Properties

Label 8007.2.a.f.1.36
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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 1.36
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.40476 q^{2} -1.00000 q^{3} -0.0266631 q^{4} +2.64776 q^{5} -1.40476 q^{6} -2.79354 q^{7} -2.84697 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.40476 q^{2} -1.00000 q^{3} -0.0266631 q^{4} +2.64776 q^{5} -1.40476 q^{6} -2.79354 q^{7} -2.84697 q^{8} +1.00000 q^{9} +3.71946 q^{10} +1.62137 q^{11} +0.0266631 q^{12} +0.165854 q^{13} -3.92423 q^{14} -2.64776 q^{15} -3.94596 q^{16} -1.00000 q^{17} +1.40476 q^{18} -0.0799859 q^{19} -0.0705975 q^{20} +2.79354 q^{21} +2.27763 q^{22} +4.53081 q^{23} +2.84697 q^{24} +2.01065 q^{25} +0.232985 q^{26} -1.00000 q^{27} +0.0744843 q^{28} -2.83514 q^{29} -3.71946 q^{30} +4.25529 q^{31} +0.150819 q^{32} -1.62137 q^{33} -1.40476 q^{34} -7.39662 q^{35} -0.0266631 q^{36} -3.78936 q^{37} -0.112361 q^{38} -0.165854 q^{39} -7.53809 q^{40} +8.76284 q^{41} +3.92423 q^{42} -12.2201 q^{43} -0.0432307 q^{44} +2.64776 q^{45} +6.36468 q^{46} +3.98690 q^{47} +3.94596 q^{48} +0.803846 q^{49} +2.82447 q^{50} +1.00000 q^{51} -0.00442219 q^{52} -10.2460 q^{53} -1.40476 q^{54} +4.29300 q^{55} +7.95310 q^{56} +0.0799859 q^{57} -3.98267 q^{58} -8.23446 q^{59} +0.0705975 q^{60} +8.41665 q^{61} +5.97764 q^{62} -2.79354 q^{63} +8.10379 q^{64} +0.439143 q^{65} -2.27763 q^{66} +5.72102 q^{67} +0.0266631 q^{68} -4.53081 q^{69} -10.3904 q^{70} +7.22392 q^{71} -2.84697 q^{72} -0.0542503 q^{73} -5.32312 q^{74} -2.01065 q^{75} +0.00213267 q^{76} -4.52935 q^{77} -0.232985 q^{78} -4.31406 q^{79} -10.4480 q^{80} +1.00000 q^{81} +12.3096 q^{82} -7.16554 q^{83} -0.0744843 q^{84} -2.64776 q^{85} -17.1663 q^{86} +2.83514 q^{87} -4.61598 q^{88} -12.8536 q^{89} +3.71946 q^{90} -0.463320 q^{91} -0.120805 q^{92} -4.25529 q^{93} +5.60062 q^{94} -0.211784 q^{95} -0.150819 q^{96} +2.43175 q^{97} +1.12921 q^{98} +1.62137 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40476 0.993312 0.496656 0.867948i \(-0.334561\pi\)
0.496656 + 0.867948i \(0.334561\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.0266631 −0.0133315
\(5\) 2.64776 1.18412 0.592058 0.805896i \(-0.298316\pi\)
0.592058 + 0.805896i \(0.298316\pi\)
\(6\) −1.40476 −0.573489
\(7\) −2.79354 −1.05586 −0.527929 0.849289i \(-0.677031\pi\)
−0.527929 + 0.849289i \(0.677031\pi\)
\(8\) −2.84697 −1.00655
\(9\) 1.00000 0.333333
\(10\) 3.71946 1.17620
\(11\) 1.62137 0.488861 0.244431 0.969667i \(-0.421399\pi\)
0.244431 + 0.969667i \(0.421399\pi\)
\(12\) 0.0266631 0.00769697
\(13\) 0.165854 0.0459997 0.0229998 0.999735i \(-0.492678\pi\)
0.0229998 + 0.999735i \(0.492678\pi\)
\(14\) −3.92423 −1.04880
\(15\) −2.64776 −0.683649
\(16\) −3.94596 −0.986491
\(17\) −1.00000 −0.242536
\(18\) 1.40476 0.331104
\(19\) −0.0799859 −0.0183500 −0.00917501 0.999958i \(-0.502921\pi\)
−0.00917501 + 0.999958i \(0.502921\pi\)
\(20\) −0.0705975 −0.0157861
\(21\) 2.79354 0.609600
\(22\) 2.27763 0.485592
\(23\) 4.53081 0.944739 0.472370 0.881401i \(-0.343399\pi\)
0.472370 + 0.881401i \(0.343399\pi\)
\(24\) 2.84697 0.581134
\(25\) 2.01065 0.402129
\(26\) 0.232985 0.0456920
\(27\) −1.00000 −0.192450
\(28\) 0.0744843 0.0140762
\(29\) −2.83514 −0.526472 −0.263236 0.964731i \(-0.584790\pi\)
−0.263236 + 0.964731i \(0.584790\pi\)
\(30\) −3.71946 −0.679077
\(31\) 4.25529 0.764273 0.382136 0.924106i \(-0.375188\pi\)
0.382136 + 0.924106i \(0.375188\pi\)
\(32\) 0.150819 0.0266613
\(33\) −1.62137 −0.282244
\(34\) −1.40476 −0.240914
\(35\) −7.39662 −1.25026
\(36\) −0.0266631 −0.00444385
\(37\) −3.78936 −0.622967 −0.311484 0.950252i \(-0.600826\pi\)
−0.311484 + 0.950252i \(0.600826\pi\)
\(38\) −0.112361 −0.0182273
\(39\) −0.165854 −0.0265579
\(40\) −7.53809 −1.19188
\(41\) 8.76284 1.36853 0.684263 0.729235i \(-0.260124\pi\)
0.684263 + 0.729235i \(0.260124\pi\)
\(42\) 3.92423 0.605523
\(43\) −12.2201 −1.86355 −0.931777 0.363030i \(-0.881742\pi\)
−0.931777 + 0.363030i \(0.881742\pi\)
\(44\) −0.0432307 −0.00651727
\(45\) 2.64776 0.394705
\(46\) 6.36468 0.938421
\(47\) 3.98690 0.581549 0.290775 0.956792i \(-0.406087\pi\)
0.290775 + 0.956792i \(0.406087\pi\)
\(48\) 3.94596 0.569551
\(49\) 0.803846 0.114835
\(50\) 2.82447 0.399440
\(51\) 1.00000 0.140028
\(52\) −0.00442219 −0.000613247 0
\(53\) −10.2460 −1.40740 −0.703700 0.710497i \(-0.748470\pi\)
−0.703700 + 0.710497i \(0.748470\pi\)
\(54\) −1.40476 −0.191163
\(55\) 4.29300 0.578868
\(56\) 7.95310 1.06278
\(57\) 0.0799859 0.0105944
\(58\) −3.98267 −0.522951
\(59\) −8.23446 −1.07204 −0.536018 0.844207i \(-0.680072\pi\)
−0.536018 + 0.844207i \(0.680072\pi\)
\(60\) 0.0705975 0.00911410
\(61\) 8.41665 1.07764 0.538821 0.842421i \(-0.318870\pi\)
0.538821 + 0.842421i \(0.318870\pi\)
\(62\) 5.97764 0.759161
\(63\) −2.79354 −0.351953
\(64\) 8.10379 1.01297
\(65\) 0.439143 0.0544689
\(66\) −2.27763 −0.280356
\(67\) 5.72102 0.698933 0.349467 0.936949i \(-0.386363\pi\)
0.349467 + 0.936949i \(0.386363\pi\)
\(68\) 0.0266631 0.00323337
\(69\) −4.53081 −0.545445
\(70\) −10.3904 −1.24190
\(71\) 7.22392 0.857321 0.428661 0.903466i \(-0.358986\pi\)
0.428661 + 0.903466i \(0.358986\pi\)
