Properties

Label 4029.2.a.l.1.20
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 32
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.937640 q^{2} -1.00000 q^{3} -1.12083 q^{4} +0.347083 q^{5} -0.937640 q^{6} +4.09662 q^{7} -2.92622 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.937640 q^{2} -1.00000 q^{3} -1.12083 q^{4} +0.347083 q^{5} -0.937640 q^{6} +4.09662 q^{7} -2.92622 q^{8} +1.00000 q^{9} +0.325439 q^{10} +5.59970 q^{11} +1.12083 q^{12} +4.86991 q^{13} +3.84115 q^{14} -0.347083 q^{15} -0.502078 q^{16} -1.00000 q^{17} +0.937640 q^{18} +2.01626 q^{19} -0.389021 q^{20} -4.09662 q^{21} +5.25050 q^{22} +7.46088 q^{23} +2.92622 q^{24} -4.87953 q^{25} +4.56623 q^{26} -1.00000 q^{27} -4.59161 q^{28} -1.16192 q^{29} -0.325439 q^{30} -7.75406 q^{31} +5.38166 q^{32} -5.59970 q^{33} -0.937640 q^{34} +1.42186 q^{35} -1.12083 q^{36} +5.13012 q^{37} +1.89053 q^{38} -4.86991 q^{39} -1.01564 q^{40} +12.4998 q^{41} -3.84115 q^{42} -3.07115 q^{43} -6.27631 q^{44} +0.347083 q^{45} +6.99562 q^{46} -9.52721 q^{47} +0.502078 q^{48} +9.78227 q^{49} -4.57525 q^{50} +1.00000 q^{51} -5.45835 q^{52} -12.4919 q^{53} -0.937640 q^{54} +1.94356 q^{55} -11.9876 q^{56} -2.01626 q^{57} -1.08946 q^{58} +4.14723 q^{59} +0.389021 q^{60} -4.30079 q^{61} -7.27052 q^{62} +4.09662 q^{63} +6.05022 q^{64} +1.69026 q^{65} -5.25050 q^{66} -1.33601 q^{67} +1.12083 q^{68} -7.46088 q^{69} +1.33320 q^{70} +5.13907 q^{71} -2.92622 q^{72} +8.49373 q^{73} +4.81021 q^{74} +4.87953 q^{75} -2.25988 q^{76} +22.9398 q^{77} -4.56623 q^{78} +1.00000 q^{79} -0.174263 q^{80} +1.00000 q^{81} +11.7203 q^{82} -11.4290 q^{83} +4.59161 q^{84} -0.347083 q^{85} -2.87963 q^{86} +1.16192 q^{87} -16.3859 q^{88} -12.2948 q^{89} +0.325439 q^{90} +19.9502 q^{91} -8.36238 q^{92} +7.75406 q^{93} -8.93310 q^{94} +0.699808 q^{95} -5.38166 q^{96} -14.1233 q^{97} +9.17225 q^{98} +5.59970 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.937640 0.663012 0.331506 0.943453i \(-0.392443\pi\)
0.331506 + 0.943453i \(0.392443\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.12083 −0.560415
\(5\) 0.347083 0.155220 0.0776100 0.996984i \(-0.475271\pi\)
0.0776100 + 0.996984i \(0.475271\pi\)
\(6\) −0.937640 −0.382790
\(7\) 4.09662 1.54838 0.774188 0.632956i \(-0.218159\pi\)
0.774188 + 0.632956i \(0.218159\pi\)
\(8\) −2.92622 −1.03457
\(9\) 1.00000 0.333333
\(10\) 0.325439 0.102913
\(11\) 5.59970 1.68837 0.844186 0.536050i \(-0.180084\pi\)
0.844186 + 0.536050i \(0.180084\pi\)
\(12\) 1.12083 0.323556
\(13\) 4.86991 1.35067 0.675336 0.737511i \(-0.263999\pi\)
0.675336 + 0.737511i \(0.263999\pi\)
\(14\) 3.84115 1.02659
\(15\) −0.347083 −0.0896163
\(16\) −0.502078 −0.125519
\(17\) −1.00000 −0.242536
\(18\) 0.937640 0.221004
\(19\) 2.01626 0.462562 0.231281 0.972887i \(-0.425708\pi\)
0.231281 + 0.972887i \(0.425708\pi\)
\(20\) −0.389021 −0.0869877
\(21\) −4.09662 −0.893955
\(22\) 5.25050 1.11941
\(23\) 7.46088 1.55570 0.777851 0.628449i \(-0.216310\pi\)
0.777851 + 0.628449i \(0.216310\pi\)
\(24\) 2.92622 0.597311
\(25\) −4.87953 −0.975907
\(26\) 4.56623 0.895511
\(27\) −1.00000 −0.192450
\(28\) −4.59161 −0.867733
\(29\) −1.16192 −0.215763 −0.107882 0.994164i \(-0.534407\pi\)
−0.107882 + 0.994164i \(0.534407\pi\)
\(30\) −0.325439 −0.0594167
\(31\) −7.75406 −1.39267 −0.696335 0.717717i \(-0.745187\pi\)
−0.696335 + 0.717717i \(0.745187\pi\)
\(32\) 5.38166 0.951353
\(33\) −5.59970 −0.974782
\(34\) −0.937640 −0.160804
\(35\) 1.42186 0.240339
\(36\) −1.12083 −0.186805
\(37\) 5.13012 0.843386 0.421693 0.906739i \(-0.361436\pi\)
0.421693 + 0.906739i \(0.361436\pi\)
\(38\) 1.89053 0.306684
\(39\) −4.86991 −0.779810
\(40\) −1.01564 −0.160587
\(41\) 12.4998 1.95214 0.976071 0.217453i \(-0.0697750\pi\)
0.976071 + 0.217453i \(0.0697750\pi\)
\(42\) −3.84115 −0.592703
\(43\) −3.07115 −0.468346 −0.234173 0.972195i \(-0.575238\pi\)
−0.234173 + 0.972195i \(0.575238\pi\)
\(44\) −6.27631 −0.946190
\(45\) 0.347083 0.0517400
\(46\) 6.99562 1.03145
\(47\) −9.52721 −1.38969 −0.694843 0.719161i \(-0.744526\pi\)
−0.694843 + 0.719161i \(0.744526\pi\)
\(48\) 0.502078 0.0724687
\(49\) 9.78227 1.39747
\(50\) −4.57525 −0.647038
\(51\) 1.00000 0.140028
\(52\) −5.45835 −0.756937
\(53\) −12.4919 −1.71589 −0.857944 0.513744i \(-0.828258\pi\)
−0.857944 + 0.513744i \(0.828258\pi\)
\(54\) −0.937640 −0.127597
\(55\) 1.94356 0.262069
\(56\) −11.9876 −1.60191
\(57\) −2.01626 −0.267060
\(58\) −1.08946 −0.143054
\(59\) 4.14723 0.539923 0.269961 0.962871i \(-0.412989\pi\)
0.269961 + 0.962871i \(0.412989\pi\)
\(60\) 0.389021 0.0502224
\(61\) −4.30079 −0.550660 −0.275330 0.961350i \(-0.588787\pi\)
−0.275330 + 0.961350i \(0.588787\pi\)
\(62\) −7.27052 −0.923357
\(63\) 4.09662 0.516125
\(64\) 6.05022 0.756278
\(65\) 1.69026 0.209651
\(66\) −5.25050 −0.646292
\(67\) −1.33601 −0.163220 −0.0816099 0.996664i \(-0.526006\pi\)
−0.0816099 + 0.996664i \(0.526006\pi\)
\(68\) 1.12083 0.135921
\(69\) −7.46088 −0.898185
\(70\) 1.33320 0.159348
\(71\) 5.13907 0.609895 0.304947 0.952369i \(-0.401361\pi\)
0.304947 + 0.952369i \(0.401361\pi\)
\(72\) −2.92622 −0.344858
