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Properties

Label 720.6.a.q.1.1
Level $720$
Weight $6$
Character 720.1
Self dual yes
Analytic conductor $115.476$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [720,6,Mod(1,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("720.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 720.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(115.476350265\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 15)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+25.0000 q^{5} -12.0000 q^{7} +O(q^{10})\) \(q+25.0000 q^{5} -12.0000 q^{7} +112.000 q^{11} -974.000 q^{13} -2182.00 q^{17} -1420.00 q^{19} +3216.00 q^{23} +625.000 q^{25} +4150.00 q^{29} +5688.00 q^{31} -300.000 q^{35} +6482.00 q^{37} -5402.00 q^{41} +21764.0 q^{43} -368.000 q^{47} -16663.0 q^{49} -12586.0 q^{53} +2800.00 q^{55} -25520.0 q^{59} +11782.0 q^{61} -24350.0 q^{65} +13188.0 q^{67} -35968.0 q^{71} +73186.0 q^{73} -1344.00 q^{77} +52440.0 q^{79} +69036.0 q^{83} -54550.0 q^{85} +33870.0 q^{89} +11688.0 q^{91} -35500.0 q^{95} +143042. q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) −12.0000 −0.0925627 −0.0462814 − 0.998928i \(-0.514737\pi\)
−0.0462814 + 0.998928i \(0.514737\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 112.000 0.279085 0.139542 − 0.990216i \(-0.455437\pi\)
0.139542 + 0.990216i \(0.455437\pi\)
\(12\) 0 0
\(13\) −974.000 −1.59846 −0.799228 − 0.601028i \(-0.794758\pi\)
−0.799228 + 0.601028i \(0.794758\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2182.00 −1.83119 −0.915593 − 0.402106i \(-0.868278\pi\)
−0.915593 + 0.402106i \(0.868278\pi\)
\(18\) 0 0
\(19\) −1420.00 −0.902411 −0.451205 − 0.892420i \(-0.649006\pi\)
−0.451205 + 0.892420i \(0.649006\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3216.00 1.26764 0.633821 − 0.773480i \(-0.281486\pi\)
0.633821 + 0.773480i \(0.281486\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4150.00 0.916333 0.458166 − 0.888867i \(-0.348506\pi\)
0.458166 + 0.888867i \(0.348506\pi\)
\(30\) 0 0
\(31\) 5688.00 1.06305 0.531527 − 0.847041i \(-0.321618\pi\)
0.531527 + 0.847041i \(0.321618\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −300.000 −0.0413953
\(36\) 0 0
\(37\) 6482.00 0.778403 0.389202 − 0.921153i \(-0.372751\pi\)
0.389202 + 0.921153i \(0.372751\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5402.00 −0.501874 −0.250937 − 0.968003i \(-0.580739\pi\)
−0.250937 + 0.968003i \(0.580739\pi\)
\(42\) 0 0
\(43\) 21764.0 1.79501 0.897506 − 0.441001i \(-0.145377\pi\)
0.897506 + 0.441001i \(0.145377\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −368.000 −0.0242998 −0.0121499 − 0.999926i \(-0.503868\pi\)
−0.0121499 + 0.999926i \(0.503868\pi\)
\(48\) 0 0
\(49\) −16663.0 −0.991432
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −12586.0 −0.615457 −0.307729 − 0.951474i \(-0.599569\pi\)
−0.307729 + 0.951474i \(0.599569\pi\)
\(54\) 0 0
\(55\) 2800.00 0.124811
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −25520.0 −0.954444 −0.477222 − 0.878783i \(-0.658356\pi\)
−0.477222 + 0.878783i \(0.658356\pi\)
\(60\) 0 0
\(61\) 11782.0 0.405410 0.202705 − 0.979240i \(-0.435027\pi\)
0.202705 + 0.979240i \(0.435027\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −24350.0 −0.714851
\(66\) 0 0
\(67\) 13188.0 0.358915 0.179458 − 0.983766i \(-0.442566\pi\)
0.179458 + 0.983766i \(0.442566\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −35968.0 −0.846780 −0.423390 − 0.905948i \(-0.639160\pi\)
−0.423390 + 0.905948i \(0.639160\pi\)
\(72\) 0 0
\(73\) 73186.0 1.60739 0.803694 − 0.595042i \(-0.202865\pi\)
0.803694 + 0.595042i \(0.202865\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1344.00 −0.0258329
\(78\) 0 0
\(79\) 52440.0 0.945355 0.472678 − 0.881235i \(-0.343288\pi\)
0.472678 + 0.881235i \(0.343288\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 69036.0 1.09997 0.549984 − 0.835175i \(-0.314634\pi\)
0.549984 + 0.835175i \(0.314634\pi\)
\(84\) 0 0
\(85\) −54550.0 −0.818931
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 33870.0 0.453252 0.226626 − 0.973982i \(-0.427230\pi\)
