Properties

Label 35.9.c.a.34.1
Level $35$
Weight $9$
Character 35.34
Self dual yes
Analytic conductor $14.258$
Analytic rank $0$
Dimension $1$
CM discriminant -35
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 35.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(14.2582513521\)
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

\(f(q)\) \(=\) \(q-127.000 q^{3} +256.000 q^{4} -625.000 q^{5} -2401.00 q^{7} +9568.00 q^{9} +O(q^{10})\) \(q-127.000 q^{3} +256.000 q^{4} -625.000 q^{5} -2401.00 q^{7} +9568.00 q^{9} -23953.0 q^{11} -32512.0 q^{12} +56593.0 q^{13} +79375.0 q^{15} +65536.0 q^{16} +97873.0 q^{17} -160000. q^{20} +304927. q^{21} +390625. q^{25} -381889. q^{27} -614656. q^{28} -85153.0 q^{29} +3.04203e6 q^{33} +1.50062e6 q^{35} +2.44941e6 q^{36} -7.18731e6 q^{39} -6.13197e6 q^{44} -5.98000e6 q^{45} -2.19149e6 q^{47} -8.32307e6 q^{48} +5.76480e6 q^{49} -1.24299e7 q^{51} +1.44878e7 q^{52} +1.49706e7 q^{55} +2.03200e7 q^{60} -2.29728e7 q^{63} +1.67772e7 q^{64} -3.53706e7 q^{65} +2.50555e7 q^{68} +5.07427e7 q^{71} -3.34915e7 q^{73} -4.96094e7 q^{75} +5.75112e7 q^{77} +7.01357e7 q^{79} -4.09600e7 q^{80} -1.42757e7 q^{81} +5.41867e7 q^{83} +7.80613e7 q^{84} -6.11706e7 q^{85} +1.08144e7 q^{87} -1.35880e8 q^{91} +1.65614e8 q^{97} -2.29182e8 q^{99} +O(q^{100})\)

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 \(\pi\)
\(3\) −127.000 −1.56790 −0.783951 0.620823i \(-0.786798\pi\)
−0.783951 + 0.620823i \(0.786798\pi\)
\(4\) 256.000 1.00000
\(5\) −625.000 −1.00000
\(6\) 0 0
\(7\) −2401.00 −1.00000
\(8\) 0 0
\(9\) 9568.00 1.45831
\(10\) 0 0
\(11\) −23953.0 −1.63602 −0.818011 0.575202i \(-0.804923\pi\)
−0.818011 + 0.575202i \(0.804923\pi\)
\(12\) −32512.0 −1.56790
\(13\) 56593.0 1.98148 0.990739 0.135779i \(-0.0433538\pi\)
0.990739 + 0.135779i \(0.0433538\pi\)
\(14\) 0 0
\(15\) 79375.0 1.56790
\(16\) 65536.0 1.00000
\(17\) 97873.0 1.17184 0.585919 0.810370i \(-0.300734\pi\)
0.585919 + 0.810370i \(0.300734\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −160000. −1.00000
\(21\) 304927. 1.56790
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 390625. 1.00000
\(26\) 0 0
\(27\) −381889. −0.718592
\(28\) −614656. −1.00000
\(29\) −85153.0 −0.120395 −0.0601974 0.998186i \(-0.519173\pi\)
−0.0601974 + 0.998186i \(0.519173\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 3.04203e6 2.56512
\(34\) 0 0
\(35\) 1.50062e6 1.00000
\(36\) 2.44941e6 1.45831
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) −7.18731e6 −3.10676
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −6.13197e6 −1.63602
\(45\) −5.98000e6 −1.45831
\(46\) 0 0
\(47\) −2.19149e6 −0.449105 −0.224552 0.974462i \(-0.572092\pi\)
−0.224552 + 0.974462i \(0.572092\pi\)
\(48\) −8.32307e6 −1.56790
\(49\) 5.76480e6 1.00000
\(50\) 0 0
\(51\) −1.24299e7 −1.83732
\(52\) 1.44878e7 1.98148
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 1.49706e7 1.63602
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 2.03200e7 1.56790
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) −2.29728e7 −1.45831
\(64\) 1.67772e7 1.00000
\(65\) −3.53706e7 −1.98148
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 2.50555e7 1.17184
\(69\) 0 0
\(70\) 0 0