\(73\) 8.49373 0.994116 0.497058 0.867717i \(-0.334414\pi\)
0.497058 + 0.867717i \(0.334414\pi\)
\(74\) 4.81021 0.559175
\(75\) 4.87953 0.563440
\(76\) −2.25988 −0.259227
\(77\) 22.9398 2.61424
\(78\) −4.56623 −0.517023
\(79\) 1.00000 0.112509
\(80\) −0.174263 −0.0194831
\(81\) 1.00000 0.111111
\(82\) 11.7203 1.29429
\(83\) −11.4290 −1.25450 −0.627249 0.778819i \(-0.715819\pi\)
−0.627249 + 0.778819i \(0.715819\pi\)
\(84\) 4.59161 0.500986
\(85\) −0.347083 −0.0376464
\(86\) −2.87963 −0.310519
\(87\) 1.16192 0.124571
\(88\) −16.3859 −1.74675
\(89\) −12.2948 −1.30325 −0.651624 0.758542i \(-0.725912\pi\)
−0.651624 + 0.758542i \(0.725912\pi\)
\(90\) 0.325439 0.0343042
\(91\) 19.9502 2.09135
\(92\) −8.36238 −0.871839
\(93\) 7.75406 0.804059
\(94\) −8.93310 −0.921379
\(95\) 0.699808 0.0717988
\(96\) −5.38166 −0.549264
\(97\) −14.1233 −1.43400 −0.717002 0.697071i \(-0.754486\pi\)
−0.717002 + 0.697071i \(0.754486\pi\)
\(98\) 9.17225 0.926537
\(99\) 5.59970 0.562791
\(100\) 5.46913 0.546913
\(101\) 13.1639 1.30985 0.654926 0.755693i \(-0.272700\pi\)
0.654926 + 0.755693i \(0.272700\pi\)
\(102\) 0.937640 0.0928402
\(103\) 9.89370 0.974855 0.487427 0.873163i \(-0.337935\pi\)
0.487427 + 0.873163i \(0.337935\pi\)
\(104\) −14.2504 −1.39737
\(105\) −1.42186 −0.138760
\(106\) −11.7129 −1.13765
\(107\) −17.5125 −1.69300 −0.846499 0.532390i \(-0.821294\pi\)
−0.846499 + 0.532390i \(0.821294\pi\)
\(108\) 1.12083 0.107852
\(109\) 15.6835 1.50221 0.751104 0.660184i \(-0.229522\pi\)
0.751104 + 0.660184i \(0.229522\pi\)
\(110\) 1.82236 0.173755
\(111\) −5.13012 −0.486929
\(112\) −2.05682 −0.194351
\(113\) 9.54304 0.897734 0.448867 0.893599i \(-0.351828\pi\)
0.448867 + 0.893599i \(0.351828\pi\)
\(114\) −1.89053 −0.177064
\(115\) 2.58954 0.241476
\(116\) 1.30232 0.120917
\(117\) 4.86991 0.450224
\(118\) 3.88861 0.357975
\(119\) −4.09662 −0.375536
\(120\) 1.01564 0.0927147
\(121\) 20.3566 1.85060
\(122\) −4.03260 −0.365094
\(123\) −12.4998 −1.12707
\(124\) 8.69099 0.780474
\(125\) −3.42901 −0.306700
\(126\) 3.84115 0.342197
\(127\) −2.21854 −0.196863 −0.0984317 0.995144i \(-0.531383\pi\)
−0.0984317 + 0.995144i \(0.531383\pi\)
\(128\) −5.09040 −0.449932
\(129\) 3.07115 0.270400
\(130\) 1.58486 0.139001
\(131\) 10.5499 0.921752 0.460876 0.887465i \(-0.347535\pi\)
0.460876 + 0.887465i \(0.347535\pi\)
\(132\) 6.27631 0.546283
\(133\) 8.25984 0.716219
\(134\) −1.25270 −0.108217
\(135\) −0.347083 −0.0298721
\(136\) 2.92622 0.250921
\(137\) −13.9317 −1.19026 −0.595132 0.803628i \(-0.702900\pi\)
−0.595132 + 0.803628i \(0.702900\pi\)
\(138\) −6.99562 −0.595507
\(139\) 11.2444 0.953735 0.476867 0.878975i \(-0.341772\pi\)
0.476867 + 0.878975i \(0.341772\pi\)
\(140\) −1.59367 −0.134690
\(141\) 9.52721 0.802336
\(142\) 4.81860 0.404368
\(143\) 27.2700 2.28044
\(144\) −0.502078 −0.0418398
\(145\) −0.403283 −0.0334908
\(146\) 7.96406 0.659110
\(147\) −9.78227 −0.806828
\(148\) −5.74999 −0.472647
\(149\) −19.7794 −1.62039 −0.810196 0.586159i \(-0.800639\pi\)
−0.810196 + 0.586159i \(0.800639\pi\)
\(150\) 4.57525 0.373567
\(151\) −0.247160 −0.0201136 −0.0100568 0.999949i \(-0.503201\pi\)
−0.0100568 + 0.999949i \(0.503201\pi\)
\(152\) −5.90001 −0.478554
\(153\) −1.00000 −0.0808452
\(154\) 21.5093 1.73327
\(155\) −2.69130 −0.216170
\(156\) 5.45835 0.437018
\(157\) 9.04620 0.721966 0.360983 0.932572i \(-0.382441\pi\)
0.360983 + 0.932572i \(0.382441\pi\)
\(158\) 0.937640 0.0745947
\(159\) 12.4919 0.990668
\(160\) 1.86788 0.147669
\(161\) 30.5644 2.40881
\(162\) 0.937640 0.0736680
\(163\) 19.8776 1.55694 0.778469 0.627684i \(-0.215997\pi\)
0.778469 + 0.627684i \(0.215997\pi\)
\(164\) −14.0102 −1.09401
\(165\) −1.94356 −0.151306
\(166\) −10.7163 −0.831747
\(167\) 23.2387 1.79826 0.899132 0.437677i \(-0.144199\pi\)
0.899132 + 0.437677i \(0.144199\pi\)
\(168\) 11.9876 0.924863
\(169\) 10.7161 0.824312
\(170\) −0.325439 −0.0249600
\(171\) 2.01626 0.154187
\(172\) 3.44224 0.262468
\(173\) 23.6309 1.79662 0.898310 0.439362i \(-0.144795\pi\)
0.898310 + 0.439362i \(0.144795\pi\)
\(174\) 1.08946 0.0825921
\(175\) −19.9896 −1.51107
\(176\) −2.81149 −0.211924
\(177\) −4.14723 −0.311725
\(178\) −11.5281 −0.864069
\(179\) −5.63786 −0.421393 −0.210697 0.977552i \(-0.567573\pi\)
−0.210697 + 0.977552i \(0.567573\pi\)
\(180\) −0.389021 −0.0289959
\(181\) −14.1392 −1.05096 −0.525479 0.850806i \(-0.676114\pi\)
−0.525479 + 0.850806i \(0.676114\pi\)
\(182\) 18.7061 1.38659
\(183\) 4.30079 0.317924
\(184\) −21.8322 −1.60949
\(185\) 1.78057 0.130910
\(186\) 7.27052 0.533101
\(187\) −5.59970 −0.409491
\(188\) 10.6784 0.778802
\(189\) −4.09662 −0.297985
\(190\) 0.656169 0.0476035
\(191\) 14.4235 1.04365 0.521824 0.853053i \(-0.325252\pi\)
0.521824 + 0.853053i \(0.325252\pi\)
\(192\) −6.05022 −0.436637
\(193\) 23.1697 1.66779 0.833894 0.551924i \(-0.186106\pi\)
0.833894 + 0.551924i \(0.186106\pi\)
\(194\) −13.2426 −0.950762
\(195\) −1.69026 −0.121042
\(196\) −10.9643 −0.783162
\(197\) −19.0246 −1.35545 −0.677724 0.735316i \(-0.737034\pi\)
−0.677724 + 0.735316i \(0.737034\pi\)
\(198\) 5.25050 0.373137
