Properties

Label 48.26.a.c.1.1
Level $48$
Weight $26$
Character 48.1
Self dual yes
Analytic conductor $190.078$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 48.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(190.078454377\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 6)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 48.1

$q$-expansion

\(f(q)\) \(=\) \(q+531441. q^{3} -2.92755e8 q^{5} -3.58064e9 q^{7} +2.82430e11 q^{9} +O(q^{10})\) \(q+531441. q^{3} -2.92755e8 q^{5} -3.58064e9 q^{7} +2.82430e11 q^{9} -1.51116e13 q^{11} +1.22107e12 q^{13} -1.55582e14 q^{15} +2.51825e15 q^{17} +7.99269e15 q^{19} -1.90290e15 q^{21} +9.96456e16 q^{23} -2.12318e17 q^{25} +1.50095e17 q^{27} -2.08067e18 q^{29} +4.93767e18 q^{31} -8.03091e18 q^{33} +1.04825e18 q^{35} +1.98292e19 q^{37} +6.48928e17 q^{39} +2.24696e20 q^{41} +7.22210e19 q^{43} -8.26826e19 q^{45} -1.89872e20 q^{47} -1.32825e21 q^{49} +1.33830e21 q^{51} -2.64568e21 q^{53} +4.42399e21 q^{55} +4.24764e21 q^{57} +1.64546e22 q^{59} -3.55470e22 q^{61} -1.01128e21 q^{63} -3.57475e20 q^{65} -1.06704e23 q^{67} +5.29558e22 q^{69} -7.36720e22 q^{71} -2.62403e23 q^{73} -1.12834e23 q^{75} +5.41092e22 q^{77} +1.00264e24 q^{79} +7.97664e22 q^{81} -1.55859e24 q^{83} -7.37230e23 q^{85} -1.10575e24 q^{87} +2.18167e24 q^{89} -4.37222e21 q^{91} +2.62408e24 q^{93} -2.33990e24 q^{95} -4.40165e23 q^{97} -4.26795e24 q^{99} +O(q^{100})\)

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
\(3\) 531441. 0.577350
\(4\) 0 0
\(5\) −2.92755e8 −0.536264 −0.268132 0.963382i \(-0.586406\pi\)
−0.268132 + 0.963382i \(0.586406\pi\)
\(6\) 0 0
\(7\) −3.58064e9 −0.0977768 −0.0488884 0.998804i \(-0.515568\pi\)
−0.0488884 + 0.998804i \(0.515568\pi\)
\(8\) 0 0
\(9\) 2.82430e11 0.333333
\(10\) 0 0
\(11\) −1.51116e13 −1.45178 −0.725891 0.687810i \(-0.758572\pi\)
−0.725891 + 0.687810i \(0.758572\pi\)
\(12\) 0 0
\(13\) 1.22107e12 0.0145361 0.00726807 0.999974i \(-0.497686\pi\)
0.00726807 + 0.999974i \(0.497686\pi\)
\(14\) 0 0
\(15\) −1.55582e14 −0.309612
\(16\) 0 0
\(17\) 2.51825e15 1.04830 0.524152 0.851625i \(-0.324382\pi\)
0.524152 + 0.851625i \(0.324382\pi\)
\(18\) 0 0
\(19\) 7.99269e15 0.828463 0.414232 0.910172i \(-0.364050\pi\)
0.414232 + 0.910172i \(0.364050\pi\)
\(20\) 0 0
\(21\) −1.90290e15 −0.0564514
\(22\) 0 0
\(23\) 9.96456e16 0.948114 0.474057 0.880494i \(-0.342789\pi\)
0.474057 + 0.880494i \(0.342789\pi\)
\(24\) 0 0
\(25\) −2.12318e17 −0.712420
\(26\) 0 0
\(27\) 1.50095e17 0.192450
\(28\) 0 0
\(29\) −2.08067e18 −1.09202 −0.546008 0.837780i \(-0.683853\pi\)
−0.546008 + 0.837780i \(0.683853\pi\)
\(30\) 0 0
\(31\) 4.93767e18 1.12590 0.562952 0.826490i \(-0.309666\pi\)
0.562952 + 0.826490i \(0.309666\pi\)
\(32\) 0 0
\(33\) −8.03091e18 −0.838186
\(34\) 0 0
\(35\) 1.04825e18 0.0524342
\(36\) 0 0
\(37\) 1.98292e19 0.495202 0.247601 0.968862i \(-0.420358\pi\)
0.247601 + 0.968862i \(0.420358\pi\)
\(38\) 0 0
\(39\) 6.48928e17 0.00839245
\(40\) 0 0
\(41\) 2.24696e20 1.55524 0.777620 0.628735i \(-0.216427\pi\)
0.777620 + 0.628735i \(0.216427\pi\)
\(42\) 0 0
\(43\) 7.22210e19 0.275618 0.137809 0.990459i \(-0.455994\pi\)
0.137809 + 0.990459i \(0.455994\pi\)
\(44\) 0 0
\(45\) −8.26826e19 −0.178755
\(46\) 0 0
\(47\) −1.89872e20 −0.238363 −0.119181 0.992872i \(-0.538027\pi\)
−0.119181 + 0.992872i \(0.538027\pi\)
\(48\) 0 0
\(49\) −1.32825e21 −0.990440
\(50\) 0 0
\(51\) 1.33830e21 0.605239
\(52\) 0 0
\(53\) −2.64568e21 −0.739756 −0.369878 0.929080i \(-0.620600\pi\)
−0.369878 + 0.929080i \(0.620600\pi\)
\(54\) 0 0
\(55\) 4.42399e21 0.778539
\(56\) 0 0
\(57\) 4.24764e21 0.478313
\(58\) 0 0
\(59\) 1.64546e22 1.20403 0.602015 0.798485i \(-0.294365\pi\)
0.602015 + 0.798485i \(0.294365\pi\)
\(60\) 0 0
\(61\) −3.55470e22 −1.71467 −0.857333 0.514762i \(-0.827880\pi\)
−0.857333 + 0.514762i \(0.827880\pi\)
\(62\) 0 0
\(63\) −1.01128e21 −0.0325923
\(64\) 0 0
\(65\) −3.57475e20 −0.00779522
\(66\) 0 0
\(67\) −1.06704e23 −1.59311 −0.796553 0.604569i \(-0.793345\pi\)
−0.796553 + 0.604569i \(0.793345\pi\)
\(68\) 0 0
\(69\) 5.29558e22 0.547394
\(70\) 0 0
\(71\) −7.36720e22 −0.532811 −0.266405 0.963861i \(-0.585836\pi\)
−0.266405 + 0.963861i \(0.585836\pi\)
\(72\) 0 0
\(73\) −2.62403e23 −1.34101 −0.670506 0.741904i \(-0.733923\pi\)
−0.670506 + 0.741904i \(0.733923\pi\)
\(74\) 0 0
\(75\) −1.12834e23 −0.411316
\(76\) 0 0
