Properties

Label 7350.2.a.bo.1.1
Level 7350
Weight 2
Character 7350.1
Self dual yes
Analytic conductor 58.690
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7350.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(58.6900454856\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 7350.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} -1.00000 q^{12} -2.00000 q^{13} +1.00000 q^{16} -6.00000 q^{17} +1.00000 q^{18} -4.00000 q^{22} +8.00000 q^{23} -1.00000 q^{24} -2.00000 q^{26} -1.00000 q^{27} +10.0000 q^{29} +8.00000 q^{31} +1.00000 q^{32} +4.00000 q^{33} -6.00000 q^{34} +1.00000 q^{36} -2.00000 q^{37} +2.00000 q^{39} +2.00000 q^{41} -8.00000 q^{43} -4.00000 q^{44} +8.00000 q^{46} +4.00000 q^{47} -1.00000 q^{48} +6.00000 q^{51} -2.00000 q^{52} -10.0000 q^{53} -1.00000 q^{54} +10.0000 q^{58} -4.00000 q^{59} +6.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} +4.00000 q^{66} -6.00000 q^{68} -8.00000 q^{69} -12.0000 q^{71} +1.00000 q^{72} -6.00000 q^{73} -2.00000 q^{74} +2.00000 q^{78} -8.00000 q^{79} +1.00000 q^{81} +2.00000 q^{82} -4.00000 q^{83} -8.00000 q^{86} -10.0000 q^{87} -4.00000 q^{88} -14.0000 q^{89} +8.00000 q^{92} -8.00000 q^{93} +4.00000 q^{94} -1.00000 q^{96} +2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 1.00000 0.235702
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0 0
\(26\) −2.00000 −0.392232
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 10.0000 1.85695 0.928477 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.00000 0.696311
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) 8.00000 1.17954
\(47\) 4.00000 0.583460 0.291730 0.956501i \(-0.405769\pi\)
0.291730 + 0.956501i \(0.405769\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 0 0
\(51\) 6.00000 0.840168
\(52\) −2.00000 −0.277350
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 10.0000 1.31306
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 8.00000 1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 4.00000 0.492366
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) −6.00000 −0.727607
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 1.00000 0.117851
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −2.00000 −0.232495
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 2.00000 0.226455
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 2.00000 0.220863
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) −10.0000 −1.07211
\(88\) −4.00000 −0.426401
\(89\) −14.0000 −1.48400 −0.741999 0.670402i \(-0.766122\pi\)
−0.741999 + 0.670402i \(0.766122\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 8.00000 0.834058
\(93\) −8.00000 −0.829561
\(94\) 4.00000 0.412568
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 6.00000 0.594089
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) −10.0000 −0.971286
\(107\) 4.00000 0.386695 0.193347 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −18.0000 −1.72409 −0.862044 0.506834i \(-0.830816\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 10.0000 0.928477
\(117\) −2.00000 −0.184900
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 6.00000 0.543214
\(123\) −2.00000 −0.180334
\(124\) 8.00000 0.718421
\(125\) 0 0
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 1.00000 0.0883883
\(129\) 8.00000 0.704361
\(130\) 0 0
\(131\) −4.00000 −0.349482 −0.174741 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 4.00000 0.348155
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −6.00000 −0.514496
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) −8.00000 −0.681005
