Properties

Label 4034.2.a.d.1.4
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 1.4
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.86609 q^{3} +1.00000 q^{4} +4.19184 q^{5} -2.86609 q^{6} -2.33387 q^{7} +1.00000 q^{8} +5.21449 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.86609 q^{3} +1.00000 q^{4} +4.19184 q^{5} -2.86609 q^{6} -2.33387 q^{7} +1.00000 q^{8} +5.21449 q^{9} +4.19184 q^{10} -0.675015 q^{11} -2.86609 q^{12} -1.98527 q^{13} -2.33387 q^{14} -12.0142 q^{15} +1.00000 q^{16} -6.70776 q^{17} +5.21449 q^{18} -4.86703 q^{19} +4.19184 q^{20} +6.68908 q^{21} -0.675015 q^{22} +2.94081 q^{23} -2.86609 q^{24} +12.5715 q^{25} -1.98527 q^{26} -6.34693 q^{27} -2.33387 q^{28} +4.30484 q^{29} -12.0142 q^{30} +4.10790 q^{31} +1.00000 q^{32} +1.93466 q^{33} -6.70776 q^{34} -9.78321 q^{35} +5.21449 q^{36} +2.03177 q^{37} -4.86703 q^{38} +5.68997 q^{39} +4.19184 q^{40} +10.3862 q^{41} +6.68908 q^{42} -0.266265 q^{43} -0.675015 q^{44} +21.8583 q^{45} +2.94081 q^{46} +4.61312 q^{47} -2.86609 q^{48} -1.55306 q^{49} +12.5715 q^{50} +19.2251 q^{51} -1.98527 q^{52} +4.75749 q^{53} -6.34693 q^{54} -2.82956 q^{55} -2.33387 q^{56} +13.9494 q^{57} +4.30484 q^{58} +3.51797 q^{59} -12.0142 q^{60} +7.78117 q^{61} +4.10790 q^{62} -12.1699 q^{63} +1.00000 q^{64} -8.32194 q^{65} +1.93466 q^{66} +4.54817 q^{67} -6.70776 q^{68} -8.42865 q^{69} -9.78321 q^{70} -5.83849 q^{71} +5.21449 q^{72} +14.6370 q^{73} +2.03177 q^{74} -36.0312 q^{75} -4.86703 q^{76} +1.57540 q^{77} +5.68997 q^{78} -12.7319 q^{79} +4.19184 q^{80} +2.54743 q^{81} +10.3862 q^{82} +5.69532 q^{83} +6.68908 q^{84} -28.1179 q^{85} -0.266265 q^{86} -12.3381 q^{87} -0.675015 q^{88} +4.51471 q^{89} +21.8583 q^{90} +4.63336 q^{91} +2.94081 q^{92} -11.7736 q^{93} +4.61312 q^{94} -20.4018 q^{95} -2.86609 q^{96} -2.04866 q^{97} -1.55306 q^{98} -3.51986 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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
\(3\) −2.86609 −1.65474 −0.827370 0.561658i \(-0.810164\pi\)
−0.827370 + 0.561658i \(0.810164\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.19184 1.87465 0.937324 0.348458i \(-0.113295\pi\)
0.937324 + 0.348458i \(0.113295\pi\)
\(6\) −2.86609 −1.17008
\(7\) −2.33387 −0.882119 −0.441060 0.897478i \(-0.645397\pi\)
−0.441060 + 0.897478i \(0.645397\pi\)
\(8\) 1.00000 0.353553
\(9\) 5.21449 1.73816
\(10\) 4.19184 1.32558
\(11\) −0.675015 −0.203525 −0.101762 0.994809i \(-0.532448\pi\)
−0.101762 + 0.994809i \(0.532448\pi\)
\(12\) −2.86609 −0.827370
\(13\) −1.98527 −0.550615 −0.275307 0.961356i \(-0.588780\pi\)
−0.275307 + 0.961356i \(0.588780\pi\)
\(14\) −2.33387 −0.623752
\(15\) −12.0142 −3.10206
\(16\) 1.00000 0.250000
\(17\) −6.70776 −1.62687 −0.813435 0.581656i \(-0.802405\pi\)
−0.813435 + 0.581656i \(0.802405\pi\)
\(18\) 5.21449 1.22907
\(19\) −4.86703 −1.11657 −0.558286 0.829648i \(-0.688541\pi\)
−0.558286 + 0.829648i \(0.688541\pi\)
\(20\) 4.19184 0.937324
\(21\) 6.68908 1.45968
\(22\) −0.675015 −0.143914
\(23\) 2.94081 0.613202 0.306601 0.951838i \(-0.400808\pi\)
0.306601 + 0.951838i \(0.400808\pi\)
\(24\) −2.86609 −0.585039
\(25\) 12.5715 2.51431
\(26\) −1.98527 −0.389343
\(27\) −6.34693 −1.22147
\(28\) −2.33387 −0.441060
\(29\) 4.30484 0.799389 0.399695 0.916648i \(-0.369116\pi\)
0.399695 + 0.916648i \(0.369116\pi\)
\(30\) −12.0142 −2.19348
\(31\) 4.10790 0.737801 0.368900 0.929469i \(-0.379734\pi\)
0.368900 + 0.929469i \(0.379734\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.93466 0.336781
\(34\) −6.70776 −1.15037
\(35\) −9.78321 −1.65366
\(36\) 5.21449 0.869082
\(37\) 2.03177 0.334021 0.167011 0.985955i \(-0.446589\pi\)
0.167011 + 0.985955i \(0.446589\pi\)
\(38\) −4.86703 −0.789536
\(39\) 5.68997 0.911124
\(40\) 4.19184 0.662788
\(41\) 10.3862 1.62205 0.811026 0.585010i \(-0.198909\pi\)
0.811026 + 0.585010i \(0.198909\pi\)
\(42\) 6.68908 1.03215
\(43\) −0.266265 −0.0406051 −0.0203025 0.999794i \(-0.506463\pi\)
−0.0203025 + 0.999794i \(0.506463\pi\)
\(44\) −0.675015 −0.101762
\(45\) 21.8583 3.25845
\(46\) 2.94081 0.433599
\(47\) 4.61312 0.672892 0.336446 0.941703i \(-0.390775\pi\)
0.336446 + 0.941703i \(0.390775\pi\)
\(48\) −2.86609 −0.413685
\(49\) −1.55306 −0.221866
\(50\) 12.5715 1.77788
\(51\) 19.2251 2.69205
\(52\) −1.98527 −0.275307
\(53\) 4.75749 0.653491 0.326746 0.945112i \(-0.394048\pi\)
0.326746 + 0.945112i \(0.394048\pi\)
\(54\) −6.34693 −0.863708
\(55\) −2.82956 −0.381537
\(56\) −2.33387 −0.311876
\(57\) 13.9494 1.84764
\(58\) 4.30484 0.565254
\(59\) 3.51797 0.458001 0.229001 0.973426i \(-0.426454\pi\)
0.229001 + 0.973426i \(0.426454\pi\)
\(60\) −12.0142 −1.55103
\(61\) 7.78117 0.996277 0.498138 0.867098i \(-0.334017\pi\)
0.498138 + 0.867098i \(0.334017\pi\)
\(62\) 4.10790 0.521704
\(63\) −12.1699 −1.53327
\(64\) 1.00000 0.125000
\(65\) −8.32194 −1.03221
\(66\) 1.93466 0.238140
\(67\) 4.54817 0.555647 0.277824 0.960632i \(-0.410387\pi\)
0.277824 + 0.960632i \(0.410387\pi\)
\(68\) −6.70776 −0.813435
\(69\) −8.42865 −1.01469
\(70\) −9.78321 −1.16932
\(71\) −5.83849 −0.692902 −0.346451 0.938068i \(-0.612613\pi\)
