Properties

Label 1152.4.a.i.1.1
Level $1152$
Weight $4$
Character 1152.1
Self dual yes
Analytic conductor $67.970$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1152.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(67.9702003266\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 128)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1152.1

$q$-expansion

\(f(q)\) \(=\) \(q+6.00000 q^{5} -20.0000 q^{7} +O(q^{10})\) \(q+6.00000 q^{5} -20.0000 q^{7} -14.0000 q^{11} -54.0000 q^{13} +66.0000 q^{17} +162.000 q^{19} +172.000 q^{23} -89.0000 q^{25} -2.00000 q^{29} +128.000 q^{31} -120.000 q^{35} -158.000 q^{37} -202.000 q^{41} -298.000 q^{43} -408.000 q^{47} +57.0000 q^{49} -690.000 q^{53} -84.0000 q^{55} +322.000 q^{59} +298.000 q^{61} -324.000 q^{65} +202.000 q^{67} -700.000 q^{71} -418.000 q^{73} +280.000 q^{77} -744.000 q^{79} +678.000 q^{83} +396.000 q^{85} +82.0000 q^{89} +1080.00 q^{91} +972.000 q^{95} -1122.00 q^{97} +O(q^{100})\)

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
\(5\) 6.00000 0.536656 0.268328 0.963328i \(-0.413529\pi\)
0.268328 + 0.963328i \(0.413529\pi\)
\(6\) 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
\(11\) −14.0000 −0.383742 −0.191871 0.981420i \(-0.561455\pi\)
−0.191871 + 0.981420i \(0.561455\pi\)
\(12\) 0 0
\(13\) −54.0000 −1.15207 −0.576035 0.817425i \(-0.695401\pi\)
−0.576035 + 0.817425i \(0.695401\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 66.0000 0.941609 0.470804 0.882238i \(-0.343964\pi\)
0.470804 + 0.882238i \(0.343964\pi\)
\(18\) 0 0
\(19\) 162.000 1.95607 0.978035 0.208438i \(-0.0668381\pi\)
0.978035 + 0.208438i \(0.0668381\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 172.000 1.55933 0.779663 0.626200i \(-0.215391\pi\)
0.779663 + 0.626200i \(0.215391\pi\)
\(24\) 0 0
\(25\) −89.0000 −0.712000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.00000 −0.0128066 −0.00640329 0.999979i \(-0.502038\pi\)
−0.00640329 + 0.999979i \(0.502038\pi\)
\(30\) 0 0
\(31\) 128.000 0.741596 0.370798 0.928714i \(-0.379084\pi\)
0.370798 + 0.928714i \(0.379084\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −120.000 −0.579534
\(36\) 0 0
\(37\) −158.000 −0.702028 −0.351014 0.936370i \(-0.614163\pi\)
−0.351014 + 0.936370i \(0.614163\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −202.000 −0.769441 −0.384721 0.923033i \(-0.625702\pi\)
−0.384721 + 0.923033i \(0.625702\pi\)
\(42\) 0 0
\(43\) −298.000 −1.05685 −0.528425 0.848980i \(-0.677217\pi\)
−0.528425 + 0.848980i \(0.677217\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −408.000 −1.26623 −0.633116 0.774057i \(-0.718224\pi\)
−0.633116 + 0.774057i \(0.718224\pi\)
\(48\) 0 0
\(49\) 57.0000 0.166181
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −690.000 −1.78828 −0.894140 0.447788i \(-0.852212\pi\)
−0.894140 + 0.447788i \(0.852212\pi\)
\(54\) 0 0
\(55\) −84.0000 −0.205937
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 322.000 0.710523 0.355261 0.934767i \(-0.384392\pi\)
0.355261 + 0.934767i \(0.384392\pi\)
\(60\) 0 0
\(61\) 298.000 0.625492 0.312746 0.949837i \(-0.398751\pi\)
0.312746 + 0.949837i \(0.398751\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −324.000 −0.618265
\(66\) 0 0
\(67\) 202.000 0.368332 0.184166 0.982895i \(-0.441042\pi\)
0.184166 + 0.982895i \(0.441042\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −700.000 −1.17007 −0.585033 0.811009i \(-0.698919\pi\)
−0.585033 + 0.811009i \(0.698919\pi\)
\(72\) 0 0
\(73\) −418.000 −0.670181 −0.335090 0.942186i \(-0.608767\pi\)
−0.335090 + 0.942186i \(0.608767\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 280.000 0.414402
\(78\) 0 0
\(79\) −744.000 −1.05958 −0.529788 0.848130i \(-0.677729\pi\)
−0.529788 + 0.848130i \(0.677729\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 678.000 0.896629 0.448314 0.893876i \(-0.352025\pi\)
0.448314 + 0.893876i \(0.352025\pi\)
\(84\) 0 0
\(85\) 396.000 0.505320
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 82.0000 0.0976627 0.0488314 0.998807i \(-0.484450\pi\)
