↑

Properties

Label 1584.4.a.p.1.1
Level $1584$
Weight $4$
Character 1584.1
Self dual yes
Analytic conductor $93.459$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1584,4,Mod(1,1584)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1584, 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("1584.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1584.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: \(93.4590254491\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 44)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1584.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+7.00000 q^{5} +26.0000 q^{7} +O(q^{10})\) \(q+7.00000 q^{5} +26.0000 q^{7} -11.0000 q^{11} +52.0000 q^{13} -46.0000 q^{17} +96.0000 q^{19} +27.0000 q^{23} -76.0000 q^{25} -16.0000 q^{29} +293.000 q^{31} +182.000 q^{35} -29.0000 q^{37} +472.000 q^{41} +110.000 q^{43} -224.000 q^{47} +333.000 q^{49} -754.000 q^{53} -77.0000 q^{55} +825.000 q^{59} -548.000 q^{61} +364.000 q^{65} +123.000 q^{67} +1001.00 q^{71} -1020.00 q^{73} -286.000 q^{77} -526.000 q^{79} -158.000 q^{83} -322.000 q^{85} +1217.00 q^{89} +1352.00 q^{91} +672.000 q^{95} -263.000 q^{97} +O(q^{100})\)

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
\(5\) 7.00000 0.626099 0.313050 − 0.949737i \(-0.398649\pi\)
0.313050 + 0.949737i \(0.398649\pi\)
\(6\) 0 0
\(7\) 26.0000 1.40387 0.701934 − 0.712242i \(-0.252320\pi\)
0.701934 + 0.712242i \(0.252320\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −11.0000 −0.301511
\(12\) 0 0
\(13\) 52.0000 1.10940 0.554700 − 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −46.0000 −0.656273 −0.328136 − 0.944630i \(-0.606421\pi\)
−0.328136 + 0.944630i \(0.606421\pi\)
\(18\) 0 0
\(19\) 96.0000 1.15915 0.579577 − 0.814918i \(-0.303218\pi\)
0.579577 + 0.814918i \(0.303218\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 27.0000 0.244778 0.122389 − 0.992482i \(-0.460944\pi\)
0.122389 + 0.992482i \(0.460944\pi\)
\(24\) 0 0
\(25\) −76.0000 −0.608000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −16.0000 −0.102453 −0.0512263 − 0.998687i \(-0.516313\pi\)
−0.0512263 + 0.998687i \(0.516313\pi\)
\(30\) 0 0
\(31\) 293.000 1.69756 0.848780 − 0.528746i \(-0.177338\pi\)
0.848780 + 0.528746i \(0.177338\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 182.000 0.878960
\(36\) 0 0
\(37\) −29.0000 −0.128853 −0.0644266 − 0.997922i \(-0.520522\pi\)
−0.0644266 + 0.997922i \(0.520522\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 472.000 1.79790 0.898951 − 0.438048i \(-0.144330\pi\)
0.898951 + 0.438048i \(0.144330\pi\)
\(42\) 0 0
\(43\) 110.000 0.390113 0.195056 − 0.980792i \(-0.437511\pi\)
0.195056 + 0.980792i \(0.437511\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −224.000 −0.695186 −0.347593 − 0.937645i \(-0.613001\pi\)
−0.347593 + 0.937645i \(0.613001\pi\)
\(48\) 0 0
\(49\) 333.000 0.970845
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −754.000 −1.95415 −0.977074 − 0.212899i \(-0.931709\pi\)
−0.977074 + 0.212899i \(0.931709\pi\)
\(54\) 0 0
\(55\) −77.0000 −0.188776
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 825.000 1.82044 0.910219 − 0.414127i \(-0.135913\pi\)
0.910219 + 0.414127i \(0.135913\pi\)
\(60\) 0 0
\(61\) −548.000 −1.15023 −0.575116 − 0.818072i \(-0.695043\pi\)
−0.575116 + 0.818072i \(0.695043\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 364.000 0.694595
\(66\) 0 0
\(67\) 123.000 0.224281 0.112141 − 0.993692i \(-0.464229\pi\)
0.112141 + 0.993692i \(0.464229\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1001.00 1.67319 0.836597 − 0.547818i \(-0.184541\pi\)
0.836597 + 0.547818i \(0.184541\pi\)
\(72\) 0 0
\(73\) −1020.00 −1.63537 −0.817685 − 0.575666i \(-0.804743\pi\)
−0.817685 + 0.575666i \(0.804743\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −286.000 −0.423282
\(78\) 0 0
\(79\) −526.000 −0.749109 −0.374555 − 0.927205i \(-0.622204\pi\)
−0.374555 + 0.927205i \(0.622204\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −158.000 −0.208949 −0.104474 − 0.994528i \(-0.533316\pi\)
