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Properties

Label 1440.4.a.d.1.1
Level $1440$
Weight $4$
Character 1440.1
Self dual yes
Analytic conductor $84.963$
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] = [1440,4,Mod(1,1440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1440, 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("1440.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1440.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: \(84.9627504083\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 480)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1440.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{5} -12.0000 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} -12.0000 q^{7} +24.0000 q^{11} +38.0000 q^{13} +6.00000 q^{17} +104.000 q^{19} -100.000 q^{23} +25.0000 q^{25} -230.000 q^{29} -56.0000 q^{31} +60.0000 q^{35} +190.000 q^{37} -202.000 q^{41} -148.000 q^{43} -124.000 q^{47} -199.000 q^{49} -206.000 q^{53} -120.000 q^{55} +128.000 q^{59} +190.000 q^{61} -190.000 q^{65} -204.000 q^{67} +440.000 q^{71} +1210.00 q^{73} -288.000 q^{77} +816.000 q^{79} +1412.00 q^{83} -30.0000 q^{85} +214.000 q^{89} -456.000 q^{91} -520.000 q^{95} +1202.00 q^{97} +O(q^{100})\)

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
\(7\) −12.0000 −0.647939 −0.323970 − 0.946068i \(-0.605018\pi\)
−0.323970 + 0.946068i \(0.605018\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 24.0000 0.657843 0.328921 − 0.944357i \(-0.393315\pi\)
0.328921 + 0.944357i \(0.393315\pi\)
\(12\) 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
\(17\) 6.00000 0.0856008 0.0428004 − 0.999084i \(-0.486372\pi\)
0.0428004 + 0.999084i \(0.486372\pi\)
\(18\) 0 0
\(19\) 104.000 1.25575 0.627875 − 0.778314i \(-0.283925\pi\)
0.627875 + 0.778314i \(0.283925\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −100.000 −0.906584 −0.453292 − 0.891362i \(-0.649751\pi\)
−0.453292 + 0.891362i \(0.649751\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −230.000 −1.47276 −0.736378 − 0.676570i \(-0.763465\pi\)
−0.736378 + 0.676570i \(0.763465\pi\)
\(30\) 0 0
\(31\) −56.0000 −0.324448 −0.162224 − 0.986754i \(-0.551867\pi\)
−0.162224 + 0.986754i \(0.551867\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 60.0000 0.289767
\(36\) 0 0
\(37\) 190.000 0.844211 0.422106 − 0.906547i \(-0.361291\pi\)
0.422106 + 0.906547i \(0.361291\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −202.000 −0.769441 −0.384721 − 0.923033i \(-0.625702\pi\)
−0.384721 + 0.923033i \(0.625702\pi\)
\(42\) 0 0
\(43\) −148.000 −0.524879 −0.262439 − 0.964948i \(-0.584527\pi\)
−0.262439 + 0.964948i \(0.584527\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −124.000 −0.384835 −0.192418 − 0.981313i \(-0.561633\pi\)
−0.192418 + 0.981313i \(0.561633\pi\)
\(48\) 0 0
\(49\) −199.000 −0.580175
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −206.000 −0.533892 −0.266946 − 0.963711i \(-0.586015\pi\)
−0.266946 + 0.963711i \(0.586015\pi\)
\(54\) 0 0
\(55\) −120.000 −0.294196
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 128.000 0.282444 0.141222 − 0.989978i \(-0.454897\pi\)
0.141222 + 0.989978i \(0.454897\pi\)
\(60\) 0 0
\(61\) 190.000 0.398803 0.199402 − 0.979918i \(-0.436100\pi\)
0.199402 + 0.979918i \(0.436100\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −190.000 −0.362563
\(66\) 0 0
\(67\) −204.000 −0.371979 −0.185989 − 0.982552i \(-0.559549\pi\)
−0.185989 + 0.982552i \(0.559549\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 440.000 0.735470 0.367735 − 0.929931i \(-0.380133\pi\)
0.367735 + 0.929931i \(0.380133\pi\)
\(72\) 0 0
\(73\) 1210.00 1.94000 0.969999 − 0.243111i \(-0.0781678\pi\)
0.969999 + 0.243111i \(0.0781678\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −288.000 −0.426242
\(78\) 0 0
\(79\) 816.000 1.16212 0.581058 − 0.813862i \(-0.302639\pi\)
0.581058 + 0.813862i \(0.302639\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1412.00 1.86731 0.933657 − 0.358167i \(-0.116598\pi\)
