Properties

Label 3150.2.a.z.1.1
Level 3150
Weight 2
Character 3150.1
Self dual yes
Analytic conductor 25.153
Analytic rank 1
Dimension 1
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(25.1528766367\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 630)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 3150.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} -4.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} -8.00000 q^{19} +8.00000 q^{23} -4.00000 q^{26} -1.00000 q^{28} -8.00000 q^{29} +4.00000 q^{31} +1.00000 q^{32} -2.00000 q^{34} +8.00000 q^{37} -8.00000 q^{38} -12.0000 q^{41} -8.00000 q^{43} +8.00000 q^{46} -4.00000 q^{47} +1.00000 q^{49} -4.00000 q^{52} -6.00000 q^{53} -1.00000 q^{56} -8.00000 q^{58} -8.00000 q^{59} -6.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} -8.00000 q^{67} -2.00000 q^{68} +4.00000 q^{73} +8.00000 q^{74} -8.00000 q^{76} +8.00000 q^{79} -12.0000 q^{82} -8.00000 q^{86} +4.00000 q^{89} +4.00000 q^{91} +8.00000 q^{92} -4.00000 q^{94} +12.0000 q^{97} +1.00000 q^{98} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) −8.00000 −1.83533 −0.917663 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −4.00000 −0.784465
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 0 0
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) −8.00000 −1.29777
\(39\) 0 0
\(40\) 0 0
\(41\) −12.0000 −1.87409 −0.937043 0.349215i \(-0.886448\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 8.00000 1.17954
\(47\) −4.00000 −0.583460 −0.291730 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) −4.00000 −0.554700
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) −8.00000 −1.05045
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 0 0
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −8.00000 −0.977356 −0.488678 0.872464i \(-0.662521\pi\)
−0.488678 + 0.872464i \(0.662521\pi\)
\(68\) −2.00000 −0.242536
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) 8.00000 0.929981
\(75\) 0 0
\(76\) −8.00000 −0.917663
\(77\) 0 0
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −12.0000 −1.32518
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) 0 0
\(88\) 0 0
\(89\) 4.00000 0.423999 0.212000 0.977270i \(-0.432002\pi\)
0.212000 + 0.977270i \(0.432002\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) 8.00000 0.834058
\(93\) 0 0
\(94\) −4.00000 −0.412568
\(95\) 0 0
\(96\) 0 0
\(97\) 12.0000 1.21842 0.609208 0.793011i \(-0.291488\pi\)
0.609208 + 0.793011i \(0.291488\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 0 0
\(101\) −12.0000 −1.19404 −0.597022 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) −4.00000 −0.392232
\(105\) 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 \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 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
\(115\) 0 0
\(116\) −8.00000 −0.742781
\(117\) 0 0
\(118\) −8.00000 −0.736460
\(119\) 2.00000 0.183340
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) −6.00000 −0.543214
\(123\) 0 0
\(124\) 4.00000 0.359211
\(125\) 0 0
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 0 0
\(133\) 8.00000 0.693688
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) −2.00000 −0.171499
\(137\) 10.0000 0.854358 0.427179 0.904167i \(-0.359507\pi\)
0.427179 + 0.904167i \(0.359507\pi\)
\(138\) 0 0
