Properties

Label 35.23.c.b.34.1
Level $35$
Weight $23$
Character 35.34
Self dual yes
Analytic conductor $107.348$
Analytic rank $0$
Dimension $1$
CM discriminant -35
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 23 \)
Character orbit: \([\chi]\) \(=\) 35.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(107.347602195\)
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 34.1
Character \(\chi\) \(=\) 35.34

$q$-expansion

\(f(q)\) \(=\) \(q+341351. q^{3} +4.19430e6 q^{4} +4.88281e7 q^{5} -1.97733e9 q^{7} +8.51394e10 q^{9} +O(q^{10})\) \(q+341351. q^{3} +4.19430e6 q^{4} +4.88281e7 q^{5} -1.97733e9 q^{7} +8.51394e10 q^{9} +3.54730e11 q^{11} +1.43173e12 q^{12} -1.43153e12 q^{13} +1.66675e13 q^{15} +1.75922e13 q^{16} -6.65471e13 q^{17} +2.04800e14 q^{20} -6.74962e14 q^{21} +2.38419e15 q^{25} +1.83505e16 q^{27} -8.29351e15 q^{28} +2.37747e16 q^{29} +1.21088e17 q^{33} -9.65492e16 q^{35} +3.57101e17 q^{36} -4.88655e17 q^{39} +1.48785e18 q^{44} +4.15720e18 q^{45} +2.60650e18 q^{47} +6.00511e18 q^{48} +3.90982e18 q^{49} -2.27159e19 q^{51} -6.00428e18 q^{52} +1.73208e19 q^{55} +6.99087e19 q^{60} -1.68349e20 q^{63} +7.37870e19 q^{64} -6.98990e19 q^{65} -2.79119e20 q^{68} -7.13315e19 q^{71} -3.31278e20 q^{73} +8.13844e20 q^{75} -7.01418e20 q^{77} -4.88366e20 q^{79} +8.58993e20 q^{80} +3.59219e21 q^{81} -7.43013e20 q^{83} -2.83100e21 q^{84} -3.24937e21 q^{85} +8.11553e21 q^{87} +2.83061e21 q^{91} -2.96499e21 q^{97} +3.02015e22 q^{99} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(-1\) \(-1\)

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 \(\pi\)
\(3\) 341351. 1.92694 0.963468 0.267823i \(-0.0863042\pi\)
0.963468 + 0.267823i \(0.0863042\pi\)
\(4\) 4.19430e6 1.00000
\(5\) 4.88281e7 1.00000
\(6\) 0 0
\(7\) −1.97733e9 −1.00000
\(8\) 0 0
\(9\) 8.51394e10 2.71308
\(10\) 0 0
\(11\) 3.54730e11 1.24331 0.621654 0.783292i \(-0.286461\pi\)
0.621654 + 0.783292i \(0.286461\pi\)
\(12\) 1.43173e12 1.92694
\(13\) −1.43153e12 −0.798774 −0.399387 0.916782i \(-0.630777\pi\)
−0.399387 + 0.916782i \(0.630777\pi\)
\(14\) 0 0
\(15\) 1.66675e13 1.92694
\(16\) 1.75922e13 1.00000
\(17\) −6.65471e13 −1.94174 −0.970870 0.239606i \(-0.922982\pi\)
−0.970870 + 0.239606i \(0.922982\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 2.04800e14 1.00000
\(21\) −6.74962e14 −1.92694
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 2.38419e15 1.00000
\(26\) 0 0
\(27\) 1.83505e16 3.30100
\(28\) −8.29351e15 −1.00000
\(29\) 2.37747e16 1.94867 0.974333 0.225110i \(-0.0722742\pi\)
0.974333 + 0.225110i \(0.0722742\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 1.21088e17 2.39578
\(34\) 0 0
\(35\) −9.65492e16 −1.00000
\(36\) 3.57101e17 2.71308
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) −4.88655e17 −1.53919
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 1.48785e18 1.24331
\(45\) 4.15720e18 2.71308
\(46\) 0 0
\(47\) 2.60650e18 1.05434 0.527171 0.849759i \(-0.323253\pi\)
0.527171 + 0.849759i \(0.323253\pi\)
\(48\) 6.00511e18 1.92694
\(49\) 3.90982e18 1.00000
\(50\) 0 0
\(51\) −2.27159e19 −3.74161
\(52\) −6.00428e18 −0.798774
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 1.73208e19 1.24331
