A quartic CM field field K is represented by invariants [D,A,B], where
K = Q[x]/(x4+Ax2+B), and D is the discriminant of the totally real
quadratic subfield (hence A2-4B = m2D for some m).
Class number:
[Non-normal]
[Cyclic]
Class number 499 non-normal (D4) quartic CM field invariants: 277 fields
K |
Quartic invariants |
Cl(OK) |
Igusa invariants |
Kr |
Reflex invariants |
Cl(OKr) |
Igusa invariants |
1) |
[5, 6718, 11128001] |
C499 |
|
263) |
[11128001, 3359, 38720] |
C499 |
2) |
[5, 9014, 20305049] |
C499 |
|
---) |
[20305049, 4507, 2000] |
C1497 |
3) |
[5, 5837, 6907361] |
C499 |
|
257) |
[6907361, 2959, 462080] |
C499 |
4) |
[5, 8398, 17626481] |
C499 |
|
272) |
[17626481, 4199, 1280] |
C499 |
5) |
[5, 9694, 23365409] |
C499 |
|
276) |
[23365409, 4847, 32000] |
C499 |
6) |
[5, 6806, 11347129] |
C499 |
|
264) |
[11347129, 3403, 58320] |
C499 |
7) |
[5, 4997, 5794001] |
C499 |
|
252) |
[5794001, 2999, 800000] |
C499 |
8) |
[5, 4917, 5293441] |
C499 |
|
250) |
[5293441, 2719, 524880] |
C499 |
9) |
[5, 6686, 11172769] |
C499 |
|
---) |
[11172769, 3343, 720] |
C5489 |
10) |
[5, 8774, 19045769] |
C499 |
|
274) |
[19045769, 4387, 50000] |
C499 |
11) |
[5, 6838, 10121561] |
C499 |
|
261) |
[10121561, 3419, 392000] |
C499 |
12) |
[5, 10574, 27951089] |
C499 |
|
277) |
[27951089, 5287, 320] |
C499 |
13) |
[5, 8521, 14678249] |
C499 |
|
268) |
[14678249, 4307, 968000] |
C499 |
14) |
[5, 7814, 15218569] |
C499 |
|
269) |
[15218569, 3907, 11520] |
C499 |
15) |
[5, 7534, 14169809] |
C499 |
|
266) |
[14169809, 3767, 5120] |
C499 |
16) |
[5, 5878, 8555801] |
C499 |
|
---) |
[8555801, 2939, 20480] |
C1497 |
17) |
[5, 7094, 12253529] |
C499 |
|
265) |
[12253529, 3547, 81920] |
C499 |
18) |
[5, 4533, 4757521] |
C499 |
|
248) |
[4757521, 2711, 648000] |
C499 |
19) |
[5, 8326, 14257289] |
C499 |
|
267) |
[14257289, 4163, 768320] |
C499 |
20) |
[8, 6526, 7034497] |
C499 |
|
258) |
[7034497, 3263, 903168] |
C499 |
21) |
[8, 5774, 6460721] |
C499 |
|
254) |
[6460721, 2887, 468512] |
C499 |
22) |
[8, 5102, 6461393] |
C499 |
|
255) |
[6461393, 2551, 11552] |
C499 |
23) |
[8, 2842, 2019041] |
C499 |
|
---) |
[2019041, 1421, 50] |
C3493 |
24) |
[8, 3790, 2361713] |
C499 |
|
244) |
[2361713, 1895, 307328] |
C499 |
25) |
[13, 3702, 3285593] |
C499 |
|
246) |
[3285593, 1851, 35152] |
C499 |
26) |
[13, 3102, 2072801] |
C499 |
|
243) |
[2072801, 1551, 83200] |
C499 |
27) |
[13, 4566, 5071481] |
C499 |
|
249) |
[5071481, 2283, 35152] |
C499 |
28) |
[13, 5118, 6145793] |
C499 |
|
253) |
[6145793, 2559, 100672] |
C499 |
29) |
[13, 9086, 19890049] |
C499 |
|
---) |
[19890049, 4543, 187200] |
C3 x C1497 |
30) |
[13, 8966, 19730377] |
C499 |
|
275) |
[19730377, 4483, 91728] |
C499 |
31) |
[17, 9542, 18845641] |
C499 |
|
273) |
[18845641, 4771, 979200] |
C499 |
32) |
[37, 6254, 7199377] |
C499 |
|
259) |
[7199377, 3127, 644688] |
C499 |
33) |
[41, 7942, 15254537] |
C499 |
|
270) |
[15254537, 3971, 128576] |
C499 |
34) |
[41, 7862, 15410777] |
C499 |
|
271) |
[15410777, 3931, 10496] |
C499 |
35) |
[41, 2186, 1075093] |
C499 |
|
---) |
[1075093, 1093, 29889] |
C4491 |
36) |
[41, 7222, 12997337] |
C499 |
|
---) |
[12997337, 3611, 10496] |
C2495 |
37) |
[41, 13270, 43981241] |
C499 |
|
---) |
[43981241, 6635, 10496] |
C10479 |
38) |
[61, 2526, 466913] |
C499 |
|
226) |
[466913, 1263, 282064] |
C499 |
39) |
[73, 6438, 10062953] |
C499 |
|
260) |
[10062953, 3219, 74752] |
C499 |
40) |
[73, 4374, 3096377] |
C499 |
|
245) |
[3096377, 2187, 421648] |
C499 |
41) |
[73, 5430, 5684633] |
C499 |
|
251) |
[5684633, 2715, 421648] |
C499 |
42) |
[73, 2738, 1850509] |
C499 |
|
241) |
[1850509, 1369, 5913] |
C499 |
43) |
[89, 950, 224201] |
C499 |
|
219) |
[224201, 475, 356] |
C499 |
44) |
[89, 6710, 10976921] |
C499 |
|
262) |
[10976921, 3355, 69776] |
C499 |
45) |
[89, 5174, 4180633] |
C499 |
|
247) |
[4180633, 2587, 627984] |
C499 |
46) |
[101, 4246, 1921529] |
C499 |
|
242) |
[1921529, 2123, 646400] |
C499 |
47) |
[109, 1722, 468821] |
C499 |
|
---) |
[468821, 861, 68125] |
C2495 |
48) |
[109, 1158, 333497] |
C499 |
|
220) |
[333497, 579, 436] |
C499 |
49) |
[113, 1930, 692117] |
C499 |
|
230) |
[692117, 965, 59777] |
C499 |
50) |
[113, 2042, 662309] |
C499 |
|
229) |
[662309, 1021, 95033] |
C499 |
51) |
[113, 5222, 6788393] |
C499 |
|
256) |
[6788393, 2611, 7232] |
C499 |
52) |
[113, 3359, 2805776] |
C499 |
|
214) |
[175361, 2951, 28928] |
C499 |
53) |
[149, 2254, 1031729] |
C499 |
|
234) |
[1031729, 1127, 59600] |
C499 |
54) |
[149, 1246, 378593] |
C499 |
|
223) |
[378593, 623, 2384] |
C499 |
55) |
[157, 4406, 1597657] |
C499 |
|
238) |
[1597657, 2203, 813888] |
C499 |
56) |
[157, 1326, 376769] |
C499 |
|
222) |
[376769, 663, 15700] |
C499 |
57) |
[157, 4790, 4289113] |
C499 |
|
---) |
[4289113, 2395, 361728] |
C24451 |
58) |
[157, 798, 149153] |
C499 |
|
211) |
[149153, 399, 2512] |
C499 |
59) |
[157, 1982, 959473] |
C499 |
|
233) |
[959473, 991, 5652] |
C499 |
60) |
[173, 1690, 707797] |
C499 |
|
231) |
[707797, 845, 1557] |
C499 |
61) |
[173, 2518, 477881] |
C499 |
|
227) |
[477881, 1259, 276800] |
C499 |
62) |
[193, 2686, 1791297] |
C499 |
|
218) |
[199033, 1343, 3088] |
C499 |
63) |
[193, 2646, 1700921] |
C499 |
|
239) |
[1700921, 1323, 12352] |
C499 |
64) |
[197, 1430, 508073] |
C499 |
|
228) |
[508073, 715, 788] |
C499 |
65) |
[233, 2534, 1545641] |
C499 |
|
236) |
[1545641, 1267, 14912] |
C499 |
66) |
[233, 842, 153941] |
C499 |
|
212) |
[153941, 421, 5825] |
C499 |
