Properties

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

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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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 40)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q-5.00000 q^{5} -16.0000 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} -16.0000 q^{7} +36.0000 q^{11} -42.0000 q^{13} +110.000 q^{17} +116.000 q^{19} +16.0000 q^{23} +25.0000 q^{25} -198.000 q^{29} -240.000 q^{31} +80.0000 q^{35} -258.000 q^{37} -442.000 q^{41} +292.000 q^{43} +392.000 q^{47} -87.0000 q^{49} -142.000 q^{53} -180.000 q^{55} -348.000 q^{59} -570.000 q^{61} +210.000 q^{65} -692.000 q^{67} +168.000 q^{71} -134.000 q^{73} -576.000 q^{77} -784.000 q^{79} +564.000 q^{83} -550.000 q^{85} -1034.00 q^{89} +672.000 q^{91} -580.000 q^{95} -382.000 q^{97} +O(q^{100})\)

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
\(7\) −16.0000 −0.863919 −0.431959 0.901893i \(-0.642178\pi\)
−0.431959 + 0.901893i \(0.642178\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 36.0000 0.986764 0.493382 0.869813i \(-0.335760\pi\)
0.493382 + 0.869813i \(0.335760\pi\)
\(12\) 0 0
\(13\) −42.0000 −0.896054 −0.448027 0.894020i \(-0.647873\pi\)
−0.448027 + 0.894020i \(0.647873\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 110.000 1.56935 0.784674 0.619909i \(-0.212830\pi\)
0.784674 + 0.619909i \(0.212830\pi\)
\(18\) 0 0
\(19\) 116.000 1.40064 0.700322 0.713827i \(-0.253040\pi\)
0.700322 + 0.713827i \(0.253040\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 16.0000 0.145054 0.0725268 0.997366i \(-0.476894\pi\)
0.0725268 + 0.997366i \(0.476894\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −198.000 −1.26785 −0.633925 0.773394i \(-0.718557\pi\)
−0.633925 + 0.773394i \(0.718557\pi\)
\(30\) 0 0
\(31\) −240.000 −1.39049 −0.695246 0.718772i \(-0.744705\pi\)
−0.695246 + 0.718772i \(0.744705\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 80.0000 0.386356
\(36\) 0 0
\(37\) −258.000 −1.14635 −0.573175 0.819433i \(-0.694288\pi\)
−0.573175 + 0.819433i \(0.694288\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −442.000 −1.68363 −0.841815 0.539767i \(-0.818512\pi\)
−0.841815 + 0.539767i \(0.818512\pi\)
\(42\) 0 0
\(43\) 292.000 1.03557 0.517786 0.855510i \(-0.326756\pi\)
0.517786 + 0.855510i \(0.326756\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 392.000 1.21658 0.608288 0.793716i \(-0.291857\pi\)
0.608288 + 0.793716i \(0.291857\pi\)
\(48\) 0 0
\(49\) −87.0000 −0.253644
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −142.000 −0.368023 −0.184011 0.982924i \(-0.558908\pi\)
−0.184011 + 0.982924i \(0.558908\pi\)
\(54\) 0 0
\(55\) −180.000 −0.441294
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −348.000 −0.767894 −0.383947 0.923355i \(-0.625435\pi\)
−0.383947 + 0.923355i \(0.625435\pi\)
\(60\) 0 0
\(61\) −570.000 −1.19641 −0.598205 0.801343i \(-0.704119\pi\)
−0.598205 + 0.801343i \(0.704119\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 210.000 0.400728
\(66\) 0 0
\(67\) −692.000 −1.26181 −0.630905 0.775860i \(-0.717316\pi\)
−0.630905 + 0.775860i \(0.717316\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 168.000 0.280816 0.140408 0.990094i \(-0.455159\pi\)
0.140408 + 0.990094i \(0.455159\pi\)
\(72\) 0 0
\(73\) −134.000 −0.214843 −0.107421 0.994214i \(-0.534259\pi\)
−0.107421 + 0.994214i \(0.534259\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −576.000 −0.852484
\(78\) 0 0
\(79\) −784.000 −1.11654 −0.558271 0.829658i \(-0.688535\pi\)
−0.558271 + 0.829658i \(0.688535\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 564.000 0.745868 0.372934 0.927858i \(-0.378352\pi\)
0.372934 + 0.927858i \(0.378352\pi\)
\(84\) 0 0
\(85\) −550.000 −0.701834
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1034.00 −1.23150 −0.615752 0.787940i \(-0.711148\pi\)
−0.615752 + 0.787940i \(0.711148\pi\)
\(90\) 0 0
\(91\) 672.000 0.774118
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −580.000 −0.626387
