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Properties

Label 612.4.a.d.1.1
Level $612$
Weight $4$
Character 612.1
Self dual yes
Analytic conductor $36.109$
Analytic rank $0$
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] = [612,4,Mod(1,612)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(612, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("612.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 612 = 2^{2} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 612.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: \(36.1091689235\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 612.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+17.0000 q^{5} +6.00000 q^{7} -17.0000 q^{11} +43.0000 q^{13} +17.0000 q^{17} +67.0000 q^{19} +51.0000 q^{23} +164.000 q^{25} +34.0000 q^{29} -124.000 q^{31} +102.000 q^{35} +106.000 q^{37} +119.000 q^{41} -387.000 q^{43} +204.000 q^{47} -307.000 q^{49} +204.000 q^{53} -289.000 q^{55} +306.000 q^{59} +242.000 q^{61} +731.000 q^{65} -732.000 q^{67} +256.000 q^{73} -102.000 q^{77} +466.000 q^{79} +476.000 q^{83} +289.000 q^{85} +1326.00 q^{89} +258.000 q^{91} +1139.00 q^{95} +712.000 q^{97} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 17.0000 1.52053 0.760263 − 0.649615i \(-0.225070\pi\)
0.760263 + 0.649615i \(0.225070\pi\)
\(6\) 0 0
\(7\) 6.00000 0.323970 0.161985 − 0.986793i \(-0.448210\pi\)
0.161985 + 0.986793i \(0.448210\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −17.0000 −0.465972 −0.232986 − 0.972480i \(-0.574850\pi\)
−0.232986 + 0.972480i \(0.574850\pi\)
\(12\) 0 0
\(13\) 43.0000 0.917389 0.458694 − 0.888594i \(-0.348317\pi\)
0.458694 + 0.888594i \(0.348317\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 17.0000 0.242536
\(18\) 0 0
\(19\) 67.0000 0.808992 0.404496 − 0.914540i \(-0.367447\pi\)
0.404496 + 0.914540i \(0.367447\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 51.0000 0.462358 0.231179 − 0.972911i \(-0.425742\pi\)
0.231179 + 0.972911i \(0.425742\pi\)
\(24\) 0 0
\(25\) 164.000 1.31200
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 34.0000 0.217712 0.108856 − 0.994058i \(-0.465281\pi\)
0.108856 + 0.994058i \(0.465281\pi\)
\(30\) 0 0
\(31\) −124.000 −0.718421 −0.359211 − 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 102.000 0.492604
\(36\) 0 0
\(37\) 106.000 0.470981 0.235490 − 0.971877i \(-0.424330\pi\)
0.235490 + 0.971877i \(0.424330\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 119.000 0.453285 0.226642 − 0.973978i \(-0.427225\pi\)
0.226642 + 0.973978i \(0.427225\pi\)
\(42\) 0 0
\(43\) −387.000 −1.37249 −0.686244 − 0.727372i \(-0.740742\pi\)
−0.686244 + 0.727372i \(0.740742\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 204.000 0.633116 0.316558 − 0.948573i \(-0.397473\pi\)
0.316558 + 0.948573i \(0.397473\pi\)
\(48\) 0 0
\(49\) −307.000 −0.895044
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 204.000 0.528709 0.264354 − 0.964426i \(-0.414841\pi\)
0.264354 + 0.964426i \(0.414841\pi\)
\(54\) 0 0
\(55\) −289.000 −0.708523
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 306.000 0.675217 0.337609 − 0.941287i \(-0.390382\pi\)
0.337609 + 0.941287i \(0.390382\pi\)
\(60\) 0 0
\(61\) 242.000 0.507950 0.253975 − 0.967211i \(-0.418262\pi\)
0.253975 + 0.967211i \(0.418262\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 731.000 1.39491
\(66\) 0 0
\(67\) −732.000 −1.33475 −0.667373 − 0.744723i \(-0.732581\pi\)
−0.667373 + 0.744723i \(0.732581\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 256.000 0.410446 0.205223 − 0.978715i \(-0.434208\pi\)
0.205223 + 0.978715i \(0.434208\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −102.000 −0.150961
\(78\) 0 0
\(79\) 466.000 0.663659 0.331830 − 0.943339i \(-0.392334\pi\)
0.331830 + 0.943339i \(0.392334\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 476.000 0.629491 0.314746 − 0.949176i \(-0.398081\pi\)
0.314746 + 0.949176i \(0.398081\pi\)
