Properties

Label 158.2.a.b.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
Root \(0\) of \(x\)
Character \(\chi\) \(=\) 158.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} -3.00000 q^{10} +1.00000 q^{12} +5.00000 q^{13} +1.00000 q^{14} +3.00000 q^{15} +1.00000 q^{16} +2.00000 q^{18} +2.00000 q^{19} +3.00000 q^{20} -1.00000 q^{21} -6.00000 q^{23} -1.00000 q^{24} +4.00000 q^{25} -5.00000 q^{26} -5.00000 q^{27} -1.00000 q^{28} -3.00000 q^{30} -4.00000 q^{31} -1.00000 q^{32} -3.00000 q^{35} -2.00000 q^{36} +2.00000 q^{37} -2.00000 q^{38} +5.00000 q^{39} -3.00000 q^{40} -12.0000 q^{41} +1.00000 q^{42} +8.00000 q^{43} -6.00000 q^{45} +6.00000 q^{46} -9.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} -4.00000 q^{50} +5.00000 q^{52} +6.00000 q^{53} +5.00000 q^{54} +1.00000 q^{56} +2.00000 q^{57} -9.00000 q^{59} +3.00000 q^{60} +8.00000 q^{61} +4.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +15.0000 q^{65} -4.00000 q^{67} -6.00000 q^{69} +3.00000 q^{70} -9.00000 q^{71} +2.00000 q^{72} +2.00000 q^{73} -2.00000 q^{74} +4.00000 q^{75} +2.00000 q^{76} -5.00000 q^{78} +1.00000 q^{79} +3.00000 q^{80} +1.00000 q^{81} +12.0000 q^{82} +18.0000 q^{83} -1.00000 q^{84} -8.00000 q^{86} +9.00000 q^{89} +6.00000 q^{90} -5.00000 q^{91} -6.00000 q^{92} -4.00000 q^{93} +9.00000 q^{94} +6.00000 q^{95} -1.00000 q^{96} +17.0000 q^{97} +6.00000 q^{98} +O(q^{100})\)

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 \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.00000 −0.666667
\(10\) −3.00000 −0.948683
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 0.288675
\(13\) 5.00000 1.38675 0.693375 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 1.00000 0.267261
\(15\) 3.00000 0.774597
\(16\) 1.00000 0.250000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 2.00000 0.471405
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 3.00000 0.670820
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) −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
\(26\) −5.00000 −0.980581
\(27\) −5.00000 −0.962250
\(28\) −1.00000 −0.188982
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −3.00000 −0.547723
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) −2.00000 −0.333333
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −2.00000 −0.324443
\(39\) 5.00000 0.800641
\(40\) −3.00000 −0.474342
\(41\) −12.0000 −1.87409 −0.937043 0.349215i \(-0.886448\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) 1.00000 0.154303
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) −6.00000 −0.894427
\(46\) 6.00000 0.884652
\(47\) −9.00000 −1.31278 −0.656392 0.754420i \(-0.727918\pi\)
−0.656392 + 0.754420i \(0.727918\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.00000 −0.857143
\(50\) −4.00000 −0.565685
\(51\) 0 0
\(52\) 5.00000 0.693375
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 5.00000 0.680414
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 2.00000 0.264906
\(58\) 0 0
\(59\) −9.00000 −1.17170 −0.585850 0.810419i \(-0.699239\pi\)
−0.585850 + 0.810419i \(0.699239\pi\)
\(60\) 3.00000 0.387298
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 4.00000 0.508001
\(63\) 2.00000 0.251976
\(64\) 1.00000 0.125000
\(65\) 15.0000 1.86052
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) −6.00000 −0.722315
\(70\) 3.00000 0.358569
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) 2.00000 0.235702
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −2.00000 −0.232495
\(75\) 4.00000 0.461880
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) −5.00000 −0.566139
\(79\) 1.00000 0.112509
\(80\) 3.00000 0.335410
\(81\) 1.00000 0.111111
\(82\) 12.0000 1.32518
\(83\) 18.0000 1.97576 0.987878 0.155230i \(-0.0496119\pi\)
0.987878 + 0.155230i \(0.0496119\pi\)
\(84\) −1.00000 −0.109109
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) 0 0
\(88\) 0 0
\(89\) 9.00000 0.953998 0.476999 0.878904i \(-0.341725\pi\)
0.476999 + 0.878904i \(0.341725\pi\)
\(90\) 6.00000 0.632456
\(91\) −5.00000 −0.524142
\(92\) −6.00000 −0.625543
\(93\) −4.00000 −0.414781
\(94\) 9.00000 0.928279
\(95\) 6.00000 0.615587
\(96\) −1.00000 −0.102062
\(97\) 17.0000 1.72609 0.863044 0.505128i \(-0.168555\pi\)
0.863044 + 0.505128i \(0.168555\pi\)
