Properties

Label 3630.2.a.r.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

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} +3.00000 q^{13} +3.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} +1.00000 q^{20} -3.00000 q^{21} +6.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +3.00000 q^{26} -1.00000 q^{27} +3.00000 q^{28} +5.00000 q^{29} -1.00000 q^{30} +1.00000 q^{32} -1.00000 q^{34} +3.00000 q^{35} +1.00000 q^{36} +3.00000 q^{37} -1.00000 q^{38} -3.00000 q^{39} +1.00000 q^{40} -4.00000 q^{41} -3.00000 q^{42} -8.00000 q^{43} +1.00000 q^{45} +6.00000 q^{46} -2.00000 q^{47} -1.00000 q^{48} +2.00000 q^{49} +1.00000 q^{50} +1.00000 q^{51} +3.00000 q^{52} -10.0000 q^{53} -1.00000 q^{54} +3.00000 q^{56} +1.00000 q^{57} +5.00000 q^{58} +14.0000 q^{59} -1.00000 q^{60} -2.00000 q^{61} +3.00000 q^{63} +1.00000 q^{64} +3.00000 q^{65} -10.0000 q^{67} -1.00000 q^{68} -6.00000 q^{69} +3.00000 q^{70} +7.00000 q^{71} +1.00000 q^{72} +8.00000 q^{73} +3.00000 q^{74} -1.00000 q^{75} -1.00000 q^{76} -3.00000 q^{78} +10.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -4.00000 q^{82} +9.00000 q^{83} -3.00000 q^{84} -1.00000 q^{85} -8.00000 q^{86} -5.00000 q^{87} +1.00000 q^{90} +9.00000 q^{91} +6.00000 q^{92} -2.00000 q^{94} -1.00000 q^{95} -1.00000 q^{96} -12.0000 q^{97} +2.00000 q^{98} +O(q^{100})\)

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
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 0 0
\(12\) −1.00000 −0.288675
\(13\) 3.00000 0.832050 0.416025 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 3.00000 0.801784
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536 −0.121268 0.992620i \(-0.538696\pi\)
−0.121268 + 0.992620i \(0.538696\pi\)
\(18\) 1.00000 0.235702
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 1.00000 0.223607
\(21\) −3.00000 −0.654654
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) 3.00000 0.588348
\(27\) −1.00000 −0.192450
\(28\) 3.00000 0.566947
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) −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
\(34\) −1.00000 −0.171499
\(35\) 3.00000 0.507093
\(36\) 1.00000 0.166667
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) −1.00000 −0.162221
\(39\) −3.00000 −0.480384
\(40\) 1.00000 0.158114
\(41\) −4.00000 −0.624695 −0.312348 0.949968i \(-0.601115\pi\)
−0.312348 + 0.949968i \(0.601115\pi\)
\(42\) −3.00000 −0.462910
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 6.00000 0.884652
\(47\) −2.00000 −0.291730 −0.145865 0.989305i \(-0.546597\pi\)
−0.145865 + 0.989305i \(0.546597\pi\)
\(48\) −1.00000 −0.144338
\(49\) 2.00000 0.285714
\(50\) 1.00000 0.141421
\(51\) 1.00000 0.140028
\(52\) 3.00000 0.416025
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) 3.00000 0.400892
\(57\) 1.00000 0.132453
\(58\) 5.00000 0.656532
\(59\) 14.0000 1.82264 0.911322 0.411693i \(-0.135063\pi\)
0.911322 + 0.411693i \(0.135063\pi\)
\(60\) −1.00000 −0.129099
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) 3.00000 0.377964
\(64\) 1.00000 0.125000
\(65\) 3.00000 0.372104
\(66\) 0 0
\(67\) −10.0000 −1.22169 −0.610847 0.791748i \(-0.709171\pi\)
−0.610847 + 0.791748i \(0.709171\pi\)
\(68\) −1.00000 −0.121268
\(69\) −6.00000 −0.722315
\(70\) 3.00000 0.358569
\(71\) 7.00000 0.830747 0.415374 0.909651i \(-0.363651\pi\)
0.415374 + 0.909651i \(0.363651\pi\)
\(72\) 1.00000 0.117851
\(73\) 8.00000 0.936329 0.468165 0.883641i \(-0.344915\pi\)
0.468165 + 0.883641i \(0.344915\pi\)
\(74\) 3.00000 0.348743
\(75\) −1.00000 −0.115470
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) −3.00000 −0.339683
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) −4.00000 −0.441726
\(83\) 9.00000 0.987878 0.493939 0.869496i \(-0.335557\pi\)
0.493939 + 0.869496i \(0.335557\pi\)
\(84\) −3.00000 −0.327327
\(85\) −1.00000 −0.108465
\(86\) −8.00000 −0.862662
\(87\) −5.00000 −0.536056
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 1.00000 0.105409
\(91\) 9.00000 0.943456
\(92\) 6.00000 0.625543
\(93\) 0 0
\(94\) −2.00000 −0.206284
\(95\) −1.00000 −0.102598
\(96\) −1.00000 −0.102062
\(97\) −12.0000 −1.21842 −0.609208 0.793011i \(-0.708512\pi\)
−0.609208 + 0.793011i \(0.708512\pi\)
\(98\) 2.00000 0.202031
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 11.0000 1.09454 0.547270 0.836956i \(-0.315667\pi\)
0.547270 + 0.836956i \(0.315667\pi\)
\(102\) 1.00000 0.0990148
\(103\) −5.00000 −0.492665 −0.246332 0.969185i \(-0.579225\pi\)
