Properties

Label 1764.4.a.c.1.1
Level $1764$
Weight $4$
Character 1764.1
Self dual yes
Analytic conductor $104.079$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1764.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(104.079369250\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 28)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1764.1

$q$-expansion

\(f(q)\) \(=\) \(q-8.00000 q^{5} +O(q^{10})\) \(q-8.00000 q^{5} +40.0000 q^{11} +12.0000 q^{13} -58.0000 q^{17} -26.0000 q^{19} +64.0000 q^{23} -61.0000 q^{25} +62.0000 q^{29} -252.000 q^{31} +26.0000 q^{37} +6.00000 q^{41} +416.000 q^{43} -396.000 q^{47} +450.000 q^{53} -320.000 q^{55} +274.000 q^{59} +576.000 q^{61} -96.0000 q^{65} -476.000 q^{67} +448.000 q^{71} +158.000 q^{73} -936.000 q^{79} +530.000 q^{83} +464.000 q^{85} -390.000 q^{89} +208.000 q^{95} -214.000 q^{97} +O(q^{100})\)

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
\(5\) −8.00000 −0.715542 −0.357771 0.933809i \(-0.616463\pi\)
−0.357771 + 0.933809i \(0.616463\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 40.0000 1.09640 0.548202 0.836346i \(-0.315312\pi\)
0.548202 + 0.836346i \(0.315312\pi\)
\(12\) 0 0
\(13\) 12.0000 0.256015 0.128008 0.991773i \(-0.459142\pi\)
0.128008 + 0.991773i \(0.459142\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −58.0000 −0.827474 −0.413737 0.910396i \(-0.635777\pi\)
−0.413737 + 0.910396i \(0.635777\pi\)
\(18\) 0 0
\(19\) −26.0000 −0.313937 −0.156969 0.987604i \(-0.550172\pi\)
−0.156969 + 0.987604i \(0.550172\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 64.0000 0.580214 0.290107 0.956994i \(-0.406309\pi\)
0.290107 + 0.956994i \(0.406309\pi\)
\(24\) 0 0
\(25\) −61.0000 −0.488000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 62.0000 0.397004 0.198502 0.980101i \(-0.436392\pi\)
0.198502 + 0.980101i \(0.436392\pi\)
\(30\) 0 0
\(31\) −252.000 −1.46002 −0.730009 0.683438i \(-0.760484\pi\)
−0.730009 + 0.683438i \(0.760484\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 26.0000 0.115524 0.0577618 0.998330i \(-0.481604\pi\)
0.0577618 + 0.998330i \(0.481604\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.00000 0.0228547 0.0114273 0.999935i \(-0.496362\pi\)
0.0114273 + 0.999935i \(0.496362\pi\)
\(42\) 0 0
\(43\) 416.000 1.47534 0.737668 0.675164i \(-0.235927\pi\)
0.737668 + 0.675164i \(0.235927\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −396.000 −1.22899 −0.614495 0.788921i \(-0.710640\pi\)
−0.614495 + 0.788921i \(0.710640\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 450.000 1.16627 0.583134 0.812376i \(-0.301826\pi\)
0.583134 + 0.812376i \(0.301826\pi\)
\(54\) 0 0
\(55\) −320.000 −0.784523
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 274.000 0.604606 0.302303 0.953212i \(-0.402245\pi\)
0.302303 + 0.953212i \(0.402245\pi\)
\(60\) 0 0
\(61\) 576.000 1.20900 0.604502 0.796604i \(-0.293372\pi\)
0.604502 + 0.796604i \(0.293372\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −96.0000 −0.183190
\(66\) 0 0
\(67\) −476.000 −0.867950 −0.433975 0.900925i \(-0.642889\pi\)
−0.433975 + 0.900925i \(0.642889\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 448.000 0.748843 0.374421 0.927259i \(-0.377841\pi\)
0.374421 + 0.927259i \(0.377841\pi\)
\(72\) 0 0
\(73\) 158.000 0.253322 0.126661 0.991946i \(-0.459574\pi\)
0.126661 + 0.991946i \(0.459574\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −936.000 −1.33302 −0.666508 0.745498i \(-0.732212\pi\)
−0.666508 + 0.745498i \(0.732212\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 530.000 0.700904 0.350452 0.936581i \(-0.386028\pi\)
0.350452 + 0.936581i \(0.386028\pi\)
\(84\) 0 0
\(85\) 464.000 0.592093
\(86\) 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
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 208.000 0.224635
