Properties

Label 1950.2.a.k.1.1
Level $1950$
Weight $2$
Character 1950.1
Self dual yes
Analytic conductor $15.571$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1950.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +4.00000 q^{11} +1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{16} +6.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} -4.00000 q^{22} -8.00000 q^{23} -1.00000 q^{24} +1.00000 q^{26} +1.00000 q^{27} +6.00000 q^{29} -8.00000 q^{31} -1.00000 q^{32} +4.00000 q^{33} -6.00000 q^{34} +1.00000 q^{36} +10.0000 q^{37} -4.00000 q^{38} -1.00000 q^{39} -6.00000 q^{41} -4.00000 q^{43} +4.00000 q^{44} +8.00000 q^{46} +1.00000 q^{48} -7.00000 q^{49} +6.00000 q^{51} -1.00000 q^{52} +10.0000 q^{53} -1.00000 q^{54} +4.00000 q^{57} -6.00000 q^{58} +4.00000 q^{59} -2.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} -4.00000 q^{66} +12.0000 q^{67} +6.00000 q^{68} -8.00000 q^{69} +16.0000 q^{71} -1.00000 q^{72} -2.00000 q^{73} -10.0000 q^{74} +4.00000 q^{76} +1.00000 q^{78} -16.0000 q^{79} +1.00000 q^{81} +6.00000 q^{82} +12.0000 q^{83} +4.00000 q^{86} +6.00000 q^{87} -4.00000 q^{88} +10.0000 q^{89} -8.00000 q^{92} -8.00000 q^{93} -1.00000 q^{96} +6.00000 q^{97} +7.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 1.00000 0.288675
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) −1.00000 −0.235702
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) −8.00000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0 0
\(26\) 1.00000 0.196116
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.00000 0.696311
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) −4.00000 −0.648886
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 4.00000 0.603023
\(45\) 0 0
\(46\) 8.00000 1.17954
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.00000 0.144338
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 6.00000 0.840168
\(52\) −1.00000 −0.138675
\(53\) 10.0000 1.37361 0.686803 0.726844i \(-0.259014\pi\)
0.686803 + 0.726844i \(0.259014\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) 0 0
\(57\) 4.00000 0.529813
\(58\) −6.00000 −0.787839
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 8.00000 1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −4.00000 −0.492366
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) 6.00000 0.727607
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) 16.0000 1.89885 0.949425 0.313993i \(-0.101667\pi\)
0.949425 + 0.313993i \(0.101667\pi\)
\(72\) −1.00000 −0.117851
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −10.0000 −1.16248
\(75\) 0 0
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 1.00000 0.113228
\(79\) −16.0000 −1.80014 −0.900070 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 4.00000 0.431331
\(87\) 6.00000 0.643268
\(88\) −4.00000 −0.426401
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −8.00000 −0.834058
\(93\) −8.00000 −0.829561
\(94\) 0 0
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 7.00000 0.707107
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −2.00000 −0.199007 −0.0995037 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) −6.00000 −0.594089
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) −10.0000 −0.971286
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 1.00000 0.0962250
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 10.0000 0.949158
\(112\) 0 0
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) −4.00000 −0.374634
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) −1.00000 −0.0924500
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 2.00000 0.181071
