Properties

Label 7800.2.a.l.1.1
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(62.2833135766\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1560)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +5.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +5.00000 q^{7} +1.00000 q^{9} +5.00000 q^{11} -1.00000 q^{13} +3.00000 q^{17} -4.00000 q^{19} -5.00000 q^{21} -5.00000 q^{23} -1.00000 q^{27} -4.00000 q^{29} -5.00000 q^{33} +7.00000 q^{37} +1.00000 q^{39} +11.0000 q^{41} +12.0000 q^{43} -6.00000 q^{47} +18.0000 q^{49} -3.00000 q^{51} -1.00000 q^{53} +4.00000 q^{57} +12.0000 q^{59} -7.00000 q^{61} +5.00000 q^{63} -4.00000 q^{67} +5.00000 q^{69} -7.00000 q^{71} +14.0000 q^{73} +25.0000 q^{77} -5.00000 q^{79} +1.00000 q^{81} +2.00000 q^{83} +4.00000 q^{87} -3.00000 q^{89} -5.00000 q^{91} +1.00000 q^{97} +5.00000 q^{99} +O(q^{100})\)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 5.00000 1.88982 0.944911 0.327327i \(-0.106148\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) −5.00000 −1.09109
\(22\) 0 0
\(23\) −5.00000 −1.04257 −0.521286 0.853382i \(-0.674548\pi\)
−0.521286 + 0.853382i \(0.674548\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) −5.00000 −0.870388
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 7.00000 1.15079 0.575396 0.817875i \(-0.304848\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) 11.0000 1.71791 0.858956 0.512050i \(-0.171114\pi\)
0.858956 + 0.512050i \(0.171114\pi\)
\(42\) 0 0
\(43\) 12.0000 1.82998 0.914991 0.403473i \(-0.132197\pi\)
0.914991 + 0.403473i \(0.132197\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0 0
\(49\) 18.0000 2.57143
\(50\) 0 0
\(51\) −3.00000 −0.420084
\(52\) 0 0
\(53\) −1.00000 −0.137361 −0.0686803 0.997639i \(-0.521879\pi\)
−0.0686803 + 0.997639i \(0.521879\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4.00000 0.529813
\(58\) 0 0
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) −7.00000 −0.896258 −0.448129 0.893969i \(-0.647910\pi\)
−0.448129 + 0.893969i \(0.647910\pi\)
\(62\) 0 0
\(63\) 5.00000 0.629941
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 5.00000 0.601929
\(70\) 0 0
\(71\) −7.00000 −0.830747 −0.415374 0.909651i \(-0.636349\pi\)
−0.415374 + 0.909651i \(0.636349\pi\)
\(72\) 0 0
\(73\) 14.0000 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 25.0000 2.84901
\(78\) 0 0
\(79\) −5.00000 −0.562544 −0.281272 0.959628i \(-0.590756\pi\)
−0.281272 + 0.959628i \(0.590756\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 4.00000 0.428845
\(88\) 0 0
\(89\) −3.00000 −0.317999 −0.159000 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 0 0
\(91\) −5.00000 −0.524142
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.00000 0.101535 0.0507673 0.998711i \(-0.483833\pi\)
0.0507673 + 0.998711i \(0.483833\pi\)
\(98\) 0 0
\(99\) 5.00000 0.502519
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.0000 1.06341 0.531705 0.846930i \(-0.321551\pi\)
0.531705 + 0.846930i \(0.321551\pi\)
\(108\) 0 0
\(109\) −12.0000 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) 0 0
\(111\) −7.00000 −0.664411
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) 15.0000 1.37505
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 0 0
\(123\) −11.0000 −0.991837
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −6.00000 −0.532414 −0.266207 0.963916i \(-0.585770\pi\)
