Properties

Label 4029.2.a.l.1.8
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 1.8
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.67650 q^{2} -1.00000 q^{3} +0.810659 q^{4} -3.83953 q^{5} +1.67650 q^{6} -4.72769 q^{7} +1.99393 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.67650 q^{2} -1.00000 q^{3} +0.810659 q^{4} -3.83953 q^{5} +1.67650 q^{6} -4.72769 q^{7} +1.99393 q^{8} +1.00000 q^{9} +6.43697 q^{10} +6.37239 q^{11} -0.810659 q^{12} +6.95110 q^{13} +7.92599 q^{14} +3.83953 q^{15} -4.96415 q^{16} -1.00000 q^{17} -1.67650 q^{18} +6.78856 q^{19} -3.11255 q^{20} +4.72769 q^{21} -10.6833 q^{22} +5.35418 q^{23} -1.99393 q^{24} +9.74196 q^{25} -11.6535 q^{26} -1.00000 q^{27} -3.83255 q^{28} -3.88066 q^{29} -6.43697 q^{30} -4.37999 q^{31} +4.33454 q^{32} -6.37239 q^{33} +1.67650 q^{34} +18.1521 q^{35} +0.810659 q^{36} -1.41918 q^{37} -11.3810 q^{38} -6.95110 q^{39} -7.65575 q^{40} +6.61973 q^{41} -7.92599 q^{42} +11.3206 q^{43} +5.16583 q^{44} -3.83953 q^{45} -8.97629 q^{46} +3.03205 q^{47} +4.96415 q^{48} +15.3511 q^{49} -16.3324 q^{50} +1.00000 q^{51} +5.63497 q^{52} -3.69509 q^{53} +1.67650 q^{54} -24.4669 q^{55} -9.42670 q^{56} -6.78856 q^{57} +6.50593 q^{58} -0.276229 q^{59} +3.11255 q^{60} +4.92566 q^{61} +7.34307 q^{62} -4.72769 q^{63} +2.66143 q^{64} -26.6889 q^{65} +10.6833 q^{66} -4.08227 q^{67} -0.810659 q^{68} -5.35418 q^{69} -30.4320 q^{70} -10.7630 q^{71} +1.99393 q^{72} +1.10125 q^{73} +2.37926 q^{74} -9.74196 q^{75} +5.50321 q^{76} -30.1267 q^{77} +11.6535 q^{78} +1.00000 q^{79} +19.0600 q^{80} +1.00000 q^{81} -11.0980 q^{82} -3.30768 q^{83} +3.83255 q^{84} +3.83953 q^{85} -18.9790 q^{86} +3.88066 q^{87} +12.7061 q^{88} +9.92560 q^{89} +6.43697 q^{90} -32.8627 q^{91} +4.34041 q^{92} +4.37999 q^{93} -5.08324 q^{94} -26.0648 q^{95} -4.33454 q^{96} +10.7466 q^{97} -25.7361 q^{98} +6.37239 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.67650 −1.18547 −0.592733 0.805399i \(-0.701951\pi\)
−0.592733 + 0.805399i \(0.701951\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.810659 0.405330
\(5\) −3.83953 −1.71709 −0.858544 0.512740i \(-0.828631\pi\)
−0.858544 + 0.512740i \(0.828631\pi\)
\(6\) 1.67650 0.684429
\(7\) −4.72769 −1.78690 −0.893450 0.449162i \(-0.851722\pi\)
−0.893450 + 0.449162i \(0.851722\pi\)
\(8\) 1.99393 0.704962
\(9\) 1.00000 0.333333
\(10\) 6.43697 2.03555
\(11\) 6.37239 1.92135 0.960673 0.277681i \(-0.0895657\pi\)
0.960673 + 0.277681i \(0.0895657\pi\)
\(12\) −0.810659 −0.234017
\(13\) 6.95110 1.92789 0.963944 0.266105i \(-0.0857369\pi\)
0.963944 + 0.266105i \(0.0857369\pi\)
\(14\) 7.92599 2.11831
\(15\) 3.83953 0.991361
\(16\) −4.96415 −1.24104
\(17\) −1.00000 −0.242536
\(18\) −1.67650 −0.395155
\(19\) 6.78856 1.55740 0.778701 0.627396i \(-0.215879\pi\)
0.778701 + 0.627396i \(0.215879\pi\)
\(20\) −3.11255 −0.695987
\(21\) 4.72769 1.03167
\(22\) −10.6833 −2.27769
\(23\) 5.35418 1.11642 0.558212 0.829699i \(-0.311488\pi\)
0.558212 + 0.829699i \(0.311488\pi\)
\(24\) −1.99393 −0.407010
\(25\) 9.74196 1.94839
\(26\) −11.6535 −2.28545
\(27\) −1.00000 −0.192450
\(28\) −3.83255 −0.724284
\(29\) −3.88066 −0.720620 −0.360310 0.932833i \(-0.617329\pi\)
−0.360310 + 0.932833i \(0.617329\pi\)
\(30\) −6.43697 −1.17523
\(31\) −4.37999 −0.786670 −0.393335 0.919395i \(-0.628679\pi\)
−0.393335 + 0.919395i \(0.628679\pi\)
\(32\) 4.33454 0.766246
\(33\) −6.37239 −1.10929
\(34\) 1.67650 0.287518
\(35\) 18.1521 3.06827
\(36\) 0.810659 0.135110
\(37\) −1.41918 −0.233312 −0.116656 0.993172i \(-0.537217\pi\)
−0.116656 + 0.993172i \(0.537217\pi\)
\(38\) −11.3810 −1.84625
\(39\) −6.95110 −1.11307
\(40\) −7.65575 −1.21048
\(41\) 6.61973 1.03383 0.516914 0.856037i \(-0.327081\pi\)
0.516914 + 0.856037i \(0.327081\pi\)
\(42\) −7.92599 −1.22301
\(43\) 11.3206 1.72637 0.863186 0.504886i \(-0.168466\pi\)
0.863186 + 0.504886i \(0.168466\pi\)
\(44\) 5.16583 0.778779
\(45\) −3.83953 −0.572363
\(46\) −8.97629 −1.32348
\(47\) 3.03205 0.442270 0.221135 0.975243i \(-0.429024\pi\)
0.221135 + 0.975243i \(0.429024\pi\)
\(48\) 4.96415 0.716513
\(49\) 15.3511 2.19301
\(50\) −16.3324 −2.30975
\(51\) 1.00000 0.140028
\(52\) 5.63497 0.781430
\(53\) −3.69509 −0.507559 −0.253780 0.967262i \(-0.581674\pi\)
−0.253780 + 0.967262i \(0.581674\pi\)
\(54\) 1.67650 0.228143
\(55\) −24.4669 −3.29912
\(56\) −9.42670 −1.25970
\(57\) −6.78856 −0.899166
\(58\) 6.50593 0.854271
\(59\) −0.276229 −0.0359619 −0.0179810 0.999838i \(-0.505724\pi\)
−0.0179810 + 0.999838i \(0.505724\pi\)
\(60\) 3.11255 0.401828
\(61\) 4.92566 0.630666 0.315333 0.948981i \(-0.397884\pi\)
0.315333 + 0.948981i \(0.397884\pi\)
\(62\) 7.34307 0.932571
\(63\) −4.72769 −0.595633
\(64\) 2.66143 0.332679
\(65\) −26.6889 −3.31035
\(66\) 10.6833 1.31503
\(67\) −4.08227 −0.498729 −0.249364 0.968410i \(-0.580222\pi\)
−0.249364 + 0.968410i \(0.580222\pi\)
\(68\) −0.810659 −0.0983069
\(69\) −5.35418 −0.644567
\(70\) −30.4320 −3.63732
\(71\) −10.7630 −1.27733 −0.638667 0.769483i \(-0.720514\pi\)
−0.638667 + 0.769483i \(0.720514\pi\)
\(72\) 1.99393 0.234987
