Properties

Label 158.2.a.d.1.1
Level $158$
Weight $2$
Character 158.1
Self dual yes
Analytic conductor $1.262$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 158 = 2 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 158.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.26163635194\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 158.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +1.00000 q^{10} +2.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +3.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} -2.00000 q^{18} +1.00000 q^{20} -3.00000 q^{21} +2.00000 q^{22} -6.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} -1.00000 q^{26} +5.00000 q^{27} +3.00000 q^{28} -10.0000 q^{29} -1.00000 q^{30} +2.00000 q^{31} +1.00000 q^{32} -2.00000 q^{33} -2.00000 q^{34} +3.00000 q^{35} -2.00000 q^{36} -2.00000 q^{37} +1.00000 q^{39} +1.00000 q^{40} +2.00000 q^{41} -3.00000 q^{42} +4.00000 q^{43} +2.00000 q^{44} -2.00000 q^{45} -6.00000 q^{46} +3.00000 q^{47} -1.00000 q^{48} +2.00000 q^{49} -4.00000 q^{50} +2.00000 q^{51} -1.00000 q^{52} +4.00000 q^{53} +5.00000 q^{54} +2.00000 q^{55} +3.00000 q^{56} -10.0000 q^{58} +5.00000 q^{59} -1.00000 q^{60} +12.0000 q^{61} +2.00000 q^{62} -6.00000 q^{63} +1.00000 q^{64} -1.00000 q^{65} -2.00000 q^{66} +8.00000 q^{67} -2.00000 q^{68} +6.00000 q^{69} +3.00000 q^{70} -13.0000 q^{71} -2.00000 q^{72} -6.00000 q^{73} -2.00000 q^{74} +4.00000 q^{75} +6.00000 q^{77} +1.00000 q^{78} -1.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} -6.00000 q^{83} -3.00000 q^{84} -2.00000 q^{85} +4.00000 q^{86} +10.0000 q^{87} +2.00000 q^{88} -15.0000 q^{89} -2.00000 q^{90} -3.00000 q^{91} -6.00000 q^{92} -2.00000 q^{93} +3.00000 q^{94} -1.00000 q^{96} +13.0000 q^{97} +2.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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
\(3\) −1.00000 −0.577350 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) −1.00000 −0.408248
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) 1.00000 0.316228
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 3.00000 0.801784
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) −2.00000 −0.471405
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 1.00000 0.223607
\(21\) −3.00000 −0.654654
\(22\) 2.00000 0.426401
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) −1.00000 −0.204124
\(25\) −4.00000 −0.800000
\(26\) −1.00000 −0.196116
\(27\) 5.00000 0.962250
\(28\) 3.00000 0.566947
\(29\) −10.0000 −1.85695 −0.928477 0.371391i \(-0.878881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) −1.00000 −0.182574
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.00000 −0.348155
\(34\) −2.00000 −0.342997
\(35\) 3.00000 0.507093
\(36\) −2.00000 −0.333333
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 1.00000 0.158114
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) −3.00000 −0.462910
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 2.00000 0.301511
\(45\) −2.00000 −0.298142
\(46\) −6.00000 −0.884652
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) −1.00000 −0.144338
\(49\) 2.00000 0.285714
\(50\) −4.00000 −0.565685
\(51\) 2.00000 0.280056
\(52\) −1.00000 −0.138675
\(53\) 4.00000 0.549442 0.274721 0.961524i \(-0.411414\pi\)
0.274721 + 0.961524i \(0.411414\pi\)
\(54\) 5.00000 0.680414
\(55\) 2.00000 0.269680
\(56\) 3.00000 0.400892
\(57\) 0 0
\(58\) −10.0000 −1.31306
\(59\) 5.00000 0.650945 0.325472 0.945552i \(-0.394477\pi\)
0.325472 + 0.945552i \(0.394477\pi\)
\(60\) −1.00000 −0.129099
\(61\) 12.0000 1.53644 0.768221 0.640184i \(-0.221142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) 2.00000 0.254000
\(63\) −6.00000 −0.755929
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) −2.00000 −0.246183
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) −2.00000 −0.242536
\(69\) 6.00000 0.722315
\(70\) 3.00000 0.358569
\(71\) −13.0000 −1.54282 −0.771408 0.636341i \(-0.780447\pi\)
−0.771408 + 0.636341i \(0.780447\pi\)
\(72\) −2.00000 −0.235702
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −2.00000 −0.232495
\(75\) 4.00000 0.461880
\(76\) 0 0
\(77\) 6.00000 0.683763
\(78\) 1.00000 0.113228
\(79\) −1.00000 −0.112509
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 2.00000 0.220863
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −3.00000 −0.327327
\(85\) −2.00000 −0.216930
\(86\) 4.00000 0.431331
\(87\) 10.0000 1.07211
\(88\) 2.00000 0.213201
\(89\) −15.0000 −1.59000 −0.794998 0.606612i \(-0.792528\pi\)
−0.794998 + 0.606612i \(0.792528\pi\)
\(90\) −2.00000 −0.210819
\(91\) −3.00000 −0.314485
\(92\) −6.00000 −0.625543
\(93\) −2.00000 −0.207390
