Properties

Label 280.6.a.g.1.3
Level $280$
Weight $6$
Character 280.1
Self dual yes
Analytic conductor $44.907$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.9074695476\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - 2 x^{3} - 232 x^{2} + 60 x + 5808\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(15.2911\) of defining polynomial
Character \(\chi\) \(=\) 280.1

$q$-expansion

\(f(q)\) \(=\) \(q+6.08191 q^{3} +25.0000 q^{5} +49.0000 q^{7} -206.010 q^{9} +O(q^{10})\) \(q+6.08191 q^{3} +25.0000 q^{5} +49.0000 q^{7} -206.010 q^{9} +407.671 q^{11} -1075.68 q^{13} +152.048 q^{15} -1775.88 q^{17} +2156.68 q^{19} +298.014 q^{21} -4540.75 q^{23} +625.000 q^{25} -2730.84 q^{27} +6114.50 q^{29} -2856.57 q^{31} +2479.42 q^{33} +1225.00 q^{35} -7036.59 q^{37} -6542.17 q^{39} -11206.3 q^{41} +10684.8 q^{43} -5150.26 q^{45} -7637.19 q^{47} +2401.00 q^{49} -10800.7 q^{51} +19261.2 q^{53} +10191.8 q^{55} +13116.8 q^{57} -9188.24 q^{59} -33709.8 q^{61} -10094.5 q^{63} -26891.9 q^{65} -29762.1 q^{67} -27616.4 q^{69} -29860.8 q^{71} -40725.0 q^{73} +3801.19 q^{75} +19975.9 q^{77} -39180.1 q^{79} +33451.8 q^{81} +34423.7 q^{83} -44396.9 q^{85} +37187.8 q^{87} -7995.49 q^{89} -52708.2 q^{91} -17373.4 q^{93} +53917.1 q^{95} -58573.9 q^{97} -83984.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 13 q^{3} + 100 q^{5} + 196 q^{7} - 193 q^{9} + O(q^{10}) \) \( 4 q - 13 q^{3} + 100 q^{5} + 196 q^{7} - 193 q^{9} - 595 q^{11} - 969 q^{13} - 325 q^{15} - 1315 q^{17} - 1090 q^{19} - 637 q^{21} - 1534 q^{23} + 2500 q^{25} + 173 q^{27} + 4099 q^{29} - 4820 q^{31} + 4149 q^{33} + 4900 q^{35} + 7692 q^{37} - 6371 q^{39} - 9722 q^{41} - 20610 q^{43} - 4825 q^{45} - 1661 q^{47} + 9604 q^{49} - 73361 q^{51} - 28898 q^{53} - 14875 q^{55} - 21246 q^{57} - 101872 q^{59} - 24742 q^{61} - 9457 q^{63} - 24225 q^{65} - 82060 q^{67} + 16914 q^{69} - 102784 q^{71} - 80652 q^{73} - 8125 q^{75} - 29155 q^{77} - 117801 q^{79} - 141052 q^{81} - 155440 q^{83} - 32875 q^{85} - 82519 q^{87} + 56426 q^{89} - 47481 q^{91} - 17332 q^{93} - 27250 q^{95} - 261031 q^{97} - 61686 q^{99} + O(q^{100}) \)

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
\(3\) 6.08191 0.390155 0.195077 0.980788i \(-0.437504\pi\)
0.195077 + 0.980788i \(0.437504\pi\)
\(4\) 0 0
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) −206.010 −0.847779
\(10\) 0 0
\(11\) 407.671 1.01585 0.507924 0.861402i \(-0.330413\pi\)
0.507924 + 0.861402i \(0.330413\pi\)
\(12\) 0 0
\(13\) −1075.68 −1.76532 −0.882661 0.470011i \(-0.844250\pi\)
−0.882661 + 0.470011i \(0.844250\pi\)
\(14\) 0 0
\(15\) 152.048 0.174482
\(16\) 0 0
\(17\) −1775.88 −1.49036 −0.745178 0.666865i \(-0.767636\pi\)
−0.745178 + 0.666865i \(0.767636\pi\)
\(18\) 0 0
\(19\) 2156.68 1.37057 0.685287 0.728273i \(-0.259677\pi\)
0.685287 + 0.728273i \(0.259677\pi\)
\(20\) 0 0
\(21\) 298.014 0.147465
\(22\) 0 0
\(23\) −4540.75 −1.78981 −0.894907 0.446253i \(-0.852758\pi\)
−0.894907 + 0.446253i \(0.852758\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) −2730.84 −0.720920
\(28\) 0 0
\(29\) 6114.50 1.35010 0.675050 0.737772i \(-0.264122\pi\)
0.675050 + 0.737772i \(0.264122\pi\)
\(30\) 0 0
\(31\) −2856.57 −0.533876 −0.266938 0.963714i \(-0.586012\pi\)
−0.266938 + 0.963714i \(0.586012\pi\)
\(32\) 0 0
\(33\) 2479.42 0.396337
\(34\) 0 0
\(35\) 1225.00 0.169031
\(36\) 0 0
\(37\) −7036.59 −0.845002 −0.422501 0.906362i \(-0.638848\pi\)
−0.422501 + 0.906362i \(0.638848\pi\)
\(38\) 0 0
\(39\) −6542.17 −0.688748
\(40\) 0 0
\(41\) −11206.3 −1.04113 −0.520563 0.853824i \(-0.674278\pi\)
−0.520563 + 0.853824i \(0.674278\pi\)
\(42\) 0 0
\(43\) 10684.8 0.881241 0.440620 0.897694i \(-0.354758\pi\)
0.440620 + 0.897694i \(0.354758\pi\)
\(44\) 0 0
\(45\) −5150.26 −0.379138
\(46\) 0 0
\(47\) −7637.19 −0.504300 −0.252150 0.967688i \(-0.581138\pi\)
−0.252150 + 0.967688i \(0.581138\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) −10800.7 −0.581469
\(52\) 0 0
\(53\) 19261.2 0.941875 0.470937 0.882167i \(-0.343916\pi\)
0.470937 + 0.882167i \(0.343916\pi\)
\(54\) 0 0
\(55\) 10191.8 0.454301
\(56\) 0 0
\(57\) 13116.8 0.534736
\(58\) 0 0
\(59\) −9188.24 −0.343639 −0.171819 0.985128i \(-0.554965\pi\)
−0.171819 + 0.985128i \(0.554965\pi\)
\(60\) 0 0
\(61\) −33709.8 −1.15993 −0.579964 0.814642i \(-0.696933\pi\)