\(98\) 6.00000 0.606092
\(99\) 0 0
\(100\) 4.00000 0.400000
\(101\) −15.0000 −1.49256 −0.746278 0.665635i \(-0.768161\pi\)
−0.746278 + 0.665635i \(0.768161\pi\)
\(102\) 0 0
\(103\) −13.0000 −1.28093 −0.640464 0.767988i \(-0.721258\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) −5.00000 −0.490290
\(105\) −3.00000 −0.292770
\(106\) −6.00000 −0.582772
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) −5.00000 −0.481125
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) −1.00000 −0.0944911
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) −2.00000 −0.187317
\(115\) −18.0000 −1.67851
\(116\) 0 0
\(117\) −10.0000 −0.924500
\(118\) 9.00000 0.828517
\(119\) 0 0
\(120\) −3.00000 −0.273861
\(121\) −11.0000 −1.00000
\(122\) −8.00000 −0.724286
\(123\) −12.0000 −1.08200
\(124\) −4.00000 −0.359211
\(125\) −3.00000 −0.268328
\(126\) −2.00000 −0.178174
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 8.00000 0.704361
\(130\) −15.0000 −1.31559
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) −2.00000 −0.173422
\(134\) 4.00000 0.345547
\(135\) −15.0000 −1.29099
\(136\) 0 0
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 6.00000 0.510754
\(139\) 5.00000 0.424094 0.212047 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(140\) −3.00000 −0.253546
\(141\) −9.00000 −0.757937
\(142\) 9.00000 0.755263
\(143\) 0 0
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) −6.00000 −0.494872
\(148\) 2.00000 0.164399
\(149\) 12.0000 0.983078 0.491539 0.870855i \(-0.336434\pi\)
0.491539 + 0.870855i \(0.336434\pi\)
\(150\) −4.00000 −0.326599
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) −2.00000 −0.162221
\(153\) 0 0
\(154\) 0 0
\(155\) −12.0000 −0.963863
\(156\) 5.00000 0.400320
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) −1.00000 −0.0795557
\(159\) 6.00000 0.475831
\(160\) −3.00000 −0.237171
\(161\) 6.00000 0.472866
\(162\) −1.00000 −0.0785674
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) −12.0000 −0.937043
\(165\) 0 0
\(166\) −18.0000 −1.39707
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 1.00000 0.0771517
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −4.00000 −0.305888
\(172\) 8.00000 0.609994
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 0 0
\(175\) −4.00000 −0.302372
\(176\) 0 0
\(177\) −9.00000 −0.676481
\(178\) −9.00000 −0.674579
\(179\) 18.0000 1.34538 0.672692 0.739923i \(-0.265138\pi\)
0.672692 + 0.739923i \(0.265138\pi\)
\(180\) −6.00000 −0.447214
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 5.00000 0.370625
\(183\) 8.00000 0.591377
\(184\) 6.00000 0.442326
\(185\) 6.00000 0.441129
\(186\) 4.00000 0.293294
\(187\) 0 0
\(188\) −9.00000 −0.656392
\(189\) 5.00000 0.363696
\(190\) −6.00000 −0.435286
\(191\) −15.0000 −1.08536 −0.542681 0.839939i \(-0.682591\pi\)
−0.542681 + 0.839939i \(0.682591\pi\)
\(192\) 1.00000 0.0721688
\(193\) −22.0000 −1.58359 −0.791797 0.610784i \(-0.790854\pi\)
−0.791797 + 0.610784i \(0.790854\pi\)
\(194\) −17.0000 −1.22053
\(195\) 15.0000 1.07417
\(196\) −6.00000 −0.428571
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) 11.0000 0.779769 0.389885 0.920864i \(-0.372515\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(200\) −4.00000 −0.282843
\(201\) −4.00000 −0.282138
\(202\) 15.0000 1.05540
\(203\) 0 0
\(204\) 0 0
\(205\) −36.0000 −2.51435
\(206\) 13.0000 0.905753
\(207\) 12.0000 0.834058
\(208\) 5.00000 0.346688
\(209\) 0 0
\(210\) 3.00000 0.207020
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 6.00000 0.412082
\(213\) −9.00000 −0.616670
\(214\) −3.00000 −0.205076
\(215\) 24.0000 1.63679
\(216\) 5.00000 0.340207
\(217\) 4.00000 0.271538
\(218\) −2.00000 −0.135457
\(219\) 2.00000 0.135147
\(220\) 0 0
\(221\) 0 0
\(222\) −2.00000 −0.134231
\(223\) 26.0000 1.74109 0.870544 0.492090i \(-0.163767\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(224\) 1.00000 0.0668153
\(225\) −8.00000 −0.533333
\(226\) −18.0000 −1.19734
\(227\) 12.0000 0.796468 0.398234 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 2.00000 0.132453
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 18.0000 1.18688
\(231\) 0 0
\(232\) 0 0
\(233\) −12.0000 −0.786146 −0.393073 0.919507i \(-0.628588\pi\)
−0.393073 + 0.919507i \(0.628588\pi\)
