Properties

Label 400.6.a.u.1.1
Level $400$
Weight $6$
Character 400.1
Self dual yes
Analytic conductor $64.154$
Analytic rank $0$
Dimension $2$
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: \(2\)
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: no (minimal twist has level 200)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-7.26209\) of defining polynomial
Character \(\chi\) \(=\) 400.1

$q$-expansion

\(f(q)\) \(=\) \(q-11.5242 q^{3} +27.0483 q^{7} -110.193 q^{9} +O(q^{10})\) \(q-11.5242 q^{3} +27.0483 q^{7} -110.193 q^{9} -226.008 q^{11} -511.257 q^{13} -387.387 q^{17} +1335.93 q^{19} -311.710 q^{21} +545.369 q^{23} +4070.26 q^{27} -4637.58 q^{29} -2991.56 q^{31} +2604.55 q^{33} +1263.70 q^{37} +5891.82 q^{39} -17197.6 q^{41} -16592.0 q^{43} +13036.0 q^{47} -16075.4 q^{49} +4464.31 q^{51} +28994.7 q^{53} -15395.4 q^{57} +34429.9 q^{59} -24149.1 q^{61} -2980.55 q^{63} +29389.7 q^{67} -6284.93 q^{69} -9064.32 q^{71} +55528.7 q^{73} -6113.13 q^{77} +101587. q^{79} -20129.4 q^{81} +73240.4 q^{83} +53444.3 q^{87} -42498.5 q^{89} -13828.7 q^{91} +34475.2 q^{93} -10565.9 q^{97} +24904.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 8 q^{3} - 8 q^{7} + 28 q^{9}+O(q^{10}) \) 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
\(3\) −11.5242 −0.739276 −0.369638 0.929176i \(-0.620518\pi\)
−0.369638 + 0.929176i \(0.620518\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 27.0483 0.208639 0.104320 0.994544i \(-0.466734\pi\)
0.104320 + 0.994544i \(0.466734\pi\)
\(8\) 0 0
\(9\) −110.193 −0.453471
\(10\) 0 0
\(11\) −226.008 −0.563173 −0.281586 0.959536i \(-0.590861\pi\)
−0.281586 + 0.959536i \(0.590861\pi\)
\(12\) 0 0
\(13\) −511.257 −0.839037 −0.419518 0.907747i \(-0.637801\pi\)
−0.419518 + 0.907747i \(0.637801\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −387.387 −0.325104 −0.162552 0.986700i \(-0.551973\pi\)
−0.162552 + 0.986700i \(0.551973\pi\)
\(18\) 0 0
\(19\) 1335.93 0.848982 0.424491 0.905432i \(-0.360453\pi\)
0.424491 + 0.905432i \(0.360453\pi\)
\(20\) 0 0
\(21\) −311.710 −0.154242
\(22\) 0 0
\(23\) 545.369 0.214967 0.107483 0.994207i \(-0.465721\pi\)
0.107483 + 0.994207i \(0.465721\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4070.26 1.07452
\(28\) 0 0
\(29\) −4637.58 −1.02399 −0.511996 0.858988i \(-0.671094\pi\)
−0.511996 + 0.858988i \(0.671094\pi\)
\(30\) 0 0
\(31\) −2991.56 −0.559105 −0.279552 0.960130i \(-0.590186\pi\)
−0.279552 + 0.960130i \(0.590186\pi\)
\(32\) 0 0
\(33\) 2604.55 0.416340
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1263.70 0.151754 0.0758770 0.997117i \(-0.475824\pi\)
0.0758770 + 0.997117i \(0.475824\pi\)
\(38\) 0 0
\(39\) 5891.82 0.620280
\(40\) 0 0
\(41\) −17197.6 −1.59775 −0.798875 0.601497i \(-0.794571\pi\)
−0.798875 + 0.601497i \(0.794571\pi\)
\(42\) 0 0
\(43\) −16592.0 −1.36845 −0.684223 0.729272i \(-0.739859\pi\)
−0.684223 + 0.729272i \(0.739859\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 13036.0 0.860795 0.430397 0.902639i \(-0.358373\pi\)
0.430397 + 0.902639i \(0.358373\pi\)
\(48\) 0 0
\(49\) −16075.4 −0.956470
\(50\) 0 0
\(51\) 4464.31 0.240342
\(52\) 0 0
\(53\) 28994.7 1.41785 0.708923 0.705286i \(-0.249181\pi\)
0.708923 + 0.705286i \(0.249181\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −15395.4 −0.627632
\(58\) 0 0
\(59\) 34429.9 1.28768 0.643838 0.765162i \(-0.277341\pi\)
0.643838 + 0.765162i \(0.277341\pi\)
\(60\) 0 0
\(61\) −24149.1 −0.830952 −0.415476 0.909604i \(-0.636385\pi\)
−0.415476 + 0.909604i \(0.636385\pi\)
\(62\) 0 0
\(63\) −2980.55 −0.0946117
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 29389.7 0.799849 0.399925 0.916548i \(-0.369036\pi\)
0.399925 + 0.916548i \(0.369036\pi\)
\(68\) 0 0
\(69\) −6284.93 −0.158920
\(70\) 0 0
\(71\) −9064.32 −0.213397 −0.106699 0.994291i \(-0.534028\pi\)
−0.106699 + 0.994291i \(0.534028\pi\)
\(72\) 0 0
\(73\) 55528.7 1.21958 0.609791 0.792563i \(-0.291254\pi\)
0.609791 + 0.792563i \(0.291254\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6113.13 −0.117500
\(78\) 0 0
\(79\) 101587. 1.83135 0.915673 0.401924i \(-0.131658\pi\)
0.915673 + 0.401924i \(0.131658\pi\)
