Properties

Label 1800.4.a.e.1.1
Level $1800$
Weight $4$
Character 1800.1
Self dual yes
Analytic conductor $106.203$
Analytic rank $0$
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: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 120)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q-20.0000 q^{7} +O(q^{10})\) \(q-20.0000 q^{7} -16.0000 q^{11} -58.0000 q^{13} +38.0000 q^{17} +4.00000 q^{19} -80.0000 q^{23} -82.0000 q^{29} -8.00000 q^{31} -426.000 q^{37} +246.000 q^{41} +524.000 q^{43} -464.000 q^{47} +57.0000 q^{49} -702.000 q^{53} +592.000 q^{59} +574.000 q^{61} +172.000 q^{67} -768.000 q^{71} +558.000 q^{73} +320.000 q^{77} +408.000 q^{79} +164.000 q^{83} +510.000 q^{89} +1160.00 q^{91} -514.000 q^{97} +O(q^{100})\)

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
\(7\) −20.0000 −1.07990 −0.539949 0.841698i \(-0.681557\pi\)
−0.539949 + 0.841698i \(0.681557\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −16.0000 −0.438562 −0.219281 0.975662i \(-0.570371\pi\)
−0.219281 + 0.975662i \(0.570371\pi\)
\(12\) 0 0
\(13\) −58.0000 −1.23741 −0.618704 0.785624i \(-0.712342\pi\)
−0.618704 + 0.785624i \(0.712342\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 38.0000 0.542138 0.271069 0.962560i \(-0.412623\pi\)
0.271069 + 0.962560i \(0.412623\pi\)
\(18\) 0 0
\(19\) 4.00000 0.0482980 0.0241490 0.999708i \(-0.492312\pi\)
0.0241490 + 0.999708i \(0.492312\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −80.0000 −0.725268 −0.362634 0.931932i \(-0.618122\pi\)
−0.362634 + 0.931932i \(0.618122\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −82.0000 −0.525070 −0.262535 0.964923i \(-0.584558\pi\)
−0.262535 + 0.964923i \(0.584558\pi\)
\(30\) 0 0
\(31\) −8.00000 −0.0463498 −0.0231749 0.999731i \(-0.507377\pi\)
−0.0231749 + 0.999731i \(0.507377\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −426.000 −1.89281 −0.946405 0.322982i \(-0.895315\pi\)
−0.946405 + 0.322982i \(0.895315\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 246.000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 524.000 1.85835 0.929177 0.369634i \(-0.120517\pi\)
0.929177 + 0.369634i \(0.120517\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −464.000 −1.44003 −0.720014 0.693959i \(-0.755865\pi\)
−0.720014 + 0.693959i \(0.755865\pi\)
\(48\) 0 0
\(49\) 57.0000 0.166181
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −702.000 −1.81938 −0.909690 0.415288i \(-0.863681\pi\)
−0.909690 + 0.415288i \(0.863681\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 592.000 1.30630 0.653151 0.757228i \(-0.273447\pi\)
0.653151 + 0.757228i \(0.273447\pi\)
\(60\) 0 0
\(61\) 574.000 1.20481 0.602403 0.798192i \(-0.294210\pi\)
0.602403 + 0.798192i \(0.294210\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 172.000 0.313629 0.156815 0.987628i \(-0.449878\pi\)
0.156815 + 0.987628i \(0.449878\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −768.000 −1.28373 −0.641865 0.766818i \(-0.721839\pi\)
−0.641865 + 0.766818i \(0.721839\pi\)
\(72\) 0 0
\(73\) 558.000 0.894643 0.447322 0.894373i \(-0.352378\pi\)
0.447322 + 0.894373i \(0.352378\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 320.000 0.473602
\(78\) 0 0
\(79\) 408.000 0.581058 0.290529 0.956866i \(-0.406169\pi\)
0.290529 + 0.956866i \(0.406169\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 164.000 0.216884 0.108442 0.994103i \(-0.465414\pi\)
0.108442 + 0.994103i \(0.465414\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 510.000 0.607415 0.303707 0.952765i \(-0.401776\pi\)
0.303707 + 0.952765i \(0.401776\pi\)
\(90\) 0 0
\(91\) 1160.00 1.33628