\(234\) 10.0000 0.653720
\(235\) −27.0000 −1.76129
\(236\) −9.00000 −0.585850
\(237\) 1.00000 0.0649570
\(238\) 0 0
\(239\) 18.0000 1.16432 0.582162 0.813073i \(-0.302207\pi\)
0.582162 + 0.813073i \(0.302207\pi\)
\(240\) 3.00000 0.193649
\(241\) 17.0000 1.09507 0.547533 0.836784i \(-0.315567\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) 11.0000 0.707107
\(243\) 16.0000 1.02640
\(244\) 8.00000 0.512148
\(245\) −18.0000 −1.14998
\(246\) 12.0000 0.765092
\(247\) 10.0000 0.636285
\(248\) 4.00000 0.254000
\(249\) 18.0000 1.14070
\(250\) 3.00000 0.189737
\(251\) −27.0000 −1.70422 −0.852112 0.523359i \(-0.824679\pi\)
−0.852112 + 0.523359i \(0.824679\pi\)
\(252\) 2.00000 0.125988
\(253\) 0 0
\(254\) 7.00000 0.439219
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −18.0000 −1.12281 −0.561405 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(258\) −8.00000 −0.498058
\(259\) −2.00000 −0.124274
\(260\) 15.0000 0.930261
\(261\) 0 0
\(262\) −6.00000 −0.370681
\(263\) −18.0000 −1.10993 −0.554964 0.831875i \(-0.687268\pi\)
−0.554964 + 0.831875i \(0.687268\pi\)
\(264\) 0 0
\(265\) 18.0000 1.10573
\(266\) 2.00000 0.122628
\(267\) 9.00000 0.550791
\(268\) −4.00000 −0.244339
\(269\) −21.0000 −1.28039 −0.640196 0.768211i \(-0.721147\pi\)
−0.640196 + 0.768211i \(0.721147\pi\)
\(270\) 15.0000 0.912871
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 0 0
\(273\) −5.00000 −0.302614
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) −6.00000 −0.361158
\(277\) 17.0000 1.02143 0.510716 0.859750i \(-0.329381\pi\)
0.510716 + 0.859750i \(0.329381\pi\)
\(278\) −5.00000 −0.299880
\(279\) 8.00000 0.478947
\(280\) 3.00000 0.179284
\(281\) 15.0000 0.894825 0.447412 0.894328i \(-0.352346\pi\)
0.447412 + 0.894328i \(0.352346\pi\)
\(282\) 9.00000 0.535942
\(283\) 14.0000 0.832214 0.416107 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) −9.00000 −0.534052
\(285\) 6.00000 0.355409
\(286\) 0 0
\(287\) 12.0000 0.708338
\(288\) 2.00000 0.117851
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 17.0000 0.996558
\(292\) 2.00000 0.117041
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 6.00000 0.349927
\(295\) −27.0000 −1.57200
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) −12.0000 −0.695141
\(299\) −30.0000 −1.73494
\(300\) 4.00000 0.230940
\(301\) −8.00000 −0.461112
\(302\) −8.00000 −0.460348
\(303\) −15.0000 −0.861727
\(304\) 2.00000 0.114708
\(305\) 24.0000 1.37424
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) −13.0000 −0.739544
\(310\) 12.0000 0.681554
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) −5.00000 −0.283069
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 4.00000 0.225733
\(315\) 6.00000 0.338062
\(316\) 1.00000 0.0562544
\(317\) −15.0000 −0.842484 −0.421242 0.906948i \(-0.638406\pi\)
−0.421242 + 0.906948i \(0.638406\pi\)
\(318\) −6.00000 −0.336463
\(319\) 0 0
\(320\) 3.00000 0.167705
\(321\) 3.00000 0.167444
\(322\) −6.00000 −0.334367
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 20.0000 1.10940
\(326\) −20.0000 −1.10770
\(327\) 2.00000 0.110600
\(328\) 12.0000 0.662589
\(329\) 9.00000 0.496186
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 18.0000 0.987878
\(333\) −4.00000 −0.219199
\(334\) −12.0000 −0.656611
\(335\) −12.0000 −0.655630
\(336\) −1.00000 −0.0545545
\(337\) −13.0000 −0.708155 −0.354078 0.935216i \(-0.615205\pi\)
−0.354078 + 0.935216i \(0.615205\pi\)
\(338\) −12.0000 −0.652714
\(339\) 18.0000 0.977626
\(340\) 0 0
\(341\) 0 0
\(342\) 4.00000 0.216295
\(343\) 13.0000 0.701934
\(344\) −8.00000 −0.431331
\(345\) −18.0000 −0.969087
\(346\) 6.00000 0.322562
\(347\) −6.00000 −0.322097 −0.161048 0.986947i \(-0.551488\pi\)
−0.161048 + 0.986947i \(0.551488\pi\)
\(348\) 0 0
\(349\) −28.0000 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) 4.00000 0.213809
\(351\) −25.0000 −1.33440
\(352\) 0 0
\(353\) 24.0000 1.27739 0.638696 0.769460i \(-0.279474\pi\)
0.638696 + 0.769460i \(0.279474\pi\)
\(354\) 9.00000 0.478345
\(355\) −27.0000 −1.43301
\(356\) 9.00000 0.476999
\(357\) 0 0
\(358\) −18.0000 −0.951330
\(359\) −15.0000 −0.791670 −0.395835 0.918322i \(-0.629545\pi\)
−0.395835 + 0.918322i \(0.629545\pi\)
\(360\) 6.00000 0.316228
\(361\) −15.0000 −0.789474
\(362\) −2.00000 −0.105118