−0.346451 + 0.938068i \(0.612613\pi\)
\(72\) 5.21449 0.614534
\(73\) 14.6370 1.71313 0.856565 0.516040i \(-0.172594\pi\)
0.856565 + 0.516040i \(0.172594\pi\)
\(74\) 2.03177 0.236189
\(75\) −36.0312 −4.16052
\(76\) −4.86703 −0.558286
\(77\) 1.57540 0.179533
\(78\) 5.68997 0.644262
\(79\) −12.7319 −1.43245 −0.716225 0.697869i \(-0.754132\pi\)
−0.716225 + 0.697869i \(0.754132\pi\)
\(80\) 4.19184 0.468662
\(81\) 2.54743 0.283048
\(82\) 10.3862 1.14696
\(83\) 5.69532 0.625142 0.312571 0.949894i \(-0.398810\pi\)
0.312571 + 0.949894i \(0.398810\pi\)
\(84\) 6.68908 0.729839
\(85\) −28.1179 −3.04981
\(86\) −0.266265 −0.0287121
\(87\) −12.3381 −1.32278
\(88\) −0.675015 −0.0719569
\(89\) 4.51471 0.478558 0.239279 0.970951i \(-0.423089\pi\)
0.239279 + 0.970951i \(0.423089\pi\)
\(90\) 21.8583 2.30407
\(91\) 4.63336 0.485708
\(92\) 2.94081 0.306601
\(93\) −11.7736 −1.22087
\(94\) 4.61312 0.475807
\(95\) −20.4018 −2.09318
\(96\) −2.86609 −0.292519
\(97\) −2.04866 −0.208010 −0.104005 0.994577i \(-0.533166\pi\)
−0.104005 + 0.994577i \(0.533166\pi\)
\(98\) −1.55306 −0.156883
\(99\) −3.51986 −0.353759
\(100\) 12.5715 1.25715
\(101\) −6.24503 −0.621404 −0.310702 0.950507i \(-0.600564\pi\)
−0.310702 + 0.950507i \(0.600564\pi\)
\(102\) 19.2251 1.90356
\(103\) 5.35319 0.527465 0.263733 0.964596i \(-0.415046\pi\)
0.263733 + 0.964596i \(0.415046\pi\)
\(104\) −1.98527 −0.194672
\(105\) 28.0396 2.73638
\(106\) 4.75749 0.462088
\(107\) −11.8267 −1.14333 −0.571665 0.820487i \(-0.693702\pi\)
−0.571665 + 0.820487i \(0.693702\pi\)
\(108\) −6.34693 −0.610734
\(109\) 7.93604 0.760135 0.380067 0.924959i \(-0.375901\pi\)
0.380067 + 0.924959i \(0.375901\pi\)
\(110\) −2.82956 −0.269788
\(111\) −5.82325 −0.552718
\(112\) −2.33387 −0.220530
\(113\) 0.577304 0.0543082 0.0271541 0.999631i \(-0.491356\pi\)
0.0271541 + 0.999631i \(0.491356\pi\)
\(114\) 13.9494 1.30648
\(115\) 12.3274 1.14954
\(116\) 4.30484 0.399695
\(117\) −10.3522 −0.957058
\(118\) 3.51797 0.323856
\(119\) 15.6550 1.43509
\(120\) −12.0142 −1.09674
\(121\) −10.5444 −0.958578
\(122\) 7.78117 0.704474
\(123\) −29.7678 −2.68408
\(124\) 4.10790 0.368900
\(125\) 31.7387 2.83879
\(126\) −12.1699 −1.08418
\(127\) 6.21845 0.551798 0.275899 0.961187i \(-0.411024\pi\)
0.275899 + 0.961187i \(0.411024\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0.763141 0.0671908
\(130\) −8.32194 −0.729882
\(131\) 21.7917 1.90395 0.951973 0.306182i \(-0.0990515\pi\)
0.951973 + 0.306182i \(0.0990515\pi\)
\(132\) 1.93466 0.168390
\(133\) 11.3590 0.984950
\(134\) 4.54817 0.392902
\(135\) −26.6053 −2.28982
\(136\) −6.70776 −0.575186
\(137\) 15.5640 1.32972 0.664860 0.746968i \(-0.268491\pi\)
0.664860 + 0.746968i \(0.268491\pi\)
\(138\) −8.42865 −0.717494
\(139\) 11.2750 0.956331 0.478166 0.878270i \(-0.341302\pi\)
0.478166 + 0.878270i \(0.341302\pi\)
\(140\) −9.78321 −0.826832
\(141\) −13.2216 −1.11346
\(142\) −5.83849 −0.489956
\(143\) 1.34009 0.112064
\(144\) 5.21449 0.434541
\(145\) 18.0452 1.49857
\(146\) 14.6370 1.21137
\(147\) 4.45121 0.367130
\(148\) 2.03177 0.167011
\(149\) 2.17011 0.177782 0.0888911 0.996041i \(-0.471668\pi\)
0.0888911 + 0.996041i \(0.471668\pi\)
\(150\) −36.0312 −2.94193
\(151\) 12.5121 1.01822 0.509112 0.860700i \(-0.329974\pi\)
0.509112 + 0.860700i \(0.329974\pi\)
\(152\) −4.86703 −0.394768
\(153\) −34.9775 −2.82777
\(154\) 1.57540 0.126949
\(155\) 17.2197 1.38312
\(156\) 5.68997 0.455562
\(157\) 15.5108 1.23790 0.618948 0.785432i \(-0.287559\pi\)
0.618948 + 0.785432i \(0.287559\pi\)
\(158\) −12.7319 −1.01290
\(159\) −13.6354 −1.08136
\(160\) 4.19184 0.331394
\(161\) −6.86347 −0.540917
\(162\) 2.54743 0.200145
\(163\) −23.3727 −1.83069 −0.915345 0.402671i \(-0.868082\pi\)
−0.915345 + 0.402671i \(0.868082\pi\)
\(164\) 10.3862 0.811026
\(165\) 8.10978 0.631345
\(166\) 5.69532 0.442042
\(167\) 3.09247 0.239302 0.119651 0.992816i \(-0.461822\pi\)
0.119651 + 0.992816i \(0.461822\pi\)
\(168\) 6.68908 0.516074
\(169\) −9.05870 −0.696823
\(170\) −28.1179 −2.15654
\(171\) −25.3791 −1.94079
\(172\) −0.266265 −0.0203025
\(173\) −10.2048 −0.775858 −0.387929 0.921689i \(-0.626809\pi\)
−0.387929 + 0.921689i \(0.626809\pi\)
\(174\) −12.3381 −0.935347
\(175\) −29.3403 −2.21792
\(176\) −0.675015 −0.0508812
\(177\) −10.0828 −0.757873
\(178\) 4.51471 0.338392
\(179\) 6.40496 0.478729 0.239365 0.970930i \(-0.423061\pi\)
0.239365 + 0.970930i \(0.423061\pi\)
\(180\) 21.8583 1.62922
\(181\) 10.7629 0.800001 0.400000 0.916515i \(-0.369010\pi\)
0.400000 + 0.916515i \(0.369010\pi\)
\(182\) 4.63336 0.343447
\(183\) −22.3016 −1.64858
\(184\) 2.94081 0.216800
\(185\) 8.51687 0.626173
\(186\) −11.7736 −0.863284
\(187\) 4.52784 0.331108
\(188\) 4.61312 0.336446
\(189\) 14.8129 1.07748
\(190\) −20.4018 −1.48010
\(191\) −6.65398 −0.481465 −0.240732 0.970592i \(-0.577388\pi\)
−0.240732 + 0.970592i \(0.577388\pi\)
\(192\) −2.86609 −0.206842
\(193\) −12.7410 −0.917116 −0.458558 0.888664i \(-0.651634\pi\)
−0.458558 + 0.888664i \(0.651634\pi\)
\(194\) −2.04866 −0.147085
\(195\) 23.8514 1.70804