\(80\) 0 0
\(81\) −20129.4 −0.340893
\(82\) 0 0
\(83\) 73240.4 1.16696 0.583479 0.812128i \(-0.301691\pi\)
0.583479 + 0.812128i \(0.301691\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 53444.3 0.757012
\(88\) 0 0
\(89\) −42498.5 −0.568719 −0.284360 0.958718i \(-0.591781\pi\)
−0.284360 + 0.958718i \(0.591781\pi\)
\(90\) 0 0
\(91\) −13828.7 −0.175056
\(92\) 0 0
\(93\) 34475.2 0.413333
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −10565.9 −0.114019 −0.0570093 0.998374i \(-0.518156\pi\)
−0.0570093 + 0.998374i \(0.518156\pi\)
\(98\) 0 0
\(99\) 24904.6 0.255382
\(100\) 0 0
\(101\) 46486.0 0.453439 0.226719 0.973960i \(-0.427200\pi\)
0.226719 + 0.973960i \(0.427200\pi\)
\(102\) 0 0
\(103\) 119526. 1.11012 0.555059 0.831811i \(-0.312696\pi\)
0.555059 + 0.831811i \(0.312696\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −22922.4 −0.193553 −0.0967765 0.995306i \(-0.530853\pi\)
−0.0967765 + 0.995306i \(0.530853\pi\)
\(108\) 0 0
\(109\) 210121. 1.69396 0.846980 0.531624i \(-0.178418\pi\)
0.846980 + 0.531624i \(0.178418\pi\)
\(110\) 0 0
\(111\) −14563.1 −0.112188
\(112\) 0 0
\(113\) 203886. 1.50208 0.751039 0.660258i \(-0.229553\pi\)
0.751039 + 0.660258i \(0.229553\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 56337.2 0.380479
\(118\) 0 0
\(119\) −10478.2 −0.0678294
\(120\) 0 0
\(121\) −109972. −0.682837
\(122\) 0 0
\(123\) 198188. 1.18118
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −175022. −0.962905 −0.481453 0.876472i \(-0.659891\pi\)
−0.481453 + 0.876472i \(0.659891\pi\)
\(128\) 0 0
\(129\) 191209. 1.01166
\(130\) 0 0
\(131\) −149218. −0.759701 −0.379850 0.925048i \(-0.624025\pi\)
−0.379850 + 0.925048i \(0.624025\pi\)
\(132\) 0 0
\(133\) 36134.6 0.177131
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 212180. 0.965836 0.482918 0.875666i \(-0.339577\pi\)
0.482918 + 0.875666i \(0.339577\pi\)
\(138\) 0 0
\(139\) −77082.5 −0.338391 −0.169195 0.985583i \(-0.554117\pi\)
−0.169195 + 0.985583i \(0.554117\pi\)
\(140\) 0 0
\(141\) −150229. −0.636365
\(142\) 0 0
\(143\) 115548. 0.472522
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 185256. 0.707095
\(148\) 0 0
\(149\) 470139. 1.73485 0.867423 0.497571i \(-0.165775\pi\)
0.867423 + 0.497571i \(0.165775\pi\)
\(150\) 0 0
\(151\) −311118. −1.11041 −0.555205 0.831714i \(-0.687360\pi\)
−0.555205 + 0.831714i \(0.687360\pi\)
\(152\) 0 0
\(153\) 42687.5 0.147425
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 543649. 1.76023 0.880115 0.474760i \(-0.157465\pi\)
0.880115 + 0.474760i \(0.157465\pi\)
\(158\) 0 0
\(159\) −334140. −1.04818
\(160\) 0 0
\(161\) 14751.3 0.0448504
\(162\) 0 0
\(163\) 298673. 0.880495 0.440248 0.897876i \(-0.354891\pi\)
0.440248 + 0.897876i \(0.354891\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −65486.6 −0.181703 −0.0908513 0.995864i \(-0.528959\pi\)
−0.0908513 + 0.995864i \(0.528959\pi\)
\(168\) 0 0
\(169\) −109909. −0.296017
\(170\) 0 0
\(171\) −147210. −0.384989
\(172\) 0 0
\(173\) −355092. −0.902040 −0.451020 0.892514i \(-0.648940\pi\)
−0.451020 + 0.892514i \(0.648940\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −396777. −0.951947
\(178\) 0 0
\(179\) 39265.7 0.0915970 0.0457985 0.998951i \(-0.485417\pi\)
0.0457985 + 0.998951i \(0.485417\pi\)
\(180\) 0 0
\(181\) 99638.2 0.226063 0.113031 0.993591i \(-0.463944\pi\)
0.113031 + 0.993591i \(0.463944\pi\)
\(182\) 0 0
\(183\) 278298. 0.614303
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 87552.4 0.183090
\(188\) 0 0
\(189\) 110094. 0.224186
\(190\) 0 0
\(191\) −380336. −0.754369 −0.377185 0.926138i \(-0.623108\pi\)
−0.377185 + 0.926138i \(0.623108\pi\)
\(192\) 0 0
\(193\) −126401. −0.244262 −0.122131 0.992514i \(-0.538973\pi\)
−0.122131 + 0.992514i \(0.538973\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 326136. 0.598733 0.299366 0.954138i \(-0.403225\pi\)
0.299366 + 0.954138i \(0.403225\pi\)
\(198\) 0 0
\(199\) 498559. 0.892451 0.446225 0.894921i \(-0.352768\pi\)
0.446225 + 0.894921i \(0.352768\pi\)
\(200\) 0 0
\(201\) −338692. −0.591309
\(202\) 0 0
\(203\) −125439. −0.213645
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −60096.1 −0.0974811
