Properties

Label 6017.2.a.f.1.18
Level 6017
Weight 2
Character 6017.1
Self dual yes
Analytic conductor 48.046
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.25579 q^{2} -2.77556 q^{3} +3.08857 q^{4} +0.288075 q^{5} +6.26106 q^{6} +1.78637 q^{7} -2.45557 q^{8} +4.70373 q^{9} +O(q^{10})\) \(q-2.25579 q^{2} -2.77556 q^{3} +3.08857 q^{4} +0.288075 q^{5} +6.26106 q^{6} +1.78637 q^{7} -2.45557 q^{8} +4.70373 q^{9} -0.649836 q^{10} -1.00000 q^{11} -8.57250 q^{12} +5.07395 q^{13} -4.02967 q^{14} -0.799570 q^{15} -0.637886 q^{16} -2.51700 q^{17} -10.6106 q^{18} -2.44919 q^{19} +0.889740 q^{20} -4.95818 q^{21} +2.25579 q^{22} -7.23846 q^{23} +6.81559 q^{24} -4.91701 q^{25} -11.4457 q^{26} -4.72879 q^{27} +5.51733 q^{28} -7.48543 q^{29} +1.80366 q^{30} -3.19569 q^{31} +6.35008 q^{32} +2.77556 q^{33} +5.67780 q^{34} +0.514610 q^{35} +14.5278 q^{36} -11.0014 q^{37} +5.52485 q^{38} -14.0830 q^{39} -0.707390 q^{40} +9.46750 q^{41} +11.1846 q^{42} +7.61735 q^{43} -3.08857 q^{44} +1.35503 q^{45} +16.3284 q^{46} -9.12690 q^{47} +1.77049 q^{48} -3.80887 q^{49} +11.0917 q^{50} +6.98607 q^{51} +15.6712 q^{52} -8.32897 q^{53} +10.6671 q^{54} -0.288075 q^{55} -4.38657 q^{56} +6.79787 q^{57} +16.8855 q^{58} +3.22138 q^{59} -2.46953 q^{60} +10.1317 q^{61} +7.20878 q^{62} +8.40261 q^{63} -13.0487 q^{64} +1.46168 q^{65} -6.26106 q^{66} +15.3378 q^{67} -7.77391 q^{68} +20.0908 q^{69} -1.16085 q^{70} -4.64867 q^{71} -11.5504 q^{72} -11.1549 q^{73} +24.8168 q^{74} +13.6475 q^{75} -7.56449 q^{76} -1.78637 q^{77} +31.7683 q^{78} -0.0153161 q^{79} -0.183759 q^{80} -0.986136 q^{81} -21.3566 q^{82} +1.08217 q^{83} -15.3137 q^{84} -0.725085 q^{85} -17.1831 q^{86} +20.7763 q^{87} +2.45557 q^{88} -14.0979 q^{89} -3.05665 q^{90} +9.06396 q^{91} -22.3565 q^{92} +8.86982 q^{93} +20.5883 q^{94} -0.705551 q^{95} -17.6250 q^{96} -8.81029 q^{97} +8.59200 q^{98} -4.70373 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.25579 −1.59508 −0.797541 0.603265i \(-0.793866\pi\)
−0.797541 + 0.603265i \(0.793866\pi\)
\(3\) −2.77556 −1.60247 −0.801235 0.598350i \(-0.795823\pi\)
−0.801235 + 0.598350i \(0.795823\pi\)
\(4\) 3.08857 1.54428
\(5\) 0.288075 0.128831 0.0644156 0.997923i \(-0.479482\pi\)
0.0644156 + 0.997923i \(0.479482\pi\)
\(6\) 6.26106 2.55607
\(7\) 1.78637 0.675185 0.337593 0.941292i \(-0.390387\pi\)
0.337593 + 0.941292i \(0.390387\pi\)
\(8\) −2.45557 −0.868177
\(9\) 4.70373 1.56791
\(10\) −0.649836 −0.205496
\(11\) −1.00000 −0.301511
\(12\) −8.57250 −2.47467
\(13\) 5.07395 1.40726 0.703630 0.710567i \(-0.251561\pi\)
0.703630 + 0.710567i \(0.251561\pi\)
\(14\) −4.02967 −1.07698
\(15\) −0.799570 −0.206448
\(16\) −0.637886 −0.159471
\(17\) −2.51700 −0.610461 −0.305231 0.952278i \(-0.598734\pi\)
−0.305231 + 0.952278i \(0.598734\pi\)
\(18\) −10.6106 −2.50094
\(19\) −2.44919 −0.561883 −0.280941 0.959725i \(-0.590647\pi\)
−0.280941 + 0.959725i \(0.590647\pi\)
\(20\) 0.889740 0.198952
\(21\) −4.95818 −1.08196
\(22\) 2.25579 0.480935
\(23\) −7.23846 −1.50932 −0.754661 0.656114i \(-0.772199\pi\)
−0.754661 + 0.656114i \(0.772199\pi\)
\(24\) 6.81559 1.39123
\(25\) −4.91701 −0.983403
\(26\) −11.4457 −2.24469
\(27\) −4.72879 −0.910057
\(28\) 5.51733 1.04268
\(29\) −7.48543 −1.39001 −0.695005 0.719005i \(-0.744598\pi\)
−0.695005 + 0.719005i \(0.744598\pi\)
\(30\) 1.80366 0.329301
\(31\) −3.19569 −0.573962 −0.286981 0.957936i \(-0.592652\pi\)
−0.286981 + 0.957936i \(0.592652\pi\)
\(32\) 6.35008 1.12255
\(33\) 2.77556 0.483163
\(34\) 5.67780 0.973735
\(35\) 0.514610 0.0869849
\(36\) 14.5278 2.42130
\(37\) −11.0014 −1.80862 −0.904309 0.426879i \(-0.859613\pi\)
−0.904309 + 0.426879i \(0.859613\pi\)
\(38\) 5.52485 0.896249
\(39\) −14.0830 −2.25509
\(40\) −0.707390 −0.111848
\(41\) 9.46750 1.47857 0.739287 0.673390i \(-0.235163\pi\)
0.739287 + 0.673390i \(0.235163\pi\)
\(42\) 11.1846 1.72582
\(43\) 7.61735 1.16164 0.580818 0.814034i \(-0.302733\pi\)
0.580818 + 0.814034i \(0.302733\pi\)
\(44\) −3.08857 −0.465619
\(45\) 1.35503 0.201996
\(46\) 16.3284 2.40749
\(47\) −9.12690 −1.33130 −0.665648 0.746266i \(-0.731845\pi\)
−0.665648 + 0.746266i \(0.731845\pi\)
\(48\) 1.77049 0.255548
\(49\) −3.80887 −0.544125
\(50\) 11.0917 1.56861
\(51\) 6.98607 0.978246
\(52\) 15.6712 2.17321
\(53\) −8.32897 −1.14407 −0.572036 0.820228i \(-0.693846\pi\)
−0.572036 + 0.820228i \(0.693846\pi\)
\(54\) 10.6671 1.45161
\(55\) −0.288075 −0.0388441
\(56\) −4.38657 −0.586180
\(57\) 6.79787 0.900400
\(58\) 16.8855 2.21718
\(59\) 3.22138 0.419388 0.209694 0.977767i \(-0.432753\pi\)
0.209694 + 0.977767i \(0.432753\pi\)
\(60\) −2.46953 −0.318814
\(61\) 10.1317 1.29724 0.648618 0.761114i \(-0.275347\pi\)
0.648618 + 0.761114i \(0.275347\pi\)
\(62\) 7.20878 0.915516
\(63\) 8.40261 1.05863
\(64\) −13.0487 −1.63108
\(65\) 1.46168 0.181299
\(66\) −6.26106 −0.770684
\(67\) 15.3378 1.87381 0.936905 0.349583i \(-0.113677\pi\)
0.936905 + 0.349583i \(0.113677\pi\)
\(68\) −7.77391 −0.942726
\(69\) 20.0908 2.41864
\(70\) −1.16085 −0.138748
\(71\) −4.64867 −0.551696 −0.275848 0.961201i \(-0.588959\pi\)
