Properties

Label 80.6.a.b.1.1
Level $80$
Weight $6$
Character 80.1
Self dual yes
Analytic conductor $12.831$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 80.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(12.8307055850\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 20)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 80.1

$q$-expansion

\(f(q)\) \(=\) \(q-22.0000 q^{3} -25.0000 q^{5} -218.000 q^{7} +241.000 q^{9} +O(q^{10})\) \(q-22.0000 q^{3} -25.0000 q^{5} -218.000 q^{7} +241.000 q^{9} +480.000 q^{11} -622.000 q^{13} +550.000 q^{15} +186.000 q^{17} +1204.00 q^{19} +4796.00 q^{21} +3186.00 q^{23} +625.000 q^{25} +44.0000 q^{27} +5526.00 q^{29} -9356.00 q^{31} -10560.0 q^{33} +5450.00 q^{35} +5618.00 q^{37} +13684.0 q^{39} -14394.0 q^{41} +370.000 q^{43} -6025.00 q^{45} -16146.0 q^{47} +30717.0 q^{49} -4092.00 q^{51} -4374.00 q^{53} -12000.0 q^{55} -26488.0 q^{57} +11748.0 q^{59} +13202.0 q^{61} -52538.0 q^{63} +15550.0 q^{65} +11542.0 q^{67} -70092.0 q^{69} +29532.0 q^{71} +33698.0 q^{73} -13750.0 q^{75} -104640. q^{77} -31208.0 q^{79} -59531.0 q^{81} +38466.0 q^{83} -4650.00 q^{85} -121572. q^{87} +119514. q^{89} +135596. q^{91} +205832. q^{93} -30100.0 q^{95} +94658.0 q^{97} +115680. q^{99} +O(q^{100})\)

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
\(3\) −22.0000 −1.41130 −0.705650 0.708560i \(-0.749345\pi\)
−0.705650 + 0.708560i \(0.749345\pi\)
\(4\) 0 0
\(5\) −25.0000 −0.447214
\(6\) 0 0
\(7\) −218.000 −1.68156 −0.840778 0.541380i \(-0.817902\pi\)
−0.840778 + 0.541380i \(0.817902\pi\)
\(8\) 0 0
\(9\) 241.000 0.991770
\(10\) 0 0
\(11\) 480.000 1.19608 0.598039 0.801467i \(-0.295947\pi\)
0.598039 + 0.801467i \(0.295947\pi\)
\(12\) 0 0
\(13\) −622.000 −1.02078 −0.510390 0.859943i \(-0.670499\pi\)
−0.510390 + 0.859943i \(0.670499\pi\)
\(14\) 0 0
\(15\) 550.000 0.631153
\(16\) 0 0
\(17\) 186.000 0.156096 0.0780478 0.996950i \(-0.475131\pi\)
0.0780478 + 0.996950i \(0.475131\pi\)
\(18\) 0 0
\(19\) 1204.00 0.765143 0.382571 0.923926i \(-0.375039\pi\)
0.382571 + 0.923926i \(0.375039\pi\)
\(20\) 0 0
\(21\) 4796.00 2.37318
\(22\) 0 0
\(23\) 3186.00 1.25582 0.627908 0.778287i \(-0.283911\pi\)
0.627908 + 0.778287i \(0.283911\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 44.0000 0.0116156
\(28\) 0 0
\(29\) 5526.00 1.22016 0.610079 0.792341i \(-0.291138\pi\)
0.610079 + 0.792341i \(0.291138\pi\)
\(30\) 0 0
\(31\) −9356.00 −1.74858 −0.874291 0.485402i \(-0.838673\pi\)
−0.874291 + 0.485402i \(0.838673\pi\)
\(32\) 0 0
\(33\) −10560.0 −1.68803
\(34\) 0 0
\(35\) 5450.00 0.752015
\(36\) 0 0
\(37\) 5618.00 0.674648 0.337324 0.941389i \(-0.390478\pi\)
0.337324 + 0.941389i \(0.390478\pi\)
\(38\) 0 0
\(39\) 13684.0 1.44063
\(40\) 0 0
\(41\) −14394.0 −1.33728 −0.668639 0.743587i \(-0.733123\pi\)
−0.668639 + 0.743587i \(0.733123\pi\)
\(42\) 0 0
\(43\) 370.000 0.0305162 0.0152581 0.999884i \(-0.495143\pi\)
0.0152581 + 0.999884i \(0.495143\pi\)
\(44\) 0 0
\(45\) −6025.00 −0.443533
\(46\) 0 0
\(47\) −16146.0 −1.06615 −0.533077 0.846066i \(-0.678965\pi\)
−0.533077 + 0.846066i \(0.678965\pi\)
\(48\) 0 0
\(49\) 30717.0 1.82763
\(50\) 0 0
\(51\) −4092.00 −0.220298
\(52\) 0 0
\(53\) −4374.00 −0.213889 −0.106945 0.994265i \(-0.534107\pi\)
−0.106945 + 0.994265i \(0.534107\pi\)
\(54\) 0 0
\(55\) −12000.0 −0.534902
\(56\) 0 0
\(57\) −26488.0 −1.07985
\(58\) 0 0
\(59\) 11748.0 0.439374 0.219687 0.975570i \(-0.429496\pi\)
0.219687 + 0.975570i \(0.429496\pi\)
\(60\) 0 0
\(61\) 13202.0 0.454271 0.227136 0.973863i \(-0.427064\pi\)
0.227136 + 0.973863i \(0.427064\pi\)
\(62\) 0 0
\(63\) −52538.0 −1.66772
\(64\) 0 0
\(65\) 15550.0 0.456507
\(66\) 0 0
\(67\) 11542.0 0.314119 0.157059 0.987589i \(-0.449799\pi\)
0.157059 + 0.987589i \(0.449799\pi\)
\(68\) 0 0
\(69\) −70092.0 −1.77233
\(70\) 0 0
\(71\) 29532.0 0.695260 0.347630 0.937632i \(-0.386987\pi\)
0.347630 + 0.937632i \(0.386987\pi\)
\(72\) 0 0
\(73\) 33698.0 0.740111 0.370056 0.929010i \(-0.379339\pi\)
0.370056 + 0.929010i \(0.379339\pi\)
\(74\) 0 0
\(75\) −13750.0 −0.282260
\(76\) 0 0
\(77\) −104640. −2.01127
\(78\) 0 0
\(79\) −31208.0 −0.562598 −0.281299 0.959620i \(-0.590765\pi\)
−0.281299 + 0.959620i \(0.590765\pi\)
\(80\) 0 0
\(81\) −59531.0 −1.00816
\(82\) 0 0
\(83\) 38466.0 0.612889 0.306444 0.951889i \(-0.400861\pi\)