\(96\) 0 0
\(97\) −214.000 −0.224004 −0.112002 0.993708i \(-0.535726\pi\)
−0.112002 + 0.993708i \(0.535726\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1432.00 1.41079 0.705393 0.708817i \(-0.250771\pi\)
0.705393 + 0.708817i \(0.250771\pi\)
\(102\) 0 0
\(103\) −764.000 −0.730866 −0.365433 0.930838i \(-0.619079\pi\)
−0.365433 + 0.930838i \(0.619079\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −324.000 −0.292731 −0.146366 0.989231i \(-0.546758\pi\)
−0.146366 + 0.989231i \(0.546758\pi\)
\(108\) 0 0
\(109\) −1334.00 −1.17224 −0.586119 0.810225i \(-0.699345\pi\)
−0.586119 + 0.810225i \(0.699345\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1798.00 −1.49683 −0.748414 0.663232i \(-0.769184\pi\)
−0.748414 + 0.663232i \(0.769184\pi\)
\(114\) 0 0
\(115\) −512.000 −0.415167
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 269.000 0.202104
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1488.00 1.06473
\(126\) 0 0
\(127\) −384.000 −0.268303 −0.134152 0.990961i \(-0.542831\pi\)
−0.134152 + 0.990961i \(0.542831\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1814.00 −1.20985 −0.604923 0.796284i \(-0.706796\pi\)
−0.604923 + 0.796284i \(0.706796\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1666.00 −1.03895 −0.519474 0.854486i \(-0.673872\pi\)
−0.519474 + 0.854486i \(0.673872\pi\)
\(138\) 0 0
\(139\) −1126.00 −0.687094 −0.343547 0.939135i \(-0.611628\pi\)
−0.343547 + 0.939135i \(0.611628\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 480.000 0.280697
\(144\) 0 0
\(145\) −496.000 −0.284073
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2694.00 −1.48122 −0.740608 0.671938i \(-0.765462\pi\)
−0.740608 + 0.671938i \(0.765462\pi\)
\(150\) 0 0
\(151\) −2648.00 −1.42709 −0.713547 0.700607i \(-0.752912\pi\)
−0.713547 + 0.700607i \(0.752912\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2016.00 1.04470
\(156\) 0 0
\(157\) 556.000 0.282635 0.141317 0.989964i \(-0.454866\pi\)
0.141317 + 0.989964i \(0.454866\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −328.000 −0.157613 −0.0788066 0.996890i \(-0.525111\pi\)
−0.0788066 + 0.996890i \(0.525111\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4268.00 −1.97765 −0.988826 0.149077i \(-0.952370\pi\)
−0.988826 + 0.149077i \(0.952370\pi\)
\(168\) 0 0
\(169\) −2053.00 −0.934456
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3476.00 −1.52760 −0.763802 0.645451i \(-0.776669\pi\)
−0.763802 + 0.645451i \(0.776669\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2268.00 −0.947029 −0.473515 0.880786i \(-0.657015\pi\)
−0.473515 + 0.880786i \(0.657015\pi\)
\(180\) 0 0
\(181\) 276.000 0.113342 0.0566710 0.998393i \(-0.481951\pi\)
0.0566710 + 0.998393i \(0.481951\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −208.000 −0.0826620
\(186\) 0 0
\(187\) −2320.00 −0.907247
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3000.00 1.13650 0.568252 0.822854i \(-0.307620\pi\)
0.568252 + 0.822854i \(0.307620\pi\)
\(192\) 0 0
\(193\) 3278.00 1.22257 0.611284 0.791411i \(-0.290653\pi\)
0.611284 + 0.791411i \(0.290653\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2362.00 0.854241 0.427121 0.904195i \(-0.359528\pi\)
0.427121 + 0.904195i \(0.359528\pi\)
\(198\) 0 0
\(199\) 1036.00 0.369046 0.184523 0.982828i \(-0.440926\pi\)
0.184523 + 0.982828i \(0.440926\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −48.0000 −0.0163535
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1040.00 −0.344202
\(210\) 0 0
\(211\) 3524.00 1.14977 0.574887 0.818233i \(-0.305046\pi\)
0.574887 + 0.818233i \(0.305046\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3328.00 −1.05566
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −696.000 −0.211846
\(222\) 0 0
\(223\) 1336.00 0.401189 0.200595 0.979674i \(-0.435713\pi\)
