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Properties

Label 1575.4.a.f.1.1
Level $1575$
Weight $4$
Character 1575.1
Self dual yes
Analytic conductor $92.928$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1575,4,Mod(1,1575)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1575, 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("1575.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1575.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: \(92.9280082590\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 105)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1575.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-8.00000 q^{4} -7.00000 q^{7} +O(q^{10})\) \(q-8.00000 q^{4} -7.00000 q^{7} -42.0000 q^{11} -20.0000 q^{13} +64.0000 q^{16} +66.0000 q^{17} +38.0000 q^{19} +12.0000 q^{23} +56.0000 q^{28} +258.000 q^{29} +146.000 q^{31} -434.000 q^{37} +282.000 q^{41} -20.0000 q^{43} +336.000 q^{44} -72.0000 q^{47} +49.0000 q^{49} +160.000 q^{52} +336.000 q^{53} +360.000 q^{59} -682.000 q^{61} -512.000 q^{64} -812.000 q^{67} -528.000 q^{68} -810.000 q^{71} +124.000 q^{73} -304.000 q^{76} +294.000 q^{77} +1136.00 q^{79} +156.000 q^{83} +1038.00 q^{89} +140.000 q^{91} -96.0000 q^{92} -1208.00 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) 0 0
\(4\) −8.00000 −1.00000
\(5\) 0 0
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −42.0000 −1.15123 −0.575613 − 0.817723i \(-0.695236\pi\)
−0.575613 + 0.817723i \(0.695236\pi\)
\(12\) 0 0
\(13\) −20.0000 −0.426692 −0.213346 − 0.976977i \(-0.568436\pi\)
−0.213346 + 0.976977i \(0.568436\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 64.0000 1.00000
\(17\) 66.0000 0.941609 0.470804 − 0.882238i \(-0.343964\pi\)
0.470804 + 0.882238i \(0.343964\pi\)
\(18\) 0 0
\(19\) 38.0000 0.458831 0.229416 − 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 12.0000 0.108790 0.0543951 − 0.998519i \(-0.482677\pi\)
0.0543951 + 0.998519i \(0.482677\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 56.0000 0.377964
\(29\) 258.000 1.65205 0.826024 − 0.563635i \(-0.190597\pi\)
0.826024 + 0.563635i \(0.190597\pi\)
\(30\) 0 0
\(31\) 146.000 0.845883 0.422942 − 0.906157i \(-0.360998\pi\)
0.422942 + 0.906157i \(0.360998\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −434.000 −1.92836 −0.964178 − 0.265257i \(-0.914543\pi\)
−0.964178 + 0.265257i \(0.914543\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 282.000 1.07417 0.537085 − 0.843528i \(-0.319525\pi\)
0.537085 + 0.843528i \(0.319525\pi\)
\(42\) 0 0
\(43\) −20.0000 −0.0709296 −0.0354648 − 0.999371i \(-0.511291\pi\)
−0.0354648 + 0.999371i \(0.511291\pi\)
\(44\) 336.000 1.15123
\(45\) 0 0
\(46\) 0 0
\(47\) −72.0000 −0.223453 −0.111726 − 0.993739i \(-0.535638\pi\)
−0.111726 + 0.993739i \(0.535638\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 160.000 0.426692
\(53\) 336.000 0.870814 0.435407 − 0.900234i \(-0.356604\pi\)
0.435407 + 0.900234i \(0.356604\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 360.000 0.794373 0.397187 − 0.917738i \(-0.369987\pi\)
0.397187 + 0.917738i \(0.369987\pi\)
\(60\) 0 0
\(61\) −682.000 −1.43149 −0.715747 − 0.698360i \(-0.753914\pi\)
−0.715747 + 0.698360i \(0.753914\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −512.000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −812.000 −1.48062 −0.740310 − 0.672265i \(-0.765321\pi\)
−0.740310 + 0.672265i \(0.765321\pi\)
\(68\) −528.000 −0.941609
\(69\) 0 0
\(70\) 0 0
\(71\) −810.000 −1.35393 −0.676967 − 0.736013i \(-0.736706\pi\)
−0.676967 + 0.736013i \(0.736706\pi\)
\(72\) 0 0
\(73\) 124.000 0.198810 0.0994048 − 0.995047i \(-0.468306\pi\)
0.0994048 + 0.995047i \(0.468306\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −304.000 −0.458831
\(77\) 294.000 0.435122
\(78\) 0 0
\(79\) 1136.00 1.61785 0.808924 − 0.587913i \(-0.200050\pi\)
