Properties

Label 784.4.a.l.1.1
Level $784$
Weight $4$
Character 784.1
Self dual yes
Analytic conductor $46.257$
Analytic rank $1$
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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 784.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +7.00000 q^{5} -26.0000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +7.00000 q^{5} -26.0000 q^{9} -35.0000 q^{11} +66.0000 q^{13} +7.00000 q^{15} +59.0000 q^{17} -137.000 q^{19} +7.00000 q^{23} -76.0000 q^{25} -53.0000 q^{27} +106.000 q^{29} -75.0000 q^{31} -35.0000 q^{33} +11.0000 q^{37} +66.0000 q^{39} -498.000 q^{41} -260.000 q^{43} -182.000 q^{45} +171.000 q^{47} +59.0000 q^{51} -417.000 q^{53} -245.000 q^{55} -137.000 q^{57} +17.0000 q^{59} +51.0000 q^{61} +462.000 q^{65} -439.000 q^{67} +7.00000 q^{69} +784.000 q^{71} +295.000 q^{73} -76.0000 q^{75} +495.000 q^{79} +649.000 q^{81} -932.000 q^{83} +413.000 q^{85} +106.000 q^{87} -873.000 q^{89} -75.0000 q^{93} -959.000 q^{95} -290.000 q^{97} +910.000 q^{99} +O(q^{100})\)

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
\(3\) 1.00000 0.192450 0.0962250 0.995360i \(-0.469323\pi\)
0.0962250 + 0.995360i \(0.469323\pi\)
\(4\) 0 0
\(5\) 7.00000 0.626099 0.313050 0.949737i \(-0.398649\pi\)
0.313050 + 0.949737i \(0.398649\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −26.0000 −0.962963
\(10\) 0 0
\(11\) −35.0000 −0.959354 −0.479677 0.877445i \(-0.659246\pi\)
−0.479677 + 0.877445i \(0.659246\pi\)
\(12\) 0 0
\(13\) 66.0000 1.40809 0.704043 0.710158i \(-0.251376\pi\)
0.704043 + 0.710158i \(0.251376\pi\)
\(14\) 0 0
\(15\) 7.00000 0.120493
\(16\) 0 0
\(17\) 59.0000 0.841741 0.420871 0.907121i \(-0.361725\pi\)
0.420871 + 0.907121i \(0.361725\pi\)
\(18\) 0 0
\(19\) −137.000 −1.65421 −0.827104 0.562049i \(-0.810013\pi\)
−0.827104 + 0.562049i \(0.810013\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.00000 0.0634609 0.0317305 0.999496i \(-0.489898\pi\)
0.0317305 + 0.999496i \(0.489898\pi\)
\(24\) 0 0
\(25\) −76.0000 −0.608000
\(26\) 0 0
\(27\) −53.0000 −0.377772
\(28\) 0 0
\(29\) 106.000 0.678748 0.339374 0.940651i \(-0.389785\pi\)
0.339374 + 0.940651i \(0.389785\pi\)
\(30\) 0 0
\(31\) −75.0000 −0.434529 −0.217264 0.976113i \(-0.569713\pi\)
−0.217264 + 0.976113i \(0.569713\pi\)
\(32\) 0 0
\(33\) −35.0000 −0.184628
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 11.0000 0.0488754 0.0244377 0.999701i \(-0.492220\pi\)
0.0244377 + 0.999701i \(0.492220\pi\)
\(38\) 0 0
\(39\) 66.0000 0.270986
\(40\) 0 0
\(41\) −498.000 −1.89694 −0.948470 0.316867i \(-0.897369\pi\)
−0.948470 + 0.316867i \(0.897369\pi\)
\(42\) 0 0
\(43\) −260.000 −0.922084 −0.461042 0.887378i \(-0.652524\pi\)
−0.461042 + 0.887378i \(0.652524\pi\)
\(44\) 0 0
\(45\) −182.000 −0.602910
\(46\) 0 0
\(47\) 171.000 0.530700 0.265350 0.964152i \(-0.414512\pi\)
0.265350 + 0.964152i \(0.414512\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 59.0000 0.161993
\(52\) 0 0
\(53\) −417.000 −1.08074 −0.540371 0.841427i \(-0.681716\pi\)
−0.540371 + 0.841427i \(0.681716\pi\)
\(54\) 0 0
\(55\) −245.000 −0.600651
\(56\) 0 0
\(57\) −137.000 −0.318353
\(58\) 0 0
\(59\) 17.0000 0.0375121 0.0187560 0.999824i \(-0.494029\pi\)
0.0187560 + 0.999824i \(0.494029\pi\)
\(60\) 0 0
\(61\) 51.0000 0.107047 0.0535236 0.998567i \(-0.482955\pi\)
0.0535236 + 0.998567i \(0.482955\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 462.000 0.881601
\(66\) 0 0
\(67\) −439.000 −0.800483 −0.400242 0.916410i \(-0.631074\pi\)
−0.400242 + 0.916410i \(0.631074\pi\)
\(68\) 0 0
\(69\) 7.00000 0.0122131
\(70\) 0 0
\(71\) 784.000 1.31047 0.655237 0.755423i \(-0.272569\pi\)
0.655237 + 0.755423i \(0.272569\pi\)
\(72\) 0 0
\(73\) 295.000 0.472974 0.236487 0.971635i \(-0.424004\pi\)
0.236487 + 0.971635i \(0.424004\pi\)
\(74\) 0 0
\(75\) −76.0000 −0.117010
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 495.000 0.704960 0.352480 0.935819i \(-0.385338\pi\)
0.352480 + 0.935819i \(0.385338\pi\)
\(80\) 0 0
\(81\) 649.000 0.890261
\(82\) 0 0
\(83\) −932.000 −1.23253 −0.616267 0.787537i \(-0.711356\pi\)
−0.616267 + 0.787537i \(0.711356\pi\)
\(84\) 0 0
\(85\) 413.000 0.527013
\(86\) 0 0
\(87\) 106.000 0.130625
\(88\) 0 0
\(89\) −873.000 −1.03975 −0.519875 0.854242i \(-0.674022\pi\)
