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Properties

Label 1008.4.a.s.1.1
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,4,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, 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("1008.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.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: \(59.4739252858\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+14.0000 q^{5} +7.00000 q^{7} +O(q^{10})\) \(q+14.0000 q^{5} +7.00000 q^{7} -28.0000 q^{11} +18.0000 q^{13} -74.0000 q^{17} -80.0000 q^{19} -112.000 q^{23} +71.0000 q^{25} -190.000 q^{29} -72.0000 q^{31} +98.0000 q^{35} -346.000 q^{37} -162.000 q^{41} +412.000 q^{43} +24.0000 q^{47} +49.0000 q^{49} -318.000 q^{53} -392.000 q^{55} -200.000 q^{59} -198.000 q^{61} +252.000 q^{65} +716.000 q^{67} +392.000 q^{71} +538.000 q^{73} -196.000 q^{77} -240.000 q^{79} -1072.00 q^{83} -1036.00 q^{85} -810.000 q^{89} +126.000 q^{91} -1120.00 q^{95} +1354.00 q^{97} +O(q^{100})\)

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
\(5\) 14.0000 1.25220 0.626099 − 0.779744i \(-0.284651\pi\)
0.626099 + 0.779744i \(0.284651\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −28.0000 −0.767483 −0.383742 − 0.923440i \(-0.625365\pi\)
−0.383742 + 0.923440i \(0.625365\pi\)
\(12\) 0 0
\(13\) 18.0000 0.384023 0.192012 − 0.981393i \(-0.438499\pi\)
0.192012 + 0.981393i \(0.438499\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −74.0000 −1.05574 −0.527872 − 0.849324i \(-0.677010\pi\)
−0.527872 + 0.849324i \(0.677010\pi\)
\(18\) 0 0
\(19\) −80.0000 −0.965961 −0.482980 − 0.875631i \(-0.660446\pi\)
−0.482980 + 0.875631i \(0.660446\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −112.000 −1.01537 −0.507687 − 0.861541i \(-0.669499\pi\)
−0.507687 + 0.861541i \(0.669499\pi\)
\(24\) 0 0
\(25\) 71.0000 0.568000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −190.000 −1.21662 −0.608312 − 0.793698i \(-0.708153\pi\)
−0.608312 + 0.793698i \(0.708153\pi\)
\(30\) 0 0
\(31\) −72.0000 −0.417148 −0.208574 − 0.978007i \(-0.566882\pi\)
−0.208574 + 0.978007i \(0.566882\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 98.0000 0.473286
\(36\) 0 0
\(37\) −346.000 −1.53735 −0.768676 − 0.639638i \(-0.779084\pi\)
−0.768676 + 0.639638i \(0.779084\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −162.000 −0.617077 −0.308538 − 0.951212i \(-0.599840\pi\)
−0.308538 + 0.951212i \(0.599840\pi\)
\(42\) 0 0
\(43\) 412.000 1.46115 0.730575 − 0.682833i \(-0.239252\pi\)
0.730575 + 0.682833i \(0.239252\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 24.0000 0.0744843 0.0372421 − 0.999306i \(-0.488143\pi\)
0.0372421 + 0.999306i \(0.488143\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −318.000 −0.824163 −0.412082 − 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) −392.000 −0.961041
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −200.000 −0.441318 −0.220659 − 0.975351i \(-0.570821\pi\)
−0.220659 + 0.975351i \(0.570821\pi\)
\(60\) 0 0
\(61\) −198.000 −0.415595 −0.207798 − 0.978172i \(-0.566630\pi\)
−0.207798 + 0.978172i \(0.566630\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 252.000 0.480873
\(66\) 0 0
\(67\) 716.000 1.30557 0.652786 − 0.757542i \(-0.273600\pi\)
0.652786 + 0.757542i \(0.273600\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 392.000 0.655237 0.327619 − 0.944810i \(-0.393754\pi\)
0.327619 + 0.944810i \(0.393754\pi\)
\(72\) 0 0
\(73\) 538.000 0.862577 0.431289 − 0.902214i \(-0.358059\pi\)
0.431289 + 0.902214i \(0.358059\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −196.000 −0.290081
\(78\) 0 0
\(79\) −240.000 −0.341799 −0.170899 − 0.985288i \(-0.554667\pi\)
−0.170899 + 0.985288i \(0.554667\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1072.00 −1.41768 −0.708839 − 0.705370i \(-0.750781\pi\)
−0.708839 + 0.705370i \(0.750781\pi\)
\(84\) 0 0
\(85\) −1036.00 −1.32200
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −810.000 −0.964717 −0.482359 − 0.875974i \(-0.660220\pi\)
−0.482359 + 0.875974i \(0.660220\pi\)
\(90\) 0 0
\(91\) 126.000 0.145147