\(208\) 0 0
\(209\) −301930. −0.478123
\(210\) 0 0
\(211\) 310763. 0.480532 0.240266 0.970707i \(-0.422765\pi\)
0.240266 + 0.970707i \(0.422765\pi\)
\(212\) 0 0
\(213\) 104459. 0.157760
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −80916.7 −0.116651
\(218\) 0 0
\(219\) −639923. −0.901607
\(220\) 0 0
\(221\) 198054. 0.272774
\(222\) 0 0
\(223\) −627285. −0.844700 −0.422350 0.906433i \(-0.638795\pi\)
−0.422350 + 0.906433i \(0.638795\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 450131. 0.579794 0.289897 0.957058i \(-0.406379\pi\)
0.289897 + 0.957058i \(0.406379\pi\)
\(228\) 0 0
\(229\) −461485. −0.581526 −0.290763 0.956795i \(-0.593909\pi\)
−0.290763 + 0.956795i \(0.593909\pi\)
\(230\) 0 0
\(231\) 70448.8 0.0868648
\(232\) 0 0
\(233\) 675812. 0.815523 0.407761 0.913089i \(-0.366310\pi\)
0.407761 + 0.913089i \(0.366310\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.17071e6 −1.35387
\(238\) 0 0
\(239\) 1.00730e6 1.14068 0.570338 0.821410i \(-0.306812\pi\)
0.570338 + 0.821410i \(0.306812\pi\)
\(240\) 0 0
\(241\) −232091. −0.257404 −0.128702 0.991683i \(-0.541081\pi\)
−0.128702 + 0.991683i \(0.541081\pi\)
\(242\) 0 0
\(243\) −757099. −0.822502
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −683002. −0.712327
\(248\) 0 0
\(249\) −844035. −0.862704
\(250\) 0 0
\(251\) 1.77096e6 1.77429 0.887143 0.461494i \(-0.152686\pi\)
0.887143 + 0.461494i \(0.152686\pi\)
\(252\) 0 0
\(253\) −123258. −0.121063
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −528458. −0.499088 −0.249544 0.968363i \(-0.580281\pi\)
−0.249544 + 0.968363i \(0.580281\pi\)
\(258\) 0 0
\(259\) 34181.0 0.0316618
\(260\) 0 0
\(261\) 511030. 0.464350
\(262\) 0 0
\(263\) −1.69907e6 −1.51469 −0.757344 0.653016i \(-0.773503\pi\)
−0.757344 + 0.653016i \(0.773503\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 489760. 0.420441
\(268\) 0 0
\(269\) −648393. −0.546333 −0.273167 0.961967i \(-0.588071\pi\)
−0.273167 + 0.961967i \(0.588071\pi\)
\(270\) 0 0
\(271\) 1.94947e6 1.61248 0.806239 0.591590i \(-0.201500\pi\)
0.806239 + 0.591590i \(0.201500\pi\)
\(272\) 0 0
\(273\) 159364. 0.129415
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −313195. −0.245254 −0.122627 0.992453i \(-0.539132\pi\)
−0.122627 + 0.992453i \(0.539132\pi\)
\(278\) 0 0
\(279\) 329650. 0.253538
\(280\) 0 0
\(281\) 1.72743e6 1.30507 0.652537 0.757757i \(-0.273705\pi\)
0.652537 + 0.757757i \(0.273705\pi\)
\(282\) 0 0
\(283\) −205142. −0.152261 −0.0761306 0.997098i \(-0.524257\pi\)
−0.0761306 + 0.997098i \(0.524257\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −465167. −0.333353
\(288\) 0 0
\(289\) −1.26979e6 −0.894307
\(290\) 0 0
\(291\) 121763. 0.0842912
\(292\) 0 0
\(293\) −390309. −0.265607 −0.132804 0.991142i \(-0.542398\pi\)
−0.132804 + 0.991142i \(0.542398\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −919911. −0.605138
\(298\) 0 0
\(299\) −278824. −0.180365
\(300\) 0 0
\(301\) −448787. −0.285511
\(302\) 0 0
\(303\) −535713. −0.335217
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.10708e6 0.670401 0.335201 0.942147i \(-0.391196\pi\)
0.335201 + 0.942147i \(0.391196\pi\)
\(308\) 0 0
\(309\) −1.37744e6 −0.820684
\(310\) 0 0
\(311\) −2.19106e6 −1.28455 −0.642277 0.766472i \(-0.722010\pi\)
−0.642277 + 0.766472i \(0.722010\pi\)
\(312\) 0 0
\(313\) −2.89050e6 −1.66768 −0.833840 0.552006i \(-0.813862\pi\)
−0.833840 + 0.552006i \(0.813862\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.46652e6 −0.819671 −0.409835 0.912160i \(-0.634414\pi\)
−0.409835 + 0.912160i \(0.634414\pi\)
\(318\) 0 0
\(319\) 1.04813e6 0.576684
\(320\) 0 0
\(321\) 264161. 0.143089
\(322\) 0 0
\(323\) −517520. −0.276008
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −2.42147e6 −1.25230
\(328\) 0 0
\(329\) 352602. 0.179595
\(330\) 0 0
\(331\) 2.23500e6 1.12126 0.560632 0.828065i \(-0.310558\pi\)
0.560632 + 0.828065i \(0.310558\pi\)
\(332\) 0 0
\(333\) −139251. −0.0688160
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.48851e6 0.713966 0.356983 0.934111i \(-0.383805\pi\)
0.356983 + 0.934111i \(0.383805\pi\)
\(338\) 0 0
\(339\) −2.34962e6 −1.11045
