Properties

Label 4010.2.a.i.1.10
Level 4010
Weight 2
Character 4010.1
Self dual yes
Analytic conductor 32.020
Analytic rank 1
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(2.54891\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.40579 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.40579 q^{6} -1.75221 q^{7} -1.00000 q^{8} +2.78781 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.40579 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.40579 q^{6} -1.75221 q^{7} -1.00000 q^{8} +2.78781 q^{9} -1.00000 q^{10} -5.60615 q^{11} +2.40579 q^{12} -0.293332 q^{13} +1.75221 q^{14} +2.40579 q^{15} +1.00000 q^{16} -4.41428 q^{17} -2.78781 q^{18} +5.95884 q^{19} +1.00000 q^{20} -4.21545 q^{21} +5.60615 q^{22} +0.532230 q^{23} -2.40579 q^{24} +1.00000 q^{25} +0.293332 q^{26} -0.510485 q^{27} -1.75221 q^{28} +3.48505 q^{29} -2.40579 q^{30} -8.31509 q^{31} -1.00000 q^{32} -13.4872 q^{33} +4.41428 q^{34} -1.75221 q^{35} +2.78781 q^{36} -6.82337 q^{37} -5.95884 q^{38} -0.705695 q^{39} -1.00000 q^{40} -3.49734 q^{41} +4.21545 q^{42} +9.84698 q^{43} -5.60615 q^{44} +2.78781 q^{45} -0.532230 q^{46} +6.31687 q^{47} +2.40579 q^{48} -3.92975 q^{49} -1.00000 q^{50} -10.6198 q^{51} -0.293332 q^{52} +11.0638 q^{53} +0.510485 q^{54} -5.60615 q^{55} +1.75221 q^{56} +14.3357 q^{57} -3.48505 q^{58} +7.19256 q^{59} +2.40579 q^{60} -13.8248 q^{61} +8.31509 q^{62} -4.88484 q^{63} +1.00000 q^{64} -0.293332 q^{65} +13.4872 q^{66} -13.3508 q^{67} -4.41428 q^{68} +1.28043 q^{69} +1.75221 q^{70} -1.33532 q^{71} -2.78781 q^{72} -10.1801 q^{73} +6.82337 q^{74} +2.40579 q^{75} +5.95884 q^{76} +9.82317 q^{77} +0.705695 q^{78} -2.23194 q^{79} +1.00000 q^{80} -9.59155 q^{81} +3.49734 q^{82} -4.18417 q^{83} -4.21545 q^{84} -4.41428 q^{85} -9.84698 q^{86} +8.38428 q^{87} +5.60615 q^{88} -13.2291 q^{89} -2.78781 q^{90} +0.513981 q^{91} +0.532230 q^{92} -20.0043 q^{93} -6.31687 q^{94} +5.95884 q^{95} -2.40579 q^{96} -10.0926 q^{97} +3.92975 q^{98} -15.6289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} + O(q^{10}) \) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} - 10q^{10} - 11q^{11} - 4q^{12} + 6q^{13} + 3q^{14} - 4q^{15} + 10q^{16} + 9q^{17} - 6q^{18} - 13q^{19} + 10q^{20} - 24q^{21} + 11q^{22} - 3q^{23} + 4q^{24} + 10q^{25} - 6q^{26} - 10q^{27} - 3q^{28} - 4q^{29} + 4q^{30} - 17q^{31} - 10q^{32} - 2q^{33} - 9q^{34} - 3q^{35} + 6q^{36} - 15q^{37} + 13q^{38} - 6q^{39} - 10q^{40} - 11q^{41} + 24q^{42} - 11q^{43} - 11q^{44} + 6q^{45} + 3q^{46} + 3q^{47} - 4q^{48} - 5q^{49} - 10q^{50} - 21q^{51} + 6q^{52} + 25q^{53} + 10q^{54} - 11q^{55} + 3q^{56} + 31q^{57} + 4q^{58} - 46q^{59} - 4q^{60} - 54q^{61} + 17q^{62} - 6q^{63} + 10q^{64} + 6q^{65} + 2q^{66} - 26q^{67} + 9q^{68} - 9q^{69} + 3q^{70} - 16q^{71} - 6q^{72} + 4q^{73} + 15q^{74} - 4q^{75} - 13q^{76} + 11q^{77} + 6q^{78} - 19q^{79} + 10q^{80} - 6q^{81} + 11q^{82} + 19q^{83} - 24q^{84} + 9q^{85} + 11q^{86} + 28q^{87} + 11q^{88} - 30q^{89} - 6q^{90} - 38q^{91} - 3q^{92} - 18q^{93} - 3q^{94} - 13q^{95} + 4q^{96} - 16q^{97} + 5q^{98} - 59q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 2.40579 1.38898 0.694491 0.719502i \(-0.255630\pi\)
0.694491 + 0.719502i \(0.255630\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −2.40579 −0.982158
\(7\) −1.75221 −0.662274 −0.331137 0.943583i \(-0.607432\pi\)
−0.331137 + 0.943583i \(0.607432\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.78781 0.929270
\(10\) −1.00000 −0.316228
\(11\) −5.60615 −1.69032 −0.845159 0.534515i \(-0.820494\pi\)
−0.845159 + 0.534515i \(0.820494\pi\)
\(12\) 2.40579 0.694491
\(13\) −0.293332 −0.0813558 −0.0406779 0.999172i \(-0.512952\pi\)
−0.0406779 + 0.999172i \(0.512952\pi\)
\(14\) 1.75221 0.468299
\(15\) 2.40579 0.621171
\(16\) 1.00000 0.250000
\(17\) −4.41428 −1.07062 −0.535310 0.844656i \(-0.679805\pi\)
−0.535310 + 0.844656i \(0.679805\pi\)
\(18\) −2.78781 −0.657093
\(19\) 5.95884 1.36705 0.683525 0.729927i \(-0.260446\pi\)
0.683525 + 0.729927i \(0.260446\pi\)
\(20\) 1.00000 0.223607
\(21\) −4.21545 −0.919887
\(22\) 5.60615 1.19523
\(23\) 0.532230 0.110978 0.0554888 0.998459i \(-0.482328\pi\)
0.0554888 + 0.998459i \(0.482328\pi\)
\(24\) −2.40579 −0.491079
\(25\) 1.00000 0.200000
\(26\) 0.293332 0.0575272
\(27\) −0.510485 −0.0982428
\(28\) −1.75221 −0.331137
\(29\) 3.48505 0.647157 0.323578 0.946201i \(-0.395114\pi\)
0.323578 + 0.946201i \(0.395114\pi\)
\(30\) −2.40579 −0.439235
\(31\) −8.31509 −1.49343 −0.746717 0.665142i \(-0.768371\pi\)
−0.746717 + 0.665142i \(0.768371\pi\)
\(32\) −1.00000 −0.176777
\(33\) −13.4872 −2.34782
\(34\) 4.41428 0.757042
\(35\) −1.75221 −0.296178
\(36\) 2.78781 0.464635
\(37\) −6.82337 −1.12176 −0.560878 0.827899i \(-0.689536\pi\)
−0.560878 + 0.827899i \(0.689536\pi\)
\(38\) −5.95884 −0.966651
\(39\) −0.705695 −0.113002
\(40\) −1.00000 −0.158114
\(41\) −3.49734 −0.546192 −0.273096 0.961987i \(-0.588048\pi\)
−0.273096 + 0.961987i \(0.588048\pi\)
\(42\) 4.21545 0.650458
\(43\) 9.84698 1.50165 0.750825 0.660501i \(-0.229656\pi\)
0.750825 + 0.660501i \(0.229656\pi\)
\(44\) −5.60615 −0.845159
\(45\) 2.78781 0.415582
\(46\) −0.532230 −0.0784730
\(47\) 6.31687 0.921410 0.460705 0.887553i \(-0.347597\pi\)
0.460705 + 0.887553i \(0.347597\pi\)