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1120.00 −1.20957
\(96\) 0 0
\(97\) 1354.00 1.41730 0.708649 − 0.705561i \(-0.249305\pi\)
0.708649 + 0.705561i \(0.249305\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1358.00 1.33788 0.668941 − 0.743316i \(-0.266748\pi\)
0.668941 + 0.743316i \(0.266748\pi\)
\(102\) 0 0
\(103\) 832.000 0.795916 0.397958 − 0.917404i \(-0.369719\pi\)
0.397958 + 0.917404i \(0.369719\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 444.000 0.401150 0.200575 − 0.979678i \(-0.435719\pi\)
0.200575 + 0.979678i \(0.435719\pi\)
\(108\) 0 0
\(109\) 1870.00 1.64324 0.821622 − 0.570033i \(-0.193070\pi\)
0.821622 + 0.570033i \(0.193070\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1378.00 −1.14718 −0.573590 − 0.819143i \(-0.694450\pi\)
−0.573590 + 0.819143i \(0.694450\pi\)
\(114\) 0 0
\(115\) −1568.00 −1.27145
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −518.000 −0.399033
\(120\) 0 0
\(121\) −547.000 −0.410969
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −756.000 −0.540950
\(126\) 0 0
\(127\) −1944.00 −1.35828 −0.679142 − 0.734007i \(-0.737648\pi\)
−0.679142 + 0.734007i \(0.737648\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −848.000 −0.565573 −0.282787 − 0.959183i \(-0.591259\pi\)
−0.282787 + 0.959183i \(0.591259\pi\)
\(132\) 0 0
\(133\) −560.000 −0.365099
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2966.00 1.84965 0.924827 − 0.380389i \(-0.124210\pi\)
0.924827 + 0.380389i \(0.124210\pi\)
\(138\) 0 0
\(139\) −2800.00 −1.70858 −0.854291 − 0.519795i \(-0.826008\pi\)
−0.854291 + 0.519795i \(0.826008\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −504.000 −0.294731
\(144\) 0 0
\(145\) −2660.00 −1.52346
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −510.000 −0.280408 −0.140204 − 0.990123i \(-0.544776\pi\)
−0.140204 + 0.990123i \(0.544776\pi\)
\(150\) 0 0
\(151\) −592.000 −0.319048 −0.159524 − 0.987194i \(-0.550996\pi\)
−0.159524 + 0.987194i \(0.550996\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1008.00 −0.522352
\(156\) 0 0
\(157\) −2686.00 −1.36539 −0.682695 − 0.730704i \(-0.739192\pi\)
−0.682695 + 0.730704i \(0.739192\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −784.000 −0.383776
\(162\) 0 0
\(163\) 1012.00 0.486294 0.243147 − 0.969989i \(-0.421820\pi\)
0.243147 + 0.969989i \(0.421820\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 544.000 0.252072 0.126036 − 0.992026i \(-0.459775\pi\)
0.126036 + 0.992026i \(0.459775\pi\)
\(168\) 0 0
\(169\) −1873.00 −0.852526
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1858.00 −0.816538 −0.408269 − 0.912862i \(-0.633868\pi\)
−0.408269 + 0.912862i \(0.633868\pi\)
\(174\) 0 0
\(175\) 497.000 0.214684
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −300.000 −0.125268 −0.0626342 − 0.998037i \(-0.519950\pi\)
−0.0626342 + 0.998037i \(0.519950\pi\)
\(180\) 0 0
\(181\) −2358.00 −0.968336 −0.484168 − 0.874975i \(-0.660878\pi\)
−0.484168 + 0.874975i \(0.660878\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4844.00 −1.92507
\(186\) 0 0
\(187\) 2072.00 0.810265
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1392.00 0.527338 0.263669 − 0.964613i \(-0.415067\pi\)
0.263669 + 0.964613i \(0.415067\pi\)
\(192\) 0 0
\(193\) 1778.00 0.663126 0.331563 − 0.943433i \(-0.392424\pi\)
0.331563 + 0.943433i \(0.392424\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1214.00 −0.439055 −0.219528 − 0.975606i \(-0.570452\pi\)
−0.219528 + 0.975606i \(0.570452\pi\)
\(198\) 0 0
\(199\) −1040.00 −0.370471 −0.185235 − 0.982694i \(-0.559305\pi\)
−0.185235 + 0.982694i \(0.559305\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1330.00 −0.459841
\(204\) 0 0
\(205\) −2268.00 −0.772702
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2240.00 0.741359
\(210\) 0 0
\(211\) 3868.00 1.26201 0.631005 − 0.775779i \(-0.282643\pi\)
0.631005 + 0.775779i \(0.282643\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 5768.00 1.82965
\(216\) 0 0
\(217\) −504.000 −0.157667
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1332.00 −0.405430
\(222\) 0 0
