Properties

Label 720.4.a.j.1.1
Level $720$
Weight $4$
Character 720.1
Self dual yes
Analytic conductor $42.481$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 720.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(42.4813752041\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 10)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 720.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.00000 q^{5} +4.00000 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} +4.00000 q^{7} +12.0000 q^{11} -58.0000 q^{13} -66.0000 q^{17} +100.000 q^{19} +132.000 q^{23} +25.0000 q^{25} +90.0000 q^{29} -152.000 q^{31} -20.0000 q^{35} -34.0000 q^{37} +438.000 q^{41} -32.0000 q^{43} -204.000 q^{47} -327.000 q^{49} -222.000 q^{53} -60.0000 q^{55} +420.000 q^{59} +902.000 q^{61} +290.000 q^{65} +1024.00 q^{67} +432.000 q^{71} +362.000 q^{73} +48.0000 q^{77} +160.000 q^{79} +72.0000 q^{83} +330.000 q^{85} -810.000 q^{89} -232.000 q^{91} -500.000 q^{95} +1106.00 q^{97} +O(q^{100})\)

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
\(7\) 4.00000 0.215980 0.107990 0.994152i \(-0.465559\pi\)
0.107990 + 0.994152i \(0.465559\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 12.0000 0.328921 0.164461 0.986384i \(-0.447412\pi\)
0.164461 + 0.986384i \(0.447412\pi\)
\(12\) 0 0
\(13\) −58.0000 −1.23741 −0.618704 0.785624i \(-0.712342\pi\)
−0.618704 + 0.785624i \(0.712342\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −66.0000 −0.941609 −0.470804 0.882238i \(-0.656036\pi\)
−0.470804 + 0.882238i \(0.656036\pi\)
\(18\) 0 0
\(19\) 100.000 1.20745 0.603726 0.797192i \(-0.293682\pi\)
0.603726 + 0.797192i \(0.293682\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 132.000 1.19669 0.598346 0.801238i \(-0.295825\pi\)
0.598346 + 0.801238i \(0.295825\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 90.0000 0.576296 0.288148 0.957586i \(-0.406961\pi\)
0.288148 + 0.957586i \(0.406961\pi\)
\(30\) 0 0
\(31\) −152.000 −0.880645 −0.440323 0.897840i \(-0.645136\pi\)
−0.440323 + 0.897840i \(0.645136\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −20.0000 −0.0965891
\(36\) 0 0
\(37\) −34.0000 −0.151069 −0.0755347 0.997143i \(-0.524066\pi\)
−0.0755347 + 0.997143i \(0.524066\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 438.000 1.66839 0.834196 0.551467i \(-0.185932\pi\)
0.834196 + 0.551467i \(0.185932\pi\)
\(42\) 0 0
\(43\) −32.0000 −0.113487 −0.0567437 0.998389i \(-0.518072\pi\)
−0.0567437 + 0.998389i \(0.518072\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −204.000 −0.633116 −0.316558 0.948573i \(-0.602527\pi\)
−0.316558 + 0.948573i \(0.602527\pi\)
\(48\) 0 0
\(49\) −327.000 −0.953353
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −222.000 −0.575359 −0.287680 0.957727i \(-0.592884\pi\)
−0.287680 + 0.957727i \(0.592884\pi\)
\(54\) 0 0
\(55\) −60.0000 −0.147098
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 420.000 0.926769 0.463384 0.886157i \(-0.346635\pi\)
0.463384 + 0.886157i \(0.346635\pi\)
\(60\) 0 0
\(61\) 902.000 1.89327 0.946633 0.322312i \(-0.104460\pi\)
0.946633 + 0.322312i \(0.104460\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 290.000 0.553386
\(66\) 0 0
\(67\) 1024.00 1.86719 0.933593 0.358334i \(-0.116655\pi\)
0.933593 + 0.358334i \(0.116655\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 432.000 0.722098 0.361049 0.932547i \(-0.382419\pi\)
0.361049 + 0.932547i \(0.382419\pi\)
\(72\) 0 0
\(73\) 362.000 0.580396 0.290198 0.956967i \(-0.406279\pi\)
0.290198 + 0.956967i \(0.406279\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 48.0000 0.0710404
\(78\) 0 0
\(79\) 160.000 0.227866 0.113933 0.993488i \(-0.463655\pi\)
0.113933 + 0.993488i \(0.463655\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 72.0000 0.0952172 0.0476086 0.998866i \(-0.484840\pi\)
0.0476086 + 0.998866i \(0.484840\pi\)
\(84\) 0 0
\(85\) 330.000 0.421100
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −810.000 −0.964717 −0.482359 0.875974i \(-0.660220\pi\)
−0.482359 + 0.875974i \(0.660220\pi\)
\(90\) 0 0
\(91\) −232.000 −0.267255
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −500.000 −0.539989