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 6.99087e19 1.92694
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) −1.68349e20 −2.71308
\(64\) 7.37870e19 1.00000
\(65\) −6.98990e19 −0.798774
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −2.79119e20 −1.94174
\(69\) 0 0
\(70\) 0 0
\(71\) −7.13315e19 −0.308631 −0.154316 0.988022i \(-0.549317\pi\)
−0.154316 + 0.988022i \(0.549317\pi\)
\(72\) 0 0
\(73\) −3.31278e20 −1.05594 −0.527972 0.849262i \(-0.677048\pi\)
−0.527972 + 0.849262i \(0.677048\pi\)
\(74\) 0 0
\(75\) 8.13844e20 1.92694
\(76\) 0 0
\(77\) −7.01418e20 −1.24331
\(78\) 0 0
\(79\) −4.88366e20 −0.652901 −0.326451 0.945214i \(-0.605853\pi\)
−0.326451 + 0.945214i \(0.605853\pi\)
\(80\) 8.58993e20 1.00000
\(81\) 3.59219e21 3.64774
\(82\) 0 0
\(83\) −7.43013e20 −0.576949 −0.288474 0.957488i \(-0.593148\pi\)
−0.288474 + 0.957488i \(0.593148\pi\)
\(84\) −2.83100e21 −1.92694
\(85\) −3.24937e21 −1.94174
\(86\) 0 0
\(87\) 8.11553e21 3.75496
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 2.83061e21 0.798774
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −2.96499e21 −0.414509 −0.207254 0.978287i \(-0.566453\pi\)
−0.207254 + 0.978287i \(0.566453\pi\)
\(98\) 0 0
\(99\) 3.02015e22 3.37320
\(100\) 1.00000e22 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −2.67126e22 −1.92978 −0.964888 0.262662i \(-0.915400\pi\)
−0.964888 + 0.262662i \(0.915400\pi\)
\(104\) 0 0
\(105\) −3.29572e22 −1.92694
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 7.69675e22 3.30100
\(109\) −4.83009e22 −1.87182 −0.935909 0.352241i \(-0.885420\pi\)
−0.935909 + 0.352241i \(0.885420\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −3.47855e22 −1.00000
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 9.97184e22 1.94867
\(117\) −1.21880e23 −2.16714
\(118\) 0 0
\(119\) 1.31585e23 1.94174
\(120\) 0 0
\(121\) 4.44308e22 0.545814
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.16415e23 1.00000
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 5.07878e23 2.39578
\(133\) 0 0
\(134\) 0 0
\(135\) 8.96019e23 3.30100
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) −4.04957e23 −1.00000
\(141\) 8.89731e23 2.03165
\(142\) 0 0
\(143\) −5.07808e23 −0.993123
\(144\) 1.49779e24 2.71308
\(145\) 1.16088e24 1.94867
\(146\) 0 0
\(147\) 1.33462e24 1.92694
\(148\) 0 0
\(149\) −1.09615e24 −1.36402 −0.682011 0.731342i \(-0.738894\pi\)
−0.682011 + 0.731342i \(0.738894\pi\)
\(150\) 0 0
\(151\) 8.48941e23 0.912286 0.456143 0.889906i \(-0.349231\pi\)
0.456143 + 0.889906i \(0.349231\pi\)
\(152\) 0 0
\(153\) −5.66579e24 −5.26811
\(154\) 0 0
\(155\) 0 0
\(156\) −2.04957e24 −1.53919
\(157\) −2.83014e24 −1.98113 −0.990564 0.137054i \(-0.956237\pi\)
−0.990564 + 0.137054i \(0.956237\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 5.91248e24 2.39578
\(166\) 0 0
\(167\) 4.70119e24 1.66850 0.834250 0.551386i \(-0.185901\pi\)
0.834250 + 0.551386i \(0.185901\pi\)
\(168\) 0 0
\(169\) −1.16255e24 −0.361959
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 8.08485e24 1.94610 0.973049 0.230599i \(-0.0740686\pi\)
0.973049 + 0.230599i \(0.0740686\pi\)
\(174\) 0 0
\(175\) −4.71431e24 −1.00000
\(176\) 6.24048e24 1.24331
\(177\) 0 0
\(178\) 0 0
