Properties

Label 8035.2.a.e.1.4
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.68656 q^{2} -0.551136 q^{3} +5.21758 q^{4} +1.00000 q^{5} +1.48066 q^{6} -4.17471 q^{7} -8.64421 q^{8} -2.69625 q^{9} +O(q^{10})\) \(q-2.68656 q^{2} -0.551136 q^{3} +5.21758 q^{4} +1.00000 q^{5} +1.48066 q^{6} -4.17471 q^{7} -8.64421 q^{8} -2.69625 q^{9} -2.68656 q^{10} +2.50730 q^{11} -2.87560 q^{12} +5.38461 q^{13} +11.2156 q^{14} -0.551136 q^{15} +12.7880 q^{16} -0.137490 q^{17} +7.24362 q^{18} -5.14076 q^{19} +5.21758 q^{20} +2.30083 q^{21} -6.73601 q^{22} -4.07872 q^{23} +4.76414 q^{24} +1.00000 q^{25} -14.4661 q^{26} +3.13941 q^{27} -21.7819 q^{28} -3.45665 q^{29} +1.48066 q^{30} +1.69309 q^{31} -17.0672 q^{32} -1.38187 q^{33} +0.369374 q^{34} -4.17471 q^{35} -14.0679 q^{36} -4.56807 q^{37} +13.8110 q^{38} -2.96765 q^{39} -8.64421 q^{40} +9.05723 q^{41} -6.18132 q^{42} -5.50216 q^{43} +13.0821 q^{44} -2.69625 q^{45} +10.9577 q^{46} -7.93476 q^{47} -7.04792 q^{48} +10.4282 q^{49} -2.68656 q^{50} +0.0757755 q^{51} +28.0947 q^{52} -1.18174 q^{53} -8.43419 q^{54} +2.50730 q^{55} +36.0871 q^{56} +2.83326 q^{57} +9.28649 q^{58} +6.06653 q^{59} -2.87560 q^{60} +4.55268 q^{61} -4.54859 q^{62} +11.2561 q^{63} +20.2761 q^{64} +5.38461 q^{65} +3.71246 q^{66} +5.60322 q^{67} -0.717364 q^{68} +2.24793 q^{69} +11.2156 q^{70} +1.37739 q^{71} +23.3070 q^{72} -2.10680 q^{73} +12.2724 q^{74} -0.551136 q^{75} -26.8224 q^{76} -10.4673 q^{77} +7.97276 q^{78} -13.2753 q^{79} +12.7880 q^{80} +6.35851 q^{81} -24.3328 q^{82} -3.44693 q^{83} +12.0048 q^{84} -0.137490 q^{85} +14.7819 q^{86} +1.90508 q^{87} -21.6737 q^{88} +1.03400 q^{89} +7.24362 q^{90} -22.4792 q^{91} -21.2810 q^{92} -0.933125 q^{93} +21.3172 q^{94} -5.14076 q^{95} +9.40637 q^{96} -6.36595 q^{97} -28.0160 q^{98} -6.76032 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q + 18q^{2} + 7q^{3} + 176q^{4} + 153q^{5} + 19q^{6} + 5q^{7} + 57q^{8} + 206q^{9} + O(q^{10}) \) \( 153q + 18q^{2} + 7q^{3} + 176q^{4} + 153q^{5} + 19q^{6} + 5q^{7} + 57q^{8} + 206q^{9} + 18q^{10} + 38q^{11} + 14q^{12} + 28q^{13} + 53q^{14} + 7q^{15} + 214q^{16} + 50q^{17} + 47q^{18} + 65q^{19} + 176q^{20} + 109q^{21} + 13q^{22} + 52q^{23} + 66q^{24} + 153q^{25} + 36q^{26} + 19q^{27} + 26q^{28} + 172q^{29} + 19q^{30} + 60q^{31} + 107q^{32} + 4q^{33} + 40q^{34} + 5q^{35} + 241q^{36} + 65q^{37} + 29q^{38} + 56q^{39} + 57q^{40} + 152q^{41} - 19q^{42} + 22q^{43} + 97q^{44} + 206q^{45} + 86q^{46} + 37q^{47} - 4q^{48} + 260q^{49} + 18q^{50} + 102q^{51} - 6q^{52} + 169q^{53} + 64q^{54} + 38q^{55} + 146q^{56} + 40q^{57} - 9q^{58} + 64q^{59} + 14q^{60} + 164q^{61} + 12q^{62} + 19q^{63} + 259q^{64} + 28q^{65} + 6q^{66} + 5q^{67} + 112q^{68} + 119q^{69} + 53q^{70} + 100q^{71} + 77q^{72} + 10q^{73} + 98q^{74} + 7q^{75} + 126q^{76} + 80q^{77} - 4q^{78} + 110q^{79} + 214q^{80} + 305q^{81} - 27q^{82} + 36q^{83} + 172q^{84} + 50q^{85} + 44q^{86} + 23q^{87} + 47q^{88} + 143q^{89} + 47q^{90} + 82q^{91} + 130q^{92} + 31q^{93} + 77q^{94} + 65q^{95} + 57q^{96} + 11q^{97} + 29q^{98} + 99q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68656 −1.89968 −0.949841 0.312734i \(-0.898755\pi\)
−0.949841 + 0.312734i \(0.898755\pi\)
\(3\) −0.551136 −0.318198 −0.159099 0.987263i \(-0.550859\pi\)
−0.159099 + 0.987263i \(0.550859\pi\)
\(4\) 5.21758 2.60879
\(5\) 1.00000 0.447214
\(6\) 1.48066 0.604476
\(7\) −4.17471 −1.57789 −0.788947 0.614462i \(-0.789373\pi\)
−0.788947 + 0.614462i \(0.789373\pi\)
\(8\) −8.64421 −3.05619
\(9\) −2.69625 −0.898750
\(10\) −2.68656 −0.849564
\(11\) 2.50730 0.755981 0.377990 0.925810i \(-0.376615\pi\)
0.377990 + 0.925810i \(0.376615\pi\)
\(12\) −2.87560 −0.830113
\(13\) 5.38461 1.49342 0.746711 0.665148i \(-0.231632\pi\)
0.746711 + 0.665148i \(0.231632\pi\)
\(14\) 11.2156 2.99749
\(15\) −0.551136 −0.142303
\(16\) 12.7880 3.19700
\(17\) −0.137490 −0.0333461 −0.0166731 0.999861i \(-0.505307\pi\)
−0.0166731 + 0.999861i \(0.505307\pi\)
\(18\) 7.24362 1.70734
\(19\) −5.14076 −1.17937 −0.589686 0.807633i \(-0.700749\pi\)
−0.589686 + 0.807633i \(0.700749\pi\)
\(20\) 5.21758 1.16669
\(21\) 2.30083 0.502083
\(22\) −6.73601 −1.43612
\(23\) −4.07872 −0.850471 −0.425236 0.905083i \(-0.639809\pi\)
−0.425236 + 0.905083i \(0.639809\pi\)
\(24\) 4.76414 0.972475
\(25\) 1.00000 0.200000
\(26\) −14.4661 −2.83703
\(27\) 3.13941 0.604179
\(28\) −21.7819 −4.11639
\(29\) −3.45665 −0.641884 −0.320942 0.947099i \(-0.603999\pi\)
−0.320942 + 0.947099i \(0.603999\pi\)
\(30\) 1.48066 0.270330
\(31\) 1.69309 0.304089 0.152044 0.988374i \(-0.451414\pi\)
0.152044 + 0.988374i \(0.451414\pi\)
\(32\) −17.0672 −3.01709
\(33\) −1.38187 −0.240552
\(34\) 0.369374 0.0633471
\(35\) −4.17471 −0.705655
\(36\) −14.0679 −2.34465
\(37\) −4.56807 −0.750986 −0.375493 0.926825i \(-0.622527\pi\)
−0.375493 + 0.926825i \(0.622527\pi\)
\(38\) 13.8110 2.24043
\(39\) −2.96765 −0.475205
\(40\) −8.64421 −1.36677
\(41\) 9.05723 1.41450 0.707251 0.706962i \(-0.249935\pi\)
0.707251 + 0.706962i \(0.249935\pi\)
\(42\) −6.18132 −0.953798
\(43\) −5.50216 −0.839072 −0.419536 0.907739i \(-0.637807\pi\)
−0.419536 + 0.907739i \(0.637807\pi\)
\(44\) 13.0821 1.97220
\(45\) −2.69625 −0.401933
\(46\) 10.9577 1.61562