−0.104474 + 0.994528i \(0.533316\pi\)
\(84\) 0 0
\(85\) −322.000 −0.410892
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1217.00 1.44946 0.724729 − 0.689034i \(-0.241965\pi\)
0.724729 + 0.689034i \(0.241965\pi\)
\(90\) 0 0
\(91\) 1352.00 1.55745
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 672.000 0.725745
\(96\) 0 0
\(97\) −263.000 −0.275295 −0.137647 − 0.990481i \(-0.543954\pi\)
−0.137647 + 0.990481i \(0.543954\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 814.000 0.801941 0.400970 − 0.916091i \(-0.368673\pi\)
0.400970 + 0.916091i \(0.368673\pi\)
\(102\) 0 0
\(103\) −376.000 −0.359693 −0.179847 − 0.983695i \(-0.557560\pi\)
−0.179847 + 0.983695i \(0.557560\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1494.00 −1.34982 −0.674909 − 0.737901i \(-0.735817\pi\)
−0.674909 + 0.737901i \(0.735817\pi\)
\(108\) 0 0
\(109\) 842.000 0.739899 0.369949 − 0.929052i \(-0.379375\pi\)
0.369949 + 0.929052i \(0.379375\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1281.00 −1.06643 −0.533214 − 0.845980i \(-0.679016\pi\)
−0.533214 + 0.845980i \(0.679016\pi\)
\(114\) 0 0
\(115\) 189.000 0.153255
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1196.00 −0.921321
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1407.00 −1.00677
\(126\) 0 0
\(127\) −1736.00 −1.21295 −0.606477 − 0.795101i \(-0.707418\pi\)
−0.606477 + 0.795101i \(0.707418\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.00000 0.00400170 0.00200085 − 0.999998i \(-0.499363\pi\)
0.00200085 + 0.999998i \(0.499363\pi\)
\(132\) 0 0
\(133\) 2496.00 1.62730
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1439.00 0.897387 0.448694 − 0.893686i \(-0.351889\pi\)
0.448694 + 0.893686i \(0.351889\pi\)
\(138\) 0 0
\(139\) 318.000 0.194046 0.0970231 − 0.995282i \(-0.469068\pi\)
0.0970231 + 0.995282i \(0.469068\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −572.000 −0.334497
\(144\) 0 0
\(145\) −112.000 −0.0641455
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 922.000 0.506934 0.253467 − 0.967344i \(-0.418429\pi\)
0.253467 + 0.967344i \(0.418429\pi\)
\(150\) 0 0
\(151\) 1030.00 0.555101 0.277550 − 0.960711i \(-0.410477\pi\)
0.277550 + 0.960711i \(0.410477\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2051.00 1.06284
\(156\) 0 0
\(157\) 1017.00 0.516977 0.258489 − 0.966014i \(-0.416776\pi\)
0.258489 + 0.966014i \(0.416776\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 702.000 0.343636
\(162\) 0 0
\(163\) 2444.00 1.17441 0.587205 − 0.809438i \(-0.300228\pi\)
0.587205 + 0.809438i \(0.300228\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1452.00 −0.672809 −0.336405 − 0.941718i \(-0.609211\pi\)
−0.336405 + 0.941718i \(0.609211\pi\)
\(168\) 0 0
\(169\) 507.000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1914.00 −0.841149 −0.420574 − 0.907258i \(-0.638171\pi\)
−0.420574 + 0.907258i \(0.638171\pi\)
\(174\) 0 0
\(175\) −1976.00 −0.853552
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1293.00 0.539907 0.269954 − 0.962873i \(-0.412992\pi\)
0.269954 + 0.962873i \(0.412992\pi\)
\(180\) 0 0
\(181\) 455.000 0.186850 0.0934251 − 0.995626i \(-0.470218\pi\)
0.0934251 + 0.995626i \(0.470218\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −203.000 −0.0806749
\(186\) 0 0
\(187\) 506.000 0.197874
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1115.00 −0.422401 −0.211200 − 0.977443i \(-0.567737\pi\)
−0.211200 + 0.977443i \(0.567737\pi\)
\(192\) 0 0
\(193\) 5012.00 1.86928 0.934642 − 0.355591i \(-0.115720\pi\)
0.934642 + 0.355591i \(0.115720\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4146.00 1.49944 0.749721 − 0.661753i \(-0.230187\pi\)
0.749721 + 0.661753i \(0.230187\pi\)
\(198\) 0 0
\(199\) 1240.00 0.441715 0.220857 − 0.975306i \(-0.429114\pi\)
0.220857 + 0.975306i \(0.429114\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −416.000 −0.143830
\(204\) 0 0
\(205\) 3304.00 1.12567
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1056.00 −0.349498
\(210\) 0 0
\(211\) 2820.00 0.920080 0.460040 − 0.887898i \(-0.347835\pi\)