\(196\) −1.55306 −0.110933
\(197\) −10.1559 −0.723575 −0.361787 0.932261i \(-0.617833\pi\)
−0.361787 + 0.932261i \(0.617833\pi\)
\(198\) −3.51986 −0.250146
\(199\) 15.7480 1.11635 0.558173 0.829724i \(-0.311502\pi\)
0.558173 + 0.829724i \(0.311502\pi\)
\(200\) 12.5715 0.888942
\(201\) −13.0355 −0.919452
\(202\) −6.24503 −0.439399
\(203\) −10.0469 −0.705157
\(204\) 19.2251 1.34602
\(205\) 43.5373 3.04078
\(206\) 5.35319 0.372974
\(207\) 15.3348 1.06585
\(208\) −1.98527 −0.137654
\(209\) 3.28532 0.227250
\(210\) 28.0396 1.93491
\(211\) −4.05048 −0.278846 −0.139423 0.990233i \(-0.544525\pi\)
−0.139423 + 0.990233i \(0.544525\pi\)
\(212\) 4.75749 0.326746
\(213\) 16.7337 1.14657
\(214\) −11.8267 −0.808457
\(215\) −1.11614 −0.0761202
\(216\) −6.34693 −0.431854
\(217\) −9.58730 −0.650828
\(218\) 7.93604 0.537497
\(219\) −41.9510 −2.83478
\(220\) −2.82956 −0.190769
\(221\) 13.3167 0.895779
\(222\) −5.82325 −0.390831
\(223\) −8.33886 −0.558411 −0.279206 0.960231i \(-0.590071\pi\)
−0.279206 + 0.960231i \(0.590071\pi\)
\(224\) −2.33387 −0.155938
\(225\) 65.5542 4.37028
\(226\) 0.577304 0.0384017
\(227\) 12.2350 0.812063 0.406032 0.913859i \(-0.366912\pi\)
0.406032 + 0.913859i \(0.366912\pi\)
\(228\) 13.9494 0.923818
\(229\) 9.58349 0.633295 0.316647 0.948543i \(-0.397443\pi\)
0.316647 + 0.948543i \(0.397443\pi\)
\(230\) 12.3274 0.812847
\(231\) −4.51523 −0.297081
\(232\) 4.30484 0.282627
\(233\) −17.5840 −1.15196 −0.575982 0.817462i \(-0.695380\pi\)
−0.575982 + 0.817462i \(0.695380\pi\)
\(234\) −10.3522 −0.676742
\(235\) 19.3375 1.26144
\(236\) 3.51797 0.229001
\(237\) 36.4908 2.37033
\(238\) 15.6550 1.01476
\(239\) −0.716956 −0.0463761 −0.0231880 0.999731i \(-0.507382\pi\)
−0.0231880 + 0.999731i \(0.507382\pi\)
\(240\) −12.0142 −0.775514
\(241\) −16.7905 −1.08157 −0.540784 0.841161i \(-0.681872\pi\)
−0.540784 + 0.841161i \(0.681872\pi\)
\(242\) −10.5444 −0.677817
\(243\) 11.7396 0.753097
\(244\) 7.78117 0.498138
\(245\) −6.51018 −0.415920
\(246\) −29.7678 −1.89793
\(247\) 9.66236 0.614801
\(248\) 4.10790 0.260852
\(249\) −16.3233 −1.03445
\(250\) 31.7387 2.00733
\(251\) 21.6505 1.36657 0.683283 0.730154i \(-0.260552\pi\)
0.683283 + 0.730154i \(0.260552\pi\)
\(252\) −12.1699 −0.766634
\(253\) −1.98510 −0.124802
\(254\) 6.21845 0.390180
\(255\) 80.5884 5.04664
\(256\) 1.00000 0.0625000
\(257\) 22.2381 1.38718 0.693588 0.720372i \(-0.256029\pi\)
0.693588 + 0.720372i \(0.256029\pi\)
\(258\) 0.763141 0.0475111
\(259\) −4.74189 −0.294647
\(260\) −8.32194 −0.516105
\(261\) 22.4476 1.38947
\(262\) 21.7917 1.34629
\(263\) −3.17475 −0.195763 −0.0978816 0.995198i \(-0.531207\pi\)
−0.0978816 + 0.995198i \(0.531207\pi\)
\(264\) 1.93466 0.119070
\(265\) 19.9426 1.22507
\(266\) 11.3590 0.696465
\(267\) −12.9396 −0.791889
\(268\) 4.54817 0.277824
\(269\) 23.2201 1.41575 0.707876 0.706337i \(-0.249654\pi\)
0.707876 + 0.706337i \(0.249654\pi\)
\(270\) −26.6053 −1.61915
\(271\) 16.7033 1.01465 0.507327 0.861754i \(-0.330634\pi\)
0.507327 + 0.861754i \(0.330634\pi\)
\(272\) −6.70776 −0.406718
\(273\) −13.2796 −0.803720
\(274\) 15.5640 0.940254
\(275\) −8.48598 −0.511724
\(276\) −8.42865 −0.507345
\(277\) −28.9839 −1.74148 −0.870738 0.491747i \(-0.836358\pi\)
−0.870738 + 0.491747i \(0.836358\pi\)
\(278\) 11.2750 0.676228
\(279\) 21.4206 1.28242
\(280\) −9.78321 −0.584658
\(281\) 25.5445 1.52386 0.761930 0.647660i \(-0.224252\pi\)
0.761930 + 0.647660i \(0.224252\pi\)
\(282\) −13.2216 −0.787336
\(283\) −16.5337 −0.982826 −0.491413 0.870927i \(-0.663519\pi\)
−0.491413 + 0.870927i \(0.663519\pi\)
\(284\) −5.83849 −0.346451
\(285\) 58.4735 3.46367
\(286\) 1.34009 0.0792410
\(287\) −24.2400 −1.43084
\(288\) 5.21449 0.307267
\(289\) 27.9940 1.64671
\(290\) 18.0452 1.05965
\(291\) 5.87166 0.344203
\(292\) 14.6370 0.856565
\(293\) 4.91877 0.287358 0.143679 0.989624i \(-0.454107\pi\)
0.143679 + 0.989624i \(0.454107\pi\)
\(294\) 4.45121 0.259600
\(295\) 14.7468 0.858591
\(296\) 2.03177 0.118094
\(297\) 4.28428 0.248599
\(298\) 2.17011 0.125711
\(299\) −5.83831 −0.337638
\(300\) −36.0312 −2.08026
\(301\) 0.621428 0.0358185
\(302\) 12.5121 0.719993
\(303\) 17.8988 1.02826
\(304\) −4.86703 −0.279143
\(305\) 32.6174 1.86767
\(306\) −34.9775 −1.99953
\(307\) −27.2017 −1.55248 −0.776240 0.630437i \(-0.782876\pi\)
−0.776240 + 0.630437i \(0.782876\pi\)
\(308\) 1.57540 0.0897666
\(309\) −15.3427 −0.872818
\(310\) 17.2197 0.978012
\(311\) 22.4381 1.27235 0.636173 0.771546i \(-0.280516\pi\)
0.636173 + 0.771546i \(0.280516\pi\)
\(312\) 5.68997 0.322131
\(313\) −27.6891 −1.56508 −0.782540 0.622601i \(-0.786076\pi\)
−0.782540 + 0.622601i \(0.786076\pi\)
\(314\) 15.5108 0.875324
\(315\) −51.0144 −2.87434
\(316\) −12.7319 −0.716225
\(317\) −28.5233 −1.60203 −0.801015 0.598644i \(-0.795706\pi\)
−0.801015 + 0.598644i \(0.795706\pi\)
\(318\) −13.6354 −0.764636
\(319\) −2.90584 −0.162696
\(320\) 4.19184 0.234331
\(321\) 33.8964 1.89191
\(322\) −6.86347 −0.382486
\(323\) 32.6468 1.81652
\(324\) 2.54743 0.141524
\(325\) −24.9579 −1.38441
\(326\) −23.3727 −1.29449
\(327\) −22.7454 −1.25783
