Properties

Label 1872.4.a.ba.1.2
Level $1872$
Weight $4$
Character 1872.1
Self dual yes
Analytic conductor $110.452$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1872.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(110.451575531\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{7}) \)
Defining polynomial: \( x^{2} - 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 117)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.64575\) of defining polynomial
Character \(\chi\) \(=\) 1872.1

$q$-expansion

\(f(q)\) \(=\) \(q+10.5830 q^{5} +22.0000 q^{7} +O(q^{10})\) \(q+10.5830 q^{5} +22.0000 q^{7} -5.29150 q^{11} +13.0000 q^{13} -116.413 q^{17} +126.000 q^{19} +31.7490 q^{23} -13.0000 q^{25} -52.9150 q^{29} +182.000 q^{31} +232.826 q^{35} -86.0000 q^{37} +444.486 q^{41} -96.0000 q^{43} +365.114 q^{47} +141.000 q^{49} +190.494 q^{53} -56.0000 q^{55} -587.357 q^{59} +574.000 q^{61} +137.579 q^{65} +530.000 q^{67} +809.600 q^{71} -154.000 q^{73} -116.413 q^{77} +460.000 q^{79} -322.782 q^{83} -1232.00 q^{85} -1439.29 q^{89} +286.000 q^{91} +1333.46 q^{95} +70.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 44 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 44 q^{7} + 26 q^{13} + 252 q^{19} - 26 q^{25} + 364 q^{31} - 172 q^{37} - 192 q^{43} + 282 q^{49} - 112 q^{55} + 1148 q^{61} + 1060 q^{67} - 308 q^{73} + 920 q^{79} - 2464 q^{85} + 572 q^{91} + 140 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) 10.5830 0.946573 0.473286 0.880909i \(-0.343068\pi\)
0.473286 + 0.880909i \(0.343068\pi\)
\(6\) 0 0
\(7\) 22.0000 1.18789 0.593944 0.804506i \(-0.297570\pi\)
0.593944 + 0.804506i \(0.297570\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −5.29150 −0.145041 −0.0725204 0.997367i \(-0.523104\pi\)
−0.0725204 + 0.997367i \(0.523104\pi\)
\(12\) 0 0
\(13\) 13.0000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −116.413 −1.66084 −0.830421 0.557136i \(-0.811900\pi\)
−0.830421 + 0.557136i \(0.811900\pi\)
\(18\) 0 0
\(19\) 126.000 1.52139 0.760694 0.649110i \(-0.224859\pi\)
0.760694 + 0.649110i \(0.224859\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 31.7490 0.287832 0.143916 0.989590i \(-0.454031\pi\)
0.143916 + 0.989590i \(0.454031\pi\)
\(24\) 0 0
\(25\) −13.0000 −0.104000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −52.9150 −0.338830 −0.169415 0.985545i \(-0.554188\pi\)
−0.169415 + 0.985545i \(0.554188\pi\)
\(30\) 0 0
\(31\) 182.000 1.05446 0.527228 0.849724i \(-0.323231\pi\)
0.527228 + 0.849724i \(0.323231\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 232.826 1.12442
\(36\) 0 0
\(37\) −86.0000 −0.382117 −0.191058 0.981579i \(-0.561192\pi\)
−0.191058 + 0.981579i \(0.561192\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 444.486 1.69310 0.846550 0.532310i \(-0.178676\pi\)
0.846550 + 0.532310i \(0.178676\pi\)
\(42\) 0 0
\(43\) −96.0000 −0.340462 −0.170231 0.985404i \(-0.554451\pi\)
−0.170231 + 0.985404i \(0.554451\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 365.114 1.13313 0.566567 0.824016i \(-0.308271\pi\)
0.566567 + 0.824016i \(0.308271\pi\)
\(48\) 0 0
\(49\) 141.000 0.411079
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 190.494 0.493705 0.246853 0.969053i \(-0.420604\pi\)
0.246853 + 0.969053i \(0.420604\pi\)
\(54\) 0 0
\(55\) −56.0000 −0.137292
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −587.357 −1.29606 −0.648028 0.761616i \(-0.724406\pi\)
−0.648028 + 0.761616i \(0.724406\pi\)
\(60\) 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
\(65\) 137.579 0.262532
\(66\) 0 0
\(67\) 530.000 0.966415 0.483208 0.875506i \(-0.339472\pi\)
0.483208 + 0.875506i \(0.339472\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 809.600 1.35327 0.676633 0.736321i \(-0.263439\pi\)
0.676633 + 0.736321i \(0.263439\pi\)
\(72\) 0 0
\(73\) −154.000 −0.246909 −0.123454 0.992350i \(-0.539397\pi\)
−0.123454 + 0.992350i \(0.539397\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −116.413 −0.172292
\(78\) 0 0