\(340\) 0 0
\(341\) 676115. 0.314872
\(342\) 0 0
\(343\) −889414. −0.408196
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.34245e6 1.04435 0.522177 0.852837i \(-0.325120\pi\)
0.522177 + 0.852837i \(0.325120\pi\)
\(348\) 0 0
\(349\) −119901. −0.0526940 −0.0263470 0.999653i \(-0.508387\pi\)
−0.0263470 + 0.999653i \(0.508387\pi\)
\(350\) 0 0
\(351\) −2.08095e6 −0.901559
\(352\) 0 0
\(353\) −2.49528e6 −1.06582 −0.532909 0.846173i \(-0.678901\pi\)
−0.532909 + 0.846173i \(0.678901\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 120752. 0.0501447
\(358\) 0 0
\(359\) −3.43398e6 −1.40625 −0.703124 0.711068i \(-0.748212\pi\)
−0.703124 + 0.711068i \(0.748212\pi\)
\(360\) 0 0
\(361\) −691400. −0.279230
\(362\) 0 0
\(363\) 1.26733e6 0.504805
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −4.67310e6 −1.81109 −0.905545 0.424249i \(-0.860538\pi\)
−0.905545 + 0.424249i \(0.860538\pi\)
\(368\) 0 0
\(369\) 1.89507e6 0.724533
\(370\) 0 0
\(371\) 784259. 0.295818
\(372\) 0 0
\(373\) −2.03766e6 −0.758333 −0.379167 0.925328i \(-0.623789\pi\)
−0.379167 + 0.925328i \(0.623789\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.37099e6 0.859166
\(378\) 0 0
\(379\) −1.78978e6 −0.640032 −0.320016 0.947412i \(-0.603688\pi\)
−0.320016 + 0.947412i \(0.603688\pi\)
\(380\) 0 0
\(381\) 2.01698e6 0.711853
\(382\) 0 0
\(383\) −2.04521e6 −0.712429 −0.356214 0.934404i \(-0.615933\pi\)
−0.356214 + 0.934404i \(0.615933\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.82833e6 0.620551
\(388\) 0 0
\(389\) 234191. 0.0784687 0.0392344 0.999230i \(-0.487508\pi\)
0.0392344 + 0.999230i \(0.487508\pi\)
\(390\) 0 0
\(391\) −211269. −0.0698865
\(392\) 0 0
\(393\) 1.71961e6 0.561629
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 2.81706e6 0.897058 0.448529 0.893768i \(-0.351948\pi\)
0.448529 + 0.893768i \(0.351948\pi\)
\(398\) 0 0
\(399\) −416421. −0.130949
\(400\) 0 0
\(401\) 735044. 0.228272 0.114136 0.993465i \(-0.463590\pi\)
0.114136 + 0.993465i \(0.463590\pi\)
\(402\) 0 0
\(403\) 1.52946e6 0.469109
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −285606. −0.0854636
\(408\) 0 0
\(409\) 6.08894e6 1.79984 0.899918 0.436058i \(-0.143626\pi\)
0.899918 + 0.436058i \(0.143626\pi\)
\(410\) 0 0
\(411\) −2.44520e6 −0.714020
\(412\) 0 0
\(413\) 931273. 0.268659
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 888312. 0.250164
\(418\) 0 0
\(419\) −5.65964e6 −1.57490 −0.787452 0.616376i \(-0.788600\pi\)
−0.787452 + 0.616376i \(0.788600\pi\)
\(420\) 0 0
\(421\) −6.34902e6 −1.74583 −0.872914 0.487873i \(-0.837773\pi\)
−0.872914 + 0.487873i \(0.837773\pi\)
\(422\) 0 0
\(423\) −1.43648e6 −0.390345
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −653192. −0.173369
\(428\) 0 0
\(429\) −1.33160e6 −0.349325
\(430\) 0 0
\(431\) −3.03516e6 −0.787024 −0.393512 0.919320i \(-0.628740\pi\)
−0.393512 + 0.919320i \(0.628740\pi\)
\(432\) 0 0
\(433\) −3.50633e6 −0.898739 −0.449369 0.893346i \(-0.648351\pi\)
−0.449369 + 0.893346i \(0.648351\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 728573. 0.182503
\(438\) 0 0
\(439\) 6.08849e6 1.50782 0.753908 0.656980i \(-0.228166\pi\)
0.753908 + 0.656980i \(0.228166\pi\)
\(440\) 0 0
\(441\) 1.77140e6 0.433731
\(442\) 0 0
\(443\) 6.03357e6 1.46071 0.730357 0.683066i \(-0.239354\pi\)
0.730357 + 0.683066i \(0.239354\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −5.41797e6 −1.28253
\(448\) 0 0
\(449\) 3.97943e6 0.931548 0.465774 0.884904i \(-0.345776\pi\)
0.465774 + 0.884904i \(0.345776\pi\)
\(450\) 0 0
\(451\) 3.88680e6 0.899809
\(452\) 0 0
\(453\) 3.58538e6 0.820899
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −430533. −0.0964308 −0.0482154 0.998837i \(-0.515353\pi\)
−0.0482154 + 0.998837i \(0.515353\pi\)
\(458\) 0 0
\(459\) −1.57677e6 −0.349330
\(460\) 0 0
\(461\) 3.80383e6 0.833622 0.416811 0.908993i \(-0.363148\pi\)
0.416811 + 0.908993i \(0.363148\pi\)
\(462\) 0 0
\(463\) 7.62853e6 1.65382 0.826911 0.562333i \(-0.190096\pi\)
0.826911 + 0.562333i \(0.190096\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 9.05102e6 1.92046 0.960230 0.279209i \(-0.0900722\pi\)
0.960230 + 0.279209i \(0.0900722\pi\)