\(96\) 0 0
\(97\) −382.000 −0.399858 −0.199929 0.979810i \(-0.564071\pi\)
−0.199929 + 0.979810i \(0.564071\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 674.000 0.664015 0.332007 0.943277i \(-0.392274\pi\)
0.332007 + 0.943277i \(0.392274\pi\)
\(102\) 0 0
\(103\) 992.000 0.948977 0.474489 0.880262i \(-0.342633\pi\)
0.474489 + 0.880262i \(0.342633\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −500.000 −0.451746 −0.225873 0.974157i \(-0.572523\pi\)
−0.225873 + 0.974157i \(0.572523\pi\)
\(108\) 0 0
\(109\) 1046.00 0.919162 0.459581 0.888136i \(-0.348000\pi\)
0.459581 + 0.888136i \(0.348000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 558.000 0.464533 0.232266 0.972652i \(-0.425386\pi\)
0.232266 + 0.972652i \(0.425386\pi\)
\(114\) 0 0
\(115\) −80.0000 −0.0648699
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1760.00 −1.35579
\(120\) 0 0
\(121\) −35.0000 −0.0262960
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 328.000 0.229176 0.114588 0.993413i \(-0.463445\pi\)
0.114588 + 0.993413i \(0.463445\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −212.000 −0.141393 −0.0706967 0.997498i \(-0.522522\pi\)
−0.0706967 + 0.997498i \(0.522522\pi\)
\(132\) 0 0
\(133\) −1856.00 −1.21004
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1434.00 −0.894269 −0.447135 0.894467i \(-0.647556\pi\)
−0.447135 + 0.894467i \(0.647556\pi\)
\(138\) 0 0
\(139\) −2196.00 −1.34002 −0.670008 0.742354i \(-0.733709\pi\)
−0.670008 + 0.742354i \(0.733709\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1512.00 −0.884194
\(144\) 0 0
\(145\) 990.000 0.567000
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2418.00 1.32946 0.664732 0.747081i \(-0.268546\pi\)
0.664732 + 0.747081i \(0.268546\pi\)
\(150\) 0 0
\(151\) −3672.00 −1.97896 −0.989481 0.144666i \(-0.953789\pi\)
−0.989481 + 0.144666i \(0.953789\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1200.00 0.621847
\(156\) 0 0
\(157\) 358.000 0.181984 0.0909921 0.995852i \(-0.470996\pi\)
0.0909921 + 0.995852i \(0.470996\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −256.000 −0.125314
\(162\) 0 0
\(163\) −2564.00 −1.23207 −0.616037 0.787717i \(-0.711263\pi\)
−0.616037 + 0.787717i \(0.711263\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3056.00 −1.41605 −0.708025 0.706187i \(-0.750414\pi\)
−0.708025 + 0.706187i \(0.750414\pi\)
\(168\) 0 0
\(169\) −433.000 −0.197087
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 234.000 0.102836 0.0514182 0.998677i \(-0.483626\pi\)
0.0514182 + 0.998677i \(0.483626\pi\)
\(174\) 0 0
\(175\) −400.000 −0.172784
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 524.000 0.218802 0.109401 0.993998i \(-0.465107\pi\)
0.109401 + 0.993998i \(0.465107\pi\)
\(180\) 0 0
\(181\) −1138.00 −0.467331 −0.233665 0.972317i \(-0.575072\pi\)
−0.233665 + 0.972317i \(0.575072\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1290.00 0.512663
\(186\) 0 0
\(187\) 3960.00 1.54858
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1520.00 0.575829 0.287915 0.957656i \(-0.407038\pi\)
0.287915 + 0.957656i \(0.407038\pi\)
\(192\) 0 0
\(193\) −2142.00 −0.798884 −0.399442 0.916759i \(-0.630796\pi\)
−0.399442 + 0.916759i \(0.630796\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2306.00 0.833988 0.416994 0.908909i \(-0.363084\pi\)
0.416994 + 0.908909i \(0.363084\pi\)
\(198\) 0 0
\(199\) −3288.00 −1.17126 −0.585628 0.810580i \(-0.699152\pi\)
−0.585628 + 0.810580i \(0.699152\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3168.00 1.09532
\(204\) 0 0
\(205\) 2210.00 0.752942
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4176.00 1.38211
\(210\) 0 0
\(211\) 3876.00 1.26462 0.632310 0.774715i \(-0.282107\pi\)
0.632310 + 0.774715i \(0.282107\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1460.00 −0.463122
\(216\) 0 0
\(217\) 3840.00 1.20127
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4620.00 −1.40622
\(222\) 0 0
\(223\) 5688.00 1.70806 0.854028 0.520226i \(-0.174152\pi\)
