Properties

Label 2160.4.a.b.1.1
Level $2160$
Weight $4$
Character 2160.1
Self dual yes
Analytic conductor $127.444$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2160.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(127.444125612\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 270)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2160.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.00000 q^{5} -14.0000 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} -14.0000 q^{7} +3.00000 q^{11} +47.0000 q^{13} +39.0000 q^{17} -32.0000 q^{19} -99.0000 q^{23} +25.0000 q^{25} -51.0000 q^{29} -83.0000 q^{31} +70.0000 q^{35} +314.000 q^{37} +108.000 q^{41} -299.000 q^{43} +531.000 q^{47} -147.000 q^{49} -564.000 q^{53} -15.0000 q^{55} +12.0000 q^{59} +230.000 q^{61} -235.000 q^{65} +268.000 q^{67} +120.000 q^{71} +1106.00 q^{73} -42.0000 q^{77} +739.000 q^{79} +1086.00 q^{83} -195.000 q^{85} +120.000 q^{89} -658.000 q^{91} +160.000 q^{95} -1642.00 q^{97} +O(q^{100})\)

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
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) −14.0000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.00000 0.0822304 0.0411152 0.999154i \(-0.486909\pi\)
0.0411152 + 0.999154i \(0.486909\pi\)
\(12\) 0 0
\(13\) 47.0000 1.00273 0.501364 0.865237i \(-0.332832\pi\)
0.501364 + 0.865237i \(0.332832\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 39.0000 0.556405 0.278203 0.960522i \(-0.410261\pi\)
0.278203 + 0.960522i \(0.410261\pi\)
\(18\) 0 0
\(19\) −32.0000 −0.386384 −0.193192 0.981161i \(-0.561884\pi\)
−0.193192 + 0.981161i \(0.561884\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −99.0000 −0.897519 −0.448759 0.893653i \(-0.648134\pi\)
−0.448759 + 0.893653i \(0.648134\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −51.0000 −0.326568 −0.163284 0.986579i \(-0.552209\pi\)
−0.163284 + 0.986579i \(0.552209\pi\)
\(30\) 0 0
\(31\) −83.0000 −0.480879 −0.240439 0.970664i \(-0.577292\pi\)
−0.240439 + 0.970664i \(0.577292\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 70.0000 0.338062
\(36\) 0 0
\(37\) 314.000 1.39517 0.697585 0.716502i \(-0.254258\pi\)
0.697585 + 0.716502i \(0.254258\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 108.000 0.411385 0.205692 0.978617i \(-0.434055\pi\)
0.205692 + 0.978617i \(0.434055\pi\)
\(42\) 0 0
\(43\) −299.000 −1.06040 −0.530199 0.847874i \(-0.677883\pi\)
−0.530199 + 0.847874i \(0.677883\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 531.000 1.64796 0.823982 0.566616i \(-0.191748\pi\)
0.823982 + 0.566616i \(0.191748\pi\)
\(48\) 0 0
\(49\) −147.000 −0.428571
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −564.000 −1.46172 −0.730862 0.682525i \(-0.760882\pi\)
−0.730862 + 0.682525i \(0.760882\pi\)
\(54\) 0 0
\(55\) −15.0000 −0.0367745
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.0000 0.0264791 0.0132396 0.999912i \(-0.495786\pi\)
0.0132396 + 0.999912i \(0.495786\pi\)
\(60\) 0 0
\(61\) 230.000 0.482762 0.241381 0.970430i \(-0.422400\pi\)
0.241381 + 0.970430i \(0.422400\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −235.000 −0.448433
\(66\) 0 0
\(67\) 268.000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 120.000 0.200583 0.100291 0.994958i \(-0.468022\pi\)
0.100291 + 0.994958i \(0.468022\pi\)
\(72\) 0 0
\(73\) 1106.00 1.77325 0.886627 0.462486i \(-0.153042\pi\)
0.886627 + 0.462486i \(0.153042\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −42.0000 −0.0621603
\(78\) 0 0
\(79\) 739.000 1.05246 0.526228 0.850344i \(-0.323606\pi\)
0.526228 + 0.850344i \(0.323606\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1086.00 1.43619 0.718096 0.695944i \(-0.245014\pi\)
0.718096 + 0.695944i \(0.245014\pi\)
\(84\) 0 0
\(85\) −195.000 −0.248832
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 120.000 0.142921 0.0714605 0.997443i \(-0.477234\pi\)
0.0714605 + 0.997443i \(0.477234\pi\)
\(90\) 0 0
\(91\) −658.000 −0.757991
