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Properties

Label 59.7.b.a.58.1
Level $59$
Weight $7$
Character 59.58
Self dual yes
Analytic conductor $13.573$
Analytic rank $0$
Dimension $1$
CM discriminant -59
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [59,7,Mod(58,59)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(59, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("59.58");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 59 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 59.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(13.5731909336\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 58.1
Character \(\chi\) \(=\) 59.58

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{3} +64.0000 q^{4} +191.000 q^{5} +155.000 q^{7} -704.000 q^{9} +O(q^{10})\) \(q-5.00000 q^{3} +64.0000 q^{4} +191.000 q^{5} +155.000 q^{7} -704.000 q^{9} -320.000 q^{12} -955.000 q^{15} +4096.00 q^{16} +6050.00 q^{17} +443.000 q^{19} +12224.0 q^{20} -775.000 q^{21} +20856.0 q^{25} +7165.00 q^{27} +9920.00 q^{28} -23497.0 q^{29} +29605.0 q^{35} -45056.0 q^{36} +137783. q^{41} -134464. q^{45} -20480.0 q^{48} -93624.0 q^{49} -30250.0 q^{51} -190825. q^{53} -2215.00 q^{57} -205379. q^{59} -61120.0 q^{60} -109120. q^{63} +262144. q^{64} +387200. q^{68} -683422. q^{71} -104280. q^{75} +28352.0 q^{76} -288853. q^{79} +782336. q^{80} +477391. q^{81} -49600.0 q^{84} +1.15555e6 q^{85} +117485. q^{87} +84613.0 q^{95} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/59\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) −5.00000 −0.185185 −0.0925926 − 0.995704i \(-0.529515\pi\)
−0.0925926 + 0.995704i \(0.529515\pi\)
\(4\) 64.0000 1.00000
\(5\) 191.000 1.52800 0.764000 − 0.645216i \(-0.223233\pi\)
0.764000 + 0.645216i \(0.223233\pi\)
\(6\) 0 0
\(7\) 155.000 0.451895 0.225948 − 0.974139i \(-0.427452\pi\)
0.225948 + 0.974139i \(0.427452\pi\)
\(8\) 0 0
\(9\) −704.000 −0.965706
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −320.000 −0.185185
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) −955.000 −0.282963
\(16\) 4096.00 1.00000
\(17\) 6050.00 1.23143 0.615713 − 0.787970i \(-0.288868\pi\)
0.615713 + 0.787970i \(0.288868\pi\)
\(18\) 0 0
\(19\) 443.000 0.0645867 0.0322933 − 0.999478i \(-0.489719\pi\)
0.0322933 + 0.999478i \(0.489719\pi\)
\(20\) 12224.0 1.52800
\(21\) −775.000 −0.0836843
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 20856.0 1.33478
\(26\) 0 0
\(27\) 7165.00 0.364020
\(28\) 9920.00 0.451895
\(29\) −23497.0 −0.963426 −0.481713 − 0.876329i \(-0.659985\pi\)
−0.481713 + 0.876329i \(0.659985\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 29605.0 0.690496
\(36\) −45056.0 −0.965706
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 137783. 1.99914 0.999572 − 0.0292552i \(-0.00931356\pi\)
0.999572 + 0.0292552i \(0.00931356\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) −134464. −1.47560
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −20480.0 −0.185185
\(49\) −93624.0 −0.795791
\(50\) 0 0
\(51\) −30250.0 −0.228042
\(52\) 0 0
\(53\) −190825. −1.28176 −0.640881 − 0.767640i \(-0.721431\pi\)
−0.640881 + 0.767640i \(0.721431\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −2215.00 −0.0119605
\(58\) 0 0
\(59\) −205379. −1.00000
\(60\) −61120.0 −0.282963
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) −109120. −0.436398
\(64\) 262144. 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 387200. 1.23143