\(468\) 0 0
\(469\) 794943. 0.166880
\(470\) 0 0
\(471\) −6.26511e6 −1.30130
\(472\) 0 0
\(473\) 3.74992e6 0.770672
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −3.19502e6 −0.642952
\(478\) 0 0
\(479\) 8.51621e6 1.69593 0.847964 0.530054i \(-0.177828\pi\)
0.847964 + 0.530054i \(0.177828\pi\)
\(480\) 0 0
\(481\) −646076. −0.127327
\(482\) 0 0
\(483\) −169997. −0.0331569
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −2.65770e6 −0.507789 −0.253895 0.967232i \(-0.581712\pi\)
−0.253895 + 0.967232i \(0.581712\pi\)
\(488\) 0 0
\(489\) −3.44196e6 −0.650929
\(490\) 0 0
\(491\) 5.05116e6 0.945557 0.472779 0.881181i \(-0.343251\pi\)
0.472779 + 0.881181i \(0.343251\pi\)
\(492\) 0 0
\(493\) 1.79654e6 0.332904
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −245175. −0.0445230
\(498\) 0 0
\(499\) 2.15003e6 0.386538 0.193269 0.981146i \(-0.438091\pi\)
0.193269 + 0.981146i \(0.438091\pi\)
\(500\) 0 0
\(501\) 754679. 0.134328
\(502\) 0 0
\(503\) −1.79475e6 −0.316289 −0.158144 0.987416i \(-0.550551\pi\)
−0.158144 + 0.987416i \(0.550551\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.26661e6 0.218839
\(508\) 0 0
\(509\) 697940. 0.119405 0.0597027 0.998216i \(-0.480985\pi\)
0.0597027 + 0.998216i \(0.480985\pi\)
\(510\) 0 0
\(511\) 1.50196e6 0.254452
\(512\) 0 0
\(513\) 5.43757e6 0.912245
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −2.94624e6 −0.484776
\(518\) 0 0
\(519\) 4.09214e6 0.666857
\(520\) 0 0
\(521\) −1.14928e6 −0.185495 −0.0927475 0.995690i \(-0.529565\pi\)
−0.0927475 + 0.995690i \(0.529565\pi\)
\(522\) 0 0
\(523\) 7.22071e6 1.15432 0.577159 0.816632i \(-0.304161\pi\)
0.577159 + 0.816632i \(0.304161\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.15889e6 0.181767
\(528\) 0 0
\(529\) −6.13892e6 −0.953789
\(530\) 0 0
\(531\) −3.79395e6 −0.583923
\(532\) 0 0
\(533\) 8.79241e6 1.34057
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −452505. −0.0677155
\(538\) 0 0
\(539\) 3.63316e6 0.538657
\(540\) 0 0
\(541\) −1.24720e7 −1.83207 −0.916035 0.401099i \(-0.868628\pi\)
−0.916035 + 0.401099i \(0.868628\pi\)
\(542\) 0 0
\(543\) −1.14825e6 −0.167123
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 8.58966e6 1.22746 0.613730 0.789516i \(-0.289668\pi\)
0.613730 + 0.789516i \(0.289668\pi\)
\(548\) 0 0
\(549\) 2.66107e6 0.376812
\(550\) 0 0
\(551\) −6.19546e6 −0.869350
\(552\) 0 0
\(553\) 2.74776e6 0.382090
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3.38207e6 0.461896 0.230948 0.972966i \(-0.425817\pi\)
0.230948 + 0.972966i \(0.425817\pi\)
\(558\) 0 0
\(559\) 8.48278e6 1.14818
\(560\) 0 0
\(561\) −1.00897e6 −0.135354
\(562\) 0 0
\(563\) −1.50247e6 −0.199772 −0.0998859 0.994999i \(-0.531848\pi\)
−0.0998859 + 0.994999i \(0.531848\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −544468. −0.0711237
\(568\) 0 0
\(569\) 1.87838e6 0.243222 0.121611 0.992578i \(-0.461194\pi\)
0.121611 + 0.992578i \(0.461194\pi\)
\(570\) 0 0
\(571\) 1.49628e7 1.92053 0.960267 0.279082i \(-0.0900301\pi\)
0.960267 + 0.279082i \(0.0900301\pi\)
\(572\) 0 0
\(573\) 4.38306e6 0.557687
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 4.03660e6 0.504750 0.252375 0.967630i \(-0.418788\pi\)
0.252375 + 0.967630i \(0.418788\pi\)
\(578\) 0 0
\(579\) 1.45666e6 0.180577
\(580\) 0 0
\(581\) 1.98103e6 0.243473
\(582\) 0 0
\(583\) −6.55303e6 −0.798492
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.57983e7 1.89241 0.946203 0.323574i \(-0.104885\pi\)
0.946203 + 0.323574i \(0.104885\pi\)
\(588\) 0 0
\(589\) −3.99650e6 −0.474670
\(590\) 0 0
\(591\) −3.75845e6 −0.442629
\(592\) 0 0
\(593\) 1.37947e7 1.61092 0.805462 0.592647i \(-0.201917\pi\)
0.805462 + 0.592647i \(0.201917\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −5.74549e6 −0.659768
\(598\) 0 0
\(599\) 814106. 0.0927073 0.0463537 0.998925i \(-0.485240\pi\)
0.0463537 + 0.998925i \(0.485240\pi\)
\(600\) 0 0
\(601\) −1.55613e7 −1.75736 −0.878679 0.477413i \(-0.841574\pi\)
−0.878679 + 0.477413i \(0.841574\pi\)
\(602\) 0 0
\(603\) −3.23855e6 −0.362708
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −1.63191e7 −1.79773 −0.898865 0.438226i \(-0.855607\pi\)
