Properties

Label 832.6.a.d.1.1
Level $832$
Weight $6$
Character 832.1
Self dual yes
Analytic conductor $133.439$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [832,6,Mod(1,832)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(832, 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("832.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 832 = 2^{6} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 832.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: \(133.439338084\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 832.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+14.0000 q^{5} -170.000 q^{7} -243.000 q^{9} +O(q^{10})\) \(q+14.0000 q^{5} -170.000 q^{7} -243.000 q^{9} +250.000 q^{11} +169.000 q^{13} +1062.00 q^{17} +78.0000 q^{19} +1576.00 q^{23} -2929.00 q^{25} -2578.00 q^{29} -8654.00 q^{31} -2380.00 q^{35} -10986.0 q^{37} +1050.00 q^{41} +5900.00 q^{43} -3402.00 q^{45} -5962.00 q^{47} +12093.0 q^{49} -29046.0 q^{53} +3500.00 q^{55} +13922.0 q^{59} +32882.0 q^{61} +41310.0 q^{63} +2366.00 q^{65} +69566.0 q^{67} -50542.0 q^{71} -46750.0 q^{73} -42500.0 q^{77} -19348.0 q^{79} +59049.0 q^{81} +87438.0 q^{83} +14868.0 q^{85} +94170.0 q^{89} -28730.0 q^{91} +1092.00 q^{95} +182786. q^{97} -60750.0 q^{99} +O(q^{100})\)

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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) 14.0000 0.250440 0.125220 0.992129i \(-0.460036\pi\)
0.125220 + 0.992129i \(0.460036\pi\)
\(6\) 0 0
\(7\) −170.000 −1.31131 −0.655653 0.755063i \(-0.727606\pi\)
−0.655653 + 0.755063i \(0.727606\pi\)
\(8\) 0 0
\(9\) −243.000 −1.00000
\(10\) 0 0
\(11\) 250.000 0.622957 0.311479 0.950253i \(-0.399176\pi\)
0.311479 + 0.950253i \(0.399176\pi\)
\(12\) 0 0
\(13\) 169.000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1062.00 0.891255 0.445628 0.895218i \(-0.352981\pi\)
0.445628 + 0.895218i \(0.352981\pi\)
\(18\) 0 0
\(19\) 78.0000 0.0495691 0.0247845 0.999693i \(-0.492110\pi\)
0.0247845 + 0.999693i \(0.492110\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1576.00 0.621207 0.310604 0.950539i \(-0.399469\pi\)
0.310604 + 0.950539i \(0.399469\pi\)
\(24\) 0 0
\(25\) −2929.00 −0.937280
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2578.00 −0.569230 −0.284615 0.958642i \(-0.591866\pi\)
−0.284615 + 0.958642i \(0.591866\pi\)
\(30\) 0 0
\(31\) −8654.00 −1.61738 −0.808691 0.588234i \(-0.799824\pi\)
−0.808691 + 0.588234i \(0.799824\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2380.00 −0.328403
\(36\) 0 0
\(37\) −10986.0 −1.31927 −0.659637 0.751584i \(-0.729290\pi\)
−0.659637 + 0.751584i \(0.729290\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1050.00 0.0975505 0.0487753 0.998810i \(-0.484468\pi\)
0.0487753 + 0.998810i \(0.484468\pi\)
\(42\) 0 0
\(43\) 5900.00 0.486610 0.243305 0.969950i \(-0.421768\pi\)
0.243305 + 0.969950i \(0.421768\pi\)
\(44\) 0 0
\(45\) −3402.00 −0.250440
\(46\) 0 0
\(47\) −5962.00 −0.393684 −0.196842 0.980435i \(-0.563069\pi\)
−0.196842 + 0.980435i \(0.563069\pi\)
\(48\) 0 0
\(49\) 12093.0 0.719522
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −29046.0 −1.42035 −0.710177 0.704023i \(-0.751385\pi\)
−0.710177 + 0.704023i \(0.751385\pi\)
\(54\) 0 0
\(55\) 3500.00 0.156013
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 13922.0 0.520681 0.260340 0.965517i \(-0.416165\pi\)
0.260340 + 0.965517i \(0.416165\pi\)
\(60\) 0 0
\(61\) 32882.0 1.13145 0.565723 0.824596i \(-0.308597\pi\)
0.565723 + 0.824596i \(0.308597\pi\)
\(62\) 0 0
\(63\) 41310.0 1.31131
\(64\) 0 0
\(65\) 2366.00 0.0694595
\(66\) 0 0
\(67\) 69566.0 1.89326 0.946629 0.322324i \(-0.104464\pi\)
0.946629 + 0.322324i \(0.104464\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −50542.0 −1.18989 −0.594945 0.803767i \(-0.702826\pi\)
−0.594945 + 0.803767i \(0.702826\pi\)
\(72\) 0 0
\(73\) −46750.0 −1.02677 −0.513387 0.858157i \(-0.671609\pi\)
−0.513387 + 0.858157i \(0.671609\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −42500.0 −0.816887
\(78\) 0 0
\(79\) −19348.0 −0.348793 −0.174397 0.984675i \(-0.555798\pi\)
−0.174397 + 0.984675i \(0.555798\pi\)
