Properties

Label 6480.2.a.bp.1.1
Level $6480$
Weight $2$
Character 6480.1
Self dual yes
Analytic conductor $51.743$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6480,2,Mod(1,6480)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6480, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6480.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6480 = 2^{4} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6480.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: \(51.7430605098\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{12})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1620)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.73205\) of defining polynomial
Character \(\chi\) \(=\) 6480.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{5} -0.732051 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} -0.732051 q^{7} -1.73205 q^{11} -1.46410 q^{13} +1.26795 q^{17} -2.46410 q^{19} -3.46410 q^{23} +1.00000 q^{25} +4.26795 q^{29} +7.92820 q^{31} -0.732051 q^{35} +4.19615 q^{37} +0.803848 q^{41} -6.73205 q^{43} -4.73205 q^{47} -6.46410 q^{49} +10.7321 q^{53} -1.73205 q^{55} -4.26795 q^{59} -4.00000 q^{61} -1.46410 q^{65} +14.3923 q^{67} -0.803848 q^{71} +10.1962 q^{73} +1.26795 q^{77} -6.39230 q^{79} +9.12436 q^{83} +1.26795 q^{85} +5.19615 q^{89} +1.07180 q^{91} -2.46410 q^{95} -2.73205 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{5} + 2 q^{7} + 4 q^{13} + 6 q^{17} + 2 q^{19} + 2 q^{25} + 12 q^{29} + 2 q^{31} + 2 q^{35} - 2 q^{37} + 12 q^{41} - 10 q^{43} - 6 q^{47} - 6 q^{49} + 18 q^{53} - 12 q^{59} - 8 q^{61} + 4 q^{65} + 8 q^{67} - 12 q^{71} + 10 q^{73} + 6 q^{77} + 8 q^{79} - 6 q^{83} + 6 q^{85} + 16 q^{91} + 2 q^{95} - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −0.732051 −0.276689 −0.138345 0.990384i \(-0.544178\pi\)
−0.138345 + 0.990384i \(0.544178\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.73205 −0.522233 −0.261116 0.965307i \(-0.584091\pi\)
−0.261116 + 0.965307i \(0.584091\pi\)
\(12\) 0 0
\(13\) −1.46410 −0.406069 −0.203034 0.979172i \(-0.565080\pi\)
−0.203034 + 0.979172i \(0.565080\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.26795 0.307523 0.153761 0.988108i \(-0.450861\pi\)
0.153761 + 0.988108i \(0.450861\pi\)
\(18\) 0 0
\(19\) −2.46410 −0.565304 −0.282652 0.959223i \(-0.591214\pi\)
−0.282652 + 0.959223i \(0.591214\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.46410 −0.722315 −0.361158 0.932505i \(-0.617618\pi\)
−0.361158 + 0.932505i \(0.617618\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.26795 0.792538 0.396269 0.918134i \(-0.370305\pi\)
0.396269 + 0.918134i \(0.370305\pi\)
\(30\) 0 0
\(31\) 7.92820 1.42395 0.711974 0.702206i \(-0.247802\pi\)
0.711974 + 0.702206i \(0.247802\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.732051 −0.123739
\(36\) 0 0
\(37\) 4.19615 0.689843 0.344922 0.938631i \(-0.387905\pi\)
0.344922 + 0.938631i \(0.387905\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.803848 0.125540 0.0627700 0.998028i \(-0.480007\pi\)
0.0627700 + 0.998028i \(0.480007\pi\)
\(42\) 0 0
\(43\) −6.73205 −1.02663 −0.513314 0.858201i \(-0.671582\pi\)
−0.513314 + 0.858201i \(0.671582\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.73205 −0.690241 −0.345120 0.938558i \(-0.612162\pi\)
−0.345120 + 0.938558i \(0.612162\pi\)
\(48\) 0 0
\(49\) −6.46410 −0.923443
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 10.7321 1.47416 0.737080 0.675805i \(-0.236204\pi\)
0.737080 + 0.675805i \(0.236204\pi\)
\(54\) 0 0
\(55\) −1.73205 −0.233550
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.26795 −0.555640 −0.277820 0.960633i \(-0.589612\pi\)
−0.277820 + 0.960633i \(0.589612\pi\)
\(60\) 0 0
\(61\) −4.00000 −0.512148 −0.256074 0.966657i \(-0.582429\pi\)
−0.256074 + 0.966657i \(0.582429\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.46410 −0.181599
\(66\) 0 0
\(67\) 14.3923 1.75830 0.879150 0.476545i \(-0.158111\pi\)
0.879150 + 0.476545i \(0.158111\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.803848 −0.0953992 −0.0476996 0.998862i \(-0.515189\pi\)