\(96\) 0 0
\(97\) 1106.00 1.15770 0.578852 0.815433i \(-0.303501\pi\)
0.578852 + 0.815433i \(0.303501\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 258.000 0.254178 0.127089 0.991891i \(-0.459437\pi\)
0.127089 + 0.991891i \(0.459437\pi\)
\(102\) 0 0
\(103\) 988.000 0.945151 0.472575 0.881290i \(-0.343324\pi\)
0.472575 + 0.881290i \(0.343324\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −24.0000 −0.0216838 −0.0108419 0.999941i \(-0.503451\pi\)
−0.0108419 + 0.999941i \(0.503451\pi\)
\(108\) 0 0
\(109\) 950.000 0.834803 0.417401 0.908722i \(-0.362941\pi\)
0.417401 + 0.908722i \(0.362941\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1038.00 0.864131 0.432066 0.901842i \(-0.357785\pi\)
0.432066 + 0.901842i \(0.357785\pi\)
\(114\) 0 0
\(115\) −660.000 −0.535177
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −264.000 −0.203368
\(120\) 0 0
\(121\) −1187.00 −0.891811
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 124.000 0.0866395 0.0433198 0.999061i \(-0.486207\pi\)
0.0433198 + 0.999061i \(0.486207\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 132.000 0.0880374 0.0440187 0.999031i \(-0.485984\pi\)
0.0440187 + 0.999031i \(0.485984\pi\)
\(132\) 0 0
\(133\) 400.000 0.260785
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1254.00 0.782018 0.391009 0.920387i \(-0.372126\pi\)
0.391009 + 0.920387i \(0.372126\pi\)
\(138\) 0 0
\(139\) 2860.00 1.74519 0.872597 0.488440i \(-0.162434\pi\)
0.872597 + 0.488440i \(0.162434\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −696.000 −0.407010
\(144\) 0 0
\(145\) −450.000 −0.257727
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −750.000 −0.412365 −0.206183 0.978514i \(-0.566104\pi\)
−0.206183 + 0.978514i \(0.566104\pi\)
\(150\) 0 0
\(151\) 448.000 0.241442 0.120721 0.992686i \(-0.461479\pi\)
0.120721 + 0.992686i \(0.461479\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 760.000 0.393837
\(156\) 0 0
\(157\) 2246.00 1.14172 0.570861 0.821047i \(-0.306610\pi\)
0.570861 + 0.821047i \(0.306610\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 528.000 0.258461
\(162\) 0 0
\(163\) 568.000 0.272940 0.136470 0.990644i \(-0.456424\pi\)
0.136470 + 0.990644i \(0.456424\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1524.00 −0.706172 −0.353086 0.935591i \(-0.614868\pi\)
−0.353086 + 0.935591i \(0.614868\pi\)
\(168\) 0 0
\(169\) 1167.00 0.531179
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3702.00 −1.62692 −0.813462 0.581618i \(-0.802420\pi\)
−0.813462 + 0.581618i \(0.802420\pi\)
\(174\) 0 0
\(175\) 100.000 0.0431959
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3180.00 1.32785 0.663923 0.747801i \(-0.268890\pi\)
0.663923 + 0.747801i \(0.268890\pi\)
\(180\) 0 0
\(181\) −2098.00 −0.861564 −0.430782 0.902456i \(-0.641762\pi\)
−0.430782 + 0.902456i \(0.641762\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 170.000 0.0675603
\(186\) 0 0
\(187\) −792.000 −0.309715
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4392.00 1.66384 0.831921 0.554894i \(-0.187241\pi\)
0.831921 + 0.554894i \(0.187241\pi\)
\(192\) 0 0
\(193\) −2158.00 −0.804851 −0.402425 0.915453i \(-0.631833\pi\)
−0.402425 + 0.915453i \(0.631833\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1074.00 0.388423 0.194212 0.980960i \(-0.437785\pi\)
0.194212 + 0.980960i \(0.437785\pi\)
\(198\) 0 0
\(199\) −2840.00 −1.01167 −0.505835 0.862630i \(-0.668815\pi\)
−0.505835 + 0.862630i \(0.668815\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 360.000 0.124468
\(204\) 0 0
\(205\) −2190.00 −0.746128
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1200.00 0.397157
\(210\) 0 0
\(211\) 2668.00 0.870487 0.435243 0.900313i \(-0.356662\pi\)
0.435243 + 0.900313i \(0.356662\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 160.000 0.0507531
\(216\) 0 0
\(217\) −608.000 −0.190202
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3828.00 1.16515
\(222\) 0 0
\(223\) −1772.00 −0.532116 −0.266058 0.963957i \(-0.585721\pi\)
−0.266058 + 0.963957i \(0.585721\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2784.00 −0.814011 −0.407006 0.913426i \(-0.633427\pi\)