−0.266207 + 0.963916i \(0.585770\pi\)
\(128\) 0 0
\(129\) −12.0000 −1.05654
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) −20.0000 −1.73422
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 14.0000 1.19610 0.598050 0.801459i \(-0.295942\pi\)
0.598050 + 0.801459i \(0.295942\pi\)
\(138\) 0 0
\(139\) −11.0000 −0.933008 −0.466504 0.884519i \(-0.654487\pi\)
−0.466504 + 0.884519i \(0.654487\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) −5.00000 −0.418121
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −18.0000 −1.48461
\(148\) 0 0
\(149\) −15.0000 −1.22885 −0.614424 0.788976i \(-0.710612\pi\)
−0.614424 + 0.788976i \(0.710612\pi\)
\(150\) 0 0
\(151\) −2.00000 −0.162758 −0.0813788 0.996683i \(-0.525932\pi\)
−0.0813788 + 0.996683i \(0.525932\pi\)
\(152\) 0 0
\(153\) 3.00000 0.242536
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) 0 0
\(159\) 1.00000 0.0793052
\(160\) 0 0
\(161\) −25.0000 −1.97028
\(162\) 0 0
\(163\) −7.00000 −0.548282 −0.274141 0.961689i \(-0.588394\pi\)
−0.274141 + 0.961689i \(0.588394\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −18.0000 −1.39288 −0.696441 0.717614i \(-0.745234\pi\)
−0.696441 + 0.717614i \(0.745234\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −4.00000 −0.305888
\(172\) 0 0
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −12.0000 −0.901975
\(178\) 0 0
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 0 0
\(181\) −23.0000 −1.70958 −0.854788 0.518977i \(-0.826313\pi\)
−0.854788 + 0.518977i \(0.826313\pi\)
\(182\) 0 0
\(183\) 7.00000 0.517455
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 15.0000 1.09691
\(188\) 0 0
\(189\) −5.00000 −0.363696
\(190\) 0 0
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) 0 0
\(193\) 23.0000 1.65558 0.827788 0.561041i \(-0.189599\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 0 0
\(201\) 4.00000 0.282138
\(202\) 0 0
\(203\) −20.0000 −1.40372
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −5.00000 −0.347524
\(208\) 0 0
\(209\) −20.0000 −1.38343
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) 7.00000 0.479632
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −14.0000 −0.946032
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) 24.0000 1.60716 0.803579 0.595198i \(-0.202926\pi\)
0.803579 + 0.595198i \(0.202926\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −20.0000 −1.32745 −0.663723 0.747978i \(-0.731025\pi\)
−0.663723 + 0.747978i \(0.731025\pi\)
\(228\) 0 0
\(229\) −6.00000 −0.396491 −0.198246 0.980152i \(-0.563524\pi\)
−0.198246 + 0.980152i \(0.563524\pi\)
\(230\) 0 0
\(231\) −25.0000 −1.64488
\(232\) 0 0
\(233\) 9.00000 0.589610 0.294805 0.955557i \(-0.404745\pi\)
0.294805 + 0.955557i \(0.404745\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 5.00000 0.324785
\(238\) 0 0
\(239\) 5.00000 0.323423 0.161712 0.986838i \(-0.448299\pi\)
0.161712 + 0.986838i \(0.448299\pi\)
\(240\) 0 0
\(241\) −4.00000 −0.257663 −0.128831 0.991667i \(-0.541123\pi\)
−0.128831 + 0.991667i \(0.541123\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 4.00000 0.254514
\(248\) 0 0
\(249\) −2.00000 −0.126745
\(250\) 0 0
\(251\) −2.00000 −0.126239 −0.0631194 0.998006i \(-0.520105\pi\)
−0.0631194 + 0.998006i \(0.520105\pi\)
\(252\) 0 0
\(253\) −25.0000 −1.57174
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) 35.0000 2.17479
\(260\) 0 0
\(261\) −4.00000 −0.247594