\(223\) −3968.00 −1.19156 −0.595778 − 0.803149i \(-0.703156\pi\)
−0.595778 + 0.803149i \(0.703156\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3936.00 −1.15084 −0.575422 − 0.817857i \(-0.695162\pi\)
−0.575422 + 0.817857i \(0.695162\pi\)
\(228\) 0 0
\(229\) 4810.00 1.38801 0.694004 − 0.719971i \(-0.255845\pi\)
0.694004 + 0.719971i \(0.255845\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2182.00 0.613509 0.306754 − 0.951789i \(-0.400757\pi\)
0.306754 + 0.951789i \(0.400757\pi\)
\(234\) 0 0
\(235\) 336.000 0.0932690
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3000.00 −0.811941 −0.405970 − 0.913886i \(-0.633066\pi\)
−0.405970 + 0.913886i \(0.633066\pi\)
\(240\) 0 0
\(241\) 2042.00 0.545796 0.272898 − 0.962043i \(-0.412018\pi\)
0.272898 + 0.962043i \(0.412018\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 686.000 0.178885
\(246\) 0 0
\(247\) −1440.00 −0.370951
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −528.000 −0.132777 −0.0663886 − 0.997794i \(-0.521148\pi\)
−0.0663886 + 0.997794i \(0.521148\pi\)
\(252\) 0 0
\(253\) 3136.00 0.779283
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5634.00 −1.36747 −0.683734 − 0.729731i \(-0.739645\pi\)
−0.683734 + 0.729731i \(0.739645\pi\)
\(258\) 0 0
\(259\) −2422.00 −0.581065
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 168.000 0.0393891 0.0196945 − 0.999806i \(-0.493731\pi\)
0.0196945 + 0.999806i \(0.493731\pi\)
\(264\) 0 0
\(265\) −4452.00 −1.03202
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1310.00 0.296922 0.148461 − 0.988918i \(-0.452568\pi\)
0.148461 + 0.988918i \(0.452568\pi\)
\(270\) 0 0
\(271\) 2208.00 0.494932 0.247466 − 0.968897i \(-0.420402\pi\)
0.247466 + 0.968897i \(0.420402\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1988.00 −0.435931
\(276\) 0 0
\(277\) 5294.00 1.14832 0.574162 − 0.818742i \(-0.305328\pi\)
0.574162 + 0.818742i \(0.305328\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3242.00 −0.688262 −0.344131 − 0.938922i \(-0.611826\pi\)
−0.344131 + 0.938922i \(0.611826\pi\)
\(282\) 0 0
\(283\) 1592.00 0.334398 0.167199 − 0.985923i \(-0.446528\pi\)
0.167199 + 0.985923i \(0.446528\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1134.00 −0.233233
\(288\) 0 0
\(289\) 563.000 0.114594
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 5022.00 1.00133 0.500663 − 0.865642i \(-0.333090\pi\)
0.500663 + 0.865642i \(0.333090\pi\)
\(294\) 0 0
\(295\) −2800.00 −0.552618
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2016.00 −0.389927
\(300\) 0 0
\(301\) 2884.00 0.552262
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2772.00 −0.520407
\(306\) 0 0
\(307\) 9536.00 1.77280 0.886398 − 0.462924i \(-0.153200\pi\)
0.886398 + 0.462924i \(0.153200\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −968.000 −0.176496 −0.0882480 − 0.996099i \(-0.528127\pi\)
−0.0882480 + 0.996099i \(0.528127\pi\)
\(312\) 0 0
\(313\) 3058.00 0.552231 0.276116 − 0.961124i \(-0.410953\pi\)
0.276116 + 0.961124i \(0.410953\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4986.00 0.883412 0.441706 − 0.897160i \(-0.354373\pi\)
0.441706 + 0.897160i \(0.354373\pi\)
\(318\) 0 0
\(319\) 5320.00 0.933739
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5920.00 1.01981
\(324\) 0 0
\(325\) 1278.00 0.218125
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 168.000 0.0281524
\(330\) 0 0
\(331\) −8612.00 −1.43009 −0.715043 − 0.699081i \(-0.753593\pi\)
−0.715043 + 0.699081i \(0.753593\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 10024.0 1.63483
\(336\) 0 0
\(337\) −10206.0 −1.64972 −0.824861 − 0.565336i \(-0.808747\pi\)
−0.824861 + 0.565336i \(0.808747\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2016.00 0.320154
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2004.00 0.310030 0.155015 − 0.987912i \(-0.450457\pi\)
0.155015 + 0.987912i \(0.450457\pi\)
\(348\) 0 0
\(349\) 1330.00 0.203992 0.101996 − 0.994785i \(-0.467477\pi\)
0.101996 + 0.994785i \(0.467477\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −978.000 −0.147461 −0.0737304 − 0.997278i \(-0.523490\pi\)
