Properties

Label 1008.4.a.b.1.1
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.4739252858\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1008.1

$q$-expansion

\(f(q)\) \(=\) \(q-18.0000 q^{5} -7.00000 q^{7} +O(q^{10})\) \(q-18.0000 q^{5} -7.00000 q^{7} -72.0000 q^{11} -34.0000 q^{13} -6.00000 q^{17} -92.0000 q^{19} -180.000 q^{23} +199.000 q^{25} +114.000 q^{29} -56.0000 q^{31} +126.000 q^{35} -34.0000 q^{37} -6.00000 q^{41} -164.000 q^{43} +168.000 q^{47} +49.0000 q^{49} -654.000 q^{53} +1296.00 q^{55} -492.000 q^{59} -250.000 q^{61} +612.000 q^{65} +124.000 q^{67} +36.0000 q^{71} +1010.00 q^{73} +504.000 q^{77} -56.0000 q^{79} +228.000 q^{83} +108.000 q^{85} -390.000 q^{89} +238.000 q^{91} +1656.00 q^{95} -70.0000 q^{97} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −18.0000 −1.60997 −0.804984 0.593296i \(-0.797826\pi\)
−0.804984 + 0.593296i \(0.797826\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −72.0000 −1.97353 −0.986764 0.162160i \(-0.948154\pi\)
−0.986764 + 0.162160i \(0.948154\pi\)
\(12\) 0 0
\(13\) −34.0000 −0.725377 −0.362689 0.931910i \(-0.618141\pi\)
−0.362689 + 0.931910i \(0.618141\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.00000 −0.0856008 −0.0428004 0.999084i \(-0.513628\pi\)
−0.0428004 + 0.999084i \(0.513628\pi\)
\(18\) 0 0
\(19\) −92.0000 −1.11086 −0.555428 0.831565i \(-0.687445\pi\)
−0.555428 + 0.831565i \(0.687445\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −180.000 −1.63185 −0.815926 0.578156i \(-0.803772\pi\)
−0.815926 + 0.578156i \(0.803772\pi\)
\(24\) 0 0
\(25\) 199.000 1.59200
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 114.000 0.729975 0.364987 0.931012i \(-0.381073\pi\)
0.364987 + 0.931012i \(0.381073\pi\)
\(30\) 0 0
\(31\) −56.0000 −0.324448 −0.162224 0.986754i \(-0.551867\pi\)
−0.162224 + 0.986754i \(0.551867\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 126.000 0.608511
\(36\) 0 0
\(37\) −34.0000 −0.151069 −0.0755347 0.997143i \(-0.524066\pi\)
−0.0755347 + 0.997143i \(0.524066\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −6.00000 −0.0228547 −0.0114273 0.999935i \(-0.503638\pi\)
−0.0114273 + 0.999935i \(0.503638\pi\)
\(42\) 0 0
\(43\) −164.000 −0.581622 −0.290811 0.956780i \(-0.593925\pi\)
−0.290811 + 0.956780i \(0.593925\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 168.000 0.521390 0.260695 0.965421i \(-0.416048\pi\)
0.260695 + 0.965421i \(0.416048\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −654.000 −1.69498 −0.847489 0.530813i \(-0.821887\pi\)
−0.847489 + 0.530813i \(0.821887\pi\)
\(54\) 0 0
\(55\) 1296.00 3.17732
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −492.000 −1.08564 −0.542822 0.839848i \(-0.682644\pi\)
−0.542822 + 0.839848i \(0.682644\pi\)
\(60\) 0 0
\(61\) −250.000 −0.524741 −0.262371 0.964967i \(-0.584504\pi\)
−0.262371 + 0.964967i \(0.584504\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 612.000 1.16783
\(66\) 0 0
\(67\) 124.000 0.226105 0.113052 0.993589i \(-0.463937\pi\)
0.113052 + 0.993589i \(0.463937\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 36.0000 0.0601748 0.0300874 0.999547i \(-0.490421\pi\)
0.0300874 + 0.999547i \(0.490421\pi\)
\(72\) 0 0
\(73\) 1010.00 1.61934 0.809668 0.586888i \(-0.199647\pi\)
0.809668 + 0.586888i \(0.199647\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 504.000 0.745924
\(78\) 0 0
\(79\) −56.0000 −0.0797531 −0.0398765 0.999205i \(-0.512696\pi\)
−0.0398765 + 0.999205i \(0.512696\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 228.000 0.301521 0.150761 0.988570i \(-0.451828\pi\)
0.150761 + 0.988570i \(0.451828\pi\)
\(84\) 0 0
\(85\) 108.000 0.137815
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −390.000 −0.464493 −0.232247 0.972657i \(-0.574608\pi\)
−0.232247 + 0.972657i \(0.574608\pi\)
\(90\) 0 0
\(91\) 238.000 0.274167
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1656.00 1.78844
\(96\) 0 0
\(97\) −70.0000 −0.0732724 −0.0366362 0.999329i \(-0.511664\pi\)