\(123\) −6.00000 −0.541002
\(124\) −8.00000 −0.718421
\(125\) 0 0
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 4.00000 0.348155
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) −6.00000 −0.514496
\(137\) −10.0000 −0.854358 −0.427179 0.904167i \(-0.640493\pi\)
−0.427179 + 0.904167i \(0.640493\pi\)
\(138\) 8.00000 0.681005
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −16.0000 −1.34269
\(143\) −4.00000 −0.334497
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 2.00000 0.165521
\(147\) −7.00000 −0.577350
\(148\) 10.0000 0.821995
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) −4.00000 −0.324443
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) −1.00000 −0.0800641
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 16.0000 1.27289
\(159\) 10.0000 0.793052
\(160\) 0 0
\(161\) 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
\(166\) −12.0000 −0.931381
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 4.00000 0.305888
\(172\) −4.00000 −0.304997
\(173\) 18.0000 1.36851 0.684257 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) −6.00000 −0.454859
\(175\) 0 0
\(176\) 4.00000 0.301511
\(177\) 4.00000 0.300658
\(178\) −10.0000 −0.749532
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 0 0
\(183\) −2.00000 −0.147844
\(184\) 8.00000 0.589768
\(185\) 0 0
\(186\) 8.00000 0.586588
\(187\) 24.0000 1.75505
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.00000 0.0721688
\(193\) −10.0000 −0.719816 −0.359908 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) −7.00000 −0.500000
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) −4.00000 −0.284268
\(199\) −8.00000 −0.567105 −0.283552 0.958957i \(-0.591513\pi\)
−0.283552 + 0.958957i \(0.591513\pi\)
\(200\) 0 0
\(201\) 12.0000 0.846415
\(202\) 2.00000 0.140720
\(203\) 0 0
\(204\) 6.00000 0.420084
\(205\) 0 0
\(206\) 0 0
\(207\) −8.00000 −0.556038
\(208\) −1.00000 −0.0693375
\(209\) 16.0000 1.10674
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 10.0000 0.686803
\(213\) 16.0000 1.09630
\(214\) −12.0000 −0.820303
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 10.0000 0.677285
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) −6.00000 −0.403604
\(222\) −10.0000 −0.671156
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 10.0000 0.665190
\(227\) −4.00000 −0.265489 −0.132745 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) 4.00000 0.264906
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 14.0000 0.917170 0.458585 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) 1.00000 0.0653720
\(235\) 0 0
\(236\) 4.00000 0.260378
\(237\) −16.0000 −1.03931
\(238\) 0 0
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 0 0
\(241\) 18.0000 1.15948 0.579741 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) −5.00000 −0.321412
\(243\) 1.00000 0.0641500
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) 6.00000 0.382546
\(247\) −4.00000 −0.254514
\(248\) 8.00000 0.508001
\(249\) 12.0000 0.760469
\(250\) 0 0
\(251\) −28.0000 −1.76734 −0.883672 0.468106i \(-0.844936\pi\)
−0.883672 + 0.468106i \(0.844936\pi\)
\(252\) 0 0
\(253\) −32.0000 −2.01182
\(254\) 8.00000 0.501965
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 4.00000 0.249029
\(259\) 0 0
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) −12.0000 −0.741362
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) −4.00000 −0.246183
\(265\) 0 0
\(266\) 0 0
\(267\) 10.0000 0.611990
\(268\) 12.0000 0.733017
\(269\) −26.0000 −1.58525 −0.792624 0.609711i \(-0.791286\pi\)
