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Properties

Label 2160.4.a.i.1.1
Level $2160$
Weight $4$
Character 2160.1
Self dual yes
Analytic conductor $127.444$
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] = [2160,4,Mod(1,2160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2160, 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("2160.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2160.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: \(127.444125612\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 270)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2160.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{5} +22.0000 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} +22.0000 q^{7} +12.0000 q^{11} +38.0000 q^{13} -105.000 q^{17} +157.000 q^{19} +117.000 q^{23} +25.0000 q^{25} +66.0000 q^{29} +25.0000 q^{31} -110.000 q^{35} +314.000 q^{37} -504.000 q^{41} -380.000 q^{43} +252.000 q^{47} +141.000 q^{49} +3.00000 q^{53} -60.0000 q^{55} +318.000 q^{59} +293.000 q^{61} -190.000 q^{65} +322.000 q^{67} +120.000 q^{71} +44.0000 q^{73} +264.000 q^{77} -917.000 q^{79} -309.000 q^{83} +525.000 q^{85} +1272.00 q^{89} +836.000 q^{91} -785.000 q^{95} +1328.00 q^{97} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) 22.0000 1.18789 0.593944 − 0.804506i \(-0.297570\pi\)
0.593944 + 0.804506i \(0.297570\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 12.0000 0.328921 0.164461 − 0.986384i \(-0.447412\pi\)
0.164461 + 0.986384i \(0.447412\pi\)
\(12\) 0 0
\(13\) 38.0000 0.810716 0.405358 − 0.914158i \(-0.367147\pi\)
0.405358 + 0.914158i \(0.367147\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −105.000 −1.49801 −0.749007 − 0.662562i \(-0.769469\pi\)
−0.749007 + 0.662562i \(0.769469\pi\)
\(18\) 0 0
\(19\) 157.000 1.89570 0.947849 − 0.318719i \(-0.103253\pi\)
0.947849 + 0.318719i \(0.103253\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 117.000 1.06070 0.530352 − 0.847778i \(-0.322060\pi\)
0.530352 + 0.847778i \(0.322060\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 66.0000 0.422617 0.211308 − 0.977419i \(-0.432228\pi\)
0.211308 + 0.977419i \(0.432228\pi\)
\(30\) 0 0
\(31\) 25.0000 0.144843 0.0724215 − 0.997374i \(-0.476927\pi\)
0.0724215 + 0.997374i \(0.476927\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −110.000 −0.531240
\(36\) 0 0
\(37\) 314.000 1.39517 0.697585 − 0.716502i \(-0.254258\pi\)
0.697585 + 0.716502i \(0.254258\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −504.000 −1.91979 −0.959897 − 0.280352i \(-0.909549\pi\)
−0.959897 + 0.280352i \(0.909549\pi\)
\(42\) 0 0
\(43\) −380.000 −1.34766 −0.673831 − 0.738886i \(-0.735352\pi\)
−0.673831 + 0.738886i \(0.735352\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 252.000 0.782085 0.391042 − 0.920373i \(-0.372115\pi\)
0.391042 + 0.920373i \(0.372115\pi\)
\(48\) 0 0
\(49\) 141.000 0.411079
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.00000 0.00777513 0.00388756 − 0.999992i \(-0.498763\pi\)
0.00388756 + 0.999992i \(0.498763\pi\)
\(54\) 0 0
\(55\) −60.0000 −0.147098
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 318.000 0.701696 0.350848 − 0.936432i \(-0.385893\pi\)
0.350848 + 0.936432i \(0.385893\pi\)
\(60\) 0 0
\(61\) 293.000 0.614997 0.307498 − 0.951549i \(-0.400508\pi\)
0.307498 + 0.951549i \(0.400508\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −190.000 −0.362563
\(66\) 0 0
\(67\) 322.000 0.587143 0.293571 − 0.955937i \(-0.405156\pi\)
0.293571 + 0.955937i \(0.405156\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 120.000 0.200583 0.100291 − 0.994958i \(-0.468022\pi\)
0.100291 + 0.994958i \(0.468022\pi\)
\(72\) 0 0
\(73\) 44.0000 0.0705453 0.0352727 − 0.999378i \(-0.488770\pi\)
0.0352727 + 0.999378i \(0.488770\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 264.000 0.390722
\(78\) 0 0
\(79\) −917.000 −1.30596 −0.652978 − 0.757377i \(-0.726481\pi\)
−0.652978 + 0.757377i \(0.726481\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −309.000 −0.408640 −0.204320 − 0.978904i \(-0.565498\pi\)
