Properties

Label 1800.4.a.bc.1.1
Level $1800$
Weight $4$
Character 1800.1
Self dual yes
Analytic conductor $106.203$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(106.203438010\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 360)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1800.1

$q$-expansion

\(f(q)\) \(=\) \(q+18.0000 q^{7} +O(q^{10})\) \(q+18.0000 q^{7} -34.0000 q^{11} -12.0000 q^{13} -102.000 q^{17} +164.000 q^{19} +48.0000 q^{23} -146.000 q^{29} +100.000 q^{31} -328.000 q^{37} +288.000 q^{41} -120.000 q^{43} +16.0000 q^{47} -19.0000 q^{49} -126.000 q^{53} -642.000 q^{59} +602.000 q^{61} -436.000 q^{67} -652.000 q^{71} -1062.00 q^{73} -612.000 q^{77} +388.000 q^{79} -444.000 q^{83} +820.000 q^{89} -216.000 q^{91} +766.000 q^{97} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 18.0000 0.971909 0.485954 0.873984i \(-0.338472\pi\)
0.485954 + 0.873984i \(0.338472\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −34.0000 −0.931944 −0.465972 0.884799i \(-0.654295\pi\)
−0.465972 + 0.884799i \(0.654295\pi\)
\(12\) 0 0
\(13\) −12.0000 −0.256015 −0.128008 0.991773i \(-0.540858\pi\)
−0.128008 + 0.991773i \(0.540858\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −102.000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 0 0
\(19\) 164.000 1.98022 0.990110 0.140293i \(-0.0448045\pi\)
0.990110 + 0.140293i \(0.0448045\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 48.0000 0.435161 0.217580 0.976042i \(-0.430184\pi\)
0.217580 + 0.976042i \(0.430184\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −146.000 −0.934880 −0.467440 0.884025i \(-0.654824\pi\)
−0.467440 + 0.884025i \(0.654824\pi\)
\(30\) 0 0
\(31\) 100.000 0.579372 0.289686 0.957122i \(-0.406449\pi\)
0.289686 + 0.957122i \(0.406449\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −328.000 −1.45737 −0.728687 0.684846i \(-0.759869\pi\)
−0.728687 + 0.684846i \(0.759869\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 288.000 1.09703 0.548513 0.836142i \(-0.315194\pi\)
0.548513 + 0.836142i \(0.315194\pi\)
\(42\) 0 0
\(43\) −120.000 −0.425577 −0.212789 0.977098i \(-0.568255\pi\)
−0.212789 + 0.977098i \(0.568255\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 16.0000 0.0496562 0.0248281 0.999692i \(-0.492096\pi\)
0.0248281 + 0.999692i \(0.492096\pi\)
\(48\) 0 0
\(49\) −19.0000 −0.0553936
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −126.000 −0.326555 −0.163278 0.986580i \(-0.552207\pi\)
−0.163278 + 0.986580i \(0.552207\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −642.000 −1.41663 −0.708316 0.705896i \(-0.750545\pi\)
−0.708316 + 0.705896i \(0.750545\pi\)
\(60\) 0 0
\(61\) 602.000 1.26358 0.631789 0.775141i \(-0.282321\pi\)
0.631789 + 0.775141i \(0.282321\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −436.000 −0.795013 −0.397507 0.917599i \(-0.630124\pi\)
−0.397507 + 0.917599i \(0.630124\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −652.000 −1.08983 −0.544917 0.838490i \(-0.683439\pi\)
−0.544917 + 0.838490i \(0.683439\pi\)
\(72\) 0 0
\(73\) −1062.00 −1.70271 −0.851354 0.524591i \(-0.824218\pi\)
−0.851354 + 0.524591i \(0.824218\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −612.000 −0.905765
\(78\) 0 0
\(79\) 388.000 0.552575 0.276287 0.961075i \(-0.410896\pi\)
0.276287 + 0.961075i \(0.410896\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −444.000 −0.587173 −0.293586 0.955933i \(-0.594849\pi\)
−0.293586 + 0.955933i \(0.594849\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 820.000 0.976627 0.488314 0.872668i \(-0.337612\pi\)
0.488314 + 0.872668i \(0.337612\pi\)
