Properties

Label 2200.4.a.f.1.1
Level $2200$
Weight $4$
Character 2200.1
Self dual yes
Analytic conductor $129.804$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2200,4,Mod(1,2200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("2200.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2200.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: \(129.804202013\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 88)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2200.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{3} +6.00000 q^{7} -26.0000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +6.00000 q^{7} -26.0000 q^{9} -11.0000 q^{11} +40.0000 q^{13} +78.0000 q^{17} +36.0000 q^{19} +6.00000 q^{21} -7.00000 q^{23} -53.0000 q^{27} +8.00000 q^{29} +183.000 q^{31} -11.0000 q^{33} -227.000 q^{37} +40.0000 q^{39} -36.0000 q^{41} -322.000 q^{43} +184.000 q^{47} -307.000 q^{49} +78.0000 q^{51} +6.00000 q^{53} +36.0000 q^{57} -99.0000 q^{59} +164.000 q^{61} -156.000 q^{63} +695.000 q^{67} -7.00000 q^{69} -987.000 q^{71} +248.000 q^{73} -66.0000 q^{77} -242.000 q^{79} +649.000 q^{81} +1494.00 q^{83} +8.00000 q^{87} -905.000 q^{89} +240.000 q^{91} +183.000 q^{93} +1031.00 q^{97} +286.000 q^{99} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.192450 0.0962250 0.995360i \(-0.469323\pi\)
0.0962250 + 0.995360i \(0.469323\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 6.00000 0.323970 0.161985 0.986793i \(-0.448210\pi\)
0.161985 + 0.986793i \(0.448210\pi\)
\(8\) 0 0
\(9\) −26.0000 −0.962963
\(10\) 0 0
\(11\) −11.0000 −0.301511
\(12\) 0 0
\(13\) 40.0000 0.853385 0.426692 0.904397i \(-0.359679\pi\)
0.426692 + 0.904397i \(0.359679\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 78.0000 1.11281 0.556405 0.830911i \(-0.312180\pi\)
0.556405 + 0.830911i \(0.312180\pi\)
\(18\) 0 0
\(19\) 36.0000 0.434682 0.217341 0.976096i \(-0.430262\pi\)
0.217341 + 0.976096i \(0.430262\pi\)
\(20\) 0 0
\(21\) 6.00000 0.0623480
\(22\) 0 0
\(23\) −7.00000 −0.0634609 −0.0317305 0.999496i \(-0.510102\pi\)
−0.0317305 + 0.999496i \(0.510102\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −53.0000 −0.377772
\(28\) 0 0
\(29\) 8.00000 0.0512263 0.0256132 0.999672i \(-0.491846\pi\)
0.0256132 + 0.999672i \(0.491846\pi\)
\(30\) 0 0
\(31\) 183.000 1.06025 0.530125 0.847919i \(-0.322145\pi\)
0.530125 + 0.847919i \(0.322145\pi\)
\(32\) 0 0
\(33\) −11.0000 −0.0580259
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −227.000 −1.00861 −0.504305 0.863526i \(-0.668251\pi\)
−0.504305 + 0.863526i \(0.668251\pi\)
\(38\) 0 0
\(39\) 40.0000 0.164234
\(40\) 0 0
\(41\) −36.0000 −0.137128 −0.0685641 0.997647i \(-0.521842\pi\)
−0.0685641 + 0.997647i \(0.521842\pi\)
\(42\) 0 0
\(43\) −322.000 −1.14197 −0.570983 0.820962i \(-0.693438\pi\)
−0.570983 + 0.820962i \(0.693438\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 184.000 0.571046 0.285523 0.958372i \(-0.407833\pi\)
0.285523 + 0.958372i \(0.407833\pi\)
\(48\) 0 0
\(49\) −307.000 −0.895044
\(50\) 0 0
\(51\) 78.0000 0.214160
\(52\) 0 0
\(53\) 6.00000 0.0155503 0.00777513 0.999970i \(-0.497525\pi\)
0.00777513 + 0.999970i \(0.497525\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 36.0000 0.0836547
\(58\) 0 0
\(59\) −99.0000 −0.218453 −0.109226 0.994017i \(-0.534837\pi\)
−0.109226 + 0.994017i \(0.534837\pi\)
\(60\) 0 0
\(61\) 164.000 0.344230 0.172115 0.985077i \(-0.444940\pi\)
0.172115 + 0.985077i \(0.444940\pi\)
\(62\) 0 0
\(63\) −156.000 −0.311971
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 695.000 1.26728 0.633640 0.773628i \(-0.281560\pi\)
0.633640 + 0.773628i \(0.281560\pi\)
\(68\) 0 0
\(69\) −7.00000 −0.0122131
\(70\) 0 0
\(71\) −987.000 −1.64979 −0.824897 0.565283i \(-0.808767\pi\)
−0.824897 + 0.565283i \(0.808767\pi\)
\(72\) 0 0
\(73\) 248.000 0.397619 0.198810 0.980038i \(-0.436292\pi\)
0.198810 + 0.980038i \(0.436292\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −66.0000 −0.0976805
\(78\) 0 0
\(79\) −242.000 −0.344647 −0.172324 0.985040i \(-0.555127\pi\)
−0.172324 + 0.985040i \(0.555127\pi\)
