Properties

Label 4029.2.a.k.1.10
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 31
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: \(31\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.26690 q^{2} +1.00000 q^{3} -0.394972 q^{4} +3.60603 q^{5} -1.26690 q^{6} -2.46109 q^{7} +3.03418 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.26690 q^{2} +1.00000 q^{3} -0.394972 q^{4} +3.60603 q^{5} -1.26690 q^{6} -2.46109 q^{7} +3.03418 q^{8} +1.00000 q^{9} -4.56847 q^{10} +4.32670 q^{11} -0.394972 q^{12} +6.87794 q^{13} +3.11794 q^{14} +3.60603 q^{15} -3.05405 q^{16} +1.00000 q^{17} -1.26690 q^{18} +1.02429 q^{19} -1.42428 q^{20} -2.46109 q^{21} -5.48148 q^{22} +3.18429 q^{23} +3.03418 q^{24} +8.00349 q^{25} -8.71364 q^{26} +1.00000 q^{27} +0.972059 q^{28} +2.11000 q^{29} -4.56847 q^{30} +11.0198 q^{31} -2.19919 q^{32} +4.32670 q^{33} -1.26690 q^{34} -8.87476 q^{35} -0.394972 q^{36} -3.84497 q^{37} -1.29767 q^{38} +6.87794 q^{39} +10.9414 q^{40} -3.71450 q^{41} +3.11794 q^{42} +5.79832 q^{43} -1.70892 q^{44} +3.60603 q^{45} -4.03416 q^{46} -10.7508 q^{47} -3.05405 q^{48} -0.943060 q^{49} -10.1396 q^{50} +1.00000 q^{51} -2.71659 q^{52} -1.67641 q^{53} -1.26690 q^{54} +15.6022 q^{55} -7.46738 q^{56} +1.02429 q^{57} -2.67315 q^{58} +1.63966 q^{59} -1.42428 q^{60} -7.36202 q^{61} -13.9609 q^{62} -2.46109 q^{63} +8.89426 q^{64} +24.8021 q^{65} -5.48148 q^{66} +2.03979 q^{67} -0.394972 q^{68} +3.18429 q^{69} +11.2434 q^{70} -3.93293 q^{71} +3.03418 q^{72} -7.02232 q^{73} +4.87118 q^{74} +8.00349 q^{75} -0.404566 q^{76} -10.6484 q^{77} -8.71364 q^{78} +1.00000 q^{79} -11.0130 q^{80} +1.00000 q^{81} +4.70588 q^{82} +2.00730 q^{83} +0.972059 q^{84} +3.60603 q^{85} -7.34587 q^{86} +2.11000 q^{87} +13.1280 q^{88} +3.75596 q^{89} -4.56847 q^{90} -16.9272 q^{91} -1.25770 q^{92} +11.0198 q^{93} +13.6201 q^{94} +3.69363 q^{95} -2.19919 q^{96} -0.409835 q^{97} +1.19476 q^{98} +4.32670 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + O(q^{10}) \) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + 5q^{10} + 26q^{11} + 34q^{12} + 7q^{13} + 19q^{14} + 11q^{15} + 40q^{16} + 31q^{17} + 4q^{18} + 32q^{19} + 23q^{20} + 4q^{21} + 2q^{22} + 29q^{23} + 12q^{24} + 32q^{25} + 13q^{26} + 31q^{27} - 13q^{28} + 25q^{29} + 5q^{30} + 22q^{31} + 28q^{32} + 26q^{33} + 4q^{34} + 20q^{35} + 34q^{36} - 4q^{37} + 19q^{38} + 7q^{39} - 3q^{40} + 33q^{41} + 19q^{42} + 6q^{43} + 30q^{44} + 11q^{45} - 11q^{46} + 23q^{47} + 40q^{48} + 31q^{49} + 6q^{50} + 31q^{51} - 7q^{52} + 12q^{53} + 4q^{54} + 40q^{56} + 32q^{57} + 9q^{58} + 27q^{59} + 23q^{60} - 4q^{61} + 25q^{62} + 4q^{63} + 10q^{64} + 54q^{65} + 2q^{66} + 34q^{68} + 29q^{69} - 59q^{70} + 35q^{71} + 12q^{72} + 5q^{73} + 48q^{74} + 32q^{75} + 32q^{76} + 42q^{77} + 13q^{78} + 31q^{79} + 24q^{80} + 31q^{81} + 5q^{82} + 67q^{83} - 13q^{84} + 11q^{85} - 20q^{86} + 25q^{87} - 7q^{88} + 22q^{89} + 5q^{90} + 16q^{91} + 57q^{92} + 22q^{93} + 45q^{94} + 73q^{95} + 28q^{96} - 13q^{97} - 19q^{98} + 26q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26690 −0.895831 −0.447916 0.894076i \(-0.647834\pi\)
−0.447916 + 0.894076i \(0.647834\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.394972 −0.197486
\(5\) 3.60603 1.61267 0.806334 0.591461i \(-0.201448\pi\)
0.806334 + 0.591461i \(0.201448\pi\)
\(6\) −1.26690 −0.517209
\(7\) −2.46109 −0.930203 −0.465101 0.885257i \(-0.653982\pi\)
−0.465101 + 0.885257i \(0.653982\pi\)
\(8\) 3.03418 1.07275
\(9\) 1.00000 0.333333
\(10\) −4.56847 −1.44468
\(11\) 4.32670 1.30455 0.652274 0.757983i \(-0.273815\pi\)
0.652274 + 0.757983i \(0.273815\pi\)
\(12\) −0.394972 −0.114019
\(13\) 6.87794 1.90760 0.953799 0.300446i \(-0.0971355\pi\)
0.953799 + 0.300446i \(0.0971355\pi\)
\(14\) 3.11794 0.833305
\(15\) 3.60603 0.931074
\(16\) −3.05405 −0.763513
\(17\) 1.00000 0.242536
\(18\) −1.26690 −0.298610
\(19\) 1.02429 0.234988 0.117494 0.993074i \(-0.462514\pi\)
0.117494 + 0.993074i \(0.462514\pi\)
\(20\) −1.42428 −0.318479
\(21\) −2.46109 −0.537053
\(22\) −5.48148 −1.16866
\(23\) 3.18429 0.663969 0.331985 0.943285i \(-0.392282\pi\)
0.331985 + 0.943285i \(0.392282\pi\)
\(24\) 3.03418 0.619350
\(25\) 8.00349 1.60070
\(26\) −8.71364 −1.70889
\(27\) 1.00000 0.192450
\(28\) 0.972059 0.183702
\(29\) 2.11000 0.391816 0.195908 0.980622i \(-0.437235\pi\)
0.195908 + 0.980622i \(0.437235\pi\)
\(30\) −4.56847 −0.834086
\(31\) 11.0198 1.97921 0.989607 0.143801i \(-0.0459326\pi\)
0.989607 + 0.143801i \(0.0459326\pi\)
\(32\) −2.19919 −0.388766
\(33\) 4.32670 0.753181
\(34\) −1.26690 −0.217271
\(35\) −8.87476 −1.50011
\(36\) −0.394972 −0.0658286
\(37\) −3.84497 −0.632108 −0.316054 0.948741i \(-0.602358\pi\)
−0.316054 + 0.948741i \(0.602358\pi\)
\(38\) −1.29767 −0.210510
\(39\) 6.87794 1.10135
\(40\) 10.9414 1.72998
\(41\) −3.71450 −0.580107 −0.290053 0.957010i \(-0.593673\pi\)
−0.290053 + 0.957010i \(0.593673\pi\)
\(42\) 3.11794 0.481109
\(43\) 5.79832 0.884235 0.442118 0.896957i \(-0.354227\pi\)
0.442118 + 0.896957i \(0.354227\pi\)
\(44\) −1.70892 −0.257630
\(45\) 3.60603 0.537556
\(46\) −4.03416 −0.594805
\(47\) −10.7508 −1.56816 −0.784079 0.620661i \(-0.786864\pi\)
−0.784079 + 0.620661i \(0.786864\pi\)
\(48\) −3.05405 −0.440815