\(47\) −7.93476 −1.15740 −0.578702 0.815539i \(-0.696441\pi\)
−0.578702 + 0.815539i \(0.696441\pi\)
\(48\) −7.04792 −1.01728
\(49\) 10.4282 1.48975
\(50\) −2.68656 −0.379936
\(51\) 0.0757755 0.0106107
\(52\) 28.0947 3.89603
\(53\) −1.18174 −0.162324 −0.0811620 0.996701i \(-0.525863\pi\)
−0.0811620 + 0.996701i \(0.525863\pi\)
\(54\) −8.43419 −1.14775
\(55\) 2.50730 0.338085
\(56\) 36.0871 4.82234
\(57\) 2.83326 0.375274
\(58\) 9.28649 1.21938
\(59\) 6.06653 0.789795 0.394897 0.918725i \(-0.370780\pi\)
0.394897 + 0.918725i \(0.370780\pi\)
\(60\) −2.87560 −0.371238
\(61\) 4.55268 0.582911 0.291456 0.956584i \(-0.405860\pi\)
0.291456 + 0.956584i \(0.405860\pi\)
\(62\) −4.54859 −0.577672
\(63\) 11.2561 1.41813
\(64\) 20.2761 2.53451
\(65\) 5.38461 0.667879
\(66\) 3.71246 0.456972
\(67\) 5.60322 0.684542 0.342271 0.939601i \(-0.388804\pi\)
0.342271 + 0.939601i \(0.388804\pi\)
\(68\) −0.717364 −0.0869931
\(69\) 2.24793 0.270619
\(70\) 11.2156 1.34052
\(71\) 1.37739 0.163466 0.0817328 0.996654i \(-0.473955\pi\)
0.0817328 + 0.996654i \(0.473955\pi\)
\(72\) 23.3070 2.74675
\(73\) −2.10680 −0.246582 −0.123291 0.992371i \(-0.539345\pi\)
−0.123291 + 0.992371i \(0.539345\pi\)
\(74\) 12.2724 1.42664
\(75\) −0.551136 −0.0636397
\(76\) −26.8224 −3.07674
\(77\) −10.4673 −1.19286
\(78\) 7.97276 0.902738
\(79\) −13.2753 −1.49359 −0.746794 0.665055i \(-0.768408\pi\)
−0.746794 + 0.665055i \(0.768408\pi\)
\(80\) 12.7880 1.42974
\(81\) 6.35851 0.706501
\(82\) −24.3328 −2.68710
\(83\) −3.44693 −0.378350 −0.189175 0.981943i \(-0.560581\pi\)
−0.189175 + 0.981943i \(0.560581\pi\)
\(84\) 12.0048 1.30983
\(85\) −0.137490 −0.0149128
\(86\) 14.7819 1.59397
\(87\) 1.90508 0.204246
\(88\) −21.6737 −2.31042
\(89\) 1.03400 0.109604 0.0548018 0.998497i \(-0.482547\pi\)
0.0548018 + 0.998497i \(0.482547\pi\)
\(90\) 7.24362 0.763545
\(91\) −22.4792 −2.35646
\(92\) −21.2810 −2.21870
\(93\) −0.933125 −0.0967606
\(94\) 21.3172 2.19870
\(95\) −5.14076 −0.527431
\(96\) 9.40637 0.960033
\(97\) −6.36595 −0.646365 −0.323182 0.946337i \(-0.604753\pi\)
−0.323182 + 0.946337i \(0.604753\pi\)
\(98\) −28.0160 −2.83004
\(99\) −6.76032 −0.679438
\(100\) 5.21758 0.521758
\(101\) 9.34813 0.930174 0.465087 0.885265i \(-0.346023\pi\)
0.465087 + 0.885265i \(0.346023\pi\)
\(102\) −0.203575 −0.0201569
\(103\) −10.2631 −1.01125 −0.505625 0.862753i \(-0.668738\pi\)
−0.505625 + 0.862753i \(0.668738\pi\)
\(104\) −46.5457 −4.56419
\(105\) 2.30083 0.224538
\(106\) 3.17480 0.308364
\(107\) −6.17808 −0.597257 −0.298629 0.954369i \(-0.596529\pi\)
−0.298629 + 0.954369i \(0.596529\pi\)
\(108\) 16.3801 1.57618
\(109\) −2.26953 −0.217381 −0.108691 0.994076i \(-0.534666\pi\)
−0.108691 + 0.994076i \(0.534666\pi\)
\(110\) −6.73601 −0.642254
\(111\) 2.51763 0.238963
\(112\) −53.3862 −5.04452
\(113\) −4.42636 −0.416397 −0.208198 0.978087i \(-0.566760\pi\)
−0.208198 + 0.978087i \(0.566760\pi\)
\(114\) −7.61171 −0.712902
\(115\) −4.07872 −0.380342
\(116\) −18.0354 −1.67454
\(117\) −14.5183 −1.34221
\(118\) −16.2981 −1.50036
\(119\) 0.573980 0.0526167
\(120\) 4.76414 0.434904
\(121\) −4.71342 −0.428493
\(122\) −12.2310 −1.10735
\(123\) −4.99177 −0.450092
\(124\) 8.83386 0.793304
\(125\) 1.00000 0.0894427
\(126\) −30.2401 −2.69400
\(127\) 19.0217 1.68790 0.843950 0.536421i \(-0.180224\pi\)
0.843950 + 0.536421i \(0.180224\pi\)
\(128\) −20.3384 −1.79768
\(129\) 3.03244 0.266991
\(130\) −14.4661 −1.26876
\(131\) −8.92416 −0.779708 −0.389854 0.920877i \(-0.627474\pi\)
−0.389854 + 0.920877i \(0.627474\pi\)
\(132\) −7.21000 −0.627550
\(133\) 21.4612 1.86092
\(134\) −15.0534 −1.30041
\(135\) 3.13941 0.270197
\(136\) 1.18849 0.101912
\(137\) −14.1239 −1.20669 −0.603344 0.797481i \(-0.706165\pi\)
−0.603344 + 0.797481i \(0.706165\pi\)
\(138\) −6.03918 −0.514089
\(139\) 9.55889 0.810774 0.405387 0.914145i \(-0.367137\pi\)
0.405387 + 0.914145i \(0.367137\pi\)
\(140\) −21.7819 −1.84091
\(141\) 4.37313 0.368284
\(142\) −3.70042 −0.310533
\(143\) 13.5009 1.12900
\(144\) −34.4796 −2.87330
\(145\) −3.45665 −0.287059
\(146\) 5.66003 0.468427
\(147\) −5.74737 −0.474035
\(148\) −23.8343 −1.95917
\(149\) 21.8435 1.78949 0.894745 0.446578i \(-0.147357\pi\)
0.894745 + 0.446578i \(0.147357\pi\)
\(150\) 1.48066 0.120895
\(151\) 7.11517 0.579024 0.289512 0.957174i \(-0.406507\pi\)
0.289512 + 0.957174i \(0.406507\pi\)
\(152\) 44.4379 3.60439
\(153\) 0.370706 0.0299698
\(154\) 28.1209 2.26605
\(155\) 1.69309 0.135993
\(156\) −15.4840 −1.23971
\(157\) −0.751237 −0.0599552 −0.0299776 0.999551i \(-0.509544\pi\)
−0.0299776 + 0.999551i \(0.509544\pi\)
\(158\) 35.6648 2.83734
\(159\) 0.651298 0.0516513
\(160\) −17.0672 −1.34928
\(161\) 17.0275 1.34195
\(162\) −17.0825 −1.34213
\(163\) −0.301965 −0.0236517 −0.0118258 0.999930i \(-0.503764\pi\)
−0.0118258 + 0.999930i \(0.503764\pi\)
\(164\) 47.2569 3.69014
\(165\) −1.38187 −0.107578
\(166\) 9.26038 0.718745
\(167\) −15.3675 −1.18918 −0.594588 0.804030i \(-0.702685\pi\)
−0.594588 + 0.804030i \(0.702685\pi\)
\(168\) −19.8889 −1.53446
\(169\) 15.9941 1.23031
\(170\) 0.369374 0.0283297
\(171\) 13.8608 1.05996
\(172\) −28.7080 −2.18896
\(173\) 16.7019 1.26982 0.634912 0.772584i \(-0.281036\pi\)
0.634912 + 0.772584i \(0.281036\pi\)
