Properties

Label 7350.2.a.a.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

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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: \(0\)
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

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -5.00000 q^{11} -1.00000 q^{12} -5.00000 q^{13} +1.00000 q^{16} -4.00000 q^{17} -1.00000 q^{18} +7.00000 q^{19} +5.00000 q^{22} -1.00000 q^{23} +1.00000 q^{24} +5.00000 q^{26} -1.00000 q^{27} +2.00000 q^{31} -1.00000 q^{32} +5.00000 q^{33} +4.00000 q^{34} +1.00000 q^{36} -1.00000 q^{37} -7.00000 q^{38} +5.00000 q^{39} -5.00000 q^{41} -12.0000 q^{43} -5.00000 q^{44} +1.00000 q^{46} -11.0000 q^{47} -1.00000 q^{48} +4.00000 q^{51} -5.00000 q^{52} +9.00000 q^{53} +1.00000 q^{54} -7.00000 q^{57} -4.00000 q^{59} -4.00000 q^{61} -2.00000 q^{62} +1.00000 q^{64} -5.00000 q^{66} +12.0000 q^{67} -4.00000 q^{68} +1.00000 q^{69} +2.00000 q^{71} -1.00000 q^{72} +10.0000 q^{73} +1.00000 q^{74} +7.00000 q^{76} -5.00000 q^{78} -12.0000 q^{79} +1.00000 q^{81} +5.00000 q^{82} -12.0000 q^{83} +12.0000 q^{86} +5.00000 q^{88} -14.0000 q^{89} -1.00000 q^{92} -2.00000 q^{93} +11.0000 q^{94} +1.00000 q^{96} -8.00000 q^{97} -5.00000 q^{99} +O(q^{100})\)

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
\(11\) −5.00000 −1.50756 −0.753778 0.657129i \(-0.771771\pi\)
−0.753778 + 0.657129i \(0.771771\pi\)
\(12\) −1.00000 −0.288675
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −4.00000 −0.970143 −0.485071 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) −1.00000 −0.235702
\(19\) 7.00000 1.60591 0.802955 0.596040i \(-0.203260\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 5.00000 1.06600
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) 1.00000 0.204124
\(25\) 0 0
\(26\) 5.00000 0.980581
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.00000 0.870388
\(34\) 4.00000 0.685994
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) −7.00000 −1.13555
\(39\) 5.00000 0.800641
\(40\) 0 0
\(41\) −5.00000 −0.780869 −0.390434 0.920631i \(-0.627675\pi\)
−0.390434 + 0.920631i \(0.627675\pi\)
\(42\) 0 0
\(43\) −12.0000 −1.82998 −0.914991 0.403473i \(-0.867803\pi\)
−0.914991 + 0.403473i \(0.867803\pi\)
\(44\) −5.00000 −0.753778
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) −11.0000 −1.60451 −0.802257 0.596978i \(-0.796368\pi\)
−0.802257 + 0.596978i \(0.796368\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 0 0
\(51\) 4.00000 0.560112
\(52\) −5.00000 −0.693375
\(53\) 9.00000 1.23625 0.618123 0.786082i \(-0.287894\pi\)
0.618123 + 0.786082i \(0.287894\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) 0 0
\(57\) −7.00000 −0.927173
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −4.00000 −0.512148 −0.256074 0.966657i \(-0.582429\pi\)
−0.256074 + 0.966657i \(0.582429\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −5.00000 −0.615457
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) −4.00000 −0.485071
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −1.00000 −0.117851
\(73\) 10.0000 1.17041 0.585206 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) 7.00000 0.802955
\(77\) 0 0
\(78\) −5.00000 −0.566139
\(79\) −12.0000 −1.35011 −0.675053 0.737769i \(-0.735879\pi\)
−0.675053 + 0.737769i \(0.735879\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 5.00000 0.552158
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 12.0000 1.29399
\(87\) 0 0
\(88\) 5.00000 0.533002
\(89\) −14.0000 −1.48400 −0.741999 0.670402i \(-0.766122\pi\)
−0.741999 + 0.670402i \(0.766122\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.00000 −0.104257
\(93\) −2.00000 −0.207390
\(94\) 11.0000 1.13456
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −8.00000 −0.812277 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) 0 0
\(99\) −5.00000 −0.502519
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) −4.00000 −0.396059
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 5.00000 0.490290
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) 2.00000 0.193347 0.0966736 0.995316i \(-0.469180\pi\)
0.0966736 + 0.995316i \(0.469180\pi\)
