Properties

Label 7350.2.a.bc.1.1
Level 7350
Weight 2
Character 7350.1
Self dual yes
Analytic conductor 58.690
Analytic rank 0
Dimension 1
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1470)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{12} -2.00000 q^{13} +1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{18} +2.00000 q^{19} +8.00000 q^{23} -1.00000 q^{24} +2.00000 q^{26} +1.00000 q^{27} -8.00000 q^{29} +4.00000 q^{31} -1.00000 q^{32} +2.00000 q^{34} +1.00000 q^{36} -6.00000 q^{37} -2.00000 q^{38} -2.00000 q^{39} +10.0000 q^{41} +2.00000 q^{43} -8.00000 q^{46} -6.00000 q^{47} +1.00000 q^{48} -2.00000 q^{51} -2.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} +2.00000 q^{57} +8.00000 q^{58} +12.0000 q^{59} +2.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} -14.0000 q^{67} -2.00000 q^{68} +8.00000 q^{69} +6.00000 q^{71} -1.00000 q^{72} -10.0000 q^{73} +6.00000 q^{74} +2.00000 q^{76} +2.00000 q^{78} +4.00000 q^{79} +1.00000 q^{81} -10.0000 q^{82} +12.0000 q^{83} -2.00000 q^{86} -8.00000 q^{87} -14.0000 q^{89} +8.00000 q^{92} +4.00000 q^{93} +6.00000 q^{94} -1.00000 q^{96} +14.0000 q^{97} +O(q^{100})\)

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
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 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
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) −1.00000 −0.235702
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0 0
\(26\) 2.00000 0.392232
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −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
\(36\) 1.00000 0.166667
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) −2.00000 −0.324443
\(39\) −2.00000 −0.320256
\(40\) 0 0
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −8.00000 −1.17954
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 1.00000 0.144338
\(49\) 0 0
\(50\) 0 0
\(51\) −2.00000 −0.280056
\(52\) −2.00000 −0.277350
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) 8.00000 1.05045
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −14.0000 −1.71037 −0.855186 0.518321i \(-0.826557\pi\)
−0.855186 + 0.518321i \(0.826557\pi\)
\(68\) −2.00000 −0.242536
\(69\) 8.00000 0.963087
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) −1.00000 −0.117851
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 6.00000 0.697486
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) 2.00000 0.226455
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −10.0000 −1.10432
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.00000 −0.215666
\(87\) −8.00000 −0.857690
\(88\) 0 0
\(89\) −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
\(93\) 4.00000 0.414781
\(94\) 6.00000 0.618853
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 2.00000 0.198030
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 1.00000 0.0962250
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 0 0
\(111\) −6.00000 −0.569495
\(112\) 0 0
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) −2.00000 −0.187317
\(115\) 0 0
\(116\) −8.00000 −0.742781
\(117\) −2.00000 −0.184900
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) −2.00000 −0.181071
\(123\) 10.0000 0.901670
\(124\) 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
\(129\) 2.00000 0.176090
\(130\) 0 0
\(131\) 8.00000 0.698963 0.349482 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 14.0000 1.20942
\(135\) 0 0
\(136\) 2.00000 0.171499
\(137\) −2.00000 −0.170872 −0.0854358 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) −8.00000 −0.681005
\(139\) 22.0000 1.86602 0.933008 0.359856i \(-0.117174\pi\)