0.460040 + 0.887898i \(0.347835\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 770.000 0.244249
\(216\) 0 0
\(217\) 7618.00 2.38315
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2392.00 −0.728069
\(222\) 0 0
\(223\) −3695.00 −1.10958 −0.554788 − 0.831992i \(-0.687201\pi\)
−0.554788 + 0.831992i \(0.687201\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −486.000 −0.142101 −0.0710506 − 0.997473i \(-0.522635\pi\)
−0.0710506 + 0.997473i \(0.522635\pi\)
\(228\) 0 0
\(229\) 4231.00 1.22093 0.610464 − 0.792044i \(-0.290983\pi\)
0.610464 + 0.792044i \(0.290983\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3336.00 0.937977 0.468988 − 0.883204i \(-0.344619\pi\)
0.468988 + 0.883204i \(0.344619\pi\)
\(234\) 0 0
\(235\) −1568.00 −0.435255
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3610.00 0.977036 0.488518 − 0.872554i \(-0.337538\pi\)
0.488518 + 0.872554i \(0.337538\pi\)
\(240\) 0 0
\(241\) −6408.00 −1.71276 −0.856381 − 0.516345i \(-0.827292\pi\)
−0.856381 + 0.516345i \(0.827292\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2331.00 0.607845
\(246\) 0 0
\(247\) 4992.00 1.28596
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1787.00 −0.449380 −0.224690 − 0.974430i \(-0.572137\pi\)
−0.224690 + 0.974430i \(0.572137\pi\)
\(252\) 0 0
\(253\) −297.000 −0.0738033
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 354.000 0.0859218 0.0429609 − 0.999077i \(-0.486321\pi\)
0.0429609 + 0.999077i \(0.486321\pi\)
\(258\) 0 0
\(259\) −754.000 −0.180893
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2026.00 −0.475013 −0.237507 − 0.971386i \(-0.576330\pi\)
−0.237507 + 0.971386i \(0.576330\pi\)
\(264\) 0 0
\(265\) −5278.00 −1.22349
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 8750.00 1.98326 0.991630 − 0.129112i \(-0.0412128\pi\)
0.991630 + 0.129112i \(0.0412128\pi\)
\(270\) 0 0
\(271\) 5036.00 1.12884 0.564419 − 0.825488i \(-0.309100\pi\)
0.564419 + 0.825488i \(0.309100\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 836.000 0.183319
\(276\) 0 0
\(277\) −4306.00 −0.934016 −0.467008 − 0.884253i \(-0.654668\pi\)
−0.467008 + 0.884253i \(0.654668\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1202.00 0.255179 0.127590 − 0.991827i \(-0.459276\pi\)
0.127590 + 0.991827i \(0.459276\pi\)
\(282\) 0 0
\(283\) 6620.00 1.39052 0.695262 − 0.718757i \(-0.255288\pi\)
0.695262 + 0.718757i \(0.255288\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 12272.0 2.52402
\(288\) 0 0
\(289\) −2797.00 −0.569306
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6968.00 −1.38933 −0.694667 − 0.719331i \(-0.744448\pi\)
−0.694667 + 0.719331i \(0.744448\pi\)
\(294\) 0 0
\(295\) 5775.00 1.13977
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1404.00 0.271557
\(300\) 0 0
\(301\) 2860.00 0.547667
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3836.00 −0.720160
\(306\) 0 0
\(307\) −7640.00 −1.42032 −0.710159 − 0.704041i \(-0.751377\pi\)
−0.710159 + 0.704041i \(0.751377\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −652.000 −0.118880 −0.0594398 − 0.998232i \(-0.518931\pi\)
−0.0594398 + 0.998232i \(0.518931\pi\)
\(312\) 0 0
\(313\) 8055.00 1.45462 0.727309 − 0.686310i \(-0.240771\pi\)
0.727309 + 0.686310i \(0.240771\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5675.00 1.00549 0.502744 − 0.864435i \(-0.332324\pi\)
0.502744 + 0.864435i \(0.332324\pi\)
\(318\) 0 0
\(319\) 176.000 0.0308906
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4416.00 −0.760721
\(324\) 0 0
\(325\) −3952.00 −0.674515
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −5824.00 −0.975950
\(330\) 0 0
\(331\) 2245.00 0.372799 0.186399 − 0.982474i \(-0.440318\pi\)
0.186399 + 0.982474i \(0.440318\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 861.000 0.140422
\(336\) 0 0
\(337\) −694.000 −0.112180 −0.0560899 − 0.998426i \(-0.517863\pi\)
−0.0560899 + 0.998426i \(0.517863\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3223.00 −0.511834
\(342\) 0 0
\(343\) −260.000 −0.0409291