\(139\) 16.0000 1.35710 0.678551 0.734553i \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) 0 0
\(148\) 8.00000 0.657596
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) −8.00000 −0.648886
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −12.0000 −0.957704 −0.478852 0.877896i \(-0.658947\pi\)
−0.478852 + 0.877896i \(0.658947\pi\)
\(158\) 8.00000 0.636446
\(159\) 0 0
\(160\) 0 0
\(161\) −8.00000 −0.630488
\(162\) 0 0
\(163\) −24.0000 −1.87983 −0.939913 0.341415i \(-0.889094\pi\)
−0.939913 + 0.341415i \(0.889094\pi\)
\(164\) −12.0000 −0.937043
\(165\) 0 0
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) −8.00000 −0.609994
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 4.00000 0.299813
\(179\) −16.0000 −1.19590 −0.597948 0.801535i \(-0.704017\pi\)
−0.597948 + 0.801535i \(0.704017\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 4.00000 0.296500
\(183\) 0 0
\(184\) 8.00000 0.589768
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −4.00000 −0.291730
\(189\) 0 0
\(190\) 0 0
\(191\) −16.0000 −1.15772 −0.578860 0.815427i \(-0.696502\pi\)
−0.578860 + 0.815427i \(0.696502\pi\)
\(192\) 0 0
\(193\) 16.0000 1.15171 0.575853 0.817554i \(-0.304670\pi\)
0.575853 + 0.817554i \(0.304670\pi\)
\(194\) 12.0000 0.861550
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) 0 0
\(199\) −12.0000 −0.850657 −0.425329 0.905039i \(-0.639842\pi\)
−0.425329 + 0.905039i \(0.639842\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −12.0000 −0.844317
\(203\) 8.00000 0.561490
\(204\) 0 0
\(205\) 0 0
\(206\) 8.00000 0.557386
\(207\) 0 0
\(208\) −4.00000 −0.277350
\(209\) 0 0
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −6.00000 −0.412082
\(213\) 0 0
\(214\) −4.00000 −0.273434
\(215\) 0 0
\(216\) 0 0
\(217\) −4.00000 −0.271538
\(218\) 2.00000 0.135457
\(219\) 0 0
\(220\) 0 0
\(221\) 8.00000 0.538138
\(222\) 0 0
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) 2.00000 0.133038
\(227\) −24.0000 −1.59294 −0.796468 0.604681i \(-0.793301\pi\)
−0.796468 + 0.604681i \(0.793301\pi\)
\(228\) 0 0
\(229\) −2.00000 −0.132164 −0.0660819 0.997814i \(-0.521050\pi\)
−0.0660819 + 0.997814i \(0.521050\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −8.00000 −0.525226
\(233\) −26.0000 −1.70332 −0.851658 0.524097i \(-0.824403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −8.00000 −0.520756
\(237\) 0 0
\(238\) 2.00000 0.129641
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) 18.0000 1.15948 0.579741 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) −11.0000 −0.707107
\(243\) 0 0
\(244\) −6.00000 −0.384111
\(245\) 0 0
\(246\) 0 0
\(247\) 32.0000 2.03611
\(248\) 4.00000 0.254000
\(249\) 0 0
\(250\) 0 0
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 8.00000 0.501965
\(255\) 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
\(259\) −8.00000 −0.497096
\(260\) 0 0
\(261\) 0 0
\(262\) −8.00000 −0.494242
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 8.00000 0.490511
\(267\) 0 0
\(268\) −8.00000 −0.488678
\(269\) 28.0000 1.70719 0.853595 0.520937i \(-0.174417\pi\)
0.853595 + 0.520937i \(0.174417\pi\)
\(270\) 0 0
\(271\) −12.0000 −0.728948 −0.364474 0.931214i \(-0.618751\pi\)
−0.364474 + 0.931214i \(0.618751\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) 10.0000 0.604122
\(275\) 0 0
\(276\) 0 0
\(277\) 32.0000 1.92269 0.961347 0.275340i \(-0.0887905\pi\)