0.200595 + 0.979674i \(0.435713\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1290.00 0.377182 0.188591 0.982056i \(-0.439608\pi\)
0.188591 + 0.982056i \(0.439608\pi\)
\(228\) 0 0
\(229\) −5524.00 −1.59404 −0.797022 0.603950i \(-0.793593\pi\)
−0.797022 + 0.603950i \(0.793593\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6314.00 −1.77530 −0.887648 0.460523i \(-0.847662\pi\)
−0.887648 + 0.460523i \(0.847662\pi\)
\(234\) 0 0
\(235\) 3168.00 0.879394
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3960.00 1.07176 0.535881 0.844294i \(-0.319980\pi\)
0.535881 + 0.844294i \(0.319980\pi\)
\(240\) 0 0
\(241\) 7018.00 1.87581 0.937903 0.346898i \(-0.112765\pi\)
0.937903 + 0.346898i \(0.112765\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −312.000 −0.0803728
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2394.00 −0.602024 −0.301012 0.953620i \(-0.597324\pi\)
−0.301012 + 0.953620i \(0.597324\pi\)
\(252\) 0 0
\(253\) 2560.00 0.636149
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2766.00 −0.671355 −0.335678 0.941977i \(-0.608965\pi\)
−0.335678 + 0.941977i \(0.608965\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −7968.00 −1.86817 −0.934084 0.357055i \(-0.883781\pi\)
−0.934084 + 0.357055i \(0.883781\pi\)
\(264\) 0 0
\(265\) −3600.00 −0.834514
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2900.00 −0.657309 −0.328654 0.944450i \(-0.606595\pi\)
−0.328654 + 0.944450i \(0.606595\pi\)
\(270\) 0 0
\(271\) −2640.00 −0.591766 −0.295883 0.955224i \(-0.595614\pi\)
−0.295883 + 0.955224i \(0.595614\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2440.00 −0.535046
\(276\) 0 0
\(277\) −1522.00 −0.330138 −0.165069 0.986282i \(-0.552785\pi\)
−0.165069 + 0.986282i \(0.552785\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4534.00 0.962547 0.481274 0.876570i \(-0.340174\pi\)
0.481274 + 0.876570i \(0.340174\pi\)
\(282\) 0 0
\(283\) −4834.00 −1.01538 −0.507688 0.861541i \(-0.669500\pi\)
−0.507688 + 0.861541i \(0.669500\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1549.00 −0.315286
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4656.00 −0.928350 −0.464175 0.885744i \(-0.653649\pi\)
−0.464175 + 0.885744i \(0.653649\pi\)
\(294\) 0 0
\(295\) −2192.00 −0.432621
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 768.000 0.148544
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4608.00 −0.865093
\(306\) 0 0
\(307\) 7238.00 1.34558 0.672792 0.739831i \(-0.265095\pi\)
0.672792 + 0.739831i \(0.265095\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1096.00 0.199834 0.0999171 0.994996i \(-0.468142\pi\)
0.0999171 + 0.994996i \(0.468142\pi\)
\(312\) 0 0
\(313\) 3818.00 0.689476 0.344738 0.938699i \(-0.387968\pi\)
0.344738 + 0.938699i \(0.387968\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1998.00 −0.354003 −0.177001 0.984211i \(-0.556640\pi\)
−0.177001 + 0.984211i \(0.556640\pi\)
\(318\) 0 0
\(319\) 2480.00 0.435277
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1508.00 0.259775
\(324\) 0 0
\(325\) −732.000 −0.124936
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −7936.00 −1.31783 −0.658915 0.752217i \(-0.728984\pi\)
−0.658915 + 0.752217i \(0.728984\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3808.00 0.621055
\(336\) 0 0
\(337\) 2766.00 0.447103 0.223551 0.974692i \(-0.428235\pi\)
0.223551 + 0.974692i \(0.428235\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −10080.0 −1.60077
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −8352.00 −1.29210 −0.646050 0.763295i \(-0.723580\pi\)
−0.646050 + 0.763295i \(0.723580\pi\)
\(348\) 0 0
\(349\) 5924.00 0.908609 0.454304 0.890847i \(-0.349888\pi\)
0.454304 + 0.890847i \(0.349888\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2226.00 0.335632 0.167816 0.985818i \(-0.446329\pi\)