\(179\) −9.60940e24 −1.58969 −0.794846 0.606811i \(-0.792448\pi\)
−0.794846 + 0.606811i \(0.792448\pi\)
\(180\) 1.74366e25 2.71308
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.36063e25 −2.41418
\(188\) 1.09325e25 1.05434
\(189\) −3.62849e25 −3.30100
\(190\) 0 0
\(191\) 8.17437e23 0.0662349 0.0331175 0.999451i \(-0.489456\pi\)
0.0331175 + 0.999451i \(0.489456\pi\)
\(192\) 2.51873e25 1.92694
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) −2.38601e25 −1.53919
\(196\) 1.63990e25 1.00000
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −4.70104e25 −1.94867
\(204\) −9.52775e25 −3.74161
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −2.51838e25 −0.798774
\(209\) 0 0
\(210\) 0 0
\(211\) −2.33390e25 −0.632376 −0.316188 0.948697i \(-0.602403\pi\)
−0.316188 + 0.948697i \(0.602403\pi\)
\(212\) 0 0
\(213\) −2.43491e25 −0.594713
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1.13082e26 −2.03474
\(220\) 7.26488e25 1.24331
\(221\) 9.52644e25 1.55101
\(222\) 0 0
\(223\) −3.63740e25 −0.536336 −0.268168 0.963372i \(-0.586418\pi\)
−0.268168 + 0.963372i \(0.586418\pi\)
\(224\) 0 0
\(225\) 2.02988e26 2.71308
\(226\) 0 0
\(227\) 1.50666e26 1.82696 0.913482 0.406880i \(-0.133383\pi\)
0.913482 + 0.406880i \(0.133383\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) −2.39430e26 −2.39578
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 1.27270e26 1.05434
\(236\) 0 0
\(237\) −1.66704e26 −1.25810
\(238\) 0 0
\(239\) −2.84004e26 −1.95410 −0.977050 0.213010i \(-0.931673\pi\)
−0.977050 + 0.213010i \(0.931673\pi\)
\(240\) 2.93218e26 1.92694
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 6.50340e26 3.72796
\(244\) 0 0
\(245\) 1.90909e26 1.00000
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −2.53628e26 −1.11174
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −7.06105e26 −2.71308
\(253\) 0 0
\(254\) 0 0
\(255\) −1.10918e27 −3.74161
\(256\) 3.09485e26 1.00000
\(257\) 6.44812e26 1.99604 0.998019 0.0629069i \(-0.0200371\pi\)
0.998019 + 0.0629069i \(0.0200371\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −2.93178e26 −0.798774
\(261\) 2.02417e27 5.28690
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −1.17071e27 −1.94174
\(273\) 9.66230e26 1.53919
\(274\) 0 0
\(275\) 8.45743e26 1.24331
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.24918e27 −1.44829 −0.724144 0.689649i \(-0.757765\pi\)
−0.724144 + 0.689649i \(0.757765\pi\)
\(282\) 0 0
\(283\) −2.98973e26 −0.320613 −0.160306 0.987067i \(-0.551248\pi\)
−0.160306 + 0.987067i \(0.551248\pi\)
\(284\) −2.99186e26 −0.308631
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 3.25396e27 2.77036
\(290\) 0 0
\(291\) −1.01210e27 −0.798732
\(292\) −1.38948e27 −1.05594
\(293\) −9.54220e26 −0.698401 −0.349201 0.937048i \(-0.613547\pi\)
−0.349201 + 0.937048i \(0.613547\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 6.50947e27 4.10416
\(298\) 0 0
\(299\) 0 0
\(300\) 3.41351e27 1.92694
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.08748e27 0.914325 0.457163 0.889383i \(-0.348866\pi\)
0.457163 + 0.889383i \(0.348866\pi\)
\(308\) −2.94196e27 −1.24331
\(309\) −9.11838e27 −3.71856
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) −4.15891e27 −1.47228 −0.736142 0.676827i \(-0.763354\pi\)
