Properties

Label 720.6.a.j.1.1
Level $720$
Weight $6$
Character 720.1
Self dual yes
Analytic conductor $115.476$
Analytic rank $1$
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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 10)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-25.0000 q^{5} +172.000 q^{7} +O(q^{10})\) \(q-25.0000 q^{5} +172.000 q^{7} +132.000 q^{11} -946.000 q^{13} +222.000 q^{17} -500.000 q^{19} +3564.00 q^{23} +625.000 q^{25} -2190.00 q^{29} -2312.00 q^{31} -4300.00 q^{35} -11242.0 q^{37} -1242.00 q^{41} -20624.0 q^{43} +6588.00 q^{47} +12777.0 q^{49} +21066.0 q^{53} -3300.00 q^{55} +7980.00 q^{59} +16622.0 q^{61} +23650.0 q^{65} -1808.00 q^{67} -24528.0 q^{71} +20474.0 q^{73} +22704.0 q^{77} +46240.0 q^{79} -51576.0 q^{83} -5550.00 q^{85} +110310. q^{89} -162712. q^{91} +12500.0 q^{95} -78382.0 q^{97} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −25.0000 −0.447214
\(6\) 0 0
\(7\) 172.000 1.32673 0.663366 0.748295i \(-0.269127\pi\)
0.663366 + 0.748295i \(0.269127\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 132.000 0.328921 0.164461 0.986384i \(-0.447412\pi\)
0.164461 + 0.986384i \(0.447412\pi\)
\(12\) 0 0
\(13\) −946.000 −1.55250 −0.776252 0.630423i \(-0.782882\pi\)
−0.776252 + 0.630423i \(0.782882\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 222.000 0.186308 0.0931538 0.995652i \(-0.470305\pi\)
0.0931538 + 0.995652i \(0.470305\pi\)
\(18\) 0 0
\(19\) −500.000 −0.317750 −0.158875 0.987299i \(-0.550787\pi\)
−0.158875 + 0.987299i \(0.550787\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3564.00 1.40481 0.702406 0.711777i \(-0.252109\pi\)
0.702406 + 0.711777i \(0.252109\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2190.00 −0.483559 −0.241779 0.970331i \(-0.577731\pi\)
−0.241779 + 0.970331i \(0.577731\pi\)
\(30\) 0 0
\(31\) −2312.00 −0.432099 −0.216050 0.976382i \(-0.569317\pi\)
−0.216050 + 0.976382i \(0.569317\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4300.00 −0.593333
\(36\) 0 0
\(37\) −11242.0 −1.35002 −0.675009 0.737810i \(-0.735860\pi\)
−0.675009 + 0.737810i \(0.735860\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1242.00 −0.115388 −0.0576942 0.998334i \(-0.518375\pi\)
−0.0576942 + 0.998334i \(0.518375\pi\)
\(42\) 0 0
\(43\) −20624.0 −1.70099 −0.850495 0.525983i \(-0.823697\pi\)
−0.850495 + 0.525983i \(0.823697\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6588.00 0.435020 0.217510 0.976058i \(-0.430207\pi\)
0.217510 + 0.976058i \(0.430207\pi\)
\(48\) 0 0
\(49\) 12777.0 0.760219
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 21066.0 1.03013 0.515065 0.857151i \(-0.327768\pi\)
0.515065 + 0.857151i \(0.327768\pi\)
\(54\) 0 0
\(55\) −3300.00 −0.147098
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 7980.00 0.298451 0.149225 0.988803i \(-0.452322\pi\)
0.149225 + 0.988803i \(0.452322\pi\)
\(60\) 0 0
\(61\) 16622.0 0.571951 0.285975 0.958237i \(-0.407682\pi\)
0.285975 + 0.958237i \(0.407682\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 23650.0 0.694301
\(66\) 0 0
\(67\) −1808.00 −0.0492052 −0.0246026 0.999697i \(-0.507832\pi\)
−0.0246026 + 0.999697i \(0.507832\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −24528.0 −0.577452 −0.288726 0.957412i \(-0.593232\pi\)
−0.288726 + 0.957412i \(0.593232\pi\)
\(72\) 0 0
\(73\) 20474.0 0.449672 0.224836 0.974397i \(-0.427815\pi\)
0.224836 + 0.974397i \(0.427815\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 22704.0 0.436391
\(78\) 0 0
\(79\) 46240.0 0.833585 0.416793 0.909002i \(-0.363154\pi\)
0.416793 + 0.909002i \(0.363154\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −51576.0 −0.821774 −0.410887 0.911686i \(-0.634781\pi\)
−0.410887 + 0.911686i \(0.634781\pi\)
\(84\) 0 0
\(85\) −5550.00 −0.0833193
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 110310. 1.47618 0.738091 0.674701i \(-0.235728\pi\)
0.738091 + 0.674701i \(0.235728\pi\)
\(90\) 0 0
\(91\) −162712. −2.05976
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 12500.0 0.142102
