Properties

Label 400.6.a.a.1.1
Level 400
Weight 6
Character 400.1
Self dual yes
Analytic conductor 64.154
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 400.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1535279252\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 10)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 400.1

$q$-expansion

\(f(q)\) \(=\) \(q-26.0000 q^{3} -22.0000 q^{7} +433.000 q^{9} +O(q^{10})\) \(q-26.0000 q^{3} -22.0000 q^{7} +433.000 q^{9} +768.000 q^{11} +46.0000 q^{13} -378.000 q^{17} -1100.00 q^{19} +572.000 q^{21} -1986.00 q^{23} -4940.00 q^{27} -5610.00 q^{29} +3988.00 q^{31} -19968.0 q^{33} +142.000 q^{37} -1196.00 q^{39} +1542.00 q^{41} -5026.00 q^{43} +24738.0 q^{47} -16323.0 q^{49} +9828.00 q^{51} +14166.0 q^{53} +28600.0 q^{57} -28380.0 q^{59} +5522.00 q^{61} -9526.00 q^{63} -24742.0 q^{67} +51636.0 q^{69} -42372.0 q^{71} +52126.0 q^{73} -16896.0 q^{77} +39640.0 q^{79} +23221.0 q^{81} -59826.0 q^{83} +145860. q^{87} +57690.0 q^{89} -1012.00 q^{91} -103688. q^{93} +144382. q^{97} +332544. q^{99} +O(q^{100})\)

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
\(3\) −26.0000 −1.66790 −0.833950 0.551839i \(-0.813926\pi\)
−0.833950 + 0.551839i \(0.813926\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −22.0000 −0.169698 −0.0848492 0.996394i \(-0.527041\pi\)
−0.0848492 + 0.996394i \(0.527041\pi\)
\(8\) 0 0
\(9\) 433.000 1.78189
\(10\) 0 0
\(11\) 768.000 1.91372 0.956862 0.290541i \(-0.0938354\pi\)
0.956862 + 0.290541i \(0.0938354\pi\)
\(12\) 0 0
\(13\) 46.0000 0.0754917 0.0377459 0.999287i \(-0.487982\pi\)
0.0377459 + 0.999287i \(0.487982\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −378.000 −0.317227 −0.158613 0.987341i \(-0.550702\pi\)
−0.158613 + 0.987341i \(0.550702\pi\)
\(18\) 0 0
\(19\) −1100.00 −0.699051 −0.349525 0.936927i \(-0.613657\pi\)
−0.349525 + 0.936927i \(0.613657\pi\)
\(20\) 0 0
\(21\) 572.000 0.283040
\(22\) 0 0
\(23\) −1986.00 −0.782816 −0.391408 0.920217i \(-0.628012\pi\)
−0.391408 + 0.920217i \(0.628012\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −4940.00 −1.30412
\(28\) 0 0
\(29\) −5610.00 −1.23870 −0.619352 0.785113i \(-0.712605\pi\)
−0.619352 + 0.785113i \(0.712605\pi\)
\(30\) 0 0
\(31\) 3988.00 0.745334 0.372667 0.927965i \(-0.378443\pi\)
0.372667 + 0.927965i \(0.378443\pi\)
\(32\) 0 0
\(33\) −19968.0 −3.19190
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 142.000 0.0170523 0.00852617 0.999964i \(-0.497286\pi\)
0.00852617 + 0.999964i \(0.497286\pi\)
\(38\) 0 0
\(39\) −1196.00 −0.125913
\(40\) 0 0
\(41\) 1542.00 0.143260 0.0716300 0.997431i \(-0.477180\pi\)
0.0716300 + 0.997431i \(0.477180\pi\)
\(42\) 0 0
\(43\) −5026.00 −0.414526 −0.207263 0.978285i \(-0.566456\pi\)
−0.207263 + 0.978285i \(0.566456\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 24738.0 1.63350 0.816752 0.576990i \(-0.195773\pi\)
0.816752 + 0.576990i \(0.195773\pi\)
\(48\) 0 0
\(49\) −16323.0 −0.971202
\(50\) 0 0
\(51\) 9828.00 0.529102
\(52\) 0 0
\(53\) 14166.0 0.692720 0.346360 0.938102i \(-0.387418\pi\)
0.346360 + 0.938102i \(0.387418\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 28600.0 1.16595
\(58\) 0 0
\(59\) −28380.0 −1.06141 −0.530704 0.847557i \(-0.678072\pi\)
−0.530704 + 0.847557i \(0.678072\pi\)
\(60\) 0 0
\(61\) 5522.00 0.190008 0.0950040 0.995477i \(-0.469714\pi\)
0.0950040 + 0.995477i \(0.469714\pi\)
\(62\) 0 0
\(63\) −9526.00 −0.302384
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −24742.0 −0.673361 −0.336680 0.941619i \(-0.609304\pi\)
−0.336680 + 0.941619i \(0.609304\pi\)
\(68\) 0 0
\(69\) 51636.0 1.30566
\(70\) 0 0
\(71\) −42372.0 −0.997546 −0.498773 0.866733i \(-0.666216\pi\)
−0.498773 + 0.866733i \(0.666216\pi\)
\(72\) 0 0
\(73\) 52126.0 1.14485 0.572423 0.819958i \(-0.306003\pi\)
0.572423 + 0.819958i \(0.306003\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −16896.0 −0.324756
\(78\) 0 0
\(79\) 39640.0 0.714605 0.357302 0.933989i \(-0.383697\pi\)
0.357302 + 0.933989i \(0.383697\pi\)
\(80\) 0 0
\(81\) 23221.0 0.393250
\(82\) 0 0
\(83\) −59826.0 −0.953223 −0.476612 0.879114i \(-0.658135\pi\)
