Properties

Label 7800.2.a.bt.1.4
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $1$
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: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.30056.1
Defining polynomial: \(x^{4} - 11 x^{2} + 26\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 1560)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.85431\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.65573 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.65573 q^{7} +1.00000 q^{9} -2.94848 q^{11} +1.00000 q^{13} -1.46738 q^{17} -1.65573 q^{21} -0.532621 q^{23} -1.00000 q^{27} +5.70861 q^{29} +2.94848 q^{33} -8.77883 q^{37} -1.00000 q^{39} +1.23987 q^{41} +1.70861 q^{43} -2.70725 q^{47} -4.25857 q^{49} +1.46738 q^{51} +8.77883 q^{53} -3.83035 q^{59} -0.241231 q^{61} +1.65573 q^{63} -2.58550 q^{67} +0.532621 q^{69} -2.55132 q^{71} -0.188347 q^{73} -4.88187 q^{77} -11.0729 q^{79} +1.00000 q^{81} +7.91566 q^{83} -5.70861 q^{87} +15.9685 q^{89} +1.65573 q^{91} -16.8641 q^{97} -2.94848 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{3} - 7q^{7} + 4q^{9} + O(q^{10}) \) \( 4q - 4q^{3} - 7q^{7} + 4q^{9} + q^{11} + 4q^{13} - 3q^{17} + 7q^{21} - 5q^{23} - 4q^{27} + 8q^{29} - q^{33} - 5q^{37} - 4q^{39} + 7q^{41} - 8q^{43} - 10q^{47} + 9q^{49} + 3q^{51} + 5q^{53} + 2q^{59} + 11q^{61} - 7q^{63} - 12q^{67} + 5q^{69} + 15q^{71} + 10q^{73} - 15q^{77} - q^{79} + 4q^{81} - 22q^{83} - 8q^{87} + 9q^{89} - 7q^{91} - q^{97} + q^{99} + O(q^{100}) \)

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
\(7\) 1.65573 0.625806 0.312903 0.949785i \(-0.398699\pi\)
0.312903 + 0.949785i \(0.398699\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −2.94848 −0.889000 −0.444500 0.895779i \(-0.646619\pi\)
−0.444500 + 0.895779i \(0.646619\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.46738 −0.355892 −0.177946 0.984040i \(-0.556945\pi\)
−0.177946 + 0.984040i \(0.556945\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) −1.65573 −0.361309
\(22\) 0 0
\(23\) −0.532621 −0.111059 −0.0555296 0.998457i \(-0.517685\pi\)
−0.0555296 + 0.998457i \(0.517685\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 5.70861 1.06006 0.530031 0.847978i \(-0.322180\pi\)
0.530031 + 0.847978i \(0.322180\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 2.94848 0.513264
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.77883 −1.44323 −0.721616 0.692294i \(-0.756600\pi\)
−0.721616 + 0.692294i \(0.756600\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 1.23987 0.193635 0.0968175 0.995302i \(-0.469134\pi\)
0.0968175 + 0.995302i \(0.469134\pi\)
\(42\) 0 0
\(43\) 1.70861 0.260561 0.130280 0.991477i \(-0.458412\pi\)
0.130280 + 0.991477i \(0.458412\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.70725 −0.394893 −0.197446 0.980314i \(-0.563265\pi\)
−0.197446 + 0.980314i \(0.563265\pi\)
\(48\) 0 0
\(49\) −4.25857 −0.608367
\(50\) 0 0
\(51\) 1.46738 0.205474
\(52\) 0 0
\(53\) 8.77883 1.20587 0.602933 0.797792i \(-0.293999\pi\)
0.602933 + 0.797792i \(0.293999\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.83035 −0.498670 −0.249335 0.968417i \(-0.580212\pi\)
−0.249335 + 0.968417i \(0.580212\pi\)
\(60\) 0 0
\(61\) −0.241231 −0.0308865 −0.0154432 0.999881i \(-0.504916\pi\)
−0.0154432 + 0.999881i \(0.504916\pi\)
\(62\) 0 0
\(63\) 1.65573 0.208602
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.58550 −0.315870 −0.157935 0.987450i \(-0.550484\pi\)
−0.157935 + 0.987450i \(0.550484\pi\)
\(68\) 0 0
\(69\) 0.532621 0.0641200
\(70\) 0 0
\(71\) −2.55132 −0.302786 −0.151393 0.988474i \(-0.548376\pi\)
−0.151393 + 0.988474i \(0.548376\pi\)
\(72\) 0 0
\(73\) −0.188347 −0.0220444 −0.0110222 0.999939i \(-0.503509\pi\)
−0.0110222 + 0.999939i \(0.503509\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.88187 −0.556341
\(78\) 0 0
\(79\) −11.0729 −1.24580 −0.622902 0.782300i \(-0.714046\pi\)