0.226626 + 0.973982i \(0.427230\pi\)
\(90\) 0 0
\(91\) 11688.0 0.147957
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −35500.0 −0.403570
\(96\) 0 0
\(97\) 143042. 1.54360 0.771799 − 0.635867i \(-0.219357\pi\)
0.771799 + 0.635867i \(0.219357\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −63042.0 −0.614931 −0.307466 − 0.951559i \(-0.599481\pi\)
−0.307466 + 0.951559i \(0.599481\pi\)
\(102\) 0 0
\(103\) −38636.0 −0.358839 −0.179419 − 0.983773i \(-0.557422\pi\)
−0.179419 + 0.983773i \(0.557422\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −69228.0 −0.584551 −0.292275 − 0.956334i \(-0.594412\pi\)
−0.292275 + 0.956334i \(0.594412\pi\)
\(108\) 0 0
\(109\) 51590.0 0.415910 0.207955 − 0.978138i \(-0.433319\pi\)
0.207955 + 0.978138i \(0.433319\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −20206.0 −0.148862 −0.0744311 − 0.997226i \(-0.523714\pi\)
−0.0744311 + 0.997226i \(0.523714\pi\)
\(114\) 0 0
\(115\) 80400.0 0.566907
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 26184.0 0.169500
\(120\) 0 0
\(121\) −148507. −0.922112
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) 198908. 1.09432 0.547158 − 0.837029i \(-0.315710\pi\)
0.547158 + 0.837029i \(0.315710\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 150672. 0.767104 0.383552 − 0.923519i \(-0.374701\pi\)
0.383552 + 0.923519i \(0.374701\pi\)
\(132\) 0 0
\(133\) 17040.0 0.0835296
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 19098.0 0.0869334 0.0434667 − 0.999055i \(-0.486160\pi\)
0.0434667 + 0.999055i \(0.486160\pi\)
\(138\) 0 0
\(139\) −196460. −0.862456 −0.431228 − 0.902243i \(-0.641920\pi\)
−0.431228 + 0.902243i \(0.641920\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −109088. −0.446105
\(144\) 0 0
\(145\) 103750. 0.409796
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 362710. 1.33842 0.669212 − 0.743071i \(-0.266632\pi\)
0.669212 + 0.743071i \(0.266632\pi\)
\(150\) 0 0
\(151\) −76072.0 −0.271508 −0.135754 − 0.990743i \(-0.543346\pi\)
−0.135754 + 0.990743i \(0.543346\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 142200. 0.475412
\(156\) 0 0
\(157\) 252722. 0.818265 0.409132 − 0.912475i \(-0.365831\pi\)
0.409132 + 0.912475i \(0.365831\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −38592.0 −0.117336
\(162\) 0 0
\(163\) −85916.0 −0.253282 −0.126641 − 0.991949i \(-0.540420\pi\)
−0.126641 + 0.991949i \(0.540420\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 316272. 0.877545 0.438773 − 0.898598i \(-0.355413\pi\)
0.438773 + 0.898598i \(0.355413\pi\)
\(168\) 0 0
\(169\) 577383. 1.55506
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 597534. 1.51791 0.758957 − 0.651140i \(-0.225709\pi\)
0.758957 + 0.651140i \(0.225709\pi\)
\(174\) 0 0
\(175\) −7500.00 −0.0185125
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −282680. −0.659421 −0.329710 − 0.944082i \(-0.606951\pi\)
−0.329710 + 0.944082i \(0.606951\pi\)
\(180\) 0 0
\(181\) −294658. −0.668531 −0.334266 − 0.942479i \(-0.608488\pi\)
−0.334266 + 0.942479i \(0.608488\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 162050. 0.348113
\(186\) 0 0
\(187\) −244384. −0.511056
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 723272. 1.43456 0.717279 − 0.696786i \(-0.245387\pi\)
0.717279 + 0.696786i \(0.245387\pi\)
\(192\) 0 0
\(193\) 80426.0 0.155419 0.0777093 − 0.996976i \(-0.475239\pi\)
0.0777093 + 0.996976i \(0.475239\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −509802. −0.935914 −0.467957 − 0.883751i \(-0.655010\pi\)
−0.467957 + 0.883751i \(0.655010\pi\)
\(198\) 0 0
\(199\) 435320. 0.779248 0.389624 − 0.920974i \(-0.372605\pi\)
0.389624 + 0.920974i \(0.372605\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −49800.0 −0.0848182
\(204\) 0 0
\(205\) −135050. −0.224445
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −159040. −0.251849
\(210\) 0 0
\(211\) 1.12275e6 1.73611 0.868053 − 0.496472i \(-0.165371\pi\)
0.868053 + 0.496472i \(0.165371\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 544100. 0.802754
\(216\) 0 0