0.854028 + 0.520226i \(0.174152\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2796.00 −0.817520 −0.408760 0.912642i \(-0.634039\pi\)
−0.408760 + 0.912642i \(0.634039\pi\)
\(228\) 0 0
\(229\) 4446.00 1.28297 0.641485 0.767136i \(-0.278319\pi\)
0.641485 + 0.767136i \(0.278319\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2522.00 −0.709106 −0.354553 0.935036i \(-0.615367\pi\)
−0.354553 + 0.935036i \(0.615367\pi\)
\(234\) 0 0
\(235\) −1960.00 −0.544069
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 816.000 0.220848 0.110424 0.993885i \(-0.464779\pi\)
0.110424 + 0.993885i \(0.464779\pi\)
\(240\) 0 0
\(241\) −5422.00 −1.44922 −0.724609 0.689160i \(-0.757980\pi\)
−0.724609 + 0.689160i \(0.757980\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 435.000 0.113433
\(246\) 0 0
\(247\) −4872.00 −1.25505
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5900.00 −1.48368 −0.741842 0.670575i \(-0.766048\pi\)
−0.741842 + 0.670575i \(0.766048\pi\)
\(252\) 0 0
\(253\) 576.000 0.143134
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5250.00 −1.27426 −0.637132 0.770754i \(-0.719880\pi\)
−0.637132 + 0.770754i \(0.719880\pi\)
\(258\) 0 0
\(259\) 4128.00 0.990353
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6240.00 1.46302 0.731511 0.681829i \(-0.238815\pi\)
0.731511 + 0.681829i \(0.238815\pi\)
\(264\) 0 0
\(265\) 710.000 0.164585
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 714.000 0.161834 0.0809170 0.996721i \(-0.474215\pi\)
0.0809170 + 0.996721i \(0.474215\pi\)
\(270\) 0 0
\(271\) −2144.00 −0.480586 −0.240293 0.970700i \(-0.577243\pi\)
−0.240293 + 0.970700i \(0.577243\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 900.000 0.197353
\(276\) 0 0
\(277\) −4466.00 −0.968722 −0.484361 0.874868i \(-0.660948\pi\)
−0.484361 + 0.874868i \(0.660948\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5302.00 1.12559 0.562795 0.826596i \(-0.309726\pi\)
0.562795 + 0.826596i \(0.309726\pi\)
\(282\) 0 0
\(283\) 6932.00 1.45606 0.728029 0.685546i \(-0.240436\pi\)
0.728029 + 0.685546i \(0.240436\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 7072.00 1.45452
\(288\) 0 0
\(289\) 7187.00 1.46285
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4034.00 0.804330 0.402165 0.915567i \(-0.368258\pi\)
0.402165 + 0.915567i \(0.368258\pi\)
\(294\) 0 0
\(295\) 1740.00 0.343413
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −672.000 −0.129976
\(300\) 0 0
\(301\) −4672.00 −0.894650
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2850.00 0.535051
\(306\) 0 0
\(307\) 3836.00 0.713134 0.356567 0.934270i \(-0.383947\pi\)
0.356567 + 0.934270i \(0.383947\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 664.000 0.121067 0.0605337 0.998166i \(-0.480720\pi\)
0.0605337 + 0.998166i \(0.480720\pi\)
\(312\) 0 0
\(313\) 2986.00 0.539229 0.269615 0.962968i \(-0.413104\pi\)
0.269615 + 0.962968i \(0.413104\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2726.00 −0.482989 −0.241494 0.970402i \(-0.577638\pi\)
−0.241494 + 0.970402i \(0.577638\pi\)
\(318\) 0 0
\(319\) −7128.00 −1.25107
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 12760.0 2.19810
\(324\) 0 0
\(325\) −1050.00 −0.179211
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −6272.00 −1.05102
\(330\) 0 0
\(331\) 9212.00 1.52972 0.764860 0.644197i \(-0.222808\pi\)
0.764860 + 0.644197i \(0.222808\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3460.00 0.564298
\(336\) 0 0
\(337\) −3278.00 −0.529864 −0.264932 0.964267i \(-0.585349\pi\)
−0.264932 + 0.964267i \(0.585349\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −8640.00 −1.37209
\(342\) 0 0
\(343\) 6880.00 1.08305
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4956.00 0.766721 0.383360 0.923599i \(-0.374767\pi\)
0.383360 + 0.923599i \(0.374767\pi\)
\(348\) 0 0
\(349\) 4678.00 0.717500 0.358750 0.933434i \(-0.383203\pi\)
0.358750 + 0.933434i \(0.383203\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1890.00 −0.284970 −0.142485 0.989797i \(-0.545509\pi\)
−0.142485 + 0.989797i \(0.545509\pi\)
\(354\) 0 0