−0.519875 + 0.854242i \(0.674022\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −75.0000 −0.0836251
\(94\) 0 0
\(95\) −959.000 −1.03570
\(96\) 0 0
\(97\) −290.000 −0.303557 −0.151779 0.988415i \(-0.548500\pi\)
−0.151779 + 0.988415i \(0.548500\pi\)
\(98\) 0 0
\(99\) 910.000 0.923823
\(100\) 0 0
\(101\) −1085.00 −1.06893 −0.534463 0.845192i \(-0.679486\pi\)
−0.534463 + 0.845192i \(0.679486\pi\)
\(102\) 0 0
\(103\) −1553.00 −1.48565 −0.742823 0.669487i \(-0.766514\pi\)
−0.742823 + 0.669487i \(0.766514\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −129.000 −0.116550 −0.0582752 0.998301i \(-0.518560\pi\)
−0.0582752 + 0.998301i \(0.518560\pi\)
\(108\) 0 0
\(109\) −965.000 −0.847984 −0.423992 0.905666i \(-0.639372\pi\)
−0.423992 + 0.905666i \(0.639372\pi\)
\(110\) 0 0
\(111\) 11.0000 0.00940607
\(112\) 0 0
\(113\) −50.0000 −0.0416248 −0.0208124 0.999783i \(-0.506625\pi\)
−0.0208124 + 0.999783i \(0.506625\pi\)
\(114\) 0 0
\(115\) 49.0000 0.0397328
\(116\) 0 0
\(117\) −1716.00 −1.35593
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −106.000 −0.0796394
\(122\) 0 0
\(123\) −498.000 −0.365066
\(124\) 0 0
\(125\) −1407.00 −1.00677
\(126\) 0 0
\(127\) −936.000 −0.653989 −0.326994 0.945026i \(-0.606036\pi\)
−0.326994 + 0.945026i \(0.606036\pi\)
\(128\) 0 0
\(129\) −260.000 −0.177455
\(130\) 0 0
\(131\) 755.000 0.503547 0.251773 0.967786i \(-0.418986\pi\)
0.251773 + 0.967786i \(0.418986\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −371.000 −0.236523
\(136\) 0 0
\(137\) −2357.00 −1.46987 −0.734935 0.678138i \(-0.762787\pi\)
−0.734935 + 0.678138i \(0.762787\pi\)
\(138\) 0 0
\(139\) −28.0000 −0.0170858 −0.00854291 0.999964i \(-0.502719\pi\)
−0.00854291 + 0.999964i \(0.502719\pi\)
\(140\) 0 0
\(141\) 171.000 0.102133
\(142\) 0 0
\(143\) −2310.00 −1.35085
\(144\) 0 0
\(145\) 742.000 0.424964
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2295.00 1.26184 0.630919 0.775849i \(-0.282678\pi\)
0.630919 + 0.775849i \(0.282678\pi\)
\(150\) 0 0
\(151\) 1109.00 0.597676 0.298838 0.954304i \(-0.403401\pi\)
0.298838 + 0.954304i \(0.403401\pi\)
\(152\) 0 0
\(153\) −1534.00 −0.810566
\(154\) 0 0
\(155\) −525.000 −0.272058
\(156\) 0 0
\(157\) 1559.00 0.792495 0.396248 0.918144i \(-0.370312\pi\)
0.396248 + 0.918144i \(0.370312\pi\)
\(158\) 0 0
\(159\) −417.000 −0.207989
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2251.00 1.08167 0.540834 0.841129i \(-0.318109\pi\)
0.540834 + 0.841129i \(0.318109\pi\)
\(164\) 0 0
\(165\) −245.000 −0.115595
\(166\) 0 0
\(167\) −2788.00 −1.29187 −0.645934 0.763393i \(-0.723532\pi\)
−0.645934 + 0.763393i \(0.723532\pi\)
\(168\) 0 0
\(169\) 2159.00 0.982704
\(170\) 0 0
\(171\) 3562.00 1.59294
\(172\) 0 0
\(173\) 1579.00 0.693926 0.346963 0.937879i \(-0.387213\pi\)
0.346963 + 0.937879i \(0.387213\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 17.0000 0.00721920
\(178\) 0 0
\(179\) −2451.00 −1.02344 −0.511722 0.859151i \(-0.670992\pi\)
−0.511722 + 0.859151i \(0.670992\pi\)
\(180\) 0 0
\(181\) −1170.00 −0.480472 −0.240236 0.970715i \(-0.577225\pi\)
−0.240236 + 0.970715i \(0.577225\pi\)
\(182\) 0 0
\(183\) 51.0000 0.0206012
\(184\) 0 0
\(185\) 77.0000 0.0306008
\(186\) 0 0
\(187\) −2065.00 −0.807528
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1275.00 0.483014 0.241507 0.970399i \(-0.422358\pi\)
0.241507 + 0.970399i \(0.422358\pi\)
\(192\) 0 0
\(193\) 35.0000 0.0130537 0.00652683 0.999979i \(-0.497922\pi\)
0.00652683 + 0.999979i \(0.497922\pi\)
\(194\) 0 0
\(195\) 462.000 0.169664
\(196\) 0 0
\(197\) −2734.00 −0.988779 −0.494389 0.869241i \(-0.664608\pi\)
−0.494389 + 0.869241i \(0.664608\pi\)
\(198\) 0 0
\(199\) −2243.00 −0.799005 −0.399503 0.916732i \(-0.630817\pi\)
−0.399503 + 0.916732i \(0.630817\pi\)
\(200\) 0 0
\(201\) −439.000 −0.154053
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −3486.00 −1.18767
\(206\) 0 0
\(207\) −182.000 −0.0611105
\(208\) 0 0
\(209\) 4795.00 1.58697
\(210\) 0 0
\(211\) −1172.00 −0.382388 −0.191194 0.981552i \(-0.561236\pi\)
−0.191194 + 0.981552i \(0.561236\pi\)
\(212\) 0 0
\(213\) 784.000 0.252201
\(214\) 0 0
\(215\) −1820.00 −0.577316
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 295.000 0.0910240
\(220\) 0 0
