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Properties

Label 720.6.a.m.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 30)
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)
 
\(f(q)\) \(=\) \(q+25.0000 q^{5} -164.000 q^{7} +O(q^{10})\) \(q+25.0000 q^{5} -164.000 q^{7} +720.000 q^{11} +698.000 q^{13} +2226.00 q^{17} -356.000 q^{19} -1800.00 q^{23} +625.000 q^{25} -714.000 q^{29} -848.000 q^{31} -4100.00 q^{35} -11302.0 q^{37} -9354.00 q^{41} +5956.00 q^{43} -11160.0 q^{47} +10089.0 q^{49} -14106.0 q^{53} +18000.0 q^{55} +7920.00 q^{59} -13450.0 q^{61} +17450.0 q^{65} +65476.0 q^{67} +34560.0 q^{71} +86258.0 q^{73} -118080. q^{77} +108832. q^{79} +10668.0 q^{83} +55650.0 q^{85} -10818.0 q^{89} -114472. q^{91} -8900.00 q^{95} +4418.00 q^{97} +O(q^{100})\)

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
\(7\) −164.000 −1.26502 −0.632512 − 0.774551i \(-0.717976\pi\)
−0.632512 + 0.774551i \(0.717976\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 720.000 1.79412 0.897059 − 0.441912i \(-0.145700\pi\)
0.897059 + 0.441912i \(0.145700\pi\)
\(12\) 0 0
\(13\) 698.000 1.14551 0.572753 − 0.819728i \(-0.305876\pi\)
0.572753 + 0.819728i \(0.305876\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2226.00 1.86811 0.934056 − 0.357127i \(-0.116244\pi\)
0.934056 + 0.357127i \(0.116244\pi\)
\(18\) 0 0
\(19\) −356.000 −0.226238 −0.113119 − 0.993581i \(-0.536084\pi\)
−0.113119 + 0.993581i \(0.536084\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1800.00 −0.709501 −0.354750 − 0.934961i \(-0.615434\pi\)
−0.354750 + 0.934961i \(0.615434\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −714.000 −0.157653 −0.0788267 − 0.996888i \(-0.525117\pi\)
−0.0788267 + 0.996888i \(0.525117\pi\)
\(30\) 0 0
\(31\) −848.000 −0.158486 −0.0792431 − 0.996855i \(-0.525250\pi\)
−0.0792431 + 0.996855i \(0.525250\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4100.00 −0.565736
\(36\) 0 0
\(37\) −11302.0 −1.35722 −0.678611 − 0.734498i \(-0.737418\pi\)
−0.678611 + 0.734498i \(0.737418\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −9354.00 −0.869036 −0.434518 − 0.900663i \(-0.643081\pi\)
−0.434518 + 0.900663i \(0.643081\pi\)
\(42\) 0 0
\(43\) 5956.00 0.491228 0.245614 − 0.969368i \(-0.421010\pi\)
0.245614 + 0.969368i \(0.421010\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11160.0 −0.736919 −0.368459 − 0.929644i \(-0.620115\pi\)
−0.368459 + 0.929644i \(0.620115\pi\)
\(48\) 0 0
\(49\) 10089.0 0.600286
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −14106.0 −0.689786 −0.344893 − 0.938642i \(-0.612085\pi\)
−0.344893 + 0.938642i \(0.612085\pi\)
\(54\) 0 0
\(55\) 18000.0 0.802354
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 7920.00 0.296207 0.148103 − 0.988972i \(-0.452683\pi\)
0.148103 + 0.988972i \(0.452683\pi\)
\(60\) 0 0
\(61\) −13450.0 −0.462805 −0.231402 − 0.972858i \(-0.574331\pi\)
−0.231402 + 0.972858i \(0.574331\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 17450.0 0.512285
\(66\) 0 0
\(67\) 65476.0 1.78195 0.890974 − 0.454054i \(-0.150023\pi\)
0.890974 + 0.454054i \(0.150023\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 34560.0 0.813632 0.406816 − 0.913510i \(-0.366639\pi\)
0.406816 + 0.913510i \(0.366639\pi\)
\(72\) 0 0
\(73\) 86258.0 1.89449 0.947245 − 0.320511i \(-0.103855\pi\)
0.947245 + 0.320511i \(0.103855\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −118080. −2.26960
\(78\) 0 0
\(79\) 108832. 1.96195 0.980977 − 0.194123i \(-0.0621862\pi\)
0.980977 + 0.194123i \(0.0621862\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 10668.0 0.169976 0.0849880 − 0.996382i \(-0.472915\pi\)
0.0849880 + 0.996382i \(0.472915\pi\)
\(84\) 0 0
\(85\) 55650.0 0.835445
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −10818.0 −0.144768 −0.0723839 − 0.997377i \(-0.523061\pi\)
−0.0723839 + 0.997377i \(0.523061\pi\)
\(90\) 0 0
\(91\) −114472. −1.44909
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −8900.00 −0.101177
\(96\) 0 0
\(97\) 4418.00 0.0476756 0.0238378 − 0.999716i \(-0.492411\pi\)
