Properties

Label 4029.2.a.l.1.9
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 32
CM no
Inner twists 1

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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 1.9
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.61915 q^{2} -1.00000 q^{3} +0.621643 q^{4} +1.62143 q^{5} +1.61915 q^{6} +3.15810 q^{7} +2.23177 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.61915 q^{2} -1.00000 q^{3} +0.621643 q^{4} +1.62143 q^{5} +1.61915 q^{6} +3.15810 q^{7} +2.23177 q^{8} +1.00000 q^{9} -2.62534 q^{10} -2.23329 q^{11} -0.621643 q^{12} -1.49187 q^{13} -5.11343 q^{14} -1.62143 q^{15} -4.85685 q^{16} -1.00000 q^{17} -1.61915 q^{18} -3.38353 q^{19} +1.00795 q^{20} -3.15810 q^{21} +3.61602 q^{22} +7.59577 q^{23} -2.23177 q^{24} -2.37096 q^{25} +2.41555 q^{26} -1.00000 q^{27} +1.96321 q^{28} -6.67740 q^{29} +2.62534 q^{30} -2.84320 q^{31} +3.40043 q^{32} +2.23329 q^{33} +1.61915 q^{34} +5.12064 q^{35} +0.621643 q^{36} +7.70590 q^{37} +5.47843 q^{38} +1.49187 q^{39} +3.61865 q^{40} +1.42941 q^{41} +5.11343 q^{42} +8.92330 q^{43} -1.38831 q^{44} +1.62143 q^{45} -12.2987 q^{46} -8.52767 q^{47} +4.85685 q^{48} +2.97359 q^{49} +3.83894 q^{50} +1.00000 q^{51} -0.927408 q^{52} +7.27256 q^{53} +1.61915 q^{54} -3.62112 q^{55} +7.04814 q^{56} +3.38353 q^{57} +10.8117 q^{58} +1.82717 q^{59} -1.00795 q^{60} +1.27446 q^{61} +4.60356 q^{62} +3.15810 q^{63} +4.20790 q^{64} -2.41896 q^{65} -3.61602 q^{66} +12.5098 q^{67} -0.621643 q^{68} -7.59577 q^{69} -8.29108 q^{70} -13.6580 q^{71} +2.23177 q^{72} +13.7920 q^{73} -12.4770 q^{74} +2.37096 q^{75} -2.10334 q^{76} -7.05294 q^{77} -2.41555 q^{78} +1.00000 q^{79} -7.87504 q^{80} +1.00000 q^{81} -2.31442 q^{82} +11.4169 q^{83} -1.96321 q^{84} -1.62143 q^{85} -14.4482 q^{86} +6.67740 q^{87} -4.98417 q^{88} +13.6742 q^{89} -2.62534 q^{90} -4.71146 q^{91} +4.72186 q^{92} +2.84320 q^{93} +13.8076 q^{94} -5.48615 q^{95} -3.40043 q^{96} +3.88801 q^{97} -4.81469 q^{98} -2.23329 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.61915 −1.14491 −0.572456 0.819936i \(-0.694009\pi\)
−0.572456 + 0.819936i \(0.694009\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.621643 0.310821
\(5\) 1.62143 0.725126 0.362563 0.931959i \(-0.381902\pi\)
0.362563 + 0.931959i \(0.381902\pi\)
\(6\) 1.61915 0.661015
\(7\) 3.15810 1.19365 0.596825 0.802372i \(-0.296429\pi\)
0.596825 + 0.802372i \(0.296429\pi\)
\(8\) 2.23177 0.789048
\(9\) 1.00000 0.333333
\(10\) −2.62534 −0.830205
\(11\) −2.23329 −0.673361 −0.336681 0.941619i \(-0.609304\pi\)
−0.336681 + 0.941619i \(0.609304\pi\)
\(12\) −0.621643 −0.179453
\(13\) −1.49187 −0.413769 −0.206885 0.978365i \(-0.566332\pi\)
−0.206885 + 0.978365i \(0.566332\pi\)
\(14\) −5.11343 −1.36662
\(15\) −1.62143 −0.418652
\(16\) −4.85685 −1.21421
\(17\) −1.00000 −0.242536
\(18\) −1.61915 −0.381637
\(19\) −3.38353 −0.776234 −0.388117 0.921610i \(-0.626874\pi\)
−0.388117 + 0.921610i \(0.626874\pi\)
\(20\) 1.00795 0.225385
\(21\) −3.15810 −0.689154
\(22\) 3.61602 0.770939
\(23\) 7.59577 1.58383 0.791914 0.610633i \(-0.209085\pi\)
0.791914 + 0.610633i \(0.209085\pi\)
\(24\) −2.23177 −0.455557
\(25\) −2.37096 −0.474192
\(26\) 2.41555 0.473729
\(27\) −1.00000 −0.192450
\(28\) 1.96321 0.371012
\(29\) −6.67740 −1.23996 −0.619981 0.784617i \(-0.712860\pi\)
−0.619981 + 0.784617i \(0.712860\pi\)
\(30\) 2.62534 0.479319
\(31\) −2.84320 −0.510653 −0.255327 0.966855i \(-0.582183\pi\)
−0.255327 + 0.966855i \(0.582183\pi\)
\(32\) 3.40043 0.601116
\(33\) 2.23329 0.388765
\(34\) 1.61915 0.277682
\(35\) 5.12064 0.865546
\(36\) 0.621643 0.103607
\(37\) 7.70590 1.26684 0.633421 0.773807i \(-0.281650\pi\)
0.633421 + 0.773807i \(0.281650\pi\)
\(38\) 5.47843 0.888719
\(39\) 1.49187 0.238890
\(40\) 3.61865 0.572159
\(41\) 1.42941 0.223236 0.111618 0.993751i \(-0.464397\pi\)
0.111618 + 0.993751i \(0.464397\pi\)
\(42\) 5.11343 0.789020
\(43\) 8.92330 1.36079 0.680396 0.732845i \(-0.261808\pi\)
0.680396 + 0.732845i \(0.261808\pi\)
\(44\) −1.38831 −0.209295
\(45\) 1.62143 0.241709
\(46\) −12.2987 −1.81334
\(47\) −8.52767 −1.24389 −0.621944 0.783062i \(-0.713657\pi\)
−0.621944 + 0.783062i \(0.713657\pi\)
\(48\) 4.85685 0.701025
\(49\) 2.97359 0.424799
\(50\) 3.83894 0.542908
\(51\) 1.00000 0.140028
\(52\) −0.927408 −0.128608
\(53\) 7.27256 0.998963 0.499482 0.866325i \(-0.333524\pi\)
0.499482 + 0.866325i \(0.333524\pi\)
\(54\) 1.61915 0.220338
\(55\) −3.62112 −0.488272
\(56\) 7.04814 0.941847
\(57\) 3.38353 0.448159
\(58\) 10.8117 1.41965
\(59\) 1.82717 0.237877 0.118939 0.992902i \(-0.462051\pi\)
0.118939 + 0.992902i \(0.462051\pi\)
\(60\) −1.00795 −0.130126
\(61\) 1.27446 0.163177 0.0815887 0.996666i \(-0.474001\pi\)
0.0815887 + 0.996666i \(0.474001\pi\)
\(62\) 4.60356 0.584652
\(63\) 3.15810 0.397883
\(64\) 4.20790 0.525987
\(65\) −2.41896 −0.300035
\(66\) −3.61602 −0.445102
\(67\) 12.5098 1.52831 0.764156 0.645032i \(-0.223156\pi\)
0.764156 + 0.645032i \(0.223156\pi\)
\(68\) −0.621643 −0.0753853
\(69\) −7.59577 −0.914423
\(70\) −8.29108 −0.990974