0.961347 + 0.275340i \(0.0887905\pi\)
\(278\) 16.0000 0.959616
\(279\) 0 0
\(280\) 0 0
\(281\) −24.0000 −1.43172 −0.715860 0.698244i \(-0.753965\pi\)
−0.715860 + 0.698244i \(0.753965\pi\)
\(282\) 0 0
\(283\) 16.0000 0.951101 0.475551 0.879688i \(-0.342249\pi\)
0.475551 + 0.879688i \(0.342249\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 12.0000 0.708338
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 4.00000 0.234082
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 8.00000 0.464991
\(297\) 0 0
\(298\) 0 0
\(299\) −32.0000 −1.85061
\(300\) 0 0
\(301\) 8.00000 0.461112
\(302\) 0 0
\(303\) 0 0
\(304\) −8.00000 −0.458831
\(305\) 0 0
\(306\) 0 0
\(307\) 16.0000 0.913168 0.456584 0.889680i \(-0.349073\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 28.0000 1.58265 0.791327 0.611393i \(-0.209391\pi\)
0.791327 + 0.611393i \(0.209391\pi\)
\(314\) −12.0000 −0.677199
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) −14.0000 −0.786318 −0.393159 0.919470i \(-0.628618\pi\)
−0.393159 + 0.919470i \(0.628618\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) −8.00000 −0.445823
\(323\) 16.0000 0.890264
\(324\) 0 0
\(325\) 0 0
\(326\) −24.0000 −1.32924
\(327\) 0 0
\(328\) −12.0000 −0.662589
\(329\) 4.00000 0.220527
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) 0 0
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) 3.00000 0.163178
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) 36.0000 1.93258 0.966291 0.257454i \(-0.0828835\pi\)
0.966291 + 0.257454i \(0.0828835\pi\)
\(348\) 0 0
\(349\) −6.00000 −0.321173 −0.160586 0.987022i \(-0.551338\pi\)
−0.160586 + 0.987022i \(0.551338\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −18.0000 −0.958043 −0.479022 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 4.00000 0.212000
\(357\) 0 0
\(358\) −16.0000 −0.845626
\(359\) −16.0000 −0.844448 −0.422224 0.906492i \(-0.638750\pi\)
−0.422224 + 0.906492i \(0.638750\pi\)
\(360\) 0 0
\(361\) 45.0000 2.36842
\(362\) 2.00000 0.105118
\(363\) 0 0
\(364\) 4.00000 0.209657
\(365\) 0 0
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 8.00000 0.417029
\(369\) 0 0
\(370\) 0 0
\(371\) 6.00000 0.311504
\(372\) 0 0
\(373\) 16.0000 0.828449 0.414224 0.910175i \(-0.364053\pi\)
0.414224 + 0.910175i \(0.364053\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −4.00000 −0.206284
\(377\) 32.0000 1.64808
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −16.0000 −0.818631
\(383\) −12.0000 −0.613171 −0.306586 0.951843i \(-0.599187\pi\)
−0.306586 + 0.951843i \(0.599187\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 16.0000 0.814379
\(387\) 0 0
\(388\) 12.0000 0.609208
\(389\) −24.0000 −1.21685 −0.608424 0.793612i \(-0.708198\pi\)
−0.608424 + 0.793612i \(0.708198\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) 22.0000 1.10834
\(395\) 0 0
\(396\) 0 0
\(397\) −4.00000 −0.200754 −0.100377 0.994949i \(-0.532005\pi\)
−0.100377 + 0.994949i \(0.532005\pi\)
\(398\) −12.0000 −0.601506
\(399\) 0 0
\(400\) 0 0
\(401\) 24.0000 1.19850 0.599251 0.800561i \(-0.295465\pi\)
0.599251 + 0.800561i \(0.295465\pi\)
\(402\) 0 0
\(403\) −16.0000 −0.797017
\(404\) −12.0000 −0.597022
\(405\) 0 0
\(406\) 8.00000 0.397033
\(407\) 0 0
\(408\) 0 0
\(409\) 22.0000 1.08783 0.543915 0.839140i \(-0.316941\pi\)
0.543915 + 0.839140i \(0.316941\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 8.00000 0.394132