0.933657 + 0.358167i \(0.116598\pi\)
\(84\) 0 0
\(85\) −30.0000 −0.0382818
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 214.000 0.254876 0.127438 − 0.991847i \(-0.459325\pi\)
0.127438 + 0.991847i \(0.459325\pi\)
\(90\) 0 0
\(91\) −456.000 −0.525294
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −520.000 −0.561588
\(96\) 0 0
\(97\) 1202.00 1.25819 0.629096 − 0.777328i \(-0.283425\pi\)
0.629096 + 0.777328i \(0.283425\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1342.00 −1.32212 −0.661059 − 0.750334i \(-0.729893\pi\)
−0.661059 + 0.750334i \(0.729893\pi\)
\(102\) 0 0
\(103\) 908.000 0.868620 0.434310 − 0.900763i \(-0.356992\pi\)
0.434310 + 0.900763i \(0.356992\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 876.000 0.791459 0.395730 − 0.918367i \(-0.370492\pi\)
0.395730 + 0.918367i \(0.370492\pi\)
\(108\) 0 0
\(109\) 302.000 0.265379 0.132690 − 0.991158i \(-0.457639\pi\)
0.132690 + 0.991158i \(0.457639\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 998.000 0.830831 0.415416 − 0.909632i \(-0.363636\pi\)
0.415416 + 0.909632i \(0.363636\pi\)
\(114\) 0 0
\(115\) 500.000 0.405437
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −72.0000 −0.0554641
\(120\) 0 0
\(121\) −755.000 −0.567243
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 836.000 0.584118 0.292059 − 0.956400i \(-0.405660\pi\)
0.292059 + 0.956400i \(0.405660\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1480.00 0.987085 0.493543 − 0.869722i \(-0.335702\pi\)
0.493543 + 0.869722i \(0.335702\pi\)
\(132\) 0 0
\(133\) −1248.00 −0.813649
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1346.00 −0.839391 −0.419695 − 0.907665i \(-0.637863\pi\)
−0.419695 + 0.907665i \(0.637863\pi\)
\(138\) 0 0
\(139\) 824.000 0.502811 0.251406 − 0.967882i \(-0.419107\pi\)
0.251406 + 0.967882i \(0.419107\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 912.000 0.533324
\(144\) 0 0
\(145\) 1150.00 0.658637
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2450.00 1.34706 0.673530 − 0.739160i \(-0.264777\pi\)
0.673530 + 0.739160i \(0.264777\pi\)
\(150\) 0 0
\(151\) 2696.00 1.45296 0.726481 − 0.687186i \(-0.241154\pi\)
0.726481 + 0.687186i \(0.241154\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 280.000 0.145098
\(156\) 0 0
\(157\) −554.000 −0.281618 −0.140809 − 0.990037i \(-0.544970\pi\)
−0.140809 + 0.990037i \(0.544970\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1200.00 0.587411
\(162\) 0 0
\(163\) −1364.00 −0.655440 −0.327720 − 0.944775i \(-0.606280\pi\)
−0.327720 + 0.944775i \(0.606280\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2004.00 0.928588 0.464294 − 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) −753.000 −0.342740
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1546.00 0.679423 0.339712 − 0.940530i \(-0.389671\pi\)
0.339712 + 0.940530i \(0.389671\pi\)
\(174\) 0 0
\(175\) −300.000 −0.129588
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1072.00 0.447626 0.223813 − 0.974632i \(-0.428150\pi\)
0.223813 + 0.974632i \(0.428150\pi\)
\(180\) 0 0
\(181\) −3754.00 −1.54162 −0.770808 − 0.637067i \(-0.780147\pi\)
−0.770808 + 0.637067i \(0.780147\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −950.000 −0.377543
\(186\) 0 0
\(187\) 144.000 0.0563119
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1224.00 −0.463694 −0.231847 − 0.972752i \(-0.574477\pi\)
−0.231847 + 0.972752i \(0.574477\pi\)
\(192\) 0 0
\(193\) −1694.00 −0.631797 −0.315898 − 0.948793i \(-0.602306\pi\)
−0.315898 + 0.948793i \(0.602306\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3134.00 −1.13344 −0.566721 − 0.823909i \(-0.691788\pi\)
−0.566721 + 0.823909i \(0.691788\pi\)
\(198\) 0 0
\(199\) 2560.00 0.911928 0.455964 − 0.889998i \(-0.349295\pi\)
0.455964 + 0.889998i \(0.349295\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2760.00 0.954256
\(204\) 0 0
\(205\) 1010.00 0.344105
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2496.00 0.826086
\(210\) 0 0