0.933008 + 0.359856i \(0.117174\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) −6.00000 −0.503509
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 10.0000 0.827606
\(147\) 0 0
\(148\) −6.00000 −0.493197
\(149\) 20.0000 1.63846 0.819232 0.573462i \(-0.194400\pi\)
0.819232 + 0.573462i \(0.194400\pi\)
\(150\) 0 0
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) −2.00000 −0.162221
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) −2.00000 −0.160128
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) −4.00000 −0.318223
\(159\) 6.00000 0.475831
\(160\) 0 0
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) 10.0000 0.780869
\(165\) 0 0
\(166\) −12.0000 −0.931381
\(167\) −2.00000 −0.154765 −0.0773823 0.997001i \(-0.524656\pi\)
−0.0773823 + 0.997001i \(0.524656\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 2.00000 0.152944
\(172\) 2.00000 0.152499
\(173\) 12.0000 0.912343 0.456172 0.889892i \(-0.349220\pi\)
0.456172 + 0.889892i \(0.349220\pi\)
\(174\) 8.00000 0.606478
\(175\) 0 0
\(176\) 0 0
\(177\) 12.0000 0.901975
\(178\) 14.0000 1.04934
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) −8.00000 −0.589768
\(185\) 0 0
\(186\) −4.00000 −0.293294
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) 22.0000 1.59186 0.795932 0.605386i \(-0.206981\pi\)
0.795932 + 0.605386i \(0.206981\pi\)
\(192\) 1.00000 0.0721688
\(193\) −20.0000 −1.43963 −0.719816 0.694165i \(-0.755774\pi\)
−0.719816 + 0.694165i \(0.755774\pi\)
\(194\) −14.0000 −1.00514
\(195\) 0 0
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 0 0
\(201\) −14.0000 −0.987484
\(202\) 6.00000 0.422159
\(203\) 0 0
\(204\) −2.00000 −0.140028
\(205\) 0 0
\(206\) 4.00000 0.278693
\(207\) 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 \(0.543966\pi\)
\(212\) 6.00000 0.412082
\(213\) 6.00000 0.411113
\(214\) 0 0
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) −10.0000 −0.675737
\(220\) 0 0
\(221\) 4.00000 0.269069
\(222\) 6.00000 0.402694
\(223\) 20.0000 1.33930 0.669650 0.742677i \(-0.266444\pi\)
0.669650 + 0.742677i \(0.266444\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −10.0000 −0.665190
\(227\) −16.0000 −1.06196 −0.530979 0.847385i \(-0.678176\pi\)
−0.530979 + 0.847385i \(0.678176\pi\)
\(228\) 2.00000 0.132453
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.00000 0.525226
\(233\) −14.0000 −0.917170 −0.458585 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) 2.00000 0.130744
\(235\) 0 0
\(236\) 12.0000 0.781133
\(237\) 4.00000 0.259828
\(238\) 0 0
\(239\) 18.0000 1.16432 0.582162 0.813073i \(-0.302207\pi\)
0.582162 + 0.813073i \(0.302207\pi\)
\(240\) 0 0
\(241\) 24.0000 1.54598 0.772988 0.634421i \(-0.218761\pi\)
0.772988 + 0.634421i \(0.218761\pi\)
\(242\) 11.0000 0.707107
\(243\) 1.00000 0.0641500
\(244\) 2.00000 0.128037
\(245\) 0 0
\(246\) −10.0000 −0.637577
\(247\) −4.00000 −0.254514
\(248\) −4.00000 −0.254000
\(249\) 12.0000 0.760469
\(250\) 0 0
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −8.00000 −0.501965
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −30.0000 −1.87135 −0.935674 0.352865i \(-0.885208\pi\)
−0.935674 + 0.352865i \(0.885208\pi\)
\(258\) −2.00000 −0.124515
\(259\) 0 0
\(260\) 0 0
\(261\) −8.00000 −0.495188
\(262\) −8.00000 −0.494242
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −14.0000 −0.856786
\(268\) −14.0000 −0.855186
\(269\) 30.0000 1.82913 0.914566 0.404436i \(-0.132532\pi\)
0.914566 + 0.404436i \(0.132532\pi\)
\(270\) 0 0
\(271\) −20.0000 −1.21491 −0.607457 0.794353i \(-0.707810\pi\)
−0.607457 + 0.794353i \(0.707810\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) 0 0
