Properties

Label 784.4.a.a.1.1
Level $784$
Weight $4$
Character 784.1
Self dual yes
Analytic conductor $46.257$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(46.2574974445\)
Analytic rank: \(0\)
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 \(\chi\) \(=\) 784.1

$q$-expansion

\(f(q)\) \(=\) \(q-10.0000 q^{3} +8.00000 q^{5} +73.0000 q^{9} +O(q^{10})\) \(q-10.0000 q^{3} +8.00000 q^{5} +73.0000 q^{9} +40.0000 q^{11} +12.0000 q^{13} -80.0000 q^{15} +58.0000 q^{17} +26.0000 q^{19} +64.0000 q^{23} -61.0000 q^{25} -460.000 q^{27} -62.0000 q^{29} +252.000 q^{31} -400.000 q^{33} +26.0000 q^{37} -120.000 q^{39} -6.00000 q^{41} -416.000 q^{43} +584.000 q^{45} -396.000 q^{47} -580.000 q^{51} -450.000 q^{53} +320.000 q^{55} -260.000 q^{57} +274.000 q^{59} +576.000 q^{61} +96.0000 q^{65} +476.000 q^{67} -640.000 q^{69} +448.000 q^{71} +158.000 q^{73} +610.000 q^{75} +936.000 q^{79} +2629.00 q^{81} +530.000 q^{83} +464.000 q^{85} +620.000 q^{87} +390.000 q^{89} -2520.00 q^{93} +208.000 q^{95} -214.000 q^{97} +2920.00 q^{99} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −10.0000 −1.92450 −0.962250 0.272166i \(-0.912260\pi\)
−0.962250 + 0.272166i \(0.912260\pi\)
\(4\) 0 0
\(5\) 8.00000 0.715542 0.357771 0.933809i \(-0.383537\pi\)
0.357771 + 0.933809i \(0.383537\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 73.0000 2.70370
\(10\) 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
\(15\) −80.0000 −1.37706
\(16\) 0 0
\(17\) 58.0000 0.827474 0.413737 0.910396i \(-0.364223\pi\)
0.413737 + 0.910396i \(0.364223\pi\)
\(18\) 0 0
\(19\) 26.0000 0.313937 0.156969 0.987604i \(-0.449828\pi\)
0.156969 + 0.987604i \(0.449828\pi\)
\(20\) 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
\(27\) −460.000 −3.27878
\(28\) 0 0
\(29\) −62.0000 −0.397004 −0.198502 0.980101i \(-0.563608\pi\)
−0.198502 + 0.980101i \(0.563608\pi\)
\(30\) 0 0
\(31\) 252.000 1.46002 0.730009 0.683438i \(-0.239516\pi\)
0.730009 + 0.683438i \(0.239516\pi\)
\(32\) 0 0
\(33\) −400.000 −2.11003
\(34\) 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
\(39\) −120.000 −0.492702
\(40\) 0 0
\(41\) −6.00000 −0.0228547 −0.0114273 0.999935i \(-0.503638\pi\)
−0.0114273 + 0.999935i \(0.503638\pi\)
\(42\) 0 0
\(43\) −416.000 −1.47534 −0.737668 0.675164i \(-0.764073\pi\)
−0.737668 + 0.675164i \(0.764073\pi\)
\(44\) 0 0
\(45\) 584.000 1.93461
\(46\) 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
\(51\) −580.000 −1.59248
\(52\) 0 0
\(53\) −450.000 −1.16627 −0.583134 0.812376i \(-0.698174\pi\)
−0.583134 + 0.812376i \(0.698174\pi\)
\(54\) 0 0
\(55\) 320.000 0.784523
\(56\) 0 0
\(57\) −260.000 −0.604173
\(58\) 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 \(-0.357111\pi\)
0.433975 + 0.900925i \(0.357111\pi\)
\(68\) 0 0
\(69\) −640.000 −1.11662
\(70\) 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
\(75\) 610.000 0.939156
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 936.000 1.33302 0.666508 0.745498i \(-0.267788\pi\)
0.666508 + 0.745498i \(0.267788\pi\)