\(94\) 3.00000 0.309426
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 13.0000 1.31995 0.659975 0.751288i \(-0.270567\pi\)
0.659975 + 0.751288i \(0.270567\pi\)
\(98\) 2.00000 0.202031
\(99\) −4.00000 −0.402015
\(100\) −4.00000 −0.400000
\(101\) 7.00000 0.696526 0.348263 0.937397i \(-0.386772\pi\)
0.348263 + 0.937397i \(0.386772\pi\)
\(102\) 2.00000 0.198030
\(103\) 19.0000 1.87213 0.936063 0.351833i \(-0.114441\pi\)
0.936063 + 0.351833i \(0.114441\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −3.00000 −0.292770
\(106\) 4.00000 0.388514
\(107\) 13.0000 1.25676 0.628379 0.777908i \(-0.283719\pi\)
0.628379 + 0.777908i \(0.283719\pi\)
\(108\) 5.00000 0.481125
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 2.00000 0.190693
\(111\) 2.00000 0.189832
\(112\) 3.00000 0.283473
\(113\) 4.00000 0.376288 0.188144 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) 0 0
\(115\) −6.00000 −0.559503
\(116\) −10.0000 −0.928477
\(117\) 2.00000 0.184900
\(118\) 5.00000 0.460287
\(119\) −6.00000 −0.550019
\(120\) −1.00000 −0.0912871
\(121\) −7.00000 −0.636364
\(122\) 12.0000 1.08643
\(123\) −2.00000 −0.180334
\(124\) 2.00000 0.179605
\(125\) −9.00000 −0.804984
\(126\) −6.00000 −0.534522
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.00000 −0.352180
\(130\) −1.00000 −0.0877058
\(131\) −18.0000 −1.57267 −0.786334 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) −2.00000 −0.174078
\(133\) 0 0
\(134\) 8.00000 0.691095
\(135\) 5.00000 0.430331
\(136\) −2.00000 −0.171499
\(137\) −12.0000 −1.02523 −0.512615 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) 6.00000 0.510754
\(139\) −5.00000 −0.424094 −0.212047 0.977259i \(-0.568013\pi\)
−0.212047 + 0.977259i \(0.568013\pi\)
\(140\) 3.00000 0.253546
\(141\) −3.00000 −0.252646
\(142\) −13.0000 −1.09094
\(143\) −2.00000 −0.167248
\(144\) −2.00000 −0.166667
\(145\) −10.0000 −0.830455
\(146\) −6.00000 −0.496564
\(147\) −2.00000 −0.164957
\(148\) −2.00000 −0.164399
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 4.00000 0.326599
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 0 0
\(153\) 4.00000 0.323381
\(154\) 6.00000 0.483494
\(155\) 2.00000 0.160644
\(156\) 1.00000 0.0800641
\(157\) 18.0000 1.43656 0.718278 0.695756i \(-0.244931\pi\)
0.718278 + 0.695756i \(0.244931\pi\)
\(158\) −1.00000 −0.0795557
\(159\) −4.00000 −0.317221
\(160\) 1.00000 0.0790569
\(161\) −18.0000 −1.41860
\(162\) 1.00000 0.0785674
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 2.00000 0.156174
\(165\) −2.00000 −0.155700
\(166\) −6.00000 −0.465690
\(167\) −2.00000 −0.154765 −0.0773823 0.997001i \(-0.524656\pi\)
−0.0773823 + 0.997001i \(0.524656\pi\)
\(168\) −3.00000 −0.231455
\(169\) −12.0000 −0.923077
\(170\) −2.00000 −0.153393
\(171\) 0 0
\(172\) 4.00000 0.304997
\(173\) 4.00000 0.304114 0.152057 0.988372i \(-0.451410\pi\)
0.152057 + 0.988372i \(0.451410\pi\)
\(174\) 10.0000 0.758098
\(175\) −12.0000 −0.907115
\(176\) 2.00000 0.150756
\(177\) −5.00000 −0.375823
\(178\) −15.0000 −1.12430
\(179\) 20.0000 1.49487 0.747435 0.664335i \(-0.231285\pi\)
0.747435 + 0.664335i \(0.231285\pi\)
\(180\) −2.00000 −0.149071
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) −3.00000 −0.222375
\(183\) −12.0000 −0.887066
\(184\) −6.00000 −0.442326
\(185\) −2.00000 −0.147043
\(186\) −2.00000 −0.146647
\(187\) −4.00000 −0.292509
\(188\) 3.00000 0.218797
\(189\) 15.0000 1.09109
\(190\) 0 0
\(191\) −3.00000 −0.217072 −0.108536 0.994092i \(-0.534616\pi\)
−0.108536 + 0.994092i \(0.534616\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 13.0000 0.933346
\(195\) 1.00000 0.0716115
\(196\) 2.00000 0.142857
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) −4.00000 −0.284268
\(199\) 15.0000 1.06332 0.531661 0.846957i \(-0.321568\pi\)
0.531661 + 0.846957i \(0.321568\pi\)
\(200\) −4.00000 −0.282843
\(201\) −8.00000 −0.564276
\(202\) 7.00000 0.492518
\(203\) −30.0000 −2.10559
\(204\) 2.00000 0.140028
\(205\) 2.00000 0.139686
\(206\) 19.0000 1.32379
\(207\) 12.0000 0.834058
\(208\) −1.00000 −0.0693375
\(209\) 0 0
\(210\) −3.00000 −0.207020
\(211\) −28.0000 −1.92760 −0.963800 0.266627i \(-0.914091\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(212\) 4.00000 0.274721
\(213\) 13.0000 0.890745
\(214\) 13.0000 0.888662
\(215\) 4.00000 0.272798
\(216\) 5.00000 0.340207
\(217\) 6.00000 0.407307
\(218\) 10.0000 0.677285
\(219\) 6.00000 0.405442
\(220\) 2.00000 0.134840
\(221\) 2.00000 0.134535
\(222\) 2.00000 0.134231
\(223\) 14.0000 0.937509 0.468755 0.883328i \(-0.344703\pi\)
0.468755 + 0.883328i \(0.344703\pi\)
\(224\) 3.00000 0.200446
\(225\) 8.00000 0.533333
