Properties

Label 6037.2.a.b.1.5
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 1.5
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.64523 q^{2} +1.84208 q^{3} +4.99727 q^{4} +3.41959 q^{5} -4.87275 q^{6} +2.32041 q^{7} -7.92847 q^{8} +0.393274 q^{9} +O(q^{10})\) \(q-2.64523 q^{2} +1.84208 q^{3} +4.99727 q^{4} +3.41959 q^{5} -4.87275 q^{6} +2.32041 q^{7} -7.92847 q^{8} +0.393274 q^{9} -9.04562 q^{10} +5.19178 q^{11} +9.20539 q^{12} -0.0581155 q^{13} -6.13803 q^{14} +6.29918 q^{15} +10.9781 q^{16} +2.10063 q^{17} -1.04030 q^{18} -0.713359 q^{19} +17.0886 q^{20} +4.27439 q^{21} -13.7335 q^{22} -6.51049 q^{23} -14.6049 q^{24} +6.69361 q^{25} +0.153729 q^{26} -4.80181 q^{27} +11.5957 q^{28} +6.22765 q^{29} -16.6628 q^{30} +4.81404 q^{31} -13.1828 q^{32} +9.56369 q^{33} -5.55667 q^{34} +7.93486 q^{35} +1.96530 q^{36} +1.73351 q^{37} +1.88700 q^{38} -0.107054 q^{39} -27.1121 q^{40} -1.43097 q^{41} -11.3068 q^{42} +1.24497 q^{43} +25.9447 q^{44} +1.34484 q^{45} +17.2218 q^{46} -0.930089 q^{47} +20.2227 q^{48} -1.61569 q^{49} -17.7062 q^{50} +3.86954 q^{51} -0.290419 q^{52} +7.34647 q^{53} +12.7019 q^{54} +17.7538 q^{55} -18.3973 q^{56} -1.31407 q^{57} -16.4736 q^{58} +2.49443 q^{59} +31.4787 q^{60} -4.42290 q^{61} -12.7343 q^{62} +0.912558 q^{63} +12.9154 q^{64} -0.198731 q^{65} -25.2982 q^{66} +12.8794 q^{67} +10.4974 q^{68} -11.9929 q^{69} -20.9896 q^{70} -13.6439 q^{71} -3.11806 q^{72} -4.24298 q^{73} -4.58554 q^{74} +12.3302 q^{75} -3.56485 q^{76} +12.0471 q^{77} +0.283182 q^{78} -1.43461 q^{79} +37.5408 q^{80} -10.0252 q^{81} +3.78526 q^{82} +7.23231 q^{83} +21.3603 q^{84} +7.18331 q^{85} -3.29323 q^{86} +11.4719 q^{87} -41.1629 q^{88} -12.8322 q^{89} -3.55741 q^{90} -0.134852 q^{91} -32.5347 q^{92} +8.86786 q^{93} +2.46031 q^{94} -2.43940 q^{95} -24.2839 q^{96} +3.69283 q^{97} +4.27388 q^{98} +2.04179 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.64523 −1.87046 −0.935232 0.354036i \(-0.884809\pi\)
−0.935232 + 0.354036i \(0.884809\pi\)
\(3\) 1.84208 1.06353 0.531764 0.846893i \(-0.321529\pi\)
0.531764 + 0.846893i \(0.321529\pi\)
\(4\) 4.99727 2.49863
\(5\) 3.41959 1.52929 0.764644 0.644453i \(-0.222915\pi\)
0.764644 + 0.644453i \(0.222915\pi\)
\(6\) −4.87275 −1.98929
\(7\) 2.32041 0.877033 0.438517 0.898723i \(-0.355504\pi\)
0.438517 + 0.898723i \(0.355504\pi\)
\(8\) −7.92847 −2.80314
\(9\) 0.393274 0.131091
\(10\) −9.04562 −2.86048
\(11\) 5.19178 1.56538 0.782690 0.622412i \(-0.213847\pi\)
0.782690 + 0.622412i \(0.213847\pi\)
\(12\) 9.20539 2.65737
\(13\) −0.0581155 −0.0161183 −0.00805917 0.999968i \(-0.502565\pi\)
−0.00805917 + 0.999968i \(0.502565\pi\)
\(14\) −6.13803 −1.64046
\(15\) 6.29918 1.62644
\(16\) 10.9781 2.74454
\(17\) 2.10063 0.509478 0.254739 0.967010i \(-0.418010\pi\)
0.254739 + 0.967010i \(0.418010\pi\)
\(18\) −1.04030 −0.245202
\(19\) −0.713359 −0.163656 −0.0818279 0.996646i \(-0.526076\pi\)
−0.0818279 + 0.996646i \(0.526076\pi\)
\(20\) 17.0886 3.82113
\(21\) 4.27439 0.932749
\(22\) −13.7335 −2.92799
\(23\) −6.51049 −1.35753 −0.678766 0.734355i \(-0.737485\pi\)
−0.678766 + 0.734355i \(0.737485\pi\)
\(24\) −14.6049 −2.98122
\(25\) 6.69361 1.33872
\(26\) 0.153729 0.0301488
\(27\) −4.80181 −0.924108
\(28\) 11.5957 2.19138
\(29\) 6.22765 1.15645 0.578223 0.815879i \(-0.303746\pi\)
0.578223 + 0.815879i \(0.303746\pi\)
\(30\) −16.6628 −3.04220
\(31\) 4.81404 0.864627 0.432313 0.901723i \(-0.357697\pi\)
0.432313 + 0.901723i \(0.357697\pi\)
\(32\) −13.1828 −2.33041
\(33\) 9.56369 1.66483
\(34\) −5.55667 −0.952961
\(35\) 7.93486 1.34124
\(36\) 1.96530 0.327549
\(37\) 1.73351 0.284987 0.142494 0.989796i \(-0.454488\pi\)
0.142494 + 0.989796i \(0.454488\pi\)
\(38\) 1.88700 0.306112
\(39\) −0.107054 −0.0171423
\(40\) −27.1121 −4.28681
\(41\) −1.43097 −0.223480 −0.111740 0.993737i \(-0.535642\pi\)
−0.111740 + 0.993737i \(0.535642\pi\)
\(42\) −11.3068 −1.74467
\(43\) 1.24497 0.189856 0.0949279 0.995484i \(-0.469738\pi\)
0.0949279 + 0.995484i \(0.469738\pi\)
\(44\) 25.9447 3.91131
\(45\) 1.34484 0.200476
\(46\) 17.2218 2.53921
\(47\) −0.930089 −0.135667 −0.0678337 0.997697i \(-0.521609\pi\)
−0.0678337 + 0.997697i \(0.521609\pi\)
\(48\) 20.2227 2.91889
\(49\) −1.61569 −0.230813
\(50\) −17.7062 −2.50403
\(51\) 3.86954 0.541844
\(52\) −0.290419 −0.0402738
\(53\) 7.34647 1.00911 0.504557 0.863378i \(-0.331656\pi\)
0.504557 + 0.863378i \(0.331656\pi\)
\(54\) 12.7019 1.72851
\(55\) 17.7538 2.39392
\(56\) −18.3973 −2.45845
\(57\) −1.31407 −0.174053
\(58\) −16.4736 −2.16309
\(59\) 2.49443 0.324747 0.162374 0.986729i \(-0.448085\pi\)
0.162374 + 0.986729i \(0.448085\pi\)
\(60\) 31.4787 4.06388
\(61\) −4.42290 −0.566294 −0.283147 0.959076i \(-0.591378\pi\)
−0.283147 + 0.959076i \(0.591378\pi\)
\(62\) −12.7343 −1.61725
\(63\) 0.912558 0.114971
\(64\) 12.9154 1.61442
\(65\) −0.198731 −0.0246496
\(66\) −25.2982 −3.11399
\(67\) 12.8794 1.57347 0.786733 0.617294i \(-0.211771\pi\)
0.786733 + 0.617294i \(0.211771\pi\)
\(68\) 10.4974 1.27300
\(69\) −11.9929 −1.44377
\(70\) −20.9896 −2.50873
\(71\) −13.6439 −1.61924 −0.809619 0.586956i \(-0.800326\pi\)