\(96\) 0 0
\(97\) −78382.0 −0.845838 −0.422919 0.906168i \(-0.638994\pi\)
−0.422919 + 0.906168i \(0.638994\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −141942. −1.38455 −0.692273 0.721636i \(-0.743391\pi\)
−0.692273 + 0.721636i \(0.743391\pi\)
\(102\) 0 0
\(103\) 436.000 0.00404943 0.00202471 0.999998i \(-0.499356\pi\)
0.00202471 + 0.999998i \(0.499356\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 232968. 1.96715 0.983574 0.180508i \(-0.0577742\pi\)
0.983574 + 0.180508i \(0.0577742\pi\)
\(108\) 0 0
\(109\) −174850. −1.40961 −0.704806 0.709400i \(-0.748966\pi\)
−0.704806 + 0.709400i \(0.748966\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −182994. −1.34816 −0.674079 0.738659i \(-0.735459\pi\)
−0.674079 + 0.738659i \(0.735459\pi\)
\(114\) 0 0
\(115\) −89100.0 −0.628251
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 38184.0 0.247180
\(120\) 0 0
\(121\) −143627. −0.891811
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) 122452. 0.673685 0.336842 0.941561i \(-0.390641\pi\)
0.336842 + 0.941561i \(0.390641\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −241908. −1.23161 −0.615803 0.787900i \(-0.711168\pi\)
−0.615803 + 0.787900i \(0.711168\pi\)
\(132\) 0 0
\(133\) −86000.0 −0.421570
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −277098. −1.26134 −0.630670 0.776051i \(-0.717220\pi\)
−0.630670 + 0.776051i \(0.717220\pi\)
\(138\) 0 0
\(139\) 193540. 0.849638 0.424819 0.905278i \(-0.360338\pi\)
0.424819 + 0.905278i \(0.360338\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −124872. −0.510652
\(144\) 0 0
\(145\) 54750.0 0.216254
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −140550. −0.518639 −0.259320 0.965792i \(-0.583498\pi\)
−0.259320 + 0.965792i \(0.583498\pi\)
\(150\) 0 0
\(151\) −433952. −1.54881 −0.774407 0.632688i \(-0.781952\pi\)
−0.774407 + 0.632688i \(0.781952\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 57800.0 0.193241
\(156\) 0 0
\(157\) −555922. −1.79997 −0.899984 0.435923i \(-0.856422\pi\)
−0.899984 + 0.435923i \(0.856422\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 613008. 1.86381
\(162\) 0 0
\(163\) 66616.0 0.196386 0.0981928 0.995167i \(-0.468694\pi\)
0.0981928 + 0.995167i \(0.468694\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −205692. −0.570724 −0.285362 0.958420i \(-0.592114\pi\)
−0.285362 + 0.958420i \(0.592114\pi\)
\(168\) 0 0
\(169\) 523623. 1.41027
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −433854. −1.10212 −0.551059 0.834466i \(-0.685776\pi\)
−0.551059 + 0.834466i \(0.685776\pi\)
\(174\) 0 0
\(175\) 107500. 0.265346
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −489180. −1.14113 −0.570566 0.821252i \(-0.693276\pi\)
−0.570566 + 0.821252i \(0.693276\pi\)
\(180\) 0 0
\(181\) 719462. 1.63234 0.816172 0.577810i \(-0.196092\pi\)
0.816172 + 0.577810i \(0.196092\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 281050. 0.603746
\(186\) 0 0
\(187\) 29304.0 0.0612806
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −185928. −0.368775 −0.184387 0.982854i \(-0.559030\pi\)
−0.184387 + 0.982854i \(0.559030\pi\)
\(192\) 0 0
\(193\) −591406. −1.14286 −0.571429 0.820651i \(-0.693611\pi\)
−0.571429 + 0.820651i \(0.693611\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −449478. −0.825169 −0.412584 0.910919i \(-0.635374\pi\)
−0.412584 + 0.910919i \(0.635374\pi\)
\(198\) 0 0
\(199\) −157160. −0.281326 −0.140663 0.990058i \(-0.544923\pi\)
−0.140663 + 0.990058i \(0.544923\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −376680. −0.641553
\(204\) 0 0
\(205\) 31050.0 0.0516032
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −66000.0 −0.104515
\(210\) 0 0
\(211\) −253052. −0.391294 −0.195647 0.980674i \(-0.562681\pi\)
−0.195647 + 0.980674i \(0.562681\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 515600. 0.760706
\(216\) 0 0
\(217\) −397664. −0.573280
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −210012. −0.289243
\(222\) 0 0
\(223\) −1.07344e6 −1.44550 −0.722749 0.691111i \(-0.757122\pi\)