\(71\) −13.6580 −1.62091 −0.810456 0.585800i \(-0.800780\pi\)
−0.810456 + 0.585800i \(0.800780\pi\)
\(72\) 2.23177 0.263016
\(73\) 13.7920 1.61423 0.807116 0.590393i \(-0.201027\pi\)
0.807116 + 0.590393i \(0.201027\pi\)
\(74\) −12.4770 −1.45042
\(75\) 2.37096 0.273775
\(76\) −2.10334 −0.241270
\(77\) −7.05294 −0.803757
\(78\) −2.41555 −0.273508
\(79\) 1.00000 0.112509
\(80\) −7.87504 −0.880456
\(81\) 1.00000 0.111111
\(82\) −2.31442 −0.255585
\(83\) 11.4169 1.25316 0.626581 0.779356i \(-0.284454\pi\)
0.626581 + 0.779356i \(0.284454\pi\)
\(84\) −1.96321 −0.214204
\(85\) −1.62143 −0.175869
\(86\) −14.4482 −1.55798
\(87\) 6.67740 0.715892
\(88\) −4.98417 −0.531314
\(89\) 13.6742 1.44947 0.724734 0.689029i \(-0.241963\pi\)
0.724734 + 0.689029i \(0.241963\pi\)
\(90\) −2.62534 −0.276735
\(91\) −4.71146 −0.493896
\(92\) 4.72186 0.492288
\(93\) 2.84320 0.294826
\(94\) 13.8076 1.42414
\(95\) −5.48615 −0.562867
\(96\) −3.40043 −0.347055
\(97\) 3.88801 0.394768 0.197384 0.980326i \(-0.436755\pi\)
0.197384 + 0.980326i \(0.436755\pi\)
\(98\) −4.81469 −0.486357
\(99\) −2.23329 −0.224454
\(100\) −1.47389 −0.147389
\(101\) −14.4066 −1.43351 −0.716753 0.697327i \(-0.754373\pi\)
−0.716753 + 0.697327i \(0.754373\pi\)
\(102\) −1.61915 −0.160320
\(103\) −7.88588 −0.777019 −0.388510 0.921445i \(-0.627010\pi\)
−0.388510 + 0.921445i \(0.627010\pi\)
\(104\) −3.32950 −0.326484
\(105\) −5.12064 −0.499723
\(106\) −11.7754 −1.14372
\(107\) −0.677395 −0.0654862 −0.0327431 0.999464i \(-0.510424\pi\)
−0.0327431 + 0.999464i \(0.510424\pi\)
\(108\) −0.621643 −0.0598176
\(109\) 13.4125 1.28469 0.642344 0.766417i \(-0.277962\pi\)
0.642344 + 0.766417i \(0.277962\pi\)
\(110\) 5.86313 0.559028
\(111\) −7.70590 −0.731412
\(112\) −15.3384 −1.44934
\(113\) 0.679348 0.0639077 0.0319539 0.999489i \(-0.489827\pi\)
0.0319539 + 0.999489i \(0.489827\pi\)
\(114\) −5.47843 −0.513102
\(115\) 12.3160 1.14847
\(116\) −4.15096 −0.385407
\(117\) −1.49187 −0.137923
\(118\) −2.95846 −0.272349
\(119\) −3.15810 −0.289503
\(120\) −3.61865 −0.330336
\(121\) −6.01243 −0.546585
\(122\) −2.06353 −0.186824
\(123\) −1.42941 −0.128885
\(124\) −1.76745 −0.158722
\(125\) −11.9515 −1.06898
\(126\) −5.11343 −0.455541
\(127\) 5.60828 0.497655 0.248827 0.968548i \(-0.419955\pi\)
0.248827 + 0.968548i \(0.419955\pi\)
\(128\) −13.6141 −1.20332
\(129\) −8.92330 −0.785653
\(130\) 3.91665 0.343513
\(131\) 6.09821 0.532803 0.266401 0.963862i \(-0.414165\pi\)
0.266401 + 0.963862i \(0.414165\pi\)
\(132\) 1.38831 0.120837
\(133\) −10.6855 −0.926551
\(134\) −20.2552 −1.74978
\(135\) −1.62143 −0.139551
\(136\) −2.23177 −0.191372
\(137\) 22.0911 1.88737 0.943685 0.330844i \(-0.107334\pi\)
0.943685 + 0.330844i \(0.107334\pi\)
\(138\) 12.2987 1.04693
\(139\) 8.05904 0.683559 0.341779 0.939780i \(-0.388970\pi\)
0.341779 + 0.939780i \(0.388970\pi\)
\(140\) 3.18321 0.269030
\(141\) 8.52767 0.718159
\(142\) 22.1144 1.85580
\(143\) 3.33177 0.278616
\(144\) −4.85685 −0.404737
\(145\) −10.8269 −0.899128
\(146\) −22.3313 −1.84815
\(147\) −2.97359 −0.245258
\(148\) 4.79032 0.393762
\(149\) −23.4401 −1.92028 −0.960142 0.279512i \(-0.909827\pi\)
−0.960142 + 0.279512i \(0.909827\pi\)
\(150\) −3.83894 −0.313448
\(151\) −15.4947 −1.26094 −0.630472 0.776212i \(-0.717139\pi\)
−0.630472 + 0.776212i \(0.717139\pi\)
\(152\) −7.55123 −0.612486
\(153\) −1.00000 −0.0808452
\(154\) 11.4198 0.920231
\(155\) −4.61005 −0.370288
\(156\) 0.927408 0.0742521
\(157\) 3.22759 0.257590 0.128795 0.991671i \(-0.458889\pi\)
0.128795 + 0.991671i \(0.458889\pi\)
\(158\) −1.61915 −0.128813
\(159\) −7.27256 −0.576752
\(160\) 5.51356 0.435885
\(161\) 23.9882 1.89054
\(162\) −1.61915 −0.127212
\(163\) −6.80575 −0.533068 −0.266534 0.963826i \(-0.585878\pi\)
−0.266534 + 0.963826i \(0.585878\pi\)
\(164\) 0.888580 0.0693864
\(165\) 3.62112 0.281904
\(166\) −18.4856 −1.43476
\(167\) 1.23692 0.0957155 0.0478577 0.998854i \(-0.484761\pi\)
0.0478577 + 0.998854i \(0.484761\pi\)
\(168\) −7.04814 −0.543776
\(169\) −10.7743 −0.828795
\(170\) 2.62534 0.201354
\(171\) −3.38353 −0.258745
\(172\) 5.54711 0.422963
\(173\) −19.4167 −1.47622 −0.738111 0.674679i \(-0.764282\pi\)
−0.738111 + 0.674679i \(0.764282\pi\)
\(174\) −10.8117 −0.819633
\(175\) −7.48773 −0.566020
\(176\) 10.8467 0.817603
\(177\) −1.82717 −0.137339
\(178\) −22.1406 −1.65951
\(179\) 8.45691 0.632099 0.316049 0.948743i \(-0.397643\pi\)
0.316049 + 0.948743i \(0.397643\pi\)
\(180\) 1.00795 0.0751282
\(181\) 7.73082 0.574628 0.287314 0.957837i \(-0.407238\pi\)
0.287314 + 0.957837i \(0.407238\pi\)
\(182\) 7.62856 0.565467
\(183\) −1.27446 −0.0942105
\(184\) 16.9520 1.24972
\(185\) 12.4946 0.918620
\(186\) −4.60356 −0.337549
\(187\) 2.23329 0.163314
\(188\) −5.30117 −0.386627
\(189\) −3.15810 −0.229718
\(190\) 8.88290 0.644433
\(191\) 2.07150 0.149888 0.0749442 0.997188i \(-0.476122\pi\)
0.0749442 + 0.997188i \(0.476122\pi\)
\(192\) −4.20790 −0.303679
\(193\) 23.1956 1.66965 0.834827 0.550512i \(-0.185567\pi\)
0.834827 + 0.550512i \(0.185567\pi\)
\(194\) −6.29527 −0.451974
\(195\) 2.41896 0.173225
\(196\) 1.84851 0.132037