\(69\) 0 0
\(70\) 0 0
\(71\) −683422. −1.90947 −0.954737 − 0.297450i \(-0.903864\pi\)
−0.954737 + 0.297450i \(0.903864\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) −104280. −0.247182
\(76\) 28352.0 0.0645867
\(77\) 0 0
\(78\) 0 0
\(79\) −288853. −0.585862 −0.292931 − 0.956134i \(-0.594631\pi\)
−0.292931 + 0.956134i \(0.594631\pi\)
\(80\) 782336. 1.52800
\(81\) 477391. 0.898295
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −49600.0 −0.0836843
\(85\) 1.15555e6 1.88162
\(86\) 0 0
\(87\) 117485. 0.178412
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 84613.0 0.0986884
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.33478e6 1.33478
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) −148025. −0.127870
\(106\) 0 0
\(107\) −2.40968e6 −1.96702 −0.983510 − 0.180852i \(-0.942115\pi\)
−0.983510 + 0.180852i \(0.942115\pi\)
\(108\) 458560. 0.364020
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 634880. 0.451895
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.50381e6 −0.963426
\(117\) 0 0
\(118\) 0 0
\(119\) 937750. 0.556476
\(120\) 0 0
\(121\) 1.77156e6 1.00000
\(122\) 0 0
\(123\) −688915. −0.370212
\(124\) 0 0
\(125\) 999121. 0.511550
\(126\) 0 0
\(127\) −3.42272e6 −1.67094 −0.835470 − 0.549536i \(-0.814804\pi\)
−0.835470 + 0.549536i \(0.814804\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 68665.0 0.0291864
\(134\) 0 0
\(135\) 1.36852e6 0.556222
\(136\) 0 0
\(137\) −4.92086e6 −1.91373 −0.956863 − 0.290540i \(-0.906165\pi\)
−0.956863 + 0.290540i \(0.906165\pi\)
\(138\) 0 0
\(139\) −1.52964e6 −0.569566 −0.284783 − 0.958592i \(-0.591922\pi\)
−0.284783 + 0.958592i \(0.591922\pi\)
\(140\) 1.89472e6 0.690496
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −2.88358e6 −0.965706
\(145\) −4.48793e6 −1.47212
\(146\) 0 0
\(147\) 468120. 0.147369
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) −4.25920e6 −1.18920
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 954125. 0.237363
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 7.72481e6 1.78371 0.891857 − 0.452318i \(-0.149403\pi\)
0.891857 + 0.452318i \(0.149403\pi\)
\(164\) 8.81811e6 1.99914
\(165\) 0 0
\(166\) 0 0
\(167\) −1.74692e6 −0.375081 −0.187540 − 0.982257i \(-0.560052\pi\)
−0.187540 + 0.982257i \(0.560052\pi\)
\(168\) 0 0
\(169\) 4.82681e6 1.00000
\(170\) 0 0
\(171\) −311872. −0.0623718
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 3.23268e6 0.603182
\(176\) 0 0
\(177\) 1.02690e6 0.185185
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −8.60570e6 −1.47560
\(181\) 1.11325e7 1.87741 0.938704 − 0.344724i \(-0.112028\pi\)
0.938704 + 0.344724i \(0.112028\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 1.11058e6 0.164499
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −1.31072e6 −0.185185
\(193\) −1.06261e7 −1.47810 −0.739050 − 0.673651i \(-0.764725\pi\)
−0.739050 + 0.673651i \(0.764725\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −5.99194e6 −0.795791
\(197\) −1.40767e6 −0.184121 −0.0920603 − 0.995753i \(-0.529345\pi\)
−0.0920603 + 0.995753i \(0.529345\pi\)
\(198\) 0 0
\(199\) 1.35177e7 1.71532 0.857658 − 0.514220i \(-0.171918\pi\)
0.857658 + 0.514220i \(0.171918\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.64204e6 −0.435367
\(204\) −1.93600e6 −0.228042
\(205\) 2.63166e7 3.05469
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −1.22128e7 −1.28176
\(213\) 3.41711e6 0.353606