\(174\) −5.11812 −0.388003
\(175\) −4.17471 −0.315579
\(176\) 32.0634 2.41687
\(177\) −3.34348 −0.251311
\(178\) −2.77789 −0.208212
\(179\) −8.36947 −0.625563 −0.312782 0.949825i \(-0.601261\pi\)
−0.312782 + 0.949825i \(0.601261\pi\)
\(180\) −14.0679 −1.04856
\(181\) 0.123471 0.00917756 0.00458878 0.999989i \(-0.498539\pi\)
0.00458878 + 0.999989i \(0.498539\pi\)
\(182\) 60.3917 4.47653
\(183\) −2.50915 −0.185481
\(184\) 35.2573 2.59920
\(185\) −4.56807 −0.335851
\(186\) 2.50689 0.183814
\(187\) −0.344729 −0.0252090
\(188\) −41.4003 −3.01943
\(189\) −13.1061 −0.953330
\(190\) 13.8110 1.00195
\(191\) 5.71354 0.413417 0.206709 0.978403i \(-0.433725\pi\)
0.206709 + 0.978403i \(0.433725\pi\)
\(192\) −11.1749 −0.806478
\(193\) −10.5684 −0.760732 −0.380366 0.924836i \(-0.624202\pi\)
−0.380366 + 0.924836i \(0.624202\pi\)
\(194\) 17.1025 1.22789
\(195\) −2.96765 −0.212518
\(196\) 54.4101 3.88644
\(197\) −10.1228 −0.721222 −0.360611 0.932716i \(-0.617432\pi\)
−0.360611 + 0.932716i \(0.617432\pi\)
\(198\) 18.1620 1.29072
\(199\) −14.9223 −1.05782 −0.528908 0.848679i \(-0.677398\pi\)
−0.528908 + 0.848679i \(0.677398\pi\)
\(200\) −8.64421 −0.611238
\(201\) −3.08813 −0.217820
\(202\) −25.1143 −1.76703
\(203\) 14.4305 1.01282
\(204\) 0.395365 0.0276811
\(205\) 9.05723 0.632585
\(206\) 27.5723 1.92105
\(207\) 10.9972 0.764361
\(208\) 68.8584 4.77447
\(209\) −12.8895 −0.891583
\(210\) −6.18132 −0.426551
\(211\) −23.4320 −1.61313 −0.806564 0.591146i \(-0.798676\pi\)
−0.806564 + 0.591146i \(0.798676\pi\)
\(212\) −6.16581 −0.423470
\(213\) −0.759126 −0.0520145
\(214\) 16.5977 1.13460
\(215\) −5.50216 −0.375245
\(216\) −27.1377 −1.84649
\(217\) −7.06818 −0.479820
\(218\) 6.09721 0.412955
\(219\) 1.16113 0.0784620
\(220\) 13.0821 0.881993
\(221\) −0.740329 −0.0497999
\(222\) −6.76375 −0.453953
\(223\) −14.7466 −0.987505 −0.493752 0.869603i \(-0.664375\pi\)
−0.493752 + 0.869603i \(0.664375\pi\)
\(224\) 71.2508 4.76065
\(225\) −2.69625 −0.179750
\(226\) 11.8917 0.791021
\(227\) 25.2136 1.67349 0.836743 0.547596i \(-0.184457\pi\)
0.836743 + 0.547596i \(0.184457\pi\)
\(228\) 14.7828 0.979012
\(229\) 4.51510 0.298366 0.149183 0.988810i \(-0.452336\pi\)
0.149183 + 0.988810i \(0.452336\pi\)
\(230\) 10.9577 0.722529
\(231\) 5.76889 0.379565
\(232\) 29.8800 1.96172
\(233\) 20.1643 1.32101 0.660503 0.750824i \(-0.270343\pi\)
0.660503 + 0.750824i \(0.270343\pi\)
\(234\) 39.0041 2.54978
\(235\) −7.93476 −0.517607
\(236\) 31.6526 2.06041
\(237\) 7.31649 0.475257
\(238\) −1.54203 −0.0999549
\(239\) −22.5189 −1.45663 −0.728314 0.685243i \(-0.759696\pi\)
−0.728314 + 0.685243i \(0.759696\pi\)
\(240\) −7.04792 −0.454941
\(241\) 0.214386 0.0138098 0.00690491 0.999976i \(-0.497802\pi\)
0.00690491 + 0.999976i \(0.497802\pi\)
\(242\) 12.6629 0.814000
\(243\) −12.9226 −0.828987
\(244\) 23.7540 1.52069
\(245\) 10.4282 0.666235
\(246\) 13.4107 0.855032
\(247\) −27.6810 −1.76130
\(248\) −14.6355 −0.929353
\(249\) 1.89973 0.120390
\(250\) −2.68656 −0.169913
\(251\) 16.4492 1.03826 0.519131 0.854694i \(-0.326256\pi\)
0.519131 + 0.854694i \(0.326256\pi\)
\(252\) 58.7295 3.69961
\(253\) −10.2266 −0.642940
\(254\) −51.1028 −3.20647
\(255\) 0.0757755 0.00474524
\(256\) 14.0880 0.880502
\(257\) −12.5060 −0.780101 −0.390050 0.920793i \(-0.627542\pi\)
−0.390050 + 0.920793i \(0.627542\pi\)
\(258\) −8.14682 −0.507199
\(259\) 19.0704 1.18498
\(260\) 28.0947 1.74236
\(261\) 9.32000 0.576893
\(262\) 23.9753 1.48120
\(263\) 4.20507 0.259296 0.129648 0.991560i \(-0.458615\pi\)
0.129648 + 0.991560i \(0.458615\pi\)
\(264\) 11.9451 0.735173
\(265\) −1.18174 −0.0725935
\(266\) −57.6568 −3.53516
\(267\) −0.569873 −0.0348757
\(268\) 29.2352 1.78583
\(269\) 7.18939 0.438345 0.219172 0.975686i \(-0.429664\pi\)
0.219172 + 0.975686i \(0.429664\pi\)
\(270\) −8.43419 −0.513289
\(271\) 26.8734 1.63245 0.816223 0.577737i \(-0.196064\pi\)
0.816223 + 0.577737i \(0.196064\pi\)
\(272\) −1.75822 −0.106608
\(273\) 12.3891 0.749822
\(274\) 37.9447 2.29232
\(275\) 2.50730 0.151196
\(276\) 11.7287 0.705987
\(277\) −20.5493 −1.23469 −0.617343 0.786694i \(-0.711791\pi\)
−0.617343 + 0.786694i \(0.711791\pi\)
\(278\) −25.6805 −1.54021
\(279\) −4.56501 −0.273300
\(280\) 36.0871 2.15662
\(281\) 12.2280 0.729459 0.364730 0.931114i \(-0.381161\pi\)
0.364730 + 0.931114i \(0.381161\pi\)
\(282\) −11.7487 −0.699623
\(283\) 16.4398 0.977247 0.488623 0.872495i \(-0.337499\pi\)
0.488623 + 0.872495i \(0.337499\pi\)
\(284\) 7.18662 0.426447
\(285\) 2.83326 0.167828
\(286\) −36.2708 −2.14474
\(287\) −37.8114 −2.23193
\(288\) 46.0175 2.71161
\(289\) −16.9811 −0.998888
\(290\) 9.28649 0.545321
\(291\) 3.50851 0.205672
\(292\) −10.9924 −0.643281
\(293\) 4.35771 0.254580 0.127290 0.991866i \(-0.459372\pi\)
0.127290 + 0.991866i \(0.459372\pi\)
\(294\) 15.4406 0.900516
\(295\) 6.06653 0.353207
\(296\) 39.4874 2.29516
\(297\) 7.87145 0.456748
\(298\) −58.6838 −3.39946
\(299\) −21.9623 −1.27011
\(300\) −2.87560 −0.166023
\(301\) 22.9700 1.32397
\(302\) −19.1153 −1.09996
\(303\) −5.15209 −0.295980
\(304\) −65.7401 −3.77045
\(305\) 4.55268 0.260686
\(306\) −0.995924 −0.0569332
\(307\) −5.57201 −0.318012 −0.159006 0.987278i \(-0.550829\pi\)