\(48\) 2.40579 0.347245
\(49\) −3.92975 −0.561393
\(50\) −1.00000 −0.141421
\(51\) −10.6198 −1.48707
\(52\) −0.293332 −0.0406779
\(53\) 11.0638 1.51973 0.759864 0.650083i \(-0.225266\pi\)
0.759864 + 0.650083i \(0.225266\pi\)
\(54\) 0.510485 0.0694682
\(55\) −5.60615 −0.755933
\(56\) 1.75221 0.234149
\(57\) 14.3357 1.89881
\(58\) −3.48505 −0.457609
\(59\) 7.19256 0.936392 0.468196 0.883625i \(-0.344904\pi\)
0.468196 + 0.883625i \(0.344904\pi\)
\(60\) 2.40579 0.310586
\(61\) −13.8248 −1.77008 −0.885040 0.465515i \(-0.845869\pi\)
−0.885040 + 0.465515i \(0.845869\pi\)
\(62\) 8.31509 1.05602
\(63\) −4.88484 −0.615431
\(64\) 1.00000 0.125000
\(65\) −0.293332 −0.0363834
\(66\) 13.4872 1.66016
\(67\) −13.3508 −1.63106 −0.815529 0.578717i \(-0.803554\pi\)
−0.815529 + 0.578717i \(0.803554\pi\)
\(68\) −4.41428 −0.535310
\(69\) 1.28043 0.154146
\(70\) 1.75221 0.209429
\(71\) −1.33532 −0.158473 −0.0792367 0.996856i \(-0.525248\pi\)
−0.0792367 + 0.996856i \(0.525248\pi\)
\(72\) −2.78781 −0.328547
\(73\) −10.1801 −1.19148 −0.595742 0.803176i \(-0.703142\pi\)
−0.595742 + 0.803176i \(0.703142\pi\)
\(74\) 6.82337 0.793201
\(75\) 2.40579 0.277796
\(76\) 5.95884 0.683525
\(77\) 9.82317 1.11945
\(78\) 0.705695 0.0799042
\(79\) −2.23194 −0.251112 −0.125556 0.992087i \(-0.540072\pi\)
−0.125556 + 0.992087i \(0.540072\pi\)
\(80\) 1.00000 0.111803
\(81\) −9.59155 −1.06573
\(82\) 3.49734 0.386216
\(83\) −4.18417 −0.459272 −0.229636 0.973277i \(-0.573754\pi\)
−0.229636 + 0.973277i \(0.573754\pi\)
\(84\) −4.21545 −0.459943
\(85\) −4.41428 −0.478796
\(86\) −9.84698 −1.06183
\(87\) 8.38428 0.898889
\(88\) 5.60615 0.597617
\(89\) −13.2291 −1.40228 −0.701139 0.713025i \(-0.747325\pi\)
−0.701139 + 0.713025i \(0.747325\pi\)
\(90\) −2.78781 −0.293861
\(91\) 0.513981 0.0538798
\(92\) 0.532230 0.0554888
\(93\) −20.0043 −2.07435
\(94\) −6.31687 −0.651536
\(95\) 5.95884 0.611364
\(96\) −2.40579 −0.245540
\(97\) −10.0926 −1.02474 −0.512372 0.858763i \(-0.671233\pi\)
−0.512372 + 0.858763i \(0.671233\pi\)
\(98\) 3.92975 0.396965
\(99\) −15.6289 −1.57076
\(100\) 1.00000 0.100000
\(101\) −9.78984 −0.974125 −0.487063 0.873367i \(-0.661932\pi\)
−0.487063 + 0.873367i \(0.661932\pi\)
\(102\) 10.6198 1.05152
\(103\) −13.3534 −1.31575 −0.657874 0.753128i \(-0.728544\pi\)
−0.657874 + 0.753128i \(0.728544\pi\)
\(104\) 0.293332 0.0287636
\(105\) −4.21545 −0.411386
\(106\) −11.0638 −1.07461
\(107\) −1.99022 −0.192402 −0.0962009 0.995362i \(-0.530669\pi\)
−0.0962009 + 0.995362i \(0.530669\pi\)
\(108\) −0.510485 −0.0491214
\(109\) −2.34125 −0.224251 −0.112126 0.993694i \(-0.535766\pi\)
−0.112126 + 0.993694i \(0.535766\pi\)
\(110\) 5.60615 0.534525
\(111\) −16.4156 −1.55810
\(112\) −1.75221 −0.165569
\(113\) 15.4709 1.45538 0.727690 0.685906i \(-0.240594\pi\)
0.727690 + 0.685906i \(0.240594\pi\)
\(114\) −14.3357 −1.34266
\(115\) 0.532230 0.0496307
\(116\) 3.48505 0.323578
\(117\) −0.817755 −0.0756015
\(118\) −7.19256 −0.662129
\(119\) 7.73475 0.709043
\(120\) −2.40579 −0.219617
\(121\) 20.4289 1.85717
\(122\) 13.8248 1.25164
\(123\) −8.41385 −0.758651
\(124\) −8.31509 −0.746717
\(125\) 1.00000 0.0894427
\(126\) 4.88484 0.435176
\(127\) −18.6217 −1.65241 −0.826203 0.563372i \(-0.809504\pi\)
−0.826203 + 0.563372i \(0.809504\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 23.6897 2.08576
\(130\) 0.293332 0.0257270
\(131\) −5.69531 −0.497602 −0.248801 0.968555i \(-0.580036\pi\)
−0.248801 + 0.968555i \(0.580036\pi\)
\(132\) −13.4872 −1.17391
\(133\) −10.4411 −0.905362
\(134\) 13.3508 1.15333
\(135\) −0.510485 −0.0439355
\(136\) 4.41428 0.378521
\(137\) −10.5675 −0.902844 −0.451422 0.892311i \(-0.649083\pi\)
−0.451422 + 0.892311i \(0.649083\pi\)
\(138\) −1.28043 −0.108998
\(139\) 9.57211 0.811896 0.405948 0.913896i \(-0.366941\pi\)
0.405948 + 0.913896i \(0.366941\pi\)
\(140\) −1.75221 −0.148089
\(141\) 15.1970 1.27982
\(142\) 1.33532 0.112058
\(143\) 1.64446 0.137517
\(144\) 2.78781 0.232317
\(145\) 3.48505 0.289417
\(146\) 10.1801 0.842507
\(147\) −9.45414 −0.779764
\(148\) −6.82337 −0.560878
\(149\) −11.9011 −0.974979 −0.487489 0.873129i \(-0.662087\pi\)
−0.487489 + 0.873129i \(0.662087\pi\)
\(150\) −2.40579 −0.196432
\(151\) −4.48113 −0.364669 −0.182335 0.983237i \(-0.558365\pi\)
−0.182335 + 0.983237i \(0.558365\pi\)
\(152\) −5.95884 −0.483325
\(153\) −12.3062 −0.994894
\(154\) −9.82317 −0.791573
\(155\) −8.31509 −0.667884
\(156\) −0.705695 −0.0565008
\(157\) 2.69235 0.214873 0.107436 0.994212i \(-0.465736\pi\)
0.107436 + 0.994212i \(0.465736\pi\)
\(158\) 2.23194 0.177563
\(159\) 26.6171 2.11087
\(160\) −1.00000 −0.0790569
\(161\) −0.932580 −0.0734976
\(162\) 9.59155 0.753583
\(163\) −23.1986 −1.81706 −0.908529 0.417822i \(-0.862794\pi\)
−0.908529 + 0.417822i \(0.862794\pi\)
\(164\) −3.49734 −0.273096
\(165\) −13.4872 −1.04998
\(166\) 4.18417 0.324755
\(167\) −10.5614 −0.817268 −0.408634 0.912698i \(-0.633995\pi\)
−0.408634 + 0.912698i \(0.633995\pi\)
\(168\) 4.21545 0.325229
\(169\) −12.9140 −0.993381
\(170\) 4.41428 0.338560
\(171\) 16.6121 1.27036
\(172\) 9.84698 0.750825
\(173\) 19.0268 1.44658 0.723291 0.690543i \(-0.242628\pi\)
0.723291 + 0.690543i \(0.242628\pi\)
\(174\) −8.38428 −0.635610
\(175\) −1.75221 −0.132455
