Properties

Label 200.6.a.e.1.1
Level $200$
Weight $6$
Character 200.1
Self dual yes
Analytic conductor $32.077$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 200.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0767639626\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{241}) \)
Defining polynomial: \( x^{2} - x - 60 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(8.26209\) of defining polynomial
Character \(\chi\) \(=\) 200.1

$q$-expansion

\(f(q)\) \(=\) \(q-19.5242 q^{3} +35.0483 q^{7} +138.193 q^{9} +O(q^{10})\) \(q-19.5242 q^{3} +35.0483 q^{7} +138.193 q^{9} -426.008 q^{11} +1103.26 q^{13} +109.387 q^{17} +495.926 q^{19} -684.290 q^{21} +2497.37 q^{23} +2046.26 q^{27} -42.4221 q^{29} -7999.56 q^{31} +8317.45 q^{33} -13763.7 q^{37} -21540.2 q^{39} +11863.6 q^{41} -16816.0 q^{43} -13036.0 q^{47} -15578.6 q^{49} -2135.69 q^{51} +17817.3 q^{53} -9682.55 q^{57} -47346.1 q^{59} -22782.9 q^{61} +4843.45 q^{63} -39418.3 q^{67} -48759.1 q^{69} -1616.32 q^{71} +53293.3 q^{73} -14930.9 q^{77} -6516.98 q^{79} -73532.6 q^{81} +46016.4 q^{83} +828.257 q^{87} +113488. q^{89} +38667.3 q^{91} +156185. q^{93} +107418. q^{97} -58871.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 8 q^{3} + 8 q^{7} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 8 q^{3} + 8 q^{7} + 28 q^{9} - 200 q^{11} + 592 q^{13} - 278 q^{17} - 840 q^{19} - 996 q^{21} + 1952 q^{23} - 2024 q^{27} - 4680 q^{29} - 5008 q^{31} + 10922 q^{33} - 12500 q^{37} - 27432 q^{39} - 5334 q^{41} - 224 q^{43} - 26072 q^{47} - 31654 q^{49} - 6600 q^{51} + 46812 q^{53} - 25078 q^{57} - 81776 q^{59} - 46932 q^{61} + 7824 q^{63} - 68808 q^{67} - 55044 q^{69} + 7448 q^{71} + 108822 q^{73} - 21044 q^{77} - 108104 q^{79} - 93662 q^{81} - 27224 q^{83} - 52616 q^{87} + 70990 q^{89} + 52496 q^{91} + 190660 q^{93} + 96852 q^{97} - 83776 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) −19.5242 −1.25248 −0.626238 0.779632i \(-0.715406\pi\)
−0.626238 + 0.779632i \(0.715406\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 35.0483 0.270348 0.135174 0.990822i \(-0.456841\pi\)
0.135174 + 0.990822i \(0.456841\pi\)
\(8\) 0 0
\(9\) 138.193 0.568697
\(10\) 0 0
\(11\) −426.008 −1.06154 −0.530769 0.847516i \(-0.678097\pi\)
−0.530769 + 0.847516i \(0.678097\pi\)
\(12\) 0 0
\(13\) 1103.26 1.81058 0.905291 0.424791i \(-0.139653\pi\)
0.905291 + 0.424791i \(0.139653\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 109.387 0.0918000 0.0459000 0.998946i \(-0.485384\pi\)
0.0459000 + 0.998946i \(0.485384\pi\)
\(18\) 0 0
\(19\) 495.926 0.315161 0.157581 0.987506i \(-0.449631\pi\)
0.157581 + 0.987506i \(0.449631\pi\)
\(20\) 0 0
\(21\) −684.290 −0.338604
\(22\) 0 0
\(23\) 2497.37 0.984381 0.492190 0.870488i \(-0.336196\pi\)
0.492190 + 0.870488i \(0.336196\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2046.26 0.540197
\(28\) 0 0
\(29\) −42.4221 −0.00936694 −0.00468347 0.999989i \(-0.501491\pi\)
−0.00468347 + 0.999989i \(0.501491\pi\)
\(30\) 0 0
\(31\) −7999.56 −1.49507 −0.747535 0.664222i \(-0.768763\pi\)
−0.747535 + 0.664222i \(0.768763\pi\)
\(32\) 0 0
\(33\) 8317.45 1.32955
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −13763.7 −1.65284 −0.826420 0.563054i \(-0.809626\pi\)
−0.826420 + 0.563054i \(0.809626\pi\)
\(38\) 0 0
\(39\) −21540.2 −2.26771
\(40\) 0 0
\(41\) 11863.6 1.10219 0.551097 0.834441i \(-0.314210\pi\)
0.551097 + 0.834441i \(0.314210\pi\)
\(42\) 0 0
\(43\) −16816.0 −1.38692 −0.693461 0.720494i \(-0.743915\pi\)
−0.693461 + 0.720494i \(0.743915\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −13036.0 −0.860795 −0.430397 0.902639i \(-0.641627\pi\)
−0.430397 + 0.902639i \(0.641627\pi\)
\(48\) 0 0
\(49\) −15578.6 −0.926912
\(50\) 0 0
\(51\) −2135.69 −0.114977
\(52\) 0 0
\(53\) 17817.3 0.871269 0.435634 0.900124i \(-0.356524\pi\)
0.435634 + 0.900124i \(0.356524\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −9682.55 −0.394732
\(58\) 0 0
\(59\) −47346.1 −1.77074 −0.885368 0.464891i \(-0.846094\pi\)
−0.885368 + 0.464891i \(0.846094\pi\)
\(60\) 0 0
\(61\) −22782.9 −0.783944 −0.391972 0.919977i \(-0.628207\pi\)
−0.391972 + 0.919977i \(0.628207\pi\)
\(62\) 0 0
\(63\) 4843.45 0.153746
