Properties

Label 882.6.a.j.1.1
Level $882$
Weight $6$
Character 882.1
Self dual yes
Analytic conductor $141.459$
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] = [882,6,Mod(1,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("882.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 882.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: \(141.458529075\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 882.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000 q^{2} +16.0000 q^{4} +76.0000 q^{5} -64.0000 q^{8} +O(q^{10})\) \(q-4.00000 q^{2} +16.0000 q^{4} +76.0000 q^{5} -64.0000 q^{8} -304.000 q^{10} -650.000 q^{11} -762.000 q^{13} +256.000 q^{16} -556.000 q^{17} +2452.00 q^{19} +1216.00 q^{20} +2600.00 q^{22} +2950.00 q^{23} +2651.00 q^{25} +3048.00 q^{26} +674.000 q^{29} +3024.00 q^{31} -1024.00 q^{32} +2224.00 q^{34} +7730.00 q^{37} -9808.00 q^{38} -4864.00 q^{40} -17016.0 q^{41} +21836.0 q^{43} -10400.0 q^{44} -11800.0 q^{46} -23940.0 q^{47} -10604.0 q^{50} -12192.0 q^{52} -15594.0 q^{53} -49400.0 q^{55} -2696.00 q^{58} +5608.00 q^{59} -150.000 q^{61} -12096.0 q^{62} +4096.00 q^{64} -57912.0 q^{65} -43784.0 q^{67} -8896.00 q^{68} +39178.0 q^{71} +23570.0 q^{73} -30920.0 q^{74} +39232.0 q^{76} -17892.0 q^{79} +19456.0 q^{80} +68064.0 q^{82} +38972.0 q^{83} -42256.0 q^{85} -87344.0 q^{86} +41600.0 q^{88} +6024.00 q^{89} +47200.0 q^{92} +95760.0 q^{94} +186352. q^{95} -108430. q^{97} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.00000 −0.707107
\(3\) 0 0
\(4\) 16.0000 0.500000
\(5\) 76.0000 1.35953 0.679765 0.733430i \(-0.262082\pi\)
0.679765 + 0.733430i \(0.262082\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −64.0000 −0.353553
\(9\) 0 0
\(10\) −304.000 −0.961332
\(11\) −650.000 −1.61969 −0.809845 0.586645i \(-0.800449\pi\)
−0.809845 + 0.586645i \(0.800449\pi\)
\(12\) 0 0
\(13\) −762.000 −1.25054 −0.625269 0.780410i \(-0.715011\pi\)
−0.625269 + 0.780410i \(0.715011\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 256.000 0.250000
\(17\) −556.000 −0.466608 −0.233304 0.972404i \(-0.574954\pi\)
−0.233304 + 0.972404i \(0.574954\pi\)
\(18\) 0 0
\(19\) 2452.00 1.55825 0.779124 0.626870i \(-0.215664\pi\)
0.779124 + 0.626870i \(0.215664\pi\)
\(20\) 1216.00 0.679765
\(21\) 0 0
\(22\) 2600.00 1.14529
\(23\) 2950.00 1.16279 0.581397 0.813620i \(-0.302507\pi\)
0.581397 + 0.813620i \(0.302507\pi\)
\(24\) 0 0
\(25\) 2651.00 0.848320
\(26\) 3048.00 0.884263
\(27\) 0 0
\(28\) 0 0
\(29\) 674.000 0.148821 0.0744106 0.997228i \(-0.476292\pi\)
0.0744106 + 0.997228i \(0.476292\pi\)
\(30\) 0 0
\(31\) 3024.00 0.565168 0.282584 0.959243i \(-0.408808\pi\)
0.282584 + 0.959243i \(0.408808\pi\)
\(32\) −1024.00 −0.176777
\(33\) 0 0
\(34\) 2224.00 0.329942
\(35\) 0 0
\(36\) 0 0
\(37\) 7730.00 0.928272 0.464136 0.885764i \(-0.346365\pi\)
0.464136 + 0.885764i \(0.346365\pi\)
\(38\) −9808.00 −1.10185
\(39\) 0 0
\(40\) −4864.00 −0.480666
\(41\) −17016.0 −1.58088 −0.790438 0.612542i \(-0.790147\pi\)
−0.790438 + 0.612542i \(0.790147\pi\)
\(42\) 0 0
\(43\) 21836.0 1.80095 0.900476 0.434907i \(-0.143219\pi\)
0.900476 + 0.434907i \(0.143219\pi\)
\(44\) −10400.0 −0.809845
\(45\) 0 0
\(46\) −11800.0 −0.822219
\(47\) −23940.0 −1.58081 −0.790405 0.612585i \(-0.790130\pi\)
−0.790405 + 0.612585i \(0.790130\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −10604.0 −0.599853
\(51\) 0 0
\(52\) −12192.0 −0.625269
\(53\) −15594.0 −0.762549 −0.381275 0.924462i \(-0.624515\pi\)
−0.381275 + 0.924462i \(0.624515\pi\)
\(54\) 0 0
\(55\) −49400.0 −2.20201
\(56\) 0 0
\(57\) 0 0
\(58\) −2696.00 −0.105233
\(59\) 5608.00 0.209738 0.104869 0.994486i \(-0.466558\pi\)
0.104869 + 0.994486i \(0.466558\pi\)
\(60\) 0 0
\(61\) −150.000 −0.00516139 −0.00258069 0.999997i \(-0.500821\pi\)
−0.00258069 + 0.999997i \(0.500821\pi\)
\(62\) −12096.0 −0.399634
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) −57912.0 −1.70014
\(66\) 0 0
\(67\) −43784.0 −1.19159 −0.595797 0.803135i \(-0.703164\pi\)
−0.595797 + 0.803135i \(0.703164\pi\)
\(68\) −8896.00 −0.233304
\(69\) 0 0
\(70\) 0 0
\(71\) 39178.0 0.922351 0.461176 0.887309i \(-0.347428\pi\)
0.461176 + 0.887309i \(0.347428\pi\)
\(72\) 0 0
\(73\) 23570.0 0.517669 0.258835 0.965922i \(-0.416662\pi\)
0.258835 + 0.965922i \(0.416662\pi\)
\(74\) −30920.0 −0.656387
\(75\) 0 0
\(76\) 39232.0 0.779124
\(77\) 0 0
\(78\) 0 0
\(79\) −17892.0 −0.322546 −0.161273 0.986910i \(-0.551560\pi\)
−0.161273 + 0.986910i \(0.551560\pi\)
\(80\) 19456.0 0.339882
\(81\) 0 0
