Properties

Label 6037.2.a.b.1.15
Level 6037
Weight 2
Character 6037.1
Self dual yes
Analytic conductor 48.206
Analytic rank 0
Dimension 259
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 6037 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6037.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2056877002\)
Analytic rank: \(0\)
Dimension: \(259\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.46237 q^{2} -0.199276 q^{3} +4.06325 q^{4} -0.688498 q^{5} +0.490692 q^{6} +0.363231 q^{7} -5.08049 q^{8} -2.96029 q^{9} +O(q^{10})\) \(q-2.46237 q^{2} -0.199276 q^{3} +4.06325 q^{4} -0.688498 q^{5} +0.490692 q^{6} +0.363231 q^{7} -5.08049 q^{8} -2.96029 q^{9} +1.69534 q^{10} +0.608305 q^{11} -0.809710 q^{12} +1.23967 q^{13} -0.894407 q^{14} +0.137201 q^{15} +4.38352 q^{16} +0.714168 q^{17} +7.28932 q^{18} -3.65294 q^{19} -2.79754 q^{20} -0.0723833 q^{21} -1.49787 q^{22} -8.98401 q^{23} +1.01242 q^{24} -4.52597 q^{25} -3.05251 q^{26} +1.18774 q^{27} +1.47590 q^{28} -4.08453 q^{29} -0.337840 q^{30} -2.25338 q^{31} -0.632868 q^{32} -0.121221 q^{33} -1.75854 q^{34} -0.250084 q^{35} -12.0284 q^{36} -1.99307 q^{37} +8.99489 q^{38} -0.247036 q^{39} +3.49791 q^{40} +1.90939 q^{41} +0.178234 q^{42} -9.31067 q^{43} +2.47170 q^{44} +2.03815 q^{45} +22.1219 q^{46} +10.6828 q^{47} -0.873533 q^{48} -6.86806 q^{49} +11.1446 q^{50} -0.142317 q^{51} +5.03708 q^{52} +7.83367 q^{53} -2.92466 q^{54} -0.418817 q^{55} -1.84539 q^{56} +0.727945 q^{57} +10.0576 q^{58} +2.96694 q^{59} +0.557484 q^{60} +4.72291 q^{61} +5.54865 q^{62} -1.07527 q^{63} -7.20869 q^{64} -0.853508 q^{65} +0.298490 q^{66} -5.88429 q^{67} +2.90185 q^{68} +1.79030 q^{69} +0.615798 q^{70} -5.19133 q^{71} +15.0397 q^{72} -16.0982 q^{73} +4.90767 q^{74} +0.901919 q^{75} -14.8428 q^{76} +0.220955 q^{77} +0.608294 q^{78} +14.5062 q^{79} -3.01805 q^{80} +8.64418 q^{81} -4.70161 q^{82} -12.9259 q^{83} -0.294112 q^{84} -0.491704 q^{85} +22.9263 q^{86} +0.813951 q^{87} -3.09049 q^{88} +11.5823 q^{89} -5.01868 q^{90} +0.450285 q^{91} -36.5043 q^{92} +0.449045 q^{93} -26.3051 q^{94} +2.51504 q^{95} +0.126116 q^{96} -13.6450 q^{97} +16.9117 q^{98} -1.80076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46237 −1.74116 −0.870578 0.492030i \(-0.836255\pi\)
−0.870578 + 0.492030i \(0.836255\pi\)
\(3\) −0.199276 −0.115052 −0.0575261 0.998344i \(-0.518321\pi\)
−0.0575261 + 0.998344i \(0.518321\pi\)
\(4\) 4.06325 2.03163
\(5\) −0.688498 −0.307906 −0.153953 0.988078i \(-0.549200\pi\)
−0.153953 + 0.988078i \(0.549200\pi\)
\(6\) 0.490692 0.200324
\(7\) 0.363231 0.137288 0.0686441 0.997641i \(-0.478133\pi\)
0.0686441 + 0.997641i \(0.478133\pi\)
\(8\) −5.08049 −1.79622
\(9\) −2.96029 −0.986763
\(10\) 1.69534 0.536112
\(11\) 0.608305 0.183411 0.0917054 0.995786i \(-0.470768\pi\)
0.0917054 + 0.995786i \(0.470768\pi\)
\(12\) −0.809710 −0.233743
\(13\) 1.23967 0.343821 0.171911 0.985113i \(-0.445006\pi\)
0.171911 + 0.985113i \(0.445006\pi\)
\(14\) −0.894407 −0.239040
\(15\) 0.137201 0.0354253
\(16\) 4.38352 1.09588
\(17\) 0.714168 0.173211 0.0866056 0.996243i \(-0.472398\pi\)
0.0866056 + 0.996243i \(0.472398\pi\)
\(18\) 7.28932 1.71811
\(19\) −3.65294 −0.838042 −0.419021 0.907976i \(-0.637627\pi\)
−0.419021 + 0.907976i \(0.637627\pi\)
\(20\) −2.79754 −0.625550
\(21\) −0.0723833 −0.0157953
\(22\) −1.49787 −0.319347
\(23\) −8.98401 −1.87330 −0.936648 0.350273i \(-0.886089\pi\)
−0.936648 + 0.350273i \(0.886089\pi\)
\(24\) 1.01242 0.206660
\(25\) −4.52597 −0.905194
\(26\) −3.05251 −0.598647
\(27\) 1.18774 0.228582
\(28\) 1.47590 0.278919
\(29\) −4.08453 −0.758479 −0.379239 0.925299i \(-0.623814\pi\)
−0.379239 + 0.925299i \(0.623814\pi\)
\(30\) −0.337840 −0.0616809
\(31\) −2.25338 −0.404719 −0.202359 0.979311i \(-0.564861\pi\)
−0.202359 + 0.979311i \(0.564861\pi\)
\(32\) −0.632868 −0.111876
\(33\) −0.121221 −0.0211018
\(34\) −1.75854 −0.301588
\(35\) −0.250084 −0.0422719
\(36\) −12.0284 −2.00473
\(37\) −1.99307 −0.327659 −0.163829 0.986489i \(-0.552385\pi\)
−0.163829 + 0.986489i \(0.552385\pi\)
\(38\) 8.99489 1.45916
\(39\) −0.247036 −0.0395574
\(40\) 3.49791 0.553068
\(41\) 1.90939 0.298196 0.149098 0.988822i \(-0.452363\pi\)
0.149098 + 0.988822i \(0.452363\pi\)
\(42\) 0.178234 0.0275021
\(43\) −9.31067 −1.41986 −0.709932 0.704270i \(-0.751274\pi\)
−0.709932 + 0.704270i \(0.751274\pi\)
\(44\) 2.47170 0.372622
\(45\) 2.03815 0.303830
\(46\) 22.1219 3.26170
\(47\) 10.6828 1.55825 0.779126 0.626867i \(-0.215663\pi\)
0.779126 + 0.626867i \(0.215663\pi\)
\(48\) −0.873533 −0.126084
\(49\) −6.86806 −0.981152
\(50\) 11.1446 1.57608
\(51\) −0.142317 −0.0199283
\(52\) 5.03708 0.698517
\(53\) 7.83367 1.07604 0.538019 0.842933i \(-0.319173\pi\)
0.538019 + 0.842933i \(0.319173\pi\)
\(54\) −2.92466 −0.397996
\(55\) −0.418817 −0.0564732
\(56\) −1.84539 −0.246601
\(57\) 0.727945 0.0964187
\(58\) 10.0576 1.32063
\(59\) 2.96694 0.386262 0.193131 0.981173i \(-0.438136\pi\)
0.193131 + 0.981173i \(0.438136\pi\)
\(60\) 0.557484 0.0719709
\(61\) 4.72291 0.604707 0.302353 0.953196i \(-0.402228\pi\)
0.302353 + 0.953196i \(0.402228\pi\)
\(62\) 5.54865 0.704679
\(63\) −1.07527 −0.135471
\(64\) −7.20869 −0.901087