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −39418.3 −1.07278 −0.536390 0.843970i \(-0.680213\pi\)
−0.536390 + 0.843970i \(0.680213\pi\)
\(68\) 0 0
\(69\) −48759.1 −1.23291
\(70\) 0 0
\(71\) −1616.32 −0.0380523 −0.0190261 0.999819i \(-0.506057\pi\)
−0.0190261 + 0.999819i \(0.506057\pi\)
\(72\) 0 0
\(73\) 53293.3 1.17048 0.585242 0.810859i \(-0.301000\pi\)
0.585242 + 0.810859i \(0.301000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −14930.9 −0.286984
\(78\) 0 0
\(79\) −6516.98 −0.117484 −0.0587420 0.998273i \(-0.518709\pi\)
−0.0587420 + 0.998273i \(0.518709\pi\)
\(80\) 0 0
\(81\) −73532.6 −1.24528
\(82\) 0 0
\(83\) 46016.4 0.733191 0.366595 0.930380i \(-0.380523\pi\)
0.366595 + 0.930380i \(0.380523\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 828.257 0.0117319
\(88\) 0 0
\(89\) 113488. 1.51872 0.759358 0.650673i \(-0.225513\pi\)
0.759358 + 0.650673i \(0.225513\pi\)
\(90\) 0 0
\(91\) 38667.3 0.489487
\(92\) 0 0
\(93\) 156185. 1.87254
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 107418. 1.15917 0.579585 0.814912i \(-0.303215\pi\)
0.579585 + 0.814912i \(0.303215\pi\)
\(98\) 0 0
\(99\) −58871.4 −0.603694
\(100\) 0 0
\(101\) −197554. −1.92700 −0.963502 0.267703i \(-0.913736\pi\)
−0.963502 + 0.267703i \(0.913736\pi\)
\(102\) 0 0
\(103\) −81026.0 −0.752543 −0.376272 0.926509i \(-0.622794\pi\)
−0.376272 + 0.926509i \(0.622794\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −137442. −1.16054 −0.580271 0.814423i \(-0.697054\pi\)
−0.580271 + 0.814423i \(0.697054\pi\)
\(108\) 0 0
\(109\) −68693.1 −0.553792 −0.276896 0.960900i \(-0.589306\pi\)
−0.276896 + 0.960900i \(0.589306\pi\)
\(110\) 0 0
\(111\) 268725. 2.07014
\(112\) 0 0
\(113\) −139632. −1.02870 −0.514352 0.857579i \(-0.671967\pi\)
−0.514352 + 0.857579i \(0.671967\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 152463. 1.02967
\(118\) 0 0
\(119\) 3833.83 0.0248179
\(120\) 0 0
\(121\) 20431.5 0.126864
\(122\) 0 0
\(123\) −231628. −1.38047
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −65230.1 −0.358871 −0.179436 0.983770i \(-0.557427\pi\)
−0.179436 + 0.983770i \(0.557427\pi\)
\(128\) 0 0
\(129\) 328319. 1.73709
\(130\) 0 0
\(131\) 118542. 0.603524 0.301762 0.953383i \(-0.402425\pi\)
0.301762 + 0.953383i \(0.402425\pi\)
\(132\) 0 0
\(133\) 17381.4 0.0852031
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 84757.8 0.385814 0.192907 0.981217i \(-0.438208\pi\)
0.192907 + 0.981217i \(0.438208\pi\)
\(138\) 0 0
\(139\) 168334. 0.738982 0.369491 0.929234i \(-0.379532\pi\)
0.369491 + 0.929234i \(0.379532\pi\)
\(140\) 0 0
\(141\) 254517. 1.07813
\(142\) 0 0
\(143\) −469996. −1.92200
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 304160. 1.16094
\(148\) 0 0
\(149\) 67628.6 0.249554 0.124777 0.992185i \(-0.460178\pi\)
0.124777 + 0.992185i \(0.460178\pi\)
\(150\) 0 0
\(151\) −65622.3 −0.234212 −0.117106 0.993119i \(-0.537362\pi\)
−0.117106 + 0.993119i \(0.537362\pi\)
\(152\) 0 0
\(153\) 15116.5 0.0522064
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −297885. −0.964495 −0.482247 0.876035i \(-0.660179\pi\)
−0.482247 + 0.876035i \(0.660179\pi\)
\(158\) 0 0
\(159\) −347868. −1.09124
\(160\) 0 0
\(161\) 87528.7 0.266125
\(162\) 0 0
\(163\) −473879. −1.39701 −0.698503 0.715607i \(-0.746150\pi\)
−0.698503 + 0.715607i \(0.746150\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 267673. 0.742701 0.371351 0.928493i \(-0.378895\pi\)
0.371351 + 0.928493i \(0.378895\pi\)
\(168\) 0 0
\(169\) 845883. 2.27821
\(170\) 0 0
\(171\) 68533.7 0.179231
\(172\) 0 0
\(173\) 703284. 1.78655 0.893276 0.449509i \(-0.148401\pi\)
0.893276 + 0.449509i \(0.148401\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 924393. 2.21780
\(178\) 0 0
\(179\) 635322. 1.48204 0.741022 0.671481i \(-0.234341\pi\)
0.741022 + 0.671481i \(0.234341\pi\)
\(180\) 0 0
\(181\) −547906. −1.24311 −0.621555 0.783370i \(-0.713499\pi\)
−0.621555 + 0.783370i \(0.713499\pi\)
\(182\) 0 0
\(183\) 444818. 0.981872
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −46599.6 −0.0974492
\(188\) 0 0
\(189\) 71718.1 0.146041
\(190\) 0 0
\(191\) −80607.9 −0.159880 −0.0799400 0.996800i \(-0.525473\pi\)
−0.0799400 + 0.996800i \(0.525473\pi\)
\(192\) 0 0
\(193\) −26549.3 −0.0513049 −0.0256525 0.999671i \(-0.508166\pi\)