0.0488314 + 0.998807i \(0.484450\pi\)
\(90\) 0 0
\(91\) 1080.00 1.24412
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 972.000 1.04974
\(96\) 0 0
\(97\) −1122.00 −1.17445 −0.587226 0.809423i \(-0.699780\pi\)
−0.587226 + 0.809423i \(0.699780\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1390.00 1.36941 0.684704 0.728821i \(-0.259932\pi\)
0.684704 + 0.728821i \(0.259932\pi\)
\(102\) 0 0
\(103\) −788.000 −0.753825 −0.376912 0.926249i \(-0.623014\pi\)
−0.376912 + 0.926249i \(0.623014\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1614.00 −1.45824 −0.729118 0.684388i \(-0.760070\pi\)
−0.729118 + 0.684388i \(0.760070\pi\)
\(108\) 0 0
\(109\) −2014.00 −1.76978 −0.884891 0.465798i \(-0.845767\pi\)
−0.884891 + 0.465798i \(0.845767\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 542.000 0.451213 0.225607 0.974219i \(-0.427564\pi\)
0.225607 + 0.974219i \(0.427564\pi\)
\(114\) 0 0
\(115\) 1032.00 0.836822
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1320.00 −1.01684
\(120\) 0 0
\(121\) −1135.00 −0.852742
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1284.00 −0.918756
\(126\) 0 0
\(127\) −1712.00 −1.19618 −0.598092 0.801427i \(-0.704074\pi\)
−0.598092 + 0.801427i \(0.704074\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2118.00 1.41260 0.706300 0.707913i \(-0.250363\pi\)
0.706300 + 0.707913i \(0.250363\pi\)
\(132\) 0 0
\(133\) −3240.00 −2.11236
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 486.000 0.303079 0.151539 0.988451i \(-0.451577\pi\)
0.151539 + 0.988451i \(0.451577\pi\)
\(138\) 0 0
\(139\) 1286.00 0.784727 0.392364 0.919810i \(-0.371657\pi\)
0.392364 + 0.919810i \(0.371657\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 756.000 0.442097
\(144\) 0 0
\(145\) −12.0000 −0.00687273
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2666.00 −1.46582 −0.732910 0.680325i \(-0.761838\pi\)
−0.732910 + 0.680325i \(0.761838\pi\)
\(150\) 0 0
\(151\) −172.000 −0.0926964 −0.0463482 0.998925i \(-0.514758\pi\)
−0.0463482 + 0.998925i \(0.514758\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 768.000 0.397982
\(156\) 0 0
\(157\) −838.000 −0.425985 −0.212993 0.977054i \(-0.568321\pi\)
−0.212993 + 0.977054i \(0.568321\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −3440.00 −1.68391
\(162\) 0 0
\(163\) 1346.00 0.646791 0.323395 0.946264i \(-0.395176\pi\)
0.323395 + 0.946264i \(0.395176\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1052.00 −0.487462 −0.243731 0.969843i \(-0.578371\pi\)
−0.243731 + 0.969843i \(0.578371\pi\)
\(168\) 0 0
\(169\) 719.000 0.327264
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 38.0000 0.0166999 0.00834996 0.999965i \(-0.497342\pi\)
0.00834996 + 0.999965i \(0.497342\pi\)
\(174\) 0 0
\(175\) 1780.00 0.768888
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2790.00 1.16500 0.582498 0.812832i \(-0.302075\pi\)
0.582498 + 0.812832i \(0.302075\pi\)
\(180\) 0 0
\(181\) 3418.00 1.40364 0.701818 0.712357i \(-0.252372\pi\)
0.701818 + 0.712357i \(0.252372\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −948.000 −0.376748
\(186\) 0 0
\(187\) −924.000 −0.361335
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1968.00 −0.745547 −0.372774 0.927922i \(-0.621593\pi\)
−0.372774 + 0.927922i \(0.621593\pi\)
\(192\) 0 0
\(193\) −1058.00 −0.394593 −0.197297 0.980344i \(-0.563216\pi\)
−0.197297 + 0.980344i \(0.563216\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 726.000 0.262565 0.131283 0.991345i \(-0.458090\pi\)
0.131283 + 0.991345i \(0.458090\pi\)
\(198\) 0 0
\(199\) −4116.00 −1.46621 −0.733104 0.680116i \(-0.761929\pi\)
−0.733104 + 0.680116i \(0.761929\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 40.0000 0.0138298
\(204\) 0 0
\(205\) −1212.00 −0.412926
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2268.00 −0.750626
\(210\) 0 0
\(211\) 1482.00 0.483531 0.241766 0.970335i \(-0.422273\pi\)
0.241766 + 0.970335i \(0.422273\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1788.00 −0.567166