0.167816 + 0.985818i \(0.446329\pi\)
\(354\) 0 0
\(355\) −3584.00 −0.535828
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3880.00 −0.570414 −0.285207 0.958466i \(-0.592062\pi\)
−0.285207 + 0.958466i \(0.592062\pi\)
\(360\) 0 0
\(361\) −6183.00 −0.901443
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1264.00 −0.181262
\(366\) 0 0
\(367\) 2584.00 0.367531 0.183765 0.982970i \(-0.441171\pi\)
0.183765 + 0.982970i \(0.441171\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 10534.0 1.46228 0.731139 0.682228i \(-0.238989\pi\)
0.731139 + 0.682228i \(0.238989\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 744.000 0.101639
\(378\) 0 0
\(379\) −4472.00 −0.606098 −0.303049 0.952975i \(-0.598005\pi\)
−0.303049 + 0.952975i \(0.598005\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2468.00 0.329266 0.164633 0.986355i \(-0.447356\pi\)
0.164633 + 0.986355i \(0.447356\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1046.00 0.136335 0.0681675 0.997674i \(-0.478285\pi\)
0.0681675 + 0.997674i \(0.478285\pi\)
\(390\) 0 0
\(391\) −3712.00 −0.480112
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7488.00 0.953828
\(396\) 0 0
\(397\) −2124.00 −0.268515 −0.134258 0.990946i \(-0.542865\pi\)
−0.134258 + 0.990946i \(0.542865\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11598.0 −1.44433 −0.722165 0.691721i \(-0.756853\pi\)
−0.722165 + 0.691721i \(0.756853\pi\)
\(402\) 0 0
\(403\) −3024.00 −0.373787
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1040.00 0.126661
\(408\) 0 0
\(409\) 2770.00 0.334884 0.167442 0.985882i \(-0.446449\pi\)
0.167442 + 0.985882i \(0.446449\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −4240.00 −0.501526
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 9438.00 1.10042 0.550211 0.835026i \(-0.314547\pi\)
0.550211 + 0.835026i \(0.314547\pi\)
\(420\) 0 0
\(421\) 5550.00 0.642495 0.321248 0.946995i \(-0.395898\pi\)
0.321248 + 0.946995i \(0.395898\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3538.00 0.403808
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3000.00 0.335278 0.167639 0.985848i \(-0.446386\pi\)
0.167639 + 0.985848i \(0.446386\pi\)
\(432\) 0 0
\(433\) −12926.0 −1.43460 −0.717302 0.696762i \(-0.754623\pi\)
−0.717302 + 0.696762i \(0.754623\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1664.00 −0.182151
\(438\) 0 0
\(439\) 408.000 0.0443571 0.0221786 0.999754i \(-0.492940\pi\)
0.0221786 + 0.999754i \(0.492940\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14452.0 1.54997 0.774983 0.631982i \(-0.217758\pi\)
0.774983 + 0.631982i \(0.217758\pi\)
\(444\) 0 0
\(445\) 3120.00 0.332364
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10258.0 −1.07818 −0.539092 0.842247i \(-0.681233\pi\)
−0.539092 + 0.842247i \(0.681233\pi\)
\(450\) 0 0
\(451\) 240.000 0.0250580
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5498.00 −0.562769 −0.281385 0.959595i \(-0.590794\pi\)
−0.281385 + 0.959595i \(0.590794\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −16316.0 −1.64840 −0.824199 0.566300i \(-0.808375\pi\)
−0.824199 + 0.566300i \(0.808375\pi\)
\(462\) 0 0
\(463\) 8944.00 0.897760 0.448880 0.893592i \(-0.351823\pi\)
0.448880 + 0.893592i \(0.351823\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9422.00 −0.933615 −0.466807 0.884359i \(-0.654596\pi\)
−0.466807 + 0.884359i \(0.654596\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 16640.0 1.61756
\(474\) 0 0
\(475\) 1586.00 0.153201
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 13820.0 1.31827 0.659136 0.752024i \(-0.270922\pi\)
0.659136 + 0.752024i \(0.270922\pi\)
\(480\) 0 0
\(481\) 312.000 0.0295758
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1712.00 0.160284
\(486\) 0 0