0.306444 + 0.951889i \(0.400861\pi\)
\(84\) 0 0
\(85\) −4650.00 −0.0698081
\(86\) 0 0
\(87\) −121572. −1.72201
\(88\) 0 0
\(89\) 119514. 1.59935 0.799675 0.600432i \(-0.205005\pi\)
0.799675 + 0.600432i \(0.205005\pi\)
\(90\) 0 0
\(91\) 135596. 1.71650
\(92\) 0 0
\(93\) 205832. 2.46777
\(94\) 0 0
\(95\) −30100.0 −0.342182
\(96\) 0 0
\(97\) 94658.0 1.02148 0.510738 0.859737i \(-0.329372\pi\)
0.510738 + 0.859737i \(0.329372\pi\)
\(98\) 0 0
\(99\) 115680. 1.18623
\(100\) 0 0
\(101\) 101046. 0.985634 0.492817 0.870133i \(-0.335967\pi\)
0.492817 + 0.870133i \(0.335967\pi\)
\(102\) 0 0
\(103\) 143434. 1.33217 0.666084 0.745877i \(-0.267969\pi\)
0.666084 + 0.745877i \(0.267969\pi\)
\(104\) 0 0
\(105\) −119900. −1.06132
\(106\) 0 0
\(107\) 57054.0 0.481755 0.240878 0.970555i \(-0.422565\pi\)
0.240878 + 0.970555i \(0.422565\pi\)
\(108\) 0 0
\(109\) −3118.00 −0.0251368 −0.0125684 0.999921i \(-0.504001\pi\)
−0.0125684 + 0.999921i \(0.504001\pi\)
\(110\) 0 0
\(111\) −123596. −0.952132
\(112\) 0 0
\(113\) −54534.0 −0.401764 −0.200882 0.979615i \(-0.564381\pi\)
−0.200882 + 0.979615i \(0.564381\pi\)
\(114\) 0 0
\(115\) −79650.0 −0.561618
\(116\) 0 0
\(117\) −149902. −1.01238
\(118\) 0 0
\(119\) −40548.0 −0.262484
\(120\) 0 0
\(121\) 69349.0 0.430603
\(122\) 0 0
\(123\) 316668. 1.88730
\(124\) 0 0
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) −24698.0 −0.135879 −0.0679395 0.997689i \(-0.521642\pi\)
−0.0679395 + 0.997689i \(0.521642\pi\)
\(128\) 0 0
\(129\) −8140.00 −0.0430675
\(130\) 0 0
\(131\) −236640. −1.20479 −0.602393 0.798200i \(-0.705786\pi\)
−0.602393 + 0.798200i \(0.705786\pi\)
\(132\) 0 0
\(133\) −262472. −1.28663
\(134\) 0 0
\(135\) −1100.00 −0.00519467
\(136\) 0 0
\(137\) −22158.0 −0.100862 −0.0504312 0.998728i \(-0.516060\pi\)
−0.0504312 + 0.998728i \(0.516060\pi\)
\(138\) 0 0
\(139\) 193204. 0.848163 0.424081 0.905624i \(-0.360597\pi\)
0.424081 + 0.905624i \(0.360597\pi\)
\(140\) 0 0
\(141\) 355212. 1.50467
\(142\) 0 0
\(143\) −298560. −1.22093
\(144\) 0 0
\(145\) −138150. −0.545671
\(146\) 0 0
\(147\) −675774. −2.57934
\(148\) 0 0
\(149\) 448554. 1.65519 0.827597 0.561322i \(-0.189707\pi\)
0.827597 + 0.561322i \(0.189707\pi\)
\(150\) 0 0
\(151\) 140860. 0.502742 0.251371 0.967891i \(-0.419119\pi\)
0.251371 + 0.967891i \(0.419119\pi\)
\(152\) 0 0
\(153\) 44826.0 0.154811
\(154\) 0 0
\(155\) 233900. 0.781990
\(156\) 0 0
\(157\) −335878. −1.08751 −0.543754 0.839245i \(-0.682998\pi\)
−0.543754 + 0.839245i \(0.682998\pi\)
\(158\) 0 0
\(159\) 96228.0 0.301862
\(160\) 0 0
\(161\) −694548. −2.11173
\(162\) 0 0
\(163\) 101650. 0.299667 0.149833 0.988711i \(-0.452126\pi\)
0.149833 + 0.988711i \(0.452126\pi\)
\(164\) 0 0
\(165\) 264000. 0.754908
\(166\) 0 0
\(167\) −139242. −0.386348 −0.193174 0.981164i \(-0.561878\pi\)
−0.193174 + 0.981164i \(0.561878\pi\)
\(168\) 0 0
\(169\) 15591.0 0.0419911
\(170\) 0 0
\(171\) 290164. 0.758845
\(172\) 0 0
\(173\) −265014. −0.673215 −0.336607 0.941645i \(-0.609279\pi\)
−0.336607 + 0.941645i \(0.609279\pi\)
\(174\) 0 0
\(175\) −136250. −0.336311
\(176\) 0 0
\(177\) −258456. −0.620088
\(178\) 0 0
\(179\) 142812. 0.333144 0.166572 0.986029i \(-0.446730\pi\)
0.166572 + 0.986029i \(0.446730\pi\)
\(180\) 0 0
\(181\) 109670. 0.248824 0.124412 0.992231i \(-0.460296\pi\)
0.124412 + 0.992231i \(0.460296\pi\)
\(182\) 0 0
\(183\) −290444. −0.641113
\(184\) 0 0
\(185\) −140450. −0.301712
\(186\) 0 0
\(187\) 89280.0 0.186703
\(188\) 0 0
\(189\) −9592.00 −0.0195324
\(190\) 0 0
\(191\) −294948. −0.585008 −0.292504 0.956264i \(-0.594489\pi\)
−0.292504 + 0.956264i \(0.594489\pi\)
\(192\) 0 0
\(193\) 1.00303e6 1.93831 0.969153 0.246459i \(-0.0792672\pi\)
0.969153 + 0.246459i \(0.0792672\pi\)
\(194\) 0 0
\(195\) −342100. −0.644268
\(196\) 0 0
\(197\) −823998. −1.51273 −0.756364 0.654151i \(-0.773026\pi\)
−0.756364 + 0.654151i \(0.773026\pi\)
\(198\) 0 0
\(199\) 906712. 1.62307 0.811534 0.584305i \(-0.198633\pi\)
0.811534 + 0.584305i \(0.198633\pi\)
\(200\) 0 0
\(201\) −253924. −0.443316
\(202\) 0 0
\(203\) −1.20467e6 −2.05176
\(204\) 0 0
\(205\) 359850. 0.598049
\(206\) 0 0
\(207\) 767826. 1.24548
\(208\) 0 0
\(209\) 577920. 0.915170
\(210\) 0 0
\(211\) −506384. −0.783022 −0.391511 0.920173i \(-0.628047\pi\)
−0.391511 + 0.920173i \(0.628047\pi\)