\(84\) 0 0
\(85\) 289.000 0.368782
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1326.00 1.57928 0.789639 − 0.613572i \(-0.210268\pi\)
0.789639 + 0.613572i \(0.210268\pi\)
\(90\) 0 0
\(91\) 258.000 0.297206
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1139.00 1.23009
\(96\) 0 0
\(97\) 712.000 0.745285 0.372643 − 0.927975i \(-0.378452\pi\)
0.372643 + 0.927975i \(0.378452\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 748.000 0.736919 0.368459 − 0.929644i \(-0.379885\pi\)
0.368459 + 0.929644i \(0.379885\pi\)
\(102\) 0 0
\(103\) −167.000 −0.159757 −0.0798786 − 0.996805i \(-0.525453\pi\)
−0.0798786 + 0.996805i \(0.525453\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 799.000 0.721890 0.360945 − 0.932587i \(-0.382454\pi\)
0.360945 + 0.932587i \(0.382454\pi\)
\(108\) 0 0
\(109\) 1136.00 0.998248 0.499124 − 0.866530i \(-0.333655\pi\)
0.499124 + 0.866530i \(0.333655\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −935.000 −0.778384 −0.389192 − 0.921157i \(-0.627246\pi\)
−0.389192 + 0.921157i \(0.627246\pi\)
\(114\) 0 0
\(115\) 867.000 0.703028
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 102.000 0.0785742
\(120\) 0 0
\(121\) −1042.00 −0.782870
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 663.000 0.474404
\(126\) 0 0
\(127\) 279.000 0.194939 0.0974695 − 0.995239i \(-0.468925\pi\)
0.0974695 + 0.995239i \(0.468925\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −663.000 −0.442188 −0.221094 − 0.975253i \(-0.570963\pi\)
−0.221094 + 0.975253i \(0.570963\pi\)
\(132\) 0 0
\(133\) 402.000 0.262089
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 782.000 0.487670 0.243835 − 0.969817i \(-0.421594\pi\)
0.243835 + 0.969817i \(0.421594\pi\)
\(138\) 0 0
\(139\) −1510.00 −0.921414 −0.460707 − 0.887552i \(-0.652404\pi\)
−0.460707 + 0.887552i \(0.652404\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −731.000 −0.427478
\(144\) 0 0
\(145\) 578.000 0.331036
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3298.00 1.81331 0.906653 − 0.421876i \(-0.138628\pi\)
0.906653 + 0.421876i \(0.138628\pi\)
\(150\) 0 0
\(151\) 1368.00 0.737260 0.368630 − 0.929576i \(-0.379827\pi\)
0.368630 + 0.929576i \(0.379827\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2108.00 −1.09238
\(156\) 0 0
\(157\) −1661.00 −0.844345 −0.422173 − 0.906515i \(-0.638732\pi\)
−0.422173 + 0.906515i \(0.638732\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 306.000 0.149790
\(162\) 0 0
\(163\) −2504.00 −1.20324 −0.601621 − 0.798782i \(-0.705478\pi\)
−0.601621 + 0.798782i \(0.705478\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1547.00 0.716829 0.358415 − 0.933563i \(-0.383317\pi\)
0.358415 + 0.933563i \(0.383317\pi\)
\(168\) 0 0
\(169\) −348.000 −0.158398
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1479.00 −0.649979 −0.324989 − 0.945718i \(-0.605361\pi\)
−0.324989 + 0.945718i \(0.605361\pi\)
\(174\) 0 0
\(175\) 984.000 0.425048
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −4692.00 −1.95920 −0.979599 − 0.200961i \(-0.935594\pi\)
−0.979599 + 0.200961i \(0.935594\pi\)
\(180\) 0 0
\(181\) −2638.00 −1.08332 −0.541660 − 0.840598i \(-0.682204\pi\)
−0.541660 + 0.840598i \(0.682204\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1802.00 0.716139
\(186\) 0 0
\(187\) −289.000 −0.113015
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1462.00 0.553857 0.276928 − 0.960891i \(-0.410684\pi\)
0.276928 + 0.960891i \(0.410684\pi\)
\(192\) 0 0
\(193\) −4068.00 −1.51721 −0.758604 − 0.651552i \(-0.774118\pi\)
−0.758604 + 0.651552i \(0.774118\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4165.00 1.50631 0.753157 − 0.657841i \(-0.228530\pi\)
0.753157 + 0.657841i \(0.228530\pi\)
\(198\) 0 0
\(199\) 2112.00 0.752340 0.376170 − 0.926551i \(-0.377241\pi\)
0.376170 + 0.926551i \(0.377241\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 204.000 0.0705320
\(204\) 0 0
\(205\) 2023.00 0.689231