\(73\) 1.10125 0.128891 0.0644456 0.997921i \(-0.479472\pi\)
0.0644456 + 0.997921i \(0.479472\pi\)
\(74\) 2.37926 0.276583
\(75\) −9.74196 −1.12490
\(76\) 5.50321 0.631261
\(77\) −30.1267 −3.43326
\(78\) 11.6535 1.31950
\(79\) 1.00000 0.112509
\(80\) 19.0600 2.13097
\(81\) 1.00000 0.111111
\(82\) −11.0980 −1.22557
\(83\) −3.30768 −0.363066 −0.181533 0.983385i \(-0.558106\pi\)
−0.181533 + 0.983385i \(0.558106\pi\)
\(84\) 3.83255 0.418165
\(85\) 3.83953 0.416455
\(86\) −18.9790 −2.04655
\(87\) 3.88066 0.416050
\(88\) 12.7061 1.35448
\(89\) 9.92560 1.05211 0.526056 0.850450i \(-0.323670\pi\)
0.526056 + 0.850450i \(0.323670\pi\)
\(90\) 6.43697 0.678517
\(91\) −32.8627 −3.44494
\(92\) 4.34041 0.452519
\(93\) 4.37999 0.454184
\(94\) −5.08324 −0.524296
\(95\) −26.0648 −2.67420
\(96\) −4.33454 −0.442392
\(97\) 10.7466 1.09116 0.545578 0.838060i \(-0.316310\pi\)
0.545578 + 0.838060i \(0.316310\pi\)
\(98\) −25.7361 −2.59974
\(99\) 6.37239 0.640449
\(100\) 7.89741 0.789741
\(101\) −2.96492 −0.295021 −0.147510 0.989061i \(-0.547126\pi\)
−0.147510 + 0.989061i \(0.547126\pi\)
\(102\) −1.67650 −0.165998
\(103\) 3.79769 0.374197 0.187099 0.982341i \(-0.440092\pi\)
0.187099 + 0.982341i \(0.440092\pi\)
\(104\) 13.8600 1.35909
\(105\) −18.1521 −1.77146
\(106\) 6.19482 0.601694
\(107\) −4.59844 −0.444548 −0.222274 0.974984i \(-0.571348\pi\)
−0.222274 + 0.974984i \(0.571348\pi\)
\(108\) −0.810659 −0.0780057
\(109\) 3.43875 0.329372 0.164686 0.986346i \(-0.447339\pi\)
0.164686 + 0.986346i \(0.447339\pi\)
\(110\) 41.0189 3.91100
\(111\) 1.41918 0.134703
\(112\) 23.4690 2.21761
\(113\) 2.48008 0.233306 0.116653 0.993173i \(-0.462783\pi\)
0.116653 + 0.993173i \(0.462783\pi\)
\(114\) 11.3810 1.06593
\(115\) −20.5575 −1.91700
\(116\) −3.14589 −0.292089
\(117\) 6.95110 0.642629
\(118\) 0.463098 0.0426316
\(119\) 4.72769 0.433387
\(120\) 7.65575 0.698872
\(121\) 29.6073 2.69157
\(122\) −8.25787 −0.747633
\(123\) −6.61973 −0.596881
\(124\) −3.55068 −0.318861
\(125\) −18.2069 −1.62847
\(126\) 7.92599 0.706103
\(127\) 0.406380 0.0360604 0.0180302 0.999837i \(-0.494260\pi\)
0.0180302 + 0.999837i \(0.494260\pi\)
\(128\) −13.1310 −1.16063
\(129\) −11.3206 −0.996721
\(130\) 44.7440 3.92431
\(131\) 18.2641 1.59574 0.797869 0.602831i \(-0.205961\pi\)
0.797869 + 0.602831i \(0.205961\pi\)
\(132\) −5.16583 −0.449628
\(133\) −32.0942 −2.78292
\(134\) 6.84394 0.591226
\(135\) 3.83953 0.330454
\(136\) −1.99393 −0.170978
\(137\) −21.4296 −1.83086 −0.915429 0.402480i \(-0.868148\pi\)
−0.915429 + 0.402480i \(0.868148\pi\)
\(138\) 8.97629 0.764112
\(139\) −6.87852 −0.583428 −0.291714 0.956506i \(-0.594226\pi\)
−0.291714 + 0.956506i \(0.594226\pi\)
\(140\) 14.7152 1.24366
\(141\) −3.03205 −0.255345
\(142\) 18.0442 1.51424
\(143\) 44.2951 3.70414
\(144\) −4.96415 −0.413679
\(145\) 14.8999 1.23737
\(146\) −1.84624 −0.152796
\(147\) −15.3511 −1.26614
\(148\) −1.15047 −0.0945682
\(149\) 12.5327 1.02672 0.513361 0.858173i \(-0.328400\pi\)
0.513361 + 0.858173i \(0.328400\pi\)
\(150\) 16.3324 1.33354
\(151\) 5.31777 0.432754 0.216377 0.976310i \(-0.430576\pi\)
0.216377 + 0.976310i \(0.430576\pi\)
\(152\) 13.5359 1.09791
\(153\) −1.00000 −0.0808452
\(154\) 50.5075 4.07001
\(155\) 16.8171 1.35078
\(156\) −5.63497 −0.451159
\(157\) 9.23022 0.736652 0.368326 0.929697i \(-0.379931\pi\)
0.368326 + 0.929697i \(0.379931\pi\)
\(158\) −1.67650 −0.133375
\(159\) 3.69509 0.293039
\(160\) −16.6426 −1.31571
\(161\) −25.3129 −1.99494
\(162\) −1.67650 −0.131718
\(163\) −2.51559 −0.197037 −0.0985183 0.995135i \(-0.531410\pi\)
−0.0985183 + 0.995135i \(0.531410\pi\)
\(164\) 5.36635 0.419041
\(165\) 24.4669 1.90475
\(166\) 5.54534 0.430402
\(167\) −9.03274 −0.698975 −0.349487 0.936941i \(-0.613644\pi\)
−0.349487 + 0.936941i \(0.613644\pi\)
\(168\) 9.42670 0.727286
\(169\) 35.3178 2.71675
\(170\) −6.43697 −0.493693
\(171\) 6.78856 0.519134
\(172\) 9.17713 0.699750
\(173\) −19.7222 −1.49945 −0.749725 0.661750i \(-0.769814\pi\)
−0.749725 + 0.661750i \(0.769814\pi\)
\(174\) −6.50593 −0.493214
\(175\) −46.0570 −3.48158
\(176\) −31.6335 −2.38446
\(177\) 0.276229 0.0207626
\(178\) −16.6403 −1.24724
\(179\) −9.96833 −0.745068 −0.372534 0.928018i \(-0.621511\pi\)
−0.372534 + 0.928018i \(0.621511\pi\)
\(180\) −3.11255 −0.231996
\(181\) 17.2092 1.27915 0.639576 0.768728i \(-0.279110\pi\)
0.639576 + 0.768728i \(0.279110\pi\)
\(182\) 55.0943 4.08386
\(183\) −4.92566 −0.364115
\(184\) 10.6759 0.787035
\(185\) 5.44898 0.400617
\(186\) −7.34307 −0.538420
\(187\) −6.37239 −0.465995
\(188\) 2.45796 0.179265
\(189\) 4.72769 0.343889
\(190\) 43.6978 3.17017
\(191\) −5.04833 −0.365284 −0.182642 0.983179i \(-0.558465\pi\)
−0.182642 + 0.983179i \(0.558465\pi\)
\(192\) −2.66143 −0.192072
\(193\) −11.0035 −0.792049 −0.396024 0.918240i \(-0.629610\pi\)
−0.396024 + 0.918240i \(0.629610\pi\)
\(194\) −18.0168 −1.29353
\(195\) 26.6889 1.91123
\(196\) 12.4445 0.888893
\(197\) 18.2973 1.30363 0.651813 0.758380i \(-0.274009\pi\)
0.651813 + 0.758380i \(0.274009\pi\)
\(198\) −10.6833 −0.759230