\(197\) −3.91514 −0.278942 −0.139471 0.990226i \(-0.544540\pi\)
−0.139471 + 0.990226i \(0.544540\pi\)
\(198\) 3.61602 0.256980
\(199\) 5.24348 0.371701 0.185850 0.982578i \(-0.440496\pi\)
0.185850 + 0.982578i \(0.440496\pi\)
\(200\) −5.29143 −0.374161
\(201\) −12.5098 −0.882371
\(202\) 23.3264 1.64124
\(203\) −21.0879 −1.48008
\(204\) 0.621643 0.0435237
\(205\) 2.31768 0.161874
\(206\) 12.7684 0.889618
\(207\) 7.59577 0.527943
\(208\) 7.24577 0.502404
\(209\) 7.55638 0.522686
\(210\) 8.29108 0.572139
\(211\) 18.9281 1.30306 0.651532 0.758621i \(-0.274127\pi\)
0.651532 + 0.758621i \(0.274127\pi\)
\(212\) 4.52094 0.310499
\(213\) 13.6580 0.935834
\(214\) 1.09680 0.0749759
\(215\) 14.4685 0.986745
\(216\) −2.23177 −0.151852
\(217\) −8.97910 −0.609541
\(218\) −21.7169 −1.47085
\(219\) −13.7920 −0.931977
\(220\) −2.25104 −0.151765
\(221\) 1.49187 0.100354
\(222\) 12.4770 0.837402
\(223\) 5.30056 0.354952 0.177476 0.984125i \(-0.443207\pi\)
0.177476 + 0.984125i \(0.443207\pi\)
\(224\) 10.7389 0.717522
\(225\) −2.37096 −0.158064
\(226\) −1.09997 −0.0731687
\(227\) 23.4772 1.55824 0.779118 0.626877i \(-0.215667\pi\)
0.779118 + 0.626877i \(0.215667\pi\)
\(228\) 2.10334 0.139297
\(229\) 27.5049 1.81758 0.908788 0.417259i \(-0.137009\pi\)
0.908788 + 0.417259i \(0.137009\pi\)
\(230\) −19.9415 −1.31490
\(231\) 7.05294 0.464050
\(232\) −14.9024 −0.978389
\(233\) 3.58508 0.234866 0.117433 0.993081i \(-0.462533\pi\)
0.117433 + 0.993081i \(0.462533\pi\)
\(234\) 2.41555 0.157910
\(235\) −13.8270 −0.901976
\(236\) 1.13585 0.0739374
\(237\) −1.00000 −0.0649570
\(238\) 5.11343 0.331455
\(239\) 5.46987 0.353817 0.176908 0.984227i \(-0.443390\pi\)
0.176908 + 0.984227i \(0.443390\pi\)
\(240\) 7.87504 0.508332
\(241\) 3.55333 0.228890 0.114445 0.993430i \(-0.463491\pi\)
0.114445 + 0.993430i \(0.463491\pi\)
\(242\) 9.73502 0.625791
\(243\) −1.00000 −0.0641500
\(244\) 0.792256 0.0507190
\(245\) 4.82148 0.308033
\(246\) 2.31442 0.147562
\(247\) 5.04777 0.321182
\(248\) −6.34535 −0.402930
\(249\) −11.4169 −0.723514
\(250\) 19.3513 1.22388
\(251\) 7.07969 0.446866 0.223433 0.974719i \(-0.428274\pi\)
0.223433 + 0.974719i \(0.428274\pi\)
\(252\) 1.96321 0.123671
\(253\) −16.9635 −1.06649
\(254\) −9.08065 −0.569771
\(255\) 1.62143 0.101538
\(256\) 13.6274 0.851713
\(257\) −23.4337 −1.46175 −0.730876 0.682510i \(-0.760888\pi\)
−0.730876 + 0.682510i \(0.760888\pi\)
\(258\) 14.4482 0.899503
\(259\) 24.3360 1.51217
\(260\) −1.50373 −0.0932573
\(261\) −6.67740 −0.413320
\(262\) −9.87391 −0.610012
\(263\) −26.7469 −1.64928 −0.824642 0.565655i \(-0.808623\pi\)
−0.824642 + 0.565655i \(0.808623\pi\)
\(264\) 4.98417 0.306755
\(265\) 11.7920 0.724374
\(266\) 17.3014 1.06082
\(267\) −13.6742 −0.836850
\(268\) 7.77661 0.475032
\(269\) 11.0733 0.675149 0.337575 0.941299i \(-0.390393\pi\)
0.337575 + 0.941299i \(0.390393\pi\)
\(270\) 2.62534 0.159773
\(271\) 10.7445 0.652682 0.326341 0.945252i \(-0.394184\pi\)
0.326341 + 0.945252i \(0.394184\pi\)
\(272\) 4.85685 0.294490
\(273\) 4.71146 0.285151
\(274\) −35.7688 −2.16087
\(275\) 5.29504 0.319303
\(276\) −4.72186 −0.284222
\(277\) 17.5287 1.05320 0.526598 0.850114i \(-0.323467\pi\)
0.526598 + 0.850114i \(0.323467\pi\)
\(278\) −13.0488 −0.782614
\(279\) −2.84320 −0.170218
\(280\) 11.4281 0.682958
\(281\) 27.0469 1.61348 0.806740 0.590906i \(-0.201230\pi\)
0.806740 + 0.590906i \(0.201230\pi\)
\(282\) −13.8076 −0.822229
\(283\) 15.0432 0.894228 0.447114 0.894477i \(-0.352452\pi\)
0.447114 + 0.894477i \(0.352452\pi\)
\(284\) −8.49043 −0.503814
\(285\) 5.48615 0.324972
\(286\) −5.39463 −0.318991
\(287\) 4.51420 0.266465
\(288\) 3.40043 0.200372
\(289\) 1.00000 0.0588235
\(290\) 17.5304 1.02942
\(291\) −3.88801 −0.227919
\(292\) 8.57370 0.501738
\(293\) −7.92022 −0.462704 −0.231352 0.972870i \(-0.574315\pi\)
−0.231352 + 0.972870i \(0.574315\pi\)
\(294\) 4.81469 0.280799
\(295\) 2.96263 0.172491
\(296\) 17.1978 0.999600
\(297\) 2.23329 0.129588
\(298\) 37.9529 2.19855
\(299\) −11.3319 −0.655339
\(300\) 1.47389 0.0850952
\(301\) 28.1807 1.62431
\(302\) 25.0883 1.44367
\(303\) 14.4066 0.827635
\(304\) 16.4333 0.942512
\(305\) 2.06644 0.118324
\(306\) 1.61915 0.0925606
\(307\) 6.65605 0.379881 0.189940 0.981796i \(-0.439171\pi\)
0.189940 + 0.981796i \(0.439171\pi\)
\(308\) −4.38441 −0.249825
\(309\) 7.88588 0.448612
\(310\) 7.46435 0.423947
\(311\) 13.5489 0.768286 0.384143 0.923274i \(-0.374497\pi\)
0.384143 + 0.923274i \(0.374497\pi\)
\(312\) 3.32950 0.188496
\(313\) 6.26533 0.354138 0.177069 0.984198i \(-0.443338\pi\)
0.177069 + 0.984198i \(0.443338\pi\)
\(314\) −5.22595 −0.294917
\(315\) 5.12064 0.288515
\(316\) 0.621643 0.0349701
\(317\) −6.35895 −0.357154 −0.178577 0.983926i \(-0.557149\pi\)
−0.178577 + 0.983926i \(0.557149\pi\)
\(318\) 11.7754 0.660329
\(319\) 14.9125 0.834942
\(320\) 6.82281 0.381407
\(321\) 0.677395 0.0378085
\(322\) −38.8405 −2.16449
\(323\) 3.38353 0.188264
\(324\) 0.621643 0.0345357
\(325\) 3.53716 0.196206
\(326\) 11.0195 0.610315
\(327\) −13.4125 −0.741714
\(328\) 3.19010 0.176144
\(329\) −26.9312 −1.48477
\(330\) −5.86313 −0.322755
