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Properties

Label 576.4.a.v.1.1
Level $576$
Weight $4$
Character 576.1
Self dual yes
Analytic conductor $33.985$
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] = [576,4,Mod(1,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("576.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 576.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: \(33.9851001633\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 24)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 576.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+14.0000 q^{5} +24.0000 q^{7} +O(q^{10})\) \(q+14.0000 q^{5} +24.0000 q^{7} +28.0000 q^{11} +74.0000 q^{13} -82.0000 q^{17} +92.0000 q^{19} +8.00000 q^{23} +71.0000 q^{25} -138.000 q^{29} -80.0000 q^{31} +336.000 q^{35} -30.0000 q^{37} -282.000 q^{41} +4.00000 q^{43} +240.000 q^{47} +233.000 q^{49} -130.000 q^{53} +392.000 q^{55} -596.000 q^{59} +218.000 q^{61} +1036.00 q^{65} -436.000 q^{67} +856.000 q^{71} -998.000 q^{73} +672.000 q^{77} +32.0000 q^{79} +1508.00 q^{83} -1148.00 q^{85} +246.000 q^{89} +1776.00 q^{91} +1288.00 q^{95} +866.000 q^{97} +O(q^{100})\)

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
\(5\) 14.0000 1.25220 0.626099 − 0.779744i \(-0.284651\pi\)
0.626099 + 0.779744i \(0.284651\pi\)
\(6\) 0 0
\(7\) 24.0000 1.29588 0.647939 − 0.761692i \(-0.275631\pi\)
0.647939 + 0.761692i \(0.275631\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 28.0000 0.767483 0.383742 − 0.923440i \(-0.374635\pi\)
0.383742 + 0.923440i \(0.374635\pi\)
\(12\) 0 0
\(13\) 74.0000 1.57876 0.789381 − 0.613904i \(-0.210402\pi\)
0.789381 + 0.613904i \(0.210402\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −82.0000 −1.16988 −0.584939 − 0.811077i \(-0.698882\pi\)
−0.584939 + 0.811077i \(0.698882\pi\)
\(18\) 0 0
\(19\) 92.0000 1.11086 0.555428 − 0.831565i \(-0.312555\pi\)
0.555428 + 0.831565i \(0.312555\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 8.00000 0.0725268 0.0362634 − 0.999342i \(-0.488454\pi\)
0.0362634 + 0.999342i \(0.488454\pi\)
\(24\) 0 0
\(25\) 71.0000 0.568000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −138.000 −0.883654 −0.441827 − 0.897100i \(-0.645669\pi\)
−0.441827 + 0.897100i \(0.645669\pi\)
\(30\) 0 0
\(31\) −80.0000 −0.463498 −0.231749 − 0.972776i \(-0.574445\pi\)
−0.231749 + 0.972776i \(0.574445\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 336.000 1.62270
\(36\) 0 0
\(37\) −30.0000 −0.133296 −0.0666482 − 0.997777i \(-0.521231\pi\)
−0.0666482 + 0.997777i \(0.521231\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −282.000 −1.07417 −0.537085 − 0.843528i \(-0.680475\pi\)
−0.537085 + 0.843528i \(0.680475\pi\)
\(42\) 0 0
\(43\) 4.00000 0.0141859 0.00709296 − 0.999975i \(-0.497742\pi\)
0.00709296 + 0.999975i \(0.497742\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 240.000 0.744843 0.372421 − 0.928064i \(-0.378528\pi\)
0.372421 + 0.928064i \(0.378528\pi\)
\(48\) 0 0
\(49\) 233.000 0.679300
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −130.000 −0.336922 −0.168461 − 0.985708i \(-0.553880\pi\)
−0.168461 + 0.985708i \(0.553880\pi\)
\(54\) 0 0
\(55\) 392.000 0.961041
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −596.000 −1.31513 −0.657564 − 0.753398i \(-0.728413\pi\)
−0.657564 + 0.753398i \(0.728413\pi\)
\(60\) 0 0
\(61\) 218.000 0.457574 0.228787 − 0.973476i \(-0.426524\pi\)
0.228787 + 0.973476i \(0.426524\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1036.00 1.97692
\(66\) 0 0
\(67\) −436.000 −0.795013 −0.397507 − 0.917599i \(-0.630124\pi\)
−0.397507 + 0.917599i \(0.630124\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 856.000 1.43082 0.715412 − 0.698703i \(-0.246239\pi\)
0.715412 + 0.698703i \(0.246239\pi\)
\(72\) 0 0
\(73\) −998.000 −1.60010 −0.800048 − 0.599935i \(-0.795193\pi\)
−0.800048 + 0.599935i \(0.795193\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 672.000 0.994565
\(78\) 0 0
\(79\) 32.0000 0.0455732 0.0227866 − 0.999740i \(-0.492746\pi\)
0.0227866 + 0.999740i \(0.492746\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1508.00 1.99427 0.997136 − 0.0756351i \(-0.0240984\pi\)
0.997136 + 0.0756351i \(0.0240984\pi\)
\(84\) 0 0
\(85\) −1148.00 −1.46492
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 246.000 0.292988 0.146494 − 0.989212i \(-0.453201\pi\)