\(226\) 4.00000 0.266076
\(227\) 8.00000 0.530979 0.265489 0.964114i \(-0.414466\pi\)
0.265489 + 0.964114i \(0.414466\pi\)
\(228\) 0 0
\(229\) 20.0000 1.32164 0.660819 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) −6.00000 −0.395628
\(231\) −6.00000 −0.394771
\(232\) −10.0000 −0.656532
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 2.00000 0.130744
\(235\) 3.00000 0.195698
\(236\) 5.00000 0.325472
\(237\) 1.00000 0.0649570
\(238\) −6.00000 −0.388922
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 17.0000 1.09507 0.547533 0.836784i \(-0.315567\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) −7.00000 −0.449977
\(243\) −16.0000 −1.02640
\(244\) 12.0000 0.768221
\(245\) 2.00000 0.127775
\(246\) −2.00000 −0.127515
\(247\) 0 0
\(248\) 2.00000 0.127000
\(249\) 6.00000 0.380235
\(250\) −9.00000 −0.569210
\(251\) 27.0000 1.70422 0.852112 0.523359i \(-0.175321\pi\)
0.852112 + 0.523359i \(0.175321\pi\)
\(252\) −6.00000 −0.377964
\(253\) −12.0000 −0.754434
\(254\) −7.00000 −0.439219
\(255\) 2.00000 0.125245
\(256\) 1.00000 0.0625000
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) −4.00000 −0.249029
\(259\) −6.00000 −0.372822
\(260\) −1.00000 −0.0620174
\(261\) 20.0000 1.23797
\(262\) −18.0000 −1.11204
\(263\) −6.00000 −0.369976 −0.184988 0.982741i \(-0.559225\pi\)
−0.184988 + 0.982741i \(0.559225\pi\)
\(264\) −2.00000 −0.123091
\(265\) 4.00000 0.245718
\(266\) 0 0
\(267\) 15.0000 0.917985
\(268\) 8.00000 0.488678
\(269\) 25.0000 1.52428 0.762138 0.647414i \(-0.224150\pi\)
0.762138 + 0.647414i \(0.224150\pi\)
\(270\) 5.00000 0.304290
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −2.00000 −0.121268
\(273\) 3.00000 0.181568
\(274\) −12.0000 −0.724947
\(275\) −8.00000 −0.482418
\(276\) 6.00000 0.361158
\(277\) −17.0000 −1.02143 −0.510716 0.859750i \(-0.670619\pi\)
−0.510716 + 0.859750i \(0.670619\pi\)
\(278\) −5.00000 −0.299880
\(279\) −4.00000 −0.239474
\(280\) 3.00000 0.179284
\(281\) −33.0000 −1.96861 −0.984307 0.176462i \(-0.943535\pi\)
−0.984307 + 0.176462i \(0.943535\pi\)
\(282\) −3.00000 −0.178647
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) −13.0000 −0.771408
\(285\) 0 0
\(286\) −2.00000 −0.118262
\(287\) 6.00000 0.354169
\(288\) −2.00000 −0.117851
\(289\) −13.0000 −0.764706
\(290\) −10.0000 −0.587220
\(291\) −13.0000 −0.762073
\(292\) −6.00000 −0.351123
\(293\) 24.0000 1.40209 0.701047 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) −2.00000 −0.116642
\(295\) 5.00000 0.291111
\(296\) −2.00000 −0.116248
\(297\) 10.0000 0.580259
\(298\) −10.0000 −0.579284
\(299\) 6.00000 0.346989
\(300\) 4.00000 0.230940
\(301\) 12.0000 0.691669
\(302\) 2.00000 0.115087
\(303\) −7.00000 −0.402139
\(304\) 0 0
\(305\) 12.0000 0.687118
\(306\) 4.00000 0.228665
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 6.00000 0.341882
\(309\) −19.0000 −1.08087
\(310\) 2.00000 0.113592
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 1.00000 0.0566139
\(313\) 14.0000 0.791327 0.395663 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) 18.0000 1.01580
\(315\) −6.00000 −0.338062
\(316\) −1.00000 −0.0562544
\(317\) 3.00000 0.168497 0.0842484 0.996445i \(-0.473151\pi\)
0.0842484 + 0.996445i \(0.473151\pi\)
\(318\) −4.00000 −0.224309
\(319\) −20.0000 −1.11979
\(320\) 1.00000 0.0559017
\(321\) −13.0000 −0.725589
\(322\) −18.0000 −1.00310
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 4.00000 0.221880
\(326\) 4.00000 0.221540
\(327\) −10.0000 −0.553001
\(328\) 2.00000 0.110432
\(329\) 9.00000 0.496186
\(330\) −2.00000 −0.110096
\(331\) −28.0000 −1.53902 −0.769510 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) −6.00000 −0.329293
\(333\) 4.00000 0.219199
\(334\) −2.00000 −0.109435
\(335\) 8.00000 0.437087
\(336\) −3.00000 −0.163663
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) −12.0000 −0.652714
\(339\) −4.00000 −0.217250
\(340\) −2.00000 −0.108465
\(341\) 4.00000 0.216612
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) 4.00000 0.215666
\(345\) 6.00000 0.323029
\(346\) 4.00000 0.215041
\(347\) 18.0000 0.966291 0.483145 0.875540i \(-0.339494\pi\)
0.483145 + 0.875540i \(0.339494\pi\)
\(348\) 10.0000 0.536056
\(349\) −20.0000 −1.07058 −0.535288 0.844670i \(-0.679797\pi\)
−0.535288 + 0.844670i \(0.679797\pi\)
\(350\) −12.0000 −0.641427
\(351\) −5.00000 −0.266880
\(352\) 2.00000 0.106600
\(353\) −36.0000 −1.91609 −0.958043 0.286623i \(-0.907467\pi\)
−0.958043 + 0.286623i \(0.907467\pi\)
\(354\) −5.00000 −0.265747
\(355\) −13.0000 −0.689968
\(356\) −15.0000 −0.794998
\(357\) 6.00000 0.317554
\(358\) 20.0000 1.05703
\(359\) 25.0000 1.31945 0.659725 0.751507i \(-0.270673\pi\)