−0.275848 + 0.961201i \(0.588959\pi\)
\(72\) −11.5504 −1.36122
\(73\) −11.1549 −1.30558 −0.652789 0.757540i \(-0.726401\pi\)
−0.652789 + 0.757540i \(0.726401\pi\)
\(74\) 24.8168 2.88489
\(75\) 13.6475 1.57587
\(76\) −7.56449 −0.867707
\(77\) −1.78637 −0.203576
\(78\) 31.7683 3.59705
\(79\) −0.0153161 −0.00172320 −0.000861599 1.00000i \(-0.500274\pi\)
−0.000861599 1.00000i \(0.500274\pi\)
\(80\) −0.183759 −0.0205449
\(81\) −0.986136 −0.109571
\(82\) −21.3566 −2.35845
\(83\) 1.08217 0.118784 0.0593918 0.998235i \(-0.481084\pi\)
0.0593918 + 0.998235i \(0.481084\pi\)
\(84\) −15.3137 −1.67086
\(85\) −0.725085 −0.0786465
\(86\) −17.1831 −1.85290
\(87\) 20.7763 2.22745
\(88\) 2.45557 0.261765
\(89\) −14.0979 −1.49438 −0.747188 0.664612i \(-0.768597\pi\)
−0.747188 + 0.664612i \(0.768597\pi\)
\(90\) −3.05665 −0.322199
\(91\) 9.06396 0.950161
\(92\) −22.3565 −2.33082
\(93\) 8.86982 0.919757
\(94\) 20.5883 2.12352
\(95\) −0.705551 −0.0723880
\(96\) −17.6250 −1.79885
\(97\) −8.81029 −0.894549 −0.447275 0.894397i \(-0.647605\pi\)
−0.447275 + 0.894397i \(0.647605\pi\)
\(98\) 8.59200 0.867923
\(99\) −4.70373 −0.472742
\(100\) −15.1865 −1.51865
\(101\) −3.04863 −0.303350 −0.151675 0.988430i \(-0.548467\pi\)
−0.151675 + 0.988430i \(0.548467\pi\)
\(102\) −15.7591 −1.56038
\(103\) 2.82491 0.278347 0.139173 0.990268i \(-0.455555\pi\)
0.139173 + 0.990268i \(0.455555\pi\)
\(104\) −12.4595 −1.22175
\(105\) −1.42833 −0.139391
\(106\) 18.7884 1.82489
\(107\) 3.00220 0.290234 0.145117 0.989415i \(-0.453644\pi\)
0.145117 + 0.989415i \(0.453644\pi\)
\(108\) −14.6052 −1.40539
\(109\) 9.08395 0.870085 0.435043 0.900410i \(-0.356733\pi\)
0.435043 + 0.900410i \(0.356733\pi\)
\(110\) 0.649836 0.0619594
\(111\) 30.5350 2.89825
\(112\) −1.13950 −0.107673
\(113\) 10.0100 0.941665 0.470832 0.882223i \(-0.343954\pi\)
0.470832 + 0.882223i \(0.343954\pi\)
\(114\) −15.3345 −1.43621
\(115\) −2.08522 −0.194448
\(116\) −23.1193 −2.14657
\(117\) 23.8665 2.20645
\(118\) −7.26675 −0.668958
\(119\) −4.49629 −0.412175
\(120\) 1.96340 0.179233
\(121\) 1.00000 0.0909091
\(122\) −22.8550 −2.06920
\(123\) −26.2776 −2.36937
\(124\) −9.87009 −0.886361
\(125\) −2.85685 −0.255524
\(126\) −18.9545 −1.68860
\(127\) 20.5104 1.82001 0.910004 0.414600i \(-0.136078\pi\)
0.910004 + 0.414600i \(0.136078\pi\)
\(128\) 16.7348 1.47916
\(129\) −21.1424 −1.86149
\(130\) −3.29723 −0.289186
\(131\) 11.4704 1.00217 0.501087 0.865397i \(-0.332934\pi\)
0.501087 + 0.865397i \(0.332934\pi\)
\(132\) 8.57250 0.746140
\(133\) −4.37517 −0.379375
\(134\) −34.5988 −2.98888
\(135\) −1.36225 −0.117244
\(136\) 6.18067 0.529988
\(137\) 17.2674 1.47525 0.737625 0.675211i \(-0.235947\pi\)
0.737625 + 0.675211i \(0.235947\pi\)
\(138\) −45.3205 −3.85793
\(139\) 1.71425 0.145401 0.0727005 0.997354i \(-0.476838\pi\)
0.0727005 + 0.997354i \(0.476838\pi\)
\(140\) 1.58941 0.134329
\(141\) 25.3322 2.13336
\(142\) 10.4864 0.879999
\(143\) −5.07395 −0.424305
\(144\) −3.00044 −0.250037
\(145\) −2.15637 −0.179077
\(146\) 25.1630 2.08250
\(147\) 10.5718 0.871943
\(148\) −33.9785 −2.79302
\(149\) −7.57899 −0.620895 −0.310448 0.950591i \(-0.600479\pi\)
−0.310448 + 0.950591i \(0.600479\pi\)
\(150\) −30.7857 −2.51364
\(151\) −6.95030 −0.565607 −0.282804 0.959178i \(-0.591264\pi\)
−0.282804 + 0.959178i \(0.591264\pi\)
\(152\) 6.01417 0.487814
\(153\) −11.8393 −0.957148
\(154\) 4.02967 0.324720
\(155\) −0.920598 −0.0739442
\(156\) −43.4964 −3.48250
\(157\) 11.9607 0.954570 0.477285 0.878748i \(-0.341621\pi\)
0.477285 + 0.878748i \(0.341621\pi\)
\(158\) 0.0345499 0.00274864
\(159\) 23.1176 1.83334
\(160\) 1.82930 0.144619
\(161\) −12.9306 −1.01907
\(162\) 2.22451 0.174774
\(163\) 6.51570 0.510349 0.255175 0.966895i \(-0.417867\pi\)
0.255175 + 0.966895i \(0.417867\pi\)
\(164\) 29.2410 2.28334
\(165\) 0.799570 0.0622464
\(166\) −2.44114 −0.189470
\(167\) −7.28437 −0.563682 −0.281841 0.959461i \(-0.590945\pi\)
−0.281841 + 0.959461i \(0.590945\pi\)
\(168\) 12.1752 0.939336
\(169\) 12.7449 0.980379
\(170\) 1.63564 0.125447
\(171\) −11.5203 −0.880981
\(172\) 23.5267 1.79390
\(173\) −26.2169 −1.99324 −0.996618 0.0821761i \(-0.973813\pi\)
−0.996618 + 0.0821761i \(0.973813\pi\)
\(174\) −46.8668 −3.55296
\(175\) −8.78362 −0.663979
\(176\) 0.637886 0.0480824
\(177\) −8.94114 −0.672057
\(178\) 31.8019 2.38365
\(179\) −3.05232 −0.228141 −0.114071 0.993473i \(-0.536389\pi\)
−0.114071 + 0.993473i \(0.536389\pi\)
\(180\) 4.18509 0.311938
\(181\) −14.3626 −1.06756 −0.533781 0.845623i \(-0.679229\pi\)
−0.533781 + 0.845623i \(0.679229\pi\)
\(182\) −20.4463 −1.51558
\(183\) −28.1212 −2.07878
\(184\) 17.7746 1.31036
\(185\) −3.16923 −0.233006
\(186\) −20.0084 −1.46709
\(187\) 2.51700 0.184061
\(188\) −28.1890 −2.05590
\(189\) −8.44739 −0.614457
\(190\) 1.59157 0.115465
\(191\) 6.83561 0.494608 0.247304 0.968938i \(-0.420455\pi\)
0.247304 + 0.968938i \(0.420455\pi\)
\(192\) 36.2173 2.61376
\(193\) 23.1093 1.66345 0.831723 0.555191i \(-0.187355\pi\)
0.831723 + 0.555191i \(0.187355\pi\)
\(194\) 19.8741 1.42688
\(195\) −4.05697 −0.290526