−0.407006 + 0.913426i \(0.633427\pi\)
\(228\) 0 0
\(229\) 350.000 0.100998 0.0504992 0.998724i \(-0.483919\pi\)
0.0504992 + 0.998724i \(0.483919\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1962.00 −0.551652 −0.275826 0.961208i \(-0.588951\pi\)
−0.275826 + 0.961208i \(0.588951\pi\)
\(234\) 0 0
\(235\) 1020.00 0.283138
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −4320.00 −1.16919 −0.584597 0.811324i \(-0.698748\pi\)
−0.584597 + 0.811324i \(0.698748\pi\)
\(240\) 0 0
\(241\) −478.000 −0.127762 −0.0638811 0.997958i \(-0.520348\pi\)
−0.0638811 + 0.997958i \(0.520348\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1635.00 0.426352
\(246\) 0 0
\(247\) −5800.00 −1.49411
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2652.00 0.666903 0.333452 0.942767i \(-0.391787\pi\)
0.333452 + 0.942767i \(0.391787\pi\)
\(252\) 0 0
\(253\) 1584.00 0.393617
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2334.00 0.566502 0.283251 0.959046i \(-0.408587\pi\)
0.283251 + 0.959046i \(0.408587\pi\)
\(258\) 0 0
\(259\) −136.000 −0.0326279
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3948.00 −0.925643 −0.462822 0.886451i \(-0.653163\pi\)
−0.462822 + 0.886451i \(0.653163\pi\)
\(264\) 0 0
\(265\) 1110.00 0.257309
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1590.00 −0.360387 −0.180193 0.983631i \(-0.557672\pi\)
−0.180193 + 0.983631i \(0.557672\pi\)
\(270\) 0 0
\(271\) −4952.00 −1.11001 −0.555005 0.831847i \(-0.687284\pi\)
−0.555005 + 0.831847i \(0.687284\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 300.000 0.0657843
\(276\) 0 0
\(277\) 1646.00 0.357034 0.178517 0.983937i \(-0.442870\pi\)
0.178517 + 0.983937i \(0.442870\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1158.00 0.245838 0.122919 0.992417i \(-0.460774\pi\)
0.122919 + 0.992417i \(0.460774\pi\)
\(282\) 0 0
\(283\) −6992.00 −1.46866 −0.734331 0.678792i \(-0.762504\pi\)
−0.734331 + 0.678792i \(0.762504\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1752.00 0.360339
\(288\) 0 0
\(289\) −557.000 −0.113373
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 258.000 0.0514421 0.0257210 0.999669i \(-0.491812\pi\)
0.0257210 + 0.999669i \(0.491812\pi\)
\(294\) 0 0
\(295\) −2100.00 −0.414463
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −7656.00 −1.48080
\(300\) 0 0
\(301\) −128.000 −0.0245110
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4510.00 −0.846695
\(306\) 0 0
\(307\) 8944.00 1.66274 0.831370 0.555720i \(-0.187557\pi\)
0.831370 + 0.555720i \(0.187557\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1392.00 0.253804 0.126902 0.991915i \(-0.459497\pi\)
0.126902 + 0.991915i \(0.459497\pi\)
\(312\) 0 0
\(313\) −5878.00 −1.06148 −0.530742 0.847534i \(-0.678087\pi\)
−0.530742 + 0.847534i \(0.678087\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10326.0 −1.82955 −0.914773 0.403969i \(-0.867630\pi\)
−0.914773 + 0.403969i \(0.867630\pi\)
\(318\) 0 0
\(319\) 1080.00 0.189556
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −6600.00 −1.13695
\(324\) 0 0
\(325\) −1450.00 −0.247482
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −816.000 −0.136740
\(330\) 0 0
\(331\) 4228.00 0.702090 0.351045 0.936359i \(-0.385826\pi\)
0.351045 + 0.936359i \(0.385826\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5120.00 −0.835031
\(336\) 0 0
\(337\) 1106.00 0.178776 0.0893882 0.995997i \(-0.471509\pi\)
0.0893882 + 0.995997i \(0.471509\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1824.00 −0.289663
\(342\) 0 0
\(343\) −2680.00 −0.421885
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9336.00 1.44433 0.722165 0.691720i \(-0.243147\pi\)
0.722165 + 0.691720i \(0.243147\pi\)
\(348\) 0 0
\(349\) −11770.0 −1.80525 −0.902627 0.430424i \(-0.858364\pi\)
−0.902627 + 0.430424i \(0.858364\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −8322.00 −1.25477 −0.627387 0.778707i \(-0.715876\pi\)
−0.627387 + 0.778707i \(0.715876\pi\)
\(354\) 0 0
\(355\) −2160.00 −0.322932
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10680.0 1.57011 0.785054 0.619427i \(-0.212635\pi\)
0.785054 + 0.619427i \(0.212635\pi\)