\(328\) 10.3862 0.573482
\(329\) −10.7664 −0.593571
\(330\) 8.10978 0.446428
\(331\) 9.85582 0.541725 0.270862 0.962618i \(-0.412691\pi\)
0.270862 + 0.962618i \(0.412691\pi\)
\(332\) 5.69532 0.312571
\(333\) 10.5947 0.580584
\(334\) 3.09247 0.169212
\(335\) 19.0652 1.04164
\(336\) 6.68908 0.364919
\(337\) −19.0226 −1.03623 −0.518115 0.855311i \(-0.673366\pi\)
−0.518115 + 0.855311i \(0.673366\pi\)
\(338\) −9.05870 −0.492729
\(339\) −1.65461 −0.0898659
\(340\) −28.1179 −1.52491
\(341\) −2.77290 −0.150161
\(342\) −25.3791 −1.37234
\(343\) 19.9617 1.07783
\(344\) −0.266265 −0.0143561
\(345\) −35.3316 −1.90219
\(346\) −10.2048 −0.548614
\(347\) 0.372005 0.0199703 0.00998513 0.999950i \(-0.496822\pi\)
0.00998513 + 0.999950i \(0.496822\pi\)
\(348\) −12.3381 −0.661391
\(349\) −22.1482 −1.18557 −0.592783 0.805363i \(-0.701971\pi\)
−0.592783 + 0.805363i \(0.701971\pi\)
\(350\) −29.3403 −1.56831
\(351\) 12.6004 0.672558
\(352\) −0.675015 −0.0359784
\(353\) 2.25416 0.119977 0.0599885 0.998199i \(-0.480894\pi\)
0.0599885 + 0.998199i \(0.480894\pi\)
\(354\) −10.0828 −0.535897
\(355\) −24.4740 −1.29895
\(356\) 4.51471 0.239279
\(357\) −44.8688 −2.37471
\(358\) 6.40496 0.338513
\(359\) 29.3350 1.54824 0.774121 0.633037i \(-0.218192\pi\)
0.774121 + 0.633037i \(0.218192\pi\)
\(360\) 21.8583 1.15203
\(361\) 4.68795 0.246734
\(362\) 10.7629 0.565686
\(363\) 30.2211 1.58620
\(364\) 4.63336 0.242854
\(365\) 61.3559 3.21152
\(366\) −22.3016 −1.16572
\(367\) −18.2816 −0.954293 −0.477146 0.878824i \(-0.658329\pi\)
−0.477146 + 0.878824i \(0.658329\pi\)
\(368\) 2.94081 0.153301
\(369\) 54.1588 2.81939
\(370\) 8.51687 0.442771
\(371\) −11.1034 −0.576457
\(372\) −11.7736 −0.610434
\(373\) −28.9312 −1.49800 −0.749001 0.662569i \(-0.769466\pi\)
−0.749001 + 0.662569i \(0.769466\pi\)
\(374\) 4.52784 0.234129
\(375\) −90.9660 −4.69747
\(376\) 4.61312 0.237903
\(377\) −8.54627 −0.440155
\(378\) 14.8129 0.761894
\(379\) 1.18879 0.0610638 0.0305319 0.999534i \(-0.490280\pi\)
0.0305319 + 0.999534i \(0.490280\pi\)
\(380\) −20.4018 −1.04659
\(381\) −17.8226 −0.913082
\(382\) −6.65398 −0.340447
\(383\) −6.34725 −0.324329 −0.162165 0.986764i \(-0.551848\pi\)
−0.162165 + 0.986764i \(0.551848\pi\)
\(384\) −2.86609 −0.146260
\(385\) 6.60381 0.336562
\(386\) −12.7410 −0.648499
\(387\) −1.38844 −0.0705782
\(388\) −2.04866 −0.104005
\(389\) 26.4943 1.34331 0.671656 0.740863i \(-0.265583\pi\)
0.671656 + 0.740863i \(0.265583\pi\)
\(390\) 23.8514 1.20776
\(391\) −19.7263 −0.997600
\(392\) −1.55306 −0.0784414
\(393\) −62.4569 −3.15054
\(394\) −10.1559 −0.511645
\(395\) −53.3701 −2.68534
\(396\) −3.51986 −0.176880
\(397\) −5.62513 −0.282317 −0.141159 0.989987i \(-0.545083\pi\)
−0.141159 + 0.989987i \(0.545083\pi\)
\(398\) 15.7480 0.789376
\(399\) −32.5559 −1.62984
\(400\) 12.5715 0.628577
\(401\) 21.8952 1.09340 0.546698 0.837330i \(-0.315885\pi\)
0.546698 + 0.837330i \(0.315885\pi\)
\(402\) −13.0355 −0.650151
\(403\) −8.15529 −0.406244
\(404\) −6.24503 −0.310702
\(405\) 10.6784 0.530616
\(406\) −10.0469 −0.498621
\(407\) −1.37148 −0.0679816
\(408\) 19.2251 0.951782
\(409\) 25.7435 1.27294 0.636468 0.771303i \(-0.280395\pi\)
0.636468 + 0.771303i \(0.280395\pi\)
\(410\) 43.5373 2.15016
\(411\) −44.6078 −2.20034
\(412\) 5.35319 0.263733
\(413\) −8.21048 −0.404012
\(414\) 15.3348 0.753667
\(415\) 23.8739 1.17192
\(416\) −1.98527 −0.0973359
\(417\) −32.3151 −1.58248
\(418\) 3.28532 0.160690
\(419\) −4.25727 −0.207981 −0.103991 0.994578i \(-0.533161\pi\)
−0.103991 + 0.994578i \(0.533161\pi\)
\(420\) 28.0396 1.36819
\(421\) −4.81894 −0.234861 −0.117430 0.993081i \(-0.537466\pi\)
−0.117430 + 0.993081i \(0.537466\pi\)
\(422\) −4.05048 −0.197174
\(423\) 24.0550 1.16960
\(424\) 4.75749 0.231044
\(425\) −84.3268 −4.09045
\(426\) 16.7337 0.810749
\(427\) −18.1602 −0.878835
\(428\) −11.8267 −0.571665
\(429\) −3.84082 −0.185436
\(430\) −1.11614 −0.0538251
\(431\) 3.30507 0.159200 0.0795999 0.996827i \(-0.474636\pi\)
0.0795999 + 0.996827i \(0.474636\pi\)
\(432\) −6.34693 −0.305367
\(433\) 39.0239 1.87537 0.937686 0.347485i \(-0.112964\pi\)
0.937686 + 0.347485i \(0.112964\pi\)
\(434\) −9.58730 −0.460205
\(435\) −51.7193 −2.47975
\(436\) 7.93604 0.380067
\(437\) −14.3130 −0.684685
\(438\) −41.9510 −2.00449
\(439\) 6.52392 0.311370 0.155685 0.987807i \(-0.450242\pi\)
0.155685 + 0.987807i \(0.450242\pi\)
\(440\) −2.82956 −0.134894
\(441\) −8.09841 −0.385639
\(442\) 13.3167 0.633411
\(443\) −21.4714 −1.02013 −0.510067 0.860134i \(-0.670380\pi\)
−0.510067 + 0.860134i \(0.670380\pi\)
\(444\) −5.82325 −0.276359
\(445\) 18.9249 0.897128
\(446\) −8.33886 −0.394856
\(447\) −6.21973 −0.294183
\(448\) −2.33387 −0.110265
\(449\) 12.1596 0.573849 0.286924 0.957953i \(-0.407367\pi\)
0.286924 + 0.957953i \(0.407367\pi\)
\(450\) 65.5542 3.09025
\(451\) −7.01085 −0.330128
\(452\) 0.577304 0.0271541
\(453\) −35.8610 −1.68490
\(454\) 12.2350 0.574215
\(455\) 19.4223 0.910532
\(456\) 13.9494 0.653238
\(457\) −2.82134 −0.131977 −0.0659884 0.997820i \(-0.521020\pi\)
−0.0659884 + 0.997820i \(0.521020\pi\)
\(458\) 9.58349 0.447807
