Properties

Label 182.2.a.c.1.1
Level $182$
Weight $2$
Character 182.1
Self dual yes
Analytic conductor $1.453$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 182.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.45327731679\)
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 \(\chi\) \(=\) 182.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{7} +1.00000 q^{8} -3.00000 q^{9} +2.00000 q^{10} +4.00000 q^{11} -1.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} -3.00000 q^{18} +2.00000 q^{20} +4.00000 q^{22} +8.00000 q^{23} -1.00000 q^{25} -1.00000 q^{26} -1.00000 q^{28} -10.0000 q^{29} -8.00000 q^{31} +1.00000 q^{32} -6.00000 q^{34} -2.00000 q^{35} -3.00000 q^{36} +6.00000 q^{37} +2.00000 q^{40} -6.00000 q^{41} +4.00000 q^{43} +4.00000 q^{44} -6.00000 q^{45} +8.00000 q^{46} -8.00000 q^{47} +1.00000 q^{49} -1.00000 q^{50} -1.00000 q^{52} +6.00000 q^{53} +8.00000 q^{55} -1.00000 q^{56} -10.0000 q^{58} +8.00000 q^{59} +10.0000 q^{61} -8.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} -2.00000 q^{65} +4.00000 q^{67} -6.00000 q^{68} -2.00000 q^{70} -8.00000 q^{71} -3.00000 q^{72} +2.00000 q^{73} +6.00000 q^{74} -4.00000 q^{77} +8.00000 q^{79} +2.00000 q^{80} +9.00000 q^{81} -6.00000 q^{82} -12.0000 q^{85} +4.00000 q^{86} +4.00000 q^{88} +18.0000 q^{89} -6.00000 q^{90} +1.00000 q^{91} +8.00000 q^{92} -8.00000 q^{94} +2.00000 q^{97} +1.00000 q^{98} -12.0000 q^{99} +O(q^{100})\)

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
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) −3.00000 −1.00000
\(10\) 2.00000 0.632456
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) −3.00000 −0.707107
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) 4.00000 0.852803
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −1.00000 −0.196116
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) −10.0000 −1.85695 −0.928477 0.371391i \(-0.878881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 0 0
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −6.00000 −1.02899
\(35\) −2.00000 −0.338062
\(36\) −3.00000 −0.500000
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 2.00000 0.316228
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 4.00000 0.603023
\(45\) −6.00000 −0.894427
\(46\) 8.00000 1.17954
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) −1.00000 −0.138675
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 8.00000 1.07872
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) −10.0000 −1.31306
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 0 0
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) −8.00000 −1.01600
\(63\) 3.00000 0.377964
\(64\) 1.00000 0.125000
\(65\) −2.00000 −0.248069
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) −6.00000 −0.727607
\(69\) 0 0
\(70\) −2.00000 −0.239046
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) −3.00000 −0.353553
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 6.00000 0.697486
\(75\) 0 0
\(76\) 0 0
\(77\) −4.00000 −0.455842
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 2.00000 0.223607
\(81\) 9.00000 1.00000
\(82\) −6.00000 −0.662589
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −12.0000 −1.30158
\(86\) 4.00000 0.431331
\(87\) 0 0
\(88\) 4.00000 0.426401
\(89\) 18.0000 1.90800 0.953998 0.299813i \(-0.0969242\pi\)
0.953998 + 0.299813i \(0.0969242\pi\)
\(90\) −6.00000 −0.632456
\(91\) 1.00000 0.104828
\(92\) 8.00000 0.834058
\(93\) 0 0
\(94\) −8.00000 −0.825137
\(95\) 0 0
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 1.00000 0.101015
\(99\) −12.0000 −1.20605
\(100\) −1.00000 −0.100000
\(101\) −14.0000 −1.39305 −0.696526 0.717532i \(-0.745272\pi\)
−0.696526 + 0.717532i \(0.745272\pi\)
\(102\) 0 0