67) |
[241, 1082, 291717] |
C499 |
|
---) |
[32413, 541, 241] |
C1497 |
68) |
[281, 1203, 64996] |
C499 |
|
193) |
[16249, 1899, 702500] |
C499 |
69) |
[281, 794, 102533] |
C499 |
|
207) |
[102533, 397, 13769] |
C499 |
70) |
[293, 1006, 178001] |
C499 |
|
215) |
[178001, 503, 18752] |
C499 |
71) |
[293, 1301, 401981] |
C499 |
|
225) |
[401981, 2602, 84677] |
C499 |
72) |
[313, 3366, 1550441] |
C499 |
|
237) |
[1550441, 1683, 320512] |
C499 |
73) |
[397, 1262, 169489] |
C499 |
|
213) |
[169489, 631, 57168] |
C499 |
74) |
[409, 4950, 1701881] |
C499 |
|
240) |
[1701881, 2475, 1105936] |
C499 |
75) |
[461, 4174, 106993] |
C499 |
|
208) |
[106993, 2087, 1062144] |
C499 |
76) |
[521, 1654, 8713] |
C499 |
|
---) |
[8713, 827, 168804] |
C1497 |
77) |
[541, 906, 99173] |
C499 |
|
206) |
[99173, 453, 26509] |
C499 |
78) |
[593, 2911, 944192] |
C499 |
|
187) |
[14753, 2207, 151808] |
C499 |
79) |
[593, 2126, 1120481] |
C499 |
|
235) |
[1120481, 1063, 2372] |
C499 |
80) |
[677, 1033, 192133] |
C499 |
|
217) |
[192133, 2066, 298557] |
C499 |
81) |
[853, 241, 12601] |
C499 |
|
179) |
[12601, 482, 7677] |
C499 |
82) |
[857, 2339, 30596] |
C499 |
|
165) |
[7649, 2539, 3428] |
C499 |
83) |
[857, 3718, 768329] |
C499 |
|
232) |
[768329, 1859, 671888] |
C499 |
84) |
[881, 974, 11633] |
C499 |
|
174) |
[11633, 487, 56384] |
C499 |
85) |
[977, 679, 60304] |
C499 |
|
131) |
[3769, 1358, 219825] |
C499 |
86) |
[997, 873, 160373] |
C499 |
|
---) |
[160373, 1746, 120637] |
C1497 |
87) |
[1013, 877, 192029] |
C499 |
|
216) |
[192029, 1754, 1013] |
C499 |
88) |
[1049, 1622, 640937] |
C499 |
|
---) |
[5297, 811, 4196] |
C1497 |
89) |
[1049, 1039, 154228] |
C499 |
|
203) |
[38557, 2078, 462609] |
C499 |
90) |
[1549, 789, 145949] |
C499 |
|
209) |
[145949, 1578, 38725] |
C499 |
91) |
[1553, 1414, 400457] |
C499 |
|
224) |
[400457, 707, 24848] |
C499 |
92) |
[1613, 1114, 148949] |
C499 |
|
210) |
[148949, 557, 40325] |
C499 |
93) |
[1693, 954, 58229] |
C499 |
|
204) |
[58229, 477, 42325] |
C499 |
94) |
[1693, 1049, 51201] |
C499 |
|
156) |
[5689, 2098, 895597] |
C499 |
95) |
[1741, 297, 21617] |
C499 |
|
201) |
[21617, 594, 1741] |
C499 |
96) |
[1997, 602, 82613] |
C499 |
|
205) |
[82613, 301, 1997] |
C499 |
97) |
[2053, 3057, 894593] |
C499 |
|
---) |
[18257, 6114, 5766877] |
C1497 |
98) |
[2069, 1921, 735833] |
C499 |
|
188) |
[15017, 3842, 746909] |
C499 |
99) |
[2137, 2642, 300429] |
C499 |
|
129) |
[3709, 1321, 361153] |
C499 |
100) |
[2141, 2005, 15329] |
C499 |
|
189) |
[15329, 4010, 3958709] |
C499 |
101) |
[2269, 1269, 306725] |
C499 |
|
---) |
[12269, 2538, 383461] |
C1497 |
102) |
[2293, 1322, 354373] |
C499 |
|
221) |
[354373, 661, 20637] |
C499 |
103) |
[2333, 373, 20201] |
C499 |
|
200) |
[20201, 746, 58325] |
C499 |
104) |
[2341, 1182, 311825] |
C499 |
|
178) |
[12473, 591, 9364] |
C499 |
105) |
[2377, 3934, 65889] |
C499 |
|
163) |
[7321, 1967, 950800] |
C499 |
106) |
[2389, 3358, 1442977] |
C499 |
|
148) |
[4993, 1679, 344016] |
C499 |
107) |
[2593, 4754, 163341] |
C499 |
|
198) |
[18149, 2377, 1371697] |
C499 |
108) |
[2729, 2175, 248656] |
C499 |
|
190) |
[15541, 4350, 3736001] |
C499 |
109) |
[2741, 2157, 11257] |
C499 |
|
---) |
[11257, 4314, 4607621] |
C8483 |
110) |
[2749, 5529, 351425] |
C499 |
|
184) |
[14057, 3583, 3177844] |
C499 |
111) |
[2753, 674, 14461] |
C499 |
|
186) |
[14461, 337, 24777] |
C499 |
112) |
[2789, 4677, 5434417] |
C499 |
|
---) |
[10273, 4759, 4919796] |
C4491 |
113) |
[2801, 2203, 1195796] |
C499 |
|
161) |
[6101, 4405, 1481729] |
C499 |
114) |
[2833, 6234, 2633189] |
C499 |
|
191) |
[15581, 3117, 1770625] |
C499 |
115) |
[2861, 3894, 3058393] |
C499 |
|
---) |
[18097, 1947, 183104] |
C1497 |
116) |
[2969, 6039, 7032400] |
C499 |
|
---) |
[17581, 5325, 1071809] |
C1497 |
117) |
[3041, 6402, 16477] |
C499 |
|
---) |
[16477, 3201, 2557481] |
C1497 |
118) |
[3041, 1630, 469601] |
C499 |
|
135) |
[3881, 815, 48656] |
C499 |
119) |
[3049, 1330, 430029] |
C499 |
|
151) |
[5309, 665, 3049] |
C499 |
120) |
[3089, 6218, 1943381] |
C499 |
|
192) |
[16061, 3109, 1930625] |
C499 |
121) |
[3217, 5151, 262736] |
C499 |
|
194) |
[16421, 7341, 4404073] |
C499 |
122) |
[3217, 1094, 93321] |
C499 |
|
170) |
[10369, 547, 51472] |
C499 |
123) |
[3517, 5045, 6045597] |
C499 |
|
168) |
[8293, 3557, 2563893] |
C499 |
124) |
[3517, 2273, 1037529] |
C499 |
|
180) |
[12809, 4546, 1016413] |
C499 |
125) |
[3529, 2666, 1423989] |
C499 |
|
---) |
[3229, 1333, 88225] |
C1497 |
126) |
[3541, 5489, 1136349] |
C499 |
|
183) |
[14029, 5045, 1561581] |
C499 |
127) |
[3677, 6337, 1390169] |
C499 |
|
173) |
[11489, 4751, 2882768] |
C499 |
128) |
[3677, 5401, 11321] |
C499 |
|
---) |
[11321, 5563, 941312] |
C7485 |
129) |
[3709, 1321, 361153] |
C499 |
|
99) |
[2137, 2642, 300429] |
C499 |
130) |
[3709, 2046, 97025] |
C499 |
|
134) |
[3881, 1023, 237376] |
C499 |
131) |
[3769, 1358, 219825] |
C499 |
|
85) |
[977, 679, 60304] |
C499 |
132) |
[3793, 5983, 8735716] |
C499 |
|
197) |
[18049, 5963, 546192] |
C499 |
133) |
[3833, 5015, 6278932] |
C499 |
|
181) |
[12973, 5345, 1690353] |
C499 |
134) |
[3881, 1023, 237376] |
C499 |
|
130) |
[3709, 2046, 97025] |
C499 |
135) |
[3881, 815, 48656] |
C499 |
|
118) |
[3041, 1630, 469601] |
C499 |
136) |
[3989, 5606, 6835625] |
C499 |
|
172) |
[10937, 2803, 255296] |
C499 |
137) |
[4021, 4257, 4360625] |
C499 |
|
162) |
[6977, 3903, 2718196] |
C499 |
138) |
[4057, 779, 69556] |
C499 |
|
195) |
[17389, 1558, 328617] |
