Properties

Label 2160.4.a.d.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 135)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q-5.00000 q^{5} +O(q^{10})\) \(q-5.00000 q^{5} +10.0000 q^{11} -80.0000 q^{13} -7.00000 q^{17} +113.000 q^{19} -81.0000 q^{23} +25.0000 q^{25} +220.000 q^{29} +189.000 q^{31} +170.000 q^{37} +130.000 q^{41} -10.0000 q^{43} +160.000 q^{47} -343.000 q^{49} -631.000 q^{53} -50.0000 q^{55} -560.000 q^{59} +229.000 q^{61} +400.000 q^{65} -750.000 q^{67} +890.000 q^{71} -890.000 q^{73} +27.0000 q^{79} +429.000 q^{83} +35.0000 q^{85} +750.000 q^{89} -565.000 q^{95} -1480.00 q^{97} +O(q^{100})\)

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
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 10.0000 0.274101 0.137051 0.990564i \(-0.456238\pi\)
0.137051 + 0.990564i \(0.456238\pi\)
\(12\) 0 0
\(13\) −80.0000 −1.70677 −0.853385 0.521281i \(-0.825454\pi\)
−0.853385 + 0.521281i \(0.825454\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −7.00000 −0.0998676 −0.0499338 0.998753i \(-0.515901\pi\)
−0.0499338 + 0.998753i \(0.515901\pi\)
\(18\) 0 0
\(19\) 113.000 1.36442 0.682210 0.731156i \(-0.261019\pi\)
0.682210 + 0.731156i \(0.261019\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −81.0000 −0.734333 −0.367167 0.930155i \(-0.619672\pi\)
−0.367167 + 0.930155i \(0.619672\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 220.000 1.40872 0.704362 0.709841i \(-0.251233\pi\)
0.704362 + 0.709841i \(0.251233\pi\)
\(30\) 0 0
\(31\) 189.000 1.09501 0.547506 0.836801i \(-0.315577\pi\)
0.547506 + 0.836801i \(0.315577\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 170.000 0.755347 0.377673 0.925939i \(-0.376724\pi\)
0.377673 + 0.925939i \(0.376724\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 130.000 0.495185 0.247593 0.968864i \(-0.420361\pi\)
0.247593 + 0.968864i \(0.420361\pi\)
\(42\) 0 0
\(43\) −10.0000 −0.0354648 −0.0177324 0.999843i \(-0.505645\pi\)
−0.0177324 + 0.999843i \(0.505645\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 160.000 0.496562 0.248281 0.968688i \(-0.420134\pi\)
0.248281 + 0.968688i \(0.420134\pi\)
\(48\) 0 0
\(49\) −343.000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −631.000 −1.63537 −0.817684 0.575667i \(-0.804742\pi\)
−0.817684 + 0.575667i \(0.804742\pi\)
\(54\) 0 0
\(55\) −50.0000 −0.122582
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −560.000 −1.23569 −0.617846 0.786299i \(-0.711994\pi\)
−0.617846 + 0.786299i \(0.711994\pi\)
\(60\) 0 0
\(61\) 229.000 0.480663 0.240332 0.970691i \(-0.422744\pi\)
0.240332 + 0.970691i \(0.422744\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 400.000 0.763291
\(66\) 0 0
\(67\) −750.000 −1.36757 −0.683784 0.729684i \(-0.739667\pi\)
−0.683784 + 0.729684i \(0.739667\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 890.000 1.48766 0.743828 0.668371i \(-0.233008\pi\)
0.743828 + 0.668371i \(0.233008\pi\)
\(72\) 0 0
\(73\) −890.000 −1.42694 −0.713470 0.700686i \(-0.752878\pi\)
−0.713470 + 0.700686i \(0.752878\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 27.0000 0.0384524 0.0192262 0.999815i \(-0.493880\pi\)
0.0192262 + 0.999815i \(0.493880\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 429.000 0.567336 0.283668 0.958923i \(-0.408449\pi\)
0.283668 + 0.958923i \(0.408449\pi\)
\(84\) 0 0
\(85\) 35.0000 0.0446622
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 750.000 0.893257 0.446628 0.894720i \(-0.352625\pi\)
0.446628 + 0.894720i \(0.352625\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −565.000 −0.610187
\(96\) 0 0
\(97\) −1480.00 −1.54919 −0.774594 0.632459i \(-0.782046\pi\)
−0.774594 + 0.632459i \(0.782046\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1500.00 1.47778 0.738889 0.673827i \(-0.235351\pi\)