\(176\) −5.60615 −0.422579
\(177\) 17.3038 1.30063
\(178\) 13.2291 0.991560
\(179\) 17.9349 1.34052 0.670260 0.742126i \(-0.266183\pi\)
0.670260 + 0.742126i \(0.266183\pi\)
\(180\) 2.78781 0.207791
\(181\) 15.9037 1.18211 0.591055 0.806631i \(-0.298711\pi\)
0.591055 + 0.806631i \(0.298711\pi\)
\(182\) −0.513981 −0.0380988
\(183\) −33.2594 −2.45861
\(184\) −0.532230 −0.0392365
\(185\) −6.82337 −0.501664
\(186\) 20.0043 1.46679
\(187\) 24.7471 1.80969
\(188\) 6.31687 0.460705
\(189\) 0.894478 0.0650637
\(190\) −5.95884 −0.432299
\(191\) −17.0814 −1.23596 −0.617982 0.786192i \(-0.712050\pi\)
−0.617982 + 0.786192i \(0.712050\pi\)
\(192\) 2.40579 0.173623
\(193\) 23.0755 1.66101 0.830505 0.557011i \(-0.188052\pi\)
0.830505 + 0.557011i \(0.188052\pi\)
\(194\) 10.0926 0.724604
\(195\) −0.705695 −0.0505359
\(196\) −3.92975 −0.280696
\(197\) 19.5317 1.39158 0.695789 0.718246i \(-0.255055\pi\)
0.695789 + 0.718246i \(0.255055\pi\)
\(198\) 15.6289 1.11070
\(199\) 7.42826 0.526576 0.263288 0.964717i \(-0.415193\pi\)
0.263288 + 0.964717i \(0.415193\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −32.1191 −2.26551
\(202\) 9.78984 0.688811
\(203\) −6.10654 −0.428595
\(204\) −10.6198 −0.743535
\(205\) −3.49734 −0.244265
\(206\) 13.3534 0.930375
\(207\) 1.48376 0.103128
\(208\) −0.293332 −0.0203389
\(209\) −33.4061 −2.31075
\(210\) 4.21545 0.290894
\(211\) 7.26922 0.500434 0.250217 0.968190i \(-0.419498\pi\)
0.250217 + 0.968190i \(0.419498\pi\)
\(212\) 11.0638 0.759864
\(213\) −3.21250 −0.220117
\(214\) 1.99022 0.136049
\(215\) 9.84698 0.671558
\(216\) 0.510485 0.0347341
\(217\) 14.5698 0.989063
\(218\) 2.34125 0.158570
\(219\) −24.4910 −1.65495
\(220\) −5.60615 −0.377966
\(221\) 1.29485 0.0871011
\(222\) 16.4156 1.10174
\(223\) −20.1554 −1.34971 −0.674853 0.737952i \(-0.735793\pi\)
−0.674853 + 0.737952i \(0.735793\pi\)
\(224\) 1.75221 0.117075
\(225\) 2.78781 0.185854
\(226\) −15.4709 −1.02911
\(227\) 25.1632 1.67014 0.835071 0.550142i \(-0.185427\pi\)
0.835071 + 0.550142i \(0.185427\pi\)
\(228\) 14.3357 0.949404
\(229\) −7.80188 −0.515563 −0.257781 0.966203i \(-0.582991\pi\)
−0.257781 + 0.966203i \(0.582991\pi\)
\(230\) −0.532230 −0.0350942
\(231\) 23.6324 1.55490
\(232\) −3.48505 −0.228804
\(233\) −8.21279 −0.538038 −0.269019 0.963135i \(-0.586699\pi\)
−0.269019 + 0.963135i \(0.586699\pi\)
\(234\) 0.817755 0.0534583
\(235\) 6.31687 0.412067
\(236\) 7.19256 0.468196
\(237\) −5.36956 −0.348791
\(238\) −7.73475 −0.501369
\(239\) −17.3544 −1.12256 −0.561280 0.827626i \(-0.689691\pi\)
−0.561280 + 0.827626i \(0.689691\pi\)
\(240\) 2.40579 0.155293
\(241\) −0.0952985 −0.00613871 −0.00306936 0.999995i \(-0.500977\pi\)
−0.00306936 + 0.999995i \(0.500977\pi\)
\(242\) −20.4289 −1.31322
\(243\) −21.5438 −1.38203
\(244\) −13.8248 −0.885040
\(245\) −3.92975 −0.251063
\(246\) 8.41385 0.536447
\(247\) −1.74792 −0.111217
\(248\) 8.31509 0.528009
\(249\) −10.0662 −0.637921
\(250\) −1.00000 −0.0632456
\(251\) 2.70106 0.170489 0.0852447 0.996360i \(-0.472833\pi\)
0.0852447 + 0.996360i \(0.472833\pi\)
\(252\) −4.88484 −0.307716
\(253\) −2.98376 −0.187587
\(254\) 18.6217 1.16843
\(255\) −10.6198 −0.665038
\(256\) 1.00000 0.0625000
\(257\) −23.6741 −1.47675 −0.738376 0.674389i \(-0.764407\pi\)
−0.738376 + 0.674389i \(0.764407\pi\)
\(258\) −23.6897 −1.47486
\(259\) 11.9560 0.742910
\(260\) −0.293332 −0.0181917
\(261\) 9.71564 0.601383
\(262\) 5.69531 0.351858
\(263\) 4.31583 0.266126 0.133063 0.991108i \(-0.457519\pi\)
0.133063 + 0.991108i \(0.457519\pi\)
\(264\) 13.4872 0.830080
\(265\) 11.0638 0.679643
\(266\) 10.4411 0.640188
\(267\) −31.8263 −1.94774
\(268\) −13.3508 −0.815529
\(269\) 14.2846 0.870948 0.435474 0.900201i \(-0.356581\pi\)
0.435474 + 0.900201i \(0.356581\pi\)
\(270\) 0.510485 0.0310671
\(271\) 4.17693 0.253730 0.126865 0.991920i \(-0.459508\pi\)
0.126865 + 0.991920i \(0.459508\pi\)
\(272\) −4.41428 −0.267655
\(273\) 1.23653 0.0748381
\(274\) 10.5675 0.638407
\(275\) −5.60615 −0.338063
\(276\) 1.28043 0.0770729
\(277\) 31.1285 1.87033 0.935165 0.354212i \(-0.115251\pi\)
0.935165 + 0.354212i \(0.115251\pi\)
\(278\) −9.57211 −0.574097
\(279\) −23.1809 −1.38780
\(280\) 1.75221 0.104715
\(281\) 31.5560 1.88247 0.941236 0.337751i \(-0.109666\pi\)
0.941236 + 0.337751i \(0.109666\pi\)
\(282\) −15.1970 −0.904971
\(283\) 28.7658 1.70995 0.854973 0.518672i \(-0.173573\pi\)
0.854973 + 0.518672i \(0.173573\pi\)
\(284\) −1.33532 −0.0792367
\(285\) 14.3357 0.849173
\(286\) −1.64446 −0.0972392
\(287\) 6.12808 0.361729
\(288\) −2.78781 −0.164273
\(289\) 2.48584 0.146226
\(290\) −3.48505 −0.204649
\(291\) −24.2806 −1.42335
\(292\) −10.1801 −0.595742
\(293\) 17.5541 1.02552 0.512760 0.858532i \(-0.328623\pi\)
0.512760 + 0.858532i \(0.328623\pi\)
\(294\) 9.45414 0.551377
\(295\) 7.19256 0.418767
\(296\) 6.82337 0.396600
\(297\) 2.86185 0.166062
\(298\) 11.9011 0.689414
\(299\) −0.156120 −0.00902867
\(300\) 2.40579 0.138898
\(301\) −17.2540 −0.994504
\(302\) 4.48113 0.257860
\(303\) −23.5523 −1.35304
\(304\) 5.95884 0.341763
\(305\) −13.8248 −0.791604
\(306\) 12.3062 0.703497
\(307\) 0.103139 0.00588646 0.00294323 0.999996i \(-0.499063\pi\)
0.00294323 + 0.999996i \(0.499063\pi\)
\(308\) 9.82317 0.559727