\(71\) 5.07427e7 1.99683 0.998413 0.0563101i \(-0.0179335\pi\)
0.998413 + 0.0563101i \(0.0179335\pi\)
\(72\) 0 0
\(73\) −3.34915e7 −1.17935 −0.589676 0.807640i \(-0.700745\pi\)
−0.589676 + 0.807640i \(0.700745\pi\)
\(74\) 0 0
\(75\) −4.96094e7 −1.56790
\(76\) 0 0
\(77\) 5.75112e7 1.63602
\(78\) 0 0
\(79\) 7.01357e7 1.80066 0.900328 0.435211i \(-0.143326\pi\)
0.900328 + 0.435211i \(0.143326\pi\)
\(80\) −4.09600e7 −1.00000
\(81\) −1.42757e7 −0.331634
\(82\) 0 0
\(83\) 5.41867e7 1.14177 0.570887 0.821028i \(-0.306599\pi\)
0.570887 + 0.821028i \(0.306599\pi\)
\(84\) 7.80613e7 1.56790
\(85\) −6.11706e7 −1.17184
\(86\) 0 0
\(87\) 1.08144e7 0.188767
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −1.35880e8 −1.98148
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.65614e8 1.87072 0.935362 0.353692i \(-0.115074\pi\)
0.935362 + 0.353692i \(0.115074\pi\)
\(98\) 0 0
\(99\) −2.29182e8 −2.38583
\(100\) 1.00000e8 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −1.12833e8 −1.00251 −0.501253 0.865301i \(-0.667127\pi\)
−0.501253 + 0.865301i \(0.667127\pi\)
\(104\) 0 0
\(105\) −1.90579e8 −1.56790
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −9.77636e7 −0.718592
\(109\) −7.63077e7 −0.540583 −0.270292 0.962779i \(-0.587120\pi\)
−0.270292 + 0.962779i \(0.587120\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.57352e8 −1.00000
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2.17992e7 −0.120395
\(117\) 5.41482e8 2.88962
\(118\) 0 0
\(119\) −2.34993e8 −1.17184
\(120\) 0 0
\(121\) 3.59387e8 1.67657
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −2.44141e8 −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 \(\pi\)
\(132\) 7.78760e8 2.56512
\(133\) 0 0
\(134\) 0 0
\(135\) 2.38681e8 0.718592
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 3.84160e8 1.00000
\(141\) 2.78319e8 0.704152
\(142\) 0 0
\(143\) −1.35557e9 −3.24174
\(144\) 6.27048e8 1.45831
\(145\) 5.32206e7 0.120395
\(146\) 0 0
\(147\) −7.32130e8 −1.56790
\(148\) 0 0
\(149\) −3.98094e8 −0.807683 −0.403841 0.914829i \(-0.632325\pi\)
−0.403841 + 0.914829i \(0.632325\pi\)
\(150\) 0 0
\(151\) 1.02439e9 1.97041 0.985204 0.171388i \(-0.0548253\pi\)
0.985204 + 0.171388i \(0.0548253\pi\)
\(152\) 0 0
\(153\) 9.36449e8 1.70891
\(154\) 0 0
\(155\) 0 0
\(156\) −1.83995e9 −3.10676
\(157\) 2.32825e8 0.383206 0.191603 0.981473i \(-0.438631\pi\)
0.191603 + 0.981473i \(0.438631\pi\)
\(158\) 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
\(165\) −1.90127e9 −2.56512
\(166\) 0 0
\(167\) 1.24361e9 1.59889 0.799445 0.600739i \(-0.205127\pi\)
0.799445 + 0.600739i \(0.205127\pi\)
\(168\) 0 0
\(169\) 2.38704e9 2.92626
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.67012e9 1.86450 0.932250 0.361816i \(-0.117843\pi\)
0.932250 + 0.361816i \(0.117843\pi\)
\(174\) 0 0
\(175\) −9.37891e8 −1.00000
\(176\) −1.56978e9 −1.63602
\(177\) 0 0
\(178\) 0 0
\(179\) −1.77908e9 −1.73294 −0.866472 0.499226i \(-0.833618\pi\)
−0.866472 + 0.499226i \(0.833618\pi\)
\(180\) −1.53088e9 −1.45831
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.34435e9 −1.91715
\(188\) −5.61021e8 −0.449105
\(189\) 9.16915e8 0.718592
\(190\) 0 0
\(191\) −4.10509e8 −0.308453 −0.154227 0.988036i \(-0.549289\pi\)
−0.154227 + 0.988036i \(0.549289\pi\)