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 160.000 0.172796
\(96\) 0 0
\(97\) −1642.00 −1.71876 −0.859381 0.511336i \(-0.829151\pi\)
−0.859381 + 0.511336i \(0.829151\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −33.0000 −0.0325111 −0.0162556 0.999868i \(-0.505175\pi\)
−0.0162556 + 0.999868i \(0.505175\pi\)
\(102\) 0 0
\(103\) 1198.00 1.14604 0.573022 0.819540i \(-0.305771\pi\)
0.573022 + 0.819540i \(0.305771\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1542.00 −1.39318 −0.696592 0.717467i \(-0.745301\pi\)
−0.696592 + 0.717467i \(0.745301\pi\)
\(108\) 0 0
\(109\) −556.000 −0.488579 −0.244290 0.969702i \(-0.578555\pi\)
−0.244290 + 0.969702i \(0.578555\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1605.00 −1.33616 −0.668078 0.744091i \(-0.732883\pi\)
−0.668078 + 0.744091i \(0.732883\pi\)
\(114\) 0 0
\(115\) 495.000 0.401383
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −546.000 −0.420603
\(120\) 0 0
\(121\) −1322.00 −0.993238
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −1334.00 −0.932074 −0.466037 0.884765i \(-0.654319\pi\)
−0.466037 + 0.884765i \(0.654319\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2883.00 −1.92282 −0.961408 0.275127i \(-0.911280\pi\)
−0.961408 + 0.275127i \(0.911280\pi\)
\(132\) 0 0
\(133\) 448.000 0.292079
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −282.000 −0.175860 −0.0879302 0.996127i \(-0.528025\pi\)
−0.0879302 + 0.996127i \(0.528025\pi\)
\(138\) 0 0
\(139\) 2494.00 1.52186 0.760929 0.648835i \(-0.224743\pi\)
0.760929 + 0.648835i \(0.224743\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 141.000 0.0824546
\(144\) 0 0
\(145\) 255.000 0.146045
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2595.00 −1.42678 −0.713392 0.700766i \(-0.752842\pi\)
−0.713392 + 0.700766i \(0.752842\pi\)
\(150\) 0 0
\(151\) −1229.00 −0.662348 −0.331174 0.943570i \(-0.607445\pi\)
−0.331174 + 0.943570i \(0.607445\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 415.000 0.215055
\(156\) 0 0
\(157\) −1591.00 −0.808762 −0.404381 0.914591i \(-0.632513\pi\)
−0.404381 + 0.914591i \(0.632513\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1386.00 0.678460
\(162\) 0 0
\(163\) 457.000 0.219601 0.109801 0.993954i \(-0.464979\pi\)
0.109801 + 0.993954i \(0.464979\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1164.00 −0.539359 −0.269680 0.962950i \(-0.586918\pi\)
−0.269680 + 0.962950i \(0.586918\pi\)
\(168\) 0 0
\(169\) 12.0000 0.00546199
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3942.00 −1.73240 −0.866199 0.499700i \(-0.833444\pi\)
−0.866199 + 0.499700i \(0.833444\pi\)
\(174\) 0 0
\(175\) −350.000 −0.151186
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1212.00 −0.506085 −0.253042 0.967455i \(-0.581431\pi\)
−0.253042 + 0.967455i \(0.581431\pi\)
\(180\) 0 0
\(181\) 2288.00 0.939590 0.469795 0.882776i \(-0.344328\pi\)
0.469795 + 0.882776i \(0.344328\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1570.00 −0.623939
\(186\) 0 0
\(187\) 117.000 0.0457534
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1938.00 −0.734182 −0.367091 0.930185i \(-0.619646\pi\)
−0.367091 + 0.930185i \(0.619646\pi\)
\(192\) 0 0
\(193\) −1498.00 −0.558696 −0.279348 0.960190i \(-0.590118\pi\)
−0.279348 + 0.960190i \(0.590118\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2124.00 0.768166 0.384083 0.923299i \(-0.374518\pi\)
0.384083 + 0.923299i \(0.374518\pi\)
\(198\) 0 0
\(199\) 385.000 0.137145 0.0685727 0.997646i \(-0.478155\pi\)
0.0685727 + 0.997646i \(0.478155\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 714.000 0.246862
\(204\) 0 0
\(205\) −540.000 −0.183977
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −96.0000 −0.0317725
\(210\) 0 0
\(211\) −3170.00 −1.03427 −0.517137 0.855903i \(-0.673002\pi\)
−0.517137 + 0.855903i \(0.673002\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1495.00 0.474224
\(216\) 0 0
\(217\) 1162.00 0.363510
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1833.00 0.557923