−0.0476996 + 0.998862i \(0.515189\pi\)
\(72\) 0 0
\(73\) 10.1962 1.19337 0.596685 0.802476i \(-0.296484\pi\)
0.596685 + 0.802476i \(0.296484\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.26795 0.144496
\(78\) 0 0
\(79\) −6.39230 −0.719190 −0.359595 0.933108i \(-0.617085\pi\)
−0.359595 + 0.933108i \(0.617085\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 9.12436 1.00153 0.500764 0.865584i \(-0.333052\pi\)
0.500764 + 0.865584i \(0.333052\pi\)
\(84\) 0 0
\(85\) 1.26795 0.137528
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.19615 0.550791 0.275396 0.961331i \(-0.411191\pi\)
0.275396 + 0.961331i \(0.411191\pi\)
\(90\) 0 0
\(91\) 1.07180 0.112355
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.46410 −0.252811
\(96\) 0 0
\(97\) −2.73205 −0.277398 −0.138699 0.990335i \(-0.544292\pi\)
−0.138699 + 0.990335i \(0.544292\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 18.1244 1.80344 0.901720 0.432320i \(-0.142305\pi\)
0.901720 + 0.432320i \(0.142305\pi\)
\(102\) 0 0
\(103\) 2.39230 0.235721 0.117860 0.993030i \(-0.462396\pi\)
0.117860 + 0.993030i \(0.462396\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.46410 −0.334887 −0.167444 0.985882i \(-0.553551\pi\)
−0.167444 + 0.985882i \(0.553551\pi\)
\(108\) 0 0
\(109\) 5.92820 0.567819 0.283909 0.958851i \(-0.408368\pi\)
0.283909 + 0.958851i \(0.408368\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 17.6603 1.66134 0.830668 0.556767i \(-0.187959\pi\)
0.830668 + 0.556767i \(0.187959\pi\)
\(114\) 0 0
\(115\) −3.46410 −0.323029
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.928203 −0.0850883
\(120\) 0 0
\(121\) −8.00000 −0.727273
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 6.19615 0.549820 0.274910 0.961470i \(-0.411352\pi\)
0.274910 + 0.961470i \(0.411352\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 13.7321 1.19977 0.599887 0.800084i \(-0.295212\pi\)
0.599887 + 0.800084i \(0.295212\pi\)
\(132\) 0 0
\(133\) 1.80385 0.156413
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 16.3923 1.40049 0.700245 0.713903i \(-0.253074\pi\)
0.700245 + 0.713903i \(0.253074\pi\)
\(138\) 0 0
\(139\) 5.39230 0.457369 0.228685 0.973501i \(-0.426558\pi\)
0.228685 + 0.973501i \(0.426558\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.53590 0.212062
\(144\) 0 0
\(145\) 4.26795 0.354434
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) −3.39230 −0.276062 −0.138031 0.990428i \(-0.544077\pi\)
−0.138031 + 0.990428i \(0.544077\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 7.92820 0.636809
\(156\) 0 0
\(157\) 6.73205 0.537276 0.268638 0.963241i \(-0.413426\pi\)
0.268638 + 0.963241i \(0.413426\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.53590 0.199857
\(162\) 0 0
\(163\) −15.2679 −1.19588 −0.597939 0.801542i \(-0.704014\pi\)
−0.597939 + 0.801542i \(0.704014\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3.12436 0.241770 0.120885 0.992667i \(-0.461427\pi\)
0.120885 + 0.992667i \(0.461427\pi\)
\(168\) 0 0
\(169\) −10.8564 −0.835108
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −24.2487 −1.84360 −0.921798 0.387671i \(-0.873280\pi\)
−0.921798 + 0.387671i \(0.873280\pi\)
\(174\) 0 0
\(175\) −0.732051 −0.0553378
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 12.1244 0.906217 0.453108 0.891455i \(-0.350315\pi\)
0.453108 + 0.891455i \(0.350315\pi\)
\(180\) 0 0
\(181\) −9.53590 −0.708798 −0.354399 0.935094i \(-0.615314\pi\)
−0.354399 + 0.935094i \(0.615314\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.19615 0.308507
\(186\) 0 0
\(187\) −2.19615 −0.160599
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −19.0526 −1.37859 −0.689297 0.724479i \(-0.742081\pi\)
−0.689297 + 0.724479i \(0.742081\pi\)
\(192\) 0 0
\(193\) 20.5885 1.48199 0.740995 0.671511i \(-0.234354\pi\)
0.740995 + 0.671511i \(0.234354\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −13.8564 −0.987228 −0.493614 0.869681i \(-0.664324\pi\)
−0.493614 + 0.869681i \(0.664324\pi\)
\(198\) 0 0