\(80\) 0 0
\(81\) 649.000 0.890261
\(82\) 0 0
\(83\) 1494.00 1.97576 0.987878 0.155230i \(-0.0496119\pi\)
0.987878 + 0.155230i \(0.0496119\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 8.00000 0.00985851
\(88\) 0 0
\(89\) −905.000 −1.07786 −0.538932 0.842350i \(-0.681172\pi\)
−0.538932 + 0.842350i \(0.681172\pi\)
\(90\) 0 0
\(91\) 240.000 0.276471
\(92\) 0 0
\(93\) 183.000 0.204045
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1031.00 1.07920 0.539599 0.841922i \(-0.318576\pi\)
0.539599 + 0.841922i \(0.318576\pi\)
\(98\) 0 0
\(99\) 286.000 0.290344
\(100\) 0 0
\(101\) 630.000 0.620667 0.310333 0.950628i \(-0.399559\pi\)
0.310333 + 0.950628i \(0.399559\pi\)
\(102\) 0 0
\(103\) −1328.00 −1.27041 −0.635203 0.772346i \(-0.719083\pi\)
−0.635203 + 0.772346i \(0.719083\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −526.000 −0.475237 −0.237618 0.971359i \(-0.576367\pi\)
−0.237618 + 0.971359i \(0.576367\pi\)
\(108\) 0 0
\(109\) 2234.00 1.96310 0.981552 0.191194i \(-0.0612360\pi\)
0.981552 + 0.191194i \(0.0612360\pi\)
\(110\) 0 0
\(111\) −227.000 −0.194107
\(112\) 0 0
\(113\) 1239.00 1.03146 0.515731 0.856750i \(-0.327520\pi\)
0.515731 + 0.856750i \(0.327520\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1040.00 −0.821778
\(118\) 0 0
\(119\) 468.000 0.360517
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) −36.0000 −0.0263903
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −132.000 −0.0922292 −0.0461146 0.998936i \(-0.514684\pi\)
−0.0461146 + 0.998936i \(0.514684\pi\)
\(128\) 0 0
\(129\) −322.000 −0.219771
\(130\) 0 0
\(131\) 1218.00 0.812345 0.406172 0.913796i \(-0.366863\pi\)
0.406172 + 0.913796i \(0.366863\pi\)
\(132\) 0 0
\(133\) 216.000 0.140824
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2775.00 1.73054 0.865271 0.501304i \(-0.167146\pi\)
0.865271 + 0.501304i \(0.167146\pi\)
\(138\) 0 0
\(139\) 1222.00 0.745674 0.372837 0.927897i \(-0.378385\pi\)
0.372837 + 0.927897i \(0.378385\pi\)
\(140\) 0 0
\(141\) 184.000 0.109898
\(142\) 0 0
\(143\) −440.000 −0.257305
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −307.000 −0.172251
\(148\) 0 0
\(149\) −1038.00 −0.570713 −0.285357 0.958421i \(-0.592112\pi\)
−0.285357 + 0.958421i \(0.592112\pi\)
\(150\) 0 0
\(151\) 3042.00 1.63943 0.819717 0.572769i \(-0.194131\pi\)
0.819717 + 0.572769i \(0.194131\pi\)
\(152\) 0 0
\(153\) −2028.00 −1.07160
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1943.00 0.987696 0.493848 0.869548i \(-0.335590\pi\)
0.493848 + 0.869548i \(0.335590\pi\)
\(158\) 0 0
\(159\) 6.00000 0.00299265
\(160\) 0 0
\(161\) −42.0000 −0.0205594
\(162\) 0 0
\(163\) −2292.00 −1.10137 −0.550685 0.834713i \(-0.685633\pi\)
−0.550685 + 0.834713i \(0.685633\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3832.00 1.77562 0.887812 0.460207i \(-0.152225\pi\)
0.887812 + 0.460207i \(0.152225\pi\)
\(168\) 0 0
\(169\) −597.000 −0.271734
\(170\) 0 0
\(171\) −936.000 −0.418583
\(172\) 0 0
\(173\) 1734.00 0.762044 0.381022 0.924566i \(-0.375572\pi\)
0.381022 + 0.924566i \(0.375572\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −99.0000 −0.0420412
\(178\) 0 0
\(179\) −2295.00 −0.958304 −0.479152 0.877732i \(-0.659056\pi\)
−0.479152 + 0.877732i \(0.659056\pi\)
\(180\) 0 0
\(181\) −2865.00 −1.17654 −0.588270 0.808665i \(-0.700191\pi\)
−0.588270 + 0.808665i \(0.700191\pi\)
\(182\) 0 0
\(183\) 164.000 0.0662472
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −858.000 −0.335525
\(188\) 0 0
\(189\) −318.000 −0.122387
\(190\) 0 0
\(191\) 2441.00 0.924736 0.462368 0.886688i \(-0.347000\pi\)
0.462368 + 0.886688i \(0.347000\pi\)
\(192\) 0 0
\(193\) 1532.00 0.571377 0.285689 0.958323i \(-0.407778\pi\)
0.285689 + 0.958323i \(0.407778\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2958.00 −1.06979 −0.534895 0.844918i \(-0.679649\pi\)
−0.534895 + 0.844918i \(0.679649\pi\)
\(198\) 0 0
\(199\) −2968.00 −1.05727 −0.528633 0.848850i \(-0.677295\pi\)
−0.528633 + 0.848850i \(0.677295\pi\)
\(200\) 0 0
\(201\) 695.000 0.243888
\(202\) 0 0
\(203\) 48.0000 0.0165958
