Properties

Label 3630.2.a.b.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

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} -1.00000 q^{13} +3.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +7.00000 q^{17} -1.00000 q^{18} +5.00000 q^{19} -1.00000 q^{20} +3.00000 q^{21} -8.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} -3.00000 q^{28} +5.00000 q^{29} -1.00000 q^{30} -10.0000 q^{31} -1.00000 q^{32} -7.00000 q^{34} +3.00000 q^{35} +1.00000 q^{36} +7.00000 q^{37} -5.00000 q^{38} +1.00000 q^{39} +1.00000 q^{40} -6.00000 q^{41} -3.00000 q^{42} -10.0000 q^{43} -1.00000 q^{45} +8.00000 q^{46} -10.0000 q^{47} -1.00000 q^{48} +2.00000 q^{49} -1.00000 q^{50} -7.00000 q^{51} -1.00000 q^{52} -4.00000 q^{53} +1.00000 q^{54} +3.00000 q^{56} -5.00000 q^{57} -5.00000 q^{58} +4.00000 q^{59} +1.00000 q^{60} +10.0000 q^{62} -3.00000 q^{63} +1.00000 q^{64} +1.00000 q^{65} -6.00000 q^{67} +7.00000 q^{68} +8.00000 q^{69} -3.00000 q^{70} +9.00000 q^{71} -1.00000 q^{72} +2.00000 q^{73} -7.00000 q^{74} -1.00000 q^{75} +5.00000 q^{76} -1.00000 q^{78} -6.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} +7.00000 q^{83} +3.00000 q^{84} -7.00000 q^{85} +10.0000 q^{86} -5.00000 q^{87} +1.00000 q^{90} +3.00000 q^{91} -8.00000 q^{92} +10.0000 q^{93} +10.0000 q^{94} -5.00000 q^{95} +1.00000 q^{96} -14.0000 q^{97} -2.00000 q^{98} +O(q^{100})\)

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
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 3.00000 0.801784
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 7.00000 1.69775 0.848875 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) −1.00000 −0.235702
\(19\) 5.00000 1.14708 0.573539 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) −1.00000 −0.223607
\(21\) 3.00000 0.654654
\(22\) 0 0
\(23\) −8.00000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 1.00000 0.196116
\(27\) −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
\(31\) −10.0000 −1.79605 −0.898027 0.439941i \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −7.00000 −1.20049
\(35\) 3.00000 0.507093
\(36\) 1.00000 0.166667
\(37\) 7.00000 1.15079 0.575396 0.817875i \(-0.304848\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(38\) −5.00000 −0.811107
\(39\) 1.00000 0.160128
\(40\) 1.00000 0.158114
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) −3.00000 −0.462910
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 8.00000 1.17954
\(47\) −10.0000 −1.45865 −0.729325 0.684167i \(-0.760166\pi\)
−0.729325 + 0.684167i \(0.760166\pi\)
\(48\) −1.00000 −0.144338
\(49\) 2.00000 0.285714
\(50\) −1.00000 −0.141421
\(51\) −7.00000 −0.980196
\(52\) −1.00000 −0.138675
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) 3.00000 0.400892
\(57\) −5.00000 −0.662266
\(58\) −5.00000 −0.656532
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 1.00000 0.129099
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 10.0000 1.27000
\(63\) −3.00000 −0.377964
\(64\) 1.00000 0.125000
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) −6.00000 −0.733017 −0.366508 0.930415i \(-0.619447\pi\)
−0.366508 + 0.930415i \(0.619447\pi\)
\(68\) 7.00000 0.848875
\(69\) 8.00000 0.963087
\(70\) −3.00000 −0.358569
\(71\) 9.00000 1.06810 0.534052 0.845452i \(-0.320669\pi\)
0.534052 + 0.845452i \(0.320669\pi\)
\(72\) −1.00000 −0.117851
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −7.00000 −0.813733
\(75\) −1.00000 −0.115470
\(76\) 5.00000 0.573539
\(77\) 0 0
\(78\) −1.00000 −0.113228
\(79\) −6.00000 −0.675053 −0.337526 0.941316i \(-0.609590\pi\)
−0.337526 + 0.941316i \(0.609590\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) 7.00000 0.768350 0.384175 0.923260i \(-0.374486\pi\)
0.384175 + 0.923260i \(0.374486\pi\)
\(84\) 3.00000 0.327327
\(85\) −7.00000 −0.759257
\(86\) 10.0000 1.07833
\(87\) −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
\(91\) 3.00000 0.314485
\(92\) −8.00000 −0.834058
\(93\) 10.0000 1.03695
\(94\) 10.0000 1.03142
\(95\) −5.00000 −0.512989
\(96\) 1.00000 0.102062
\(97\) −14.0000 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) −2.00000 −0.202031
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 15.0000 1.49256 0.746278 0.665635i \(-0.231839\pi\)
0.746278 + 0.665635i \(0.231839\pi\)
\(102\) 7.00000 0.693103
\(103\) 13.0000 1.28093 0.640464 0.767988i \(-0.278742\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) 1.00000 0.0980581
\(105\) −3.00000 −0.292770