\(80\) 0 0
\(81\) 59049.0 1.00000
\(82\) 0 0
\(83\) 87438.0 1.39317 0.696586 0.717473i \(-0.254701\pi\)
0.696586 + 0.717473i \(0.254701\pi\)
\(84\) 0 0
\(85\) 14868.0 0.223206
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 94170.0 1.26019 0.630097 0.776516i \(-0.283015\pi\)
0.630097 + 0.776516i \(0.283015\pi\)
\(90\) 0 0
\(91\) −28730.0 −0.363691
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1092.00 0.0124141
\(96\) 0 0
\(97\) 182786. 1.97248 0.986242 0.165307i \(-0.0528613\pi\)
0.986242 + 0.165307i \(0.0528613\pi\)
\(98\) 0 0
\(99\) −60750.0 −0.622957
\(100\) 0 0
\(101\) 18514.0 0.180591 0.0902957 0.995915i \(-0.471219\pi\)
0.0902957 + 0.995915i \(0.471219\pi\)
\(102\) 0 0
\(103\) 116056. 1.07789 0.538945 0.842341i \(-0.318823\pi\)
0.538945 + 0.842341i \(0.318823\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −153520. −1.29630 −0.648150 0.761513i \(-0.724457\pi\)
−0.648150 + 0.761513i \(0.724457\pi\)
\(108\) 0 0
\(109\) 178622. 1.44002 0.720010 0.693963i \(-0.244137\pi\)
0.720010 + 0.693963i \(0.244137\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −244754. −1.80316 −0.901579 0.432615i \(-0.857591\pi\)
−0.901579 + 0.432615i \(0.857591\pi\)
\(114\) 0 0
\(115\) 22064.0 0.155575
\(116\) 0 0
\(117\) −41067.0 −0.277350
\(118\) 0 0
\(119\) −180540. −1.16871
\(120\) 0 0
\(121\) −98551.0 −0.611924
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −84756.0 −0.485172
\(126\) 0 0
\(127\) 256600. 1.41172 0.705858 0.708353i \(-0.250562\pi\)
0.705858 + 0.708353i \(0.250562\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 262736. 1.33765 0.668823 0.743421i \(-0.266798\pi\)
0.668823 + 0.743421i \(0.266798\pi\)
\(132\) 0 0
\(133\) −13260.0 −0.0650002
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −38286.0 −0.174276 −0.0871382 0.996196i \(-0.527772\pi\)
−0.0871382 + 0.996196i \(0.527772\pi\)
\(138\) 0 0
\(139\) 57776.0 0.253636 0.126818 0.991926i \(-0.459524\pi\)
0.126818 + 0.991926i \(0.459524\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 42250.0 0.172777
\(144\) 0 0
\(145\) −36092.0 −0.142558
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −28866.0 −0.106517 −0.0532587 0.998581i \(-0.516961\pi\)
−0.0532587 + 0.998581i \(0.516961\pi\)
\(150\) 0 0
\(151\) 39870.0 0.142300 0.0711498 0.997466i \(-0.477333\pi\)
0.0711498 + 0.997466i \(0.477333\pi\)
\(152\) 0 0
\(153\) −258066. −0.891255
\(154\) 0 0
\(155\) −121156. −0.405057
\(156\) 0 0
\(157\) −161042. −0.521423 −0.260711 0.965417i \(-0.583957\pi\)
−0.260711 + 0.965417i \(0.583957\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −267920. −0.814593
\(162\) 0 0
\(163\) −312830. −0.922230 −0.461115 0.887340i \(-0.652550\pi\)
−0.461115 + 0.887340i \(0.652550\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 532926. 1.47869 0.739343 0.673329i \(-0.235136\pi\)
0.739343 + 0.673329i \(0.235136\pi\)
\(168\) 0 0
\(169\) 28561.0 0.0769231
\(170\) 0 0
\(171\) −18954.0 −0.0495691
\(172\) 0 0
\(173\) 630458. 1.60155 0.800776 0.598964i \(-0.204421\pi\)
0.800776 + 0.598964i \(0.204421\pi\)
\(174\) 0 0
\(175\) 497930. 1.22906
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 674916. 1.57441 0.787204 0.616693i \(-0.211528\pi\)
0.787204 + 0.616693i \(0.211528\pi\)
\(180\) 0 0
\(181\) −186282. −0.422644 −0.211322 0.977417i \(-0.567777\pi\)
−0.211322 + 0.977417i \(0.567777\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −153804. −0.330399
\(186\) 0 0
\(187\) 265500. 0.555214
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 812180. 1.61090 0.805451 0.592663i \(-0.201923\pi\)
0.805451 + 0.592663i \(0.201923\pi\)
\(192\) 0 0
\(193\) −150142. −0.290141 −0.145070 0.989421i \(-0.546341\pi\)
−0.145070 + 0.989421i \(0.546341\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −236394. −0.433981 −0.216991 0.976174i \(-0.569624\pi\)
−0.216991 + 0.976174i \(0.569624\pi\)
\(198\) 0 0
\(199\) −39376.0 −0.0704854 −0.0352427 0.999379i \(-0.511220\pi\)
−0.0352427 + 0.999379i \(0.511220\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 438260. 0.746435
\(204\) 0 0
\(205\) 14700.0 0.0244305
\(206\) 0 0
\(207\) −382968. −0.621207
