Properties

Label 4029.2.a.l.1.4
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 1.4
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.50856 q^{2} -1.00000 q^{3} +4.29286 q^{4} -2.69434 q^{5} +2.50856 q^{6} +3.74400 q^{7} -5.75176 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.50856 q^{2} -1.00000 q^{3} +4.29286 q^{4} -2.69434 q^{5} +2.50856 q^{6} +3.74400 q^{7} -5.75176 q^{8} +1.00000 q^{9} +6.75889 q^{10} -1.71911 q^{11} -4.29286 q^{12} -0.139018 q^{13} -9.39205 q^{14} +2.69434 q^{15} +5.84290 q^{16} -1.00000 q^{17} -2.50856 q^{18} +5.54406 q^{19} -11.5664 q^{20} -3.74400 q^{21} +4.31249 q^{22} +5.39210 q^{23} +5.75176 q^{24} +2.25944 q^{25} +0.348734 q^{26} -1.00000 q^{27} +16.0725 q^{28} +7.20257 q^{29} -6.75889 q^{30} -6.35822 q^{31} -3.15372 q^{32} +1.71911 q^{33} +2.50856 q^{34} -10.0876 q^{35} +4.29286 q^{36} -9.56660 q^{37} -13.9076 q^{38} +0.139018 q^{39} +15.4972 q^{40} +0.327658 q^{41} +9.39205 q^{42} +11.0164 q^{43} -7.37990 q^{44} -2.69434 q^{45} -13.5264 q^{46} -8.65194 q^{47} -5.84290 q^{48} +7.01757 q^{49} -5.66794 q^{50} +1.00000 q^{51} -0.596784 q^{52} +2.07677 q^{53} +2.50856 q^{54} +4.63187 q^{55} -21.5346 q^{56} -5.54406 q^{57} -18.0680 q^{58} +2.59407 q^{59} +11.5664 q^{60} +15.1344 q^{61} +15.9500 q^{62} +3.74400 q^{63} -3.77451 q^{64} +0.374561 q^{65} -4.31249 q^{66} +4.21389 q^{67} -4.29286 q^{68} -5.39210 q^{69} +25.3053 q^{70} +8.71318 q^{71} -5.75176 q^{72} +10.0129 q^{73} +23.9984 q^{74} -2.25944 q^{75} +23.7998 q^{76} -6.43637 q^{77} -0.348734 q^{78} +1.00000 q^{79} -15.7427 q^{80} +1.00000 q^{81} -0.821949 q^{82} -16.7409 q^{83} -16.0725 q^{84} +2.69434 q^{85} -27.6354 q^{86} -7.20257 q^{87} +9.88792 q^{88} -0.176143 q^{89} +6.75889 q^{90} -0.520484 q^{91} +23.1475 q^{92} +6.35822 q^{93} +21.7039 q^{94} -14.9376 q^{95} +3.15372 q^{96} -9.72863 q^{97} -17.6040 q^{98} -1.71911 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.50856 −1.77382 −0.886909 0.461945i \(-0.847152\pi\)
−0.886909 + 0.461945i \(0.847152\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.29286 2.14643
\(5\) −2.69434 −1.20494 −0.602472 0.798140i \(-0.705817\pi\)
−0.602472 + 0.798140i \(0.705817\pi\)
\(6\) 2.50856 1.02411
\(7\) 3.74400 1.41510 0.707550 0.706663i \(-0.249800\pi\)
0.707550 + 0.706663i \(0.249800\pi\)
\(8\) −5.75176 −2.03355
\(9\) 1.00000 0.333333
\(10\) 6.75889 2.13735
\(11\) −1.71911 −0.518332 −0.259166 0.965833i \(-0.583448\pi\)
−0.259166 + 0.965833i \(0.583448\pi\)
\(12\) −4.29286 −1.23924
\(13\) −0.139018 −0.0385566 −0.0192783 0.999814i \(-0.506137\pi\)
−0.0192783 + 0.999814i \(0.506137\pi\)
\(14\) −9.39205 −2.51013
\(15\) 2.69434 0.695674
\(16\) 5.84290 1.46072
\(17\) −1.00000 −0.242536
\(18\) −2.50856 −0.591272
\(19\) 5.54406 1.27189 0.635947 0.771732i \(-0.280610\pi\)
0.635947 + 0.771732i \(0.280610\pi\)
\(20\) −11.5664 −2.58632
\(21\) −3.74400 −0.817009
\(22\) 4.31249 0.919427
\(23\) 5.39210 1.12433 0.562165 0.827025i \(-0.309968\pi\)
0.562165 + 0.827025i \(0.309968\pi\)
\(24\) 5.75176 1.17407
\(25\) 2.25944 0.451888
\(26\) 0.348734 0.0683924
\(27\) −1.00000 −0.192450
\(28\) 16.0725 3.03741
\(29\) 7.20257 1.33748 0.668741 0.743495i \(-0.266833\pi\)
0.668741 + 0.743495i \(0.266833\pi\)
\(30\) −6.75889 −1.23400
\(31\) −6.35822 −1.14197 −0.570985 0.820961i \(-0.693439\pi\)
−0.570985 + 0.820961i \(0.693439\pi\)
\(32\) −3.15372 −0.557504
\(33\) 1.71911 0.299259
\(34\) 2.50856 0.430214
\(35\) −10.0876 −1.70512
\(36\) 4.29286 0.715476
\(37\) −9.56660 −1.57274 −0.786370 0.617756i \(-0.788042\pi\)
−0.786370 + 0.617756i \(0.788042\pi\)
\(38\) −13.9076 −2.25611
\(39\) 0.139018 0.0222607
\(40\) 15.4972 2.45032
\(41\) 0.327658 0.0511716 0.0255858 0.999673i \(-0.491855\pi\)
0.0255858 + 0.999673i \(0.491855\pi\)
\(42\) 9.39205 1.44922
\(43\) 11.0164 1.67999 0.839996 0.542592i \(-0.182557\pi\)
0.839996 + 0.542592i \(0.182557\pi\)
\(44\) −7.37990 −1.11256
\(45\) −2.69434 −0.401648
\(46\) −13.5264 −1.99436
\(47\) −8.65194 −1.26202 −0.631008 0.775777i \(-0.717358\pi\)
−0.631008 + 0.775777i \(0.717358\pi\)
\(48\) −5.84290 −0.843349
\(49\) 7.01757 1.00251
\(50\) −5.66794 −0.801568
\(51\) 1.00000 0.140028
\(52\) −0.596784 −0.0827590
\(53\) 2.07677 0.285267 0.142633 0.989776i \(-0.454443\pi\)
0.142633 + 0.989776i \(0.454443\pi\)
\(54\) 2.50856 0.341371
\(55\) 4.63187 0.624561
\(56\) −21.5346 −2.87768
\(57\) −5.54406 −0.734329
\(58\) −18.0680 −2.37245
\(59\) 2.59407 0.337719 0.168860 0.985640i \(-0.445992\pi\)
0.168860 + 0.985640i \(0.445992\pi\)
\(60\) 11.5664 1.49321
\(61\) 15.1344 1.93776 0.968882 0.247522i \(-0.0796164\pi\)
0.968882 + 0.247522i \(0.0796164\pi\)
\(62\) 15.9500 2.02565
\(63\) 3.74400 0.471700
\(64\) −3.77451 −0.471814
\(65\) 0.374561 0.0464585
\(66\) −4.31249 −0.530831
\(67\) 4.21389 0.514809 0.257404 0.966304i \(-0.417133\pi\)
0.257404 + 0.966304i \(0.417133\pi\)
\(68\) −4.29286 −0.520585
\(69\) −5.39210 −0.649133
\(70\) 25.3053 3.02456
\(71\) 8.71318 1.03406 0.517032 0.855966i \(-0.327037\pi\)
0.517032 + 0.855966i \(0.327037\pi\)
\(72\) −5.75176 −0.677851