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 182.000 0.0611105
\(208\) 0 0
\(209\) −396.000 −0.131062
\(210\) 0 0
\(211\) 60.0000 0.0195762 0.00978808 0.999952i \(-0.496884\pi\)
0.00978808 + 0.999952i \(0.496884\pi\)
\(212\) 0 0
\(213\) −987.000 −0.317503
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 1098.00 0.343489
\(218\) 0 0
\(219\) 248.000 0.0765219
\(220\) 0 0
\(221\) 3120.00 0.949656
\(222\) 0 0
\(223\) −723.000 −0.217111 −0.108555 0.994090i \(-0.534622\pi\)
−0.108555 + 0.994090i \(0.534622\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4466.00 1.30581 0.652905 0.757440i \(-0.273550\pi\)
0.652905 + 0.757440i \(0.273550\pi\)
\(228\) 0 0
\(229\) −4609.00 −1.33001 −0.665003 0.746841i \(-0.731570\pi\)
−0.665003 + 0.746841i \(0.731570\pi\)
\(230\) 0 0
\(231\) −66.0000 −0.0187986
\(232\) 0 0
\(233\) −4768.00 −1.34061 −0.670305 0.742086i \(-0.733837\pi\)
−0.670305 + 0.742086i \(0.733837\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −242.000 −0.0663274
\(238\) 0 0
\(239\) 4802.00 1.29965 0.649823 0.760085i \(-0.274843\pi\)
0.649823 + 0.760085i \(0.274843\pi\)
\(240\) 0 0
\(241\) 3920.00 1.04776 0.523878 0.851793i \(-0.324485\pi\)
0.523878 + 0.851793i \(0.324485\pi\)
\(242\) 0 0
\(243\) 2080.00 0.549103
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1440.00 0.370951
\(248\) 0 0
\(249\) 1494.00 0.380235
\(250\) 0 0
\(251\) 6057.00 1.52317 0.761583 0.648068i \(-0.224423\pi\)
0.761583 + 0.648068i \(0.224423\pi\)
\(252\) 0 0
\(253\) 77.0000 0.0191342
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3270.00 −0.793685 −0.396842 0.917887i \(-0.629894\pi\)
−0.396842 + 0.917887i \(0.629894\pi\)
\(258\) 0 0
\(259\) −1362.00 −0.326759
\(260\) 0 0
\(261\) −208.000 −0.0493290
\(262\) 0 0
\(263\) 6102.00 1.43067 0.715334 0.698783i \(-0.246275\pi\)
0.715334 + 0.698783i \(0.246275\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −905.000 −0.207435
\(268\) 0 0
\(269\) −1166.00 −0.264284 −0.132142 0.991231i \(-0.542185\pi\)
−0.132142 + 0.991231i \(0.542185\pi\)
\(270\) 0 0
\(271\) 6680.00 1.49735 0.748674 0.662939i \(-0.230691\pi\)
0.748674 + 0.662939i \(0.230691\pi\)
\(272\) 0 0
\(273\) 240.000 0.0532068
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1014.00 −0.219947 −0.109974 0.993935i \(-0.535077\pi\)
−0.109974 + 0.993935i \(0.535077\pi\)
\(278\) 0 0
\(279\) −4758.00 −1.02098
\(280\) 0 0
\(281\) 8326.00 1.76757 0.883786 0.467892i \(-0.154986\pi\)
0.883786 + 0.467892i \(0.154986\pi\)
\(282\) 0 0
\(283\) −1308.00 −0.274744 −0.137372 0.990520i \(-0.543866\pi\)
−0.137372 + 0.990520i \(0.543866\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −216.000 −0.0444254
\(288\) 0 0
\(289\) 1171.00 0.238347
\(290\) 0 0
\(291\) 1031.00 0.207692
\(292\) 0 0
\(293\) 3516.00 0.701047 0.350524 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 583.000 0.113903
\(298\) 0 0
\(299\) −280.000 −0.0541566
\(300\) 0 0
\(301\) −1932.00 −0.369962
\(302\) 0 0
\(303\) 630.000 0.119447
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 9652.00 1.79436 0.897180 0.441664i \(-0.145612\pi\)
0.897180 + 0.441664i \(0.145612\pi\)
\(308\) 0 0
\(309\) −1328.00 −0.244490
\(310\) 0 0
\(311\) −852.000 −0.155346 −0.0776728 0.996979i \(-0.524749\pi\)
−0.0776728 + 0.996979i \(0.524749\pi\)
\(312\) 0 0
\(313\) 3313.00 0.598281 0.299140 0.954209i \(-0.403300\pi\)
0.299140 + 0.954209i \(0.403300\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3035.00 0.537737 0.268868 0.963177i \(-0.413350\pi\)
0.268868 + 0.963177i \(0.413350\pi\)
\(318\) 0 0
\(319\) −88.0000 −0.0154453
\(320\) 0 0
\(321\) −526.000 −0.0914594
\(322\) 0 0
\(323\) 2808.00 0.483719
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 2234.00 0.377800
\(328\) 0 0
\(329\) 1104.00 0.185001
\(330\) 0 0
\(331\) 1655.00 0.274825 0.137412 0.990514i \(-0.456121\pi\)
0.137412 + 0.990514i \(0.456121\pi\)
\(332\) 0 0
\(333\) 5902.00 0.971254
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 6130.00 0.990868 0.495434 0.868646i \(-0.335009\pi\)
0.495434 + 0.868646i \(0.335009\pi\)
\(338\) 0 0