\(80\) 0 0
\(81\) 2629.00 3.60631
\(82\) 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
\(87\) 620.000 0.764034
\(88\) 0 0
\(89\) 390.000 0.464493 0.232247 0.972657i \(-0.425392\pi\)
0.232247 + 0.972657i \(0.425392\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −2520.00 −2.80980
\(94\) 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
\(99\) 2920.00 2.96435
\(100\) 0 0
\(101\) −1432.00 −1.41079 −0.705393 0.708817i \(-0.749229\pi\)
−0.705393 + 0.708817i \(0.749229\pi\)
\(102\) 0 0
\(103\) 764.000 0.730866 0.365433 0.930838i \(-0.380921\pi\)
0.365433 + 0.930838i \(0.380921\pi\)
\(104\) 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
\(111\) −260.000 −0.222325
\(112\) 0 0
\(113\) 1798.00 1.49683 0.748414 0.663232i \(-0.230816\pi\)
0.748414 + 0.663232i \(0.230816\pi\)
\(114\) 0 0
\(115\) 512.000 0.415167
\(116\) 0 0
\(117\) 876.000 0.692190
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 269.000 0.202104
\(122\) 0 0
\(123\) 60.0000 0.0439839
\(124\) 0 0
\(125\) −1488.00 −1.06473
\(126\) 0 0
\(127\) 384.000 0.268303 0.134152 0.990961i \(-0.457169\pi\)
0.134152 + 0.990961i \(0.457169\pi\)
\(128\) 0 0
\(129\) 4160.00 2.83928
\(130\) 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
\(135\) −3680.00 −2.34610
\(136\) 0 0
\(137\) 1666.00 1.03895 0.519474 0.854486i \(-0.326128\pi\)
0.519474 + 0.854486i \(0.326128\pi\)
\(138\) 0 0
\(139\) 1126.00 0.687094 0.343547 0.939135i \(-0.388372\pi\)
0.343547 + 0.939135i \(0.388372\pi\)
\(140\) 0 0
\(141\) 3960.00 2.36519
\(142\) 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 \(-0.234538\pi\)
0.740608 + 0.671938i \(0.234538\pi\)
\(150\) 0 0
\(151\) 2648.00 1.42709 0.713547 0.700607i \(-0.247088\pi\)
0.713547 + 0.700607i \(0.247088\pi\)
\(152\) 0 0
\(153\) 4234.00 2.23725
\(154\) 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
\(159\) 4500.00 2.24449
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 328.000 0.157613 0.0788066 0.996890i \(-0.474889\pi\)
0.0788066 + 0.996890i \(0.474889\pi\)
\(164\) 0 0
\(165\) −3200.00 −1.50982
\(166\) 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
\(171\) 1898.00 0.848793
\(172\) 0 0
\(173\) 3476.00 1.52760 0.763802 0.645451i \(-0.223331\pi\)
0.763802 + 0.645451i \(0.223331\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −2740.00 −1.16357
\(178\) 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
\(183\) −5760.00 −2.32673
\(184\) 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
\(195\) −960.000 −0.352549
\(196\) 0 0
\(197\) −2362.00 −0.854241 −0.427121 0.904195i \(-0.640472\pi\)
−0.427121 + 0.904195i \(0.640472\pi\)
\(198\) 0 0
\(199\) −1036.00 −0.369046 −0.184523 0.982828i \(-0.559074\pi\)
−0.184523 + 0.982828i \(0.559074\pi\)
\(200\) 0 0
\(201\) −4760.00 −1.67037
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −48.0000 −0.0163535
\(206\) 0 0
\(207\) 4672.00 1.56873
\(208\) 0 0
\(209\) 1040.00 0.344202
\(210\) 0 0
\(211\) −3524.00 −1.14977 −0.574887 0.818233i \(-0.694954\pi\)
−0.574887 + 0.818233i \(0.694954\pi\)