−0.792624 + 0.609711i \(0.791286\pi\)
\(270\) 0 0
\(271\) 24.0000 1.45790 0.728948 0.684569i \(-0.240010\pi\)
0.728948 + 0.684569i \(0.240010\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) 10.0000 0.604122
\(275\) 0 0
\(276\) −8.00000 −0.481543
\(277\) 10.0000 0.600842 0.300421 0.953807i \(-0.402873\pi\)
0.300421 + 0.953807i \(0.402873\pi\)
\(278\) −12.0000 −0.719712
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) −20.0000 −1.18888 −0.594438 0.804141i \(-0.702626\pi\)
−0.594438 + 0.804141i \(0.702626\pi\)
\(284\) 16.0000 0.949425
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 6.00000 0.351726
\(292\) −2.00000 −0.117041
\(293\) 26.0000 1.51894 0.759468 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) 7.00000 0.408248
\(295\) 0 0
\(296\) −10.0000 −0.581238
\(297\) 4.00000 0.232104
\(298\) −6.00000 −0.347571
\(299\) 8.00000 0.462652
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −2.00000 −0.114897
\(304\) 4.00000 0.229416
\(305\) 0 0
\(306\) −6.00000 −0.342997
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 1.00000 0.0566139
\(313\) 22.0000 1.24351 0.621757 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) 2.00000 0.112331 0.0561656 0.998421i \(-0.482113\pi\)
0.0561656 + 0.998421i \(0.482113\pi\)
\(318\) −10.0000 −0.560772
\(319\) 24.0000 1.34374
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 24.0000 1.33540
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 4.00000 0.221540
\(327\) −10.0000 −0.553001
\(328\) 6.00000 0.331295
\(329\) 0 0
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) 12.0000 0.658586
\(333\) 10.0000 0.547997
\(334\) 8.00000 0.437741
\(335\) 0 0
\(336\) 0 0
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −10.0000 −0.543125
\(340\) 0 0
\(341\) −32.0000 −1.73290
\(342\) −4.00000 −0.216295
\(343\) 0 0
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) −18.0000 −0.967686
\(347\) −20.0000 −1.07366 −0.536828 0.843692i \(-0.680378\pi\)
−0.536828 + 0.843692i \(0.680378\pi\)
\(348\) 6.00000 0.321634
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) −4.00000 −0.213201
\(353\) 30.0000 1.59674 0.798369 0.602168i \(-0.205696\pi\)
0.798369 + 0.602168i \(0.205696\pi\)
\(354\) −4.00000 −0.212598
\(355\) 0 0
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) 16.0000 0.844448 0.422224 0.906492i \(-0.361250\pi\)
0.422224 + 0.906492i \(0.361250\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) −6.00000 −0.315353
\(363\) 5.00000 0.262432
\(364\) 0 0
\(365\) 0 0
\(366\) 2.00000 0.104542
\(367\) 24.0000 1.25279 0.626395 0.779506i \(-0.284530\pi\)
0.626395 + 0.779506i \(0.284530\pi\)
\(368\) −8.00000 −0.417029
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) 0 0
\(372\) −8.00000 −0.414781
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) −24.0000 −1.24101
\(375\) 0 0
\(376\) 0 0
\(377\) −6.00000 −0.309016
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) −8.00000 −0.409852
\(382\) 0 0
\(383\) −32.0000 −1.63512 −0.817562 0.575841i \(-0.804675\pi\)
−0.817562 + 0.575841i \(0.804675\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) −4.00000 −0.203331
\(388\) 6.00000 0.304604
\(389\) −34.0000 −1.72387 −0.861934 0.507020i \(-0.830747\pi\)
−0.861934 + 0.507020i \(0.830747\pi\)
\(390\) 0 0
\(391\) −48.0000 −2.42746
\(392\) 7.00000 0.353553
\(393\) 12.0000 0.605320
\(394\) 6.00000 0.302276
\(395\) 0 0
\(396\) 4.00000 0.201008
\(397\) −30.0000 −1.50566 −0.752828 0.658217i \(-0.771311\pi\)
−0.752828 + 0.658217i \(0.771311\pi\)
\(398\) 8.00000 0.401004
\(399\) 0 0
\(400\) 0 0