\(309\) −32.1254 −1.82755
\(310\) 8.31509 0.472265
\(311\) 25.3389 1.43684 0.718419 0.695611i \(-0.244866\pi\)
0.718419 + 0.695611i \(0.244866\pi\)
\(312\) 0.705695 0.0399521
\(313\) 17.7254 1.00190 0.500950 0.865476i \(-0.332984\pi\)
0.500950 + 0.865476i \(0.332984\pi\)
\(314\) −2.69235 −0.151938
\(315\) −4.88484 −0.275229
\(316\) −2.23194 −0.125556
\(317\) 11.4292 0.641927 0.320964 0.947092i \(-0.395993\pi\)
0.320964 + 0.947092i \(0.395993\pi\)
\(318\) −26.6171 −1.49261
\(319\) −19.5377 −1.09390
\(320\) 1.00000 0.0559017
\(321\) −4.78804 −0.267242
\(322\) 0.932580 0.0519707
\(323\) −26.3039 −1.46359
\(324\) −9.59155 −0.532864
\(325\) −0.293332 −0.0162712
\(326\) 23.1986 1.28485
\(327\) −5.63256 −0.311481
\(328\) 3.49734 0.193108
\(329\) −11.0685 −0.610226
\(330\) 13.4872 0.742446
\(331\) −2.57374 −0.141465 −0.0707326 0.997495i \(-0.522534\pi\)
−0.0707326 + 0.997495i \(0.522534\pi\)
\(332\) −4.18417 −0.229636
\(333\) −19.0223 −1.04241
\(334\) 10.5614 0.577896
\(335\) −13.3508 −0.729431
\(336\) −4.21545 −0.229972
\(337\) 23.1351 1.26025 0.630124 0.776494i \(-0.283004\pi\)
0.630124 + 0.776494i \(0.283004\pi\)
\(338\) 12.9140 0.702427
\(339\) 37.2197 2.02150
\(340\) −4.41428 −0.239398
\(341\) 46.6156 2.52438
\(342\) −16.6121 −0.898279
\(343\) 19.1512 1.03407
\(344\) −9.84698 −0.530913
\(345\) 1.28043 0.0689361
\(346\) −19.0268 −1.02289
\(347\) −5.29245 −0.284114 −0.142057 0.989859i \(-0.545372\pi\)
−0.142057 + 0.989859i \(0.545372\pi\)
\(348\) 8.38428 0.449444
\(349\) 31.2995 1.67543 0.837713 0.546111i \(-0.183892\pi\)
0.837713 + 0.546111i \(0.183892\pi\)
\(350\) 1.75221 0.0936597
\(351\) 0.149742 0.00799262
\(352\) 5.60615 0.298809
\(353\) 24.8184 1.32095 0.660475 0.750848i \(-0.270355\pi\)
0.660475 + 0.750848i \(0.270355\pi\)
\(354\) −17.3038 −0.919685
\(355\) −1.33532 −0.0708715
\(356\) −13.2291 −0.701139
\(357\) 18.6082 0.984848
\(358\) −17.9349 −0.947891
\(359\) 6.33468 0.334332 0.167166 0.985929i \(-0.446538\pi\)
0.167166 + 0.985929i \(0.446538\pi\)
\(360\) −2.78781 −0.146930
\(361\) 16.5077 0.868827
\(362\) −15.9037 −0.835878
\(363\) 49.1476 2.57958
\(364\) 0.513981 0.0269399
\(365\) −10.1801 −0.532848
\(366\) 33.2594 1.73850
\(367\) −31.1149 −1.62418 −0.812092 0.583529i \(-0.801671\pi\)
−0.812092 + 0.583529i \(0.801671\pi\)
\(368\) 0.532230 0.0277444
\(369\) −9.74991 −0.507560
\(370\) 6.82337 0.354730
\(371\) −19.3861 −1.00648
\(372\) −20.0043 −1.03718
\(373\) 20.0301 1.03712 0.518559 0.855042i \(-0.326469\pi\)
0.518559 + 0.855042i \(0.326469\pi\)
\(374\) −24.7471 −1.27964
\(375\) 2.40579 0.124234
\(376\) −6.31687 −0.325768
\(377\) −1.02228 −0.0526499
\(378\) −0.894478 −0.0460070
\(379\) −32.5737 −1.67320 −0.836600 0.547814i \(-0.815460\pi\)
−0.836600 + 0.547814i \(0.815460\pi\)
\(380\) 5.95884 0.305682
\(381\) −44.7998 −2.29516
\(382\) 17.0814 0.873958
\(383\) 10.7995 0.551830 0.275915 0.961182i \(-0.411019\pi\)
0.275915 + 0.961182i \(0.411019\pi\)
\(384\) −2.40579 −0.122770
\(385\) 9.82317 0.500635
\(386\) −23.0755 −1.17451
\(387\) 27.4515 1.39544
\(388\) −10.0926 −0.512372
\(389\) −3.29764 −0.167197 −0.0835985 0.996500i \(-0.526641\pi\)
−0.0835985 + 0.996500i \(0.526641\pi\)
\(390\) 0.705695 0.0357343
\(391\) −2.34941 −0.118815
\(392\) 3.92975 0.198482
\(393\) −13.7017 −0.691160
\(394\) −19.5317 −0.983994
\(395\) −2.23194 −0.112301
\(396\) −15.6289 −0.785381
\(397\) 30.4380 1.52764 0.763819 0.645431i \(-0.223322\pi\)
0.763819 + 0.645431i \(0.223322\pi\)
\(398\) −7.42826 −0.372345
\(399\) −25.1192 −1.25753
\(400\) 1.00000 0.0500000
\(401\) 1.00000 0.0499376
\(402\) 32.1191 1.60196
\(403\) 2.43909 0.121500
\(404\) −9.78984 −0.487063
\(405\) −9.59155 −0.476608
\(406\) 6.10654 0.303063
\(407\) 38.2528 1.89612
\(408\) 10.6198 0.525759
\(409\) −2.25032 −0.111271 −0.0556355 0.998451i \(-0.517718\pi\)
−0.0556355 + 0.998451i \(0.517718\pi\)
\(410\) 3.49734 0.172721
\(411\) −25.4232 −1.25403
\(412\) −13.3534 −0.657874
\(413\) −12.6029 −0.620148
\(414\) −1.48376 −0.0729226
\(415\) −4.18417 −0.205393
\(416\) 0.293332 0.0143818
\(417\) 23.0284 1.12771
\(418\) 33.4061 1.63395
\(419\) −20.2395 −0.988763 −0.494381 0.869245i \(-0.664605\pi\)
−0.494381 + 0.869245i \(0.664605\pi\)
\(420\) −4.21545 −0.205693
\(421\) −6.12535 −0.298531 −0.149266 0.988797i \(-0.547691\pi\)
−0.149266 + 0.988797i \(0.547691\pi\)
\(422\) −7.26922 −0.353860
\(423\) 17.6102 0.856239
\(424\) −11.0638 −0.537305
\(425\) −4.41428 −0.214124
\(426\) 3.21250 0.155646
\(427\) 24.2239 1.17228
\(428\) −1.99022 −0.0962009
\(429\) 3.95623 0.191009
\(430\) −9.84698 −0.474863
\(431\) 16.8163 0.810011 0.405005 0.914314i \(-0.367270\pi\)
0.405005 + 0.914314i \(0.367270\pi\)
\(432\) −0.510485 −0.0245607
\(433\) −1.18090 −0.0567503 −0.0283752 0.999597i \(-0.509033\pi\)
−0.0283752 + 0.999597i \(0.509033\pi\)
\(434\) −14.5698 −0.699373
\(435\) 8.38428 0.401995
\(436\) −2.34125 −0.112126
\(437\) 3.17147 0.151712
\(438\) 24.4910 1.17023
\(439\) −25.4663 −1.21544 −0.607720 0.794151i \(-0.707916\pi\)
−0.607720 + 0.794151i \(0.707916\pi\)
\(440\) 5.60615 0.267263
\(441\) −10.9554 −0.521686
\(442\) −1.29485 −0.0615897
\(443\) −16.4471 −0.781426 −0.390713 0.920513i \(-0.627772\pi\)
−0.390713 + 0.920513i \(0.627772\pi\)
\(444\) −16.4156 −0.779049