\(262\) 0 0
\(263\) 24.0000 1.47990 0.739952 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 3.00000 0.183597
\(268\) 0 0
\(269\) −6.00000 −0.365826 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) 0 0
\(273\) 5.00000 0.302614
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 30.0000 1.80253 0.901263 0.433273i \(-0.142641\pi\)
0.901263 + 0.433273i \(0.142641\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 18.0000 1.06999 0.534994 0.844856i \(-0.320314\pi\)
0.534994 + 0.844856i \(0.320314\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 55.0000 3.24655
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) −1.00000 −0.0586210
\(292\) 0 0
\(293\) −20.0000 −1.16841 −0.584206 0.811605i \(-0.698594\pi\)
−0.584206 + 0.811605i \(0.698594\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −5.00000 −0.290129
\(298\) 0 0
\(299\) 5.00000 0.289157
\(300\) 0 0
\(301\) 60.0000 3.45834
\(302\) 0 0
\(303\) 6.00000 0.344691
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 25.0000 1.42683 0.713413 0.700744i \(-0.247149\pi\)
0.713413 + 0.700744i \(0.247149\pi\)
\(308\) 0 0
\(309\) −14.0000 −0.796432
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 20.0000 1.13047 0.565233 0.824931i \(-0.308786\pi\)
0.565233 + 0.824931i \(0.308786\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −24.0000 −1.34797 −0.673987 0.738743i \(-0.735420\pi\)
−0.673987 + 0.738743i \(0.735420\pi\)
\(318\) 0 0
\(319\) −20.0000 −1.11979
\(320\) 0 0
\(321\) −11.0000 −0.613960
\(322\) 0 0
\(323\) −12.0000 −0.667698
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 12.0000 0.663602
\(328\) 0 0
\(329\) −30.0000 −1.65395
\(330\) 0 0
\(331\) 4.00000 0.219860 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) 0 0
\(333\) 7.00000 0.383598
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) 0 0
\(339\) 14.0000 0.760376
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 55.0000 2.96972
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.00000 0.375780 0.187890 0.982190i \(-0.439835\pi\)
0.187890 + 0.982190i \(0.439835\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) −30.0000 −1.59674 −0.798369 0.602168i \(-0.794304\pi\)
−0.798369 + 0.602168i \(0.794304\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −15.0000 −0.793884
\(358\) 0 0
\(359\) −32.0000 −1.68890 −0.844448 0.535638i \(-0.820071\pi\)
−0.844448 + 0.535638i \(0.820071\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) −14.0000 −0.734809
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 22.0000 1.14839 0.574195 0.818718i \(-0.305315\pi\)
0.574195 + 0.818718i \(0.305315\pi\)
\(368\) 0 0
\(369\) 11.0000 0.572637
\(370\) 0 0
\(371\) −5.00000 −0.259587
\(372\) 0 0
\(373\) −14.0000 −0.724893 −0.362446 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) 32.0000 1.64373 0.821865 0.569683i \(-0.192934\pi\)
0.821865 + 0.569683i \(0.192934\pi\)
\(380\) 0 0
\(381\) 6.00000 0.307389
\(382\) 0 0
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 12.0000 0.609994
\(388\) 0 0
\(389\) −24.0000 −1.21685 −0.608424 0.793612i \(-0.708198\pi\)
−0.608424 + 0.793612i \(0.708198\pi\)
\(390\) 0 0
\(391\) −15.0000 −0.758583
\(392\) 0 0
\(393\) −12.0000 −0.605320
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 3.00000 0.150566 0.0752828 0.997162i \(-0.476014\pi\)
0.0752828 + 0.997162i \(0.476014\pi\)
\(398\) 0 0