\(192\) −2.13071e9 −1.56790
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 4.49207e9 3.10676
\(196\) 1.47579e9 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
\(203\) 2.04452e8 0.120395
\(204\) −3.18205e9 −1.83732
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 3.70888e9 1.98148
\(209\) 0 0
\(210\) 0 0
\(211\) 2.05643e9 1.03749 0.518746 0.854928i \(-0.326399\pi\)
0.518746 + 0.854928i \(0.326399\pi\)
\(212\) 0 0
\(213\) −6.44433e9 −3.13083
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 4.25342e9 1.84911
\(220\) 3.83248e9 1.63602
\(221\) 5.53893e9 2.32197
\(222\) 0 0
\(223\) 1.18298e9 0.478365 0.239182 0.970975i \(-0.423121\pi\)
0.239182 + 0.970975i \(0.423121\pi\)
\(224\) 0 0
\(225\) 3.73750e9 1.45831
\(226\) 0 0
\(227\) 2.82814e9 1.06512 0.532560 0.846393i \(-0.321230\pi\)
0.532560 + 0.846393i \(0.321230\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) −7.30392e9 −2.56512
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 1.36968e9 0.449105
\(236\) 0 0
\(237\) −8.90724e9 −2.82325
\(238\) 0 0
\(239\) −4.64492e9 −1.42360 −0.711798 0.702384i \(-0.752119\pi\)
−0.711798 + 0.702384i \(0.752119\pi\)
\(240\) 5.20192e9 1.56790
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 4.31859e9 1.23856
\(244\) 0 0
\(245\) −3.60300e9 −1.00000
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −6.88171e9 −1.79019
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −5.88103e9 −1.45831
\(253\) 0 0
\(254\) 0 0
\(255\) 7.76867e9 1.83732
\(256\) 4.29497e9 1.00000
\(257\) −3.80518e9 −0.872252 −0.436126 0.899886i \(-0.643650\pi\)
−0.436126 + 0.899886i \(0.643650\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −9.05488e9 −1.98148
\(261\) −8.14744e8 −0.175574
\(262\) 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 \(\pi\)
\(272\) 6.41420e9 1.17184
\(273\) 1.72567e10 3.10676
\(274\) 0 0
\(275\) −9.35664e9 −1.63602
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.88404e9 0.302179 0.151090 0.988520i \(-0.451722\pi\)
0.151090 + 0.988520i \(0.451722\pi\)
\(282\) 0 0
\(283\) −1.03677e10 −1.61636 −0.808178 0.588938i \(-0.799546\pi\)
−0.808178 + 0.588938i \(0.799546\pi\)
\(284\) 1.29901e10 1.99683
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2.60337e9 0.373202
\(290\) 0 0
\(291\) −2.10330e10 −2.93311
\(292\) −8.57383e9 −1.17935
\(293\) −1.46163e10 −1.98320 −0.991599 0.129352i \(-0.958710\pi\)
−0.991599 + 0.129352i \(0.958710\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 9.14739e9 1.17563
\(298\) 0 0
\(299\) 0 0
\(300\) −1.27000e10 −1.56790
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −5.30331e8 −0.0597027 −0.0298513 0.999554i \(-0.509503\pi\)
−0.0298513 + 0.999554i \(0.509503\pi\)
\(308\) 1.47229e10 1.63602
\(309\) 1.43298e10 1.57183
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) −2.44168e9 −0.254396 −0.127198 0.991877i \(-0.540598\pi\)
−0.127198 + 0.991877i \(0.540598\pi\)
\(314\) 0 0
\(315\) 1.43580e10 1.45831
\(316\) 1.79547e10 1.80066
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 2.03967e9 0.196969
\(320\) −1.04858e10 −1.00000
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −3.65459e9 −0.331634
\(325\) 2.21066e10 1.98148
\(326\) 0 0
\(327\) 9.69108e9 0.847581
