Properties

Label 966.2.a.i.1.1
Level $966$
Weight $2$
Character 966.1
Self dual yes
Analytic conductor $7.714$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.71354883526\)
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 \(\chi\) \(=\) 966.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.00000 q^{10} +1.00000 q^{12} +5.00000 q^{13} +1.00000 q^{14} -3.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} +8.00000 q^{19} -3.00000 q^{20} +1.00000 q^{21} -1.00000 q^{23} +1.00000 q^{24} +4.00000 q^{25} +5.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} +3.00000 q^{29} -3.00000 q^{30} +2.00000 q^{31} +1.00000 q^{32} -3.00000 q^{35} +1.00000 q^{36} -7.00000 q^{37} +8.00000 q^{38} +5.00000 q^{39} -3.00000 q^{40} +9.00000 q^{41} +1.00000 q^{42} -1.00000 q^{43} -3.00000 q^{45} -1.00000 q^{46} -3.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.00000 q^{50} +5.00000 q^{52} -12.0000 q^{53} +1.00000 q^{54} +1.00000 q^{56} +8.00000 q^{57} +3.00000 q^{58} -6.00000 q^{59} -3.00000 q^{60} +14.0000 q^{61} +2.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} -15.0000 q^{65} -4.00000 q^{67} -1.00000 q^{69} -3.00000 q^{70} +6.00000 q^{71} +1.00000 q^{72} -4.00000 q^{73} -7.00000 q^{74} +4.00000 q^{75} +8.00000 q^{76} +5.00000 q^{78} -16.0000 q^{79} -3.00000 q^{80} +1.00000 q^{81} +9.00000 q^{82} -12.0000 q^{83} +1.00000 q^{84} -1.00000 q^{86} +3.00000 q^{87} +6.00000 q^{89} -3.00000 q^{90} +5.00000 q^{91} -1.00000 q^{92} +2.00000 q^{93} -3.00000 q^{94} -24.0000 q^{95} +1.00000 q^{96} -1.00000 q^{97} +1.00000 q^{98} +O(q^{100})\)

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
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 1.00000 0.408248
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −3.00000 −0.948683
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 0.288675
\(13\) 5.00000 1.38675 0.693375 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 1.00000 0.267261
\(15\) −3.00000 −0.774597
\(16\) 1.00000 0.250000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 1.00000 0.235702
\(19\) 8.00000 1.83533 0.917663 0.397360i \(-0.130073\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) −3.00000 −0.670820
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 1.00000 0.204124
\(25\) 4.00000 0.800000
\(26\) 5.00000 0.980581
\(27\) 1.00000 0.192450
\(28\) 1.00000 0.188982
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) −3.00000 −0.547723
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) 1.00000 0.166667
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) 8.00000 1.29777
\(39\) 5.00000 0.800641
\(40\) −3.00000 −0.474342
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 1.00000 0.154303
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 0 0
\(45\) −3.00000 −0.447214
\(46\) −1.00000 −0.147442
\(47\) −3.00000 −0.437595 −0.218797 0.975770i \(-0.570213\pi\)
−0.218797 + 0.975770i \(0.570213\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) 4.00000 0.565685
\(51\) 0 0
\(52\) 5.00000 0.693375
\(53\) −12.0000 −1.64833 −0.824163 0.566352i \(-0.808354\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 8.00000 1.05963
\(58\) 3.00000 0.393919
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) −3.00000 −0.387298
\(61\) 14.0000 1.79252 0.896258 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 2.00000 0.254000
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) −15.0000 −1.86052
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) −1.00000 −0.120386
\(70\) −3.00000 −0.358569
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 1.00000 0.117851
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) −7.00000 −0.813733
\(75\) 4.00000 0.461880
\(76\) 8.00000 0.917663
\(77\) 0 0
\(78\) 5.00000 0.566139
\(79\) −16.0000 −1.80014 −0.900070 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) −3.00000 −0.335410
\(81\) 1.00000 0.111111
\(82\) 9.00000 0.993884
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 1.00000 0.109109
\(85\) 0 0
\(86\) −1.00000 −0.107833
\(87\) 3.00000 0.321634
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −3.00000 −0.316228
\(91\) 5.00000 0.524142
\(92\) −1.00000 −0.104257
\(93\) 2.00000 0.207390
\(94\) −3.00000 −0.309426
\(95\) −24.0000 −2.46235
\(96\) 1.00000 0.102062