\(199\) 3.98259 0.282319 0.141159 0.989987i \(-0.454917\pi\)
0.141159 + 0.989987i \(0.454917\pi\)
\(200\) 19.4248 1.37354
\(201\) 4.08227 0.287941
\(202\) 4.97070 0.349737
\(203\) 18.3466 1.28768
\(204\) 0.810659 0.0567575
\(205\) −25.4166 −1.77518
\(206\) −6.36683 −0.443598
\(207\) 5.35418 0.372141
\(208\) −34.5063 −2.39258
\(209\) 43.2593 2.99231
\(210\) 30.4320 2.10001
\(211\) 19.0801 1.31353 0.656766 0.754095i \(-0.271924\pi\)
0.656766 + 0.754095i \(0.271924\pi\)
\(212\) −2.99546 −0.205729
\(213\) 10.7630 0.737470
\(214\) 7.70929 0.526996
\(215\) −43.4656 −2.96433
\(216\) −1.99393 −0.135670
\(217\) 20.7073 1.40570
\(218\) −5.76506 −0.390459
\(219\) −1.10125 −0.0744154
\(220\) −19.8344 −1.33723
\(221\) −6.95110 −0.467581
\(222\) −2.37926 −0.159685
\(223\) 13.1357 0.879630 0.439815 0.898088i \(-0.355044\pi\)
0.439815 + 0.898088i \(0.355044\pi\)
\(224\) −20.4924 −1.36921
\(225\) 9.74196 0.649464
\(226\) −4.15785 −0.276576
\(227\) −17.1471 −1.13810 −0.569048 0.822304i \(-0.692688\pi\)
−0.569048 + 0.822304i \(0.692688\pi\)
\(228\) −5.50321 −0.364459
\(229\) −11.9431 −0.789220 −0.394610 0.918849i \(-0.629120\pi\)
−0.394610 + 0.918849i \(0.629120\pi\)
\(230\) 34.4647 2.27253
\(231\) 30.1267 1.98219
\(232\) −7.73777 −0.508010
\(233\) −1.82958 −0.119860 −0.0599299 0.998203i \(-0.519088\pi\)
−0.0599299 + 0.998203i \(0.519088\pi\)
\(234\) −11.6535 −0.761815
\(235\) −11.6416 −0.759417
\(236\) −0.223927 −0.0145764
\(237\) −1.00000 −0.0649570
\(238\) −7.92599 −0.513766
\(239\) 17.2064 1.11299 0.556495 0.830851i \(-0.312146\pi\)
0.556495 + 0.830851i \(0.312146\pi\)
\(240\) −19.0600 −1.23032
\(241\) −6.89593 −0.444206 −0.222103 0.975023i \(-0.571292\pi\)
−0.222103 + 0.975023i \(0.571292\pi\)
\(242\) −49.6367 −3.19077
\(243\) −1.00000 −0.0641500
\(244\) 3.99303 0.255628
\(245\) −58.9409 −3.76560
\(246\) 11.0980 0.707582
\(247\) 47.1879 3.00250
\(248\) −8.73341 −0.554572
\(249\) 3.30768 0.209616
\(250\) 30.5239 1.93050
\(251\) −29.6853 −1.87372 −0.936860 0.349705i \(-0.886282\pi\)
−0.936860 + 0.349705i \(0.886282\pi\)
\(252\) −3.83255 −0.241428
\(253\) 34.1189 2.14504
\(254\) −0.681298 −0.0427484
\(255\) −3.83953 −0.240440
\(256\) 16.6913 1.04320
\(257\) −3.05355 −0.190475 −0.0952375 0.995455i \(-0.530361\pi\)
−0.0952375 + 0.995455i \(0.530361\pi\)
\(258\) 18.9790 1.18158
\(259\) 6.70945 0.416905
\(260\) −21.6356 −1.34178
\(261\) −3.88066 −0.240207
\(262\) −30.6197 −1.89169
\(263\) −5.81981 −0.358865 −0.179432 0.983770i \(-0.557426\pi\)
−0.179432 + 0.983770i \(0.557426\pi\)
\(264\) −12.7061 −0.782007
\(265\) 14.1874 0.871524
\(266\) 53.8060 3.29906
\(267\) −9.92560 −0.607437
\(268\) −3.30933 −0.202150
\(269\) −2.35629 −0.143666 −0.0718328 0.997417i \(-0.522885\pi\)
−0.0718328 + 0.997417i \(0.522885\pi\)
\(270\) −6.43697 −0.391742
\(271\) 29.5281 1.79370 0.896852 0.442330i \(-0.145848\pi\)
0.896852 + 0.442330i \(0.145848\pi\)
\(272\) 4.96415 0.300996
\(273\) 32.8627 1.98894
\(274\) 35.9268 2.17042
\(275\) 62.0795 3.74354
\(276\) −4.34041 −0.261262
\(277\) −14.5426 −0.873781 −0.436890 0.899515i \(-0.643920\pi\)
−0.436890 + 0.899515i \(0.643920\pi\)
\(278\) 11.5318 0.691634
\(279\) −4.37999 −0.262223
\(280\) 36.1941 2.16301
\(281\) −16.1433 −0.963031 −0.481515 0.876438i \(-0.659913\pi\)
−0.481515 + 0.876438i \(0.659913\pi\)
\(282\) 5.08324 0.302703
\(283\) −9.45035 −0.561765 −0.280882 0.959742i \(-0.590627\pi\)
−0.280882 + 0.959742i \(0.590627\pi\)
\(284\) −8.72514 −0.517742
\(285\) 26.0648 1.54395
\(286\) −74.2608 −4.39113
\(287\) −31.2961 −1.84735
\(288\) 4.33454 0.255415
\(289\) 1.00000 0.0588235
\(290\) −24.9797 −1.46686
\(291\) −10.7466 −0.629979
\(292\) 0.892736 0.0522434
\(293\) 5.12156 0.299204 0.149602 0.988746i \(-0.452201\pi\)
0.149602 + 0.988746i \(0.452201\pi\)
\(294\) 25.7361 1.50096
\(295\) 1.06059 0.0617498
\(296\) −2.82975 −0.164476
\(297\) −6.37239 −0.369763
\(298\) −21.0112 −1.21714
\(299\) 37.2174 2.15234
\(300\) −7.89741 −0.455957
\(301\) −53.5202 −3.08485
\(302\) −8.91526 −0.513016
\(303\) 2.96492 0.170330
\(304\) −33.6994 −1.93279
\(305\) −18.9122 −1.08291
\(306\) 1.67650 0.0958392
\(307\) −13.2993 −0.759028 −0.379514 0.925186i \(-0.623909\pi\)
−0.379514 + 0.925186i \(0.623909\pi\)
\(308\) −24.4225 −1.39160
\(309\) −3.79769 −0.216043
\(310\) −28.1939 −1.60131
\(311\) 7.15879 0.405938 0.202969 0.979185i \(-0.434941\pi\)
0.202969 + 0.979185i \(0.434941\pi\)
\(312\) −13.8600 −0.784669
\(313\) −6.89071 −0.389486 −0.194743 0.980854i \(-0.562387\pi\)
−0.194743 + 0.980854i \(0.562387\pi\)
\(314\) −15.4745 −0.873275
\(315\) 18.1521 1.02276
\(316\) 0.810659 0.0456031
\(317\) −21.4196 −1.20304 −0.601522 0.798856i \(-0.705439\pi\)
−0.601522 + 0.798856i \(0.705439\pi\)
\(318\) −6.19482 −0.347388
\(319\) −24.7291 −1.38456
\(320\) −10.2186 −0.571239
\(321\) 4.59844 0.256660
\(322\) 42.4371 2.36493
\(323\) −6.78856 −0.377725
\(324\) 0.810659 0.0450366
\(325\) 67.7173 3.75628
\(326\) 4.21740 0.233580
\(327\) −3.43875 −0.190163
\(328\) 13.1993 0.728809
\(329\) −14.3346 −0.790293
\(330\) −41.0189 −2.25802