\(222\) 0 0
\(223\) −1388.00 −0.416804 −0.208402 0.978043i \(-0.566826\pi\)
−0.208402 + 0.978043i \(0.566826\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4644.00 −1.35786 −0.678928 0.734205i \(-0.737555\pi\)
−0.678928 + 0.734205i \(0.737555\pi\)
\(228\) 0 0
\(229\) 4736.00 1.36665 0.683327 0.730113i \(-0.260532\pi\)
0.683327 + 0.730113i \(0.260532\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2814.00 −0.791207 −0.395604 0.918421i \(-0.629465\pi\)
−0.395604 + 0.918421i \(0.629465\pi\)
\(234\) 0 0
\(235\) −2655.00 −0.736992
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2202.00 −0.595965 −0.297982 0.954571i \(-0.596314\pi\)
−0.297982 + 0.954571i \(0.596314\pi\)
\(240\) 0 0
\(241\) 3485.00 0.931488 0.465744 0.884920i \(-0.345787\pi\)
0.465744 + 0.884920i \(0.345787\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 735.000 0.191663
\(246\) 0 0
\(247\) −1504.00 −0.387438
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −6345.00 −1.59559 −0.797795 0.602929i \(-0.794000\pi\)
−0.797795 + 0.602929i \(0.794000\pi\)
\(252\) 0 0
\(253\) −297.000 −0.0738033
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −525.000 −0.127426 −0.0637132 0.997968i \(-0.520294\pi\)
−0.0637132 + 0.997968i \(0.520294\pi\)
\(258\) 0 0
\(259\) −4396.00 −1.05465
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 5196.00 1.21825 0.609124 0.793075i \(-0.291521\pi\)
0.609124 + 0.793075i \(0.291521\pi\)
\(264\) 0 0
\(265\) 2820.00 0.653703
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7479.00 1.69518 0.847589 0.530654i \(-0.178054\pi\)
0.847589 + 0.530654i \(0.178054\pi\)
\(270\) 0 0
\(271\) 856.000 0.191876 0.0959378 0.995387i \(-0.469415\pi\)
0.0959378 + 0.995387i \(0.469415\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 75.0000 0.0164461
\(276\) 0 0
\(277\) −7054.00 −1.53009 −0.765043 0.643979i \(-0.777282\pi\)
−0.765043 + 0.643979i \(0.777282\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1014.00 −0.215268 −0.107634 0.994191i \(-0.534327\pi\)
−0.107634 + 0.994191i \(0.534327\pi\)
\(282\) 0 0
\(283\) −992.000 −0.208368 −0.104184 0.994558i \(-0.533223\pi\)
−0.104184 + 0.994558i \(0.533223\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1512.00 −0.310977
\(288\) 0 0
\(289\) −3392.00 −0.690413
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4950.00 0.986970 0.493485 0.869754i \(-0.335723\pi\)
0.493485 + 0.869754i \(0.335723\pi\)
\(294\) 0 0
\(295\) −60.0000 −0.0118418
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4653.00 −0.899966
\(300\) 0 0
\(301\) 4186.00 0.801585
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1150.00 −0.215898
\(306\) 0 0
\(307\) 4777.00 0.888071 0.444035 0.896009i \(-0.353546\pi\)
0.444035 + 0.896009i \(0.353546\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −7692.00 −1.40249 −0.701243 0.712922i \(-0.747371\pi\)
−0.701243 + 0.712922i \(0.747371\pi\)
\(312\) 0 0
\(313\) −2932.00 −0.529477 −0.264739 0.964320i \(-0.585286\pi\)
−0.264739 + 0.964320i \(0.585286\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8352.00 −1.47980 −0.739898 0.672720i \(-0.765126\pi\)
−0.739898 + 0.672720i \(0.765126\pi\)
\(318\) 0 0
\(319\) −153.000 −0.0268538
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1248.00 −0.214986
\(324\) 0 0
\(325\) 1175.00 0.200545
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −7434.00 −1.24574
\(330\) 0 0
\(331\) 3070.00 0.509796 0.254898 0.966968i \(-0.417958\pi\)
0.254898 + 0.966968i \(0.417958\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1340.00 −0.218543
\(336\) 0 0
\(337\) −1672.00 −0.270266 −0.135133 0.990827i \(-0.543146\pi\)
−0.135133 + 0.990827i \(0.543146\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −249.000 −0.0395428
\(342\) 0 0
\(343\) 6860.00 1.07990
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5076.00 −0.785285 −0.392643 0.919691i \(-0.628439\pi\)
−0.392643 + 0.919691i \(0.628439\pi\)
\(348\) 0 0
\(349\) 8594.00 1.31813 0.659063 0.752087i \(-0.270953\pi\)