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4092.00 0.633055 0.316527 − 0.948583i \(-0.397483\pi\)
0.316527 + 0.948583i \(0.397483\pi\)
\(348\) 0 0
\(349\) 334.000 0.0512281 0.0256141 − 0.999672i \(-0.491846\pi\)
0.0256141 + 0.999672i \(0.491846\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −891.000 −0.134343 −0.0671716 − 0.997741i \(-0.521397\pi\)
−0.0671716 + 0.997741i \(0.521397\pi\)
\(354\) 0 0
\(355\) 7007.00 1.04759
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2476.00 0.364006 0.182003 − 0.983298i \(-0.441742\pi\)
0.182003 + 0.983298i \(0.441742\pi\)
\(360\) 0 0
\(361\) 2357.00 0.343636
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −7140.00 −1.02390
\(366\) 0 0
\(367\) −1379.00 −0.196140 −0.0980698 − 0.995180i \(-0.531267\pi\)
−0.0980698 + 0.995180i \(0.531267\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −19604.0 −2.74337
\(372\) 0 0
\(373\) −6266.00 −0.869816 −0.434908 − 0.900475i \(-0.643219\pi\)
−0.434908 + 0.900475i \(0.643219\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −832.000 −0.113661
\(378\) 0 0
\(379\) −151.000 −0.0204653 −0.0102327 − 0.999948i \(-0.503257\pi\)
−0.0102327 + 0.999948i \(0.503257\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1989.00 −0.265361 −0.132680 − 0.991159i \(-0.542358\pi\)
−0.132680 + 0.991159i \(0.542358\pi\)
\(384\) 0 0
\(385\) −2002.00 −0.265017
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −6817.00 −0.888523 −0.444262 − 0.895897i \(-0.646534\pi\)
−0.444262 + 0.895897i \(0.646534\pi\)
\(390\) 0 0
\(391\) −1242.00 −0.160641
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3682.00 −0.469017
\(396\) 0 0
\(397\) −4170.00 −0.527170 −0.263585 − 0.964636i \(-0.584905\pi\)
−0.263585 + 0.964636i \(0.584905\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10914.0 −1.35915 −0.679575 − 0.733606i \(-0.737836\pi\)
−0.679575 + 0.733606i \(0.737836\pi\)
\(402\) 0 0
\(403\) 15236.0 1.88327
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 319.000 0.0388507
\(408\) 0 0
\(409\) −1102.00 −0.133228 −0.0666142 − 0.997779i \(-0.521220\pi\)
−0.0666142 + 0.997779i \(0.521220\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 21450.0 2.55565
\(414\) 0 0
\(415\) −1106.00 −0.130823
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 11028.0 1.28581 0.642903 − 0.765947i \(-0.277730\pi\)
0.642903 + 0.765947i \(0.277730\pi\)
\(420\) 0 0
\(421\) 2622.00 0.303536 0.151768 − 0.988416i \(-0.451503\pi\)
0.151768 + 0.988416i \(0.451503\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3496.00 0.399014
\(426\) 0 0
\(427\) −14248.0 −1.61478
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 16598.0 1.85498 0.927491 − 0.373845i \(-0.121961\pi\)
0.927491 + 0.373845i \(0.121961\pi\)
\(432\) 0 0
\(433\) −5763.00 −0.639612 −0.319806 − 0.947483i \(-0.603618\pi\)
−0.319806 + 0.947483i \(0.603618\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2592.00 0.283735
\(438\) 0 0
\(439\) 3128.00 0.340071 0.170036 − 0.985438i \(-0.445612\pi\)
0.170036 + 0.985438i \(0.445612\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6369.00 0.683071 0.341535 − 0.939869i \(-0.389053\pi\)
0.341535 + 0.939869i \(0.389053\pi\)
\(444\) 0 0
\(445\) 8519.00 0.907504
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −8691.00 −0.913483 −0.456741 − 0.889600i \(-0.650983\pi\)
−0.456741 + 0.889600i \(0.650983\pi\)
\(450\) 0 0
\(451\) −5192.00 −0.542088
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 9464.00 0.975119
\(456\) 0 0
\(457\) 2260.00 0.231331 0.115666 − 0.993288i \(-0.463100\pi\)
0.115666 + 0.993288i \(0.463100\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 12756.0 1.28873 0.644367 − 0.764717i \(-0.277121\pi\)
0.644367 + 0.764717i \(0.277121\pi\)
\(462\) 0 0
\(463\) 6887.00 0.691287 0.345644 − 0.938366i \(-0.387661\pi\)
0.345644 + 0.938366i \(0.387661\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1535.00 −0.152101 −0.0760507 − 0.997104i \(-0.524231\pi\)
−0.0760507 + 0.997104i \(0.524231\pi\)
\(468\) 0 0
\(469\) 3198.00 0.314861
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1210.00 −0.117623