\(77\) 5.41092e22 0.141950
\(78\) 0 0
\(79\) 1.00264e24 1.90901 0.954503 0.298201i \(-0.0963866\pi\)
0.954503 + 0.298201i \(0.0963866\pi\)
\(80\) 0 0
\(81\) 7.97664e22 0.111111
\(82\) 0 0
\(83\) −1.55859e24 −1.60050 −0.800249 0.599667i \(-0.795300\pi\)
−0.800249 + 0.599667i \(0.795300\pi\)
\(84\) 0 0
\(85\) −7.37230e23 −0.562169
\(86\) 0 0
\(87\) −1.10575e24 −0.630475
\(88\) 0 0
\(89\) 2.18167e24 0.936298 0.468149 0.883650i \(-0.344921\pi\)
0.468149 + 0.883650i \(0.344921\pi\)
\(90\) 0 0
\(91\) −4.37222e21 −0.00142130
\(92\) 0 0
\(93\) 2.62408e24 0.650041
\(94\) 0 0
\(95\) −2.33990e24 −0.444275
\(96\) 0 0
\(97\) −4.40165e23 −0.0644123 −0.0322062 0.999481i \(-0.510253\pi\)
−0.0322062 + 0.999481i \(0.510253\pi\)
\(98\) 0 0
\(99\) −4.26795e24 −0.483927
\(100\) 0 0
\(101\) −5.02582e24 −0.443802 −0.221901 0.975069i \(-0.571226\pi\)
−0.221901 + 0.975069i \(0.571226\pi\)
\(102\) 0 0
\(103\) 1.52311e25 1.05261 0.526304 0.850296i \(-0.323577\pi\)
0.526304 + 0.850296i \(0.323577\pi\)
\(104\) 0 0
\(105\) 5.57084e23 0.0302729
\(106\) 0 0
\(107\) 2.47232e25 1.06123 0.530613 0.847614i \(-0.321962\pi\)
0.530613 + 0.847614i \(0.321962\pi\)
\(108\) 0 0
\(109\) −2.85771e25 −0.973166 −0.486583 0.873634i \(-0.661757\pi\)
−0.486583 + 0.873634i \(0.661757\pi\)
\(110\) 0 0
\(111\) 1.05380e25 0.285905
\(112\) 0 0
\(113\) −1.73240e25 −0.375982 −0.187991 0.982171i \(-0.560198\pi\)
−0.187991 + 0.982171i \(0.560198\pi\)
\(114\) 0 0
\(115\) −2.91717e25 −0.508440
\(116\) 0 0
\(117\) 3.44867e23 0.00484538
\(118\) 0 0
\(119\) −9.01696e24 −0.102500
\(120\) 0 0
\(121\) 1.20013e26 1.10767
\(122\) 0 0
\(123\) 1.19413e26 0.897918
\(124\) 0 0
\(125\) 1.49405e26 0.918310
\(126\) 0 0
\(127\) −3.23349e26 −1.62976 −0.814882 0.579627i \(-0.803198\pi\)
−0.814882 + 0.579627i \(0.803198\pi\)
\(128\) 0 0
\(129\) 3.83812e25 0.159128
\(130\) 0 0
\(131\) 3.63273e26 1.24263 0.621315 0.783561i \(-0.286599\pi\)
0.621315 + 0.783561i \(0.286599\pi\)
\(132\) 0 0
\(133\) −2.86190e25 −0.0810044
\(134\) 0 0
\(135\) −4.39409e25 −0.103204
\(136\) 0 0
\(137\) −6.56742e26 −1.28348 −0.641738 0.766924i \(-0.721786\pi\)
−0.641738 + 0.766924i \(0.721786\pi\)
\(138\) 0 0
\(139\) −6.72509e26 −1.09651 −0.548256 0.836311i \(-0.684708\pi\)
−0.548256 + 0.836311i \(0.684708\pi\)
\(140\) 0 0
\(141\) −1.00906e26 −0.137619
\(142\) 0 0
\(143\) −1.84523e25 −0.0211033
\(144\) 0 0
\(145\) 6.09127e26 0.585609
\(146\) 0 0
\(147\) −7.05885e26 −0.571831
\(148\) 0 0
\(149\) −7.98627e26 −0.546406 −0.273203 0.961956i \(-0.588083\pi\)
−0.273203 + 0.961956i \(0.588083\pi\)
\(150\) 0 0
\(151\) 1.03633e27 0.600187 0.300093 0.953910i \(-0.402982\pi\)
0.300093 + 0.953910i \(0.402982\pi\)
\(152\) 0 0
\(153\) 7.11228e26 0.349435
\(154\) 0 0
\(155\) −1.44553e27 −0.603782
\(156\) 0 0
\(157\) −3.36346e27 −1.19685 −0.598427 0.801178i \(-0.704207\pi\)
−0.598427 + 0.801178i \(0.704207\pi\)
\(158\) 0 0
\(159\) −1.40602e27 −0.427098
\(160\) 0 0
\(161\) −3.56796e26 −0.0927035
\(162\) 0 0
\(163\) −8.00443e26 −0.178232 −0.0891159 0.996021i \(-0.528404\pi\)
−0.0891159 + 0.996021i \(0.528404\pi\)
\(164\) 0 0
\(165\) 2.35109e27 0.449489
\(166\) 0 0
\(167\) 5.17982e27 0.851842 0.425921 0.904760i \(-0.359950\pi\)
0.425921 + 0.904760i \(0.359950\pi\)
\(168\) 0 0
\(169\) −7.05492e27 −0.999789
\(170\) 0 0
\(171\) 2.25737e27 0.276154
\(172\) 0 0
\(173\) −3.40880e27 −0.360599 −0.180300 0.983612i \(-0.557707\pi\)
−0.180300 + 0.983612i \(0.557707\pi\)
\(174\) 0 0
\(175\) 7.60235e26 0.0696582
\(176\) 0 0
\(177\) 8.74465e27 0.695147
\(178\) 0 0
\(179\) 1.23610e28 0.853870 0.426935 0.904282i \(-0.359593\pi\)
0.426935 + 0.904282i \(0.359593\pi\)
\(180\) 0 0
\(181\) 3.38516e27 0.203516 0.101758 0.994809i \(-0.467553\pi\)
0.101758 + 0.994809i \(0.467553\pi\)
\(182\) 0 0
\(183\) −1.88911e28 −0.989963
\(184\) 0 0
\(185\) −5.80508e27 −0.265559
\(186\) 0 0
\(187\) −3.80547e28 −1.52191
\(188\) 0 0
\(189\) −5.37435e26 −0.0188171
\(190\) 0 0
\(191\) −3.81140e28 −1.16995 −0.584975 0.811052i \(-0.698896\pi\)
−0.584975 + 0.811052i \(0.698896\pi\)
\(192\) 0 0
\(193\) 6.38842e28 1.72158 0.860790 0.508961i \(-0.169970\pi\)
0.860790 + 0.508961i \(0.169970\pi\)
\(194\) 0 0
\(195\) −1.89977e26 −0.00450057
\(196\) 0 0
\(197\) −8.73680e28 −1.82190 −0.910950 0.412517i \(-0.864650\pi\)
−0.910950 + 0.412517i \(0.864650\pi\)
\(198\) 0 0
\(199\) −2.76766e28 −0.508686 −0.254343 0.967114i \(-0.581859\pi\)