−0.204320 + 0.978904i \(0.565498\pi\)
\(84\) 0 0
\(85\) 525.000 0.669932
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1272.00 1.51496 0.757482 − 0.652856i \(-0.226430\pi\)
0.757482 + 0.652856i \(0.226430\pi\)
\(90\) 0 0
\(91\) 836.000 0.963040
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −785.000 −0.847782
\(96\) 0 0
\(97\) 1328.00 1.39008 0.695041 − 0.718970i \(-0.255386\pi\)
0.695041 + 0.718970i \(0.255386\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −492.000 −0.484711 −0.242356 − 0.970187i \(-0.577920\pi\)
−0.242356 + 0.970187i \(0.577920\pi\)
\(102\) 0 0
\(103\) −548.000 −0.524233 −0.262117 − 0.965036i \(-0.584421\pi\)
−0.262117 + 0.965036i \(0.584421\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −732.000 −0.661356 −0.330678 − 0.943744i \(-0.607277\pi\)
−0.330678 + 0.943744i \(0.607277\pi\)
\(108\) 0 0
\(109\) −907.000 −0.797017 −0.398508 − 0.917165i \(-0.630472\pi\)
−0.398508 + 0.917165i \(0.630472\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1542.00 −1.28371 −0.641855 − 0.766826i \(-0.721835\pi\)
−0.641855 + 0.766826i \(0.721835\pi\)
\(114\) 0 0
\(115\) −585.000 −0.474361
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2310.00 −1.77947
\(120\) 0 0
\(121\) −1187.00 −0.891811
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 2554.00 1.78449 0.892247 − 0.451547i \(-0.149128\pi\)
0.892247 + 0.451547i \(0.149128\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 150.000 0.100042 0.0500212 − 0.998748i \(-0.484071\pi\)
0.0500212 + 0.998748i \(0.484071\pi\)
\(132\) 0 0
\(133\) 3454.00 2.25188
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1653.00 1.03084 0.515421 − 0.856937i \(-0.327636\pi\)
0.515421 + 0.856937i \(0.327636\pi\)
\(138\) 0 0
\(139\) −1124.00 −0.685874 −0.342937 − 0.939358i \(-0.611422\pi\)
−0.342937 + 0.939358i \(0.611422\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 456.000 0.266662
\(144\) 0 0
\(145\) −330.000 −0.189000
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1608.00 0.884111 0.442055 − 0.896988i \(-0.354249\pi\)
0.442055 + 0.896988i \(0.354249\pi\)
\(150\) 0 0
\(151\) 2488.00 1.34086 0.670432 − 0.741971i \(-0.266109\pi\)
0.670432 + 0.741971i \(0.266109\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −125.000 −0.0647758
\(156\) 0 0
\(157\) −2968.00 −1.50874 −0.754370 − 0.656449i \(-0.772058\pi\)
−0.754370 + 0.656449i \(0.772058\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2574.00 1.26000
\(162\) 0 0
\(163\) −3170.00 −1.52327 −0.761637 − 0.648004i \(-0.775604\pi\)
−0.761637 + 0.648004i \(0.775604\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −327.000 −0.151521 −0.0757605 − 0.997126i \(-0.524138\pi\)
−0.0757605 + 0.997126i \(0.524138\pi\)
\(168\) 0 0
\(169\) −753.000 −0.342740
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1305.00 0.573510 0.286755 − 0.958004i \(-0.407423\pi\)
0.286755 + 0.958004i \(0.407423\pi\)
\(174\) 0 0
\(175\) 550.000 0.237578
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 4044.00 1.68862 0.844309 − 0.535856i \(-0.180011\pi\)
0.844309 + 0.535856i \(0.180011\pi\)
\(180\) 0 0
\(181\) −1051.00 −0.431603 −0.215802 − 0.976437i \(-0.569236\pi\)
−0.215802 + 0.976437i \(0.569236\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1570.00 −0.623939
\(186\) 0 0
\(187\) −1260.00 −0.492729
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2598.00 0.984213 0.492106 − 0.870535i \(-0.336227\pi\)
0.492106 + 0.870535i \(0.336227\pi\)
\(192\) 0 0
\(193\) 4370.00 1.62984 0.814921 − 0.579572i \(-0.196780\pi\)
0.814921 + 0.579572i \(0.196780\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2943.00 −1.06437 −0.532183 − 0.846629i \(-0.678628\pi\)
−0.532183 + 0.846629i \(0.678628\pi\)
\(198\) 0 0
\(199\) 4768.00 1.69847 0.849233 − 0.528019i \(-0.177065\pi\)
0.849233 + 0.528019i \(0.177065\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1452.00 0.502022
\(204\) 0 0
\(205\) 2520.00 0.858558
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1884.00 0.623536
\(210\) 0 0
\(211\) 1267.00 0.413383 0.206692 − 0.978406i \(-0.433730\pi\)