\(108\) −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
\(111\) 1.00000 0.0949158
\(112\) 0 0
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 7.00000 0.655610
\(115\) 0 0
\(116\) 0 0
\(117\) −5.00000 −0.462250
\(118\) 4.00000 0.368230
\(119\) 0 0
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 4.00000 0.362143
\(123\) 5.00000 0.450835
\(124\) 2.00000 0.179605
\(125\) 0 0
\(126\) 0 0
\(127\) −9.00000 −0.798621 −0.399310 0.916816i \(-0.630750\pi\)
−0.399310 + 0.916816i \(0.630750\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 12.0000 1.05654
\(130\) 0 0
\(131\) 9.00000 0.786334 0.393167 0.919467i \(-0.371379\pi\)
0.393167 + 0.919467i \(0.371379\pi\)
\(132\) 5.00000 0.435194
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) 4.00000 0.342997
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) −1.00000 −0.0851257
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 11.0000 0.926367
\(142\) −2.00000 −0.167836
\(143\) 25.0000 2.09061
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −10.0000 −0.827606
\(147\) 0 0
\(148\) −1.00000 −0.0821995
\(149\) 12.0000 0.983078 0.491539 0.870855i \(-0.336434\pi\)
0.491539 + 0.870855i \(0.336434\pi\)
\(150\) 0 0
\(151\) 14.0000 1.13930 0.569652 0.821886i \(-0.307078\pi\)
0.569652 + 0.821886i \(0.307078\pi\)
\(152\) −7.00000 −0.567775
\(153\) −4.00000 −0.323381
\(154\) 0 0
\(155\) 0 0
\(156\) 5.00000 0.400320
\(157\) 11.0000 0.877896 0.438948 0.898513i \(-0.355351\pi\)
0.438948 + 0.898513i \(0.355351\pi\)
\(158\) 12.0000 0.954669
\(159\) −9.00000 −0.713746
\(160\) 0 0
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 24.0000 1.87983 0.939913 0.341415i \(-0.110906\pi\)
0.939913 + 0.341415i \(0.110906\pi\)
\(164\) −5.00000 −0.390434
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 11.0000 0.851206 0.425603 0.904910i \(-0.360062\pi\)
0.425603 + 0.904910i \(0.360062\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 7.00000 0.535303
\(172\) −12.0000 −0.914991
\(173\) −13.0000 −0.988372 −0.494186 0.869356i \(-0.664534\pi\)
−0.494186 + 0.869356i \(0.664534\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −5.00000 −0.376889
\(177\) 4.00000 0.300658
\(178\) 14.0000 1.04934
\(179\) −23.0000 −1.71910 −0.859550 0.511051i \(-0.829256\pi\)
−0.859550 + 0.511051i \(0.829256\pi\)
\(180\) 0 0
\(181\) −20.0000 −1.48659 −0.743294 0.668965i \(-0.766738\pi\)
−0.743294 + 0.668965i \(0.766738\pi\)
\(182\) 0 0
\(183\) 4.00000 0.295689
\(184\) 1.00000 0.0737210
\(185\) 0 0
\(186\) 2.00000 0.146647
\(187\) 20.0000 1.46254
\(188\) −11.0000 −0.802257
\(189\) 0 0
\(190\) 0 0
\(191\) 14.0000 1.01300 0.506502 0.862239i \(-0.330938\pi\)
0.506502 + 0.862239i \(0.330938\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −10.0000 −0.719816 −0.359908 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) 8.00000 0.574367
\(195\) 0 0
\(196\) 0 0
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 5.00000 0.355335
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 0 0
\(201\) −12.0000 −0.846415
\(202\) 0 0
\(203\) 0 0
\(204\) 4.00000 0.280056
\(205\) 0 0
\(206\) −8.00000 −0.557386
\(207\) −1.00000 −0.0695048
\(208\) −5.00000 −0.346688
\(209\) −35.0000 −2.42100
\(210\) 0 0
\(211\) 17.0000 1.17033 0.585164 0.810915i \(-0.301030\pi\)
0.585164 + 0.810915i \(0.301030\pi\)
\(212\) 9.00000 0.618123
\(213\) −2.00000 −0.137038
\(214\) −2.00000 −0.136717
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) −10.0000 −0.675737
\(220\) 0 0
\(221\) 20.0000 1.34535
\(222\) −1.00000 −0.0671156
\(223\) −12.0000 −0.803579 −0.401790 0.915732i \(-0.631612\pi\)
−0.401790 + 0.915732i \(0.631612\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −14.0000 −0.931266
\(227\) −12.0000 −0.796468 −0.398234 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) −7.00000 −0.463586
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.0000 0.917170 0.458585 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) 5.00000 0.326860
\(235\) 0 0
\(236\) −4.00000 −0.260378
\(237\) 12.0000 0.779484
\(238\) 0 0
\(239\) −22.0000 −1.42306 −0.711531 0.702655i \(-0.751998\pi\)
−0.711531 + 0.702655i \(0.751998\pi\)
\(240\) 0 0