0.0238378 + 0.999716i \(0.492411\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 102942. 1.00413 0.502064 − 0.864830i \(-0.332574\pi\)
0.502064 + 0.864830i \(0.332574\pi\)
\(102\) 0 0
\(103\) 69436.0 0.644899 0.322449 − 0.946587i \(-0.395494\pi\)
0.322449 + 0.946587i \(0.395494\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 17412.0 0.147024 0.0735122 − 0.997294i \(-0.476579\pi\)
0.0735122 + 0.997294i \(0.476579\pi\)
\(108\) 0 0
\(109\) −203770. −1.64276 −0.821380 − 0.570382i \(-0.806795\pi\)
−0.821380 + 0.570382i \(0.806795\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 212202. 1.56334 0.781670 − 0.623692i \(-0.214368\pi\)
0.781670 + 0.623692i \(0.214368\pi\)
\(114\) 0 0
\(115\) −45000.0 −0.317298
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −365064. −2.36321
\(120\) 0 0
\(121\) 357349. 2.21886
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) −6140.00 −0.0337800 −0.0168900 − 0.999857i \(-0.505377\pi\)
−0.0168900 + 0.999857i \(0.505377\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −205920. −1.04838 −0.524192 − 0.851600i \(-0.675633\pi\)
−0.524192 + 0.851600i \(0.675633\pi\)
\(132\) 0 0
\(133\) 58384.0 0.286197
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −230334. −1.04847 −0.524236 − 0.851573i \(-0.675649\pi\)
−0.524236 + 0.851573i \(0.675649\pi\)
\(138\) 0 0
\(139\) −260756. −1.14471 −0.572357 − 0.820004i \(-0.693971\pi\)
−0.572357 + 0.820004i \(0.693971\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 502560. 2.05517
\(144\) 0 0
\(145\) −17850.0 −0.0705047
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 29526.0 0.108953 0.0544765 − 0.998515i \(-0.482651\pi\)
0.0544765 + 0.998515i \(0.482651\pi\)
\(150\) 0 0
\(151\) −125168. −0.446736 −0.223368 − 0.974734i \(-0.571705\pi\)
−0.223368 + 0.974734i \(0.571705\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −21200.0 −0.0708772
\(156\) 0 0
\(157\) −43222.0 −0.139944 −0.0699722 − 0.997549i \(-0.522291\pi\)
−0.0699722 + 0.997549i \(0.522291\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 295200. 0.897536
\(162\) 0 0
\(163\) 293476. 0.865174 0.432587 − 0.901592i \(-0.357601\pi\)
0.432587 + 0.901592i \(0.357601\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 322200. 0.893993 0.446997 − 0.894536i \(-0.352494\pi\)
0.446997 + 0.894536i \(0.352494\pi\)
\(168\) 0 0
\(169\) 115911. 0.312182
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 261918. 0.665350 0.332675 − 0.943042i \(-0.392049\pi\)
0.332675 + 0.943042i \(0.392049\pi\)
\(174\) 0 0
\(175\) −102500. −0.253005
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 623544. 1.45457 0.727285 − 0.686336i \(-0.240782\pi\)
0.727285 + 0.686336i \(0.240782\pi\)
\(180\) 0 0
\(181\) −61186.0 −0.138821 −0.0694106 − 0.997588i \(-0.522112\pi\)
−0.0694106 + 0.997588i \(0.522112\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −282550. −0.606968
\(186\) 0 0
\(187\) 1.60272e6 3.35161
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 737256. 1.46229 0.731147 − 0.682220i \(-0.238985\pi\)
0.731147 + 0.682220i \(0.238985\pi\)
\(192\) 0 0
\(193\) 539162. 1.04190 0.520950 − 0.853587i \(-0.325578\pi\)
0.520950 + 0.853587i \(0.325578\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 651174. 1.19545 0.597725 − 0.801701i \(-0.296071\pi\)
0.597725 + 0.801701i \(0.296071\pi\)
\(198\) 0 0
\(199\) −157328. −0.281626 −0.140813 − 0.990036i \(-0.544972\pi\)
−0.140813 + 0.990036i \(0.544972\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 117096. 0.199435
\(204\) 0 0
\(205\) −233850. −0.388645
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −256320. −0.405898
\(210\) 0 0
\(211\) −707180. −1.09351 −0.546756 − 0.837292i \(-0.684138\pi\)
−0.546756 + 0.837292i \(0.684138\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 148900. 0.219684
\(216\) 0 0
\(217\) 139072. 0.200489
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.55375e6 2.13993
\(222\) 0 0
\(223\) 530740. 0.714693 0.357347 − 0.933972i \(-0.383681\pi\)