−0.246332 + 0.969185i \(0.579225\pi\)
\(104\) 3.00000 0.294174
\(105\) −3.00000 −0.292770
\(106\) −10.0000 −0.971286
\(107\) 20.0000 1.93347 0.966736 0.255774i \(-0.0823304\pi\)
0.966736 + 0.255774i \(0.0823304\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) −3.00000 −0.284747
\(112\) 3.00000 0.283473
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 1.00000 0.0936586
\(115\) 6.00000 0.559503
\(116\) 5.00000 0.464238
\(117\) 3.00000 0.277350
\(118\) 14.0000 1.28880
\(119\) −3.00000 −0.275010
\(120\) −1.00000 −0.0912871
\(121\) 0 0
\(122\) −2.00000 −0.181071
\(123\) 4.00000 0.360668
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 3.00000 0.267261
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 1.00000 0.0883883
\(129\) 8.00000 0.704361
\(130\) 3.00000 0.263117
\(131\) −10.0000 −0.873704 −0.436852 0.899533i \(-0.643907\pi\)
−0.436852 + 0.899533i \(0.643907\pi\)
\(132\) 0 0
\(133\) −3.00000 −0.260133
\(134\) −10.0000 −0.863868
\(135\) −1.00000 −0.0860663
\(136\) −1.00000 −0.0857493
\(137\) −15.0000 −1.28154 −0.640768 0.767734i \(-0.721384\pi\)
−0.640768 + 0.767734i \(0.721384\pi\)
\(138\) −6.00000 −0.510754
\(139\) −11.0000 −0.933008 −0.466504 0.884519i \(-0.654487\pi\)
−0.466504 + 0.884519i \(0.654487\pi\)
\(140\) 3.00000 0.253546
\(141\) 2.00000 0.168430
\(142\) 7.00000 0.587427
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 5.00000 0.415227
\(146\) 8.00000 0.662085
\(147\) −2.00000 −0.164957
\(148\) 3.00000 0.246598
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) −1.00000 −0.0816497
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −1.00000 −0.0808452
\(154\) 0 0
\(155\) 0 0
\(156\) −3.00000 −0.240192
\(157\) 21.0000 1.67598 0.837991 0.545684i \(-0.183730\pi\)
0.837991 + 0.545684i \(0.183730\pi\)
\(158\) 10.0000 0.795557
\(159\) 10.0000 0.793052
\(160\) 1.00000 0.0790569
\(161\) 18.0000 1.41860
\(162\) 1.00000 0.0785674
\(163\) 22.0000 1.72317 0.861586 0.507611i \(-0.169471\pi\)
0.861586 + 0.507611i \(0.169471\pi\)
\(164\) −4.00000 −0.312348
\(165\) 0 0
\(166\) 9.00000 0.698535
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) −3.00000 −0.231455
\(169\) −4.00000 −0.307692
\(170\) −1.00000 −0.0766965
\(171\) −1.00000 −0.0764719
\(172\) −8.00000 −0.609994
\(173\) 14.0000 1.06440 0.532200 0.846619i \(-0.321365\pi\)
0.532200 + 0.846619i \(0.321365\pi\)
\(174\) −5.00000 −0.379049
\(175\) 3.00000 0.226779
\(176\) 0 0
\(177\) −14.0000 −1.05230
\(178\) 0 0
\(179\) −18.0000 −1.34538 −0.672692 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) 1.00000 0.0745356
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 9.00000 0.667124
\(183\) 2.00000 0.147844
\(184\) 6.00000 0.442326
\(185\) 3.00000 0.220564
\(186\) 0 0
\(187\) 0 0
\(188\) −2.00000 −0.145865
\(189\) −3.00000 −0.218218
\(190\) −1.00000 −0.0725476
\(191\) 9.00000 0.651217 0.325609 0.945505i \(-0.394431\pi\)
0.325609 + 0.945505i \(0.394431\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 16.0000 1.15171 0.575853 0.817554i \(-0.304670\pi\)
0.575853 + 0.817554i \(0.304670\pi\)
\(194\) −12.0000 −0.861550
\(195\) −3.00000 −0.214834
\(196\) 2.00000 0.142857
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 1.00000 0.0707107
\(201\) 10.0000 0.705346
\(202\) 11.0000 0.773957
\(203\) 15.0000 1.05279
\(204\) 1.00000 0.0700140
\(205\) −4.00000 −0.279372
\(206\) −5.00000 −0.348367
\(207\) 6.00000 0.417029
\(208\) 3.00000 0.208013
\(209\) 0 0
\(210\) −3.00000 −0.207020
\(211\) 19.0000 1.30801 0.654007 0.756489i \(-0.273087\pi\)
0.654007 + 0.756489i \(0.273087\pi\)
\(212\) −10.0000 −0.686803
\(213\) −7.00000 −0.479632
\(214\) 20.0000 1.36717
\(215\) −8.00000 −0.545595
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) −16.0000 −1.08366
\(219\) −8.00000 −0.540590
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) −3.00000 −0.201347
\(223\) 9.00000 0.602685 0.301342 0.953516i \(-0.402565\pi\)
0.301342 + 0.953516i \(0.402565\pi\)
\(224\) 3.00000 0.200446
\(225\) 1.00000 0.0666667
\(226\) −10.0000 −0.665190
\(227\) 28.0000 1.85843 0.929213 0.369546i \(-0.120487\pi\)
0.929213 + 0.369546i \(0.120487\pi\)
\(228\) 1.00000 0.0662266
\(229\) −20.0000 −1.32164 −0.660819 0.750546i \(-0.729791\pi\)
−0.660819 + 0.750546i \(0.729791\pi\)
\(230\) 6.00000 0.395628
\(231\) 0 0
\(232\) 5.00000 0.328266
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 3.00000 0.196116
\(235\) −2.00000 −0.130466