\(72\) −2.84697 −0.335518
\(73\) −0.0542503 −0.00634952 −0.00317476 0.999995i \(-0.501011\pi\)
−0.00317476 + 0.999995i \(0.501011\pi\)
\(74\) −5.32312 −0.618801
\(75\) −2.01065 −0.232170
\(76\) 0.00213267 0.000244634 0
\(77\) −4.52935 −0.516168
\(78\) −0.232985 −0.0263803
\(79\) −4.31406 −0.485370 −0.242685 0.970105i \(-0.578028\pi\)
−0.242685 + 0.970105i \(0.578028\pi\)
\(80\) −10.4480 −1.16812
\(81\) 1.00000 0.111111
\(82\) 12.3096 1.35937
\(83\) −7.16554 −0.786520 −0.393260 0.919427i \(-0.628653\pi\)
−0.393260 + 0.919427i \(0.628653\pi\)
\(84\) −0.0744843 −0.00812691
\(85\) −2.64776 −0.287190
\(86\) −17.1663 −1.85109
\(87\) 2.83514 0.303959
\(88\) −4.61598 −0.492065
\(89\) −12.8536 −1.36248 −0.681239 0.732061i \(-0.738559\pi\)
−0.681239 + 0.732061i \(0.738559\pi\)
\(90\) 3.71946 0.392065
\(91\) −0.463320 −0.0485691
\(92\) −0.120805 −0.0125948
\(93\) −4.25529 −0.441253
\(94\) 5.60062 0.577660
\(95\) −0.211784 −0.0217285
\(96\) −0.150819 −0.0153929
\(97\) 2.43175 0.246907 0.123453 0.992350i \(-0.460603\pi\)
0.123453 + 0.992350i \(0.460603\pi\)
\(98\) 1.12921 0.114067
\(99\) 1.62137 0.162954
\(100\) −0.0536101 −0.00536101
\(101\) −15.6388 −1.55612 −0.778059 0.628191i \(-0.783796\pi\)
−0.778059 + 0.628191i \(0.783796\pi\)
\(102\) 1.40476 0.139091
\(103\) −6.59769 −0.650090 −0.325045 0.945699i \(-0.605379\pi\)
−0.325045 + 0.945699i \(0.605379\pi\)
\(104\) −0.472181 −0.0463012
\(105\) 7.39662 0.721836
\(106\) −14.3932 −1.39799
\(107\) 15.4981 1.49826 0.749128 0.662426i \(-0.230473\pi\)
0.749128 + 0.662426i \(0.230473\pi\)
\(108\) 0.0266631 0.00256566
\(109\) −10.2838 −0.985008 −0.492504 0.870310i \(-0.663918\pi\)
−0.492504 + 0.870310i \(0.663918\pi\)
\(110\) 6.03061 0.574996
\(111\) 3.78936 0.359670
\(112\) 11.0232 1.04159
\(113\) −10.1906 −0.958650 −0.479325 0.877637i \(-0.659119\pi\)
−0.479325 + 0.877637i \(0.659119\pi\)
\(114\) 0.112361 0.0105235
\(115\) 11.9965 1.11868
\(116\) 0.0755935 0.00701868
\(117\) 0.165854 0.0153332
\(118\) −11.5674 −1.06487
\(119\) 2.79354 0.256083
\(120\) 7.53809 0.688130
\(121\) −8.37116 −0.761015
\(122\) 11.8233 1.07043
\(123\) −8.76284 −0.790119
\(124\) −0.113459 −0.0101889
\(125\) −7.91510 −0.707948
\(126\) −3.92423 −0.349599
\(127\) −6.48200 −0.575184 −0.287592 0.957753i \(-0.592855\pi\)
−0.287592 + 0.957753i \(0.592855\pi\)
\(128\) 11.0822 0.979538
\(129\) 12.2201 1.07592
\(130\) 0.616888 0.0541046
\(131\) −2.31920 −0.202629 −0.101315 0.994854i \(-0.532305\pi\)
−0.101315 + 0.994854i \(0.532305\pi\)
\(132\) 0.0432307 0.00376275
\(133\) 0.223443 0.0193750
\(134\) 8.03663 0.694259
\(135\) −2.64776 −0.227883
\(136\) 2.84697 0.244125
\(137\) 10.3119 0.881003 0.440501 0.897752i \(-0.354801\pi\)
0.440501 + 0.897752i \(0.354801\pi\)
\(138\) −6.36468 −0.541797
\(139\) −7.72575 −0.655289 −0.327645 0.944801i \(-0.606255\pi\)
−0.327645 + 0.944801i \(0.606255\pi\)
\(140\) 0.197217 0.0166679
\(141\) −3.98690 −0.335758
\(142\) 10.1478 0.851587
\(143\) 0.268911 0.0224875
\(144\) −3.94596 −0.328830
\(145\) −7.50677 −0.623403
\(146\) −0.0762084 −0.00630705
\(147\) −0.803846 −0.0663001
\(148\) 0.101036 0.00830511
\(149\) 18.1734 1.48883 0.744413 0.667719i \(-0.232729\pi\)
0.744413 + 0.667719i \(0.232729\pi\)
\(150\) −2.82447 −0.230617
\(151\) −8.80913 −0.716877 −0.358438 0.933553i \(-0.616691\pi\)
−0.358438 + 0.933553i \(0.616691\pi\)
\(152\) 0.227717 0.0184703
\(153\) −1.00000 −0.0808452
\(154\) −6.36263 −0.512715
\(155\) 11.2670 0.904987
\(156\) 0.00442219 0.000354058 0
\(157\) −1.00000 −0.0798087
\(158\) −6.06020 −0.482123
\(159\) 10.2460 0.812563
\(160\) 0.399333 0.0315701
\(161\) −12.6570 −0.997510
\(162\) 1.40476 0.110368
\(163\) 10.9456 0.857327 0.428663 0.903464i \(-0.358985\pi\)
0.428663 + 0.903464i \(0.358985\pi\)
\(164\) −0.233644 −0.0182446
\(165\) −4.29300 −0.334210
\(166\) −10.0658 −0.781260
\(167\) −7.78150 −0.602151 −0.301075 0.953600i \(-0.597346\pi\)
−0.301075 + 0.953600i \(0.597346\pi\)
\(168\) −7.95310 −0.613595
\(169\) −12.9725 −0.997884
\(170\) −3.71946 −0.285269
\(171\) −0.0799859 −0.00611667
\(172\) 0.325827 0.0248441
\(173\) −15.7573 −1.19800 −0.599001 0.800748i \(-0.704436\pi\)
−0.599001 + 0.800748i \(0.704436\pi\)
\(174\) 3.98267 0.301926
\(175\) −5.61682 −0.424591
\(176\) −6.39786 −0.482257
\(177\) 8.23446 0.618940
\(178\) −18.0561 −1.35337
\(179\) −5.69874 −0.425944 −0.212972 0.977058i \(-0.568314\pi\)
−0.212972 + 0.977058i \(0.568314\pi\)
\(180\) −0.0705975 −0.00526203
\(181\) 9.01042 0.669739 0.334870 0.942264i \(-0.391308\pi\)
0.334870 + 0.942264i \(0.391308\pi\)
\(182\) −0.650851 −0.0482443
\(183\) −8.41665 −0.622176
\(184\) −12.8991 −0.950931
\(185\) −10.0333 −0.737665
\(186\) −5.97764 −0.438302
\(187\) −1.62137 −0.118566
\(188\) −0.106303 −0.00775295
\(189\) 2.79354 0.203200
\(190\) −0.297504 −0.0215832
\(191\) 12.6905 0.918255 0.459127 0.888370i \(-0.348162\pi\)
0.459127 + 0.888370i \(0.348162\pi\)
\(192\) −8.10379 −0.584841
\(193\) −17.2372 −1.24076 −0.620380 0.784301i \(-0.713022\pi\)
−0.620380 + 0.784301i \(0.713022\pi\)
\(194\) 3.41601 0.245255
\(195\) −0.439143 −0.0314477
\(196\) −0.0214330 −0.00153093
\(197\) −24.3145 −1.73233 −0.866167 0.499754i \(-0.833424\pi\)