−0.254343 + 0.967114i \(0.581859\pi\)
\(200\) 0 0
\(201\) −5.67067e28 −0.919780
\(202\) 0 0
\(203\) 7.45015e27 0.106774
\(204\) 0 0
\(205\) −6.57809e28 −0.834020
\(206\) 0 0
\(207\) 2.81429e28 0.316038
\(208\) 0 0
\(209\) −1.20782e29 −1.20275
\(210\) 0 0
\(211\) 2.08479e28 0.184303 0.0921513 0.995745i \(-0.470626\pi\)
0.0921513 + 0.995745i \(0.470626\pi\)
\(212\) 0 0
\(213\) −3.91523e28 −0.307619
\(214\) 0 0
\(215\) −2.11431e28 −0.147804
\(216\) 0 0
\(217\) −1.76800e28 −0.110087
\(218\) 0 0
\(219\) −1.39452e29 −0.774234
\(220\) 0 0
\(221\) 3.07496e27 0.0152383
\(222\) 0 0
\(223\) −2.90506e29 −1.28630 −0.643152 0.765739i \(-0.722374\pi\)
−0.643152 + 0.765739i \(0.722374\pi\)
\(224\) 0 0
\(225\) −5.99648e28 −0.237473
\(226\) 0 0
\(227\) −3.23765e29 −1.14791 −0.573954 0.818887i \(-0.694591\pi\)
−0.573954 + 0.818887i \(0.694591\pi\)
\(228\) 0 0
\(229\) −5.11099e29 −1.62391 −0.811954 0.583721i \(-0.801596\pi\)
−0.811954 + 0.583721i \(0.801596\pi\)
\(230\) 0 0
\(231\) 2.87558e28 0.0819551
\(232\) 0 0
\(233\) −1.20130e29 −0.307399 −0.153700 0.988118i \(-0.549119\pi\)
−0.153700 + 0.988118i \(0.549119\pi\)
\(234\) 0 0
\(235\) 5.55861e28 0.127826
\(236\) 0 0
\(237\) 5.32845e29 1.10217
\(238\) 0 0
\(239\) −3.34916e29 −0.623681 −0.311840 0.950135i \(-0.600945\pi\)
−0.311840 + 0.950135i \(0.600945\pi\)
\(240\) 0 0
\(241\) −3.53238e29 −0.592727 −0.296363 0.955075i \(-0.595774\pi\)
−0.296363 + 0.955075i \(0.595774\pi\)
\(242\) 0 0
\(243\) 4.23912e28 0.0641500
\(244\) 0 0
\(245\) 3.88851e29 0.531138
\(246\) 0 0
\(247\) 9.75965e27 0.0120427
\(248\) 0 0
\(249\) −8.28298e29 −0.924048
\(250\) 0 0
\(251\) −1.07603e30 −1.08619 −0.543093 0.839673i \(-0.682747\pi\)
−0.543093 + 0.839673i \(0.682747\pi\)
\(252\) 0 0
\(253\) −1.50580e30 −1.37645
\(254\) 0 0
\(255\) −3.91794e29 −0.324568
\(256\) 0 0
\(257\) 6.56258e27 0.00493073 0.00246536 0.999997i \(-0.499215\pi\)
0.00246536 + 0.999997i \(0.499215\pi\)
\(258\) 0 0
\(259\) −7.10011e28 −0.0484193
\(260\) 0 0
\(261\) −5.87643e29 −0.364005
\(262\) 0 0
\(263\) −2.03818e30 −1.14761 −0.573807 0.818990i \(-0.694534\pi\)
−0.573807 + 0.818990i \(0.694534\pi\)
\(264\) 0 0
\(265\) 7.74534e29 0.396705
\(266\) 0 0
\(267\) 1.15943e30 0.540572
\(268\) 0 0
\(269\) 1.30216e30 0.553046 0.276523 0.961007i \(-0.410818\pi\)
0.276523 + 0.961007i \(0.410818\pi\)
\(270\) 0 0
\(271\) −2.73384e30 −1.05842 −0.529209 0.848492i \(-0.677511\pi\)
−0.529209 + 0.848492i \(0.677511\pi\)
\(272\) 0 0
\(273\) −2.32358e27 −0.000820586 0
\(274\) 0 0
\(275\) 3.20846e30 1.03428
\(276\) 0 0
\(277\) −4.83846e29 −0.142466 −0.0712329 0.997460i \(-0.522693\pi\)
−0.0712329 + 0.997460i \(0.522693\pi\)
\(278\) 0 0
\(279\) 1.39454e30 0.375301
\(280\) 0 0
\(281\) −7.57818e30 −1.86525 −0.932623 0.360853i \(-0.882486\pi\)
−0.932623 + 0.360853i \(0.882486\pi\)
\(282\) 0 0
\(283\) 1.30443e30 0.293827 0.146914 0.989149i \(-0.453066\pi\)
0.146914 + 0.989149i \(0.453066\pi\)
\(284\) 0 0
\(285\) −1.24352e30 −0.256502
\(286\) 0 0
\(287\) −8.04557e29 −0.152066
\(288\) 0 0
\(289\) 5.70960e29 0.0989424
\(290\) 0 0
\(291\) −2.33922e29 −0.0371885
\(292\) 0 0
\(293\) −4.04021e29 −0.0589601 −0.0294800 0.999565i \(-0.509385\pi\)
−0.0294800 + 0.999565i \(0.509385\pi\)
\(294\) 0 0
\(295\) −4.81717e30 −0.645679
\(296\) 0 0
\(297\) −2.26817e30 −0.279395
\(298\) 0 0
\(299\) 1.21674e29 0.0137819
\(300\) 0 0
\(301\) −2.58598e29 −0.0269491
\(302\) 0 0
\(303\) −2.67092e30 −0.256229
\(304\) 0 0
\(305\) 1.04065e31 0.919514
\(306\) 0 0
\(307\) −6.95636e30 −0.566438 −0.283219 0.959055i \(-0.591402\pi\)
−0.283219 + 0.959055i \(0.591402\pi\)
\(308\) 0 0
\(309\) 8.09445e30 0.607724
\(310\) 0 0
\(311\) −2.74913e30 −0.190410 −0.0952051 0.995458i \(-0.530351\pi\)
−0.0952051 + 0.995458i \(0.530351\pi\)
\(312\) 0 0
\(313\) 9.39383e30 0.600535 0.300267 0.953855i \(-0.402924\pi\)
0.300267 + 0.953855i \(0.402924\pi\)
\(314\) 0 0
\(315\) 2.96057e29 0.0174781
\(316\) 0 0
\(317\) 1.86543e31 1.01751 0.508755 0.860912i \(-0.330106\pi\)
0.508755 + 0.860912i \(0.330106\pi\)
\(318\) 0 0
\(319\) 3.14422e31 1.58537
\(320\) 0 0
\(321\) 1.31389e31 0.612699
\(322\) 0 0
\(323\) 2.01276e31 0.868482
\(324\) 0 0
\(325\) −2.59255e29 −0.0103558
\(326\) 0 0
\(327\) −1.51870e31 −0.561857
\(328\) 0 0
\(329\) 6.79866e29 0.0233064
\(330\) 0 0
\(331\) 4.71638e31 1.49885 0.749426 0.662088i \(-0.230330\pi\)