\(217\) −68256.0 −0.0983992
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.12527e6 2.92707
\(222\) 0 0
\(223\) 325084. 0.437757 0.218879 − 0.975752i \(-0.429760\pi\)
0.218879 + 0.975752i \(0.429760\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −311308. −0.400983 −0.200491 − 0.979695i \(-0.564254\pi\)
−0.200491 + 0.979695i \(0.564254\pi\)
\(228\) 0 0
\(229\) −615450. −0.775540 −0.387770 − 0.921756i \(-0.626754\pi\)
−0.387770 + 0.921756i \(0.626754\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 304434. 0.367370 0.183685 − 0.982985i \(-0.441197\pi\)
0.183685 + 0.982985i \(0.441197\pi\)
\(234\) 0 0
\(235\) −9200.00 −0.0108672
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 780760. 0.884144 0.442072 − 0.896980i \(-0.354244\pi\)
0.442072 + 0.896980i \(0.354244\pi\)
\(240\) 0 0
\(241\) 635842. 0.705191 0.352595 − 0.935776i \(-0.385299\pi\)
0.352595 + 0.935776i \(0.385299\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −416575. −0.443382
\(246\) 0 0
\(247\) 1.38308e6 1.44246
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.20559e6 1.20786 0.603929 − 0.797038i \(-0.293601\pi\)
0.603929 + 0.797038i \(0.293601\pi\)
\(252\) 0 0
\(253\) 360192. 0.353780
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.96702e6 −1.85770 −0.928852 − 0.370452i \(-0.879203\pi\)
−0.928852 + 0.370452i \(0.879203\pi\)
\(258\) 0 0
\(259\) −77784.0 −0.0720511
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −625264. −0.557409 −0.278705 − 0.960377i \(-0.589905\pi\)
−0.278705 + 0.960377i \(0.589905\pi\)
\(264\) 0 0
\(265\) −314650. −0.275241
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −527050. −0.444090 −0.222045 − 0.975036i \(-0.571273\pi\)
−0.222045 + 0.975036i \(0.571273\pi\)
\(270\) 0 0
\(271\) −2.10923e6 −1.74462 −0.872311 − 0.488952i \(-0.837379\pi\)
−0.872311 + 0.488952i \(0.837379\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 70000.0 0.0558170
\(276\) 0 0
\(277\) −267438. −0.209423 −0.104711 − 0.994503i \(-0.533392\pi\)
−0.104711 + 0.994503i \(0.533392\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −838002. −0.633110 −0.316555 − 0.948574i \(-0.602526\pi\)
−0.316555 + 0.948574i \(0.602526\pi\)
\(282\) 0 0
\(283\) 2.23772e6 1.66089 0.830444 − 0.557102i \(-0.188087\pi\)
0.830444 + 0.557102i \(0.188087\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 64824.0 0.0464549
\(288\) 0 0
\(289\) 3.34127e6 2.35324
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −785706. −0.534676 −0.267338 − 0.963603i \(-0.586144\pi\)
−0.267338 + 0.963603i \(0.586144\pi\)
\(294\) 0 0
\(295\) −638000. −0.426841
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.13238e6 −2.02627
\(300\) 0 0
\(301\) −261168. −0.166151
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 294550. 0.181305
\(306\) 0 0
\(307\) 2.94955e6 1.78612 0.893058 − 0.449942i \(-0.148555\pi\)
0.893058 + 0.449942i \(0.148555\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3.07757e6 −1.80429 −0.902146 − 0.431431i \(-0.858009\pi\)
−0.902146 + 0.431431i \(0.858009\pi\)
\(312\) 0 0
\(313\) 1.61367e6 0.931007 0.465503 − 0.885046i \(-0.345873\pi\)
0.465503 + 0.885046i \(0.345873\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.00496e6 1.12062 0.560308 − 0.828284i \(-0.310683\pi\)
0.560308 + 0.828284i \(0.310683\pi\)
\(318\) 0 0
\(319\) 464800. 0.255735
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.09844e6 1.65248
\(324\) 0 0
\(325\) −608750. −0.319691
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4416.00 0.00224926
\(330\) 0 0
\(331\) −470772. −0.236179 −0.118089 − 0.993003i \(-0.537677\pi\)
−0.118089 + 0.993003i \(0.537677\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 329700. 0.160512
\(336\) 0 0
\(337\) 2.31548e6 1.11062 0.555311 − 0.831642i \(-0.312599\pi\)
0.555311 + 0.831642i \(0.312599\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 637056. 0.296682
\(342\) 0 0
\(343\) 401640. 0.184332
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.25393e6 0.559050 0.279525 − 0.960138i \(-0.409823\pi\)
0.279525 + 0.960138i \(0.409823\pi\)
