Properties

Label 3630.2.a.d.1.1
Level $3630$
Weight $2$
Character 3630.1
Self dual yes
Analytic conductor $28.986$
Analytic rank $1$
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: \(1\)
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 \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) −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 \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) 3.00000 0.801784
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.00000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 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 \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 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 \(-0.398885\pi\)
0.312348 + 0.949968i \(0.398885\pi\)
\(42\) −3.00000 −0.462910
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 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 \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 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 \(-0.655085\pi\)
−0.468165 + 0.883641i \(0.655085\pi\)
\(74\) −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 \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) −4.00000 −0.441726
\(83\) −9.00000 −0.987878 −0.493939 0.869496i \(-0.664443\pi\)
−0.493939 + 0.869496i \(0.664443\pi\)
\(84\) 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 \(-0.684333\pi\)
−0.547270 + 0.836956i \(0.684333\pi\)
\(102\) 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 \(-0.917670\pi\)
−0.966736 + 0.255774i \(0.917670\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 16.0000 1.53252 0.766261 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) 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 \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −8.00000 −0.704361
\(130\) 3.00000 0.263117
\(131\) 10.0000 0.873704 0.436852 0.899533i \(-0.356093\pi\)
0.436852 + 0.899533i \(0.356093\pi\)
\(132\) 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 \(-0.345513\pi\)
0.466504 + 0.884519i \(0.345513\pi\)
\(140\) −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 \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 1.00000 0.0816497
\(151\) 10.0000 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) −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 \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) −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 \(-0.678635\pi\)
−0.532200 + 0.846619i \(0.678635\pi\)
\(174\) −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 \(-0.695330\pi\)
−0.575853 + 0.817554i \(0.695330\pi\)
\(194\) 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 \(-0.726913\pi\)
−0.654007 + 0.756489i \(0.726913\pi\)
\(212\) −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 \(-0.879513\pi\)
−0.929213 + 0.369546i \(0.879513\pi\)
\(228\) −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 \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 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 \(-0.384220\pi\)
0.355765 + 0.934575i \(0.384220\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −21.0000 −1.35273 −0.676364 0.736567i \(-0.736446\pi\)
−0.676364 + 0.736567i \(0.736446\pi\)
\(242\) 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 \(-0.732936\pi\)
−0.668202 + 0.743980i \(0.732936\pi\)
\(272\) 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 \(-0.557691\pi\)
−0.180253 + 0.983620i \(0.557691\pi\)
\(278\) −11.0000 −0.659736
\(279\) 0 0
\(280\) 3.00000 0.179284
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) −2.00000 −0.119098
\(283\) 24.0000 1.42665 0.713326 0.700832i \(-0.247188\pi\)
0.713326 + 0.700832i \(0.247188\pi\)
\(284\) 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 \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) 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 \(-0.316630\pi\)
0.544735 + 0.838608i \(0.316630\pi\)
\(338\) 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 \(-0.631901\pi\)
−0.402621 + 0.915367i \(0.631901\pi\)
\(348\) 5.00000 0.268028
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) 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 \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(360\) −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 \(-0.253627\pi\)
0.699004 + 0.715118i \(0.253627\pi\)
\(374\) 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 \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) −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 \(-0.461576\pi\)
0.120421 + 0.992723i \(0.461576\pi\)
\(432\) −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 \(-0.324065\pi\)
0.525001 + 0.851101i \(0.324065\pi\)
\(440\) 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 \(-0.638322\pi\)
−0.421002 + 0.907060i \(0.638322\pi\)
\(458\) 20.0000 0.934539
\(459\) −1.00000 −0.0466760
\(460\) 6.00000 0.279751
\(461\) 15.0000 0.698620 0.349310 0.937007i \(-0.386416\pi\)