\(339\) 1239.00 0.198505
\(340\) 0 0
\(341\) −2013.00 −0.319678
\(342\) 0 0
\(343\) −3900.00 −0.613936
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 696.000 0.107675 0.0538375 0.998550i \(-0.482855\pi\)
0.0538375 + 0.998550i \(0.482855\pi\)
\(348\) 0 0
\(349\) −12526.0 −1.92121 −0.960604 0.277922i \(-0.910354\pi\)
−0.960604 + 0.277922i \(0.910354\pi\)
\(350\) 0 0
\(351\) −2120.00 −0.322385
\(352\) 0 0
\(353\) −7411.00 −1.11742 −0.558708 0.829365i \(-0.688703\pi\)
−0.558708 + 0.829365i \(0.688703\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 468.000 0.0693815
\(358\) 0 0
\(359\) 4096.00 0.602169 0.301084 0.953597i \(-0.402651\pi\)
0.301084 + 0.953597i \(0.402651\pi\)
\(360\) 0 0
\(361\) −5563.00 −0.811051
\(362\) 0 0
\(363\) 121.000 0.0174955
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 6721.00 0.955949 0.477975 0.878374i \(-0.341371\pi\)
0.477975 + 0.878374i \(0.341371\pi\)
\(368\) 0 0
\(369\) 936.000 0.132049
\(370\) 0 0
\(371\) 36.0000 0.00503781
\(372\) 0 0
\(373\) 6854.00 0.951439 0.475719 0.879597i \(-0.342188\pi\)
0.475719 + 0.879597i \(0.342188\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 320.000 0.0437158
\(378\) 0 0
\(379\) 12155.0 1.64739 0.823694 0.567034i \(-0.191909\pi\)
0.823694 + 0.567034i \(0.191909\pi\)
\(380\) 0 0
\(381\) −132.000 −0.0177495
\(382\) 0 0
\(383\) −10447.0 −1.39378 −0.696889 0.717179i \(-0.745433\pi\)
−0.696889 + 0.717179i \(0.745433\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 8372.00 1.09967
\(388\) 0 0
\(389\) −7863.00 −1.02486 −0.512429 0.858729i \(-0.671254\pi\)
−0.512429 + 0.858729i \(0.671254\pi\)
\(390\) 0 0
\(391\) −546.000 −0.0706200
\(392\) 0 0
\(393\) 1218.00 0.156336
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −6142.00 −0.776469 −0.388234 0.921561i \(-0.626915\pi\)
−0.388234 + 0.921561i \(0.626915\pi\)
\(398\) 0 0
\(399\) 216.000 0.0271016
\(400\) 0 0
\(401\) 12074.0 1.50361 0.751804 0.659387i \(-0.229184\pi\)
0.751804 + 0.659387i \(0.229184\pi\)
\(402\) 0 0
\(403\) 7320.00 0.904802
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2497.00 0.304107
\(408\) 0 0
\(409\) −1454.00 −0.175784 −0.0878920 0.996130i \(-0.528013\pi\)
−0.0878920 + 0.996130i \(0.528013\pi\)
\(410\) 0 0
\(411\) 2775.00 0.333043
\(412\) 0 0
\(413\) −594.000 −0.0707720
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1222.00 0.143505
\(418\) 0 0
\(419\) 5308.00 0.618885 0.309442 0.950918i \(-0.399858\pi\)
0.309442 + 0.950918i \(0.399858\pi\)
\(420\) 0 0
\(421\) 13030.0 1.50842 0.754208 0.656635i \(-0.228021\pi\)
0.754208 + 0.656635i \(0.228021\pi\)
\(422\) 0 0
\(423\) −4784.00 −0.549896
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 984.000 0.111520
\(428\) 0 0
\(429\) −440.000 −0.0495184
\(430\) 0 0
\(431\) 2194.00 0.245200 0.122600 0.992456i \(-0.460877\pi\)
0.122600 + 0.992456i \(0.460877\pi\)
\(432\) 0 0
\(433\) 5459.00 0.605873 0.302936 0.953011i \(-0.402033\pi\)
0.302936 + 0.953011i \(0.402033\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −252.000 −0.0275853
\(438\) 0 0
\(439\) −12208.0 −1.32723 −0.663617 0.748072i \(-0.730980\pi\)
−0.663617 + 0.748072i \(0.730980\pi\)
\(440\) 0 0
\(441\) 7982.00 0.861894
\(442\) 0 0
\(443\) −10997.0 −1.17942 −0.589710 0.807615i \(-0.700758\pi\)
−0.589710 + 0.807615i \(0.700758\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −1038.00 −0.109834
\(448\) 0 0
\(449\) 891.000 0.0936501 0.0468250 0.998903i \(-0.485090\pi\)
0.0468250 + 0.998903i \(0.485090\pi\)
\(450\) 0 0
\(451\) 396.000 0.0413457
\(452\) 0 0
\(453\) 3042.00 0.315509
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −10396.0 −1.06412 −0.532062 0.846706i \(-0.678583\pi\)
−0.532062 + 0.846706i \(0.678583\pi\)
\(458\) 0 0
\(459\) −4134.00 −0.420389
\(460\) 0 0
\(461\) −3708.00 −0.374618 −0.187309 0.982301i \(-0.559977\pi\)
−0.187309 + 0.982301i \(0.559977\pi\)
\(462\) 0 0
\(463\) 2651.00 0.266096 0.133048 0.991110i \(-0.457524\pi\)
0.133048 + 0.991110i \(0.457524\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1061.00 −0.105133 −0.0525666 0.998617i \(-0.516740\pi\)