−0.622902 + 0.782300i \(0.714046\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 7.91566 0.868856 0.434428 0.900706i \(-0.356950\pi\)
0.434428 + 0.900706i \(0.356950\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −5.70861 −0.612027
\(88\) 0 0
\(89\) 15.9685 1.69266 0.846331 0.532657i \(-0.178807\pi\)
0.846331 + 0.532657i \(0.178807\pi\)
\(90\) 0 0
\(91\) 1.65573 0.173567
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −16.8641 −1.71229 −0.856147 0.516733i \(-0.827148\pi\)
−0.856147 + 0.516733i \(0.827148\pi\)
\(98\) 0 0
\(99\) −2.94848 −0.296333
\(100\) 0 0
\(101\) −4.64337 −0.462032 −0.231016 0.972950i \(-0.574205\pi\)
−0.231016 + 0.972950i \(0.574205\pi\)
\(102\) 0 0
\(103\) −9.66071 −0.951898 −0.475949 0.879473i \(-0.657895\pi\)
−0.475949 + 0.879473i \(0.657895\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −11.9498 −1.15523 −0.577617 0.816308i \(-0.696017\pi\)
−0.577617 + 0.816308i \(0.696017\pi\)
\(108\) 0 0
\(109\) 11.8970 1.13952 0.569761 0.821810i \(-0.307036\pi\)
0.569761 + 0.821810i \(0.307036\pi\)
\(110\) 0 0
\(111\) 8.77883 0.833250
\(112\) 0 0
\(113\) −2.37669 −0.223581 −0.111790 0.993732i \(-0.535659\pi\)
−0.111790 + 0.993732i \(0.535659\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) −2.42958 −0.222719
\(120\) 0 0
\(121\) −2.30647 −0.209679
\(122\) 0 0
\(123\) −1.23987 −0.111795
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −2.87689 −0.255283 −0.127642 0.991820i \(-0.540741\pi\)
−0.127642 + 0.991820i \(0.540741\pi\)
\(128\) 0 0
\(129\) −1.70861 −0.150435
\(130\) 0 0
\(131\) 19.3968 1.69470 0.847351 0.531033i \(-0.178196\pi\)
0.847351 + 0.531033i \(0.178196\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −0.357994 −0.0305855 −0.0152927 0.999883i \(-0.504868\pi\)
−0.0152927 + 0.999883i \(0.504868\pi\)
\(138\) 0 0
\(139\) −4.88187 −0.414075 −0.207038 0.978333i \(-0.566382\pi\)
−0.207038 + 0.978333i \(0.566382\pi\)
\(140\) 0 0
\(141\) 2.70725 0.227991
\(142\) 0 0
\(143\) −2.94848 −0.246564
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 4.25857 0.351241
\(148\) 0 0
\(149\) 20.6092 1.68837 0.844185 0.536052i \(-0.180085\pi\)
0.844185 + 0.536052i \(0.180085\pi\)
\(150\) 0 0
\(151\) −3.89423 −0.316908 −0.158454 0.987366i \(-0.550651\pi\)
−0.158454 + 0.987366i \(0.550651\pi\)
\(152\) 0 0
\(153\) −1.46738 −0.118631
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −9.22887 −0.736544 −0.368272 0.929718i \(-0.620051\pi\)
−0.368272 + 0.929718i \(0.620051\pi\)
\(158\) 0 0
\(159\) −8.77883 −0.696207
\(160\) 0 0
\(161\) −0.881875 −0.0695015
\(162\) 0 0
\(163\) −16.5700 −1.29786 −0.648932 0.760846i \(-0.724784\pi\)
−0.648932 + 0.760846i \(0.724784\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −15.5390 −1.20244 −0.601221 0.799083i \(-0.705319\pi\)
−0.601221 + 0.799083i \(0.705319\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3.17101 −0.241087 −0.120544 0.992708i \(-0.538464\pi\)
−0.120544 + 0.992708i \(0.538464\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 3.83035 0.287907
\(178\) 0 0
\(179\) 2.29411 0.171470 0.0857351 0.996318i \(-0.472676\pi\)
0.0857351 + 0.996318i \(0.472676\pi\)
\(180\) 0 0
\(181\) −17.6105 −1.30898 −0.654491 0.756070i \(-0.727117\pi\)
−0.654491 + 0.756070i \(0.727117\pi\)
\(182\) 0 0
\(183\) 0.241231 0.0178323
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 4.32654 0.316388
\(188\) 0 0
\(189\) −1.65573 −0.120436
\(190\) 0 0
\(191\) −0.105767 −0.00765304 −0.00382652 0.999993i \(-0.501218\pi\)
−0.00382652 + 0.999993i \(0.501218\pi\)
\(192\) 0 0
\(193\) 3.27903 0.236030 0.118015 0.993012i \(-0.462347\pi\)
0.118015 + 0.993012i \(0.462347\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.01598 −0.428621 −0.214310 0.976766i \(-0.568750\pi\)
−0.214310 + 0.976766i \(0.568750\pi\)
\(198\) 0 0
\(199\) −5.33192 −0.377969 −0.188985 0.981980i \(-0.560520\pi\)
−0.188985 + 0.981980i \(0.560520\pi\)
\(200\) 0 0
\(201\) 2.58550 0.182367
\(202\) 0 0
\(203\) 9.45190 0.663393
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.532621 −0.0370197