\(82\) 68064.0 1.11785
\(83\) 38972.0 0.620951 0.310476 0.950581i \(-0.399512\pi\)
0.310476 + 0.950581i \(0.399512\pi\)
\(84\) 0 0
\(85\) −42256.0 −0.634368
\(86\) −87344.0 −1.27346
\(87\) 0 0
\(88\) 41600.0 0.572647
\(89\) 6024.00 0.0806139 0.0403070 0.999187i \(-0.487166\pi\)
0.0403070 + 0.999187i \(0.487166\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 47200.0 0.581397
\(93\) 0 0
\(94\) 95760.0 1.11780
\(95\) 186352. 2.11848
\(96\) 0 0
\(97\) −108430. −1.17009 −0.585046 0.811000i \(-0.698924\pi\)
−0.585046 + 0.811000i \(0.698924\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 42416.0 0.424160
\(101\) −70424.0 −0.686938 −0.343469 0.939164i \(-0.611602\pi\)
−0.343469 + 0.939164i \(0.611602\pi\)
\(102\) 0 0
\(103\) 31552.0 0.293045 0.146522 0.989207i \(-0.453192\pi\)
0.146522 + 0.989207i \(0.453192\pi\)
\(104\) 48768.0 0.442132
\(105\) 0 0
\(106\) 62376.0 0.539204
\(107\) −108282. −0.914317 −0.457159 0.889385i \(-0.651133\pi\)
−0.457159 + 0.889385i \(0.651133\pi\)
\(108\) 0 0
\(109\) −72146.0 −0.581629 −0.290814 0.956779i \(-0.593926\pi\)
−0.290814 + 0.956779i \(0.593926\pi\)
\(110\) 197600. 1.55706
\(111\) 0 0
\(112\) 0 0
\(113\) −220906. −1.62746 −0.813732 0.581240i \(-0.802568\pi\)
−0.813732 + 0.581240i \(0.802568\pi\)
\(114\) 0 0
\(115\) 224200. 1.58085
\(116\) 10784.0 0.0744106
\(117\) 0 0
\(118\) −22432.0 −0.148307
\(119\) 0 0
\(120\) 0 0
\(121\) 261449. 1.62339
\(122\) 600.000 0.00364965
\(123\) 0 0
\(124\) 48384.0 0.282584
\(125\) −36024.0 −0.206213
\(126\) 0 0
\(127\) −239652. −1.31847 −0.659237 0.751935i \(-0.729121\pi\)
−0.659237 + 0.751935i \(0.729121\pi\)
\(128\) −16384.0 −0.0883883
\(129\) 0 0
\(130\) 231648. 1.20218
\(131\) −274172. −1.39587 −0.697935 0.716161i \(-0.745897\pi\)
−0.697935 + 0.716161i \(0.745897\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 175136. 0.842584
\(135\) 0 0
\(136\) 35584.0 0.164971
\(137\) 391154. 1.78052 0.890259 0.455455i \(-0.150523\pi\)
0.890259 + 0.455455i \(0.150523\pi\)
\(138\) 0 0
\(139\) −339364. −1.48980 −0.744901 0.667175i \(-0.767503\pi\)
−0.744901 + 0.667175i \(0.767503\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −156712. −0.652201
\(143\) 495300. 2.02548
\(144\) 0 0
\(145\) 51224.0 0.202327
\(146\) −94280.0 −0.366047
\(147\) 0 0
\(148\) 123680. 0.464136
\(149\) 29334.0 0.108244 0.0541222 0.998534i \(-0.482764\pi\)
0.0541222 + 0.998534i \(0.482764\pi\)
\(150\) 0 0
\(151\) 71608.0 0.255575 0.127788 0.991802i \(-0.459212\pi\)
0.127788 + 0.991802i \(0.459212\pi\)
\(152\) −156928. −0.550924
\(153\) 0 0
\(154\) 0 0
\(155\) 229824. 0.768362
\(156\) 0 0
\(157\) −296318. −0.959420 −0.479710 0.877427i \(-0.659258\pi\)
−0.479710 + 0.877427i \(0.659258\pi\)
\(158\) 71568.0 0.228074
\(159\) 0 0
\(160\) −77824.0 −0.240333
\(161\) 0 0
\(162\) 0 0
\(163\) −480400. −1.41623 −0.708115 0.706097i \(-0.750454\pi\)
−0.708115 + 0.706097i \(0.750454\pi\)
\(164\) −272256. −0.790438
\(165\) 0 0
\(166\) −155888. −0.439079
\(167\) 160180. 0.444444 0.222222 0.974996i \(-0.428669\pi\)
0.222222 + 0.974996i \(0.428669\pi\)
\(168\) 0 0
\(169\) 209351. 0.563843
\(170\) 169024. 0.448566
\(171\) 0 0
\(172\) 349376. 0.900476
\(173\) −8984.00 −0.0228220 −0.0114110 0.999935i \(-0.503632\pi\)
−0.0114110 + 0.999935i \(0.503632\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −166400. −0.404922
\(177\) 0 0
\(178\) −24096.0 −0.0570026
\(179\) −182886. −0.426627 −0.213313 0.976984i \(-0.568425\pi\)
−0.213313 + 0.976984i \(0.568425\pi\)
\(180\) 0 0
\(181\) −138330. −0.313848 −0.156924 0.987611i \(-0.550158\pi\)
−0.156924 + 0.987611i \(0.550158\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −188800. −0.411109
\(185\) 587480. 1.26201
\(186\) 0 0
\(187\) 361400. 0.755760
\(188\) −383040. −0.790405
\(189\) 0 0
\(190\) −745408. −1.49799
\(191\) −327222. −0.649021 −0.324511 0.945882i \(-0.605200\pi\)
−0.324511 + 0.945882i \(0.605200\pi\)
\(192\) 0 0
\(193\) 786902. 1.52064 0.760322 0.649547i \(-0.225041\pi\)
0.760322 + 0.649547i \(0.225041\pi\)
\(194\) 433720. 0.827380
\(195\) 0 0
\(196\) 0 0
\(197\) −423098. −0.776740 −0.388370 0.921504i \(-0.626962\pi\)
−0.388370 + 0.921504i \(0.626962\pi\)
\(198\) 0 0
\(199\) −1.02392e6 −1.83288 −0.916439 0.400175i \(-0.868949\pi\)
−0.916439 + 0.400175i \(0.868949\pi\)
\(200\) −169664. −0.299926
\(201\) 0 0
\(202\) 281696. 0.485738
\(203\) 0 0
\(204\) 0 0
\(205\) −1.29322e6 −2.14925
\(206\) −126208. −0.207214
\(207\) 0 0
\(208\) −195072. −0.312634
\(209\) −1.59380e6 −2.52388
\(210\) 0 0
