Properties

Label 4034.2.a.d.1.1
Level 4034
Weight 2
Character 4034.1
Self dual yes
Analytic conductor 32.212
Analytic rank 0
Dimension 52
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(52\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.35325 q^{3} +1.00000 q^{4} -0.0968667 q^{5} -3.35325 q^{6} -2.67437 q^{7} +1.00000 q^{8} +8.24428 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.35325 q^{3} +1.00000 q^{4} -0.0968667 q^{5} -3.35325 q^{6} -2.67437 q^{7} +1.00000 q^{8} +8.24428 q^{9} -0.0968667 q^{10} -3.55769 q^{11} -3.35325 q^{12} -5.20042 q^{13} -2.67437 q^{14} +0.324818 q^{15} +1.00000 q^{16} +1.84555 q^{17} +8.24428 q^{18} -0.434911 q^{19} -0.0968667 q^{20} +8.96782 q^{21} -3.55769 q^{22} -9.44828 q^{23} -3.35325 q^{24} -4.99062 q^{25} -5.20042 q^{26} -17.5854 q^{27} -2.67437 q^{28} +5.88214 q^{29} +0.324818 q^{30} +9.65979 q^{31} +1.00000 q^{32} +11.9298 q^{33} +1.84555 q^{34} +0.259057 q^{35} +8.24428 q^{36} +3.05031 q^{37} -0.434911 q^{38} +17.4383 q^{39} -0.0968667 q^{40} -10.0990 q^{41} +8.96782 q^{42} +4.43508 q^{43} -3.55769 q^{44} -0.798596 q^{45} -9.44828 q^{46} -5.75080 q^{47} -3.35325 q^{48} +0.152234 q^{49} -4.99062 q^{50} -6.18859 q^{51} -5.20042 q^{52} -12.0959 q^{53} -17.5854 q^{54} +0.344621 q^{55} -2.67437 q^{56} +1.45836 q^{57} +5.88214 q^{58} +7.87428 q^{59} +0.324818 q^{60} +6.56172 q^{61} +9.65979 q^{62} -22.0482 q^{63} +1.00000 q^{64} +0.503748 q^{65} +11.9298 q^{66} -9.40136 q^{67} +1.84555 q^{68} +31.6824 q^{69} +0.259057 q^{70} -14.8968 q^{71} +8.24428 q^{72} +4.93530 q^{73} +3.05031 q^{74} +16.7348 q^{75} -0.434911 q^{76} +9.51456 q^{77} +17.4383 q^{78} +2.09798 q^{79} -0.0968667 q^{80} +34.2353 q^{81} -10.0990 q^{82} -0.871999 q^{83} +8.96782 q^{84} -0.178772 q^{85} +4.43508 q^{86} -19.7243 q^{87} -3.55769 q^{88} +1.39518 q^{89} -0.798596 q^{90} +13.9078 q^{91} -9.44828 q^{92} -32.3917 q^{93} -5.75080 q^{94} +0.0421284 q^{95} -3.35325 q^{96} +17.0595 q^{97} +0.152234 q^{98} -29.3306 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.35325 −1.93600 −0.968000 0.250952i \(-0.919257\pi\)
−0.968000 + 0.250952i \(0.919257\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.0968667 −0.0433201 −0.0216600 0.999765i \(-0.506895\pi\)
−0.0216600 + 0.999765i \(0.506895\pi\)
\(6\) −3.35325 −1.36896
\(7\) −2.67437 −1.01082 −0.505408 0.862881i \(-0.668658\pi\)
−0.505408 + 0.862881i \(0.668658\pi\)
\(8\) 1.00000 0.353553
\(9\) 8.24428 2.74809
\(10\) −0.0968667 −0.0306319
\(11\) −3.55769 −1.07268 −0.536342 0.844001i \(-0.680194\pi\)
−0.536342 + 0.844001i \(0.680194\pi\)
\(12\) −3.35325 −0.968000
\(13\) −5.20042 −1.44234 −0.721169 0.692759i \(-0.756395\pi\)
−0.721169 + 0.692759i \(0.756395\pi\)
\(14\) −2.67437 −0.714754
\(15\) 0.324818 0.0838677
\(16\) 1.00000 0.250000
\(17\) 1.84555 0.447612 0.223806 0.974634i \(-0.428152\pi\)
0.223806 + 0.974634i \(0.428152\pi\)
\(18\) 8.24428 1.94320
\(19\) −0.434911 −0.0997754 −0.0498877 0.998755i \(-0.515886\pi\)
−0.0498877 + 0.998755i \(0.515886\pi\)
\(20\) −0.0968667 −0.0216600
\(21\) 8.96782 1.95694
\(22\) −3.55769 −0.758502
\(23\) −9.44828 −1.97010 −0.985051 0.172262i \(-0.944892\pi\)
−0.985051 + 0.172262i \(0.944892\pi\)
\(24\) −3.35325 −0.684479
\(25\) −4.99062 −0.998123
\(26\) −5.20042 −1.01989
\(27\) −17.5854 −3.38431
\(28\) −2.67437 −0.505408
\(29\) 5.88214 1.09229 0.546143 0.837692i \(-0.316095\pi\)
0.546143 + 0.837692i \(0.316095\pi\)
\(30\) 0.324818 0.0593034
\(31\) 9.65979 1.73495 0.867475 0.497481i \(-0.165742\pi\)
0.867475 + 0.497481i \(0.165742\pi\)
\(32\) 1.00000 0.176777
\(33\) 11.9298 2.07671
\(34\) 1.84555 0.316509
\(35\) 0.259057 0.0437886
\(36\) 8.24428 1.37405
\(37\) 3.05031 0.501469 0.250734 0.968056i \(-0.419328\pi\)
0.250734 + 0.968056i \(0.419328\pi\)
\(38\) −0.434911 −0.0705518
\(39\) 17.4383 2.79236
\(40\) −0.0968667 −0.0153160
\(41\) −10.0990 −1.57720 −0.788602 0.614904i \(-0.789195\pi\)
−0.788602 + 0.614904i \(0.789195\pi\)
\(42\) 8.96782 1.38376
\(43\) 4.43508 0.676344 0.338172 0.941084i \(-0.390191\pi\)
0.338172 + 0.941084i \(0.390191\pi\)
\(44\) −3.55769 −0.536342
\(45\) −0.798596 −0.119048
\(46\) −9.44828 −1.39307
\(47\) −5.75080 −0.838841 −0.419420 0.907792i \(-0.637767\pi\)
−0.419420 + 0.907792i \(0.637767\pi\)
\(48\) −3.35325 −0.484000
\(49\) 0.152234 0.0217478
\(50\) −4.99062 −0.705780
\(51\) −6.18859 −0.866576
\(52\) −5.20042 −0.721169
\(53\) −12.0959 −1.66150 −0.830750 0.556645i \(-0.812088\pi\)
−0.830750 + 0.556645i \(0.812088\pi\)
\(54\) −17.5854 −2.39307
\(55\) 0.344621 0.0464687
\(56\) −2.67437 −0.357377
\(57\) 1.45836 0.193165
\(58\) 5.88214 0.772363
\(59\) 7.87428 1.02514 0.512572 0.858644i \(-0.328693\pi\)
0.512572 + 0.858644i \(0.328693\pi\)
\(60\) 0.324818 0.0419338
\(61\) 6.56172 0.840142 0.420071 0.907491i \(-0.362005\pi\)
0.420071 + 0.907491i \(0.362005\pi\)
\(62\) 9.65979 1.22679
\(63\) −22.0482 −2.77782
\(64\) 1.00000 0.125000
\(65\) 0.503748 0.0624822
\(66\) 11.9298 1.46846
\(67\) −9.40136 −1.14856 −0.574280 0.818659i \(-0.694718\pi\)
−0.574280 + 0.818659i \(0.694718\pi\)
\(68\) 1.84555 0.223806
\(69\) 31.6824 3.81412
\(70\) 0.259057 0.0309632