0.808924 + 0.587913i \(0.200050\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 156.000 0.206304 0.103152 − 0.994666i \(-0.467107\pi\)
0.103152 + 0.994666i \(0.467107\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1038.00 1.23627 0.618134 − 0.786073i \(-0.287889\pi\)
0.618134 + 0.786073i \(0.287889\pi\)
\(90\) 0 0
\(91\) 140.000 0.161275
\(92\) −96.0000 −0.108790
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1208.00 −1.26447 −0.632236 − 0.774776i \(-0.717863\pi\)
−0.632236 + 0.774776i \(0.717863\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −546.000 −0.537911 −0.268956 − 0.963153i \(-0.586678\pi\)
−0.268956 + 0.963153i \(0.586678\pi\)
\(102\) 0 0
\(103\) 520.000 0.497448 0.248724 − 0.968574i \(-0.419989\pi\)
0.248724 + 0.968574i \(0.419989\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1212.00 1.09503 0.547516 − 0.836795i \(-0.315573\pi\)
0.547516 + 0.836795i \(0.315573\pi\)
\(108\) 0 0
\(109\) −1078.00 −0.947281 −0.473641 − 0.880718i \(-0.657060\pi\)
−0.473641 + 0.880718i \(0.657060\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −448.000 −0.377964
\(113\) −1452.00 −1.20878 −0.604392 − 0.796687i \(-0.706584\pi\)
−0.604392 + 0.796687i \(0.706584\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2064.00 −1.65205
\(117\) 0 0
\(118\) 0 0
\(119\) −462.000 −0.355895
\(120\) 0 0
\(121\) 433.000 0.325319
\(122\) 0 0
\(123\) 0 0
\(124\) −1168.00 −0.845883
\(125\) 0 0
\(126\) 0 0
\(127\) 1312.00 0.916702 0.458351 − 0.888771i \(-0.348440\pi\)
0.458351 + 0.888771i \(0.348440\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1356.00 0.904384 0.452192 − 0.891921i \(-0.350642\pi\)
0.452192 + 0.891921i \(0.350642\pi\)
\(132\) 0 0
\(133\) −266.000 −0.173422
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −984.000 −0.613641 −0.306820 − 0.951767i \(-0.599265\pi\)
−0.306820 + 0.951767i \(0.599265\pi\)
\(138\) 0 0
\(139\) −394.000 −0.240422 −0.120211 − 0.992748i \(-0.538357\pi\)
−0.120211 + 0.992748i \(0.538357\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 840.000 0.491219
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 3472.00 1.92836
\(149\) 1014.00 0.557518 0.278759 − 0.960361i \(-0.410077\pi\)
0.278759 + 0.960361i \(0.410077\pi\)
\(150\) 0 0
\(151\) −1996.00 −1.07571 −0.537855 − 0.843037i \(-0.680765\pi\)
−0.537855 + 0.843037i \(0.680765\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 2392.00 1.21594 0.607969 − 0.793960i \(-0.291984\pi\)
0.607969 + 0.793960i \(0.291984\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −84.0000 −0.0411188
\(162\) 0 0
\(163\) −2036.00 −0.978355 −0.489177 − 0.872184i \(-0.662703\pi\)
−0.489177 + 0.872184i \(0.662703\pi\)
\(164\) −2256.00 −1.07417
\(165\) 0 0
\(166\) 0 0
\(167\) −3936.00 −1.82381 −0.911907 − 0.410398i \(-0.865390\pi\)
−0.911907 + 0.410398i \(0.865390\pi\)
\(168\) 0 0
\(169\) −1797.00 −0.817934
\(170\) 0 0
\(171\) 0 0
\(172\) 160.000 0.0709296
\(173\) 378.000 0.166120 0.0830601 − 0.996545i \(-0.473531\pi\)
0.0830601 + 0.996545i \(0.473531\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2688.00 −1.15123
\(177\) 0 0
\(178\) 0 0
\(179\) 222.000 0.0926987 0.0463493 − 0.998925i \(-0.485241\pi\)
0.0463493 + 0.998925i \(0.485241\pi\)
\(180\) 0 0
\(181\) −2590.00 −1.06361 −0.531804 − 0.846867i \(-0.678486\pi\)
−0.531804 + 0.846867i \(0.678486\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2772.00 −1.08400
\(188\) 576.000 0.223453
\(189\) 0 0
\(190\) 0 0
\(191\) −2214.00 −0.838740 −0.419370 − 0.907815i \(-0.637749\pi\)
−0.419370 + 0.907815i \(0.637749\pi\)
\(192\) 0 0
\(193\) −4178.00 −1.55823 −0.779117 − 0.626879i \(-0.784332\pi\)
−0.779117 + 0.626879i \(0.784332\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −392.000 −0.142857
\(197\) −3060.00 −1.10668 −0.553340 − 0.832955i \(-0.686647\pi\)
−0.553340 + 0.832955i \(0.686647\pi\)
\(198\) 0 0
\(199\) 2666.00 0.949687 0.474844 − 0.880070i \(-0.342505\pi\)
0.474844 + 0.880070i \(0.342505\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1806.00 −0.624416