−0.898865 + 0.438226i \(0.855607\pi\)
\(608\) 0 0
\(609\) 1.44558e6 0.157942
\(610\) 0 0
\(611\) −6.66475e6 −0.722239
\(612\) 0 0
\(613\) −5.38233e6 −0.578520 −0.289260 0.957250i \(-0.593409\pi\)
−0.289260 + 0.957250i \(0.593409\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5.83565e6 −0.617130 −0.308565 0.951203i \(-0.599849\pi\)
−0.308565 + 0.951203i \(0.599849\pi\)
\(618\) 0 0
\(619\) 3.36289e6 0.352765 0.176383 0.984322i \(-0.443560\pi\)
0.176383 + 0.984322i \(0.443560\pi\)
\(620\) 0 0
\(621\) 2.21980e6 0.230985
\(622\) 0 0
\(623\) −1.14951e6 −0.118657
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 3.47949e6 0.353465
\(628\) 0 0
\(629\) −489541. −0.0493358
\(630\) 0 0
\(631\) −8.10425e6 −0.810288 −0.405144 0.914253i \(-0.632779\pi\)
−0.405144 + 0.914253i \(0.632779\pi\)
\(632\) 0 0
\(633\) −3.58128e6 −0.355246
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 8.21866e6 0.802513
\(638\) 0 0
\(639\) 998828. 0.0967695
\(640\) 0 0
\(641\) 7.08523e6 0.681097 0.340548 0.940227i \(-0.389387\pi\)
0.340548 + 0.940227i \(0.389387\pi\)
\(642\) 0 0
\(643\) 5.72946e6 0.546495 0.273247 0.961944i \(-0.411902\pi\)
0.273247 + 0.961944i \(0.411902\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.17751e6 0.204503 0.102251 0.994759i \(-0.467395\pi\)
0.102251 + 0.994759i \(0.467395\pi\)
\(648\) 0 0
\(649\) −7.78143e6 −0.725183
\(650\) 0 0
\(651\) 932498. 0.0862374
\(652\) 0 0
\(653\) −1.42048e7 −1.30363 −0.651813 0.758379i \(-0.725991\pi\)
−0.651813 + 0.758379i \(0.725991\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −6.11890e6 −0.553044
\(658\) 0 0
\(659\) −1.54033e7 −1.38166 −0.690829 0.723018i \(-0.742754\pi\)
−0.690829 + 0.723018i \(0.742754\pi\)
\(660\) 0 0
\(661\) −544048. −0.0484322 −0.0242161 0.999707i \(-0.507709\pi\)
−0.0242161 + 0.999707i \(0.507709\pi\)
\(662\) 0 0
\(663\) −2.28241e6 −0.201656
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −2.52919e6 −0.220124
\(668\) 0 0
\(669\) 7.22894e6 0.624467
\(670\) 0 0
\(671\) 5.45787e6 0.467969
\(672\) 0 0
\(673\) −1.37093e7 −1.16675 −0.583374 0.812203i \(-0.698268\pi\)
−0.583374 + 0.812203i \(0.698268\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.49910e7 1.25707 0.628536 0.777781i \(-0.283655\pi\)
0.628536 + 0.777781i \(0.283655\pi\)
\(678\) 0 0
\(679\) −285789. −0.0237887
\(680\) 0 0
\(681\) −5.18738e6 −0.428628
\(682\) 0 0
\(683\) 3.47996e6 0.285445 0.142723 0.989763i \(-0.454414\pi\)
0.142723 + 0.989763i \(0.454414\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 5.31824e6 0.429908
\(688\) 0 0
\(689\) −1.48237e7 −1.18962
\(690\) 0 0
\(691\) −5.09436e6 −0.405877 −0.202939 0.979191i \(-0.565049\pi\)
−0.202939 + 0.979191i \(0.565049\pi\)
\(692\) 0 0
\(693\) 673627. 0.0532827
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 6.66213e6 0.519435
\(698\) 0 0
\(699\) −7.78817e6 −0.602896
\(700\) 0 0
\(701\) 1.75839e7 1.35151 0.675755 0.737126i \(-0.263818\pi\)
0.675755 + 0.737126i \(0.263818\pi\)
\(702\) 0 0
\(703\) 1.68821e6 0.128836
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.25737e6 0.0946051
\(708\) 0 0
\(709\) 1.35383e7 1.01146 0.505730 0.862692i \(-0.331223\pi\)
0.505730 + 0.862692i \(0.331223\pi\)
\(710\) 0 0
\(711\) −1.11942e7 −0.830462
\(712\) 0 0
\(713\) −1.63150e6 −0.120189
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −1.16083e7 −0.843275
\(718\) 0 0
\(719\) −1.27911e7 −0.922756 −0.461378 0.887204i \(-0.652645\pi\)
−0.461378 + 0.887204i \(0.652645\pi\)
\(720\) 0 0
\(721\) 3.23298e6 0.231614
\(722\) 0 0
\(723\) 2.67466e6 0.190293
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −2.11509e7 −1.48420 −0.742100 0.670289i \(-0.766170\pi\)
−0.742100 + 0.670289i \(0.766170\pi\)
\(728\) 0 0
\(729\) 1.36164e7 0.948949
\(730\) 0 0
\(731\) 6.42753e6 0.444888
\(732\) 0 0
\(733\) −1.23015e7 −0.845667 −0.422833 0.906207i \(-0.638964\pi\)
−0.422833 + 0.906207i \(0.638964\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6.64230e6 −0.450453
\(738\) 0 0
\(739\) −1.04425e7 −0.703383 −0.351691 0.936116i \(-0.614393\pi\)
−0.351691 + 0.936116i \(0.614393\pi\)
\(740\) 0 0
\(741\) 7.87103e6 0.526606