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −514.000 −0.538029 −0.269014 0.963136i \(-0.586698\pi\)
−0.269014 + 0.963136i \(0.586698\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −666.000 −0.656133 −0.328067 0.944655i \(-0.606397\pi\)
−0.328067 + 0.944655i \(0.606397\pi\)
\(102\) 0 0
\(103\) 1100.00 1.05229 0.526147 0.850394i \(-0.323636\pi\)
0.526147 + 0.850394i \(0.323636\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1212.00 1.09503 0.547516 0.836795i \(-0.315573\pi\)
0.547516 + 0.836795i \(0.315573\pi\)
\(108\) 0 0
\(109\) 2078.00 1.82602 0.913011 0.407936i \(-0.133751\pi\)
0.913011 + 0.407936i \(0.133751\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1458.00 −1.21378 −0.606890 0.794786i \(-0.707583\pi\)
−0.606890 + 0.794786i \(0.707583\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −760.000 −0.585455
\(120\) 0 0
\(121\) −1075.00 −0.807663
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2436.00 1.70205 0.851024 0.525127i \(-0.175982\pi\)
0.851024 + 0.525127i \(0.175982\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2544.00 −1.69672 −0.848360 0.529420i \(-0.822410\pi\)
−0.848360 + 0.529420i \(0.822410\pi\)
\(132\) 0 0
\(133\) −80.0000 −0.0521570
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 694.000 0.432791 0.216396 0.976306i \(-0.430570\pi\)
0.216396 + 0.976306i \(0.430570\pi\)
\(138\) 0 0
\(139\) 516.000 0.314867 0.157434 0.987530i \(-0.449678\pi\)
0.157434 + 0.987530i \(0.449678\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 928.000 0.542680
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −770.000 −0.423361 −0.211681 0.977339i \(-0.567894\pi\)
−0.211681 + 0.977339i \(0.567894\pi\)
\(150\) 0 0
\(151\) −424.000 −0.228507 −0.114254 0.993452i \(-0.536448\pi\)
−0.114254 + 0.993452i \(0.536448\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −922.000 −0.468685 −0.234343 0.972154i \(-0.575294\pi\)
−0.234343 + 0.972154i \(0.575294\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1600.00 0.783215
\(162\) 0 0
\(163\) 3788.00 1.82024 0.910120 0.414345i \(-0.135989\pi\)
0.910120 + 0.414345i \(0.135989\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −48.0000 −0.0222416 −0.0111208 0.999938i \(-0.503540\pi\)
−0.0111208 + 0.999938i \(0.503540\pi\)
\(168\) 0 0
\(169\) 1167.00 0.531179
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3242.00 1.42477 0.712384 0.701790i \(-0.247616\pi\)
0.712384 + 0.701790i \(0.247616\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2728.00 1.13911 0.569554 0.821954i \(-0.307116\pi\)
0.569554 + 0.821954i \(0.307116\pi\)
\(180\) 0 0
\(181\) −4090.00 −1.67960 −0.839799 0.542897i \(-0.817327\pi\)
−0.839799 + 0.542897i \(0.817327\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −608.000 −0.237761
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1480.00 0.560676 0.280338 0.959901i \(-0.409554\pi\)
0.280338 + 0.959901i \(0.409554\pi\)
\(192\) 0 0
\(193\) 1622.00 0.604944 0.302472 0.953158i \(-0.402188\pi\)
0.302472 + 0.953158i \(0.402188\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2530.00 0.915000 0.457500 0.889210i \(-0.348745\pi\)
0.457500 + 0.889210i \(0.348745\pi\)
\(198\) 0 0
\(199\) −2440.00 −0.869181 −0.434590 0.900628i \(-0.643107\pi\)
−0.434590 + 0.900628i \(0.643107\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1640.00 0.567022
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −64.0000 −0.0211817
\(210\) 0 0
\(211\) −148.000 −0.0482879 −0.0241439 0.999708i \(-0.507686\pi\)
−0.0241439 + 0.999708i \(0.507686\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 160.000 0.0500530
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2204.00 −0.670847