\(49\) −0.943060 −0.134723
\(50\) −10.1396 −1.43395
\(51\) 1.00000 0.140028
\(52\) −2.71659 −0.376724
\(53\) −1.67641 −0.230272 −0.115136 0.993350i \(-0.536730\pi\)
−0.115136 + 0.993350i \(0.536730\pi\)
\(54\) −1.26690 −0.172403
\(55\) 15.6022 2.10380
\(56\) −7.46738 −0.997871
\(57\) 1.02429 0.135671
\(58\) −2.67315 −0.351002
\(59\) 1.63966 0.213465 0.106733 0.994288i \(-0.465961\pi\)
0.106733 + 0.994288i \(0.465961\pi\)
\(60\) −1.42428 −0.183874
\(61\) −7.36202 −0.942611 −0.471305 0.881970i \(-0.656217\pi\)
−0.471305 + 0.881970i \(0.656217\pi\)
\(62\) −13.9609 −1.77304
\(63\) −2.46109 −0.310068
\(64\) 8.89426 1.11178
\(65\) 24.8021 3.07632
\(66\) −5.48148 −0.674724
\(67\) 2.03979 0.249200 0.124600 0.992207i \(-0.460235\pi\)
0.124600 + 0.992207i \(0.460235\pi\)
\(68\) −0.394972 −0.0478974
\(69\) 3.18429 0.383343
\(70\) 11.2434 1.34384
\(71\) −3.93293 −0.466753 −0.233376 0.972386i \(-0.574977\pi\)
−0.233376 + 0.972386i \(0.574977\pi\)
\(72\) 3.03418 0.357582
\(73\) −7.02232 −0.821901 −0.410950 0.911658i \(-0.634803\pi\)
−0.410950 + 0.911658i \(0.634803\pi\)
\(74\) 4.87118 0.566263
\(75\) 8.00349 0.924163
\(76\) −0.404566 −0.0464069
\(77\) −10.6484 −1.21349
\(78\) −8.71364 −0.986626
\(79\) 1.00000 0.112509
\(80\) −11.0130 −1.23129
\(81\) 1.00000 0.111111
\(82\) 4.70588 0.519678
\(83\) 2.00730 0.220330 0.110165 0.993913i \(-0.464862\pi\)
0.110165 + 0.993913i \(0.464862\pi\)
\(84\) 0.972059 0.106060
\(85\) 3.60603 0.391129
\(86\) −7.34587 −0.792126
\(87\) 2.11000 0.226215
\(88\) 13.1280 1.39945
\(89\) 3.75596 0.398131 0.199066 0.979986i \(-0.436209\pi\)
0.199066 + 0.979986i \(0.436209\pi\)
\(90\) −4.56847 −0.481560
\(91\) −16.9272 −1.77445
\(92\) −1.25770 −0.131125
\(93\) 11.0198 1.14270
\(94\) 13.6201 1.40481
\(95\) 3.69363 0.378958
\(96\) −2.19919 −0.224454
\(97\) −0.409835 −0.0416124 −0.0208062 0.999784i \(-0.506623\pi\)
−0.0208062 + 0.999784i \(0.506623\pi\)
\(98\) 1.19476 0.120689
\(99\) 4.32670 0.434849
\(100\) −3.16115 −0.316115
\(101\) −13.6638 −1.35960 −0.679802 0.733396i \(-0.737934\pi\)
−0.679802 + 0.733396i \(0.737934\pi\)
\(102\) −1.26690 −0.125442
\(103\) −12.4933 −1.23100 −0.615499 0.788137i \(-0.711046\pi\)
−0.615499 + 0.788137i \(0.711046\pi\)
\(104\) 20.8689 2.04637
\(105\) −8.87476 −0.866088
\(106\) 2.12383 0.206285
\(107\) −2.33864 −0.226085 −0.113043 0.993590i \(-0.536060\pi\)
−0.113043 + 0.993590i \(0.536060\pi\)
\(108\) −0.394972 −0.0380062
\(109\) −9.08357 −0.870049 −0.435024 0.900419i \(-0.643260\pi\)
−0.435024 + 0.900419i \(0.643260\pi\)
\(110\) −19.7664 −1.88465
\(111\) −3.84497 −0.364948
\(112\) 7.51629 0.710222
\(113\) −13.4114 −1.26164 −0.630820 0.775929i \(-0.717282\pi\)
−0.630820 + 0.775929i \(0.717282\pi\)
\(114\) −1.29767 −0.121538
\(115\) 11.4826 1.07076
\(116\) −0.833389 −0.0773782
\(117\) 6.87794 0.635866
\(118\) −2.07728 −0.191229
\(119\) −2.46109 −0.225607
\(120\) 10.9414 0.998806
\(121\) 7.72031 0.701847
\(122\) 9.32693 0.844420
\(123\) −3.71450 −0.334925
\(124\) −4.35251 −0.390867
\(125\) 10.8307 0.968725
\(126\) 3.11794 0.277768
\(127\) −2.05867 −0.182678 −0.0913388 0.995820i \(-0.529115\pi\)
−0.0913388 + 0.995820i \(0.529115\pi\)
\(128\) −6.86972 −0.607203
\(129\) 5.79832 0.510513
\(130\) −31.4217 −2.75587
\(131\) 12.4435 1.08719 0.543596 0.839347i \(-0.317062\pi\)
0.543596 + 0.839347i \(0.317062\pi\)
\(132\) −1.70892 −0.148743
\(133\) −2.52087 −0.218587
\(134\) −2.58420 −0.223241
\(135\) 3.60603 0.310358
\(136\) 3.03418 0.260179
\(137\) −6.62722 −0.566201 −0.283101 0.959090i \(-0.591363\pi\)
−0.283101 + 0.959090i \(0.591363\pi\)
\(138\) −4.03416 −0.343411
\(139\) 8.97590 0.761326 0.380663 0.924714i \(-0.375696\pi\)
0.380663 + 0.924714i \(0.375696\pi\)
\(140\) 3.50528 0.296250
\(141\) −10.7508 −0.905377
\(142\) 4.98262 0.418132
\(143\) 29.7588 2.48855
\(144\) −3.05405 −0.254504
\(145\) 7.60872 0.631870
\(146\) 8.89656 0.736285
\(147\) −0.943060 −0.0777823
\(148\) 1.51865 0.124833
\(149\) 1.81441 0.148642 0.0743210 0.997234i \(-0.476321\pi\)
0.0743210 + 0.997234i \(0.476321\pi\)
\(150\) −10.1396 −0.827894
\(151\) −16.4110 −1.33551 −0.667753 0.744383i \(-0.732744\pi\)
−0.667753 + 0.744383i \(0.732744\pi\)
\(152\) 3.10788 0.252083
\(153\) 1.00000 0.0808452
\(154\) 13.4904 1.08709
\(155\) 39.7378 3.19181
\(156\) −2.71659 −0.217502
\(157\) 8.32711 0.664576 0.332288 0.943178i \(-0.392179\pi\)
0.332288 + 0.943178i \(0.392179\pi\)
\(158\) −1.26690 −0.100789
\(159\) −1.67641 −0.132948
\(160\) −7.93037 −0.626951
\(161\) −7.83680 −0.617626
\(162\) −1.26690 −0.0995368
\(163\) −7.54315 −0.590825 −0.295412 0.955370i \(-0.595457\pi\)
−0.295412 + 0.955370i \(0.595457\pi\)
\(164\) 1.46712 0.114563
\(165\) 15.6022 1.21463
\(166\) −2.54304 −0.197378
\(167\) −0.0281472 −0.00217810 −0.00108905 0.999999i \(-0.500347\pi\)
−0.00108905 + 0.999999i \(0.500347\pi\)
\(168\) −7.46738 −0.576121
\(169\) 34.3061 2.63893
\(170\) −4.56847 −0.350386
\(171\) 1.02429 0.0783294
\(172\) −2.29017 −0.174624
\(173\) 23.8128 1.81045 0.905225 0.424932i \(-0.139702\pi\)
0.905225 + 0.424932i \(0.139702\pi\)
\(174\) −2.67315 −0.202651
\(175\) −19.6973 −1.48897
\(176\) −13.2140 −0.996040
\(177\) 1.63966 0.123244
\(178\) −4.75842 −0.356659
\(179\) 9.65959 0.721992 0.360996 0.932567i \(-0.382437\pi\)