\(199\) −12.5654 −0.890735 −0.445368 0.895348i \(-0.646927\pi\)
−0.445368 + 0.895348i \(0.646927\pi\)
\(200\) 14.2786 1.00965
\(201\) 1.33601 0.0942350
\(202\) 12.3430 0.868448
\(203\) −4.75995 −0.334083
\(204\) −1.12083 −0.0784738
\(205\) 4.33846 0.303011
\(206\) 9.27673 0.646340
\(207\) 7.46088 0.518567
\(208\) −2.44508 −0.169536
\(209\) 11.2904 0.780976
\(210\) −1.33320 −0.0919994
\(211\) −6.71501 −0.462280 −0.231140 0.972920i \(-0.574246\pi\)
−0.231140 + 0.972920i \(0.574246\pi\)
\(212\) 14.0012 0.961610
\(213\) −5.13907 −0.352123
\(214\) −16.4204 −1.12248
\(215\) −1.06594 −0.0726967
\(216\) 2.92622 0.199104
\(217\) −31.7654 −2.15638
\(218\) 14.7055 0.995982
\(219\) −8.49373 −0.573953
\(220\) −2.17840 −0.146868
\(221\) −4.86991 −0.327586
\(222\) −4.81021 −0.322840
\(223\) −9.14970 −0.612709 −0.306355 0.951917i \(-0.599109\pi\)
−0.306355 + 0.951917i \(0.599109\pi\)
\(224\) 22.0466 1.47305
\(225\) −4.87953 −0.325302
\(226\) 8.94794 0.595208
\(227\) −4.22399 −0.280356 −0.140178 0.990126i \(-0.544768\pi\)
−0.140178 + 0.990126i \(0.544768\pi\)
\(228\) 2.25988 0.149665
\(229\) −2.37348 −0.156844 −0.0784219 0.996920i \(-0.524988\pi\)
−0.0784219 + 0.996920i \(0.524988\pi\)
\(230\) 2.42806 0.160101
\(231\) −22.9398 −1.50933
\(232\) 3.40003 0.223223
\(233\) 10.7498 0.704240 0.352120 0.935955i \(-0.385461\pi\)
0.352120 + 0.935955i \(0.385461\pi\)
\(234\) 4.56623 0.298504
\(235\) −3.30673 −0.215707
\(236\) −4.64834 −0.302581
\(237\) −1.00000 −0.0649570
\(238\) −3.84115 −0.248985
\(239\) −27.1869 −1.75858 −0.879288 0.476290i \(-0.841981\pi\)
−0.879288 + 0.476290i \(0.841981\pi\)
\(240\) 0.174263 0.0112486
\(241\) 15.8635 1.02186 0.510928 0.859623i \(-0.329302\pi\)
0.510928 + 0.859623i \(0.329302\pi\)
\(242\) 19.0872 1.22697
\(243\) −1.00000 −0.0641500
\(244\) 4.82046 0.308598
\(245\) 3.39526 0.216915
\(246\) −11.7203 −0.747260
\(247\) 9.81901 0.624769
\(248\) 22.6901 1.44082
\(249\) 11.4290 0.724284
\(250\) −3.21518 −0.203346
\(251\) −1.56038 −0.0984902 −0.0492451 0.998787i \(-0.515682\pi\)
−0.0492451 + 0.998787i \(0.515682\pi\)
\(252\) −4.59161 −0.289244
\(253\) 41.7787 2.62660
\(254\) −2.08019 −0.130523
\(255\) 0.347083 0.0217352
\(256\) −16.8734 −1.05459
\(257\) 12.8005 0.798476 0.399238 0.916847i \(-0.369275\pi\)
0.399238 + 0.916847i \(0.369275\pi\)
\(258\) 2.87963 0.179278
\(259\) 21.0161 1.30588
\(260\) −1.89450 −0.117492
\(261\) −1.16192 −0.0719211
\(262\) 9.89204 0.611132
\(263\) −17.2751 −1.06523 −0.532614 0.846358i \(-0.678790\pi\)
−0.532614 + 0.846358i \(0.678790\pi\)
\(264\) 16.3859 1.00848
\(265\) −4.33570 −0.266340
\(266\) 7.74476 0.474862
\(267\) 12.2948 0.752431
\(268\) 1.49744 0.0914708
\(269\) 13.5428 0.825722 0.412861 0.910794i \(-0.364530\pi\)
0.412861 + 0.910794i \(0.364530\pi\)
\(270\) −0.325439 −0.0198056
\(271\) −5.09831 −0.309700 −0.154850 0.987938i \(-0.549489\pi\)
−0.154850 + 0.987938i \(0.549489\pi\)
\(272\) 0.502078 0.0304429
\(273\) −19.9502 −1.20744
\(274\) −13.0629 −0.789159
\(275\) −27.3239 −1.64769
\(276\) 8.36238 0.503356
\(277\) 6.00075 0.360550 0.180275 0.983616i \(-0.442301\pi\)
0.180275 + 0.983616i \(0.442301\pi\)
\(278\) 10.5432 0.632337
\(279\) −7.75406 −0.464224
\(280\) −4.16068 −0.248648
\(281\) 7.17807 0.428208 0.214104 0.976811i \(-0.431317\pi\)
0.214104 + 0.976811i \(0.431317\pi\)
\(282\) 8.93310 0.531958
\(283\) 20.0080 1.18935 0.594675 0.803966i \(-0.297281\pi\)
0.594675 + 0.803966i \(0.297281\pi\)
\(284\) −5.76002 −0.341794
\(285\) −0.699808 −0.0414531
\(286\) 25.5695 1.51196
\(287\) 51.2069 3.02265
\(288\) 5.38166 0.317118
\(289\) 1.00000 0.0588235
\(290\) −0.378134 −0.0222048
\(291\) 14.1233 0.827923
\(292\) −9.52003 −0.557118
\(293\) −28.3559 −1.65657 −0.828285 0.560308i \(-0.810683\pi\)
−0.828285 + 0.560308i \(0.810683\pi\)
\(294\) −9.17225 −0.534937
\(295\) 1.43943 0.0838068
\(296\) −15.0118 −0.872545
\(297\) −5.59970 −0.324927
\(298\) −18.5460 −1.07434
\(299\) 36.3338 2.10124
\(300\) −5.46913 −0.315760
\(301\) −12.5813 −0.725176
\(302\) −0.231747 −0.0133355
\(303\) −13.1639 −0.756244
\(304\) −1.01232 −0.0580605
\(305\) −1.49273 −0.0854734
\(306\) −0.937640 −0.0536013
\(307\) −23.4856 −1.34039 −0.670196 0.742184i \(-0.733790\pi\)
−0.670196 + 0.742184i \(0.733790\pi\)
\(308\) −25.7117 −1.46506
\(309\) −9.89370 −0.562833
\(310\) −2.52347 −0.143324
\(311\) −9.82176 −0.556941 −0.278470 0.960445i \(-0.589827\pi\)
−0.278470 + 0.960445i \(0.589827\pi\)
\(312\) 14.2504 0.806771
\(313\) 11.7000 0.661323 0.330662 0.943749i \(-0.392728\pi\)
0.330662 + 0.943749i \(0.392728\pi\)
\(314\) 8.48209 0.478672
\(315\) 1.42186 0.0801130
\(316\) −1.12083 −0.0630516
\(317\) −20.3892 −1.14517 −0.572586 0.819845i \(-0.694060\pi\)
−0.572586 + 0.819845i \(0.694060\pi\)
\(318\) 11.7129 0.656825
\(319\) −6.50641 −0.364289
\(320\) 2.09993 0.117389
\(321\) 17.5125 0.977453
\(322\) 28.6584 1.59707
\(323\) −2.01626 −0.112188
\(324\) −1.12083 −0.0622684
\(325\) −23.7629 −1.31813
\(326\) 18.6381 1.03227
\(327\) −15.6835 −0.867300
\(328\) −36.5771 −2.01963
\(329\) −39.0293 −2.15176
\(330\) −1.82236 −0.100318