−0.0525666 + 0.998617i \(0.516740\pi\)
\(468\) 0 0
\(469\) 4170.00 0.410560
\(470\) 0 0
\(471\) 1943.00 0.190082
\(472\) 0 0
\(473\) 3542.00 0.344316
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −156.000 −0.0149743
\(478\) 0 0
\(479\) 6752.00 0.644064 0.322032 0.946729i \(-0.395634\pi\)
0.322032 + 0.946729i \(0.395634\pi\)
\(480\) 0 0
\(481\) −9080.00 −0.860733
\(482\) 0 0
\(483\) −42.0000 −0.00395666
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 13073.0 1.21642 0.608208 0.793778i \(-0.291889\pi\)
0.608208 + 0.793778i \(0.291889\pi\)
\(488\) 0 0
\(489\) −2292.00 −0.211959
\(490\) 0 0
\(491\) −4072.00 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(492\) 0 0
\(493\) 624.000 0.0570052
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5922.00 −0.534483
\(498\) 0 0
\(499\) −16060.0 −1.44077 −0.720385 0.693574i \(-0.756035\pi\)
−0.720385 + 0.693574i \(0.756035\pi\)
\(500\) 0 0
\(501\) 3832.00 0.341719
\(502\) 0 0
\(503\) 7650.00 0.678125 0.339062 0.940764i \(-0.389890\pi\)
0.339062 + 0.940764i \(0.389890\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −597.000 −0.0522953
\(508\) 0 0
\(509\) −3777.00 −0.328905 −0.164452 0.986385i \(-0.552586\pi\)
−0.164452 + 0.986385i \(0.552586\pi\)
\(510\) 0 0
\(511\) 1488.00 0.128817
\(512\) 0 0
\(513\) −1908.00 −0.164211
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −2024.00 −0.172177
\(518\) 0 0
\(519\) 1734.00 0.146655
\(520\) 0 0
\(521\) −10883.0 −0.915149 −0.457575 0.889171i \(-0.651282\pi\)
−0.457575 + 0.889171i \(0.651282\pi\)
\(522\) 0 0
\(523\) −12748.0 −1.06583 −0.532917 0.846168i \(-0.678904\pi\)
−0.532917 + 0.846168i \(0.678904\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14274.0 1.17986
\(528\) 0 0
\(529\) −12118.0 −0.995973
\(530\) 0 0
\(531\) 2574.00 0.210362
\(532\) 0 0
\(533\) −1440.00 −0.117023
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −2295.00 −0.184426
\(538\) 0 0
\(539\) 3377.00 0.269866
\(540\) 0 0
\(541\) 23012.0 1.82877 0.914384 0.404849i \(-0.132676\pi\)
0.914384 + 0.404849i \(0.132676\pi\)
\(542\) 0 0
\(543\) −2865.00 −0.226425
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 8400.00 0.656596 0.328298 0.944574i \(-0.393525\pi\)
0.328298 + 0.944574i \(0.393525\pi\)
\(548\) 0 0
\(549\) −4264.00 −0.331481
\(550\) 0 0
\(551\) 288.000 0.0222672
\(552\) 0 0
\(553\) −1452.00 −0.111655
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2426.00 −0.184547 −0.0922737 0.995734i \(-0.529413\pi\)
−0.0922737 + 0.995734i \(0.529413\pi\)
\(558\) 0 0
\(559\) −12880.0 −0.974537
\(560\) 0 0
\(561\) −858.000 −0.0645718
\(562\) 0 0
\(563\) 14484.0 1.08424 0.542121 0.840301i \(-0.317622\pi\)
0.542121 + 0.840301i \(0.317622\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 3894.00 0.288417
\(568\) 0 0
\(569\) 1784.00 0.131440 0.0657198 0.997838i \(-0.479066\pi\)
0.0657198 + 0.997838i \(0.479066\pi\)
\(570\) 0 0
\(571\) −3564.00 −0.261206 −0.130603 0.991435i \(-0.541691\pi\)
−0.130603 + 0.991435i \(0.541691\pi\)
\(572\) 0 0
\(573\) 2441.00 0.177966
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1081.00 −0.0779941 −0.0389971 0.999239i \(-0.512416\pi\)
−0.0389971 + 0.999239i \(0.512416\pi\)
\(578\) 0 0
\(579\) 1532.00 0.109962
\(580\) 0 0
\(581\) 8964.00 0.640085
\(582\) 0 0
\(583\) −66.0000 −0.00468858
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9324.00 0.655609 0.327805 0.944746i \(-0.393691\pi\)
0.327805 + 0.944746i \(0.393691\pi\)
\(588\) 0 0
\(589\) 6588.00 0.460872
\(590\) 0 0
\(591\) −2958.00 −0.205881
\(592\) 0 0
\(593\) 8548.00 0.591947 0.295973 0.955196i \(-0.404356\pi\)
0.295973 + 0.955196i \(0.404356\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2968.00 −0.203471
\(598\) 0 0
\(599\) 4512.00 0.307772 0.153886 0.988089i \(-0.450821\pi\)
0.153886 + 0.988089i \(0.450821\pi\)
\(600\) 0 0
\(601\) −14242.0 −0.966628 −0.483314 0.875447i \(-0.660567\pi\)
−0.483314 + 0.875447i \(0.660567\pi\)
\(602\) 0 0
\(603\) −18070.0 −1.22034
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −24386.0 −1.63064 −0.815319 0.579012i \(-0.803438\pi\)