\(212\) 0 0
\(213\) −4480.00 −1.44115
\(214\) 0 0
\(215\) −3328.00 −1.05566
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1580.00 −0.487518
\(220\) 0 0
\(221\) 696.000 0.211846
\(222\) 0 0
\(223\) −1336.00 −0.401189 −0.200595 0.979674i \(-0.564287\pi\)
−0.200595 + 0.979674i \(0.564287\pi\)
\(224\) 0 0
\(225\) −4453.00 −1.31941
\(226\) 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 \(-0.152338\pi\)
0.887648 + 0.460523i \(0.152338\pi\)
\(234\) 0 0
\(235\) −3168.00 −0.879394
\(236\) 0 0
\(237\) −9360.00 −2.56539
\(238\) 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
\(243\) −13870.0 −3.66157
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 312.000 0.0803728
\(248\) 0 0
\(249\) −5300.00 −1.34889
\(250\) 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
\(255\) −4640.00 −1.13948
\(256\) 0 0
\(257\) 2766.00 0.671355 0.335678 0.941977i \(-0.391035\pi\)
0.335678 + 0.941977i \(0.391035\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −4526.00 −1.07338
\(262\) 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
\(267\) −3900.00 −0.893918
\(268\) 0 0
\(269\) 2900.00 0.657309 0.328654 0.944450i \(-0.393405\pi\)
0.328654 + 0.944450i \(0.393405\pi\)
\(270\) 0 0
\(271\) 2640.00 0.591766 0.295883 0.955224i \(-0.404386\pi\)
0.295883 + 0.955224i \(0.404386\pi\)
\(272\) 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
\(279\) 18396.0 3.94745
\(280\) 0 0
\(281\) −4534.00 −0.962547 −0.481274 0.876570i \(-0.659826\pi\)
−0.481274 + 0.876570i \(0.659826\pi\)
\(282\) 0 0
\(283\) 4834.00 1.01538 0.507688 0.861541i \(-0.330500\pi\)
0.507688 + 0.861541i \(0.330500\pi\)
\(284\) 0 0
\(285\) −2080.00 −0.432311
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1549.00 −0.315286
\(290\) 0 0
\(291\) 2140.00 0.431096
\(292\) 0 0
\(293\) 4656.00 0.928350 0.464175 0.885744i \(-0.346351\pi\)
0.464175 + 0.885744i \(0.346351\pi\)
\(294\) 0 0
\(295\) 2192.00 0.432621
\(296\) 0 0
\(297\) −18400.0 −3.59487
\(298\) 0 0
\(299\) 768.000 0.148544
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 14320.0 2.71506
\(304\) 0 0
\(305\) 4608.00 0.865093
\(306\) 0 0
\(307\) −7238.00 −1.34558 −0.672792 0.739831i \(-0.734905\pi\)
−0.672792 + 0.739831i \(0.734905\pi\)
\(308\) 0 0
\(309\) −7640.00 −1.40655
\(310\) 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 \(-0.443360\pi\)
0.177001 + 0.984211i \(0.443360\pi\)
\(318\) 0 0
\(319\) −2480.00 −0.435277
\(320\) 0 0
\(321\) 3240.00 0.563362
\(322\) 0 0
\(323\) 1508.00 0.259775
\(324\) 0 0
\(325\) −732.000 −0.124936
\(326\) 0 0
\(327\) 13340.0 2.25597
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 7936.00 1.31783 0.658915 0.752217i \(-0.271016\pi\)
0.658915 + 0.752217i \(0.271016\pi\)
\(332\) 0 0
\(333\) 1898.00 0.312342
\(334\) 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
\(339\) −17980.0 −2.88065
\(340\) 0 0
\(341\) 10080.0 1.60077
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −5120.00 −0.798990
\(346\) 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