\(331\) −15.2254 −0.836863 −0.418431 0.908248i \(-0.637420\pi\)
−0.418431 + 0.908248i \(0.637420\pi\)
\(332\) 12.8100 0.703039
\(333\) 5.13012 0.281129
\(334\) 21.7895 1.19227
\(335\) −0.463706 −0.0253350
\(336\) 2.05682 0.112209
\(337\) 13.5123 0.736062 0.368031 0.929814i \(-0.380032\pi\)
0.368031 + 0.929814i \(0.380032\pi\)
\(338\) 10.0478 0.546529
\(339\) −9.54304 −0.518307
\(340\) 0.389021 0.0210976
\(341\) −43.4204 −2.35135
\(342\) 1.89053 0.102228
\(343\) 11.3979 0.615429
\(344\) 8.98685 0.484539
\(345\) −2.58954 −0.139416
\(346\) 22.1572 1.19118
\(347\) −3.83122 −0.205671 −0.102835 0.994698i \(-0.532791\pi\)
−0.102835 + 0.994698i \(0.532791\pi\)
\(348\) −1.30232 −0.0698115
\(349\) 30.8043 1.64891 0.824457 0.565924i \(-0.191481\pi\)
0.824457 + 0.565924i \(0.191481\pi\)
\(350\) −18.7430 −1.00186
\(351\) −4.86991 −0.259937
\(352\) 30.1357 1.60624
\(353\) −17.2001 −0.915471 −0.457735 0.889088i \(-0.651339\pi\)
−0.457735 + 0.889088i \(0.651339\pi\)
\(354\) −3.88861 −0.206677
\(355\) 1.78368 0.0946679
\(356\) 13.7804 0.730360
\(357\) 4.09662 0.216816
\(358\) −5.28628 −0.279389
\(359\) −22.4491 −1.18482 −0.592410 0.805637i \(-0.701823\pi\)
−0.592410 + 0.805637i \(0.701823\pi\)
\(360\) −1.01564 −0.0535289
\(361\) −14.9347 −0.786037
\(362\) −13.2575 −0.696798
\(363\) −20.3566 −1.06845
\(364\) −22.3608 −1.17202
\(365\) 2.94802 0.154307
\(366\) 4.03260 0.210787
\(367\) −25.8969 −1.35181 −0.675903 0.736990i \(-0.736246\pi\)
−0.675903 + 0.736990i \(0.736246\pi\)
\(368\) −3.74594 −0.195271
\(369\) 12.4998 0.650714
\(370\) 1.66954 0.0867952
\(371\) −51.1743 −2.65684
\(372\) −8.69099 −0.450607
\(373\) 15.4291 0.798890 0.399445 0.916757i \(-0.369203\pi\)
0.399445 + 0.916757i \(0.369203\pi\)
\(374\) −5.25050 −0.271497
\(375\) 3.42901 0.177074
\(376\) 27.8787 1.43773
\(377\) −5.65845 −0.291425
\(378\) −3.84115 −0.197568
\(379\) −2.04604 −0.105098 −0.0525489 0.998618i \(-0.516735\pi\)
−0.0525489 + 0.998618i \(0.516735\pi\)
\(380\) −0.784367 −0.0402372
\(381\) 2.21854 0.113659
\(382\) 13.5241 0.691952
\(383\) −0.154093 −0.00787380 −0.00393690 0.999992i \(-0.501253\pi\)
−0.00393690 + 0.999992i \(0.501253\pi\)
\(384\) 5.09040 0.259768
\(385\) 7.96201 0.405782
\(386\) 21.7248 1.10576
\(387\) −3.07115 −0.156115
\(388\) 15.8298 0.803638
\(389\) 18.0285 0.914083 0.457041 0.889445i \(-0.348909\pi\)
0.457041 + 0.889445i \(0.348909\pi\)
\(390\) −1.58486 −0.0802524
\(391\) −7.46088 −0.377313
\(392\) −28.6250 −1.44578
\(393\) −10.5499 −0.532174
\(394\) −17.8383 −0.898678
\(395\) 0.347083 0.0174636
\(396\) −6.27631 −0.315397
\(397\) −5.83195 −0.292697 −0.146348 0.989233i \(-0.546752\pi\)
−0.146348 + 0.989233i \(0.546752\pi\)
\(398\) −11.7818 −0.590568
\(399\) −8.25984 −0.413509
\(400\) 2.44991 0.122495
\(401\) −4.36405 −0.217930 −0.108965 0.994046i \(-0.534754\pi\)
−0.108965 + 0.994046i \(0.534754\pi\)
\(402\) 1.25270 0.0624789
\(403\) −37.7616 −1.88104
\(404\) −14.7545 −0.734061
\(405\) 0.347083 0.0172467
\(406\) −4.46312 −0.221501
\(407\) 28.7271 1.42395
\(408\) −2.92622 −0.144869
\(409\) −19.4906 −0.963747 −0.481873 0.876241i \(-0.660043\pi\)
−0.481873 + 0.876241i \(0.660043\pi\)
\(410\) 4.06792 0.200900
\(411\) 13.9317 0.687199
\(412\) −11.0892 −0.546324
\(413\) 16.9896 0.836003
\(414\) 6.99562 0.343816
\(415\) −3.96681 −0.194723
\(416\) 26.2082 1.28496
\(417\) −11.2444 −0.550639
\(418\) 10.5864 0.517797
\(419\) 12.9774 0.633987 0.316993 0.948428i \(-0.397327\pi\)
0.316993 + 0.948428i \(0.397327\pi\)
\(420\) 1.59367 0.0777631
\(421\) 22.8680 1.11452 0.557258 0.830339i \(-0.311853\pi\)
0.557258 + 0.830339i \(0.311853\pi\)
\(422\) −6.29626 −0.306497
\(423\) −9.52721 −0.463229
\(424\) 36.5539 1.77521
\(425\) 4.87953 0.236692
\(426\) −4.81860 −0.233462
\(427\) −17.6187 −0.852628
\(428\) 19.6286 0.948782
\(429\) −27.2700 −1.31661
\(430\) −0.999471 −0.0481988
\(431\) −4.19097 −0.201872 −0.100936 0.994893i \(-0.532184\pi\)
−0.100936 + 0.994893i \(0.532184\pi\)
\(432\) 0.502078 0.0241562
\(433\) −26.4514 −1.27117 −0.635586 0.772030i \(-0.719242\pi\)
−0.635586 + 0.772030i \(0.719242\pi\)
\(434\) −29.7845 −1.42970
\(435\) 0.403283 0.0193359
\(436\) −17.5786 −0.841860
\(437\) 15.0431 0.719608
\(438\) −7.96406 −0.380538
\(439\) 12.3154 0.587784 0.293892 0.955839i \(-0.405049\pi\)
0.293892 + 0.955839i \(0.405049\pi\)
\(440\) −5.68727 −0.271130
\(441\) 9.78227 0.465822
\(442\) −4.56623 −0.217193
\(443\) 18.7289 0.889837 0.444918 0.895571i \(-0.353233\pi\)
0.444918 + 0.895571i \(0.353233\pi\)
\(444\) 5.74999 0.272883
\(445\) −4.26732 −0.202290
\(446\) −8.57913 −0.406233
\(447\) 19.7794 0.935534
\(448\) 24.7854 1.17100
\(449\) 11.6254 0.548636 0.274318 0.961639i \(-0.411548\pi\)
0.274318 + 0.961639i \(0.411548\pi\)
\(450\) −4.57525 −0.215679
\(451\) 69.9951 3.29594
\(452\) −10.6961 −0.503104
\(453\) 0.247160 0.0116126
\(454\) −3.96059 −0.185880
\(455\) 6.92436 0.324619
\(456\) 5.90001 0.276293
\(457\) 17.8919 0.836945 0.418473 0.908229i \(-0.362566\pi\)
0.418473 + 0.908229i \(0.362566\pi\)
\(458\) −2.22547 −0.103989
\(459\) 1.00000 0.0466760
\(460\) −2.90244 −0.135327
