Properties

Label 630.6.a.i.1.1
Level $630$
Weight $6$
Character 630.1
Self dual yes
Analytic conductor $101.042$
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] = [630,6,Mod(1,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("630.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 630.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: \(101.041806482\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 630.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{2} +16.0000 q^{4} -25.0000 q^{5} -49.0000 q^{7} +64.0000 q^{8} +O(q^{10})\) \(q+4.00000 q^{2} +16.0000 q^{4} -25.0000 q^{5} -49.0000 q^{7} +64.0000 q^{8} -100.000 q^{10} +187.000 q^{11} +627.000 q^{13} -196.000 q^{14} +256.000 q^{16} -1813.00 q^{17} +258.000 q^{19} -400.000 q^{20} +748.000 q^{22} -2970.00 q^{23} +625.000 q^{25} +2508.00 q^{26} -784.000 q^{28} -1299.00 q^{29} +1916.00 q^{31} +1024.00 q^{32} -7252.00 q^{34} +1225.00 q^{35} +6578.00 q^{37} +1032.00 q^{38} -1600.00 q^{40} -6676.00 q^{41} +3178.00 q^{43} +2992.00 q^{44} -11880.0 q^{46} +22001.0 q^{47} +2401.00 q^{49} +2500.00 q^{50} +10032.0 q^{52} -26168.0 q^{53} -4675.00 q^{55} -3136.00 q^{56} -5196.00 q^{58} -3932.00 q^{59} -48740.0 q^{61} +7664.00 q^{62} +4096.00 q^{64} -15675.0 q^{65} -44832.0 q^{67} -29008.0 q^{68} +4900.00 q^{70} -63736.0 q^{71} +60470.0 q^{73} +26312.0 q^{74} +4128.00 q^{76} -9163.00 q^{77} -43721.0 q^{79} -6400.00 q^{80} -26704.0 q^{82} -97276.0 q^{83} +45325.0 q^{85} +12712.0 q^{86} +11968.0 q^{88} -45560.0 q^{89} -30723.0 q^{91} -47520.0 q^{92} +88004.0 q^{94} -6450.00 q^{95} -57295.0 q^{97} +9604.00 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 0.707107
\(3\) 0 0
\(4\) 16.0000 0.500000
\(5\) −25.0000 −0.447214
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 64.0000 0.353553
\(9\) 0 0
\(10\) −100.000 −0.316228
\(11\) 187.000 0.465972 0.232986 0.972480i \(-0.425150\pi\)
0.232986 + 0.972480i \(0.425150\pi\)
\(12\) 0 0
\(13\) 627.000 1.02899 0.514493 0.857495i \(-0.327980\pi\)
0.514493 + 0.857495i \(0.327980\pi\)
\(14\) −196.000 −0.267261
\(15\) 0 0
\(16\) 256.000 0.250000
\(17\) −1813.00 −1.52151 −0.760756 0.649038i \(-0.775172\pi\)
−0.760756 + 0.649038i \(0.775172\pi\)
\(18\) 0 0
\(19\) 258.000 0.163959 0.0819796 0.996634i \(-0.473876\pi\)
0.0819796 + 0.996634i \(0.473876\pi\)
\(20\) −400.000 −0.223607
\(21\) 0 0
\(22\) 748.000 0.329492
\(23\) −2970.00 −1.17068 −0.585338 0.810789i \(-0.699038\pi\)
−0.585338 + 0.810789i \(0.699038\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 2508.00 0.727602
\(27\) 0 0
\(28\) −784.000 −0.188982
\(29\) −1299.00 −0.286823 −0.143412 0.989663i \(-0.545807\pi\)
−0.143412 + 0.989663i \(0.545807\pi\)
\(30\) 0 0
\(31\) 1916.00 0.358089 0.179045 0.983841i \(-0.442699\pi\)
0.179045 + 0.983841i \(0.442699\pi\)
\(32\) 1024.00 0.176777
\(33\) 0 0
\(34\) −7252.00 −1.07587
\(35\) 1225.00 0.169031
\(36\) 0 0
\(37\) 6578.00 0.789932 0.394966 0.918696i \(-0.370756\pi\)
0.394966 + 0.918696i \(0.370756\pi\)
\(38\) 1032.00 0.115937
\(39\) 0 0
\(40\) −1600.00 −0.158114
\(41\) −6676.00 −0.620236 −0.310118 0.950698i \(-0.600368\pi\)
−0.310118 + 0.950698i \(0.600368\pi\)
\(42\) 0 0
\(43\) 3178.00 0.262109 0.131055 0.991375i \(-0.458164\pi\)
0.131055 + 0.991375i \(0.458164\pi\)
\(44\) 2992.00 0.232986
\(45\) 0 0
\(46\) −11880.0 −0.827793
\(47\) 22001.0 1.45277 0.726387 0.687286i \(-0.241198\pi\)
0.726387 + 0.687286i \(0.241198\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 2500.00 0.141421
\(51\) 0 0
\(52\) 10032.0 0.514493
\(53\) −26168.0 −1.27962 −0.639810 0.768533i \(-0.720987\pi\)
−0.639810 + 0.768533i \(0.720987\pi\)
\(54\) 0 0
\(55\) −4675.00 −0.208389
\(56\) −3136.00 −0.133631
\(57\) 0 0
\(58\) −5196.00 −0.202815
\(59\) −3932.00 −0.147056 −0.0735281 0.997293i \(-0.523426\pi\)
−0.0735281 + 0.997293i \(0.523426\pi\)
\(60\) 0 0
\(61\) −48740.0 −1.67711 −0.838554 0.544819i \(-0.816598\pi\)
−0.838554 + 0.544819i \(0.816598\pi\)
\(62\) 7664.00 0.253207
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) −15675.0 −0.460176
\(66\) 0 0
\(67\) −44832.0 −1.22012 −0.610058 0.792357i \(-0.708854\pi\)
−0.610058 + 0.792357i \(0.708854\pi\)
\(68\) −29008.0 −0.760756
\(69\) 0 0
\(70\) 4900.00 0.119523
\(71\) −63736.0 −1.50051 −0.750255 0.661148i \(-0.770069\pi\)
−0.750255 + 0.661148i \(0.770069\pi\)
\(72\) 0 0
\(73\) 60470.0 1.32811 0.664053 0.747685i \(-0.268835\pi\)
0.664053 + 0.747685i \(0.268835\pi\)
\(74\) 26312.0 0.558566
\(75\) 0 0
\(76\) 4128.00 0.0819796
\(77\) −9163.00 −0.176121
\(78\) 0 0
\(79\) −43721.0 −0.788174 −0.394087 0.919073i \(-0.628939\pi\)