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −1280.00 −0.426692
\(209\) −1596.00 −0.528218
\(210\) 0 0
\(211\) −1348.00 −0.439811 −0.219906 − 0.975521i \(-0.570575\pi\)
−0.219906 + 0.975521i \(0.570575\pi\)
\(212\) −2688.00 −0.870814
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1022.00 −0.319714
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1320.00 −0.401777
\(222\) 0 0
\(223\) −3188.00 −0.957329 −0.478664 − 0.877998i \(-0.658879\pi\)
−0.478664 + 0.877998i \(0.658879\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3396.00 −0.992953 −0.496477 − 0.868050i \(-0.665373\pi\)
−0.496477 + 0.868050i \(0.665373\pi\)
\(228\) 0 0
\(229\) 5294.00 1.52767 0.763837 − 0.645409i \(-0.223313\pi\)
0.763837 + 0.645409i \(0.223313\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 852.000 0.239555 0.119778 − 0.992801i \(-0.461782\pi\)
0.119778 + 0.992801i \(0.461782\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −2880.00 −0.794373
\(237\) 0 0
\(238\) 0 0
\(239\) −4866.00 −1.31697 −0.658484 − 0.752595i \(-0.728802\pi\)
−0.658484 + 0.752595i \(0.728802\pi\)
\(240\) 0 0
\(241\) −2050.00 −0.547934 −0.273967 − 0.961739i \(-0.588336\pi\)
−0.273967 + 0.961739i \(0.588336\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 5456.00 1.43149
\(245\) 0 0
\(246\) 0 0
\(247\) −760.000 −0.195780
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1152.00 0.289696 0.144848 − 0.989454i \(-0.453731\pi\)
0.144848 + 0.989454i \(0.453731\pi\)
\(252\) 0 0
\(253\) −504.000 −0.125242
\(254\) 0 0
\(255\) 0 0
\(256\) 4096.00 1.00000
\(257\) −6450.00 −1.56553 −0.782763 − 0.622321i \(-0.786190\pi\)
−0.782763 + 0.622321i \(0.786190\pi\)
\(258\) 0 0
\(259\) 3038.00 0.728850
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1968.00 0.461415 0.230707 − 0.973023i \(-0.425896\pi\)
0.230707 + 0.973023i \(0.425896\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 6496.00 1.48062
\(269\) 3894.00 0.882607 0.441304 − 0.897358i \(-0.354516\pi\)
0.441304 + 0.897358i \(0.354516\pi\)
\(270\) 0 0
\(271\) 7094.00 1.59015 0.795073 − 0.606513i \(-0.207432\pi\)
0.795073 + 0.606513i \(0.207432\pi\)
\(272\) 4224.00 0.941609
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 3310.00 0.717973 0.358987 − 0.933343i \(-0.383122\pi\)
0.358987 + 0.933343i \(0.383122\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −7158.00 −1.51961 −0.759805 − 0.650151i \(-0.774706\pi\)
−0.759805 + 0.650151i \(0.774706\pi\)
\(282\) 0 0
\(283\) 5164.00 1.08469 0.542346 − 0.840155i \(-0.317536\pi\)
0.542346 + 0.840155i \(0.317536\pi\)
\(284\) 6480.00 1.35393
\(285\) 0 0
\(286\) 0 0
\(287\) −1974.00 −0.405998
\(288\) 0 0
\(289\) −557.000 −0.113373
\(290\) 0 0
\(291\) 0 0
\(292\) −992.000 −0.198810
\(293\) −8598.00 −1.71434 −0.857168 − 0.515037i \(-0.827778\pi\)
−0.857168 + 0.515037i \(0.827778\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −240.000 −0.0464199
\(300\) 0 0
\(301\) 140.000 0.0268089
\(302\) 0 0
\(303\) 0 0
\(304\) 2432.00 0.458831
\(305\) 0 0
\(306\) 0 0
\(307\) 448.000 0.0832857 0.0416429 − 0.999133i \(-0.486741\pi\)
0.0416429 + 0.999133i \(0.486741\pi\)
\(308\) −2352.00 −0.435122
\(309\) 0 0
\(310\) 0 0
\(311\) 5832.00 1.06335 0.531676 − 0.846948i \(-0.321562\pi\)
0.531676 + 0.846948i \(0.321562\pi\)
\(312\) 0 0
\(313\) −9848.00 −1.77841 −0.889204 − 0.457510i \(-0.848741\pi\)
−0.889204 + 0.457510i \(0.848741\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −9088.00 −1.61785
\(317\) −5616.00 −0.995035 −0.497517 − 0.867454i \(-0.665755\pi\)
−0.497517 + 0.867454i \(0.665755\pi\)
\(318\) 0 0
\(319\) −10836.0 −1.90188
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2508.00 0.432040
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 504.000 0.0844572
\(330\) 0 0
\(331\) 452.000 0.0750579 0.0375290 − 0.999296i \(-0.488051\pi\)
0.0375290 + 0.999296i \(0.488051\pi\)
\(332\) −1248.00 −0.206304