\(399\) 20.0000 1.00125
\(400\) 0 0
\(401\) −14.0000 −0.699127 −0.349563 0.936913i \(-0.613670\pi\)
−0.349563 + 0.936913i \(0.613670\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 35.0000 1.73489
\(408\) 0 0
\(409\) 20.0000 0.988936 0.494468 0.869196i \(-0.335363\pi\)
0.494468 + 0.869196i \(0.335363\pi\)
\(410\) 0 0
\(411\) −14.0000 −0.690569
\(412\) 0 0
\(413\) 60.0000 2.95241
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 11.0000 0.538672
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −14.0000 −0.682318 −0.341159 0.940006i \(-0.610819\pi\)
−0.341159 + 0.940006i \(0.610819\pi\)
\(422\) 0 0
\(423\) −6.00000 −0.291730
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −35.0000 −1.69377
\(428\) 0 0
\(429\) 5.00000 0.241402
\(430\) 0 0
\(431\) 4.00000 0.192673 0.0963366 0.995349i \(-0.469287\pi\)
0.0963366 + 0.995349i \(0.469287\pi\)
\(432\) 0 0
\(433\) 18.0000 0.865025 0.432512 0.901628i \(-0.357627\pi\)
0.432512 + 0.901628i \(0.357627\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 20.0000 0.956730
\(438\) 0 0
\(439\) −27.0000 −1.28864 −0.644320 0.764756i \(-0.722859\pi\)
−0.644320 + 0.764756i \(0.722859\pi\)
\(440\) 0 0
\(441\) 18.0000 0.857143
\(442\) 0 0
\(443\) −21.0000 −0.997740 −0.498870 0.866677i \(-0.666252\pi\)
−0.498870 + 0.866677i \(0.666252\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 15.0000 0.709476
\(448\) 0 0
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) 55.0000 2.58985
\(452\) 0 0
\(453\) 2.00000 0.0939682
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −39.0000 −1.82434 −0.912172 0.409809i \(-0.865595\pi\)
−0.912172 + 0.409809i \(0.865595\pi\)
\(458\) 0 0
\(459\) −3.00000 −0.140028
\(460\) 0 0
\(461\) −33.0000 −1.53696 −0.768482 0.639872i \(-0.778987\pi\)
−0.768482 + 0.639872i \(0.778987\pi\)
\(462\) 0 0
\(463\) 1.00000 0.0464739 0.0232370 0.999730i \(-0.492603\pi\)
0.0232370 + 0.999730i \(0.492603\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15.0000 0.694117 0.347059 0.937843i \(-0.387180\pi\)
0.347059 + 0.937843i \(0.387180\pi\)
\(468\) 0 0
\(469\) −20.0000 −0.923514
\(470\) 0 0
\(471\) 4.00000 0.184310
\(472\) 0 0
\(473\) 60.0000 2.75880
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.00000 −0.0457869
\(478\) 0 0
\(479\) 11.0000 0.502603 0.251301 0.967909i \(-0.419141\pi\)
0.251301 + 0.967909i \(0.419141\pi\)
\(480\) 0 0
\(481\) −7.00000 −0.319173
\(482\) 0 0
\(483\) 25.0000 1.13754
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 23.0000 1.04223 0.521115 0.853487i \(-0.325516\pi\)
0.521115 + 0.853487i \(0.325516\pi\)
\(488\) 0 0
\(489\) 7.00000 0.316551
\(490\) 0 0
\(491\) −22.0000 −0.992846 −0.496423 0.868081i \(-0.665354\pi\)
−0.496423 + 0.868081i \(0.665354\pi\)
\(492\) 0 0
\(493\) −12.0000 −0.540453
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −35.0000 −1.56996
\(498\) 0 0
\(499\) 14.0000 0.626726 0.313363 0.949633i \(-0.398544\pi\)
0.313363 + 0.949633i \(0.398544\pi\)
\(500\) 0 0
\(501\) 18.0000 0.804181
\(502\) 0 0
\(503\) 8.00000 0.356702 0.178351 0.983967i \(-0.442924\pi\)
0.178351 + 0.983967i \(0.442924\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) 13.0000 0.576215 0.288107 0.957598i \(-0.406974\pi\)
0.288107 + 0.957598i \(0.406974\pi\)
\(510\) 0 0
\(511\) 70.0000 3.09662
\(512\) 0 0
\(513\) 4.00000 0.176604
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −30.0000 −1.31940