\(211\) 461516. 0.713642 0.356821 0.934173i \(-0.383861\pi\)
0.356821 + 0.934173i \(0.383861\pi\)
\(212\) −249504. −0.381275
\(213\) 0 0
\(214\) 433128. 0.646520
\(215\) 1.65954e6 2.44845
\(216\) 0 0
\(217\) 0 0
\(218\) 288584. 0.411274
\(219\) 0 0
\(220\) −790400. −1.10101
\(221\) 423672. 0.583511
\(222\) 0 0
\(223\) −995048. −1.33993 −0.669965 0.742393i \(-0.733691\pi\)
−0.669965 + 0.742393i \(0.733691\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 883624. 1.15079
\(227\) −95568.0 −0.123097 −0.0615486 0.998104i \(-0.519604\pi\)
−0.0615486 + 0.998104i \(0.519604\pi\)
\(228\) 0 0
\(229\) 1.04409e6 1.31567 0.657836 0.753161i \(-0.271472\pi\)
0.657836 + 0.753161i \(0.271472\pi\)
\(230\) −896800. −1.11783
\(231\) 0 0
\(232\) −43136.0 −0.0526163
\(233\) 1.16941e6 1.41116 0.705581 0.708629i \(-0.250686\pi\)
0.705581 + 0.708629i \(0.250686\pi\)
\(234\) 0 0
\(235\) −1.81944e6 −2.14916
\(236\) 89728.0 0.104869
\(237\) 0 0
\(238\) 0 0
\(239\) 27342.0 0.0309625 0.0154812 0.999880i \(-0.495072\pi\)
0.0154812 + 0.999880i \(0.495072\pi\)
\(240\) 0 0
\(241\) 907714. 1.00671 0.503357 0.864078i \(-0.332098\pi\)
0.503357 + 0.864078i \(0.332098\pi\)
\(242\) −1.04580e6 −1.14791
\(243\) 0 0
\(244\) −2400.00 −0.00258069
\(245\) 0 0
\(246\) 0 0
\(247\) −1.86842e6 −1.94865
\(248\) −193536. −0.199817
\(249\) 0 0
\(250\) 144096. 0.145815
\(251\) 44088.0 0.0441709 0.0220854 0.999756i \(-0.492969\pi\)
0.0220854 + 0.999756i \(0.492969\pi\)
\(252\) 0 0
\(253\) −1.91750e6 −1.88336
\(254\) 958608. 0.932302
\(255\) 0 0
\(256\) 65536.0 0.0625000
\(257\) −829200. −0.783117 −0.391558 0.920153i \(-0.628064\pi\)
−0.391558 + 0.920153i \(0.628064\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −926592. −0.850071
\(261\) 0 0
\(262\) 1.09669e6 0.987029
\(263\) −1.31947e6 −1.17627 −0.588137 0.808761i \(-0.700139\pi\)
−0.588137 + 0.808761i \(0.700139\pi\)
\(264\) 0 0
\(265\) −1.18514e6 −1.03671
\(266\) 0 0
\(267\) 0 0
\(268\) −700544. −0.595797
\(269\) −783788. −0.660416 −0.330208 0.943908i \(-0.607119\pi\)
−0.330208 + 0.943908i \(0.607119\pi\)
\(270\) 0 0
\(271\) −955080. −0.789981 −0.394990 0.918685i \(-0.629252\pi\)
−0.394990 + 0.918685i \(0.629252\pi\)
\(272\) −142336. −0.116652
\(273\) 0 0
\(274\) −1.56462e6 −1.25902
\(275\) −1.72315e6 −1.37401
\(276\) 0 0
\(277\) 1.91273e6 1.49780 0.748901 0.662682i \(-0.230582\pi\)
0.748901 + 0.662682i \(0.230582\pi\)
\(278\) 1.35746e6 1.05345
\(279\) 0 0
\(280\) 0 0
\(281\) 1.02620e6 0.775295 0.387648 0.921808i \(-0.373288\pi\)
0.387648 + 0.921808i \(0.373288\pi\)
\(282\) 0 0
\(283\) −1.74668e6 −1.29642 −0.648211 0.761461i \(-0.724482\pi\)
−0.648211 + 0.761461i \(0.724482\pi\)
\(284\) 626848. 0.461176
\(285\) 0 0
\(286\) −1.98120e6 −1.43223
\(287\) 0 0
\(288\) 0 0
\(289\) −1.11072e6 −0.782277
\(290\) −204896. −0.143067
\(291\) 0 0
\(292\) 377120. 0.258835
\(293\) 2.23212e6 1.51897 0.759484 0.650526i \(-0.225452\pi\)
0.759484 + 0.650526i \(0.225452\pi\)
\(294\) 0 0
\(295\) 426208. 0.285146
\(296\) −494720. −0.328194
\(297\) 0 0
\(298\) −117336. −0.0765404
\(299\) −2.24790e6 −1.45412
\(300\) 0 0
\(301\) 0 0
\(302\) −286432. −0.180719
\(303\) 0 0
\(304\) 627712. 0.389562
\(305\) −11400.0 −0.00701706
\(306\) 0 0
\(307\) −1.85324e6 −1.12224 −0.561119 0.827735i \(-0.689629\pi\)
−0.561119 + 0.827735i \(0.689629\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −919296. −0.543314
\(311\) −450956. −0.264383 −0.132191 0.991224i \(-0.542201\pi\)
−0.132191 + 0.991224i \(0.542201\pi\)
\(312\) 0 0
\(313\) −1.60263e6 −0.924642 −0.462321 0.886713i \(-0.652983\pi\)
−0.462321 + 0.886713i \(0.652983\pi\)
\(314\) 1.18527e6 0.678413
\(315\) 0 0
\(316\) −286272. −0.161273
\(317\) 20862.0 0.0116602 0.00583012 0.999983i \(-0.498144\pi\)
0.00583012 + 0.999983i \(0.498144\pi\)
\(318\) 0 0
\(319\) −438100. −0.241044
\(320\) 311296. 0.169941
\(321\) 0 0
\(322\) 0 0
\(323\) −1.36331e6 −0.727091
\(324\) 0 0
\(325\) −2.02006e6 −1.06086
\(326\) 1.92160e6 1.00143
\(327\) 0 0
\(328\) 1.08902e6 0.558924
\(329\) 0 0
\(330\) 0 0
\(331\) 2.07621e6 1.04160 0.520801 0.853678i \(-0.325633\pi\)
0.520801 + 0.853678i \(0.325633\pi\)
\(332\) 623552. 0.310476
\(333\) 0 0
\(334\) −640720. −0.314269
\(335\) −3.32758e6 −1.62001
\(336\) 0 0
\(337\) 1.20508e6 0.578019 0.289009 0.957326i \(-0.406674\pi\)
0.289009 + 0.957326i \(0.406674\pi\)
\(338\) −837404. −0.398697
\(339\) 0 0
\(340\) −676096. −0.317184
\(341\) −1.96560e6 −0.915396
\(342\) 0 0
\(343\) 0 0
\(344\) −1.39750e6 −0.636732
\(345\) 0 0