\(211\) −1856.00 −0.605556 −0.302778 − 0.953061i \(-0.597914\pi\)
−0.302778 + 0.953061i \(0.597914\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 740.000 0.234733
\(216\) 0 0
\(217\) 672.000 0.210223
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 228.000 0.0693979
\(222\) 0 0
\(223\) 1596.00 0.479265 0.239632 − 0.970864i \(-0.422973\pi\)
0.239632 + 0.970864i \(0.422973\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3996.00 1.16839 0.584193 − 0.811614i \(-0.301411\pi\)
0.584193 + 0.811614i \(0.301411\pi\)
\(228\) 0 0
\(229\) −6090.00 −1.75737 −0.878687 − 0.477399i \(-0.841580\pi\)
−0.878687 + 0.477399i \(0.841580\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 894.000 0.251364 0.125682 − 0.992071i \(-0.459888\pi\)
0.125682 + 0.992071i \(0.459888\pi\)
\(234\) 0 0
\(235\) 620.000 0.172104
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6336.00 1.71482 0.857410 − 0.514635i \(-0.172072\pi\)
0.857410 + 0.514635i \(0.172072\pi\)
\(240\) 0 0
\(241\) 338.000 0.0903423 0.0451711 − 0.998979i \(-0.485617\pi\)
0.0451711 + 0.998979i \(0.485617\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 995.000 0.259462
\(246\) 0 0
\(247\) 3952.00 1.01806
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4872.00 1.22517 0.612585 − 0.790404i \(-0.290130\pi\)
0.612585 + 0.790404i \(0.290130\pi\)
\(252\) 0 0
\(253\) −2400.00 −0.596390
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1878.00 0.455823 0.227911 − 0.973682i \(-0.426810\pi\)
0.227911 + 0.973682i \(0.426810\pi\)
\(258\) 0 0
\(259\) −2280.00 −0.546997
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2244.00 −0.526125 −0.263063 − 0.964779i \(-0.584733\pi\)
−0.263063 + 0.964779i \(0.584733\pi\)
\(264\) 0 0
\(265\) 1030.00 0.238764
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4314.00 0.977804 0.488902 − 0.872339i \(-0.337398\pi\)
0.488902 + 0.872339i \(0.337398\pi\)
\(270\) 0 0
\(271\) −6392.00 −1.43279 −0.716395 − 0.697694i \(-0.754209\pi\)
−0.716395 + 0.697694i \(0.754209\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 600.000 0.131569
\(276\) 0 0
\(277\) 4398.00 0.953972 0.476986 − 0.878911i \(-0.341729\pi\)
0.476986 + 0.878911i \(0.341729\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 7622.00 1.61812 0.809058 − 0.587729i \(-0.199978\pi\)
0.809058 + 0.587729i \(0.199978\pi\)
\(282\) 0 0
\(283\) 1020.00 0.214250 0.107125 − 0.994246i \(-0.465836\pi\)
0.107125 + 0.994246i \(0.465836\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2424.00 0.498551
\(288\) 0 0
\(289\) −4877.00 −0.992673
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3746.00 0.746907 0.373453 − 0.927649i \(-0.378174\pi\)
0.373453 + 0.927649i \(0.378174\pi\)
\(294\) 0 0
\(295\) −640.000 −0.126313
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3800.00 −0.734982
\(300\) 0 0
\(301\) 1776.00 0.340089
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −950.000 −0.178350
\(306\) 0 0
\(307\) 9700.00 1.80328 0.901642 − 0.432483i \(-0.142362\pi\)
0.901642 + 0.432483i \(0.142362\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4152.00 −0.757036 −0.378518 − 0.925594i \(-0.623566\pi\)
−0.378518 + 0.925594i \(0.623566\pi\)
\(312\) 0 0
\(313\) 6362.00 1.14889 0.574443 − 0.818544i \(-0.305219\pi\)
0.574443 + 0.818544i \(0.305219\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10886.0 −1.92877 −0.964383 − 0.264511i \(-0.914790\pi\)
−0.964383 + 0.264511i \(0.914790\pi\)
\(318\) 0 0
\(319\) −5520.00 −0.968842
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 624.000 0.107493
\(324\) 0 0
\(325\) 950.000 0.162143
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1488.00 0.249350
\(330\) 0 0
\(331\) 4128.00 0.685485 0.342742 − 0.939429i \(-0.388644\pi\)
0.342742 + 0.939429i \(0.388644\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1020.00 0.166354
\(336\) 0 0
\(337\) 12002.0 1.94003 0.970016 − 0.243042i \(-0.0781453\pi\)
0.970016 + 0.243042i \(0.0781453\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1344.00 −0.213436