\(222\) 0 0
\(223\) 676.000 0.202997 0.101498 0.994836i \(-0.467636\pi\)
0.101498 + 0.994836i \(0.467636\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6276.00 −1.83503 −0.917517 0.397696i \(-0.869810\pi\)
−0.917517 + 0.397696i \(0.869810\pi\)
\(228\) 0 0
\(229\) 6190.00 1.78623 0.893115 0.449828i \(-0.148515\pi\)
0.893115 + 0.449828i \(0.148515\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5406.00 1.52000 0.759998 0.649926i \(-0.225200\pi\)
0.759998 + 0.649926i \(0.225200\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 600.000 0.162388 0.0811941 0.996698i \(-0.474127\pi\)
0.0811941 + 0.996698i \(0.474127\pi\)
\(240\) 0 0
\(241\) −1054.00 −0.281718 −0.140859 0.990030i \(-0.544986\pi\)
−0.140859 + 0.990030i \(0.544986\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −232.000 −0.0597644
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2232.00 0.561285 0.280643 0.959812i \(-0.409452\pi\)
0.280643 + 0.959812i \(0.409452\pi\)
\(252\) 0 0
\(253\) 1280.00 0.318075
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3630.00 0.881063 0.440531 0.897737i \(-0.354790\pi\)
0.440531 + 0.897737i \(0.354790\pi\)
\(258\) 0 0
\(259\) 8520.00 2.04404
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6960.00 1.63183 0.815916 0.578170i \(-0.196233\pi\)
0.815916 + 0.578170i \(0.196233\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2062.00 0.467369 0.233685 0.972312i \(-0.424922\pi\)
0.233685 + 0.972312i \(0.424922\pi\)
\(270\) 0 0
\(271\) −2544.00 −0.570247 −0.285124 0.958491i \(-0.592035\pi\)
−0.285124 + 0.958491i \(0.592035\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 694.000 0.150536 0.0752679 0.997163i \(-0.476019\pi\)
0.0752679 + 0.997163i \(0.476019\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1982.00 0.420769 0.210385 0.977619i \(-0.432528\pi\)
0.210385 + 0.977619i \(0.432528\pi\)
\(282\) 0 0
\(283\) −5228.00 −1.09814 −0.549068 0.835778i \(-0.685017\pi\)
−0.549068 + 0.835778i \(0.685017\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4920.00 −1.01191
\(288\) 0 0
\(289\) −3469.00 −0.706086
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7454.00 −1.48624 −0.743118 0.669160i \(-0.766654\pi\)
−0.743118 + 0.669160i \(0.766654\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4640.00 0.897452
\(300\) 0 0
\(301\) −10480.0 −2.00683
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1316.00 0.244652 0.122326 0.992490i \(-0.460965\pi\)
0.122326 + 0.992490i \(0.460965\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 832.000 0.151699 0.0758495 0.997119i \(-0.475833\pi\)
0.0758495 + 0.997119i \(0.475833\pi\)
\(312\) 0 0
\(313\) −6770.00 −1.22257 −0.611283 0.791412i \(-0.709346\pi\)
−0.611283 + 0.791412i \(0.709346\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6582.00 −1.16619 −0.583095 0.812404i \(-0.698158\pi\)
−0.583095 + 0.812404i \(0.698158\pi\)
\(318\) 0 0
\(319\) 1312.00 0.230276
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 152.000 0.0261842
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 9280.00 1.55508
\(330\) 0 0
\(331\) 11292.0 1.87512 0.937560 0.347825i \(-0.113080\pi\)
0.937560 + 0.347825i \(0.113080\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 8006.00 1.29411 0.647054 0.762444i \(-0.276001\pi\)
0.647054 + 0.762444i \(0.276001\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 128.000 0.0203272
\(342\) 0 0
\(343\) 5720.00 0.900440
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −316.000 −0.0488869 −0.0244435 0.999701i \(-0.507781\pi\)
−0.0244435 + 0.999701i \(0.507781\pi\)
\(348\) 0 0
\(349\) 4926.00 0.755538 0.377769 0.925900i \(-0.376691\pi\)