\(90\) 0 0
\(91\) −216.000 −0.248824
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 766.000 0.801809 0.400905 0.916120i \(-0.368696\pi\)
0.400905 + 0.916120i \(0.368696\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 798.000 0.786178 0.393089 0.919500i \(-0.371406\pi\)
0.393089 + 0.919500i \(0.371406\pi\)
\(102\) 0 0
\(103\) 402.000 0.384565 0.192283 0.981340i \(-0.438411\pi\)
0.192283 + 0.981340i \(0.438411\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1444.00 1.30464 0.652321 0.757943i \(-0.273795\pi\)
0.652321 + 0.757943i \(0.273795\pi\)
\(108\) 0 0
\(109\) −198.000 −0.173990 −0.0869952 0.996209i \(-0.527726\pi\)
−0.0869952 + 0.996209i \(0.527726\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2010.00 −1.67332 −0.836659 0.547724i \(-0.815494\pi\)
−0.836659 + 0.547724i \(0.815494\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1836.00 −1.41433
\(120\) 0 0
\(121\) −175.000 −0.131480
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 866.000 0.605079 0.302540 0.953137i \(-0.402166\pi\)
0.302540 + 0.953137i \(0.402166\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2098.00 1.39926 0.699630 0.714505i \(-0.253348\pi\)
0.699630 + 0.714505i \(0.253348\pi\)
\(132\) 0 0
\(133\) 2952.00 1.92459
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 886.000 0.552526 0.276263 0.961082i \(-0.410904\pi\)
0.276263 + 0.961082i \(0.410904\pi\)
\(138\) 0 0
\(139\) −500.000 −0.305104 −0.152552 0.988295i \(-0.548749\pi\)
−0.152552 + 0.988295i \(0.548749\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 408.000 0.238592
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2302.00 −1.26569 −0.632843 0.774280i \(-0.718112\pi\)
−0.632843 + 0.774280i \(0.718112\pi\)
\(150\) 0 0
\(151\) −2384.00 −1.28482 −0.642408 0.766363i \(-0.722064\pi\)
−0.642408 + 0.766363i \(0.722064\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1452.00 −0.738103 −0.369052 0.929409i \(-0.620317\pi\)
−0.369052 + 0.929409i \(0.620317\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 864.000 0.422936
\(162\) 0 0
\(163\) −604.000 −0.290239 −0.145119 0.989414i \(-0.546357\pi\)
−0.145119 + 0.989414i \(0.546357\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −664.000 −0.307676 −0.153838 0.988096i \(-0.549163\pi\)
−0.153838 + 0.988096i \(0.549163\pi\)
\(168\) 0 0
\(169\) −2053.00 −0.934456
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −4118.00 −1.80974 −0.904872 0.425684i \(-0.860034\pi\)
−0.904872 + 0.425684i \(0.860034\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1746.00 −0.729062 −0.364531 0.931191i \(-0.618771\pi\)
−0.364531 + 0.931191i \(0.618771\pi\)
\(180\) 0 0
\(181\) −1270.00 −0.521538 −0.260769 0.965401i \(-0.583976\pi\)
−0.260769 + 0.965401i \(0.583976\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 3468.00 1.35618
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2676.00 −1.01376 −0.506881 0.862016i \(-0.669202\pi\)
−0.506881 + 0.862016i \(0.669202\pi\)
\(192\) 0 0
\(193\) 3146.00 1.17334 0.586668 0.809827i \(-0.300439\pi\)
0.586668 + 0.809827i \(0.300439\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3674.00 −1.32874 −0.664370 0.747404i \(-0.731300\pi\)
−0.664370 + 0.747404i \(0.731300\pi\)
\(198\) 0 0
\(199\) −1392.00 −0.495861 −0.247930 0.968778i \(-0.579750\pi\)
−0.247930 + 0.968778i \(0.579750\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2628.00 −0.908618
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5576.00 −1.84545
\(210\) 0 0
\(211\) −540.000 −0.176185 −0.0880927 0.996112i \(-0.528077\pi\)
−0.0880927 + 0.996112i \(0.528077\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 1800.00 0.563097