−0.0366362 + 0.999329i \(0.511664\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1350.00 1.33000 0.665000 0.746843i \(-0.268431\pi\)
0.665000 + 0.746843i \(0.268431\pi\)
\(102\) 0 0
\(103\) −2000.00 −1.91326 −0.956630 0.291305i \(-0.905911\pi\)
−0.956630 + 0.291305i \(0.905911\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 696.000 0.628830 0.314415 0.949286i \(-0.398192\pi\)
0.314415 + 0.949286i \(0.398192\pi\)
\(108\) 0 0
\(109\) −1114.00 −0.978916 −0.489458 0.872027i \(-0.662805\pi\)
−0.489458 + 0.872027i \(0.662805\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 462.000 0.384613 0.192307 0.981335i \(-0.438403\pi\)
0.192307 + 0.981335i \(0.438403\pi\)
\(114\) 0 0
\(115\) 3240.00 2.62723
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 42.0000 0.0323541
\(120\) 0 0
\(121\) 3853.00 2.89482
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1332.00 −0.953102
\(126\) 0 0
\(127\) −1064.00 −0.743423 −0.371712 0.928348i \(-0.621229\pi\)
−0.371712 + 0.928348i \(0.621229\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 180.000 0.120051 0.0600255 0.998197i \(-0.480882\pi\)
0.0600255 + 0.998197i \(0.480882\pi\)
\(132\) 0 0
\(133\) 644.000 0.419864
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2718.00 1.69500 0.847498 0.530799i \(-0.178108\pi\)
0.847498 + 0.530799i \(0.178108\pi\)
\(138\) 0 0
\(139\) 1348.00 0.822560 0.411280 0.911509i \(-0.365082\pi\)
0.411280 + 0.911509i \(0.365082\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2448.00 1.43155
\(144\) 0 0
\(145\) −2052.00 −1.17524
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −558.000 −0.306800 −0.153400 0.988164i \(-0.549022\pi\)
−0.153400 + 0.988164i \(0.549022\pi\)
\(150\) 0 0
\(151\) −1928.00 −1.03906 −0.519531 0.854451i \(-0.673893\pi\)
−0.519531 + 0.854451i \(0.673893\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1008.00 0.522352
\(156\) 0 0
\(157\) −2410.00 −1.22509 −0.612544 0.790436i \(-0.709854\pi\)
−0.612544 + 0.790436i \(0.709854\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1260.00 0.616782
\(162\) 0 0
\(163\) −740.000 −0.355591 −0.177795 0.984067i \(-0.556896\pi\)
−0.177795 + 0.984067i \(0.556896\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3984.00 1.84605 0.923027 0.384734i \(-0.125707\pi\)
0.923027 + 0.384734i \(0.125707\pi\)
\(168\) 0 0
\(169\) −1041.00 −0.473828
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1038.00 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) −1393.00 −0.601719
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2568.00 −1.07230 −0.536149 0.844123i \(-0.680121\pi\)
−0.536149 + 0.844123i \(0.680121\pi\)
\(180\) 0 0
\(181\) −2698.00 −1.10796 −0.553980 0.832530i \(-0.686892\pi\)
−0.553980 + 0.832530i \(0.686892\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 612.000 0.243217
\(186\) 0 0
\(187\) 432.000 0.168936
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4116.00 −1.55928 −0.779642 0.626225i \(-0.784599\pi\)
−0.779642 + 0.626225i \(0.784599\pi\)
\(192\) 0 0
\(193\) −3310.00 −1.23450 −0.617251 0.786766i \(-0.711754\pi\)
−0.617251 + 0.786766i \(0.711754\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1278.00 −0.462202 −0.231101 0.972930i \(-0.574233\pi\)
−0.231101 + 0.972930i \(0.574233\pi\)
\(198\) 0 0
\(199\) −2936.00 −1.04587 −0.522933 0.852374i \(-0.675162\pi\)
−0.522933 + 0.852374i \(0.675162\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −798.000 −0.275905
\(204\) 0 0
\(205\) 108.000 0.0367954
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 6624.00 2.19230
\(210\) 0 0
\(211\) 3508.00 1.14455 0.572276 0.820061i \(-0.306060\pi\)
0.572276 + 0.820061i \(0.306060\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2952.00 0.936394
\(216\) 0 0
\(217\) 392.000 0.122630
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 204.000 0.0620929
\(222\) 0 0
\(223\) 1888.00 0.566950 0.283475 0.958980i \(-0.408513\pi\)
0.283475 + 0.958980i \(0.408513\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3564.00 1.04207 0.521037 0.853534i \(-0.325545\pi\)