0.360996 + 0.932567i \(0.382437\pi\)
\(180\) −1.42428 −0.106160
\(181\) −13.6390 −1.01378 −0.506888 0.862012i \(-0.669204\pi\)
−0.506888 + 0.862012i \(0.669204\pi\)
\(182\) 21.4450 1.58961
\(183\) −7.36202 −0.544216
\(184\) 9.66170 0.712270
\(185\) −13.8651 −1.01938
\(186\) −13.9609 −1.02367
\(187\) 4.32670 0.316399
\(188\) 4.24624 0.309689
\(189\) −2.46109 −0.179018
\(190\) −4.67944 −0.339483
\(191\) 6.60493 0.477916 0.238958 0.971030i \(-0.423194\pi\)
0.238958 + 0.971030i \(0.423194\pi\)
\(192\) 8.89426 0.641888
\(193\) −4.38819 −0.315869 −0.157935 0.987450i \(-0.550483\pi\)
−0.157935 + 0.987450i \(0.550483\pi\)
\(194\) 0.519219 0.0372777
\(195\) 24.8021 1.77611
\(196\) 0.372482 0.0266059
\(197\) −4.55343 −0.324418 −0.162209 0.986756i \(-0.551862\pi\)
−0.162209 + 0.986756i \(0.551862\pi\)
\(198\) −5.48148 −0.389552
\(199\) −20.1322 −1.42714 −0.713568 0.700586i \(-0.752922\pi\)
−0.713568 + 0.700586i \(0.752922\pi\)
\(200\) 24.2840 1.71714
\(201\) 2.03979 0.143876
\(202\) 17.3107 1.21798
\(203\) −5.19288 −0.364469
\(204\) −0.394972 −0.0276536
\(205\) −13.3946 −0.935520
\(206\) 15.8277 1.10277
\(207\) 3.18429 0.221323
\(208\) −21.0056 −1.45648
\(209\) 4.43180 0.306554
\(210\) 11.2434 0.775869
\(211\) 23.4148 1.61194 0.805970 0.591957i \(-0.201644\pi\)
0.805970 + 0.591957i \(0.201644\pi\)
\(212\) 0.662133 0.0454755
\(213\) −3.93293 −0.269480
\(214\) 2.96282 0.202534
\(215\) 20.9089 1.42598
\(216\) 3.03418 0.206450
\(217\) −27.1206 −1.84107
\(218\) 11.5080 0.779417
\(219\) −7.02232 −0.474525
\(220\) −6.16244 −0.415472
\(221\) 6.87794 0.462660
\(222\) 4.87118 0.326932
\(223\) −8.99029 −0.602034 −0.301017 0.953619i \(-0.597326\pi\)
−0.301017 + 0.953619i \(0.597326\pi\)
\(224\) 5.41240 0.361631
\(225\) 8.00349 0.533566
\(226\) 16.9909 1.13022
\(227\) −13.9699 −0.927212 −0.463606 0.886041i \(-0.653445\pi\)
−0.463606 + 0.886041i \(0.653445\pi\)
\(228\) −0.404566 −0.0267930
\(229\) −7.43085 −0.491044 −0.245522 0.969391i \(-0.578959\pi\)
−0.245522 + 0.969391i \(0.578959\pi\)
\(230\) −14.5473 −0.959222
\(231\) −10.6484 −0.700611
\(232\) 6.40211 0.420319
\(233\) −29.6762 −1.94415 −0.972075 0.234671i \(-0.924599\pi\)
−0.972075 + 0.234671i \(0.924599\pi\)
\(234\) −8.71364 −0.569629
\(235\) −38.7676 −2.52892
\(236\) −0.647619 −0.0421564
\(237\) 1.00000 0.0649570
\(238\) 3.11794 0.202106
\(239\) −20.5697 −1.33054 −0.665272 0.746601i \(-0.731684\pi\)
−0.665272 + 0.746601i \(0.731684\pi\)
\(240\) −11.0130 −0.710888
\(241\) −25.5963 −1.64880 −0.824402 0.566005i \(-0.808488\pi\)
−0.824402 + 0.566005i \(0.808488\pi\)
\(242\) −9.78084 −0.628736
\(243\) 1.00000 0.0641500
\(244\) 2.90779 0.186152
\(245\) −3.40071 −0.217263
\(246\) 4.70588 0.300036
\(247\) 7.04501 0.448263
\(248\) 33.4361 2.12319
\(249\) 2.00730 0.127207
\(250\) −13.7213 −0.867814
\(251\) −6.78324 −0.428154 −0.214077 0.976817i \(-0.568674\pi\)
−0.214077 + 0.976817i \(0.568674\pi\)
\(252\) 0.972059 0.0612340
\(253\) 13.7774 0.866180
\(254\) 2.60813 0.163648
\(255\) 3.60603 0.225819
\(256\) −9.08529 −0.567830
\(257\) 19.9073 1.24178 0.620890 0.783898i \(-0.286771\pi\)
0.620890 + 0.783898i \(0.286771\pi\)
\(258\) −7.34587 −0.457334
\(259\) 9.46279 0.587989
\(260\) −9.79613 −0.607530
\(261\) 2.11000 0.130605
\(262\) −15.7646 −0.973940
\(263\) 17.3086 1.06730 0.533649 0.845706i \(-0.320821\pi\)
0.533649 + 0.845706i \(0.320821\pi\)
\(264\) 13.1280 0.807972
\(265\) −6.04517 −0.371352
\(266\) 3.19368 0.195817
\(267\) 3.75596 0.229861
\(268\) −0.805660 −0.0492135
\(269\) −20.7982 −1.26809 −0.634046 0.773296i \(-0.718607\pi\)
−0.634046 + 0.773296i \(0.718607\pi\)
\(270\) −4.56847 −0.278029
\(271\) 12.1348 0.737136 0.368568 0.929601i \(-0.379848\pi\)
0.368568 + 0.929601i \(0.379848\pi\)
\(272\) −3.05405 −0.185179
\(273\) −16.9272 −1.02448
\(274\) 8.39600 0.507221
\(275\) 34.6287 2.08819
\(276\) −1.25770 −0.0757048
\(277\) 26.2300 1.57601 0.788004 0.615671i \(-0.211115\pi\)
0.788004 + 0.615671i \(0.211115\pi\)
\(278\) −11.3715 −0.682020
\(279\) 11.0198 0.659738
\(280\) −26.9276 −1.60923
\(281\) 0.603688 0.0360130 0.0180065 0.999838i \(-0.494268\pi\)
0.0180065 + 0.999838i \(0.494268\pi\)
\(282\) 13.6201 0.811065
\(283\) 12.5103 0.743659 0.371830 0.928301i \(-0.378731\pi\)
0.371830 + 0.928301i \(0.378731\pi\)
\(284\) 1.55340 0.0921771
\(285\) 3.69363 0.218792
\(286\) −37.7013 −2.22932
\(287\) 9.14169 0.539617
\(288\) −2.19919 −0.129589
\(289\) 1.00000 0.0588235
\(290\) −9.63946 −0.566049
\(291\) −0.409835 −0.0240250
\(292\) 2.77362 0.162314
\(293\) −20.1930 −1.17969 −0.589843 0.807518i \(-0.700810\pi\)
−0.589843 + 0.807518i \(0.700810\pi\)
\(294\) 1.19476 0.0696798
\(295\) 5.91266 0.344249
\(296\) −11.6663 −0.678092
\(297\) 4.32670 0.251060
\(298\) −2.29867 −0.133158
\(299\) 21.9013 1.26659
\(300\) −3.16115 −0.182509
\(301\) −14.2702 −0.822518
\(302\) 20.7910 1.19639
\(303\) −13.6638 −0.784968
\(304\) −3.12824 −0.179417
\(305\) −26.5477 −1.52012
\(306\) −1.26690 −0.0724237
\(307\) −1.30351 −0.0743955 −0.0371977 0.999308i \(-0.511843\pi\)
−0.0371977 + 0.999308i \(0.511843\pi\)
\(308\) 4.20581 0.239648
\(309\) −12.4933 −0.710718
\(310\) −50.3436 −2.85933
\(311\) −1.43428 −0.0813306 −0.0406653 0.999173i \(-0.512948\pi\)