−0.476612 + 0.879114i \(0.658135\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 145860. 2.06604
\(88\) 0 0
\(89\) 57690.0 0.772015 0.386007 0.922496i \(-0.373854\pi\)
0.386007 + 0.922496i \(0.373854\pi\)
\(90\) 0 0
\(91\) −1012.00 −0.0128108
\(92\) 0 0
\(93\) −103688. −1.24314
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 144382. 1.55806 0.779029 0.626988i \(-0.215712\pi\)
0.779029 + 0.626988i \(0.215712\pi\)
\(98\) 0 0
\(99\) 332544. 3.41005
\(100\) 0 0
\(101\) −141258. −1.37787 −0.688937 0.724821i \(-0.741922\pi\)
−0.688937 + 0.724821i \(0.741922\pi\)
\(102\) 0 0
\(103\) 139814. 1.29855 0.649273 0.760555i \(-0.275073\pi\)
0.649273 + 0.760555i \(0.275073\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 86418.0 0.729701 0.364850 0.931066i \(-0.381120\pi\)
0.364850 + 0.931066i \(0.381120\pi\)
\(108\) 0 0
\(109\) 218450. 1.76111 0.880554 0.473947i \(-0.157171\pi\)
0.880554 + 0.473947i \(0.157171\pi\)
\(110\) 0 0
\(111\) −3692.00 −0.0284416
\(112\) 0 0
\(113\) 28806.0 0.212220 0.106110 0.994354i \(-0.466160\pi\)
0.106110 + 0.994354i \(0.466160\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 19918.0 0.134518
\(118\) 0 0
\(119\) 8316.00 0.0538328
\(120\) 0 0
\(121\) 428773. 2.66234
\(122\) 0 0
\(123\) −40092.0 −0.238943
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −216502. −1.19111 −0.595556 0.803314i \(-0.703068\pi\)
−0.595556 + 0.803314i \(0.703068\pi\)
\(128\) 0 0
\(129\) 130676. 0.691388
\(130\) 0 0
\(131\) 244608. 1.24535 0.622676 0.782479i \(-0.286045\pi\)
0.622676 + 0.782479i \(0.286045\pi\)
\(132\) 0 0
\(133\) 24200.0 0.118628
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 239502. 1.09020 0.545102 0.838370i \(-0.316491\pi\)
0.545102 + 0.838370i \(0.316491\pi\)
\(138\) 0 0
\(139\) −30860.0 −0.135475 −0.0677375 0.997703i \(-0.521578\pi\)
−0.0677375 + 0.997703i \(0.521578\pi\)
\(140\) 0 0
\(141\) −643188. −2.72452
\(142\) 0 0
\(143\) 35328.0 0.144470
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 424398. 1.61987
\(148\) 0 0
\(149\) −100950. −0.372512 −0.186256 0.982501i \(-0.559635\pi\)
−0.186256 + 0.982501i \(0.559635\pi\)
\(150\) 0 0
\(151\) −12452.0 −0.0444423 −0.0222212 0.999753i \(-0.507074\pi\)
−0.0222212 + 0.999753i \(0.507074\pi\)
\(152\) 0 0
\(153\) −163674. −0.565264
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 6022.00 0.0194981 0.00974903 0.999952i \(-0.496897\pi\)
0.00974903 + 0.999952i \(0.496897\pi\)
\(158\) 0 0
\(159\) −368316. −1.15539
\(160\) 0 0
\(161\) 43692.0 0.132843
\(162\) 0 0
\(163\) −500866. −1.47656 −0.738282 0.674492i \(-0.764363\pi\)
−0.738282 + 0.674492i \(0.764363\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 555258. 1.54065 0.770324 0.637652i \(-0.220094\pi\)
0.770324 + 0.637652i \(0.220094\pi\)
\(168\) 0 0
\(169\) −369177. −0.994301
\(170\) 0 0
\(171\) −476300. −1.24563
\(172\) 0 0
\(173\) −417354. −1.06020 −0.530102 0.847934i \(-0.677846\pi\)
−0.530102 + 0.847934i \(0.677846\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 737880. 1.77032
\(178\) 0 0
\(179\) 52380.0 0.122189 0.0610946 0.998132i \(-0.480541\pi\)
0.0610946 + 0.998132i \(0.480541\pi\)
\(180\) 0 0
\(181\) 546662. 1.24029 0.620144 0.784488i \(-0.287074\pi\)
0.620144 + 0.784488i \(0.287074\pi\)
\(182\) 0 0
\(183\) −143572. −0.316914
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −290304. −0.607084
\(188\) 0 0
\(189\) 108680. 0.221307
\(190\) 0 0
\(191\) 452028. 0.896565 0.448283 0.893892i \(-0.352036\pi\)
0.448283 + 0.893892i \(0.352036\pi\)
\(192\) 0 0
\(193\) −485594. −0.938383 −0.469191 0.883097i \(-0.655455\pi\)
−0.469191 + 0.883097i \(0.655455\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.01018e6 −1.85452 −0.927262 0.374414i \(-0.877844\pi\)
−0.927262 + 0.374414i \(0.877844\pi\)
\(198\) 0 0
\(199\) 807640. 1.44572 0.722862 0.690993i \(-0.242826\pi\)
0.722862 + 0.690993i \(0.242826\pi\)
\(200\) 0 0
\(201\) 643292. 1.12310
\(202\) 0 0
\(203\) 123420. 0.210206
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −859938. −1.39489
\(208\) 0 0
\(209\) −844800. −1.33779
\(210\) 0 0
\(211\) −149552. −0.231252 −0.115626 0.993293i \(-0.536887\pi\)
−0.115626 + 0.993293i \(0.536887\pi\)
\(212\) 0 0
\(213\) 1.10167e6 1.66381