\(97\) −1.00000 −0.101535 −0.0507673 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 4.00000 0.400000
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) −1.00000 −0.0985329 −0.0492665 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) 5.00000 0.490290
\(105\) −3.00000 −0.292770
\(106\) −12.0000 −1.16554
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 1.00000 0.0962250
\(109\) −19.0000 −1.81987 −0.909935 0.414751i \(-0.863869\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(110\) 0 0
\(111\) −7.00000 −0.664411
\(112\) 1.00000 0.0944911
\(113\) 15.0000 1.41108 0.705541 0.708669i \(-0.250704\pi\)
0.705541 + 0.708669i \(0.250704\pi\)
\(114\) 8.00000 0.749269
\(115\) 3.00000 0.279751
\(116\) 3.00000 0.278543
\(117\) 5.00000 0.462250
\(118\) −6.00000 −0.552345
\(119\) 0 0
\(120\) −3.00000 −0.273861
\(121\) −11.0000 −1.00000
\(122\) 14.0000 1.26750
\(123\) 9.00000 0.811503
\(124\) 2.00000 0.179605
\(125\) 3.00000 0.268328
\(126\) 1.00000 0.0890871
\(127\) −13.0000 −1.15356 −0.576782 0.816898i \(-0.695692\pi\)
−0.576782 + 0.816898i \(0.695692\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.00000 −0.0880451
\(130\) −15.0000 −1.31559
\(131\) −18.0000 −1.57267 −0.786334 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) 0 0
\(133\) 8.00000 0.693688
\(134\) −4.00000 −0.345547
\(135\) −3.00000 −0.258199
\(136\) 0 0
\(137\) −9.00000 −0.768922 −0.384461 0.923141i \(-0.625613\pi\)
−0.384461 + 0.923141i \(0.625613\pi\)
\(138\) −1.00000 −0.0851257
\(139\) 5.00000 0.424094 0.212047 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(140\) −3.00000 −0.253546
\(141\) −3.00000 −0.252646
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −9.00000 −0.747409
\(146\) −4.00000 −0.331042
\(147\) 1.00000 0.0824786
\(148\) −7.00000 −0.575396
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 4.00000 0.326599
\(151\) 11.0000 0.895167 0.447584 0.894242i \(-0.352285\pi\)
0.447584 + 0.894242i \(0.352285\pi\)
\(152\) 8.00000 0.648886
\(153\) 0 0
\(154\) 0 0
\(155\) −6.00000 −0.481932
\(156\) 5.00000 0.400320
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) −16.0000 −1.27289
\(159\) −12.0000 −0.951662
\(160\) −3.00000 −0.237171
\(161\) −1.00000 −0.0788110
\(162\) 1.00000 0.0785674
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 9.00000 0.702782
\(165\) 0 0
\(166\) −12.0000 −0.931381
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 1.00000 0.0771517
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 8.00000 0.611775
\(172\) −1.00000 −0.0762493
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 3.00000 0.227429
\(175\) 4.00000 0.302372
\(176\) 0 0
\(177\) −6.00000 −0.450988
\(178\) 6.00000 0.449719
\(179\) 15.0000 1.12115 0.560576 0.828103i \(-0.310580\pi\)
0.560576 + 0.828103i \(0.310580\pi\)
\(180\) −3.00000 −0.223607
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 5.00000 0.370625
\(183\) 14.0000 1.03491
\(184\) −1.00000 −0.0737210
\(185\) 21.0000 1.54395
\(186\) 2.00000 0.146647
\(187\) 0 0
\(188\) −3.00000 −0.218797
\(189\) 1.00000 0.0727393
\(190\) −24.0000 −1.74114
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 1.00000 0.0721688
\(193\) −1.00000 −0.0719816 −0.0359908 0.999352i \(-0.511459\pi\)
−0.0359908 + 0.999352i \(0.511459\pi\)
\(194\) −1.00000 −0.0717958
\(195\) −15.0000 −1.07417
\(196\) 1.00000 0.0714286
\(197\) 9.00000 0.641223 0.320612 0.947211i \(-0.396112\pi\)
0.320612 + 0.947211i \(0.396112\pi\)
\(198\) 0 0
\(199\) 17.0000 1.20510 0.602549 0.798082i \(-0.294152\pi\)
0.602549 + 0.798082i \(0.294152\pi\)
\(200\) 4.00000 0.282843
\(201\) −4.00000 −0.282138
\(202\) −6.00000 −0.422159
\(203\) 3.00000 0.210559
\(204\) 0 0
\(205\) −27.0000 −1.88576
\(206\) −1.00000 −0.0696733
\(207\) −1.00000 −0.0695048
\(208\) 5.00000 0.346688
\(209\) 0 0
\(210\) −3.00000 −0.207020
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) −12.0000 −0.824163
\(213\) 6.00000 0.411113
\(214\) 12.0000 0.820303
\(215\) 3.00000 0.204598
\(216\) 1.00000 0.0680414
\(217\) 2.00000 0.135769
\(218\) −19.0000 −1.28684
\(219\) −4.00000 −0.270295
\(220\) 0 0
\(221\) 0 0
\(222\) −7.00000 −0.469809
\(223\) 14.0000 0.937509 0.468755 0.883328i \(-0.344703\pi\)
0.468755 + 0.883328i \(0.344703\pi\)
\(224\) 1.00000 0.0668153
\(225\) 4.00000 0.266667
\(226\) 15.0000 0.997785
\(227\) −15.0000 −0.995585 −0.497792 0.867296i \(-0.665856\pi\)