−0.159006 + 0.987278i \(0.550829\pi\)
\(308\) −54.6139 −3.11191
\(309\) 5.65635 0.321778
\(310\) −4.54859 −0.258343
\(311\) 8.45195 0.479266 0.239633 0.970864i \(-0.422973\pi\)
0.239633 + 0.970864i \(0.422973\pi\)
\(312\) 25.6530 1.45232
\(313\) 21.7270 1.22808 0.614041 0.789274i \(-0.289543\pi\)
0.614041 + 0.789274i \(0.289543\pi\)
\(314\) 2.01824 0.113896
\(315\) 11.2561 0.634208
\(316\) −69.2650 −3.89646
\(317\) 6.21933 0.349312 0.174656 0.984629i \(-0.444119\pi\)
0.174656 + 0.984629i \(0.444119\pi\)
\(318\) −1.74975 −0.0981210
\(319\) −8.66688 −0.485252
\(320\) 20.2761 1.13347
\(321\) 3.40496 0.190046
\(322\) −45.7452 −2.54928
\(323\) 0.706802 0.0393275
\(324\) 33.1760 1.84311
\(325\) 5.38461 0.298685
\(326\) 0.811245 0.0449307
\(327\) 1.25082 0.0691704
\(328\) −78.2927 −4.32299
\(329\) 33.1254 1.82626
\(330\) 3.71246 0.204364
\(331\) −1.60605 −0.0882764 −0.0441382 0.999025i \(-0.514054\pi\)
−0.0441382 + 0.999025i \(0.514054\pi\)
\(332\) −17.9847 −0.987036
\(333\) 12.3167 0.674949
\(334\) 41.2858 2.25906
\(335\) 5.60322 0.306136
\(336\) 29.4231 1.60516
\(337\) 19.7668 1.07676 0.538382 0.842701i \(-0.319036\pi\)
0.538382 + 0.842701i \(0.319036\pi\)
\(338\) −42.9689 −2.33720
\(339\) 2.43952 0.132497
\(340\) −0.717364 −0.0389045
\(341\) 4.24510 0.229885
\(342\) −37.2378 −2.01359
\(343\) −14.3119 −0.772768
\(344\) 47.5619 2.56437
\(345\) 2.24793 0.121024
\(346\) −44.8707 −2.41226
\(347\) 28.4597 1.52780 0.763899 0.645336i \(-0.223283\pi\)
0.763899 + 0.645336i \(0.223283\pi\)
\(348\) 9.93993 0.532836
\(349\) −9.69739 −0.519090 −0.259545 0.965731i \(-0.583573\pi\)
−0.259545 + 0.965731i \(0.583573\pi\)
\(350\) 11.2156 0.599499
\(351\) 16.9045 0.902295
\(352\) −42.7928 −2.28086
\(353\) −1.88103 −0.100117 −0.0500586 0.998746i \(-0.515941\pi\)
−0.0500586 + 0.998746i \(0.515941\pi\)
\(354\) 8.98245 0.477412
\(355\) 1.37739 0.0731040
\(356\) 5.39497 0.285933
\(357\) −0.316341 −0.0167425
\(358\) 22.4850 1.18837
\(359\) −14.2015 −0.749528 −0.374764 0.927120i \(-0.622276\pi\)
−0.374764 + 0.927120i \(0.622276\pi\)
\(360\) 23.3070 1.22838
\(361\) 7.42746 0.390919
\(362\) −0.331713 −0.0174344
\(363\) 2.59774 0.136346
\(364\) −117.287 −6.14752
\(365\) −2.10680 −0.110275
\(366\) 6.74096 0.352356
\(367\) 26.2555 1.37053 0.685264 0.728295i \(-0.259687\pi\)
0.685264 + 0.728295i \(0.259687\pi\)
\(368\) −52.1586 −2.71896
\(369\) −24.4206 −1.27128
\(370\) 12.2724 0.638011
\(371\) 4.93341 0.256130
\(372\) −4.86866 −0.252428
\(373\) −20.6020 −1.06673 −0.533366 0.845884i \(-0.679073\pi\)
−0.533366 + 0.845884i \(0.679073\pi\)
\(374\) 0.926132 0.0478892
\(375\) −0.551136 −0.0284605
\(376\) 68.5898 3.53725
\(377\) −18.6127 −0.958604
\(378\) 35.2103 1.81102
\(379\) −31.7907 −1.63298 −0.816489 0.577361i \(-0.804083\pi\)
−0.816489 + 0.577361i \(0.804083\pi\)
\(380\) −26.8224 −1.37596
\(381\) −10.4835 −0.537087
\(382\) −15.3497 −0.785361
\(383\) −18.7585 −0.958516 −0.479258 0.877674i \(-0.659094\pi\)
−0.479258 + 0.877674i \(0.659094\pi\)
\(384\) 11.2092 0.572018
\(385\) −10.4673 −0.533462
\(386\) 28.3927 1.44515
\(387\) 14.8352 0.754116
\(388\) −33.2149 −1.68623
\(389\) 15.3497 0.778259 0.389129 0.921183i \(-0.372776\pi\)
0.389129 + 0.921183i \(0.372776\pi\)
\(390\) 7.97276 0.403717
\(391\) 0.560781 0.0283599
\(392\) −90.1438 −4.55295
\(393\) 4.91843 0.248102
\(394\) 27.1956 1.37009
\(395\) −13.2753 −0.667953
\(396\) −35.2725 −1.77251
\(397\) 6.77136 0.339845 0.169923 0.985457i \(-0.445648\pi\)
0.169923 + 0.985457i \(0.445648\pi\)
\(398\) 40.0897 2.00951
\(399\) −11.8280 −0.592143
\(400\) 12.7880 0.639400
\(401\) −1.40707 −0.0702657 −0.0351329 0.999383i \(-0.511185\pi\)
−0.0351329 + 0.999383i \(0.511185\pi\)
\(402\) 8.29644 0.413789
\(403\) 9.11666 0.454133
\(404\) 48.7747 2.42663
\(405\) 6.35851 0.315957
\(406\) −38.7684 −1.92404
\(407\) −11.4535 −0.567731
\(408\) −0.655019 −0.0324283
\(409\) 12.2604 0.606238 0.303119 0.952953i \(-0.401972\pi\)
0.303119 + 0.952953i \(0.401972\pi\)
\(410\) −24.3328 −1.20171
\(411\) 7.78420 0.383966
\(412\) −53.5484 −2.63814
\(413\) −25.3260 −1.24621
\(414\) −29.5447 −1.45204
\(415\) −3.44693 −0.169203
\(416\) −91.9005 −4.50579
\(417\) −5.26825 −0.257987
\(418\) 34.6283 1.69372
\(419\) −7.10863 −0.347279 −0.173640 0.984809i \(-0.555553\pi\)
−0.173640 + 0.984809i \(0.555553\pi\)
\(420\) 12.0048 0.585774
\(421\) −13.0499 −0.636013 −0.318007 0.948088i \(-0.603013\pi\)
−0.318007 + 0.948088i \(0.603013\pi\)
\(422\) 62.9515 3.06443
\(423\) 21.3941 1.04022
\(424\) 10.2152 0.496093
\(425\) −0.137490 −0.00666923
\(426\) 2.03943 0.0988109
\(427\) −19.0061 −0.919772
\(428\) −32.2346 −1.55812
\(429\) −7.44081 −0.359246
\(430\) 14.7819 0.712845
\(431\) 7.98782 0.384760 0.192380 0.981321i \(-0.438379\pi\)
0.192380 + 0.981321i \(0.438379\pi\)
\(432\) 40.1467 1.93156
\(433\) −23.3731 −1.12324 −0.561619 0.827396i \(-0.689821\pi\)
−0.561619 + 0.827396i \(0.689821\pi\)
\(434\) 18.9891 0.911505
\(435\) 1.90508 0.0913418
\(436\) −11.8414 −0.567102
\(437\) 20.9677 1.00302
\(438\) −3.11944 −0.149053
\(439\) −35.4872 −1.69371 −0.846855 0.531824i \(-0.821507\pi\)
−0.846855 + 0.531824i \(0.821507\pi\)
\(440\) −21.6737 −1.03325
\(441\) −28.1171 −1.33891
\(442\) 1.98893 0.0946040