\(742\) 0 0
\(743\) −3.63296e6 −0.241429 −0.120714 0.992687i \(-0.538519\pi\)
−0.120714 + 0.992687i \(0.538519\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −8.07060e6 −0.529181
\(748\) 0 0
\(749\) −620012. −0.0403827
\(750\) 0 0
\(751\) 1.77346e7 1.14741 0.573707 0.819060i \(-0.305505\pi\)
0.573707 + 0.819060i \(0.305505\pi\)
\(752\) 0 0
\(753\) −2.04088e7 −1.31169
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 7.89094e6 0.500483 0.250241 0.968183i \(-0.419490\pi\)
0.250241 + 0.968183i \(0.419490\pi\)
\(758\) 0 0
\(759\) 1.42044e6 0.0894992
\(760\) 0 0
\(761\) 1.98455e7 1.24223 0.621114 0.783721i \(-0.286681\pi\)
0.621114 + 0.783721i \(0.286681\pi\)
\(762\) 0 0
\(763\) 5.68343e6 0.353426
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.76026e7 −1.08041
\(768\) 0 0
\(769\) 3.89976e6 0.237806 0.118903 0.992906i \(-0.462062\pi\)
0.118903 + 0.992906i \(0.462062\pi\)
\(770\) 0 0
\(771\) 6.09004e6 0.368964
\(772\) 0 0
\(773\) 2.33736e6 0.140695 0.0703474 0.997523i \(-0.477589\pi\)
0.0703474 + 0.997523i \(0.477589\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −393908. −0.0234068
\(778\) 0 0
\(779\) −2.29748e7 −1.35646
\(780\) 0 0
\(781\) 2.04860e6 0.120180
\(782\) 0 0
\(783\) −1.88762e7 −1.10030
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −1.52903e7 −0.879993 −0.439997 0.897999i \(-0.645020\pi\)
−0.439997 + 0.897999i \(0.645020\pi\)
\(788\) 0 0
\(789\) 1.95804e7 1.11977
\(790\) 0 0
\(791\) 5.51479e6 0.313392
\(792\) 0 0
\(793\) 1.23464e7 0.697199
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.25972e7 0.702468 0.351234 0.936288i \(-0.385762\pi\)
0.351234 + 0.936288i \(0.385762\pi\)
\(798\) 0 0
\(799\) −5.04997e6 −0.279848
\(800\) 0 0
\(801\) 4.68305e6 0.257898
\(802\) 0 0
\(803\) −1.25499e7 −0.686835
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 7.47219e6 0.403891
\(808\) 0 0
\(809\) −1.13476e7 −0.609584 −0.304792 0.952419i \(-0.598587\pi\)
−0.304792 + 0.952419i \(0.598587\pi\)
\(810\) 0 0
\(811\) 1.91000e7 1.01972 0.509860 0.860257i \(-0.329697\pi\)
0.509860 + 0.860257i \(0.329697\pi\)
\(812\) 0 0
\(813\) −2.24661e7 −1.19207
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −2.21657e7 −1.16179
\(818\) 0 0
\(819\) 1.52383e6 0.0793827
\(820\) 0 0
\(821\) 1.25668e6 0.0650678 0.0325339 0.999471i \(-0.489642\pi\)
0.0325339 + 0.999471i \(0.489642\pi\)
\(822\) 0 0
\(823\) −6.95590e6 −0.357976 −0.178988 0.983851i \(-0.557282\pi\)
−0.178988 + 0.983851i \(0.557282\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −9.04638e6 −0.459950 −0.229975 0.973197i \(-0.573864\pi\)
−0.229975 + 0.973197i \(0.573864\pi\)
\(828\) 0 0
\(829\) −1.54026e7 −0.778407 −0.389203 0.921152i \(-0.627250\pi\)
−0.389203 + 0.921152i \(0.627250\pi\)
\(830\) 0 0
\(831\) 3.60932e6 0.181310
\(832\) 0 0
\(833\) 6.22739e6 0.310952
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1.21764e7 −0.600767
\(838\) 0 0
\(839\) −1.75941e7 −0.862903 −0.431451 0.902136i \(-0.641998\pi\)
−0.431451 + 0.902136i \(0.641998\pi\)
\(840\) 0 0
\(841\) 995979. 0.0485580
\(842\) 0 0
\(843\) −1.99072e7 −0.964809
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −2.97455e6 −0.142466
\(848\) 0 0
\(849\) 2.36410e6 0.112563
\(850\) 0 0
\(851\) 689183. 0.0326220
\(852\) 0 0
\(853\) −2.06755e7 −0.972934 −0.486467 0.873699i \(-0.661715\pi\)
−0.486467 + 0.873699i \(0.661715\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2.16205e7 1.00557 0.502786 0.864411i \(-0.332308\pi\)
0.502786 + 0.864411i \(0.332308\pi\)
\(858\) 0 0
\(859\) 1.70061e7 0.786362 0.393181 0.919461i \(-0.371375\pi\)
0.393181 + 0.919461i \(0.371375\pi\)
\(860\) 0 0
\(861\) 5.36067e6 0.246440
\(862\) 0 0
\(863\) 2.96043e7 1.35309 0.676547 0.736399i \(-0.263475\pi\)
0.676547 + 0.736399i \(0.263475\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 1.46333e7 0.661140
\(868\) 0 0
\(869\) −2.29594e7 −1.03136
\(870\) 0 0
\(871\) −1.50257e7 −0.671103
\(872\) 0 0
\(873\) 1.16429e6 0.0517041
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −2.77691e7 −1.21917 −0.609583 0.792722i \(-0.708663\pi\)
−0.609583 + 0.792722i \(0.708663\pi\)
\(878\) 0 0
\(879\) 4.49799e6 0.196357