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) −14.0000 −0.613351 −0.306676 0.951814i \(-0.599217\pi\)
−0.306676 + 0.951814i \(0.599217\pi\)
\(522\) 0 0
\(523\) −38.0000 −1.66162 −0.830812 0.556553i \(-0.812124\pi\)
−0.830812 + 0.556553i \(0.812124\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 2.00000 0.0869565
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) −11.0000 −0.476463
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 10.0000 0.431532
\(538\) 0 0
\(539\) 90.0000 3.87657
\(540\) 0 0
\(541\) 16.0000 0.687894 0.343947 0.938989i \(-0.388236\pi\)
0.343947 + 0.938989i \(0.388236\pi\)
\(542\) 0 0
\(543\) 23.0000 0.987024
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 0 0
\(549\) −7.00000 −0.298753
\(550\) 0 0
\(551\) 16.0000 0.681623
\(552\) 0 0
\(553\) −25.0000 −1.06311
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) −12.0000 −0.507546
\(560\) 0 0
\(561\) −15.0000 −0.633300
\(562\) 0 0
\(563\) 39.0000 1.64365 0.821827 0.569737i \(-0.192955\pi\)
0.821827 + 0.569737i \(0.192955\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 5.00000 0.209980
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 43.0000 1.79949 0.899747 0.436412i \(-0.143751\pi\)
0.899747 + 0.436412i \(0.143751\pi\)
\(572\) 0 0
\(573\) −6.00000 −0.250654
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 17.0000 0.707719 0.353860 0.935299i \(-0.384869\pi\)
0.353860 + 0.935299i \(0.384869\pi\)
\(578\) 0 0
\(579\) −23.0000 −0.955847
\(580\) 0 0
\(581\) 10.0000 0.414870
\(582\) 0 0
\(583\) −5.00000 −0.207079
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −34.0000 −1.40333 −0.701665 0.712507i \(-0.747560\pi\)
−0.701665 + 0.712507i \(0.747560\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −18.0000 −0.740421
\(592\) 0 0
\(593\) −16.0000 −0.657041 −0.328521 0.944497i \(-0.606550\pi\)
−0.328521 + 0.944497i \(0.606550\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −16.0000 −0.654836
\(598\) 0 0
\(599\) 34.0000 1.38920 0.694601 0.719395i \(-0.255581\pi\)
0.694601 + 0.719395i \(0.255581\pi\)
\(600\) 0 0
\(601\) 15.0000 0.611863 0.305931 0.952054i \(-0.401032\pi\)
0.305931 + 0.952054i \(0.401032\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −32.0000 −1.29884 −0.649420 0.760430i \(-0.724988\pi\)
−0.649420 + 0.760430i \(0.724988\pi\)
\(608\) 0 0
\(609\) 20.0000 0.810441
\(610\) 0 0
\(611\) 6.00000 0.242734
\(612\) 0 0
\(613\) −11.0000 −0.444286 −0.222143 0.975014i \(-0.571305\pi\)
−0.222143 + 0.975014i \(0.571305\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.00000 0.161034 0.0805170 0.996753i \(-0.474343\pi\)
0.0805170 + 0.996753i \(0.474343\pi\)
\(618\) 0 0
\(619\) 10.0000 0.401934 0.200967 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(620\) 0 0
\(621\) 5.00000 0.200643
\(622\) 0 0
\(623\) −15.0000 −0.600962
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 20.0000 0.798723
\(628\) 0 0
\(629\) 21.0000 0.837325
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 0 0
\(633\) −4.00000 −0.158986
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −18.0000 −0.713186
\(638\) 0 0
\(639\) −7.00000 −0.276916
\(640\) 0 0
\(641\) −36.0000 −1.42191 −0.710957 0.703235i \(-0.751738\pi\)
−0.710957 + 0.703235i \(0.751738\pi\)
\(642\) 0 0
\(643\) −39.0000 −1.53801 −0.769005 0.639243i \(-0.779248\pi\)