\(443\) 13.6082 0.646543 0.323272 0.946306i \(-0.395217\pi\)
0.323272 + 0.946306i \(0.395217\pi\)
\(444\) 13.1359 0.623404
\(445\) 1.03400 0.0490162
\(446\) 39.6175 1.87595
\(447\) −12.0387 −0.569413
\(448\) −84.6469 −3.99919
\(449\) 16.2595 0.767331 0.383666 0.923472i \(-0.374662\pi\)
0.383666 + 0.923472i \(0.374662\pi\)
\(450\) 7.24362 0.341468
\(451\) 22.7092 1.06934
\(452\) −23.0949 −1.08629
\(453\) −3.92142 −0.184244
\(454\) −67.7377 −3.17909
\(455\) −22.4792 −1.05384
\(456\) −24.4913 −1.14691
\(457\) −22.0888 −1.03327 −0.516636 0.856205i \(-0.672816\pi\)
−0.516636 + 0.856205i \(0.672816\pi\)
\(458\) −12.1301 −0.566801
\(459\) −0.431636 −0.0201470
\(460\) −21.2810 −0.992233
\(461\) 21.2236 0.988484 0.494242 0.869324i \(-0.335446\pi\)
0.494242 + 0.869324i \(0.335446\pi\)
\(462\) −15.4984 −0.721053
\(463\) 3.75121 0.174334 0.0871668 0.996194i \(-0.472219\pi\)
0.0871668 + 0.996194i \(0.472219\pi\)
\(464\) −44.2037 −2.05210
\(465\) −0.933125 −0.0432726
\(466\) −54.1724 −2.50949
\(467\) 22.7424 1.05239 0.526196 0.850363i \(-0.323618\pi\)
0.526196 + 0.850363i \(0.323618\pi\)
\(468\) −75.7502 −3.50155
\(469\) −23.3918 −1.08013
\(470\) 21.3172 0.983288
\(471\) 0.414034 0.0190777
\(472\) −52.4404 −2.41376
\(473\) −13.7956 −0.634323
\(474\) −19.6562 −0.902838
\(475\) −5.14076 −0.235874
\(476\) 2.99479 0.137266
\(477\) 3.18626 0.145889
\(478\) 60.4984 2.76713
\(479\) 16.3008 0.744803 0.372401 0.928072i \(-0.378534\pi\)
0.372401 + 0.928072i \(0.378534\pi\)
\(480\) 9.40637 0.429340
\(481\) −24.5973 −1.12154
\(482\) −0.575960 −0.0262343
\(483\) −9.38445 −0.427007
\(484\) −24.5927 −1.11785
\(485\) −6.36595 −0.289063
\(486\) 34.7173 1.57481
\(487\) 6.81584 0.308855 0.154428 0.988004i \(-0.450647\pi\)
0.154428 + 0.988004i \(0.450647\pi\)
\(488\) −39.3544 −1.78149
\(489\) 0.166424 0.00752593
\(490\) −28.0160 −1.26563
\(491\) −7.37205 −0.332696 −0.166348 0.986067i \(-0.553197\pi\)
−0.166348 + 0.986067i \(0.553197\pi\)
\(492\) −26.0449 −1.17420
\(493\) 0.475254 0.0214044
\(494\) 74.3666 3.34591
\(495\) −6.76032 −0.303854
\(496\) 21.6513 0.972172
\(497\) −5.75019 −0.257931
\(498\) −5.10373 −0.228703
\(499\) −19.3192 −0.864848 −0.432424 0.901670i \(-0.642342\pi\)
−0.432424 + 0.901670i \(0.642342\pi\)
\(500\) 5.21758 0.233337
\(501\) 8.46961 0.378394
\(502\) −44.1916 −1.97237
\(503\) 38.1145 1.69944 0.849722 0.527231i \(-0.176770\pi\)
0.849722 + 0.527231i \(0.176770\pi\)
\(504\) −97.2998 −4.33408
\(505\) 9.34813 0.415986
\(506\) 27.4743 1.22138
\(507\) −8.81490 −0.391483
\(508\) 99.2472 4.40338
\(509\) 16.5328 0.732803 0.366401 0.930457i \(-0.380590\pi\)
0.366401 + 0.930457i \(0.380590\pi\)
\(510\) −0.203575 −0.00901445
\(511\) 8.79527 0.389080
\(512\) 2.82850 0.125003
\(513\) −16.1390 −0.712552
\(514\) 33.5980 1.48194
\(515\) −10.2631 −0.452245
\(516\) 15.8220 0.696525
\(517\) −19.8949 −0.874975
\(518\) −51.2337 −2.25108
\(519\) −9.20503 −0.404056
\(520\) −46.5457 −2.04117
\(521\) −9.38900 −0.411340 −0.205670 0.978621i \(-0.565937\pi\)
−0.205670 + 0.978621i \(0.565937\pi\)
\(522\) −25.0387 −1.09591
\(523\) 44.8717 1.96210 0.981052 0.193744i \(-0.0620632\pi\)
0.981052 + 0.193744i \(0.0620632\pi\)
\(524\) −46.5626 −2.03409
\(525\) 2.30083 0.100417
\(526\) −11.2971 −0.492579
\(527\) −0.232783 −0.0101402
\(528\) −17.6713 −0.769044
\(529\) −6.36408 −0.276699
\(530\) 3.17480 0.137905
\(531\) −16.3569 −0.709828
\(532\) 111.976 4.85476
\(533\) 48.7697 2.11245
\(534\) 1.53100 0.0662527
\(535\) −6.17808 −0.267101
\(536\) −48.4354 −2.09209
\(537\) 4.61271 0.199053
\(538\) −19.3147 −0.832716
\(539\) 26.1467 1.12622
\(540\) 16.3801 0.704888
\(541\) 35.1182 1.50985 0.754924 0.655812i \(-0.227674\pi\)
0.754924 + 0.655812i \(0.227674\pi\)
\(542\) −72.1970 −3.10113
\(543\) −0.0680496 −0.00292029
\(544\) 2.34657 0.100608
\(545\) −2.26953 −0.0972159
\(546\) −33.2840 −1.42442
\(547\) −32.2773 −1.38008 −0.690038 0.723773i \(-0.742406\pi\)
−0.690038 + 0.723773i \(0.742406\pi\)
\(548\) −73.6927 −3.14800
\(549\) −12.2752 −0.523891
\(550\) −6.73601 −0.287225
\(551\) 17.7698 0.757020
\(552\) −19.4316 −0.827062
\(553\) 55.4206 2.35672
\(554\) 55.2068 2.34551
\(555\) 2.51763 0.106867
\(556\) 49.8743 2.11514
\(557\) 13.0377 0.552426 0.276213 0.961096i \(-0.410920\pi\)
0.276213 + 0.961096i \(0.410920\pi\)
\(558\) 12.2641 0.519183
\(559\) −29.6270 −1.25309
\(560\) −53.3862 −2.25598
\(561\) 0.189992 0.00802148
\(562\) −32.8511 −1.38574
\(563\) −42.3308 −1.78403 −0.892014 0.452007i \(-0.850708\pi\)
−0.892014 + 0.452007i \(0.850708\pi\)
\(564\) 22.8172 0.960776
\(565\) −4.42636 −0.186218
\(566\) −44.1665 −1.85646
\(567\) −26.5449 −1.11478
\(568\) −11.9064 −0.499582
\(569\) 41.0841 1.72234 0.861168 0.508320i \(-0.169733\pi\)
0.861168 + 0.508320i \(0.169733\pi\)
\(570\) −7.61171 −0.318819
\(571\) −26.1998 −1.09643 −0.548213 0.836339i \(-0.684692\pi\)
−0.548213 + 0.836339i \(0.684692\pi\)
\(572\) 70.4419 2.94532
\(573\) −3.14893 −0.131549
\(574\) 101.582 4.23996
\(575\) −4.07872 −0.170094
\(576\) −54.6694 −2.27789
\(577\) −13.4846 −0.561370 −0.280685 0.959800i \(-0.590562\pi\)
−0.280685 + 0.959800i \(0.590562\pi\)
\(578\) 45.6207 1.89757
\(579\) 5.82464 0.242064
\(580\) −18.0354 −0.748878