\(348\) 0 0
\(349\) 616390. 0.270889 0.135445 − 0.990785i \(-0.456754\pi\)
0.135445 + 0.990785i \(0.456754\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 281274. 0.120141 0.0600707 − 0.998194i \(-0.480867\pi\)
0.0600707 + 0.998194i \(0.480867\pi\)
\(354\) 0 0
\(355\) −899200. −0.378691
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.19148e6 −0.487922 −0.243961 − 0.969785i \(-0.578447\pi\)
−0.243961 + 0.969785i \(0.578447\pi\)
\(360\) 0 0
\(361\) −459699. −0.185655
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.82965e6 0.718846
\(366\) 0 0
\(367\) 793068. 0.307359 0.153679 − 0.988121i \(-0.450888\pi\)
0.153679 + 0.988121i \(0.450888\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 151032. 0.0569684
\(372\) 0 0
\(373\) 635626. 0.236554 0.118277 − 0.992981i \(-0.462263\pi\)
0.118277 + 0.992981i \(0.462263\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.04210e6 −1.46472
\(378\) 0 0
\(379\) 2.12834e6 0.761102 0.380551 − 0.924760i \(-0.375734\pi\)
0.380551 + 0.924760i \(0.375734\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4.88174e6 −1.70051 −0.850253 − 0.526375i \(-0.823551\pi\)
−0.850253 + 0.526375i \(0.823551\pi\)
\(384\) 0 0
\(385\) −33600.0 −0.0115528
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.30607e6 0.772678 0.386339 − 0.922357i \(-0.373740\pi\)
0.386339 + 0.922357i \(0.373740\pi\)
\(390\) 0 0
\(391\) −7.01731e6 −2.32129
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.31100e6 0.422776
\(396\) 0 0
\(397\) −423398. −0.134826 −0.0674128 − 0.997725i \(-0.521474\pi\)
−0.0674128 + 0.997725i \(0.521474\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.60756e6 0.809791 0.404896 − 0.914363i \(-0.367308\pi\)
0.404896 + 0.914363i \(0.367308\pi\)
\(402\) 0 0
\(403\) −5.54011e6 −1.69924
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 725984. 0.217241
\(408\) 0 0
\(409\) −4.80871e6 −1.42141 −0.710707 − 0.703489i \(-0.751625\pi\)
−0.710707 + 0.703489i \(0.751625\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 306240. 0.0883460
\(414\) 0 0
\(415\) 1.72590e6 0.491921
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 139760. 0.0388909 0.0194454 − 0.999811i \(-0.493810\pi\)
0.0194454 + 0.999811i \(0.493810\pi\)
\(420\) 0 0
\(421\) −3.00310e6 −0.825780 −0.412890 − 0.910781i \(-0.635481\pi\)
−0.412890 + 0.910781i \(0.635481\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.36375e6 −0.366237
\(426\) 0 0
\(427\) −141384. −0.0375259
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5.97955e6 1.55051 0.775257 − 0.631646i \(-0.217621\pi\)
0.775257 + 0.631646i \(0.217621\pi\)
\(432\) 0 0
\(433\) 1.75235e6 0.449159 0.224580 − 0.974456i \(-0.427899\pi\)
0.224580 + 0.974456i \(0.427899\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.56672e6 −1.14393
\(438\) 0 0
\(439\) 4.72556e6 1.17029 0.585143 − 0.810930i \(-0.301038\pi\)
0.585143 + 0.810930i \(0.301038\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.48584e6 0.601815 0.300908 − 0.953653i \(-0.402710\pi\)
0.300908 + 0.953653i \(0.402710\pi\)
\(444\) 0 0
\(445\) 846750. 0.202701
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.46233e6 −0.342318 −0.171159 − 0.985243i \(-0.554751\pi\)
−0.171159 + 0.985243i \(0.554751\pi\)
\(450\) 0 0
\(451\) −605024. −0.140066
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 292200. 0.0661686
\(456\) 0 0
\(457\) −1.45684e6 −0.326303 −0.163151 − 0.986601i \(-0.552166\pi\)
−0.163151 + 0.986601i \(0.552166\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4.32280e6 −0.947356 −0.473678 − 0.880698i \(-0.657074\pi\)
−0.473678 + 0.880698i \(0.657074\pi\)
\(462\) 0 0
\(463\) −1.07848e6 −0.233807 −0.116904 − 0.993143i \(-0.537297\pi\)
−0.116904 + 0.993143i \(0.537297\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3.40023e6 −0.721466 −0.360733 − 0.932669i \(-0.617473\pi\)
−0.360733 + 0.932669i \(0.617473\pi\)
\(468\) 0 0
\(469\) −158256. −0.0332222
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.43757e6 0.500961
\(474\) 0 0
\(475\) −887500. −0.180482
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.75268e6 0.548172 0.274086 − 0.961705i \(-0.411625\pi\)