\(445\) −13.2291 −0.627118
\(446\) 20.1554 0.954387
\(447\) −28.6316 −1.35423
\(448\) −1.75221 −0.0827843
\(449\) 9.13398 0.431059 0.215530 0.976497i \(-0.430852\pi\)
0.215530 + 0.976497i \(0.430852\pi\)
\(450\) −2.78781 −0.131419
\(451\) 19.6066 0.923238
\(452\) 15.4709 0.727690
\(453\) −10.7806 −0.506519
\(454\) −25.1632 −1.18097
\(455\) 0.513981 0.0240958
\(456\) −14.3357 −0.671330
\(457\) −27.2144 −1.27304 −0.636518 0.771262i \(-0.719626\pi\)
−0.636518 + 0.771262i \(0.719626\pi\)
\(458\) 7.80188 0.364558
\(459\) 2.25342 0.105181
\(460\) 0.532230 0.0248154
\(461\) −7.78685 −0.362670 −0.181335 0.983421i \(-0.558042\pi\)
−0.181335 + 0.983421i \(0.558042\pi\)
\(462\) −23.6324 −1.09948
\(463\) 24.6432 1.14527 0.572633 0.819812i \(-0.305922\pi\)
0.572633 + 0.819812i \(0.305922\pi\)
\(464\) 3.48505 0.161789
\(465\) −20.0043 −0.927679
\(466\) 8.21279 0.380450
\(467\) −4.37222 −0.202322 −0.101161 0.994870i \(-0.532256\pi\)
−0.101161 + 0.994870i \(0.532256\pi\)
\(468\) −0.817755 −0.0378007
\(469\) 23.3934 1.08021
\(470\) −6.31687 −0.291376
\(471\) 6.47722 0.298454
\(472\) −7.19256 −0.331064
\(473\) −55.2036 −2.53827
\(474\) 5.36956 0.246632
\(475\) 5.95884 0.273410
\(476\) 7.73475 0.354522
\(477\) 30.8437 1.41224
\(478\) 17.3544 0.793770
\(479\) 12.8369 0.586531 0.293266 0.956031i \(-0.405258\pi\)
0.293266 + 0.956031i \(0.405258\pi\)
\(480\) −2.40579 −0.109809
\(481\) 2.00152 0.0912613
\(482\) 0.0952985 0.00434073
\(483\) −2.24359 −0.102087
\(484\) 20.4289 0.928587
\(485\) −10.0926 −0.458280
\(486\) 21.5438 0.977245
\(487\) −17.4018 −0.788552 −0.394276 0.918992i \(-0.629005\pi\)
−0.394276 + 0.918992i \(0.629005\pi\)
\(488\) 13.8248 0.625818
\(489\) −55.8110 −2.52386
\(490\) 3.92975 0.177528
\(491\) −38.1358 −1.72104 −0.860522 0.509413i \(-0.829863\pi\)
−0.860522 + 0.509413i \(0.829863\pi\)
\(492\) −8.41385 −0.379325
\(493\) −15.3840 −0.692858
\(494\) 1.74792 0.0786426
\(495\) −15.6289 −0.702466
\(496\) −8.31509 −0.373359
\(497\) 2.33977 0.104953
\(498\) 10.0662 0.451078
\(499\) −33.3663 −1.49368 −0.746841 0.665003i \(-0.768430\pi\)
−0.746841 + 0.665003i \(0.768430\pi\)
\(500\) 1.00000 0.0447214
\(501\) −25.4086 −1.13517
\(502\) −2.70106 −0.120554
\(503\) −5.78208 −0.257810 −0.128905 0.991657i \(-0.541146\pi\)
−0.128905 + 0.991657i \(0.541146\pi\)
\(504\) 4.88484 0.217588
\(505\) −9.78984 −0.435642
\(506\) 2.98376 0.132644
\(507\) −31.0682 −1.37979
\(508\) −18.6217 −0.826203
\(509\) 2.32636 0.103114 0.0515571 0.998670i \(-0.483582\pi\)
0.0515571 + 0.998670i \(0.483582\pi\)
\(510\) 10.6198 0.470253
\(511\) 17.8376 0.789090
\(512\) −1.00000 −0.0441942
\(513\) −3.04189 −0.134303
\(514\) 23.6741 1.04422
\(515\) −13.3534 −0.588421
\(516\) 23.6897 1.04288
\(517\) −35.4133 −1.55748
\(518\) −11.9560 −0.525316
\(519\) 45.7745 2.00928
\(520\) 0.293332 0.0128635
\(521\) −7.39413 −0.323943 −0.161971 0.986795i \(-0.551785\pi\)
−0.161971 + 0.986795i \(0.551785\pi\)
\(522\) −9.71564 −0.425242
\(523\) −41.3423 −1.80777 −0.903886 0.427774i \(-0.859298\pi\)
−0.903886 + 0.427774i \(0.859298\pi\)
\(524\) −5.69531 −0.248801
\(525\) −4.21545 −0.183977
\(526\) −4.31583 −0.188179
\(527\) 36.7051 1.59890
\(528\) −13.4872 −0.586955
\(529\) −22.7167 −0.987684
\(530\) −11.0638 −0.480580
\(531\) 20.0515 0.870161
\(532\) −10.4411 −0.452681
\(533\) 1.02588 0.0444359
\(534\) 31.8263 1.37726
\(535\) −1.99022 −0.0860447
\(536\) 13.3508 0.576666
\(537\) 43.1476 1.86196
\(538\) −14.2846 −0.615853
\(539\) 22.0308 0.948932
\(540\) −0.510485 −0.0219678
\(541\) −4.07929 −0.175382 −0.0876912 0.996148i \(-0.527949\pi\)
−0.0876912 + 0.996148i \(0.527949\pi\)
\(542\) −4.17693 −0.179414
\(543\) 38.2608 1.64193
\(544\) 4.41428 0.189261
\(545\) −2.34125 −0.100288
\(546\) −1.23653 −0.0529185
\(547\) −9.99288 −0.427265 −0.213632 0.976914i \(-0.568529\pi\)
−0.213632 + 0.976914i \(0.568529\pi\)
\(548\) −10.5675 −0.451422
\(549\) −38.5408 −1.64488
\(550\) 5.60615 0.239047
\(551\) 20.7668 0.884696
\(552\) −1.28043 −0.0544988
\(553\) 3.91083 0.166305
\(554\) −31.1285 −1.32252
\(555\) −16.4156 −0.696802
\(556\) 9.57211 0.405948
\(557\) 0.828239 0.0350936 0.0175468 0.999846i \(-0.494414\pi\)
0.0175468 + 0.999846i \(0.494414\pi\)
\(558\) 23.1809 0.981325
\(559\) −2.88844 −0.122168
\(560\) −1.75221 −0.0740445
\(561\) 59.5362 2.51362
\(562\) −31.5560 −1.33111
\(563\) 0.532790 0.0224544 0.0112272 0.999937i \(-0.496426\pi\)
0.0112272 + 0.999937i \(0.496426\pi\)
\(564\) 15.1970 0.639911
\(565\) 15.4709 0.650866
\(566\) −28.7658 −1.20911
\(567\) 16.8064 0.705804
\(568\) 1.33532 0.0560288
\(569\) −17.8871 −0.749865 −0.374932 0.927052i \(-0.622334\pi\)
−0.374932 + 0.927052i \(0.622334\pi\)
\(570\) −14.3357 −0.600456
\(571\) 13.6191 0.569943 0.284971 0.958536i \(-0.408016\pi\)
0.284971 + 0.958536i \(0.408016\pi\)
\(572\) 1.64446 0.0687585
\(573\) −41.0941 −1.71673
\(574\) −6.12808 −0.255781
\(575\) 0.532230 0.0221955
\(576\) 2.78781 0.116159
\(577\) −21.2418 −0.884310 −0.442155 0.896939i \(-0.645786\pi\)
−0.442155 + 0.896939i \(0.645786\pi\)
\(578\) −2.48584 −0.103397
\(579\) 55.5147 2.30711
\(580\) 3.48505 0.144709
\(581\) 7.33156 0.304164
\(582\) 24.2806 1.00646
\(583\) −62.0252 −2.56882
\(584\) 10.1801 0.421253
\(585\) −0.817755 −0.0338100