\(328\) 0 0
\(329\) 5.26176e9 0.449105
\(330\) 0 0
\(331\) −4.82996e9 −0.402376 −0.201188 0.979553i \(-0.564480\pi\)
−0.201188 + 0.979553i \(0.564480\pi\)
\(332\) 1.38718e10 1.14177
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 1.99837e10 1.56790
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) −1.56597e10 −1.17184
\(341\) 0 0
\(342\) 0 0
\(343\) −1.38413e10 −1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 2.76849e9 0.188767
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) −2.16122e10 −1.42387
\(352\) 0 0
\(353\) −2.17978e10 −1.40383 −0.701915 0.712261i \(-0.747671\pi\)
−0.701915 + 0.712261i \(0.747671\pi\)
\(354\) 0 0
\(355\) −3.17142e10 −1.99683
\(356\) 0 0
\(357\) 2.98441e10 1.83732
\(358\) 0 0
\(359\) −2.73956e10 −1.64931 −0.824656 0.565635i \(-0.808631\pi\)
−0.824656 + 0.565635i \(0.808631\pi\)
\(360\) 0 0
\(361\) 1.69836e10 1.00000
\(362\) 0 0
\(363\) −4.56422e10 −2.62869
\(364\) −3.47852e10 −1.98148
\(365\) 2.09322e10 1.17935
\(366\) 0 0
\(367\) 2.27107e10 1.25189 0.625945 0.779867i \(-0.284713\pi\)
0.625945 + 0.779867i \(0.284713\pi\)
\(368\) 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
\(375\) 3.10059e10 1.56790
\(376\) 0 0
\(377\) −4.81906e9 −0.238560
\(378\) 0 0
\(379\) −4.00209e10 −1.93968 −0.969841 0.243740i \(-0.921626\pi\)
−0.969841 + 0.243740i \(0.921626\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.21837e10 1.96042 0.980212 0.197951i \(-0.0634288\pi\)
0.980212 + 0.197951i \(0.0634288\pi\)
\(384\) 0 0
\(385\) −3.59445e10 −1.63602
\(386\) 0 0
\(387\) 0 0
\(388\) 4.23972e10 1.87072
\(389\) 1.64078e10 0.716557 0.358279 0.933615i \(-0.383364\pi\)
0.358279 + 0.933615i \(0.383364\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.38348e10 −1.80066
\(396\) −5.86707e10 −2.38583
\(397\) 2.28190e10 0.918616 0.459308 0.888277i \(-0.348097\pi\)
0.459308 + 0.888277i \(0.348097\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 2.56000e10 1.00000
\(401\) 4.83147e10 1.86854 0.934268 0.356570i \(-0.116054\pi\)
0.934268 + 0.356570i \(0.116054\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 8.92234e9 0.331634
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −2.88852e10 −1.00251
\(413\) 0 0
\(414\) 0 0
\(415\) −3.38667e10 −1.14177
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) −4.87883e10 −1.56790
\(421\) −5.69377e10 −1.81247 −0.906237 0.422770i \(-0.861058\pi\)
−0.906237 + 0.422770i \(0.861058\pi\)
\(422\) 0 0
\(423\) −2.09681e10 −0.654936
\(424\) 0 0
\(425\) 3.82316e10 1.17184
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 1.72158e11 5.08273
\(430\) 0 0
\(431\) 5.77837e10 1.67454 0.837271 0.546789i \(-0.184150\pi\)
0.837271 + 0.546789i \(0.184150\pi\)
\(432\) −2.50275e10 −0.718592
\(433\) 3.28473e10 0.934433 0.467216 0.884143i \(-0.345257\pi\)
0.467216 + 0.884143i \(0.345257\pi\)
\(434\) 0 0
\(435\) −6.75902e9 −0.188767
\(436\) −1.95348e10 −0.540583
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 5.51576e10 1.45831
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 5.05580e10 1.26637
\(448\) −4.02821e10 −1.00000
\(449\) −1.14383e10 −0.281434 −0.140717 0.990050i \(-0.544941\pi\)
−0.140717 + 0.990050i \(0.544941\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −1.30097e11 −3.08940