\(355\) −840.000 −0.125585
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6472.00 −0.951474 −0.475737 0.879588i \(-0.657819\pi\)
−0.475737 + 0.879588i \(0.657819\pi\)
\(360\) 0 0
\(361\) 6597.00 0.961802
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 670.000 0.0960806
\(366\) 0 0
\(367\) −1960.00 −0.278777 −0.139389 0.990238i \(-0.544514\pi\)
−0.139389 + 0.990238i \(0.544514\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2272.00 0.317942
\(372\) 0 0
\(373\) 8750.00 1.21463 0.607316 0.794460i \(-0.292246\pi\)
0.607316 + 0.794460i \(0.292246\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8316.00 1.13606
\(378\) 0 0
\(379\) 380.000 0.0515021 0.0257510 0.999668i \(-0.491802\pi\)
0.0257510 + 0.999668i \(0.491802\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −9688.00 −1.29252 −0.646258 0.763119i \(-0.723667\pi\)
−0.646258 + 0.763119i \(0.723667\pi\)
\(384\) 0 0
\(385\) 2880.00 0.381243
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3870.00 −0.504413 −0.252207 0.967673i \(-0.581156\pi\)
−0.252207 + 0.967673i \(0.581156\pi\)
\(390\) 0 0
\(391\) 1760.00 0.227639
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3920.00 0.499333
\(396\) 0 0
\(397\) 1622.00 0.205053 0.102526 0.994730i \(-0.467307\pi\)
0.102526 + 0.994730i \(0.467307\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9906.00 −1.23362 −0.616811 0.787112i \(-0.711576\pi\)
−0.616811 + 0.787112i \(0.711576\pi\)
\(402\) 0 0
\(403\) 10080.0 1.24596
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −9288.00 −1.13118
\(408\) 0 0
\(409\) −4214.00 −0.509459 −0.254730 0.967012i \(-0.581986\pi\)
−0.254730 + 0.967012i \(0.581986\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5568.00 0.663398
\(414\) 0 0
\(415\) −2820.00 −0.333562
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7012.00 −0.817562 −0.408781 0.912632i \(-0.634046\pi\)
−0.408781 + 0.912632i \(0.634046\pi\)
\(420\) 0 0
\(421\) −1602.00 −0.185455 −0.0927277 0.995692i \(-0.529559\pi\)
−0.0927277 + 0.995692i \(0.529559\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2750.00 0.313870
\(426\) 0 0
\(427\) 9120.00 1.03360
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −3584.00 −0.400546 −0.200273 0.979740i \(-0.564183\pi\)
−0.200273 + 0.979740i \(0.564183\pi\)
\(432\) 0 0
\(433\) −3470.00 −0.385121 −0.192561 0.981285i \(-0.561679\pi\)
−0.192561 + 0.981285i \(0.561679\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1856.00 0.203168
\(438\) 0 0
\(439\) 3416.00 0.371382 0.185691 0.982608i \(-0.440548\pi\)
0.185691 + 0.982608i \(0.440548\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9708.00 1.04118 0.520588 0.853808i \(-0.325713\pi\)
0.520588 + 0.853808i \(0.325713\pi\)
\(444\) 0 0
\(445\) 5170.00 0.550745
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 10366.0 1.08954 0.544768 0.838587i \(-0.316618\pi\)
0.544768 + 0.838587i \(0.316618\pi\)
\(450\) 0 0
\(451\) −15912.0 −1.66135
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3360.00 −0.346196
\(456\) 0 0
\(457\) −16742.0 −1.71369 −0.856847 0.515572i \(-0.827580\pi\)
−0.856847 + 0.515572i \(0.827580\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1258.00 0.127095 0.0635476 0.997979i \(-0.479759\pi\)
0.0635476 + 0.997979i \(0.479759\pi\)
\(462\) 0 0
\(463\) −13528.0 −1.35788 −0.678941 0.734193i \(-0.737561\pi\)
−0.678941 + 0.734193i \(0.737561\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6916.00 0.685298 0.342649 0.939463i \(-0.388676\pi\)
0.342649 + 0.939463i \(0.388676\pi\)
\(468\) 0 0
\(469\) 11072.0 1.09010
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 10512.0 1.02187
\(474\) 0 0
\(475\) 2900.00 0.280129
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1728.00 0.164832 0.0824158 0.996598i \(-0.473736\pi\)
0.0824158 + 0.996598i \(0.473736\pi\)
\(480\) 0 0
\(481\) 10836.0 1.02719
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1910.00 0.178822
\(486\) 0 0
\(487\) −16656.0 −1.54981 −0.774903 0.632080i \(-0.782201\pi\)