\(586\) −17.5541 −0.725153
\(587\) 26.6077 1.09822 0.549109 0.835750i \(-0.314967\pi\)
0.549109 + 0.835750i \(0.314967\pi\)
\(588\) −9.45414 −0.389882
\(589\) −49.5483 −2.04160
\(590\) −7.19256 −0.296113
\(591\) 46.9892 1.93288
\(592\) −6.82337 −0.280439
\(593\) 31.0830 1.27643 0.638213 0.769860i \(-0.279674\pi\)
0.638213 + 0.769860i \(0.279674\pi\)
\(594\) −2.86185 −0.117423
\(595\) 7.73475 0.317094
\(596\) −11.9011 −0.487489
\(597\) 17.8708 0.731404
\(598\) 0.156120 0.00638423
\(599\) −13.0196 −0.531965 −0.265983 0.963978i \(-0.585696\pi\)
−0.265983 + 0.963978i \(0.585696\pi\)
\(600\) −2.40579 −0.0982158
\(601\) −11.9314 −0.486691 −0.243345 0.969940i \(-0.578245\pi\)
−0.243345 + 0.969940i \(0.578245\pi\)
\(602\) 17.2540 0.703221
\(603\) −37.2194 −1.51569
\(604\) −4.48113 −0.182335
\(605\) 20.4289 0.830553
\(606\) 23.5523 0.956745
\(607\) 28.3130 1.14919 0.574595 0.818438i \(-0.305160\pi\)
0.574595 + 0.818438i \(0.305160\pi\)
\(608\) −5.95884 −0.241663
\(609\) −14.6910 −0.595311
\(610\) 13.8248 0.559748
\(611\) −1.85294 −0.0749621
\(612\) −12.3062 −0.497447
\(613\) 27.8312 1.12409 0.562046 0.827106i \(-0.310014\pi\)
0.562046 + 0.827106i \(0.310014\pi\)
\(614\) −0.103139 −0.00416235
\(615\) −8.41385 −0.339279
\(616\) −9.82317 −0.395787
\(617\) 15.7270 0.633146 0.316573 0.948568i \(-0.397468\pi\)
0.316573 + 0.948568i \(0.397468\pi\)
\(618\) 32.1254 1.29227
\(619\) −5.82742 −0.234224 −0.117112 0.993119i \(-0.537364\pi\)
−0.117112 + 0.993119i \(0.537364\pi\)
\(620\) −8.31509 −0.333942
\(621\) −0.271695 −0.0109028
\(622\) −25.3389 −1.01600
\(623\) 23.1801 0.928692
\(624\) −0.705695 −0.0282504
\(625\) 1.00000 0.0400000
\(626\) −17.7254 −0.708450
\(627\) −80.3680 −3.20959
\(628\) 2.69235 0.107436
\(629\) 30.1202 1.20097
\(630\) 4.88484 0.194617
\(631\) 1.93094 0.0768693 0.0384347 0.999261i \(-0.487763\pi\)
0.0384347 + 0.999261i \(0.487763\pi\)
\(632\) 2.23194 0.0887817
\(633\) 17.4882 0.695094
\(634\) −11.4292 −0.453911
\(635\) −18.6217 −0.738979
\(636\) 26.6171 1.05544
\(637\) 1.15272 0.0456726
\(638\) 19.5377 0.773504
\(639\) −3.72262 −0.147265
\(640\) −1.00000 −0.0395285
\(641\) −18.6773 −0.737710 −0.368855 0.929487i \(-0.620250\pi\)
−0.368855 + 0.929487i \(0.620250\pi\)
\(642\) 4.78804 0.188969
\(643\) 43.3949 1.71133 0.855665 0.517531i \(-0.173149\pi\)
0.855665 + 0.517531i \(0.173149\pi\)
\(644\) −0.932580 −0.0367488
\(645\) 23.6897 0.932782
\(646\) 26.3039 1.03491
\(647\) 11.3229 0.445150 0.222575 0.974916i \(-0.428554\pi\)
0.222575 + 0.974916i \(0.428554\pi\)
\(648\) 9.59155 0.376792
\(649\) −40.3226 −1.58280
\(650\) 0.293332 0.0115054
\(651\) 35.0519 1.37379
\(652\) −23.1986 −0.908529
\(653\) −30.3222 −1.18660 −0.593300 0.804982i \(-0.702175\pi\)
−0.593300 + 0.804982i \(0.702175\pi\)
\(654\) 5.63256 0.220250
\(655\) −5.69531 −0.222534
\(656\) −3.49734 −0.136548
\(657\) −28.3800 −1.10721
\(658\) 11.0685 0.431495
\(659\) 10.2859 0.400681 0.200340 0.979726i \(-0.435795\pi\)
0.200340 + 0.979726i \(0.435795\pi\)
\(660\) −13.4872 −0.524988
\(661\) −14.2306 −0.553505 −0.276753 0.960941i \(-0.589258\pi\)
−0.276753 + 0.960941i \(0.589258\pi\)
\(662\) 2.57374 0.100031
\(663\) 3.11513 0.120982
\(664\) 4.18417 0.162377
\(665\) −10.4411 −0.404890
\(666\) 19.0223 0.737098
\(667\) 1.85485 0.0718199
\(668\) −10.5614 −0.408634
\(669\) −48.4896 −1.87472
\(670\) 13.3508 0.515786
\(671\) 77.5037 2.99200
\(672\) 4.21545 0.162615
\(673\) −22.9868 −0.886076 −0.443038 0.896503i \(-0.646099\pi\)
−0.443038 + 0.896503i \(0.646099\pi\)
\(674\) −23.1351 −0.891130
\(675\) −0.510485 −0.0196486
\(676\) −12.9140 −0.496691
\(677\) −13.3790 −0.514199 −0.257099 0.966385i \(-0.582767\pi\)
−0.257099 + 0.966385i \(0.582767\pi\)
\(678\) −37.2197 −1.42941
\(679\) 17.6843 0.678662
\(680\) 4.41428 0.169280
\(681\) 60.5374 2.31980
\(682\) −46.6156 −1.78501
\(683\) 20.1226 0.769970 0.384985 0.922923i \(-0.374207\pi\)
0.384985 + 0.922923i \(0.374207\pi\)
\(684\) 16.6121 0.635179
\(685\) −10.5675 −0.403764
\(686\) −19.1512 −0.731198
\(687\) −18.7697 −0.716107
\(688\) 9.84698 0.375413
\(689\) −3.24536 −0.123639
\(690\) −1.28043 −0.0487452
\(691\) −8.07108 −0.307038 −0.153519 0.988146i \(-0.549061\pi\)
−0.153519 + 0.988146i \(0.549061\pi\)
\(692\) 19.0268 0.723291
\(693\) 27.3851 1.04027
\(694\) 5.29245 0.200899
\(695\) 9.57211 0.363091
\(696\) −8.38428 −0.317805
\(697\) 15.4382 0.584764
\(698\) −31.2995 −1.18471
\(699\) −19.7582 −0.747325
\(700\) −1.75221 −0.0662274
\(701\) −4.74431 −0.179190 −0.0895951 0.995978i \(-0.528557\pi\)
−0.0895951 + 0.995978i \(0.528557\pi\)
\(702\) −0.149742 −0.00565163
\(703\) −40.6593 −1.53350
\(704\) −5.60615 −0.211290
\(705\) 15.1970 0.572354
\(706\) −24.8184 −0.934052
\(707\) 17.1539 0.645138
\(708\) 17.3038 0.650315
\(709\) −4.01101 −0.150636 −0.0753182 0.997160i \(-0.523997\pi\)
−0.0753182 + 0.997160i \(0.523997\pi\)
\(710\) 1.33532 0.0501137
\(711\) −6.22221 −0.233351
\(712\) 13.2291 0.495780
\(713\) −4.42554 −0.165738
\(714\) −18.6082 −0.696393
\(715\) 1.64446 0.0614995
\(716\) 17.9349 0.670260
\(717\) −41.7509 −1.55922
\(718\) −6.33468 −0.236408
\(719\) 31.3475 1.16906 0.584532 0.811371i \(-0.301278\pi\)
0.584532 + 0.811371i \(0.301278\pi\)
\(720\) 2.78781 0.103896
\(721\) 23.3980 0.871386