\(103\) 16.0000 1.57653 0.788263 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 8.00000 0.762770
\(111\) 0 0
\(112\) −1.00000 −0.0944911
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) 16.0000 1.49201
\(116\) −10.0000 −0.928477
\(117\) 3.00000 0.277350
\(118\) 8.00000 0.736460
\(119\) 6.00000 0.550019
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 10.0000 0.905357
\(123\) 0 0
\(124\) −8.00000 −0.718421
\(125\) −12.0000 −1.07331
\(126\) 3.00000 0.267261
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) −2.00000 −0.175412
\(131\) 8.00000 0.698963 0.349482 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) −6.00000 −0.514496
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) −2.00000 −0.169031
\(141\) 0 0
\(142\) −8.00000 −0.671345
\(143\) −4.00000 −0.334497
\(144\) −3.00000 −0.250000
\(145\) −20.0000 −1.66091
\(146\) 2.00000 0.165521
\(147\) 0 0
\(148\) 6.00000 0.493197
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 18.0000 1.45521
\(154\) −4.00000 −0.322329
\(155\) −16.0000 −1.28515
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 8.00000 0.636446
\(159\) 0 0
\(160\) 2.00000 0.158114
\(161\) −8.00000 −0.630488
\(162\) 9.00000 0.707107
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −12.0000 −0.920358
\(171\) 0 0
\(172\) 4.00000 0.304997
\(173\) 2.00000 0.152057 0.0760286 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 4.00000 0.301511
\(177\) 0 0
\(178\) 18.0000 1.34916
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) −6.00000 −0.447214
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 1.00000 0.0741249
\(183\) 0 0
\(184\) 8.00000 0.589768
\(185\) 12.0000 0.882258
\(186\) 0 0
\(187\) −24.0000 −1.75505
\(188\) −8.00000 −0.583460
\(189\) 0 0
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 0 0
\(193\) 2.00000 0.143963 0.0719816 0.997406i \(-0.477068\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 2.00000 0.143592
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) −12.0000 −0.852803
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0 0
\(202\) −14.0000 −0.985037
\(203\) 10.0000 0.701862
\(204\) 0 0
\(205\) −12.0000 −0.838116
\(206\) 16.0000 1.11477
\(207\) −24.0000 −1.66812
\(208\) −1.00000 −0.0693375
\(209\) 0 0
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 6.00000 0.412082
\(213\) 0 0
\(214\) −4.00000 −0.273434
\(215\) 8.00000 0.545595
\(216\) 0 0
\(217\) 8.00000 0.543075
\(218\) −2.00000 −0.135457
\(219\) 0 0
\(220\) 8.00000 0.539360
\(221\) 6.00000 0.403604
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 3.00000 0.200000
\(226\) 2.00000 0.133038
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) −6.00000 −0.396491 −0.198246 0.980152i \(-0.563524\pi\)
−0.198246 + 0.980152i \(0.563524\pi\)
\(230\) 16.0000 1.05501
\(231\) 0 0
\(232\) −10.0000 −0.656532
\(233\) 10.0000 0.655122 0.327561 0.944830i \(-0.393773\pi\)
0.327561 + 0.944830i \(0.393773\pi\)
\(234\) 3.00000 0.196116
\(235\) −16.0000 −1.04372
\(236\) 8.00000 0.520756
\(237\) 0 0
\(238\) 6.00000 0.388922
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) 18.0000 1.15948 0.579741 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) 5.00000 0.321412
\(243\) 0 0
\(244\) 10.0000 0.640184
\(245\) 2.00000 0.127775
\(246\) 0 0
\(247\) 0 0
\(248\) −8.00000 −0.508001
\(249\) 0 0
\(250\) −12.0000 −0.758947
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 3.00000 0.188982
\(253\) 32.0000 2.01182
\(254\) 16.0000 1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 0 0
\(259\) −6.00000 −0.372822
\(260\) −2.00000 −0.124035
\(261\) 30.0000 1.85695
\(262\) 8.00000 0.494242
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 12.0000 0.737154
\(266\) 0 0
\(267\) 0 0
\(268\) 4.00000 0.244339
\(269\) −30.0000 −1.82913 −0.914566 0.404436i \(-0.867468\pi\)