−0.0256525 + 0.999671i \(0.508166\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −703676. −1.29184 −0.645918 0.763407i \(-0.723525\pi\)
−0.645918 + 0.763407i \(0.723525\pi\)
\(198\) 0 0
\(199\) 73599.5 0.131747 0.0658737 0.997828i \(-0.479017\pi\)
0.0658737 + 0.997828i \(0.479017\pi\)
\(200\) 0 0
\(201\) 769610. 1.34363
\(202\) 0 0
\(203\) −1486.83 −0.00253233
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 345120. 0.559815
\(208\) 0 0
\(209\) −211268. −0.334556
\(210\) 0 0
\(211\) −1.00808e6 −1.55879 −0.779395 0.626533i \(-0.784474\pi\)
−0.779395 + 0.626533i \(0.784474\pi\)
\(212\) 0 0
\(213\) 31557.2 0.0476596
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −280371. −0.404189
\(218\) 0 0
\(219\) −1.04051e6 −1.46600
\(220\) 0 0
\(221\) 120682. 0.166211
\(222\) 0 0
\(223\) 141067. 0.189961 0.0949805 0.995479i \(-0.469721\pi\)
0.0949805 + 0.995479i \(0.469721\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.14301e6 −1.47226 −0.736129 0.676842i \(-0.763348\pi\)
−0.736129 + 0.676842i \(0.763348\pi\)
\(228\) 0 0
\(229\) −1.29731e6 −1.63476 −0.817380 0.576099i \(-0.804574\pi\)
−0.817380 + 0.576099i \(0.804574\pi\)
\(230\) 0 0
\(231\) 291513. 0.359441
\(232\) 0 0
\(233\) −626232. −0.755693 −0.377846 0.925868i \(-0.623335\pi\)
−0.377846 + 0.925868i \(0.623335\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 127239. 0.147146
\(238\) 0 0
\(239\) 270281. 0.306070 0.153035 0.988221i \(-0.451095\pi\)
0.153035 + 0.988221i \(0.451095\pi\)
\(240\) 0 0
\(241\) −694339. −0.770068 −0.385034 0.922902i \(-0.625810\pi\)
−0.385034 + 0.922902i \(0.625810\pi\)
\(242\) 0 0
\(243\) 938421. 1.01949
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 547134. 0.570626
\(248\) 0 0
\(249\) −898431. −0.918304
\(250\) 0 0
\(251\) 864085. 0.865710 0.432855 0.901464i \(-0.357506\pi\)
0.432855 + 0.901464i \(0.357506\pi\)
\(252\) 0 0
\(253\) −1.06390e6 −1.04496
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.00660e6 −0.950660 −0.475330 0.879808i \(-0.657671\pi\)
−0.475330 + 0.879808i \(0.657671\pi\)
\(258\) 0 0
\(259\) −482395. −0.446841
\(260\) 0 0
\(261\) −5862.46 −0.00532695
\(262\) 0 0
\(263\) 931373. 0.830299 0.415149 0.909753i \(-0.363729\pi\)
0.415149 + 0.909753i \(0.363729\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −2.21577e6 −1.90216
\(268\) 0 0
\(269\) −1.96236e6 −1.65348 −0.826738 0.562587i \(-0.809806\pi\)
−0.826738 + 0.562587i \(0.809806\pi\)
\(270\) 0 0
\(271\) 1.12152e6 0.927649 0.463825 0.885927i \(-0.346477\pi\)
0.463825 + 0.885927i \(0.346477\pi\)
\(272\) 0 0
\(273\) −754948. −0.613070
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −105917. −0.0829401 −0.0414701 0.999140i \(-0.513204\pi\)
−0.0414701 + 0.999140i \(0.513204\pi\)
\(278\) 0 0
\(279\) −1.10549e6 −0.850242
\(280\) 0 0
\(281\) −1.05276e6 −0.795362 −0.397681 0.917524i \(-0.630185\pi\)
−0.397681 + 0.917524i \(0.630185\pi\)
\(282\) 0 0
\(283\) 950210. 0.705267 0.352633 0.935762i \(-0.385286\pi\)
0.352633 + 0.935762i \(0.385286\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 415801. 0.297975
\(288\) 0 0
\(289\) −1.40789e6 −0.991573
\(290\) 0 0
\(291\) −2.09725e6 −1.45183
\(292\) 0 0
\(293\) 381801. 0.259817 0.129909 0.991526i \(-0.458532\pi\)
0.129909 + 0.991526i \(0.458532\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −871723. −0.573440
\(298\) 0 0
\(299\) 2.75524e6 1.78230
\(300\) 0 0
\(301\) −589373. −0.374951
\(302\) 0 0
\(303\) 3.85708e6 2.41353
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.61048e6 0.975238 0.487619 0.873057i \(-0.337866\pi\)
0.487619 + 0.873057i \(0.337866\pi\)
\(308\) 0 0
\(309\) 1.58197e6 0.942543
\(310\) 0 0
\(311\) −2.15652e6 −1.26431 −0.632153 0.774843i \(-0.717829\pi\)
−0.632153 + 0.774843i \(0.717829\pi\)
\(312\) 0 0
\(313\) 364108. 0.210073 0.105036 0.994468i \(-0.466504\pi\)
0.105036 + 0.994468i \(0.466504\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.03846e6 0.580420 0.290210 0.956963i \(-0.406275\pi\)
0.290210 + 0.956963i \(0.406275\pi\)
\(318\) 0 0
\(319\) 18072.2 0.00994336
\(320\) 0 0
\(321\) 2.68345e6 1.45355
\(322\) 0 0
\(323\) 54247.8 0.0289318
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.34118e6 0.693612