\(487\) −13264.0 −1.23419 −0.617094 0.786890i \(-0.711690\pi\)
−0.617094 + 0.786890i \(0.711690\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5940.00 0.545964 0.272982 0.962019i \(-0.411990\pi\)
0.272982 + 0.962019i \(0.411990\pi\)
\(492\) 0 0
\(493\) −3596.00 −0.328511
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −8252.00 −0.740301 −0.370151 0.928972i \(-0.620694\pi\)
−0.370151 + 0.928972i \(0.620694\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4704.00 0.416980 0.208490 0.978024i \(-0.433145\pi\)
0.208490 + 0.978024i \(0.433145\pi\)
\(504\) 0 0
\(505\) −11456.0 −1.00948
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −10788.0 −0.939430 −0.469715 0.882818i \(-0.655643\pi\)
−0.469715 + 0.882818i \(0.655643\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6112.00 0.522965
\(516\) 0 0
\(517\) −15840.0 −1.34747
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −14586.0 −1.22653 −0.613267 0.789876i \(-0.710145\pi\)
−0.613267 + 0.789876i \(0.710145\pi\)
\(522\) 0 0
\(523\) −26.0000 −0.00217381 −0.00108690 0.999999i \(-0.500346\pi\)
−0.00108690 + 0.999999i \(0.500346\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14616.0 1.20813
\(528\) 0 0
\(529\) −8071.00 −0.663352
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 72.0000 0.00585116
\(534\) 0 0
\(535\) 2592.00 0.209462
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 11214.0 0.891178 0.445589 0.895238i \(-0.352994\pi\)
0.445589 + 0.895238i \(0.352994\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 10672.0 0.838786
\(546\) 0 0
\(547\) −5424.00 −0.423973 −0.211987 0.977273i \(-0.567993\pi\)
−0.211987 + 0.977273i \(0.567993\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1612.00 −0.124634
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 17618.0 1.34021 0.670106 0.742265i \(-0.266248\pi\)
0.670106 + 0.742265i \(0.266248\pi\)
\(558\) 0 0
\(559\) 4992.00 0.377709
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3562.00 −0.266644 −0.133322 0.991073i \(-0.542564\pi\)
−0.133322 + 0.991073i \(0.542564\pi\)
\(564\) 0 0
\(565\) 14384.0 1.07104
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2838.00 −0.209095 −0.104548 0.994520i \(-0.533339\pi\)
−0.104548 + 0.994520i \(0.533339\pi\)
\(570\) 0 0
\(571\) −360.000 −0.0263845 −0.0131922 0.999913i \(-0.504199\pi\)
−0.0131922 + 0.999913i \(0.504199\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3904.00 −0.283144
\(576\) 0 0
\(577\) −22018.0 −1.58860 −0.794299 0.607527i \(-0.792162\pi\)
−0.794299 + 0.607527i \(0.792162\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 18000.0 1.27870
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1454.00 0.102237 0.0511184 0.998693i \(-0.483721\pi\)
0.0511184 + 0.998693i \(0.483721\pi\)
\(588\) 0 0
\(589\) 6552.00 0.458354
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 13818.0 0.956892 0.478446 0.878117i \(-0.341200\pi\)
0.478446 + 0.878117i \(0.341200\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6696.00 −0.456746 −0.228373 0.973574i \(-0.573341\pi\)
−0.228373 + 0.973574i \(0.573341\pi\)
\(600\) 0 0
\(601\) −10010.0 −0.679395 −0.339698 0.940535i \(-0.610325\pi\)
−0.339698 + 0.940535i \(0.610325\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2152.00 −0.144614
\(606\) 0 0
\(607\) −2880.00 −0.192579 −0.0962896 0.995353i \(-0.530697\pi\)
−0.0962896 + 0.995353i \(0.530697\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4752.00 −0.314640
\(612\) 0 0
\(613\) 6522.00 0.429724 0.214862 0.976644i \(-0.431070\pi\)
0.214862 + 0.976644i \(0.431070\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −6614.00 −0.431555 −0.215778 0.976443i \(-0.569229\pi\)
−0.215778 + 0.976443i \(0.569229\pi\)
\(618\) 0 0
\(619\) −5266.00 −0.341936 −0.170968 0.985277i \(-0.554689\pi\)