\(360\) 0 0
\(361\) 3141.00 0.457938
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1810.00 −0.259561
\(366\) 0 0
\(367\) 5884.00 0.836900 0.418450 0.908240i \(-0.362574\pi\)
0.418450 + 0.908240i \(0.362574\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −888.000 −0.124266
\(372\) 0 0
\(373\) −2098.00 −0.291234 −0.145617 0.989341i \(-0.546517\pi\)
−0.145617 + 0.989341i \(0.546517\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5220.00 −0.713113
\(378\) 0 0
\(379\) −3860.00 −0.523153 −0.261576 0.965183i \(-0.584242\pi\)
−0.261576 + 0.965183i \(0.584242\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −9588.00 −1.27917 −0.639587 0.768718i \(-0.720895\pi\)
−0.639587 + 0.768718i \(0.720895\pi\)
\(384\) 0 0
\(385\) −240.000 −0.0317702
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 13410.0 1.74785 0.873925 0.486060i \(-0.161566\pi\)
0.873925 + 0.486060i \(0.161566\pi\)
\(390\) 0 0
\(391\) −8712.00 −1.12682
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −800.000 −0.101905
\(396\) 0 0
\(397\) −13114.0 −1.65787 −0.828933 0.559348i \(-0.811052\pi\)
−0.828933 + 0.559348i \(0.811052\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5838.00 0.727022 0.363511 0.931590i \(-0.381578\pi\)
0.363511 + 0.931590i \(0.381578\pi\)
\(402\) 0 0
\(403\) 8816.00 1.08972
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −408.000 −0.0496899
\(408\) 0 0
\(409\) 9530.00 1.15215 0.576074 0.817398i \(-0.304584\pi\)
0.576074 + 0.817398i \(0.304584\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1680.00 0.200163
\(414\) 0 0
\(415\) −360.000 −0.0425824
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7260.00 0.846478 0.423239 0.906018i \(-0.360893\pi\)
0.423239 + 0.906018i \(0.360893\pi\)
\(420\) 0 0
\(421\) 12062.0 1.39636 0.698178 0.715924i \(-0.253994\pi\)
0.698178 + 0.715924i \(0.253994\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1650.00 −0.188322
\(426\) 0 0
\(427\) 3608.00 0.408907
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −13608.0 −1.52082 −0.760411 0.649442i \(-0.775002\pi\)
−0.760411 + 0.649442i \(0.775002\pi\)
\(432\) 0 0
\(433\) −3838.00 −0.425964 −0.212982 0.977056i \(-0.568318\pi\)
−0.212982 + 0.977056i \(0.568318\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 13200.0 1.44495
\(438\) 0 0
\(439\) −7400.00 −0.804516 −0.402258 0.915526i \(-0.631775\pi\)
−0.402258 + 0.915526i \(0.631775\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8352.00 0.895746 0.447873 0.894097i \(-0.352182\pi\)
0.447873 + 0.894097i \(0.352182\pi\)
\(444\) 0 0
\(445\) 4050.00 0.431435
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10770.0 −1.13200 −0.566000 0.824405i \(-0.691510\pi\)
−0.566000 + 0.824405i \(0.691510\pi\)
\(450\) 0 0
\(451\) 5256.00 0.548770
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1160.00 0.119520
\(456\) 0 0
\(457\) −6694.00 −0.685191 −0.342595 0.939483i \(-0.611306\pi\)
−0.342595 + 0.939483i \(0.611306\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3018.00 0.304907 0.152454 0.988311i \(-0.451283\pi\)
0.152454 + 0.988311i \(0.451283\pi\)
\(462\) 0 0
\(463\) −14492.0 −1.45464 −0.727322 0.686296i \(-0.759235\pi\)
−0.727322 + 0.686296i \(0.759235\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7776.00 0.770515 0.385257 0.922809i \(-0.374113\pi\)
0.385257 + 0.922809i \(0.374113\pi\)
\(468\) 0 0
\(469\) 4096.00 0.403274
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −384.000 −0.0373284
\(474\) 0 0
\(475\) 2500.00 0.241490
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −13680.0 −1.30492 −0.652458 0.757825i \(-0.726262\pi\)
−0.652458 + 0.757825i \(0.726262\pi\)
\(480\) 0 0
\(481\) 1972.00 0.186934
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −5530.00 −0.517741
\(486\) 0 0
\(487\) −7916.00 −0.736567 −0.368284 0.929714i \(-0.620054\pi\)
−0.368284 + 0.929714i \(0.620054\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 13932.0 1.28053 0.640267 0.768152i \(-0.278824\pi\)
0.640267 + 0.768152i \(0.278824\pi\)
\(492\) 0 0
\(493\) −5940.00 −0.542645
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1728.00 0.155959
\(498\) 0 0
