Properties

Label 3630.2.a.z.1.1
Level $3630$
Weight $2$
Character 3630.1
Self dual yes
Analytic conductor $28.986$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3630.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.9856959337\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 3630.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} +2.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} +2.00000 q^{19} +1.00000 q^{20} +2.00000 q^{21} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} +2.00000 q^{28} +6.00000 q^{29} +1.00000 q^{30} +1.00000 q^{32} +2.00000 q^{34} +2.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} +2.00000 q^{38} +1.00000 q^{40} -6.00000 q^{41} +2.00000 q^{42} +2.00000 q^{43} +1.00000 q^{45} -4.00000 q^{47} +1.00000 q^{48} -3.00000 q^{49} +1.00000 q^{50} +2.00000 q^{51} +2.00000 q^{53} +1.00000 q^{54} +2.00000 q^{56} +2.00000 q^{57} +6.00000 q^{58} -8.00000 q^{59} +1.00000 q^{60} +2.00000 q^{63} +1.00000 q^{64} +4.00000 q^{67} +2.00000 q^{68} +2.00000 q^{70} +12.0000 q^{71} +1.00000 q^{72} +16.0000 q^{73} -6.00000 q^{74} +1.00000 q^{75} +2.00000 q^{76} -2.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} +8.00000 q^{83} +2.00000 q^{84} +2.00000 q^{85} +2.00000 q^{86} +6.00000 q^{87} -6.00000 q^{89} +1.00000 q^{90} -4.00000 q^{94} +2.00000 q^{95} +1.00000 q^{96} +10.0000 q^{97} -3.00000 q^{98} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 1.00000 0.408248
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 0 0
\(12\) 1.00000 0.288675
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 2.00000 0.534522
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 1.00000 0.235702
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 1.00000 0.223607
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 2.00000 0.377964
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 1.00000 0.182574
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 2.00000 0.338062
\(36\) 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
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 2.00000 0.308607
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) −4.00000 −0.583460 −0.291730 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.00000 −0.428571
\(50\) 1.00000 0.141421
\(51\) 2.00000 0.280056
\(52\) 0 0
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) 2.00000 0.267261
\(57\) 2.00000 0.264906
\(58\) 6.00000 0.787839
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 1.00000 0.129099
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 2.00000 0.251976
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 2.00000 0.242536
\(69\) 0 0
\(70\) 2.00000 0.239046
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 1.00000 0.117851
\(73\) 16.0000 1.87266 0.936329 0.351123i \(-0.114200\pi\)
0.936329 + 0.351123i \(0.114200\pi\)
\(74\) −6.00000 −0.697486
\(75\) 1.00000 0.115470
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) 0 0
\(79\) −2.00000 −0.225018 −0.112509 0.993651i \(-0.535889\pi\)
−0.112509 + 0.993651i \(0.535889\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) −6.00000 −0.662589
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) 2.00000 0.218218
\(85\) 2.00000 0.216930
\(86\) 2.00000 0.215666
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 1.00000 0.105409
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) −4.00000 −0.412568
\(95\) 2.00000 0.205196
\(96\) 1.00000 0.102062
\(97\) 10.0000 1.01535 0.507673 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) −3.00000 −0.303046
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 2.00000 0.198030
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) 0 0
\(105\) 2.00000 0.195180
\(106\) 2.00000 0.194257
\(107\) −16.0000 −1.54678 −0.773389 0.633932i \(-0.781440\pi\)
−0.773389 + 0.633932i \(0.781440\pi\)
\(108\) 1.00000 0.0962250
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) −6.00000 −0.569495