−0.809619 + 0.586956i \(0.800326\pi\)
\(72\) −3.11806 −0.367467
\(73\) −4.24298 −0.496603 −0.248301 0.968683i \(-0.579872\pi\)
−0.248301 + 0.968683i \(0.579872\pi\)
\(74\) −4.58554 −0.533058
\(75\) 12.3302 1.42377
\(76\) −3.56485 −0.408916
\(77\) 12.0471 1.37289
\(78\) 0.283182 0.0320641
\(79\) −1.43461 −0.161406 −0.0807031 0.996738i \(-0.525717\pi\)
−0.0807031 + 0.996738i \(0.525717\pi\)
\(80\) 37.5408 4.19719
\(81\) −10.0252 −1.11391
\(82\) 3.78526 0.418012
\(83\) 7.23231 0.793849 0.396925 0.917851i \(-0.370077\pi\)
0.396925 + 0.917851i \(0.370077\pi\)
\(84\) 21.3603 2.33060
\(85\) 7.18331 0.779139
\(86\) −3.29323 −0.355118
\(87\) 11.4719 1.22991
\(88\) −41.1629 −4.38798
\(89\) −12.8322 −1.36021 −0.680103 0.733116i \(-0.738065\pi\)
−0.680103 + 0.733116i \(0.738065\pi\)
\(90\) −3.55741 −0.374984
\(91\) −0.134852 −0.0141363
\(92\) −32.5347 −3.39197
\(93\) 8.86786 0.919555
\(94\) 2.46031 0.253761
\(95\) −2.43940 −0.250277
\(96\) −24.2839 −2.47846
\(97\) 3.69283 0.374950 0.187475 0.982269i \(-0.439970\pi\)
0.187475 + 0.982269i \(0.439970\pi\)
\(98\) 4.27388 0.431727
\(99\) 2.04179 0.205208
\(100\) 33.4498 3.34498
\(101\) −3.59853 −0.358067 −0.179034 0.983843i \(-0.557297\pi\)
−0.179034 + 0.983843i \(0.557297\pi\)
\(102\) −10.2359 −1.01350
\(103\) −9.80860 −0.966470 −0.483235 0.875491i \(-0.660538\pi\)
−0.483235 + 0.875491i \(0.660538\pi\)
\(104\) 0.460767 0.0451820
\(105\) 14.6167 1.42644
\(106\) −19.4331 −1.88751
\(107\) 3.02709 0.292640 0.146320 0.989237i \(-0.453257\pi\)
0.146320 + 0.989237i \(0.453257\pi\)
\(108\) −23.9959 −2.30901
\(109\) −6.80667 −0.651960 −0.325980 0.945377i \(-0.605694\pi\)
−0.325980 + 0.945377i \(0.605694\pi\)
\(110\) −46.9629 −4.47773
\(111\) 3.19327 0.303092
\(112\) 25.4738 2.40705
\(113\) 7.21078 0.678333 0.339167 0.940726i \(-0.389855\pi\)
0.339167 + 0.940726i \(0.389855\pi\)
\(114\) 3.47602 0.325559
\(115\) −22.2632 −2.07606
\(116\) 31.1212 2.88953
\(117\) −0.0228553 −0.00211298
\(118\) −6.59835 −0.607428
\(119\) 4.87433 0.446829
\(120\) −49.9429 −4.55914
\(121\) 15.9546 1.45041
\(122\) 11.6996 1.05923
\(123\) −2.63597 −0.237677
\(124\) 24.0570 2.16039
\(125\) 5.79145 0.518003
\(126\) −2.41393 −0.215050
\(127\) 13.3896 1.18813 0.594066 0.804416i \(-0.297522\pi\)
0.594066 + 0.804416i \(0.297522\pi\)
\(128\) −7.79851 −0.689298
\(129\) 2.29333 0.201917
\(130\) 0.525691 0.0461062
\(131\) 15.9538 1.39389 0.696945 0.717125i \(-0.254542\pi\)
0.696945 + 0.717125i \(0.254542\pi\)
\(132\) 47.7923 4.15979
\(133\) −1.65529 −0.143532
\(134\) −34.0690 −2.94311
\(135\) −16.4202 −1.41323
\(136\) −16.6548 −1.42814
\(137\) 8.97426 0.766722 0.383361 0.923598i \(-0.374766\pi\)
0.383361 + 0.923598i \(0.374766\pi\)
\(138\) 31.7240 2.70052
\(139\) −3.49221 −0.296205 −0.148103 0.988972i \(-0.547317\pi\)
−0.148103 + 0.988972i \(0.547317\pi\)
\(140\) 39.6526 3.35126
\(141\) −1.71330 −0.144286
\(142\) 36.0914 3.02873
\(143\) −0.301723 −0.0252313
\(144\) 4.31742 0.359785
\(145\) 21.2960 1.76854
\(146\) 11.2237 0.928878
\(147\) −2.97624 −0.245476
\(148\) 8.66280 0.712078
\(149\) 12.9567 1.06145 0.530726 0.847543i \(-0.321919\pi\)
0.530726 + 0.847543i \(0.321919\pi\)
\(150\) −32.6163 −2.66311
\(151\) −4.51215 −0.367194 −0.183597 0.983002i \(-0.558774\pi\)
−0.183597 + 0.983002i \(0.558774\pi\)
\(152\) 5.65585 0.458750
\(153\) 0.826125 0.0667882
\(154\) −31.8673 −2.56794
\(155\) 16.4620 1.32226
\(156\) −0.534976 −0.0428323
\(157\) 14.4989 1.15714 0.578569 0.815634i \(-0.303611\pi\)
0.578569 + 0.815634i \(0.303611\pi\)
\(158\) 3.79488 0.301904
\(159\) 13.5328 1.07322
\(160\) −45.0798 −3.56387
\(161\) −15.1070 −1.19060
\(162\) 26.5189 2.08352
\(163\) −23.4553 −1.83716 −0.918582 0.395230i \(-0.870665\pi\)
−0.918582 + 0.395230i \(0.870665\pi\)
\(164\) −7.15095 −0.558395
\(165\) 32.7039 2.54600
\(166\) −19.1312 −1.48487
\(167\) −0.0685580 −0.00530518 −0.00265259 0.999996i \(-0.500844\pi\)
−0.00265259 + 0.999996i \(0.500844\pi\)
\(168\) −33.8894 −2.61463
\(169\) −12.9966 −0.999740
\(170\) −19.0015 −1.45735
\(171\) −0.280546 −0.0214539
\(172\) 6.22143 0.474380
\(173\) −10.2040 −0.775799 −0.387900 0.921702i \(-0.626799\pi\)
−0.387900 + 0.921702i \(0.626799\pi\)
\(174\) −30.3458 −2.30051
\(175\) 15.5319 1.17410
\(176\) 56.9961 4.29624
\(177\) 4.59495 0.345378
\(178\) 33.9441 2.54422
\(179\) 18.5912 1.38957 0.694785 0.719217i \(-0.255499\pi\)
0.694785 + 0.719217i \(0.255499\pi\)
\(180\) 6.72051 0.500917
\(181\) −4.17063 −0.310001 −0.155000 0.987914i \(-0.549538\pi\)
−0.155000 + 0.987914i \(0.549538\pi\)
\(182\) 0.356715 0.0264415
\(183\) −8.14735 −0.602270
\(184\) 51.6183 3.80535
\(185\) 5.92789 0.435827
\(186\) −23.4576 −1.71999
\(187\) 10.9060 0.797527
\(188\) −4.64791 −0.338983
\(189\) −11.1422 −0.810474
\(190\) 6.45278 0.468134
\(191\) 14.1651 1.02495 0.512476 0.858701i \(-0.328728\pi\)
0.512476 + 0.858701i \(0.328728\pi\)
\(192\) 23.7912 1.71698
\(193\) 19.1396 1.37770 0.688848 0.724906i \(-0.258117\pi\)
0.688848 + 0.724906i \(0.258117\pi\)
\(194\) −9.76840 −0.701330
\(195\) −0.366080 −0.0262155
\(196\) −8.07404 −0.576717