−0.866167 + 0.499754i \(0.833424\pi\)
\(198\) 2.27763 0.161864
\(199\) −12.9913 −0.920930 −0.460465 0.887678i \(-0.652317\pi\)
−0.460465 + 0.887678i \(0.652317\pi\)
\(200\) −5.72424 −0.404765
\(201\) −5.72102 −0.403529
\(202\) −21.9687 −1.54571
\(203\) 7.92006 0.555879
\(204\) −0.0266631 −0.00186679
\(205\) 23.2019 1.62049
\(206\) −9.26814 −0.645742
\(207\) 4.53081 0.314913
\(208\) −0.654455 −0.0453783
\(209\) −0.129687 −0.00897061
\(210\) 10.3904 0.717009
\(211\) 14.7598 1.01611 0.508053 0.861326i \(-0.330365\pi\)
0.508053 + 0.861326i \(0.330365\pi\)
\(212\) 0.273191 0.0187628
\(213\) −7.22392 −0.494975
\(214\) 21.7710 1.48823
\(215\) −32.3560 −2.20666
\(216\) 2.84697 0.193711
\(217\) −11.8873 −0.806963
\(218\) −14.4462 −0.978420
\(219\) 0.0542503 0.00366590
\(220\) −0.114465 −0.00771721
\(221\) −0.165854 −0.0111566
\(222\) 5.32312 0.357265
\(223\) −1.98824 −0.133143 −0.0665713 0.997782i \(-0.521206\pi\)
−0.0665713 + 0.997782i \(0.521206\pi\)
\(224\) −0.421319 −0.0281505
\(225\) 2.01065 0.134043
\(226\) −14.3153 −0.952239
\(227\) −9.25134 −0.614033 −0.307016 0.951704i \(-0.599331\pi\)
−0.307016 + 0.951704i \(0.599331\pi\)
\(228\) −0.00213267 −0.000141240 0
\(229\) 7.45096 0.492373 0.246187 0.969222i \(-0.420822\pi\)
0.246187 + 0.969222i \(0.420822\pi\)
\(230\) 16.8522 1.11120
\(231\) 4.52935 0.298010
\(232\) 8.07154 0.529922
\(233\) −20.0603 −1.31420 −0.657098 0.753805i \(-0.728216\pi\)
−0.657098 + 0.753805i \(0.728216\pi\)
\(234\) 0.232985 0.0152307
\(235\) 10.5564 0.688622
\(236\) 0.219556 0.0142919
\(237\) 4.31406 0.280228
\(238\) 3.92423 0.254370
\(239\) 20.8806 1.35066 0.675328 0.737518i \(-0.264002\pi\)
0.675328 + 0.737518i \(0.264002\pi\)
\(240\) 10.4480 0.674414
\(241\) −17.9054 −1.15339 −0.576695 0.816959i \(-0.695658\pi\)
−0.576695 + 0.816959i \(0.695658\pi\)
\(242\) −11.7594 −0.755925
\(243\) −1.00000 −0.0641500
\(244\) −0.224414 −0.0143666
\(245\) 2.12839 0.135978
\(246\) −12.3096 −0.784834
\(247\) −0.0132660 −0.000844095 0
\(248\) −12.1147 −0.769282
\(249\) 7.16554 0.454098
\(250\) −11.1188 −0.703213
\(251\) −26.5402 −1.67520 −0.837601 0.546283i \(-0.816042\pi\)
−0.837601 + 0.546283i \(0.816042\pi\)
\(252\) 0.0744843 0.00469207
\(253\) 7.34611 0.461846
\(254\) −9.10562 −0.571337
\(255\) 2.64776 0.165809
\(256\) −0.639800 −0.0399875
\(257\) 1.12775 0.0703470 0.0351735 0.999381i \(-0.488802\pi\)
0.0351735 + 0.999381i \(0.488802\pi\)
\(258\) 17.1663 1.06873
\(259\) 10.5857 0.657764
\(260\) −0.0117089 −0.000726155 0
\(261\) −2.83514 −0.175491
\(262\) −3.25790 −0.201274
\(263\) −1.17905 −0.0727033 −0.0363516 0.999339i \(-0.511574\pi\)
−0.0363516 + 0.999339i \(0.511574\pi\)
\(264\) 4.61598 0.284094
\(265\) −27.1291 −1.66652
\(266\) 0.313883 0.0192454
\(267\) 12.8536 0.786627
\(268\) −0.152540 −0.00931786
\(269\) −27.3165 −1.66552 −0.832759 0.553635i \(-0.813240\pi\)
−0.832759 + 0.553635i \(0.813240\pi\)
\(270\) −3.71946 −0.226359
\(271\) −4.75613 −0.288914 −0.144457 0.989511i \(-0.546144\pi\)
−0.144457 + 0.989511i \(0.546144\pi\)
\(272\) 3.94596 0.239259
\(273\) 0.463320 0.0280414
\(274\) 14.4857 0.875110
\(275\) 3.26000 0.196585
\(276\) 0.120805 0.00727163
\(277\) 15.6079 0.937791 0.468895 0.883254i \(-0.344652\pi\)
0.468895 + 0.883254i \(0.344652\pi\)
\(278\) −10.8528 −0.650907
\(279\) 4.25529 0.254758
\(280\) 21.0579 1.25845
\(281\) −9.15864 −0.546358 −0.273179 0.961963i \(-0.588075\pi\)
−0.273179 + 0.961963i \(0.588075\pi\)
\(282\) −5.60062 −0.333512
\(283\) 30.4383 1.80937 0.904684 0.426083i \(-0.140107\pi\)
0.904684 + 0.426083i \(0.140107\pi\)
\(284\) −0.192612 −0.0114294
\(285\) 0.211784 0.0125450
\(286\) 0.377754 0.0223371
\(287\) −24.4793 −1.44497
\(288\) 0.150819 0.00888710
\(289\) 1.00000 0.0588235
\(290\) −10.5452 −0.619234
\(291\) −2.43175 −0.142552
\(292\) 0.00144648 8.46489e−5 0
\(293\) −0.983388 −0.0574501 −0.0287251 0.999587i \(-0.509145\pi\)
−0.0287251 + 0.999587i \(0.509145\pi\)
\(294\) −1.12921 −0.0658566
\(295\) −21.8029 −1.26941
\(296\) 10.7882 0.627050
\(297\) −1.62137 −0.0940814
\(298\) 25.5292 1.47887
\(299\) 0.751454 0.0434577
\(300\) 0.0536101 0.00309518
\(301\) 34.1374 1.96765
\(302\) −12.3747 −0.712082
\(303\) 15.6388 0.898425
\(304\) 0.315621 0.0181021
\(305\) 22.2853 1.27605
\(306\) −1.40476 −0.0803045
\(307\) −7.42666 −0.423862 −0.211931 0.977285i \(-0.567975\pi\)
−0.211931 + 0.977285i \(0.567975\pi\)
\(308\) 0.120767 0.00688131
\(309\) 6.59769 0.375330
\(310\) 15.8274 0.898934
\(311\) 24.4279 1.38518 0.692590 0.721331i \(-0.256469\pi\)
0.692590 + 0.721331i \(0.256469\pi\)
\(312\) 0.472181 0.0267320
\(313\) −20.0203 −1.13161 −0.565806 0.824538i \(-0.691435\pi\)
−0.565806 + 0.824538i \(0.691435\pi\)
\(314\) −1.40476 −0.0792749
\(315\) −7.39662 −0.416752
\(316\) 0.115026 0.00647073
\(317\) −21.5021 −1.20768 −0.603838 0.797107i \(-0.706363\pi\)
−0.603838 + 0.797107i \(0.706363\pi\)
\(318\) 14.3932 0.807128
\(319\) −4.59680 −0.257372
\(320\) 21.4569 1.19948
\(321\) −15.4981 −0.865018
\(322\) −17.7800 −0.990838
\(323\) 0.0799859 0.00445053
\(324\) −0.0266631 −0.00148128
\(325\) 0.333474 0.0184978
\(326\) 15.3759 0.851593
\(327\) 10.2838 0.568695
\(328\) −24.9475 −1.37750