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 2302.00 0.372101 0.186050 − 0.982540i \(-0.440431\pi\)
0.186050 + 0.982540i \(0.440431\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6132.00 −0.973802
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1584.00 0.245054 0.122527 − 0.992465i \(-0.460900\pi\)
0.122527 + 0.992465i \(0.460900\pi\)
\(348\) 0 0
\(349\) 8174.00 1.25371 0.626854 − 0.779137i \(-0.284342\pi\)
0.626854 + 0.779137i \(0.284342\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8610.00 1.29820 0.649099 − 0.760704i \(-0.275146\pi\)
0.649099 + 0.760704i \(0.275146\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −8304.00 −1.23627
\(357\) 0 0
\(358\) 0 0
\(359\) 2154.00 0.316668 0.158334 − 0.987386i \(-0.449388\pi\)
0.158334 + 0.987386i \(0.449388\pi\)
\(360\) 0 0
\(361\) −5415.00 −0.789474
\(362\) 0 0
\(363\) 0 0
\(364\) −1120.00 −0.161275
\(365\) 0 0
\(366\) 0 0
\(367\) −6644.00 −0.944997 −0.472499 − 0.881331i \(-0.656648\pi\)
−0.472499 + 0.881331i \(0.656648\pi\)
\(368\) 768.000 0.108790
\(369\) 0 0
\(370\) 0 0
\(371\) −2352.00 −0.329137
\(372\) 0 0
\(373\) −7958.00 −1.10469 −0.552345 − 0.833615i \(-0.686267\pi\)
−0.552345 + 0.833615i \(0.686267\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5160.00 −0.704917
\(378\) 0 0
\(379\) 3440.00 0.466229 0.233115 − 0.972449i \(-0.425108\pi\)
0.233115 + 0.972449i \(0.425108\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12936.0 1.72585 0.862923 − 0.505336i \(-0.168631\pi\)
0.862923 + 0.505336i \(0.168631\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 9664.00 1.26447
\(389\) 14862.0 1.93710 0.968552 − 0.248812i \(-0.0800401\pi\)
0.968552 + 0.248812i \(0.0800401\pi\)
\(390\) 0 0
\(391\) 792.000 0.102438
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −10460.0 −1.32235 −0.661174 − 0.750232i \(-0.729942\pi\)
−0.661174 + 0.750232i \(0.729942\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9150.00 1.13947 0.569737 − 0.821827i \(-0.307045\pi\)
0.569737 + 0.821827i \(0.307045\pi\)
\(402\) 0 0
\(403\) −2920.00 −0.360932
\(404\) 4368.00 0.537911
\(405\) 0 0
\(406\) 0 0
\(407\) 18228.0 2.21997
\(408\) 0 0
\(409\) −4894.00 −0.591669 −0.295835 − 0.955239i \(-0.595598\pi\)
−0.295835 + 0.955239i \(0.595598\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4160.00 −0.497448
\(413\) −2520.00 −0.300245
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1668.00 0.194480 0.0972400 − 0.995261i \(-0.468999\pi\)
0.0972400 + 0.995261i \(0.468999\pi\)
\(420\) 0 0
\(421\) −12418.0 −1.43757 −0.718784 − 0.695233i \(-0.755301\pi\)
−0.718784 + 0.695233i \(0.755301\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 4774.00 0.541054
\(428\) −9696.00 −1.09503
\(429\) 0 0
\(430\) 0 0
\(431\) −15186.0 −1.69718 −0.848589 − 0.529052i \(-0.822548\pi\)
−0.848589 + 0.529052i \(0.822548\pi\)
\(432\) 0 0
\(433\) 5704.00 0.633064 0.316532 − 0.948582i \(-0.397482\pi\)
0.316532 + 0.948582i \(0.397482\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 8624.00 0.947281
\(437\) 456.000 0.0499163
\(438\) 0 0
\(439\) −17206.0 −1.87061 −0.935305 − 0.353843i \(-0.884875\pi\)
−0.935305 + 0.353843i \(0.884875\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3456.00 0.370654 0.185327 − 0.982677i \(-0.440666\pi\)
0.185327 + 0.982677i \(0.440666\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 3584.00 0.377964
\(449\) −16074.0 −1.68949 −0.844743 − 0.535173i \(-0.820247\pi\)
−0.844743 + 0.535173i \(0.820247\pi\)
\(450\) 0 0
\(451\) −11844.0 −1.23661
\(452\) 11616.0 1.20878
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −7526.00 −0.770353 −0.385177 − 0.922843i \(-0.625859\pi\)
−0.385177 + 0.922843i \(0.625859\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2274.00 0.229741 0.114871 − 0.993380i \(-0.463355\pi\)
0.114871 + 0.993380i \(0.463355\pi\)
\(462\) 0 0
\(463\) 10024.0 1.00617 0.503083 − 0.864238i \(-0.332199\pi\)
0.503083 + 0.864238i \(0.332199\pi\)