\(196\) −11.7640 −0.840283
\(197\) 3.43700 0.244876 0.122438 0.992476i \(-0.460929\pi\)
0.122438 + 0.992476i \(0.460929\pi\)
\(198\) 10.6106 0.754062
\(199\) −9.64110 −0.683439 −0.341720 0.939802i \(-0.611009\pi\)
−0.341720 + 0.939802i \(0.611009\pi\)
\(200\) 12.0741 0.853767
\(201\) −42.5710 −3.00272
\(202\) 6.87704 0.483867
\(203\) −13.3718 −0.938515
\(204\) 21.5770 1.51069
\(205\) 2.72735 0.190486
\(206\) −6.37239 −0.443986
\(207\) −34.0477 −2.36648
\(208\) −3.23660 −0.224418
\(209\) 2.44919 0.169414
\(210\) 3.22201 0.222339
\(211\) −0.611647 −0.0421075 −0.0210537 0.999778i \(-0.506702\pi\)
−0.0210537 + 0.999778i \(0.506702\pi\)
\(212\) −25.7246 −1.76677
\(213\) 12.9027 0.884076
\(214\) −6.77232 −0.462947
\(215\) 2.19437 0.149655
\(216\) 11.6119 0.790090
\(217\) −5.70869 −0.387531
\(218\) −20.4915 −1.38786
\(219\) 30.9610 2.09215
\(220\) −0.889740 −0.0599863
\(221\) −12.7711 −0.859078
\(222\) −68.8804 −4.62295
\(223\) 28.3451 1.89813 0.949064 0.315083i \(-0.102032\pi\)
0.949064 + 0.315083i \(0.102032\pi\)
\(224\) 11.3436 0.757927
\(225\) −23.1283 −1.54189
\(226\) −22.5805 −1.50203
\(227\) 12.0971 0.802914 0.401457 0.915878i \(-0.368504\pi\)
0.401457 + 0.915878i \(0.368504\pi\)
\(228\) 20.9957 1.39047
\(229\) −9.03285 −0.596908 −0.298454 0.954424i \(-0.596471\pi\)
−0.298454 + 0.954424i \(0.596471\pi\)
\(230\) 4.70381 0.310160
\(231\) 4.95818 0.326224
\(232\) 18.3810 1.20677
\(233\) −8.87297 −0.581288 −0.290644 0.956831i \(-0.593869\pi\)
−0.290644 + 0.956831i \(0.593869\pi\)
\(234\) −53.8376 −3.51947
\(235\) −2.62923 −0.171512
\(236\) 9.94946 0.647655
\(237\) 0.0425108 0.00276137
\(238\) 10.1427 0.657452
\(239\) 1.01325 0.0655414 0.0327707 0.999463i \(-0.489567\pi\)
0.0327707 + 0.999463i \(0.489567\pi\)
\(240\) 0.510034 0.0329226
\(241\) 10.8492 0.698860 0.349430 0.936962i \(-0.386375\pi\)
0.349430 + 0.936962i \(0.386375\pi\)
\(242\) −2.25579 −0.145007
\(243\) 16.9235 1.08564
\(244\) 31.2925 2.00330
\(245\) −1.09724 −0.0701002
\(246\) 59.2766 3.77934
\(247\) −12.4271 −0.790715
\(248\) 7.84725 0.498301
\(249\) −3.00363 −0.190347
\(250\) 6.44443 0.407582
\(251\) −19.2506 −1.21509 −0.607544 0.794286i \(-0.707845\pi\)
−0.607544 + 0.794286i \(0.707845\pi\)
\(252\) 25.9520 1.63482
\(253\) 7.23846 0.455078
\(254\) −46.2672 −2.90306
\(255\) 2.01251 0.126029
\(256\) −11.6528 −0.728300
\(257\) −7.91006 −0.493416 −0.246708 0.969090i \(-0.579349\pi\)
−0.246708 + 0.969090i \(0.579349\pi\)
\(258\) 47.6927 2.96922
\(259\) −19.6526 −1.22115
\(260\) 4.51449 0.279977
\(261\) −35.2094 −2.17941
\(262\) −25.8748 −1.59855
\(263\) 11.4691 0.707212 0.353606 0.935394i \(-0.384955\pi\)
0.353606 + 0.935394i \(0.384955\pi\)
\(264\) −6.81559 −0.419471
\(265\) −2.39937 −0.147392
\(266\) 9.86944 0.605134
\(267\) 39.1296 2.39469
\(268\) 47.3718 2.89370
\(269\) −12.8929 −0.786092 −0.393046 0.919519i \(-0.628579\pi\)
−0.393046 + 0.919519i \(0.628579\pi\)
\(270\) 3.07294 0.187013
\(271\) −12.8690 −0.781736 −0.390868 0.920447i \(-0.627825\pi\)
−0.390868 + 0.920447i \(0.627825\pi\)
\(272\) 1.60556 0.0973511
\(273\) −25.1575 −1.52260
\(274\) −38.9514 −2.35314
\(275\) 4.91701 0.296507
\(276\) 62.0517 3.73507
\(277\) −22.1645 −1.33174 −0.665869 0.746069i \(-0.731939\pi\)
−0.665869 + 0.746069i \(0.731939\pi\)
\(278\) −3.86699 −0.231926
\(279\) −15.0316 −0.899920
\(280\) −1.26366 −0.0755183
\(281\) 7.94582 0.474008 0.237004 0.971509i \(-0.423835\pi\)
0.237004 + 0.971509i \(0.423835\pi\)
\(282\) −57.1441 −3.40288
\(283\) 10.1913 0.605810 0.302905 0.953021i \(-0.402043\pi\)
0.302905 + 0.953021i \(0.402043\pi\)
\(284\) −14.3577 −0.851975
\(285\) 1.95830 0.116000
\(286\) 11.4457 0.676800
\(287\) 16.9125 0.998312
\(288\) 29.8691 1.76005
\(289\) −10.6647 −0.627337
\(290\) 4.86430 0.285642
\(291\) 24.4535 1.43349
\(292\) −34.4525 −2.01618
\(293\) 2.36782 0.138329 0.0691647 0.997605i \(-0.477967\pi\)
0.0691647 + 0.997605i \(0.477967\pi\)
\(294\) −23.8476 −1.39082
\(295\) 0.928001 0.0540303
\(296\) 27.0147 1.57020
\(297\) 4.72879 0.274392
\(298\) 17.0966 0.990378
\(299\) −36.7275 −2.12401
\(300\) 42.1511 2.43359
\(301\) 13.6074 0.784319
\(302\) 15.6784 0.902189
\(303\) 8.46164 0.486108
\(304\) 1.56230 0.0896042
\(305\) 2.91870 0.167124
\(306\) 26.7068 1.52673
\(307\) 19.9300 1.13747 0.568734 0.822522i \(-0.307433\pi\)
0.568734 + 0.822522i \(0.307433\pi\)
\(308\) −5.51733 −0.314379
\(309\) −7.84070 −0.446042
\(310\) 2.07667 0.117947
\(311\) 27.0353 1.53303 0.766515 0.642227i \(-0.221989\pi\)
0.766515 + 0.642227i \(0.221989\pi\)
\(312\) 34.5819 1.95782
\(313\) −3.88262 −0.219459 −0.109729 0.993961i \(-0.534998\pi\)
−0.109729 + 0.993961i \(0.534998\pi\)
\(314\) −26.9808 −1.52262
\(315\) 2.42058 0.136384
\(316\) −0.0473049 −0.00266111
\(317\) 15.5513 0.873449 0.436724 0.899595i \(-0.356139\pi\)
0.436724 + 0.899595i \(0.356139\pi\)
\(318\) −52.1482 −2.92433
\(319\) 7.48543 0.419104
\(320\) −3.75899 −0.210134
\(321\) −8.33279 −0.465091
\(322\) 29.1686 1.62550
\(323\) 6.16460 0.343008
\(324\) −3.04575 −0.169208
\(325\) −24.9487 −1.38390
\(326\) −14.6980 −0.814048