\(79\) 460.000 0.655114 0.327557 0.944831i \(-0.393775\pi\)
0.327557 + 0.944831i \(0.393775\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −322.782 −0.426866 −0.213433 0.976958i \(-0.568465\pi\)
−0.213433 + 0.976958i \(0.568465\pi\)
\(84\) 0 0
\(85\) −1232.00 −1.57211
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1439.29 −1.71421 −0.857103 0.515145i \(-0.827738\pi\)
−0.857103 + 0.515145i \(0.827738\pi\)
\(90\) 0 0
\(91\) 286.000 0.329461
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1333.46 1.44010
\(96\) 0 0
\(97\) 70.0000 0.0732724 0.0366362 0.999329i \(-0.488336\pi\)
0.0366362 + 0.999329i \(0.488336\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1460.45 1.43882 0.719409 0.694586i \(-0.244413\pi\)
0.719409 + 0.694586i \(0.244413\pi\)
\(102\) 0 0
\(103\) 1428.00 1.36607 0.683034 0.730387i \(-0.260660\pi\)
0.683034 + 0.730387i \(0.260660\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1619.20 −1.46293 −0.731467 0.681877i \(-0.761164\pi\)
−0.731467 + 0.681877i \(0.761164\pi\)
\(108\) 0 0
\(109\) −338.000 −0.297014 −0.148507 0.988911i \(-0.547447\pi\)
−0.148507 + 0.988911i \(0.547447\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1682.70 1.40084 0.700420 0.713731i \(-0.252996\pi\)
0.700420 + 0.713731i \(0.252996\pi\)
\(114\) 0 0
\(115\) 336.000 0.272454
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2561.09 −1.97289
\(120\) 0 0
\(121\) −1303.00 −0.978963
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1460.45 −1.04502
\(126\) 0 0
\(127\) 376.000 0.262713 0.131357 0.991335i \(-0.458067\pi\)
0.131357 + 0.991335i \(0.458067\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −687.895 −0.458792 −0.229396 0.973333i \(-0.573675\pi\)
−0.229396 + 0.973333i \(0.573675\pi\)
\(132\) 0 0
\(133\) 2772.00 1.80724
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1396.96 −0.871168 −0.435584 0.900148i \(-0.643458\pi\)
−0.435584 + 0.900148i \(0.643458\pi\)
\(138\) 0 0
\(139\) −2100.00 −1.28144 −0.640718 0.767776i \(-0.721363\pi\)
−0.640718 + 0.767776i \(0.721363\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −68.7895 −0.0402271
\(144\) 0 0
\(145\) −560.000 −0.320727
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2000.19 1.09974 0.549872 0.835249i \(-0.314677\pi\)
0.549872 + 0.835249i \(0.314677\pi\)
\(150\) 0 0
\(151\) −3526.00 −1.90028 −0.950138 0.311828i \(-0.899059\pi\)
−0.950138 + 0.311828i \(0.899059\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1926.11 0.998120
\(156\) 0 0
\(157\) 3066.00 1.55856 0.779278 0.626678i \(-0.215586\pi\)
0.779278 + 0.626678i \(0.215586\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 698.478 0.341912
\(162\) 0 0
\(163\) 3442.00 1.65398 0.826988 0.562219i \(-0.190052\pi\)
0.826988 + 0.562219i \(0.190052\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2693.37 1.24802 0.624011 0.781416i \(-0.285502\pi\)
0.624011 + 0.781416i \(0.285502\pi\)
\(168\) 0 0
\(169\) 169.000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3492.39 −1.53481 −0.767404 0.641164i \(-0.778452\pi\)
−0.767404 + 0.641164i \(0.778452\pi\)
\(174\) 0 0
\(175\) −286.000 −0.123540
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 169.328 0.0707049 0.0353524 0.999375i \(-0.488745\pi\)
0.0353524 + 0.999375i \(0.488745\pi\)
\(180\) 0 0
\(181\) 3374.00 1.38557 0.692783 0.721146i \(-0.256384\pi\)
0.692783 + 0.721146i \(0.256384\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −910.138 −0.361701
\(186\) 0 0
\(187\) 616.000 0.240890
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1185.30 −0.449032 −0.224516 0.974470i \(-0.572080\pi\)
−0.224516 + 0.974470i \(0.572080\pi\)
\(192\) 0 0
\(193\) −1542.00 −0.575107 −0.287553 0.957765i \(-0.592842\pi\)
−0.287553 + 0.957765i \(0.592842\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2127.18 −0.769318 −0.384659 0.923059i \(-0.625681\pi\)
−0.384659 + 0.923059i \(0.625681\pi\)
\(198\) 0 0
\(199\) 952.000 0.339123 0.169562 0.985520i \(-0.445765\pi\)