−0.722749 + 0.691111i \(0.757122\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −626832. −0.807396 −0.403698 0.914892i \(-0.632275\pi\)
−0.403698 + 0.914892i \(0.632275\pi\)
\(228\) 0 0
\(229\) −116650. −0.146993 −0.0734964 0.997295i \(-0.523416\pi\)
−0.0734964 + 0.997295i \(0.523416\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 743046. 0.896656 0.448328 0.893869i \(-0.352020\pi\)
0.448328 + 0.893869i \(0.352020\pi\)
\(234\) 0 0
\(235\) −164700. −0.194547
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 978720. 1.10832 0.554158 0.832411i \(-0.313040\pi\)
0.554158 + 0.832411i \(0.313040\pi\)
\(240\) 0 0
\(241\) −1.13280e6 −1.25635 −0.628174 0.778073i \(-0.716197\pi\)
−0.628174 + 0.778073i \(0.716197\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −319425. −0.339980
\(246\) 0 0
\(247\) 473000. 0.493309
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 905652. 0.907355 0.453677 0.891166i \(-0.350112\pi\)
0.453677 + 0.891166i \(0.350112\pi\)
\(252\) 0 0
\(253\) 470448. 0.462073
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.93994e6 −1.83212 −0.916062 0.401036i \(-0.868650\pi\)
−0.916062 + 0.401036i \(0.868650\pi\)
\(258\) 0 0
\(259\) −1.93362e6 −1.79111
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −805476. −0.718064 −0.359032 0.933325i \(-0.616893\pi\)
−0.359032 + 0.933325i \(0.616893\pi\)
\(264\) 0 0
\(265\) −526650. −0.460689
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 858690. 0.723529 0.361764 0.932270i \(-0.382175\pi\)
0.361764 + 0.932270i \(0.382175\pi\)
\(270\) 0 0
\(271\) 383608. 0.317296 0.158648 0.987335i \(-0.449287\pi\)
0.158648 + 0.987335i \(0.449287\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 82500.0 0.0657843
\(276\) 0 0
\(277\) 2.01076e6 1.57456 0.787282 0.616593i \(-0.211488\pi\)
0.787282 + 0.616593i \(0.211488\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −202602. −0.153066 −0.0765329 0.997067i \(-0.524385\pi\)
−0.0765329 + 0.997067i \(0.524385\pi\)
\(282\) 0 0
\(283\) 221536. 0.164429 0.0822145 0.996615i \(-0.473801\pi\)
0.0822145 + 0.996615i \(0.473801\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −213624. −0.153089
\(288\) 0 0
\(289\) −1.37057e6 −0.965289
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 322506. 0.219467 0.109733 0.993961i \(-0.465000\pi\)
0.109733 + 0.993961i \(0.465000\pi\)
\(294\) 0 0
\(295\) −199500. −0.133471
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.37154e6 −2.18098
\(300\) 0 0
\(301\) −3.54733e6 −2.25676
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −415550. −0.255784
\(306\) 0 0
\(307\) −1.44301e6 −0.873822 −0.436911 0.899505i \(-0.643927\pi\)
−0.436911 + 0.899505i \(0.643927\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 171312. 0.100435 0.0502177 0.998738i \(-0.484008\pi\)
0.0502177 + 0.998738i \(0.484008\pi\)
\(312\) 0 0
\(313\) −1.02689e6 −0.592463 −0.296232 0.955116i \(-0.595730\pi\)
−0.296232 + 0.955116i \(0.595730\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −752958. −0.420845 −0.210423 0.977610i \(-0.567484\pi\)
−0.210423 + 0.977610i \(0.567484\pi\)
\(318\) 0 0
\(319\) −289080. −0.159053
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −111000. −0.0591993
\(324\) 0 0
\(325\) −591250. −0.310501
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.13314e6 0.577155
\(330\) 0 0
\(331\) −1.99413e6 −1.00042 −0.500212 0.865903i \(-0.666745\pi\)
−0.500212 + 0.865903i \(0.666745\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 45200.0 0.0220053
\(336\) 0 0
\(337\) −987022. −0.473426 −0.236713 0.971580i \(-0.576070\pi\)
−0.236713 + 0.971580i \(0.576070\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −305184. −0.142127
\(342\) 0 0
\(343\) −693160. −0.318125
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.20601e6 0.983520 0.491760 0.870731i \(-0.336354\pi\)
0.491760 + 0.870731i \(0.336354\pi\)
\(348\) 0 0
\(349\) 2.74187e6 1.20499 0.602495 0.798123i \(-0.294173\pi\)
0.602495 + 0.798123i \(0.294173\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.38957e6 1.02066 0.510331 0.859978i \(-0.329523\pi\)