0.357347 + 0.933972i \(0.383681\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 120372. 0.155046 0.0775230 − 0.996991i \(-0.475299\pi\)
0.0775230 + 0.996991i \(0.475299\pi\)
\(228\) 0 0
\(229\) 772310. 0.973202 0.486601 − 0.873624i \(-0.338237\pi\)
0.486601 + 0.873624i \(0.338237\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8838.00 −0.0106651 −0.00533254 − 0.999986i \(-0.501697\pi\)
−0.00533254 + 0.999986i \(0.501697\pi\)
\(234\) 0 0
\(235\) −279000. −0.329560
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −775416. −0.878092 −0.439046 − 0.898465i \(-0.644683\pi\)
−0.439046 + 0.898465i \(0.644683\pi\)
\(240\) 0 0
\(241\) −373438. −0.414167 −0.207084 − 0.978323i \(-0.566397\pi\)
−0.207084 + 0.978323i \(0.566397\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 252225. 0.268456
\(246\) 0 0
\(247\) −248488. −0.259157
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 71976.0 0.0721113 0.0360557 − 0.999350i \(-0.488521\pi\)
0.0360557 + 0.999350i \(0.488521\pi\)
\(252\) 0 0
\(253\) −1.29600e6 −1.27293
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.59356e6 −1.50500 −0.752498 − 0.658595i \(-0.771151\pi\)
−0.752498 + 0.658595i \(0.771151\pi\)
\(258\) 0 0
\(259\) 1.85353e6 1.71692
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.05452e6 −1.83156 −0.915780 − 0.401681i \(-0.868426\pi\)
−0.915780 + 0.401681i \(0.868426\pi\)
\(264\) 0 0
\(265\) −352650. −0.308482
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 258486. 0.217799 0.108900 − 0.994053i \(-0.465267\pi\)
0.108900 + 0.994053i \(0.465267\pi\)
\(270\) 0 0
\(271\) 1.98398e6 1.64102 0.820509 − 0.571634i \(-0.193690\pi\)
0.820509 + 0.571634i \(0.193690\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 450000. 0.358823
\(276\) 0 0
\(277\) 1.61326e6 1.26329 0.631647 − 0.775256i \(-0.282379\pi\)
0.631647 + 0.775256i \(0.282379\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.37882e6 −1.04170 −0.520848 − 0.853649i \(-0.674384\pi\)
−0.520848 + 0.853649i \(0.674384\pi\)
\(282\) 0 0
\(283\) −1.45831e6 −1.08239 −0.541194 − 0.840898i \(-0.682028\pi\)
−0.541194 + 0.840898i \(0.682028\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.53406e6 1.09935
\(288\) 0 0
\(289\) 3.53522e6 2.48984
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 988134. 0.672430 0.336215 − 0.941785i \(-0.390853\pi\)
0.336215 + 0.941785i \(0.390853\pi\)
\(294\) 0 0
\(295\) 198000. 0.132468
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.25640e6 −0.812737
\(300\) 0 0
\(301\) −976784. −0.621416
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −336250. −0.206973
\(306\) 0 0
\(307\) 393820. 0.238480 0.119240 − 0.992865i \(-0.461954\pi\)
0.119240 + 0.992865i \(0.461954\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.55448e6 0.911348 0.455674 − 0.890147i \(-0.349398\pi\)
0.455674 + 0.890147i \(0.349398\pi\)
\(312\) 0 0
\(313\) 1.76050e6 1.01572 0.507861 − 0.861439i \(-0.330436\pi\)
0.507861 + 0.861439i \(0.330436\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.37112e6 −1.32527 −0.662637 − 0.748941i \(-0.730563\pi\)
−0.662637 + 0.748941i \(0.730563\pi\)
\(318\) 0 0
\(319\) −514080. −0.282849
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −792456. −0.422638
\(324\) 0 0
\(325\) 436250. 0.229101
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.83024e6 0.932220
\(330\) 0 0
\(331\) 980068. 0.491684 0.245842 − 0.969310i \(-0.420936\pi\)
0.245842 + 0.969310i \(0.420936\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.63690e6 0.796912
\(336\) 0 0
\(337\) 905834. 0.434484 0.217242 − 0.976118i \(-0.430294\pi\)
0.217242 + 0.976118i \(0.430294\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −610560. −0.284343
\(342\) 0 0
\(343\) 1.10175e6 0.505648
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.95069e6 −1.31553 −0.657764 − 0.753224i \(-0.728498\pi\)
−0.657764 + 0.753224i \(0.728498\pi\)
\(348\) 0 0
\(349\) −2.15761e6 −0.948221 −0.474110 − 0.880465i \(-0.657230\pi\)
−0.474110 + 0.880465i \(0.657230\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.28873e6 −0.550461 −0.275230 − 0.961378i \(-0.588754\pi\)