0.206692 + 0.978406i \(0.433730\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1900.00 0.602693
\(216\) 0 0
\(217\) 550.000 0.172057
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3990.00 −1.21446
\(222\) 0 0
\(223\) 2986.00 0.896670 0.448335 − 0.893866i \(-0.352017\pi\)
0.448335 + 0.893866i \(0.352017\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5409.00 −1.58153 −0.790766 − 0.612118i \(-0.790318\pi\)
−0.790766 + 0.612118i \(0.790318\pi\)
\(228\) 0 0
\(229\) 4331.00 1.24978 0.624892 − 0.780711i \(-0.285143\pi\)
0.624892 + 0.780711i \(0.285143\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2586.00 0.727101 0.363550 − 0.931575i \(-0.381564\pi\)
0.363550 + 0.931575i \(0.381564\pi\)
\(234\) 0 0
\(235\) −1260.00 −0.349759
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −510.000 −0.138030 −0.0690150 − 0.997616i \(-0.521986\pi\)
−0.0690150 + 0.997616i \(0.521986\pi\)
\(240\) 0 0
\(241\) −205.000 −0.0547934 −0.0273967 − 0.999625i \(-0.508722\pi\)
−0.0273967 + 0.999625i \(0.508722\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −705.000 −0.183840
\(246\) 0 0
\(247\) 5966.00 1.53687
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4680.00 1.17689 0.588444 − 0.808538i \(-0.299741\pi\)
0.588444 + 0.808538i \(0.299741\pi\)
\(252\) 0 0
\(253\) 1404.00 0.348888
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6159.00 −1.49489 −0.747447 − 0.664321i \(-0.768721\pi\)
−0.747447 + 0.664321i \(0.768721\pi\)
\(258\) 0 0
\(259\) 6908.00 1.65731
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6240.00 1.46302 0.731511 − 0.681829i \(-0.238815\pi\)
0.731511 + 0.681829i \(0.238815\pi\)
\(264\) 0 0
\(265\) −15.0000 −0.00347714
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7758.00 −1.75841 −0.879207 − 0.476439i \(-0.841927\pi\)
−0.879207 + 0.476439i \(0.841927\pi\)
\(270\) 0 0
\(271\) 7345.00 1.64641 0.823205 − 0.567745i \(-0.192184\pi\)
0.823205 + 0.567745i \(0.192184\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 300.000 0.0657843
\(276\) 0 0
\(277\) −3004.00 −0.651599 −0.325799 − 0.945439i \(-0.605633\pi\)
−0.325799 + 0.945439i \(0.605633\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2046.00 0.434356 0.217178 − 0.976132i \(-0.430315\pi\)
0.217178 + 0.976132i \(0.430315\pi\)
\(282\) 0 0
\(283\) 5488.00 1.15275 0.576374 − 0.817186i \(-0.304467\pi\)
0.576374 + 0.817186i \(0.304467\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −11088.0 −2.28050
\(288\) 0 0
\(289\) 6112.00 1.24405
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 333.000 0.0663961 0.0331981 − 0.999449i \(-0.489431\pi\)
0.0331981 + 0.999449i \(0.489431\pi\)
\(294\) 0 0
\(295\) −1590.00 −0.313808
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4446.00 0.859929
\(300\) 0 0
\(301\) −8360.00 −1.60087
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1465.00 −0.275035
\(306\) 0 0
\(307\) −2918.00 −0.542472 −0.271236 − 0.962513i \(-0.587432\pi\)
−0.271236 + 0.962513i \(0.587432\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5754.00 1.04913 0.524565 − 0.851370i \(-0.324228\pi\)
0.524565 + 0.851370i \(0.324228\pi\)
\(312\) 0 0
\(313\) 3368.00 0.608213 0.304106 − 0.952638i \(-0.401642\pi\)
0.304106 + 0.952638i \(0.401642\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2871.00 0.508680 0.254340 − 0.967115i \(-0.418142\pi\)
0.254340 + 0.967115i \(0.418142\pi\)
\(318\) 0 0
\(319\) 792.000 0.139008
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −16485.0 −2.83978
\(324\) 0 0
\(325\) 950.000 0.162143
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 5544.00 0.929029
\(330\) 0 0
\(331\) 10540.0 1.75024 0.875122 − 0.483902i \(-0.160781\pi\)
0.875122 + 0.483902i \(0.160781\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1610.00 −0.262578
\(336\) 0 0
\(337\) 5006.00 0.809182 0.404591 − 0.914498i \(-0.367414\pi\)
0.404591 + 0.914498i \(0.367414\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 300.000 0.0476420
\(342\) 0 0
\(343\) −4444.00 −0.699573