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.20668e7 1.08812 0.544060 − 0.839047i \(-0.316887\pi\)
0.544060 + 0.839047i \(0.316887\pi\)
\(224\) 0 0
\(225\) −1.46826e7 −1.28901
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) −141760. −0.0119605
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.31443e7 −1.00000
\(237\) 1.44426e6 0.108493
\(238\) 0 0
\(239\) −2.23086e7 −1.63410 −0.817050 − 0.576566i \(-0.804392\pi\)
−0.817050 + 0.576566i \(0.804392\pi\)
\(240\) −3.91168e6 −0.282963
\(241\) 5.67977e6 0.405769 0.202885 − 0.979203i \(-0.434968\pi\)
0.202885 + 0.979203i \(0.434968\pi\)
\(242\) 0 0
\(243\) −7.61024e6 −0.530371
\(244\) 0 0
\(245\) −1.78822e7 −1.21597
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2.84403e7 −1.79851 −0.899255 − 0.437426i \(-0.855890\pi\)
−0.899255 + 0.437426i \(0.855890\pi\)
\(252\) −6.98368e6 −0.436398
\(253\) 0 0
\(254\) 0 0
\(255\) −5.77775e6 −0.348448
\(256\) 1.67772e7 1.00000
\(257\) 2.28873e7 1.34833 0.674164 − 0.738581i \(-0.264504\pi\)
0.674164 + 0.738581i \(0.264504\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1.65419e7 0.930387
\(262\) 0 0
\(263\) −3.48774e7 −1.91724 −0.958620 − 0.284689i \(-0.908110\pi\)
−0.958620 + 0.284689i \(0.908110\pi\)
\(264\) 0 0
\(265\) −3.64476e7 −1.95853
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 3.37256e7 1.69454 0.847270 − 0.531162i \(-0.178245\pi\)
0.847270 + 0.531162i \(0.178245\pi\)
\(272\) 2.47808e7 1.23143
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 4.12329e7 1.94001 0.970007 − 0.243076i \(-0.0781565\pi\)
0.970007 + 0.243076i \(0.0781565\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4.43038e7 1.99674 0.998371 − 0.0570503i \(-0.0181695\pi\)
0.998371 + 0.0570503i \(0.0181695\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) −4.37390e7 −1.90947
\(285\) −423065. −0.0182756
\(286\) 0 0
\(287\) 2.13564e7 0.903403
\(288\) 0 0
\(289\) 1.24649e7 0.516412
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.13149e7 0.847383 0.423691 − 0.905807i \(-0.360734\pi\)
0.423691 + 0.905807i \(0.360734\pi\)
\(294\) 0 0
\(295\) −3.92274e7 −1.52800
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −6.67392e6 −0.247182
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 1.81453e6 0.0645867
\(305\) 0 0
\(306\) 0 0
\(307\) −4.44660e7 −1.53678 −0.768392 − 0.639980i \(-0.778943\pi\)
−0.768392 + 0.639980i \(0.778943\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.58448e7 −0.526752 −0.263376 − 0.964693i \(-0.584836\pi\)
−0.263376 + 0.964693i \(0.584836\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) −2.08419e7 −0.666816
\(316\) −1.84866e7 −0.585862
\(317\) 6.36638e7 1.99855 0.999274 − 0.0380992i \(-0.0121303\pi\)
0.999274 + 0.0380992i \(0.0121303\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 5.00695e7 1.52800
\(321\) 1.20484e7 0.364263
\(322\) 0 0
\(323\) 2.68015e6 0.0795338
\(324\) 3.05530e7 0.898295
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 7.18789e7 1.98206 0.991032 − 0.133628i \(-0.0426627\pi\)
0.991032 + 0.133628i \(0.0426627\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −3.17440e6 −0.0836843
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 7.39552e7 1.88162
\(341\) 0 0
\(342\) 0 0
\(343\) −3.27473e7 −0.811509
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 7.51904e6 0.178412
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) −1.30534e8 −2.91768
\(356\) 0 0
\(357\) −4.68875e6 −0.103051
\(358\) 0 0