\(197\) 19.9650 1.42245 0.711223 0.702966i \(-0.248141\pi\)
0.711223 + 0.702966i \(0.248141\pi\)
\(198\) −5.40102 −0.383834
\(199\) −6.35378 −0.450408 −0.225204 0.974312i \(-0.572305\pi\)
−0.225204 + 0.974312i \(0.572305\pi\)
\(200\) −53.0701 −3.75262
\(201\) 23.7249 1.67342
\(202\) 9.51896 0.669752
\(203\) 14.4507 1.01424
\(204\) 19.3371 1.35387
\(205\) −4.89334 −0.341766
\(206\) 25.9461 1.80775
\(207\) −2.56041 −0.177961
\(208\) −0.638000 −0.0442374
\(209\) −3.70360 −0.256184
\(210\) −38.6646 −2.66811
\(211\) −7.81369 −0.537917 −0.268958 0.963152i \(-0.586679\pi\)
−0.268958 + 0.963152i \(0.586679\pi\)
\(212\) 36.7123 2.52141
\(213\) −25.1333 −1.72211
\(214\) −8.00738 −0.547373
\(215\) 4.25728 0.290344
\(216\) 38.0710 2.59040
\(217\) 11.1705 0.758306
\(218\) 18.0052 1.21947
\(219\) −7.81592 −0.528151
\(220\) 88.7203 5.98152
\(221\) −0.122079 −0.00821195
\(222\) −8.44694 −0.566922
\(223\) 12.3591 0.827630 0.413815 0.910361i \(-0.364196\pi\)
0.413815 + 0.910361i \(0.364196\pi\)
\(224\) −30.5896 −2.04385
\(225\) 2.63242 0.175495
\(226\) −19.0742 −1.26880
\(227\) −7.75973 −0.515031 −0.257516 0.966274i \(-0.582904\pi\)
−0.257516 + 0.966274i \(0.582904\pi\)
\(228\) −6.56675 −0.434894
\(229\) −18.1275 −1.19790 −0.598949 0.800787i \(-0.704415\pi\)
−0.598949 + 0.800787i \(0.704415\pi\)
\(230\) 58.8915 3.88319
\(231\) 22.1917 1.46011
\(232\) −49.3758 −3.24168
\(233\) 7.17043 0.469750 0.234875 0.972026i \(-0.424532\pi\)
0.234875 + 0.972026i \(0.424532\pi\)
\(234\) 0.0604577 0.00395224
\(235\) −3.18053 −0.207475
\(236\) 12.4653 0.811424
\(237\) −2.64267 −0.171660
\(238\) −12.8938 −0.835778
\(239\) 7.95581 0.514619 0.257309 0.966329i \(-0.417164\pi\)
0.257309 + 0.966329i \(0.417164\pi\)
\(240\) 69.1533 4.46382
\(241\) −0.143103 −0.00921810 −0.00460905 0.999989i \(-0.501467\pi\)
−0.00460905 + 0.999989i \(0.501467\pi\)
\(242\) −42.2036 −2.71295
\(243\) −4.06176 −0.260562
\(244\) −22.1024 −1.41496
\(245\) −5.52500 −0.352979
\(246\) 6.97276 0.444567
\(247\) 0.0414572 0.00263786
\(248\) −38.1680 −2.42367
\(249\) 13.3225 0.844281
\(250\) −15.3198 −0.968906
\(251\) 9.42872 0.595135 0.297568 0.954701i \(-0.403825\pi\)
0.297568 + 0.954701i \(0.403825\pi\)
\(252\) 4.56029 0.287272
\(253\) −33.8010 −2.12505
\(254\) −35.4185 −2.22236
\(255\) 13.2323 0.828636
\(256\) −5.20181 −0.325113
\(257\) 3.94320 0.245970 0.122985 0.992409i \(-0.460753\pi\)
0.122985 + 0.992409i \(0.460753\pi\)
\(258\) −6.06641 −0.377678
\(259\) 4.02245 0.249943
\(260\) −0.993114 −0.0615903
\(261\) 2.44917 0.151600
\(262\) −42.2015 −2.60722
\(263\) 1.55944 0.0961590 0.0480795 0.998844i \(-0.484690\pi\)
0.0480795 + 0.998844i \(0.484690\pi\)
\(264\) −75.8255 −4.66674
\(265\) 25.1219 1.54323
\(266\) 4.37862 0.268471
\(267\) −23.6379 −1.44662
\(268\) 64.3617 3.93151
\(269\) −17.6451 −1.07584 −0.537919 0.842996i \(-0.680790\pi\)
−0.537919 + 0.842996i \(0.680790\pi\)
\(270\) 43.4354 2.64339
\(271\) −18.2237 −1.10701 −0.553505 0.832846i \(-0.686710\pi\)
−0.553505 + 0.832846i \(0.686710\pi\)
\(272\) 23.0611 1.39828
\(273\) −0.248409 −0.0150344
\(274\) −23.7390 −1.43413
\(275\) 34.7517 2.09561
\(276\) −59.9316 −3.60746
\(277\) 10.4162 0.625848 0.312924 0.949778i \(-0.398691\pi\)
0.312924 + 0.949778i \(0.398691\pi\)
\(278\) 9.23770 0.554041
\(279\) 1.89324 0.113345
\(280\) −62.9113 −3.75967
\(281\) −20.8411 −1.24328 −0.621639 0.783304i \(-0.713533\pi\)
−0.621639 + 0.783304i \(0.713533\pi\)
\(282\) 4.53209 0.269882
\(283\) 12.9470 0.769619 0.384810 0.922996i \(-0.374267\pi\)
0.384810 + 0.922996i \(0.374267\pi\)
\(284\) −68.1824 −4.04588
\(285\) −4.49358 −0.266176
\(286\) 0.798128 0.0471943
\(287\) −3.32044 −0.196000
\(288\) −5.18446 −0.305497
\(289\) −12.5873 −0.740432
\(290\) −56.3330 −3.30799
\(291\) 6.80250 0.398770
\(292\) −21.2033 −1.24083
\(293\) −22.1695 −1.29516 −0.647578 0.761999i \(-0.724218\pi\)
−0.647578 + 0.761999i \(0.724218\pi\)
\(294\) 7.87285 0.459154
\(295\) 8.52993 0.496632
\(296\) −13.7441 −0.798858
\(297\) −24.9299 −1.44658
\(298\) −34.2735 −1.98541
\(299\) 0.378361 0.0218812
\(300\) 61.6173 3.55747
\(301\) 2.88884 0.166510
\(302\) 11.9357 0.686822
\(303\) −6.62880 −0.380815
\(304\) −7.83136 −0.449159
\(305\) −15.1245 −0.866027
\(306\) −2.18529 −0.124925
\(307\) −33.1302 −1.89084 −0.945421 0.325852i \(-0.894349\pi\)
−0.945421 + 0.325852i \(0.894349\pi\)
\(308\) 60.2024 3.43035
\(309\) −18.0683 −1.02787
\(310\) −43.5460 −2.47325
\(311\) −6.99237 −0.396501 −0.198251 0.980151i \(-0.563526\pi\)
−0.198251 + 0.980151i \(0.563526\pi\)
\(312\) 0.848772 0.0480523
\(313\) −15.4922 −0.875671 −0.437836 0.899055i \(-0.644255\pi\)
−0.437836 + 0.899055i \(0.644255\pi\)
\(314\) −38.3530 −2.16438
\(315\) 3.12057 0.175824
\(316\) −7.16913 −0.403295
\(317\) 23.4067 1.31465 0.657325 0.753607i \(-0.271688\pi\)
0.657325 + 0.753607i \(0.271688\pi\)
\(318\) −35.7975 −2.00742
\(319\) 32.3326 1.81028
\(320\) 44.1652 2.46891
\(321\) 5.57616 0.311231
\(322\) 39.9616 2.22697
\(323\) −1.49851 −0.0833791
\(324\) −50.0984 −2.78324
\(325\) −0.389003 −0.0215780
\(326\) 62.0449 3.43635