\(363\) −11.0000 −0.577350
\(364\) −5.00000 −0.262071
\(365\) 6.00000 0.314054
\(366\) −8.00000 −0.418167
\(367\) −28.0000 −1.46159 −0.730794 0.682598i \(-0.760850\pi\)
−0.730794 + 0.682598i \(0.760850\pi\)
\(368\) −6.00000 −0.312772
\(369\) 24.0000 1.24939
\(370\) −6.00000 −0.311925
\(371\) −6.00000 −0.311504
\(372\) −4.00000 −0.207390
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 0 0
\(375\) −3.00000 −0.154919
\(376\) 9.00000 0.464140
\(377\) 0 0
\(378\) −5.00000 −0.257172
\(379\) 11.0000 0.565032 0.282516 0.959263i \(-0.408831\pi\)
0.282516 + 0.959263i \(0.408831\pi\)
\(380\) 6.00000 0.307794
\(381\) −7.00000 −0.358621
\(382\) 15.0000 0.767467
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 22.0000 1.11977
\(387\) −16.0000 −0.813326
\(388\) 17.0000 0.863044
\(389\) 9.00000 0.456318 0.228159 0.973624i \(-0.426729\pi\)
0.228159 + 0.973624i \(0.426729\pi\)
\(390\) −15.0000 −0.759555
\(391\) 0 0
\(392\) 6.00000 0.303046
\(393\) 6.00000 0.302660
\(394\) −6.00000 −0.302276
\(395\) 3.00000 0.150946
\(396\) 0 0
\(397\) −7.00000 −0.351320 −0.175660 0.984451i \(-0.556206\pi\)
−0.175660 + 0.984451i \(0.556206\pi\)
\(398\) −11.0000 −0.551380
\(399\) −2.00000 −0.100125
\(400\) 4.00000 0.200000
\(401\) −6.00000 −0.299626 −0.149813 0.988714i \(-0.547867\pi\)
−0.149813 + 0.988714i \(0.547867\pi\)
\(402\) 4.00000 0.199502
\(403\) −20.0000 −0.996271
\(404\) −15.0000 −0.746278
\(405\) 3.00000 0.149071
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −22.0000 −1.08783 −0.543915 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 36.0000 1.77791
\(411\) 12.0000 0.591916
\(412\) −13.0000 −0.640464
\(413\) 9.00000 0.442861
\(414\) −12.0000 −0.589768
\(415\) 54.0000 2.65076
\(416\) −5.00000 −0.245145
\(417\) 5.00000 0.244851
\(418\) 0 0
\(419\) 27.0000 1.31904 0.659518 0.751689i \(-0.270760\pi\)
0.659518 + 0.751689i \(0.270760\pi\)
\(420\) −3.00000 −0.146385
\(421\) 17.0000 0.828529 0.414265 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) 4.00000 0.194717
\(423\) 18.0000 0.875190
\(424\) −6.00000 −0.291386
\(425\) 0 0
\(426\) 9.00000 0.436051
\(427\) −8.00000 −0.387147
\(428\) 3.00000 0.145010
\(429\) 0 0
\(430\) −24.0000 −1.15738
\(431\) −6.00000 −0.289010 −0.144505 0.989504i \(-0.546159\pi\)
−0.144505 + 0.989504i \(0.546159\pi\)
\(432\) −5.00000 −0.240563
\(433\) 29.0000 1.39365 0.696826 0.717241i \(-0.254595\pi\)
0.696826 + 0.717241i \(0.254595\pi\)
\(434\) −4.00000 −0.192006
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) −12.0000 −0.574038
\(438\) −2.00000 −0.0955637
\(439\) 26.0000 1.24091 0.620456 0.784241i \(-0.286947\pi\)
0.620456 + 0.784241i \(0.286947\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) 2.00000 0.0949158
\(445\) 27.0000 1.27992
\(446\) −26.0000 −1.23114
\(447\) 12.0000 0.567581
\(448\) −1.00000 −0.0472456
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 8.00000 0.377124
\(451\) 0 0
\(452\) 18.0000 0.846649
\(453\) 8.00000 0.375873
\(454\) −12.0000 −0.563188
\(455\) −15.0000 −0.703211
\(456\) −2.00000 −0.0936586
\(457\) −37.0000 −1.73079 −0.865393 0.501093i \(-0.832931\pi\)
−0.865393 + 0.501093i \(0.832931\pi\)
\(458\) 22.0000 1.02799
\(459\) 0 0
\(460\) −18.0000 −0.839254
\(461\) 42.0000 1.95614 0.978068 0.208288i \(-0.0667892\pi\)
0.978068 + 0.208288i \(0.0667892\pi\)
\(462\) 0 0
\(463\) 41.0000 1.90543 0.952716 0.303863i \(-0.0982765\pi\)
0.952716 + 0.303863i \(0.0982765\pi\)
\(464\) 0 0
\(465\) −12.0000 −0.556487
\(466\) 12.0000 0.555889
\(467\) 6.00000 0.277647 0.138823 0.990317i \(-0.455668\pi\)
0.138823 + 0.990317i \(0.455668\pi\)
\(468\) −10.0000 −0.462250
\(469\) 4.00000 0.184703
\(470\) 27.0000 1.24542
\(471\) −4.00000 −0.184310
\(472\) 9.00000 0.414259
\(473\) 0 0
\(474\) −1.00000 −0.0459315
\(475\) 8.00000 0.367065
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) −18.0000 −0.823301
\(479\) −18.0000 −0.822441 −0.411220 0.911536i \(-0.634897\pi\)
−0.411220 + 0.911536i \(0.634897\pi\)
\(480\) −3.00000 −0.136931
\(481\) 10.0000 0.455961
\(482\) −17.0000 −0.774329
\(483\) 6.00000 0.273009
\(484\) −11.0000 −0.500000
\(485\) 51.0000 2.31579
\(486\) −16.0000 −0.725775
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −8.00000 −0.362143
\(489\) 20.0000 0.904431
\(490\) 18.0000 0.813157