\(722\) −16.5077 −0.614354
\(723\) −0.229268 −0.00852656
\(724\) 15.9037 0.591055
\(725\) 3.48505 0.129431
\(726\) −49.1476 −1.82404
\(727\) −7.19320 −0.266781 −0.133390 0.991064i \(-0.542586\pi\)
−0.133390 + 0.991064i \(0.542586\pi\)
\(728\) −0.513981 −0.0190494
\(729\) −23.0551 −0.853891
\(730\) 10.1801 0.376781
\(731\) −43.4673 −1.60770
\(732\) −33.2594 −1.22930
\(733\) 20.0145 0.739254 0.369627 0.929180i \(-0.379486\pi\)
0.369627 + 0.929180i \(0.379486\pi\)
\(734\) 31.1149 1.14847
\(735\) −9.45414 −0.348721
\(736\) −0.532230 −0.0196183
\(737\) 74.8465 2.75700
\(738\) 9.74991 0.358899
\(739\) −11.0093 −0.404984 −0.202492 0.979284i \(-0.564904\pi\)
−0.202492 + 0.979284i \(0.564904\pi\)
\(740\) −6.82337 −0.250832
\(741\) −4.20512 −0.154479
\(742\) 19.3861 0.711686
\(743\) −38.7143 −1.42029 −0.710144 0.704056i \(-0.751370\pi\)
−0.710144 + 0.704056i \(0.751370\pi\)
\(744\) 20.0043 0.733395
\(745\) −11.9011 −0.436024
\(746\) −20.0301 −0.733353
\(747\) −11.6647 −0.426788
\(748\) 24.7471 0.904843
\(749\) 3.48729 0.127423
\(750\) −2.40579 −0.0878469
\(751\) 20.5252 0.748974 0.374487 0.927232i \(-0.377819\pi\)
0.374487 + 0.927232i \(0.377819\pi\)
\(752\) 6.31687 0.230353
\(753\) 6.49817 0.236807
\(754\) 1.02228 0.0372291
\(755\) −4.48113 −0.163085
\(756\) 0.894478 0.0325318
\(757\) 17.1690 0.624019 0.312009 0.950079i \(-0.398998\pi\)
0.312009 + 0.950079i \(0.398998\pi\)
\(758\) 32.5737 1.18313
\(759\) −7.17829 −0.260555
\(760\) −5.95884 −0.216150
\(761\) 21.7443 0.788231 0.394115 0.919061i \(-0.371051\pi\)
0.394115 + 0.919061i \(0.371051\pi\)
\(762\) 44.7998 1.62292
\(763\) 4.10238 0.148516
\(764\) −17.0814 −0.617982
\(765\) −12.3062 −0.444930
\(766\) −10.7995 −0.390202
\(767\) −2.10981 −0.0761809
\(768\) 2.40579 0.0868114
\(769\) −24.0187 −0.866136 −0.433068 0.901361i \(-0.642569\pi\)
−0.433068 + 0.901361i \(0.642569\pi\)
\(770\) −9.82317 −0.354002
\(771\) −56.9549 −2.05118
\(772\) 23.0755 0.830505
\(773\) −46.2409 −1.66317 −0.831585 0.555397i \(-0.812566\pi\)
−0.831585 + 0.555397i \(0.812566\pi\)
\(774\) −27.4515 −0.986724
\(775\) −8.31509 −0.298687
\(776\) 10.0926 0.362302
\(777\) 28.7636 1.03189
\(778\) 3.29764 0.118226
\(779\) −20.8401 −0.746672
\(780\) −0.705695 −0.0252679
\(781\) 7.48601 0.267870
\(782\) 2.34941 0.0840148
\(783\) −1.77906 −0.0635785
\(784\) −3.92975 −0.140348
\(785\) 2.69235 0.0960940
\(786\) 13.7017 0.488724
\(787\) 10.0082 0.356754 0.178377 0.983962i \(-0.442915\pi\)
0.178377 + 0.983962i \(0.442915\pi\)
\(788\) 19.5317 0.695789
\(789\) 10.3830 0.369644
\(790\) 2.23194 0.0794087
\(791\) −27.1083 −0.963861
\(792\) 15.6289 0.555348
\(793\) 4.05525 0.144006
\(794\) −30.4380 −1.08020
\(795\) 26.6171 0.944011
\(796\) 7.42826 0.263288
\(797\) 13.5133 0.478667 0.239333 0.970937i \(-0.423071\pi\)
0.239333 + 0.970937i \(0.423071\pi\)
\(798\) 25.1192 0.889209
\(799\) −27.8844 −0.986480
\(800\) −1.00000 −0.0353553
\(801\) −36.8801 −1.30309
\(802\) −1.00000 −0.0353112
\(803\) 57.0709 2.01399
\(804\) −32.1191 −1.13275
\(805\) −0.932580 −0.0328691
\(806\) −2.43909 −0.0859131
\(807\) 34.3657 1.20973
\(808\) 9.78984 0.344405
\(809\) −28.2194 −0.992141 −0.496071 0.868282i \(-0.665224\pi\)
−0.496071 + 0.868282i \(0.665224\pi\)
\(810\) 9.59155 0.337013
\(811\) −36.6501 −1.28696 −0.643480 0.765463i \(-0.722510\pi\)
−0.643480 + 0.765463i \(0.722510\pi\)
\(812\) −6.10654 −0.214298
\(813\) 10.0488 0.352427
\(814\) −38.2528 −1.34076
\(815\) −23.1986 −0.812613
\(816\) −10.6198 −0.371768
\(817\) 58.6765 2.05283
\(818\) 2.25032 0.0786804
\(819\) 1.43288 0.0500689
\(820\) −3.49734 −0.122132
\(821\) 49.5635 1.72978 0.864889 0.501963i \(-0.167389\pi\)
0.864889 + 0.501963i \(0.167389\pi\)
\(822\) 25.4232 0.886736
\(823\) 37.7484 1.31583 0.657913 0.753094i \(-0.271439\pi\)
0.657913 + 0.753094i \(0.271439\pi\)
\(824\) 13.3534 0.465187
\(825\) −13.4872 −0.469564
\(826\) 12.6029 0.438511
\(827\) 31.1848 1.08440 0.542201 0.840249i \(-0.317591\pi\)
0.542201 + 0.840249i \(0.317591\pi\)
\(828\) 1.48376 0.0515641
\(829\) 37.5310 1.30350 0.651752 0.758432i \(-0.274034\pi\)
0.651752 + 0.758432i \(0.274034\pi\)
\(830\) 4.18417 0.145235
\(831\) 74.8885 2.59785
\(832\) −0.293332 −0.0101695
\(833\) 17.3470 0.601038
\(834\) −23.0284 −0.797410
\(835\) −10.5614 −0.365493
\(836\) −33.4061 −1.15537
\(837\) 4.24473 0.146719
\(838\) 20.2395 0.699161
\(839\) −25.7680 −0.889611 −0.444806 0.895627i \(-0.646727\pi\)
−0.444806 + 0.895627i \(0.646727\pi\)
\(840\) 4.21545 0.145447
\(841\) −16.8545 −0.581188
\(842\) 6.12535 0.211094
\(843\) 75.9169 2.61472
\(844\) 7.26922 0.250217
\(845\) −12.9140 −0.444254
\(846\) −17.6102 −0.605452
\(847\) −35.7958 −1.22996
\(848\) 11.0638 0.379932
\(849\) 69.2043 2.37508
\(850\) 4.41428 0.151408
\(851\) −3.63160 −0.124490
\(852\) −3.21250 −0.110058
\(853\) 52.8961 1.81113 0.905564 0.424209i \(-0.139448\pi\)
0.905564 + 0.424209i \(0.139448\pi\)
\(854\) −24.2239 −0.828926
\(855\) 16.6121 0.568122
\(856\) 1.99022 0.0680243
\(857\) −8.61059 −0.294132 −0.147066 0.989127i \(-0.546983\pi\)
−0.147066 + 0.989127i \(0.546983\pi\)
\(858\) −3.95623 −0.135064
\(859\) −7.84399 −0.267633 −0.133817 0.991006i \(-0.542723\pi\)
−0.133817 + 0.991006i \(0.542723\pi\)
\(860\) 9.84698 0.335779
\(861\) 14.7428 0.502435