\(112\) 2.00000 0.188982
\(113\) −18.0000 −1.69330 −0.846649 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 2.00000 0.187317
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) 0 0
\(118\) −8.00000 −0.736460
\(119\) 4.00000 0.366679
\(120\) 1.00000 0.0912871
\(121\) 0 0
\(122\) 0 0
\(123\) −6.00000 −0.541002
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 2.00000 0.178174
\(127\) 10.0000 0.887357 0.443678 0.896186i \(-0.353673\pi\)
0.443678 + 0.896186i \(0.353673\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.00000 0.176090
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 4.00000 0.346844
\(134\) 4.00000 0.345547
\(135\) 1.00000 0.0860663
\(136\) 2.00000 0.171499
\(137\) −2.00000 −0.170872 −0.0854358 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) 0 0
\(139\) 18.0000 1.52674 0.763370 0.645961i \(-0.223543\pi\)
0.763370 + 0.645961i \(0.223543\pi\)
\(140\) 2.00000 0.169031
\(141\) −4.00000 −0.336861
\(142\) 12.0000 1.00702
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 6.00000 0.498273
\(146\) 16.0000 1.32417
\(147\) −3.00000 −0.247436
\(148\) −6.00000 −0.493197
\(149\) −14.0000 −1.14692 −0.573462 0.819232i \(-0.694400\pi\)
−0.573462 + 0.819232i \(0.694400\pi\)
\(150\) 1.00000 0.0816497
\(151\) −18.0000 −1.46482 −0.732410 0.680864i \(-0.761604\pi\)
−0.732410 + 0.680864i \(0.761604\pi\)
\(152\) 2.00000 0.162221
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −22.0000 −1.75579 −0.877896 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) −2.00000 −0.159111
\(159\) 2.00000 0.158610
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 8.00000 0.620920
\(167\) 24.0000 1.85718 0.928588 0.371113i \(-0.121024\pi\)
0.928588 + 0.371113i \(0.121024\pi\)
\(168\) 2.00000 0.154303
\(169\) −13.0000 −1.00000
\(170\) 2.00000 0.153393
\(171\) 2.00000 0.152944
\(172\) 2.00000 0.152499
\(173\) −22.0000 −1.67263 −0.836315 0.548250i \(-0.815294\pi\)
−0.836315 + 0.548250i \(0.815294\pi\)
\(174\) 6.00000 0.454859
\(175\) 2.00000 0.151186
\(176\) 0 0
\(177\) −8.00000 −0.601317
\(178\) −6.00000 −0.449719
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 1.00000 0.0745356
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −6.00000 −0.441129
\(186\) 0 0
\(187\) 0 0
\(188\) −4.00000 −0.291730
\(189\) 2.00000 0.145479
\(190\) 2.00000 0.145095
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 1.00000 0.0721688
\(193\) 12.0000 0.863779 0.431889 0.901927i \(-0.357847\pi\)
0.431889 + 0.901927i \(0.357847\pi\)
\(194\) 10.0000 0.717958
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 1.00000 0.0707107
\(201\) 4.00000 0.282138
\(202\) 6.00000 0.422159
\(203\) 12.0000 0.842235
\(204\) 2.00000 0.140028
\(205\) −6.00000 −0.419058
\(206\) −16.0000 −1.11477
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 2.00000 0.138013
\(211\) −6.00000 −0.413057 −0.206529 0.978441i \(-0.566217\pi\)
−0.206529 + 0.978441i \(0.566217\pi\)
\(212\) 2.00000 0.137361
\(213\) 12.0000 0.822226
\(214\) −16.0000 −1.09374
\(215\) 2.00000 0.136399
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 4.00000 0.270914
\(219\) 16.0000 1.08118
\(220\) 0 0
\(221\) 0 0
\(222\) −6.00000 −0.402694
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 2.00000 0.133631
\(225\) 1.00000 0.0666667
\(226\) −18.0000 −1.19734
\(227\) −24.0000 −1.59294 −0.796468 0.604681i \(-0.793301\pi\)
−0.796468 + 0.604681i \(0.793301\pi\)
\(228\) 2.00000 0.132453
\(229\) −6.00000 −0.396491 −0.198246 0.980152i \(-0.563524\pi\)
−0.198246 + 0.980152i \(0.563524\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) −4.00000 −0.260931
\(236\) −8.00000 −0.520756
\(237\) −2.00000 −0.129914
\(238\) 4.00000 0.259281
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 1.00000 0.0645497
\(241\) 28.0000 1.80364 0.901819 0.432113i \(-0.142232\pi\)
0.901819 + 0.432113i \(0.142232\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −3.00000 −0.191663