0.274086 + 0.961705i \(0.411625\pi\)
\(480\) 0 0
\(481\) −6.31347e6 −1.24424
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.57605e6 0.690318
\(486\) 0 0
\(487\) −3.56997e6 −0.682091 −0.341046 − 0.940047i \(-0.610781\pi\)
−0.341046 + 0.940047i \(0.610781\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.96455e6 0.367756 0.183878 − 0.982949i \(-0.441135\pi\)
0.183878 + 0.982949i \(0.441135\pi\)
\(492\) 0 0
\(493\) −9.05530e6 −1.67798
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 431616. 0.0783802
\(498\) 0 0
\(499\) −5.14798e6 −0.925519 −0.462760 − 0.886484i \(-0.653141\pi\)
−0.462760 + 0.886484i \(0.653141\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 1.97502e6 0.348057 0.174029 − 0.984741i \(-0.444321\pi\)
0.174029 + 0.984741i \(0.444321\pi\)
\(504\) 0 0
\(505\) −1.57605e6 −0.275006
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3.32447e6 0.568759 0.284379 − 0.958712i \(-0.408213\pi\)
0.284379 + 0.958712i \(0.408213\pi\)
\(510\) 0 0
\(511\) −878232. −0.148784
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −965900. −0.160477
\(516\) 0 0
\(517\) −41216.0 −0.00678171
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.97960e6 0.480910 0.240455 − 0.970660i \(-0.422703\pi\)
0.240455 + 0.970660i \(0.422703\pi\)
\(522\) 0 0
\(523\) 6.19108e6 0.989720 0.494860 − 0.868973i \(-0.335219\pi\)
0.494860 + 0.868973i \(0.335219\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.24112e7 −1.94665
\(528\) 0 0
\(529\) 3.90631e6 0.606915
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5.26155e6 0.802224
\(534\) 0 0
\(535\) −1.73070e6 −0.261419
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.86626e6 −0.276694
\(540\) 0 0
\(541\) −8.55398e6 −1.25654 −0.628268 − 0.777997i \(-0.716236\pi\)
−0.628268 + 0.777997i \(0.716236\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.28975e6 0.186001
\(546\) 0 0
\(547\) 2.54371e6 0.363495 0.181748 − 0.983345i \(-0.441825\pi\)
0.181748 + 0.983345i \(0.441825\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −5.89300e6 −0.826908
\(552\) 0 0
\(553\) −629280. −0.0875046
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −7.58704e6 −1.03618 −0.518089 − 0.855327i \(-0.673356\pi\)
−0.518089 + 0.855327i \(0.673356\pi\)
\(558\) 0 0
\(559\) −2.11981e7 −2.86925
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7.50940e6 0.998468 0.499234 − 0.866467i \(-0.333615\pi\)
0.499234 + 0.866467i \(0.333615\pi\)
\(564\) 0 0
\(565\) −505150. −0.0665732
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.38890e7 −1.79842 −0.899209 − 0.437519i \(-0.855857\pi\)
−0.899209 + 0.437519i \(0.855857\pi\)
\(570\) 0 0
\(571\) 1.93539e6 0.248415 0.124207 − 0.992256i \(-0.460361\pi\)
0.124207 + 0.992256i \(0.460361\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.01000e6 0.253528
\(576\) 0 0
\(577\) −4.89408e6 −0.611972 −0.305986 − 0.952036i \(-0.598986\pi\)
−0.305986 + 0.952036i \(0.598986\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −828432. −0.101816
\(582\) 0 0
\(583\) −1.40963e6 −0.171765
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −6.43883e6 −0.771279 −0.385640 − 0.922650i \(-0.626019\pi\)
−0.385640 + 0.922650i \(0.626019\pi\)
\(588\) 0 0
\(589\) −8.07696e6 −0.959312
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −4.30365e6 −0.502574 −0.251287 − 0.967913i \(-0.580854\pi\)
−0.251287 + 0.967913i \(0.580854\pi\)
\(594\) 0 0
\(595\) 654600. 0.0758025
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −4.50988e6 −0.513568 −0.256784 − 0.966469i \(-0.582663\pi\)
−0.256784 + 0.966469i \(0.582663\pi\)
\(600\) 0 0
\(601\) −5.11596e6 −0.577751 −0.288876 − 0.957367i \(-0.593281\pi\)
−0.288876 + 0.957367i \(0.593281\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.71267e6 −0.412381
\(606\) 0 0
\(607\) −1.61925e7 −1.78378 −0.891891 − 0.452250i \(-0.850622\pi\)
−0.891891 + 0.452250i \(0.850622\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 358432. 0.0388422
\(612\) 0 0
\(613\) 1.55525e7 1.67166 0.835830 − 0.548988i \(-0.184987\pi\)