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1224.00 0.372557
\(222\) 0 0
\(223\) −4166.00 −1.25101 −0.625507 0.780219i \(-0.715108\pi\)
−0.625507 + 0.780219i \(0.715108\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5024.00 −1.46896 −0.734481 0.678629i \(-0.762575\pi\)
−0.734481 + 0.678629i \(0.762575\pi\)
\(228\) 0 0
\(229\) 4454.00 1.28528 0.642639 0.766169i \(-0.277840\pi\)
0.642639 + 0.766169i \(0.277840\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1526.00 −0.429063 −0.214531 0.976717i \(-0.568822\pi\)
−0.214531 + 0.976717i \(0.568822\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6828.00 −1.84798 −0.923989 0.382420i \(-0.875091\pi\)
−0.923989 + 0.382420i \(0.875091\pi\)
\(240\) 0 0
\(241\) 5782.00 1.54544 0.772721 0.634746i \(-0.218895\pi\)
0.772721 + 0.634746i \(0.218895\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1968.00 −0.506967
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6394.00 1.60791 0.803956 0.594689i \(-0.202725\pi\)
0.803956 + 0.594689i \(0.202725\pi\)
\(252\) 0 0
\(253\) −1632.00 −0.405545
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1862.00 0.451939 0.225970 0.974134i \(-0.427445\pi\)
0.225970 + 0.974134i \(0.427445\pi\)
\(258\) 0 0
\(259\) −5904.00 −1.41644
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6504.00 −1.52492 −0.762460 0.647036i \(-0.776008\pi\)
−0.762460 + 0.647036i \(0.776008\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −8298.00 −1.88081 −0.940405 0.340056i \(-0.889554\pi\)
−0.940405 + 0.340056i \(0.889554\pi\)
\(270\) 0 0
\(271\) 1848.00 0.414236 0.207118 0.978316i \(-0.433592\pi\)
0.207118 + 0.978316i \(0.433592\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −2824.00 −0.612555 −0.306277 0.951942i \(-0.599084\pi\)
−0.306277 + 0.951942i \(0.599084\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1940.00 0.411853 0.205927 0.978567i \(-0.433979\pi\)
0.205927 + 0.978567i \(0.433979\pi\)
\(282\) 0 0
\(283\) −6548.00 −1.37540 −0.687700 0.725995i \(-0.741380\pi\)
−0.687700 + 0.725995i \(0.741380\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5184.00 1.06621
\(288\) 0 0
\(289\) 5491.00 1.11765
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6566.00 1.30918 0.654590 0.755984i \(-0.272841\pi\)
0.654590 + 0.755984i \(0.272841\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −576.000 −0.111408
\(300\) 0 0
\(301\) −2160.00 −0.413622
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −8432.00 −1.56756 −0.783778 0.621041i \(-0.786710\pi\)
−0.783778 + 0.621041i \(0.786710\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4916.00 0.896337 0.448168 0.893949i \(-0.352076\pi\)
0.448168 + 0.893949i \(0.352076\pi\)
\(312\) 0 0
\(313\) 10106.0 1.82500 0.912500 0.409077i \(-0.134149\pi\)
0.912500 + 0.409077i \(0.134149\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3382.00 0.599218 0.299609 0.954062i \(-0.403144\pi\)
0.299609 + 0.954062i \(0.403144\pi\)
\(318\) 0 0
\(319\) 4964.00 0.871256
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −16728.0 −2.88164
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 288.000 0.0482613
\(330\) 0 0
\(331\) −6460.00 −1.07273 −0.536365 0.843986i \(-0.680203\pi\)
−0.536365 + 0.843986i \(0.680203\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −5294.00 −0.855735 −0.427867 0.903842i \(-0.640735\pi\)
−0.427867 + 0.903842i \(0.640735\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3400.00 −0.539942
\(342\) 0 0
\(343\) −6516.00 −1.02575
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −12096.0 −1.87132 −0.935659 0.352906i \(-0.885194\pi\)