0.749426 + 0.662088i \(0.230330\pi\)
\(332\) 0 0
\(333\) 5.60034e30 0.165067
\(334\) 0 0
\(335\) 3.12380e31 0.854326
\(336\) 0 0
\(337\) 1.85792e31 0.471686 0.235843 0.971791i \(-0.424215\pi\)
0.235843 + 0.971791i \(0.424215\pi\)
\(338\) 0 0
\(339\) −9.20668e30 −0.217074
\(340\) 0 0
\(341\) −7.46160e31 −1.63456
\(342\) 0 0
\(343\) 9.55787e30 0.194619
\(344\) 0 0
\(345\) −1.55031e31 −0.293548
\(346\) 0 0
\(347\) 7.27635e31 1.28173 0.640863 0.767655i \(-0.278577\pi\)
0.640863 + 0.767655i \(0.278577\pi\)
\(348\) 0 0
\(349\) 1.19713e32 1.96256 0.981282 0.192574i \(-0.0616835\pi\)
0.981282 + 0.192574i \(0.0616835\pi\)
\(350\) 0 0
\(351\) 1.83276e29 0.00279748
\(352\) 0 0
\(353\) 6.99722e31 0.994813 0.497407 0.867517i \(-0.334286\pi\)
0.497407 + 0.867517i \(0.334286\pi\)
\(354\) 0 0
\(355\) 2.15678e31 0.285728
\(356\) 0 0
\(357\) −4.79198e30 −0.0591783
\(358\) 0 0
\(359\) −6.06364e31 −0.698317 −0.349159 0.937064i \(-0.613533\pi\)
−0.349159 + 0.937064i \(0.613533\pi\)
\(360\) 0 0
\(361\) −2.91933e31 −0.313649
\(362\) 0 0
\(363\) 6.37796e31 0.639513
\(364\) 0 0
\(365\) 7.68197e31 0.719137
\(366\) 0 0
\(367\) −2.22539e32 −1.94572 −0.972860 0.231394i \(-0.925671\pi\)
−0.972860 + 0.231394i \(0.925671\pi\)
\(368\) 0 0
\(369\) 6.34608e31 0.518413
\(370\) 0 0
\(371\) 9.47322e30 0.0723309
\(372\) 0 0
\(373\) −1.15379e32 −0.823695 −0.411848 0.911253i \(-0.635116\pi\)
−0.411848 + 0.911253i \(0.635116\pi\)
\(374\) 0 0
\(375\) 7.93998e31 0.530187
\(376\) 0 0
\(377\) −2.54065e30 −0.0158737
\(378\) 0 0
\(379\) −5.47213e31 −0.320012 −0.160006 0.987116i \(-0.551151\pi\)
−0.160006 + 0.987116i \(0.551151\pi\)
\(380\) 0 0
\(381\) −1.71841e32 −0.940945
\(382\) 0 0
\(383\) 1.98130e32 1.01617 0.508085 0.861307i \(-0.330354\pi\)
0.508085 + 0.861307i \(0.330354\pi\)
\(384\) 0 0
\(385\) −1.58407e31 −0.0761230
\(386\) 0 0
\(387\) 2.03973e31 0.0918727
\(388\) 0 0
\(389\) 4.19098e31 0.176989 0.0884945 0.996077i \(-0.471794\pi\)
0.0884945 + 0.996077i \(0.471794\pi\)
\(390\) 0 0
\(391\) 2.50933e32 0.993912
\(392\) 0 0
\(393\) 1.93058e32 0.717433
\(394\) 0 0
\(395\) −2.93528e32 −1.02373
\(396\) 0 0
\(397\) 2.64500e32 0.866053 0.433027 0.901381i \(-0.357446\pi\)
0.433027 + 0.901381i \(0.357446\pi\)
\(398\) 0 0
\(399\) −1.52093e31 −0.0467679
\(400\) 0 0
\(401\) 2.33767e32 0.675273 0.337636 0.941277i \(-0.390373\pi\)
0.337636 + 0.941277i \(0.390373\pi\)
\(402\) 0 0
\(403\) 6.02925e30 0.0163663
\(404\) 0 0
\(405\) −2.33520e31 −0.0595849
\(406\) 0 0
\(407\) −2.99650e32 −0.718925
\(408\) 0 0
\(409\) −5.48497e32 −1.23775 −0.618875 0.785490i \(-0.712411\pi\)
−0.618875 + 0.785490i \(0.712411\pi\)
\(410\) 0 0
\(411\) −3.49020e32 −0.741015
\(412\) 0 0
\(413\) −5.89181e31 −0.117726
\(414\) 0 0
\(415\) 4.56284e32 0.858291
\(416\) 0 0
\(417\) −3.57399e32 −0.633071
\(418\) 0 0
\(419\) −3.41488e31 −0.0569771 −0.0284885 0.999594i \(-0.509069\pi\)
−0.0284885 + 0.999594i \(0.509069\pi\)
\(420\) 0 0
\(421\) −5.71127e32 −0.897856 −0.448928 0.893568i \(-0.648194\pi\)
−0.448928 + 0.893568i \(0.648194\pi\)
\(422\) 0 0
\(423\) −5.36256e31 −0.0794543
\(424\) 0 0
\(425\) −5.34670e32 −0.746834
\(426\) 0 0
\(427\) 1.27281e32 0.167654
\(428\) 0 0
\(429\) −9.80632e30 −0.0121840
\(430\) 0 0
\(431\) −5.26390e32 −0.617081 −0.308540 0.951211i \(-0.599840\pi\)
−0.308540 + 0.951211i \(0.599840\pi\)
\(432\) 0 0
\(433\) −7.00633e32 −0.775160 −0.387580 0.921836i \(-0.626689\pi\)
−0.387580 + 0.921836i \(0.626689\pi\)
\(434\) 0 0
\(435\) 3.23715e32 0.338102
\(436\) 0 0
\(437\) 7.96437e32 0.785477
\(438\) 0 0
\(439\) −5.29542e32 −0.493280 −0.246640 0.969107i \(-0.579327\pi\)
−0.246640 + 0.969107i \(0.579327\pi\)
\(440\) 0 0
\(441\) −3.75136e32 −0.330147
\(442\) 0 0
\(443\) −4.49792e32 −0.374080 −0.187040 0.982352i \(-0.559889\pi\)
−0.187040 + 0.982352i \(0.559889\pi\)
\(444\) 0 0
\(445\) −6.38695e32 −0.502103
\(446\) 0 0
\(447\) −4.24423e32 −0.315468
\(448\) 0 0
\(449\) −9.88741e32 −0.695030 −0.347515 0.937674i \(-0.612974\pi\)
−0.347515 + 0.937674i \(0.612974\pi\)
\(450\) 0 0
\(451\) −3.39551e33 −2.25787
\(452\) 0 0
\(453\) 5.50748e32 0.346518
\(454\) 0 0
\(455\) 1.27999e30 0.000762191 0
\(456\) 0 0
\(457\) 2.93791e33 1.65610 0.828050 0.560654i \(-0.189450\pi\)
0.828050 + 0.560654i \(0.189450\pi\)
\(458\) 0 0
\(459\) 3.77976e32 0.201746
\(460\) 0 0
\(461\) −2.14053e33 −1.08208 −0.541039 0.840997i \(-0.681969\pi\)
