Properties

Label 8041.2.a.i.1.15
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.90003 q^{2} +1.99775 q^{3} +1.61013 q^{4} -3.13238 q^{5} -3.79579 q^{6} -0.279659 q^{7} +0.740768 q^{8} +0.990997 q^{9} +O(q^{10})\) \(q-1.90003 q^{2} +1.99775 q^{3} +1.61013 q^{4} -3.13238 q^{5} -3.79579 q^{6} -0.279659 q^{7} +0.740768 q^{8} +0.990997 q^{9} +5.95163 q^{10} +1.00000 q^{11} +3.21663 q^{12} -1.37133 q^{13} +0.531361 q^{14} -6.25770 q^{15} -4.62774 q^{16} -1.00000 q^{17} -1.88293 q^{18} +2.56782 q^{19} -5.04353 q^{20} -0.558688 q^{21} -1.90003 q^{22} -5.56968 q^{23} +1.47987 q^{24} +4.81179 q^{25} +2.60557 q^{26} -4.01348 q^{27} -0.450287 q^{28} -5.48031 q^{29} +11.8898 q^{30} -2.40258 q^{31} +7.31133 q^{32} +1.99775 q^{33} +1.90003 q^{34} +0.875997 q^{35} +1.59563 q^{36} -6.44814 q^{37} -4.87895 q^{38} -2.73957 q^{39} -2.32037 q^{40} +5.16443 q^{41} +1.06153 q^{42} -1.00000 q^{43} +1.61013 q^{44} -3.10418 q^{45} +10.5826 q^{46} +4.29668 q^{47} -9.24506 q^{48} -6.92179 q^{49} -9.14257 q^{50} -1.99775 q^{51} -2.20802 q^{52} +3.96910 q^{53} +7.62575 q^{54} -3.13238 q^{55} -0.207162 q^{56} +5.12986 q^{57} +10.4128 q^{58} -0.143220 q^{59} -10.0757 q^{60} +13.9770 q^{61} +4.56498 q^{62} -0.277141 q^{63} -4.63629 q^{64} +4.29552 q^{65} -3.79579 q^{66} -9.52542 q^{67} -1.61013 q^{68} -11.1268 q^{69} -1.66442 q^{70} +12.7841 q^{71} +0.734099 q^{72} -10.1584 q^{73} +12.2517 q^{74} +9.61275 q^{75} +4.13453 q^{76} -0.279659 q^{77} +5.20528 q^{78} +2.40998 q^{79} +14.4958 q^{80} -10.9909 q^{81} -9.81259 q^{82} -13.6597 q^{83} -0.899560 q^{84} +3.13238 q^{85} +1.90003 q^{86} -10.9483 q^{87} +0.740768 q^{88} +11.1325 q^{89} +5.89804 q^{90} +0.383505 q^{91} -8.96791 q^{92} -4.79974 q^{93} -8.16383 q^{94} -8.04339 q^{95} +14.6062 q^{96} -7.90060 q^{97} +13.1516 q^{98} +0.990997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.90003 −1.34353 −0.671763 0.740766i \(-0.734463\pi\)
−0.671763 + 0.740766i \(0.734463\pi\)
\(3\) 1.99775 1.15340 0.576700 0.816956i \(-0.304340\pi\)
0.576700 + 0.816956i \(0.304340\pi\)
\(4\) 1.61013 0.805065
\(5\) −3.13238 −1.40084 −0.700421 0.713730i \(-0.747004\pi\)
−0.700421 + 0.713730i \(0.747004\pi\)
\(6\) −3.79579 −1.54962
\(7\) −0.279659 −0.105701 −0.0528506 0.998602i \(-0.516831\pi\)
−0.0528506 + 0.998602i \(0.516831\pi\)
\(8\) 0.740768 0.261901
\(9\) 0.990997 0.330332
\(10\) 5.95163 1.88207
\(11\) 1.00000 0.301511
\(12\) 3.21663 0.928562
\(13\) −1.37133 −0.380338 −0.190169 0.981751i \(-0.560904\pi\)
−0.190169 + 0.981751i \(0.560904\pi\)
\(14\) 0.531361 0.142012
\(15\) −6.25770 −1.61573
\(16\) −4.62774 −1.15694
\(17\) −1.00000 −0.242536
\(18\) −1.88293 −0.443810
\(19\) 2.56782 0.589099 0.294550 0.955636i \(-0.404830\pi\)
0.294550 + 0.955636i \(0.404830\pi\)
\(20\) −5.04353 −1.12777
\(21\) −0.558688 −0.121916
\(22\) −1.90003 −0.405089
\(23\) −5.56968 −1.16136 −0.580680 0.814132i \(-0.697213\pi\)
−0.580680 + 0.814132i \(0.697213\pi\)
\(24\) 1.47987 0.302077
\(25\) 4.81179 0.962359
\(26\) 2.60557 0.510995
\(27\) −4.01348 −0.772395
\(28\) −0.450287 −0.0850962
\(29\) −5.48031 −1.01767 −0.508834 0.860865i \(-0.669923\pi\)
−0.508834 + 0.860865i \(0.669923\pi\)
\(30\) 11.8898 2.17078
\(31\) −2.40258 −0.431516 −0.215758 0.976447i \(-0.569222\pi\)
−0.215758 + 0.976447i \(0.569222\pi\)
\(32\) 7.31133 1.29247
\(33\) 1.99775 0.347763
\(34\) 1.90003 0.325853
\(35\) 0.875997 0.148071
\(36\) 1.59563 0.265939
\(37\) −6.44814 −1.06007 −0.530034 0.847977i \(-0.677821\pi\)
−0.530034 + 0.847977i \(0.677821\pi\)
\(38\) −4.87895 −0.791471
\(39\) −2.73957 −0.438683
\(40\) −2.32037 −0.366882
\(41\) 5.16443 0.806548 0.403274 0.915079i \(-0.367872\pi\)
0.403274 + 0.915079i \(0.367872\pi\)
\(42\) 1.06153 0.163797
\(43\) −1.00000 −0.152499
\(44\) 1.61013 0.242736
\(45\) −3.10418 −0.462743
\(46\) 10.5826 1.56032
\(47\) 4.29668 0.626735 0.313367 0.949632i \(-0.398543\pi\)
0.313367 + 0.949632i \(0.398543\pi\)
\(48\) −9.24506 −1.33441
\(49\) −6.92179 −0.988827
\(50\) −9.14257 −1.29295
\(51\) −1.99775 −0.279741
\(52\) −2.20802 −0.306197
\(53\) 3.96910 0.545198 0.272599 0.962128i \(-0.412117\pi\)
0.272599 + 0.962128i \(0.412117\pi\)
\(54\) 7.62575 1.03773
\(55\) −3.13238 −0.422370
\(56\) −0.207162 −0.0276832
\(57\) 5.12986 0.679467
\(58\) 10.4128 1.36726
\(59\) −0.143220 −0.0186457 −0.00932285 0.999957i \(-0.502968\pi\)
−0.00932285 + 0.999957i \(0.502968\pi\)
\(60\) −10.0757 −1.30077
\(61\) 13.9770 1.78957 0.894785 0.446496i \(-0.147328\pi\)
0.894785 + 0.446496i \(0.147328\pi\)
\(62\) 4.56498 0.579753
\(63\) −0.277141 −0.0349165
\(64\) −4.63629 −0.579537
\(65\) 4.29552 0.532794
\(66\) −3.79579 −0.467229
\(67\) −9.52542 −1.16371 −0.581857 0.813291i \(-0.697674\pi\)
−0.581857 + 0.813291i \(0.697674\pi\)
\(68\) −1.61013 −0.195257
\(69\) −11.1268 −1.33951
\(70\) −1.66442 −0.198937
\(71\) 12.7841 1.51720 0.758600 0.651557i \(-0.225884\pi\)
0.758600 + 0.651557i \(0.225884\pi\)
\(72\) 0.734099 0.0865144
\(73\) −10.1584 −1.18896 −0.594478 0.804112i \(-0.702641\pi\)
−0.594478 + 0.804112i \(0.702641\pi\)
\(74\) 12.2517 1.42423