\(212\) 0 0
\(213\) −649704. −0.981220
\(214\) 0 0
\(215\) −9250.00 −0.0136473
\(216\) 0 0
\(217\) 2.03961e6 2.94034
\(218\) 0 0
\(219\) −741356. −1.04452
\(220\) 0 0
\(221\) −115692. −0.159339
\(222\) 0 0
\(223\) 542050. 0.729923 0.364962 0.931023i \(-0.381082\pi\)
0.364962 + 0.931023i \(0.381082\pi\)
\(224\) 0 0
\(225\) 150625. 0.198354
\(226\) 0 0
\(227\) 1.44857e6 1.86585 0.932924 0.360075i \(-0.117249\pi\)
0.932924 + 0.360075i \(0.117249\pi\)
\(228\) 0 0
\(229\) −478786. −0.603327 −0.301663 0.953414i \(-0.597542\pi\)
−0.301663 + 0.953414i \(0.597542\pi\)
\(230\) 0 0
\(231\) 2.30208e6 2.83851
\(232\) 0 0
\(233\) 374106. 0.451445 0.225723 0.974192i \(-0.427526\pi\)
0.225723 + 0.974192i \(0.427526\pi\)
\(234\) 0 0
\(235\) 403650. 0.476799
\(236\) 0 0
\(237\) 686576. 0.793995
\(238\) 0 0
\(239\) −169416. −0.191849 −0.0959245 0.995389i \(-0.530581\pi\)
−0.0959245 + 0.995389i \(0.530581\pi\)
\(240\) 0 0
\(241\) −353746. −0.392328 −0.196164 0.980571i \(-0.562848\pi\)
−0.196164 + 0.980571i \(0.562848\pi\)
\(242\) 0 0
\(243\) 1.29899e6 1.41121
\(244\) 0 0
\(245\) −767925. −0.817342
\(246\) 0 0
\(247\) −748888. −0.781042
\(248\) 0 0
\(249\) −846252. −0.864971
\(250\) 0 0
\(251\) −1.25520e6 −1.25756 −0.628780 0.777583i \(-0.716445\pi\)
−0.628780 + 0.777583i \(0.716445\pi\)
\(252\) 0 0
\(253\) 1.52928e6 1.50205
\(254\) 0 0
\(255\) 102300. 0.0985202
\(256\) 0 0
\(257\) −1.12877e6 −1.06604 −0.533021 0.846102i \(-0.678943\pi\)
−0.533021 + 0.846102i \(0.678943\pi\)
\(258\) 0 0
\(259\) −1.22472e6 −1.13446
\(260\) 0 0
\(261\) 1.33177e6 1.21012
\(262\) 0 0
\(263\) 263082. 0.234532 0.117266 0.993101i \(-0.462587\pi\)
0.117266 + 0.993101i \(0.462587\pi\)
\(264\) 0 0
\(265\) 109350. 0.0956542
\(266\) 0 0
\(267\) −2.62931e6 −2.25717
\(268\) 0 0
\(269\) −1.18774e6 −1.00079 −0.500393 0.865798i \(-0.666811\pi\)
−0.500393 + 0.865798i \(0.666811\pi\)
\(270\) 0 0
\(271\) −431300. −0.356744 −0.178372 0.983963i \(-0.557083\pi\)
−0.178372 + 0.983963i \(0.557083\pi\)
\(272\) 0 0
\(273\) −2.98311e6 −2.42250
\(274\) 0 0
\(275\) 300000. 0.239216
\(276\) 0 0
\(277\) 743114. 0.581910 0.290955 0.956737i \(-0.406027\pi\)
0.290955 + 0.956737i \(0.406027\pi\)
\(278\) 0 0
\(279\) −2.25480e6 −1.73419
\(280\) 0 0
\(281\) 1.92193e6 1.45201 0.726007 0.687687i \(-0.241374\pi\)
0.726007 + 0.687687i \(0.241374\pi\)
\(282\) 0 0
\(283\) 1.63071e6 1.21035 0.605176 0.796092i \(-0.293103\pi\)
0.605176 + 0.796092i \(0.293103\pi\)
\(284\) 0 0
\(285\) 662200. 0.482922
\(286\) 0 0
\(287\) 3.13789e6 2.24871
\(288\) 0 0
\(289\) −1.38526e6 −0.975634
\(290\) 0 0
\(291\) −2.08248e6 −1.44161
\(292\) 0 0
\(293\) 71250.0 0.0484859 0.0242430 0.999706i \(-0.492282\pi\)
0.0242430 + 0.999706i \(0.492282\pi\)
\(294\) 0 0
\(295\) −293700. −0.196494
\(296\) 0 0
\(297\) 21120.0 0.0138932
\(298\) 0 0
\(299\) −1.98169e6 −1.28191
\(300\) 0 0
\(301\) −80660.0 −0.0513147
\(302\) 0 0
\(303\) −2.22301e6 −1.39103
\(304\) 0 0
\(305\) −330050. −0.203156
\(306\) 0 0
\(307\) 1.61762e6 0.979560 0.489780 0.871846i \(-0.337077\pi\)
0.489780 + 0.871846i \(0.337077\pi\)
\(308\) 0 0
\(309\) −3.15555e6 −1.88009
\(310\) 0 0
\(311\) 682788. 0.400299 0.200150 0.979765i \(-0.435857\pi\)
0.200150 + 0.979765i \(0.435857\pi\)
\(312\) 0 0
\(313\) −2.70444e6 −1.56033 −0.780165 0.625574i \(-0.784865\pi\)
−0.780165 + 0.625574i \(0.784865\pi\)
\(314\) 0 0
\(315\) 1.31345e6 0.745825
\(316\) 0 0
\(317\) 2.60347e6 1.45514 0.727568 0.686035i \(-0.240650\pi\)
0.727568 + 0.686035i \(0.240650\pi\)
\(318\) 0 0
\(319\) 2.65248e6 1.45940
\(320\) 0 0
\(321\) −1.25519e6 −0.679902
\(322\) 0 0
\(323\) 223944. 0.119435
\(324\) 0 0
\(325\) −388750. −0.204156
\(326\) 0 0
\(327\) 68596.0 0.0354756
\(328\) 0 0
\(329\) 3.51983e6 1.79280
\(330\) 0 0
\(331\) 661432. 0.331830 0.165915 0.986140i \(-0.446942\pi\)
0.165915 + 0.986140i \(0.446942\pi\)
\(332\) 0 0
\(333\) 1.35394e6 0.669096
\(334\) 0 0
\(335\) −288550. −0.140478
\(336\) 0 0
\(337\) 1.71706e6 0.823588 0.411794 0.911277i \(-0.364902\pi\)
0.411794 + 0.911277i \(0.364902\pi\)
\(338\) 0 0
\(339\) 1.19975e6 0.567010
\(340\) 0 0
\(341\) −4.49088e6 −2.09144
\(342\) 0 0
\(343\) −3.03238e6 −1.39171
\(344\) 0 0
\(345\) 1.75230e6 0.792612
\(346\) 0 0
\(347\) −131370. −0.0585696 −0.0292848 0.999571i \(-0.509323\pi\)