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 14.5777 1.00357 0.501786 0.864992i \(-0.332676\pi\)
0.501786 + 0.864992i \(0.332676\pi\)
\(212\) 0 0
\(213\) 2.55132 0.174814
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0.188347 0.0127273
\(220\) 0 0
\(221\) −1.46738 −0.0987066
\(222\) 0 0
\(223\) −19.8518 −1.32937 −0.664687 0.747122i \(-0.731435\pi\)
−0.664687 + 0.747122i \(0.731435\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.85042 0.454678 0.227339 0.973816i \(-0.426997\pi\)
0.227339 + 0.973816i \(0.426997\pi\)
\(228\) 0 0
\(229\) 18.0374 1.19195 0.595973 0.803005i \(-0.296767\pi\)
0.595973 + 0.803005i \(0.296767\pi\)
\(230\) 0 0
\(231\) 4.88187 0.321204
\(232\) 0 0
\(233\) −14.4049 −0.943694 −0.471847 0.881680i \(-0.656413\pi\)
−0.471847 + 0.881680i \(0.656413\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 11.0729 0.719265
\(238\) 0 0
\(239\) 21.7350 1.40592 0.702961 0.711229i \(-0.251861\pi\)
0.702961 + 0.711229i \(0.251861\pi\)
\(240\) 0 0
\(241\) 17.5604 1.13116 0.565582 0.824692i \(-0.308652\pi\)
0.565582 + 0.824692i \(0.308652\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −7.91566 −0.501634
\(250\) 0 0
\(251\) −22.7082 −1.43333 −0.716665 0.697418i \(-0.754332\pi\)
−0.716665 + 0.697418i \(0.754332\pi\)
\(252\) 0 0
\(253\) 1.57042 0.0987316
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.58278 −0.410623 −0.205311 0.978697i \(-0.565821\pi\)
−0.205311 + 0.978697i \(0.565821\pi\)
\(258\) 0 0
\(259\) −14.5353 −0.903182
\(260\) 0 0
\(261\) 5.70861 0.353354
\(262\) 0 0
\(263\) −4.24349 −0.261665 −0.130832 0.991405i \(-0.541765\pi\)
−0.130832 + 0.991405i \(0.541765\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −15.9685 −0.977259
\(268\) 0 0
\(269\) 12.6434 0.770880 0.385440 0.922733i \(-0.374050\pi\)
0.385440 + 0.922733i \(0.374050\pi\)
\(270\) 0 0
\(271\) −23.7665 −1.44371 −0.721855 0.692044i \(-0.756710\pi\)
−0.721855 + 0.692044i \(0.756710\pi\)
\(272\) 0 0
\(273\) −1.65573 −0.100209
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −17.8765 −1.07409 −0.537047 0.843552i \(-0.680460\pi\)
−0.537047 + 0.843552i \(0.680460\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8.39540 0.500827 0.250414 0.968139i \(-0.419433\pi\)
0.250414 + 0.968139i \(0.419433\pi\)
\(282\) 0 0
\(283\) 13.9344 0.828312 0.414156 0.910206i \(-0.364077\pi\)
0.414156 + 0.910206i \(0.364077\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.05288 0.121178
\(288\) 0 0
\(289\) −14.8468 −0.873341
\(290\) 0 0
\(291\) 16.8641 0.988593
\(292\) 0 0
\(293\) −11.4085 −0.666491 −0.333245 0.942840i \(-0.608144\pi\)
−0.333245 + 0.942840i \(0.608144\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 2.94848 0.171088
\(298\) 0 0
\(299\) −0.532621 −0.0308023
\(300\) 0 0
\(301\) 2.82899 0.163060
\(302\) 0 0
\(303\) 4.64337 0.266755
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.50790 0.143134 0.0715668 0.997436i \(-0.477200\pi\)
0.0715668 + 0.997436i \(0.477200\pi\)
\(308\) 0 0
\(309\) 9.66071 0.549578
\(310\) 0 0
\(311\) −6.96220 −0.394790 −0.197395 0.980324i \(-0.563248\pi\)
−0.197395 + 0.980324i \(0.563248\pi\)
\(312\) 0 0
\(313\) 16.0880 0.909349 0.454675 0.890658i \(-0.349756\pi\)
0.454675 + 0.890658i \(0.349756\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.25263 −0.0703545 −0.0351772 0.999381i \(-0.511200\pi\)
−0.0351772 + 0.999381i \(0.511200\pi\)
\(318\) 0 0
\(319\) −16.8317 −0.942395
\(320\) 0 0
\(321\) 11.9498 0.666975
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −11.8970 −0.657903
\(328\) 0 0
\(329\) −4.48246 −0.247126
\(330\) 0 0
\(331\) −8.24349 −0.453103 −0.226552 0.973999i \(-0.572745\pi\)
−0.226552 + 0.973999i \(0.572745\pi\)
\(332\) 0 0
\(333\) −8.77883 −0.481077
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 22.1227 1.20510 0.602550 0.798081i \(-0.294151\pi\)
0.602550 + 0.798081i \(0.294151\pi\)
\(338\) 0 0
\(339\) 2.37669 0.129084
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −18.6411 −1.00653