\(73\) 10.0129 1.17192 0.585962 0.810339i \(-0.300717\pi\)
0.585962 + 0.810339i \(0.300717\pi\)
\(74\) 23.9984 2.78975
\(75\) −2.25944 −0.260898
\(76\) 23.7998 2.73003
\(77\) −6.43637 −0.733492
\(78\) −0.348734 −0.0394864
\(79\) 1.00000 0.112509
\(80\) −15.7427 −1.76009
\(81\) 1.00000 0.111111
\(82\) −0.821949 −0.0907691
\(83\) −16.7409 −1.83755 −0.918776 0.394779i \(-0.870821\pi\)
−0.918776 + 0.394779i \(0.870821\pi\)
\(84\) −16.0725 −1.75365
\(85\) 2.69434 0.292242
\(86\) −27.6354 −2.98000
\(87\) −7.20257 −0.772196
\(88\) 9.88792 1.05406
\(89\) −0.176143 −0.0186711 −0.00933555 0.999956i \(-0.502972\pi\)
−0.00933555 + 0.999956i \(0.502972\pi\)
\(90\) 6.75889 0.712450
\(91\) −0.520484 −0.0545615
\(92\) 23.1475 2.41329
\(93\) 6.35822 0.659317
\(94\) 21.7039 2.23858
\(95\) −14.9376 −1.53256
\(96\) 3.15372 0.321875
\(97\) −9.72863 −0.987793 −0.493896 0.869521i \(-0.664428\pi\)
−0.493896 + 0.869521i \(0.664428\pi\)
\(98\) −17.6040 −1.77827
\(99\) −1.71911 −0.172777
\(100\) 9.69946 0.969946
\(101\) −3.07310 −0.305785 −0.152892 0.988243i \(-0.548859\pi\)
−0.152892 + 0.988243i \(0.548859\pi\)
\(102\) −2.50856 −0.248384
\(103\) 15.7707 1.55393 0.776966 0.629542i \(-0.216757\pi\)
0.776966 + 0.629542i \(0.216757\pi\)
\(104\) 0.799597 0.0784069
\(105\) 10.0876 0.984449
\(106\) −5.20971 −0.506011
\(107\) 0.106214 0.0102681 0.00513403 0.999987i \(-0.498366\pi\)
0.00513403 + 0.999987i \(0.498366\pi\)
\(108\) −4.29286 −0.413080
\(109\) −19.5268 −1.87033 −0.935163 0.354219i \(-0.884747\pi\)
−0.935163 + 0.354219i \(0.884747\pi\)
\(110\) −11.6193 −1.10786
\(111\) 9.56660 0.908021
\(112\) 21.8758 2.06707
\(113\) 10.4099 0.979277 0.489639 0.871925i \(-0.337129\pi\)
0.489639 + 0.871925i \(0.337129\pi\)
\(114\) 13.9076 1.30256
\(115\) −14.5281 −1.35475
\(116\) 30.9196 2.87081
\(117\) −0.139018 −0.0128522
\(118\) −6.50737 −0.599052
\(119\) −3.74400 −0.343212
\(120\) −15.4972 −1.41469
\(121\) −8.04465 −0.731332
\(122\) −37.9656 −3.43724
\(123\) −0.327658 −0.0295440
\(124\) −27.2949 −2.45116
\(125\) 7.38398 0.660443
\(126\) −9.39205 −0.836710
\(127\) −18.6065 −1.65106 −0.825532 0.564356i \(-0.809125\pi\)
−0.825532 + 0.564356i \(0.809125\pi\)
\(128\) 15.7760 1.39442
\(129\) −11.0164 −0.969944
\(130\) −0.939607 −0.0824090
\(131\) −5.45234 −0.476373 −0.238187 0.971219i \(-0.576553\pi\)
−0.238187 + 0.971219i \(0.576553\pi\)
\(132\) 7.37990 0.642338
\(133\) 20.7570 1.79986
\(134\) −10.5708 −0.913177
\(135\) 2.69434 0.231891
\(136\) 5.75176 0.493209
\(137\) 3.81445 0.325890 0.162945 0.986635i \(-0.447901\pi\)
0.162945 + 0.986635i \(0.447901\pi\)
\(138\) 13.5264 1.15144
\(139\) −3.66939 −0.311233 −0.155617 0.987818i \(-0.549736\pi\)
−0.155617 + 0.987818i \(0.549736\pi\)
\(140\) −43.3046 −3.65991
\(141\) 8.65194 0.728625
\(142\) −21.8575 −1.83424
\(143\) 0.238987 0.0199851
\(144\) 5.84290 0.486908
\(145\) −19.4061 −1.61159
\(146\) −25.1180 −2.07878
\(147\) −7.01757 −0.578799
\(148\) −41.0680 −3.37577
\(149\) 10.2266 0.837799 0.418900 0.908032i \(-0.362416\pi\)
0.418900 + 0.908032i \(0.362416\pi\)
\(150\) 5.66794 0.462785
\(151\) −15.0719 −1.22654 −0.613268 0.789875i \(-0.710146\pi\)
−0.613268 + 0.789875i \(0.710146\pi\)
\(152\) −31.8881 −2.58647
\(153\) −1.00000 −0.0808452
\(154\) 16.1460 1.30108
\(155\) 17.1312 1.37601
\(156\) 0.596784 0.0477809
\(157\) 2.91823 0.232900 0.116450 0.993197i \(-0.462848\pi\)
0.116450 + 0.993197i \(0.462848\pi\)
\(158\) −2.50856 −0.199570
\(159\) −2.07677 −0.164699
\(160\) 8.49718 0.671761
\(161\) 20.1880 1.59104
\(162\) −2.50856 −0.197091
\(163\) −19.6064 −1.53569 −0.767845 0.640635i \(-0.778671\pi\)
−0.767845 + 0.640635i \(0.778671\pi\)
\(164\) 1.40659 0.109836
\(165\) −4.63187 −0.360590
\(166\) 41.9955 3.25948
\(167\) −9.66602 −0.747979 −0.373990 0.927433i \(-0.622010\pi\)
−0.373990 + 0.927433i \(0.622010\pi\)
\(168\) 21.5346 1.66143
\(169\) −12.9807 −0.998513
\(170\) −6.75889 −0.518383
\(171\) 5.54406 0.423965
\(172\) 47.2920 3.60598
\(173\) 23.4494 1.78282 0.891411 0.453195i \(-0.149716\pi\)
0.891411 + 0.453195i \(0.149716\pi\)
\(174\) 18.0680 1.36973
\(175\) 8.45936 0.639468
\(176\) −10.0446 −0.757140
\(177\) −2.59407 −0.194982
\(178\) 0.441864 0.0331191
\(179\) 22.0195 1.64582 0.822909 0.568173i \(-0.192350\pi\)
0.822909 + 0.568173i \(0.192350\pi\)
\(180\) −11.5664 −0.862108
\(181\) 8.02793 0.596712 0.298356 0.954455i \(-0.403562\pi\)
0.298356 + 0.954455i \(0.403562\pi\)
\(182\) 1.30566 0.0967821
\(183\) −15.1344 −1.11877
\(184\) −31.0140 −2.28639
\(185\) 25.7756 1.89506
\(186\) −15.9500 −1.16951
\(187\) 1.71911 0.125714
\(188\) −37.1415 −2.70882
\(189\) −3.74400 −0.272336
\(190\) 37.4717 2.71848
\(191\) −18.3556 −1.32816 −0.664082 0.747660i \(-0.731177\pi\)
−0.664082 + 0.747660i \(0.731177\pi\)
\(192\) 3.77451 0.272402
\(193\) −10.0684 −0.724741 −0.362370 0.932034i \(-0.618032\pi\)
−0.362370 + 0.932034i \(0.618032\pi\)
\(194\) 24.4048 1.75216
\(195\) −0.374561 −0.0268229
\(196\) 30.1254 2.15181
\(197\) −15.7115 −1.11940 −0.559701 0.828695i \(-0.689084\pi\)
−0.559701 + 0.828695i \(0.689084\pi\)