\(75\) 9.61275 1.10998
\(76\) 4.13453 0.474263
\(77\) −0.279659 −0.0318701
\(78\) 5.20528 0.589382
\(79\) 2.40998 0.271143 0.135572 0.990768i \(-0.456713\pi\)
0.135572 + 0.990768i \(0.456713\pi\)
\(80\) 14.4958 1.62068
\(81\) −10.9909 −1.22121
\(82\) −9.81259 −1.08362
\(83\) −13.6597 −1.49934 −0.749671 0.661811i \(-0.769788\pi\)
−0.749671 + 0.661811i \(0.769788\pi\)
\(84\) −0.899560 −0.0981500
\(85\) 3.13238 0.339754
\(86\) 1.90003 0.204886
\(87\) −10.9483 −1.17378
\(88\) 0.740768 0.0789661
\(89\) 11.1325 1.18005 0.590023 0.807386i \(-0.299119\pi\)
0.590023 + 0.807386i \(0.299119\pi\)
\(90\) 5.89804 0.621708
\(91\) 0.383505 0.0402022
\(92\) −8.96791 −0.934969
\(93\) −4.79974 −0.497710
\(94\) −8.16383 −0.842035
\(95\) −8.04339 −0.825235
\(96\) 14.6062 1.49074
\(97\) −7.90060 −0.802184 −0.401092 0.916038i \(-0.631369\pi\)
−0.401092 + 0.916038i \(0.631369\pi\)
\(98\) 13.1516 1.32852
\(99\) 0.990997 0.0995989
\(100\) 7.74761 0.774761
\(101\) 9.50281 0.945565 0.472783 0.881179i \(-0.343250\pi\)
0.472783 + 0.881179i \(0.343250\pi\)
\(102\) 3.79579 0.375839
\(103\) 11.4954 1.13267 0.566336 0.824175i \(-0.308361\pi\)
0.566336 + 0.824175i \(0.308361\pi\)
\(104\) −1.01584 −0.0996110
\(105\) 1.75002 0.170785
\(106\) −7.54142 −0.732488
\(107\) 6.70439 0.648138 0.324069 0.946033i \(-0.394949\pi\)
0.324069 + 0.946033i \(0.394949\pi\)
\(108\) −6.46222 −0.621828
\(109\) 3.19350 0.305882 0.152941 0.988235i \(-0.451126\pi\)
0.152941 + 0.988235i \(0.451126\pi\)
\(110\) 5.95163 0.567465
\(111\) −12.8818 −1.22268
\(112\) 1.29419 0.122289
\(113\) 2.62618 0.247050 0.123525 0.992341i \(-0.460580\pi\)
0.123525 + 0.992341i \(0.460580\pi\)
\(114\) −9.74692 −0.912882
\(115\) 17.4464 1.62688
\(116\) −8.82401 −0.819288
\(117\) −1.35898 −0.125638
\(118\) 0.272123 0.0250510
\(119\) 0.279659 0.0256363
\(120\) −4.63551 −0.423162
\(121\) 1.00000 0.0909091
\(122\) −26.5568 −2.40434
\(123\) 10.3172 0.930273
\(124\) −3.86846 −0.347398
\(125\) 0.589532 0.0527294
\(126\) 0.526577 0.0469112
\(127\) 18.1135 1.60731 0.803657 0.595093i \(-0.202885\pi\)
0.803657 + 0.595093i \(0.202885\pi\)
\(128\) −5.81355 −0.513850
\(129\) −1.99775 −0.175892
\(130\) −8.16164 −0.715823
\(131\) −0.628464 −0.0549092 −0.0274546 0.999623i \(-0.508740\pi\)
−0.0274546 + 0.999623i \(0.508740\pi\)
\(132\) 3.21663 0.279972
\(133\) −0.718115 −0.0622684
\(134\) 18.0986 1.56348
\(135\) 12.5717 1.08200
\(136\) −0.740768 −0.0635203
\(137\) −6.27047 −0.535723 −0.267861 0.963457i \(-0.586317\pi\)
−0.267861 + 0.963457i \(0.586317\pi\)
\(138\) 21.1413 1.79967
\(139\) 12.7449 1.08101 0.540503 0.841342i \(-0.318234\pi\)
0.540503 + 0.841342i \(0.318234\pi\)
\(140\) 1.41047 0.119206
\(141\) 8.58367 0.722876
\(142\) −24.2903 −2.03840
\(143\) −1.37133 −0.114676
\(144\) −4.58608 −0.382173
\(145\) 17.1664 1.42559
\(146\) 19.3014 1.59739
\(147\) −13.8280 −1.14051
\(148\) −10.3823 −0.853422
\(149\) −8.36079 −0.684942 −0.342471 0.939528i \(-0.611264\pi\)
−0.342471 + 0.939528i \(0.611264\pi\)
\(150\) −18.2646 −1.49129
\(151\) −11.2795 −0.917915 −0.458958 0.888458i \(-0.651777\pi\)
−0.458958 + 0.888458i \(0.651777\pi\)
\(152\) 1.90216 0.154286
\(153\) −0.990997 −0.0801173
\(154\) 0.531361 0.0428183
\(155\) 7.52578 0.604485
\(156\) −4.41106 −0.353168
\(157\) −17.8591 −1.42531 −0.712657 0.701513i \(-0.752508\pi\)
−0.712657 + 0.701513i \(0.752508\pi\)
\(158\) −4.57903 −0.364288
\(159\) 7.92926 0.628831
\(160\) −22.9019 −1.81055
\(161\) 1.55761 0.122757
\(162\) 20.8831 1.64073
\(163\) −13.4824 −1.05602 −0.528010 0.849238i \(-0.677062\pi\)
−0.528010 + 0.849238i \(0.677062\pi\)
\(164\) 8.31539 0.649323
\(165\) −6.25770 −0.487161
\(166\) 25.9538 2.01441
\(167\) −0.721942 −0.0558656 −0.0279328 0.999610i \(-0.508892\pi\)
−0.0279328 + 0.999610i \(0.508892\pi\)
\(168\) −0.413858 −0.0319298
\(169\) −11.1195 −0.855343
\(170\) −5.95163 −0.456469
\(171\) 2.54470 0.194598
\(172\) −1.61013 −0.122771
\(173\) −24.9192 −1.89457 −0.947284 0.320395i \(-0.896184\pi\)
−0.947284 + 0.320395i \(0.896184\pi\)
\(174\) 20.8021 1.57700
\(175\) −1.34566 −0.101722
\(176\) −4.62774 −0.348829
\(177\) −0.286118 −0.0215060
\(178\) −21.1522 −1.58542
\(179\) 3.50222 0.261768 0.130884 0.991398i \(-0.458218\pi\)
0.130884 + 0.991398i \(0.458218\pi\)
\(180\) −4.99813 −0.372538
\(181\) 0.594036 0.0441544 0.0220772 0.999756i \(-0.492972\pi\)
0.0220772 + 0.999756i \(0.492972\pi\)
\(182\) −0.728672 −0.0540127
\(183\) 27.9225 2.06409
\(184\) −4.12584 −0.304161
\(185\) 20.1980 1.48499
\(186\) 9.11967 0.668687
\(187\) −1.00000 −0.0731272
\(188\) 6.91820 0.504562
\(189\) 1.12241 0.0816430
\(190\) 15.2827 1.10873
\(191\) −3.71613 −0.268889 −0.134445 0.990921i \(-0.542925\pi\)
−0.134445 + 0.990921i \(0.542925\pi\)
\(192\) −9.26215 −0.668438
\(193\) −7.08417 −0.509929 −0.254965 0.966950i \(-0.582064\pi\)
−0.254965 + 0.966950i \(0.582064\pi\)
\(194\) 15.0114 1.07776
\(195\) 8.58137 0.614525
\(196\) −11.1450 −0.796070
\(197\) 20.0268 1.42685 0.713424 0.700733i \(-0.247143\pi\)
0.713424 + 0.700733i \(0.247143\pi\)
\(198\) −1.88293 −0.133814