\(327\) −12.5385 −0.693378
\(328\) 11.3454 0.626446
\(329\) −2.15819 −0.118985
\(330\) −86.5096 −4.76219
\(331\) −0.400810 −0.0220305 −0.0110153 0.999939i \(-0.503506\pi\)
−0.0110153 + 0.999939i \(0.503506\pi\)
\(332\) 36.1418 1.98354
\(333\) 0.681744 0.0373593
\(334\) 0.181352 0.00992314
\(335\) 44.0422 2.40628
\(336\) 46.9249 2.55996
\(337\) −5.56005 −0.302875 −0.151438 0.988467i \(-0.548390\pi\)
−0.151438 + 0.988467i \(0.548390\pi\)
\(338\) 34.3791 1.86998
\(339\) 13.2829 0.721426
\(340\) 35.8969 1.94678
\(341\) 24.9934 1.35347
\(342\) 0.742109 0.0401287
\(343\) −19.9919 −1.07946
\(344\) −9.87069 −0.532192
\(345\) −41.0107 −2.20794
\(346\) 26.9921 1.45110
\(347\) 11.8695 0.637187 0.318593 0.947892i \(-0.396790\pi\)
0.318593 + 0.947892i \(0.396790\pi\)
\(348\) 57.3279 3.07310
\(349\) 4.90896 0.262771 0.131385 0.991331i \(-0.458057\pi\)
0.131385 + 0.991331i \(0.458057\pi\)
\(350\) −41.0856 −2.19612
\(351\) 0.279060 0.0148951
\(352\) −68.4422 −3.64798
\(353\) −9.40347 −0.500496 −0.250248 0.968182i \(-0.580512\pi\)
−0.250248 + 0.968182i \(0.580512\pi\)
\(354\) −12.1547 −0.646016
\(355\) −46.6567 −2.47628
\(356\) −64.1257 −3.39866
\(357\) 8.97893 0.475216
\(358\) −49.1781 −2.59914
\(359\) 14.4132 0.760697 0.380349 0.924843i \(-0.375804\pi\)
0.380349 + 0.924843i \(0.375804\pi\)
\(360\) −10.6625 −0.561963
\(361\) −18.4911 −0.973217
\(362\) 11.0323 0.579845
\(363\) 29.3896 1.54256
\(364\) −0.673891 −0.0353215
\(365\) −14.5093 −0.759449
\(366\) 21.5517 1.12652
\(367\) 25.9169 1.35285 0.676425 0.736511i \(-0.263528\pi\)
0.676425 + 0.736511i \(0.263528\pi\)
\(368\) −71.4731 −3.72579
\(369\) −0.562764 −0.0292963
\(370\) −15.6807 −0.815199
\(371\) 17.0468 0.885027
\(372\) 44.3151 2.29763
\(373\) −22.6577 −1.17317 −0.586585 0.809888i \(-0.699528\pi\)
−0.586585 + 0.809888i \(0.699528\pi\)
\(374\) −28.8490 −1.49175
\(375\) 10.6683 0.550911
\(376\) 7.37419 0.380295
\(377\) −0.361923 −0.0186400
\(378\) 29.4737 1.51596
\(379\) −19.4114 −0.997098 −0.498549 0.866862i \(-0.666134\pi\)
−0.498549 + 0.866862i \(0.666134\pi\)
\(380\) −12.1903 −0.625350
\(381\) 24.6647 1.26361
\(382\) −37.4701 −1.91714
\(383\) −22.3188 −1.14044 −0.570220 0.821492i \(-0.693142\pi\)
−0.570220 + 0.821492i \(0.693142\pi\)
\(384\) −14.3655 −0.733087
\(385\) 41.1960 2.09954
\(386\) −50.6286 −2.57693
\(387\) 0.489613 0.0248884
\(388\) 18.4541 0.936863
\(389\) 5.03268 0.255167 0.127584 0.991828i \(-0.459278\pi\)
0.127584 + 0.991828i \(0.459278\pi\)
\(390\) 0.968367 0.0490352
\(391\) −13.6762 −0.691633
\(392\) 12.8100 0.647001
\(393\) 29.3882 1.48244
\(394\) −52.8121 −2.66063
\(395\) −4.90578 −0.246837
\(396\) 10.2034 0.512739
\(397\) −38.7478 −1.94470 −0.972349 0.233535i \(-0.924971\pi\)
−0.972349 + 0.233535i \(0.924971\pi\)
\(398\) 16.8073 0.842471
\(399\) −3.04918 −0.152650
\(400\) 73.4834 3.67417
\(401\) −8.43229 −0.421089 −0.210544 0.977584i \(-0.567524\pi\)
−0.210544 + 0.977584i \(0.567524\pi\)
\(402\) −62.7579 −3.13008
\(403\) −0.279770 −0.0139364
\(404\) −17.9828 −0.894679
\(405\) −34.2819 −1.70348
\(406\) −38.2255 −1.89710
\(407\) 8.99999 0.446113
\(408\) −30.6796 −1.51887
\(409\) 13.9214 0.688371 0.344186 0.938902i \(-0.388155\pi\)
0.344186 + 0.938902i \(0.388155\pi\)
\(410\) 12.9440 0.639260
\(411\) 16.5313 0.815431
\(412\) −49.0162 −2.41486
\(413\) 5.78810 0.284814
\(414\) 6.77288 0.332869
\(415\) 24.7315 1.21402
\(416\) 0.766126 0.0375624
\(417\) −6.43294 −0.315022
\(418\) 9.79690 0.479182
\(419\) −26.7345 −1.30606 −0.653032 0.757330i \(-0.726503\pi\)
−0.653032 + 0.757330i \(0.726503\pi\)
\(420\) 73.0435 3.56416
\(421\) −32.9303 −1.60492 −0.802462 0.596704i \(-0.796477\pi\)
−0.802462 + 0.596704i \(0.796477\pi\)
\(422\) 20.6691 1.00615
\(423\) −0.365780 −0.0177848
\(424\) −58.2463 −2.82869
\(425\) 14.0608 0.682050
\(426\) 66.4835 3.22113
\(427\) −10.2629 −0.496659
\(428\) 15.1272 0.731201
\(429\) −0.555799 −0.0268342
\(430\) −11.2615 −0.543078
\(431\) −20.4037 −0.982813 −0.491407 0.870930i \(-0.663517\pi\)
−0.491407 + 0.870930i \(0.663517\pi\)
\(432\) −52.7149 −2.53625
\(433\) 31.9531 1.53557 0.767783 0.640709i \(-0.221360\pi\)
0.767783 + 0.640709i \(0.221360\pi\)
\(434\) −29.5487 −1.41838
\(435\) 39.2291 1.88089
\(436\) −34.0147 −1.62901
\(437\) 4.64432 0.222168
\(438\) 20.6749 0.987887
\(439\) −4.54105 −0.216733 −0.108366 0.994111i \(-0.534562\pi\)
−0.108366 + 0.994111i \(0.534562\pi\)
\(440\) −140.760 −6.71048
\(441\) −0.635409 −0.0302576
\(442\) 0.322929 0.0153601
\(443\) −1.49264 −0.0709175 −0.0354588 0.999371i \(-0.511289\pi\)
−0.0354588 + 0.999371i \(0.511289\pi\)
\(444\) 15.9576 0.757315
\(445\) −43.8808 −2.08015
\(446\) −32.6928 −1.54805
\(447\) 23.8673 1.12888
\(448\) 29.9689 1.41590
\(449\) 19.3172 0.911635 0.455817 0.890073i \(-0.349347\pi\)
0.455817 + 0.890073i \(0.349347\pi\)
\(450\) −6.96338 −0.328257
\(451\) −7.42929 −0.349832
\(452\) 36.0342 1.69491
\(453\) −8.31176 −0.390521
\(454\) 20.5263 0.963347
\(455\) −0.461139 −0.0216185
\(456\) 10.4186 0.487893
\(457\) 15.8292 0.740457 0.370229 0.928941i \(-0.379279\pi\)
0.370229 + 0.928941i \(0.379279\pi\)