\(276\) 8.00000 0.481543
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −22.0000 −1.31947
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 6.00000 0.357295
\(283\) −20.0000 −1.18888 −0.594438 0.804141i \(-0.702626\pi\)
−0.594438 + 0.804141i \(0.702626\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 14.0000 0.820695
\(292\) −10.0000 −0.585206
\(293\) 24.0000 1.40209 0.701047 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) −20.0000 −1.15857
\(299\) −16.0000 −0.925304
\(300\) 0 0
\(301\) 0 0
\(302\) −20.0000 −1.15087
\(303\) −6.00000 −0.344691
\(304\) 2.00000 0.114708
\(305\) 0 0
\(306\) 2.00000 0.114332
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 2.00000 0.113228
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) 34.0000 1.90963 0.954815 0.297200i \(-0.0960529\pi\)
0.954815 + 0.297200i \(0.0960529\pi\)
\(318\) −6.00000 −0.336463
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.00000 −0.222566
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −2.00000 −0.110770
\(327\) −2.00000 −0.110600
\(328\) −10.0000 −0.552158
\(329\) 0 0
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 12.0000 0.658586
\(333\) −6.00000 −0.328798
\(334\) 2.00000 0.109435
\(335\) 0 0
\(336\) 0 0
\(337\) −12.0000 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(338\) 9.00000 0.489535
\(339\) 10.0000 0.543125
\(340\) 0 0
\(341\) 0 0
\(342\) −2.00000 −0.108148
\(343\) 0 0
\(344\) −2.00000 −0.107833
\(345\) 0 0
\(346\) −12.0000 −0.645124
\(347\) 28.0000 1.50312 0.751559 0.659665i \(-0.229302\pi\)
0.751559 + 0.659665i \(0.229302\pi\)
\(348\) −8.00000 −0.428845
\(349\) 30.0000 1.60586 0.802932 0.596071i \(-0.203272\pi\)
0.802932 + 0.596071i \(0.203272\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) −12.0000 −0.637793
\(355\) 0 0
\(356\) −14.0000 −0.741999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) −14.0000 −0.738892 −0.369446 0.929252i \(-0.620452\pi\)
−0.369446 + 0.929252i \(0.620452\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) −2.00000 −0.105118
\(363\) −11.0000 −0.577350
\(364\) 0 0
\(365\) 0 0
\(366\) −2.00000 −0.104542
\(367\) −16.0000 −0.835193 −0.417597 0.908633i \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) 8.00000 0.417029
\(369\) 10.0000 0.520579
\(370\) 0 0
\(371\) 0 0
\(372\) 4.00000 0.207390
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) 16.0000 0.824042
\(378\) 0 0
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) 0 0
\(381\) 8.00000 0.409852
\(382\) −22.0000 −1.12562
\(383\) 26.0000 1.32854 0.664269 0.747494i \(-0.268743\pi\)
0.664269 + 0.747494i \(0.268743\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 20.0000 1.01797
\(387\) 2.00000 0.101666
\(388\) 14.0000 0.710742
\(389\) −4.00000 −0.202808 −0.101404 0.994845i \(-0.532333\pi\)
−0.101404 + 0.994845i \(0.532333\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) 8.00000 0.403547
\(394\) 6.00000 0.302276
\(395\) 0 0
\(396\) 0 0
\(397\) 38.0000 1.90717 0.953583 0.301131i \(-0.0973643\pi\)
0.953583 + 0.301131i \(0.0973643\pi\)
\(398\) −16.0000 −0.802008
\(399\) 0 0
\(400\) 0 0
\(401\) 10.0000 0.499376 0.249688 0.968326i \(-0.419672\pi\)
0.249688 + 0.968326i \(0.419672\pi\)
\(402\) 14.0000 0.698257
\(403\) −8.00000 −0.398508
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 2.00000 0.0990148
\(409\) 24.0000 1.18672 0.593362 0.804936i \(-0.297800\pi\)
0.593362 + 0.804936i \(0.297800\pi\)
\(410\) 0 0
\(411\) −2.00000 −0.0986527
\(412\) −4.00000 −0.197066
\(413\) 0 0
\(414\) −8.00000 −0.393179
\(415\) 0 0
\(416\) 2.00000 0.0980581
\(417\) 22.0000 1.07734