\(65\) −0.853508 −0.105865
\(66\) 0.298490 0.0367416
\(67\) −5.88429 −0.718880 −0.359440 0.933168i \(-0.617032\pi\)
−0.359440 + 0.933168i \(0.617032\pi\)
\(68\) 2.90185 0.351901
\(69\) 1.79030 0.215527
\(70\) 0.615798 0.0736019
\(71\) −5.19133 −0.616098 −0.308049 0.951370i \(-0.599676\pi\)
−0.308049 + 0.951370i \(0.599676\pi\)
\(72\) 15.0397 1.77245
\(73\) −16.0982 −1.88415 −0.942076 0.335398i \(-0.891129\pi\)
−0.942076 + 0.335398i \(0.891129\pi\)
\(74\) 4.90767 0.570505
\(75\) 0.901919 0.104145
\(76\) −14.8428 −1.70259
\(77\) 0.220955 0.0251802
\(78\) 0.608294 0.0688757
\(79\) 14.5062 1.63208 0.816038 0.577998i \(-0.196166\pi\)
0.816038 + 0.577998i \(0.196166\pi\)
\(80\) −3.01805 −0.337428
\(81\) 8.64418 0.960464
\(82\) −4.70161 −0.519206
\(83\) −12.9259 −1.41881 −0.709404 0.704803i \(-0.751036\pi\)
−0.709404 + 0.704803i \(0.751036\pi\)
\(84\) −0.294112 −0.0320902
\(85\) −0.491704 −0.0533328
\(86\) 22.9263 2.47221
\(87\) 0.813951 0.0872647
\(88\) −3.09049 −0.329447
\(89\) 11.5823 1.22772 0.613859 0.789416i \(-0.289616\pi\)
0.613859 + 0.789416i \(0.289616\pi\)
\(90\) −5.01868 −0.529016
\(91\) 0.450285 0.0472027
\(92\) −36.5043 −3.80584
\(93\) 0.449045 0.0465638
\(94\) −26.3051 −2.71316
\(95\) 2.51504 0.258038
\(96\) 0.126116 0.0128716
\(97\) −13.6450 −1.38544 −0.692722 0.721204i \(-0.743589\pi\)
−0.692722 + 0.721204i \(0.743589\pi\)
\(98\) 16.9117 1.70834
\(99\) −1.80076 −0.180983
\(100\) −18.3902 −1.83902
\(101\) 8.25853 0.821755 0.410877 0.911691i \(-0.365222\pi\)
0.410877 + 0.911691i \(0.365222\pi\)
\(102\) 0.350436 0.0346984
\(103\) 11.8042 1.16310 0.581551 0.813510i \(-0.302446\pi\)
0.581551 + 0.813510i \(0.302446\pi\)
\(104\) −6.29811 −0.617580
\(105\) 0.0498358 0.00486347
\(106\) −19.2894 −1.87355
\(107\) 5.57492 0.538948 0.269474 0.963008i \(-0.413150\pi\)
0.269474 + 0.963008i \(0.413150\pi\)
\(108\) 4.82611 0.464392
\(109\) −10.2275 −0.979618 −0.489809 0.871830i \(-0.662933\pi\)
−0.489809 + 0.871830i \(0.662933\pi\)
\(110\) 1.03128 0.0983288
\(111\) 0.397172 0.0376979
\(112\) 1.59223 0.150452
\(113\) 0.255742 0.0240581 0.0120291 0.999928i \(-0.496171\pi\)
0.0120291 + 0.999928i \(0.496171\pi\)
\(114\) −1.79247 −0.167880
\(115\) 6.18548 0.576799
\(116\) −16.5965 −1.54095
\(117\) −3.66977 −0.339270
\(118\) −7.30569 −0.672543
\(119\) 0.259408 0.0237799
\(120\) −0.697051 −0.0636317
\(121\) −10.6300 −0.966360
\(122\) −11.6295 −1.05289
\(123\) −0.380495 −0.0343081
\(124\) −9.15605 −0.822238
\(125\) 6.55862 0.586620
\(126\) 2.64770 0.235876
\(127\) 14.6336 1.29852 0.649261 0.760566i \(-0.275078\pi\)
0.649261 + 0.760566i \(0.275078\pi\)
\(128\) 19.0162 1.68081
\(129\) 1.85540 0.163359
\(130\) 2.10165 0.184327
\(131\) 2.22423 0.194331 0.0971657 0.995268i \(-0.469022\pi\)
0.0971657 + 0.995268i \(0.469022\pi\)
\(132\) −0.492551 −0.0428710
\(133\) −1.32686 −0.115053
\(134\) 14.4893 1.25168
\(135\) −0.817760 −0.0703816
\(136\) −3.62832 −0.311126
\(137\) 3.75673 0.320959 0.160479 0.987039i \(-0.448696\pi\)
0.160479 + 0.987039i \(0.448696\pi\)
\(138\) −4.40838 −0.375266
\(139\) 0.575436 0.0488079 0.0244039 0.999702i \(-0.492231\pi\)
0.0244039 + 0.999702i \(0.492231\pi\)
\(140\) −1.01615 −0.0858807
\(141\) −2.12884 −0.179280
\(142\) 12.7830 1.07272
\(143\) 0.754094 0.0630605
\(144\) −12.9765 −1.08137
\(145\) 2.81219 0.233540
\(146\) 39.6397 3.28061
\(147\) 1.36864 0.112884
\(148\) −8.09835 −0.665680
\(149\) 8.71682 0.714109 0.357055 0.934083i \(-0.383781\pi\)
0.357055 + 0.934083i \(0.383781\pi\)
\(150\) −2.22086 −0.181332
\(151\) 1.59710 0.129970 0.0649851 0.997886i \(-0.479300\pi\)
0.0649851 + 0.997886i \(0.479300\pi\)
\(152\) 18.5587 1.50531
\(153\) −2.11414 −0.170918
\(154\) −0.544072 −0.0438426
\(155\) 1.55145 0.124615
\(156\) −1.00377 −0.0803659
\(157\) 9.73833 0.777204 0.388602 0.921406i \(-0.372958\pi\)
0.388602 + 0.921406i \(0.372958\pi\)
\(158\) −35.7196 −2.84170
\(159\) −1.56107 −0.123801
\(160\) 0.435729 0.0344474
\(161\) −3.26327 −0.257182
\(162\) −21.2851 −1.67232
\(163\) 6.99321 0.547751 0.273875 0.961765i \(-0.411694\pi\)
0.273875 + 0.961765i \(0.411694\pi\)
\(164\) 7.75832 0.605823
\(165\) 0.0834603 0.00649738
\(166\) 31.8284 2.47037
\(167\) −1.83769 −0.142205 −0.0711025 0.997469i \(-0.522652\pi\)
−0.0711025 + 0.997469i \(0.522652\pi\)
\(168\) 0.367743 0.0283720
\(169\) −11.4632 −0.881787
\(170\) 1.21076 0.0928607
\(171\) 10.8138 0.826949
\(172\) −37.8316 −2.88463
\(173\) 13.0373 0.991204 0.495602 0.868550i \(-0.334948\pi\)
0.495602 + 0.868550i \(0.334948\pi\)
\(174\) −2.00425 −0.151942
\(175\) −1.64397 −0.124273
\(176\) 2.66652 0.200996
\(177\) −0.591240 −0.0444403
\(178\) −28.5198 −2.13765
\(179\) −12.8342 −0.959269 −0.479635 0.877468i \(-0.659231\pi\)
−0.479635 + 0.877468i \(0.659231\pi\)
\(180\) 8.28154 0.617269
\(181\) 8.53462 0.634373 0.317187 0.948363i \(-0.397262\pi\)
0.317187 + 0.948363i \(0.397262\pi\)
\(182\) −1.10877 −0.0821872
\(183\) −0.941164 −0.0695729
\(184\) 45.6432 3.36486
\(185\) 1.37223 0.100888
\(186\) −1.10571 −0.0810749
\(187\) 0.434432 0.0317688
\(188\) 43.4071 3.16579
\(189\) 0.431425 0.0313816
\(190\) −6.19297 −0.449285
\(191\) 13.3780 0.968000 0.484000 0.875068i \(-0.339184\pi\)