0.738889 + 0.673827i \(0.235351\pi\)
\(102\) 0 0
\(103\) 460.000 0.440050 0.220025 0.975494i \(-0.429386\pi\)
0.220025 + 0.975494i \(0.429386\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −420.000 −0.379467 −0.189733 0.981836i \(-0.560762\pi\)
−0.189733 + 0.981836i \(0.560762\pi\)
\(108\) 0 0
\(109\) −607.000 −0.533395 −0.266698 0.963780i \(-0.585932\pi\)
−0.266698 + 0.963780i \(0.585932\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2170.00 −1.80652 −0.903259 0.429097i \(-0.858832\pi\)
−0.903259 + 0.429097i \(0.858832\pi\)
\(114\) 0 0
\(115\) 405.000 0.328404
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1231.00 −0.924869
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 1610.00 1.12492 0.562458 0.826826i \(-0.309856\pi\)
0.562458 + 0.826826i \(0.309856\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2370.00 1.58067 0.790335 0.612674i \(-0.209906\pi\)
0.790335 + 0.612674i \(0.209906\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1797.00 −1.12064 −0.560321 0.828275i \(-0.689322\pi\)
−0.560321 + 0.828275i \(0.689322\pi\)
\(138\) 0 0
\(139\) 124.000 0.0756658 0.0378329 0.999284i \(-0.487955\pi\)
0.0378329 + 0.999284i \(0.487955\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −800.000 −0.467828
\(144\) 0 0
\(145\) −1100.00 −0.630000
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 70.0000 0.0384874 0.0192437 0.999815i \(-0.493874\pi\)
0.0192437 + 0.999815i \(0.493874\pi\)
\(150\) 0 0
\(151\) −2248.00 −1.21152 −0.605760 0.795647i \(-0.707131\pi\)
−0.605760 + 0.795647i \(0.707131\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −945.000 −0.489705
\(156\) 0 0
\(157\) 1010.00 0.513419 0.256709 0.966489i \(-0.417362\pi\)
0.256709 + 0.966489i \(0.417362\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −590.000 −0.283511 −0.141756 0.989902i \(-0.545275\pi\)
−0.141756 + 0.989902i \(0.545275\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2403.00 1.11347 0.556736 0.830690i \(-0.312054\pi\)
0.556736 + 0.830690i \(0.312054\pi\)
\(168\) 0 0
\(169\) 4203.00 1.91306
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −801.000 −0.352017 −0.176008 0.984389i \(-0.556319\pi\)
−0.176008 + 0.984389i \(0.556319\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2360.00 −0.985445 −0.492723 0.870186i \(-0.663998\pi\)
−0.492723 + 0.870186i \(0.663998\pi\)
\(180\) 0 0
\(181\) 1241.00 0.509629 0.254814 0.966990i \(-0.417986\pi\)
0.254814 + 0.966990i \(0.417986\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −850.000 −0.337801
\(186\) 0 0
\(187\) −70.0000 −0.0273738
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4990.00 −1.89039 −0.945193 0.326512i \(-0.894127\pi\)
−0.945193 + 0.326512i \(0.894127\pi\)
\(192\) 0 0
\(193\) −2260.00 −0.842893 −0.421447 0.906853i \(-0.638477\pi\)
−0.421447 + 0.906853i \(0.638477\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2247.00 0.812650 0.406325 0.913729i \(-0.366810\pi\)
0.406325 + 0.913729i \(0.366810\pi\)
\(198\) 0 0
\(199\) −4564.00 −1.62580 −0.812898 0.582406i \(-0.802111\pi\)
−0.812898 + 0.582406i \(0.802111\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −650.000 −0.221454
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1130.00 0.373989
\(210\) 0 0
\(211\) −4949.00 −1.61471 −0.807354 0.590068i \(-0.799101\pi\)
−0.807354 + 0.590068i \(0.799101\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 50.0000 0.0158603
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 560.000 0.170451
\(222\) 0 0
\(223\) −3890.00 −1.16813 −0.584067 0.811706i \(-0.698539\pi\)
−0.584067 + 0.811706i \(0.698539\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2453.00 0.717231 0.358615 0.933485i \(-0.383249\pi\)