\(106\) 4.00000 0.388514
\(107\) 8.00000 0.773389 0.386695 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 12.0000 1.14939 0.574696 0.818367i \(-0.305120\pi\)
0.574696 + 0.818367i \(0.305120\pi\)
\(110\) 0 0
\(111\) −7.00000 −0.664411
\(112\) −3.00000 −0.283473
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 5.00000 0.468293
\(115\) 8.00000 0.746004
\(116\) 5.00000 0.464238
\(117\) −1.00000 −0.0924500
\(118\) −4.00000 −0.368230
\(119\) −21.0000 −1.92507
\(120\) −1.00000 −0.0912871
\(121\) 0 0
\(122\) 0 0
\(123\) 6.00000 0.541002
\(124\) −10.0000 −0.898027
\(125\) −1.00000 −0.0894427
\(126\) 3.00000 0.267261
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 10.0000 0.880451
\(130\) −1.00000 −0.0877058
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) −15.0000 −1.30066
\(134\) 6.00000 0.518321
\(135\) 1.00000 0.0860663
\(136\) −7.00000 −0.600245
\(137\) 5.00000 0.427179 0.213589 0.976924i \(-0.431485\pi\)
0.213589 + 0.976924i \(0.431485\pi\)
\(138\) −8.00000 −0.681005
\(139\) 7.00000 0.593732 0.296866 0.954919i \(-0.404058\pi\)
0.296866 + 0.954919i \(0.404058\pi\)
\(140\) 3.00000 0.253546
\(141\) 10.0000 0.842152
\(142\) −9.00000 −0.755263
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −5.00000 −0.415227
\(146\) −2.00000 −0.165521
\(147\) −2.00000 −0.164957
\(148\) 7.00000 0.575396
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 1.00000 0.0816497
\(151\) 4.00000 0.325515 0.162758 0.986666i \(-0.447961\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) −5.00000 −0.405554
\(153\) 7.00000 0.565916
\(154\) 0 0
\(155\) 10.0000 0.803219
\(156\) 1.00000 0.0800641
\(157\) −23.0000 −1.83560 −0.917800 0.397043i \(-0.870036\pi\)
−0.917800 + 0.397043i \(0.870036\pi\)
\(158\) 6.00000 0.477334
\(159\) 4.00000 0.317221
\(160\) 1.00000 0.0790569
\(161\) 24.0000 1.89146
\(162\) −1.00000 −0.0785674
\(163\) 8.00000 0.626608 0.313304 0.949653i \(-0.398564\pi\)
0.313304 + 0.949653i \(0.398564\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) −7.00000 −0.543305
\(167\) 16.0000 1.23812 0.619059 0.785345i \(-0.287514\pi\)
0.619059 + 0.785345i \(0.287514\pi\)
\(168\) −3.00000 −0.231455
\(169\) −12.0000 −0.923077
\(170\) 7.00000 0.536875
\(171\) 5.00000 0.382360
\(172\) −10.0000 −0.762493
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 5.00000 0.379049
\(175\) −3.00000 −0.226779
\(176\) 0 0
\(177\) −4.00000 −0.300658
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 16.0000 1.18927 0.594635 0.803996i \(-0.297296\pi\)
0.594635 + 0.803996i \(0.297296\pi\)
\(182\) −3.00000 −0.222375
\(183\) 0 0
\(184\) 8.00000 0.589768
\(185\) −7.00000 −0.514650
\(186\) −10.0000 −0.733236
\(187\) 0 0
\(188\) −10.0000 −0.729325
\(189\) 3.00000 0.218218
\(190\) 5.00000 0.362738
\(191\) 3.00000 0.217072 0.108536 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 14.0000 1.00514
\(195\) −1.00000 −0.0716115
\(196\) 2.00000 0.142857
\(197\) −8.00000 −0.569976 −0.284988 0.958531i \(-0.591990\pi\)
−0.284988 + 0.958531i \(0.591990\pi\)
\(198\) 0 0
\(199\) −12.0000 −0.850657 −0.425329 0.905039i \(-0.639842\pi\)
−0.425329 + 0.905039i \(0.639842\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 6.00000 0.423207
\(202\) −15.0000 −1.05540
\(203\) −15.0000 −1.05279
\(204\) −7.00000 −0.490098
\(205\) 6.00000 0.419058
\(206\) −13.0000 −0.905753
\(207\) −8.00000 −0.556038
\(208\) −1.00000 −0.0693375
\(209\) 0 0
\(210\) 3.00000 0.207020
\(211\) −3.00000 −0.206529 −0.103264 0.994654i \(-0.532929\pi\)
−0.103264 + 0.994654i \(0.532929\pi\)
\(212\) −4.00000 −0.274721
\(213\) −9.00000 −0.616670
\(214\) −8.00000 −0.546869
\(215\) 10.0000 0.681994
\(216\) 1.00000 0.0680414
\(217\) 30.0000 2.03653
\(218\) −12.0000 −0.812743
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) −7.00000 −0.470871
\(222\) 7.00000 0.469809
\(223\) 23.0000 1.54019 0.770097 0.637927i \(-0.220208\pi\)
0.770097 + 0.637927i \(0.220208\pi\)
\(224\) 3.00000 0.200446
\(225\) 1.00000 0.0666667
\(226\) −14.0000 −0.931266
\(227\) −24.0000 −1.59294 −0.796468 0.604681i \(-0.793301\pi\)
−0.796468 + 0.604681i \(0.793301\pi\)
\(228\) −5.00000 −0.331133
\(229\) −4.00000 −0.264327 −0.132164 0.991228i \(-0.542192\pi\)
−0.132164 + 0.991228i \(0.542192\pi\)
\(230\) −8.00000 −0.527504
\(231\) 0 0
\(232\) −5.00000 −0.328266
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 1.00000 0.0653720
\(235\) 10.0000 0.652328
\(236\) 4.00000 0.260378
\(237\) 6.00000 0.389742