\(351\) −5520.00 −0.839418
\(352\) 0 0
\(353\) −2226.00 −0.335632 −0.167816 0.985818i \(-0.553671\pi\)
−0.167816 + 0.985818i \(0.553671\pi\)
\(354\) 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
\(363\) −2690.00 −0.388949
\(364\) 0 0
\(365\) 1264.00 0.181262
\(366\) 0 0
\(367\) −2584.00 −0.367531 −0.183765 0.982970i \(-0.558829\pi\)
−0.183765 + 0.982970i \(0.558829\pi\)
\(368\) 0 0
\(369\) −438.000 −0.0617923
\(370\) 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
\(375\) 14880.0 2.04907
\(376\) 0 0
\(377\) −744.000 −0.101639
\(378\) 0 0
\(379\) 4472.00 0.606098 0.303049 0.952975i \(-0.401995\pi\)
0.303049 + 0.952975i \(0.401995\pi\)
\(380\) 0 0
\(381\) −3840.00 −0.516350
\(382\) 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
\(387\) −30368.0 −3.98887
\(388\) 0 0
\(389\) −1046.00 −0.136335 −0.0681675 0.997674i \(-0.521715\pi\)
−0.0681675 + 0.997674i \(0.521715\pi\)
\(390\) 0 0
\(391\) 3712.00 0.480112
\(392\) 0 0
\(393\) 18140.0 2.32835
\(394\) 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 \(-0.243147\pi\)
0.722165 + 0.691721i \(0.243147\pi\)
\(402\) 0 0
\(403\) 3024.00 0.373787
\(404\) 0 0
\(405\) 21032.0 2.58047
\(406\) 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
\(411\) −16660.0 −1.99946
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 4240.00 0.501526
\(416\) 0 0
\(417\) −11260.0 −1.32231
\(418\) 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
\(423\) −28908.0 −3.32283
\(424\) 0 0
\(425\) −3538.00 −0.403808
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −4800.00 −0.540201
\(430\) 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
\(435\) 4960.00 0.546698
\(436\) 0 0
\(437\) 1664.00 0.182151
\(438\) 0 0
\(439\) −408.000 −0.0443571 −0.0221786 0.999754i \(-0.507060\pi\)
−0.0221786 + 0.999754i \(0.507060\pi\)
\(440\) 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
\(447\) −26940.0 −2.85060
\(448\) 0 0
\(449\) 10258.0 1.07818 0.539092 0.842247i \(-0.318767\pi\)
0.539092 + 0.842247i \(0.318767\pi\)
\(450\) 0 0
\(451\) −240.000 −0.0250580
\(452\) 0 0
\(453\) −26480.0 −2.74644
\(454\) 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
\(459\) −26680.0 −2.71311
\(460\) 0 0
\(461\) 16316.0 1.64840 0.824199 0.566300i \(-0.191625\pi\)
0.824199 + 0.566300i \(0.191625\pi\)
\(462\) 0 0
\(463\) −8944.00 −0.897760 −0.448880 0.893592i \(-0.648177\pi\)
−0.448880 + 0.893592i \(0.648177\pi\)
\(464\) 0 0
\(465\) −20160.0 −2.01053
\(466\) 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
\(471\) −5560.00 −0.543931
\(472\) 0 0
\(473\) −16640.0 −1.61756
\(474\) 0 0
\(475\) −1586.00 −0.153201
\(476\) 0 0
\(477\) −32850.0 −3.15325
\(478\) 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 \(-0.288310\pi\)
0.617094 + 0.786890i \(0.288310\pi\)
\(488\) 0 0
\(489\) −3280.00 −0.303327
\(490\) 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
\(495\) 23360.0 2.12112
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 8252.00 0.740301 0.370151 0.928972i \(-0.379306\pi\)
0.370151 + 0.928972i \(0.379306\pi\)