0.358615 + 0.933485i \(0.383249\pi\)
\(228\) 0 0
\(229\) −6213.00 −1.79287 −0.896434 0.443178i \(-0.853851\pi\)
−0.896434 + 0.443178i \(0.853851\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3450.00 0.970030 0.485015 0.874506i \(-0.338814\pi\)
0.485015 + 0.874506i \(0.338814\pi\)
\(234\) 0 0
\(235\) −800.000 −0.222069
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6490.00 1.75650 0.878249 0.478203i \(-0.158712\pi\)
0.878249 + 0.478203i \(0.158712\pi\)
\(240\) 0 0
\(241\) −3401.00 −0.909036 −0.454518 0.890738i \(-0.650188\pi\)
−0.454518 + 0.890738i \(0.650188\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1715.00 0.447214
\(246\) 0 0
\(247\) −9040.00 −2.32875
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4980.00 −1.25233 −0.626165 0.779691i \(-0.715376\pi\)
−0.626165 + 0.779691i \(0.715376\pi\)
\(252\) 0 0
\(253\) −810.000 −0.201282
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3357.00 −0.814801 −0.407401 0.913250i \(-0.633565\pi\)
−0.407401 + 0.913250i \(0.633565\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4540.00 −1.06444 −0.532221 0.846605i \(-0.678643\pi\)
−0.532221 + 0.846605i \(0.678643\pi\)
\(264\) 0 0
\(265\) 3155.00 0.731359
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −8410.00 −1.90620 −0.953098 0.302662i \(-0.902125\pi\)
−0.953098 + 0.302662i \(0.902125\pi\)
\(270\) 0 0
\(271\) −259.000 −0.0580558 −0.0290279 0.999579i \(-0.509241\pi\)
−0.0290279 + 0.999579i \(0.509241\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 250.000 0.0548202
\(276\) 0 0
\(277\) −4170.00 −0.904516 −0.452258 0.891887i \(-0.649381\pi\)
−0.452258 + 0.891887i \(0.649381\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1740.00 0.369394 0.184697 0.982796i \(-0.440870\pi\)
0.184697 + 0.982796i \(0.440870\pi\)
\(282\) 0 0
\(283\) 5070.00 1.06495 0.532474 0.846446i \(-0.321262\pi\)
0.532474 + 0.846446i \(0.321262\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −4864.00 −0.990026
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 159.000 0.0317027 0.0158513 0.999874i \(-0.494954\pi\)
0.0158513 + 0.999874i \(0.494954\pi\)
\(294\) 0 0
\(295\) 2800.00 0.552618
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6480.00 1.25334
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1145.00 −0.214959
\(306\) 0 0
\(307\) −6490.00 −1.20653 −0.603264 0.797542i \(-0.706133\pi\)
−0.603264 + 0.797542i \(0.706133\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −8220.00 −1.49876 −0.749379 0.662142i \(-0.769648\pi\)
−0.749379 + 0.662142i \(0.769648\pi\)
\(312\) 0 0
\(313\) −4660.00 −0.841530 −0.420765 0.907170i \(-0.638238\pi\)
−0.420765 + 0.907170i \(0.638238\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6817.00 1.20783 0.603913 0.797050i \(-0.293607\pi\)
0.603913 + 0.797050i \(0.293607\pi\)
\(318\) 0 0
\(319\) 2200.00 0.386133
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −791.000 −0.136261
\(324\) 0 0
\(325\) −2000.00 −0.341354
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −192.000 −0.0318830 −0.0159415 0.999873i \(-0.505075\pi\)
−0.0159415 + 0.999873i \(0.505075\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3750.00 0.611595
\(336\) 0 0
\(337\) 4840.00 0.782349 0.391174 0.920317i \(-0.372069\pi\)
0.391174 + 0.920317i \(0.372069\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1890.00 0.300144
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −860.000 −0.133047 −0.0665234 0.997785i \(-0.521191\pi\)
−0.0665234 + 0.997785i \(0.521191\pi\)
\(348\) 0 0
\(349\) 5377.00 0.824711 0.412356 0.911023i \(-0.364706\pi\)
0.412356 + 0.911023i \(0.364706\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8010.00 1.20773 0.603866 0.797086i \(-0.293626\pi\)
0.603866 + 0.797086i \(0.293626\pi\)