\(328\) 0 0
\(329\) −456890. −0.232714
\(330\) 0 0
\(331\) −2.82942e6 −1.41948 −0.709738 0.704466i \(-0.751186\pi\)
−0.709738 + 0.704466i \(0.751186\pi\)
\(332\) 0 0
\(333\) −1.90205e6 −0.939966
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −804843. −0.386043 −0.193022 0.981194i \(-0.561829\pi\)
−0.193022 + 0.981194i \(0.561829\pi\)
\(338\) 0 0
\(339\) 2.72621e6 1.28843
\(340\) 0 0
\(341\) 3.40787e6 1.58708
\(342\) 0 0
\(343\) −1.13506e6 −0.520936
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −759889. −0.338787 −0.169393 0.985549i \(-0.554181\pi\)
−0.169393 + 0.985549i \(0.554181\pi\)
\(348\) 0 0
\(349\) 580673. 0.255193 0.127596 0.991826i \(-0.459274\pi\)
0.127596 + 0.991826i \(0.459274\pi\)
\(350\) 0 0
\(351\) 2.25755e6 0.978071
\(352\) 0 0
\(353\) 1.64210e6 0.701393 0.350697 0.936489i \(-0.385945\pi\)
0.350697 + 0.936489i \(0.385945\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −74852.3 −0.0310838
\(358\) 0 0
\(359\) −2.88181e6 −1.18013 −0.590065 0.807356i \(-0.700898\pi\)
−0.590065 + 0.807356i \(0.700898\pi\)
\(360\) 0 0
\(361\) −2.23016e6 −0.900673
\(362\) 0 0
\(363\) −398909. −0.158894
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 3.83418e6 1.48596 0.742980 0.669314i \(-0.233412\pi\)
0.742980 + 0.669314i \(0.233412\pi\)
\(368\) 0 0
\(369\) 1.63947e6 0.626814
\(370\) 0 0
\(371\) 624467. 0.235545
\(372\) 0 0
\(373\) −3.19341e6 −1.18845 −0.594227 0.804298i \(-0.702542\pi\)
−0.594227 + 0.804298i \(0.702542\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −46802.5 −0.0169596
\(378\) 0 0
\(379\) 3.47338e6 1.24209 0.621046 0.783774i \(-0.286708\pi\)
0.621046 + 0.783774i \(0.286708\pi\)
\(380\) 0 0
\(381\) 1.27356e6 0.449478
\(382\) 0 0
\(383\) −1.56341e6 −0.544599 −0.272299 0.962213i \(-0.587784\pi\)
−0.272299 + 0.962213i \(0.587784\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −2.32386e6 −0.788738
\(388\) 0 0
\(389\) 4.98980e6 1.67190 0.835949 0.548808i \(-0.184918\pi\)
0.835949 + 0.548808i \(0.184918\pi\)
\(390\) 0 0
\(391\) 273179. 0.0903661
\(392\) 0 0
\(393\) −2.31444e6 −0.755899
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1.37245e6 0.437038 0.218519 0.975833i \(-0.429877\pi\)
0.218519 + 0.975833i \(0.429877\pi\)
\(398\) 0 0
\(399\) −339357. −0.106715
\(400\) 0 0
\(401\) 5.44247e6 1.69019 0.845094 0.534617i \(-0.179544\pi\)
0.845094 + 0.534617i \(0.179544\pi\)
\(402\) 0 0
\(403\) −8.82557e6 −2.70695
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.86344e6 1.75455
\(408\) 0 0
\(409\) −6.03830e6 −1.78487 −0.892435 0.451176i \(-0.851005\pi\)
−0.892435 + 0.451176i \(0.851005\pi\)
\(410\) 0 0
\(411\) −1.65483e6 −0.483223
\(412\) 0 0
\(413\) −1.65940e6 −0.478714
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −3.28657e6 −0.925557
\(418\) 0 0
\(419\) 770366. 0.214369 0.107184 0.994239i \(-0.465816\pi\)
0.107184 + 0.994239i \(0.465816\pi\)
\(420\) 0 0
\(421\) 2.00249e6 0.550636 0.275318 0.961353i \(-0.411217\pi\)
0.275318 + 0.961353i \(0.411217\pi\)
\(422\) 0 0
\(423\) −1.80149e6 −0.489532
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −798504. −0.211937
\(428\) 0 0
\(429\) 9.17628e6 2.40726
\(430\) 0 0
\(431\) 5.56690e6 1.44351 0.721756 0.692148i \(-0.243335\pi\)
0.721756 + 0.692148i \(0.243335\pi\)
\(432\) 0 0
\(433\) 2.22941e6 0.571441 0.285720 0.958313i \(-0.407767\pi\)
0.285720 + 0.958313i \(0.407767\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.23851e6 0.310239
\(438\) 0 0
\(439\) 543061. 0.134489 0.0672446 0.997737i \(-0.478579\pi\)
0.0672446 + 0.997737i \(0.478579\pi\)
\(440\) 0 0
\(441\) −2.15286e6 −0.527132
\(442\) 0 0
\(443\) 4.53358e6 1.09757 0.548785 0.835964i \(-0.315091\pi\)
0.548785 + 0.835964i \(0.315091\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −1.32039e6 −0.312561
\(448\) 0 0
\(449\) −3.39468e6 −0.794662 −0.397331 0.917675i \(-0.630064\pi\)
−0.397331 + 0.917675i \(0.630064\pi\)
\(450\) 0 0
\(451\) −5.05400e6 −1.17002
\(452\) 0 0
\(453\) 1.28122e6 0.293345
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 8.34100e6 1.86822 0.934109 0.356988i \(-0.116196\pi\)
0.934109 + 0.356988i \(0.116196\pi\)
\(458\) 0 0
\(459\) 223834. 0.0495900
\(460\) 0 0
\(461\) −3.18453e6 −0.697900 −0.348950 0.937141i \(-0.613462\pi\)