−0.541039 + 0.840997i \(0.681969\pi\)
\(462\) 0 0
\(463\) −8.71982e32 −0.417585 −0.208793 0.977960i \(-0.566953\pi\)
−0.208793 + 0.977960i \(0.566953\pi\)
\(464\) 0 0
\(465\) −7.68213e32 −0.348594
\(466\) 0 0
\(467\) 6.01153e32 0.258538 0.129269 0.991610i \(-0.458737\pi\)
0.129269 + 0.991610i \(0.458737\pi\)
\(468\) 0 0
\(469\) 3.82068e32 0.155769
\(470\) 0 0
\(471\) −1.78748e33 −0.691003
\(472\) 0 0
\(473\) −1.09137e33 −0.400137
\(474\) 0 0
\(475\) −1.69699e33 −0.590214
\(476\) 0 0
\(477\) −7.47217e32 −0.246585
\(478\) 0 0
\(479\) 3.01870e33 0.945423 0.472711 0.881217i \(-0.343275\pi\)
0.472711 + 0.881217i \(0.343275\pi\)
\(480\) 0 0
\(481\) 2.42128e31 0.00719833
\(482\) 0 0
\(483\) −1.89616e32 −0.0535224
\(484\) 0 0
\(485\) 1.28861e32 0.0345421
\(486\) 0 0
\(487\) 5.24137e33 1.33454 0.667272 0.744814i \(-0.267462\pi\)
0.667272 + 0.744814i \(0.267462\pi\)
\(488\) 0 0
\(489\) −4.25388e32 −0.102902
\(490\) 0 0
\(491\) 3.08172e33 0.708393 0.354197 0.935171i \(-0.384754\pi\)
0.354197 + 0.935171i \(0.384754\pi\)
\(492\) 0 0
\(493\) −5.23966e33 −1.14476
\(494\) 0 0
\(495\) 1.24946e33 0.259513
\(496\) 0 0
\(497\) 2.63793e32 0.0520965
\(498\) 0 0
\(499\) 1.64910e33 0.309734 0.154867 0.987935i \(-0.450505\pi\)
0.154867 + 0.987935i \(0.450505\pi\)
\(500\) 0 0
\(501\) 2.75277e33 0.491811
\(502\) 0 0
\(503\) 2.47162e32 0.0420128 0.0210064 0.999779i \(-0.493313\pi\)
0.0210064 + 0.999779i \(0.493313\pi\)
\(504\) 0 0
\(505\) 1.47133e33 0.237995
\(506\) 0 0
\(507\) −3.74927e33 −0.577228
\(508\) 0 0
\(509\) 6.26740e33 0.918577 0.459288 0.888287i \(-0.348105\pi\)
0.459288 + 0.888287i \(0.348105\pi\)
\(510\) 0 0
\(511\) 9.39571e32 0.131120
\(512\) 0 0
\(513\) 1.19966e33 0.159438
\(514\) 0 0
\(515\) −4.45899e33 −0.564477
\(516\) 0 0
\(517\) 2.86927e33 0.346051
\(518\) 0 0
\(519\) −1.81158e33 −0.208192
\(520\) 0 0
\(521\) 1.64678e34 1.80370 0.901850 0.432049i \(-0.142209\pi\)
0.901850 + 0.432049i \(0.142209\pi\)
\(522\) 0 0
\(523\) 3.45969e33 0.361216 0.180608 0.983555i \(-0.442194\pi\)
0.180608 + 0.983555i \(0.442194\pi\)
\(524\) 0 0
\(525\) 4.04020e32 0.0402172
\(526\) 0 0
\(527\) 1.24343e34 1.18029
\(528\) 0 0
\(529\) −1.11651e33 −0.101081
\(530\) 0 0
\(531\) 4.64727e33 0.401343
\(532\) 0 0
\(533\) 2.74370e32 0.0226072
\(534\) 0 0
\(535\) −7.23785e33 −0.569098
\(536\) 0 0
\(537\) 6.56916e33 0.492982
\(538\) 0 0
\(539\) 2.00719e34 1.43790
\(540\) 0 0
\(541\) −2.31144e33 −0.158094 −0.0790472 0.996871i \(-0.525188\pi\)
−0.0790472 + 0.996871i \(0.525188\pi\)
\(542\) 0 0
\(543\) 1.79902e33 0.117500
\(544\) 0 0
\(545\) 8.36608e33 0.521874
\(546\) 0 0
\(547\) 4.04733e33 0.241172 0.120586 0.992703i \(-0.461523\pi\)
0.120586 + 0.992703i \(0.461523\pi\)
\(548\) 0 0
\(549\) −1.00395e34 −0.571555
\(550\) 0 0
\(551\) −1.66302e34 −0.904694
\(552\) 0 0
\(553\) −3.59010e33 −0.186656
\(554\) 0 0
\(555\) −3.08506e33 −0.153321
\(556\) 0 0
\(557\) 2.32181e34 1.10315 0.551577 0.834124i \(-0.314026\pi\)
0.551577 + 0.834124i \(0.314026\pi\)
\(558\) 0 0
\(559\) 8.81870e31 0.00400643
\(560\) 0 0
\(561\) −2.02238e34 −0.878674
\(562\) 0 0
\(563\) 2.70103e34 1.12247 0.561235 0.827656i \(-0.310326\pi\)
0.561235 + 0.827656i \(0.310326\pi\)
\(564\) 0 0
\(565\) 5.07168e33 0.201626
\(566\) 0 0
\(567\) −2.85615e32 −0.0108641
\(568\) 0 0
\(569\) −2.32147e33 −0.0845007 −0.0422504 0.999107i \(-0.513453\pi\)
−0.0422504 + 0.999107i \(0.513453\pi\)
\(570\) 0 0
\(571\) −2.55837e34 −0.891276 −0.445638 0.895213i \(-0.647023\pi\)
−0.445638 + 0.895213i \(0.647023\pi\)
\(572\) 0 0
\(573\) −2.02553e34 −0.675470
\(574\) 0 0
\(575\) −2.11565e34 −0.675455
\(576\) 0 0
\(577\) 1.95952e34 0.599035 0.299517 0.954091i \(-0.403174\pi\)
0.299517 + 0.954091i \(0.403174\pi\)
\(578\) 0 0
\(579\) 3.39507e34 0.993954
\(580\) 0 0
\(581\) 5.58075e33 0.156492
\(582\) 0 0
\(583\) 3.99803e34 1.07396
\(584\) 0 0
\(585\) −1.00961e32 −0.00259841
\(586\) 0 0
\(587\) −5.98783e33 −0.147670 −0.0738352 0.997270i \(-0.523524\pi\)
−0.0738352 + 0.997270i \(0.523524\pi\)
\(588\) 0 0
\(589\) 3.94653e34 0.932769
\(590\) 0 0
\(591\) −4.64309e34 −1.05187
\(592\) 0 0
\(593\) 1.57169e34 0.341338 0.170669 0.985328i \(-0.445407\pi\)
0.170669 + 0.985328i \(0.445407\pi\)
\(594\) 0 0
\(595\) 2.63976e33 0.0549670
\(596\) 0 0
\(597\) −1.47085e34 −0.293690
\(598\) 0 0
\(599\) 7.90989e34 1.51473 0.757364 0.652992i \(-0.226487\pi\)