−0.774903 + 0.632080i \(0.782201\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1084.00 −0.0996339 −0.0498169 0.998758i \(-0.515864\pi\)
−0.0498169 + 0.998758i \(0.515864\pi\)
\(492\) 0 0
\(493\) −21780.0 −1.98970
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2688.00 −0.242602
\(498\) 0 0
\(499\) −5804.00 −0.520687 −0.260343 0.965516i \(-0.583836\pi\)
−0.260343 + 0.965516i \(0.583836\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 10512.0 0.931823 0.465911 0.884831i \(-0.345727\pi\)
0.465911 + 0.884831i \(0.345727\pi\)
\(504\) 0 0
\(505\) −3370.00 −0.296956
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4314.00 0.375667 0.187834 0.982201i \(-0.439853\pi\)
0.187834 + 0.982201i \(0.439853\pi\)
\(510\) 0 0
\(511\) 2144.00 0.185607
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4960.00 −0.424396
\(516\) 0 0
\(517\) 14112.0 1.20047
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1190.00 0.100067 0.0500334 0.998748i \(-0.484067\pi\)
0.0500334 + 0.998748i \(0.484067\pi\)
\(522\) 0 0
\(523\) 3780.00 0.316038 0.158019 0.987436i \(-0.449489\pi\)
0.158019 + 0.987436i \(0.449489\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −26400.0 −2.18217
\(528\) 0 0
\(529\) −11911.0 −0.978959
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 18564.0 1.50862
\(534\) 0 0
\(535\) 2500.00 0.202027
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3132.00 −0.250287
\(540\) 0 0
\(541\) −11002.0 −0.874331 −0.437165 0.899381i \(-0.644018\pi\)
−0.437165 + 0.899381i \(0.644018\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5230.00 −0.411062
\(546\) 0 0
\(547\) −5908.00 −0.461806 −0.230903 0.972977i \(-0.574168\pi\)
−0.230903 + 0.972977i \(0.574168\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −22968.0 −1.77581
\(552\) 0 0
\(553\) 12544.0 0.964602
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14806.0 −1.12630 −0.563151 0.826354i \(-0.690411\pi\)
−0.563151 + 0.826354i \(0.690411\pi\)
\(558\) 0 0
\(559\) −12264.0 −0.927928
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −684.000 −0.0512028 −0.0256014 0.999672i \(-0.508150\pi\)
−0.0256014 + 0.999672i \(0.508150\pi\)
\(564\) 0 0
\(565\) −2790.00 −0.207745
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2582.00 0.190234 0.0951169 0.995466i \(-0.469677\pi\)
0.0951169 + 0.995466i \(0.469677\pi\)
\(570\) 0 0
\(571\) 2540.00 0.186157 0.0930785 0.995659i \(-0.470329\pi\)
0.0930785 + 0.995659i \(0.470329\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 400.000 0.0290107
\(576\) 0 0
\(577\) 22786.0 1.64401 0.822005 0.569480i \(-0.192856\pi\)
0.822005 + 0.569480i \(0.192856\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −9024.00 −0.644369
\(582\) 0 0
\(583\) −5112.00 −0.363152
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7884.00 0.554357 0.277178 0.960818i \(-0.410601\pi\)
0.277178 + 0.960818i \(0.410601\pi\)
\(588\) 0 0
\(589\) −27840.0 −1.94758
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 21902.0 1.51671 0.758354 0.651843i \(-0.226004\pi\)
0.758354 + 0.651843i \(0.226004\pi\)
\(594\) 0 0
\(595\) 8800.00 0.606327
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 15080.0 1.02863 0.514317 0.857600i \(-0.328045\pi\)
0.514317 + 0.857600i \(0.328045\pi\)
\(600\) 0 0
\(601\) −19702.0 −1.33721 −0.668603 0.743619i \(-0.733108\pi\)
−0.668603 + 0.743619i \(0.733108\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 175.000 0.0117599
\(606\) 0 0
\(607\) −7320.00 −0.489472 −0.244736 0.969590i \(-0.578701\pi\)
−0.244736 + 0.969590i \(0.578701\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −16464.0 −1.09012
\(612\) 0 0
\(613\) 24350.0 1.60438 0.802192 0.597066i \(-0.203667\pi\)
0.802192 + 0.597066i \(0.203667\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −19546.0 −1.27535 −0.637676 0.770305i \(-0.720104\pi\)
−0.637676 + 0.770305i \(0.720104\pi\)
\(618\) 0 0
\(619\) −3476.00 −0.225706 −0.112853 0.993612i \(-0.535999\pi\)
−0.112853 + 0.993612i \(0.535999\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 16544.0 1.06392