\(459\) 42.5737 1.98717
\(460\) 12.3274 0.574769
\(461\) 24.5352 1.14272 0.571359 0.820700i \(-0.306417\pi\)
0.571359 + 0.820700i \(0.306417\pi\)
\(462\) −4.51523 −0.210068
\(463\) 22.8312 1.06105 0.530527 0.847668i \(-0.321994\pi\)
0.530527 + 0.847668i \(0.321994\pi\)
\(464\) 4.30484 0.199847
\(465\) −49.3532 −2.28870
\(466\) −17.5840 −0.814562
\(467\) 26.9331 1.24632 0.623158 0.782096i \(-0.285849\pi\)
0.623158 + 0.782096i \(0.285849\pi\)
\(468\) −10.3522 −0.478529
\(469\) −10.6148 −0.490147
\(470\) 19.3375 0.891970
\(471\) −44.4554 −2.04839
\(472\) 3.51797 0.161928
\(473\) 0.179733 0.00826414
\(474\) 36.4908 1.67608
\(475\) −61.1860 −2.80741
\(476\) 15.6550 0.717547
\(477\) 24.8079 1.13587
\(478\) −0.716956 −0.0327928
\(479\) −11.3564 −0.518889 −0.259445 0.965758i \(-0.583539\pi\)
−0.259445 + 0.965758i \(0.583539\pi\)
\(480\) −12.0142 −0.548371
\(481\) −4.03362 −0.183917
\(482\) −16.7905 −0.764784
\(483\) 19.6714 0.895078
\(484\) −10.5444 −0.479289
\(485\) −8.58767 −0.389946
\(486\) 11.7396 0.532520
\(487\) 5.28079 0.239295 0.119648 0.992816i \(-0.461824\pi\)
0.119648 + 0.992816i \(0.461824\pi\)
\(488\) 7.78117 0.352237
\(489\) 66.9883 3.02931
\(490\) −6.51018 −0.294100
\(491\) −29.4378 −1.32851 −0.664254 0.747507i \(-0.731251\pi\)
−0.664254 + 0.747507i \(0.731251\pi\)
\(492\) −29.7678 −1.34204
\(493\) −28.8758 −1.30050
\(494\) 9.66236 0.434730
\(495\) −14.7547 −0.663174
\(496\) 4.10790 0.184450
\(497\) 13.6263 0.611222
\(498\) −16.3233 −0.731465
\(499\) −17.5255 −0.784547 −0.392274 0.919849i \(-0.628311\pi\)
−0.392274 + 0.919849i \(0.628311\pi\)
\(500\) 31.7387 1.41940
\(501\) −8.86330 −0.395983
\(502\) 21.6505 0.966308
\(503\) −2.51695 −0.112225 −0.0561126 0.998424i \(-0.517871\pi\)
−0.0561126 + 0.998424i \(0.517871\pi\)
\(504\) −12.1699 −0.542092
\(505\) −26.1782 −1.16491
\(506\) −1.98510 −0.0882482
\(507\) 25.9631 1.15306
\(508\) 6.21845 0.275899
\(509\) −37.2868 −1.65271 −0.826355 0.563150i \(-0.809589\pi\)
−0.826355 + 0.563150i \(0.809589\pi\)
\(510\) 80.5884 3.56851
\(511\) −34.1608 −1.51118
\(512\) 1.00000 0.0441942
\(513\) 30.8907 1.36386
\(514\) 22.2381 0.980881
\(515\) 22.4397 0.988812
\(516\) 0.763141 0.0335954
\(517\) −3.11392 −0.136950
\(518\) −4.74189 −0.208347
\(519\) 29.2480 1.28384
\(520\) −8.32194 −0.364941
\(521\) 17.9478 0.786305 0.393153 0.919473i \(-0.371384\pi\)
0.393153 + 0.919473i \(0.371384\pi\)
\(522\) 22.4476 0.982503
\(523\) 35.2811 1.54273 0.771366 0.636391i \(-0.219574\pi\)
0.771366 + 0.636391i \(0.219574\pi\)
\(524\) 21.7917 0.951973
\(525\) 84.0921 3.67008
\(526\) −3.17475 −0.138425
\(527\) −27.5548 −1.20031
\(528\) 1.93466 0.0841951
\(529\) −14.3516 −0.623983
\(530\) 19.9426 0.866253
\(531\) 18.3444 0.796081
\(532\) 11.3590 0.492475
\(533\) −20.6194 −0.893126
\(534\) −12.9396 −0.559950
\(535\) −49.5757 −2.14334
\(536\) 4.54817 0.196451
\(537\) −18.3572 −0.792172
\(538\) 23.2201 1.00109
\(539\) 1.04834 0.0451552
\(540\) −26.6053 −1.14491
\(541\) 0.808670 0.0347674 0.0173837 0.999849i \(-0.494466\pi\)
0.0173837 + 0.999849i \(0.494466\pi\)
\(542\) 16.7033 0.717469
\(543\) −30.8475 −1.32379
\(544\) −6.70776 −0.287593
\(545\) 33.2666 1.42499
\(546\) −13.2796 −0.568316
\(547\) −35.5790 −1.52125 −0.760625 0.649192i \(-0.775107\pi\)
−0.760625 + 0.649192i \(0.775107\pi\)
\(548\) 15.5640 0.664860
\(549\) 40.5748 1.73169
\(550\) −8.48598 −0.361843
\(551\) −20.9518 −0.892576
\(552\) −8.42865 −0.358747
\(553\) 29.7146 1.26359
\(554\) −28.9839 −1.23141
\(555\) −24.4101 −1.03615
\(556\) 11.2750 0.478166
\(557\) 1.04732 0.0443764 0.0221882 0.999754i \(-0.492937\pi\)
0.0221882 + 0.999754i \(0.492937\pi\)
\(558\) 21.4206 0.906807
\(559\) 0.528608 0.0223578
\(560\) −9.78321 −0.413416
\(561\) −12.9772 −0.547898
\(562\) 25.5445 1.07753
\(563\) −43.1417 −1.81821 −0.909103 0.416572i \(-0.863232\pi\)
−0.909103 + 0.416572i \(0.863232\pi\)
\(564\) −13.2216 −0.556731
\(565\) 2.41997 0.101809
\(566\) −16.5337 −0.694963
\(567\) −5.94538 −0.249682
\(568\) −5.83849 −0.244978
\(569\) −14.5268 −0.608993 −0.304497 0.952513i \(-0.598488\pi\)
−0.304497 + 0.952513i \(0.598488\pi\)
\(570\) 58.4735 2.44918
\(571\) 21.7766 0.911324 0.455662 0.890153i \(-0.349403\pi\)
0.455662 + 0.890153i \(0.349403\pi\)
\(572\) 1.34009 0.0560319
\(573\) 19.0709 0.796699
\(574\) −24.2400 −1.01176
\(575\) 36.9706 1.54178
\(576\) 5.21449 0.217270
\(577\) −45.4087 −1.89039 −0.945194 0.326510i \(-0.894127\pi\)
−0.945194 + 0.326510i \(0.894127\pi\)
\(578\) 27.9940 1.16440
\(579\) 36.5169 1.51759
\(580\) 18.0452 0.749287
\(581\) −13.2921 −0.551450
\(582\) 5.87166 0.243388
\(583\) −3.21138 −0.133002
\(584\) 14.6370 0.605683
\(585\) −43.3947 −1.79415
\(586\) 4.91877 0.203193
\(587\) 0.811212 0.0334823 0.0167412 0.999860i \(-0.494671\pi\)
0.0167412 + 0.999860i \(0.494671\pi\)
\(588\) 4.45121 0.183565
\(589\) −19.9933 −0.823808
\(590\) 14.7468 0.607116
\(591\) 29.1076 1.19733
\(592\) 2.03177 0.0835053
\(593\) 9.59267 0.393924 0.196962 0.980411i \(-0.436892\pi\)
0.196962 + 0.980411i \(0.436892\pi\)
\(594\) 4.28428 0.175786
\(595\) 65.6234 2.69030