\(499\) 8260.00 0.741019 0.370509 0.928829i \(-0.379183\pi\)
0.370509 + 0.928829i \(0.379183\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −11148.0 −0.988200 −0.494100 0.869405i \(-0.664502\pi\)
−0.494100 + 0.869405i \(0.664502\pi\)
\(504\) 0 0
\(505\) −1290.00 −0.113672
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 9690.00 0.843815 0.421907 0.906639i \(-0.361361\pi\)
0.421907 + 0.906639i \(0.361361\pi\)
\(510\) 0 0
\(511\) 1448.00 0.125354
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4940.00 −0.422684
\(516\) 0 0
\(517\) −2448.00 −0.208245
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 16038.0 1.34863 0.674316 0.738443i \(-0.264438\pi\)
0.674316 + 0.738443i \(0.264438\pi\)
\(522\) 0 0
\(523\) −992.000 −0.0829391 −0.0414695 0.999140i \(-0.513204\pi\)
−0.0414695 + 0.999140i \(0.513204\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10032.0 0.829223
\(528\) 0 0
\(529\) 5257.00 0.432070
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −25404.0 −2.06448
\(534\) 0 0
\(535\) 120.000 0.00969729
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3924.00 −0.313578
\(540\) 0 0
\(541\) 7142.00 0.567576 0.283788 0.958887i \(-0.408409\pi\)
0.283788 + 0.958887i \(0.408409\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −4750.00 −0.373335
\(546\) 0 0
\(547\) −7616.00 −0.595314 −0.297657 0.954673i \(-0.596205\pi\)
−0.297657 + 0.954673i \(0.596205\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 9000.00 0.695849
\(552\) 0 0
\(553\) 640.000 0.0492144
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 10314.0 0.784593 0.392296 0.919839i \(-0.371681\pi\)
0.392296 + 0.919839i \(0.371681\pi\)
\(558\) 0 0
\(559\) 1856.00 0.140430
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7128.00 −0.533587 −0.266793 0.963754i \(-0.585964\pi\)
−0.266793 + 0.963754i \(0.585964\pi\)
\(564\) 0 0
\(565\) −5190.00 −0.386451
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2010.00 −0.148091 −0.0740453 0.997255i \(-0.523591\pi\)
−0.0740453 + 0.997255i \(0.523591\pi\)
\(570\) 0 0
\(571\) 23188.0 1.69945 0.849726 0.527224i \(-0.176767\pi\)
0.849726 + 0.527224i \(0.176767\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3300.00 0.239338
\(576\) 0 0
\(577\) 22466.0 1.62092 0.810461 0.585793i \(-0.199217\pi\)
0.810461 + 0.585793i \(0.199217\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 288.000 0.0205650
\(582\) 0 0
\(583\) −2664.00 −0.189248
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 22776.0 1.60148 0.800738 0.599015i \(-0.204441\pi\)
0.800738 + 0.599015i \(0.204441\pi\)
\(588\) 0 0
\(589\) −15200.0 −1.06334
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 21198.0 1.46796 0.733978 0.679174i \(-0.237662\pi\)
0.733978 + 0.679174i \(0.237662\pi\)
\(594\) 0 0
\(595\) 1320.00 0.0909491
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 15960.0 1.08866 0.544330 0.838871i \(-0.316784\pi\)
0.544330 + 0.838871i \(0.316784\pi\)
\(600\) 0 0
\(601\) 5882.00 0.399221 0.199610 0.979875i \(-0.436032\pi\)
0.199610 + 0.979875i \(0.436032\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5935.00 0.398830
\(606\) 0 0
\(607\) −8516.00 −0.569446 −0.284723 0.958610i \(-0.591902\pi\)
−0.284723 + 0.958610i \(0.591902\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 11832.0 0.783423
\(612\) 0 0
\(613\) 8462.00 0.557548 0.278774 0.960357i \(-0.410072\pi\)
0.278774 + 0.960357i \(0.410072\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11094.0 0.723870 0.361935 0.932203i \(-0.382116\pi\)
0.361935 + 0.932203i \(0.382116\pi\)
\(618\) 0 0
\(619\) −2180.00 −0.141553 −0.0707767 0.997492i \(-0.522548\pi\)
−0.0707767 + 0.997492i \(0.522548\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3240.00 −0.208359
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2244.00 0.142248
\(630\) 0 0
\(631\) 26848.0 1.69382 0.846911 0.531734i \(-0.178459\pi\)
0.846911 + 0.531734i \(0.178459\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −620.000 −0.0387464
\(636\) 0 0
\(637\) 18966.0 1.17969
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −26322.0 −1.62193 −0.810965 0.585095i \(-0.801057\pi\)