0.659063 + 0.752087i \(0.270953\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −12711.0 −1.91654 −0.958269 0.285866i \(-0.907719\pi\)
−0.958269 + 0.285866i \(0.907719\pi\)
\(354\) 0 0
\(355\) −600.000 −0.0897034
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1464.00 −0.215228 −0.107614 0.994193i \(-0.534321\pi\)
−0.107614 + 0.994193i \(0.534321\pi\)
\(360\) 0 0
\(361\) −5835.00 −0.850707
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −5530.00 −0.793023
\(366\) 0 0
\(367\) 7630.00 1.08524 0.542620 0.839979i \(-0.317433\pi\)
0.542620 + 0.839979i \(0.317433\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 7896.00 1.10496
\(372\) 0 0
\(373\) −3883.00 −0.539019 −0.269510 0.962998i \(-0.586862\pi\)
−0.269510 + 0.962998i \(0.586862\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2397.00 −0.327458
\(378\) 0 0
\(379\) 13768.0 1.86600 0.933001 0.359874i \(-0.117180\pi\)
0.933001 + 0.359874i \(0.117180\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −14139.0 −1.88634 −0.943171 0.332307i \(-0.892173\pi\)
−0.943171 + 0.332307i \(0.892173\pi\)
\(384\) 0 0
\(385\) 210.000 0.0277989
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −567.000 −0.0739024 −0.0369512 0.999317i \(-0.511765\pi\)
−0.0369512 + 0.999317i \(0.511765\pi\)
\(390\) 0 0
\(391\) −3861.00 −0.499384
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3695.00 −0.470672
\(396\) 0 0
\(397\) −6685.00 −0.845115 −0.422557 0.906336i \(-0.638867\pi\)
−0.422557 + 0.906336i \(0.638867\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4572.00 −0.569364 −0.284682 0.958622i \(-0.591888\pi\)
−0.284682 + 0.958622i \(0.591888\pi\)
\(402\) 0 0
\(403\) −3901.00 −0.482190
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 942.000 0.114725
\(408\) 0 0
\(409\) −25.0000 −0.00302242 −0.00151121 0.999999i \(-0.500481\pi\)
−0.00151121 + 0.999999i \(0.500481\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −168.000 −0.0200163
\(414\) 0 0
\(415\) −5430.00 −0.642285
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 12453.0 1.45195 0.725977 0.687719i \(-0.241388\pi\)
0.725977 + 0.687719i \(0.241388\pi\)
\(420\) 0 0
\(421\) 5048.00 0.584381 0.292191 0.956360i \(-0.405616\pi\)
0.292191 + 0.956360i \(0.405616\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 975.000 0.111281
\(426\) 0 0
\(427\) −3220.00 −0.364934
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5400.00 0.603501 0.301750 0.953387i \(-0.402429\pi\)
0.301750 + 0.953387i \(0.402429\pi\)
\(432\) 0 0
\(433\) −6298.00 −0.698990 −0.349495 0.936938i \(-0.613647\pi\)
−0.349495 + 0.936938i \(0.613647\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3168.00 0.346787
\(438\) 0 0
\(439\) 6208.00 0.674924 0.337462 0.941339i \(-0.390432\pi\)
0.337462 + 0.941339i \(0.390432\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3360.00 −0.360358 −0.180179 0.983634i \(-0.557668\pi\)
−0.180179 + 0.983634i \(0.557668\pi\)
\(444\) 0 0
\(445\) −600.000 −0.0639162
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −14394.0 −1.51291 −0.756453 0.654048i \(-0.773069\pi\)
−0.756453 + 0.654048i \(0.773069\pi\)
\(450\) 0 0
\(451\) 324.000 0.0338283
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3290.00 0.338984
\(456\) 0 0
\(457\) −916.000 −0.0937608 −0.0468804 0.998901i \(-0.514928\pi\)
−0.0468804 + 0.998901i \(0.514928\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8550.00 −0.863803 −0.431902 0.901921i \(-0.642157\pi\)
−0.431902 + 0.901921i \(0.642157\pi\)
\(462\) 0 0
\(463\) −3734.00 −0.374803 −0.187401 0.982283i \(-0.560007\pi\)
−0.187401 + 0.982283i \(0.560007\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 9840.00 0.975034 0.487517 0.873113i \(-0.337903\pi\)
0.487517 + 0.873113i \(0.337903\pi\)
\(468\) 0 0
\(469\) −3752.00 −0.369406
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −897.000 −0.0871968
\(474\) 0 0
\(475\) −800.000 −0.0772769
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −17280.0 −1.64832 −0.824158 0.566360i \(-0.808351\pi\)