0.169562 + 0.985520i \(0.445765\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1164.13 −0.402492
\(204\) 0 0
\(205\) 4704.00 1.60264
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −666.729 −0.220663
\(210\) 0 0
\(211\) 1640.00 0.535082 0.267541 0.963547i \(-0.413789\pi\)
0.267541 + 0.963547i \(0.413789\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1015.97 −0.322272
\(216\) 0 0
\(217\) 4004.00 1.25258
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1513.37 −0.460635
\(222\) 0 0
\(223\) 4886.00 1.46722 0.733612 0.679569i \(-0.237833\pi\)
0.733612 + 0.679569i \(0.237833\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1867.90 0.546154 0.273077 0.961992i \(-0.411959\pi\)
0.273077 + 0.961992i \(0.411959\pi\)
\(228\) 0 0
\(229\) 5558.00 1.60386 0.801928 0.597421i \(-0.203808\pi\)
0.801928 + 0.597421i \(0.203808\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3577.06 1.00575 0.502877 0.864358i \(-0.332275\pi\)
0.502877 + 0.864358i \(0.332275\pi\)
\(234\) 0 0
\(235\) 3864.00 1.07259
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2936.78 −0.794832 −0.397416 0.917639i \(-0.630093\pi\)
−0.397416 + 0.917639i \(0.630093\pi\)
\(240\) 0 0
\(241\) −602.000 −0.160906 −0.0804528 0.996758i \(-0.525637\pi\)
−0.0804528 + 0.996758i \(0.525637\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1492.20 0.389116
\(246\) 0 0
\(247\) 1638.00 0.421957
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −3524.14 −0.886222 −0.443111 0.896467i \(-0.646125\pi\)
−0.443111 + 0.896467i \(0.646125\pi\)
\(252\) 0 0
\(253\) −168.000 −0.0417473
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2942.08 −0.714092 −0.357046 0.934087i \(-0.616216\pi\)
−0.357046 + 0.934087i \(0.616216\pi\)
\(258\) 0 0
\(259\) −1892.00 −0.453912
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 857.223 0.200984 0.100492 0.994938i \(-0.467958\pi\)
0.100492 + 0.994938i \(0.467958\pi\)
\(264\) 0 0
\(265\) 2016.00 0.467328
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −328.073 −0.0743605 −0.0371802 0.999309i \(-0.511838\pi\)
−0.0371802 + 0.999309i \(0.511838\pi\)
\(270\) 0 0
\(271\) 2814.00 0.630769 0.315384 0.948964i \(-0.397867\pi\)
0.315384 + 0.948964i \(0.397867\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 68.7895 0.0150842
\(276\) 0 0
\(277\) −3190.00 −0.691944 −0.345972 0.938245i \(-0.612451\pi\)
−0.345972 + 0.938245i \(0.612451\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6116.98 −1.29861 −0.649303 0.760530i \(-0.724939\pi\)
−0.649303 + 0.760530i \(0.724939\pi\)
\(282\) 0 0
\(283\) 4788.00 1.00571 0.502857 0.864370i \(-0.332282\pi\)
0.502857 + 0.864370i \(0.332282\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 9778.70 2.01121
\(288\) 0 0
\(289\) 8639.00 1.75840
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6699.04 1.33571 0.667854 0.744293i \(-0.267213\pi\)
0.667854 + 0.744293i \(0.267213\pi\)
\(294\) 0 0
\(295\) −6216.00 −1.22681
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 412.737 0.0798301
\(300\) 0 0
\(301\) −2112.00 −0.404431
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6074.65 1.14044
\(306\) 0 0
\(307\) 406.000 0.0754777 0.0377388 0.999288i \(-0.487985\pi\)
0.0377388 + 0.999288i \(0.487985\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 8286.49 1.51088 0.755440 0.655217i \(-0.227423\pi\)
0.755440 + 0.655217i \(0.227423\pi\)
\(312\) 0 0
\(313\) −5586.00 −1.00875 −0.504376 0.863484i \(-0.668277\pi\)
−0.504376 + 0.863484i \(0.668277\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8392.32 1.48694 0.743470 0.668770i \(-0.233179\pi\)
0.743470 + 0.668770i \(0.233179\pi\)
\(318\) 0 0
\(319\) 280.000 0.0491442
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −14668.0 −2.52679
\(324\) 0 0
\(325\) −169.000 −0.0288444
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 8032.50 1.34604
\(330\) 0 0
\(331\) 4426.00 0.734970 0.367485 0.930030i \(-0.380219\pi\)
0.367485 + 0.930030i \(0.380219\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5608.99 0.914782
\(336\) 0 0