0.484000 + 0.875068i \(0.339184\pi\)
\(192\) 1.43652 0.103672
\(193\) 17.5520 1.26342 0.631711 0.775204i \(-0.282353\pi\)
0.631711 + 0.775204i \(0.282353\pi\)
\(194\) 33.5991 2.41228
\(195\) 0.170084 0.0121800
\(196\) −27.9067 −1.99333
\(197\) −4.38499 −0.312417 −0.156209 0.987724i \(-0.549927\pi\)
−0.156209 + 0.987724i \(0.549927\pi\)
\(198\) 4.43413 0.315120
\(199\) −3.34431 −0.237072 −0.118536 0.992950i \(-0.537820\pi\)
−0.118536 + 0.992950i \(0.537820\pi\)
\(200\) 22.9941 1.62593
\(201\) 1.17260 0.0827088
\(202\) −20.3355 −1.43080
\(203\) −1.48363 −0.104130
\(204\) −0.578270 −0.0404870
\(205\) −1.31461 −0.0918162
\(206\) −29.0663 −2.02514
\(207\) 26.5953 1.84850
\(208\) 5.43410 0.376787
\(209\) −2.22210 −0.153706
\(210\) −0.122714 −0.00846807
\(211\) −21.5889 −1.48624 −0.743121 0.669157i \(-0.766655\pi\)
−0.743121 + 0.669157i \(0.766655\pi\)
\(212\) 31.8302 2.18611
\(213\) 1.03451 0.0708835
\(214\) −13.7275 −0.938393
\(215\) 6.41038 0.437185
\(216\) −6.03432 −0.410584
\(217\) −0.818497 −0.0555632
\(218\) 25.1839 1.70567
\(219\) 3.20799 0.216776
\(220\) −1.70176 −0.114733
\(221\) 0.885330 0.0595537
\(222\) −0.977983 −0.0656379
\(223\) 12.1800 0.815636 0.407818 0.913063i \(-0.366290\pi\)
0.407818 + 0.913063i \(0.366290\pi\)
\(224\) −0.229877 −0.0153593
\(225\) 13.3982 0.893212
\(226\) −0.629730 −0.0418890
\(227\) −16.3201 −1.08321 −0.541603 0.840635i \(-0.682182\pi\)
−0.541603 + 0.840635i \(0.682182\pi\)
\(228\) 2.95783 0.195887
\(229\) −1.05865 −0.0699574 −0.0349787 0.999388i \(-0.511136\pi\)
−0.0349787 + 0.999388i \(0.511136\pi\)
\(230\) −15.2309 −1.00430
\(231\) −0.0440311 −0.00289703
\(232\) 20.7514 1.36240
\(233\) −18.7423 −1.22785 −0.613923 0.789366i \(-0.710410\pi\)
−0.613923 + 0.789366i \(0.710410\pi\)
\(234\) 9.03632 0.590723
\(235\) −7.35512 −0.479795
\(236\) 12.0554 0.784741
\(237\) −2.89075 −0.187774
\(238\) −0.638757 −0.0414045
\(239\) −8.37904 −0.541995 −0.270997 0.962580i \(-0.587354\pi\)
−0.270997 + 0.962580i \(0.587354\pi\)
\(240\) 0.601426 0.0388219
\(241\) −7.94408 −0.511723 −0.255862 0.966713i \(-0.582359\pi\)
−0.255862 + 0.966713i \(0.582359\pi\)
\(242\) 26.1749 1.68259
\(243\) −5.28581 −0.339085
\(244\) 19.1904 1.22854
\(245\) 4.72865 0.302102
\(246\) 0.936919 0.0597358
\(247\) −4.52843 −0.288137
\(248\) 11.4483 0.726966
\(249\) 2.57584 0.163237
\(250\) −16.1497 −1.02140
\(251\) 15.6797 0.989693 0.494847 0.868980i \(-0.335224\pi\)
0.494847 + 0.868980i \(0.335224\pi\)
\(252\) −4.36909 −0.275227
\(253\) −5.46501 −0.343583
\(254\) −36.0333 −2.26093
\(255\) 0.0979849 0.00613605
\(256\) −32.4075 −2.02547
\(257\) −2.31076 −0.144141 −0.0720707 0.997400i \(-0.522961\pi\)
−0.0720707 + 0.997400i \(0.522961\pi\)
\(258\) −4.56867 −0.284433
\(259\) −0.723944 −0.0449837
\(260\) −3.46802 −0.215077
\(261\) 12.0914 0.748439
\(262\) −5.47686 −0.338362
\(263\) 0.559168 0.0344798 0.0172399 0.999851i \(-0.494512\pi\)
0.0172399 + 0.999851i \(0.494512\pi\)
\(264\) 0.615861 0.0379036
\(265\) −5.39347 −0.331318
\(266\) 3.26722 0.200326
\(267\) −2.30807 −0.141252
\(268\) −23.9094 −1.46050
\(269\) −11.9395 −0.727965 −0.363982 0.931406i \(-0.618583\pi\)
−0.363982 + 0.931406i \(0.618583\pi\)
\(270\) 2.01363 0.122545
\(271\) −6.23189 −0.378560 −0.189280 0.981923i \(-0.560615\pi\)
−0.189280 + 0.981923i \(0.560615\pi\)
\(272\) 3.13057 0.189819
\(273\) −0.0897311 −0.00543077
\(274\) −9.25044 −0.558839
\(275\) −2.75317 −0.166022
\(276\) 7.27445 0.437870
\(277\) −26.6442 −1.60089 −0.800447 0.599404i \(-0.795404\pi\)
−0.800447 + 0.599404i \(0.795404\pi\)
\(278\) −1.41694 −0.0849821
\(279\) 6.67065 0.399362
\(280\) 1.27055 0.0759297
\(281\) 11.9020 0.710012 0.355006 0.934864i \(-0.384479\pi\)
0.355006 + 0.934864i \(0.384479\pi\)
\(282\) 5.24198 0.312155
\(283\) 9.26386 0.550679 0.275340 0.961347i \(-0.411210\pi\)
0.275340 + 0.961347i \(0.411210\pi\)
\(284\) −21.0937 −1.25168
\(285\) −0.501189 −0.0296879
\(286\) −1.85686 −0.109798
\(287\) 0.693547 0.0409388
\(288\) 1.87347 0.110395
\(289\) −16.4900 −0.969998
\(290\) −6.92466 −0.406630
\(291\) 2.71914 0.159399
\(292\) −65.4111 −3.82790
\(293\) 14.7360 0.860886 0.430443 0.902618i \(-0.358357\pi\)
0.430443 + 0.902618i \(0.358357\pi\)
\(294\) −3.37010 −0.196548
\(295\) −2.04273 −0.118932
\(296\) 10.1258 0.588548
\(297\) 0.722511 0.0419243
\(298\) −21.4640 −1.24338
\(299\) −11.1372 −0.644079
\(300\) 3.66473 0.211583
\(301\) −3.38192 −0.194931
\(302\) −3.93265 −0.226299
\(303\) −1.64573 −0.0945447
\(304\) −16.0128 −0.918395
\(305\) −3.25172 −0.186193
\(306\) 5.20580 0.297596
\(307\) 29.3661 1.67601 0.838006 0.545661i \(-0.183721\pi\)
0.838006 + 0.545661i \(0.183721\pi\)
\(308\) 0.897796 0.0511567
\(309\) −2.35230 −0.133817
\(310\) −3.82024 −0.216975
\(311\) −19.6726 −1.11553 −0.557764 0.829999i \(-0.688341\pi\)
−0.557764 + 0.829999i \(0.688341\pi\)
\(312\) 1.25506 0.0710540
\(313\) −7.33952 −0.414854 −0.207427 0.978250i \(-0.566509\pi\)
−0.207427 + 0.978250i \(0.566509\pi\)
\(314\) −23.9794 −1.35323
\(315\) 0.740320 0.0417123
\(316\) 58.9424 3.31577
\(317\) 16.3228 0.916781 0.458390 0.888751i \(-0.348426\pi\)
0.458390 + 0.888751i \(0.348426\pi\)
\(318\) 3.84392 0.215556