−0.824158 + 0.566360i \(0.808351\pi\)
\(480\) 0 0
\(481\) 14758.0 1.39897
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8210.00 0.768653
\(486\) 0 0
\(487\) 4588.00 0.426904 0.213452 0.976954i \(-0.431529\pi\)
0.213452 + 0.976954i \(0.431529\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 636.000 0.0584568 0.0292284 0.999573i \(-0.490695\pi\)
0.0292284 + 0.999573i \(0.490695\pi\)
\(492\) 0 0
\(493\) −1989.00 −0.181704
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1680.00 −0.151626
\(498\) 0 0
\(499\) 11716.0 1.05106 0.525531 0.850774i \(-0.323867\pi\)
0.525531 + 0.850774i \(0.323867\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4653.00 0.412459 0.206230 0.978504i \(-0.433881\pi\)
0.206230 + 0.978504i \(0.433881\pi\)
\(504\) 0 0
\(505\) 165.000 0.0145394
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16479.0 −1.43501 −0.717504 0.696555i \(-0.754715\pi\)
−0.717504 + 0.696555i \(0.754715\pi\)
\(510\) 0 0
\(511\) −15484.0 −1.34045
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5990.00 −0.512526
\(516\) 0 0
\(517\) 1593.00 0.135513
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3120.00 −0.262360 −0.131180 0.991359i \(-0.541877\pi\)
−0.131180 + 0.991359i \(0.541877\pi\)
\(522\) 0 0
\(523\) −17645.0 −1.47526 −0.737631 0.675204i \(-0.764056\pi\)
−0.737631 + 0.675204i \(0.764056\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3237.00 −0.267563
\(528\) 0 0
\(529\) −2366.00 −0.194460
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5076.00 0.412507
\(534\) 0 0
\(535\) 7710.00 0.623051
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −441.000 −0.0352416
\(540\) 0 0
\(541\) −2182.00 −0.173404 −0.0867019 0.996234i \(-0.527633\pi\)
−0.0867019 + 0.996234i \(0.527633\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2780.00 0.218499
\(546\) 0 0
\(547\) 4033.00 0.315244 0.157622 0.987499i \(-0.449617\pi\)
0.157622 + 0.987499i \(0.449617\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1632.00 0.126181
\(552\) 0 0
\(553\) −10346.0 −0.795582
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 960.000 0.0730278 0.0365139 0.999333i \(-0.488375\pi\)
0.0365139 + 0.999333i \(0.488375\pi\)
\(558\) 0 0
\(559\) −14053.0 −1.06329
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −23754.0 −1.77817 −0.889087 0.457739i \(-0.848660\pi\)
−0.889087 + 0.457739i \(0.848660\pi\)
\(564\) 0 0
\(565\) 8025.00 0.597547
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 22536.0 1.66038 0.830192 0.557478i \(-0.188231\pi\)
0.830192 + 0.557478i \(0.188231\pi\)
\(570\) 0 0
\(571\) −17726.0 −1.29914 −0.649571 0.760301i \(-0.725051\pi\)
−0.649571 + 0.760301i \(0.725051\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2475.00 −0.179504
\(576\) 0 0
\(577\) 17168.0 1.23867 0.619336 0.785126i \(-0.287402\pi\)
0.619336 + 0.785126i \(0.287402\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −15204.0 −1.08566
\(582\) 0 0
\(583\) −1692.00 −0.120198
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7542.00 0.530309 0.265155 0.964206i \(-0.414577\pi\)
0.265155 + 0.964206i \(0.414577\pi\)
\(588\) 0 0
\(589\) 2656.00 0.185804
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 15543.0 1.07635 0.538174 0.842834i \(-0.319114\pi\)
0.538174 + 0.842834i \(0.319114\pi\)
\(594\) 0 0
\(595\) 2730.00 0.188099
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 16026.0 1.09316 0.546581 0.837406i \(-0.315929\pi\)
0.546581 + 0.837406i \(0.315929\pi\)
\(600\) 0 0
\(601\) 10469.0 0.710548 0.355274 0.934762i \(-0.384388\pi\)
0.355274 + 0.934762i \(0.384388\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6610.00 0.444190
\(606\) 0 0
\(607\) 8074.00 0.539891 0.269945 0.962876i \(-0.412994\pi\)
0.269945 + 0.962876i \(0.412994\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 24957.0 1.65246
\(612\) 0 0
\(613\) 26855.0 1.76943 0.884717 0.466128i \(-0.154351\pi\)
0.884717 + 0.466128i \(0.154351\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −24447.0 −1.59514 −0.797568 0.603229i \(-0.793881\pi\)
