Properties

Label 8007.2.a.f.1.40
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.40
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.85165 q^{2} -1.00000 q^{3} +1.42859 q^{4} +1.52272 q^{5} -1.85165 q^{6} +0.592895 q^{7} -1.05805 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.85165 q^{2} -1.00000 q^{3} +1.42859 q^{4} +1.52272 q^{5} -1.85165 q^{6} +0.592895 q^{7} -1.05805 q^{8} +1.00000 q^{9} +2.81954 q^{10} +5.80574 q^{11} -1.42859 q^{12} +0.790537 q^{13} +1.09783 q^{14} -1.52272 q^{15} -4.81631 q^{16} -1.00000 q^{17} +1.85165 q^{18} -8.36055 q^{19} +2.17535 q^{20} -0.592895 q^{21} +10.7502 q^{22} -4.55046 q^{23} +1.05805 q^{24} -2.68131 q^{25} +1.46379 q^{26} -1.00000 q^{27} +0.847005 q^{28} +4.33100 q^{29} -2.81954 q^{30} -10.2152 q^{31} -6.80201 q^{32} -5.80574 q^{33} -1.85165 q^{34} +0.902816 q^{35} +1.42859 q^{36} -6.10080 q^{37} -15.4808 q^{38} -0.790537 q^{39} -1.61111 q^{40} -7.36631 q^{41} -1.09783 q^{42} -3.95148 q^{43} +8.29402 q^{44} +1.52272 q^{45} -8.42583 q^{46} -6.98813 q^{47} +4.81631 q^{48} -6.64847 q^{49} -4.96484 q^{50} +1.00000 q^{51} +1.12935 q^{52} -8.60881 q^{53} -1.85165 q^{54} +8.84053 q^{55} -0.627311 q^{56} +8.36055 q^{57} +8.01947 q^{58} +10.5893 q^{59} -2.17535 q^{60} +9.55763 q^{61} -18.9149 q^{62} +0.592895 q^{63} -2.96228 q^{64} +1.20377 q^{65} -10.7502 q^{66} +4.56547 q^{67} -1.42859 q^{68} +4.55046 q^{69} +1.67169 q^{70} -8.15323 q^{71} -1.05805 q^{72} +12.0222 q^{73} -11.2965 q^{74} +2.68131 q^{75} -11.9438 q^{76} +3.44219 q^{77} -1.46379 q^{78} +12.3113 q^{79} -7.33391 q^{80} +1.00000 q^{81} -13.6398 q^{82} +8.32039 q^{83} -0.847005 q^{84} -1.52272 q^{85} -7.31673 q^{86} -4.33100 q^{87} -6.14274 q^{88} -17.9096 q^{89} +2.81954 q^{90} +0.468706 q^{91} -6.50074 q^{92} +10.2152 q^{93} -12.9395 q^{94} -12.7308 q^{95} +6.80201 q^{96} +15.2579 q^{97} -12.3106 q^{98} +5.80574 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.85165 1.30931 0.654656 0.755927i \(-0.272814\pi\)
0.654656 + 0.755927i \(0.272814\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.42859 0.714296
\(5\) 1.52272 0.680983 0.340491 0.940248i \(-0.389407\pi\)
0.340491 + 0.940248i \(0.389407\pi\)
\(6\) −1.85165 −0.755931
\(7\) 0.592895 0.224093 0.112047 0.993703i \(-0.464259\pi\)
0.112047 + 0.993703i \(0.464259\pi\)
\(8\) −1.05805 −0.374076
\(9\) 1.00000 0.333333
\(10\) 2.81954 0.891618
\(11\) 5.80574 1.75050 0.875248 0.483675i \(-0.160698\pi\)
0.875248 + 0.483675i \(0.160698\pi\)
\(12\) −1.42859 −0.412399
\(13\) 0.790537 0.219255 0.109628 0.993973i \(-0.465034\pi\)
0.109628 + 0.993973i \(0.465034\pi\)
\(14\) 1.09783 0.293408
\(15\) −1.52272 −0.393166
\(16\) −4.81631 −1.20408
\(17\) −1.00000 −0.242536
\(18\) 1.85165 0.436437
\(19\) −8.36055 −1.91804 −0.959021 0.283336i \(-0.908559\pi\)
−0.959021 + 0.283336i \(0.908559\pi\)
\(20\) 2.17535 0.486423
\(21\) −0.592895 −0.129380
\(22\) 10.7502 2.29194
\(23\) −4.55046 −0.948836 −0.474418 0.880300i \(-0.657341\pi\)
−0.474418 + 0.880300i \(0.657341\pi\)
\(24\) 1.05805 0.215973
\(25\) −2.68131 −0.536263
\(26\) 1.46379 0.287074
\(27\) −1.00000 −0.192450
\(28\) 0.847005 0.160069
\(29\) 4.33100 0.804246 0.402123 0.915586i \(-0.368272\pi\)
0.402123 + 0.915586i \(0.368272\pi\)
\(30\) −2.81954 −0.514776
\(31\) −10.2152 −1.83470 −0.917350 0.398081i \(-0.869676\pi\)
−0.917350 + 0.398081i \(0.869676\pi\)
\(32\) −6.80201 −1.20244
\(33\) −5.80574 −1.01065
\(34\) −1.85165 −0.317555
\(35\) 0.902816 0.152604
\(36\) 1.42859 0.238099
\(37\) −6.10080 −1.00297 −0.501483 0.865168i \(-0.667212\pi\)
−0.501483 + 0.865168i \(0.667212\pi\)
\(38\) −15.4808 −2.51131
\(39\) −0.790537 −0.126587
\(40\) −1.61111 −0.254739
\(41\) −7.36631 −1.15042 −0.575212 0.818004i \(-0.695081\pi\)
−0.575212 + 0.818004i \(0.695081\pi\)
\(42\) −1.09783 −0.169399
\(43\) −3.95148 −0.602594 −0.301297 0.953530i \(-0.597420\pi\)
−0.301297 + 0.953530i \(0.597420\pi\)
\(44\) 8.29402 1.25037
\(45\) 1.52272 0.226994
\(46\) −8.42583 −1.24232
\(47\) −6.98813 −1.01932 −0.509662 0.860375i \(-0.670229\pi\)
−0.509662 + 0.860375i \(0.670229\pi\)
\(48\) 4.81631 0.695174
\(49\) −6.64847 −0.949782
\(50\) −4.96484 −0.702135
\(51\) 1.00000 0.140028
\(52\) 1.12935 0.156613
\(53\) −8.60881 −1.18251 −0.591256 0.806484i \(-0.701368\pi\)
−0.591256 + 0.806484i \(0.701368\pi\)
\(54\) −1.85165 −0.251977
\(55\) 8.84053 1.19206
\(56\) −0.627311 −0.0838279
\(57\) 8.36055 1.10738
\(58\) 8.01947 1.05301
\(59\) 10.5893 1.37861 0.689306 0.724471i \(-0.257916\pi\)
0.689306 + 0.724471i \(0.257916\pi\)
\(60\) −2.17535 −0.280836
\(61\) 9.55763 1.22373 0.611864 0.790963i \(-0.290420\pi\)
0.611864 + 0.790963i \(0.290420\pi\)
\(62\) −18.9149 −2.40219
\(63\) 0.592895 0.0746978
\(64\) −2.96228 −0.370285
\(65\) 1.20377 0.149309
\(66\) −10.7502 −1.32325
\(67\) 4.56547 0.557761 0.278881 0.960326i \(-0.410037\pi\)
0.278881 + 0.960326i \(0.410037\pi\)
\(68\) −1.42859 −0.173242
\(69\) 4.55046 0.547811
\(70\) 1.67169 0.199806
\(71\) −8.15323 −0.967611 −0.483805 0.875176i \(-0.660746\pi\)
−0.483805 + 0.875176i \(0.660746\pi\)
\(72\) −1.05805 −0.124692