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −87736.0 −0.126482
\(218\) 0 0
\(219\) −1.35528e6 −1.90949
\(220\) 0 0
\(221\) −17388.0 −0.0239480
\(222\) 0 0
\(223\) −443506. −0.597224 −0.298612 0.954375i \(-0.596524\pi\)
−0.298612 + 0.954375i \(0.596524\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 420018. 0.541007 0.270504 0.962719i \(-0.412810\pi\)
0.270504 + 0.962719i \(0.412810\pi\)
\(228\) 0 0
\(229\) 1.05875e6 1.33415 0.667075 0.744990i \(-0.267546\pi\)
0.667075 + 0.744990i \(0.267546\pi\)
\(230\) 0 0
\(231\) 439296. 0.541661
\(232\) 0 0
\(233\) 1.27345e6 1.53671 0.768353 0.640026i \(-0.221077\pi\)
0.768353 + 0.640026i \(0.221077\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.03064e6 −1.19189
\(238\) 0 0
\(239\) 370680. 0.419763 0.209882 0.977727i \(-0.432692\pi\)
0.209882 + 0.977727i \(0.432692\pi\)
\(240\) 0 0
\(241\) −561298. −0.622517 −0.311258 0.950325i \(-0.600750\pi\)
−0.311258 + 0.950325i \(0.600750\pi\)
\(242\) 0 0
\(243\) 596674. 0.648219
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −50600.0 −0.0527726
\(248\) 0 0
\(249\) 1.55548e6 1.58988
\(250\) 0 0
\(251\) −577152. −0.578237 −0.289119 0.957293i \(-0.593362\pi\)
−0.289119 + 0.957293i \(0.593362\pi\)
\(252\) 0 0
\(253\) −1.52525e6 −1.49809
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 651462. 0.615257 0.307628 0.951507i \(-0.400465\pi\)
0.307628 + 0.951507i \(0.400465\pi\)
\(258\) 0 0
\(259\) −3124.00 −0.00289375
\(260\) 0 0
\(261\) −2.42913e6 −2.20724
\(262\) 0 0
\(263\) 917574. 0.817997 0.408999 0.912535i \(-0.365878\pi\)
0.408999 + 0.912535i \(0.365878\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −1.49994e6 −1.28764
\(268\) 0 0
\(269\) −735390. −0.619637 −0.309818 0.950796i \(-0.600268\pi\)
−0.309818 + 0.950796i \(0.600268\pi\)
\(270\) 0 0
\(271\) 1.12131e6 0.927474 0.463737 0.885973i \(-0.346508\pi\)
0.463737 + 0.885973i \(0.346508\pi\)
\(272\) 0 0
\(273\) 26312.0 0.0213672
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.66034e6 1.30016 0.650082 0.759864i \(-0.274735\pi\)
0.650082 + 0.759864i \(0.274735\pi\)
\(278\) 0 0
\(279\) 1.72680e6 1.32811
\(280\) 0 0
\(281\) 1.45210e6 1.09706 0.548531 0.836130i \(-0.315187\pi\)
0.548531 + 0.836130i \(0.315187\pi\)
\(282\) 0 0
\(283\) 309014. 0.229357 0.114679 0.993403i \(-0.463416\pi\)
0.114679 + 0.993403i \(0.463416\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −33924.0 −0.0243110
\(288\) 0 0
\(289\) −1.27697e6 −0.899367
\(290\) 0 0
\(291\) −3.75393e6 −2.59869
\(292\) 0 0
\(293\) 1.59301e6 1.08405 0.542024 0.840363i \(-0.317658\pi\)
0.542024 + 0.840363i \(0.317658\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −3.79392e6 −2.49573
\(298\) 0 0
\(299\) −91356.0 −0.0590961
\(300\) 0 0
\(301\) 110572. 0.0703443
\(302\) 0 0
\(303\) 3.67271e6 2.29816
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.24726e6 0.755284 0.377642 0.925952i \(-0.376735\pi\)
0.377642 + 0.925952i \(0.376735\pi\)
\(308\) 0 0
\(309\) −3.63516e6 −2.16585
\(310\) 0 0
\(311\) 665988. 0.390450 0.195225 0.980758i \(-0.437456\pi\)
0.195225 + 0.980758i \(0.437456\pi\)
\(312\) 0 0
\(313\) 591286. 0.341143 0.170572 0.985345i \(-0.445439\pi\)
0.170572 + 0.985345i \(0.445439\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 516342. 0.288595 0.144298 0.989534i \(-0.453908\pi\)
0.144298 + 0.989534i \(0.453908\pi\)
\(318\) 0 0
\(319\) −4.30848e6 −2.37054
\(320\) 0 0
\(321\) −2.24687e6 −1.21707
\(322\) 0 0
\(323\) 415800. 0.221757
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −5.67970e6 −2.93735
\(328\) 0 0
\(329\) −544236. −0.277203
\(330\) 0 0
\(331\) 3.29577e6 1.65343 0.826717 0.562619i \(-0.190206\pi\)
0.826717 + 0.562619i \(0.190206\pi\)
\(332\) 0 0
\(333\) 61486.0 0.0303854
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.91098e6 −0.916602 −0.458301 0.888797i \(-0.651542\pi\)
−0.458301 + 0.888797i \(0.651542\pi\)
\(338\) 0 0
\(339\) −748956. −0.353962
\(340\) 0 0
\(341\) 3.06278e6 1.42636
\(342\) 0 0
\(343\) 728860. 0.334510
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.42006e6 1.07895 0.539476 0.842001i \(-0.318622\pi\)
0.539476 + 0.842001i \(0.318622\pi\)
\(348\) 0 0