\(331\) 20.0992 1.10475 0.552375 0.833596i \(-0.313722\pi\)
0.552375 + 0.833596i \(0.313722\pi\)
\(332\) −2.68141 −0.147161
\(333\) −1.41918 −0.0777706
\(334\) 15.1434 0.828611
\(335\) 15.6740 0.856362
\(336\) −23.4690 −1.28034
\(337\) 22.7664 1.24016 0.620082 0.784537i \(-0.287099\pi\)
0.620082 + 0.784537i \(0.287099\pi\)
\(338\) −59.2103 −3.22062
\(339\) −2.48008 −0.134699
\(340\) 3.11255 0.168802
\(341\) −27.9110 −1.51147
\(342\) −11.3810 −0.615416
\(343\) −39.4814 −2.13179
\(344\) 22.5725 1.21703
\(345\) 20.5575 1.10678
\(346\) 33.0643 1.77755
\(347\) −17.6912 −0.949712 −0.474856 0.880063i \(-0.657500\pi\)
−0.474856 + 0.880063i \(0.657500\pi\)
\(348\) 3.14589 0.168638
\(349\) 5.42603 0.290449 0.145224 0.989399i \(-0.453610\pi\)
0.145224 + 0.989399i \(0.453610\pi\)
\(350\) 77.2147 4.12730
\(351\) −6.95110 −0.371022
\(352\) 27.6214 1.47222
\(353\) 0.406109 0.0216150 0.0108075 0.999942i \(-0.496560\pi\)
0.0108075 + 0.999942i \(0.496560\pi\)
\(354\) −0.463098 −0.0246134
\(355\) 41.3249 2.19330
\(356\) 8.04628 0.426452
\(357\) −4.72769 −0.250216
\(358\) 16.7119 0.883253
\(359\) −36.9440 −1.94983 −0.974915 0.222576i \(-0.928554\pi\)
−0.974915 + 0.222576i \(0.928554\pi\)
\(360\) −7.65575 −0.403494
\(361\) 27.0845 1.42550
\(362\) −28.8513 −1.51639
\(363\) −29.6073 −1.55398
\(364\) −26.6404 −1.39634
\(365\) −4.22827 −0.221318
\(366\) 8.25787 0.431646
\(367\) −11.3105 −0.590406 −0.295203 0.955435i \(-0.595387\pi\)
−0.295203 + 0.955435i \(0.595387\pi\)
\(368\) −26.5789 −1.38552
\(369\) 6.61973 0.344610
\(370\) −9.13523 −0.474918
\(371\) 17.4692 0.906957
\(372\) 3.55068 0.184094
\(373\) −31.0020 −1.60523 −0.802613 0.596501i \(-0.796557\pi\)
−0.802613 + 0.596501i \(0.796557\pi\)
\(374\) 10.6833 0.552421
\(375\) 18.2069 0.940199
\(376\) 6.04571 0.311784
\(377\) −26.9748 −1.38928
\(378\) −7.92599 −0.407669
\(379\) 37.7767 1.94046 0.970230 0.242187i \(-0.0778648\pi\)
0.970230 + 0.242187i \(0.0778648\pi\)
\(380\) −21.1297 −1.08393
\(381\) −0.406380 −0.0208195
\(382\) 8.46353 0.433032
\(383\) 31.6180 1.61560 0.807802 0.589454i \(-0.200657\pi\)
0.807802 + 0.589454i \(0.200657\pi\)
\(384\) 13.1310 0.670087
\(385\) 115.672 5.89520
\(386\) 18.4474 0.938947
\(387\) 11.3206 0.575457
\(388\) 8.71186 0.442278
\(389\) −3.85735 −0.195576 −0.0977878 0.995207i \(-0.531177\pi\)
−0.0977878 + 0.995207i \(0.531177\pi\)
\(390\) −44.7440 −2.26570
\(391\) −5.35418 −0.270772
\(392\) 30.6090 1.54599
\(393\) −18.2641 −0.921300
\(394\) −30.6754 −1.54540
\(395\) −3.83953 −0.193188
\(396\) 5.16583 0.259593
\(397\) −32.8523 −1.64881 −0.824404 0.566002i \(-0.808490\pi\)
−0.824404 + 0.566002i \(0.808490\pi\)
\(398\) −6.67683 −0.334679
\(399\) 32.0942 1.60672
\(400\) −48.3606 −2.41803
\(401\) 19.8461 0.991066 0.495533 0.868589i \(-0.334973\pi\)
0.495533 + 0.868589i \(0.334973\pi\)
\(402\) −6.84394 −0.341345
\(403\) −30.4458 −1.51661
\(404\) −2.40354 −0.119581
\(405\) −3.83953 −0.190788
\(406\) −30.7581 −1.52650
\(407\) −9.04357 −0.448273
\(408\) 1.99393 0.0987144
\(409\) 15.7146 0.777036 0.388518 0.921441i \(-0.372987\pi\)
0.388518 + 0.921441i \(0.372987\pi\)
\(410\) 42.6110 2.10441
\(411\) 21.4296 1.05705
\(412\) 3.07863 0.151673
\(413\) 1.30592 0.0642603
\(414\) −8.97629 −0.441161
\(415\) 12.6999 0.623416
\(416\) 30.1298 1.47724
\(417\) 6.87852 0.336842
\(418\) −72.5243 −3.54728
\(419\) 2.73740 0.133731 0.0668655 0.997762i \(-0.478700\pi\)
0.0668655 + 0.997762i \(0.478700\pi\)
\(420\) −14.7152 −0.718027
\(421\) −27.3254 −1.33176 −0.665879 0.746060i \(-0.731943\pi\)
−0.665879 + 0.746060i \(0.731943\pi\)
\(422\) −31.9879 −1.55715
\(423\) 3.03205 0.147423
\(424\) −7.36775 −0.357810
\(425\) −9.74196 −0.472554
\(426\) −18.0442 −0.874245
\(427\) −23.2870 −1.12694
\(428\) −3.72777 −0.180188
\(429\) −44.2951 −2.13859
\(430\) 72.8702 3.51412
\(431\) −11.5588 −0.556770 −0.278385 0.960470i \(-0.589799\pi\)
−0.278385 + 0.960470i \(0.589799\pi\)
\(432\) 4.96415 0.238838
\(433\) −18.3469 −0.881695 −0.440848 0.897582i \(-0.645322\pi\)
−0.440848 + 0.897582i \(0.645322\pi\)
\(434\) −34.7158 −1.66641
\(435\) −14.8999 −0.714395
\(436\) 2.78765 0.133504
\(437\) 36.3471 1.73872
\(438\) 1.84624 0.0882169
\(439\) 0.900201 0.0429643 0.0214821 0.999769i \(-0.493161\pi\)
0.0214821 + 0.999769i \(0.493161\pi\)
\(440\) −48.7854 −2.32575
\(441\) 15.3511 0.731004
\(442\) 11.6535 0.554302
\(443\) −0.0573528 −0.00272491 −0.00136246 0.999999i \(-0.500434\pi\)
−0.00136246 + 0.999999i \(0.500434\pi\)
\(444\) 1.15047 0.0545990
\(445\) −38.1096 −1.80657
\(446\) −22.0220 −1.04277
\(447\) −12.5327 −0.592778
\(448\) −12.5824 −0.594463
\(449\) 33.9099 1.60030 0.800152 0.599797i \(-0.204752\pi\)
0.800152 + 0.599797i \(0.204752\pi\)
\(450\) −16.3324 −0.769918
\(451\) 42.1835 1.98634
\(452\) 2.01050 0.0945658
\(453\) −5.31777 −0.249851
\(454\) 28.7472 1.34917
\(455\) 126.177 5.91527
\(456\) −13.5359 −0.633878
\(457\) −40.9848 −1.91719 −0.958594 0.284777i \(-0.908081\pi\)
−0.958594 + 0.284777i \(0.908081\pi\)
\(458\) 20.0226 0.935594
\(459\) 1.00000 0.0466760
\(460\) −16.6651 −0.777016