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −28380.0 −1.79902
\(630\) 0 0
\(631\) −21880.0 −1.38039 −0.690197 0.723621i \(-0.742476\pi\)
−0.690197 + 0.723621i \(0.742476\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1640.00 −0.102490
\(636\) 0 0
\(637\) 3654.00 0.227279
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −20994.0 −1.29362 −0.646812 0.762649i \(-0.723898\pi\)
−0.646812 + 0.762649i \(0.723898\pi\)
\(642\) 0 0
\(643\) 18204.0 1.11648 0.558239 0.829680i \(-0.311477\pi\)
0.558239 + 0.829680i \(0.311477\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2064.00 −0.125416 −0.0627080 0.998032i \(-0.519974\pi\)
−0.0627080 + 0.998032i \(0.519974\pi\)
\(648\) 0 0
\(649\) −12528.0 −0.757730
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9942.00 −0.595805 −0.297902 0.954596i \(-0.596287\pi\)
−0.297902 + 0.954596i \(0.596287\pi\)
\(654\) 0 0
\(655\) 1060.00 0.0632330
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 24236.0 1.43263 0.716313 0.697779i \(-0.245828\pi\)
0.716313 + 0.697779i \(0.245828\pi\)
\(660\) 0 0
\(661\) 17614.0 1.03647 0.518234 0.855239i \(-0.326590\pi\)
0.518234 + 0.855239i \(0.326590\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 9280.00 0.541147
\(666\) 0 0
\(667\) −3168.00 −0.183906
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −20520.0 −1.18057
\(672\) 0 0
\(673\) 13058.0 0.747918 0.373959 0.927445i \(-0.378000\pi\)
0.373959 + 0.927445i \(0.378000\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 33186.0 1.88396 0.941980 0.335668i \(-0.108962\pi\)
0.941980 + 0.335668i \(0.108962\pi\)
\(678\) 0 0
\(679\) 6112.00 0.345445
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −31716.0 −1.77684 −0.888418 0.459035i \(-0.848195\pi\)
−0.888418 + 0.459035i \(0.848195\pi\)
\(684\) 0 0
\(685\) 7170.00 0.399929
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 5964.00 0.329768
\(690\) 0 0
\(691\) 2084.00 0.114731 0.0573655 0.998353i \(-0.481730\pi\)
0.0573655 + 0.998353i \(0.481730\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 10980.0 0.599274
\(696\) 0 0
\(697\) −48620.0 −2.64220
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 7418.00 0.399678 0.199839 0.979829i \(-0.435958\pi\)
0.199839 + 0.979829i \(0.435958\pi\)
\(702\) 0 0
\(703\) −29928.0 −1.60563
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10784.0 −0.573655
\(708\) 0 0
\(709\) −18242.0 −0.966280 −0.483140 0.875543i \(-0.660504\pi\)
−0.483140 + 0.875543i \(0.660504\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3840.00 −0.201696
\(714\) 0 0
\(715\) 7560.00 0.395424
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 3024.00 0.156851 0.0784257 0.996920i \(-0.475011\pi\)
0.0784257 + 0.996920i \(0.475011\pi\)
\(720\) 0 0
\(721\) −15872.0 −0.819839
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4950.00 −0.253570
\(726\) 0 0
\(727\) 26176.0 1.33537 0.667685 0.744444i \(-0.267285\pi\)
0.667685 + 0.744444i \(0.267285\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 32120.0 1.62517
\(732\) 0 0
\(733\) −17818.0 −0.897848 −0.448924 0.893570i \(-0.648193\pi\)
−0.448924 + 0.893570i \(0.648193\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −24912.0 −1.24511
\(738\) 0 0
\(739\) 22052.0 1.09769 0.548847 0.835923i \(-0.315067\pi\)
0.548847 + 0.835923i \(0.315067\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 15840.0 0.782117 0.391059 0.920366i \(-0.372109\pi\)
0.391059 + 0.920366i \(0.372109\pi\)
\(744\) 0 0
\(745\) −12090.0 −0.594555
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 8000.00 0.390272
\(750\) 0 0
\(751\) −21024.0 −1.02154 −0.510770 0.859717i \(-0.670640\pi\)
−0.510770 + 0.859717i \(0.670640\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 18360.0 0.885018
\(756\) 0 0
\(757\) −38034.0 −1.82612 −0.913058 0.407831i \(-0.866285\pi\)
−0.913058 + 0.407831i \(0.866285\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −37802.0 −1.80069 −0.900343 0.435182i \(-0.856684\pi\)
−0.900343 + 0.435182i \(0.856684\pi\)
\(762\) 0 0
\(763\) −16736.0 −0.794081