−0.275230 + 0.961378i \(0.588754\pi\)
\(354\) 0 0
\(355\) 864000. 0.363867
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.26946e6 −0.929367 −0.464683 − 0.885477i \(-0.653832\pi\)
−0.464683 + 0.885477i \(0.653832\pi\)
\(360\) 0 0
\(361\) −2.34936e6 −0.948816
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.15645e6 0.847242
\(366\) 0 0
\(367\) −1.04659e6 −0.405612 −0.202806 − 0.979219i \(-0.565006\pi\)
−0.202806 + 0.979219i \(0.565006\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2.31338e6 0.872595
\(372\) 0 0
\(373\) 1.79827e6 0.669243 0.334621 − 0.942353i \(-0.391392\pi\)
0.334621 + 0.942353i \(0.391392\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −498372. −0.180593
\(378\) 0 0
\(379\) 2.18412e6 0.781051 0.390525 − 0.920592i \(-0.372293\pi\)
0.390525 + 0.920592i \(0.372293\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.78452e6 0.621619 0.310810 − 0.950472i \(-0.399400\pi\)
0.310810 + 0.950472i \(0.399400\pi\)
\(384\) 0 0
\(385\) −2.95200e6 −1.01500
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1.10953e6 0.371761 0.185880 − 0.982572i \(-0.440486\pi\)
0.185880 + 0.982572i \(0.440486\pi\)
\(390\) 0 0
\(391\) −4.00680e6 −1.32543
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.72080e6 0.877413
\(396\) 0 0
\(397\) 3.89568e6 1.24053 0.620265 − 0.784392i \(-0.287025\pi\)
0.620265 + 0.784392i \(0.287025\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.20673e6 0.374755 0.187378 − 0.982288i \(-0.440001\pi\)
0.187378 + 0.982288i \(0.440001\pi\)
\(402\) 0 0
\(403\) −591904. −0.181547
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −8.13744e6 −2.43502
\(408\) 0 0
\(409\) 5.61363e6 1.65934 0.829670 − 0.558255i \(-0.188529\pi\)
0.829670 + 0.558255i \(0.188529\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.29888e6 −0.374709
\(414\) 0 0
\(415\) 266700. 0.0760156
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.15056e6 0.320165 0.160083 − 0.987104i \(-0.448824\pi\)
0.160083 + 0.987104i \(0.448824\pi\)
\(420\) 0 0
\(421\) −3.83089e6 −1.05340 −0.526701 − 0.850050i \(-0.676571\pi\)
−0.526701 + 0.850050i \(0.676571\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.39125e6 0.373622
\(426\) 0 0
\(427\) 2.20580e6 0.585459
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 155520. 0.0403267 0.0201634 − 0.999797i \(-0.493581\pi\)
0.0201634 + 0.999797i \(0.493581\pi\)
\(432\) 0 0
\(433\) 4.14391e6 1.06216 0.531081 − 0.847321i \(-0.321786\pi\)
0.531081 + 0.847321i \(0.321786\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 640800. 0.160516
\(438\) 0 0
\(439\) −6.23653e6 −1.54448 −0.772239 − 0.635332i \(-0.780863\pi\)
−0.772239 + 0.635332i \(0.780863\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.52507e6 1.09551 0.547754 − 0.836639i \(-0.315483\pi\)
0.547754 + 0.836639i \(0.315483\pi\)
\(444\) 0 0
\(445\) −270450. −0.0647421
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.56463e6 −0.600357 −0.300178 − 0.953883i \(-0.597046\pi\)
−0.300178 + 0.953883i \(0.597046\pi\)
\(450\) 0 0
\(451\) −6.73488e6 −1.55915
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.86180e6 −0.648053
\(456\) 0 0
\(457\) −5.53409e6 −1.23953 −0.619763 − 0.784789i \(-0.712771\pi\)
−0.619763 + 0.784789i \(0.712771\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 7.19211e6 1.57617 0.788087 − 0.615564i \(-0.211072\pi\)
0.788087 + 0.615564i \(0.211072\pi\)
\(462\) 0 0
\(463\) 1.13936e6 0.247006 0.123503 − 0.992344i \(-0.460587\pi\)
0.123503 + 0.992344i \(0.460587\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.36168e6 1.56201 0.781006 − 0.624523i \(-0.214707\pi\)
0.781006 + 0.624523i \(0.214707\pi\)
\(468\) 0 0
\(469\) −1.07381e7 −2.25421
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.28832e6 0.881321
\(474\) 0 0
\(475\) −222500. −0.0452476
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1.36226e6 −0.271283 −0.135641 − 0.990758i \(-0.543310\pi\)
−0.135641 + 0.990758i \(0.543310\pi\)
\(480\) 0 0
\(481\) −7.88880e6 −1.55471