0.757364 + 0.652992i \(0.226487\pi\)
\(600\) 0 0
\(601\) −9.50067e34 −1.74511 −0.872556 0.488514i \(-0.837539\pi\)
−0.872556 + 0.488514i \(0.837539\pi\)
\(602\) 0 0
\(603\) −3.01363e34 −0.531035
\(604\) 0 0
\(605\) −3.51343e34 −0.594003
\(606\) 0 0
\(607\) 3.98588e32 0.00646644 0.00323322 0.999995i \(-0.498971\pi\)
0.00323322 + 0.999995i \(0.498971\pi\)
\(608\) 0 0
\(609\) 3.95931e33 0.0616458
\(610\) 0 0
\(611\) −2.31848e32 −0.00346488
\(612\) 0 0
\(613\) −6.82592e34 −0.979276 −0.489638 0.871926i \(-0.662871\pi\)
−0.489638 + 0.871926i \(0.662871\pi\)
\(614\) 0 0
\(615\) −3.49586e34 −0.481521
\(616\) 0 0
\(617\) 1.15084e35 1.52212 0.761062 0.648679i \(-0.224678\pi\)
0.761062 + 0.648679i \(0.224678\pi\)
\(618\) 0 0
\(619\) −4.34788e34 −0.552261 −0.276131 0.961120i \(-0.589052\pi\)
−0.276131 + 0.961120i \(0.589052\pi\)
\(620\) 0 0
\(621\) 1.49563e34 0.182465
\(622\) 0 0
\(623\) −7.81178e33 −0.0915482
\(624\) 0 0
\(625\) 1.95367e34 0.219963
\(626\) 0 0
\(627\) −6.41886e34 −0.694406
\(628\) 0 0
\(629\) 4.99348e34 0.519123
\(630\) 0 0
\(631\) −1.27302e35 −1.27195 −0.635974 0.771711i \(-0.719401\pi\)
−0.635974 + 0.771711i \(0.719401\pi\)
\(632\) 0 0
\(633\) 1.10794e34 0.106407
\(634\) 0 0
\(635\) 9.46619e34 0.873985
\(636\) 0 0
\(637\) −1.62189e33 −0.0143972
\(638\) 0 0
\(639\) −2.08072e34 −0.177604
\(640\) 0 0
\(641\) −9.45454e33 −0.0776096 −0.0388048 0.999247i \(-0.512355\pi\)
−0.0388048 + 0.999247i \(0.512355\pi\)
\(642\) 0 0
\(643\) −8.31941e34 −0.656834 −0.328417 0.944533i \(-0.606515\pi\)
−0.328417 + 0.944533i \(0.606515\pi\)
\(644\) 0 0
\(645\) −1.12363e34 −0.0853348
\(646\) 0 0
\(647\) −2.34992e35 −1.71692 −0.858460 0.512880i \(-0.828579\pi\)
−0.858460 + 0.512880i \(0.828579\pi\)
\(648\) 0 0
\(649\) −2.48655e35 −1.74799
\(650\) 0 0
\(651\) −9.39590e33 −0.0635589
\(652\) 0 0
\(653\) −1.75276e35 −1.14106 −0.570530 0.821277i \(-0.693262\pi\)
−0.570530 + 0.821277i \(0.693262\pi\)
\(654\) 0 0
\(655\) −1.06350e35 −0.666379
\(656\) 0 0
\(657\) −7.41103e34 −0.447004
\(658\) 0 0
\(659\) 2.48211e35 1.44130 0.720648 0.693301i \(-0.243844\pi\)
0.720648 + 0.693301i \(0.243844\pi\)
\(660\) 0 0
\(661\) −3.37345e35 −1.88606 −0.943030 0.332707i \(-0.892038\pi\)
−0.943030 + 0.332707i \(0.892038\pi\)
\(662\) 0 0
\(663\) 1.63416e33 0.00879784
\(664\) 0 0
\(665\) 8.37835e33 0.0434398
\(666\) 0 0
\(667\) −2.07330e35 −1.03535
\(668\) 0 0
\(669\) −1.54387e35 −0.742648
\(670\) 0 0
\(671\) 5.37170e35 2.48932
\(672\) 0 0
\(673\) 2.99045e35 1.33521 0.667604 0.744517i \(-0.267320\pi\)
0.667604 + 0.744517i \(0.267320\pi\)
\(674\) 0 0
\(675\) −3.18678e34 −0.137105
\(676\) 0 0
\(677\) 5.69058e34 0.235938 0.117969 0.993017i \(-0.462362\pi\)
0.117969 + 0.993017i \(0.462362\pi\)
\(678\) 0 0
\(679\) 1.57608e33 0.00629803
\(680\) 0 0
\(681\) −1.72062e35 −0.662745
\(682\) 0 0
\(683\) −1.38059e35 −0.512633 −0.256317 0.966593i \(-0.582509\pi\)
−0.256317 + 0.966593i \(0.582509\pi\)
\(684\) 0 0
\(685\) 1.92264e35 0.688283
\(686\) 0 0
\(687\) −2.71619e35 −0.937564
\(688\) 0 0
\(689\) −3.23056e33 −0.0107532
\(690\) 0 0
\(691\) −1.16343e35 −0.373479 −0.186739 0.982409i \(-0.559792\pi\)
−0.186739 + 0.982409i \(0.559792\pi\)
\(692\) 0 0
\(693\) 1.52820e34 0.0473168
\(694\) 0 0
\(695\) 1.96880e35 0.588020
\(696\) 0 0
\(697\) 5.65841e35 1.63036
\(698\) 0 0
\(699\) −6.38421e34 −0.177477
\(700\) 0 0
\(701\) 6.30496e35 1.69125 0.845624 0.533779i \(-0.179229\pi\)
0.845624 + 0.533779i \(0.179229\pi\)
\(702\) 0 0
\(703\) 1.58488e35 0.410257
\(704\) 0 0
\(705\) 2.95407e34 0.0738001
\(706\) 0 0
\(707\) 1.79957e34 0.0433935
\(708\) 0 0
\(709\) −7.52844e35 −1.75238 −0.876188 0.481970i \(-0.839921\pi\)
−0.876188 + 0.481970i \(0.839921\pi\)
\(710\) 0 0
\(711\) 2.83176e35 0.636335
\(712\) 0 0
\(713\) 4.92018e35 1.06748
\(714\) 0 0
\(715\) 5.40200e33 0.0113170
\(716\) 0 0
\(717\) −1.77988e35 −0.360082
\(718\) 0 0
\(719\) 1.28708e35 0.251475 0.125738 0.992064i \(-0.459870\pi\)
0.125738 + 0.992064i \(0.459870\pi\)
\(720\) 0 0
\(721\) −5.45373e34 −0.102921
\(722\) 0 0
\(723\) −1.87725e35 −0.342211
\(724\) 0 0
\(725\) 4.41764e35 0.777974
\(726\) 0 0
\(727\) −4.39640e35 −0.748027 −0.374014 0.927423i \(-0.622019\pi\)
−0.374014 + 0.927423i \(0.622019\pi\)
\(728\) 0 0
\(729\) 2.25284e34 0.0370370
\(730\) 0 0
\(731\) 1.81871e35 0.288932
\(732\) 0 0