0.835830 + 0.548988i \(0.184987\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.46710e7 1.55148 0.775740 − 0.631053i \(-0.217377\pi\)
0.775740 + 0.631053i \(0.217377\pi\)
\(618\) 0 0
\(619\) 9.66826e6 1.01420 0.507098 − 0.861889i \(-0.330718\pi\)
0.507098 + 0.861889i \(0.330718\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −406440. −0.0419543
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.41437e7 −1.42540
\(630\) 0 0
\(631\) 1.16557e6 0.116537 0.0582686 − 0.998301i \(-0.481442\pi\)
0.0582686 + 0.998301i \(0.481442\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.97270e6 0.489393
\(636\) 0 0
\(637\) 1.62298e7 1.58476
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.95088e6 −0.187537 −0.0937683 − 0.995594i \(-0.529891\pi\)
−0.0937683 + 0.995594i \(0.529891\pi\)
\(642\) 0 0
\(643\) 1.17387e7 1.11968 0.559839 − 0.828601i \(-0.310863\pi\)
0.559839 + 0.828601i \(0.310863\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.01369e7 −0.952015 −0.476008 − 0.879441i \(-0.657917\pi\)
−0.476008 + 0.879441i \(0.657917\pi\)
\(648\) 0 0
\(649\) −2.85824e6 −0.266371
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2.47095e6 −0.226767 −0.113384 − 0.993551i \(-0.536169\pi\)
−0.113384 + 0.993551i \(0.536169\pi\)
\(654\) 0 0
\(655\) 3.76680e6 0.343059
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.62242e7 1.45529 0.727644 − 0.685955i \(-0.240616\pi\)
0.727644 + 0.685955i \(0.240616\pi\)
\(660\) 0 0
\(661\) 1.54679e7 1.37698 0.688490 − 0.725246i \(-0.258274\pi\)
0.688490 + 0.725246i \(0.258274\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 426000. 0.0373556
\(666\) 0 0
\(667\) 1.33464e7 1.16158
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.31958e6 0.113144
\(672\) 0 0
\(673\) −1.94441e7 −1.65482 −0.827410 − 0.561598i \(-0.810187\pi\)
−0.827410 + 0.561598i \(0.810187\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −643242. −0.0539390 −0.0269695 − 0.999636i \(-0.508586\pi\)
−0.0269695 + 0.999636i \(0.508586\pi\)
\(678\) 0 0
\(679\) −1.71650e6 −0.142880
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.14412e6 0.0938465 0.0469233 − 0.998898i \(-0.485058\pi\)
0.0469233 + 0.998898i \(0.485058\pi\)
\(684\) 0 0
\(685\) 477450. 0.0388778
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.22588e7 0.983781
\(690\) 0 0
\(691\) −1.63625e6 −0.130363 −0.0651816 − 0.997873i \(-0.520763\pi\)
−0.0651816 + 0.997873i \(0.520763\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4.91150e6 −0.385702
\(696\) 0 0
\(697\) 1.17872e7 0.919025
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.58303e7 −1.21673 −0.608364 − 0.793658i \(-0.708174\pi\)
−0.608364 + 0.793658i \(0.708174\pi\)
\(702\) 0 0
\(703\) −9.20444e6 −0.702440
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 756504. 0.0569197
\(708\) 0 0
\(709\) 910870. 0.0680520 0.0340260 − 0.999421i \(-0.489167\pi\)
0.0340260 + 0.999421i \(0.489167\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.82926e7 1.34757
\(714\) 0 0
\(715\) −2.72720e6 −0.199504
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.52246e7 −1.09831 −0.549155 − 0.835721i \(-0.685050\pi\)
−0.549155 + 0.835721i \(0.685050\pi\)
\(720\) 0 0
\(721\) 463632. 0.0332151
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.59375e6 0.183267
\(726\) 0 0
\(727\) −1.81793e7 −1.27567 −0.637837 − 0.770171i \(-0.720171\pi\)
−0.637837 + 0.770171i \(0.720171\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.74890e7 −3.28700
\(732\) 0 0
\(733\) 2.08512e7 1.43341 0.716707 − 0.697374i \(-0.245648\pi\)
0.716707 + 0.697374i \(0.245648\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.47706e6 0.100168
\(738\) 0 0
\(739\) 2.12513e7 1.43144 0.715722 − 0.698385i \(-0.246098\pi\)
0.715722 + 0.698385i \(0.246098\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 7.12262e6 0.473334 0.236667 − 0.971591i \(-0.423945\pi\)
0.236667 + 0.971591i \(0.423945\pi\)
\(744\) 0 0
\(745\) 9.06775e6 0.598562
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 830736. 0.0541076
\(750\) 0 0
\(751\) 1.00277e7 0.648785 0.324393 − 0.945923i \(-0.394840\pi\)