\(241\) −15.0000 −0.966235 −0.483117 0.875556i \(-0.660496\pi\)
−0.483117 + 0.875556i \(0.660496\pi\)
\(242\) −14.0000 −0.899954
\(243\) −1.00000 −0.0641500
\(244\) −4.00000 −0.256074
\(245\) 0 0
\(246\) −5.00000 −0.318788
\(247\) −35.0000 −2.22700
\(248\) −2.00000 −0.127000
\(249\) 12.0000 0.760469
\(250\) 0 0
\(251\) −1.00000 −0.0631194 −0.0315597 0.999502i \(-0.510047\pi\)
−0.0315597 + 0.999502i \(0.510047\pi\)
\(252\) 0 0
\(253\) 5.00000 0.314347
\(254\) 9.00000 0.564710
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −16.0000 −0.998053 −0.499026 0.866587i \(-0.666309\pi\)
−0.499026 + 0.866587i \(0.666309\pi\)
\(258\) −12.0000 −0.747087
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −9.00000 −0.556022
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) −5.00000 −0.307729
\(265\) 0 0
\(266\) 0 0
\(267\) 14.0000 0.856786
\(268\) 12.0000 0.733017
\(269\) 24.0000 1.46331 0.731653 0.681677i \(-0.238749\pi\)
0.731653 + 0.681677i \(0.238749\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) −4.00000 −0.242536
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 0 0
\(276\) 1.00000 0.0601929
\(277\) −14.0000 −0.841178 −0.420589 0.907251i \(-0.638177\pi\)
−0.420589 + 0.907251i \(0.638177\pi\)
\(278\) −4.00000 −0.239904
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) 7.00000 0.417585 0.208792 0.977960i \(-0.433047\pi\)
0.208792 + 0.977960i \(0.433047\pi\)
\(282\) −11.0000 −0.655040
\(283\) −10.0000 −0.594438 −0.297219 0.954809i \(-0.596059\pi\)
−0.297219 + 0.954809i \(0.596059\pi\)
\(284\) 2.00000 0.118678
\(285\) 0 0
\(286\) −25.0000 −1.47828
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 8.00000 0.468968
\(292\) 10.0000 0.585206
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.00000 0.0581238
\(297\) 5.00000 0.290129
\(298\) −12.0000 −0.695141
\(299\) 5.00000 0.289157
\(300\) 0 0
\(301\) 0 0
\(302\) −14.0000 −0.805609
\(303\) 0 0
\(304\) 7.00000 0.401478
\(305\) 0 0
\(306\) 4.00000 0.228665
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) −5.00000 −0.283069
\(313\) 16.0000 0.904373 0.452187 0.891923i \(-0.350644\pi\)
0.452187 + 0.891923i \(0.350644\pi\)
\(314\) −11.0000 −0.620766
\(315\) 0 0
\(316\) −12.0000 −0.675053
\(317\) 22.0000 1.23564 0.617822 0.786318i \(-0.288015\pi\)
0.617822 + 0.786318i \(0.288015\pi\)
\(318\) 9.00000 0.504695
\(319\) 0 0
\(320\) 0 0
\(321\) −2.00000 −0.111629
\(322\) 0 0
\(323\) −28.0000 −1.55796
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −24.0000 −1.32924
\(327\) 2.00000 0.110600
\(328\) 5.00000 0.276079
\(329\) 0 0
\(330\) 0 0
\(331\) 31.0000 1.70391 0.851957 0.523612i \(-0.175416\pi\)
0.851957 + 0.523612i \(0.175416\pi\)
\(332\) −12.0000 −0.658586
\(333\) −1.00000 −0.0547997
\(334\) −11.0000 −0.601893
\(335\) 0 0
\(336\) 0 0
\(337\) 16.0000 0.871576 0.435788 0.900049i \(-0.356470\pi\)
0.435788 + 0.900049i \(0.356470\pi\)
\(338\) −12.0000 −0.652714
\(339\) −14.0000 −0.760376
\(340\) 0 0
\(341\) −10.0000 −0.541530
\(342\) −7.00000 −0.378517
\(343\) 0 0
\(344\) 12.0000 0.646997
\(345\) 0 0
\(346\) 13.0000 0.698884
\(347\) 18.0000 0.966291 0.483145 0.875540i \(-0.339494\pi\)
0.483145 + 0.875540i \(0.339494\pi\)
\(348\) 0 0
\(349\) 4.00000 0.214115 0.107058 0.994253i \(-0.465857\pi\)
0.107058 + 0.994253i \(0.465857\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 5.00000 0.266501
\(353\) 24.0000 1.27739 0.638696 0.769460i \(-0.279474\pi\)
0.638696 + 0.769460i \(0.279474\pi\)
\(354\) −4.00000 −0.212598
\(355\) 0 0
\(356\) −14.0000 −0.741999
\(357\) 0 0
\(358\) 23.0000 1.21559
\(359\) −20.0000 −1.05556 −0.527780 0.849381i \(-0.676975\pi\)
−0.527780 + 0.849381i \(0.676975\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) 20.0000 1.05118
\(363\) −14.0000 −0.734809
\(364\) 0 0
\(365\) 0 0
\(366\) −4.00000 −0.209083
\(367\) 7.00000 0.365397 0.182699 0.983169i \(-0.441517\pi\)
0.182699 + 0.983169i \(0.441517\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −5.00000 −0.260290
\(370\) 0 0
\(371\) 0 0
\(372\) −2.00000 −0.103695
\(373\) 22.0000 1.13912 0.569558 0.821951i \(-0.307114\pi\)
0.569558 + 0.821951i \(0.307114\pi\)
\(374\) −20.0000 −1.03418
\(375\) 0 0
\(376\) 11.0000 0.567282