−0.394087 + 0.919073i \(0.628939\pi\)
\(80\) −6400.00 −0.111803
\(81\) 0 0
\(82\) −26704.0 −0.438573
\(83\) −97276.0 −1.54992 −0.774962 0.632008i \(-0.782231\pi\)
−0.774962 + 0.632008i \(0.782231\pi\)
\(84\) 0 0
\(85\) 45325.0 0.680441
\(86\) 12712.0 0.185339
\(87\) 0 0
\(88\) 11968.0 0.164746
\(89\) −45560.0 −0.609689 −0.304845 0.952402i \(-0.598605\pi\)
−0.304845 + 0.952402i \(0.598605\pi\)
\(90\) 0 0
\(91\) −30723.0 −0.388920
\(92\) −47520.0 −0.585338
\(93\) 0 0
\(94\) 88004.0 1.02727
\(95\) −6450.00 −0.0733248
\(96\) 0 0
\(97\) −57295.0 −0.618283 −0.309142 0.951016i \(-0.600042\pi\)
−0.309142 + 0.951016i \(0.600042\pi\)
\(98\) 9604.00 0.101015
\(99\) 0 0
\(100\) 10000.0 0.100000
\(101\) 44970.0 0.438651 0.219326 0.975652i \(-0.429614\pi\)
0.219326 + 0.975652i \(0.429614\pi\)
\(102\) 0 0
\(103\) −101405. −0.941817 −0.470908 0.882182i \(-0.656074\pi\)
−0.470908 + 0.882182i \(0.656074\pi\)
\(104\) 40128.0 0.363801
\(105\) 0 0
\(106\) −104672. −0.904828
\(107\) 166002. 1.40170 0.700848 0.713311i \(-0.252805\pi\)
0.700848 + 0.713311i \(0.252805\pi\)
\(108\) 0 0
\(109\) 8289.00 0.0668245 0.0334123 0.999442i \(-0.489363\pi\)
0.0334123 + 0.999442i \(0.489363\pi\)
\(110\) −18700.0 −0.147353
\(111\) 0 0
\(112\) −12544.0 −0.0944911
\(113\) −263206. −1.93910 −0.969549 0.244898i \(-0.921245\pi\)
−0.969549 + 0.244898i \(0.921245\pi\)
\(114\) 0 0
\(115\) 74250.0 0.523542
\(116\) −20784.0 −0.143412
\(117\) 0 0
\(118\) −15728.0 −0.103984
\(119\) 88837.0 0.575078
\(120\) 0 0
\(121\) −126082. −0.782870
\(122\) −194960. −1.18589
\(123\) 0 0
\(124\) 30656.0 0.179045
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) 30052.0 0.165335 0.0826674 0.996577i \(-0.473656\pi\)
0.0826674 + 0.996577i \(0.473656\pi\)
\(128\) 16384.0 0.0883883
\(129\) 0 0
\(130\) −62700.0 −0.325394
\(131\) 120050. 0.611201 0.305600 0.952160i \(-0.401143\pi\)
0.305600 + 0.952160i \(0.401143\pi\)
\(132\) 0 0
\(133\) −12642.0 −0.0619707
\(134\) −179328. −0.862752
\(135\) 0 0
\(136\) −116032. −0.537936
\(137\) −31776.0 −0.144643 −0.0723216 0.997381i \(-0.523041\pi\)
−0.0723216 + 0.997381i \(0.523041\pi\)
\(138\) 0 0
\(139\) −200162. −0.878708 −0.439354 0.898314i \(-0.644793\pi\)
−0.439354 + 0.898314i \(0.644793\pi\)
\(140\) 19600.0 0.0845154
\(141\) 0 0
\(142\) −254944. −1.06102
\(143\) 117249. 0.479478
\(144\) 0 0
\(145\) 32475.0 0.128271
\(146\) 241880. 0.939113
\(147\) 0 0
\(148\) 105248. 0.394966
\(149\) −309642. −1.14260 −0.571300 0.820741i \(-0.693561\pi\)
−0.571300 + 0.820741i \(0.693561\pi\)
\(150\) 0 0
\(151\) −208657. −0.744716 −0.372358 0.928089i \(-0.621451\pi\)
−0.372358 + 0.928089i \(0.621451\pi\)
\(152\) 16512.0 0.0579683
\(153\) 0 0
\(154\) −36652.0 −0.124536
\(155\) −47900.0 −0.160142
\(156\) 0 0
\(157\) 36010.0 0.116593 0.0582967 0.998299i \(-0.481433\pi\)
0.0582967 + 0.998299i \(0.481433\pi\)
\(158\) −174884. −0.557324
\(159\) 0 0
\(160\) −25600.0 −0.0790569
\(161\) 145530. 0.442474
\(162\) 0 0
\(163\) 175670. 0.517879 0.258940 0.965893i \(-0.416627\pi\)
0.258940 + 0.965893i \(0.416627\pi\)
\(164\) −106816. −0.310118
\(165\) 0 0
\(166\) −389104. −1.09596
\(167\) 157413. 0.436767 0.218383 0.975863i \(-0.429922\pi\)
0.218383 + 0.975863i \(0.429922\pi\)
\(168\) 0 0
\(169\) 21836.0 0.0588107
\(170\) 181300. 0.481144
\(171\) 0 0
\(172\) 50848.0 0.131055
\(173\) 23471.0 0.0596233 0.0298117 0.999556i \(-0.490509\pi\)
0.0298117 + 0.999556i \(0.490509\pi\)
\(174\) 0 0
\(175\) −30625.0 −0.0755929
\(176\) 47872.0 0.116493
\(177\) 0 0
\(178\) −182240. −0.431116
\(179\) −612228. −1.42817 −0.714086 0.700058i \(-0.753158\pi\)
−0.714086 + 0.700058i \(0.753158\pi\)
\(180\) 0 0
\(181\) 528832. 1.19983 0.599917 0.800062i \(-0.295200\pi\)
0.599917 + 0.800062i \(0.295200\pi\)
\(182\) −122892. −0.275008
\(183\) 0 0
\(184\) −190080. −0.413897
\(185\) −164450. −0.353268
\(186\) 0 0
\(187\) −339031. −0.708982
\(188\) 352016. 0.726387
\(189\) 0 0
\(190\) −25800.0 −0.0518484
\(191\) −540369. −1.07178 −0.535892 0.844287i \(-0.680024\pi\)
−0.535892 + 0.844287i \(0.680024\pi\)
\(192\) 0 0
\(193\) 960320. 1.85576 0.927882 0.372874i \(-0.121628\pi\)
0.927882 + 0.372874i \(0.121628\pi\)
\(194\) −229180. −0.437192
\(195\) 0 0
\(196\) 38416.0 0.0714286
\(197\) −761944. −1.39881 −0.699403 0.714728i \(-0.746551\pi\)
−0.699403 + 0.714728i \(0.746551\pi\)
\(198\) 0 0
\(199\) 125084. 0.223908 0.111954 0.993713i \(-0.464289\pi\)
0.111954 + 0.993713i \(0.464289\pi\)
\(200\) 40000.0 0.0707107
\(201\) 0 0
\(202\) 179880. 0.310173
\(203\) 63651.0 0.108409
\(204\) 0 0
\(205\) 166900. 0.277378
\(206\) −405620. −0.665965