−0.579964 + 0.814642i \(0.696933\pi\)
\(62\) 0 0
\(63\) −10094.5 −0.320430
\(64\) 0 0
\(65\) −26891.9 −0.789476
\(66\) 0 0
\(67\) −29762.1 −0.809985 −0.404993 0.914320i \(-0.632726\pi\)
−0.404993 + 0.914320i \(0.632726\pi\)
\(68\) 0 0
\(69\) −27616.4 −0.698304
\(70\) 0 0
\(71\) −29860.8 −0.703001 −0.351500 0.936188i \(-0.614328\pi\)
−0.351500 + 0.936188i \(0.614328\pi\)
\(72\) 0 0
\(73\) −40725.0 −0.894445 −0.447222 0.894423i \(-0.647587\pi\)
−0.447222 + 0.894423i \(0.647587\pi\)
\(74\) 0 0
\(75\) 3801.19 0.0780309
\(76\) 0 0
\(77\) 19975.9 0.383954
\(78\) 0 0
\(79\) −39180.1 −0.706313 −0.353157 0.935564i \(-0.614892\pi\)
−0.353157 + 0.935564i \(0.614892\pi\)
\(80\) 0 0
\(81\) 33451.8 0.566509
\(82\) 0 0
\(83\) 34423.7 0.548483 0.274241 0.961661i \(-0.411573\pi\)
0.274241 + 0.961661i \(0.411573\pi\)
\(84\) 0 0
\(85\) −44396.9 −0.666508
\(86\) 0 0
\(87\) 37187.8 0.526748
\(88\) 0 0
\(89\) −7995.49 −0.106997 −0.0534983 0.998568i \(-0.517037\pi\)
−0.0534983 + 0.998568i \(0.517037\pi\)
\(90\) 0 0
\(91\) −52708.2 −0.667229
\(92\) 0 0
\(93\) −17373.4 −0.208294
\(94\) 0 0
\(95\) 53917.1 0.612940
\(96\) 0 0
\(97\) −58573.9 −0.632084 −0.316042 0.948745i \(-0.602354\pi\)
−0.316042 + 0.948745i \(0.602354\pi\)
\(98\) 0 0
\(99\) −83984.5 −0.861214
\(100\) 0 0
\(101\) 159709. 1.55785 0.778925 0.627117i \(-0.215765\pi\)
0.778925 + 0.627117i \(0.215765\pi\)
\(102\) 0 0
\(103\) −69774.5 −0.648043 −0.324021 0.946050i \(-0.605035\pi\)
−0.324021 + 0.946050i \(0.605035\pi\)
\(104\) 0 0
\(105\) 7450.34 0.0659482
\(106\) 0 0
\(107\) −136651. −1.15386 −0.576929 0.816794i \(-0.695749\pi\)
−0.576929 + 0.816794i \(0.695749\pi\)
\(108\) 0 0
\(109\) −164476. −1.32598 −0.662990 0.748628i \(-0.730713\pi\)
−0.662990 + 0.748628i \(0.730713\pi\)
\(110\) 0 0
\(111\) −42795.9 −0.329682
\(112\) 0 0
\(113\) −57417.3 −0.423006 −0.211503 0.977377i \(-0.567836\pi\)
−0.211503 + 0.977377i \(0.567836\pi\)
\(114\) 0 0
\(115\) −113519. −0.800429
\(116\) 0 0
\(117\) 221601. 1.49660
\(118\) 0 0
\(119\) −87017.9 −0.563302
\(120\) 0 0
\(121\) 5144.87 0.0319456
\(122\) 0 0
\(123\) −68155.7 −0.406200
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) −132464. −0.728766 −0.364383 0.931249i \(-0.618720\pi\)
−0.364383 + 0.931249i \(0.618720\pi\)
\(128\) 0 0
\(129\) 64983.9 0.343820
\(130\) 0 0
\(131\) 68982.8 0.351206 0.175603 0.984461i \(-0.443812\pi\)
0.175603 + 0.984461i \(0.443812\pi\)
\(132\) 0 0
\(133\) 105678. 0.518028
\(134\) 0 0
\(135\) −68271.0 −0.322405
\(136\) 0 0
\(137\) −379201. −1.72611 −0.863055 0.505110i \(-0.831452\pi\)
−0.863055 + 0.505110i \(0.831452\pi\)
\(138\) 0 0
\(139\) 87581.5 0.384481 0.192241 0.981348i \(-0.438425\pi\)
0.192241 + 0.981348i \(0.438425\pi\)
\(140\) 0 0
\(141\) −46448.7 −0.196755
\(142\) 0 0
\(143\) −438523. −1.79330
\(144\) 0 0
\(145\) 152863. 0.603783
\(146\) 0 0
\(147\) 14602.7 0.0557364
\(148\) 0 0
\(149\) 278024. 1.02593 0.512963 0.858411i \(-0.328548\pi\)
0.512963 + 0.858411i \(0.328548\pi\)
\(150\) 0 0
\(151\) 214016. 0.763843 0.381921 0.924195i \(-0.375263\pi\)
0.381921 + 0.924195i \(0.375263\pi\)
\(152\) 0 0
\(153\) 365849. 1.26349
\(154\) 0 0
\(155\) −71414.2 −0.238757
\(156\) 0 0
\(157\) 372088. 1.20475 0.602374 0.798214i \(-0.294222\pi\)
0.602374 + 0.798214i \(0.294222\pi\)
\(158\) 0 0
\(159\) 117145. 0.367477
\(160\) 0 0
\(161\) −222497. −0.676486
\(162\) 0 0
\(163\) 505449. 1.49008 0.745038 0.667022i \(-0.232432\pi\)
0.745038 + 0.667022i \(0.232432\pi\)
\(164\) 0 0
\(165\) 61985.5 0.177248
\(166\) 0 0
\(167\) −210214. −0.583271 −0.291635 0.956530i \(-0.594199\pi\)
−0.291635 + 0.956530i \(0.594199\pi\)
\(168\) 0 0
\(169\) 785790. 2.11636
\(170\) 0 0
\(171\) −444299. −1.16194
\(172\) 0 0
\(173\) 126094. 0.320316 0.160158 0.987091i \(-0.448800\pi\)
0.160158 + 0.987091i \(0.448800\pi\)
\(174\) 0 0
\(175\) 30625.0 0.0755929
\(176\) 0 0
\(177\) −55882.0 −0.134072
\(178\) 0 0
\(179\) −133191. −0.310701 −0.155350 0.987859i \(-0.549651\pi\)
−0.155350 + 0.987859i \(0.549651\pi\)
\(180\) 0 0
\(181\) 137432. 0.311810 0.155905 0.987772i \(-0.450171\pi\)
0.155905 + 0.987772i \(0.450171\pi\)
\(182\) 0 0
\(183\) −205020. −0.452551
\(184\) 0 0
\(185\) −175915. −0.377897
\(186\) 0 0
\(187\) −723973. −1.51397
\(188\) 0 0
\(189\) −133811. −0.272482
\(190\) 0 0