−0.497792 + 0.867296i \(0.665856\pi\)
\(228\) 8.00000 0.529813
\(229\) −4.00000 −0.264327 −0.132164 0.991228i \(-0.542192\pi\)
−0.132164 + 0.991228i \(0.542192\pi\)
\(230\) 3.00000 0.197814
\(231\) 0 0
\(232\) 3.00000 0.196960
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 5.00000 0.326860
\(235\) 9.00000 0.587095
\(236\) −6.00000 −0.390567
\(237\) −16.0000 −1.03931
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) −3.00000 −0.193649
\(241\) −19.0000 −1.22390 −0.611949 0.790897i \(-0.709614\pi\)
−0.611949 + 0.790897i \(0.709614\pi\)
\(242\) −11.0000 −0.707107
\(243\) 1.00000 0.0641500
\(244\) 14.0000 0.896258
\(245\) −3.00000 −0.191663
\(246\) 9.00000 0.573819
\(247\) 40.0000 2.54514
\(248\) 2.00000 0.127000
\(249\) −12.0000 −0.760469
\(250\) 3.00000 0.189737
\(251\) −15.0000 −0.946792 −0.473396 0.880850i \(-0.656972\pi\)
−0.473396 + 0.880850i \(0.656972\pi\)
\(252\) 1.00000 0.0629941
\(253\) 0 0
\(254\) −13.0000 −0.815693
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) −1.00000 −0.0622573
\(259\) −7.00000 −0.434959
\(260\) −15.0000 −0.930261
\(261\) 3.00000 0.185695
\(262\) −18.0000 −1.11204
\(263\) −9.00000 −0.554964 −0.277482 0.960731i \(-0.589500\pi\)
−0.277482 + 0.960731i \(0.589500\pi\)
\(264\) 0 0
\(265\) 36.0000 2.21146
\(266\) 8.00000 0.490511
\(267\) 6.00000 0.367194
\(268\) −4.00000 −0.244339
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) −3.00000 −0.182574
\(271\) −28.0000 −1.70088 −0.850439 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 0 0
\(273\) 5.00000 0.302614
\(274\) −9.00000 −0.543710
\(275\) 0 0
\(276\) −1.00000 −0.0601929
\(277\) −4.00000 −0.240337 −0.120168 0.992754i \(-0.538343\pi\)
−0.120168 + 0.992754i \(0.538343\pi\)
\(278\) 5.00000 0.299880
\(279\) 2.00000 0.119737
\(280\) −3.00000 −0.179284
\(281\) −15.0000 −0.894825 −0.447412 0.894328i \(-0.647654\pi\)
−0.447412 + 0.894328i \(0.647654\pi\)
\(282\) −3.00000 −0.178647
\(283\) 14.0000 0.832214 0.416107 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) 6.00000 0.356034
\(285\) −24.0000 −1.42164
\(286\) 0 0
\(287\) 9.00000 0.531253
\(288\) 1.00000 0.0589256
\(289\) −17.0000 −1.00000
\(290\) −9.00000 −0.528498
\(291\) −1.00000 −0.0586210
\(292\) −4.00000 −0.234082
\(293\) −30.0000 −1.75262 −0.876309 0.481749i \(-0.840002\pi\)
−0.876309 + 0.481749i \(0.840002\pi\)
\(294\) 1.00000 0.0583212
\(295\) 18.0000 1.04800
\(296\) −7.00000 −0.406867
\(297\) 0 0
\(298\) 0 0
\(299\) −5.00000 −0.289157
\(300\) 4.00000 0.230940
\(301\) −1.00000 −0.0576390
\(302\) 11.0000 0.632979
\(303\) −6.00000 −0.344691
\(304\) 8.00000 0.458831
\(305\) −42.0000 −2.40491
\(306\) 0 0
\(307\) 11.0000 0.627803 0.313902 0.949456i \(-0.398364\pi\)
0.313902 + 0.949456i \(0.398364\pi\)
\(308\) 0 0
\(309\) −1.00000 −0.0568880
\(310\) −6.00000 −0.340777
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 5.00000 0.283069
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) −4.00000 −0.225733
\(315\) −3.00000 −0.169031
\(316\) −16.0000 −0.900070
\(317\) −27.0000 −1.51647 −0.758236 0.651981i \(-0.773938\pi\)
−0.758236 + 0.651981i \(0.773938\pi\)
\(318\) −12.0000 −0.672927
\(319\) 0 0
\(320\) −3.00000 −0.167705
\(321\) 12.0000 0.669775
\(322\) −1.00000 −0.0557278
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 20.0000 1.10940
\(326\) 20.0000 1.10770
\(327\) −19.0000 −1.05070
\(328\) 9.00000 0.496942
\(329\) −3.00000 −0.165395
\(330\) 0 0
\(331\) −16.0000 −0.879440 −0.439720 0.898135i \(-0.644922\pi\)
−0.439720 + 0.898135i \(0.644922\pi\)
\(332\) −12.0000 −0.658586
\(333\) −7.00000 −0.383598
\(334\) −12.0000 −0.656611
\(335\) 12.0000 0.655630
\(336\) 1.00000 0.0545545
\(337\) −4.00000 −0.217894 −0.108947 0.994048i \(-0.534748\pi\)
−0.108947 + 0.994048i \(0.534748\pi\)
\(338\) 12.0000 0.652714
\(339\) 15.0000 0.814688
\(340\) 0 0
\(341\) 0 0
\(342\) 8.00000 0.432590
\(343\) 1.00000 0.0539949
\(344\) −1.00000 −0.0539164
\(345\) 3.00000 0.161515
\(346\) 6.00000 0.322562
\(347\) 3.00000 0.161048 0.0805242 0.996753i \(-0.474341\pi\)
0.0805242 + 0.996753i \(0.474341\pi\)
\(348\) 3.00000 0.160817
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 4.00000 0.213809
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) 27.0000 1.43706 0.718532 0.695493i \(-0.244814\pi\)
0.718532 + 0.695493i \(0.244814\pi\)
\(354\) −6.00000 −0.318896
\(355\) −18.0000 −0.955341