0.659725 + 0.751507i \(0.270673\pi\)
\(360\) −2.00000 −0.105409
\(361\) −19.0000 −1.00000
\(362\) −18.0000 −0.946059
\(363\) 7.00000 0.367405
\(364\) −3.00000 −0.157243
\(365\) −6.00000 −0.314054
\(366\) −12.0000 −0.627250
\(367\) −22.0000 −1.14839 −0.574195 0.818718i \(-0.694685\pi\)
−0.574195 + 0.818718i \(0.694685\pi\)
\(368\) −6.00000 −0.312772
\(369\) −4.00000 −0.208232
\(370\) −2.00000 −0.103975
\(371\) 12.0000 0.623009
\(372\) −2.00000 −0.103695
\(373\) 14.0000 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) −4.00000 −0.206835
\(375\) 9.00000 0.464758
\(376\) 3.00000 0.154713
\(377\) 10.0000 0.515026
\(378\) 15.0000 0.771517
\(379\) −15.0000 −0.770498 −0.385249 0.922813i \(-0.625884\pi\)
−0.385249 + 0.922813i \(0.625884\pi\)
\(380\) 0 0
\(381\) 7.00000 0.358621
\(382\) −3.00000 −0.153493
\(383\) −6.00000 −0.306586 −0.153293 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 6.00000 0.305788
\(386\) 14.0000 0.712581
\(387\) −8.00000 −0.406663
\(388\) 13.0000 0.659975
\(389\) −5.00000 −0.253510 −0.126755 0.991934i \(-0.540456\pi\)
−0.126755 + 0.991934i \(0.540456\pi\)
\(390\) 1.00000 0.0506370
\(391\) 12.0000 0.606866
\(392\) 2.00000 0.101015
\(393\) 18.0000 0.907980
\(394\) 18.0000 0.906827
\(395\) −1.00000 −0.0503155
\(396\) −4.00000 −0.201008
\(397\) −37.0000 −1.85698 −0.928488 0.371361i \(-0.878891\pi\)
−0.928488 + 0.371361i \(0.878891\pi\)
\(398\) 15.0000 0.751882
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) −8.00000 −0.399004
\(403\) −2.00000 −0.0996271
\(404\) 7.00000 0.348263
\(405\) 1.00000 0.0496904
\(406\) −30.0000 −1.48888
\(407\) −4.00000 −0.198273
\(408\) 2.00000 0.0990148
\(409\) −20.0000 −0.988936 −0.494468 0.869196i \(-0.664637\pi\)
−0.494468 + 0.869196i \(0.664637\pi\)
\(410\) 2.00000 0.0987730
\(411\) 12.0000 0.591916
\(412\) 19.0000 0.936063
\(413\) 15.0000 0.738102
\(414\) 12.0000 0.589768
\(415\) −6.00000 −0.294528
\(416\) −1.00000 −0.0490290
\(417\) 5.00000 0.244851
\(418\) 0 0
\(419\) 25.0000 1.22133 0.610665 0.791889i \(-0.290902\pi\)
0.610665 + 0.791889i \(0.290902\pi\)
\(420\) −3.00000 −0.146385
\(421\) 7.00000 0.341159 0.170580 0.985344i \(-0.445436\pi\)
0.170580 + 0.985344i \(0.445436\pi\)
\(422\) −28.0000 −1.36302
\(423\) −6.00000 −0.291730
\(424\) 4.00000 0.194257
\(425\) 8.00000 0.388057
\(426\) 13.0000 0.629852
\(427\) 36.0000 1.74216
\(428\) 13.0000 0.628379
\(429\) 2.00000 0.0965609
\(430\) 4.00000 0.192897
\(431\) 32.0000 1.54139 0.770693 0.637207i \(-0.219910\pi\)
0.770693 + 0.637207i \(0.219910\pi\)
\(432\) 5.00000 0.240563
\(433\) −11.0000 −0.528626 −0.264313 0.964437i \(-0.585145\pi\)
−0.264313 + 0.964437i \(0.585145\pi\)
\(434\) 6.00000 0.288009
\(435\) 10.0000 0.479463
\(436\) 10.0000 0.478913
\(437\) 0 0
\(438\) 6.00000 0.286691
\(439\) −40.0000 −1.90910 −0.954548 0.298057i \(-0.903661\pi\)
−0.954548 + 0.298057i \(0.903661\pi\)
\(440\) 2.00000 0.0953463
\(441\) −4.00000 −0.190476
\(442\) 2.00000 0.0951303
\(443\) 4.00000 0.190046 0.0950229 0.995475i \(-0.469708\pi\)
0.0950229 + 0.995475i \(0.469708\pi\)
\(444\) 2.00000 0.0949158
\(445\) −15.0000 −0.711068
\(446\) 14.0000 0.662919
\(447\) 10.0000 0.472984
\(448\) 3.00000 0.141737
\(449\) −10.0000 −0.471929 −0.235965 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 8.00000 0.377124
\(451\) 4.00000 0.188353
\(452\) 4.00000 0.188144
\(453\) −2.00000 −0.0939682
\(454\) 8.00000 0.375459
\(455\) −3.00000 −0.140642
\(456\) 0 0
\(457\) 23.0000 1.07589 0.537947 0.842978i \(-0.319200\pi\)
0.537947 + 0.842978i \(0.319200\pi\)
\(458\) 20.0000 0.934539
\(459\) −10.0000 −0.466760
\(460\) −6.00000 −0.279751
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) −6.00000 −0.279145
\(463\) −31.0000 −1.44069 −0.720346 0.693615i \(-0.756017\pi\)
−0.720346 + 0.693615i \(0.756017\pi\)
\(464\) −10.0000 −0.464238
\(465\) −2.00000 −0.0927478
\(466\) −6.00000 −0.277945
\(467\) −42.0000 −1.94353 −0.971764 0.235954i \(-0.924178\pi\)
−0.971764 + 0.235954i \(0.924178\pi\)
\(468\) 2.00000 0.0924500
\(469\) 24.0000 1.10822
\(470\) 3.00000 0.138380
\(471\) −18.0000 −0.829396
\(472\) 5.00000 0.230144
\(473\) 8.00000 0.367840
\(474\) 1.00000 0.0459315
\(475\) 0 0
\(476\) −6.00000 −0.275010
\(477\) −8.00000 −0.366295
\(478\) 0 0
\(479\) −20.0000 −0.913823 −0.456912 0.889512i \(-0.651044\pi\)
−0.456912 + 0.889512i \(0.651044\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 2.00000 0.0911922
\(482\) 17.0000 0.774329
\(483\) 18.0000 0.819028
\(484\) −7.00000 −0.318182
\(485\) 13.0000 0.590300
\(486\) −16.0000 −0.725775
\(487\) 38.0000 1.72194 0.860972 0.508652i \(-0.169856\pi\)
0.860972 + 0.508652i \(0.169856\pi\)