\(349\) 2.50727e6 1.10189 0.550944 0.834542i \(-0.314268\pi\)
0.550944 + 0.834542i \(0.314268\pi\)
\(350\) 0 0
\(351\) −227240. −0.0984503
\(352\) 0 0
\(353\) 413166. 0.176477 0.0882384 0.996099i \(-0.471876\pi\)
0.0882384 + 0.996099i \(0.471876\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −216216. −0.0897878
\(358\) 0 0
\(359\) −1.73772e6 −0.711613 −0.355806 0.934560i \(-0.615794\pi\)
−0.355806 + 0.934560i \(0.615794\pi\)
\(360\) 0 0
\(361\) −1.26610e6 −0.511328
\(362\) 0 0
\(363\) −1.11481e7 −4.44052
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1.16098e6 0.449944 0.224972 0.974365i \(-0.427771\pi\)
0.224972 + 0.974365i \(0.427771\pi\)
\(368\) 0 0
\(369\) 667686. 0.255274
\(370\) 0 0
\(371\) −311652. −0.117553
\(372\) 0 0
\(373\) −343754. −0.127931 −0.0639655 0.997952i \(-0.520375\pi\)
−0.0639655 + 0.997952i \(0.520375\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −258060. −0.0935120
\(378\) 0 0
\(379\) −573140. −0.204957 −0.102478 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(380\) 0 0
\(381\) 5.62905e6 1.98666
\(382\) 0 0
\(383\) −2.88055e6 −1.00341 −0.501704 0.865039i \(-0.667293\pi\)
−0.501704 + 0.865039i \(0.667293\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −2.17626e6 −0.738640
\(388\) 0 0
\(389\) −3.08559e6 −1.03387 −0.516933 0.856026i \(-0.672926\pi\)
−0.516933 + 0.856026i \(0.672926\pi\)
\(390\) 0 0
\(391\) 750708. 0.248330
\(392\) 0 0
\(393\) −6.35981e6 −2.07712
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −885458. −0.281963 −0.140981 0.990012i \(-0.545026\pi\)
−0.140981 + 0.990012i \(0.545026\pi\)
\(398\) 0 0
\(399\) −629200. −0.197859
\(400\) 0 0
\(401\) −3.75344e6 −1.16565 −0.582825 0.812598i \(-0.698053\pi\)
−0.582825 + 0.812598i \(0.698053\pi\)
\(402\) 0 0
\(403\) 183448. 0.0562666
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 109056. 0.0326335
\(408\) 0 0
\(409\) −1.94653e6 −0.575377 −0.287689 0.957724i \(-0.592887\pi\)
−0.287689 + 0.957724i \(0.592887\pi\)
\(410\) 0 0
\(411\) −6.22705e6 −1.81835
\(412\) 0 0
\(413\) 624360. 0.180119
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 802360. 0.225959
\(418\) 0 0
\(419\) 2.99166e6 0.832486 0.416243 0.909253i \(-0.363346\pi\)
0.416243 + 0.909253i \(0.363346\pi\)
\(420\) 0 0
\(421\) 3.96660e6 1.09072 0.545360 0.838202i \(-0.316393\pi\)
0.545360 + 0.838202i \(0.316393\pi\)
\(422\) 0 0
\(423\) 1.07116e7 2.91073
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −121484. −0.0322440
\(428\) 0 0
\(429\) −918528. −0.240962
\(430\) 0 0
\(431\) 5.17115e6 1.34089 0.670446 0.741958i \(-0.266103\pi\)
0.670446 + 0.741958i \(0.266103\pi\)
\(432\) 0 0
\(433\) 4.53485e6 1.16237 0.581183 0.813773i \(-0.302590\pi\)
0.581183 + 0.813773i \(0.302590\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.18460e6 0.547228
\(438\) 0 0
\(439\) 1.08220e6 0.268007 0.134004 0.990981i \(-0.457217\pi\)
0.134004 + 0.990981i \(0.457217\pi\)
\(440\) 0 0
\(441\) −7.06786e6 −1.73058
\(442\) 0 0
\(443\) −1.08079e6 −0.261656 −0.130828 0.991405i \(-0.541764\pi\)
−0.130828 + 0.991405i \(0.541764\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 2.62470e6 0.621314
\(448\) 0 0
\(449\) 2.61783e6 0.612810 0.306405 0.951901i \(-0.400874\pi\)
0.306405 + 0.951901i \(0.400874\pi\)
\(450\) 0 0
\(451\) 1.18426e6 0.274160
\(452\) 0 0
\(453\) 323752. 0.0741254
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.59046e6 −0.356231 −0.178115 0.984010i \(-0.557000\pi\)
−0.178115 + 0.984010i \(0.557000\pi\)
\(458\) 0 0
\(459\) 1.86732e6 0.413701
\(460\) 0 0
\(461\) 4.25470e6 0.932431 0.466216 0.884671i \(-0.345617\pi\)
0.466216 + 0.884671i \(0.345617\pi\)
\(462\) 0 0
\(463\) 3.26605e6 0.708061 0.354031 0.935234i \(-0.384811\pi\)
0.354031 + 0.935234i \(0.384811\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −601542. −0.127636 −0.0638181 0.997962i \(-0.520328\pi\)
−0.0638181 + 0.997962i \(0.520328\pi\)
\(468\) 0 0
\(469\) 544324. 0.114268
\(470\) 0 0
\(471\) −156572. −0.0325208
\(472\) 0 0
\(473\) −3.85997e6 −0.793288
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 6.13388e6 1.23435
\(478\) 0 0
\(479\) 4.57932e6 0.911931 0.455966 0.889997i \(-0.349294\pi\)