\(359\) 2.83535e7 0.612806 0.306403 − 0.951902i \(-0.400875\pi\)
0.306403 + 0.951902i \(0.400875\pi\)
\(360\) 0 0
\(361\) −4.68496e7 −0.995829
\(362\) 0 0
\(363\) −8.85780e6 −0.185185
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) −9.69992e7 −1.93059
\(370\) 0 0
\(371\) −2.95779e7 −0.579222
\(372\) 0 0
\(373\) −7.97998e7 −1.53771 −0.768857 − 0.639421i \(-0.779174\pi\)
−0.768857 + 0.639421i \(0.779174\pi\)
\(374\) 0 0
\(375\) −4.99560e6 −0.0947315
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 6.07707e7 1.11629 0.558145 − 0.829744i \(-0.311513\pi\)
0.558145 + 0.829744i \(0.311513\pi\)
\(380\) 5.41523e6 0.0986884
\(381\) 1.71136e7 0.309433
\(382\) 0 0
\(383\) −8.43585e7 −1.50153 −0.750763 − 0.660572i \(-0.770314\pi\)
−0.750763 + 0.660572i \(0.770314\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.21967e7 −0.377085 −0.188542 − 0.982065i \(-0.560376\pi\)
−0.188542 + 0.982065i \(0.560376\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −5.51709e7 −0.895198
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) −343325. −0.00540489
\(400\) 8.54262e7 1.33478
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 9.11817e7 1.37260
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 2.46043e7 0.354394
\(412\) 0 0
\(413\) −3.18337e7 −0.451895
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 7.64819e6 0.105475
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) −9.47360e6 −0.127870
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.26179e8 1.64369
\(426\) 0 0
\(427\) 0 0
\(428\) −1.54220e8 −1.96702
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 2.93478e7 0.364020
\(433\) 5.14667e7 0.633961 0.316980 − 0.948432i \(-0.397331\pi\)
0.316980 + 0.948432i \(0.397331\pi\)
\(434\) 0 0
\(435\) 2.24396e7 0.272614
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −1.58841e8 −1.87745 −0.938724 − 0.344669i \(-0.887991\pi\)
−0.938724 + 0.344669i \(0.887991\pi\)
\(440\) 0 0
\(441\) 6.59113e7 0.768500
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 4.06323e7 0.451895
\(449\) 9.25008e7 1.02190 0.510948 − 0.859612i \(-0.329295\pi\)
0.510948 + 0.859612i \(0.329295\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 4.33482e7 0.448264
\(460\) 0 0
\(461\) 1.40157e7 0.143058 0.0715292 − 0.997439i \(-0.477212\pi\)
0.0715292 + 0.997439i \(0.477212\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) −9.62437e7 −0.963426
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 9.23921e6 0.0862093
\(476\) 6.00160e7 0.556476
\(477\) 1.34341e8 1.23781
\(478\) 0 0
\(479\) 2.17675e8 1.98062 0.990310 − 0.138874i \(-0.0443484\pi\)
0.990310 + 0.138874i \(0.0443484\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.13380e8 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 1.57915e8 1.36722 0.683608 − 0.729849i \(-0.260410\pi\)
0.683608 + 0.729849i \(0.260410\pi\)
\(488\) 0 0
\(489\) −3.86240e7 −0.330317
\(490\) 0 0
\(491\) 1.37797e8 1.16411 0.582057 − 0.813148i \(-0.302248\pi\)
0.582057 + 0.813148i \(0.302248\pi\)
\(492\) −4.40906e7 −0.370212
\(493\) −1.42157e8 −1.18639
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.05930e8 −0.862882
\(498\) 0 0
\(499\) −1.58044e8 −1.27197 −0.635984 − 0.771702i \(-0.719405\pi\)
−0.635984 + 0.771702i \(0.719405\pi\)
\(500\) 6.39437e7 0.511550
\(501\) 8.73462e6 0.0694594
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2.41340e7 −0.185185
\(508\) −2.19054e8 −1.67094
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 3.17410e6 0.0235108