\(208\) 0 0
\(209\) 19500.0 0.0308794
\(210\) 0 0
\(211\) 410776. 0.635183 0.317592 0.948228i \(-0.397126\pi\)
0.317592 + 0.948228i \(0.397126\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 82600.0 0.121866
\(216\) 0 0
\(217\) 1.47118e6 2.12088
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 179478. 0.247190
\(222\) 0 0
\(223\) 1.08688e6 1.46359 0.731796 0.681523i \(-0.238682\pi\)
0.731796 + 0.681523i \(0.238682\pi\)
\(224\) 0 0
\(225\) 711747. 0.937280
\(226\) 0 0
\(227\) 256470. 0.330348 0.165174 0.986264i \(-0.447181\pi\)
0.165174 + 0.986264i \(0.447181\pi\)
\(228\) 0 0
\(229\) 298110. 0.375654 0.187827 0.982202i \(-0.439856\pi\)
0.187827 + 0.982202i \(0.439856\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −611926. −0.738430 −0.369215 0.929344i \(-0.620373\pi\)
−0.369215 + 0.929344i \(0.620373\pi\)
\(234\) 0 0
\(235\) −83468.0 −0.0985940
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 36570.0 0.0414124 0.0207062 0.999786i \(-0.493409\pi\)
0.0207062 + 0.999786i \(0.493409\pi\)
\(240\) 0 0
\(241\) 380922. 0.422468 0.211234 0.977436i \(-0.432252\pi\)
0.211234 + 0.977436i \(0.432252\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 169302. 0.180197
\(246\) 0 0
\(247\) 13182.0 0.0137480
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.22807e6 1.23038 0.615188 0.788380i \(-0.289080\pi\)
0.615188 + 0.788380i \(0.289080\pi\)
\(252\) 0 0
\(253\) 394000. 0.386986
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −439278. −0.414865 −0.207432 0.978249i \(-0.566511\pi\)
−0.207432 + 0.978249i \(0.566511\pi\)
\(258\) 0 0
\(259\) 1.86762e6 1.72997
\(260\) 0 0
\(261\) 626454. 0.569230
\(262\) 0 0
\(263\) −1.67987e6 −1.49757 −0.748783 0.662816i \(-0.769361\pi\)
−0.748783 + 0.662816i \(0.769361\pi\)
\(264\) 0 0
\(265\) −406644. −0.355713
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.93840e6 −1.63329 −0.816645 0.577141i \(-0.804168\pi\)
−0.816645 + 0.577141i \(0.804168\pi\)
\(270\) 0 0
\(271\) −695498. −0.575271 −0.287636 0.957740i \(-0.592869\pi\)
−0.287636 + 0.957740i \(0.592869\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −732250. −0.583885
\(276\) 0 0
\(277\) 1.13138e6 0.885948 0.442974 0.896534i \(-0.353923\pi\)
0.442974 + 0.896534i \(0.353923\pi\)
\(278\) 0 0
\(279\) 2.10292e6 1.61738
\(280\) 0 0
\(281\) 1.73122e6 1.30793 0.653967 0.756523i \(-0.273103\pi\)
0.653967 + 0.756523i \(0.273103\pi\)
\(282\) 0 0
\(283\) 1.47124e6 1.09199 0.545995 0.837788i \(-0.316152\pi\)
0.545995 + 0.837788i \(0.316152\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −178500. −0.127919
\(288\) 0 0
\(289\) −292013. −0.205664
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2.88855e6 −1.96567 −0.982834 0.184491i \(-0.940936\pi\)
−0.982834 + 0.184491i \(0.940936\pi\)
\(294\) 0 0
\(295\) 194908. 0.130399
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 266344. 0.172292
\(300\) 0 0
\(301\) −1.00300e6 −0.638094
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 460348. 0.283359
\(306\) 0 0
\(307\) −874118. −0.529327 −0.264664 0.964341i \(-0.585261\pi\)
−0.264664 + 0.964341i \(0.585261\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.68224e6 1.57252 0.786261 0.617895i \(-0.212014\pi\)
0.786261 + 0.617895i \(0.212014\pi\)
\(312\) 0 0
\(313\) −1.34459e6 −0.775761 −0.387880 0.921710i \(-0.626793\pi\)
−0.387880 + 0.921710i \(0.626793\pi\)
\(314\) 0 0
\(315\) 578340. 0.328403
\(316\) 0 0
\(317\) −1.32074e6 −0.738191 −0.369095 0.929392i \(-0.620332\pi\)
−0.369095 + 0.929392i \(0.620332\pi\)
\(318\) 0 0
\(319\) −644500. −0.354606
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 82836.0 0.0441787
\(324\) 0 0
\(325\) −495001. −0.259955
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.01354e6 0.516239
\(330\) 0 0
\(331\) 2.05728e6 1.03210 0.516051 0.856558i \(-0.327401\pi\)
0.516051 + 0.856558i \(0.327401\pi\)
\(332\) 0 0
\(333\) 2.66960e6 1.31927
\(334\) 0 0
\(335\) 973924. 0.474147
\(336\) 0 0
\(337\) 453398. 0.217473 0.108736 0.994071i \(-0.465320\pi\)
0.108736 + 0.994071i \(0.465320\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.16350e6 −1.00756