\(191\) 223165. 0.442631 0.221316 0.975202i \(-0.428965\pi\)
0.221316 + 0.975202i \(0.428965\pi\)
\(192\) 0 0
\(193\) 849159. 1.64095 0.820476 0.571681i \(-0.193708\pi\)
0.820476 + 0.571681i \(0.193708\pi\)
\(194\) 0 0
\(195\) −163554. −0.308018
\(196\) 0 0
\(197\) −198502. −0.364418 −0.182209 0.983260i \(-0.558325\pi\)
−0.182209 + 0.983260i \(0.558325\pi\)
\(198\) 0 0
\(199\) −485537. −0.869139 −0.434570 0.900638i \(-0.643100\pi\)
−0.434570 + 0.900638i \(0.643100\pi\)
\(200\) 0 0
\(201\) −181011. −0.316020
\(202\) 0 0
\(203\) 299611. 0.510290
\(204\) 0 0
\(205\) −280158. −0.465605
\(206\) 0 0
\(207\) 935441. 1.51737
\(208\) 0 0
\(209\) 879218. 1.39229
\(210\) 0 0
\(211\) 1.03186e6 1.59557 0.797785 0.602943i \(-0.206005\pi\)
0.797785 + 0.602943i \(0.206005\pi\)
\(212\) 0 0
\(213\) −181611. −0.274279
\(214\) 0 0
\(215\) 267120. 0.394103
\(216\) 0 0
\(217\) −139972. −0.201786
\(218\) 0 0
\(219\) −247685. −0.348972
\(220\) 0 0
\(221\) 1.91027e6 2.63096
\(222\) 0 0
\(223\) 1.24200e6 1.67247 0.836235 0.548372i \(-0.184752\pi\)
0.836235 + 0.548372i \(0.184752\pi\)
\(224\) 0 0
\(225\) −128756. −0.169556
\(226\) 0 0
\(227\) 1.45644e6 1.87597 0.937987 0.346670i \(-0.112688\pi\)
0.937987 + 0.346670i \(0.112688\pi\)
\(228\) 0 0
\(229\) −602646. −0.759406 −0.379703 0.925109i \(-0.623974\pi\)
−0.379703 + 0.925109i \(0.623974\pi\)
\(230\) 0 0
\(231\) 121492. 0.149801
\(232\) 0 0
\(233\) 754395. 0.910351 0.455175 0.890402i \(-0.349577\pi\)
0.455175 + 0.890402i \(0.349577\pi\)
\(234\) 0 0
\(235\) −190930. −0.225530
\(236\) 0 0
\(237\) −238290. −0.275571
\(238\) 0 0
\(239\) −43290.4 −0.0490226 −0.0245113 0.999700i \(-0.507803\pi\)
−0.0245113 + 0.999700i \(0.507803\pi\)
\(240\) 0 0
\(241\) 696883. 0.772890 0.386445 0.922313i \(-0.373703\pi\)
0.386445 + 0.922313i \(0.373703\pi\)
\(242\) 0 0
\(243\) 867045. 0.941946
\(244\) 0 0
\(245\) 60025.0 0.0638877
\(246\) 0 0
\(247\) −2.31990e6 −2.41950
\(248\) 0 0
\(249\) 209362. 0.213993
\(250\) 0 0
\(251\) −1.98194e6 −1.98566 −0.992831 0.119529i \(-0.961862\pi\)
−0.992831 + 0.119529i \(0.961862\pi\)
\(252\) 0 0
\(253\) −1.85113e6 −1.81818
\(254\) 0 0
\(255\) −270018. −0.260041
\(256\) 0 0
\(257\) 160003. 0.151110 0.0755552 0.997142i \(-0.475927\pi\)
0.0755552 + 0.997142i \(0.475927\pi\)
\(258\) 0 0
\(259\) −344793. −0.319381
\(260\) 0 0
\(261\) −1.25965e6 −1.14459
\(262\) 0 0
\(263\) −913315. −0.814200 −0.407100 0.913384i \(-0.633460\pi\)
−0.407100 + 0.913384i \(0.633460\pi\)
\(264\) 0 0
\(265\) 481529. 0.421219
\(266\) 0 0
\(267\) −48627.8 −0.0417452
\(268\) 0 0
\(269\) 842402. 0.709805 0.354902 0.934903i \(-0.384514\pi\)
0.354902 + 0.934903i \(0.384514\pi\)
\(270\) 0 0
\(271\) −1.25079e6 −1.03457 −0.517285 0.855813i \(-0.673057\pi\)
−0.517285 + 0.855813i \(0.673057\pi\)
\(272\) 0 0
\(273\) −320567. −0.260322
\(274\) 0 0
\(275\) 254795. 0.203169
\(276\) 0 0
\(277\) −370062. −0.289784 −0.144892 0.989447i \(-0.546284\pi\)
−0.144892 + 0.989447i \(0.546284\pi\)
\(278\) 0 0
\(279\) 588483. 0.452609
\(280\) 0 0
\(281\) 1.08198e6 0.817435 0.408717 0.912661i \(-0.365976\pi\)
0.408717 + 0.912661i \(0.365976\pi\)
\(282\) 0 0
\(283\) 2.17327e6 1.61305 0.806525 0.591200i \(-0.201346\pi\)
0.806525 + 0.591200i \(0.201346\pi\)
\(284\) 0 0
\(285\) 327919. 0.239141
\(286\) 0 0
\(287\) −549109. −0.393508
\(288\) 0 0
\(289\) 1.73388e6 1.22116
\(290\) 0 0
\(291\) −356241. −0.246611
\(292\) 0 0
\(293\) −2.06185e6 −1.40310 −0.701550 0.712620i \(-0.747508\pi\)
−0.701550 + 0.712620i \(0.747508\pi\)
\(294\) 0 0
\(295\) −229706. −0.153680
\(296\) 0 0
\(297\) −1.11329e6 −0.732344
\(298\) 0 0
\(299\) 4.88438e6 3.15960
\(300\) 0 0
\(301\) 523554. 0.333078
\(302\) 0 0
\(303\) 971335. 0.607803
\(304\) 0 0
\(305\) −842744. −0.518736
\(306\) 0 0
\(307\) −1.45256e6 −0.879603 −0.439802 0.898095i \(-0.644951\pi\)
−0.439802 + 0.898095i \(0.644951\pi\)
\(308\) 0 0
\(309\) −424362. −0.252837
\(310\) 0 0
\(311\) −2.66514e6 −1.56250 −0.781248 0.624221i \(-0.785417\pi\)
−0.781248 + 0.624221i \(0.785417\pi\)
\(312\) 0 0
\(313\) −1.21556e6 −0.701317 −0.350658 0.936503i \(-0.614042\pi\)
−0.350658 + 0.936503i \(0.614042\pi\)
\(314\) 0 0
\(315\) −252363. −0.143301
\(316\) 0 0
\(317\) 2.41341e6 1.34891 0.674455 0.738316i \(-0.264379\pi\)
0.674455 + 0.738316i \(0.264379\pi\)
\(318\) 0 0
\(319\) 2.49271e6 1.37150