\(354\) 0 0
\(355\) −4450.00 −0.665300
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 12930.0 1.90089 0.950445 0.310894i \(-0.100628\pi\)
0.950445 + 0.310894i \(0.100628\pi\)
\(360\) 0 0
\(361\) 5910.00 0.861642
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4450.00 0.638147
\(366\) 0 0
\(367\) 6000.00 0.853399 0.426700 0.904393i \(-0.359676\pi\)
0.426700 + 0.904393i \(0.359676\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −140.000 −0.0194341 −0.00971706 0.999953i \(-0.503093\pi\)
−0.00971706 + 0.999953i \(0.503093\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −17600.0 −2.40437
\(378\) 0 0
\(379\) −6217.00 −0.842601 −0.421301 0.906921i \(-0.638426\pi\)
−0.421301 + 0.906921i \(0.638426\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4551.00 0.607168 0.303584 0.952805i \(-0.401817\pi\)
0.303584 + 0.952805i \(0.401817\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2310.00 0.301084 0.150542 0.988604i \(-0.451898\pi\)
0.150542 + 0.988604i \(0.451898\pi\)
\(390\) 0 0
\(391\) 567.000 0.0733361
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −135.000 −0.0171964
\(396\) 0 0
\(397\) −2900.00 −0.366617 −0.183308 0.983055i \(-0.558681\pi\)
−0.183308 + 0.983055i \(0.558681\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2250.00 −0.280199 −0.140099 0.990137i \(-0.544742\pi\)
−0.140099 + 0.990137i \(0.544742\pi\)
\(402\) 0 0
\(403\) −15120.0 −1.86894
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1700.00 0.207041
\(408\) 0 0
\(409\) −11263.0 −1.36166 −0.680831 0.732441i \(-0.738381\pi\)
−0.680831 + 0.732441i \(0.738381\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −2145.00 −0.253720
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6910.00 −0.805670 −0.402835 0.915273i \(-0.631975\pi\)
−0.402835 + 0.915273i \(0.631975\pi\)
\(420\) 0 0
\(421\) −5249.00 −0.607650 −0.303825 0.952728i \(-0.598264\pi\)
−0.303825 + 0.952728i \(0.598264\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −175.000 −0.0199735
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −11880.0 −1.32770 −0.663851 0.747865i \(-0.731079\pi\)
−0.663851 + 0.747865i \(0.731079\pi\)
\(432\) 0 0
\(433\) −4280.00 −0.475020 −0.237510 0.971385i \(-0.576331\pi\)
−0.237510 + 0.971385i \(0.576331\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −9153.00 −1.00194
\(438\) 0 0
\(439\) −6463.00 −0.702647 −0.351324 0.936254i \(-0.614268\pi\)
−0.351324 + 0.936254i \(0.614268\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11721.0 1.25707 0.628534 0.777782i \(-0.283655\pi\)
0.628534 + 0.777782i \(0.283655\pi\)
\(444\) 0 0
\(445\) −3750.00 −0.399477
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2180.00 0.229133 0.114566 0.993416i \(-0.463452\pi\)
0.114566 + 0.993416i \(0.463452\pi\)
\(450\) 0 0
\(451\) 1300.00 0.135731
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −17840.0 −1.82608 −0.913042 0.407866i \(-0.866273\pi\)
−0.913042 + 0.407866i \(0.866273\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2250.00 0.227317 0.113658 0.993520i \(-0.463743\pi\)
0.113658 + 0.993520i \(0.463743\pi\)
\(462\) 0 0
\(463\) −1230.00 −0.123462 −0.0617310 0.998093i \(-0.519662\pi\)
−0.0617310 + 0.998093i \(0.519662\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5813.00 0.576003 0.288002 0.957630i \(-0.407009\pi\)
0.288002 + 0.957630i \(0.407009\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −100.000 −0.00972094
\(474\) 0 0
\(475\) 2825.00 0.272884
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6750.00 −0.643873 −0.321937 0.946761i \(-0.604334\pi\)
−0.321937 + 0.946761i \(0.604334\pi\)
\(480\) 0 0
\(481\) −13600.0 −1.28920
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7400.00 0.692818