\(342\) 0 0
\(343\) 6504.00 1.02386
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6276.00 −0.970932 −0.485466 − 0.874256i \(-0.661350\pi\)
−0.485466 + 0.874256i \(0.661350\pi\)
\(348\) 0 0
\(349\) −9362.00 −1.43592 −0.717960 − 0.696084i \(-0.754924\pi\)
−0.717960 + 0.696084i \(0.754924\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 838.000 0.126352 0.0631760 − 0.998002i \(-0.479877\pi\)
0.0631760 + 0.998002i \(0.479877\pi\)
\(354\) 0 0
\(355\) −2200.00 −0.328912
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6896.00 1.01381 0.506904 − 0.862003i \(-0.330790\pi\)
0.506904 + 0.862003i \(0.330790\pi\)
\(360\) 0 0
\(361\) 3957.00 0.576906
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −6050.00 −0.867593
\(366\) 0 0
\(367\) −1132.00 −0.161008 −0.0805040 − 0.996754i \(-0.525653\pi\)
−0.0805040 + 0.996754i \(0.525653\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2472.00 0.345930
\(372\) 0 0
\(373\) −12578.0 −1.74602 −0.873008 − 0.487705i \(-0.837834\pi\)
−0.873008 + 0.487705i \(0.837834\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8740.00 −1.19399
\(378\) 0 0
\(379\) 11752.0 1.59277 0.796385 − 0.604790i \(-0.206743\pi\)
0.796385 + 0.604790i \(0.206743\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 7372.00 0.983529 0.491764 − 0.870728i \(-0.336352\pi\)
0.491764 + 0.870728i \(0.336352\pi\)
\(384\) 0 0
\(385\) 1440.00 0.190621
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −6654.00 −0.867278 −0.433639 − 0.901087i \(-0.642771\pi\)
−0.433639 + 0.901087i \(0.642771\pi\)
\(390\) 0 0
\(391\) −600.000 −0.0776044
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4080.00 −0.519714
\(396\) 0 0
\(397\) 4278.00 0.540823 0.270411 − 0.962745i \(-0.412840\pi\)
0.270411 + 0.962745i \(0.412840\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9074.00 −1.13001 −0.565005 − 0.825088i \(-0.691126\pi\)
−0.565005 + 0.825088i \(0.691126\pi\)
\(402\) 0 0
\(403\) −2128.00 −0.263035
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4560.00 0.555358
\(408\) 0 0
\(409\) 6682.00 0.807833 0.403916 − 0.914796i \(-0.367649\pi\)
0.403916 + 0.914796i \(0.367649\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1536.00 −0.183006
\(414\) 0 0
\(415\) −7060.00 −0.835089
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −4832.00 −0.563386 −0.281693 − 0.959505i \(-0.590896\pi\)
−0.281693 + 0.959505i \(0.590896\pi\)
\(420\) 0 0
\(421\) 3974.00 0.460050 0.230025 − 0.973185i \(-0.426119\pi\)
0.230025 + 0.973185i \(0.426119\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 150.000 0.0171202
\(426\) 0 0
\(427\) −2280.00 −0.258400
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1112.00 −0.124276 −0.0621382 − 0.998068i \(-0.519792\pi\)
−0.0621382 + 0.998068i \(0.519792\pi\)
\(432\) 0 0
\(433\) 1106.00 0.122751 0.0613753 − 0.998115i \(-0.480451\pi\)
0.0613753 + 0.998115i \(0.480451\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −10400.0 −1.13844
\(438\) 0 0
\(439\) −9280.00 −1.00891 −0.504454 − 0.863439i \(-0.668306\pi\)
−0.504454 + 0.863439i \(0.668306\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −7004.00 −0.751174 −0.375587 − 0.926787i \(-0.622559\pi\)
−0.375587 + 0.926787i \(0.622559\pi\)
\(444\) 0 0
\(445\) −1070.00 −0.113984
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 11502.0 1.20894 0.604469 − 0.796629i \(-0.293385\pi\)
0.604469 + 0.796629i \(0.293385\pi\)
\(450\) 0 0
\(451\) −4848.00 −0.506172
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2280.00 0.234919
\(456\) 0 0
\(457\) 11578.0 1.18511 0.592556 − 0.805529i \(-0.298119\pi\)
0.592556 + 0.805529i \(0.298119\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6362.00 0.642750 0.321375 − 0.946952i \(-0.395855\pi\)
0.321375 + 0.946952i \(0.395855\pi\)
\(462\) 0 0
\(463\) 2892.00 0.290286 0.145143 − 0.989411i \(-0.453636\pi\)
0.145143 + 0.989411i \(0.453636\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 11036.0 1.09354 0.546772 − 0.837281i \(-0.315856\pi\)
0.546772 + 0.837281i \(0.315856\pi\)