\(320\) 0 0
\(321\) −831097. −0.450183
\(322\) 0 0
\(323\) −3.83000e6 −2.04264
\(324\) 0 0
\(325\) −672299. −0.353064
\(326\) 0 0
\(327\) −1.00033e6 −0.517338
\(328\) 0 0
\(329\) −374223. −0.190608
\(330\) 0 0
\(331\) 1.47548e6 0.740226 0.370113 0.928987i \(-0.379319\pi\)
0.370113 + 0.928987i \(0.379319\pi\)
\(332\) 0 0
\(333\) 1.44961e6 0.716376
\(334\) 0 0
\(335\) −744054. −0.362236
\(336\) 0 0
\(337\) −1.98021e6 −0.949812 −0.474906 0.880037i \(-0.657518\pi\)
−0.474906 + 0.880037i \(0.657518\pi\)
\(338\) 0 0
\(339\) −349207. −0.165038
\(340\) 0 0
\(341\) −1.16454e6 −0.542337
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) −690410. −0.312291
\(346\) 0 0
\(347\) −212122. −0.0945720 −0.0472860 0.998881i \(-0.515057\pi\)
−0.0472860 + 0.998881i \(0.515057\pi\)
\(348\) 0 0
\(349\) −852633. −0.374713 −0.187356 0.982292i \(-0.559992\pi\)
−0.187356 + 0.982292i \(0.559992\pi\)
\(350\) 0 0
\(351\) 2.93750e6 1.27265
\(352\) 0 0
\(353\) −987395. −0.421749 −0.210875 0.977513i \(-0.567631\pi\)
−0.210875 + 0.977513i \(0.567631\pi\)
\(354\) 0 0
\(355\) −746520. −0.314391
\(356\) 0 0
\(357\) −529235. −0.219775
\(358\) 0 0
\(359\) −940935. −0.385322 −0.192661 0.981265i \(-0.561712\pi\)
−0.192661 + 0.981265i \(0.561712\pi\)
\(360\) 0 0
\(361\) 2.17519e6 0.878474
\(362\) 0 0
\(363\) 31290.6 0.0124637
\(364\) 0 0
\(365\) −1.01812e6 −0.400008
\(366\) 0 0
\(367\) −4.12708e6 −1.59948 −0.799739 0.600348i \(-0.795029\pi\)
−0.799739 + 0.600348i \(0.795029\pi\)
\(368\) 0 0
\(369\) 2.30862e6 0.882644
\(370\) 0 0
\(371\) 943798. 0.355995
\(372\) 0 0
\(373\) 2.26644e6 0.843476 0.421738 0.906718i \(-0.361420\pi\)
0.421738 + 0.906718i \(0.361420\pi\)
\(374\) 0 0
\(375\) 95029.8 0.0348965
\(376\) 0 0
\(377\) −6.57723e6 −2.38336
\(378\) 0 0
\(379\) −2.24173e6 −0.801653 −0.400826 0.916154i \(-0.631277\pi\)
−0.400826 + 0.916154i \(0.631277\pi\)
\(380\) 0 0
\(381\) −805633. −0.284331
\(382\) 0 0
\(383\) 1.03804e6 0.361591 0.180795 0.983521i \(-0.442133\pi\)
0.180795 + 0.983521i \(0.442133\pi\)
\(384\) 0 0
\(385\) 499397. 0.171710
\(386\) 0 0
\(387\) −2.20118e6 −0.747098
\(388\) 0 0
\(389\) −259366. −0.0869040 −0.0434520 0.999056i \(-0.513836\pi\)
−0.0434520 + 0.999056i \(0.513836\pi\)
\(390\) 0 0
\(391\) 8.06380e6 2.66746
\(392\) 0 0
\(393\) 419547. 0.137025
\(394\) 0 0
\(395\) −979502. −0.315873
\(396\) 0 0
\(397\) −2.75320e6 −0.876720 −0.438360 0.898799i \(-0.644441\pi\)
−0.438360 + 0.898799i \(0.644441\pi\)
\(398\) 0 0
\(399\) 642721. 0.202111
\(400\) 0 0
\(401\) −5.92473e6 −1.83996 −0.919979 0.391968i \(-0.871794\pi\)
−0.919979 + 0.391968i \(0.871794\pi\)
\(402\) 0 0
\(403\) 3.07275e6 0.942463
\(404\) 0 0
\(405\) 836295. 0.253351
\(406\) 0 0
\(407\) −2.86862e6 −0.858393
\(408\) 0 0
\(409\) 3.69799e6 1.09309 0.546547 0.837428i \(-0.315942\pi\)
0.546547 + 0.837428i \(0.315942\pi\)
\(410\) 0 0
\(411\) −2.30627e6 −0.673450
\(412\) 0 0
\(413\) −450224. −0.129883
\(414\) 0 0
\(415\) 860594. 0.245289
\(416\) 0 0
\(417\) 532662. 0.150007
\(418\) 0 0
\(419\) −4.15994e6 −1.15758 −0.578791 0.815476i \(-0.696475\pi\)
−0.578791 + 0.815476i \(0.696475\pi\)
\(420\) 0 0
\(421\) −5.20770e6 −1.43199 −0.715996 0.698104i \(-0.754027\pi\)
−0.715996 + 0.698104i \(0.754027\pi\)
\(422\) 0 0
\(423\) 1.57334e6 0.427535
\(424\) 0 0
\(425\) −1.10992e6 −0.298071
\(426\) 0 0
\(427\) −1.65178e6 −0.438412
\(428\) 0 0
\(429\) −2.66706e6 −0.699663
\(430\) 0 0
\(431\) 1.68636e6 0.437276 0.218638 0.975806i \(-0.429839\pi\)
0.218638 + 0.975806i \(0.429839\pi\)
\(432\) 0 0
\(433\) −3.10555e6 −0.796010 −0.398005 0.917383i \(-0.630297\pi\)
−0.398005 + 0.917383i \(0.630297\pi\)
\(434\) 0 0
\(435\) 929696. 0.235569
\(436\) 0 0
\(437\) −9.79296e6 −2.45307
\(438\) 0 0
\(439\) 1.22048e6 0.302252 0.151126 0.988515i \(-0.451710\pi\)
0.151126 + 0.988515i \(0.451710\pi\)
\(440\) 0 0
\(441\) −494631. −0.121111
\(442\) 0 0
\(443\) 2.25319e6 0.545493 0.272747 0.962086i \(-0.412068\pi\)
0.272747 + 0.962086i \(0.412068\pi\)
\(444\) 0 0
\(445\) −199887. −0.0478503
\(446\) 0 0
\(447\) 1.69091e6 0.400270
\(448\) 0 0
\(449\) 7.67885e6 1.79755 0.898774 0.438412i \(-0.144459\pi\)
0.898774 + 0.438412i \(0.144459\pi\)
\(450\) 0 0
\(451\) −4.56849e6 −1.05762
\(452\) 0 0
\(453\) 1.30163e6 0.298017
\(454\) 0 0
\(455\) −1.31771e6 −0.298394
\(456\) 0 0