\(199\) 8.38545 0.594429 0.297214 0.954811i \(-0.403942\pi\)
0.297214 + 0.954811i \(0.403942\pi\)
\(200\) 3.56442 0.252043
\(201\) −19.0294 −1.34223
\(202\) −18.0557 −1.27039
\(203\) 1.53262 0.107569
\(204\) −3.21663 −0.225209
\(205\) −16.1769 −1.12985
\(206\) −21.8416 −1.52177
\(207\) −5.51954 −0.383634
\(208\) 6.34616 0.440027
\(209\) 2.56782 0.177620
\(210\) −3.32510 −0.229454
\(211\) −23.2674 −1.60179 −0.800896 0.598803i \(-0.795643\pi\)
−0.800896 + 0.598803i \(0.795643\pi\)
\(212\) 6.39076 0.438919
\(213\) 25.5395 1.74994
\(214\) −12.7386 −0.870791
\(215\) 3.13238 0.213626
\(216\) −2.97306 −0.202291
\(217\) 0.671902 0.0456117
\(218\) −6.06776 −0.410961
\(219\) −20.2940 −1.37134
\(220\) −5.04353 −0.340035
\(221\) 1.37133 0.0922456
\(222\) 24.4758 1.64271
\(223\) 8.70863 0.583173 0.291586 0.956544i \(-0.405817\pi\)
0.291586 + 0.956544i \(0.405817\pi\)
\(224\) −2.04468 −0.136616
\(225\) 4.76847 0.317898
\(226\) −4.98982 −0.331918
\(227\) −20.6202 −1.36861 −0.684304 0.729197i \(-0.739894\pi\)
−0.684304 + 0.729197i \(0.739894\pi\)
\(228\) 8.25974 0.547015
\(229\) −4.02643 −0.266074 −0.133037 0.991111i \(-0.542473\pi\)
−0.133037 + 0.991111i \(0.542473\pi\)
\(230\) −33.1487 −2.18576
\(231\) −0.558688 −0.0367590
\(232\) −4.05964 −0.266528
\(233\) 3.95740 0.259258 0.129629 0.991563i \(-0.458621\pi\)
0.129629 + 0.991563i \(0.458621\pi\)
\(234\) 2.58211 0.168798
\(235\) −13.4588 −0.877956
\(236\) −0.230603 −0.0150110
\(237\) 4.81452 0.312737
\(238\) −0.531361 −0.0344430
\(239\) 17.1361 1.10844 0.554222 0.832369i \(-0.313016\pi\)
0.554222 + 0.832369i \(0.313016\pi\)
\(240\) 28.9590 1.86930
\(241\) −0.676038 −0.0435474 −0.0217737 0.999763i \(-0.506931\pi\)
−0.0217737 + 0.999763i \(0.506931\pi\)
\(242\) −1.90003 −0.122139
\(243\) −9.91663 −0.636152
\(244\) 22.5048 1.44072
\(245\) 21.6817 1.38519
\(246\) −19.6031 −1.24985
\(247\) −3.52133 −0.224057
\(248\) −1.77975 −0.113014
\(249\) −27.2885 −1.72934
\(250\) −1.12013 −0.0708433
\(251\) 29.9133 1.88811 0.944057 0.329783i \(-0.106976\pi\)
0.944057 + 0.329783i \(0.106976\pi\)
\(252\) −0.446233 −0.0281100
\(253\) −5.56968 −0.350163
\(254\) −34.4163 −2.15947
\(255\) 6.25770 0.391873
\(256\) 20.3185 1.26991
\(257\) 22.3669 1.39521 0.697605 0.716483i \(-0.254249\pi\)
0.697605 + 0.716483i \(0.254249\pi\)
\(258\) 3.79579 0.236315
\(259\) 1.80328 0.112050
\(260\) 6.91635 0.428934
\(261\) −5.43097 −0.336169
\(262\) 1.19410 0.0737720
\(263\) −7.61166 −0.469355 −0.234677 0.972073i \(-0.575403\pi\)
−0.234677 + 0.972073i \(0.575403\pi\)
\(264\) 1.47987 0.0910796
\(265\) −12.4327 −0.763736
\(266\) 1.36444 0.0836593
\(267\) 22.2400 1.36107
\(268\) −15.3371 −0.936865
\(269\) 6.21577 0.378982 0.189491 0.981882i \(-0.439316\pi\)
0.189491 + 0.981882i \(0.439316\pi\)
\(270\) −23.8867 −1.45370
\(271\) −26.7843 −1.62703 −0.813514 0.581546i \(-0.802448\pi\)
−0.813514 + 0.581546i \(0.802448\pi\)
\(272\) 4.62774 0.280598
\(273\) 0.766145 0.0463692
\(274\) 11.9141 0.719758
\(275\) 4.81179 0.290162
\(276\) −17.9156 −1.07839
\(277\) 13.8827 0.834130 0.417065 0.908877i \(-0.363059\pi\)
0.417065 + 0.908877i \(0.363059\pi\)
\(278\) −24.2157 −1.45236
\(279\) −2.38095 −0.142544
\(280\) 0.648911 0.0387798
\(281\) 1.67650 0.100012 0.0500059 0.998749i \(-0.484076\pi\)
0.0500059 + 0.998749i \(0.484076\pi\)
\(282\) −16.3093 −0.971203
\(283\) −5.63197 −0.334786 −0.167393 0.985890i \(-0.553535\pi\)
−0.167393 + 0.985890i \(0.553535\pi\)
\(284\) 20.5841 1.22144
\(285\) −16.0687 −0.951826
\(286\) 2.60557 0.154071
\(287\) −1.44428 −0.0852530
\(288\) 7.24551 0.426946
\(289\) 1.00000 0.0588235
\(290\) −32.6167 −1.91532
\(291\) −15.7834 −0.925239
\(292\) −16.3564 −0.957186
\(293\) 27.0382 1.57959 0.789794 0.613372i \(-0.210187\pi\)
0.789794 + 0.613372i \(0.210187\pi\)
\(294\) 26.2737 1.53231
\(295\) 0.448620 0.0261197
\(296\) −4.77657 −0.277633
\(297\) −4.01348 −0.232886
\(298\) 15.8858 0.920239
\(299\) 7.63787 0.441710
\(300\) 15.4778 0.893610
\(301\) 0.279659 0.0161193
\(302\) 21.4315 1.23324
\(303\) 18.9842 1.09062
\(304\) −11.8832 −0.681550
\(305\) −43.7812 −2.50691
\(306\) 1.88293 0.107640
\(307\) 6.70606 0.382735 0.191368 0.981518i \(-0.438708\pi\)
0.191368 + 0.981518i \(0.438708\pi\)
\(308\) −0.450287 −0.0256575
\(309\) 22.9648 1.30642
\(310\) −14.2992 −0.812142
\(311\) 28.3030 1.60492 0.802459 0.596708i \(-0.203525\pi\)
0.802459 + 0.596708i \(0.203525\pi\)
\(312\) −2.02939 −0.114891
\(313\) −4.58151 −0.258962 −0.129481 0.991582i \(-0.541331\pi\)
−0.129481 + 0.991582i \(0.541331\pi\)
\(314\) 33.9330 1.91495
\(315\) 0.868111 0.0489125
\(316\) 3.88037 0.218288
\(317\) 0.164102 0.00921687 0.00460844 0.999989i \(-0.498533\pi\)
0.00460844 + 0.999989i \(0.498533\pi\)
\(318\) −15.0659 −0.844852
\(319\) −5.48031 −0.306838
\(320\) 14.5226 0.811840
\(321\) 13.3937 0.747562
\(322\) −2.95951 −0.164927
\(323\) −2.56782 −0.142878
\(324\) −17.6968 −0.983155
\(325\) −6.59856 −0.366022
\(326\) 25.6169 1.41879
\(327\) 6.37981 0.352805
\(328\) 3.82564 0.211236
\(329\) −1.20160 −0.0662465
\(330\) 11.8898 0.654515