\(221\) 3894.00 1.18524
\(222\) 0 0
\(223\) −2024.00 −0.607790 −0.303895 0.952706i \(-0.598287\pi\)
−0.303895 + 0.952706i \(0.598287\pi\)
\(224\) 0 0
\(225\) 1976.00 0.585481
\(226\) 0 0
\(227\) −2571.00 −0.751732 −0.375866 0.926674i \(-0.622655\pi\)
−0.375866 + 0.926674i \(0.622655\pi\)
\(228\) 0 0
\(229\) 895.000 0.258268 0.129134 0.991627i \(-0.458780\pi\)
0.129134 + 0.991627i \(0.458780\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1787.00 0.502447 0.251224 0.967929i \(-0.419167\pi\)
0.251224 + 0.967929i \(0.419167\pi\)
\(234\) 0 0
\(235\) 1197.00 0.332271
\(236\) 0 0
\(237\) 495.000 0.135670
\(238\) 0 0
\(239\) 5100.00 1.38030 0.690150 0.723667i \(-0.257545\pi\)
0.690150 + 0.723667i \(0.257545\pi\)
\(240\) 0 0
\(241\) −4177.00 −1.11645 −0.558225 0.829690i \(-0.688517\pi\)
−0.558225 + 0.829690i \(0.688517\pi\)
\(242\) 0 0
\(243\) 2080.00 0.549103
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −9042.00 −2.32927
\(248\) 0 0
\(249\) −932.000 −0.237201
\(250\) 0 0
\(251\) 4680.00 1.17689 0.588444 0.808538i \(-0.299741\pi\)
0.588444 + 0.808538i \(0.299741\pi\)
\(252\) 0 0
\(253\) −245.000 −0.0608815
\(254\) 0 0
\(255\) 413.000 0.101424
\(256\) 0 0
\(257\) −1749.00 −0.424512 −0.212256 0.977214i \(-0.568081\pi\)
−0.212256 + 0.977214i \(0.568081\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −2756.00 −0.653610
\(262\) 0 0
\(263\) 4473.00 1.04873 0.524367 0.851492i \(-0.324302\pi\)
0.524367 + 0.851492i \(0.324302\pi\)
\(264\) 0 0
\(265\) −2919.00 −0.676652
\(266\) 0 0
\(267\) −873.000 −0.200100
\(268\) 0 0
\(269\) 1975.00 0.447650 0.223825 0.974629i \(-0.428146\pi\)
0.223825 + 0.974629i \(0.428146\pi\)
\(270\) 0 0
\(271\) 8439.00 1.89163 0.945817 0.324701i \(-0.105264\pi\)
0.945817 + 0.324701i \(0.105264\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2660.00 0.583287
\(276\) 0 0
\(277\) 527.000 0.114312 0.0571559 0.998365i \(-0.481797\pi\)
0.0571559 + 0.998365i \(0.481797\pi\)
\(278\) 0 0
\(279\) 1950.00 0.418435
\(280\) 0 0
\(281\) −202.000 −0.0428837 −0.0214418 0.999770i \(-0.506826\pi\)
−0.0214418 + 0.999770i \(0.506826\pi\)
\(282\) 0 0
\(283\) 7949.00 1.66968 0.834839 0.550494i \(-0.185561\pi\)
0.834839 + 0.550494i \(0.185561\pi\)
\(284\) 0 0
\(285\) −959.000 −0.199320
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1432.00 −0.291472
\(290\) 0 0
\(291\) −290.000 −0.0584196
\(292\) 0 0
\(293\) 318.000 0.0634053 0.0317027 0.999497i \(-0.489907\pi\)
0.0317027 + 0.999497i \(0.489907\pi\)
\(294\) 0 0
\(295\) 119.000 0.0234863
\(296\) 0 0
\(297\) 1855.00 0.362418
\(298\) 0 0
\(299\) 462.000 0.0893584
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −1085.00 −0.205715
\(304\) 0 0
\(305\) 357.000 0.0670222
\(306\) 0 0
\(307\) 8132.00 1.51178 0.755892 0.654696i \(-0.227203\pi\)
0.755892 + 0.654696i \(0.227203\pi\)
\(308\) 0 0
\(309\) −1553.00 −0.285913
\(310\) 0 0
\(311\) 929.000 0.169385 0.0846925 0.996407i \(-0.473009\pi\)
0.0846925 + 0.996407i \(0.473009\pi\)
\(312\) 0 0
\(313\) −209.000 −0.0377424 −0.0188712 0.999822i \(-0.506007\pi\)
−0.0188712 + 0.999822i \(0.506007\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7131.00 1.26346 0.631730 0.775188i \(-0.282345\pi\)
0.631730 + 0.775188i \(0.282345\pi\)
\(318\) 0 0
\(319\) −3710.00 −0.651160
\(320\) 0 0
\(321\) −129.000 −0.0224301
\(322\) 0 0
\(323\) −8083.00 −1.39242
\(324\) 0 0
\(325\) −5016.00 −0.856116
\(326\) 0 0
\(327\) −965.000 −0.163195
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 6571.00 1.09116 0.545581 0.838058i \(-0.316309\pi\)
0.545581 + 0.838058i \(0.316309\pi\)
\(332\) 0 0
\(333\) −286.000 −0.0470652
\(334\) 0 0
\(335\) −3073.00 −0.501182
\(336\) 0 0
\(337\) −11466.0 −1.85339 −0.926696 0.375813i \(-0.877364\pi\)
−0.926696 + 0.375813i \(0.877364\pi\)
\(338\) 0 0
\(339\) −50.0000 −0.00801070
\(340\) 0 0
\(341\) 2625.00 0.416867
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 49.0000 0.00764658
\(346\) 0 0
\(347\) 9777.00 1.51256 0.756278 0.654251i \(-0.227016\pi\)
0.756278 + 0.654251i \(0.227016\pi\)
\(348\) 0 0
\(349\) 11914.0 1.82734 0.913670 0.406456i \(-0.133236\pi\)
0.913670 + 0.406456i \(0.133236\pi\)
\(350\) 0 0
\(351\) −3498.00 −0.531936
\(352\) 0 0
\(353\) 9123.00 1.37555 0.687774 0.725925i \(-0.258588\pi\)