\(216\) 0 0
\(217\) −2560.00 −0.800848
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3564.00 −1.08480
\(222\) 0 0
\(223\) 896.000 0.269061 0.134530 0.990909i \(-0.457047\pi\)
0.134530 + 0.990909i \(0.457047\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3410.00 −0.997047 −0.498523 0.866876i \(-0.666124\pi\)
−0.498523 + 0.866876i \(0.666124\pi\)
\(228\) 0 0
\(229\) −4502.00 −1.29913 −0.649564 0.760307i \(-0.725049\pi\)
−0.649564 + 0.760307i \(0.725049\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2302.00 −0.647249 −0.323625 0.946186i \(-0.604901\pi\)
−0.323625 + 0.946186i \(0.604901\pi\)
\(234\) 0 0
\(235\) −2448.00 −0.679532
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4024.00 1.08908 0.544542 0.838734i \(-0.316704\pi\)
0.544542 + 0.838734i \(0.316704\pi\)
\(240\) 0 0
\(241\) −3586.00 −0.958484 −0.479242 0.877683i \(-0.659088\pi\)
−0.479242 + 0.877683i \(0.659088\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 342.000 0.0891820
\(246\) 0 0
\(247\) −8748.00 −2.25353
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1250.00 0.314340 0.157170 0.987572i \(-0.449763\pi\)
0.157170 + 0.987572i \(0.449763\pi\)
\(252\) 0 0
\(253\) −2408.00 −0.598378
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6638.00 1.61116 0.805578 0.592490i \(-0.201855\pi\)
0.805578 + 0.592490i \(0.201855\pi\)
\(258\) 0 0
\(259\) 3160.00 0.758119
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1724.00 −0.404207 −0.202103 0.979364i \(-0.564778\pi\)
−0.202103 + 0.979364i \(0.564778\pi\)
\(264\) 0 0
\(265\) −4140.00 −0.959691
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4814.00 1.09113 0.545566 0.838068i \(-0.316315\pi\)
0.545566 + 0.838068i \(0.316315\pi\)
\(270\) 0 0
\(271\) 1640.00 0.367612 0.183806 0.982963i \(-0.441158\pi\)
0.183806 + 0.982963i \(0.441158\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1246.00 0.273224
\(276\) 0 0
\(277\) −3982.00 −0.863737 −0.431869 0.901937i \(-0.642146\pi\)
−0.431869 + 0.901937i \(0.642146\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4126.00 −0.875931 −0.437965 0.898992i \(-0.644301\pi\)
−0.437965 + 0.898992i \(0.644301\pi\)
\(282\) 0 0
\(283\) 3446.00 0.723828 0.361914 0.932211i \(-0.382123\pi\)
0.361914 + 0.932211i \(0.382123\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4040.00 0.830919
\(288\) 0 0
\(289\) −557.000 −0.113373
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1514.00 −0.301873 −0.150937 0.988543i \(-0.548229\pi\)
−0.150937 + 0.988543i \(0.548229\pi\)
\(294\) 0 0
\(295\) 1932.00 0.381306
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −9288.00 −1.79645
\(300\) 0 0
\(301\) 5960.00 1.14129
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1788.00 0.335674
\(306\) 0 0
\(307\) 5490.00 1.02062 0.510311 0.859990i \(-0.329530\pi\)
0.510311 + 0.859990i \(0.329530\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5556.00 −1.01303 −0.506514 0.862232i \(-0.669066\pi\)
−0.506514 + 0.862232i \(0.669066\pi\)
\(312\) 0 0
\(313\) −2054.00 −0.370923 −0.185462 0.982652i \(-0.559378\pi\)
−0.185462 + 0.982652i \(0.559378\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2494.00 0.441883 0.220942 0.975287i \(-0.429087\pi\)
0.220942 + 0.975287i \(0.429087\pi\)
\(318\) 0 0
\(319\) 28.0000 0.00491442
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 10692.0 1.84185
\(324\) 0 0
\(325\) 4806.00 0.820274
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 8160.00 1.36740
\(330\) 0 0
\(331\) −2914.00 −0.483891 −0.241946 0.970290i \(-0.577786\pi\)
−0.241946 + 0.970290i \(0.577786\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1212.00 0.197668
\(336\) 0 0
\(337\) 7186.00 1.16156 0.580781 0.814060i \(-0.302747\pi\)
0.580781 + 0.814060i \(0.302747\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1792.00 −0.284581
\(342\) 0 0
\(343\) 5720.00 0.900440
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4446.00 −0.687821 −0.343910 0.939002i \(-0.611752\pi\)