−0.935659 + 0.352906i \(0.885194\pi\)
\(348\) 0 0
\(349\) −862.000 −0.132211 −0.0661057 0.997813i \(-0.521057\pi\)
−0.0661057 + 0.997813i \(0.521057\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6878.00 −1.03705 −0.518525 0.855062i \(-0.673519\pi\)
−0.518525 + 0.855062i \(0.673519\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6216.00 −0.913838 −0.456919 0.889508i \(-0.651047\pi\)
−0.456919 + 0.889508i \(0.651047\pi\)
\(360\) 0 0
\(361\) 20037.0 2.92127
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 13274.0 1.88800 0.944002 0.329941i \(-0.107029\pi\)
0.944002 + 0.329941i \(0.107029\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2268.00 −0.317382
\(372\) 0 0
\(373\) −1300.00 −0.180460 −0.0902298 0.995921i \(-0.528760\pi\)
−0.0902298 + 0.995921i \(0.528760\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1752.00 0.239344
\(378\) 0 0
\(379\) 13324.0 1.80583 0.902913 0.429824i \(-0.141424\pi\)
0.902913 + 0.429824i \(0.141424\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 6192.00 0.826100 0.413050 0.910708i \(-0.364463\pi\)
0.413050 + 0.910708i \(0.364463\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2022.00 −0.263546 −0.131773 0.991280i \(-0.542067\pi\)
−0.131773 + 0.991280i \(0.542067\pi\)
\(390\) 0 0
\(391\) −4896.00 −0.633252
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −7856.00 −0.993152 −0.496576 0.867993i \(-0.665410\pi\)
−0.496576 + 0.867993i \(0.665410\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1148.00 −0.142964 −0.0714818 0.997442i \(-0.522773\pi\)
−0.0714818 + 0.997442i \(0.522773\pi\)
\(402\) 0 0
\(403\) −1200.00 −0.148328
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 11152.0 1.35819
\(408\) 0 0
\(409\) −6310.00 −0.762859 −0.381430 0.924398i \(-0.624568\pi\)
−0.381430 + 0.924398i \(0.624568\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −11556.0 −1.37684
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 13362.0 1.55794 0.778969 0.627062i \(-0.215743\pi\)
0.778969 + 0.627062i \(0.215743\pi\)
\(420\) 0 0
\(421\) −5146.00 −0.595726 −0.297863 0.954609i \(-0.596274\pi\)
−0.297863 + 0.954609i \(0.596274\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 10836.0 1.22808
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6368.00 0.711684 0.355842 0.934546i \(-0.384194\pi\)
0.355842 + 0.934546i \(0.384194\pi\)
\(432\) 0 0
\(433\) 6138.00 0.681232 0.340616 0.940202i \(-0.389364\pi\)
0.340616 + 0.940202i \(0.389364\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7872.00 0.861714
\(438\) 0 0
\(439\) −4424.00 −0.480970 −0.240485 0.970653i \(-0.577307\pi\)
−0.240485 + 0.970653i \(0.577307\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −488.000 −0.0523377 −0.0261688 0.999658i \(-0.508331\pi\)
−0.0261688 + 0.999658i \(0.508331\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −16884.0 −1.77462 −0.887311 0.461172i \(-0.847429\pi\)
−0.887311 + 0.461172i \(0.847429\pi\)
\(450\) 0 0
\(451\) −9792.00 −1.02237
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 5398.00 0.552533 0.276267 0.961081i \(-0.410903\pi\)
0.276267 + 0.961081i \(0.410903\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6122.00 0.618503 0.309252 0.950980i \(-0.399921\pi\)
0.309252 + 0.950980i \(0.399921\pi\)
\(462\) 0 0
\(463\) −8162.00 −0.819266 −0.409633 0.912250i \(-0.634343\pi\)
−0.409633 + 0.912250i \(0.634343\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2660.00 −0.263576 −0.131788 0.991278i \(-0.542072\pi\)
−0.131788 + 0.991278i \(0.542072\pi\)
\(468\) 0 0
\(469\) −7848.00 −0.772680
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4080.00 0.396614