0.687774 + 0.725925i \(0.258588\pi\)
\(354\) 0 0
\(355\) 5488.00 0.820487
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8149.00 −1.19802 −0.599008 0.800743i \(-0.704438\pi\)
−0.599008 + 0.800743i \(0.704438\pi\)
\(360\) 0 0
\(361\) 11910.0 1.73640
\(362\) 0 0
\(363\) −106.000 −0.0153266
\(364\) 0 0
\(365\) 2065.00 0.296129
\(366\) 0 0
\(367\) −9671.00 −1.37554 −0.687769 0.725930i \(-0.741410\pi\)
−0.687769 + 0.725930i \(0.741410\pi\)
\(368\) 0 0
\(369\) 12948.0 1.82668
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −4109.00 −0.570391 −0.285196 0.958469i \(-0.592059\pi\)
−0.285196 + 0.958469i \(0.592059\pi\)
\(374\) 0 0
\(375\) −1407.00 −0.193752
\(376\) 0 0
\(377\) 6996.00 0.955736
\(378\) 0 0
\(379\) 3488.00 0.472735 0.236367 0.971664i \(-0.424043\pi\)
0.236367 + 0.971664i \(0.424043\pi\)
\(380\) 0 0
\(381\) −936.000 −0.125860
\(382\) 0 0
\(383\) −8717.00 −1.16297 −0.581485 0.813557i \(-0.697528\pi\)
−0.581485 + 0.813557i \(0.697528\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 6760.00 0.887933
\(388\) 0 0
\(389\) 163.000 0.0212453 0.0106227 0.999944i \(-0.496619\pi\)
0.0106227 + 0.999944i \(0.496619\pi\)
\(390\) 0 0
\(391\) 413.000 0.0534177
\(392\) 0 0
\(393\) 755.000 0.0969077
\(394\) 0 0
\(395\) 3465.00 0.441375
\(396\) 0 0
\(397\) 999.000 0.126293 0.0631466 0.998004i \(-0.479886\pi\)
0.0631466 + 0.998004i \(0.479886\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −14757.0 −1.83773 −0.918865 0.394573i \(-0.870893\pi\)
−0.918865 + 0.394573i \(0.870893\pi\)
\(402\) 0 0
\(403\) −4950.00 −0.611854
\(404\) 0 0
\(405\) 4543.00 0.557391
\(406\) 0 0
\(407\) −385.000 −0.0468888
\(408\) 0 0
\(409\) −133.000 −0.0160793 −0.00803964 0.999968i \(-0.502559\pi\)
−0.00803964 + 0.999968i \(0.502559\pi\)
\(410\) 0 0
\(411\) −2357.00 −0.282876
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −6524.00 −0.771688
\(416\) 0 0
\(417\) −28.0000 −0.00328817
\(418\) 0 0
\(419\) 6420.00 0.748538 0.374269 0.927320i \(-0.377894\pi\)
0.374269 + 0.927320i \(0.377894\pi\)
\(420\) 0 0
\(421\) 10266.0 1.18844 0.594221 0.804302i \(-0.297460\pi\)
0.594221 + 0.804302i \(0.297460\pi\)
\(422\) 0 0
\(423\) −4446.00 −0.511045
\(424\) 0 0
\(425\) −4484.00 −0.511779
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −2310.00 −0.259972
\(430\) 0 0
\(431\) 15213.0 1.70020 0.850098 0.526625i \(-0.176543\pi\)
0.850098 + 0.526625i \(0.176543\pi\)
\(432\) 0 0
\(433\) −1378.00 −0.152939 −0.0764693 0.997072i \(-0.524365\pi\)
−0.0764693 + 0.997072i \(0.524365\pi\)
\(434\) 0 0
\(435\) 742.000 0.0817843
\(436\) 0 0
\(437\) −959.000 −0.104978
\(438\) 0 0
\(439\) 2763.00 0.300389 0.150195 0.988656i \(-0.452010\pi\)
0.150195 + 0.988656i \(0.452010\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5849.00 −0.627301 −0.313651 0.949538i \(-0.601552\pi\)
−0.313651 + 0.949538i \(0.601552\pi\)
\(444\) 0 0
\(445\) −6111.00 −0.650987
\(446\) 0 0
\(447\) 2295.00 0.242841
\(448\) 0 0
\(449\) 4582.00 0.481599 0.240799 0.970575i \(-0.422590\pi\)
0.240799 + 0.970575i \(0.422590\pi\)
\(450\) 0 0
\(451\) 17430.0 1.81984
\(452\) 0 0
\(453\) 1109.00 0.115023
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 11551.0 1.18235 0.591174 0.806544i \(-0.298665\pi\)
0.591174 + 0.806544i \(0.298665\pi\)
\(458\) 0 0
\(459\) −3127.00 −0.317987
\(460\) 0 0
\(461\) −9494.00 −0.959175 −0.479587 0.877494i \(-0.659214\pi\)
−0.479587 + 0.877494i \(0.659214\pi\)
\(462\) 0 0
\(463\) 10160.0 1.01982 0.509908 0.860229i \(-0.329679\pi\)
0.509908 + 0.860229i \(0.329679\pi\)
\(464\) 0 0
\(465\) −525.000 −0.0523576
\(466\) 0 0
\(467\) 1307.00 0.129509 0.0647545 0.997901i \(-0.479374\pi\)
0.0647545 + 0.997901i \(0.479374\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 1559.00 0.152516
\(472\) 0 0
\(473\) 9100.00 0.884606
\(474\) 0 0
\(475\) 10412.0 1.00576
\(476\) 0 0
\(477\) 10842.0 1.04072
\(478\) 0 0
\(479\) −18287.0 −1.74437 −0.872186 0.489174i \(-0.837298\pi\)
−0.872186 + 0.489174i \(0.837298\pi\)
\(480\) 0 0
\(481\) 726.000 0.0688207
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2030.00 −0.190057
\(486\) 0 0
\(487\) 14953.0 1.39135 0.695673 0.718359i \(-0.255106\pi\)
0.695673 + 0.718359i \(0.255106\pi\)
\(488\) 0 0
\(489\) 2251.00 0.208167
\(490\) 0 0