\(238\) 21.0000 1.36123
\(239\) 19.0000 1.22901 0.614504 0.788914i \(-0.289356\pi\)
0.614504 + 0.788914i \(0.289356\pi\)
\(240\) 1.00000 0.0645497
\(241\) −15.0000 −0.966235 −0.483117 0.875556i \(-0.660496\pi\)
−0.483117 + 0.875556i \(0.660496\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −2.00000 −0.127775
\(246\) −6.00000 −0.382546
\(247\) −5.00000 −0.318142
\(248\) 10.0000 0.635001
\(249\) −7.00000 −0.443607
\(250\) 1.00000 0.0632456
\(251\) 28.0000 1.76734 0.883672 0.468106i \(-0.155064\pi\)
0.883672 + 0.468106i \(0.155064\pi\)
\(252\) −3.00000 −0.188982
\(253\) 0 0
\(254\) 4.00000 0.250982
\(255\) 7.00000 0.438357
\(256\) 1.00000 0.0625000
\(257\) 23.0000 1.43470 0.717350 0.696713i \(-0.245355\pi\)
0.717350 + 0.696713i \(0.245355\pi\)
\(258\) −10.0000 −0.622573
\(259\) −21.0000 −1.30488
\(260\) 1.00000 0.0620174
\(261\) 5.00000 0.309492
\(262\) −12.0000 −0.741362
\(263\) 30.0000 1.84988 0.924940 0.380114i \(-0.124115\pi\)
0.924940 + 0.380114i \(0.124115\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) 15.0000 0.919709
\(267\) 0 0
\(268\) −6.00000 −0.366508
\(269\) −1.00000 −0.0609711 −0.0304855 0.999535i \(-0.509705\pi\)
−0.0304855 + 0.999535i \(0.509705\pi\)
\(270\) −1.00000 −0.0608581
\(271\) −18.0000 −1.09342 −0.546711 0.837321i \(-0.684120\pi\)
−0.546711 + 0.837321i \(0.684120\pi\)
\(272\) 7.00000 0.424437
\(273\) −3.00000 −0.181568
\(274\) −5.00000 −0.302061
\(275\) 0 0
\(276\) 8.00000 0.481543
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −7.00000 −0.419832
\(279\) −10.0000 −0.598684
\(280\) −3.00000 −0.179284
\(281\) 20.0000 1.19310 0.596550 0.802576i \(-0.296538\pi\)
0.596550 + 0.802576i \(0.296538\pi\)
\(282\) −10.0000 −0.595491
\(283\) 28.0000 1.66443 0.832214 0.554455i \(-0.187073\pi\)
0.832214 + 0.554455i \(0.187073\pi\)
\(284\) 9.00000 0.534052
\(285\) 5.00000 0.296174
\(286\) 0 0
\(287\) 18.0000 1.06251
\(288\) −1.00000 −0.0589256
\(289\) 32.0000 1.88235
\(290\) 5.00000 0.293610
\(291\) 14.0000 0.820695
\(292\) 2.00000 0.117041
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 2.00000 0.116642
\(295\) −4.00000 −0.232889
\(296\) −7.00000 −0.406867
\(297\) 0 0
\(298\) −10.0000 −0.579284
\(299\) 8.00000 0.462652
\(300\) −1.00000 −0.0577350
\(301\) 30.0000 1.72917
\(302\) −4.00000 −0.230174
\(303\) −15.0000 −0.861727
\(304\) 5.00000 0.286770
\(305\) 0 0
\(306\) −7.00000 −0.400163
\(307\) −6.00000 −0.342438 −0.171219 0.985233i \(-0.554771\pi\)
−0.171219 + 0.985233i \(0.554771\pi\)
\(308\) 0 0
\(309\) −13.0000 −0.739544
\(310\) −10.0000 −0.567962
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) −1.00000 −0.0566139
\(313\) 18.0000 1.01742 0.508710 0.860938i \(-0.330123\pi\)
0.508710 + 0.860938i \(0.330123\pi\)
\(314\) 23.0000 1.29797
\(315\) 3.00000 0.169031
\(316\) −6.00000 −0.337526
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) −4.00000 −0.224309
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) −8.00000 −0.446516
\(322\) −24.0000 −1.33747
\(323\) 35.0000 1.94745
\(324\) 1.00000 0.0555556
\(325\) −1.00000 −0.0554700
\(326\) −8.00000 −0.443079
\(327\) −12.0000 −0.663602
\(328\) 6.00000 0.331295
\(329\) 30.0000 1.65395
\(330\) 0 0
\(331\) 3.00000 0.164895 0.0824475 0.996595i \(-0.473726\pi\)
0.0824475 + 0.996595i \(0.473726\pi\)
\(332\) 7.00000 0.384175
\(333\) 7.00000 0.383598
\(334\) −16.0000 −0.875481
\(335\) 6.00000 0.327815
\(336\) 3.00000 0.163663
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 12.0000 0.652714
\(339\) −14.0000 −0.760376
\(340\) −7.00000 −0.379628
\(341\) 0 0
\(342\) −5.00000 −0.270369
\(343\) 15.0000 0.809924
\(344\) 10.0000 0.539164
\(345\) −8.00000 −0.430706
\(346\) 0 0
\(347\) 25.0000 1.34207 0.671035 0.741426i \(-0.265850\pi\)
0.671035 + 0.741426i \(0.265850\pi\)
\(348\) −5.00000 −0.268028
\(349\) 18.0000 0.963518 0.481759 0.876304i \(-0.339998\pi\)
0.481759 + 0.876304i \(0.339998\pi\)
\(350\) 3.00000 0.160357
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) 26.0000 1.38384 0.691920 0.721974i \(-0.256765\pi\)
0.691920 + 0.721974i \(0.256765\pi\)
\(354\) 4.00000 0.212598
\(355\) −9.00000 −0.477670
\(356\) 0 0
\(357\) 21.0000 1.11144
\(358\) 0 0
\(359\) −8.00000 −0.422224 −0.211112 0.977462i \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) 1.00000 0.0527046
\(361\) 6.00000 0.315789
\(362\) −16.0000 −0.840941
\(363\) 0 0
\(364\) 3.00000 0.157243
\(365\) −2.00000 −0.104685
\(366\) 0 0
\(367\) −11.0000 −0.574195 −0.287098 0.957901i \(-0.592690\pi\)