\(329\) −11.1376 −0.614033
\(330\) −6.03061 −0.331974
\(331\) 14.6065 0.802845 0.401422 0.915893i \(-0.368516\pi\)
0.401422 + 0.915893i \(0.368516\pi\)
\(332\) 0.191056 0.0104855
\(333\) −3.78936 −0.207656
\(334\) −10.9311 −0.598123
\(335\) 15.1479 0.827618
\(336\) −11.0232 −0.601364
\(337\) 19.1280 1.04197 0.520983 0.853567i \(-0.325565\pi\)
0.520983 + 0.853567i \(0.325565\pi\)
\(338\) −18.2232 −0.991210
\(339\) 10.1906 0.553477
\(340\) 0.0705975 0.00382869
\(341\) 6.89939 0.373623
\(342\) −0.112361 −0.00607576
\(343\) 17.3092 0.934608
\(344\) 34.7903 1.87577
\(345\) −11.9965 −0.645870
\(346\) −22.1351 −1.18999
\(347\) −9.50133 −0.510058 −0.255029 0.966933i \(-0.582085\pi\)
−0.255029 + 0.966933i \(0.582085\pi\)
\(348\) −0.0755935 −0.00405224
\(349\) 35.0893 1.87829 0.939143 0.343526i \(-0.111621\pi\)
0.939143 + 0.343526i \(0.111621\pi\)
\(350\) −7.89025 −0.421752
\(351\) −0.165854 −0.00885264
\(352\) 0.244533 0.0130337
\(353\) −16.7172 −0.889764 −0.444882 0.895589i \(-0.646754\pi\)
−0.444882 + 0.895589i \(0.646754\pi\)
\(354\) 11.5674 0.614801
\(355\) 19.1272 1.01517
\(356\) 0.342716 0.0181639
\(357\) −2.79354 −0.147850
\(358\) −8.00533 −0.423095
\(359\) −12.8173 −0.676473 −0.338236 0.941061i \(-0.609830\pi\)
−0.338236 + 0.941061i \(0.609830\pi\)
\(360\) −7.53809 −0.397292
\(361\) −18.9936 −0.999663
\(362\) 12.6574 0.665260
\(363\) 8.37116 0.439372
\(364\) 0.0123535 0.000647501 0
\(365\) −0.143642 −0.00751856
\(366\) −11.8233 −0.618015
\(367\) −12.2019 −0.636933 −0.318467 0.947934i \(-0.603168\pi\)
−0.318467 + 0.947934i \(0.603168\pi\)
\(368\) −17.8784 −0.931976
\(369\) 8.76284 0.456175
\(370\) −14.0944 −0.732731
\(371\) 28.6227 1.48601
\(372\) 0.113459 0.00588258
\(373\) 6.88413 0.356447 0.178223 0.983990i \(-0.442965\pi\)
0.178223 + 0.983990i \(0.442965\pi\)
\(374\) −2.27763 −0.117773
\(375\) 7.91510 0.408734
\(376\) −11.3506 −0.585361
\(377\) −0.470220 −0.0242175
\(378\) 3.92423 0.201841
\(379\) 34.1792 1.75567 0.877834 0.478966i \(-0.158988\pi\)
0.877834 + 0.478966i \(0.158988\pi\)
\(380\) 0.00564681 0.000289675 0
\(381\) 6.48200 0.332083
\(382\) 17.8271 0.912113
\(383\) −22.4535 −1.14732 −0.573661 0.819093i \(-0.694477\pi\)
−0.573661 + 0.819093i \(0.694477\pi\)
\(384\) −11.0822 −0.565536
\(385\) −11.9927 −0.611202
\(386\) −24.2140 −1.23246
\(387\) −12.2201 −0.621185
\(388\) −0.0648380 −0.00329165
\(389\) −17.9346 −0.909320 −0.454660 0.890665i \(-0.650239\pi\)
−0.454660 + 0.890665i \(0.650239\pi\)
\(390\) −0.616888 −0.0312373
\(391\) −4.53081 −0.229133
\(392\) −2.28852 −0.115588
\(393\) 2.31920 0.116988
\(394\) −34.1559 −1.72075
\(395\) −11.4226 −0.574734
\(396\) −0.0432307 −0.00217242
\(397\) −28.1059 −1.41060 −0.705299 0.708910i \(-0.749187\pi\)
−0.705299 + 0.708910i \(0.749187\pi\)
\(398\) −18.2496 −0.914771
\(399\) −0.223443 −0.0111862
\(400\) −7.93394 −0.396697
\(401\) −23.0560 −1.15136 −0.575681 0.817675i \(-0.695263\pi\)
−0.575681 + 0.817675i \(0.695263\pi\)
\(402\) −8.03663 −0.400831
\(403\) 0.705758 0.0351563
\(404\) 0.416979 0.0207455
\(405\) 2.64776 0.131568
\(406\) 11.1257 0.552161
\(407\) −6.14395 −0.304544
\(408\) −2.84697 −0.140946
\(409\) 19.0173 0.940345 0.470173 0.882574i \(-0.344192\pi\)
0.470173 + 0.882574i \(0.344192\pi\)
\(410\) 32.5930 1.60965
\(411\) −10.3119 −0.508647
\(412\) 0.175915 0.00866670
\(413\) 23.0033 1.13192
\(414\) 6.36468 0.312807
\(415\) −18.9727 −0.931331
\(416\) 0.0250140 0.00122641
\(417\) 7.72575 0.378331
\(418\) −0.182178 −0.00891061
\(419\) 39.0848 1.90942 0.954710 0.297538i \(-0.0961657\pi\)
0.954710 + 0.297538i \(0.0961657\pi\)
\(420\) −0.197217 −0.00962319
\(421\) 7.19257 0.350545 0.175272 0.984520i \(-0.443919\pi\)
0.175272 + 0.984520i \(0.443919\pi\)
\(422\) 20.7339 1.00931
\(423\) 3.98690 0.193850
\(424\) 29.1701 1.41662
\(425\) −2.01065 −0.0975307
\(426\) −10.1478 −0.491664
\(427\) −23.5122 −1.13784
\(428\) −0.413227 −0.0199741
\(429\) −0.268911 −0.0129831
\(430\) −45.4523 −2.19191
\(431\) −15.5779 −0.750363 −0.375182 0.926951i \(-0.622420\pi\)
−0.375182 + 0.926951i \(0.622420\pi\)
\(432\) 3.94596 0.189850
\(433\) 37.7488 1.81409 0.907047 0.421030i \(-0.138331\pi\)
0.907047 + 0.421030i \(0.138331\pi\)
\(434\) −16.6988 −0.801566
\(435\) 7.50677 0.359922
\(436\) 0.274198 0.0131317
\(437\) −0.362401 −0.0173360
\(438\) 0.0762084 0.00364138
\(439\) −33.0220 −1.57606 −0.788028 0.615640i \(-0.788898\pi\)
−0.788028 + 0.615640i \(0.788898\pi\)
\(440\) −12.2220 −0.582662
\(441\) 0.803846 0.0382784
\(442\) −0.232985 −0.0110819
\(443\) −12.2710 −0.583015 −0.291507 0.956569i \(-0.594157\pi\)
−0.291507 + 0.956569i \(0.594157\pi\)
\(444\) −0.101036 −0.00479496
\(445\) −34.0333 −1.61333
\(446\) −2.79299 −0.132252
\(447\) −18.1734 −0.859574
\(448\) −22.6382 −1.06956
\(449\) 33.3696 1.57481 0.787404 0.616437i \(-0.211425\pi\)
0.787404 + 0.616437i \(0.211425\pi\)
\(450\) 2.82447 0.133147
\(451\) 14.2078 0.669019
\(452\) 0.271713 0.0127803
\(453\) 8.80913 0.413889
\(454\) −12.9959 −0.609926
\(455\) −1.22676 −0.0575114
\(456\) −0.227717 −0.0106638
\(457\) −21.0599 −0.985142 −0.492571 0.870272i \(-0.663943\pi\)
−0.492571 + 0.870272i \(0.663943\pi\)
\(458\) 10.4668 0.489080
\(459\) 1.00000 0.0466760