−0.736142 + 0.676827i \(0.763354\pi\)
\(314\) 0 0
\(315\) −8.22014e27 −2.71308
\(316\) −2.04836e27 −0.652901
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 8.43361e27 2.42279
\(320\) 3.60288e27 1.00000
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.50667e28 3.64774
\(325\) −3.41304e27 −0.798774
\(326\) 0 0
\(327\) −1.64876e28 −3.60688
\(328\) 0 0
\(329\) −5.15390e27 −1.05434
\(330\) 0 0
\(331\) −1.71002e27 −0.327261 −0.163630 0.986522i \(-0.552320\pi\)
−0.163630 + 0.986522i \(0.552320\pi\)
\(332\) −3.11642e27 −0.576949
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −1.18741e28 −1.92694
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) −1.36289e28 −1.94174
\(341\) 0 0
\(342\) 0 0
\(343\) −7.73099e27 −1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 3.40390e28 3.75496
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) −2.62693e28 −2.63676
\(352\) 0 0
\(353\) −1.73953e28 −1.64025 −0.820125 0.572185i \(-0.806096\pi\)
−0.820125 + 0.572185i \(0.806096\pi\)
\(354\) 0 0
\(355\) −3.48299e27 −0.308631
\(356\) 0 0
\(357\) 4.49168e28 3.74161
\(358\) 0 0
\(359\) 1.94797e28 1.52596 0.762980 0.646422i \(-0.223736\pi\)
0.762980 + 0.646422i \(0.223736\pi\)
\(360\) 0 0
\(361\) 1.35700e28 1.00000
\(362\) 0 0
\(363\) 1.51665e28 1.05175
\(364\) 1.18724e28 0.798774
\(365\) −1.61757e28 −1.05594
\(366\) 0 0
\(367\) 3.36310e27 0.206735 0.103367 0.994643i \(-0.467038\pi\)
0.103367 + 0.994643i \(0.467038\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 3.97385e28 1.92694
\(376\) 0 0
\(377\) −3.40343e28 −1.55655
\(378\) 0 0
\(379\) 4.60797e28 1.98828 0.994142 0.108082i \(-0.0344709\pi\)
0.994142 + 0.108082i \(0.0344709\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −5.05662e28 −1.94390 −0.971950 0.235189i \(-0.924429\pi\)
−0.971950 + 0.235189i \(0.924429\pi\)
\(384\) 0 0
\(385\) −3.42489e28 −1.24331
\(386\) 0 0
\(387\) 0 0
\(388\) −1.24361e28 −0.414509
\(389\) −6.08327e28 −1.97102 −0.985511 0.169609i \(-0.945750\pi\)
−0.985511 + 0.169609i \(0.945750\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.38460e28 −0.652901
\(396\) 1.26674e29 3.37320
\(397\) −4.68028e28 −1.21221 −0.606103 0.795386i \(-0.707268\pi\)
−0.606103 + 0.795386i \(0.707268\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 4.19430e28 1.00000
\(401\) 7.26758e28 1.68578 0.842892 0.538083i \(-0.180851\pi\)
0.842892 + 0.538083i \(0.180851\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.75400e29 3.64774
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.12041e29 −1.92978
\(413\) 0 0
\(414\) 0 0
\(415\) −3.62799e28 −0.576949
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) −1.38232e29 −1.92694
\(421\) −1.34776e29 −1.83025 −0.915125 0.403169i \(-0.867909\pi\)
−0.915125 + 0.403169i \(0.867909\pi\)
\(422\) 0 0
\(423\) 2.21916e29 2.86052
\(424\) 0 0
\(425\) −1.58661e29 −1.94174
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −1.73341e29 −1.91368
\(430\) 0 0
\(431\) 3.84058e27 0.0402853 0.0201427 0.999797i \(-0.493588\pi\)
0.0201427 + 0.999797i \(0.493588\pi\)
\(432\) 3.22825e29 3.30100
\(433\) 1.62515e29 1.62004 0.810019 0.586403i \(-0.199457\pi\)