0.521037 + 0.853534i \(0.325545\pi\)
\(228\) 0 0
\(229\) 1334.00 0.384948 0.192474 0.981302i \(-0.438349\pi\)
0.192474 + 0.981302i \(0.438349\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2658.00 −0.747345 −0.373672 0.927561i \(-0.621902\pi\)
−0.373672 + 0.927561i \(0.621902\pi\)
\(234\) 0 0
\(235\) −3024.00 −0.839421
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −588.000 −0.159140 −0.0795702 0.996829i \(-0.525355\pi\)
−0.0795702 + 0.996829i \(0.525355\pi\)
\(240\) 0 0
\(241\) 5690.00 1.52085 0.760426 0.649425i \(-0.224990\pi\)
0.760426 + 0.649425i \(0.224990\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −882.000 −0.229996
\(246\) 0 0
\(247\) 3128.00 0.805789
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 180.000 0.0452649 0.0226325 0.999744i \(-0.492795\pi\)
0.0226325 + 0.999744i \(0.492795\pi\)
\(252\) 0 0
\(253\) 12960.0 3.22051
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5310.00 −1.28883 −0.644414 0.764677i \(-0.722899\pi\)
−0.644414 + 0.764677i \(0.722899\pi\)
\(258\) 0 0
\(259\) 238.000 0.0570988
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 828.000 0.194132 0.0970659 0.995278i \(-0.469054\pi\)
0.0970659 + 0.995278i \(0.469054\pi\)
\(264\) 0 0
\(265\) 11772.0 2.72886
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4134.00 0.937005 0.468503 0.883462i \(-0.344794\pi\)
0.468503 + 0.883462i \(0.344794\pi\)
\(270\) 0 0
\(271\) 2968.00 0.665288 0.332644 0.943052i \(-0.392059\pi\)
0.332644 + 0.943052i \(0.392059\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −14328.0 −3.14186
\(276\) 0 0
\(277\) −4786.00 −1.03813 −0.519067 0.854734i \(-0.673720\pi\)
−0.519067 + 0.854734i \(0.673720\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4398.00 0.933675 0.466838 0.884343i \(-0.345393\pi\)
0.466838 + 0.884343i \(0.345393\pi\)
\(282\) 0 0
\(283\) −4772.00 −1.00235 −0.501177 0.865345i \(-0.667099\pi\)
−0.501177 + 0.865345i \(0.667099\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 42.0000 0.00863826
\(288\) 0 0
\(289\) −4877.00 −0.992673
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6522.00 −1.30041 −0.650204 0.759760i \(-0.725316\pi\)
−0.650204 + 0.759760i \(0.725316\pi\)
\(294\) 0 0
\(295\) 8856.00 1.74785
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6120.00 1.18371
\(300\) 0 0
\(301\) 1148.00 0.219833
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4500.00 0.844817
\(306\) 0 0
\(307\) 6244.00 1.16079 0.580397 0.814333i \(-0.302897\pi\)
0.580397 + 0.814333i \(0.302897\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −528.000 −0.0962705 −0.0481353 0.998841i \(-0.515328\pi\)
−0.0481353 + 0.998841i \(0.515328\pi\)
\(312\) 0 0
\(313\) −5830.00 −1.05281 −0.526407 0.850232i \(-0.676461\pi\)
−0.526407 + 0.850232i \(0.676461\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5046.00 −0.894043 −0.447021 0.894523i \(-0.647515\pi\)
−0.447021 + 0.894523i \(0.647515\pi\)
\(318\) 0 0
\(319\) −8208.00 −1.44063
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 552.000 0.0950901
\(324\) 0 0
\(325\) −6766.00 −1.15480
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1176.00 −0.197067
\(330\) 0 0
\(331\) 5020.00 0.833608 0.416804 0.908996i \(-0.363150\pi\)
0.416804 + 0.908996i \(0.363150\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2232.00 −0.364021
\(336\) 0 0
\(337\) −7486.00 −1.21005 −0.605027 0.796205i \(-0.706838\pi\)
−0.605027 + 0.796205i \(0.706838\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 4032.00 0.640308
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10032.0 −1.55201 −0.776003 0.630729i \(-0.782756\pi\)
−0.776003 + 0.630729i \(0.782756\pi\)
\(348\) 0 0
\(349\) 5942.00 0.911370 0.455685 0.890141i \(-0.349394\pi\)
0.455685 + 0.890141i \(0.349394\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 90.0000 0.0135700 0.00678501 0.999977i \(-0.497840\pi\)
0.00678501 + 0.999977i \(0.497840\pi\)
\(354\) 0 0
\(355\) −648.000 −0.0968796