−0.287098 + 0.957901i \(0.592690\pi\)
\(368\) −8.00000 −0.417029
\(369\) −6.00000 −0.312348
\(370\) 7.00000 0.363913
\(371\) 12.0000 0.623009
\(372\) 10.0000 0.518476
\(373\) −31.0000 −1.60512 −0.802560 0.596572i \(-0.796529\pi\)
−0.802560 + 0.596572i \(0.796529\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) 10.0000 0.515711
\(377\) −5.00000 −0.257513
\(378\) −3.00000 −0.154303
\(379\) −27.0000 −1.38690 −0.693448 0.720506i \(-0.743909\pi\)
−0.693448 + 0.720506i \(0.743909\pi\)
\(380\) −5.00000 −0.256495
\(381\) 4.00000 0.204926
\(382\) −3.00000 −0.153493
\(383\) −6.00000 −0.306586 −0.153293 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 4.00000 0.203595
\(387\) −10.0000 −0.508329
\(388\) −14.0000 −0.710742
\(389\) 14.0000 0.709828 0.354914 0.934899i \(-0.384510\pi\)
0.354914 + 0.934899i \(0.384510\pi\)
\(390\) 1.00000 0.0506370
\(391\) −56.0000 −2.83204
\(392\) −2.00000 −0.101015
\(393\) −12.0000 −0.605320
\(394\) 8.00000 0.403034
\(395\) 6.00000 0.301893
\(396\) 0 0
\(397\) 31.0000 1.55585 0.777923 0.628360i \(-0.216273\pi\)
0.777923 + 0.628360i \(0.216273\pi\)
\(398\) 12.0000 0.601506
\(399\) 15.0000 0.750939
\(400\) 1.00000 0.0500000
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) −6.00000 −0.299253
\(403\) 10.0000 0.498135
\(404\) 15.0000 0.746278
\(405\) −1.00000 −0.0496904
\(406\) 15.0000 0.744438
\(407\) 0 0
\(408\) 7.00000 0.346552
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) −6.00000 −0.296319
\(411\) −5.00000 −0.246632
\(412\) 13.0000 0.640464
\(413\) −12.0000 −0.590481
\(414\) 8.00000 0.393179
\(415\) −7.00000 −0.343616
\(416\) 1.00000 0.0490290
\(417\) −7.00000 −0.342791
\(418\) 0 0
\(419\) −14.0000 −0.683945 −0.341972 0.939710i \(-0.611095\pi\)
−0.341972 + 0.939710i \(0.611095\pi\)
\(420\) −3.00000 −0.146385
\(421\) −34.0000 −1.65706 −0.828529 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) 3.00000 0.146038
\(423\) −10.0000 −0.486217
\(424\) 4.00000 0.194257
\(425\) 7.00000 0.339550
\(426\) 9.00000 0.436051
\(427\) 0 0
\(428\) 8.00000 0.386695
\(429\) 0 0
\(430\) −10.0000 −0.482243
\(431\) −15.0000 −0.722525 −0.361262 0.932464i \(-0.617654\pi\)
−0.361262 + 0.932464i \(0.617654\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 8.00000 0.384455 0.192228 0.981350i \(-0.438429\pi\)
0.192228 + 0.981350i \(0.438429\pi\)
\(434\) −30.0000 −1.44005
\(435\) 5.00000 0.239732
\(436\) 12.0000 0.574696
\(437\) −40.0000 −1.91346
\(438\) 2.00000 0.0955637
\(439\) 26.0000 1.24091 0.620456 0.784241i \(-0.286947\pi\)
0.620456 + 0.784241i \(0.286947\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) 7.00000 0.332956
\(443\) −19.0000 −0.902717 −0.451359 0.892343i \(-0.649060\pi\)
−0.451359 + 0.892343i \(0.649060\pi\)
\(444\) −7.00000 −0.332205
\(445\) 0 0
\(446\) −23.0000 −1.08908
\(447\) −10.0000 −0.472984
\(448\) −3.00000 −0.141737
\(449\) 34.0000 1.60456 0.802280 0.596948i \(-0.203620\pi\)
0.802280 + 0.596948i \(0.203620\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 0 0
\(452\) 14.0000 0.658505
\(453\) −4.00000 −0.187936
\(454\) 24.0000 1.12638
\(455\) −3.00000 −0.140642
\(456\) 5.00000 0.234146
\(457\) 28.0000 1.30978 0.654892 0.755722i \(-0.272714\pi\)
0.654892 + 0.755722i \(0.272714\pi\)
\(458\) 4.00000 0.186908
\(459\) −7.00000 −0.326732
\(460\) 8.00000 0.373002
\(461\) 21.0000 0.978068 0.489034 0.872265i \(-0.337349\pi\)
0.489034 + 0.872265i \(0.337349\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 5.00000 0.232119
\(465\) −10.0000 −0.463739
\(466\) 6.00000 0.277945
\(467\) −21.0000 −0.971764 −0.485882 0.874024i \(-0.661502\pi\)
−0.485882 + 0.874024i \(0.661502\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 18.0000 0.831163
\(470\) −10.0000 −0.461266
\(471\) 23.0000 1.05978
\(472\) −4.00000 −0.184115
\(473\) 0 0
\(474\) −6.00000 −0.275589
\(475\) 5.00000 0.229416
\(476\) −21.0000 −0.962533
\(477\) −4.00000 −0.183147
\(478\) −19.0000 −0.869040
\(479\) 3.00000 0.137073 0.0685367 0.997649i \(-0.478167\pi\)
0.0685367 + 0.997649i \(0.478167\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −7.00000 −0.319173
\(482\) 15.0000 0.683231
\(483\) −24.0000 −1.09204
\(484\) 0 0
\(485\) 14.0000 0.635707
\(486\) 1.00000 0.0453609
\(487\) 29.0000 1.31412 0.657058 0.753840i \(-0.271801\pi\)
0.657058 + 0.753840i \(0.271801\pi\)
\(488\) 0 0
\(489\) −8.00000 −0.361773
\(490\) 2.00000 0.0903508
\(491\) 18.0000 0.812329 0.406164 0.913800i \(-0.366866\pi\)