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 36.0000 0.00556940 0.00278470 − 0.999996i \(-0.499114\pi\)
0.00278470 + 0.999996i \(0.499114\pi\)
\(348\) 0 0
\(349\) −6715.00 −1.02993 −0.514965 − 0.857211i \(-0.672195\pi\)
−0.514965 + 0.857211i \(0.672195\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 12822.0 1.93328 0.966638 − 0.256148i \(-0.0824533\pi\)
0.966638 + 0.256148i \(0.0824533\pi\)
\(354\) 0 0
\(355\) −600.000 −0.0897034
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5478.00 −0.805342 −0.402671 − 0.915345i \(-0.631918\pi\)
−0.402671 + 0.915345i \(0.631918\pi\)
\(360\) 0 0
\(361\) 17790.0 2.59367
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −220.000 −0.0315488
\(366\) 0 0
\(367\) 2446.00 0.347902 0.173951 − 0.984754i \(-0.444347\pi\)
0.173951 + 0.984754i \(0.444347\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 66.0000 0.00923598
\(372\) 0 0
\(373\) 11696.0 1.62358 0.811791 − 0.583948i \(-0.198493\pi\)
0.811791 + 0.583948i \(0.198493\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2508.00 0.342622
\(378\) 0 0
\(379\) 2095.00 0.283939 0.141970 − 0.989871i \(-0.454656\pi\)
0.141970 + 0.989871i \(0.454656\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 11313.0 1.50931 0.754657 − 0.656119i \(-0.227803\pi\)
0.754657 + 0.656119i \(0.227803\pi\)
\(384\) 0 0
\(385\) −1320.00 −0.174736
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2124.00 0.276841 0.138420 − 0.990374i \(-0.455797\pi\)
0.138420 + 0.990374i \(0.455797\pi\)
\(390\) 0 0
\(391\) −12285.0 −1.58895
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4585.00 0.584041
\(396\) 0 0
\(397\) 6410.00 0.810349 0.405175 − 0.914239i \(-0.367211\pi\)
0.405175 + 0.914239i \(0.367211\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9882.00 −1.23063 −0.615316 − 0.788280i \(-0.710972\pi\)
−0.615316 + 0.788280i \(0.710972\pi\)
\(402\) 0 0
\(403\) 950.000 0.117426
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3768.00 0.458901
\(408\) 0 0
\(409\) 5897.00 0.712929 0.356464 − 0.934309i \(-0.383982\pi\)
0.356464 + 0.934309i \(0.383982\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 6996.00 0.833537
\(414\) 0 0
\(415\) 1545.00 0.182750
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6852.00 −0.798907 −0.399454 − 0.916753i \(-0.630800\pi\)
−0.399454 + 0.916753i \(0.630800\pi\)
\(420\) 0 0
\(421\) 323.000 0.0373921 0.0186960 − 0.999825i \(-0.494049\pi\)
0.0186960 + 0.999825i \(0.494049\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2625.00 −0.299603
\(426\) 0 0
\(427\) 6446.00 0.730548
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −10242.0 −1.14464 −0.572320 − 0.820030i \(-0.693956\pi\)
−0.572320 + 0.820030i \(0.693956\pi\)
\(432\) 0 0
\(433\) −14398.0 −1.59798 −0.798988 − 0.601347i \(-0.794631\pi\)
−0.798988 + 0.601347i \(0.794631\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 18369.0 2.01077
\(438\) 0 0
\(439\) −4079.00 −0.443463 −0.221731 − 0.975108i \(-0.571171\pi\)
−0.221731 + 0.975108i \(0.571171\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5781.00 −0.620008 −0.310004 − 0.950735i \(-0.600330\pi\)
−0.310004 + 0.950735i \(0.600330\pi\)
\(444\) 0 0
\(445\) −6360.00 −0.677512
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −15078.0 −1.58480 −0.792400 − 0.610002i \(-0.791168\pi\)
−0.792400 + 0.610002i \(0.791168\pi\)
\(450\) 0 0
\(451\) −6048.00 −0.631462
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4180.00 −0.430684
\(456\) 0 0
\(457\) 4268.00 0.436868 0.218434 − 0.975852i \(-0.429905\pi\)
0.218434 + 0.975852i \(0.429905\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −5634.00 −0.569201 −0.284600 − 0.958646i \(-0.591861\pi\)
−0.284600 + 0.958646i \(0.591861\pi\)
\(462\) 0 0
\(463\) −4526.00 −0.454300 −0.227150 − 0.973860i \(-0.572941\pi\)
−0.227150 + 0.973860i \(0.572941\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −969.000 −0.0960171 −0.0480085 − 0.998847i \(-0.515287\pi\)
−0.0480085 + 0.998847i \(0.515287\pi\)
\(468\) 0 0
\(469\) 7084.00 0.697460
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4560.00 −0.443275
\(474\) 0 0