−0.769005 + 0.639243i \(0.779248\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 29.0000 1.14011 0.570054 0.821607i \(-0.306922\pi\)
0.570054 + 0.821607i \(0.306922\pi\)
\(648\) 0 0
\(649\) 60.0000 2.35521
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −18.0000 −0.704394 −0.352197 0.935926i \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 14.0000 0.546192
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −46.0000 −1.78919 −0.894596 0.446875i \(-0.852537\pi\)
−0.894596 + 0.446875i \(0.852537\pi\)
\(662\) 0 0
\(663\) 3.00000 0.116510
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 20.0000 0.774403
\(668\) 0 0
\(669\) −24.0000 −0.927894
\(670\) 0 0
\(671\) −35.0000 −1.35116
\(672\) 0 0
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15.0000 0.576497 0.288248 0.957556i \(-0.406927\pi\)
0.288248 + 0.957556i \(0.406927\pi\)
\(678\) 0 0
\(679\) 5.00000 0.191882
\(680\) 0 0
\(681\) 20.0000 0.766402
\(682\) 0 0
\(683\) −14.0000 −0.535695 −0.267848 0.963461i \(-0.586312\pi\)
−0.267848 + 0.963461i \(0.586312\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 6.00000 0.228914
\(688\) 0 0
\(689\) 1.00000 0.0380970
\(690\) 0 0
\(691\) −18.0000 −0.684752 −0.342376 0.939563i \(-0.611232\pi\)
−0.342376 + 0.939563i \(0.611232\pi\)
\(692\) 0 0
\(693\) 25.0000 0.949671
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 33.0000 1.24996
\(698\) 0 0
\(699\) −9.00000 −0.340411
\(700\) 0 0
\(701\) 4.00000 0.151078 0.0755390 0.997143i \(-0.475932\pi\)
0.0755390 + 0.997143i \(0.475932\pi\)
\(702\) 0 0
\(703\) −28.0000 −1.05604
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −30.0000 −1.12827
\(708\) 0 0
\(709\) −20.0000 −0.751116 −0.375558 0.926799i \(-0.622549\pi\)
−0.375558 + 0.926799i \(0.622549\pi\)
\(710\) 0 0
\(711\) −5.00000 −0.187515
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −5.00000 −0.186728
\(718\) 0 0
\(719\) 22.0000 0.820462 0.410231 0.911982i \(-0.365448\pi\)
0.410231 + 0.911982i \(0.365448\pi\)
\(720\) 0 0
\(721\) 70.0000 2.60694
\(722\) 0 0
\(723\) 4.00000 0.148762
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 36.0000 1.33151
\(732\) 0 0
\(733\) 3.00000 0.110808 0.0554038 0.998464i \(-0.482355\pi\)
0.0554038 + 0.998464i \(0.482355\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −20.0000 −0.736709
\(738\) 0 0
\(739\) 24.0000 0.882854 0.441427 0.897297i \(-0.354472\pi\)
0.441427 + 0.897297i \(0.354472\pi\)
\(740\) 0 0
\(741\) −4.00000 −0.146944
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 2.00000 0.0731762
\(748\) 0 0
\(749\) 55.0000 2.00966
\(750\) 0 0
\(751\) 17.0000 0.620339 0.310169 0.950681i \(-0.399614\pi\)
0.310169 + 0.950681i \(0.399614\pi\)
\(752\) 0 0
\(753\) 2.00000 0.0728841
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) 0 0
\(759\) 25.0000 0.907443
\(760\) 0 0
\(761\) 10.0000 0.362500 0.181250 0.983437i \(-0.441986\pi\)
0.181250 + 0.983437i \(0.441986\pi\)
\(762\) 0 0
\(763\) −60.0000 −2.17215
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −12.0000 −0.433295
\(768\) 0 0
\(769\) 46.0000 1.65880 0.829401 0.558653i \(-0.188682\pi\)
0.829401 + 0.558653i \(0.188682\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) 0 0
\(773\) −2.00000 −0.0719350 −0.0359675 0.999353i \(-0.511451\pi\)
−0.0359675 + 0.999353i \(0.511451\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −35.0000 −1.25562
\(778\) 0 0
\(779\) −44.0000 −1.57646
\(780\) 0 0