\(491\) 15.0000 0.676941 0.338470 0.940977i \(-0.390091\pi\)
0.338470 + 0.940977i \(0.390091\pi\)
\(492\) −12.0000 −0.541002
\(493\) 0 0
\(494\) −10.0000 −0.449921
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 9.00000 0.403705
\(498\) −18.0000 −0.806599
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) −3.00000 −0.134164
\(501\) 12.0000 0.536120
\(502\) 27.0000 1.20507
\(503\) −21.0000 −0.936344 −0.468172 0.883637i \(-0.655087\pi\)
−0.468172 + 0.883637i \(0.655087\pi\)
\(504\) −2.00000 −0.0890871
\(505\) −45.0000 −2.00247
\(506\) 0 0
\(507\) 12.0000 0.532939
\(508\) −7.00000 −0.310575
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) −2.00000 −0.0884748
\(512\) −1.00000 −0.0441942
\(513\) −10.0000 −0.441511
\(514\) 18.0000 0.793946
\(515\) −39.0000 −1.71855
\(516\) 8.00000 0.352180
\(517\) 0 0
\(518\) 2.00000 0.0878750
\(519\) −6.00000 −0.263371
\(520\) −15.0000 −0.657794
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) 0 0
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) 6.00000 0.262111
\(525\) −4.00000 −0.174574
\(526\) 18.0000 0.784837
\(527\) 0 0
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) −18.0000 −0.781870
\(531\) 18.0000 0.781133
\(532\) −2.00000 −0.0867110
\(533\) −60.0000 −2.59889
\(534\) −9.00000 −0.389468
\(535\) 9.00000 0.389104
\(536\) 4.00000 0.172774
\(537\) 18.0000 0.776757
\(538\) 21.0000 0.905374
\(539\) 0 0
\(540\) −15.0000 −0.645497
\(541\) 29.0000 1.24681 0.623404 0.781900i \(-0.285749\pi\)
0.623404 + 0.781900i \(0.285749\pi\)
\(542\) 16.0000 0.687259
\(543\) 2.00000 0.0858282
\(544\) 0 0
\(545\) 6.00000 0.257012
\(546\) 5.00000 0.213980
\(547\) 26.0000 1.11168 0.555840 0.831289i \(-0.312397\pi\)
0.555840 + 0.831289i \(0.312397\pi\)
\(548\) 12.0000 0.512615
\(549\) −16.0000 −0.682863
\(550\) 0 0
\(551\) 0 0
\(552\) 6.00000 0.255377
\(553\) −1.00000 −0.0425243
\(554\) −17.0000 −0.722261
\(555\) 6.00000 0.254686
\(556\) 5.00000 0.212047
\(557\) 15.0000 0.635570 0.317785 0.948163i \(-0.397061\pi\)
0.317785 + 0.948163i \(0.397061\pi\)
\(558\) −8.00000 −0.338667
\(559\) 40.0000 1.69182
\(560\) −3.00000 −0.126773
\(561\) 0 0
\(562\) −15.0000 −0.632737
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) −9.00000 −0.378968
\(565\) 54.0000 2.27180
\(566\) −14.0000 −0.588464
\(567\) −1.00000 −0.0419961
\(568\) 9.00000 0.377632
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) −6.00000 −0.251312
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) 0 0
\(573\) −15.0000 −0.626634
\(574\) −12.0000 −0.500870
\(575\) −24.0000 −1.00087
\(576\) −2.00000 −0.0833333
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) 17.0000 0.707107
\(579\) −22.0000 −0.914289
\(580\) 0 0
\(581\) −18.0000 −0.746766
\(582\) −17.0000 −0.704673
\(583\) 0 0
\(584\) −2.00000 −0.0827606
\(585\) −30.0000 −1.24035
\(586\) 6.00000 0.247858
\(587\) −21.0000 −0.866763 −0.433381 0.901211i \(-0.642680\pi\)
−0.433381 + 0.901211i \(0.642680\pi\)
\(588\) −6.00000 −0.247436
\(589\) −8.00000 −0.329634
\(590\) 27.0000 1.11157
\(591\) 6.00000 0.246807
\(592\) 2.00000 0.0821995
\(593\) −21.0000 −0.862367 −0.431183 0.902264i \(-0.641904\pi\)
−0.431183 + 0.902264i \(0.641904\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12.0000 0.491539
\(597\) 11.0000 0.450200
\(598\) 30.0000 1.22679
\(599\) 6.00000 0.245153 0.122577 0.992459i \(-0.460884\pi\)
0.122577 + 0.992459i \(0.460884\pi\)
\(600\) −4.00000 −0.163299
\(601\) −28.0000 −1.14214 −0.571072 0.820900i \(-0.693472\pi\)
−0.571072 + 0.820900i \(0.693472\pi\)
\(602\) 8.00000 0.326056
\(603\) 8.00000 0.325785
\(604\) 8.00000 0.325515
\(605\) −33.0000 −1.34164
\(606\) 15.0000 0.609333
\(607\) 5.00000 0.202944 0.101472 0.994838i \(-0.467645\pi\)
0.101472 + 0.994838i \(0.467645\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 0 0
\(610\) −24.0000 −0.971732
\(611\) −45.0000 −1.82051
\(612\) 0 0
\(613\) 2.00000 0.0807792 0.0403896 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) −20.0000 −0.807134
\(615\) −36.0000 −1.45166
\(616\) 0 0
\(617\) −39.0000 −1.57008 −0.785040 0.619445i \(-0.787358\pi\)
−0.785040 + 0.619445i \(0.787358\pi\)
\(618\) 13.0000 0.522937
\(619\) −1.00000 −0.0401934 −0.0200967 0.999798i \(-0.506397\pi\)
−0.0200967 + 0.999798i \(0.506397\pi\)