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −18.4395 −0.989886 −0.494943 0.868925i \(-0.664811\pi\)
−0.494943 + 0.868925i \(0.664811\pi\)
\(348\) 0 0
\(349\) 19.6634 1.05256 0.526280 0.850312i \(-0.323586\pi\)
0.526280 + 0.850312i \(0.323586\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 1.18971 0.0633219 0.0316609 0.999499i \(-0.489920\pi\)
0.0316609 + 0.999499i \(0.489920\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 2.42958 0.128587
\(358\) 0 0
\(359\) 4.98090 0.262882 0.131441 0.991324i \(-0.458040\pi\)
0.131441 + 0.991324i \(0.458040\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) 2.30647 0.121058
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −10.7160 −0.559370 −0.279685 0.960092i \(-0.590230\pi\)
−0.279685 + 0.960092i \(0.590230\pi\)
\(368\) 0 0
\(369\) 1.23987 0.0645450
\(370\) 0 0
\(371\) 14.5353 0.754638
\(372\) 0 0
\(373\) −22.8691 −1.18412 −0.592059 0.805895i \(-0.701685\pi\)
−0.592059 + 0.805895i \(0.701685\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.70861 0.294008
\(378\) 0 0
\(379\) 26.5325 1.36289 0.681443 0.731871i \(-0.261353\pi\)
0.681443 + 0.731871i \(0.261353\pi\)
\(380\) 0 0
\(381\) 2.87689 0.147388
\(382\) 0 0
\(383\) −38.3325 −1.95870 −0.979349 0.202176i \(-0.935199\pi\)
−0.979349 + 0.202176i \(0.935199\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.70861 0.0868535
\(388\) 0 0
\(389\) −7.87650 −0.399354 −0.199677 0.979862i \(-0.563989\pi\)
−0.199677 + 0.979862i \(0.563989\pi\)
\(390\) 0 0
\(391\) 0.781557 0.0395250
\(392\) 0 0
\(393\) −19.3968 −0.978437
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0.673065 0.0337802 0.0168901 0.999857i \(-0.494623\pi\)
0.0168901 + 0.999857i \(0.494623\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −26.3981 −1.31826 −0.659130 0.752029i \(-0.729075\pi\)
−0.659130 + 0.752029i \(0.729075\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 25.8842 1.28303
\(408\) 0 0
\(409\) −33.4646 −1.65472 −0.827359 0.561674i \(-0.810157\pi\)
−0.827359 + 0.561674i \(0.810157\pi\)
\(410\) 0 0
\(411\) 0.357994 0.0176585
\(412\) 0 0
\(413\) −6.34202 −0.312070
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 4.88187 0.239066
\(418\) 0 0
\(419\) −32.3068 −1.57829 −0.789145 0.614207i \(-0.789476\pi\)
−0.789145 + 0.614207i \(0.789476\pi\)
\(420\) 0 0
\(421\) 2.33929 0.114010 0.0570051 0.998374i \(-0.481845\pi\)
0.0570051 + 0.998374i \(0.481845\pi\)
\(422\) 0 0
\(423\) −2.70725 −0.131631
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.399413 −0.0193289
\(428\) 0 0
\(429\) 2.94848 0.142354
\(430\) 0 0
\(431\) −20.5138 −0.988117 −0.494059 0.869429i \(-0.664487\pi\)
−0.494059 + 0.869429i \(0.664487\pi\)
\(432\) 0 0
\(433\) 24.8514 1.19428 0.597141 0.802137i \(-0.296303\pi\)
0.597141 + 0.802137i \(0.296303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −8.18337 −0.390571 −0.195285 0.980746i \(-0.562563\pi\)
−0.195285 + 0.980746i \(0.562563\pi\)
\(440\) 0 0
\(441\) −4.25857 −0.202789
\(442\) 0 0
\(443\) −26.1961 −1.24461 −0.622306 0.782774i \(-0.713804\pi\)
−0.622306 + 0.782774i \(0.713804\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −20.6092 −0.974781
\(448\) 0 0
\(449\) −11.8034 −0.557036 −0.278518 0.960431i \(-0.589843\pi\)
−0.278518 + 0.960431i \(0.589843\pi\)
\(450\) 0 0
\(451\) −3.65573 −0.172141
\(452\) 0 0
\(453\) 3.89423 0.182967
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.86454 −0.0872193 −0.0436097 0.999049i \(-0.513886\pi\)
−0.0436097 + 0.999049i \(0.513886\pi\)
\(458\) 0 0
\(459\) 1.46738 0.0684914
\(460\) 0 0
\(461\) 7.42822 0.345967 0.172983 0.984925i \(-0.444659\pi\)
0.172983 + 0.984925i \(0.444659\pi\)
\(462\) 0 0
\(463\) −29.0829 −1.35160 −0.675799 0.737086i \(-0.736201\pi\)
−0.675799 + 0.737086i \(0.736201\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −10.5727 −0.489248 −0.244624 0.969618i \(-0.578665\pi\)
−0.244624 + 0.969618i \(0.578665\pi\)
\(468\) 0 0
\(469\) −4.28089 −0.197673