\(319\) −2.48464 −0.139113
\(320\) 4.96317 0.277450
\(321\) −1.11095 −0.0620072
\(322\) 8.03536 0.447793
\(323\) −2.60882 −0.145158
\(324\) 35.1235 1.95130
\(325\) −5.61069 −0.311225
\(326\) −17.2199 −0.953720
\(327\) 2.03810 0.112707
\(328\) −9.70061 −0.535627
\(329\) 3.88034 0.213930
\(330\) −0.205510 −0.0113129
\(331\) 4.51222 0.248014 0.124007 0.992281i \(-0.460425\pi\)
0.124007 + 0.992281i \(0.460425\pi\)
\(332\) −52.5214 −2.88249
\(333\) 5.90006 0.323321
\(334\) 4.52508 0.247601
\(335\) 4.05132 0.221347
\(336\) −0.317294 −0.0173098
\(337\) 2.41213 0.131397 0.0656986 0.997840i \(-0.479072\pi\)
0.0656986 + 0.997840i \(0.479072\pi\)
\(338\) 28.2267 1.53533
\(339\) −0.0509633 −0.00276794
\(340\) −1.99792 −0.108352
\(341\) −1.37074 −0.0742298
\(342\) −26.6275 −1.43985
\(343\) −5.03731 −0.271989
\(344\) 47.3028 2.55039
\(345\) −1.23262 −0.0663620
\(346\) −32.1025 −1.72584
\(347\) −4.17830 −0.224303 −0.112151 0.993691i \(-0.535774\pi\)
−0.112151 + 0.993691i \(0.535774\pi\)
\(348\) 3.30729 0.177289
\(349\) 6.84288 0.366291 0.183146 0.983086i \(-0.441372\pi\)
0.183146 + 0.983086i \(0.441372\pi\)
\(350\) 4.04806 0.216378
\(351\) 1.47241 0.0785912
\(352\) −0.384977 −0.0205193
\(353\) −26.3267 −1.40123 −0.700613 0.713541i \(-0.747090\pi\)
−0.700613 + 0.713541i \(0.747090\pi\)
\(354\) 1.45585 0.0773776
\(355\) 3.57423 0.189700
\(356\) 47.0617 2.49427
\(357\) −0.0516938 −0.00273593
\(358\) 31.6024 1.67024
\(359\) −17.5566 −0.926602 −0.463301 0.886201i \(-0.653335\pi\)
−0.463301 + 0.886201i \(0.653335\pi\)
\(360\) −10.3548 −0.545747
\(361\) −5.65601 −0.297685
\(362\) −21.0154 −1.10454
\(363\) 2.11830 0.111182
\(364\) 1.82962 0.0958982
\(365\) 11.0836 0.580142
\(366\) 2.31749 0.121137
\(367\) 28.1724 1.47059 0.735293 0.677750i \(-0.237045\pi\)
0.735293 + 0.677750i \(0.237045\pi\)
\(368\) −39.3816 −2.05291
\(369\) −5.65233 −0.294249
\(370\) −3.37892 −0.175662
\(371\) 2.84543 0.147727
\(372\) 1.82459 0.0946003
\(373\) 5.57630 0.288730 0.144365 0.989525i \(-0.453886\pi\)
0.144365 + 0.989525i \(0.453886\pi\)
\(374\) −1.06973 −0.0553145
\(375\) −1.30698 −0.0674920
\(376\) −54.2741 −2.79897
\(377\) −5.06346 −0.260781
\(378\) −1.06233 −0.0546402
\(379\) −15.0356 −0.772327 −0.386163 0.922430i \(-0.626200\pi\)
−0.386163 + 0.922430i \(0.626200\pi\)
\(380\) 10.2193 0.524237
\(381\) −2.91613 −0.149398
\(382\) −32.9416 −1.68544
\(383\) 23.8340 1.21786 0.608929 0.793224i \(-0.291599\pi\)
0.608929 + 0.793224i \(0.291599\pi\)
\(384\) −3.78948 −0.193381
\(385\) −0.152127 −0.00775312
\(386\) −43.2195 −2.19982
\(387\) 27.5623 1.40107
\(388\) −55.4433 −2.81471
\(389\) 8.34022 0.422866 0.211433 0.977392i \(-0.432187\pi\)
0.211433 + 0.977392i \(0.432187\pi\)
\(390\) −0.418809 −0.0212072
\(391\) −6.41609 −0.324476
\(392\) 34.8931 1.76237
\(393\) −0.443236 −0.0223583
\(394\) 10.7975 0.543968
\(395\) −9.98750 −0.502526
\(396\) −7.31694 −0.367690
\(397\) 11.7351 0.588967 0.294483 0.955657i \(-0.404852\pi\)
0.294483 + 0.955657i \(0.404852\pi\)
\(398\) 8.23493 0.412780
\(399\) 0.264412 0.0132372
\(400\) −19.8397 −0.991985
\(401\) 17.5279 0.875301 0.437650 0.899145i \(-0.355811\pi\)
0.437650 + 0.899145i \(0.355811\pi\)
\(402\) −2.88737 −0.144009
\(403\) −2.79344 −0.139151
\(404\) 33.5565 1.66950
\(405\) −5.95150 −0.295733
\(406\) 3.65324 0.181307
\(407\) −1.21239 −0.0600961
\(408\) 0.723039 0.0357958
\(409\) 34.8728 1.72435 0.862176 0.506610i \(-0.169101\pi\)
0.862176 + 0.506610i \(0.169101\pi\)
\(410\) 3.23705 0.159866
\(411\) −0.748627 −0.0369270
\(412\) 47.9634 2.36299
\(413\) 1.07768 0.0530293
\(414\) −65.4873 −3.21853
\(415\) 8.89949 0.436859
\(416\) −0.784545 −0.0384655
\(417\) −0.114671 −0.00561546
\(418\) 5.47163 0.267626
\(419\) −10.3102 −0.503686 −0.251843 0.967768i \(-0.581037\pi\)
−0.251843 + 0.967768i \(0.581037\pi\)
\(420\) 0.202495 0.00988076
\(421\) −5.72609 −0.279073 −0.139536 0.990217i \(-0.544561\pi\)
−0.139536 + 0.990217i \(0.544561\pi\)
\(422\) 53.1598 2.58778
\(423\) −31.6243 −1.53763
\(424\) −39.7989 −1.93280
\(425\) −3.23230 −0.156790
\(426\) −2.54734 −0.123419
\(427\) 1.71551 0.0830191
\(428\) 22.6523 1.09494
\(429\) −0.150273 −0.00725526
\(430\) −15.7847 −0.761207
\(431\) −5.94644 −0.286430 −0.143215 0.989692i \(-0.545744\pi\)
−0.143215 + 0.989692i \(0.545744\pi\)
\(432\) 5.20651 0.250498
\(433\) 24.9052 1.19687 0.598435 0.801172i \(-0.295790\pi\)
0.598435 + 0.801172i \(0.295790\pi\)
\(434\) 2.01544 0.0967442
\(435\) −0.560404 −0.0268693
\(436\) −41.5570 −1.99022
\(437\) 32.8181 1.56990
\(438\) −7.89926 −0.377441
\(439\) −2.94598 −0.140604 −0.0703019 0.997526i \(-0.522396\pi\)
−0.0703019 + 0.997526i \(0.522396\pi\)
\(440\) 2.12779 0.101439
\(441\) 20.3315 0.968164
\(442\) −2.18001 −0.103692
\(443\) −12.1746 −0.578431 −0.289216 0.957264i \(-0.593394\pi\)
−0.289216 + 0.957264i \(0.593394\pi\)
\(444\) 1.61381 0.0765880
\(445\) −7.97438 −0.378022
\(446\) −29.9917 −1.42015
\(447\) −1.73706 −0.0821599
\(448\) −2.61842 −0.123709
\(449\) 24.3684 1.15001 0.575007 0.818149i \(-0.304999\pi\)
0.575007 + 0.818149i \(0.304999\pi\)
\(450\) −32.9912 −1.55522
\(451\) 1.16149 0.0546923
\(452\) 1.03914 0.0488772
\(453\) −0.318264 −0.0149534
