Properties

Label 7800.2.a.bu.1.3
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $0$
Dimension $4$
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: \(4\)
Coefficient field: 4.4.461844.1
Defining polynomial: \(x^{4} - x^{3} - 14 x^{2} - 12 x + 6\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.352593\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -0.647407 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -0.647407 q^{7} +1.00000 q^{9} +0.502467 q^{11} -1.00000 q^{13} +4.73074 q^{17} -6.58086 q^{19} +0.647407 q^{21} -2.85013 q^{23} -1.00000 q^{27} +0.294814 q^{29} +2.20272 q^{31} -0.502467 q^{33} -7.28605 q^{37} +1.00000 q^{39} +7.58580 q^{41} -0.444688 q^{43} -8.07840 q^{47} -6.58086 q^{49} -4.73074 q^{51} +12.7220 q^{53} +6.58086 q^{57} +10.8141 q^{59} +11.4359 q^{61} -0.647407 q^{63} +8.63864 q^{67} +2.85013 q^{69} -2.58086 q^{71} -10.6114 q^{73} -0.325301 q^{77} +5.28605 q^{79} +1.00000 q^{81} -5.35259 q^{83} -0.294814 q^{87} +4.99507 q^{89} +0.647407 q^{91} -2.20272 q^{93} +1.29481 q^{97} +0.502467 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{3} - 3q^{7} + 4q^{9} + O(q^{10}) \) \( 4q - 4q^{3} - 3q^{7} + 4q^{9} + 5q^{11} - 4q^{13} - 7q^{17} + 3q^{19} + 3q^{21} - 8q^{23} - 4q^{27} + 2q^{29} + 5q^{31} - 5q^{33} + q^{37} + 4q^{39} + 7q^{41} - 6q^{43} + 3q^{49} + 7q^{51} - 6q^{53} - 3q^{57} - 9q^{59} + 19q^{61} - 3q^{63} + 4q^{67} + 8q^{69} + 19q^{71} + 6q^{73} + 17q^{77} - 9q^{79} + 4q^{81} - 21q^{83} - 2q^{87} + 14q^{89} + 3q^{91} - 5q^{93} + 6q^{97} + 5q^{99} + O(q^{100}) \)

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
\(7\) −0.647407 −0.244697 −0.122348 0.992487i \(-0.539043\pi\)
−0.122348 + 0.992487i \(0.539043\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.502467 0.151500 0.0757498 0.997127i \(-0.475865\pi\)
0.0757498 + 0.997127i \(0.475865\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.73074 1.14737 0.573686 0.819075i \(-0.305513\pi\)
0.573686 + 0.819075i \(0.305513\pi\)
\(18\) 0 0
\(19\) −6.58086 −1.50975 −0.754877 0.655867i \(-0.772303\pi\)
−0.754877 + 0.655867i \(0.772303\pi\)
\(20\) 0 0
\(21\) 0.647407 0.141276
\(22\) 0 0
\(23\) −2.85013 −0.594292 −0.297146 0.954832i \(-0.596035\pi\)
−0.297146 + 0.954832i \(0.596035\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 0.294814 0.0547456 0.0273728 0.999625i \(-0.491286\pi\)
0.0273728 + 0.999625i \(0.491286\pi\)
\(30\) 0 0
\(31\) 2.20272 0.395620 0.197810 0.980240i \(-0.436617\pi\)
0.197810 + 0.980240i \(0.436617\pi\)
\(32\) 0 0
\(33\) −0.502467 −0.0874683
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −7.28605 −1.19782 −0.598910 0.800817i \(-0.704399\pi\)
−0.598910 + 0.800817i \(0.704399\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) 7.58580 1.18470 0.592351 0.805680i \(-0.298200\pi\)
0.592351 + 0.805680i \(0.298200\pi\)
\(42\) 0 0
\(43\) −0.444688 −0.0678143 −0.0339072 0.999425i \(-0.510795\pi\)
−0.0339072 + 0.999425i \(0.510795\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.07840 −1.17836 −0.589178 0.808004i \(-0.700548\pi\)
−0.589178 + 0.808004i \(0.700548\pi\)
\(48\) 0 0
\(49\) −6.58086 −0.940123
\(50\) 0 0
\(51\) −4.73074 −0.662436
\(52\) 0 0
\(53\) 12.7220 1.74750 0.873749 0.486377i \(-0.161682\pi\)
0.873749 + 0.486377i \(0.161682\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 6.58086 0.871657
\(58\) 0 0
\(59\) 10.8141 1.40787 0.703936 0.710263i \(-0.251424\pi\)
0.703936 + 0.710263i \(0.251424\pi\)
\(60\) 0 0
\(61\) 11.4359 1.46422 0.732110 0.681186i \(-0.238536\pi\)
0.732110 + 0.681186i \(0.238536\pi\)
\(62\) 0 0
\(63\) −0.647407 −0.0815656
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 8.63864 1.05538 0.527689 0.849438i \(-0.323059\pi\)
0.527689 + 0.849438i \(0.323059\pi\)
\(68\) 0 0
\(69\) 2.85013 0.343115
\(70\) 0 0
\(71\) −2.58086 −0.306292 −0.153146 0.988204i \(-0.548941\pi\)
−0.153146 + 0.988204i \(0.548941\pi\)
\(72\) 0 0
\(73\) −10.6114 −1.24196 −0.620982 0.783825i \(-0.713266\pi\)
−0.620982 + 0.783825i \(0.713266\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.325301 −0.0370715