\(73\) 12.0222 1.40709 0.703546 0.710650i \(-0.251599\pi\)
0.703546 + 0.710650i \(0.251599\pi\)
\(74\) −11.2965 −1.31319
\(75\) 2.68131 0.309611
\(76\) −11.9438 −1.37005
\(77\) 3.44219 0.392274
\(78\) −1.46379 −0.165742
\(79\) 12.3113 1.38513 0.692564 0.721357i \(-0.256481\pi\)
0.692564 + 0.721357i \(0.256481\pi\)
\(80\) −7.33391 −0.819956
\(81\) 1.00000 0.111111
\(82\) −13.6398 −1.50626
\(83\) 8.32039 0.913281 0.456641 0.889651i \(-0.349053\pi\)
0.456641 + 0.889651i \(0.349053\pi\)
\(84\) −0.847005 −0.0924159
\(85\) −1.52272 −0.165163
\(86\) −7.31673 −0.788983
\(87\) −4.33100 −0.464332
\(88\) −6.14274 −0.654818
\(89\) −17.9096 −1.89841 −0.949205 0.314657i \(-0.898110\pi\)
−0.949205 + 0.314657i \(0.898110\pi\)
\(90\) 2.81954 0.297206
\(91\) 0.468706 0.0491337
\(92\) −6.50074 −0.677749
\(93\) 10.2152 1.05926
\(94\) −12.9395 −1.33461
\(95\) −12.7308 −1.30615
\(96\) 6.80201 0.694227
\(97\) 15.2579 1.54921 0.774603 0.632448i \(-0.217950\pi\)
0.774603 + 0.632448i \(0.217950\pi\)
\(98\) −12.3106 −1.24356
\(99\) 5.80574 0.583498
\(100\) −3.83050 −0.383050
\(101\) −13.9391 −1.38699 −0.693496 0.720460i \(-0.743931\pi\)
−0.693496 + 0.720460i \(0.743931\pi\)
\(102\) 1.85165 0.183340
\(103\) 7.10387 0.699966 0.349983 0.936756i \(-0.386187\pi\)
0.349983 + 0.936756i \(0.386187\pi\)
\(104\) −0.836425 −0.0820182
\(105\) −0.902816 −0.0881058
\(106\) −15.9405 −1.54828
\(107\) 9.74860 0.942433 0.471217 0.882018i \(-0.343815\pi\)
0.471217 + 0.882018i \(0.343815\pi\)
\(108\) −1.42859 −0.137466
\(109\) −0.523599 −0.0501517 −0.0250759 0.999686i \(-0.507983\pi\)
−0.0250759 + 0.999686i \(0.507983\pi\)
\(110\) 16.3695 1.56077
\(111\) 6.10080 0.579063
\(112\) −2.85557 −0.269826
\(113\) 5.93044 0.557889 0.278945 0.960307i \(-0.410015\pi\)
0.278945 + 0.960307i \(0.410015\pi\)
\(114\) 15.4808 1.44991
\(115\) −6.92909 −0.646141
\(116\) 6.18722 0.574469
\(117\) 0.790537 0.0730852
\(118\) 19.6077 1.80503
\(119\) −0.592895 −0.0543506
\(120\) 1.61111 0.147074
\(121\) 22.7066 2.06423
\(122\) 17.6973 1.60224
\(123\) 7.36631 0.664198
\(124\) −14.5933 −1.31052
\(125\) −11.6965 −1.04617
\(126\) 1.09783 0.0978027
\(127\) −8.40692 −0.745994 −0.372997 0.927833i \(-0.621670\pi\)
−0.372997 + 0.927833i \(0.621670\pi\)
\(128\) 8.11891 0.717617
\(129\) 3.95148 0.347908
\(130\) 2.22895 0.195492
\(131\) 9.32937 0.815111 0.407555 0.913181i \(-0.366381\pi\)
0.407555 + 0.913181i \(0.366381\pi\)
\(132\) −8.29402 −0.721902
\(133\) −4.95693 −0.429820
\(134\) 8.45364 0.730283
\(135\) −1.52272 −0.131055
\(136\) 1.05805 0.0907267
\(137\) −22.4372 −1.91694 −0.958469 0.285198i \(-0.907941\pi\)
−0.958469 + 0.285198i \(0.907941\pi\)
\(138\) 8.42583 0.717255
\(139\) −14.3859 −1.22019 −0.610097 0.792326i \(-0.708870\pi\)
−0.610097 + 0.792326i \(0.708870\pi\)
\(140\) 1.28975 0.109004
\(141\) 6.98813 0.588507
\(142\) −15.0969 −1.26690
\(143\) 4.58965 0.383806
\(144\) −4.81631 −0.401359
\(145\) 6.59491 0.547677
\(146\) 22.2608 1.84232
\(147\) 6.64847 0.548357
\(148\) −8.71555 −0.716414
\(149\) −20.9710 −1.71801 −0.859005 0.511967i \(-0.828917\pi\)
−0.859005 + 0.511967i \(0.828917\pi\)
\(150\) 4.96484 0.405378
\(151\) 1.75453 0.142781 0.0713906 0.997448i \(-0.477256\pi\)
0.0713906 + 0.997448i \(0.477256\pi\)
\(152\) 8.84585 0.717493
\(153\) −1.00000 −0.0808452
\(154\) 6.37372 0.513609
\(155\) −15.5549 −1.24940
\(156\) −1.12935 −0.0904207
\(157\) −1.00000 −0.0798087
\(158\) 22.7961 1.81356
\(159\) 8.60881 0.682723
\(160\) −10.3576 −0.818838
\(161\) −2.69795 −0.212628
\(162\) 1.85165 0.145479
\(163\) 9.79492 0.767198 0.383599 0.923500i \(-0.374685\pi\)
0.383599 + 0.923500i \(0.374685\pi\)
\(164\) −10.5234 −0.821743
\(165\) −8.84053 −0.688234
\(166\) 15.4064 1.19577
\(167\) 21.4686 1.66129 0.830647 0.556800i \(-0.187971\pi\)
0.830647 + 0.556800i \(0.187971\pi\)
\(168\) 0.627311 0.0483981
\(169\) −12.3751 −0.951927
\(170\) −2.81954 −0.216249
\(171\) −8.36055 −0.639347
\(172\) −5.64504 −0.430430
\(173\) −10.3683 −0.788286 −0.394143 0.919049i \(-0.628959\pi\)
−0.394143 + 0.919049i \(0.628959\pi\)
\(174\) −8.01947 −0.607955
\(175\) −1.58974 −0.120173
\(176\) −27.9622 −2.10773
\(177\) −10.5893 −0.795942
\(178\) −33.1622 −2.48561
\(179\) −18.4231 −1.37701 −0.688503 0.725234i \(-0.741732\pi\)
−0.688503 + 0.725234i \(0.741732\pi\)
\(180\) 2.17535 0.162141
\(181\) 14.4873 1.07684 0.538418 0.842678i \(-0.319022\pi\)
0.538418 + 0.842678i \(0.319022\pi\)
\(182\) 0.867877 0.0643313
\(183\) −9.55763 −0.706520
\(184\) 4.81459 0.354937
\(185\) −9.28984 −0.683002
\(186\) 18.9149 1.38691
\(187\) −5.80574 −0.424557
\(188\) −9.98318 −0.728098
\(189\) −0.592895 −0.0431268
\(190\) −23.5729 −1.71016
\(191\) 12.3486 0.893515 0.446758 0.894655i \(-0.352579\pi\)
0.446758 + 0.894655i \(0.352579\pi\)
\(192\) 2.96228 0.213784
\(193\) −16.8294 −1.21140 −0.605702 0.795692i \(-0.707108\pi\)
−0.605702 + 0.795692i \(0.707108\pi\)
\(194\) 28.2522 2.02839
\(195\) −1.20377 −0.0862037
\(196\) −9.49795 −0.678425
\(197\) 7.85567 0.559693 0.279847 0.960045i \(-0.409716\pi\)
0.279847 + 0.960045i \(0.409716\pi\)
\(198\) 10.7502 0.763981