−0.914566 + 0.404436i \(0.867468\pi\)
\(270\) 0 0
\(271\) −32.0000 −1.94386 −0.971931 0.235267i \(-0.924404\pi\)
−0.971931 + 0.235267i \(0.924404\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) −4.00000 −0.241209
\(276\) 0 0
\(277\) 6.00000 0.360505 0.180253 0.983620i \(-0.442309\pi\)
0.180253 + 0.983620i \(0.442309\pi\)
\(278\) −8.00000 −0.479808
\(279\) 24.0000 1.43684
\(280\) −2.00000 −0.119523
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) 16.0000 0.951101 0.475551 0.879688i \(-0.342249\pi\)
0.475551 + 0.879688i \(0.342249\pi\)
\(284\) −8.00000 −0.474713
\(285\) 0 0
\(286\) −4.00000 −0.236525
\(287\) 6.00000 0.354169
\(288\) −3.00000 −0.176777
\(289\) 19.0000 1.11765
\(290\) −20.0000 −1.17444
\(291\) 0 0
\(292\) 2.00000 0.117041
\(293\) −14.0000 −0.817889 −0.408944 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) 0 0
\(295\) 16.0000 0.931556
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) −18.0000 −1.04271
\(299\) −8.00000 −0.462652
\(300\) 0 0
\(301\) −4.00000 −0.230556
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 20.0000 1.14520
\(306\) 18.0000 1.02899
\(307\) 32.0000 1.82634 0.913168 0.407583i \(-0.133628\pi\)
0.913168 + 0.407583i \(0.133628\pi\)
\(308\) −4.00000 −0.227921
\(309\) 0 0
\(310\) −16.0000 −0.908739
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) 2.00000 0.112867
\(315\) 6.00000 0.338062
\(316\) 8.00000 0.450035
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 0 0
\(319\) −40.0000 −2.23957
\(320\) 2.00000 0.111803
\(321\) 0 0
\(322\) −8.00000 −0.445823
\(323\) 0 0
\(324\) 9.00000 0.500000
\(325\) 1.00000 0.0554700
\(326\) −4.00000 −0.221540
\(327\) 0 0
\(328\) −6.00000 −0.331295
\(329\) 8.00000 0.441054
\(330\) 0 0
\(331\) −28.0000 −1.53902 −0.769510 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) 0 0
\(333\) −18.0000 −0.986394
\(334\) 0 0
\(335\) 8.00000 0.437087
\(336\) 0 0
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 1.00000 0.0543928
\(339\) 0 0
\(340\) −12.0000 −0.650791
\(341\) −32.0000 −1.73290
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 2.00000 0.107521
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 1.00000 0.0534522
\(351\) 0 0
\(352\) 4.00000 0.213201
\(353\) 10.0000 0.532246 0.266123 0.963939i \(-0.414257\pi\)
0.266123 + 0.963939i \(0.414257\pi\)
\(354\) 0 0
\(355\) −16.0000 −0.849192
\(356\) 18.0000 0.953998
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −6.00000 −0.316228
\(361\) −19.0000 −1.00000
\(362\) −6.00000 −0.315353
\(363\) 0 0
\(364\) 1.00000 0.0524142
\(365\) 4.00000 0.209370
\(366\) 0 0
\(367\) −16.0000 −0.835193 −0.417597 0.908633i \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) 8.00000 0.417029
\(369\) 18.0000 0.937043
\(370\) 12.0000 0.623850
\(371\) −6.00000 −0.311504
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) −24.0000 −1.24101
\(375\) 0 0
\(376\) −8.00000 −0.412568
\(377\) 10.0000 0.515026
\(378\) 0 0
\(379\) 4.00000 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −8.00000 −0.409316
\(383\) 24.0000 1.22634 0.613171 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 0 0
\(385\) −8.00000 −0.407718
\(386\) 2.00000 0.101797
\(387\) −12.0000 −0.609994
\(388\) 2.00000 0.101535
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 0 0
\(391\) −48.0000 −2.42746
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) −18.0000 −0.906827
\(395\) 16.0000 0.805047
\(396\) −12.0000 −0.603023
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) −16.0000 −0.802008
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) 8.00000 0.398508
\(404\) −14.0000 −0.696526
\(405\) 18.0000 0.894427
\(406\) 10.0000 0.496292
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) −38.0000 −1.87898 −0.939490 0.342578i \(-0.888700\pi\)