−0.343910 + 0.939002i \(0.611752\pi\)
\(348\) 0 0
\(349\) −430.000 −0.0659524 −0.0329762 0.999456i \(-0.510499\pi\)
−0.0329762 + 0.999456i \(0.510499\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −850.000 −0.128161 −0.0640806 0.997945i \(-0.520411\pi\)
−0.0640806 + 0.997945i \(0.520411\pi\)
\(354\) 0 0
\(355\) −4200.00 −0.627924
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10988.0 −1.61539 −0.807694 0.589602i \(-0.799285\pi\)
−0.807694 + 0.589602i \(0.799285\pi\)
\(360\) 0 0
\(361\) 19385.0 2.82621
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2508.00 −0.359657
\(366\) 0 0
\(367\) −872.000 −0.124027 −0.0620137 0.998075i \(-0.519752\pi\)
−0.0620137 + 0.998075i \(0.519752\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 13800.0 1.93116
\(372\) 0 0
\(373\) −3454.00 −0.479467 −0.239734 0.970839i \(-0.577060\pi\)
−0.239734 + 0.970839i \(0.577060\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 108.000 0.0147541
\(378\) 0 0
\(379\) −1490.00 −0.201942 −0.100971 0.994889i \(-0.532195\pi\)
−0.100971 + 0.994889i \(0.532195\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 10240.0 1.36616 0.683080 0.730343i \(-0.260640\pi\)
0.683080 + 0.730343i \(0.260640\pi\)
\(384\) 0 0
\(385\) 1680.00 0.222392
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7458.00 −0.972071 −0.486035 0.873939i \(-0.661557\pi\)
−0.486035 + 0.873939i \(0.661557\pi\)
\(390\) 0 0
\(391\) 11352.0 1.46827
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4464.00 −0.568628
\(396\) 0 0
\(397\) 4706.00 0.594930 0.297465 0.954733i \(-0.403859\pi\)
0.297465 + 0.954733i \(0.403859\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5598.00 −0.697134 −0.348567 0.937284i \(-0.613332\pi\)
−0.348567 + 0.937284i \(0.613332\pi\)
\(402\) 0 0
\(403\) −6912.00 −0.854370
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2212.00 0.269397
\(408\) 0 0
\(409\) −838.000 −0.101312 −0.0506558 0.998716i \(-0.516131\pi\)
−0.0506558 + 0.998716i \(0.516131\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −6440.00 −0.767292
\(414\) 0 0
\(415\) 4068.00 0.481181
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −26.0000 −0.00303146 −0.00151573 0.999999i \(-0.500482\pi\)
−0.00151573 + 0.999999i \(0.500482\pi\)
\(420\) 0 0
\(421\) 15578.0 1.80339 0.901693 0.432377i \(-0.142325\pi\)
0.901693 + 0.432377i \(0.142325\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5874.00 −0.670426
\(426\) 0 0
\(427\) −5960.00 −0.675467
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6792.00 −0.759070 −0.379535 0.925177i \(-0.623916\pi\)
−0.379535 + 0.925177i \(0.623916\pi\)
\(432\) 0 0
\(433\) −9314.00 −1.03372 −0.516862 0.856069i \(-0.672900\pi\)
−0.516862 + 0.856069i \(0.672900\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 27864.0 3.05015
\(438\) 0 0
\(439\) 3828.00 0.416174 0.208087 0.978110i \(-0.433276\pi\)
0.208087 + 0.978110i \(0.433276\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −15414.0 −1.65314 −0.826570 0.562834i \(-0.809711\pi\)
−0.826570 + 0.562834i \(0.809711\pi\)
\(444\) 0 0
\(445\) 492.000 0.0524113
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3650.00 0.383640 0.191820 0.981430i \(-0.438561\pi\)
0.191820 + 0.981430i \(0.438561\pi\)
\(450\) 0 0
\(451\) 2828.00 0.295267
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6480.00 0.667664
\(456\) 0 0
\(457\) −15862.0 −1.62362 −0.811809 0.583924i \(-0.801517\pi\)
−0.811809 + 0.583924i \(0.801517\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 78.0000 0.00788031 0.00394015 0.999992i \(-0.498746\pi\)
0.00394015 + 0.999992i \(0.498746\pi\)
\(462\) 0 0
\(463\) 4376.00 0.439244 0.219622 0.975585i \(-0.429518\pi\)
0.219622 + 0.975585i \(0.429518\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −13714.0 −1.35890 −0.679452 0.733720i \(-0.737782\pi\)
−0.679452 + 0.733720i \(0.737782\pi\)
\(468\) 0 0
\(469\) −4040.00 −0.397761
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4172.00 0.405558
\(474\) 0 0
\(475\) −14418.0 −1.39272