\(78\) 0 0
\(79\) 5.28605 0.594727 0.297364 0.954764i \(-0.403893\pi\)
0.297364 + 0.954764i \(0.403893\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −5.35259 −0.587523 −0.293762 0.955879i \(-0.594907\pi\)
−0.293762 + 0.955879i \(0.594907\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.294814 −0.0316074
\(88\) 0 0
\(89\) 4.99507 0.529476 0.264738 0.964320i \(-0.414715\pi\)
0.264738 + 0.964320i \(0.414715\pi\)
\(90\) 0 0
\(91\) 0.647407 0.0678667
\(92\) 0 0
\(93\) −2.20272 −0.228411
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.29481 0.131468 0.0657342 0.997837i \(-0.479061\pi\)
0.0657342 + 0.997837i \(0.479061\pi\)
\(98\) 0 0
\(99\) 0.502467 0.0504999
\(100\) 0 0
\(101\) −4.28605 −0.426478 −0.213239 0.977000i \(-0.568401\pi\)
−0.213239 + 0.977000i \(0.568401\pi\)
\(102\) 0 0
\(103\) −7.25556 −0.714912 −0.357456 0.933930i \(-0.616356\pi\)
−0.357456 + 0.933930i \(0.616356\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −10.1362 −0.979901 −0.489951 0.871750i \(-0.662985\pi\)
−0.489951 + 0.871750i \(0.662985\pi\)
\(108\) 0 0
\(109\) 17.4527 1.67167 0.835833 0.548983i \(-0.184985\pi\)
0.835833 + 0.548983i \(0.184985\pi\)
\(110\) 0 0
\(111\) 7.28605 0.691561
\(112\) 0 0
\(113\) −15.8669 −1.49263 −0.746317 0.665591i \(-0.768180\pi\)
−0.746317 + 0.665591i \(0.768180\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) −3.06271 −0.280758
\(120\) 0 0
\(121\) −10.7475 −0.977048
\(122\) 0 0
\(123\) −7.58580 −0.683988
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −9.99124 −0.886579 −0.443289 0.896379i \(-0.646189\pi\)
−0.443289 + 0.896379i \(0.646189\pi\)
\(128\) 0 0
\(129\) 0.444688 0.0391526
\(130\) 0 0
\(131\) 16.2811 1.42249 0.711244 0.702945i \(-0.248132\pi\)
0.711244 + 0.702945i \(0.248132\pi\)
\(132\) 0 0
\(133\) 4.26050 0.369432
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.73567 −0.404596 −0.202298 0.979324i \(-0.564841\pi\)
−0.202298 + 0.979324i \(0.564841\pi\)
\(138\) 0 0
\(139\) −17.4615 −1.48106 −0.740532 0.672022i \(-0.765426\pi\)
−0.740532 + 0.672022i \(0.765426\pi\)
\(140\) 0 0
\(141\) 8.07840 0.680324
\(142\) 0 0
\(143\) −0.502467 −0.0420184
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 6.58086 0.542781
\(148\) 0 0
\(149\) 5.29481 0.433768 0.216884 0.976197i \(-0.430411\pi\)
0.216884 + 0.976197i \(0.430411\pi\)
\(150\) 0 0
\(151\) 18.5143 1.50667 0.753337 0.657635i \(-0.228443\pi\)
0.753337 + 0.657635i \(0.228443\pi\)
\(152\) 0 0
\(153\) 4.73074 0.382458
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 17.5809 1.40311 0.701553 0.712617i \(-0.252490\pi\)
0.701553 + 0.712617i \(0.252490\pi\)
\(158\) 0 0
\(159\) −12.7220 −1.00892
\(160\) 0 0
\(161\) 1.84519 0.145421
\(162\) 0 0
\(163\) 10.0119 0.784189 0.392094 0.919925i \(-0.371751\pi\)
0.392094 + 0.919925i \(0.371751\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.69642 0.672949 0.336475 0.941693i \(-0.390765\pi\)
0.336475 + 0.941693i \(0.390765\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −6.58086 −0.503251
\(172\) 0 0
\(173\) −18.0069 −1.36904 −0.684520 0.728994i \(-0.739988\pi\)
−0.684520 + 0.728994i \(0.739988\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −10.8141 −0.812835
\(178\) 0 0
\(179\) −2.73457 −0.204391 −0.102196 0.994764i \(-0.532587\pi\)
−0.102196 + 0.994764i \(0.532587\pi\)
\(180\) 0 0
\(181\) 16.8757 1.25436 0.627180 0.778875i \(-0.284209\pi\)
0.627180 + 0.778875i \(0.284209\pi\)
\(182\) 0 0
\(183\) −11.4359 −0.845368
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2.37704 0.173826
\(188\) 0 0
\(189\) 0.647407 0.0470919
\(190\) 0 0
\(191\) 12.5896 0.910954 0.455477 0.890248i \(-0.349469\pi\)
0.455477 + 0.890248i \(0.349469\pi\)
\(192\) 0 0
\(193\) 20.0728 1.44487 0.722437 0.691437i \(-0.243022\pi\)
0.722437 + 0.691437i \(0.243022\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.6163 1.11261 0.556307 0.830977i \(-0.312218\pi\)
0.556307 + 0.830977i \(0.312218\pi\)
\(198\) 0 0
\(199\) −15.7307 −1.11512 −0.557561 0.830136i \(-0.688263\pi\)