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 15.0000 0.792775
\(359\) 21.0000 1.10834 0.554169 0.832404i \(-0.313036\pi\)
0.554169 + 0.832404i \(0.313036\pi\)
\(360\) −3.00000 −0.158114
\(361\) 45.0000 2.36842
\(362\) 2.00000 0.105118
\(363\) −11.0000 −0.577350
\(364\) 5.00000 0.262071
\(365\) 12.0000 0.628109
\(366\) 14.0000 0.731792
\(367\) 29.0000 1.51379 0.756894 0.653538i \(-0.226716\pi\)
0.756894 + 0.653538i \(0.226716\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 9.00000 0.468521
\(370\) 21.0000 1.09174
\(371\) −12.0000 −0.623009
\(372\) 2.00000 0.103695
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 0 0
\(375\) 3.00000 0.154919
\(376\) −3.00000 −0.154713
\(377\) 15.0000 0.772539
\(378\) 1.00000 0.0514344
\(379\) 29.0000 1.48963 0.744815 0.667271i \(-0.232538\pi\)
0.744815 + 0.667271i \(0.232538\pi\)
\(380\) −24.0000 −1.23117
\(381\) −13.0000 −0.666010
\(382\) −12.0000 −0.613973
\(383\) 36.0000 1.83951 0.919757 0.392488i \(-0.128386\pi\)
0.919757 + 0.392488i \(0.128386\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −1.00000 −0.0508987
\(387\) −1.00000 −0.0508329
\(388\) −1.00000 −0.0507673
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) −15.0000 −0.759555
\(391\) 0 0
\(392\) 1.00000 0.0505076
\(393\) −18.0000 −0.907980
\(394\) 9.00000 0.453413
\(395\) 48.0000 2.41514
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 17.0000 0.852133
\(399\) 8.00000 0.400501
\(400\) 4.00000 0.200000
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) −4.00000 −0.199502
\(403\) 10.0000 0.498135
\(404\) −6.00000 −0.298511
\(405\) −3.00000 −0.149071
\(406\) 3.00000 0.148888
\(407\) 0 0
\(408\) 0 0
\(409\) 32.0000 1.58230 0.791149 0.611623i \(-0.209483\pi\)
0.791149 + 0.611623i \(0.209483\pi\)
\(410\) −27.0000 −1.33343
\(411\) −9.00000 −0.443937
\(412\) −1.00000 −0.0492665
\(413\) −6.00000 −0.295241
\(414\) −1.00000 −0.0491473
\(415\) 36.0000 1.76717
\(416\) 5.00000 0.245145
\(417\) 5.00000 0.244851
\(418\) 0 0
\(419\) 36.0000 1.75872 0.879358 0.476162i \(-0.157972\pi\)
0.879358 + 0.476162i \(0.157972\pi\)
\(420\) −3.00000 −0.146385
\(421\) −19.0000 −0.926003 −0.463002 0.886357i \(-0.653228\pi\)
−0.463002 + 0.886357i \(0.653228\pi\)
\(422\) 8.00000 0.389434
\(423\) −3.00000 −0.145865
\(424\) −12.0000 −0.582772
\(425\) 0 0
\(426\) 6.00000 0.290701
\(427\) 14.0000 0.677507
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 3.00000 0.144673
\(431\) 15.0000 0.722525 0.361262 0.932464i \(-0.382346\pi\)
0.361262 + 0.932464i \(0.382346\pi\)
\(432\) 1.00000 0.0481125
\(433\) 17.0000 0.816968 0.408484 0.912766i \(-0.366058\pi\)
0.408484 + 0.912766i \(0.366058\pi\)
\(434\) 2.00000 0.0960031
\(435\) −9.00000 −0.431517
\(436\) −19.0000 −0.909935
\(437\) −8.00000 −0.382692
\(438\) −4.00000 −0.191127
\(439\) 26.0000 1.24091 0.620456 0.784241i \(-0.286947\pi\)
0.620456 + 0.784241i \(0.286947\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −27.0000 −1.28281 −0.641404 0.767203i \(-0.721648\pi\)
−0.641404 + 0.767203i \(0.721648\pi\)
\(444\) −7.00000 −0.332205
\(445\) −18.0000 −0.853282
\(446\) 14.0000 0.662919
\(447\) 0 0
\(448\) 1.00000 0.0472456
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 4.00000 0.188562
\(451\) 0 0
\(452\) 15.0000 0.705541
\(453\) 11.0000 0.516825
\(454\) −15.0000 −0.703985
\(455\) −15.0000 −0.703211
\(456\) 8.00000 0.374634
\(457\) −28.0000 −1.30978 −0.654892 0.755722i \(-0.727286\pi\)
−0.654892 + 0.755722i \(0.727286\pi\)
\(458\) −4.00000 −0.186908
\(459\) 0 0
\(460\) 3.00000 0.139876
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 0 0
\(463\) −31.0000 −1.44069 −0.720346 0.693615i \(-0.756017\pi\)
−0.720346 + 0.693615i \(0.756017\pi\)
\(464\) 3.00000 0.139272
\(465\) −6.00000 −0.278243
\(466\) −6.00000 −0.277945
\(467\) −33.0000 −1.52706 −0.763529 0.645774i \(-0.776535\pi\)
−0.763529 + 0.645774i \(0.776535\pi\)
\(468\) 5.00000 0.231125
\(469\) −4.00000 −0.184703
\(470\) 9.00000 0.415139
\(471\) −4.00000 −0.184310
\(472\) −6.00000 −0.276172
\(473\) 0 0
\(474\) −16.0000 −0.734904
\(475\) 32.0000 1.46826
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) 12.0000 0.548867
\(479\) −6.00000 −0.274147 −0.137073 0.990561i \(-0.543770\pi\)
−0.137073 + 0.990561i \(0.543770\pi\)
\(480\) −3.00000 −0.136931
\(481\) −35.0000 −1.59586
\(482\) −19.0000 −0.865426