0.377769 + 0.925900i \(0.376691\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2438.00 0.367597 0.183798 0.982964i \(-0.441161\pi\)
0.183798 + 0.982964i \(0.441161\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3336.00 0.490438 0.245219 0.969468i \(-0.421140\pi\)
0.245219 + 0.969468i \(0.421140\pi\)
\(360\) 0 0
\(361\) −6843.00 −0.997667
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −44.0000 −0.00625826 −0.00312913 0.999995i \(-0.500996\pi\)
−0.00312913 + 0.999995i \(0.500996\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 14040.0 1.96475
\(372\) 0 0
\(373\) 11966.0 1.66106 0.830531 0.556973i \(-0.188037\pi\)
0.830531 + 0.556973i \(0.188037\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4756.00 0.649725
\(378\) 0 0
\(379\) 12676.0 1.71800 0.859001 0.511975i \(-0.171086\pi\)
0.859001 + 0.511975i \(0.171086\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 6672.00 0.890139 0.445070 0.895496i \(-0.353179\pi\)
0.445070 + 0.895496i \(0.353179\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −354.000 −0.0461401 −0.0230701 0.999734i \(-0.507344\pi\)
−0.0230701 + 0.999734i \(0.507344\pi\)
\(390\) 0 0
\(391\) −3040.00 −0.393195
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 5054.00 0.638924 0.319462 0.947599i \(-0.396498\pi\)
0.319462 + 0.947599i \(0.396498\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10266.0 −1.27845 −0.639226 0.769019i \(-0.720745\pi\)
−0.639226 + 0.769019i \(0.720745\pi\)
\(402\) 0 0
\(403\) 464.000 0.0573536
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6816.00 0.830114
\(408\) 0 0
\(409\) −1526.00 −0.184489 −0.0922443 0.995736i \(-0.529404\pi\)
−0.0922443 + 0.995736i \(0.529404\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −11840.0 −1.41067
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2064.00 −0.240652 −0.120326 0.992734i \(-0.538394\pi\)
−0.120326 + 0.992734i \(0.538394\pi\)
\(420\) 0 0
\(421\) 4590.00 0.531361 0.265680 0.964061i \(-0.414403\pi\)
0.265680 + 0.964061i \(0.414403\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −11480.0 −1.30107
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5536.00 0.618700 0.309350 0.950948i \(-0.399889\pi\)
0.309350 + 0.950948i \(0.399889\pi\)
\(432\) 0 0
\(433\) −1850.00 −0.205324 −0.102662 0.994716i \(-0.532736\pi\)
−0.102662 + 0.994716i \(0.532736\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −320.000 −0.0350290
\(438\) 0 0
\(439\) 11704.0 1.27244 0.636220 0.771507i \(-0.280497\pi\)
0.636220 + 0.771507i \(0.280497\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6948.00 0.745168 0.372584 0.927998i \(-0.378472\pi\)
0.372584 + 0.927998i \(0.378472\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −12090.0 −1.27074 −0.635370 0.772208i \(-0.719152\pi\)
−0.635370 + 0.772208i \(0.719152\pi\)
\(450\) 0 0
\(451\) −3936.00 −0.410951
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −11626.0 −1.19002 −0.595012 0.803717i \(-0.702853\pi\)
−0.595012 + 0.803717i \(0.702853\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −16314.0 −1.64820 −0.824098 0.566447i \(-0.808318\pi\)
−0.824098 + 0.566447i \(0.808318\pi\)
\(462\) 0 0
\(463\) 15756.0 1.58152 0.790760 0.612127i \(-0.209686\pi\)
0.790760 + 0.612127i \(0.209686\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5684.00 0.563221 0.281610 0.959529i \(-0.409131\pi\)
0.281610 + 0.959529i \(0.409131\pi\)
\(468\) 0 0
\(469\) −3440.00 −0.338688
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −8384.00 −0.815004
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3368.00 0.321269 0.160634 0.987014i \(-0.448646\pi\)
0.160634 + 0.987014i \(0.448646\pi\)
\(480\) 0 0