\(461\) −19.8599 −0.924967 −0.462484 0.886628i \(-0.653042\pi\)
−0.462484 + 0.886628i \(0.653042\pi\)
\(462\) −50.5075 −2.34982
\(463\) −14.5222 −0.674902 −0.337451 0.941343i \(-0.609565\pi\)
−0.337451 + 0.941343i \(0.609565\pi\)
\(464\) 19.2642 0.894317
\(465\) −16.8171 −0.779874
\(466\) 3.06730 0.142090
\(467\) 32.6267 1.50978 0.754891 0.655850i \(-0.227690\pi\)
0.754891 + 0.655850i \(0.227690\pi\)
\(468\) 5.63497 0.260477
\(469\) 19.2997 0.891179
\(470\) 19.5172 0.900263
\(471\) −9.23022 −0.425306
\(472\) −0.550781 −0.0253518
\(473\) 72.1391 3.31696
\(474\) 1.67650 0.0770043
\(475\) 66.1338 3.03443
\(476\) 3.83255 0.175665
\(477\) −3.69509 −0.169186
\(478\) −28.8466 −1.31941
\(479\) 32.7846 1.49797 0.748984 0.662589i \(-0.230542\pi\)
0.748984 + 0.662589i \(0.230542\pi\)
\(480\) 16.6426 0.759627
\(481\) −9.86487 −0.449799
\(482\) 11.5610 0.526591
\(483\) 25.3129 1.15178
\(484\) 24.0014 1.09097
\(485\) −41.2620 −1.87361
\(486\) 1.67650 0.0760477
\(487\) 23.7069 1.07426 0.537130 0.843499i \(-0.319508\pi\)
0.537130 + 0.843499i \(0.319508\pi\)
\(488\) 9.82143 0.444595
\(489\) 2.51559 0.113759
\(490\) 98.8145 4.46399
\(491\) 9.44727 0.426349 0.213175 0.977014i \(-0.431620\pi\)
0.213175 + 0.977014i \(0.431620\pi\)
\(492\) −5.36635 −0.241934
\(493\) 3.88066 0.174776
\(494\) −79.1106 −3.55936
\(495\) −24.4669 −1.09971
\(496\) 21.7429 0.976287
\(497\) 50.8842 2.28247
\(498\) −5.54534 −0.248493
\(499\) 6.44483 0.288510 0.144255 0.989541i \(-0.453921\pi\)
0.144255 + 0.989541i \(0.453921\pi\)
\(500\) −14.7596 −0.660068
\(501\) 9.03274 0.403553
\(502\) 49.7675 2.22123
\(503\) 2.88139 0.128475 0.0642373 0.997935i \(-0.479539\pi\)
0.0642373 + 0.997935i \(0.479539\pi\)
\(504\) −9.42670 −0.419899
\(505\) 11.3839 0.506577
\(506\) −57.2004 −2.54287
\(507\) −35.3178 −1.56852
\(508\) 0.329436 0.0146164
\(509\) 6.19045 0.274387 0.137193 0.990544i \(-0.456192\pi\)
0.137193 + 0.990544i \(0.456192\pi\)
\(510\) 6.43697 0.285034
\(511\) −5.20636 −0.230316
\(512\) −1.72097 −0.0760567
\(513\) −6.78856 −0.299722
\(514\) 5.11928 0.225802
\(515\) −14.5813 −0.642530
\(516\) −9.17713 −0.404001
\(517\) 19.3214 0.849755
\(518\) −11.2484 −0.494227
\(519\) 19.7222 0.865708
\(520\) −53.2159 −2.33367
\(521\) 29.6116 1.29731 0.648655 0.761083i \(-0.275332\pi\)
0.648655 + 0.761083i \(0.275332\pi\)
\(522\) 6.50593 0.284757
\(523\) −18.8165 −0.822787 −0.411393 0.911458i \(-0.634958\pi\)
−0.411393 + 0.911458i \(0.634958\pi\)
\(524\) 14.8059 0.646800
\(525\) 46.0570 2.01009
\(526\) 9.75692 0.425422
\(527\) 4.37999 0.190795
\(528\) 31.6335 1.37667
\(529\) 5.66721 0.246400
\(530\) −23.7852 −1.03316
\(531\) −0.276229 −0.0119873
\(532\) −26.0175 −1.12800
\(533\) 46.0144 1.99311
\(534\) 16.6403 0.720096
\(535\) 17.6558 0.763328
\(536\) −8.13977 −0.351585
\(537\) 9.96833 0.430165
\(538\) 3.95033 0.170311
\(539\) 97.8231 4.21354
\(540\) 3.11255 0.133943
\(541\) −11.9511 −0.513819 −0.256910 0.966435i \(-0.582704\pi\)
−0.256910 + 0.966435i \(0.582704\pi\)
\(542\) −49.5039 −2.12638
\(543\) −17.2092 −0.738518
\(544\) −4.33454 −0.185842
\(545\) −13.2032 −0.565561
\(546\) −55.0943 −2.35782
\(547\) 2.57315 0.110020 0.0550100 0.998486i \(-0.482481\pi\)
0.0550100 + 0.998486i \(0.482481\pi\)
\(548\) −17.3721 −0.742101
\(549\) 4.92566 0.210222
\(550\) −104.076 −4.43784
\(551\) −26.3441 −1.12230
\(552\) −10.6759 −0.454395
\(553\) −4.72769 −0.201042
\(554\) 24.3807 1.03584
\(555\) −5.44898 −0.231296
\(556\) −5.57613 −0.236481
\(557\) 27.6812 1.17289 0.586446 0.809988i \(-0.300527\pi\)
0.586446 + 0.809988i \(0.300527\pi\)
\(558\) 7.34307 0.310857
\(559\) 78.6904 3.32825
\(560\) −90.1098 −3.80783
\(561\) 6.37239 0.269042
\(562\) 27.0643 1.14164
\(563\) 25.1911 1.06168 0.530840 0.847472i \(-0.321877\pi\)
0.530840 + 0.847472i \(0.321877\pi\)
\(564\) −2.45796 −0.103499
\(565\) −9.52232 −0.400607
\(566\) 15.8435 0.665953
\(567\) −4.72769 −0.198544
\(568\) −21.4607 −0.900472
\(569\) 14.4312 0.604986 0.302493 0.953152i \(-0.402181\pi\)
0.302493 + 0.953152i \(0.402181\pi\)
\(570\) −43.6978 −1.83030
\(571\) 23.9711 1.00316 0.501581 0.865111i \(-0.332752\pi\)
0.501581 + 0.865111i \(0.332752\pi\)
\(572\) 35.9082 1.50140
\(573\) 5.04833 0.210897
\(574\) 52.4679 2.18997
\(575\) 52.1602 2.17523
\(576\) 2.66143 0.110893
\(577\) −3.12979 −0.130295 −0.0651475 0.997876i \(-0.520752\pi\)
−0.0651475 + 0.997876i \(0.520752\pi\)
\(578\) −1.67650 −0.0697333
\(579\) 11.0035 0.457290
\(580\) 12.0787 0.501542
\(581\) 15.6377 0.648762
\(582\) 18.0168 0.746819
\(583\) −23.5465 −0.975197
\(584\) 2.19581 0.0908633
\(585\) −26.6889 −1.10345
\(586\) −8.58630 −0.354697
\(587\) −13.5379 −0.558768 −0.279384 0.960180i \(-0.590130\pi\)
−0.279384 + 0.960180i \(0.590130\pi\)
\(588\) −12.4445 −0.513203
\(589\) −29.7338 −1.22516
\(590\) −1.77808 −0.0732022
\(591\) −18.2973 −0.752649
\(592\) 7.04503 0.289549
\(593\) 9.33997 0.383546 0.191773 0.981439i \(-0.438576\pi\)
0.191773 + 0.981439i \(0.438576\pi\)
\(594\) 10.6833 0.438342
\(595\) −18.1521 −0.744164
\(596\) 10.1598 0.416161
\(597\) −3.98259 −0.162997