−0.557561 + 0.830136i \(0.688263\pi\)
\(200\) 0 0
\(201\) −8.63864 −0.609323
\(202\) 0 0
\(203\) −0.190865 −0.0133961
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −2.85013 −0.198097
\(208\) 0 0
\(209\) −3.30667 −0.228727
\(210\) 0 0
\(211\) 6.85013 0.471582 0.235791 0.971804i \(-0.424232\pi\)
0.235791 + 0.971804i \(0.424232\pi\)
\(212\) 0 0
\(213\) 2.58086 0.176838
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1.42606 −0.0968070
\(218\) 0 0
\(219\) 10.6114 0.717049
\(220\) 0 0
\(221\) −4.73074 −0.318224
\(222\) 0 0
\(223\) 1.15974 0.0776621 0.0388311 0.999246i \(-0.487637\pi\)
0.0388311 + 0.999246i \(0.487637\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 26.1207 1.73369 0.866847 0.498574i \(-0.166143\pi\)
0.866847 + 0.498574i \(0.166143\pi\)
\(228\) 0 0
\(229\) −4.02062 −0.265690 −0.132845 0.991137i \(-0.542411\pi\)
−0.132845 + 0.991137i \(0.542411\pi\)
\(230\) 0 0
\(231\) 0.325301 0.0214032
\(232\) 0 0
\(233\) −6.99507 −0.458262 −0.229131 0.973396i \(-0.573588\pi\)
−0.229131 + 0.973396i \(0.573588\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −5.28605 −0.343366
\(238\) 0 0
\(239\) −15.4037 −0.996382 −0.498191 0.867067i \(-0.666002\pi\)
−0.498191 + 0.867067i \(0.666002\pi\)
\(240\) 0 0
\(241\) 5.14987 0.331733 0.165866 0.986148i \(-0.446958\pi\)
0.165866 + 0.986148i \(0.446958\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 6.58086 0.418730
\(248\) 0 0
\(249\) 5.35259 0.339207
\(250\) 0 0
\(251\) 17.5858 1.11001 0.555003 0.831848i \(-0.312717\pi\)
0.555003 + 0.831848i \(0.312717\pi\)
\(252\) 0 0
\(253\) −1.43209 −0.0900350
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 15.3421 0.957013 0.478507 0.878084i \(-0.341178\pi\)
0.478507 + 0.878084i \(0.341178\pi\)
\(258\) 0 0
\(259\) 4.71704 0.293103
\(260\) 0 0
\(261\) 0.294814 0.0182485
\(262\) 0 0
\(263\) −21.0168 −1.29595 −0.647975 0.761661i \(-0.724384\pi\)
−0.647975 + 0.761661i \(0.724384\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −4.99507 −0.305693
\(268\) 0 0
\(269\) −5.57210 −0.339737 −0.169868 0.985467i \(-0.554334\pi\)
−0.169868 + 0.985467i \(0.554334\pi\)
\(270\) 0 0
\(271\) −5.50939 −0.334671 −0.167336 0.985900i \(-0.553516\pi\)
−0.167336 + 0.985900i \(0.553516\pi\)
\(272\) 0 0
\(273\) −0.647407 −0.0391829
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 29.5672 1.77652 0.888259 0.459342i \(-0.151915\pi\)
0.888259 + 0.459342i \(0.151915\pi\)
\(278\) 0 0
\(279\) 2.20272 0.131873
\(280\) 0 0
\(281\) −5.14111 −0.306693 −0.153346 0.988172i \(-0.549005\pi\)
−0.153346 + 0.988172i \(0.549005\pi\)
\(282\) 0 0
\(283\) −14.3509 −0.853070 −0.426535 0.904471i \(-0.640266\pi\)
−0.426535 + 0.904471i \(0.640266\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.91110 −0.289893
\(288\) 0 0
\(289\) 5.37989 0.316464
\(290\) 0 0
\(291\) −1.29481 −0.0759033
\(292\) 0 0
\(293\) 15.4516 0.902693 0.451346 0.892349i \(-0.350944\pi\)
0.451346 + 0.892349i \(0.350944\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −0.502467 −0.0291561
\(298\) 0 0
\(299\) 2.85013 0.164827
\(300\) 0 0
\(301\) 0.287894 0.0165940
\(302\) 0 0
\(303\) 4.28605 0.246227
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.12432 0.121241 0.0606207 0.998161i \(-0.480692\pi\)
0.0606207 + 0.998161i \(0.480692\pi\)
\(308\) 0 0
\(309\) 7.25556 0.412755
\(310\) 0 0
\(311\) 32.6331 1.85045 0.925226 0.379417i \(-0.123875\pi\)
0.925226 + 0.379417i \(0.123875\pi\)
\(312\) 0 0
\(313\) −18.7318 −1.05879 −0.529393 0.848377i \(-0.677580\pi\)
−0.529393 + 0.848377i \(0.677580\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −26.3452 −1.47969 −0.739846 0.672776i \(-0.765102\pi\)
−0.739846 + 0.672776i \(0.765102\pi\)
\(318\) 0 0
\(319\) 0.148134 0.00829393
\(320\) 0 0
\(321\) 10.1362 0.565746
\(322\) 0 0
\(323\) −31.1323 −1.73225
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −17.4527 −0.965137
\(328\) 0 0
\(329\) 5.23001 0.288340
\(330\) 0 0
\(331\) 24.3116 1.33629 0.668143 0.744033i \(-0.267089\pi\)
0.668143 + 0.744033i \(0.267089\pi\)