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 19072.0 1.81925 0.909626 0.415428i \(-0.136368\pi\)
0.909626 + 0.415428i \(0.136368\pi\)
\(480\) 0 0
\(481\) 8532.00 0.808785
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6732.00 −0.630277
\(486\) 0 0
\(487\) −19428.0 −1.80773 −0.903867 0.427813i \(-0.859284\pi\)
−0.903867 + 0.427813i \(0.859284\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2490.00 0.228864 0.114432 0.993431i \(-0.463495\pi\)
0.114432 + 0.993431i \(0.463495\pi\)
\(492\) 0 0
\(493\) −132.000 −0.0120588
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 14000.0 1.26355
\(498\) 0 0
\(499\) 2826.00 0.253525 0.126763 0.991933i \(-0.459541\pi\)
0.126763 + 0.991933i \(0.459541\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2268.00 0.201044 0.100522 0.994935i \(-0.467949\pi\)
0.100522 + 0.994935i \(0.467949\pi\)
\(504\) 0 0
\(505\) 8340.00 0.734901
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 10534.0 0.917311 0.458656 0.888614i \(-0.348331\pi\)
0.458656 + 0.888614i \(0.348331\pi\)
\(510\) 0 0
\(511\) 8360.00 0.723727
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4728.00 −0.404545
\(516\) 0 0
\(517\) 5712.00 0.485906
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 9478.00 0.797003 0.398502 0.917168i \(-0.369530\pi\)
0.398502 + 0.917168i \(0.369530\pi\)
\(522\) 0 0
\(523\) −5858.00 −0.489775 −0.244888 0.969551i \(-0.578751\pi\)
−0.244888 + 0.969551i \(0.578751\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8448.00 0.698293
\(528\) 0 0
\(529\) 17417.0 1.43150
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 10908.0 0.886450
\(534\) 0 0
\(535\) −9684.00 −0.782572
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −798.000 −0.0637705
\(540\) 0 0
\(541\) −1910.00 −0.151788 −0.0758940 0.997116i \(-0.524181\pi\)
−0.0758940 + 0.997116i \(0.524181\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −12084.0 −0.949765
\(546\) 0 0
\(547\) 1754.00 0.137104 0.0685518 0.997648i \(-0.478162\pi\)
0.0685518 + 0.997648i \(0.478162\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −324.000 −0.0250506
\(552\) 0 0
\(553\) 14880.0 1.14424
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2294.00 0.174506 0.0872531 0.996186i \(-0.472191\pi\)
0.0872531 + 0.996186i \(0.472191\pi\)
\(558\) 0 0
\(559\) 16092.0 1.21757
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −16242.0 −1.21584 −0.607921 0.793998i \(-0.707996\pi\)
−0.607921 + 0.793998i \(0.707996\pi\)
\(564\) 0 0
\(565\) 3252.00 0.242146
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 15990.0 1.17809 0.589047 0.808099i \(-0.299503\pi\)
0.589047 + 0.808099i \(0.299503\pi\)
\(570\) 0 0
\(571\) −21674.0 −1.58849 −0.794246 0.607597i \(-0.792134\pi\)
−0.794246 + 0.607597i \(0.792134\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −15308.0 −1.11024
\(576\) 0 0
\(577\) −12542.0 −0.904905 −0.452453 0.891788i \(-0.649451\pi\)
−0.452453 + 0.891788i \(0.649451\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −13560.0 −0.968268
\(582\) 0 0
\(583\) 9660.00 0.686237
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18578.0 1.30630 0.653148 0.757230i \(-0.273448\pi\)
0.653148 + 0.757230i \(0.273448\pi\)
\(588\) 0 0
\(589\) 20736.0 1.45061
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −14514.0 −1.00509 −0.502545 0.864551i \(-0.667603\pi\)
−0.502545 + 0.864551i \(0.667603\pi\)
\(594\) 0 0
\(595\) −7920.00 −0.545695
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3460.00 −0.236013 −0.118006 0.993013i \(-0.537650\pi\)
−0.118006 + 0.993013i \(0.537650\pi\)
\(600\) 0 0
\(601\) 20686.0 1.40399 0.701996 0.712181i \(-0.252292\pi\)
0.701996 + 0.712181i \(0.252292\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6810.00 −0.457630
\(606\) 0 0
\(607\) 9776.00 0.653700 0.326850 0.945076i \(-0.394013\pi\)
0.326850 + 0.945076i \(0.394013\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 22032.0 1.45879
\(612\) 0 0
\(613\) 8794.00 0.579423 0.289712 0.957114i \(-0.406441\pi\)