\(246\) −6.00000 −0.382546
\(247\) 0 0
\(248\) 0 0
\(249\) 8.00000 0.506979
\(250\) 1.00000 0.0632456
\(251\) −20.0000 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 2.00000 0.125988
\(253\) 0 0
\(254\) 10.0000 0.627456
\(255\) 2.00000 0.125245
\(256\) 1.00000 0.0625000
\(257\) 10.0000 0.623783 0.311891 0.950118i \(-0.399037\pi\)
0.311891 + 0.950118i \(0.399037\pi\)
\(258\) 2.00000 0.124515
\(259\) −12.0000 −0.745644
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 0 0
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) 2.00000 0.122859
\(266\) 4.00000 0.245256
\(267\) −6.00000 −0.367194
\(268\) 4.00000 0.244339
\(269\) 2.00000 0.121942 0.0609711 0.998140i \(-0.480580\pi\)
0.0609711 + 0.998140i \(0.480580\pi\)
\(270\) 1.00000 0.0608581
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 0 0
\(276\) 0 0
\(277\) 24.0000 1.44202 0.721010 0.692925i \(-0.243678\pi\)
0.721010 + 0.692925i \(0.243678\pi\)
\(278\) 18.0000 1.07957
\(279\) 0 0
\(280\) 2.00000 0.119523
\(281\) −14.0000 −0.835170 −0.417585 0.908638i \(-0.637123\pi\)
−0.417585 + 0.908638i \(0.637123\pi\)
\(282\) −4.00000 −0.238197
\(283\) −6.00000 −0.356663 −0.178331 0.983970i \(-0.557070\pi\)
−0.178331 + 0.983970i \(0.557070\pi\)
\(284\) 12.0000 0.712069
\(285\) 2.00000 0.118470
\(286\) 0 0
\(287\) −12.0000 −0.708338
\(288\) 1.00000 0.0589256
\(289\) −13.0000 −0.764706
\(290\) 6.00000 0.352332
\(291\) 10.0000 0.586210
\(292\) 16.0000 0.936329
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) −3.00000 −0.174964
\(295\) −8.00000 −0.465778
\(296\) −6.00000 −0.348743
\(297\) 0 0
\(298\) −14.0000 −0.810998
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) 4.00000 0.230556
\(302\) −18.0000 −1.03578
\(303\) 6.00000 0.344691
\(304\) 2.00000 0.114708
\(305\) 0 0
\(306\) 2.00000 0.114332
\(307\) 14.0000 0.799022 0.399511 0.916728i \(-0.369180\pi\)
0.399511 + 0.916728i \(0.369180\pi\)
\(308\) 0 0
\(309\) −16.0000 −0.910208
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) −22.0000 −1.24153
\(315\) 2.00000 0.112687
\(316\) −2.00000 −0.112509
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 2.00000 0.112154
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) −16.0000 −0.893033
\(322\) 0 0
\(323\) 4.00000 0.222566
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −4.00000 −0.221540
\(327\) 4.00000 0.221201
\(328\) −6.00000 −0.331295
\(329\) −8.00000 −0.441054
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 8.00000 0.439057
\(333\) −6.00000 −0.328798
\(334\) 24.0000 1.31322
\(335\) 4.00000 0.218543
\(336\) 2.00000 0.109109
\(337\) −8.00000 −0.435788 −0.217894 0.975972i \(-0.569919\pi\)
−0.217894 + 0.975972i \(0.569919\pi\)
\(338\) −13.0000 −0.707107
\(339\) −18.0000 −0.977626
\(340\) 2.00000 0.108465
\(341\) 0 0
\(342\) 2.00000 0.108148
\(343\) −20.0000 −1.07990
\(344\) 2.00000 0.107833
\(345\) 0 0
\(346\) −22.0000 −1.18273
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 6.00000 0.321634
\(349\) 24.0000 1.28469 0.642345 0.766415i \(-0.277962\pi\)
0.642345 + 0.766415i \(0.277962\pi\)
\(350\) 2.00000 0.106904
\(351\) 0 0
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) −8.00000 −0.425195
\(355\) 12.0000 0.636894
\(356\) −6.00000 −0.317999
\(357\) 4.00000 0.211702
\(358\) 4.00000 0.211407
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 1.00000 0.0527046
\(361\) −15.0000 −0.789474
\(362\) 14.0000 0.735824
\(363\) 0 0
\(364\) 0 0
\(365\) 16.0000 0.837478
\(366\) 0 0
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 0 0
\(369\) −6.00000 −0.312348
\(370\) −6.00000 −0.311925
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) 4.00000 0.207112 0.103556 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) −4.00000 −0.206284
\(377\) 0 0
\(378\) 2.00000 0.102869
\(379\) 4.00000 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) 2.00000 0.102598