\(331\) −4.40814 −0.242293 −0.121147 0.992635i \(-0.538657\pi\)
−0.121147 + 0.992635i \(0.538657\pi\)
\(332\) −21.9938 −1.20707
\(333\) −6.39008 −0.350174
\(334\) 1.37171 0.0750569
\(335\) 29.8372 1.63018
\(336\) 2.58546 0.141049
\(337\) 28.9901 1.57919 0.789595 0.613628i \(-0.210291\pi\)
0.789595 + 0.613628i \(0.210291\pi\)
\(338\) 21.1273 1.14918
\(339\) 5.24644 0.284947
\(340\) 5.04353 0.273524
\(341\) −2.40258 −0.130107
\(342\) −4.83503 −0.261448
\(343\) 3.89335 0.210221
\(344\) −0.740768 −0.0399395
\(345\) 34.8534 1.87645
\(346\) 47.3472 2.54540
\(347\) 26.4139 1.41797 0.708987 0.705221i \(-0.249152\pi\)
0.708987 + 0.705221i \(0.249152\pi\)
\(348\) −17.6281 −0.944967
\(349\) 0.263510 0.0141053 0.00705267 0.999975i \(-0.497755\pi\)
0.00705267 + 0.999975i \(0.497755\pi\)
\(350\) 2.55680 0.136667
\(351\) 5.50381 0.293772
\(352\) 7.31133 0.389695
\(353\) −24.6920 −1.31422 −0.657112 0.753793i \(-0.728222\pi\)
−0.657112 + 0.753793i \(0.728222\pi\)
\(354\) 0.543634 0.0288938
\(355\) −40.0448 −2.12536
\(356\) 17.9248 0.950013
\(357\) 0.558688 0.0295689
\(358\) −6.65433 −0.351693
\(359\) 27.8514 1.46994 0.734970 0.678099i \(-0.237196\pi\)
0.734970 + 0.678099i \(0.237196\pi\)
\(360\) −2.29947 −0.121193
\(361\) −12.4063 −0.652962
\(362\) −1.12869 −0.0593226
\(363\) 1.99775 0.104855
\(364\) 0.617492 0.0323654
\(365\) 31.8201 1.66554
\(366\) −53.0537 −2.77316
\(367\) 29.9724 1.56454 0.782272 0.622937i \(-0.214061\pi\)
0.782272 + 0.622937i \(0.214061\pi\)
\(368\) 25.7751 1.34362
\(369\) 5.11793 0.266429
\(370\) −38.3769 −1.99512
\(371\) −1.10999 −0.0576280
\(372\) −7.72821 −0.400689
\(373\) 2.64767 0.137091 0.0685456 0.997648i \(-0.478164\pi\)
0.0685456 + 0.997648i \(0.478164\pi\)
\(374\) 1.90003 0.0982484
\(375\) 1.17774 0.0608181
\(376\) 3.18284 0.164142
\(377\) 7.51531 0.387058
\(378\) −2.13261 −0.109690
\(379\) 19.7109 1.01248 0.506241 0.862392i \(-0.331035\pi\)
0.506241 + 0.862392i \(0.331035\pi\)
\(380\) −12.9509 −0.664367
\(381\) 36.1862 1.85388
\(382\) 7.06077 0.361260
\(383\) 25.7703 1.31680 0.658400 0.752668i \(-0.271234\pi\)
0.658400 + 0.752668i \(0.271234\pi\)
\(384\) −11.6140 −0.592675
\(385\) 0.875997 0.0446450
\(386\) 13.4602 0.685104
\(387\) −0.990997 −0.0503752
\(388\) −12.7210 −0.645810
\(389\) −23.4021 −1.18654 −0.593268 0.805005i \(-0.702162\pi\)
−0.593268 + 0.805005i \(0.702162\pi\)
\(390\) −16.3049 −0.825631
\(391\) 5.56968 0.281671
\(392\) −5.12744 −0.258975
\(393\) −1.25551 −0.0633323
\(394\) −38.0515 −1.91701
\(395\) −7.54895 −0.379829
\(396\) 1.59563 0.0801836
\(397\) 8.67600 0.435436 0.217718 0.976012i \(-0.430139\pi\)
0.217718 + 0.976012i \(0.430139\pi\)
\(398\) −15.9326 −0.798631
\(399\) −1.43461 −0.0718204
\(400\) −22.2677 −1.11339
\(401\) 8.81082 0.439992 0.219996 0.975501i \(-0.429396\pi\)
0.219996 + 0.975501i \(0.429396\pi\)
\(402\) 36.1565 1.80332
\(403\) 3.29473 0.164122
\(404\) 15.3008 0.761241
\(405\) 34.4277 1.71073
\(406\) −2.91202 −0.144521
\(407\) −6.44814 −0.319622
\(408\) −1.47987 −0.0732644
\(409\) 2.45455 0.121370 0.0606849 0.998157i \(-0.480672\pi\)
0.0606849 + 0.998157i \(0.480672\pi\)
\(410\) 30.7367 1.51798
\(411\) −12.5268 −0.617903
\(412\) 18.5090 0.911873
\(413\) 0.0400528 0.00197087
\(414\) 10.4873 0.515423
\(415\) 42.7872 2.10034
\(416\) −10.0262 −0.491577
\(417\) 25.4610 1.24683
\(418\) −4.87895 −0.238637
\(419\) 30.4297 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(420\) 2.81776 0.137493
\(421\) 36.3478 1.77148 0.885742 0.464178i \(-0.153650\pi\)
0.885742 + 0.464178i \(0.153650\pi\)
\(422\) 44.2088 2.15205
\(423\) 4.25799 0.207031
\(424\) 2.94018 0.142788
\(425\) −4.81179 −0.233406
\(426\) −48.5259 −2.35109
\(427\) −3.90879 −0.189160
\(428\) 10.7949 0.521793
\(429\) −2.73957 −0.132268
\(430\) −5.95163 −0.287013
\(431\) 9.80739 0.472406 0.236203 0.971704i \(-0.424097\pi\)
0.236203 + 0.971704i \(0.424097\pi\)
\(432\) 18.5734 0.893611
\(433\) 16.2718 0.781971 0.390986 0.920397i \(-0.372134\pi\)
0.390986 + 0.920397i \(0.372134\pi\)
\(434\) −1.27664 −0.0612805
\(435\) 34.2941 1.64428
\(436\) 5.14195 0.246255
\(437\) −14.3020 −0.684156
\(438\) 38.5593 1.84243
\(439\) −13.4609 −0.642452 −0.321226 0.947003i \(-0.604095\pi\)
−0.321226 + 0.947003i \(0.604095\pi\)
\(440\) −2.32037 −0.110619
\(441\) −6.85947 −0.326642
\(442\) −2.60557 −0.123934
\(443\) −40.5473 −1.92646 −0.963230 0.268678i \(-0.913413\pi\)
−0.963230 + 0.268678i \(0.913413\pi\)
\(444\) −20.7413 −0.984338
\(445\) −34.8713 −1.65306
\(446\) −16.5467 −0.783508
\(447\) −16.7027 −0.790013
\(448\) 1.29658 0.0612577
\(449\) 34.2317 1.61549 0.807747 0.589529i \(-0.200687\pi\)
0.807747 + 0.589529i \(0.200687\pi\)
\(450\) −9.06026 −0.427105
\(451\) 5.16443 0.243183
\(452\) 4.22848 0.198891
\(453\) −22.5337 −1.05872
\(454\) 39.1790 1.83876
\(455\) −1.20128 −0.0563169
\(456\) 3.80004 0.177953
\(457\) 25.9727 1.21495 0.607476 0.794338i \(-0.292182\pi\)
0.607476 + 0.794338i \(0.292182\pi\)
\(458\) 7.65036 0.357478
\(459\) 4.01348 0.187333
\(460\) 28.0909 1.30974
\(461\) 24.0311 1.11924 0.559621 0.828749i \(-0.310947\pi\)