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1139.00 −0.376968
\(210\) 0 0
\(211\) −2764.00 −0.901809 −0.450904 − 0.892572i \(-0.648898\pi\)
−0.450904 + 0.892572i \(0.648898\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6579.00 −2.08690
\(216\) 0 0
\(217\) −744.000 −0.232747
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 731.000 0.222499
\(222\) 0 0
\(223\) 3667.00 1.10117 0.550584 − 0.834780i \(-0.314405\pi\)
0.550584 + 0.834780i \(0.314405\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5083.00 −1.48621 −0.743107 − 0.669173i \(-0.766649\pi\)
−0.743107 + 0.669173i \(0.766649\pi\)
\(228\) 0 0
\(229\) −74.0000 −0.0213540 −0.0106770 − 0.999943i \(-0.503399\pi\)
−0.0106770 + 0.999943i \(0.503399\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2057.00 −0.578363 −0.289181 − 0.957274i \(-0.593383\pi\)
−0.289181 + 0.957274i \(0.593383\pi\)
\(234\) 0 0
\(235\) 3468.00 0.962670
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6120.00 −1.65636 −0.828180 − 0.560463i \(-0.810623\pi\)
−0.828180 + 0.560463i \(0.810623\pi\)
\(240\) 0 0
\(241\) 1538.00 0.411084 0.205542 − 0.978648i \(-0.434104\pi\)
0.205542 + 0.978648i \(0.434104\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −5219.00 −1.36094
\(246\) 0 0
\(247\) 2881.00 0.742160
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 5270.00 1.32526 0.662628 − 0.748948i \(-0.269441\pi\)
0.662628 + 0.748948i \(0.269441\pi\)
\(252\) 0 0
\(253\) −867.000 −0.215446
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5066.00 −1.22960 −0.614802 − 0.788681i \(-0.710764\pi\)
−0.614802 + 0.788681i \(0.710764\pi\)
\(258\) 0 0
\(259\) 636.000 0.152583
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1462.00 −0.342779 −0.171389 − 0.985203i \(-0.554826\pi\)
−0.171389 + 0.985203i \(0.554826\pi\)
\(264\) 0 0
\(265\) 3468.00 0.803915
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3519.00 0.797610 0.398805 − 0.917036i \(-0.369425\pi\)
0.398805 + 0.917036i \(0.369425\pi\)
\(270\) 0 0
\(271\) 4159.00 0.932256 0.466128 − 0.884717i \(-0.345649\pi\)
0.466128 + 0.884717i \(0.345649\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2788.00 −0.611355
\(276\) 0 0
\(277\) −2964.00 −0.642922 −0.321461 − 0.946923i \(-0.604174\pi\)
−0.321461 + 0.946923i \(0.604174\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4386.00 −0.931127 −0.465564 − 0.885014i \(-0.654148\pi\)
−0.465564 + 0.885014i \(0.654148\pi\)
\(282\) 0 0
\(283\) 1338.00 0.281045 0.140523 − 0.990077i \(-0.455122\pi\)
0.140523 + 0.990077i \(0.455122\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 714.000 0.146850
\(288\) 0 0
\(289\) 289.000 0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2006.00 0.399972 0.199986 − 0.979799i \(-0.435910\pi\)
0.199986 + 0.979799i \(0.435910\pi\)
\(294\) 0 0
\(295\) 5202.00 1.02669
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2193.00 0.424162
\(300\) 0 0
\(301\) −2322.00 −0.444644
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4114.00 0.772351
\(306\) 0 0
\(307\) −9060.00 −1.68430 −0.842152 − 0.539240i \(-0.818712\pi\)
−0.842152 + 0.539240i \(0.818712\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −6936.00 −1.26464 −0.632322 − 0.774705i \(-0.717898\pi\)
−0.632322 + 0.774705i \(0.717898\pi\)
\(312\) 0 0
\(313\) 16.0000 0.00288937 0.00144469 − 0.999999i \(-0.499540\pi\)
0.00144469 + 0.999999i \(0.499540\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10098.0 −1.78915 −0.894574 − 0.446919i \(-0.852521\pi\)
−0.894574 + 0.446919i \(0.852521\pi\)
\(318\) 0 0
\(319\) −578.000 −0.101448
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1139.00 0.196209
\(324\) 0 0
\(325\) 7052.00 1.20361
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1224.00 0.205110
\(330\) 0 0
\(331\) −7853.00 −1.30405 −0.652024 − 0.758198i \(-0.726080\pi\)
−0.652024 + 0.758198i \(0.726080\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −12444.0 −2.02952
\(336\) 0 0
\(337\) −1802.00 −0.291280 −0.145640 − 0.989338i \(-0.546524\pi\)