0.810019 + 0.586403i \(0.199457\pi\)
\(434\) 0 0
\(435\) 3.96266e29 3.75496
\(436\) −2.02589e29 −1.87182
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 3.32880e29 2.71308
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −3.74172e29 −2.62838
\(448\) −1.45901e29 −1.00000
\(449\) 1.32742e27 0.00887768 0.00443884 0.999990i \(-0.498587\pi\)
0.00443884 + 0.999990i \(0.498587\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 2.89787e29 1.75792
\(454\) 0 0
\(455\) 1.38213e29 0.798774
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) −1.22117e30 −6.40969
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 4.18249e29 1.94867
\(465\) 0 0
\(466\) 0 0
\(467\) −2.78546e29 −1.20896 −0.604479 0.796621i \(-0.706619\pi\)
−0.604479 + 0.796621i \(0.706619\pi\)
\(468\) −5.11201e29 −2.16714
\(469\) 0 0
\(470\) 0 0
\(471\) −9.66072e29 −3.81751
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 5.51909e29 1.94174
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.86356e29 0.545814
\(485\) −1.44775e29 −0.414509
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.45628e29 −1.86477 −0.932386 0.361464i \(-0.882277\pi\)
−0.932386 + 0.361464i \(0.882277\pi\)
\(492\) 0 0
\(493\) −1.58214e30 −3.78381
\(494\) 0 0
\(495\) 1.47468e30 3.37320
\(496\) 0 0
\(497\) 1.41046e29 0.308631
\(498\) 0 0
\(499\) −8.65465e29 −1.81194 −0.905970 0.423343i \(-0.860857\pi\)
−0.905970 + 0.423343i \(0.860857\pi\)
\(500\) 4.88281e29 1.00000
\(501\) 1.60475e30 3.21509
\(502\) 0 0
\(503\) 1.00928e30 1.93537 0.967684 0.252166i \(-0.0811429\pi\)
0.967684 + 0.252166i \(0.0811429\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −3.96839e29 −0.697473
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 6.55045e29 1.05594
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.30433e30 −1.92978
\(516\) 0 0
\(517\) 9.24604e29 1.31087
\(518\) 0 0
\(519\) 2.75977e30 3.75001
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −5.41321e29 −0.675984 −0.337992 0.941149i \(-0.609748\pi\)
−0.337992 + 0.941149i \(0.609748\pi\)
\(524\) 0 0
\(525\) −1.60924e30 −1.92694
\(526\) 0 0
\(527\) 0 0
\(528\) 2.13019e30 2.39578
\(529\) 9.07846e29 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −3.28018e30 −3.06324
\(538\) 0 0
\(539\) 1.38693e30 1.24331
\(540\) 3.75818e30 3.30100
\(541\) −1.59737e30 −1.37479 −0.687395 0.726284i \(-0.741246\pi\)
−0.687395 + 0.726284i \(0.741246\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.35844e30 −1.87182
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 9.65659e29 0.652901
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −1.69851e30 −1.00000
\(561\) −8.05803e30 −4.65197
\(562\) 0 0
\(563\) 1.23528e30 0.685760 0.342880 0.939379i \(-0.388598\pi\)
0.342880 + 0.939379i \(0.388598\pi\)
\(564\) 3.73180e30 2.03165
\(565\) 0 0
\(566\) 0 0
\(567\) −7.10293e30 −3.64774
\(568\) 0 0
\(569\) 3.77809e30 1.86654 0.933271 0.359174i \(-0.116941\pi\)
0.933271 + 0.359174i \(0.116941\pi\)
\(570\) 0 0
\(571\) 3.82070e30 1.81613 0.908063 0.418835i \(-0.137561\pi\)
0.908063 + 0.418835i \(0.137561\pi\)
\(572\) −2.12990e30 −0.993123
\(573\) 2.79033e29 0.127630
\(574\) 0 0
\(575\) 0 0
\(576\) 6.28218e30 2.71308
\(577\) 1.28839e30 0.545901 0.272951 0.962028i \(-0.412000\pi\)