\(199\) −3.33007 −0.236062 −0.118031 0.993010i \(-0.537658\pi\)
−0.118031 + 0.993010i \(0.537658\pi\)
\(200\) 2.83695 0.200603
\(201\) −4.56547 −0.322024
\(202\) −25.8103 −1.81600
\(203\) 2.56783 0.180226
\(204\) 1.42859 0.100021
\(205\) −11.2169 −0.783419
\(206\) 13.1539 0.916473
\(207\) −4.55046 −0.316279
\(208\) −3.80747 −0.264001
\(209\) −48.5391 −3.35752
\(210\) −1.67169 −0.115358
\(211\) −25.0736 −1.72614 −0.863070 0.505085i \(-0.831461\pi\)
−0.863070 + 0.505085i \(0.831461\pi\)
\(212\) −12.2985 −0.844663
\(213\) 8.15323 0.558650
\(214\) 18.0510 1.23394
\(215\) −6.01700 −0.410356
\(216\) 1.05805 0.0719909
\(217\) −6.05653 −0.411144
\(218\) −0.969521 −0.0656642
\(219\) −12.0222 −0.812384
\(220\) 12.6295 0.851481
\(221\) −0.790537 −0.0531773
\(222\) 11.2965 0.758173
\(223\) −2.69549 −0.180503 −0.0902516 0.995919i \(-0.528767\pi\)
−0.0902516 + 0.995919i \(0.528767\pi\)
\(224\) −4.03288 −0.269458
\(225\) −2.68131 −0.178754
\(226\) 10.9811 0.730450
\(227\) −27.4607 −1.82263 −0.911315 0.411710i \(-0.864932\pi\)
−0.911315 + 0.411710i \(0.864932\pi\)
\(228\) 11.9438 0.790998
\(229\) −3.09977 −0.204838 −0.102419 0.994741i \(-0.532658\pi\)
−0.102419 + 0.994741i \(0.532658\pi\)
\(230\) −12.8302 −0.845999
\(231\) −3.44219 −0.226480
\(232\) −4.58240 −0.300849
\(233\) 20.0319 1.31233 0.656166 0.754616i \(-0.272177\pi\)
0.656166 + 0.754616i \(0.272177\pi\)
\(234\) 1.46379 0.0956912
\(235\) −10.6410 −0.694141
\(236\) 15.1278 0.984736
\(237\) −12.3113 −0.799704
\(238\) −1.09783 −0.0711619
\(239\) −17.0924 −1.10562 −0.552808 0.833309i \(-0.686444\pi\)
−0.552808 + 0.833309i \(0.686444\pi\)
\(240\) 7.33391 0.473402
\(241\) 17.3130 1.11523 0.557615 0.830100i \(-0.311717\pi\)
0.557615 + 0.830100i \(0.311717\pi\)
\(242\) 42.0445 2.70272
\(243\) −1.00000 −0.0641500
\(244\) 13.6539 0.874104
\(245\) −10.1238 −0.646785
\(246\) 13.6398 0.869642
\(247\) −6.60932 −0.420541
\(248\) 10.8081 0.686317
\(249\) −8.32039 −0.527283
\(250\) −21.6578 −1.36976
\(251\) 18.0587 1.13985 0.569926 0.821696i \(-0.306972\pi\)
0.569926 + 0.821696i \(0.306972\pi\)
\(252\) 0.847005 0.0533563
\(253\) −26.4187 −1.66093
\(254\) −15.5666 −0.976738
\(255\) 1.52272 0.0953566
\(256\) 20.9579 1.30987
\(257\) −1.98632 −0.123903 −0.0619517 0.998079i \(-0.519732\pi\)
−0.0619517 + 0.998079i \(0.519732\pi\)
\(258\) 7.31673 0.455520
\(259\) −3.61714 −0.224758
\(260\) 1.71969 0.106651
\(261\) 4.33100 0.268082
\(262\) 17.2747 1.06723
\(263\) 1.85794 0.114565 0.0572827 0.998358i \(-0.481756\pi\)
0.0572827 + 0.998358i \(0.481756\pi\)
\(264\) 6.14274 0.378059
\(265\) −13.1088 −0.805270
\(266\) −9.17848 −0.562769
\(267\) 17.9096 1.09605
\(268\) 6.52219 0.398406
\(269\) 16.4997 1.00600 0.503001 0.864286i \(-0.332229\pi\)
0.503001 + 0.864286i \(0.332229\pi\)
\(270\) −2.81954 −0.171592
\(271\) 17.2735 1.04929 0.524645 0.851321i \(-0.324198\pi\)
0.524645 + 0.851321i \(0.324198\pi\)
\(272\) 4.81631 0.292032
\(273\) −0.468706 −0.0283674
\(274\) −41.5457 −2.50987
\(275\) −15.5670 −0.938725
\(276\) 6.50074 0.391299
\(277\) 19.5227 1.17300 0.586502 0.809948i \(-0.300505\pi\)
0.586502 + 0.809948i \(0.300505\pi\)
\(278\) −26.6376 −1.59761
\(279\) −10.2152 −0.611567
\(280\) −0.955221 −0.0570854
\(281\) −6.83926 −0.407996 −0.203998 0.978971i \(-0.565394\pi\)
−0.203998 + 0.978971i \(0.565394\pi\)
\(282\) 12.9395 0.770538
\(283\) 1.47130 0.0874599 0.0437299 0.999043i \(-0.486076\pi\)
0.0437299 + 0.999043i \(0.486076\pi\)
\(284\) −11.6476 −0.691160
\(285\) 12.7308 0.754108
\(286\) 8.49840 0.502521
\(287\) −4.36745 −0.257803
\(288\) −6.80201 −0.400812
\(289\) 1.00000 0.0588235
\(290\) 12.2114 0.717080
\(291\) −15.2579 −0.894434
\(292\) 17.1748 1.00508
\(293\) −15.0191 −0.877423 −0.438711 0.898628i \(-0.644565\pi\)
−0.438711 + 0.898628i \(0.644565\pi\)
\(294\) 12.3106 0.717970
\(295\) 16.1246 0.938810
\(296\) 6.45493 0.375185
\(297\) −5.80574 −0.336883
\(298\) −38.8308 −2.24941
\(299\) −3.59730 −0.208037
\(300\) 3.83050 0.221154
\(301\) −2.34281 −0.135037
\(302\) 3.24876 0.186945
\(303\) 13.9391 0.800780
\(304\) 40.2670 2.30947
\(305\) 14.5536 0.833338
\(306\) −1.85165 −0.105852
\(307\) 24.0001 1.36976 0.684878 0.728658i \(-0.259855\pi\)
0.684878 + 0.728658i \(0.259855\pi\)
\(308\) 4.91749 0.280200
\(309\) −7.10387 −0.404125
\(310\) −28.8021 −1.63585
\(311\) 29.6667 1.68225 0.841123 0.540844i \(-0.181895\pi\)
0.841123 + 0.540844i \(0.181895\pi\)
\(312\) 0.836425 0.0473532
\(313\) 5.39192 0.304769 0.152385 0.988321i \(-0.451305\pi\)
0.152385 + 0.988321i \(0.451305\pi\)
\(314\) −1.85165 −0.104494
\(315\) 0.902816 0.0508679
\(316\) 17.5878 0.989390
\(317\) −9.67677 −0.543501 −0.271751 0.962368i \(-0.587603\pi\)
−0.271751 + 0.962368i \(0.587603\pi\)
\(318\) 15.9405 0.893897
\(319\) 25.1446 1.40783
\(320\) −4.51074 −0.252158
\(321\) −9.74860 −0.544114
\(322\) −4.99564 −0.278396
\(323\) 8.36055 0.465193
\(324\) 1.42859 0.0793662
\(325\) −2.11968 −0.117579
\(326\) 18.1367 1.00450
\(327\) 0.523599 0.0289551
\(328\) 7.79390 0.430346
\(329\) −4.14323 −0.228424
\(330\) −16.3695 −0.901113