−0.145640 + 0.989338i \(0.546524\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2108.00 0.334764
\(342\) 0 0
\(343\) −3900.00 −0.613936
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −7684.00 −1.18876 −0.594379 − 0.804185i \(-0.702602\pi\)
−0.594379 + 0.804185i \(0.702602\pi\)
\(348\) 0 0
\(349\) −8935.00 −1.37043 −0.685214 − 0.728342i \(-0.740291\pi\)
−0.685214 + 0.728342i \(0.740291\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 11730.0 1.76863 0.884313 − 0.466895i \(-0.154627\pi\)
0.884313 + 0.466895i \(0.154627\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8670.00 −1.27461 −0.637305 − 0.770612i \(-0.719951\pi\)
−0.637305 + 0.770612i \(0.719951\pi\)
\(360\) 0 0
\(361\) −2370.00 −0.345531
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4352.00 0.624093
\(366\) 0 0
\(367\) 198.000 0.0281622 0.0140811 − 0.999901i \(-0.495518\pi\)
0.0140811 + 0.999901i \(0.495518\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1224.00 0.171285
\(372\) 0 0
\(373\) −378.000 −0.0524721 −0.0262361 − 0.999656i \(-0.508352\pi\)
−0.0262361 + 0.999656i \(0.508352\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1462.00 0.199726
\(378\) 0 0
\(379\) −9718.00 −1.31710 −0.658549 − 0.752538i \(-0.728829\pi\)
−0.658549 + 0.752538i \(0.728829\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4964.00 −0.662268 −0.331134 − 0.943584i \(-0.607431\pi\)
−0.331134 + 0.943584i \(0.607431\pi\)
\(384\) 0 0
\(385\) −1734.00 −0.229540
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6698.00 0.873013 0.436507 − 0.899701i \(-0.356216\pi\)
0.436507 + 0.899701i \(0.356216\pi\)
\(390\) 0 0
\(391\) 867.000 0.112138
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7922.00 1.00911
\(396\) 0 0
\(397\) 10540.0 1.33246 0.666231 − 0.745745i \(-0.267906\pi\)
0.666231 + 0.745745i \(0.267906\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7463.00 0.929388 0.464694 − 0.885471i \(-0.346164\pi\)
0.464694 + 0.885471i \(0.346164\pi\)
\(402\) 0 0
\(403\) −5332.00 −0.659072
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1802.00 −0.219464
\(408\) 0 0
\(409\) 8045.00 0.972615 0.486308 − 0.873788i \(-0.338343\pi\)
0.486308 + 0.873788i \(0.338343\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1836.00 0.218750
\(414\) 0 0
\(415\) 8092.00 0.957158
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 476.000 0.0554991 0.0277495 − 0.999615i \(-0.491166\pi\)
0.0277495 + 0.999615i \(0.491166\pi\)
\(420\) 0 0
\(421\) −5981.00 −0.692390 −0.346195 − 0.938163i \(-0.612526\pi\)
−0.346195 + 0.938163i \(0.612526\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2788.00 0.318207
\(426\) 0 0
\(427\) 1452.00 0.164560
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4216.00 −0.471178 −0.235589 − 0.971853i \(-0.575702\pi\)
−0.235589 + 0.971853i \(0.575702\pi\)
\(432\) 0 0
\(433\) 1495.00 0.165924 0.0829620 − 0.996553i \(-0.473562\pi\)
0.0829620 + 0.996553i \(0.473562\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3417.00 0.374044
\(438\) 0 0
\(439\) 2668.00 0.290061 0.145030 − 0.989427i \(-0.453672\pi\)
0.145030 + 0.989427i \(0.453672\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12308.0 −1.32002 −0.660012 − 0.751255i \(-0.729449\pi\)
−0.660012 + 0.751255i \(0.729449\pi\)
\(444\) 0 0
\(445\) 22542.0 2.40133
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −782.000 −0.0821935 −0.0410967 − 0.999155i \(-0.513085\pi\)
−0.0410967 + 0.999155i \(0.513085\pi\)
\(450\) 0 0
\(451\) −2023.00 −0.211218
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 4386.00 0.451910
\(456\) 0 0
\(457\) 2281.00 0.233481 0.116740 − 0.993162i \(-0.462755\pi\)
0.116740 + 0.993162i \(0.462755\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −918.000 −0.0927452 −0.0463726 − 0.998924i \(-0.514766\pi\)
−0.0463726 + 0.998924i \(0.514766\pi\)
\(462\) 0 0
\(463\) −5224.00 −0.524363 −0.262181 − 0.965019i \(-0.584442\pi\)