\(457\) 7.98138e6 1.78767 0.893835 0.448396i \(-0.148005\pi\)
0.893835 + 0.448396i \(0.148005\pi\)
\(458\) 0 0
\(459\) 4.84963e6 1.07443
\(460\) 0 0
\(461\) −6.10635e6 −1.33823 −0.669113 0.743161i \(-0.733326\pi\)
−0.669113 + 0.743161i \(0.733326\pi\)
\(462\) 0 0
\(463\) 7.69353e6 1.66791 0.833957 0.551830i \(-0.186070\pi\)
0.833957 + 0.551830i \(0.186070\pi\)
\(464\) 0 0
\(465\) −434335. −0.0931520
\(466\) 0 0
\(467\) 4.41567e6 0.936924 0.468462 0.883484i \(-0.344808\pi\)
0.468462 + 0.883484i \(0.344808\pi\)
\(468\) 0 0
\(469\) −1.45835e6 −0.306146
\(470\) 0 0
\(471\) 2.26300e6 0.470038
\(472\) 0 0
\(473\) 4.35588e6 0.895206
\(474\) 0 0
\(475\) 1.34793e6 0.274115
\(476\) 0 0
\(477\) −3.96800e6 −0.798502
\(478\) 0 0
\(479\) −2.46498e6 −0.490878 −0.245439 0.969412i \(-0.578932\pi\)
−0.245439 + 0.969412i \(0.578932\pi\)
\(480\) 0 0
\(481\) 7.56910e6 1.49170
\(482\) 0 0
\(483\) −1.35320e6 −0.263934
\(484\) 0 0
\(485\) −1.46435e6 −0.282677
\(486\) 0 0
\(487\) 29208.5 0.00558068 0.00279034 0.999996i \(-0.499112\pi\)
0.00279034 + 0.999996i \(0.499112\pi\)
\(488\) 0 0
\(489\) 3.07409e6 0.581360
\(490\) 0 0
\(491\) −1.41942e6 −0.265710 −0.132855 0.991135i \(-0.542414\pi\)
−0.132855 + 0.991135i \(0.542414\pi\)
\(492\) 0 0
\(493\) −1.08586e7 −2.01213
\(494\) 0 0
\(495\) −2.09961e6 −0.385147
\(496\) 0 0
\(497\) −1.46318e6 −0.265709
\(498\) 0 0
\(499\) 6.68747e6 1.20229 0.601147 0.799138i \(-0.294711\pi\)
0.601147 + 0.799138i \(0.294711\pi\)
\(500\) 0 0
\(501\) −1.27850e6 −0.227566
\(502\) 0 0
\(503\) −5.12274e6 −0.902782 −0.451391 0.892326i \(-0.649072\pi\)
−0.451391 + 0.892326i \(0.649072\pi\)
\(504\) 0 0
\(505\) 3.99272e6 0.696692
\(506\) 0 0
\(507\) 4.77910e6 0.825708
\(508\) 0 0
\(509\) 2.78484e6 0.476438 0.238219 0.971211i \(-0.423436\pi\)
0.238219 + 0.971211i \(0.423436\pi\)
\(510\) 0 0
\(511\) −1.99552e6 −0.338068
\(512\) 0 0
\(513\) −5.88956e6 −0.988074
\(514\) 0 0
\(515\) −1.74436e6 −0.289814
\(516\) 0 0
\(517\) −3.11346e6 −0.512292
\(518\) 0 0
\(519\) 766891. 0.124973
\(520\) 0 0
\(521\) 6.73984e6 1.08781 0.543907 0.839145i \(-0.316944\pi\)
0.543907 + 0.839145i \(0.316944\pi\)
\(522\) 0 0
\(523\) 6.94281e6 1.10989 0.554947 0.831886i \(-0.312739\pi\)
0.554947 + 0.831886i \(0.312739\pi\)
\(524\) 0 0
\(525\) 186258. 0.0294929
\(526\) 0 0
\(527\) 5.07291e6 0.795666
\(528\) 0 0
\(529\) 1.41820e7 2.20343
\(530\) 0 0
\(531\) 1.89287e6 0.291330
\(532\) 0 0
\(533\) 1.20544e7 1.83792
\(534\) 0 0
\(535\) −3.41627e6 −0.516021
\(536\) 0 0
\(537\) −810055. −0.121221
\(538\) 0 0
\(539\) 978819. 0.145121
\(540\) 0 0
\(541\) 5.25286e6 0.771619 0.385810 0.922578i \(-0.373922\pi\)
0.385810 + 0.922578i \(0.373922\pi\)
\(542\) 0 0
\(543\) 835847. 0.121654
\(544\) 0 0
\(545\) −4.11191e6 −0.592997
\(546\) 0 0
\(547\) −8.43518e6 −1.20539 −0.602693 0.797974i \(-0.705905\pi\)
−0.602693 + 0.797974i \(0.705905\pi\)
\(548\) 0 0
\(549\) 6.94456e6 0.983363
\(550\) 0 0
\(551\) 1.31871e7 1.85041
\(552\) 0 0
\(553\) −1.91982e6 −0.266961
\(554\) 0 0
\(555\) −1.06990e6 −0.147438
\(556\) 0 0
\(557\) −8.14320e6 −1.11213 −0.556067 0.831137i \(-0.687690\pi\)
−0.556067 + 0.831137i \(0.687690\pi\)
\(558\) 0 0
\(559\) −1.14934e7 −1.55567
\(560\) 0 0
\(561\) −4.40314e6 −0.590684
\(562\) 0 0
\(563\) 5.32372e6 0.707854 0.353927 0.935273i \(-0.384846\pi\)
0.353927 + 0.935273i \(0.384846\pi\)
\(564\) 0 0
\(565\) −1.43543e6 −0.189174
\(566\) 0 0
\(567\) 1.63914e6 0.214120
\(568\) 0 0
\(569\) 594659. 0.0769994 0.0384997 0.999259i \(-0.487742\pi\)
0.0384997 + 0.999259i \(0.487742\pi\)
\(570\) 0 0
\(571\) 5.08376e6 0.652521 0.326260 0.945280i \(-0.394211\pi\)
0.326260 + 0.945280i \(0.394211\pi\)
\(572\) 0 0
\(573\) 1.35727e6 0.172695
\(574\) 0 0
\(575\) −2.83797e6 −0.357963
\(576\) 0 0
\(577\) 6.83943e6 0.855225 0.427612 0.903962i \(-0.359355\pi\)
0.427612 + 0.903962i \(0.359355\pi\)
\(578\) 0 0
\(579\) 5.16451e6 0.640225
\(580\) 0 0
\(581\) 1.68676e6 0.207307
\(582\) 0 0
\(583\) 7.85223e6 0.956801
\(584\) 0 0
\(585\) 5.54002e6 0.669301
\(586\) 0 0
\(587\) −1.24602e7 −1.49256 −0.746278 0.665634i \(-0.768161\pi\)
−0.746278 + 0.665634i \(0.768161\pi\)
\(588\) 0 0
\(589\) −6.16072e6 −0.731717
\(590\) 0 0
\(591\) −1.20727e6 −0.142179
\(592\) 0 0
\(593\) −1.04774e7 −1.22353 −0.611765 0.791039i \(-0.709540\pi\)
−0.611765 + 0.791039i \(0.709540\pi\)