0.289712 + 0.957114i \(0.406441\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −16398.0 −1.06995 −0.534975 0.844868i \(-0.679679\pi\)
−0.534975 + 0.844868i \(0.679679\pi\)
\(618\) 0 0
\(619\) 21374.0 1.38787 0.693937 0.720036i \(-0.255875\pi\)
0.693937 + 0.720036i \(0.255875\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1640.00 −0.105466
\(624\) 0 0
\(625\) 3421.00 0.218944
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −10428.0 −0.661036
\(630\) 0 0
\(631\) 18916.0 1.19340 0.596699 0.802465i \(-0.296479\pi\)
0.596699 + 0.802465i \(0.296479\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −10272.0 −0.641940
\(636\) 0 0
\(637\) −3078.00 −0.191452
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5250.00 0.323498 0.161749 0.986832i \(-0.448286\pi\)
0.161749 + 0.986832i \(0.448286\pi\)
\(642\) 0 0
\(643\) −4502.00 −0.276114 −0.138057 0.990424i \(-0.544086\pi\)
−0.138057 + 0.990424i \(0.544086\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 11076.0 0.673018 0.336509 0.941680i \(-0.390754\pi\)
0.336509 + 0.941680i \(0.390754\pi\)
\(648\) 0 0
\(649\) −4508.00 −0.272657
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 30766.0 1.84375 0.921873 0.387491i \(-0.126658\pi\)
0.921873 + 0.387491i \(0.126658\pi\)
\(654\) 0 0
\(655\) 12708.0 0.758080
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 20518.0 1.21285 0.606425 0.795141i \(-0.292603\pi\)
0.606425 + 0.795141i \(0.292603\pi\)
\(660\) 0 0
\(661\) −70.0000 −0.00411904 −0.00205952 0.999998i \(-0.500656\pi\)
−0.00205952 + 0.999998i \(0.500656\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −19440.0 −1.13361
\(666\) 0 0
\(667\) −344.000 −0.0199696
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4172.00 −0.240027
\(672\) 0 0
\(673\) 23070.0 1.32137 0.660686 0.750663i \(-0.270266\pi\)
0.660686 + 0.750663i \(0.270266\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2622.00 0.148850 0.0744251 0.997227i \(-0.476288\pi\)
0.0744251 + 0.997227i \(0.476288\pi\)
\(678\) 0 0
\(679\) 22440.0 1.26829
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 14682.0 0.822535 0.411267 0.911515i \(-0.365086\pi\)
0.411267 + 0.911515i \(0.365086\pi\)
\(684\) 0 0
\(685\) 2916.00 0.162649
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 37260.0 2.06022
\(690\) 0 0
\(691\) −23270.0 −1.28109 −0.640545 0.767921i \(-0.721291\pi\)
−0.640545 + 0.767921i \(0.721291\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 7716.00 0.421129
\(696\) 0 0
\(697\) −13332.0 −0.724513
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −31530.0 −1.69882 −0.849409 0.527735i \(-0.823041\pi\)
−0.849409 + 0.527735i \(0.823041\pi\)
\(702\) 0 0
\(703\) −25596.0 −1.37322
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −27800.0 −1.47882
\(708\) 0 0
\(709\) −22014.0 −1.16608 −0.583042 0.812442i \(-0.698138\pi\)
−0.583042 + 0.812442i \(0.698138\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 22016.0 1.15639
\(714\) 0 0
\(715\) 4536.00 0.237254
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 19016.0 0.986338 0.493169 0.869933i \(-0.335838\pi\)
0.493169 + 0.869933i \(0.335838\pi\)
\(720\) 0 0
\(721\) 15760.0 0.814054
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 178.000 0.00911828
\(726\) 0 0
\(727\) −15996.0 −0.816037 −0.408018 0.912974i \(-0.633780\pi\)
−0.408018 + 0.912974i \(0.633780\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −19668.0 −0.995140
\(732\) 0 0
\(733\) −10622.0 −0.535242 −0.267621 0.963524i \(-0.586238\pi\)
−0.267621 + 0.963524i \(0.586238\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2828.00 −0.141344
\(738\) 0 0
\(739\) −8878.00 −0.441925 −0.220962 0.975282i \(-0.570920\pi\)
−0.220962 + 0.975282i \(0.570920\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −21852.0 −1.07897 −0.539483 0.841996i \(-0.681380\pi\)
−0.539483 + 0.841996i \(0.681380\pi\)
\(744\) 0 0
\(745\) −15996.0 −0.786642
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 32280.0 1.57475
\(750\) 0 0