0.455966 + 0.889997i \(0.349294\pi\)
\(480\) 0 0
\(481\) 6532.00 0.00128731
\(482\) 0 0
\(483\) −1.13599e6 −0.221568
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 7.05226e6 1.34743 0.673714 0.738992i \(-0.264698\pi\)
0.673714 + 0.738992i \(0.264698\pi\)
\(488\) 0 0
\(489\) 1.30225e7 2.46276
\(490\) 0 0
\(491\) 2.62349e6 0.491106 0.245553 0.969383i \(-0.421030\pi\)
0.245553 + 0.969383i \(0.421030\pi\)
\(492\) 0 0
\(493\) 2.12058e6 0.392950
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 932184. 0.169282
\(498\) 0 0
\(499\) 3.61234e6 0.649437 0.324719 0.945811i \(-0.394730\pi\)
0.324719 + 0.945811i \(0.394730\pi\)
\(500\) 0 0
\(501\) −1.44367e7 −2.56965
\(502\) 0 0
\(503\) 9.15629e6 1.61361 0.806807 0.590815i \(-0.201194\pi\)
0.806807 + 0.590815i \(0.201194\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 9.59860e6 1.65840
\(508\) 0 0
\(509\) 7.26159e6 1.24233 0.621165 0.783679i \(-0.286660\pi\)
0.621165 + 0.783679i \(0.286660\pi\)
\(510\) 0 0
\(511\) −1.14677e6 −0.194279
\(512\) 0 0
\(513\) 5.43400e6 0.911646
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1.89988e7 3.12608
\(518\) 0 0
\(519\) 1.08512e7 1.76831
\(520\) 0 0
\(521\) 5.81020e6 0.937771 0.468886 0.883259i \(-0.344656\pi\)
0.468886 + 0.883259i \(0.344656\pi\)
\(522\) 0 0
\(523\) −8.17067e6 −1.30618 −0.653090 0.757280i \(-0.726528\pi\)
−0.653090 + 0.757280i \(0.726528\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.50746e6 −0.236440
\(528\) 0 0
\(529\) −2.49215e6 −0.387199
\(530\) 0 0
\(531\) −1.22885e7 −1.89132
\(532\) 0 0
\(533\) 70932.0 0.0108149
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.36188e6 −0.203800
\(538\) 0 0
\(539\) −1.25361e7 −1.85861
\(540\) 0 0
\(541\) −817378. −0.120069 −0.0600343 0.998196i \(-0.519121\pi\)
−0.0600343 + 0.998196i \(0.519121\pi\)
\(542\) 0 0
\(543\) −1.42132e7 −2.06868
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −3.50750e6 −0.501221 −0.250611 0.968088i \(-0.580631\pi\)
−0.250611 + 0.968088i \(0.580631\pi\)
\(548\) 0 0
\(549\) 2.39103e6 0.338574
\(550\) 0 0
\(551\) 6.17100e6 0.865918
\(552\) 0 0
\(553\) −872080. −0.121267
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.61490e6 −1.31313 −0.656563 0.754271i \(-0.727991\pi\)
−0.656563 + 0.754271i \(0.727991\pi\)
\(558\) 0 0
\(559\) −231196. −0.0312933
\(560\) 0 0
\(561\) 7.54790e6 1.01256
\(562\) 0 0
\(563\) 2.01941e6 0.268506 0.134253 0.990947i \(-0.457136\pi\)
0.134253 + 0.990947i \(0.457136\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −510862. −0.0667338
\(568\) 0 0
\(569\) 1.37859e6 0.178507 0.0892533 0.996009i \(-0.471552\pi\)
0.0892533 + 0.996009i \(0.471552\pi\)
\(570\) 0 0
\(571\) −8.54295e6 −1.09652 −0.548261 0.836307i \(-0.684710\pi\)
−0.548261 + 0.836307i \(0.684710\pi\)
\(572\) 0 0
\(573\) −1.17527e7 −1.49538
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 2.31458e6 0.289423 0.144711 0.989474i \(-0.453775\pi\)
0.144711 + 0.989474i \(0.453775\pi\)
\(578\) 0 0
\(579\) 1.26254e7 1.56513
\(580\) 0 0
\(581\) 1.31617e6 0.161760
\(582\) 0 0
\(583\) 1.08795e7 1.32568
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 928338. 0.111202 0.0556008 0.998453i \(-0.482293\pi\)
0.0556008 + 0.998453i \(0.482293\pi\)
\(588\) 0 0
\(589\) −4.38680e6 −0.521026
\(590\) 0 0
\(591\) 2.62646e7 3.09316
\(592\) 0 0
\(593\) 909486. 0.106209 0.0531043 0.998589i \(-0.483088\pi\)
0.0531043 + 0.998589i \(0.483088\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.09986e7 −2.41132
\(598\) 0 0
\(599\) 8.51136e6 0.969241 0.484621 0.874724i \(-0.338958\pi\)
0.484621 + 0.874724i \(0.338958\pi\)
\(600\) 0 0
\(601\) 6.12498e6 0.691701 0.345851 0.938290i \(-0.387590\pi\)
0.345851 + 0.938290i \(0.387590\pi\)
\(602\) 0 0
\(603\) −1.07133e7 −1.19986
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −4.51646e6 −0.497538 −0.248769 0.968563i \(-0.580026\pi\)
−0.248769 + 0.968563i \(0.580026\pi\)
\(608\) 0 0
\(609\) −3.20892e6 −0.350603
\(610\) 0 0
\(611\) 1.13795e6 0.123316
\(612\) 0 0
\(613\) −9.63979e6 −1.03614 −0.518068 0.855340i \(-0.673349\pi\)
−0.518068 + 0.855340i \(0.673349\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.92650e6 1.04974 0.524872 0.851181i \(-0.324113\pi\)