0.272951 + 0.962028i \(0.412000\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 4.86906e30 1.94867
\(581\) 1.46918e30 0.576949
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −5.95116e30 −2.16714
\(586\) 0 0
\(587\) 3.35072e30 1.17522 0.587610 0.809144i \(-0.300069\pi\)
0.587610 + 0.809144i \(0.300069\pi\)
\(588\) 5.59781e30 1.92694
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.53477e30 0.481330 0.240665 0.970608i \(-0.422635\pi\)
0.240665 + 0.970608i \(0.422635\pi\)
\(594\) 0 0
\(595\) 6.42507e30 1.94174
\(596\) −4.59759e30 −1.36402
\(597\) 0 0
\(598\) 0 0
\(599\) −9.84624e29 −0.276424 −0.138212 0.990403i \(-0.544135\pi\)
−0.138212 + 0.990403i \(0.544135\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 3.56072e30 0.912286
\(605\) 2.16947e30 0.545814
\(606\) 0 0
\(607\) 8.12599e30 1.97152 0.985758 0.168168i \(-0.0537852\pi\)
0.985758 + 0.168168i \(0.0537852\pi\)
\(608\) 0 0
\(609\) −1.60470e31 −3.75496
\(610\) 0 0
\(611\) −3.73129e30 −0.842181
\(612\) −2.37640e31 −5.26811
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −8.59651e30 −1.53919
\(625\) 5.68434e30 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) −1.18705e31 −1.98113
\(629\) 0 0
\(630\) 0 0
\(631\) −1.12879e30 −0.178769 −0.0893845 0.995997i \(-0.528490\pi\)
−0.0893845 + 0.995997i \(0.528490\pi\)
\(632\) 0 0
\(633\) −7.96680e30 −1.21855
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −5.59703e30 −0.798774
\(638\) 0 0
\(639\) −6.07313e30 −0.837342
\(640\) 0 0
\(641\) 2.11566e30 0.281843 0.140922 0.990021i \(-0.454993\pi\)
0.140922 + 0.990021i \(0.454993\pi\)
\(642\) 0 0
\(643\) 1.51516e31 1.95046 0.975230 0.221192i \(-0.0709947\pi\)
0.975230 + 0.221192i \(0.0709947\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.48066e29 0.101972 0.0509862 0.998699i \(-0.483764\pi\)
0.0509862 + 0.998699i \(0.483764\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −2.82048e31 −2.86487
\(658\) 0 0
\(659\) −1.67930e31 −1.64964 −0.824819 0.565396i \(-0.808723\pi\)
−0.824819 + 0.565396i \(0.808723\pi\)
\(660\) 2.47987e31 2.39578
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 3.25186e31 2.98870
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.97182e31 1.66850
\(669\) −1.24163e31 −1.03349
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 4.37510e31 3.30100
\(676\) −4.87611e30 −0.361959
\(677\) −2.66811e31 −1.94863 −0.974313 0.225196i \(-0.927698\pi\)
−0.974313 + 0.225196i \(0.927698\pi\)
\(678\) 0 0
\(679\) 5.86275e30 0.414509
\(680\) 0 0
\(681\) 5.14299e31 3.52044
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 3.39103e31 1.94610
\(693\) −5.97183e31 −3.37320
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −1.97733e31 −1.00000
\(701\) 2.47870e31 1.23403 0.617015 0.786952i \(-0.288342\pi\)
0.617015 + 0.786952i \(0.288342\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 2.61745e31 1.24331
\(705\) 4.34439e31 2.03165
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −4.16841e31 −1.83173 −0.915865 0.401485i \(-0.868494\pi\)
−0.915865 + 0.401485i \(0.868494\pi\)
\(710\) 0 0
\(711\) −4.15792e31 −1.77138
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −2.47953e31 −0.993123