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −18.0000 −0.877266 −0.438633 0.898666i \(-0.644537\pi\)
−0.438633 + 0.898666i \(0.644537\pi\)
\(422\) 4.00000 0.194717
\(423\) −6.00000 −0.291730
\(424\) −6.00000 −0.291386
\(425\) 0 0
\(426\) −6.00000 −0.290701
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −10.0000 −0.481683 −0.240842 0.970564i \(-0.577423\pi\)
−0.240842 + 0.970564i \(0.577423\pi\)
\(432\) 1.00000 0.0481125
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2.00000 −0.0957826
\(437\) 16.0000 0.765384
\(438\) 10.0000 0.477818
\(439\) −36.0000 −1.71819 −0.859093 0.511819i \(-0.828972\pi\)
−0.859093 + 0.511819i \(0.828972\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −4.00000 −0.190261
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) −6.00000 −0.284747
\(445\) 0 0
\(446\) −20.0000 −0.947027
\(447\) 20.0000 0.945968
\(448\) 0 0
\(449\) −26.0000 −1.22702 −0.613508 0.789689i \(-0.710242\pi\)
−0.613508 + 0.789689i \(0.710242\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 10.0000 0.470360
\(453\) 20.0000 0.939682
\(454\) 16.0000 0.750917
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) −32.0000 −1.49690 −0.748448 0.663193i \(-0.769201\pi\)
−0.748448 + 0.663193i \(0.769201\pi\)
\(458\) 10.0000 0.467269
\(459\) −2.00000 −0.0933520
\(460\) 0 0
\(461\) −14.0000 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 0 0
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) −8.00000 −0.371391
\(465\) 0 0
\(466\) 14.0000 0.648537
\(467\) 36.0000 1.66588 0.832941 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) 0 0
\(471\) 2.00000 0.0921551
\(472\) −12.0000 −0.552345
\(473\) 0 0
\(474\) −4.00000 −0.183726
\(475\) 0 0
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) −18.0000 −0.823301
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) 12.0000 0.547153
\(482\) −24.0000 −1.09317
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) −32.0000 −1.45006 −0.725029 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(488\) −2.00000 −0.0905357
\(489\) 2.00000 0.0904431
\(490\) 0 0
\(491\) −4.00000 −0.180517 −0.0902587 0.995918i \(-0.528769\pi\)
−0.0902587 + 0.995918i \(0.528769\pi\)
\(492\) 10.0000 0.450835
\(493\) 16.0000 0.720604
\(494\) 4.00000 0.179969
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) −12.0000 −0.537733
\(499\) −12.0000 −0.537194 −0.268597 0.963253i \(-0.586560\pi\)
−0.268597 + 0.963253i \(0.586560\pi\)
\(500\) 0 0
\(501\) −2.00000 −0.0893534
\(502\) −24.0000 −1.07117
\(503\) −26.0000 −1.15928 −0.579641 0.814872i \(-0.696807\pi\)
−0.579641 + 0.814872i \(0.696807\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −9.00000 −0.399704
\(508\) 8.00000 0.354943
\(509\) 14.0000 0.620539 0.310270 0.950649i \(-0.399581\pi\)
0.310270 + 0.950649i \(0.399581\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 2.00000 0.0883022
\(514\) 30.0000 1.32324
\(515\) 0 0
\(516\) 2.00000 0.0880451
\(517\) 0 0
\(518\) 0 0
\(519\) 12.0000 0.526742
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 8.00000 0.350150
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) 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
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) −20.0000 −0.866296
\(534\) 14.0000 0.605839
\(535\) 0 0
\(536\) 14.0000 0.604708
\(537\) −12.0000 −0.517838
\(538\) −30.0000 −1.29339
\(539\) 0 0
\(540\) 0 0
\(541\) −30.0000 −1.28980 −0.644900 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) 20.0000 0.859074
\(543\) 2.00000 0.0858282
\(544\) 2.00000 0.0857493
\(545\) 0 0
\(546\) 0 0
\(547\) 26.0000 1.11168 0.555840 0.831289i \(-0.312397\pi\)
0.555840 + 0.831289i \(0.312397\pi\)