\(377\) 0 0
\(378\) 0 0
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) 0 0
\(381\) 9.00000 0.461084
\(382\) −14.0000 −0.716302
\(383\) 21.0000 1.07305 0.536525 0.843884i \(-0.319737\pi\)
0.536525 + 0.843884i \(0.319737\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) −12.0000 −0.609994
\(388\) −8.00000 −0.406138
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 0 0
\(393\) −9.00000 −0.453990
\(394\) −3.00000 −0.151138
\(395\) 0 0
\(396\) −5.00000 −0.251259
\(397\) −14.0000 −0.702640 −0.351320 0.936255i \(-0.614267\pi\)
−0.351320 + 0.936255i \(0.614267\pi\)
\(398\) −4.00000 −0.200502
\(399\) 0 0
\(400\) 0 0
\(401\) −21.0000 −1.04869 −0.524345 0.851506i \(-0.675690\pi\)
−0.524345 + 0.851506i \(0.675690\pi\)
\(402\) 12.0000 0.598506
\(403\) −10.0000 −0.498135
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.00000 0.247841
\(408\) −4.00000 −0.198030
\(409\) −10.0000 −0.494468 −0.247234 0.968956i \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) 0 0
\(411\) −2.00000 −0.0986527
\(412\) 8.00000 0.394132
\(413\) 0 0
\(414\) 1.00000 0.0491473
\(415\) 0 0
\(416\) 5.00000 0.245145
\(417\) −4.00000 −0.195881
\(418\) 35.0000 1.71191
\(419\) −15.0000 −0.732798 −0.366399 0.930458i \(-0.619409\pi\)
−0.366399 + 0.930458i \(0.619409\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) −17.0000 −0.827547
\(423\) −11.0000 −0.534838
\(424\) −9.00000 −0.437079
\(425\) 0 0
\(426\) 2.00000 0.0969003
\(427\) 0 0
\(428\) 2.00000 0.0966736
\(429\) −25.0000 −1.20701
\(430\) 0 0
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 24.0000 1.15337 0.576683 0.816968i \(-0.304347\pi\)
0.576683 + 0.816968i \(0.304347\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2.00000 −0.0957826
\(437\) −7.00000 −0.334855
\(438\) 10.0000 0.477818
\(439\) 40.0000 1.90910 0.954548 0.298057i \(-0.0963387\pi\)
0.954548 + 0.298057i \(0.0963387\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −20.0000 −0.951303
\(443\) 28.0000 1.33032 0.665160 0.746701i \(-0.268363\pi\)
0.665160 + 0.746701i \(0.268363\pi\)
\(444\) 1.00000 0.0474579
\(445\) 0 0
\(446\) 12.0000 0.568216
\(447\) −12.0000 −0.567581
\(448\) 0 0
\(449\) −29.0000 −1.36859 −0.684297 0.729203i \(-0.739891\pi\)
−0.684297 + 0.729203i \(0.739891\pi\)
\(450\) 0 0
\(451\) 25.0000 1.17720
\(452\) 14.0000 0.658505
\(453\) −14.0000 −0.657777
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 7.00000 0.327805
\(457\) 14.0000 0.654892 0.327446 0.944870i \(-0.393812\pi\)
0.327446 + 0.944870i \(0.393812\pi\)
\(458\) 10.0000 0.467269
\(459\) 4.00000 0.186704
\(460\) 0 0
\(461\) 4.00000 0.186299 0.0931493 0.995652i \(-0.470307\pi\)
0.0931493 + 0.995652i \(0.470307\pi\)
\(462\) 0 0
\(463\) 19.0000 0.883005 0.441502 0.897260i \(-0.354446\pi\)
0.441502 + 0.897260i \(0.354446\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −14.0000 −0.648537
\(467\) −20.0000 −0.925490 −0.462745 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) −5.00000 −0.231125
\(469\) 0 0
\(470\) 0 0
\(471\) −11.0000 −0.506853
\(472\) 4.00000 0.184115
\(473\) 60.0000 2.75880
\(474\) −12.0000 −0.551178
\(475\) 0 0
\(476\) 0 0
\(477\) 9.00000 0.412082
\(478\) 22.0000 1.00626
\(479\) −18.0000 −0.822441 −0.411220 0.911536i \(-0.634897\pi\)
−0.411220 + 0.911536i \(0.634897\pi\)
\(480\) 0 0
\(481\) 5.00000 0.227980
\(482\) 15.0000 0.683231
\(483\) 0 0
\(484\) 14.0000 0.636364
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 4.00000 0.181071
\(489\) −24.0000 −1.08532
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 5.00000 0.225417
\(493\) 0 0
\(494\) 35.0000 1.57472
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) −12.0000 −0.537733
\(499\) 40.0000 1.79065 0.895323 0.445418i \(-0.146945\pi\)
0.895323 + 0.445418i \(0.146945\pi\)
\(500\) 0 0
\(501\) −11.0000 −0.491444
\(502\) 1.00000 0.0446322
\(503\) −20.0000 −0.891756 −0.445878 0.895094i \(-0.647108\pi\)
−0.445878 + 0.895094i \(0.647108\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −5.00000 −0.222277
\(507\) −12.0000 −0.532939
\(508\) −9.00000 −0.399310
\(509\) 10.0000 0.443242 0.221621 0.975133i \(-0.428865\pi\)
0.221621 + 0.975133i \(0.428865\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −7.00000 −0.309058