\(342\) 0 0
\(343\) 801380. 0.367793
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.23065e6 0.548669 0.274334 0.961634i \(-0.411543\pi\)
0.274334 + 0.961634i \(0.411543\pi\)
\(348\) 0 0
\(349\) 2.43825e6 1.07155 0.535777 0.844360i \(-0.320019\pi\)
0.535777 + 0.844360i \(0.320019\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2.68315e6 −1.14606 −0.573031 0.819534i \(-0.694233\pi\)
−0.573031 + 0.819534i \(0.694233\pi\)
\(354\) 0 0
\(355\) −707588. −0.297995
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.58693e6 0.649864 0.324932 0.945737i \(-0.394659\pi\)
0.324932 + 0.945737i \(0.394659\pi\)
\(360\) 0 0
\(361\) −2.47002e6 −0.997543
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −654500. −0.257145
\(366\) 0 0
\(367\) −60052.0 −0.0232735 −0.0116368 0.999932i \(-0.503704\pi\)
−0.0116368 + 0.999932i \(0.503704\pi\)
\(368\) 0 0
\(369\) −255150. −0.0975505
\(370\) 0 0
\(371\) 4.93782e6 1.86252
\(372\) 0 0
\(373\) 4.01853e6 1.49553 0.747766 0.663963i \(-0.231127\pi\)
0.747766 + 0.663963i \(0.231127\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −435682. −0.157876
\(378\) 0 0
\(379\) −1.67581e6 −0.599276 −0.299638 0.954053i \(-0.596866\pi\)
−0.299638 + 0.954053i \(0.596866\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 687258. 0.239399 0.119700 0.992810i \(-0.461807\pi\)
0.119700 + 0.992810i \(0.461807\pi\)
\(384\) 0 0
\(385\) −595000. −0.204581
\(386\) 0 0
\(387\) −1.43370e6 −0.486610
\(388\) 0 0
\(389\) −1.37611e6 −0.461082 −0.230541 0.973063i \(-0.574050\pi\)
−0.230541 + 0.973063i \(0.574050\pi\)
\(390\) 0 0
\(391\) 1.67371e6 0.553655
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −270872. −0.0873517
\(396\) 0 0
\(397\) 721198. 0.229656 0.114828 0.993385i \(-0.463368\pi\)
0.114828 + 0.993385i \(0.463368\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.22681e6 0.691548 0.345774 0.938318i \(-0.387616\pi\)
0.345774 + 0.938318i \(0.387616\pi\)
\(402\) 0 0
\(403\) −1.46253e6 −0.448581
\(404\) 0 0
\(405\) 826686. 0.250440
\(406\) 0 0
\(407\) −2.74650e6 −0.821852
\(408\) 0 0
\(409\) 2.00783e6 0.593496 0.296748 0.954956i \(-0.404098\pi\)
0.296748 + 0.954956i \(0.404098\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.36674e6 −0.682772
\(414\) 0 0
\(415\) 1.22413e6 0.348906
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.99378e6 −1.66788 −0.833942 0.551852i \(-0.813921\pi\)
−0.833942 + 0.551852i \(0.813921\pi\)
\(420\) 0 0
\(421\) 5.32737e6 1.46490 0.732449 0.680822i \(-0.238377\pi\)
0.732449 + 0.680822i \(0.238377\pi\)
\(422\) 0 0
\(423\) 1.44877e6 0.393684
\(424\) 0 0
\(425\) −3.11060e6 −0.835356
\(426\) 0 0
\(427\) −5.58994e6 −1.48367
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.42972e6 −1.40794 −0.703970 0.710230i \(-0.748591\pi\)
−0.703970 + 0.710230i \(0.748591\pi\)
\(432\) 0 0
\(433\) 7.43979e6 1.90696 0.953479 0.301459i \(-0.0974737\pi\)
0.953479 + 0.301459i \(0.0974737\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 122928. 0.0307927
\(438\) 0 0
\(439\) 6.86418e6 1.69991 0.849957 0.526852i \(-0.176628\pi\)
0.849957 + 0.526852i \(0.176628\pi\)
\(440\) 0 0
\(441\) −2.93860e6 −0.719522
\(442\) 0 0
\(443\) 3.46630e6 0.839182 0.419591 0.907713i \(-0.362173\pi\)
0.419591 + 0.907713i \(0.362173\pi\)
\(444\) 0 0
\(445\) 1.31838e6 0.315603
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.40426e6 −0.328725 −0.164362 0.986400i \(-0.552557\pi\)
−0.164362 + 0.986400i \(0.552557\pi\)
\(450\) 0 0
\(451\) 262500. 0.0607698
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −402220. −0.0910825
\(456\) 0 0
\(457\) −5.95072e6 −1.33284 −0.666421 0.745575i \(-0.732175\pi\)
−0.666421 + 0.745575i \(0.732175\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.25465e6 1.37073 0.685363 0.728202i \(-0.259644\pi\)
0.685363 + 0.728202i \(0.259644\pi\)
\(462\) 0 0
\(463\) −1.55055e6 −0.336149 −0.168075 0.985774i \(-0.553755\pi\)
−0.168075 + 0.985774i \(0.553755\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.80480e6 0.382945 0.191472 0.981498i \(-0.438674\pi\)
0.191472 + 0.981498i \(0.438674\pi\)
\(468\) 0 0
\(469\) −1.18262e7 −2.48264