0.510331 + 0.859978i \(0.329523\pi\)
\(354\) 0 0
\(355\) 613200. 0.258245
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −279480. −0.114450 −0.0572248 0.998361i \(-0.518225\pi\)
−0.0572248 + 0.998361i \(0.518225\pi\)
\(360\) 0 0
\(361\) −2.22610e6 −0.899035
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −511850. −0.201099
\(366\) 0 0
\(367\) 2.47637e6 0.959734 0.479867 0.877341i \(-0.340685\pi\)
0.479867 + 0.877341i \(0.340685\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.62335e6 1.36671
\(372\) 0 0
\(373\) 2.74525e6 1.02167 0.510835 0.859679i \(-0.329336\pi\)
0.510835 + 0.859679i \(0.329336\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.07174e6 0.750727
\(378\) 0 0
\(379\) 1.18906e6 0.425212 0.212606 0.977138i \(-0.431805\pi\)
0.212606 + 0.977138i \(0.431805\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.25760e6 1.13475 0.567377 0.823458i \(-0.307958\pi\)
0.567377 + 0.823458i \(0.307958\pi\)
\(384\) 0 0
\(385\) −567600. −0.195160
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.98351e6 −0.664600 −0.332300 0.943174i \(-0.607825\pi\)
−0.332300 + 0.943174i \(0.607825\pi\)
\(390\) 0 0
\(391\) 791208. 0.261727
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.15600e6 −0.372791
\(396\) 0 0
\(397\) 4.97416e6 1.58396 0.791978 0.610549i \(-0.209051\pi\)
0.791978 + 0.610549i \(0.209051\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.34264e6 0.416963 0.208482 0.978026i \(-0.433148\pi\)
0.208482 + 0.978026i \(0.433148\pi\)
\(402\) 0 0
\(403\) 2.18715e6 0.670836
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.48394e6 −0.444050
\(408\) 0 0
\(409\) −1.09423e6 −0.323445 −0.161722 0.986836i \(-0.551705\pi\)
−0.161722 + 0.986836i \(0.551705\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.37256e6 0.395964
\(414\) 0 0
\(415\) 1.28940e6 0.367509
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −954060. −0.265485 −0.132743 0.991151i \(-0.542378\pi\)
−0.132743 + 0.991151i \(0.542378\pi\)
\(420\) 0 0
\(421\) −1.59390e6 −0.438284 −0.219142 0.975693i \(-0.570326\pi\)
−0.219142 + 0.975693i \(0.570326\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 138750. 0.0372615
\(426\) 0 0
\(427\) 2.85898e6 0.758826
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.64665e6 −0.686283 −0.343141 0.939284i \(-0.611491\pi\)
−0.343141 + 0.939284i \(0.611491\pi\)
\(432\) 0 0
\(433\) 3.72355e6 0.954416 0.477208 0.878790i \(-0.341649\pi\)
0.477208 + 0.878790i \(0.341649\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.78200e6 −0.446379
\(438\) 0 0
\(439\) 2.58340e6 0.639780 0.319890 0.947455i \(-0.396354\pi\)
0.319890 + 0.947455i \(0.396354\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7.56206e6 1.83076 0.915379 0.402593i \(-0.131891\pi\)
0.915379 + 0.402593i \(0.131891\pi\)
\(444\) 0 0
\(445\) −2.75775e6 −0.660169
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −4.30773e6 −1.00840 −0.504200 0.863587i \(-0.668212\pi\)
−0.504200 + 0.863587i \(0.668212\pi\)
\(450\) 0 0
\(451\) −163944. −0.0379537
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 4.06780e6 0.921152
\(456\) 0 0
\(457\) −2.24354e6 −0.502509 −0.251254 0.967921i \(-0.580843\pi\)
−0.251254 + 0.967921i \(0.580843\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.65670e6 −0.363071 −0.181536 0.983384i \(-0.558107\pi\)
−0.181536 + 0.983384i \(0.558107\pi\)
\(462\) 0 0
\(463\) 2.89160e6 0.626881 0.313441 0.949608i \(-0.398518\pi\)
0.313441 + 0.949608i \(0.398518\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6.52699e6 −1.38491 −0.692454 0.721462i \(-0.743470\pi\)
−0.692454 + 0.721462i \(0.743470\pi\)
\(468\) 0 0
\(469\) −310976. −0.0652822
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.72237e6 −0.559492
\(474\) 0 0
\(475\) −312500. −0.0635501
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5.96232e6 −1.18734 −0.593672 0.804707i \(-0.702322\pi\)
−0.593672 + 0.804707i \(0.702322\pi\)
\(480\) 0 0
\(481\) 1.06349e7 2.09591
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.95955e6 0.378270