\(598\) −62.3951 −2.55152
\(599\) 24.2391 0.990382 0.495191 0.868784i \(-0.335098\pi\)
0.495191 + 0.868784i \(0.335098\pi\)
\(600\) −19.4248 −0.793014
\(601\) −18.4338 −0.751932 −0.375966 0.926634i \(-0.622689\pi\)
−0.375966 + 0.926634i \(0.622689\pi\)
\(602\) 89.7267 3.65699
\(603\) −4.08227 −0.166243
\(604\) 4.31090 0.175408
\(605\) −113.678 −4.62167
\(606\) −4.97070 −0.201921
\(607\) 29.5438 1.19914 0.599572 0.800321i \(-0.295338\pi\)
0.599572 + 0.800321i \(0.295338\pi\)
\(608\) 29.4253 1.19335
\(609\) −18.3466 −0.743440
\(610\) 31.7063 1.28375
\(611\) 21.0761 0.852648
\(612\) −0.810659 −0.0327690
\(613\) −12.4238 −0.501794 −0.250897 0.968014i \(-0.580726\pi\)
−0.250897 + 0.968014i \(0.580726\pi\)
\(614\) 22.2962 0.899802
\(615\) 25.4166 1.02490
\(616\) −60.0706 −2.42031
\(617\) −20.7760 −0.836409 −0.418205 0.908353i \(-0.637341\pi\)
−0.418205 + 0.908353i \(0.637341\pi\)
\(618\) 6.36683 0.256112
\(619\) −7.95561 −0.319763 −0.159882 0.987136i \(-0.551111\pi\)
−0.159882 + 0.987136i \(0.551111\pi\)
\(620\) 13.6329 0.547512
\(621\) −5.35418 −0.214856
\(622\) −12.0017 −0.481226
\(623\) −46.9252 −1.88002
\(624\) 34.5063 1.38136
\(625\) 21.1960 0.847840
\(626\) 11.5523 0.461722
\(627\) −43.2593 −1.72761
\(628\) 7.48256 0.298587
\(629\) 1.41918 0.0565865
\(630\) −30.4320 −1.21244
\(631\) 7.35370 0.292746 0.146373 0.989229i \(-0.453240\pi\)
0.146373 + 0.989229i \(0.453240\pi\)
\(632\) 1.99393 0.0793144
\(633\) −19.0801 −0.758368
\(634\) 35.9100 1.42617
\(635\) −1.56031 −0.0619189
\(636\) 2.99546 0.118778
\(637\) 106.707 4.22788
\(638\) 41.4583 1.64135
\(639\) −10.7630 −0.425778
\(640\) 50.4167 1.99290
\(641\) −23.9838 −0.947302 −0.473651 0.880713i \(-0.657064\pi\)
−0.473651 + 0.880713i \(0.657064\pi\)
\(642\) −7.70929 −0.304262
\(643\) 39.8466 1.57140 0.785698 0.618610i \(-0.212304\pi\)
0.785698 + 0.618610i \(0.212304\pi\)
\(644\) −20.5201 −0.808607
\(645\) 43.4656 1.71146
\(646\) 11.3810 0.447781
\(647\) −23.7285 −0.932863 −0.466432 0.884557i \(-0.654461\pi\)
−0.466432 + 0.884557i \(0.654461\pi\)
\(648\) 1.99393 0.0783291
\(649\) −1.76024 −0.0690953
\(650\) −113.528 −4.45294
\(651\) −20.7073 −0.811582
\(652\) −2.03929 −0.0798648
\(653\) 18.3307 0.717337 0.358669 0.933465i \(-0.383231\pi\)
0.358669 + 0.933465i \(0.383231\pi\)
\(654\) 5.76506 0.225432
\(655\) −70.1253 −2.74002
\(656\) −32.8614 −1.28302
\(657\) 1.10125 0.0429637
\(658\) 24.0320 0.936865
\(659\) 1.28907 0.0502151 0.0251075 0.999685i \(-0.492007\pi\)
0.0251075 + 0.999685i \(0.492007\pi\)
\(660\) 19.8344 0.772051
\(661\) 9.08212 0.353254 0.176627 0.984278i \(-0.443481\pi\)
0.176627 + 0.984278i \(0.443481\pi\)
\(662\) −33.6963 −1.30964
\(663\) 6.95110 0.269958
\(664\) −6.59530 −0.255947
\(665\) 123.227 4.77852
\(666\) 2.37926 0.0921944
\(667\) −20.7777 −0.804517
\(668\) −7.32248 −0.283315
\(669\) −13.1357 −0.507855
\(670\) −26.2775 −1.01519
\(671\) 31.3882 1.21173
\(672\) 20.4924 0.790511
\(673\) 2.47132 0.0952624 0.0476312 0.998865i \(-0.484833\pi\)
0.0476312 + 0.998865i \(0.484833\pi\)
\(674\) −38.1679 −1.47017
\(675\) −9.74196 −0.374968
\(676\) 28.6307 1.10118
\(677\) 0.0788017 0.00302860 0.00151430 0.999999i \(-0.499518\pi\)
0.00151430 + 0.999999i \(0.499518\pi\)
\(678\) 4.15785 0.159681
\(679\) −50.8068 −1.94979
\(680\) 7.65575 0.293585
\(681\) 17.1471 0.657080
\(682\) 46.7929 1.79179
\(683\) −49.1204 −1.87954 −0.939770 0.341806i \(-0.888961\pi\)
−0.939770 + 0.341806i \(0.888961\pi\)
\(684\) 5.50321 0.210420
\(685\) 82.2797 3.14374
\(686\) 66.1906 2.52717
\(687\) 11.9431 0.455656
\(688\) −56.1970 −2.14249
\(689\) −25.6849 −0.978517
\(690\) −34.4647 −1.31205
\(691\) −1.60298 −0.0609802 −0.0304901 0.999535i \(-0.509707\pi\)
−0.0304901 + 0.999535i \(0.509707\pi\)
\(692\) −15.9880 −0.607771
\(693\) −30.1267 −1.14442
\(694\) 29.6593 1.12585
\(695\) 26.4102 1.00180
\(696\) 7.73777 0.293299
\(697\) −6.61973 −0.250740
\(698\) −9.09675 −0.344317
\(699\) 1.82958 0.0692011
\(700\) −37.3365 −1.41119
\(701\) −30.6068 −1.15600 −0.578001 0.816036i \(-0.696167\pi\)
−0.578001 + 0.816036i \(0.696167\pi\)
\(702\) 11.6535 0.439834
\(703\) −9.63419 −0.363360
\(704\) 16.9597 0.639191
\(705\) 11.6416 0.438450
\(706\) −0.680843 −0.0256239
\(707\) 14.0172 0.527173
\(708\) 0.223927 0.00841570
\(709\) −21.8444 −0.820385 −0.410193 0.911999i \(-0.634538\pi\)
−0.410193 + 0.911999i \(0.634538\pi\)
\(710\) −69.2812 −2.60008
\(711\) 1.00000 0.0375029
\(712\) 19.7910 0.741698
\(713\) −23.4513 −0.878256
\(714\) 7.92599 0.296623
\(715\) −170.072 −6.36034
\(716\) −8.08092 −0.301998
\(717\) −17.2064 −0.642585
\(718\) 61.9367 2.31146
\(719\) −29.7035 −1.10775 −0.553877 0.832598i \(-0.686852\pi\)
−0.553877 + 0.832598i \(0.686852\pi\)
\(720\) 19.0600 0.710324
\(721\) −17.9543 −0.668653
\(722\) −45.4072 −1.68988
\(723\) 6.89593 0.256462
\(724\) 13.9508 0.518478
\(725\) −37.8052 −1.40405
\(726\) 49.6367 1.84219
\(727\) −5.55713 −0.206103 −0.103051 0.994676i \(-0.532861\pi\)
−0.103051 + 0.994676i \(0.532861\pi\)
\(728\) −65.5259 −2.42855
\(729\) 1.00000 0.0370370