\(207\) 0 0
\(208\) 160512. 0.257246
\(209\) 48246.0 0.0764004
\(210\) 0 0
\(211\) 627547. 0.970376 0.485188 0.874410i \(-0.338751\pi\)
0.485188 + 0.874410i \(0.338751\pi\)
\(212\) −418688. −0.639810
\(213\) 0 0
\(214\) 664008. 0.991149
\(215\) −79450.0 −0.117219
\(216\) 0 0
\(217\) −93884.0 −0.135345
\(218\) 33156.0 0.0472521
\(219\) 0 0
\(220\) −74800.0 −0.104195
\(221\) −1.13675e6 −1.56561
\(222\) 0 0
\(223\) −1.22110e6 −1.64433 −0.822166 0.569248i \(-0.807234\pi\)
−0.822166 + 0.569248i \(0.807234\pi\)
\(224\) −50176.0 −0.0668153
\(225\) 0 0
\(226\) −1.05282e6 −1.37115
\(227\) −390547. −0.503047 −0.251524 0.967851i \(-0.580932\pi\)
−0.251524 + 0.967851i \(0.580932\pi\)
\(228\) 0 0
\(229\) −712124. −0.897360 −0.448680 0.893692i \(-0.648106\pi\)
−0.448680 + 0.893692i \(0.648106\pi\)
\(230\) 297000. 0.370200
\(231\) 0 0
\(232\) −83136.0 −0.101407
\(233\) −561576. −0.677671 −0.338835 0.940846i \(-0.610033\pi\)
−0.338835 + 0.940846i \(0.610033\pi\)
\(234\) 0 0
\(235\) −550025. −0.649700
\(236\) −62912.0 −0.0735281
\(237\) 0 0
\(238\) 355348. 0.406641
\(239\) 1.36084e6 1.54103 0.770515 0.637421i \(-0.219999\pi\)
0.770515 + 0.637421i \(0.219999\pi\)
\(240\) 0 0
\(241\) 530050. 0.587860 0.293930 0.955827i \(-0.405037\pi\)
0.293930 + 0.955827i \(0.405037\pi\)
\(242\) −504328. −0.553573
\(243\) 0 0
\(244\) −779840. −0.838554
\(245\) −60025.0 −0.0638877
\(246\) 0 0
\(247\) 161766. 0.168712
\(248\) 122624. 0.126604
\(249\) 0 0
\(250\) −62500.0 −0.0632456
\(251\) −990330. −0.992192 −0.496096 0.868268i \(-0.665234\pi\)
−0.496096 + 0.868268i \(0.665234\pi\)
\(252\) 0 0
\(253\) −555390. −0.545503
\(254\) 120208. 0.116909
\(255\) 0 0
\(256\) 65536.0 0.0625000
\(257\) 1.81643e6 1.71548 0.857740 0.514083i \(-0.171868\pi\)
0.857740 + 0.514083i \(0.171868\pi\)
\(258\) 0 0
\(259\) −322322. −0.298566
\(260\) −250800. −0.230088
\(261\) 0 0
\(262\) 480200. 0.432184
\(263\) 1.95847e6 1.74594 0.872968 0.487777i \(-0.162192\pi\)
0.872968 + 0.487777i \(0.162192\pi\)
\(264\) 0 0
\(265\) 654200. 0.572263
\(266\) −50568.0 −0.0438199
\(267\) 0 0
\(268\) −717312. −0.610058
\(269\) −218034. −0.183715 −0.0918573 0.995772i \(-0.529280\pi\)
−0.0918573 + 0.995772i \(0.529280\pi\)
\(270\) 0 0
\(271\) 1.26265e6 1.04438 0.522192 0.852828i \(-0.325114\pi\)
0.522192 + 0.852828i \(0.325114\pi\)
\(272\) −464128. −0.380378
\(273\) 0 0
\(274\) −127104. −0.102278
\(275\) 116875. 0.0931944
\(276\) 0 0
\(277\) −1.10264e6 −0.863443 −0.431721 0.902007i \(-0.642094\pi\)
−0.431721 + 0.902007i \(0.642094\pi\)
\(278\) −800648. −0.621340
\(279\) 0 0
\(280\) 78400.0 0.0597614
\(281\) 998213. 0.754149 0.377075 0.926183i \(-0.376930\pi\)
0.377075 + 0.926183i \(0.376930\pi\)
\(282\) 0 0
\(283\) −386371. −0.286773 −0.143387 0.989667i \(-0.545799\pi\)
−0.143387 + 0.989667i \(0.545799\pi\)
\(284\) −1.01978e6 −0.750255
\(285\) 0 0
\(286\) 468996. 0.339042
\(287\) 327124. 0.234427
\(288\) 0 0
\(289\) 1.86711e6 1.31500
\(290\) 129900. 0.0907014
\(291\) 0 0
\(292\) 967520. 0.664053
\(293\) 783571. 0.533224 0.266612 0.963804i \(-0.414096\pi\)
0.266612 + 0.963804i \(0.414096\pi\)
\(294\) 0 0
\(295\) 98300.0 0.0657656
\(296\) 420992. 0.279283
\(297\) 0 0
\(298\) −1.23857e6 −0.807940
\(299\) −1.86219e6 −1.20461
\(300\) 0 0
\(301\) −155722. −0.0990681
\(302\) −834628. −0.526594
\(303\) 0 0
\(304\) 66048.0 0.0409898
\(305\) 1.21850e6 0.750025
\(306\) 0 0
\(307\) 2.81773e6 1.70629 0.853147 0.521670i \(-0.174691\pi\)
0.853147 + 0.521670i \(0.174691\pi\)
\(308\) −146608. −0.0880604
\(309\) 0 0
\(310\) −191600. −0.113238
\(311\) 847398. 0.496806 0.248403 0.968657i \(-0.420094\pi\)
0.248403 + 0.968657i \(0.420094\pi\)
\(312\) 0 0
\(313\) 364955. 0.210561 0.105281 0.994443i \(-0.466426\pi\)
0.105281 + 0.994443i \(0.466426\pi\)
\(314\) 144040. 0.0824440
\(315\) 0 0
\(316\) −699536. −0.394087
\(317\) −1.93744e6 −1.08288 −0.541439 0.840740i \(-0.682120\pi\)
−0.541439 + 0.840740i \(0.682120\pi\)
\(318\) 0 0
\(319\) −242913. −0.133652
\(320\) −102400. −0.0559017
\(321\) 0 0
\(322\) 582120. 0.312876
\(323\) −467754. −0.249466
\(324\) 0 0
\(325\) 391875. 0.205797
\(326\) 702680. 0.366196
\(327\) 0 0
\(328\) −427264. −0.219286
\(329\) −1.07805e6 −0.549097
\(330\) 0 0
\(331\) −61460.0 −0.0308335 −0.0154167 0.999881i \(-0.504907\pi\)
−0.0154167 + 0.999881i \(0.504907\pi\)
\(332\) −1.55642e6 −0.774962
\(333\) 0 0
\(334\) 629652. 0.308841
\(335\) 1.12080e6 0.545652
\(336\) 0 0
\(337\) −3.74116e6 −1.79445 −0.897225 0.441574i \(-0.854420\pi\)
−0.897225 + 0.441574i \(0.854420\pi\)
\(338\) 87344.0 0.0415854
\(339\) 0 0
\(340\) 725200. 0.340221