\(474\) 0 0
\(475\) −7296.00 −0.704765
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −17564.0 −1.67541 −0.837703 − 0.546126i \(-0.816102\pi\)
−0.837703 + 0.546126i \(0.816102\pi\)
\(480\) 0 0
\(481\) −1508.00 −0.142950
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1841.00 −0.172362
\(486\) 0 0
\(487\) 7541.00 0.701674 0.350837 − 0.936437i \(-0.385897\pi\)
0.350837 + 0.936437i \(0.385897\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12552.0 1.15369 0.576847 − 0.816852i \(-0.304283\pi\)
0.576847 + 0.816852i \(0.304283\pi\)
\(492\) 0 0
\(493\) 736.000 0.0672369
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 26026.0 2.34894
\(498\) 0 0
\(499\) 8396.00 0.753220 0.376610 − 0.926372i \(-0.377090\pi\)
0.376610 + 0.926372i \(0.377090\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12194.0 −1.08092 −0.540461 − 0.841369i \(-0.681750\pi\)
−0.540461 + 0.841369i \(0.681750\pi\)
\(504\) 0 0
\(505\) 5698.00 0.502094
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −18295.0 −1.59315 −0.796573 − 0.604542i \(-0.793356\pi\)
−0.796573 + 0.604542i \(0.793356\pi\)
\(510\) 0 0
\(511\) −26520.0 −2.29584
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2632.00 −0.225203
\(516\) 0 0
\(517\) 2464.00 0.209607
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7101.00 −0.597122 −0.298561 − 0.954391i \(-0.596507\pi\)
−0.298561 + 0.954391i \(0.596507\pi\)
\(522\) 0 0
\(523\) 4912.00 0.410682 0.205341 − 0.978690i \(-0.434170\pi\)
0.205341 + 0.978690i \(0.434170\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −13478.0 −1.11406
\(528\) 0 0
\(529\) −11438.0 −0.940084
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 24544.0 1.99459
\(534\) 0 0
\(535\) −10458.0 −0.845119
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3663.00 −0.292721
\(540\) 0 0
\(541\) 11496.0 0.913589 0.456794 − 0.889572i \(-0.348997\pi\)
0.456794 + 0.889572i \(0.348997\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5894.00 0.463250
\(546\) 0 0
\(547\) −19048.0 −1.48891 −0.744455 − 0.667673i \(-0.767291\pi\)
−0.744455 + 0.667673i \(0.767291\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1536.00 −0.118758
\(552\) 0 0
\(553\) −13676.0 −1.05165
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −10718.0 −0.815325 −0.407663 − 0.913133i \(-0.633656\pi\)
−0.407663 + 0.913133i \(0.633656\pi\)
\(558\) 0 0
\(559\) 5720.00 0.432791
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6660.00 0.498553 0.249277 − 0.968432i \(-0.419807\pi\)
0.249277 + 0.968432i \(0.419807\pi\)
\(564\) 0 0
\(565\) −8967.00 −0.667689
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 10960.0 0.807499 0.403750 − 0.914870i \(-0.367707\pi\)
0.403750 + 0.914870i \(0.367707\pi\)
\(570\) 0 0
\(571\) −18596.0 −1.36290 −0.681452 − 0.731863i \(-0.738651\pi\)
−0.681452 + 0.731863i \(0.738651\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2052.00 −0.148825
\(576\) 0 0
\(577\) −21119.0 −1.52374 −0.761868 − 0.647733i \(-0.775717\pi\)
−0.761868 + 0.647733i \(0.775717\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4108.00 −0.293337
\(582\) 0 0
\(583\) 8294.00 0.589198
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2836.00 −0.199411 −0.0997055 − 0.995017i \(-0.531790\pi\)
−0.0997055 + 0.995017i \(0.531790\pi\)
\(588\) 0 0
\(589\) 28128.0 1.96773
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −18044.0 −1.24954 −0.624771 − 0.780808i \(-0.714808\pi\)
−0.624771 + 0.780808i \(0.714808\pi\)
\(594\) 0 0
\(595\) −8372.00 −0.576838
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −9264.00 −0.631914 −0.315957 − 0.948773i \(-0.602326\pi\)
−0.315957 + 0.948773i \(0.602326\pi\)
\(600\) 0 0
\(601\) −19326.0 −1.31169 −0.655844 − 0.754897i \(-0.727687\pi\)
−0.655844 + 0.754897i \(0.727687\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 847.000 0.0569181
\(606\) 0 0
\(607\) −10082.0 −0.674161 −0.337081 − 0.941476i \(-0.609439\pi\)
−0.337081 + 0.941476i \(0.609439\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −11648.0 −0.771240