\(198\) 4.31249 0.306476
\(199\) 10.4890 0.743543 0.371772 0.928324i \(-0.378750\pi\)
0.371772 + 0.928324i \(0.378750\pi\)
\(200\) −12.9958 −0.918939
\(201\) −4.21389 −0.297225
\(202\) 7.70904 0.542406
\(203\) 26.9664 1.89267
\(204\) 4.29286 0.300560
\(205\) −0.882821 −0.0616589
\(206\) −39.5617 −2.75639
\(207\) 5.39210 0.374777
\(208\) −0.812267 −0.0563206
\(209\) −9.53087 −0.659264
\(210\) −25.3053 −1.74623
\(211\) 17.5312 1.20690 0.603449 0.797401i \(-0.293793\pi\)
0.603449 + 0.797401i \(0.293793\pi\)
\(212\) 8.91529 0.612305
\(213\) −8.71318 −0.597017
\(214\) −0.266443 −0.0182137
\(215\) −29.6820 −2.02430
\(216\) 5.75176 0.391357
\(217\) −23.8052 −1.61600
\(218\) 48.9840 3.31762
\(219\) −10.0129 −0.676610
\(220\) 19.8839 1.34057
\(221\) 0.139018 0.00935136
\(222\) −23.9984 −1.61066
\(223\) 1.07333 0.0718756 0.0359378 0.999354i \(-0.488558\pi\)
0.0359378 + 0.999354i \(0.488558\pi\)
\(224\) −11.8075 −0.788924
\(225\) 2.25944 0.150629
\(226\) −26.1137 −1.73706
\(227\) −6.66723 −0.442520 −0.221260 0.975215i \(-0.571017\pi\)
−0.221260 + 0.975215i \(0.571017\pi\)
\(228\) −23.7998 −1.57618
\(229\) 20.5325 1.35683 0.678414 0.734680i \(-0.262668\pi\)
0.678414 + 0.734680i \(0.262668\pi\)
\(230\) 36.4446 2.40309
\(231\) 6.43637 0.423482
\(232\) −41.4274 −2.71984
\(233\) −26.4189 −1.73076 −0.865378 0.501119i \(-0.832922\pi\)
−0.865378 + 0.501119i \(0.832922\pi\)
\(234\) 0.348734 0.0227975
\(235\) 23.3112 1.52066
\(236\) 11.1360 0.724890
\(237\) −1.00000 −0.0649570
\(238\) 9.39205 0.608796
\(239\) −12.3541 −0.799120 −0.399560 0.916707i \(-0.630837\pi\)
−0.399560 + 0.916707i \(0.630837\pi\)
\(240\) 15.7427 1.01619
\(241\) 4.32551 0.278630 0.139315 0.990248i \(-0.455510\pi\)
0.139315 + 0.990248i \(0.455510\pi\)
\(242\) 20.1805 1.29725
\(243\) −1.00000 −0.0641500
\(244\) 64.9699 4.15927
\(245\) −18.9077 −1.20797
\(246\) 0.821949 0.0524056
\(247\) −0.770724 −0.0490400
\(248\) 36.5709 2.32226
\(249\) 16.7409 1.06091
\(250\) −18.5231 −1.17151
\(251\) 19.3106 1.21887 0.609436 0.792835i \(-0.291396\pi\)
0.609436 + 0.792835i \(0.291396\pi\)
\(252\) 16.0725 1.01247
\(253\) −9.26963 −0.582777
\(254\) 46.6756 2.92868
\(255\) −2.69434 −0.168726
\(256\) −32.0260 −2.00162
\(257\) 23.6722 1.47663 0.738315 0.674456i \(-0.235622\pi\)
0.738315 + 0.674456i \(0.235622\pi\)
\(258\) 27.6354 1.72050
\(259\) −35.8174 −2.22558
\(260\) 1.60794 0.0997199
\(261\) 7.20257 0.445828
\(262\) 13.6775 0.844999
\(263\) −9.98045 −0.615421 −0.307710 0.951480i \(-0.599563\pi\)
−0.307710 + 0.951480i \(0.599563\pi\)
\(264\) −9.88792 −0.608559
\(265\) −5.59553 −0.343730
\(266\) −52.0701 −3.19262
\(267\) 0.176143 0.0107798
\(268\) 18.0896 1.10500
\(269\) 1.01465 0.0618644 0.0309322 0.999521i \(-0.490152\pi\)
0.0309322 + 0.999521i \(0.490152\pi\)
\(270\) −6.75889 −0.411333
\(271\) −0.893528 −0.0542780 −0.0271390 0.999632i \(-0.508640\pi\)
−0.0271390 + 0.999632i \(0.508640\pi\)
\(272\) −5.84290 −0.354278
\(273\) 0.520484 0.0315011
\(274\) −9.56875 −0.578069
\(275\) −3.88424 −0.234228
\(276\) −23.1475 −1.39332
\(277\) −2.86557 −0.172176 −0.0860878 0.996288i \(-0.527437\pi\)
−0.0860878 + 0.996288i \(0.527437\pi\)
\(278\) 9.20486 0.552071
\(279\) −6.35822 −0.380657
\(280\) 58.0214 3.46744
\(281\) −6.62580 −0.395262 −0.197631 0.980276i \(-0.563325\pi\)
−0.197631 + 0.980276i \(0.563325\pi\)
\(282\) −21.7039 −1.29245
\(283\) −12.7835 −0.759900 −0.379950 0.925007i \(-0.624059\pi\)
−0.379950 + 0.925007i \(0.624059\pi\)
\(284\) 37.4044 2.21954
\(285\) 14.9376 0.884825
\(286\) −0.599514 −0.0354500
\(287\) 1.22675 0.0724130
\(288\) −3.15372 −0.185835
\(289\) 1.00000 0.0588235
\(290\) 48.6814 2.85867
\(291\) 9.72863 0.570302
\(292\) 42.9840 2.51545
\(293\) 11.8071 0.689780 0.344890 0.938643i \(-0.387916\pi\)
0.344890 + 0.938643i \(0.387916\pi\)
\(294\) 17.6040 1.02668
\(295\) −6.98930 −0.406933
\(296\) 55.0247 3.19825
\(297\) 1.71911 0.0997531
\(298\) −25.6541 −1.48610
\(299\) −0.749598 −0.0433504
\(300\) −9.69946 −0.559999
\(301\) 41.2456 2.37736
\(302\) 37.8088 2.17565
\(303\) 3.07310 0.176545
\(304\) 32.3934 1.85789
\(305\) −40.7772 −2.33490
\(306\) 2.50856 0.143405
\(307\) 18.2181 1.03976 0.519880 0.854239i \(-0.325977\pi\)
0.519880 + 0.854239i \(0.325977\pi\)
\(308\) −27.6304 −1.57439
\(309\) −15.7707 −0.897164
\(310\) −42.9745 −2.44079
\(311\) 10.1159 0.573620 0.286810 0.957987i \(-0.407405\pi\)
0.286810 + 0.957987i \(0.407405\pi\)
\(312\) −0.799597 −0.0452683
\(313\) −16.4058 −0.927310 −0.463655 0.886016i \(-0.653462\pi\)
−0.463655 + 0.886016i \(0.653462\pi\)
\(314\) −7.32055 −0.413122
\(315\) −10.0876 −0.568372
\(316\) 4.29286 0.241492
\(317\) 12.8397 0.721148 0.360574 0.932731i \(-0.382581\pi\)
0.360574 + 0.932731i \(0.382581\pi\)
\(318\) 5.20971 0.292146
\(319\) −12.3820 −0.693260
\(320\) 10.1698 0.568509
\(321\) −0.106214 −0.00592827
\(322\) −50.6428 −2.82222
\(323\) −5.54406 −0.308480
\(324\) 4.29286 0.238492
\(325\) −0.314103 −0.0174233
\(326\) 49.1837 2.72403
\(327\) 19.5268 1.07983
\(328\) −1.88461 −0.104060
\(329\) −32.3929 −1.78588
\(330\) 11.6193 0.639621