\(454\) 40.1862 1.88603
\(455\) −0.310020 −0.0145340
\(456\) −3.69832 −0.173190
\(457\) −13.3343 −0.623753 −0.311877 0.950123i \(-0.600958\pi\)
−0.311877 + 0.950123i \(0.600958\pi\)
\(458\) 2.60678 0.121807
\(459\) 0.848250 0.0395929
\(460\) 25.1332 1.17184
\(461\) 20.2808 0.944573 0.472286 0.881445i \(-0.343429\pi\)
0.472286 + 0.881445i \(0.343429\pi\)
\(462\) 0.108421 0.00504419
\(463\) 23.5324 1.09364 0.546822 0.837249i \(-0.315837\pi\)
0.546822 + 0.837249i \(0.315837\pi\)
\(464\) −17.9046 −0.831202
\(465\) −0.309167 −0.0143373
\(466\) 46.1503 2.13787
\(467\) 14.0058 0.648109 0.324055 0.946038i \(-0.394954\pi\)
0.324055 + 0.946038i \(0.394954\pi\)
\(468\) −14.9112 −0.689271
\(469\) −2.13735 −0.0986939
\(470\) 18.1110 0.835398
\(471\) −1.94062 −0.0894190
\(472\) −15.0735 −0.693813
\(473\) −5.66373 −0.260418
\(474\) 7.11808 0.326944
\(475\) 16.5331 0.758591
\(476\) 1.05404 0.0483118
\(477\) −23.1899 −1.06179
\(478\) 20.6323 0.943698
\(479\) −36.0014 −1.64494 −0.822472 0.568805i \(-0.807406\pi\)
−0.822472 + 0.568805i \(0.807406\pi\)
\(480\) −0.0868304 −0.00396325
\(481\) −2.47074 −0.112656
\(482\) 19.5612 0.890990
\(483\) 0.650292 0.0295893
\(484\) −43.1922 −1.96328
\(485\) 9.39460 0.426587
\(486\) 13.0156 0.590400
\(487\) −1.23392 −0.0559143 −0.0279572 0.999609i \(-0.508900\pi\)
−0.0279572 + 0.999609i \(0.508900\pi\)
\(488\) −23.9947 −1.08619
\(489\) −1.39358 −0.0630200
\(490\) −11.6437 −0.526008
\(491\) 4.38378 0.197837 0.0989187 0.995096i \(-0.468462\pi\)
0.0989187 + 0.995096i \(0.468462\pi\)
\(492\) −1.54605 −0.0697013
\(493\) −2.91704 −0.131377
\(494\) 11.1507 0.501692
\(495\) 1.23982 0.0557257
\(496\) −9.87774 −0.443524
\(497\) −1.88565 −0.0845830
\(498\) −6.34266 −0.284221
\(499\) −32.9660 −1.47576 −0.737881 0.674931i \(-0.764173\pi\)
−0.737881 + 0.674931i \(0.764173\pi\)
\(500\) 26.6493 1.19179
\(501\) 0.366209 0.0163610
\(502\) −38.6092 −1.72321
\(503\) 3.32925 0.148444 0.0742220 0.997242i \(-0.476353\pi\)
0.0742220 + 0.997242i \(0.476353\pi\)
\(504\) 5.46289 0.243336
\(505\) −5.68599 −0.253023
\(506\) 13.4569 0.598231
\(507\) 2.28435 0.101452
\(508\) 59.4600 2.63811
\(509\) −25.5006 −1.13029 −0.565147 0.824990i \(-0.691180\pi\)
−0.565147 + 0.824990i \(0.691180\pi\)
\(510\) −0.241275 −0.0106838
\(511\) −5.84736 −0.258672
\(512\) 41.7667 1.84584
\(513\) −4.33876 −0.191561
\(514\) 5.68995 0.250973
\(515\) −8.12717 −0.358126
\(516\) 7.53895 0.331884
\(517\) 6.49842 0.285800
\(518\) 1.78262 0.0783237
\(519\) −2.59802 −0.114040
\(520\) 4.33624 0.190157
\(521\) −7.13807 −0.312724 −0.156362 0.987700i \(-0.549977\pi\)
−0.156362 + 0.987700i \(0.549977\pi\)
\(522\) −29.7735 −1.30315
\(523\) −10.2309 −0.447367 −0.223683 0.974662i \(-0.571808\pi\)
−0.223683 + 0.974662i \(0.571808\pi\)
\(524\) 9.03759 0.394809
\(525\) 0.327605 0.0142978
\(526\) −1.37688 −0.0600347
\(527\) −1.60929 −0.0701019
\(528\) −0.531374 −0.0231251
\(529\) 57.7124 2.50924
\(530\) 13.2807 0.576877
\(531\) −8.78299 −0.381149
\(532\) −5.39137 −0.233746
\(533\) 2.36700 0.102526
\(534\) 5.68332 0.245942
\(535\) −3.83832 −0.165945
\(536\) 29.8951 1.29127
\(537\) 2.55754 0.110366
\(538\) 29.3995 1.26750
\(539\) −4.17788 −0.179954
\(540\) −3.32277 −0.142989
\(541\) −14.3939 −0.618841 −0.309420 0.950925i \(-0.600135\pi\)
−0.309420 + 0.950925i \(0.600135\pi\)
\(542\) 15.3452 0.659132
\(543\) −1.70075 −0.0729861
\(544\) −0.451974 −0.0193782
\(545\) 7.04163 0.301630
\(546\) 0.220951 0.00945583
\(547\) −0.0309924 −0.00132514 −0.000662569 1.00000i \(-0.500211\pi\)
−0.000662569 1.00000i \(0.500211\pi\)
\(548\) 15.2645 0.652068
\(549\) −13.9812 −0.596702
\(550\) 6.77931 0.289071
\(551\) 14.9206 0.635637
\(552\) −9.09560 −0.387135
\(553\) 5.26910 0.224065
\(554\) 65.6078 2.78741
\(555\) −0.273452 −0.0116074
\(556\) 2.33814 0.0991594
\(557\) 12.4387 0.527043 0.263522 0.964654i \(-0.415116\pi\)
0.263522 + 0.964654i \(0.415116\pi\)
\(558\) −16.4256 −0.695351
\(559\) −11.5421 −0.488180
\(560\) −1.09625 −0.0463249
\(561\) −0.0865720 −0.00365507
\(562\) −29.3070 −1.23624
\(563\) 35.7047 1.50477 0.752387 0.658721i \(-0.228902\pi\)
0.752387 + 0.658721i \(0.228902\pi\)
\(564\) −8.65001 −0.364231
\(565\) −0.176078 −0.00740764
\(566\) −22.8110 −0.958819
\(567\) 3.13983 0.131860
\(568\) 26.3745 1.10665
\(569\) 27.5053 1.15308 0.576541 0.817068i \(-0.304402\pi\)
0.576541 + 0.817068i \(0.304402\pi\)
\(570\) 1.23411 0.0516912
\(571\) 20.8980 0.874556 0.437278 0.899326i \(-0.355943\pi\)
0.437278 + 0.899326i \(0.355943\pi\)
\(572\) 3.06408 0.128116
\(573\) −2.66592 −0.111371
\(574\) −1.70777 −0.0712809
\(575\) 40.6614 1.69570
\(576\) 21.3398 0.889159
\(577\) 6.99681 0.291281 0.145641 0.989338i \(-0.453476\pi\)
0.145641 + 0.989338i \(0.453476\pi\)
\(578\) 40.6044 1.68892
\(579\) −3.49770 −0.145360
\(580\) 11.4267 0.474466
\(581\) −4.69510 −0.194786
\(582\) −6.69551 −0.277538
\(583\) 4.76526 0.197357
\(584\) 81.7868 3.38436
\(585\) 2.52663 0.104463
\(586\) −36.2854 −1.49894
\(587\) 15.0302 0.620363 0.310181 0.950677i \(-0.399610\pi\)
0.310181 + 0.950677i \(0.399610\pi\)
\(588\) 5.56114 0.229338
\(589\) 8.23147 0.339172
\(590\) 5.02995 0.207080
\(591\) 0.873825 0.0359443