−0.348950 + 0.937141i \(0.613462\pi\)
\(462\) 0 0
\(463\) 4.05943e6 0.880061 0.440030 0.897983i \(-0.354968\pi\)
0.440030 + 0.897983i \(0.354968\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.98706e6 −1.69471 −0.847353 0.531029i \(-0.821805\pi\)
−0.847353 + 0.531029i \(0.821805\pi\)
\(468\) 0 0
\(469\) −1.38155e6 −0.290024
\(470\) 0 0
\(471\) 5.81596e6 1.20801
\(472\) 0 0
\(473\) 7.16375e6 1.47227
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 2.46223e6 0.495488
\(478\) 0 0
\(479\) 5.27553e6 1.05058 0.525288 0.850924i \(-0.323958\pi\)
0.525288 + 0.850924i \(0.323958\pi\)
\(480\) 0 0
\(481\) −1.51849e7 −2.99260
\(482\) 0 0
\(483\) −1.70892e6 −0.333315
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 8.76969e6 1.67557 0.837784 0.546002i \(-0.183851\pi\)
0.837784 + 0.546002i \(0.183851\pi\)
\(488\) 0 0
\(489\) 9.25209e6 1.74972
\(490\) 0 0
\(491\) 7.83080e6 1.46589 0.732946 0.680286i \(-0.238145\pi\)
0.732946 + 0.680286i \(0.238145\pi\)
\(492\) 0 0
\(493\) −4640.42 −0.000859885 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −56649.2 −0.0102873
\(498\) 0 0
\(499\) −6.54560e6 −1.17679 −0.588394 0.808574i \(-0.700240\pi\)
−0.588394 + 0.808574i \(0.700240\pi\)
\(500\) 0 0
\(501\) −5.22610e6 −0.930216
\(502\) 0 0
\(503\) −2.07773e6 −0.366158 −0.183079 0.983098i \(-0.558606\pi\)
−0.183079 + 0.983098i \(0.558606\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.65152e7 −2.85340
\(508\) 0 0
\(509\) −6.25093e6 −1.06942 −0.534712 0.845034i \(-0.679580\pi\)
−0.534712 + 0.845034i \(0.679580\pi\)
\(510\) 0 0
\(511\) 1.86784e6 0.316437
\(512\) 0 0
\(513\) 1.01480e6 0.170249
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 5.55344e6 0.913767
\(518\) 0 0
\(519\) −1.37310e7 −2.23761
\(520\) 0 0
\(521\) 2.19897e6 0.354916 0.177458 0.984128i \(-0.443213\pi\)
0.177458 + 0.984128i \(0.443213\pi\)
\(522\) 0 0
\(523\) −2.10298e6 −0.336187 −0.168093 0.985771i \(-0.553761\pi\)
−0.168093 + 0.985771i \(0.553761\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −875046. −0.137247
\(528\) 0 0
\(529\) −199490. −0.0309944
\(530\) 0 0
\(531\) −6.54291e6 −1.00701
\(532\) 0 0
\(533\) 1.30886e7 1.99561
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.24041e7 −1.85623
\(538\) 0 0
\(539\) 6.63661e6 0.983953
\(540\) 0 0
\(541\) −1.83729e6 −0.269889 −0.134944 0.990853i \(-0.543086\pi\)
−0.134944 + 0.990853i \(0.543086\pi\)
\(542\) 0 0
\(543\) 1.06974e7 1.55697
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 4.31872e6 0.617145 0.308572 0.951201i \(-0.400149\pi\)
0.308572 + 0.951201i \(0.400149\pi\)
\(548\) 0 0
\(549\) −3.14845e6 −0.445827
\(550\) 0 0
\(551\) −21038.3 −0.00295210
\(552\) 0 0
\(553\) −228409. −0.0317615
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4.26837e6 −0.582940 −0.291470 0.956580i \(-0.594144\pi\)
−0.291470 + 0.956580i \(0.594144\pi\)
\(558\) 0 0
\(559\) −1.85524e7 −2.51114
\(560\) 0 0
\(561\) 909819. 0.122053
\(562\) 0 0
\(563\) −1.26350e7 −1.67998 −0.839988 0.542605i \(-0.817438\pi\)
−0.839988 + 0.542605i \(0.817438\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2.57720e6 −0.336659
\(568\) 0 0
\(569\) −8.67409e6 −1.12316 −0.561582 0.827421i \(-0.689807\pi\)
−0.561582 + 0.827421i \(0.689807\pi\)
\(570\) 0 0
\(571\) 3.28781e6 0.422004 0.211002 0.977486i \(-0.432327\pi\)
0.211002 + 0.977486i \(0.432327\pi\)
\(572\) 0 0
\(573\) 1.57380e6 0.200246
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −117668. −0.0147135 −0.00735677 0.999973i \(-0.502342\pi\)
−0.00735677 + 0.999973i \(0.502342\pi\)
\(578\) 0 0
\(579\) 518352. 0.0642582
\(580\) 0 0
\(581\) 1.61280e6 0.198216
\(582\) 0 0
\(583\) −7.59031e6 −0.924885
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.10151e7 −1.31945 −0.659723 0.751509i \(-0.729326\pi\)
−0.659723 + 0.751509i \(0.729326\pi\)
\(588\) 0 0
\(589\) −3.96719e6 −0.471189
\(590\) 0 0
\(591\) 1.37387e7 1.61799
\(592\) 0 0
\(593\) −5.33879e6 −0.623456 −0.311728 0.950171i \(-0.600908\pi\)
−0.311728 + 0.950171i \(0.600908\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1.43697e6 −0.165011
\(598\) 0 0
\(599\) −7.17784e6 −0.817385 −0.408692 0.912672i \(-0.634015\pi\)
−0.408692 + 0.912672i \(0.634015\pi\)
\(600\) 0 0