\(594\) 0 0
\(595\) −2.17545e6 −0.251916
\(596\) 0 0
\(597\) −2.95299e6 −0.339099
\(598\) 0 0
\(599\) 2.01252e6 0.229179 0.114589 0.993413i \(-0.463445\pi\)
0.114589 + 0.993413i \(0.463445\pi\)
\(600\) 0 0
\(601\) −9.45258e6 −1.06749 −0.533746 0.845645i \(-0.679216\pi\)
−0.533746 + 0.845645i \(0.679216\pi\)
\(602\) 0 0
\(603\) 6.13131e6 0.686689
\(604\) 0 0
\(605\) 128622. 0.0142865
\(606\) 0 0
\(607\) 1.58379e7 1.74473 0.872363 0.488859i \(-0.162587\pi\)
0.872363 + 0.488859i \(0.162587\pi\)
\(608\) 0 0
\(609\) 1.82220e6 0.199092
\(610\) 0 0
\(611\) 8.21516e6 0.890252
\(612\) 0 0
\(613\) 1.15645e7 1.24301 0.621505 0.783410i \(-0.286521\pi\)
0.621505 + 0.783410i \(0.286521\pi\)
\(614\) 0 0
\(615\) −1.70389e6 −0.181658
\(616\) 0 0
\(617\) −1.24967e6 −0.132154 −0.0660771 0.997815i \(-0.521048\pi\)
−0.0660771 + 0.997815i \(0.521048\pi\)
\(618\) 0 0
\(619\) −1.11632e6 −0.117101 −0.0585505 0.998284i \(-0.518648\pi\)
−0.0585505 + 0.998284i \(0.518648\pi\)
\(620\) 0 0
\(621\) 1.24001e7 1.29031
\(622\) 0 0
\(623\) −391779. −0.0404409
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 5.34733e6 0.543210
\(628\) 0 0
\(629\) 1.24961e7 1.25935
\(630\) 0 0
\(631\) −1.52038e7 −1.52012 −0.760062 0.649851i \(-0.774831\pi\)
−0.760062 + 0.649851i \(0.774831\pi\)
\(632\) 0 0
\(633\) 6.27569e6 0.622519
\(634\) 0 0
\(635\) −3.31160e6 −0.325914
\(636\) 0 0
\(637\) −2.58270e6 −0.252189
\(638\) 0 0
\(639\) 6.15164e6 0.595989
\(640\) 0 0
\(641\) 1.02239e7 0.982814 0.491407 0.870930i \(-0.336483\pi\)
0.491407 + 0.870930i \(0.336483\pi\)
\(642\) 0 0
\(643\) −1.70419e6 −0.162551 −0.0812757 0.996692i \(-0.525899\pi\)
−0.0812757 + 0.996692i \(0.525899\pi\)
\(644\) 0 0
\(645\) 1.62460e6 0.153761
\(646\) 0 0
\(647\) −1.34708e7 −1.26512 −0.632560 0.774512i \(-0.717996\pi\)
−0.632560 + 0.774512i \(0.717996\pi\)
\(648\) 0 0
\(649\) −3.74578e6 −0.349085
\(650\) 0 0
\(651\) −851296. −0.0787278
\(652\) 0 0
\(653\) −1.55928e7 −1.43100 −0.715500 0.698612i \(-0.753801\pi\)
−0.715500 + 0.698612i \(0.753801\pi\)
\(654\) 0 0
\(655\) 1.72457e6 0.157064
\(656\) 0 0
\(657\) 8.38976e6 0.758292
\(658\) 0 0
\(659\) −2.02390e7 −1.81542 −0.907708 0.419603i \(-0.862169\pi\)
−0.907708 + 0.419603i \(0.862169\pi\)
\(660\) 0 0
\(661\) −5.28966e6 −0.470895 −0.235448 0.971887i \(-0.575656\pi\)
−0.235448 + 0.971887i \(0.575656\pi\)
\(662\) 0 0
\(663\) 1.16181e7 1.02648
\(664\) 0 0
\(665\) 2.64194e6 0.231669
\(666\) 0 0
\(667\) −2.77644e7 −2.41643
\(668\) 0 0
\(669\) 7.55371e6 0.652522
\(670\) 0 0
\(671\) −1.37425e7 −1.17831
\(672\) 0 0
\(673\) 7.68769e6 0.654271 0.327136 0.944977i \(-0.393917\pi\)
0.327136 + 0.944977i \(0.393917\pi\)
\(674\) 0 0
\(675\) −1.70678e6 −0.144184
\(676\) 0 0
\(677\) −1.13880e7 −0.954939 −0.477469 0.878648i \(-0.658446\pi\)
−0.477469 + 0.878648i \(0.658446\pi\)
\(678\) 0 0
\(679\) −2.87012e6 −0.238905
\(680\) 0 0
\(681\) 8.85791e6 0.731920
\(682\) 0 0
\(683\) 1.15735e7 0.949320 0.474660 0.880169i \(-0.342571\pi\)
0.474660 + 0.880169i \(0.342571\pi\)
\(684\) 0 0
\(685\) −9.48003e6 −0.771940
\(686\) 0 0
\(687\) −3.66524e6 −0.296286
\(688\) 0 0
\(689\) −2.07188e7 −1.66271
\(690\) 0 0
\(691\) 1.33398e7 1.06281 0.531404 0.847119i \(-0.321665\pi\)
0.531404 + 0.847119i \(0.321665\pi\)
\(692\) 0 0
\(693\) −4.11524e6 −0.325508
\(694\) 0 0
\(695\) 2.18954e6 0.171945
\(696\) 0 0
\(697\) 1.99010e7 1.55165
\(698\) 0 0
\(699\) 4.58816e6 0.355178
\(700\) 0 0
\(701\) −4.67569e6 −0.359377 −0.179689 0.983724i \(-0.557509\pi\)
−0.179689 + 0.983724i \(0.557509\pi\)
\(702\) 0 0
\(703\) −1.51757e7 −1.15814
\(704\) 0 0
\(705\) −1.16122e6 −0.0879916
\(706\) 0 0
\(707\) 7.82574e6 0.588812
\(708\) 0 0
\(709\) 2.08491e7 1.55766 0.778829 0.627236i \(-0.215814\pi\)
0.778829 + 0.627236i \(0.215814\pi\)
\(710\) 0 0
\(711\) 8.07150e6 0.598798
\(712\) 0 0
\(713\) 1.29710e7 0.955539
\(714\) 0 0
\(715\) −1.09631e7 −0.801987
\(716\) 0 0
\(717\) −263288. −0.0191264
\(718\) 0 0
\(719\) −1.97250e7 −1.42297 −0.711485 0.702702i \(-0.751977\pi\)
−0.711485 + 0.702702i \(0.751977\pi\)
\(720\) 0 0
\(721\) −3.41895e6 −0.244937
\(722\) 0 0
\(723\) 4.23838e6 0.301547
\(724\) 0 0
\(725\) 3.82156e6 0.270020
\(726\) 0 0
\(727\) 1.84776e7 1.29661 0.648306 0.761380i \(-0.275478\pi\)
0.648306 + 0.761380i \(0.275478\pi\)
\(728\) 0 0
\(729\) −2.85550e6 −0.199005