\(199\) 11.8564 0.840478 0.420239 0.907413i \(-0.361946\pi\)
0.420239 + 0.907413i \(0.361946\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.12436 −0.219287
\(204\) 0 0
\(205\) 0.803848 0.0561432
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4.26795 0.295220
\(210\) 0 0
\(211\) 6.07180 0.418000 0.209000 0.977916i \(-0.432979\pi\)
0.209000 + 0.977916i \(0.432979\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6.73205 −0.459122
\(216\) 0 0
\(217\) −5.80385 −0.393991
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.85641 −0.124875
\(222\) 0 0
\(223\) −21.8564 −1.46361 −0.731807 0.681512i \(-0.761323\pi\)
−0.731807 + 0.681512i \(0.761323\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 15.8038 1.04894 0.524469 0.851429i \(-0.324264\pi\)
0.524469 + 0.851429i \(0.324264\pi\)
\(228\) 0 0
\(229\) 9.85641 0.651330 0.325665 0.945485i \(-0.394412\pi\)
0.325665 + 0.945485i \(0.394412\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.58846 0.431624 0.215812 0.976435i \(-0.430760\pi\)
0.215812 + 0.976435i \(0.430760\pi\)
\(234\) 0 0
\(235\) −4.73205 −0.308685
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 15.4641 1.00029 0.500145 0.865942i \(-0.333280\pi\)
0.500145 + 0.865942i \(0.333280\pi\)
\(240\) 0 0
\(241\) −24.3205 −1.56662 −0.783311 0.621630i \(-0.786471\pi\)
−0.783311 + 0.621630i \(0.786471\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −6.46410 −0.412976
\(246\) 0 0
\(247\) 3.60770 0.229552
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 27.4641 1.73352 0.866759 0.498727i \(-0.166199\pi\)
0.866759 + 0.498727i \(0.166199\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8.53590 −0.532455 −0.266227 0.963910i \(-0.585777\pi\)
−0.266227 + 0.963910i \(0.585777\pi\)
\(258\) 0 0
\(259\) −3.07180 −0.190872
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 24.2487 1.49524 0.747620 0.664127i \(-0.231197\pi\)
0.747620 + 0.664127i \(0.231197\pi\)
\(264\) 0 0
\(265\) 10.7321 0.659265
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 19.7321 1.20308 0.601542 0.798841i \(-0.294553\pi\)
0.601542 + 0.798841i \(0.294553\pi\)
\(270\) 0 0
\(271\) 24.7846 1.50556 0.752779 0.658273i \(-0.228713\pi\)
0.752779 + 0.658273i \(0.228713\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.73205 −0.104447
\(276\) 0 0
\(277\) −19.1244 −1.14907 −0.574536 0.818480i \(-0.694817\pi\)
−0.574536 + 0.818480i \(0.694817\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5.32051 0.317395 0.158697 0.987327i \(-0.449271\pi\)
0.158697 + 0.987327i \(0.449271\pi\)
\(282\) 0 0
\(283\) −23.4641 −1.39480 −0.697398 0.716684i \(-0.745659\pi\)
−0.697398 + 0.716684i \(0.745659\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.588457 −0.0347355
\(288\) 0 0
\(289\) −15.3923 −0.905430
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6.58846 0.384902 0.192451 0.981307i \(-0.438356\pi\)
0.192451 + 0.981307i \(0.438356\pi\)
\(294\) 0 0
\(295\) −4.26795 −0.248490
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.07180 0.293310
\(300\) 0 0
\(301\) 4.92820 0.284057
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.00000 −0.229039
\(306\) 0 0
\(307\) 12.1962 0.696071 0.348036 0.937481i \(-0.386849\pi\)
0.348036 + 0.937481i \(0.386849\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 28.5167 1.61703 0.808516 0.588475i \(-0.200271\pi\)
0.808516 + 0.588475i \(0.200271\pi\)
\(312\) 0 0
\(313\) 1.07180 0.0605815 0.0302908 0.999541i \(-0.490357\pi\)
0.0302908 + 0.999541i \(0.490357\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 21.1244 1.18646 0.593231 0.805032i \(-0.297852\pi\)
0.593231 + 0.805032i \(0.297852\pi\)
\(318\) 0 0
\(319\) −7.39230 −0.413890
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.12436 −0.173844
\(324\) 0 0
\(325\) −1.46410 −0.0812137
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3.46410 0.190982
\(330\) 0 0
\(331\) 8.60770 0.473122 0.236561 0.971617i \(-0.423980\pi\)
0.236561 + 0.971617i \(0.423980\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 14.3923 0.786336
\(336\) 0 0