\(401\) 34.0000 1.69788 0.848939 0.528490i \(-0.177242\pi\)
0.848939 + 0.528490i \(0.177242\pi\)
\(402\) −12.0000 −0.598506
\(403\) 8.00000 0.398508
\(404\) −2.00000 −0.0995037
\(405\) 0 0
\(406\) 0 0
\(407\) 40.0000 1.98273
\(408\) −6.00000 −0.297044
\(409\) −22.0000 −1.08783 −0.543915 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 0 0
\(411\) −10.0000 −0.493264
\(412\) 0 0
\(413\) 0 0
\(414\) 8.00000 0.393179
\(415\) 0 0
\(416\) 1.00000 0.0490290
\(417\) 12.0000 0.587643
\(418\) −16.0000 −0.782586
\(419\) −4.00000 −0.195413 −0.0977064 0.995215i \(-0.531151\pi\)
−0.0977064 + 0.995215i \(0.531151\pi\)
\(420\) 0 0
\(421\) −34.0000 −1.65706 −0.828529 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) 12.0000 0.584151
\(423\) 0 0
\(424\) −10.0000 −0.485643
\(425\) 0 0
\(426\) −16.0000 −0.775203
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) −4.00000 −0.193122
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 1.00000 0.0481125
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −10.0000 −0.478913
\(437\) −32.0000 −1.53077
\(438\) 2.00000 0.0955637
\(439\) −40.0000 −1.90910 −0.954548 0.298057i \(-0.903661\pi\)
−0.954548 + 0.298057i \(0.903661\pi\)
\(440\) 0 0
\(441\) −7.00000 −0.333333
\(442\) 6.00000 0.285391
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) 10.0000 0.474579
\(445\) 0 0
\(446\) 8.00000 0.378811
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 0 0
\(451\) −24.0000 −1.13012
\(452\) −10.0000 −0.470360
\(453\) 0 0
\(454\) 4.00000 0.187729
\(455\) 0 0
\(456\) −4.00000 −0.187317
\(457\) −34.0000 −1.59045 −0.795226 0.606313i \(-0.792648\pi\)
−0.795226 + 0.606313i \(0.792648\pi\)
\(458\) −14.0000 −0.654177
\(459\) 6.00000 0.280056
\(460\) 0 0
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) −14.0000 −0.648537
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 0 0
\(470\) 0 0
\(471\) 2.00000 0.0921551
\(472\) −4.00000 −0.184115
\(473\) −16.0000 −0.735681
\(474\) 16.0000 0.734904
\(475\) 0 0
\(476\) 0 0
\(477\) 10.0000 0.457869
\(478\) 8.00000 0.365911
\(479\) −8.00000 −0.365529 −0.182765 0.983157i \(-0.558505\pi\)
−0.182765 + 0.983157i \(0.558505\pi\)
\(480\) 0 0
\(481\) −10.0000 −0.455961
\(482\) −18.0000 −0.819878
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 16.0000 0.725029 0.362515 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) 2.00000 0.0905357
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 4.00000 0.180517 0.0902587 0.995918i \(-0.471231\pi\)
0.0902587 + 0.995918i \(0.471231\pi\)
\(492\) −6.00000 −0.270501
\(493\) 36.0000 1.62136
\(494\) 4.00000 0.179969
\(495\) 0 0
\(496\) −8.00000 −0.359211
\(497\) 0 0
\(498\) −12.0000 −0.537733
\(499\) 20.0000 0.895323 0.447661 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 0 0
\(501\) −8.00000 −0.357414
\(502\) 28.0000 1.24970
\(503\) −8.00000 −0.356702 −0.178351 0.983967i \(-0.557076\pi\)
−0.178351 + 0.983967i \(0.557076\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 32.0000 1.42257
\(507\) 1.00000 0.0444116
\(508\) −8.00000 −0.354943
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 4.00000 0.176604
\(514\) −6.00000 −0.264649
\(515\) 0 0
\(516\) −4.00000 −0.176090
\(517\) 0 0
\(518\) 0 0
\(519\) 18.0000 0.790112
\(520\) 0 0
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) −6.00000 −0.262613
\(523\) −36.0000 −1.57417 −0.787085 0.616844i \(-0.788411\pi\)
−0.787085 + 0.616844i \(0.788411\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) −48.0000 −2.09091
\(528\) 4.00000 0.174078
\(529\) 41.0000 1.78261
\(530\) 0 0
\(531\) 4.00000 0.173585
\(532\) 0 0