\(481\) 24708.0 2.34218
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 5588.00 0.519952 0.259976 0.965615i \(-0.416285\pi\)
0.259976 + 0.965615i \(0.416285\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −10584.0 −0.972809 −0.486405 0.873734i \(-0.661692\pi\)
−0.486405 + 0.873734i \(0.661692\pi\)
\(492\) 0 0
\(493\) −3116.00 −0.284660
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 15360.0 1.38630
\(498\) 0 0
\(499\) −12220.0 −1.09628 −0.548139 0.836388i \(-0.684663\pi\)
−0.548139 + 0.836388i \(0.684663\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 16152.0 1.43177 0.715887 0.698216i \(-0.246023\pi\)
0.715887 + 0.698216i \(0.246023\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −10642.0 −0.926716 −0.463358 0.886171i \(-0.653356\pi\)
−0.463358 + 0.886171i \(0.653356\pi\)
\(510\) 0 0
\(511\) −11160.0 −0.966124
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 7424.00 0.631542
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −22882.0 −1.92414 −0.962072 0.272797i \(-0.912051\pi\)
−0.962072 + 0.272797i \(0.912051\pi\)
\(522\) 0 0
\(523\) 10052.0 0.840427 0.420213 0.907425i \(-0.361955\pi\)
0.420213 + 0.907425i \(0.361955\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −304.000 −0.0251280
\(528\) 0 0
\(529\) −5767.00 −0.473987
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −14268.0 −1.15950
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −912.000 −0.0728806
\(540\) 0 0
\(541\) −6530.00 −0.518940 −0.259470 0.965751i \(-0.583548\pi\)
−0.259470 + 0.965751i \(0.583548\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −16652.0 −1.30162 −0.650812 0.759239i \(-0.725571\pi\)
−0.650812 + 0.759239i \(0.725571\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −328.000 −0.0253598
\(552\) 0 0
\(553\) −8160.00 −0.627484
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −12886.0 −0.980247 −0.490123 0.871653i \(-0.663048\pi\)
−0.490123 + 0.871653i \(0.663048\pi\)
\(558\) 0 0
\(559\) −30392.0 −2.29954
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −11108.0 −0.831521 −0.415761 0.909474i \(-0.636485\pi\)
−0.415761 + 0.909474i \(0.636485\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 9214.00 0.678859 0.339430 0.940631i \(-0.389766\pi\)
0.339430 + 0.940631i \(0.389766\pi\)
\(570\) 0 0
\(571\) −4052.00 −0.296972 −0.148486 0.988915i \(-0.547440\pi\)
−0.148486 + 0.988915i \(0.547440\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 8446.00 0.609379 0.304689 0.952452i \(-0.401447\pi\)
0.304689 + 0.952452i \(0.401447\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3280.00 −0.234212
\(582\) 0 0
\(583\) 11232.0 0.797911
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2172.00 0.152722 0.0763612 0.997080i \(-0.475670\pi\)
0.0763612 + 0.997080i \(0.475670\pi\)
\(588\) 0 0
\(589\) −32.0000 −0.00223860
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1218.00 −0.0843461 −0.0421731 0.999110i \(-0.513428\pi\)
−0.0421731 + 0.999110i \(0.513428\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −21240.0 −1.44882 −0.724410 0.689370i \(-0.757888\pi\)
−0.724410 + 0.689370i \(0.757888\pi\)
\(600\) 0 0
\(601\) 17626.0 1.19631 0.598153 0.801382i \(-0.295902\pi\)
0.598153 + 0.801382i \(0.295902\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −2580.00 −0.172519 −0.0862594 0.996273i \(-0.527491\pi\)
−0.0862594 + 0.996273i \(0.527491\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 26912.0 1.78190
\(612\) 0 0
\(613\) 14166.0 0.933376 0.466688 0.884422i \(-0.345447\pi\)
0.466688 + 0.884422i \(0.345447\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −21426.0 −1.39802 −0.699010 0.715112i \(-0.746376\pi\)