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.49383e8 1.05630 0.528149 − 0.849151i \(-0.322886\pi\)
0.528149 + 0.849151i \(0.322886\pi\)
\(522\) 0 0
\(523\) −2.48079e8 −1.73415 −0.867073 − 0.498181i \(-0.834002\pi\)
−0.867073 + 0.498181i \(0.834002\pi\)
\(524\) 0 0
\(525\) −1.61634e7 −0.111700
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.48036e8 1.00000
\(530\) 0 0
\(531\) 1.44587e8 0.965706
\(532\) 4.39456e6 0.0291864
\(533\) 0 0
\(534\) 0 0
\(535\) −4.60250e8 −3.00561
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 8.75850e7 0.556222
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −5.56627e7 −0.347668
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.68171e8 −1.02752 −0.513759 − 0.857934i \(-0.671748\pi\)
−0.513759 + 0.857934i \(0.671748\pi\)
\(548\) −3.14935e8 −1.91373
\(549\) 0 0
\(550\) 0 0
\(551\) −1.04092e7 −0.0622245
\(552\) 0 0
\(553\) −4.47722e7 −0.264748
\(554\) 0 0
\(555\) 0 0
\(556\) −9.78968e7 −0.569566
\(557\) 2.81434e8 1.62859 0.814294 − 0.580452i \(-0.197124\pi\)
0.814294 + 0.580452i \(0.197124\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.21262e8 0.690496
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 7.39956e7 0.405935
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −1.84549e8 −0.965706
\(577\) −2.92634e8 −1.52334 −0.761672 − 0.647963i \(-0.775621\pi\)
−0.761672 + 0.647963i \(0.775621\pi\)
\(578\) 0 0
\(579\) 5.31307e7 0.273722
\(580\) −2.87227e8 −1.47212
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 2.99597e7 0.147369
\(589\) 0 0
\(590\) 0 0
\(591\) 7.03835e6 0.0340964
\(592\) 0 0
\(593\) 3.71262e8 1.78040 0.890198 − 0.455574i \(-0.150566\pi\)
0.890198 + 0.455574i \(0.150566\pi\)
\(594\) 0 0
\(595\) 1.79110e8 0.850295
\(596\) 0 0
\(597\) −6.75886e7 −0.317651
\(598\) 0 0
\(599\) −1.68666e8 −0.784777 −0.392388 − 0.919800i \(-0.628351\pi\)
−0.392388 + 0.919800i \(0.628351\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3.38368e8 1.52800
\(606\) 0 0
\(607\) 1.93755e8 0.866336 0.433168 − 0.901313i \(-0.357396\pi\)
0.433168 + 0.901313i \(0.357396\pi\)
\(608\) 0 0
\(609\) 1.82102e7 0.0806236
\(610\) 0 0
\(611\) 0 0
\(612\) −2.72589e8 −1.18920
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) −1.31583e8 −0.565684
\(616\) 0 0
\(617\) 2.07843e8 0.884870 0.442435 − 0.896801i \(-0.354115\pi\)
0.442435 + 0.896801i \(0.354115\pi\)
\(618\) 0 0
\(619\) 4.54982e8 1.91832 0.959162 − 0.282856i \(-0.0912817\pi\)
0.959162 + 0.282856i \(0.0912817\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −1.35043e8 −0.553136
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 3.89140e8 1.54888 0.774441 − 0.632646i \(-0.218031\pi\)
0.774441 + 0.632646i \(0.218031\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.53740e8 −2.55320
\(636\) 6.10640e7 0.237363
\(637\) 0 0
\(638\) 0 0
\(639\) 4.81129e8 1.84399
\(640\) 0 0
\(641\) 2.30711e8 0.875980 0.437990 − 0.898980i \(-0.355690\pi\)
0.437990 + 0.898980i \(0.355690\pi\)
\(642\) 0 0
\(643\) −1.74221e8 −0.655340 −0.327670 − 0.944792i \(-0.606263\pi\)
−0.327670 + 0.944792i \(0.606263\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5.40621e8 −1.99609 −0.998045 − 0.0624952i \(-0.980094\pi\)
−0.998045 + 0.0624952i \(0.980094\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 4.94388e8 1.78371
\(653\) −6.28506e7 −0.225720 −0.112860 − 0.993611i \(-0.536001\pi\)
−0.112860 + 0.993611i \(0.536001\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 5.64359e8 1.99914