−0.170968 + 0.985277i \(0.554689\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −4279.00 −0.273856
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1508.00 −0.0955928
\(630\) 0 0
\(631\) 3344.00 0.210971 0.105485 0.994421i \(-0.466360\pi\)
0.105485 + 0.994421i \(0.466360\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3072.00 0.191982
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4882.00 0.300823 0.150411 0.988623i \(-0.451940\pi\)
0.150411 + 0.988623i \(0.451940\pi\)
\(642\) 0 0
\(643\) 15898.0 0.975048 0.487524 0.873110i \(-0.337900\pi\)
0.487524 + 0.873110i \(0.337900\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6132.00 0.372602 0.186301 0.982493i \(-0.440350\pi\)
0.186301 + 0.982493i \(0.440350\pi\)
\(648\) 0 0
\(649\) 10960.0 0.662893
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 24198.0 1.45014 0.725070 0.688676i \(-0.241808\pi\)
0.725070 + 0.688676i \(0.241808\pi\)
\(654\) 0 0
\(655\) 14512.0 0.865696
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −17456.0 −1.03185 −0.515925 0.856634i \(-0.672552\pi\)
−0.515925 + 0.856634i \(0.672552\pi\)
\(660\) 0 0
\(661\) 656.000 0.0386013 0.0193006 0.999814i \(-0.493856\pi\)
0.0193006 + 0.999814i \(0.493856\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 3968.00 0.230347
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 23040.0 1.32556
\(672\) 0 0
\(673\) −18214.0 −1.04324 −0.521618 0.853179i \(-0.674671\pi\)
−0.521618 + 0.853179i \(0.674671\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 30252.0 1.71740 0.858699 0.512480i \(-0.171273\pi\)
0.858699 + 0.512480i \(0.171273\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 10836.0 0.607069 0.303534 0.952820i \(-0.401833\pi\)
0.303534 + 0.952820i \(0.401833\pi\)
\(684\) 0 0
\(685\) 13328.0 0.743411
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 5400.00 0.298583
\(690\) 0 0
\(691\) −9578.00 −0.527300 −0.263650 0.964618i \(-0.584926\pi\)
−0.263650 + 0.964618i \(0.584926\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9008.00 0.491644
\(696\) 0 0
\(697\) −348.000 −0.0189117
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −12442.0 −0.670368 −0.335184 0.942153i \(-0.608798\pi\)
−0.335184 + 0.942153i \(0.608798\pi\)
\(702\) 0 0
\(703\) −676.000 −0.0362672
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −25174.0 −1.33347 −0.666734 0.745295i \(-0.732308\pi\)
−0.666734 + 0.745295i \(0.732308\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −16128.0 −0.847123
\(714\) 0 0
\(715\) −3840.00 −0.200850
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 34188.0 1.77329 0.886646 0.462448i \(-0.153029\pi\)
0.886646 + 0.462448i \(0.153029\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3782.00 −0.193738
\(726\) 0 0
\(727\) 5204.00 0.265482 0.132741 0.991151i \(-0.457622\pi\)
0.132741 + 0.991151i \(0.457622\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −24128.0 −1.22080
\(732\) 0 0
\(733\) 32880.0 1.65682 0.828411 0.560121i \(-0.189245\pi\)
0.828411 + 0.560121i \(0.189245\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −19040.0 −0.951625
\(738\) 0 0
\(739\) −3912.00 −0.194730 −0.0973648 0.995249i \(-0.531041\pi\)
−0.0973648 + 0.995249i \(0.531041\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 16008.0 0.790413 0.395206 0.918592i \(-0.370673\pi\)
0.395206 + 0.918592i \(0.370673\pi\)
\(744\) 0 0
\(745\) 21552.0 1.05987
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 9960.00 0.483949 0.241974 0.970283i \(-0.422205\pi\)
0.241974 + 0.970283i \(0.422205\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 21184.0 1.02115
\(756\) 0 0
\(757\) 12378.0 0.594301 0.297151 0.954831i \(-0.403964\pi\)
0.297151 + 0.954831i \(0.403964\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 34670.0 1.65149 0.825747 0.564041i \(-0.190754\pi\)