\(337\) 8370.00 1.35295 0.676473 0.736467i \(-0.263507\pi\)
0.676473 + 0.736467i \(0.263507\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −963.053 −0.152939
\(342\) 0 0
\(343\) −4444.00 −0.699573
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6095.81 0.943056 0.471528 0.881851i \(-0.343703\pi\)
0.471528 + 0.881851i \(0.343703\pi\)
\(348\) 0 0
\(349\) 4354.00 0.667806 0.333903 0.942607i \(-0.391634\pi\)
0.333903 + 0.942607i \(0.391634\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3407.73 −0.513810 −0.256905 0.966437i \(-0.582703\pi\)
−0.256905 + 0.966437i \(0.582703\pi\)
\(354\) 0 0
\(355\) 8568.00 1.28096
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7762.63 −1.14121 −0.570607 0.821223i \(-0.693292\pi\)
−0.570607 + 0.821223i \(0.693292\pi\)
\(360\) 0 0
\(361\) 9017.00 1.31462
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1629.78 −0.233717
\(366\) 0 0
\(367\) 7784.00 1.10714 0.553572 0.832802i \(-0.313265\pi\)
0.553572 + 0.832802i \(0.313265\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4190.87 0.586467
\(372\) 0 0
\(373\) −8510.00 −1.18132 −0.590658 0.806922i \(-0.701132\pi\)
−0.590658 + 0.806922i \(0.701132\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −687.895 −0.0939746
\(378\) 0 0
\(379\) −1650.00 −0.223627 −0.111814 0.993729i \(-0.535666\pi\)
−0.111814 + 0.993729i \(0.535666\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8662.19 −1.15566 −0.577829 0.816158i \(-0.696100\pi\)
−0.577829 + 0.816158i \(0.696100\pi\)
\(384\) 0 0
\(385\) −1232.00 −0.163087
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2423.51 −0.315879 −0.157939 0.987449i \(-0.550485\pi\)
−0.157939 + 0.987449i \(0.550485\pi\)
\(390\) 0 0
\(391\) −3696.00 −0.478043
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4868.18 0.620114
\(396\) 0 0
\(397\) −1414.00 −0.178757 −0.0893786 0.995998i \(-0.528488\pi\)
−0.0893786 + 0.995998i \(0.528488\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5228.00 0.651058 0.325529 0.945532i \(-0.394458\pi\)
0.325529 + 0.945532i \(0.394458\pi\)
\(402\) 0 0
\(403\) 2366.00 0.292454
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 455.069 0.0554225
\(408\) 0 0
\(409\) 5782.00 0.699026 0.349513 0.936932i \(-0.386347\pi\)
0.349513 + 0.936932i \(0.386347\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −12921.8 −1.53957
\(414\) 0 0
\(415\) −3416.00 −0.404060
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −11482.6 −1.33881 −0.669403 0.742899i \(-0.733450\pi\)
−0.669403 + 0.742899i \(0.733450\pi\)
\(420\) 0 0
\(421\) −14194.0 −1.64317 −0.821583 0.570088i \(-0.806909\pi\)
−0.821583 + 0.570088i \(0.806909\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1513.37 0.172728
\(426\) 0 0
\(427\) 12628.0 1.43118
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5222.71 0.583687 0.291844 0.956466i \(-0.405731\pi\)
0.291844 + 0.956466i \(0.405731\pi\)
\(432\) 0 0
\(433\) −686.000 −0.0761364 −0.0380682 0.999275i \(-0.512120\pi\)
−0.0380682 + 0.999275i \(0.512120\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4000.38 0.437904
\(438\) 0 0
\(439\) 1372.00 0.149162 0.0745809 0.997215i \(-0.476238\pi\)
0.0745809 + 0.997215i \(0.476238\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2338.84 0.250839 0.125420 0.992104i \(-0.459972\pi\)
0.125420 + 0.992104i \(0.459972\pi\)
\(444\) 0 0
\(445\) −15232.0 −1.62262
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −17250.3 −1.81312 −0.906561 0.422074i \(-0.861302\pi\)
−0.906561 + 0.422074i \(0.861302\pi\)
\(450\) 0 0
\(451\) −2352.00 −0.245568
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3026.74 0.311859
\(456\) 0 0
\(457\) −17866.0 −1.82874 −0.914372 0.404875i \(-0.867315\pi\)
−0.914372 + 0.404875i \(0.867315\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2106.02 −0.212770 −0.106385 0.994325i \(-0.533928\pi\)
−0.106385 + 0.994325i \(0.533928\pi\)
\(462\) 0 0
\(463\) 13718.0 1.37695 0.688477 0.725258i \(-0.258280\pi\)