−0.0737304 + 0.997278i \(0.523490\pi\)
\(354\) 0 0
\(355\) 5488.00 0.820487
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9680.00 −1.42309 −0.711547 − 0.702638i \(-0.752005\pi\)
−0.711547 + 0.702638i \(0.752005\pi\)
\(360\) 0 0
\(361\) −459.000 −0.0669194
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 7532.00 1.08012
\(366\) 0 0
\(367\) 8656.00 1.23117 0.615585 − 0.788070i \(-0.288920\pi\)
0.615585 + 0.788070i \(0.288920\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2226.00 −0.311504
\(372\) 0 0
\(373\) 5278.00 0.732666 0.366333 − 0.930484i \(-0.380613\pi\)
0.366333 + 0.930484i \(0.380613\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3420.00 −0.467212
\(378\) 0 0
\(379\) −6340.00 −0.859272 −0.429636 − 0.903002i \(-0.641358\pi\)
−0.429636 + 0.903002i \(0.641358\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6232.00 −0.831437 −0.415718 − 0.909493i \(-0.636470\pi\)
−0.415718 + 0.909493i \(0.636470\pi\)
\(384\) 0 0
\(385\) −2744.00 −0.363239
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 14810.0 1.93033 0.965163 − 0.261649i \(-0.0842664\pi\)
0.965163 + 0.261649i \(0.0842664\pi\)
\(390\) 0 0
\(391\) 8288.00 1.07197
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3360.00 −0.428000
\(396\) 0 0
\(397\) 5154.00 0.651566 0.325783 − 0.945445i \(-0.394372\pi\)
0.325783 + 0.945445i \(0.394372\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3282.00 −0.408716 −0.204358 − 0.978896i \(-0.565511\pi\)
−0.204358 + 0.978896i \(0.565511\pi\)
\(402\) 0 0
\(403\) −1296.00 −0.160194
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9688.00 1.17989
\(408\) 0 0
\(409\) 5810.00 0.702411 0.351205 − 0.936298i \(-0.385772\pi\)
0.351205 + 0.936298i \(0.385772\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1400.00 −0.166803
\(414\) 0 0
\(415\) −15008.0 −1.77521
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 13560.0 1.58102 0.790512 − 0.612446i \(-0.209814\pi\)
0.790512 + 0.612446i \(0.209814\pi\)
\(420\) 0 0
\(421\) −738.000 −0.0854345 −0.0427172 − 0.999087i \(-0.513601\pi\)
−0.0427172 + 0.999087i \(0.513601\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5254.00 −0.599662
\(426\) 0 0
\(427\) −1386.00 −0.157080
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1272.00 0.142158 0.0710790 − 0.997471i \(-0.477356\pi\)
0.0710790 + 0.997471i \(0.477356\pi\)
\(432\) 0 0
\(433\) −5062.00 −0.561811 −0.280906 − 0.959735i \(-0.590635\pi\)
−0.280906 + 0.959735i \(0.590635\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8960.00 0.980812
\(438\) 0 0
\(439\) −5640.00 −0.613172 −0.306586 − 0.951843i \(-0.599187\pi\)
−0.306586 + 0.951843i \(0.599187\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 13388.0 1.43585 0.717927 − 0.696119i \(-0.245091\pi\)
0.717927 + 0.696119i \(0.245091\pi\)
\(444\) 0 0
\(445\) −11340.0 −1.20802
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3230.00 0.339495 0.169747 − 0.985488i \(-0.445705\pi\)
0.169747 + 0.985488i \(0.445705\pi\)
\(450\) 0 0
\(451\) 4536.00 0.473596
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1764.00 0.181753
\(456\) 0 0
\(457\) −10646.0 −1.08971 −0.544857 − 0.838529i \(-0.683416\pi\)
−0.544857 + 0.838529i \(0.683416\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7282.00 −0.735698 −0.367849 − 0.929886i \(-0.619906\pi\)
−0.367849 + 0.929886i \(0.619906\pi\)
\(462\) 0 0
\(463\) −12688.0 −1.27357 −0.636783 − 0.771043i \(-0.719735\pi\)
−0.636783 + 0.771043i \(0.719735\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2816.00 −0.279034 −0.139517 − 0.990220i \(-0.544555\pi\)
−0.139517 + 0.990220i \(0.544555\pi\)
\(468\) 0 0
\(469\) 5012.00 0.493460
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −11536.0 −1.12141
\(474\) 0 0
\(475\) −5680.00 −0.548666
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3160.00 −0.301428 −0.150714 − 0.988577i \(-0.548157\pi\)
−0.150714 + 0.988577i \(0.548157\pi\)
\(480\) 0 0
\(481\) −6228.00 −0.590379
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 18956.0 1.77474
\(486\) 0 0
\(487\) 14176.0 1.31905 0.659523 − 0.751684i \(-0.270758\pi\)