\(514\) 16.0000 0.705730
\(515\) 0 0
\(516\) 12.0000 0.528271
\(517\) 55.0000 2.41890
\(518\) 0 0
\(519\) 13.0000 0.570637
\(520\) 0 0
\(521\) 33.0000 1.44576 0.722878 0.690976i \(-0.242819\pi\)
0.722878 + 0.690976i \(0.242819\pi\)
\(522\) 0 0
\(523\) −22.0000 −0.961993 −0.480996 0.876723i \(-0.659725\pi\)
−0.480996 + 0.876723i \(0.659725\pi\)
\(524\) 9.00000 0.393167
\(525\) 0 0
\(526\) 0 0
\(527\) −8.00000 −0.348485
\(528\) 5.00000 0.217597
\(529\) −22.0000 −0.956522
\(530\) 0 0
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) 25.0000 1.08287
\(534\) −14.0000 −0.605839
\(535\) 0 0
\(536\) −12.0000 −0.518321
\(537\) 23.0000 0.992523
\(538\) −24.0000 −1.03471
\(539\) 0 0
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 0 0
\(543\) 20.0000 0.858282
\(544\) 4.00000 0.171499
\(545\) 0 0
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 2.00000 0.0854358
\(549\) −4.00000 −0.170716
\(550\) 0 0
\(551\) 0 0
\(552\) −1.00000 −0.0425628
\(553\) 0 0
\(554\) 14.0000 0.594803
\(555\) 0 0
\(556\) 4.00000 0.169638
\(557\) −37.0000 −1.56774 −0.783870 0.620925i \(-0.786757\pi\)
−0.783870 + 0.620925i \(0.786757\pi\)
\(558\) −2.00000 −0.0846668
\(559\) 60.0000 2.53773
\(560\) 0 0
\(561\) −20.0000 −0.844401
\(562\) −7.00000 −0.295277
\(563\) −18.0000 −0.758610 −0.379305 0.925272i \(-0.623837\pi\)
−0.379305 + 0.925272i \(0.623837\pi\)
\(564\) 11.0000 0.463184
\(565\) 0 0
\(566\) 10.0000 0.420331
\(567\) 0 0
\(568\) −2.00000 −0.0839181
\(569\) 39.0000 1.63497 0.817483 0.575953i \(-0.195369\pi\)
0.817483 + 0.575953i \(0.195369\pi\)
\(570\) 0 0
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) 25.0000 1.04530
\(573\) −14.0000 −0.584858
\(574\) 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 \(0.317971\pi\)
\(578\) 1.00000 0.0415945
\(579\) 10.0000 0.415586
\(580\) 0 0
\(581\) 0 0
\(582\) −8.00000 −0.331611
\(583\) −45.0000 −1.86371
\(584\) −10.0000 −0.413803
\(585\) 0 0
\(586\) −9.00000 −0.371787
\(587\) −30.0000 −1.23823 −0.619116 0.785299i \(-0.712509\pi\)
−0.619116 + 0.785299i \(0.712509\pi\)
\(588\) 0 0
\(589\) 14.0000 0.576860
\(590\) 0 0
\(591\) −3.00000 −0.123404
\(592\) −1.00000 −0.0410997
\(593\) 36.0000 1.47834 0.739171 0.673517i \(-0.235217\pi\)
0.739171 + 0.673517i \(0.235217\pi\)
\(594\) −5.00000 −0.205152
\(595\) 0 0
\(596\) 12.0000 0.491539
\(597\) −4.00000 −0.163709
\(598\) −5.00000 −0.204465
\(599\) −10.0000 −0.408589 −0.204294 0.978909i \(-0.565490\pi\)
−0.204294 + 0.978909i \(0.565490\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 14.0000 0.569652
\(605\) 0 0
\(606\) 0 0
\(607\) −27.0000 −1.09590 −0.547948 0.836512i \(-0.684591\pi\)
−0.547948 + 0.836512i \(0.684591\pi\)
\(608\) −7.00000 −0.283887
\(609\) 0 0
\(610\) 0 0
\(611\) 55.0000 2.22506
\(612\) −4.00000 −0.161690
\(613\) 43.0000 1.73675 0.868377 0.495905i \(-0.165164\pi\)
0.868377 + 0.495905i \(0.165164\pi\)
\(614\) −8.00000 −0.322854
\(615\) 0 0
\(616\) 0 0
\(617\) 8.00000 0.322068 0.161034 0.986949i \(-0.448517\pi\)
0.161034 + 0.986949i \(0.448517\pi\)
\(618\) 8.00000 0.321807
\(619\) −25.0000 −1.00483 −0.502417 0.864625i \(-0.667556\pi\)
−0.502417 + 0.864625i \(0.667556\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 8.00000 0.320771
\(623\) 0 0
\(624\) 5.00000 0.200160
\(625\) 0 0
\(626\) −16.0000 −0.639489
\(627\) 35.0000 1.39777
\(628\) 11.0000 0.438948
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) 6.00000 0.238856 0.119428 0.992843i \(-0.461894\pi\)
0.119428 + 0.992843i \(0.461894\pi\)
\(632\) 12.0000 0.477334
\(633\) −17.0000 −0.675689
\(634\) −22.0000 −0.873732
\(635\) 0 0
\(636\) −9.00000 −0.356873
\(637\) 0 0
\(638\) 0 0
\(639\) 2.00000 0.0791188
\(640\) 0 0
\(641\) 21.0000 0.829450 0.414725 0.909947i \(-0.363878\pi\)
0.414725 + 0.909947i \(0.363878\pi\)
\(642\) 2.00000 0.0789337
\(643\) 34.0000 1.34083 0.670415 0.741987i \(-0.266116\pi\)
0.670415 + 0.741987i \(0.266116\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 28.0000 1.10165
\(647\) −23.0000 −0.904223 −0.452112 0.891961i \(-0.649329\pi\)
−0.452112 + 0.891961i \(0.649329\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 20.0000 0.785069