\(483\) −1.00000 −0.0455016
\(484\) −11.0000 −0.500000
\(485\) 3.00000 0.136223
\(486\) 1.00000 0.0453609
\(487\) −31.0000 −1.40474 −0.702372 0.711810i \(-0.747876\pi\)
−0.702372 + 0.711810i \(0.747876\pi\)
\(488\) 14.0000 0.633750
\(489\) 20.0000 0.904431
\(490\) −3.00000 −0.135526
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 9.00000 0.405751
\(493\) 0 0
\(494\) 40.0000 1.79969
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 6.00000 0.269137
\(498\) −12.0000 −0.537733
\(499\) 14.0000 0.626726 0.313363 0.949633i \(-0.398544\pi\)
0.313363 + 0.949633i \(0.398544\pi\)
\(500\) 3.00000 0.134164
\(501\) −12.0000 −0.536120
\(502\) −15.0000 −0.669483
\(503\) 18.0000 0.802580 0.401290 0.915951i \(-0.368562\pi\)
0.401290 + 0.915951i \(0.368562\pi\)
\(504\) 1.00000 0.0445435
\(505\) 18.0000 0.800989
\(506\) 0 0
\(507\) 12.0000 0.532939
\(508\) −13.0000 −0.576782
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) −4.00000 −0.176950
\(512\) 1.00000 0.0441942
\(513\) 8.00000 0.353209
\(514\) 6.00000 0.264649
\(515\) 3.00000 0.132196
\(516\) −1.00000 −0.0440225
\(517\) 0 0
\(518\) −7.00000 −0.307562
\(519\) 6.00000 0.263371
\(520\) −15.0000 −0.657794
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 3.00000 0.131306
\(523\) 26.0000 1.13690 0.568450 0.822718i \(-0.307543\pi\)
0.568450 + 0.822718i \(0.307543\pi\)
\(524\) −18.0000 −0.786334
\(525\) 4.00000 0.174574
\(526\) −9.00000 −0.392419
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 36.0000 1.56374
\(531\) −6.00000 −0.260378
\(532\) 8.00000 0.346844
\(533\) 45.0000 1.94917
\(534\) 6.00000 0.259645
\(535\) −36.0000 −1.55642
\(536\) −4.00000 −0.172774
\(537\) 15.0000 0.647298
\(538\) −18.0000 −0.776035
\(539\) 0 0
\(540\) −3.00000 −0.129099
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) −28.0000 −1.20270
\(543\) 2.00000 0.0858282
\(544\) 0 0
\(545\) 57.0000 2.44161
\(546\) 5.00000 0.213980
\(547\) −10.0000 −0.427569 −0.213785 0.976881i \(-0.568579\pi\)
−0.213785 + 0.976881i \(0.568579\pi\)
\(548\) −9.00000 −0.384461
\(549\) 14.0000 0.597505
\(550\) 0 0
\(551\) 24.0000 1.02243
\(552\) −1.00000 −0.0425628
\(553\) −16.0000 −0.680389
\(554\) −4.00000 −0.169944
\(555\) 21.0000 0.891400
\(556\) 5.00000 0.212047
\(557\) 24.0000 1.01691 0.508456 0.861088i \(-0.330216\pi\)
0.508456 + 0.861088i \(0.330216\pi\)
\(558\) 2.00000 0.0846668
\(559\) −5.00000 −0.211477
\(560\) −3.00000 −0.126773
\(561\) 0 0
\(562\) −15.0000 −0.632737
\(563\) −3.00000 −0.126435 −0.0632175 0.998000i \(-0.520136\pi\)
−0.0632175 + 0.998000i \(0.520136\pi\)
\(564\) −3.00000 −0.126323
\(565\) −45.0000 −1.89316
\(566\) 14.0000 0.588464
\(567\) 1.00000 0.0419961
\(568\) 6.00000 0.251754
\(569\) 45.0000 1.88650 0.943249 0.332086i \(-0.107752\pi\)
0.943249 + 0.332086i \(0.107752\pi\)
\(570\) −24.0000 −1.00525
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) −12.0000 −0.501307
\(574\) 9.00000 0.375653
\(575\) −4.00000 −0.166812
\(576\) 1.00000 0.0416667
\(577\) 26.0000 1.08239 0.541197 0.840896i \(-0.317971\pi\)
0.541197 + 0.840896i \(0.317971\pi\)
\(578\) −17.0000 −0.707107
\(579\) −1.00000 −0.0415586
\(580\) −9.00000 −0.373705
\(581\) −12.0000 −0.497844
\(582\) −1.00000 −0.0414513
\(583\) 0 0
\(584\) −4.00000 −0.165521
\(585\) −15.0000 −0.620174
\(586\) −30.0000 −1.23929
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 1.00000 0.0412393
\(589\) 16.0000 0.659269
\(590\) 18.0000 0.741048
\(591\) 9.00000 0.370211
\(592\) −7.00000 −0.287698
\(593\) −27.0000 −1.10876 −0.554379 0.832265i \(-0.687044\pi\)
−0.554379 + 0.832265i \(0.687044\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 17.0000 0.695764
\(598\) −5.00000 −0.204465
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 4.00000 0.163299
\(601\) −16.0000 −0.652654 −0.326327 0.945257i \(-0.605811\pi\)
−0.326327 + 0.945257i \(0.605811\pi\)
\(602\) −1.00000 −0.0407570
\(603\) −4.00000 −0.162893
\(604\) 11.0000 0.447584
\(605\) 33.0000 1.34164
\(606\) −6.00000 −0.243733
\(607\) 14.0000 0.568242 0.284121 0.958788i \(-0.408298\pi\)
0.284121 + 0.958788i \(0.408298\pi\)
\(608\) 8.00000 0.324443
\(609\) 3.00000 0.121566
\(610\) −42.0000 −1.70053
\(611\) −15.0000 −0.606835
\(612\) 0 0
\(613\) −1.00000 −0.0403896 −0.0201948 0.999796i \(-0.506429\pi\)
−0.0201948 + 0.999796i \(0.506429\pi\)
\(614\) 11.0000 0.443924