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10596.0 1.55776 0.778880 0.627174i \(-0.215788\pi\)
0.778880 + 0.627174i \(0.215788\pi\)
\(360\) 0 0
\(361\) 1605.00 0.233999
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −18180.0 −2.60708
\(366\) 0 0
\(367\) −4016.00 −0.571208 −0.285604 0.958348i \(-0.592194\pi\)
−0.285604 + 0.958348i \(0.592194\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4578.00 0.640641
\(372\) 0 0
\(373\) 3278.00 0.455036 0.227518 0.973774i \(-0.426939\pi\)
0.227518 + 0.973774i \(0.426939\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3876.00 −0.529507
\(378\) 0 0
\(379\) −4628.00 −0.627241 −0.313621 0.949548i \(-0.601542\pi\)
−0.313621 + 0.949548i \(0.601542\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2880.00 −0.384233 −0.192116 0.981372i \(-0.561535\pi\)
−0.192116 + 0.981372i \(0.561535\pi\)
\(384\) 0 0
\(385\) −9072.00 −1.20091
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7974.00 −1.03933 −0.519663 0.854371i \(-0.673943\pi\)
−0.519663 + 0.854371i \(0.673943\pi\)
\(390\) 0 0
\(391\) 1080.00 0.139688
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1008.00 0.128400
\(396\) 0 0
\(397\) −12346.0 −1.56078 −0.780388 0.625296i \(-0.784978\pi\)
−0.780388 + 0.625296i \(0.784978\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9738.00 −1.21270 −0.606350 0.795198i \(-0.707367\pi\)
−0.606350 + 0.795198i \(0.707367\pi\)
\(402\) 0 0
\(403\) 1904.00 0.235347
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2448.00 0.298140
\(408\) 0 0
\(409\) −430.000 −0.0519857 −0.0259928 0.999662i \(-0.508275\pi\)
−0.0259928 + 0.999662i \(0.508275\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3444.00 0.410335
\(414\) 0 0
\(415\) −4104.00 −0.485440
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1812.00 −0.211270 −0.105635 0.994405i \(-0.533687\pi\)
−0.105635 + 0.994405i \(0.533687\pi\)
\(420\) 0 0
\(421\) −10690.0 −1.23753 −0.618763 0.785577i \(-0.712366\pi\)
−0.618763 + 0.785577i \(0.712366\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1194.00 −0.136276
\(426\) 0 0
\(427\) 1750.00 0.198334
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4116.00 −0.460002 −0.230001 0.973190i \(-0.573873\pi\)
−0.230001 + 0.973190i \(0.573873\pi\)
\(432\) 0 0
\(433\) 9938.00 1.10298 0.551489 0.834182i \(-0.314060\pi\)
0.551489 + 0.834182i \(0.314060\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 16560.0 1.81275
\(438\) 0 0
\(439\) −1784.00 −0.193954 −0.0969769 0.995287i \(-0.530917\pi\)
−0.0969769 + 0.995287i \(0.530917\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −11712.0 −1.25610 −0.628052 0.778172i \(-0.716147\pi\)
−0.628052 + 0.778172i \(0.716147\pi\)
\(444\) 0 0
\(445\) 7020.00 0.747820
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −7650.00 −0.804066 −0.402033 0.915625i \(-0.631696\pi\)
−0.402033 + 0.915625i \(0.631696\pi\)
\(450\) 0 0
\(451\) 432.000 0.0451044
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4284.00 −0.441400
\(456\) 0 0
\(457\) 3674.00 0.376067 0.188033 0.982163i \(-0.439789\pi\)
0.188033 + 0.982163i \(0.439789\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3102.00 0.313394 0.156697 0.987647i \(-0.449915\pi\)
0.156697 + 0.987647i \(0.449915\pi\)
\(462\) 0 0
\(463\) −8984.00 −0.901775 −0.450888 0.892581i \(-0.648892\pi\)
−0.450888 + 0.892581i \(0.648892\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3612.00 0.357909 0.178954 0.983857i \(-0.442729\pi\)
0.178954 + 0.983857i \(0.442729\pi\)
\(468\) 0 0
\(469\) −868.000 −0.0854595
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 11808.0 1.14785
\(474\) 0 0
\(475\) −18308.0 −1.76848
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9288.00 −0.885970 −0.442985 0.896529i \(-0.646080\pi\)
−0.442985 + 0.896529i \(0.646080\pi\)
\(480\) 0 0
\(481\) 1156.00 0.109582
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1260.00 0.117966
\(486\) 0 0
\(487\) 5848.00 0.544144 0.272072 0.962277i \(-0.412291\pi\)
0.272072 + 0.962277i \(0.412291\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5952.00 −0.547067 −0.273534 0.961862i \(-0.588192\pi\)