\(533\) 6.00000 0.259889
\(534\) −10.0000 −0.432742
\(535\) 0 0
\(536\) −12.0000 −0.518321
\(537\) 12.0000 0.517838
\(538\) 26.0000 1.12094
\(539\) −28.0000 −1.20605
\(540\) 0 0
\(541\) 22.0000 0.945854 0.472927 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) −24.0000 −1.03089
\(543\) 6.00000 0.257485
\(544\) −6.00000 −0.257248
\(545\) 0 0
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) −10.0000 −0.427179
\(549\) −2.00000 −0.0853579
\(550\) 0 0
\(551\) 24.0000 1.02243
\(552\) 8.00000 0.340503
\(553\) 0 0
\(554\) −10.0000 −0.424859
\(555\) 0 0
\(556\) 12.0000 0.508913
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 8.00000 0.338667
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) 24.0000 1.01328
\(562\) −10.0000 −0.421825
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 20.0000 0.840663
\(567\) 0 0
\(568\) −16.0000 −0.671345
\(569\) 10.0000 0.419222 0.209611 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 0 0
\(571\) 28.0000 1.17176 0.585882 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) −4.00000 −0.167248
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −42.0000 −1.74848 −0.874241 0.485491i \(-0.838641\pi\)
−0.874241 + 0.485491i \(0.838641\pi\)
\(578\) −19.0000 −0.790296
\(579\) −10.0000 −0.415586
\(580\) 0 0
\(581\) 0 0
\(582\) −6.00000 −0.248708
\(583\) 40.0000 1.65663
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) −26.0000 −1.07405
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) −7.00000 −0.288675
\(589\) −32.0000 −1.31854
\(590\) 0 0
\(591\) −6.00000 −0.246807
\(592\) 10.0000 0.410997
\(593\) −34.0000 −1.39621 −0.698106 0.715994i \(-0.745974\pi\)
−0.698106 + 0.715994i \(0.745974\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) −8.00000 −0.327418
\(598\) −8.00000 −0.327144
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) −6.00000 −0.244745 −0.122373 0.992484i \(-0.539050\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 0 0
\(605\) 0 0
\(606\) 2.00000 0.0812444
\(607\) 8.00000 0.324710 0.162355 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(608\) −4.00000 −0.162221
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 6.00000 0.242536
\(613\) 10.0000 0.403896 0.201948 0.979396i \(-0.435273\pi\)
0.201948 + 0.979396i \(0.435273\pi\)
\(614\) −12.0000 −0.484281
\(615\) 0 0
\(616\) 0 0
\(617\) −42.0000 −1.69086 −0.845428 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0 0
\(621\) −8.00000 −0.321029
\(622\) 24.0000 0.962312
\(623\) 0 0
\(624\) −1.00000 −0.0400320
\(625\) 0 0
\(626\) −22.0000 −0.879297
\(627\) 16.0000 0.638978
\(628\) 2.00000 0.0798087
\(629\) 60.0000 2.39236
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 16.0000 0.636446
\(633\) −12.0000 −0.476957
\(634\) −2.00000 −0.0794301
\(635\) 0 0
\(636\) 10.0000 0.396526
\(637\) 7.00000 0.277350
\(638\) −24.0000 −0.950169
\(639\) 16.0000 0.632950
\(640\) 0 0
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) −12.0000 −0.473602
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −24.0000 −0.944267
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 16.0000 0.628055
\(650\) 0 0
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) 34.0000 1.33052 0.665261 0.746611i \(-0.268320\pi\)
0.665261 + 0.746611i \(0.268320\pi\)
\(654\) 10.0000 0.391031
\(655\) 0 0
\(656\) −6.00000 −0.234261
\(657\) −2.00000 −0.0780274
\(658\) 0 0
\(659\) −20.0000 −0.779089 −0.389545 0.921008i \(-0.627368\pi\)
−0.389545 + 0.921008i \(0.627368\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 20.0000 0.777322
\(663\) −6.00000 −0.233021