\(460\) −0.319864 −0.0149137
\(461\) 8.76368 0.408165 0.204083 0.978954i \(-0.434579\pi\)
0.204083 + 0.978954i \(0.434579\pi\)
\(462\) 6.36263 0.296016
\(463\) 17.7281 0.823893 0.411946 0.911208i \(-0.364849\pi\)
0.411946 + 0.911208i \(0.364849\pi\)
\(464\) 11.1873 0.519360
\(465\) −11.2670 −0.522495
\(466\) −28.1798 −1.30541
\(467\) 3.78890 0.175329 0.0876647 0.996150i \(-0.472060\pi\)
0.0876647 + 0.996150i \(0.472060\pi\)
\(468\) −0.00442219 −0.000204416 0
\(469\) −15.9819 −0.737974
\(470\) 14.8291 0.684016
\(471\) 1.00000 0.0460776
\(472\) 23.4432 1.07906
\(473\) −19.8134 −0.911019
\(474\) 6.06020 0.278354
\(475\) −0.160823 −0.00737908
\(476\) −0.0744843 −0.00341398
\(477\) −10.2460 −0.469133
\(478\) 29.3322 1.34162
\(479\) 12.5790 0.574750 0.287375 0.957818i \(-0.407217\pi\)
0.287375 + 0.957818i \(0.407217\pi\)
\(480\) −0.399333 −0.0182270
\(481\) −0.628481 −0.0286563
\(482\) −25.1528 −1.14568
\(483\) 12.6570 0.575913
\(484\) 0.223201 0.0101455
\(485\) 6.43870 0.292366
\(486\) −1.40476 −0.0637210
\(487\) 1.03149 0.0467412 0.0233706 0.999727i \(-0.492560\pi\)
0.0233706 + 0.999727i \(0.492560\pi\)
\(488\) −23.9619 −1.08470
\(489\) −10.9456 −0.494978
\(490\) 2.98987 0.135069
\(491\) −0.817532 −0.0368947 −0.0184473 0.999830i \(-0.505872\pi\)
−0.0184473 + 0.999830i \(0.505872\pi\)
\(492\) 0.233644 0.0105335
\(493\) 2.83514 0.127688
\(494\) −0.0186355 −0.000838450 0
\(495\) 4.29300 0.192956
\(496\) −16.7912 −0.753948
\(497\) −20.1803 −0.905209
\(498\) 10.0658 0.451061
\(499\) −26.2294 −1.17419 −0.587095 0.809518i \(-0.699728\pi\)
−0.587095 + 0.809518i \(0.699728\pi\)
\(500\) 0.211041 0.00943804
\(501\) 7.78150 0.347652
\(502\) −37.2824 −1.66400
\(503\) 3.68823 0.164450 0.0822249 0.996614i \(-0.473797\pi\)
0.0822249 + 0.996614i \(0.473797\pi\)
\(504\) 7.95310 0.354259
\(505\) −41.4078 −1.84262
\(506\) 10.3195 0.458757
\(507\) 12.9725 0.576129
\(508\) 0.172830 0.00766810
\(509\) −28.6257 −1.26881 −0.634407 0.772999i \(-0.718755\pi\)
−0.634407 + 0.772999i \(0.718755\pi\)
\(510\) 3.71946 0.164700
\(511\) 0.151550 0.00670419
\(512\) −23.0632 −1.01926
\(513\) 0.0799859 0.00353146
\(514\) 1.58421 0.0698766
\(515\) −17.4691 −0.769782
\(516\) −0.325827 −0.0143437
\(517\) 6.46424 0.284297
\(518\) 14.8703 0.653365
\(519\) 15.7573 0.691667
\(520\) −1.25022 −0.0548259
\(521\) −12.5187 −0.548453 −0.274227 0.961665i \(-0.588422\pi\)
−0.274227 + 0.961665i \(0.588422\pi\)
\(522\) −3.98267 −0.174317
\(523\) 4.08363 0.178565 0.0892824 0.996006i \(-0.471543\pi\)
0.0892824 + 0.996006i \(0.471543\pi\)
\(524\) 0.0618369 0.00270136
\(525\) 5.61682 0.245138
\(526\) −1.65628 −0.0722170
\(527\) −4.25529 −0.185363
\(528\) 6.39786 0.278431
\(529\) −2.47176 −0.107468
\(530\) −38.1097 −1.65538
\(531\) −8.23446 −0.357345
\(532\) −0.00595769 −0.000258299 0
\(533\) 1.45335 0.0629518
\(534\) 18.0561 0.781366
\(535\) 41.0352 1.77411
\(536\) −16.2875 −0.703514
\(537\) 5.69874 0.245919
\(538\) −38.3730 −1.65438
\(539\) 1.30333 0.0561384
\(540\) 0.0705975 0.00303803
\(541\) 28.6584 1.23212 0.616060 0.787699i \(-0.288728\pi\)
0.616060 + 0.787699i \(0.288728\pi\)
\(542\) −6.68120 −0.286982
\(543\) −9.01042 −0.386674
\(544\) −0.150819 −0.00646632
\(545\) −27.2290 −1.16636
\(546\) 0.650851 0.0278538
\(547\) 13.0821 0.559349 0.279675 0.960095i \(-0.409773\pi\)
0.279675 + 0.960095i \(0.409773\pi\)
\(548\) −0.274946 −0.0117451
\(549\) 8.41665 0.359214
\(550\) 4.57950 0.195271
\(551\) 0.226771 0.00966077
\(552\) 12.8991 0.549020
\(553\) 12.0515 0.512481
\(554\) 21.9253 0.931519
\(555\) 10.0333 0.425891
\(556\) 0.205992 0.00873602
\(557\) −21.2269 −0.899414 −0.449707 0.893176i \(-0.648472\pi\)
−0.449707 + 0.893176i \(0.648472\pi\)
\(558\) 5.97764 0.253054
\(559\) −2.02676 −0.0857229
\(560\) 29.1868 1.23337
\(561\) 1.62137 0.0684542
\(562\) −12.8656 −0.542704
\(563\) −22.8671 −0.963734 −0.481867 0.876245i \(-0.660041\pi\)
−0.481867 + 0.876245i \(0.660041\pi\)
\(564\) 0.106303 0.00447617
\(565\) −26.9823 −1.13515
\(566\) 42.7583 1.79727
\(567\) −2.79354 −0.117318
\(568\) −20.5662 −0.862940
\(569\) −15.5530 −0.652017 −0.326008 0.945367i \(-0.605704\pi\)
−0.326008 + 0.945367i \(0.605704\pi\)
\(570\) 0.297504 0.0124611
\(571\) 1.61833 0.0677250 0.0338625 0.999427i \(-0.489219\pi\)
0.0338625 + 0.999427i \(0.489219\pi\)
\(572\) −0.00717000 −0.000299793 0
\(573\) −12.6905 −0.530155
\(574\) −34.3874 −1.43530
\(575\) 9.10986 0.379907
\(576\) 8.10379 0.337658
\(577\) −6.54500 −0.272472 −0.136236 0.990676i \(-0.543501\pi\)
−0.136236 + 0.990676i \(0.543501\pi\)
\(578\) 1.40476 0.0584301
\(579\) 17.2372 0.716353
\(580\) 0.200154 0.00831093
\(581\) 20.0172 0.830454
\(582\) −3.41601 −0.141598
\(583\) −16.6126 −0.688023
\(584\) 0.154449 0.00639113
\(585\) 0.439143 0.0181563
\(586\) −1.38142 −0.0570659
\(587\) −35.9655 −1.48446 −0.742228 0.670147i \(-0.766231\pi\)
−0.742228 + 0.670147i \(0.766231\pi\)
\(588\) 0.0214330 0.000883882 0
\(589\) −0.340363 −0.0140244
\(590\) −30.6277 −1.26092
\(591\) 24.3145 1.00016
\(592\) 14.9527 0.614551
\(593\) −18.7859 −0.771443 −0.385722 0.922615i \(-0.626047\pi\)
−0.385722 + 0.922615i \(0.626047\pi\)
\(594\) −2.27763 −0.0934521
\(595\) 7.39662 0.303232