\(341\) 358292. 0.166860
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 203392. 0.0926697
\(345\) 0 0
\(346\) 93884.0 0.0421601
\(347\) −211334. −0.0942206 −0.0471103 0.998890i \(-0.515001\pi\)
−0.0471103 + 0.998890i \(0.515001\pi\)
\(348\) 0 0
\(349\) 3.39558e6 1.49228 0.746140 0.665789i \(-0.231905\pi\)
0.746140 + 0.665789i \(0.231905\pi\)
\(350\) −122500. −0.0534522
\(351\) 0 0
\(352\) 191488. 0.0823730
\(353\) 3.88094e6 1.65768 0.828838 0.559489i \(-0.189003\pi\)
0.828838 + 0.559489i \(0.189003\pi\)
\(354\) 0 0
\(355\) 1.59340e6 0.671049
\(356\) −728960. −0.304845
\(357\) 0 0
\(358\) −2.44891e6 −1.00987
\(359\) −3.24210e6 −1.32767 −0.663836 0.747878i \(-0.731073\pi\)
−0.663836 + 0.747878i \(0.731073\pi\)
\(360\) 0 0
\(361\) −2.40954e6 −0.973117
\(362\) 2.11533e6 0.848411
\(363\) 0 0
\(364\) −491568. −0.194460
\(365\) −1.51175e6 −0.593947
\(366\) 0 0
\(367\) 1.44430e6 0.559749 0.279874 0.960037i \(-0.409707\pi\)
0.279874 + 0.960037i \(0.409707\pi\)
\(368\) −760320. −0.292669
\(369\) 0 0
\(370\) −657800. −0.249798
\(371\) 1.28223e6 0.483651
\(372\) 0 0
\(373\) 3.43542e6 1.27852 0.639260 0.768991i \(-0.279241\pi\)
0.639260 + 0.768991i \(0.279241\pi\)
\(374\) −1.35612e6 −0.501326
\(375\) 0 0
\(376\) 1.40806e6 0.513633
\(377\) −814473. −0.295137
\(378\) 0 0
\(379\) −1.68635e6 −0.603044 −0.301522 0.953459i \(-0.597495\pi\)
−0.301522 + 0.953459i \(0.597495\pi\)
\(380\) −103200. −0.0366624
\(381\) 0 0
\(382\) −2.16148e6 −0.757865
\(383\) −2.64354e6 −0.920850 −0.460425 0.887699i \(-0.652303\pi\)
−0.460425 + 0.887699i \(0.652303\pi\)
\(384\) 0 0
\(385\) 229075. 0.0787637
\(386\) 3.84128e6 1.31222
\(387\) 0 0
\(388\) −916720. −0.309142
\(389\) 452099. 0.151481 0.0757407 0.997128i \(-0.475868\pi\)
0.0757407 + 0.997128i \(0.475868\pi\)
\(390\) 0 0
\(391\) 5.38461e6 1.78120
\(392\) 153664. 0.0505076
\(393\) 0 0
\(394\) −3.04778e6 −0.989105
\(395\) 1.09302e6 0.352482
\(396\) 0 0
\(397\) −1.95530e6 −0.622641 −0.311321 0.950305i \(-0.600771\pi\)
−0.311321 + 0.950305i \(0.600771\pi\)
\(398\) 500336. 0.158327
\(399\) 0 0
\(400\) 160000. 0.0500000
\(401\) 4.76737e6 1.48053 0.740266 0.672314i \(-0.234700\pi\)
0.740266 + 0.672314i \(0.234700\pi\)
\(402\) 0 0
\(403\) 1.20133e6 0.368469
\(404\) 719520. 0.219326
\(405\) 0 0
\(406\) 254604. 0.0766567
\(407\) 1.23009e6 0.368086
\(408\) 0 0
\(409\) −4.13199e6 −1.22138 −0.610690 0.791870i \(-0.709108\pi\)
−0.610690 + 0.791870i \(0.709108\pi\)
\(410\) 667600. 0.196136
\(411\) 0 0
\(412\) −1.62248e6 −0.470908
\(413\) 192668. 0.0555820
\(414\) 0 0
\(415\) 2.43190e6 0.693147
\(416\) 642048. 0.181901
\(417\) 0 0
\(418\) 192984. 0.0540232
\(419\) −190512. −0.0530136 −0.0265068 0.999649i \(-0.508438\pi\)
−0.0265068 + 0.999649i \(0.508438\pi\)
\(420\) 0 0
\(421\) −5.19186e6 −1.42764 −0.713818 0.700332i \(-0.753035\pi\)
−0.713818 + 0.700332i \(0.753035\pi\)
\(422\) 2.51019e6 0.686160
\(423\) 0 0
\(424\) −1.67475e6 −0.452414
\(425\) −1.13312e6 −0.304302
\(426\) 0 0
\(427\) 2.38826e6 0.633887
\(428\) 2.65603e6 0.700848
\(429\) 0 0
\(430\) −317800. −0.0828863
\(431\) 4.21781e6 1.09369 0.546845 0.837234i \(-0.315829\pi\)
0.546845 + 0.837234i \(0.315829\pi\)
\(432\) 0 0
\(433\) −4.86027e6 −1.24578 −0.622890 0.782310i \(-0.714041\pi\)
−0.622890 + 0.782310i \(0.714041\pi\)
\(434\) −375536. −0.0957034
\(435\) 0 0
\(436\) 132624. 0.0334123
\(437\) −766260. −0.191943
\(438\) 0 0
\(439\) −2.03113e6 −0.503011 −0.251505 0.967856i \(-0.580926\pi\)
−0.251505 + 0.967856i \(0.580926\pi\)
\(440\) −299200. −0.0736767
\(441\) 0 0
\(442\) −4.54700e6 −1.10706
\(443\) −2.84199e6 −0.688038 −0.344019 0.938963i \(-0.611789\pi\)
−0.344019 + 0.938963i \(0.611789\pi\)
\(444\) 0 0
\(445\) 1.13900e6 0.272661
\(446\) −4.88440e6 −1.16272
\(447\) 0 0
\(448\) −200704. −0.0472456
\(449\) 4.59682e6 1.07607 0.538037 0.842921i \(-0.319166\pi\)
0.538037 + 0.842921i \(0.319166\pi\)
\(450\) 0 0
\(451\) −1.24841e6 −0.289012
\(452\) −4.21130e6 −0.969549
\(453\) 0 0
\(454\) −1.56219e6 −0.355708
\(455\) 768075. 0.173930
\(456\) 0 0
\(457\) 4.93367e6 1.10504 0.552522 0.833498i \(-0.313665\pi\)
0.552522 + 0.833498i \(0.313665\pi\)
\(458\) −2.84850e6 −0.634530
\(459\) 0 0
\(460\) 1.18800e6 0.261771
\(461\) 4.75667e6 1.04244 0.521220 0.853422i \(-0.325477\pi\)
0.521220 + 0.853422i \(0.325477\pi\)
\(462\) 0 0
\(463\) 4.08619e6 0.885862 0.442931 0.896556i \(-0.353939\pi\)
0.442931 + 0.896556i \(0.353939\pi\)
\(464\) −332544. −0.0717058
\(465\) 0 0
\(466\) −2.24630e6 −0.479186
\(467\) 4.15932e6 0.882531 0.441266 0.897377i \(-0.354530\pi\)
0.441266 + 0.897377i \(0.354530\pi\)