0.688477 + 0.725258i \(0.258280\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4095.62 0.405830 0.202915 0.979196i \(-0.434958\pi\)
0.202915 + 0.979196i \(0.434958\pi\)
\(468\) 0 0
\(469\) 11660.0 1.14799
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 507.984 0.0493808
\(474\) 0 0
\(475\) −1638.00 −0.158224
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8715.10 0.831322 0.415661 0.909520i \(-0.363550\pi\)
0.415661 + 0.909520i \(0.363550\pi\)
\(480\) 0 0
\(481\) −1118.00 −0.105980
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 740.810 0.0693577
\(486\) 0 0
\(487\) −4506.00 −0.419274 −0.209637 0.977779i \(-0.567228\pi\)
−0.209637 + 0.977779i \(0.567228\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −21621.1 −1.98726 −0.993631 0.112683i \(-0.964056\pi\)
−0.993631 + 0.112683i \(0.964056\pi\)
\(492\) 0 0
\(493\) 6160.00 0.562743
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 17811.2 1.60753
\(498\) 0 0
\(499\) 786.000 0.0705134 0.0352567 0.999378i \(-0.488775\pi\)
0.0352567 + 0.999378i \(0.488775\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2106.02 0.186685 0.0933426 0.995634i \(-0.470245\pi\)
0.0933426 + 0.995634i \(0.470245\pi\)
\(504\) 0 0
\(505\) 15456.0 1.36195
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8392.32 −0.730812 −0.365406 0.930848i \(-0.619070\pi\)
−0.365406 + 0.930848i \(0.619070\pi\)
\(510\) 0 0
\(511\) −3388.00 −0.293300
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 15112.5 1.29308
\(516\) 0 0
\(517\) −1932.00 −0.164351
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3905.13 −0.328382 −0.164191 0.986429i \(-0.552501\pi\)
−0.164191 + 0.986429i \(0.552501\pi\)
\(522\) 0 0
\(523\) 17668.0 1.47718 0.738592 0.674152i \(-0.235491\pi\)
0.738592 + 0.674152i \(0.235491\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −21187.2 −1.75129
\(528\) 0 0
\(529\) −11159.0 −0.917153
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5778.32 0.469581
\(534\) 0 0
\(535\) −17136.0 −1.38477
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −746.102 −0.0596232
\(540\) 0 0
\(541\) −1650.00 −0.131126 −0.0655629 0.997848i \(-0.520884\pi\)
−0.0655629 + 0.997848i \(0.520884\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3577.06 −0.281145
\(546\) 0 0
\(547\) −3796.00 −0.296719 −0.148359 0.988934i \(-0.547399\pi\)
−0.148359 + 0.988934i \(0.547399\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −6667.29 −0.515492
\(552\) 0 0
\(553\) 10120.0 0.778203
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2063.69 0.156986 0.0784930 0.996915i \(-0.474989\pi\)
0.0784930 + 0.996915i \(0.474989\pi\)
\(558\) 0 0
\(559\) −1248.00 −0.0944271
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 26034.2 1.94886 0.974432 0.224683i \(-0.0721346\pi\)
0.974432 + 0.224683i \(0.0721346\pi\)
\(564\) 0 0
\(565\) 17808.0 1.32600
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3640.55 0.268225 0.134112 0.990966i \(-0.457182\pi\)
0.134112 + 0.990966i \(0.457182\pi\)
\(570\) 0 0
\(571\) 19612.0 1.43737 0.718684 0.695337i \(-0.244745\pi\)
0.718684 + 0.695337i \(0.244745\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −412.737 −0.0299345
\(576\) 0 0
\(577\) 15722.0 1.13434 0.567171 0.823600i \(-0.308038\pi\)
0.567171 + 0.823600i \(0.308038\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −7101.20 −0.507069
\(582\) 0 0
\(583\) −1008.00 −0.0716074
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2725.12 0.191615 0.0958074 0.995400i \(-0.469457\pi\)
0.0958074 + 0.995400i \(0.469457\pi\)
\(588\) 0 0
\(589\) 22932.0 1.60424
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −18012.3 −1.24734 −0.623672 0.781686i \(-0.714360\pi\)
−0.623672 + 0.781686i \(0.714360\pi\)
\(594\) 0 0
\(595\) −27104.0 −1.86749
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 12181.0 0.830891 0.415446 0.909618i \(-0.363626\pi\)
0.415446 + 0.909618i \(0.363626\pi\)
\(600\) 0 0
\(601\) 5950.00 0.403836 0.201918 0.979402i \(-0.435283\pi\)