\(337\) 14.2487 0.776177 0.388088 0.921622i \(-0.373136\pi\)
0.388088 + 0.921622i \(0.373136\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −13.7321 −0.743632
\(342\) 0 0
\(343\) 9.85641 0.532196
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 32.1962 1.72838 0.864190 0.503166i \(-0.167831\pi\)
0.864190 + 0.503166i \(0.167831\pi\)
\(348\) 0 0
\(349\) −25.0000 −1.33822 −0.669110 0.743164i \(-0.733324\pi\)
−0.669110 + 0.743164i \(0.733324\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −22.9808 −1.22314 −0.611571 0.791189i \(-0.709462\pi\)
−0.611571 + 0.791189i \(0.709462\pi\)
\(354\) 0 0
\(355\) −0.803848 −0.0426638
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 26.6603 1.40707 0.703537 0.710658i \(-0.251603\pi\)
0.703537 + 0.710658i \(0.251603\pi\)
\(360\) 0 0
\(361\) −12.9282 −0.680432
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 10.1962 0.533691
\(366\) 0 0
\(367\) 5.60770 0.292719 0.146360 0.989231i \(-0.453244\pi\)
0.146360 + 0.989231i \(0.453244\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −7.85641 −0.407884
\(372\) 0 0
\(373\) 24.0526 1.24539 0.622697 0.782463i \(-0.286037\pi\)
0.622697 + 0.782463i \(0.286037\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6.24871 −0.321825
\(378\) 0 0
\(379\) −11.4641 −0.588871 −0.294436 0.955671i \(-0.595132\pi\)
−0.294436 + 0.955671i \(0.595132\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −30.2487 −1.54564 −0.772818 0.634627i \(-0.781154\pi\)
−0.772818 + 0.634627i \(0.781154\pi\)
\(384\) 0 0
\(385\) 1.26795 0.0646207
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −20.5359 −1.04121 −0.520606 0.853797i \(-0.674294\pi\)
−0.520606 + 0.853797i \(0.674294\pi\)
\(390\) 0 0
\(391\) −4.39230 −0.222128
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6.39230 −0.321632
\(396\) 0 0
\(397\) 2.67949 0.134480 0.0672399 0.997737i \(-0.478581\pi\)
0.0672399 + 0.997737i \(0.478581\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −26.7846 −1.33756 −0.668780 0.743461i \(-0.733183\pi\)
−0.668780 + 0.743461i \(0.733183\pi\)
\(402\) 0 0
\(403\) −11.6077 −0.578220
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7.26795 −0.360259
\(408\) 0 0
\(409\) 9.85641 0.487368 0.243684 0.969855i \(-0.421644\pi\)
0.243684 + 0.969855i \(0.421644\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3.12436 0.153739
\(414\) 0 0
\(415\) 9.12436 0.447897
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 14.5359 0.710125 0.355063 0.934843i \(-0.384460\pi\)
0.355063 + 0.934843i \(0.384460\pi\)
\(420\) 0 0
\(421\) −27.7846 −1.35414 −0.677070 0.735919i \(-0.736750\pi\)
−0.677070 + 0.735919i \(0.736750\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.26795 0.0615046
\(426\) 0 0
\(427\) 2.92820 0.141706
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.41154 −0.116160 −0.0580800 0.998312i \(-0.518498\pi\)
−0.0580800 + 0.998312i \(0.518498\pi\)
\(432\) 0 0
\(433\) 4.53590 0.217981 0.108991 0.994043i \(-0.465238\pi\)
0.108991 + 0.994043i \(0.465238\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.53590 0.408327
\(438\) 0 0
\(439\) −27.3923 −1.30736 −0.653682 0.756770i \(-0.726776\pi\)
−0.653682 + 0.756770i \(0.726776\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 40.7321 1.93524 0.967619 0.252415i \(-0.0812248\pi\)
0.967619 + 0.252415i \(0.0812248\pi\)
\(444\) 0 0
\(445\) 5.19615 0.246321
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.124356 0.00586871 0.00293435 0.999996i \(-0.499066\pi\)
0.00293435 + 0.999996i \(0.499066\pi\)
\(450\) 0 0
\(451\) −1.39230 −0.0655611
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.07180 0.0502466
\(456\) 0 0
\(457\) 11.8038 0.552161 0.276080 0.961135i \(-0.410964\pi\)
0.276080 + 0.961135i \(0.410964\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 21.5885 1.00547 0.502737 0.864439i \(-0.332326\pi\)
0.502737 + 0.864439i \(0.332326\pi\)
\(462\) 0 0
\(463\) −18.3923 −0.854763 −0.427381 0.904071i \(-0.640564\pi\)
−0.427381 + 0.904071i \(0.640564\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15.8038 0.731315 0.365657 0.930750i \(-0.380844\pi\)