\(464\) 16512.0 1.65205
\(465\) 0 0
\(466\) 0 0
\(467\) −2460.00 −0.243759 −0.121879 − 0.992545i \(-0.538892\pi\)
−0.121879 + 0.992545i \(0.538892\pi\)
\(468\) 0 0
\(469\) 5684.00 0.559622
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 840.000 0.0816559
\(474\) 0 0
\(475\) 0 0
\(476\) 3696.00 0.355895
\(477\) 0 0
\(478\) 0 0
\(479\) −19320.0 −1.84291 −0.921454 − 0.388486i \(-0.872998\pi\)
−0.921454 + 0.388486i \(0.872998\pi\)
\(480\) 0 0
\(481\) 8680.00 0.822815
\(482\) 0 0
\(483\) 0 0
\(484\) −3464.00 −0.325319
\(485\) 0 0
\(486\) 0 0
\(487\) 12544.0 1.16719 0.583596 − 0.812044i \(-0.301645\pi\)
0.583596 + 0.812044i \(0.301645\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 15510.0 1.42557 0.712787 − 0.701381i \(-0.247433\pi\)
0.712787 + 0.701381i \(0.247433\pi\)
\(492\) 0 0
\(493\) 17028.0 1.55558
\(494\) 0 0
\(495\) 0 0
\(496\) 9344.00 0.845883
\(497\) 5670.00 0.511739
\(498\) 0 0
\(499\) −14344.0 −1.28682 −0.643412 − 0.765520i \(-0.722482\pi\)
−0.643412 + 0.765520i \(0.722482\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −21384.0 −1.89556 −0.947779 − 0.318929i \(-0.896677\pi\)
−0.947779 + 0.318929i \(0.896677\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) −10496.0 −0.916702
\(509\) 7134.00 0.621236 0.310618 − 0.950535i \(-0.399464\pi\)
0.310618 + 0.950535i \(0.399464\pi\)
\(510\) 0 0
\(511\) −868.000 −0.0751430
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 3024.00 0.257244
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 19122.0 1.60797 0.803983 − 0.594653i \(-0.202710\pi\)
0.803983 + 0.594653i \(0.202710\pi\)
\(522\) 0 0
\(523\) 15640.0 1.30763 0.653814 − 0.756655i \(-0.273168\pi\)
0.653814 + 0.756655i \(0.273168\pi\)
\(524\) −10848.0 −0.904384
\(525\) 0 0
\(526\) 0 0
\(527\) 9636.00 0.796491
\(528\) 0 0
\(529\) −12023.0 −0.988165
\(530\) 0 0
\(531\) 0 0
\(532\) 2128.00 0.173422
\(533\) −5640.00 −0.458341
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2058.00 −0.164461
\(540\) 0 0
\(541\) 2846.00 0.226172 0.113086 − 0.993585i \(-0.463926\pi\)
0.113086 + 0.993585i \(0.463926\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 4444.00 0.347371 0.173685 − 0.984801i \(-0.444432\pi\)
0.173685 + 0.984801i \(0.444432\pi\)
\(548\) 7872.00 0.613641
\(549\) 0 0
\(550\) 0 0
\(551\) 9804.00 0.758012
\(552\) 0 0
\(553\) −7952.00 −0.611489
\(554\) 0 0
\(555\) 0 0
\(556\) 3152.00 0.240422
\(557\) 18552.0 1.41126 0.705631 − 0.708579i \(-0.250663\pi\)
0.705631 + 0.708579i \(0.250663\pi\)
\(558\) 0 0
\(559\) 400.000 0.0302651
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −16452.0 −1.23156 −0.615781 − 0.787918i \(-0.711159\pi\)
−0.615781 + 0.787918i \(0.711159\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −7722.00 −0.568933 −0.284467 − 0.958686i \(-0.591817\pi\)
−0.284467 + 0.958686i \(0.591817\pi\)
\(570\) 0 0
\(571\) 2576.00 0.188796 0.0943978 − 0.995535i \(-0.469907\pi\)
0.0943978 + 0.995535i \(0.469907\pi\)
\(572\) −6720.00 −0.491219
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 2464.00 0.177778 0.0888888 − 0.996042i \(-0.471668\pi\)
0.0888888 + 0.996042i \(0.471668\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1092.00 −0.0779755
\(582\) 0 0
\(583\) −14112.0 −1.00250
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1452.00 0.102096 0.0510481 − 0.998696i \(-0.483744\pi\)
0.0510481 + 0.998696i \(0.483744\pi\)
\(588\) 0 0
\(589\) 5548.00 0.388118
\(590\) 0 0
\(591\) 0 0
\(592\) −27776.0 −1.92836
\(593\) 10698.0 0.740833 0.370417 − 0.928866i \(-0.379215\pi\)
0.370417 + 0.928866i \(0.379215\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −8112.00 −0.557518
\(597\) 0 0
\(598\) 0 0
\(599\) 8730.00 0.595489 0.297745 − 0.954646i \(-0.403766\pi\)
0.297745 + 0.954646i \(0.403766\pi\)
\(600\) 0 0
\(601\) 1910.00 0.129635 0.0648174 − 0.997897i \(-0.479354\pi\)
0.0648174 + 0.997897i \(0.479354\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 15968.0 1.07571