\(139\) 16.0000 1.35710 0.678551 0.734553i \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0 0
\(141\) −4.00000 −0.336861
\(142\) −12.0000 −1.00702
\(143\) 8.00000 0.668994
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −6.00000 −0.496564
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) 2.00000 0.160128
\(157\) −10.0000 −0.798087 −0.399043 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(158\) −8.00000 −0.636446
\(159\) 10.0000 0.793052
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) −4.00000 −0.310460
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) −8.00000 −0.609994
\(173\) 18.0000 1.36851 0.684257 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) −10.0000 −0.758098
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 4.00000 0.300658
\(178\) −14.0000 −1.04934
\(179\) −4.00000 −0.298974 −0.149487 0.988764i \(-0.547762\pi\)
−0.149487 + 0.988764i \(0.547762\pi\)
\(180\) 0 0
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 0 0
\(183\) −6.00000 −0.443533
\(184\) 8.00000 0.589768
\(185\) 0 0
\(186\) −8.00000 −0.586588
\(187\) 24.0000 1.75505
\(188\) 4.00000 0.291730
\(189\) 0 0
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −10.0000 −0.719816 −0.359908 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) 2.00000 0.143592
\(195\) 0 0
\(196\) 0 0
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) −4.00000 −0.284268
\(199\) −24.0000 −1.70131 −0.850657 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 6.00000 0.422159
\(203\) 0 0
\(204\) 6.00000 0.420084
\(205\) 0 0
\(206\) −16.0000 −1.11477
\(207\) 8.00000 0.556038
\(208\) −2.00000 −0.138675
\(209\) 0 0
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) −10.0000 −0.686803
\(213\) 12.0000 0.822226
\(214\) 4.00000 0.273434
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) −18.0000 −1.21911
\(219\) 6.00000 0.405442
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 2.00000 0.134231
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) 20.0000 1.32745 0.663723 0.747978i \(-0.268975\pi\)
0.663723 + 0.747978i \(0.268975\pi\)
\(228\) 0 0
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 10.0000 0.656532
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) −2.00000 −0.130744
\(235\) 0 0
\(236\) −4.00000 −0.260378
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 5.00000 0.321412
\(243\) −1.00000 −0.0641500
\(244\) 6.00000 0.384111
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) 0 0
\(248\) 8.00000 0.508001
\(249\) 4.00000 0.253490
\(250\) 0 0
\(251\) 20.0000 1.26239 0.631194 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) 0 0
\(253\) −32.0000 −2.01182
\(254\) −16.0000 −1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −14.0000 −0.873296 −0.436648 0.899632i \(-0.643834\pi\)
−0.436648 + 0.899632i \(0.643834\pi\)
\(258\) 8.00000 0.498058
\(259\) 0 0
\(260\) 0 0
\(261\) 10.0000 0.618984
\(262\) −4.00000 −0.247121
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 4.00000 0.246183
\(265\) 0 0
\(266\) 0 0
\(267\) 14.0000 0.856786
\(268\) 0 0
\(269\) −2.00000 −0.121942 −0.0609711 0.998140i \(-0.519420\pi\)
−0.0609711 + 0.998140i \(0.519420\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) 0 0
\(276\) −8.00000 −0.481543
\(277\) 22.0000 1.32185 0.660926 0.750451i \(-0.270164\pi\)
0.660926 + 0.750451i \(0.270164\pi\)
\(278\) 16.0000 0.959616
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) −22.0000 −1.31241 −0.656205 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) −4.00000 −0.238197
\(283\) 28.0000 1.66443 0.832214 0.554455i \(-0.187073\pi\)
0.832214 + 0.554455i \(0.187073\pi\)