\(491\) −14352.0 −1.31914 −0.659569 0.751644i \(-0.729261\pi\)
−0.659569 + 0.751644i \(0.729261\pi\)
\(492\) 0 0
\(493\) 6254.00 0.571331
\(494\) 0 0
\(495\) 6370.00 0.578404
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 5531.00 0.496196 0.248098 0.968735i \(-0.420195\pi\)
0.248098 + 0.968735i \(0.420195\pi\)
\(500\) 0 0
\(501\) −2788.00 −0.248620
\(502\) 0 0
\(503\) −8400.00 −0.744607 −0.372304 0.928111i \(-0.621432\pi\)
−0.372304 + 0.928111i \(0.621432\pi\)
\(504\) 0 0
\(505\) −7595.00 −0.669254
\(506\) 0 0
\(507\) 2159.00 0.189121
\(508\) 0 0
\(509\) −2385.00 −0.207688 −0.103844 0.994594i \(-0.533114\pi\)
−0.103844 + 0.994594i \(0.533114\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 7261.00 0.624914
\(514\) 0 0
\(515\) −10871.0 −0.930162
\(516\) 0 0
\(517\) −5985.00 −0.509130
\(518\) 0 0
\(519\) 1579.00 0.133546
\(520\) 0 0
\(521\) −9153.00 −0.769674 −0.384837 0.922985i \(-0.625742\pi\)
−0.384837 + 0.922985i \(0.625742\pi\)
\(522\) 0 0
\(523\) 13807.0 1.15437 0.577187 0.816612i \(-0.304150\pi\)
0.577187 + 0.816612i \(0.304150\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4425.00 −0.365761
\(528\) 0 0
\(529\) −12118.0 −0.995973
\(530\) 0 0
\(531\) −442.000 −0.0361227
\(532\) 0 0
\(533\) −32868.0 −2.67105
\(534\) 0 0
\(535\) −903.000 −0.0729721
\(536\) 0 0
\(537\) −2451.00 −0.196962
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 8175.00 0.649669 0.324834 0.945771i \(-0.394691\pi\)
0.324834 + 0.945771i \(0.394691\pi\)
\(542\) 0 0
\(543\) −1170.00 −0.0924669
\(544\) 0 0
\(545\) −6755.00 −0.530922
\(546\) 0 0
\(547\) −4656.00 −0.363942 −0.181971 0.983304i \(-0.558248\pi\)
−0.181971 + 0.983304i \(0.558248\pi\)
\(548\) 0 0
\(549\) −1326.00 −0.103083
\(550\) 0 0
\(551\) −14522.0 −1.12279
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 77.0000 0.00588913
\(556\) 0 0
\(557\) 7003.00 0.532723 0.266361 0.963873i \(-0.414179\pi\)
0.266361 + 0.963873i \(0.414179\pi\)
\(558\) 0 0
\(559\) −17160.0 −1.29837
\(560\) 0 0
\(561\) −2065.00 −0.155409
\(562\) 0 0
\(563\) 19753.0 1.47867 0.739334 0.673339i \(-0.235141\pi\)
0.739334 + 0.673339i \(0.235141\pi\)
\(564\) 0 0
\(565\) −350.000 −0.0260613
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6897.00 −0.508150 −0.254075 0.967185i \(-0.581771\pi\)
−0.254075 + 0.967185i \(0.581771\pi\)
\(570\) 0 0
\(571\) −24915.0 −1.82603 −0.913013 0.407932i \(-0.866250\pi\)
−0.913013 + 0.407932i \(0.866250\pi\)
\(572\) 0 0
\(573\) 1275.00 0.0929562
\(574\) 0 0
\(575\) −532.000 −0.0385842
\(576\) 0 0
\(577\) 127.000 0.00916305 0.00458152 0.999990i \(-0.498542\pi\)
0.00458152 + 0.999990i \(0.498542\pi\)
\(578\) 0 0
\(579\) 35.0000 0.00251218
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 14595.0 1.03681
\(584\) 0 0
\(585\) −12012.0 −0.848949
\(586\) 0 0
\(587\) −9044.00 −0.635921 −0.317961 0.948104i \(-0.602998\pi\)
−0.317961 + 0.948104i \(0.602998\pi\)
\(588\) 0 0
\(589\) 10275.0 0.718801
\(590\) 0 0
\(591\) −2734.00 −0.190291
\(592\) 0 0
\(593\) −10701.0 −0.741041 −0.370521 0.928824i \(-0.620821\pi\)
−0.370521 + 0.928824i \(0.620821\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2243.00 −0.153769
\(598\) 0 0
\(599\) −20799.0 −1.41874 −0.709369 0.704837i \(-0.751020\pi\)
−0.709369 + 0.704837i \(0.751020\pi\)
\(600\) 0 0
\(601\) −1402.00 −0.0951560 −0.0475780 0.998868i \(-0.515150\pi\)
−0.0475780 + 0.998868i \(0.515150\pi\)
\(602\) 0 0
\(603\) 11414.0 0.770836
\(604\) 0 0
\(605\) −742.000 −0.0498621
\(606\) 0 0
\(607\) −6525.00 −0.436312 −0.218156 0.975914i \(-0.570004\pi\)
−0.218156 + 0.975914i \(0.570004\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 11286.0 0.747271
\(612\) 0 0
\(613\) 15051.0 0.991687 0.495844 0.868412i \(-0.334859\pi\)
0.495844 + 0.868412i \(0.334859\pi\)
\(614\) 0 0
\(615\) −3486.00 −0.228568
\(616\) 0 0
\(617\) 11150.0 0.727524 0.363762 0.931492i \(-0.381492\pi\)
0.363762 + 0.931492i \(0.381492\pi\)
\(618\) 0 0
\(619\) −3415.00 −0.221745 −0.110873 0.993835i \(-0.535365\pi\)
−0.110873 + 0.993835i \(0.535365\pi\)
\(620\) 0 0
\(621\) −371.000 −0.0239738
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −349.000 −0.0223360
\(626\) 0 0
\(627\) 4795.00 0.305413
\(628\) 0 0
\(629\) 649.000 0.0411404
\(630\) 0 0