−0.699010 + 0.715112i \(0.746376\pi\)
\(618\) 0 0
\(619\) 3668.00 0.238173 0.119087 0.992884i \(-0.462003\pi\)
0.119087 + 0.992884i \(0.462003\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −10200.0 −0.655946
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −16188.0 −1.02617
\(630\) 0 0
\(631\) 20032.0 1.26381 0.631903 0.775048i \(-0.282274\pi\)
0.631903 + 0.775048i \(0.282274\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −3306.00 −0.205633
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7458.00 −0.459553 −0.229776 0.973243i \(-0.573799\pi\)
−0.229776 + 0.973243i \(0.573799\pi\)
\(642\) 0 0
\(643\) −7092.00 −0.434963 −0.217481 0.976064i \(-0.569784\pi\)
−0.217481 + 0.976064i \(0.569784\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3384.00 0.205624 0.102812 0.994701i \(-0.467216\pi\)
0.102812 + 0.994701i \(0.467216\pi\)
\(648\) 0 0
\(649\) −9472.00 −0.572894
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −29398.0 −1.76177 −0.880883 0.473335i \(-0.843050\pi\)
−0.880883 + 0.473335i \(0.843050\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6624.00 0.391554 0.195777 0.980648i \(-0.437277\pi\)
0.195777 + 0.980648i \(0.437277\pi\)
\(660\) 0 0
\(661\) 8646.00 0.508760 0.254380 0.967104i \(-0.418129\pi\)
0.254380 + 0.967104i \(0.418129\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 6560.00 0.380816
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −9184.00 −0.528382
\(672\) 0 0
\(673\) −28698.0 −1.64372 −0.821862 0.569686i \(-0.807065\pi\)
−0.821862 + 0.569686i \(0.807065\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 19426.0 1.10281 0.551405 0.834238i \(-0.314092\pi\)
0.551405 + 0.834238i \(0.314092\pi\)
\(678\) 0 0
\(679\) 10280.0 0.581016
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 8604.00 0.482025 0.241012 0.970522i \(-0.422521\pi\)
0.241012 + 0.970522i \(0.422521\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 40716.0 2.25132
\(690\) 0 0
\(691\) 12980.0 0.714591 0.357296 0.933991i \(-0.383699\pi\)
0.357296 + 0.933991i \(0.383699\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 9348.00 0.508007
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 19630.0 1.05765 0.528827 0.848730i \(-0.322632\pi\)
0.528827 + 0.848730i \(0.322632\pi\)
\(702\) 0 0
\(703\) −1704.00 −0.0914190
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 13320.0 0.708558
\(708\) 0 0
\(709\) 8030.00 0.425350 0.212675 0.977123i \(-0.431782\pi\)
0.212675 + 0.977123i \(0.431782\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 640.000 0.0336160
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −22720.0 −1.17846 −0.589230 0.807965i \(-0.700569\pi\)
−0.589230 + 0.807965i \(0.700569\pi\)
\(720\) 0 0
\(721\) −22000.0 −1.13637
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −27116.0 −1.38332 −0.691662 0.722221i \(-0.743121\pi\)
−0.691662 + 0.722221i \(0.743121\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 19912.0 1.00749
\(732\) 0 0
\(733\) −30882.0 −1.55614 −0.778071 0.628176i \(-0.783802\pi\)
−0.778071 + 0.628176i \(0.783802\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2752.00 −0.137546
\(738\) 0 0
\(739\) −13836.0 −0.688722 −0.344361 0.938837i \(-0.611904\pi\)
−0.344361 + 0.938837i \(0.611904\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 32712.0 1.61519 0.807595 0.589737i \(-0.200769\pi\)
0.807595 + 0.589737i \(0.200769\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −24240.0 −1.18252
\(750\) 0 0
\(751\) −8472.00 −0.411648 −0.205824 0.978589i \(-0.565987\pi\)
−0.205824 + 0.978589i \(0.565987\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −9866.00 −0.473693 −0.236847 0.971547i \(-0.576114\pi\)