−0.0406653 + 0.999173i \(0.512948\pi\)
\(312\) 20.8689 1.18147
\(313\) −1.80053 −0.101772 −0.0508860 0.998704i \(-0.516205\pi\)
−0.0508860 + 0.998704i \(0.516205\pi\)
\(314\) −10.5496 −0.595348
\(315\) −8.87476 −0.500036
\(316\) −0.394972 −0.0222189
\(317\) 19.0499 1.06995 0.534974 0.844869i \(-0.320321\pi\)
0.534974 + 0.844869i \(0.320321\pi\)
\(318\) 2.12383 0.119099
\(319\) 9.12932 0.511144
\(320\) 32.0730 1.79294
\(321\) −2.33864 −0.130530
\(322\) 9.92841 0.553289
\(323\) 1.02429 0.0569930
\(324\) −0.394972 −0.0219429
\(325\) 55.0475 3.05349
\(326\) 9.55639 0.529279
\(327\) −9.08357 −0.502323
\(328\) −11.2705 −0.622307
\(329\) 26.4585 1.45871
\(330\) −19.7664 −1.08811
\(331\) −4.54377 −0.249748 −0.124874 0.992173i \(-0.539853\pi\)
−0.124874 + 0.992173i \(0.539853\pi\)
\(332\) −0.792826 −0.0435120
\(333\) −3.84497 −0.210703
\(334\) 0.0356596 0.00195121
\(335\) 7.35555 0.401877
\(336\) 7.51629 0.410047
\(337\) −3.10873 −0.169343 −0.0846717 0.996409i \(-0.526984\pi\)
−0.0846717 + 0.996409i \(0.526984\pi\)
\(338\) −43.4623 −2.36404
\(339\) −13.4114 −0.728409
\(340\) −1.42428 −0.0772425
\(341\) 47.6793 2.58198
\(342\) −1.29767 −0.0701700
\(343\) 19.5485 1.05552
\(344\) 17.5932 0.948559
\(345\) 11.4826 0.618205
\(346\) −30.1683 −1.62186
\(347\) −5.27170 −0.283000 −0.141500 0.989938i \(-0.545192\pi\)
−0.141500 + 0.989938i \(0.545192\pi\)
\(348\) −0.833389 −0.0446743
\(349\) 34.5823 1.85115 0.925573 0.378569i \(-0.123584\pi\)
0.925573 + 0.378569i \(0.123584\pi\)
\(350\) 24.9544 1.33387
\(351\) 6.87794 0.367117
\(352\) −9.51525 −0.507164
\(353\) −20.9297 −1.11398 −0.556989 0.830520i \(-0.688043\pi\)
−0.556989 + 0.830520i \(0.688043\pi\)
\(354\) −2.07728 −0.110406
\(355\) −14.1823 −0.752717
\(356\) −1.48350 −0.0786254
\(357\) −2.46109 −0.130254
\(358\) −12.2377 −0.646783
\(359\) 7.75726 0.409412 0.204706 0.978823i \(-0.434376\pi\)
0.204706 + 0.978823i \(0.434376\pi\)
\(360\) 10.9414 0.576661
\(361\) −17.9508 −0.944780
\(362\) 17.2792 0.908172
\(363\) 7.72031 0.405211
\(364\) 6.68577 0.350429
\(365\) −25.3227 −1.32545
\(366\) 9.32693 0.487526
\(367\) −20.1465 −1.05164 −0.525819 0.850596i \(-0.676241\pi\)
−0.525819 + 0.850596i \(0.676241\pi\)
\(368\) −9.72498 −0.506949
\(369\) −3.71450 −0.193369
\(370\) 17.5656 0.913193
\(371\) 4.12578 0.214200
\(372\) −4.35251 −0.225667
\(373\) −18.3044 −0.947768 −0.473884 0.880587i \(-0.657148\pi\)
−0.473884 + 0.880587i \(0.657148\pi\)
\(374\) −5.48148 −0.283441
\(375\) 10.8307 0.559294
\(376\) −32.6197 −1.68223
\(377\) 14.5124 0.747428
\(378\) 3.11794 0.160370
\(379\) −6.98642 −0.358868 −0.179434 0.983770i \(-0.557427\pi\)
−0.179434 + 0.983770i \(0.557427\pi\)
\(380\) −1.45888 −0.0748389
\(381\) −2.05867 −0.105469
\(382\) −8.36777 −0.428132
\(383\) 36.0036 1.83970 0.919849 0.392272i \(-0.128311\pi\)
0.919849 + 0.392272i \(0.128311\pi\)
\(384\) −6.86972 −0.350569
\(385\) −38.3984 −1.95696
\(386\) 5.55939 0.282965
\(387\) 5.79832 0.294745
\(388\) 0.161873 0.00821787
\(389\) −17.4498 −0.884742 −0.442371 0.896832i \(-0.645863\pi\)
−0.442371 + 0.896832i \(0.645863\pi\)
\(390\) −31.4217 −1.59110
\(391\) 3.18429 0.161036
\(392\) −2.86142 −0.144523
\(393\) 12.4435 0.627690
\(394\) 5.76872 0.290624
\(395\) 3.60603 0.181439
\(396\) −1.70892 −0.0858767
\(397\) 12.3394 0.619296 0.309648 0.950851i \(-0.399789\pi\)
0.309648 + 0.950851i \(0.399789\pi\)
\(398\) 25.5055 1.27847
\(399\) −2.52087 −0.126201
\(400\) −24.4431 −1.22215
\(401\) −3.69472 −0.184505 −0.0922527 0.995736i \(-0.529407\pi\)
−0.0922527 + 0.995736i \(0.529407\pi\)
\(402\) −2.58420 −0.128888
\(403\) 75.7935 3.77554
\(404\) 5.39684 0.268503
\(405\) 3.60603 0.179185
\(406\) 6.57884 0.326503
\(407\) −16.6360 −0.824616
\(408\) 3.03418 0.150214
\(409\) −27.6938 −1.36937 −0.684686 0.728838i \(-0.740061\pi\)
−0.684686 + 0.728838i \(0.740061\pi\)
\(410\) 16.9696 0.838068
\(411\) −6.62722 −0.326896
\(412\) 4.93449 0.243105
\(413\) −4.03534 −0.198566
\(414\) −4.03416 −0.198268
\(415\) 7.23839 0.355318
\(416\) −15.1259 −0.741610
\(417\) 8.97590 0.439552
\(418\) −5.61463 −0.274620
\(419\) 27.1998 1.32880 0.664398 0.747379i \(-0.268688\pi\)
0.664398 + 0.747379i \(0.268688\pi\)
\(420\) 3.50528 0.171040
\(421\) 18.4806 0.900687 0.450344 0.892855i \(-0.351301\pi\)
0.450344 + 0.892855i \(0.351301\pi\)
\(422\) −29.6641 −1.44403
\(423\) −10.7508 −0.522719
\(424\) −5.08652 −0.247023
\(425\) 8.00349 0.388226
\(426\) 4.98262 0.241409
\(427\) 18.1186 0.876819
\(428\) 0.923699 0.0446487
\(429\) 29.7588 1.43677
\(430\) −26.4895 −1.27744
\(431\) 32.6876 1.57451 0.787254 0.616629i \(-0.211502\pi\)
0.787254 + 0.616629i \(0.211502\pi\)
\(432\) −3.05405 −0.146938
\(433\) 23.9317 1.15008 0.575041 0.818125i \(-0.304986\pi\)
0.575041 + 0.818125i \(0.304986\pi\)
\(434\) 34.3591 1.64929
\(435\) 7.60872 0.364810
\(436\) 3.58776 0.171822
\(437\) 3.26163 0.156025
\(438\) 8.89656 0.425094
\(439\) 36.2900 1.73203 0.866013 0.500022i \(-0.166675\pi\)
0.866013 + 0.500022i \(0.166675\pi\)
\(440\) 47.3400 2.25685
\(441\) −0.943060 −0.0449076
\(442\) −8.71364 −0.414466
\(443\) 1.85387 0.0880798 0.0440399 0.999030i \(-0.485977\pi\)
0.0440399 + 0.999030i \(0.485977\pi\)
\(444\) 1.51865 0.0720721
\(445\) 13.5441 0.642054