\(486\) 0 0
\(487\) −2.99191e6 −0.571644 −0.285822 0.958283i \(-0.592267\pi\)
−0.285822 + 0.958283i \(0.592267\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.20419e6 −0.225419 −0.112710 0.993628i \(-0.535953\pi\)
−0.112710 + 0.993628i \(0.535953\pi\)
\(492\) 0 0
\(493\) −486180. −0.0900907
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.21882e6 −0.766125
\(498\) 0 0
\(499\) −9.20546e6 −1.65499 −0.827493 0.561477i \(-0.810233\pi\)
−0.827493 + 0.561477i \(0.810233\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3.35956e6 −0.592055 −0.296027 0.955179i \(-0.595662\pi\)
−0.296027 + 0.955179i \(0.595662\pi\)
\(504\) 0 0
\(505\) 3.54855e6 0.619188
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2.53701e6 0.434038 0.217019 0.976167i \(-0.430367\pi\)
0.217019 + 0.976167i \(0.430367\pi\)
\(510\) 0 0
\(511\) 3.52153e6 0.596594
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −10900.0 −0.00181096
\(516\) 0 0
\(517\) 869616. 0.143087
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 9.31580e6 1.50358 0.751789 0.659404i \(-0.229191\pi\)
0.751789 + 0.659404i \(0.229191\pi\)
\(522\) 0 0
\(523\) 5.02802e6 0.803790 0.401895 0.915686i \(-0.368352\pi\)
0.401895 + 0.915686i \(0.368352\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −513264. −0.0805034
\(528\) 0 0
\(529\) 6.26575e6 0.973496
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.17493e6 0.179141
\(534\) 0 0
\(535\) −5.82420e6 −0.879735
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.68656e6 0.250052
\(540\) 0 0
\(541\) 134222. 0.0197165 0.00985827 0.999951i \(-0.496862\pi\)
0.00985827 + 0.999951i \(0.496862\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.37125e6 0.630397
\(546\) 0 0
\(547\) −605648. −0.0865470 −0.0432735 0.999063i \(-0.513779\pi\)
−0.0432735 + 0.999063i \(0.513779\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.09500e6 0.153651
\(552\) 0 0
\(553\) 7.95328e6 1.10594
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.06240e6 0.964527 0.482264 0.876026i \(-0.339815\pi\)
0.482264 + 0.876026i \(0.339815\pi\)
\(558\) 0 0
\(559\) 1.95103e7 2.64079
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.03029e7 −1.36990 −0.684952 0.728588i \(-0.740177\pi\)
−0.684952 + 0.728588i \(0.740177\pi\)
\(564\) 0 0
\(565\) 4.57485e6 0.602915
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.04769e6 −0.135660 −0.0678300 0.997697i \(-0.521608\pi\)
−0.0678300 + 0.997697i \(0.521608\pi\)
\(570\) 0 0
\(571\) −1.40765e7 −1.80677 −0.903385 0.428830i \(-0.858926\pi\)
−0.903385 + 0.428830i \(0.858926\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.22750e6 0.280962
\(576\) 0 0
\(577\) 1.62682e6 0.203423 0.101711 0.994814i \(-0.467568\pi\)
0.101711 + 0.994814i \(0.467568\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −8.87107e6 −1.09027
\(582\) 0 0
\(583\) 2.78071e6 0.338832
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6.96089e6 0.833814 0.416907 0.908949i \(-0.363114\pi\)
0.416907 + 0.908949i \(0.363114\pi\)
\(588\) 0 0
\(589\) 1.15600e6 0.137300
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.13639e7 1.32706 0.663529 0.748150i \(-0.269058\pi\)
0.663529 + 0.748150i \(0.269058\pi\)
\(594\) 0 0
\(595\) −954600. −0.110542
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.48688e7 1.69321 0.846603 0.532224i \(-0.178644\pi\)
0.846603 + 0.532224i \(0.178644\pi\)
\(600\) 0 0
\(601\) −1.23612e6 −0.139596 −0.0697981 0.997561i \(-0.522236\pi\)
−0.0697981 + 0.997561i \(0.522236\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3.59067e6 0.398830
\(606\) 0 0
\(607\) 1.24498e7 1.37149 0.685743 0.727844i \(-0.259478\pi\)
0.685743 + 0.727844i \(0.259478\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.23225e6 −0.675370
\(612\) 0 0
\(613\) −8.73491e6 −0.938873 −0.469437 0.882966i \(-0.655543\pi\)
−0.469437 + 0.882966i \(0.655543\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.25495e7 −1.32713 −0.663565 0.748119i \(-0.730957\pi\)
−0.663565 + 0.748119i \(0.730957\pi\)
\(618\) 0 0