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9788.00 −0.933664 −0.466832 0.884346i \(-0.654605\pi\)
−0.466832 + 0.884346i \(0.654605\pi\)
\(480\) 0 0
\(481\) 3936.00 0.373111
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −4714.00 −0.438628 −0.219314 0.975654i \(-0.570382\pi\)
−0.219314 + 0.975654i \(0.570382\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6690.00 0.614899 0.307450 0.951564i \(-0.400524\pi\)
0.307450 + 0.951564i \(0.400524\pi\)
\(492\) 0 0
\(493\) 14892.0 1.36045
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −11736.0 −1.05922
\(498\) 0 0
\(499\) −20636.0 −1.85129 −0.925646 0.378392i \(-0.876477\pi\)
−0.925646 + 0.378392i \(0.876477\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 15952.0 1.41404 0.707022 0.707191i \(-0.250038\pi\)
0.707022 + 0.707191i \(0.250038\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2230.00 0.194191 0.0970953 0.995275i \(-0.469045\pi\)
0.0970953 + 0.995275i \(0.469045\pi\)
\(510\) 0 0
\(511\) −19116.0 −1.65488
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −544.000 −0.0462768
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1260.00 −0.105953 −0.0529766 0.998596i \(-0.516871\pi\)
−0.0529766 + 0.998596i \(0.516871\pi\)
\(522\) 0 0
\(523\) −2900.00 −0.242463 −0.121231 0.992624i \(-0.538684\pi\)
−0.121231 + 0.992624i \(0.538684\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −10200.0 −0.843110
\(528\) 0 0
\(529\) −9863.00 −0.810635
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3456.00 −0.280855
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 646.000 0.0516237
\(540\) 0 0
\(541\) 19554.0 1.55396 0.776980 0.629526i \(-0.216751\pi\)
0.776980 + 0.629526i \(0.216751\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −2664.00 −0.208235 −0.104117 0.994565i \(-0.533202\pi\)
−0.104117 + 0.994565i \(0.533202\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −23944.0 −1.85127
\(552\) 0 0
\(553\) 6984.00 0.537052
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −11358.0 −0.864011 −0.432005 0.901871i \(-0.642194\pi\)
−0.432005 + 0.901871i \(0.642194\pi\)
\(558\) 0 0
\(559\) 1440.00 0.108954
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −2440.00 −0.182653 −0.0913266 0.995821i \(-0.529111\pi\)
−0.0913266 + 0.995821i \(0.529111\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 24156.0 1.77974 0.889870 0.456214i \(-0.150795\pi\)
0.889870 + 0.456214i \(0.150795\pi\)
\(570\) 0 0
\(571\) −2220.00 −0.162704 −0.0813521 0.996685i \(-0.525924\pi\)
−0.0813521 + 0.996685i \(0.525924\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 5782.00 0.417171 0.208586 0.978004i \(-0.433114\pi\)
0.208586 + 0.978004i \(0.433114\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −7992.00 −0.570678
\(582\) 0 0
\(583\) 4284.00 0.304331
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1684.00 0.118409 0.0592045 0.998246i \(-0.481144\pi\)
0.0592045 + 0.998246i \(0.481144\pi\)
\(588\) 0 0
\(589\) 16400.0 1.14728
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 15246.0 1.05578 0.527891 0.849312i \(-0.322983\pi\)
0.527891 + 0.849312i \(0.322983\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −9016.00 −0.614998 −0.307499 0.951548i \(-0.599492\pi\)
−0.307499 + 0.951548i \(0.599492\pi\)
\(600\) 0 0
\(601\) −18682.0 −1.26798 −0.633989 0.773342i \(-0.718584\pi\)
−0.633989 + 0.773342i \(0.718584\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 22022.0 1.47256 0.736281 0.676676i \(-0.236580\pi\)
0.736281 + 0.676676i \(0.236580\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −192.000 −0.0127127