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 110450. 0.0213212
\(486\) 0 0
\(487\) −606428. −0.115866 −0.0579331 − 0.998320i \(-0.518451\pi\)
−0.0579331 + 0.998320i \(0.518451\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5.84278e6 −1.09374 −0.546872 − 0.837216i \(-0.684181\pi\)
−0.546872 + 0.837216i \(0.684181\pi\)
\(492\) 0 0
\(493\) −1.58936e6 −0.294514
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.66784e6 −1.02926
\(498\) 0 0
\(499\) 1.15044e6 0.206830 0.103415 − 0.994638i \(-0.467023\pi\)
0.103415 + 0.994638i \(0.467023\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −869664. −0.153261 −0.0766305 − 0.997060i \(-0.524416\pi\)
−0.0766305 + 0.997060i \(0.524416\pi\)
\(504\) 0 0
\(505\) 2.57355e6 0.449060
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.43495e6 −0.245495 −0.122748 − 0.992438i \(-0.539171\pi\)
−0.122748 + 0.992438i \(0.539171\pi\)
\(510\) 0 0
\(511\) −1.41463e7 −2.39657
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.73590e6 0.288408
\(516\) 0 0
\(517\) −8.03520e6 −1.32212
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.04371e7 −1.68456 −0.842281 − 0.539038i \(-0.818788\pi\)
−0.842281 + 0.539038i \(0.818788\pi\)
\(522\) 0 0
\(523\) 7.75942e6 1.24044 0.620219 − 0.784429i \(-0.287044\pi\)
0.620219 + 0.784429i \(0.287044\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.88765e6 −0.296070
\(528\) 0 0
\(529\) −3.19634e6 −0.496609
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −6.52909e6 −0.995485
\(534\) 0 0
\(535\) 435300. 0.0657513
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 7.26408e6 1.07698
\(540\) 0 0
\(541\) −1.10233e6 −0.161927 −0.0809633 − 0.996717i \(-0.525800\pi\)
−0.0809633 + 0.996717i \(0.525800\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5.09425e6 −0.734664
\(546\) 0 0
\(547\) −2.48263e6 −0.354767 −0.177384 − 0.984142i \(-0.556763\pi\)
−0.177384 + 0.984142i \(0.556763\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 254184. 0.0356672
\(552\) 0 0
\(553\) −1.78484e7 −2.48192
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.73568e6 −0.783334 −0.391667 − 0.920107i \(-0.628102\pi\)
−0.391667 + 0.920107i \(0.628102\pi\)
\(558\) 0 0
\(559\) 4.15729e6 0.562705
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 517092. 0.0687538 0.0343769 − 0.999409i \(-0.489055\pi\)
0.0343769 + 0.999409i \(0.489055\pi\)
\(564\) 0 0
\(565\) 5.30505e6 0.699147
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 6.72766e6 0.871131 0.435566 − 0.900157i \(-0.356548\pi\)
0.435566 + 0.900157i \(0.356548\pi\)
\(570\) 0 0
\(571\) 1.03290e7 1.32577 0.662883 − 0.748723i \(-0.269332\pi\)
0.662883 + 0.748723i \(0.269332\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.12500e6 −0.141900
\(576\) 0 0
\(577\) 9.25834e6 1.15769 0.578847 − 0.815436i \(-0.303503\pi\)
0.578847 + 0.815436i \(0.303503\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.74955e6 −0.215024
\(582\) 0 0
\(583\) −1.01563e7 −1.23756
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −9.57155e6 −1.14653 −0.573267 − 0.819369i \(-0.694324\pi\)
−0.573267 + 0.819369i \(0.694324\pi\)
\(588\) 0 0
\(589\) 301888. 0.0358557
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.12388e7 1.31245 0.656226 − 0.754564i \(-0.272152\pi\)
0.656226 + 0.754564i \(0.272152\pi\)
\(594\) 0 0
\(595\) −9.12660e6 −1.05686
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 3.72670e6 0.424382 0.212191 − 0.977228i \(-0.431940\pi\)
0.212191 + 0.977228i \(0.431940\pi\)
\(600\) 0 0
\(601\) 6.74734e6 0.761985 0.380992 − 0.924578i \(-0.375582\pi\)
0.380992 + 0.924578i \(0.375582\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 8.93372e6 0.992303
\(606\) 0 0
\(607\) 6.83384e6 0.752823 0.376411 − 0.926453i \(-0.377158\pi\)
0.376411 + 0.926453i \(0.377158\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −7.78968e6 −0.844144
\(612\) 0 0
\(613\) −433222. −0.0465650 −0.0232825 − 0.999729i \(-0.507412\pi\)
−0.0232825 + 0.999729i \(0.507412\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.17569e6 0.547338 0.273669 − 0.961824i \(-0.411763\pi\)