−0.797568 + 0.603229i \(0.793881\pi\)
\(618\) 0 0
\(619\) −1850.00 −0.120126 −0.0600628 0.998195i \(-0.519130\pi\)
−0.0600628 + 0.998195i \(0.519130\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1680.00 −0.108038
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 12246.0 0.776280
\(630\) 0 0
\(631\) −21728.0 −1.37081 −0.685403 0.728164i \(-0.740374\pi\)
−0.685403 + 0.728164i \(0.740374\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6670.00 0.416836
\(636\) 0 0
\(637\) −6909.00 −0.429740
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −23862.0 −1.47035 −0.735173 0.677879i \(-0.762899\pi\)
−0.735173 + 0.677879i \(0.762899\pi\)
\(642\) 0 0
\(643\) −10523.0 −0.645391 −0.322696 0.946503i \(-0.604589\pi\)
−0.322696 + 0.946503i \(0.604589\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5484.00 0.333228 0.166614 0.986022i \(-0.446717\pi\)
0.166614 + 0.986022i \(0.446717\pi\)
\(648\) 0 0
\(649\) 36.0000 0.00217739
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 26784.0 1.60511 0.802557 0.596576i \(-0.203473\pi\)
0.802557 + 0.596576i \(0.203473\pi\)
\(654\) 0 0
\(655\) 14415.0 0.859909
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −12120.0 −0.716431 −0.358216 0.933639i \(-0.616615\pi\)
−0.358216 + 0.933639i \(0.616615\pi\)
\(660\) 0 0
\(661\) −18226.0 −1.07248 −0.536240 0.844066i \(-0.680156\pi\)
−0.536240 + 0.844066i \(0.680156\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2240.00 −0.130622
\(666\) 0 0
\(667\) 5049.00 0.293101
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 690.000 0.0396977
\(672\) 0 0
\(673\) −11062.0 −0.633594 −0.316797 0.948493i \(-0.602607\pi\)
−0.316797 + 0.948493i \(0.602607\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 9348.00 0.530684 0.265342 0.964154i \(-0.414515\pi\)
0.265342 + 0.964154i \(0.414515\pi\)
\(678\) 0 0
\(679\) 22988.0 1.29926
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 19248.0 1.07834 0.539169 0.842198i \(-0.318739\pi\)
0.539169 + 0.842198i \(0.318739\pi\)
\(684\) 0 0
\(685\) 1410.00 0.0786472
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −26508.0 −1.46571
\(690\) 0 0
\(691\) 17710.0 0.974993 0.487496 0.873125i \(-0.337910\pi\)
0.487496 + 0.873125i \(0.337910\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −12470.0 −0.680596
\(696\) 0 0
\(697\) 4212.00 0.228897
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 19437.0 1.04725 0.523627 0.851947i \(-0.324578\pi\)
0.523627 + 0.851947i \(0.324578\pi\)
\(702\) 0 0
\(703\) −10048.0 −0.539072
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 462.000 0.0245761
\(708\) 0 0
\(709\) −19516.0 −1.03376 −0.516882 0.856057i \(-0.672907\pi\)
−0.516882 + 0.856057i \(0.672907\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8217.00 0.431598
\(714\) 0 0
\(715\) −705.000 −0.0368748
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 17358.0 0.900340 0.450170 0.892943i \(-0.351363\pi\)
0.450170 + 0.892943i \(0.351363\pi\)
\(720\) 0 0
\(721\) −16772.0 −0.866327
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1275.00 −0.0653135
\(726\) 0 0
\(727\) −24428.0 −1.24620 −0.623098 0.782144i \(-0.714126\pi\)
−0.623098 + 0.782144i \(0.714126\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −11661.0 −0.590010
\(732\) 0 0
\(733\) −21418.0 −1.07925 −0.539626 0.841905i \(-0.681434\pi\)
−0.539626 + 0.841905i \(0.681434\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 804.000 0.0401842
\(738\) 0 0
\(739\) 664.000 0.0330523 0.0165261 0.999863i \(-0.494739\pi\)
0.0165261 + 0.999863i \(0.494739\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −34209.0 −1.68911 −0.844553 0.535471i \(-0.820134\pi\)
−0.844553 + 0.535471i \(0.820134\pi\)
\(744\) 0 0
\(745\) 12975.0 0.638077
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 21588.0 1.05315
\(750\) 0 0
\(751\) −6857.00 −0.333176 −0.166588 0.986027i \(-0.553275\pi\)
−0.166588 + 0.986027i \(0.553275\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 6145.00 0.296211