\(733\) −1.18297e36 −1.81625 −0.908124 0.418702i \(-0.862485\pi\)
−0.908124 + 0.418702i \(0.862485\pi\)
\(734\) 0 0
\(735\) 2.06651e35 0.306652
\(736\) 0 0
\(737\) 1.61246e36 2.31284
\(738\) 0 0
\(739\) 8.13836e35 1.12845 0.564224 0.825622i \(-0.309175\pi\)
0.564224 + 0.825622i \(0.309175\pi\)
\(740\) 0 0
\(741\) 5.18668e33 0.00695283
\(742\) 0 0
\(743\) 1.02640e36 1.33033 0.665164 0.746698i \(-0.268362\pi\)
0.665164 + 0.746698i \(0.268362\pi\)
\(744\) 0 0
\(745\) 2.33802e35 0.293018
\(746\) 0 0
\(747\) −4.40191e35 −0.533500
\(748\) 0 0
\(749\) −8.85251e34 −0.103763
\(750\) 0 0
\(751\) 1.43129e36 1.62266 0.811332 0.584586i \(-0.198743\pi\)
0.811332 + 0.584586i \(0.198743\pi\)
\(752\) 0 0
\(753\) −5.71848e35 −0.627110
\(754\) 0 0
\(755\) −3.03391e35 −0.321859
\(756\) 0 0
\(757\) 8.68697e35 0.891600 0.445800 0.895133i \(-0.352919\pi\)
0.445800 + 0.895133i \(0.352919\pi\)
\(758\) 0 0
\(759\) −8.00245e35 −0.794696
\(760\) 0 0
\(761\) 5.51250e34 0.0529713 0.0264857 0.999649i \(-0.491568\pi\)
0.0264857 + 0.999649i \(0.491568\pi\)
\(762\) 0 0
\(763\) 1.02324e35 0.0951530
\(764\) 0 0
\(765\) −2.08216e35 −0.187390
\(766\) 0 0
\(767\) 2.00923e34 0.0175020
\(768\) 0 0
\(769\) −4.98681e35 −0.420479 −0.210239 0.977650i \(-0.567424\pi\)
−0.210239 + 0.977650i \(0.567424\pi\)
\(770\) 0 0
\(771\) 3.48763e33 0.00284676
\(772\) 0 0
\(773\) 4.79467e35 0.378892 0.189446 0.981891i \(-0.439331\pi\)
0.189446 + 0.981891i \(0.439331\pi\)
\(774\) 0 0
\(775\) −1.04836e36 −0.802116
\(776\) 0 0
\(777\) −3.77329e34 −0.0279549
\(778\) 0 0
\(779\) 1.79593e36 1.28846
\(780\) 0 0
\(781\) 1.11330e36 0.773525
\(782\) 0 0
\(783\) −3.12298e35 −0.210158
\(784\) 0 0
\(785\) 9.84670e35 0.641830
\(786\) 0 0
\(787\) −1.22599e36 −0.774111 −0.387055 0.922056i \(-0.626508\pi\)
−0.387055 + 0.922056i \(0.626508\pi\)
\(788\) 0 0
\(789\) −1.08317e36 −0.662576
\(790\) 0 0
\(791\) 6.20311e34 0.0367623
\(792\) 0 0
\(793\) −4.34054e34 −0.0249246
\(794\) 0 0
\(795\) 4.11619e35 0.229038
\(796\) 0 0
\(797\) −3.12403e36 −1.68456 −0.842278 0.539043i \(-0.818786\pi\)
−0.842278 + 0.539043i \(0.818786\pi\)
\(798\) 0 0
\(799\) −4.78146e35 −0.249877
\(800\) 0 0
\(801\) 6.16168e35 0.312099
\(802\) 0 0
\(803\) 3.96532e36 1.94686
\(804\) 0 0
\(805\) 1.04454e35 0.0497136
\(806\) 0 0
\(807\) 6.92021e35 0.319301
\(808\) 0 0
\(809\) 4.16982e36 1.86535 0.932675 0.360717i \(-0.117468\pi\)
0.932675 + 0.360717i \(0.117468\pi\)
\(810\) 0 0
\(811\) −7.93102e35 −0.344008 −0.172004 0.985096i \(-0.555024\pi\)
−0.172004 + 0.985096i \(0.555024\pi\)
\(812\) 0 0
\(813\) −1.45287e36 −0.611078
\(814\) 0 0
\(815\) 2.34334e35 0.0955794
\(816\) 0 0
\(817\) 5.77240e35 0.228339
\(818\) 0 0
\(819\) −1.23484e33 −0.000473766 0
\(820\) 0 0
\(821\) 2.22198e35 0.0826896 0.0413448 0.999145i \(-0.486836\pi\)
0.0413448 + 0.999145i \(0.486836\pi\)
\(822\) 0 0
\(823\) −4.63197e36 −1.67212 −0.836061 0.548637i \(-0.815147\pi\)
−0.836061 + 0.548637i \(0.815147\pi\)
\(824\) 0 0
\(825\) 1.70511e36 0.597141
\(826\) 0 0
\(827\) −5.60825e36 −1.90550 −0.952748 0.303760i \(-0.901758\pi\)
−0.952748 + 0.303760i \(0.901758\pi\)
\(828\) 0 0
\(829\) −3.61387e36 −1.19135 −0.595677 0.803224i \(-0.703116\pi\)
−0.595677 + 0.803224i \(0.703116\pi\)
\(830\) 0 0
\(831\) −2.57136e35 −0.0822526
\(832\) 0 0
\(833\) −3.34486e36 −1.03828
\(834\) 0 0
\(835\) −1.51642e36 −0.456813
\(836\) 0 0
\(837\) 7.41118e35 0.216680
\(838\) 0 0
\(839\) 3.53738e36 1.00382 0.501911 0.864919i \(-0.332630\pi\)
0.501911 + 0.864919i \(0.332630\pi\)
\(840\) 0 0
\(841\) 6.98837e35 0.192498
\(842\) 0 0
\(843\) −4.02736e36 −1.07690
\(844\) 0 0
\(845\) 2.06536e36 0.536151
\(846\) 0 0
\(847\) −4.29722e35 −0.108304
\(848\) 0 0
\(849\) 6.93230e35 0.169641
\(850\) 0 0
\(851\) 1.97589e36 0.469508
\(852\) 0 0
\(853\) −5.36485e36 −1.23792 −0.618962 0.785421i \(-0.712447\pi\)
−0.618962 + 0.785421i \(0.712447\pi\)
\(854\) 0 0
\(855\) −6.60857e35 −0.148092
\(856\) 0 0
\(857\) 1.12850e36 0.245607 0.122803 0.992431i \(-0.460812\pi\)
0.122803 + 0.992431i \(0.460812\pi\)
\(858\) 0 0
\(859\) 6.05620e36 1.28022 0.640111 0.768282i \(-0.278888\pi\)
0.640111 + 0.768282i \(0.278888\pi\)
\(860\) 0 0
\(861\) −4.27574e35 −0.0877955
\(862\) 0 0
\(863\) −5.30956e35 −0.105907 −0.0529533 0.998597i \(-0.516863\pi\)
−0.0529533 + 0.998597i \(0.516863\pi\)
\(864\) 0 0
\(865\) 9.97942e35 0.193377
\(866\) 0 0
\(867\) 3.03432e35 0.0571244