\(461\) −30.5920 −1.42481 −0.712405 0.701769i \(-0.752394\pi\)
−0.712405 + 0.701769i \(0.752394\pi\)
\(462\) −21.5093 −1.00070
\(463\) 32.2386 1.49825 0.749126 0.662427i \(-0.230474\pi\)
0.749126 + 0.662427i \(0.230474\pi\)
\(464\) 0.583375 0.0270825
\(465\) 2.69130 0.124806
\(466\) 10.0794 0.466920
\(467\) 15.9870 0.739791 0.369896 0.929073i \(-0.379393\pi\)
0.369896 + 0.929073i \(0.379393\pi\)
\(468\) −5.45835 −0.252312
\(469\) −5.47313 −0.252726
\(470\) −3.10052 −0.143016
\(471\) −9.04620 −0.416827
\(472\) −12.1357 −0.558590
\(473\) −17.1975 −0.790743
\(474\) −0.937640 −0.0430672
\(475\) −9.83841 −0.451417
\(476\) 4.59161 0.210456
\(477\) −12.4919 −0.571963
\(478\) −25.4916 −1.16596
\(479\) 13.0677 0.597079 0.298540 0.954397i \(-0.403501\pi\)
0.298540 + 0.954397i \(0.403501\pi\)
\(480\) −1.86788 −0.0852568
\(481\) 24.9832 1.13914
\(482\) 14.8742 0.677503
\(483\) −30.5644 −1.39073
\(484\) −22.8163 −1.03711
\(485\) −4.90195 −0.222586
\(486\) −0.937640 −0.0425322
\(487\) −22.1941 −1.00571 −0.502854 0.864371i \(-0.667717\pi\)
−0.502854 + 0.864371i \(0.667717\pi\)
\(488\) 12.5850 0.569698
\(489\) −19.8776 −0.898898
\(490\) 3.18353 0.143817
\(491\) −10.0490 −0.453503 −0.226752 0.973953i \(-0.572811\pi\)
−0.226752 + 0.973953i \(0.572811\pi\)
\(492\) 14.0102 0.631627
\(493\) 1.16192 0.0523303
\(494\) 9.20670 0.414229
\(495\) 1.94356 0.0873564
\(496\) 3.89314 0.174807
\(497\) 21.0528 0.944346
\(498\) 10.7163 0.480209
\(499\) −17.5225 −0.784414 −0.392207 0.919877i \(-0.628288\pi\)
−0.392207 + 0.919877i \(0.628288\pi\)
\(500\) 3.84334 0.171880
\(501\) −23.2387 −1.03823
\(502\) −1.46307 −0.0653002
\(503\) 2.04147 0.0910247 0.0455123 0.998964i \(-0.485508\pi\)
0.0455123 + 0.998964i \(0.485508\pi\)
\(504\) −11.9876 −0.533970
\(505\) 4.56895 0.203315
\(506\) 39.1734 1.74147
\(507\) −10.7161 −0.475917
\(508\) 2.48661 0.110325
\(509\) −39.9557 −1.77101 −0.885504 0.464633i \(-0.846186\pi\)
−0.885504 + 0.464633i \(0.846186\pi\)
\(510\) 0.325439 0.0144107
\(511\) 34.7955 1.53926
\(512\) −5.64039 −0.249273
\(513\) −2.01626 −0.0890200
\(514\) 12.0023 0.529399
\(515\) 3.43393 0.151317
\(516\) −3.44224 −0.151536
\(517\) −53.3495 −2.34631
\(518\) 19.7056 0.865813
\(519\) −23.6309 −1.03728
\(520\) −4.94607 −0.216900
\(521\) 10.3033 0.451397 0.225699 0.974197i \(-0.427534\pi\)
0.225699 + 0.974197i \(0.427534\pi\)
\(522\) −1.08946 −0.0476845
\(523\) 6.43225 0.281263 0.140631 0.990062i \(-0.455087\pi\)
0.140631 + 0.990062i \(0.455087\pi\)
\(524\) −11.8247 −0.516564
\(525\) 19.9896 0.872417
\(526\) −16.1978 −0.706259
\(527\) 7.75406 0.337772
\(528\) 2.81149 0.122354
\(529\) 32.6647 1.42021
\(530\) −4.06533 −0.176587
\(531\) 4.14723 0.179974
\(532\) −9.25788 −0.401380
\(533\) 60.8730 2.63670
\(534\) 11.5281 0.498871
\(535\) −6.07829 −0.262787
\(536\) 3.90946 0.168863
\(537\) 5.63786 0.243291
\(538\) 12.6983 0.547463
\(539\) 54.7778 2.35945
\(540\) 0.389021 0.0167408
\(541\) 23.1879 0.996927 0.498463 0.866911i \(-0.333898\pi\)
0.498463 + 0.866911i \(0.333898\pi\)
\(542\) −4.78038 −0.205335
\(543\) 14.1392 0.606771
\(544\) −5.38166 −0.230737
\(545\) 5.44347 0.233173
\(546\) −18.7061 −0.800547
\(547\) −11.2899 −0.482721 −0.241361 0.970435i \(-0.577594\pi\)
−0.241361 + 0.970435i \(0.577594\pi\)
\(548\) 15.6151 0.667042
\(549\) −4.30079 −0.183553
\(550\) −25.6200 −1.09244
\(551\) −2.34273 −0.0998038
\(552\) 21.8322 0.929238
\(553\) 4.09662 0.174206
\(554\) 5.62654 0.239049
\(555\) −1.78057 −0.0755812
\(556\) −12.6030 −0.534487
\(557\) −24.3062 −1.02989 −0.514943 0.857224i \(-0.672187\pi\)
−0.514943 + 0.857224i \(0.672187\pi\)
\(558\) −7.27052 −0.307786
\(559\) −14.9562 −0.632581
\(560\) −0.713887 −0.0301672
\(561\) 5.59970 0.236419
\(562\) 6.73045 0.283907
\(563\) 36.5673 1.54113 0.770563 0.637364i \(-0.219975\pi\)
0.770563 + 0.637364i \(0.219975\pi\)
\(564\) −10.6784 −0.449641
\(565\) 3.31222 0.139346
\(566\) 18.7603 0.788553
\(567\) 4.09662 0.172042
\(568\) −15.0380 −0.630981
\(569\) −17.3740 −0.728354 −0.364177 0.931330i \(-0.618650\pi\)
−0.364177 + 0.931330i \(0.618650\pi\)
\(570\) −0.656169 −0.0274839
\(571\) 18.8824 0.790204 0.395102 0.918637i \(-0.370709\pi\)
0.395102 + 0.918637i \(0.370709\pi\)
\(572\) −30.5651 −1.27799
\(573\) −14.4235 −0.602551
\(574\) 48.0137 2.00405
\(575\) −36.4056 −1.51822
\(576\) 6.05022 0.252093
\(577\) 8.23163 0.342687 0.171344 0.985211i \(-0.445189\pi\)
0.171344 + 0.985211i \(0.445189\pi\)
\(578\) 0.937640 0.0390007
\(579\) −23.1697 −0.962898
\(580\) 0.452011 0.0187687
\(581\) −46.8203 −1.94243
\(582\) 13.2426 0.548923
\(583\) −69.9506 −2.89706
\(584\) −24.8545 −1.02849
\(585\) 1.69026 0.0698837
\(586\) −26.5876 −1.09832
\(587\) 6.53172 0.269593 0.134796 0.990873i \(-0.456962\pi\)
0.134796 + 0.990873i \(0.456962\pi\)
\(588\) 10.9643 0.452159
\(589\) −15.6342 −0.644196
\(590\) 1.34967 0.0555649
\(591\) 19.0246 0.782568
\(592\) −2.57572 −0.105861
\(593\) −11.1777 −0.459013 −0.229506 0.973307i \(-0.573711\pi\)
−0.229506 + 0.973307i \(0.573711\pi\)
\(594\) −5.25050 −0.215431
\(595\) −1.42186 −0.0582908
\(596\) 22.1694 0.908092
\(597\) 12.5654 0.514266