0.201918 + 0.979402i \(0.435283\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −13789.7 −0.926660
\(606\) 0 0
\(607\) −14168.0 −0.947383 −0.473691 0.880691i \(-0.657079\pi\)
−0.473691 + 0.880691i \(0.657079\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 4746.48 0.314275
\(612\) 0 0
\(613\) −6326.00 −0.416810 −0.208405 0.978043i \(-0.566827\pi\)
−0.208405 + 0.978043i \(0.566827\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8805.06 −0.574519 −0.287260 0.957853i \(-0.592744\pi\)
−0.287260 + 0.957853i \(0.592744\pi\)
\(618\) 0 0
\(619\) 24486.0 1.58994 0.794972 0.606646i \(-0.207485\pi\)
0.794972 + 0.606646i \(0.207485\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −31664.4 −2.03628
\(624\) 0 0
\(625\) −13831.0 −0.885184
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 10011.5 0.634635
\(630\) 0 0
\(631\) −22430.0 −1.41509 −0.707547 0.706666i \(-0.750198\pi\)
−0.707547 + 0.706666i \(0.750198\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3979.21 0.248677
\(636\) 0 0
\(637\) 1833.00 0.114013
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −27484.1 −1.69353 −0.846767 0.531964i \(-0.821454\pi\)
−0.846767 + 0.531964i \(0.821454\pi\)
\(642\) 0 0
\(643\) −16478.0 −1.01062 −0.505310 0.862938i \(-0.668622\pi\)
−0.505310 + 0.862938i \(0.668622\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −26563.3 −1.61408 −0.807042 0.590494i \(-0.798933\pi\)
−0.807042 + 0.590494i \(0.798933\pi\)
\(648\) 0 0
\(649\) 3108.00 0.187981
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 20287.6 1.21580 0.607899 0.794014i \(-0.292013\pi\)
0.607899 + 0.794014i \(0.292013\pi\)
\(654\) 0 0
\(655\) −7280.00 −0.434280
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −656.146 −0.0387858 −0.0193929 0.999812i \(-0.506173\pi\)
−0.0193929 + 0.999812i \(0.506173\pi\)
\(660\) 0 0
\(661\) −14238.0 −0.837812 −0.418906 0.908030i \(-0.637586\pi\)
−0.418906 + 0.908030i \(0.637586\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 29336.1 1.71068
\(666\) 0 0
\(667\) −1680.00 −0.0975260
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3037.32 −0.174746
\(672\) 0 0
\(673\) −4874.00 −0.279166 −0.139583 0.990210i \(-0.544576\pi\)
−0.139583 + 0.990210i \(0.544576\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 21801.0 1.23764 0.618818 0.785534i \(-0.287612\pi\)
0.618818 + 0.785534i \(0.287612\pi\)
\(678\) 0 0
\(679\) 1540.00 0.0870394
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −8746.85 −0.490028 −0.245014 0.969520i \(-0.578793\pi\)
−0.245014 + 0.969520i \(0.578793\pi\)
\(684\) 0 0
\(685\) −14784.0 −0.824624
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2476.42 0.136929
\(690\) 0 0
\(691\) −294.000 −0.0161857 −0.00809283 0.999967i \(-0.502576\pi\)
−0.00809283 + 0.999967i \(0.502576\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −22224.3 −1.21297
\(696\) 0 0
\(697\) −51744.0 −2.81197
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 15758.1 0.849037 0.424519 0.905419i \(-0.360443\pi\)
0.424519 + 0.905419i \(0.360443\pi\)
\(702\) 0 0
\(703\) −10836.0 −0.581348
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 32130.0 1.70916
\(708\) 0 0
\(709\) −6722.00 −0.356065 −0.178032 0.984025i \(-0.556973\pi\)
−0.178032 + 0.984025i \(0.556973\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 5778.32 0.303506
\(714\) 0 0
\(715\) −728.000 −0.0380778
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 31.7490 0.00164679 0.000823393 1.00000i \(-0.499738\pi\)
0.000823393 1.00000i \(0.499738\pi\)
\(720\) 0 0
\(721\) 31416.0 1.62274
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 687.895 0.0352383
\(726\) 0 0
\(727\) −12824.0 −0.654217 −0.327109 0.944987i \(-0.606074\pi\)
−0.327109 + 0.944987i \(0.606074\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 11175.7 0.565453
\(732\) 0 0
\(733\) −29610.0 −1.49205 −0.746023 0.665920i \(-0.768039\pi\)
−0.746023 + 0.665920i \(0.768039\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2804.50 −0.140170
\(738\) 0 0
\(739\) 15622.0 0.777625 0.388812 0.921317i \(-0.372885\pi\)