−0.0292848 + 0.999571i \(0.509323\pi\)
\(348\) 0 0
\(349\) 3.50951e6 1.54235 0.771175 0.636623i \(-0.219669\pi\)
0.771175 + 0.636623i \(0.219669\pi\)
\(350\) 0 0
\(351\) −27368.0 −0.0118570
\(352\) 0 0
\(353\) 2.21992e6 0.948202 0.474101 0.880470i \(-0.342773\pi\)
0.474101 + 0.880470i \(0.342773\pi\)
\(354\) 0 0
\(355\) −738300. −0.310930
\(356\) 0 0
\(357\) 892056. 0.370443
\(358\) 0 0
\(359\) −4.39730e6 −1.80074 −0.900369 0.435128i \(-0.856703\pi\)
−0.900369 + 0.435128i \(0.856703\pi\)
\(360\) 0 0
\(361\) −1.02648e6 −0.414557
\(362\) 0 0
\(363\) −1.52568e6 −0.607710
\(364\) 0 0
\(365\) −842450. −0.330988
\(366\) 0 0
\(367\) 2.29824e6 0.890697 0.445348 0.895357i \(-0.353080\pi\)
0.445348 + 0.895357i \(0.353080\pi\)
\(368\) 0 0
\(369\) −3.46895e6 −1.32627
\(370\) 0 0
\(371\) 953532. 0.359667
\(372\) 0 0
\(373\) −1.73561e6 −0.645920 −0.322960 0.946413i \(-0.604678\pi\)
−0.322960 + 0.946413i \(0.604678\pi\)
\(374\) 0 0
\(375\) 343750. 0.126231
\(376\) 0 0
\(377\) −3.43717e6 −1.24551
\(378\) 0 0
\(379\) 5.39115e6 1.92789 0.963947 0.266094i \(-0.0857331\pi\)
0.963947 + 0.266094i \(0.0857331\pi\)
\(380\) 0 0
\(381\) 543356. 0.191766
\(382\) 0 0
\(383\) −3.27281e6 −1.14005 −0.570026 0.821627i \(-0.693067\pi\)
−0.570026 + 0.821627i \(0.693067\pi\)
\(384\) 0 0
\(385\) 2.61600e6 0.899468
\(386\) 0 0
\(387\) 89170.0 0.0302650
\(388\) 0 0
\(389\) 603114. 0.202081 0.101040 0.994882i \(-0.467783\pi\)
0.101040 + 0.994882i \(0.467783\pi\)
\(390\) 0 0
\(391\) 592596. 0.196027
\(392\) 0 0
\(393\) 5.20608e6 1.70032
\(394\) 0 0
\(395\) 780200. 0.251601
\(396\) 0 0
\(397\) −749422. −0.238644 −0.119322 0.992856i \(-0.538072\pi\)
−0.119322 + 0.992856i \(0.538072\pi\)
\(398\) 0 0
\(399\) 5.77438e6 1.81582
\(400\) 0 0
\(401\) 5.31357e6 1.65016 0.825079 0.565018i \(-0.191131\pi\)
0.825079 + 0.565018i \(0.191131\pi\)
\(402\) 0 0
\(403\) 5.81943e6 1.78492
\(404\) 0 0
\(405\) 1.48827e6 0.450864
\(406\) 0 0
\(407\) 2.69664e6 0.806932
\(408\) 0 0
\(409\) 999326. 0.295392 0.147696 0.989033i \(-0.452814\pi\)
0.147696 + 0.989033i \(0.452814\pi\)
\(410\) 0 0
\(411\) 487476. 0.142347
\(412\) 0 0
\(413\) −2.56106e6 −0.738831
\(414\) 0 0
\(415\) −961650. −0.274092
\(416\) 0 0
\(417\) −4.25049e6 −1.19701
\(418\) 0 0
\(419\) −2.03740e6 −0.566944 −0.283472 0.958980i \(-0.591486\pi\)
−0.283472 + 0.958980i \(0.591486\pi\)
\(420\) 0 0
\(421\) −5.11461e6 −1.40640 −0.703198 0.710994i \(-0.748245\pi\)
−0.703198 + 0.710994i \(0.748245\pi\)
\(422\) 0 0
\(423\) −3.89119e6 −1.05738
\(424\) 0 0
\(425\) 116250. 0.0312191
\(426\) 0 0
\(427\) −2.87804e6 −0.763882
\(428\) 0 0
\(429\) 6.56832e6 1.72310
\(430\) 0 0
\(431\) 3.30404e6 0.856747 0.428374 0.903602i \(-0.359087\pi\)
0.428374 + 0.903602i \(0.359087\pi\)
\(432\) 0 0
\(433\) −2.01638e6 −0.516836 −0.258418 0.966033i \(-0.583201\pi\)
−0.258418 + 0.966033i \(0.583201\pi\)
\(434\) 0 0
\(435\) 3.03930e6 0.770106
\(436\) 0 0
\(437\) 3.83594e6 0.960879
\(438\) 0 0
\(439\) −6.58321e6 −1.63033 −0.815166 0.579227i \(-0.803355\pi\)
−0.815166 + 0.579227i \(0.803355\pi\)
\(440\) 0 0
\(441\) 7.40280e6 1.81259
\(442\) 0 0
\(443\) 4.81783e6 1.16638 0.583192 0.812334i \(-0.301803\pi\)
0.583192 + 0.812334i \(0.301803\pi\)
\(444\) 0 0
\(445\) −2.98785e6 −0.715251
\(446\) 0 0
\(447\) −9.86819e6 −2.33598
\(448\) 0 0
\(449\) −6.20399e6 −1.45230 −0.726149 0.687538i \(-0.758692\pi\)
−0.726149 + 0.687538i \(0.758692\pi\)
\(450\) 0 0
\(451\) −6.90912e6 −1.59949
\(452\) 0 0
\(453\) −3.09892e6 −0.709520
\(454\) 0 0
\(455\) −3.38990e6 −0.767641
\(456\) 0 0
\(457\) 2.84383e6 0.636962 0.318481 0.947929i \(-0.396827\pi\)
0.318481 + 0.947929i \(0.396827\pi\)
\(458\) 0 0
\(459\) 8184.00 0.00181315
\(460\) 0 0
\(461\) −1.75605e6 −0.384844 −0.192422 0.981312i \(-0.561634\pi\)
−0.192422 + 0.981312i \(0.561634\pi\)
\(462\) 0 0
\(463\) −7.66857e6 −1.66250 −0.831250 0.555899i \(-0.812374\pi\)
−0.831250 + 0.555899i \(0.812374\pi\)
\(464\) 0 0
\(465\) −5.14580e6 −1.10362
\(466\) 0 0
\(467\) 1.35903e6 0.288361 0.144181 0.989551i \(-0.453945\pi\)
0.144181 + 0.989551i \(0.453945\pi\)
\(468\) 0 0
\(469\) −2.51616e6 −0.528209
\(470\) 0 0
\(471\) 7.38932e6 1.53480
\(472\) 0 0
\(473\) 177600. 0.0364998
\(474\) 0 0
\(475\) 752500. 0.153029
\(476\) 0 0
\(477\) −1.05413e6 −0.212129
\(478\) 0 0