\(596\) 2.17011 0.0888911
\(597\) −45.1353 −1.84726
\(598\) −5.83831 −0.238746
\(599\) 31.6283 1.29230 0.646148 0.763212i \(-0.276379\pi\)
0.646148 + 0.763212i \(0.276379\pi\)
\(600\) −36.0312 −1.47097
\(601\) 10.2853 0.419548 0.209774 0.977750i \(-0.432727\pi\)
0.209774 + 0.977750i \(0.432727\pi\)
\(602\) 0.621428 0.0253275
\(603\) 23.7164 0.965806
\(604\) 12.5121 0.509112
\(605\) −44.2003 −1.79700
\(606\) 17.8988 0.727091
\(607\) −45.4036 −1.84287 −0.921437 0.388528i \(-0.872984\pi\)
−0.921437 + 0.388528i \(0.872984\pi\)
\(608\) −4.86703 −0.197384
\(609\) 28.7955 1.16685
\(610\) 32.6174 1.32064
\(611\) −9.15828 −0.370504
\(612\) −34.9775 −1.41388
\(613\) 43.7185 1.76577 0.882887 0.469586i \(-0.155597\pi\)
0.882887 + 0.469586i \(0.155597\pi\)
\(614\) −27.2017 −1.09777
\(615\) −124.782 −5.03170
\(616\) 1.57540 0.0634745
\(617\) 34.1578 1.37514 0.687571 0.726118i \(-0.258677\pi\)
0.687571 + 0.726118i \(0.258677\pi\)
\(618\) −15.3427 −0.617175
\(619\) −20.9780 −0.843177 −0.421588 0.906787i \(-0.638527\pi\)
−0.421588 + 0.906787i \(0.638527\pi\)
\(620\) 17.2197 0.691559
\(621\) −18.6652 −0.749007
\(622\) 22.4381 0.899685
\(623\) −10.5367 −0.422145
\(624\) 5.68997 0.227781
\(625\) 70.1859 2.80743
\(626\) −27.6891 −1.10668
\(627\) −9.41603 −0.376040
\(628\) 15.5108 0.618948
\(629\) −13.6286 −0.543410
\(630\) −51.0144 −2.03246
\(631\) −2.19076 −0.0872129 −0.0436064 0.999049i \(-0.513885\pi\)
−0.0436064 + 0.999049i \(0.513885\pi\)
\(632\) −12.7319 −0.506448
\(633\) 11.6090 0.461418
\(634\) −28.5233 −1.13281
\(635\) 26.0667 1.03443
\(636\) −13.6354 −0.540679
\(637\) 3.08324 0.122163
\(638\) −2.90584 −0.115043
\(639\) −30.4448 −1.20438
\(640\) 4.19184 0.165697
\(641\) −22.1513 −0.874925 −0.437463 0.899237i \(-0.644123\pi\)
−0.437463 + 0.899237i \(0.644123\pi\)
\(642\) 33.8964 1.33779
\(643\) 26.7731 1.05583 0.527914 0.849298i \(-0.322974\pi\)
0.527914 + 0.849298i \(0.322974\pi\)
\(644\) −6.86347 −0.270459
\(645\) 3.19897 0.125959
\(646\) 32.6468 1.28447
\(647\) −22.6579 −0.890774 −0.445387 0.895338i \(-0.646934\pi\)
−0.445387 + 0.895338i \(0.646934\pi\)
\(648\) 2.54743 0.100073
\(649\) −2.37469 −0.0932146
\(650\) −24.9579 −0.978929
\(651\) 27.4781 1.07695
\(652\) −23.3727 −0.915345
\(653\) 14.8451 0.580932 0.290466 0.956885i \(-0.406190\pi\)
0.290466 + 0.956885i \(0.406190\pi\)
\(654\) −22.7454 −0.889417
\(655\) 91.3472 3.56923
\(656\) 10.3862 0.405513
\(657\) 76.3244 2.97770
\(658\) −10.7664 −0.419718
\(659\) −17.5433 −0.683390 −0.341695 0.939811i \(-0.611001\pi\)
−0.341695 + 0.939811i \(0.611001\pi\)
\(660\) 8.10978 0.315673
\(661\) −51.0049 −1.98386 −0.991929 0.126791i \(-0.959532\pi\)
−0.991929 + 0.126791i \(0.959532\pi\)
\(662\) 9.85582 0.383057
\(663\) −38.1669 −1.48228
\(664\) 5.69532 0.221021
\(665\) 47.6151 1.84644
\(666\) 10.5947 0.410535
\(667\) 12.6597 0.490187
\(668\) 3.09247 0.119651
\(669\) 23.8999 0.924025
\(670\) 19.0652 0.736553
\(671\) −5.25241 −0.202767
\(672\) 6.68908 0.258037
\(673\) −4.87423 −0.187888 −0.0939438 0.995577i \(-0.529947\pi\)
−0.0939438 + 0.995577i \(0.529947\pi\)
\(674\) −19.0226 −0.732725
\(675\) −79.7907 −3.07115
\(676\) −9.05870 −0.348412
\(677\) 5.70616 0.219305 0.109653 0.993970i \(-0.465026\pi\)
0.109653 + 0.993970i \(0.465026\pi\)
\(678\) −1.65461 −0.0635448
\(679\) 4.78131 0.183490
\(680\) −28.1179 −1.07827
\(681\) −35.0666 −1.34375
\(682\) −2.77290 −0.106180
\(683\) 26.2411 1.00409 0.502044 0.864842i \(-0.332582\pi\)
0.502044 + 0.864842i \(0.332582\pi\)
\(684\) −25.3791 −0.970393
\(685\) 65.2417 2.49276
\(686\) 19.9617 0.762142
\(687\) −27.4672 −1.04794
\(688\) −0.266265 −0.0101513
\(689\) −9.44490 −0.359822
\(690\) −35.3316 −1.34505
\(691\) 14.9282 0.567894 0.283947 0.958840i \(-0.408356\pi\)
0.283947 + 0.958840i \(0.408356\pi\)
\(692\) −10.2048 −0.387929
\(693\) 8.21489 0.312058
\(694\) 0.372005 0.0141211
\(695\) 47.2629 1.79279
\(696\) −12.3381 −0.467674
\(697\) −69.6682 −2.63887
\(698\) −22.1482 −0.838321
\(699\) 50.3973 1.90620
\(700\) −29.3403 −1.10896
\(701\) 38.7391 1.46316 0.731578 0.681758i \(-0.238784\pi\)
0.731578 + 0.681758i \(0.238784\pi\)
\(702\) 12.6004 0.475571
\(703\) −9.88869 −0.372959
\(704\) −0.675015 −0.0254406
\(705\) −55.4229 −2.08735
\(706\) 2.25416 0.0848365
\(707\) 14.5751 0.548152
\(708\) −10.0828 −0.378936
\(709\) −22.6710 −0.851429 −0.425715 0.904858i \(-0.639977\pi\)
−0.425715 + 0.904858i \(0.639977\pi\)
\(710\) −24.4740 −0.918495
\(711\) −66.3904 −2.48983
\(712\) 4.51471 0.169196
\(713\) 12.0806 0.452421
\(714\) −44.8688 −1.67917
\(715\) 5.61744 0.210080
\(716\) 6.40496 0.239365
\(717\) 2.05486 0.0767403
\(718\) 29.3350 1.09477
\(719\) −31.9796 −1.19264 −0.596319 0.802747i \(-0.703371\pi\)
−0.596319 + 0.802747i \(0.703371\pi\)
\(720\) 21.8583 0.814611
\(721\) −12.4936 −0.465287
\(722\) 4.68795 0.174467
\(723\) 48.1230 1.78971
\(724\) 10.7629 0.400000
\(725\) 54.1185 2.00991
\(726\) 30.2211 1.12161
\(727\) −21.9154 −0.812798 −0.406399 0.913696i \(-0.633216\pi\)
−0.406399 + 0.913696i \(0.633216\pi\)
\(728\) 4.63336 0.171724
\(729\) −41.2891 −1.52923