\(475\) 3925.00 0.379140
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9756.00 −0.930612 −0.465306 − 0.885150i \(-0.654056\pi\)
−0.465306 + 0.885150i \(0.654056\pi\)
\(480\) 0 0
\(481\) 11932.0 1.13109
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6640.00 −0.621664
\(486\) 0 0
\(487\) −8768.00 −0.815844 −0.407922 − 0.913017i \(-0.633746\pi\)
−0.407922 + 0.913017i \(0.633746\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2274.00 0.209011 0.104505 − 0.994524i \(-0.466674\pi\)
0.104505 + 0.994524i \(0.466674\pi\)
\(492\) 0 0
\(493\) −6930.00 −0.633086
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2640.00 0.238270
\(498\) 0 0
\(499\) 1969.00 0.176642 0.0883212 − 0.996092i \(-0.471850\pi\)
0.0883212 + 0.996092i \(0.471850\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 10701.0 0.948577 0.474288 − 0.880370i \(-0.342705\pi\)
0.474288 + 0.880370i \(0.342705\pi\)
\(504\) 0 0
\(505\) 2460.00 0.216769
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 12420.0 1.08155 0.540773 − 0.841169i \(-0.318132\pi\)
0.540773 + 0.841169i \(0.318132\pi\)
\(510\) 0 0
\(511\) 968.000 0.0838000
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2740.00 0.234444
\(516\) 0 0
\(517\) 3024.00 0.257244
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −18816.0 −1.58223 −0.791117 − 0.611665i \(-0.790500\pi\)
−0.791117 + 0.611665i \(0.790500\pi\)
\(522\) 0 0
\(523\) 16798.0 1.40445 0.702223 − 0.711957i \(-0.252191\pi\)
0.702223 + 0.711957i \(0.252191\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2625.00 −0.216977
\(528\) 0 0
\(529\) 1522.00 0.125092
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −19152.0 −1.55641
\(534\) 0 0
\(535\) 3660.00 0.295767
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1692.00 0.135213
\(540\) 0 0
\(541\) −5890.00 −0.468079 −0.234040 − 0.972227i \(-0.575195\pi\)
−0.234040 + 0.972227i \(0.575195\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4535.00 0.356437
\(546\) 0 0
\(547\) −5516.00 −0.431165 −0.215582 − 0.976486i \(-0.569165\pi\)
−0.215582 + 0.976486i \(0.569165\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 10362.0 0.801154
\(552\) 0 0
\(553\) −20174.0 −1.55133
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4146.00 0.315389 0.157694 − 0.987488i \(-0.449594\pi\)
0.157694 + 0.987488i \(0.449594\pi\)
\(558\) 0 0
\(559\) −14440.0 −1.09257
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 21444.0 1.60525 0.802626 − 0.596483i \(-0.203436\pi\)
0.802626 + 0.596483i \(0.203436\pi\)
\(564\) 0 0
\(565\) 7710.00 0.574092
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 14778.0 1.08880 0.544399 − 0.838826i \(-0.316758\pi\)
0.544399 + 0.838826i \(0.316758\pi\)
\(570\) 0 0
\(571\) −9131.00 −0.669213 −0.334606 − 0.942358i \(-0.608603\pi\)
−0.334606 + 0.942358i \(0.608603\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2925.00 0.212141
\(576\) 0 0
\(577\) −2344.00 −0.169120 −0.0845598 − 0.996418i \(-0.526948\pi\)
−0.0845598 + 0.996418i \(0.526948\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −6798.00 −0.485419
\(582\) 0 0
\(583\) 36.0000 0.00255741
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 26829.0 1.88646 0.943229 − 0.332142i \(-0.107771\pi\)
0.943229 + 0.332142i \(0.107771\pi\)
\(588\) 0 0
\(589\) 3925.00 0.274579
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8181.00 0.566532 0.283266 − 0.959041i \(-0.408582\pi\)
0.283266 + 0.959041i \(0.408582\pi\)
\(594\) 0 0
\(595\) 11550.0 0.795805
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −24078.0 −1.64240 −0.821202 − 0.570637i \(-0.806696\pi\)
−0.821202 + 0.570637i \(0.806696\pi\)
\(600\) 0 0
\(601\) 22565.0 1.53152 0.765762 − 0.643124i \(-0.222362\pi\)
0.765762 + 0.643124i \(0.222362\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5935.00 0.398830
\(606\) 0 0
\(607\) 14716.0 0.984026 0.492013 − 0.870588i \(-0.336261\pi\)
0.492013 + 0.870588i \(0.336261\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 9576.00 0.634048
\(612\) 0 0
\(613\) −7552.00 −0.497590 −0.248795 − 0.968556i \(-0.580034\pi\)