\(454\) 0 0
\(455\) 8.49249e10 1.98148
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) −3.73766e10 −0.842072
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) −5.58059e9 −0.120395
\(465\) 0 0
\(466\) 0 0
\(467\) −8.85676e9 −0.186212 −0.0931060 0.995656i \(-0.529680\pi\)
−0.0931060 + 0.995656i \(0.529680\pi\)
\(468\) 1.38619e11 2.88962
\(469\) 0 0
\(470\) 0 0
\(471\) −2.95688e10 −0.600828
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) −6.01582e10 −1.17184
\(477\) 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
\(484\) 9.20032e10 1.67657
\(485\) −1.03509e11 −1.87072
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.05331e11 1.81229 0.906147 0.422963i \(-0.139010\pi\)
0.906147 + 0.422963i \(0.139010\pi\)
\(492\) 0 0
\(493\) −8.33418e9 −0.141083
\(494\) 0 0
\(495\) 1.43239e11 2.38583
\(496\) 0 0
\(497\) −1.21833e11 −1.99683
\(498\) 0 0
\(499\) −1.23010e11 −1.98398 −0.991992 0.126304i \(-0.959688\pi\)
−0.991992 + 0.126304i \(0.959688\pi\)
\(500\) −6.25000e10 −1.00000
\(501\) −1.57939e11 −2.50690
\(502\) 0 0
\(503\) 2.98721e10 0.466653 0.233326 0.972398i \(-0.425039\pi\)
0.233326 + 0.972398i \(0.425039\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −3.03154e11 −4.58808
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 8.04131e10 1.17935
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7.05206e10 1.00251
\(516\) 0 0
\(517\) 5.24927e10 0.734745
\(518\) 0 0
\(519\) −2.12105e11 −2.92335
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −4.46525e10 −0.596815 −0.298407 0.954439i \(-0.596455\pi\)
−0.298407 + 0.954439i \(0.596455\pi\)
\(524\) 0 0
\(525\) 1.19112e11 1.56790
\(526\) 0 0
\(527\) 0 0
\(528\) 1.99363e11 2.56512
\(529\) 7.83110e10 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 2.25944e11 2.71708
\(538\) 0 0
\(539\) −1.38084e11 −1.63602
\(540\) 6.11022e10 0.718592
\(541\) −1.71316e11 −1.99990 −0.999950 0.0100005i \(-0.996817\pi\)
−0.999950 + 0.0100005i \(0.996817\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.76923e10 0.540583
\(546\) 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
\(553\) −1.68396e11 −1.80066
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 9.83450e10 1.00000
\(561\) 2.97733e11 3.00590
\(562\) 0 0
\(563\) 1.84055e11 1.83195 0.915975 0.401235i \(-0.131419\pi\)
0.915975 + 0.401235i \(0.131419\pi\)
\(564\) 7.12496e10 0.704152
\(565\) 0 0
\(566\) 0 0
\(567\) 3.42761e10 0.331634
\(568\) 0 0
\(569\) 1.11713e11 1.06575 0.532873 0.846195i \(-0.321112\pi\)
0.532873 + 0.846195i \(0.321112\pi\)
\(570\) 0 0
\(571\) 1.94640e11 1.83100 0.915499 0.402319i \(-0.131796\pi\)
0.915499 + 0.402319i \(0.131796\pi\)
\(572\) −3.47026e11 −3.24174
\(573\) 5.21346e10 0.483624
\(574\) 0 0
\(575\) 0 0
\(576\) 1.60524e11 1.45831
\(577\) −2.20564e11 −1.98990 −0.994951 0.100361i \(-0.968000\pi\)
−0.994951 + 0.100361i \(0.968000\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 1.36245e10 0.120395
\(581\) −1.30102e11 −1.14177
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −3.38426e11 −2.88962
\(586\) 0 0
\(587\) −2.03017e10 −0.170993 −0.0854967 0.996338i \(-0.527248\pi\)
−0.0854967 + 0.996338i \(0.527248\pi\)
\(588\) −1.87425e11 −1.56790