\(598\) 34.0681 1.39315
\(599\) 14.5485 0.594435 0.297217 0.954810i \(-0.403941\pi\)
0.297217 + 0.954810i \(0.403941\pi\)
\(600\) −14.2786 −0.582920
\(601\) −14.4650 −0.590040 −0.295020 0.955491i \(-0.595326\pi\)
−0.295020 + 0.955491i \(0.595326\pi\)
\(602\) −11.7968 −0.480800
\(603\) −1.33601 −0.0544066
\(604\) 0.277024 0.0112720
\(605\) 7.06543 0.287251
\(606\) −12.3430 −0.501399
\(607\) 10.7009 0.434336 0.217168 0.976134i \(-0.430318\pi\)
0.217168 + 0.976134i \(0.430318\pi\)
\(608\) 10.8508 0.440059
\(609\) 4.75995 0.192883
\(610\) −1.39964 −0.0566699
\(611\) −46.3967 −1.87701
\(612\) 1.12083 0.0453069
\(613\) −20.8403 −0.841731 −0.420865 0.907123i \(-0.638273\pi\)
−0.420865 + 0.907123i \(0.638273\pi\)
\(614\) −22.0210 −0.888695
\(615\) −4.33846 −0.174944
\(616\) −67.1269 −2.70462
\(617\) −17.3444 −0.698260 −0.349130 0.937074i \(-0.613523\pi\)
−0.349130 + 0.937074i \(0.613523\pi\)
\(618\) −9.27673 −0.373165
\(619\) 3.24893 0.130585 0.0652927 0.997866i \(-0.479202\pi\)
0.0652927 + 0.997866i \(0.479202\pi\)
\(620\) 3.01649 0.121145
\(621\) −7.46088 −0.299395
\(622\) −9.20928 −0.369258
\(623\) −50.3672 −2.01792
\(624\) 2.44508 0.0978814
\(625\) 23.2075 0.928301
\(626\) 10.9704 0.438465
\(627\) −11.2904 −0.450897
\(628\) −10.1393 −0.404601
\(629\) −5.13012 −0.204551
\(630\) 1.33320 0.0531159
\(631\) 33.4493 1.33159 0.665797 0.746133i \(-0.268092\pi\)
0.665797 + 0.746133i \(0.268092\pi\)
\(632\) −2.92622 −0.116399
\(633\) 6.71501 0.266898
\(634\) −19.1177 −0.759263
\(635\) −0.770016 −0.0305571
\(636\) −14.0012 −0.555186
\(637\) 47.6388 1.88752
\(638\) −6.10067 −0.241528
\(639\) 5.13907 0.203298
\(640\) −1.76679 −0.0698384
\(641\) −17.3263 −0.684348 −0.342174 0.939637i \(-0.611163\pi\)
−0.342174 + 0.939637i \(0.611163\pi\)
\(642\) 16.4204 0.648063
\(643\) 12.7906 0.504414 0.252207 0.967673i \(-0.418844\pi\)
0.252207 + 0.967673i \(0.418844\pi\)
\(644\) −34.2575 −1.34993
\(645\) 1.06594 0.0419715
\(646\) −1.89053 −0.0743818
\(647\) −20.2770 −0.797170 −0.398585 0.917131i \(-0.630499\pi\)
−0.398585 + 0.917131i \(0.630499\pi\)
\(648\) −2.92622 −0.114953
\(649\) 23.2232 0.911591
\(650\) −22.2811 −0.873935
\(651\) 31.7654 1.24499
\(652\) −22.2795 −0.872531
\(653\) −7.45780 −0.291846 −0.145923 0.989296i \(-0.546615\pi\)
−0.145923 + 0.989296i \(0.546615\pi\)
\(654\) −14.7055 −0.575030
\(655\) 3.66170 0.143074
\(656\) −6.27588 −0.245032
\(657\) 8.49373 0.331372
\(658\) −36.5955 −1.42664
\(659\) −13.1328 −0.511583 −0.255791 0.966732i \(-0.582336\pi\)
−0.255791 + 0.966732i \(0.582336\pi\)
\(660\) 2.17840 0.0847941
\(661\) −17.9357 −0.697616 −0.348808 0.937194i \(-0.613413\pi\)
−0.348808 + 0.937194i \(0.613413\pi\)
\(662\) −14.2759 −0.554850
\(663\) 4.86991 0.189132
\(664\) 33.4438 1.29787
\(665\) 2.86685 0.111172
\(666\) 4.81021 0.186392
\(667\) −8.66895 −0.335663
\(668\) −26.0466 −1.00778
\(669\) 9.14970 0.353748
\(670\) −0.434790 −0.0167974
\(671\) −24.0831 −0.929719
\(672\) −22.0466 −0.850467
\(673\) −7.09535 −0.273506 −0.136753 0.990605i \(-0.543667\pi\)
−0.136753 + 0.990605i \(0.543667\pi\)
\(674\) 12.6697 0.488018
\(675\) 4.87953 0.187813
\(676\) −12.0109 −0.461957
\(677\) 36.6573 1.40885 0.704426 0.709777i \(-0.251204\pi\)
0.704426 + 0.709777i \(0.251204\pi\)
\(678\) −8.94794 −0.343644
\(679\) −57.8578 −2.22038
\(680\) 1.01564 0.0389480
\(681\) 4.22399 0.161864
\(682\) −40.7127 −1.55897
\(683\) −8.43662 −0.322818 −0.161409 0.986888i \(-0.551604\pi\)
−0.161409 + 0.986888i \(0.551604\pi\)
\(684\) −2.25988 −0.0864089
\(685\) −4.83544 −0.184753
\(686\) 10.6871 0.408037
\(687\) 2.37348 0.0905538
\(688\) 1.54196 0.0587866
\(689\) −60.8342 −2.31760
\(690\) −2.42806 −0.0924346
\(691\) 12.5285 0.476606 0.238303 0.971191i \(-0.423409\pi\)
0.238303 + 0.971191i \(0.423409\pi\)
\(692\) −26.4862 −1.00685
\(693\) 22.9398 0.871412
\(694\) −3.59231 −0.136362
\(695\) 3.90272 0.148039
\(696\) −3.40003 −0.128878
\(697\) −12.4998 −0.473464
\(698\) 28.8833 1.09325
\(699\) −10.7498 −0.406593
\(700\) 22.4049 0.846827
\(701\) −31.0482 −1.17268 −0.586338 0.810066i \(-0.699431\pi\)
−0.586338 + 0.810066i \(0.699431\pi\)
\(702\) −4.56623 −0.172341
\(703\) 10.3436 0.390118
\(704\) 33.8794 1.27688
\(705\) 3.30673 0.124539
\(706\) −16.1275 −0.606968
\(707\) 53.9273 2.02814
\(708\) 4.64834 0.174695
\(709\) −45.1159 −1.69436 −0.847182 0.531303i \(-0.821702\pi\)
−0.847182 + 0.531303i \(0.821702\pi\)
\(710\) 1.67245 0.0627659
\(711\) 1.00000 0.0375029
\(712\) 35.9773 1.34831
\(713\) −57.8521 −2.16658
\(714\) 3.84115 0.143752
\(715\) 9.46496 0.353969
\(716\) 6.31908 0.236155
\(717\) 27.1869 1.01531
\(718\) −21.0492 −0.785550
\(719\) −30.1870 −1.12578 −0.562892 0.826530i \(-0.690311\pi\)
−0.562892 + 0.826530i \(0.690311\pi\)
\(720\) −0.174263 −0.00649438
\(721\) 40.5307 1.50944
\(722\) −14.0034 −0.521152
\(723\) −15.8635 −0.589969
\(724\) 15.8476 0.588973
\(725\) 5.66963 0.210565
\(726\) −19.0872 −0.708392
\(727\) 39.6179 1.46934 0.734672 0.678422i \(-0.237336\pi\)
0.734672 + 0.678422i \(0.237336\pi\)
\(728\) −58.3785 −2.16365
\(729\) 1.00000 0.0370370
\(730\) 2.76419 0.102307