\(236\) 14.0000 0.911322
\(237\) −10.0000 −0.649570
\(238\) −3.00000 −0.194461
\(239\) −11.0000 −0.711531 −0.355765 0.934575i \(-0.615780\pi\)
−0.355765 + 0.934575i \(0.615780\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 21.0000 1.35273 0.676364 0.736567i \(-0.263554\pi\)
0.676364 + 0.736567i \(0.263554\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) −2.00000 −0.128037
\(245\) 2.00000 0.127775
\(246\) 4.00000 0.255031
\(247\) −3.00000 −0.190885
\(248\) 0 0
\(249\) −9.00000 −0.570352
\(250\) 1.00000 0.0632456
\(251\) 8.00000 0.504956 0.252478 0.967603i \(-0.418755\pi\)
0.252478 + 0.967603i \(0.418755\pi\)
\(252\) 3.00000 0.188982
\(253\) 0 0
\(254\) −16.0000 −1.00393
\(255\) 1.00000 0.0626224
\(256\) 1.00000 0.0625000
\(257\) −17.0000 −1.06043 −0.530215 0.847863i \(-0.677889\pi\)
−0.530215 + 0.847863i \(0.677889\pi\)
\(258\) 8.00000 0.498058
\(259\) 9.00000 0.559233
\(260\) 3.00000 0.186052
\(261\) 5.00000 0.309492
\(262\) −10.0000 −0.617802
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −10.0000 −0.614295
\(266\) −3.00000 −0.183942
\(267\) 0 0
\(268\) −10.0000 −0.610847
\(269\) −17.0000 −1.03651 −0.518254 0.855227i \(-0.673418\pi\)
−0.518254 + 0.855227i \(0.673418\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 22.0000 1.33640 0.668202 0.743980i \(-0.267064\pi\)
0.668202 + 0.743980i \(0.267064\pi\)
\(272\) −1.00000 −0.0606339
\(273\) −9.00000 −0.544705
\(274\) −15.0000 −0.906183
\(275\) 0 0
\(276\) −6.00000 −0.361158
\(277\) 6.00000 0.360505 0.180253 0.983620i \(-0.442309\pi\)
0.180253 + 0.983620i \(0.442309\pi\)
\(278\) −11.0000 −0.659736
\(279\) 0 0
\(280\) 3.00000 0.179284
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 2.00000 0.119098
\(283\) −24.0000 −1.42665 −0.713326 0.700832i \(-0.752812\pi\)
−0.713326 + 0.700832i \(0.752812\pi\)
\(284\) 7.00000 0.415374
\(285\) 1.00000 0.0592349
\(286\) 0 0
\(287\) −12.0000 −0.708338
\(288\) 1.00000 0.0589256
\(289\) −16.0000 −0.941176
\(290\) 5.00000 0.293610
\(291\) 12.0000 0.703452
\(292\) 8.00000 0.468165
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) −2.00000 −0.116642
\(295\) 14.0000 0.815112
\(296\) 3.00000 0.174371
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 18.0000 1.04097
\(300\) −1.00000 −0.0577350
\(301\) −24.0000 −1.38334
\(302\) −10.0000 −0.575435
\(303\) −11.0000 −0.631933
\(304\) −1.00000 −0.0573539
\(305\) −2.00000 −0.114520
\(306\) −1.00000 −0.0571662
\(307\) 16.0000 0.913168 0.456584 0.889680i \(-0.349073\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(308\) 0 0
\(309\) 5.00000 0.284440
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) −3.00000 −0.169842
\(313\) 24.0000 1.35656 0.678280 0.734803i \(-0.262726\pi\)
0.678280 + 0.734803i \(0.262726\pi\)
\(314\) 21.0000 1.18510
\(315\) 3.00000 0.169031
\(316\) 10.0000 0.562544
\(317\) 2.00000 0.112331 0.0561656 0.998421i \(-0.482113\pi\)
0.0561656 + 0.998421i \(0.482113\pi\)
\(318\) 10.0000 0.560772
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) −20.0000 −1.11629
\(322\) 18.0000 1.00310
\(323\) 1.00000 0.0556415
\(324\) 1.00000 0.0555556
\(325\) 3.00000 0.166410
\(326\) 22.0000 1.21847
\(327\) 16.0000 0.884802
\(328\) −4.00000 −0.220863
\(329\) −6.00000 −0.330791
\(330\) 0 0
\(331\) 5.00000 0.274825 0.137412 0.990514i \(-0.456121\pi\)
0.137412 + 0.990514i \(0.456121\pi\)
\(332\) 9.00000 0.493939
\(333\) 3.00000 0.164399
\(334\) 12.0000 0.656611
\(335\) −10.0000 −0.546358
\(336\) −3.00000 −0.163663
\(337\) −20.0000 −1.08947 −0.544735 0.838608i \(-0.683370\pi\)
−0.544735 + 0.838608i \(0.683370\pi\)
\(338\) −4.00000 −0.217571
\(339\) 10.0000 0.543125
\(340\) −1.00000 −0.0542326
\(341\) 0 0
\(342\) −1.00000 −0.0540738
\(343\) −15.0000 −0.809924
\(344\) −8.00000 −0.431331
\(345\) −6.00000 −0.323029
\(346\) 14.0000 0.752645
\(347\) 15.0000 0.805242 0.402621 0.915367i \(-0.368099\pi\)
0.402621 + 0.915367i \(0.368099\pi\)
\(348\) −5.00000 −0.268028
\(349\) −6.00000 −0.321173 −0.160586 0.987022i \(-0.551338\pi\)
−0.160586 + 0.987022i \(0.551338\pi\)
\(350\) 3.00000 0.160357
\(351\) −3.00000 −0.160128
\(352\) 0 0
\(353\) 10.0000 0.532246 0.266123 0.963939i \(-0.414257\pi\)
0.266123 + 0.963939i \(0.414257\pi\)
\(354\) −14.0000 −0.744092
\(355\) 7.00000 0.371521
\(356\) 0 0
\(357\) 3.00000 0.158777
\(358\) −18.0000 −0.951330
\(359\) −8.00000 −0.422224 −0.211112 0.977462i \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) 1.00000 0.0527046