\(327\) −25.2131 −1.39428
\(328\) −23.2481 −1.28366
\(329\) −16.3040 −0.898871
\(330\) −1.80366 −0.0992881
\(331\) −33.7134 −1.85305 −0.926527 0.376228i \(-0.877221\pi\)
−0.926527 + 0.376228i \(0.877221\pi\)
\(332\) 3.34236 0.183436
\(333\) −51.7475 −2.83575
\(334\) 16.4320 0.899118
\(335\) 4.41844 0.241405
\(336\) 3.16275 0.172542
\(337\) 9.27816 0.505414 0.252707 0.967543i \(-0.418679\pi\)
0.252707 + 0.967543i \(0.418679\pi\)
\(338\) −28.7498 −1.56378
\(339\) −27.7834 −1.50899
\(340\) −2.23947 −0.121452
\(341\) 3.19569 0.173056
\(342\) 25.9874 1.40524
\(343\) −19.3087 −1.04257
\(344\) −18.7050 −1.00851
\(345\) 5.78765 0.311597
\(346\) 59.1397 3.17937
\(347\) 22.4488 1.20512 0.602558 0.798075i \(-0.294148\pi\)
0.602558 + 0.798075i \(0.294148\pi\)
\(348\) 64.1689 3.43981
\(349\) 24.4644 1.30955 0.654773 0.755825i \(-0.272764\pi\)
0.654773 + 0.755825i \(0.272764\pi\)
\(350\) 19.8140 1.05910
\(351\) −23.9936 −1.28069
\(352\) −6.35008 −0.338461
\(353\) −19.1090 −1.01707 −0.508534 0.861042i \(-0.669812\pi\)
−0.508534 + 0.861042i \(0.669812\pi\)
\(354\) 20.1693 1.07199
\(355\) −1.33917 −0.0710756
\(356\) −43.5424 −2.30774
\(357\) 12.4797 0.660497
\(358\) 6.88539 0.363904
\(359\) 21.1199 1.11467 0.557333 0.830289i \(-0.311825\pi\)
0.557333 + 0.830289i \(0.311825\pi\)
\(360\) −3.32737 −0.175368
\(361\) −13.0015 −0.684288
\(362\) 32.3989 1.70285
\(363\) −2.77556 −0.145679
\(364\) 27.9946 1.46732
\(365\) −3.21344 −0.168199
\(366\) 63.4354 3.31582
\(367\) 10.5128 0.548764 0.274382 0.961621i \(-0.411527\pi\)
0.274382 + 0.961621i \(0.411527\pi\)
\(368\) 4.61731 0.240694
\(369\) 44.5325 2.31827
\(370\) 7.14910 0.371664
\(371\) −14.8787 −0.772461
\(372\) 27.3950 1.42037
\(373\) 18.8868 0.977922 0.488961 0.872306i \(-0.337376\pi\)
0.488961 + 0.872306i \(0.337376\pi\)
\(374\) −5.67780 −0.293592
\(375\) 7.92934 0.409470
\(376\) 22.4118 1.15580
\(377\) −37.9807 −1.95610
\(378\) 19.0555 0.980109
\(379\) 3.07004 0.157698 0.0788488 0.996887i \(-0.474876\pi\)
0.0788488 + 0.996887i \(0.474876\pi\)
\(380\) −2.17914 −0.111788
\(381\) −56.9279 −2.91651
\(382\) −15.4197 −0.788939
\(383\) −5.52189 −0.282155 −0.141078 0.989999i \(-0.545057\pi\)
−0.141078 + 0.989999i \(0.545057\pi\)
\(384\) −46.4484 −2.37031
\(385\) −0.514610 −0.0262269
\(386\) −52.1297 −2.65333
\(387\) 35.8300 1.82134
\(388\) −27.2112 −1.38144
\(389\) −24.8161 −1.25823 −0.629113 0.777314i \(-0.716582\pi\)
−0.629113 + 0.777314i \(0.716582\pi\)
\(390\) 9.15166 0.463412
\(391\) 18.2192 0.921383
\(392\) 9.35297 0.472396
\(393\) −31.8368 −1.60595
\(394\) −7.75314 −0.390598
\(395\) −0.00441220 −0.000222002 0
\(396\) −14.5278 −0.730048
\(397\) 3.47733 0.174522 0.0872611 0.996185i \(-0.472189\pi\)
0.0872611 + 0.996185i \(0.472189\pi\)
\(398\) 21.7482 1.09014
\(399\) 12.1435 0.607937
\(400\) 3.13649 0.156825
\(401\) 24.6427 1.23060 0.615300 0.788293i \(-0.289035\pi\)
0.615300 + 0.788293i \(0.289035\pi\)
\(402\) 96.0310 4.78959
\(403\) −16.2147 −0.807714
\(404\) −9.41588 −0.468458
\(405\) −0.284082 −0.0141161
\(406\) 30.1639 1.49701
\(407\) 11.0014 0.545319
\(408\) −17.1548 −0.849290
\(409\) 0.657742 0.0325233 0.0162616 0.999868i \(-0.494824\pi\)
0.0162616 + 0.999868i \(0.494824\pi\)
\(410\) −6.15232 −0.303841
\(411\) −47.9265 −2.36404
\(412\) 8.72493 0.429846
\(413\) 5.75459 0.283165
\(414\) 76.8044 3.77473
\(415\) 0.311747 0.0153030
\(416\) 32.2200 1.57971
\(417\) −4.75801 −0.233001
\(418\) −5.52485 −0.270229
\(419\) −13.2258 −0.646120 −0.323060 0.946378i \(-0.604712\pi\)
−0.323060 + 0.946378i \(0.604712\pi\)
\(420\) −4.41149 −0.215259
\(421\) 13.4481 0.655419 0.327709 0.944779i \(-0.393723\pi\)
0.327709 + 0.944779i \(0.393723\pi\)
\(422\) 1.37974 0.0671649
\(423\) −42.9304 −2.08735
\(424\) 20.4524 0.993257
\(425\) 12.3761 0.600329
\(426\) −29.1056 −1.41017
\(427\) 18.0990 0.875874
\(428\) 9.27250 0.448203
\(429\) 14.0830 0.679935
\(430\) −4.95003 −0.238712
\(431\) −1.75557 −0.0845629 −0.0422815 0.999106i \(-0.513463\pi\)
−0.0422815 + 0.999106i \(0.513463\pi\)
\(432\) 3.01643 0.145128
\(433\) 13.8354 0.664885 0.332443 0.943123i \(-0.392127\pi\)
0.332443 + 0.943123i \(0.392127\pi\)
\(434\) 12.8776 0.618143
\(435\) 5.98513 0.286965
\(436\) 28.0564 1.34366
\(437\) 17.7284 0.848063
\(438\) −69.8413 −3.33715
\(439\) 22.1007 1.05481 0.527404 0.849615i \(-0.323165\pi\)
0.527404 + 0.849615i \(0.323165\pi\)
\(440\) 0.707390 0.0337235
\(441\) −17.9159 −0.853138
\(442\) 28.8089 1.37030
\(443\) 33.1485 1.57493 0.787467 0.616357i \(-0.211392\pi\)
0.787467 + 0.616357i \(0.211392\pi\)
\(444\) 94.3094 4.47573
\(445\) −4.06126 −0.192522
\(446\) −63.9405 −3.02767
\(447\) 21.0359 0.994966
\(448\) −23.3098 −1.10128
\(449\) −9.06740 −0.427917 −0.213959 0.976843i \(-0.568636\pi\)
−0.213959 + 0.976843i \(0.568636\pi\)
\(450\) 52.1724 2.45943
\(451\) −9.46750 −0.445807
\(452\) 30.9167 1.45420
\(453\) 19.2910 0.906368
\(454\) −27.2885 −1.28071
\(455\) 2.61110 0.122410
\(456\) −16.6927 −0.781706
\(457\) 4.27152 0.199813 0.0999067 0.994997i \(-0.468146\pi\)
0.0999067 + 0.994997i \(0.468146\pi\)