0.349310 + 0.937007i \(0.386416\pi\)
\(462\) 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 \(-0.565918\pi\)
−0.205610 + 0.978634i \(0.565918\pi\)
\(480\) 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 \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) −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 \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 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 \(-0.692457\pi\)
−0.568450 + 0.822718i \(0.692457\pi\)
\(524\) 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 \(-0.105227\pi\)
0.945854 + 0.324593i \(0.105227\pi\)
\(542\) 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 \(-0.344136\pi\)
0.470326 + 0.882493i \(0.344136\pi\)
\(548\) −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 \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 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 \(-0.354084\pi\)
0.442522 + 0.896758i \(0.354084\pi\)
\(564\) 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 \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 1.00000 0.0418854
\(571\) −12.0000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) 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 \(-0.592809\pi\)
−0.287456 + 0.957794i \(0.592809\pi\)
\(594\) 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 \(-0.290420\pi\)
0.611863 + 0.790964i \(0.290420\pi\)
\(602\) 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 \(-0.428337\pi\)
0.223238 + 0.974764i \(0.428337\pi\)
\(608\) −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 \(-0.467804\pi\)
0.100974 + 0.994889i \(0.467804\pi\)
\(614\) 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 \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) 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 \(-0.219785\pi\)
0.770943 + 0.636904i \(0.219785\pi\)
\(674\) −20.0000 −0.770371
\(675\) −1.00000 −0.0384900
\(676\) −4.00000 −0.153846
\(677\) −28.0000 −1.07613 −0.538064 0.842904i \(-0.680844\pi\)
−0.538064 + 0.842904i \(0.680844\pi\)
\(678\) −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 \(-0.506012\pi\)
−0.0188847 + 0.999822i \(0.506012\pi\)
\(702\) −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 \(-0.392134\pi\)
0.332423 + 0.943131i \(0.392134\pi\)
\(734\) 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 \(-0.435152\pi\)
0.202321 + 0.979319i \(0.435152\pi\)
\(740\) 3.00000 0.110282
\(741\) 3.00000 0.110208
\(742\) −30.0000 −1.10133
\(743\) 30.0000 1.10059 0.550297 0.834969i \(-0.314515\pi\)
0.550297 + 0.834969i \(0.314515\pi\)
\(744\) 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 \(-0.430210\pi\)
0.217500 + 0.976060i \(0.430210\pi\)
\(762\) 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 \(-0.494260\pi\)
0.0180305 + 0.999837i \(0.494260\pi\)
\(770\) 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 \(-0.263160\pi\)
0.677277 + 0.735728i \(0.263160\pi\)
\(788\) 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 \(-0.361364\pi\)
0.421898 + 0.906644i \(0.361364\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −43.0000 −1.50993 −0.754967 0.655763i \(-0.772347\pi\)
−0.754967 + 0.655763i \(0.772347\pi\)
\(812\) 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 \(-0.466612\pi\)
0.104701 + 0.994504i \(0.466612\pi\)
\(822\) −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 \(-0.494465\pi\)
0.0173867 + 0.999849i \(0.494465\pi\)
\(828\) 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 \(-0.472720\pi\)
0.0855984 + 0.996330i \(0.472720\pi\)
\(854\) 6.00000 0.205316
\(855\) 1.00000 0.0341993
\(856\) 20.0000 0.683586
\(857\) −47.0000 −1.60549 −0.802745 0.596323i \(-0.796628\pi\)
−0.802745 + 0.596323i \(0.796628\pi\)
\(858\) 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 \(-0.324664\pi\)
0.523398 + 0.852088i \(0.324664\pi\)
\(878\) −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 \(-0.764554\pi\)
−0.738688 + 0.674048i \(0.764554\pi\)
\(888\) 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 \(-0.191359\pi\)
0.824674 + 0.565608i \(0.191359\pi\)
\(920\) −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 \(-0.312578\pi\)
0.555366 + 0.831606i \(0.312578\pi\)
\(938\) −30.0000 −0.979535
\(939\) −24.0000 −0.783210
\(940\) −2.00000 −0.0652328
\(941\) 19.0000 0.619382 0.309691 0.950837i \(-0.399774\pi\)
0.309691 + 0.950837i \(0.399774\pi\)
\(942\) 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 \(-0.261868\pi\)
0.680257 + 0.732974i \(0.261868\pi\)
\(954\) 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 \(-0.626107\pi\)
−0.385894 + 0.922543i \(0.626107\pi\)
\(968\) 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 \(-0.565998\pi\)
−0.205857 + 0.978582i \(0.565998\pi\)
\(998\) 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.d.1.1 1
11.10 odd 2 3630.2.a.r.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3630.2.a.d.1.1 1 1.1 even 1 trivial
3630.2.a.r.1.1 yes 1 11.10 odd 2