0.146494 + 0.989212i \(0.453201\pi\)
\(90\) 0 0
\(91\) 1776.00 2.04588
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1288.00 1.39101
\(96\) 0 0
\(97\) 866.000 0.906484 0.453242 − 0.891387i \(-0.350267\pi\)
0.453242 + 0.891387i \(0.350267\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 270.000 0.266000 0.133000 − 0.991116i \(-0.457539\pi\)
0.133000 + 0.991116i \(0.457539\pi\)
\(102\) 0 0
\(103\) 1496.00 1.43112 0.715560 − 0.698552i \(-0.246172\pi\)
0.715560 + 0.698552i \(0.246172\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1692.00 1.52871 0.764354 − 0.644797i \(-0.223058\pi\)
0.764354 + 0.644797i \(0.223058\pi\)
\(108\) 0 0
\(109\) −406.000 −0.356768 −0.178384 − 0.983961i \(-0.557087\pi\)
−0.178384 + 0.983961i \(0.557087\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −786.000 −0.654342 −0.327171 − 0.944965i \(-0.606095\pi\)
−0.327171 + 0.944965i \(0.606095\pi\)
\(114\) 0 0
\(115\) 112.000 0.0908179
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1968.00 −1.51602
\(120\) 0 0
\(121\) −547.000 −0.410969
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −756.000 −0.540950
\(126\) 0 0
\(127\) −1744.00 −1.21854 −0.609272 − 0.792962i \(-0.708538\pi\)
−0.609272 + 0.792962i \(0.708538\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −652.000 −0.434851 −0.217426 − 0.976077i \(-0.569766\pi\)
−0.217426 + 0.976077i \(0.569766\pi\)
\(132\) 0 0
\(133\) 2208.00 1.43953
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1530.00 −0.954137 −0.477068 − 0.878866i \(-0.658301\pi\)
−0.477068 + 0.878866i \(0.658301\pi\)
\(138\) 0 0
\(139\) 516.000 0.314867 0.157434 − 0.987530i \(-0.449678\pi\)
0.157434 + 0.987530i \(0.449678\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2072.00 1.21167
\(144\) 0 0
\(145\) −1932.00 −1.10651
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1342.00 0.737859 0.368929 − 0.929457i \(-0.379724\pi\)
0.368929 + 0.929457i \(0.379724\pi\)
\(150\) 0 0
\(151\) 424.000 0.228507 0.114254 − 0.993452i \(-0.463552\pi\)
0.114254 + 0.993452i \(0.463552\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1120.00 −0.580391
\(156\) 0 0
\(157\) −262.000 −0.133184 −0.0665920 − 0.997780i \(-0.521213\pi\)
−0.0665920 + 0.997780i \(0.521213\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 192.000 0.0939858
\(162\) 0 0
\(163\) −2292.00 −1.10137 −0.550685 − 0.834713i \(-0.685633\pi\)
−0.550685 + 0.834713i \(0.685633\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1896.00 −0.878544 −0.439272 − 0.898354i \(-0.644764\pi\)
−0.439272 + 0.898354i \(0.644764\pi\)
\(168\) 0 0
\(169\) 3279.00 1.49249
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2874.00 −1.26304 −0.631521 − 0.775359i \(-0.717569\pi\)
−0.631521 + 0.775359i \(0.717569\pi\)
\(174\) 0 0
\(175\) 1704.00 0.736059
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1188.00 0.496063 0.248032 − 0.968752i \(-0.420216\pi\)
0.248032 + 0.968752i \(0.420216\pi\)
\(180\) 0 0
\(181\) 3474.00 1.42663 0.713316 − 0.700843i \(-0.247192\pi\)
0.713316 + 0.700843i \(0.247192\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −420.000 −0.166914
\(186\) 0 0
\(187\) −2296.00 −0.897862
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 192.000 0.0727363 0.0363681 − 0.999338i \(-0.488421\pi\)
0.0363681 + 0.999338i \(0.488421\pi\)
\(192\) 0 0
\(193\) 4802.00 1.79096 0.895481 − 0.445100i \(-0.146832\pi\)
0.895481 + 0.445100i \(0.146832\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1518.00 0.549000 0.274500 − 0.961587i \(-0.411488\pi\)
0.274500 + 0.961587i \(0.411488\pi\)
\(198\) 0 0
\(199\) −5128.00 −1.82670 −0.913352 − 0.407170i \(-0.866516\pi\)
−0.913352 + 0.407170i \(0.866516\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3312.00 −1.14511
\(204\) 0 0
\(205\) −3948.00 −1.34507
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2576.00 0.852563
\(210\) 0 0
\(211\) 1084.00 0.353676 0.176838 − 0.984240i \(-0.443413\pi\)
0.176838 + 0.984240i \(0.443413\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 56.0000 0.0177636
\(216\) 0 0
\(217\) −1920.00 −0.600636
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6068.00 −1.84696
\(222\) 0 0
\(223\) −688.000 −0.206600 −0.103300 − 0.994650i \(-0.532940\pi\)