0.524872 + 0.851181i \(0.324113\pi\)
\(618\) 0 0
\(619\) −7.63322e6 −0.800721 −0.400360 0.916358i \(-0.631115\pi\)
−0.400360 + 0.916358i \(0.631115\pi\)
\(620\) 0 0
\(621\) 9.81084e6 1.02089
\(622\) 0 0
\(623\) −1.26918e6 −0.131010
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 2.19648e7 2.23130
\(628\) 0 0
\(629\) −53676.0 −0.00540946
\(630\) 0 0
\(631\) −1.80314e7 −1.80284 −0.901418 0.432949i \(-0.857473\pi\)
−0.901418 + 0.432949i \(0.857473\pi\)
\(632\) 0 0
\(633\) 3.88835e6 0.385706
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −750858. −0.0733178
\(638\) 0 0
\(639\) −1.83471e7 −1.77752
\(640\) 0 0
\(641\) 9.30190e6 0.894184 0.447092 0.894488i \(-0.352460\pi\)
0.447092 + 0.894488i \(0.352460\pi\)
\(642\) 0 0
\(643\) −1.38332e7 −1.31946 −0.659730 0.751503i \(-0.729329\pi\)
−0.659730 + 0.751503i \(0.729329\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.48997e7 −1.39932 −0.699658 0.714478i \(-0.746664\pi\)
−0.699658 + 0.714478i \(0.746664\pi\)
\(648\) 0 0
\(649\) −2.17958e7 −2.03124
\(650\) 0 0
\(651\) 2.28114e6 0.210959
\(652\) 0 0
\(653\) 1.93306e7 1.77403 0.887016 0.461738i \(-0.152774\pi\)
0.887016 + 0.461738i \(0.152774\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.25706e7 2.03999
\(658\) 0 0
\(659\) 4.06110e6 0.364276 0.182138 0.983273i \(-0.441698\pi\)
0.182138 + 0.983273i \(0.441698\pi\)
\(660\) 0 0
\(661\) −1.35152e7 −1.20315 −0.601575 0.798816i \(-0.705460\pi\)
−0.601575 + 0.798816i \(0.705460\pi\)
\(662\) 0 0
\(663\) 452088. 0.0399429
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1.11415e7 0.969678
\(668\) 0 0
\(669\) 1.15312e7 0.996111
\(670\) 0 0
\(671\) 4.24090e6 0.363623
\(672\) 0 0
\(673\) −1.43520e7 −1.22144 −0.610722 0.791845i \(-0.709121\pi\)
−0.610722 + 0.791845i \(0.709121\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.89530e6 −0.158930 −0.0794650 0.996838i \(-0.525321\pi\)
−0.0794650 + 0.996838i \(0.525321\pi\)
\(678\) 0 0
\(679\) −3.17640e6 −0.264400
\(680\) 0 0
\(681\) −1.09205e7 −0.902347
\(682\) 0 0
\(683\) 2.91641e6 0.239220 0.119610 0.992821i \(-0.461836\pi\)
0.119610 + 0.992821i \(0.461836\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −2.75275e7 −2.22523
\(688\) 0 0
\(689\) 651636. 0.0522946
\(690\) 0 0
\(691\) −1.44278e7 −1.14949 −0.574743 0.818334i \(-0.694898\pi\)
−0.574743 + 0.818334i \(0.694898\pi\)
\(692\) 0 0
\(693\) −7.31597e6 −0.578680
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −582876. −0.0454458
\(698\) 0 0
\(699\) −3.31096e7 −2.56307
\(700\) 0 0
\(701\) −1.58679e7 −1.21962 −0.609811 0.792547i \(-0.708754\pi\)
−0.609811 + 0.792547i \(0.708754\pi\)
\(702\) 0 0
\(703\) −156200. −0.0119205
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.10768e6 0.233823
\(708\) 0 0
\(709\) −301810. −0.0225485 −0.0112743 0.999936i \(-0.503589\pi\)
−0.0112743 + 0.999936i \(0.503589\pi\)
\(710\) 0 0
\(711\) 1.71641e7 1.27335
\(712\) 0 0
\(713\) −7.92017e6 −0.583459
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −9.63768e6 −0.700123
\(718\) 0 0
\(719\) −2.12677e7 −1.53426 −0.767130 0.641492i \(-0.778316\pi\)
−0.767130 + 0.641492i \(0.778316\pi\)
\(720\) 0 0
\(721\) −3.07591e6 −0.220361
\(722\) 0 0
\(723\) 1.45937e7 1.03830
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1.55009e7 1.08773 0.543863 0.839174i \(-0.316961\pi\)
0.543863 + 0.839174i \(0.316961\pi\)
\(728\) 0 0
\(729\) −2.11562e7 −1.47441
\(730\) 0 0
\(731\) 1.89983e6 0.131499
\(732\) 0 0
\(733\) 1.21850e7 0.837653 0.418827 0.908066i \(-0.362441\pi\)
0.418827 + 0.908066i \(0.362441\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.90019e7 −1.28863
\(738\) 0 0
\(739\) 2.90282e7 1.95528 0.977641 0.210282i \(-0.0674382\pi\)
0.977641 + 0.210282i \(0.0674382\pi\)
\(740\) 0 0
\(741\) 1.31560e6 0.0880194
\(742\) 0 0
\(743\) 1.61145e7 1.07089 0.535445 0.844570i \(-0.320144\pi\)
0.535445 + 0.844570i \(0.320144\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −2.59047e7 −1.69854
\(748\) 0 0
\(749\) −1.90120e6 −0.123829
\(750\) 0 0
\(751\) 2.92431e6 0.189201 0.0946005 0.995515i \(-0.469843\pi\)
0.0946005 + 0.995515i \(0.469843\pi\)
\(752\) 0 0
\(753\) 1.50060e7 0.964442