\(284\) −12.0000 −0.712069
\(285\) 0 0
\(286\) 8.00000 0.473050
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) −2.00000 −0.117242
\(292\) −6.00000 −0.351123
\(293\) −30.0000 −1.75262 −0.876309 0.481749i \(-0.840002\pi\)
−0.876309 + 0.481749i \(0.840002\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) 4.00000 0.232104
\(298\) −6.00000 −0.347571
\(299\) −16.0000 −0.925304
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −6.00000 −0.344691
\(304\) 0 0
\(305\) 0 0
\(306\) −6.00000 −0.342997
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 2.00000 0.113228
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) −10.0000 −0.564333
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 30.0000 1.68497 0.842484 0.538721i \(-0.181092\pi\)
0.842484 + 0.538721i \(0.181092\pi\)
\(318\) 10.0000 0.560772
\(319\) −40.0000 −2.23957
\(320\) 0 0
\(321\) −4.00000 −0.223258
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −16.0000 −0.886158
\(327\) 18.0000 0.995402
\(328\) 2.00000 0.110432
\(329\) 0 0
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) −4.00000 −0.219529
\(333\) −2.00000 −0.109599
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) 0 0
\(337\) 6.00000 0.326841 0.163420 0.986557i \(-0.447747\pi\)
0.163420 + 0.986557i \(0.447747\pi\)
\(338\) −9.00000 −0.489535
\(339\) 6.00000 0.325875
\(340\) 0 0
\(341\) −32.0000 −1.73290
\(342\) 0 0
\(343\) 0 0
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) 18.0000 0.967686
\(347\) −20.0000 −1.07366 −0.536828 0.843692i \(-0.680378\pi\)
−0.536828 + 0.843692i \(0.680378\pi\)
\(348\) −10.0000 −0.536056
\(349\) −18.0000 −0.963518 −0.481759 0.876304i \(-0.660002\pi\)
−0.481759 + 0.876304i \(0.660002\pi\)
\(350\) 0 0
\(351\) 2.00000 0.106752
\(352\) −4.00000 −0.213201
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 4.00000 0.212598
\(355\) 0 0
\(356\) −14.0000 −0.741999
\(357\) 0 0
\(358\) −4.00000 −0.211407
\(359\) −20.0000 −1.05556 −0.527780 0.849381i \(-0.676975\pi\)
−0.527780 + 0.849381i \(0.676975\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) −18.0000 −0.946059
\(363\) −5.00000 −0.262432
\(364\) 0 0
\(365\) 0 0
\(366\) −6.00000 −0.313625
\(367\) 16.0000 0.835193 0.417597 0.908633i \(-0.362873\pi\)
0.417597 + 0.908633i \(0.362873\pi\)
\(368\) 8.00000 0.417029
\(369\) 2.00000 0.104116
\(370\) 0 0
\(371\) 0 0
\(372\) −8.00000 −0.414781
\(373\) 30.0000 1.55334 0.776671 0.629907i \(-0.216907\pi\)
0.776671 + 0.629907i \(0.216907\pi\)
\(374\) 24.0000 1.24101
\(375\) 0 0
\(376\) 4.00000 0.206284
\(377\) −20.0000 −1.03005
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 0 0
\(381\) 16.0000 0.819705
\(382\) 12.0000 0.613973
\(383\) −28.0000 −1.43073 −0.715367 0.698749i \(-0.753740\pi\)
−0.715367 + 0.698749i \(0.753740\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) −8.00000 −0.406663
\(388\) 2.00000 0.101535
\(389\) 10.0000 0.507020 0.253510 0.967333i \(-0.418415\pi\)
0.253510 + 0.967333i \(0.418415\pi\)
\(390\) 0 0
\(391\) −48.0000 −2.42746
\(392\) 0 0
\(393\) 4.00000 0.201773
\(394\) 22.0000 1.10834
\(395\) 0 0
\(396\) −4.00000 −0.201008
\(397\) 14.0000 0.702640 0.351320 0.936255i \(-0.385733\pi\)
0.351320 + 0.936255i \(0.385733\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) 0 0
\(401\) 34.0000 1.69788 0.848939 0.528490i \(-0.177242\pi\)
0.848939 + 0.528490i \(0.177242\pi\)
\(402\) 0 0
\(403\) −16.0000 −0.797017
\(404\) 6.00000 0.298511
\(405\) 0 0
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) 6.00000 0.297044
\(409\) −26.0000 −1.28562 −0.642809 0.766027i \(-0.722231\pi\)
−0.642809 + 0.766027i \(0.722231\pi\)