\(730\) 0 0
\(731\) −1.89748e7 −1.31336
\(732\) 0 0
\(733\) 1.95578e6 0.134449 0.0672247 0.997738i \(-0.478586\pi\)
0.0672247 + 0.997738i \(0.478586\pi\)
\(734\) 0 0
\(735\) 365067. 0.0249261
\(736\) 0 0
\(737\) −1.21332e7 −0.822821
\(738\) 0 0
\(739\) −1.55560e7 −1.04782 −0.523911 0.851773i \(-0.675528\pi\)
−0.523911 + 0.851773i \(0.675528\pi\)
\(740\) 0 0
\(741\) −1.41094e7 −0.943981
\(742\) 0 0
\(743\) −1.21540e7 −0.807694 −0.403847 0.914827i \(-0.632327\pi\)
−0.403847 + 0.914827i \(0.632327\pi\)
\(744\) 0 0
\(745\) 6.95059e6 0.458808
\(746\) 0 0
\(747\) −7.09165e6 −0.464992
\(748\) 0 0
\(749\) −6.69588e6 −0.436117
\(750\) 0 0
\(751\) −7.81290e6 −0.505490 −0.252745 0.967533i \(-0.581333\pi\)
−0.252745 + 0.967533i \(0.581333\pi\)
\(752\) 0 0
\(753\) −1.20540e7 −0.774715
\(754\) 0 0
\(755\) 5.35040e6 0.341601
\(756\) 0 0
\(757\) 2.04844e7 1.29922 0.649610 0.760268i \(-0.274932\pi\)
0.649610 + 0.760268i \(0.274932\pi\)
\(758\) 0 0
\(759\) −1.12584e7 −0.709370
\(760\) 0 0
\(761\) −8.17274e6 −0.511571 −0.255786 0.966734i \(-0.582334\pi\)
−0.255786 + 0.966734i \(0.582334\pi\)
\(762\) 0 0
\(763\) −8.05934e6 −0.501174
\(764\) 0 0
\(765\) 9.14622e6 0.565051
\(766\) 0 0
\(767\) 9.88359e6 0.606633
\(768\) 0 0
\(769\) 6.09119e6 0.371438 0.185719 0.982603i \(-0.440539\pi\)
0.185719 + 0.982603i \(0.440539\pi\)
\(770\) 0 0
\(771\) 973122. 0.0589564
\(772\) 0 0
\(773\) −2.91960e7 −1.75741 −0.878707 0.477361i \(-0.841593\pi\)
−0.878707 + 0.477361i \(0.841593\pi\)
\(774\) 0 0
\(775\) −1.78536e6 −0.106775
\(776\) 0 0
\(777\) −2.09700e6 −0.124608
\(778\) 0 0
\(779\) −2.41685e7 −1.42694
\(780\) 0 0
\(781\) −1.21734e7 −0.714141
\(782\) 0 0
\(783\) −1.66977e7 −0.973314
\(784\) 0 0
\(785\) 9.30219e6 0.538780
\(786\) 0 0
\(787\) −9.27644e6 −0.533881 −0.266940 0.963713i \(-0.586013\pi\)
−0.266940 + 0.963713i \(0.586013\pi\)
\(788\) 0 0
\(789\) −5.55470e6 −0.317664
\(790\) 0 0
\(791\) −2.81345e6 −0.159881
\(792\) 0 0
\(793\) 3.62608e7 2.04765
\(794\) 0 0
\(795\) 2.92862e6 0.164341
\(796\) 0 0
\(797\) −3.37629e7 −1.88275 −0.941377 0.337356i \(-0.890467\pi\)
−0.941377 + 0.337356i \(0.890467\pi\)
\(798\) 0 0
\(799\) 1.35627e7 0.751587
\(800\) 0 0
\(801\) 1.64715e6 0.0907095
\(802\) 0 0
\(803\) −1.66024e7 −0.908619
\(804\) 0 0
\(805\) −5.56242e6 −0.302534
\(806\) 0 0
\(807\) 5.12341e6 0.276934
\(808\) 0 0
\(809\) 2.68549e7 1.44262 0.721312 0.692611i \(-0.243540\pi\)
0.721312 + 0.692611i \(0.243540\pi\)
\(810\) 0 0
\(811\) 8.99843e6 0.480413 0.240206 0.970722i \(-0.422785\pi\)
0.240206 + 0.970722i \(0.422785\pi\)
\(812\) 0 0
\(813\) −7.60717e6 −0.403642
\(814\) 0 0
\(815\) 1.26362e7 0.666382
\(816\) 0 0
\(817\) 2.30437e7 1.20781
\(818\) 0 0
\(819\) 1.08584e7 0.565663
\(820\) 0 0
\(821\) −2.53478e7 −1.31245 −0.656225 0.754565i \(-0.727848\pi\)
−0.656225 + 0.754565i \(0.727848\pi\)
\(822\) 0 0
\(823\) −2.80232e7 −1.44217 −0.721087 0.692844i \(-0.756357\pi\)
−0.721087 + 0.692844i \(0.756357\pi\)
\(824\) 0 0
\(825\) 1.54964e6 0.0792675
\(826\) 0 0
\(827\) −1.08632e7 −0.552325 −0.276162 0.961111i \(-0.589063\pi\)
−0.276162 + 0.961111i \(0.589063\pi\)
\(828\) 0 0
\(829\) 2.61760e7 1.32287 0.661435 0.750002i \(-0.269948\pi\)
0.661435 + 0.750002i \(0.269948\pi\)
\(830\) 0 0
\(831\) −2.25068e6 −0.113061
\(832\) 0 0
\(833\) −4.26388e6 −0.212908
\(834\) 0 0
\(835\) −5.25535e6 −0.260847
\(836\) 0 0
\(837\) 7.80083e6 0.384882
\(838\) 0 0
\(839\) −5.33086e6 −0.261452 −0.130726 0.991419i \(-0.541731\pi\)
−0.130726 + 0.991419i \(0.541731\pi\)
\(840\) 0 0
\(841\) 1.68760e7 0.822771
\(842\) 0 0
\(843\) 6.58050e6 0.318926
\(844\) 0 0
\(845\) 1.96447e7 0.946465
\(846\) 0 0
\(847\) 252098. 0.0120743
\(848\) 0 0
\(849\) 1.32176e7 0.629339
\(850\) 0 0
\(851\) 3.19514e7 1.51240
\(852\) 0 0
\(853\) −3.52267e7 −1.65768 −0.828838 0.559488i \(-0.810998\pi\)
−0.828838 + 0.559488i \(0.810998\pi\)
\(854\) 0 0
\(855\) −1.11075e7 −0.519638
\(856\) 0 0
\(857\) −1.93997e6 −0.0902283 −0.0451141 0.998982i \(-0.514365\pi\)
−0.0451141 + 0.998982i \(0.514365\pi\)
\(858\) 0 0
\(859\) −2.90322e7 −1.34245 −0.671223 0.741255i \(-0.734231\pi\)
−0.671223 + 0.741255i \(0.734231\pi\)
\(860\) 0 0
\(861\) −3.33963e6 −0.153529
\(862\) 0 0
\(863\) 3.76000e7 1.71854 0.859272 0.511518i \(-0.170917\pi\)
0.859272 + 0.511518i \(0.170917\pi\)