\(601\) −809127. −0.0913756 −0.0456878 0.998956i \(-0.514548\pi\)
−0.0456878 + 0.998956i \(0.514548\pi\)
\(602\) 0 0
\(603\) −5.44735e6 −0.610087
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 591991. 0.0652143 0.0326072 0.999468i \(-0.489619\pi\)
0.0326072 + 0.999468i \(0.489619\pi\)
\(608\) 0 0
\(609\) 29029.1 0.00317168
\(610\) 0 0
\(611\) −1.43821e7 −1.55854
\(612\) 0 0
\(613\) −4.01173e6 −0.431201 −0.215601 0.976482i \(-0.569171\pi\)
−0.215601 + 0.976482i \(0.569171\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 8.24093e6 0.871491 0.435746 0.900070i \(-0.356485\pi\)
0.435746 + 0.900070i \(0.356485\pi\)
\(618\) 0 0
\(619\) 1.96985e6 0.206636 0.103318 0.994648i \(-0.467054\pi\)
0.103318 + 0.994648i \(0.467054\pi\)
\(620\) 0 0
\(621\) 5.11027e6 0.531759
\(622\) 0 0
\(623\) 3.97758e6 0.410581
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 4.12484e6 0.419024
\(628\) 0 0
\(629\) −1.50557e6 −0.151731
\(630\) 0 0
\(631\) −1.82360e7 −1.82329 −0.911646 0.410977i \(-0.865187\pi\)
−0.911646 + 0.410977i \(0.865187\pi\)
\(632\) 0 0
\(633\) 1.96819e7 1.95235
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1.71872e7 −1.67825
\(638\) 0 0
\(639\) −223364. −0.0216402
\(640\) 0 0
\(641\) 7.65378e6 0.735752 0.367876 0.929875i \(-0.380085\pi\)
0.367876 + 0.929875i \(0.380085\pi\)
\(642\) 0 0
\(643\) 2.47762e6 0.236323 0.118162 0.992994i \(-0.462300\pi\)
0.118162 + 0.992994i \(0.462300\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4.79533e6 0.450358 0.225179 0.974317i \(-0.427703\pi\)
0.225179 + 0.974317i \(0.427703\pi\)
\(648\) 0 0
\(649\) 2.01698e7 1.87970
\(650\) 0 0
\(651\) 5.47402e6 0.506237
\(652\) 0 0
\(653\) 1.67125e7 1.53376 0.766881 0.641789i \(-0.221807\pi\)
0.766881 + 0.641789i \(0.221807\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 7.36478e6 0.665650
\(658\) 0 0
\(659\) 3.28380e6 0.294553 0.147277 0.989095i \(-0.452949\pi\)
0.147277 + 0.989095i \(0.452949\pi\)
\(660\) 0 0
\(661\) −1.98880e7 −1.77047 −0.885234 0.465145i \(-0.846002\pi\)
−0.885234 + 0.465145i \(0.846002\pi\)
\(662\) 0 0
\(663\) −2.35621e6 −0.208176
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −105944. −0.00922063
\(668\) 0 0
\(669\) −2.75423e6 −0.237922
\(670\) 0 0
\(671\) 9.70571e6 0.832187
\(672\) 0 0
\(673\) −1.39915e7 −1.19076 −0.595381 0.803443i \(-0.702999\pi\)
−0.595381 + 0.803443i \(0.702999\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.13032e6 0.262493 0.131246 0.991350i \(-0.458102\pi\)
0.131246 + 0.991350i \(0.458102\pi\)
\(678\) 0 0
\(679\) 3.76482e6 0.313379
\(680\) 0 0
\(681\) 2.23162e7 1.84397
\(682\) 0 0
\(683\) 8.94034e6 0.733335 0.366667 0.930352i \(-0.380499\pi\)
0.366667 + 0.930352i \(0.380499\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 2.53288e7 2.04750
\(688\) 0 0
\(689\) 1.96571e7 1.57750
\(690\) 0 0
\(691\) −2.38378e7 −1.89920 −0.949599 0.313466i \(-0.898510\pi\)
−0.949599 + 0.313466i \(0.898510\pi\)
\(692\) 0 0
\(693\) −2.06335e6 −0.163207
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 1.29772e6 0.101181
\(698\) 0 0
\(699\) 1.22267e7 0.946487
\(700\) 0 0
\(701\) 1.57226e7 1.20845 0.604225 0.796814i \(-0.293483\pi\)
0.604225 + 0.796814i \(0.293483\pi\)
\(702\) 0 0
\(703\) −6.82578e6 −0.520912
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6.92394e6 −0.520961
\(708\) 0 0
\(709\) −3.05866e6 −0.228515 −0.114258 0.993451i \(-0.536449\pi\)
−0.114258 + 0.993451i \(0.536449\pi\)
\(710\) 0 0
\(711\) −900603. −0.0668128
\(712\) 0 0
\(713\) −1.99778e7 −1.47172
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −5.27701e6 −0.383345
\(718\) 0 0
\(719\) 2.16146e7 1.55929 0.779643 0.626224i \(-0.215400\pi\)
0.779643 + 0.626224i \(0.215400\pi\)
\(720\) 0 0
\(721\) −2.83983e6 −0.203448
\(722\) 0 0
\(723\) 1.35564e7 0.964492
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 2.73589e7 1.91983 0.959916 0.280287i \(-0.0904297\pi\)
0.959916 + 0.280287i \(0.0904297\pi\)
\(728\) 0 0
\(729\) −453482. −0.0316039
\(730\) 0 0
\(731\) −1.83945e6 −0.127319
\(732\) 0 0
\(733\) −1.54693e7 −1.06344 −0.531718 0.846921i \(-0.678453\pi\)
−0.531718 + 0.846921i \(0.678453\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.67925e7 1.13880
\(738\) 0 0