C499 |
139) |
[4177, 1567, 312084] |
C499 |
|
169) |
[8669, 3134, 1207153] |
C499 |
140) |
[4201, 4475, 2484756] |
C499 |
|
166) |
[7669, 4513, 105025] |
C499 |
141) |
[4421, 377, 7901] |
C499 |
|
167) |
[7901, 754, 110525] |
C499 |
142) |
[4457, 4135, 3337472] |
C499 |
|
182) |
[13037, 7813, 12519713] |
C499 |
143) |
[4517, 442, 30773] |
C499 |
|
202) |
[30773, 221, 4517] |
C499 |
144) |
[4621, 1777, 67401] |
C499 |
|
164) |
[7489, 3554, 2888125] |
C499 |
145) |
[4801, 1795, 660276] |
C499 |
|
199) |
[18341, 3590, 580921] |
C499 |
146) |
[4877, 3289, 11057] |
C499 |
|
---) |
[11057, 6578, 10773293] |
C1497 |
147) |
[4877, 2822, 1912889] |
C499 |
|
---) |
[15809, 1411, 19508] |
C3493 |
148) |
[4993, 1679, 344016] |
C499 |
|
106) |
[2389, 3358, 1442977] |
C499 |
149) |
[5153, 1435, 49748] |
C499 |
|
177) |
[12437, 2870, 1860233] |
C499 |
150) |
[5233, 2259, 1054676] |
C499 |
|
152) |
[5381, 4518, 884377] |
C499 |
151) |
[5309, 665, 3049] |
C499 |
|
119) |
[3049, 1330, 430029] |
C499 |
152) |
[5381, 4518, 884377] |
C499 |
|
150) |
[5233, 2259, 1054676] |
C499 |
153) |
[5437, 2973, 2175701] |
C499 |
|
196) |
[17981, 5946, 135925] |
C499 |
154) |
[5641, 1655, 672064] |
C499 |
|
171) |
[10501, 3310, 50769] |
C499 |
155) |
[5669, 4145, 1674761] |
C499 |
|
---) |
[13841, 8290, 10481981] |
C2495 |
156) |
[5689, 2098, 895597] |
C499 |
|
94) |
[1693, 1049, 51201] |
C499 |
157) |
[5801, 7507, 1000256] |
C499 |
|
---) |
[15629, 8297, 701921] |
C4491 |
158) |
[5813, 7962, 3548053] |
C499 |
|
176) |
[12277, 3981, 3075077] |
C499 |
159) |
[5849, 4594, 12109] |
C499 |
|
175) |
[12109, 2297, 1316025] |
C499 |
160) |
[5861, 9921, 1712029] |
C499 |
|
185) |
[14149, 5385, 709181] |
C499 |
161) |
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C499 |
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113) |
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C499 |
162) |
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C499 |
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137) |
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C499 |
163) |
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C499 |
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105) |
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C499 |
164) |
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C499 |
|
144) |
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C499 |
165) |
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C499 |
|
82) |
[857, 2339, 30596] |
C499 |
166) |
[7669, 4513, 105025] |
C499 |
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140) |
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C499 |
167) |
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C499 |
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141) |
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C499 |
168) |
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C499 |
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123) |
[3517, 5045, 6045597] |
C499 |
169) |
[8669, 3134, 1207153] |
C499 |
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139) |
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C499 |
170) |
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C499 |
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122) |
[3217, 1094, 93321] |
C499 |
171) |
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C499 |
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154) |
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C499 |
172) |
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C499 |
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136) |
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C499 |
173) |
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C499 |
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127) |
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C499 |
174) |
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C499 |
|
84) |
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C499 |
175) |
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C499 |
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159) |
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C499 |
176) |
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C499 |
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158) |
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C499 |
177) |
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C499 |
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149) |
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C499 |
178) |
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C499 |
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104) |
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C499 |
179) |
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C499 |
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81) |
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C499 |
180) |
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C499 |
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124) |
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C499 |
181) |
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C499 |
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133) |
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C499 |
182) |
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C499 |
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142) |