\(410\) 0 0
\(411\) 6.00000 0.295958
\(412\) −16.0000 −0.788263
\(413\) 0 0
\(414\) 8.00000 0.393179
\(415\) 0 0
\(416\) −2.00000 −0.0980581
\(417\) −16.0000 −0.783523
\(418\) 0 0
\(419\) −28.0000 −1.36789 −0.683945 0.729534i \(-0.739737\pi\)
−0.683945 + 0.729534i \(0.739737\pi\)
\(420\) 0 0
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) −4.00000 −0.194717
\(423\) 4.00000 0.194487
\(424\) −10.0000 −0.485643
\(425\) 0 0
\(426\) 12.0000 0.581402
\(427\) 0 0
\(428\) 4.00000 0.193347
\(429\) −8.00000 −0.386244
\(430\) 0 0
\(431\) −36.0000 −1.73406 −0.867029 0.498257i \(-0.833974\pi\)
−0.867029 + 0.498257i \(0.833974\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 34.0000 1.63394 0.816968 0.576683i \(-0.195653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −18.0000 −0.862044
\(437\) 0 0
\(438\) 6.00000 0.286691
\(439\) −32.0000 −1.52728 −0.763638 0.645644i \(-0.776589\pi\)
−0.763638 + 0.645644i \(0.776589\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) 2.00000 0.0949158
\(445\) 0 0
\(446\) −24.0000 −1.13643
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) 0 0
\(451\) −8.00000 −0.376705
\(452\) −6.00000 −0.282216
\(453\) 0 0
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) 0 0
\(457\) 6.00000 0.280668 0.140334 0.990104i \(-0.455182\pi\)
0.140334 + 0.990104i \(0.455182\pi\)
\(458\) 22.0000 1.02799
\(459\) 6.00000 0.280056
\(460\) 0 0
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 10.0000 0.464238
\(465\) 0 0
\(466\) 18.0000 0.833834
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) 0 0
\(471\) 10.0000 0.460776
\(472\) −4.00000 −0.184115
\(473\) 32.0000 1.47136
\(474\) 8.00000 0.367452
\(475\) 0 0
\(476\) 0 0
\(477\) −10.0000 −0.457869
\(478\) −12.0000 −0.548867
\(479\) 8.00000 0.365529 0.182765 0.983157i \(-0.441495\pi\)
0.182765 + 0.983157i \(0.441495\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) 14.0000 0.637683
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) −8.00000 −0.362515 −0.181257 0.983436i \(-0.558017\pi\)
−0.181257 + 0.983436i \(0.558017\pi\)
\(488\) 6.00000 0.271607
\(489\) 16.0000 0.723545
\(490\) 0 0
\(491\) 20.0000 0.902587 0.451294 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) −2.00000 −0.0901670
\(493\) −60.0000 −2.70226
\(494\) 0 0
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) 4.00000 0.179244
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) 0 0
\(501\) 12.0000 0.536120
\(502\) 20.0000 0.892644
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −32.0000 −1.42257
\(507\) 9.00000 0.399704
\(508\) −16.0000 −0.709885
\(509\) −2.00000 −0.0886484 −0.0443242 0.999017i \(-0.514113\pi\)
−0.0443242 + 0.999017i \(0.514113\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −14.0000 −0.617514
\(515\) 0 0
\(516\) 8.00000 0.352180
\(517\) −16.0000 −0.703679
\(518\) 0 0
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 10.0000 0.437688
\(523\) −28.0000 −1.22435 −0.612177 0.790721i \(-0.709706\pi\)
−0.612177 + 0.790721i \(0.709706\pi\)
\(524\) −4.00000 −0.174741
\(525\) 0 0
\(526\) 0 0
\(527\) −48.0000 −2.09091
\(528\) 4.00000 0.174078
\(529\) 41.0000 1.78261
\(530\) 0 0
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) −4.00000 −0.173259
\(534\) 14.0000 0.605839
\(535\) 0 0
\(536\) 0 0
\(537\) 4.00000 0.172613
\(538\) −2.00000 −0.0862261
\(539\) 0 0
\(540\) 0 0
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) −8.00000 −0.343629
\(543\) 18.0000 0.772454
\(544\) −6.00000 −0.257248
\(545\) 0 0
\(546\) 0 0
\(547\) 32.0000 1.36822 0.684111 0.729378i \(-0.260191\pi\)
0.684111 + 0.729378i \(0.260191\pi\)