\(446\) 11.3898 0.539321
\(447\) 1.81441 0.0858185
\(448\) −21.8895 −1.03418
\(449\) 14.0063 0.660996 0.330498 0.943807i \(-0.392783\pi\)
0.330498 + 0.943807i \(0.392783\pi\)
\(450\) −10.1396 −0.477985
\(451\) −16.0715 −0.756778
\(452\) 5.29714 0.249156
\(453\) −16.4110 −0.771055
\(454\) 17.6984 0.830626
\(455\) −61.0401 −2.86160
\(456\) 3.10788 0.145540
\(457\) −5.32504 −0.249095 −0.124548 0.992214i \(-0.539748\pi\)
−0.124548 + 0.992214i \(0.539748\pi\)
\(458\) 9.41412 0.439893
\(459\) 1.00000 0.0466760
\(460\) −4.53532 −0.211460
\(461\) 13.0886 0.609595 0.304798 0.952417i \(-0.401411\pi\)
0.304798 + 0.952417i \(0.401411\pi\)
\(462\) 13.4904 0.627630
\(463\) 4.15712 0.193198 0.0965988 0.995323i \(-0.469204\pi\)
0.0965988 + 0.995323i \(0.469204\pi\)
\(464\) −6.44404 −0.299157
\(465\) 39.7378 1.84279
\(466\) 37.5966 1.74163
\(467\) −13.7026 −0.634081 −0.317040 0.948412i \(-0.602689\pi\)
−0.317040 + 0.948412i \(0.602689\pi\)
\(468\) −2.71659 −0.125575
\(469\) −5.02010 −0.231807
\(470\) 49.1145 2.26548
\(471\) 8.32711 0.383693
\(472\) 4.97502 0.228994
\(473\) 25.0876 1.15353
\(474\) −1.26690 −0.0581905
\(475\) 8.19789 0.376145
\(476\) 0.972059 0.0445543
\(477\) −1.67641 −0.0767573
\(478\) 26.0597 1.19194
\(479\) 11.6636 0.532923 0.266462 0.963846i \(-0.414145\pi\)
0.266462 + 0.963846i \(0.414145\pi\)
\(480\) −7.93037 −0.361970
\(481\) −26.4454 −1.20581
\(482\) 32.4279 1.47705
\(483\) −7.83680 −0.356587
\(484\) −3.04931 −0.138605
\(485\) −1.47788 −0.0671071
\(486\) −1.26690 −0.0574676
\(487\) 33.5884 1.52203 0.761017 0.648732i \(-0.224700\pi\)
0.761017 + 0.648732i \(0.224700\pi\)
\(488\) −22.3377 −1.01118
\(489\) −7.54315 −0.341113
\(490\) 4.30835 0.194631
\(491\) −11.3079 −0.510318 −0.255159 0.966899i \(-0.582128\pi\)
−0.255159 + 0.966899i \(0.582128\pi\)
\(492\) 1.46712 0.0661430
\(493\) 2.11000 0.0950294
\(494\) −8.92530 −0.401568
\(495\) 15.6022 0.701268
\(496\) −33.6550 −1.51116
\(497\) 9.67928 0.434175
\(498\) −2.54304 −0.113956
\(499\) −23.0773 −1.03308 −0.516541 0.856262i \(-0.672781\pi\)
−0.516541 + 0.856262i \(0.672781\pi\)
\(500\) −4.27781 −0.191310
\(501\) −0.0281472 −0.00125752
\(502\) 8.59367 0.383554
\(503\) 36.0050 1.60538 0.802692 0.596393i \(-0.203400\pi\)
0.802692 + 0.596393i \(0.203400\pi\)
\(504\) −7.46738 −0.332624
\(505\) −49.2723 −2.19259
\(506\) −17.4546 −0.775952
\(507\) 34.3061 1.52359
\(508\) 0.813118 0.0360763
\(509\) 39.6681 1.75826 0.879129 0.476583i \(-0.158125\pi\)
0.879129 + 0.476583i \(0.158125\pi\)
\(510\) −4.56847 −0.202295
\(511\) 17.2825 0.764535
\(512\) 25.2496 1.11588
\(513\) 1.02429 0.0452235
\(514\) −25.2204 −1.11243
\(515\) −45.0512 −1.98519
\(516\) −2.29017 −0.100819
\(517\) −46.5152 −2.04574
\(518\) −11.9884 −0.526739
\(519\) 23.8128 1.04526
\(520\) 75.2541 3.30011
\(521\) 28.9891 1.27003 0.635017 0.772498i \(-0.280993\pi\)
0.635017 + 0.772498i \(0.280993\pi\)
\(522\) −2.67315 −0.117001
\(523\) −15.3834 −0.672669 −0.336334 0.941743i \(-0.609187\pi\)
−0.336334 + 0.941743i \(0.609187\pi\)
\(524\) −4.91482 −0.214705
\(525\) −19.6973 −0.859659
\(526\) −21.9283 −0.956118
\(527\) 11.0198 0.480030
\(528\) −13.2140 −0.575064
\(529\) −12.8603 −0.559145
\(530\) 7.65861 0.332669
\(531\) 1.63966 0.0711551
\(532\) 0.995671 0.0431678
\(533\) −25.5481 −1.10661
\(534\) −4.75842 −0.205917
\(535\) −8.43323 −0.364601
\(536\) 6.18910 0.267328
\(537\) 9.65959 0.416842
\(538\) 26.3492 1.13600
\(539\) −4.08034 −0.175752
\(540\) −1.42428 −0.0612913
\(541\) −11.9733 −0.514774 −0.257387 0.966308i \(-0.582861\pi\)
−0.257387 + 0.966308i \(0.582861\pi\)
\(542\) −15.3735 −0.660350
\(543\) −13.6390 −0.585304
\(544\) −2.19919 −0.0942897
\(545\) −32.7557 −1.40310
\(546\) 21.4450 0.917762
\(547\) −9.94841 −0.425363 −0.212682 0.977122i \(-0.568220\pi\)
−0.212682 + 0.977122i \(0.568220\pi\)
\(548\) 2.61756 0.111817
\(549\) −7.36202 −0.314204
\(550\) −43.8710 −1.87066
\(551\) 2.16125 0.0920723
\(552\) 9.66170 0.411229
\(553\) −2.46109 −0.104656
\(554\) −33.2307 −1.41184
\(555\) −13.8651 −0.588540
\(556\) −3.54523 −0.150351
\(557\) −16.1566 −0.684575 −0.342288 0.939595i \(-0.611202\pi\)
−0.342288 + 0.939595i \(0.611202\pi\)
\(558\) −13.9609 −0.591014
\(559\) 39.8805 1.68676
\(560\) 27.1040 1.14535
\(561\) 4.32670 0.182673
\(562\) −0.764810 −0.0322616
\(563\) 41.9107 1.76633 0.883163 0.469065i \(-0.155409\pi\)
0.883163 + 0.469065i \(0.155409\pi\)
\(564\) 4.24624 0.178799
\(565\) −48.3621 −2.03461
\(566\) −15.8492 −0.666193
\(567\) −2.46109 −0.103356
\(568\) −11.9332 −0.500707
\(569\) −14.2557 −0.597630 −0.298815 0.954311i \(-0.596591\pi\)
−0.298815 + 0.954311i \(0.596591\pi\)
\(570\) −4.67944 −0.196000
\(571\) 27.0724 1.13294 0.566472 0.824081i \(-0.308308\pi\)
0.566472 + 0.824081i \(0.308308\pi\)
\(572\) −11.7539 −0.491454
\(573\) 6.60493 0.275925
\(574\) −11.5816 −0.483406
\(575\) 25.4854 1.06281
\(576\) 8.89426 0.370594
\(577\) −32.2946 −1.34444 −0.672221 0.740351i \(-0.734660\pi\)
−0.672221 + 0.740351i \(0.734660\pi\)
\(578\) −1.26690 −0.0526960
\(579\) −4.38819 −0.182367
\(580\) −3.00523 −0.124785
\(581\) −4.94013 −0.204951
\(582\) 0.519219 0.0215223
\(583\) −7.25330 −0.300401
\(584\) −21.3070 −0.881691
\(585\) 24.8021 1.02544
\(586\) 25.5824 1.05680