\(413\) 8.00000 0.393654
\(414\) 0 0
\(415\) 0 0
\(416\) −4.00000 −0.196116
\(417\) 0 0
\(418\) 0 0
\(419\) 40.0000 1.95413 0.977064 0.212946i \(-0.0683059\pi\)
0.977064 + 0.212946i \(0.0683059\pi\)
\(420\) 0 0
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) −12.0000 −0.584151
\(423\) 0 0
\(424\) −6.00000 −0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) 6.00000 0.290360
\(428\) −4.00000 −0.193347
\(429\) 0 0
\(430\) 0 0
\(431\) 16.0000 0.770693 0.385346 0.922772i \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) 0 0
\(433\) −4.00000 −0.192228 −0.0961139 0.995370i \(-0.530641\pi\)
−0.0961139 + 0.995370i \(0.530641\pi\)
\(434\) −4.00000 −0.192006
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) −64.0000 −3.06154
\(438\) 0 0
\(439\) −28.0000 −1.33637 −0.668184 0.743996i \(-0.732928\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 8.00000 0.380521
\(443\) 12.0000 0.570137 0.285069 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 8.00000 0.378811
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) 16.0000 0.755087 0.377543 0.925992i \(-0.376769\pi\)
0.377543 + 0.925992i \(0.376769\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 2.00000 0.0940721
\(453\) 0 0
\(454\) −24.0000 −1.12638
\(455\) 0 0
\(456\) 0 0
\(457\) 16.0000 0.748448 0.374224 0.927338i \(-0.377909\pi\)
0.374224 + 0.927338i \(0.377909\pi\)
\(458\) −2.00000 −0.0934539
\(459\) 0 0
\(460\) 0 0
\(461\) 20.0000 0.931493 0.465746 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) −8.00000 −0.371391
\(465\) 0 0
\(466\) −26.0000 −1.20443
\(467\) −32.0000 −1.48078 −0.740392 0.672176i \(-0.765360\pi\)
−0.740392 + 0.672176i \(0.765360\pi\)
\(468\) 0 0
\(469\) 8.00000 0.369406
\(470\) 0 0
\(471\) 0 0
\(472\) −8.00000 −0.368230
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 2.00000 0.0916698
\(477\) 0 0
\(478\) 16.0000 0.731823
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −32.0000 −1.45907
\(482\) 18.0000 0.819878
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) 0 0
\(487\) −40.0000 −1.81257 −0.906287 0.422664i \(-0.861095\pi\)
−0.906287 + 0.422664i \(0.861095\pi\)
\(488\) −6.00000 −0.271607
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 16.0000 0.720604
\(494\) 32.0000 1.43975
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −8.00000 −0.357057
\(503\) 28.0000 1.24846 0.624229 0.781241i \(-0.285413\pi\)
0.624229 + 0.781241i \(0.285413\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 8.00000 0.354943
\(509\) 4.00000 0.177297 0.0886484 0.996063i \(-0.471745\pi\)
0.0886484 + 0.996063i \(0.471745\pi\)
\(510\) 0 0
\(511\) −4.00000 −0.176950
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 18.0000 0.793946
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −8.00000 −0.351500
\(519\) 0 0
\(520\) 0 0
\(521\) −12.0000 −0.525730 −0.262865 0.964833i \(-0.584667\pi\)
−0.262865 + 0.964833i \(0.584667\pi\)
\(522\) 0 0
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) −8.00000 −0.349482
\(525\) 0 0
\(526\) 0 0
\(527\) −8.00000 −0.348485
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) 0 0
\(531\) 0 0
\(532\) 8.00000 0.346844
\(533\) 48.0000 2.07911
\(534\) 0 0
\(535\) 0 0
\(536\) −8.00000 −0.345547
\(537\) 0 0
\(538\) 28.0000 1.20717
\(539\) 0 0
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) −12.0000 −0.515444