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) −10.0000 −0.387492
\(667\) −48.0000 −1.85857
\(668\) −8.00000 −0.309529
\(669\) −8.00000 −0.309298
\(670\) 0 0
\(671\) −8.00000 −0.308837
\(672\) 0 0
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 2.00000 0.0770371
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) −22.0000 −0.845529 −0.422764 0.906240i \(-0.638940\pi\)
−0.422764 + 0.906240i \(0.638940\pi\)
\(678\) 10.0000 0.384048
\(679\) 0 0
\(680\) 0 0
\(681\) −4.00000 −0.153280
\(682\) 32.0000 1.22534
\(683\) −28.0000 −1.07139 −0.535695 0.844411i \(-0.679950\pi\)
−0.535695 + 0.844411i \(0.679950\pi\)
\(684\) 4.00000 0.152944
\(685\) 0 0
\(686\) 0 0
\(687\) 14.0000 0.534133
\(688\) −4.00000 −0.152499
\(689\) −10.0000 −0.380970
\(690\) 0 0
\(691\) −12.0000 −0.456502 −0.228251 0.973602i \(-0.573301\pi\)
−0.228251 + 0.973602i \(0.573301\pi\)
\(692\) 18.0000 0.684257
\(693\) 0 0
\(694\) 20.0000 0.759190
\(695\) 0 0
\(696\) −6.00000 −0.227429
\(697\) −36.0000 −1.36360
\(698\) −6.00000 −0.227103
\(699\) 14.0000 0.529529
\(700\) 0 0
\(701\) 22.0000 0.830929 0.415464 0.909610i \(-0.363619\pi\)
0.415464 + 0.909610i \(0.363619\pi\)
\(702\) 1.00000 0.0377426
\(703\) 40.0000 1.50863
\(704\) 4.00000 0.150756
\(705\) 0 0
\(706\) −30.0000 −1.12906
\(707\) 0 0
\(708\) 4.00000 0.150329
\(709\) −50.0000 −1.87779 −0.938895 0.344204i \(-0.888149\pi\)
−0.938895 + 0.344204i \(0.888149\pi\)
\(710\) 0 0
\(711\) −16.0000 −0.600047
\(712\) −10.0000 −0.374766
\(713\) 64.0000 2.39682
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) −8.00000 −0.298765
\(718\) −16.0000 −0.597115
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) 18.0000 0.669427
\(724\) 6.00000 0.222988
\(725\) 0 0
\(726\) −5.00000 −0.185567
\(727\) 16.0000 0.593407 0.296704 0.954970i \(-0.404113\pi\)
0.296704 + 0.954970i \(0.404113\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −24.0000 −0.887672
\(732\) −2.00000 −0.0739221
\(733\) 50.0000 1.84679 0.923396 0.383849i \(-0.125402\pi\)
0.923396 + 0.383849i \(0.125402\pi\)
\(734\) −24.0000 −0.885856
\(735\) 0 0
\(736\) 8.00000 0.294884
\(737\) 48.0000 1.76810
\(738\) 6.00000 0.220863
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 0 0
\(741\) −4.00000 −0.146944
\(742\) 0 0
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 8.00000 0.293294
\(745\) 0 0
\(746\) 22.0000 0.805477
\(747\) 12.0000 0.439057
\(748\) 24.0000 0.877527
\(749\) 0 0
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 0 0
\(753\) −28.0000 −1.02038
\(754\) 6.00000 0.218507
\(755\) 0 0
\(756\) 0 0
\(757\) 42.0000 1.52652 0.763258 0.646094i \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(758\) 4.00000 0.145287
\(759\) −32.0000 −1.16153
\(760\) 0 0
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 8.00000 0.289809
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 32.0000 1.15621
\(767\) −4.00000 −0.144432
\(768\) 1.00000 0.0360844
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) 6.00000 0.216085
\(772\) −10.0000 −0.359908
\(773\) −38.0000 −1.36677 −0.683383 0.730061i \(-0.739492\pi\)
−0.683383 + 0.730061i \(0.739492\pi\)
\(774\) 4.00000 0.143777
\(775\) 0 0
\(776\) −6.00000 −0.215387
\(777\) 0 0
\(778\) 34.0000 1.21896
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 64.0000 2.29010
\(782\) 48.0000 1.71648
\(783\) 6.00000 0.214423
\(784\) −7.00000 −0.250000
\(785\) 0 0
\(786\) −12.0000 −0.428026
\(787\) −4.00000 −0.142585 −0.0712923 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) −6.00000 −0.213741
\(789\) −24.0000 −0.854423
\(790\) 0 0
\(791\) 0 0
\(792\) −4.00000 −0.142134