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C499 |
183) |
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C499 |
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126) |
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C499 |
184) |
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C499 |
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110) |
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C499 |
185) |
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C499 |
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160) |
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C499 |
186) |
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C499 |
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111) |
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C499 |
187) |
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C499 |
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78) |
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C499 |
188) |
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C499 |
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98) |
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C499 |
189) |
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C499 |
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100) |
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C499 |
190) |
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C499 |
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108) |
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C499 |
191) |
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C499 |
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114) |
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C499 |
192) |
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C499 |
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120) |
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C499 |
193) |
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C499 |
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68) |
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C499 |
194) |
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C499 |
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121) |
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C499 |
195) |
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C499 |
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138) |
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C499 |
196) |
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C499 |
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153) |
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C499 |
197) |
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C499 |
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132) |
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C499 |
198) |
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C499 |
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107) |
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C499 |
199) |
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C499 |
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145) |
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C499 |
200) |
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C499 |
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103) |
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C499 |
201) |
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C499 |
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95) |
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C499 |
202) |
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C499 |
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143) |
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C499 |
203) |
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C499 |
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89) |
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C499 |
204) |
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C499 |
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93) |
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C499 |
205) |
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C499 |
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96) |
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C499 |
206) |
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C499 |
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77) |
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C499 |
207) |
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C499 |
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69) |
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C499 |
208) |
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C499 |
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75) |
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C499 |
209) |
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C499 |
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90) |
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C499 |
210) |
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C499 |
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92) |
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C499 |
211) |
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C499 |
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58) |