\(331\) 32.1823 1.76890 0.884451 0.466634i \(-0.154533\pi\)
0.884451 + 0.466634i \(0.154533\pi\)
\(332\) −71.8663 −3.94417
\(333\) −9.56660 −0.524246
\(334\) 24.2478 1.32678
\(335\) −11.3536 −0.620316
\(336\) −21.8758 −1.19342
\(337\) 31.9269 1.73917 0.869584 0.493786i \(-0.164387\pi\)
0.869584 + 0.493786i \(0.164387\pi\)
\(338\) 32.5628 1.77118
\(339\) −10.4099 −0.565386
\(340\) 11.5664 0.627276
\(341\) 10.9305 0.591920
\(342\) −13.9076 −0.752036
\(343\) 0.0657671 0.00355109
\(344\) −63.3639 −3.41635
\(345\) 14.5281 0.782168
\(346\) −58.8241 −3.16240
\(347\) 2.87151 0.154151 0.0770755 0.997025i \(-0.475442\pi\)
0.0770755 + 0.997025i \(0.475442\pi\)
\(348\) −30.9196 −1.65746
\(349\) 21.8859 1.17152 0.585762 0.810483i \(-0.300795\pi\)
0.585762 + 0.810483i \(0.300795\pi\)
\(350\) −21.2208 −1.13430
\(351\) 0.139018 0.00742023
\(352\) 5.42160 0.288972
\(353\) 30.1911 1.60691 0.803455 0.595365i \(-0.202993\pi\)
0.803455 + 0.595365i \(0.202993\pi\)
\(354\) 6.50737 0.345863
\(355\) −23.4762 −1.24599
\(356\) −0.756155 −0.0400761
\(357\) 3.74400 0.198154
\(358\) −55.2373 −2.91938
\(359\) 28.3388 1.49567 0.747833 0.663887i \(-0.231095\pi\)
0.747833 + 0.663887i \(0.231095\pi\)
\(360\) 15.4972 0.816772
\(361\) 11.7366 0.617716
\(362\) −20.1385 −1.05846
\(363\) 8.04465 0.422235
\(364\) −2.23436 −0.117112
\(365\) −26.9781 −1.41210
\(366\) 37.9656 1.98449
\(367\) −24.0440 −1.25509 −0.627543 0.778582i \(-0.715940\pi\)
−0.627543 + 0.778582i \(0.715940\pi\)
\(368\) 31.5055 1.64234
\(369\) 0.327658 0.0170572
\(370\) −64.6596 −3.36149
\(371\) 7.77545 0.403681
\(372\) 27.2949 1.41518
\(373\) −5.63709 −0.291878 −0.145939 0.989294i \(-0.546620\pi\)
−0.145939 + 0.989294i \(0.546620\pi\)
\(374\) −4.31249 −0.222994
\(375\) −7.38398 −0.381307
\(376\) 49.7639 2.56638
\(377\) −1.00129 −0.0515688
\(378\) 9.39205 0.483075
\(379\) 33.3778 1.71450 0.857250 0.514901i \(-0.172171\pi\)
0.857250 + 0.514901i \(0.172171\pi\)
\(380\) −64.1248 −3.28953
\(381\) 18.6065 0.953242
\(382\) 46.0460 2.35592
\(383\) −11.5476 −0.590054 −0.295027 0.955489i \(-0.595329\pi\)
−0.295027 + 0.955489i \(0.595329\pi\)
\(384\) −15.7760 −0.805066
\(385\) 17.3417 0.883816
\(386\) 25.2572 1.28556
\(387\) 11.0164 0.559997
\(388\) −41.7636 −2.12023
\(389\) −7.53981 −0.382283 −0.191142 0.981562i \(-0.561219\pi\)
−0.191142 + 0.981562i \(0.561219\pi\)
\(390\) 0.939607 0.0475788
\(391\) −5.39210 −0.272690
\(392\) −40.3633 −2.03866
\(393\) 5.45234 0.275034
\(394\) 39.4133 1.98561
\(395\) −2.69434 −0.135567
\(396\) −7.37990 −0.370854
\(397\) −18.5849 −0.932747 −0.466373 0.884588i \(-0.654440\pi\)
−0.466373 + 0.884588i \(0.654440\pi\)
\(398\) −26.3122 −1.31891
\(399\) −20.7570 −1.03915
\(400\) 13.2017 0.660084
\(401\) 2.06309 0.103026 0.0515128 0.998672i \(-0.483596\pi\)
0.0515128 + 0.998672i \(0.483596\pi\)
\(402\) 10.5708 0.527223
\(403\) 0.883906 0.0440305
\(404\) −13.1924 −0.656344
\(405\) −2.69434 −0.133883
\(406\) −67.6468 −3.35726
\(407\) 16.4461 0.815201
\(408\) −5.75176 −0.284754
\(409\) 11.2813 0.557824 0.278912 0.960317i \(-0.410026\pi\)
0.278912 + 0.960317i \(0.410026\pi\)
\(410\) 2.21461 0.109372
\(411\) −3.81445 −0.188153
\(412\) 67.7013 3.33540
\(413\) 9.71221 0.477907
\(414\) −13.5264 −0.664786
\(415\) 45.1056 2.21415
\(416\) 0.438423 0.0214955
\(417\) 3.66939 0.179691
\(418\) 23.9087 1.16941
\(419\) −13.1347 −0.641671 −0.320835 0.947135i \(-0.603964\pi\)
−0.320835 + 0.947135i \(0.603964\pi\)
\(420\) 43.3046 2.11305
\(421\) 37.6913 1.83696 0.918480 0.395467i \(-0.129417\pi\)
0.918480 + 0.395467i \(0.129417\pi\)
\(422\) −43.9780 −2.14082
\(423\) −8.65194 −0.420672
\(424\) −11.9451 −0.580105
\(425\) −2.25944 −0.109599
\(426\) 21.8575 1.05900
\(427\) 56.6633 2.74213
\(428\) 0.455960 0.0220397
\(429\) −0.238987 −0.0115384
\(430\) 74.4590 3.59073
\(431\) 38.0414 1.83239 0.916194 0.400735i \(-0.131245\pi\)
0.916194 + 0.400735i \(0.131245\pi\)
\(432\) −5.84290 −0.281116
\(433\) 35.0692 1.68532 0.842659 0.538448i \(-0.180989\pi\)
0.842659 + 0.538448i \(0.180989\pi\)
\(434\) 59.7167 2.86649
\(435\) 19.4061 0.930452
\(436\) −83.8256 −4.01452
\(437\) 29.8941 1.43003
\(438\) 25.1180 1.20018
\(439\) 7.87788 0.375991 0.187995 0.982170i \(-0.439801\pi\)
0.187995 + 0.982170i \(0.439801\pi\)
\(440\) −26.6414 −1.27008
\(441\) 7.01757 0.334170
\(442\) −0.348734 −0.0165876
\(443\) 3.69444 0.175528 0.0877641 0.996141i \(-0.472028\pi\)
0.0877641 + 0.996141i \(0.472028\pi\)
\(444\) 41.0680 1.94900
\(445\) 0.474588 0.0224976
\(446\) −2.69251 −0.127494
\(447\) −10.2266 −0.483704
\(448\) −14.1318 −0.667664
\(449\) −3.62828 −0.171229 −0.0856146 0.996328i \(-0.527285\pi\)
−0.0856146 + 0.996328i \(0.527285\pi\)
\(450\) −5.66794 −0.267189
\(451\) −0.563282 −0.0265239
\(452\) 44.6880 2.10195
\(453\) 15.0719 0.708141
\(454\) 16.7251 0.784949
\(455\) 1.40236 0.0657435
\(456\) 31.8881 1.49330
\(457\) −7.63909 −0.357342 −0.178671 0.983909i \(-0.557180\pi\)
−0.178671 + 0.983909i \(0.557180\pi\)
\(458\) −51.5070 −2.40677
\(459\) 1.00000 0.0466760
\(460\) −62.3671 −2.90788