−0.939490 + 0.342578i \(0.888700\pi\)
\(410\) −12.0000 −0.592638
\(411\) 0 0
\(412\) 16.0000 0.788263
\(413\) −8.00000 −0.393654
\(414\) −24.0000 −1.17954
\(415\) 0 0
\(416\) −1.00000 −0.0490290
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) 20.0000 0.973585
\(423\) 24.0000 1.16692
\(424\) 6.00000 0.291386
\(425\) 6.00000 0.291043
\(426\) 0 0
\(427\) −10.0000 −0.483934
\(428\) −4.00000 −0.193347
\(429\) 0 0
\(430\) 8.00000 0.385794
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) −38.0000 −1.82616 −0.913082 0.407777i \(-0.866304\pi\)
−0.913082 + 0.407777i \(0.866304\pi\)
\(434\) 8.00000 0.384012
\(435\) 0 0
\(436\) −2.00000 −0.0957826
\(437\) 0 0
\(438\) 0 0
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 8.00000 0.381385
\(441\) −3.00000 −0.142857
\(442\) 6.00000 0.285391
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) 0 0
\(445\) 36.0000 1.70656
\(446\) 0 0
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) −14.0000 −0.660701 −0.330350 0.943858i \(-0.607167\pi\)
−0.330350 + 0.943858i \(0.607167\pi\)
\(450\) 3.00000 0.141421
\(451\) −24.0000 −1.13012
\(452\) 2.00000 0.0940721
\(453\) 0 0
\(454\) 0 0
\(455\) 2.00000 0.0937614
\(456\) 0 0
\(457\) 10.0000 0.467780 0.233890 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) −6.00000 −0.280362
\(459\) 0 0
\(460\) 16.0000 0.746004
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) −10.0000 −0.464238
\(465\) 0 0
\(466\) 10.0000 0.463241
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 3.00000 0.138675
\(469\) −4.00000 −0.184703
\(470\) −16.0000 −0.738025
\(471\) 0 0
\(472\) 8.00000 0.368230
\(473\) 16.0000 0.735681
\(474\) 0 0
\(475\) 0 0
\(476\) 6.00000 0.275010
\(477\) −18.0000 −0.824163
\(478\) −24.0000 −1.09773
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) 18.0000 0.819878
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 4.00000 0.181631
\(486\) 0 0
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) 10.0000 0.452679
\(489\) 0 0
\(490\) 2.00000 0.0903508
\(491\) 28.0000 1.26362 0.631811 0.775122i \(-0.282312\pi\)
0.631811 + 0.775122i \(0.282312\pi\)
\(492\) 0 0
\(493\) 60.0000 2.70226
\(494\) 0 0
\(495\) −24.0000 −1.07872
\(496\) −8.00000 −0.359211
\(497\) 8.00000 0.358849
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) −12.0000 −0.536656
\(501\) 0 0
\(502\) 24.0000 1.07117
\(503\) −8.00000 −0.356702 −0.178351 0.983967i \(-0.557076\pi\)
−0.178351 + 0.983967i \(0.557076\pi\)
\(504\) 3.00000 0.133631
\(505\) −28.0000 −1.24598
\(506\) 32.0000 1.42257
\(507\) 0 0
\(508\) 16.0000 0.709885
\(509\) −14.0000 −0.620539 −0.310270 0.950649i \(-0.600419\pi\)
−0.310270 + 0.950649i \(0.600419\pi\)
\(510\) 0 0
\(511\) −2.00000 −0.0884748
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 18.0000 0.793946
\(515\) 32.0000 1.41009
\(516\) 0 0
\(517\) −32.0000 −1.40736
\(518\) −6.00000 −0.263625
\(519\) 0 0
\(520\) −2.00000 −0.0877058
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 30.0000 1.31306
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 8.00000 0.349482
\(525\) 0 0
\(526\) 0 0
\(527\) 48.0000 2.09091
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) 12.0000 0.521247
\(531\) −24.0000 −1.04151
\(532\) 0 0
\(533\) 6.00000 0.259889
\(534\) 0 0
\(535\) −8.00000 −0.345870
\(536\) 4.00000 0.172774
\(537\) 0 0
\(538\) −30.0000 −1.29339
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) −32.0000 −1.37452
\(543\) 0 0
\(544\) −6.00000 −0.257248
\(545\) −4.00000 −0.171341
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) −6.00000 −0.256307
\(549\) −30.0000 −1.28037
\(550\) −4.00000 −0.170561
\(551\) 0 0
\(552\) 0 0
\(553\) −8.00000 −0.340195
\(554\) 6.00000 0.254916
\(555\) 0 0
\(556\) −8.00000 −0.339276