0.659523 + 0.751684i \(0.270758\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −11268.0 −1.03568 −0.517839 − 0.855478i \(-0.673263\pi\)
−0.517839 + 0.855478i \(0.673263\pi\)
\(492\) 0 0
\(493\) 14060.0 1.28444
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2744.00 0.247656
\(498\) 0 0
\(499\) 4460.00 0.400114 0.200057 − 0.979784i \(-0.435887\pi\)
0.200057 + 0.979784i \(0.435887\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1512.00 −0.134029 −0.0670147 − 0.997752i \(-0.521347\pi\)
−0.0670147 + 0.997752i \(0.521347\pi\)
\(504\) 0 0
\(505\) 19012.0 1.67529
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 11790.0 1.02668 0.513342 − 0.858184i \(-0.328407\pi\)
0.513342 + 0.858184i \(0.328407\pi\)
\(510\) 0 0
\(511\) 3766.00 0.326024
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 11648.0 0.996645
\(516\) 0 0
\(517\) −672.000 −0.0571654
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1362.00 −0.114530 −0.0572652 − 0.998359i \(-0.518238\pi\)
−0.0572652 + 0.998359i \(0.518238\pi\)
\(522\) 0 0
\(523\) −6968.00 −0.582580 −0.291290 − 0.956635i \(-0.594084\pi\)
−0.291290 + 0.956635i \(0.594084\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5328.00 0.440401
\(528\) 0 0
\(529\) 377.000 0.0309855
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2916.00 −0.236972
\(534\) 0 0
\(535\) 6216.00 0.502320
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1372.00 −0.109640
\(540\) 0 0
\(541\) 7062.00 0.561218 0.280609 − 0.959822i \(-0.409464\pi\)
0.280609 + 0.959822i \(0.409464\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 26180.0 2.05767
\(546\) 0 0
\(547\) 8196.00 0.640650 0.320325 − 0.947308i \(-0.396208\pi\)
0.320325 + 0.947308i \(0.396208\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 15200.0 1.17521
\(552\) 0 0
\(553\) −1680.00 −0.129188
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7466.00 0.567944 0.283972 − 0.958833i \(-0.408348\pi\)
0.283972 + 0.958833i \(0.408348\pi\)
\(558\) 0 0
\(559\) 7416.00 0.561115
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 24968.0 1.86905 0.934526 − 0.355896i \(-0.115824\pi\)
0.934526 + 0.355896i \(0.115824\pi\)
\(564\) 0 0
\(565\) −19292.0 −1.43650
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −14250.0 −1.04990 −0.524948 − 0.851134i \(-0.675915\pi\)
−0.524948 + 0.851134i \(0.675915\pi\)
\(570\) 0 0
\(571\) −6372.00 −0.467005 −0.233503 − 0.972356i \(-0.575019\pi\)
−0.233503 + 0.972356i \(0.575019\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −7952.00 −0.576733
\(576\) 0 0
\(577\) −8366.00 −0.603607 −0.301803 − 0.953370i \(-0.597589\pi\)
−0.301803 + 0.953370i \(0.597589\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −7504.00 −0.535832
\(582\) 0 0
\(583\) 8904.00 0.632532
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 20384.0 1.43328 0.716642 − 0.697441i \(-0.245678\pi\)
0.716642 + 0.697441i \(0.245678\pi\)
\(588\) 0 0
\(589\) 5760.00 0.402948
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −9378.00 −0.649424 −0.324712 − 0.945813i \(-0.605267\pi\)
−0.324712 + 0.945813i \(0.605267\pi\)
\(594\) 0 0
\(595\) −7252.00 −0.499669
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −9000.00 −0.613907 −0.306953 − 0.951725i \(-0.599310\pi\)
−0.306953 + 0.951725i \(0.599310\pi\)
\(600\) 0 0
\(601\) 7562.00 0.513245 0.256623 − 0.966512i \(-0.417390\pi\)
0.256623 + 0.966512i \(0.417390\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7658.00 −0.514615
\(606\) 0 0
\(607\) 2976.00 0.198999 0.0994993 − 0.995038i \(-0.468276\pi\)
0.0994993 + 0.995038i \(0.468276\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 432.000 0.0286037
\(612\) 0 0
\(613\) 4278.00 0.281871 0.140935 − 0.990019i \(-0.454989\pi\)
0.140935 + 0.990019i \(0.454989\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −18794.0 −1.22629 −0.613143 − 0.789972i \(-0.710095\pi\)
−0.613143 + 0.789972i \(0.710095\pi\)
\(618\) 0 0
\(619\) −18040.0 −1.17139 −0.585694 − 0.810532i \(-0.699178\pi\)
−0.585694 + 0.810532i \(0.699178\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −5670.00 −0.364629
\(624\) 0 0
\(625\) −19459.0 −1.24538