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 4.30135e8 1.48936 0.744682 − 0.667419i \(-0.232601\pi\)
0.744682 + 0.667419i \(0.232601\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.31150e7 0.0445968
\(666\) 0 0
\(667\) 0 0
\(668\) −1.11803e8 −0.375081
\(669\) −6.03338e7 −0.201504
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 1.49433e8 0.485888
\(676\) 3.08916e8 1.00000
\(677\) −4.94824e8 −1.59472 −0.797360 − 0.603504i \(-0.793771\pi\)
−0.797360 + 0.603504i \(0.793771\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −1.99598e7 −0.0623718
\(685\) −9.39885e8 −2.92417
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.92161e8 −0.870297
\(696\) 0 0
\(697\) 8.33587e8 2.46180
\(698\) 0 0
\(699\) 0 0
\(700\) 2.06892e8 0.603182
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 6.57213e7 0.185185
\(709\) −4.89927e8 −1.37465 −0.687325 − 0.726350i \(-0.741215\pi\)
−0.687325 + 0.726350i \(0.741215\pi\)
\(710\) 0 0
\(711\) 2.03353e8 0.565771
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 1.11543e8 0.302611
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −5.50765e8 −1.47560
\(721\) 0 0
\(722\) 0 0
\(723\) −2.83988e7 −0.0751425
\(724\) 7.12483e8 1.87741
\(725\) −4.90053e8 −1.28597
\(726\) 0 0
\(727\) 7.61580e8 1.98204 0.991020 − 0.133713i \(-0.0426900\pi\)
0.991020 + 0.133713i \(0.0426900\pi\)
\(728\) 0 0
\(729\) −3.09967e8 −0.800079
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −6.89695e8 −1.75124 −0.875619 − 0.483002i \(-0.839546\pi\)
−0.875619 + 0.483002i \(0.839546\pi\)
\(734\) 0 0
\(735\) 8.94109e7 0.225179
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4.46619e8 −1.08886 −0.544428 − 0.838808i \(-0.683253\pi\)
−0.544428 + 0.838808i \(0.683253\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.73501e8 −0.888887
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 1.42201e8 0.333057
\(754\) 0 0
\(755\) 0 0
\(756\) 7.10768e7 0.164499
\(757\) −4.73137e8 −1.09068 −0.545342 − 0.838213i \(-0.683600\pi\)
−0.545342 + 0.838213i \(0.683600\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.03260e8 −0.688116 −0.344058 − 0.938948i \(-0.611802\pi\)
−0.344058 + 0.938948i \(0.611802\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −8.13507e8 −1.81709
\(766\) 0 0
\(767\) 0 0
\(768\) −8.38861e7 −0.185185
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) −1.14437e8 −0.249691
\(772\) −6.80073e8 −1.47810
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.10379e7 0.129118
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −1.68356e8 −0.350706
\(784\) −3.83484e8 −0.795791
\(785\) 0 0
\(786\) 0 0
\(787\) 8.55584e8 1.75525 0.877624 − 0.479350i \(-0.159128\pi\)
0.877624 + 0.479350i \(0.159128\pi\)
\(788\) −9.00909e7 −0.184121
\(789\) 1.74387e8 0.355044
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 1.82238e8 0.362691
\(796\) 8.65134e8 1.71532
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) −2.33090e8 −0.435367
\(813\) −1.68628e8 −0.313804
\(814\) 0 0
\(815\) 1.47544e9 2.72551
\(816\) −1.23904e8 −0.228042
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 1.68426e9 3.05469
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 7.85120e8 1.38810 0.694048 − 0.719929i \(-0.255826\pi\)
0.694048 + 0.719929i \(0.255826\pi\)
\(828\) 0 0
\(829\) −3.50341e8 −0.614933 −0.307466 − 0.951559i \(-0.599481\pi\)
−0.307466 + 0.951559i \(0.599481\pi\)
\(830\) 0 0
\(831\) −2.06165e8 −0.359262
\(832\) 0 0