\(458\) 20.3762 0.952116
\(459\) 11.9024 0.555554
\(460\) −6.44034 −0.300283
\(461\) 8.05656 0.375231 0.187616 0.982243i \(-0.439924\pi\)
0.187616 + 0.982243i \(0.439924\pi\)
\(462\) −11.1846 −0.520354
\(463\) 27.1442 1.26150 0.630748 0.775988i \(-0.282748\pi\)
0.630748 + 0.775988i \(0.282748\pi\)
\(464\) 4.77485 0.221667
\(465\) 2.55517 0.118493
\(466\) 20.0155 0.927201
\(467\) −4.10416 −0.189918 −0.0949589 0.995481i \(-0.530272\pi\)
−0.0949589 + 0.995481i \(0.530272\pi\)
\(468\) 73.7132 3.40739
\(469\) 27.3990 1.26517
\(470\) 5.93099 0.273576
\(471\) −33.1977 −1.52967
\(472\) −7.91035 −0.364103
\(473\) −7.61735 −0.350246
\(474\) −0.0958952 −0.00440461
\(475\) 12.0427 0.552557
\(476\) −13.8871 −0.636515
\(477\) −39.1772 −1.79380
\(478\) −2.28566 −0.104544
\(479\) 27.6482 1.26328 0.631638 0.775263i \(-0.282383\pi\)
0.631638 + 0.775263i \(0.282383\pi\)
\(480\) −5.07733 −0.231748
\(481\) −55.8205 −2.54519
\(482\) −24.4735 −1.11474
\(483\) 35.8896 1.63303
\(484\) 3.08857 0.140389
\(485\) −2.53803 −0.115246
\(486\) −38.1757 −1.73168
\(487\) 9.87200 0.447343 0.223671 0.974665i \(-0.428196\pi\)
0.223671 + 0.974665i \(0.428196\pi\)
\(488\) −24.8792 −1.12623
\(489\) −18.0847 −0.817819
\(490\) 2.47514 0.111816
\(491\) −15.5527 −0.701884 −0.350942 0.936397i \(-0.614139\pi\)
−0.350942 + 0.936397i \(0.614139\pi\)
\(492\) −81.1601 −3.65898
\(493\) 18.8408 0.848548
\(494\) 28.0328 1.26125
\(495\) −1.35503 −0.0609039
\(496\) 2.03848 0.0915306
\(497\) −8.30426 −0.372497
\(498\) 6.77554 0.303619
\(499\) 2.85994 0.128029 0.0640143 0.997949i \(-0.479610\pi\)
0.0640143 + 0.997949i \(0.479610\pi\)
\(500\) −8.82356 −0.394602
\(501\) 20.2182 0.903283
\(502\) 43.4252 1.93816
\(503\) 12.6095 0.562230 0.281115 0.959674i \(-0.409296\pi\)
0.281115 + 0.959674i \(0.409296\pi\)
\(504\) −20.6332 −0.919077
\(505\) −0.878233 −0.0390809
\(506\) −16.3284 −0.725886
\(507\) −35.3743 −1.57103
\(508\) 63.3479 2.81061
\(509\) −35.0444 −1.55331 −0.776657 0.629924i \(-0.783086\pi\)
−0.776657 + 0.629924i \(0.783086\pi\)
\(510\) −4.53980 −0.201026
\(511\) −19.9267 −0.881507
\(512\) −7.18338 −0.317463
\(513\) 11.5817 0.511345
\(514\) 17.8434 0.787039
\(515\) 0.813787 0.0358597
\(516\) −65.2998 −2.87466
\(517\) 9.12690 0.401401
\(518\) 44.3320 1.94784
\(519\) 72.7666 3.19410
\(520\) −3.58926 −0.157399
\(521\) 21.9940 0.963576 0.481788 0.876288i \(-0.339987\pi\)
0.481788 + 0.876288i \(0.339987\pi\)
\(522\) 79.4249 3.47633
\(523\) −7.76336 −0.339468 −0.169734 0.985490i \(-0.554291\pi\)
−0.169734 + 0.985490i \(0.554291\pi\)
\(524\) 35.4271 1.54764
\(525\) 24.3794 1.06401
\(526\) −25.8717 −1.12806
\(527\) 8.04353 0.350382
\(528\) −1.77049 −0.0770506
\(529\) 29.3953 1.27806
\(530\) 5.41247 0.235103
\(531\) 15.1525 0.657563
\(532\) −13.5130 −0.585863
\(533\) 48.0376 2.08074
\(534\) −88.2680 −3.81973
\(535\) 0.864860 0.0373912
\(536\) −37.6631 −1.62680
\(537\) 8.47190 0.365590
\(538\) 29.0836 1.25388
\(539\) 3.80887 0.164060
\(540\) −4.20740 −0.181057
\(541\) 3.16004 0.135861 0.0679303 0.997690i \(-0.478360\pi\)
0.0679303 + 0.997690i \(0.478360\pi\)
\(542\) 29.0297 1.24693
\(543\) 39.8642 1.71074
\(544\) −15.9831 −0.685271
\(545\) 2.61686 0.112094
\(546\) 56.7500 2.42868
\(547\) 1.00000 0.0427569
\(548\) 53.3314 2.27820
\(549\) 47.6569 2.03395
\(550\) −11.0917 −0.472953
\(551\) 18.3333 0.781023
\(552\) −49.3344 −2.09981
\(553\) −0.0273603 −0.00116348
\(554\) 49.9984 2.12423
\(555\) 8.79638 0.373385
\(556\) 5.29459 0.224540
\(557\) −9.88589 −0.418879 −0.209439 0.977822i \(-0.567164\pi\)
−0.209439 + 0.977822i \(0.567164\pi\)
\(558\) 33.9081 1.43545
\(559\) 38.6500 1.63472
\(560\) −0.328262 −0.0138716
\(561\) −6.98607 −0.294952
\(562\) −17.9241 −0.756081
\(563\) 32.8492 1.38443 0.692214 0.721692i \(-0.256635\pi\)
0.692214 + 0.721692i \(0.256635\pi\)
\(564\) 78.2404 3.29451
\(565\) 2.88364 0.121316
\(566\) −22.9894 −0.966316
\(567\) −1.76161 −0.0739805
\(568\) 11.4152 0.478969
\(569\) −11.0057 −0.461384 −0.230692 0.973027i \(-0.574099\pi\)
−0.230692 + 0.973027i \(0.574099\pi\)
\(570\) −4.41750 −0.185029
\(571\) −17.5138 −0.732930 −0.366465 0.930432i \(-0.619432\pi\)
−0.366465 + 0.930432i \(0.619432\pi\)
\(572\) −15.6712 −0.655247
\(573\) −18.9726 −0.792594
\(574\) −38.1509 −1.59239
\(575\) 35.5916 1.48427
\(576\) −61.3773 −2.55739
\(577\) 47.2193 1.96576 0.982882 0.184236i \(-0.0589812\pi\)
0.982882 + 0.184236i \(0.0589812\pi\)
\(578\) 24.0573 1.00065
\(579\) −64.1413 −2.66562
\(580\) −6.66009 −0.276545
\(581\) 1.93316 0.0802010
\(582\) −55.1618 −2.28653
\(583\) 8.32897 0.344951
\(584\) 27.3916 1.13347
\(585\) 6.87534 0.284260
\(586\) −5.34129 −0.220647
\(587\) −28.5617 −1.17887 −0.589433 0.807817i \(-0.700649\pi\)
−0.589433 + 0.807817i \(0.700649\pi\)
\(588\) 32.6516 1.34653
\(589\) 7.82684 0.322500
\(590\) −2.09337 −0.0861827
\(591\) −9.53960 −0.392407
\(592\) 7.01763 0.288423
\(593\) 35.0155 1.43791 0.718957 0.695054i \(-0.244620\pi\)
0.718957 + 0.695054i \(0.244620\pi\)
\(594\) −10.6671 −0.437678
\(595\) −1.29527 −0.0531009
\(596\) −23.4082 −0.958838