\(868\) 0 0
\(869\) −1.51515e37 −2.77146
\(870\) 0 0
\(871\) −1.30293e35 −0.0231576
\(872\) 0 0
\(873\) −1.24316e35 −0.0214708
\(874\) 0 0
\(875\) −5.34965e35 −0.0897894
\(876\) 0 0
\(877\) −5.83031e36 −0.951035 −0.475518 0.879706i \(-0.657739\pi\)
−0.475518 + 0.879706i \(0.657739\pi\)
\(878\) 0 0
\(879\) −2.14713e35 −0.0340406
\(880\) 0 0
\(881\) 7.57293e36 1.16698 0.583492 0.812119i \(-0.301686\pi\)
0.583492 + 0.812119i \(0.301686\pi\)
\(882\) 0 0
\(883\) 2.59184e36 0.388239 0.194119 0.980978i \(-0.437815\pi\)
0.194119 + 0.980978i \(0.437815\pi\)
\(884\) 0 0
\(885\) −2.56004e36 −0.372783
\(886\) 0 0
\(887\) −7.96686e36 −1.12782 −0.563912 0.825835i \(-0.690704\pi\)
−0.563912 + 0.825835i \(0.690704\pi\)
\(888\) 0 0
\(889\) 1.15780e36 0.159353
\(890\) 0 0
\(891\) −1.20540e36 −0.161309
\(892\) 0 0
\(893\) −1.51759e36 −0.197475
\(894\) 0 0
\(895\) −3.61875e36 −0.457900
\(896\) 0 0
\(897\) 6.46628e34 0.00795699
\(898\) 0 0
\(899\) −1.02737e37 −1.22950
\(900\) 0 0
\(901\) −6.66248e36 −0.775489
\(902\) 0 0
\(903\) −1.37429e35 −0.0155590
\(904\) 0 0
\(905\) −9.91023e35 −0.109138
\(906\) 0 0
\(907\) 4.86506e36 0.521191 0.260596 0.965448i \(-0.416081\pi\)
0.260596 + 0.965448i \(0.416081\pi\)
\(908\) 0 0
\(909\) −1.41944e36 −0.147934
\(910\) 0 0
\(911\) −1.10036e37 −1.11572 −0.557859 0.829936i \(-0.688377\pi\)
−0.557859 + 0.829936i \(0.688377\pi\)
\(912\) 0 0
\(913\) 2.35527e37 2.32357
\(914\) 0 0
\(915\) 5.53046e36 0.530882
\(916\) 0 0
\(917\) −1.30075e36 −0.121500
\(918\) 0 0
\(919\) −1.10577e37 −1.00513 −0.502564 0.864540i \(-0.667610\pi\)
−0.502564 + 0.864540i \(0.667610\pi\)
\(920\) 0 0
\(921\) −3.69689e36 −0.327033
\(922\) 0 0
\(923\) −8.99588e34 −0.00774502
\(924\) 0 0
\(925\) −4.21008e36 −0.352792
\(926\) 0 0
\(927\) 4.30172e36 0.350870
\(928\) 0 0
\(929\) 1.82435e37 1.44848 0.724239 0.689549i \(-0.242191\pi\)
0.724239 + 0.689549i \(0.242191\pi\)
\(930\) 0 0
\(931\) −1.06163e37 −0.820543
\(932\) 0 0
\(933\) −1.46100e36 −0.109933
\(934\) 0 0
\(935\) 1.11407e37 0.816146
\(936\) 0 0
\(937\) 9.54074e36 0.680514 0.340257 0.940332i \(-0.389486\pi\)
0.340257 + 0.940332i \(0.389486\pi\)
\(938\) 0 0
\(939\) 4.99226e36 0.346719
\(940\) 0 0
\(941\) −7.72127e36 −0.522178 −0.261089 0.965315i \(-0.584082\pi\)
−0.261089 + 0.965315i \(0.584082\pi\)
\(942\) 0 0
\(943\) 2.23900e37 1.47454
\(944\) 0 0
\(945\) 1.57337e35 0.0100910
\(946\) 0 0
\(947\) 1.89183e37 1.18170 0.590849 0.806782i \(-0.298793\pi\)
0.590849 + 0.806782i \(0.298793\pi\)
\(948\) 0 0
\(949\) −3.20413e35 −0.0194932
\(950\) 0 0
\(951\) 9.91366e36 0.587459
\(952\) 0 0
\(953\) −1.61494e37 −0.932172 −0.466086 0.884739i \(-0.654336\pi\)
−0.466086 + 0.884739i \(0.654336\pi\)
\(954\) 0 0
\(955\) 1.11580e37 0.627402
\(956\) 0 0
\(957\) 1.67097e37 0.915312
\(958\) 0 0
\(959\) 2.35156e36 0.125494
\(960\) 0 0
\(961\) 5.14781e36 0.267658
\(962\) 0 0
\(963\) 6.98257e36 0.353742
\(964\) 0 0
\(965\) −1.87024e37 −0.923222
\(966\) 0 0
\(967\) 2.64645e37 1.27301 0.636507 0.771271i \(-0.280379\pi\)
0.636507 + 0.771271i \(0.280379\pi\)
\(968\) 0 0
\(969\) 1.06966e37 0.501418
\(970\) 0 0
\(971\) −2.73601e37 −1.24990 −0.624952 0.780663i \(-0.714882\pi\)
−0.624952 + 0.780663i \(0.714882\pi\)
\(972\) 0 0
\(973\) 2.40802e36 0.107213
\(974\) 0 0
\(975\) −1.37779e35 −0.00597895
\(976\) 0 0
\(977\) 3.04743e37 1.28900 0.644498 0.764606i \(-0.277066\pi\)
0.644498 + 0.764606i \(0.277066\pi\)
\(978\) 0 0
\(979\) −3.29685e37 −1.35930
\(980\) 0 0
\(981\) −8.07101e36 −0.324389
\(982\) 0 0
\(983\) −3.84516e36 −0.150659 −0.0753296 0.997159i \(-0.524001\pi\)
−0.0753296 + 0.997159i \(0.524001\pi\)
\(984\) 0 0
\(985\) 2.55774e37 0.977020
\(986\) 0 0
\(987\) 3.61308e35 0.0134559
\(988\) 0 0
\(989\) 7.19651e36 0.261317
\(990\) 0 0
\(991\) 4.30043e37 1.52262 0.761309 0.648389i \(-0.224557\pi\)
0.761309 + 0.648389i \(0.224557\pi\)
\(992\) 0 0
\(993\) 2.50648e37 0.865363
\(994\) 0 0
\(995\) 8.10246e36 0.272790
\(996\) 0 0
\(997\) −1.52317e37 −0.500103 −0.250051 0.968233i \(-0.580447\pi\)
−0.250051 + 0.968233i \(0.580447\pi\)
\(998\) 0 0
\(999\) 2.97625e36 0.0953017
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 48.26.a.c.1.1 1
4.3 odd 2 6.26.a.a.1.1 1
12.11 even 2 18.26.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6.26.a.a.1.1 1 4.3 odd 2
18.26.a.d.1.1 1 12.11 even 2
48.26.a.c.1.1 1 1.1 even 1 trivial