\(557\) −42.0000 −1.77960 −0.889799 0.456354i \(-0.849155\pi\)
−0.889799 + 0.456354i \(0.849155\pi\)
\(558\) 24.0000 1.01600
\(559\) −4.00000 −0.169182
\(560\) −2.00000 −0.0845154
\(561\) 0 0
\(562\) 10.0000 0.421825
\(563\) −16.0000 −0.674320 −0.337160 0.941447i \(-0.609466\pi\)
−0.337160 + 0.941447i \(0.609466\pi\)
\(564\) 0 0
\(565\) 4.00000 0.168281
\(566\) 16.0000 0.672530
\(567\) −9.00000 −0.377964
\(568\) −8.00000 −0.335673
\(569\) −38.0000 −1.59304 −0.796521 0.604610i \(-0.793329\pi\)
−0.796521 + 0.604610i \(0.793329\pi\)
\(570\) 0 0
\(571\) −12.0000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) −4.00000 −0.167248
\(573\) 0 0
\(574\) 6.00000 0.250435
\(575\) −8.00000 −0.333623
\(576\) −3.00000 −0.125000
\(577\) 42.0000 1.74848 0.874241 0.485491i \(-0.161359\pi\)
0.874241 + 0.485491i \(0.161359\pi\)
\(578\) 19.0000 0.790296
\(579\) 0 0
\(580\) −20.0000 −0.830455
\(581\) 0 0
\(582\) 0 0
\(583\) 24.0000 0.993978
\(584\) 2.00000 0.0827606
\(585\) 6.00000 0.248069
\(586\) −14.0000 −0.578335
\(587\) −16.0000 −0.660391 −0.330195 0.943913i \(-0.607115\pi\)
−0.330195 + 0.943913i \(0.607115\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 16.0000 0.658710
\(591\) 0 0
\(592\) 6.00000 0.246598
\(593\) −22.0000 −0.903432 −0.451716 0.892162i \(-0.649188\pi\)
−0.451716 + 0.892162i \(0.649188\pi\)
\(594\) 0 0
\(595\) 12.0000 0.491952
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) −8.00000 −0.327144
\(599\) 16.0000 0.653742 0.326871 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) −4.00000 −0.163028
\(603\) −12.0000 −0.488678
\(604\) 0 0
\(605\) 10.0000 0.406558
\(606\) 0 0
\(607\) −48.0000 −1.94826 −0.974130 0.225989i \(-0.927439\pi\)
−0.974130 + 0.225989i \(0.927439\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 20.0000 0.809776
\(611\) 8.00000 0.323645
\(612\) 18.0000 0.727607
\(613\) 38.0000 1.53481 0.767403 0.641165i \(-0.221549\pi\)
0.767403 + 0.641165i \(0.221549\pi\)
\(614\) 32.0000 1.29141
\(615\) 0 0
\(616\) −4.00000 −0.161165
\(617\) 10.0000 0.402585 0.201292 0.979531i \(-0.435486\pi\)
0.201292 + 0.979531i \(0.435486\pi\)
\(618\) 0 0
\(619\) 40.0000 1.60774 0.803868 0.594808i \(-0.202772\pi\)
0.803868 + 0.594808i \(0.202772\pi\)
\(620\) −16.0000 −0.642575
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) −18.0000 −0.721155
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 2.00000 0.0799361
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) −36.0000 −1.43541
\(630\) 6.00000 0.239046
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 8.00000 0.318223
\(633\) 0 0
\(634\) 6.00000 0.238290
\(635\) 32.0000 1.26988
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) −40.0000 −1.58362
\(639\) 24.0000 0.949425
\(640\) 2.00000 0.0790569
\(641\) 34.0000 1.34292 0.671460 0.741041i \(-0.265668\pi\)
0.671460 + 0.741041i \(0.265668\pi\)
\(642\) 0 0
\(643\) 8.00000 0.315489 0.157745 0.987480i \(-0.449578\pi\)
0.157745 + 0.987480i \(0.449578\pi\)
\(644\) −8.00000 −0.315244
\(645\) 0 0
\(646\) 0 0
\(647\) −32.0000 −1.25805 −0.629025 0.777385i \(-0.716546\pi\)
−0.629025 + 0.777385i \(0.716546\pi\)
\(648\) 9.00000 0.353553
\(649\) 32.0000 1.25611
\(650\) 1.00000 0.0392232
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) −42.0000 −1.64359 −0.821794 0.569785i \(-0.807026\pi\)
−0.821794 + 0.569785i \(0.807026\pi\)
\(654\) 0 0
\(655\) 16.0000 0.625172
\(656\) −6.00000 −0.234261
\(657\) −6.00000 −0.234082
\(658\) 8.00000 0.311872
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) 2.00000 0.0777910 0.0388955 0.999243i \(-0.487616\pi\)
0.0388955 + 0.999243i \(0.487616\pi\)
\(662\) −28.0000 −1.08825
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −18.0000 −0.697486
\(667\) −80.0000 −3.09761
\(668\) 0 0