\(587\) 12.9438 0.534248 0.267124 0.963662i \(-0.413927\pi\)
0.267124 + 0.963662i \(0.413927\pi\)
\(588\) 0.372482 0.0153609
\(589\) 11.2875 0.465092
\(590\) −7.49074 −0.308389
\(591\) −4.55343 −0.187303
\(592\) 11.7427 0.482623
\(593\) −26.5076 −1.08854 −0.544268 0.838911i \(-0.683193\pi\)
−0.544268 + 0.838911i \(0.683193\pi\)
\(594\) −5.48148 −0.224908
\(595\) −8.87476 −0.363830
\(596\) −0.716640 −0.0293547
\(597\) −20.1322 −0.823957
\(598\) −27.7467 −1.13465
\(599\) −22.6635 −0.926004 −0.463002 0.886357i \(-0.653228\pi\)
−0.463002 + 0.886357i \(0.653228\pi\)
\(600\) 24.2840 0.991392
\(601\) 19.2843 0.786623 0.393312 0.919405i \(-0.371329\pi\)
0.393312 + 0.919405i \(0.371329\pi\)
\(602\) 18.0788 0.736837
\(603\) 2.03979 0.0830667
\(604\) 6.48187 0.263744
\(605\) 27.8397 1.13185
\(606\) 17.3107 0.703199
\(607\) −33.4003 −1.35568 −0.677839 0.735211i \(-0.737083\pi\)
−0.677839 + 0.735211i \(0.737083\pi\)
\(608\) −2.25261 −0.0913555
\(609\) −5.19288 −0.210426
\(610\) 33.6332 1.36177
\(611\) −73.9430 −2.99141
\(612\) −0.394972 −0.0159658
\(613\) 28.2913 1.14267 0.571337 0.820716i \(-0.306425\pi\)
0.571337 + 0.820716i \(0.306425\pi\)
\(614\) 1.65142 0.0666458
\(615\) −13.3946 −0.540123
\(616\) −32.3091 −1.30177
\(617\) 41.5676 1.67345 0.836725 0.547624i \(-0.184468\pi\)
0.836725 + 0.547624i \(0.184468\pi\)
\(618\) 15.8277 0.636683
\(619\) 45.5246 1.82979 0.914893 0.403696i \(-0.132275\pi\)
0.914893 + 0.403696i \(0.132275\pi\)
\(620\) −15.6953 −0.630338
\(621\) 3.18429 0.127781
\(622\) 1.81709 0.0728585
\(623\) −9.24375 −0.370343
\(624\) −21.0056 −0.840897
\(625\) −0.961643 −0.0384657
\(626\) 2.28109 0.0911705
\(627\) 4.43180 0.176989
\(628\) −3.28897 −0.131244
\(629\) −3.84497 −0.153309
\(630\) 11.2434 0.447948
\(631\) −26.0677 −1.03774 −0.518868 0.854854i \(-0.673647\pi\)
−0.518868 + 0.854854i \(0.673647\pi\)
\(632\) 3.03418 0.120693
\(633\) 23.4148 0.930654
\(634\) −24.1342 −0.958493
\(635\) −7.42364 −0.294598
\(636\) 0.662133 0.0262553
\(637\) −6.48631 −0.256997
\(638\) −11.5659 −0.457898
\(639\) −3.93293 −0.155584
\(640\) −24.7725 −0.979217
\(641\) 13.6719 0.540009 0.270004 0.962859i \(-0.412975\pi\)
0.270004 + 0.962859i \(0.412975\pi\)
\(642\) 2.96282 0.116933
\(643\) −24.6783 −0.973218 −0.486609 0.873620i \(-0.661766\pi\)
−0.486609 + 0.873620i \(0.661766\pi\)
\(644\) 3.09531 0.121972
\(645\) 20.9089 0.823288
\(646\) −1.29767 −0.0510562
\(647\) −2.12641 −0.0835979 −0.0417989 0.999126i \(-0.513309\pi\)
−0.0417989 + 0.999126i \(0.513309\pi\)
\(648\) 3.03418 0.119194
\(649\) 7.09431 0.278476
\(650\) −69.7395 −2.73541
\(651\) −27.1206 −1.06294
\(652\) 2.97933 0.116680
\(653\) −11.3322 −0.443463 −0.221732 0.975108i \(-0.571171\pi\)
−0.221732 + 0.975108i \(0.571171\pi\)
\(654\) 11.5080 0.449997
\(655\) 44.8716 1.75328
\(656\) 11.3443 0.442919
\(657\) −7.02232 −0.273967
\(658\) −33.5202 −1.30675
\(659\) 35.2566 1.37340 0.686701 0.726940i \(-0.259058\pi\)
0.686701 + 0.726940i \(0.259058\pi\)
\(660\) −6.16244 −0.239873
\(661\) −17.7745 −0.691349 −0.345674 0.938355i \(-0.612350\pi\)
−0.345674 + 0.938355i \(0.612350\pi\)
\(662\) 5.75649 0.223732
\(663\) 6.87794 0.267117
\(664\) 6.09051 0.236358
\(665\) −9.09033 −0.352508
\(666\) 4.87118 0.188754
\(667\) 6.71883 0.260154
\(668\) 0.0111174 0.000430143 0
\(669\) −8.99029 −0.347585
\(670\) −9.31873 −0.360014
\(671\) −31.8533 −1.22968
\(672\) 5.41240 0.208788
\(673\) −22.9469 −0.884538 −0.442269 0.896883i \(-0.645826\pi\)
−0.442269 + 0.896883i \(0.645826\pi\)
\(674\) 3.93844 0.151703
\(675\) 8.00349 0.308054
\(676\) −13.5499 −0.521151
\(677\) −24.0602 −0.924710 −0.462355 0.886695i \(-0.652995\pi\)
−0.462355 + 0.886695i \(0.652995\pi\)
\(678\) 16.9909 0.652531
\(679\) 1.00864 0.0387080
\(680\) 10.9414 0.419582
\(681\) −13.9699 −0.535326
\(682\) −60.4048 −2.31302
\(683\) −13.5985 −0.520334 −0.260167 0.965564i \(-0.583778\pi\)
−0.260167 + 0.965564i \(0.583778\pi\)
\(684\) −0.404566 −0.0154690
\(685\) −23.8980 −0.913094
\(686\) −24.7660 −0.945570
\(687\) −7.43085 −0.283504
\(688\) −17.7084 −0.675125
\(689\) −11.5302 −0.439266
\(690\) −14.5473 −0.553807
\(691\) −33.1769 −1.26211 −0.631055 0.775738i \(-0.717378\pi\)
−0.631055 + 0.775738i \(0.717378\pi\)
\(692\) −9.40537 −0.357539
\(693\) −10.6484 −0.404498
\(694\) 6.67870 0.253520
\(695\) 32.3674 1.22777
\(696\) 6.40211 0.242671
\(697\) −3.71450 −0.140697
\(698\) −43.8122 −1.65832
\(699\) −29.6762 −1.12246
\(700\) 7.77986 0.294051
\(701\) 25.0473 0.946022 0.473011 0.881056i \(-0.343167\pi\)
0.473011 + 0.881056i \(0.343167\pi\)
\(702\) −8.71364 −0.328875
\(703\) −3.93836 −0.148538
\(704\) 38.4828 1.45037
\(705\) −38.7676 −1.46007
\(706\) 26.5158 0.997936
\(707\) 33.6279 1.26471
\(708\) −0.647619 −0.0243390
\(709\) 19.7256 0.740809 0.370404 0.928871i \(-0.379219\pi\)
0.370404 + 0.928871i \(0.379219\pi\)
\(710\) 17.9675 0.674308
\(711\) 1.00000 0.0375029
\(712\) 11.3963 0.427094
\(713\) 35.0902 1.31414
\(714\) 3.11794 0.116686
\(715\) 107.311 4.01321
\(716\) −3.81527 −0.142583
\(717\) −20.5697 −0.768190
\(718\) −9.82765 −0.366764
\(719\) −43.5503 −1.62415 −0.812076 0.583551i \(-0.801663\pi\)
−0.812076 + 0.583551i \(0.801663\pi\)
\(720\) −11.0130 −0.410431
\(721\) 30.7470 1.14508
\(722\) 22.7419 0.846364