\(71\) −14.8968 −1.76792 −0.883962 0.467559i \(-0.845134\pi\)
−0.883962 + 0.467559i \(0.845134\pi\)
\(72\) 8.24428 0.971598
\(73\) 4.93530 0.577633 0.288817 0.957384i \(-0.406738\pi\)
0.288817 + 0.957384i \(0.406738\pi\)
\(74\) 3.05031 0.354592
\(75\) 16.7348 1.93237
\(76\) −0.434911 −0.0498877
\(77\) 9.51456 1.08428
\(78\) 17.4383 1.97450
\(79\) 2.09798 0.236041 0.118020 0.993011i \(-0.462345\pi\)
0.118020 + 0.993011i \(0.462345\pi\)
\(80\) −0.0968667 −0.0108300
\(81\) 34.2353 3.80392
\(82\) −10.0990 −1.11525
\(83\) −0.871999 −0.0957143 −0.0478571 0.998854i \(-0.515239\pi\)
−0.0478571 + 0.998854i \(0.515239\pi\)
\(84\) 8.96782 0.978469
\(85\) −0.178772 −0.0193906
\(86\) 4.43508 0.478247
\(87\) −19.7243 −2.11467
\(88\) −3.55769 −0.379251
\(89\) 1.39518 0.147888 0.0739441 0.997262i \(-0.476441\pi\)
0.0739441 + 0.997262i \(0.476441\pi\)
\(90\) −0.798596 −0.0841794
\(91\) 13.9078 1.45794
\(92\) −9.44828 −0.985051
\(93\) −32.3917 −3.35886
\(94\) −5.75080 −0.593150
\(95\) 0.0421284 0.00432228
\(96\) −3.35325 −0.342240
\(97\) 17.0595 1.73213 0.866066 0.499930i \(-0.166641\pi\)
0.866066 + 0.499930i \(0.166641\pi\)
\(98\) 0.152234 0.0153780
\(99\) −29.3306 −2.94783
\(100\) −4.99062 −0.499062
\(101\) 12.3779 1.23165 0.615825 0.787883i \(-0.288823\pi\)
0.615825 + 0.787883i \(0.288823\pi\)
\(102\) −6.18859 −0.612762
\(103\) −11.5723 −1.14025 −0.570126 0.821557i \(-0.693106\pi\)
−0.570126 + 0.821557i \(0.693106\pi\)
\(104\) −5.20042 −0.509943
\(105\) −0.868683 −0.0847747
\(106\) −12.0959 −1.17486
\(107\) 16.6889 1.61338 0.806690 0.590975i \(-0.201257\pi\)
0.806690 + 0.590975i \(0.201257\pi\)
\(108\) −17.5854 −1.69215
\(109\) 3.60668 0.345457 0.172729 0.984969i \(-0.444742\pi\)
0.172729 + 0.984969i \(0.444742\pi\)
\(110\) 0.344621 0.0328584
\(111\) −10.2285 −0.970843
\(112\) −2.67437 −0.252704
\(113\) −7.81554 −0.735224 −0.367612 0.929979i \(-0.619825\pi\)
−0.367612 + 0.929979i \(0.619825\pi\)
\(114\) 1.45836 0.136588
\(115\) 0.915223 0.0853450
\(116\) 5.88214 0.546143
\(117\) −42.8737 −3.96368
\(118\) 7.87428 0.724886
\(119\) −4.93568 −0.452453
\(120\) 0.324818 0.0296517
\(121\) 1.65714 0.150649
\(122\) 6.56172 0.594070
\(123\) 33.8646 3.05347
\(124\) 9.65979 0.867475
\(125\) 0.967758 0.0865589
\(126\) −22.0482 −1.96421
\(127\) −5.31971 −0.472048 −0.236024 0.971747i \(-0.575844\pi\)
−0.236024 + 0.971747i \(0.575844\pi\)
\(128\) 1.00000 0.0883883
\(129\) −14.8719 −1.30940
\(130\) 0.503748 0.0441816
\(131\) −0.580813 −0.0507459 −0.0253729 0.999678i \(-0.508077\pi\)
−0.0253729 + 0.999678i \(0.508077\pi\)
\(132\) 11.9298 1.03836
\(133\) 1.16311 0.100854
\(134\) −9.40136 −0.812154
\(135\) 1.70344 0.146609
\(136\) 1.84555 0.158255
\(137\) −6.92694 −0.591808 −0.295904 0.955218i \(-0.595621\pi\)
−0.295904 + 0.955218i \(0.595621\pi\)
\(138\) 31.6824 2.69699
\(139\) 16.5579 1.40442 0.702210 0.711970i \(-0.252197\pi\)
0.702210 + 0.711970i \(0.252197\pi\)
\(140\) 0.259057 0.0218943
\(141\) 19.2839 1.62400
\(142\) −14.8968 −1.25011
\(143\) 18.5015 1.54717
\(144\) 8.24428 0.687023
\(145\) −0.569784 −0.0473180
\(146\) 4.93530 0.408448
\(147\) −0.510480 −0.0421037
\(148\) 3.05031 0.250734
\(149\) 19.6408 1.60904 0.804518 0.593928i \(-0.202424\pi\)
0.804518 + 0.593928i \(0.202424\pi\)
\(150\) 16.7348 1.36639
\(151\) −20.3563 −1.65657 −0.828286 0.560305i \(-0.810684\pi\)
−0.828286 + 0.560305i \(0.810684\pi\)
\(152\) −0.434911 −0.0352759
\(153\) 15.2152 1.23008
\(154\) 9.51456 0.766705
\(155\) −0.935712 −0.0751582
\(156\) 17.4383 1.39618
\(157\) 8.99323 0.717738 0.358869 0.933388i \(-0.383162\pi\)
0.358869 + 0.933388i \(0.383162\pi\)
\(158\) 2.09798 0.166906
\(159\) 40.5606 3.21666
\(160\) −0.0968667 −0.00765798
\(161\) 25.2682 1.99141
\(162\) 34.2353 2.68978
\(163\) −19.6081 −1.53582 −0.767912 0.640556i \(-0.778704\pi\)
−0.767912 + 0.640556i \(0.778704\pi\)
\(164\) −10.0990 −0.788602
\(165\) −1.15560 −0.0899635
\(166\) −0.871999 −0.0676802
\(167\) 18.5732 1.43724 0.718619 0.695404i \(-0.244775\pi\)
0.718619 + 0.695404i \(0.244775\pi\)
\(168\) 8.96782 0.691882
\(169\) 14.0444 1.08034
\(170\) −0.178772 −0.0137112
\(171\) −3.58553 −0.274192
\(172\) 4.43508 0.338172
\(173\) 21.6896 1.64903 0.824516 0.565839i \(-0.191448\pi\)
0.824516 + 0.565839i \(0.191448\pi\)
\(174\) −19.7243 −1.49530
\(175\) 13.3467 1.00892
\(176\) −3.55769 −0.268171
\(177\) −26.4044 −1.98468
\(178\) 1.39518 0.104573
\(179\) 5.69226 0.425460 0.212730 0.977111i \(-0.431765\pi\)
0.212730 + 0.977111i \(0.431765\pi\)
\(180\) −0.798596 −0.0595238
\(181\) 13.2984 0.988463 0.494232 0.869330i \(-0.335449\pi\)
0.494232 + 0.869330i \(0.335449\pi\)
\(182\) 13.9078 1.03092
\(183\) −22.0031 −1.62651
\(184\) −9.44828 −0.696536
\(185\) −0.295474 −0.0217237
\(186\) −32.3917 −2.37507
\(187\) −6.56589 −0.480146
\(188\) −5.75080 −0.419420
\(189\) 47.0297 3.42091
\(190\) 0.0421284 0.00305631
\(191\) 2.77312 0.200656 0.100328 0.994954i \(-0.468011\pi\)
0.100328 + 0.994954i \(0.468011\pi\)
\(192\) −3.35325 −0.242000
\(193\) 12.1561 0.875015 0.437507 0.899215i \(-0.355861\pi\)
0.437507 + 0.899215i \(0.355861\pi\)
\(194\) 17.0595 1.22480
\(195\) −1.68919 −0.120966