−0.815319 + 0.579012i \(0.803438\pi\)
\(608\) 0 0
\(609\) 48.0000 0.00319386
\(610\) 0 0
\(611\) 7360.00 0.487322
\(612\) 0 0
\(613\) −26608.0 −1.75316 −0.876580 0.481256i \(-0.840181\pi\)
−0.876580 + 0.481256i \(0.840181\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5246.00 0.342295 0.171147 0.985245i \(-0.445253\pi\)
0.171147 + 0.985245i \(0.445253\pi\)
\(618\) 0 0
\(619\) 20823.0 1.35210 0.676048 0.736858i \(-0.263691\pi\)
0.676048 + 0.736858i \(0.263691\pi\)
\(620\) 0 0
\(621\) 371.000 0.0239738
\(622\) 0 0
\(623\) −5430.00 −0.349195
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −396.000 −0.0252228
\(628\) 0 0
\(629\) −17706.0 −1.12239
\(630\) 0 0
\(631\) 29279.0 1.84719 0.923596 0.383366i \(-0.125235\pi\)
0.923596 + 0.383366i \(0.125235\pi\)
\(632\) 0 0
\(633\) 60.0000 0.00376743
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −12280.0 −0.763817
\(638\) 0 0
\(639\) 25662.0 1.58869
\(640\) 0 0
\(641\) −9209.00 −0.567447 −0.283724 0.958906i \(-0.591570\pi\)
−0.283724 + 0.958906i \(0.591570\pi\)
\(642\) 0 0
\(643\) 21331.0 1.30826 0.654131 0.756381i \(-0.273034\pi\)
0.654131 + 0.756381i \(0.273034\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 18135.0 1.10195 0.550974 0.834522i \(-0.314256\pi\)
0.550974 + 0.834522i \(0.314256\pi\)
\(648\) 0 0
\(649\) 1089.00 0.0658659
\(650\) 0 0
\(651\) 1098.00 0.0661045
\(652\) 0 0
\(653\) 3193.00 0.191350 0.0956751 0.995413i \(-0.469499\pi\)
0.0956751 + 0.995413i \(0.469499\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −6448.00 −0.382893
\(658\) 0 0
\(659\) 31778.0 1.87844 0.939222 0.343309i \(-0.111548\pi\)
0.939222 + 0.343309i \(0.111548\pi\)
\(660\) 0 0
\(661\) −14747.0 −0.867764 −0.433882 0.900970i \(-0.642856\pi\)
−0.433882 + 0.900970i \(0.642856\pi\)
\(662\) 0 0
\(663\) 3120.00 0.182761
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −56.0000 −0.00325087
\(668\) 0 0
\(669\) −723.000 −0.0417830
\(670\) 0 0
\(671\) −1804.00 −0.103789
\(672\) 0 0
\(673\) −62.0000 −0.00355115 −0.00177558 0.999998i \(-0.500565\pi\)
−0.00177558 + 0.999998i \(0.500565\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 12670.0 0.719273 0.359636 0.933093i \(-0.382901\pi\)
0.359636 + 0.933093i \(0.382901\pi\)
\(678\) 0 0
\(679\) 6186.00 0.349627
\(680\) 0 0
\(681\) 4466.00 0.251303
\(682\) 0 0
\(683\) −11816.0 −0.661972 −0.330986 0.943636i \(-0.607381\pi\)
−0.330986 + 0.943636i \(0.607381\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −4609.00 −0.255960
\(688\) 0 0
\(689\) 240.000 0.0132704
\(690\) 0 0
\(691\) 3441.00 0.189438 0.0947191 0.995504i \(-0.469805\pi\)
0.0947191 + 0.995504i \(0.469805\pi\)
\(692\) 0 0
\(693\) 1716.00 0.0940627
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −2808.00 −0.152598
\(698\) 0 0
\(699\) −4768.00 −0.258000
\(700\) 0 0
\(701\) −13690.0 −0.737609 −0.368805 0.929507i \(-0.620233\pi\)
−0.368805 + 0.929507i \(0.620233\pi\)
\(702\) 0 0
\(703\) −8172.00 −0.438425
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3780.00 0.201077
\(708\) 0 0
\(709\) 71.0000 0.00376088 0.00188044 0.999998i \(-0.499401\pi\)
0.00188044 + 0.999998i \(0.499401\pi\)
\(710\) 0 0
\(711\) 6292.00 0.331882
\(712\) 0 0
\(713\) −1281.00 −0.0672845
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 4802.00 0.250117
\(718\) 0 0
\(719\) 26503.0 1.37468 0.687340 0.726336i \(-0.258778\pi\)
0.687340 + 0.726336i \(0.258778\pi\)
\(720\) 0 0
\(721\) −7968.00 −0.411573
\(722\) 0 0
\(723\) 3920.00 0.201641
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 18165.0 0.926689 0.463344 0.886178i \(-0.346649\pi\)
0.463344 + 0.886178i \(0.346649\pi\)
\(728\) 0 0
\(729\) −15443.0 −0.784586
\(730\) 0 0
\(731\) −25116.0 −1.27079
\(732\) 0 0
\(733\) 572.000 0.0288231 0.0144115 0.999896i \(-0.495413\pi\)
0.0144115 + 0.999896i \(0.495413\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7645.00 −0.382099
\(738\) 0 0
\(739\) 17026.0 0.847512 0.423756 0.905776i \(-0.360711\pi\)
0.423756 + 0.905776i \(0.360711\pi\)
\(740\) 0 0
\(741\) 1440.00 0.0713896
\(742\) 0 0
\(743\) −1028.00 −0.0507586 −0.0253793 0.999678i \(-0.508079\pi\)