\(597\) 26.7594 1.09519
\(598\) 82.8495 3.38797
\(599\) −17.4246 −0.711950 −0.355975 0.934495i \(-0.615851\pi\)
−0.355975 + 0.934495i \(0.615851\pi\)
\(600\) −33.5124 −1.36814
\(601\) 33.5374 1.36802 0.684010 0.729472i \(-0.260234\pi\)
0.684010 + 0.729472i \(0.260234\pi\)
\(602\) −30.6954 −1.25105
\(603\) 72.1448 2.93796
\(604\) −21.4665 −0.873458
\(605\) 0.288075 0.0117119
\(606\) −19.0876 −0.775382
\(607\) −4.68848 −0.190300 −0.0951498 0.995463i \(-0.530333\pi\)
−0.0951498 + 0.995463i \(0.530333\pi\)
\(608\) −15.5526 −0.630740
\(609\) 37.1141 1.50394
\(610\) −6.58396 −0.266577
\(611\) −46.3094 −1.87348
\(612\) −36.5664 −1.47811
\(613\) 19.2799 0.778708 0.389354 0.921088i \(-0.372698\pi\)
0.389354 + 0.921088i \(0.372698\pi\)
\(614\) −44.9579 −1.81435
\(615\) −7.56992 −0.305249
\(616\) 4.38657 0.176740
\(617\) 5.77895 0.232652 0.116326 0.993211i \(-0.462888\pi\)
0.116326 + 0.993211i \(0.462888\pi\)
\(618\) 17.6869 0.711473
\(619\) −36.3348 −1.46042 −0.730209 0.683224i \(-0.760577\pi\)
−0.730209 + 0.683224i \(0.760577\pi\)
\(620\) −2.84333 −0.114191
\(621\) 34.2292 1.37357
\(622\) −60.9858 −2.44531
\(623\) −25.1841 −1.00898
\(624\) 8.98337 0.359622
\(625\) 23.7621 0.950483
\(626\) 8.75836 0.350055
\(627\) −6.79787 −0.271481
\(628\) 36.9415 1.47413
\(629\) 27.6905 1.10409
\(630\) −5.46032 −0.217544
\(631\) −22.0364 −0.877254 −0.438627 0.898669i \(-0.644535\pi\)
−0.438627 + 0.898669i \(0.644535\pi\)
\(632\) 0.0376099 0.00149604
\(633\) 1.69766 0.0674760
\(634\) −35.0804 −1.39322
\(635\) 5.90855 0.234474
\(636\) 71.4001 2.83120
\(637\) −19.3260 −0.765725
\(638\) −16.8855 −0.668505
\(639\) −21.8661 −0.865009
\(640\) 4.82088 0.190562
\(641\) −23.7688 −0.938812 −0.469406 0.882982i \(-0.655532\pi\)
−0.469406 + 0.882982i \(0.655532\pi\)
\(642\) 18.7970 0.741858
\(643\) −33.5561 −1.32332 −0.661662 0.749802i \(-0.730149\pi\)
−0.661662 + 0.749802i \(0.730149\pi\)
\(644\) −39.9370 −1.57374
\(645\) −6.09061 −0.239817
\(646\) −13.9060 −0.547125
\(647\) 25.8699 1.01705 0.508525 0.861047i \(-0.330191\pi\)
0.508525 + 0.861047i \(0.330191\pi\)
\(648\) 2.42153 0.0951268
\(649\) −3.22138 −0.126450
\(650\) 56.2788 2.20744
\(651\) 15.8448 0.621006
\(652\) 20.1242 0.788124
\(653\) 10.4800 0.410115 0.205057 0.978750i \(-0.434262\pi\)
0.205057 + 0.978750i \(0.434262\pi\)
\(654\) 56.8752 2.22400
\(655\) 3.30434 0.129111
\(656\) −6.03918 −0.235790
\(657\) −52.4694 −2.04703
\(658\) 36.7784 1.43377
\(659\) 5.39149 0.210023 0.105011 0.994471i \(-0.466512\pi\)
0.105011 + 0.994471i \(0.466512\pi\)
\(660\) 2.46953 0.0961261
\(661\) 37.8691 1.47294 0.736469 0.676471i \(-0.236492\pi\)
0.736469 + 0.676471i \(0.236492\pi\)
\(662\) 76.0501 2.95577
\(663\) 35.4470 1.37665
\(664\) −2.65735 −0.103125
\(665\) −1.26038 −0.0488753
\(666\) 116.731 4.52325
\(667\) 54.1830 2.09797
\(668\) −22.4983 −0.870485
\(669\) −78.6735 −3.04169
\(670\) −9.96706 −0.385061
\(671\) −10.1317 −0.391131
\(672\) −31.4849 −1.21456
\(673\) −35.0557 −1.35130 −0.675649 0.737223i \(-0.736137\pi\)
−0.675649 + 0.737223i \(0.736137\pi\)
\(674\) −20.9295 −0.806176
\(675\) 23.2515 0.894952
\(676\) 39.3636 1.51398
\(677\) −18.4429 −0.708818 −0.354409 0.935090i \(-0.615318\pi\)
−0.354409 + 0.935090i \(0.615318\pi\)
\(678\) 62.6735 2.40696
\(679\) −15.7385 −0.603987
\(680\) 1.78050 0.0682790
\(681\) −33.5763 −1.28665
\(682\) −7.20878 −0.276039
\(683\) −43.2287 −1.65410 −0.827051 0.562127i \(-0.809983\pi\)
−0.827051 + 0.562127i \(0.809983\pi\)
\(684\) −35.5813 −1.36048
\(685\) 4.97430 0.190058
\(686\) 43.5562 1.66298
\(687\) 25.0712 0.956527
\(688\) −4.85900 −0.185248
\(689\) −42.2608 −1.61001
\(690\) −13.0557 −0.497022
\(691\) −43.9096 −1.67040 −0.835201 0.549945i \(-0.814649\pi\)
−0.835201 + 0.549945i \(0.814649\pi\)
\(692\) −80.9727 −3.07812
\(693\) −8.40261 −0.319189
\(694\) −50.6397 −1.92226
\(695\) 0.493834 0.0187322
\(696\) −51.0177 −1.93382
\(697\) −23.8297 −0.902613
\(698\) −55.1863 −2.08883
\(699\) 24.6275 0.931496
\(700\) −27.1288 −1.02537
\(701\) 0.275808 0.0104171 0.00520856 0.999986i \(-0.498342\pi\)
0.00520856 + 0.999986i \(0.498342\pi\)
\(702\) 54.1245 2.04280
\(703\) 26.9445 1.01623
\(704\) 13.0487 0.491790
\(705\) 7.29759 0.274843
\(706\) 43.1058 1.62231
\(707\) −5.44598 −0.204817
\(708\) −27.6153 −1.03785
\(709\) 42.0342 1.57863 0.789313 0.613991i \(-0.210437\pi\)
0.789313 + 0.613991i \(0.210437\pi\)
\(710\) 3.02087 0.113371
\(711\) −0.0720428 −0.00270182
\(712\) 34.6185 1.29738
\(713\) 23.1318 0.866294
\(714\) −28.1516 −1.05355
\(715\) −1.46168 −0.0546637
\(716\) −9.42731 −0.352315
\(717\) −2.81232 −0.105028
\(718\) −47.6420 −1.77798
\(719\) 40.3075 1.50321 0.751607 0.659611i \(-0.229279\pi\)
0.751607 + 0.659611i \(0.229279\pi\)
\(720\) −0.864352 −0.0322125
\(721\) 5.04634 0.187936
\(722\) 29.3285 1.09149
\(723\) −30.1127 −1.11990
\(724\) −44.3598 −1.64862
\(725\) 36.8060 1.36694
\(726\) 6.26106 0.232370
\(727\) 10.3962 0.385575 0.192788 0.981240i \(-0.438247\pi\)
0.192788 + 0.981240i \(0.438247\pi\)
\(728\) −22.2572 −0.824908
\(729\) −44.0136 −1.63014
\(730\) 7.24883 0.268291