\(470\) 0 0
\(471\) 9.22887 0.425244
\(472\) 0 0
\(473\) −5.03780 −0.231638
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 8.77883 0.401955
\(478\) 0 0
\(479\) −19.6166 −0.896304 −0.448152 0.893957i \(-0.647918\pi\)
−0.448152 + 0.893957i \(0.647918\pi\)
\(480\) 0 0
\(481\) −8.77883 −0.400280
\(482\) 0 0
\(483\) 0.881875 0.0401267
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −0.235782 −0.0106843 −0.00534215 0.999986i \(-0.501700\pi\)
−0.00534215 + 0.999986i \(0.501700\pi\)
\(488\) 0 0
\(489\) 16.5700 0.749322
\(490\) 0 0
\(491\) −23.6183 −1.06588 −0.532938 0.846154i \(-0.678912\pi\)
−0.532938 + 0.846154i \(0.678912\pi\)
\(492\) 0 0
\(493\) −8.37669 −0.377267
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.22429 −0.189485
\(498\) 0 0
\(499\) −18.2737 −0.818041 −0.409021 0.912525i \(-0.634130\pi\)
−0.409021 + 0.912525i \(0.634130\pi\)
\(500\) 0 0
\(501\) 15.5390 0.694230
\(502\) 0 0
\(503\) 27.8722 1.24276 0.621381 0.783509i \(-0.286572\pi\)
0.621381 + 0.783509i \(0.286572\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) 17.2878 0.766267 0.383134 0.923693i \(-0.374845\pi\)
0.383134 + 0.923693i \(0.374845\pi\)
\(510\) 0 0
\(511\) −0.311852 −0.0137955
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 7.98226 0.351060
\(518\) 0 0
\(519\) 3.17101 0.139192
\(520\) 0 0
\(521\) 26.9474 1.18059 0.590294 0.807188i \(-0.299012\pi\)
0.590294 + 0.807188i \(0.299012\pi\)
\(522\) 0 0
\(523\) −0.150946 −0.00660040 −0.00330020 0.999995i \(-0.501050\pi\)
−0.00330020 + 0.999995i \(0.501050\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −22.7163 −0.987666
\(530\) 0 0
\(531\) −3.83035 −0.166223
\(532\) 0 0
\(533\) 1.23987 0.0537047
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −2.29411 −0.0989983
\(538\) 0 0
\(539\) 12.5563 0.540838
\(540\) 0 0
\(541\) −1.97256 −0.0848069 −0.0424035 0.999101i \(-0.513501\pi\)
−0.0424035 + 0.999101i \(0.513501\pi\)
\(542\) 0 0
\(543\) 17.6105 0.755741
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 21.6128 0.924097 0.462048 0.886855i \(-0.347115\pi\)
0.462048 + 0.886855i \(0.347115\pi\)
\(548\) 0 0
\(549\) −0.241231 −0.0102955
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −18.3338 −0.779631
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −36.1619 −1.53223 −0.766114 0.642705i \(-0.777812\pi\)
−0.766114 + 0.642705i \(0.777812\pi\)
\(558\) 0 0
\(559\) 1.70861 0.0722665
\(560\) 0 0
\(561\) −4.32654 −0.182666
\(562\) 0 0
\(563\) 9.05248 0.381517 0.190758 0.981637i \(-0.438905\pi\)
0.190758 + 0.981637i \(0.438905\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1.65573 0.0695340
\(568\) 0 0
\(569\) 17.7255 0.743094 0.371547 0.928414i \(-0.378828\pi\)
0.371547 + 0.928414i \(0.378828\pi\)
\(570\) 0 0
\(571\) −17.4095 −0.728566 −0.364283 0.931288i \(-0.618686\pi\)
−0.364283 + 0.931288i \(0.618686\pi\)
\(572\) 0 0
\(573\) 0.105767 0.00441848
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −27.0729 −1.12706 −0.563531 0.826095i \(-0.690557\pi\)
−0.563531 + 0.826095i \(0.690557\pi\)
\(578\) 0 0
\(579\) −3.27903 −0.136272
\(580\) 0 0
\(581\) 13.1062 0.543735
\(582\) 0 0
\(583\) −25.8842 −1.07201
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 21.5417 0.889121 0.444560 0.895749i \(-0.353360\pi\)
0.444560 + 0.895749i \(0.353360\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 6.01598 0.247464
\(592\) 0 0
\(593\) 0.542087 0.0222608 0.0111304 0.999938i \(-0.496457\pi\)
0.0111304 + 0.999938i \(0.496457\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 5.33192 0.218221
\(598\) 0 0
\(599\) −4.72595 −0.193097 −0.0965485 0.995328i \(-0.530780\pi\)
−0.0965485 + 0.995328i \(0.530780\pi\)
\(600\) 0 0
\(601\) −2.47203 −0.100836 −0.0504182 0.998728i \(-0.516055\pi\)
−0.0504182 + 0.998728i \(0.516055\pi\)
\(602\) 0 0
\(603\) −2.58550 −0.105290
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −42.8966 −1.74112 −0.870559 0.492064i \(-0.836242\pi\)
−0.870559 + 0.492064i \(0.836242\pi\)