\(486\) 0 0
\(487\) 6610.00 0.615047 0.307523 0.951541i \(-0.400500\pi\)
0.307523 + 0.951541i \(0.400500\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4990.00 −0.458647 −0.229323 0.973350i \(-0.573651\pi\)
−0.229323 + 0.973350i \(0.573651\pi\)
\(492\) 0 0
\(493\) −1540.00 −0.140686
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −1483.00 −0.133042 −0.0665212 0.997785i \(-0.521190\pi\)
−0.0665212 + 0.997785i \(0.521190\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −11641.0 −1.03190 −0.515951 0.856618i \(-0.672561\pi\)
−0.515951 + 0.856618i \(0.672561\pi\)
\(504\) 0 0
\(505\) −7500.00 −0.660882
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −2620.00 −0.228152 −0.114076 0.993472i \(-0.536391\pi\)
−0.114076 + 0.993472i \(0.536391\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2300.00 −0.196796
\(516\) 0 0
\(517\) 1600.00 0.136108
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 13690.0 1.15119 0.575595 0.817735i \(-0.304771\pi\)
0.575595 + 0.817735i \(0.304771\pi\)
\(522\) 0 0
\(523\) 10220.0 0.854473 0.427237 0.904140i \(-0.359487\pi\)
0.427237 + 0.904140i \(0.359487\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1323.00 −0.109356
\(528\) 0 0
\(529\) −5606.00 −0.460754
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −10400.0 −0.845167
\(534\) 0 0
\(535\) 2100.00 0.169703
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3430.00 −0.274101
\(540\) 0 0
\(541\) −2778.00 −0.220768 −0.110384 0.993889i \(-0.535208\pi\)
−0.110384 + 0.993889i \(0.535208\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3035.00 0.238541
\(546\) 0 0
\(547\) 12830.0 1.00287 0.501436 0.865195i \(-0.332805\pi\)
0.501436 + 0.865195i \(0.332805\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 24860.0 1.92209
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4950.00 0.376550 0.188275 0.982116i \(-0.439710\pi\)
0.188275 + 0.982116i \(0.439710\pi\)
\(558\) 0 0
\(559\) 800.000 0.0605302
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6540.00 0.489570 0.244785 0.969577i \(-0.421283\pi\)
0.244785 + 0.969577i \(0.421283\pi\)
\(564\) 0 0
\(565\) 10850.0 0.807899
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 15240.0 1.12284 0.561418 0.827532i \(-0.310256\pi\)
0.561418 + 0.827532i \(0.310256\pi\)
\(570\) 0 0
\(571\) 5281.00 0.387045 0.193523 0.981096i \(-0.438009\pi\)
0.193523 + 0.981096i \(0.438009\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2025.00 −0.146867
\(576\) 0 0
\(577\) −10510.0 −0.758296 −0.379148 0.925336i \(-0.623783\pi\)
−0.379148 + 0.925336i \(0.623783\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −6310.00 −0.448256
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4107.00 0.288780 0.144390 0.989521i \(-0.453878\pi\)
0.144390 + 0.989521i \(0.453878\pi\)
\(588\) 0 0
\(589\) 21357.0 1.49406
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −26129.0 −1.80943 −0.904713 0.426022i \(-0.859915\pi\)
−0.904713 + 0.426022i \(0.859915\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −4360.00 −0.297404 −0.148702 0.988882i \(-0.547509\pi\)
−0.148702 + 0.988882i \(0.547509\pi\)
\(600\) 0 0
\(601\) −16639.0 −1.12932 −0.564658 0.825325i \(-0.690992\pi\)
−0.564658 + 0.825325i \(0.690992\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6155.00 0.413614
\(606\) 0 0
\(607\) −490.000 −0.0327652 −0.0163826 0.999866i \(-0.505215\pi\)
−0.0163826 + 0.999866i \(0.505215\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −12800.0 −0.847516
\(612\) 0 0
\(613\) 18400.0 1.21235 0.606174 0.795332i \(-0.292704\pi\)
0.606174 + 0.795332i \(0.292704\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7827.00 −0.510702 −0.255351 0.966848i \(-0.582191\pi\)
−0.255351 + 0.966848i \(0.582191\pi\)