\(479\) 2.02706e6 0.403672 0.201836 0.979419i \(-0.435309\pi\)
0.201836 + 0.979419i \(0.435309\pi\)
\(480\) 0 0
\(481\) −3.49440e6 −0.688667
\(482\) 0 0
\(483\) 1.52801e7 2.98028
\(484\) 0 0
\(485\) −2.36645e6 −0.456818
\(486\) 0 0
\(487\) −2.46427e6 −0.470833 −0.235416 0.971895i \(-0.575645\pi\)
−0.235416 + 0.971895i \(0.575645\pi\)
\(488\) 0 0
\(489\) −2.23630e6 −0.422920
\(490\) 0 0
\(491\) −1.03848e7 −1.94399 −0.971996 0.234998i \(-0.924492\pi\)
−0.971996 + 0.234998i \(0.924492\pi\)
\(492\) 0 0
\(493\) 1.02784e6 0.190461
\(494\) 0 0
\(495\) −2.89200e6 −0.530500
\(496\) 0 0
\(497\) −6.43798e6 −1.16912
\(498\) 0 0
\(499\) −6.49416e6 −1.16754 −0.583769 0.811919i \(-0.698423\pi\)
−0.583769 + 0.811919i \(0.698423\pi\)
\(500\) 0 0
\(501\) 3.06332e6 0.545254
\(502\) 0 0
\(503\) 1.03565e7 1.82513 0.912565 0.408931i \(-0.134098\pi\)
0.912565 + 0.408931i \(0.134098\pi\)
\(504\) 0 0
\(505\) −2.52615e6 −0.440789
\(506\) 0 0
\(507\) −343002. −0.0592621
\(508\) 0 0
\(509\) 5.87305e6 1.00478 0.502388 0.864643i \(-0.332455\pi\)
0.502388 + 0.864643i \(0.332455\pi\)
\(510\) 0 0
\(511\) −7.34616e6 −1.24454
\(512\) 0 0
\(513\) 52976.0 0.00888763
\(514\) 0 0
\(515\) −3.58585e6 −0.595764
\(516\) 0 0
\(517\) −7.75008e6 −1.27520
\(518\) 0 0
\(519\) 5.83031e6 0.950108
\(520\) 0 0
\(521\) 2.17295e6 0.350717 0.175358 0.984505i \(-0.443892\pi\)
0.175358 + 0.984505i \(0.443892\pi\)
\(522\) 0 0
\(523\) −1.07361e6 −0.171629 −0.0858145 0.996311i \(-0.527349\pi\)
−0.0858145 + 0.996311i \(0.527349\pi\)
\(524\) 0 0
\(525\) 2.99750e6 0.474636
\(526\) 0 0
\(527\) −1.74022e6 −0.272946
\(528\) 0 0
\(529\) 3.71425e6 0.577075
\(530\) 0 0
\(531\) 2.83127e6 0.435757
\(532\) 0 0
\(533\) 8.95307e6 1.36507
\(534\) 0 0
\(535\) −1.42635e6 −0.215448
\(536\) 0 0
\(537\) −3.14186e6 −0.470166
\(538\) 0 0
\(539\) 1.47442e7 2.18599
\(540\) 0 0
\(541\) 7.09033e6 1.04153 0.520767 0.853699i \(-0.325646\pi\)
0.520767 + 0.853699i \(0.325646\pi\)
\(542\) 0 0
\(543\) −2.41274e6 −0.351165
\(544\) 0 0
\(545\) 77950.0 0.0112415
\(546\) 0 0
\(547\) −6.69763e6 −0.957091 −0.478545 0.878063i \(-0.658836\pi\)
−0.478545 + 0.878063i \(0.658836\pi\)
\(548\) 0 0
\(549\) 3.18168e6 0.450532
\(550\) 0 0
\(551\) 6.65330e6 0.933595
\(552\) 0 0
\(553\) 6.80334e6 0.946040
\(554\) 0 0
\(555\) 3.08990e6 0.425806
\(556\) 0 0
\(557\) 1.19008e7 1.62532 0.812662 0.582735i \(-0.198018\pi\)
0.812662 + 0.582735i \(0.198018\pi\)
\(558\) 0 0
\(559\) −230140. −0.0311503
\(560\) 0 0
\(561\) −1.96416e6 −0.263493
\(562\) 0 0
\(563\) −8.75636e6 −1.16427 −0.582133 0.813093i \(-0.697782\pi\)
−0.582133 + 0.813093i \(0.697782\pi\)
\(564\) 0 0
\(565\) 1.36335e6 0.179674
\(566\) 0 0
\(567\) 1.29778e7 1.69528
\(568\) 0 0
\(569\) −1.15677e6 −0.149784 −0.0748922 0.997192i \(-0.523861\pi\)
−0.0748922 + 0.997192i \(0.523861\pi\)
\(570\) 0 0
\(571\) 7.07807e6 0.908500 0.454250 0.890874i \(-0.349907\pi\)
0.454250 + 0.890874i \(0.349907\pi\)
\(572\) 0 0
\(573\) 6.48886e6 0.825623
\(574\) 0 0
\(575\) 1.99125e6 0.251163
\(576\) 0 0
\(577\) −3.13404e6 −0.391890 −0.195945 0.980615i \(-0.562777\pi\)
−0.195945 + 0.980615i \(0.562777\pi\)
\(578\) 0 0
\(579\) −2.20667e7 −2.73553
\(580\) 0 0
\(581\) −8.38559e6 −1.03061
\(582\) 0 0
\(583\) −2.09952e6 −0.255828
\(584\) 0 0
\(585\) 3.74755e6 0.452749
\(586\) 0 0
\(587\) −1.13833e7 −1.36355 −0.681776 0.731561i \(-0.738792\pi\)
−0.681776 + 0.731561i \(0.738792\pi\)
\(588\) 0 0
\(589\) −1.12646e7 −1.33791
\(590\) 0 0
\(591\) 1.81280e7 2.13491
\(592\) 0 0
\(593\) −1.58655e7 −1.85275 −0.926376 0.376599i \(-0.877094\pi\)
−0.926376 + 0.376599i \(0.877094\pi\)
\(594\) 0 0
\(595\) 1.01370e6 0.117386
\(596\) 0 0
\(597\) −1.99477e7 −2.29064
\(598\) 0 0
\(599\) 1.50998e7 1.71951 0.859756 0.510705i \(-0.170615\pi\)
0.859756 + 0.510705i \(0.170615\pi\)
\(600\) 0 0
\(601\) −8.08705e6 −0.913280 −0.456640 0.889652i \(-0.650947\pi\)
−0.456640 + 0.889652i \(0.650947\pi\)
\(602\) 0 0
\(603\) 2.78162e6 0.311534
\(604\) 0 0
\(605\) −1.73373e6 −0.192571
\(606\) 0 0
\(607\) 710398. 0.0782582 0.0391291 0.999234i \(-0.487542\pi\)
0.0391291 + 0.999234i \(0.487542\pi\)
\(608\) 0 0
\(609\) 2.65027e7 2.89566
\(610\) 0 0
\(611\) 1.00428e7 1.08831
\(612\) 0 0
\(613\) 5.96434e6 0.641078 0.320539 0.947235i \(-0.396136\pi\)
0.320539 + 0.947235i \(0.396136\pi\)
\(614\) 0 0