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.47500e6 0.303137
\(474\) 0 0
\(475\) −228462. −0.0464601
\(476\) 0 0
\(477\) 7.05818e6 1.42035
\(478\) 0 0
\(479\) 2.21809e6 0.441712 0.220856 0.975306i \(-0.429115\pi\)
0.220856 + 0.975306i \(0.429115\pi\)
\(480\) 0 0
\(481\) −1.85663e6 −0.365901
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.55900e6 0.493988
\(486\) 0 0
\(487\) −6.14268e6 −1.17364 −0.586821 0.809717i \(-0.699621\pi\)
−0.586821 + 0.809717i \(0.699621\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6.44486e6 −1.20645 −0.603226 0.797571i \(-0.706118\pi\)
−0.603226 + 0.797571i \(0.706118\pi\)
\(492\) 0 0
\(493\) −2.73784e6 −0.507330
\(494\) 0 0
\(495\) −850500. −0.156013
\(496\) 0 0
\(497\) 8.59214e6 1.56031
\(498\) 0 0
\(499\) −4.25838e6 −0.765584 −0.382792 0.923835i \(-0.625037\pi\)
−0.382792 + 0.923835i \(0.625037\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3.56242e6 −0.627806 −0.313903 0.949455i \(-0.601637\pi\)
−0.313903 + 0.949455i \(0.601637\pi\)
\(504\) 0 0
\(505\) 259196. 0.0452272
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4.23936e6 −0.725281 −0.362640 0.931929i \(-0.618125\pi\)
−0.362640 + 0.931929i \(0.618125\pi\)
\(510\) 0 0
\(511\) 7.94750e6 1.34641
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.62478e6 0.269946
\(516\) 0 0
\(517\) −1.49050e6 −0.245248
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.38657e6 0.385194 0.192597 0.981278i \(-0.438309\pi\)
0.192597 + 0.981278i \(0.438309\pi\)
\(522\) 0 0
\(523\) 8.84129e6 1.41339 0.706694 0.707519i \(-0.250186\pi\)
0.706694 + 0.707519i \(0.250186\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −9.19055e6 −1.44150
\(528\) 0 0
\(529\) −3.95257e6 −0.614101
\(530\) 0 0
\(531\) −3.38305e6 −0.520681
\(532\) 0 0
\(533\) 177450. 0.0270557
\(534\) 0 0
\(535\) −2.14928e6 −0.324645
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3.02325e6 0.448231
\(540\) 0 0
\(541\) −70058.0 −0.0102912 −0.00514558 0.999987i \(-0.501638\pi\)
−0.00514558 + 0.999987i \(0.501638\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.50071e6 0.360638
\(546\) 0 0
\(547\) 6.60752e6 0.944213 0.472107 0.881541i \(-0.343494\pi\)
0.472107 + 0.881541i \(0.343494\pi\)
\(548\) 0 0
\(549\) −7.99033e6 −1.13145
\(550\) 0 0
\(551\) −201084. −0.0282162
\(552\) 0 0
\(553\) 3.28916e6 0.457375
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.10726e7 1.51221 0.756107 0.654448i \(-0.227099\pi\)
0.756107 + 0.654448i \(0.227099\pi\)
\(558\) 0 0
\(559\) 997100. 0.134961
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.43532e6 0.190843 0.0954216 0.995437i \(-0.469580\pi\)
0.0954216 + 0.995437i \(0.469580\pi\)
\(564\) 0 0
\(565\) −3.42656e6 −0.451582
\(566\) 0 0
\(567\) −1.00383e7 −1.31131
\(568\) 0 0
\(569\) −1.17051e7 −1.51564 −0.757818 0.652466i \(-0.773734\pi\)
−0.757818 + 0.652466i \(0.773734\pi\)
\(570\) 0 0
\(571\) −4.81885e6 −0.618519 −0.309260 0.950978i \(-0.600081\pi\)
−0.309260 + 0.950978i \(0.600081\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.61610e6 −0.582245
\(576\) 0 0
\(577\) −1.35572e6 −0.169523 −0.0847617 0.996401i \(-0.527013\pi\)
−0.0847617 + 0.996401i \(0.527013\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.48645e7 −1.82687
\(582\) 0 0
\(583\) −7.26150e6 −0.884820
\(584\) 0 0
\(585\) −574938. −0.0694595
\(586\) 0 0
\(587\) −5.03941e6 −0.603649 −0.301824 0.953364i \(-0.597596\pi\)
−0.301824 + 0.953364i \(0.597596\pi\)
\(588\) 0 0
\(589\) −675012. −0.0801721
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 9.16124e6 1.06984 0.534919 0.844904i \(-0.320342\pi\)
0.534919 + 0.844904i \(0.320342\pi\)
\(594\) 0 0
\(595\) −2.52756e6 −0.292691
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6.46635e6 −0.736363 −0.368182 0.929754i \(-0.620020\pi\)
−0.368182 + 0.929754i \(0.620020\pi\)
\(600\) 0 0
\(601\) −1.18021e7 −1.33282 −0.666411 0.745585i \(-0.732170\pi\)
−0.666411 + 0.745585i \(0.732170\pi\)
\(602\) 0 0
\(603\) −1.69045e7 −1.89326
\(604\) 0 0
\(605\) −1.37971e6 −0.153250
\(606\) 0 0
\(607\) 2.25748e6 0.248686 0.124343 0.992239i \(-0.460318\pi\)