0.406164 + 0.913800i \(0.366866\pi\)
\(492\) 6.00000 0.270501
\(493\) 35.0000 1.57632
\(494\) 5.00000 0.224961
\(495\) 0 0
\(496\) −10.0000 −0.449013
\(497\) −27.0000 −1.21112
\(498\) 7.00000 0.313678
\(499\) 13.0000 0.581960 0.290980 0.956729i \(-0.406019\pi\)
0.290980 + 0.956729i \(0.406019\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −16.0000 −0.714827
\(502\) −28.0000 −1.24970
\(503\) −36.0000 −1.60516 −0.802580 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 3.00000 0.133631
\(505\) −15.0000 −0.667491
\(506\) 0 0
\(507\) 12.0000 0.532939
\(508\) −4.00000 −0.177471
\(509\) 2.00000 0.0886484 0.0443242 0.999017i \(-0.485887\pi\)
0.0443242 + 0.999017i \(0.485887\pi\)
\(510\) −7.00000 −0.309965
\(511\) −6.00000 −0.265424
\(512\) −1.00000 −0.0441942
\(513\) −5.00000 −0.220755
\(514\) −23.0000 −1.01449
\(515\) −13.0000 −0.572848
\(516\) 10.0000 0.440225
\(517\) 0 0
\(518\) 21.0000 0.922687
\(519\) 0 0
\(520\) −1.00000 −0.0438529
\(521\) 16.0000 0.700973 0.350486 0.936568i \(-0.386016\pi\)
0.350486 + 0.936568i \(0.386016\pi\)
\(522\) −5.00000 −0.218844
\(523\) 36.0000 1.57417 0.787085 0.616844i \(-0.211589\pi\)
0.787085 + 0.616844i \(0.211589\pi\)
\(524\) 12.0000 0.524222
\(525\) 3.00000 0.130931
\(526\) −30.0000 −1.30806
\(527\) −70.0000 −3.04925
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) −4.00000 −0.173749
\(531\) 4.00000 0.173585
\(532\) −15.0000 −0.650332
\(533\) 6.00000 0.259889
\(534\) 0 0
\(535\) −8.00000 −0.345870
\(536\) 6.00000 0.259161
\(537\) 0 0
\(538\) 1.00000 0.0431131
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) −22.0000 −0.945854 −0.472927 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) 18.0000 0.773166
\(543\) −16.0000 −0.686626
\(544\) −7.00000 −0.300123
\(545\) −12.0000 −0.514024
\(546\) 3.00000 0.128388
\(547\) 26.0000 1.11168 0.555840 0.831289i \(-0.312397\pi\)
0.555840 + 0.831289i \(0.312397\pi\)
\(548\) 5.00000 0.213589
\(549\) 0 0
\(550\) 0 0
\(551\) 25.0000 1.06504
\(552\) −8.00000 −0.340503
\(553\) 18.0000 0.765438
\(554\) 2.00000 0.0849719
\(555\) 7.00000 0.297133
\(556\) 7.00000 0.296866
\(557\) −10.0000 −0.423714 −0.211857 0.977301i \(-0.567951\pi\)
−0.211857 + 0.977301i \(0.567951\pi\)
\(558\) 10.0000 0.423334
\(559\) 10.0000 0.422955
\(560\) 3.00000 0.126773
\(561\) 0 0
\(562\) −20.0000 −0.843649
\(563\) 13.0000 0.547885 0.273942 0.961746i \(-0.411672\pi\)
0.273942 + 0.961746i \(0.411672\pi\)
\(564\) 10.0000 0.421076
\(565\) −14.0000 −0.588984
\(566\) −28.0000 −1.17693
\(567\) −3.00000 −0.125988
\(568\) −9.00000 −0.377632
\(569\) −34.0000 −1.42535 −0.712677 0.701492i \(-0.752517\pi\)
−0.712677 + 0.701492i \(0.752517\pi\)
\(570\) −5.00000 −0.209427
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 0 0
\(573\) −3.00000 −0.125327
\(574\) −18.0000 −0.751305
\(575\) −8.00000 −0.333623
\(576\) 1.00000 0.0416667
\(577\) 42.0000 1.74848 0.874241 0.485491i \(-0.161359\pi\)
0.874241 + 0.485491i \(0.161359\pi\)
\(578\) −32.0000 −1.33102
\(579\) 4.00000 0.166234
\(580\) −5.00000 −0.207614
\(581\) −21.0000 −0.871227
\(582\) −14.0000 −0.580319
\(583\) 0 0
\(584\) −2.00000 −0.0827606
\(585\) 1.00000 0.0413449
\(586\) 24.0000 0.991431
\(587\) 21.0000 0.866763 0.433381 0.901211i \(-0.357320\pi\)
0.433381 + 0.901211i \(0.357320\pi\)
\(588\) −2.00000 −0.0824786
\(589\) −50.0000 −2.06021
\(590\) 4.00000 0.164677
\(591\) 8.00000 0.329076
\(592\) 7.00000 0.287698
\(593\) 34.0000 1.39621 0.698106 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) 0 0
\(595\) 21.0000 0.860916
\(596\) 10.0000 0.409616
\(597\) 12.0000 0.491127
\(598\) −8.00000 −0.327144
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 1.00000 0.0408248
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) −30.0000 −1.22271
\(603\) −6.00000 −0.244339
\(604\) 4.00000 0.162758
\(605\) 0 0
\(606\) 15.0000 0.609333
\(607\) −41.0000 −1.66414 −0.832069 0.554672i \(-0.812844\pi\)
−0.832069 + 0.554672i \(0.812844\pi\)
\(608\) −5.00000 −0.202777
\(609\) 15.0000 0.607831
\(610\) 0 0
\(611\) 10.0000 0.404557
\(612\) 7.00000 0.282958
\(613\) −17.0000 −0.686624 −0.343312 0.939222i \(-0.611549\pi\)
−0.343312 + 0.939222i \(0.611549\pi\)
\(614\) 6.00000 0.242140
\(615\) −6.00000 −0.241943
\(616\) 0 0
\(617\) −3.00000 −0.120775 −0.0603877 0.998175i \(-0.519234\pi\)
−0.0603877 + 0.998175i \(0.519234\pi\)
\(618\) 13.0000 0.522937
\(619\) −11.0000 −0.442127 −0.221064 0.975259i \(-0.570953\pi\)
−0.221064 + 0.975259i \(0.570953\pi\)