−0.0253793 + 0.999678i \(0.508079\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −38844.0 −1.90258
\(748\) 0 0
\(749\) −3156.00 −0.153962
\(750\) 0 0
\(751\) −37527.0 −1.82341 −0.911704 0.410847i \(-0.865233\pi\)
−0.911704 + 0.410847i \(0.865233\pi\)
\(752\) 0 0
\(753\) 6057.00 0.293133
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −29330.0 −1.40821 −0.704106 0.710095i \(-0.748652\pi\)
−0.704106 + 0.710095i \(0.748652\pi\)
\(758\) 0 0
\(759\) 77.0000 0.00368238
\(760\) 0 0
\(761\) −30520.0 −1.45381 −0.726905 0.686738i \(-0.759042\pi\)
−0.726905 + 0.686738i \(0.759042\pi\)
\(762\) 0 0
\(763\) 13404.0 0.635986
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3960.00 −0.186424
\(768\) 0 0
\(769\) −25816.0 −1.21060 −0.605298 0.795999i \(-0.706946\pi\)
−0.605298 + 0.795999i \(0.706946\pi\)
\(770\) 0 0
\(771\) −3270.00 −0.152745
\(772\) 0 0
\(773\) 37182.0 1.73007 0.865035 0.501712i \(-0.167296\pi\)
0.865035 + 0.501712i \(0.167296\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −1362.00 −0.0628848
\(778\) 0 0
\(779\) −1296.00 −0.0596072
\(780\) 0 0
\(781\) 10857.0 0.497432
\(782\) 0 0
\(783\) −424.000 −0.0193519
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 7848.00 0.355465 0.177733 0.984079i \(-0.443124\pi\)
0.177733 + 0.984079i \(0.443124\pi\)
\(788\) 0 0
\(789\) 6102.00 0.275332
\(790\) 0 0
\(791\) 7434.00 0.334163
\(792\) 0 0
\(793\) 6560.00 0.293761
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 6267.00 0.278530 0.139265 0.990255i \(-0.455526\pi\)
0.139265 + 0.990255i \(0.455526\pi\)
\(798\) 0 0
\(799\) 14352.0 0.635466
\(800\) 0 0
\(801\) 23530.0 1.03794
\(802\) 0 0
\(803\) −2728.00 −0.119887
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −1166.00 −0.0508614
\(808\) 0 0
\(809\) −10332.0 −0.449016 −0.224508 0.974472i \(-0.572077\pi\)
−0.224508 + 0.974472i \(0.572077\pi\)
\(810\) 0 0
\(811\) −24926.0 −1.07925 −0.539624 0.841906i \(-0.681434\pi\)
−0.539624 + 0.841906i \(0.681434\pi\)
\(812\) 0 0
\(813\) 6680.00 0.288165
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −11592.0 −0.496393
\(818\) 0 0
\(819\) −6240.00 −0.266231
\(820\) 0 0
\(821\) 11366.0 0.483162 0.241581 0.970381i \(-0.422334\pi\)
0.241581 + 0.970381i \(0.422334\pi\)
\(822\) 0 0
\(823\) 35337.0 1.49668 0.748342 0.663313i \(-0.230850\pi\)
0.748342 + 0.663313i \(0.230850\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 13128.0 0.552002 0.276001 0.961157i \(-0.410991\pi\)
0.276001 + 0.961157i \(0.410991\pi\)
\(828\) 0 0
\(829\) 25185.0 1.05514 0.527570 0.849512i \(-0.323103\pi\)
0.527570 + 0.849512i \(0.323103\pi\)
\(830\) 0 0
\(831\) −1014.00 −0.0423288
\(832\) 0 0
\(833\) −23946.0 −0.996014
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −9699.00 −0.400533
\(838\) 0 0
\(839\) −37821.0 −1.55629 −0.778144 0.628086i \(-0.783839\pi\)
−0.778144 + 0.628086i \(0.783839\pi\)
\(840\) 0 0
\(841\) −24325.0 −0.997376
\(842\) 0 0
\(843\) 8326.00 0.340169
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 726.000 0.0294518
\(848\) 0 0
\(849\) −1308.00 −0.0528745
\(850\) 0 0
\(851\) 1589.00 0.0640073
\(852\) 0 0
\(853\) −6638.00 −0.266449 −0.133224 0.991086i \(-0.542533\pi\)
−0.133224 + 0.991086i \(0.542533\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −42408.0 −1.69035 −0.845175 0.534490i \(-0.820504\pi\)
−0.845175 + 0.534490i \(0.820504\pi\)
\(858\) 0 0
\(859\) −16591.0 −0.658996 −0.329498 0.944156i \(-0.606880\pi\)
−0.329498 + 0.944156i \(0.606880\pi\)
\(860\) 0 0
\(861\) −216.000 −0.00854966
\(862\) 0 0
\(863\) −8128.00 −0.320603 −0.160301 0.987068i \(-0.551247\pi\)
−0.160301 + 0.987068i \(0.551247\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 1171.00 0.0458699
\(868\) 0 0
\(869\) 2662.00 0.103915
\(870\) 0 0
\(871\) 27800.0 1.08148
\(872\) 0 0
\(873\) −26806.0 −1.03923
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −32128.0 −1.23704 −0.618521 0.785768i \(-0.712268\pi\)
−0.618521 + 0.785768i \(0.712268\pi\)
\(878\) 0 0
\(879\) 3516.00 0.134917
\(880\) 0 0
\(881\) −25619.0 −0.979712 −0.489856 0.871803i \(-0.662951\pi\)