\(346\) 35936.0 0.0161376
\(347\) 876642. 0.390840 0.195420 0.980720i \(-0.437393\pi\)
0.195420 + 0.980720i \(0.437393\pi\)
\(348\) 0 0
\(349\) 1.29593e6 0.569532 0.284766 0.958597i \(-0.408084\pi\)
0.284766 + 0.958597i \(0.408084\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 665600. 0.286323
\(353\) −3.99040e6 −1.70443 −0.852215 0.523192i \(-0.824741\pi\)
−0.852215 + 0.523192i \(0.824741\pi\)
\(354\) 0 0
\(355\) 2.97753e6 1.25396
\(356\) 96384.0 0.0403070
\(357\) 0 0
\(358\) 731544. 0.301671
\(359\) −4.06452e6 −1.66446 −0.832229 0.554432i \(-0.812936\pi\)
−0.832229 + 0.554432i \(0.812936\pi\)
\(360\) 0 0
\(361\) 3.53620e6 1.42814
\(362\) 553320. 0.221924
\(363\) 0 0
\(364\) 0 0
\(365\) 1.79132e6 0.703787
\(366\) 0 0
\(367\) 1.67243e6 0.648162 0.324081 0.946029i \(-0.394945\pi\)
0.324081 + 0.946029i \(0.394945\pi\)
\(368\) 755200. 0.290698
\(369\) 0 0
\(370\) −2.34992e6 −0.892378
\(371\) 0 0
\(372\) 0 0
\(373\) 3.16769e6 1.17888 0.589441 0.807812i \(-0.299348\pi\)
0.589441 + 0.807812i \(0.299348\pi\)
\(374\) −1.44560e6 −0.534403
\(375\) 0 0
\(376\) 1.53216e6 0.558901
\(377\) −513588. −0.186106
\(378\) 0 0
\(379\) −4.20388e6 −1.50332 −0.751662 0.659548i \(-0.770748\pi\)
−0.751662 + 0.659548i \(0.770748\pi\)
\(380\) 2.98163e6 1.05924
\(381\) 0 0
\(382\) 1.30889e6 0.458927
\(383\) −342616. −0.119347 −0.0596734 0.998218i \(-0.519006\pi\)
−0.0596734 + 0.998218i \(0.519006\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −3.14761e6 −1.07526
\(387\) 0 0
\(388\) −1.73488e6 −0.585046
\(389\) 3.83959e6 1.28650 0.643252 0.765654i \(-0.277585\pi\)
0.643252 + 0.765654i \(0.277585\pi\)
\(390\) 0 0
\(391\) −1.64020e6 −0.542569
\(392\) 0 0
\(393\) 0 0
\(394\) 1.69239e6 0.549238
\(395\) −1.35979e6 −0.438510
\(396\) 0 0
\(397\) −3.43894e6 −1.09509 −0.547543 0.836777i \(-0.684437\pi\)
−0.547543 + 0.836777i \(0.684437\pi\)
\(398\) 4.09568e6 1.29604
\(399\) 0 0
\(400\) 678656. 0.212080
\(401\) 3.89421e6 1.20937 0.604684 0.796466i \(-0.293299\pi\)
0.604684 + 0.796466i \(0.293299\pi\)
\(402\) 0 0
\(403\) −2.30429e6 −0.706764
\(404\) −1.12678e6 −0.343469
\(405\) 0 0
\(406\) 0 0
\(407\) −5.02450e6 −1.50351
\(408\) 0 0
\(409\) 1.64679e6 0.486778 0.243389 0.969929i \(-0.421741\pi\)
0.243389 + 0.969929i \(0.421741\pi\)
\(410\) 5.17286e6 1.51975
\(411\) 0 0
\(412\) 504832. 0.146522
\(413\) 0 0
\(414\) 0 0
\(415\) 2.96187e6 0.844201
\(416\) 780288. 0.221066
\(417\) 0 0
\(418\) 6.37520e6 1.78465
\(419\) −1.67659e6 −0.466544 −0.233272 0.972412i \(-0.574943\pi\)
−0.233272 + 0.972412i \(0.574943\pi\)
\(420\) 0 0
\(421\) −566742. −0.155840 −0.0779202 0.996960i \(-0.524828\pi\)
−0.0779202 + 0.996960i \(0.524828\pi\)
\(422\) −1.84606e6 −0.504621
\(423\) 0 0
\(424\) 998016. 0.269602
\(425\) −1.47396e6 −0.395833
\(426\) 0 0
\(427\) 0 0
\(428\) −1.73251e6 −0.457159
\(429\) 0 0
\(430\) −6.63814e6 −1.73131
\(431\) −6.68468e6 −1.73335 −0.866677 0.498870i \(-0.833749\pi\)
−0.866677 + 0.498870i \(0.833749\pi\)
\(432\) 0 0
\(433\) −6.91337e6 −1.77203 −0.886013 0.463661i \(-0.846536\pi\)
−0.886013 + 0.463661i \(0.846536\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.15434e6 −0.290814
\(437\) 7.23340e6 1.81192
\(438\) 0 0
\(439\) 4.56281e6 1.12998 0.564990 0.825098i \(-0.308880\pi\)
0.564990 + 0.825098i \(0.308880\pi\)
\(440\) 3.16160e6 0.778530
\(441\) 0 0
\(442\) −1.69469e6 −0.412605
\(443\) −4.59760e6 −1.11307 −0.556534 0.830825i \(-0.687869\pi\)
−0.556534 + 0.830825i \(0.687869\pi\)
\(444\) 0 0
\(445\) 457824. 0.109597
\(446\) 3.98019e6 0.947473
\(447\) 0 0
\(448\) 0 0
\(449\) −1.70658e6 −0.399494 −0.199747 0.979848i \(-0.564012\pi\)
−0.199747 + 0.979848i \(0.564012\pi\)
\(450\) 0 0
\(451\) 1.10604e7 2.56053
\(452\) −3.53450e6 −0.813732
\(453\) 0 0
\(454\) 382272. 0.0870428
\(455\) 0 0
\(456\) 0 0
\(457\) −6.93916e6 −1.55423 −0.777117 0.629356i \(-0.783319\pi\)
−0.777117 + 0.629356i \(0.783319\pi\)
\(458\) −4.17634e6 −0.930320
\(459\) 0 0
\(460\) 3.58720e6 0.790426
\(461\) −2.61805e6 −0.573753 −0.286877 0.957968i \(-0.592617\pi\)
−0.286877 + 0.957968i \(0.592617\pi\)
\(462\) 0 0
\(463\) 7.13602e6 1.54705 0.773524 0.633767i \(-0.218492\pi\)
0.773524 + 0.633767i \(0.218492\pi\)
\(464\) 172544. 0.0372053
\(465\) 0 0
\(466\) −4.67764e6 −0.997843
\(467\) −2.17398e6 −0.461278 −0.230639 0.973039i \(-0.574082\pi\)
−0.230639 + 0.973039i \(0.574082\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 7.27776e6 1.51968
\(471\) 0 0
\(472\) −358912. −0.0741537
\(473\) −1.41934e7 −2.91698
\(474\) 0 0