\(331\) 20.0192 1.10036 0.550178 0.835048i \(-0.314560\pi\)
0.550178 + 0.835048i \(0.314560\pi\)
\(332\) 7.09721 0.389510
\(333\) 7.70590 0.422281
\(334\) −2.00275 −0.109586
\(335\) 20.2837 1.10822
\(336\) 15.3384 0.836779
\(337\) 15.4402 0.841081 0.420541 0.907274i \(-0.361840\pi\)
0.420541 + 0.907274i \(0.361840\pi\)
\(338\) 17.4452 0.948896
\(339\) −0.679348 −0.0368971
\(340\) −1.00795 −0.0546638
\(341\) 6.34967 0.343854
\(342\) 5.47843 0.296240
\(343\) −12.7158 −0.686588
\(344\) 19.9147 1.07373
\(345\) −12.3160 −0.663072
\(346\) 31.4385 1.69014
\(347\) 21.6927 1.16453 0.582263 0.813001i \(-0.302168\pi\)
0.582263 + 0.813001i \(0.302168\pi\)
\(348\) 4.15096 0.222515
\(349\) −14.0246 −0.750717 −0.375359 0.926880i \(-0.622480\pi\)
−0.375359 + 0.926880i \(0.622480\pi\)
\(350\) 12.1238 0.648042
\(351\) 1.49187 0.0796300
\(352\) −7.59413 −0.404768
\(353\) 27.8115 1.48026 0.740128 0.672466i \(-0.234765\pi\)
0.740128 + 0.672466i \(0.234765\pi\)
\(354\) 2.95846 0.157240
\(355\) −22.1456 −1.17536
\(356\) 8.50050 0.450526
\(357\) 3.15810 0.167144
\(358\) −13.6930 −0.723697
\(359\) −31.1804 −1.64564 −0.822819 0.568304i \(-0.807600\pi\)
−0.822819 + 0.568304i \(0.807600\pi\)
\(360\) 3.61865 0.190720
\(361\) −7.55176 −0.397461
\(362\) −12.5174 −0.657897
\(363\) 6.01243 0.315571
\(364\) −2.92885 −0.153513
\(365\) 22.3628 1.17052
\(366\) 2.06353 0.107863
\(367\) 3.54416 0.185004 0.0925018 0.995713i \(-0.470514\pi\)
0.0925018 + 0.995713i \(0.470514\pi\)
\(368\) −36.8915 −1.92310
\(369\) 1.42941 0.0744119
\(370\) −20.2306 −1.05174
\(371\) 22.9675 1.19241
\(372\) 1.76745 0.0916382
\(373\) 16.1948 0.838534 0.419267 0.907863i \(-0.362287\pi\)
0.419267 + 0.907863i \(0.362287\pi\)
\(374\) −3.61602 −0.186980
\(375\) 11.9515 0.617173
\(376\) −19.0318 −0.981488
\(377\) 9.96178 0.513058
\(378\) 5.11343 0.263007
\(379\) 0.305843 0.0157101 0.00785505 0.999969i \(-0.497500\pi\)
0.00785505 + 0.999969i \(0.497500\pi\)
\(380\) −3.41043 −0.174951
\(381\) −5.60828 −0.287321
\(382\) −3.35407 −0.171609
\(383\) 27.8990 1.42557 0.712786 0.701381i \(-0.247433\pi\)
0.712786 + 0.701381i \(0.247433\pi\)
\(384\) 13.6141 0.694740
\(385\) −11.4359 −0.582825
\(386\) −37.5571 −1.91161
\(387\) 8.92330 0.453597
\(388\) 2.41695 0.122702
\(389\) −29.9450 −1.51827 −0.759135 0.650933i \(-0.774378\pi\)
−0.759135 + 0.650933i \(0.774378\pi\)
\(390\) −3.91665 −0.198328
\(391\) −7.59577 −0.384135
\(392\) 6.63637 0.335187
\(393\) −6.09821 −0.307614
\(394\) 6.33920 0.319364
\(395\) 1.62143 0.0815830
\(396\) −1.38831 −0.0697651
\(397\) −13.7321 −0.689192 −0.344596 0.938751i \(-0.611984\pi\)
−0.344596 + 0.938751i \(0.611984\pi\)
\(398\) −8.48998 −0.425564
\(399\) 10.6855 0.534945
\(400\) 11.5154 0.575770
\(401\) −39.1935 −1.95723 −0.978614 0.205706i \(-0.934051\pi\)
−0.978614 + 0.205706i \(0.934051\pi\)
\(402\) 20.2552 1.01024
\(403\) 4.24167 0.211293
\(404\) −8.95574 −0.445565
\(405\) 1.62143 0.0805695
\(406\) 34.1444 1.69456
\(407\) −17.2095 −0.853043
\(408\) 2.23177 0.110489
\(409\) −29.4352 −1.45548 −0.727738 0.685856i \(-0.759428\pi\)
−0.727738 + 0.685856i \(0.759428\pi\)
\(410\) −3.75267 −0.185331
\(411\) −22.0911 −1.08967
\(412\) −4.90220 −0.241514
\(413\) 5.77039 0.283942
\(414\) −12.2987 −0.604447
\(415\) 18.5116 0.908701
\(416\) −5.07298 −0.248723
\(417\) −8.05904 −0.394653
\(418\) −12.2349 −0.598429
\(419\) −31.4106 −1.53451 −0.767255 0.641342i \(-0.778378\pi\)
−0.767255 + 0.641342i \(0.778378\pi\)
\(420\) −3.18321 −0.155325
\(421\) −11.5289 −0.561884 −0.280942 0.959725i \(-0.590647\pi\)
−0.280942 + 0.959725i \(0.590647\pi\)
\(422\) −30.6474 −1.49189
\(423\) −8.52767 −0.414630
\(424\) 16.2306 0.788230
\(425\) 2.37096 0.115009
\(426\) −22.1144 −1.07145
\(427\) 4.02486 0.194777
\(428\) −0.421098 −0.0203545
\(429\) −3.33177 −0.160859
\(430\) −23.4267 −1.12974
\(431\) −18.6217 −0.896974 −0.448487 0.893789i \(-0.648037\pi\)
−0.448487 + 0.893789i \(0.648037\pi\)
\(432\) 4.85685 0.233675
\(433\) 13.9508 0.670433 0.335216 0.942141i \(-0.391191\pi\)
0.335216 + 0.942141i \(0.391191\pi\)
\(434\) 14.5385 0.697870
\(435\) 10.8269 0.519112
\(436\) 8.33780 0.399308
\(437\) −25.7005 −1.22942
\(438\) 22.3313 1.06703
\(439\) 32.2939 1.54130 0.770651 0.637257i \(-0.219931\pi\)
0.770651 + 0.637257i \(0.219931\pi\)
\(440\) −8.08149 −0.385270
\(441\) 2.97359 0.141600
\(442\) −2.41555 −0.114896
\(443\) −29.6455 −1.40850 −0.704249 0.709953i \(-0.748716\pi\)
−0.704249 + 0.709953i \(0.748716\pi\)
\(444\) −4.79032 −0.227339
\(445\) 22.1718 1.05105
\(446\) −8.58240 −0.406388
\(447\) 23.4401 1.10868
\(448\) 13.2890 0.627844
\(449\) −3.37451 −0.159253 −0.0796265 0.996825i \(-0.525373\pi\)
−0.0796265 + 0.996825i \(0.525373\pi\)
\(450\) 3.83894 0.180969
\(451\) −3.19227 −0.150318
\(452\) 0.422312 0.0198639
\(453\) 15.4947 0.728007
\(454\) −38.0131 −1.78404
\(455\) −7.63931 −0.358137
\(456\) 7.55123 0.353619
\(457\) 3.92810 0.183749 0.0918745 0.995771i \(-0.470714\pi\)
0.0918745 + 0.995771i \(0.470714\pi\)
\(458\) −44.5345 −2.08096
\(459\) 1.00000 0.0466760
\(460\) 7.65617 0.356971