\(862\) −16.8163 −0.572764
\(863\) −21.3242 −0.725885 −0.362943 0.931811i \(-0.618228\pi\)
−0.362943 + 0.931811i \(0.618228\pi\)
\(864\) 0.510485 0.0173670
\(865\) 19.0268 0.646931
\(866\) 1.18090 0.0401285
\(867\) 5.98039 0.203105
\(868\) 14.5698 0.494532
\(869\) 12.5126 0.424460
\(870\) −8.38428 −0.284254
\(871\) 3.91622 0.132696
\(872\) 2.34125 0.0792849
\(873\) −28.1361 −0.952264
\(874\) −3.17147 −0.107277
\(875\) −1.75221 −0.0592356
\(876\) −24.4910 −0.827475
\(877\) −52.8173 −1.78351 −0.891757 0.452515i \(-0.850527\pi\)
−0.891757 + 0.452515i \(0.850527\pi\)
\(878\) 25.4663 0.859446
\(879\) 42.2314 1.42443
\(880\) −5.60615 −0.188983
\(881\) −36.3310 −1.22402 −0.612011 0.790849i \(-0.709639\pi\)
−0.612011 + 0.790849i \(0.709639\pi\)
\(882\) 10.9554 0.368887
\(883\) −22.7038 −0.764044 −0.382022 0.924153i \(-0.624772\pi\)
−0.382022 + 0.924153i \(0.624772\pi\)
\(884\) 1.29485 0.0435505
\(885\) 17.3038 0.581660
\(886\) 16.4471 0.552552
\(887\) −24.5134 −0.823081 −0.411540 0.911392i \(-0.635009\pi\)
−0.411540 + 0.911392i \(0.635009\pi\)
\(888\) 16.4156 0.550871
\(889\) 32.6291 1.09435
\(890\) 13.2291 0.443439
\(891\) 53.7716 1.80142
\(892\) −20.1554 −0.674853
\(893\) 37.6412 1.25961
\(894\) 28.6316 0.957584
\(895\) 17.9349 0.599499
\(896\) 1.75221 0.0585373
\(897\) −0.375592 −0.0125407
\(898\) −9.13398 −0.304805
\(899\) −28.9785 −0.966486
\(900\) 2.78781 0.0929270
\(901\) −48.8386 −1.62705
\(902\) −19.6066 −0.652828
\(903\) −41.5094 −1.38135
\(904\) −15.4709 −0.514555
\(905\) 15.9037 0.528656
\(906\) 10.7806 0.358163
\(907\) 45.0931 1.49729 0.748646 0.662971i \(-0.230705\pi\)
0.748646 + 0.662971i \(0.230705\pi\)
\(908\) 25.1632 0.835071
\(909\) −27.2922 −0.905225
\(910\) −0.513981 −0.0170383
\(911\) −50.8279 −1.68400 −0.842002 0.539474i \(-0.818623\pi\)
−0.842002 + 0.539474i \(0.818623\pi\)
\(912\) 14.3357 0.474702
\(913\) 23.4571 0.776316
\(914\) 27.2144 0.900173
\(915\) −33.2594 −1.09952
\(916\) −7.80188 −0.257781
\(917\) 9.97940 0.329549
\(918\) −2.25342 −0.0743739
\(919\) −20.8817 −0.688823 −0.344412 0.938819i \(-0.611922\pi\)
−0.344412 + 0.938819i \(0.611922\pi\)
\(920\) −0.532230 −0.0175471
\(921\) 0.248131 0.00817618
\(922\) 7.78685 0.256446
\(923\) 0.391693 0.0128927
\(924\) 23.6324 0.777450
\(925\) −6.82337 −0.224351
\(926\) −24.6432 −0.809826
\(927\) −37.2267 −1.22269
\(928\) −3.48505 −0.114402
\(929\) −43.9574 −1.44220 −0.721098 0.692833i \(-0.756362\pi\)
−0.721098 + 0.692833i \(0.756362\pi\)
\(930\) 20.0043 0.655968
\(931\) −23.4167 −0.767453
\(932\) −8.21279 −0.269019
\(933\) 60.9600 1.99574
\(934\) 4.37222 0.143063
\(935\) 24.7471 0.809316
\(936\) 0.817755 0.0267292
\(937\) −54.3703 −1.77620 −0.888099 0.459652i \(-0.847974\pi\)
−0.888099 + 0.459652i \(0.847974\pi\)
\(938\) −23.3934 −0.763822
\(939\) 42.6435 1.39162
\(940\) 6.31687 0.206034
\(941\) 16.6596 0.543086 0.271543 0.962426i \(-0.412466\pi\)
0.271543 + 0.962426i \(0.412466\pi\)
\(942\) −6.47722 −0.211039
\(943\) −1.86139 −0.0606151
\(944\) 7.19256 0.234098
\(945\) 0.894478 0.0290974
\(946\) 55.2036 1.79482
\(947\) 38.2608 1.24331 0.621654 0.783292i \(-0.286461\pi\)
0.621654 + 0.783292i \(0.286461\pi\)
\(948\) −5.36956 −0.174395
\(949\) 2.98614 0.0969342
\(950\) −5.95884 −0.193330
\(951\) 27.4962 0.891625
\(952\) −7.73475 −0.250685
\(953\) 29.5278 0.956498 0.478249 0.878224i \(-0.341272\pi\)
0.478249 + 0.878224i \(0.341272\pi\)
\(954\) −30.8437 −0.998602
\(955\) −17.0814 −0.552740
\(956\) −17.3544 −0.561280
\(957\) −47.0035 −1.51941
\(958\) −12.8369 −0.414740
\(959\) 18.5165 0.597930
\(960\) 2.40579 0.0776464
\(961\) 38.1407 1.23035
\(962\) −2.00152 −0.0645315
\(963\) −5.54835 −0.178793
\(964\) −0.0952985 −0.00306936
\(965\) 23.0755 0.742826
\(966\) 2.24359 0.0721863
\(967\) 22.1456 0.712155 0.356078 0.934456i \(-0.384114\pi\)
0.356078 + 0.934456i \(0.384114\pi\)
\(968\) −20.4289 −0.656610
\(969\) −63.2817 −2.03290
\(970\) 10.0926 0.324053
\(971\) −14.7008 −0.471770 −0.235885 0.971781i \(-0.575799\pi\)
−0.235885 + 0.971781i \(0.575799\pi\)
\(972\) −21.5438 −0.691016
\(973\) −16.7724 −0.537697
\(974\) 17.4018 0.557591
\(975\) −0.705695 −0.0226003
\(976\) −13.8248 −0.442520
\(977\) −8.97781 −0.287225 −0.143613 0.989634i \(-0.545872\pi\)
−0.143613 + 0.989634i \(0.545872\pi\)
\(978\) 55.8110 1.78464
\(979\) 74.1641 2.37029
\(980\) −3.92975 −0.125531
\(981\) −6.52697 −0.208390
\(982\) 38.1358 1.21696
\(983\) −17.1411 −0.546715 −0.273358 0.961913i \(-0.588134\pi\)
−0.273358 + 0.961913i \(0.588134\pi\)
\(984\) 8.41385 0.268224
\(985\) 19.5317 0.622332
\(986\) 15.3840 0.489925
\(987\) −26.6285 −0.847593
\(988\) −1.74792 −0.0556087
\(989\) 5.24086 0.166650
\(990\) 15.6289 0.496718
\(991\) 34.1073 1.08345 0.541727 0.840554i \(-0.317771\pi\)
0.541727 + 0.840554i \(0.317771\pi\)
\(992\) 8.31509 0.264004
\(993\) −6.19186 −0.196493
\(994\) −2.33977 −0.0742129
\(995\) 7.42826 0.235492
\(996\) −10.0662 −0.318961
\(997\) −36.2444 −1.14787 −0.573936 0.818900i \(-0.694584\pi\)
−0.573936 + 0.818900i \(0.694584\pi\)
\(998\) 33.3663 1.05619
\(999\) 3.48323 0.110204
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4010.2.a.i.1.10 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4010.2.a.i.1.10 10 1.1 even 1 trivial