\(618\) 0 0
\(619\) 19756.0 1.28281 0.641406 0.767202i \(-0.278351\pi\)
0.641406 + 0.767202i \(0.278351\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1190.00 −0.0754347
\(630\) 0 0
\(631\) −9829.00 −0.620105 −0.310053 0.950719i \(-0.600347\pi\)
−0.310053 + 0.950719i \(0.600347\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8050.00 −0.503078
\(636\) 0 0
\(637\) 27440.0 1.70677
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 6000.00 0.369713 0.184856 0.982766i \(-0.440818\pi\)
0.184856 + 0.982766i \(0.440818\pi\)
\(642\) 0 0
\(643\) −8280.00 −0.507825 −0.253912 0.967227i \(-0.581717\pi\)
−0.253912 + 0.967227i \(0.581717\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −16637.0 −1.01092 −0.505462 0.862849i \(-0.668678\pi\)
−0.505462 + 0.862849i \(0.668678\pi\)
\(648\) 0 0
\(649\) −5600.00 −0.338705
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −19751.0 −1.18364 −0.591820 0.806070i \(-0.701590\pi\)
−0.591820 + 0.806070i \(0.701590\pi\)
\(654\) 0 0
\(655\) −11850.0 −0.706897
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 14260.0 0.842930 0.421465 0.906845i \(-0.361516\pi\)
0.421465 + 0.906845i \(0.361516\pi\)
\(660\) 0 0
\(661\) 22318.0 1.31327 0.656634 0.754210i \(-0.271980\pi\)
0.656634 + 0.754210i \(0.271980\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −17820.0 −1.03447
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2290.00 0.131750
\(672\) 0 0
\(673\) 20040.0 1.14782 0.573912 0.818917i \(-0.305425\pi\)
0.573912 + 0.818917i \(0.305425\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2310.00 0.131138 0.0655691 0.997848i \(-0.479114\pi\)
0.0655691 + 0.997848i \(0.479114\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −26739.0 −1.49801 −0.749004 0.662566i \(-0.769468\pi\)
−0.749004 + 0.662566i \(0.769468\pi\)
\(684\) 0 0
\(685\) 8985.00 0.501167
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 50480.0 2.79120
\(690\) 0 0
\(691\) −5101.00 −0.280827 −0.140413 0.990093i \(-0.544843\pi\)
−0.140413 + 0.990093i \(0.544843\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −620.000 −0.0338388
\(696\) 0 0
\(697\) −910.000 −0.0494530
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −26030.0 −1.40248 −0.701241 0.712925i \(-0.747370\pi\)
−0.701241 + 0.712925i \(0.747370\pi\)
\(702\) 0 0
\(703\) 19210.0 1.03061
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −3854.00 −0.204147 −0.102073 0.994777i \(-0.532548\pi\)
−0.102073 + 0.994777i \(0.532548\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −15309.0 −0.804105
\(714\) 0 0
\(715\) 4000.00 0.209219
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −870.000 −0.0451259 −0.0225630 0.999745i \(-0.507183\pi\)
−0.0225630 + 0.999745i \(0.507183\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 5500.00 0.281745
\(726\) 0 0
\(727\) −35780.0 −1.82532 −0.912659 0.408721i \(-0.865975\pi\)
−0.912659 + 0.408721i \(0.865975\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 70.0000 0.00354178
\(732\) 0 0
\(733\) −3400.00 −0.171326 −0.0856629 0.996324i \(-0.527301\pi\)
−0.0856629 + 0.996324i \(0.527301\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7500.00 −0.374852
\(738\) 0 0
\(739\) 683.000 0.0339981 0.0169990 0.999856i \(-0.494589\pi\)
0.0169990 + 0.999856i \(0.494589\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −13400.0 −0.661640 −0.330820 0.943694i \(-0.607325\pi\)
−0.330820 + 0.943694i \(0.607325\pi\)
\(744\) 0 0
\(745\) −350.000 −0.0172121
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 23219.0 1.12819 0.564097 0.825709i \(-0.309224\pi\)
0.564097 + 0.825709i \(0.309224\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 11240.0 0.541809
\(756\) 0 0
\(757\) 19630.0 0.942489 0.471245 0.882003i \(-0.343805\pi\)