−0.248795 + 0.968556i \(0.580034\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3981.00 −0.259755 −0.129878 − 0.991530i \(-0.541458\pi\)
−0.129878 + 0.991530i \(0.541458\pi\)
\(618\) 0 0
\(619\) −13928.0 −0.904384 −0.452192 − 0.891921i \(-0.649358\pi\)
−0.452192 + 0.891921i \(0.649358\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 27984.0 1.79961
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −32970.0 −2.08998
\(630\) 0 0
\(631\) −18605.0 −1.17378 −0.586889 − 0.809668i \(-0.699647\pi\)
−0.586889 + 0.809668i \(0.699647\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −12770.0 −0.798050
\(636\) 0 0
\(637\) 5358.00 0.333268
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 14928.0 0.919845 0.459922 − 0.887959i \(-0.347877\pi\)
0.459922 + 0.887959i \(0.347877\pi\)
\(642\) 0 0
\(643\) 6082.00 0.373018 0.186509 − 0.982453i \(-0.440283\pi\)
0.186509 + 0.982453i \(0.440283\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −4875.00 −0.296223 −0.148111 − 0.988971i \(-0.547319\pi\)
−0.148111 + 0.988971i \(0.547319\pi\)
\(648\) 0 0
\(649\) 3816.00 0.230803
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −5157.00 −0.309049 −0.154525 − 0.987989i \(-0.549385\pi\)
−0.154525 + 0.987989i \(0.549385\pi\)
\(654\) 0 0
\(655\) −750.000 −0.0447403
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1506.00 0.0890219 0.0445109 − 0.999009i \(-0.485827\pi\)
0.0445109 + 0.999009i \(0.485827\pi\)
\(660\) 0 0
\(661\) −2386.00 −0.140400 −0.0702002 − 0.997533i \(-0.522364\pi\)
−0.0702002 + 0.997533i \(0.522364\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −17270.0 −1.00707
\(666\) 0 0
\(667\) 7722.00 0.448271
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3516.00 0.202286
\(672\) 0 0
\(673\) 21158.0 1.21186 0.605929 − 0.795518i \(-0.292801\pi\)
0.605929 + 0.795518i \(0.292801\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 26826.0 1.52291 0.761453 − 0.648220i \(-0.224486\pi\)
0.761453 + 0.648220i \(0.224486\pi\)
\(678\) 0 0
\(679\) 29216.0 1.65126
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −32493.0 −1.82037 −0.910183 − 0.414206i \(-0.864059\pi\)
−0.910183 + 0.414206i \(0.864059\pi\)
\(684\) 0 0
\(685\) −8265.00 −0.461006
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 114.000 0.00630342
\(690\) 0 0
\(691\) 7531.00 0.414606 0.207303 − 0.978277i \(-0.433531\pi\)
0.207303 + 0.978277i \(0.433531\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5620.00 0.306732
\(696\) 0 0
\(697\) 52920.0 2.87588
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 24306.0 1.30959 0.654797 − 0.755805i \(-0.272754\pi\)
0.654797 + 0.755805i \(0.272754\pi\)
\(702\) 0 0
\(703\) 49298.0 2.64482
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10824.0 −0.575783
\(708\) 0 0
\(709\) −27454.0 −1.45424 −0.727120 − 0.686510i \(-0.759142\pi\)
−0.727120 + 0.686510i \(0.759142\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2925.00 0.153635
\(714\) 0 0
\(715\) −2280.00 −0.119255
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 5334.00 0.276668 0.138334 − 0.990386i \(-0.455825\pi\)
0.138334 + 0.990386i \(0.455825\pi\)
\(720\) 0 0
\(721\) −12056.0 −0.622731
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1650.00 0.0845234
\(726\) 0 0
\(727\) −26048.0 −1.32884 −0.664420 − 0.747359i \(-0.731321\pi\)
−0.664420 + 0.747359i \(0.731321\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 39900.0 2.01882
\(732\) 0 0
\(733\) −33136.0 −1.66972 −0.834861 − 0.550461i \(-0.814452\pi\)
−0.834861 + 0.550461i \(0.814452\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3864.00 0.193124
\(738\) 0 0
\(739\) 11599.0 0.577370 0.288685 − 0.957424i \(-0.406782\pi\)
0.288685 + 0.957424i \(0.406782\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −26424.0 −1.30471 −0.652357 − 0.757912i \(-0.726220\pi\)
−0.652357 + 0.757912i \(0.726220\pi\)
\(744\) 0 0
\(745\) −8040.00 −0.395386
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −16104.0 −0.785617
\(750\) 0 0
\(751\) −13661.0 −0.663778 −0.331889 − 0.943319i \(-0.607686\pi\)