\(331\) −13.8446 −0.760969 −0.380485 0.924787i \(-0.624243\pi\)
−0.380485 + 0.924787i \(0.624243\pi\)
\(332\) 11.8864 0.652353
\(333\) −6.10080 −0.334322
\(334\) 39.7523 2.17515
\(335\) 6.95195 0.379826
\(336\) 2.85557 0.155784
\(337\) −9.10708 −0.496094 −0.248047 0.968748i \(-0.579789\pi\)
−0.248047 + 0.968748i \(0.579789\pi\)
\(338\) −22.9142 −1.24637
\(339\) −5.93044 −0.322097
\(340\) −2.17535 −0.117975
\(341\) −59.3066 −3.21163
\(342\) −15.4808 −0.837104
\(343\) −8.09212 −0.436933
\(344\) 4.18084 0.225416
\(345\) 6.92909 0.373050
\(346\) −19.1984 −1.03211
\(347\) −30.5201 −1.63840 −0.819202 0.573505i \(-0.805583\pi\)
−0.819202 + 0.573505i \(0.805583\pi\)
\(348\) −6.18722 −0.331670
\(349\) −18.7346 −1.00284 −0.501420 0.865204i \(-0.667189\pi\)
−0.501420 + 0.865204i \(0.667189\pi\)
\(350\) −2.94363 −0.157344
\(351\) −0.790537 −0.0421957
\(352\) −39.4906 −2.10486
\(353\) −0.0549497 −0.00292468 −0.00146234 0.999999i \(-0.500465\pi\)
−0.00146234 + 0.999999i \(0.500465\pi\)
\(354\) −19.6077 −1.04214
\(355\) −12.4151 −0.658926
\(356\) −25.5855 −1.35603
\(357\) 0.592895 0.0313794
\(358\) −34.1130 −1.80293
\(359\) −1.15478 −0.0609468 −0.0304734 0.999536i \(-0.509701\pi\)
−0.0304734 + 0.999536i \(0.509701\pi\)
\(360\) −1.61111 −0.0849131
\(361\) 50.8988 2.67888
\(362\) 26.8254 1.40991
\(363\) −22.7066 −1.19179
\(364\) 0.669589 0.0350960
\(365\) 18.3065 0.958205
\(366\) −17.6973 −0.925055
\(367\) −9.32154 −0.486580 −0.243290 0.969954i \(-0.578227\pi\)
−0.243290 + 0.969954i \(0.578227\pi\)
\(368\) 21.9164 1.14247
\(369\) −7.36631 −0.383475
\(370\) −17.2015 −0.894262
\(371\) −5.10413 −0.264993
\(372\) 14.5933 0.756628
\(373\) −24.8604 −1.28722 −0.643611 0.765353i \(-0.722564\pi\)
−0.643611 + 0.765353i \(0.722564\pi\)
\(374\) −10.7502 −0.555878
\(375\) 11.6965 0.604005
\(376\) 7.39376 0.381304
\(377\) 3.42381 0.176335
\(378\) −1.09783 −0.0564664
\(379\) −15.2568 −0.783688 −0.391844 0.920032i \(-0.628163\pi\)
−0.391844 + 0.920032i \(0.628163\pi\)
\(380\) −18.1871 −0.932979
\(381\) 8.40692 0.430700
\(382\) 22.8653 1.16989
\(383\) 37.6542 1.92404 0.962020 0.272979i \(-0.0880089\pi\)
0.962020 + 0.272979i \(0.0880089\pi\)
\(384\) −8.11891 −0.414316
\(385\) 5.24151 0.267132
\(386\) −31.1620 −1.58611
\(387\) −3.95148 −0.200865
\(388\) 21.7973 1.10659
\(389\) 2.08505 0.105716 0.0528581 0.998602i \(-0.483167\pi\)
0.0528581 + 0.998602i \(0.483167\pi\)
\(390\) −2.22895 −0.112867
\(391\) 4.55046 0.230127
\(392\) 7.03440 0.355291
\(393\) −9.32937 −0.470604
\(394\) 14.5459 0.732813
\(395\) 18.7467 0.943248
\(396\) 8.29402 0.416790
\(397\) −19.3637 −0.971836 −0.485918 0.874005i \(-0.661515\pi\)
−0.485918 + 0.874005i \(0.661515\pi\)
\(398\) −6.16611 −0.309079
\(399\) 4.95693 0.248157
\(400\) 12.9140 0.645702
\(401\) 36.2545 1.81046 0.905231 0.424920i \(-0.139698\pi\)
0.905231 + 0.424920i \(0.139698\pi\)
\(402\) −8.45364 −0.421629
\(403\) −8.07548 −0.402268
\(404\) −19.9133 −0.990722
\(405\) 1.52272 0.0756647
\(406\) 4.75471 0.235972
\(407\) −35.4196 −1.75569
\(408\) −1.05805 −0.0523811
\(409\) 26.0246 1.28683 0.643416 0.765517i \(-0.277517\pi\)
0.643416 + 0.765517i \(0.277517\pi\)
\(410\) −20.7696 −1.02574
\(411\) 22.4372 1.10674
\(412\) 10.1485 0.499982
\(413\) 6.27836 0.308938
\(414\) −8.42583 −0.414107
\(415\) 12.6696 0.621929
\(416\) −5.37724 −0.263641
\(417\) 14.3859 0.704480
\(418\) −89.8773 −4.39604
\(419\) 8.94675 0.437077 0.218539 0.975828i \(-0.429871\pi\)
0.218539 + 0.975828i \(0.429871\pi\)
\(420\) −1.28975 −0.0629336
\(421\) −19.3800 −0.944523 −0.472261 0.881459i \(-0.656562\pi\)
−0.472261 + 0.881459i \(0.656562\pi\)
\(422\) −46.4275 −2.26005
\(423\) −6.98813 −0.339774
\(424\) 9.10852 0.442349
\(425\) 2.68131 0.130063
\(426\) 15.0969 0.731447
\(427\) 5.66667 0.274230
\(428\) 13.9268 0.673176
\(429\) −4.58965 −0.221590
\(430\) −11.1414 −0.537284
\(431\) 24.5160 1.18089 0.590446 0.807077i \(-0.298952\pi\)
0.590446 + 0.807077i \(0.298952\pi\)
\(432\) 4.81631 0.231725
\(433\) 6.54669 0.314614 0.157307 0.987550i \(-0.449719\pi\)
0.157307 + 0.987550i \(0.449719\pi\)
\(434\) −11.2146 −0.538316
\(435\) −6.59491 −0.316202
\(436\) −0.748010 −0.0358232
\(437\) 38.0443 1.81991
\(438\) −22.2608 −1.06366
\(439\) 22.4568 1.07180 0.535902 0.844280i \(-0.319972\pi\)
0.535902 + 0.844280i \(0.319972\pi\)
\(440\) −9.35369 −0.445920
\(441\) −6.64847 −0.316594
\(442\) −1.46379 −0.0696256
\(443\) 28.8903 1.37262 0.686309 0.727310i \(-0.259230\pi\)
0.686309 + 0.727310i \(0.259230\pi\)
\(444\) 8.71555 0.413622
\(445\) −27.2713 −1.29278
\(446\) −4.99109 −0.236335
\(447\) 20.9710 0.991894
\(448\) −1.75632 −0.0829785
\(449\) −15.6886 −0.740390 −0.370195 0.928954i \(-0.620709\pi\)
−0.370195 + 0.928954i \(0.620709\pi\)
\(450\) −4.96484 −0.234045
\(451\) −42.7669 −2.01381
\(452\) 8.47218 0.398498
\(453\) −1.75453 −0.0824348
\(454\) −50.8475 −2.38639
\(455\) 0.713709 0.0334592
\(456\) −8.84585 −0.414245
\(457\) 4.99318 0.233571 0.116786 0.993157i \(-0.462741\pi\)
0.116786 + 0.993157i \(0.462741\pi\)
\(458\) −5.73967 −0.268197
\(459\) 1.00000 0.0466760
\(460\) −9.89883 −0.461536