\(332\) 0 0
\(333\) −7.28605 −0.399273
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.72382 0.0939024 0.0469512 0.998897i \(-0.485049\pi\)
0.0469512 + 0.998897i \(0.485049\pi\)
\(338\) 0 0
\(339\) 15.8669 0.861772
\(340\) 0 0
\(341\) 1.10679 0.0599362
\(342\) 0 0
\(343\) 8.79235 0.474742
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.44086 −0.184715 −0.0923575 0.995726i \(-0.529440\pi\)
−0.0923575 + 0.995726i \(0.529440\pi\)
\(348\) 0 0
\(349\) 12.2059 0.653368 0.326684 0.945134i \(-0.394069\pi\)
0.326684 + 0.945134i \(0.394069\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) 16.3967 0.872707 0.436353 0.899775i \(-0.356270\pi\)
0.436353 + 0.899775i \(0.356270\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 3.06271 0.162096
\(358\) 0 0
\(359\) 0.511231 0.0269817 0.0134909 0.999909i \(-0.495706\pi\)
0.0134909 + 0.999909i \(0.495706\pi\)
\(360\) 0 0
\(361\) 24.3078 1.27936
\(362\) 0 0
\(363\) 10.7475 0.564099
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 16.3028 0.851001 0.425501 0.904958i \(-0.360098\pi\)
0.425501 + 0.904958i \(0.360098\pi\)
\(368\) 0 0
\(369\) 7.58580 0.394901
\(370\) 0 0
\(371\) −8.23630 −0.427607
\(372\) 0 0
\(373\) 32.3372 1.67435 0.837177 0.546932i \(-0.184204\pi\)
0.837177 + 0.546932i \(0.184204\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.294814 −0.0151837
\(378\) 0 0
\(379\) 9.36445 0.481019 0.240510 0.970647i \(-0.422685\pi\)
0.240510 + 0.970647i \(0.422685\pi\)
\(380\) 0 0
\(381\) 9.99124 0.511867
\(382\) 0 0
\(383\) 10.0423 0.513140 0.256570 0.966526i \(-0.417408\pi\)
0.256570 + 0.966526i \(0.417408\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.444688 −0.0226048
\(388\) 0 0
\(389\) 35.8974 1.82007 0.910035 0.414531i \(-0.136054\pi\)
0.910035 + 0.414531i \(0.136054\pi\)
\(390\) 0 0
\(391\) −13.4832 −0.681875
\(392\) 0 0
\(393\) −16.2811 −0.821274
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 39.2979 1.97231 0.986153 0.165840i \(-0.0530336\pi\)
0.986153 + 0.165840i \(0.0530336\pi\)
\(398\) 0 0
\(399\) −4.26050 −0.213292
\(400\) 0 0
\(401\) −2.69333 −0.134499 −0.0672493 0.997736i \(-0.521422\pi\)
−0.0672493 + 0.997736i \(0.521422\pi\)
\(402\) 0 0
\(403\) −2.20272 −0.109725
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.66100 −0.181469
\(408\) 0 0
\(409\) 25.8963 1.28049 0.640245 0.768171i \(-0.278833\pi\)
0.640245 + 0.768171i \(0.278833\pi\)
\(410\) 0 0
\(411\) 4.73567 0.233594
\(412\) 0 0
\(413\) −7.00110 −0.344502
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 17.4615 0.855092
\(418\) 0 0
\(419\) −19.0374 −0.930038 −0.465019 0.885301i \(-0.653953\pi\)
−0.465019 + 0.885301i \(0.653953\pi\)
\(420\) 0 0
\(421\) 22.5721 1.10010 0.550048 0.835133i \(-0.314609\pi\)
0.550048 + 0.835133i \(0.314609\pi\)
\(422\) 0 0
\(423\) −8.07840 −0.392785
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −7.40370 −0.358290
\(428\) 0 0
\(429\) 0.502467 0.0242593
\(430\) 0 0
\(431\) −9.75246 −0.469760 −0.234880 0.972024i \(-0.575470\pi\)
−0.234880 + 0.972024i \(0.575470\pi\)
\(432\) 0 0
\(433\) 8.14604 0.391474 0.195737 0.980656i \(-0.437290\pi\)
0.195737 + 0.980656i \(0.437290\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 18.7563 0.897235
\(438\) 0 0
\(439\) 0.870744 0.0415583 0.0207792 0.999784i \(-0.493385\pi\)
0.0207792 + 0.999784i \(0.493385\pi\)
\(440\) 0 0
\(441\) −6.58086 −0.313374
\(442\) 0 0
\(443\) −33.3470 −1.58436 −0.792182 0.610284i \(-0.791055\pi\)
−0.792182 + 0.610284i \(0.791055\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −5.29481 −0.250436
\(448\) 0 0
\(449\) 38.0641 1.79635 0.898177 0.439634i \(-0.144892\pi\)
0.898177 + 0.439634i \(0.144892\pi\)
\(450\) 0 0
\(451\) 3.81161 0.179482
\(452\) 0 0
\(453\) −18.5143 −0.869879
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.0938351 0.00438942 0.00219471 0.999998i \(-0.499301\pi\)
0.00219471 + 0.999998i \(0.499301\pi\)
\(458\) 0 0
\(459\) −4.73074 −0.220812
\(460\) 0 0
\(461\) −31.1617 −1.45135 −0.725673 0.688040i \(-0.758472\pi\)