−0.331889 + 0.943319i \(0.607686\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −12440.0 −0.599653
\(756\) 0 0
\(757\) −22846.0 −1.09690 −0.548449 − 0.836184i \(-0.684782\pi\)
−0.548449 + 0.836184i \(0.684782\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 20862.0 0.993754 0.496877 − 0.867821i \(-0.334480\pi\)
0.496877 + 0.867821i \(0.334480\pi\)
\(762\) 0 0
\(763\) −19954.0 −0.946767
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12084.0 0.568876
\(768\) 0 0
\(769\) −22219.0 −1.04192 −0.520961 − 0.853581i \(-0.674426\pi\)
−0.520961 + 0.853581i \(0.674426\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 17619.0 0.819808 0.409904 − 0.912129i \(-0.365562\pi\)
0.409904 + 0.912129i \(0.365562\pi\)
\(774\) 0 0
\(775\) 625.000 0.0289686
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −79128.0 −3.63935
\(780\) 0 0
\(781\) 1440.00 0.0659760
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 14840.0 0.674729
\(786\) 0 0
\(787\) −15584.0 −0.705857 −0.352929 − 0.935650i \(-0.614814\pi\)
−0.352929 + 0.935650i \(0.614814\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −33924.0 −1.52490
\(792\) 0 0
\(793\) 11134.0 0.498588
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −13023.0 −0.578793 −0.289397 − 0.957209i \(-0.593455\pi\)
−0.289397 + 0.957209i \(0.593455\pi\)
\(798\) 0 0
\(799\) −26460.0 −1.17157
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 528.000 0.0232039
\(804\) 0 0
\(805\) −12870.0 −0.563488
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −25872.0 −1.12436 −0.562182 − 0.827013i \(-0.690038\pi\)
−0.562182 + 0.827013i \(0.690038\pi\)
\(810\) 0 0
\(811\) −22052.0 −0.954809 −0.477405 − 0.878684i \(-0.658422\pi\)
−0.477405 + 0.878684i \(0.658422\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 15850.0 0.681229
\(816\) 0 0
\(817\) −59660.0 −2.55476
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1914.00 0.0813630 0.0406815 − 0.999172i \(-0.487047\pi\)
0.0406815 + 0.999172i \(0.487047\pi\)
\(822\) 0 0
\(823\) 11068.0 0.468780 0.234390 − 0.972143i \(-0.424691\pi\)
0.234390 + 0.972143i \(0.424691\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 21405.0 0.900030 0.450015 − 0.893021i \(-0.351419\pi\)
0.450015 + 0.893021i \(0.351419\pi\)
\(828\) 0 0
\(829\) −40042.0 −1.67758 −0.838791 − 0.544453i \(-0.816737\pi\)
−0.838791 + 0.544453i \(0.816737\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −14805.0 −0.615802
\(834\) 0 0
\(835\) 1635.00 0.0677623
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −17904.0 −0.736728 −0.368364 − 0.929682i \(-0.620082\pi\)
−0.368364 + 0.929682i \(0.620082\pi\)
\(840\) 0 0
\(841\) −20033.0 −0.821395
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 3765.00 0.153278
\(846\) 0 0
\(847\) −26114.0 −1.05937
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 36738.0 1.47986
\(852\) 0 0
\(853\) −21580.0 −0.866219 −0.433110 − 0.901341i \(-0.642584\pi\)
−0.433110 + 0.901341i \(0.642584\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 17151.0 0.683625 0.341813 − 0.939768i \(-0.388959\pi\)
0.341813 + 0.939768i \(0.388959\pi\)
\(858\) 0 0
\(859\) −33425.0 −1.32764 −0.663822 − 0.747891i \(-0.731067\pi\)
−0.663822 + 0.747891i \(0.731067\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −6603.00 −0.260450 −0.130225 − 0.991484i \(-0.541570\pi\)
−0.130225 + 0.991484i \(0.541570\pi\)
\(864\) 0 0
\(865\) −6525.00 −0.256482
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −11004.0 −0.429557
\(870\) 0 0
\(871\) 12236.0 0.476006
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2750.00 −0.106248
\(876\) 0 0
\(877\) −43384.0 −1.67044 −0.835219 − 0.549918i \(-0.814659\pi\)
−0.835219 + 0.549918i \(0.814659\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 12726.0 0.486663 0.243331 − 0.969943i \(-0.421760\pi\)
0.243331 + 0.969943i \(0.421760\pi\)
\(882\) 0 0
\(883\) −2786.00 −0.106179 −0.0530897 − 0.998590i \(-0.516907\pi\)
−0.0530897 + 0.998590i \(0.516907\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 4389.00 0.166142 0.0830711 − 0.996544i \(-0.473527\pi\)