\(739\) 5.56327e6 0.374731 0.187365 0.982290i \(-0.440005\pi\)
0.187365 + 0.982290i \(0.440005\pi\)
\(740\) 0 0
\(741\) −1.06823e7 −0.714695
\(742\) 0 0
\(743\) 1.55089e7 1.03064 0.515322 0.856997i \(-0.327672\pi\)
0.515322 + 0.856997i \(0.327672\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 6.35916e6 0.416963
\(748\) 0 0
\(749\) −4.81713e6 −0.313750
\(750\) 0 0
\(751\) 2.20221e7 1.42482 0.712409 0.701765i \(-0.247604\pi\)
0.712409 + 0.701765i \(0.247604\pi\)
\(752\) 0 0
\(753\) −1.68706e7 −1.08428
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.75653e6 0.111408 0.0557040 0.998447i \(-0.482260\pi\)
0.0557040 + 0.998447i \(0.482260\pi\)
\(758\) 0 0
\(759\) 2.07717e7 1.30879
\(760\) 0 0
\(761\) −2.16974e6 −0.135814 −0.0679072 0.997692i \(-0.521632\pi\)
−0.0679072 + 0.997692i \(0.521632\pi\)
\(762\) 0 0
\(763\) −2.40758e6 −0.149716
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.22349e7 −3.20606
\(768\) 0 0
\(769\) −1.12131e7 −0.683769 −0.341884 0.939742i \(-0.611065\pi\)
−0.341884 + 0.939742i \(0.611065\pi\)
\(770\) 0 0
\(771\) 1.96531e7 1.19068
\(772\) 0 0
\(773\) −1.43367e7 −0.862980 −0.431490 0.902118i \(-0.642012\pi\)
−0.431490 + 0.902118i \(0.642012\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 9.41836e6 0.559658
\(778\) 0 0
\(779\) 5.88348e6 0.347369
\(780\) 0 0
\(781\) 688563. 0.0403939
\(782\) 0 0
\(783\) −86806.8 −0.00505999
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −2.00549e6 −0.115421 −0.0577103 0.998333i \(-0.518380\pi\)
−0.0577103 + 0.998333i \(0.518380\pi\)
\(788\) 0 0
\(789\) −1.81843e7 −1.03993
\(790\) 0 0
\(791\) −4.89389e6 −0.278108
\(792\) 0 0
\(793\) −2.51354e7 −1.41940
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −448115. −0.0249887 −0.0124944 0.999922i \(-0.503977\pi\)
−0.0124944 + 0.999922i \(0.503977\pi\)
\(798\) 0 0
\(799\) −1.42597e6 −0.0790210
\(800\) 0 0
\(801\) 1.56834e7 0.863690
\(802\) 0 0
\(803\) −2.27033e7 −1.24251
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 3.83134e7 2.07094
\(808\) 0 0
\(809\) 1.28425e7 0.689889 0.344944 0.938623i \(-0.387898\pi\)
0.344944 + 0.938623i \(0.387898\pi\)
\(810\) 0 0
\(811\) 1.78700e7 0.954054 0.477027 0.878889i \(-0.341714\pi\)
0.477027 + 0.878889i \(0.341714\pi\)
\(812\) 0 0
\(813\) −2.18968e7 −1.16186
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −8.33950e6 −0.437104
\(818\) 0 0
\(819\) 5.34357e6 0.278370
\(820\) 0 0
\(821\) 2.73336e7 1.41527 0.707634 0.706580i \(-0.249763\pi\)
0.707634 + 0.706580i \(0.249763\pi\)
\(822\) 0 0
\(823\) −3.05819e6 −0.157385 −0.0786927 0.996899i \(-0.525075\pi\)
−0.0786927 + 0.996899i \(0.525075\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.23961e7 −0.630261 −0.315131 0.949048i \(-0.602048\pi\)
−0.315131 + 0.949048i \(0.602048\pi\)
\(828\) 0 0
\(829\) −399873. −0.0202086 −0.0101043 0.999949i \(-0.503216\pi\)
−0.0101043 + 0.999949i \(0.503216\pi\)
\(830\) 0 0
\(831\) 2.06793e6 0.103881
\(832\) 0 0
\(833\) −1.70409e6 −0.0850905
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1.63692e7 −0.807632
\(838\) 0 0
\(839\) −2.08411e6 −0.102215 −0.0511075 0.998693i \(-0.516275\pi\)
−0.0511075 + 0.998693i \(0.516275\pi\)
\(840\) 0 0
\(841\) −2.05093e7 −0.999912
\(842\) 0 0
\(843\) 2.05543e7 0.996172
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 716092. 0.0342973
\(848\) 0 0
\(849\) −1.85521e7 −0.883330
\(850\) 0 0
\(851\) −3.43730e7 −1.62702
\(852\) 0 0
\(853\) 2.14298e7 1.00843 0.504214 0.863579i \(-0.331782\pi\)
0.504214 + 0.863579i \(0.331782\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3.49123e6 0.162377 0.0811887 0.996699i \(-0.474128\pi\)
0.0811887 + 0.996699i \(0.474128\pi\)
\(858\) 0 0
\(859\) −568043. −0.0262662 −0.0131331 0.999914i \(-0.504181\pi\)
−0.0131331 + 0.999914i \(0.504181\pi\)
\(860\) 0 0
\(861\) −8.11816e6 −0.373207
\(862\) 0 0
\(863\) 3.28678e7 1.50226 0.751128 0.660157i \(-0.229510\pi\)
0.751128 + 0.660157i \(0.229510\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 2.74879e7 1.24192
\(868\) 0 0
\(869\) 2.77628e6 0.124714
\(870\) 0 0
\(871\) −4.34885e7 −1.94236
\(872\) 0 0
\(873\) 1.48444e7 0.659217
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 2.92945e7 1.28614 0.643069 0.765808i \(-0.277661\pi\)