\(730\) 61.3559 2.27088
\(731\) 1.78604 0.0660592
\(732\) −22.3016 −0.824289
\(733\) −13.0679 −0.482673 −0.241336 0.970442i \(-0.577586\pi\)
−0.241336 + 0.970442i \(0.577586\pi\)
\(734\) −18.2816 −0.674787
\(735\) 18.6588 0.688240
\(736\) 2.94081 0.108400
\(737\) −3.07009 −0.113088
\(738\) 54.1588 1.99361
\(739\) −41.3654 −1.52165 −0.760826 0.648956i \(-0.775206\pi\)
−0.760826 + 0.648956i \(0.775206\pi\)
\(740\) 8.51687 0.313086
\(741\) −27.6932 −1.01734
\(742\) −11.1034 −0.407617
\(743\) −26.9462 −0.988560 −0.494280 0.869303i \(-0.664568\pi\)
−0.494280 + 0.869303i \(0.664568\pi\)
\(744\) −11.7736 −0.431642
\(745\) 9.09675 0.333279
\(746\) −28.9312 −1.05925
\(747\) 29.6982 1.08660
\(748\) 4.52784 0.165554
\(749\) 27.6020 1.00855
\(750\) −90.9660 −3.32161
\(751\) −19.8725 −0.725157 −0.362578 0.931953i \(-0.618103\pi\)
−0.362578 + 0.931953i \(0.618103\pi\)
\(752\) 4.61312 0.168223
\(753\) −62.0523 −2.26131
\(754\) −8.54627 −0.311237
\(755\) 52.4489 1.90881
\(756\) 14.8129 0.538740
\(757\) −13.7202 −0.498668 −0.249334 0.968418i \(-0.580212\pi\)
−0.249334 + 0.968418i \(0.580212\pi\)
\(758\) 1.18879 0.0431786
\(759\) 5.68947 0.206515
\(760\) −20.4018 −0.740051
\(761\) −18.7184 −0.678540 −0.339270 0.940689i \(-0.610180\pi\)
−0.339270 + 0.940689i \(0.610180\pi\)
\(762\) −17.8226 −0.645646
\(763\) −18.5217 −0.670530
\(764\) −6.65398 −0.240732
\(765\) −146.620 −5.30107
\(766\) −6.34725 −0.229335
\(767\) −6.98412 −0.252182
\(768\) −2.86609 −0.103421
\(769\) 13.4883 0.486400 0.243200 0.969976i \(-0.421803\pi\)
0.243200 + 0.969976i \(0.421803\pi\)
\(770\) 6.60381 0.237985
\(771\) −63.7365 −2.29541
\(772\) −12.7410 −0.458558
\(773\) 26.6255 0.957652 0.478826 0.877910i \(-0.341062\pi\)
0.478826 + 0.877910i \(0.341062\pi\)
\(774\) −1.38844 −0.0499064
\(775\) 51.6426 1.85506
\(776\) −2.04866 −0.0735427
\(777\) 13.5907 0.487564
\(778\) 26.4943 0.949866
\(779\) −50.5499 −1.81114
\(780\) 23.8514 0.854019
\(781\) 3.94107 0.141023
\(782\) −19.7263 −0.705410
\(783\) −27.3226 −0.976428
\(784\) −1.55306 −0.0554664
\(785\) 65.0188 2.32062
\(786\) −62.4569 −2.22776
\(787\) −18.7897 −0.669779 −0.334890 0.942257i \(-0.608699\pi\)
−0.334890 + 0.942257i \(0.608699\pi\)
\(788\) −10.1559 −0.361787
\(789\) 9.09912 0.323937
\(790\) −53.3701 −1.89882
\(791\) −1.34735 −0.0479063
\(792\) −3.51986 −0.125073
\(793\) −15.4477 −0.548565
\(794\) −5.62513 −0.199628
\(795\) −57.1575 −2.02717
\(796\) 15.7480 0.558173
\(797\) −7.13496 −0.252733 −0.126367 0.991984i \(-0.540332\pi\)
−0.126367 + 0.991984i \(0.540332\pi\)
\(798\) −32.5559 −1.15247
\(799\) −30.9437 −1.09471
\(800\) 12.5715 0.444471
\(801\) 23.5419 0.831812
\(802\) 21.8952 0.773148
\(803\) −9.88019 −0.348664
\(804\) −13.0355 −0.459726
\(805\) −28.7706 −1.01403
\(806\) −8.15529 −0.287258
\(807\) −66.5509 −2.34270
\(808\) −6.24503 −0.219699
\(809\) −24.7847 −0.871384 −0.435692 0.900096i \(-0.643496\pi\)
−0.435692 + 0.900096i \(0.643496\pi\)
\(810\) 10.6784 0.375202
\(811\) 31.2352 1.09682 0.548408 0.836211i \(-0.315234\pi\)
0.548408 + 0.836211i \(0.315234\pi\)
\(812\) −10.0469 −0.352578
\(813\) −47.8733 −1.67899
\(814\) −1.37148 −0.0480703
\(815\) −97.9746 −3.43190
\(816\) 19.2251 0.673012
\(817\) 1.29592 0.0453385
\(818\) 25.7435 0.900102
\(819\) 24.1606 0.844240
\(820\) 43.5373 1.52039
\(821\) 54.8782 1.91526 0.957631 0.287999i \(-0.0929900\pi\)
0.957631 + 0.287999i \(0.0929900\pi\)
\(822\) −44.6078 −1.55588
\(823\) 53.2055 1.85463 0.927314 0.374283i \(-0.122111\pi\)
0.927314 + 0.374283i \(0.122111\pi\)
\(824\) 5.35319 0.186487
\(825\) 24.3216 0.846770
\(826\) −8.21048 −0.285679
\(827\) 35.9683 1.25074 0.625369 0.780329i \(-0.284948\pi\)
0.625369 + 0.780329i \(0.284948\pi\)
\(828\) 15.3348 0.532923
\(829\) 3.71339 0.128971 0.0644857 0.997919i \(-0.479459\pi\)
0.0644857 + 0.997919i \(0.479459\pi\)
\(830\) 23.8739 0.828674
\(831\) 83.0707 2.88169
\(832\) −1.98527 −0.0688268
\(833\) 10.4175 0.360947
\(834\) −32.3151 −1.11898
\(835\) 12.9631 0.448608
\(836\) 3.28532 0.113625
\(837\) −26.0726 −0.901200
\(838\) −4.25727 −0.147065
\(839\) −1.44433 −0.0498637 −0.0249319 0.999689i \(-0.507937\pi\)
−0.0249319 + 0.999689i \(0.507937\pi\)
\(840\) 28.0396 0.967457
\(841\) −10.4683 −0.360977
\(842\) −4.81894 −0.166072
\(843\) −73.2130 −2.52159
\(844\) −4.05048 −0.139423
\(845\) −37.9727 −1.30630
\(846\) 24.0550 0.827030
\(847\) 24.6091 0.845580
\(848\) 4.75749 0.163373
\(849\) 47.3871 1.62632
\(850\) −84.3268 −2.89239
\(851\) 5.97507 0.204823
\(852\) 16.7337 0.573286
\(853\) 39.2726 1.34467 0.672334 0.740248i \(-0.265292\pi\)
0.672334 + 0.740248i \(0.265292\pi\)
\(854\) −18.1602 −0.621430
\(855\) −106.385 −3.63829
\(856\) −11.8267 −0.404228
\(857\) −15.3486 −0.524298 −0.262149 0.965027i \(-0.584431\pi\)
−0.262149 + 0.965027i \(0.584431\pi\)
\(858\) −3.84082 −0.131123
\(859\) 8.71946 0.297504 0.148752 0.988875i \(-0.452474\pi\)
0.148752 + 0.988875i \(0.452474\pi\)
\(860\) −1.11614 −0.0380601
\(861\) 69.4742 2.36767
\(862\) 3.30507 0.112571
\(863\) −11.9056 −0.405270 −0.202635 0.979254i \(-0.564951\pi\)
−0.202635 + 0.979254i \(0.564951\pi\)