\(458\) 47.9515 2.24062
\(459\) −10.0868 −0.470813
\(460\) −111.255 −5.18731
\(461\) 41.8837 1.95072 0.975359 0.220625i \(-0.0708098\pi\)
0.975359 + 0.220625i \(0.0708098\pi\)
\(462\) −58.7023 −2.73108
\(463\) −4.56067 −0.211952 −0.105976 0.994369i \(-0.533797\pi\)
−0.105976 + 0.994369i \(0.533797\pi\)
\(464\) 68.3681 3.17391
\(465\) 30.3245 1.40626
\(466\) −18.9675 −0.878651
\(467\) −29.8059 −1.37925 −0.689627 0.724164i \(-0.742226\pi\)
−0.689627 + 0.724164i \(0.742226\pi\)
\(468\) −0.114214 −0.00527955
\(469\) 29.8854 1.37998
\(470\) 8.41324 0.388074
\(471\) 26.7082 1.23065
\(472\) −19.7770 −0.910311
\(473\) 6.46359 0.297196
\(474\) 6.99049 0.321084
\(475\) −4.77495 −0.219090
\(476\) 24.3583 1.11646
\(477\) 2.88917 0.132286
\(478\) −21.0450 −0.962575
\(479\) −11.2690 −0.514895 −0.257447 0.966292i \(-0.582881\pi\)
−0.257447 + 0.966292i \(0.582881\pi\)
\(480\) −83.0409 −3.79028
\(481\) −0.100744 −0.00459352
\(482\) 0.378542 0.0172421
\(483\) −27.8284 −1.26624
\(484\) 79.7292 3.62405
\(485\) 12.6280 0.573407
\(486\) 10.7443 0.487372
\(487\) 16.0998 0.729554 0.364777 0.931095i \(-0.381145\pi\)
0.364777 + 0.931095i \(0.381145\pi\)
\(488\) 35.0668 1.58740
\(489\) −43.2067 −1.95388
\(490\) 14.6149 0.660235
\(491\) −4.27274 −0.192826 −0.0964130 0.995341i \(-0.530737\pi\)
−0.0964130 + 0.995341i \(0.530737\pi\)
\(492\) −13.1726 −0.593869
\(493\) 13.0820 0.589184
\(494\) −0.109664 −0.00493402
\(495\) 6.98209 0.313822
\(496\) 52.8492 2.37300
\(497\) −31.6596 −1.42013
\(498\) −35.2412 −1.57920
\(499\) 9.35834 0.418937 0.209468 0.977815i \(-0.432827\pi\)
0.209468 + 0.977815i \(0.432827\pi\)
\(500\) 28.9414 1.29430
\(501\) −0.126290 −0.00564220
\(502\) −24.9412 −1.11318
\(503\) 30.3031 1.35115 0.675575 0.737291i \(-0.263895\pi\)
0.675575 + 0.737291i \(0.263895\pi\)
\(504\) −7.23519 −0.322281
\(505\) −12.3055 −0.547588
\(506\) 89.4117 3.97483
\(507\) −23.9409 −1.06325
\(508\) 66.9112 2.96871
\(509\) 10.7840 0.477990 0.238995 0.971021i \(-0.423182\pi\)
0.238995 + 0.971021i \(0.423182\pi\)
\(510\) −35.0024 −1.54993
\(511\) −9.84545 −0.435537
\(512\) 29.3570 1.29741
\(513\) 3.42541 0.151236
\(514\) −10.4307 −0.460077
\(515\) −33.5414 −1.47801
\(516\) 11.4604 0.504516
\(517\) −4.82882 −0.212371
\(518\) −10.6403 −0.467509
\(519\) −18.7967 −0.825084
\(520\) 1.57564 0.0690962
\(521\) −25.4407 −1.11458 −0.557289 0.830318i \(-0.688159\pi\)
−0.557289 + 0.830318i \(0.688159\pi\)
\(522\) −6.47864 −0.283562
\(523\) −39.9406 −1.74648 −0.873239 0.487292i \(-0.837985\pi\)
−0.873239 + 0.487292i \(0.837985\pi\)
\(524\) 79.7254 3.48282
\(525\) 28.6111 1.24869
\(526\) −4.12508 −0.179862
\(527\) 10.1125 0.440509
\(528\) 104.992 4.56917
\(529\) 19.3865 0.842892
\(530\) −66.4534 −2.88655
\(531\) 0.980995 0.0425715
\(532\) −8.27191 −0.358633
\(533\) 0.0831617 0.00360213
\(534\) 62.5278 2.70584
\(535\) 10.3514 0.447531
\(536\) −102.114 −4.41064
\(537\) 34.2465 1.47785
\(538\) 46.6754 2.01232
\(539\) −8.38831 −0.361310
\(540\) −82.0563 −3.53114
\(541\) −27.5899 −1.18618 −0.593090 0.805136i \(-0.702092\pi\)
−0.593090 + 0.805136i \(0.702092\pi\)
\(542\) 48.2059 2.07062
\(543\) −7.68265 −0.329694
\(544\) −27.6923 −1.18730
\(545\) −23.2760 −0.997035
\(546\) 0.657099 0.0281212
\(547\) −23.9891 −1.02570 −0.512850 0.858478i \(-0.671410\pi\)
−0.512850 + 0.858478i \(0.671410\pi\)
\(548\) 44.8468 1.91576
\(549\) −1.73941 −0.0742363
\(550\) −91.9265 −3.91976
\(551\) −4.44255 −0.189259
\(552\) 95.0852 4.04710
\(553\) −3.32888 −0.141559
\(554\) −27.5533 −1.17063
\(555\) 10.9197 0.463514
\(556\) −17.4515 −0.740108
\(557\) 40.0814 1.69830 0.849152 0.528148i \(-0.177113\pi\)
0.849152 + 0.528148i \(0.177113\pi\)
\(558\) −5.00805 −0.212008
\(559\) −0.0723519 −0.00306016
\(560\) 87.1100 3.68107
\(561\) 20.0898 0.848192
\(562\) 55.1297 2.32551
\(563\) 20.4006 0.859781 0.429891 0.902881i \(-0.358552\pi\)
0.429891 + 0.902881i \(0.358552\pi\)
\(564\) −8.56183 −0.360518
\(565\) 24.6579 1.03737
\(566\) −34.2478 −1.43954
\(567\) −23.2625 −0.976933
\(568\) 108.176 4.53895
\(569\) 25.5676 1.07185 0.535925 0.844266i \(-0.319963\pi\)
0.535925 + 0.844266i \(0.319963\pi\)
\(570\) 11.8866 0.497873
\(571\) 46.8061 1.95877 0.979386 0.201997i \(-0.0647430\pi\)
0.979386 + 0.201997i \(0.0647430\pi\)
\(572\) −1.50779 −0.0630439
\(573\) 26.0934 1.09007
\(574\) 8.78335 0.366610
\(575\) −43.5787 −1.81736
\(576\) 5.07927 0.211636
\(577\) −34.6628 −1.44303 −0.721515 0.692399i \(-0.756554\pi\)
−0.721515 + 0.692399i \(0.756554\pi\)
\(578\) 33.2965 1.38495
\(579\) 35.2567 1.46522
\(580\) 106.422 4.41893
\(581\) 16.7819 0.696232
\(582\) −17.9942 −0.745884
\(583\) 38.1412 1.57965
\(584\) 33.6403 1.39205
\(585\) −0.0781559 −0.00323135
\(586\) 58.6435 2.42254
\(587\) −18.6552 −0.769984 −0.384992 0.922920i \(-0.625796\pi\)
−0.384992 + 0.922920i \(0.625796\pi\)
\(588\) −14.8731 −0.613354
\(589\) −3.43414 −0.141501
\(590\) −22.5637 −0.928932
\(591\) 36.7772 1.51281
\(592\) 19.0307 0.782157
\(593\) 16.0408 0.658715 0.329358 0.944205i \(-0.393168\pi\)
0.329358 + 0.944205i \(0.393168\pi\)
\(594\) 65.9455 2.70578
\(595\) 16.6682 0.683331