\(751\) −32024.0 −1.55602 −0.778011 0.628251i \(-0.783771\pi\)
−0.778011 + 0.628251i \(0.783771\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1032.00 −0.0497461
\(756\) 0 0
\(757\) 26602.0 1.27723 0.638617 0.769525i \(-0.279507\pi\)
0.638617 + 0.769525i \(0.279507\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13958.0 0.664885 0.332442 0.943124i \(-0.392127\pi\)
0.332442 + 0.943124i \(0.392127\pi\)
\(762\) 0 0
\(763\) 40280.0 1.91118
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −17388.0 −0.818571
\(768\) 0 0
\(769\) −11970.0 −0.561312 −0.280656 0.959808i \(-0.590552\pi\)
−0.280656 + 0.959808i \(0.590552\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 12318.0 0.573154 0.286577 0.958057i \(-0.407483\pi\)
0.286577 + 0.958057i \(0.407483\pi\)
\(774\) 0 0
\(775\) −11392.0 −0.528016
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −32724.0 −1.50508
\(780\) 0 0
\(781\) 9800.00 0.449003
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −5028.00 −0.228608
\(786\) 0 0
\(787\) 26698.0 1.20925 0.604626 0.796510i \(-0.293323\pi\)
0.604626 + 0.796510i \(0.293323\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −10840.0 −0.487264
\(792\) 0 0
\(793\) −16092.0 −0.720610
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −4794.00 −0.213064 −0.106532 0.994309i \(-0.533975\pi\)
−0.106532 + 0.994309i \(0.533975\pi\)
\(798\) 0 0
\(799\) −26928.0 −1.19230
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 5852.00 0.257176
\(804\) 0 0
\(805\) −20640.0 −0.903683
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −39114.0 −1.69985 −0.849923 0.526907i \(-0.823351\pi\)
−0.849923 + 0.526907i \(0.823351\pi\)
\(810\) 0 0
\(811\) −1090.00 −0.0471949 −0.0235975 0.999722i \(-0.507512\pi\)
−0.0235975 + 0.999722i \(0.507512\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 8076.00 0.347104
\(816\) 0 0
\(817\) −48276.0 −2.06727
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −9730.00 −0.413617 −0.206808 0.978381i \(-0.566308\pi\)
−0.206808 + 0.978381i \(0.566308\pi\)
\(822\) 0 0
\(823\) −1100.00 −0.0465900 −0.0232950 0.999729i \(-0.507416\pi\)
−0.0232950 + 0.999729i \(0.507416\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 38074.0 1.60092 0.800461 0.599385i \(-0.204588\pi\)
0.800461 + 0.599385i \(0.204588\pi\)
\(828\) 0 0
\(829\) −24230.0 −1.01513 −0.507565 0.861613i \(-0.669454\pi\)
−0.507565 + 0.861613i \(0.669454\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3762.00 0.156477
\(834\) 0 0
\(835\) −6312.00 −0.261600
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 16820.0 0.692123 0.346061 0.938212i \(-0.387519\pi\)
0.346061 + 0.938212i \(0.387519\pi\)
\(840\) 0 0
\(841\) −24385.0 −0.999836
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 4314.00 0.175629
\(846\) 0 0
\(847\) 22700.0 0.920875
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −27176.0 −1.09469
\(852\) 0 0
\(853\) 22162.0 0.889581 0.444790 0.895635i \(-0.353278\pi\)
0.444790 + 0.895635i \(0.353278\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 8790.00 0.350363 0.175181 0.984536i \(-0.443949\pi\)
0.175181 + 0.984536i \(0.443949\pi\)
\(858\) 0 0
\(859\) 10558.0 0.419365 0.209682 0.977770i \(-0.432757\pi\)
0.209682 + 0.977770i \(0.432757\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −7392.00 −0.291572 −0.145786 0.989316i \(-0.546571\pi\)
−0.145786 + 0.989316i \(0.546571\pi\)
\(864\) 0 0
\(865\) 228.000 0.00896212
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 10416.0 0.406604
\(870\) 0 0
\(871\) −10908.0 −0.424344
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 25680.0 0.992163
\(876\) 0 0
\(877\) −6574.00 −0.253122 −0.126561 0.991959i \(-0.540394\pi\)
−0.126561 + 0.991959i \(0.540394\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −47154.0 −1.80324 −0.901622 0.432524i \(-0.857623\pi\)
−0.901622 + 0.432524i \(0.857623\pi\)
\(882\) 0 0
\(883\) 642.000 0.0244677 0.0122339 0.999925i \(-0.496106\pi\)