\(631\) 21184.0 1.33648 0.668242 0.743944i \(-0.267047\pi\)
0.668242 + 0.743944i \(0.267047\pi\)
\(632\) 0 0
\(633\) −1172.00 −0.0735905
\(634\) 0 0
\(635\) −6552.00 −0.409462
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −20384.0 −1.26194
\(640\) 0 0
\(641\) −10705.0 −0.659629 −0.329814 0.944046i \(-0.606986\pi\)
−0.329814 + 0.944046i \(0.606986\pi\)
\(642\) 0 0
\(643\) −6860.00 −0.420734 −0.210367 0.977622i \(-0.567466\pi\)
−0.210367 + 0.977622i \(0.567466\pi\)
\(644\) 0 0
\(645\) −1820.00 −0.111105
\(646\) 0 0
\(647\) −14463.0 −0.878824 −0.439412 0.898286i \(-0.644813\pi\)
−0.439412 + 0.898286i \(0.644813\pi\)
\(648\) 0 0
\(649\) −595.000 −0.0359874
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5979.00 0.358310 0.179155 0.983821i \(-0.442664\pi\)
0.179155 + 0.983821i \(0.442664\pi\)
\(654\) 0 0
\(655\) 5285.00 0.315270
\(656\) 0 0
\(657\) −7670.00 −0.455457
\(658\) 0 0
\(659\) 6940.00 0.410234 0.205117 0.978737i \(-0.434243\pi\)
0.205117 + 0.978737i \(0.434243\pi\)
\(660\) 0 0
\(661\) 13399.0 0.788443 0.394221 0.919015i \(-0.371014\pi\)
0.394221 + 0.919015i \(0.371014\pi\)
\(662\) 0 0
\(663\) 3894.00 0.228100
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 742.000 0.0430740
\(668\) 0 0
\(669\) −2024.00 −0.116969
\(670\) 0 0
\(671\) −1785.00 −0.102696
\(672\) 0 0
\(673\) 29510.0 1.69023 0.845117 0.534582i \(-0.179531\pi\)
0.845117 + 0.534582i \(0.179531\pi\)
\(674\) 0 0
\(675\) 4028.00 0.229686
\(676\) 0 0
\(677\) −26001.0 −1.47607 −0.738035 0.674762i \(-0.764246\pi\)
−0.738035 + 0.674762i \(0.764246\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −2571.00 −0.144671
\(682\) 0 0
\(683\) 8805.00 0.493285 0.246643 0.969106i \(-0.420673\pi\)
0.246643 + 0.969106i \(0.420673\pi\)
\(684\) 0 0
\(685\) −16499.0 −0.920284
\(686\) 0 0
\(687\) 895.000 0.0497036
\(688\) 0 0
\(689\) −27522.0 −1.52178
\(690\) 0 0
\(691\) −28685.0 −1.57920 −0.789601 0.613620i \(-0.789713\pi\)
−0.789601 + 0.613620i \(0.789713\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −196.000 −0.0106974
\(696\) 0 0
\(697\) −29382.0 −1.59673
\(698\) 0 0
\(699\) 1787.00 0.0966961
\(700\) 0 0
\(701\) −3146.00 −0.169505 −0.0847523 0.996402i \(-0.527010\pi\)
−0.0847523 + 0.996402i \(0.527010\pi\)
\(702\) 0 0
\(703\) −1507.00 −0.0808500
\(704\) 0 0
\(705\) 1197.00 0.0639456
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1259.00 0.0666893 0.0333447 0.999444i \(-0.489384\pi\)
0.0333447 + 0.999444i \(0.489384\pi\)
\(710\) 0 0
\(711\) −12870.0 −0.678851
\(712\) 0 0
\(713\) −525.000 −0.0275756
\(714\) 0 0
\(715\) −16170.0 −0.845767
\(716\) 0 0
\(717\) 5100.00 0.265639
\(718\) 0 0
\(719\) −16425.0 −0.851946 −0.425973 0.904736i \(-0.640068\pi\)
−0.425973 + 0.904736i \(0.640068\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −4177.00 −0.214861
\(724\) 0 0
\(725\) −8056.00 −0.412679
\(726\) 0 0
\(727\) 6032.00 0.307723 0.153861 0.988092i \(-0.450829\pi\)
0.153861 + 0.988092i \(0.450829\pi\)
\(728\) 0 0
\(729\) −15443.0 −0.784586
\(730\) 0 0
\(731\) −15340.0 −0.776156
\(732\) 0 0
\(733\) 15243.0 0.768094 0.384047 0.923314i \(-0.374530\pi\)
0.384047 + 0.923314i \(0.374530\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 15365.0 0.767947
\(738\) 0 0
\(739\) 10053.0 0.500414 0.250207 0.968192i \(-0.419501\pi\)
0.250207 + 0.968192i \(0.419501\pi\)
\(740\) 0 0
\(741\) −9042.00 −0.448267
\(742\) 0 0
\(743\) −24384.0 −1.20399 −0.601993 0.798501i \(-0.705627\pi\)
−0.601993 + 0.798501i \(0.705627\pi\)
\(744\) 0 0
\(745\) 16065.0 0.790035
\(746\) 0 0
\(747\) 24232.0 1.18688
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −11589.0 −0.563101 −0.281550 0.959546i \(-0.590849\pi\)
−0.281550 + 0.959546i \(0.590849\pi\)
\(752\) 0 0
\(753\) 4680.00 0.226492
\(754\) 0 0
\(755\) 7763.00 0.374205
\(756\) 0 0
\(757\) 14562.0 0.699161 0.349581 0.936906i \(-0.386324\pi\)
0.349581 + 0.936906i \(0.386324\pi\)
\(758\) 0 0
\(759\) −245.000 −0.0117166
\(760\) 0 0
\(761\) −22765.0 −1.08440 −0.542201 0.840249i \(-0.682409\pi\)
−0.542201 + 0.840249i \(0.682409\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −10738.0 −0.507494
\(766\) 0 0
\(767\) 1122.00 0.0528202
\(768\) 0 0
\(769\) 3766.00 0.176600 0.0883000 0.996094i \(-0.471857\pi\)
0.0883000 + 0.996094i \(0.471857\pi\)
\(770\) 0 0