\(475\) 6.50025e6 1.32189
\(476\) 0 0
\(477\) 0 0
\(478\) −109368. −0.0218938
\(479\) −4.63294e6 −0.922609 −0.461305 0.887242i \(-0.652619\pi\)
−0.461305 + 0.887242i \(0.652619\pi\)
\(480\) 0 0
\(481\) −5.89026e6 −1.16084
\(482\) −3.63086e6 −0.711855
\(483\) 0 0
\(484\) 4.18318e6 0.811696
\(485\) −8.24068e6 −1.59077
\(486\) 0 0
\(487\) −4.56645e6 −0.872481 −0.436241 0.899830i \(-0.643690\pi\)
−0.436241 + 0.899830i \(0.643690\pi\)
\(488\) 9600.00 0.00182483
\(489\) 0 0
\(490\) 0 0
\(491\) 5.31429e6 0.994813 0.497407 0.867518i \(-0.334286\pi\)
0.497407 + 0.867518i \(0.334286\pi\)
\(492\) 0 0
\(493\) −374744. −0.0694412
\(494\) 7.47370e6 1.37790
\(495\) 0 0
\(496\) 774144. 0.141292
\(497\) 0 0
\(498\) 0 0
\(499\) −2.46314e6 −0.442831 −0.221415 0.975180i \(-0.571068\pi\)
−0.221415 + 0.975180i \(0.571068\pi\)
\(500\) −576384. −0.103107
\(501\) 0 0
\(502\) −176352. −0.0312335
\(503\) 2.79924e6 0.493310 0.246655 0.969103i \(-0.420669\pi\)
0.246655 + 0.969103i \(0.420669\pi\)
\(504\) 0 0
\(505\) −5.35222e6 −0.933912
\(506\) 7.67000e6 1.33174
\(507\) 0 0
\(508\) −3.83443e6 −0.659237
\(509\) 1.99914e6 0.342018 0.171009 0.985269i \(-0.445297\pi\)
0.171009 + 0.985269i \(0.445297\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −262144. −0.0441942
\(513\) 0 0
\(514\) 3.31680e6 0.553747
\(515\) 2.39795e6 0.398403
\(516\) 0 0
\(517\) 1.55610e7 2.56042
\(518\) 0 0
\(519\) 0 0
\(520\) 3.70637e6 0.601091
\(521\) 3.52160e6 0.568390 0.284195 0.958767i \(-0.408274\pi\)
0.284195 + 0.958767i \(0.408274\pi\)
\(522\) 0 0
\(523\) −2.60685e6 −0.416737 −0.208369 0.978050i \(-0.566815\pi\)
−0.208369 + 0.978050i \(0.566815\pi\)
\(524\) −4.38675e6 −0.697935
\(525\) 0 0
\(526\) 5.27786e6 0.831752
\(527\) −1.68134e6 −0.263712
\(528\) 0 0
\(529\) 2.26616e6 0.352088
\(530\) 4.74058e6 0.733063
\(531\) 0 0
\(532\) 0 0
\(533\) 1.29662e7 1.97694
\(534\) 0 0
\(535\) −8.22943e6 −1.24304
\(536\) 2.80218e6 0.421292
\(537\) 0 0
\(538\) 3.13515e6 0.466985
\(539\) 0 0
\(540\) 0 0
\(541\) −1.37441e6 −0.201894 −0.100947 0.994892i \(-0.532187\pi\)
−0.100947 + 0.994892i \(0.532187\pi\)
\(542\) 3.82032e6 0.558601
\(543\) 0 0
\(544\) 569344. 0.0824855
\(545\) −5.48310e6 −0.790742
\(546\) 0 0
\(547\) −8.78398e6 −1.25523 −0.627614 0.778524i \(-0.715968\pi\)
−0.627614 + 0.778524i \(0.715968\pi\)
\(548\) 6.25846e6 0.890259
\(549\) 0 0
\(550\) 6.89260e6 0.971575
\(551\) 1.65265e6 0.231900
\(552\) 0 0
\(553\) 0 0
\(554\) −7.65092e6 −1.05911
\(555\) 0 0
\(556\) −5.42982e6 −0.744901
\(557\) −6.29262e6 −0.859396 −0.429698 0.902973i \(-0.641380\pi\)
−0.429698 + 0.902973i \(0.641380\pi\)
\(558\) 0 0
\(559\) −1.66390e7 −2.25216
\(560\) 0 0
\(561\) 0 0
\(562\) −4.10481e6 −0.548216
\(563\) 4.86582e6 0.646971 0.323485 0.946233i \(-0.395145\pi\)
0.323485 + 0.946233i \(0.395145\pi\)
\(564\) 0 0
\(565\) −1.67889e7 −2.21259
\(566\) 6.98670e6 0.916709
\(567\) 0 0
\(568\) −2.50739e6 −0.326100
\(569\) 4.46383e6 0.577998 0.288999 0.957329i \(-0.406678\pi\)
0.288999 + 0.957329i \(0.406678\pi\)
\(570\) 0 0
\(571\) 8.17054e6 1.04872 0.524361 0.851496i \(-0.324304\pi\)
0.524361 + 0.851496i \(0.324304\pi\)
\(572\) 7.92480e6 1.01274
\(573\) 0 0
\(574\) 0 0
\(575\) 7.82045e6 0.986421
\(576\) 0 0
\(577\) 5.50343e6 0.688167 0.344084 0.938939i \(-0.388190\pi\)
0.344084 + 0.938939i \(0.388190\pi\)
\(578\) 4.44288e6 0.553153
\(579\) 0 0
\(580\) 819584. 0.101163
\(581\) 0 0
\(582\) 0 0
\(583\) 1.01361e7 1.23509
\(584\) −1.50848e6 −0.183024
\(585\) 0 0
\(586\) −8.92848e6 −1.07407
\(587\) 8.14251e6 0.975356 0.487678 0.873024i \(-0.337844\pi\)
0.487678 + 0.873024i \(0.337844\pi\)
\(588\) 0 0
\(589\) 7.41485e6 0.880672
\(590\) −1.70483e6 −0.201628
\(591\) 0 0
\(592\) 1.97888e6 0.232068
\(593\) −2.73136e6 −0.318964 −0.159482 0.987201i \(-0.550982\pi\)
−0.159482 + 0.987201i \(0.550982\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 469344. 0.0541222
\(597\) 0 0
\(598\) 8.99160e6 1.02822
\(599\) −1.23733e6 −0.140902 −0.0704510 0.997515i \(-0.522444\pi\)
−0.0704510 + 0.997515i \(0.522444\pi\)
\(600\) 0 0
\(601\) 1.59756e7 1.80414 0.902071 0.431587i \(-0.142046\pi\)
0.902071 + 0.431587i \(0.142046\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.14573e6 0.127788
\(605\) 1.98701e7 2.20705
\(606\) 0 0
\(607\) 1.88275e6 0.207406 0.103703 0.994608i \(-0.466931\pi\)
0.103703 + 0.994608i \(0.466931\pi\)
\(608\) −2.51085e6 −0.275462
\(609\) 0 0
\(610\) 45600.0 0.00496181
\(611\) 1.82423e7 1.97686
\(612\) 0 0
\(613\) −9.82804e6 −1.05637 −0.528185 0.849130i \(-0.677127\pi\)