\(620\) 10.0000 0.401610
\(621\) 8.00000 0.321029
\(622\) 8.00000 0.320771
\(623\) 0 0
\(624\) 1.00000 0.0400320
\(625\) 1.00000 0.0400000
\(626\) −18.0000 −0.719425
\(627\) 0 0
\(628\) −23.0000 −0.917800
\(629\) 49.0000 1.95376
\(630\) −3.00000 −0.119523
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 6.00000 0.238667
\(633\) 3.00000 0.119239
\(634\) 12.0000 0.476581
\(635\) 4.00000 0.158735
\(636\) 4.00000 0.158610
\(637\) −2.00000 −0.0792429
\(638\) 0 0
\(639\) 9.00000 0.356034
\(640\) 1.00000 0.0395285
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 8.00000 0.315735
\(643\) −20.0000 −0.788723 −0.394362 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(644\) 24.0000 0.945732
\(645\) −10.0000 −0.393750
\(646\) −35.0000 −1.37706
\(647\) −32.0000 −1.25805 −0.629025 0.777385i \(-0.716546\pi\)
−0.629025 + 0.777385i \(0.716546\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 1.00000 0.0392232
\(651\) −30.0000 −1.17579
\(652\) 8.00000 0.313304
\(653\) 30.0000 1.17399 0.586995 0.809590i \(-0.300311\pi\)
0.586995 + 0.809590i \(0.300311\pi\)
\(654\) 12.0000 0.469237
\(655\) −12.0000 −0.468879
\(656\) −6.00000 −0.234261
\(657\) 2.00000 0.0780274
\(658\) −30.0000 −1.16952
\(659\) 22.0000 0.856998 0.428499 0.903542i \(-0.359042\pi\)
0.428499 + 0.903542i \(0.359042\pi\)
\(660\) 0 0
\(661\) −10.0000 −0.388955 −0.194477 0.980907i \(-0.562301\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(662\) −3.00000 −0.116598
\(663\) 7.00000 0.271857
\(664\) −7.00000 −0.271653
\(665\) 15.0000 0.581675
\(666\) −7.00000 −0.271244
\(667\) −40.0000 −1.54881
\(668\) 16.0000 0.619059
\(669\) −23.0000 −0.889231
\(670\) −6.00000 −0.231800
\(671\) 0 0
\(672\) −3.00000 −0.115728
\(673\) −36.0000 −1.38770 −0.693849 0.720121i \(-0.744086\pi\)
−0.693849 + 0.720121i \(0.744086\pi\)
\(674\) 2.00000 0.0770371
\(675\) −1.00000 −0.0384900
\(676\) −12.0000 −0.461538
\(677\) 34.0000 1.30673 0.653363 0.757045i \(-0.273358\pi\)
0.653363 + 0.757045i \(0.273358\pi\)
\(678\) 14.0000 0.537667
\(679\) 42.0000 1.61181
\(680\) 7.00000 0.268438
\(681\) 24.0000 0.919682
\(682\) 0 0
\(683\) −13.0000 −0.497431 −0.248716 0.968577i \(-0.580008\pi\)
−0.248716 + 0.968577i \(0.580008\pi\)
\(684\) 5.00000 0.191180
\(685\) −5.00000 −0.191040
\(686\) −15.0000 −0.572703
\(687\) 4.00000 0.152610
\(688\) −10.0000 −0.381246
\(689\) 4.00000 0.152388
\(690\) 8.00000 0.304555
\(691\) −43.0000 −1.63580 −0.817899 0.575362i \(-0.804861\pi\)
−0.817899 + 0.575362i \(0.804861\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −25.0000 −0.948987
\(695\) −7.00000 −0.265525
\(696\) 5.00000 0.189525
\(697\) −42.0000 −1.59086
\(698\) −18.0000 −0.681310
\(699\) 6.00000 0.226941
\(700\) −3.00000 −0.113389
\(701\) 5.00000 0.188847 0.0944237 0.995532i \(-0.469899\pi\)
0.0944237 + 0.995532i \(0.469899\pi\)
\(702\) −1.00000 −0.0377426
\(703\) 35.0000 1.32005
\(704\) 0 0
\(705\) −10.0000 −0.376622
\(706\) −26.0000 −0.978523
\(707\) −45.0000 −1.69240
\(708\) −4.00000 −0.150329
\(709\) −26.0000 −0.976450 −0.488225 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) 9.00000 0.337764
\(711\) −6.00000 −0.225018
\(712\) 0 0
\(713\) 80.0000 2.99602
\(714\) −21.0000 −0.785905
\(715\) 0 0
\(716\) 0 0
\(717\) −19.0000 −0.709568
\(718\) 8.00000 0.298557
\(719\) −36.0000 −1.34257 −0.671287 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −39.0000 −1.45244
\(722\) −6.00000 −0.223297
\(723\) 15.0000 0.557856
\(724\) 16.0000 0.594635
\(725\) 5.00000 0.185695
\(726\) 0 0
\(727\) 47.0000 1.74313 0.871567 0.490277i \(-0.163104\pi\)
0.871567 + 0.490277i \(0.163104\pi\)
\(728\) −3.00000 −0.111187
\(729\) 1.00000 0.0370370
\(730\) 2.00000 0.0740233
\(731\) −70.0000 −2.58904
\(732\) 0 0
\(733\) −2.00000 −0.0738717 −0.0369358 0.999318i \(-0.511760\pi\)
−0.0369358 + 0.999318i \(0.511760\pi\)
\(734\) 11.0000 0.406017
\(735\) 2.00000 0.0737711
\(736\) 8.00000 0.294884
\(737\) 0 0
\(738\) 6.00000 0.220863
\(739\) −9.00000 −0.331070 −0.165535 0.986204i \(-0.552935\pi\)
−0.165535 + 0.986204i \(0.552935\pi\)
\(740\) −7.00000 −0.257325
\(741\) 5.00000 0.183680
\(742\) −12.0000 −0.440534
\(743\) 40.0000 1.46746 0.733729 0.679442i \(-0.237778\pi\)
0.733729 + 0.679442i \(0.237778\pi\)
\(744\) −10.0000 −0.366618
\(745\) −10.0000 −0.366372
\(746\) 31.0000 1.13499
\(747\) 7.00000 0.256117
\(748\) 0 0
\(749\) −24.0000 −0.876941
\(750\) −1.00000 −0.0365148
\(751\) 50.0000 1.82453 0.912263 0.409605i \(-0.134333\pi\)