\(548\) −6.00000 −0.256307
\(549\) 6.00000 0.256074
\(550\) 0 0
\(551\) 0 0
\(552\) −8.00000 −0.340503
\(553\) 0 0
\(554\) 22.0000 0.934690
\(555\) 0 0
\(556\) 16.0000 0.678551
\(557\) −18.0000 −0.762684 −0.381342 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) 8.00000 0.338667
\(559\) 16.0000 0.676728
\(560\) 0 0
\(561\) −24.0000 −1.01328
\(562\) −22.0000 −0.928014
\(563\) 4.00000 0.168580 0.0842900 0.996441i \(-0.473138\pi\)
0.0842900 + 0.996441i \(0.473138\pi\)
\(564\) −4.00000 −0.168430
\(565\) 0 0
\(566\) 28.0000 1.17693
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 8.00000 0.334497
\(573\) −12.0000 −0.501307
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −14.0000 −0.582828 −0.291414 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) 19.0000 0.790296
\(579\) 10.0000 0.415586
\(580\) 0 0
\(581\) 0 0
\(582\) −2.00000 −0.0829027
\(583\) 40.0000 1.65663
\(584\) −6.00000 −0.248282
\(585\) 0 0
\(586\) −30.0000 −1.23929
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −22.0000 −0.904959
\(592\) −2.00000 −0.0821995
\(593\) −38.0000 −1.56047 −0.780236 0.625485i \(-0.784901\pi\)
−0.780236 + 0.625485i \(0.784901\pi\)
\(594\) 4.00000 0.164122
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 24.0000 0.982255
\(598\) −16.0000 −0.654289
\(599\) 20.0000 0.817178 0.408589 0.912719i \(-0.366021\pi\)
0.408589 + 0.912719i \(0.366021\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) −6.00000 −0.243733
\(607\) −40.0000 −1.62355 −0.811775 0.583970i \(-0.801498\pi\)
−0.811775 + 0.583970i \(0.801498\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −8.00000 −0.323645
\(612\) −6.00000 −0.242536
\(613\) 14.0000 0.565455 0.282727 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) 20.0000 0.807134
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000 0.0805170 0.0402585 0.999189i \(-0.487182\pi\)
0.0402585 + 0.999189i \(0.487182\pi\)
\(618\) 16.0000 0.643614
\(619\) −8.00000 −0.321547 −0.160774 0.986991i \(-0.551399\pi\)
−0.160774 + 0.986991i \(0.551399\pi\)
\(620\) 0 0
\(621\) −8.00000 −0.321029
\(622\) 0 0
\(623\) 0 0
\(624\) 2.00000 0.0800641
\(625\) 0 0
\(626\) −6.00000 −0.239808
\(627\) 0 0
\(628\) −10.0000 −0.399043
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) −8.00000 −0.318223
\(633\) 4.00000 0.158986
\(634\) 30.0000 1.19145
\(635\) 0 0
\(636\) 10.0000 0.396526
\(637\) 0 0
\(638\) −40.0000 −1.58362
\(639\) −12.0000 −0.474713
\(640\) 0 0
\(641\) −6.00000 −0.236986 −0.118493 0.992955i \(-0.537806\pi\)
−0.118493 + 0.992955i \(0.537806\pi\)
\(642\) −4.00000 −0.157867
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 28.0000 1.10079 0.550397 0.834903i \(-0.314476\pi\)
0.550397 + 0.834903i \(0.314476\pi\)
\(648\) 1.00000 0.0392837
\(649\) 16.0000 0.628055
\(650\) 0 0
\(651\) 0 0
\(652\) −16.0000 −0.626608
\(653\) 14.0000 0.547862 0.273931 0.961749i \(-0.411676\pi\)
0.273931 + 0.961749i \(0.411676\pi\)
\(654\) 18.0000 0.703856
\(655\) 0 0
\(656\) 2.00000 0.0780869
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) 30.0000 1.16686 0.583432 0.812162i \(-0.301709\pi\)
0.583432 + 0.812162i \(0.301709\pi\)
\(662\) 20.0000 0.777322
\(663\) −12.0000 −0.466041
\(664\) −4.00000 −0.155230
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) 80.0000 3.09761
\(668\) −12.0000 −0.464294
\(669\) 24.0000 0.927894
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 6.00000 0.231111
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) −22.0000 −0.845529 −0.422764 0.906240i \(-0.638940\pi\)
−0.422764 + 0.906240i \(0.638940\pi\)
\(678\) 6.00000 0.230429
\(679\) 0 0