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 25604.0 1.62305
\(630\) 0 0
\(631\) 21688.0 1.36828 0.684141 − 0.729350i \(-0.260177\pi\)
0.684141 + 0.729350i \(0.260177\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −27216.0 −1.70084
\(636\) 0 0
\(637\) 882.000 0.0548605
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 10558.0 0.650571 0.325285 − 0.945616i \(-0.394540\pi\)
0.325285 + 0.945616i \(0.394540\pi\)
\(642\) 0 0
\(643\) 26152.0 1.60394 0.801971 − 0.597363i \(-0.203785\pi\)
0.801971 + 0.597363i \(0.203785\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 25584.0 1.55458 0.777288 − 0.629145i \(-0.216595\pi\)
0.777288 + 0.629145i \(0.216595\pi\)
\(648\) 0 0
\(649\) 5600.00 0.338705
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −15198.0 −0.910787 −0.455393 − 0.890290i \(-0.650501\pi\)
−0.455393 + 0.890290i \(0.650501\pi\)
\(654\) 0 0
\(655\) −11872.0 −0.708210
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −6100.00 −0.360580 −0.180290 − 0.983613i \(-0.557704\pi\)
−0.180290 + 0.983613i \(0.557704\pi\)
\(660\) 0 0
\(661\) −2318.00 −0.136399 −0.0681995 − 0.997672i \(-0.521725\pi\)
−0.0681995 + 0.997672i \(0.521725\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −7840.00 −0.457176
\(666\) 0 0
\(667\) 21280.0 1.23533
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5544.00 0.318962
\(672\) 0 0
\(673\) −10222.0 −0.585482 −0.292741 − 0.956192i \(-0.594567\pi\)
−0.292741 + 0.956192i \(0.594567\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −25434.0 −1.44388 −0.721941 − 0.691955i \(-0.756750\pi\)
−0.721941 + 0.691955i \(0.756750\pi\)
\(678\) 0 0
\(679\) 9478.00 0.535688
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −8532.00 −0.477991 −0.238996 − 0.971021i \(-0.576818\pi\)
−0.238996 + 0.971021i \(0.576818\pi\)
\(684\) 0 0
\(685\) 41524.0 2.31613
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −5724.00 −0.316498
\(690\) 0 0
\(691\) −20672.0 −1.13806 −0.569030 − 0.822317i \(-0.692681\pi\)
−0.569030 + 0.822317i \(0.692681\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −39200.0 −2.13948
\(696\) 0 0
\(697\) 11988.0 0.651475
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 21458.0 1.15614 0.578072 − 0.815985i \(-0.303805\pi\)
0.578072 + 0.815985i \(0.303805\pi\)
\(702\) 0 0
\(703\) 27680.0 1.48502
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9506.00 0.505672
\(708\) 0 0
\(709\) −9850.00 −0.521755 −0.260878 − 0.965372i \(-0.584012\pi\)
−0.260878 + 0.965372i \(0.584012\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8064.00 0.423561
\(714\) 0 0
\(715\) −7056.00 −0.369062
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −18840.0 −0.977209 −0.488605 − 0.872505i \(-0.662494\pi\)
−0.488605 + 0.872505i \(0.662494\pi\)
\(720\) 0 0
\(721\) 5824.00 0.300828
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −13490.0 −0.691043
\(726\) 0 0
\(727\) −37504.0 −1.91327 −0.956634 − 0.291291i \(-0.905915\pi\)
−0.956634 + 0.291291i \(0.905915\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −30488.0 −1.54260
\(732\) 0 0
\(733\) 13338.0 0.672101 0.336051 − 0.941844i \(-0.390909\pi\)
0.336051 + 0.941844i \(0.390909\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −20048.0 −1.00200
\(738\) 0 0
\(739\) −17100.0 −0.851196 −0.425598 − 0.904912i \(-0.639936\pi\)
−0.425598 + 0.904912i \(0.639936\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −19632.0 −0.969352 −0.484676 − 0.874694i \(-0.661062\pi\)
−0.484676 + 0.874694i \(0.661062\pi\)
\(744\) 0 0
\(745\) −7140.00 −0.351127
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 3108.00 0.151621
\(750\) 0 0
\(751\) −33912.0 −1.64776 −0.823879 − 0.566766i \(-0.808195\pi\)
−0.823879 + 0.566766i \(0.808195\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −8288.00 −0.399512
\(756\) 0 0
\(757\) −31386.0 −1.50693 −0.753463 − 0.657490i \(-0.771618\pi\)
−0.753463 + 0.657490i \(0.771618\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 34558.0 1.64616 0.823079 − 0.567927i \(-0.192254\pi\)
0.823079 + 0.567927i \(0.192254\pi\)
\(762\) 0 0
\(763\) 13090.0 0.621088