0.559621 + 0.828749i \(0.310947\pi\)
\(462\) 1.06153 0.0493867
\(463\) 26.7137 1.24149 0.620745 0.784012i \(-0.286830\pi\)
0.620745 + 0.784012i \(0.286830\pi\)
\(464\) 25.3615 1.17738
\(465\) 15.0346 0.697213
\(466\) −7.51920 −0.348320
\(467\) 18.5449 0.858157 0.429079 0.903267i \(-0.358838\pi\)
0.429079 + 0.903267i \(0.358838\pi\)
\(468\) −2.18814 −0.101147
\(469\) 2.66387 0.123006
\(470\) 25.5722 1.17956
\(471\) −35.6780 −1.64396
\(472\) −0.106093 −0.00488333
\(473\) −1.00000 −0.0459800
\(474\) −9.14776 −0.420170
\(475\) 12.3558 0.566925
\(476\) 0.450287 0.0206389
\(477\) 3.93336 0.180096
\(478\) −32.5592 −1.48923
\(479\) −24.3418 −1.11221 −0.556103 0.831114i \(-0.687704\pi\)
−0.556103 + 0.831114i \(0.687704\pi\)
\(480\) −45.7521 −2.08829
\(481\) 8.84252 0.403184
\(482\) 1.28450 0.0585072
\(483\) 3.11172 0.141588
\(484\) 1.61013 0.0731877
\(485\) 24.7477 1.12373
\(486\) 18.8419 0.854688
\(487\) −14.3721 −0.651262 −0.325631 0.945497i \(-0.605577\pi\)
−0.325631 + 0.945497i \(0.605577\pi\)
\(488\) 10.3537 0.468690
\(489\) −26.9343 −1.21801
\(490\) −41.1959 −1.86104
\(491\) −37.5048 −1.69257 −0.846285 0.532731i \(-0.821166\pi\)
−0.846285 + 0.532731i \(0.821166\pi\)
\(492\) 16.6121 0.748930
\(493\) 5.48031 0.246821
\(494\) 6.69065 0.301027
\(495\) −3.10418 −0.139522
\(496\) 11.1185 0.499236
\(497\) −3.57520 −0.160370
\(498\) 51.8492 2.32342
\(499\) 37.0309 1.65773 0.828866 0.559447i \(-0.188987\pi\)
0.828866 + 0.559447i \(0.188987\pi\)
\(500\) 0.949223 0.0424506
\(501\) −1.44226 −0.0644353
\(502\) −56.8364 −2.53673
\(503\) −10.1466 −0.452412 −0.226206 0.974079i \(-0.572632\pi\)
−0.226206 + 0.974079i \(0.572632\pi\)
\(504\) −0.205297 −0.00914466
\(505\) −29.7664 −1.32459
\(506\) 10.5826 0.470453
\(507\) −22.2139 −0.986552
\(508\) 29.1651 1.29399
\(509\) 11.4821 0.508935 0.254467 0.967081i \(-0.418100\pi\)
0.254467 + 0.967081i \(0.418100\pi\)
\(510\) −11.8898 −0.526491
\(511\) 2.84090 0.125674
\(512\) −26.9788 −1.19231
\(513\) −10.3059 −0.455017
\(514\) −42.4979 −1.87450
\(515\) −36.0078 −1.58669
\(516\) −3.21663 −0.141604
\(517\) 4.29668 0.188968
\(518\) −3.42629 −0.150543
\(519\) −49.7822 −2.18520
\(520\) 3.18199 0.139539
\(521\) −29.6638 −1.29960 −0.649798 0.760107i \(-0.725147\pi\)
−0.649798 + 0.760107i \(0.725147\pi\)
\(522\) 10.3190 0.451651
\(523\) −18.4904 −0.808530 −0.404265 0.914642i \(-0.632473\pi\)
−0.404265 + 0.914642i \(0.632473\pi\)
\(524\) −1.01191 −0.0442054
\(525\) −2.68829 −0.117327
\(526\) 14.4624 0.630591
\(527\) 2.40258 0.104658
\(528\) −9.24506 −0.402340
\(529\) 8.02138 0.348756
\(530\) 23.6226 1.02610
\(531\) −0.141931 −0.00615927
\(532\) −1.15626 −0.0501301
\(533\) −7.08213 −0.306761
\(534\) −42.2567 −1.82863
\(535\) −21.0007 −0.907939
\(536\) −7.05612 −0.304778
\(537\) 6.99655 0.301923
\(538\) −11.8102 −0.509173
\(539\) −6.92179 −0.298143
\(540\) 20.2421 0.871083
\(541\) 39.8199 1.71199 0.855996 0.516982i \(-0.172945\pi\)
0.855996 + 0.516982i \(0.172945\pi\)
\(542\) 50.8910 2.18596
\(543\) 1.18674 0.0509277
\(544\) −7.31133 −0.313471
\(545\) −10.0033 −0.428493
\(546\) −1.45570 −0.0622983
\(547\) −22.4465 −0.959743 −0.479871 0.877339i \(-0.659317\pi\)
−0.479871 + 0.877339i \(0.659317\pi\)
\(548\) −10.0963 −0.431291
\(549\) 13.8512 0.591153
\(550\) −9.14257 −0.389841
\(551\) −14.0725 −0.599507
\(552\) −8.24240 −0.350820
\(553\) −0.673971 −0.0286602
\(554\) −26.3776 −1.12068
\(555\) 40.3505 1.71278
\(556\) 20.5209 0.870279
\(557\) 44.2445 1.87470 0.937351 0.348387i \(-0.113271\pi\)
0.937351 + 0.348387i \(0.113271\pi\)
\(558\) 4.52388 0.191511
\(559\) 1.37133 0.0580011
\(560\) −4.05389 −0.171308
\(561\) −1.99775 −0.0843450
\(562\) −3.18541 −0.134369
\(563\) −3.57926 −0.150848 −0.0754240 0.997152i \(-0.524031\pi\)
−0.0754240 + 0.997152i \(0.524031\pi\)
\(564\) 13.8208 0.581962
\(565\) −8.22618 −0.346078
\(566\) 10.7009 0.449794
\(567\) 3.07371 0.129084
\(568\) 9.47009 0.397356
\(569\) −20.4397 −0.856877 −0.428438 0.903571i \(-0.640936\pi\)
−0.428438 + 0.903571i \(0.640936\pi\)
\(570\) 30.5310 1.27880
\(571\) −16.8035 −0.703206 −0.351603 0.936149i \(-0.614363\pi\)
−0.351603 + 0.936149i \(0.614363\pi\)
\(572\) −2.20802 −0.0923219
\(573\) −7.42388 −0.310137
\(574\) 2.74418 0.114540
\(575\) −26.8002 −1.11764
\(576\) −4.59455 −0.191440
\(577\) −42.8148 −1.78240 −0.891202 0.453607i \(-0.850137\pi\)
−0.891202 + 0.453607i \(0.850137\pi\)
\(578\) −1.90003 −0.0790310
\(579\) −14.1524 −0.588153
\(580\) 27.6401 1.14769
\(581\) 3.82004 0.158482
\(582\) 29.9890 1.24308
\(583\) 3.96910 0.164383
\(584\) −7.52505 −0.311389
\(585\) 4.25685 0.175999
\(586\) −51.3735 −2.12222
\(587\) −2.15540 −0.0889628 −0.0444814 0.999010i \(-0.514164\pi\)
−0.0444814 + 0.999010i \(0.514164\pi\)
\(588\) −22.2649 −0.918187
\(589\) −6.16939 −0.254205
\(590\) −0.852394 −0.0350925
\(591\) 40.0084 1.64573
\(592\) 29.8403 1.22643
\(593\) −29.3176 −1.20393 −0.601964 0.798523i \(-0.705615\pi\)
−0.601964 + 0.798523i \(0.705615\pi\)
\(594\) 7.62575 0.312888
\(595\) −0.875997 −0.0359124
\(596\) −13.4619 −0.551423