0.365657 + 0.930750i \(0.380844\pi\)
\(468\) 0 0
\(469\) −10.5359 −0.486503
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 11.6603 0.536139
\(474\) 0 0
\(475\) −2.46410 −0.113061
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −20.6603 −0.943991 −0.471996 0.881601i \(-0.656466\pi\)
−0.471996 + 0.881601i \(0.656466\pi\)
\(480\) 0 0
\(481\) −6.14359 −0.280124
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.73205 −0.124056
\(486\) 0 0
\(487\) 37.4641 1.69766 0.848830 0.528666i \(-0.177307\pi\)
0.848830 + 0.528666i \(0.177307\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.73205 −0.348943 −0.174471 0.984662i \(-0.555822\pi\)
−0.174471 + 0.984662i \(0.555822\pi\)
\(492\) 0 0
\(493\) 5.41154 0.243724
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.588457 0.0263959
\(498\) 0 0
\(499\) −6.60770 −0.295801 −0.147901 0.989002i \(-0.547252\pi\)
−0.147901 + 0.989002i \(0.547252\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −0.679492 −0.0302970 −0.0151485 0.999885i \(-0.504822\pi\)
−0.0151485 + 0.999885i \(0.504822\pi\)
\(504\) 0 0
\(505\) 18.1244 0.806523
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −14.7846 −0.655316 −0.327658 0.944796i \(-0.606259\pi\)
−0.327658 + 0.944796i \(0.606259\pi\)
\(510\) 0 0
\(511\) −7.46410 −0.330192
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.39230 0.105418
\(516\) 0 0
\(517\) 8.19615 0.360466
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −10.3923 −0.455295 −0.227648 0.973744i \(-0.573103\pi\)
−0.227648 + 0.973744i \(0.573103\pi\)
\(522\) 0 0
\(523\) −24.3923 −1.06660 −0.533301 0.845926i \(-0.679048\pi\)
−0.533301 + 0.845926i \(0.679048\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.0526 0.437896
\(528\) 0 0
\(529\) −11.0000 −0.478261
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.17691 −0.0509778
\(534\) 0 0
\(535\) −3.46410 −0.149766
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 11.1962 0.482252
\(540\) 0 0
\(541\) −4.46410 −0.191927 −0.0959634 0.995385i \(-0.530593\pi\)
−0.0959634 + 0.995385i \(0.530593\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5.92820 0.253936
\(546\) 0 0
\(547\) 36.7846 1.57280 0.786398 0.617720i \(-0.211943\pi\)
0.786398 + 0.617720i \(0.211943\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −10.5167 −0.448025
\(552\) 0 0
\(553\) 4.67949 0.198992
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −16.3923 −0.694564 −0.347282 0.937761i \(-0.612895\pi\)
−0.347282 + 0.937761i \(0.612895\pi\)
\(558\) 0 0
\(559\) 9.85641 0.416882
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 19.2679 0.812047 0.406024 0.913863i \(-0.366915\pi\)
0.406024 + 0.913863i \(0.366915\pi\)
\(564\) 0 0
\(565\) 17.6603 0.742972
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.94744 0.207408 0.103704 0.994608i \(-0.466931\pi\)
0.103704 + 0.994608i \(0.466931\pi\)
\(570\) 0 0
\(571\) 26.8564 1.12391 0.561953 0.827169i \(-0.310050\pi\)
0.561953 + 0.827169i \(0.310050\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3.46410 −0.144463
\(576\) 0 0
\(577\) 22.1962 0.924038 0.462019 0.886870i \(-0.347125\pi\)
0.462019 + 0.886870i \(0.347125\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −6.67949 −0.277112
\(582\) 0 0
\(583\) −18.5885 −0.769855
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 14.1962 0.585938 0.292969 0.956122i \(-0.405357\pi\)
0.292969 + 0.956122i \(0.405357\pi\)
\(588\) 0 0
\(589\) −19.5359 −0.804963
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 36.9282 1.51646 0.758230 0.651987i \(-0.226065\pi\)
0.758230 + 0.651987i \(0.226065\pi\)
\(594\) 0 0
\(595\) −0.928203 −0.0380526
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −45.5885 −1.86269 −0.931347 0.364133i \(-0.881365\pi\)
−0.931347 + 0.364133i \(0.881365\pi\)
\(600\) 0 0
\(601\) 10.3205 0.420982 0.210491 0.977596i \(-0.432494\pi\)
0.210491 + 0.977596i \(0.432494\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −8.00000 −0.325246
\(606\) 0 0
\(607\) 28.5885 1.16037 0.580185 0.814485i \(-0.302980\pi\)