\(615\) −27.0000 −1.08875
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) −1.00000 −0.0402259
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) −6.00000 −0.240966
\(621\) −1.00000 −0.0401286
\(622\) 12.0000 0.481156
\(623\) 6.00000 0.240385
\(624\) 5.00000 0.200160
\(625\) −29.0000 −1.16000
\(626\) −10.0000 −0.399680
\(627\) 0 0
\(628\) −4.00000 −0.159617
\(629\) 0 0
\(630\) −3.00000 −0.119523
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) −16.0000 −0.636446
\(633\) 8.00000 0.317971
\(634\) −27.0000 −1.07231
\(635\) 39.0000 1.54767
\(636\) −12.0000 −0.475831
\(637\) 5.00000 0.198107
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) −3.00000 −0.118585
\(641\) −15.0000 −0.592464 −0.296232 0.955116i \(-0.595730\pi\)
−0.296232 + 0.955116i \(0.595730\pi\)
\(642\) 12.0000 0.473602
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) −1.00000 −0.0394055
\(645\) 3.00000 0.118125
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 20.0000 0.784465
\(651\) 2.00000 0.0783862
\(652\) 20.0000 0.783260
\(653\) −9.00000 −0.352197 −0.176099 0.984373i \(-0.556348\pi\)
−0.176099 + 0.984373i \(0.556348\pi\)
\(654\) −19.0000 −0.742959
\(655\) 54.0000 2.10995
\(656\) 9.00000 0.351391
\(657\) −4.00000 −0.156055
\(658\) −3.00000 −0.116952
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −10.0000 −0.388955 −0.194477 0.980907i \(-0.562301\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(662\) −16.0000 −0.621858
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) −24.0000 −0.930680
\(666\) −7.00000 −0.271244
\(667\) −3.00000 −0.116160
\(668\) −12.0000 −0.464294
\(669\) 14.0000 0.541271
\(670\) 12.0000 0.463600
\(671\) 0 0
\(672\) 1.00000 0.0385758
\(673\) 35.0000 1.34915 0.674575 0.738206i \(-0.264327\pi\)
0.674575 + 0.738206i \(0.264327\pi\)
\(674\) −4.00000 −0.154074
\(675\) 4.00000 0.153960
\(676\) 12.0000 0.461538
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 15.0000 0.576072
\(679\) −1.00000 −0.0383765
\(680\) 0 0
\(681\) −15.0000 −0.574801
\(682\) 0 0
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 8.00000 0.305888
\(685\) 27.0000 1.03162
\(686\) 1.00000 0.0381802
\(687\) −4.00000 −0.152610
\(688\) −1.00000 −0.0381246
\(689\) −60.0000 −2.28582
\(690\) 3.00000 0.114208
\(691\) −49.0000 −1.86405 −0.932024 0.362397i \(-0.881959\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 3.00000 0.113878
\(695\) −15.0000 −0.568982
\(696\) 3.00000 0.113715
\(697\) 0 0
\(698\) −10.0000 −0.378506
\(699\) −6.00000 −0.226941
\(700\) 4.00000 0.151186
\(701\) 36.0000 1.35970 0.679851 0.733351i \(-0.262045\pi\)
0.679851 + 0.733351i \(0.262045\pi\)
\(702\) 5.00000 0.188713
\(703\) −56.0000 −2.11208
\(704\) 0 0
\(705\) 9.00000 0.338960
\(706\) 27.0000 1.01616
\(707\) −6.00000 −0.225653
\(708\) −6.00000 −0.225494
\(709\) −22.0000 −0.826227 −0.413114 0.910679i \(-0.635559\pi\)
−0.413114 + 0.910679i \(0.635559\pi\)
\(710\) −18.0000 −0.675528
\(711\) −16.0000 −0.600047
\(712\) 6.00000 0.224860
\(713\) −2.00000 −0.0749006
\(714\) 0 0
\(715\) 0 0
\(716\) 15.0000 0.560576
\(717\) 12.0000 0.448148
\(718\) 21.0000 0.783713
\(719\) 45.0000 1.67822 0.839108 0.543964i \(-0.183077\pi\)
0.839108 + 0.543964i \(0.183077\pi\)
\(720\) −3.00000 −0.111803
\(721\) −1.00000 −0.0372419
\(722\) 45.0000 1.67473
\(723\) −19.0000 −0.706618
\(724\) 2.00000 0.0743294
\(725\) 12.0000 0.445669
\(726\) −11.0000 −0.408248
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 5.00000 0.185312
\(729\) 1.00000 0.0370370
\(730\) 12.0000 0.444140
\(731\) 0 0
\(732\) 14.0000 0.517455
\(733\) 8.00000 0.295487 0.147743 0.989026i \(-0.452799\pi\)
0.147743 + 0.989026i \(0.452799\pi\)
\(734\) 29.0000 1.07041
\(735\) −3.00000 −0.110657
\(736\) −1.00000 −0.0368605
\(737\) 0 0
\(738\) 9.00000 0.331295
\(739\) 50.0000 1.83928 0.919640 0.392763i \(-0.128481\pi\)
0.919640 + 0.392763i \(0.128481\pi\)
\(740\) 21.0000 0.771975
\(741\) 40.0000 1.46944
\(742\) −12.0000 −0.440534
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 2.00000 0.0733236
\(745\) 0 0
\(746\) −22.0000 −0.805477
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) 12.0000 0.438470
\(750\) 3.00000 0.109545
\(751\) −40.0000 −1.45962 −0.729810 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) −3.00000 −0.109399
\(753\) −15.0000 −0.546630
\(754\) 15.0000 0.546268