\(597\) 16.7520 0.685614
\(598\) −14.5122 −0.593449
\(599\) −18.9069 −0.772515 −0.386258 0.922391i \(-0.626232\pi\)
−0.386258 + 0.922391i \(0.626232\pi\)
\(600\) 7.12082 0.290706
\(601\) 37.3438 1.52329 0.761643 0.647997i \(-0.224393\pi\)
0.761643 + 0.647997i \(0.224393\pi\)
\(602\) −0.531361 −0.0216567
\(603\) −9.43966 −0.384413
\(604\) −18.1615 −0.738981
\(605\) −3.13238 −0.127349
\(606\) −36.0707 −1.46527
\(607\) 8.78314 0.356497 0.178248 0.983986i \(-0.442957\pi\)
0.178248 + 0.983986i \(0.442957\pi\)
\(608\) 18.7742 0.761395
\(609\) 3.06178 0.124070
\(610\) 83.1858 3.36810
\(611\) −5.89216 −0.238371
\(612\) −1.59563 −0.0644996
\(613\) −3.76203 −0.151947 −0.0759735 0.997110i \(-0.524206\pi\)
−0.0759735 + 0.997110i \(0.524206\pi\)
\(614\) −12.7417 −0.514215
\(615\) −32.3174 −1.30317
\(616\) −0.207162 −0.00834681
\(617\) 25.6242 1.03159 0.515795 0.856712i \(-0.327496\pi\)
0.515795 + 0.856712i \(0.327496\pi\)
\(618\) −43.6339 −1.75521
\(619\) 45.8942 1.84465 0.922323 0.386421i \(-0.126289\pi\)
0.922323 + 0.386421i \(0.126289\pi\)
\(620\) 12.1175 0.486650
\(621\) 22.3538 0.897028
\(622\) −53.7767 −2.15625
\(623\) −3.11331 −0.124732
\(624\) 12.6780 0.507527
\(625\) −25.9056 −1.03622
\(626\) 8.70502 0.347922
\(627\) 5.12986 0.204867
\(628\) −28.7555 −1.14747
\(629\) 6.44814 0.257104
\(630\) −1.64944 −0.0657152
\(631\) −2.73597 −0.108917 −0.0544586 0.998516i \(-0.517343\pi\)
−0.0544586 + 0.998516i \(0.517343\pi\)
\(632\) 1.78523 0.0710127
\(633\) −46.4824 −1.84751
\(634\) −0.311799 −0.0123831
\(635\) −56.7384 −2.25159
\(636\) 12.7671 0.506250
\(637\) 9.49206 0.376089
\(638\) 10.4128 0.412246
\(639\) 12.6690 0.501180
\(640\) 18.2102 0.719823
\(641\) 18.1921 0.718546 0.359273 0.933232i \(-0.383025\pi\)
0.359273 + 0.933232i \(0.383025\pi\)
\(642\) −25.4484 −1.00437
\(643\) −17.0303 −0.671608 −0.335804 0.941932i \(-0.609008\pi\)
−0.335804 + 0.941932i \(0.609008\pi\)
\(644\) 2.50796 0.0988273
\(645\) 6.25770 0.246397
\(646\) 4.87895 0.191960
\(647\) 40.3693 1.58708 0.793541 0.608517i \(-0.208235\pi\)
0.793541 + 0.608517i \(0.208235\pi\)
\(648\) −8.14172 −0.319837
\(649\) −0.143220 −0.00562189
\(650\) 12.5375 0.491761
\(651\) 1.34229 0.0526085
\(652\) −21.7083 −0.850164
\(653\) 5.90276 0.230993 0.115496 0.993308i \(-0.463154\pi\)
0.115496 + 0.993308i \(0.463154\pi\)
\(654\) −12.1219 −0.474002
\(655\) 1.96859 0.0769191
\(656\) −23.8996 −0.933124
\(657\) −10.0670 −0.392750
\(658\) 2.28309 0.0890040
\(659\) −42.7007 −1.66338 −0.831692 0.555237i \(-0.812628\pi\)
−0.831692 + 0.555237i \(0.812628\pi\)
\(660\) −10.0757 −0.392196
\(661\) 26.4725 1.02966 0.514831 0.857291i \(-0.327855\pi\)
0.514831 + 0.857291i \(0.327855\pi\)
\(662\) 8.37561 0.325527
\(663\) 2.73957 0.106396
\(664\) −10.1186 −0.392679
\(665\) 2.24941 0.0872282
\(666\) 12.1414 0.470469
\(667\) 30.5236 1.18188
\(668\) −1.16242 −0.0449754
\(669\) 17.3976 0.672632
\(670\) −56.6917 −2.19019
\(671\) 13.9770 0.539576
\(672\) −4.08475 −0.157573
\(673\) −44.0528 −1.69811 −0.849055 0.528305i \(-0.822828\pi\)
−0.849055 + 0.528305i \(0.822828\pi\)
\(674\) −55.0821 −2.12168
\(675\) −19.3120 −0.743321
\(676\) −17.9038 −0.688606
\(677\) 26.1405 1.00466 0.502330 0.864676i \(-0.332476\pi\)
0.502330 + 0.864676i \(0.332476\pi\)
\(678\) −9.96841 −0.382834
\(679\) 2.20947 0.0847917
\(680\) 2.32037 0.0889820
\(681\) −41.1939 −1.57855
\(682\) 4.56498 0.174802
\(683\) 1.02576 0.0392496 0.0196248 0.999807i \(-0.493753\pi\)
0.0196248 + 0.999807i \(0.493753\pi\)
\(684\) 4.09730 0.156664
\(685\) 19.6415 0.750463
\(686\) −7.39750 −0.282438
\(687\) −8.04380 −0.306890
\(688\) 4.62774 0.176431
\(689\) −5.44294 −0.207360
\(690\) −66.2227 −2.52105
\(691\) 29.8452 1.13536 0.567682 0.823248i \(-0.307840\pi\)
0.567682 + 0.823248i \(0.307840\pi\)
\(692\) −40.1230 −1.52525
\(693\) −0.277141 −0.0105277
\(694\) −50.1874 −1.90509
\(695\) −39.9217 −1.51432
\(696\) −8.11013 −0.307414
\(697\) −5.16443 −0.195617
\(698\) −0.500677 −0.0189509
\(699\) 7.90590 0.299028
\(700\) −2.16669 −0.0818931
\(701\) −48.2659 −1.82298 −0.911489 0.411325i \(-0.865066\pi\)
−0.911489 + 0.411325i \(0.865066\pi\)
\(702\) −10.4574 −0.394690
\(703\) −16.5577 −0.624485
\(704\) −4.63629 −0.174737
\(705\) −26.8873 −1.01263
\(706\) 46.9157 1.76570
\(707\) −2.65755 −0.0999473
\(708\) −0.460687 −0.0173137
\(709\) −37.0975 −1.39323 −0.696613 0.717447i \(-0.745310\pi\)
−0.696613 + 0.717447i \(0.745310\pi\)
\(710\) 76.0865 2.85547
\(711\) 2.38828 0.0895674
\(712\) 8.24662 0.309055
\(713\) 13.3816 0.501145
\(714\) −1.06153 −0.0397266
\(715\) 4.29552 0.160643
\(716\) 5.63902 0.210740
\(717\) 34.2337 1.27848
\(718\) −52.9186 −1.97491
\(719\) 9.31302 0.347317 0.173658 0.984806i \(-0.444441\pi\)
0.173658 + 0.984806i \(0.444441\pi\)
\(720\) 14.3653 0.535364
\(721\) −3.21478 −0.119725
\(722\) 23.5724 0.877272
\(723\) −1.35055 −0.0502276
\(724\) 0.956475 0.0355471
\(725\) −26.3701 −0.979362
\(726\) −3.79579 −0.140875
\(727\) −15.5708 −0.577490 −0.288745 0.957406i \(-0.593238\pi\)
−0.288745 + 0.957406i \(0.593238\pi\)
\(728\) 0.284088 0.0105290