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3600.00 −0.169476
\(768\) 0 0
\(769\) 39130.0 1.83493 0.917467 − 0.397812i \(-0.130231\pi\)
0.917467 + 0.397812i \(0.130231\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 25982.0 1.20894 0.604468 − 0.796629i \(-0.293386\pi\)
0.604468 + 0.796629i \(0.293386\pi\)
\(774\) 0 0
\(775\) −5112.00 −0.236940
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 12960.0 0.596072
\(780\) 0 0
\(781\) −10976.0 −0.502884
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −37604.0 −1.70974
\(786\) 0 0
\(787\) −35424.0 −1.60448 −0.802242 − 0.596999i \(-0.796360\pi\)
−0.802242 + 0.596999i \(0.796360\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9646.00 −0.433593
\(792\) 0 0
\(793\) −3564.00 −0.159598
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 30606.0 1.36025 0.680126 − 0.733096i \(-0.261925\pi\)
0.680126 + 0.733096i \(0.261925\pi\)
\(798\) 0 0
\(799\) −1776.00 −0.0786362
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −15064.0 −0.662014
\(804\) 0 0
\(805\) −10976.0 −0.480563
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −16810.0 −0.730542 −0.365271 − 0.930901i \(-0.619024\pi\)
−0.365271 + 0.930901i \(0.619024\pi\)
\(810\) 0 0
\(811\) 9368.00 0.405616 0.202808 − 0.979218i \(-0.434993\pi\)
0.202808 + 0.979218i \(0.434993\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 14168.0 0.608937
\(816\) 0 0
\(817\) −32960.0 −1.41141
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −34382.0 −1.46156 −0.730780 − 0.682614i \(-0.760843\pi\)
−0.730780 + 0.682614i \(0.760843\pi\)
\(822\) 0 0
\(823\) 4472.00 0.189410 0.0947048 − 0.995505i \(-0.469809\pi\)
0.0947048 + 0.995505i \(0.469809\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1716.00 −0.0721538 −0.0360769 − 0.999349i \(-0.511486\pi\)
−0.0360769 + 0.999349i \(0.511486\pi\)
\(828\) 0 0
\(829\) −7910.00 −0.331394 −0.165697 − 0.986177i \(-0.552987\pi\)
−0.165697 + 0.986177i \(0.552987\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −3626.00 −0.150820
\(834\) 0 0
\(835\) 7616.00 0.315644
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −19360.0 −0.796641 −0.398320 − 0.917246i \(-0.630407\pi\)
−0.398320 + 0.917246i \(0.630407\pi\)
\(840\) 0 0
\(841\) 11711.0 0.480175
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −26222.0 −1.06753
\(846\) 0 0
\(847\) −3829.00 −0.155332
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 38752.0 1.56099
\(852\) 0 0
\(853\) 698.000 0.0280177 0.0140088 − 0.999902i \(-0.495541\pi\)
0.0140088 + 0.999902i \(0.495541\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 23406.0 0.932945 0.466472 − 0.884536i \(-0.345525\pi\)
0.466472 + 0.884536i \(0.345525\pi\)
\(858\) 0 0
\(859\) −7280.00 −0.289162 −0.144581 − 0.989493i \(-0.546183\pi\)
−0.144581 + 0.989493i \(0.546183\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 9808.00 0.386869 0.193435 − 0.981113i \(-0.438037\pi\)
0.193435 + 0.981113i \(0.438037\pi\)
\(864\) 0 0
\(865\) −26012.0 −1.02247
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 6720.00 0.262325
\(870\) 0 0
\(871\) 12888.0 0.501370
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −5292.00 −0.204460
\(876\) 0 0
\(877\) −8066.00 −0.310570 −0.155285 − 0.987870i \(-0.549630\pi\)
−0.155285 + 0.987870i \(0.549630\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −25842.0 −0.988240 −0.494120 − 0.869394i \(-0.664510\pi\)
−0.494120 + 0.869394i \(0.664510\pi\)
\(882\) 0 0
\(883\) 5692.00 0.216932 0.108466 − 0.994100i \(-0.465406\pi\)
0.108466 + 0.994100i \(0.465406\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −13536.0 −0.512395 −0.256198 − 0.966624i \(-0.582470\pi\)
−0.256198 + 0.966624i \(0.582470\pi\)
\(888\) 0 0
\(889\) −13608.0 −0.513383
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1920.00 −0.0719489
\(894\) 0 0
\(895\) −4200.00 −0.156861
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 13680.0 0.507512
\(900\) 0 0
\(901\) 23532.0 0.870105
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −33012.0 −1.21255
\(906\) 0 0
\(907\) −17004.0 −0.622501 −0.311251 − 0.950328i \(-0.600748\pi\)