\(731\) 3.07115 0.113591
\(732\) −4.82046 −0.178169
\(733\) −0.841789 −0.0310922 −0.0155461 0.999879i \(-0.504949\pi\)
−0.0155461 + 0.999879i \(0.504949\pi\)
\(734\) −24.2820 −0.896264
\(735\) −3.39526 −0.125236
\(736\) 40.1520 1.48002
\(737\) −7.48126 −0.275576
\(738\) 11.7203 0.431431
\(739\) 42.6030 1.56718 0.783589 0.621280i \(-0.213387\pi\)
0.783589 + 0.621280i \(0.213387\pi\)
\(740\) −1.99572 −0.0733642
\(741\) −9.81901 −0.360710
\(742\) −47.9831 −1.76152
\(743\) 12.7733 0.468609 0.234304 0.972163i \(-0.424719\pi\)
0.234304 + 0.972163i \(0.424719\pi\)
\(744\) −22.6901 −0.831858
\(745\) −6.86509 −0.251517
\(746\) 14.4670 0.529673
\(747\) −11.4290 −0.418166
\(748\) 6.27631 0.229485
\(749\) −71.7420 −2.62140
\(750\) 3.21518 0.117402
\(751\) 26.1462 0.954090 0.477045 0.878879i \(-0.341708\pi\)
0.477045 + 0.878879i \(0.341708\pi\)
\(752\) 4.78340 0.174433
\(753\) 1.56038 0.0568634
\(754\) −5.30560 −0.193218
\(755\) −0.0857849 −0.00312203
\(756\) 4.59161 0.166995
\(757\) −22.6111 −0.821816 −0.410908 0.911677i \(-0.634788\pi\)
−0.410908 + 0.911677i \(0.634788\pi\)
\(758\) −1.91845 −0.0696811
\(759\) −41.7787 −1.51647
\(760\) −2.04779 −0.0742812
\(761\) −41.3831 −1.50013 −0.750067 0.661362i \(-0.769979\pi\)
−0.750067 + 0.661362i \(0.769979\pi\)
\(762\) 2.08019 0.0753574
\(763\) 64.2493 2.32598
\(764\) −16.1663 −0.584877
\(765\) −0.347083 −0.0125488
\(766\) −0.144484 −0.00522043
\(767\) 20.1966 0.729258
\(768\) 16.8734 0.608867
\(769\) −16.6357 −0.599898 −0.299949 0.953955i \(-0.596970\pi\)
−0.299949 + 0.953955i \(0.596970\pi\)
\(770\) 7.46550 0.269038
\(771\) −12.8005 −0.461000
\(772\) −25.9693 −0.934654
\(773\) 23.6869 0.851959 0.425980 0.904733i \(-0.359930\pi\)
0.425980 + 0.904733i \(0.359930\pi\)
\(774\) −2.87963 −0.103506
\(775\) 37.8362 1.35912
\(776\) 41.3278 1.48358
\(777\) −21.0161 −0.753950
\(778\) 16.9043 0.606048
\(779\) 25.2028 0.902986
\(780\) 1.89450 0.0678339
\(781\) 28.7772 1.02973
\(782\) −6.99562 −0.250163
\(783\) 1.16192 0.0415237
\(784\) −4.91146 −0.175409
\(785\) 3.13978 0.112064
\(786\) −9.89204 −0.352837
\(787\) −45.5145 −1.62242 −0.811208 0.584758i \(-0.801190\pi\)
−0.811208 + 0.584758i \(0.801190\pi\)
\(788\) 21.3234 0.759614
\(789\) 17.2751 0.615009
\(790\) 0.325439 0.0115786
\(791\) 39.0942 1.39003
\(792\) −16.3859 −0.582249
\(793\) −20.9445 −0.743760
\(794\) −5.46827 −0.194062
\(795\) 4.33570 0.153772
\(796\) 14.0836 0.499182
\(797\) −28.6934 −1.01637 −0.508186 0.861247i \(-0.669684\pi\)
−0.508186 + 0.861247i \(0.669684\pi\)
\(798\) −7.74476 −0.274162
\(799\) 9.52721 0.337049
\(800\) −26.2600 −0.928432
\(801\) −12.2948 −0.434416
\(802\) −4.09191 −0.144490
\(803\) 47.5623 1.67844
\(804\) −1.49744 −0.0528107
\(805\) 10.6084 0.373896
\(806\) −35.4068 −1.24715
\(807\) −13.5428 −0.476731
\(808\) −38.5203 −1.35514
\(809\) −16.1541 −0.567947 −0.283973 0.958832i \(-0.591653\pi\)
−0.283973 + 0.958832i \(0.591653\pi\)
\(810\) 0.325439 0.0114347
\(811\) −21.7220 −0.762763 −0.381381 0.924418i \(-0.624552\pi\)
−0.381381 + 0.924418i \(0.624552\pi\)
\(812\) 5.33509 0.187225
\(813\) 5.09831 0.178805
\(814\) 26.9357 0.944096
\(815\) 6.89918 0.241668
\(816\) −0.502078 −0.0175762
\(817\) −6.19224 −0.216639
\(818\) −18.2751 −0.638975
\(819\) 19.9502 0.697115
\(820\) −4.86268 −0.169812
\(821\) 3.79658 0.132502 0.0662508 0.997803i \(-0.478896\pi\)
0.0662508 + 0.997803i \(0.478896\pi\)
\(822\) 13.0629 0.455621
\(823\) 15.3534 0.535185 0.267592 0.963532i \(-0.413772\pi\)
0.267592 + 0.963532i \(0.413772\pi\)
\(824\) −28.9511 −1.00856
\(825\) 27.3239 0.951297
\(826\) 15.9301 0.554280
\(827\) −7.28594 −0.253357 −0.126679 0.991944i \(-0.540432\pi\)
−0.126679 + 0.991944i \(0.540432\pi\)
\(828\) −8.36238 −0.290613
\(829\) 37.4118 1.29937 0.649683 0.760205i \(-0.274902\pi\)
0.649683 + 0.760205i \(0.274902\pi\)
\(830\) −3.71944 −0.129104
\(831\) −6.00075 −0.208164
\(832\) 29.4641 1.02148
\(833\) −9.78227 −0.338936
\(834\) −10.5432 −0.365080
\(835\) 8.06575 0.279127
\(836\) −12.6547 −0.437671
\(837\) 7.75406 0.268020
\(838\) 12.1681 0.420341
\(839\) 7.15124 0.246888 0.123444 0.992352i \(-0.460606\pi\)
0.123444 + 0.992352i \(0.460606\pi\)
\(840\) 4.16068 0.143557
\(841\) −27.6499 −0.953446
\(842\) 21.4419 0.738938
\(843\) −7.17807 −0.247226
\(844\) 7.52638 0.259069
\(845\) 3.71936 0.127950
\(846\) −8.93310 −0.307126
\(847\) 83.3933 2.86543
\(848\) 6.27188 0.215377
\(849\) −20.0080 −0.686671
\(850\) 4.57525 0.156930
\(851\) 38.2752 1.31206
\(852\) 5.76002 0.197335
\(853\) −17.0402 −0.583444 −0.291722 0.956503i \(-0.594228\pi\)
−0.291722 + 0.956503i \(0.594228\pi\)
\(854\) −16.5200 −0.565303
\(855\) 0.699808 0.0239329
\(856\) 51.2454 1.75153
\(857\) −31.6694 −1.08181 −0.540904 0.841085i \(-0.681918\pi\)
−0.540904 + 0.841085i \(0.681918\pi\)
\(858\) −25.5695 −0.872928
\(859\) 11.0215 0.376050 0.188025 0.982164i \(-0.439791\pi\)
0.188025 + 0.982164i \(0.439791\pi\)
\(860\) 1.19474 0.0407403
\(861\) −51.2069 −1.74513
\(862\) −3.92962 −0.133844
\(863\) 10.8817 0.370416 0.185208 0.982699i \(-0.440704\pi\)
0.185208 + 0.982699i \(0.440704\pi\)