0.324393 + 0.945923i \(0.394840\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.90180e6 −0.121422
\(756\) 0 0
\(757\) −2.18303e7 −1.38459 −0.692294 − 0.721616i \(-0.743400\pi\)
−0.692294 + 0.721616i \(0.743400\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.56780e7 −1.60731 −0.803655 − 0.595096i \(-0.797114\pi\)
−0.803655 + 0.595096i \(0.797114\pi\)
\(762\) 0 0
\(763\) −619080. −0.0384978
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.48565e7 1.52564
\(768\) 0 0
\(769\) 5.81453e6 0.354567 0.177284 − 0.984160i \(-0.443269\pi\)
0.177284 + 0.984160i \(0.443269\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.55507e7 −0.936057 −0.468029 − 0.883713i \(-0.655036\pi\)
−0.468029 + 0.883713i \(0.655036\pi\)
\(774\) 0 0
\(775\) 3.55500e6 0.212611
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7.67084e6 0.452897
\(780\) 0 0
\(781\) −4.02842e6 −0.236323
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 6.31805e6 0.365939
\(786\) 0 0
\(787\) −2.35987e7 −1.35816 −0.679079 − 0.734065i \(-0.737621\pi\)
−0.679079 + 0.734065i \(0.737621\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 242472. 0.0137791
\(792\) 0 0
\(793\) −1.14757e7 −0.648030
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.01127e7 1.12157 0.560783 − 0.827963i \(-0.310500\pi\)
0.560783 + 0.827963i \(0.310500\pi\)
\(798\) 0 0
\(799\) 802976. 0.0444975
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 8.19683e6 0.448598
\(804\) 0 0
\(805\) −964800. −0.0524744
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 4.24111e6 0.227829 0.113914 − 0.993491i \(-0.463661\pi\)
0.113914 + 0.993491i \(0.463661\pi\)
\(810\) 0 0
\(811\) −6.04321e6 −0.322638 −0.161319 − 0.986902i \(-0.551575\pi\)
−0.161319 + 0.986902i \(0.551575\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −2.14790e6 −0.113271
\(816\) 0 0
\(817\) −3.09049e7 −1.61984
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.66230e7 −0.860702 −0.430351 − 0.902662i \(-0.641610\pi\)
−0.430351 + 0.902662i \(0.641610\pi\)
\(822\) 0 0
\(823\) 2.59172e7 1.33380 0.666898 − 0.745149i \(-0.267622\pi\)
0.666898 + 0.745149i \(0.267622\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.67704e7 0.852668 0.426334 − 0.904566i \(-0.359805\pi\)
0.426334 + 0.904566i \(0.359805\pi\)
\(828\) 0 0
\(829\) 6.15999e6 0.311310 0.155655 − 0.987811i \(-0.450251\pi\)
0.155655 + 0.987811i \(0.450251\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.63587e7 1.81550
\(834\) 0 0
\(835\) 7.90680e6 0.392450
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.80172e6 0.137410 0.0687052 − 0.997637i \(-0.478113\pi\)
0.0687052 + 0.997637i \(0.478113\pi\)
\(840\) 0 0
\(841\) −3.28865e6 −0.160335
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.44346e7 0.695444
\(846\) 0 0
\(847\) 1.78208e6 0.0853532
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.08461e7 0.986736
\(852\) 0 0
\(853\) 2.54991e7 1.19992 0.599960 − 0.800030i \(-0.295183\pi\)
0.599960 + 0.800030i \(0.295183\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.19499e7 0.555794 0.277897 − 0.960611i \(-0.410363\pi\)
0.277897 + 0.960611i \(0.410363\pi\)
\(858\) 0 0
\(859\) 1.01568e7 0.469651 0.234825 − 0.972038i \(-0.424548\pi\)
0.234825 + 0.972038i \(0.424548\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 3.66497e7 1.67511 0.837556 − 0.546351i \(-0.183984\pi\)
0.837556 + 0.546351i \(0.183984\pi\)
\(864\) 0 0
\(865\) 1.49384e7 0.678832
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 5.87328e6 0.263834
\(870\) 0 0
\(871\) −1.28451e7 −0.573710
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −187500. −0.00827906
\(876\) 0 0
\(877\) −8.08232e6 −0.354844 −0.177422 − 0.984135i \(-0.556776\pi\)
−0.177422 + 0.984135i \(0.556776\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −288202. −0.0125100 −0.00625500 − 0.999980i \(-0.501991\pi\)
−0.00625500 + 0.999980i \(0.501991\pi\)
\(882\) 0 0
\(883\) −6.20688e6 −0.267899 −0.133950 − 0.990988i \(-0.542766\pi\)
−0.133950 + 0.990988i \(0.542766\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.49976e7 −0.640050 −0.320025 − 0.947409i \(-0.603691\pi\)