\(833\) −5.66425e8 −0.979958
\(834\) 0 0
\(835\) −3.33663e8 −0.573123
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) −4.27143e7 −0.0718101
\(842\) 0 0
\(843\) −2.21519e8 −0.369767
\(844\) 0 0
\(845\) 9.21921e8 1.52800
\(846\) 0 0
\(847\) 2.74592e8 0.451895
\(848\) −7.81619e8 −1.28176
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 2.18695e8 0.353606
\(853\) −1.04940e9 −1.69080 −0.845400 − 0.534134i \(-0.820638\pi\)
−0.845400 + 0.534134i \(0.820638\pi\)
\(854\) 0 0
\(855\) −5.95676e7 −0.0953041
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) −1.06782e8 −0.167297
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −6.23247e7 −0.0956319
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.54864e8 0.231167
\(876\) 0 0
\(877\) 1.21040e9 1.79444 0.897220 − 0.441583i \(-0.145583\pi\)
0.897220 + 0.441583i \(0.145583\pi\)
\(878\) 0 0
\(879\) −1.06574e8 −0.156923
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 1.37690e9 1.99996 0.999981 − 0.00614755i \(-0.00195684\pi\)
0.999981 + 0.00614755i \(0.00195684\pi\)
\(884\) 0 0
\(885\) 1.96137e8 0.282963
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −5.30522e8 −0.755089
\(890\) 0 0
\(891\) 0 0
\(892\) 7.72273e8 1.08812
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −9.39688e8 −1.28901
\(901\) −1.15449e9 −1.57840
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.12632e9 2.86868
\(906\) 0 0
\(907\) −1.05677e9 −1.41631 −0.708156 − 0.706056i \(-0.750472\pi\)
−0.708156 + 0.706056i \(0.750472\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.43149e9 1.89336 0.946679 − 0.322177i \(-0.104415\pi\)
0.946679 + 0.322177i \(0.104415\pi\)
\(912\) −9.07264e6 −0.0119605
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 2.22330e8 0.284589
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) −4.14754e7 −0.0513975
\(932\) 0 0
\(933\) 7.92241e7 0.0975466
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −8.41232e8 −1.00000
\(945\) 2.12120e8 0.251354
\(946\) 0 0
\(947\) −1.31514e9 −1.54854 −0.774270 − 0.632856i \(-0.781883\pi\)
−0.774270 + 0.632856i \(0.781883\pi\)
\(948\) 9.24330e7 0.108493
\(949\) 0 0
\(950\) 0 0
\(951\) −3.18319e8 −0.370101
\(952\) 0 0
\(953\) −1.44415e9 −1.66853 −0.834264 − 0.551364i \(-0.814107\pi\)
−0.834264 + 0.551364i \(0.814107\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −1.42775e9 −1.63410
\(957\) 0 0
\(958\) 0 0
\(959\) −7.62734e8 −0.864803
\(960\) −2.50348e8 −0.282963
\(961\) 8.87504e8 1.00000
\(962\) 0 0
\(963\) 1.69642e9 1.89956
\(964\) 3.63505e8 0.405769
\(965\) −2.02959e9 −2.25854
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0 0
\(969\) −1.34008e7 −0.0147285
\(970\) 0 0
\(971\) −1.43048e9 −1.56251 −0.781256 − 0.624211i \(-0.785421\pi\)
−0.781256 + 0.624211i \(0.785421\pi\)
\(972\) −4.87055e8 −0.530371
\(973\) −2.37094e8 −0.257384
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −1.14446e9 −1.21597
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) −2.68865e8 −0.281336
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) −3.59395e8 −0.367049
\(994\) 0 0
\(995\) 2.58189e9 2.62100
\(996\) 0 0
\(997\) 1.84448e9 1.86118 0.930591 − 0.366060i \(-0.119294\pi\)
0.930591 + 0.366060i \(0.119294\pi\)
\(998\) 0 0
\(999\) 0 0
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 59.7.b.a.58.1 ✓ 1
59.58 odd 2 CM 59.7.b.a.58.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
59.7.b.a.58.1 ✓ 1 1.1 even 1 trivial
59.7.b.a.58.1 ✓ 1 59.58 odd 2 CM