\(461\) −0.727123 −0.0338655 −0.0169328 0.999857i \(-0.505390\pi\)
−0.0169328 + 0.999857i \(0.505390\pi\)
\(462\) −11.4198 −0.531295
\(463\) −18.4544 −0.857648 −0.428824 0.903388i \(-0.641072\pi\)
−0.428824 + 0.903388i \(0.641072\pi\)
\(464\) 32.4311 1.50558
\(465\) 4.61005 0.213786
\(466\) −5.80477 −0.268901
\(467\) 26.1401 1.20962 0.604811 0.796369i \(-0.293249\pi\)
0.604811 + 0.796369i \(0.293249\pi\)
\(468\) −0.927408 −0.0428695
\(469\) 39.5071 1.82427
\(470\) 22.3880 1.03268
\(471\) −3.22759 −0.148719
\(472\) 4.07782 0.187697
\(473\) −19.9283 −0.916304
\(474\) 1.61915 0.0743700
\(475\) 8.02221 0.368084
\(476\) −1.96321 −0.0899836
\(477\) 7.27256 0.332988
\(478\) −8.85654 −0.405089
\(479\) 38.7912 1.77242 0.886209 0.463287i \(-0.153330\pi\)
0.886209 + 0.463287i \(0.153330\pi\)
\(480\) −5.51356 −0.251658
\(481\) −11.4962 −0.524181
\(482\) −5.75338 −0.262059
\(483\) −23.9882 −1.09150
\(484\) −3.73759 −0.169890
\(485\) 6.30414 0.286256
\(486\) 1.61915 0.0734461
\(487\) 27.5492 1.24837 0.624186 0.781276i \(-0.285431\pi\)
0.624186 + 0.781276i \(0.285431\pi\)
\(488\) 2.84429 0.128755
\(489\) 6.80575 0.307767
\(490\) −7.80669 −0.352670
\(491\) −1.85799 −0.0838500 −0.0419250 0.999121i \(-0.513349\pi\)
−0.0419250 + 0.999121i \(0.513349\pi\)
\(492\) −0.888580 −0.0400603
\(493\) 6.67740 0.300735
\(494\) −8.17309 −0.367725
\(495\) −3.62112 −0.162757
\(496\) 13.8090 0.620041
\(497\) −43.1335 −1.93480
\(498\) 18.4856 0.828359
\(499\) −13.4717 −0.603076 −0.301538 0.953454i \(-0.597500\pi\)
−0.301538 + 0.953454i \(0.597500\pi\)
\(500\) −7.42957 −0.332260
\(501\) −1.23692 −0.0552614
\(502\) −11.4631 −0.511622
\(503\) 13.6458 0.608434 0.304217 0.952603i \(-0.401605\pi\)
0.304217 + 0.952603i \(0.401605\pi\)
\(504\) 7.04814 0.313949
\(505\) −23.3592 −1.03947
\(506\) 27.4665 1.22103
\(507\) 10.7743 0.478505
\(508\) 3.48635 0.154682
\(509\) −24.1992 −1.07261 −0.536305 0.844025i \(-0.680180\pi\)
−0.536305 + 0.844025i \(0.680180\pi\)
\(510\) −2.62534 −0.116252
\(511\) 43.5565 1.92683
\(512\) 5.16333 0.228189
\(513\) 3.38353 0.149386
\(514\) 37.9426 1.67358
\(515\) −12.7864 −0.563437
\(516\) −5.54711 −0.244198
\(517\) 19.0447 0.837586
\(518\) −39.4036 −1.73130
\(519\) 19.4167 0.852297
\(520\) −5.39855 −0.236742
\(521\) 16.0480 0.703075 0.351538 0.936174i \(-0.385659\pi\)
0.351538 + 0.936174i \(0.385659\pi\)
\(522\) 10.8117 0.473215
\(523\) 25.0399 1.09492 0.547459 0.836833i \(-0.315595\pi\)
0.547459 + 0.836833i \(0.315595\pi\)
\(524\) 3.79091 0.165607
\(525\) 7.48773 0.326792
\(526\) 43.3072 1.88828
\(527\) 2.84320 0.123852
\(528\) −10.8467 −0.472043
\(529\) 34.6957 1.50851
\(530\) −19.0929 −0.829344
\(531\) 1.82717 0.0792925
\(532\) −6.64257 −0.287992
\(533\) −2.13248 −0.0923680
\(534\) 22.1406 0.958119
\(535\) −1.09835 −0.0474858
\(536\) 27.9189 1.20591
\(537\) −8.45691 −0.364942
\(538\) −17.9293 −0.772986
\(539\) −6.64089 −0.286043
\(540\) −1.00795 −0.0433753
\(541\) −42.3879 −1.82240 −0.911199 0.411966i \(-0.864842\pi\)
−0.911199 + 0.411966i \(0.864842\pi\)
\(542\) −17.3969 −0.747263
\(543\) −7.73082 −0.331761
\(544\) −3.40043 −0.145792
\(545\) 21.7475 0.931560
\(546\) −7.62856 −0.326472
\(547\) 7.39993 0.316398 0.158199 0.987407i \(-0.449431\pi\)
0.158199 + 0.987407i \(0.449431\pi\)
\(548\) 13.7328 0.586635
\(549\) 1.27446 0.0543924
\(550\) −8.57345 −0.365573
\(551\) 22.5931 0.962500
\(552\) −16.9520 −0.721524
\(553\) 3.15810 0.134296
\(554\) −28.3815 −1.20582
\(555\) −12.4946 −0.530366
\(556\) 5.00985 0.212465
\(557\) 28.3930 1.20305 0.601525 0.798854i \(-0.294560\pi\)
0.601525 + 0.798854i \(0.294560\pi\)
\(558\) 4.60356 0.194884
\(559\) −13.3124 −0.563054
\(560\) −24.8702 −1.05096
\(561\) −2.23329 −0.0942894
\(562\) −43.7929 −1.84729
\(563\) 5.18365 0.218465 0.109232 0.994016i \(-0.465161\pi\)
0.109232 + 0.994016i \(0.465161\pi\)
\(564\) 5.30117 0.223219
\(565\) 1.10152 0.0463411
\(566\) −24.3572 −1.02381
\(567\) 3.15810 0.132628
\(568\) −30.4815 −1.27898
\(569\) −30.8799 −1.29455 −0.647276 0.762256i \(-0.724092\pi\)
−0.647276 + 0.762256i \(0.724092\pi\)
\(570\) −8.88290 −0.372064
\(571\) 41.5963 1.74075 0.870375 0.492389i \(-0.163876\pi\)
0.870375 + 0.492389i \(0.163876\pi\)
\(572\) 2.07117 0.0865999
\(573\) −2.07150 −0.0865381
\(574\) −7.30917 −0.305079
\(575\) −18.0093 −0.751039
\(576\) 4.20790 0.175329
\(577\) −23.3328 −0.971356 −0.485678 0.874138i \(-0.661427\pi\)
−0.485678 + 0.874138i \(0.661427\pi\)
\(578\) −1.61915 −0.0673477
\(579\) −23.1956 −0.963976
\(580\) −6.73049 −0.279468
\(581\) 36.0556 1.49584
\(582\) 6.29527 0.260947
\(583\) −16.2417 −0.672663
\(584\) 30.7805 1.27371
\(585\) −2.41896 −0.100012
\(586\) 12.8240 0.529755
\(587\) 15.2426 0.629130 0.314565 0.949236i \(-0.398141\pi\)
0.314565 + 0.949236i \(0.398141\pi\)
\(588\) −1.84851 −0.0762314
\(589\) 9.62003 0.396386
\(590\) −4.79694 −0.197487
\(591\) 3.91514 0.161048
\(592\) −37.4264 −1.53821
\(593\) 16.9063 0.694259 0.347129 0.937817i \(-0.387156\pi\)
0.347129 + 0.937817i \(0.387156\pi\)
\(594\) −3.61602 −0.148367
\(595\) −5.12064 −0.209926
\(596\) −14.5713 −0.596866
\(597\) −5.24348 −0.214601
\(598\) 18.3480 0.750305