\(468\) 0 0
\(469\) 2.19677e6 0.461160
\(470\) −2.20010e6 −0.459407
\(471\) 0 0
\(472\) −251648. −0.0519922
\(473\) 594286. 0.122136
\(474\) 0 0
\(475\) 161250. 0.0327918
\(476\) 1.42139e6 0.287539
\(477\) 0 0
\(478\) 5.44335e6 1.08967
\(479\) 3.36040e6 0.669195 0.334597 0.942361i \(-0.391400\pi\)
0.334597 + 0.942361i \(0.391400\pi\)
\(480\) 0 0
\(481\) 4.12441e6 0.812828
\(482\) 2.12020e6 0.415680
\(483\) 0 0
\(484\) −2.01731e6 −0.391435
\(485\) 1.43238e6 0.276505
\(486\) 0 0
\(487\) 7.05243e6 1.34746 0.673730 0.738977i \(-0.264691\pi\)
0.673730 + 0.738977i \(0.264691\pi\)
\(488\) −3.11936e6 −0.592947
\(489\) 0 0
\(490\) −240100. −0.0451754
\(491\) 83937.0 0.0157127 0.00785633 0.999969i \(-0.497499\pi\)
0.00785633 + 0.999969i \(0.497499\pi\)
\(492\) 0 0
\(493\) 2.35509e6 0.436405
\(494\) 647064. 0.119297
\(495\) 0 0
\(496\) 490496. 0.0895223
\(497\) 3.12306e6 0.567140
\(498\) 0 0
\(499\) −7.10526e6 −1.27741 −0.638703 0.769454i \(-0.720529\pi\)
−0.638703 + 0.769454i \(0.720529\pi\)
\(500\) −250000. −0.0447214
\(501\) 0 0
\(502\) −3.96132e6 −0.701586
\(503\) −2.89147e6 −0.509564 −0.254782 0.966999i \(-0.582004\pi\)
−0.254782 + 0.966999i \(0.582004\pi\)
\(504\) 0 0
\(505\) −1.12425e6 −0.196171
\(506\) −2.22156e6 −0.385729
\(507\) 0 0
\(508\) 480832. 0.0826674
\(509\) −1.03548e6 −0.177153 −0.0885764 0.996069i \(-0.528232\pi\)
−0.0885764 + 0.996069i \(0.528232\pi\)
\(510\) 0 0
\(511\) −2.96303e6 −0.501977
\(512\) 262144. 0.0441942
\(513\) 0 0
\(514\) 7.26572e6 1.21303
\(515\) 2.53513e6 0.421193
\(516\) 0 0
\(517\) 4.11419e6 0.676952
\(518\) −1.28929e6 −0.211118
\(519\) 0 0
\(520\) −1.00320e6 −0.162697
\(521\) 7.49715e6 1.21005 0.605023 0.796208i \(-0.293164\pi\)
0.605023 + 0.796208i \(0.293164\pi\)
\(522\) 0 0
\(523\) 3.53223e6 0.564670 0.282335 0.959316i \(-0.408891\pi\)
0.282335 + 0.959316i \(0.408891\pi\)
\(524\) 1.92080e6 0.305600
\(525\) 0 0
\(526\) 7.83390e6 1.23456
\(527\) −3.47371e6 −0.544837
\(528\) 0 0
\(529\) 2.38456e6 0.370483
\(530\) 2.61680e6 0.404651
\(531\) 0 0
\(532\) −202272. −0.0309854
\(533\) −4.18585e6 −0.638213
\(534\) 0 0
\(535\) −4.15005e6 −0.626858
\(536\) −2.86925e6 −0.431376
\(537\) 0 0
\(538\) −872136. −0.129906
\(539\) 448987. 0.0665674
\(540\) 0 0
\(541\) −4.99188e6 −0.733281 −0.366641 0.930363i \(-0.619492\pi\)
−0.366641 + 0.930363i \(0.619492\pi\)
\(542\) 5.05061e6 0.738491
\(543\) 0 0
\(544\) −1.85651e6 −0.268968
\(545\) −207225. −0.0298848
\(546\) 0 0
\(547\) 5.12634e6 0.732553 0.366277 0.930506i \(-0.380632\pi\)
0.366277 + 0.930506i \(0.380632\pi\)
\(548\) −508416. −0.0723216
\(549\) 0 0
\(550\) 467500. 0.0658984
\(551\) −335142. −0.0470273
\(552\) 0 0
\(553\) 2.14233e6 0.297902
\(554\) −4.41055e6 −0.610546
\(555\) 0 0
\(556\) −3.20259e6 −0.439354
\(557\) −8.86866e6 −1.21121 −0.605606 0.795765i \(-0.707069\pi\)
−0.605606 + 0.795765i \(0.707069\pi\)
\(558\) 0 0
\(559\) 1.99261e6 0.269707
\(560\) 313600. 0.0422577
\(561\) 0 0
\(562\) 3.99285e6 0.533264
\(563\) −9.07277e6 −1.20634 −0.603169 0.797613i \(-0.706096\pi\)
−0.603169 + 0.797613i \(0.706096\pi\)
\(564\) 0 0
\(565\) 6.58015e6 0.867191
\(566\) −1.54548e6 −0.202779
\(567\) 0 0
\(568\) −4.07910e6 −0.530510
\(569\) −2.08310e6 −0.269730 −0.134865 0.990864i \(-0.543060\pi\)
−0.134865 + 0.990864i \(0.543060\pi\)
\(570\) 0 0
\(571\) −5.46368e6 −0.701286 −0.350643 0.936509i \(-0.614037\pi\)
−0.350643 + 0.936509i \(0.614037\pi\)
\(572\) 1.87598e6 0.239739
\(573\) 0 0
\(574\) 1.30850e6 0.165765
\(575\) −1.85625e6 −0.234135
\(576\) 0 0
\(577\) 7.66246e6 0.958140 0.479070 0.877777i \(-0.340974\pi\)
0.479070 + 0.877777i \(0.340974\pi\)
\(578\) 7.46845e6 0.929845
\(579\) 0 0
\(580\) 519600. 0.0641356
\(581\) 4.76652e6 0.585816
\(582\) 0 0
\(583\) −4.89342e6 −0.596267
\(584\) 3.87008e6 0.469556
\(585\) 0 0
\(586\) 3.13428e6 0.377046
\(587\) 1.57465e7 1.88620 0.943100 0.332510i \(-0.107896\pi\)
0.943100 + 0.332510i \(0.107896\pi\)
\(588\) 0 0
\(589\) 494328. 0.0587120
\(590\) 393200. 0.0465033
\(591\) 0 0
\(592\) 1.68397e6 0.197483
\(593\) 1.62409e7 1.89658 0.948292 0.317398i \(-0.102809\pi\)
0.948292 + 0.317398i \(0.102809\pi\)
\(594\) 0 0
\(595\) −2.22093e6 −0.257183
\(596\) −4.95427e6 −0.571300
\(597\) 0 0
\(598\) −7.44876e6 −0.851787
\(599\) 1.90793e6 0.217268 0.108634 0.994082i \(-0.465352\pi\)
0.108634 + 0.994082i \(0.465352\pi\)
\(600\) 0 0
\(601\) 3.52970e6 0.398613 0.199306 0.979937i \(-0.436131\pi\)
0.199306 + 0.979937i \(0.436131\pi\)
\(602\) −622888. −0.0700517
\(603\) 0 0
\(604\) −3.33851e6 −0.372358
\(605\) 3.15205e6 0.350110
\(606\) 0 0
\(607\) 3.37799e6 0.372123 0.186061 0.982538i \(-0.440428\pi\)