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −2.60325e7 −1.65111 −0.825557 0.564319i \(-0.809139\pi\)
−0.825557 + 0.564319i \(0.809139\pi\)
\(758\) 0 0
\(759\) 3.96564e7 2.49867
\(760\) 0 0
\(761\) 1.63263e7 1.02194 0.510970 0.859598i \(-0.329286\pi\)
0.510970 + 0.859598i \(0.329286\pi\)
\(762\) 0 0
\(763\) −4.80590e6 −0.298857
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.30548e6 −0.0801275
\(768\) 0 0
\(769\) 2.58132e7 1.57408 0.787040 0.616902i \(-0.211612\pi\)
0.787040 + 0.616902i \(0.211612\pi\)
\(770\) 0 0
\(771\) −1.69380e7 −1.02619
\(772\) 0 0
\(773\) 1.90592e7 1.14725 0.573624 0.819119i \(-0.305537\pi\)
0.573624 + 0.819119i \(0.305537\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 81224.0 0.00482649
\(778\) 0 0
\(779\) −1.69620e6 −0.100146
\(780\) 0 0
\(781\) −3.25417e7 −1.90903
\(782\) 0 0
\(783\) 2.77134e7 1.61542
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −1.73411e7 −0.998021 −0.499011 0.866596i \(-0.666303\pi\)
−0.499011 + 0.866596i \(0.666303\pi\)
\(788\) 0 0
\(789\) −2.38569e7 −1.36434
\(790\) 0 0
\(791\) −633732. −0.0360134
\(792\) 0 0
\(793\) 254012. 0.0143440
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.58169e7 1.43965 0.719827 0.694153i \(-0.244221\pi\)
0.719827 + 0.694153i \(0.244221\pi\)
\(798\) 0 0
\(799\) −9.35096e6 −0.518190
\(800\) 0 0
\(801\) 2.49798e7 1.37565
\(802\) 0 0
\(803\) 4.00328e7 2.19092
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1.91201e7 1.03349
\(808\) 0 0
\(809\) 8.88489e6 0.477288 0.238644 0.971107i \(-0.423297\pi\)
0.238644 + 0.971107i \(0.423297\pi\)
\(810\) 0 0
\(811\) 2.46396e7 1.31547 0.657735 0.753249i \(-0.271515\pi\)
0.657735 + 0.753249i \(0.271515\pi\)
\(812\) 0 0
\(813\) −2.91540e7 −1.54693
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 5.52860e6 0.289774
\(818\) 0 0
\(819\) −438196. −0.0228275
\(820\) 0 0
\(821\) 1.13768e7 0.589062 0.294531 0.955642i \(-0.404837\pi\)
0.294531 + 0.955642i \(0.404837\pi\)
\(822\) 0 0
\(823\) −1.30783e7 −0.673057 −0.336529 0.941673i \(-0.609253\pi\)
−0.336529 + 0.941673i \(0.609253\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −3.57188e7 −1.81607 −0.908037 0.418891i \(-0.862419\pi\)
−0.908037 + 0.418891i \(0.862419\pi\)
\(828\) 0 0
\(829\) 1.61880e7 0.818103 0.409052 0.912511i \(-0.365860\pi\)
0.409052 + 0.912511i \(0.365860\pi\)
\(830\) 0 0
\(831\) −4.31689e7 −2.16854
\(832\) 0 0
\(833\) 6.17009e6 0.308091
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1.97007e7 −0.972005
\(838\) 0 0
\(839\) 2.55497e7 1.25309 0.626543 0.779387i \(-0.284469\pi\)
0.626543 + 0.779387i \(0.284469\pi\)
\(840\) 0 0
\(841\) 1.09610e7 0.534390
\(842\) 0 0
\(843\) −3.77547e7 −1.82979
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −9.43301e6 −0.451795
\(848\) 0 0
\(849\) −8.03436e6 −0.382545
\(850\) 0 0
\(851\) −282012. −0.0133488
\(852\) 0 0
\(853\) 2.22953e7 1.04916 0.524579 0.851362i \(-0.324223\pi\)
0.524579 + 0.851362i \(0.324223\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.96872e7 −0.915656 −0.457828 0.889041i \(-0.651372\pi\)
−0.457828 + 0.889041i \(0.651372\pi\)
\(858\) 0 0
\(859\) −6.77582e6 −0.313313 −0.156657 0.987653i \(-0.550072\pi\)
−0.156657 + 0.987653i \(0.550072\pi\)
\(860\) 0 0
\(861\) 882024. 0.0405483
\(862\) 0 0
\(863\) −2.63804e7 −1.20574 −0.602871 0.797839i \(-0.705977\pi\)
−0.602871 + 0.797839i \(0.705977\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 3.32013e7 1.50006
\(868\) 0 0
\(869\) 3.04435e7 1.36756
\(870\) 0 0
\(871\) −1.13813e6 −0.0508332
\(872\) 0 0
\(873\) 6.25174e7 2.77629
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −2.95161e7 −1.29587 −0.647934 0.761697i \(-0.724367\pi\)
−0.647934 + 0.761697i \(0.724367\pi\)
\(878\) 0 0
\(879\) −4.14182e7 −1.80808
\(880\) 0 0
\(881\) −1.48565e7 −0.644877 −0.322438 0.946590i \(-0.604502\pi\)
−0.322438 + 0.946590i \(0.604502\pi\)
\(882\) 0 0
\(883\) −1.45340e7 −0.627313 −0.313656 0.949537i \(-0.601554\pi\)
−0.313656 + 0.949537i \(0.601554\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.72028e7 −0.734160 −0.367080 0.930189i \(-0.619642\pi\)
−0.367080 + 0.930189i \(0.619642\pi\)
\(888\) 0 0
\(889\) 4.76304e6 0.202130
\(890\) 0 0