\(599\) −20.0032 −0.817309 −0.408655 0.912689i \(-0.634002\pi\)
−0.408655 + 0.912689i \(0.634002\pi\)
\(600\) 5.29143 0.216022
\(601\) 17.8073 0.726375 0.363187 0.931716i \(-0.381688\pi\)
0.363187 + 0.931716i \(0.381688\pi\)
\(602\) −45.6287 −1.85969
\(603\) 12.5098 0.509437
\(604\) −9.63220 −0.391929
\(605\) −9.74874 −0.396343
\(606\) −23.3264 −0.947569
\(607\) 36.1296 1.46646 0.733228 0.679983i \(-0.238013\pi\)
0.733228 + 0.679983i \(0.238013\pi\)
\(608\) −11.5054 −0.466607
\(609\) 21.0879 0.854524
\(610\) −3.34588 −0.135471
\(611\) 12.7221 0.514683
\(612\) −0.621643 −0.0251284
\(613\) −18.2027 −0.735200 −0.367600 0.929984i \(-0.619821\pi\)
−0.367600 + 0.929984i \(0.619821\pi\)
\(614\) −10.7771 −0.434930
\(615\) −2.31768 −0.0934579
\(616\) −15.7405 −0.634203
\(617\) −12.7703 −0.514114 −0.257057 0.966396i \(-0.582753\pi\)
−0.257057 + 0.966396i \(0.582753\pi\)
\(618\) −12.7684 −0.513621
\(619\) 36.1586 1.45334 0.726668 0.686989i \(-0.241068\pi\)
0.726668 + 0.686989i \(0.241068\pi\)
\(620\) −2.86580 −0.115093
\(621\) −7.59577 −0.304808
\(622\) −21.9376 −0.879619
\(623\) 43.1846 1.73016
\(624\) −7.24577 −0.290063
\(625\) −7.52373 −0.300949
\(626\) −10.1445 −0.405456
\(627\) −7.55638 −0.301773
\(628\) 2.00641 0.0800644
\(629\) −7.70590 −0.307254
\(630\) −8.29108 −0.330325
\(631\) 14.5792 0.580390 0.290195 0.956967i \(-0.406280\pi\)
0.290195 + 0.956967i \(0.406280\pi\)
\(632\) 2.23177 0.0887749
\(633\) −18.9281 −0.752324
\(634\) 10.2961 0.408910
\(635\) 9.09345 0.360862
\(636\) −4.52094 −0.179267
\(637\) −4.43621 −0.175769
\(638\) −24.1456 −0.955934
\(639\) −13.6580 −0.540304
\(640\) −22.0743 −0.872562
\(641\) −44.9190 −1.77420 −0.887098 0.461582i \(-0.847282\pi\)
−0.887098 + 0.461582i \(0.847282\pi\)
\(642\) −1.09680 −0.0432874
\(643\) 30.2735 1.19387 0.596935 0.802290i \(-0.296385\pi\)
0.596935 + 0.802290i \(0.296385\pi\)
\(644\) 14.9121 0.587619
\(645\) −14.4685 −0.569697
\(646\) −5.47843 −0.215546
\(647\) −14.7042 −0.578080 −0.289040 0.957317i \(-0.593336\pi\)
−0.289040 + 0.957317i \(0.593336\pi\)
\(648\) 2.23177 0.0876720
\(649\) −4.08060 −0.160177
\(650\) −5.72719 −0.224639
\(651\) 8.97910 0.351919
\(652\) −4.23075 −0.165689
\(653\) −20.0540 −0.784773 −0.392386 0.919800i \(-0.628350\pi\)
−0.392386 + 0.919800i \(0.628350\pi\)
\(654\) 21.7169 0.849197
\(655\) 9.88782 0.386349
\(656\) −6.94240 −0.271055
\(657\) 13.7920 0.538077
\(658\) 43.6057 1.69993
\(659\) 30.2599 1.17876 0.589379 0.807857i \(-0.299373\pi\)
0.589379 + 0.807857i \(0.299373\pi\)
\(660\) 2.25104 0.0876218
\(661\) −2.25883 −0.0878584 −0.0439292 0.999035i \(-0.513988\pi\)
−0.0439292 + 0.999035i \(0.513988\pi\)
\(662\) −32.4141 −1.25981
\(663\) −1.49187 −0.0579393
\(664\) 25.4797 0.988806
\(665\) −17.3258 −0.671866
\(666\) −12.4770 −0.483474
\(667\) −50.7200 −1.96388
\(668\) 0.768921 0.0297504
\(669\) −5.30056 −0.204932
\(670\) −32.8424 −1.26881
\(671\) −2.84622 −0.109877
\(672\) −10.7389 −0.414261
\(673\) −47.7731 −1.84152 −0.920759 0.390132i \(-0.872429\pi\)
−0.920759 + 0.390132i \(0.872429\pi\)
\(674\) −25.0000 −0.962964
\(675\) 2.37096 0.0912584
\(676\) −6.69779 −0.257607
\(677\) 22.6881 0.871975 0.435988 0.899953i \(-0.356399\pi\)
0.435988 + 0.899953i \(0.356399\pi\)
\(678\) 1.09997 0.0422439
\(679\) 12.2787 0.471214
\(680\) −3.61865 −0.138769
\(681\) −23.4772 −0.899648
\(682\) −10.2811 −0.393682
\(683\) 43.5046 1.66466 0.832328 0.554284i \(-0.187008\pi\)
0.832328 + 0.554284i \(0.187008\pi\)
\(684\) −2.10334 −0.0804234
\(685\) 35.8192 1.36858
\(686\) 20.5888 0.786082
\(687\) −27.5049 −1.04938
\(688\) −43.3391 −1.65229
\(689\) −10.8497 −0.413340
\(690\) 19.9415 0.759159
\(691\) −43.9353 −1.67138 −0.835689 0.549204i \(-0.814931\pi\)
−0.835689 + 0.549204i \(0.814931\pi\)
\(692\) −12.0702 −0.458842
\(693\) −7.05294 −0.267919
\(694\) −35.1237 −1.33328
\(695\) 13.0672 0.495666
\(696\) 14.9024 0.564873
\(697\) −1.42941 −0.0541426
\(698\) 22.7078 0.859505
\(699\) −3.58508 −0.135600
\(700\) −4.65470 −0.175931
\(701\) 40.0941 1.51433 0.757167 0.653221i \(-0.226583\pi\)
0.757167 + 0.653221i \(0.226583\pi\)
\(702\) −2.41555 −0.0911692
\(703\) −26.0731 −0.983366
\(704\) −9.39744 −0.354179
\(705\) 13.8270 0.520756
\(706\) −45.0310 −1.69476
\(707\) −45.4974 −1.71110
\(708\) −1.13585 −0.0426878
\(709\) 49.7636 1.86891 0.934455 0.356082i \(-0.115887\pi\)
0.934455 + 0.356082i \(0.115887\pi\)
\(710\) 35.8570 1.34569
\(711\) 1.00000 0.0375029
\(712\) 30.5177 1.14370
\(713\) −21.5963 −0.808787
\(714\) −5.11343 −0.191365
\(715\) 5.40223 0.202032
\(716\) 5.25718 0.196470
\(717\) −5.46987 −0.204276
\(718\) 50.4857 1.88411
\(719\) 15.8344 0.590524 0.295262 0.955416i \(-0.404593\pi\)
0.295262 + 0.955416i \(0.404593\pi\)
\(720\) −7.87504 −0.293485
\(721\) −24.9044 −0.927488
\(722\) 12.2274 0.455057
\(723\) −3.55333 −0.132150
\(724\) 4.80581 0.178607
\(725\) 15.8318 0.587980
\(726\) −9.73502 −0.361300
\(727\) −14.8752 −0.551692 −0.275846 0.961202i \(-0.588958\pi\)
−0.275846 + 0.961202i \(0.588958\pi\)
\(728\) −10.5149 −0.389707
\(729\) 1.00000 0.0370370
\(730\) −36.2087 −1.34014