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 14616.0 0.688075
\(768\) 0 0
\(769\) 15042.0 0.705369 0.352684 0.935742i \(-0.385269\pi\)
0.352684 + 0.935742i \(0.385269\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −5950.00 −0.276852 −0.138426 0.990373i \(-0.544204\pi\)
−0.138426 + 0.990373i \(0.544204\pi\)
\(774\) 0 0
\(775\) −6000.00 −0.278099
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −51272.0 −2.35816
\(780\) 0 0
\(781\) 6048.00 0.277099
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1790.00 −0.0813858
\(786\) 0 0
\(787\) −23364.0 −1.05824 −0.529121 0.848546i \(-0.677478\pi\)
−0.529121 + 0.848546i \(0.677478\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −8928.00 −0.401319
\(792\) 0 0
\(793\) 23940.0 1.07205
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −19846.0 −0.882034 −0.441017 0.897499i \(-0.645382\pi\)
−0.441017 + 0.897499i \(0.645382\pi\)
\(798\) 0 0
\(799\) 43120.0 1.90923
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4824.00 −0.211999
\(804\) 0 0
\(805\) 1280.00 0.0560423
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −24762.0 −1.07613 −0.538063 0.842905i \(-0.680844\pi\)
−0.538063 + 0.842905i \(0.680844\pi\)
\(810\) 0 0
\(811\) −16644.0 −0.720653 −0.360327 0.932826i \(-0.617335\pi\)
−0.360327 + 0.932826i \(0.617335\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 12820.0 0.551000
\(816\) 0 0
\(817\) 33872.0 1.45047
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3182.00 −0.135265 −0.0676325 0.997710i \(-0.521545\pi\)
−0.0676325 + 0.997710i \(0.521545\pi\)
\(822\) 0 0
\(823\) 7504.00 0.317829 0.158914 0.987292i \(-0.449201\pi\)
0.158914 + 0.987292i \(0.449201\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 12604.0 0.529969 0.264984 0.964253i \(-0.414633\pi\)
0.264984 + 0.964253i \(0.414633\pi\)
\(828\) 0 0
\(829\) 12230.0 0.512383 0.256191 0.966626i \(-0.417532\pi\)
0.256191 + 0.966626i \(0.417532\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −9570.00 −0.398056
\(834\) 0 0
\(835\) 15280.0 0.633277
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 9656.00 0.397333 0.198666 0.980067i \(-0.436339\pi\)
0.198666 + 0.980067i \(0.436339\pi\)
\(840\) 0 0
\(841\) 14815.0 0.607446
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2165.00 0.0881400
\(846\) 0 0
\(847\) 560.000 0.0227176
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −4128.00 −0.166282
\(852\) 0 0
\(853\) 5806.00 0.233052 0.116526 0.993188i \(-0.462824\pi\)
0.116526 + 0.993188i \(0.462824\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 39094.0 1.55826 0.779128 0.626865i \(-0.215662\pi\)
0.779128 + 0.626865i \(0.215662\pi\)
\(858\) 0 0
\(859\) 18876.0 0.749756 0.374878 0.927074i \(-0.377685\pi\)
0.374878 + 0.927074i \(0.377685\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 32296.0 1.27389 0.636946 0.770909i \(-0.280197\pi\)
0.636946 + 0.770909i \(0.280197\pi\)
\(864\) 0 0
\(865\) −1170.00 −0.0459898
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −28224.0 −1.10176
\(870\) 0 0
\(871\) 29064.0 1.13065
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2000.00 0.0772712
\(876\) 0 0
\(877\) −9578.00 −0.368787 −0.184393 0.982853i \(-0.559032\pi\)
−0.184393 + 0.982853i \(0.559032\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 41710.0 1.59506 0.797529 0.603281i \(-0.206140\pi\)
0.797529 + 0.603281i \(0.206140\pi\)
\(882\) 0 0
\(883\) −2260.00 −0.0861326 −0.0430663 0.999072i \(-0.513713\pi\)
−0.0430663 + 0.999072i \(0.513713\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −33696.0 −1.27554 −0.637768 0.770228i \(-0.720142\pi\)
−0.637768 + 0.770228i \(0.720142\pi\)
\(888\) 0 0
\(889\) −5248.00 −0.197989
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 45472.0 1.70399
\(894\) 0 0
\(895\) −2620.00 −0.0978513
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 47520.0 1.76294
\(900\) 0 0
\(901\) −15620.0 −0.577556
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5690.00 0.208997
\(906\) 0 0
\(907\) −7756.00 −0.283940 −0.141970 0.989871i \(-0.545344\pi\)