\(650\) 0 0
\(651\) 0 0
\(652\) 24.0000 0.939913
\(653\) 19.0000 0.743527 0.371764 0.928327i \(-0.378753\pi\)
0.371764 + 0.928327i \(0.378753\pi\)
\(654\) −2.00000 −0.0782062
\(655\) 0 0
\(656\) −5.00000 −0.195217
\(657\) 10.0000 0.390137
\(658\) 0 0
\(659\) −20.0000 −0.779089 −0.389545 0.921008i \(-0.627368\pi\)
−0.389545 + 0.921008i \(0.627368\pi\)
\(660\) 0 0
\(661\) 40.0000 1.55582 0.777910 0.628376i \(-0.216280\pi\)
0.777910 + 0.628376i \(0.216280\pi\)
\(662\) −31.0000 −1.20485
\(663\) −20.0000 −0.776736
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) 1.00000 0.0387492
\(667\) 0 0
\(668\) 11.0000 0.425603
\(669\) 12.0000 0.463947
\(670\) 0 0
\(671\) 20.0000 0.772091
\(672\) 0 0
\(673\) 4.00000 0.154189 0.0770943 0.997024i \(-0.475436\pi\)
0.0770943 + 0.997024i \(0.475436\pi\)
\(674\) −16.0000 −0.616297
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) 33.0000 1.26829 0.634147 0.773213i \(-0.281352\pi\)
0.634147 + 0.773213i \(0.281352\pi\)
\(678\) 14.0000 0.537667
\(679\) 0 0
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 10.0000 0.382920
\(683\) 4.00000 0.153056 0.0765279 0.997067i \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) 7.00000 0.267652
\(685\) 0 0
\(686\) 0 0
\(687\) 10.0000 0.381524
\(688\) −12.0000 −0.457496
\(689\) −45.0000 −1.71436
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) −13.0000 −0.494186
\(693\) 0 0
\(694\) −18.0000 −0.683271
\(695\) 0 0
\(696\) 0 0
\(697\) 20.0000 0.757554
\(698\) −4.00000 −0.151402
\(699\) −14.0000 −0.529529
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) −5.00000 −0.188713
\(703\) −7.00000 −0.264010
\(704\) −5.00000 −0.188445
\(705\) 0 0
\(706\) −24.0000 −0.903252
\(707\) 0 0
\(708\) 4.00000 0.150329
\(709\) 28.0000 1.05156 0.525781 0.850620i \(-0.323773\pi\)
0.525781 + 0.850620i \(0.323773\pi\)
\(710\) 0 0
\(711\) −12.0000 −0.450035
\(712\) 14.0000 0.524672
\(713\) −2.00000 −0.0749006
\(714\) 0 0
\(715\) 0 0
\(716\) −23.0000 −0.859550
\(717\) 22.0000 0.821605
\(718\) 20.0000 0.746393
\(719\) 6.00000 0.223762 0.111881 0.993722i \(-0.464312\pi\)
0.111881 + 0.993722i \(0.464312\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −30.0000 −1.11648
\(723\) 15.0000 0.557856
\(724\) −20.0000 −0.743294
\(725\) 0 0
\(726\) 14.0000 0.519589
\(727\) −3.00000 −0.111264 −0.0556319 0.998451i \(-0.517717\pi\)
−0.0556319 + 0.998451i \(0.517717\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 48.0000 1.77534
\(732\) 4.00000 0.147844
\(733\) 9.00000 0.332423 0.166211 0.986090i \(-0.446847\pi\)
0.166211 + 0.986090i \(0.446847\pi\)
\(734\) −7.00000 −0.258375
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) −60.0000 −2.21013
\(738\) 5.00000 0.184053
\(739\) −15.0000 −0.551784 −0.275892 0.961189i \(-0.588973\pi\)
−0.275892 + 0.961189i \(0.588973\pi\)
\(740\) 0 0
\(741\) 35.0000 1.28576
\(742\) 0 0
\(743\) −15.0000 −0.550297 −0.275148 0.961402i \(-0.588727\pi\)
−0.275148 + 0.961402i \(0.588727\pi\)
\(744\) 2.00000 0.0733236
\(745\) 0 0
\(746\) −22.0000 −0.805477
\(747\) −12.0000 −0.439057
\(748\) 20.0000 0.731272
\(749\) 0 0
\(750\) 0 0
\(751\) −50.0000 −1.82453 −0.912263 0.409605i \(-0.865667\pi\)
−0.912263 + 0.409605i \(0.865667\pi\)
\(752\) −11.0000 −0.401129
\(753\) 1.00000 0.0364420
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 34.0000 1.23575 0.617876 0.786276i \(-0.287994\pi\)
0.617876 + 0.786276i \(0.287994\pi\)
\(758\) −1.00000 −0.0363216
\(759\) −5.00000 −0.181489
\(760\) 0 0
\(761\) 37.0000 1.34125 0.670624 0.741797i \(-0.266026\pi\)
0.670624 + 0.741797i \(0.266026\pi\)
\(762\) −9.00000 −0.326036
\(763\) 0 0
\(764\) 14.0000 0.506502
\(765\) 0 0
\(766\) −21.0000 −0.758761
\(767\) 20.0000 0.722158
\(768\) −1.00000 −0.0360844
\(769\) 5.00000 0.180305 0.0901523 0.995928i \(-0.471265\pi\)
0.0901523 + 0.995928i \(0.471265\pi\)
\(770\) 0 0
\(771\) 16.0000 0.576226
\(772\) −10.0000 −0.359908
\(773\) −5.00000 −0.179838 −0.0899188 0.995949i \(-0.528661\pi\)
−0.0899188 + 0.995949i \(0.528661\pi\)
\(774\) 12.0000 0.431331
\(775\) 0 0
\(776\) 8.00000 0.287183
\(777\) 0 0
\(778\) −18.0000 −0.645331
\(779\) −35.0000 −1.25401
\(780\) 0 0
\(781\) −10.0000 −0.357828