−0.262181 + 0.965019i \(0.584442\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15402.0 1.52617 0.763083 − 0.646300i \(-0.223685\pi\)
0.763083 + 0.646300i \(0.223685\pi\)
\(468\) 0 0
\(469\) −4392.00 −0.432417
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 6579.00 0.639541
\(474\) 0 0
\(475\) 10988.0 1.06140
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 663.000 0.0632427 0.0316213 − 0.999500i \(-0.489933\pi\)
0.0316213 + 0.999500i \(0.489933\pi\)
\(480\) 0 0
\(481\) 4558.00 0.432073
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12104.0 1.13323
\(486\) 0 0
\(487\) −15598.0 −1.45136 −0.725681 − 0.688032i \(-0.758475\pi\)
−0.725681 + 0.688032i \(0.758475\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1836.00 0.168753 0.0843763 − 0.996434i \(-0.473110\pi\)
0.0843763 + 0.996434i \(0.473110\pi\)
\(492\) 0 0
\(493\) 578.000 0.0528029
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −80.0000 −0.00717694 −0.00358847 − 0.999994i \(-0.501142\pi\)
−0.00358847 + 0.999994i \(0.501142\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 12597.0 1.11665 0.558323 − 0.829624i \(-0.311445\pi\)
0.558323 + 0.829624i \(0.311445\pi\)
\(504\) 0 0
\(505\) 12716.0 1.12050
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6732.00 0.586229 0.293115 − 0.956077i \(-0.405308\pi\)
0.293115 + 0.956077i \(0.405308\pi\)
\(510\) 0 0
\(511\) 1536.00 0.132972
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2839.00 −0.242915
\(516\) 0 0
\(517\) −3468.00 −0.295014
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1003.00 0.0843421 0.0421710 − 0.999110i \(-0.486573\pi\)
0.0421710 + 0.999110i \(0.486573\pi\)
\(522\) 0 0
\(523\) 308.000 0.0257512 0.0128756 − 0.999917i \(-0.495901\pi\)
0.0128756 + 0.999917i \(0.495901\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2108.00 −0.174243
\(528\) 0 0
\(529\) −9566.00 −0.786225
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5117.00 0.415838
\(534\) 0 0
\(535\) 13583.0 1.09765
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5219.00 0.417065
\(540\) 0 0
\(541\) 11630.0 0.924238 0.462119 − 0.886818i \(-0.347089\pi\)
0.462119 + 0.886818i \(0.347089\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 19312.0 1.51786
\(546\) 0 0
\(547\) −8790.00 −0.687081 −0.343540 − 0.939138i \(-0.611626\pi\)
−0.343540 + 0.939138i \(0.611626\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2278.00 0.176127
\(552\) 0 0
\(553\) 2796.00 0.215005
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 15538.0 1.18199 0.590993 − 0.806677i \(-0.298736\pi\)
0.590993 + 0.806677i \(0.298736\pi\)
\(558\) 0 0
\(559\) −16641.0 −1.25910
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 8568.00 0.641382 0.320691 − 0.947184i \(-0.396085\pi\)
0.320691 + 0.947184i \(0.396085\pi\)
\(564\) 0 0
\(565\) −15895.0 −1.18355
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −13056.0 −0.961926 −0.480963 − 0.876741i \(-0.659713\pi\)
−0.480963 + 0.876741i \(0.659713\pi\)
\(570\) 0 0
\(571\) −11924.0 −0.873912 −0.436956 − 0.899483i \(-0.643943\pi\)
−0.436956 + 0.899483i \(0.643943\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 8364.00 0.606614
\(576\) 0 0
\(577\) 14717.0 1.06183 0.530916 − 0.847425i \(-0.321848\pi\)
0.530916 + 0.847425i \(0.321848\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2856.00 0.203936
\(582\) 0 0
\(583\) −3468.00 −0.246363
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5440.00 −0.382509 −0.191255 − 0.981540i \(-0.561256\pi\)
−0.191255 + 0.981540i \(0.561256\pi\)
\(588\) 0 0
\(589\) −8308.00 −0.581197
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14756.0 1.02185 0.510924 − 0.859626i \(-0.329303\pi\)
0.510924 + 0.859626i \(0.329303\pi\)
\(594\) 0 0
\(595\) 1734.00 0.119474
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3910.00 −0.266708 −0.133354 − 0.991068i \(-0.542575\pi\)
−0.133354 + 0.991068i \(0.542575\pi\)
\(600\) 0 0
\(601\) −21672.0 −1.47091 −0.735457 − 0.677571i \(-0.763032\pi\)