0.186061 + 0.982538i \(0.440428\pi\)
\(608\) 264192. 0.0289842
\(609\) 0 0
\(610\) 4.87400e6 0.530348
\(611\) 1.37946e7 1.49488
\(612\) 0 0
\(613\) 1.20412e6 0.129425 0.0647127 0.997904i \(-0.479387\pi\)
0.0647127 + 0.997904i \(0.479387\pi\)
\(614\) 1.12709e7 1.20653
\(615\) 0 0
\(616\) −586432. −0.0622681
\(617\) 5.47330e6 0.578810 0.289405 0.957207i \(-0.406543\pi\)
0.289405 + 0.957207i \(0.406543\pi\)
\(618\) 0 0
\(619\) 3.22662e6 0.338471 0.169236 0.985576i \(-0.445870\pi\)
0.169236 + 0.985576i \(0.445870\pi\)
\(620\) −766400. −0.0800712
\(621\) 0 0
\(622\) 3.38959e6 0.351295
\(623\) 2.23244e6 0.230441
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 1.45982e6 0.148889
\(627\) 0 0
\(628\) 576160. 0.0582967
\(629\) −1.19259e7 −1.20189
\(630\) 0 0
\(631\) 1.36282e7 1.36259 0.681297 0.732007i \(-0.261416\pi\)
0.681297 + 0.732007i \(0.261416\pi\)
\(632\) −2.79814e6 −0.278662
\(633\) 0 0
\(634\) −7.74975e6 −0.765711
\(635\) −751300. −0.0739399
\(636\) 0 0
\(637\) 1.50543e6 0.146998
\(638\) −971652. −0.0945059
\(639\) 0 0
\(640\) −409600. −0.0395285
\(641\) 1.92472e7 1.85021 0.925106 0.379710i \(-0.123976\pi\)
0.925106 + 0.379710i \(0.123976\pi\)
\(642\) 0 0
\(643\) −1.28399e7 −1.22472 −0.612358 0.790580i \(-0.709779\pi\)
−0.612358 + 0.790580i \(0.709779\pi\)
\(644\) 2.32848e6 0.221237
\(645\) 0 0
\(646\) −1.87102e6 −0.176399
\(647\) −2.00233e7 −1.88050 −0.940251 0.340481i \(-0.889410\pi\)
−0.940251 + 0.340481i \(0.889410\pi\)
\(648\) 0 0
\(649\) −735284. −0.0685241
\(650\) 1.56750e6 0.145520
\(651\) 0 0
\(652\) 2.81072e6 0.258940
\(653\) 7.23655e6 0.664124 0.332062 0.943258i \(-0.392256\pi\)
0.332062 + 0.943258i \(0.392256\pi\)
\(654\) 0 0
\(655\) −3.00125e6 −0.273337
\(656\) −1.70906e6 −0.155059
\(657\) 0 0
\(658\) −4.31220e6 −0.388270
\(659\) −1.42474e7 −1.27798 −0.638989 0.769216i \(-0.720647\pi\)
−0.638989 + 0.769216i \(0.720647\pi\)
\(660\) 0 0
\(661\) 1.49265e7 1.32878 0.664391 0.747385i \(-0.268691\pi\)
0.664391 + 0.747385i \(0.268691\pi\)
\(662\) −245840. −0.0218026
\(663\) 0 0
\(664\) −6.22566e6 −0.547981
\(665\) 316050. 0.0277142
\(666\) 0 0
\(667\) 3.85803e6 0.335777
\(668\) 2.51861e6 0.218383
\(669\) 0 0
\(670\) 4.48320e6 0.385835
\(671\) −9.11438e6 −0.781485
\(672\) 0 0
\(673\) −1.55062e7 −1.31967 −0.659837 0.751409i \(-0.729375\pi\)
−0.659837 + 0.751409i \(0.729375\pi\)
\(674\) −1.49646e7 −1.26887
\(675\) 0 0
\(676\) 349376. 0.0294053
\(677\) 7.80065e6 0.654122 0.327061 0.945003i \(-0.393942\pi\)
0.327061 + 0.945003i \(0.393942\pi\)
\(678\) 0 0
\(679\) 2.80745e6 0.233689
\(680\) 2.90080e6 0.240572
\(681\) 0 0
\(682\) 1.43317e6 0.117988
\(683\) −1.58547e7 −1.30049 −0.650243 0.759727i \(-0.725333\pi\)
−0.650243 + 0.759727i \(0.725333\pi\)
\(684\) 0 0
\(685\) 794400. 0.0646864
\(686\) −470596. −0.0381802
\(687\) 0 0
\(688\) 813568. 0.0655274
\(689\) −1.64073e7 −1.31671
\(690\) 0 0
\(691\) 2.03656e7 1.62257 0.811284 0.584652i \(-0.198769\pi\)
0.811284 + 0.584652i \(0.198769\pi\)
\(692\) 375536. 0.0298117
\(693\) 0 0
\(694\) −845336. −0.0666240
\(695\) 5.00405e6 0.392970
\(696\) 0 0
\(697\) 1.21036e7 0.943696
\(698\) 1.35823e7 1.05520
\(699\) 0 0
\(700\) −490000. −0.0377964
\(701\) −2.48036e7 −1.90643 −0.953213 0.302300i \(-0.902246\pi\)
−0.953213 + 0.302300i \(0.902246\pi\)
\(702\) 0 0
\(703\) 1.69712e6 0.129517
\(704\) 765952. 0.0582465
\(705\) 0 0
\(706\) 1.55237e7 1.17215
\(707\) −2.20353e6 −0.165795
\(708\) 0 0
\(709\) 1.81917e7 1.35912 0.679560 0.733620i \(-0.262171\pi\)
0.679560 + 0.733620i \(0.262171\pi\)
\(710\) 6.37360e6 0.474503
\(711\) 0 0
\(712\) −2.91584e6 −0.215558
\(713\) −5.69052e6 −0.419207
\(714\) 0 0
\(715\) −2.93122e6 −0.214429
\(716\) −9.79565e6 −0.714086
\(717\) 0 0
\(718\) −1.29684e7 −0.938806
\(719\) 1.66202e7 1.19899 0.599493 0.800380i \(-0.295369\pi\)
0.599493 + 0.800380i \(0.295369\pi\)
\(720\) 0 0
\(721\) 4.96884e6 0.355973
\(722\) −9.63814e6 −0.688098
\(723\) 0 0
\(724\) 8.46131e6 0.599917
\(725\) −811875. −0.0573646
\(726\) 0 0
\(727\) −1.57591e7 −1.10585 −0.552925 0.833231i \(-0.686489\pi\)
−0.552925 + 0.833231i \(0.686489\pi\)
\(728\) −1.96627e6 −0.137504
\(729\) 0 0
\(730\) −6.04700e6 −0.419984
\(731\) −5.76171e6 −0.398803
\(732\) 0 0
\(733\) −2.15238e6 −0.147965 −0.0739827 0.997260i \(-0.523571\pi\)
−0.0739827 + 0.997260i \(0.523571\pi\)
\(734\) 5.77721e6 0.395802
\(735\) 0 0
\(736\) −3.04128e6 −0.206948
\(737\) −8.38358e6 −0.568540
\(738\) 0 0
\(739\) −2.27267e7 −1.53083 −0.765413 0.643540i \(-0.777465\pi\)
−0.765413 + 0.643540i \(0.777465\pi\)
\(740\) −2.63120e6 −0.176634