−0.273534 + 0.961862i \(0.588192\pi\)
\(492\) 0 0
\(493\) −684.000 −0.0624864
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −252.000 −0.0227440
\(498\) 0 0
\(499\) −10748.0 −0.964222 −0.482111 0.876110i \(-0.660130\pi\)
−0.482111 + 0.876110i \(0.660130\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −16488.0 −1.46156 −0.730779 0.682614i \(-0.760843\pi\)
−0.730779 + 0.682614i \(0.760843\pi\)
\(504\) 0 0
\(505\) −24300.0 −2.14126
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −14058.0 −1.22418 −0.612092 0.790786i \(-0.709672\pi\)
−0.612092 + 0.790786i \(0.709672\pi\)
\(510\) 0 0
\(511\) −7070.00 −0.612052
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 36000.0 3.08029
\(516\) 0 0
\(517\) −12096.0 −1.02898
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 14466.0 1.21644 0.608222 0.793767i \(-0.291883\pi\)
0.608222 + 0.793767i \(0.291883\pi\)
\(522\) 0 0
\(523\) −18524.0 −1.54875 −0.774377 0.632725i \(-0.781936\pi\)
−0.774377 + 0.632725i \(0.781936\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 336.000 0.0277730
\(528\) 0 0
\(529\) 20233.0 1.66294
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 204.000 0.0165783
\(534\) 0 0
\(535\) −12528.0 −1.01240
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3528.00 −0.281933
\(540\) 0 0
\(541\) 4358.00 0.346331 0.173165 0.984893i \(-0.444600\pi\)
0.173165 + 0.984893i \(0.444600\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 20052.0 1.57602
\(546\) 0 0
\(547\) 2140.00 0.167276 0.0836378 0.996496i \(-0.473346\pi\)
0.0836378 + 0.996496i \(0.473346\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −10488.0 −0.810896
\(552\) 0 0
\(553\) 392.000 0.0301438
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2022.00 −0.153815 −0.0769074 0.997038i \(-0.524505\pi\)
−0.0769074 + 0.997038i \(0.524505\pi\)
\(558\) 0 0
\(559\) 5576.00 0.421896
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7356.00 0.550654 0.275327 0.961351i \(-0.411214\pi\)
0.275327 + 0.961351i \(0.411214\pi\)
\(564\) 0 0
\(565\) −8316.00 −0.619215
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11202.0 −0.825329 −0.412665 0.910883i \(-0.635402\pi\)
−0.412665 + 0.910883i \(0.635402\pi\)
\(570\) 0 0
\(571\) 10564.0 0.774238 0.387119 0.922030i \(-0.373470\pi\)
0.387119 + 0.922030i \(0.373470\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −35820.0 −2.59791
\(576\) 0 0
\(577\) −18574.0 −1.34011 −0.670057 0.742310i \(-0.733730\pi\)
−0.670057 + 0.742310i \(0.733730\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1596.00 −0.113964
\(582\) 0 0
\(583\) 47088.0 3.34509
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 13188.0 0.927303 0.463652 0.886018i \(-0.346539\pi\)
0.463652 + 0.886018i \(0.346539\pi\)
\(588\) 0 0
\(589\) 5152.00 0.360415
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 22506.0 1.55853 0.779267 0.626692i \(-0.215592\pi\)
0.779267 + 0.626692i \(0.215592\pi\)
\(594\) 0 0
\(595\) −756.000 −0.0520890
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 10596.0 0.722773 0.361386 0.932416i \(-0.382304\pi\)
0.361386 + 0.932416i \(0.382304\pi\)
\(600\) 0 0
\(601\) 14618.0 0.992148 0.496074 0.868280i \(-0.334775\pi\)
0.496074 + 0.868280i \(0.334775\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −69354.0 −4.66056
\(606\) 0 0
\(607\) −5168.00 −0.345573 −0.172786 0.984959i \(-0.555277\pi\)
−0.172786 + 0.984959i \(0.555277\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5712.00 −0.378204
\(612\) 0 0
\(613\) 5726.00 0.377277 0.188639 0.982047i \(-0.439593\pi\)
0.188639 + 0.982047i \(0.439593\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7806.00 0.509332 0.254666 0.967029i \(-0.418035\pi\)
0.254666 + 0.967029i \(0.418035\pi\)
\(618\) 0 0
\(619\) 18052.0 1.17217 0.586083 0.810251i \(-0.300669\pi\)
0.586083 + 0.810251i \(0.300669\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2730.00 0.175562
\(624\) 0 0
\(625\) −899.000 −0.0575360