\(756\) 0 0
\(757\) −23719.0 −1.13881 −0.569407 0.822056i \(-0.692827\pi\)
−0.569407 + 0.822056i \(0.692827\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 14418.0 0.686796 0.343398 0.939190i \(-0.388422\pi\)
0.343398 + 0.939190i \(0.388422\pi\)
\(762\) 0 0
\(763\) 7784.00 0.369331
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 564.000 0.0265513
\(768\) 0 0
\(769\) −4849.00 −0.227385 −0.113693 0.993516i \(-0.536268\pi\)
−0.113693 + 0.993516i \(0.536268\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 36258.0 1.68708 0.843538 0.537070i \(-0.180469\pi\)
0.843538 + 0.537070i \(0.180469\pi\)
\(774\) 0 0
\(775\) −2075.00 −0.0961757
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3456.00 −0.158953
\(780\) 0 0
\(781\) 360.000 0.0164940
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 7955.00 0.361689
\(786\) 0 0
\(787\) 18877.0 0.855009 0.427505 0.904013i \(-0.359393\pi\)
0.427505 + 0.904013i \(0.359393\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 22470.0 1.01004
\(792\) 0 0
\(793\) 10810.0 0.484079
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 16200.0 0.719992 0.359996 0.932954i \(-0.382778\pi\)
0.359996 + 0.932954i \(0.382778\pi\)
\(798\) 0 0
\(799\) 20709.0 0.916936
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 3318.00 0.145815
\(804\) 0 0
\(805\) −6930.00 −0.303417
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 26760.0 1.16296 0.581478 0.813562i \(-0.302475\pi\)
0.581478 + 0.813562i \(0.302475\pi\)
\(810\) 0 0
\(811\) 10510.0 0.455063 0.227531 0.973771i \(-0.426935\pi\)
0.227531 + 0.973771i \(0.426935\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −2285.00 −0.0982087
\(816\) 0 0
\(817\) 9568.00 0.409721
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 28230.0 1.20004 0.600021 0.799985i \(-0.295159\pi\)
0.600021 + 0.799985i \(0.295159\pi\)
\(822\) 0 0
\(823\) 39868.0 1.68859 0.844296 0.535877i \(-0.180019\pi\)
0.844296 + 0.535877i \(0.180019\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 32394.0 1.36209 0.681046 0.732241i \(-0.261525\pi\)
0.681046 + 0.732241i \(0.261525\pi\)
\(828\) 0 0
\(829\) 34820.0 1.45880 0.729402 0.684085i \(-0.239798\pi\)
0.729402 + 0.684085i \(0.239798\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −5733.00 −0.238459
\(834\) 0 0
\(835\) 5820.00 0.241209
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −1146.00 −0.0471565 −0.0235783 0.999722i \(-0.507506\pi\)
−0.0235783 + 0.999722i \(0.507506\pi\)
\(840\) 0 0
\(841\) −21788.0 −0.893354
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −60.0000 −0.00244268
\(846\) 0 0
\(847\) 18508.0 0.750817
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −31086.0 −1.25219
\(852\) 0 0
\(853\) −19393.0 −0.778433 −0.389217 0.921146i \(-0.627254\pi\)
−0.389217 + 0.921146i \(0.627254\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 8430.00 0.336013 0.168007 0.985786i \(-0.446267\pi\)
0.168007 + 0.985786i \(0.446267\pi\)
\(858\) 0 0
\(859\) −15470.0 −0.614470 −0.307235 0.951634i \(-0.599404\pi\)
−0.307235 + 0.951634i \(0.599404\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 5871.00 0.231577 0.115789 0.993274i \(-0.463060\pi\)
0.115789 + 0.993274i \(0.463060\pi\)
\(864\) 0 0
\(865\) 19710.0 0.774752
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 2217.00 0.0865438
\(870\) 0 0
\(871\) 12596.0 0.490011
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1750.00 0.0676123
\(876\) 0 0
\(877\) −11299.0 −0.435051 −0.217526 0.976055i \(-0.569799\pi\)
−0.217526 + 0.976055i \(0.569799\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −29682.0 −1.13509 −0.567544 0.823343i \(-0.692106\pi\)
−0.567544 + 0.823343i \(0.692106\pi\)
\(882\) 0 0
\(883\) −40316.0 −1.53651 −0.768257 0.640142i \(-0.778876\pi\)
−0.768257 + 0.640142i \(0.778876\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −21945.0 −0.830711 −0.415356 0.909659i \(-0.636343\pi\)
−0.415356 + 0.909659i \(0.636343\pi\)