0.825747 + 0.564041i \(0.190754\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3288.00 0.154789
\(768\) 0 0
\(769\) 10898.0 0.511043 0.255521 0.966803i \(-0.417753\pi\)
0.255521 + 0.966803i \(0.417753\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −25808.0 −1.20084 −0.600420 0.799685i \(-0.705000\pi\)
−0.600420 + 0.799685i \(0.705000\pi\)
\(774\) 0 0
\(775\) 15372.0 0.712488
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −156.000 −0.00717494
\(780\) 0 0
\(781\) 17920.0 0.821035
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4448.00 −0.202237
\(786\) 0 0
\(787\) 21054.0 0.953614 0.476807 0.879008i \(-0.341794\pi\)
0.476807 + 0.879008i \(0.341794\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6912.00 0.309524
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −24276.0 −1.07892 −0.539461 0.842011i \(-0.681372\pi\)
−0.539461 + 0.842011i \(0.681372\pi\)
\(798\) 0 0
\(799\) 22968.0 1.01696
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 6320.00 0.277743
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −21526.0 −0.935493 −0.467747 0.883863i \(-0.654934\pi\)
−0.467747 + 0.883863i \(0.654934\pi\)
\(810\) 0 0
\(811\) 12806.0 0.554475 0.277238 0.960801i \(-0.410581\pi\)
0.277238 + 0.960801i \(0.410581\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 2624.00 0.112779
\(816\) 0 0
\(817\) −10816.0 −0.463163
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −13214.0 −0.561720 −0.280860 0.959749i \(-0.590620\pi\)
−0.280860 + 0.959749i \(0.590620\pi\)
\(822\) 0 0
\(823\) 32248.0 1.36585 0.682925 0.730488i \(-0.260708\pi\)
0.682925 + 0.730488i \(0.260708\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 14316.0 0.601954 0.300977 0.953631i \(-0.402687\pi\)
0.300977 + 0.953631i \(0.402687\pi\)
\(828\) 0 0
\(829\) −25168.0 −1.05443 −0.527214 0.849733i \(-0.676763\pi\)
−0.527214 + 0.849733i \(0.676763\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 34144.0 1.41509
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 9356.00 0.384988 0.192494 0.981298i \(-0.438342\pi\)
0.192494 + 0.981298i \(0.438342\pi\)
\(840\) 0 0
\(841\) −20545.0 −0.842388
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 16424.0 0.668642
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1664.00 0.0670284
\(852\) 0 0
\(853\) −2372.00 −0.0952119 −0.0476059 0.998866i \(-0.515159\pi\)
−0.0476059 + 0.998866i \(0.515159\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 11694.0 0.466114 0.233057 0.972463i \(-0.425127\pi\)
0.233057 + 0.972463i \(0.425127\pi\)
\(858\) 0 0
\(859\) 20506.0 0.814500 0.407250 0.913317i \(-0.366488\pi\)
0.407250 + 0.913317i \(0.366488\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 28136.0 1.10980 0.554902 0.831916i \(-0.312756\pi\)
0.554902 + 0.831916i \(0.312756\pi\)
\(864\) 0 0
\(865\) 27808.0 1.09306
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −37440.0 −1.46152
\(870\) 0 0
\(871\) −5712.00 −0.222209
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −37070.0 −1.42733 −0.713663 0.700489i \(-0.752965\pi\)
−0.713663 + 0.700489i \(0.752965\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −6198.00 −0.237021 −0.118511 0.992953i \(-0.537812\pi\)
−0.118511 + 0.992953i \(0.537812\pi\)
\(882\) 0 0
\(883\) −31876.0 −1.21485 −0.607425 0.794377i \(-0.707798\pi\)
−0.607425 + 0.794377i \(0.707798\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −132.000 −0.00499676 −0.00249838 0.999997i \(-0.500795\pi\)
−0.00249838 + 0.999997i \(0.500795\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 10296.0 0.385826
\(894\) 0 0
\(895\) 18144.0 0.677639
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −15624.0 −0.579632
\(900\) 0 0
\(901\) −26100.0 −0.965058
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2208.00 −0.0811010
\(906\) 0 0