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.44826e11 1.17119 0.585597 0.810602i \(-0.300860\pi\)
0.585597 + 0.810602i \(0.300860\pi\)
\(594\) 0 0
\(595\) 1.46871e11 1.17184
\(596\) −1.01912e11 −0.807683
\(597\) 0 0
\(598\) 0 0
\(599\) 1.18627e11 0.921463 0.460732 0.887540i \(-0.347587\pi\)
0.460732 + 0.887540i \(0.347587\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 2.62243e11 1.97041
\(605\) −2.24617e11 −1.67657
\(606\) 0 0
\(607\) 2.64717e11 1.94996 0.974982 0.222283i \(-0.0713509\pi\)
0.974982 + 0.222283i \(0.0713509\pi\)
\(608\) 0 0
\(609\) −2.59654e10 −0.188767
\(610\) 0 0
\(611\) −1.24023e11 −0.889891
\(612\) 2.39731e11 1.70891
\(613\) 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
\(624\) −4.71028e11 −3.10676
\(625\) 1.52588e11 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 5.96033e10 0.383206
\(629\) 0 0
\(630\) 0 0
\(631\) −3.06967e11 −1.93631 −0.968153 0.250360i \(-0.919451\pi\)
−0.968153 + 0.250360i \(0.919451\pi\)
\(632\) 0 0
\(633\) −2.61167e11 −1.62669
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 3.26247e11 1.98148
\(638\) 0 0
\(639\) 4.85506e11 2.91200
\(640\) 0 0
\(641\) −3.28430e11 −1.94541 −0.972704 0.232049i \(-0.925457\pi\)
−0.972704 + 0.232049i \(0.925457\pi\)
\(642\) 0 0
\(643\) −1.66750e11 −0.975487 −0.487744 0.872987i \(-0.662180\pi\)
−0.487744 + 0.872987i \(0.662180\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3.38044e11 1.92911 0.964553 0.263888i \(-0.0850049\pi\)
0.964553 + 0.263888i \(0.0850049\pi\)
\(648\) 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
\(657\) −3.20447e11 −1.71987
\(658\) 0 0
\(659\) 2.27348e11 1.20545 0.602726 0.797948i \(-0.294081\pi\)
0.602726 + 0.797948i \(0.294081\pi\)
\(660\) −4.86725e11 −2.56512
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) −7.03444e11 −3.64062
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 3.18364e11 1.59889
\(669\) −1.50239e11 −0.750029
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) −1.49175e11 −0.718592
\(676\) 6.11081e11 2.92626
\(677\) −1.42404e11 −0.677901 −0.338950 0.940804i \(-0.610072\pi\)
−0.338950 + 0.940804i \(0.610072\pi\)
\(678\) 0 0
\(679\) −3.97639e11 −1.87072
\(680\) 0 0
\(681\) −3.59174e11 −1.67000
\(682\) 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 \(\pi\)
\(692\) 4.27550e11 1.86450
\(693\) 5.50267e11 2.38583
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −2.40100e11 −1.00000
\(701\) 2.99980e11 1.24228 0.621140 0.783700i \(-0.286670\pi\)
0.621140 + 0.783700i \(0.286670\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −4.01865e11 −1.63602
\(705\) −1.73949e11 −0.704152
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 4.99684e11 1.97747 0.988736 0.149668i \(-0.0478203\pi\)
0.988736 + 0.149668i \(0.0478203\pi\)
\(710\) 0 0
\(711\) 6.71059e11 2.62592
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 8.47233e11 3.24174
\(716\) −4.55446e11 −1.73294
\(717\) 5.89905e11 2.23206
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −3.91905e11 −1.45831
\(721\) 2.70912e11 1.00251
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3.32629e10 −0.120395
\(726\) 0 0
\(727\) −3.94706e11 −1.41298 −0.706491 0.707722i \(-0.749723\pi\)
−0.706491 + 0.707722i \(0.749723\pi\)