\(592\) −8.73667 −0.359075
\(593\) 16.5479 0.679542 0.339771 0.940508i \(-0.389650\pi\)
0.339771 + 0.940508i \(0.389650\pi\)
\(594\) −1.77909 −0.0729968
\(595\) −0.178602 −0.00732196
\(596\) 35.4186 1.45080
\(597\) 0.666443 0.0272757
\(598\) 27.4238 1.12144
\(599\) 15.3528 0.627299 0.313650 0.949539i \(-0.398448\pi\)
0.313650 + 0.949539i \(0.398448\pi\)
\(600\) −4.58219 −0.187067
\(601\) −4.00835 −0.163504 −0.0817521 0.996653i \(-0.526052\pi\)
−0.0817521 + 0.996653i \(0.526052\pi\)
\(602\) 8.32754 0.339405
\(603\) 17.4192 0.709365
\(604\) 6.48943 0.264051
\(605\) 7.31871 0.297548
\(606\) 4.05239 0.164617
\(607\) 30.4854 1.23736 0.618682 0.785642i \(-0.287667\pi\)
0.618682 + 0.785642i \(0.287667\pi\)
\(608\) 2.31183 0.0937571
\(609\) 0.295652 0.0119804
\(610\) 8.00692 0.324191
\(611\) 13.2432 0.535761
\(612\) −8.59030 −0.347242
\(613\) 0.946597 0.0382327 0.0191163 0.999817i \(-0.493915\pi\)
0.0191163 + 0.999817i \(0.493915\pi\)
\(614\) −72.3101 −2.91820
\(615\) 0.261970 0.0105637
\(616\) −1.12256 −0.0452292
\(617\) 32.1592 1.29468 0.647341 0.762201i \(-0.275881\pi\)
0.647341 + 0.762201i \(0.275881\pi\)
\(618\) 5.79222 0.232997
\(619\) −42.7938 −1.72003 −0.860014 0.510270i \(-0.829545\pi\)
−0.860014 + 0.510270i \(0.829545\pi\)
\(620\) 6.30393 0.253172
\(621\) −10.6707 −0.428201
\(622\) 48.4411 1.94231
\(623\) 4.20704 0.168551
\(624\) −1.08289 −0.0433502
\(625\) 18.1143 0.724570
\(626\) 18.0726 0.722326
\(627\) 0.442812 0.0176842
\(628\) 39.5693 1.57899
\(629\) −1.42339 −0.0567542
\(630\) −1.82294 −0.0726277
\(631\) 13.5830 0.540730 0.270365 0.962758i \(-0.412856\pi\)
0.270365 + 0.962758i \(0.412856\pi\)
\(632\) −73.6986 −2.93157
\(633\) 4.30216 0.170996
\(634\) −40.1928 −1.59626
\(635\) −10.0752 −0.399822
\(636\) −6.34300 −0.251516
\(637\) −8.51410 −0.337341
\(638\) 6.11810 0.242218
\(639\) 15.3678 0.607943
\(640\) −13.0926 −0.517531
\(641\) −38.1110 −1.50529 −0.752647 0.658424i \(-0.771223\pi\)
−0.752647 + 0.658424i \(0.771223\pi\)
\(642\) 2.73557 0.107964
\(643\) −4.72788 −0.186449 −0.0932246 0.995645i \(-0.529717\pi\)
−0.0932246 + 0.995645i \(0.529717\pi\)
\(644\) −13.2595 −0.522497
\(645\) −1.27744 −0.0502991
\(646\) 6.42386 0.252743
\(647\) 24.7026 0.971159 0.485579 0.874193i \(-0.338609\pi\)
0.485579 + 0.874193i \(0.338609\pi\)
\(648\) −43.9166 −1.72521
\(649\) 1.80480 0.0708446
\(650\) 13.8156 0.541892
\(651\) 0.163107 0.00639267
\(652\) 28.4152 1.11283
\(653\) −15.7362 −0.615805 −0.307902 0.951418i \(-0.599627\pi\)
−0.307902 + 0.951418i \(0.599627\pi\)
\(654\) −5.01856 −0.196241
\(655\) −1.53138 −0.0598358
\(656\) 8.36983 0.326787
\(657\) 47.6554 1.85921
\(658\) −9.55481 −0.372485
\(659\) −5.03185 −0.196013 −0.0980066 0.995186i \(-0.531247\pi\)
−0.0980066 + 0.995186i \(0.531247\pi\)
\(660\) 0.339120 0.0132002
\(661\) 25.0643 0.974888 0.487444 0.873154i \(-0.337929\pi\)
0.487444 + 0.873154i \(0.337929\pi\)
\(662\) −11.1107 −0.431831
\(663\) −0.176425 −0.00685179
\(664\) 65.6701 2.54850
\(665\) 0.913541 0.0354256
\(666\) −14.5281 −0.562953
\(667\) 36.6955 1.42085
\(668\) −7.46702 −0.288908
\(669\) −2.42719 −0.0938407
\(670\) −9.97585 −0.385401
\(671\) 2.87297 0.110910
\(672\) 0.0458091 0.00176712
\(673\) −12.4768 −0.480945 −0.240472 0.970656i \(-0.577302\pi\)
−0.240472 + 0.970656i \(0.577302\pi\)
\(674\) −5.93956 −0.228783
\(675\) −5.37570 −0.206911
\(676\) −46.5780 −1.79146
\(677\) 15.5776 0.598696 0.299348 0.954144i \(-0.403231\pi\)
0.299348 + 0.954144i \(0.403231\pi\)
\(678\) 0.125490 0.00481942
\(679\) −4.95630 −0.190205
\(680\) 2.49810 0.0957976
\(681\) 3.25222 0.124625
\(682\) 3.37527 0.129246
\(683\) 25.3107 0.968488 0.484244 0.874933i \(-0.339095\pi\)
0.484244 + 0.874933i \(0.339095\pi\)
\(684\) 43.9391 1.68005
\(685\) −2.58650 −0.0988251
\(686\) 12.4037 0.473575
\(687\) 0.210963 0.00804876
\(688\) −40.8136 −1.55600
\(689\) 9.71113 0.369965
\(690\) 3.03516 0.115547
\(691\) 31.9905 1.21698 0.608489 0.793563i \(-0.291776\pi\)
0.608489 + 0.793563i \(0.291776\pi\)
\(692\) 52.9737 2.01376
\(693\) −0.654090 −0.0248468
\(694\) 10.2885 0.390546
\(695\) −0.396187 −0.0150282
\(696\) −4.13527 −0.156747
\(697\) 1.36362 0.0516509
\(698\) −16.8497 −0.637770
\(699\) 3.73489 0.141267
\(700\) −6.67987 −0.252475
\(701\) 23.1733 0.875244 0.437622 0.899159i \(-0.355821\pi\)
0.437622 + 0.899159i \(0.355821\pi\)
\(702\) −3.62561 −0.136840
\(703\) 7.28057 0.274592
\(704\) −4.38508 −0.165269
\(705\) 1.46570 0.0552015
\(706\) 64.8259 2.43975
\(707\) 2.99975 0.112817
\(708\) −2.40236 −0.0902862
\(709\) −43.4701 −1.63255 −0.816277 0.577660i \(-0.803966\pi\)
−0.816277 + 0.577660i \(0.803966\pi\)
\(710\) −8.80106 −0.330298
\(711\) −42.9426 −1.61047
\(712\) −58.8436 −2.20526
\(713\) 20.2444 0.758158
\(714\) 0.127289 0.00476368
\(715\) −0.519193 −0.0194167
\(716\) −52.1484 −1.94888
\(717\) 1.66974 0.0623577
\(718\) 43.2308 1.61336
\(719\) 39.6940 1.48034 0.740169 0.672421i \(-0.234746\pi\)
0.740169 + 0.672421i \(0.234746\pi\)
\(720\) 8.93430 0.332962
\(721\) 4.28764 0.159680
\(722\) 13.9272 0.518316
\(723\) 1.58307 0.0588749
\(724\) 34.6783 1.28881
\(725\) 18.4865 0.686570
\(726\) −5.21604 −0.193585