\(548\) −2.00000 −0.0854358
\(549\) 2.00000 0.0853579
\(550\) 0 0
\(551\) −16.0000 −0.681623
\(552\) −8.00000 −0.340503
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) 22.0000 0.933008
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) −4.00000 −0.169334
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 0 0
\(562\) −18.0000 −0.759284
\(563\) −24.0000 −1.01148 −0.505740 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) −6.00000 −0.252646
\(565\) 0 0
\(566\) 20.0000 0.840663
\(567\) 0 0
\(568\) −6.00000 −0.251754
\(569\) 10.0000 0.419222 0.209611 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 0 0
\(573\) 22.0000 0.919063
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 26.0000 1.08239 0.541197 0.840896i \(-0.317971\pi\)
0.541197 + 0.840896i \(0.317971\pi\)
\(578\) 13.0000 0.540729
\(579\) −20.0000 −0.831172
\(580\) 0 0
\(581\) 0 0
\(582\) −14.0000 −0.580319
\(583\) 0 0
\(584\) 10.0000 0.413803
\(585\) 0 0
\(586\) −24.0000 −0.991431
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 8.00000 0.329634
\(590\) 0 0
\(591\) −6.00000 −0.246807
\(592\) −6.00000 −0.246598
\(593\) 14.0000 0.574911 0.287456 0.957794i \(-0.407191\pi\)
0.287456 + 0.957794i \(0.407191\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 20.0000 0.819232
\(597\) 16.0000 0.654836
\(598\) 16.0000 0.654289
\(599\) −34.0000 −1.38920 −0.694601 0.719395i \(-0.744419\pi\)
−0.694601 + 0.719395i \(0.744419\pi\)
\(600\) 0 0
\(601\) 8.00000 0.326327 0.163163 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) 0 0
\(603\) −14.0000 −0.570124
\(604\) 20.0000 0.813788
\(605\) 0 0
\(606\) 6.00000 0.243733
\(607\) 12.0000 0.487065 0.243532 0.969893i \(-0.421694\pi\)
0.243532 + 0.969893i \(0.421694\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) −2.00000 −0.0808452
\(613\) 10.0000 0.403896 0.201948 0.979396i \(-0.435273\pi\)
0.201948 + 0.979396i \(0.435273\pi\)
\(614\) 12.0000 0.484281
\(615\) 0 0
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 4.00000 0.160904
\(619\) −22.0000 −0.884255 −0.442127 0.896952i \(-0.645776\pi\)
−0.442127 + 0.896952i \(0.645776\pi\)
\(620\) 0 0
\(621\) 8.00000 0.321029
\(622\) −8.00000 −0.320771
\(623\) 0 0
\(624\) −2.00000 −0.0800641
\(625\) 0 0
\(626\) 6.00000 0.239808
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −24.0000 −0.955425 −0.477712 0.878516i \(-0.658534\pi\)
−0.477712 + 0.878516i \(0.658534\pi\)
\(632\) −4.00000 −0.159111
\(633\) −4.00000 −0.158986
\(634\) −34.0000 −1.35031
\(635\) 0 0
\(636\) 6.00000 0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) −42.0000 −1.65890 −0.829450 0.558581i \(-0.811346\pi\)
−0.829450 + 0.558581i \(0.811346\pi\)
\(642\) 0 0
\(643\) 36.0000 1.41970 0.709851 0.704352i \(-0.248762\pi\)
0.709851 + 0.704352i \(0.248762\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 4.00000 0.157378
\(647\) −14.0000 −0.550397 −0.275198 0.961387i \(-0.588744\pi\)
−0.275198 + 0.961387i \(0.588744\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 2.00000 0.0783260
\(653\) 14.0000 0.547862 0.273931 0.961749i \(-0.411676\pi\)
0.273931 + 0.961749i \(0.411676\pi\)
\(654\) 2.00000 0.0782062
\(655\) 0 0
\(656\) 10.0000 0.390434
\(657\) −10.0000 −0.390137
\(658\) 0 0
\(659\) 16.0000 0.623272 0.311636 0.950202i \(-0.399123\pi\)
0.311636 + 0.950202i \(0.399123\pi\)
\(660\) 0 0
\(661\) −22.0000 −0.855701 −0.427850 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) −28.0000 −1.08825
\(663\) 4.00000 0.155347
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) −64.0000 −2.47809
\(668\) −2.00000 −0.0773823
\(669\) 20.0000 0.773245