\(619\) 1.46658e7 1.53843 0.769216 0.638988i \(-0.220647\pi\)
0.769216 + 0.638988i \(0.220647\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.89733e7 1.95850
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.49572e6 −0.251519
\(630\) 0 0
\(631\) 196288. 0.0196255 0.00981274 0.999952i \(-0.496876\pi\)
0.00981274 + 0.999952i \(0.496876\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3.06130e6 −0.301281
\(636\) 0 0
\(637\) −1.20870e7 −1.18024
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.11596e7 1.07276 0.536381 0.843976i \(-0.319791\pi\)
0.536381 + 0.843976i \(0.319791\pi\)
\(642\) 0 0
\(643\) 2.25158e6 0.214763 0.107381 0.994218i \(-0.465753\pi\)
0.107381 + 0.994218i \(0.465753\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.05319e6 0.756323 0.378161 0.925740i \(-0.376556\pi\)
0.378161 + 0.925740i \(0.376556\pi\)
\(648\) 0 0
\(649\) 1.05336e6 0.0981669
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 416466. 0.0382205 0.0191103 0.999817i \(-0.493917\pi\)
0.0191103 + 0.999817i \(0.493917\pi\)
\(654\) 0 0
\(655\) 6.04770e6 0.550791
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.31721e7 1.18152 0.590761 0.806847i \(-0.298828\pi\)
0.590761 + 0.806847i \(0.298828\pi\)
\(660\) 0 0
\(661\) −1.69494e6 −0.150886 −0.0754432 0.997150i \(-0.524037\pi\)
−0.0754432 + 0.997150i \(0.524037\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.15000e6 0.188532
\(666\) 0 0
\(667\) −7.80516e6 −0.679309
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.19410e6 0.188127
\(672\) 0 0
\(673\) −8.91605e6 −0.758813 −0.379406 0.925230i \(-0.623872\pi\)
−0.379406 + 0.925230i \(0.623872\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.42894e7 1.19824 0.599118 0.800661i \(-0.295518\pi\)
0.599118 + 0.800661i \(0.295518\pi\)
\(678\) 0 0
\(679\) −1.34817e7 −1.12220
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −5.33314e6 −0.437452 −0.218726 0.975786i \(-0.570190\pi\)
−0.218726 + 0.975786i \(0.570190\pi\)
\(684\) 0 0
\(685\) 6.92745e6 0.564088
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.99284e7 −1.59928
\(690\) 0 0
\(691\) −698252. −0.0556310 −0.0278155 0.999613i \(-0.508855\pi\)
−0.0278155 + 0.999613i \(0.508855\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4.83850e6 −0.379969
\(696\) 0 0
\(697\) −275724. −0.0214977
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.79880e7 −1.38257 −0.691285 0.722582i \(-0.742955\pi\)
−0.691285 + 0.722582i \(0.742955\pi\)
\(702\) 0 0
\(703\) 5.62100e6 0.428968
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.44140e7 −1.83692
\(708\) 0 0
\(709\) −1.39464e7 −1.04195 −0.520975 0.853572i \(-0.674432\pi\)
−0.520975 + 0.853572i \(0.674432\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −8.23997e6 −0.607018
\(714\) 0 0
\(715\) 3.12180e6 0.228370
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.22272e6 0.448909 0.224454 0.974485i \(-0.427940\pi\)
0.224454 + 0.974485i \(0.427940\pi\)
\(720\) 0 0
\(721\) 74992.0 0.00537250
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.36875e6 −0.0967117
\(726\) 0 0
\(727\) 7.76729e6 0.545047 0.272523 0.962149i \(-0.412142\pi\)
0.272523 + 0.962149i \(0.412142\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.57853e6 −0.316907
\(732\) 0 0
\(733\) 2.42083e7 1.66420 0.832099 0.554627i \(-0.187139\pi\)
0.832099 + 0.554627i \(0.187139\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −238656. −0.0161847
\(738\) 0 0
\(739\) −1.26850e7 −0.854434 −0.427217 0.904149i \(-0.640506\pi\)
−0.427217 + 0.904149i \(0.640506\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.97632e7 1.31337 0.656684 0.754166i \(-0.271959\pi\)
0.656684 + 0.754166i \(0.271959\pi\)
\(744\) 0 0
\(745\) 3.51375e6 0.231942
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.00705e7 2.60988
\(750\) 0 0
\(751\) 9.01761e6 0.583434 0.291717 0.956505i \(-0.405774\pi\)
0.291717 + 0.956505i \(0.405774\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.08488e7 0.692651
\(756\) 0 0
\(757\) −1.12556e6 −0.0713887 −0.0356944 0.999363i \(-0.511364\pi\)