−0.735457 + 0.677571i \(0.763032\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −17714.0 −1.19037
\(606\) 0 0
\(607\) 7890.00 0.527587 0.263793 − 0.964579i \(-0.415026\pi\)
0.263793 + 0.964579i \(0.415026\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 8772.00 0.580814
\(612\) 0 0
\(613\) −25153.0 −1.65729 −0.828646 − 0.559773i \(-0.810888\pi\)
−0.828646 + 0.559773i \(0.810888\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11934.0 0.778679 0.389339 − 0.921094i \(-0.372703\pi\)
0.389339 + 0.921094i \(0.372703\pi\)
\(618\) 0 0
\(619\) 26506.0 1.72111 0.860554 − 0.509359i \(-0.170117\pi\)
0.860554 + 0.509359i \(0.170117\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 7956.00 0.511638
\(624\) 0 0
\(625\) −9229.00 −0.590656
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1802.00 0.114230
\(630\) 0 0
\(631\) −4281.00 −0.270085 −0.135043 − 0.990840i \(-0.543117\pi\)
−0.135043 + 0.990840i \(0.543117\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4743.00 0.296410
\(636\) 0 0
\(637\) −13201.0 −0.821103
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 3145.00 0.193791 0.0968955 − 0.995295i \(-0.469109\pi\)
0.0968955 + 0.995295i \(0.469109\pi\)
\(642\) 0 0
\(643\) 23852.0 1.46288 0.731439 − 0.681906i \(-0.238849\pi\)
0.731439 + 0.681906i \(0.238849\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −7922.00 −0.481369 −0.240685 − 0.970603i \(-0.577372\pi\)
−0.240685 + 0.970603i \(0.577372\pi\)
\(648\) 0 0
\(649\) −5202.00 −0.314632
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7089.00 0.424830 0.212415 − 0.977180i \(-0.431867\pi\)
0.212415 + 0.977180i \(0.431867\pi\)
\(654\) 0 0
\(655\) −11271.0 −0.672358
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −28050.0 −1.65808 −0.829039 − 0.559191i \(-0.811112\pi\)
−0.829039 + 0.559191i \(0.811112\pi\)
\(660\) 0 0
\(661\) 6945.00 0.408667 0.204334 − 0.978901i \(-0.434497\pi\)
0.204334 + 0.978901i \(0.434497\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 6834.00 0.398513
\(666\) 0 0
\(667\) 1734.00 0.100661
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4114.00 −0.236690
\(672\) 0 0
\(673\) −21532.0 −1.23328 −0.616640 − 0.787245i \(-0.711507\pi\)
−0.616640 + 0.787245i \(0.711507\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −29257.0 −1.66091 −0.830456 − 0.557084i \(-0.811920\pi\)
−0.830456 + 0.557084i \(0.811920\pi\)
\(678\) 0 0
\(679\) 4272.00 0.241450
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 18377.0 1.02954 0.514770 − 0.857328i \(-0.327877\pi\)
0.514770 + 0.857328i \(0.327877\pi\)
\(684\) 0 0
\(685\) 13294.0 0.741515
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 8772.00 0.485031
\(690\) 0 0
\(691\) 17768.0 0.978186 0.489093 − 0.872232i \(-0.337328\pi\)
0.489093 + 0.872232i \(0.337328\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −25670.0 −1.40103
\(696\) 0 0
\(697\) 2023.00 0.109938
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −5440.00 −0.293104 −0.146552 − 0.989203i \(-0.546818\pi\)
−0.146552 + 0.989203i \(0.546818\pi\)
\(702\) 0 0
\(703\) 7102.00 0.381020
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4488.00 0.238739
\(708\) 0 0
\(709\) −128.000 −0.00678017 −0.00339009 − 0.999994i \(-0.501079\pi\)
−0.00339009 + 0.999994i \(0.501079\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −6324.00 −0.332168
\(714\) 0 0
\(715\) −12427.0 −0.649991
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −3655.00 −0.189581 −0.0947903 − 0.995497i \(-0.530218\pi\)
−0.0947903 + 0.995497i \(0.530218\pi\)
\(720\) 0 0
\(721\) −1002.00 −0.0517565
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 5576.00 0.285638
\(726\) 0 0
\(727\) 6556.00 0.334455 0.167227 − 0.985918i \(-0.446519\pi\)
0.167227 + 0.985918i \(0.446519\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −6579.00 −0.332877
\(732\) 0 0
\(733\) 17746.0 0.894220 0.447110 − 0.894479i \(-0.352453\pi\)
0.447110 + 0.894479i \(0.352453\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 12444.0 0.621955