\(543\) 0 0
\(544\) −2.00000 −0.0857493
\(545\) 0 0
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 10.0000 0.427179
\(549\) 0 0
\(550\) 0 0
\(551\) 64.0000 2.72649
\(552\) 0 0
\(553\) −8.00000 −0.340195
\(554\) 32.0000 1.35955
\(555\) 0 0
\(556\) 16.0000 0.678551
\(557\) 2.00000 0.0847427 0.0423714 0.999102i \(-0.486509\pi\)
0.0423714 + 0.999102i \(0.486509\pi\)
\(558\) 0 0
\(559\) 32.0000 1.35346
\(560\) 0 0
\(561\) 0 0
\(562\) −24.0000 −1.01238
\(563\) −40.0000 −1.68580 −0.842900 0.538071i \(-0.819153\pi\)
−0.842900 + 0.538071i \(0.819153\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 16.0000 0.672530
\(567\) 0 0
\(568\) 0 0
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 12.0000 0.500870
\(575\) 0 0
\(576\) 0 0
\(577\) 28.0000 1.16566 0.582828 0.812596i \(-0.301946\pi\)
0.582828 + 0.812596i \(0.301946\pi\)
\(578\) −13.0000 −0.540729
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 4.00000 0.165521
\(585\) 0 0
\(586\) −18.0000 −0.743573
\(587\) 16.0000 0.660391 0.330195 0.943913i \(-0.392885\pi\)
0.330195 + 0.943913i \(0.392885\pi\)
\(588\) 0 0
\(589\) −32.0000 −1.31854
\(590\) 0 0
\(591\) 0 0
\(592\) 8.00000 0.328798
\(593\) −30.0000 −1.23195 −0.615976 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −32.0000 −1.30858
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 8.00000 0.326056
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −8.00000 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) −8.00000 −0.324443
\(609\) 0 0
\(610\) 0 0
\(611\) 16.0000 0.647291
\(612\) 0 0
\(613\) 24.0000 0.969351 0.484675 0.874694i \(-0.338938\pi\)
0.484675 + 0.874694i \(0.338938\pi\)
\(614\) 16.0000 0.645707
\(615\) 0 0
\(616\) 0 0
\(617\) 38.0000 1.52982 0.764911 0.644136i \(-0.222783\pi\)
0.764911 + 0.644136i \(0.222783\pi\)
\(618\) 0 0
\(619\) 16.0000 0.643094 0.321547 0.946894i \(-0.395797\pi\)
0.321547 + 0.946894i \(0.395797\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4.00000 −0.160257
\(624\) 0 0
\(625\) 0 0
\(626\) 28.0000 1.11911
\(627\) 0 0
\(628\) −12.0000 −0.478852
\(629\) −16.0000 −0.637962
\(630\) 0 0
\(631\) −24.0000 −0.955425 −0.477712 0.878516i \(-0.658534\pi\)
−0.477712 + 0.878516i \(0.658534\pi\)
\(632\) 8.00000 0.318223
\(633\) 0 0
\(634\) −14.0000 −0.556011
\(635\) 0 0
\(636\) 0 0
\(637\) −4.00000 −0.158486
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8.00000 0.315981 0.157991 0.987441i \(-0.449498\pi\)
0.157991 + 0.987441i \(0.449498\pi\)
\(642\) 0 0
\(643\) −16.0000 −0.630978 −0.315489 0.948929i \(-0.602169\pi\)
−0.315489 + 0.948929i \(0.602169\pi\)
\(644\) −8.00000 −0.315244
\(645\) 0 0
\(646\) 16.0000 0.629512
\(647\) −36.0000 −1.41531 −0.707653 0.706560i \(-0.750246\pi\)
−0.707653 + 0.706560i \(0.750246\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −24.0000 −0.939913
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −12.0000 −0.468521
\(657\) 0 0
\(658\) 4.00000 0.155936
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −14.0000 −0.544537 −0.272268 0.962221i \(-0.587774\pi\)
−0.272268 + 0.962221i \(0.587774\pi\)
\(662\) 20.0000 0.777322
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −64.0000 −2.47809
\(668\) −12.0000 −0.464294
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 40.0000 1.54189 0.770943 0.636904i \(-0.219785\pi\)
0.770943 + 0.636904i \(0.219785\pi\)
\(674\) 8.00000 0.308148