\(581\) 14.3900 0.596996
\(582\) −9.42580 −0.390712
\(583\) −2.96298 −0.122714
\(584\) 18.2116 0.753602
\(585\) −14.5183 −0.600256
\(586\) −11.7072 −0.483621
\(587\) −39.6361 −1.63596 −0.817979 0.575248i \(-0.804906\pi\)
−0.817979 + 0.575248i \(0.804906\pi\)
\(588\) −29.9874 −1.23666
\(589\) −8.70380 −0.358634
\(590\) −16.2981 −0.670981
\(591\) 5.57906 0.229492
\(592\) −58.4165 −2.40090
\(593\) −17.9368 −0.736577 −0.368288 0.929712i \(-0.620056\pi\)
−0.368288 + 0.929712i \(0.620056\pi\)
\(594\) −21.1471 −0.867676
\(595\) 0.573980 0.0235309
\(596\) 113.970 4.66840
\(597\) 8.22424 0.336596
\(598\) 59.0030 2.41281
\(599\) −21.7227 −0.887565 −0.443782 0.896135i \(-0.646364\pi\)
−0.443782 + 0.896135i \(0.646364\pi\)
\(600\) 4.76414 0.194495
\(601\) 26.5987 1.08498 0.542491 0.840061i \(-0.317481\pi\)
0.542491 + 0.840061i \(0.317481\pi\)
\(602\) −61.7101 −2.51511
\(603\) −15.1077 −0.615232
\(604\) 37.1240 1.51055
\(605\) −4.71342 −0.191628
\(606\) 13.8414 0.562268
\(607\) 17.9496 0.728553 0.364277 0.931291i \(-0.381316\pi\)
0.364277 + 0.931291i \(0.381316\pi\)
\(608\) 87.7387 3.55827
\(609\) −7.95318 −0.322279
\(610\) −12.2310 −0.495220
\(611\) −42.7256 −1.72849
\(612\) 1.93419 0.0781851
\(613\) −5.66539 −0.228823 −0.114412 0.993433i \(-0.536498\pi\)
−0.114412 + 0.993433i \(0.536498\pi\)
\(614\) 14.9695 0.604121
\(615\) −4.99177 −0.201287
\(616\) 90.4814 3.64560
\(617\) −10.5310 −0.423963 −0.211982 0.977274i \(-0.567992\pi\)
−0.211982 + 0.977274i \(0.567992\pi\)
\(618\) −15.1961 −0.611276
\(619\) 22.2872 0.895799 0.447900 0.894084i \(-0.352172\pi\)
0.447900 + 0.894084i \(0.352172\pi\)
\(620\) 8.83386 0.354776
\(621\) −12.8047 −0.513837
\(622\) −22.7066 −0.910454
\(623\) −4.31664 −0.172943
\(624\) −37.9503 −1.51923
\(625\) 1.00000 0.0400000
\(626\) −58.3708 −2.33296
\(627\) 7.10384 0.283700
\(628\) −3.91964 −0.156411
\(629\) 0.628063 0.0250425
\(630\) −30.2401 −1.20479
\(631\) 41.9274 1.66910 0.834552 0.550930i \(-0.185727\pi\)
0.834552 + 0.550930i \(0.185727\pi\)
\(632\) 114.755 4.56469
\(633\) 12.9142 0.513295
\(634\) −16.7086 −0.663583
\(635\) 19.0217 0.754852
\(636\) 3.39820 0.134747
\(637\) 56.1520 2.22482
\(638\) 23.2841 0.921825
\(639\) −3.71377 −0.146915
\(640\) −20.3384 −0.803946
\(641\) 20.7974 0.821447 0.410723 0.911760i \(-0.365276\pi\)
0.410723 + 0.911760i \(0.365276\pi\)
\(642\) −9.14761 −0.361027
\(643\) 43.7406 1.72496 0.862480 0.506091i \(-0.168910\pi\)
0.862480 + 0.506091i \(0.168910\pi\)
\(644\) 88.8422 3.50087
\(645\) 3.03244 0.119402
\(646\) −1.89886 −0.0747098
\(647\) 49.3297 1.93935 0.969675 0.244397i \(-0.0785899\pi\)
0.969675 + 0.244397i \(0.0785899\pi\)
\(648\) −54.9643 −2.15920
\(649\) 15.2106 0.597070
\(650\) −14.4661 −0.567406
\(651\) 3.89553 0.152678
\(652\) −1.57553 −0.0617023
\(653\) 7.98269 0.312387 0.156193 0.987727i \(-0.450078\pi\)
0.156193 + 0.987727i \(0.450078\pi\)
\(654\) −3.36039 −0.131402
\(655\) −8.92416 −0.348696
\(656\) 115.824 4.52216
\(657\) 5.68045 0.221615
\(658\) −88.9931 −3.46931
\(659\) 42.2683 1.64654 0.823270 0.567649i \(-0.192147\pi\)
0.823270 + 0.567649i \(0.192147\pi\)
\(660\) −7.21000 −0.280649
\(661\) 10.4675 0.407138 0.203569 0.979061i \(-0.434746\pi\)
0.203569 + 0.979061i \(0.434746\pi\)
\(662\) 4.31474 0.167697
\(663\) 0.408022 0.0158462
\(664\) 29.7960 1.15631
\(665\) 21.4612 0.832230
\(666\) −33.0894 −1.28219
\(667\) 14.0987 0.545904
\(668\) −80.1814 −3.10231
\(669\) 8.12737 0.314222
\(670\) −15.0534 −0.581562
\(671\) 11.4150 0.440670
\(672\) −39.2689 −1.51483
\(673\) 45.1154 1.73907 0.869536 0.493870i \(-0.164418\pi\)
0.869536 + 0.493870i \(0.164418\pi\)
\(674\) −53.1046 −2.04551
\(675\) 3.13941 0.120836
\(676\) 83.4503 3.20963
\(677\) 4.12144 0.158400 0.0791999 0.996859i \(-0.474763\pi\)
0.0791999 + 0.996859i \(0.474763\pi\)
\(678\) −6.55392 −0.251702
\(679\) 26.5760 1.01989
\(680\) 1.18849 0.0455765
\(681\) −13.8961 −0.532500
\(682\) −11.4047 −0.436709
\(683\) 10.8404 0.414797 0.207399 0.978257i \(-0.433500\pi\)
0.207399 + 0.978257i \(0.433500\pi\)
\(684\) 72.3198 2.76522
\(685\) −14.1239 −0.539647
\(686\) 38.4496 1.46801
\(687\) −2.48843 −0.0949397
\(688\) −70.3617 −2.68251
\(689\) −6.36320 −0.242418
\(690\) −6.03918 −0.229908
\(691\) −2.42507 −0.0922541 −0.0461270 0.998936i \(-0.514688\pi\)
−0.0461270 + 0.998936i \(0.514688\pi\)
\(692\) 87.1437 3.31271
\(693\) 28.2224 1.07208
\(694\) −76.4586 −2.90233
\(695\) 9.55889 0.362589
\(696\) −16.4680 −0.624216
\(697\) −1.24528 −0.0471682
\(698\) 26.0526 0.986105
\(699\) −11.1132 −0.420342
\(700\) −21.7819 −0.823279
\(701\) 4.92637 0.186066 0.0930332 0.995663i \(-0.470344\pi\)
0.0930332 + 0.995663i \(0.470344\pi\)
\(702\) −45.4149 −1.71407
\(703\) 23.4834 0.885693
\(704\) 50.8384 1.91604
\(705\) 4.37313 0.164702
\(706\) 5.05350 0.190191
\(707\) −39.0258 −1.46772
\(708\) −17.4449 −0.655619
\(709\) −17.3908 −0.653126 −0.326563 0.945175i \(-0.605891\pi\)
−0.326563 + 0.945175i \(0.605891\pi\)
\(710\) −3.70042 −0.138874
\(711\) 35.7935 1.34236
\(712\) −8.93810 −0.334969
\(713\) −6.90565 −0.258619
\(714\) 0.849867 0.0318055
\(715\) 13.5009 0.504904
\(716\) −43.6684 −1.63196
\(717\) 12.4110 0.463497
\(718\) 38.1532 1.42386
\(719\) −25.8386 −0.963617 −0.481809 0.876277i \(-0.660020\pi\)