0.643069 + 0.765808i \(0.277661\pi\)
\(878\) 0 0
\(879\) −7.45435e6 −0.325415
\(880\) 0 0
\(881\) 2.88332e6 0.125156 0.0625782 0.998040i \(-0.480068\pi\)
0.0625782 + 0.998040i \(0.480068\pi\)
\(882\) 0 0
\(883\) 2.79477e7 1.20627 0.603135 0.797639i \(-0.293918\pi\)
0.603135 + 0.797639i \(0.293918\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.89567e7 −1.23578 −0.617888 0.786266i \(-0.712011\pi\)
−0.617888 + 0.786266i \(0.712011\pi\)
\(888\) 0 0
\(889\) −2.28621e6 −0.0970199
\(890\) 0 0
\(891\) 3.13254e7 1.32191
\(892\) 0 0
\(893\) −6.46490e6 −0.271289
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −5.37938e7 −2.23229
\(898\) 0 0
\(899\) 339358. 0.0140042
\(900\) 0 0
\(901\) 1.94898e6 0.0799825
\(902\) 0 0
\(903\) 1.15070e7 0.469617
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −1.18508e6 −0.0478333 −0.0239166 0.999714i \(-0.507614\pi\)
−0.0239166 + 0.999714i \(0.507614\pi\)
\(908\) 0 0
\(909\) −2.73007e7 −1.09588
\(910\) 0 0
\(911\) −1.14346e7 −0.456485 −0.228242 0.973604i \(-0.573298\pi\)
−0.228242 + 0.973604i \(0.573298\pi\)
\(912\) 0 0
\(913\) −1.96033e7 −0.778310
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 4.15471e6 0.163161
\(918\) 0 0
\(919\) −1.48904e7 −0.581589 −0.290795 0.956785i \(-0.593920\pi\)
−0.290795 + 0.956785i \(0.593920\pi\)
\(920\) 0 0
\(921\) −3.14434e7 −1.22146
\(922\) 0 0
\(923\) −1.78321e6 −0.0688968
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −1.11973e7 −0.427969
\(928\) 0 0
\(929\) −2.02580e7 −0.770117 −0.385058 0.922892i \(-0.625819\pi\)
−0.385058 + 0.922892i \(0.625819\pi\)
\(930\) 0 0
\(931\) −7.72584e6 −0.292127
\(932\) 0 0
\(933\) 4.21043e7 1.58351
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −1.96237e7 −0.730182 −0.365091 0.930972i \(-0.618962\pi\)
−0.365091 + 0.930972i \(0.618962\pi\)
\(938\) 0 0
\(939\) −7.10891e6 −0.263111
\(940\) 0 0
\(941\) 7.62854e6 0.280846 0.140423 0.990092i \(-0.455154\pi\)
0.140423 + 0.990092i \(0.455154\pi\)
\(942\) 0 0
\(943\) 2.96279e7 1.08498
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.93605e7 1.42622 0.713108 0.701054i \(-0.247287\pi\)
0.713108 + 0.701054i \(0.247287\pi\)
\(948\) 0 0
\(949\) 5.87962e7 2.11926
\(950\) 0 0
\(951\) −2.02751e7 −0.726963
\(952\) 0 0
\(953\) 5.09953e7 1.81886 0.909428 0.415861i \(-0.136520\pi\)
0.909428 + 0.415861i \(0.136520\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −352844. −0.0124538
\(958\) 0 0
\(959\) 2.97062e6 0.104304
\(960\) 0 0
\(961\) 3.53638e7 1.23524
\(962\) 0 0
\(963\) −1.89936e7 −0.659997
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −5.17740e7 −1.78051 −0.890257 0.455458i \(-0.849476\pi\)
−0.890257 + 0.455458i \(0.849476\pi\)
\(968\) 0 0
\(969\) −1.05914e6 −0.0362364
\(970\) 0 0
\(971\) −3.69158e7 −1.25651 −0.628253 0.778009i \(-0.716230\pi\)
−0.628253 + 0.778009i \(0.716230\pi\)
\(972\) 0 0
\(973\) 5.89981e6 0.199782
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 3.14468e7 1.05400 0.526999 0.849866i \(-0.323317\pi\)
0.526999 + 0.849866i \(0.323317\pi\)
\(978\) 0 0
\(979\) −4.83470e7 −1.61218
\(980\) 0 0
\(981\) −9.49293e6 −0.314940
\(982\) 0 0
\(983\) −5.15823e7 −1.70262 −0.851308 0.524667i \(-0.824190\pi\)
−0.851308 + 0.524667i \(0.824190\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 8.92041e6 0.291469
\(988\) 0 0
\(989\) −4.19958e7 −1.36526
\(990\) 0 0
\(991\) −1.30562e7 −0.422312 −0.211156 0.977452i \(-0.567723\pi\)
−0.211156 + 0.977452i \(0.567723\pi\)
\(992\) 0 0
\(993\) 5.52421e7 1.77786
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −4.97672e7 −1.58564 −0.792821 0.609454i \(-0.791389\pi\)
−0.792821 + 0.609454i \(0.791389\pi\)
\(998\) 0 0
\(999\) −2.81641e7 −0.892859
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 200.6.a.e.1.1 2
4.3 odd 2 400.6.a.u.1.2 2
5.2 odd 4 200.6.c.f.49.4 4
5.3 odd 4 200.6.c.f.49.1 4
5.4 even 2 200.6.a.f.1.2 yes 2
20.3 even 4 400.6.c.o.49.4 4
20.7 even 4 400.6.c.o.49.1 4
20.19 odd 2 400.6.a.r.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
200.6.a.e.1.1 2 1.1 even 1 trivial
200.6.a.f.1.2 yes 2 5.4 even 2
200.6.c.f.49.1 4 5.3 odd 4
200.6.c.f.49.4 4 5.2 odd 4
400.6.a.r.1.1 2 20.19 odd 2
400.6.a.u.1.2 2 4.3 odd 2
400.6.c.o.49.1 4 20.7 even 4
400.6.c.o.49.4 4 20.3 even 4