\(738\) 0 0
\(739\) 7471.00 0.371888 0.185944 − 0.982560i \(-0.440466\pi\)
0.185944 + 0.982560i \(0.440466\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 17884.0 0.883042 0.441521 − 0.897251i \(-0.354439\pi\)
0.441521 + 0.897251i \(0.354439\pi\)
\(744\) 0 0
\(745\) 56066.0 2.75718
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4794.00 0.233870
\(750\) 0 0
\(751\) 38672.0 1.87904 0.939522 − 0.342490i \(-0.111270\pi\)
0.939522 + 0.342490i \(0.111270\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 23256.0 1.12102
\(756\) 0 0
\(757\) −14335.0 −0.688262 −0.344131 − 0.938922i \(-0.611826\pi\)
−0.344131 + 0.938922i \(0.611826\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −30396.0 −1.44790 −0.723951 − 0.689851i \(-0.757676\pi\)
−0.723951 + 0.689851i \(0.757676\pi\)
\(762\) 0 0
\(763\) 6816.00 0.323402
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 13158.0 0.619437
\(768\) 0 0
\(769\) −34179.0 −1.60276 −0.801382 − 0.598152i \(-0.795902\pi\)
−0.801382 + 0.598152i \(0.795902\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −14756.0 −0.686593 −0.343297 − 0.939227i \(-0.611544\pi\)
−0.343297 + 0.939227i \(0.611544\pi\)
\(774\) 0 0
\(775\) −20336.0 −0.942569
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7973.00 0.366704
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −28237.0 −1.28385
\(786\) 0 0
\(787\) 1708.00 0.0773617 0.0386808 − 0.999252i \(-0.487684\pi\)
0.0386808 + 0.999252i \(0.487684\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −5610.00 −0.252173
\(792\) 0 0
\(793\) 10406.0 0.465987
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −27812.0 −1.23607 −0.618037 − 0.786149i \(-0.712072\pi\)
−0.618037 + 0.786149i \(0.712072\pi\)
\(798\) 0 0
\(799\) 3468.00 0.153553
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4352.00 −0.191256
\(804\) 0 0
\(805\) 5202.00 0.227760
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −39185.0 −1.70293 −0.851466 − 0.524411i \(-0.824286\pi\)
−0.851466 + 0.524411i \(0.824286\pi\)
\(810\) 0 0
\(811\) 5704.00 0.246972 0.123486 − 0.992346i \(-0.460593\pi\)
0.123486 + 0.992346i \(0.460593\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −42568.0 −1.82956
\(816\) 0 0
\(817\) −25929.0 −1.11033
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 10489.0 0.445881 0.222941 − 0.974832i \(-0.428434\pi\)
0.222941 + 0.974832i \(0.428434\pi\)
\(822\) 0 0
\(823\) −12298.0 −0.520876 −0.260438 − 0.965491i \(-0.583867\pi\)
−0.260438 + 0.965491i \(0.583867\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 41429.0 1.74199 0.870996 − 0.491290i \(-0.163474\pi\)
0.870996 + 0.491290i \(0.163474\pi\)
\(828\) 0 0
\(829\) 24086.0 1.00910 0.504548 − 0.863383i \(-0.331659\pi\)
0.504548 + 0.863383i \(0.331659\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −5219.00 −0.217080
\(834\) 0 0
\(835\) 26299.0 1.08996
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −43503.0 −1.79010 −0.895048 − 0.445970i \(-0.852859\pi\)
−0.895048 + 0.445970i \(0.852859\pi\)
\(840\) 0 0
\(841\) −23233.0 −0.952602
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −5916.00 −0.240848
\(846\) 0 0
\(847\) −6252.00 −0.253626
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 5406.00 0.217762
\(852\) 0 0
\(853\) 10366.0 0.416090 0.208045 − 0.978119i \(-0.433290\pi\)
0.208045 + 0.978119i \(0.433290\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3978.00 0.158560 0.0792800 − 0.996852i \(-0.474738\pi\)
0.0792800 + 0.996852i \(0.474738\pi\)
\(858\) 0 0
\(859\) −25812.0 −1.02526 −0.512628 − 0.858611i \(-0.671328\pi\)
−0.512628 + 0.858611i \(0.671328\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −27982.0 −1.10373 −0.551865 − 0.833934i \(-0.686083\pi\)
−0.551865 + 0.833934i \(0.686083\pi\)
\(864\) 0 0
\(865\) −25143.0 −0.988309
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −7922.00 −0.309247
\(870\) 0 0
\(871\) −31476.0 −1.22448