\(500\) 0 0
\(501\) 42680.0 3.80599
\(502\) 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
\(507\) 20530.0 1.79836
\(508\) 0 0
\(509\) 10788.0 0.939430 0.469715 0.882818i \(-0.344357\pi\)
0.469715 + 0.882818i \(0.344357\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −11960.0 −1.02933
\(514\) 0 0
\(515\) 6112.00 0.522965
\(516\) 0 0
\(517\) −15840.0 −1.34747
\(518\) 0 0
\(519\) −34760.0 −2.93987
\(520\) 0 0
\(521\) 14586.0 1.22653 0.613267 0.789876i \(-0.289855\pi\)
0.613267 + 0.789876i \(0.289855\pi\)
\(522\) 0 0
\(523\) 26.0000 0.00217381 0.00108690 0.999999i \(-0.499654\pi\)
0.00108690 + 0.999999i \(0.499654\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14616.0 1.20813
\(528\) 0 0
\(529\) −8071.00 −0.663352
\(530\) 0 0
\(531\) 20002.0 1.63468
\(532\) 0 0
\(533\) −72.0000 −0.00585116
\(534\) 0 0
\(535\) −2592.00 −0.209462
\(536\) 0 0
\(537\) 22680.0 1.82256
\(538\) 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
\(543\) −2760.00 −0.218127
\(544\) 0 0
\(545\) −10672.0 −0.838786
\(546\) 0 0
\(547\) 5424.00 0.423973 0.211987 0.977273i \(-0.432007\pi\)
0.211987 + 0.977273i \(0.432007\pi\)
\(548\) 0 0
\(549\) 42048.0 3.26879
\(550\) 0 0
\(551\) −1612.00 −0.124634
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −2080.00 −0.159083
\(556\) 0 0
\(557\) −17618.0 −1.34021 −0.670106 0.742265i \(-0.733752\pi\)
−0.670106 + 0.742265i \(0.733752\pi\)
\(558\) 0 0
\(559\) −4992.00 −0.377709
\(560\) 0 0
\(561\) −23200.0 −1.74600
\(562\) 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 \(-0.466661\pi\)
0.104548 + 0.994520i \(0.466661\pi\)
\(570\) 0 0
\(571\) 360.000 0.0263845 0.0131922 0.999913i \(-0.495801\pi\)
0.0131922 + 0.999913i \(0.495801\pi\)
\(572\) 0 0
\(573\) −30000.0 −2.18720
\(574\) 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
\(579\) −32780.0 −2.35283
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −18000.0 −1.27870
\(584\) 0 0
\(585\) 7008.00 0.495291
\(586\) 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
\(591\) 23620.0 1.64399
\(592\) 0 0
\(593\) −13818.0 −0.956892 −0.478446 0.878117i \(-0.658800\pi\)
−0.478446 + 0.878117i \(0.658800\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 10360.0 0.710229
\(598\) 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
\(603\) 34748.0 2.34668
\(604\) 0 0
\(605\) 2152.00 0.144614
\(606\) 0 0
\(607\) 2880.00 0.192579 0.0962896 0.995353i \(-0.469303\pi\)
0.0962896 + 0.995353i \(0.469303\pi\)
\(608\) 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
\(615\) 480.000 0.0314723
\(616\) 0 0
\(617\) 6614.00 0.431555 0.215778 0.976443i \(-0.430771\pi\)
0.215778 + 0.976443i \(0.430771\pi\)
\(618\) 0 0
\(619\) 5266.00 0.341936 0.170968 0.985277i \(-0.445311\pi\)
0.170968 + 0.985277i \(0.445311\pi\)
\(620\) 0 0
\(621\) −29440.0 −1.90239
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −4279.00 −0.273856
\(626\) 0 0
\(627\) −10400.0 −0.662418
\(628\) 0 0
\(629\) 1508.00 0.0955928
\(630\) 0 0
\(631\) −3344.00 −0.210971 −0.105485 0.994421i \(-0.533640\pi\)