−0.725673 + 0.688040i \(0.758472\pi\)
\(462\) 0 0
\(463\) 16.7748 0.779592 0.389796 0.920901i \(-0.372546\pi\)
0.389796 + 0.920901i \(0.372546\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −24.7594 −1.14573 −0.572864 0.819651i \(-0.694168\pi\)
−0.572864 + 0.819651i \(0.694168\pi\)
\(468\) 0 0
\(469\) −5.59272 −0.258248
\(470\) 0 0
\(471\) −17.5809 −0.810083
\(472\) 0 0
\(473\) −0.223441 −0.0102738
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 12.7220 0.582499
\(478\) 0 0
\(479\) 16.8130 0.768204 0.384102 0.923291i \(-0.374511\pi\)
0.384102 + 0.923291i \(0.374511\pi\)
\(480\) 0 0
\(481\) 7.28605 0.332215
\(482\) 0 0
\(483\) −1.84519 −0.0839591
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −5.78741 −0.262253 −0.131126 0.991366i \(-0.541859\pi\)
−0.131126 + 0.991366i \(0.541859\pi\)
\(488\) 0 0
\(489\) −10.0119 −0.452752
\(490\) 0 0
\(491\) −0.650602 −0.0293612 −0.0146806 0.999892i \(-0.504673\pi\)
−0.0146806 + 0.999892i \(0.504673\pi\)
\(492\) 0 0
\(493\) 1.39469 0.0628136
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.67087 0.0749487
\(498\) 0 0
\(499\) −31.5300 −1.41148 −0.705738 0.708472i \(-0.749385\pi\)
−0.705738 + 0.708472i \(0.749385\pi\)
\(500\) 0 0
\(501\) −8.69642 −0.388527
\(502\) 0 0
\(503\) −2.61135 −0.116434 −0.0582172 0.998304i \(-0.518542\pi\)
−0.0582172 + 0.998304i \(0.518542\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) −2.27037 −0.100632 −0.0503161 0.998733i \(-0.516023\pi\)
−0.0503161 + 0.998733i \(0.516023\pi\)
\(510\) 0 0
\(511\) 6.86986 0.303905
\(512\) 0 0
\(513\) 6.58086 0.290552
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −4.05913 −0.178520
\(518\) 0 0
\(519\) 18.0069 0.790416
\(520\) 0 0
\(521\) 2.87185 0.125818 0.0629090 0.998019i \(-0.479962\pi\)
0.0629090 + 0.998019i \(0.479962\pi\)
\(522\) 0 0
\(523\) −14.1469 −0.618602 −0.309301 0.950964i \(-0.600095\pi\)
−0.309301 + 0.950964i \(0.600095\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.4205 0.453924
\(528\) 0 0
\(529\) −14.8768 −0.646817
\(530\) 0 0
\(531\) 10.8141 0.469291
\(532\) 0 0
\(533\) −7.58580 −0.328577
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 2.73457 0.118005
\(538\) 0 0
\(539\) −3.30667 −0.142428
\(540\) 0 0
\(541\) 14.5504 0.625570 0.312785 0.949824i \(-0.398738\pi\)
0.312785 + 0.949824i \(0.398738\pi\)
\(542\) 0 0
\(543\) −16.8757 −0.724205
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −13.5378 −0.578834 −0.289417 0.957203i \(-0.593461\pi\)
−0.289417 + 0.957203i \(0.593461\pi\)
\(548\) 0 0
\(549\) 11.4359 0.488073
\(550\) 0 0
\(551\) −1.94013 −0.0826524
\(552\) 0 0
\(553\) −3.42223 −0.145528
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3.20098 0.135630 0.0678149 0.997698i \(-0.478397\pi\)
0.0678149 + 0.997698i \(0.478397\pi\)
\(558\) 0 0
\(559\) 0.444688 0.0188083
\(560\) 0 0
\(561\) −2.37704 −0.100359
\(562\) 0 0
\(563\) −14.0088 −0.590399 −0.295200 0.955436i \(-0.595386\pi\)
−0.295200 + 0.955436i \(0.595386\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.647407 −0.0271885
\(568\) 0 0
\(569\) 28.0571 1.17622 0.588108 0.808782i \(-0.299873\pi\)
0.588108 + 0.808782i \(0.299873\pi\)
\(570\) 0 0
\(571\) 43.4733 1.81930 0.909651 0.415373i \(-0.136349\pi\)
0.909651 + 0.415373i \(0.136349\pi\)
\(572\) 0 0
\(573\) −12.5896 −0.525939
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 41.6281 1.73300 0.866501 0.499175i \(-0.166364\pi\)
0.866501 + 0.499175i \(0.166364\pi\)
\(578\) 0 0
\(579\) −20.0728 −0.834198
\(580\) 0 0
\(581\) 3.46531 0.143765
\(582\) 0 0
\(583\) 6.39237 0.264745
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 41.2489 1.70252 0.851262 0.524741i \(-0.175838\pi\)
0.851262 + 0.524741i \(0.175838\pi\)
\(588\) 0 0
\(589\) −14.4958 −0.597289
\(590\) 0 0
\(591\) −15.6163 −0.642368
\(592\) 0 0
\(593\) −20.5416 −0.843543 −0.421771 0.906702i \(-0.638592\pi\)
−0.421771 + 0.906702i \(0.638592\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 15.7307 0.643816
\(598\) 0 0
\(599\) 14.0316 0.573315 0.286658 0.958033i \(-0.407456\pi\)