\(361\) −18.0000 −0.947368
\(362\) 14.0000 0.735824
\(363\) 0 0
\(364\) 9.00000 0.471728
\(365\) 8.00000 0.418739
\(366\) 2.00000 0.104542
\(367\) −17.0000 −0.887393 −0.443696 0.896177i \(-0.646333\pi\)
−0.443696 + 0.896177i \(0.646333\pi\)
\(368\) 6.00000 0.312772
\(369\) −4.00000 −0.208232
\(370\) 3.00000 0.155963
\(371\) −30.0000 −1.55752
\(372\) 0 0
\(373\) −27.0000 −1.39801 −0.699004 0.715118i \(-0.746373\pi\)
−0.699004 + 0.715118i \(0.746373\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) −2.00000 −0.103142
\(377\) 15.0000 0.772539
\(378\) −3.00000 −0.154303
\(379\) 3.00000 0.154100 0.0770498 0.997027i \(-0.475450\pi\)
0.0770498 + 0.997027i \(0.475450\pi\)
\(380\) −1.00000 −0.0512989
\(381\) 16.0000 0.819705
\(382\) 9.00000 0.460480
\(383\) 10.0000 0.510976 0.255488 0.966812i \(-0.417764\pi\)
0.255488 + 0.966812i \(0.417764\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 16.0000 0.814379
\(387\) −8.00000 −0.406663
\(388\) −12.0000 −0.609208
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) −3.00000 −0.151911
\(391\) −6.00000 −0.303433
\(392\) 2.00000 0.101015
\(393\) 10.0000 0.504433
\(394\) 0 0
\(395\) 10.0000 0.503155
\(396\) 0 0
\(397\) −29.0000 −1.45547 −0.727734 0.685859i \(-0.759427\pi\)
−0.727734 + 0.685859i \(0.759427\pi\)
\(398\) −16.0000 −0.802008
\(399\) 3.00000 0.150188
\(400\) 1.00000 0.0500000
\(401\) −28.0000 −1.39825 −0.699127 0.714998i \(-0.746428\pi\)
−0.699127 + 0.714998i \(0.746428\pi\)
\(402\) 10.0000 0.498755
\(403\) 0 0
\(404\) 11.0000 0.547270
\(405\) 1.00000 0.0496904
\(406\) 15.0000 0.744438
\(407\) 0 0
\(408\) 1.00000 0.0495074
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) −4.00000 −0.197546
\(411\) 15.0000 0.739895
\(412\) −5.00000 −0.246332
\(413\) 42.0000 2.06668
\(414\) 6.00000 0.294884
\(415\) 9.00000 0.441793
\(416\) 3.00000 0.147087
\(417\) 11.0000 0.538672
\(418\) 0 0
\(419\) 18.0000 0.879358 0.439679 0.898155i \(-0.355092\pi\)
0.439679 + 0.898155i \(0.355092\pi\)
\(420\) −3.00000 −0.146385
\(421\) −40.0000 −1.94948 −0.974740 0.223341i \(-0.928304\pi\)
−0.974740 + 0.223341i \(0.928304\pi\)
\(422\) 19.0000 0.924906
\(423\) −2.00000 −0.0972433
\(424\) −10.0000 −0.485643
\(425\) −1.00000 −0.0485071
\(426\) −7.00000 −0.339151
\(427\) −6.00000 −0.290360
\(428\) 20.0000 0.966736
\(429\) 0 0
\(430\) −8.00000 −0.385794
\(431\) −5.00000 −0.240842 −0.120421 0.992723i \(-0.538424\pi\)
−0.120421 + 0.992723i \(0.538424\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) 0 0
\(435\) −5.00000 −0.239732
\(436\) −16.0000 −0.766261
\(437\) −6.00000 −0.287019
\(438\) −8.00000 −0.382255
\(439\) −22.0000 −1.05000 −0.525001 0.851101i \(-0.675935\pi\)
−0.525001 + 0.851101i \(0.675935\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) −3.00000 −0.142695
\(443\) −17.0000 −0.807694 −0.403847 0.914826i \(-0.632327\pi\)
−0.403847 + 0.914826i \(0.632327\pi\)
\(444\) −3.00000 −0.142374
\(445\) 0 0
\(446\) 9.00000 0.426162
\(447\) −6.00000 −0.283790
\(448\) 3.00000 0.141737
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) −10.0000 −0.470360
\(453\) 10.0000 0.469841
\(454\) 28.0000 1.31411
\(455\) 9.00000 0.421927
\(456\) 1.00000 0.0468293
\(457\) 18.0000 0.842004 0.421002 0.907060i \(-0.361678\pi\)
0.421002 + 0.907060i \(0.361678\pi\)
\(458\) −20.0000 −0.934539
\(459\) 1.00000 0.0466760
\(460\) 6.00000 0.279751
\(461\) −15.0000 −0.698620 −0.349310 0.937007i \(-0.613584\pi\)
−0.349310 + 0.937007i \(0.613584\pi\)
\(462\) 0 0
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) 5.00000 0.232119
\(465\) 0 0
\(466\) 18.0000 0.833834
\(467\) −43.0000 −1.98980 −0.994901 0.100853i \(-0.967843\pi\)
−0.994901 + 0.100853i \(0.967843\pi\)
\(468\) 3.00000 0.138675
\(469\) −30.0000 −1.38527
\(470\) −2.00000 −0.0922531
\(471\) −21.0000 −0.967629
\(472\) 14.0000 0.644402
\(473\) 0 0
\(474\) −10.0000 −0.459315
\(475\) −1.00000 −0.0458831
\(476\) −3.00000 −0.137505
\(477\) −10.0000 −0.457869
\(478\) −11.0000 −0.503128
\(479\) 9.00000 0.411220 0.205610 0.978634i \(-0.434082\pi\)
0.205610 + 0.978634i \(0.434082\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 9.00000 0.410365
\(482\) 21.0000 0.956524
\(483\) −18.0000 −0.819028
\(484\) 0 0
\(485\) −12.0000 −0.544892
\(486\) −1.00000 −0.0453609
\(487\) 27.0000 1.22349 0.611743 0.791056i \(-0.290469\pi\)
0.611743 + 0.791056i \(0.290469\pi\)
\(488\) −2.00000 −0.0905357
\(489\) −22.0000 −0.994874
\(490\) 2.00000 0.0903508