\(196\) 0.152234 0.0108739
\(197\) 21.4380 1.52740 0.763698 0.645573i \(-0.223382\pi\)
0.763698 + 0.645573i \(0.223382\pi\)
\(198\) −29.3306 −2.08443
\(199\) −10.8941 −0.772262 −0.386131 0.922444i \(-0.626189\pi\)
−0.386131 + 0.922444i \(0.626189\pi\)
\(200\) −4.99062 −0.352890
\(201\) 31.5251 2.22361
\(202\) 12.3779 0.870908
\(203\) −15.7310 −1.10410
\(204\) −6.18859 −0.433288
\(205\) 0.978260 0.0683247
\(206\) −11.5723 −0.806280
\(207\) −77.8943 −5.41402
\(208\) −5.20042 −0.360584
\(209\) 1.54728 0.107027
\(210\) −0.868683 −0.0599448
\(211\) 11.3189 0.779228 0.389614 0.920978i \(-0.372608\pi\)
0.389614 + 0.920978i \(0.372608\pi\)
\(212\) −12.0959 −0.830750
\(213\) 49.9526 3.42270
\(214\) 16.6889 1.14083
\(215\) −0.429612 −0.0292993
\(216\) −17.5854 −1.19653
\(217\) −25.8338 −1.75371
\(218\) 3.60668 0.244275
\(219\) −16.5493 −1.11830
\(220\) 0.344621 0.0232344
\(221\) −9.59764 −0.645607
\(222\) −10.2285 −0.686490
\(223\) 21.1149 1.41396 0.706978 0.707236i \(-0.250058\pi\)
0.706978 + 0.707236i \(0.250058\pi\)
\(224\) −2.67437 −0.178689
\(225\) −41.1440 −2.74294
\(226\) −7.81554 −0.519882
\(227\) 9.39551 0.623602 0.311801 0.950147i \(-0.399068\pi\)
0.311801 + 0.950147i \(0.399068\pi\)
\(228\) 1.45836 0.0965825
\(229\) −12.9210 −0.853842 −0.426921 0.904289i \(-0.640402\pi\)
−0.426921 + 0.904289i \(0.640402\pi\)
\(230\) 0.915223 0.0603480
\(231\) −31.9047 −2.09917
\(232\) 5.88214 0.386182
\(233\) −4.38813 −0.287476 −0.143738 0.989616i \(-0.545912\pi\)
−0.143738 + 0.989616i \(0.545912\pi\)
\(234\) −42.8737 −2.80274
\(235\) 0.557061 0.0363387
\(236\) 7.87428 0.512572
\(237\) −7.03504 −0.456975
\(238\) −4.93568 −0.319933
\(239\) 18.0144 1.16526 0.582629 0.812738i \(-0.302024\pi\)
0.582629 + 0.812738i \(0.302024\pi\)
\(240\) 0.324818 0.0209669
\(241\) 19.8422 1.27815 0.639075 0.769144i \(-0.279317\pi\)
0.639075 + 0.769144i \(0.279317\pi\)
\(242\) 1.65714 0.106525
\(243\) −62.0434 −3.98009
\(244\) 6.56172 0.420071
\(245\) −0.0147464 −0.000942115 0
\(246\) 33.8646 2.15913
\(247\) 2.26172 0.143910
\(248\) 9.65979 0.613397
\(249\) 2.92403 0.185303
\(250\) 0.967758 0.0612064
\(251\) −15.4721 −0.976588 −0.488294 0.872679i \(-0.662381\pi\)
−0.488294 + 0.872679i \(0.662381\pi\)
\(252\) −22.0482 −1.38891
\(253\) 33.6140 2.11330
\(254\) −5.31971 −0.333788
\(255\) 0.599468 0.0375402
\(256\) 1.00000 0.0625000
\(257\) 9.32801 0.581865 0.290933 0.956744i \(-0.406034\pi\)
0.290933 + 0.956744i \(0.406034\pi\)
\(258\) −14.8719 −0.925887
\(259\) −8.15766 −0.506892
\(260\) 0.503748 0.0312411
\(261\) 48.4940 3.00171
\(262\) −0.580813 −0.0358828
\(263\) 18.4406 1.13710 0.568549 0.822649i \(-0.307505\pi\)
0.568549 + 0.822649i \(0.307505\pi\)
\(264\) 11.9298 0.734229
\(265\) 1.17169 0.0719764
\(266\) 1.16311 0.0713149
\(267\) −4.67837 −0.286312
\(268\) −9.40136 −0.574280
\(269\) 15.6567 0.954609 0.477304 0.878738i \(-0.341614\pi\)
0.477304 + 0.878738i \(0.341614\pi\)
\(270\) 1.70344 0.103668
\(271\) −7.53205 −0.457539 −0.228770 0.973481i \(-0.573470\pi\)
−0.228770 + 0.973481i \(0.573470\pi\)
\(272\) 1.84555 0.111903
\(273\) −46.6364 −2.82257
\(274\) −6.92694 −0.418472
\(275\) 17.7551 1.07067
\(276\) 31.6824 1.90706
\(277\) −1.69550 −0.101873 −0.0509363 0.998702i \(-0.516221\pi\)
−0.0509363 + 0.998702i \(0.516221\pi\)
\(278\) 16.5579 0.993075
\(279\) 79.6380 4.76780
\(280\) 0.259057 0.0154816
\(281\) −30.5556 −1.82280 −0.911399 0.411525i \(-0.864996\pi\)
−0.911399 + 0.411525i \(0.864996\pi\)
\(282\) 19.2839 1.14834
\(283\) 1.71177 0.101754 0.0508771 0.998705i \(-0.483798\pi\)
0.0508771 + 0.998705i \(0.483798\pi\)
\(284\) −14.8968 −0.883962
\(285\) −0.141267 −0.00836793
\(286\) 18.5015 1.09402
\(287\) 27.0085 1.59426
\(288\) 8.24428 0.485799
\(289\) −13.5939 −0.799644
\(290\) −0.569784 −0.0334589
\(291\) −57.2048 −3.35341
\(292\) 4.93530 0.288817
\(293\) 10.3651 0.605537 0.302769 0.953064i \(-0.402089\pi\)
0.302769 + 0.953064i \(0.402089\pi\)
\(294\) −0.510480 −0.0297718
\(295\) −0.762755 −0.0444093
\(296\) 3.05031 0.177296
\(297\) 62.5633 3.63029
\(298\) 19.6408 1.13776
\(299\) 49.1350 2.84155
\(300\) 16.7348 0.966183
\(301\) −11.8610 −0.683659
\(302\) −20.3563 −1.17137
\(303\) −41.5063 −2.38447
\(304\) −0.434911 −0.0249438
\(305\) −0.635612 −0.0363950
\(306\) 15.2152 0.869797
\(307\) −14.8531 −0.847711 −0.423856 0.905730i \(-0.639324\pi\)
−0.423856 + 0.905730i \(0.639324\pi\)
\(308\) 9.51456 0.542142
\(309\) 38.8048 2.20753
\(310\) −0.935712 −0.0531449
\(311\) −19.6436 −1.11389 −0.556943 0.830551i \(-0.688026\pi\)
−0.556943 + 0.830551i \(0.688026\pi\)
\(312\) 17.4383 0.987250
\(313\) 4.73213 0.267476 0.133738 0.991017i \(-0.457302\pi\)
0.133738 + 0.991017i \(0.457302\pi\)
\(314\) 8.99323 0.507518
\(315\) 2.13574 0.120335
\(316\) 2.09798 0.118020
\(317\) −27.7729 −1.55988 −0.779941 0.625853i \(-0.784751\pi\)
−0.779941 + 0.625853i \(0.784751\pi\)
\(318\) 40.5606 2.27452
\(319\) −20.9268 −1.17168
\(320\) −0.0968667 −0.00541501
\(321\) −55.9621 −3.12350
\(322\) 25.2682 1.40814
\(323\) −0.802650 −0.0446606
\(324\) 34.2353 1.90196
\(325\) 25.9533 1.43963
\(326\) −19.6081 −1.08599