\(488\) 12.0000 0.543214
\(489\) −4.00000 −0.180886
\(490\) 2.00000 0.0903508
\(491\) −3.00000 −0.135388 −0.0676941 0.997706i \(-0.521564\pi\)
−0.0676941 + 0.997706i \(0.521564\pi\)
\(492\) −2.00000 −0.0901670
\(493\) 20.0000 0.900755
\(494\) 0 0
\(495\) −4.00000 −0.179787
\(496\) 2.00000 0.0898027
\(497\) −39.0000 −1.74939
\(498\) 6.00000 0.268866
\(499\) −10.0000 −0.447661 −0.223831 0.974628i \(-0.571856\pi\)
−0.223831 + 0.974628i \(0.571856\pi\)
\(500\) −9.00000 −0.402492
\(501\) 2.00000 0.0893534
\(502\) 27.0000 1.20507
\(503\) 39.0000 1.73892 0.869462 0.494000i \(-0.164466\pi\)
0.869462 + 0.494000i \(0.164466\pi\)
\(504\) −6.00000 −0.267261
\(505\) 7.00000 0.311496
\(506\) −12.0000 −0.533465
\(507\) 12.0000 0.532939
\(508\) −7.00000 −0.310575
\(509\) −20.0000 −0.886484 −0.443242 0.896402i \(-0.646172\pi\)
−0.443242 + 0.896402i \(0.646172\pi\)
\(510\) 2.00000 0.0885615
\(511\) −18.0000 −0.796273
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −2.00000 −0.0882162
\(515\) 19.0000 0.837240
\(516\) −4.00000 −0.176090
\(517\) 6.00000 0.263880
\(518\) −6.00000 −0.263625
\(519\) −4.00000 −0.175581
\(520\) −1.00000 −0.0438529
\(521\) 12.0000 0.525730 0.262865 0.964833i \(-0.415333\pi\)
0.262865 + 0.964833i \(0.415333\pi\)
\(522\) 20.0000 0.875376
\(523\) −26.0000 −1.13690 −0.568450 0.822718i \(-0.692457\pi\)
−0.568450 + 0.822718i \(0.692457\pi\)
\(524\) −18.0000 −0.786334
\(525\) 12.0000 0.523723
\(526\) −6.00000 −0.261612
\(527\) −4.00000 −0.174243
\(528\) −2.00000 −0.0870388
\(529\) 13.0000 0.565217
\(530\) 4.00000 0.173749
\(531\) −10.0000 −0.433963
\(532\) 0 0
\(533\) −2.00000 −0.0866296
\(534\) 15.0000 0.649113
\(535\) 13.0000 0.562039
\(536\) 8.00000 0.345547
\(537\) −20.0000 −0.863064
\(538\) 25.0000 1.07783
\(539\) 4.00000 0.172292
\(540\) 5.00000 0.215166
\(541\) 7.00000 0.300954 0.150477 0.988614i \(-0.451919\pi\)
0.150477 + 0.988614i \(0.451919\pi\)
\(542\) −8.00000 −0.343629
\(543\) 18.0000 0.772454
\(544\) −2.00000 −0.0857493
\(545\) 10.0000 0.428353
\(546\) 3.00000 0.128388
\(547\) −2.00000 −0.0855138 −0.0427569 0.999086i \(-0.513614\pi\)
−0.0427569 + 0.999086i \(0.513614\pi\)
\(548\) −12.0000 −0.512615
\(549\) −24.0000 −1.02430
\(550\) −8.00000 −0.341121
\(551\) 0 0
\(552\) 6.00000 0.255377
\(553\) −3.00000 −0.127573
\(554\) −17.0000 −0.722261
\(555\) 2.00000 0.0848953
\(556\) −5.00000 −0.212047
\(557\) −7.00000 −0.296600 −0.148300 0.988942i \(-0.547380\pi\)
−0.148300 + 0.988942i \(0.547380\pi\)
\(558\) −4.00000 −0.169334
\(559\) −4.00000 −0.169182
\(560\) 3.00000 0.126773
\(561\) 4.00000 0.168880
\(562\) −33.0000 −1.39202
\(563\) 14.0000 0.590030 0.295015 0.955493i \(-0.404675\pi\)
0.295015 + 0.955493i \(0.404675\pi\)
\(564\) −3.00000 −0.126323
\(565\) 4.00000 0.168281
\(566\) 4.00000 0.168133
\(567\) 3.00000 0.125988
\(568\) −13.0000 −0.545468
\(569\) −30.0000 −1.25767 −0.628833 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) 0 0
\(571\) 22.0000 0.920671 0.460336 0.887745i \(-0.347729\pi\)
0.460336 + 0.887745i \(0.347729\pi\)
\(572\) −2.00000 −0.0836242
\(573\) 3.00000 0.125327
\(574\) 6.00000 0.250435
\(575\) 24.0000 1.00087
\(576\) −2.00000 −0.0833333
\(577\) −12.0000 −0.499567 −0.249783 0.968302i \(-0.580359\pi\)
−0.249783 + 0.968302i \(0.580359\pi\)
\(578\) −13.0000 −0.540729
\(579\) −14.0000 −0.581820
\(580\) −10.0000 −0.415227
\(581\) −18.0000 −0.746766
\(582\) −13.0000 −0.538867
\(583\) 8.00000 0.331326
\(584\) −6.00000 −0.248282
\(585\) 2.00000 0.0826898
\(586\) 24.0000 0.991431
\(587\) −7.00000 −0.288921 −0.144460 0.989511i \(-0.546145\pi\)
−0.144460 + 0.989511i \(0.546145\pi\)
\(588\) −2.00000 −0.0824786
\(589\) 0 0
\(590\) 5.00000 0.205847
\(591\) −18.0000 −0.740421
\(592\) −2.00000 −0.0821995
\(593\) −21.0000 −0.862367 −0.431183 0.902264i \(-0.641904\pi\)
−0.431183 + 0.902264i \(0.641904\pi\)
\(594\) 10.0000 0.410305
\(595\) −6.00000 −0.245976
\(596\) −10.0000 −0.409616
\(597\) −15.0000 −0.613909
\(598\) 6.00000 0.245358
\(599\) 40.0000 1.63436 0.817178 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 4.00000 0.163299
\(601\) 12.0000 0.489490 0.244745 0.969587i \(-0.421296\pi\)
0.244745 + 0.969587i \(0.421296\pi\)
\(602\) 12.0000 0.489083
\(603\) −16.0000 −0.651570
\(604\) 2.00000 0.0813788
\(605\) −7.00000 −0.284590
\(606\) −7.00000 −0.284356
\(607\) 33.0000 1.33943 0.669714 0.742619i \(-0.266417\pi\)
0.669714 + 0.742619i \(0.266417\pi\)
\(608\) 0 0
\(609\) 30.0000 1.21566
\(610\) 12.0000 0.485866
\(611\) −3.00000 −0.121367
\(612\) 4.00000 0.161690
\(613\) 14.0000 0.565455 0.282727 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) −12.0000 −0.484281
\(615\) −2.00000 −0.0806478