\(716\) −4.03048e31 −1.58969
\(717\) −9.69449e31 −3.76543
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 7.31342e31 2.71308
\(721\) 5.28196e31 1.92978
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 5.66834e31 1.94867
\(726\) 0 0
\(727\) −3.34349e31 −1.11512 −0.557560 0.830137i \(-0.688262\pi\)
−0.557560 + 0.830137i \(0.688262\pi\)
\(728\) 0 0
\(729\) 1.09267e32 3.53580
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 3.28167e31 0.999889 0.499944 0.866057i \(-0.333354\pi\)
0.499944 + 0.866057i \(0.333354\pi\)
\(734\) 0 0
\(735\) 6.51671e31 1.92694
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1.63960e31 0.456719 0.228359 0.973577i \(-0.426664\pi\)
0.228359 + 0.973577i \(0.426664\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) −5.35230e31 −1.36402
\(746\) 0 0
\(747\) −6.32597e31 −1.56531
\(748\) −9.90119e31 −2.41418
\(749\) 0 0
\(750\) 0 0
\(751\) −4.52385e31 −1.05553 −0.527763 0.849392i \(-0.676969\pi\)
−0.527763 + 0.849392i \(0.676969\pi\)
\(752\) 4.58540e31 1.05434
\(753\) 0 0
\(754\) 0 0
\(755\) 4.14522e31 0.912286
\(756\) −1.52190e32 −3.30100
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 9.55067e31 1.87182
\(764\) 3.42858e30 0.0662349
\(765\) −2.76650e32 −5.26811
\(766\) 0 0
\(767\) 0 0
\(768\) 1.05643e32 1.92694
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 2.20107e32 3.84624
\(772\) 0 0
\(773\) −7.45844e31 −1.26670 −0.633350 0.773866i \(-0.718321\pi\)
−0.633350 + 0.773866i \(0.718321\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −1.00077e32 −1.53919
\(781\) −2.53035e31 −0.383724
\(782\) 0 0
\(783\) 4.36278e32 6.43256
\(784\) 6.87823e31 1.00000
\(785\) −1.38191e32 −1.98113
\(786\) 0 0
\(787\) −5.80416e30 −0.0809128 −0.0404564 0.999181i \(-0.512881\pi\)
−0.0404564 + 0.999181i \(0.512881\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.64720e32 −1.99851 −0.999253 0.0386338i \(-0.987699\pi\)
−0.999253 + 0.0386338i \(0.987699\pi\)
\(798\) 0 0
\(799\) −1.73455e32 −2.04726
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.17514e32 −1.31286
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.19103e32 1.22600 0.613000 0.790083i \(-0.289963\pi\)
0.613000 + 0.790083i \(0.289963\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) −1.97176e32 −1.94867
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) −3.99623e32 −3.74161
\(817\) 0 0
\(818\) 0 0
\(819\) 2.40996e32 2.16714
\(820\) 0 0
\(821\) −1.47953e32 −1.29524 −0.647620 0.761964i \(-0.724235\pi\)
−0.647620 + 0.761964i \(0.724235\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 2.88695e32 2.39578
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.05628e32 −0.798774
\(833\) −2.60187e32 −1.94174
\(834\) 0 0
\(835\) 2.29550e32 1.66850
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 4.16385e32 2.79730
\(842\) 0 0
\(843\) −4.26408e32 −2.79076
\(844\) −9.78909e31 −0.632376
\(845\) −5.67654e31 −0.361959
\(846\) 0 0
\(847\) −8.78542e31 −0.545814
\(848\) 0 0
\(849\) −1.02055e32 −0.617801
\(850\) 0 0
\(851\) 0 0
\(852\) −1.02127e32 −0.594713
\(853\) 1.83256e32 1.05346 0.526730 0.850033i \(-0.323418\pi\)
0.526730 + 0.850033i \(0.323418\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3.65955e32 1.99820 0.999099 0.0424323i \(-0.0135107\pi\)