\(327\) −12.0941 −0.668805
\(328\) −10.0990 −0.557626
\(329\) 15.3798 0.847913
\(330\) −1.15560 −0.0636138
\(331\) −0.154355 −0.00848413 −0.00424206 0.999991i \(-0.501350\pi\)
−0.00424206 + 0.999991i \(0.501350\pi\)
\(332\) −0.871999 −0.0478571
\(333\) 25.1476 1.37808
\(334\) 18.5732 1.01628
\(335\) 0.910679 0.0497557
\(336\) 8.96782 0.489234
\(337\) 9.01822 0.491254 0.245627 0.969364i \(-0.421006\pi\)
0.245627 + 0.969364i \(0.421006\pi\)
\(338\) 14.0444 0.763914
\(339\) 26.2075 1.42339
\(340\) −0.178772 −0.00969529
\(341\) −34.3665 −1.86105
\(342\) −3.58553 −0.193883
\(343\) 18.3134 0.988832
\(344\) 4.43508 0.239124
\(345\) −3.06897 −0.165228
\(346\) 21.6896 1.16604
\(347\) 14.4946 0.778108 0.389054 0.921215i \(-0.372802\pi\)
0.389054 + 0.921215i \(0.372802\pi\)
\(348\) −19.7243 −1.05733
\(349\) 0.809288 0.0433202 0.0216601 0.999765i \(-0.493105\pi\)
0.0216601 + 0.999765i \(0.493105\pi\)
\(350\) 13.3467 0.713413
\(351\) 91.4514 4.88131
\(352\) −3.55769 −0.189625
\(353\) 18.2823 0.973066 0.486533 0.873662i \(-0.338261\pi\)
0.486533 + 0.873662i \(0.338261\pi\)
\(354\) −26.4044 −1.40338
\(355\) 1.44300 0.0765866
\(356\) 1.39518 0.0739441
\(357\) 16.5506 0.875948
\(358\) 5.69226 0.300846
\(359\) 1.09243 0.0576560 0.0288280 0.999584i \(-0.490822\pi\)
0.0288280 + 0.999584i \(0.490822\pi\)
\(360\) −0.798596 −0.0420897
\(361\) −18.8109 −0.990045
\(362\) 13.2984 0.698949
\(363\) −5.55681 −0.291657
\(364\) 13.9078 0.728969
\(365\) −0.478066 −0.0250231
\(366\) −22.0031 −1.15012
\(367\) 18.8528 0.984109 0.492054 0.870564i \(-0.336246\pi\)
0.492054 + 0.870564i \(0.336246\pi\)
\(368\) −9.44828 −0.492526
\(369\) −83.2593 −4.33431
\(370\) −0.295474 −0.0153610
\(371\) 32.3489 1.67947
\(372\) −32.3917 −1.67943
\(373\) −22.1298 −1.14584 −0.572918 0.819613i \(-0.694189\pi\)
−0.572918 + 0.819613i \(0.694189\pi\)
\(374\) −6.56589 −0.339514
\(375\) −3.24513 −0.167578
\(376\) −5.75080 −0.296575
\(377\) −30.5896 −1.57545
\(378\) 47.0297 2.41895
\(379\) 30.4741 1.56535 0.782676 0.622430i \(-0.213854\pi\)
0.782676 + 0.622430i \(0.213854\pi\)
\(380\) 0.0421284 0.00216114
\(381\) 17.8383 0.913884
\(382\) 2.77312 0.141885
\(383\) −25.8440 −1.32057 −0.660283 0.751017i \(-0.729564\pi\)
−0.660283 + 0.751017i \(0.729564\pi\)
\(384\) −3.35325 −0.171120
\(385\) −0.921644 −0.0469713
\(386\) 12.1561 0.618729
\(387\) 36.5641 1.85866
\(388\) 17.0595 0.866066
\(389\) −7.87194 −0.399123 −0.199562 0.979885i \(-0.563952\pi\)
−0.199562 + 0.979885i \(0.563952\pi\)
\(390\) −1.68919 −0.0855355
\(391\) −17.4373 −0.881841
\(392\) 0.152234 0.00768900
\(393\) 1.94761 0.0982440
\(394\) 21.4380 1.08003
\(395\) −0.203224 −0.0102253
\(396\) −29.3306 −1.47392
\(397\) −20.4955 −1.02864 −0.514320 0.857598i \(-0.671956\pi\)
−0.514320 + 0.857598i \(0.671956\pi\)
\(398\) −10.8941 −0.546072
\(399\) −3.90020 −0.195254
\(400\) −4.99062 −0.249531
\(401\) −14.0710 −0.702673 −0.351337 0.936249i \(-0.614273\pi\)
−0.351337 + 0.936249i \(0.614273\pi\)
\(402\) 31.5251 1.57233
\(403\) −50.2350 −2.50238
\(404\) 12.3779 0.615825
\(405\) −3.31626 −0.164786
\(406\) −15.7310 −0.780717
\(407\) −10.8521 −0.537917
\(408\) −6.18859 −0.306381
\(409\) −18.4117 −0.910401 −0.455200 0.890389i \(-0.650432\pi\)
−0.455200 + 0.890389i \(0.650432\pi\)
\(410\) 0.978260 0.0483128
\(411\) 23.2278 1.14574
\(412\) −11.5723 −0.570126
\(413\) −21.0587 −1.03623
\(414\) −77.8943 −3.82829
\(415\) 0.0844676 0.00414635
\(416\) −5.20042 −0.254972
\(417\) −55.5227 −2.71896
\(418\) 1.54728 0.0756798
\(419\) 23.7870 1.16207 0.581035 0.813879i \(-0.302648\pi\)
0.581035 + 0.813879i \(0.302648\pi\)
\(420\) −0.868683 −0.0423874
\(421\) −6.87293 −0.334966 −0.167483 0.985875i \(-0.553564\pi\)
−0.167483 + 0.985875i \(0.553564\pi\)
\(422\) 11.3189 0.550997
\(423\) −47.4112 −2.30521
\(424\) −12.0959 −0.587429
\(425\) −9.21044 −0.446772
\(426\) 49.9526 2.42021
\(427\) −17.5484 −0.849228
\(428\) 16.6889 0.806690
\(429\) −62.0401 −2.99532
\(430\) −0.429612 −0.0207177
\(431\) −34.4500 −1.65940 −0.829700 0.558210i \(-0.811488\pi\)
−0.829700 + 0.558210i \(0.811488\pi\)
\(432\) −17.5854 −0.846077
\(433\) −11.9923 −0.576312 −0.288156 0.957583i \(-0.593042\pi\)
−0.288156 + 0.957583i \(0.593042\pi\)
\(434\) −25.8338 −1.24006
\(435\) 1.91063 0.0916076
\(436\) 3.60668 0.172729
\(437\) 4.10916 0.196568
\(438\) −16.5493 −0.790756
\(439\) 0.762424 0.0363885 0.0181943 0.999834i \(-0.494208\pi\)
0.0181943 + 0.999834i \(0.494208\pi\)
\(440\) 0.344621 0.0164292
\(441\) 1.25506 0.0597649
\(442\) −9.59764 −0.456513
\(443\) 4.91551 0.233543 0.116771 0.993159i \(-0.462745\pi\)
0.116771 + 0.993159i \(0.462745\pi\)
\(444\) −10.2285 −0.485421
\(445\) −0.135146 −0.00640654
\(446\) 21.1149 0.999817
\(447\) −65.8604 −3.11509
\(448\) −2.67437 −0.126352
\(449\) −7.50630 −0.354244 −0.177122 0.984189i \(-0.556679\pi\)
−0.177122 + 0.984189i \(0.556679\pi\)
\(450\) −41.1440 −1.93955
\(451\) 35.9292 1.69184
\(452\) −7.81554 −0.367612
\(453\) 68.2597 3.20712
\(454\) 9.39551 0.440953
\(455\) −1.34721 −0.0631580
\(456\) 1.45836 0.0682941
\(457\) 25.1784 1.17780 0.588898 0.808207i \(-0.299562\pi\)
0.588898 + 0.808207i \(0.299562\pi\)