\(731\) −19.1729 −0.709134
\(732\) −86.8543 −3.21023
\(733\) −35.4616 −1.30980 −0.654901 0.755715i \(-0.727290\pi\)
−0.654901 + 0.755715i \(0.727290\pi\)
\(734\) −23.7146 −0.875323
\(735\) 3.04546 0.112333
\(736\) −45.9648 −1.69429
\(737\) −15.3378 −0.564975
\(738\) −100.456 −3.69783
\(739\) 41.3307 1.52037 0.760186 0.649705i \(-0.225108\pi\)
0.760186 + 0.649705i \(0.225108\pi\)
\(740\) −9.78837 −0.359828
\(741\) 34.4920 1.26710
\(742\) 33.5630 1.23214
\(743\) 33.3636 1.22399 0.611996 0.790861i \(-0.290367\pi\)
0.611996 + 0.790861i \(0.290367\pi\)
\(744\) −21.7805 −0.798512
\(745\) −2.18332 −0.0799906
\(746\) −42.6046 −1.55986
\(747\) 5.09023 0.186242
\(748\) 7.77391 0.284242
\(749\) 5.36305 0.195962
\(750\) −17.8869 −0.653137
\(751\) 20.1232 0.734308 0.367154 0.930160i \(-0.380332\pi\)
0.367154 + 0.930160i \(0.380332\pi\)
\(752\) 5.82192 0.212303
\(753\) 53.4312 1.94714
\(754\) 85.6763 3.12015
\(755\) −2.00221 −0.0728678
\(756\) −26.0903 −0.948896
\(757\) 12.8664 0.467636 0.233818 0.972280i \(-0.424878\pi\)
0.233818 + 0.972280i \(0.424878\pi\)
\(758\) −6.92536 −0.251540
\(759\) −20.0908 −0.729249
\(760\) 1.73253 0.0628456
\(761\) −53.4169 −1.93636 −0.968181 0.250252i \(-0.919487\pi\)
−0.968181 + 0.250252i \(0.919487\pi\)
\(762\) 128.417 4.65206
\(763\) 16.2273 0.587469
\(764\) 21.1123 0.763815
\(765\) −3.41060 −0.123310
\(766\) 12.4562 0.450061
\(767\) 16.3451 0.590188
\(768\) 32.3430 1.16708
\(769\) 9.15986 0.330313 0.165157 0.986267i \(-0.447187\pi\)
0.165157 + 0.986267i \(0.447187\pi\)
\(770\) 1.16085 0.0418341
\(771\) 21.9548 0.790684
\(772\) 71.3747 2.56883
\(773\) −12.3881 −0.445569 −0.222784 0.974868i \(-0.571515\pi\)
−0.222784 + 0.974868i \(0.571515\pi\)
\(774\) −80.8247 −2.90518
\(775\) 15.7132 0.564436
\(776\) 21.6343 0.776627
\(777\) 54.5469 1.95686
\(778\) 55.9797 2.00697
\(779\) −23.1877 −0.830786
\(780\) −12.5302 −0.448655
\(781\) 4.64867 0.166343
\(782\) −41.0985 −1.46968
\(783\) 35.3971 1.26499
\(784\) 2.42963 0.0867723
\(785\) 3.44559 0.122978
\(786\) 71.8169 2.56163
\(787\) 5.70568 0.203385 0.101693 0.994816i \(-0.467574\pi\)
0.101693 + 0.994816i \(0.467574\pi\)
\(788\) 10.6154 0.378159
\(789\) −31.8330 −1.13329
\(790\) 0.00995297 0.000354111 0
\(791\) 17.8816 0.635798
\(792\) 11.5504 0.410424
\(793\) 51.4079 1.82555
\(794\) −7.84411 −0.278377
\(795\) 6.65960 0.236192
\(796\) −29.7772 −1.05542
\(797\) 7.58111 0.268537 0.134268 0.990945i \(-0.457132\pi\)
0.134268 + 0.990945i \(0.457132\pi\)
\(798\) −27.3932 −0.969709
\(799\) 22.9724 0.812704
\(800\) −31.2234 −1.10392
\(801\) −66.3128 −2.34305
\(802\) −55.5887 −1.96291
\(803\) 11.1549 0.393646
\(804\) −131.483 −4.63706
\(805\) −3.72498 −0.131288
\(806\) 36.5770 1.28837
\(807\) 35.7849 1.25969
\(808\) 7.48613 0.263361
\(809\) −3.58109 −0.125904 −0.0629522 0.998017i \(-0.520052\pi\)
−0.0629522 + 0.998017i \(0.520052\pi\)
\(810\) 0.640827 0.0225164
\(811\) −24.6170 −0.864419 −0.432210 0.901773i \(-0.642266\pi\)
−0.432210 + 0.901773i \(0.642266\pi\)
\(812\) −41.2996 −1.44933
\(813\) 35.7187 1.25271
\(814\) −24.8168 −0.869827
\(815\) 1.87701 0.0657489
\(816\) −4.45632 −0.156002
\(817\) −18.6564 −0.652703
\(818\) −1.48373 −0.0518772
\(819\) 42.6344 1.48977
\(820\) 8.42361 0.294165
\(821\) 10.3674 0.361826 0.180913 0.983499i \(-0.442095\pi\)
0.180913 + 0.983499i \(0.442095\pi\)
\(822\) 108.112 3.77084
\(823\) −14.7998 −0.515890 −0.257945 0.966160i \(-0.583045\pi\)
−0.257945 + 0.966160i \(0.583045\pi\)
\(824\) −6.93678 −0.241654
\(825\) −13.6475 −0.475143
\(826\) −12.9811 −0.451671
\(827\) −52.8232 −1.83684 −0.918421 0.395606i \(-0.870535\pi\)
−0.918421 + 0.395606i \(0.870535\pi\)
\(828\) −105.159 −3.65452
\(829\) −13.7974 −0.479202 −0.239601 0.970871i \(-0.577017\pi\)
−0.239601 + 0.970871i \(0.577017\pi\)
\(830\) −0.703233 −0.0244096
\(831\) 61.5190 2.13407
\(832\) −66.2082 −2.29535
\(833\) 9.58692 0.332167
\(834\) 10.7330 0.371655
\(835\) −2.09845 −0.0726198
\(836\) 7.56449 0.261623
\(837\) 15.1117 0.522338
\(838\) 29.8345 1.03061
\(839\) −29.6222 −1.02267 −0.511336 0.859381i \(-0.670849\pi\)
−0.511336 + 0.859381i \(0.670849\pi\)
\(840\) 3.50737 0.121016
\(841\) 27.0317 0.932128
\(842\) −30.3360 −1.04545
\(843\) −22.0541 −0.759583
\(844\) −1.88911 −0.0650259
\(845\) 3.67150 0.126303
\(846\) 96.8419 3.32949
\(847\) 1.78637 0.0613805
\(848\) 5.31293 0.182447
\(849\) −28.2866 −0.970792
\(850\) −27.9178 −0.957574
\(851\) 79.6331 2.72979
\(852\) 39.8507 1.36526
\(853\) −41.9044 −1.43478 −0.717390 0.696671i \(-0.754664\pi\)
−0.717390 + 0.696671i \(0.754664\pi\)
\(854\) −40.8276 −1.39709
\(855\) −3.31872 −0.113498
\(856\) −7.37213 −0.251974
\(857\) −32.4509 −1.10850 −0.554252 0.832349i \(-0.686995\pi\)
−0.554252 + 0.832349i \(0.686995\pi\)
\(858\) −31.7683 −1.08455
\(859\) 19.4611 0.664005 0.332003 0.943278i \(-0.392276\pi\)
0.332003 + 0.943278i \(0.392276\pi\)
\(860\) 6.77746 0.231110
\(861\) −46.9416 −1.59976
\(862\) 3.96019 0.134885
\(863\) 25.8898 0.881300 0.440650 0.897679i \(-0.354748\pi\)
0.440650 + 0.897679i \(0.354748\pi\)
\(864\) −30.0282 −1.02158