\(781\) −35.0000 −1.25240
\(782\) 0 0
\(783\) 4.00000 0.142948
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −32.0000 −1.14068 −0.570338 0.821410i \(-0.693188\pi\)
−0.570338 + 0.821410i \(0.693188\pi\)
\(788\) 0 0
\(789\) −24.0000 −0.854423
\(790\) 0 0
\(791\) −70.0000 −2.48891
\(792\) 0 0
\(793\) 7.00000 0.248577
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 45.0000 1.59398 0.796991 0.603991i \(-0.206424\pi\)
0.796991 + 0.603991i \(0.206424\pi\)
\(798\) 0 0
\(799\) −18.0000 −0.636794
\(800\) 0 0
\(801\) −3.00000 −0.106000
\(802\) 0 0
\(803\) 70.0000 2.47025
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 6.00000 0.211210
\(808\) 0 0
\(809\) 24.0000 0.843795 0.421898 0.906644i \(-0.361364\pi\)
0.421898 + 0.906644i \(0.361364\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) −2.00000 −0.0701431
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −48.0000 −1.67931
\(818\) 0 0
\(819\) −5.00000 −0.174714
\(820\) 0 0
\(821\) 3.00000 0.104701 0.0523504 0.998629i \(-0.483329\pi\)
0.0523504 + 0.998629i \(0.483329\pi\)
\(822\) 0 0
\(823\) −26.0000 −0.906303 −0.453152 0.891434i \(-0.649700\pi\)
−0.453152 + 0.891434i \(0.649700\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −18.0000 −0.625921 −0.312961 0.949766i \(-0.601321\pi\)
−0.312961 + 0.949766i \(0.601321\pi\)
\(828\) 0 0
\(829\) 10.0000 0.347314 0.173657 0.984806i \(-0.444442\pi\)
0.173657 + 0.984806i \(0.444442\pi\)
\(830\) 0 0
\(831\) −30.0000 −1.04069
\(832\) 0 0
\(833\) 54.0000 1.87099
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −3.00000 −0.103572 −0.0517858 0.998658i \(-0.516491\pi\)
−0.0517858 + 0.998658i \(0.516491\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 0 0
\(843\) −6.00000 −0.206651
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 70.0000 2.40523
\(848\) 0 0
\(849\) −18.0000 −0.617758
\(850\) 0 0
\(851\) −35.0000 −1.19978
\(852\) 0 0
\(853\) 49.0000 1.67773 0.838864 0.544341i \(-0.183220\pi\)
0.838864 + 0.544341i \(0.183220\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −11.0000 −0.375753 −0.187876 0.982193i \(-0.560160\pi\)
−0.187876 + 0.982193i \(0.560160\pi\)
\(858\) 0 0
\(859\) 1.00000 0.0341196 0.0170598 0.999854i \(-0.494569\pi\)
0.0170598 + 0.999854i \(0.494569\pi\)
\(860\) 0 0
\(861\) −55.0000 −1.87439
\(862\) 0 0
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 8.00000 0.271694
\(868\) 0 0
\(869\) −25.0000 −0.848067
\(870\) 0 0
\(871\) 4.00000 0.135535
\(872\) 0 0
\(873\) 1.00000 0.0338449
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 2.00000 0.0675352 0.0337676 0.999430i \(-0.489249\pi\)
0.0337676 + 0.999430i \(0.489249\pi\)
\(878\) 0 0
\(879\) 20.0000 0.674583
\(880\) 0 0
\(881\) 34.0000 1.14549 0.572745 0.819734i \(-0.305879\pi\)
0.572745 + 0.819734i \(0.305879\pi\)
\(882\) 0 0
\(883\) −22.0000 −0.740359 −0.370179 0.928960i \(-0.620704\pi\)
−0.370179 + 0.928960i \(0.620704\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 9.00000 0.302190 0.151095 0.988519i \(-0.451720\pi\)
0.151095 + 0.988519i \(0.451720\pi\)
\(888\) 0 0
\(889\) −30.0000 −1.00617
\(890\) 0 0
\(891\) 5.00000 0.167506
\(892\) 0 0
\(893\) 24.0000 0.803129
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −5.00000 −0.166945
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) −3.00000 −0.0999445
\(902\) 0 0
\(903\) −60.0000 −1.99667