\(669\) 0 0
\(670\) 8.00000 0.309067
\(671\) 40.0000 1.54418
\(672\) 0 0
\(673\) −14.0000 −0.539660 −0.269830 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) 2.00000 0.0770371
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) 42.0000 1.61419 0.807096 0.590421i \(-0.201038\pi\)
0.807096 + 0.590421i \(0.201038\pi\)
\(678\) 0 0
\(679\) −2.00000 −0.0767530
\(680\) −12.0000 −0.460179
\(681\) 0 0
\(682\) −32.0000 −1.22534
\(683\) 28.0000 1.07139 0.535695 0.844411i \(-0.320050\pi\)
0.535695 + 0.844411i \(0.320050\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) −1.00000 −0.0381802
\(687\) 0 0
\(688\) 4.00000 0.152499
\(689\) −6.00000 −0.228582
\(690\) 0 0
\(691\) 16.0000 0.608669 0.304334 0.952565i \(-0.401566\pi\)
0.304334 + 0.952565i \(0.401566\pi\)
\(692\) 2.00000 0.0760286
\(693\) 12.0000 0.455842
\(694\) −12.0000 −0.455514
\(695\) −16.0000 −0.606915
\(696\) 0 0
\(697\) 36.0000 1.36360
\(698\) −14.0000 −0.529908
\(699\) 0 0
\(700\) 1.00000 0.0377964
\(701\) −42.0000 −1.58632 −0.793159 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 4.00000 0.150756
\(705\) 0 0
\(706\) 10.0000 0.376355
\(707\) 14.0000 0.526524
\(708\) 0 0
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) −16.0000 −0.600469
\(711\) −24.0000 −0.900070
\(712\) 18.0000 0.674579
\(713\) −64.0000 −2.39682
\(714\) 0 0
\(715\) −8.00000 −0.299183
\(716\) −12.0000 −0.448461
\(717\) 0 0
\(718\) 0 0
\(719\) 8.00000 0.298350 0.149175 0.988811i \(-0.452338\pi\)
0.149175 + 0.988811i \(0.452338\pi\)
\(720\) −6.00000 −0.223607
\(721\) −16.0000 −0.595871
\(722\) −19.0000 −0.707107
\(723\) 0 0
\(724\) −6.00000 −0.222988
\(725\) 10.0000 0.371391
\(726\) 0 0
\(727\) 16.0000 0.593407 0.296704 0.954970i \(-0.404113\pi\)
0.296704 + 0.954970i \(0.404113\pi\)
\(728\) 1.00000 0.0370625
\(729\) −27.0000 −1.00000
\(730\) 4.00000 0.148047
\(731\) −24.0000 −0.887672
\(732\) 0 0
\(733\) 26.0000 0.960332 0.480166 0.877178i \(-0.340576\pi\)
0.480166 + 0.877178i \(0.340576\pi\)
\(734\) −16.0000 −0.590571
\(735\) 0 0
\(736\) 8.00000 0.294884
\(737\) 16.0000 0.589368
\(738\) 18.0000 0.662589
\(739\) −36.0000 −1.32428 −0.662141 0.749380i \(-0.730352\pi\)
−0.662141 + 0.749380i \(0.730352\pi\)
\(740\) 12.0000 0.441129
\(741\) 0 0
\(742\) −6.00000 −0.220267
\(743\) 16.0000 0.586983 0.293492 0.955962i \(-0.405183\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(744\) 0 0
\(745\) −36.0000 −1.31894
\(746\) −10.0000 −0.366126
\(747\) 0 0
\(748\) −24.0000 −0.877527
\(749\) 4.00000 0.146157
\(750\) 0 0
\(751\) 48.0000 1.75154 0.875772 0.482724i \(-0.160353\pi\)
0.875772 + 0.482724i \(0.160353\pi\)
\(752\) −8.00000 −0.291730
\(753\) 0 0
\(754\) 10.0000 0.364179
\(755\) 0 0
\(756\) 0 0
\(757\) 30.0000 1.09037 0.545184 0.838316i \(-0.316460\pi\)
0.545184 + 0.838316i \(0.316460\pi\)
\(758\) 4.00000 0.145287
\(759\) 0 0
\(760\) 0 0
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) 0 0
\(763\) 2.00000 0.0724049
\(764\) −8.00000 −0.289430
\(765\) 36.0000 1.30158
\(766\) 24.0000 0.867155
\(767\) −8.00000 −0.288863
\(768\) 0 0
\(769\) −30.0000 −1.08183 −0.540914 0.841078i \(-0.681921\pi\)
−0.540914 + 0.841078i \(0.681921\pi\)
\(770\) −8.00000 −0.288300
\(771\) 0 0
\(772\) 2.00000 0.0719816
\(773\) −46.0000 −1.65451 −0.827253 0.561830i \(-0.810097\pi\)
−0.827253 + 0.561830i \(0.810097\pi\)
\(774\) −12.0000 −0.431331
\(775\) 8.00000 0.287368
\(776\) 2.00000 0.0717958
\(777\) 0 0
\(778\) 30.0000 1.07555
\(779\) 0 0
\(780\) 0 0
\(781\) −32.0000 −1.14505
\(782\) −48.0000 −1.71648
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 4.00000 0.142766
\(786\) 0 0
\(787\) 32.0000 1.14068 0.570338 0.821410i \(-0.306812\pi\)
0.570338 + 0.821410i \(0.306812\pi\)
\(788\) −18.0000 −0.641223
\(789\) 0 0
\(790\) 16.0000 0.569254