0.580185 + 0.814485i \(0.302980\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.92820 0.280285
\(612\) 0 0
\(613\) 3.60770 0.145713 0.0728567 0.997342i \(-0.476788\pi\)
0.0728567 + 0.997342i \(0.476788\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000 0.483102 0.241551 0.970388i \(-0.422344\pi\)
0.241551 + 0.970388i \(0.422344\pi\)
\(618\) 0 0
\(619\) 10.0000 0.401934 0.200967 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.80385 −0.152398
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.32051 0.212143
\(630\) 0 0
\(631\) 13.9282 0.554473 0.277237 0.960802i \(-0.410581\pi\)
0.277237 + 0.960802i \(0.410581\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6.19615 0.245887
\(636\) 0 0
\(637\) 9.46410 0.374981
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 23.1962 0.916193 0.458096 0.888902i \(-0.348531\pi\)
0.458096 + 0.888902i \(0.348531\pi\)
\(642\) 0 0
\(643\) 16.5885 0.654185 0.327092 0.944992i \(-0.393931\pi\)
0.327092 + 0.944992i \(0.393931\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −48.2487 −1.89685 −0.948426 0.316998i \(-0.897325\pi\)
−0.948426 + 0.316998i \(0.897325\pi\)
\(648\) 0 0
\(649\) 7.39230 0.290173
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.46410 0.370359 0.185179 0.982705i \(-0.440713\pi\)
0.185179 + 0.982705i \(0.440713\pi\)
\(654\) 0 0
\(655\) 13.7321 0.536556
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −9.46410 −0.368669 −0.184335 0.982864i \(-0.559013\pi\)
−0.184335 + 0.982864i \(0.559013\pi\)
\(660\) 0 0
\(661\) −5.39230 −0.209736 −0.104868 0.994486i \(-0.533442\pi\)
−0.104868 + 0.994486i \(0.533442\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.80385 0.0699502
\(666\) 0 0
\(667\) −14.7846 −0.572462
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6.92820 0.267460
\(672\) 0 0
\(673\) −17.6077 −0.678727 −0.339363 0.940655i \(-0.610212\pi\)
−0.339363 + 0.940655i \(0.610212\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 28.6410 1.10076 0.550382 0.834913i \(-0.314482\pi\)
0.550382 + 0.834913i \(0.314482\pi\)
\(678\) 0 0
\(679\) 2.00000 0.0767530
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 14.5359 0.556201 0.278100 0.960552i \(-0.410295\pi\)
0.278100 + 0.960552i \(0.410295\pi\)
\(684\) 0 0
\(685\) 16.3923 0.626318
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −15.7128 −0.598610
\(690\) 0 0
\(691\) 10.0000 0.380418 0.190209 0.981744i \(-0.439083\pi\)
0.190209 + 0.981744i \(0.439083\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5.39230 0.204542
\(696\) 0 0
\(697\) 1.01924 0.0386064
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 42.1244 1.59101 0.795507 0.605944i \(-0.207204\pi\)
0.795507 + 0.605944i \(0.207204\pi\)
\(702\) 0 0
\(703\) −10.3397 −0.389971
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −13.2679 −0.498993
\(708\) 0 0
\(709\) 17.4641 0.655878 0.327939 0.944699i \(-0.393646\pi\)
0.327939 + 0.944699i \(0.393646\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −27.4641 −1.02854
\(714\) 0 0
\(715\) 2.53590 0.0948372
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −6.80385 −0.253741 −0.126870 0.991919i \(-0.540493\pi\)
−0.126870 + 0.991919i \(0.540493\pi\)
\(720\) 0 0
\(721\) −1.75129 −0.0652214
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 4.26795 0.158508
\(726\) 0 0
\(727\) −33.1769 −1.23046 −0.615232 0.788346i \(-0.710938\pi\)
−0.615232 + 0.788346i \(0.710938\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −8.53590 −0.315712
\(732\) 0 0
\(733\) −39.5692 −1.46152 −0.730761 0.682633i \(-0.760835\pi\)
−0.730761 + 0.682633i \(0.760835\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −24.9282 −0.918242
\(738\) 0 0
\(739\) −36.1769 −1.33079 −0.665395 0.746492i \(-0.731737\pi\)
−0.665395 + 0.746492i \(0.731737\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −36.5885 −1.34230 −0.671150 0.741321i \(-0.734199\pi\)
−0.671150 + 0.741321i \(0.734199\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.53590 0.0926597
\(750\) 0 0
\(751\) 0.784610 0.0286308 0.0143154 0.999898i \(-0.495443\pi\)