−0.105485 + 0.994421i \(0.533640\pi\)
\(632\) 0 0
\(633\) 35240.0 2.21274
\(634\) 0 0
\(635\) 3072.00 0.191982
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 32704.0 2.02465
\(640\) 0 0
\(641\) −4882.00 −0.300823 −0.150411 0.988623i \(-0.548060\pi\)
−0.150411 + 0.988623i \(0.548060\pi\)
\(642\) 0 0
\(643\) −15898.0 −0.975048 −0.487524 0.873110i \(-0.662100\pi\)
−0.487524 + 0.873110i \(0.662100\pi\)
\(644\) 0 0
\(645\) 33280.0 2.03163
\(646\) 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 \(-0.758192\pi\)
−0.725070 + 0.688676i \(0.758192\pi\)
\(654\) 0 0
\(655\) −14512.0 −0.865696
\(656\) 0 0
\(657\) 11534.0 0.684907
\(658\) 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
\(663\) −6960.00 −0.407698
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −3968.00 −0.230347
\(668\) 0 0
\(669\) 13360.0 0.772089
\(670\) 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
\(675\) 28060.0 1.60004
\(676\) 0 0
\(677\) −30252.0 −1.71740 −0.858699 0.512480i \(-0.828727\pi\)
−0.858699 + 0.512480i \(0.828727\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −12900.0 −0.725887
\(682\) 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
\(687\) 55240.0 3.06774
\(688\) 0 0
\(689\) −5400.00 −0.298583
\(690\) 0 0
\(691\) 9578.00 0.527300 0.263650 0.964618i \(-0.415074\pi\)
0.263650 + 0.964618i \(0.415074\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9008.00 0.491644
\(696\) 0 0
\(697\) −348.000 −0.0189117
\(698\) 0 0
\(699\) −63140.0 −3.41656
\(700\) 0 0
\(701\) 12442.0 0.670368 0.335184 0.942153i \(-0.391202\pi\)
0.335184 + 0.942153i \(0.391202\pi\)
\(702\) 0 0
\(703\) 676.000 0.0362672
\(704\) 0 0
\(705\) 31680.0 1.69239
\(706\) 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
\(711\) 68328.0 3.60408
\(712\) 0 0
\(713\) 16128.0 0.847123
\(714\) 0 0
\(715\) 3840.00 0.200850
\(716\) 0 0
\(717\) −39600.0 −2.06261
\(718\) 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
\(723\) −70180.0 −3.60999
\(724\) 0 0
\(725\) 3782.00 0.193738
\(726\) 0 0
\(727\) −5204.00 −0.265482 −0.132741 0.991151i \(-0.542378\pi\)
−0.132741 + 0.991151i \(0.542378\pi\)
\(728\) 0 0
\(729\) 67717.0 3.44038
\(730\) 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 \(-0.468959\pi\)
0.0973648 + 0.995249i \(0.468959\pi\)
\(740\) 0 0
\(741\) −3120.00 −0.154678
\(742\) 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
\(747\) 38690.0 1.89504
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −9960.00 −0.483949 −0.241974 0.970283i \(-0.577795\pi\)
−0.241974 + 0.970283i \(0.577795\pi\)
\(752\) 0 0
\(753\) 23940.0 1.15860
\(754\) 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
\(759\) −25600.0 −1.22427
\(760\) 0 0
\(761\) −34670.0 −1.65149 −0.825747 0.564041i \(-0.809246\pi\)
−0.825747 + 0.564041i \(0.809246\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 33872.0 1.60084
\(766\) 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
\(771\) −27660.0 −1.29202
\(772\) 0 0
\(773\) 25808.0 1.20084 0.600420 0.799685i \(-0.295000\pi\)