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 4.00000 0.180334
\(493\) −5.00000 −0.225189
\(494\) −3.00000 −0.134976
\(495\) 0 0
\(496\) 0 0
\(497\) 21.0000 0.941979
\(498\) −9.00000 −0.403300
\(499\) −13.0000 −0.581960 −0.290980 0.956729i \(-0.593981\pi\)
−0.290980 + 0.956729i \(0.593981\pi\)
\(500\) 1.00000 0.0447214
\(501\) −12.0000 −0.536120
\(502\) 8.00000 0.357057
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 3.00000 0.133631
\(505\) 11.0000 0.489494
\(506\) 0 0
\(507\) 4.00000 0.177646
\(508\) −16.0000 −0.709885
\(509\) −34.0000 −1.50702 −0.753512 0.657434i \(-0.771642\pi\)
−0.753512 + 0.657434i \(0.771642\pi\)
\(510\) 1.00000 0.0442807
\(511\) 24.0000 1.06170
\(512\) 1.00000 0.0441942
\(513\) 1.00000 0.0441511
\(514\) −17.0000 −0.749838
\(515\) −5.00000 −0.220326
\(516\) 8.00000 0.352180
\(517\) 0 0
\(518\) 9.00000 0.395437
\(519\) −14.0000 −0.614532
\(520\) 3.00000 0.131559
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) 5.00000 0.218844
\(523\) 26.0000 1.13690 0.568450 0.822718i \(-0.307543\pi\)
0.568450 + 0.822718i \(0.307543\pi\)
\(524\) −10.0000 −0.436852
\(525\) −3.00000 −0.130931
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) −10.0000 −0.434372
\(531\) 14.0000 0.607548
\(532\) −3.00000 −0.130066
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) 20.0000 0.864675
\(536\) −10.0000 −0.431934
\(537\) 18.0000 0.776757
\(538\) −17.0000 −0.732922
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) −44.0000 −1.89171 −0.945854 0.324593i \(-0.894773\pi\)
−0.945854 + 0.324593i \(0.894773\pi\)
\(542\) 22.0000 0.944981
\(543\) −14.0000 −0.600798
\(544\) −1.00000 −0.0428746
\(545\) −16.0000 −0.685365
\(546\) −9.00000 −0.385164
\(547\) −22.0000 −0.940652 −0.470326 0.882493i \(-0.655864\pi\)
−0.470326 + 0.882493i \(0.655864\pi\)
\(548\) −15.0000 −0.640768
\(549\) −2.00000 −0.0853579
\(550\) 0 0
\(551\) −5.00000 −0.213007
\(552\) −6.00000 −0.255377
\(553\) 30.0000 1.27573
\(554\) 6.00000 0.254916
\(555\) −3.00000 −0.127343
\(556\) −11.0000 −0.466504
\(557\) −18.0000 −0.762684 −0.381342 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) 0 0
\(559\) −24.0000 −1.01509
\(560\) 3.00000 0.126773
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) −21.0000 −0.885044 −0.442522 0.896758i \(-0.645916\pi\)
−0.442522 + 0.896758i \(0.645916\pi\)
\(564\) 2.00000 0.0842152
\(565\) −10.0000 −0.420703
\(566\) −24.0000 −1.00880
\(567\) 3.00000 0.125988
\(568\) 7.00000 0.293713
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 1.00000 0.0418854
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 0 0
\(573\) −9.00000 −0.375980
\(574\) −12.0000 −0.500870
\(575\) 6.00000 0.250217
\(576\) 1.00000 0.0416667
\(577\) −46.0000 −1.91501 −0.957503 0.288425i \(-0.906868\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) −16.0000 −0.665512
\(579\) −16.0000 −0.664937
\(580\) 5.00000 0.207614
\(581\) 27.0000 1.12015
\(582\) 12.0000 0.497416
\(583\) 0 0
\(584\) 8.00000 0.331042
\(585\) 3.00000 0.124035
\(586\) 0 0
\(587\) 27.0000 1.11441 0.557205 0.830375i \(-0.311874\pi\)
0.557205 + 0.830375i \(0.311874\pi\)
\(588\) −2.00000 −0.0824786
\(589\) 0 0
\(590\) 14.0000 0.576371
\(591\) 0 0
\(592\) 3.00000 0.123299
\(593\) 14.0000 0.574911 0.287456 0.957794i \(-0.407191\pi\)
0.287456 + 0.957794i \(0.407191\pi\)
\(594\) 0 0
\(595\) −3.00000 −0.122988
\(596\) 6.00000 0.245770
\(597\) 16.0000 0.654836
\(598\) 18.0000 0.736075
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −30.0000 −1.22373 −0.611863 0.790964i \(-0.709580\pi\)
−0.611863 + 0.790964i \(0.709580\pi\)
\(602\) −24.0000 −0.978167
\(603\) −10.0000 −0.407231
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) −11.0000 −0.446844
\(607\) −11.0000 −0.446476 −0.223238 0.974764i \(-0.571663\pi\)
−0.223238 + 0.974764i \(0.571663\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −15.0000 −0.607831
\(610\) −2.00000 −0.0809776
\(611\) −6.00000 −0.242734
\(612\) −1.00000 −0.0404226
\(613\) −5.00000 −0.201948 −0.100974 0.994889i \(-0.532196\pi\)
−0.100974 + 0.994889i \(0.532196\pi\)
\(614\) 16.0000 0.645707
\(615\) 4.00000 0.161296
\(616\) 0 0
\(617\) −7.00000 −0.281809 −0.140905 0.990023i \(-0.545001\pi\)
−0.140905 + 0.990023i \(0.545001\pi\)
\(618\) 5.00000 0.201129
\(619\) −25.0000 −1.00483 −0.502417 0.864625i \(-0.667556\pi\)
−0.502417 + 0.864625i \(0.667556\pi\)
\(620\) 0 0
\(621\) −6.00000 −0.240772
\(622\) −24.0000 −0.962312
\(623\) 0 0