\(458\) −12.9210 −0.603757
\(459\) −32.4547 −1.51486
\(460\) 0.915223 0.0426725
\(461\) −32.8403 −1.52952 −0.764762 0.644313i \(-0.777143\pi\)
−0.764762 + 0.644313i \(0.777143\pi\)
\(462\) −31.9047 −1.48434
\(463\) 20.3737 0.946848 0.473424 0.880835i \(-0.343018\pi\)
0.473424 + 0.880835i \(0.343018\pi\)
\(464\) 5.88214 0.273072
\(465\) 3.13768 0.145506
\(466\) −4.38813 −0.203276
\(467\) −9.48846 −0.439073 −0.219537 0.975604i \(-0.570455\pi\)
−0.219537 + 0.975604i \(0.570455\pi\)
\(468\) −42.8737 −1.98184
\(469\) 25.1427 1.16098
\(470\) 0.557061 0.0256953
\(471\) −30.1566 −1.38954
\(472\) 7.87428 0.362443
\(473\) −15.7786 −0.725503
\(474\) −7.03504 −0.323130
\(475\) 2.17047 0.0995881
\(476\) −4.93568 −0.226226
\(477\) −99.7220 −4.56596
\(478\) 18.0144 0.823961
\(479\) −27.3667 −1.25042 −0.625208 0.780458i \(-0.714986\pi\)
−0.625208 + 0.780458i \(0.714986\pi\)
\(480\) 0.324818 0.0148259
\(481\) −15.8629 −0.723287
\(482\) 19.8422 0.903789
\(483\) −84.7304 −3.85537
\(484\) 1.65714 0.0753247
\(485\) −1.65250 −0.0750361
\(486\) −62.0434 −2.81435
\(487\) 17.4059 0.788735 0.394367 0.918953i \(-0.370964\pi\)
0.394367 + 0.918953i \(0.370964\pi\)
\(488\) 6.56172 0.297035
\(489\) 65.7508 2.97335
\(490\) −0.0147464 −0.000666176 0
\(491\) 0.790617 0.0356801 0.0178400 0.999841i \(-0.494321\pi\)
0.0178400 + 0.999841i \(0.494321\pi\)
\(492\) 33.8646 1.52673
\(493\) 10.8558 0.488920
\(494\) 2.26172 0.101760
\(495\) 2.84116 0.127700
\(496\) 9.65979 0.433737
\(497\) 39.8395 1.78704
\(498\) 2.92403 0.131029
\(499\) 28.7338 1.28630 0.643150 0.765740i \(-0.277627\pi\)
0.643150 + 0.765740i \(0.277627\pi\)
\(500\) 0.967758 0.0432795
\(501\) −62.2806 −2.78249
\(502\) −15.4721 −0.690552
\(503\) −17.8810 −0.797276 −0.398638 0.917108i \(-0.630517\pi\)
−0.398638 + 0.917108i \(0.630517\pi\)
\(504\) −22.0482 −0.982106
\(505\) −1.19901 −0.0533552
\(506\) 33.6140 1.49433
\(507\) −47.0943 −2.09153
\(508\) −5.31971 −0.236024
\(509\) −36.0819 −1.59930 −0.799650 0.600466i \(-0.794982\pi\)
−0.799650 + 0.600466i \(0.794982\pi\)
\(510\) 0.599468 0.0265449
\(511\) −13.1988 −0.583881
\(512\) 1.00000 0.0441942
\(513\) 7.64807 0.337670
\(514\) 9.32801 0.411441
\(515\) 1.12097 0.0493958
\(516\) −14.8719 −0.654701
\(517\) 20.4596 0.899810
\(518\) −8.15766 −0.358427
\(519\) −72.7307 −3.19252
\(520\) 0.503748 0.0220908
\(521\) 1.50359 0.0658736 0.0329368 0.999457i \(-0.489514\pi\)
0.0329368 + 0.999457i \(0.489514\pi\)
\(522\) 48.4940 2.12253
\(523\) −16.6308 −0.727215 −0.363608 0.931552i \(-0.618455\pi\)
−0.363608 + 0.931552i \(0.618455\pi\)
\(524\) −0.580813 −0.0253729
\(525\) −44.7549 −1.95327
\(526\) 18.4406 0.804050
\(527\) 17.8276 0.776584
\(528\) 11.9298 0.519179
\(529\) 66.2700 2.88130
\(530\) 1.17169 0.0508950
\(531\) 64.9178 2.81719
\(532\) 1.16311 0.0504272
\(533\) 52.5193 2.27486
\(534\) −4.67837 −0.202453
\(535\) −1.61660 −0.0698918
\(536\) −9.40136 −0.406077
\(537\) −19.0876 −0.823690
\(538\) 15.6567 0.675010
\(539\) −0.541602 −0.0233285
\(540\) 1.70344 0.0733043
\(541\) 29.0539 1.24913 0.624563 0.780975i \(-0.285277\pi\)
0.624563 + 0.780975i \(0.285277\pi\)
\(542\) −7.53205 −0.323529
\(543\) −44.5929 −1.91366
\(544\) 1.84555 0.0791273
\(545\) −0.349367 −0.0149652
\(546\) −46.6364 −1.99585
\(547\) 5.65284 0.241698 0.120849 0.992671i \(-0.461438\pi\)
0.120849 + 0.992671i \(0.461438\pi\)
\(548\) −6.92694 −0.295904
\(549\) 54.0966 2.30879
\(550\) 17.7551 0.757078
\(551\) −2.55821 −0.108983
\(552\) 31.6824 1.34849
\(553\) −5.61076 −0.238594
\(554\) −1.69550 −0.0720348
\(555\) 0.990797 0.0420570
\(556\) 16.5579 0.702210
\(557\) −2.27382 −0.0963450 −0.0481725 0.998839i \(-0.515340\pi\)
−0.0481725 + 0.998839i \(0.515340\pi\)
\(558\) 79.6380 3.37135
\(559\) −23.0643 −0.975516
\(560\) 0.259057 0.0109472
\(561\) 22.0171 0.929562
\(562\) −30.5556 −1.28891
\(563\) 20.8280 0.877796 0.438898 0.898537i \(-0.355369\pi\)
0.438898 + 0.898537i \(0.355369\pi\)
\(564\) 19.2839 0.811998
\(565\) 0.757065 0.0318500
\(566\) 1.71177 0.0719511
\(567\) −91.5578 −3.84506
\(568\) −14.8968 −0.625055
\(569\) 10.0113 0.419693 0.209847 0.977734i \(-0.432703\pi\)
0.209847 + 0.977734i \(0.432703\pi\)
\(570\) −0.141267 −0.00591702
\(571\) −2.42776 −0.101599 −0.0507993 0.998709i \(-0.516177\pi\)
−0.0507993 + 0.998709i \(0.516177\pi\)
\(572\) 18.5015 0.773586
\(573\) −9.29897 −0.388470
\(574\) 27.0085 1.12731
\(575\) 47.1527 1.96641
\(576\) 8.24428 0.343512
\(577\) −31.5109 −1.31181 −0.655907 0.754842i \(-0.727714\pi\)
−0.655907 + 0.754842i \(0.727714\pi\)
\(578\) −13.5939 −0.565433
\(579\) −40.7624 −1.69403
\(580\) −0.569784 −0.0236590
\(581\) 2.33204 0.0967495
\(582\) −57.2048 −2.37122
\(583\) 43.0335 1.78226
\(584\) 4.93530 0.204224
\(585\) 4.15304 0.171707
\(586\) 10.3651 0.428179
\(587\) 2.15284 0.0888574 0.0444287 0.999013i \(-0.485853\pi\)
0.0444287 + 0.999013i \(0.485853\pi\)
\(588\) −0.510480 −0.0210518
\(589\) −4.20115 −0.173105
\(590\) −0.762755 −0.0314021
\(591\) −71.8871 −2.95704
\(592\) 3.05031 0.125367
\(593\) −4.18523 −0.171867 −0.0859335 0.996301i \(-0.527387\pi\)
−0.0859335 + 0.996301i \(0.527387\pi\)
\(594\) 62.5633 2.56700