−0.810965 + 0.585095i \(0.801057\pi\)
\(642\) 0 0
\(643\) 10168.0 0.623619 0.311809 0.950145i \(-0.399065\pi\)
0.311809 + 0.950145i \(0.399065\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −23604.0 −1.43426 −0.717132 0.696937i \(-0.754546\pi\)
−0.717132 + 0.696937i \(0.754546\pi\)
\(648\) 0 0
\(649\) 5040.00 0.304834
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −16422.0 −0.984139 −0.492069 0.870556i \(-0.663759\pi\)
−0.492069 + 0.870556i \(0.663759\pi\)
\(654\) 0 0
\(655\) −660.000 −0.0393715
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −26100.0 −1.54281 −0.771405 0.636345i \(-0.780446\pi\)
−0.771405 + 0.636345i \(0.780446\pi\)
\(660\) 0 0
\(661\) −3058.00 −0.179943 −0.0899716 0.995944i \(-0.528678\pi\)
−0.0899716 + 0.995944i \(0.528678\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2000.00 −0.116627
\(666\) 0 0
\(667\) 11880.0 0.689648
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 10824.0 0.622736
\(672\) 0 0
\(673\) 10802.0 0.618702 0.309351 0.950948i \(-0.399888\pi\)
0.309351 + 0.950948i \(0.399888\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10674.0 0.605960 0.302980 0.952997i \(-0.402018\pi\)
0.302980 + 0.952997i \(0.402018\pi\)
\(678\) 0 0
\(679\) 4424.00 0.250041
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −28608.0 −1.60272 −0.801358 0.598185i \(-0.795889\pi\)
−0.801358 + 0.598185i \(0.795889\pi\)
\(684\) 0 0
\(685\) −6270.00 −0.349729
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 12876.0 0.711954
\(690\) 0 0
\(691\) 2428.00 0.133669 0.0668346 0.997764i \(-0.478710\pi\)
0.0668346 + 0.997764i \(0.478710\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −14300.0 −0.780475
\(696\) 0 0
\(697\) −28908.0 −1.57097
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 6618.00 0.356574 0.178287 0.983979i \(-0.442944\pi\)
0.178287 + 0.983979i \(0.442944\pi\)
\(702\) 0 0
\(703\) −3400.00 −0.182409
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1032.00 0.0548972
\(708\) 0 0
\(709\) 20510.0 1.08642 0.543208 0.839598i \(-0.317209\pi\)
0.543208 + 0.839598i \(0.317209\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −20064.0 −1.05386
\(714\) 0 0
\(715\) 3480.00 0.182020
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 31680.0 1.64321 0.821603 0.570061i \(-0.193080\pi\)
0.821603 + 0.570061i \(0.193080\pi\)
\(720\) 0 0
\(721\) 3952.00 0.204133
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2250.00 0.115259
\(726\) 0 0
\(727\) −13196.0 −0.673195 −0.336597 0.941649i \(-0.609276\pi\)
−0.336597 + 0.941649i \(0.609276\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2112.00 0.106861
\(732\) 0 0
\(733\) 8102.00 0.408259 0.204130 0.978944i \(-0.434564\pi\)
0.204130 + 0.978944i \(0.434564\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 12288.0 0.614158
\(738\) 0 0
\(739\) 12580.0 0.626201 0.313101 0.949720i \(-0.398632\pi\)
0.313101 + 0.949720i \(0.398632\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 29892.0 1.47595 0.737975 0.674828i \(-0.235782\pi\)
0.737975 + 0.674828i \(0.235782\pi\)
\(744\) 0 0
\(745\) 3750.00 0.184415
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −96.0000 −0.00468326
\(750\) 0 0
\(751\) 40408.0 1.96339 0.981697 0.190450i \(-0.0609946\pi\)
0.981697 + 0.190450i \(0.0609946\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2240.00 −0.107976
\(756\) 0 0
\(757\) 32366.0 1.55398 0.776990 0.629513i \(-0.216746\pi\)
0.776990 + 0.629513i \(0.216746\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 17238.0 0.821126 0.410563 0.911832i \(-0.365332\pi\)
0.410563 + 0.911832i \(0.365332\pi\)
\(762\) 0 0
\(763\) 3800.00 0.180300
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −24360.0 −1.14679
\(768\) 0 0
\(769\) 10850.0 0.508792 0.254396 0.967100i \(-0.418123\pi\)
0.254396 + 0.967100i \(0.418123\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9102.00 −0.423514 −0.211757 0.977322i \(-0.567919\pi\)
−0.211757 + 0.977322i \(0.567919\pi\)
\(774\) 0 0
\(775\) −3800.00 −0.176129
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 43800.0 2.01450
\(780\) 0 0
\(781\) 5184.00 0.237514
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −11230.0 −0.510593