0.0143154 + 0.999898i \(0.495443\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −3.39230 −0.123459
\(756\) 0 0
\(757\) 0.392305 0.0142586 0.00712928 0.999975i \(-0.497731\pi\)
0.00712928 + 0.999975i \(0.497731\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 5.87564 0.212992 0.106496 0.994313i \(-0.466037\pi\)
0.106496 + 0.994313i \(0.466037\pi\)
\(762\) 0 0
\(763\) −4.33975 −0.157109
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6.24871 0.225628
\(768\) 0 0
\(769\) −13.2487 −0.477761 −0.238880 0.971049i \(-0.576780\pi\)
−0.238880 + 0.971049i \(0.576780\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.339746 −0.0122198 −0.00610991 0.999981i \(-0.501945\pi\)
−0.00610991 + 0.999981i \(0.501945\pi\)
\(774\) 0 0
\(775\) 7.92820 0.284789
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.98076 −0.0709682
\(780\) 0 0
\(781\) 1.39230 0.0498206
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 6.73205 0.240277
\(786\) 0 0
\(787\) 25.8038 0.919808 0.459904 0.887969i \(-0.347884\pi\)
0.459904 + 0.887969i \(0.347884\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −12.9282 −0.459674
\(792\) 0 0
\(793\) 5.85641 0.207967
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11.3205 0.400993 0.200496 0.979694i \(-0.435744\pi\)
0.200496 + 0.979694i \(0.435744\pi\)
\(798\) 0 0
\(799\) −6.00000 −0.212265
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −17.6603 −0.623217
\(804\) 0 0
\(805\) 2.53590 0.0893787
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 39.5885 1.39186 0.695928 0.718112i \(-0.254993\pi\)
0.695928 + 0.718112i \(0.254993\pi\)
\(810\) 0 0
\(811\) −23.2487 −0.816373 −0.408186 0.912899i \(-0.633839\pi\)
−0.408186 + 0.912899i \(0.633839\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −15.2679 −0.534813
\(816\) 0 0
\(817\) 16.5885 0.580357
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −20.6603 −0.721048 −0.360524 0.932750i \(-0.617402\pi\)
−0.360524 + 0.932750i \(0.617402\pi\)
\(822\) 0 0
\(823\) 3.07180 0.107076 0.0535381 0.998566i \(-0.482950\pi\)
0.0535381 + 0.998566i \(0.482950\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −38.5359 −1.34002 −0.670012 0.742350i \(-0.733711\pi\)
−0.670012 + 0.742350i \(0.733711\pi\)
\(828\) 0 0
\(829\) −10.2154 −0.354795 −0.177398 0.984139i \(-0.556768\pi\)
−0.177398 + 0.984139i \(0.556768\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −8.19615 −0.283980
\(834\) 0 0
\(835\) 3.12436 0.108123
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −39.5885 −1.36675 −0.683373 0.730070i \(-0.739488\pi\)
−0.683373 + 0.730070i \(0.739488\pi\)
\(840\) 0 0
\(841\) −10.7846 −0.371883
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −10.8564 −0.373472
\(846\) 0 0
\(847\) 5.85641 0.201229
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −14.5359 −0.498284
\(852\) 0 0
\(853\) 10.1962 0.349110 0.174555 0.984647i \(-0.444151\pi\)
0.174555 + 0.984647i \(0.444151\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 42.9282 1.46640 0.733200 0.680013i \(-0.238026\pi\)
0.733200 + 0.680013i \(0.238026\pi\)
\(858\) 0 0
\(859\) 33.7846 1.15272 0.576358 0.817197i \(-0.304473\pi\)
0.576358 + 0.817197i \(0.304473\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −4.48334 −0.152615 −0.0763073 0.997084i \(-0.524313\pi\)
−0.0763073 + 0.997084i \(0.524313\pi\)
\(864\) 0 0
\(865\) −24.2487 −0.824481
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 11.0718 0.375585
\(870\) 0 0
\(871\) −21.0718 −0.713991
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −0.732051 −0.0247478
\(876\) 0 0
\(877\) −34.2487 −1.15650 −0.578248 0.815861i \(-0.696264\pi\)
−0.578248 + 0.815861i \(0.696264\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −17.1962 −0.579353 −0.289677 0.957125i \(-0.593548\pi\)
−0.289677 + 0.957125i \(0.593548\pi\)
\(882\) 0 0
\(883\) −32.8372 −1.10506 −0.552529 0.833493i \(-0.686337\pi\)
−0.552529 + 0.833493i \(0.686337\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 16.7321 0.561807 0.280904 0.959736i \(-0.409366\pi\)