\(596\) 64.7480 2.65218
\(597\) −11.7042 −0.479021
\(598\) −1.00085 −0.0409279
\(599\) −25.6413 −1.04767 −0.523837 0.851819i \(-0.675500\pi\)
−0.523837 + 0.851819i \(0.675500\pi\)
\(600\) −97.7596 −3.99102
\(601\) −30.9986 −1.26446 −0.632230 0.774781i \(-0.717860\pi\)
−0.632230 + 0.774781i \(0.717860\pi\)
\(602\) −7.64165 −0.311450
\(603\) 5.06512 0.206268
\(604\) −22.5484 −0.917482
\(605\) 54.5581 2.21810
\(606\) 17.5347 0.712300
\(607\) −25.7761 −1.04622 −0.523111 0.852265i \(-0.675229\pi\)
−0.523111 + 0.852265i \(0.675229\pi\)
\(608\) 9.40408 0.381386
\(609\) 26.6194 1.07867
\(610\) 40.0079 1.61987
\(611\) 0.0540526 0.00218674
\(612\) 4.12836 0.166879
\(613\) 14.1549 0.571709 0.285855 0.958273i \(-0.407723\pi\)
0.285855 + 0.958273i \(0.407723\pi\)
\(614\) 87.6372 3.53675
\(615\) −9.01394 −0.363477
\(616\) −95.5148 −3.84840
\(617\) 0.762338 0.0306906 0.0153453 0.999882i \(-0.495115\pi\)
0.0153453 + 0.999882i \(0.495115\pi\)
\(618\) 47.7948 1.92259
\(619\) 47.3150 1.90175 0.950876 0.309572i \(-0.100186\pi\)
0.950876 + 0.309572i \(0.100186\pi\)
\(620\) 82.2652 3.30385
\(621\) 31.2621 1.25451
\(622\) 18.4965 0.741641
\(623\) −29.7759 −1.19295
\(624\) −1.17525 −0.0470477
\(625\) −13.6636 −0.546546
\(626\) 40.9805 1.63791
\(627\) −6.82235 −0.272458
\(628\) 72.4548 2.89126
\(629\) 3.64147 0.145195
\(630\) −8.25465 −0.328873
\(631\) −41.5514 −1.65414 −0.827068 0.562102i \(-0.809993\pi\)
−0.827068 + 0.562102i \(0.809993\pi\)
\(632\) 11.3743 0.452444
\(633\) −14.3935 −0.572089
\(634\) −61.9161 −2.45900
\(635\) 45.7869 1.81700
\(636\) 67.6271 2.68159
\(637\) 0.0938967 0.00372032
\(638\) −85.5273 −3.38606
\(639\) −5.36581 −0.212268
\(640\) −26.6677 −1.05413
\(641\) 3.09194 0.122124 0.0610621 0.998134i \(-0.480551\pi\)
0.0610621 + 0.998134i \(0.480551\pi\)
\(642\) −14.7503 −0.582146
\(643\) 10.2815 0.405461 0.202731 0.979235i \(-0.435018\pi\)
0.202731 + 0.979235i \(0.435018\pi\)
\(644\) −75.4938 −2.97487
\(645\) 7.84227 0.308789
\(646\) 3.96390 0.155958
\(647\) −9.41355 −0.370085 −0.185042 0.982731i \(-0.559242\pi\)
−0.185042 + 0.982731i \(0.559242\pi\)
\(648\) 79.4842 3.12243
\(649\) 12.9505 0.508353
\(650\) 1.02900 0.0403608
\(651\) 20.5771 0.806480
\(652\) −117.213 −4.59040
\(653\) −2.29527 −0.0898208 −0.0449104 0.998991i \(-0.514300\pi\)
−0.0449104 + 0.998991i \(0.514300\pi\)
\(654\) 33.1672 1.29694
\(655\) 54.5555 2.13166
\(656\) −15.7094 −0.613350
\(657\) −1.66865 −0.0651004
\(658\) 5.70892 0.222557
\(659\) −9.80371 −0.381898 −0.190949 0.981600i \(-0.561157\pi\)
−0.190949 + 0.981600i \(0.561157\pi\)
\(660\) 163.430 6.36151
\(661\) −33.6238 −1.30782 −0.653908 0.756574i \(-0.726872\pi\)
−0.653908 + 0.756574i \(0.726872\pi\)
\(662\) 1.06024 0.0412072
\(663\) −0.224881 −0.00873364
\(664\) −57.3412 −2.22527
\(665\) −5.66041 −0.219501
\(666\) −1.80337 −0.0698793
\(667\) −40.5451 −1.56991
\(668\) −0.342603 −0.0132557
\(669\) 22.7666 0.880207
\(670\) −116.502 −4.50086
\(671\) −22.9627 −0.886466
\(672\) −56.3485 −2.17369
\(673\) 5.07110 0.195476 0.0977382 0.995212i \(-0.468839\pi\)
0.0977382 + 0.995212i \(0.468839\pi\)
\(674\) 14.7076 0.566517
\(675\) −32.1414 −1.23712
\(676\) −64.9476 −2.49798
\(677\) −9.78191 −0.375949 −0.187975 0.982174i \(-0.560192\pi\)
−0.187975 + 0.982174i \(0.560192\pi\)
\(678\) −35.1363 −1.34940
\(679\) 8.56888 0.328844
\(680\) −56.9527 −2.18404
\(681\) −14.2941 −0.547750
\(682\) −66.1135 −2.53161
\(683\) 30.9517 1.18433 0.592166 0.805816i \(-0.298273\pi\)
0.592166 + 0.805816i \(0.298273\pi\)
\(684\) −1.40196 −0.0536053
\(685\) 30.6883 1.17254
\(686\) 52.8834 2.01910
\(687\) −33.3924 −1.27400
\(688\) 13.6674 0.521066
\(689\) −0.426944 −0.0162653
\(690\) 108.483 4.12988
\(691\) −7.88528 −0.299970 −0.149985 0.988688i \(-0.547923\pi\)
−0.149985 + 0.988688i \(0.547923\pi\)
\(692\) −50.9923 −1.93844
\(693\) 4.73780 0.179974
\(694\) −31.3975 −1.19183
\(695\) −11.9419 −0.452983
\(696\) −90.9543 −3.44762
\(697\) −3.00595 −0.113858
\(698\) −12.9854 −0.491503
\(699\) 13.2085 0.499592
\(700\) 77.6172 2.93365
\(701\) 42.5856 1.60844 0.804218 0.594335i \(-0.202585\pi\)
0.804218 + 0.594335i \(0.202585\pi\)
\(702\) −0.738178 −0.0278607
\(703\) −1.23661 −0.0466398
\(704\) 67.0537 2.52718
\(705\) −5.85880 −0.220655
\(706\) 24.8744 0.936160
\(707\) −8.35007 −0.314037
\(708\) 22.9622 0.862972
\(709\) 37.1217 1.39413 0.697067 0.717006i \(-0.254488\pi\)
0.697067 + 0.717006i \(0.254488\pi\)
\(710\) 123.418 4.63179
\(711\) −0.564195 −0.0211590
\(712\) 101.739 3.81285
\(713\) −31.3418 −1.17376
\(714\) −23.7514 −0.888873
\(715\) −1.03177 −0.0385860
\(716\) 92.9051 3.47203
\(717\) 14.6553 0.547311
\(718\) −38.1262 −1.42286
\(719\) 11.2596 0.419911 0.209955 0.977711i \(-0.432668\pi\)
0.209955 + 0.977711i \(0.432668\pi\)
\(720\) 14.7638 0.550215
\(721\) −22.7600 −0.847627
\(722\) 48.9133 1.82037
\(723\) −0.263609 −0.00980371
\(724\) −20.8418 −0.774578
\(725\) 41.6855 1.54816
\(726\) −77.7425 −2.88530
\(727\) −36.2194 −1.34330 −0.671652 0.740867i \(-0.734415\pi\)
−0.671652 + 0.740867i \(0.734415\pi\)
\(728\) 1.06917 0.0396261