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) −14.0000 −0.538064 −0.269032 0.963131i \(-0.586704\pi\)
−0.269032 + 0.963131i \(0.586704\pi\)
\(678\) 0 0
\(679\) −12.0000 −0.460518
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.00000 0.153056 0.0765279 0.997067i \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.00000 −0.0381802
\(687\) 0 0
\(688\) −8.00000 −0.304997
\(689\) 24.0000 0.914327
\(690\) 0 0
\(691\) −32.0000 −1.21734 −0.608669 0.793424i \(-0.708296\pi\)
−0.608669 + 0.793424i \(0.708296\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 36.0000 1.36654
\(695\) 0 0
\(696\) 0 0
\(697\) 24.0000 0.909065
\(698\) −6.00000 −0.227103
\(699\) 0 0
\(700\) 0 0
\(701\) 40.0000 1.51078 0.755390 0.655276i \(-0.227448\pi\)
0.755390 + 0.655276i \(0.227448\pi\)
\(702\) 0 0
\(703\) −64.0000 −2.41381
\(704\) 0 0
\(705\) 0 0
\(706\) −18.0000 −0.677439
\(707\) 12.0000 0.451306
\(708\) 0 0
\(709\) −42.0000 −1.57734 −0.788672 0.614815i \(-0.789231\pi\)
−0.788672 + 0.614815i \(0.789231\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 4.00000 0.149906
\(713\) 32.0000 1.19841
\(714\) 0 0
\(715\) 0 0
\(716\) −16.0000 −0.597948
\(717\) 0 0
\(718\) −16.0000 −0.597115
\(719\) 16.0000 0.596699 0.298350 0.954457i \(-0.403564\pi\)
0.298350 + 0.954457i \(0.403564\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 45.0000 1.67473
\(723\) 0 0
\(724\) 2.00000 0.0743294
\(725\) 0 0
\(726\) 0 0
\(727\) −40.0000 −1.48352 −0.741759 0.670667i \(-0.766008\pi\)
−0.741759 + 0.670667i \(0.766008\pi\)
\(728\) 4.00000 0.148250
\(729\) 0 0
\(730\) 0 0
\(731\) 16.0000 0.591781
\(732\) 0 0
\(733\) −20.0000 −0.738717 −0.369358 0.929287i \(-0.620423\pi\)
−0.369358 + 0.929287i \(0.620423\pi\)
\(734\) 8.00000 0.295285
\(735\) 0 0
\(736\) 8.00000 0.294884
\(737\) 0 0
\(738\) 0 0
\(739\) 4.00000 0.147142 0.0735712 0.997290i \(-0.476560\pi\)
0.0735712 + 0.997290i \(0.476560\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 6.00000 0.220267
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 16.0000 0.585802
\(747\) 0 0
\(748\) 0 0
\(749\) 4.00000 0.146157
\(750\) 0 0
\(751\) 40.0000 1.45962 0.729810 0.683650i \(-0.239608\pi\)
0.729810 + 0.683650i \(0.239608\pi\)
\(752\) −4.00000 −0.145865
\(753\) 0 0
\(754\) 32.0000 1.16537
\(755\) 0 0
\(756\) 0 0
\(757\) −24.0000 −0.872295 −0.436147 0.899875i \(-0.643657\pi\)
−0.436147 + 0.899875i \(0.643657\pi\)
\(758\) −20.0000 −0.726433
\(759\) 0 0
\(760\) 0 0
\(761\) −4.00000 −0.145000 −0.0724999 0.997368i \(-0.523098\pi\)
−0.0724999 + 0.997368i \(0.523098\pi\)
\(762\) 0 0
\(763\) −2.00000 −0.0724049
\(764\) −16.0000 −0.578860
\(765\) 0 0
\(766\) −12.0000 −0.433578
\(767\) 32.0000 1.15545
\(768\) 0 0
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 16.0000 0.575853
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 12.0000 0.430775
\(777\) 0 0
\(778\) −24.0000 −0.860442
\(779\) 96.0000 3.43956
\(780\) 0 0
\(781\) 0 0
\(782\) −16.0000 −0.572159
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 22.0000 0.783718
\(789\) 0 0
\(790\) 0 0
\(791\) −2.00000 −0.0711118
\(792\) 0 0
\(793\) 24.0000 0.852265
\(794\) −4.00000 −0.141955
\(795\) 0 0
\(796\) −12.0000 −0.425329
\(797\) −26.0000 −0.920967 −0.460484 0.887668i \(-0.652324\pi\)
−0.460484 + 0.887668i \(0.652324\pi\)
\(798\) 0 0
\(799\) 8.00000 0.283020
\(800\) 0 0
\(801\) 0 0