\(786\) 0 0
\(787\) 25504.0 1.15517 0.577585 0.816330i \(-0.303995\pi\)
0.577585 + 0.816330i \(0.303995\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 4152.00 0.186635
\(792\) 0 0
\(793\) −52316.0 −2.34274
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −14166.0 −0.629593 −0.314796 0.949159i \(-0.601936\pi\)
−0.314796 + 0.949159i \(0.601936\pi\)
\(798\) 0 0
\(799\) 13464.0 0.596148
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4344.00 0.190905
\(804\) 0 0
\(805\) −2640.00 −0.115587
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −33210.0 −1.44327 −0.721633 0.692276i \(-0.756608\pi\)
−0.721633 + 0.692276i \(0.756608\pi\)
\(810\) 0 0
\(811\) −39212.0 −1.69780 −0.848902 0.528550i \(-0.822736\pi\)
−0.848902 + 0.528550i \(0.822736\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −2840.00 −0.122062
\(816\) 0 0
\(817\) −3200.00 −0.137030
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −6222.00 −0.264494 −0.132247 0.991217i \(-0.542219\pi\)
−0.132247 + 0.991217i \(0.542219\pi\)
\(822\) 0 0
\(823\) −31172.0 −1.32028 −0.660138 0.751144i \(-0.729502\pi\)
−0.660138 + 0.751144i \(0.729502\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −264.000 −0.0111006 −0.00555029 0.999985i \(-0.501767\pi\)
−0.00555029 + 0.999985i \(0.501767\pi\)
\(828\) 0 0
\(829\) −29050.0 −1.21707 −0.608533 0.793528i \(-0.708242\pi\)
−0.608533 + 0.793528i \(0.708242\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 21582.0 0.897685
\(834\) 0 0
\(835\) 7620.00 0.315810
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −21720.0 −0.893752 −0.446876 0.894596i \(-0.647463\pi\)
−0.446876 + 0.894596i \(0.647463\pi\)
\(840\) 0 0
\(841\) −16289.0 −0.667883
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −5835.00 −0.237550
\(846\) 0 0
\(847\) −4748.00 −0.192613
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −4488.00 −0.180783
\(852\) 0 0
\(853\) −6658.00 −0.267252 −0.133626 0.991032i \(-0.542662\pi\)
−0.133626 + 0.991032i \(0.542662\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 13974.0 0.556993 0.278496 0.960437i \(-0.410164\pi\)
0.278496 + 0.960437i \(0.410164\pi\)
\(858\) 0 0
\(859\) −23780.0 −0.944544 −0.472272 0.881453i \(-0.656566\pi\)
−0.472272 + 0.881453i \(0.656566\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −12228.0 −0.482324 −0.241162 0.970485i \(-0.577529\pi\)
−0.241162 + 0.970485i \(0.577529\pi\)
\(864\) 0 0
\(865\) 18510.0 0.727583
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1920.00 0.0749500
\(870\) 0 0
\(871\) −59392.0 −2.31047
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −500.000 −0.0193178
\(876\) 0 0
\(877\) 11606.0 0.446872 0.223436 0.974719i \(-0.428273\pi\)
0.223436 + 0.974719i \(0.428273\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 32958.0 1.26037 0.630183 0.776446i \(-0.282980\pi\)
0.630183 + 0.776446i \(0.282980\pi\)
\(882\) 0 0
\(883\) −8072.00 −0.307638 −0.153819 0.988099i \(-0.549157\pi\)
−0.153819 + 0.988099i \(0.549157\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 15756.0 0.596431 0.298216 0.954498i \(-0.403609\pi\)
0.298216 + 0.954498i \(0.403609\pi\)
\(888\) 0 0
\(889\) 496.000 0.0187124
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −20400.0 −0.764457
\(894\) 0 0
\(895\) −15900.0 −0.593831
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −13680.0 −0.507512
\(900\) 0 0
\(901\) 14652.0 0.541763
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 10490.0 0.385303
\(906\) 0 0
\(907\) −18776.0 −0.687372 −0.343686 0.939085i \(-0.611676\pi\)
−0.343686 + 0.939085i \(0.611676\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −20568.0 −0.748022 −0.374011 0.927424i \(-0.622018\pi\)
−0.374011 + 0.927424i \(0.622018\pi\)
\(912\) 0 0
\(913\) 864.000 0.0313190
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 528.000 0.0190143
\(918\) 0 0
\(919\) 6280.00 0.225417 0.112708 0.993628i \(-0.464047\pi\)
0.112708 + 0.993628i \(0.464047\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −25056.0 −0.893530
\(924\) 0 0
\(925\) −850.000 −0.0302139
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 20430.0 0.721514 0.360757 0.932660i \(-0.382518\pi\)