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C499 |
212) |
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C499 |
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66) |
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C499 |
213) |
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C499 |
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73) |
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C499 |
214) |
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C499 |
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52) |
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C499 |
215) |
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C499 |
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70) |
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C499 |
216) |
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C499 |
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87) |
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C499 |
217) |
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C499 |
|
80) |
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C499 |
218) |
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C499 |
|
62) |
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C499 |
219) |
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C499 |
|
43) |
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C499 |
220) |
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C499 |
|
48) |
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C499 |
221) |
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C499 |
|
102) |
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C499 |
222) |
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C499 |
|
56) |
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C499 |
223) |
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C499 |
|
54) |
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C499 |
224) |
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C499 |
|
91) |
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C499 |
225) |
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C499 |
|
71) |
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C499 |
226) |
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C499 |
|
38) |
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C499 |
227) |
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C499 |
|
61) |
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C499 |
228) |
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C499 |
|
64) |
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C499 |
229) |
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C499 |
|
50) |
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C499 |
230) |
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C499 |
|
49) |
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C499 |
231) |
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C499 |
|
60) |
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C499 |
232) |
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C499 |
|
83) |
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C499 |
233) |
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C499 |
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59) |
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C499 |
234) |
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C499 |
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53) |
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C499 |
235) |
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C499 |
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79) |
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C499 |
236) |
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C499 |
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65) |
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C499 |
237) |
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C499 |
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72) |
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C499 |
238) |
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C499 |
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55) |
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C499 |
239) |
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C499 |
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63) |
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C499 |
240) |
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C499 |
|
74) |
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C499 |
241) |
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C499 |
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42) |
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C499 |
242) |
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C499 |
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46) |
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C499 |
243) |
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C499 |
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26) |
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C499 |
244) |
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C499 |
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C499 |
245) |
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C499 |
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C499 |
246) |