\(755\) −33.0000 −1.20099
\(756\) 1.00000 0.0363696
\(757\) −34.0000 −1.23575 −0.617876 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) 29.0000 1.05333
\(759\) 0 0
\(760\) −24.0000 −0.870572
\(761\) 30.0000 1.08750 0.543750 0.839248i \(-0.317004\pi\)
0.543750 + 0.839248i \(0.317004\pi\)
\(762\) −13.0000 −0.470940
\(763\) −19.0000 −0.687846
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) 36.0000 1.30073
\(767\) −30.0000 −1.08324
\(768\) 1.00000 0.0360844
\(769\) −37.0000 −1.33425 −0.667127 0.744944i \(-0.732476\pi\)
−0.667127 + 0.744944i \(0.732476\pi\)
\(770\) 0 0
\(771\) 6.00000 0.216085
\(772\) −1.00000 −0.0359908
\(773\) −51.0000 −1.83434 −0.917171 0.398493i \(-0.869533\pi\)
−0.917171 + 0.398493i \(0.869533\pi\)
\(774\) −1.00000 −0.0359443
\(775\) 8.00000 0.287368
\(776\) −1.00000 −0.0358979
\(777\) −7.00000 −0.251124
\(778\) −30.0000 −1.07555
\(779\) 72.0000 2.57967
\(780\) −15.0000 −0.537086
\(781\) 0 0
\(782\) 0 0
\(783\) 3.00000 0.107211
\(784\) 1.00000 0.0357143
\(785\) 12.0000 0.428298
\(786\) −18.0000 −0.642039
\(787\) −4.00000 −0.142585 −0.0712923 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) 9.00000 0.320612
\(789\) −9.00000 −0.320408
\(790\) 48.0000 1.70776
\(791\) 15.0000 0.533339
\(792\) 0 0
\(793\) 70.0000 2.48577
\(794\) −22.0000 −0.780751
\(795\) 36.0000 1.27679
\(796\) 17.0000 0.602549
\(797\) 33.0000 1.16892 0.584460 0.811423i \(-0.301306\pi\)
0.584460 + 0.811423i \(0.301306\pi\)
\(798\) 8.00000 0.283197
\(799\) 0 0
\(800\) 4.00000 0.141421
\(801\) 6.00000 0.212000
\(802\) 18.0000 0.635602
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) 3.00000 0.105736
\(806\) 10.0000 0.352235
\(807\) −18.0000 −0.633630
\(808\) −6.00000 −0.211079
\(809\) −12.0000 −0.421898 −0.210949 0.977497i \(-0.567655\pi\)
−0.210949 + 0.977497i \(0.567655\pi\)
\(810\) −3.00000 −0.105409
\(811\) 5.00000 0.175574 0.0877869 0.996139i \(-0.472021\pi\)
0.0877869 + 0.996139i \(0.472021\pi\)
\(812\) 3.00000 0.105279
\(813\) −28.0000 −0.982003
\(814\) 0 0
\(815\) −60.0000 −2.10171
\(816\) 0 0
\(817\) −8.00000 −0.279885
\(818\) 32.0000 1.11885
\(819\) 5.00000 0.174714
\(820\) −27.0000 −0.942881
\(821\) −30.0000 −1.04701 −0.523504 0.852023i \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) −9.00000 −0.313911
\(823\) −13.0000 −0.453152 −0.226576 0.973994i \(-0.572753\pi\)
−0.226576 + 0.973994i \(0.572753\pi\)
\(824\) −1.00000 −0.0348367
\(825\) 0 0
\(826\) −6.00000 −0.208767
\(827\) 6.00000 0.208640 0.104320 0.994544i \(-0.466733\pi\)
0.104320 + 0.994544i \(0.466733\pi\)
\(828\) −1.00000 −0.0347524
\(829\) −10.0000 −0.347314 −0.173657 0.984806i \(-0.555558\pi\)
−0.173657 + 0.984806i \(0.555558\pi\)
\(830\) 36.0000 1.24958
\(831\) −4.00000 −0.138758
\(832\) 5.00000 0.173344
\(833\) 0 0
\(834\) 5.00000 0.173136
\(835\) 36.0000 1.24583
\(836\) 0 0
\(837\) 2.00000 0.0691301
\(838\) 36.0000 1.24360
\(839\) 6.00000 0.207143 0.103572 0.994622i \(-0.466973\pi\)
0.103572 + 0.994622i \(0.466973\pi\)
\(840\) −3.00000 −0.103510
\(841\) −20.0000 −0.689655
\(842\) −19.0000 −0.654783
\(843\) −15.0000 −0.516627
\(844\) 8.00000 0.275371
\(845\) −36.0000 −1.23844
\(846\) −3.00000 −0.103142
\(847\) −11.0000 −0.377964
\(848\) −12.0000 −0.412082
\(849\) 14.0000 0.480479
\(850\) 0 0
\(851\) 7.00000 0.239957
\(852\) 6.00000 0.205557
\(853\) −49.0000 −1.67773 −0.838864 0.544341i \(-0.816780\pi\)
−0.838864 + 0.544341i \(0.816780\pi\)
\(854\) 14.0000 0.479070
\(855\) −24.0000 −0.820783
\(856\) 12.0000 0.410152
\(857\) −15.0000 −0.512390 −0.256195 0.966625i \(-0.582469\pi\)
−0.256195 + 0.966625i \(0.582469\pi\)
\(858\) 0 0
\(859\) −31.0000 −1.05771 −0.528853 0.848713i \(-0.677378\pi\)
−0.528853 + 0.848713i \(0.677378\pi\)
\(860\) 3.00000 0.102299
\(861\) 9.00000 0.306719
\(862\) 15.0000 0.510902
\(863\) 12.0000 0.408485 0.204242 0.978920i \(-0.434527\pi\)
0.204242 + 0.978920i \(0.434527\pi\)
\(864\) 1.00000 0.0340207
\(865\) −18.0000 −0.612018
\(866\) 17.0000 0.577684
\(867\) −17.0000 −0.577350
\(868\) 2.00000 0.0678844
\(869\) 0 0
\(870\) −9.00000 −0.305129
\(871\) −20.0000 −0.677674
\(872\) −19.0000 −0.643421
\(873\) −1.00000 −0.0338449
\(874\) −8.00000 −0.270604
\(875\) 3.00000 0.101419
\(876\) −4.00000 −0.135147
\(877\) −40.0000 −1.35070 −0.675352 0.737496i \(-0.736008\pi\)
−0.675352 + 0.737496i \(0.736008\pi\)
\(878\) 26.0000 0.877457