\(615\) −7.91670e6 −0.844027
\(616\) 0 0
\(617\) 1.48432e7 1.56970 0.784848 0.619689i \(-0.212741\pi\)
0.784848 + 0.619689i \(0.212741\pi\)
\(618\) 0 0
\(619\) 1.82042e7 1.90961 0.954807 0.297227i \(-0.0960620\pi\)
0.954807 + 0.297227i \(0.0960620\pi\)
\(620\) 0 0
\(621\) 140184. 0.0145871
\(622\) 0 0
\(623\) −2.60541e7 −2.68940
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) −1.27142e7 −1.29158
\(628\) 0 0
\(629\) 1.04495e6 0.105310
\(630\) 0 0
\(631\) −1.09461e6 −0.109443 −0.0547214 0.998502i \(-0.517427\pi\)
−0.0547214 + 0.998502i \(0.517427\pi\)
\(632\) 0 0
\(633\) 1.11404e7 1.10508
\(634\) 0 0
\(635\) 617450. 0.0607670
\(636\) 0 0
\(637\) −1.91060e7 −1.86561
\(638\) 0 0
\(639\) 7.11721e6 0.689537
\(640\) 0 0
\(641\) 7.44046e6 0.715245 0.357622 0.933866i \(-0.383587\pi\)
0.357622 + 0.933866i \(0.383587\pi\)
\(642\) 0 0
\(643\) 1.07915e7 1.02933 0.514665 0.857391i \(-0.327916\pi\)
0.514665 + 0.857391i \(0.327916\pi\)
\(644\) 0 0
\(645\) 203500. 0.0192604
\(646\) 0 0
\(647\) 9.62998e6 0.904409 0.452204 0.891914i \(-0.350638\pi\)
0.452204 + 0.891914i \(0.350638\pi\)
\(648\) 0 0
\(649\) 5.63904e6 0.525525
\(650\) 0 0
\(651\) −4.48714e7 −4.14970
\(652\) 0 0
\(653\) −1.00019e7 −0.917905 −0.458953 0.888461i \(-0.651775\pi\)
−0.458953 + 0.888461i \(0.651775\pi\)
\(654\) 0 0
\(655\) 5.91600e6 0.538797
\(656\) 0 0
\(657\) 8.12122e6 0.734020
\(658\) 0 0
\(659\) 4.01060e6 0.359746 0.179873 0.983690i \(-0.442431\pi\)
0.179873 + 0.983690i \(0.442431\pi\)
\(660\) 0 0
\(661\) 1.20338e7 1.07127 0.535636 0.844449i \(-0.320072\pi\)
0.535636 + 0.844449i \(0.320072\pi\)
\(662\) 0 0
\(663\) 2.54522e6 0.224876
\(664\) 0 0
\(665\) 6.56180e6 0.575399
\(666\) 0 0
\(667\) 1.76058e7 1.53229
\(668\) 0 0
\(669\) −1.19251e7 −1.03014
\(670\) 0 0
\(671\) 6.33696e6 0.543344
\(672\) 0 0
\(673\) 2.01231e6 0.171260 0.0856301 0.996327i \(-0.472710\pi\)
0.0856301 + 0.996327i \(0.472710\pi\)
\(674\) 0 0
\(675\) 27500.0 0.00232313
\(676\) 0 0
\(677\) 1.62410e7 1.36188 0.680942 0.732337i \(-0.261571\pi\)
0.680942 + 0.732337i \(0.261571\pi\)
\(678\) 0 0
\(679\) −2.06354e7 −1.71767
\(680\) 0 0
\(681\) −3.18686e7 −2.63327
\(682\) 0 0
\(683\) −4.62910e6 −0.379704 −0.189852 0.981813i \(-0.560801\pi\)
−0.189852 + 0.981813i \(0.560801\pi\)
\(684\) 0 0
\(685\) 553950. 0.0451070
\(686\) 0 0
\(687\) 1.05333e7 0.851476
\(688\) 0 0
\(689\) 2.72063e6 0.218334
\(690\) 0 0
\(691\) −1.16794e7 −0.930517 −0.465258 0.885175i \(-0.654039\pi\)
−0.465258 + 0.885175i \(0.654039\pi\)
\(692\) 0 0
\(693\) −2.52182e7 −1.99472
\(694\) 0 0
\(695\) −4.83010e6 −0.379310
\(696\) 0 0
\(697\) −2.67728e6 −0.208743
\(698\) 0 0
\(699\) −8.23033e6 −0.637125
\(700\) 0 0
\(701\) 1.99543e7 1.53370 0.766851 0.641825i \(-0.221822\pi\)
0.766851 + 0.641825i \(0.221822\pi\)
\(702\) 0 0
\(703\) 6.76407e6 0.516202
\(704\) 0 0
\(705\) −8.88030e6 −0.672907
\(706\) 0 0
\(707\) −2.20280e7 −1.65740
\(708\) 0 0
\(709\) −4.88331e6 −0.364837 −0.182419 0.983221i \(-0.558393\pi\)
−0.182419 + 0.983221i \(0.558393\pi\)
\(710\) 0 0
\(711\) −7.52113e6 −0.557968
\(712\) 0 0
\(713\) −2.98082e7 −2.19590
\(714\) 0 0
\(715\) 7.46400e6 0.546017
\(716\) 0 0
\(717\) 3.72715e6 0.270757
\(718\) 0 0
\(719\) 1.35778e7 0.979505 0.489753 0.871861i \(-0.337087\pi\)
0.489753 + 0.871861i \(0.337087\pi\)
\(720\) 0 0
\(721\) −3.12686e7 −2.24012
\(722\) 0 0
\(723\) 7.78241e6 0.553692
\(724\) 0 0
\(725\) 3.45375e6 0.244031
\(726\) 0 0
\(727\) −6.42411e6 −0.450792 −0.225396 0.974267i \(-0.572368\pi\)
−0.225396 + 0.974267i \(0.572368\pi\)
\(728\) 0 0
\(729\) −1.41117e7 −0.983472
\(730\) 0 0
\(731\) 68820.0 0.00476345
\(732\) 0 0
\(733\) 9.08556e6 0.624585 0.312293 0.949986i \(-0.398903\pi\)
0.312293 + 0.949986i \(0.398903\pi\)
\(734\) 0 0
\(735\) 1.68944e7 1.15351
\(736\) 0 0
\(737\) 5.54016e6 0.375711
\(738\) 0 0
\(739\) −2.02457e7 −1.36371 −0.681854 0.731488i \(-0.738826\pi\)
−0.681854 + 0.731488i \(0.738826\pi\)
\(740\) 0 0
\(741\) 1.64755e7 1.10229
\(742\) 0 0
\(743\) 5.44831e6 0.362067 0.181034 0.983477i \(-0.442056\pi\)
0.181034 + 0.983477i \(0.442056\pi\)
\(744\) 0 0
\(745\) −1.12138e7 −0.740226
\(746\) 0 0
\(747\) 9.27031e6 0.607845
\(748\) 0 0
\(749\) −1.24378e7 −0.810099
\(750\) 0 0
\(751\) 1.14072e6 0.0738041 0.0369021 0.999319i \(-0.488251\pi\)
0.0369021 + 0.999319i \(0.488251\pi\)