0.273669 + 0.961824i \(0.411763\pi\)
\(618\) 0 0
\(619\) 151996. 0.0159443 0.00797215 − 0.999968i \(-0.497462\pi\)
0.00797215 + 0.999968i \(0.497462\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.77415e6 0.183135
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.51583e7 −2.53544
\(630\) 0 0
\(631\) −1.05635e7 −1.05617 −0.528086 − 0.849191i \(-0.677090\pi\)
−0.528086 + 0.849191i \(0.677090\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −153500. −0.0151069
\(636\) 0 0
\(637\) 7.04212e6 0.687630
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5.53755e6 0.532320 0.266160 − 0.963929i \(-0.414245\pi\)
0.266160 + 0.963929i \(0.414245\pi\)
\(642\) 0 0
\(643\) −8.89132e6 −0.848084 −0.424042 − 0.905642i \(-0.639389\pi\)
−0.424042 + 0.905642i \(0.639389\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.29474e6 0.215512 0.107756 − 0.994177i \(-0.465633\pi\)
0.107756 + 0.994177i \(0.465633\pi\)
\(648\) 0 0
\(649\) 5.70240e6 0.531430
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.36338e7 1.25122 0.625608 − 0.780137i \(-0.284851\pi\)
0.625608 + 0.780137i \(0.284851\pi\)
\(654\) 0 0
\(655\) −5.14800e6 −0.468851
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.31234e7 −1.17715 −0.588576 − 0.808442i \(-0.700311\pi\)
−0.588576 + 0.808442i \(0.700311\pi\)
\(660\) 0 0
\(661\) 1.78522e7 1.58923 0.794616 − 0.607112i \(-0.207672\pi\)
0.794616 + 0.607112i \(0.207672\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.45960e6 0.127991
\(666\) 0 0
\(667\) 1.28520e6 0.111855
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −9.68400e6 −0.830326
\(672\) 0 0
\(673\) 1.32471e7 1.12741 0.563707 − 0.825975i \(-0.309375\pi\)
0.563707 + 0.825975i \(0.309375\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.04491e7 −0.876205 −0.438103 − 0.898925i \(-0.644349\pi\)
−0.438103 + 0.898925i \(0.644349\pi\)
\(678\) 0 0
\(679\) −724552. −0.0603108
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −613308. −0.0503068 −0.0251534 − 0.999684i \(-0.508007\pi\)
−0.0251534 + 0.999684i \(0.508007\pi\)
\(684\) 0 0
\(685\) −5.75835e6 −0.468891
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −9.84599e6 −0.790153
\(690\) 0 0
\(691\) 2.13992e7 1.70491 0.852457 − 0.522798i \(-0.175112\pi\)
0.852457 + 0.522798i \(0.175112\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −6.51890e6 −0.511932
\(696\) 0 0
\(697\) −2.08220e7 −1.62346
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.09778e7 −0.843765 −0.421883 − 0.906650i \(-0.638631\pi\)
−0.421883 + 0.906650i \(0.638631\pi\)
\(702\) 0 0
\(703\) 4.02351e6 0.307056
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.68825e7 −1.27025
\(708\) 0 0
\(709\) 1.69732e6 0.126808 0.0634041 − 0.997988i \(-0.479804\pi\)
0.0634041 + 0.997988i \(0.479804\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.52640e6 0.112446
\(714\) 0 0
\(715\) 1.25640e7 0.919100
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 3.71304e6 0.267860 0.133930 − 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(720\) 0 0
\(721\) −1.13875e7 −0.815813
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −446250. −0.0315307
\(726\) 0 0
\(727\) −1.38067e6 −0.0968843 −0.0484421 − 0.998826i \(-0.515426\pi\)
−0.0484421 + 0.998826i \(0.515426\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.32581e7 0.917670
\(732\) 0 0
\(733\) 1.38156e7 0.949751 0.474876 − 0.880053i \(-0.342493\pi\)
0.474876 + 0.880053i \(0.342493\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.71427e7 3.19702
\(738\) 0 0
\(739\) −4.59463e6 −0.309485 −0.154742 − 0.987955i \(-0.549455\pi\)
−0.154742 + 0.987955i \(0.549455\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 8.51174e6 0.565648 0.282824 − 0.959172i \(-0.408729\pi\)
0.282824 + 0.959172i \(0.408729\pi\)
\(744\) 0 0
\(745\) 738150. 0.0487252
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2.85557e6 −0.185989
\(750\) 0 0
\(751\) −1.71224e7 −1.10781 −0.553904 − 0.832580i \(-0.686863\pi\)