\(605\) 0 0
\(606\) 0 0
\(607\) 5596.00 0.374192 0.187096 − 0.982342i \(-0.440092\pi\)
0.187096 + 0.982342i \(0.440092\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1440.00 0.0953456
\(612\) 0 0
\(613\) −28586.0 −1.88349 −0.941744 − 0.336332i \(-0.890814\pi\)
−0.941744 + 0.336332i \(0.890814\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −19236.0 −1.25513 −0.627563 − 0.778566i \(-0.715947\pi\)
−0.627563 + 0.778566i \(0.715947\pi\)
\(618\) 0 0
\(619\) 6734.00 0.437257 0.218629 − 0.975808i \(-0.429842\pi\)
0.218629 + 0.975808i \(0.429842\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −7266.00 −0.467265
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) −19136.0 −1.21594
\(629\) −28644.0 −1.81576
\(630\) 0 0
\(631\) 7184.00 0.453234 0.226617 − 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −980.000 −0.0609561
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −510.000 −0.0314256 −0.0157128 − 0.999877i \(-0.505002\pi\)
−0.0157128 + 0.999877i \(0.505002\pi\)
\(642\) 0 0
\(643\) 20752.0 1.27275 0.636376 − 0.771379i \(-0.280433\pi\)
0.636376 + 0.771379i \(0.280433\pi\)
\(644\) 672.000 0.0411188
\(645\) 0 0
\(646\) 0 0
\(647\) 21072.0 1.28041 0.640205 − 0.768204i \(-0.278849\pi\)
0.640205 + 0.768204i \(0.278849\pi\)
\(648\) 0 0
\(649\) −15120.0 −0.914502
\(650\) 0 0
\(651\) 0 0
\(652\) 16288.0 0.978355
\(653\) 2892.00 0.173312 0.0866560 − 0.996238i \(-0.472382\pi\)
0.0866560 + 0.996238i \(0.472382\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 18048.0 1.07417
\(657\) 0 0
\(658\) 0 0
\(659\) −750.000 −0.0443336 −0.0221668 − 0.999754i \(-0.507056\pi\)
−0.0221668 + 0.999754i \(0.507056\pi\)
\(660\) 0 0
\(661\) 30062.0 1.76895 0.884475 − 0.466587i \(-0.154517\pi\)
0.884475 + 0.466587i \(0.154517\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 3096.00 0.179727
\(668\) 31488.0 1.82381
\(669\) 0 0
\(670\) 0 0
\(671\) 28644.0 1.64797
\(672\) 0 0
\(673\) −15446.0 −0.884695 −0.442347 − 0.896844i \(-0.645854\pi\)
−0.442347 + 0.896844i \(0.645854\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 14376.0 0.817934
\(677\) −25110.0 −1.42549 −0.712744 − 0.701424i \(-0.752548\pi\)
−0.712744 + 0.701424i \(0.752548\pi\)
\(678\) 0 0
\(679\) 8456.00 0.477926
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 7968.00 0.446394 0.223197 − 0.974773i \(-0.428351\pi\)
0.223197 + 0.974773i \(0.428351\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1280.00 −0.0709296
\(689\) −6720.00 −0.371570
\(690\) 0 0
\(691\) −14398.0 −0.792657 −0.396328 − 0.918109i \(-0.629716\pi\)
−0.396328 + 0.918109i \(0.629716\pi\)
\(692\) −3024.00 −0.166120
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 18612.0 1.01145
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 9234.00 0.497523 0.248761 − 0.968565i \(-0.419977\pi\)
0.248761 + 0.968565i \(0.419977\pi\)
\(702\) 0 0
\(703\) −16492.0 −0.884790
\(704\) 21504.0 1.15123
\(705\) 0 0
\(706\) 0 0
\(707\) 3822.00 0.203311
\(708\) 0 0
\(709\) 8030.00 0.425350 0.212675 − 0.977123i \(-0.431782\pi\)
0.212675 + 0.977123i \(0.431782\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1752.00 0.0920237
\(714\) 0 0
\(715\) 0 0
\(716\) −1776.00 −0.0926987
\(717\) 0 0
\(718\) 0 0
\(719\) −27060.0 −1.40357 −0.701786 − 0.712388i \(-0.747614\pi\)
−0.701786 + 0.712388i \(0.747614\pi\)
\(720\) 0 0
\(721\) −3640.00 −0.188018
\(722\) 0 0
\(723\) 0 0
\(724\) 20720.0 1.06361
\(725\) 0 0
\(726\) 0 0
\(727\) 3724.00 0.189980 0.0949900 − 0.995478i \(-0.469718\pi\)
0.0949900 + 0.995478i \(0.469718\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1320.00 −0.0667879
\(732\) 0 0
\(733\) 5668.00 0.285610 0.142805 − 0.989751i \(-0.454388\pi\)
0.142805 + 0.989751i \(0.454388\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 34104.0 1.70453
\(738\) 0 0
\(739\) −16072.0 −0.800024 −0.400012 − 0.916510i \(-0.630994\pi\)