\(731\) −8.92330 −0.330040
\(732\) −0.792256 −0.0292826
\(733\) −27.6577 −1.02156 −0.510780 0.859712i \(-0.670643\pi\)
−0.510780 + 0.859712i \(0.670643\pi\)
\(734\) −5.73852 −0.211813
\(735\) −4.82148 −0.177843
\(736\) 25.8289 0.952064
\(737\) −27.9379 −1.02911
\(738\) −2.31442 −0.0851950
\(739\) −12.5623 −0.462111 −0.231056 0.972941i \(-0.574218\pi\)
−0.231056 + 0.972941i \(0.574218\pi\)
\(740\) 7.76717 0.285527
\(741\) −5.04777 −0.185434
\(742\) −37.1878 −1.36521
\(743\) −13.5845 −0.498368 −0.249184 0.968456i \(-0.580162\pi\)
−0.249184 + 0.968456i \(0.580162\pi\)
\(744\) 6.34535 0.232632
\(745\) −38.0064 −1.39245
\(746\) −26.2218 −0.960047
\(747\) 11.4169 0.417721
\(748\) 1.38831 0.0507615
\(749\) −2.13928 −0.0781676
\(750\) −19.3513 −0.706608
\(751\) −7.06287 −0.257728 −0.128864 0.991662i \(-0.541133\pi\)
−0.128864 + 0.991662i \(0.541133\pi\)
\(752\) 41.4176 1.51034
\(753\) −7.07969 −0.257998
\(754\) −16.1296 −0.587406
\(755\) −25.1237 −0.914344
\(756\) −1.96321 −0.0714013
\(757\) −15.0811 −0.548131 −0.274065 0.961711i \(-0.588368\pi\)
−0.274065 + 0.961711i \(0.588368\pi\)
\(758\) −0.495205 −0.0179867
\(759\) 16.9635 0.615737
\(760\) −12.2438 −0.444129
\(761\) −3.89985 −0.141370 −0.0706848 0.997499i \(-0.522518\pi\)
−0.0706848 + 0.997499i \(0.522518\pi\)
\(762\) 9.08065 0.328957
\(763\) 42.3581 1.53347
\(764\) 1.28773 0.0465885
\(765\) −1.62143 −0.0586230
\(766\) −45.1726 −1.63215
\(767\) −2.72590 −0.0984264
\(768\) −13.6274 −0.491736
\(769\) 22.9657 0.828163 0.414081 0.910240i \(-0.364103\pi\)
0.414081 + 0.910240i \(0.364103\pi\)
\(770\) 18.5164 0.667283
\(771\) 23.4337 0.843943
\(772\) 14.4194 0.518965
\(773\) 37.3634 1.34387 0.671933 0.740611i \(-0.265464\pi\)
0.671933 + 0.740611i \(0.265464\pi\)
\(774\) −14.4482 −0.519328
\(775\) 6.74111 0.242148
\(776\) 8.67713 0.311491
\(777\) −24.3360 −0.873049
\(778\) 48.4854 1.73829
\(779\) −4.83643 −0.173283
\(780\) 1.50373 0.0538421
\(781\) 30.5023 1.09146
\(782\) 12.2987 0.439800
\(783\) 6.67740 0.238631
\(784\) −14.4423 −0.515796
\(785\) 5.23331 0.186785
\(786\) 9.87391 0.352191
\(787\) −3.15418 −0.112434 −0.0562172 0.998419i \(-0.517904\pi\)
−0.0562172 + 0.998419i \(0.517904\pi\)
\(788\) −2.43382 −0.0867013
\(789\) 26.7469 0.952214
\(790\) −2.62534 −0.0934053
\(791\) 2.14545 0.0762834
\(792\) −4.98417 −0.177105
\(793\) −1.90132 −0.0675178
\(794\) 22.2342 0.789064
\(795\) −11.7920 −0.418218
\(796\) 3.25957 0.115533
\(797\) 49.4204 1.75056 0.875281 0.483615i \(-0.160676\pi\)
0.875281 + 0.483615i \(0.160676\pi\)
\(798\) −17.3014 −0.612464
\(799\) 8.52767 0.301687
\(800\) −8.06228 −0.285045
\(801\) 13.6742 0.483156
\(802\) 63.4600 2.24085
\(803\) −30.8015 −1.08696
\(804\) −7.77661 −0.274260
\(805\) 38.8952 1.37088
\(806\) −6.86789 −0.241911
\(807\) −11.0733 −0.389798
\(808\) −32.1521 −1.13111
\(809\) −32.1831 −1.13150 −0.565748 0.824578i \(-0.691413\pi\)
−0.565748 + 0.824578i \(0.691413\pi\)
\(810\) −2.62534 −0.0922450
\(811\) 45.7157 1.60530 0.802648 0.596453i \(-0.203424\pi\)
0.802648 + 0.596453i \(0.203424\pi\)
\(812\) −13.1091 −0.460040
\(813\) −10.7445 −0.376826
\(814\) 27.8647 0.976658
\(815\) −11.0351 −0.386541
\(816\) −4.85685 −0.170024
\(817\) −30.1922 −1.05629
\(818\) 47.6599 1.66639
\(819\) −4.71146 −0.164632
\(820\) 1.44077 0.0503139
\(821\) −4.37264 −0.152606 −0.0763032 0.997085i \(-0.524312\pi\)
−0.0763032 + 0.997085i \(0.524312\pi\)
\(822\) 35.7688 1.24758
\(823\) −6.74665 −0.235173 −0.117587 0.993063i \(-0.537516\pi\)
−0.117587 + 0.993063i \(0.537516\pi\)
\(824\) −17.5994 −0.613105
\(825\) −5.29504 −0.184350
\(826\) −9.34312 −0.325089
\(827\) 11.4276 0.397377 0.198688 0.980063i \(-0.436332\pi\)
0.198688 + 0.980063i \(0.436332\pi\)
\(828\) 4.72186 0.164096
\(829\) −37.9600 −1.31840 −0.659202 0.751966i \(-0.729106\pi\)
−0.659202 + 0.751966i \(0.729106\pi\)
\(830\) −29.9731 −1.04038
\(831\) −17.5287 −0.608063
\(832\) −6.27762 −0.217637
\(833\) −2.97359 −0.103029
\(834\) 13.0488 0.451843
\(835\) 2.00557 0.0694058
\(836\) 4.69737 0.162462
\(837\) 2.84320 0.0982752
\(838\) 50.8585 1.75688
\(839\) −24.5052 −0.846014 −0.423007 0.906126i \(-0.639025\pi\)
−0.423007 + 0.906126i \(0.639025\pi\)
\(840\) −11.4281 −0.394306
\(841\) 15.5876 0.537504
\(842\) 18.6670 0.643308
\(843\) −27.0469 −0.931544
\(844\) 11.7665 0.405020
\(845\) −17.4698 −0.600981
\(846\) 13.8076 0.474714
\(847\) −18.9879 −0.652430
\(848\) −35.3217 −1.21295
\(849\) −15.0432 −0.516283
\(850\) −3.83894 −0.131675
\(851\) 58.5323 2.00646
\(852\) 8.49043 0.290877
\(853\) −39.6239 −1.35670 −0.678348 0.734740i \(-0.737304\pi\)
−0.678348 + 0.734740i \(0.737304\pi\)
\(854\) −6.51684 −0.223002
\(855\) −5.48615 −0.187622
\(856\) −1.51179 −0.0516718
\(857\) −56.5569 −1.93195 −0.965974 0.258641i \(-0.916725\pi\)
−0.965974 + 0.258641i \(0.916725\pi\)
\(858\) 5.39463 0.184169
\(859\) 26.9328 0.918935 0.459467 0.888195i \(-0.348040\pi\)
0.459467 + 0.888195i \(0.348040\pi\)
\(860\) 8.99425 0.306702
\(861\) −4.51420 −0.153844
\(862\) 30.1512 1.02696
\(863\) −44.6636 −1.52037 −0.760183 0.649709i \(-0.774891\pi\)
−0.760183 + 0.649709i \(0.774891\pi\)