\(612\) 0 0
\(613\) 22808.0 1.50278 0.751392 0.659856i \(-0.229383\pi\)
0.751392 + 0.659856i \(0.229383\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9422.00 −0.614774 −0.307387 0.951585i \(-0.599455\pi\)
−0.307387 + 0.951585i \(0.599455\pi\)
\(618\) 0 0
\(619\) 4172.00 0.270900 0.135450 0.990784i \(-0.456752\pi\)
0.135450 + 0.990784i \(0.456752\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 14760.0 0.949192
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 33456.0 2.12079
\(630\) 0 0
\(631\) −11572.0 −0.730070 −0.365035 0.930994i \(-0.618943\pi\)
−0.365035 + 0.930994i \(0.618943\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 228.000 0.0141816
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 936.000 0.0576752 0.0288376 0.999584i \(-0.490819\pi\)
0.0288376 + 0.999584i \(0.490819\pi\)
\(642\) 0 0
\(643\) −15892.0 −0.974680 −0.487340 0.873212i \(-0.662033\pi\)
−0.487340 + 0.873212i \(0.662033\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 25056.0 1.52249 0.761247 0.648463i \(-0.224588\pi\)
0.761247 + 0.648463i \(0.224588\pi\)
\(648\) 0 0
\(649\) 21828.0 1.32022
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4054.00 0.242948 0.121474 0.992595i \(-0.461238\pi\)
0.121474 + 0.992595i \(0.461238\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −6758.00 −0.399475 −0.199738 0.979849i \(-0.564009\pi\)
−0.199738 + 0.979849i \(0.564009\pi\)
\(660\) 0 0
\(661\) 25098.0 1.47685 0.738426 0.674335i \(-0.235569\pi\)
0.738426 + 0.674335i \(0.235569\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −7008.00 −0.406823
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −20468.0 −1.17758
\(672\) 0 0
\(673\) −2830.00 −0.162093 −0.0810464 0.996710i \(-0.525826\pi\)
−0.0810464 + 0.996710i \(0.525826\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10654.0 0.604825 0.302412 0.953177i \(-0.402208\pi\)
0.302412 + 0.953177i \(0.402208\pi\)
\(678\) 0 0
\(679\) 13788.0 0.779286
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 17156.0 0.961136 0.480568 0.876957i \(-0.340430\pi\)
0.480568 + 0.876957i \(0.340430\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1512.00 0.0836032
\(690\) 0 0
\(691\) −812.000 −0.0447032 −0.0223516 0.999750i \(-0.507115\pi\)
−0.0223516 + 0.999750i \(0.507115\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −29376.0 −1.59641
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 30270.0 1.63093 0.815465 0.578806i \(-0.196481\pi\)
0.815465 + 0.578806i \(0.196481\pi\)
\(702\) 0 0
\(703\) −53792.0 −2.88592
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 14364.0 0.764093
\(708\) 0 0
\(709\) −394.000 −0.0208702 −0.0104351 0.999946i \(-0.503322\pi\)
−0.0104351 + 0.999946i \(0.503322\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4800.00 0.252120
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 37224.0 1.93077 0.965383 0.260836i \(-0.0839982\pi\)
0.965383 + 0.260836i \(0.0839982\pi\)
\(720\) 0 0
\(721\) 7236.00 0.373762
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 12614.0 0.643504 0.321752 0.946824i \(-0.395728\pi\)
0.321752 + 0.946824i \(0.395728\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 12240.0 0.619306
\(732\) 0 0
\(733\) 25664.0 1.29321 0.646604 0.762826i \(-0.276189\pi\)
0.646604 + 0.762826i \(0.276189\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 14824.0 0.740908
\(738\) 0 0
\(739\) −18772.0 −0.934424 −0.467212 0.884145i \(-0.654741\pi\)
−0.467212 + 0.884145i \(0.654741\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −19376.0 −0.956711 −0.478356 0.878166i \(-0.658767\pi\)