\(879\) −30.0000 −1.01187
\(880\) 0 0
\(881\) 30.0000 1.01073 0.505363 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) 1.00000 0.0336718
\(883\) 26.0000 0.874970 0.437485 0.899226i \(-0.355869\pi\)
0.437485 + 0.899226i \(0.355869\pi\)
\(884\) 0 0
\(885\) 18.0000 0.605063
\(886\) −27.0000 −0.907083
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) −7.00000 −0.234905
\(889\) −13.0000 −0.436006
\(890\) −18.0000 −0.603361
\(891\) 0 0
\(892\) 14.0000 0.468755
\(893\) −24.0000 −0.803129
\(894\) 0 0
\(895\) −45.0000 −1.50418
\(896\) 1.00000 0.0334077
\(897\) −5.00000 −0.166945
\(898\) 18.0000 0.600668
\(899\) 6.00000 0.200111
\(900\) 4.00000 0.133333
\(901\) 0 0
\(902\) 0 0
\(903\) −1.00000 −0.0332779
\(904\) 15.0000 0.498893
\(905\) −6.00000 −0.199447
\(906\) 11.0000 0.365451
\(907\) 41.0000 1.36138 0.680691 0.732570i \(-0.261680\pi\)
0.680691 + 0.732570i \(0.261680\pi\)
\(908\) −15.0000 −0.497792
\(909\) −6.00000 −0.199007
\(910\) −15.0000 −0.497245
\(911\) 21.0000 0.695761 0.347881 0.937539i \(-0.386901\pi\)
0.347881 + 0.937539i \(0.386901\pi\)
\(912\) 8.00000 0.264906
\(913\) 0 0
\(914\) −28.0000 −0.926158
\(915\) −42.0000 −1.38848
\(916\) −4.00000 −0.132164
\(917\) −18.0000 −0.594412
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 3.00000 0.0989071
\(921\) 11.0000 0.362462
\(922\) −30.0000 −0.987997
\(923\) 30.0000 0.987462
\(924\) 0 0
\(925\) −28.0000 −0.920634
\(926\) −31.0000 −1.01872
\(927\) −1.00000 −0.0328443
\(928\) 3.00000 0.0984798
\(929\) 33.0000 1.08269 0.541347 0.840799i \(-0.317914\pi\)
0.541347 + 0.840799i \(0.317914\pi\)
\(930\) −6.00000 −0.196748
\(931\) 8.00000 0.262189
\(932\) −6.00000 −0.196537
\(933\) 12.0000 0.392862
\(934\) −33.0000 −1.07979
\(935\) 0 0
\(936\) 5.00000 0.163430
\(937\) −25.0000 −0.816714 −0.408357 0.912822i \(-0.633898\pi\)
−0.408357 + 0.912822i \(0.633898\pi\)
\(938\) −4.00000 −0.130605
\(939\) −10.0000 −0.326338
\(940\) 9.00000 0.293548
\(941\) −51.0000 −1.66255 −0.831276 0.555860i \(-0.812389\pi\)
−0.831276 + 0.555860i \(0.812389\pi\)
\(942\) −4.00000 −0.130327
\(943\) −9.00000 −0.293080
\(944\) −6.00000 −0.195283
\(945\) −3.00000 −0.0975900
\(946\) 0 0
\(947\) −3.00000 −0.0974869 −0.0487435 0.998811i \(-0.515522\pi\)
−0.0487435 + 0.998811i \(0.515522\pi\)
\(948\) −16.0000 −0.519656
\(949\) −20.0000 −0.649227
\(950\) 32.0000 1.03822
\(951\) −27.0000 −0.875535
\(952\) 0 0
\(953\) −18.0000 −0.583077 −0.291539 0.956559i \(-0.594167\pi\)
−0.291539 + 0.956559i \(0.594167\pi\)
\(954\) −12.0000 −0.388514
\(955\) 36.0000 1.16493
\(956\) 12.0000 0.388108
\(957\) 0 0
\(958\) −6.00000 −0.193851
\(959\) −9.00000 −0.290625
\(960\) −3.00000 −0.0968246
\(961\) −27.0000 −0.870968
\(962\) −35.0000 −1.12845
\(963\) 12.0000 0.386695
\(964\) −19.0000 −0.611949
\(965\) 3.00000 0.0965734
\(966\) −1.00000 −0.0321745
\(967\) 44.0000 1.41494 0.707472 0.706741i \(-0.249835\pi\)
0.707472 + 0.706741i \(0.249835\pi\)
\(968\) −11.0000 −0.353553
\(969\) 0 0
\(970\) 3.00000 0.0963242
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 1.00000 0.0320750
\(973\) 5.00000 0.160293
\(974\) −31.0000 −0.993304
\(975\) 20.0000 0.640513
\(976\) 14.0000 0.448129
\(977\) −21.0000 −0.671850 −0.335925 0.941889i \(-0.609049\pi\)
−0.335925 + 0.941889i \(0.609049\pi\)
\(978\) 20.0000 0.639529
\(979\) 0 0
\(980\) −3.00000 −0.0958315
\(981\) −19.0000 −0.606623
\(982\) 12.0000 0.382935
\(983\) 30.0000 0.956851 0.478426 0.878128i \(-0.341208\pi\)
0.478426 + 0.878128i \(0.341208\pi\)
\(984\) 9.00000 0.286910
\(985\) −27.0000 −0.860292
\(986\) 0 0
\(987\) −3.00000 −0.0954911
\(988\) 40.0000 1.27257
\(989\) 1.00000 0.0317982
\(990\) 0 0
\(991\) −28.0000 −0.889449 −0.444725 0.895667i \(-0.646698\pi\)
−0.444725 + 0.895667i \(0.646698\pi\)
\(992\) 2.00000 0.0635001
\(993\) −16.0000 −0.507745
\(994\) 6.00000 0.190308
\(995\) −51.0000 −1.61681
\(996\) −12.0000 −0.380235
\(997\) 26.0000 0.823428 0.411714 0.911313i \(-0.364930\pi\)
0.411714 + 0.911313i \(0.364930\pi\)
\(998\) 14.0000 0.443162
\(999\) −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 966.2.a.i.1.1 1
3.2 odd 2 2898.2.a.j.1.1 1
4.3 odd 2 7728.2.a.a.1.1 1
7.6 odd 2 6762.2.a.bd.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.a.i.1.1 1 1.1 even 1 trivial
2898.2.a.j.1.1 1 3.2 odd 2
6762.2.a.bd.1.1 1 7.6 odd 2
7728.2.a.a.1.1 1 4.3 odd 2