\(461\) 9.76476 0.454790 0.227395 0.973803i \(-0.426979\pi\)
0.227395 + 0.973803i \(0.426979\pi\)
\(462\) −6.37372 −0.296532
\(463\) −6.34394 −0.294828 −0.147414 0.989075i \(-0.547095\pi\)
−0.147414 + 0.989075i \(0.547095\pi\)
\(464\) −20.8594 −0.968374
\(465\) 15.5549 0.721341
\(466\) 37.0920 1.71825
\(467\) −18.0623 −0.835822 −0.417911 0.908488i \(-0.637238\pi\)
−0.417911 + 0.908488i \(0.637238\pi\)
\(468\) 1.12935 0.0522044
\(469\) 2.70685 0.124991
\(470\) −19.7033 −0.908847
\(471\) 1.00000 0.0460776
\(472\) −11.2040 −0.515705
\(473\) −22.9412 −1.05484
\(474\) −22.7961 −1.04706
\(475\) 22.4172 1.02857
\(476\) −0.847005 −0.0388224
\(477\) −8.60881 −0.394170
\(478\) −31.6491 −1.44759
\(479\) −20.6472 −0.943395 −0.471698 0.881760i \(-0.656359\pi\)
−0.471698 + 0.881760i \(0.656359\pi\)
\(480\) 10.3576 0.472756
\(481\) −4.82291 −0.219906
\(482\) 32.0576 1.46018
\(483\) 2.69795 0.122761
\(484\) 32.4384 1.47447
\(485\) 23.2336 1.05498
\(486\) −1.85165 −0.0839923
\(487\) −18.3023 −0.829356 −0.414678 0.909968i \(-0.636106\pi\)
−0.414678 + 0.909968i \(0.636106\pi\)
\(488\) −10.1124 −0.457767
\(489\) −9.79492 −0.442942
\(490\) −18.7457 −0.846843
\(491\) −2.68600 −0.121218 −0.0606089 0.998162i \(-0.519304\pi\)
−0.0606089 + 0.998162i \(0.519304\pi\)
\(492\) 10.5234 0.474434
\(493\) −4.33100 −0.195058
\(494\) −12.2381 −0.550619
\(495\) 8.84053 0.397352
\(496\) 49.1995 2.20912
\(497\) −4.83402 −0.216835
\(498\) −15.4064 −0.690378
\(499\) −28.0367 −1.25509 −0.627547 0.778579i \(-0.715941\pi\)
−0.627547 + 0.778579i \(0.715941\pi\)
\(500\) −16.7095 −0.747273
\(501\) −21.4686 −0.959148
\(502\) 33.4382 1.49242
\(503\) 9.14819 0.407898 0.203949 0.978982i \(-0.434622\pi\)
0.203949 + 0.978982i \(0.434622\pi\)
\(504\) −0.627311 −0.0279426
\(505\) −21.2254 −0.944518
\(506\) −48.9182 −2.17468
\(507\) 12.3751 0.549595
\(508\) −12.0101 −0.532860
\(509\) 25.2113 1.11747 0.558735 0.829346i \(-0.311287\pi\)
0.558735 + 0.829346i \(0.311287\pi\)
\(510\) 2.81954 0.124852
\(511\) 7.12790 0.315320
\(512\) 22.5688 0.997410
\(513\) 8.36055 0.369127
\(514\) −3.67797 −0.162228
\(515\) 10.8172 0.476664
\(516\) 5.64504 0.248509
\(517\) −40.5712 −1.78432
\(518\) −6.69766 −0.294278
\(519\) 10.3683 0.455117
\(520\) −1.27364 −0.0558530
\(521\) −11.7648 −0.515426 −0.257713 0.966222i \(-0.582969\pi\)
−0.257713 + 0.966222i \(0.582969\pi\)
\(522\) 8.01947 0.351003
\(523\) −12.9905 −0.568033 −0.284016 0.958819i \(-0.591667\pi\)
−0.284016 + 0.958819i \(0.591667\pi\)
\(524\) 13.3279 0.582230
\(525\) 1.58974 0.0693819
\(526\) 3.44025 0.150002
\(527\) 10.2152 0.444980
\(528\) 27.9622 1.21690
\(529\) −2.29334 −0.0997105
\(530\) −24.2729 −1.05435
\(531\) 10.5893 0.459537
\(532\) −7.08143 −0.307019
\(533\) −5.82334 −0.252237
\(534\) 33.1622 1.43507
\(535\) 14.8444 0.641780
\(536\) −4.83048 −0.208645
\(537\) 18.4231 0.795015
\(538\) 30.5515 1.31717
\(539\) −38.5993 −1.66259
\(540\) −2.17535 −0.0936121
\(541\) −24.5817 −1.05685 −0.528426 0.848980i \(-0.677217\pi\)
−0.528426 + 0.848980i \(0.677217\pi\)
\(542\) 31.9844 1.37385
\(543\) −14.4873 −0.621711
\(544\) 6.80201 0.291634
\(545\) −0.797297 −0.0341525
\(546\) −0.867877 −0.0371417
\(547\) −10.7030 −0.457629 −0.228814 0.973470i \(-0.573485\pi\)
−0.228814 + 0.973470i \(0.573485\pi\)
\(548\) −32.0536 −1.36926
\(549\) 9.55763 0.407910
\(550\) −28.8246 −1.22908
\(551\) −36.2095 −1.54258
\(552\) −4.81459 −0.204923
\(553\) 7.29930 0.310398
\(554\) 36.1491 1.53583
\(555\) 9.28984 0.394332
\(556\) −20.5515 −0.871580
\(557\) 16.9136 0.716654 0.358327 0.933596i \(-0.383347\pi\)
0.358327 + 0.933596i \(0.383347\pi\)
\(558\) −18.9149 −0.800731
\(559\) −3.12379 −0.132122
\(560\) −4.34824 −0.183747
\(561\) 5.80574 0.245118
\(562\) −12.6639 −0.534194
\(563\) −21.7343 −0.915990 −0.457995 0.888955i \(-0.651432\pi\)
−0.457995 + 0.888955i \(0.651432\pi\)
\(564\) 9.98318 0.420368
\(565\) 9.03042 0.379913
\(566\) 2.72433 0.114512
\(567\) 0.592895 0.0248993
\(568\) 8.62650 0.361960
\(569\) −38.6392 −1.61984 −0.809920 0.586541i \(-0.800489\pi\)
−0.809920 + 0.586541i \(0.800489\pi\)
\(570\) 23.5729 0.987362
\(571\) 20.8146 0.871065 0.435533 0.900173i \(-0.356560\pi\)
0.435533 + 0.900173i \(0.356560\pi\)
\(572\) 6.55673 0.274151
\(573\) −12.3486 −0.515871
\(574\) −8.08697 −0.337544
\(575\) 12.2012 0.508825
\(576\) −2.96228 −0.123428
\(577\) −46.1050 −1.91938 −0.959688 0.281066i \(-0.909312\pi\)
−0.959688 + 0.281066i \(0.909312\pi\)
\(578\) 1.85165 0.0770183
\(579\) 16.8294 0.699405
\(580\) 9.42143 0.391204
\(581\) 4.93312 0.204660
\(582\) −28.2522 −1.17109
\(583\) −49.9805 −2.06998
\(584\) −12.7200 −0.526359
\(585\) 1.20377 0.0497697
\(586\) −27.8100 −1.14882
\(587\) −26.9114 −1.11075 −0.555376 0.831600i \(-0.687426\pi\)
−0.555376 + 0.831600i \(0.687426\pi\)
\(588\) 9.49795 0.391689
\(589\) 85.4045 3.51903
\(590\) 29.8570 1.22919
\(591\) −7.85567 −0.323139
\(592\) 29.3834 1.20765
\(593\) 2.40357 0.0987028 0.0493514 0.998781i \(-0.484285\pi\)
0.0493514 + 0.998781i \(0.484285\pi\)
\(594\) −10.7502 −0.441085
\(595\) −0.902816 −0.0370118
\(596\) −29.9590 −1.22717