0.0830711 + 0.996544i \(0.473527\pi\)
\(888\) 0 0
\(889\) 56188.0 2.11978
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 39564.0 1.48260
\(894\) 0 0
\(895\) −20220.0 −0.755173
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1650.00 0.0612131
\(900\) 0 0
\(901\) −315.000 −0.0116472
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5255.00 0.193019
\(906\) 0 0
\(907\) 24868.0 0.910395 0.455198 − 0.890390i \(-0.349569\pi\)
0.455198 + 0.890390i \(0.349569\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 126.000 0.00458240 0.00229120 − 0.999997i \(-0.499271\pi\)
0.00229120 + 0.999997i \(0.499271\pi\)
\(912\) 0 0
\(913\) −3708.00 −0.134411
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3300.00 0.118839
\(918\) 0 0
\(919\) 16144.0 0.579479 0.289740 − 0.957106i \(-0.406431\pi\)
0.289740 + 0.957106i \(0.406431\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 4560.00 0.162616
\(924\) 0 0
\(925\) 7850.00 0.279034
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −42192.0 −1.49007 −0.745035 − 0.667026i \(-0.767567\pi\)
−0.745035 + 0.667026i \(0.767567\pi\)
\(930\) 0 0
\(931\) 22137.0 0.779281
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 6300.00 0.220355
\(936\) 0 0
\(937\) 3272.00 0.114079 0.0570393 − 0.998372i \(-0.481834\pi\)
0.0570393 + 0.998372i \(0.481834\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 20838.0 0.721891 0.360945 − 0.932587i \(-0.382454\pi\)
0.360945 + 0.932587i \(0.382454\pi\)
\(942\) 0 0
\(943\) −58968.0 −2.03633
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −13353.0 −0.458199 −0.229099 − 0.973403i \(-0.573578\pi\)
−0.229099 + 0.973403i \(0.573578\pi\)
\(948\) 0 0
\(949\) 1672.00 0.0571922
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 13098.0 0.445211 0.222605 − 0.974909i \(-0.428544\pi\)
0.222605 + 0.974909i \(0.428544\pi\)
\(954\) 0 0
\(955\) −12990.0 −0.440153
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 36366.0 1.22452
\(960\) 0 0
\(961\) −29166.0 −0.979021
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −21850.0 −0.728887
\(966\) 0 0
\(967\) −19826.0 −0.659319 −0.329659 − 0.944100i \(-0.606934\pi\)
−0.329659 + 0.944100i \(0.606934\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −23322.0 −0.770792 −0.385396 − 0.922751i \(-0.625935\pi\)
−0.385396 + 0.922751i \(0.625935\pi\)
\(972\) 0 0
\(973\) −24728.0 −0.814741
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −47346.0 −1.55039 −0.775196 − 0.631721i \(-0.782349\pi\)
−0.775196 + 0.631721i \(0.782349\pi\)
\(978\) 0 0
\(979\) 15264.0 0.498304
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 33033.0 1.07181 0.535905 − 0.844278i \(-0.319971\pi\)
0.535905 + 0.844278i \(0.319971\pi\)
\(984\) 0 0
\(985\) 14715.0 0.475999
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −44460.0 −1.42947
\(990\) 0 0
\(991\) −6017.00 −0.192872 −0.0964361 − 0.995339i \(-0.530744\pi\)
−0.0964361 + 0.995339i \(0.530744\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −23840.0 −0.759577
\(996\) 0 0
\(997\) −34216.0 −1.08689 −0.543446 − 0.839444i \(-0.682881\pi\)
−0.543446 + 0.839444i \(0.682881\pi\)
\(998\) 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 2160.4.a.i.1.1 1
3.2 odd 2 2160.4.a.r.1.1 1
4.3 odd 2 270.4.a.g.1.1 yes 1
12.11 even 2 270.4.a.c.1.1 ✓ 1
20.3 even 4 1350.4.c.i.649.1 2
20.7 even 4 1350.4.c.i.649.2 2
20.19 odd 2 1350.4.a.l.1.1 1
36.7 odd 6 810.4.e.k.271.1 2
36.11 even 6 810.4.e.s.271.1 2
36.23 even 6 810.4.e.s.541.1 2
36.31 odd 6 810.4.e.k.541.1 2
60.23 odd 4 1350.4.c.l.649.2 2
60.47 odd 4 1350.4.c.l.649.1 2
60.59 even 2 1350.4.a.z.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.4.a.c.1.1 ✓ 1 12.11 even 2
270.4.a.g.1.1 yes 1 4.3 odd 2
810.4.e.k.271.1 2 36.7 odd 6
810.4.e.k.541.1 2 36.31 odd 6
810.4.e.s.271.1 2 36.11 even 6
810.4.e.s.541.1 2 36.23 even 6
1350.4.a.l.1.1 1 20.19 odd 2
1350.4.a.z.1.1 1 60.59 even 2
1350.4.c.i.649.1 2 20.3 even 4
1350.4.c.i.649.2 2 20.7 even 4
1350.4.c.l.649.1 2 60.47 odd 4
1350.4.c.l.649.2 2 60.23 odd 4
2160.4.a.i.1.1 1 1.1 even 1 trivial
2160.4.a.r.1.1 1 3.2 odd 2