\(680\) 0 0
\(681\) −20.0000 −0.766402
\(682\) −32.0000 −1.22534
\(683\) −28.0000 −1.07139 −0.535695 0.844411i \(-0.679950\pi\)
−0.535695 + 0.844411i \(0.679950\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −22.0000 −0.839352
\(688\) −8.00000 −0.304997
\(689\) 20.0000 0.761939
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 18.0000 0.684257
\(693\) 0 0
\(694\) −20.0000 −0.759190
\(695\) 0 0
\(696\) −10.0000 −0.379049
\(697\) −12.0000 −0.454532
\(698\) −18.0000 −0.681310
\(699\) −18.0000 −0.680823
\(700\) 0 0
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 2.00000 0.0754851
\(703\) 0 0
\(704\) −4.00000 −0.150756
\(705\) 0 0
\(706\) 18.0000 0.677439
\(707\) 0 0
\(708\) 4.00000 0.150329
\(709\) 14.0000 0.525781 0.262891 0.964826i \(-0.415324\pi\)
0.262891 + 0.964826i \(0.415324\pi\)
\(710\) 0 0
\(711\) −8.00000 −0.300023
\(712\) −14.0000 −0.524672
\(713\) 64.0000 2.39682
\(714\) 0 0
\(715\) 0 0
\(716\) −4.00000 −0.149487
\(717\) 12.0000 0.448148
\(718\) −20.0000 −0.746393
\(719\) −8.00000 −0.298350 −0.149175 0.988811i \(-0.547662\pi\)
−0.149175 + 0.988811i \(0.547662\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −19.0000 −0.707107
\(723\) −14.0000 −0.520666
\(724\) −18.0000 −0.668965
\(725\) 0 0
\(726\) −5.00000 −0.185567
\(727\) −16.0000 −0.593407 −0.296704 0.954970i \(-0.595887\pi\)
−0.296704 + 0.954970i \(0.595887\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 48.0000 1.77534
\(732\) −6.00000 −0.221766
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) 16.0000 0.590571
\(735\) 0 0
\(736\) 8.00000 0.294884
\(737\) 0 0
\(738\) 2.00000 0.0736210
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 8.00000 0.293492 0.146746 0.989174i \(-0.453120\pi\)
0.146746 + 0.989174i \(0.453120\pi\)
\(744\) −8.00000 −0.293294
\(745\) 0 0
\(746\) 30.0000 1.09838
\(747\) −4.00000 −0.146352
\(748\) 24.0000 0.877527
\(749\) 0 0
\(750\) 0 0
\(751\) −16.0000 −0.583848 −0.291924 0.956441i \(-0.594295\pi\)
−0.291924 + 0.956441i \(0.594295\pi\)
\(752\) 4.00000 0.145865
\(753\) −20.0000 −0.728841
\(754\) −20.0000 −0.728357
\(755\) 0 0
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −28.0000 −1.01701
\(759\) 32.0000 1.16153
\(760\) 0 0
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 16.0000 0.579619
\(763\) 0 0
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) −28.0000 −1.01168
\(767\) 8.00000 0.288863
\(768\) −1.00000 −0.0360844
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) 14.0000 0.504198
\(772\) −10.0000 −0.359908
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) −8.00000 −0.287554
\(775\) 0 0
\(776\) 2.00000 0.0717958
\(777\) 0 0
\(778\) 10.0000 0.358517
\(779\) 0 0
\(780\) 0 0
\(781\) 48.0000 1.71758
\(782\) −48.0000 −1.71648
\(783\) −10.0000 −0.357371
\(784\) 0 0
\(785\) 0 0
\(786\) 4.00000 0.142675
\(787\) 4.00000 0.142585 0.0712923 0.997455i \(-0.477288\pi\)
0.0712923 + 0.997455i \(0.477288\pi\)
\(788\) 22.0000 0.783718
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −4.00000 −0.142134
\(793\) −12.0000 −0.426132
\(794\) 14.0000 0.496841
\(795\) 0 0
\(796\) −24.0000 −0.850657
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 0 0
\(799\) −24.0000 −0.849059
\(800\) 0 0
\(801\) −14.0000 −0.494666
\(802\) 34.0000 1.20058
\(803\) 24.0000 0.846942
\(804\) 0 0
\(805\) 0 0
\(806\) −16.0000 −0.563576
\(807\) 2.00000 0.0704033
\(808\) 6.00000 0.211079
\(809\) 42.0000 1.47664 0.738321 0.674450i \(-0.235619\pi\)
0.738321 + 0.674450i \(0.235619\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 8.00000 0.280572
\(814\) 8.00000 0.280400
\(815\) 0 0