−0.0356944 + 0.999363i \(0.511364\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.25747e7 −1.41306 −0.706529 0.707684i \(-0.749740\pi\)
−0.706529 + 0.707684i \(0.749740\pi\)
\(762\) 0 0
\(763\) −3.00742e7 −1.87018
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7.54908e6 −0.463346
\(768\) 0 0
\(769\) −632350. −0.0385604 −0.0192802 0.999814i \(-0.506137\pi\)
−0.0192802 + 0.999814i \(0.506137\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.25867e7 0.757643 0.378822 0.925470i \(-0.376329\pi\)
0.378822 + 0.925470i \(0.376329\pi\)
\(774\) 0 0
\(775\) −1.44500e6 −0.0864199
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 621000. 0.0366647
\(780\) 0 0
\(781\) −3.23770e6 −0.189937
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.38980e7 0.804970
\(786\) 0 0
\(787\) −2.15792e7 −1.24194 −0.620968 0.783836i \(-0.713260\pi\)
−0.620968 + 0.783836i \(0.713260\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3.14750e7 −1.78864
\(792\) 0 0
\(793\) −1.57244e7 −0.887956
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.09760e7 1.72735 0.863673 0.504052i \(-0.168158\pi\)
0.863673 + 0.504052i \(0.168158\pi\)
\(798\) 0 0
\(799\) 1.46254e6 0.0810475
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.70257e6 0.147907
\(804\) 0 0
\(805\) −1.53252e7 −0.833521
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −4.24929e6 −0.228268 −0.114134 0.993465i \(-0.536409\pi\)
−0.114134 + 0.993465i \(0.536409\pi\)
\(810\) 0 0
\(811\) −3.42333e6 −0.182767 −0.0913833 0.995816i \(-0.529129\pi\)
−0.0913833 + 0.995816i \(0.529129\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.66540e6 −0.0878263
\(816\) 0 0
\(817\) 1.03120e7 0.540490
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3.10571e7 −1.60806 −0.804030 0.594588i \(-0.797315\pi\)
−0.804030 + 0.594588i \(0.797315\pi\)
\(822\) 0 0
\(823\) 3.11904e7 1.60517 0.802584 0.596538i \(-0.203458\pi\)
0.802584 + 0.596538i \(0.203458\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −8.28487e6 −0.421233 −0.210616 0.977569i \(-0.567547\pi\)
−0.210616 + 0.977569i \(0.567547\pi\)
\(828\) 0 0
\(829\) −1.81688e7 −0.918208 −0.459104 0.888383i \(-0.651829\pi\)
−0.459104 + 0.888383i \(0.651829\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.83649e6 0.141635
\(834\) 0 0
\(835\) 5.14230e6 0.255236
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −1.02743e7 −0.503902 −0.251951 0.967740i \(-0.581072\pi\)
−0.251951 + 0.967740i \(0.581072\pi\)
\(840\) 0 0
\(841\) −1.57150e7 −0.766171
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.30906e7 −0.630691
\(846\) 0 0
\(847\) −2.47038e7 −1.18319
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −4.00665e7 −1.89652
\(852\) 0 0
\(853\) 6.28597e6 0.295801 0.147901 0.989002i \(-0.452748\pi\)
0.147901 + 0.989002i \(0.452748\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.54050e7 −0.716490 −0.358245 0.933628i \(-0.616625\pi\)
−0.358245 + 0.933628i \(0.616625\pi\)
\(858\) 0 0
\(859\) −1.43526e7 −0.663664 −0.331832 0.943338i \(-0.607667\pi\)
−0.331832 + 0.943338i \(0.607667\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.33278e7 0.609158 0.304579 0.952487i \(-0.401484\pi\)
0.304579 + 0.952487i \(0.401484\pi\)
\(864\) 0 0
\(865\) 1.08464e7 0.492882
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 6.10368e6 0.274184
\(870\) 0 0
\(871\) 1.71037e6 0.0763913
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2.68750e6 −0.118667
\(876\) 0 0
\(877\) 3.24846e7 1.42620 0.713098 0.701065i \(-0.247292\pi\)
0.713098 + 0.701065i \(0.247292\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.54600e7 −0.671073 −0.335537 0.942027i \(-0.608918\pi\)
−0.335537 + 0.942027i \(0.608918\pi\)
\(882\) 0 0
\(883\) 1.69478e6 0.0731494 0.0365747 0.999331i \(-0.488355\pi\)
0.0365747 + 0.999331i \(0.488355\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.87257e6 −0.122592 −0.0612960 0.998120i \(-0.519523\pi\)
−0.0612960 + 0.998120i \(0.519523\pi\)
\(888\) 0 0
\(889\) 2.10617e7 0.893799