−0.320025 + 0.947409i \(0.603691\pi\)
\(888\) 0 0
\(889\) −2.38690e6 −0.101293
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 522560. 0.0219284
\(894\) 0 0
\(895\) −7.06700e6 −0.294902
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 2.36052e7 0.974111
\(900\) 0 0
\(901\) 2.74627e7 1.12702
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −7.36645e6 −0.298976
\(906\) 0 0
\(907\) 3.92150e7 1.58283 0.791415 − 0.611279i \(-0.209345\pi\)
0.791415 + 0.611279i \(0.209345\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −3.72997e7 −1.48905 −0.744526 − 0.667594i \(-0.767324\pi\)
−0.744526 + 0.667594i \(0.767324\pi\)
\(912\) 0 0
\(913\) 7.73203e6 0.306985
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.80806e6 −0.0710052
\(918\) 0 0
\(919\) −5.78776e6 −0.226059 −0.113029 − 0.993592i \(-0.536055\pi\)
−0.113029 + 0.993592i \(0.536055\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 3.50328e7 1.35354
\(924\) 0 0
\(925\) 4.05125e6 0.155681
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.62700e7 −0.618513 −0.309256 − 0.950979i \(-0.600080\pi\)
−0.309256 + 0.950979i \(0.600080\pi\)
\(930\) 0 0
\(931\) 2.36615e7 0.894679
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −6.10960e6 −0.228551
\(936\) 0 0
\(937\) −1.20396e7 −0.447983 −0.223992 − 0.974591i \(-0.571909\pi\)
−0.223992 + 0.974591i \(0.571909\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −3.10171e7 −1.14190 −0.570949 − 0.820985i \(-0.693425\pi\)
−0.570949 + 0.820985i \(0.693425\pi\)
\(942\) 0 0
\(943\) −1.73728e7 −0.636197
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.27325e6 0.118605 0.0593027 − 0.998240i \(-0.481112\pi\)
0.0593027 + 0.998240i \(0.481112\pi\)
\(948\) 0 0
\(949\) −7.12832e7 −2.56934
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2.62021e7 0.934552 0.467276 − 0.884112i \(-0.345235\pi\)
0.467276 + 0.884112i \(0.345235\pi\)
\(954\) 0 0
\(955\) 1.80818e7 0.641554
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −229176. −0.00804679
\(960\) 0 0
\(961\) 3.72419e6 0.130084
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 2.01065e6 0.0695053
\(966\) 0 0
\(967\) 2.01481e7 0.692897 0.346449 − 0.938069i \(-0.387387\pi\)
0.346449 + 0.938069i \(0.387387\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.57046e7 −0.534537 −0.267269 − 0.963622i \(-0.586121\pi\)
−0.267269 + 0.963622i \(0.586121\pi\)
\(972\) 0 0
\(973\) 2.35752e6 0.0798313
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.84554e7 −0.953736 −0.476868 − 0.878975i \(-0.658228\pi\)
−0.476868 + 0.878975i \(0.658228\pi\)
\(978\) 0 0
\(979\) 3.79344e6 0.126496
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −7.50074e6 −0.247583 −0.123791 − 0.992308i \(-0.539505\pi\)
−0.123791 + 0.992308i \(0.539505\pi\)
\(984\) 0 0
\(985\) −1.27450e7 −0.418553
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 6.99930e7 2.27543
\(990\) 0 0
\(991\) −3.22184e7 −1.04212 −0.521062 − 0.853519i \(-0.674464\pi\)
−0.521062 + 0.853519i \(0.674464\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1.08830e7 0.348490
\(996\) 0 0
\(997\) 1.22112e7 0.389065 0.194532 − 0.980896i \(-0.437681\pi\)
0.194532 + 0.980896i \(0.437681\pi\)
\(998\) 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 720.6.a.q.1.1 1
3.2 odd 2 240.6.a.b.1.1 1
4.3 odd 2 45.6.a.a.1.1 1
12.11 even 2 15.6.a.b.1.1 ✓ 1
20.3 even 4 225.6.b.a.199.2 2
20.7 even 4 225.6.b.a.199.1 2
20.19 odd 2 225.6.a.h.1.1 1
24.5 odd 2 960.6.a.x.1.1 1
24.11 even 2 960.6.a.k.1.1 1
60.23 odd 4 75.6.b.a.49.1 2
60.47 odd 4 75.6.b.a.49.2 2
60.59 even 2 75.6.a.a.1.1 1
84.83 odd 2 735.6.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.6.a.b.1.1 ✓ 1 12.11 even 2
45.6.a.a.1.1 1 4.3 odd 2
75.6.a.a.1.1 1 60.59 even 2
75.6.b.a.49.1 2 60.23 odd 4
75.6.b.a.49.2 2 60.47 odd 4
225.6.a.h.1.1 1 20.19 odd 2
225.6.b.a.199.1 2 20.7 even 4
225.6.b.a.199.2 2 20.3 even 4
240.6.a.b.1.1 1 3.2 odd 2
720.6.a.q.1.1 1 1.1 even 1 trivial
735.6.a.b.1.1 1 84.83 odd 2
960.6.a.k.1.1 1 24.11 even 2
960.6.a.x.1.1 1 24.5 odd 2