\(608\) 0 0
\(609\) −9.45190 −0.383010
\(610\) 0 0
\(611\) −2.70725 −0.109524
\(612\) 0 0
\(613\) 39.5175 1.59610 0.798048 0.602594i \(-0.205866\pi\)
0.798048 + 0.602594i \(0.205866\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −32.2951 −1.30015 −0.650075 0.759870i \(-0.725263\pi\)
−0.650075 + 0.759870i \(0.725263\pi\)
\(618\) 0 0
\(619\) −17.4793 −0.702554 −0.351277 0.936272i \(-0.614252\pi\)
−0.351277 + 0.936272i \(0.614252\pi\)
\(620\) 0 0
\(621\) 0.532621 0.0213733
\(622\) 0 0
\(623\) 26.4395 1.05928
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 12.8819 0.513634
\(630\) 0 0
\(631\) −0.376695 −0.0149960 −0.00749799 0.999972i \(-0.502387\pi\)
−0.00749799 + 0.999972i \(0.502387\pi\)
\(632\) 0 0
\(633\) −14.5777 −0.579413
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −4.25857 −0.168731
\(638\) 0 0
\(639\) −2.55132 −0.100929
\(640\) 0 0
\(641\) 30.3921 1.20042 0.600208 0.799844i \(-0.295084\pi\)
0.600208 + 0.799844i \(0.295084\pi\)
\(642\) 0 0
\(643\) 17.3918 0.685865 0.342932 0.939360i \(-0.388580\pi\)
0.342932 + 0.939360i \(0.388580\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −34.1331 −1.34191 −0.670956 0.741497i \(-0.734116\pi\)
−0.670956 + 0.741497i \(0.734116\pi\)
\(648\) 0 0
\(649\) 11.2937 0.443317
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 20.6284 0.807250 0.403625 0.914925i \(-0.367750\pi\)
0.403625 + 0.914925i \(0.367750\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −0.188347 −0.00734814
\(658\) 0 0
\(659\) −17.3940 −0.677575 −0.338788 0.940863i \(-0.610017\pi\)
−0.338788 + 0.940863i \(0.610017\pi\)
\(660\) 0 0
\(661\) −9.04053 −0.351636 −0.175818 0.984423i \(-0.556257\pi\)
−0.175818 + 0.984423i \(0.556257\pi\)
\(662\) 0 0
\(663\) 1.46738 0.0569883
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −3.04053 −0.117730
\(668\) 0 0
\(669\) 19.8518 0.767514
\(670\) 0 0
\(671\) 0.711265 0.0274581
\(672\) 0 0
\(673\) 12.7634 0.491991 0.245996 0.969271i \(-0.420885\pi\)
0.245996 + 0.969271i \(0.420885\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15.9251 −0.612052 −0.306026 0.952023i \(-0.598999\pi\)
−0.306026 + 0.952023i \(0.598999\pi\)
\(678\) 0 0
\(679\) −27.9224 −1.07156
\(680\) 0 0
\(681\) −6.85042 −0.262509
\(682\) 0 0
\(683\) 9.04927 0.346261 0.173130 0.984899i \(-0.444612\pi\)
0.173130 + 0.984899i \(0.444612\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −18.0374 −0.688170
\(688\) 0 0
\(689\) 8.77883 0.334447
\(690\) 0 0
\(691\) −41.4848 −1.57816 −0.789078 0.614293i \(-0.789441\pi\)
−0.789078 + 0.614293i \(0.789441\pi\)
\(692\) 0 0
\(693\) −4.88187 −0.185447
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −1.81936 −0.0689131
\(698\) 0 0
\(699\) 14.4049 0.544842
\(700\) 0 0
\(701\) 1.08298 0.0409036 0.0204518 0.999791i \(-0.493490\pi\)
0.0204518 + 0.999791i \(0.493490\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7.68815 −0.289143
\(708\) 0 0
\(709\) −29.9371 −1.12431 −0.562155 0.827032i \(-0.690028\pi\)
−0.562155 + 0.827032i \(0.690028\pi\)
\(710\) 0 0
\(711\) −11.0729 −0.415268
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −21.7350 −0.811709
\(718\) 0 0
\(719\) −29.4793 −1.09939 −0.549697 0.835364i \(-0.685257\pi\)
−0.549697 + 0.835364i \(0.685257\pi\)
\(720\) 0 0
\(721\) −15.9955 −0.595703
\(722\) 0 0
\(723\) −17.5604 −0.653078
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 8.43456 0.312820 0.156410 0.987692i \(-0.450008\pi\)
0.156410 + 0.987692i \(0.450008\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −2.50718 −0.0927314
\(732\) 0 0
\(733\) 11.5449 0.426421 0.213210 0.977006i \(-0.431608\pi\)
0.213210 + 0.977006i \(0.431608\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7.62331 0.280808
\(738\) 0 0
\(739\) 14.2891 0.525632 0.262816 0.964846i \(-0.415349\pi\)
0.262816 + 0.964846i \(0.415349\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.60693 −0.0956390 −0.0478195 0.998856i \(-0.515227\pi\)