0.280904 + 0.959736i \(0.409366\pi\)
\(888\) 0 0
\(889\) −4.53590 −0.152129
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 11.6603 0.390196
\(894\) 0 0
\(895\) 12.1244 0.405273
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 33.8372 1.12853
\(900\) 0 0
\(901\) 13.6077 0.453338
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −9.53590 −0.316984
\(906\) 0 0
\(907\) 42.7846 1.42064 0.710320 0.703879i \(-0.248550\pi\)
0.710320 + 0.703879i \(0.248550\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −17.1962 −0.569734 −0.284867 0.958567i \(-0.591949\pi\)
−0.284867 + 0.958567i \(0.591949\pi\)
\(912\) 0 0
\(913\) −15.8038 −0.523031
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −10.0526 −0.331965
\(918\) 0 0
\(919\) −30.6077 −1.00965 −0.504827 0.863220i \(-0.668444\pi\)
−0.504827 + 0.863220i \(0.668444\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1.17691 0.0387386
\(924\) 0 0
\(925\) 4.19615 0.137969
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −46.5167 −1.52616 −0.763081 0.646303i \(-0.776314\pi\)
−0.763081 + 0.646303i \(0.776314\pi\)
\(930\) 0 0
\(931\) 15.9282 0.522026
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2.19615 −0.0718219
\(936\) 0 0
\(937\) 32.9282 1.07572 0.537859 0.843035i \(-0.319233\pi\)
0.537859 + 0.843035i \(0.319233\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 15.4641 0.504115 0.252058 0.967712i \(-0.418893\pi\)
0.252058 + 0.967712i \(0.418893\pi\)
\(942\) 0 0
\(943\) −2.78461 −0.0906794
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 16.6410 0.540760 0.270380 0.962754i \(-0.412851\pi\)
0.270380 + 0.962754i \(0.412851\pi\)
\(948\) 0 0
\(949\) −14.9282 −0.484590
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 9.46410 0.306572 0.153286 0.988182i \(-0.451014\pi\)
0.153286 + 0.988182i \(0.451014\pi\)
\(954\) 0 0
\(955\) −19.0526 −0.616526
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −12.0000 −0.387500
\(960\) 0 0
\(961\) 31.8564 1.02763
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 20.5885 0.662766
\(966\) 0 0
\(967\) −38.5885 −1.24092 −0.620461 0.784238i \(-0.713054\pi\)
−0.620461 + 0.784238i \(0.713054\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 25.7321 0.825781 0.412890 0.910781i \(-0.364519\pi\)
0.412890 + 0.910781i \(0.364519\pi\)
\(972\) 0 0
\(973\) −3.94744 −0.126549
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 16.3923 0.524436 0.262218 0.965009i \(-0.415546\pi\)
0.262218 + 0.965009i \(0.415546\pi\)
\(978\) 0 0
\(979\) −9.00000 −0.287641
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −49.2679 −1.57140 −0.785702 0.618605i \(-0.787698\pi\)
−0.785702 + 0.618605i \(0.787698\pi\)
\(984\) 0 0
\(985\) −13.8564 −0.441502
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 23.3205 0.741549
\(990\) 0 0
\(991\) −14.2154 −0.451567 −0.225783 0.974178i \(-0.572494\pi\)
−0.225783 + 0.974178i \(0.572494\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 11.8564 0.375873
\(996\) 0 0
\(997\) 41.8038 1.32394 0.661971 0.749530i \(-0.269720\pi\)
0.661971 + 0.749530i \(0.269720\pi\)
\(998\) 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 6480.2.a.bp.1.1 2
3.2 odd 2 6480.2.a.bh.1.1 2
4.3 odd 2 1620.2.a.h.1.2 yes 2
12.11 even 2 1620.2.a.g.1.2 2
20.3 even 4 8100.2.d.l.649.2 4
20.7 even 4 8100.2.d.l.649.3 4
20.19 odd 2 8100.2.a.s.1.1 2
36.7 odd 6 1620.2.i.m.1081.1 4
36.11 even 6 1620.2.i.n.1081.1 4
36.23 even 6 1620.2.i.n.541.1 4
36.31 odd 6 1620.2.i.m.541.1 4
60.23 odd 4 8100.2.d.m.649.2 4
60.47 odd 4 8100.2.d.m.649.3 4
60.59 even 2 8100.2.a.t.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1620.2.a.g.1.2 2 12.11 even 2
1620.2.a.h.1.2 yes 2 4.3 odd 2
1620.2.i.m.541.1 4 36.31 odd 6
1620.2.i.m.1081.1 4 36.7 odd 6
1620.2.i.n.541.1 4 36.23 even 6
1620.2.i.n.1081.1 4 36.11 even 6
6480.2.a.bh.1.1 2 3.2 odd 2
6480.2.a.bp.1.1 2 1.1 even 1 trivial
8100.2.a.s.1.1 2 20.19 odd 2
8100.2.a.t.1.1 2 60.59 even 2
8100.2.d.l.649.2 4 20.3 even 4
8100.2.d.l.649.3 4 20.7 even 4
8100.2.d.m.649.2 4 60.23 odd 4
8100.2.d.m.649.3 4 60.47 odd 4