\(723\) −25.5963 −0.951937
\(724\) 5.38700 0.200206
\(725\) 16.8873 0.627179
\(726\) −9.78084 −0.363001
\(727\) −25.7710 −0.955792 −0.477896 0.878416i \(-0.658600\pi\)
−0.477896 + 0.878416i \(0.658600\pi\)
\(728\) −51.3602 −1.90354
\(729\) 1.00000 0.0370370
\(730\) 32.0813 1.18738
\(731\) 5.79832 0.214458
\(732\) 2.90779 0.107475
\(733\) −18.6401 −0.688488 −0.344244 0.938880i \(-0.611865\pi\)
−0.344244 + 0.938880i \(0.611865\pi\)
\(734\) 25.5235 0.942091
\(735\) −3.40071 −0.125437
\(736\) −7.00286 −0.258129
\(737\) 8.82556 0.325094
\(738\) 4.70588 0.173226
\(739\) −7.27703 −0.267690 −0.133845 0.991002i \(-0.542732\pi\)
−0.133845 + 0.991002i \(0.542732\pi\)
\(740\) 5.47632 0.201313
\(741\) 7.04501 0.258805
\(742\) −5.22693 −0.191887
\(743\) 20.8378 0.764464 0.382232 0.924066i \(-0.375156\pi\)
0.382232 + 0.924066i \(0.375156\pi\)
\(744\) 33.4361 1.22583
\(745\) 6.54281 0.239710
\(746\) 23.1899 0.849041
\(747\) 2.00730 0.0734432
\(748\) −1.70892 −0.0624844
\(749\) 5.75560 0.210305
\(750\) −13.7213 −0.501033
\(751\) −52.3594 −1.91062 −0.955311 0.295603i \(-0.904480\pi\)
−0.955311 + 0.295603i \(0.904480\pi\)
\(752\) 32.8334 1.19731
\(753\) −6.78324 −0.247195
\(754\) −18.3858 −0.669570
\(755\) −59.1785 −2.15373
\(756\) 0.972059 0.0353535
\(757\) −30.3943 −1.10470 −0.552350 0.833612i \(-0.686269\pi\)
−0.552350 + 0.833612i \(0.686269\pi\)
\(758\) 8.85107 0.321486
\(759\) 13.7774 0.500089
\(760\) 11.2071 0.406526
\(761\) −37.2863 −1.35163 −0.675814 0.737073i \(-0.736208\pi\)
−0.675814 + 0.737073i \(0.736208\pi\)
\(762\) 2.60813 0.0944824
\(763\) 22.3554 0.809322
\(764\) −2.60876 −0.0943817
\(765\) 3.60603 0.130376
\(766\) −45.6129 −1.64806
\(767\) 11.2775 0.407206
\(768\) −9.08529 −0.327837
\(769\) 7.59774 0.273981 0.136991 0.990572i \(-0.456257\pi\)
0.136991 + 0.990572i \(0.456257\pi\)
\(770\) 48.6468 1.75311
\(771\) 19.9073 0.716942
\(772\) 1.73321 0.0623797
\(773\) 5.98933 0.215421 0.107711 0.994182i \(-0.465648\pi\)
0.107711 + 0.994182i \(0.465648\pi\)
\(774\) −7.34587 −0.264042
\(775\) 88.1968 3.16812
\(776\) −1.24351 −0.0446396
\(777\) 9.46279 0.339476
\(778\) 22.1071 0.792580
\(779\) −3.80472 −0.136318
\(780\) −9.79613 −0.350758
\(781\) −17.0166 −0.608902
\(782\) −4.03416 −0.144261
\(783\) 2.11000 0.0754051
\(784\) 2.88016 0.102863
\(785\) 30.0279 1.07174
\(786\) −15.7646 −0.562305
\(787\) −9.32781 −0.332501 −0.166250 0.986084i \(-0.553166\pi\)
−0.166250 + 0.986084i \(0.553166\pi\)
\(788\) 1.79848 0.0640680
\(789\) 17.3086 0.616204
\(790\) −4.56847 −0.162539
\(791\) 33.0067 1.17358
\(792\) 13.1280 0.466483
\(793\) −50.6356 −1.79812
\(794\) −15.6327 −0.554785
\(795\) −6.04517 −0.214400
\(796\) 7.95166 0.281839
\(797\) −2.97478 −0.105372 −0.0526861 0.998611i \(-0.516778\pi\)
−0.0526861 + 0.998611i \(0.516778\pi\)
\(798\) 3.19368 0.113055
\(799\) −10.7508 −0.380334
\(800\) −17.6012 −0.622297
\(801\) 3.75596 0.132710
\(802\) 4.68083 0.165286
\(803\) −30.3835 −1.07221
\(804\) −0.805660 −0.0284134
\(805\) −28.2598 −0.996026
\(806\) −96.0225 −3.38225
\(807\) −20.7982 −0.732133
\(808\) −41.4586 −1.45851
\(809\) 26.3095 0.924991 0.462496 0.886622i \(-0.346954\pi\)
0.462496 + 0.886622i \(0.346954\pi\)
\(810\) −4.56847 −0.160520
\(811\) 33.1979 1.16574 0.582868 0.812567i \(-0.301930\pi\)
0.582868 + 0.812567i \(0.301930\pi\)
\(812\) 2.05104 0.0719774
\(813\) 12.1348 0.425586
\(814\) 21.0761 0.738717
\(815\) −27.2008 −0.952804
\(816\) −3.05405 −0.106913
\(817\) 5.93916 0.207785
\(818\) 35.0852 1.22673
\(819\) −16.9272 −0.591484
\(820\) 5.29049 0.184752
\(821\) −3.06087 −0.106825 −0.0534126 0.998573i \(-0.517010\pi\)
−0.0534126 + 0.998573i \(0.517010\pi\)
\(822\) 8.39600 0.292844
\(823\) 47.0026 1.63841 0.819204 0.573502i \(-0.194416\pi\)
0.819204 + 0.573502i \(0.194416\pi\)
\(824\) −37.9069 −1.32055
\(825\) 34.6287 1.20562
\(826\) 5.11236 0.177882
\(827\) −54.9477 −1.91072 −0.955360 0.295445i \(-0.904532\pi\)
−0.955360 + 0.295445i \(0.904532\pi\)
\(828\) −1.25770 −0.0437082
\(829\) −11.7361 −0.407612 −0.203806 0.979011i \(-0.565331\pi\)
−0.203806 + 0.979011i \(0.565331\pi\)
\(830\) −9.17029 −0.318305
\(831\) 26.2300 0.909908
\(832\) 61.1742 2.12083
\(833\) −0.943060 −0.0326751
\(834\) −11.3715 −0.393764
\(835\) −0.101500 −0.00351254
\(836\) −1.75043 −0.0605400
\(837\) 11.0198 0.380900
\(838\) −34.4593 −1.19038
\(839\) −32.6383 −1.12680 −0.563399 0.826185i \(-0.690507\pi\)
−0.563399 + 0.826185i \(0.690507\pi\)
\(840\) −26.9276 −0.929092
\(841\) −24.5479 −0.846480
\(842\) −23.4130 −0.806864
\(843\) 0.603688 0.0207921
\(844\) −9.24818 −0.318335
\(845\) 123.709 4.25572
\(846\) 13.6201 0.468268
\(847\) −19.0004 −0.652860
\(848\) 5.11983 0.175816
\(849\) 12.5103 0.429352
\(850\) −10.1396 −0.347785
\(851\) −12.2435 −0.419701
\(852\) 1.55340 0.0532185
\(853\) −41.1697 −1.40962 −0.704812 0.709395i \(-0.748968\pi\)
−0.704812 + 0.709395i \(0.748968\pi\)
\(854\) −22.9544 −0.785482
\(855\) 3.69363 0.126319
\(856\) −7.09588 −0.242532
\(857\) −37.4206 −1.27826 −0.639132 0.769097i \(-0.720706\pi\)
−0.639132 + 0.769097i \(0.720706\pi\)
\(858\) −37.7013 −1.28710
\(859\) 52.4913 1.79098 0.895490 0.445081i \(-0.146825\pi\)
0.895490 + 0.445081i \(0.146825\pi\)
\(860\) −8.25844 −0.281610
\(861\) 9.14169 0.311548