\(802\) 24.0000 0.847469
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) −16.0000 −0.563576
\(807\) 0 0
\(808\) −12.0000 −0.422159
\(809\) 32.0000 1.12506 0.562530 0.826777i \(-0.309828\pi\)
0.562530 + 0.826777i \(0.309828\pi\)
\(810\) 0 0
\(811\) 24.0000 0.842754 0.421377 0.906886i \(-0.361547\pi\)
0.421377 + 0.906886i \(0.361547\pi\)
\(812\) 8.00000 0.280745
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 64.0000 2.23908
\(818\) 22.0000 0.769212
\(819\) 0 0
\(820\) 0 0
\(821\) 48.0000 1.67521 0.837606 0.546275i \(-0.183955\pi\)
0.837606 + 0.546275i \(0.183955\pi\)
\(822\) 0 0
\(823\) −24.0000 −0.836587 −0.418294 0.908312i \(-0.637372\pi\)
−0.418294 + 0.908312i \(0.637372\pi\)
\(824\) 8.00000 0.278693
\(825\) 0 0
\(826\) 8.00000 0.278356
\(827\) 20.0000 0.695468 0.347734 0.937593i \(-0.386951\pi\)
0.347734 + 0.937593i \(0.386951\pi\)
\(828\) 0 0
\(829\) 10.0000 0.347314 0.173657 0.984806i \(-0.444442\pi\)
0.173657 + 0.984806i \(0.444442\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −4.00000 −0.138675
\(833\) −2.00000 −0.0692959
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 40.0000 1.38178
\(839\) −32.0000 −1.10476 −0.552381 0.833592i \(-0.686281\pi\)
−0.552381 + 0.833592i \(0.686281\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) −26.0000 −0.896019
\(843\) 0 0
\(844\) −12.0000 −0.413057
\(845\) 0 0
\(846\) 0 0
\(847\) 11.0000 0.377964
\(848\) −6.00000 −0.206041
\(849\) 0 0
\(850\) 0 0
\(851\) 64.0000 2.19389
\(852\) 0 0
\(853\) 28.0000 0.958702 0.479351 0.877623i \(-0.340872\pi\)
0.479351 + 0.877623i \(0.340872\pi\)
\(854\) 6.00000 0.205316
\(855\) 0 0
\(856\) −4.00000 −0.136717
\(857\) −58.0000 −1.98124 −0.990621 0.136637i \(-0.956370\pi\)
−0.990621 + 0.136637i \(0.956370\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 16.0000 0.544962
\(863\) −32.0000 −1.08929 −0.544646 0.838666i \(-0.683336\pi\)
−0.544646 + 0.838666i \(0.683336\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −4.00000 −0.135926
\(867\) 0 0
\(868\) −4.00000 −0.135769
\(869\) 0 0
\(870\) 0 0
\(871\) 32.0000 1.08428
\(872\) 2.00000 0.0677285
\(873\) 0 0
\(874\) −64.0000 −2.16483
\(875\) 0 0
\(876\) 0 0
\(877\) −40.0000 −1.35070 −0.675352 0.737496i \(-0.736008\pi\)
−0.675352 + 0.737496i \(0.736008\pi\)
\(878\) −28.0000 −0.944954
\(879\) 0 0
\(880\) 0 0
\(881\) 12.0000 0.404290 0.202145 0.979356i \(-0.435209\pi\)
0.202145 + 0.979356i \(0.435209\pi\)
\(882\) 0 0
\(883\) −40.0000 −1.34611 −0.673054 0.739594i \(-0.735018\pi\)
−0.673054 + 0.739594i \(0.735018\pi\)
\(884\) 8.00000 0.269069
\(885\) 0 0
\(886\) 12.0000 0.403148
\(887\) 12.0000 0.402921 0.201460 0.979497i \(-0.435431\pi\)
0.201460 + 0.979497i \(0.435431\pi\)
\(888\) 0 0
\(889\) −8.00000 −0.268311
\(890\) 0 0
\(891\) 0 0
\(892\) 8.00000 0.267860
\(893\) 32.0000 1.07084
\(894\) 0 0
\(895\) 0 0
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) 16.0000 0.533927
\(899\) −32.0000 −1.06726
\(900\) 0 0
\(901\) 12.0000 0.399778
\(902\) 0 0
\(903\) 0 0
\(904\) 2.00000 0.0665190
\(905\) 0 0
\(906\) 0 0
\(907\) 40.0000 1.32818 0.664089 0.747653i \(-0.268820\pi\)
0.664089 + 0.747653i \(0.268820\pi\)
\(908\) −24.0000 −0.796468
\(909\) 0 0
\(910\) 0 0
\(911\) −32.0000 −1.06021 −0.530104 0.847933i \(-0.677847\pi\)
−0.530104 + 0.847933i \(0.677847\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 16.0000 0.529233