\(864\) −5.38166 −0.183088
\(865\) 8.20186 0.278871
\(866\) −24.8019 −0.842803
\(867\) −1.00000 −0.0339618
\(868\) 35.6037 1.20847
\(869\) 5.59970 0.189957
\(870\) 0.378134 0.0128199
\(871\) −6.50626 −0.220456
\(872\) −45.8934 −1.55415
\(873\) −14.1233 −0.478001
\(874\) 14.1050 0.477108
\(875\) −14.0474 −0.474887
\(876\) 9.52003 0.321652
\(877\) −23.8840 −0.806504 −0.403252 0.915089i \(-0.632120\pi\)
−0.403252 + 0.915089i \(0.632120\pi\)
\(878\) 11.5475 0.389708
\(879\) 28.3559 0.956421
\(880\) −0.975818 −0.0328948
\(881\) −33.5982 −1.13195 −0.565976 0.824422i \(-0.691500\pi\)
−0.565976 + 0.824422i \(0.691500\pi\)
\(882\) 9.17225 0.308846
\(883\) −22.1669 −0.745976 −0.372988 0.927836i \(-0.621667\pi\)
−0.372988 + 0.927836i \(0.621667\pi\)
\(884\) 5.45835 0.183584
\(885\) −1.43943 −0.0483859
\(886\) 17.5610 0.589972
\(887\) 25.1366 0.844005 0.422002 0.906595i \(-0.361327\pi\)
0.422002 + 0.906595i \(0.361327\pi\)
\(888\) 15.0118 0.503764
\(889\) −9.08850 −0.304819
\(890\) −4.00121 −0.134121
\(891\) 5.59970 0.187597
\(892\) 10.2553 0.343372
\(893\) −19.2093 −0.642816
\(894\) 18.5460 0.620270
\(895\) −1.95680 −0.0654087
\(896\) −20.8534 −0.696663
\(897\) −36.3338 −1.21315
\(898\) 10.9004 0.363752
\(899\) 9.00961 0.300487
\(900\) 5.46913 0.182304
\(901\) 12.4919 0.416164
\(902\) 65.6303 2.18525
\(903\) 12.5813 0.418680
\(904\) −27.9250 −0.928772
\(905\) −4.90747 −0.163130
\(906\) 0.231747 0.00769928
\(907\) 40.2360 1.33601 0.668006 0.744155i \(-0.267148\pi\)
0.668006 + 0.744155i \(0.267148\pi\)
\(908\) 4.73438 0.157116
\(909\) 13.1639 0.436618
\(910\) 6.49256 0.215226
\(911\) 28.3165 0.938166 0.469083 0.883154i \(-0.344584\pi\)
0.469083 + 0.883154i \(0.344584\pi\)
\(912\) 1.01232 0.0335212
\(913\) −63.9990 −2.11806
\(914\) 16.7761 0.554905
\(915\) 1.49273 0.0493481
\(916\) 2.66027 0.0878977
\(917\) 43.2190 1.42722
\(918\) 0.937640 0.0309467
\(919\) 22.4403 0.740238 0.370119 0.928984i \(-0.379317\pi\)
0.370119 + 0.928984i \(0.379317\pi\)
\(920\) −7.57756 −0.249825
\(921\) 23.4856 0.773875
\(922\) −28.6843 −0.944666
\(923\) 25.0268 0.823767
\(924\) 25.7117 0.845851
\(925\) −25.0326 −0.823066
\(926\) 30.2282 0.993359
\(927\) 9.89370 0.324952
\(928\) −6.25307 −0.205267
\(929\) 12.5436 0.411541 0.205770 0.978600i \(-0.434030\pi\)
0.205770 + 0.978600i \(0.434030\pi\)
\(930\) 2.52347 0.0827479
\(931\) 19.7236 0.646415
\(932\) −12.0487 −0.394667
\(933\) 9.82176 0.321550
\(934\) 14.9901 0.490490
\(935\) −1.94356 −0.0635611
\(936\) −14.2504 −0.465790
\(937\) −0.969152 −0.0316608 −0.0158304 0.999875i \(-0.505039\pi\)
−0.0158304 + 0.999875i \(0.505039\pi\)
\(938\) −5.13182 −0.167560
\(939\) −11.7000 −0.381815
\(940\) 3.70628 0.120886
\(941\) 23.9777 0.781651 0.390825 0.920465i \(-0.372190\pi\)
0.390825 + 0.920465i \(0.372190\pi\)
\(942\) −8.48209 −0.276361
\(943\) 93.2596 3.03695
\(944\) −2.08223 −0.0677708
\(945\) −1.42186 −0.0462533
\(946\) −16.1251 −0.524272
\(947\) −21.7920 −0.708146 −0.354073 0.935218i \(-0.615204\pi\)
−0.354073 + 0.935218i \(0.615204\pi\)
\(948\) 1.12083 0.0364029
\(949\) 41.3637 1.34272
\(950\) −9.22489 −0.299295
\(951\) 20.3892 0.661165
\(952\) 11.9876 0.388520
\(953\) 39.6953 1.28586 0.642928 0.765927i \(-0.277720\pi\)
0.642928 + 0.765927i \(0.277720\pi\)
\(954\) −11.7129 −0.379218
\(955\) 5.00615 0.161995
\(956\) 30.4719 0.985533
\(957\) 6.50641 0.210322
\(958\) 12.2528 0.395871
\(959\) −57.0728 −1.84298
\(960\) −2.09993 −0.0677748
\(961\) 29.1255 0.939532
\(962\) 23.4253 0.755262
\(963\) −17.5125 −0.564333
\(964\) −17.7803 −0.572664
\(965\) 8.04179 0.258874
\(966\) −28.6584 −0.922069
\(967\) −31.3976 −1.00968 −0.504840 0.863213i \(-0.668449\pi\)
−0.504840 + 0.863213i \(0.668449\pi\)
\(968\) −59.5679 −1.91458
\(969\) 2.01626 0.0647716
\(970\) −4.59627 −0.147577
\(971\) 55.6249 1.78509 0.892545 0.450959i \(-0.148918\pi\)
0.892545 + 0.450959i \(0.148918\pi\)
\(972\) 1.12083 0.0359507
\(973\) 46.0639 1.47674
\(974\) −20.8100 −0.666797
\(975\) 23.7629 0.761022
\(976\) 2.15933 0.0691185
\(977\) −46.3798 −1.48382 −0.741910 0.670499i \(-0.766080\pi\)
−0.741910 + 0.670499i \(0.766080\pi\)
\(978\) −18.6381 −0.595980
\(979\) −68.8473 −2.20037
\(980\) −3.80551 −0.121562
\(981\) 15.6835 0.500736
\(982\) −9.42231 −0.300678
\(983\) −2.24807 −0.0717024 −0.0358512 0.999357i \(-0.511414\pi\)
−0.0358512 + 0.999357i \(0.511414\pi\)
\(984\) 36.5771 1.16604
\(985\) −6.60312 −0.210393
\(986\) 1.08946 0.0346956
\(987\) 39.0293 1.24232
\(988\) −11.0054 −0.350130
\(989\) −22.9135 −0.728606
\(990\) 1.82236 0.0579183
\(991\) −5.02645 −0.159670 −0.0798351 0.996808i \(-0.525439\pi\)
−0.0798351 + 0.996808i \(0.525439\pi\)
\(992\) −41.7298 −1.32492
\(993\) 15.2254 0.483163
\(994\) 19.7399 0.626113
\(995\) −4.36122 −0.138260
\(996\) −12.8100 −0.405900
\(997\) 40.7833 1.29162 0.645810 0.763498i \(-0.276520\pi\)
0.645810 + 0.763498i \(0.276520\pi\)
\(998\) −16.4298 −0.520076
\(999\) −5.13012 −0.162310
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 4029.2.a.l.1.20 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.20 32 1.1 even 1 trivial