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −3.29400e6 −0.138228
\(894\) 0 0
\(895\) 1.22295e7 0.510330
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 5.06328e6 0.208945
\(900\) 0 0
\(901\) 4.67665e6 0.191921
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.79866e7 −0.730006
\(906\) 0 0
\(907\) −3.95422e7 −1.59603 −0.798017 0.602635i \(-0.794118\pi\)
−0.798017 + 0.602635i \(0.794118\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.13178e7 0.451819 0.225909 0.974148i \(-0.427465\pi\)
0.225909 + 0.974148i \(0.427465\pi\)
\(912\) 0 0
\(913\) −6.80803e6 −0.270299
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4.16082e7 −1.63401
\(918\) 0 0
\(919\) −8.51348e6 −0.332520 −0.166260 0.986082i \(-0.553169\pi\)
−0.166260 + 0.986082i \(0.553169\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.32035e7 0.896497
\(924\) 0 0
\(925\) −7.02625e6 −0.270003
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 7.54587e6 0.286860 0.143430 0.989660i \(-0.454187\pi\)
0.143430 + 0.989660i \(0.454187\pi\)
\(930\) 0 0
\(931\) −6.38850e6 −0.241560
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −732600. −0.0274055
\(936\) 0 0
\(937\) −1.84500e7 −0.686512 −0.343256 0.939242i \(-0.611530\pi\)
−0.343256 + 0.939242i \(0.611530\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −6.75046e6 −0.248519 −0.124259 0.992250i \(-0.539656\pi\)
−0.124259 + 0.992250i \(0.539656\pi\)
\(942\) 0 0
\(943\) −4.42649e6 −0.162099
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 6.45677e6 0.233959 0.116980 0.993134i \(-0.462679\pi\)
0.116980 + 0.993134i \(0.462679\pi\)
\(948\) 0 0
\(949\) −1.93684e7 −0.698117
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 3.96648e7 1.41473 0.707364 0.706849i \(-0.249884\pi\)
0.707364 + 0.706849i \(0.249884\pi\)
\(954\) 0 0
\(955\) 4.64820e6 0.164921
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −4.76609e7 −1.67346
\(960\) 0 0
\(961\) −2.32838e7 −0.813290
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.47851e7 0.511102
\(966\) 0 0
\(967\) 3.43015e7 1.17963 0.589816 0.807538i \(-0.299200\pi\)
0.589816 + 0.807538i \(0.299200\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −5.77115e6 −0.196433 −0.0982164 0.995165i \(-0.531314\pi\)
−0.0982164 + 0.995165i \(0.531314\pi\)
\(972\) 0 0
\(973\) 3.32889e7 1.12724
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −7.08746e6 −0.237549 −0.118775 0.992921i \(-0.537897\pi\)
−0.118775 + 0.992921i \(0.537897\pi\)
\(978\) 0 0
\(979\) 1.45609e7 0.485548
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 4.59362e7 1.51625 0.758126 0.652108i \(-0.226115\pi\)
0.758126 + 0.652108i \(0.226115\pi\)
\(984\) 0 0
\(985\) 1.12370e7 0.369027
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −7.35039e7 −2.38957
\(990\) 0 0
\(991\) 4.50298e7 1.45652 0.728260 0.685301i \(-0.240329\pi\)
0.728260 + 0.685301i \(0.240329\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 3.92900e6 0.125813
\(996\) 0 0
\(997\) −2.37364e7 −0.756271 −0.378136 0.925750i \(-0.623435\pi\)
−0.378136 + 0.925750i \(0.623435\pi\)
\(998\) 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.j.1.1 1
3.2 odd 2 80.6.a.a.1.1 1
4.3 odd 2 90.6.a.d.1.1 1
12.11 even 2 10.6.a.b.1.1 1
15.2 even 4 400.6.c.b.49.2 2
15.8 even 4 400.6.c.b.49.1 2
15.14 odd 2 400.6.a.n.1.1 1
20.3 even 4 450.6.c.h.199.1 2
20.7 even 4 450.6.c.h.199.2 2
20.19 odd 2 450.6.a.l.1.1 1
24.5 odd 2 320.6.a.o.1.1 1
24.11 even 2 320.6.a.b.1.1 1
60.23 odd 4 50.6.b.a.49.2 2
60.47 odd 4 50.6.b.a.49.1 2
60.59 even 2 50.6.a.d.1.1 1
84.83 odd 2 490.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.6.a.b.1.1 1 12.11 even 2
50.6.a.d.1.1 1 60.59 even 2
50.6.b.a.49.1 2 60.47 odd 4
50.6.b.a.49.2 2 60.23 odd 4
80.6.a.a.1.1 1 3.2 odd 2
90.6.a.d.1.1 1 4.3 odd 2
320.6.a.b.1.1 1 24.11 even 2
320.6.a.o.1.1 1 24.5 odd 2
400.6.a.n.1.1 1 15.14 odd 2
400.6.c.b.49.1 2 15.8 even 4
400.6.c.b.49.2 2 15.2 even 4
450.6.a.l.1.1 1 20.19 odd 2
450.6.c.h.199.1 2 20.3 even 4
450.6.c.h.199.2 2 20.7 even 4
490.6.a.a.1.1 1 84.83 odd 2
720.6.a.j.1.1 1 1.1 even 1 trivial