0.124343 + 0.992239i \(0.460318\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.00758e6 −0.109188
\(612\) 0 0
\(613\) 2.75378e6 0.295991 0.147995 0.988988i \(-0.452718\pi\)
0.147995 + 0.988988i \(0.452718\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.41607e6 0.361255 0.180627 0.983552i \(-0.442187\pi\)
0.180627 + 0.983552i \(0.442187\pi\)
\(618\) 0 0
\(619\) −9.43169e6 −0.989379 −0.494690 0.869070i \(-0.664718\pi\)
−0.494690 + 0.869070i \(0.664718\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.60089e7 −1.65250
\(624\) 0 0
\(625\) 7.96654e6 0.815774
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.16671e7 −1.17581
\(630\) 0 0
\(631\) −4.87474e6 −0.487391 −0.243696 0.969852i \(-0.578360\pi\)
−0.243696 + 0.969852i \(0.578360\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3.59240e6 0.353550
\(636\) 0 0
\(637\) 2.04372e6 0.199559
\(638\) 0 0
\(639\) 1.22817e7 1.18989
\(640\) 0 0
\(641\) 9.74279e6 0.936566 0.468283 0.883579i \(-0.344873\pi\)
0.468283 + 0.883579i \(0.344873\pi\)
\(642\) 0 0
\(643\) −1.63894e6 −0.156327 −0.0781637 0.996941i \(-0.524906\pi\)
−0.0781637 + 0.996941i \(0.524906\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.59069e6 −0.149391 −0.0746955 0.997206i \(-0.523798\pi\)
−0.0746955 + 0.997206i \(0.523798\pi\)
\(648\) 0 0
\(649\) 3.48050e6 0.324362
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.59778e7 −1.46634 −0.733170 0.680045i \(-0.761960\pi\)
−0.733170 + 0.680045i \(0.761960\pi\)
\(654\) 0 0
\(655\) 3.67830e6 0.335000
\(656\) 0 0
\(657\) 1.13602e7 1.02677
\(658\) 0 0
\(659\) 6.02458e6 0.540397 0.270199 0.962805i \(-0.412911\pi\)
0.270199 + 0.962805i \(0.412911\pi\)
\(660\) 0 0
\(661\) 2.00705e7 1.78671 0.893355 0.449352i \(-0.148345\pi\)
0.893355 + 0.449352i \(0.148345\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −185640. −0.0162786
\(666\) 0 0
\(667\) −4.06293e6 −0.353610
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 8.22050e6 0.704842
\(672\) 0 0
\(673\) −5.48575e6 −0.466873 −0.233436 0.972372i \(-0.574997\pi\)
−0.233436 + 0.972372i \(0.574997\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.74926e6 0.398248 0.199124 0.979974i \(-0.436190\pi\)
0.199124 + 0.979974i \(0.436190\pi\)
\(678\) 0 0
\(679\) −3.10736e7 −2.58653
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 6.13964e6 0.503606 0.251803 0.967778i \(-0.418976\pi\)
0.251803 + 0.967778i \(0.418976\pi\)
\(684\) 0 0
\(685\) −536004. −0.0436457
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −4.90877e6 −0.393935
\(690\) 0 0
\(691\) −1.57617e7 −1.25577 −0.627883 0.778308i \(-0.716078\pi\)
−0.627883 + 0.778308i \(0.716078\pi\)
\(692\) 0 0
\(693\) 1.03275e7 0.816887
\(694\) 0 0
\(695\) 808864. 0.0635204
\(696\) 0 0
\(697\) 1.11510e6 0.0869424
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.42036e7 1.09170 0.545851 0.837882i \(-0.316207\pi\)
0.545851 + 0.837882i \(0.316207\pi\)
\(702\) 0 0
\(703\) −856908. −0.0653952
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3.14738e6 −0.236810
\(708\) 0 0
\(709\) −1.60718e7 −1.20074 −0.600369 0.799723i \(-0.704980\pi\)
−0.600369 + 0.799723i \(0.704980\pi\)
\(710\) 0 0
\(711\) 4.70156e6 0.348793
\(712\) 0 0
\(713\) −1.36387e7 −1.00473
\(714\) 0 0
\(715\) 591500. 0.0432703
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.07078e7 −1.49387 −0.746933 0.664900i \(-0.768474\pi\)
−0.746933 + 0.664900i \(0.768474\pi\)
\(720\) 0 0
\(721\) −1.97295e7 −1.41344
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 7.55096e6 0.533528
\(726\) 0 0
\(727\) 5.04803e6 0.354231 0.177115 0.984190i \(-0.443323\pi\)
0.177115 + 0.984190i \(0.443323\pi\)
\(728\) 0 0
\(729\) −1.43489e7 −1.00000
\(730\) 0 0
\(731\) 6.26580e6 0.433694
\(732\) 0 0
\(733\) 2.10377e7 1.44623 0.723115 0.690728i \(-0.242710\pi\)
0.723115 + 0.690728i \(0.242710\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.73915e7 1.17942
\(738\) 0 0
\(739\) −1.38992e7 −0.936218 −0.468109 0.883671i \(-0.655065\pi\)
−0.468109 + 0.883671i \(0.655065\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.23267e6 0.0819169 0.0409584 0.999161i \(-0.486959\pi\)
0.0409584 + 0.999161i \(0.486959\pi\)