\(620\) −12.0000 −0.481932
\(621\) 30.0000 1.20386
\(622\) −12.0000 −0.481156
\(623\) −9.00000 −0.360577
\(624\) 5.00000 0.200160
\(625\) −29.0000 −1.16000
\(626\) 10.0000 0.399680
\(627\) 0 0
\(628\) −4.00000 −0.159617
\(629\) 0 0
\(630\) −6.00000 −0.239046
\(631\) −43.0000 −1.71180 −0.855901 0.517139i \(-0.826997\pi\)
−0.855901 + 0.517139i \(0.826997\pi\)
\(632\) −1.00000 −0.0397779
\(633\) −4.00000 −0.158986
\(634\) 15.0000 0.595726
\(635\) −21.0000 −0.833360
\(636\) 6.00000 0.237915
\(637\) −30.0000 −1.18864
\(638\) 0 0
\(639\) 18.0000 0.712069
\(640\) −3.00000 −0.118585
\(641\) 27.0000 1.06644 0.533218 0.845978i \(-0.320983\pi\)
0.533218 + 0.845978i \(0.320983\pi\)
\(642\) −3.00000 −0.118401
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) 6.00000 0.236433
\(645\) 24.0000 0.944999
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) −20.0000 −0.784465
\(651\) 4.00000 0.156772
\(652\) 20.0000 0.783260
\(653\) −21.0000 −0.821794 −0.410897 0.911682i \(-0.634784\pi\)
−0.410897 + 0.911682i \(0.634784\pi\)
\(654\) −2.00000 −0.0782062
\(655\) 18.0000 0.703318
\(656\) −12.0000 −0.468521
\(657\) −4.00000 −0.156055
\(658\) −9.00000 −0.350857
\(659\) 21.0000 0.818044 0.409022 0.912525i \(-0.365870\pi\)
0.409022 + 0.912525i \(0.365870\pi\)
\(660\) 0 0
\(661\) −4.00000 −0.155582 −0.0777910 0.996970i \(-0.524787\pi\)
−0.0777910 + 0.996970i \(0.524787\pi\)
\(662\) −8.00000 −0.310929
\(663\) 0 0
\(664\) −18.0000 −0.698535
\(665\) −6.00000 −0.232670
\(666\) 4.00000 0.154997
\(667\) 0 0
\(668\) 12.0000 0.464294
\(669\) 26.0000 1.00522
\(670\) 12.0000 0.463600
\(671\) 0 0
\(672\) 1.00000 0.0385758
\(673\) −28.0000 −1.07932 −0.539660 0.841883i \(-0.681447\pi\)
−0.539660 + 0.841883i \(0.681447\pi\)
\(674\) 13.0000 0.500741
\(675\) −20.0000 −0.769800
\(676\) 12.0000 0.461538
\(677\) 15.0000 0.576497 0.288248 0.957556i \(-0.406927\pi\)
0.288248 + 0.957556i \(0.406927\pi\)
\(678\) −18.0000 −0.691286
\(679\) −17.0000 −0.652400
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) 30.0000 1.14792 0.573959 0.818884i \(-0.305407\pi\)
0.573959 + 0.818884i \(0.305407\pi\)
\(684\) −4.00000 −0.152944
\(685\) 36.0000 1.37549
\(686\) −13.0000 −0.496342
\(687\) −22.0000 −0.839352
\(688\) 8.00000 0.304997
\(689\) 30.0000 1.14291
\(690\) 18.0000 0.685248
\(691\) 35.0000 1.33146 0.665731 0.746191i \(-0.268120\pi\)
0.665731 + 0.746191i \(0.268120\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) 6.00000 0.227757
\(695\) 15.0000 0.568982
\(696\) 0 0
\(697\) 0 0
\(698\) 28.0000 1.05982
\(699\) −12.0000 −0.453882
\(700\) −4.00000 −0.151186
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 25.0000 0.943564
\(703\) 4.00000 0.150863
\(704\) 0 0
\(705\) −27.0000 −1.01688
\(706\) −24.0000 −0.903252
\(707\) 15.0000 0.564133
\(708\) −9.00000 −0.338241
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 27.0000 1.01329
\(711\) −2.00000 −0.0750059
\(712\) −9.00000 −0.337289
\(713\) 24.0000 0.898807
\(714\) 0 0
\(715\) 0 0
\(716\) 18.0000 0.672692
\(717\) 18.0000 0.672222
\(718\) 15.0000 0.559795
\(719\) −18.0000 −0.671287 −0.335643 0.941989i \(-0.608954\pi\)
−0.335643 + 0.941989i \(0.608954\pi\)
\(720\) −6.00000 −0.223607
\(721\) 13.0000 0.484145
\(722\) 15.0000 0.558242
\(723\) 17.0000 0.632237
\(724\) 2.00000 0.0743294
\(725\) 0 0
\(726\) 11.0000 0.408248
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 5.00000 0.185312
\(729\) 13.0000 0.481481
\(730\) −6.00000 −0.222070
\(731\) 0 0
\(732\) 8.00000 0.295689
\(733\) 50.0000 1.84679 0.923396 0.383849i \(-0.125402\pi\)
0.923396 + 0.383849i \(0.125402\pi\)
\(734\) 28.0000 1.03350
\(735\) −18.0000 −0.663940
\(736\) 6.00000 0.221163
\(737\) 0 0
\(738\) −24.0000 −0.883452
\(739\) −43.0000 −1.58178 −0.790890 0.611958i \(-0.790382\pi\)
−0.790890 + 0.611958i \(0.790382\pi\)
\(740\) 6.00000 0.220564
\(741\) 10.0000 0.367359
\(742\) 6.00000 0.220267
\(743\) −6.00000 −0.220119 −0.110059 0.993925i \(-0.535104\pi\)
−0.110059 + 0.993925i \(0.535104\pi\)
\(744\) 4.00000 0.146647
\(745\) 36.0000 1.31894
\(746\) 22.0000 0.805477
\(747\) −36.0000 −1.31717
\(748\) 0 0
\(749\) −3.00000 −0.109618
\(750\) 3.00000 0.109545
\(751\) 50.0000 1.82453 0.912263 0.409605i \(-0.134333\pi\)
0.912263 + 0.409605i \(0.134333\pi\)
\(752\) −9.00000 −0.328196