0.286658 + 0.958033i \(0.407456\pi\)
\(600\) 0 0
\(601\) −14.6610 −0.598035 −0.299017 0.954248i \(-0.596659\pi\)
−0.299017 + 0.954248i \(0.596659\pi\)
\(602\) 0 0
\(603\) 8.63864 0.351793
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −21.8875 −0.888388 −0.444194 0.895931i \(-0.646510\pi\)
−0.444194 + 0.895931i \(0.646510\pi\)
\(608\) 0 0
\(609\) 0.190865 0.00773423
\(610\) 0 0
\(611\) 8.07840 0.326817
\(612\) 0 0
\(613\) 24.0099 0.969749 0.484875 0.874584i \(-0.338865\pi\)
0.484875 + 0.874584i \(0.338865\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −2.21468 −0.0891595 −0.0445798 0.999006i \(-0.514195\pi\)
−0.0445798 + 0.999006i \(0.514195\pi\)
\(618\) 0 0
\(619\) 12.4348 0.499798 0.249899 0.968272i \(-0.419603\pi\)
0.249899 + 0.968272i \(0.419603\pi\)
\(620\) 0 0
\(621\) 2.85013 0.114372
\(622\) 0 0
\(623\) −3.23384 −0.129561
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 3.30667 0.132056
\(628\) 0 0
\(629\) −34.4684 −1.37434
\(630\) 0 0
\(631\) 26.4684 1.05369 0.526845 0.849961i \(-0.323375\pi\)
0.526845 + 0.849961i \(0.323375\pi\)
\(632\) 0 0
\(633\) −6.85013 −0.272268
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 6.58086 0.260743
\(638\) 0 0
\(639\) −2.58086 −0.102097
\(640\) 0 0
\(641\) −6.44852 −0.254701 −0.127351 0.991858i \(-0.540647\pi\)
−0.127351 + 0.991858i \(0.540647\pi\)
\(642\) 0 0
\(643\) 2.01863 0.0796071 0.0398035 0.999208i \(-0.487327\pi\)
0.0398035 + 0.999208i \(0.487327\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.142954 −0.00562012 −0.00281006 0.999996i \(-0.500894\pi\)
−0.00281006 + 0.999996i \(0.500894\pi\)
\(648\) 0 0
\(649\) 5.43371 0.213292
\(650\) 0 0
\(651\) 1.42606 0.0558915
\(652\) 0 0
\(653\) 22.1823 0.868062 0.434031 0.900898i \(-0.357091\pi\)
0.434031 + 0.900898i \(0.357091\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −10.6114 −0.413988
\(658\) 0 0
\(659\) 28.4989 1.11016 0.555079 0.831797i \(-0.312688\pi\)
0.555079 + 0.831797i \(0.312688\pi\)
\(660\) 0 0
\(661\) −21.8680 −0.850567 −0.425284 0.905060i \(-0.639826\pi\)
−0.425284 + 0.905060i \(0.639826\pi\)
\(662\) 0 0
\(663\) 4.73074 0.183727
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.840257 −0.0325349
\(668\) 0 0
\(669\) −1.15974 −0.0448382
\(670\) 0 0
\(671\) 5.74618 0.221829
\(672\) 0 0
\(673\) 10.0679 0.388089 0.194044 0.980993i \(-0.437839\pi\)
0.194044 + 0.980993i \(0.437839\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 27.7003 1.06461 0.532304 0.846554i \(-0.321326\pi\)
0.532304 + 0.846554i \(0.321326\pi\)
\(678\) 0 0
\(679\) −0.838272 −0.0321699
\(680\) 0 0
\(681\) −26.1207 −1.00095
\(682\) 0 0
\(683\) −7.73631 −0.296022 −0.148011 0.988986i \(-0.547287\pi\)
−0.148011 + 0.988986i \(0.547287\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 4.02062 0.153396
\(688\) 0 0
\(689\) −12.7220 −0.484669
\(690\) 0 0
\(691\) 46.7115 1.77699 0.888494 0.458888i \(-0.151752\pi\)
0.888494 + 0.458888i \(0.151752\pi\)
\(692\) 0 0
\(693\) −0.325301 −0.0123572
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 35.8864 1.35930
\(698\) 0 0
\(699\) 6.99507 0.264578
\(700\) 0 0
\(701\) −39.7670 −1.50198 −0.750990 0.660313i \(-0.770423\pi\)
−0.750990 + 0.660313i \(0.770423\pi\)
\(702\) 0 0
\(703\) 47.9485 1.80841
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.77482 0.104358
\(708\) 0 0
\(709\) −35.5988 −1.33694 −0.668470 0.743739i \(-0.733050\pi\)
−0.668470 + 0.743739i \(0.733050\pi\)
\(710\) 0 0
\(711\) 5.28605 0.198242
\(712\) 0 0
\(713\) −6.27803 −0.235114
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 15.4037 0.575262
\(718\) 0 0
\(719\) 38.6995 1.44325 0.721624 0.692285i \(-0.243396\pi\)
0.721624 + 0.692285i \(0.243396\pi\)
\(720\) 0 0
\(721\) 4.69730 0.174937
\(722\) 0 0
\(723\) −5.14987 −0.191526
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 19.8788 0.737263 0.368631 0.929576i \(-0.379826\pi\)
0.368631 + 0.929576i \(0.379826\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −2.10370 −0.0778083
\(732\) 0 0
\(733\) 14.2693 0.527047 0.263524 0.964653i \(-0.415115\pi\)