\(596\) −0.484560 −0.0198484
\(597\) 12.9913 0.531699
\(598\) 1.05561 0.0431670
\(599\) −14.8180 −0.605447 −0.302724 0.953078i \(-0.597896\pi\)
−0.302724 + 0.953078i \(0.597896\pi\)
\(600\) 5.72424 0.233691
\(601\) 25.4852 1.03956 0.519782 0.854299i \(-0.326013\pi\)
0.519782 + 0.854299i \(0.326013\pi\)
\(602\) 47.9547 1.95449
\(603\) 5.72102 0.232978
\(604\) 0.234879 0.00955707
\(605\) −22.1649 −0.901129
\(606\) 21.9687 0.892416
\(607\) −12.2513 −0.497265 −0.248632 0.968598i \(-0.579981\pi\)
−0.248632 + 0.968598i \(0.579981\pi\)
\(608\) −0.0120634 −0.000489235 0
\(609\) −7.92006 −0.320937
\(610\) 31.3054 1.26752
\(611\) 0.661244 0.0267511
\(612\) 0.0266631 0.00107779
\(613\) −7.16214 −0.289276 −0.144638 0.989485i \(-0.546202\pi\)
−0.144638 + 0.989485i \(0.546202\pi\)
\(614\) −10.4326 −0.421027
\(615\) −23.2019 −0.935592
\(616\) 12.8949 0.519551
\(617\) 21.0326 0.846742 0.423371 0.905956i \(-0.360847\pi\)
0.423371 + 0.905956i \(0.360847\pi\)
\(618\) 9.26814 0.372819
\(619\) 23.8020 0.956685 0.478343 0.878173i \(-0.341238\pi\)
0.478343 + 0.878173i \(0.341238\pi\)
\(620\) −0.300413 −0.0120649
\(621\) −4.53081 −0.181815
\(622\) 34.3153 1.37592
\(623\) 35.9070 1.43858
\(624\) 0.654455 0.0261992
\(625\) −31.0105 −1.24042
\(626\) −28.1236 −1.12404
\(627\) 0.129687 0.00517918
\(628\) 0.0266631 0.00106397
\(629\) 3.78936 0.151092
\(630\) −10.3904 −0.413965
\(631\) −30.7538 −1.22429 −0.612144 0.790746i \(-0.709693\pi\)
−0.612144 + 0.790746i \(0.709693\pi\)
\(632\) 12.2820 0.488551
\(633\) −14.7598 −0.586649
\(634\) −30.2051 −1.19960
\(635\) −17.1628 −0.681085
\(636\) −0.273191 −0.0108327
\(637\) 0.133321 0.00528238
\(638\) −6.45738 −0.255650
\(639\) 7.22392 0.285774
\(640\) 29.3430 1.15989
\(641\) 32.8289 1.29666 0.648332 0.761358i \(-0.275467\pi\)
0.648332 + 0.761358i \(0.275467\pi\)
\(642\) −21.7710 −0.859233
\(643\) 5.23782 0.206559 0.103280 0.994652i \(-0.467066\pi\)
0.103280 + 0.994652i \(0.467066\pi\)
\(644\) 0.337474 0.0132983
\(645\) 32.3560 1.27402
\(646\) 0.112361 0.00442077
\(647\) −18.3072 −0.719728 −0.359864 0.933005i \(-0.617177\pi\)
−0.359864 + 0.933005i \(0.617177\pi\)
\(648\) −2.84697 −0.111839
\(649\) −13.3511 −0.524077
\(650\) 0.468450 0.0183741
\(651\) 11.8873 0.465900
\(652\) −0.291844 −0.0114295
\(653\) 30.9887 1.21268 0.606341 0.795204i \(-0.292636\pi\)
0.606341 + 0.795204i \(0.292636\pi\)
\(654\) 14.4462 0.564891
\(655\) −6.14068 −0.239936
\(656\) −34.5778 −1.35004
\(657\) −0.0542503 −0.00211651
\(658\) −15.6455 −0.609927
\(659\) 46.0606 1.79427 0.897134 0.441759i \(-0.145645\pi\)
0.897134 + 0.441759i \(0.145645\pi\)
\(660\) 0.114465 0.00445553
\(661\) 1.98525 0.0772174 0.0386087 0.999254i \(-0.487707\pi\)
0.0386087 + 0.999254i \(0.487707\pi\)
\(662\) 20.5185 0.797475
\(663\) 0.165854 0.00644124
\(664\) 20.4000 0.791675
\(665\) 0.591625 0.0229422
\(666\) −5.32312 −0.206267
\(667\) −12.8455 −0.497379
\(668\) 0.207479 0.00802760
\(669\) 1.98824 0.0768699
\(670\) 21.2791 0.822083
\(671\) 13.6465 0.526817
\(672\) 0.421319 0.0162527
\(673\) 24.6657 0.950792 0.475396 0.879772i \(-0.342305\pi\)
0.475396 + 0.879772i \(0.342305\pi\)
\(674\) 26.8701 1.03500
\(675\) −2.01065 −0.0773899
\(676\) 0.345887 0.0133033
\(677\) 19.4476 0.747431 0.373715 0.927543i \(-0.378084\pi\)
0.373715 + 0.927543i \(0.378084\pi\)
\(678\) 14.3153 0.549775
\(679\) −6.79318 −0.260698
\(680\) 7.53809 0.289073
\(681\) 9.25134 0.354512
\(682\) 9.69196 0.371124
\(683\) −26.7815 −1.02476 −0.512382 0.858757i \(-0.671237\pi\)
−0.512382 + 0.858757i \(0.671237\pi\)
\(684\) 0.00213267 8.15447e−5 0
\(685\) 27.3034 1.04321
\(686\) 24.3152 0.928357
\(687\) −7.45096 −0.284272
\(688\) 48.2202 1.83838
\(689\) −1.69935 −0.0647400
\(690\) −16.8522 −0.641551
\(691\) 36.3670 1.38346 0.691732 0.722154i \(-0.256848\pi\)
0.691732 + 0.722154i \(0.256848\pi\)
\(692\) 0.420137 0.0159712
\(693\) −4.52935 −0.172056
\(694\) −13.3470 −0.506647
\(695\) −20.4559 −0.775938
\(696\) −8.07154 −0.305951
\(697\) −8.76284 −0.331916
\(698\) 49.2918 1.86572
\(699\) 20.0603 0.758751
\(700\) 0.149762 0.00566046
\(701\) 20.3410 0.768270 0.384135 0.923277i \(-0.374500\pi\)
0.384135 + 0.923277i \(0.374500\pi\)
\(702\) −0.232985 −0.00879344
\(703\) 0.303095 0.0114315
\(704\) 13.1392 0.495203
\(705\) −10.5564 −0.397576
\(706\) −23.4835 −0.883814
\(707\) 43.6875 1.64304
\(708\) −0.219556 −0.00825143
\(709\) −44.2214 −1.66077 −0.830384 0.557191i \(-0.811879\pi\)
−0.830384 + 0.557191i \(0.811879\pi\)
\(710\) 26.8691 1.00838
\(711\) −4.31406 −0.161790
\(712\) 36.5937 1.37141
\(713\) 19.2799 0.722038
\(714\) −3.92423 −0.146861
\(715\) 0.712012 0.0266277
\(716\) 0.151946 0.00567849
\(717\) −20.8806 −0.779802
\(718\) −18.0052 −0.671948
\(719\) −44.1380 −1.64607 −0.823034 0.567992i \(-0.807720\pi\)
−0.823034 + 0.567992i \(0.807720\pi\)
\(720\) −10.4480 −0.389373
\(721\) 18.4309 0.686402
\(722\) −26.6814 −0.992977
\(723\) 17.9054 0.665910
\(724\) −0.240246 −0.00892866
\(725\) −5.70046 −0.211710
\(726\) 11.7594 0.436434
\(727\) −41.6842 −1.54598 −0.772991 0.634418i \(-0.781240\pi\)
−0.772991 + 0.634418i \(0.781240\pi\)
\(728\) 1.31906 0.0488874
\(729\) 1.00000 0.0370370
\(730\) −0.201782 −0.00746828