\(616\) 6.00000 0.241747
\(617\) −27.0000 −1.08698 −0.543490 0.839416i \(-0.682897\pi\)
−0.543490 + 0.839416i \(0.682897\pi\)
\(618\) −19.0000 −0.764292
\(619\) −35.0000 −1.40677 −0.703384 0.710810i \(-0.748329\pi\)
−0.703384 + 0.710810i \(0.748329\pi\)
\(620\) 2.00000 0.0803219
\(621\) −30.0000 −1.20386
\(622\) 12.0000 0.481156
\(623\) −45.0000 −1.80289
\(624\) 1.00000 0.0400320
\(625\) 11.0000 0.440000
\(626\) 14.0000 0.559553
\(627\) 0 0
\(628\) 18.0000 0.718278
\(629\) 4.00000 0.159490
\(630\) −6.00000 −0.239046
\(631\) 37.0000 1.47295 0.736473 0.676467i \(-0.236490\pi\)
0.736473 + 0.676467i \(0.236490\pi\)
\(632\) −1.00000 −0.0397779
\(633\) 28.0000 1.11290
\(634\) 3.00000 0.119145
\(635\) −7.00000 −0.277787
\(636\) −4.00000 −0.158610
\(637\) −2.00000 −0.0792429
\(638\) −20.0000 −0.791808
\(639\) 26.0000 1.02854
\(640\) 1.00000 0.0395285
\(641\) −33.0000 −1.30342 −0.651711 0.758468i \(-0.725948\pi\)
−0.651711 + 0.758468i \(0.725948\pi\)
\(642\) −13.0000 −0.513069
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) −18.0000 −0.709299
\(645\) −4.00000 −0.157500
\(646\) 0 0
\(647\) −32.0000 −1.25805 −0.629025 0.777385i \(-0.716546\pi\)
−0.629025 + 0.777385i \(0.716546\pi\)
\(648\) 1.00000 0.0392837
\(649\) 10.0000 0.392534
\(650\) 4.00000 0.156893
\(651\) −6.00000 −0.235159
\(652\) 4.00000 0.156652
\(653\) −11.0000 −0.430463 −0.215232 0.976563i \(-0.569051\pi\)
−0.215232 + 0.976563i \(0.569051\pi\)
\(654\) −10.0000 −0.391031
\(655\) −18.0000 −0.703318
\(656\) 2.00000 0.0780869
\(657\) 12.0000 0.468165
\(658\) 9.00000 0.350857
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) −2.00000 −0.0778499
\(661\) 2.00000 0.0777910 0.0388955 0.999243i \(-0.487616\pi\)
0.0388955 + 0.999243i \(0.487616\pi\)
\(662\) −28.0000 −1.08825
\(663\) −2.00000 −0.0776736
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 60.0000 2.32321
\(668\) −2.00000 −0.0773823
\(669\) −14.0000 −0.541271
\(670\) 8.00000 0.309067
\(671\) 24.0000 0.926510
\(672\) −3.00000 −0.115728
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 23.0000 0.885927
\(675\) −20.0000 −0.769800
\(676\) −12.0000 −0.461538
\(677\) −27.0000 −1.03769 −0.518847 0.854867i \(-0.673639\pi\)
−0.518847 + 0.854867i \(0.673639\pi\)
\(678\) −4.00000 −0.153619
\(679\) 39.0000 1.49668
\(680\) −2.00000 −0.0766965
\(681\) −8.00000 −0.306561
\(682\) 4.00000 0.153168
\(683\) 4.00000 0.153056 0.0765279 0.997067i \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) −15.0000 −0.572703
\(687\) −20.0000 −0.763048
\(688\) 4.00000 0.152499
\(689\) −4.00000 −0.152388
\(690\) 6.00000 0.228416
\(691\) 17.0000 0.646710 0.323355 0.946278i \(-0.395189\pi\)
0.323355 + 0.946278i \(0.395189\pi\)
\(692\) 4.00000 0.152057
\(693\) −12.0000 −0.455842
\(694\) 18.0000 0.683271
\(695\) −5.00000 −0.189661
\(696\) 10.0000 0.379049
\(697\) −4.00000 −0.151511
\(698\) −20.0000 −0.757011
\(699\) 6.00000 0.226941
\(700\) −12.0000 −0.453557
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) −5.00000 −0.188713
\(703\) 0 0
\(704\) 2.00000 0.0753778
\(705\) −3.00000 −0.112987
\(706\) −36.0000 −1.35488
\(707\) 21.0000 0.789786
\(708\) −5.00000 −0.187912
\(709\) −50.0000 −1.87779 −0.938895 0.344204i \(-0.888149\pi\)
−0.938895 + 0.344204i \(0.888149\pi\)
\(710\) −13.0000 −0.487881
\(711\) 2.00000 0.0750059
\(712\) −15.0000 −0.562149
\(713\) −12.0000 −0.449404
\(714\) 6.00000 0.224544
\(715\) −2.00000 −0.0747958
\(716\) 20.0000 0.747435
\(717\) 0 0
\(718\) 25.0000 0.932992
\(719\) 30.0000 1.11881 0.559406 0.828894i \(-0.311029\pi\)
0.559406 + 0.828894i \(0.311029\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 57.0000 2.12279
\(722\) −19.0000 −0.707107
\(723\) −17.0000 −0.632237
\(724\) −18.0000 −0.668965
\(725\) 40.0000 1.48556
\(726\) 7.00000 0.259794
\(727\) 18.0000 0.667583 0.333792 0.942647i \(-0.391672\pi\)
0.333792 + 0.942647i \(0.391672\pi\)
\(728\) −3.00000 −0.111187
\(729\) 13.0000 0.481481
\(730\) −6.00000 −0.222070
\(731\) −8.00000 −0.295891
\(732\) −12.0000 −0.443533
\(733\) 34.0000 1.25582 0.627909 0.778287i \(-0.283911\pi\)
0.627909 + 0.778287i \(0.283911\pi\)
\(734\) −22.0000 −0.812035
\(735\) −2.00000 −0.0737711
\(736\) −6.00000 −0.221163
\(737\) 16.0000 0.589368
\(738\) −4.00000 −0.147242
\(739\) −5.00000 −0.183928 −0.0919640 0.995762i \(-0.529314\pi\)
−0.0919640 + 0.995762i \(0.529314\pi\)
\(740\) −2.00000 −0.0735215
\(741\) 0 0
\(742\) 12.0000 0.440534
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) −2.00000 −0.0733236
\(745\) −10.0000 −0.366372
\(746\) 14.0000 0.512576
\(747\) 12.0000 0.439057
\(748\) −4.00000 −0.146254
\(749\) 39.0000 1.42503
\(750\) 9.00000 0.328634