\(381\) 10.0000 0.512316
\(382\) 12.0000 0.613973
\(383\) −16.0000 −0.817562 −0.408781 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 12.0000 0.610784
\(387\) 2.00000 0.101666
\(388\) 10.0000 0.507673
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −3.00000 −0.151523
\(393\) 0 0
\(394\) 2.00000 0.100759
\(395\) −2.00000 −0.100631
\(396\) 0 0
\(397\) −18.0000 −0.903394 −0.451697 0.892171i \(-0.649181\pi\)
−0.451697 + 0.892171i \(0.649181\pi\)
\(398\) 0 0
\(399\) 4.00000 0.200250
\(400\) 1.00000 0.0500000
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 4.00000 0.199502
\(403\) 0 0
\(404\) 6.00000 0.298511
\(405\) 1.00000 0.0496904
\(406\) 12.0000 0.595550
\(407\) 0 0
\(408\) 2.00000 0.0990148
\(409\) −28.0000 −1.38451 −0.692255 0.721653i \(-0.743383\pi\)
−0.692255 + 0.721653i \(0.743383\pi\)
\(410\) −6.00000 −0.296319
\(411\) −2.00000 −0.0986527
\(412\) −16.0000 −0.788263
\(413\) −16.0000 −0.787309
\(414\) 0 0
\(415\) 8.00000 0.392705
\(416\) 0 0
\(417\) 18.0000 0.881464
\(418\) 0 0
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 2.00000 0.0975900
\(421\) −30.0000 −1.46211 −0.731055 0.682318i \(-0.760972\pi\)
−0.731055 + 0.682318i \(0.760972\pi\)
\(422\) −6.00000 −0.292075
\(423\) −4.00000 −0.194487
\(424\) 2.00000 0.0971286
\(425\) 2.00000 0.0970143
\(426\) 12.0000 0.581402
\(427\) 0 0
\(428\) −16.0000 −0.773389
\(429\) 0 0
\(430\) 2.00000 0.0964486
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 1.00000 0.0481125
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) 6.00000 0.287678
\(436\) 4.00000 0.191565
\(437\) 0 0
\(438\) 16.0000 0.764510
\(439\) −14.0000 −0.668184 −0.334092 0.942541i \(-0.608430\pi\)
−0.334092 + 0.942541i \(0.608430\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) −6.00000 −0.284747
\(445\) −6.00000 −0.284427
\(446\) 0 0
\(447\) −14.0000 −0.662177
\(448\) 2.00000 0.0944911
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) −18.0000 −0.846649
\(453\) −18.0000 −0.845714
\(454\) −24.0000 −1.12638
\(455\) 0 0
\(456\) 2.00000 0.0936586
\(457\) 32.0000 1.49690 0.748448 0.663193i \(-0.230799\pi\)
0.748448 + 0.663193i \(0.230799\pi\)
\(458\) −6.00000 −0.280362
\(459\) 2.00000 0.0933520
\(460\) 0 0
\(461\) −38.0000 −1.76984 −0.884918 0.465746i \(-0.845786\pi\)
−0.884918 + 0.465746i \(0.845786\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) 6.00000 0.277945
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 8.00000 0.369406
\(470\) −4.00000 −0.184506
\(471\) −22.0000 −1.01371
\(472\) −8.00000 −0.368230
\(473\) 0 0
\(474\) −2.00000 −0.0918630
\(475\) 2.00000 0.0917663
\(476\) 4.00000 0.183340
\(477\) 2.00000 0.0915737
\(478\) −20.0000 −0.914779
\(479\) −28.0000 −1.27935 −0.639676 0.768644i \(-0.720932\pi\)
−0.639676 + 0.768644i \(0.720932\pi\)
\(480\) 1.00000 0.0456435
\(481\) 0 0
\(482\) 28.0000 1.27537
\(483\) 0 0
\(484\) 0 0
\(485\) 10.0000 0.454077
\(486\) 1.00000 0.0453609
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) −3.00000 −0.135526
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −6.00000 −0.270501
\(493\) 12.0000 0.540453
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 24.0000 1.07655
\(498\) 8.00000 0.358489
\(499\) −28.0000 −1.25345 −0.626726 0.779240i \(-0.715605\pi\)
−0.626726 + 0.779240i \(0.715605\pi\)
\(500\) 1.00000 0.0447214
\(501\) 24.0000 1.07224
\(502\) −20.0000 −0.892644
\(503\) 8.00000 0.356702 0.178351 0.983967i \(-0.442924\pi\)
0.178351 + 0.983967i \(0.442924\pi\)
\(504\) 2.00000 0.0890871
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) −13.0000 −0.577350
\(508\) 10.0000 0.443678
\(509\) −22.0000 −0.975133 −0.487566 0.873086i \(-0.662115\pi\)
−0.487566 + 0.873086i \(0.662115\pi\)
\(510\) 2.00000 0.0885615
\(511\) 32.0000 1.41560
\(512\) 1.00000 0.0441942
\(513\) 2.00000 0.0883022
\(514\) 10.0000 0.441081
\(515\) −16.0000 −0.705044
\(516\) 2.00000 0.0880451
\(517\) 0 0
\(518\) −12.0000 −0.527250