−0.481809 + 0.876277i \(0.660020\pi\)
\(720\) −34.4796 −1.28498
\(721\) 42.8454 1.59565
\(722\) −19.9543 −0.742621
\(723\) −0.118156 −0.00439427
\(724\) 0.644223 0.0239423
\(725\) −3.45665 −0.128377
\(726\) −6.97896 −0.259014
\(727\) 14.0373 0.520614 0.260307 0.965526i \(-0.416176\pi\)
0.260307 + 0.965526i \(0.416176\pi\)
\(728\) 194.315 7.20180
\(729\) −11.9534 −0.442719
\(730\) 5.66003 0.209487
\(731\) 0.756491 0.0279798
\(732\) −13.0917 −0.483882
\(733\) 47.7566 1.76393 0.881966 0.471314i \(-0.156220\pi\)
0.881966 + 0.471314i \(0.156220\pi\)
\(734\) −70.5370 −2.60357
\(735\) −5.74737 −0.211995
\(736\) 69.6124 2.56595
\(737\) 14.0490 0.517500
\(738\) 65.6072 2.41503
\(739\) −53.1000 −1.95331 −0.976657 0.214804i \(-0.931089\pi\)
−0.976657 + 0.214804i \(0.931089\pi\)
\(740\) −23.8343 −0.876166
\(741\) 15.2560 0.560443
\(742\) −13.2539 −0.486566
\(743\) 47.3435 1.73686 0.868432 0.495808i \(-0.165128\pi\)
0.868432 + 0.495808i \(0.165128\pi\)
\(744\) 8.06613 0.295719
\(745\) 21.8435 0.800284
\(746\) 55.3485 2.02645
\(747\) 9.29379 0.340042
\(748\) −1.79865 −0.0657651
\(749\) 25.7917 0.942408
\(750\) 1.48066 0.0540659
\(751\) −30.4409 −1.11081 −0.555403 0.831581i \(-0.687436\pi\)
−0.555403 + 0.831581i \(0.687436\pi\)
\(752\) −101.470 −3.70022
\(753\) −9.06573 −0.330374
\(754\) 50.0041 1.82104
\(755\) 7.11517 0.258947
\(756\) −68.3823 −2.48704
\(757\) −22.3310 −0.811633 −0.405817 0.913955i \(-0.633013\pi\)
−0.405817 + 0.913955i \(0.633013\pi\)
\(758\) 85.4075 3.10214
\(759\) 5.63624 0.204582
\(760\) 44.4379 1.61193
\(761\) 42.4805 1.53992 0.769959 0.638093i \(-0.220276\pi\)
0.769959 + 0.638093i \(0.220276\pi\)
\(762\) 28.1646 1.02029
\(763\) 9.47462 0.343004
\(764\) 29.8108 1.07852
\(765\) 0.370706 0.0134029
\(766\) 50.3959 1.82088
\(767\) 32.6659 1.17950
\(768\) −7.76442 −0.280174
\(769\) −51.5033 −1.85726 −0.928628 0.371012i \(-0.879011\pi\)
−0.928628 + 0.371012i \(0.879011\pi\)
\(770\) 28.1209 1.01341
\(771\) 6.89249 0.248227
\(772\) −55.1416 −1.98459
\(773\) −2.56997 −0.0924355 −0.0462177 0.998931i \(-0.514717\pi\)
−0.0462177 + 0.998931i \(0.514717\pi\)
\(774\) −39.8556 −1.43258
\(775\) 1.69309 0.0608178
\(776\) 55.0287 1.97541
\(777\) −10.5104 −0.377058
\(778\) −41.2377 −1.47844
\(779\) −46.5611 −1.66822
\(780\) −15.4840 −0.554415
\(781\) 3.45352 0.123577
\(782\) −1.50657 −0.0538748
\(783\) −10.8518 −0.387813
\(784\) 133.356 4.76272
\(785\) −0.751237 −0.0268128
\(786\) −13.2136 −0.471314
\(787\) −17.4009 −0.620277 −0.310138 0.950691i \(-0.600375\pi\)
−0.310138 + 0.950691i \(0.600375\pi\)
\(788\) −52.8167 −1.88152
\(789\) −2.31756 −0.0825074
\(790\) 35.6648 1.26890
\(791\) 18.4788 0.657029
\(792\) 58.4376 2.07649
\(793\) 24.5144 0.870533
\(794\) −18.1916 −0.645597
\(795\) 0.651298 0.0230991
\(796\) −77.8585 −2.75962
\(797\) 44.9685 1.59287 0.796433 0.604727i \(-0.206718\pi\)
0.796433 + 0.604727i \(0.206718\pi\)
\(798\) 31.7767 1.12488
\(799\) 1.09095 0.0385950
\(800\) −17.0672 −0.603418
\(801\) −2.78792 −0.0985062
\(802\) 3.78017 0.133482
\(803\) −5.28238 −0.186411
\(804\) −16.1126 −0.568247
\(805\) 17.0275 0.600139
\(806\) −24.4924 −0.862708
\(807\) −3.96233 −0.139481
\(808\) −80.8073 −2.84279
\(809\) 14.0536 0.494098 0.247049 0.969003i \(-0.420539\pi\)
0.247049 + 0.969003i \(0.420539\pi\)
\(810\) −17.0825 −0.600217
\(811\) −45.9069 −1.61201 −0.806005 0.591909i \(-0.798375\pi\)
−0.806005 + 0.591909i \(0.798375\pi\)
\(812\) 75.2925 2.64225
\(813\) −14.8109 −0.519442
\(814\) 30.7706 1.07851
\(815\) −0.301965 −0.0105774
\(816\) 0.969017 0.0339224
\(817\) 28.2853 0.989578
\(818\) −32.9383 −1.15166
\(819\) 60.6096 2.11787
\(820\) 47.2569 1.65028
\(821\) 45.4069 1.58471 0.792357 0.610058i \(-0.208854\pi\)
0.792357 + 0.610058i \(0.208854\pi\)
\(822\) −20.9127 −0.729414
\(823\) 39.5396 1.37826 0.689132 0.724635i \(-0.257992\pi\)
0.689132 + 0.724635i \(0.257992\pi\)
\(824\) 88.7162 3.09057
\(825\) −1.38187 −0.0481104
\(826\) 68.0398 2.36741
\(827\) 42.7376 1.48613 0.743067 0.669218i \(-0.233371\pi\)
0.743067 + 0.669218i \(0.233371\pi\)
\(828\) 57.3790 1.99406
\(829\) −21.3426 −0.741259 −0.370630 0.928781i \(-0.620858\pi\)
−0.370630 + 0.928781i \(0.620858\pi\)
\(830\) 9.26038 0.321432
\(831\) 11.3254 0.392875
\(832\) 109.179 3.78510
\(833\) −1.43377 −0.0496773
\(834\) 14.1534 0.490093
\(835\) −15.3675 −0.531816
\(836\) −67.2518 −2.32595
\(837\) 5.31531 0.183724
\(838\) 19.0977 0.659720
\(839\) 17.2492 0.595509 0.297755 0.954642i \(-0.403762\pi\)
0.297755 + 0.954642i \(0.403762\pi\)
\(840\) −19.8889 −0.686232
\(841\) −17.0516 −0.587985
\(842\) 35.0593 1.20822
\(843\) −6.73927 −0.232113
\(844\) −122.259 −4.20832
\(845\) 15.9941 0.550212
\(846\) −57.4764 −1.97608
\(847\) 19.6772 0.676116
\(848\) −15.1121 −0.518950
\(849\) −9.06058 −0.310958
\(850\) 0.369374 0.0126694
\(851\) 18.6319 0.638692
\(852\) −3.96080 −0.135695
\(853\) 3.39166 0.116128 0.0580641 0.998313i \(-0.481507\pi\)
0.0580641 + 0.998313i \(0.481507\pi\)
\(854\) 51.0611 1.74727
\(855\) 13.8608 0.474029
\(856\) 53.4046 1.82533
\(857\) −11.1756 −0.381750 −0.190875 0.981614i \(-0.561132\pi\)
−0.190875 + 0.981614i \(0.561132\pi\)
\(858\) 19.9902 0.682453