−0.553904 + 0.832580i \(0.686863\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −3.12920e6 −0.199786
\(756\) 0 0
\(757\) −1.22018e6 −0.0773900 −0.0386950 − 0.999251i \(-0.512320\pi\)
−0.0386950 + 0.999251i \(0.512320\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.20327e7 −0.753182 −0.376591 − 0.926380i \(-0.622904\pi\)
−0.376591 + 0.926380i \(0.622904\pi\)
\(762\) 0 0
\(763\) 3.34183e7 2.07813
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5.52816e6 0.339307
\(768\) 0 0
\(769\) −1.88952e7 −1.15222 −0.576110 − 0.817372i \(-0.695430\pi\)
−0.576110 + 0.817372i \(0.695430\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.72115e7 −1.03602 −0.518012 − 0.855373i \(-0.673328\pi\)
−0.518012 + 0.855373i \(0.673328\pi\)
\(774\) 0 0
\(775\) −530000. −0.0316973
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.33002e6 0.196609
\(780\) 0 0
\(781\) 2.48832e7 1.45975
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.08055e6 −0.0625851
\(786\) 0 0
\(787\) −1.32970e7 −0.765274 −0.382637 − 0.923899i \(-0.624984\pi\)
−0.382637 + 0.923899i \(0.624984\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3.48011e7 −1.97766
\(792\) 0 0
\(793\) −9.38810e6 −0.530145
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.15632e7 −1.20245 −0.601227 − 0.799078i \(-0.705321\pi\)
−0.601227 + 0.799078i \(0.705321\pi\)
\(798\) 0 0
\(799\) −2.48422e7 −1.37665
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 6.21058e7 3.39894
\(804\) 0 0
\(805\) 7.38000e6 0.401390
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −2.65355e7 −1.42547 −0.712733 − 0.701436i \(-0.752543\pi\)
−0.712733 + 0.701436i \(0.752543\pi\)
\(810\) 0 0
\(811\) 1.40015e7 0.747518 0.373759 − 0.927526i \(-0.378069\pi\)
0.373759 + 0.927526i \(0.378069\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 7.33690e6 0.386918
\(816\) 0 0
\(817\) −2.12034e6 −0.111135
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.32286e7 −0.684944 −0.342472 − 0.939528i \(-0.611264\pi\)
−0.342472 + 0.939528i \(0.611264\pi\)
\(822\) 0 0
\(823\) 7.25818e6 0.373532 0.186766 − 0.982404i \(-0.440199\pi\)
0.186766 + 0.982404i \(0.440199\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.84527e7 0.938204 0.469102 − 0.883144i \(-0.344578\pi\)
0.469102 + 0.883144i \(0.344578\pi\)
\(828\) 0 0
\(829\) −2.43640e7 −1.23130 −0.615649 − 0.788021i \(-0.711106\pi\)
−0.615649 + 0.788021i \(0.711106\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.24581e7 1.12140
\(834\) 0 0
\(835\) 8.05500e6 0.399806
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −1.55793e7 −0.764089 −0.382045 − 0.924144i \(-0.624780\pi\)
−0.382045 + 0.924144i \(0.624780\pi\)
\(840\) 0 0
\(841\) −2.00014e7 −0.975145
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.89777e6 0.139612
\(846\) 0 0
\(847\) −5.86052e7 −2.80691
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.03436e7 0.962950
\(852\) 0 0
\(853\) 3.08062e7 1.44966 0.724829 − 0.688929i \(-0.241919\pi\)
0.724829 + 0.688929i \(0.241919\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2.02084e6 0.0939897 0.0469949 − 0.998895i \(-0.485036\pi\)
0.0469949 + 0.998895i \(0.485036\pi\)
\(858\) 0 0
\(859\) 2.24790e7 1.03943 0.519714 − 0.854340i \(-0.326039\pi\)
0.519714 + 0.854340i \(0.326039\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −9.20942e6 −0.420926 −0.210463 − 0.977602i \(-0.567497\pi\)
−0.210463 + 0.977602i \(0.567497\pi\)
\(864\) 0 0
\(865\) 6.54795e6 0.297554
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 7.83590e7 3.51998
\(870\) 0 0
\(871\) 4.57022e7 2.04123
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2.56250e6 −0.113147
\(876\) 0 0
\(877\) −5.36258e6 −0.235437 −0.117719 − 0.993047i \(-0.537558\pi\)
−0.117719 + 0.993047i \(0.537558\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.38347e7 −0.600525 −0.300263 − 0.953857i \(-0.597074\pi\)
−0.300263 + 0.953857i \(0.597074\pi\)
\(882\) 0 0
\(883\) 1.66004e6 0.0716499 0.0358250 − 0.999358i \(-0.488594\pi\)