\(519\) −22.0000 −0.965693
\(520\) 0 0
\(521\) 14.0000 0.613351 0.306676 0.951814i \(-0.400783\pi\)
0.306676 + 0.951814i \(0.400783\pi\)
\(522\) 6.00000 0.262613
\(523\) −6.00000 −0.262362 −0.131181 0.991358i \(-0.541877\pi\)
−0.131181 + 0.991358i \(0.541877\pi\)
\(524\) 0 0
\(525\) 2.00000 0.0872872
\(526\) −16.0000 −0.697633
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 2.00000 0.0868744
\(531\) −8.00000 −0.347170
\(532\) 4.00000 0.173422
\(533\) 0 0
\(534\) −6.00000 −0.259645
\(535\) −16.0000 −0.691740
\(536\) 4.00000 0.172774
\(537\) 4.00000 0.172613
\(538\) 2.00000 0.0862261
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) −28.0000 −1.20381 −0.601907 0.798566i \(-0.705592\pi\)
−0.601907 + 0.798566i \(0.705592\pi\)
\(542\) 2.00000 0.0859074
\(543\) 14.0000 0.600798
\(544\) 2.00000 0.0857493
\(545\) 4.00000 0.171341
\(546\) 0 0
\(547\) 34.0000 1.45374 0.726868 0.686778i \(-0.240975\pi\)
0.726868 + 0.686778i \(0.240975\pi\)
\(548\) −2.00000 −0.0854358
\(549\) 0 0
\(550\) 0 0
\(551\) 12.0000 0.511217
\(552\) 0 0
\(553\) −4.00000 −0.170097
\(554\) 24.0000 1.01966
\(555\) −6.00000 −0.254686
\(556\) 18.0000 0.763370
\(557\) −42.0000 −1.77960 −0.889799 0.456354i \(-0.849155\pi\)
−0.889799 + 0.456354i \(0.849155\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 2.00000 0.0845154
\(561\) 0 0
\(562\) −14.0000 −0.590554
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) −4.00000 −0.168430
\(565\) −18.0000 −0.757266
\(566\) −6.00000 −0.252199
\(567\) 2.00000 0.0839921
\(568\) 12.0000 0.503509
\(569\) −10.0000 −0.419222 −0.209611 0.977785i \(-0.567220\pi\)
−0.209611 + 0.977785i \(0.567220\pi\)
\(570\) 2.00000 0.0837708
\(571\) 14.0000 0.585882 0.292941 0.956131i \(-0.405366\pi\)
0.292941 + 0.956131i \(0.405366\pi\)
\(572\) 0 0
\(573\) 12.0000 0.501307
\(574\) −12.0000 −0.500870
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 30.0000 1.24892 0.624458 0.781058i \(-0.285320\pi\)
0.624458 + 0.781058i \(0.285320\pi\)
\(578\) −13.0000 −0.540729
\(579\) 12.0000 0.498703
\(580\) 6.00000 0.249136
\(581\) 16.0000 0.663792
\(582\) 10.0000 0.414513
\(583\) 0 0
\(584\) 16.0000 0.662085
\(585\) 0 0
\(586\) 6.00000 0.247858
\(587\) 8.00000 0.330195 0.165098 0.986277i \(-0.447206\pi\)
0.165098 + 0.986277i \(0.447206\pi\)
\(588\) −3.00000 −0.123718
\(589\) 0 0
\(590\) −8.00000 −0.329355
\(591\) 2.00000 0.0822690
\(592\) −6.00000 −0.246598
\(593\) −34.0000 −1.39621 −0.698106 0.715994i \(-0.745974\pi\)
−0.698106 + 0.715994i \(0.745974\pi\)
\(594\) 0 0
\(595\) 4.00000 0.163984
\(596\) −14.0000 −0.573462
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 1.00000 0.0408248
\(601\) −40.0000 −1.63163 −0.815817 0.578310i \(-0.803712\pi\)
−0.815817 + 0.578310i \(0.803712\pi\)
\(602\) 4.00000 0.163028
\(603\) 4.00000 0.162893
\(604\) −18.0000 −0.732410
\(605\) 0 0
\(606\) 6.00000 0.243733
\(607\) 18.0000 0.730597 0.365299 0.930890i \(-0.380967\pi\)
0.365299 + 0.930890i \(0.380967\pi\)
\(608\) 2.00000 0.0811107
\(609\) 12.0000 0.486265
\(610\) 0 0
\(611\) 0 0
\(612\) 2.00000 0.0808452
\(613\) −4.00000 −0.161558 −0.0807792 0.996732i \(-0.525741\pi\)
−0.0807792 + 0.996732i \(0.525741\pi\)
\(614\) 14.0000 0.564994
\(615\) −6.00000 −0.241943
\(616\) 0 0
\(617\) −26.0000 −1.04672 −0.523360 0.852111i \(-0.675322\pi\)
−0.523360 + 0.852111i \(0.675322\pi\)
\(618\) −16.0000 −0.643614
\(619\) 36.0000 1.44696 0.723481 0.690344i \(-0.242541\pi\)
0.723481 + 0.690344i \(0.242541\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) −12.0000 −0.480770
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −10.0000 −0.399680
\(627\) 0 0
\(628\) −22.0000 −0.877896
\(629\) −12.0000 −0.478471
\(630\) 2.00000 0.0796819
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) −2.00000 −0.0795557
\(633\) −6.00000 −0.238479
\(634\) 6.00000 0.238290
\(635\) 10.0000 0.396838
\(636\) 2.00000 0.0793052
\(637\) 0 0