−0.400012 + 0.916510i \(0.630994\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −8256.00 −0.407649 −0.203825 − 0.979007i \(-0.565337\pi\)
−0.203825 + 0.979007i \(0.565337\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 22176.0 1.08400
\(749\) −8484.00 −0.413883
\(750\) 0 0
\(751\) −6352.00 −0.308639 −0.154319 − 0.988021i \(-0.549318\pi\)
−0.154319 + 0.988021i \(0.549318\pi\)
\(752\) −4608.00 −0.223453
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −11558.0 −0.554931 −0.277465 − 0.960736i \(-0.589494\pi\)
−0.277465 + 0.960736i \(0.589494\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −7770.00 −0.370121 −0.185061 − 0.982727i \(-0.559248\pi\)
−0.185061 + 0.982727i \(0.559248\pi\)
\(762\) 0 0
\(763\) 7546.00 0.358039
\(764\) 17712.0 0.838740
\(765\) 0 0
\(766\) 0 0
\(767\) −7200.00 −0.338953
\(768\) 0 0
\(769\) 22646.0 1.06194 0.530972 − 0.847389i \(-0.321827\pi\)
0.530972 + 0.847389i \(0.321827\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 33424.0 1.55823
\(773\) −35502.0 −1.65190 −0.825950 − 0.563744i \(-0.809361\pi\)
−0.825950 + 0.563744i \(0.809361\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 10716.0 0.492863
\(780\) 0 0
\(781\) 34020.0 1.55868
\(782\) 0 0
\(783\) 0 0
\(784\) 3136.00 0.142857
\(785\) 0 0
\(786\) 0 0
\(787\) 17080.0 0.773617 0.386808 − 0.922160i \(-0.373578\pi\)
0.386808 + 0.922160i \(0.373578\pi\)
\(788\) 24480.0 1.10668
\(789\) 0 0
\(790\) 0 0
\(791\) 10164.0 0.456878
\(792\) 0 0
\(793\) 13640.0 0.610808
\(794\) 0 0
\(795\) 0 0
\(796\) −21328.0 −0.949687
\(797\) 5730.00 0.254664 0.127332 − 0.991860i \(-0.459359\pi\)
0.127332 + 0.991860i \(0.459359\pi\)
\(798\) 0 0
\(799\) −4752.00 −0.210405
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −5208.00 −0.228875
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −2550.00 −0.110820 −0.0554099 − 0.998464i \(-0.517647\pi\)
−0.0554099 + 0.998464i \(0.517647\pi\)
\(810\) 0 0
\(811\) −27538.0 −1.19234 −0.596171 − 0.802857i \(-0.703312\pi\)
−0.596171 + 0.802857i \(0.703312\pi\)
\(812\) 14448.0 0.624416
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −760.000 −0.0325447
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 19242.0 0.817966 0.408983 − 0.912542i \(-0.365883\pi\)
0.408983 + 0.912542i \(0.365883\pi\)
\(822\) 0 0
\(823\) 11752.0 0.497751 0.248875 − 0.968536i \(-0.419939\pi\)
0.248875 + 0.968536i \(0.419939\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −28692.0 −1.20643 −0.603216 − 0.797578i \(-0.706114\pi\)
−0.603216 + 0.797578i \(0.706114\pi\)
\(828\) 0 0
\(829\) 28442.0 1.19159 0.595797 − 0.803135i \(-0.296836\pi\)
0.595797 + 0.803135i \(0.296836\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 10240.0 0.426692
\(833\) 3234.00 0.134516
\(834\) 0 0
\(835\) 0 0
\(836\) 12768.0 0.528218
\(837\) 0 0
\(838\) 0 0
\(839\) −20172.0 −0.830053 −0.415027 − 0.909809i \(-0.636228\pi\)
−0.415027 + 0.909809i \(0.636228\pi\)
\(840\) 0 0
\(841\) 42175.0 1.72926
\(842\) 0 0
\(843\) 0 0
\(844\) 10784.0 0.439811
\(845\) 0 0
\(846\) 0 0
\(847\) −3031.00 −0.122959
\(848\) 21504.0 0.870814
\(849\) 0 0
\(850\) 0 0
\(851\) −5208.00 −0.209786
\(852\) 0 0
\(853\) −19820.0 −0.795573 −0.397787 − 0.917478i \(-0.630222\pi\)
−0.397787 + 0.917478i \(0.630222\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −10290.0 −0.410151 −0.205076 − 0.978746i \(-0.565744\pi\)
−0.205076 + 0.978746i \(0.565744\pi\)
\(858\) 0 0
\(859\) −31606.0 −1.25539 −0.627697 − 0.778458i \(-0.716002\pi\)
−0.627697 + 0.778458i \(0.716002\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 23172.0 0.914002 0.457001 − 0.889466i \(-0.348924\pi\)
0.457001 + 0.889466i \(0.348924\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 8176.00 0.319714
\(869\) −47712.0 −1.86251
\(870\) 0 0
\(871\) 16240.0 0.631770
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 15550.0 0.598730 0.299365 − 0.954139i \(-0.403225\pi\)
0.299365 + 0.954139i \(0.403225\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −28530.0 −1.09103 −0.545517 − 0.838100i \(-0.683666\pi\)