\(864\) −6.34693 −0.215927
\(865\) −42.7770 −1.45446
\(866\) 39.0239 1.32609
\(867\) −80.2335 −2.72487
\(868\) −9.58730 −0.325414
\(869\) 8.59423 0.291539
\(870\) −51.7193 −1.75345
\(871\) −9.02934 −0.305948
\(872\) 7.93604 0.268748
\(873\) −10.6827 −0.361556
\(874\) −14.3130 −0.484145
\(875\) −74.0739 −2.50416
\(876\) −41.9510 −1.41739
\(877\) 11.4537 0.386764 0.193382 0.981123i \(-0.438054\pi\)
0.193382 + 0.981123i \(0.438054\pi\)
\(878\) 6.52392 0.220172
\(879\) −14.0977 −0.475502
\(880\) −2.82956 −0.0953844
\(881\) −38.4270 −1.29464 −0.647319 0.762219i \(-0.724110\pi\)
−0.647319 + 0.762219i \(0.724110\pi\)
\(882\) −8.09841 −0.272688
\(883\) 4.64106 0.156184 0.0780920 0.996946i \(-0.475117\pi\)
0.0780920 + 0.996946i \(0.475117\pi\)
\(884\) 13.3167 0.447889
\(885\) −42.2657 −1.42074
\(886\) −21.4714 −0.721344
\(887\) 43.4295 1.45822 0.729110 0.684397i \(-0.239934\pi\)
0.729110 + 0.684397i \(0.239934\pi\)
\(888\) −5.82325 −0.195415
\(889\) −14.5130 −0.486752
\(890\) 18.9249 0.634365
\(891\) −1.71956 −0.0576073
\(892\) −8.33886 −0.279206
\(893\) −22.4522 −0.751333
\(894\) −6.21973 −0.208019
\(895\) 26.8486 0.897449
\(896\) −2.33387 −0.0779691
\(897\) 16.7331 0.558703
\(898\) 12.1596 0.405772
\(899\) 17.6839 0.589790
\(900\) 65.5542 2.18514
\(901\) −31.9121 −1.06315
\(902\) −7.01085 −0.233436
\(903\) −1.78107 −0.0592703
\(904\) 0.577304 0.0192009
\(905\) 45.1164 1.49972
\(906\) −35.8610 −1.19140
\(907\) −12.1002 −0.401781 −0.200891 0.979614i \(-0.564384\pi\)
−0.200891 + 0.979614i \(0.564384\pi\)
\(908\) 12.2350 0.406032
\(909\) −32.5647 −1.08010
\(910\) 19.4223 0.643843
\(911\) −41.3820 −1.37105 −0.685524 0.728050i \(-0.740427\pi\)
−0.685524 + 0.728050i \(0.740427\pi\)
\(912\) 13.9494 0.461909
\(913\) −3.84443 −0.127232
\(914\) −2.82134 −0.0933217
\(915\) −93.4846 −3.09051
\(916\) 9.58349 0.316647
\(917\) −50.8589 −1.67951
\(918\) 42.5737 1.40514
\(919\) 34.6940 1.14445 0.572225 0.820097i \(-0.306081\pi\)
0.572225 + 0.820097i \(0.306081\pi\)
\(920\) 12.3274 0.406423
\(921\) 77.9625 2.56895
\(922\) 24.5352 0.808023
\(923\) 11.5910 0.381522
\(924\) −4.51523 −0.148540
\(925\) 25.5425 0.839832
\(926\) 22.8312 0.750278
\(927\) 27.9141 0.916821
\(928\) 4.30484 0.141313
\(929\) −35.0234 −1.14908 −0.574540 0.818476i \(-0.694819\pi\)
−0.574540 + 0.818476i \(0.694819\pi\)
\(930\) −49.3532 −1.61835
\(931\) 7.55878 0.247729
\(932\) −17.5840 −0.575982
\(933\) −64.3096 −2.10540
\(934\) 26.9331 0.881279
\(935\) 18.9800 0.620712
\(936\) −10.3522 −0.338371
\(937\) −53.7612 −1.75630 −0.878151 0.478384i \(-0.841223\pi\)
−0.878151 + 0.478384i \(0.841223\pi\)
\(938\) −10.6148 −0.346586
\(939\) 79.3595 2.58980
\(940\) 19.3375 0.630718
\(941\) −13.5022 −0.440160 −0.220080 0.975482i \(-0.570632\pi\)
−0.220080 + 0.975482i \(0.570632\pi\)
\(942\) −44.4554 −1.44843
\(943\) 30.5439 0.994646
\(944\) 3.51797 0.114500
\(945\) 62.0934 2.01990
\(946\) 0.179733 0.00584363
\(947\) 57.4128 1.86566 0.932832 0.360312i \(-0.117330\pi\)
0.932832 + 0.360312i \(0.117330\pi\)
\(948\) 36.4908 1.18517
\(949\) −29.0584 −0.943274
\(950\) −61.1860 −1.98514
\(951\) 81.7505 2.65094
\(952\) 15.6550 0.507382
\(953\) −20.8615 −0.675772 −0.337886 0.941187i \(-0.609712\pi\)
−0.337886 + 0.941187i \(0.609712\pi\)
\(954\) 24.8079 0.803185
\(955\) −27.8924 −0.902578
\(956\) −0.716956 −0.0231880
\(957\) 8.32839 0.269219
\(958\) −11.3564 −0.366910
\(959\) −36.3243 −1.17297
\(960\) −12.0142 −0.387757
\(961\) −14.1252 −0.455650
\(962\) −4.03362 −0.130049
\(963\) −61.6702 −1.98730
\(964\) −16.7905 −0.540784
\(965\) −53.4082 −1.71927
\(966\) 19.6714 0.632915
\(967\) −39.5217 −1.27093 −0.635465 0.772129i \(-0.719192\pi\)
−0.635465 + 0.772129i \(0.719192\pi\)
\(968\) −10.5444 −0.338908
\(969\) −93.5689 −3.00587
\(970\) −8.58767 −0.275733
\(971\) 4.17106 0.133856 0.0669279 0.997758i \(-0.478680\pi\)
0.0669279 + 0.997758i \(0.478680\pi\)
\(972\) 11.7396 0.376548
\(973\) −26.3143 −0.843598
\(974\) 5.28079 0.169207
\(975\) 71.5316 2.29085
\(976\) 7.78117 0.249069
\(977\) −49.3663 −1.57937 −0.789684 0.613513i \(-0.789756\pi\)
−0.789684 + 0.613513i \(0.789756\pi\)
\(978\) 66.9883 2.14205
\(979\) −3.04750 −0.0973984
\(980\) −6.51018 −0.207960
\(981\) 41.3824 1.32124
\(982\) −29.4378 −0.939397
\(983\) −15.8263 −0.504780 −0.252390 0.967626i \(-0.581217\pi\)
−0.252390 + 0.967626i \(0.581217\pi\)
\(984\) −29.7678 −0.948964
\(985\) −42.5717 −1.35645
\(986\) −28.8758 −0.919594
\(987\) 30.8575 0.982206
\(988\) 9.66236 0.307401
\(989\) −0.783037 −0.0248991
\(990\) −14.7547 −0.468935
\(991\) 47.4299 1.50666 0.753330 0.657642i \(-0.228446\pi\)
0.753330 + 0.657642i \(0.228446\pi\)
\(992\) 4.10790 0.130426
\(993\) −28.2477 −0.896413
\(994\) 13.6263 0.432199
\(995\) 66.0132 2.09276
\(996\) −16.3233 −0.517224
\(997\) 10.3279 0.327088 0.163544 0.986536i \(-0.447707\pi\)
0.163544 + 0.986536i \(0.447707\pi\)
\(998\) −17.5255 −0.554759
\(999\) −12.8955 −0.407996
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.1.4 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.4 52 1.1 even 1 trivial