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −20.0000 −0.770943 −0.385472 0.922720i \(-0.625961\pi\)
−0.385472 + 0.922720i \(0.625961\pi\)
\(674\) 12.0000 0.462223
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) 12.0000 0.461197 0.230599 0.973049i \(-0.425932\pi\)
0.230599 + 0.973049i \(0.425932\pi\)
\(678\) −10.0000 −0.384048
\(679\) 0 0
\(680\) 0 0
\(681\) −16.0000 −0.613121
\(682\) 0 0
\(683\) 24.0000 0.918334 0.459167 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) 2.00000 0.0764719
\(685\) 0 0
\(686\) 0 0
\(687\) −10.0000 −0.381524
\(688\) 2.00000 0.0762493
\(689\) −12.0000 −0.457164
\(690\) 0 0
\(691\) 34.0000 1.29342 0.646710 0.762736i \(-0.276144\pi\)
0.646710 + 0.762736i \(0.276144\pi\)
\(692\) 12.0000 0.456172
\(693\) 0 0
\(694\) −28.0000 −1.06287
\(695\) 0 0
\(696\) 8.00000 0.303239
\(697\) −20.0000 −0.757554
\(698\) −30.0000 −1.13552
\(699\) −14.0000 −0.529529
\(700\) 0 0
\(701\) −8.00000 −0.302156 −0.151078 0.988522i \(-0.548274\pi\)
−0.151078 + 0.988522i \(0.548274\pi\)
\(702\) 2.00000 0.0754851
\(703\) −12.0000 −0.452589
\(704\) 0 0
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) 12.0000 0.450988
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 0 0
\(711\) 4.00000 0.150012
\(712\) 14.0000 0.524672
\(713\) 32.0000 1.19841
\(714\) 0 0
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) 18.0000 0.672222
\(718\) 14.0000 0.522475
\(719\) 8.00000 0.298350 0.149175 0.988811i \(-0.452338\pi\)
0.149175 + 0.988811i \(0.452338\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 15.0000 0.558242
\(723\) 24.0000 0.892570
\(724\) 2.00000 0.0743294
\(725\) 0 0
\(726\) 11.0000 0.408248
\(727\) −36.0000 −1.33517 −0.667583 0.744535i \(-0.732671\pi\)
−0.667583 + 0.744535i \(0.732671\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −4.00000 −0.147945
\(732\) 2.00000 0.0739221
\(733\) −2.00000 −0.0738717 −0.0369358 0.999318i \(-0.511760\pi\)
−0.0369358 + 0.999318i \(0.511760\pi\)
\(734\) 16.0000 0.590571
\(735\) 0 0
\(736\) −8.00000 −0.294884
\(737\) 0 0
\(738\) −10.0000 −0.368105
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) 0 0
\(741\) −4.00000 −0.146944
\(742\) 0 0
\(743\) −32.0000 −1.17397 −0.586983 0.809599i \(-0.699684\pi\)
−0.586983 + 0.809599i \(0.699684\pi\)
\(744\) −4.00000 −0.146647
\(745\) 0 0
\(746\) 22.0000 0.805477
\(747\) 12.0000 0.439057
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −24.0000 −0.875772 −0.437886 0.899030i \(-0.644273\pi\)
−0.437886 + 0.899030i \(0.644273\pi\)
\(752\) −6.00000 −0.218797
\(753\) 24.0000 0.874609
\(754\) −16.0000 −0.582686
\(755\) 0 0
\(756\) 0 0
\(757\) 34.0000 1.23575 0.617876 0.786276i \(-0.287994\pi\)
0.617876 + 0.786276i \(0.287994\pi\)
\(758\) −12.0000 −0.435860
\(759\) 0 0
\(760\) 0 0
\(761\) −34.0000 −1.23250 −0.616250 0.787551i \(-0.711349\pi\)
−0.616250 + 0.787551i \(0.711349\pi\)
\(762\) −8.00000 −0.289809
\(763\) 0 0
\(764\) 22.0000 0.795932
\(765\) 0 0
\(766\) −26.0000 −0.939418
\(767\) −24.0000 −0.866590
\(768\) 1.00000 0.0360844
\(769\) −20.0000 −0.721218 −0.360609 0.932717i \(-0.617431\pi\)
−0.360609 + 0.932717i \(0.617431\pi\)
\(770\) 0 0
\(771\) −30.0000 −1.08042
\(772\) −20.0000 −0.719816
\(773\) 24.0000 0.863220 0.431610 0.902060i \(-0.357946\pi\)
0.431610 + 0.902060i \(0.357946\pi\)
\(774\) −2.00000 −0.0718885
\(775\) 0 0
\(776\) −14.0000 −0.502571
\(777\) 0 0
\(778\) 4.00000 0.143407
\(779\) 20.0000 0.716574
\(780\) 0 0
\(781\) 0 0
\(782\) 16.0000 0.572159
\(783\) −8.00000 −0.285897
\(784\) 0 0
\(785\) 0 0
\(786\) −8.00000 −0.285351
\(787\) 28.0000 0.998092 0.499046 0.866575i \(-0.333684\pi\)
0.499046 + 0.866575i \(0.333684\pi\)
\(788\) −6.00000 −0.213741