\(624\) −3.00000 −0.120096
\(625\) 1.00000 0.0400000
\(626\) 24.0000 0.959233
\(627\) 0 0
\(628\) 21.0000 0.837991
\(629\) −3.00000 −0.119618
\(630\) 3.00000 0.119523
\(631\) −18.0000 −0.716569 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(632\) 10.0000 0.397779
\(633\) −19.0000 −0.755182
\(634\) 2.00000 0.0794301
\(635\) −16.0000 −0.634941
\(636\) 10.0000 0.396526
\(637\) 6.00000 0.237729
\(638\) 0 0
\(639\) 7.00000 0.276916
\(640\) 1.00000 0.0395285
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) −20.0000 −0.789337
\(643\) −20.0000 −0.788723 −0.394362 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(644\) 18.0000 0.709299
\(645\) 8.00000 0.315000
\(646\) 1.00000 0.0393445
\(647\) 24.0000 0.943537 0.471769 0.881722i \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 3.00000 0.117670
\(651\) 0 0
\(652\) 22.0000 0.861586
\(653\) 44.0000 1.72185 0.860927 0.508729i \(-0.169885\pi\)
0.860927 + 0.508729i \(0.169885\pi\)
\(654\) 16.0000 0.625650
\(655\) −10.0000 −0.390732
\(656\) −4.00000 −0.156174
\(657\) 8.00000 0.312110
\(658\) −6.00000 −0.233904
\(659\) −6.00000 −0.233727 −0.116863 0.993148i \(-0.537284\pi\)
−0.116863 + 0.993148i \(0.537284\pi\)
\(660\) 0 0
\(661\) 8.00000 0.311164 0.155582 0.987823i \(-0.450275\pi\)
0.155582 + 0.987823i \(0.450275\pi\)
\(662\) 5.00000 0.194331
\(663\) 3.00000 0.116510
\(664\) 9.00000 0.349268
\(665\) −3.00000 −0.116335
\(666\) 3.00000 0.116248
\(667\) 30.0000 1.16160
\(668\) 12.0000 0.464294
\(669\) −9.00000 −0.347960
\(670\) −10.0000 −0.386334
\(671\) 0 0
\(672\) −3.00000 −0.115728
\(673\) −40.0000 −1.54189 −0.770943 0.636904i \(-0.780215\pi\)
−0.770943 + 0.636904i \(0.780215\pi\)
\(674\) −20.0000 −0.770371
\(675\) −1.00000 −0.0384900
\(676\) −4.00000 −0.153846
\(677\) 28.0000 1.07613 0.538064 0.842904i \(-0.319156\pi\)
0.538064 + 0.842904i \(0.319156\pi\)
\(678\) 10.0000 0.384048
\(679\) −36.0000 −1.38155
\(680\) −1.00000 −0.0383482
\(681\) −28.0000 −1.07296
\(682\) 0 0
\(683\) 29.0000 1.10965 0.554827 0.831966i \(-0.312784\pi\)
0.554827 + 0.831966i \(0.312784\pi\)
\(684\) −1.00000 −0.0382360
\(685\) −15.0000 −0.573121
\(686\) −15.0000 −0.572703
\(687\) 20.0000 0.763048
\(688\) −8.00000 −0.304997
\(689\) −30.0000 −1.14291
\(690\) −6.00000 −0.228416
\(691\) 43.0000 1.63580 0.817899 0.575362i \(-0.195139\pi\)
0.817899 + 0.575362i \(0.195139\pi\)
\(692\) 14.0000 0.532200
\(693\) 0 0
\(694\) 15.0000 0.569392
\(695\) −11.0000 −0.417254
\(696\) −5.00000 −0.189525
\(697\) 4.00000 0.151511
\(698\) −6.00000 −0.227103
\(699\) −18.0000 −0.680823
\(700\) 3.00000 0.113389
\(701\) 1.00000 0.0377695 0.0188847 0.999822i \(-0.493988\pi\)
0.0188847 + 0.999822i \(0.493988\pi\)
\(702\) −3.00000 −0.113228
\(703\) −3.00000 −0.113147
\(704\) 0 0
\(705\) 2.00000 0.0753244
\(706\) 10.0000 0.376355
\(707\) 33.0000 1.24109
\(708\) −14.0000 −0.526152
\(709\) 20.0000 0.751116 0.375558 0.926799i \(-0.377451\pi\)
0.375558 + 0.926799i \(0.377451\pi\)
\(710\) 7.00000 0.262705
\(711\) 10.0000 0.375029
\(712\) 0 0
\(713\) 0 0
\(714\) 3.00000 0.112272
\(715\) 0 0
\(716\) −18.0000 −0.672692
\(717\) 11.0000 0.410803
\(718\) −8.00000 −0.298557
\(719\) −8.00000 −0.298350 −0.149175 0.988811i \(-0.547662\pi\)
−0.149175 + 0.988811i \(0.547662\pi\)
\(720\) 1.00000 0.0372678
\(721\) −15.0000 −0.558629
\(722\) −18.0000 −0.669891
\(723\) −21.0000 −0.780998
\(724\) 14.0000 0.520306
\(725\) 5.00000 0.185695
\(726\) 0 0
\(727\) −19.0000 −0.704671 −0.352335 0.935874i \(-0.614612\pi\)
−0.352335 + 0.935874i \(0.614612\pi\)
\(728\) 9.00000 0.333562
\(729\) 1.00000 0.0370370
\(730\) 8.00000 0.296093
\(731\) 8.00000 0.295891
\(732\) 2.00000 0.0739221
\(733\) −18.0000 −0.664845 −0.332423 0.943131i \(-0.607866\pi\)
−0.332423 + 0.943131i \(0.607866\pi\)
\(734\) −17.0000 −0.627481
\(735\) −2.00000 −0.0737711
\(736\) 6.00000 0.221163
\(737\) 0 0
\(738\) −4.00000 −0.147242
\(739\) −11.0000 −0.404642 −0.202321 0.979319i \(-0.564848\pi\)
−0.202321 + 0.979319i \(0.564848\pi\)
\(740\) 3.00000 0.110282
\(741\) 3.00000 0.110208
\(742\) −30.0000 −1.10133
\(743\) −30.0000 −1.10059 −0.550297 0.834969i \(-0.685485\pi\)
−0.550297 + 0.834969i \(0.685485\pi\)
\(744\) 0 0
\(745\) 6.00000 0.219823
\(746\) −27.0000 −0.988540
\(747\) 9.00000 0.329293
\(748\) 0 0
\(749\) 60.0000 2.19235
\(750\) −1.00000 −0.0365148
\(751\) −16.0000 −0.583848 −0.291924 0.956441i \(-0.594295\pi\)
−0.291924 + 0.956441i \(0.594295\pi\)
\(752\) −2.00000 −0.0729325