\(864\) −3.40043 −0.115685
\(865\) −31.4828 −1.07045
\(866\) −22.5884 −0.767586
\(867\) −1.00000 −0.0339618
\(868\) −5.58179 −0.189458
\(869\) −2.23329 −0.0757591
\(870\) −17.5304 −0.594337
\(871\) −18.6629 −0.632369
\(872\) 29.9336 1.01368
\(873\) 3.88801 0.131589
\(874\) 41.6129 1.40758
\(875\) −37.7440 −1.27598
\(876\) −8.57370 −0.289679
\(877\) 9.47023 0.319787 0.159893 0.987134i \(-0.448885\pi\)
0.159893 + 0.987134i \(0.448885\pi\)
\(878\) −52.2886 −1.76465
\(879\) 7.92022 0.267142
\(880\) 17.5872 0.592865
\(881\) −0.573540 −0.0193230 −0.00966152 0.999953i \(-0.503075\pi\)
−0.00966152 + 0.999953i \(0.503075\pi\)
\(882\) −4.81469 −0.162119
\(883\) −35.0880 −1.18080 −0.590402 0.807109i \(-0.701031\pi\)
−0.590402 + 0.807109i \(0.701031\pi\)
\(884\) 0.927408 0.0311921
\(885\) −2.96263 −0.0995878
\(886\) 48.0004 1.61261
\(887\) 10.4708 0.351575 0.175787 0.984428i \(-0.443753\pi\)
0.175787 + 0.984428i \(0.443753\pi\)
\(888\) −17.1978 −0.577119
\(889\) 17.7115 0.594025
\(890\) −35.8995 −1.20335
\(891\) −2.23329 −0.0748179
\(892\) 3.29506 0.110327
\(893\) 28.8536 0.965548
\(894\) −37.9529 −1.26934
\(895\) 13.7123 0.458351
\(896\) −42.9946 −1.43635
\(897\) 11.3319 0.378360
\(898\) 5.46384 0.182331
\(899\) 18.9851 0.633190
\(900\) −1.47389 −0.0491297
\(901\) −7.27256 −0.242284
\(902\) 5.16876 0.172101
\(903\) −28.1807 −0.937794
\(904\) 1.51615 0.0504263
\(905\) 12.5350 0.416677
\(906\) −25.0883 −0.833503
\(907\) −23.5870 −0.783194 −0.391597 0.920137i \(-0.628077\pi\)
−0.391597 + 0.920137i \(0.628077\pi\)
\(908\) 14.5944 0.484333
\(909\) −14.4066 −0.477836
\(910\) 12.3692 0.410035
\(911\) 36.7261 1.21679 0.608395 0.793634i \(-0.291814\pi\)
0.608395 + 0.793634i \(0.291814\pi\)
\(912\) −16.4333 −0.544160
\(913\) −25.4971 −0.843831
\(914\) −6.36018 −0.210376
\(915\) −2.06644 −0.0683145
\(916\) 17.0982 0.564941
\(917\) 19.2588 0.635980
\(918\) −1.61915 −0.0534399
\(919\) 5.83442 0.192460 0.0962298 0.995359i \(-0.469322\pi\)
0.0962298 + 0.995359i \(0.469322\pi\)
\(920\) 27.4865 0.906202
\(921\) −6.65605 −0.219324
\(922\) 1.17732 0.0387730
\(923\) 20.3760 0.670684
\(924\) 4.38441 0.144237
\(925\) −18.2704 −0.600727
\(926\) 29.8804 0.981931
\(927\) −7.88588 −0.259006
\(928\) −22.7060 −0.745361
\(929\) −31.9313 −1.04763 −0.523815 0.851832i \(-0.675492\pi\)
−0.523815 + 0.851832i \(0.675492\pi\)
\(930\) −7.46435 −0.244766
\(931\) −10.0612 −0.329744
\(932\) 2.22864 0.0730014
\(933\) −13.5489 −0.443570
\(934\) −42.3248 −1.38491
\(935\) 3.62112 0.118423
\(936\) −3.32950 −0.108828
\(937\) 19.3220 0.631223 0.315611 0.948889i \(-0.397790\pi\)
0.315611 + 0.948889i \(0.397790\pi\)
\(938\) −63.9679 −2.08863
\(939\) −6.26533 −0.204461
\(940\) −8.59547 −0.280353
\(941\) −8.27759 −0.269842 −0.134921 0.990856i \(-0.543078\pi\)
−0.134921 + 0.990856i \(0.543078\pi\)
\(942\) 5.22595 0.170271
\(943\) 10.8574 0.353567
\(944\) −8.87429 −0.288834
\(945\) −5.12064 −0.166574
\(946\) 32.2669 1.04909
\(947\) 37.9224 1.23231 0.616155 0.787625i \(-0.288689\pi\)
0.616155 + 0.787625i \(0.288689\pi\)
\(948\) −0.621643 −0.0201900
\(949\) −20.5758 −0.667920
\(950\) −12.9892 −0.421424
\(951\) 6.35895 0.206203
\(952\) −7.04814 −0.228431
\(953\) 32.2004 1.04307 0.521537 0.853229i \(-0.325359\pi\)
0.521537 + 0.853229i \(0.325359\pi\)
\(954\) −11.7754 −0.381241
\(955\) 3.35879 0.108688
\(956\) 3.40031 0.109974
\(957\) −14.9125 −0.482054
\(958\) −62.8088 −2.02926
\(959\) 69.7659 2.25286
\(960\) −6.82281 −0.220205
\(961\) −22.9162 −0.739233
\(962\) 18.6140 0.600140
\(963\) −0.677395 −0.0218287
\(964\) 2.20891 0.0711441
\(965\) 37.6100 1.21071
\(966\) 38.8405 1.24967
\(967\) 49.6081 1.59529 0.797644 0.603128i \(-0.206079\pi\)
0.797644 + 0.603128i \(0.206079\pi\)
\(968\) −13.4183 −0.431282
\(969\) −3.38353 −0.108694
\(970\) −10.2073 −0.327738
\(971\) 52.9617 1.69962 0.849811 0.527087i \(-0.176716\pi\)
0.849811 + 0.527087i \(0.176716\pi\)
\(972\) −0.621643 −0.0199392
\(973\) 25.4513 0.815930
\(974\) −44.6062 −1.42928
\(975\) −3.53716 −0.113280
\(976\) −6.18983 −0.198132
\(977\) 42.1723 1.34921 0.674605 0.738179i \(-0.264314\pi\)
0.674605 + 0.738179i \(0.264314\pi\)
\(978\) −11.0195 −0.352366
\(979\) −30.5385 −0.976015
\(980\) 2.99724 0.0957433
\(981\) 13.4125 0.428229
\(982\) 3.00837 0.0960008
\(983\) 5.06917 0.161682 0.0808408 0.996727i \(-0.474239\pi\)
0.0808408 + 0.996727i \(0.474239\pi\)
\(984\) −3.19010 −0.101697
\(985\) −6.34814 −0.202268
\(986\) −10.8117 −0.344315
\(987\) 26.9312 0.857231
\(988\) 3.13791 0.0998302
\(989\) 67.7794 2.15526
\(990\) 5.86313 0.186343
\(991\) −31.7938 −1.00996 −0.504982 0.863130i \(-0.668501\pi\)
−0.504982 + 0.863130i \(0.668501\pi\)
\(992\) −9.66808 −0.306962
\(993\) −20.0192 −0.635290
\(994\) 69.8395 2.21517
\(995\) 8.50195 0.269530
\(996\) −7.09721 −0.224884
\(997\) −40.1702 −1.27220 −0.636101 0.771605i \(-0.719454\pi\)
−0.636101 + 0.771605i \(0.719454\pi\)
\(998\) 21.8127 0.690469
\(999\) −7.70590 −0.243804
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.1.9 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.9 32 1.1 even 1 trivial