\(751\) 42.0000 1.53260 0.766301 0.642482i \(-0.222095\pi\)
0.766301 + 0.642482i \(0.222095\pi\)
\(752\) 3.00000 0.109399
\(753\) −27.0000 −0.983935
\(754\) 10.0000 0.364179
\(755\) 2.00000 0.0727875
\(756\) 15.0000 0.545545
\(757\) −37.0000 −1.34479 −0.672394 0.740193i \(-0.734734\pi\)
−0.672394 + 0.740193i \(0.734734\pi\)
\(758\) −15.0000 −0.544825
\(759\) 12.0000 0.435572
\(760\) 0 0
\(761\) 22.0000 0.797499 0.398750 0.917060i \(-0.369444\pi\)
0.398750 + 0.917060i \(0.369444\pi\)
\(762\) 7.00000 0.253583
\(763\) 30.0000 1.08607
\(764\) −3.00000 −0.108536
\(765\) 4.00000 0.144620
\(766\) −6.00000 −0.216789
\(767\) −5.00000 −0.180540
\(768\) −1.00000 −0.0360844
\(769\) −40.0000 −1.44244 −0.721218 0.692708i \(-0.756418\pi\)
−0.721218 + 0.692708i \(0.756418\pi\)
\(770\) 6.00000 0.216225
\(771\) 2.00000 0.0720282
\(772\) 14.0000 0.503871
\(773\) 34.0000 1.22290 0.611448 0.791285i \(-0.290588\pi\)
0.611448 + 0.791285i \(0.290588\pi\)
\(774\) −8.00000 −0.287554
\(775\) −8.00000 −0.287368
\(776\) 13.0000 0.466673
\(777\) 6.00000 0.215249
\(778\) −5.00000 −0.179259
\(779\) 0 0
\(780\) 1.00000 0.0358057
\(781\) −26.0000 −0.930353
\(782\) 12.0000 0.429119
\(783\) −50.0000 −1.78685
\(784\) 2.00000 0.0714286
\(785\) 18.0000 0.642448
\(786\) 18.0000 0.642039
\(787\) 18.0000 0.641631 0.320815 0.947142i \(-0.396043\pi\)
0.320815 + 0.947142i \(0.396043\pi\)
\(788\) 18.0000 0.641223
\(789\) 6.00000 0.213606
\(790\) −1.00000 −0.0355784
\(791\) 12.0000 0.426671
\(792\) −4.00000 −0.142134
\(793\) −12.0000 −0.426132
\(794\) −37.0000 −1.31308
\(795\) −4.00000 −0.141865
\(796\) 15.0000 0.531661
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0
\(799\) −6.00000 −0.212265
\(800\) −4.00000 −0.141421
\(801\) 30.0000 1.06000
\(802\) 2.00000 0.0706225
\(803\) −12.0000 −0.423471
\(804\) −8.00000 −0.282138
\(805\) −18.0000 −0.634417
\(806\) −2.00000 −0.0704470
\(807\) −25.0000 −0.880042
\(808\) 7.00000 0.246259
\(809\) 15.0000 0.527372 0.263686 0.964609i \(-0.415062\pi\)
0.263686 + 0.964609i \(0.415062\pi\)
\(810\) 1.00000 0.0351364
\(811\) 22.0000 0.772524 0.386262 0.922389i \(-0.373766\pi\)
0.386262 + 0.922389i \(0.373766\pi\)
\(812\) −30.0000 −1.05279
\(813\) 8.00000 0.280572
\(814\) −4.00000 −0.140200
\(815\) 4.00000 0.140114
\(816\) 2.00000 0.0700140
\(817\) 0 0
\(818\) −20.0000 −0.699284
\(819\) 6.00000 0.209657
\(820\) 2.00000 0.0698430
\(821\) 42.0000 1.46581 0.732905 0.680331i \(-0.238164\pi\)
0.732905 + 0.680331i \(0.238164\pi\)
\(822\) 12.0000 0.418548
\(823\) −16.0000 −0.557725 −0.278862 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) 19.0000 0.661896
\(825\) 8.00000 0.278524
\(826\) 15.0000 0.521917
\(827\) 23.0000 0.799788 0.399894 0.916561i \(-0.369047\pi\)
0.399894 + 0.916561i \(0.369047\pi\)
\(828\) 12.0000 0.417029
\(829\) −20.0000 −0.694629 −0.347314 0.937749i \(-0.612906\pi\)
−0.347314 + 0.937749i \(0.612906\pi\)
\(830\) −6.00000 −0.208263
\(831\) 17.0000 0.589723
\(832\) −1.00000 −0.0346688
\(833\) −4.00000 −0.138592
\(834\) 5.00000 0.173136
\(835\) −2.00000 −0.0692129
\(836\) 0 0
\(837\) 10.0000 0.345651
\(838\) 25.0000 0.863611
\(839\) 20.0000 0.690477 0.345238 0.938515i \(-0.387798\pi\)
0.345238 + 0.938515i \(0.387798\pi\)
\(840\) −3.00000 −0.103510
\(841\) 71.0000 2.44828
\(842\) 7.00000 0.241236
\(843\) 33.0000 1.13658
\(844\) −28.0000 −0.963800
\(845\) −12.0000 −0.412813
\(846\) −6.00000 −0.206284
\(847\) −21.0000 −0.721569
\(848\) 4.00000 0.137361
\(849\) −4.00000 −0.137280
\(850\) 8.00000 0.274398
\(851\) 12.0000 0.411355
\(852\) 13.0000 0.445373
\(853\) −16.0000 −0.547830 −0.273915 0.961754i \(-0.588319\pi\)
−0.273915 + 0.961754i \(0.588319\pi\)
\(854\) 36.0000 1.23189
\(855\) 0 0
\(856\) 13.0000 0.444331
\(857\) 33.0000 1.12726 0.563629 0.826028i \(-0.309405\pi\)
0.563629 + 0.826028i \(0.309405\pi\)
\(858\) 2.00000 0.0682789
\(859\) −35.0000 −1.19418 −0.597092 0.802173i \(-0.703677\pi\)
−0.597092 + 0.802173i \(0.703677\pi\)
\(860\) 4.00000 0.136399
\(861\) −6.00000 −0.204479
\(862\) 32.0000 1.08992
\(863\) −46.0000 −1.56586 −0.782929 0.622111i \(-0.786275\pi\)
−0.782929 + 0.622111i \(0.786275\pi\)
\(864\) 5.00000 0.170103
\(865\) 4.00000 0.136004
\(866\) −11.0000 −0.373795
\(867\) 13.0000 0.441503
\(868\) 6.00000 0.203653
\(869\) −2.00000 −0.0678454
\(870\) 10.0000 0.339032
\(871\) −8.00000 −0.271070
\(872\) 10.0000 0.338643
\(873\) −26.0000 −0.879967
\(874\) 0 0
\(875\) −27.0000 −0.912767
\(876\) 6.00000 0.202721
\(877\) 58.0000 1.95852 0.979260 0.202606i \(-0.0649409\pi\)
0.979260 + 0.202606i \(0.0649409\pi\)
\(878\) −40.0000 −1.34993
\(879\) −24.0000 −0.809500
\(880\) 2.00000 0.0674200