\(793\) 2.00000 0.0710221
\(794\) 30.0000 1.06466
\(795\) 0 0
\(796\) −8.00000 −0.283552
\(797\) 2.00000 0.0708436 0.0354218 0.999372i \(-0.488723\pi\)
0.0354218 + 0.999372i \(0.488723\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 10.0000 0.353333
\(802\) −34.0000 −1.20058
\(803\) −8.00000 −0.282314
\(804\) 12.0000 0.423207
\(805\) 0 0
\(806\) −8.00000 −0.281788
\(807\) −26.0000 −0.915243
\(808\) 2.00000 0.0703598
\(809\) 42.0000 1.47664 0.738321 0.674450i \(-0.235619\pi\)
0.738321 + 0.674450i \(0.235619\pi\)
\(810\) 0 0
\(811\) 12.0000 0.421377 0.210688 0.977553i \(-0.432429\pi\)
0.210688 + 0.977553i \(0.432429\pi\)
\(812\) 0 0
\(813\) 24.0000 0.841717
\(814\) −40.0000 −1.40200
\(815\) 0 0
\(816\) 6.00000 0.210042
\(817\) −16.0000 −0.559769
\(818\) 22.0000 0.769212
\(819\) 0 0
\(820\) 0 0
\(821\) 6.00000 0.209401 0.104701 0.994504i \(-0.466612\pi\)
0.104701 + 0.994504i \(0.466612\pi\)
\(822\) 10.0000 0.348790
\(823\) −16.0000 −0.557725 −0.278862 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 36.0000 1.25184 0.625921 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) −8.00000 −0.278019
\(829\) −2.00000 −0.0694629 −0.0347314 0.999397i \(-0.511058\pi\)
−0.0347314 + 0.999397i \(0.511058\pi\)
\(830\) 0 0
\(831\) 10.0000 0.346896
\(832\) −1.00000 −0.0346688
\(833\) −42.0000 −1.45521
\(834\) −12.0000 −0.415526
\(835\) 0 0
\(836\) 16.0000 0.553372
\(837\) −8.00000 −0.276520
\(838\) 4.00000 0.138178
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 34.0000 1.17172
\(843\) 10.0000 0.344418
\(844\) −12.0000 −0.413057
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 10.0000 0.343401
\(849\) −20.0000 −0.686398
\(850\) 0 0
\(851\) −80.0000 −2.74236
\(852\) 16.0000 0.548151
\(853\) 26.0000 0.890223 0.445112 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −12.0000 −0.410152
\(857\) −18.0000 −0.614868 −0.307434 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(858\) 4.00000 0.136558
\(859\) −20.0000 −0.682391 −0.341196 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 24.0000 0.817443
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 0 0
\(866\) 34.0000 1.15537
\(867\) 19.0000 0.645274
\(868\) 0 0
\(869\) −64.0000 −2.17105
\(870\) 0 0
\(871\) −12.0000 −0.406604
\(872\) 10.0000 0.338643
\(873\) 6.00000 0.203069
\(874\) 32.0000 1.08242
\(875\) 0 0
\(876\) −2.00000 −0.0675737
\(877\) −14.0000 −0.472746 −0.236373 0.971662i \(-0.575959\pi\)
−0.236373 + 0.971662i \(0.575959\pi\)
\(878\) 40.0000 1.34993
\(879\) 26.0000 0.876958
\(880\) 0 0
\(881\) 2.00000 0.0673817 0.0336909 0.999432i \(-0.489274\pi\)
0.0336909 + 0.999432i \(0.489274\pi\)
\(882\) 7.00000 0.235702
\(883\) 36.0000 1.21150 0.605748 0.795656i \(-0.292874\pi\)
0.605748 + 0.795656i \(0.292874\pi\)
\(884\) −6.00000 −0.201802
\(885\) 0 0
\(886\) 36.0000 1.20944
\(887\) −8.00000 −0.268614 −0.134307 0.990940i \(-0.542881\pi\)
−0.134307 + 0.990940i \(0.542881\pi\)
\(888\) −10.0000 −0.335578
\(889\) 0 0
\(890\) 0 0
\(891\) 4.00000 0.134005
\(892\) −8.00000 −0.267860
\(893\) 0 0
\(894\) −6.00000 −0.200670
\(895\) 0 0
\(896\) 0 0
\(897\) 8.00000 0.267112
\(898\) −18.0000 −0.600668
\(899\) −48.0000 −1.60089
\(900\) 0 0
\(901\) 60.0000 1.99889
\(902\) 24.0000 0.799113
\(903\) 0 0
\(904\) 10.0000 0.332595
\(905\) 0 0
\(906\) 0 0
\(907\) 12.0000 0.398453 0.199227 0.979953i \(-0.436157\pi\)
0.199227 + 0.979953i \(0.436157\pi\)
\(908\) −4.00000 −0.132745
\(909\) −2.00000 −0.0663358
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 4.00000 0.132453
\(913\) 48.0000 1.58857
\(914\) 34.0000 1.12462
\(915\) 0 0