\(753\) −27.0000 −0.983935
\(754\) 0 0
\(755\) 24.0000 0.873449
\(756\) 5.00000 0.181848
\(757\) 29.0000 1.05402 0.527011 0.849858i \(-0.323312\pi\)
0.527011 + 0.849858i \(0.323312\pi\)
\(758\) −11.0000 −0.399538
\(759\) 0 0
\(760\) −6.00000 −0.217643
\(761\) 30.0000 1.08750 0.543750 0.839248i \(-0.317004\pi\)
0.543750 + 0.839248i \(0.317004\pi\)
\(762\) 7.00000 0.253583
\(763\) −2.00000 −0.0724049
\(764\) −15.0000 −0.542681
\(765\) 0 0
\(766\) −6.00000 −0.216789
\(767\) −45.0000 −1.62486
\(768\) 1.00000 0.0360844
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) −22.0000 −0.791797
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) 16.0000 0.575108
\(775\) −16.0000 −0.574737
\(776\) −17.0000 −0.610264
\(777\) −2.00000 −0.0717496
\(778\) −9.00000 −0.322666
\(779\) −24.0000 −0.859889
\(780\) 15.0000 0.537086
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −6.00000 −0.214286
\(785\) −12.0000 −0.428298
\(786\) −6.00000 −0.214013
\(787\) −4.00000 −0.142585 −0.0712923 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) 6.00000 0.213741
\(789\) −18.0000 −0.640817
\(790\) −3.00000 −0.106735
\(791\) −18.0000 −0.640006
\(792\) 0 0
\(793\) 40.0000 1.42044
\(794\) 7.00000 0.248421
\(795\) 18.0000 0.638394
\(796\) 11.0000 0.389885
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 2.00000 0.0707992
\(799\) 0 0
\(800\) −4.00000 −0.141421
\(801\) −18.0000 −0.635999
\(802\) 6.00000 0.211867
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) 18.0000 0.634417
\(806\) 20.0000 0.704470
\(807\) −21.0000 −0.739235
\(808\) 15.0000 0.527698
\(809\) 15.0000 0.527372 0.263686 0.964609i \(-0.415062\pi\)
0.263686 + 0.964609i \(0.415062\pi\)
\(810\) −3.00000 −0.105409
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 0 0
\(813\) −16.0000 −0.561144
\(814\) 0 0
\(815\) 60.0000 2.10171
\(816\) 0 0
\(817\) 16.0000 0.559769
\(818\) 22.0000 0.769212
\(819\) 10.0000 0.349428
\(820\) −36.0000 −1.25717
\(821\) −18.0000 −0.628204 −0.314102 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) −12.0000 −0.418548
\(823\) −40.0000 −1.39431 −0.697156 0.716919i \(-0.745552\pi\)
−0.697156 + 0.716919i \(0.745552\pi\)
\(824\) 13.0000 0.452876
\(825\) 0 0
\(826\) −9.00000 −0.313150
\(827\) 21.0000 0.730242 0.365121 0.930960i \(-0.381028\pi\)
0.365121 + 0.930960i \(0.381028\pi\)
\(828\) 12.0000 0.417029
\(829\) −16.0000 −0.555703 −0.277851 0.960624i \(-0.589622\pi\)
−0.277851 + 0.960624i \(0.589622\pi\)
\(830\) −54.0000 −1.87437
\(831\) 17.0000 0.589723
\(832\) 5.00000 0.173344
\(833\) 0 0
\(834\) −5.00000 −0.173136
\(835\) 36.0000 1.24583
\(836\) 0 0
\(837\) 20.0000 0.691301
\(838\) −27.0000 −0.932700
\(839\) −48.0000 −1.65714 −0.828572 0.559883i \(-0.810846\pi\)
−0.828572 + 0.559883i \(0.810846\pi\)
\(840\) 3.00000 0.103510
\(841\) −29.0000 −1.00000
\(842\) −17.0000 −0.585859
\(843\) 15.0000 0.516627
\(844\) −4.00000 −0.137686
\(845\) 36.0000 1.23844
\(846\) −18.0000 −0.618853
\(847\) 11.0000 0.377964
\(848\) 6.00000 0.206041
\(849\) 14.0000 0.480479
\(850\) 0 0
\(851\) −12.0000 −0.411355
\(852\) −9.00000 −0.308335
\(853\) 26.0000 0.890223 0.445112 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(854\) 8.00000 0.273754
\(855\) −12.0000 −0.410391
\(856\) −3.00000 −0.102538
\(857\) 21.0000 0.717346 0.358673 0.933463i \(-0.383229\pi\)
0.358673 + 0.933463i \(0.383229\pi\)
\(858\) 0 0
\(859\) 23.0000 0.784750 0.392375 0.919805i \(-0.371654\pi\)
0.392375 + 0.919805i \(0.371654\pi\)
\(860\) 24.0000 0.818393
\(861\) 12.0000 0.408959
\(862\) 6.00000 0.204361
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 5.00000 0.170103
\(865\) −18.0000 −0.612018
\(866\) −29.0000 −0.985460
\(867\) −17.0000 −0.577350
\(868\) 4.00000 0.135769
\(869\) 0 0
\(870\) 0 0
\(871\) −20.0000 −0.677674
\(872\) −2.00000 −0.0677285
\(873\) −34.0000 −1.15073
\(874\) 12.0000 0.405906
\(875\) 3.00000 0.101419
\(876\) 2.00000 0.0675737
\(877\) 14.0000 0.472746 0.236373 0.971662i \(-0.424041\pi\)
0.236373 + 0.971662i \(0.424041\pi\)
\(878\) −26.0000 −0.877457
\(879\) −6.00000 −0.202375
\(880\) 0 0
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) −12.0000 −0.404061
\(883\) 29.0000 0.975928 0.487964 0.872864i \(-0.337740\pi\)
0.487964 + 0.872864i \(0.337740\pi\)
\(884\) 0 0
\(885\) −27.0000 −0.907595