0.600420 + 0.799685i \(0.295000\pi\)
\(774\) 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
\(783\) 28520.0 1.30169
\(784\) 0 0
\(785\) 4448.00 0.202237
\(786\) 0 0
\(787\) −21054.0 −0.953614 −0.476807 0.879008i \(-0.658206\pi\)
−0.476807 + 0.879008i \(0.658206\pi\)
\(788\) 0 0
\(789\) 79680.0 3.59529
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6912.00 0.309524
\(794\) 0 0
\(795\) 36000.0 1.60602
\(796\) 0 0
\(797\) 24276.0 1.07892 0.539461 0.842011i \(-0.318628\pi\)
0.539461 + 0.842011i \(0.318628\pi\)
\(798\) 0 0
\(799\) −22968.0 −1.01696
\(800\) 0 0
\(801\) 28470.0 1.25585
\(802\) 0 0
\(803\) 6320.00 0.277743
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −29000.0 −1.26499
\(808\) 0 0
\(809\) 21526.0 0.935493 0.467747 0.883863i \(-0.345066\pi\)
0.467747 + 0.883863i \(0.345066\pi\)
\(810\) 0 0
\(811\) −12806.0 −0.554475 −0.277238 0.960801i \(-0.589419\pi\)
−0.277238 + 0.960801i \(0.589419\pi\)
\(812\) 0 0
\(813\) −26400.0 −1.13885
\(814\) 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 \(-0.409380\pi\)
0.280860 + 0.959749i \(0.409380\pi\)
\(822\) 0 0
\(823\) −32248.0 −1.36585 −0.682925 0.730488i \(-0.739292\pi\)
−0.682925 + 0.730488i \(0.739292\pi\)
\(824\) 0 0
\(825\) 24400.0 1.02970
\(826\) 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
\(831\) 15220.0 0.635350
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −34144.0 −1.41509
\(836\) 0 0
\(837\) −115920. −4.78707
\(838\) 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
\(843\) 45340.0 1.85242
\(844\) 0 0
\(845\) −16424.0 −0.668642
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −48340.0 −1.95409
\(850\) 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
\(855\) 15184.0 0.607347
\(856\) 0 0
\(857\) −11694.0 −0.466114 −0.233057 0.972463i \(-0.574873\pi\)
−0.233057 + 0.972463i \(0.574873\pi\)
\(858\) 0 0
\(859\) −20506.0 −0.814500 −0.407250 0.913317i \(-0.633512\pi\)
−0.407250 + 0.913317i \(0.633512\pi\)
\(860\) 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
\(867\) 15490.0 0.606768
\(868\) 0 0
\(869\) 37440.0 1.46152
\(870\) 0 0
\(871\) 5712.00 0.222209
\(872\) 0 0
\(873\) −15622.0 −0.605641
\(874\) 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
\(879\) −46560.0 −1.78661
\(880\) 0 0
\(881\) 6198.00 0.237021 0.118511 0.992953i \(-0.462188\pi\)
0.118511 + 0.992953i \(0.462188\pi\)
\(882\) 0 0
\(883\) 31876.0 1.21485 0.607425 0.794377i \(-0.292202\pi\)
0.607425 + 0.794377i \(0.292202\pi\)
\(884\) 0 0
\(885\) −21920.0 −0.832579
\(886\) 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
\(891\) 105160. 3.95398
\(892\) 0 0
\(893\) −10296.0 −0.385826
\(894\) 0 0
\(895\) −18144.0 −0.677639
\(896\) 0 0
\(897\) −7680.00 −0.285873
\(898\) 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 \(-0.746834\pi\)
−0.700039 + 0.714104i \(0.746834\pi\)
\(908\) 0 0
\(909\) −104536. −3.81435
\(910\) 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
\(915\) −46080.0 −1.66487