−0.0478195 + 0.998856i \(0.515227\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 7.91566 0.289619
\(748\) 0 0
\(749\) −19.7857 −0.722953
\(750\) 0 0
\(751\) −46.1277 −1.68322 −0.841612 0.540083i \(-0.818393\pi\)
−0.841612 + 0.540083i \(0.818393\pi\)
\(752\) 0 0
\(753\) 22.7082 0.827533
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −20.6229 −0.749552 −0.374776 0.927115i \(-0.622280\pi\)
−0.374776 + 0.927115i \(0.622280\pi\)
\(758\) 0 0
\(759\) −1.57042 −0.0570027
\(760\) 0 0
\(761\) 52.6872 1.90991 0.954954 0.296752i \(-0.0959036\pi\)
0.954954 + 0.296752i \(0.0959036\pi\)
\(762\) 0 0
\(763\) 19.6981 0.713119
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.83035 −0.138306
\(768\) 0 0
\(769\) 31.2458 1.12675 0.563376 0.826200i \(-0.309502\pi\)
0.563376 + 0.826200i \(0.309502\pi\)
\(770\) 0 0
\(771\) 6.58278 0.237073
\(772\) 0 0
\(773\) −41.0584 −1.47677 −0.738385 0.674380i \(-0.764411\pi\)
−0.738385 + 0.674380i \(0.764411\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 14.5353 0.521453
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 7.52252 0.269177
\(782\) 0 0
\(783\) −5.70861 −0.204009
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −26.7067 −0.951990 −0.475995 0.879448i \(-0.657912\pi\)
−0.475995 + 0.879448i \(0.657912\pi\)
\(788\) 0 0
\(789\) 4.24349 0.151072
\(790\) 0 0
\(791\) −3.93516 −0.139918
\(792\) 0 0
\(793\) −0.241231 −0.00856636
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 15.8293 0.560703 0.280352 0.959897i \(-0.409549\pi\)
0.280352 + 0.959897i \(0.409549\pi\)
\(798\) 0 0
\(799\) 3.97256 0.140539
\(800\) 0 0
\(801\) 15.9685 0.564221
\(802\) 0 0
\(803\) 0.555339 0.0195975
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −12.6434 −0.445068
\(808\) 0 0
\(809\) −20.3894 −0.716852 −0.358426 0.933558i \(-0.616687\pi\)
−0.358426 + 0.933558i \(0.616687\pi\)
\(810\) 0 0
\(811\) −35.7445 −1.25516 −0.627579 0.778553i \(-0.715954\pi\)
−0.627579 + 0.778553i \(0.715954\pi\)
\(812\) 0 0
\(813\) 23.7665 0.833527
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 1.65573 0.0578558
\(820\) 0 0
\(821\) 32.4660 1.13307 0.566536 0.824037i \(-0.308283\pi\)
0.566536 + 0.824037i \(0.308283\pi\)
\(822\) 0 0
\(823\) 36.0775 1.25758 0.628792 0.777574i \(-0.283550\pi\)
0.628792 + 0.777574i \(0.283550\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 10.7247 0.372935 0.186468 0.982461i \(-0.440296\pi\)
0.186468 + 0.982461i \(0.440296\pi\)
\(828\) 0 0
\(829\) 44.6206 1.54974 0.774868 0.632123i \(-0.217816\pi\)
0.774868 + 0.632123i \(0.217816\pi\)
\(830\) 0 0
\(831\) 17.8765 0.620129
\(832\) 0 0
\(833\) 6.24894 0.216513
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −34.8786 −1.20414 −0.602071 0.798442i \(-0.705658\pi\)
−0.602071 + 0.798442i \(0.705658\pi\)
\(840\) 0 0
\(841\) 3.58823 0.123732
\(842\) 0 0
\(843\) −8.39540 −0.289153
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −3.81889 −0.131219
\(848\) 0 0
\(849\) −13.9344 −0.478226
\(850\) 0 0
\(851\) 4.67579 0.160284
\(852\) 0 0
\(853\) 20.5673 0.704211 0.352105 0.935960i \(-0.385466\pi\)
0.352105 + 0.935960i \(0.385466\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −36.7060 −1.25385 −0.626926 0.779079i \(-0.715687\pi\)
−0.626926 + 0.779079i \(0.715687\pi\)
\(858\) 0 0
\(859\) −13.2543 −0.452231 −0.226116 0.974100i \(-0.572603\pi\)
−0.226116 + 0.974100i \(0.572603\pi\)
\(860\) 0 0
\(861\) −2.05288 −0.0699621
\(862\) 0 0
\(863\) 21.0966 0.718138 0.359069 0.933311i \(-0.383094\pi\)
0.359069 + 0.933311i \(0.383094\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 14.8468 0.504224
\(868\) 0 0
\(869\) 32.6483 1.10752
\(870\) 0 0
\(871\) −2.58550 −0.0876065
\(872\) 0 0
\(873\) −16.8641 −0.570765
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 5.54498 0.187241 0.0936203 0.995608i \(-0.470156\pi\)
0.0936203 + 0.995608i \(0.470156\pi\)
\(878\) 0 0
\(879\) 11.4085 0.384798
\(880\) 0 0
\(881\) −15.0378 −0.506636 −0.253318 0.967383i \(-0.581522\pi\)