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 204.000 0.0129317
\(630\) 0 0
\(631\) 6208.00 0.391659 0.195829 0.980638i \(-0.437260\pi\)
0.195829 + 0.980638i \(0.437260\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 19152.0 1.19689
\(636\) 0 0
\(637\) −1666.00 −0.103625
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 21510.0 1.32542 0.662710 0.748876i \(-0.269406\pi\)
0.662710 + 0.748876i \(0.269406\pi\)
\(642\) 0 0
\(643\) 11140.0 0.683233 0.341616 0.939839i \(-0.389026\pi\)
0.341616 + 0.939839i \(0.389026\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9312.00 0.565831 0.282915 0.959145i \(-0.408698\pi\)
0.282915 + 0.959145i \(0.408698\pi\)
\(648\) 0 0
\(649\) 35424.0 2.14255
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4878.00 −0.292329 −0.146165 0.989260i \(-0.546693\pi\)
−0.146165 + 0.989260i \(0.546693\pi\)
\(654\) 0 0
\(655\) −3240.00 −0.193278
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −9744.00 −0.575982 −0.287991 0.957633i \(-0.592987\pi\)
−0.287991 + 0.957633i \(0.592987\pi\)
\(660\) 0 0
\(661\) 2990.00 0.175942 0.0879709 0.996123i \(-0.471962\pi\)
0.0879709 + 0.996123i \(0.471962\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −11592.0 −0.675968
\(666\) 0 0
\(667\) −20520.0 −1.19121
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 18000.0 1.03559
\(672\) 0 0
\(673\) 33266.0 1.90536 0.952682 0.303969i \(-0.0983118\pi\)
0.952682 + 0.303969i \(0.0983118\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −5370.00 −0.304854 −0.152427 0.988315i \(-0.548709\pi\)
−0.152427 + 0.988315i \(0.548709\pi\)
\(678\) 0 0
\(679\) 490.000 0.0276944
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 384.000 0.0215130 0.0107565 0.999942i \(-0.496576\pi\)
0.0107565 + 0.999942i \(0.496576\pi\)
\(684\) 0 0
\(685\) −48924.0 −2.72889
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 22236.0 1.22950
\(690\) 0 0
\(691\) 14524.0 0.799593 0.399797 0.916604i \(-0.369081\pi\)
0.399797 + 0.916604i \(0.369081\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −24264.0 −1.32430
\(696\) 0 0
\(697\) 36.0000 0.00195638
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −24750.0 −1.33352 −0.666758 0.745274i \(-0.732318\pi\)
−0.666758 + 0.745274i \(0.732318\pi\)
\(702\) 0 0
\(703\) 3128.00 0.167816
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9450.00 −0.502693
\(708\) 0 0
\(709\) −1042.00 −0.0551948 −0.0275974 0.999619i \(-0.508786\pi\)
−0.0275974 + 0.999619i \(0.508786\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 10080.0 0.529452
\(714\) 0 0
\(715\) −44064.0 −2.30476
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −36960.0 −1.91707 −0.958536 0.284970i \(-0.908016\pi\)
−0.958536 + 0.284970i \(0.908016\pi\)
\(720\) 0 0
\(721\) 14000.0 0.723145
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 22686.0 1.16212
\(726\) 0 0
\(727\) 16288.0 0.830933 0.415467 0.909608i \(-0.363618\pi\)
0.415467 + 0.909608i \(0.363618\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 984.000 0.0497874
\(732\) 0 0
\(733\) −7810.00 −0.393546 −0.196773 0.980449i \(-0.563046\pi\)
−0.196773 + 0.980449i \(0.563046\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −8928.00 −0.446224
\(738\) 0 0
\(739\) 36700.0 1.82684 0.913418 0.407024i \(-0.133433\pi\)
0.913418 + 0.407024i \(0.133433\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 29508.0 1.45699 0.728495 0.685051i \(-0.240220\pi\)
0.728495 + 0.685051i \(0.240220\pi\)
\(744\) 0 0
\(745\) 10044.0 0.493938
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −4872.00 −0.237676
\(750\) 0 0
\(751\) 15136.0 0.735447 0.367723 0.929935i \(-0.380137\pi\)
0.367723 + 0.929935i \(0.380137\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 34704.0 1.67286
\(756\) 0 0
\(757\) 3422.00 0.164299 0.0821497 0.996620i \(-0.473821\pi\)
0.0821497 + 0.996620i \(0.473821\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −31446.0 −1.49792 −0.748960 0.662616i \(-0.769446\pi\)
−0.748960 + 0.662616i \(0.769446\pi\)