0.0122339 + 0.999925i \(0.496106\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 23308.0 0.882307 0.441153 0.897432i \(-0.354569\pi\)
0.441153 + 0.897432i \(0.354569\pi\)
\(888\) 0 0
\(889\) 34240.0 1.29176
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −66096.0 −2.47684
\(894\) 0 0
\(895\) 16740.0 0.625203
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −256.000 −0.00949731
\(900\) 0 0
\(901\) −45540.0 −1.68386
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 20508.0 0.753270
\(906\) 0 0
\(907\) −21450.0 −0.785265 −0.392633 0.919695i \(-0.628436\pi\)
−0.392633 + 0.919695i \(0.628436\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −40904.0 −1.48761 −0.743804 0.668398i \(-0.766980\pi\)
−0.743804 + 0.668398i \(0.766980\pi\)
\(912\) 0 0
\(913\) −9492.00 −0.344074
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −42360.0 −1.52546
\(918\) 0 0
\(919\) 27380.0 0.982789 0.491394 0.870937i \(-0.336487\pi\)
0.491394 + 0.870937i \(0.336487\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 37800.0 1.34800
\(924\) 0 0
\(925\) 14062.0 0.499844
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −10302.0 −0.363830 −0.181915 0.983314i \(-0.558230\pi\)
−0.181915 + 0.983314i \(0.558230\pi\)
\(930\) 0 0
\(931\) 9234.00 0.325061
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −5544.00 −0.193912
\(936\) 0 0
\(937\) 5054.00 0.176208 0.0881040 0.996111i \(-0.471919\pi\)
0.0881040 + 0.996111i \(0.471919\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 30462.0 1.05530 0.527648 0.849463i \(-0.323074\pi\)
0.527648 + 0.849463i \(0.323074\pi\)
\(942\) 0 0
\(943\) −34744.0 −1.19981
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −32082.0 −1.10087 −0.550436 0.834878i \(-0.685538\pi\)
−0.550436 + 0.834878i \(0.685538\pi\)
\(948\) 0 0
\(949\) 22572.0 0.772095
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −12970.0 −0.440860 −0.220430 0.975403i \(-0.570746\pi\)
−0.220430 + 0.975403i \(0.570746\pi\)
\(954\) 0 0
\(955\) −11808.0 −0.400103
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −9720.00 −0.327294
\(960\) 0 0
\(961\) −13407.0 −0.450035
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −6348.00 −0.211761
\(966\) 0 0
\(967\) −1652.00 −0.0549377 −0.0274688 0.999623i \(-0.508745\pi\)
−0.0274688 + 0.999623i \(0.508745\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 24650.0 0.814682 0.407341 0.913276i \(-0.366456\pi\)
0.407341 + 0.913276i \(0.366456\pi\)
\(972\) 0 0
\(973\) −25720.0 −0.847426
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −23646.0 −0.774312 −0.387156 0.922014i \(-0.626542\pi\)
−0.387156 + 0.922014i \(0.626542\pi\)
\(978\) 0 0
\(979\) −1148.00 −0.0374773
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 38108.0 1.23648 0.618238 0.785991i \(-0.287847\pi\)
0.618238 + 0.785991i \(0.287847\pi\)
\(984\) 0 0
\(985\) 4356.00 0.140907
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −51256.0 −1.64797
\(990\) 0 0
\(991\) 18640.0 0.597497 0.298748 0.954332i \(-0.403431\pi\)
0.298748 + 0.954332i \(0.403431\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −24696.0 −0.786850
\(996\) 0 0
\(997\) −29022.0 −0.921902 −0.460951 0.887426i \(-0.652492\pi\)
−0.460951 + 0.887426i \(0.652492\pi\)
\(998\) 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 1152.4.a.i.1.1 1
3.2 odd 2 128.4.a.c.1.1 yes 1
4.3 odd 2 1152.4.a.j.1.1 1
8.3 odd 2 1152.4.a.d.1.1 1
8.5 even 2 1152.4.a.c.1.1 1
12.11 even 2 128.4.a.a.1.1 1
24.5 odd 2 128.4.a.b.1.1 yes 1
24.11 even 2 128.4.a.d.1.1 yes 1
48.5 odd 4 256.4.b.f.129.1 2
48.11 even 4 256.4.b.b.129.2 2
48.29 odd 4 256.4.b.f.129.2 2
48.35 even 4 256.4.b.b.129.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.4.a.a.1.1 1 12.11 even 2
128.4.a.b.1.1 yes 1 24.5 odd 2
128.4.a.c.1.1 yes 1 3.2 odd 2
128.4.a.d.1.1 yes 1 24.11 even 2
256.4.b.b.129.1 2 48.35 even 4
256.4.b.b.129.2 2 48.11 even 4
256.4.b.f.129.1 2 48.5 odd 4
256.4.b.f.129.2 2 48.29 odd 4
1152.4.a.c.1.1 1 8.5 even 2
1152.4.a.d.1.1 1 8.3 odd 2
1152.4.a.i.1.1 1 1.1 even 1 trivial
1152.4.a.j.1.1 1 4.3 odd 2