0.999099 + 0.0424323i \(0.0135107\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 3.94768e32 1.94610
\(866\) 0 0
\(867\) 1.11074e33 5.33830
\(868\) 0 0
\(869\) −1.73238e32 −0.811757
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −2.52437e32 −1.12460
\(874\) 0 0
\(875\) −2.30191e32 −1.00000
\(876\) −4.74301e32 −2.03474
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) −3.25724e32 −1.34577
\(880\) 3.04711e32 1.24331
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 3.99568e32 1.55101
\(885\) 0 0
\(886\) 0 0
\(887\) 2.00085e31 0.0748264 0.0374132 0.999300i \(-0.488088\pi\)
0.0374132 + 0.999300i \(0.488088\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1.27426e33 4.53526
\(892\) −1.52563e32 −0.536336
\(893\) 0 0
\(894\) 0 0
\(895\) −4.69209e32 −1.58969
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 8.51394e32 2.71308
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 6.31938e32 1.82696
\(909\) 0 0
\(910\) 0 0
\(911\) 2.18633e32 0.609557 0.304778 0.952423i \(-0.401418\pi\)
0.304778 + 0.952423i \(0.401418\pi\)
\(912\) 0 0
\(913\) −2.63569e32 −0.717325
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 1.85644e31 0.0470121 0.0235060 0.999724i \(-0.492517\pi\)
0.0235060 + 0.999724i \(0.492517\pi\)
\(920\) 0 0
\(921\) 7.12564e32 1.76185
\(922\) 0 0
\(923\) 1.02113e32 0.246527
\(924\) −1.00424e33 −2.39578
\(925\) 0 0
\(926\) 0 0
\(927\) −2.27430e33 −5.23564
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.15265e33 −2.41418
\(936\) 0 0
\(937\) 7.31013e32 1.49551 0.747756 0.663974i \(-0.231131\pi\)
0.747756 + 0.663974i \(0.231131\pi\)
\(938\) 0 0
\(939\) −1.41965e33 −2.83700
\(940\) 5.33811e32 1.05434
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) −1.77172e33 −3.30100
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) −6.99208e32 −1.25810
\(949\) 4.74235e32 0.843462
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 3.99139e31 0.0662349
\(956\) −1.19120e33 −1.95410
\(957\) 2.87882e33 4.66857
\(958\) 0 0
\(959\) 0 0
\(960\) 1.22985e33 1.92694
\(961\) 6.45591e32 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 2.72772e33 3.72796
\(973\) 0 0
\(974\) 0 0
\(975\) −1.16504e33 −1.53919
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 8.00731e32 1.00000
\(981\) −4.11231e33 −5.07840
\(982\) 0 0
\(983\) 6.31158e32 0.762165 0.381083 0.924541i \(-0.375551\pi\)
0.381083 + 0.924541i \(0.375551\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −1.75929e33 −2.03165
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 1.48313e33 1.63821 0.819103 0.573647i \(-0.194472\pi\)
0.819103 + 0.573647i \(0.194472\pi\)
\(992\) 0 0
\(993\) −5.83718e32 −0.630610
\(994\) 0 0
\(995\) 0 0
\(996\) −1.06379e33 −1.11174
\(997\) 1.86741e33 1.93016 0.965081 0.261951i \(-0.0843659\pi\)
0.965081 + 0.261951i \(0.0843659\pi\)
\(998\) 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 35.23.c.b.34.1 yes 1
5.4 even 2 35.23.c.a.34.1 1
7.6 odd 2 35.23.c.a.34.1 1
35.34 odd 2 CM 35.23.c.b.34.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.23.c.a.34.1 1 5.4 even 2
35.23.c.a.34.1 1 7.6 odd 2
35.23.c.b.34.1 yes 1 1.1 even 1 trivial
35.23.c.b.34.1 yes 1 35.34 odd 2 CM