\(762\) 0 0
\(763\) 7798.00 0.369995
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 16728.0 0.787501
\(768\) 0 0
\(769\) −18718.0 −0.877748 −0.438874 0.898549i \(-0.644623\pi\)
−0.438874 + 0.898549i \(0.644623\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1686.00 0.0784492 0.0392246 0.999230i \(-0.487511\pi\)
0.0392246 + 0.999230i \(0.487511\pi\)
\(774\) 0 0
\(775\) −11144.0 −0.516522
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 552.000 0.0253883
\(780\) 0 0
\(781\) −2592.00 −0.118757
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 43380.0 1.97235
\(786\) 0 0
\(787\) −5492.00 −0.248753 −0.124377 0.992235i \(-0.539693\pi\)
−0.124377 + 0.992235i \(0.539693\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3234.00 −0.145370
\(792\) 0 0
\(793\) 8500.00 0.380635
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 17310.0 0.769325 0.384662 0.923057i \(-0.374318\pi\)
0.384662 + 0.923057i \(0.374318\pi\)
\(798\) 0 0
\(799\) −1008.00 −0.0446314
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −72720.0 −3.19581
\(804\) 0 0
\(805\) −22680.0 −0.993000
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −35754.0 −1.55382 −0.776912 0.629609i \(-0.783215\pi\)
−0.776912 + 0.629609i \(0.783215\pi\)
\(810\) 0 0
\(811\) −33644.0 −1.45672 −0.728360 0.685194i \(-0.759717\pi\)
−0.728360 + 0.685194i \(0.759717\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 13320.0 0.572490
\(816\) 0 0
\(817\) 15088.0 0.646098
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −28734.0 −1.22147 −0.610733 0.791837i \(-0.709125\pi\)
−0.610733 + 0.791837i \(0.709125\pi\)
\(822\) 0 0
\(823\) 28672.0 1.21439 0.607195 0.794553i \(-0.292295\pi\)
0.607195 + 0.794553i \(0.292295\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −15912.0 −0.669062 −0.334531 0.942385i \(-0.608578\pi\)
−0.334531 + 0.942385i \(0.608578\pi\)
\(828\) 0 0
\(829\) 17534.0 0.734597 0.367299 0.930103i \(-0.380283\pi\)
0.367299 + 0.930103i \(0.380283\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −294.000 −0.0122287
\(834\) 0 0
\(835\) −71712.0 −2.97209
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 40656.0 1.67295 0.836473 0.548009i \(-0.184614\pi\)
0.836473 + 0.548009i \(0.184614\pi\)
\(840\) 0 0
\(841\) −11393.0 −0.467137
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 18738.0 0.762848
\(846\) 0 0
\(847\) −26971.0 −1.09414
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 6120.00 0.246523
\(852\) 0 0
\(853\) 23870.0 0.958140 0.479070 0.877777i \(-0.340974\pi\)
0.479070 + 0.877777i \(0.340974\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 29610.0 1.18023 0.590116 0.807319i \(-0.299082\pi\)
0.590116 + 0.807319i \(0.299082\pi\)
\(858\) 0 0
\(859\) 45484.0 1.80663 0.903314 0.428979i \(-0.141127\pi\)
0.903314 + 0.428979i \(0.141127\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 46164.0 1.82090 0.910452 0.413614i \(-0.135734\pi\)
0.910452 + 0.413614i \(0.135734\pi\)
\(864\) 0 0
\(865\) −18684.0 −0.734422
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 4032.00 0.157395
\(870\) 0 0
\(871\) −4216.00 −0.164011
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 9324.00 0.360239
\(876\) 0 0
\(877\) −2986.00 −0.114972 −0.0574858 0.998346i \(-0.518308\pi\)
−0.0574858 + 0.998346i \(0.518308\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −6534.00 −0.249871 −0.124935 0.992165i \(-0.539872\pi\)
−0.124935 + 0.992165i \(0.539872\pi\)
\(882\) 0 0
\(883\) −29756.0 −1.13405 −0.567027 0.823699i \(-0.691906\pi\)
−0.567027 + 0.823699i \(0.691906\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 29952.0 1.13381 0.566905 0.823783i \(-0.308141\pi\)
0.566905 + 0.823783i \(0.308141\pi\)
\(888\) 0 0
\(889\) 7448.00 0.280988
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −15456.0 −0.579188
\(894\) 0 0
\(895\) 46224.0 1.72637
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −6384.00 −0.236839
\(900\) 0 0
\(901\) 3924.00 0.145091
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 48564.0 1.78378