0.471245 + 0.882003i \(0.343805\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2940.00 −0.140046 −0.0700229 0.997545i \(-0.522307\pi\)
−0.0700229 + 0.997545i \(0.522307\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 44800.0 2.10904
\(768\) 0 0
\(769\) −13987.0 −0.655896 −0.327948 0.944696i \(-0.606357\pi\)
−0.327948 + 0.944696i \(0.606357\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −19839.0 −0.923104 −0.461552 0.887113i \(-0.652707\pi\)
−0.461552 + 0.887113i \(0.652707\pi\)
\(774\) 0 0
\(775\) 4725.00 0.219003
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 14690.0 0.675640
\(780\) 0 0
\(781\) 8900.00 0.407768
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −5050.00 −0.229608
\(786\) 0 0
\(787\) 38390.0 1.73883 0.869413 0.494086i \(-0.164497\pi\)
0.869413 + 0.494086i \(0.164497\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −18320.0 −0.820381
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 28027.0 1.24563 0.622815 0.782369i \(-0.285989\pi\)
0.622815 + 0.782369i \(0.285989\pi\)
\(798\) 0 0
\(799\) −1120.00 −0.0495904
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −8900.00 −0.391126
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −8630.00 −0.375049 −0.187525 0.982260i \(-0.560046\pi\)
−0.187525 + 0.982260i \(0.560046\pi\)
\(810\) 0 0
\(811\) 1932.00 0.0836519 0.0418260 0.999125i \(-0.486683\pi\)
0.0418260 + 0.999125i \(0.486683\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 2950.00 0.126790
\(816\) 0 0
\(817\) −1130.00 −0.0483889
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 18090.0 0.768996 0.384498 0.923126i \(-0.374375\pi\)
0.384498 + 0.923126i \(0.374375\pi\)
\(822\) 0 0
\(823\) −12890.0 −0.545950 −0.272975 0.962021i \(-0.588008\pi\)
−0.272975 + 0.962021i \(0.588008\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 14887.0 0.625963 0.312982 0.949759i \(-0.398672\pi\)
0.312982 + 0.949759i \(0.398672\pi\)
\(828\) 0 0
\(829\) 12666.0 0.530649 0.265325 0.964159i \(-0.414521\pi\)
0.265325 + 0.964159i \(0.414521\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2401.00 0.0998676
\(834\) 0 0
\(835\) −12015.0 −0.497960
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 43820.0 1.80314 0.901570 0.432633i \(-0.142416\pi\)
0.901570 + 0.432633i \(0.142416\pi\)
\(840\) 0 0
\(841\) 24011.0 0.984501
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −21015.0 −0.855548
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −13770.0 −0.554676
\(852\) 0 0
\(853\) 19320.0 0.775503 0.387752 0.921764i \(-0.373252\pi\)
0.387752 + 0.921764i \(0.373252\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3653.00 0.145606 0.0728029 0.997346i \(-0.476806\pi\)
0.0728029 + 0.997346i \(0.476806\pi\)
\(858\) 0 0
\(859\) −24373.0 −0.968098 −0.484049 0.875041i \(-0.660834\pi\)
−0.484049 + 0.875041i \(0.660834\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −17629.0 −0.695363 −0.347681 0.937613i \(-0.613031\pi\)
−0.347681 + 0.937613i \(0.613031\pi\)
\(864\) 0 0
\(865\) 4005.00 0.157427
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 270.000 0.0105398
\(870\) 0 0
\(871\) 60000.0 2.33412
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −21210.0 −0.816660 −0.408330 0.912834i \(-0.633889\pi\)
−0.408330 + 0.912834i \(0.633889\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −39340.0 −1.50442 −0.752212 0.658921i \(-0.771013\pi\)
−0.752212 + 0.658921i \(0.771013\pi\)
\(882\) 0 0
\(883\) 4240.00 0.161594 0.0807969 0.996731i \(-0.474253\pi\)
0.0807969 + 0.996731i \(0.474253\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −15933.0 −0.603132 −0.301566 0.953445i \(-0.597509\pi\)
−0.301566 + 0.953445i \(0.597509\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 18080.0 0.677519