\(730\) 7.08870 0.262364
\(731\) −11.3206 −0.418707
\(732\) −3.99303 −0.147587
\(733\) −12.8972 −0.476368 −0.238184 0.971220i \(-0.576552\pi\)
−0.238184 + 0.971220i \(0.576552\pi\)
\(734\) 18.9622 0.699906
\(735\) 58.9409 2.17407
\(736\) 23.2079 0.855455
\(737\) −26.0138 −0.958231
\(738\) −11.0980 −0.408523
\(739\) −18.9291 −0.696319 −0.348159 0.937435i \(-0.613193\pi\)
−0.348159 + 0.937435i \(0.613193\pi\)
\(740\) 4.41727 0.162382
\(741\) −47.1879 −1.73349
\(742\) −29.2872 −1.07517
\(743\) 21.2235 0.778616 0.389308 0.921108i \(-0.372714\pi\)
0.389308 + 0.921108i \(0.372714\pi\)
\(744\) 8.73341 0.320182
\(745\) −48.1198 −1.76297
\(746\) 51.9750 1.90294
\(747\) −3.30768 −0.121022
\(748\) −5.16583 −0.188882
\(749\) 21.7400 0.794363
\(750\) −30.5239 −1.11457
\(751\) 13.0781 0.477227 0.238613 0.971115i \(-0.423307\pi\)
0.238613 + 0.971115i \(0.423307\pi\)
\(752\) −15.0516 −0.548874
\(753\) 29.6853 1.08179
\(754\) 45.2234 1.64694
\(755\) −20.4177 −0.743077
\(756\) 3.83255 0.139388
\(757\) 22.0581 0.801715 0.400857 0.916140i \(-0.368712\pi\)
0.400857 + 0.916140i \(0.368712\pi\)
\(758\) −63.3327 −2.30035
\(759\) −34.1189 −1.23844
\(760\) −51.9715 −1.88521
\(761\) 14.2847 0.517820 0.258910 0.965901i \(-0.416637\pi\)
0.258910 + 0.965901i \(0.416637\pi\)
\(762\) 0.681298 0.0246808
\(763\) −16.2573 −0.588555
\(764\) −4.09247 −0.148061
\(765\) 3.83953 0.138818
\(766\) −53.0076 −1.91524
\(767\) −1.92009 −0.0693305
\(768\) −16.6913 −0.602294
\(769\) 32.7936 1.18257 0.591284 0.806464i \(-0.298621\pi\)
0.591284 + 0.806464i \(0.298621\pi\)
\(770\) −193.925 −6.98856
\(771\) 3.05355 0.109971
\(772\) −8.92008 −0.321041
\(773\) −20.6646 −0.743252 −0.371626 0.928382i \(-0.621200\pi\)
−0.371626 + 0.928382i \(0.621200\pi\)
\(774\) −18.9790 −0.682185
\(775\) −42.6697 −1.53274
\(776\) 21.4281 0.769223
\(777\) −6.70945 −0.240700
\(778\) 6.46686 0.231848
\(779\) 44.9384 1.61009
\(780\) 21.6356 0.774680
\(781\) −68.5861 −2.45420
\(782\) 8.97629 0.320991
\(783\) 3.88066 0.138683
\(784\) −76.2051 −2.72161
\(785\) −35.4397 −1.26490
\(786\) 30.6197 1.09217
\(787\) 21.9481 0.782365 0.391183 0.920313i \(-0.372066\pi\)
0.391183 + 0.920313i \(0.372066\pi\)
\(788\) 14.8328 0.528398
\(789\) 5.81981 0.207191
\(790\) 6.43697 0.229017
\(791\) −11.7250 −0.416894
\(792\) 12.7061 0.451492
\(793\) 34.2387 1.21585
\(794\) 55.0769 1.95461
\(795\) −14.1874 −0.503174
\(796\) 3.22853 0.114432
\(797\) 51.0625 1.80873 0.904364 0.426762i \(-0.140346\pi\)
0.904364 + 0.426762i \(0.140346\pi\)
\(798\) −53.8060 −1.90471
\(799\) −3.03205 −0.107266
\(800\) 42.2270 1.49295
\(801\) 9.92560 0.350704
\(802\) −33.2720 −1.17488
\(803\) 7.01757 0.247645
\(804\) 3.30933 0.116711
\(805\) 97.1896 3.42548
\(806\) 51.0424 1.79789
\(807\) 2.35629 0.0829454
\(808\) −5.91186 −0.207978
\(809\) −37.7956 −1.32882 −0.664412 0.747367i \(-0.731318\pi\)
−0.664412 + 0.747367i \(0.731318\pi\)
\(810\) 6.43697 0.226172
\(811\) −15.2981 −0.537190 −0.268595 0.963253i \(-0.586559\pi\)
−0.268595 + 0.963253i \(0.586559\pi\)
\(812\) 14.8728 0.521934
\(813\) −29.5281 −1.03560
\(814\) 15.1616 0.531413
\(815\) 9.65869 0.338329
\(816\) −4.96415 −0.173780
\(817\) 76.8504 2.68865
\(818\) −26.3455 −0.921150
\(819\) −32.8627 −1.14831
\(820\) −20.6042 −0.719531
\(821\) −10.4100 −0.363312 −0.181656 0.983362i \(-0.558146\pi\)
−0.181656 + 0.983362i \(0.558146\pi\)
\(822\) −35.9268 −1.25309
\(823\) 22.1248 0.771223 0.385612 0.922661i \(-0.373990\pi\)
0.385612 + 0.922661i \(0.373990\pi\)
\(824\) 7.57233 0.263795
\(825\) −62.0795 −2.16133
\(826\) −2.18938 −0.0761784
\(827\) −22.8024 −0.792918 −0.396459 0.918052i \(-0.629761\pi\)
−0.396459 + 0.918052i \(0.629761\pi\)
\(828\) 4.34041 0.150840
\(829\) −46.4492 −1.61325 −0.806624 0.591065i \(-0.798708\pi\)
−0.806624 + 0.591065i \(0.798708\pi\)
\(830\) −21.2915 −0.739038
\(831\) 14.5426 0.504478
\(832\) 18.4999 0.641367
\(833\) −15.3511 −0.531884
\(834\) −11.5318 −0.399315
\(835\) 34.6815 1.20020
\(836\) 35.0686 1.21287
\(837\) 4.37999 0.151395
\(838\) −4.58926 −0.158533
\(839\) 23.1115 0.797898 0.398949 0.916973i \(-0.369375\pi\)
0.398949 + 0.916973i \(0.369375\pi\)
\(840\) −36.1941 −1.24881
\(841\) −13.9405 −0.480706
\(842\) 45.8111 1.57875
\(843\) 16.1433 0.556006
\(844\) 15.4675 0.532413
\(845\) −135.603 −4.66490
\(846\) −5.08324 −0.174765
\(847\) −139.974 −4.80957
\(848\) 18.3430 0.629900
\(849\) 9.45035 0.324335
\(850\) 16.3324 0.560197
\(851\) −7.59855 −0.260475
\(852\) 8.72514 0.298918
\(853\) 42.8850 1.46835 0.734177 0.678958i \(-0.237568\pi\)
0.734177 + 0.678958i \(0.237568\pi\)
\(854\) 39.0407 1.33595
\(855\) −26.0648 −0.891399
\(856\) −9.16898 −0.313389
\(857\) 51.2242 1.74979 0.874893 0.484316i \(-0.160932\pi\)
0.874893 + 0.484316i \(0.160932\pi\)
\(858\) 74.2608 2.53522
\(859\) −5.55864 −0.189658 −0.0948291 0.995494i \(-0.530230\pi\)
−0.0948291 + 0.995494i \(0.530230\pi\)
\(860\) −35.2358 −1.20153
\(861\) 31.2961 1.06657
\(862\) 19.3784 0.660032
\(863\) 33.4681 1.13927 0.569633 0.821899i \(-0.307085\pi\)
0.569633 + 0.821899i \(0.307085\pi\)