\(864\) 0 0
\(865\) 3.15235e6 0.143250
\(866\) 0 0
\(867\) 1.05453e7 0.476442
\(868\) 0 0
\(869\) −1.59726e7 −0.717506
\(870\) 0 0
\(871\) 3.20145e7 1.42988
\(872\) 0 0
\(873\) 1.20668e7 0.535868
\(874\) 0 0
\(875\) 765625. 0.0338062
\(876\) 0 0
\(877\) −2.05117e7 −0.900539 −0.450269 0.892893i \(-0.648672\pi\)
−0.450269 + 0.892893i \(0.648672\pi\)
\(878\) 0 0
\(879\) −1.25400e7 −0.547426
\(880\) 0 0
\(881\) −1.36918e7 −0.594322 −0.297161 0.954827i \(-0.596040\pi\)
−0.297161 + 0.954827i \(0.596040\pi\)
\(882\) 0 0
\(883\) −2.73738e7 −1.18150 −0.590750 0.806855i \(-0.701168\pi\)
−0.590750 + 0.806855i \(0.701168\pi\)
\(884\) 0 0
\(885\) −1.39705e6 −0.0599590
\(886\) 0 0
\(887\) −1.44173e7 −0.615284 −0.307642 0.951502i \(-0.599540\pi\)
−0.307642 + 0.951502i \(0.599540\pi\)
\(888\) 0 0
\(889\) −6.49073e6 −0.275448
\(890\) 0 0
\(891\) 1.36373e7 0.575487
\(892\) 0 0
\(893\) −1.64710e7 −0.691181
\(894\) 0 0
\(895\) −3.32977e6 −0.138950
\(896\) 0 0
\(897\) 2.97064e7 1.23273
\(898\) 0 0
\(899\) −1.74665e7 −0.720786
\(900\) 0 0
\(901\) −3.42054e7 −1.40373
\(902\) 0 0
\(903\) 3.18421e6 0.129952
\(904\) 0 0
\(905\) 3.43579e6 0.139446
\(906\) 0 0
\(907\) 2.74482e7 1.10789 0.553944 0.832554i \(-0.313122\pi\)
0.553944 + 0.832554i \(0.313122\pi\)
\(908\) 0 0
\(909\) −3.29017e7 −1.32071
\(910\) 0 0
\(911\) −3.10414e7 −1.23921 −0.619607 0.784913i \(-0.712708\pi\)
−0.619607 + 0.784913i \(0.712708\pi\)
\(912\) 0 0
\(913\) 1.40336e7 0.557175
\(914\) 0 0
\(915\) −5.12549e6 −0.202387
\(916\) 0 0
\(917\) 3.38016e6 0.132744
\(918\) 0 0
\(919\) −1.13810e7 −0.444519 −0.222260 0.974988i \(-0.571343\pi\)
−0.222260 + 0.974988i \(0.571343\pi\)
\(920\) 0 0
\(921\) −8.83431e6 −0.343181
\(922\) 0 0
\(923\) 3.21206e7 1.24102
\(924\) 0 0
\(925\) −4.39787e6 −0.169000
\(926\) 0 0
\(927\) 1.43743e7 0.549397
\(928\) 0 0
\(929\) 1.77569e7 0.675038 0.337519 0.941319i \(-0.390412\pi\)
0.337519 + 0.941319i \(0.390412\pi\)
\(930\) 0 0
\(931\) 5.17820e6 0.195796
\(932\) 0 0
\(933\) −1.62091e7 −0.609615
\(934\) 0 0
\(935\) −1.80993e7 −0.677070
\(936\) 0 0
\(937\) −1.93662e7 −0.720602 −0.360301 0.932836i \(-0.617326\pi\)
−0.360301 + 0.932836i \(0.617326\pi\)
\(938\) 0 0
\(939\) −7.39290e6 −0.273622
\(940\) 0 0
\(941\) 2.75371e7 1.01378 0.506891 0.862010i \(-0.330795\pi\)
0.506891 + 0.862010i \(0.330795\pi\)
\(942\) 0 0
\(943\) 5.08850e7 1.86342
\(944\) 0 0
\(945\) −3.34528e6 −0.121858
\(946\) 0 0
\(947\) 4.71647e7 1.70900 0.854501 0.519450i \(-0.173863\pi\)
0.854501 + 0.519450i \(0.173863\pi\)
\(948\) 0 0
\(949\) 4.38069e7 1.57898
\(950\) 0 0
\(951\) 1.46781e7 0.526283
\(952\) 0 0
\(953\) −3.72865e7 −1.32990 −0.664951 0.746887i \(-0.731547\pi\)
−0.664951 + 0.746887i \(0.731547\pi\)
\(954\) 0 0
\(955\) 5.57912e6 0.197951
\(956\) 0 0
\(957\) 1.51604e7 0.535095
\(958\) 0 0
\(959\) −1.85809e7 −0.652408
\(960\) 0 0
\(961\) −2.04692e7 −0.714976
\(962\) 0 0
\(963\) 2.81515e7 0.978217
\(964\) 0 0
\(965\) 2.12290e7 0.733856
\(966\) 0 0
\(967\) −2.46193e7 −0.846662 −0.423331 0.905975i \(-0.639139\pi\)
−0.423331 + 0.905975i \(0.639139\pi\)
\(968\) 0 0
\(969\) −2.32937e7 −0.796947
\(970\) 0 0
\(971\) −2.00471e6 −0.0682344 −0.0341172 0.999418i \(-0.510862\pi\)
−0.0341172 + 0.999418i \(0.510862\pi\)
\(972\) 0 0
\(973\) 4.29149e6 0.145320
\(974\) 0 0
\(975\) −4.08886e6 −0.137750
\(976\) 0 0
\(977\) 2.77180e7 0.929022 0.464511 0.885567i \(-0.346230\pi\)
0.464511 + 0.885567i \(0.346230\pi\)
\(978\) 0 0
\(979\) −3.25953e6 −0.108692
\(980\) 0 0
\(981\) 3.38838e7 1.12414
\(982\) 0 0
\(983\) −1.79222e7 −0.591573 −0.295787 0.955254i \(-0.595582\pi\)
−0.295787 + 0.955254i \(0.595582\pi\)
\(984\) 0 0
\(985\) −4.96255e6 −0.162973
\(986\) 0 0
\(987\) −2.27599e6 −0.0743664
\(988\) 0 0
\(989\) −4.85169e7 −1.57726
\(990\) 0 0
\(991\) −1.38359e7 −0.447532 −0.223766 0.974643i \(-0.571835\pi\)
−0.223766 + 0.974643i \(0.571835\pi\)
\(992\) 0 0
\(993\) 8.97375e6 0.288803
\(994\) 0 0
\(995\) −1.21384e7 −0.388691
\(996\) 0 0
\(997\) 3.19988e7 1.01952 0.509761 0.860316i \(-0.329734\pi\)
0.509761 + 0.860316i \(0.329734\pi\)
\(998\) 0 0
\(999\) 1.92158e7 0.609179
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 280.6.a.g.1.3 4
4.3 odd 2 560.6.a.x.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.6.a.g.1.3 4 1.1 even 1 trivial
560.6.a.x.1.2 4 4.3 odd 2