−0.489856 + 0.871803i \(0.662951\pi\)
\(882\) 0 0
\(883\) −50044.0 −1.90726 −0.953632 0.300974i \(-0.902688\pi\)
−0.953632 + 0.300974i \(0.902688\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −39938.0 −1.51182 −0.755911 0.654674i \(-0.772806\pi\)
−0.755911 + 0.654674i \(0.772806\pi\)
\(888\) 0 0
\(889\) −792.000 −0.0298794
\(890\) 0 0
\(891\) −7139.00 −0.268424
\(892\) 0 0
\(893\) 6624.00 0.248224
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −280.000 −0.0104224
\(898\) 0 0
\(899\) 1464.00 0.0543127
\(900\) 0 0
\(901\) 468.000 0.0173045
\(902\) 0 0
\(903\) −1932.00 −0.0711993
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 49196.0 1.80102 0.900511 0.434834i \(-0.143193\pi\)
0.900511 + 0.434834i \(0.143193\pi\)
\(908\) 0 0
\(909\) −16380.0 −0.597679
\(910\) 0 0
\(911\) −32644.0 −1.18721 −0.593603 0.804758i \(-0.702295\pi\)
−0.593603 + 0.804758i \(0.702295\pi\)
\(912\) 0 0
\(913\) −16434.0 −0.595713
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 7308.00 0.263175
\(918\) 0 0
\(919\) 24370.0 0.874747 0.437373 0.899280i \(-0.355909\pi\)
0.437373 + 0.899280i \(0.355909\pi\)
\(920\) 0 0
\(921\) 9652.00 0.345325
\(922\) 0 0
\(923\) −39480.0 −1.40791
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 34528.0 1.22335
\(928\) 0 0
\(929\) 2202.00 0.0777667 0.0388834 0.999244i \(-0.487620\pi\)
0.0388834 + 0.999244i \(0.487620\pi\)
\(930\) 0 0
\(931\) −11052.0 −0.389060
\(932\) 0 0
\(933\) −852.000 −0.0298963
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −28092.0 −0.979430 −0.489715 0.871883i \(-0.662899\pi\)
−0.489715 + 0.871883i \(0.662899\pi\)
\(938\) 0 0
\(939\) 3313.00 0.115139
\(940\) 0 0
\(941\) −31070.0 −1.07636 −0.538179 0.842831i \(-0.680888\pi\)
−0.538179 + 0.842831i \(0.680888\pi\)
\(942\) 0 0
\(943\) 252.000 0.00870228
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −33461.0 −1.14819 −0.574095 0.818789i \(-0.694646\pi\)
−0.574095 + 0.818789i \(0.694646\pi\)
\(948\) 0 0
\(949\) 9920.00 0.339322
\(950\) 0 0
\(951\) 3035.00 0.103488
\(952\) 0 0
\(953\) −21702.0 −0.737667 −0.368834 0.929495i \(-0.620243\pi\)
−0.368834 + 0.929495i \(0.620243\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −88.0000 −0.00297245
\(958\) 0 0
\(959\) 16650.0 0.560643
\(960\) 0 0
\(961\) 3698.00 0.124131
\(962\) 0 0
\(963\) 13676.0 0.457635
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 8744.00 0.290784 0.145392 0.989374i \(-0.453556\pi\)
0.145392 + 0.989374i \(0.453556\pi\)
\(968\) 0 0
\(969\) 2808.00 0.0930918
\(970\) 0 0
\(971\) 18303.0 0.604914 0.302457 0.953163i \(-0.402193\pi\)
0.302457 + 0.953163i \(0.402193\pi\)
\(972\) 0 0
\(973\) 7332.00 0.241576
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −34917.0 −1.14339 −0.571696 0.820466i \(-0.693714\pi\)
−0.571696 + 0.820466i \(0.693714\pi\)
\(978\) 0 0
\(979\) 9955.00 0.324988
\(980\) 0 0
\(981\) −58084.0 −1.89040
\(982\) 0 0
\(983\) −31375.0 −1.01801 −0.509007 0.860763i \(-0.669987\pi\)
−0.509007 + 0.860763i \(0.669987\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 1104.00 0.0356036
\(988\) 0 0
\(989\) 2254.00 0.0724702
\(990\) 0 0
\(991\) −28064.0 −0.899579 −0.449789 0.893135i \(-0.648501\pi\)
−0.449789 + 0.893135i \(0.648501\pi\)
\(992\) 0 0
\(993\) 1655.00 0.0528901
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 25534.0 0.811103 0.405552 0.914072i \(-0.367079\pi\)
0.405552 + 0.914072i \(0.367079\pi\)
\(998\) 0 0
\(999\) 12031.0 0.381025
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 2200.4.a.f.1.1 1
5.4 even 2 88.4.a.a.1.1 1
15.14 odd 2 792.4.a.e.1.1 1
20.19 odd 2 176.4.a.d.1.1 1
40.19 odd 2 704.4.a.f.1.1 1
40.29 even 2 704.4.a.h.1.1 1
55.54 odd 2 968.4.a.d.1.1 1
60.59 even 2 1584.4.a.o.1.1 1
220.219 even 2 1936.4.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
88.4.a.a.1.1 1 5.4 even 2
176.4.a.d.1.1 1 20.19 odd 2
704.4.a.f.1.1 1 40.19 odd 2
704.4.a.h.1.1 1 40.29 even 2
792.4.a.e.1.1 1 15.14 odd 2
968.4.a.d.1.1 1 55.54 odd 2
1584.4.a.o.1.1 1 60.59 even 2
1936.4.a.i.1.1 1 220.219 even 2
2200.4.a.f.1.1 1 1.1 even 1 trivial