\(612\) 0 0
\(613\) 13088.0 0.862348 0.431174 − 0.902269i \(-0.358100\pi\)
0.431174 + 0.902269i \(0.358100\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −23426.0 −1.52852 −0.764259 − 0.644910i \(-0.776895\pi\)
−0.764259 + 0.644910i \(0.776895\pi\)
\(618\) 0 0
\(619\) −23587.0 −1.53157 −0.765785 − 0.643097i \(-0.777649\pi\)
−0.765785 + 0.643097i \(0.777649\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 31642.0 2.03485
\(624\) 0 0
\(625\) −349.000 −0.0223360
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1334.00 0.0845629
\(630\) 0 0
\(631\) −19683.0 −1.24179 −0.620894 − 0.783895i \(-0.713230\pi\)
−0.620894 + 0.783895i \(0.713230\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −12152.0 −0.759429
\(636\) 0 0
\(637\) 17316.0 1.07706
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −375.000 −0.0231070 −0.0115535 − 0.999933i \(-0.503678\pi\)
−0.0115535 + 0.999933i \(0.503678\pi\)
\(642\) 0 0
\(643\) 21055.0 1.29133 0.645667 − 0.763619i \(-0.276579\pi\)
0.645667 + 0.763619i \(0.276579\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −6427.00 −0.390528 −0.195264 − 0.980751i \(-0.562556\pi\)
−0.195264 + 0.980751i \(0.562556\pi\)
\(648\) 0 0
\(649\) −9075.00 −0.548883
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7617.00 0.456472 0.228236 − 0.973606i \(-0.426704\pi\)
0.228236 + 0.973606i \(0.426704\pi\)
\(654\) 0 0
\(655\) 42.0000 0.00250546
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −17630.0 −1.04214 −0.521068 − 0.853515i \(-0.674466\pi\)
−0.521068 + 0.853515i \(0.674466\pi\)
\(660\) 0 0
\(661\) 4605.00 0.270974 0.135487 − 0.990779i \(-0.456740\pi\)
0.135487 + 0.990779i \(0.456740\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 17472.0 1.01885
\(666\) 0 0
\(667\) −432.000 −0.0250781
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6028.00 0.346808
\(672\) 0 0
\(673\) −2818.00 −0.161406 −0.0807028 − 0.996738i \(-0.525716\pi\)
−0.0807028 + 0.996738i \(0.525716\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −8438.00 −0.479023 −0.239512 − 0.970894i \(-0.576987\pi\)
−0.239512 + 0.970894i \(0.576987\pi\)
\(678\) 0 0
\(679\) −6838.00 −0.386478
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −17344.0 −0.971669 −0.485834 − 0.874051i \(-0.661484\pi\)
−0.485834 + 0.874051i \(0.661484\pi\)
\(684\) 0 0
\(685\) 10073.0 0.561853
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −39208.0 −2.16793
\(690\) 0 0
\(691\) 3947.00 0.217295 0.108648 − 0.994080i \(-0.465348\pi\)
0.108648 + 0.994080i \(0.465348\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2226.00 0.121492
\(696\) 0 0
\(697\) −21712.0 −1.17991
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 7998.00 0.430928 0.215464 − 0.976512i \(-0.430874\pi\)
0.215464 + 0.976512i \(0.430874\pi\)
\(702\) 0 0
\(703\) −2784.00 −0.149361
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 21164.0 1.12582
\(708\) 0 0
\(709\) −881.000 −0.0466666 −0.0233333 − 0.999728i \(-0.507428\pi\)
−0.0233333 + 0.999728i \(0.507428\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 7911.00 0.415525
\(714\) 0 0
\(715\) −4004.00 −0.209428
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −26093.0 −1.35341 −0.676707 − 0.736252i \(-0.736594\pi\)
−0.676707 + 0.736252i \(0.736594\pi\)
\(720\) 0 0
\(721\) −9776.00 −0.504962
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1216.00 0.0622912
\(726\) 0 0
\(727\) 7481.00 0.381644 0.190822 − 0.981625i \(-0.438885\pi\)
0.190822 + 0.981625i \(0.438885\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −5060.00 −0.256020
\(732\) 0 0
\(733\) 17788.0 0.896337 0.448168 − 0.893949i \(-0.352077\pi\)
0.448168 + 0.893949i \(0.352077\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1353.00 −0.0676233
\(738\) 0 0
\(739\) 32182.0 1.60194 0.800970 − 0.598704i \(-0.204317\pi\)
0.800970 + 0.598704i \(0.204317\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −32044.0 −1.58221 −0.791104 − 0.611682i \(-0.790493\pi\)
−0.791104 + 0.611682i \(0.790493\pi\)
\(744\) 0 0
\(745\) 6454.00 0.317391