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) 1.00000 0.0395285
\(641\) 2.00000 0.0789953 0.0394976 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) −16.0000 −0.631470
\(643\) −12.0000 −0.473234 −0.236617 0.971603i \(-0.576039\pi\)
−0.236617 + 0.971603i \(0.576039\pi\)
\(644\) 0 0
\(645\) 2.00000 0.0787499
\(646\) 4.00000 0.157378
\(647\) −40.0000 −1.57256 −0.786281 0.617869i \(-0.787996\pi\)
−0.786281 + 0.617869i \(0.787996\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) 4.00000 0.156412
\(655\) 0 0
\(656\) −6.00000 −0.234261
\(657\) 16.0000 0.624219
\(658\) −8.00000 −0.311872
\(659\) −40.0000 −1.55818 −0.779089 0.626913i \(-0.784318\pi\)
−0.779089 + 0.626913i \(0.784318\pi\)
\(660\) 0 0
\(661\) 26.0000 1.01128 0.505641 0.862744i \(-0.331256\pi\)
0.505641 + 0.862744i \(0.331256\pi\)
\(662\) 28.0000 1.08825
\(663\) 0 0
\(664\) 8.00000 0.310460
\(665\) 4.00000 0.155113
\(666\) −6.00000 −0.232495
\(667\) 0 0
\(668\) 24.0000 0.928588
\(669\) 0 0
\(670\) 4.00000 0.154533
\(671\) 0 0
\(672\) 2.00000 0.0771517
\(673\) −4.00000 −0.154189 −0.0770943 0.997024i \(-0.524564\pi\)
−0.0770943 + 0.997024i \(0.524564\pi\)
\(674\) −8.00000 −0.308148
\(675\) 1.00000 0.0384900
\(676\) −13.0000 −0.500000
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −18.0000 −0.691286
\(679\) 20.0000 0.767530
\(680\) 2.00000 0.0766965
\(681\) −24.0000 −0.919682
\(682\) 0 0
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 2.00000 0.0764719
\(685\) −2.00000 −0.0764161
\(686\) −20.0000 −0.763604
\(687\) −6.00000 −0.228914
\(688\) 2.00000 0.0762493
\(689\) 0 0
\(690\) 0 0
\(691\) −4.00000 −0.152167 −0.0760836 0.997101i \(-0.524242\pi\)
−0.0760836 + 0.997101i \(0.524242\pi\)
\(692\) −22.0000 −0.836315
\(693\) 0 0
\(694\) 0 0
\(695\) 18.0000 0.682779
\(696\) 6.00000 0.227429
\(697\) −12.0000 −0.454532
\(698\) 24.0000 0.908413
\(699\) 6.00000 0.226941
\(700\) 2.00000 0.0755929
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) −12.0000 −0.452589
\(704\) 0 0
\(705\) −4.00000 −0.150649
\(706\) −6.00000 −0.225813
\(707\) 12.0000 0.451306
\(708\) −8.00000 −0.300658
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 12.0000 0.450352
\(711\) −2.00000 −0.0750059
\(712\) −6.00000 −0.224860
\(713\) 0 0
\(714\) 4.00000 0.149696
\(715\) 0 0
\(716\) 4.00000 0.149487
\(717\) −20.0000 −0.746914
\(718\) 24.0000 0.895672
\(719\) −20.0000 −0.745874 −0.372937 0.927857i \(-0.621649\pi\)
−0.372937 + 0.927857i \(0.621649\pi\)
\(720\) 1.00000 0.0372678
\(721\) −32.0000 −1.19174
\(722\) −15.0000 −0.558242
\(723\) 28.0000 1.04133
\(724\) 14.0000 0.520306
\(725\) 6.00000 0.222834
\(726\) 0 0
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 16.0000 0.592187
\(731\) 4.00000 0.147945
\(732\) 0 0
\(733\) 16.0000 0.590973 0.295487 0.955347i \(-0.404518\pi\)
0.295487 + 0.955347i \(0.404518\pi\)
\(734\) −8.00000 −0.295285
\(735\) −3.00000 −0.110657
\(736\) 0 0
\(737\) 0 0
\(738\) −6.00000 −0.220863
\(739\) −50.0000 −1.83928 −0.919640 0.392763i \(-0.871519\pi\)
−0.919640 + 0.392763i \(0.871519\pi\)
\(740\) −6.00000 −0.220564
\(741\) 0 0
\(742\) 4.00000 0.146845
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 0 0
\(745\) −14.0000 −0.512920
\(746\) 4.00000 0.146450
\(747\) 8.00000 0.292705
\(748\) 0 0
\(749\) −32.0000 −1.16925
\(750\) 1.00000 0.0365148
\(751\) 24.0000 0.875772 0.437886 0.899030i \(-0.355727\pi\)
0.437886 + 0.899030i \(0.355727\pi\)
\(752\) −4.00000 −0.145865
\(753\) −20.0000 −0.728841
\(754\) 0 0
\(755\) −18.0000 −0.655087
\(756\) 2.00000 0.0727393
\(757\) 42.0000 1.52652 0.763258 0.646094i \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(758\) 4.00000 0.145287
\(759\) 0 0
\(760\) 2.00000 0.0725476
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 10.0000 0.362262
\(763\) 8.00000 0.289619
\(764\) 12.0000 0.434145
\(765\) 2.00000 0.0723102
\(766\) −16.0000 −0.578103