\(741\) 0 0
\(742\) 5.12893e6 0.341993
\(743\) −1.21153e7 −0.805123 −0.402561 0.915393i \(-0.631880\pi\)
−0.402561 + 0.915393i \(0.631880\pi\)
\(744\) 0 0
\(745\) 7.74105e6 0.510986
\(746\) 1.37417e7 0.904050
\(747\) 0 0
\(748\) −5.42450e6 −0.354491
\(749\) −8.13410e6 −0.529791
\(750\) 0 0
\(751\) −2.07590e7 −1.34310 −0.671549 0.740961i \(-0.734371\pi\)
−0.671549 + 0.740961i \(0.734371\pi\)
\(752\) 5.63226e6 0.363193
\(753\) 0 0
\(754\) −3.25789e6 −0.208693
\(755\) 5.21642e6 0.333047
\(756\) 0 0
\(757\) −1.86222e7 −1.18111 −0.590556 0.806997i \(-0.701091\pi\)
−0.590556 + 0.806997i \(0.701091\pi\)
\(758\) −6.74539e6 −0.426417
\(759\) 0 0
\(760\) −412800. −0.0259242
\(761\) −2.65336e7 −1.66087 −0.830434 0.557117i \(-0.811907\pi\)
−0.830434 + 0.557117i \(0.811907\pi\)
\(762\) 0 0
\(763\) −406161. −0.0252573
\(764\) −8.64590e6 −0.535892
\(765\) 0 0
\(766\) −1.05742e7 −0.651139
\(767\) −2.46536e6 −0.151319
\(768\) 0 0
\(769\) −2.01595e7 −1.22931 −0.614657 0.788794i \(-0.710706\pi\)
−0.614657 + 0.788794i \(0.710706\pi\)
\(770\) 916300. 0.0556943
\(771\) 0 0
\(772\) 1.53651e7 0.927882
\(773\) 5.86488e6 0.353029 0.176514 0.984298i \(-0.443518\pi\)
0.176514 + 0.984298i \(0.443518\pi\)
\(774\) 0 0
\(775\) 1.19750e6 0.0716178
\(776\) −3.66688e6 −0.218596
\(777\) 0 0
\(778\) 1.80840e6 0.107114
\(779\) −1.72241e6 −0.101693
\(780\) 0 0
\(781\) −1.19186e7 −0.699196
\(782\) 2.15384e7 1.25950
\(783\) 0 0
\(784\) 614656. 0.0357143
\(785\) −900250. −0.0521422
\(786\) 0 0
\(787\) −1.63347e6 −0.0940100 −0.0470050 0.998895i \(-0.514968\pi\)
−0.0470050 + 0.998895i \(0.514968\pi\)
\(788\) −1.21911e7 −0.699403
\(789\) 0 0
\(790\) 4.37210e6 0.249243
\(791\) 1.28971e7 0.732910
\(792\) 0 0
\(793\) −3.05600e7 −1.72572
\(794\) −7.82121e6 −0.440274
\(795\) 0 0
\(796\) 2.00134e6 0.111954
\(797\) −2.07673e7 −1.15807 −0.579034 0.815303i \(-0.696570\pi\)
−0.579034 + 0.815303i \(0.696570\pi\)
\(798\) 0 0
\(799\) −3.98878e7 −2.21041
\(800\) 640000. 0.0353553
\(801\) 0 0
\(802\) 1.90695e7 1.04689
\(803\) 1.13079e7 0.618860
\(804\) 0 0
\(805\) −3.63825e6 −0.197880
\(806\) 4.80533e6 0.260547
\(807\) 0 0
\(808\) 2.87808e6 0.155087
\(809\) −3.53936e6 −0.190131 −0.0950656 0.995471i \(-0.530306\pi\)
−0.0950656 + 0.995471i \(0.530306\pi\)
\(810\) 0 0
\(811\) −2.11480e7 −1.12906 −0.564530 0.825412i \(-0.690943\pi\)
−0.564530 + 0.825412i \(0.690943\pi\)
\(812\) 1.01842e6 0.0542045
\(813\) 0 0
\(814\) 4.92034e6 0.260276
\(815\) −4.39175e6 −0.231603
\(816\) 0 0
\(817\) 819924. 0.0429753
\(818\) −1.65280e7 −0.863646
\(819\) 0 0
\(820\) 2.67040e6 0.138689
\(821\) −265389. −0.0137412 −0.00687061 0.999976i \(-0.502187\pi\)
−0.00687061 + 0.999976i \(0.502187\pi\)
\(822\) 0 0
\(823\) 3.09261e7 1.59157 0.795785 0.605579i \(-0.207058\pi\)
0.795785 + 0.605579i \(0.207058\pi\)
\(824\) −6.48992e6 −0.332982
\(825\) 0 0
\(826\) 770672. 0.0393024
\(827\) 2.84152e7 1.44473 0.722367 0.691510i \(-0.243054\pi\)
0.722367 + 0.691510i \(0.243054\pi\)
\(828\) 0 0
\(829\) −3.33547e7 −1.68566 −0.842832 0.538177i \(-0.819113\pi\)
−0.842832 + 0.538177i \(0.819113\pi\)
\(830\) 9.72760e6 0.490129
\(831\) 0 0
\(832\) 2.56819e6 0.128623
\(833\) −4.35301e6 −0.217359
\(834\) 0 0
\(835\) −3.93532e6 −0.195328
\(836\) 771936. 0.0382002
\(837\) 0 0
\(838\) −762048. −0.0374863
\(839\) 5.66205e6 0.277695 0.138848 0.990314i \(-0.455660\pi\)
0.138848 + 0.990314i \(0.455660\pi\)
\(840\) 0 0
\(841\) −1.88237e7 −0.917732
\(842\) −2.07674e7 −1.00949
\(843\) 0 0
\(844\) 1.00408e7 0.485188
\(845\) −545900. −0.0263009
\(846\) 0 0
\(847\) 6.17802e6 0.295897
\(848\) −6.69901e6 −0.319905
\(849\) 0 0
\(850\) −4.53250e6 −0.215174
\(851\) −1.95367e7 −0.924754
\(852\) 0 0
\(853\) 2.19983e7 1.03518 0.517592 0.855628i \(-0.326829\pi\)
0.517592 + 0.855628i \(0.326829\pi\)
\(854\) 9.55304e6 0.448226
\(855\) 0 0
\(856\) 1.06241e7 0.495574
\(857\) 2.17568e7 1.01191 0.505956 0.862559i \(-0.331140\pi\)
0.505956 + 0.862559i \(0.331140\pi\)
\(858\) 0 0
\(859\) −4.09384e7 −1.89299 −0.946494 0.322721i \(-0.895402\pi\)
−0.946494 + 0.322721i \(0.895402\pi\)
\(860\) −1.27120e6 −0.0586095
\(861\) 0 0
\(862\) 1.68712e7 0.773355
\(863\) −5.65597e6 −0.258512 −0.129256 0.991611i \(-0.541259\pi\)
−0.129256 + 0.991611i \(0.541259\pi\)
\(864\) 0 0
\(865\) −586775. −0.0266644
\(866\) −1.94411e7 −0.880899
\(867\) 0 0
\(868\) −1.50214e6 −0.0676725
\(869\) −8.17583e6 −0.367267
\(870\) 0 0
\(871\) −2.81097e7 −1.25548
\(872\) 530496. 0.0236260
\(873\) 0 0
\(874\) −3.06504e6 −0.135724
\(875\) 765625. 0.0338062
\(876\) 0 0
\(877\) 2.61067e7 1.14618 0.573089 0.819493i \(-0.305745\pi\)