\(752\) 0 0
\(753\) 2.76144e7 1.77479
\(754\) 0 0
\(755\) −3.52150e6 −0.224833
\(756\) 0 0
\(757\) 1.90153e7 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(758\) 0 0
\(759\) −3.36442e7 −2.11985
\(760\) 0 0
\(761\) 2.23551e7 1.39931 0.699656 0.714480i \(-0.253337\pi\)
0.699656 + 0.714480i \(0.253337\pi\)
\(762\) 0 0
\(763\) 679724. 0.0422689
\(764\) 0 0
\(765\) −1.12065e6 −0.0692335
\(766\) 0 0
\(767\) −7.30726e6 −0.448504
\(768\) 0 0
\(769\) −1.00704e7 −0.614088 −0.307044 0.951695i \(-0.599340\pi\)
−0.307044 + 0.951695i \(0.599340\pi\)
\(770\) 0 0
\(771\) 2.48330e7 1.50451
\(772\) 0 0
\(773\) −4.05963e6 −0.244364 −0.122182 0.992508i \(-0.538989\pi\)
−0.122182 + 0.992508i \(0.538989\pi\)
\(774\) 0 0
\(775\) −5.84750e6 −0.349716
\(776\) 0 0
\(777\) 2.69439e7 1.60106
\(778\) 0 0
\(779\) −1.73304e7 −1.02321
\(780\) 0 0
\(781\) 1.41754e7 0.831585
\(782\) 0 0
\(783\) 243144. 0.0141729
\(784\) 0 0
\(785\) 8.39695e6 0.486348
\(786\) 0 0
\(787\) 1.72256e7 0.991372 0.495686 0.868502i \(-0.334917\pi\)
0.495686 + 0.868502i \(0.334917\pi\)
\(788\) 0 0
\(789\) −5.78780e6 −0.330995
\(790\) 0 0
\(791\) 1.18884e7 0.675589
\(792\) 0 0
\(793\) −8.21164e6 −0.463711
\(794\) 0 0
\(795\) −2.40570e6 −0.134997
\(796\) 0 0
\(797\) −2.10793e7 −1.17547 −0.587733 0.809055i \(-0.699980\pi\)
−0.587733 + 0.809055i \(0.699980\pi\)
\(798\) 0 0
\(799\) −3.00316e6 −0.166422
\(800\) 0 0
\(801\) 2.88029e7 1.58619
\(802\) 0 0
\(803\) 1.61750e7 0.885231
\(804\) 0 0
\(805\) 1.73637e7 0.944393
\(806\) 0 0
\(807\) 2.61303e7 1.41241
\(808\) 0 0
\(809\) −1.87877e7 −1.00926 −0.504629 0.863336i \(-0.668371\pi\)
−0.504629 + 0.863336i \(0.668371\pi\)
\(810\) 0 0
\(811\) 1.32456e7 0.707164 0.353582 0.935404i \(-0.384964\pi\)
0.353582 + 0.935404i \(0.384964\pi\)
\(812\) 0 0
\(813\) 9.48860e6 0.503473
\(814\) 0 0
\(815\) −2.54125e6 −0.134015
\(816\) 0 0
\(817\) 445480. 0.0233493
\(818\) 0 0
\(819\) 3.26786e7 1.70237
\(820\) 0 0
\(821\) −7.66925e6 −0.397096 −0.198548 0.980091i \(-0.563623\pi\)
−0.198548 + 0.980091i \(0.563623\pi\)
\(822\) 0 0
\(823\) 8.82786e6 0.454314 0.227157 0.973858i \(-0.427057\pi\)
0.227157 + 0.973858i \(0.427057\pi\)
\(824\) 0 0
\(825\) −6.60000e6 −0.337605
\(826\) 0 0
\(827\) 3.06923e7 1.56051 0.780254 0.625463i \(-0.215090\pi\)
0.780254 + 0.625463i \(0.215090\pi\)
\(828\) 0 0
\(829\) 3.28414e7 1.65972 0.829860 0.557972i \(-0.188420\pi\)
0.829860 + 0.557972i \(0.188420\pi\)
\(830\) 0 0
\(831\) −1.63485e7 −0.821250
\(832\) 0 0
\(833\) 5.71336e6 0.285285
\(834\) 0 0
\(835\) 3.48105e6 0.172780
\(836\) 0 0
\(837\) −411664. −0.0203109
\(838\) 0 0
\(839\) 8.42117e6 0.413017 0.206508 0.978445i \(-0.433790\pi\)
0.206508 + 0.978445i \(0.433790\pi\)
\(840\) 0 0
\(841\) 1.00255e7 0.488784
\(842\) 0 0
\(843\) −4.22824e7 −2.04923
\(844\) 0 0
\(845\) −389775. −0.0187790
\(846\) 0 0
\(847\) −1.51181e7 −0.724083
\(848\) 0 0
\(849\) −3.58757e7 −1.70817
\(850\) 0 0
\(851\) 1.78989e7 0.847234
\(852\) 0 0
\(853\) 2.35126e7 1.10644 0.553221 0.833035i \(-0.313399\pi\)
0.553221 + 0.833035i \(0.313399\pi\)
\(854\) 0 0
\(855\) −7.25410e6 −0.339366
\(856\) 0 0
\(857\) −1.13050e7 −0.525799 −0.262900 0.964823i \(-0.584679\pi\)
−0.262900 + 0.964823i \(0.584679\pi\)
\(858\) 0 0
\(859\) −1.00078e7 −0.462758 −0.231379 0.972864i \(-0.574324\pi\)
−0.231379 + 0.972864i \(0.574324\pi\)
\(860\) 0 0
\(861\) −6.90336e7 −3.17360
\(862\) 0 0
\(863\) −2.61429e7 −1.19489 −0.597443 0.801911i \(-0.703817\pi\)
−0.597443 + 0.801911i \(0.703817\pi\)
\(864\) 0 0
\(865\) 6.62535e6 0.301071
\(866\) 0 0
\(867\) 3.04757e7 1.37691
\(868\) 0 0
\(869\) −1.49798e7 −0.672911
\(870\) 0 0
\(871\) −7.17912e6 −0.320646
\(872\) 0 0
\(873\) 2.28126e7 1.01307
\(874\) 0 0
\(875\) 3.40625e6 0.150403
\(876\) 0 0
\(877\) −1.92041e6 −0.0843129 −0.0421565 0.999111i \(-0.513423\pi\)
−0.0421565 + 0.999111i \(0.513423\pi\)
\(878\) 0 0
\(879\) −1.56750e6 −0.0684282
\(880\) 0 0
\(881\) −2.56594e7 −1.11380 −0.556899 0.830580i \(-0.688009\pi\)
−0.556899 + 0.830580i \(0.688009\pi\)
\(882\) 0 0
\(883\) 2.05643e7 0.887590 0.443795 0.896128i \(-0.353632\pi\)
0.443795 + 0.896128i \(0.353632\pi\)
\(884\) 0 0
\(885\) 6.46140e6 0.277312
\(886\) 0 0
\(887\) −3.16868e7 −1.35229 −0.676143 0.736770i \(-0.736350\pi\)
−0.676143 + 0.736770i \(0.736350\pi\)
\(888\) 0 0