−0.311251 + 0.950328i \(0.600748\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −14568.0 −0.529813 −0.264906 − 0.964274i \(-0.585341\pi\)
−0.264906 + 0.964274i \(0.585341\pi\)
\(912\) 0 0
\(913\) 30016.0 1.08804
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −5936.00 −0.213767
\(918\) 0 0
\(919\) 1400.00 0.0502522 0.0251261 − 0.999684i \(-0.492001\pi\)
0.0251261 + 0.999684i \(0.492001\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 7056.00 0.251626
\(924\) 0 0
\(925\) −24566.0 −0.873216
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 13830.0 0.488426 0.244213 − 0.969722i \(-0.421470\pi\)
0.244213 + 0.969722i \(0.421470\pi\)
\(930\) 0 0
\(931\) −3920.00 −0.137994
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 29008.0 1.01461
\(936\) 0 0
\(937\) −24166.0 −0.842549 −0.421275 − 0.906933i \(-0.638417\pi\)
−0.421275 + 0.906933i \(0.638417\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 10838.0 0.375461 0.187730 − 0.982221i \(-0.439887\pi\)
0.187730 + 0.982221i \(0.439887\pi\)
\(942\) 0 0
\(943\) 18144.0 0.626564
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −40916.0 −1.40400 −0.702002 − 0.712175i \(-0.747710\pi\)
−0.702002 + 0.712175i \(0.747710\pi\)
\(948\) 0 0
\(949\) 9684.00 0.331250
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −56618.0 −1.92449 −0.962244 − 0.272189i \(-0.912253\pi\)
−0.962244 + 0.272189i \(0.912253\pi\)
\(954\) 0 0
\(955\) 19488.0 0.660332
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 20762.0 0.699103
\(960\) 0 0
\(961\) −24607.0 −0.825988
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 24892.0 0.830365
\(966\) 0 0
\(967\) −17504.0 −0.582100 −0.291050 − 0.956708i \(-0.594005\pi\)
−0.291050 + 0.956708i \(0.594005\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 23112.0 0.763851 0.381926 − 0.924193i \(-0.375261\pi\)
0.381926 + 0.924193i \(0.375261\pi\)
\(972\) 0 0
\(973\) −19600.0 −0.645783
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −23874.0 −0.781778 −0.390889 − 0.920438i \(-0.627832\pi\)
−0.390889 + 0.920438i \(0.627832\pi\)
\(978\) 0 0
\(979\) 22680.0 0.740404
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −15312.0 −0.496823 −0.248411 − 0.968655i \(-0.579909\pi\)
−0.248411 + 0.968655i \(0.579909\pi\)
\(984\) 0 0
\(985\) −16996.0 −0.549784
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −46144.0 −1.48361
\(990\) 0 0
\(991\) 16528.0 0.529797 0.264899 − 0.964276i \(-0.414661\pi\)
0.264899 + 0.964276i \(0.414661\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −14560.0 −0.463903
\(996\) 0 0
\(997\) −28606.0 −0.908687 −0.454344 − 0.890827i \(-0.650126\pi\)
−0.454344 + 0.890827i \(0.650126\pi\)
\(998\) 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 1008.4.a.s.1.1 1
3.2 odd 2 112.4.a.a.1.1 1
4.3 odd 2 126.4.a.h.1.1 1
12.11 even 2 14.4.a.a.1.1 ✓ 1
21.20 even 2 784.4.a.s.1.1 1
24.5 odd 2 448.4.a.o.1.1 1
24.11 even 2 448.4.a.b.1.1 1
28.3 even 6 882.4.g.k.667.1 2
28.11 odd 6 882.4.g.b.667.1 2
28.19 even 6 882.4.g.k.361.1 2
28.23 odd 6 882.4.g.b.361.1 2
28.27 even 2 882.4.a.i.1.1 1
60.23 odd 4 350.4.c.b.99.2 2
60.47 odd 4 350.4.c.b.99.1 2
60.59 even 2 350.4.a.l.1.1 1
84.11 even 6 98.4.c.d.79.1 2
84.23 even 6 98.4.c.d.67.1 2
84.47 odd 6 98.4.c.f.67.1 2
84.59 odd 6 98.4.c.f.79.1 2
84.83 odd 2 98.4.a.a.1.1 1
132.131 odd 2 1694.4.a.g.1.1 1
156.155 even 2 2366.4.a.h.1.1 1
420.419 odd 2 2450.4.a.bo.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.4.a.a.1.1 ✓ 1 12.11 even 2
98.4.a.a.1.1 1 84.83 odd 2
98.4.c.d.67.1 2 84.23 even 6
98.4.c.d.79.1 2 84.11 even 6
98.4.c.f.67.1 2 84.47 odd 6
98.4.c.f.79.1 2 84.59 odd 6
112.4.a.a.1.1 1 3.2 odd 2
126.4.a.h.1.1 1 4.3 odd 2
350.4.a.l.1.1 1 60.59 even 2
350.4.c.b.99.1 2 60.47 odd 4
350.4.c.b.99.2 2 60.23 odd 4
448.4.a.b.1.1 1 24.11 even 2
448.4.a.o.1.1 1 24.5 odd 2
784.4.a.s.1.1 1 21.20 even 2
882.4.a.i.1.1 1 28.27 even 2
882.4.g.b.361.1 2 28.23 odd 6
882.4.g.b.667.1 2 28.11 odd 6
882.4.g.k.361.1 2 28.19 even 6
882.4.g.k.667.1 2 28.3 even 6
1008.4.a.s.1.1 1 1.1 even 1 trivial
1694.4.a.g.1.1 1 132.131 odd 2
2366.4.a.h.1.1 1 156.155 even 2
2450.4.a.bo.1.1 1 420.419 odd 2