\(915\) 0 0
\(916\) −2.00000 −0.0660819
\(917\) 8.00000 0.264183
\(918\) 0 0
\(919\) −40.0000 −1.31948 −0.659739 0.751495i \(-0.729333\pi\)
−0.659739 + 0.751495i \(0.729333\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 20.0000 0.658665
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 8.00000 0.262896
\(927\) 0 0
\(928\) −8.00000 −0.262613
\(929\) 12.0000 0.393707 0.196854 0.980433i \(-0.436928\pi\)
0.196854 + 0.980433i \(0.436928\pi\)
\(930\) 0 0
\(931\) −8.00000 −0.262189
\(932\) −26.0000 −0.851658
\(933\) 0 0
\(934\) −32.0000 −1.04707
\(935\) 0 0
\(936\) 0 0
\(937\) −28.0000 −0.914720 −0.457360 0.889282i \(-0.651205\pi\)
−0.457360 + 0.889282i \(0.651205\pi\)
\(938\) 8.00000 0.261209
\(939\) 0 0
\(940\) 0 0
\(941\) 28.0000 0.912774 0.456387 0.889781i \(-0.349143\pi\)
0.456387 + 0.889781i \(0.349143\pi\)
\(942\) 0 0
\(943\) −96.0000 −3.12619
\(944\) −8.00000 −0.260378
\(945\) 0 0
\(946\) 0 0
\(947\) −60.0000 −1.94974 −0.974869 0.222779i \(-0.928487\pi\)
−0.974869 + 0.222779i \(0.928487\pi\)
\(948\) 0 0
\(949\) −16.0000 −0.519382
\(950\) 0 0
\(951\) 0 0
\(952\) 2.00000 0.0648204
\(953\) −54.0000 −1.74923 −0.874616 0.484817i \(-0.838886\pi\)
−0.874616 + 0.484817i \(0.838886\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 16.0000 0.517477
\(957\) 0 0
\(958\) 0 0
\(959\) −10.0000 −0.322917
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) −32.0000 −1.03172
\(963\) 0 0
\(964\) 18.0000 0.579741
\(965\) 0 0
\(966\) 0 0
\(967\) −8.00000 −0.257263 −0.128631 0.991692i \(-0.541058\pi\)
−0.128631 + 0.991692i \(0.541058\pi\)
\(968\) −11.0000 −0.353553
\(969\) 0 0
\(970\) 0 0
\(971\) −24.0000 −0.770197 −0.385098 0.922876i \(-0.625832\pi\)
−0.385098 + 0.922876i \(0.625832\pi\)
\(972\) 0 0
\(973\) −16.0000 −0.512936
\(974\) −40.0000 −1.28168
\(975\) 0 0
\(976\) −6.00000 −0.192055
\(977\) 30.0000 0.959785 0.479893 0.877327i \(-0.340676\pi\)
0.479893 + 0.877327i \(0.340676\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 4.00000 0.127580 0.0637901 0.997963i \(-0.479681\pi\)
0.0637901 + 0.997963i \(0.479681\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 16.0000 0.509544
\(987\) 0 0
\(988\) 32.0000 1.01806
\(989\) −64.0000 −2.03508
\(990\) 0 0
\(991\) −32.0000 −1.01651 −0.508257 0.861206i \(-0.669710\pi\)
−0.508257 + 0.861206i \(0.669710\pi\)
\(992\) 4.00000 0.127000
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −4.00000 −0.126681 −0.0633406 0.997992i \(-0.520175\pi\)
−0.0633406 + 0.997992i \(0.520175\pi\)
\(998\) 28.0000 0.886325
\(999\) 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 3150.2.a.z.1.1 1
3.2 odd 2 3150.2.a.e.1.1 1
5.2 odd 4 630.2.g.f.379.2 yes 2
5.3 odd 4 630.2.g.f.379.1 yes 2
5.4 even 2 3150.2.a.p.1.1 1
15.2 even 4 630.2.g.a.379.1 2
15.8 even 4 630.2.g.a.379.2 yes 2
15.14 odd 2 3150.2.a.bn.1.1 1
20.3 even 4 5040.2.t.q.1009.2 2
20.7 even 4 5040.2.t.q.1009.1 2
60.23 odd 4 5040.2.t.b.1009.1 2
60.47 odd 4 5040.2.t.b.1009.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.g.a.379.1 2 15.2 even 4
630.2.g.a.379.2 yes 2 15.8 even 4
630.2.g.f.379.1 yes 2 5.3 odd 4
630.2.g.f.379.2 yes 2 5.2 odd 4
3150.2.a.e.1.1 1 3.2 odd 2
3150.2.a.p.1.1 1 5.4 even 2
3150.2.a.z.1.1 1 1.1 even 1 trivial
3150.2.a.bn.1.1 1 15.14 odd 2
5040.2.t.b.1009.1 2 60.23 odd 4
5040.2.t.b.1009.2 2 60.47 odd 4
5040.2.t.q.1009.1 2 20.7 even 4
5040.2.t.q.1009.2 2 20.3 even 4