0.573089 + 0.819493i \(0.305745\pi\)
\(878\) −8.12454e6 −0.355682
\(879\) 0 0
\(880\) −1.19680e6 −0.0520973
\(881\) −1.44294e6 −0.0626339 −0.0313170 0.999510i \(-0.509970\pi\)
−0.0313170 + 0.999510i \(0.509970\pi\)
\(882\) 0 0
\(883\) −1.52432e7 −0.657921 −0.328960 0.944344i \(-0.606698\pi\)
−0.328960 + 0.944344i \(0.606698\pi\)
\(884\) −1.81880e7 −0.782807
\(885\) 0 0
\(886\) −1.13679e7 −0.486517
\(887\) 3.31500e7 1.41473 0.707366 0.706847i \(-0.249883\pi\)
0.707366 + 0.706847i \(0.249883\pi\)
\(888\) 0 0
\(889\) −1.47255e6 −0.0624907
\(890\) 4.55600e6 0.192801
\(891\) 0 0
\(892\) −1.95376e7 −0.822166
\(893\) 5.67626e6 0.238195
\(894\) 0 0
\(895\) 1.53057e7 0.638698
\(896\) −802816. −0.0334077
\(897\) 0 0
\(898\) 1.83873e7 0.760899
\(899\) −2.48888e6 −0.102708
\(900\) 0 0
\(901\) 4.74426e7 1.94696
\(902\) −4.99365e6 −0.204363
\(903\) 0 0
\(904\) −1.68452e7 −0.685575
\(905\) −1.32208e7 −0.536582
\(906\) 0 0
\(907\) 1.16963e7 0.472096 0.236048 0.971741i \(-0.424148\pi\)
0.236048 + 0.971741i \(0.424148\pi\)
\(908\) −6.24875e6 −0.251524
\(909\) 0 0
\(910\) 3.07230e6 0.122987
\(911\) −2.89321e7 −1.15501 −0.577503 0.816389i \(-0.695973\pi\)
−0.577503 + 0.816389i \(0.695973\pi\)
\(912\) 0 0
\(913\) −1.81906e7 −0.722221
\(914\) 1.97347e7 0.781384
\(915\) 0 0
\(916\) −1.13940e7 −0.448680
\(917\) −5.88245e6 −0.231012
\(918\) 0 0
\(919\) −4.57838e7 −1.78823 −0.894115 0.447838i \(-0.852194\pi\)
−0.894115 + 0.447838i \(0.852194\pi\)
\(920\) 4.75200e6 0.185100
\(921\) 0 0
\(922\) 1.90267e7 0.737116
\(923\) −3.99625e7 −1.54400
\(924\) 0 0
\(925\) 4.11125e6 0.157986
\(926\) 1.63448e7 0.626399
\(927\) 0 0
\(928\) −1.33018e6 −0.0507036
\(929\) −2.46947e7 −0.938782 −0.469391 0.882990i \(-0.655526\pi\)
−0.469391 + 0.882990i \(0.655526\pi\)
\(930\) 0 0
\(931\) 619458. 0.0234227
\(932\) −8.98522e6 −0.338835
\(933\) 0 0
\(934\) 1.66373e7 0.624044
\(935\) 8.47578e6 0.317067
\(936\) 0 0
\(937\) −1.98926e7 −0.740187 −0.370094 0.928994i \(-0.620674\pi\)
−0.370094 + 0.928994i \(0.620674\pi\)
\(938\) 8.78707e6 0.326090
\(939\) 0 0
\(940\) −8.80040e6 −0.324850
\(941\) 3.73454e7 1.37488 0.687438 0.726243i \(-0.258735\pi\)
0.687438 + 0.726243i \(0.258735\pi\)
\(942\) 0 0
\(943\) 1.98277e7 0.726095
\(944\) −1.00659e6 −0.0367641
\(945\) 0 0
\(946\) 2.37714e6 0.0863630
\(947\) −5.10396e7 −1.84941 −0.924703 0.380689i \(-0.875687\pi\)
−0.924703 + 0.380689i \(0.875687\pi\)
\(948\) 0 0
\(949\) 3.79147e7 1.36660
\(950\) 645000. 0.0231873
\(951\) 0 0
\(952\) 5.68557e6 0.203321
\(953\) −254832. −0.00908912 −0.00454456 0.999990i \(-0.501447\pi\)
−0.00454456 + 0.999990i \(0.501447\pi\)
\(954\) 0 0
\(955\) 1.35092e7 0.479316
\(956\) 2.17734e7 0.770515
\(957\) 0 0
\(958\) 1.34416e7 0.473192
\(959\) 1.55702e6 0.0546700
\(960\) 0 0
\(961\) −2.49581e7 −0.871772
\(962\) 1.64976e7 0.574756
\(963\) 0 0
\(964\) 8.48080e6 0.293930
\(965\) −2.40080e7 −0.829923
\(966\) 0 0
\(967\) 1.17012e7 0.402405 0.201203 0.979550i \(-0.435515\pi\)
0.201203 + 0.979550i \(0.435515\pi\)
\(968\) −8.06925e6 −0.276786
\(969\) 0 0
\(970\) 5.72950e6 0.195518
\(971\) −3.59080e7 −1.22220 −0.611101 0.791553i \(-0.709273\pi\)
−0.611101 + 0.791553i \(0.709273\pi\)
\(972\) 0 0
\(973\) 9.80794e6 0.332120
\(974\) 2.82097e7 0.952799
\(975\) 0 0
\(976\) −1.24774e7 −0.419277
\(977\) 5.50592e7 1.84541 0.922706 0.385504i \(-0.125972\pi\)
0.922706 + 0.385504i \(0.125972\pi\)
\(978\) 0 0
\(979\) −8.51972e6 −0.284098
\(980\) −960400. −0.0319438
\(981\) 0 0
\(982\) 335748. 0.0111105
\(983\) 1.81317e7 0.598488 0.299244 0.954177i \(-0.403266\pi\)
0.299244 + 0.954177i \(0.403266\pi\)
\(984\) 0 0
\(985\) 1.90486e7 0.625565
\(986\) 9.42035e6 0.308585
\(987\) 0 0
\(988\) 2.58826e6 0.0843558
\(989\) −9.43866e6 −0.306845
\(990\) 0 0
\(991\) −2.02908e7 −0.656318 −0.328159 0.944623i \(-0.606428\pi\)
−0.328159 + 0.944623i \(0.606428\pi\)
\(992\) 1.96198e6 0.0633018
\(993\) 0 0
\(994\) 1.24923e7 0.401028
\(995\) −3.12710e6 −0.100135
\(996\) 0 0
\(997\) 4.75390e7 1.51465 0.757325 0.653038i \(-0.226506\pi\)
0.757325 + 0.653038i \(0.226506\pi\)
\(998\) −2.84211e7 −0.903262
\(999\) 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 630.6.a.i.1.1 1
3.2 odd 2 70.6.a.b.1.1 1
12.11 even 2 560.6.a.e.1.1 1
15.2 even 4 350.6.c.g.99.1 2
15.8 even 4 350.6.c.g.99.2 2
15.14 odd 2 350.6.a.l.1.1 1
21.20 even 2 490.6.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.6.a.b.1.1 1 3.2 odd 2
350.6.a.l.1.1 1 15.14 odd 2
350.6.c.g.99.1 2 15.2 even 4
350.6.c.g.99.2 2 15.8 even 4
490.6.a.g.1.1 1 21.20 even 2
560.6.a.e.1.1 1 12.11 even 2
630.6.a.i.1.1 1 1.1 even 1 trivial