−0.253318 + 0.967383i \(0.581522\pi\)
\(882\) 0 0
\(883\) 6.55806 0.220696 0.110348 0.993893i \(-0.464803\pi\)
0.110348 + 0.993893i \(0.464803\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −20.3045 −0.681760 −0.340880 0.940107i \(-0.610725\pi\)
−0.340880 + 0.940107i \(0.610725\pi\)
\(888\) 0 0
\(889\) −4.76335 −0.159758
\(890\) 0 0
\(891\) −2.94848 −0.0987778
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0.532621 0.0177837
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) −12.8819 −0.429157
\(902\) 0 0
\(903\) −2.82899 −0.0941429
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −32.8791 −1.09173 −0.545866 0.837873i \(-0.683799\pi\)
−0.545866 + 0.837873i \(0.683799\pi\)
\(908\) 0 0
\(909\) −4.64337 −0.154011
\(910\) 0 0
\(911\) 8.27638 0.274209 0.137104 0.990557i \(-0.456220\pi\)
0.137104 + 0.990557i \(0.456220\pi\)
\(912\) 0 0
\(913\) −23.3392 −0.772413
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 32.1157 1.06055
\(918\) 0 0
\(919\) 53.4997 1.76479 0.882397 0.470506i \(-0.155929\pi\)
0.882397 + 0.470506i \(0.155929\pi\)
\(920\) 0 0
\(921\) −2.50790 −0.0826383
\(922\) 0 0
\(923\) −2.55132 −0.0839778
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −9.66071 −0.317299
\(928\) 0 0
\(929\) −25.9384 −0.851011 −0.425505 0.904956i \(-0.639904\pi\)
−0.425505 + 0.904956i \(0.639904\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 6.96220 0.227932
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 14.1537 0.462380 0.231190 0.972909i \(-0.425738\pi\)
0.231190 + 0.972909i \(0.425738\pi\)
\(938\) 0 0
\(939\) −16.0880 −0.525013
\(940\) 0 0
\(941\) 26.9458 0.878406 0.439203 0.898388i \(-0.355261\pi\)
0.439203 + 0.898388i \(0.355261\pi\)
\(942\) 0 0
\(943\) −0.660380 −0.0215049
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 48.6570 1.58114 0.790570 0.612371i \(-0.209784\pi\)
0.790570 + 0.612371i \(0.209784\pi\)
\(948\) 0 0
\(949\) −0.188347 −0.00611402
\(950\) 0 0
\(951\) 1.25263 0.0406192
\(952\) 0 0
\(953\) −41.7911 −1.35375 −0.676874 0.736099i \(-0.736666\pi\)
−0.676874 + 0.736099i \(0.736666\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 16.8317 0.544092
\(958\) 0 0
\(959\) −0.592740 −0.0191406
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) −11.9498 −0.385078
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −0.524916 −0.0168802 −0.00844008 0.999964i \(-0.502687\pi\)
−0.00844008 + 0.999964i \(0.502687\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 60.4036 1.93844 0.969222 0.246189i \(-0.0791784\pi\)
0.969222 + 0.246189i \(0.0791784\pi\)
\(972\) 0 0
\(973\) −8.08305 −0.259131
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 41.6412 1.33222 0.666110 0.745853i \(-0.267958\pi\)
0.666110 + 0.745853i \(0.267958\pi\)
\(978\) 0 0
\(979\) −47.0829 −1.50478
\(980\) 0 0
\(981\) 11.8970 0.379841
\(982\) 0 0
\(983\) 58.6498 1.87064 0.935319 0.353806i \(-0.115113\pi\)
0.935319 + 0.353806i \(0.115113\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 4.48246 0.142678
\(988\) 0 0
\(989\) −0.910041 −0.0289376
\(990\) 0 0
\(991\) −59.2987 −1.88369 −0.941843 0.336054i \(-0.890907\pi\)
−0.941843 + 0.336054i \(0.890907\pi\)
\(992\) 0 0
\(993\) 8.24349 0.261599
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 36.9170 1.16917 0.584587 0.811331i \(-0.301257\pi\)
0.584587 + 0.811331i \(0.301257\pi\)
\(998\) 0 0
\(999\) 8.77883 0.277750
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.bt.1.4 4
5.2 odd 4 1560.2.l.d.1249.5 yes 8
5.3 odd 4 1560.2.l.d.1249.1 8
5.4 even 2 7800.2.a.by.1.1 4
15.2 even 4 4680.2.l.g.2809.7 8
15.8 even 4 4680.2.l.g.2809.8 8
20.3 even 4 3120.2.l.n.1249.5 8
20.7 even 4 3120.2.l.n.1249.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1560.2.l.d.1249.1 8 5.3 odd 4
1560.2.l.d.1249.5 yes 8 5.2 odd 4
3120.2.l.n.1249.1 8 20.7 even 4
3120.2.l.n.1249.5 8 20.3 even 4
4680.2.l.g.2809.7 8 15.2 even 4
4680.2.l.g.2809.8 8 15.8 even 4
7800.2.a.bt.1.4 4 1.1 even 1 trivial
7800.2.a.by.1.1 4 5.4 even 2