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −48.0000 −1.73092 −0.865462 0.500974i \(-0.832975\pi\)
−0.865462 + 0.500974i \(0.832975\pi\)
\(770\) 0 0
\(771\) 10.0000 0.360141
\(772\) 12.0000 0.431889
\(773\) −46.0000 −1.65451 −0.827253 0.561830i \(-0.810097\pi\)
−0.827253 + 0.561830i \(0.810097\pi\)
\(774\) 2.00000 0.0718885
\(775\) 0 0
\(776\) 10.0000 0.358979
\(777\) −12.0000 −0.430498
\(778\) 6.00000 0.215110
\(779\) −12.0000 −0.429945
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 6.00000 0.214423
\(784\) −3.00000 −0.107143
\(785\) −22.0000 −0.785214
\(786\) 0 0
\(787\) 50.0000 1.78231 0.891154 0.453701i \(-0.149897\pi\)
0.891154 + 0.453701i \(0.149897\pi\)
\(788\) 2.00000 0.0712470
\(789\) −16.0000 −0.569615
\(790\) −2.00000 −0.0711568
\(791\) −36.0000 −1.28001
\(792\) 0 0
\(793\) 0 0
\(794\) −18.0000 −0.638796
\(795\) 2.00000 0.0709327
\(796\) 0 0
\(797\) −10.0000 −0.354218 −0.177109 0.984191i \(-0.556675\pi\)
−0.177109 + 0.984191i \(0.556675\pi\)
\(798\) 4.00000 0.141598
\(799\) −8.00000 −0.283020
\(800\) 1.00000 0.0353553
\(801\) −6.00000 −0.212000
\(802\) −18.0000 −0.635602
\(803\) 0 0
\(804\) 4.00000 0.141069
\(805\) 0 0
\(806\) 0 0
\(807\) 2.00000 0.0704033
\(808\) 6.00000 0.211079
\(809\) −18.0000 −0.632846 −0.316423 0.948618i \(-0.602482\pi\)
−0.316423 + 0.948618i \(0.602482\pi\)
\(810\) 1.00000 0.0351364
\(811\) 2.00000 0.0702295 0.0351147 0.999383i \(-0.488820\pi\)
0.0351147 + 0.999383i \(0.488820\pi\)
\(812\) 12.0000 0.421117
\(813\) 2.00000 0.0701431
\(814\) 0 0
\(815\) −4.00000 −0.140114
\(816\) 2.00000 0.0700140
\(817\) 4.00000 0.139942
\(818\) −28.0000 −0.978997
\(819\) 0 0
\(820\) −6.00000 −0.209529
\(821\) 6.00000 0.209401 0.104701 0.994504i \(-0.466612\pi\)
0.104701 + 0.994504i \(0.466612\pi\)
\(822\) −2.00000 −0.0697580
\(823\) 24.0000 0.836587 0.418294 0.908312i \(-0.362628\pi\)
0.418294 + 0.908312i \(0.362628\pi\)
\(824\) −16.0000 −0.557386
\(825\) 0 0
\(826\) −16.0000 −0.556711
\(827\) 16.0000 0.556375 0.278187 0.960527i \(-0.410266\pi\)
0.278187 + 0.960527i \(0.410266\pi\)
\(828\) 0 0
\(829\) −2.00000 −0.0694629 −0.0347314 0.999397i \(-0.511058\pi\)
−0.0347314 + 0.999397i \(0.511058\pi\)
\(830\) 8.00000 0.277684
\(831\) 24.0000 0.832551
\(832\) 0 0
\(833\) −6.00000 −0.207888
\(834\) 18.0000 0.623289
\(835\) 24.0000 0.830554
\(836\) 0 0
\(837\) 0 0
\(838\) −20.0000 −0.690889
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 2.00000 0.0690066
\(841\) 7.00000 0.241379
\(842\) −30.0000 −1.03387
\(843\) −14.0000 −0.482186
\(844\) −6.00000 −0.206529
\(845\) −13.0000 −0.447214
\(846\) −4.00000 −0.137523
\(847\) 0 0
\(848\) 2.00000 0.0686803
\(849\) −6.00000 −0.205919
\(850\) 2.00000 0.0685994
\(851\) 0 0
\(852\) 12.0000 0.411113
\(853\) −4.00000 −0.136957 −0.0684787 0.997653i \(-0.521815\pi\)
−0.0684787 + 0.997653i \(0.521815\pi\)
\(854\) 0 0
\(855\) 2.00000 0.0683986
\(856\) −16.0000 −0.546869
\(857\) −6.00000 −0.204956 −0.102478 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(858\) 0 0
\(859\) 36.0000 1.22830 0.614152 0.789188i \(-0.289498\pi\)
0.614152 + 0.789188i \(0.289498\pi\)
\(860\) 2.00000 0.0681994
\(861\) −12.0000 −0.408959
\(862\) 12.0000 0.408722
\(863\) 48.0000 1.63394 0.816970 0.576681i \(-0.195652\pi\)
0.816970 + 0.576681i \(0.195652\pi\)
\(864\) 1.00000 0.0340207
\(865\) −22.0000 −0.748022
\(866\) 2.00000 0.0679628
\(867\) −13.0000 −0.441503
\(868\) 0 0
\(869\) 0 0
\(870\) 6.00000 0.203419
\(871\) 0 0
\(872\) 4.00000 0.135457
\(873\) 10.0000 0.338449
\(874\) 0 0
\(875\) 2.00000 0.0676123
\(876\) 16.0000 0.540590
\(877\) 44.0000 1.48577 0.742887 0.669417i \(-0.233456\pi\)
0.742887 + 0.669417i \(0.233456\pi\)
\(878\) −14.0000 −0.472477
\(879\) 6.00000 0.202375
\(880\) 0 0
\(881\) 30.0000 1.01073 0.505363 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) −3.00000 −0.101015
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 0 0
\(885\) −8.00000 −0.268917
\(886\) −24.0000 −0.806296