\(729\) 22.5934 0.836792
\(730\) 38.3804 1.42052
\(731\) 2.61522 0.0967274
\(732\) −40.7145 −1.50485
\(733\) 2.36474 0.0873438 0.0436719 0.999046i \(-0.486094\pi\)
0.0436719 + 0.999046i \(0.486094\pi\)
\(734\) −68.5563 −2.53046
\(735\) −10.1775 −0.375403
\(736\) 85.8266 3.16361
\(737\) 66.8668 2.46307
\(738\) 1.48864 0.0547977
\(739\) −2.64267 −0.0972124 −0.0486062 0.998818i \(-0.515478\pi\)
−0.0486062 + 0.998818i \(0.515478\pi\)
\(740\) 29.6233 1.08897
\(741\) 0.0763677 0.00280544
\(742\) −45.0929 −1.65541
\(743\) −28.1565 −1.03296 −0.516481 0.856299i \(-0.672758\pi\)
−0.516481 + 0.856299i \(0.672758\pi\)
\(744\) −70.3086 −2.57764
\(745\) 44.3066 1.62327
\(746\) 59.9349 2.19437
\(747\) 2.84428 0.104067
\(748\) 54.5003 1.99273
\(749\) 7.02411 0.256655
\(750\) −28.2203 −1.03046
\(751\) 17.8849 0.652628 0.326314 0.945261i \(-0.394193\pi\)
0.326314 + 0.945261i \(0.394193\pi\)
\(752\) −10.2107 −0.372344
\(753\) 17.3685 0.632943
\(754\) 0.957372 0.0348654
\(755\) −15.4297 −0.561545
\(756\) −55.6804 −2.02508
\(757\) −7.08973 −0.257681 −0.128840 0.991665i \(-0.541125\pi\)
−0.128840 + 0.991665i \(0.541125\pi\)
\(758\) 51.3478 1.86504
\(759\) −62.2644 −2.26005
\(760\) 19.3407 0.701561
\(761\) 16.7001 0.605379 0.302689 0.953089i \(-0.402116\pi\)
0.302689 + 0.953089i \(0.402116\pi\)
\(762\) −65.2439 −2.36354
\(763\) −15.7943 −0.571791
\(764\) 70.7869 2.56098
\(765\) 2.82501 0.102138
\(766\) 59.0386 2.13315
\(767\) −0.144965 −0.00523439
\(768\) −9.58216 −0.345767
\(769\) −6.03331 −0.217567 −0.108783 0.994065i \(-0.534695\pi\)
−0.108783 + 0.994065i \(0.534695\pi\)
\(770\) −108.973 −3.92712
\(771\) 7.26370 0.261596
\(772\) 95.6454 3.44236
\(773\) −27.6703 −0.995230 −0.497615 0.867398i \(-0.665791\pi\)
−0.497615 + 0.867398i \(0.665791\pi\)
\(774\) −1.29514 −0.0465529
\(775\) 32.2233 1.15749
\(776\) −29.2785 −1.05104
\(777\) 7.40970 0.265821
\(778\) −13.3126 −0.477281
\(779\) 1.02080 0.0365739
\(780\) −1.82940 −0.0655030
\(781\) −70.8363 −2.53472
\(782\) 36.1766 1.29367
\(783\) −29.9040 −1.06868
\(784\) −17.7373 −0.633474
\(785\) 49.5803 1.76960
\(786\) −77.7388 −2.77285
\(787\) −8.18533 −0.291775 −0.145888 0.989301i \(-0.546604\pi\)
−0.145888 + 0.989301i \(0.546604\pi\)
\(788\) 99.7704 3.55417
\(789\) 2.87262 0.102268
\(790\) 12.9769 0.461699
\(791\) 16.7320 0.594921
\(792\) −16.1883 −0.575226
\(793\) 0.257039 0.00912773
\(794\) 102.497 3.63748
\(795\) 46.2767 1.64126
\(796\) −31.7516 −1.12540
\(797\) −29.7002 −1.05203 −0.526017 0.850474i \(-0.676315\pi\)
−0.526017 + 0.850474i \(0.676315\pi\)
\(798\) 8.06579 0.285526
\(799\) −1.95378 −0.0691197
\(800\) −88.2406 −3.11978
\(801\) −5.04656 −0.178311
\(802\) 22.3054 0.787631
\(803\) −22.0286 −0.777372
\(804\) 118.560 4.18127
\(805\) −51.6599 −1.82077
\(806\) 0.740058 0.0260674
\(807\) −32.5037 −1.14418
\(808\) 28.5309 1.00371
\(809\) 37.8009 1.32901 0.664504 0.747284i \(-0.268643\pi\)
0.664504 + 0.747284i \(0.268643\pi\)
\(810\) 90.6838 3.18630
\(811\) −6.57643 −0.230930 −0.115465 0.993312i \(-0.536836\pi\)
−0.115465 + 0.993312i \(0.536836\pi\)
\(812\) 72.2141 2.53422
\(813\) −33.5696 −1.17734
\(814\) −23.8071 −0.834438
\(815\) −80.2077 −2.80955
\(816\) 42.4804 1.48711
\(817\) −0.888109 −0.0310710
\(818\) −36.8255 −1.28757
\(819\) −0.0530338 −0.00185315
\(820\) −24.4533 −0.853947
\(821\) −15.6248 −0.545308 −0.272654 0.962112i \(-0.587901\pi\)
−0.272654 + 0.962112i \(0.587901\pi\)
\(822\) −43.7293 −1.52523
\(823\) −14.6905 −0.512078 −0.256039 0.966666i \(-0.582418\pi\)
−0.256039 + 0.966666i \(0.582418\pi\)
\(824\) 77.7673 2.70915
\(825\) 64.0156 2.22874
\(826\) −15.3109 −0.532734
\(827\) −28.5293 −0.992060 −0.496030 0.868305i \(-0.665209\pi\)
−0.496030 + 0.868305i \(0.665209\pi\)
\(828\) −12.7950 −0.444658
\(829\) −12.2428 −0.425212 −0.212606 0.977138i \(-0.568195\pi\)
−0.212606 + 0.977138i \(0.568195\pi\)
\(830\) −65.4208 −2.27079
\(831\) 19.1875 0.665607
\(832\) −0.750583 −0.0260218
\(833\) −3.39397 −0.117594
\(834\) 17.0166 0.589238
\(835\) −0.234440 −0.00811314
\(836\) −18.5079 −0.640109
\(837\) −23.1161 −0.799009
\(838\) 70.7189 2.44294
\(839\) −5.15144 −0.177847 −0.0889237 0.996038i \(-0.528343\pi\)
−0.0889237 + 0.996038i \(0.528343\pi\)
\(840\) −115.888 −3.99852
\(841\) 9.78366 0.337367
\(842\) 87.1083 3.00195
\(843\) −38.3911 −1.32226
\(844\) −39.0471 −1.34406
\(845\) −44.4431 −1.52889
\(846\) 0.967574 0.0332659
\(847\) 37.0211 1.27206
\(848\) 80.6505 2.76955
\(849\) 23.8495 0.818511
\(850\) −37.1942 −1.27575
\(851\) −11.2860 −0.386879
\(852\) −125.598 −4.30291
\(853\) 16.5114 0.565338 0.282669 0.959218i \(-0.408780\pi\)
0.282669 + 0.959218i \(0.408780\pi\)
\(854\) 27.1479 0.928982
\(855\) −0.959352 −0.0328091
\(856\) −24.0002 −0.820311
\(857\) 23.6615 0.808260 0.404130 0.914702i \(-0.367574\pi\)
0.404130 + 0.914702i \(0.367574\pi\)
\(858\) 1.47022 0.0501924
\(859\) 18.0175 0.614748 0.307374 0.951589i \(-0.400550\pi\)
0.307374 + 0.951589i \(0.400550\pi\)
\(860\) 21.2748 0.725463
\(861\) −6.11654 −0.208451
\(862\) 53.9727 1.83832
\(863\) −47.0214 −1.60063 −0.800314 0.599581i \(-0.795334\pi\)