\(891\) 1.78337e7 0.752572
\(892\) 0 0
\(893\) −2.72118e7 −1.14190
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 2.37526e6 0.0985665
\(898\) 0 0
\(899\) −2.23727e7 −0.923249
\(900\) 0 0
\(901\) −5.35475e6 −0.219749
\(902\) 0 0
\(903\) −2.87487e6 −0.117327
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −3.44434e7 −1.39023 −0.695116 0.718897i \(-0.744647\pi\)
−0.695116 + 0.718897i \(0.744647\pi\)
\(908\) 0 0
\(909\) −6.11647e7 −2.45522
\(910\) 0 0
\(911\) 983748. 0.0392724 0.0196362 0.999807i \(-0.493749\pi\)
0.0196362 + 0.999807i \(0.493749\pi\)
\(912\) 0 0
\(913\) −4.59464e7 −1.82421
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −5.38138e6 −0.211334
\(918\) 0 0
\(919\) −3.08857e7 −1.20634 −0.603168 0.797614i \(-0.706095\pi\)
−0.603168 + 0.797614i \(0.706095\pi\)
\(920\) 0 0
\(921\) −3.24287e7 −1.25974
\(922\) 0 0
\(923\) −1.94911e6 −0.0753065
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 6.05395e7 2.31387
\(928\) 0 0
\(929\) −3.20874e7 −1.21982 −0.609909 0.792472i \(-0.708794\pi\)
−0.609909 + 0.792472i \(0.708794\pi\)
\(930\) 0 0
\(931\) 1.79553e7 0.678920
\(932\) 0 0
\(933\) −1.73157e7 −0.651232
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −1.52520e7 −0.567515 −0.283757 0.958896i \(-0.591581\pi\)
−0.283757 + 0.958896i \(0.591581\pi\)
\(938\) 0 0
\(939\) −1.53734e7 −0.568993
\(940\) 0 0
\(941\) 3.48166e6 0.128178 0.0640889 0.997944i \(-0.479586\pi\)
0.0640889 + 0.997944i \(0.479586\pi\)
\(942\) 0 0
\(943\) −3.06241e6 −0.112146
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.54010e7 −0.920398 −0.460199 0.887816i \(-0.652222\pi\)
−0.460199 + 0.887816i \(0.652222\pi\)
\(948\) 0 0
\(949\) 2.39780e6 0.0864265
\(950\) 0 0
\(951\) −1.34249e7 −0.481348
\(952\) 0 0
\(953\) 4.97352e7 1.77391 0.886955 0.461856i \(-0.152816\pi\)
0.886955 + 0.461856i \(0.152816\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 1.12020e8 3.95383
\(958\) 0 0
\(959\) −5.26904e6 −0.185006
\(960\) 0 0
\(961\) −1.27250e7 −0.444477
\(962\) 0 0
\(963\) 3.74190e7 1.30025
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 3.05173e7 1.04949 0.524747 0.851258i \(-0.324160\pi\)
0.524747 + 0.851258i \(0.324160\pi\)
\(968\) 0 0
\(969\) −1.08108e7 −0.369869
\(970\) 0 0
\(971\) −3.19854e7 −1.08869 −0.544344 0.838862i \(-0.683221\pi\)
−0.544344 + 0.838862i \(0.683221\pi\)
\(972\) 0 0
\(973\) 678920. 0.0229899
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.90786e6 −0.0974623 −0.0487312 0.998812i \(-0.515518\pi\)
−0.0487312 + 0.998812i \(0.515518\pi\)
\(978\) 0 0
\(979\) 4.43059e7 1.47742
\(980\) 0 0
\(981\) 9.45888e7 3.13810
\(982\) 0 0
\(983\) 3.49621e7 1.15402 0.577010 0.816737i \(-0.304219\pi\)
0.577010 + 0.816737i \(0.304219\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 1.41501e7 0.462347
\(988\) 0 0
\(989\) 9.98164e6 0.324497
\(990\) 0 0
\(991\) −3.00465e6 −0.0971874 −0.0485937 0.998819i \(-0.515474\pi\)
−0.0485937 + 0.998819i \(0.515474\pi\)
\(992\) 0 0
\(993\) −8.56900e7 −2.75776
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −3.20789e7 −1.02207 −0.511035 0.859560i \(-0.670738\pi\)
−0.511035 + 0.859560i \(0.670738\pi\)
\(998\) 0 0
\(999\) −701480. −0.0222383
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 400.6.a.a.1.1 1
4.3 odd 2 50.6.a.g.1.1 1
5.2 odd 4 400.6.c.a.49.2 2
5.3 odd 4 400.6.c.a.49.1 2
5.4 even 2 80.6.a.h.1.1 1
12.11 even 2 450.6.a.h.1.1 1
15.14 odd 2 720.6.a.r.1.1 1
20.3 even 4 50.6.b.d.49.1 2
20.7 even 4 50.6.b.d.49.2 2
20.19 odd 2 10.6.a.a.1.1 1
40.19 odd 2 320.6.a.p.1.1 1
40.29 even 2 320.6.a.a.1.1 1
60.23 odd 4 450.6.c.o.199.2 2
60.47 odd 4 450.6.c.o.199.1 2
60.59 even 2 90.6.a.f.1.1 1
140.139 even 2 490.6.a.j.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.6.a.a.1.1 1 20.19 odd 2
50.6.a.g.1.1 1 4.3 odd 2
50.6.b.d.49.1 2 20.3 even 4
50.6.b.d.49.2 2 20.7 even 4
80.6.a.h.1.1 1 5.4 even 2
90.6.a.f.1.1 1 60.59 even 2
320.6.a.a.1.1 1 40.29 even 2
320.6.a.p.1.1 1 40.19 odd 2
400.6.a.a.1.1 1 1.1 even 1 trivial
400.6.c.a.49.1 2 5.3 odd 4
400.6.c.a.49.2 2 5.2 odd 4
450.6.a.h.1.1 1 12.11 even 2
450.6.c.o.199.1 2 60.47 odd 4
450.6.c.o.199.2 2 60.23 odd 4
490.6.a.j.1.1 1 140.139 even 2
720.6.a.r.1.1 1 15.14 odd 2