\(461\) 38.1537 1.77700 0.888498 0.458880i \(-0.151749\pi\)
0.888498 + 0.458880i \(0.151749\pi\)
\(462\) −16.1460 −0.751179
\(463\) 4.62234 0.214818 0.107409 0.994215i \(-0.465745\pi\)
0.107409 + 0.994215i \(0.465745\pi\)
\(464\) 42.0838 1.95369
\(465\) −17.1312 −0.794439
\(466\) 66.2732 3.07005
\(467\) 14.6418 0.677540 0.338770 0.940869i \(-0.389989\pi\)
0.338770 + 0.940869i \(0.389989\pi\)
\(468\) −0.596784 −0.0275863
\(469\) 15.7768 0.728506
\(470\) −58.4775 −2.69737
\(471\) −2.91823 −0.134465
\(472\) −14.9205 −0.686770
\(473\) −18.9385 −0.870794
\(474\) 2.50856 0.115222
\(475\) 12.5265 0.574755
\(476\) −16.0725 −0.736680
\(477\) 2.07677 0.0950890
\(478\) 30.9910 1.41749
\(479\) −16.7934 −0.767311 −0.383655 0.923476i \(-0.625335\pi\)
−0.383655 + 0.923476i \(0.625335\pi\)
\(480\) −8.49718 −0.387841
\(481\) 1.32993 0.0606395
\(482\) −10.8508 −0.494239
\(483\) −20.1880 −0.918588
\(484\) −34.5345 −1.56975
\(485\) 26.2122 1.19023
\(486\) 2.50856 0.113790
\(487\) −33.0770 −1.49886 −0.749432 0.662082i \(-0.769673\pi\)
−0.749432 + 0.662082i \(0.769673\pi\)
\(488\) −87.0495 −3.94055
\(489\) 19.6064 0.886631
\(490\) 47.4310 2.14271
\(491\) −10.9250 −0.493038 −0.246519 0.969138i \(-0.579287\pi\)
−0.246519 + 0.969138i \(0.579287\pi\)
\(492\) −1.40659 −0.0634140
\(493\) −7.20257 −0.324387
\(494\) 1.93340 0.0869879
\(495\) 4.63187 0.208187
\(496\) −37.1504 −1.66810
\(497\) 32.6222 1.46331
\(498\) −41.9955 −1.88186
\(499\) 35.2632 1.57860 0.789299 0.614009i \(-0.210444\pi\)
0.789299 + 0.614009i \(0.210444\pi\)
\(500\) 31.6984 1.41759
\(501\) 9.66602 0.431846
\(502\) −48.4417 −2.16206
\(503\) −0.658137 −0.0293449 −0.0146724 0.999892i \(-0.504671\pi\)
−0.0146724 + 0.999892i \(0.504671\pi\)
\(504\) −21.5346 −0.959227
\(505\) 8.27995 0.368453
\(506\) 23.2534 1.03374
\(507\) 12.9807 0.576492
\(508\) −79.8752 −3.54389
\(509\) 9.43187 0.418060 0.209030 0.977909i \(-0.432969\pi\)
0.209030 + 0.977909i \(0.432969\pi\)
\(510\) 6.75889 0.299289
\(511\) 37.4884 1.65839
\(512\) 48.7870 2.15610
\(513\) −5.54406 −0.244776
\(514\) −59.3830 −2.61927
\(515\) −42.4915 −1.87240
\(516\) −47.2920 −2.08191
\(517\) 14.8737 0.654143
\(518\) 89.8499 3.94778
\(519\) −23.4494 −1.02931
\(520\) −2.15438 −0.0944759
\(521\) 35.4738 1.55413 0.777067 0.629418i \(-0.216707\pi\)
0.777067 + 0.629418i \(0.216707\pi\)
\(522\) −18.0680 −0.790817
\(523\) 17.7537 0.776317 0.388158 0.921593i \(-0.373111\pi\)
0.388158 + 0.921593i \(0.373111\pi\)
\(524\) −23.4061 −1.02250
\(525\) −8.45936 −0.369197
\(526\) 25.0365 1.09164
\(527\) 6.35822 0.276968
\(528\) 10.0446 0.437135
\(529\) 6.07474 0.264119
\(530\) 14.0367 0.609715
\(531\) 2.59407 0.112573
\(532\) 89.1067 3.86327
\(533\) −0.0455504 −0.00197301
\(534\) −0.441864 −0.0191213
\(535\) −0.286175 −0.0123724
\(536\) −24.2373 −1.04689
\(537\) −22.0195 −0.950213
\(538\) −2.54531 −0.109736
\(539\) −12.0640 −0.519633
\(540\) 11.5664 0.497738
\(541\) 1.45853 0.0627070 0.0313535 0.999508i \(-0.490018\pi\)
0.0313535 + 0.999508i \(0.490018\pi\)
\(542\) 2.24147 0.0962792
\(543\) −8.02793 −0.344512
\(544\) 3.15372 0.135215
\(545\) 52.6117 2.25364
\(546\) −1.30566 −0.0558772
\(547\) −27.0237 −1.15545 −0.577725 0.816232i \(-0.696059\pi\)
−0.577725 + 0.816232i \(0.696059\pi\)
\(548\) 16.3749 0.699499
\(549\) 15.1344 0.645921
\(550\) 9.74383 0.415478
\(551\) 39.9315 1.70114
\(552\) 31.0140 1.32005
\(553\) 3.74400 0.159211
\(554\) 7.18846 0.305408
\(555\) −25.7756 −1.09411
\(556\) −15.7521 −0.668040
\(557\) −34.8372 −1.47610 −0.738050 0.674746i \(-0.764253\pi\)
−0.738050 + 0.674746i \(0.764253\pi\)
\(558\) 15.9500 0.675215
\(559\) −1.53148 −0.0647748
\(560\) −58.9408 −2.49070
\(561\) −1.71911 −0.0725810
\(562\) 16.6212 0.701123
\(563\) 28.5743 1.20426 0.602131 0.798397i \(-0.294318\pi\)
0.602131 + 0.798397i \(0.294318\pi\)
\(564\) 37.1415 1.56394
\(565\) −28.0477 −1.17997
\(566\) 32.0681 1.34792
\(567\) 3.74400 0.157233
\(568\) −50.1161 −2.10282
\(569\) 28.5706 1.19774 0.598871 0.800846i \(-0.295616\pi\)
0.598871 + 0.800846i \(0.295616\pi\)
\(570\) −37.4717 −1.56952
\(571\) −4.76657 −0.199475 −0.0997373 0.995014i \(-0.531800\pi\)
−0.0997373 + 0.995014i \(0.531800\pi\)
\(572\) 1.02594 0.0428967
\(573\) 18.3556 0.766816
\(574\) −3.07738 −0.128447
\(575\) 12.1831 0.508072
\(576\) −3.77451 −0.157271
\(577\) 8.93976 0.372167 0.186084 0.982534i \(-0.440420\pi\)
0.186084 + 0.982534i \(0.440420\pi\)
\(578\) −2.50856 −0.104342
\(579\) 10.0684 0.418429
\(580\) −83.3077 −3.45916
\(581\) −62.6780 −2.60032
\(582\) −24.4048 −1.01161
\(583\) −3.57021 −0.147863
\(584\) −57.5918 −2.38317
\(585\) 0.374561 0.0154862
\(586\) −29.6188 −1.22354
\(587\) −27.6439 −1.14099 −0.570493 0.821303i \(-0.693248\pi\)
−0.570493 + 0.821303i \(0.693248\pi\)
\(588\) −30.1254 −1.24235
\(589\) −35.2503 −1.45247
\(590\) 17.5330 0.721824
\(591\) 15.7115 0.646287
\(592\) −55.8966 −2.29734
\(593\) 24.3651 1.00055 0.500277 0.865866i \(-0.333232\pi\)
0.500277 + 0.865866i \(0.333232\pi\)
\(594\) −4.31249 −0.176944
\(595\) 10.0876 0.413551
\(596\) 43.9015 1.79828
\(597\) −10.4890 −0.429285