\(597\) 3.33007 0.136291
\(598\) −6.66093 −0.272386
\(599\) 40.2253 1.64356 0.821781 0.569804i \(-0.192981\pi\)
0.821781 + 0.569804i \(0.192981\pi\)
\(600\) −2.83695 −0.115818
\(601\) −16.6753 −0.680198 −0.340099 0.940390i \(-0.610461\pi\)
−0.340099 + 0.940390i \(0.610461\pi\)
\(602\) −4.33806 −0.176806
\(603\) 4.56547 0.185920
\(604\) 2.50650 0.101988
\(605\) 34.5758 1.40571
\(606\) 25.8103 1.04847
\(607\) 17.9768 0.729657 0.364829 0.931075i \(-0.381128\pi\)
0.364829 + 0.931075i \(0.381128\pi\)
\(608\) 56.8685 2.30632
\(609\) −2.56783 −0.104054
\(610\) 26.9481 1.09110
\(611\) −5.52437 −0.223492
\(612\) −1.42859 −0.0577474
\(613\) −2.57498 −0.104003 −0.0520013 0.998647i \(-0.516560\pi\)
−0.0520013 + 0.998647i \(0.516560\pi\)
\(614\) 44.4396 1.79344
\(615\) 11.2169 0.452307
\(616\) −3.64200 −0.146740
\(617\) 19.4272 0.782110 0.391055 0.920367i \(-0.372110\pi\)
0.391055 + 0.920367i \(0.372110\pi\)
\(618\) −13.1539 −0.529126
\(619\) 38.8528 1.56162 0.780812 0.624766i \(-0.214806\pi\)
0.780812 + 0.624766i \(0.214806\pi\)
\(620\) −22.2216 −0.892440
\(621\) 4.55046 0.182604
\(622\) 54.9323 2.20258
\(623\) −10.6185 −0.425421
\(624\) 3.80747 0.152421
\(625\) −4.40399 −0.176160
\(626\) 9.98392 0.399038
\(627\) 48.5391 1.93847
\(628\) −1.42859 −0.0570070
\(629\) 6.10080 0.243255
\(630\) 1.67169 0.0666019
\(631\) 34.3397 1.36704 0.683521 0.729931i \(-0.260448\pi\)
0.683521 + 0.729931i \(0.260448\pi\)
\(632\) −13.0259 −0.518143
\(633\) 25.0736 0.996587
\(634\) −17.9179 −0.711612
\(635\) −12.8014 −0.508009
\(636\) 12.2985 0.487666
\(637\) −5.25586 −0.208245
\(638\) 46.5589 1.84329
\(639\) −8.15323 −0.322537
\(640\) 12.3629 0.488685
\(641\) −35.3955 −1.39804 −0.699019 0.715103i \(-0.746380\pi\)
−0.699019 + 0.715103i \(0.746380\pi\)
\(642\) −18.0510 −0.712414
\(643\) 16.4750 0.649709 0.324854 0.945764i \(-0.394685\pi\)
0.324854 + 0.945764i \(0.394685\pi\)
\(644\) −3.85426 −0.151879
\(645\) 6.01700 0.236919
\(646\) 15.4808 0.609083
\(647\) 13.9775 0.549512 0.274756 0.961514i \(-0.411403\pi\)
0.274756 + 0.961514i \(0.411403\pi\)
\(648\) −1.05805 −0.0415640
\(649\) 61.4788 2.41325
\(650\) −3.92489 −0.153947
\(651\) 6.05653 0.237374
\(652\) 13.9929 0.548006
\(653\) −35.0114 −1.37010 −0.685052 0.728494i \(-0.740220\pi\)
−0.685052 + 0.728494i \(0.740220\pi\)
\(654\) 0.969521 0.0379113
\(655\) 14.2060 0.555076
\(656\) 35.4784 1.38520
\(657\) 12.0222 0.469030
\(658\) −7.67179 −0.299078
\(659\) 22.7875 0.887674 0.443837 0.896107i \(-0.353617\pi\)
0.443837 + 0.896107i \(0.353617\pi\)
\(660\) −12.6295 −0.491603
\(661\) 31.6182 1.22980 0.614902 0.788604i \(-0.289196\pi\)
0.614902 + 0.788604i \(0.289196\pi\)
\(662\) −25.6353 −0.996345
\(663\) 0.790537 0.0307019
\(664\) −8.80335 −0.341636
\(665\) −7.54803 −0.292700
\(666\) −11.2965 −0.437731
\(667\) −19.7080 −0.763097
\(668\) 30.6699 1.18665
\(669\) 2.69549 0.104214
\(670\) 12.8725 0.497310
\(671\) 55.4890 2.14213
\(672\) 4.03288 0.155572
\(673\) −43.9719 −1.69499 −0.847496 0.530802i \(-0.821891\pi\)
−0.847496 + 0.530802i \(0.821891\pi\)
\(674\) −16.8631 −0.649541
\(675\) 2.68131 0.103204
\(676\) −17.6789 −0.679957
\(677\) 29.5774 1.13675 0.568377 0.822768i \(-0.307572\pi\)
0.568377 + 0.822768i \(0.307572\pi\)
\(678\) −10.9811 −0.421726
\(679\) 9.04634 0.347167
\(680\) 1.61111 0.0617833
\(681\) 27.4607 1.05230
\(682\) −109.815 −4.20503
\(683\) 16.4680 0.630130 0.315065 0.949070i \(-0.397974\pi\)
0.315065 + 0.949070i \(0.397974\pi\)
\(684\) −11.9438 −0.456683
\(685\) −34.1656 −1.30540
\(686\) −14.9837 −0.572082
\(687\) 3.09977 0.118263
\(688\) 19.0315 0.725570
\(689\) −6.80558 −0.259272
\(690\) 12.8302 0.488438
\(691\) −22.4688 −0.854754 −0.427377 0.904074i \(-0.640562\pi\)
−0.427377 + 0.904074i \(0.640562\pi\)
\(692\) −14.8120 −0.563070
\(693\) 3.44219 0.130758
\(694\) −56.5124 −2.14518
\(695\) −21.9057 −0.830931
\(696\) 4.58240 0.173695
\(697\) 7.36631 0.279019
\(698\) −34.6898 −1.31303
\(699\) −20.0319 −0.757676
\(700\) −2.27109 −0.0858390
\(701\) −10.1228 −0.382331 −0.191166 0.981558i \(-0.561227\pi\)
−0.191166 + 0.981558i \(0.561227\pi\)
\(702\) −1.46379 −0.0552473
\(703\) 51.0061 1.92373
\(704\) −17.1982 −0.648183
\(705\) 10.6410 0.400763
\(706\) −0.101747 −0.00382931
\(707\) −8.26443 −0.310816
\(708\) −15.1278 −0.568538
\(709\) 43.0622 1.61723 0.808617 0.588336i \(-0.200217\pi\)
0.808617 + 0.588336i \(0.200217\pi\)
\(710\) −22.9884 −0.862739
\(711\) 12.3113 0.461709
\(712\) 18.9492 0.710150
\(713\) 46.4837 1.74083
\(714\) 1.09783 0.0410853
\(715\) 6.98876 0.261365
\(716\) −26.3191 −0.983589
\(717\) 17.0924 0.638327
\(718\) −2.13824 −0.0797983
\(719\) −19.9392 −0.743606 −0.371803 0.928312i \(-0.621260\pi\)
−0.371803 + 0.928312i \(0.621260\pi\)
\(720\) −7.33391 −0.273319
\(721\) 4.21185 0.156858
\(722\) 94.2465 3.50749
\(723\) −17.3130 −0.643878
\(724\) 20.6965 0.769179
\(725\) −11.6128 −0.431287
\(726\) −42.0445 −1.56042
\(727\) −17.0629 −0.632827 −0.316413 0.948621i \(-0.602479\pi\)
−0.316413 + 0.948621i \(0.602479\pi\)
\(728\) −0.495912 −0.0183797
\(729\) 1.00000 0.0370370
\(730\) 33.8971 1.25459