\(595\) 0.478103 0.0196003
\(596\) 19.6408 0.804518
\(597\) 36.5306 1.49510
\(598\) 49.1350 2.00928
\(599\) 7.32978 0.299487 0.149743 0.988725i \(-0.452155\pi\)
0.149743 + 0.988725i \(0.452155\pi\)
\(600\) 16.7348 0.683195
\(601\) 16.0825 0.656019 0.328009 0.944674i \(-0.393622\pi\)
0.328009 + 0.944674i \(0.393622\pi\)
\(602\) −11.8610 −0.483420
\(603\) −77.5075 −3.15635
\(604\) −20.3563 −0.828286
\(605\) −0.160522 −0.00652615
\(606\) −41.5063 −1.68608
\(607\) −5.63187 −0.228590 −0.114295 0.993447i \(-0.536461\pi\)
−0.114295 + 0.993447i \(0.536461\pi\)
\(608\) −0.434911 −0.0176380
\(609\) 52.7500 2.13754
\(610\) −0.635612 −0.0257352
\(611\) 29.9066 1.20989
\(612\) 15.2152 0.615039
\(613\) −36.5455 −1.47606 −0.738028 0.674770i \(-0.764243\pi\)
−0.738028 + 0.674770i \(0.764243\pi\)
\(614\) −14.8531 −0.599423
\(615\) −3.28035 −0.132276
\(616\) 9.51456 0.383353
\(617\) −13.8028 −0.555680 −0.277840 0.960627i \(-0.589618\pi\)
−0.277840 + 0.960627i \(0.589618\pi\)
\(618\) 38.8048 1.56096
\(619\) 26.6908 1.07279 0.536396 0.843966i \(-0.319785\pi\)
0.536396 + 0.843966i \(0.319785\pi\)
\(620\) −0.935712 −0.0375791
\(621\) 166.152 6.66743
\(622\) −19.6436 −0.787636
\(623\) −3.73121 −0.149488
\(624\) 17.4383 0.698091
\(625\) 24.8593 0.994374
\(626\) 4.73213 0.189134
\(627\) −5.18840 −0.207205
\(628\) 8.99323 0.358869
\(629\) 5.62951 0.224463
\(630\) 2.13574 0.0850898
\(631\) 41.8744 1.66699 0.833497 0.552524i \(-0.186335\pi\)
0.833497 + 0.552524i \(0.186335\pi\)
\(632\) 2.09798 0.0834531
\(633\) −37.9552 −1.50858
\(634\) −27.7729 −1.10300
\(635\) 0.515302 0.0204491
\(636\) 40.5606 1.60833
\(637\) −0.791683 −0.0313676
\(638\) −20.9268 −0.828501
\(639\) −122.813 −4.85842
\(640\) −0.0968667 −0.00382899
\(641\) −33.0780 −1.30650 −0.653251 0.757142i \(-0.726595\pi\)
−0.653251 + 0.757142i \(0.726595\pi\)
\(642\) −55.9621 −2.20865
\(643\) −9.49992 −0.374640 −0.187320 0.982299i \(-0.559980\pi\)
−0.187320 + 0.982299i \(0.559980\pi\)
\(644\) 25.2682 0.995705
\(645\) 1.44060 0.0567234
\(646\) −0.802650 −0.0315798
\(647\) 21.0399 0.827163 0.413582 0.910467i \(-0.364278\pi\)
0.413582 + 0.910467i \(0.364278\pi\)
\(648\) 34.2353 1.34489
\(649\) −28.0142 −1.09965
\(650\) 25.9533 1.01797
\(651\) 86.6272 3.39519
\(652\) −19.6081 −0.767912
\(653\) −39.1316 −1.53134 −0.765668 0.643236i \(-0.777591\pi\)
−0.765668 + 0.643236i \(0.777591\pi\)
\(654\) −12.0941 −0.472916
\(655\) 0.0562614 0.00219832
\(656\) −10.0990 −0.394301
\(657\) 40.6880 1.58739
\(658\) 15.3798 0.599565
\(659\) 20.2896 0.790371 0.395185 0.918601i \(-0.370680\pi\)
0.395185 + 0.918601i \(0.370680\pi\)
\(660\) −1.15560 −0.0449817
\(661\) −25.0745 −0.975285 −0.487643 0.873043i \(-0.662143\pi\)
−0.487643 + 0.873043i \(0.662143\pi\)
\(662\) −0.154355 −0.00599918
\(663\) 32.1833 1.24990
\(664\) −0.871999 −0.0338401
\(665\) −0.112667 −0.00436903
\(666\) 25.1476 0.974452
\(667\) −55.5761 −2.15192
\(668\) 18.5732 0.718619
\(669\) −70.8034 −2.73742
\(670\) 0.910679 0.0351826
\(671\) −23.3445 −0.901206
\(672\) 8.96782 0.345941
\(673\) 21.6093 0.832977 0.416489 0.909141i \(-0.363261\pi\)
0.416489 + 0.909141i \(0.363261\pi\)
\(674\) 9.01822 0.347369
\(675\) 87.7619 3.37796
\(676\) 14.0444 0.540169
\(677\) 50.8691 1.95506 0.977530 0.210798i \(-0.0676063\pi\)
0.977530 + 0.210798i \(0.0676063\pi\)
\(678\) 26.2075 1.00649
\(679\) −45.6234 −1.75087
\(680\) −0.178772 −0.00685561
\(681\) −31.5055 −1.20729
\(682\) −34.3665 −1.31596
\(683\) 26.0620 0.997236 0.498618 0.866822i \(-0.333841\pi\)
0.498618 + 0.866822i \(0.333841\pi\)
\(684\) −3.58553 −0.137096
\(685\) 0.670990 0.0256372
\(686\) 18.3134 0.699210
\(687\) 43.3272 1.65304
\(688\) 4.43508 0.169086
\(689\) 62.9038 2.39644
\(690\) −3.06897 −0.116834
\(691\) 7.46053 0.283812 0.141906 0.989880i \(-0.454677\pi\)
0.141906 + 0.989880i \(0.454677\pi\)
\(692\) 21.6896 0.824516
\(693\) 78.4407 2.97972
\(694\) 14.4946 0.550206
\(695\) −1.60391 −0.0608396
\(696\) −19.7243 −0.747648
\(697\) −18.6383 −0.705975
\(698\) 0.809288 0.0306320
\(699\) 14.7145 0.556553
\(700\) 13.3467 0.504459
\(701\) 42.8964 1.62017 0.810087 0.586310i \(-0.199420\pi\)
0.810087 + 0.586310i \(0.199420\pi\)
\(702\) 91.4514 3.45161
\(703\) −1.32661 −0.0500342
\(704\) −3.55769 −0.134085
\(705\) −1.86796 −0.0703516
\(706\) 18.2823 0.688062
\(707\) −33.1031 −1.24497
\(708\) −26.4044 −0.992339
\(709\) −23.0580 −0.865961 −0.432981 0.901403i \(-0.642538\pi\)
−0.432981 + 0.901403i \(0.642538\pi\)
\(710\) 1.44300 0.0541549
\(711\) 17.2963 0.648663
\(712\) 1.39518 0.0522864
\(713\) −91.2684 −3.41803
\(714\) 16.5506 0.619389
\(715\) −1.79218 −0.0670236
\(716\) 5.69226 0.212730
\(717\) −60.4069 −2.25594
\(718\) 1.09243 0.0407690
\(719\) −30.4340 −1.13500 −0.567498 0.823375i \(-0.692089\pi\)
−0.567498 + 0.823375i \(0.692089\pi\)
\(720\) −0.798596 −0.0297619
\(721\) 30.9486 1.15258
\(722\) −18.8109 −0.700067
\(723\) −66.5360 −2.47450
\(724\) 13.2984 0.494232
\(725\) −29.3555 −1.09024
\(726\) −5.55681 −0.206233
\(727\) −2.93252 −0.108761 −0.0543806 0.998520i \(-0.517318\pi\)
−0.0543806 + 0.998520i \(0.517318\pi\)
\(728\) 13.9078 0.515459
\(729\) 105.341 3.90152