\(865\) −7.55245 −0.256791
\(866\) −31.2096 −1.06055
\(867\) 29.6006 1.00529
\(868\) −17.6317 −0.598458
\(869\) 0.0153161 0.000519564 0
\(870\) −13.5012 −0.457732
\(871\) 77.8232 2.63694
\(872\) −22.3063 −0.755388
\(873\) −41.4412 −1.40257
\(874\) −39.9914 −1.35273
\(875\) −5.10339 −0.172526
\(876\) 95.6250 3.23087
\(877\) 34.2959 1.15809 0.579046 0.815295i \(-0.303425\pi\)
0.579046 + 0.815295i \(0.303425\pi\)
\(878\) −49.8544 −1.68250
\(879\) −6.57202 −0.221669
\(880\) 0.183759 0.00619452
\(881\) 44.9275 1.51365 0.756823 0.653620i \(-0.226750\pi\)
0.756823 + 0.653620i \(0.226750\pi\)
\(882\) 40.4144 1.36082
\(883\) −46.1259 −1.55226 −0.776130 0.630573i \(-0.782820\pi\)
−0.776130 + 0.630573i \(0.782820\pi\)
\(884\) −39.4444 −1.32666
\(885\) −2.57572 −0.0865819
\(886\) −74.7759 −2.51215
\(887\) 21.6909 0.728308 0.364154 0.931339i \(-0.381358\pi\)
0.364154 + 0.931339i \(0.381358\pi\)
\(888\) −74.9810 −2.51620
\(889\) 36.6393 1.22884
\(890\) 9.16133 0.307089
\(891\) 0.986136 0.0330368
\(892\) 87.5457 2.93125
\(893\) 22.3535 0.748032
\(894\) −47.4526 −1.58705
\(895\) −0.879299 −0.0293917
\(896\) 29.8946 0.998708
\(897\) 101.939 3.40366
\(898\) 20.4541 0.682562
\(899\) 23.9211 0.797813
\(900\) −71.4333 −2.38111
\(901\) 20.9640 0.698412
\(902\) 21.3566 0.711098
\(903\) −37.7682 −1.25685
\(904\) −24.5804 −0.817531
\(905\) −4.13751 −0.137535
\(906\) −43.5163 −1.44573
\(907\) −30.5769 −1.01529 −0.507645 0.861566i \(-0.669484\pi\)
−0.507645 + 0.861566i \(0.669484\pi\)
\(908\) 37.3628 1.23993
\(909\) −14.3399 −0.475624
\(910\) −5.89009 −0.195254
\(911\) 11.6300 0.385320 0.192660 0.981266i \(-0.438289\pi\)
0.192660 + 0.981266i \(0.438289\pi\)
\(912\) −4.33626 −0.143588
\(913\) −1.08217 −0.0358146
\(914\) −9.63564 −0.318719
\(915\) −8.10103 −0.267812
\(916\) −27.8986 −0.921795
\(917\) 20.4904 0.676653
\(918\) −26.8492 −0.886154
\(919\) −1.71864 −0.0566926 −0.0283463 0.999598i \(-0.509024\pi\)
−0.0283463 + 0.999598i \(0.509024\pi\)
\(920\) 5.12042 0.168815
\(921\) −55.3170 −1.82276
\(922\) −18.1739 −0.598525
\(923\) −23.5871 −0.776379
\(924\) 15.3137 0.503783
\(925\) 54.0940 1.77860
\(926\) −61.2314 −2.01219
\(927\) 13.2876 0.436422
\(928\) −47.5331 −1.56035
\(929\) −17.5276 −0.575063 −0.287531 0.957771i \(-0.592835\pi\)
−0.287531 + 0.957771i \(0.592835\pi\)
\(930\) −5.76392 −0.189007
\(931\) 9.32866 0.305734
\(932\) −27.4048 −0.897673
\(933\) −75.0380 −2.45663
\(934\) 9.25810 0.302934
\(935\) 0.725085 0.0237128
\(936\) −58.6059 −1.91559
\(937\) −2.75255 −0.0899220 −0.0449610 0.998989i \(-0.514316\pi\)
−0.0449610 + 0.998989i \(0.514316\pi\)
\(938\) −61.8063 −2.01805
\(939\) 10.7764 0.351676
\(940\) −8.12057 −0.264864
\(941\) −18.0014 −0.586828 −0.293414 0.955985i \(-0.594791\pi\)
−0.293414 + 0.955985i \(0.594791\pi\)
\(942\) 74.8869 2.43995
\(943\) −68.5301 −2.23165
\(944\) −2.05487 −0.0668804
\(945\) −2.43348 −0.0791612
\(946\) 17.1831 0.558671
\(947\) 41.8284 1.35924 0.679620 0.733564i \(-0.262145\pi\)
0.679620 + 0.733564i \(0.262145\pi\)
\(948\) 0.131297 0.00426434
\(949\) −56.5991 −1.83729
\(950\) −27.1657 −0.881373
\(951\) −43.1636 −1.39967
\(952\) 11.0410 0.357840
\(953\) −14.2687 −0.462208 −0.231104 0.972929i \(-0.574234\pi\)
−0.231104 + 0.972929i \(0.574234\pi\)
\(954\) 88.3754 2.86126
\(955\) 1.96917 0.0637209
\(956\) 3.12948 0.101215
\(957\) −20.7763 −0.671601
\(958\) −62.3683 −2.01503
\(959\) 30.8459 0.996067
\(960\) 10.4333 0.336734
\(961\) −20.7876 −0.670567
\(962\) 125.919 4.05979
\(963\) 14.1215 0.455060
\(964\) 33.5086 1.07924
\(965\) 6.65722 0.214304
\(966\) −80.9592 −2.60482
\(967\) −40.8331 −1.31310 −0.656552 0.754281i \(-0.727986\pi\)
−0.656552 + 0.754281i \(0.727986\pi\)
\(968\) −2.45557 −0.0789252
\(969\) −17.1102 −0.549660
\(970\) 5.72524 0.183826
\(971\) −40.6696 −1.30515 −0.652575 0.757724i \(-0.726311\pi\)
−0.652575 + 0.757724i \(0.726311\pi\)
\(972\) 52.2692 1.67654
\(973\) 3.06229 0.0981726
\(974\) −22.2691 −0.713548
\(975\) 69.2465 2.21766
\(976\) −6.46288 −0.206872
\(977\) −10.5141 −0.336376 −0.168188 0.985755i \(-0.553792\pi\)
−0.168188 + 0.985755i \(0.553792\pi\)
\(978\) 40.7952 1.30449
\(979\) 14.0979 0.450571
\(980\) −3.38891 −0.108255
\(981\) 42.7284 1.36421
\(982\) 35.0836 1.11956
\(983\) 21.6369 0.690111 0.345056 0.938582i \(-0.387860\pi\)
0.345056 + 0.938582i \(0.387860\pi\)
\(984\) 64.5266 2.05703
\(985\) 0.990115 0.0315477
\(986\) −42.5008 −1.35350
\(987\) 45.2528 1.44041
\(988\) −38.3818 −1.22109
\(989\) −55.1379 −1.75328
\(990\) 3.05665 0.0971467
\(991\) −35.8843 −1.13990 −0.569951 0.821679i \(-0.693038\pi\)
−0.569951 + 0.821679i \(0.693038\pi\)
\(992\) −20.2929 −0.644299
\(993\) 93.5734 2.96946
\(994\) 18.7326 0.594163
\(995\) −2.77736 −0.0880483
\(996\) −9.27691 −0.293950
\(997\) 15.6274 0.494925 0.247463 0.968897i \(-0.420403\pi\)
0.247463 + 0.968897i \(0.420403\pi\)
\(998\) −6.45141 −0.204216
\(999\) 52.0233 1.64594
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 6017.2.a.f.1.18 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.18 121 1.1 even 1 trivial