−0.236847 + 0.971547i \(0.576114\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 3774.00 0.179773 0.0898866 0.995952i \(-0.471350\pi\)
0.0898866 + 0.995952i \(0.471350\pi\)
\(762\) 0 0
\(763\) −41560.0 −1.97192
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −34336.0 −1.61643
\(768\) 0 0
\(769\) −28670.0 −1.34443 −0.672215 0.740356i \(-0.734657\pi\)
−0.672215 + 0.740356i \(0.734657\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3246.00 −0.151036 −0.0755178 0.997144i \(-0.524061\pi\)
−0.0755178 + 0.997144i \(0.524061\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 984.000 0.0452573
\(780\) 0 0
\(781\) 12288.0 0.562995
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 19372.0 0.877430 0.438715 0.898626i \(-0.355434\pi\)
0.438715 + 0.898626i \(0.355434\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 29160.0 1.31076
\(792\) 0 0
\(793\) −33292.0 −1.49084
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −11814.0 −0.525061 −0.262530 0.964924i \(-0.584557\pi\)
−0.262530 + 0.964924i \(0.584557\pi\)
\(798\) 0 0
\(799\) −17632.0 −0.780695
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −8928.00 −0.392357
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 30054.0 1.30611 0.653055 0.757311i \(-0.273487\pi\)
0.653055 + 0.757311i \(0.273487\pi\)
\(810\) 0 0
\(811\) 2852.00 0.123486 0.0617431 0.998092i \(-0.480334\pi\)
0.0617431 + 0.998092i \(0.480334\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 2096.00 0.0897549
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −2170.00 −0.0922455 −0.0461227 0.998936i \(-0.514687\pi\)
−0.0461227 + 0.998936i \(0.514687\pi\)
\(822\) 0 0
\(823\) −19804.0 −0.838790 −0.419395 0.907804i \(-0.637758\pi\)
−0.419395 + 0.907804i \(0.637758\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 5508.00 0.231598 0.115799 0.993273i \(-0.463057\pi\)
0.115799 + 0.993273i \(0.463057\pi\)
\(828\) 0 0
\(829\) 33262.0 1.39353 0.696765 0.717299i \(-0.254622\pi\)
0.696765 + 0.717299i \(0.254622\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2166.00 0.0900930
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 4600.00 0.189284 0.0946422 0.995511i \(-0.469829\pi\)
0.0946422 + 0.995511i \(0.469829\pi\)
\(840\) 0 0
\(841\) −17665.0 −0.724302
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 21500.0 0.872195
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 34080.0 1.37279
\(852\) 0 0
\(853\) 4198.00 0.168507 0.0842537 0.996444i \(-0.473149\pi\)
0.0842537 + 0.996444i \(0.473149\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −5826.00 −0.232220 −0.116110 0.993236i \(-0.537042\pi\)
−0.116110 + 0.993236i \(0.537042\pi\)
\(858\) 0 0
\(859\) −3004.00 −0.119319 −0.0596596 0.998219i \(-0.519002\pi\)
−0.0596596 + 0.998219i \(0.519002\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −36936.0 −1.45691 −0.728457 0.685092i \(-0.759762\pi\)
−0.728457 + 0.685092i \(0.759762\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −6528.00 −0.254830
\(870\) 0 0
\(871\) −9976.00 −0.388087
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −5434.00 −0.209228 −0.104614 0.994513i \(-0.533361\pi\)
−0.104614 + 0.994513i \(0.533361\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 4758.00 0.181954 0.0909768 0.995853i \(-0.471001\pi\)
0.0909768 + 0.995853i \(0.471001\pi\)
\(882\) 0 0
\(883\) −15476.0 −0.589818 −0.294909 0.955525i \(-0.595289\pi\)
−0.294909 + 0.955525i \(0.595289\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −27440.0 −1.03872 −0.519360 0.854555i \(-0.673830\pi\)
−0.519360 + 0.854555i \(0.673830\pi\)
\(888\) 0 0
\(889\) −48720.0 −1.83804