\(881\) 12.0000 0.404290 0.202145 0.979356i \(-0.435209\pi\)
0.202145 + 0.979356i \(0.435209\pi\)
\(882\) −4.00000 −0.134687
\(883\) −1.00000 −0.0336527 −0.0168263 0.999858i \(-0.505356\pi\)
−0.0168263 + 0.999858i \(0.505356\pi\)
\(884\) 2.00000 0.0672673
\(885\) −5.00000 −0.168073
\(886\) 4.00000 0.134383
\(887\) −22.0000 −0.738688 −0.369344 0.929293i \(-0.620418\pi\)
−0.369344 + 0.929293i \(0.620418\pi\)
\(888\) 2.00000 0.0671156
\(889\) −21.0000 −0.704317
\(890\) −15.0000 −0.502801
\(891\) 2.00000 0.0670025
\(892\) 14.0000 0.468755
\(893\) 0 0
\(894\) 10.0000 0.334450
\(895\) 20.0000 0.668526
\(896\) 3.00000 0.100223
\(897\) −6.00000 −0.200334
\(898\) −10.0000 −0.333704
\(899\) −20.0000 −0.667037
\(900\) 8.00000 0.266667
\(901\) −8.00000 −0.266519
\(902\) 4.00000 0.133185
\(903\) −12.0000 −0.399335
\(904\) 4.00000 0.133038
\(905\) −18.0000 −0.598340
\(906\) −2.00000 −0.0664455
\(907\) −12.0000 −0.398453 −0.199227 0.979953i \(-0.563843\pi\)
−0.199227 + 0.979953i \(0.563843\pi\)
\(908\) 8.00000 0.265489
\(909\) −14.0000 −0.464351
\(910\) −3.00000 −0.0994490
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 0 0
\(913\) −12.0000 −0.397142
\(914\) 23.0000 0.760772
\(915\) −12.0000 −0.396708
\(916\) 20.0000 0.660819
\(917\) −54.0000 −1.78324
\(918\) −10.0000 −0.330049
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) −6.00000 −0.197814
\(921\) 12.0000 0.395413
\(922\) −18.0000 −0.592798
\(923\) 13.0000 0.427900
\(924\) −6.00000 −0.197386
\(925\) 8.00000 0.263038
\(926\) −31.0000 −1.01872
\(927\) −38.0000 −1.24808
\(928\) −10.0000 −0.328266
\(929\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) −2.00000 −0.0655826
\(931\) 0 0
\(932\) −6.00000 −0.196537
\(933\) −12.0000 −0.392862
\(934\) −42.0000 −1.37428
\(935\) −4.00000 −0.130814
\(936\) 2.00000 0.0653720
\(937\) −12.0000 −0.392023 −0.196011 0.980602i \(-0.562799\pi\)
−0.196011 + 0.980602i \(0.562799\pi\)
\(938\) 24.0000 0.783628
\(939\) −14.0000 −0.456873
\(940\) 3.00000 0.0978492
\(941\) −38.0000 −1.23876 −0.619382 0.785090i \(-0.712617\pi\)
−0.619382 + 0.785090i \(0.712617\pi\)
\(942\) −18.0000 −0.586472
\(943\) −12.0000 −0.390774
\(944\) 5.00000 0.162736
\(945\) 15.0000 0.487950
\(946\) 8.00000 0.260102
\(947\) −32.0000 −1.03986 −0.519930 0.854209i \(-0.674042\pi\)
−0.519930 + 0.854209i \(0.674042\pi\)
\(948\) 1.00000 0.0324785
\(949\) 6.00000 0.194768
\(950\) 0 0
\(951\) −3.00000 −0.0972817
\(952\) −6.00000 −0.194461
\(953\) −31.0000 −1.00419 −0.502094 0.864813i \(-0.667437\pi\)
−0.502094 + 0.864813i \(0.667437\pi\)
\(954\) −8.00000 −0.259010
\(955\) −3.00000 −0.0970777
\(956\) 0 0
\(957\) 20.0000 0.646508
\(958\) −20.0000 −0.646171
\(959\) −36.0000 −1.16250
\(960\) −1.00000 −0.0322749
\(961\) −27.0000 −0.870968
\(962\) 2.00000 0.0644826
\(963\) −26.0000 −0.837838
\(964\) 17.0000 0.547533
\(965\) 14.0000 0.450676
\(966\) 18.0000 0.579141
\(967\) −52.0000 −1.67221 −0.836104 0.548572i \(-0.815172\pi\)
−0.836104 + 0.548572i \(0.815172\pi\)
\(968\) −7.00000 −0.224989
\(969\) 0 0
\(970\) 13.0000 0.417405
\(971\) 22.0000 0.706014 0.353007 0.935621i \(-0.385159\pi\)
0.353007 + 0.935621i \(0.385159\pi\)
\(972\) −16.0000 −0.513200
\(973\) −15.0000 −0.480878
\(974\) 38.0000 1.21760
\(975\) −4.00000 −0.128103
\(976\) 12.0000 0.384111
\(977\) 58.0000 1.85558 0.927792 0.373097i \(-0.121704\pi\)
0.927792 + 0.373097i \(0.121704\pi\)
\(978\) −4.00000 −0.127906
\(979\) −30.0000 −0.958804
\(980\) 2.00000 0.0638877
\(981\) −20.0000 −0.638551
\(982\) −3.00000 −0.0957338
\(983\) 24.0000 0.765481 0.382741 0.923856i \(-0.374980\pi\)
0.382741 + 0.923856i \(0.374980\pi\)
\(984\) −2.00000 −0.0637577
\(985\) 18.0000 0.573528
\(986\) 20.0000 0.636930
\(987\) −9.00000 −0.286473
\(988\) 0 0
\(989\) −24.0000 −0.763156
\(990\) −4.00000 −0.127128
\(991\) −13.0000 −0.412959 −0.206479 0.978451i \(-0.566201\pi\)
−0.206479 + 0.978451i \(0.566201\pi\)
\(992\) 2.00000 0.0635001
\(993\) 28.0000 0.888553
\(994\) −39.0000 −1.23700
\(995\) 15.0000 0.475532
\(996\) 6.00000 0.190117
\(997\) −22.0000 −0.696747 −0.348373 0.937356i \(-0.613266\pi\)
−0.348373 + 0.937356i \(0.613266\pi\)
\(998\) −10.0000 −0.316544
\(999\) −10.0000 −0.316386
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 158.2.a.d.1.1 1
3.2 odd 2 1422.2.a.a.1.1 1
4.3 odd 2 1264.2.a.f.1.1 1
5.4 even 2 3950.2.a.d.1.1 1
7.6 odd 2 7742.2.a.m.1.1 1
8.3 odd 2 5056.2.a.e.1.1 1
8.5 even 2 5056.2.a.m.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
158.2.a.d.1.1 1 1.1 even 1 trivial
1264.2.a.f.1.1 1 4.3 odd 2
1422.2.a.a.1.1 1 3.2 odd 2
3950.2.a.d.1.1 1 5.4 even 2
5056.2.a.e.1.1 1 8.3 odd 2
5056.2.a.m.1.1 1 8.5 even 2
7742.2.a.m.1.1 1 7.6 odd 2