\(753\) −8.00000 −0.291536
\(754\) 15.0000 0.546268
\(755\) −10.0000 −0.363937
\(756\) −3.00000 −0.109109
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 3.00000 0.108965
\(759\) 0 0
\(760\) −1.00000 −0.0362738
\(761\) −12.0000 −0.435000 −0.217500 0.976060i \(-0.569790\pi\)
−0.217500 + 0.976060i \(0.569790\pi\)
\(762\) 16.0000 0.579619
\(763\) −48.0000 −1.73772
\(764\) 9.00000 0.325609
\(765\) −1.00000 −0.0361551
\(766\) 10.0000 0.361315
\(767\) 42.0000 1.51653
\(768\) −1.00000 −0.0360844
\(769\) −1.00000 −0.0360609 −0.0180305 0.999837i \(-0.505740\pi\)
−0.0180305 + 0.999837i \(0.505740\pi\)
\(770\) 0 0
\(771\) 17.0000 0.612240
\(772\) 16.0000 0.575853
\(773\) 34.0000 1.22290 0.611448 0.791285i \(-0.290588\pi\)
0.611448 + 0.791285i \(0.290588\pi\)
\(774\) −8.00000 −0.287554
\(775\) 0 0
\(776\) −12.0000 −0.430775
\(777\) −9.00000 −0.322873
\(778\) −18.0000 −0.645331
\(779\) 4.00000 0.143315
\(780\) −3.00000 −0.107417
\(781\) 0 0
\(782\) −6.00000 −0.214560
\(783\) −5.00000 −0.178685
\(784\) 2.00000 0.0714286
\(785\) 21.0000 0.749522
\(786\) 10.0000 0.356688
\(787\) −38.0000 −1.35455 −0.677277 0.735728i \(-0.736840\pi\)
−0.677277 + 0.735728i \(0.736840\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 10.0000 0.355784
\(791\) −30.0000 −1.06668
\(792\) 0 0
\(793\) −6.00000 −0.213066
\(794\) −29.0000 −1.02917
\(795\) 10.0000 0.354663
\(796\) −16.0000 −0.567105
\(797\) −54.0000 −1.91278 −0.956389 0.292096i \(-0.905647\pi\)
−0.956389 + 0.292096i \(0.905647\pi\)
\(798\) 3.00000 0.106199
\(799\) 2.00000 0.0707549
\(800\) 1.00000 0.0353553
\(801\) 0 0
\(802\) −28.0000 −0.988714
\(803\) 0 0
\(804\) 10.0000 0.352673
\(805\) 18.0000 0.634417
\(806\) 0 0
\(807\) 17.0000 0.598428
\(808\) 11.0000 0.386979
\(809\) −24.0000 −0.843795 −0.421898 0.906644i \(-0.638636\pi\)
−0.421898 + 0.906644i \(0.638636\pi\)
\(810\) 1.00000 0.0351364
\(811\) 43.0000 1.50993 0.754967 0.655763i \(-0.227653\pi\)
0.754967 + 0.655763i \(0.227653\pi\)
\(812\) 15.0000 0.526397
\(813\) −22.0000 −0.771574
\(814\) 0 0
\(815\) 22.0000 0.770626
\(816\) 1.00000 0.0350070
\(817\) 8.00000 0.279885
\(818\) 10.0000 0.349642
\(819\) 9.00000 0.314485
\(820\) −4.00000 −0.139686
\(821\) −6.00000 −0.209401 −0.104701 0.994504i \(-0.533388\pi\)
−0.104701 + 0.994504i \(0.533388\pi\)
\(822\) 15.0000 0.523185
\(823\) 29.0000 1.01088 0.505438 0.862863i \(-0.331331\pi\)
0.505438 + 0.862863i \(0.331331\pi\)
\(824\) −5.00000 −0.174183
\(825\) 0 0
\(826\) 42.0000 1.46137
\(827\) −1.00000 −0.0347734 −0.0173867 0.999849i \(-0.505535\pi\)
−0.0173867 + 0.999849i \(0.505535\pi\)
\(828\) 6.00000 0.208514
\(829\) −2.00000 −0.0694629 −0.0347314 0.999397i \(-0.511058\pi\)
−0.0347314 + 0.999397i \(0.511058\pi\)
\(830\) 9.00000 0.312395
\(831\) −6.00000 −0.208138
\(832\) 3.00000 0.104006
\(833\) −2.00000 −0.0692959
\(834\) 11.0000 0.380899
\(835\) 12.0000 0.415277
\(836\) 0 0
\(837\) 0 0
\(838\) 18.0000 0.621800
\(839\) −45.0000 −1.55357 −0.776786 0.629764i \(-0.783151\pi\)
−0.776786 + 0.629764i \(0.783151\pi\)
\(840\) −3.00000 −0.103510
\(841\) −4.00000 −0.137931
\(842\) −40.0000 −1.37849
\(843\) −6.00000 −0.206651
\(844\) 19.0000 0.654007
\(845\) −4.00000 −0.137604
\(846\) −2.00000 −0.0687614
\(847\) 0 0
\(848\) −10.0000 −0.343401
\(849\) 24.0000 0.823678
\(850\) −1.00000 −0.0342997
\(851\) 18.0000 0.617032
\(852\) −7.00000 −0.239816
\(853\) −5.00000 −0.171197 −0.0855984 0.996330i \(-0.527280\pi\)
−0.0855984 + 0.996330i \(0.527280\pi\)
\(854\) −6.00000 −0.205316
\(855\) −1.00000 −0.0341993
\(856\) 20.0000 0.683586
\(857\) 47.0000 1.60549 0.802745 0.596323i \(-0.203372\pi\)
0.802745 + 0.596323i \(0.203372\pi\)
\(858\) 0 0
\(859\) 12.0000 0.409435 0.204717 0.978821i \(-0.434372\pi\)
0.204717 + 0.978821i \(0.434372\pi\)
\(860\) −8.00000 −0.272798
\(861\) 12.0000 0.408959
\(862\) −5.00000 −0.170301
\(863\) 6.00000 0.204242 0.102121 0.994772i \(-0.467437\pi\)
0.102121 + 0.994772i \(0.467437\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 14.0000 0.476014
\(866\) −16.0000 −0.543702
\(867\) 16.0000 0.543388
\(868\) 0 0
\(869\) 0 0
\(870\) −5.00000 −0.169516
\(871\) −30.0000 −1.01651
\(872\) −16.0000 −0.541828
\(873\) −12.0000 −0.406138
\(874\) −6.00000 −0.202953
\(875\) 3.00000 0.101419
\(876\) −8.00000 −0.270295
\(877\) −31.0000 −1.04680 −0.523398 0.852088i \(-0.675336\pi\)
−0.523398 + 0.852088i \(0.675336\pi\)
\(878\) −22.0000 −0.742464
\(879\) 0 0
\(880\) 0 0