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1856.00 −0.0695506
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 656.000 0.0243368
\(900\) 0 0
\(901\) −26676.0 −0.986356
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 48924.0 1.79106 0.895532 0.444997i \(-0.146795\pi\)
0.895532 + 0.444997i \(0.146795\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 3440.00 0.125107 0.0625534 0.998042i \(-0.480076\pi\)
0.0625534 + 0.998042i \(0.480076\pi\)
\(912\) 0 0
\(913\) −2624.00 −0.0951169
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 50880.0 1.83229
\(918\) 0 0
\(919\) −27184.0 −0.975753 −0.487877 0.872913i \(-0.662228\pi\)
−0.487877 + 0.872913i \(0.662228\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 44544.0 1.58850
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −42490.0 −1.50059 −0.750297 0.661101i \(-0.770089\pi\)
−0.750297 + 0.661101i \(0.770089\pi\)
\(930\) 0 0
\(931\) 228.000 0.00802621
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −37354.0 −1.30235 −0.651175 0.758928i \(-0.725724\pi\)
−0.651175 + 0.758928i \(0.725724\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 24470.0 0.847714 0.423857 0.905729i \(-0.360676\pi\)
0.423857 + 0.905729i \(0.360676\pi\)
\(942\) 0 0
\(943\) −19680.0 −0.679607
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −34100.0 −1.17012 −0.585059 0.810991i \(-0.698929\pi\)
−0.585059 + 0.810991i \(0.698929\pi\)
\(948\) 0 0
\(949\) −32364.0 −1.10704
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1878.00 0.0638346 0.0319173 0.999491i \(-0.489839\pi\)
0.0319173 + 0.999491i \(0.489839\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −13880.0 −0.467371
\(960\) 0 0
\(961\) −29727.0 −0.997852
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −38484.0 −1.27980 −0.639898 0.768460i \(-0.721023\pi\)
−0.639898 + 0.768460i \(0.721023\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −45272.0 −1.49624 −0.748119 0.663564i \(-0.769043\pi\)
−0.748119 + 0.663564i \(0.769043\pi\)
\(972\) 0 0
\(973\) −10320.0 −0.340025
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −25354.0 −0.830242 −0.415121 0.909766i \(-0.636261\pi\)
−0.415121 + 0.909766i \(0.636261\pi\)
\(978\) 0 0
\(979\) −8160.00 −0.266389
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −18744.0 −0.608180 −0.304090 0.952643i \(-0.598352\pi\)
−0.304090 + 0.952643i \(0.598352\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −41920.0 −1.34780
\(990\) 0 0
\(991\) 59600.0 1.91045 0.955225 0.295880i \(-0.0956127\pi\)
0.955225 + 0.295880i \(0.0956127\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 17886.0 0.568160 0.284080 0.958801i \(-0.408312\pi\)
0.284080 + 0.958801i \(0.408312\pi\)
\(998\) 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.e.1.1 1
3.2 odd 2 600.4.a.a.1.1 1
5.2 odd 4 1800.4.f.k.649.1 2
5.3 odd 4 1800.4.f.k.649.2 2
5.4 even 2 360.4.a.m.1.1 1
12.11 even 2 1200.4.a.bj.1.1 1
15.2 even 4 600.4.f.f.49.2 2
15.8 even 4 600.4.f.f.49.1 2
15.14 odd 2 120.4.a.e.1.1 1
20.19 odd 2 720.4.a.s.1.1 1
60.23 odd 4 1200.4.f.h.49.2 2
60.47 odd 4 1200.4.f.h.49.1 2
60.59 even 2 240.4.a.a.1.1 1
120.29 odd 2 960.4.a.q.1.1 1
120.59 even 2 960.4.a.bd.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.4.a.e.1.1 1 15.14 odd 2
240.4.a.a.1.1 1 60.59 even 2
360.4.a.m.1.1 1 5.4 even 2
600.4.a.a.1.1 1 3.2 odd 2
600.4.f.f.49.1 2 15.8 even 4
600.4.f.f.49.2 2 15.2 even 4
720.4.a.s.1.1 1 20.19 odd 2
960.4.a.q.1.1 1 120.29 odd 2
960.4.a.bd.1.1 1 120.59 even 2
1200.4.a.bj.1.1 1 12.11 even 2
1200.4.f.h.49.1 2 60.47 odd 4
1200.4.f.h.49.2 2 60.23 odd 4
1800.4.a.e.1.1 1 1.1 even 1 trivial
1800.4.f.k.649.1 2 5.2 odd 4
1800.4.f.k.649.2 2 5.3 odd 4