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −36664.0 −1.31603 −0.658016 0.753004i \(-0.728604\pi\)
−0.658016 + 0.753004i \(0.728604\pi\)
\(920\) 0 0
\(921\) 72380.0 2.58958
\(922\) 0 0
\(923\) 5376.00 0.191715
\(924\) 0 0
\(925\) −1586.00 −0.0563755
\(926\) 0 0
\(927\) 55772.0 1.97604
\(928\) 0 0
\(929\) −45510.0 −1.60725 −0.803625 0.595136i \(-0.797098\pi\)
−0.803625 + 0.595136i \(0.797098\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −10960.0 −0.384581
\(934\) 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
\(939\) −38180.0 −1.32690
\(940\) 0 0
\(941\) 16832.0 0.583111 0.291556 0.956554i \(-0.405827\pi\)
0.291556 + 0.956554i \(0.405827\pi\)
\(942\) 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
\(951\) −19980.0 −0.681279
\(952\) 0 0
\(953\) −24070.0 −0.818157 −0.409079 0.912499i \(-0.634150\pi\)
−0.409079 + 0.912499i \(0.634150\pi\)
\(954\) 0 0
\(955\) 24000.0 0.813217
\(956\) 0 0
\(957\) 24800.0 0.837691
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 33713.0 1.13165
\(962\) 0 0
\(963\) −23652.0 −0.791459
\(964\) 0 0
\(965\) 26224.0 0.874798
\(966\) 0 0
\(967\) 17152.0 0.570394 0.285197 0.958469i \(-0.407941\pi\)
0.285197 + 0.958469i \(0.407941\pi\)
\(968\) 0 0
\(969\) −15080.0 −0.499937
\(970\) 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
\(975\) 7320.00 0.240439
\(976\) 0 0
\(977\) −6822.00 −0.223393 −0.111697 0.993742i \(-0.535628\pi\)
−0.111697 + 0.993742i \(0.535628\pi\)
\(978\) 0 0
\(979\) 15600.0 0.509273
\(980\) 0 0
\(981\) −97382.0 −3.16939
\(982\) 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 \(-0.210704\pi\)
0.788798 + 0.614652i \(0.210704\pi\)
\(992\) 0 0
\(993\) −79360.0 −2.53617
\(994\) 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
\(999\) −11960.0 −0.378776
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 784.4.a.a.1.1 1
4.3 odd 2 196.4.a.d.1.1 1
7.6 odd 2 112.4.a.g.1.1 1
12.11 even 2 1764.4.a.c.1.1 1
21.20 even 2 1008.4.a.o.1.1 1
28.3 even 6 196.4.e.f.177.1 2
28.11 odd 6 196.4.e.a.177.1 2
28.19 even 6 196.4.e.f.165.1 2
28.23 odd 6 196.4.e.a.165.1 2
28.27 even 2 28.4.a.a.1.1 1
56.13 odd 2 448.4.a.a.1.1 1
56.27 even 2 448.4.a.p.1.1 1
84.11 even 6 1764.4.k.m.1549.1 2
84.23 even 6 1764.4.k.m.361.1 2
84.47 odd 6 1764.4.k.d.361.1 2
84.59 odd 6 1764.4.k.d.1549.1 2
84.83 odd 2 252.4.a.d.1.1 1
140.27 odd 4 700.4.e.a.449.2 2
140.83 odd 4 700.4.e.a.449.1 2
140.139 even 2 700.4.a.n.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.4.a.a.1.1 1 28.27 even 2
112.4.a.g.1.1 1 7.6 odd 2
196.4.a.d.1.1 1 4.3 odd 2
196.4.e.a.165.1 2 28.23 odd 6
196.4.e.a.177.1 2 28.11 odd 6
196.4.e.f.165.1 2 28.19 even 6
196.4.e.f.177.1 2 28.3 even 6
252.4.a.d.1.1 1 84.83 odd 2
448.4.a.a.1.1 1 56.13 odd 2
448.4.a.p.1.1 1 56.27 even 2
700.4.a.n.1.1 1 140.139 even 2
700.4.e.a.449.1 2 140.83 odd 4
700.4.e.a.449.2 2 140.27 odd 4
784.4.a.a.1.1 1 1.1 even 1 trivial
1008.4.a.o.1.1 1 21.20 even 2
1764.4.a.c.1.1 1 12.11 even 2
1764.4.k.d.361.1 2 84.47 odd 6
1764.4.k.d.1549.1 2 84.59 odd 6
1764.4.k.m.361.1 2 84.23 even 6
1764.4.k.m.1549.1 2 84.11 even 6