0.388812 + 0.921317i \(0.372885\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −8588.11 −0.424047 −0.212024 0.977265i \(-0.568005\pi\)
−0.212024 + 0.977265i \(0.568005\pi\)
\(744\) 0 0
\(745\) 21168.0 1.04099
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −35622.4 −1.73780
\(750\) 0 0
\(751\) −29468.0 −1.43183 −0.715914 0.698189i \(-0.753990\pi\)
−0.715914 + 0.698189i \(0.753990\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −37315.7 −1.79875
\(756\) 0 0
\(757\) −35030.0 −1.68189 −0.840943 0.541124i \(-0.817999\pi\)
−0.840943 + 0.541124i \(0.817999\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 22330.1 1.06369 0.531844 0.846842i \(-0.321499\pi\)
0.531844 + 0.846842i \(0.321499\pi\)
\(762\) 0 0
\(763\) −7436.00 −0.352819
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7635.64 −0.359461
\(768\) 0 0
\(769\) −27342.0 −1.28216 −0.641078 0.767476i \(-0.721512\pi\)
−0.641078 + 0.767476i \(0.721512\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −11884.7 −0.552993 −0.276496 0.961015i \(-0.589173\pi\)
−0.276496 + 0.961015i \(0.589173\pi\)
\(774\) 0 0
\(775\) −2366.00 −0.109664
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 56005.3 2.57586
\(780\) 0 0
\(781\) −4284.00 −0.196279
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 32447.5 1.47529
\(786\) 0 0
\(787\) −22666.0 −1.02663 −0.513314 0.858201i \(-0.671582\pi\)
−0.513314 + 0.858201i \(0.671582\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 37019.4 1.66404
\(792\) 0 0
\(793\) 7462.00 0.334153
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −582.065 −0.0258693 −0.0129346 0.999916i \(-0.504117\pi\)
−0.0129346 + 0.999916i \(0.504117\pi\)
\(798\) 0 0
\(799\) −42504.0 −1.88196
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 814.891 0.0358118
\(804\) 0 0
\(805\) 7392.00 0.323644
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −793.725 −0.0344943 −0.0172472 0.999851i \(-0.505490\pi\)
−0.0172472 + 0.999851i \(0.505490\pi\)
\(810\) 0 0
\(811\) 9478.00 0.410379 0.205190 0.978722i \(-0.434219\pi\)
0.205190 + 0.978722i \(0.434219\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 36426.7 1.56561
\(816\) 0 0
\(817\) −12096.0 −0.517975
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3227.82 −0.137213 −0.0686063 0.997644i \(-0.521855\pi\)
−0.0686063 + 0.997644i \(0.521855\pi\)
\(822\) 0 0
\(823\) −40476.0 −1.71434 −0.857172 0.515031i \(-0.827781\pi\)
−0.857172 + 0.515031i \(0.827781\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 7169.99 0.301481 0.150741 0.988573i \(-0.451834\pi\)
0.150741 + 0.988573i \(0.451834\pi\)
\(828\) 0 0
\(829\) 27482.0 1.15137 0.575687 0.817670i \(-0.304735\pi\)
0.575687 + 0.817670i \(0.304735\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −16414.2 −0.682737
\(834\) 0 0
\(835\) 28504.0 1.18134
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 19128.8 0.787126 0.393563 0.919298i \(-0.371242\pi\)
0.393563 + 0.919298i \(0.371242\pi\)
\(840\) 0 0
\(841\) −21589.0 −0.885194
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1788.53 0.0728133
\(846\) 0 0
\(847\) −28666.0 −1.16290
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −2730.42 −0.109985
\(852\) 0 0
\(853\) 31962.0 1.28295 0.641476 0.767143i \(-0.278322\pi\)
0.641476 + 0.767143i \(0.278322\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 4931.68 0.196573 0.0982865 0.995158i \(-0.468664\pi\)
0.0982865 + 0.995158i \(0.468664\pi\)
\(858\) 0 0
\(859\) −11704.0 −0.464884 −0.232442 0.972610i \(-0.574672\pi\)
−0.232442 + 0.972610i \(0.574672\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2280.64 0.0899581 0.0449790 0.998988i \(-0.485678\pi\)
0.0449790 + 0.998988i \(0.485678\pi\)
\(864\) 0 0
\(865\) −36960.0 −1.45281
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2434.09 −0.0950183
\(870\) 0 0
\(871\) 6890.00 0.268035
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −32130.0 −1.24136
\(876\) 0 0
\(877\) −1006.00 −0.0387346 −0.0193673 0.999812i \(-0.506165\pi\)