\(731\) 12.2201 0.451978
\(732\) 0.224414 0.00829457
\(733\) 26.3265 0.972393 0.486196 0.873850i \(-0.338384\pi\)
0.486196 + 0.873850i \(0.338384\pi\)
\(734\) −17.1407 −0.632673
\(735\) −2.12839 −0.0785069
\(736\) 0.683333 0.0251880
\(737\) 9.27588 0.341681
\(738\) 12.3096 0.453124
\(739\) 6.21603 0.228660 0.114330 0.993443i \(-0.463528\pi\)
0.114330 + 0.993443i \(0.463528\pi\)
\(740\) 0.267520 0.00983421
\(741\) 0.0132660 0.000487339 0
\(742\) 40.2078 1.47608
\(743\) 2.49893 0.0916770 0.0458385 0.998949i \(-0.485404\pi\)
0.0458385 + 0.998949i \(0.485404\pi\)
\(744\) 12.1147 0.444145
\(745\) 48.1189 1.76294
\(746\) 9.67051 0.354063
\(747\) −7.16554 −0.262173
\(748\) 0.0432307 0.00158067
\(749\) −43.2944 −1.58194
\(750\) 11.1188 0.406000
\(751\) −18.1164 −0.661078 −0.330539 0.943792i \(-0.607230\pi\)
−0.330539 + 0.943792i \(0.607230\pi\)
\(752\) −15.7322 −0.573693
\(753\) 26.5402 0.967178
\(754\) −0.660543 −0.0240556
\(755\) −23.3245 −0.848865
\(756\) −0.0744843 −0.00270897
\(757\) 24.8027 0.901469 0.450734 0.892658i \(-0.351162\pi\)
0.450734 + 0.892658i \(0.351162\pi\)
\(758\) 48.0134 1.74393
\(759\) −7.34611 −0.266647
\(760\) 0.602941 0.0218710
\(761\) 18.6899 0.677509 0.338754 0.940875i \(-0.389994\pi\)
0.338754 + 0.940875i \(0.389994\pi\)
\(762\) 9.10562 0.329862
\(763\) 28.7281 1.04003
\(764\) −0.338369 −0.0122418
\(765\) −2.64776 −0.0957301
\(766\) −31.5417 −1.13965
\(767\) −1.36572 −0.0493133
\(768\) 0.639800 0.0230868
\(769\) 39.2534 1.41552 0.707758 0.706455i \(-0.249707\pi\)
0.707758 + 0.706455i \(0.249707\pi\)
\(770\) −16.8467 −0.607114
\(771\) −1.12775 −0.0406149
\(772\) 0.459597 0.0165412
\(773\) −0.561119 −0.0201821 −0.0100910 0.999949i \(-0.503212\pi\)
−0.0100910 + 0.999949i \(0.503212\pi\)
\(774\) −17.1663 −0.617030
\(775\) 8.55589 0.307337
\(776\) −6.92311 −0.248525
\(777\) −10.5857 −0.379760
\(778\) −25.1937 −0.903238
\(779\) −0.700904 −0.0251125
\(780\) 0.0117089 0.000419246 0
\(781\) 11.7126 0.419111
\(782\) −6.36468 −0.227600
\(783\) 2.83514 0.101320
\(784\) −3.17195 −0.113284
\(785\) −2.64776 −0.0945027
\(786\) 3.25790 0.116206
\(787\) 23.0313 0.820977 0.410489 0.911866i \(-0.365358\pi\)
0.410489 + 0.911866i \(0.365358\pi\)
\(788\) 0.648299 0.0230947
\(789\) 1.17905 0.0419753
\(790\) −16.0460 −0.570890
\(791\) 28.4678 1.01220
\(792\) −4.61598 −0.164022
\(793\) 1.39594 0.0495711
\(794\) −39.4820 −1.40116
\(795\) 27.1291 0.962168
\(796\) 0.346389 0.0122774
\(797\) 30.0871 1.06574 0.532869 0.846197i \(-0.321114\pi\)
0.532869 + 0.846197i \(0.321114\pi\)
\(798\) −0.313883 −0.0111114
\(799\) −3.98690 −0.141046
\(800\) 0.303244 0.0107213
\(801\) −12.8536 −0.454159
\(802\) −32.3880 −1.14366
\(803\) −0.0879598 −0.00310403
\(804\) 0.152540 0.00537967
\(805\) −33.5127 −1.18117
\(806\) 0.991417 0.0349212
\(807\) 27.3165 0.961588
\(808\) 44.5231 1.56632
\(809\) −19.7634 −0.694846 −0.347423 0.937709i \(-0.612943\pi\)
−0.347423 + 0.937709i \(0.612943\pi\)
\(810\) 3.71946 0.130688
\(811\) 17.5235 0.615332 0.307666 0.951494i \(-0.400452\pi\)
0.307666 + 0.951494i \(0.400452\pi\)
\(812\) −0.211173 −0.00741073
\(813\) 4.75613 0.166805
\(814\) −8.63075 −0.302508
\(815\) 28.9814 1.01517
\(816\) −3.94596 −0.138136
\(817\) 0.977439 0.0341963
\(818\) 26.7147 0.934056
\(819\) −0.463320 −0.0161897
\(820\) −0.618635 −0.0216037
\(821\) 24.8923 0.868746 0.434373 0.900733i \(-0.356970\pi\)
0.434373 + 0.900733i \(0.356970\pi\)
\(822\) −14.4857 −0.505245
\(823\) −10.8662 −0.378772 −0.189386 0.981903i \(-0.560650\pi\)
−0.189386 + 0.981903i \(0.560650\pi\)
\(824\) 18.7834 0.654351
\(825\) −3.26000 −0.113499
\(826\) 32.3140 1.12435
\(827\) 55.5557 1.93186 0.965931 0.258800i \(-0.0833272\pi\)
0.965931 + 0.258800i \(0.0833272\pi\)
\(828\) −0.120805 −0.00419828
\(829\) 19.9610 0.693274 0.346637 0.937999i \(-0.387324\pi\)
0.346637 + 0.937999i \(0.387324\pi\)
\(830\) −26.6519 −0.925102
\(831\) −15.6079 −0.541434
\(832\) 1.34405 0.0465965
\(833\) −0.803846 −0.0278516
\(834\) 10.8528 0.375801
\(835\) −20.6036 −0.713016
\(836\) 0.00345785 0.000119592 0
\(837\) −4.25529 −0.147084
\(838\) 54.9046 1.89665
\(839\) 37.1272 1.28177 0.640887 0.767635i \(-0.278567\pi\)
0.640887 + 0.767635i \(0.278567\pi\)
\(840\) −21.0579 −0.726567
\(841\) −20.9620 −0.722827
\(842\) 10.1038 0.348200
\(843\) 9.15864 0.315440
\(844\) −0.393542 −0.0135463
\(845\) −34.3481 −1.18161
\(846\) 5.60062 0.192553
\(847\) 23.3851 0.803523
\(848\) 40.4304 1.38839
\(849\) −30.4383 −1.04464
\(850\) −2.82447 −0.0968784
\(851\) −17.1689 −0.588541
\(852\) 0.192612 0.00659878
\(853\) −57.0401 −1.95301 −0.976507 0.215484i \(-0.930867\pi\)
−0.976507 + 0.215484i \(0.930867\pi\)
\(854\) −33.0289 −1.13023
\(855\) −0.211784 −0.00724285
\(856\) −44.1225 −1.50808
\(857\) −5.73664 −0.195960 −0.0979799 0.995188i \(-0.531238\pi\)
−0.0979799 + 0.995188i \(0.531238\pi\)
\(858\) −0.377754 −0.0128963
\(859\) −21.3659 −0.728994 −0.364497 0.931205i \(-0.618759\pi\)
−0.364497 + 0.931205i \(0.618759\pi\)
\(860\) 0.862712 0.0294182
\(861\) 24.4793 0.834253
\(862\) −21.8832 −0.745344
\(863\) 5.14888 0.175270 0.0876349 0.996153i \(-0.472069\pi\)
0.0876349 + 0.996153i \(0.472069\pi\)