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C499 |
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25) |
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C499 |
247) |
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C499 |
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45) |
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C499 |
248) |
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C499 |
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18) |
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C499 |
249) |
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C499 |
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27) |
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C499 |
250) |
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C499 |
|
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C499 |
251) |
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C499 |
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41) |
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C499 |
252) |
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C499 |
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C499 |
253) |
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C499 |
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28) |
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C499 |
254) |
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C499 |
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21) |
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C499 |
255) |
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C499 |
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22) |
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C499 |
256) |
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C499 |
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51) |
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C499 |
257) |
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C499 |
|
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C499 |
258) |
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C499 |
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20) |
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C499 |
259) |
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C499 |
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C499 |
260) |
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C499 |
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39) |
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C499 |
261) |
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C499 |
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11) |
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C499 |
262) |
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C499 |
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44) |
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C499 |
263) |
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C499 |
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1) |
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C499 |
264) |
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C499 |
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6) |
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C499 |
265) |
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C499 |
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17) |
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C499 |
266) |
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C499 |
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15) |
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C499 |
267) |
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C499 |
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19) |
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C499 |
268) |
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C499 |
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13) |
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C499 |
269) |
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C499 |
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14) |
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C499 |
270) |
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C499 |
|
33) |
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C499 |
271) |
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C499 |
|
34) |
[41, 7862, 15410777] |
C499 |
272) |
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C499 |
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[5, 8398, 17626481] |
C499 |
273) |
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C499 |
|
31) |
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C499 |
274) |
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C499 |
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10) |
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C499 |
275) |
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C499 |
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30) |
[13, 8966, 19730377] |
C499 |
276) |
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C499 |
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5) |
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C499 |
277) |
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C499 |
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12) |
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C499 |