\(729\) 13.1618 0.487475
\(730\) −60.4592 −2.23770
\(731\) 1.00000 0.0369863
\(732\) 44.9589 1.66173
\(733\) −4.38913 −0.162116 −0.0810581 0.996709i \(-0.525830\pi\)
−0.0810581 + 0.996709i \(0.525830\pi\)
\(734\) −56.9485 −2.10201
\(735\) 43.3145 1.59768
\(736\) −40.7218 −1.50103
\(737\) −9.52542 −0.350873
\(738\) −9.72424 −0.357954
\(739\) 7.84489 0.288579 0.144290 0.989536i \(-0.453910\pi\)
0.144290 + 0.989536i \(0.453910\pi\)
\(740\) 32.5214 1.19551
\(741\) −7.03474 −0.258427
\(742\) 2.10903 0.0774248
\(743\) 31.9285 1.17134 0.585672 0.810548i \(-0.300831\pi\)
0.585672 + 0.810548i \(0.300831\pi\)
\(744\) −3.55550 −0.130351
\(745\) 26.1892 0.959496
\(746\) −5.03066 −0.184186
\(747\) −13.5367 −0.495281
\(748\) −1.61013 −0.0588721
\(749\) −1.87494 −0.0685089
\(750\) −2.23774 −0.0817107
\(751\) 34.5510 1.26078 0.630391 0.776278i \(-0.282894\pi\)
0.630391 + 0.776278i \(0.282894\pi\)
\(752\) −19.8839 −0.725091
\(753\) 59.7593 2.17775
\(754\) −14.2793 −0.520023
\(755\) 35.3318 1.28585
\(756\) 1.80722 0.0657279
\(757\) −17.3235 −0.629634 −0.314817 0.949152i \(-0.601943\pi\)
−0.314817 + 0.949152i \(0.601943\pi\)
\(758\) −37.4514 −1.36030
\(759\) −11.1268 −0.403878
\(760\) −5.95829 −0.216130
\(761\) 20.2802 0.735156 0.367578 0.929993i \(-0.380187\pi\)
0.367578 + 0.929993i \(0.380187\pi\)
\(762\) −68.7551 −2.49073
\(763\) −0.893092 −0.0323321
\(764\) −5.98344 −0.216473
\(765\) 3.10418 0.112232
\(766\) −48.9644 −1.76916
\(767\) 0.196402 0.00709168
\(768\) 40.5913 1.46471
\(769\) 12.8641 0.463893 0.231947 0.972729i \(-0.425491\pi\)
0.231947 + 0.972729i \(0.425491\pi\)
\(770\) −1.66442 −0.0599817
\(771\) 44.6835 1.60924
\(772\) −11.4064 −0.410526
\(773\) 32.9580 1.18542 0.592708 0.805418i \(-0.298059\pi\)
0.592708 + 0.805418i \(0.298059\pi\)
\(774\) 1.88293 0.0676804
\(775\) −11.5607 −0.415273
\(776\) −5.85251 −0.210093
\(777\) 3.60250 0.129239
\(778\) 44.4648 1.59414
\(779\) 13.2613 0.475137
\(780\) 13.8171 0.494732
\(781\) 12.7841 0.457453
\(782\) −10.5826 −0.378433
\(783\) 21.9951 0.786042
\(784\) 32.0323 1.14401
\(785\) 55.9415 1.99664
\(786\) 2.38552 0.0850886
\(787\) −52.9292 −1.88672 −0.943362 0.331766i \(-0.892356\pi\)
−0.943362 + 0.331766i \(0.892356\pi\)
\(788\) 32.2457 1.14870
\(789\) −15.2062 −0.541354
\(790\) 14.3433 0.510311
\(791\) −0.734433 −0.0261134
\(792\) 0.734099 0.0260851
\(793\) −19.1671 −0.680643
\(794\) −16.4847 −0.585020
\(795\) −24.8374 −0.880893
\(796\) 13.5017 0.478553
\(797\) −25.4421 −0.901206 −0.450603 0.892724i \(-0.648791\pi\)
−0.450603 + 0.892724i \(0.648791\pi\)
\(798\) 2.72581 0.0964927
\(799\) −4.29668 −0.152005
\(800\) 35.1806 1.24382
\(801\) 11.0323 0.389807
\(802\) −16.7409 −0.591140
\(803\) −10.1584 −0.358484
\(804\) −30.6398 −1.08058
\(805\) −4.87903 −0.171963
\(806\) −6.26009 −0.220502
\(807\) 12.4175 0.437118
\(808\) 7.03938 0.247644
\(809\) 9.92790 0.349046 0.174523 0.984653i \(-0.444162\pi\)
0.174523 + 0.984653i \(0.444162\pi\)
\(810\) −65.4138 −2.29841
\(811\) −28.9800 −1.01763 −0.508813 0.860877i \(-0.669916\pi\)
−0.508813 + 0.860877i \(0.669916\pi\)
\(812\) 2.46771 0.0865997
\(813\) −53.5082 −1.87661
\(814\) 12.2517 0.429421
\(815\) 42.2318 1.47932
\(816\) 9.24506 0.323642
\(817\) −2.56782 −0.0898368
\(818\) −4.66373 −0.163064
\(819\) 0.380052 0.0132801
\(820\) −26.0470 −0.909599
\(821\) 29.2870 1.02212 0.511062 0.859544i \(-0.329252\pi\)
0.511062 + 0.859544i \(0.329252\pi\)
\(822\) 23.8014 0.830169
\(823\) 18.1532 0.632779 0.316390 0.948629i \(-0.397529\pi\)
0.316390 + 0.948629i \(0.397529\pi\)
\(824\) 8.51539 0.296648
\(825\) 9.61275 0.334673
\(826\) −0.0761017 −0.00264792
\(827\) 48.4707 1.68549 0.842746 0.538311i \(-0.180937\pi\)
0.842746 + 0.538311i \(0.180937\pi\)
\(828\) −8.88717 −0.308851
\(829\) −31.1040 −1.08029 −0.540143 0.841573i \(-0.681630\pi\)
−0.540143 + 0.841573i \(0.681630\pi\)
\(830\) −81.2971 −2.82186
\(831\) 27.7341 0.962086
\(832\) 6.35789 0.220420
\(833\) 6.92179 0.239826
\(834\) −48.3768 −1.67515
\(835\) 2.26140 0.0782588
\(836\) 4.13453 0.142996
\(837\) 9.64270 0.333300
\(838\) −57.8175 −1.99727
\(839\) 39.7144 1.37109 0.685546 0.728029i \(-0.259563\pi\)
0.685546 + 0.728029i \(0.259563\pi\)
\(840\) 1.29636 0.0447287
\(841\) 1.03379 0.0356481
\(842\) −69.0621 −2.38004
\(843\) 3.34923 0.115354
\(844\) −37.4635 −1.28955
\(845\) 34.8303 1.19820
\(846\) −8.09033 −0.278151
\(847\) −0.279659 −0.00960919
\(848\) −18.3680 −0.630759
\(849\) −11.2512 −0.386142
\(850\) 9.14257 0.313588
\(851\) 35.9141 1.23112
\(852\) 41.1219 1.40881
\(853\) −23.3520 −0.799557 −0.399778 0.916612i \(-0.630913\pi\)
−0.399778 + 0.916612i \(0.630913\pi\)
\(854\) 7.42684 0.254141
\(855\) −7.97098 −0.272602
\(856\) 4.96640 0.169748
\(857\) 57.5931 1.96734 0.983671 0.179975i \(-0.0576017\pi\)
0.983671 + 0.179975i \(0.0576017\pi\)
\(858\) 5.20528 0.177705
\(859\) 23.9841 0.818326 0.409163 0.912461i \(-0.365821\pi\)
0.409163 + 0.912461i \(0.365821\pi\)
\(860\) 5.04353 0.171983
\(861\) −2.88530 −0.0983309
\(862\) −18.6344 −0.634690
\(863\) 28.1685 0.958867 0.479433 0.877578i \(-0.340842\pi\)