−0.800314 + 0.599581i \(0.795334\pi\)
\(864\) 63.3014 2.15356
\(865\) −34.8937 −1.18642
\(866\) −84.5234 −2.87222
\(867\) −23.1869 −0.787470
\(868\) 55.8222 1.89473
\(869\) −7.44817 −0.252662
\(870\) −103.770 −3.51814
\(871\) −0.748491 −0.0253617
\(872\) 53.9665 1.82754
\(873\) 1.45229 0.0491527
\(874\) −12.2853 −0.415557
\(875\) 13.4386 0.454306
\(876\) −39.0582 −1.31966
\(877\) 22.7645 0.768703 0.384351 0.923187i \(-0.374425\pi\)
0.384351 + 0.923187i \(0.374425\pi\)
\(878\) 12.0122 0.405391
\(879\) −40.8381 −1.37743
\(880\) 194.903 6.57019
\(881\) −24.2189 −0.815956 −0.407978 0.912992i \(-0.633766\pi\)
−0.407978 + 0.912992i \(0.633766\pi\)
\(882\) 1.68081 0.0565957
\(883\) 21.6653 0.729095 0.364548 0.931185i \(-0.381224\pi\)
0.364548 + 0.931185i \(0.381224\pi\)
\(884\) −0.610063 −0.0205186
\(885\) 15.7129 0.528182
\(886\) 3.94839 0.132649
\(887\) 9.10194 0.305613 0.152807 0.988256i \(-0.451169\pi\)
0.152807 + 0.988256i \(0.451169\pi\)
\(888\) −25.3177 −0.849608
\(889\) 31.0693 1.04203
\(890\) 116.075 3.89084
\(891\) −52.0484 −1.74369
\(892\) 61.7620 2.06794
\(893\) 0.663488 0.0222028
\(894\) −63.1346 −2.11154
\(895\) 63.5743 2.12505
\(896\) −18.0958 −0.604537
\(897\) 0.696972 0.0232712
\(898\) −51.0985 −1.70518
\(899\) 29.9802 0.999894
\(900\) 13.1549 0.438497
\(901\) 15.4322 0.514122
\(902\) 19.6522 0.654347
\(903\) 5.32148 0.177088
\(904\) −57.1705 −1.90146
\(905\) −14.2619 −0.474080
\(906\) 21.9866 0.730454
\(907\) 4.68005 0.155398 0.0776992 0.996977i \(-0.475243\pi\)
0.0776992 + 0.996977i \(0.475243\pi\)
\(908\) −38.7774 −1.28687
\(909\) −1.41521 −0.0469395
\(910\) 1.21982 0.0404366
\(911\) −15.5766 −0.516077 −0.258039 0.966135i \(-0.583076\pi\)
−0.258039 + 0.966135i \(0.583076\pi\)
\(912\) −14.4260 −0.477693
\(913\) 37.5485 1.24268
\(914\) −41.8719 −1.38500
\(915\) −27.8606 −0.921044
\(916\) −90.5879 −2.99311
\(917\) 37.0194 1.22249
\(918\) 26.6821 0.880639
\(919\) 32.5815 1.07477 0.537383 0.843339i \(-0.319413\pi\)
0.537383 + 0.843339i \(0.319413\pi\)
\(920\) 176.513 5.81948
\(921\) −61.0287 −2.01096
\(922\) −110.792 −3.64875
\(923\) 0.792925 0.0260994
\(924\) 110.898 3.64827
\(925\) 11.6034 0.381518
\(926\) 12.0640 0.396449
\(927\) −3.85747 −0.126696
\(928\) −82.0980 −2.69500
\(929\) −5.89176 −0.193302 −0.0966512 0.995318i \(-0.530813\pi\)
−0.0966512 + 0.995318i \(0.530813\pi\)
\(930\) −80.2153 −2.63036
\(931\) 1.15257 0.0377739
\(932\) 35.8325 1.17373
\(933\) −12.8805 −0.421690
\(934\) 78.8437 2.57985
\(935\) 37.2941 1.21965
\(936\) 0.181208 0.00592296
\(937\) −6.43083 −0.210086 −0.105043 0.994468i \(-0.533498\pi\)
−0.105043 + 0.994468i \(0.533498\pi\)
\(938\) −79.0540 −2.58121
\(939\) −28.5380 −0.931301
\(940\) −15.8939 −0.518403
\(941\) −22.5880 −0.736349 −0.368175 0.929757i \(-0.620017\pi\)
−0.368175 + 0.929757i \(0.620017\pi\)
\(942\) −70.6494 −2.30188
\(943\) 9.31633 0.303382
\(944\) 27.3842 0.891280
\(945\) −38.1017 −1.23945
\(946\) −17.0977 −0.555895
\(947\) 7.90199 0.256780 0.128390 0.991724i \(-0.459019\pi\)
0.128390 + 0.991724i \(0.459019\pi\)
\(948\) −13.2061 −0.428915
\(949\) 0.246583 0.00800442
\(950\) 12.6309 0.409799
\(951\) 43.1171 1.39817
\(952\) −38.6460 −1.25253
\(953\) 3.70593 0.120047 0.0600235 0.998197i \(-0.480882\pi\)
0.0600235 + 0.998197i \(0.480882\pi\)
\(954\) −7.64254 −0.247437
\(955\) 48.4390 1.56745
\(956\) 39.7573 1.28584
\(957\) 59.5594 1.92528
\(958\) 29.8092 0.963092
\(959\) 20.8240 0.672441
\(960\) 81.3561 2.62576
\(961\) −7.82504 −0.252421
\(962\) 0.266491 0.00859201
\(963\) 1.19048 0.0383626
\(964\) −0.715126 −0.0230327
\(965\) 65.4495 2.10689
\(966\) 73.6127 2.36845
\(967\) 59.0925 1.90029 0.950143 0.311815i \(-0.100937\pi\)
0.950143 + 0.311815i \(0.100937\pi\)
\(968\) −126.495 −4.06571
\(969\) −2.76037 −0.0886760
\(970\) −33.4039 −1.07254
\(971\) −28.4465 −0.912892 −0.456446 0.889751i \(-0.650878\pi\)
−0.456446 + 0.889751i \(0.650878\pi\)
\(972\) −20.2977 −0.651049
\(973\) −8.10335 −0.259782
\(974\) −42.5879 −1.36460
\(975\) −0.716575 −0.0229488
\(976\) −48.5552 −1.55421
\(977\) 7.38506 0.236269 0.118135 0.992998i \(-0.462309\pi\)
0.118135 + 0.992998i \(0.462309\pi\)
\(978\) 114.292 3.65465
\(979\) −66.6217 −2.12924
\(980\) −27.6099 −0.881966
\(981\) −2.67689 −0.0854664
\(982\) 11.3024 0.360674
\(983\) −23.7948 −0.758936 −0.379468 0.925205i \(-0.623893\pi\)
−0.379468 + 0.925205i \(0.623893\pi\)
\(984\) 20.8992 0.666243
\(985\) 68.2721 2.17533
\(986\) −34.6050 −1.10205
\(987\) −3.97557 −0.126544
\(988\) 0.207173 0.00659105
\(989\) −8.10535 −0.257735
\(990\) −18.4693 −0.586992
\(991\) 5.56043 0.176633 0.0883164 0.996092i \(-0.471851\pi\)
0.0883164 + 0.996092i \(0.471851\pi\)
\(992\) −63.4626 −2.01494
\(993\) −0.738325 −0.0234301
\(994\) 83.7470 2.65629
\(995\) −21.7274 −0.688803
\(996\) 66.5762 2.10955
\(997\) −4.91329 −0.155606 −0.0778028 0.996969i \(-0.524790\pi\)
−0.0778028 + 0.996969i \(0.524790\pi\)
\(998\) −24.7550 −0.783606
\(999\) −8.32398 −0.263359
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.1.5 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.5 259 1.1 even 1 trivial