\(598\) 1.88041 0.0768957
\(599\) −38.3834 −1.56830 −0.784151 0.620570i \(-0.786901\pi\)
−0.784151 + 0.620570i \(0.786901\pi\)
\(600\) 12.9958 0.530550
\(601\) 10.1591 0.414399 0.207200 0.978299i \(-0.433565\pi\)
0.207200 + 0.978299i \(0.433565\pi\)
\(602\) −103.467 −4.21700
\(603\) 4.21389 0.171603
\(604\) −64.7016 −2.63267
\(605\) 21.6750 0.881213
\(606\) −7.70904 −0.313158
\(607\) 36.5524 1.48362 0.741809 0.670611i \(-0.233968\pi\)
0.741809 + 0.670611i \(0.233968\pi\)
\(608\) −17.4844 −0.709086
\(609\) −26.9664 −1.09273
\(610\) 102.292 4.14168
\(611\) 1.20277 0.0486591
\(612\) −4.29286 −0.173528
\(613\) −25.7134 −1.03855 −0.519276 0.854606i \(-0.673798\pi\)
−0.519276 + 0.854606i \(0.673798\pi\)
\(614\) −45.7011 −1.84434
\(615\) 0.882821 0.0355988
\(616\) 37.0204 1.49160
\(617\) −23.4453 −0.943871 −0.471935 0.881633i \(-0.656444\pi\)
−0.471935 + 0.881633i \(0.656444\pi\)
\(618\) 39.5617 1.59140
\(619\) 35.7309 1.43615 0.718074 0.695967i \(-0.245024\pi\)
0.718074 + 0.695967i \(0.245024\pi\)
\(620\) 73.5416 2.95350
\(621\) −5.39210 −0.216378
\(622\) −25.3763 −1.01750
\(623\) −0.659479 −0.0264215
\(624\) 0.812267 0.0325167
\(625\) −31.1921 −1.24769
\(626\) 41.1548 1.64488
\(627\) 9.53087 0.380626
\(628\) 12.5275 0.499904
\(629\) 9.56660 0.381445
\(630\) 25.3053 1.00819
\(631\) 16.7832 0.668129 0.334065 0.942550i \(-0.391580\pi\)
0.334065 + 0.942550i \(0.391580\pi\)
\(632\) −5.75176 −0.228793
\(633\) −17.5312 −0.696803
\(634\) −32.2091 −1.27919
\(635\) 50.1323 1.98944
\(636\) −8.91529 −0.353514
\(637\) −0.975567 −0.0386534
\(638\) 31.0610 1.22972
\(639\) 8.71318 0.344688
\(640\) −42.5058 −1.68019
\(641\) −29.9402 −1.18257 −0.591283 0.806464i \(-0.701378\pi\)
−0.591283 + 0.806464i \(0.701378\pi\)
\(642\) 0.266443 0.0105157
\(643\) 7.06091 0.278455 0.139228 0.990260i \(-0.455538\pi\)
0.139228 + 0.990260i \(0.455538\pi\)
\(644\) 86.6643 3.41505
\(645\) 29.6820 1.16873
\(646\) 13.9076 0.547187
\(647\) 17.0182 0.669054 0.334527 0.942386i \(-0.391423\pi\)
0.334527 + 0.942386i \(0.391423\pi\)
\(648\) −5.75176 −0.225950
\(649\) −4.45950 −0.175051
\(650\) 0.787945 0.0309057
\(651\) 23.8052 0.932999
\(652\) −84.1674 −3.29625
\(653\) 29.1632 1.14124 0.570622 0.821213i \(-0.306702\pi\)
0.570622 + 0.821213i \(0.306702\pi\)
\(654\) −48.9840 −1.91543
\(655\) 14.6904 0.574003
\(656\) 1.91447 0.0747476
\(657\) 10.0129 0.390641
\(658\) 81.2594 3.16782
\(659\) 21.4490 0.835535 0.417768 0.908554i \(-0.362813\pi\)
0.417768 + 0.908554i \(0.362813\pi\)
\(660\) −19.8839 −0.773981
\(661\) −26.4673 −1.02946 −0.514730 0.857352i \(-0.672108\pi\)
−0.514730 + 0.857352i \(0.672108\pi\)
\(662\) −80.7312 −3.13771
\(663\) −0.139018 −0.00539901
\(664\) 96.2896 3.73676
\(665\) −55.9263 −2.16873
\(666\) 23.9984 0.929917
\(667\) 38.8370 1.50377
\(668\) −41.4948 −1.60548
\(669\) −1.07333 −0.0414974
\(670\) 28.4812 1.10033
\(671\) −26.0178 −1.00441
\(672\) 11.8075 0.455486
\(673\) 5.99232 0.230987 0.115493 0.993308i \(-0.463155\pi\)
0.115493 + 0.993308i \(0.463155\pi\)
\(674\) −80.0903 −3.08496
\(675\) −2.25944 −0.0869660
\(676\) −55.7242 −2.14324
\(677\) −32.1490 −1.23559 −0.617794 0.786340i \(-0.711973\pi\)
−0.617794 + 0.786340i \(0.711973\pi\)
\(678\) 26.1137 1.00289
\(679\) −36.4240 −1.39783
\(680\) −15.4972 −0.594289
\(681\) 6.66723 0.255489
\(682\) −27.4198 −1.04996
\(683\) −30.6438 −1.17255 −0.586276 0.810111i \(-0.699407\pi\)
−0.586276 + 0.810111i \(0.699407\pi\)
\(684\) 23.7998 0.910010
\(685\) −10.2774 −0.392679
\(686\) −0.164981 −0.00629899
\(687\) −20.5325 −0.783365
\(688\) 64.3679 2.45400
\(689\) −0.288709 −0.0109989
\(690\) −36.4446 −1.38742
\(691\) −6.24184 −0.237451 −0.118725 0.992927i \(-0.537881\pi\)
−0.118725 + 0.992927i \(0.537881\pi\)
\(692\) 100.665 3.82670
\(693\) −6.43637 −0.244497
\(694\) −7.20336 −0.273436
\(695\) 9.88655 0.375018
\(696\) 41.4274 1.57030
\(697\) −0.327658 −0.0124109
\(698\) −54.9019 −2.07807
\(699\) 26.4189 0.999253
\(700\) 36.3148 1.37257
\(701\) 25.8694 0.977072 0.488536 0.872544i \(-0.337531\pi\)
0.488536 + 0.872544i \(0.337531\pi\)
\(702\) −0.348734 −0.0131621
\(703\) −53.0378 −2.00036
\(704\) 6.48881 0.244556
\(705\) −23.3112 −0.877952
\(706\) −75.7361 −2.85037
\(707\) −11.5057 −0.432716
\(708\) −11.1360 −0.418515
\(709\) −30.6086 −1.14953 −0.574766 0.818318i \(-0.694907\pi\)
−0.574766 + 0.818318i \(0.694907\pi\)
\(710\) 58.8915 2.21016
\(711\) 1.00000 0.0375029
\(712\) 1.01313 0.0379687
\(713\) −34.2842 −1.28395
\(714\) −9.39205 −0.351488
\(715\) −0.643912 −0.0240810
\(716\) 94.5267 3.53263
\(717\) 12.3541 0.461372
\(718\) −71.0895 −2.65304
\(719\) 11.5708 0.431518 0.215759 0.976447i \(-0.430777\pi\)
0.215759 + 0.976447i \(0.430777\pi\)
\(720\) −15.7427 −0.586696
\(721\) 59.0455 2.19897
\(722\) −29.4419 −1.09572
\(723\) −4.32551 −0.160867
\(724\) 34.4628 1.28080
\(725\) 16.2738 0.604393
\(726\) −20.1805 −0.748967
\(727\) −24.7108 −0.916473 −0.458237 0.888830i \(-0.651519\pi\)
−0.458237 + 0.888830i \(0.651519\pi\)
\(728\) 2.99369 0.110954
\(729\) 1.00000 0.0370370
\(730\) 67.6762 2.50481