0.912263 + 0.409605i \(0.134333\pi\)
\(752\) −10.0000 −0.364662
\(753\) −28.0000 −1.02038
\(754\) 5.00000 0.182089
\(755\) −4.00000 −0.145575
\(756\) 3.00000 0.109109
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 27.0000 0.980684
\(759\) 0 0
\(760\) 5.00000 0.181369
\(761\) −12.0000 −0.435000 −0.217500 0.976060i \(-0.569790\pi\)
−0.217500 + 0.976060i \(0.569790\pi\)
\(762\) −4.00000 −0.144905
\(763\) −36.0000 −1.30329
\(764\) 3.00000 0.108536
\(765\) −7.00000 −0.253086
\(766\) 6.00000 0.216789
\(767\) −4.00000 −0.144432
\(768\) −1.00000 −0.0360844
\(769\) 7.00000 0.252426 0.126213 0.992003i \(-0.459718\pi\)
0.126213 + 0.992003i \(0.459718\pi\)
\(770\) 0 0
\(771\) −23.0000 −0.828325
\(772\) −4.00000 −0.143963
\(773\) 28.0000 1.00709 0.503545 0.863969i \(-0.332029\pi\)
0.503545 + 0.863969i \(0.332029\pi\)
\(774\) 10.0000 0.359443
\(775\) −10.0000 −0.359211
\(776\) 14.0000 0.502571
\(777\) 21.0000 0.753371
\(778\) −14.0000 −0.501924
\(779\) −30.0000 −1.07486
\(780\) −1.00000 −0.0358057
\(781\) 0 0
\(782\) 56.0000 2.00256
\(783\) −5.00000 −0.178685
\(784\) 2.00000 0.0714286
\(785\) 23.0000 0.820905
\(786\) 12.0000 0.428026
\(787\) −8.00000 −0.285169 −0.142585 0.989783i \(-0.545541\pi\)
−0.142585 + 0.989783i \(0.545541\pi\)
\(788\) −8.00000 −0.284988
\(789\) −30.0000 −1.06803
\(790\) −6.00000 −0.213470
\(791\) −42.0000 −1.49335
\(792\) 0 0
\(793\) 0 0
\(794\) −31.0000 −1.10015
\(795\) −4.00000 −0.141865
\(796\) −12.0000 −0.425329
\(797\) −36.0000 −1.27519 −0.637593 0.770374i \(-0.720070\pi\)
−0.637593 + 0.770374i \(0.720070\pi\)
\(798\) −15.0000 −0.530994
\(799\) −70.0000 −2.47642
\(800\) −1.00000 −0.0353553
\(801\) 0 0
\(802\) −18.0000 −0.635602
\(803\) 0 0
\(804\) 6.00000 0.211604
\(805\) −24.0000 −0.845889
\(806\) −10.0000 −0.352235
\(807\) 1.00000 0.0352017
\(808\) −15.0000 −0.527698
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) 1.00000 0.0351364
\(811\) −35.0000 −1.22902 −0.614508 0.788911i \(-0.710645\pi\)
−0.614508 + 0.788911i \(0.710645\pi\)
\(812\) −15.0000 −0.526397
\(813\) 18.0000 0.631288
\(814\) 0 0
\(815\) −8.00000 −0.280228
\(816\) −7.00000 −0.245049
\(817\) −50.0000 −1.74928
\(818\) −14.0000 −0.489499
\(819\) 3.00000 0.104828
\(820\) 6.00000 0.209529
\(821\) 22.0000 0.767805 0.383903 0.923374i \(-0.374580\pi\)
0.383903 + 0.923374i \(0.374580\pi\)
\(822\) 5.00000 0.174395
\(823\) 3.00000 0.104573 0.0522867 0.998632i \(-0.483349\pi\)
0.0522867 + 0.998632i \(0.483349\pi\)
\(824\) −13.0000 −0.452876
\(825\) 0 0
\(826\) 12.0000 0.417533
\(827\) −27.0000 −0.938882 −0.469441 0.882964i \(-0.655545\pi\)
−0.469441 + 0.882964i \(0.655545\pi\)
\(828\) −8.00000 −0.278019
\(829\) −44.0000 −1.52818 −0.764092 0.645108i \(-0.776812\pi\)
−0.764092 + 0.645108i \(0.776812\pi\)
\(830\) 7.00000 0.242974
\(831\) 2.00000 0.0693792
\(832\) −1.00000 −0.0346688
\(833\) 14.0000 0.485071
\(834\) 7.00000 0.242390
\(835\) −16.0000 −0.553703
\(836\) 0 0
\(837\) 10.0000 0.345651
\(838\) 14.0000 0.483622
\(839\) 21.0000 0.725001 0.362500 0.931984i \(-0.381923\pi\)
0.362500 + 0.931984i \(0.381923\pi\)
\(840\) 3.00000 0.103510
\(841\) −4.00000 −0.137931
\(842\) 34.0000 1.17172
\(843\) −20.0000 −0.688837
\(844\) −3.00000 −0.103264
\(845\) 12.0000 0.412813
\(846\) 10.0000 0.343807
\(847\) 0 0
\(848\) −4.00000 −0.137361
\(849\) −28.0000 −0.960958
\(850\) −7.00000 −0.240098
\(851\) −56.0000 −1.91966
\(852\) −9.00000 −0.308335
\(853\) −37.0000 −1.26686 −0.633428 0.773802i \(-0.718353\pi\)
−0.633428 + 0.773802i \(0.718353\pi\)
\(854\) 0 0
\(855\) −5.00000 −0.170996
\(856\) −8.00000 −0.273434
\(857\) −21.0000 −0.717346 −0.358673 0.933463i \(-0.616771\pi\)
−0.358673 + 0.933463i \(0.616771\pi\)
\(858\) 0 0
\(859\) 4.00000 0.136478 0.0682391 0.997669i \(-0.478262\pi\)
0.0682391 + 0.997669i \(0.478262\pi\)
\(860\) 10.0000 0.340997
\(861\) −18.0000 −0.613438
\(862\) 15.0000 0.510902
\(863\) 34.0000 1.15737 0.578687 0.815550i \(-0.303565\pi\)
0.578687 + 0.815550i \(0.303565\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) −8.00000 −0.271851
\(867\) −32.0000 −1.08678
\(868\) 30.0000 1.01827
\(869\) 0 0
\(870\) −5.00000 −0.169516
\(871\) 6.00000 0.203302
\(872\) −12.0000 −0.406371
\(873\) −14.0000 −0.473828
\(874\) 40.0000 1.35302
\(875\) 3.00000 0.101419
\(876\) −2.00000 −0.0675737
\(877\) −43.0000 −1.45201 −0.726003 0.687691i \(-0.758624\pi\)
−0.726003 + 0.687691i \(0.758624\pi\)
\(878\) −26.0000 −0.877457