\(727\) 36.2404 1.34408 0.672041 0.740514i \(-0.265418\pi\)
0.672041 + 0.740514i \(0.265418\pi\)
\(728\) −2.28767 −0.0847865
\(729\) −24.8792 −0.921452
\(730\) −27.2919 −1.01012
\(731\) −6.64939 −0.245936
\(732\) −3.82419 −0.141346
\(733\) 33.0965 1.22245 0.611224 0.791457i \(-0.290677\pi\)
0.611224 + 0.791457i \(0.290677\pi\)
\(734\) −69.3707 −2.56052
\(735\) −0.942308 −0.0347576
\(736\) 5.68569 0.209577
\(737\) −3.57944 −0.131850
\(738\) 13.9181 0.512333
\(739\) −43.7389 −1.60896 −0.804480 0.593980i \(-0.797556\pi\)
−0.804480 + 0.593980i \(0.797556\pi\)
\(740\) 5.57570 0.204967
\(741\) 0.902409 0.0331508
\(742\) −7.00649 −0.257216
\(743\) −9.83063 −0.360651 −0.180325 0.983607i \(-0.557715\pi\)
−0.180325 + 0.983607i \(0.557715\pi\)
\(744\) −2.28137 −0.0836391
\(745\) −6.00151 −0.219878
\(746\) −13.7309 −0.502724
\(747\) 38.2645 1.40003
\(748\) 1.76521 0.0645424
\(749\) 2.02498 0.0739912
\(750\) 3.21826 0.117514
\(751\) 37.0100 1.35051 0.675257 0.737583i \(-0.264033\pi\)
0.675257 + 0.737583i \(0.264033\pi\)
\(752\) 46.8285 1.70766
\(753\) −3.12459 −0.113866
\(754\) 12.4681 0.454061
\(755\) −1.09960 −0.0400186
\(756\) 1.75299 0.0637557
\(757\) 15.6212 0.567760 0.283880 0.958860i \(-0.408378\pi\)
0.283880 + 0.958860i \(0.408378\pi\)
\(758\) 37.0232 1.34474
\(759\) 1.08905 0.0395299
\(760\) −12.7777 −0.463494
\(761\) −34.9672 −1.26756 −0.633780 0.773513i \(-0.718498\pi\)
−0.633780 + 0.773513i \(0.718498\pi\)
\(762\) 7.18058 0.260125
\(763\) −3.71495 −0.134490
\(764\) 54.3583 1.96661
\(765\) 1.45559 0.0526268
\(766\) −58.6880 −2.12048
\(767\) 3.67801 0.132805
\(768\) 6.45804 0.233034
\(769\) −36.1481 −1.30353 −0.651767 0.758419i \(-0.725972\pi\)
−0.651767 + 0.758419i \(0.725972\pi\)
\(770\) 0.374593 0.0134994
\(771\) 0.460481 0.0165838
\(772\) 71.3183 2.56680
\(773\) 30.5228 1.09783 0.548915 0.835878i \(-0.315041\pi\)
0.548915 + 0.835878i \(0.315041\pi\)
\(774\) −67.8685 −2.43948
\(775\) 10.1987 0.366349
\(776\) 69.3235 2.48857
\(777\) 0.144265 0.00517548
\(778\) −20.5367 −0.736276
\(779\) −6.97487 −0.249901
\(780\) 0.691094 0.0247451
\(781\) −3.15791 −0.112999
\(782\) 15.7988 0.564963
\(783\) −4.85138 −0.173374
\(784\) −30.1063 −1.07523
\(785\) −6.70483 −0.239306
\(786\) 1.09141 0.0389293
\(787\) −0.816266 −0.0290967 −0.0145484 0.999894i \(-0.504631\pi\)
−0.0145484 + 0.999894i \(0.504631\pi\)
\(788\) −17.8173 −0.634716
\(789\) −0.111429 −0.00396698
\(790\) 24.5929 0.874976
\(791\) 0.0928932 0.00330290
\(792\) 9.14873 0.325086
\(793\) 5.85483 0.207911
\(794\) −28.8961 −1.02548
\(795\) 1.07479 0.0381189
\(796\) −13.5888 −0.481642
\(797\) 24.9704 0.884496 0.442248 0.896893i \(-0.354181\pi\)
0.442248 + 0.896893i \(0.354181\pi\)
\(798\) −0.651079 −0.0230480
\(799\) 7.62934 0.269907
\(800\) 2.86434 0.101270
\(801\) −34.2869 −1.21147
\(802\) −43.1601 −1.52404
\(803\) −9.79262 −0.345574
\(804\) 4.76457 0.168033
\(805\) 2.24675 0.0791877
\(806\) 6.87847 0.242284
\(807\) 2.37926 0.0837540
\(808\) −41.9574 −1.47606
\(809\) 10.8063 0.379930 0.189965 0.981791i \(-0.439163\pi\)
0.189965 + 0.981791i \(0.439163\pi\)
\(810\) 14.6548 0.514917
\(811\) 37.7034 1.32395 0.661973 0.749527i \(-0.269719\pi\)
0.661973 + 0.749527i \(0.269719\pi\)
\(812\) −6.02836 −0.211554
\(813\) 1.24187 0.0435542
\(814\) 2.98536 0.104637
\(815\) −4.81482 −0.168656
\(816\) −0.623849 −0.0218391
\(817\) 34.0114 1.18991
\(818\) −85.8698 −3.00237
\(819\) −1.33297 −0.0465778
\(820\) −5.34159 −0.186536
\(821\) −14.7813 −0.515871 −0.257935 0.966162i \(-0.583042\pi\)
−0.257935 + 0.966162i \(0.583042\pi\)
\(822\) 1.84339 0.0642957
\(823\) −47.3909 −1.65194 −0.825972 0.563711i \(-0.809373\pi\)
−0.825972 + 0.563711i \(0.809373\pi\)
\(824\) −59.9711 −2.08919
\(825\) 0.548641 0.0191012
\(826\) −2.65365 −0.0923323
\(827\) −51.8766 −1.80393 −0.901963 0.431814i \(-0.857874\pi\)
−0.901963 + 0.431814i \(0.857874\pi\)
\(828\) 108.063 3.75546
\(829\) 8.10315 0.281434 0.140717 0.990050i \(-0.455059\pi\)
0.140717 + 0.990050i \(0.455059\pi\)
\(830\) −21.9138 −0.760640
\(831\) 5.30955 0.184186
\(832\) −8.93637 −0.309813
\(833\) −4.90495 −0.169947
\(834\) 0.282362 0.00977739
\(835\) 1.26525 0.0437858
\(836\) −9.02896 −0.312273
\(837\) −2.67644 −0.0925113
\(838\) 25.3875 0.876997
\(839\) 37.3711 1.29020 0.645098 0.764100i \(-0.276817\pi\)
0.645098 + 0.764100i \(0.276817\pi\)
\(840\) −0.253190 −0.00873589
\(841\) −12.3166 −0.424710
\(842\) 14.0997 0.485909
\(843\) −2.37178 −0.0816885
\(844\) −87.7212 −3.01949
\(845\) 7.89241 0.271507
\(846\) 77.8706 2.67725
\(847\) −3.86113 −0.132670
\(848\) 34.3391 1.17921
\(849\) −1.84607 −0.0633569
\(850\) 7.95912 0.272996
\(851\) 17.9058 0.613801
\(852\) 4.20348 0.144009
\(853\) 2.04739 0.0701012 0.0350506 0.999386i \(-0.488841\pi\)
0.0350506 + 0.999386i \(0.488841\pi\)
\(854\) −4.22420 −0.144549
\(855\) −7.44526 −0.254623
\(856\) −28.3233 −0.968071
\(857\) 11.0282 0.376716 0.188358 0.982100i \(-0.439683\pi\)
0.188358 + 0.982100i \(0.439683\pi\)
\(858\) 0.370028 0.0126325
\(859\) −14.4955 −0.494579 −0.247290 0.968942i \(-0.579540\pi\)
−0.247290 + 0.968942i \(0.579540\pi\)
\(860\) 26.0470 0.888196
\(861\) −0.138208 −0.00471010
\(862\) 14.6423 0.498719