−0.545517 + 0.838100i \(0.683666\pi\)
\(882\) 0 0
\(883\) 28780.0 1.09686 0.548428 − 0.836198i \(-0.315226\pi\)
0.548428 + 0.836198i \(0.315226\pi\)
\(884\) 10560.0 0.401777
\(885\) 0 0
\(886\) 0 0
\(887\) 22872.0 0.865802 0.432901 − 0.901441i \(-0.357490\pi\)
0.432901 + 0.901441i \(0.357490\pi\)
\(888\) 0 0
\(889\) −9184.00 −0.346481
\(890\) 0 0
\(891\) 0 0
\(892\) 25504.0 0.957329
\(893\) −2736.00 −0.102527
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 37668.0 1.39744
\(900\) 0 0
\(901\) 22176.0 0.819966
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 10708.0 0.392010 0.196005 − 0.980603i \(-0.437203\pi\)
0.196005 + 0.980603i \(0.437203\pi\)
\(908\) 27168.0 0.992953
\(909\) 0 0
\(910\) 0 0
\(911\) −1326.00 −0.0482243 −0.0241122 − 0.999709i \(-0.507676\pi\)
−0.0241122 + 0.999709i \(0.507676\pi\)
\(912\) 0 0
\(913\) −6552.00 −0.237502
\(914\) 0 0
\(915\) 0 0
\(916\) −42352.0 −1.52767
\(917\) −9492.00 −0.341825
\(918\) 0 0
\(919\) −13696.0 −0.491610 −0.245805 − 0.969319i \(-0.579052\pi\)
−0.245805 + 0.969319i \(0.579052\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 16200.0 0.577713
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −42354.0 −1.49579 −0.747895 − 0.663817i \(-0.768936\pi\)
−0.747895 + 0.663817i \(0.768936\pi\)
\(930\) 0 0
\(931\) 1862.00 0.0655474
\(932\) −6816.00 −0.239555
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −6644.00 −0.231644 −0.115822 − 0.993270i \(-0.536950\pi\)
−0.115822 + 0.993270i \(0.536950\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1350.00 −0.0467681 −0.0233840 − 0.999727i \(-0.507444\pi\)
−0.0233840 + 0.999727i \(0.507444\pi\)
\(942\) 0 0
\(943\) 3384.00 0.116859
\(944\) 23040.0 0.794373
\(945\) 0 0
\(946\) 0 0
\(947\) 49320.0 1.69238 0.846190 − 0.532881i \(-0.178891\pi\)
0.846190 + 0.532881i \(0.178891\pi\)
\(948\) 0 0
\(949\) −2480.00 −0.0848306
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 5940.00 0.201905 0.100953 − 0.994891i \(-0.467811\pi\)
0.100953 + 0.994891i \(0.467811\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 38928.0 1.31697
\(957\) 0 0
\(958\) 0 0
\(959\) 6888.00 0.231934
\(960\) 0 0
\(961\) −8475.00 −0.284482
\(962\) 0 0
\(963\) 0 0
\(964\) 16400.0 0.547934
\(965\) 0 0
\(966\) 0 0
\(967\) −47216.0 −1.57018 −0.785090 − 0.619382i \(-0.787383\pi\)
−0.785090 + 0.619382i \(0.787383\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −12552.0 −0.414843 −0.207422 − 0.978252i \(-0.566507\pi\)
−0.207422 + 0.978252i \(0.566507\pi\)
\(972\) 0 0
\(973\) 2758.00 0.0908709
\(974\) 0 0
\(975\) 0 0
\(976\) −43648.0 −1.43149
\(977\) 46908.0 1.53605 0.768025 − 0.640420i \(-0.221240\pi\)
0.768025 + 0.640420i \(0.221240\pi\)
\(978\) 0 0
\(979\) −43596.0 −1.42322
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −46128.0 −1.49670 −0.748349 − 0.663305i \(-0.769153\pi\)
−0.748349 + 0.663305i \(0.769153\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 6080.00 0.195780
\(989\) −240.000 −0.00771644
\(990\) 0 0
\(991\) −12184.0 −0.390552 −0.195276 − 0.980748i \(-0.562560\pi\)
−0.195276 + 0.980748i \(0.562560\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 5164.00 0.164038 0.0820188 − 0.996631i \(-0.473863\pi\)
0.0820188 + 0.996631i \(0.473863\pi\)
\(998\) 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 1575.4.a.f.1.1 1
3.2 odd 2 525.4.a.e.1.1 1
5.4 even 2 315.4.a.d.1.1 1
15.2 even 4 525.4.d.f.274.1 2
15.8 even 4 525.4.d.f.274.2 2
15.14 odd 2 105.4.a.a.1.1 ✓ 1
35.34 odd 2 2205.4.a.o.1.1 1
60.59 even 2 1680.4.a.s.1.1 1
105.104 even 2 735.4.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.a.a.1.1 ✓ 1 15.14 odd 2
315.4.a.d.1.1 1 5.4 even 2
525.4.a.e.1.1 1 3.2 odd 2
525.4.d.f.274.1 2 15.2 even 4
525.4.d.f.274.2 2 15.8 even 4
735.4.a.c.1.1 1 105.104 even 2
1575.4.a.f.1.1 1 1.1 even 1 trivial
1680.4.a.s.1.1 1 60.59 even 2
2205.4.a.o.1.1 1 35.34 odd 2