\(881\) −4.00000 −0.134763 −0.0673817 0.997727i \(-0.521465\pi\)
−0.0673817 + 0.997727i \(0.521465\pi\)
\(882\) 2.00000 0.0673435
\(883\) −24.0000 −0.807664 −0.403832 0.914833i \(-0.632322\pi\)
−0.403832 + 0.914833i \(0.632322\pi\)
\(884\) −3.00000 −0.100901
\(885\) −14.0000 −0.470605
\(886\) −17.0000 −0.571126
\(887\) 44.0000 1.47738 0.738688 0.674048i \(-0.235446\pi\)
0.738688 + 0.674048i \(0.235446\pi\)
\(888\) −3.00000 −0.100673
\(889\) −48.0000 −1.60987
\(890\) 0 0
\(891\) 0 0
\(892\) 9.00000 0.301342
\(893\) 2.00000 0.0669274
\(894\) −6.00000 −0.200670
\(895\) −18.0000 −0.601674
\(896\) 3.00000 0.100223
\(897\) −18.0000 −0.601003
\(898\) −18.0000 −0.600668
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) 10.0000 0.333148
\(902\) 0 0
\(903\) 24.0000 0.798670
\(904\) −10.0000 −0.332595
\(905\) 14.0000 0.465376
\(906\) 10.0000 0.332228
\(907\) −18.0000 −0.597680 −0.298840 0.954303i \(-0.596600\pi\)
−0.298840 + 0.954303i \(0.596600\pi\)
\(908\) 28.0000 0.929213
\(909\) 11.0000 0.364847
\(910\) 9.00000 0.298347
\(911\) 15.0000 0.496972 0.248486 0.968635i \(-0.420067\pi\)
0.248486 + 0.968635i \(0.420067\pi\)
\(912\) 1.00000 0.0331133
\(913\) 0 0
\(914\) 18.0000 0.595387
\(915\) 2.00000 0.0661180
\(916\) −20.0000 −0.660819
\(917\) −30.0000 −0.990687
\(918\) 1.00000 0.0330049
\(919\) −50.0000 −1.64935 −0.824674 0.565608i \(-0.808641\pi\)
−0.824674 + 0.565608i \(0.808641\pi\)
\(920\) 6.00000 0.197814
\(921\) −16.0000 −0.527218
\(922\) −15.0000 −0.493999
\(923\) 21.0000 0.691223
\(924\) 0 0
\(925\) 3.00000 0.0986394
\(926\) 4.00000 0.131448
\(927\) −5.00000 −0.164222
\(928\) 5.00000 0.164133
\(929\) 2.00000 0.0656179 0.0328089 0.999462i \(-0.489555\pi\)
0.0328089 + 0.999462i \(0.489555\pi\)
\(930\) 0 0
\(931\) −2.00000 −0.0655474
\(932\) 18.0000 0.589610
\(933\) 24.0000 0.785725
\(934\) −43.0000 −1.40700
\(935\) 0 0
\(936\) 3.00000 0.0980581
\(937\) −34.0000 −1.11073 −0.555366 0.831606i \(-0.687422\pi\)
−0.555366 + 0.831606i \(0.687422\pi\)
\(938\) −30.0000 −0.979535
\(939\) −24.0000 −0.783210
\(940\) −2.00000 −0.0652328
\(941\) −19.0000 −0.619382 −0.309691 0.950837i \(-0.600226\pi\)
−0.309691 + 0.950837i \(0.600226\pi\)
\(942\) −21.0000 −0.684217
\(943\) −24.0000 −0.781548
\(944\) 14.0000 0.455661
\(945\) −3.00000 −0.0975900
\(946\) 0 0
\(947\) 27.0000 0.877382 0.438691 0.898638i \(-0.355442\pi\)
0.438691 + 0.898638i \(0.355442\pi\)
\(948\) −10.0000 −0.324785
\(949\) 24.0000 0.779073
\(950\) −1.00000 −0.0324443
\(951\) −2.00000 −0.0648544
\(952\) −3.00000 −0.0972306
\(953\) −42.0000 −1.36051 −0.680257 0.732974i \(-0.738132\pi\)
−0.680257 + 0.732974i \(0.738132\pi\)
\(954\) −10.0000 −0.323762
\(955\) 9.00000 0.291233
\(956\) −11.0000 −0.355765
\(957\) 0 0
\(958\) 9.00000 0.290777
\(959\) −45.0000 −1.45313
\(960\) −1.00000 −0.0322749
\(961\) −31.0000 −1.00000
\(962\) 9.00000 0.290172
\(963\) 20.0000 0.644491
\(964\) 21.0000 0.676364
\(965\) 16.0000 0.515058
\(966\) −18.0000 −0.579141
\(967\) 24.0000 0.771788 0.385894 0.922543i \(-0.373893\pi\)
0.385894 + 0.922543i \(0.373893\pi\)
\(968\) 0 0
\(969\) −1.00000 −0.0321246
\(970\) −12.0000 −0.385297
\(971\) 12.0000 0.385098 0.192549 0.981287i \(-0.438325\pi\)
0.192549 + 0.981287i \(0.438325\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −33.0000 −1.05793
\(974\) 27.0000 0.865136
\(975\) −3.00000 −0.0960769
\(976\) −2.00000 −0.0640184
\(977\) 30.0000 0.959785 0.479893 0.877327i \(-0.340676\pi\)
0.479893 + 0.877327i \(0.340676\pi\)
\(978\) −22.0000 −0.703482
\(979\) 0 0
\(980\) 2.00000 0.0638877
\(981\) −16.0000 −0.510841
\(982\) 24.0000 0.765871
\(983\) 36.0000 1.14822 0.574111 0.818778i \(-0.305348\pi\)
0.574111 + 0.818778i \(0.305348\pi\)
\(984\) 4.00000 0.127515
\(985\) 0 0
\(986\) −5.00000 −0.159232
\(987\) 6.00000 0.190982
\(988\) −3.00000 −0.0954427
\(989\) −48.0000 −1.52631
\(990\) 0 0
\(991\) −26.0000 −0.825917 −0.412959 0.910750i \(-0.635505\pi\)
−0.412959 + 0.910750i \(0.635505\pi\)
\(992\) 0 0
\(993\) −5.00000 −0.158670
\(994\) 21.0000 0.666080
\(995\) −16.0000 −0.507234
\(996\) −9.00000 −0.285176
\(997\) 13.0000 0.411714 0.205857 0.978582i \(-0.434002\pi\)
0.205857 + 0.978582i \(0.434002\pi\)
\(998\) −13.0000 −0.411508
\(999\) −3.00000 −0.0949158
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.r.1.1 yes 1
11.10 odd 2 3630.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3630.2.a.d.1.1 1 11.10 odd 2
3630.2.a.r.1.1 yes 1 1.1 even 1 trivial