\(771\) −1749.00 −0.0816974
\(772\) 0 0
\(773\) −26861.0 −1.24984 −0.624918 0.780691i \(-0.714868\pi\)
−0.624918 + 0.780691i \(0.714868\pi\)
\(774\) 0 0
\(775\) 5700.00 0.264194
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 68226.0 3.13793
\(780\) 0 0
\(781\) −27440.0 −1.25721
\(782\) 0 0
\(783\) −5618.00 −0.256412
\(784\) 0 0
\(785\) 10913.0 0.496180
\(786\) 0 0
\(787\) 2097.00 0.0949809 0.0474905 0.998872i \(-0.484878\pi\)
0.0474905 + 0.998872i \(0.484878\pi\)
\(788\) 0 0
\(789\) 4473.00 0.201829
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 3366.00 0.150732
\(794\) 0 0
\(795\) −2919.00 −0.130222
\(796\) 0 0
\(797\) −35334.0 −1.57038 −0.785191 0.619254i \(-0.787435\pi\)
−0.785191 + 0.619254i \(0.787435\pi\)
\(798\) 0 0
\(799\) 10089.0 0.446712
\(800\) 0 0
\(801\) 22698.0 1.00124
\(802\) 0 0
\(803\) −10325.0 −0.453750
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1975.00 0.0861503
\(808\) 0 0
\(809\) 42535.0 1.84852 0.924259 0.381766i \(-0.124684\pi\)
0.924259 + 0.381766i \(0.124684\pi\)
\(810\) 0 0
\(811\) −30676.0 −1.32821 −0.664106 0.747638i \(-0.731188\pi\)
−0.664106 + 0.747638i \(0.731188\pi\)
\(812\) 0 0
\(813\) 8439.00 0.364045
\(814\) 0 0
\(815\) 15757.0 0.677231
\(816\) 0 0
\(817\) 35620.0 1.52532
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 37343.0 1.58743 0.793715 0.608290i \(-0.208144\pi\)
0.793715 + 0.608290i \(0.208144\pi\)
\(822\) 0 0
\(823\) −2815.00 −0.119228 −0.0596141 0.998222i \(-0.518987\pi\)
−0.0596141 + 0.998222i \(0.518987\pi\)
\(824\) 0 0
\(825\) 2660.00 0.112254
\(826\) 0 0
\(827\) 9276.00 0.390034 0.195017 0.980800i \(-0.437524\pi\)
0.195017 + 0.980800i \(0.437524\pi\)
\(828\) 0 0
\(829\) 18571.0 0.778043 0.389021 0.921229i \(-0.372813\pi\)
0.389021 + 0.921229i \(0.372813\pi\)
\(830\) 0 0
\(831\) 527.000 0.0219993
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −19516.0 −0.808837
\(836\) 0 0
\(837\) 3975.00 0.164153
\(838\) 0 0
\(839\) −29048.0 −1.19529 −0.597645 0.801761i \(-0.703897\pi\)
−0.597645 + 0.801761i \(0.703897\pi\)
\(840\) 0 0
\(841\) −13153.0 −0.539301
\(842\) 0 0
\(843\) −202.000 −0.00825297
\(844\) 0 0
\(845\) 15113.0 0.615270
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 7949.00 0.321330
\(850\) 0 0
\(851\) 77.0000 0.00310168
\(852\) 0 0
\(853\) 32090.0 1.28809 0.644045 0.764988i \(-0.277255\pi\)
0.644045 + 0.764988i \(0.277255\pi\)
\(854\) 0 0
\(855\) 24934.0 0.997339
\(856\) 0 0
\(857\) −24537.0 −0.978026 −0.489013 0.872277i \(-0.662643\pi\)
−0.489013 + 0.872277i \(0.662643\pi\)
\(858\) 0 0
\(859\) −20825.0 −0.827171 −0.413585 0.910465i \(-0.635724\pi\)
−0.413585 + 0.910465i \(0.635724\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 22847.0 0.901183 0.450591 0.892730i \(-0.351213\pi\)
0.450591 + 0.892730i \(0.351213\pi\)
\(864\) 0 0
\(865\) 11053.0 0.434466
\(866\) 0 0
\(867\) −1432.00 −0.0560937
\(868\) 0 0
\(869\) −17325.0 −0.676307
\(870\) 0 0
\(871\) −28974.0 −1.12715
\(872\) 0 0
\(873\) 7540.00 0.292314
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −42737.0 −1.64553 −0.822763 0.568385i \(-0.807568\pi\)
−0.822763 + 0.568385i \(0.807568\pi\)
\(878\) 0 0
\(879\) 318.000 0.0122024
\(880\) 0 0
\(881\) 6162.00 0.235645 0.117822 0.993035i \(-0.462409\pi\)
0.117822 + 0.993035i \(0.462409\pi\)
\(882\) 0 0
\(883\) −7748.00 −0.295290 −0.147645 0.989040i \(-0.547169\pi\)
−0.147645 + 0.989040i \(0.547169\pi\)
\(884\) 0 0
\(885\) 119.000 0.00451993
\(886\) 0 0
\(887\) 25923.0 0.981296 0.490648 0.871358i \(-0.336760\pi\)
0.490648 + 0.871358i \(0.336760\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −22715.0 −0.854075
\(892\) 0 0
\(893\) −23427.0 −0.877889
\(894\) 0 0
\(895\) −17157.0 −0.640777
\(896\) 0 0
\(897\) 462.000 0.0171970
\(898\) 0 0
\(899\) −7950.00 −0.294936
\(900\) 0 0
\(901\) −24603.0 −0.909706
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −8190.00 −0.300823
\(906\) 0 0
\(907\) −31935.0 −1.16911 −0.584556 0.811353i \(-0.698731\pi\)
−0.584556 + 0.811353i \(0.698731\pi\)
\(908\) 0 0
\(909\) 28210.0 1.02934
\(910\) 0 0
\(911\) −3408.00 −0.123943 −0.0619715 0.998078i \(-0.519739\pi\)
−0.0619715 + 0.998078i \(0.519739\pi\)
\(912\) 0 0
\(913\) 32620.0 1.18244
\(914\) 0 0
\(915\) 357.000 0.0128984