\(916\) 14.0000 0.462573
\(917\) 0 0
\(918\) −6.00000 −0.198030
\(919\) −56.0000 −1.84727 −0.923635 0.383274i \(-0.874797\pi\)
−0.923635 + 0.383274i \(0.874797\pi\)
\(920\) 0 0
\(921\) 12.0000 0.395413
\(922\) 18.0000 0.592798
\(923\) −16.0000 −0.526646
\(924\) 0 0
\(925\) 0 0
\(926\) 8.00000 0.262896
\(927\) 0 0
\(928\) −6.00000 −0.196960
\(929\) −14.0000 −0.459325 −0.229663 0.973270i \(-0.573762\pi\)
−0.229663 + 0.973270i \(0.573762\pi\)
\(930\) 0 0
\(931\) −28.0000 −0.917663
\(932\) 14.0000 0.458585
\(933\) −24.0000 −0.785725
\(934\) 12.0000 0.392652
\(935\) 0 0
\(936\) 1.00000 0.0326860
\(937\) 22.0000 0.718709 0.359354 0.933201i \(-0.382997\pi\)
0.359354 + 0.933201i \(0.382997\pi\)
\(938\) 0 0
\(939\) 22.0000 0.717943
\(940\) 0 0
\(941\) 30.0000 0.977972 0.488986 0.872292i \(-0.337367\pi\)
0.488986 + 0.872292i \(0.337367\pi\)
\(942\) −2.00000 −0.0651635
\(943\) 48.0000 1.56310
\(944\) 4.00000 0.130189
\(945\) 0 0
\(946\) 16.0000 0.520205
\(947\) −52.0000 −1.68977 −0.844886 0.534946i \(-0.820332\pi\)
−0.844886 + 0.534946i \(0.820332\pi\)
\(948\) −16.0000 −0.519656
\(949\) 2.00000 0.0649227
\(950\) 0 0
\(951\) 2.00000 0.0648544
\(952\) 0 0
\(953\) −34.0000 −1.10137 −0.550684 0.834714i \(-0.685633\pi\)
−0.550684 + 0.834714i \(0.685633\pi\)
\(954\) −10.0000 −0.323762
\(955\) 0 0
\(956\) −8.00000 −0.258738
\(957\) 24.0000 0.775810
\(958\) 8.00000 0.258468
\(959\) 0 0
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 10.0000 0.322413
\(963\) 12.0000 0.386695
\(964\) 18.0000 0.579741
\(965\) 0 0
\(966\) 0 0
\(967\) −16.0000 −0.514525 −0.257263 0.966342i \(-0.582821\pi\)
−0.257263 + 0.966342i \(0.582821\pi\)
\(968\) −5.00000 −0.160706
\(969\) 24.0000 0.770991
\(970\) 0 0
\(971\) 36.0000 1.15529 0.577647 0.816286i \(-0.303971\pi\)
0.577647 + 0.816286i \(0.303971\pi\)
\(972\) 1.00000 0.0320750
\(973\) 0 0
\(974\) −16.0000 −0.512673
\(975\) 0 0
\(976\) −2.00000 −0.0640184
\(977\) 30.0000 0.959785 0.479893 0.877327i \(-0.340676\pi\)
0.479893 + 0.877327i \(0.340676\pi\)
\(978\) 4.00000 0.127906
\(979\) 40.0000 1.27841
\(980\) 0 0
\(981\) −10.0000 −0.319275
\(982\) −4.00000 −0.127645
\(983\) −8.00000 −0.255160 −0.127580 0.991828i \(-0.540721\pi\)
−0.127580 + 0.991828i \(0.540721\pi\)
\(984\) 6.00000 0.191273
\(985\) 0 0
\(986\) −36.0000 −1.14647
\(987\) 0 0
\(988\) −4.00000 −0.127257
\(989\) 32.0000 1.01754
\(990\) 0 0
\(991\) −16.0000 −0.508257 −0.254128 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) 8.00000 0.254000
\(993\) −20.0000 −0.634681
\(994\) 0 0
\(995\) 0 0
\(996\) 12.0000 0.380235
\(997\) 58.0000 1.83688 0.918439 0.395562i \(-0.129450\pi\)
0.918439 + 0.395562i \(0.129450\pi\)
\(998\) −20.0000 −0.633089
\(999\) 10.0000 0.316386
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 1950.2.a.k.1.1 1
3.2 odd 2 5850.2.a.bo.1.1 1
5.2 odd 4 1950.2.e.g.1249.1 2
5.3 odd 4 1950.2.e.g.1249.2 2
5.4 even 2 390.2.a.f.1.1 1
15.2 even 4 5850.2.e.e.5149.2 2
15.8 even 4 5850.2.e.e.5149.1 2
15.14 odd 2 1170.2.a.a.1.1 1
20.19 odd 2 3120.2.a.w.1.1 1
60.59 even 2 9360.2.a.p.1.1 1
65.34 odd 4 5070.2.b.d.1351.2 2
65.44 odd 4 5070.2.b.d.1351.1 2
65.64 even 2 5070.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.a.f.1.1 1 5.4 even 2
1170.2.a.a.1.1 1 15.14 odd 2
1950.2.a.k.1.1 1 1.1 even 1 trivial
1950.2.e.g.1249.1 2 5.2 odd 4
1950.2.e.g.1249.2 2 5.3 odd 4
3120.2.a.w.1.1 1 20.19 odd 2
5070.2.a.a.1.1 1 65.64 even 2
5070.2.b.d.1351.1 2 65.44 odd 4
5070.2.b.d.1351.2 2 65.34 odd 4
5850.2.a.bo.1.1 1 3.2 odd 2
5850.2.e.e.5149.1 2 15.8 even 4
5850.2.e.e.5149.2 2 15.2 even 4
9360.2.a.p.1.1 1 60.59 even 2