−0.478356 + 0.878166i \(0.658767\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 25992.0 1.26799
\(750\) 0 0
\(751\) 30092.0 1.46215 0.731074 0.682299i \(-0.239020\pi\)
0.731074 + 0.682299i \(0.239020\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −18136.0 −0.870758 −0.435379 0.900247i \(-0.643386\pi\)
−0.435379 + 0.900247i \(0.643386\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −10948.0 −0.521504 −0.260752 0.965406i \(-0.583971\pi\)
−0.260752 + 0.965406i \(0.583971\pi\)
\(762\) 0 0
\(763\) −3564.00 −0.169103
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 7704.00 0.362680
\(768\) 0 0
\(769\) 1422.00 0.0666822 0.0333411 0.999444i \(-0.489385\pi\)
0.0333411 + 0.999444i \(0.489385\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 26142.0 1.21638 0.608190 0.793791i \(-0.291896\pi\)
0.608190 + 0.793791i \(0.291896\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 47232.0 2.17235
\(780\) 0 0
\(781\) 22168.0 1.01566
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −23404.0 −1.06005 −0.530027 0.847981i \(-0.677818\pi\)
−0.530027 + 0.847981i \(0.677818\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −36180.0 −1.62631
\(792\) 0 0
\(793\) −7224.00 −0.323495
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1418.00 0.0630215 0.0315108 0.999503i \(-0.489968\pi\)
0.0315108 + 0.999503i \(0.489968\pi\)
\(798\) 0 0
\(799\) −1632.00 −0.0722603
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 36108.0 1.58683
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 17304.0 0.752010 0.376005 0.926618i \(-0.377298\pi\)
0.376005 + 0.926618i \(0.377298\pi\)
\(810\) 0 0
\(811\) −28012.0 −1.21287 −0.606433 0.795135i \(-0.707400\pi\)
−0.606433 + 0.795135i \(0.707400\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −19680.0 −0.842737
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −32266.0 −1.37161 −0.685805 0.727786i \(-0.740550\pi\)
−0.685805 + 0.727786i \(0.740550\pi\)
\(822\) 0 0
\(823\) −4962.00 −0.210163 −0.105082 0.994464i \(-0.533510\pi\)
−0.105082 + 0.994464i \(0.533510\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 5064.00 0.212929 0.106465 0.994316i \(-0.466047\pi\)
0.106465 + 0.994316i \(0.466047\pi\)
\(828\) 0 0
\(829\) −8174.00 −0.342454 −0.171227 0.985232i \(-0.554773\pi\)
−0.171227 + 0.985232i \(0.554773\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1938.00 0.0806095
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 28240.0 1.16204 0.581021 0.813889i \(-0.302653\pi\)
0.581021 + 0.813889i \(0.302653\pi\)
\(840\) 0 0
\(841\) −3073.00 −0.125999
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −3150.00 −0.127787
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −15744.0 −0.634192
\(852\) 0 0
\(853\) −10472.0 −0.420345 −0.210173 0.977664i \(-0.567403\pi\)
−0.210173 + 0.977664i \(0.567403\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −32102.0 −1.27956 −0.639780 0.768558i \(-0.720975\pi\)
−0.639780 + 0.768558i \(0.720975\pi\)
\(858\) 0 0
\(859\) −11060.0 −0.439304 −0.219652 0.975578i \(-0.570492\pi\)
−0.219652 + 0.975578i \(0.570492\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 36088.0 1.42346 0.711732 0.702451i \(-0.247911\pi\)
0.711732 + 0.702451i \(0.247911\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −13192.0 −0.514969
\(870\) 0 0
\(871\) 5232.00 0.203536
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 34508.0 1.32868 0.664340 0.747431i \(-0.268713\pi\)
0.664340 + 0.747431i \(0.268713\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 6596.00 0.252242 0.126121 0.992015i \(-0.459747\pi\)
0.126121 + 0.992015i \(0.459747\pi\)
\(882\) 0 0