\(731\) 3.95148 0.146151
\(732\) −13.6539 −0.504664
\(733\) −26.2776 −0.970585 −0.485293 0.874352i \(-0.661287\pi\)
−0.485293 + 0.874352i \(0.661287\pi\)
\(734\) −17.2602 −0.637085
\(735\) 10.1238 0.373422
\(736\) 30.9522 1.14091
\(737\) 26.5059 0.976358
\(738\) −13.6398 −0.502088
\(739\) −8.07199 −0.296933 −0.148466 0.988917i \(-0.547434\pi\)
−0.148466 + 0.988917i \(0.547434\pi\)
\(740\) −13.2714 −0.487866
\(741\) 6.60932 0.242800
\(742\) −9.45103 −0.346958
\(743\) 16.8378 0.617719 0.308860 0.951108i \(-0.400053\pi\)
0.308860 + 0.951108i \(0.400053\pi\)
\(744\) −10.8081 −0.396245
\(745\) −31.9330 −1.16994
\(746\) −46.0326 −1.68537
\(747\) 8.32039 0.304427
\(748\) −8.29402 −0.303260
\(749\) 5.77990 0.211193
\(750\) 21.6578 0.790831
\(751\) 13.6448 0.497907 0.248954 0.968515i \(-0.419913\pi\)
0.248954 + 0.968515i \(0.419913\pi\)
\(752\) 33.6570 1.22734
\(753\) −18.0587 −0.658094
\(754\) 6.33969 0.230878
\(755\) 2.67166 0.0972316
\(756\) −0.847005 −0.0308053
\(757\) 20.8405 0.757460 0.378730 0.925507i \(-0.376361\pi\)
0.378730 + 0.925507i \(0.376361\pi\)
\(758\) −28.2501 −1.02609
\(759\) 26.4187 0.958940
\(760\) 13.4698 0.488600
\(761\) 13.2014 0.478552 0.239276 0.970952i \(-0.423090\pi\)
0.239276 + 0.970952i \(0.423090\pi\)
\(762\) 15.5666 0.563920
\(763\) −0.310440 −0.0112387
\(764\) 17.6411 0.638234
\(765\) −1.52272 −0.0550542
\(766\) 69.7222 2.51917
\(767\) 8.37124 0.302268
\(768\) −20.9579 −0.756254
\(769\) 12.2469 0.441634 0.220817 0.975315i \(-0.429128\pi\)
0.220817 + 0.975315i \(0.429128\pi\)
\(770\) 9.70542 0.349759
\(771\) 1.98632 0.0715357
\(772\) −24.0423 −0.865301
\(773\) −28.8898 −1.03909 −0.519546 0.854442i \(-0.673899\pi\)
−0.519546 + 0.854442i \(0.673899\pi\)
\(774\) −7.31673 −0.262994
\(775\) 27.3901 0.983881
\(776\) −16.1436 −0.579520
\(777\) 3.61714 0.129764
\(778\) 3.86077 0.138415
\(779\) 61.5864 2.20656
\(780\) −1.71969 −0.0615749
\(781\) −47.3355 −1.69380
\(782\) 8.42583 0.301307
\(783\) −4.33100 −0.154777
\(784\) 32.0211 1.14361
\(785\) −1.52272 −0.0543483
\(786\) −17.2747 −0.616168
\(787\) −5.82375 −0.207594 −0.103797 0.994598i \(-0.533099\pi\)
−0.103797 + 0.994598i \(0.533099\pi\)
\(788\) 11.2225 0.399786
\(789\) −1.85794 −0.0661444
\(790\) 34.7122 1.23500
\(791\) 3.51613 0.125019
\(792\) −6.14274 −0.218273
\(793\) 7.55566 0.268309
\(794\) −35.8547 −1.27244
\(795\) 13.1088 0.464923
\(796\) −4.75731 −0.168618
\(797\) 27.3577 0.969059 0.484529 0.874775i \(-0.338991\pi\)
0.484529 + 0.874775i \(0.338991\pi\)
\(798\) 9.17848 0.324915
\(799\) 6.98813 0.247222
\(800\) 18.2383 0.644822
\(801\) −17.9096 −0.632804
\(802\) 67.1304 2.37046
\(803\) 69.7977 2.46311
\(804\) −6.52219 −0.230020
\(805\) −4.10822 −0.144796
\(806\) −14.9529 −0.526694
\(807\) −16.4997 −0.580816
\(808\) 14.7482 0.518840
\(809\) −48.4762 −1.70433 −0.852166 0.523272i \(-0.824711\pi\)
−0.852166 + 0.523272i \(0.824711\pi\)
\(810\) 2.81954 0.0990687
\(811\) 1.62819 0.0571735 0.0285868 0.999591i \(-0.490899\pi\)
0.0285868 + 0.999591i \(0.490899\pi\)
\(812\) 3.66838 0.128735
\(813\) −17.2735 −0.605808
\(814\) −65.5846 −2.29874
\(815\) 14.9150 0.522448
\(816\) −4.81631 −0.168605
\(817\) 33.0365 1.15580
\(818\) 48.1883 1.68486
\(819\) 0.468706 0.0163779
\(820\) −16.0243 −0.559593
\(821\) 2.22097 0.0775124 0.0387562 0.999249i \(-0.487660\pi\)
0.0387562 + 0.999249i \(0.487660\pi\)
\(822\) 41.5457 1.44907
\(823\) −48.9827 −1.70743 −0.853714 0.520742i \(-0.825655\pi\)
−0.853714 + 0.520742i \(0.825655\pi\)
\(824\) −7.51623 −0.261840
\(825\) 15.5670 0.541973
\(826\) 11.6253 0.404496
\(827\) 2.95069 0.102606 0.0513028 0.998683i \(-0.483663\pi\)
0.0513028 + 0.998683i \(0.483663\pi\)
\(828\) −6.50074 −0.225916
\(829\) 35.7698 1.24234 0.621168 0.783678i \(-0.286659\pi\)
0.621168 + 0.783678i \(0.286659\pi\)
\(830\) 23.4597 0.814298
\(831\) −19.5227 −0.677234
\(832\) −2.34179 −0.0811871
\(833\) 6.64847 0.230356
\(834\) 26.6376 0.922383
\(835\) 32.6908 1.13131
\(836\) −69.3426 −2.39826
\(837\) 10.2152 0.353088
\(838\) 16.5662 0.572270
\(839\) −8.24737 −0.284731 −0.142365 0.989814i \(-0.545471\pi\)
−0.142365 + 0.989814i \(0.545471\pi\)
\(840\) 0.955221 0.0329583
\(841\) −10.2425 −0.353189
\(842\) −35.8849 −1.23667
\(843\) 6.83926 0.235557
\(844\) −35.8200 −1.23297
\(845\) −18.8438 −0.648246
\(846\) −12.9395 −0.444870
\(847\) 13.4626 0.462581
\(848\) 41.4627 1.42384
\(849\) −1.47130 −0.0504950
\(850\) 4.96484 0.170293
\(851\) 27.7614 0.951650
\(852\) 11.6476 0.399042
\(853\) 4.11677 0.140956 0.0704778 0.997513i \(-0.477548\pi\)
0.0704778 + 0.997513i \(0.477548\pi\)
\(854\) 10.4927 0.359052
\(855\) −12.7308 −0.435384
\(856\) −10.3145 −0.352541
\(857\) 14.8778 0.508216 0.254108 0.967176i \(-0.418218\pi\)
0.254108 + 0.967176i \(0.418218\pi\)
\(858\) −8.49840 −0.290131
\(859\) −14.5402 −0.496104 −0.248052 0.968747i \(-0.579790\pi\)
−0.248052 + 0.968747i \(0.579790\pi\)
\(860\) −8.59584 −0.293116
\(861\) 4.36745 0.148842
\(862\) 45.3949 1.54616
\(863\) −13.3109 −0.453109 −0.226554 0.973999i \(-0.572746\pi\)
−0.226554 + 0.973999i \(0.572746\pi\)
\(864\) 6.80201 0.231409