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −4.00000 −0.142044
\(794\) −38.0000 −1.34857
\(795\) 0 0
\(796\) 16.0000 0.567105
\(797\) 20.0000 0.708436 0.354218 0.935163i \(-0.384747\pi\)
0.354218 + 0.935163i \(0.384747\pi\)
\(798\) 0 0
\(799\) 12.0000 0.424529
\(800\) 0 0
\(801\) −14.0000 −0.494666
\(802\) −10.0000 −0.353112
\(803\) 0 0
\(804\) −14.0000 −0.493742
\(805\) 0 0
\(806\) 8.00000 0.281788
\(807\) 30.0000 1.05605
\(808\) 6.00000 0.211079
\(809\) 18.0000 0.632846 0.316423 0.948618i \(-0.397518\pi\)
0.316423 + 0.948618i \(0.397518\pi\)
\(810\) 0 0
\(811\) 22.0000 0.772524 0.386262 0.922389i \(-0.373766\pi\)
0.386262 + 0.922389i \(0.373766\pi\)
\(812\) 0 0
\(813\) −20.0000 −0.701431
\(814\) 0 0
\(815\) 0 0
\(816\) −2.00000 −0.0700140
\(817\) 4.00000 0.139942
\(818\) −24.0000 −0.839140
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 2.00000 0.0697580
\(823\) −4.00000 −0.139431 −0.0697156 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) 4.00000 0.139347
\(825\) 0 0
\(826\) 0 0
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 8.00000 0.278019
\(829\) 22.0000 0.764092 0.382046 0.924143i \(-0.375220\pi\)
0.382046 + 0.924143i \(0.375220\pi\)
\(830\) 0 0
\(831\) −2.00000 −0.0693792
\(832\) −2.00000 −0.0693375
\(833\) 0 0
\(834\) −22.0000 −0.761798
\(835\) 0 0
\(836\) 0 0
\(837\) 4.00000 0.138260
\(838\) −12.0000 −0.414533
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) 18.0000 0.620321
\(843\) 18.0000 0.619953
\(844\) −4.00000 −0.137686
\(845\) 0 0
\(846\) 6.00000 0.206284
\(847\) 0 0
\(848\) 6.00000 0.206041
\(849\) −20.0000 −0.686398
\(850\) 0 0
\(851\) −48.0000 −1.64542
\(852\) 6.00000 0.205557
\(853\) −10.0000 −0.342393 −0.171197 0.985237i \(-0.554763\pi\)
−0.171197 + 0.985237i \(0.554763\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 10.0000 0.341593 0.170797 0.985306i \(-0.445366\pi\)
0.170797 + 0.985306i \(0.445366\pi\)
\(858\) 0 0
\(859\) 42.0000 1.43302 0.716511 0.697576i \(-0.245738\pi\)
0.716511 + 0.697576i \(0.245738\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 10.0000 0.340601
\(863\) 32.0000 1.08929 0.544646 0.838666i \(-0.316664\pi\)
0.544646 + 0.838666i \(0.316664\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 0 0
\(866\) −14.0000 −0.475739
\(867\) −13.0000 −0.441503
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 28.0000 0.948744
\(872\) 2.00000 0.0677285
\(873\) 14.0000 0.473828
\(874\) −16.0000 −0.541208
\(875\) 0 0
\(876\) −10.0000 −0.337869
\(877\) −42.0000 −1.41824 −0.709120 0.705088i \(-0.750907\pi\)
−0.709120 + 0.705088i \(0.750907\pi\)
\(878\) 36.0000 1.21494
\(879\) 24.0000 0.809500
\(880\) 0 0
\(881\) −18.0000 −0.606435 −0.303218 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 0 0
\(883\) 10.0000 0.336527 0.168263 0.985742i \(-0.446184\pi\)
0.168263 + 0.985742i \(0.446184\pi\)
\(884\) 4.00000 0.134535
\(885\) 0 0
\(886\) 4.00000 0.134383
\(887\) 30.0000 1.00730 0.503651 0.863907i \(-0.331990\pi\)
0.503651 + 0.863907i \(0.331990\pi\)
\(888\) 6.00000 0.201347
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 20.0000 0.669650
\(893\) −12.0000 −0.401565
\(894\) −20.0000 −0.668900
\(895\) 0 0
\(896\) 0 0
\(897\) −16.0000 −0.534224
\(898\) 26.0000 0.867631
\(899\) −32.0000 −1.06726
\(900\) 0 0
\(901\) −12.0000 −0.399778
\(902\) 0 0
\(903\) 0 0
\(904\) −10.0000 −0.332595
\(905\) 0 0
\(906\) −20.0000 −0.664455
\(907\) −38.0000 −1.26177 −0.630885 0.775877i \(-0.717308\pi\)
−0.630885 + 0.775877i \(0.717308\pi\)
\(908\) −16.0000 −0.530979
\(909\) −6.00000 −0.199007
\(910\) 0 0
\(911\) 22.0000 0.728893 0.364446 0.931224i \(-0.381258\pi\)