\(468\) 0 0
\(469\) 2448.00 0.241019
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3552.00 −0.345288
\(474\) 0 0
\(475\) 2600.00 0.251150
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 13664.0 1.30339 0.651695 − 0.758481i \(-0.274058\pi\)
0.651695 + 0.758481i \(0.274058\pi\)
\(480\) 0 0
\(481\) 7220.00 0.684415
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6010.00 −0.562680
\(486\) 0 0
\(487\) 4820.00 0.448491 0.224245 − 0.974533i \(-0.428008\pi\)
0.224245 + 0.974533i \(0.428008\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −17464.0 −1.60517 −0.802586 − 0.596537i \(-0.796543\pi\)
−0.802586 + 0.596537i \(0.796543\pi\)
\(492\) 0 0
\(493\) −1380.00 −0.126069
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5280.00 −0.476540
\(498\) 0 0
\(499\) 13960.0 1.25238 0.626188 − 0.779672i \(-0.284614\pi\)
0.626188 + 0.779672i \(0.284614\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −20388.0 −1.80727 −0.903634 − 0.428305i \(-0.859111\pi\)
−0.903634 + 0.428305i \(0.859111\pi\)
\(504\) 0 0
\(505\) 6710.00 0.591269
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 12954.0 1.12805 0.564024 − 0.825759i \(-0.309253\pi\)
0.564024 + 0.825759i \(0.309253\pi\)
\(510\) 0 0
\(511\) −14520.0 −1.25700
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4540.00 −0.388459
\(516\) 0 0
\(517\) −2976.00 −0.253161
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3542.00 0.297846 0.148923 − 0.988849i \(-0.452419\pi\)
0.148923 + 0.988849i \(0.452419\pi\)
\(522\) 0 0
\(523\) 1532.00 0.128087 0.0640437 − 0.997947i \(-0.479600\pi\)
0.0640437 + 0.997947i \(0.479600\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −336.000 −0.0277730
\(528\) 0 0
\(529\) −2167.00 −0.178105
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −7676.00 −0.623798
\(534\) 0 0
\(535\) −4380.00 −0.353951
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4776.00 −0.381664
\(540\) 0 0
\(541\) −11826.0 −0.939814 −0.469907 − 0.882716i \(-0.655713\pi\)
−0.469907 + 0.882716i \(0.655713\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1510.00 −0.118681
\(546\) 0 0
\(547\) −11260.0 −0.880151 −0.440076 − 0.897961i \(-0.645048\pi\)
−0.440076 + 0.897961i \(0.645048\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −23920.0 −1.84941
\(552\) 0 0
\(553\) −9792.00 −0.752980
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4374.00 −0.332733 −0.166367 − 0.986064i \(-0.553203\pi\)
−0.166367 + 0.986064i \(0.553203\pi\)
\(558\) 0 0
\(559\) −5624.00 −0.425527
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 11604.0 0.868651 0.434325 − 0.900756i \(-0.356987\pi\)
0.434325 + 0.900756i \(0.356987\pi\)
\(564\) 0 0
\(565\) −4990.00 −0.371559
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 7990.00 0.588679 0.294339 − 0.955701i \(-0.404900\pi\)
0.294339 + 0.955701i \(0.404900\pi\)
\(570\) 0 0
\(571\) −26080.0 −1.91141 −0.955704 − 0.294329i \(-0.904904\pi\)
−0.955704 + 0.294329i \(0.904904\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2500.00 −0.181317
\(576\) 0 0
\(577\) 13922.0 1.00447 0.502236 − 0.864731i \(-0.332511\pi\)
0.502236 + 0.864731i \(0.332511\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −16944.0 −1.20991
\(582\) 0 0
\(583\) −4944.00 −0.351217
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −26340.0 −1.85208 −0.926038 − 0.377431i \(-0.876807\pi\)
−0.926038 + 0.377431i \(0.876807\pi\)
\(588\) 0 0
\(589\) −5824.00 −0.407426
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 9478.00 0.656349 0.328174 − 0.944617i \(-0.393567\pi\)
0.328174 + 0.944617i \(0.393567\pi\)
\(594\) 0 0
\(595\) 360.000 0.0248043
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6528.00 −0.445287 −0.222643 − 0.974900i \(-0.571469\pi\)
−0.222643 + 0.974900i \(0.571469\pi\)
\(600\) 0 0
\(601\) 2090.00 0.141852 0.0709259 − 0.997482i \(-0.477405\pi\)
0.0709259 + 0.997482i \(0.477405\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3775.00 0.253679
\(606\) 0 0
\(607\) 8788.00 0.587634 0.293817 − 0.955862i \(-0.405074\pi\)