−0.528185 + 0.849130i \(0.677127\pi\)
\(614\) 7.41294e6 0.793542
\(615\) 0 0
\(616\) 0 0
\(617\) 8.21262e6 0.868498 0.434249 0.900793i \(-0.357014\pi\)
0.434249 + 0.900793i \(0.357014\pi\)
\(618\) 0 0
\(619\) −6.98465e6 −0.732686 −0.366343 0.930480i \(-0.619390\pi\)
−0.366343 + 0.930480i \(0.619390\pi\)
\(620\) 3.67718e6 0.384181
\(621\) 0 0
\(622\) 1.80382e6 0.186947
\(623\) 0 0
\(624\) 0 0
\(625\) −1.10222e7 −1.12867
\(626\) 6.41054e6 0.653820
\(627\) 0 0
\(628\) −4.74109e6 −0.479710
\(629\) −4.29788e6 −0.433139
\(630\) 0 0
\(631\) 1.26789e7 1.26767 0.633837 0.773467i \(-0.281479\pi\)
0.633837 + 0.773467i \(0.281479\pi\)
\(632\) 1.14509e6 0.114037
\(633\) 0 0
\(634\) −83448.0 −0.00824504
\(635\) −1.82136e7 −1.79250
\(636\) 0 0
\(637\) 0 0
\(638\) 1.75240e6 0.170444
\(639\) 0 0
\(640\) −1.24518e6 −0.120167
\(641\) 1.40324e7 1.34892 0.674460 0.738311i \(-0.264376\pi\)
0.674460 + 0.738311i \(0.264376\pi\)
\(642\) 0 0
\(643\) −1.30368e6 −0.124349 −0.0621745 0.998065i \(-0.519804\pi\)
−0.0621745 + 0.998065i \(0.519804\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 5.45325e6 0.514131
\(647\) 1.57110e6 0.147551 0.0737757 0.997275i \(-0.476495\pi\)
0.0737757 + 0.997275i \(0.476495\pi\)
\(648\) 0 0
\(649\) −3.64520e6 −0.339711
\(650\) 8.08025e6 0.750138
\(651\) 0 0
\(652\) −7.68640e6 −0.708115
\(653\) 8.34115e6 0.765496 0.382748 0.923853i \(-0.374978\pi\)
0.382748 + 0.923853i \(0.374978\pi\)
\(654\) 0 0
\(655\) −2.08371e7 −1.89773
\(656\) −4.35610e6 −0.395219
\(657\) 0 0
\(658\) 0 0
\(659\) −6.18334e6 −0.554638 −0.277319 0.960778i \(-0.589446\pi\)
−0.277319 + 0.960778i \(0.589446\pi\)
\(660\) 0 0
\(661\) −928966. −0.0826982 −0.0413491 0.999145i \(-0.513166\pi\)
−0.0413491 + 0.999145i \(0.513166\pi\)
\(662\) −8.30485e6 −0.736524
\(663\) 0 0
\(664\) −2.49421e6 −0.219539
\(665\) 0 0
\(666\) 0 0
\(667\) 1.98830e6 0.173048
\(668\) 2.56288e6 0.222222
\(669\) 0 0
\(670\) 1.33103e7 1.14552
\(671\) 97500.0 0.00835985
\(672\) 0 0
\(673\) 1.79131e7 1.52452 0.762259 0.647272i \(-0.224090\pi\)
0.762259 + 0.647272i \(0.224090\pi\)
\(674\) −4.82033e6 −0.408721
\(675\) 0 0
\(676\) 3.34962e6 0.281922
\(677\) −4.96397e6 −0.416253 −0.208126 0.978102i \(-0.566737\pi\)
−0.208126 + 0.978102i \(0.566737\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 2.70438e6 0.224283
\(681\) 0 0
\(682\) 7.86240e6 0.647283
\(683\) −89526.0 −0.00734340 −0.00367170 0.999993i \(-0.501169\pi\)
−0.00367170 + 0.999993i \(0.501169\pi\)
\(684\) 0 0
\(685\) 2.97277e7 2.42067
\(686\) 0 0
\(687\) 0 0
\(688\) 5.59002e6 0.450238
\(689\) 1.18826e7 0.953596
\(690\) 0 0
\(691\) 142396. 0.0113450 0.00567248 0.999984i \(-0.498194\pi\)
0.00567248 + 0.999984i \(0.498194\pi\)
\(692\) −143744. −0.0114110
\(693\) 0 0
\(694\) −3.50657e6 −0.276365
\(695\) −2.57917e7 −2.02543
\(696\) 0 0
\(697\) 9.46090e6 0.737650
\(698\) −5.18372e6 −0.402720
\(699\) 0 0
\(700\) 0 0
\(701\) −1.03935e7 −0.798852 −0.399426 0.916765i \(-0.630791\pi\)
−0.399426 + 0.916765i \(0.630791\pi\)
\(702\) 0 0
\(703\) 1.89540e7 1.44648
\(704\) −2.66240e6 −0.202461
\(705\) 0 0
\(706\) 1.59616e7 1.20521
\(707\) 0 0
\(708\) 0 0
\(709\) 4.65503e6 0.347782 0.173891 0.984765i \(-0.444366\pi\)
0.173891 + 0.984765i \(0.444366\pi\)
\(710\) −1.19101e7 −0.886686
\(711\) 0 0
\(712\) −385536. −0.0285013
\(713\) 8.92080e6 0.657173
\(714\) 0 0
\(715\) 3.76428e7 2.75370
\(716\) −2.92618e6 −0.213313
\(717\) 0 0
\(718\) 1.62581e7 1.17695
\(719\) −6.72134e6 −0.484880 −0.242440 0.970166i \(-0.577948\pi\)
−0.242440 + 0.970166i \(0.577948\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.41448e7 −1.00984
\(723\) 0 0
\(724\) −2.21328e6 −0.156924
\(725\) 1.78677e6 0.126248
\(726\) 0 0
\(727\) 1.24076e7 0.870670 0.435335 0.900269i \(-0.356630\pi\)
0.435335 + 0.900269i \(0.356630\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −7.16528e6 −0.497652
\(731\) −1.21408e7 −0.840339
\(732\) 0 0
\(733\) −1.35958e7 −0.934641 −0.467321 0.884088i \(-0.654781\pi\)
−0.467321 + 0.884088i \(0.654781\pi\)
\(734\) −6.68973e6 −0.458319
\(735\) 0 0
\(736\) −3.02080e6 −0.205555
\(737\) 2.84596e7 1.93001
\(738\) 0 0
\(739\) 2.56819e6 0.172988 0.0864941 0.996252i \(-0.472434\pi\)
0.0864941 + 0.996252i \(0.472434\pi\)
\(740\) 9.39968e6 0.631006
\(741\) 0 0
\(742\) 0 0
\(743\) 2.02133e7 1.34327 0.671637 0.740880i \(-0.265591\pi\)
0.671637 + 0.740880i \(0.265591\pi\)
\(744\) 0 0
\(745\) 2.22938e6 0.147161
\(746\) −1.26707e7 −0.833595
\(747\) 0 0
\(748\) 5.78240e6 0.377880
\(749\) 0 0