\(879\) 24.0000 0.809500
\(880\) 0 0
\(881\) −14.0000 −0.471672 −0.235836 0.971793i \(-0.575783\pi\)
−0.235836 + 0.971793i \(0.575783\pi\)
\(882\) −2.00000 −0.0673435
\(883\) 34.0000 1.14419 0.572096 0.820187i \(-0.306131\pi\)
0.572096 + 0.820187i \(0.306131\pi\)
\(884\) −7.00000 −0.235435
\(885\) 4.00000 0.134459
\(886\) 19.0000 0.638317
\(887\) −8.00000 −0.268614 −0.134307 0.990940i \(-0.542881\pi\)
−0.134307 + 0.990940i \(0.542881\pi\)
\(888\) 7.00000 0.234905
\(889\) 12.0000 0.402467
\(890\) 0 0
\(891\) 0 0
\(892\) 23.0000 0.770097
\(893\) −50.0000 −1.67319
\(894\) 10.0000 0.334450
\(895\) 0 0
\(896\) 3.00000 0.100223
\(897\) −8.00000 −0.267112
\(898\) −34.0000 −1.13459
\(899\) −50.0000 −1.66759
\(900\) 1.00000 0.0333333
\(901\) −28.0000 −0.932815
\(902\) 0 0
\(903\) −30.0000 −0.998337
\(904\) −14.0000 −0.465633
\(905\) −16.0000 −0.531858
\(906\) 4.00000 0.132891
\(907\) 46.0000 1.52740 0.763702 0.645568i \(-0.223379\pi\)
0.763702 + 0.645568i \(0.223379\pi\)
\(908\) −24.0000 −0.796468
\(909\) 15.0000 0.497519
\(910\) 3.00000 0.0994490
\(911\) 49.0000 1.62344 0.811721 0.584045i \(-0.198531\pi\)
0.811721 + 0.584045i \(0.198531\pi\)
\(912\) −5.00000 −0.165567
\(913\) 0 0
\(914\) −28.0000 −0.926158
\(915\) 0 0
\(916\) −4.00000 −0.132164
\(917\) −36.0000 −1.18882
\(918\) 7.00000 0.231034
\(919\) 32.0000 1.05558 0.527791 0.849374i \(-0.323020\pi\)
0.527791 + 0.849374i \(0.323020\pi\)
\(920\) −8.00000 −0.263752
\(921\) 6.00000 0.197707
\(922\) −21.0000 −0.691598
\(923\) −9.00000 −0.296239
\(924\) 0 0
\(925\) 7.00000 0.230159
\(926\) 16.0000 0.525793
\(927\) 13.0000 0.426976
\(928\) −5.00000 −0.164133
\(929\) −40.0000 −1.31236 −0.656179 0.754606i \(-0.727828\pi\)
−0.656179 + 0.754606i \(0.727828\pi\)
\(930\) 10.0000 0.327913
\(931\) 10.0000 0.327737
\(932\) −6.00000 −0.196537
\(933\) 8.00000 0.261908
\(934\) 21.0000 0.687141
\(935\) 0 0
\(936\) 1.00000 0.0326860
\(937\) 54.0000 1.76410 0.882052 0.471153i \(-0.156162\pi\)
0.882052 + 0.471153i \(0.156162\pi\)
\(938\) −18.0000 −0.587721
\(939\) −18.0000 −0.587408
\(940\) 10.0000 0.326164
\(941\) 5.00000 0.162995 0.0814977 0.996674i \(-0.474030\pi\)
0.0814977 + 0.996674i \(0.474030\pi\)
\(942\) −23.0000 −0.749380
\(943\) 48.0000 1.56310
\(944\) 4.00000 0.130189
\(945\) −3.00000 −0.0975900
\(946\) 0 0
\(947\) −23.0000 −0.747400 −0.373700 0.927550i \(-0.621911\pi\)
−0.373700 + 0.927550i \(0.621911\pi\)
\(948\) 6.00000 0.194871
\(949\) −2.00000 −0.0649227
\(950\) −5.00000 −0.162221
\(951\) 12.0000 0.389127
\(952\) 21.0000 0.680614
\(953\) 26.0000 0.842223 0.421111 0.907009i \(-0.361640\pi\)
0.421111 + 0.907009i \(0.361640\pi\)
\(954\) 4.00000 0.129505
\(955\) −3.00000 −0.0970777
\(956\) 19.0000 0.614504
\(957\) 0 0
\(958\) −3.00000 −0.0969256
\(959\) −15.0000 −0.484375
\(960\) 1.00000 0.0322749
\(961\) 69.0000 2.22581
\(962\) 7.00000 0.225689
\(963\) 8.00000 0.257796
\(964\) −15.0000 −0.483117
\(965\) 4.00000 0.128765
\(966\) 24.0000 0.772187
\(967\) −32.0000 −1.02905 −0.514525 0.857475i \(-0.672032\pi\)
−0.514525 + 0.857475i \(0.672032\pi\)
\(968\) 0 0
\(969\) −35.0000 −1.12436
\(970\) −14.0000 −0.449513
\(971\) 12.0000 0.385098 0.192549 0.981287i \(-0.438325\pi\)
0.192549 + 0.981287i \(0.438325\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −21.0000 −0.673229
\(974\) −29.0000 −0.929220
\(975\) 1.00000 0.0320256
\(976\) 0 0
\(977\) −2.00000 −0.0639857 −0.0319928 0.999488i \(-0.510185\pi\)
−0.0319928 + 0.999488i \(0.510185\pi\)
\(978\) 8.00000 0.255812
\(979\) 0 0
\(980\) −2.00000 −0.0638877
\(981\) 12.0000 0.383131
\(982\) −18.0000 −0.574403
\(983\) −2.00000 −0.0637901 −0.0318950 0.999491i \(-0.510154\pi\)
−0.0318950 + 0.999491i \(0.510154\pi\)
\(984\) −6.00000 −0.191273
\(985\) 8.00000 0.254901
\(986\) −35.0000 −1.11463
\(987\) −30.0000 −0.954911
\(988\) −5.00000 −0.159071
\(989\) 80.0000 2.54385
\(990\) 0 0
\(991\) 22.0000 0.698853 0.349427 0.936964i \(-0.386376\pi\)
0.349427 + 0.936964i \(0.386376\pi\)
\(992\) 10.0000 0.317500
\(993\) −3.00000 −0.0952021
\(994\) 27.0000 0.856388
\(995\) 12.0000 0.380426
\(996\) −7.00000 −0.221803
\(997\) −43.0000 −1.36182 −0.680912 0.732365i \(-0.738416\pi\)
−0.680912 + 0.732365i \(0.738416\pi\)
\(998\) −13.0000 −0.411508
\(999\) −7.00000 −0.221470
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.b.1.1 1
11.10 odd 2 3630.2.a.p.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3630.2.a.b.1.1 1 1.1 even 1 trivial
3630.2.a.p.1.1 yes 1 11.10 odd 2