0.360757 + 0.932660i \(0.382518\pi\)
\(930\) 0 0
\(931\) −32700.0 −1.15113
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 3960.00 0.138509
\(936\) 0 0
\(937\) 8906.00 0.310508 0.155254 0.987875i \(-0.450380\pi\)
0.155254 + 0.987875i \(0.450380\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 17418.0 0.603412 0.301706 0.953401i \(-0.402444\pi\)
0.301706 + 0.953401i \(0.402444\pi\)
\(942\) 0 0
\(943\) 57816.0 1.99655
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2544.00 −0.0872956 −0.0436478 0.999047i \(-0.513898\pi\)
−0.0436478 + 0.999047i \(0.513898\pi\)
\(948\) 0 0
\(949\) −20996.0 −0.718187
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −15402.0 −0.523525 −0.261763 0.965132i \(-0.584304\pi\)
−0.261763 + 0.965132i \(0.584304\pi\)
\(954\) 0 0
\(955\) −21960.0 −0.744093
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 5016.00 0.168900
\(960\) 0 0
\(961\) −6687.00 −0.224464
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 10790.0 0.359940
\(966\) 0 0
\(967\) 49444.0 1.64427 0.822136 0.569291i \(-0.192782\pi\)
0.822136 + 0.569291i \(0.192782\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −25188.0 −0.832463 −0.416231 0.909259i \(-0.636649\pi\)
−0.416231 + 0.909259i \(0.636649\pi\)
\(972\) 0 0
\(973\) 11440.0 0.376927
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2946.00 −0.0964697 −0.0482348 0.998836i \(-0.515360\pi\)
−0.0482348 + 0.998836i \(0.515360\pi\)
\(978\) 0 0
\(979\) −9720.00 −0.317316
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 15012.0 0.487089 0.243544 0.969890i \(-0.421690\pi\)
0.243544 + 0.969890i \(0.421690\pi\)
\(984\) 0 0
\(985\) −5370.00 −0.173708
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4224.00 −0.135809
\(990\) 0 0
\(991\) 5128.00 0.164376 0.0821878 0.996617i \(-0.473809\pi\)
0.0821878 + 0.996617i \(0.473809\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 14200.0 0.452432
\(996\) 0 0
\(997\) −49714.0 −1.57920 −0.789598 0.613625i \(-0.789711\pi\)
−0.789598 + 0.613625i \(0.789711\pi\)
\(998\) 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 720.4.a.j.1.1 1
3.2 odd 2 80.4.a.f.1.1 1
4.3 odd 2 90.4.a.a.1.1 1
12.11 even 2 10.4.a.a.1.1 1
15.2 even 4 400.4.c.c.49.1 2
15.8 even 4 400.4.c.c.49.2 2
15.14 odd 2 400.4.a.b.1.1 1
20.3 even 4 450.4.c.d.199.2 2
20.7 even 4 450.4.c.d.199.1 2
20.19 odd 2 450.4.a.q.1.1 1
24.5 odd 2 320.4.a.b.1.1 1
24.11 even 2 320.4.a.m.1.1 1
36.7 odd 6 810.4.e.w.271.1 2
36.11 even 6 810.4.e.c.271.1 2
36.23 even 6 810.4.e.c.541.1 2
36.31 odd 6 810.4.e.w.541.1 2
48.5 odd 4 1280.4.d.g.641.1 2
48.11 even 4 1280.4.d.j.641.2 2
48.29 odd 4 1280.4.d.g.641.2 2
48.35 even 4 1280.4.d.j.641.1 2
60.23 odd 4 50.4.b.a.49.1 2
60.47 odd 4 50.4.b.a.49.2 2
60.59 even 2 50.4.a.c.1.1 1
84.11 even 6 490.4.e.i.471.1 2
84.23 even 6 490.4.e.i.361.1 2
84.47 odd 6 490.4.e.a.361.1 2
84.59 odd 6 490.4.e.a.471.1 2
84.83 odd 2 490.4.a.o.1.1 1
120.29 odd 2 1600.4.a.bx.1.1 1
120.59 even 2 1600.4.a.d.1.1 1
132.131 odd 2 1210.4.a.b.1.1 1
156.155 even 2 1690.4.a.a.1.1 1
420.419 odd 2 2450.4.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.4.a.a.1.1 1 12.11 even 2
50.4.a.c.1.1 1 60.59 even 2
50.4.b.a.49.1 2 60.23 odd 4
50.4.b.a.49.2 2 60.47 odd 4
80.4.a.f.1.1 1 3.2 odd 2
90.4.a.a.1.1 1 4.3 odd 2
320.4.a.b.1.1 1 24.5 odd 2
320.4.a.m.1.1 1 24.11 even 2
400.4.a.b.1.1 1 15.14 odd 2
400.4.c.c.49.1 2 15.2 even 4
400.4.c.c.49.2 2 15.8 even 4
450.4.a.q.1.1 1 20.19 odd 2
450.4.c.d.199.1 2 20.7 even 4
450.4.c.d.199.2 2 20.3 even 4
490.4.a.o.1.1 1 84.83 odd 2
490.4.e.a.361.1 2 84.47 odd 6
490.4.e.a.471.1 2 84.59 odd 6
490.4.e.i.361.1 2 84.23 even 6
490.4.e.i.471.1 2 84.11 even 6
720.4.a.j.1.1 1 1.1 even 1 trivial
810.4.e.c.271.1 2 36.11 even 6
810.4.e.c.541.1 2 36.23 even 6
810.4.e.w.271.1 2 36.7 odd 6
810.4.e.w.541.1 2 36.31 odd 6
1210.4.a.b.1.1 1 132.131 odd 2
1280.4.d.g.641.1 2 48.5 odd 4
1280.4.d.g.641.2 2 48.29 odd 4
1280.4.d.j.641.1 2 48.35 even 4
1280.4.d.j.641.2 2 48.11 even 4
1600.4.a.d.1.1 1 120.59 even 2
1600.4.a.bx.1.1 1 120.29 odd 2
1690.4.a.a.1.1 1 156.155 even 2
2450.4.a.b.1.1 1 420.419 odd 2