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 22.0000 0.730498 0.365249 0.930910i \(-0.380984\pi\)
0.365249 + 0.930910i \(0.380984\pi\)
\(908\) 0 0
\(909\) −6.00000 −0.199007
\(910\) 0 0
\(911\) −6.00000 −0.198789 −0.0993944 0.995048i \(-0.531691\pi\)
−0.0993944 + 0.995048i \(0.531691\pi\)
\(912\) 0 0
\(913\) 10.0000 0.330952
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 60.0000 1.98137
\(918\) 0 0
\(919\) 51.0000 1.68233 0.841167 0.540775i \(-0.181869\pi\)
0.841167 + 0.540775i \(0.181869\pi\)
\(920\) 0 0
\(921\) −25.0000 −0.823778
\(922\) 0 0
\(923\) 7.00000 0.230408
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 14.0000 0.459820
\(928\) 0 0
\(929\) −31.0000 −1.01708 −0.508539 0.861039i \(-0.669814\pi\)
−0.508539 + 0.861039i \(0.669814\pi\)
\(930\) 0 0
\(931\) −72.0000 −2.35970
\(932\) 0 0
\(933\) −24.0000 −0.785725
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 14.0000 0.457360 0.228680 0.973502i \(-0.426559\pi\)
0.228680 + 0.973502i \(0.426559\pi\)
\(938\) 0 0
\(939\) −20.0000 −0.652675
\(940\) 0 0
\(941\) −7.00000 −0.228193 −0.114097 0.993470i \(-0.536397\pi\)
−0.114097 + 0.993470i \(0.536397\pi\)
\(942\) 0 0
\(943\) −55.0000 −1.79105
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −30.0000 −0.974869 −0.487435 0.873160i \(-0.662067\pi\)
−0.487435 + 0.873160i \(0.662067\pi\)
\(948\) 0 0
\(949\) −14.0000 −0.454459
\(950\) 0 0
\(951\) 24.0000 0.778253
\(952\) 0 0
\(953\) 3.00000 0.0971795 0.0485898 0.998819i \(-0.484527\pi\)
0.0485898 + 0.998819i \(0.484527\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 20.0000 0.646508
\(958\) 0 0
\(959\) 70.0000 2.26042
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 11.0000 0.354470
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −40.0000 −1.28631 −0.643157 0.765735i \(-0.722376\pi\)
−0.643157 + 0.765735i \(0.722376\pi\)
\(968\) 0 0
\(969\) 12.0000 0.385496
\(970\) 0 0
\(971\) 54.0000 1.73294 0.866471 0.499227i \(-0.166383\pi\)
0.866471 + 0.499227i \(0.166383\pi\)
\(972\) 0 0
\(973\) −55.0000 −1.76322
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −46.0000 −1.47167 −0.735835 0.677161i \(-0.763210\pi\)
−0.735835 + 0.677161i \(0.763210\pi\)
\(978\) 0 0
\(979\) −15.0000 −0.479402
\(980\) 0 0
\(981\) −12.0000 −0.383131
\(982\) 0 0
\(983\) 40.0000 1.27580 0.637901 0.770118i \(-0.279803\pi\)
0.637901 + 0.770118i \(0.279803\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 30.0000 0.954911
\(988\) 0 0
\(989\) −60.0000 −1.90789
\(990\) 0 0
\(991\) 1.00000 0.0317660 0.0158830 0.999874i \(-0.494944\pi\)
0.0158830 + 0.999874i \(0.494944\pi\)
\(992\) 0 0
\(993\) −4.00000 −0.126936
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 42.0000 1.33015 0.665077 0.746775i \(-0.268399\pi\)
0.665077 + 0.746775i \(0.268399\pi\)
\(998\) 0 0
\(999\) −7.00000 −0.221470
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 7800.2.a.l.1.1 1
5.2 odd 4 1560.2.l.a.1249.2 yes 2
5.3 odd 4 1560.2.l.a.1249.1 2
5.4 even 2 7800.2.a.m.1.1 1
15.2 even 4 4680.2.l.c.2809.1 2
15.8 even 4 4680.2.l.c.2809.2 2
20.3 even 4 3120.2.l.b.1249.2 2
20.7 even 4 3120.2.l.b.1249.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1560.2.l.a.1249.1 2 5.3 odd 4
1560.2.l.a.1249.2 yes 2 5.2 odd 4
3120.2.l.b.1249.1 2 20.7 even 4
3120.2.l.b.1249.2 2 20.3 even 4
4680.2.l.c.2809.1 2 15.2 even 4
4680.2.l.c.2809.2 2 15.8 even 4
7800.2.a.l.1.1 1 1.1 even 1 trivial
7800.2.a.m.1.1 1 5.4 even 2