\(887\) −36.0000 −1.20876 −0.604381 0.796696i \(-0.706579\pi\)
−0.604381 + 0.796696i \(0.706579\pi\)
\(888\) −6.00000 −0.201347
\(889\) 20.0000 0.670778
\(890\) −6.00000 −0.201120
\(891\) 0 0
\(892\) 0 0
\(893\) −8.00000 −0.267710
\(894\) −14.0000 −0.468230
\(895\) 4.00000 0.133705
\(896\) 2.00000 0.0668153
\(897\) 0 0
\(898\) −6.00000 −0.200223
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) 4.00000 0.133259
\(902\) 0 0
\(903\) 4.00000 0.133112
\(904\) −18.0000 −0.598671
\(905\) 14.0000 0.465376
\(906\) −18.0000 −0.598010
\(907\) −20.0000 −0.664089 −0.332045 0.943264i \(-0.607738\pi\)
−0.332045 + 0.943264i \(0.607738\pi\)
\(908\) −24.0000 −0.796468
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) 20.0000 0.662630 0.331315 0.943520i \(-0.392508\pi\)
0.331315 + 0.943520i \(0.392508\pi\)
\(912\) 2.00000 0.0662266
\(913\) 0 0
\(914\) 32.0000 1.05847
\(915\) 0 0
\(916\) −6.00000 −0.198246
\(917\) 0 0
\(918\) 2.00000 0.0660098
\(919\) −38.0000 −1.25350 −0.626752 0.779219i \(-0.715616\pi\)
−0.626752 + 0.779219i \(0.715616\pi\)
\(920\) 0 0
\(921\) 14.0000 0.461316
\(922\) −38.0000 −1.25146
\(923\) 0 0
\(924\) 0 0
\(925\) −6.00000 −0.197279
\(926\) 16.0000 0.525793
\(927\) −16.0000 −0.525509
\(928\) 6.00000 0.196960
\(929\) −42.0000 −1.37798 −0.688988 0.724773i \(-0.741945\pi\)
−0.688988 + 0.724773i \(0.741945\pi\)
\(930\) 0 0
\(931\) −6.00000 −0.196642
\(932\) 6.00000 0.196537
\(933\) 24.0000 0.785725
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 28.0000 0.914720 0.457360 0.889282i \(-0.348795\pi\)
0.457360 + 0.889282i \(0.348795\pi\)
\(938\) 8.00000 0.261209
\(939\) −10.0000 −0.326338
\(940\) −4.00000 −0.130466
\(941\) 14.0000 0.456387 0.228193 0.973616i \(-0.426718\pi\)
0.228193 + 0.973616i \(0.426718\pi\)
\(942\) −22.0000 −0.716799
\(943\) 0 0
\(944\) −8.00000 −0.260378
\(945\) 2.00000 0.0650600
\(946\) 0 0
\(947\) 36.0000 1.16984 0.584921 0.811090i \(-0.301125\pi\)
0.584921 + 0.811090i \(0.301125\pi\)
\(948\) −2.00000 −0.0649570
\(949\) 0 0
\(950\) 2.00000 0.0648886
\(951\) 6.00000 0.194563
\(952\) 4.00000 0.129641
\(953\) −6.00000 −0.194359 −0.0971795 0.995267i \(-0.530982\pi\)
−0.0971795 + 0.995267i \(0.530982\pi\)
\(954\) 2.00000 0.0647524
\(955\) 12.0000 0.388311
\(956\) −20.0000 −0.646846
\(957\) 0 0
\(958\) −28.0000 −0.904639
\(959\) −4.00000 −0.129167
\(960\) 1.00000 0.0322749
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) −16.0000 −0.515593
\(964\) 28.0000 0.901819
\(965\) 12.0000 0.386294
\(966\) 0 0
\(967\) −22.0000 −0.707472 −0.353736 0.935345i \(-0.615089\pi\)
−0.353736 + 0.935345i \(0.615089\pi\)
\(968\) 0 0
\(969\) 4.00000 0.128499
\(970\) 10.0000 0.321081
\(971\) 24.0000 0.770197 0.385098 0.922876i \(-0.374168\pi\)
0.385098 + 0.922876i \(0.374168\pi\)
\(972\) 1.00000 0.0320750
\(973\) 36.0000 1.15411
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 46.0000 1.47167 0.735835 0.677161i \(-0.236790\pi\)
0.735835 + 0.677161i \(0.236790\pi\)
\(978\) −4.00000 −0.127906
\(979\) 0 0
\(980\) −3.00000 −0.0958315
\(981\) 4.00000 0.127710
\(982\) 12.0000 0.382935
\(983\) 8.00000 0.255160 0.127580 0.991828i \(-0.459279\pi\)
0.127580 + 0.991828i \(0.459279\pi\)
\(984\) −6.00000 −0.191273
\(985\) 2.00000 0.0637253
\(986\) 12.0000 0.382158
\(987\) −8.00000 −0.254643
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −24.0000 −0.762385 −0.381193 0.924496i \(-0.624487\pi\)
−0.381193 + 0.924496i \(0.624487\pi\)
\(992\) 0 0
\(993\) 28.0000 0.888553
\(994\) 24.0000 0.761234
\(995\) 0 0
\(996\) 8.00000 0.253490
\(997\) −44.0000 −1.39349 −0.696747 0.717317i \(-0.745370\pi\)
−0.696747 + 0.717317i \(0.745370\pi\)
\(998\) −28.0000 −0.886325
\(999\) −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 3630.2.a.z.1.1 yes 1
11.10 odd 2 3630.2.a.j.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3630.2.a.j.1.1 1 11.10 odd 2
3630.2.a.z.1.1 yes 1 1.1 even 1 trivial