\(744\) 0 0
\(745\) −404124. −0.0266762
\(746\) 0 0
\(747\) −2.12474e7 −1.39317
\(748\) 0 0
\(749\) 2.60984e7 1.69985
\(750\) 0 0
\(751\) −1.62624e6 −0.105217 −0.0526084 0.998615i \(-0.516753\pi\)
−0.0526084 + 0.998615i \(0.516753\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 558180. 0.0356375
\(756\) 0 0
\(757\) −3.49882e6 −0.221913 −0.110956 0.993825i \(-0.535391\pi\)
−0.110956 + 0.993825i \(0.535391\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.21713e7 1.38781 0.693905 0.720067i \(-0.255889\pi\)
0.693905 + 0.720067i \(0.255889\pi\)
\(762\) 0 0
\(763\) −3.03657e7 −1.88831
\(764\) 0 0
\(765\) −3.61292e6 −0.223206
\(766\) 0 0
\(767\) 2.35282e6 0.144411
\(768\) 0 0
\(769\) 1.08955e6 0.0664400 0.0332200 0.999448i \(-0.489424\pi\)
0.0332200 + 0.999448i \(0.489424\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.95219e6 −0.117510 −0.0587549 0.998272i \(-0.518713\pi\)
−0.0587549 + 0.998272i \(0.518713\pi\)
\(774\) 0 0
\(775\) 2.53476e7 1.51594
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 81900.0 0.00483549
\(780\) 0 0
\(781\) −1.26355e7 −0.741250
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.25459e6 −0.130585
\(786\) 0 0
\(787\) 1.44531e7 0.831809 0.415904 0.909408i \(-0.363465\pi\)
0.415904 + 0.909408i \(0.363465\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 4.16082e7 2.36449
\(792\) 0 0
\(793\) 5.55706e6 0.313807
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.23500e7 −0.688685 −0.344343 0.938844i \(-0.611898\pi\)
−0.344343 + 0.938844i \(0.611898\pi\)
\(798\) 0 0
\(799\) −6.33164e6 −0.350873
\(800\) 0 0
\(801\) −2.28833e7 −1.26019
\(802\) 0 0
\(803\) −1.16875e7 −0.639636
\(804\) 0 0
\(805\) −3.75088e6 −0.204006
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.15968e7 0.622970 0.311485 0.950251i \(-0.399174\pi\)
0.311485 + 0.950251i \(0.399174\pi\)
\(810\) 0 0
\(811\) 2.47534e7 1.32155 0.660774 0.750585i \(-0.270228\pi\)
0.660774 + 0.750585i \(0.270228\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −4.37962e6 −0.230963
\(816\) 0 0
\(817\) 460200. 0.0241208
\(818\) 0 0
\(819\) 6.98139e6 0.363691
\(820\) 0 0
\(821\) 2.47470e6 0.128134 0.0640671 0.997946i \(-0.479593\pi\)
0.0640671 + 0.997946i \(0.479593\pi\)
\(822\) 0 0
\(823\) −7.84754e6 −0.403863 −0.201932 0.979400i \(-0.564722\pi\)
−0.201932 + 0.979400i \(0.564722\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.26192e7 1.15004 0.575020 0.818140i \(-0.304994\pi\)
0.575020 + 0.818140i \(0.304994\pi\)
\(828\) 0 0
\(829\) 1.73912e7 0.878907 0.439454 0.898265i \(-0.355172\pi\)
0.439454 + 0.898265i \(0.355172\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1.28428e7 0.641278
\(834\) 0 0
\(835\) 7.46096e6 0.370321
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −3.43825e7 −1.68629 −0.843147 0.537684i \(-0.819299\pi\)
−0.843147 + 0.537684i \(0.819299\pi\)
\(840\) 0 0
\(841\) −1.38651e7 −0.675977
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 399854. 0.0192646
\(846\) 0 0
\(847\) 1.67537e7 0.802419
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.73139e7 −0.819543
\(852\) 0 0
\(853\) −2.31007e7 −1.08706 −0.543528 0.839391i \(-0.682912\pi\)
−0.543528 + 0.839391i \(0.682912\pi\)
\(854\) 0 0
\(855\) −265356. −0.0124141
\(856\) 0 0
\(857\) −7.02305e6 −0.326643 −0.163322 0.986573i \(-0.552221\pi\)
−0.163322 + 0.986573i \(0.552221\pi\)
\(858\) 0 0
\(859\) −8.82135e6 −0.407899 −0.203949 0.978981i \(-0.565378\pi\)
−0.203949 + 0.978981i \(0.565378\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.39560e7 1.09493 0.547466 0.836828i \(-0.315592\pi\)
0.547466 + 0.836828i \(0.315592\pi\)
\(864\) 0 0
\(865\) 8.82641e6 0.401092
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −4.83700e6 −0.217283
\(870\) 0 0
\(871\) 1.17567e7 0.525096
\(872\) 0 0
\(873\) −4.44170e7 −1.97248
\(874\) 0 0
\(875\) 1.44085e7 0.636208
\(876\) 0 0
\(877\) 5.79805e6 0.254556 0.127278 0.991867i \(-0.459376\pi\)
0.127278 + 0.991867i \(0.459376\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.30527e7 −0.566580 −0.283290 0.959034i \(-0.591426\pi\)
−0.283290 + 0.959034i \(0.591426\pi\)
\(882\) 0 0