\(816\) 6.00000 0.210042
\(817\) 0 0
\(818\) −26.0000 −0.909069
\(819\) 0 0
\(820\) 0 0
\(821\) 18.0000 0.628204 0.314102 0.949389i \(-0.398297\pi\)
0.314102 + 0.949389i \(0.398297\pi\)
\(822\) 6.00000 0.209274
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) −16.0000 −0.557386
\(825\) 0 0
\(826\) 0 0
\(827\) 28.0000 0.973655 0.486828 0.873498i \(-0.338154\pi\)
0.486828 + 0.873498i \(0.338154\pi\)
\(828\) 8.00000 0.278019
\(829\) −34.0000 −1.18087 −0.590434 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) 0 0
\(831\) −22.0000 −0.763172
\(832\) −2.00000 −0.0693375
\(833\) 0 0
\(834\) −16.0000 −0.554035
\(835\) 0 0
\(836\) 0 0
\(837\) −8.00000 −0.276520
\(838\) −28.0000 −0.967244
\(839\) −8.00000 −0.276191 −0.138095 0.990419i \(-0.544098\pi\)
−0.138095 + 0.990419i \(0.544098\pi\)
\(840\) 0 0
\(841\) 71.0000 2.44828
\(842\) −26.0000 −0.896019
\(843\) 22.0000 0.757720
\(844\) −4.00000 −0.137686
\(845\) 0 0
\(846\) 4.00000 0.137523
\(847\) 0 0
\(848\) −10.0000 −0.343401
\(849\) −28.0000 −0.960958
\(850\) 0 0
\(851\) −16.0000 −0.548473
\(852\) 12.0000 0.411113
\(853\) 22.0000 0.753266 0.376633 0.926363i \(-0.377082\pi\)
0.376633 + 0.926363i \(0.377082\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 4.00000 0.136717
\(857\) −38.0000 −1.29806 −0.649028 0.760765i \(-0.724824\pi\)
−0.649028 + 0.760765i \(0.724824\pi\)
\(858\) −8.00000 −0.273115
\(859\) −24.0000 −0.818869 −0.409435 0.912339i \(-0.634274\pi\)
−0.409435 + 0.912339i \(0.634274\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −36.0000 −1.22616
\(863\) 8.00000 0.272323 0.136162 0.990687i \(-0.456523\pi\)
0.136162 + 0.990687i \(0.456523\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 0 0
\(866\) 34.0000 1.15537
\(867\) −19.0000 −0.645274
\(868\) 0 0
\(869\) 32.0000 1.08553
\(870\) 0 0
\(871\) 0 0
\(872\) −18.0000 −0.609557
\(873\) 2.00000 0.0676897
\(874\) 0 0
\(875\) 0 0
\(876\) 6.00000 0.202721
\(877\) −2.00000 −0.0675352 −0.0337676 0.999430i \(-0.510751\pi\)
−0.0337676 + 0.999430i \(0.510751\pi\)
\(878\) −32.0000 −1.07995
\(879\) 30.0000 1.01187
\(880\) 0 0
\(881\) 2.00000 0.0673817 0.0336909 0.999432i \(-0.489274\pi\)
0.0336909 + 0.999432i \(0.489274\pi\)
\(882\) 0 0
\(883\) −48.0000 −1.61533 −0.807664 0.589643i \(-0.799269\pi\)
−0.807664 + 0.589643i \(0.799269\pi\)
\(884\) 12.0000 0.403604
\(885\) 0 0
\(886\) −4.00000 −0.134383
\(887\) 20.0000 0.671534 0.335767 0.941945i \(-0.391004\pi\)
0.335767 + 0.941945i \(0.391004\pi\)
\(888\) 2.00000 0.0671156
\(889\) 0 0
\(890\) 0 0
\(891\) −4.00000 −0.134005
\(892\) −24.0000 −0.803579
\(893\) 0 0
\(894\) 6.00000 0.200670
\(895\) 0 0
\(896\) 0 0
\(897\) 16.0000 0.534224
\(898\) 26.0000 0.867631
\(899\) 80.0000 2.66815
\(900\) 0 0
\(901\) 60.0000 1.99889
\(902\) −8.00000 −0.266371
\(903\) 0 0
\(904\) −6.00000 −0.199557
\(905\) 0 0
\(906\) 0 0
\(907\) −8.00000 −0.265636 −0.132818 0.991140i \(-0.542403\pi\)
−0.132818 + 0.991140i \(0.542403\pi\)
\(908\) 20.0000 0.663723
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) −20.0000 −0.662630 −0.331315 0.943520i \(-0.607492\pi\)
−0.331315 + 0.943520i \(0.607492\pi\)
\(912\) 0 0
\(913\) 16.0000 0.529523
\(914\) 6.00000 0.198462
\(915\) 0 0
\(916\) 22.0000 0.726900
\(917\) 0 0
\(918\) 6.00000 0.198030
\(919\) −24.0000 −0.791687 −0.395843 0.918318i \(-0.629548\pi\)
−0.395843 + 0.918318i \(0.629548\pi\)
\(920\) 0 0
\(921\) −20.0000 −0.659022
\(922\) −18.0000 −0.592798
\(923\) 24.0000 0.789970
\(924\) 0 0
\(925\) 0 0
\(926\) −8.00000 −0.262896
\(927\) −16.0000 −0.525509
\(928\) 10.0000 0.328266
\(929\) 18.0000 0.590561 0.295280 0.955411i \(-0.404587\pi\)