0.263524 + 0.964653i \(0.415115\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.34063 0.159889
\(738\) 0 0
\(739\) −12.3801 −0.455410 −0.227705 0.973730i \(-0.573122\pi\)
−0.227705 + 0.973730i \(0.573122\pi\)
\(740\) 0 0
\(741\) −6.58086 −0.241754
\(742\) 0 0
\(743\) 4.23321 0.155301 0.0776506 0.996981i \(-0.475258\pi\)
0.0776506 + 0.996981i \(0.475258\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −5.35259 −0.195841
\(748\) 0 0
\(749\) 6.56223 0.239779
\(750\) 0 0
\(751\) −20.6418 −0.753231 −0.376616 0.926370i \(-0.622912\pi\)
−0.376616 + 0.926370i \(0.622912\pi\)
\(752\) 0 0
\(753\) −17.5858 −0.640862
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −28.7033 −1.04324 −0.521620 0.853178i \(-0.674672\pi\)
−0.521620 + 0.853178i \(0.674672\pi\)
\(758\) 0 0
\(759\) 1.43209 0.0519817
\(760\) 0 0
\(761\) −6.53963 −0.237061 −0.118531 0.992950i \(-0.537818\pi\)
−0.118531 + 0.992950i \(0.537818\pi\)
\(762\) 0 0
\(763\) −11.2990 −0.409052
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −10.8141 −0.390473
\(768\) 0 0
\(769\) 7.58690 0.273591 0.136795 0.990599i \(-0.456320\pi\)
0.136795 + 0.990599i \(0.456320\pi\)
\(770\) 0 0
\(771\) −15.3421 −0.552532
\(772\) 0 0
\(773\) 20.7151 0.745069 0.372534 0.928018i \(-0.378489\pi\)
0.372534 + 0.928018i \(0.378489\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −4.71704 −0.169223
\(778\) 0 0
\(779\) −49.9211 −1.78861
\(780\) 0 0
\(781\) −1.29680 −0.0464031
\(782\) 0 0
\(783\) −0.294814 −0.0105358
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −52.0486 −1.85533 −0.927667 0.373410i \(-0.878189\pi\)
−0.927667 + 0.373410i \(0.878189\pi\)
\(788\) 0 0
\(789\) 21.0168 0.748217
\(790\) 0 0
\(791\) 10.2724 0.365243
\(792\) 0 0
\(793\) −11.4359 −0.406102
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −19.1796 −0.679377 −0.339689 0.940538i \(-0.610322\pi\)
−0.339689 + 0.940538i \(0.610322\pi\)
\(798\) 0 0
\(799\) −38.2168 −1.35201
\(800\) 0 0
\(801\) 4.99507 0.176492
\(802\) 0 0
\(803\) −5.33186 −0.188157
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 5.57210 0.196147
\(808\) 0 0
\(809\) 42.4803 1.49353 0.746763 0.665090i \(-0.231607\pi\)
0.746763 + 0.665090i \(0.231607\pi\)
\(810\) 0 0
\(811\) −21.5094 −0.755297 −0.377648 0.925949i \(-0.623267\pi\)
−0.377648 + 0.925949i \(0.623267\pi\)
\(812\) 0 0
\(813\) 5.50939 0.193223
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 2.92643 0.102383
\(818\) 0 0
\(819\) 0.647407 0.0226222
\(820\) 0 0
\(821\) 21.3067 0.743608 0.371804 0.928311i \(-0.378739\pi\)
0.371804 + 0.928311i \(0.378739\pi\)
\(822\) 0 0
\(823\) −7.24680 −0.252608 −0.126304 0.991992i \(-0.540311\pi\)
−0.126304 + 0.991992i \(0.540311\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 43.7076 1.51986 0.759932 0.650003i \(-0.225232\pi\)
0.759932 + 0.650003i \(0.225232\pi\)
\(828\) 0 0
\(829\) −24.3665 −0.846285 −0.423142 0.906063i \(-0.639073\pi\)
−0.423142 + 0.906063i \(0.639073\pi\)
\(830\) 0 0
\(831\) −29.5672 −1.02567
\(832\) 0 0
\(833\) −31.1323 −1.07867
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −2.20272 −0.0761371
\(838\) 0 0
\(839\) −18.0553 −0.623338 −0.311669 0.950191i \(-0.600888\pi\)
−0.311669 + 0.950191i \(0.600888\pi\)
\(840\) 0 0
\(841\) −28.9131 −0.997003
\(842\) 0 0
\(843\) 5.14111 0.177069
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 6.95802 0.239081
\(848\) 0 0
\(849\) 14.3509 0.492520
\(850\) 0 0
\(851\) 20.7662 0.711855
\(852\) 0 0
\(853\) 6.28679 0.215256 0.107628 0.994191i \(-0.465675\pi\)
0.107628 + 0.994191i \(0.465675\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −4.82074 −0.164673 −0.0823367 0.996605i \(-0.526238\pi\)
−0.0823367 + 0.996605i \(0.526238\pi\)
\(858\) 0 0
\(859\) 7.32420 0.249898 0.124949 0.992163i \(-0.460123\pi\)
0.124949 + 0.992163i \(0.460123\pi\)
\(860\) 0 0
\(861\) 4.91110 0.167370
\(862\) 0 0
\(863\) 14.0567 0.478495 0.239247 0.970959i \(-0.423099\pi\)
0.239247 + 0.970959i \(0.423099\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −5.37989 −0.182710