\(888\) 0 0
\(889\) 18676.0 0.704581
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −16992.0 −0.636748
\(894\) 0 0
\(895\) 6060.00 0.226328
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 4233.00 0.157039
\(900\) 0 0
\(901\) −21996.0 −0.813311
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −11440.0 −0.420197
\(906\) 0 0
\(907\) −24911.0 −0.911969 −0.455985 0.889988i \(-0.650713\pi\)
−0.455985 + 0.889988i \(0.650713\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 33264.0 1.20975 0.604877 0.796319i \(-0.293222\pi\)
0.604877 + 0.796319i \(0.293222\pi\)
\(912\) 0 0
\(913\) 3258.00 0.118099
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 40362.0 1.45351
\(918\) 0 0
\(919\) 23191.0 0.832427 0.416214 0.909267i \(-0.363357\pi\)
0.416214 + 0.909267i \(0.363357\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 5640.00 0.201130
\(924\) 0 0
\(925\) 7850.00 0.279034
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −2160.00 −0.0762834 −0.0381417 0.999272i \(-0.512144\pi\)
−0.0381417 + 0.999272i \(0.512144\pi\)
\(930\) 0 0
\(931\) 4704.00 0.165593
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −585.000 −0.0204615
\(936\) 0 0
\(937\) 2066.00 0.0720312 0.0360156 0.999351i \(-0.488533\pi\)
0.0360156 + 0.999351i \(0.488533\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 22233.0 0.770218 0.385109 0.922871i \(-0.374164\pi\)
0.385109 + 0.922871i \(0.374164\pi\)
\(942\) 0 0
\(943\) −10692.0 −0.369225
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −17754.0 −0.609216 −0.304608 0.952478i \(-0.598525\pi\)
−0.304608 + 0.952478i \(0.598525\pi\)
\(948\) 0 0
\(949\) 51982.0 1.77809
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −33891.0 −1.15198 −0.575990 0.817457i \(-0.695383\pi\)
−0.575990 + 0.817457i \(0.695383\pi\)
\(954\) 0 0
\(955\) 9690.00 0.328336
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 3948.00 0.132938
\(960\) 0 0
\(961\) −22902.0 −0.768756
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 7490.00 0.249857
\(966\) 0 0
\(967\) −51074.0 −1.69848 −0.849239 0.528008i \(-0.822939\pi\)
−0.849239 + 0.528008i \(0.822939\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 20967.0 0.692959 0.346479 0.938058i \(-0.387377\pi\)
0.346479 + 0.938058i \(0.387377\pi\)
\(972\) 0 0
\(973\) −34916.0 −1.15042
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −31749.0 −1.03965 −0.519826 0.854272i \(-0.674003\pi\)
−0.519826 + 0.854272i \(0.674003\pi\)
\(978\) 0 0
\(979\) 360.000 0.0117525
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 47325.0 1.53554 0.767769 0.640727i \(-0.221367\pi\)
0.767769 + 0.640727i \(0.221367\pi\)
\(984\) 0 0
\(985\) −10620.0 −0.343534
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 29601.0 0.951726
\(990\) 0 0
\(991\) −2363.00 −0.0757449 −0.0378724 0.999283i \(-0.512058\pi\)
−0.0378724 + 0.999283i \(0.512058\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1925.00 −0.0613333
\(996\) 0 0
\(997\) 45569.0 1.44753 0.723764 0.690048i \(-0.242411\pi\)
0.723764 + 0.690048i \(0.242411\pi\)
\(998\) 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 2160.4.a.b.1.1 1
3.2 odd 2 2160.4.a.l.1.1 1
4.3 odd 2 270.4.a.j.1.1 yes 1
12.11 even 2 270.4.a.f.1.1 1
20.3 even 4 1350.4.c.j.649.1 2
20.7 even 4 1350.4.c.j.649.2 2
20.19 odd 2 1350.4.a.e.1.1 1
36.7 odd 6 810.4.e.f.271.1 2
36.11 even 6 810.4.e.n.271.1 2
36.23 even 6 810.4.e.n.541.1 2
36.31 odd 6 810.4.e.f.541.1 2
60.23 odd 4 1350.4.c.k.649.2 2
60.47 odd 4 1350.4.c.k.649.1 2
60.59 even 2 1350.4.a.r.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.4.a.f.1.1 1 12.11 even 2
270.4.a.j.1.1 yes 1 4.3 odd 2
810.4.e.f.271.1 2 36.7 odd 6
810.4.e.f.541.1 2 36.31 odd 6
810.4.e.n.271.1 2 36.11 even 6
810.4.e.n.541.1 2 36.23 even 6
1350.4.a.e.1.1 1 20.19 odd 2
1350.4.a.r.1.1 1 60.59 even 2
1350.4.c.j.649.1 2 20.3 even 4
1350.4.c.j.649.2 2 20.7 even 4
1350.4.c.k.649.1 2 60.47 odd 4
1350.4.c.k.649.2 2 60.23 odd 4
2160.4.a.b.1.1 1 1.1 even 1 trivial
2160.4.a.l.1.1 1 3.2 odd 2