\(730\) −0.478066 −0.0176940
\(731\) 8.18517 0.302740
\(732\) −22.0031 −0.813257
\(733\) 33.7218 1.24554 0.622771 0.782404i \(-0.286007\pi\)
0.622771 + 0.782404i \(0.286007\pi\)
\(734\) 18.8528 0.695870
\(735\) 0.0494485 0.00182393
\(736\) −9.44828 −0.348268
\(737\) 33.4471 1.23204
\(738\) −83.2593 −3.06482
\(739\) −46.2631 −1.70182 −0.850908 0.525315i \(-0.823947\pi\)
−0.850908 + 0.525315i \(0.823947\pi\)
\(740\) −0.295474 −0.0108618
\(741\) −7.58411 −0.278609
\(742\) 32.3489 1.18756
\(743\) −9.50469 −0.348693 −0.174347 0.984684i \(-0.555781\pi\)
−0.174347 + 0.984684i \(0.555781\pi\)
\(744\) −32.3917 −1.18754
\(745\) −1.90254 −0.0697036
\(746\) −22.1298 −0.810228
\(747\) −7.18900 −0.263032
\(748\) −6.56589 −0.240073
\(749\) −44.6323 −1.63083
\(750\) −3.24513 −0.118496
\(751\) −10.0412 −0.366409 −0.183205 0.983075i \(-0.558647\pi\)
−0.183205 + 0.983075i \(0.558647\pi\)
\(752\) −5.75080 −0.209710
\(753\) 51.8817 1.89067
\(754\) −30.5896 −1.11401
\(755\) 1.97185 0.0717629
\(756\) 47.0297 1.71046
\(757\) 0.743989 0.0270407 0.0135204 0.999909i \(-0.495696\pi\)
0.0135204 + 0.999909i \(0.495696\pi\)
\(758\) 30.4741 1.10687
\(759\) −112.716 −4.09134
\(760\) 0.0421284 0.00152816
\(761\) −29.0144 −1.05177 −0.525885 0.850556i \(-0.676266\pi\)
−0.525885 + 0.850556i \(0.676266\pi\)
\(762\) 17.8383 0.646213
\(763\) −9.64558 −0.349193
\(764\) 2.77312 0.100328
\(765\) −1.47385 −0.0532871
\(766\) −25.8440 −0.933781
\(767\) −40.9496 −1.47860
\(768\) −3.35325 −0.121000
\(769\) 43.3002 1.56145 0.780723 0.624877i \(-0.214851\pi\)
0.780723 + 0.624877i \(0.214851\pi\)
\(770\) −0.921644 −0.0332137
\(771\) −31.2791 −1.12649
\(772\) 12.1561 0.437507
\(773\) −29.0108 −1.04344 −0.521722 0.853115i \(-0.674710\pi\)
−0.521722 + 0.853115i \(0.674710\pi\)
\(774\) 36.5641 1.31427
\(775\) −48.2083 −1.73169
\(776\) 17.0595 0.612401
\(777\) 27.3547 0.981343
\(778\) −7.87194 −0.282223
\(779\) 4.39218 0.157366
\(780\) −1.68919 −0.0604828
\(781\) 52.9981 1.89642
\(782\) −17.4373 −0.623556
\(783\) −103.440 −3.69663
\(784\) 0.152234 0.00543694
\(785\) −0.871145 −0.0310925
\(786\) 1.94761 0.0694690
\(787\) 23.3719 0.833120 0.416560 0.909108i \(-0.363236\pi\)
0.416560 + 0.909108i \(0.363236\pi\)
\(788\) 21.4380 0.763698
\(789\) −61.8361 −2.20142
\(790\) −0.203224 −0.00723039
\(791\) 20.9016 0.743176
\(792\) −29.3306 −1.04222
\(793\) −34.1237 −1.21177
\(794\) −20.4955 −0.727358
\(795\) −3.92897 −0.139346
\(796\) −10.8941 −0.386131
\(797\) −23.8931 −0.846335 −0.423168 0.906051i \(-0.639082\pi\)
−0.423168 + 0.906051i \(0.639082\pi\)
\(798\) −3.90020 −0.138066
\(799\) −10.6134 −0.375475
\(800\) −4.99062 −0.176445
\(801\) 11.5022 0.406411
\(802\) −14.0710 −0.496865
\(803\) −17.5583 −0.619618
\(804\) 31.5251 1.11180
\(805\) −2.44764 −0.0862681
\(806\) −50.2350 −1.76945
\(807\) −52.5010 −1.84812
\(808\) 12.3779 0.435454
\(809\) 9.70466 0.341198 0.170599 0.985341i \(-0.445430\pi\)
0.170599 + 0.985341i \(0.445430\pi\)
\(810\) −3.31626 −0.116522
\(811\) 2.96299 0.104044 0.0520222 0.998646i \(-0.483433\pi\)
0.0520222 + 0.998646i \(0.483433\pi\)
\(812\) −15.7310 −0.552050
\(813\) 25.2568 0.885796
\(814\) −10.8521 −0.380365
\(815\) 1.89937 0.0665320
\(816\) −6.18859 −0.216644
\(817\) −1.92887 −0.0674825
\(818\) −18.4117 −0.643751
\(819\) 114.660 4.00655
\(820\) 0.978260 0.0341623
\(821\) −15.2578 −0.532501 −0.266251 0.963904i \(-0.585785\pi\)
−0.266251 + 0.963904i \(0.585785\pi\)
\(822\) 23.2278 0.810161
\(823\) −16.6831 −0.581536 −0.290768 0.956794i \(-0.593911\pi\)
−0.290768 + 0.956794i \(0.593911\pi\)
\(824\) −11.5723 −0.403140
\(825\) −59.5371 −2.07282
\(826\) −21.0587 −0.732726
\(827\) −24.1917 −0.841229 −0.420615 0.907239i \(-0.638186\pi\)
−0.420615 + 0.907239i \(0.638186\pi\)
\(828\) −77.8943 −2.70701
\(829\) 7.12913 0.247605 0.123802 0.992307i \(-0.460491\pi\)
0.123802 + 0.992307i \(0.460491\pi\)
\(830\) 0.0844676 0.00293191
\(831\) 5.68543 0.197225
\(832\) −5.20042 −0.180292
\(833\) 0.280956 0.00973456
\(834\) −55.5227 −1.92259
\(835\) −1.79912 −0.0622613
\(836\) 1.54728 0.0535137
\(837\) −169.871 −5.87160
\(838\) 23.7870 0.821708
\(839\) −9.33970 −0.322442 −0.161221 0.986918i \(-0.551543\pi\)
−0.161221 + 0.986918i \(0.551543\pi\)
\(840\) −0.868683 −0.0299724
\(841\) 5.59963 0.193091
\(842\) −6.87293 −0.236857
\(843\) 102.461 3.52893
\(844\) 11.3189 0.389614
\(845\) −1.36043 −0.0468003
\(846\) −47.4112 −1.63003
\(847\) −4.43181 −0.152279
\(848\) −12.0959 −0.415375
\(849\) −5.74000 −0.196996
\(850\) −9.21044 −0.315915
\(851\) −28.8202 −0.987944
\(852\) 49.9526 1.71135
\(853\) 31.6719 1.08443 0.542213 0.840241i \(-0.317587\pi\)
0.542213 + 0.840241i \(0.317587\pi\)
\(854\) −17.5484 −0.600495
\(855\) 0.347318 0.0118780
\(856\) 16.6889 0.570416
\(857\) −38.6553 −1.32044 −0.660221 0.751072i \(-0.729537\pi\)
−0.660221 + 0.751072i \(0.729537\pi\)
\(858\) −62.0401 −2.11801
\(859\) 11.3474 0.387169 0.193585 0.981084i \(-0.437989\pi\)
0.193585 + 0.981084i \(0.437989\pi\)
\(860\) −0.429612 −0.0146496
\(861\) −90.5663 −3.08649
\(862\) −34.4500 −1.17337
\(863\) 40.0251 1.36247 0.681236 0.732064i \(-0.261443\pi\)