\(731\) −11.0164 −0.407458
\(732\) −64.9699 −2.40136
\(733\) 51.8781 1.91616 0.958080 0.286500i \(-0.0924918\pi\)
0.958080 + 0.286500i \(0.0924918\pi\)
\(734\) 60.3157 2.22629
\(735\) 18.9077 0.697420
\(736\) −17.0052 −0.626819
\(737\) −7.24416 −0.266842
\(738\) −0.821949 −0.0302564
\(739\) 44.8867 1.65118 0.825592 0.564267i \(-0.190841\pi\)
0.825592 + 0.564267i \(0.190841\pi\)
\(740\) 110.651 4.06761
\(741\) 0.770724 0.0283132
\(742\) −19.5052 −0.716057
\(743\) 30.8520 1.13185 0.565926 0.824456i \(-0.308519\pi\)
0.565926 + 0.824456i \(0.308519\pi\)
\(744\) −36.5709 −1.34076
\(745\) −27.5540 −1.00950
\(746\) 14.1410 0.517737
\(747\) −16.7409 −0.612517
\(748\) 7.37990 0.269836
\(749\) 0.397665 0.0145303
\(750\) 18.5231 0.676369
\(751\) 19.7178 0.719513 0.359757 0.933046i \(-0.382860\pi\)
0.359757 + 0.933046i \(0.382860\pi\)
\(752\) −50.5524 −1.84346
\(753\) −19.3106 −0.703716
\(754\) 2.51178 0.0914737
\(755\) 40.6089 1.47791
\(756\) −16.0725 −0.584550
\(757\) 15.8870 0.577424 0.288712 0.957416i \(-0.406773\pi\)
0.288712 + 0.957416i \(0.406773\pi\)
\(758\) −83.7300 −3.04121
\(759\) 9.26963 0.336466
\(760\) 85.9172 3.11654
\(761\) 25.0751 0.908972 0.454486 0.890754i \(-0.349823\pi\)
0.454486 + 0.890754i \(0.349823\pi\)
\(762\) −46.6756 −1.69088
\(763\) −73.1083 −2.64670
\(764\) −78.7979 −2.85081
\(765\) 2.69434 0.0974139
\(766\) 28.9677 1.04665
\(767\) −0.360622 −0.0130213
\(768\) 32.0260 1.15564
\(769\) 17.2244 0.621127 0.310564 0.950553i \(-0.399482\pi\)
0.310564 + 0.950553i \(0.399482\pi\)
\(770\) −43.5027 −1.56773
\(771\) −23.6722 −0.852533
\(772\) −43.2223 −1.55560
\(773\) 24.4961 0.881063 0.440531 0.897737i \(-0.354790\pi\)
0.440531 + 0.897737i \(0.354790\pi\)
\(774\) −27.6354 −0.993333
\(775\) −14.3660 −0.516043
\(776\) 55.9567 2.00873
\(777\) 35.8174 1.28494
\(778\) 18.9140 0.678101
\(779\) 1.81656 0.0650849
\(780\) −1.60794 −0.0575733
\(781\) −14.9789 −0.535989
\(782\) 13.5264 0.483703
\(783\) −7.20257 −0.257399
\(784\) 41.0029 1.46439
\(785\) −7.86269 −0.280632
\(786\) −13.6775 −0.487860
\(787\) −31.2735 −1.11478 −0.557389 0.830251i \(-0.688197\pi\)
−0.557389 + 0.830251i \(0.688197\pi\)
\(788\) −67.4474 −2.40271
\(789\) 9.98045 0.355313
\(790\) 6.75889 0.240471
\(791\) 38.9746 1.38578
\(792\) 9.88792 0.351352
\(793\) −2.10396 −0.0747137
\(794\) 46.6211 1.65452
\(795\) 5.59553 0.198453
\(796\) 45.0276 1.59596
\(797\) −50.7016 −1.79594 −0.897972 0.440053i \(-0.854959\pi\)
−0.897972 + 0.440053i \(0.854959\pi\)
\(798\) 52.0701 1.84326
\(799\) 8.65194 0.306084
\(800\) −7.12565 −0.251930
\(801\) −0.176143 −0.00622370
\(802\) −5.17537 −0.182749
\(803\) −17.2133 −0.607445
\(804\) −18.0896 −0.637972
\(805\) −54.3934 −1.91711
\(806\) −2.21733 −0.0781021
\(807\) −1.01465 −0.0357174
\(808\) 17.6757 0.621829
\(809\) 4.30764 0.151449 0.0757243 0.997129i \(-0.475873\pi\)
0.0757243 + 0.997129i \(0.475873\pi\)
\(810\) 6.75889 0.237483
\(811\) −9.54767 −0.335264 −0.167632 0.985850i \(-0.553612\pi\)
−0.167632 + 0.985850i \(0.553612\pi\)
\(812\) 115.763 4.06248
\(813\) 0.893528 0.0313374
\(814\) −41.2559 −1.44602
\(815\) 52.8262 1.85042
\(816\) 5.84290 0.204542
\(817\) 61.0758 2.13677
\(818\) −28.2998 −0.989478
\(819\) −0.520484 −0.0181872
\(820\) −3.78982 −0.132346
\(821\) 39.9747 1.39513 0.697564 0.716523i \(-0.254267\pi\)
0.697564 + 0.716523i \(0.254267\pi\)
\(822\) 9.56875 0.333748
\(823\) −19.6790 −0.685968 −0.342984 0.939341i \(-0.611438\pi\)
−0.342984 + 0.939341i \(0.611438\pi\)
\(824\) −90.7092 −3.16000
\(825\) 3.88424 0.135232
\(826\) −24.3636 −0.847719
\(827\) 31.9137 1.10975 0.554873 0.831935i \(-0.312767\pi\)
0.554873 + 0.831935i \(0.312767\pi\)
\(828\) 23.1475 0.804431
\(829\) −10.6270 −0.369092 −0.184546 0.982824i \(-0.559081\pi\)
−0.184546 + 0.982824i \(0.559081\pi\)
\(830\) −113.150 −3.92749
\(831\) 2.86557 0.0994057
\(832\) 0.524724 0.0181915
\(833\) −7.01757 −0.243144
\(834\) −9.20486 −0.318738
\(835\) 26.0435 0.901273
\(836\) −40.9146 −1.41506
\(837\) 6.35822 0.219772
\(838\) 32.9491 1.13821
\(839\) 10.1406 0.350091 0.175046 0.984560i \(-0.443993\pi\)
0.175046 + 0.984560i \(0.443993\pi\)
\(840\) −58.0214 −2.00193
\(841\) 22.8769 0.788860
\(842\) −94.5507 −3.25843
\(843\) 6.62580 0.228205
\(844\) 75.2590 2.59052
\(845\) 34.9743 1.20315
\(846\) 21.7039 0.746195
\(847\) −30.1192 −1.03491
\(848\) 12.1344 0.416696
\(849\) 12.7835 0.438729
\(850\) 5.66794 0.194409
\(851\) −51.5841 −1.76828
\(852\) −37.4044 −1.28145
\(853\) −19.6341 −0.672260 −0.336130 0.941816i \(-0.609118\pi\)
−0.336130 + 0.941816i \(0.609118\pi\)
\(854\) −142.143 −4.86404
\(855\) −14.9376 −0.510854
\(856\) −0.610915 −0.0208807
\(857\) −21.5317 −0.735508 −0.367754 0.929923i \(-0.619873\pi\)
−0.367754 + 0.929923i \(0.619873\pi\)
\(858\) 0.599514 0.0204671
\(859\) 30.3366 1.03507 0.517535 0.855662i \(-0.326850\pi\)
0.517535 + 0.855662i \(0.326850\pi\)
\(860\) −127.421 −4.34500
\(861\) −1.22675 −0.0418077
\(862\) −95.4289 −3.25032
\(863\) 35.4483 1.20667 0.603337 0.797486i \(-0.293837\pi\)
0.603337 + 0.797486i \(0.293837\pi\)