0.293817 + 0.955862i \(0.405074\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4712.00 −0.311992
\(612\) 0 0
\(613\) −2626.00 −0.173023 −0.0865115 − 0.996251i \(-0.527572\pi\)
−0.0865115 + 0.996251i \(0.527572\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 29214.0 1.90618 0.953089 − 0.302691i \(-0.0978852\pi\)
0.953089 + 0.302691i \(0.0978852\pi\)
\(618\) 0 0
\(619\) 22984.0 1.49242 0.746208 − 0.665713i \(-0.231873\pi\)
0.746208 + 0.665713i \(0.231873\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2568.00 −0.165144
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1140.00 0.0722651
\(630\) 0 0
\(631\) 4472.00 0.282136 0.141068 − 0.990000i \(-0.454946\pi\)
0.141068 + 0.990000i \(0.454946\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4180.00 −0.261226
\(636\) 0 0
\(637\) −7562.00 −0.470357
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8798.00 0.542122 0.271061 − 0.962562i \(-0.412626\pi\)
0.271061 + 0.962562i \(0.412626\pi\)
\(642\) 0 0
\(643\) −29428.0 −1.80486 −0.902432 − 0.430833i \(-0.858220\pi\)
−0.902432 + 0.430833i \(0.858220\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −4860.00 −0.295311 −0.147656 − 0.989039i \(-0.547173\pi\)
−0.147656 + 0.989039i \(0.547173\pi\)
\(648\) 0 0
\(649\) 3072.00 0.185804
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 6570.00 0.393727 0.196864 − 0.980431i \(-0.436924\pi\)
0.196864 + 0.980431i \(0.436924\pi\)
\(654\) 0 0
\(655\) −7400.00 −0.441438
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −26496.0 −1.56622 −0.783109 − 0.621885i \(-0.786367\pi\)
−0.783109 + 0.621885i \(0.786367\pi\)
\(660\) 0 0
\(661\) −19642.0 −1.15580 −0.577901 − 0.816107i \(-0.696128\pi\)
−0.577901 + 0.816107i \(0.696128\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 6240.00 0.363875
\(666\) 0 0
\(667\) 23000.0 1.33518
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4560.00 0.262350
\(672\) 0 0
\(673\) −19582.0 −1.12159 −0.560795 − 0.827954i \(-0.689505\pi\)
−0.560795 + 0.827954i \(0.689505\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 22914.0 1.30082 0.650411 − 0.759582i \(-0.274597\pi\)
0.650411 + 0.759582i \(0.274597\pi\)
\(678\) 0 0
\(679\) −14424.0 −0.815232
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 13764.0 0.771105 0.385553 − 0.922686i \(-0.374011\pi\)
0.385553 + 0.922686i \(0.374011\pi\)
\(684\) 0 0
\(685\) 6730.00 0.375387
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −7828.00 −0.432835
\(690\) 0 0
\(691\) −34688.0 −1.90969 −0.954843 − 0.297109i \(-0.903977\pi\)
−0.954843 + 0.297109i \(0.903977\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4120.00 −0.224864
\(696\) 0 0
\(697\) −1212.00 −0.0658648
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 17226.0 0.928127 0.464064 − 0.885802i \(-0.346391\pi\)
0.464064 + 0.885802i \(0.346391\pi\)
\(702\) 0 0
\(703\) 19760.0 1.06012
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 16104.0 0.856652
\(708\) 0 0
\(709\) −12970.0 −0.687022 −0.343511 − 0.939149i \(-0.611616\pi\)
−0.343511 + 0.939149i \(0.611616\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 5600.00 0.294140
\(714\) 0 0
\(715\) −4560.00 −0.238510
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −10832.0 −0.561843 −0.280922 − 0.959731i \(-0.590640\pi\)
−0.280922 + 0.959731i \(0.590640\pi\)
\(720\) 0 0
\(721\) −10896.0 −0.562813
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −5750.00 −0.294551
\(726\) 0 0
\(727\) 35588.0 1.81552 0.907762 − 0.419486i \(-0.137790\pi\)
0.907762 + 0.419486i \(0.137790\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −888.000 −0.0449300
\(732\) 0 0
\(733\) 19238.0 0.969402 0.484701 − 0.874680i \(-0.338928\pi\)
0.484701 + 0.874680i \(0.338928\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4896.00 −0.244703
\(738\) 0 0
\(739\) −4072.00 −0.202694 −0.101347 − 0.994851i \(-0.532315\pi\)
−0.101347 + 0.994851i \(0.532315\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −31268.0 −1.54389 −0.771946 − 0.635688i \(-0.780716\pi\)