\(864\) −0.150819 −0.00513097
\(865\) −41.7215 −1.41857
\(866\) 53.0279 1.80196
\(867\) −1.00000 −0.0339618
\(868\) 0.316952 0.0107581
\(869\) −6.99468 −0.237278
\(870\) 10.5452 0.357515
\(871\) 0.948855 0.0321507
\(872\) 29.2776 0.991464
\(873\) 2.43175 0.0823023
\(874\) −0.509084 −0.0172200
\(875\) 22.1111 0.747492
\(876\) −0.00144648 −4.88721e−5 0
\(877\) −53.5911 −1.80964 −0.904822 0.425791i \(-0.859996\pi\)
−0.904822 + 0.425791i \(0.859996\pi\)
\(878\) −46.3879 −1.56551
\(879\) 0.983388 0.0331688
\(880\) −16.9400 −0.571048
\(881\) −8.02841 −0.270484 −0.135242 0.990813i \(-0.543181\pi\)
−0.135242 + 0.990813i \(0.543181\pi\)
\(882\) 1.12921 0.0380224
\(883\) −44.8927 −1.51076 −0.755381 0.655286i \(-0.772548\pi\)
−0.755381 + 0.655286i \(0.772548\pi\)
\(884\) 0.00442219 0.000148734 0
\(885\) 21.8029 0.732897
\(886\) −17.2378 −0.579116
\(887\) 38.9754 1.30867 0.654333 0.756206i \(-0.272949\pi\)
0.654333 + 0.756206i \(0.272949\pi\)
\(888\) −10.7882 −0.362028
\(889\) 18.1077 0.607313
\(890\) −47.8084 −1.60254
\(891\) 1.62137 0.0543179
\(892\) 0.0530127 0.00177500
\(893\) −0.318896 −0.0106714
\(894\) −25.5292 −0.853825
\(895\) −15.0889 −0.504366
\(896\) −30.9585 −1.03425
\(897\) −0.751454 −0.0250903
\(898\) 46.8761 1.56428
\(899\) −12.0643 −0.402368
\(900\) −0.0536101 −0.00178700
\(901\) 10.2460 0.341345
\(902\) 19.9585 0.664545
\(903\) −34.1374 −1.13602
\(904\) 29.0123 0.964934
\(905\) 23.8575 0.793049
\(906\) 12.3747 0.411121
\(907\) −17.5592 −0.583045 −0.291522 0.956564i \(-0.594162\pi\)
−0.291522 + 0.956564i \(0.594162\pi\)
\(908\) 0.246669 0.00818601
\(909\) −15.6388 −0.518706
\(910\) −1.72330 −0.0571268
\(911\) −0.302607 −0.0100258 −0.00501291 0.999987i \(-0.501596\pi\)
−0.00501291 + 0.999987i \(0.501596\pi\)
\(912\) −0.315621 −0.0104513
\(913\) −11.6180 −0.384499
\(914\) −29.5840 −0.978553
\(915\) −22.2853 −0.736729
\(916\) −0.198666 −0.00656410
\(917\) 6.47876 0.213947
\(918\) 1.40476 0.0463638
\(919\) 57.2237 1.88764 0.943818 0.330464i \(-0.107205\pi\)
0.943818 + 0.330464i \(0.107205\pi\)
\(920\) −34.1536 −1.12601
\(921\) 7.42666 0.244717
\(922\) 12.3108 0.405435
\(923\) 1.19812 0.0394365
\(924\) −0.120767 −0.00397293
\(925\) −7.61907 −0.250513
\(926\) 24.9036 0.818382
\(927\) −6.59769 −0.216697
\(928\) −0.427593 −0.0140364
\(929\) −55.3163 −1.81487 −0.907434 0.420194i \(-0.861962\pi\)
−0.907434 + 0.420194i \(0.861962\pi\)
\(930\) −15.8274 −0.519000
\(931\) −0.0642963 −0.00210723
\(932\) 0.534870 0.0175203
\(933\) −24.4279 −0.799734
\(934\) 5.32248 0.174157
\(935\) −4.29300 −0.140396
\(936\) −0.472181 −0.0154337
\(937\) 0.891662 0.0291293 0.0145647 0.999894i \(-0.495364\pi\)
0.0145647 + 0.999894i \(0.495364\pi\)
\(938\) −22.4506 −0.733038
\(939\) 20.0203 0.653337
\(940\) −0.281465 −0.00918039
\(941\) 45.5829 1.48596 0.742981 0.669313i \(-0.233411\pi\)
0.742981 + 0.669313i \(0.233411\pi\)
\(942\) 1.40476 0.0457694
\(943\) 39.7028 1.29290
\(944\) 32.4929 1.05755
\(945\) 7.39662 0.240612
\(946\) −27.8329 −0.904926
\(947\) 18.8708 0.613217 0.306609 0.951836i \(-0.400806\pi\)
0.306609 + 0.951836i \(0.400806\pi\)
\(948\) −0.115026 −0.00373588
\(949\) −0.00899764 −0.000292076 0
\(950\) −0.225917 −0.00732973
\(951\) 21.5021 0.697252
\(952\) −7.95310 −0.257761
\(953\) 7.25899 0.235142 0.117571 0.993064i \(-0.462489\pi\)
0.117571 + 0.993064i \(0.462489\pi\)
\(954\) −14.3932 −0.465996
\(955\) 33.6015 1.08732
\(956\) −0.556742 −0.0180063
\(957\) 4.59680 0.148594
\(958\) 17.6705 0.570906
\(959\) −28.8066 −0.930213
\(960\) −21.4569 −0.692519
\(961\) −12.8925 −0.415887
\(962\) −0.882863 −0.0284646
\(963\) 15.4981 0.499418
\(964\) 0.477414 0.0153765
\(965\) −45.6400 −1.46920
\(966\) 17.7800 0.572061
\(967\) 9.20478 0.296006 0.148003 0.988987i \(-0.452715\pi\)
0.148003 + 0.988987i \(0.452715\pi\)
\(968\) 23.8324 0.766003
\(969\) −0.0799859 −0.00256952
\(970\) 9.04479 0.290411
\(971\) 22.5155 0.722557 0.361279 0.932458i \(-0.382340\pi\)
0.361279 + 0.932458i \(0.382340\pi\)
\(972\) 0.0266631 0.000855219 0
\(973\) 21.5822 0.691892
\(974\) 1.44899 0.0464285
\(975\) −0.333474 −0.0106797
\(976\) −33.2118 −1.06308
\(977\) 53.9084 1.72468 0.862342 0.506327i \(-0.168997\pi\)
0.862342 + 0.506327i \(0.168997\pi\)
\(978\) −15.3759 −0.491667
\(979\) −20.8404 −0.666062
\(980\) −0.0567495 −0.00181280
\(981\) −10.2838 −0.328336
\(982\) −1.14843 −0.0366479
\(983\) −36.3100 −1.15811 −0.579055 0.815289i \(-0.696578\pi\)
−0.579055 + 0.815289i \(0.696578\pi\)
\(984\) 24.9475 0.795297
\(985\) −64.3789 −2.05128
\(986\) 3.98267 0.126834
\(987\) 11.1376 0.354512
\(988\) 0.000353712 0 1.12531e−5 0
\(989\) −55.3672 −1.76057
\(990\) 6.03061 0.191665
\(991\) −46.1196 −1.46504 −0.732519 0.680746i \(-0.761656\pi\)
−0.732519 + 0.680746i \(0.761656\pi\)
\(992\) 0.641779 0.0203765
\(993\) −14.6065 −0.463523
\(994\) −28.3483 −0.899155
\(995\) −34.3979 −1.09049
\(996\) −0.191056 −0.00605383
\(997\) −5.94386 −0.188244 −0.0941219 0.995561i \(-0.530004\pi\)
−0.0941219 + 0.995561i \(0.530004\pi\)
\(998\) −36.8459 −1.16634
\(999\) 3.78936 0.119890
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.1.36 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.36 48 1.1 even 1 trivial