\(894\) 0 0
\(895\) 11800.0 0.440704
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 41580.0 1.54257
\(900\) 0 0
\(901\) 4417.00 0.163320
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −6205.00 −0.227913
\(906\) 0 0
\(907\) 6780.00 0.248210 0.124105 0.992269i \(-0.460394\pi\)
0.124105 + 0.992269i \(0.460394\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −24740.0 −0.899751 −0.449875 0.893091i \(-0.648532\pi\)
−0.449875 + 0.893091i \(0.648532\pi\)
\(912\) 0 0
\(913\) 4290.00 0.155507
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 48344.0 1.73528 0.867640 0.497194i \(-0.165636\pi\)
0.867640 + 0.497194i \(0.165636\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −71200.0 −2.53909
\(924\) 0 0
\(925\) 4250.00 0.151069
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 29650.0 1.04713 0.523566 0.851985i \(-0.324601\pi\)
0.523566 + 0.851985i \(0.324601\pi\)
\(930\) 0 0
\(931\) −38759.0 −1.36442
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 350.000 0.0122420
\(936\) 0 0
\(937\) 10260.0 0.357716 0.178858 0.983875i \(-0.442760\pi\)
0.178858 + 0.983875i \(0.442760\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 16270.0 0.563642 0.281821 0.959467i \(-0.409062\pi\)
0.281821 + 0.959467i \(0.409062\pi\)
\(942\) 0 0
\(943\) −10530.0 −0.363631
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −23103.0 −0.792763 −0.396382 0.918086i \(-0.629734\pi\)
−0.396382 + 0.918086i \(0.629734\pi\)
\(948\) 0 0
\(949\) 71200.0 2.43546
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 32090.0 1.09076 0.545381 0.838188i \(-0.316385\pi\)
0.545381 + 0.838188i \(0.316385\pi\)
\(954\) 0 0
\(955\) 24950.0 0.845406
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 5930.00 0.199053
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 11300.0 0.376953
\(966\) 0 0
\(967\) 42010.0 1.39705 0.698527 0.715584i \(-0.253839\pi\)
0.698527 + 0.715584i \(0.253839\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 17490.0 0.578044 0.289022 0.957322i \(-0.406670\pi\)
0.289022 + 0.957322i \(0.406670\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 22130.0 0.724669 0.362334 0.932048i \(-0.381980\pi\)
0.362334 + 0.932048i \(0.381980\pi\)
\(978\) 0 0
\(979\) 7500.00 0.244843
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 40959.0 1.32898 0.664491 0.747296i \(-0.268648\pi\)
0.664491 + 0.747296i \(0.268648\pi\)
\(984\) 0 0
\(985\) −11235.0 −0.363428
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 810.000 0.0260430
\(990\) 0 0
\(991\) −61169.0 −1.96074 −0.980372 0.197157i \(-0.936829\pi\)
−0.980372 + 0.197157i \(0.936829\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 22820.0 0.727078
\(996\) 0 0
\(997\) 26190.0 0.831941 0.415971 0.909378i \(-0.363442\pi\)
0.415971 + 0.909378i \(0.363442\pi\)
\(998\) 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.d.1.1 1
3.2 odd 2 2160.4.a.n.1.1 1
4.3 odd 2 135.4.a.d.1.1 yes 1
12.11 even 2 135.4.a.a.1.1 1
20.3 even 4 675.4.b.c.649.1 2
20.7 even 4 675.4.b.c.649.2 2
20.19 odd 2 675.4.a.b.1.1 1
36.7 odd 6 405.4.e.e.271.1 2
36.11 even 6 405.4.e.j.271.1 2
36.23 even 6 405.4.e.j.136.1 2
36.31 odd 6 405.4.e.e.136.1 2
60.23 odd 4 675.4.b.d.649.2 2
60.47 odd 4 675.4.b.d.649.1 2
60.59 even 2 675.4.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
135.4.a.a.1.1 1 12.11 even 2
135.4.a.d.1.1 yes 1 4.3 odd 2
405.4.e.e.136.1 2 36.31 odd 6
405.4.e.e.271.1 2 36.7 odd 6
405.4.e.j.136.1 2 36.23 even 6
405.4.e.j.271.1 2 36.11 even 6
675.4.a.b.1.1 1 20.19 odd 2
675.4.a.i.1.1 1 60.59 even 2
675.4.b.c.649.1 2 20.3 even 4
675.4.b.c.649.2 2 20.7 even 4
675.4.b.d.649.1 2 60.47 odd 4
675.4.b.d.649.2 2 60.23 odd 4
2160.4.a.d.1.1 1 1.1 even 1 trivial
2160.4.a.n.1.1 1 3.2 odd 2