\(883\) −4.73009e6 −0.204159 −0.102079 0.994776i \(-0.532550\pi\)
−0.102079 + 0.994776i \(0.532550\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.80737e7 1.19809 0.599046 0.800714i \(-0.295547\pi\)
0.599046 + 0.800714i \(0.295547\pi\)
\(888\) 0 0
\(889\) −4.36220e7 −1.85119
\(890\) 0 0
\(891\) 1.47622e7 0.622957
\(892\) 0 0
\(893\) −465036. −0.0195145
\(894\) 0 0
\(895\) 9.44882e6 0.394294
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 2.23100e7 0.920663
\(900\) 0 0
\(901\) −3.08469e7 −1.26590
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.60795e6 −0.105847
\(906\) 0 0
\(907\) −2.28552e7 −0.922500 −0.461250 0.887270i \(-0.652599\pi\)
−0.461250 + 0.887270i \(0.652599\pi\)
\(908\) 0 0
\(909\) −4.49890e6 −0.180591
\(910\) 0 0
\(911\) −3.27335e7 −1.30676 −0.653381 0.757029i \(-0.726650\pi\)
−0.653381 + 0.757029i \(0.726650\pi\)
\(912\) 0 0
\(913\) 2.18595e7 0.867887
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4.46651e7 −1.75406
\(918\) 0 0
\(919\) −1.27717e7 −0.498839 −0.249419 0.968396i \(-0.580240\pi\)
−0.249419 + 0.968396i \(0.580240\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −8.54160e6 −0.330016
\(924\) 0 0
\(925\) 3.21780e7 1.23653
\(926\) 0 0
\(927\) −2.82016e7 −1.07789
\(928\) 0 0
\(929\) 3.48297e7 1.32407 0.662034 0.749473i \(-0.269693\pi\)
0.662034 + 0.749473i \(0.269693\pi\)
\(930\) 0 0
\(931\) 943254. 0.0356660
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 3.71700e6 0.139048
\(936\) 0 0
\(937\) 3.00172e7 1.11692 0.558459 0.829532i \(-0.311393\pi\)
0.558459 + 0.829532i \(0.311393\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 4.50649e7 1.65907 0.829534 0.558457i \(-0.188606\pi\)
0.829534 + 0.558457i \(0.188606\pi\)
\(942\) 0 0
\(943\) 1.65480e6 0.0605991
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.99276e7 −1.08442 −0.542210 0.840243i \(-0.682412\pi\)
−0.542210 + 0.840243i \(0.682412\pi\)
\(948\) 0 0
\(949\) −7.90075e6 −0.284776
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −4.25147e7 −1.51638 −0.758188 0.652036i \(-0.773915\pi\)
−0.758188 + 0.652036i \(0.773915\pi\)
\(954\) 0 0
\(955\) 1.13705e7 0.403433
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 6.50862e6 0.228530
\(960\) 0 0
\(961\) 4.62626e7 1.61593
\(962\) 0 0
\(963\) 3.73054e7 1.29630
\(964\) 0 0
\(965\) −2.10199e6 −0.0726628
\(966\) 0 0
\(967\) −3.00251e7 −1.03257 −0.516284 0.856417i \(-0.672685\pi\)
−0.516284 + 0.856417i \(0.672685\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 4.00864e7 1.36442 0.682211 0.731155i \(-0.261018\pi\)
0.682211 + 0.731155i \(0.261018\pi\)
\(972\) 0 0
\(973\) −9.82192e6 −0.332594
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 5.12151e7 1.71657 0.858284 0.513174i \(-0.171531\pi\)
0.858284 + 0.513174i \(0.171531\pi\)
\(978\) 0 0
\(979\) 2.35425e7 0.785047
\(980\) 0 0
\(981\) −4.34051e7 −1.44002
\(982\) 0 0
\(983\) 1.82382e7 0.602004 0.301002 0.953624i \(-0.402679\pi\)
0.301002 + 0.953624i \(0.402679\pi\)
\(984\) 0 0
\(985\) −3.30952e6 −0.108686
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 9.29840e6 0.302286
\(990\) 0 0
\(991\) −3.24103e7 −1.04833 −0.524166 0.851616i \(-0.675623\pi\)
−0.524166 + 0.851616i \(0.675623\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −551264. −0.0176523
\(996\) 0 0
\(997\) 2.07867e7 0.662289 0.331145 0.943580i \(-0.392565\pi\)
0.331145 + 0.943580i \(0.392565\pi\)
\(998\) 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 832.6.a.d.1.1 1
4.3 odd 2 832.6.a.e.1.1 1
8.3 odd 2 208.6.a.b.1.1 1
8.5 even 2 26.6.a.a.1.1 1
24.5 odd 2 234.6.a.g.1.1 1
40.13 odd 4 650.6.b.a.599.2 2
40.29 even 2 650.6.a.a.1.1 1
40.37 odd 4 650.6.b.a.599.1 2
104.5 odd 4 338.6.b.a.337.2 2
104.21 odd 4 338.6.b.a.337.1 2
104.77 even 2 338.6.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
26.6.a.a.1.1 1 8.5 even 2
208.6.a.b.1.1 1 8.3 odd 2
234.6.a.g.1.1 1 24.5 odd 2
338.6.a.d.1.1 1 104.77 even 2
338.6.b.a.337.1 2 104.21 odd 4
338.6.b.a.337.2 2 104.5 odd 4
650.6.a.a.1.1 1 40.29 even 2
650.6.b.a.599.1 2 40.37 odd 4
650.6.b.a.599.2 2 40.13 odd 4
832.6.a.d.1.1 1 1.1 even 1 trivial
832.6.a.e.1.1 1 4.3 odd 2