\(750\) 0 0
\(751\) 7.04813e6 0.456010 0.228005 0.973660i \(-0.426780\pi\)
0.228005 + 0.973660i \(0.426780\pi\)
\(752\) −6.12864e6 −0.395202
\(753\) 0 0
\(754\) 2.05435e6 0.131597
\(755\) 5.44221e6 0.347462
\(756\) 0 0
\(757\) −2.04120e7 −1.29463 −0.647315 0.762223i \(-0.724108\pi\)
−0.647315 + 0.762223i \(0.724108\pi\)
\(758\) 1.68155e7 1.06301
\(759\) 0 0
\(760\) −1.19265e7 −0.748997
\(761\) −5.07974e6 −0.317965 −0.158983 0.987281i \(-0.550821\pi\)
−0.158983 + 0.987281i \(0.550821\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −5.23555e6 −0.324511
\(765\) 0 0
\(766\) 1.37046e6 0.0843909
\(767\) −4.27330e6 −0.262286
\(768\) 0 0
\(769\) −2.33898e7 −1.42630 −0.713149 0.701012i \(-0.752732\pi\)
−0.713149 + 0.701012i \(0.752732\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.25904e7 0.760322
\(773\) −1.11253e6 −0.0669672 −0.0334836 0.999439i \(-0.510660\pi\)
−0.0334836 + 0.999439i \(0.510660\pi\)
\(774\) 0 0
\(775\) 8.01662e6 0.479443
\(776\) 6.93952e6 0.413690
\(777\) 0 0
\(778\) −1.53584e7 −0.909696
\(779\) −4.17232e7 −2.46340
\(780\) 0 0
\(781\) −2.54657e7 −1.49392
\(782\) 6.56080e6 0.383654
\(783\) 0 0
\(784\) 0 0
\(785\) −2.25202e7 −1.30436
\(786\) 0 0
\(787\) −2.00812e6 −0.115572 −0.0577859 0.998329i \(-0.518404\pi\)
−0.0577859 + 0.998329i \(0.518404\pi\)
\(788\) −6.76957e6 −0.388370
\(789\) 0 0
\(790\) 5.43917e6 0.310074
\(791\) 0 0
\(792\) 0 0
\(793\) 114300. 0.00645451
\(794\) 1.37558e7 0.774343
\(795\) 0 0
\(796\) −1.63827e7 −0.916439
\(797\) 3.00897e7 1.67792 0.838961 0.544191i \(-0.183163\pi\)
0.838961 + 0.544191i \(0.183163\pi\)
\(798\) 0 0
\(799\) 1.33106e7 0.737619
\(800\) −2.71462e6 −0.149963
\(801\) 0 0
\(802\) −1.55768e7 −0.855152
\(803\) −1.53205e7 −0.838463
\(804\) 0 0
\(805\) 0 0
\(806\) 9.21715e6 0.499757
\(807\) 0 0
\(808\) 4.50714e6 0.242869
\(809\) 1.88207e6 0.101103 0.0505515 0.998721i \(-0.483902\pi\)
0.0505515 + 0.998721i \(0.483902\pi\)
\(810\) 0 0
\(811\) −4.88220e6 −0.260654 −0.130327 0.991471i \(-0.541603\pi\)
−0.130327 + 0.991471i \(0.541603\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 2.00980e7 1.06314
\(815\) −3.65104e7 −1.92541
\(816\) 0 0
\(817\) 5.35419e7 2.80633
\(818\) −6.58718e6 −0.344204
\(819\) 0 0
\(820\) −2.06915e7 −1.07462
\(821\) −8.37096e6 −0.433429 −0.216714 0.976235i \(-0.569534\pi\)
−0.216714 + 0.976235i \(0.569534\pi\)
\(822\) 0 0
\(823\) −2.02090e7 −1.04003 −0.520015 0.854157i \(-0.674074\pi\)
−0.520015 + 0.854157i \(0.674074\pi\)
\(824\) −2.01933e6 −0.103607
\(825\) 0 0
\(826\) 0 0
\(827\) 1.31059e7 0.666352 0.333176 0.942865i \(-0.391880\pi\)
0.333176 + 0.942865i \(0.391880\pi\)
\(828\) 0 0
\(829\) −3.18667e7 −1.61046 −0.805232 0.592960i \(-0.797959\pi\)
−0.805232 + 0.592960i \(0.797959\pi\)
\(830\) −1.18475e7 −0.596941
\(831\) 0 0
\(832\) −3.12115e6 −0.156317
\(833\) 0 0
\(834\) 0 0
\(835\) 1.21737e7 0.604235
\(836\) −2.55008e7 −1.26194
\(837\) 0 0
\(838\) 6.70637e6 0.329896
\(839\) 9.94742e6 0.487872 0.243936 0.969791i \(-0.421561\pi\)
0.243936 + 0.969791i \(0.421561\pi\)
\(840\) 0 0
\(841\) −2.00569e7 −0.977852
\(842\) 2.26697e6 0.110196
\(843\) 0 0
\(844\) 7.38426e6 0.356821
\(845\) 1.59107e7 0.766561
\(846\) 0 0
\(847\) 0 0
\(848\) −3.99206e6 −0.190637
\(849\) 0 0
\(850\) 5.89582e6 0.279896
\(851\) 2.28035e7 1.07939
\(852\) 0 0
\(853\) 6.52611e6 0.307102 0.153551 0.988141i \(-0.450929\pi\)
0.153551 + 0.988141i \(0.450929\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 6.93005e6 0.323260
\(857\) −8.76238e6 −0.407540 −0.203770 0.979019i \(-0.565319\pi\)
−0.203770 + 0.979019i \(0.565319\pi\)
\(858\) 0 0
\(859\) −6.47942e6 −0.299608 −0.149804 0.988716i \(-0.547864\pi\)
−0.149804 + 0.988716i \(0.547864\pi\)
\(860\) 2.65526e7 1.22422
\(861\) 0 0
\(862\) 2.67387e7 1.22567
\(863\) 1.83417e7 0.838323 0.419162 0.907912i \(-0.362324\pi\)
0.419162 + 0.907912i \(0.362324\pi\)
\(864\) 0 0
\(865\) −682784. −0.0310272
\(866\) 2.76535e7 1.25301
\(867\) 0 0
\(868\) 0 0
\(869\) 1.16298e7 0.522424
\(870\) 0 0
\(871\) 3.33634e7 1.49013
\(872\) 4.61734e6 0.205637
\(873\) 0 0
\(874\) −2.89336e7 −1.28122
\(875\) 0 0
\(876\) 0 0
\(877\) 2.69065e7 1.18129 0.590647 0.806930i \(-0.298873\pi\)
0.590647 + 0.806930i \(0.298873\pi\)
\(878\) −1.82512e7 −0.799017
\(879\) 0 0
\(880\) −1.26464e7 −0.550504
\(881\) −1.52174e7 −0.660542 −0.330271 0.943886i \(-0.607140\pi\)
−0.330271 + 0.943886i \(0.607140\pi\)
\(882\) 0 0
\(883\) −2.61520e7 −1.12877 −0.564383 0.825513i \(-0.690886\pi\)
−0.564383 + 0.825513i \(0.690886\pi\)