\(791\) −2.00000 −0.0711118
\(792\) −12.0000 −0.426401
\(793\) −10.0000 −0.355110
\(794\) 2.00000 0.0709773
\(795\) 0 0
\(796\) −16.0000 −0.567105
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 0 0
\(799\) 48.0000 1.69812
\(800\) −1.00000 −0.0353553
\(801\) −54.0000 −1.90800
\(802\) 18.0000 0.635602
\(803\) 8.00000 0.282314
\(804\) 0 0
\(805\) −16.0000 −0.563926
\(806\) 8.00000 0.281788
\(807\) 0 0
\(808\) −14.0000 −0.492518
\(809\) −6.00000 −0.210949 −0.105474 0.994422i \(-0.533636\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(810\) 18.0000 0.632456
\(811\) 8.00000 0.280918 0.140459 0.990086i \(-0.455142\pi\)
0.140459 + 0.990086i \(0.455142\pi\)
\(812\) 10.0000 0.350931
\(813\) 0 0
\(814\) 24.0000 0.841200
\(815\) −8.00000 −0.280228
\(816\) 0 0
\(817\) 0 0
\(818\) −38.0000 −1.32864
\(819\) −3.00000 −0.104828
\(820\) −12.0000 −0.419058
\(821\) 14.0000 0.488603 0.244302 0.969699i \(-0.421441\pi\)
0.244302 + 0.969699i \(0.421441\pi\)
\(822\) 0 0
\(823\) 48.0000 1.67317 0.836587 0.547833i \(-0.184547\pi\)
0.836587 + 0.547833i \(0.184547\pi\)
\(824\) 16.0000 0.557386
\(825\) 0 0
\(826\) −8.00000 −0.278356
\(827\) −36.0000 −1.25184 −0.625921 0.779886i \(-0.715277\pi\)
−0.625921 + 0.779886i \(0.715277\pi\)
\(828\) −24.0000 −0.834058
\(829\) 10.0000 0.347314 0.173657 0.984806i \(-0.444442\pi\)
0.173657 + 0.984806i \(0.444442\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.00000 −0.0346688
\(833\) −6.00000 −0.207888
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 32.0000 1.10476 0.552381 0.833592i \(-0.313719\pi\)
0.552381 + 0.833592i \(0.313719\pi\)
\(840\) 0 0
\(841\) 71.0000 2.44828
\(842\) −2.00000 −0.0689246
\(843\) 0 0
\(844\) 20.0000 0.688428
\(845\) 2.00000 0.0688021
\(846\) 24.0000 0.825137
\(847\) −5.00000 −0.171802
\(848\) 6.00000 0.206041
\(849\) 0 0
\(850\) 6.00000 0.205798
\(851\) 48.0000 1.64542
\(852\) 0 0
\(853\) 10.0000 0.342393 0.171197 0.985237i \(-0.445237\pi\)
0.171197 + 0.985237i \(0.445237\pi\)
\(854\) −10.0000 −0.342193
\(855\) 0 0
\(856\) −4.00000 −0.136717
\(857\) 34.0000 1.16142 0.580709 0.814111i \(-0.302775\pi\)
0.580709 + 0.814111i \(0.302775\pi\)
\(858\) 0 0
\(859\) 8.00000 0.272956 0.136478 0.990643i \(-0.456422\pi\)
0.136478 + 0.990643i \(0.456422\pi\)
\(860\) 8.00000 0.272798
\(861\) 0 0
\(862\) −24.0000 −0.817443
\(863\) −32.0000 −1.08929 −0.544646 0.838666i \(-0.683336\pi\)
−0.544646 + 0.838666i \(0.683336\pi\)
\(864\) 0 0
\(865\) 4.00000 0.136004
\(866\) −38.0000 −1.29129
\(867\) 0 0
\(868\) 8.00000 0.271538
\(869\) 32.0000 1.08553
\(870\) 0 0
\(871\) −4.00000 −0.135535
\(872\) −2.00000 −0.0677285
\(873\) −6.00000 −0.203069
\(874\) 0 0
\(875\) 12.0000 0.405674
\(876\) 0 0
\(877\) 30.0000 1.01303 0.506514 0.862232i \(-0.330934\pi\)
0.506514 + 0.862232i \(0.330934\pi\)
\(878\) 8.00000 0.269987
\(879\) 0 0
\(880\) 8.00000 0.269680
\(881\) −30.0000 −1.01073 −0.505363 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) −3.00000 −0.101015
\(883\) −44.0000 −1.48072 −0.740359 0.672212i \(-0.765344\pi\)
−0.740359 + 0.672212i \(0.765344\pi\)
\(884\) 6.00000 0.201802
\(885\) 0 0
\(886\) −36.0000 −1.20944
\(887\) −32.0000 −1.07445 −0.537227 0.843437i \(-0.680528\pi\)
−0.537227 + 0.843437i \(0.680528\pi\)
\(888\) 0 0
\(889\) −16.0000 −0.536623
\(890\) 36.0000 1.20672
\(891\) 36.0000 1.20605
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) −24.0000 −0.802232
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −14.0000 −0.467186
\(899\) 80.0000 2.66815
\(900\) 3.00000 0.100000
\(901\) −36.0000 −1.19933
\(902\) −24.0000 −0.799113
\(903\) 0 0
\(904\) 2.00000 0.0665190
\(905\) −12.0000 −0.398893
\(906\) 0 0
\(907\) 12.0000 0.398453 0.199227 0.979953i \(-0.436157\pi\)
0.199227 + 0.979953i \(0.436157\pi\)