−0.771946 + 0.635688i \(0.780716\pi\)
\(744\) 0 0
\(745\) −12250.0 −0.602423
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −10512.0 −0.512817
\(750\) 0 0
\(751\) −28216.0 −1.37099 −0.685497 − 0.728075i \(-0.740415\pi\)
−0.685497 + 0.728075i \(0.740415\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −13480.0 −0.649785
\(756\) 0 0
\(757\) −33874.0 −1.62638 −0.813191 − 0.581997i \(-0.802272\pi\)
−0.813191 + 0.581997i \(0.802272\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −5466.00 −0.260371 −0.130186 − 0.991490i \(-0.541557\pi\)
−0.130186 + 0.991490i \(0.541557\pi\)
\(762\) 0 0
\(763\) −3624.00 −0.171950
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4864.00 0.228982
\(768\) 0 0
\(769\) −8878.00 −0.416318 −0.208159 − 0.978095i \(-0.566747\pi\)
−0.208159 + 0.978095i \(0.566747\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 9538.00 0.443801 0.221900 − 0.975069i \(-0.428774\pi\)
0.221900 + 0.975069i \(0.428774\pi\)
\(774\) 0 0
\(775\) −1400.00 −0.0648897
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −21008.0 −0.966226
\(780\) 0 0
\(781\) 10560.0 0.483824
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2770.00 0.125943
\(786\) 0 0
\(787\) −5404.00 −0.244767 −0.122384 − 0.992483i \(-0.539054\pi\)
−0.122384 + 0.992483i \(0.539054\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −11976.0 −0.538328
\(792\) 0 0
\(793\) 7220.00 0.323316
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −16326.0 −0.725592 −0.362796 − 0.931869i \(-0.618178\pi\)
−0.362796 + 0.931869i \(0.618178\pi\)
\(798\) 0 0
\(799\) −744.000 −0.0329422
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 29040.0 1.27621
\(804\) 0 0
\(805\) −6000.00 −0.262698
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −26202.0 −1.13871 −0.569353 − 0.822093i \(-0.692806\pi\)
−0.569353 + 0.822093i \(0.692806\pi\)
\(810\) 0 0
\(811\) −26208.0 −1.13476 −0.567378 − 0.823457i \(-0.692042\pi\)
−0.567378 + 0.823457i \(0.692042\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 6820.00 0.293122
\(816\) 0 0
\(817\) −15392.0 −0.659116
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1986.00 0.0844237 0.0422119 − 0.999109i \(-0.486560\pi\)
0.0422119 + 0.999109i \(0.486560\pi\)
\(822\) 0 0
\(823\) −5236.00 −0.221769 −0.110884 − 0.993833i \(-0.535368\pi\)
−0.110884 + 0.993833i \(0.535368\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 26044.0 1.09509 0.547545 − 0.836777i \(-0.315563\pi\)
0.547545 + 0.836777i \(0.315563\pi\)
\(828\) 0 0
\(829\) 21246.0 0.890113 0.445057 − 0.895502i \(-0.353184\pi\)
0.445057 + 0.895502i \(0.353184\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1194.00 −0.0496634
\(834\) 0 0
\(835\) −10020.0 −0.415277
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 17440.0 0.717635 0.358817 − 0.933408i \(-0.383180\pi\)
0.358817 + 0.933408i \(0.383180\pi\)
\(840\) 0 0
\(841\) 28511.0 1.16901
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 3765.00 0.153278
\(846\) 0 0
\(847\) 9060.00 0.367539
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −19000.0 −0.765349
\(852\) 0 0
\(853\) 33582.0 1.34798 0.673989 − 0.738741i \(-0.264579\pi\)
0.673989 + 0.738741i \(0.264579\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 18942.0 0.755013 0.377507 − 0.926007i \(-0.376782\pi\)
0.377507 + 0.926007i \(0.376782\pi\)
\(858\) 0 0
\(859\) 25720.0 1.02160 0.510800 − 0.859699i \(-0.329349\pi\)
0.510800 + 0.859699i \(0.329349\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −32436.0 −1.27941 −0.639707 − 0.768619i \(-0.720944\pi\)
−0.639707 + 0.768619i \(0.720944\pi\)
\(864\) 0 0
\(865\) −7730.00 −0.303847
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 19584.0 0.764490
\(870\) 0 0
\(871\) −7752.00 −0.301569
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1500.00 0.0579534
\(876\) 0 0
\(877\) 8646.00 0.332902 0.166451 − 0.986050i \(-0.446769\pi\)
0.166451 + 0.986050i \(0.446769\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −27442.0 −1.04943 −0.524713 − 0.851279i \(-0.675827\pi\)