\(884\) 6.77875e6 0.291756
\(885\) 0 0
\(886\) 1.83904e7 0.787058
\(887\) −1.08021e7 −0.460997 −0.230499 0.973073i \(-0.574036\pi\)
−0.230499 + 0.973073i \(0.574036\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −1.83130e6 −0.0774968
\(891\) 0 0
\(892\) −1.59208e7 −0.669965
\(893\) −5.87009e7 −2.46329
\(894\) 0 0
\(895\) −1.38993e7 −0.580011
\(896\) 0 0
\(897\) 0 0
\(898\) 6.82631e6 0.282485
\(899\) 2.03818e6 0.0841090
\(900\) 0 0
\(901\) 8.67026e6 0.355812
\(902\) −4.42416e7 −1.81057
\(903\) 0 0
\(904\) 1.41380e7 0.575395
\(905\) −1.05131e7 −0.426686
\(906\) 0 0
\(907\) −9.84167e6 −0.397238 −0.198619 0.980077i \(-0.563646\pi\)
−0.198619 + 0.980077i \(0.563646\pi\)
\(908\) −1.52909e6 −0.0615486
\(909\) 0 0
\(910\) 0 0
\(911\) −2.72509e7 −1.08789 −0.543945 0.839121i \(-0.683070\pi\)
−0.543945 + 0.839121i \(0.683070\pi\)
\(912\) 0 0
\(913\) −2.53318e7 −1.00575
\(914\) 2.77566e7 1.09901
\(915\) 0 0
\(916\) 1.67054e7 0.657836
\(917\) 0 0
\(918\) 0 0
\(919\) 2.86432e7 1.11875 0.559374 0.828916i \(-0.311042\pi\)
0.559374 + 0.828916i \(0.311042\pi\)
\(920\) −1.43488e7 −0.558915
\(921\) 0 0
\(922\) 1.04722e7 0.405705
\(923\) −2.98536e7 −1.15343
\(924\) 0 0
\(925\) 2.04922e7 0.787472
\(926\) −2.85441e7 −1.09393
\(927\) 0 0
\(928\) −690176. −0.0263081
\(929\) 6.78492e6 0.257932 0.128966 0.991649i \(-0.458834\pi\)
0.128966 + 0.991649i \(0.458834\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 1.87106e7 0.705581
\(933\) 0 0
\(934\) 8.69590e6 0.326173
\(935\) 2.74664e7 1.02748
\(936\) 0 0
\(937\) −3.00308e7 −1.11742 −0.558712 0.829362i \(-0.688704\pi\)
−0.558712 + 0.829362i \(0.688704\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −2.91110e7 −1.07458
\(941\) 2.30725e7 0.849415 0.424707 0.905331i \(-0.360377\pi\)
0.424707 + 0.905331i \(0.360377\pi\)
\(942\) 0 0
\(943\) −5.01972e7 −1.83823
\(944\) 1.43565e6 0.0524346
\(945\) 0 0
\(946\) 5.67736e7 2.06262
\(947\) −2.71433e7 −0.983531 −0.491765 0.870728i \(-0.663648\pi\)
−0.491765 + 0.870728i \(0.663648\pi\)
\(948\) 0 0
\(949\) −1.79603e7 −0.647365
\(950\) −2.60010e7 −0.934719
\(951\) 0 0
\(952\) 0 0
\(953\) 1.61552e7 0.576209 0.288104 0.957599i \(-0.406975\pi\)
0.288104 + 0.957599i \(0.406975\pi\)
\(954\) 0 0
\(955\) −2.48689e7 −0.882364
\(956\) 437472. 0.0154812
\(957\) 0 0
\(958\) 1.85318e7 0.652383
\(959\) 0 0
\(960\) 0 0
\(961\) −1.94846e7 −0.680585
\(962\) 2.35610e7 0.820837
\(963\) 0 0
\(964\) 1.45234e7 0.503357
\(965\) 5.98046e7 2.06736
\(966\) 0 0
\(967\) −3.80323e7 −1.30793 −0.653967 0.756523i \(-0.726897\pi\)
−0.653967 + 0.756523i \(0.726897\pi\)
\(968\) −1.67327e7 −0.573956
\(969\) 0 0
\(970\) 3.29627e7 1.12485
\(971\) −2.23104e7 −0.759379 −0.379689 0.925114i \(-0.623969\pi\)
−0.379689 + 0.925114i \(0.623969\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 1.82658e7 0.616937
\(975\) 0 0
\(976\) −38400.0 −0.00129035
\(977\) −3.06930e7 −1.02873 −0.514367 0.857570i \(-0.671973\pi\)
−0.514367 + 0.857570i \(0.671973\pi\)
\(978\) 0 0
\(979\) −3.91560e6 −0.130569
\(980\) 0 0
\(981\) 0 0
\(982\) −2.12572e7 −0.703439
\(983\) −1.52706e7 −0.504048 −0.252024 0.967721i \(-0.581096\pi\)
−0.252024 + 0.967721i \(0.581096\pi\)
\(984\) 0 0
\(985\) −3.21554e7 −1.05600
\(986\) 1.49898e6 0.0491024
\(987\) 0 0
\(988\) −2.98948e7 −0.974323
\(989\) 6.44162e7 2.09413
\(990\) 0 0
\(991\) 3.16279e7 1.02303 0.511513 0.859276i \(-0.329085\pi\)
0.511513 + 0.859276i \(0.329085\pi\)
\(992\) −3.09658e6 −0.0999085
\(993\) 0 0
\(994\) 0 0
\(995\) −7.78179e7 −2.49185
\(996\) 0 0
\(997\) 3.55842e7 1.13376 0.566878 0.823802i \(-0.308151\pi\)
0.566878 + 0.823802i \(0.308151\pi\)
\(998\) 9.85256e6 0.313129
\(999\) 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 882.6.a.j.1.1 1
3.2 odd 2 294.6.a.k.1.1 1
7.6 odd 2 126.6.a.a.1.1 1
21.2 odd 6 294.6.e.c.67.1 2
21.5 even 6 294.6.e.d.67.1 2
21.11 odd 6 294.6.e.c.79.1 2
21.17 even 6 294.6.e.d.79.1 2
21.20 even 2 42.6.a.e.1.1 1
28.27 even 2 1008.6.a.d.1.1 1
84.83 odd 2 336.6.a.q.1.1 1
105.62 odd 4 1050.6.g.h.799.2 2
105.83 odd 4 1050.6.g.h.799.1 2
105.104 even 2 1050.6.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.6.a.e.1.1 1 21.20 even 2
126.6.a.a.1.1 1 7.6 odd 2
294.6.a.k.1.1 1 3.2 odd 2
294.6.e.c.67.1 2 21.2 odd 6
294.6.e.c.79.1 2 21.11 odd 6
294.6.e.d.67.1 2 21.5 even 6
294.6.e.d.79.1 2 21.17 even 6
336.6.a.q.1.1 1 84.83 odd 2
882.6.a.j.1.1 1 1.1 even 1 trivial
1008.6.a.d.1.1 1 28.27 even 2
1050.6.a.f.1.1 1 105.104 even 2
1050.6.g.h.799.1 2 105.83 odd 4
1050.6.g.h.799.2 2 105.62 odd 4