\(908\) 0 0
\(909\) 42.0000 1.39305
\(910\) 2.00000 0.0662994
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 10.0000 0.330771
\(915\) 0 0
\(916\) −6.00000 −0.198246
\(917\) −8.00000 −0.264183
\(918\) 0 0
\(919\) 48.0000 1.58337 0.791687 0.610927i \(-0.209203\pi\)
0.791687 + 0.610927i \(0.209203\pi\)
\(920\) 16.0000 0.527504
\(921\) 0 0
\(922\) 18.0000 0.592798
\(923\) 8.00000 0.263323
\(924\) 0 0
\(925\) −6.00000 −0.197279
\(926\) 16.0000 0.525793
\(927\) −48.0000 −1.57653
\(928\) −10.0000 −0.328266
\(929\) −30.0000 −0.984268 −0.492134 0.870519i \(-0.663783\pi\)
−0.492134 + 0.870519i \(0.663783\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 10.0000 0.327561
\(933\) 0 0
\(934\) 8.00000 0.261768
\(935\) −48.0000 −1.56977
\(936\) 3.00000 0.0980581
\(937\) 42.0000 1.37208 0.686040 0.727564i \(-0.259347\pi\)
0.686040 + 0.727564i \(0.259347\pi\)
\(938\) −4.00000 −0.130605
\(939\) 0 0
\(940\) −16.0000 −0.521862
\(941\) 10.0000 0.325991 0.162995 0.986627i \(-0.447884\pi\)
0.162995 + 0.986627i \(0.447884\pi\)
\(942\) 0 0
\(943\) −48.0000 −1.56310
\(944\) 8.00000 0.260378
\(945\) 0 0
\(946\) 16.0000 0.520205
\(947\) 12.0000 0.389948 0.194974 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 0 0
\(949\) −2.00000 −0.0649227
\(950\) 0 0
\(951\) 0 0
\(952\) 6.00000 0.194461
\(953\) 26.0000 0.842223 0.421111 0.907009i \(-0.361640\pi\)
0.421111 + 0.907009i \(0.361640\pi\)
\(954\) −18.0000 −0.582772
\(955\) −16.0000 −0.517748
\(956\) −24.0000 −0.776215
\(957\) 0 0
\(958\) 24.0000 0.775405
\(959\) 6.00000 0.193750
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) −6.00000 −0.193448
\(963\) 12.0000 0.386695
\(964\) 18.0000 0.579741
\(965\) 4.00000 0.128765
\(966\) 0 0
\(967\) 32.0000 1.02905 0.514525 0.857475i \(-0.327968\pi\)
0.514525 + 0.857475i \(0.327968\pi\)
\(968\) 5.00000 0.160706
\(969\) 0 0
\(970\) 4.00000 0.128432
\(971\) 48.0000 1.54039 0.770197 0.637806i \(-0.220158\pi\)
0.770197 + 0.637806i \(0.220158\pi\)
\(972\) 0 0
\(973\) 8.00000 0.256468
\(974\) −16.0000 −0.512673
\(975\) 0 0
\(976\) 10.0000 0.320092
\(977\) −30.0000 −0.959785 −0.479893 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) 0 0
\(979\) 72.0000 2.30113
\(980\) 2.00000 0.0638877
\(981\) 6.00000 0.191565
\(982\) 28.0000 0.893516
\(983\) 32.0000 1.02064 0.510321 0.859984i \(-0.329527\pi\)
0.510321 + 0.859984i \(0.329527\pi\)
\(984\) 0 0
\(985\) −36.0000 −1.14706
\(986\) 60.0000 1.91079
\(987\) 0 0
\(988\) 0 0
\(989\) 32.0000 1.01754
\(990\) −24.0000 −0.762770
\(991\) 24.0000 0.762385 0.381193 0.924496i \(-0.375513\pi\)
0.381193 + 0.924496i \(0.375513\pi\)
\(992\) −8.00000 −0.254000
\(993\) 0 0
\(994\) 8.00000 0.253745
\(995\) −32.0000 −1.01447
\(996\) 0 0
\(997\) 2.00000 0.0633406 0.0316703 0.999498i \(-0.489917\pi\)
0.0316703 + 0.999498i \(0.489917\pi\)
\(998\) 4.00000 0.126618
\(999\) 0 0
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 182.2.a.c.1.1 1
3.2 odd 2 1638.2.a.c.1.1 1
4.3 odd 2 1456.2.a.i.1.1 1
5.4 even 2 4550.2.a.g.1.1 1
7.2 even 3 1274.2.f.f.1145.1 2
7.3 odd 6 1274.2.f.g.79.1 2
7.4 even 3 1274.2.f.f.79.1 2
7.5 odd 6 1274.2.f.g.1145.1 2
7.6 odd 2 1274.2.a.l.1.1 1
8.3 odd 2 5824.2.a.m.1.1 1
8.5 even 2 5824.2.a.l.1.1 1
13.5 odd 4 2366.2.d.d.337.1 2
13.8 odd 4 2366.2.d.d.337.2 2
13.12 even 2 2366.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
182.2.a.c.1.1 1 1.1 even 1 trivial
1274.2.a.l.1.1 1 7.6 odd 2
1274.2.f.f.79.1 2 7.4 even 3
1274.2.f.f.1145.1 2 7.2 even 3
1274.2.f.g.79.1 2 7.3 odd 6
1274.2.f.g.1145.1 2 7.5 odd 6
1456.2.a.i.1.1 1 4.3 odd 2
1638.2.a.c.1.1 1 3.2 odd 2
2366.2.a.d.1.1 1 13.12 even 2
2366.2.d.d.337.1 2 13.5 odd 4
2366.2.d.d.337.2 2 13.8 odd 4
4550.2.a.g.1.1 1 5.4 even 2
5824.2.a.l.1.1 1 8.5 even 2
5824.2.a.m.1.1 1 8.3 odd 2