0.681236 + 0.732064i \(0.261443\pi\)
\(864\) −17.5854 −0.598267
\(865\) −2.10100 −0.0714362
\(866\) −11.9923 −0.407514
\(867\) 45.5839 1.54811
\(868\) −25.8338 −0.876857
\(869\) −7.46395 −0.253197
\(870\) 1.91063 0.0647763
\(871\) 48.8911 1.65661
\(872\) 3.60668 0.122138
\(873\) 140.643 4.76006
\(874\) 4.10916 0.138994
\(875\) −2.58814 −0.0874951
\(876\) −16.5493 −0.559149
\(877\) −6.22331 −0.210146 −0.105073 0.994464i \(-0.533508\pi\)
−0.105073 + 0.994464i \(0.533508\pi\)
\(878\) 0.762424 0.0257306
\(879\) −34.7568 −1.17232
\(880\) 0.344621 0.0116172
\(881\) −31.4408 −1.05927 −0.529633 0.848227i \(-0.677670\pi\)
−0.529633 + 0.848227i \(0.677670\pi\)
\(882\) 1.25506 0.0422602
\(883\) 44.1907 1.48713 0.743567 0.668661i \(-0.233132\pi\)
0.743567 + 0.668661i \(0.233132\pi\)
\(884\) −9.59764 −0.322804
\(885\) 2.55771 0.0859764
\(886\) 4.91551 0.165140
\(887\) 23.4825 0.788466 0.394233 0.919010i \(-0.371010\pi\)
0.394233 + 0.919010i \(0.371010\pi\)
\(888\) −10.2285 −0.343245
\(889\) 14.2268 0.477153
\(890\) −0.135146 −0.00453010
\(891\) −121.799 −4.08041
\(892\) 21.1149 0.706978
\(893\) 2.50109 0.0836956
\(894\) −65.8604 −2.20270
\(895\) −0.551391 −0.0184310
\(896\) −2.67437 −0.0893443
\(897\) −164.762 −5.50124
\(898\) −7.50630 −0.250489
\(899\) 56.8203 1.89506
\(900\) −41.1440 −1.37147
\(901\) −22.3236 −0.743707
\(902\) 35.9292 1.19631
\(903\) 39.7730 1.32356
\(904\) −7.81554 −0.259941
\(905\) −1.28817 −0.0428203
\(906\) 68.2597 2.26778
\(907\) −38.7529 −1.28677 −0.643384 0.765543i \(-0.722470\pi\)
−0.643384 + 0.765543i \(0.722470\pi\)
\(908\) 9.39551 0.311801
\(909\) 102.047 3.38469
\(910\) −1.34721 −0.0446594
\(911\) −14.0965 −0.467039 −0.233519 0.972352i \(-0.575024\pi\)
−0.233519 + 0.972352i \(0.575024\pi\)
\(912\) 1.45836 0.0482913
\(913\) 3.10230 0.102671
\(914\) 25.1784 0.832828
\(915\) 2.13136 0.0704607
\(916\) −12.9210 −0.426921
\(917\) 1.55331 0.0512947
\(918\) −32.4547 −1.07116
\(919\) −32.1144 −1.05936 −0.529679 0.848198i \(-0.677687\pi\)
−0.529679 + 0.848198i \(0.677687\pi\)
\(920\) 0.915223 0.0301740
\(921\) 49.8062 1.64117
\(922\) −32.8403 −1.08154
\(923\) 77.4696 2.54994
\(924\) −31.9047 −1.04959
\(925\) −15.2230 −0.500528
\(926\) 20.3737 0.669523
\(927\) −95.4053 −3.13352
\(928\) 5.88214 0.193091
\(929\) 19.4469 0.638031 0.319016 0.947749i \(-0.396648\pi\)
0.319016 + 0.947749i \(0.396648\pi\)
\(930\) 3.13768 0.102888
\(931\) −0.0662084 −0.00216989
\(932\) −4.38813 −0.143738
\(933\) 65.8699 2.15648
\(934\) −9.48846 −0.310472
\(935\) 0.636016 0.0208000
\(936\) −42.8737 −1.40137
\(937\) −10.4331 −0.340833 −0.170417 0.985372i \(-0.554511\pi\)
−0.170417 + 0.985372i \(0.554511\pi\)
\(938\) 25.1427 0.820938
\(939\) −15.8680 −0.517833
\(940\) 0.557061 0.0181693
\(941\) 8.61317 0.280781 0.140391 0.990096i \(-0.455164\pi\)
0.140391 + 0.990096i \(0.455164\pi\)
\(942\) −30.1566 −0.982554
\(943\) 95.4185 3.10725
\(944\) 7.87428 0.256286
\(945\) −4.55561 −0.148194
\(946\) −15.7786 −0.513008
\(947\) −5.20240 −0.169055 −0.0845277 0.996421i \(-0.526938\pi\)
−0.0845277 + 0.996421i \(0.526938\pi\)
\(948\) −7.03504 −0.228488
\(949\) −25.6657 −0.833142
\(950\) 2.17047 0.0704194
\(951\) 93.1294 3.01993
\(952\) −4.93568 −0.159966
\(953\) 0.814097 0.0263712 0.0131856 0.999913i \(-0.495803\pi\)
0.0131856 + 0.999913i \(0.495803\pi\)
\(954\) −99.7220 −3.22862
\(955\) −0.268623 −0.00869244
\(956\) 18.0144 0.582629
\(957\) 70.1729 2.26837
\(958\) −27.3667 −0.884177
\(959\) 18.5252 0.598209
\(960\) 0.324818 0.0104835
\(961\) 62.3116 2.01005
\(962\) −15.8629 −0.511441
\(963\) 137.588 4.43372
\(964\) 19.8422 0.639075
\(965\) −1.17752 −0.0379057
\(966\) −84.7304 −2.72616
\(967\) 20.8772 0.671367 0.335683 0.941975i \(-0.391033\pi\)
0.335683 + 0.941975i \(0.391033\pi\)
\(968\) 1.65714 0.0532626
\(969\) 2.69148 0.0864629
\(970\) −1.65250 −0.0530585
\(971\) −48.3132 −1.55045 −0.775223 0.631688i \(-0.782362\pi\)
−0.775223 + 0.631688i \(0.782362\pi\)
\(972\) −62.0434 −1.99004
\(973\) −44.2818 −1.41961
\(974\) 17.4059 0.557720
\(975\) −87.0279 −2.78712
\(976\) 6.56172 0.210035
\(977\) −31.4026 −1.00466 −0.502329 0.864677i \(-0.667523\pi\)
−0.502329 + 0.864677i \(0.667523\pi\)
\(978\) 65.7508 2.10248
\(979\) −4.96360 −0.158637
\(980\) −0.0147464 −0.000471058 0
\(981\) 29.7345 0.949348
\(982\) 0.790617 0.0252296
\(983\) 12.9766 0.413891 0.206945 0.978352i \(-0.433648\pi\)
0.206945 + 0.978352i \(0.433648\pi\)
\(984\) 33.8646 1.07956
\(985\) −2.07663 −0.0661670
\(986\) 10.8558 0.345719
\(987\) −51.5721 −1.64156
\(988\) 2.26172 0.0719549
\(989\) −41.9039 −1.33247
\(990\) 2.84116 0.0902979
\(991\) 62.3724 1.98132 0.990662 0.136340i \(-0.0435339\pi\)
0.990662 + 0.136340i \(0.0435339\pi\)
\(992\) 9.65979 0.306699
\(993\) 0.517591 0.0164253
\(994\) 39.8395 1.26363
\(995\) 1.05528 0.0334545
\(996\) 2.92403 0.0926514
\(997\) −4.81690 −0.152553 −0.0762763 0.997087i \(-0.524303\pi\)
−0.0762763 + 0.997087i \(0.524303\pi\)
\(998\) 28.7338 0.909552
\(999\) −53.6409 −1.69712
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 4034.2.a.d.1.1 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.1 52 1.1 even 1 trivial