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −38844.0 −1.89497
\(750\) 0 0
\(751\) 33779.0 1.64130 0.820648 − 0.571434i \(-0.193613\pi\)
0.820648 + 0.571434i \(0.193613\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 7210.00 0.347548
\(756\) 0 0
\(757\) −15630.0 −0.750439 −0.375219 − 0.926936i \(-0.622433\pi\)
−0.375219 + 0.926936i \(0.622433\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1948.00 −0.0927923 −0.0463962 − 0.998923i \(-0.514774\pi\)
−0.0463962 + 0.998923i \(0.514774\pi\)
\(762\) 0 0
\(763\) 21892.0 1.03872
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 42900.0 2.01959
\(768\) 0 0
\(769\) −17420.0 −0.816881 −0.408440 − 0.912785i \(-0.633927\pi\)
−0.408440 + 0.912785i \(0.633927\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −11122.0 −0.517504 −0.258752 − 0.965944i \(-0.583311\pi\)
−0.258752 + 0.965944i \(0.583311\pi\)
\(774\) 0 0
\(775\) −22268.0 −1.03212
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 45312.0 2.08404
\(780\) 0 0
\(781\) −11011.0 −0.504487
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 7119.00 0.323679
\(786\) 0 0
\(787\) −29648.0 −1.34287 −0.671434 − 0.741064i \(-0.734321\pi\)
−0.671434 + 0.741064i \(0.734321\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −33306.0 −1.49712
\(792\) 0 0
\(793\) −28496.0 −1.27607
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 23219.0 1.03194 0.515972 − 0.856606i \(-0.327431\pi\)
0.515972 + 0.856606i \(0.327431\pi\)
\(798\) 0 0
\(799\) 10304.0 0.456232
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 11220.0 0.493082
\(804\) 0 0
\(805\) 4914.00 0.215150
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −9232.00 −0.401211 −0.200606 − 0.979672i \(-0.564291\pi\)
−0.200606 + 0.979672i \(0.564291\pi\)
\(810\) 0 0
\(811\) 32286.0 1.39792 0.698961 − 0.715160i \(-0.253646\pi\)
0.698961 + 0.715160i \(0.253646\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 17108.0 0.735297
\(816\) 0 0
\(817\) 10560.0 0.452200
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 31706.0 1.34780 0.673902 − 0.738821i \(-0.264617\pi\)
0.673902 + 0.738821i \(0.264617\pi\)
\(822\) 0 0
\(823\) −41139.0 −1.74242 −0.871212 − 0.490906i \(-0.836666\pi\)
−0.871212 + 0.490906i \(0.836666\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −15252.0 −0.641311 −0.320655 − 0.947196i \(-0.603903\pi\)
−0.320655 + 0.947196i \(0.603903\pi\)
\(828\) 0 0
\(829\) 369.000 0.0154595 0.00772973 − 0.999970i \(-0.497540\pi\)
0.00772973 + 0.999970i \(0.497540\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −15318.0 −0.637140
\(834\) 0 0
\(835\) −10164.0 −0.421245
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −10257.0 −0.422063 −0.211032 − 0.977479i \(-0.567682\pi\)
−0.211032 + 0.977479i \(0.567682\pi\)
\(840\) 0 0
\(841\) −24133.0 −0.989503
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 3549.00 0.144484
\(846\) 0 0
\(847\) 3146.00 0.127624
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −783.000 −0.0315404
\(852\) 0 0
\(853\) −34386.0 −1.38025 −0.690126 − 0.723690i \(-0.742445\pi\)
−0.690126 + 0.723690i \(0.742445\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 23464.0 0.935257 0.467628 − 0.883925i \(-0.345109\pi\)
0.467628 + 0.883925i \(0.345109\pi\)
\(858\) 0 0
\(859\) 22475.0 0.892709 0.446355 − 0.894856i \(-0.352722\pi\)
0.446355 + 0.894856i \(0.352722\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2880.00 0.113599 0.0567997 − 0.998386i \(-0.481910\pi\)
0.0567997 + 0.998386i \(0.481910\pi\)
\(864\) 0 0
\(865\) −13398.0 −0.526642
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 5786.00 0.225865
\(870\) 0 0
\(871\) 6396.00 0.248818
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −36582.0 −1.41337
\(876\) 0 0
\(877\) −11084.0 −0.426773 −0.213387 − 0.976968i \(-0.568449\pi\)
−0.213387 + 0.976968i \(0.568449\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −41797.0 −1.59838 −0.799192 − 0.601076i \(-0.794739\pi\)
−0.799192 + 0.601076i \(0.794739\pi\)
\(882\) 0 0
\(883\) −23780.0 −0.906298 −0.453149 − 0.891435i \(-0.649699\pi\)