\(728\) 0 0
\(729\) −4.54798e11 −1.61031
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 5.74743e11 1.99094 0.995470 0.0950793i \(-0.0303105\pi\)
0.995470 + 0.0950793i \(0.0303105\pi\)
\(734\) 0 0
\(735\) 4.57581e11 1.56790
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −3.51852e10 −0.117973 −0.0589864 0.998259i \(-0.518787\pi\)
−0.0589864 + 0.998259i \(0.518787\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 2.48809e11 0.807683
\(746\) 0 0
\(747\) 5.18459e11 1.66507
\(748\) −6.00154e11 −1.91715
\(749\) 0 0
\(750\) 0 0
\(751\) −2.15140e11 −0.676334 −0.338167 0.941086i \(-0.609807\pi\)
−0.338167 + 0.941086i \(0.609807\pi\)
\(752\) −1.43621e11 −0.449105
\(753\) 0 0
\(754\) 0 0
\(755\) −6.40241e11 −1.97041
\(756\) 2.34730e11 0.718592
\(757\) 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
\(763\) 1.83215e11 0.540583
\(764\) −1.05090e11 −0.308453
\(765\) −5.85281e11 −1.70891
\(766\) 0 0
\(767\) 0 0
\(768\) −5.45461e11 −1.56790
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 4.83257e11 1.36761
\(772\) 0 0
\(773\) −6.77429e11 −1.89734 −0.948671 0.316265i \(-0.897571\pi\)
−0.948671 + 0.316265i \(0.897571\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 1.14997e12 3.10676
\(781\) −1.21544e12 −3.26685
\(782\) 0 0
\(783\) 3.25190e10 0.0865147
\(784\) 3.77802e11 1.00000
\(785\) −1.45516e11 −0.383206
\(786\) 0 0
\(787\) −3.08417e11 −0.803970 −0.401985 0.915646i \(-0.631680\pi\)
−0.401985 + 0.915646i \(0.631680\pi\)
\(788\) 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
\(797\) −3.45514e11 −0.856312 −0.428156 0.903705i \(-0.640837\pi\)
−0.428156 + 0.903705i \(0.640837\pi\)
\(798\) 0 0
\(799\) −2.14487e11 −0.526277
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 8.02222e11 1.92945
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 8.32147e11 1.94270 0.971351 0.237650i \(-0.0763772\pi\)
0.971351 + 0.237650i \(0.0763772\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 5.23398e10 0.120395
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) −8.14604e11 −1.83732
\(817\) 0 0
\(818\) 0 0
\(819\) −1.30010e12 −2.88962
\(820\) 0 0
\(821\) 6.14999e11 1.35364 0.676818 0.736150i \(-0.263358\pi\)
0.676818 + 0.736150i \(0.263358\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 1.18829e12 2.56512
\(826\) 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
\(832\) 9.49473e11 1.98148
\(833\) 5.64218e11 1.17184
\(834\) 0 0
\(835\) −7.77257e11 −1.59889
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) −4.92995e11 −0.985505
\(842\) 0 0
\(843\) −2.39273e11 −0.473787
\(844\) 5.26447e11 1.03749
\(845\) −1.49190e12 −2.92626
\(846\) 0 0
\(847\) −8.62889e11 −1.67657
\(848\) 0 0
\(849\) 1.31670e12 2.53429
\(850\) 0 0
\(851\) 0 0
\(852\) −1.64975e12 −3.13083
\(853\) −1.03736e12 −1.95944 −0.979722 0.200361i \(-0.935788\pi\)
−0.979722 + 0.200361i \(0.935788\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.37034e11 0.254042 0.127021 0.991900i \(-0.459458\pi\)
0.127021 + 0.991900i \(0.459458\pi\)
\(858\) 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
\(865\) −1.04382e12 −1.86450
\(866\) 0 0
\(867\) −3.30628e11 −0.585144
\(868\) 0 0
\(869\) −1.67996e12 −2.94591
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 1.58459e12 2.72810