\(862\) −41.4119 −1.41049
\(863\) −32.3238 −1.10032 −0.550158 0.835061i \(-0.685432\pi\)
−0.550158 + 0.835061i \(0.685432\pi\)
\(864\) −2.19919 −0.0748181
\(865\) 85.8696 2.91966
\(866\) −30.3189 −1.03028
\(867\) 1.00000 0.0339618
\(868\) 10.7119 0.363585
\(869\) 4.32670 0.146773
\(870\) −9.63946 −0.326808
\(871\) 14.0296 0.475373
\(872\) −27.5612 −0.933341
\(873\) −0.409835 −0.0138708
\(874\) −4.13215 −0.139772
\(875\) −26.6552 −0.901111
\(876\) 2.77362 0.0937120
\(877\) −44.3456 −1.49744 −0.748722 0.662884i \(-0.769332\pi\)
−0.748722 + 0.662884i \(0.769332\pi\)
\(878\) −45.9757 −1.55160
\(879\) −20.1930 −0.681092
\(880\) −47.6500 −1.60628
\(881\) 21.0812 0.710244 0.355122 0.934820i \(-0.384439\pi\)
0.355122 + 0.934820i \(0.384439\pi\)
\(882\) 1.19476 0.0402297
\(883\) 14.3239 0.482036 0.241018 0.970521i \(-0.422519\pi\)
0.241018 + 0.970521i \(0.422519\pi\)
\(884\) −2.71659 −0.0913689
\(885\) 5.91266 0.198752
\(886\) −2.34866 −0.0789047
\(887\) −13.5909 −0.456336 −0.228168 0.973622i \(-0.573274\pi\)
−0.228168 + 0.973622i \(0.573274\pi\)
\(888\) −11.6663 −0.391496
\(889\) 5.06657 0.169927
\(890\) −17.1590 −0.575172
\(891\) 4.32670 0.144950
\(892\) 3.55091 0.118893
\(893\) −11.0119 −0.368499
\(894\) −2.29867 −0.0768789
\(895\) 34.8328 1.16433
\(896\) 16.9070 0.564822
\(897\) 21.9013 0.731264
\(898\) −17.7445 −0.592141
\(899\) 23.2517 0.775488
\(900\) −3.16115 −0.105372
\(901\) −1.67641 −0.0558491
\(902\) 20.3609 0.677945
\(903\) −14.2702 −0.474881
\(904\) −40.6927 −1.35342
\(905\) −49.1826 −1.63488
\(906\) 20.7910 0.690735
\(907\) 24.5040 0.813641 0.406821 0.913508i \(-0.366637\pi\)
0.406821 + 0.913508i \(0.366637\pi\)
\(908\) 5.51770 0.183111
\(909\) −13.6638 −0.453201
\(910\) 77.3315 2.56351
\(911\) −49.6960 −1.64650 −0.823250 0.567678i \(-0.807842\pi\)
−0.823250 + 0.567678i \(0.807842\pi\)
\(912\) −3.12824 −0.103586
\(913\) 8.68497 0.287431
\(914\) 6.74628 0.223147
\(915\) −26.5477 −0.877640
\(916\) 2.93497 0.0969743
\(917\) −30.6245 −1.01131
\(918\) −1.26690 −0.0418138
\(919\) 59.2114 1.95321 0.976603 0.215051i \(-0.0689919\pi\)
0.976603 + 0.215051i \(0.0689919\pi\)
\(920\) 34.8404 1.14866
\(921\) −1.30351 −0.0429522
\(922\) −16.5819 −0.546094
\(923\) −27.0505 −0.890377
\(924\) 4.20581 0.138361
\(925\) −30.7731 −1.01181
\(926\) −5.26664 −0.173072
\(927\) −12.4933 −0.410333
\(928\) −4.64029 −0.152325
\(929\) −32.4081 −1.06327 −0.531637 0.846972i \(-0.678423\pi\)
−0.531637 + 0.846972i \(0.678423\pi\)
\(930\) −50.3436 −1.65083
\(931\) −0.965967 −0.0316583
\(932\) 11.7212 0.383942
\(933\) −1.43428 −0.0469562
\(934\) 17.3598 0.568030
\(935\) 15.6022 0.510247
\(936\) 20.8689 0.682122
\(937\) 12.6115 0.411999 0.205999 0.978552i \(-0.433956\pi\)
0.205999 + 0.978552i \(0.433956\pi\)
\(938\) 6.35995 0.207660
\(939\) −1.80053 −0.0587581
\(940\) 15.3121 0.499426
\(941\) −4.84264 −0.157865 −0.0789327 0.996880i \(-0.525151\pi\)
−0.0789327 + 0.996880i \(0.525151\pi\)
\(942\) −10.5496 −0.343724
\(943\) −11.8280 −0.385173
\(944\) −5.00760 −0.162984
\(945\) −8.87476 −0.288696
\(946\) −31.7834 −1.03337
\(947\) −53.6510 −1.74342 −0.871711 0.490021i \(-0.836989\pi\)
−0.871711 + 0.490021i \(0.836989\pi\)
\(948\) −0.394972 −0.0128281
\(949\) −48.2991 −1.56786
\(950\) −10.3859 −0.336963
\(951\) 19.0499 0.617735
\(952\) −7.46738 −0.242019
\(953\) 23.2884 0.754386 0.377193 0.926135i \(-0.376889\pi\)
0.377193 + 0.926135i \(0.376889\pi\)
\(954\) 2.12383 0.0687616
\(955\) 23.8176 0.770720
\(956\) 8.12446 0.262764
\(957\) 9.12932 0.295109
\(958\) −14.7766 −0.477409
\(959\) 16.3101 0.526682
\(960\) 32.0730 1.03515
\(961\) 90.4358 2.91728
\(962\) 33.5037 1.08020
\(963\) −2.33864 −0.0753618
\(964\) 10.1098 0.325616
\(965\) −15.8240 −0.509392
\(966\) 9.92841 0.319442
\(967\) 21.8121 0.701429 0.350714 0.936482i \(-0.385939\pi\)
0.350714 + 0.936482i \(0.385939\pi\)
\(968\) 23.4248 0.752903
\(969\) 1.02429 0.0329049
\(970\) 1.87232 0.0601166
\(971\) −13.3978 −0.429954 −0.214977 0.976619i \(-0.568968\pi\)
−0.214977 + 0.976619i \(0.568968\pi\)
\(972\) −0.394972 −0.0126687
\(973\) −22.0905 −0.708187
\(974\) −42.5530 −1.36349
\(975\) 55.0475 1.76293
\(976\) 22.4840 0.719696
\(977\) 34.2518 1.09581 0.547906 0.836540i \(-0.315425\pi\)
0.547906 + 0.836540i \(0.315425\pi\)
\(978\) 9.55639 0.305580
\(979\) 16.2509 0.519382
\(980\) 1.34318 0.0429064
\(981\) −9.08357 −0.290016
\(982\) 14.3259 0.457159
\(983\) 48.6071 1.55032 0.775162 0.631762i \(-0.217668\pi\)
0.775162 + 0.631762i \(0.217668\pi\)
\(984\) −11.2705 −0.359289
\(985\) −16.4198 −0.523179
\(986\) −2.67315 −0.0851304
\(987\) 26.4585 0.842184
\(988\) −2.78258 −0.0885257
\(989\) 18.4635 0.587105
\(990\) −19.7664 −0.628218
\(991\) −18.3700 −0.583542 −0.291771 0.956488i \(-0.594244\pi\)
−0.291771 + 0.956488i \(0.594244\pi\)
\(992\) −24.2347 −0.769451
\(993\) −4.54377 −0.144192
\(994\) −12.2626 −0.388948
\(995\) −72.5975 −2.30150
\(996\) −0.792826 −0.0251217
\(997\) −40.3551 −1.27806 −0.639029 0.769183i \(-0.720664\pi\)
−0.639029 + 0.769183i \(0.720664\pi\)
\(998\) 29.2366 0.925468
\(999\) −3.84497 −0.121649
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.k.1.10 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.k.1.10 31 1.1 even 1 trivial