−0.453149 + 0.891435i \(0.649699\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −14334.0 −0.542603 −0.271301 − 0.962494i \(-0.587454\pi\)
−0.271301 + 0.962494i \(0.587454\pi\)
\(888\) 0 0
\(889\) −45136.0 −1.70283
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −21504.0 −0.805827
\(894\) 0 0
\(895\) 9051.00 0.338035
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −4688.00 −0.173919
\(900\) 0 0
\(901\) 34684.0 1.28245
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 3185.00 0.116987
\(906\) 0 0
\(907\) −25716.0 −0.941440 −0.470720 − 0.882283i \(-0.656006\pi\)
−0.470720 + 0.882283i \(0.656006\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −28300.0 −1.02922 −0.514611 − 0.857424i \(-0.672064\pi\)
−0.514611 + 0.857424i \(0.672064\pi\)
\(912\) 0 0
\(913\) 1738.00 0.0630004
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 156.000 0.00561786
\(918\) 0 0
\(919\) −21410.0 −0.768499 −0.384250 − 0.923229i \(-0.625540\pi\)
−0.384250 + 0.923229i \(0.625540\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 52052.0 1.85624
\(924\) 0 0
\(925\) 2204.00 0.0783428
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −19938.0 −0.704138 −0.352069 − 0.935974i \(-0.614522\pi\)
−0.352069 + 0.935974i \(0.614522\pi\)
\(930\) 0 0
\(931\) 31968.0 1.12536
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 3542.00 0.123889
\(936\) 0 0
\(937\) 26728.0 0.931874 0.465937 − 0.884818i \(-0.345717\pi\)
0.465937 + 0.884818i \(0.345717\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −8634.00 −0.299108 −0.149554 − 0.988754i \(-0.547784\pi\)
−0.149554 + 0.988754i \(0.547784\pi\)
\(942\) 0 0
\(943\) 12744.0 0.440087
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 24841.0 0.852401 0.426201 − 0.904629i \(-0.359852\pi\)
0.426201 + 0.904629i \(0.359852\pi\)
\(948\) 0 0
\(949\) −53040.0 −1.81428
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −51234.0 −1.74148 −0.870741 − 0.491742i \(-0.836360\pi\)
−0.870741 + 0.491742i \(0.836360\pi\)
\(954\) 0 0
\(955\) −7805.00 −0.264465
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 37414.0 1.25981
\(960\) 0 0
\(961\) 56058.0 1.88171
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 35084.0 1.17036
\(966\) 0 0
\(967\) 26752.0 0.889645 0.444822 − 0.895619i \(-0.353267\pi\)
0.444822 + 0.895619i \(0.353267\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 21155.0 0.699172 0.349586 − 0.936904i \(-0.386322\pi\)
0.349586 + 0.936904i \(0.386322\pi\)
\(972\) 0 0
\(973\) 8268.00 0.272415
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 56323.0 1.84435 0.922176 − 0.386770i \(-0.126409\pi\)
0.922176 + 0.386770i \(0.126409\pi\)
\(978\) 0 0
\(979\) −13387.0 −0.437028
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 24683.0 0.800880 0.400440 − 0.916323i \(-0.368857\pi\)
0.400440 + 0.916323i \(0.368857\pi\)
\(984\) 0 0
\(985\) 29022.0 0.938800
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 2970.00 0.0954909
\(990\) 0 0
\(991\) 26816.0 0.859574 0.429787 − 0.902930i \(-0.358589\pi\)
0.429787 + 0.902930i \(0.358589\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 8680.00 0.276557
\(996\) 0 0
\(997\) 18614.0 0.591285 0.295643 − 0.955299i \(-0.404466\pi\)
0.295643 + 0.955299i \(0.404466\pi\)
\(998\) 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 1584.4.a.p.1.1 1
3.2 odd 2 176.4.a.e.1.1 1
4.3 odd 2 396.4.a.e.1.1 1
12.11 even 2 44.4.a.a.1.1 ✓ 1
24.5 odd 2 704.4.a.c.1.1 1
24.11 even 2 704.4.a.j.1.1 1
33.32 even 2 1936.4.a.m.1.1 1
60.23 odd 4 1100.4.b.c.749.1 2
60.47 odd 4 1100.4.b.c.749.2 2
60.59 even 2 1100.4.a.d.1.1 1
84.83 odd 2 2156.4.a.b.1.1 1
132.131 odd 2 484.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
44.4.a.a.1.1 ✓ 1 12.11 even 2
176.4.a.e.1.1 1 3.2 odd 2
396.4.a.e.1.1 1 4.3 odd 2
484.4.a.a.1.1 1 132.131 odd 2
704.4.a.c.1.1 1 24.5 odd 2
704.4.a.j.1.1 1 24.11 even 2
1100.4.a.d.1.1 1 60.59 even 2
1100.4.b.c.749.1 2 60.23 odd 4
1100.4.b.c.749.2 2 60.47 odd 4
1584.4.a.p.1.1 1 1.1 even 1 trivial
1936.4.a.m.1.1 1 33.32 even 2
2156.4.a.b.1.1 1 84.83 odd 2