\(889\) 5.38416e6 0.228488
\(890\) 0 0
\(891\) −2.85749e7 −1.20584
\(892\) 0 0
\(893\) −1.94398e7 −0.815761
\(894\) 0 0
\(895\) −3.57030e6 −0.148987
\(896\) 0 0
\(897\) 4.35972e7 1.80916
\(898\) 0 0
\(899\) −5.17013e7 −2.13355
\(900\) 0 0
\(901\) −813564. −0.0333872
\(902\) 0 0
\(903\) 1.77452e6 0.0724205
\(904\) 0 0
\(905\) −2.74175e6 −0.111277
\(906\) 0 0
\(907\) −3.96963e6 −0.160225 −0.0801127 0.996786i \(-0.525528\pi\)
−0.0801127 + 0.996786i \(0.525528\pi\)
\(908\) 0 0
\(909\) 2.43521e7 0.977522
\(910\) 0 0
\(911\) 1.37945e7 0.550692 0.275346 0.961345i \(-0.411208\pi\)
0.275346 + 0.961345i \(0.411208\pi\)
\(912\) 0 0
\(913\) 1.84637e7 0.733063
\(914\) 0 0
\(915\) 7.26110e6 0.286715
\(916\) 0 0
\(917\) 5.15875e7 2.02592
\(918\) 0 0
\(919\) −8.08126e6 −0.315639 −0.157819 0.987468i \(-0.550446\pi\)
−0.157819 + 0.987468i \(0.550446\pi\)
\(920\) 0 0
\(921\) −3.55877e7 −1.38245
\(922\) 0 0
\(923\) −1.83689e7 −0.709707
\(924\) 0 0
\(925\) 3.51125e6 0.134930
\(926\) 0 0
\(927\) 3.45676e7 1.32120
\(928\) 0 0
\(929\) 2.99956e7 1.14030 0.570150 0.821541i \(-0.306885\pi\)
0.570150 + 0.821541i \(0.306885\pi\)
\(930\) 0 0
\(931\) 3.69833e7 1.39840
\(932\) 0 0
\(933\) −1.50213e7 −0.564943
\(934\) 0 0
\(935\) −2.23200e6 −0.0834959
\(936\) 0 0
\(937\) −2.07620e7 −0.772540 −0.386270 0.922386i \(-0.626237\pi\)
−0.386270 + 0.922386i \(0.626237\pi\)
\(938\) 0 0
\(939\) 5.94976e7 2.20209
\(940\) 0 0
\(941\) −3.47642e6 −0.127985 −0.0639923 0.997950i \(-0.520383\pi\)
−0.0639923 + 0.997950i \(0.520383\pi\)
\(942\) 0 0
\(943\) −4.58593e7 −1.67938
\(944\) 0 0
\(945\) 239800. 0.00873514
\(946\) 0 0
\(947\) −1.86700e6 −0.0676503 −0.0338252 0.999428i \(-0.510769\pi\)
−0.0338252 + 0.999428i \(0.510769\pi\)
\(948\) 0 0
\(949\) −2.09602e7 −0.755490
\(950\) 0 0
\(951\) −5.72763e7 −2.05364
\(952\) 0 0
\(953\) −3.85501e7 −1.37497 −0.687484 0.726199i \(-0.741285\pi\)
−0.687484 + 0.726199i \(0.741285\pi\)
\(954\) 0 0
\(955\) 7.37370e6 0.261624
\(956\) 0 0
\(957\) −5.83546e7 −2.05966
\(958\) 0 0
\(959\) 4.83044e6 0.169606
\(960\) 0 0
\(961\) 5.89056e7 2.05754
\(962\) 0 0
\(963\) 1.37500e7 0.477790
\(964\) 0 0
\(965\) −2.50758e7 −0.866837
\(966\) 0 0
\(967\) −1.64875e7 −0.567008 −0.283504 0.958971i \(-0.591497\pi\)
−0.283504 + 0.958971i \(0.591497\pi\)
\(968\) 0 0
\(969\) −4.92677e6 −0.168559
\(970\) 0 0
\(971\) 2.36976e7 0.806597 0.403299 0.915068i \(-0.367864\pi\)
0.403299 + 0.915068i \(0.367864\pi\)
\(972\) 0 0
\(973\) −4.21185e7 −1.42623
\(974\) 0 0
\(975\) 8.55250e6 0.288125
\(976\) 0 0
\(977\) −5.77590e7 −1.93590 −0.967950 0.251143i \(-0.919194\pi\)
−0.967950 + 0.251143i \(0.919194\pi\)
\(978\) 0 0
\(979\) 5.73667e7 1.91295
\(980\) 0 0
\(981\) −751438. −0.0249299
\(982\) 0 0
\(983\) 1.10103e7 0.363425 0.181712 0.983352i \(-0.441836\pi\)
0.181712 + 0.983352i \(0.441836\pi\)
\(984\) 0 0
\(985\) 2.05999e7 0.676512
\(986\) 0 0
\(987\) −7.74362e7 −2.53018
\(988\) 0 0
\(989\) 1.17882e6 0.0383228
\(990\) 0 0
\(991\) −3.70807e7 −1.19940 −0.599700 0.800225i \(-0.704713\pi\)
−0.599700 + 0.800225i \(0.704713\pi\)
\(992\) 0 0
\(993\) −1.45515e7 −0.468311
\(994\) 0 0
\(995\) −2.26678e7 −0.725858
\(996\) 0 0
\(997\) 4.52935e6 0.144311 0.0721553 0.997393i \(-0.477012\pi\)
0.0721553 + 0.997393i \(0.477012\pi\)
\(998\) 0 0
\(999\) 247192. 0.00783647
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 80.6.a.b.1.1 1
3.2 odd 2 720.6.a.l.1.1 1
4.3 odd 2 20.6.a.a.1.1 1
5.2 odd 4 400.6.c.c.49.2 2
5.3 odd 4 400.6.c.c.49.1 2
5.4 even 2 400.6.a.m.1.1 1
8.3 odd 2 320.6.a.c.1.1 1
8.5 even 2 320.6.a.n.1.1 1
12.11 even 2 180.6.a.e.1.1 1
20.3 even 4 100.6.c.a.49.2 2
20.7 even 4 100.6.c.a.49.1 2
20.19 odd 2 100.6.a.a.1.1 1
28.27 even 2 980.6.a.b.1.1 1
60.23 odd 4 900.6.d.h.649.1 2
60.47 odd 4 900.6.d.h.649.2 2
60.59 even 2 900.6.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.6.a.a.1.1 1 4.3 odd 2
80.6.a.b.1.1 1 1.1 even 1 trivial
100.6.a.a.1.1 1 20.19 odd 2
100.6.c.a.49.1 2 20.7 even 4
100.6.c.a.49.2 2 20.3 even 4
180.6.a.e.1.1 1 12.11 even 2
320.6.a.c.1.1 1 8.3 odd 2
320.6.a.n.1.1 1 8.5 even 2
400.6.a.m.1.1 1 5.4 even 2
400.6.c.c.49.1 2 5.3 odd 4
400.6.c.c.49.2 2 5.2 odd 4
720.6.a.l.1.1 1 3.2 odd 2
900.6.a.b.1.1 1 60.59 even 2
900.6.d.h.649.1 2 60.23 odd 4
900.6.d.h.649.2 2 60.47 odd 4
980.6.a.b.1.1 1 28.27 even 2