0.295280 + 0.955411i \(0.404587\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 18.0000 0.589610
\(933\) 0 0
\(934\) 12.0000 0.392652
\(935\) 0 0
\(936\) −2.00000 −0.0653720
\(937\) 42.0000 1.37208 0.686040 0.727564i \(-0.259347\pi\)
0.686040 + 0.727564i \(0.259347\pi\)
\(938\) 0 0
\(939\) 6.00000 0.195803
\(940\) 0 0
\(941\) −18.0000 −0.586783 −0.293392 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) 10.0000 0.325818
\(943\) 16.0000 0.521032
\(944\) −4.00000 −0.130189
\(945\) 0 0
\(946\) 32.0000 1.04041
\(947\) −52.0000 −1.68977 −0.844886 0.534946i \(-0.820332\pi\)
−0.844886 + 0.534946i \(0.820332\pi\)
\(948\) 8.00000 0.259828
\(949\) 12.0000 0.389536
\(950\) 0 0
\(951\) −30.0000 −0.972817
\(952\) 0 0
\(953\) 50.0000 1.61966 0.809829 0.586665i \(-0.199560\pi\)
0.809829 + 0.586665i \(0.199560\pi\)
\(954\) −10.0000 −0.323762
\(955\) 0 0
\(956\) −12.0000 −0.388108
\(957\) 40.0000 1.29302
\(958\) 8.00000 0.258468
\(959\) 0 0
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 4.00000 0.128965
\(963\) 4.00000 0.128898
\(964\) 14.0000 0.450910
\(965\) 0 0
\(966\) 0 0
\(967\) 8.00000 0.257263 0.128631 0.991692i \(-0.458942\pi\)
0.128631 + 0.991692i \(0.458942\pi\)
\(968\) 5.00000 0.160706
\(969\) 0 0
\(970\) 0 0
\(971\) 36.0000 1.15529 0.577647 0.816286i \(-0.303971\pi\)
0.577647 + 0.816286i \(0.303971\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) −8.00000 −0.256337
\(975\) 0 0
\(976\) 6.00000 0.192055
\(977\) −6.00000 −0.191957 −0.0959785 0.995383i \(-0.530598\pi\)
−0.0959785 + 0.995383i \(0.530598\pi\)
\(978\) 16.0000 0.511624
\(979\) 56.0000 1.78977
\(980\) 0 0
\(981\) −18.0000 −0.574696
\(982\) 20.0000 0.638226
\(983\) 28.0000 0.893061 0.446531 0.894768i \(-0.352659\pi\)
0.446531 + 0.894768i \(0.352659\pi\)
\(984\) −2.00000 −0.0637577
\(985\) 0 0
\(986\) −60.0000 −1.91079
\(987\) 0 0
\(988\) 0 0
\(989\) −64.0000 −2.03508
\(990\) 0 0
\(991\) 16.0000 0.508257 0.254128 0.967170i \(-0.418211\pi\)
0.254128 + 0.967170i \(0.418211\pi\)
\(992\) 8.00000 0.254000
\(993\) −20.0000 −0.634681
\(994\) 0 0
\(995\) 0 0
\(996\) 4.00000 0.126745
\(997\) −10.0000 −0.316703 −0.158352 0.987383i \(-0.550618\pi\)
−0.158352 + 0.987383i \(0.550618\pi\)
\(998\) 28.0000 0.886325
\(999\) 2.00000 0.0632772
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 7350.2.a.bo.1.1 1
5.4 even 2 1470.2.a.g.1.1 1
7.6 odd 2 1050.2.a.q.1.1 1
15.14 odd 2 4410.2.a.bc.1.1 1
21.20 even 2 3150.2.a.t.1.1 1
28.27 even 2 8400.2.a.m.1.1 1
35.4 even 6 1470.2.i.n.961.1 2
35.9 even 6 1470.2.i.n.361.1 2
35.13 even 4 1050.2.g.f.799.1 2
35.19 odd 6 1470.2.i.t.361.1 2
35.24 odd 6 1470.2.i.t.961.1 2
35.27 even 4 1050.2.g.f.799.2 2
35.34 odd 2 210.2.a.a.1.1 1
105.62 odd 4 3150.2.g.t.2899.1 2
105.83 odd 4 3150.2.g.t.2899.2 2
105.104 even 2 630.2.a.i.1.1 1
140.139 even 2 1680.2.a.o.1.1 1
280.69 odd 2 6720.2.a.cg.1.1 1
280.139 even 2 6720.2.a.z.1.1 1
420.419 odd 2 5040.2.a.bg.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.a.a.1.1 1 35.34 odd 2
630.2.a.i.1.1 1 105.104 even 2
1050.2.a.q.1.1 1 7.6 odd 2
1050.2.g.f.799.1 2 35.13 even 4
1050.2.g.f.799.2 2 35.27 even 4
1470.2.a.g.1.1 1 5.4 even 2
1470.2.i.n.361.1 2 35.9 even 6
1470.2.i.n.961.1 2 35.4 even 6
1470.2.i.t.361.1 2 35.19 odd 6
1470.2.i.t.961.1 2 35.24 odd 6
1680.2.a.o.1.1 1 140.139 even 2
3150.2.a.t.1.1 1 21.20 even 2
3150.2.g.t.2899.1 2 105.62 odd 4
3150.2.g.t.2899.2 2 105.83 odd 4
4410.2.a.bc.1.1 1 15.14 odd 2
5040.2.a.bg.1.1 1 420.419 odd 2
6720.2.a.z.1.1 1 280.139 even 2
6720.2.a.cg.1.1 1 280.69 odd 2
7350.2.a.bo.1.1 1 1.1 even 1 trivial
8400.2.a.m.1.1 1 28.27 even 2