\(864\) 3.15372 0.107292
\(865\) −63.1805 −2.14820
\(866\) −87.9730 −2.98945
\(867\) −1.00000 −0.0339618
\(868\) −102.192 −3.46863
\(869\) −1.71911 −0.0583169
\(870\) −48.6814 −1.65045
\(871\) −0.585807 −0.0198493
\(872\) 112.313 3.80341
\(873\) −9.72863 −0.329264
\(874\) −74.9911 −2.53661
\(875\) 27.6457 0.934594
\(876\) −42.9840 −1.45229
\(877\) −17.4436 −0.589029 −0.294514 0.955647i \(-0.595158\pi\)
−0.294514 + 0.955647i \(0.595158\pi\)
\(878\) −19.7621 −0.666939
\(879\) −11.8071 −0.398245
\(880\) 27.0635 0.912311
\(881\) −12.5196 −0.421794 −0.210897 0.977508i \(-0.567639\pi\)
−0.210897 + 0.977508i \(0.567639\pi\)
\(882\) −17.6040 −0.592756
\(883\) −22.4719 −0.756241 −0.378120 0.925756i \(-0.623429\pi\)
−0.378120 + 0.925756i \(0.623429\pi\)
\(884\) 0.596784 0.0200720
\(885\) 6.98930 0.234943
\(886\) −9.26771 −0.311355
\(887\) 26.2816 0.882448 0.441224 0.897397i \(-0.354544\pi\)
0.441224 + 0.897397i \(0.354544\pi\)
\(888\) −55.0247 −1.84651
\(889\) −69.6630 −2.33642
\(890\) −1.19053 −0.0399066
\(891\) −1.71911 −0.0575925
\(892\) 4.60766 0.154276
\(893\) −47.9669 −1.60515
\(894\) 25.6541 0.858002
\(895\) −59.3280 −1.98312
\(896\) 59.0654 1.97324
\(897\) 0.749598 0.0250284
\(898\) 9.10175 0.303729
\(899\) −45.7955 −1.52736
\(900\) 9.69946 0.323315
\(901\) −2.07677 −0.0691874
\(902\) 1.41302 0.0470485
\(903\) −41.2456 −1.37257
\(904\) −59.8750 −1.99141
\(905\) −21.6299 −0.719004
\(906\) −37.8088 −1.25611
\(907\) −1.93038 −0.0640972 −0.0320486 0.999486i \(-0.510203\pi\)
−0.0320486 + 0.999486i \(0.510203\pi\)
\(908\) −28.6215 −0.949837
\(909\) −3.07310 −0.101928
\(910\) −3.51789 −0.116617
\(911\) 23.1841 0.768123 0.384061 0.923308i \(-0.374525\pi\)
0.384061 + 0.923308i \(0.374525\pi\)
\(912\) −32.3934 −1.07265
\(913\) 28.7795 0.952463
\(914\) 19.1631 0.633859
\(915\) 40.7772 1.34805
\(916\) 88.1432 2.91233
\(917\) −20.4136 −0.674116
\(918\) −2.50856 −0.0827947
\(919\) −30.5628 −1.00817 −0.504087 0.863653i \(-0.668171\pi\)
−0.504087 + 0.863653i \(0.668171\pi\)
\(920\) 83.5622 2.75497
\(921\) −18.2181 −0.600306
\(922\) −95.7108 −3.15207
\(923\) −1.21129 −0.0398700
\(924\) 27.6304 0.908973
\(925\) −21.6152 −0.710703
\(926\) −11.5954 −0.381049
\(927\) 15.7707 0.517978
\(928\) −22.7149 −0.745652
\(929\) 7.06537 0.231807 0.115904 0.993260i \(-0.463024\pi\)
0.115904 + 0.993260i \(0.463024\pi\)
\(930\) 42.9745 1.40919
\(931\) 38.9058 1.27509
\(932\) −113.412 −3.71494
\(933\) −10.1159 −0.331180
\(934\) −36.7297 −1.20183
\(935\) −4.63187 −0.151478
\(936\) 0.799597 0.0261356
\(937\) −16.4990 −0.538999 −0.269500 0.963000i \(-0.586858\pi\)
−0.269500 + 0.963000i \(0.586858\pi\)
\(938\) −39.5771 −1.29224
\(939\) 16.4058 0.535382
\(940\) 100.072 3.26398
\(941\) 4.21742 0.137484 0.0687420 0.997634i \(-0.478101\pi\)
0.0687420 + 0.997634i \(0.478101\pi\)
\(942\) 7.32055 0.238516
\(943\) 1.76677 0.0575338
\(944\) 15.1569 0.493315
\(945\) 10.0876 0.328150
\(946\) 47.5083 1.54463
\(947\) 8.56505 0.278327 0.139163 0.990269i \(-0.455559\pi\)
0.139163 + 0.990269i \(0.455559\pi\)
\(948\) −4.29286 −0.139425
\(949\) −1.39197 −0.0451854
\(950\) −31.4234 −1.01951
\(951\) −12.8397 −0.416355
\(952\) 21.5346 0.697940
\(953\) −59.0273 −1.91208 −0.956041 0.293231i \(-0.905269\pi\)
−0.956041 + 0.293231i \(0.905269\pi\)
\(954\) −5.20971 −0.168670
\(955\) 49.4561 1.60036
\(956\) −53.0344 −1.71525
\(957\) 12.3820 0.400254
\(958\) 42.1272 1.36107
\(959\) 14.2813 0.461167
\(960\) −10.1698 −0.328229
\(961\) 9.42695 0.304095
\(962\) −3.33620 −0.107563
\(963\) 0.106214 0.00342269
\(964\) 18.5688 0.598060
\(965\) 27.1277 0.873271
\(966\) 50.6428 1.62941
\(967\) −15.1871 −0.488385 −0.244193 0.969727i \(-0.578523\pi\)
−0.244193 + 0.969727i \(0.578523\pi\)
\(968\) 46.2709 1.48720
\(969\) 5.54406 0.178101
\(970\) −65.7547 −2.11126
\(971\) −47.5157 −1.52485 −0.762426 0.647076i \(-0.775992\pi\)
−0.762426 + 0.647076i \(0.775992\pi\)
\(972\) −4.29286 −0.137693
\(973\) −13.7382 −0.440426
\(974\) 82.9756 2.65871
\(975\) 0.314103 0.0100593
\(976\) 88.4288 2.83054
\(977\) −32.4199 −1.03720 −0.518602 0.855016i \(-0.673547\pi\)
−0.518602 + 0.855016i \(0.673547\pi\)
\(978\) −49.1837 −1.57272
\(979\) 0.302809 0.00967783
\(980\) −81.1679 −2.59281
\(981\) −19.5268 −0.623442
\(982\) 27.4059 0.874559
\(983\) 3.04172 0.0970157 0.0485078 0.998823i \(-0.484553\pi\)
0.0485078 + 0.998823i \(0.484553\pi\)
\(984\) 1.88461 0.0600792
\(985\) 42.3322 1.34881
\(986\) 18.0680 0.575404
\(987\) 32.3929 1.03108
\(988\) −3.30860 −0.105261
\(989\) 59.4018 1.88887
\(990\) −11.6193 −0.369286
\(991\) 32.8602 1.04384 0.521920 0.852995i \(-0.325216\pi\)
0.521920 + 0.852995i \(0.325216\pi\)
\(992\) 20.0520 0.636653
\(993\) −32.1823 −1.02128
\(994\) −81.8346 −2.59564
\(995\) −28.2608 −0.895927
\(996\) 71.8663 2.27717
\(997\) 22.0507 0.698352 0.349176 0.937057i \(-0.386462\pi\)
0.349176 + 0.937057i \(0.386462\pi\)
\(998\) −88.4598 −2.80014
\(999\) 9.56660 0.302674
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.1.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.4 32 1.1 even 1 trivial