\(906\) 0 0
\(907\) 36268.0 1.32774 0.663869 0.747848i \(-0.268913\pi\)
0.663869 + 0.747848i \(0.268913\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −23604.0 −0.858436 −0.429218 0.903201i \(-0.641211\pi\)
−0.429218 + 0.903201i \(0.641211\pi\)
\(912\) 0 0
\(913\) −16416.0 −0.595061
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1260.00 −0.0453750
\(918\) 0 0
\(919\) −34184.0 −1.22701 −0.613507 0.789689i \(-0.710242\pi\)
−0.613507 + 0.789689i \(0.710242\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1224.00 −0.0436495
\(924\) 0 0
\(925\) −6766.00 −0.240502
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 53922.0 1.90433 0.952165 0.305583i \(-0.0988513\pi\)
0.952165 + 0.305583i \(0.0988513\pi\)
\(930\) 0 0
\(931\) −4508.00 −0.158694
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −7776.00 −0.271981
\(936\) 0 0
\(937\) 40538.0 1.41336 0.706680 0.707533i \(-0.250192\pi\)
0.706680 + 0.707533i \(0.250192\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 3606.00 0.124923 0.0624613 0.998047i \(-0.480105\pi\)
0.0624613 + 0.998047i \(0.480105\pi\)
\(942\) 0 0
\(943\) 1080.00 0.0372955
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 14064.0 0.482596 0.241298 0.970451i \(-0.422427\pi\)
0.241298 + 0.970451i \(0.422427\pi\)
\(948\) 0 0
\(949\) −34340.0 −1.17463
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −33066.0 −1.12394 −0.561969 0.827158i \(-0.689956\pi\)
−0.561969 + 0.827158i \(0.689956\pi\)
\(954\) 0 0
\(955\) 74088.0 2.51040
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −19026.0 −0.640648
\(960\) 0 0
\(961\) −26655.0 −0.894733
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 59580.0 1.98751
\(966\) 0 0
\(967\) 26368.0 0.876875 0.438437 0.898762i \(-0.355532\pi\)
0.438437 + 0.898762i \(0.355532\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 55884.0 1.84696 0.923482 0.383641i \(-0.125330\pi\)
0.923482 + 0.383641i \(0.125330\pi\)
\(972\) 0 0
\(973\) −9436.00 −0.310899
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 51126.0 1.67417 0.837086 0.547072i \(-0.184257\pi\)
0.837086 + 0.547072i \(0.184257\pi\)
\(978\) 0 0
\(979\) 28080.0 0.916691
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −14184.0 −0.460223 −0.230112 0.973164i \(-0.573909\pi\)
−0.230112 + 0.973164i \(0.573909\pi\)
\(984\) 0 0
\(985\) 23004.0 0.744130
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 29520.0 0.949122
\(990\) 0 0
\(991\) −51680.0 −1.65658 −0.828289 0.560301i \(-0.810686\pi\)
−0.828289 + 0.560301i \(0.810686\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 52848.0 1.68381
\(996\) 0 0
\(997\) 52094.0 1.65480 0.827399 0.561615i \(-0.189820\pi\)
0.827399 + 0.561615i \(0.189820\pi\)
\(998\) 0 0
\(999\) 0 0
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 1008.4.a.b.1.1 1
3.2 odd 2 336.4.a.l.1.1 1
4.3 odd 2 126.4.a.a.1.1 1
12.11 even 2 42.4.a.a.1.1 1
21.20 even 2 2352.4.a.a.1.1 1
24.5 odd 2 1344.4.a.a.1.1 1
24.11 even 2 1344.4.a.o.1.1 1
28.3 even 6 882.4.g.o.667.1 2
28.11 odd 6 882.4.g.w.667.1 2
28.19 even 6 882.4.g.o.361.1 2
28.23 odd 6 882.4.g.w.361.1 2
28.27 even 2 882.4.a.g.1.1 1
60.23 odd 4 1050.4.g.a.799.1 2
60.47 odd 4 1050.4.g.a.799.2 2
60.59 even 2 1050.4.a.g.1.1 1
84.11 even 6 294.4.e.c.79.1 2
84.23 even 6 294.4.e.c.67.1 2
84.47 odd 6 294.4.e.b.67.1 2
84.59 odd 6 294.4.e.b.79.1 2
84.83 odd 2 294.4.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.4.a.a.1.1 1 12.11 even 2
126.4.a.a.1.1 1 4.3 odd 2
294.4.a.i.1.1 1 84.83 odd 2
294.4.e.b.67.1 2 84.47 odd 6
294.4.e.b.79.1 2 84.59 odd 6
294.4.e.c.67.1 2 84.23 even 6
294.4.e.c.79.1 2 84.11 even 6
336.4.a.l.1.1 1 3.2 odd 2
882.4.a.g.1.1 1 28.27 even 2
882.4.g.o.361.1 2 28.19 even 6
882.4.g.o.667.1 2 28.3 even 6
882.4.g.w.361.1 2 28.23 odd 6
882.4.g.w.667.1 2 28.11 odd 6
1008.4.a.b.1.1 1 1.1 even 1 trivial
1050.4.a.g.1.1 1 60.59 even 2
1050.4.g.a.799.1 2 60.23 odd 4
1050.4.g.a.799.2 2 60.47 odd 4
1344.4.a.a.1.1 1 24.5 odd 2
1344.4.a.o.1.1 1 24.11 even 2
2352.4.a.a.1.1 1 21.20 even 2