\(863\) 3.55962 0.121171 0.0605854 0.998163i \(-0.480703\pi\)
0.0605854 + 0.998163i \(0.480703\pi\)
\(864\) −0.751686 −0.0255729
\(865\) −8.97613 −0.305197
\(866\) −61.3259 −2.08394
\(867\) 3.28606 0.111600
\(868\) −3.32576 −0.112884
\(869\) 8.82420 0.299340
\(870\) 1.37992 0.0467837
\(871\) −7.29455 −0.247166
\(872\) 51.9608 1.75961
\(873\) 40.3933 1.36711
\(874\) −80.8101 −2.73344
\(875\) 2.38229 0.0805361
\(876\) 13.0349 0.440408
\(877\) −47.7955 −1.61394 −0.806970 0.590592i \(-0.798894\pi\)
−0.806970 + 0.590592i \(0.798894\pi\)
\(878\) 7.25408 0.244813
\(879\) −2.93653 −0.0990468
\(880\) −1.83589 −0.0618880
\(881\) 45.5872 1.53587 0.767936 0.640527i \(-0.221284\pi\)
0.767936 + 0.640527i \(0.221284\pi\)
\(882\) −50.0635 −1.68573
\(883\) 7.88523 0.265359 0.132680 0.991159i \(-0.457642\pi\)
0.132680 + 0.991159i \(0.457642\pi\)
\(884\) 3.59732 0.120991
\(885\) 0.407068 0.0136834
\(886\) 29.9783 1.00714
\(887\) 26.1885 0.879322 0.439661 0.898164i \(-0.355099\pi\)
0.439661 + 0.898164i \(0.355099\pi\)
\(888\) −2.01783 −0.0677138
\(889\) 5.31537 0.178272
\(890\) 19.6358 0.658195
\(891\) 5.25829 0.176159
\(892\) 49.4906 1.65707
\(893\) −39.0238 −1.30588
\(894\) 4.27727 0.143053
\(895\) 8.83629 0.295365
\(896\) 6.90726 0.230755
\(897\) 2.21937 0.0741028
\(898\) −60.0038 −2.00235
\(899\) 9.20400 0.306971
\(900\) 54.4402 1.81467
\(901\) 5.59456 0.186382
\(902\) −2.86001 −0.0952279
\(903\) 0.673937 0.0224272
\(904\) −1.29929 −0.0432138
\(905\) −5.87607 −0.195327
\(906\) 0.783684 0.0260362
\(907\) 35.4269 1.17633 0.588165 0.808741i \(-0.299851\pi\)
0.588165 + 0.808741i \(0.299851\pi\)
\(908\) −66.3128 −2.20067
\(909\) −24.4476 −0.810877
\(910\) 0.763384 0.0253059
\(911\) −12.8829 −0.426830 −0.213415 0.976962i \(-0.568459\pi\)
−0.213415 + 0.976962i \(0.568459\pi\)
\(912\) 3.19096 0.105663
\(913\) −7.86291 −0.260225
\(914\) 32.8340 1.08605
\(915\) 0.647990 0.0214219
\(916\) −4.30155 −0.142127
\(917\) 0.807907 0.0266794
\(918\) −2.08870 −0.0689374
\(919\) −24.6257 −0.812328 −0.406164 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(920\) −31.4252 −1.03606
\(921\) −5.85197 −0.192829
\(922\) −49.9389 −1.64465
\(923\) −6.43552 −0.211828
\(924\) −0.178910 −0.00588569
\(925\) 9.02057 0.296595
\(926\) −57.9455 −1.90421
\(927\) −34.9438 −1.14771
\(928\) 2.58497 0.0848558
\(929\) 43.4827 1.42662 0.713310 0.700848i \(-0.247195\pi\)
0.713310 + 0.700848i \(0.247195\pi\)
\(930\) 0.761283 0.0249634
\(931\) 25.0886 0.822247
\(932\) −76.1546 −2.49453
\(933\) 3.92028 0.128344
\(934\) −34.4873 −1.12846
\(935\) −0.299106 −0.00978180
\(936\) 18.6442 0.609405
\(937\) 46.0292 1.50371 0.751854 0.659330i \(-0.229160\pi\)
0.751854 + 0.659330i \(0.229160\pi\)
\(938\) 5.26295 0.171841
\(939\) 1.46259 0.0477299
\(940\) −29.8857 −0.974764
\(941\) −28.2566 −0.921140 −0.460570 0.887623i \(-0.652355\pi\)
−0.460570 + 0.887623i \(0.652355\pi\)
\(942\) 4.77852 0.155693
\(943\) −17.1539 −0.558609
\(944\) 13.0056 0.423297
\(945\) −0.297036 −0.00966257
\(946\) 13.9462 0.453429
\(947\) 43.5512 1.41522 0.707612 0.706601i \(-0.249772\pi\)
0.707612 + 0.706601i \(0.249772\pi\)
\(948\) −11.7458 −0.381487
\(949\) −19.9564 −0.647812
\(950\) −40.7106 −1.32083
\(951\) −3.25275 −0.105478
\(952\) −1.31792 −0.0427140
\(953\) −36.6249 −1.18640 −0.593199 0.805056i \(-0.702135\pi\)
−0.593199 + 0.805056i \(0.702135\pi\)
\(954\) 57.1021 1.84875
\(955\) −9.21075 −0.298053
\(956\) −34.0462 −1.10113
\(957\) 0.495130 0.0160053
\(958\) 88.6486 2.86411
\(959\) 1.36456 0.0440639
\(960\) −0.989043 −0.0319212
\(961\) −25.9223 −0.836203
\(962\) 6.08387 0.196152
\(963\) −16.5034 −0.531814
\(964\) −32.2788 −1.03963
\(965\) −12.0845 −0.389015
\(966\) −1.60126 −0.0515196
\(967\) −17.1291 −0.550835 −0.275418 0.961325i \(-0.588816\pi\)
−0.275418 + 0.961325i \(0.588816\pi\)
\(968\) 54.0054 1.73580
\(969\) 0.519875 0.0167008
\(970\) −23.1329 −0.742754
\(971\) 9.58860 0.307713 0.153856 0.988093i \(-0.450831\pi\)
0.153856 + 0.988093i \(0.450831\pi\)
\(972\) −21.4776 −0.688895
\(973\) 0.209016 0.00670075
\(974\) 3.03837 0.0973556
\(975\) 1.11808 0.0358071
\(976\) 20.7030 0.662686
\(977\) 3.91750 0.125332 0.0626659 0.998035i \(-0.480040\pi\)
0.0626659 + 0.998035i \(0.480040\pi\)
\(978\) 3.43151 0.109728
\(979\) 7.04555 0.225177
\(980\) 19.2137 0.613759
\(981\) 30.2764 0.966651
\(982\) −10.7945 −0.344466
\(983\) 17.0680 0.544383 0.272192 0.962243i \(-0.412252\pi\)
0.272192 + 0.962243i \(0.412252\pi\)
\(984\) 1.93310 0.0616251
\(985\) 3.01906 0.0961952
\(986\) 7.18283 0.228748
\(987\) −0.773259 −0.0246131
\(988\) −18.4001 −0.585387
\(989\) 83.6472 2.65983
\(990\) −3.05289 −0.0970272
\(991\) 30.1671 0.958288 0.479144 0.877736i \(-0.340947\pi\)
0.479144 + 0.877736i \(0.340947\pi\)
\(992\) 1.42609 0.0452785
\(993\) −0.899178 −0.0285346
\(994\) 4.64317 0.147272
\(995\) 2.30255 0.0729959
\(996\) 10.4663 0.331637
\(997\) 13.1035 0.414993 0.207497 0.978236i \(-0.433468\pi\)
0.207497 + 0.978236i \(0.433468\pi\)
\(998\) 81.1745 2.56953
\(999\) −2.36726 −0.0748967
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 6037.2.a.b.1.15 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.15 259 1.1 even 1 trivial