\(880\) 0 0
\(881\) 1.16824e7 0.507099 0.253550 0.967322i \(-0.418402\pi\)
0.253550 + 0.967322i \(0.418402\pi\)
\(882\) 0 0
\(883\) −2.66919e7 −1.15207 −0.576034 0.817426i \(-0.695400\pi\)
−0.576034 + 0.817426i \(0.695400\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 3.95714e7 1.68878 0.844388 0.535733i \(-0.179964\pi\)
0.844388 + 0.535733i \(0.179964\pi\)
\(888\) 0 0
\(889\) −4.73406e6 −0.200900
\(890\) 0 0
\(891\) 4.54940e6 0.191982
\(892\) 0 0
\(893\) 1.74151e7 0.730799
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 3.21321e6 0.133339
\(898\) 0 0
\(899\) 1.38736e7 0.572518
\(900\) 0 0
\(901\) −1.12322e7 −0.460948
\(902\) 0 0
\(903\) 5.17189e6 0.211072
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −2.79635e7 −1.12869 −0.564343 0.825541i \(-0.690870\pi\)
−0.564343 + 0.825541i \(0.690870\pi\)
\(908\) 0 0
\(909\) −5.12245e6 −0.205621
\(910\) 0 0
\(911\) 1.87296e7 0.747710 0.373855 0.927487i \(-0.378036\pi\)
0.373855 + 0.927487i \(0.378036\pi\)
\(912\) 0 0
\(913\) −1.65529e7 −0.657199
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4.03610e6 −0.158503
\(918\) 0 0
\(919\) 7.77613e6 0.303721 0.151861 0.988402i \(-0.451474\pi\)
0.151861 + 0.988402i \(0.451474\pi\)
\(920\) 0 0
\(921\) −1.27582e7 −0.495612
\(922\) 0 0
\(923\) 4.63420e6 0.179048
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −1.31710e7 −0.503406
\(928\) 0 0
\(929\) −3.88269e7 −1.47602 −0.738011 0.674788i \(-0.764235\pi\)
−0.738011 + 0.674788i \(0.764235\pi\)
\(930\) 0 0
\(931\) −2.14755e7 −0.812026
\(932\) 0 0
\(933\) 2.52501e7 0.949640
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −1.75302e7 −0.652288 −0.326144 0.945320i \(-0.605749\pi\)
−0.326144 + 0.945320i \(0.605749\pi\)
\(938\) 0 0
\(939\) 3.33107e7 1.23288
\(940\) 0 0
\(941\) −4.29638e6 −0.158172 −0.0790859 0.996868i \(-0.525200\pi\)
−0.0790859 + 0.996868i \(0.525200\pi\)
\(942\) 0 0
\(943\) −9.37905e6 −0.343463
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.43637e7 1.60751 0.803754 0.594962i \(-0.202833\pi\)
0.803754 + 0.594962i \(0.202833\pi\)
\(948\) 0 0
\(949\) −2.83895e7 −1.02327
\(950\) 0 0
\(951\) 1.69004e7 0.605963
\(952\) 0 0
\(953\) 5.71990e6 0.204012 0.102006 0.994784i \(-0.467474\pi\)
0.102006 + 0.994784i \(0.467474\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −1.20788e7 −0.426329
\(958\) 0 0
\(959\) 5.73912e6 0.201511
\(960\) 0 0
\(961\) −1.96797e7 −0.687402
\(962\) 0 0
\(963\) 2.52589e6 0.0877706
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 3.00548e7 1.03359 0.516794 0.856110i \(-0.327125\pi\)
0.516794 + 0.856110i \(0.327125\pi\)
\(968\) 0 0
\(969\) 5.96399e6 0.204046
\(970\) 0 0
\(971\) −1.89662e7 −0.645552 −0.322776 0.946475i \(-0.604616\pi\)
−0.322776 + 0.946475i \(0.604616\pi\)
\(972\) 0 0
\(973\) −2.08495e6 −0.0706015
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.45541e7 0.822975 0.411488 0.911415i \(-0.365009\pi\)
0.411488 + 0.911415i \(0.365009\pi\)
\(978\) 0 0
\(979\) 9.60498e6 0.320287
\(980\) 0 0
\(981\) −2.31540e7 −0.768162
\(982\) 0 0
\(983\) −3.35539e7 −1.10754 −0.553769 0.832670i \(-0.686811\pi\)
−0.553769 + 0.832670i \(0.686811\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −4.06345e6 −0.132771
\(988\) 0 0
\(989\) −9.04877e6 −0.294170
\(990\) 0 0
\(991\) −2.05230e7 −0.663830 −0.331915 0.943309i \(-0.607695\pi\)
−0.331915 + 0.943309i \(0.607695\pi\)
\(992\) 0 0
\(993\) −2.57565e7 −0.828924
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 1.25729e7 0.400589 0.200294 0.979736i \(-0.435810\pi\)
0.200294 + 0.979736i \(0.435810\pi\)
\(998\) 0 0
\(999\) 5.14359e6 0.163062
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.u.1.1 2
4.3 odd 2 200.6.a.e.1.2 2
5.2 odd 4 400.6.c.o.49.3 4
5.3 odd 4 400.6.c.o.49.2 4
5.4 even 2 400.6.a.r.1.2 2
20.3 even 4 200.6.c.f.49.3 4
20.7 even 4 200.6.c.f.49.2 4
20.19 odd 2 200.6.a.f.1.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
200.6.a.e.1.2 2 4.3 odd 2
200.6.a.f.1.1 yes 2 20.19 odd 2
200.6.c.f.49.2 4 20.7 even 4
200.6.c.f.49.3 4 20.3 even 4
400.6.a.r.1.2 2 5.4 even 2
400.6.a.u.1.1 2 1.1 even 1 trivial
400.6.c.o.49.2 4 5.3 odd 4
400.6.c.o.49.3 4 5.2 odd 4