\(864\) −4.33454 −0.147464
\(865\) 75.7238 2.57469
\(866\) 30.7586 1.04522
\(867\) −1.00000 −0.0339618
\(868\) 16.7865 0.569772
\(869\) 6.37239 0.216168
\(870\) 24.9797 0.846891
\(871\) −28.3763 −0.961493
\(872\) 6.85663 0.232195
\(873\) 10.7466 0.363719
\(874\) −60.9360 −2.06119
\(875\) 86.0765 2.90992
\(876\) −0.892736 −0.0301628
\(877\) −54.2213 −1.83092 −0.915462 0.402404i \(-0.868175\pi\)
−0.915462 + 0.402404i \(0.868175\pi\)
\(878\) −1.50919 −0.0509327
\(879\) −5.12156 −0.172746
\(880\) 121.458 4.09433
\(881\) 41.8045 1.40843 0.704215 0.709987i \(-0.251299\pi\)
0.704215 + 0.709987i \(0.251299\pi\)
\(882\) −25.7361 −0.866581
\(883\) −7.63546 −0.256954 −0.128477 0.991713i \(-0.541009\pi\)
−0.128477 + 0.991713i \(0.541009\pi\)
\(884\) −5.63497 −0.189525
\(885\) −1.06059 −0.0356512
\(886\) 0.0961520 0.00323029
\(887\) −26.9704 −0.905579 −0.452789 0.891617i \(-0.649571\pi\)
−0.452789 + 0.891617i \(0.649571\pi\)
\(888\) 2.82975 0.0949602
\(889\) −1.92124 −0.0644364
\(890\) 63.8908 2.14162
\(891\) 6.37239 0.213483
\(892\) 10.6486 0.356540
\(893\) 20.5833 0.688792
\(894\) 21.0112 0.702719
\(895\) 38.2737 1.27935
\(896\) 62.0792 2.07392
\(897\) −37.2174 −1.24265
\(898\) −56.8499 −1.89711
\(899\) 16.9973 0.566890
\(900\) 7.89741 0.263247
\(901\) 3.69509 0.123101
\(902\) −70.7207 −2.35474
\(903\) 53.5202 1.78104
\(904\) 4.94510 0.164472
\(905\) −66.0752 −2.19642
\(906\) 8.91526 0.296190
\(907\) 41.1282 1.36564 0.682820 0.730587i \(-0.260753\pi\)
0.682820 + 0.730587i \(0.260753\pi\)
\(908\) −13.9005 −0.461304
\(909\) −2.96492 −0.0983403
\(910\) −211.536 −7.01235
\(911\) −0.439674 −0.0145670 −0.00728352 0.999973i \(-0.502318\pi\)
−0.00728352 + 0.999973i \(0.502318\pi\)
\(912\) 33.6994 1.11590
\(913\) −21.0778 −0.697575
\(914\) 68.7111 2.27276
\(915\) 18.9122 0.625218
\(916\) −9.68176 −0.319894
\(917\) −86.3469 −2.85142
\(918\) −1.67650 −0.0553328
\(919\) −18.0160 −0.594294 −0.297147 0.954832i \(-0.596035\pi\)
−0.297147 + 0.954832i \(0.596035\pi\)
\(920\) −40.9903 −1.35141
\(921\) 13.2993 0.438225
\(922\) 33.2952 1.09652
\(923\) −74.8148 −2.46256
\(924\) 24.4225 0.803441
\(925\) −13.8256 −0.454583
\(926\) 24.3464 0.800074
\(927\) 3.79769 0.124732
\(928\) −16.8209 −0.552173
\(929\) −5.01967 −0.164690 −0.0823450 0.996604i \(-0.526241\pi\)
−0.0823450 + 0.996604i \(0.526241\pi\)
\(930\) 28.1939 0.924514
\(931\) 104.212 3.41540
\(932\) −1.48317 −0.0485827
\(933\) −7.15879 −0.234368
\(934\) −54.6987 −1.78980
\(935\) 24.4669 0.800155
\(936\) 13.8600 0.453029
\(937\) −10.0905 −0.329643 −0.164821 0.986323i \(-0.552705\pi\)
−0.164821 + 0.986323i \(0.552705\pi\)
\(938\) −32.3560 −1.05646
\(939\) 6.89071 0.224870
\(940\) −9.43741 −0.307814
\(941\) 10.1696 0.331521 0.165760 0.986166i \(-0.446992\pi\)
0.165760 + 0.986166i \(0.446992\pi\)
\(942\) 15.4745 0.504186
\(943\) 35.4432 1.15419
\(944\) 1.37124 0.0446301
\(945\) −18.1521 −0.590488
\(946\) −120.941 −3.93214
\(947\) 52.9560 1.72084 0.860420 0.509585i \(-0.170201\pi\)
0.860420 + 0.509585i \(0.170201\pi\)
\(948\) −0.810659 −0.0263290
\(949\) 7.65488 0.248488
\(950\) −110.874 −3.59721
\(951\) 21.4196 0.694578
\(952\) 9.42670 0.305521
\(953\) −7.79405 −0.252474 −0.126237 0.992000i \(-0.540290\pi\)
−0.126237 + 0.992000i \(0.540290\pi\)
\(954\) 6.19482 0.200565
\(955\) 19.3832 0.627225
\(956\) 13.9485 0.451128
\(957\) 24.7291 0.799377
\(958\) −54.9635 −1.77579
\(959\) 101.313 3.27156
\(960\) 10.2186 0.329805
\(961\) −11.8157 −0.381150
\(962\) 16.5385 0.533222
\(963\) −4.59844 −0.148183
\(964\) −5.59025 −0.180050
\(965\) 42.2482 1.36002
\(966\) −42.4371 −1.36539
\(967\) −1.56378 −0.0502878 −0.0251439 0.999684i \(-0.508004\pi\)
−0.0251439 + 0.999684i \(0.508004\pi\)
\(968\) 59.0350 1.89746
\(969\) 6.78856 0.218080
\(970\) 69.1758 2.22110
\(971\) 32.3287 1.03748 0.518738 0.854933i \(-0.326402\pi\)
0.518738 + 0.854933i \(0.326402\pi\)
\(972\) −0.810659 −0.0260019
\(973\) 32.5195 1.04253
\(974\) −39.7446 −1.27350
\(975\) −67.7173 −2.16869
\(976\) −24.4517 −0.782680
\(977\) −39.9335 −1.27758 −0.638792 0.769379i \(-0.720566\pi\)
−0.638792 + 0.769379i \(0.720566\pi\)
\(978\) −4.21740 −0.134858
\(979\) 63.2498 2.02147
\(980\) −47.7810 −1.52631
\(981\) 3.43875 0.109791
\(982\) −15.8384 −0.505423
\(983\) −30.7327 −0.980221 −0.490110 0.871660i \(-0.663044\pi\)
−0.490110 + 0.871660i \(0.663044\pi\)
\(984\) −13.1993 −0.420778
\(985\) −70.2528 −2.23844
\(986\) −6.50593 −0.207191
\(987\) 14.3346 0.456276
\(988\) 38.2533 1.21700
\(989\) 60.6124 1.92736
\(990\) 41.0189 1.30367
\(991\) −21.5490 −0.684528 −0.342264 0.939604i \(-0.611194\pi\)
−0.342264 + 0.939604i \(0.611194\pi\)
\(992\) −18.9853 −0.602783
\(993\) −20.0992 −0.637828
\(994\) −85.3075 −2.70579
\(995\) −15.2913 −0.484766
\(996\) 2.68141 0.0849636
\(997\) 0.774472 0.0245278 0.0122639 0.999925i \(-0.496096\pi\)
0.0122639 + 0.999925i \(0.496096\pi\)
\(998\) −10.8048 −0.342019
\(999\) 1.41918 0.0449009
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.1.8 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.8 32 1.1 even 1 trivial