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 3978.00 0.153693
\(876\) 0 0
\(877\) −17306.0 −0.666342 −0.333171 − 0.942866i \(-0.608119\pi\)
−0.333171 + 0.942866i \(0.608119\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −30158.0 −1.15329 −0.576645 − 0.816995i \(-0.695638\pi\)
−0.576645 + 0.816995i \(0.695638\pi\)
\(882\) 0 0
\(883\) 9087.00 0.346322 0.173161 − 0.984894i \(-0.444602\pi\)
0.173161 + 0.984894i \(0.444602\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1989.00 0.0752921 0.0376460 − 0.999291i \(-0.488014\pi\)
0.0376460 + 0.999291i \(0.488014\pi\)
\(888\) 0 0
\(889\) 1674.00 0.0631543
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 13668.0 0.512186
\(894\) 0 0
\(895\) −79764.0 −2.97901
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −4216.00 −0.156409
\(900\) 0 0
\(901\) 3468.00 0.128231
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −44846.0 −1.64722
\(906\) 0 0
\(907\) 38554.0 1.41143 0.705714 − 0.708497i \(-0.250627\pi\)
0.705714 + 0.708497i \(0.250627\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −26333.0 −0.957685 −0.478843 − 0.877901i \(-0.658944\pi\)
−0.478843 + 0.877901i \(0.658944\pi\)
\(912\) 0 0
\(913\) −8092.00 −0.293325
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −3978.00 −0.143255
\(918\) 0 0
\(919\) −16389.0 −0.588273 −0.294137 − 0.955763i \(-0.595032\pi\)
−0.294137 + 0.955763i \(0.595032\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 17384.0 0.617927
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −21131.0 −0.746271 −0.373135 − 0.927777i \(-0.621717\pi\)
−0.373135 + 0.927777i \(0.621717\pi\)
\(930\) 0 0
\(931\) −20569.0 −0.724084
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −4913.00 −0.171842
\(936\) 0 0
\(937\) 22934.0 0.799596 0.399798 − 0.916603i \(-0.369080\pi\)
0.399798 + 0.916603i \(0.369080\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 43690.0 1.51355 0.756776 − 0.653674i \(-0.226773\pi\)
0.756776 + 0.653674i \(0.226773\pi\)
\(942\) 0 0
\(943\) 6069.00 0.209580
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 10540.0 0.361673 0.180836 − 0.983513i \(-0.442120\pi\)
0.180836 + 0.983513i \(0.442120\pi\)
\(948\) 0 0
\(949\) 11008.0 0.376538
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 37128.0 1.26201 0.631004 − 0.775779i \(-0.282643\pi\)
0.631004 + 0.775779i \(0.282643\pi\)
\(954\) 0 0
\(955\) 24854.0 0.842153
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 4692.00 0.157990
\(960\) 0 0
\(961\) −14415.0 −0.483871
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −69156.0 −2.30695
\(966\) 0 0
\(967\) −45107.0 −1.50004 −0.750022 − 0.661412i \(-0.769957\pi\)
−0.750022 + 0.661412i \(0.769957\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 52768.0 1.74398 0.871991 − 0.489523i \(-0.162829\pi\)
0.871991 + 0.489523i \(0.162829\pi\)
\(972\) 0 0
\(973\) −9060.00 −0.298510
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −39746.0 −1.30152 −0.650761 − 0.759283i \(-0.725550\pi\)
−0.650761 + 0.759283i \(0.725550\pi\)
\(978\) 0 0
\(979\) −22542.0 −0.735899
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −23919.0 −0.776091 −0.388046 − 0.921640i \(-0.626850\pi\)
−0.388046 + 0.921640i \(0.626850\pi\)
\(984\) 0 0
\(985\) 70805.0 2.29039
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −19737.0 −0.634580
\(990\) 0 0
\(991\) −11476.0 −0.367858 −0.183929 − 0.982940i \(-0.558882\pi\)
−0.183929 + 0.982940i \(0.558882\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 35904.0 1.14395
\(996\) 0 0
\(997\) −4598.00 −0.146058 −0.0730291 − 0.997330i \(-0.523267\pi\)
−0.0730291 + 0.997330i \(0.523267\pi\)
\(998\) 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 612.4.a.d.1.1 yes 1
3.2 odd 2 612.4.a.a.1.1 ✓ 1
4.3 odd 2 2448.4.a.p.1.1 1
12.11 even 2 2448.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
612.4.a.a.1.1 ✓ 1 3.2 odd 2
612.4.a.d.1.1 yes 1 1.1 even 1 trivial
2448.4.a.a.1.1 1 12.11 even 2
2448.4.a.p.1.1 1 4.3 odd 2