\(865\) −15.7880 −0.536809
\(866\) 12.1221 0.411927
\(867\) −1.00000 −0.0339618
\(868\) −8.65231 −0.293679
\(869\) 71.4760 2.42466
\(870\) −12.2114 −0.414006
\(871\) 3.60917 0.122292
\(872\) 0.553992 0.0187606
\(873\) 15.2579 0.516402
\(874\) 70.4446 2.38282
\(875\) −6.93481 −0.234439
\(876\) −17.1748 −0.580283
\(877\) −45.5288 −1.53740 −0.768699 0.639611i \(-0.779096\pi\)
−0.768699 + 0.639611i \(0.779096\pi\)
\(878\) 41.5820 1.40332
\(879\) 15.0191 0.506580
\(880\) −42.5787 −1.43533
\(881\) −23.8946 −0.805030 −0.402515 0.915413i \(-0.631864\pi\)
−0.402515 + 0.915413i \(0.631864\pi\)
\(882\) −12.3106 −0.414520
\(883\) 36.5644 1.23049 0.615245 0.788336i \(-0.289057\pi\)
0.615245 + 0.788336i \(0.289057\pi\)
\(884\) −1.12935 −0.0379843
\(885\) −16.1246 −0.542022
\(886\) 53.4945 1.79718
\(887\) −56.5770 −1.89967 −0.949834 0.312753i \(-0.898749\pi\)
−0.949834 + 0.312753i \(0.898749\pi\)
\(888\) −6.45493 −0.216613
\(889\) −4.98443 −0.167172
\(890\) −50.4968 −1.69266
\(891\) 5.80574 0.194499
\(892\) −3.85075 −0.128933
\(893\) 58.4246 1.95510
\(894\) 38.8308 1.29870
\(895\) −28.0533 −0.937717
\(896\) 4.81367 0.160813
\(897\) 3.59730 0.120110
\(898\) −29.0497 −0.969401
\(899\) −44.2419 −1.47555
\(900\) −3.83050 −0.127683
\(901\) 8.60881 0.286801
\(902\) −79.1891 −2.63671
\(903\) 2.34281 0.0779639
\(904\) −6.27468 −0.208693
\(905\) 22.0602 0.733306
\(906\) −3.24876 −0.107933
\(907\) −21.7146 −0.721023 −0.360511 0.932755i \(-0.617398\pi\)
−0.360511 + 0.932755i \(0.617398\pi\)
\(908\) −39.2301 −1.30190
\(909\) −13.9391 −0.462331
\(910\) 1.32154 0.0438085
\(911\) −1.17482 −0.0389237 −0.0194618 0.999811i \(-0.506195\pi\)
−0.0194618 + 0.999811i \(0.506195\pi\)
\(912\) −40.2670 −1.33337
\(913\) 48.3060 1.59869
\(914\) 9.24560 0.305817
\(915\) −14.5536 −0.481128
\(916\) −4.42830 −0.146315
\(917\) 5.53134 0.182661
\(918\) 1.85165 0.0611134
\(919\) 43.5319 1.43599 0.717993 0.696050i \(-0.245061\pi\)
0.717993 + 0.696050i \(0.245061\pi\)
\(920\) 7.33130 0.241706
\(921\) −24.0001 −0.790829
\(922\) 18.0809 0.595462
\(923\) −6.44543 −0.212154
\(924\) −4.91749 −0.161773
\(925\) 16.3582 0.537853
\(926\) −11.7467 −0.386021
\(927\) 7.10387 0.233322
\(928\) −29.4595 −0.967054
\(929\) −31.0750 −1.01954 −0.509769 0.860311i \(-0.670269\pi\)
−0.509769 + 0.860311i \(0.670269\pi\)
\(930\) 28.8021 0.944460
\(931\) 55.5849 1.82172
\(932\) 28.6174 0.937394
\(933\) −29.6667 −0.971245
\(934\) −33.4449 −1.09435
\(935\) −8.84053 −0.289116
\(936\) −0.836425 −0.0273394
\(937\) −31.2913 −1.02224 −0.511121 0.859509i \(-0.670770\pi\)
−0.511121 + 0.859509i \(0.670770\pi\)
\(938\) 5.01212 0.163652
\(939\) −5.39192 −0.175959
\(940\) −15.2016 −0.495822
\(941\) −12.3214 −0.401665 −0.200832 0.979626i \(-0.564365\pi\)
−0.200832 + 0.979626i \(0.564365\pi\)
\(942\) 1.85165 0.0603299
\(943\) 33.5201 1.09156
\(944\) −51.0014 −1.65995
\(945\) −0.902816 −0.0293686
\(946\) −42.4790 −1.38111
\(947\) −23.6727 −0.769259 −0.384630 0.923071i \(-0.625671\pi\)
−0.384630 + 0.923071i \(0.625671\pi\)
\(948\) −17.5878 −0.571225
\(949\) 9.50399 0.308512
\(950\) 41.5088 1.34672
\(951\) 9.67677 0.313791
\(952\) 0.627311 0.0203313
\(953\) −46.1271 −1.49420 −0.747101 0.664710i \(-0.768555\pi\)
−0.747101 + 0.664710i \(0.768555\pi\)
\(954\) −15.9405 −0.516092
\(955\) 18.8035 0.608468
\(956\) −24.4181 −0.789736
\(957\) −25.1446 −0.812810
\(958\) −38.2313 −1.23520
\(959\) −13.3029 −0.429573
\(960\) 4.51074 0.145583
\(961\) 73.3499 2.36613
\(962\) −8.93032 −0.287925
\(963\) 9.74860 0.314144
\(964\) 24.7332 0.796604
\(965\) −25.6265 −0.824945
\(966\) 4.99564 0.160732
\(967\) −12.6008 −0.405213 −0.202607 0.979260i \(-0.564941\pi\)
−0.202607 + 0.979260i \(0.564941\pi\)
\(968\) −24.0246 −0.772180
\(969\) −8.36055 −0.268580
\(970\) 43.0203 1.38130
\(971\) −4.23955 −0.136054 −0.0680268 0.997683i \(-0.521670\pi\)
−0.0680268 + 0.997683i \(0.521670\pi\)
\(972\) −1.42859 −0.0458221
\(973\) −8.52932 −0.273438
\(974\) −33.8894 −1.08589
\(975\) 2.11968 0.0678840
\(976\) −46.0325 −1.47346
\(977\) −16.2196 −0.518911 −0.259455 0.965755i \(-0.583543\pi\)
−0.259455 + 0.965755i \(0.583543\pi\)
\(978\) −18.1367 −0.579949
\(979\) −103.978 −3.32316
\(980\) −14.4628 −0.461996
\(981\) −0.523599 −0.0167172
\(982\) −4.97353 −0.158712
\(983\) −3.05502 −0.0974399 −0.0487199 0.998812i \(-0.515514\pi\)
−0.0487199 + 0.998812i \(0.515514\pi\)
\(984\) −7.79390 −0.248460
\(985\) 11.9620 0.381141
\(986\) −8.01947 −0.255392
\(987\) 4.14323 0.131880
\(988\) −9.44202 −0.300391
\(989\) 17.9810 0.571763
\(990\) 16.3695 0.520258
\(991\) 45.4318 1.44319 0.721594 0.692316i \(-0.243410\pi\)
0.721594 + 0.692316i \(0.243410\pi\)
\(992\) 69.4837 2.20611
\(993\) 13.8446 0.439346
\(994\) −8.95088 −0.283905
\(995\) −5.07078 −0.160754
\(996\) −11.8864 −0.376636
\(997\) −12.1999 −0.386375 −0.193188 0.981162i \(-0.561883\pi\)
−0.193188 + 0.981162i \(0.561883\pi\)
\(998\) −51.9140 −1.64331
\(999\) 6.10080 0.193021
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 8007.2.a.f.1.40 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.40 48 1.1 even 1 trivial