\(868\) 0 0
\(869\) 2.65607 0.0901009
\(870\) 0 0
\(871\) −8.63864 −0.292709
\(872\) 0 0
\(873\) 1.29481 0.0438228
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 12.6747 0.427994 0.213997 0.976834i \(-0.431352\pi\)
0.213997 + 0.976834i \(0.431352\pi\)
\(878\) 0 0
\(879\) −15.4516 −0.521170
\(880\) 0 0
\(881\) −27.0325 −0.910747 −0.455374 0.890300i \(-0.650494\pi\)
−0.455374 + 0.890300i \(0.650494\pi\)
\(882\) 0 0
\(883\) 8.14693 0.274166 0.137083 0.990560i \(-0.456227\pi\)
0.137083 + 0.990560i \(0.456227\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −26.4173 −0.887006 −0.443503 0.896273i \(-0.646264\pi\)
−0.443503 + 0.896273i \(0.646264\pi\)
\(888\) 0 0
\(889\) 6.46840 0.216943
\(890\) 0 0
\(891\) 0.502467 0.0168333
\(892\) 0 0
\(893\) 53.1628 1.77903
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −2.85013 −0.0951629
\(898\) 0 0
\(899\) 0.649392 0.0216585
\(900\) 0 0
\(901\) 60.1843 2.00503
\(902\) 0 0
\(903\) −0.287894 −0.00958052
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −7.12815 −0.236686 −0.118343 0.992973i \(-0.537758\pi\)
−0.118343 + 0.992973i \(0.537758\pi\)
\(908\) 0 0
\(909\) −4.28605 −0.142159
\(910\) 0 0
\(911\) 17.1911 0.569567 0.284783 0.958592i \(-0.408078\pi\)
0.284783 + 0.958592i \(0.408078\pi\)
\(912\) 0 0
\(913\) −2.68950 −0.0890095
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −10.5405 −0.348078
\(918\) 0 0
\(919\) 3.35888 0.110799 0.0553996 0.998464i \(-0.482357\pi\)
0.0553996 + 0.998464i \(0.482357\pi\)
\(920\) 0 0
\(921\) −2.12432 −0.0699988
\(922\) 0 0
\(923\) 2.58086 0.0849502
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −7.25556 −0.238304
\(928\) 0 0
\(929\) 7.75048 0.254285 0.127142 0.991884i \(-0.459419\pi\)
0.127142 + 0.991884i \(0.459419\pi\)
\(930\) 0 0
\(931\) 43.3078 1.41935
\(932\) 0 0
\(933\) −32.6331 −1.06836
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 5.75320 0.187949 0.0939744 0.995575i \(-0.470043\pi\)
0.0939744 + 0.995575i \(0.470043\pi\)
\(938\) 0 0
\(939\) 18.7318 0.611291
\(940\) 0 0
\(941\) 1.43209 0.0466850 0.0233425 0.999728i \(-0.492569\pi\)
0.0233425 + 0.999728i \(0.492569\pi\)
\(942\) 0 0
\(943\) −21.6205 −0.704060
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −46.6830 −1.51699 −0.758496 0.651677i \(-0.774066\pi\)
−0.758496 + 0.651677i \(0.774066\pi\)
\(948\) 0 0
\(949\) 10.6114 0.344459
\(950\) 0 0
\(951\) 26.3452 0.854301
\(952\) 0 0
\(953\) −13.1145 −0.424819 −0.212409 0.977181i \(-0.568131\pi\)
−0.212409 + 0.977181i \(0.568131\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −0.148134 −0.00478850
\(958\) 0 0
\(959\) 3.06591 0.0990033
\(960\) 0 0
\(961\) −26.1480 −0.843485
\(962\) 0 0
\(963\) −10.1362 −0.326634
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 23.4765 0.754954 0.377477 0.926019i \(-0.376792\pi\)
0.377477 + 0.926019i \(0.376792\pi\)
\(968\) 0 0
\(969\) 31.1323 1.00012
\(970\) 0 0
\(971\) 57.3687 1.84105 0.920525 0.390683i \(-0.127761\pi\)
0.920525 + 0.390683i \(0.127761\pi\)
\(972\) 0 0
\(973\) 11.3047 0.362411
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −52.2961 −1.67310 −0.836550 0.547891i \(-0.815431\pi\)
−0.836550 + 0.547891i \(0.815431\pi\)
\(978\) 0 0
\(979\) 2.50986 0.0802154
\(980\) 0 0
\(981\) 17.4527 0.557222
\(982\) 0 0
\(983\) −17.5074 −0.558399 −0.279200 0.960233i \(-0.590069\pi\)
−0.279200 + 0.960233i \(0.590069\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −5.23001 −0.166473
\(988\) 0 0
\(989\) 1.26742 0.0403015
\(990\) 0 0
\(991\) −49.4527 −1.57092 −0.785459 0.618914i \(-0.787573\pi\)
−0.785459 + 0.618914i \(0.787573\pi\)
\(992\) 0 0
\(993\) −24.3116 −0.771505
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 40.0493 1.26837 0.634186 0.773180i \(-0.281335\pi\)
0.634186 + 0.773180i \(0.281335\pi\)
\(998\) 0 0
\(999\) 7.28605 0.230520
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.bu.1.3 4
5.4 even 2 7800.2.a.bx.1.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7800.2.a.bu.1.3 4 1.1 even 1 trivial
7800.2.a.bx.1.2 yes 4 5.4 even 2