\(874\) 0 0
\(875\) 5.86182e11 1.00000
\(876\) 1.08888e12 1.84911
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 1.85627e12 3.10946
\(880\) 9.81115e11 1.63602
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 1.41797e12 2.32197
\(885\) 0 0
\(886\) 0 0
\(887\) −5.29565e11 −0.855509 −0.427754 0.903895i \(-0.640695\pi\)
−0.427754 + 0.903895i \(0.640695\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 3.41947e11 0.542560
\(892\) 3.02844e11 0.478365
\(893\) 0 0
\(894\) 0 0
\(895\) 1.11193e12 1.73294
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 9.56800e11 1.45831
\(901\) 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 \(\pi\)
\(908\) 7.24005e11 1.06512
\(909\) 0 0
\(910\) 0 0
\(911\) −4.15670e10 −0.0603497 −0.0301749 0.999545i \(-0.509606\pi\)
−0.0301749 + 0.999545i \(0.509606\pi\)
\(912\) 0 0
\(913\) −1.29793e12 −1.86797
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −9.43384e11 −1.32259 −0.661297 0.750124i \(-0.729994\pi\)
−0.661297 + 0.750124i \(0.729994\pi\)
\(920\) 0 0
\(921\) 6.73521e10 0.0936079
\(922\) 0 0
\(923\) 2.87168e12 3.95667
\(924\) −1.86980e12 −2.56512
\(925\) 0 0
\(926\) 0 0
\(927\) −1.07959e12 −1.46197
\(928\) 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
\(935\) 1.46522e12 1.91715
\(936\) 0 0
\(937\) −9.84225e11 −1.27684 −0.638419 0.769689i \(-0.720411\pi\)
−0.638419 + 0.769689i \(0.720411\pi\)
\(938\) 0 0
\(939\) 3.10093e11 0.398868
\(940\) 3.50638e11 0.449105
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) −5.73072e11 −0.718592
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) −2.28025e12 −2.82325
\(949\) −1.89539e12 −2.33686
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 2.56568e11 0.308453
\(956\) −1.18910e12 −1.42360
\(957\) −2.59038e11 −0.308827
\(958\) 0 0
\(959\) 0 0
\(960\) 1.33169e12 1.56790
\(961\) 8.52891e11 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 \(\pi\)
\(972\) 1.10556e12 1.23856
\(973\) 0 0
\(974\) 0 0
\(975\) −2.80754e12 −3.10676
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −9.22368e11 −1.00000
\(981\) −7.30112e11 −0.788340
\(982\) 0 0
\(983\) 1.41054e12 1.51067 0.755337 0.655337i \(-0.227473\pi\)
0.755337 + 0.655337i \(0.227473\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −6.68244e11 −0.704152
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 1.52931e11 0.158562 0.0792812 0.996852i \(-0.474738\pi\)
0.0792812 + 0.996852i \(0.474738\pi\)
\(992\) 0 0
\(993\) 6.13405e11 0.630885
\(994\) 0 0
\(995\) 0 0
\(996\) −1.76172e12 −1.79019
\(997\) 1.43178e12 1.44910 0.724548 0.689225i \(-0.242049\pi\)
0.724548 + 0.689225i \(0.242049\pi\)
\(998\) 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 35.9.c.a.34.1 1
5.2 odd 4 175.9.d.c.76.2 2
5.3 odd 4 175.9.d.c.76.1 2
5.4 even 2 35.9.c.b.34.1 yes 1
7.6 odd 2 35.9.c.b.34.1 yes 1
35.13 even 4 175.9.d.c.76.2 2
35.27 even 4 175.9.d.c.76.1 2
35.34 odd 2 CM 35.9.c.a.34.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.9.c.a.34.1 1 1.1 even 1 trivial
35.9.c.a.34.1 1 35.34 odd 2 CM
35.9.c.b.34.1 yes 1 5.4 even 2
35.9.c.b.34.1 yes 1 7.6 odd 2
175.9.d.c.76.1 2 5.3 odd 4
175.9.d.c.76.1 2 35.27 even 4
175.9.d.c.76.2 2 5.2 odd 4
175.9.d.c.76.2 2 35.13 even 4