\(859\) −34.0465 −1.16165 −0.580826 0.814027i \(-0.697271\pi\)
−0.580826 + 0.814027i \(0.697271\pi\)
\(860\) −28.7080 −0.978935
\(861\) 20.8392 0.710198
\(862\) −21.4597 −0.730921
\(863\) −39.7923 −1.35455 −0.677273 0.735731i \(-0.736839\pi\)
−0.677273 + 0.735731i \(0.736839\pi\)
\(864\) −53.5810 −1.82286
\(865\) 16.7019 0.567883
\(866\) 62.7931 2.13379
\(867\) 9.35889 0.317845
\(868\) −36.8788 −1.25175
\(869\) −33.2852 −1.12912
\(870\) −5.11812 −0.173520
\(871\) 30.1711 1.02231
\(872\) 19.6183 0.664359
\(873\) 17.1642 0.580920
\(874\) −56.3309 −1.90542
\(875\) −4.17471 −0.141131
\(876\) 6.05830 0.204691
\(877\) −20.2518 −0.683853 −0.341927 0.939727i \(-0.611079\pi\)
−0.341927 + 0.939727i \(0.611079\pi\)
\(878\) 95.3383 3.21751
\(879\) −2.40169 −0.0810069
\(880\) 32.0634 1.08086
\(881\) 30.1657 1.01631 0.508154 0.861266i \(-0.330328\pi\)
0.508154 + 0.861266i \(0.330328\pi\)
\(882\) 75.5382 2.54350
\(883\) 45.4949 1.53103 0.765513 0.643421i \(-0.222485\pi\)
0.765513 + 0.643421i \(0.222485\pi\)
\(884\) −3.86273 −0.129918
\(885\) −3.34348 −0.112390
\(886\) −36.5591 −1.22823
\(887\) −3.27161 −0.109850 −0.0549250 0.998490i \(-0.517492\pi\)
−0.0549250 + 0.998490i \(0.517492\pi\)
\(888\) −21.7629 −0.730316
\(889\) −79.4100 −2.66333
\(890\) −2.77789 −0.0931152
\(891\) 15.9427 0.534101
\(892\) −76.9416 −2.57619
\(893\) 40.7907 1.36501
\(894\) 32.3427 1.08170
\(895\) −8.36947 −0.279760
\(896\) 84.9070 2.83654
\(897\) 12.1042 0.404148
\(898\) −43.6819 −1.45769
\(899\) −5.85244 −0.195190
\(900\) −14.0679 −0.468930
\(901\) 0.162477 0.00541288
\(902\) −61.0097 −2.03140
\(903\) −12.6596 −0.421284
\(904\) 38.2624 1.27259
\(905\) 0.123471 0.00410433
\(906\) 10.5351 0.350006
\(907\) −27.2913 −0.906191 −0.453096 0.891462i \(-0.649680\pi\)
−0.453096 + 0.891462i \(0.649680\pi\)
\(908\) 131.554 4.36577
\(909\) −25.2049 −0.835994
\(910\) 60.3917 2.00196
\(911\) −27.6325 −0.915506 −0.457753 0.889079i \(-0.651346\pi\)
−0.457753 + 0.889079i \(0.651346\pi\)
\(912\) 36.2317 1.19975
\(913\) −8.64251 −0.286025
\(914\) 59.3428 1.96289
\(915\) −2.50915 −0.0829498
\(916\) 23.5579 0.778376
\(917\) 37.2558 1.23030
\(918\) 1.15961 0.0382730
\(919\) 35.1920 1.16088 0.580439 0.814304i \(-0.302881\pi\)
0.580439 + 0.814304i \(0.302881\pi\)
\(920\) 35.2573 1.16240
\(921\) 3.07094 0.101191
\(922\) −57.0185 −1.87780
\(923\) 7.41669 0.244123
\(924\) 30.0997 0.990206
\(925\) −4.56807 −0.150197
\(926\) −10.0778 −0.331178
\(927\) 27.6718 0.908861
\(928\) 58.9955 1.93662
\(929\) 25.7186 0.843800 0.421900 0.906642i \(-0.361363\pi\)
0.421900 + 0.906642i \(0.361363\pi\)
\(930\) 2.50689 0.0822042
\(931\) −53.6091 −1.75697
\(932\) 105.209 3.44623
\(933\) −4.65817 −0.152502
\(934\) −61.0987 −1.99921
\(935\) −0.344729 −0.0112738
\(936\) 125.499 4.10206
\(937\) 3.14560 0.102762 0.0513811 0.998679i \(-0.483638\pi\)
0.0513811 + 0.998679i \(0.483638\pi\)
\(938\) 62.8434 2.05191
\(939\) −11.9745 −0.390774
\(940\) −41.4003 −1.35033
\(941\) −31.3154 −1.02085 −0.510427 0.859921i \(-0.670513\pi\)
−0.510427 + 0.859921i \(0.670513\pi\)
\(942\) −1.11232 −0.0362415
\(943\) −36.9419 −1.20299
\(944\) 77.5788 2.52497
\(945\) −13.1061 −0.426342
\(946\) 37.0627 1.20501
\(947\) 33.8579 1.10023 0.550117 0.835088i \(-0.314583\pi\)
0.550117 + 0.835088i \(0.314583\pi\)
\(948\) 38.1744 1.23985
\(949\) −11.3443 −0.368251
\(950\) 13.8110 0.448086
\(951\) −3.42770 −0.111151
\(952\) −4.96161 −0.160807
\(953\) 23.4153 0.758496 0.379248 0.925295i \(-0.376183\pi\)
0.379248 + 0.925295i \(0.376183\pi\)
\(954\) −8.56006 −0.277142
\(955\) 5.71354 0.184886
\(956\) −117.494 −3.80004
\(957\) 4.77663 0.154406
\(958\) −43.7930 −1.41489
\(959\) 58.9633 1.90403
\(960\) −11.1749 −0.360668
\(961\) −28.1334 −0.907530
\(962\) 66.0820 2.13057
\(963\) 16.6576 0.536785
\(964\) 1.11858 0.0360270
\(965\) −10.5684 −0.340210
\(966\) 25.2118 0.811178
\(967\) −2.38523 −0.0767040 −0.0383520 0.999264i \(-0.512211\pi\)
−0.0383520 + 0.999264i \(0.512211\pi\)
\(968\) 40.7438 1.30956
\(969\) −0.389544 −0.0125140
\(970\) 17.1025 0.549128
\(971\) 27.7365 0.890107 0.445053 0.895504i \(-0.353185\pi\)
0.445053 + 0.895504i \(0.353185\pi\)
\(972\) −67.4248 −2.16265
\(973\) −39.9056 −1.27932
\(974\) −18.3111 −0.586727
\(975\) −2.96765 −0.0950410
\(976\) 58.2197 1.86357
\(977\) −5.82297 −0.186293 −0.0931467 0.995652i \(-0.529693\pi\)
−0.0931467 + 0.995652i \(0.529693\pi\)
\(978\) −0.447106 −0.0142969
\(979\) 2.59255 0.0828582
\(980\) 54.4101 1.73807
\(981\) 6.11921 0.195371
\(982\) 19.8054 0.632016
\(983\) 57.7876 1.84314 0.921570 0.388213i \(-0.126908\pi\)
0.921570 + 0.388213i \(0.126908\pi\)
\(984\) 43.1499 1.37557
\(985\) −10.1228 −0.322541
\(986\) −1.27680 −0.0406615
\(987\) −18.2566 −0.581113
\(988\) −144.428 −4.59487
\(989\) 22.4418 0.713607
\(990\) 18.1620 0.577225
\(991\) 42.0597 1.33607 0.668035 0.744130i \(-0.267136\pi\)
0.668035 + 0.744130i \(0.267136\pi\)
\(992\) −28.8965 −0.917463
\(993\) 0.885150 0.0280894
\(994\) 15.4482 0.489987
\(995\) −14.9223 −0.473070
\(996\) 9.91199 0.314073
\(997\) 44.6992 1.41564 0.707819 0.706394i \(-0.249679\pi\)
0.707819 + 0.706394i \(0.249679\pi\)
\(998\) 51.9022 1.64294
\(999\) −14.3410 −0.453730
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))