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −13909.0 −0.499255 −0.249628 0.968342i \(-0.580308\pi\)
−0.249628 + 0.968342i \(0.580308\pi\)
\(920\) 0 0
\(921\) 8132.00 0.290943
\(922\) 0 0
\(923\) 51744.0 1.84526
\(924\) 0 0
\(925\) −836.000 −0.0297162
\(926\) 0 0
\(927\) 40378.0 1.43062
\(928\) 0 0
\(929\) −24537.0 −0.866559 −0.433279 0.901260i \(-0.642644\pi\)
−0.433279 + 0.901260i \(0.642644\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 929.000 0.0325982
\(934\) 0 0
\(935\) −14455.0 −0.505593
\(936\) 0 0
\(937\) −32758.0 −1.14211 −0.571055 0.820912i \(-0.693466\pi\)
−0.571055 + 0.820912i \(0.693466\pi\)
\(938\) 0 0
\(939\) −209.000 −0.00726353
\(940\) 0 0
\(941\) −38561.0 −1.33587 −0.667934 0.744220i \(-0.732821\pi\)
−0.667934 + 0.744220i \(0.732821\pi\)
\(942\) 0 0
\(943\) −3486.00 −0.120382
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −39661.0 −1.36094 −0.680470 0.732776i \(-0.738224\pi\)
−0.680470 + 0.732776i \(0.738224\pi\)
\(948\) 0 0
\(949\) 19470.0 0.665988
\(950\) 0 0
\(951\) 7131.00 0.243153
\(952\) 0 0
\(953\) −46618.0 −1.58458 −0.792290 0.610144i \(-0.791111\pi\)
−0.792290 + 0.610144i \(0.791111\pi\)
\(954\) 0 0
\(955\) 8925.00 0.302415
\(956\) 0 0
\(957\) −3710.00 −0.125316
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −24166.0 −0.811185
\(962\) 0 0
\(963\) 3354.00 0.112234
\(964\) 0 0
\(965\) 245.000 0.00817288
\(966\) 0 0
\(967\) −14816.0 −0.492710 −0.246355 0.969180i \(-0.579233\pi\)
−0.246355 + 0.969180i \(0.579233\pi\)
\(968\) 0 0
\(969\) −8083.00 −0.267970
\(970\) 0 0
\(971\) 16875.0 0.557718 0.278859 0.960332i \(-0.410044\pi\)
0.278859 + 0.960332i \(0.410044\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −5016.00 −0.164760
\(976\) 0 0
\(977\) −15837.0 −0.518598 −0.259299 0.965797i \(-0.583492\pi\)
−0.259299 + 0.965797i \(0.583492\pi\)
\(978\) 0 0
\(979\) 30555.0 0.997489
\(980\) 0 0
\(981\) 25090.0 0.816577
\(982\) 0 0
\(983\) −9915.00 −0.321708 −0.160854 0.986978i \(-0.551425\pi\)
−0.160854 + 0.986978i \(0.551425\pi\)
\(984\) 0 0
\(985\) −19138.0 −0.619073
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1820.00 −0.0585163
\(990\) 0 0
\(991\) 43681.0 1.40017 0.700087 0.714057i \(-0.253144\pi\)
0.700087 + 0.714057i \(0.253144\pi\)
\(992\) 0 0
\(993\) 6571.00 0.209994
\(994\) 0 0
\(995\) −15701.0 −0.500256
\(996\) 0 0
\(997\) −47113.0 −1.49657 −0.748287 0.663375i \(-0.769123\pi\)
−0.748287 + 0.663375i \(0.769123\pi\)
\(998\) 0 0
\(999\) −583.000 −0.0184638
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.l.1.1 1
4.3 odd 2 98.4.a.b.1.1 1
7.2 even 3 112.4.i.b.81.1 2
7.4 even 3 112.4.i.b.65.1 2
7.6 odd 2 784.4.a.j.1.1 1
12.11 even 2 882.4.a.k.1.1 1
20.19 odd 2 2450.4.a.bh.1.1 1
28.3 even 6 98.4.c.e.79.1 2
28.11 odd 6 14.4.c.b.9.1 2
28.19 even 6 98.4.c.e.67.1 2
28.23 odd 6 14.4.c.b.11.1 yes 2
28.27 even 2 98.4.a.c.1.1 1
56.11 odd 6 448.4.i.c.65.1 2
56.37 even 6 448.4.i.d.193.1 2
56.51 odd 6 448.4.i.c.193.1 2
56.53 even 6 448.4.i.d.65.1 2
84.11 even 6 126.4.g.c.37.1 2
84.23 even 6 126.4.g.c.109.1 2
84.47 odd 6 882.4.g.d.361.1 2
84.59 odd 6 882.4.g.d.667.1 2
84.83 odd 2 882.4.a.p.1.1 1
140.23 even 12 350.4.j.d.249.2 4
140.39 odd 6 350.4.e.b.51.1 2
140.67 even 12 350.4.j.d.149.2 4
140.79 odd 6 350.4.e.b.151.1 2
140.107 even 12 350.4.j.d.249.1 4
140.123 even 12 350.4.j.d.149.1 4
140.139 even 2 2450.4.a.bf.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.4.c.b.9.1 2 28.11 odd 6
14.4.c.b.11.1 yes 2 28.23 odd 6
98.4.a.b.1.1 1 4.3 odd 2
98.4.a.c.1.1 1 28.27 even 2
98.4.c.e.67.1 2 28.19 even 6
98.4.c.e.79.1 2 28.3 even 6
112.4.i.b.65.1 2 7.4 even 3
112.4.i.b.81.1 2 7.2 even 3
126.4.g.c.37.1 2 84.11 even 6
126.4.g.c.109.1 2 84.23 even 6
350.4.e.b.51.1 2 140.39 odd 6
350.4.e.b.151.1 2 140.79 odd 6
350.4.j.d.149.1 4 140.123 even 12
350.4.j.d.149.2 4 140.67 even 12
350.4.j.d.249.1 4 140.107 even 12
350.4.j.d.249.2 4 140.23 even 12
448.4.i.c.65.1 2 56.11 odd 6
448.4.i.c.193.1 2 56.51 odd 6
448.4.i.d.65.1 2 56.53 even 6
448.4.i.d.193.1 2 56.37 even 6
784.4.a.j.1.1 1 7.6 odd 2
784.4.a.l.1.1 1 1.1 even 1 trivial
882.4.a.k.1.1 1 12.11 even 2
882.4.a.p.1.1 1 84.83 odd 2
882.4.g.d.361.1 2 84.47 odd 6
882.4.g.d.667.1 2 84.59 odd 6
2450.4.a.bf.1.1 1 140.139 even 2
2450.4.a.bh.1.1 1 20.19 odd 2