\(883\) −17620.0 −0.671529 −0.335765 0.941946i \(-0.608995\pi\)
−0.335765 + 0.941946i \(0.608995\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −50784.0 −1.92239 −0.961195 0.275870i \(-0.911034\pi\)
−0.961195 + 0.275870i \(0.911034\pi\)
\(888\) 0 0
\(889\) 15588.0 0.588082
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2624.00 0.0983301
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −14600.0 −0.541643
\(900\) 0 0
\(901\) 12852.0 0.475208
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −16072.0 −0.588381 −0.294191 0.955747i \(-0.595050\pi\)
−0.294191 + 0.955747i \(0.595050\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 41760.0 1.51874 0.759369 0.650660i \(-0.225508\pi\)
0.759369 + 0.650660i \(0.225508\pi\)
\(912\) 0 0
\(913\) 15096.0 0.547212
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 37764.0 1.35995
\(918\) 0 0
\(919\) 34100.0 1.22400 0.612000 0.790858i \(-0.290365\pi\)
0.612000 + 0.790858i \(0.290365\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 7824.00 0.279014
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 22812.0 0.805638 0.402819 0.915280i \(-0.368030\pi\)
0.402819 + 0.915280i \(0.368030\pi\)
\(930\) 0 0
\(931\) −3116.00 −0.109691
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 38982.0 1.35911 0.679555 0.733624i \(-0.262173\pi\)
0.679555 + 0.733624i \(0.262173\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −52766.0 −1.82797 −0.913986 0.405745i \(-0.867012\pi\)
−0.913986 + 0.405745i \(0.867012\pi\)
\(942\) 0 0
\(943\) 13824.0 0.477382
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 13608.0 0.466949 0.233474 0.972363i \(-0.424990\pi\)
0.233474 + 0.972363i \(0.424990\pi\)
\(948\) 0 0
\(949\) 12744.0 0.435920
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 6446.00 0.219104 0.109552 0.993981i \(-0.465058\pi\)
0.109552 + 0.993981i \(0.465058\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 15948.0 0.537005
\(960\) 0 0
\(961\) −19791.0 −0.664328
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 42642.0 1.41807 0.709035 0.705173i \(-0.249131\pi\)
0.709035 + 0.705173i \(0.249131\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 19938.0 0.658950 0.329475 0.944164i \(-0.393128\pi\)
0.329475 + 0.944164i \(0.393128\pi\)
\(972\) 0 0
\(973\) −9000.00 −0.296533
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 49754.0 1.62924 0.814622 0.579992i \(-0.196944\pi\)
0.814622 + 0.579992i \(0.196944\pi\)
\(978\) 0 0
\(979\) −27880.0 −0.910162
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 7936.00 0.257497 0.128748 0.991677i \(-0.458904\pi\)
0.128748 + 0.991677i \(0.458904\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −5760.00 −0.185194
\(990\) 0 0
\(991\) −33248.0 −1.06575 −0.532875 0.846194i \(-0.678888\pi\)
−0.532875 + 0.846194i \(0.678888\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 20196.0 0.641538 0.320769 0.947157i \(-0.396059\pi\)
0.320769 + 0.947157i \(0.396059\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1800.4.a.bc.1.1 1
3.2 odd 2 1800.4.a.be.1.1 1
5.2 odd 4 1800.4.f.e.649.2 2
5.3 odd 4 1800.4.f.e.649.1 2
5.4 even 2 360.4.a.a.1.1 1
15.2 even 4 1800.4.f.s.649.2 2
15.8 even 4 1800.4.f.s.649.1 2
15.14 odd 2 360.4.a.j.1.1 yes 1
20.19 odd 2 720.4.a.m.1.1 1
60.59 even 2 720.4.a.z.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.4.a.a.1.1 1 5.4 even 2
360.4.a.j.1.1 yes 1 15.14 odd 2
720.4.a.m.1.1 1 20.19 odd 2
720.4.a.z.1.1 1 60.59 even 2
1800.4.a.bc.1.1 1 1.1 even 1 trivial
1800.4.a.be.1.1 1 3.2 odd 2
1800.4.f.e.649.1 2 5.3 odd 4
1800.4.f.e.649.2 2 5.2 odd 4
1800.4.f.s.649.1 2 15.8 even 4
1800.4.f.s.649.2 2 15.2 even 4