−0.0193673 + 0.999812i \(0.506165\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −40681.1 −1.55571 −0.777855 0.628444i \(-0.783692\pi\)
−0.777855 + 0.628444i \(0.783692\pi\)
\(882\) 0 0
\(883\) −124.000 −0.00472586 −0.00236293 0.999997i \(-0.500752\pi\)
−0.00236293 + 0.999997i \(0.500752\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −16573.0 −0.627358 −0.313679 0.949529i \(-0.601562\pi\)
−0.313679 + 0.949529i \(0.601562\pi\)
\(888\) 0 0
\(889\) 8272.00 0.312074
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 46004.3 1.72394
\(894\) 0 0
\(895\) 1792.00 0.0669273
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −9630.53 −0.357282
\(900\) 0 0
\(901\) −22176.0 −0.819966
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 35707.1 1.31154
\(906\) 0 0
\(907\) 42996.0 1.57404 0.787022 0.616924i \(-0.211622\pi\)
0.787022 + 0.616924i \(0.211622\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 53169.0 1.93366 0.966832 0.255413i \(-0.0822113\pi\)
0.966832 + 0.255413i \(0.0822113\pi\)
\(912\) 0 0
\(913\) 1708.00 0.0619130
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −15133.7 −0.544993
\(918\) 0 0
\(919\) −8244.00 −0.295913 −0.147957 0.988994i \(-0.547270\pi\)
−0.147957 + 0.988994i \(0.547270\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 10524.8 0.375328
\(924\) 0 0
\(925\) 1118.00 0.0397401
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −16192.0 −0.571843 −0.285922 0.958253i \(-0.592300\pi\)
−0.285922 + 0.958253i \(0.592300\pi\)
\(930\) 0 0
\(931\) 17766.0 0.625410
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 6519.13 0.228020
\(936\) 0 0
\(937\) −18214.0 −0.635032 −0.317516 0.948253i \(-0.602849\pi\)
−0.317516 + 0.948253i \(0.602849\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −13916.7 −0.482115 −0.241057 0.970511i \(-0.577494\pi\)
−0.241057 + 0.970511i \(0.577494\pi\)
\(942\) 0 0
\(943\) 14112.0 0.487328
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −40400.6 −1.38632 −0.693159 0.720784i \(-0.743782\pi\)
−0.693159 + 0.720784i \(0.743782\pi\)
\(948\) 0 0
\(949\) −2002.00 −0.0684802
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 21271.8 0.723046 0.361523 0.932363i \(-0.382257\pi\)
0.361523 + 0.932363i \(0.382257\pi\)
\(954\) 0 0
\(955\) −12544.0 −0.425041
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −30733.0 −1.03485
\(960\) 0 0
\(961\) 3333.00 0.111879
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −16319.0 −0.544380
\(966\) 0 0
\(967\) −9578.00 −0.318519 −0.159259 0.987237i \(-0.550911\pi\)
−0.159259 + 0.987237i \(0.550911\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −44956.6 −1.48581 −0.742907 0.669394i \(-0.766554\pi\)
−0.742907 + 0.669394i \(0.766554\pi\)
\(972\) 0 0
\(973\) −46200.0 −1.52220
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −32765.0 −1.07292 −0.536461 0.843925i \(-0.680239\pi\)
−0.536461 + 0.843925i \(0.680239\pi\)
\(978\) 0 0
\(979\) 7616.00 0.248630
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −47438.3 −1.53921 −0.769607 0.638518i \(-0.779548\pi\)
−0.769607 + 0.638518i \(0.779548\pi\)
\(984\) 0 0
\(985\) −22512.0 −0.728215
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −3047.91 −0.0979957
\(990\) 0 0
\(991\) 6848.00 0.219509 0.109755 0.993959i \(-0.464993\pi\)
0.109755 + 0.993959i \(0.464993\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 10075.0 0.321005
\(996\) 0 0
\(997\) −5810.00 −0.184558 −0.0922791 0.995733i \(-0.529415\pi\)
−0.0922791 + 0.995733i \(0.529415\pi\)
\(998\) 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 1872.4.a.ba.1.2 2
3.2 odd 2 inner 1872.4.a.ba.1.1 2
4.3 odd 2 117.4.a.e.1.1 2
12.11 even 2 117.4.a.e.1.2 yes 2
52.51 odd 2 1521.4.a.p.1.2 2
156.155 even 2 1521.4.a.p.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.4.a.e.1.1 2 4.3 odd 2
117.4.a.e.1.2 yes 2 12.11 even 2
1521.4.a.p.1.1 2 156.155 even 2
1521.4.a.p.1.2 2 52.51 odd 2
1872.4.a.ba.1.1 2 3.2 odd 2 inner
1872.4.a.ba.1.2 2 1.1 even 1 trivial