0.364446 + 0.931224i \(0.381258\pi\)
\(912\) 2.00000 0.0662266
\(913\) 0 0
\(914\) 32.0000 1.05847
\(915\) 0 0
\(916\) −10.0000 −0.330409
\(917\) 0 0
\(918\) 2.00000 0.0660098
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) −12.0000 −0.395413
\(922\) 14.0000 0.461065
\(923\) −12.0000 −0.394985
\(924\) 0 0
\(925\) 0 0
\(926\) 4.00000 0.131448
\(927\) −4.00000 −0.131377
\(928\) 8.00000 0.262613
\(929\) 22.0000 0.721797 0.360898 0.932605i \(-0.382470\pi\)
0.360898 + 0.932605i \(0.382470\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −14.0000 −0.458585
\(933\) 8.00000 0.261908
\(934\) −36.0000 −1.17796
\(935\) 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
\(941\) 14.0000 0.456387 0.228193 0.973616i \(-0.426718\pi\)
0.228193 + 0.973616i \(0.426718\pi\)
\(942\) −2.00000 −0.0651635
\(943\) 80.0000 2.60516
\(944\) 12.0000 0.390567
\(945\) 0 0
\(946\) 0 0
\(947\) 24.0000 0.779895 0.389948 0.920837i \(-0.372493\pi\)
0.389948 + 0.920837i \(0.372493\pi\)
\(948\) 4.00000 0.129914
\(949\) 20.0000 0.649227
\(950\) 0 0
\(951\) 34.0000 1.10253
\(952\) 0 0
\(953\) 34.0000 1.10137 0.550684 0.834714i \(-0.314367\pi\)
0.550684 + 0.834714i \(0.314367\pi\)
\(954\) −6.00000 −0.194257
\(955\) 0 0
\(956\) 18.0000 0.582162
\(957\) 0 0
\(958\) −24.0000 −0.775405
\(959\) 0 0
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) −12.0000 −0.386896
\(963\) 0 0
\(964\) 24.0000 0.772988
\(965\) 0 0
\(966\) 0 0
\(967\) 32.0000 1.02905 0.514525 0.857475i \(-0.327968\pi\)
0.514525 + 0.857475i \(0.327968\pi\)
\(968\) 11.0000 0.353553
\(969\) −4.00000 −0.128499
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 1.00000 0.0320750
\(973\) 0 0
\(974\) 32.0000 1.02535
\(975\) 0 0
\(976\) 2.00000 0.0640184
\(977\) 34.0000 1.08776 0.543878 0.839164i \(-0.316955\pi\)
0.543878 + 0.839164i \(0.316955\pi\)
\(978\) −2.00000 −0.0639529
\(979\) 0 0
\(980\) 0 0
\(981\) −2.00000 −0.0638551
\(982\) 4.00000 0.127645
\(983\) 18.0000 0.574111 0.287055 0.957914i \(-0.407324\pi\)
0.287055 + 0.957914i \(0.407324\pi\)
\(984\) −10.0000 −0.318788
\(985\) 0 0
\(986\) −16.0000 −0.509544
\(987\) 0 0
\(988\) −4.00000 −0.127257
\(989\) 16.0000 0.508770
\(990\) 0 0
\(991\) 16.0000 0.508257 0.254128 0.967170i \(-0.418211\pi\)
0.254128 + 0.967170i \(0.418211\pi\)
\(992\) −4.00000 −0.127000
\(993\) 28.0000 0.888553
\(994\) 0 0
\(995\) 0 0
\(996\) 12.0000 0.380235
\(997\) 6.00000 0.190022 0.0950110 0.995476i \(-0.469711\pi\)
0.0950110 + 0.995476i \(0.469711\pi\)
\(998\) 12.0000 0.379853
\(999\) −6.00000 −0.189832
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.bc.1.1 1
5.2 odd 4 1470.2.g.c.589.1 2
5.3 odd 4 1470.2.g.c.589.2 yes 2
5.4 even 2 7350.2.a.bx.1.1 1
7.6 odd 2 7350.2.a.m.1.1 1
35.2 odd 12 1470.2.n.e.949.1 4
35.3 even 12 1470.2.n.d.79.1 4
35.12 even 12 1470.2.n.d.949.1 4
35.13 even 4 1470.2.g.d.589.2 yes 2
35.17 even 12 1470.2.n.d.79.2 4
35.18 odd 12 1470.2.n.e.79.1 4
35.23 odd 12 1470.2.n.e.949.2 4
35.27 even 4 1470.2.g.d.589.1 yes 2
35.32 odd 12 1470.2.n.e.79.2 4
35.33 even 12 1470.2.n.d.949.2 4
35.34 odd 2 7350.2.a.cr.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1470.2.g.c.589.1 2 5.2 odd 4
1470.2.g.c.589.2 yes 2 5.3 odd 4
1470.2.g.d.589.1 yes 2 35.27 even 4
1470.2.g.d.589.2 yes 2 35.13 even 4
1470.2.n.d.79.1 4 35.3 even 12
1470.2.n.d.79.2 4 35.17 even 12
1470.2.n.d.949.1 4 35.12 even 12
1470.2.n.d.949.2 4 35.33 even 12
1470.2.n.e.79.1 4 35.18 odd 12
1470.2.n.e.79.2 4 35.32 odd 12
1470.2.n.e.949.1 4 35.2 odd 12
1470.2.n.e.949.2 4 35.23 odd 12
7350.2.a.m.1.1 1 7.6 odd 2
7350.2.a.bc.1.1 1 1.1 even 1 trivial
7350.2.a.bx.1.1 1 5.4 even 2
7350.2.a.cr.1.1 1 35.34 odd 2