\(782\) −4.00000 −0.143040
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 9.00000 0.321019
\(787\) 2.00000 0.0712923 0.0356462 0.999364i \(-0.488651\pi\)
0.0356462 + 0.999364i \(0.488651\pi\)
\(788\) 3.00000 0.106871
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 5.00000 0.177667
\(793\) 20.0000 0.710221
\(794\) 14.0000 0.496841
\(795\) 0 0
\(796\) 4.00000 0.141776
\(797\) −54.0000 −1.91278 −0.956389 0.292096i \(-0.905647\pi\)
−0.956389 + 0.292096i \(0.905647\pi\)
\(798\) 0 0
\(799\) 44.0000 1.55661
\(800\) 0 0
\(801\) −14.0000 −0.494666
\(802\) 21.0000 0.741536
\(803\) −50.0000 −1.76446
\(804\) −12.0000 −0.423207
\(805\) 0 0
\(806\) 10.0000 0.352235
\(807\) −24.0000 −0.844840
\(808\) 0 0
\(809\) 25.0000 0.878953 0.439477 0.898254i \(-0.355164\pi\)
0.439477 + 0.898254i \(0.355164\pi\)
\(810\) 0 0
\(811\) −21.0000 −0.737410 −0.368705 0.929547i \(-0.620199\pi\)
−0.368705 + 0.929547i \(0.620199\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −5.00000 −0.175250
\(815\) 0 0
\(816\) 4.00000 0.140028
\(817\) −84.0000 −2.93879
\(818\) 10.0000 0.349642
\(819\) 0 0
\(820\) 0 0
\(821\) 10.0000 0.349002 0.174501 0.984657i \(-0.444169\pi\)
0.174501 + 0.984657i \(0.444169\pi\)
\(822\) 2.00000 0.0697580
\(823\) −40.0000 −1.39431 −0.697156 0.716919i \(-0.745552\pi\)
−0.697156 + 0.716919i \(0.745552\pi\)
\(824\) −8.00000 −0.278693
\(825\) 0 0
\(826\) 0 0
\(827\) 6.00000 0.208640 0.104320 0.994544i \(-0.466733\pi\)
0.104320 + 0.994544i \(0.466733\pi\)
\(828\) −1.00000 −0.0347524
\(829\) 52.0000 1.80603 0.903017 0.429604i \(-0.141347\pi\)
0.903017 + 0.429604i \(0.141347\pi\)
\(830\) 0 0
\(831\) 14.0000 0.485655
\(832\) −5.00000 −0.173344
\(833\) 0 0
\(834\) 4.00000 0.138509
\(835\) 0 0
\(836\) −35.0000 −1.21050
\(837\) −2.00000 −0.0691301
\(838\) 15.0000 0.518166
\(839\) −12.0000 −0.414286 −0.207143 0.978311i \(-0.566417\pi\)
−0.207143 + 0.978311i \(0.566417\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) −10.0000 −0.344623
\(843\) −7.00000 −0.241093
\(844\) 17.0000 0.585164
\(845\) 0 0
\(846\) 11.0000 0.378188
\(847\) 0 0
\(848\) 9.00000 0.309061
\(849\) 10.0000 0.343199
\(850\) 0 0
\(851\) 1.00000 0.0342796
\(852\) −2.00000 −0.0685189
\(853\) −11.0000 −0.376633 −0.188316 0.982108i \(-0.560303\pi\)
−0.188316 + 0.982108i \(0.560303\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −2.00000 −0.0683586
\(857\) 2.00000 0.0683187 0.0341593 0.999416i \(-0.489125\pi\)
0.0341593 + 0.999416i \(0.489125\pi\)
\(858\) 25.0000 0.853486
\(859\) 4.00000 0.136478 0.0682391 0.997669i \(-0.478262\pi\)
0.0682391 + 0.997669i \(0.478262\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −12.0000 −0.408722
\(863\) −45.0000 −1.53182 −0.765909 0.642949i \(-0.777711\pi\)
−0.765909 + 0.642949i \(0.777711\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) −24.0000 −0.815553
\(867\) 1.00000 0.0339618
\(868\) 0 0
\(869\) 60.0000 2.03536
\(870\) 0 0
\(871\) −60.0000 −2.03302
\(872\) 2.00000 0.0677285
\(873\) −8.00000 −0.270759
\(874\) 7.00000 0.236779
\(875\) 0 0
\(876\) −10.0000 −0.337869
\(877\) 37.0000 1.24940 0.624701 0.780864i \(-0.285221\pi\)
0.624701 + 0.780864i \(0.285221\pi\)
\(878\) −40.0000 −1.34993
\(879\) −9.00000 −0.303562
\(880\) 0 0
\(881\) −3.00000 −0.101073 −0.0505363 0.998722i \(-0.516093\pi\)
−0.0505363 + 0.998722i \(0.516093\pi\)
\(882\) 0 0
\(883\) 50.0000 1.68263 0.841317 0.540542i \(-0.181781\pi\)
0.841317 + 0.540542i \(0.181781\pi\)
\(884\) 20.0000 0.672673
\(885\) 0 0
\(886\) −28.0000 −0.940678
\(887\) −44.0000 −1.47738 −0.738688 0.674048i \(-0.764554\pi\)
−0.738688 + 0.674048i \(0.764554\pi\)
\(888\) −1.00000 −0.0335578
\(889\) 0 0
\(890\) 0 0
\(891\) −5.00000 −0.167506
\(892\) −12.0000 −0.401790
\(893\) −77.0000 −2.57671
\(894\) 12.0000 0.401340
\(895\) 0 0
\(896\) 0 0
\(897\) −5.00000 −0.166945
\(898\) 29.0000 0.967743
\(899\) 0 0
\(900\) 0 0
\(901\) −36.0000 −1.19933
\(902\) −25.0000 −0.832409
\(903\) 0 0
\(904\) −14.0000 −0.465633
\(905\) 0 0
\(906\) 14.0000 0.465119
\(907\) 18.0000 0.597680 0.298840 0.954303i \(-0.403400\pi\)
0.298840 + 0.954303i \(0.403400\pi\)
\(908\) −12.0000 −0.398234
\(909\) 0 0
\(910\) 0 0