−0.524713 + 0.851279i \(0.675827\pi\)
\(882\) 0 0
\(883\) −14116.0 −0.537986 −0.268993 − 0.963142i \(-0.586691\pi\)
−0.268993 + 0.963142i \(0.586691\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −4124.00 −0.156111 −0.0780554 − 0.996949i \(-0.524871\pi\)
−0.0780554 + 0.996949i \(0.524871\pi\)
\(888\) 0 0
\(889\) −10032.0 −0.378473
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −12896.0 −0.483257
\(894\) 0 0
\(895\) −5360.00 −0.200184
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 12880.0 0.477833
\(900\) 0 0
\(901\) −1236.00 −0.0457016
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 18770.0 0.689432
\(906\) 0 0
\(907\) 42100.0 1.54124 0.770622 − 0.637293i \(-0.219946\pi\)
0.770622 + 0.637293i \(0.219946\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −34152.0 −1.24205 −0.621024 − 0.783791i \(-0.713283\pi\)
−0.621024 + 0.783791i \(0.713283\pi\)
\(912\) 0 0
\(913\) 33888.0 1.22840
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −17760.0 −0.639571
\(918\) 0 0
\(919\) 41984.0 1.50699 0.753495 − 0.657453i \(-0.228366\pi\)
0.753495 + 0.657453i \(0.228366\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 16720.0 0.596257
\(924\) 0 0
\(925\) 4750.00 0.168842
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −48434.0 −1.71051 −0.855257 − 0.518204i \(-0.826601\pi\)
−0.855257 + 0.518204i \(0.826601\pi\)
\(930\) 0 0
\(931\) −20696.0 −0.728554
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −720.000 −0.0251834
\(936\) 0 0
\(937\) −25590.0 −0.892197 −0.446099 − 0.894984i \(-0.647187\pi\)
−0.446099 + 0.894984i \(0.647187\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 18906.0 0.654961 0.327480 − 0.944858i \(-0.393800\pi\)
0.327480 + 0.944858i \(0.393800\pi\)
\(942\) 0 0
\(943\) 20200.0 0.697564
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 36316.0 1.24616 0.623079 − 0.782159i \(-0.285882\pi\)
0.623079 + 0.782159i \(0.285882\pi\)
\(948\) 0 0
\(949\) 45980.0 1.57279
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −15890.0 −0.540113 −0.270056 − 0.962844i \(-0.587042\pi\)
−0.270056 + 0.962844i \(0.587042\pi\)
\(954\) 0 0
\(955\) 6120.00 0.207370
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 16152.0 0.543874
\(960\) 0 0
\(961\) −26655.0 −0.894733
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 8470.00 0.282548
\(966\) 0 0
\(967\) 116.000 0.00385761 0.00192880 − 0.999998i \(-0.499386\pi\)
0.00192880 + 0.999998i \(0.499386\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −4744.00 −0.156789 −0.0783945 − 0.996922i \(-0.524979\pi\)
−0.0783945 + 0.996922i \(0.524979\pi\)
\(972\) 0 0
\(973\) −9888.00 −0.325791
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 18374.0 0.601675 0.300837 − 0.953675i \(-0.402734\pi\)
0.300837 + 0.953675i \(0.402734\pi\)
\(978\) 0 0
\(979\) 5136.00 0.167668
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 13036.0 0.422974 0.211487 − 0.977381i \(-0.432169\pi\)
0.211487 + 0.977381i \(0.432169\pi\)
\(984\) 0 0
\(985\) 15670.0 0.506891
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 14800.0 0.475847
\(990\) 0 0
\(991\) 15224.0 0.487998 0.243999 − 0.969775i \(-0.421541\pi\)
0.243999 + 0.969775i \(0.421541\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −12800.0 −0.407826
\(996\) 0 0
\(997\) −43794.0 −1.39114 −0.695572 − 0.718457i \(-0.744849\pi\)
−0.695572 + 0.718457i \(0.744849\pi\)
\(998\) 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 1440.4.a.d.1.1 1
3.2 odd 2 480.4.a.j.1.1 yes 1
4.3 odd 2 1440.4.a.g.1.1 1
12.11 even 2 480.4.a.e.1.1 ✓ 1
15.14 odd 2 2400.4.a.g.1.1 1
24.5 odd 2 960.4.a.d.1.1 1
24.11 even 2 960.4.a.y.1.1 1
60.59 even 2 2400.4.a.p.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
480.4.a.e.1.1 ✓ 1 12.11 even 2
480.4.a.j.1.1 yes 1 3.2 odd 2
960.4.a.d.1.1 1 24.5 odd 2
960.4.a.y.1.1 1 24.11 even 2
1440.4.a.d.1.1 1 1.1 even 1 trivial
1440.4.a.g.1.1 1 4.3 odd 2
2400.4.a.g.1.1 1 15.14 odd 2
2400.4.a.p.1.1 1 60.59 even 2