\(886\) 36.0000 1.20944
\(887\) −12.0000 −0.402921 −0.201460 0.979497i \(-0.564569\pi\)
−0.201460 + 0.979497i \(0.564569\pi\)
\(888\) −2.00000 −0.0671156
\(889\) 7.00000 0.234772
\(890\) −27.0000 −0.905042
\(891\) 0 0
\(892\) 26.0000 0.870544
\(893\) −18.0000 −0.602347
\(894\) −12.0000 −0.401340
\(895\) 54.0000 1.80502
\(896\) 1.00000 0.0334077
\(897\) −30.0000 −1.00167
\(898\) −12.0000 −0.400445
\(899\) 0 0
\(900\) −8.00000 −0.266667
\(901\) 0 0
\(902\) 0 0
\(903\) −8.00000 −0.266223
\(904\) −18.0000 −0.598671
\(905\) 6.00000 0.199447
\(906\) −8.00000 −0.265782
\(907\) −10.0000 −0.332045 −0.166022 0.986122i \(-0.553092\pi\)
−0.166022 + 0.986122i \(0.553092\pi\)
\(908\) 12.0000 0.398234
\(909\) 30.0000 0.995037
\(910\) 15.0000 0.497245
\(911\) 42.0000 1.39152 0.695761 0.718273i \(-0.255067\pi\)
0.695761 + 0.718273i \(0.255067\pi\)
\(912\) 2.00000 0.0662266
\(913\) 0 0
\(914\) 37.0000 1.22385
\(915\) 24.0000 0.793416
\(916\) −22.0000 −0.726900
\(917\) −6.00000 −0.198137
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 18.0000 0.593442
\(921\) 20.0000 0.659022
\(922\) −42.0000 −1.38320
\(923\) −45.0000 −1.48119
\(924\) 0 0
\(925\) 8.00000 0.263038
\(926\) −41.0000 −1.34734
\(927\) 26.0000 0.853952
\(928\) 0 0
\(929\) −18.0000 −0.590561 −0.295280 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) 12.0000 0.393496
\(931\) −12.0000 −0.393284
\(932\) −12.0000 −0.393073
\(933\) 12.0000 0.392862
\(934\) −6.00000 −0.196326
\(935\) 0 0
\(936\) 10.0000 0.326860
\(937\) −52.0000 −1.69877 −0.849383 0.527777i \(-0.823026\pi\)
−0.849383 + 0.527777i \(0.823026\pi\)
\(938\) −4.00000 −0.130605
\(939\) −10.0000 −0.326338
\(940\) −27.0000 −0.880643
\(941\) 30.0000 0.977972 0.488986 0.872292i \(-0.337367\pi\)
0.488986 + 0.872292i \(0.337367\pi\)
\(942\) 4.00000 0.130327
\(943\) 72.0000 2.34464
\(944\) −9.00000 −0.292925
\(945\) 15.0000 0.487950
\(946\) 0 0
\(947\) −60.0000 −1.94974 −0.974869 0.222779i \(-0.928487\pi\)
−0.974869 + 0.222779i \(0.928487\pi\)
\(948\) 1.00000 0.0324785
\(949\) 10.0000 0.324614
\(950\) −8.00000 −0.259554
\(951\) −15.0000 −0.486408
\(952\) 0 0
\(953\) −3.00000 −0.0971795 −0.0485898 0.998819i \(-0.515473\pi\)
−0.0485898 + 0.998819i \(0.515473\pi\)
\(954\) 12.0000 0.388514
\(955\) −45.0000 −1.45617
\(956\) 18.0000 0.582162
\(957\) 0 0
\(958\) 18.0000 0.581554
\(959\) −12.0000 −0.387500
\(960\) 3.00000 0.0968246
\(961\) −15.0000 −0.483871
\(962\) −10.0000 −0.322413
\(963\) −6.00000 −0.193347
\(964\) 17.0000 0.547533
\(965\) −66.0000 −2.12462
\(966\) −6.00000 −0.193047
\(967\) −22.0000 −0.707472 −0.353736 0.935345i \(-0.615089\pi\)
−0.353736 + 0.935345i \(0.615089\pi\)
\(968\) 11.0000 0.353553
\(969\) 0 0
\(970\) −51.0000 −1.63751
\(971\) 42.0000 1.34784 0.673922 0.738802i \(-0.264608\pi\)
0.673922 + 0.738802i \(0.264608\pi\)
\(972\) 16.0000 0.513200
\(973\) −5.00000 −0.160293
\(974\) 16.0000 0.512673
\(975\) 20.0000 0.640513
\(976\) 8.00000 0.256074
\(977\) 30.0000 0.959785 0.479893 0.877327i \(-0.340676\pi\)
0.479893 + 0.877327i \(0.340676\pi\)
\(978\) −20.0000 −0.639529
\(979\) 0 0
\(980\) −18.0000 −0.574989
\(981\) −4.00000 −0.127710
\(982\) −15.0000 −0.478669
\(983\) 24.0000 0.765481 0.382741 0.923856i \(-0.374980\pi\)
0.382741 + 0.923856i \(0.374980\pi\)
\(984\) 12.0000 0.382546
\(985\) 18.0000 0.573528
\(986\) 0 0
\(987\) 9.00000 0.286473
\(988\) 10.0000 0.318142
\(989\) −48.0000 −1.52631
\(990\) 0 0
\(991\) −25.0000 −0.794151 −0.397076 0.917786i \(-0.629975\pi\)
−0.397076 + 0.917786i \(0.629975\pi\)
\(992\) 4.00000 0.127000
\(993\) 8.00000 0.253872
\(994\) −9.00000 −0.285463
\(995\) 33.0000 1.04617
\(996\) 18.0000 0.570352
\(997\) −10.0000 −0.316703 −0.158352 0.987383i \(-0.550618\pi\)
−0.158352 + 0.987383i \(0.550618\pi\)
\(998\) 4.00000 0.126618
\(999\) −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.b.1.1 1
3.2 odd 2 1422.2.a.f.1.1 1
4.3 odd 2 1264.2.a.c.1.1 1
5.4 even 2 3950.2.a.g.1.1 1
7.6 odd 2 7742.2.a.b.1.1 1
8.3 odd 2 5056.2.a.l.1.1 1
8.5 even 2 5056.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
158.2.a.b.1.1 1 1.1 even 1 trivial
1264.2.a.c.1.1 1 4.3 odd 2
1422.2.a.f.1.1 1 3.2 odd 2
3950.2.a.g.1.1 1 5.4 even 2
5056.2.a.d.1.1 1 8.5 even 2
5056.2.a.l.1.1 1 8.3 odd 2
7742.2.a.b.1.1 1 7.6 odd 2