0.0358250 + 0.999358i \(0.488594\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −8.10612e6 −0.345943 −0.172971 − 0.984927i \(-0.555337\pi\)
−0.172971 + 0.984927i \(0.555337\pi\)
\(888\) 0 0
\(889\) 1.00696e6 0.0427325
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 3.97296e6 0.166719
\(894\) 0 0
\(895\) 1.55886e7 0.650503
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 605472. 0.0249859
\(900\) 0 0
\(901\) −3.14000e7 −1.28860
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.52965e6 −0.0620827
\(906\) 0 0
\(907\) −4.05360e6 −0.163615 −0.0818073 − 0.996648i \(-0.526069\pi\)
−0.0818073 + 0.996648i \(0.526069\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −1.38233e7 −0.551844 −0.275922 − 0.961180i \(-0.588983\pi\)
−0.275922 + 0.961180i \(0.588983\pi\)
\(912\) 0 0
\(913\) 7.68096e6 0.304957
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.37709e7 1.32623
\(918\) 0 0
\(919\) 3.78443e7 1.47813 0.739063 − 0.673636i \(-0.235268\pi\)
0.739063 + 0.673636i \(0.235268\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.41229e7 0.932019
\(924\) 0 0
\(925\) −7.06375e6 −0.271444
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2.72822e7 1.03715 0.518574 − 0.855033i \(-0.326463\pi\)
0.518574 + 0.855033i \(0.326463\pi\)
\(930\) 0 0
\(931\) −3.59168e6 −0.135808
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 4.00680e7 1.49889
\(936\) 0 0
\(937\) 4.32666e7 1.60992 0.804958 − 0.593332i \(-0.202188\pi\)
0.804958 + 0.593332i \(0.202188\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −8.50106e6 −0.312967 −0.156484 − 0.987681i \(-0.550016\pi\)
−0.156484 + 0.987681i \(0.550016\pi\)
\(942\) 0 0
\(943\) 1.68372e7 0.616582
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 7.10456e6 0.257432 0.128716 − 0.991681i \(-0.458914\pi\)
0.128716 + 0.991681i \(0.458914\pi\)
\(948\) 0 0
\(949\) 6.02081e7 2.17015
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 5.39741e7 1.92510 0.962551 − 0.271102i \(-0.0873882\pi\)
0.962551 + 0.271102i \(0.0873882\pi\)
\(954\) 0 0
\(955\) 1.84314e7 0.653958
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 3.77748e7 1.32634
\(960\) 0 0
\(961\) −2.79100e7 −0.974882
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.34790e7 0.465952
\(966\) 0 0
\(967\) −3.64583e7 −1.25381 −0.626903 − 0.779097i \(-0.715678\pi\)
−0.626903 + 0.779097i \(0.715678\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −5.20286e7 −1.77090 −0.885450 − 0.464734i \(-0.846150\pi\)
−0.885450 + 0.464734i \(0.846150\pi\)
\(972\) 0 0
\(973\) 4.27640e7 1.44809
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −127902. −0.00428688 −0.00214344 − 0.999998i \(-0.500682\pi\)
−0.00214344 + 0.999998i \(0.500682\pi\)
\(978\) 0 0
\(979\) −7.78896e6 −0.259730
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1.57667e7 −0.520422 −0.260211 − 0.965552i \(-0.583792\pi\)
−0.260211 + 0.965552i \(0.583792\pi\)
\(984\) 0 0
\(985\) 1.62794e7 0.534622
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.07208e7 −0.348527
\(990\) 0 0
\(991\) −2.99415e7 −0.968479 −0.484239 − 0.874936i \(-0.660904\pi\)
−0.484239 + 0.874936i \(0.660904\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −3.93320e6 −0.125947
\(996\) 0 0
\(997\) −5.07440e7 −1.61676 −0.808382 − 0.588659i \(-0.799656\pi\)
−0.808382 + 0.588659i \(0.799656\pi\)
\(998\) 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.m.1.1 1
3.2 odd 2 240.6.a.a.1.1 1
4.3 odd 2 90.6.a.g.1.1 1
12.11 even 2 30.6.a.a.1.1 ✓ 1
20.3 even 4 450.6.c.b.199.1 2
20.7 even 4 450.6.c.b.199.2 2
20.19 odd 2 450.6.a.b.1.1 1
24.5 odd 2 960.6.a.u.1.1 1
24.11 even 2 960.6.a.n.1.1 1
60.23 odd 4 150.6.c.d.49.2 2
60.47 odd 4 150.6.c.d.49.1 2
60.59 even 2 150.6.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
30.6.a.a.1.1 ✓ 1 12.11 even 2
90.6.a.g.1.1 1 4.3 odd 2
150.6.a.h.1.1 1 60.59 even 2
150.6.c.d.49.1 2 60.47 odd 4
150.6.c.d.49.2 2 60.23 odd 4
240.6.a.a.1.1 1 3.2 odd 2
450.6.a.b.1.1 1 20.19 odd 2
450.6.c.b.199.1 2 20.3 even 4
450.6.c.b.199.2 2 20.7 even 4
720.6.a.m.1.1 1 1.1 even 1 trivial
960.6.a.n.1.1 1 24.11 even 2
960.6.a.u.1.1 1 24.5 odd 2