\(911\) 30.0000 0.993944 0.496972 0.867766i \(-0.334445\pi\)
0.496972 + 0.867766i \(0.334445\pi\)
\(912\) −7.00000 −0.231793
\(913\) 60.0000 1.98571
\(914\) −14.0000 −0.463079
\(915\) 0 0
\(916\) −10.0000 −0.330409
\(917\) 0 0
\(918\) −4.00000 −0.132020
\(919\) 28.0000 0.923635 0.461817 0.886975i \(-0.347198\pi\)
0.461817 + 0.886975i \(0.347198\pi\)
\(920\) 0 0
\(921\) −8.00000 −0.263609
\(922\) −4.00000 −0.131733
\(923\) −10.0000 −0.329154
\(924\) 0 0
\(925\) 0 0
\(926\) −19.0000 −0.624379
\(927\) 8.00000 0.262754
\(928\) 0 0
\(929\) −19.0000 −0.623370 −0.311685 0.950186i \(-0.600893\pi\)
−0.311685 + 0.950186i \(0.600893\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 14.0000 0.458585
\(933\) 8.00000 0.261908
\(934\) 20.0000 0.654420
\(935\) 0 0
\(936\) 5.00000 0.163430
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) −16.0000 −0.522140
\(940\) 0 0
\(941\) 6.00000 0.195594 0.0977972 0.995206i \(-0.468820\pi\)
0.0977972 + 0.995206i \(0.468820\pi\)
\(942\) 11.0000 0.358399
\(943\) 5.00000 0.162822
\(944\) −4.00000 −0.130189
\(945\) 0 0
\(946\) −60.0000 −1.95077
\(947\) 42.0000 1.36482 0.682408 0.730971i \(-0.260933\pi\)
0.682408 + 0.730971i \(0.260933\pi\)
\(948\) 12.0000 0.389742
\(949\) −50.0000 −1.62307
\(950\) 0 0
\(951\) −22.0000 −0.713399
\(952\) 0 0
\(953\) −12.0000 −0.388718 −0.194359 0.980930i \(-0.562263\pi\)
−0.194359 + 0.980930i \(0.562263\pi\)
\(954\) −9.00000 −0.291386
\(955\) 0 0
\(956\) −22.0000 −0.711531
\(957\) 0 0
\(958\) 18.0000 0.581554
\(959\) 0 0
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) −5.00000 −0.161206
\(963\) 2.00000 0.0644491
\(964\) −15.0000 −0.483117
\(965\) 0 0
\(966\) 0 0
\(967\) −4.00000 −0.128631 −0.0643157 0.997930i \(-0.520486\pi\)
−0.0643157 + 0.997930i \(0.520486\pi\)
\(968\) −14.0000 −0.449977
\(969\) 28.0000 0.899490
\(970\) 0 0
\(971\) −15.0000 −0.481373 −0.240686 0.970603i \(-0.577373\pi\)
−0.240686 + 0.970603i \(0.577373\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −4.00000 −0.128037
\(977\) 30.0000 0.959785 0.479893 0.877327i \(-0.340676\pi\)
0.479893 + 0.877327i \(0.340676\pi\)
\(978\) 24.0000 0.767435
\(979\) 70.0000 2.23721
\(980\) 0 0
\(981\) −2.00000 −0.0638551
\(982\) 36.0000 1.14881
\(983\) −25.0000 −0.797376 −0.398688 0.917087i \(-0.630534\pi\)
−0.398688 + 0.917087i \(0.630534\pi\)
\(984\) −5.00000 −0.159394
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −35.0000 −1.11350
\(989\) 12.0000 0.381578
\(990\) 0 0
\(991\) −38.0000 −1.20711 −0.603555 0.797321i \(-0.706250\pi\)
−0.603555 + 0.797321i \(0.706250\pi\)
\(992\) −2.00000 −0.0635001
\(993\) −31.0000 −0.983755
\(994\) 0 0
\(995\) 0 0
\(996\) 12.0000 0.380235
\(997\) −22.0000 −0.696747 −0.348373 0.937356i \(-0.613266\pi\)
−0.348373 + 0.937356i \(0.613266\pi\)
\(998\) −40.0000 −1.26618
\(999\) 1.00000 0.0316386
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.a.1.1 1
5.4 even 2 1470.2.a.o.1.1 1
7.3 odd 6 1050.2.i.p.751.1 2
7.5 odd 6 1050.2.i.p.151.1 2
7.6 odd 2 7350.2.a.u.1.1 1
15.14 odd 2 4410.2.a.u.1.1 1
35.3 even 12 1050.2.o.g.499.1 4
35.4 even 6 1470.2.i.e.961.1 2
35.9 even 6 1470.2.i.e.361.1 2
35.12 even 12 1050.2.o.g.949.1 4
35.17 even 12 1050.2.o.g.499.2 4
35.19 odd 6 210.2.i.b.151.1 yes 2
35.24 odd 6 210.2.i.b.121.1 2
35.33 even 12 1050.2.o.g.949.2 4
35.34 odd 2 1470.2.a.l.1.1 1
105.59 even 6 630.2.k.g.541.1 2
105.89 even 6 630.2.k.g.361.1 2
105.104 even 2 4410.2.a.j.1.1 1
140.19 even 6 1680.2.bg.d.1201.1 2
140.59 even 6 1680.2.bg.d.961.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.i.b.121.1 2 35.24 odd 6
210.2.i.b.151.1 yes 2 35.19 odd 6
630.2.k.g.361.1 2 105.89 even 6
630.2.k.g.541.1 2 105.59 even 6
1050.2.i.p.151.1 2 7.5 odd 6
1050.2.i.p.751.1 2 7.3 odd 6
1050.2.o.g.499.1 4 35.3 even 12
1050.2.o.g.499.2 4 35.17 even 12
1050.2.o.g.949.1 4 35.12 even 12
1050.2.o.g.949.2 4 35.33 even 12
1470.2.a.l.1.1 1 35.34 odd 2
1470.2.a.o.1.1 1 5.4 even 2
1470.2.i.e.361.1 2 35.9 even 6
1470.2.i.e.961.1 2 35.4 even 6
1680.2.bg.d.961.1 2 140.59 even 6
1680.2.bg.d.1201.1 2 140.19 even 6
4410.2.a.j.1.1 1 105.104 even 2
4410.2.a.u.1.1 1 15.14 odd 2
7350.2.a.a.1.1 1 1.1 even 1 trivial
7350.2.a.u.1.1 1 7.6 odd 2