0.479433 + 0.877578i \(0.340842\pi\)
\(864\) −29.3439 −0.998300
\(865\) 78.0562 2.65399
\(866\) −30.9169 −1.05060
\(867\) 1.99775 0.0678471
\(868\) 1.08185 0.0367203
\(869\) 2.40998 0.0817528
\(870\) −65.1600 −2.20913
\(871\) 13.0625 0.442605
\(872\) 2.36565 0.0801109
\(873\) −7.82947 −0.264987
\(874\) 27.1742 0.919182
\(875\) −0.164868 −0.00557355
\(876\) −32.6760 −1.10402
\(877\) −27.4867 −0.928159 −0.464079 0.885794i \(-0.653615\pi\)
−0.464079 + 0.885794i \(0.653615\pi\)
\(878\) 25.5761 0.863152
\(879\) 54.0155 1.82190
\(880\) 14.4958 0.488655
\(881\) 11.4034 0.384190 0.192095 0.981376i \(-0.438472\pi\)
0.192095 + 0.981376i \(0.438472\pi\)
\(882\) 13.0332 0.438852
\(883\) −17.3540 −0.584010 −0.292005 0.956417i \(-0.594322\pi\)
−0.292005 + 0.956417i \(0.594322\pi\)
\(884\) 2.20802 0.0742637
\(885\) 0.896230 0.0301264
\(886\) 77.0412 2.58825
\(887\) 0.928728 0.0311836 0.0155918 0.999878i \(-0.495037\pi\)
0.0155918 + 0.999878i \(0.495037\pi\)
\(888\) −9.54239 −0.320222
\(889\) −5.06560 −0.169895
\(890\) 66.2567 2.22093
\(891\) −10.9909 −0.368210
\(892\) 14.0220 0.469492
\(893\) 11.0331 0.369209
\(894\) 31.7358 1.06140
\(895\) −10.9703 −0.366696
\(896\) 1.62581 0.0543145
\(897\) 15.2585 0.509468
\(898\) −65.0414 −2.17046
\(899\) 13.1669 0.439140
\(900\) 7.67786 0.255929
\(901\) −3.96910 −0.132230
\(902\) −9.81259 −0.326723
\(903\) 0.558688 0.0185920
\(904\) 1.94539 0.0647026
\(905\) −1.86075 −0.0618533
\(906\) 42.8147 1.42242
\(907\) −43.7530 −1.45279 −0.726397 0.687276i \(-0.758806\pi\)
−0.726397 + 0.687276i \(0.758806\pi\)
\(908\) −33.2011 −1.10182
\(909\) 9.41726 0.312351
\(910\) 2.28248 0.0756633
\(911\) −5.46050 −0.180914 −0.0904572 0.995900i \(-0.528833\pi\)
−0.0904572 + 0.995900i \(0.528833\pi\)
\(912\) −23.7397 −0.786100
\(913\) −13.6597 −0.452068
\(914\) −49.3490 −1.63232
\(915\) −87.4639 −2.89147
\(916\) −6.48308 −0.214207
\(917\) 0.175756 0.00580396
\(918\) −7.62575 −0.251687
\(919\) −39.0785 −1.28908 −0.644540 0.764570i \(-0.722951\pi\)
−0.644540 + 0.764570i \(0.722951\pi\)
\(920\) 12.9237 0.426082
\(921\) 13.3970 0.441447
\(922\) −45.6600 −1.50373
\(923\) −17.5313 −0.577049
\(924\) −0.899560 −0.0295933
\(925\) −31.0271 −1.02016
\(926\) −50.7569 −1.66798
\(927\) 11.3919 0.374158
\(928\) −40.0684 −1.31531
\(929\) 8.30350 0.272429 0.136214 0.990679i \(-0.456506\pi\)
0.136214 + 0.990679i \(0.456506\pi\)
\(930\) −28.5663 −0.936725
\(931\) −17.7739 −0.582517
\(932\) 6.37193 0.208720
\(933\) 56.5423 1.85111
\(934\) −35.2360 −1.15296
\(935\) 3.13238 0.102440
\(936\) −1.00669 −0.0329047
\(937\) 49.9655 1.63230 0.816152 0.577838i \(-0.196103\pi\)
0.816152 + 0.577838i \(0.196103\pi\)
\(938\) −5.06144 −0.165262
\(939\) −9.15269 −0.298687
\(940\) −21.6704 −0.706811
\(941\) 23.0537 0.751528 0.375764 0.926715i \(-0.377380\pi\)
0.375764 + 0.926715i \(0.377380\pi\)
\(942\) 67.7895 2.20870
\(943\) −28.7642 −0.936692
\(944\) 0.662787 0.0215719
\(945\) −3.51580 −0.114369
\(946\) 1.90003 0.0617754
\(947\) 35.5679 1.15580 0.577901 0.816107i \(-0.303872\pi\)
0.577901 + 0.816107i \(0.303872\pi\)
\(948\) 7.75200 0.251773
\(949\) 13.9306 0.452205
\(950\) −23.4765 −0.761679
\(951\) 0.327834 0.0106307
\(952\) 0.207162 0.00671417
\(953\) 7.87901 0.255226 0.127613 0.991824i \(-0.459268\pi\)
0.127613 + 0.991824i \(0.459268\pi\)
\(954\) −7.47353 −0.241964
\(955\) 11.6403 0.376672
\(956\) 27.5914 0.892370
\(957\) −10.9483 −0.353908
\(958\) 46.2503 1.49428
\(959\) 1.75359 0.0566265
\(960\) 29.0125 0.936376
\(961\) −25.2276 −0.813794
\(962\) −16.8011 −0.541689
\(963\) 6.64403 0.214101
\(964\) −1.08851 −0.0350585
\(965\) 22.1903 0.714331
\(966\) −5.91236 −0.190227
\(967\) 3.79544 0.122053 0.0610265 0.998136i \(-0.480563\pi\)
0.0610265 + 0.998136i \(0.480563\pi\)
\(968\) 0.740768 0.0238092
\(969\) −5.12986 −0.164795
\(970\) −47.0214 −1.50977
\(971\) 44.9670 1.44306 0.721529 0.692384i \(-0.243439\pi\)
0.721529 + 0.692384i \(0.243439\pi\)
\(972\) −15.9671 −0.512144
\(973\) −3.56421 −0.114263
\(974\) 27.3075 0.874989
\(975\) −13.1823 −0.422170
\(976\) −64.6819 −2.07042
\(977\) −3.36134 −0.107539 −0.0537694 0.998553i \(-0.517124\pi\)
−0.0537694 + 0.998553i \(0.517124\pi\)
\(978\) 51.1762 1.63643
\(979\) 11.1325 0.355797
\(980\) 34.9103 1.11517
\(981\) 3.16475 0.101043
\(982\) 71.2605 2.27401
\(983\) −33.0578 −1.05438 −0.527190 0.849747i \(-0.676754\pi\)
−0.527190 + 0.849747i \(0.676754\pi\)
\(984\) 7.64267 0.243639
\(985\) −62.7314 −1.99879
\(986\) −10.4128 −0.331610
\(987\) −2.40050 −0.0764088
\(988\) −5.66980 −0.180380
\(989\) 5.56968 0.177106
\(990\) 5.89804 0.187452
\(991\) 53.9622 1.71417 0.857083 0.515178i \(-0.172274\pi\)
0.857083 + 0.515178i \(0.172274\pi\)
\(992\) −17.5660 −0.557722
\(993\) −8.80635 −0.279461
\(994\) 6.79300 0.215461
\(995\) −26.2664 −0.832701
\(996\) −43.9381 −1.39223
\(997\) −17.3861 −0.550623 −0.275311 0.961355i \(-0.588781\pi\)
−0.275311 + 0.961355i \(0.588781\pi\)
\(998\) −70.3600 −2.22721
\(999\) 25.8795 0.818790
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 \(a_p\))