\(907\) 38244.0 1.40008 0.700039 0.714104i \(-0.253166\pi\)
0.700039 + 0.714104i \(0.253166\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 7008.00 0.254869 0.127434 0.991847i \(-0.459326\pi\)
0.127434 + 0.991847i \(0.459326\pi\)
\(912\) 0 0
\(913\) 21200.0 0.768475
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 36664.0 1.31603 0.658016 0.753004i \(-0.271396\pi\)
0.658016 + 0.753004i \(0.271396\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 5376.00 0.191715
\(924\) 0 0
\(925\) −1586.00 −0.0563755
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 45510.0 1.60725 0.803625 0.595136i \(-0.202902\pi\)
0.803625 + 0.595136i \(0.202902\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 18560.0 0.649173
\(936\) 0 0
\(937\) 3838.00 0.133812 0.0669061 0.997759i \(-0.478687\pi\)
0.0669061 + 0.997759i \(0.478687\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −16832.0 −0.583111 −0.291556 0.956554i \(-0.594173\pi\)
−0.291556 + 0.956554i \(0.594173\pi\)
\(942\) 0 0
\(943\) 384.000 0.0132606
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 40928.0 1.40442 0.702208 0.711972i \(-0.252198\pi\)
0.702208 + 0.711972i \(0.252198\pi\)
\(948\) 0 0
\(949\) 1896.00 0.0648543
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 24070.0 0.818157 0.409079 0.912499i \(-0.365850\pi\)
0.409079 + 0.912499i \(0.365850\pi\)
\(954\) 0 0
\(955\) −24000.0 −0.813217
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 33713.0 1.13165
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −26224.0 −0.874798
\(966\) 0 0
\(967\) −17152.0 −0.570394 −0.285197 0.958469i \(-0.592059\pi\)
−0.285197 + 0.958469i \(0.592059\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −32910.0 −1.08767 −0.543837 0.839191i \(-0.683029\pi\)
−0.543837 + 0.839191i \(0.683029\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 6822.00 0.223393 0.111697 0.993742i \(-0.464372\pi\)
0.111697 + 0.993742i \(0.464372\pi\)
\(978\) 0 0
\(979\) −15600.0 −0.509273
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −48420.0 −1.57107 −0.785533 0.618820i \(-0.787611\pi\)
−0.785533 + 0.618820i \(0.787611\pi\)
\(984\) 0 0
\(985\) −18896.0 −0.611245
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 26624.0 0.856010
\(990\) 0 0
\(991\) −49216.0 −1.57760 −0.788798 0.614652i \(-0.789296\pi\)
−0.788798 + 0.614652i \(0.789296\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −8288.00 −0.264068
\(996\) 0 0
\(997\) −35264.0 −1.12018 −0.560091 0.828431i \(-0.689234\pi\)
−0.560091 + 0.828431i \(0.689234\pi\)
\(998\) 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 1764.4.a.c.1.1 1
3.2 odd 2 196.4.a.d.1.1 1
7.2 even 3 1764.4.k.m.361.1 2
7.3 odd 6 1764.4.k.d.1549.1 2
7.4 even 3 1764.4.k.m.1549.1 2
7.5 odd 6 1764.4.k.d.361.1 2
7.6 odd 2 252.4.a.d.1.1 1
12.11 even 2 784.4.a.a.1.1 1
21.2 odd 6 196.4.e.a.165.1 2
21.5 even 6 196.4.e.f.165.1 2
21.11 odd 6 196.4.e.a.177.1 2
21.17 even 6 196.4.e.f.177.1 2
21.20 even 2 28.4.a.a.1.1 1
28.27 even 2 1008.4.a.o.1.1 1
84.83 odd 2 112.4.a.g.1.1 1
105.62 odd 4 700.4.e.a.449.2 2
105.83 odd 4 700.4.e.a.449.1 2
105.104 even 2 700.4.a.n.1.1 1
168.83 odd 2 448.4.a.a.1.1 1
168.125 even 2 448.4.a.p.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.4.a.a.1.1 1 21.20 even 2
112.4.a.g.1.1 1 84.83 odd 2
196.4.a.d.1.1 1 3.2 odd 2
196.4.e.a.165.1 2 21.2 odd 6
196.4.e.a.177.1 2 21.11 odd 6
196.4.e.f.165.1 2 21.5 even 6
196.4.e.f.177.1 2 21.17 even 6
252.4.a.d.1.1 1 7.6 odd 2
448.4.a.a.1.1 1 168.83 odd 2
448.4.a.p.1.1 1 168.125 even 2
700.4.a.n.1.1 1 105.104 even 2
700.4.e.a.449.1 2 105.83 odd 4
700.4.e.a.449.2 2 105.62 odd 4
784.4.a.a.1.1 1 12.11 even 2
1008.4.a.o.1.1 1 28.27 even 2
1764.4.a.c.1.1 1 1.1 even 1 trivial
1764.4.k.d.361.1 2 7.5 odd 6
1764.4.k.d.1549.1 2 7.3 odd 6
1764.4.k.m.361.1 2 7.2 even 3
1764.4.k.m.1549.1 2 7.4 even 3