−0.141970 + 0.989871i \(0.545344\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −5312.00 −0.193188 −0.0965941 0.995324i \(-0.530795\pi\)
−0.0965941 + 0.995324i \(0.530795\pi\)
\(912\) 0 0
\(913\) 20304.0 0.735996
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3392.00 0.122152
\(918\) 0 0
\(919\) 23576.0 0.846246 0.423123 0.906072i \(-0.360934\pi\)
0.423123 + 0.906072i \(0.360934\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −7056.00 −0.251626
\(924\) 0 0
\(925\) −6450.00 −0.229270
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 19038.0 0.672354 0.336177 0.941799i \(-0.390866\pi\)
0.336177 + 0.941799i \(0.390866\pi\)
\(930\) 0 0
\(931\) −10092.0 −0.355265
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −19800.0 −0.692545
\(936\) 0 0
\(937\) 20570.0 0.717175 0.358587 0.933496i \(-0.383259\pi\)
0.358587 + 0.933496i \(0.383259\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 21386.0 0.740875 0.370438 0.928857i \(-0.379208\pi\)
0.370438 + 0.928857i \(0.379208\pi\)
\(942\) 0 0
\(943\) −7072.00 −0.244216
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 38020.0 1.30463 0.652315 0.757948i \(-0.273798\pi\)
0.652315 + 0.757948i \(0.273798\pi\)
\(948\) 0 0
\(949\) 5628.00 0.192511
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −20202.0 −0.686681 −0.343340 0.939211i \(-0.611558\pi\)
−0.343340 + 0.939211i \(0.611558\pi\)
\(954\) 0 0
\(955\) −7600.00 −0.257519
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 22944.0 0.772576
\(960\) 0 0
\(961\) 27809.0 0.933470
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 10710.0 0.357272
\(966\) 0 0
\(967\) −29840.0 −0.992337 −0.496168 0.868226i \(-0.665260\pi\)
−0.496168 + 0.868226i \(0.665260\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −12476.0 −0.412332 −0.206166 0.978517i \(-0.566099\pi\)
−0.206166 + 0.978517i \(0.566099\pi\)
\(972\) 0 0
\(973\) 35136.0 1.15767
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 36974.0 1.21075 0.605375 0.795940i \(-0.293023\pi\)
0.605375 + 0.795940i \(0.293023\pi\)
\(978\) 0 0
\(979\) −37224.0 −1.21520
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −16368.0 −0.531087 −0.265543 0.964099i \(-0.585551\pi\)
−0.265543 + 0.964099i \(0.585551\pi\)
\(984\) 0 0
\(985\) −11530.0 −0.372971
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 4672.00 0.150213
\(990\) 0 0
\(991\) 49552.0 1.58837 0.794183 0.607678i \(-0.207899\pi\)
0.794183 + 0.607678i \(0.207899\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 16440.0 0.523802
\(996\) 0 0
\(997\) 24414.0 0.775526 0.387763 0.921759i \(-0.373248\pi\)
0.387763 + 0.921759i \(0.373248\pi\)
\(998\) 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.d.1.1 1
3.2 odd 2 80.4.a.b.1.1 1
4.3 odd 2 360.4.a.f.1.1 1
12.11 even 2 40.4.a.b.1.1 1
15.2 even 4 400.4.c.h.49.2 2
15.8 even 4 400.4.c.h.49.1 2
15.14 odd 2 400.4.a.p.1.1 1
20.3 even 4 1800.4.f.d.649.1 2
20.7 even 4 1800.4.f.d.649.2 2
20.19 odd 2 1800.4.a.h.1.1 1
24.5 odd 2 320.4.a.j.1.1 1
24.11 even 2 320.4.a.e.1.1 1
48.5 odd 4 1280.4.d.m.641.2 2
48.11 even 4 1280.4.d.d.641.1 2
48.29 odd 4 1280.4.d.m.641.1 2
48.35 even 4 1280.4.d.d.641.2 2
60.23 odd 4 200.4.c.f.49.2 2
60.47 odd 4 200.4.c.f.49.1 2
60.59 even 2 200.4.a.d.1.1 1
84.83 odd 2 1960.4.a.e.1.1 1
120.29 odd 2 1600.4.a.q.1.1 1
120.59 even 2 1600.4.a.bk.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.4.a.b.1.1 1 12.11 even 2
80.4.a.b.1.1 1 3.2 odd 2
200.4.a.d.1.1 1 60.59 even 2
200.4.c.f.49.1 2 60.47 odd 4
200.4.c.f.49.2 2 60.23 odd 4
320.4.a.e.1.1 1 24.11 even 2
320.4.a.j.1.1 1 24.5 odd 2
360.4.a.f.1.1 1 4.3 odd 2
400.4.a.p.1.1 1 15.14 odd 2
400.4.c.h.49.1 2 15.8 even 4
400.4.c.h.49.2 2 15.2 even 4
720.4.a.d.1.1 1 1.1 even 1 trivial
1280.4.d.d.641.1 2 48.11 even 4
1280.4.d.d.641.2 2 48.35 even 4
1280.4.d.m.641.1 2 48.29 odd 4
1280.4.d.m.641.2 2 48.5 odd 4
1600.4.a.q.1.1 1 120.29 odd 2
1600.4.a.bk.1.1 1 120.59 even 2
1800.4.a.h.1.1 1 20.19 odd 2
1800.4.f.d.649.1 2 20.3 even 4
1800.4.f.d.649.2 2 20.7 even 4
1960.4.a.e.1.1 1 84.83 odd 2