−0.103300 + 0.994650i \(0.532940\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4812.00 −1.40698 −0.703488 − 0.710707i \(-0.748375\pi\)
−0.703488 + 0.710707i \(0.748375\pi\)
\(228\) 0 0
\(229\) −2494.00 −0.719686 −0.359843 − 0.933013i \(-0.617170\pi\)
−0.359843 + 0.933013i \(0.617170\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −698.000 −0.196255 −0.0981277 − 0.995174i \(-0.531285\pi\)
−0.0981277 + 0.995174i \(0.531285\pi\)
\(234\) 0 0
\(235\) 3360.00 0.932690
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6320.00 −1.71049 −0.855244 − 0.518225i \(-0.826593\pi\)
−0.855244 + 0.518225i \(0.826593\pi\)
\(240\) 0 0
\(241\) −6510.00 −1.74002 −0.870012 − 0.493030i \(-0.835889\pi\)
−0.870012 + 0.493030i \(0.835889\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3262.00 0.850619
\(246\) 0 0
\(247\) 6808.00 1.75378
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −628.000 −0.157924 −0.0789622 − 0.996878i \(-0.525161\pi\)
−0.0789622 + 0.996878i \(0.525161\pi\)
\(252\) 0 0
\(253\) 224.000 0.0556631
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4862.00 1.18009 0.590045 − 0.807370i \(-0.299110\pi\)
0.590045 + 0.807370i \(0.299110\pi\)
\(258\) 0 0
\(259\) −720.000 −0.172736
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 5816.00 1.36361 0.681806 − 0.731533i \(-0.261195\pi\)
0.681806 + 0.731533i \(0.261195\pi\)
\(264\) 0 0
\(265\) −1820.00 −0.421893
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3526.00 0.799197 0.399599 − 0.916690i \(-0.369150\pi\)
0.399599 + 0.916690i \(0.369150\pi\)
\(270\) 0 0
\(271\) 256.000 0.0573834 0.0286917 − 0.999588i \(-0.490866\pi\)
0.0286917 + 0.999588i \(0.490866\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1988.00 0.435931
\(276\) 0 0
\(277\) −142.000 −0.0308013 −0.0154006 − 0.999881i \(-0.504902\pi\)
−0.0154006 + 0.999881i \(0.504902\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −8842.00 −1.87712 −0.938558 − 0.345122i \(-0.887838\pi\)
−0.938558 + 0.345122i \(0.887838\pi\)
\(282\) 0 0
\(283\) −7180.00 −1.50815 −0.754075 − 0.656788i \(-0.771915\pi\)
−0.754075 + 0.656788i \(0.771915\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6768.00 −1.39199
\(288\) 0 0
\(289\) 1811.00 0.368614
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7374.00 1.47029 0.735143 − 0.677912i \(-0.237115\pi\)
0.735143 + 0.677912i \(0.237115\pi\)
\(294\) 0 0
\(295\) −8344.00 −1.64680
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 592.000 0.114502
\(300\) 0 0
\(301\) 96.0000 0.0183832
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3052.00 0.572974
\(306\) 0 0
\(307\) 1500.00 0.278858 0.139429 − 0.990232i \(-0.455473\pi\)
0.139429 + 0.990232i \(0.455473\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −7608.00 −1.38717 −0.693585 − 0.720374i \(-0.743970\pi\)
−0.693585 + 0.720374i \(0.743970\pi\)
\(312\) 0 0
\(313\) −4758.00 −0.859227 −0.429614 − 0.903013i \(-0.641350\pi\)
−0.429614 + 0.903013i \(0.641350\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4374.00 0.774979 0.387489 − 0.921874i \(-0.373342\pi\)
0.387489 + 0.921874i \(0.373342\pi\)
\(318\) 0 0
\(319\) −3864.00 −0.678190
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −7544.00 −1.29956
\(324\) 0 0
\(325\) 5254.00 0.896737
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 5760.00 0.965225
\(330\) 0 0
\(331\) −7804.00 −1.29591 −0.647956 − 0.761678i \(-0.724376\pi\)
−0.647956 + 0.761678i \(0.724376\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −6104.00 −0.995514
\(336\) 0 0
\(337\) 5106.00 0.825346 0.412673 − 0.910879i \(-0.364595\pi\)
0.412673 + 0.910879i \(0.364595\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2240.00 −0.355727
\(342\) 0 0
\(343\) −2640.00 −0.415588
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4716.00 0.729591 0.364796 − 0.931088i \(-0.381139\pi\)
0.364796 + 0.931088i \(0.381139\pi\)
\(348\) 0 0
\(349\) −7302.00 −1.11996 −0.559982 − 0.828505i \(-0.689192\pi\)
−0.559982 + 0.828505i \(0.689192\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4382.00 0.660709 0.330355 − 0.943857i \(-0.392832\pi\)
0.330355 + 0.943857i \(0.392832\pi\)
\(354\) 0 0
\(355\) 11984.0 1.79168
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7224.00 1.06203 0.531014 − 0.847363i \(-0.321811\pi\)
0.531014 + 0.847363i \(0.321811\pi\)
\(360\) 0 0
\(361\) 1605.00 0.233999
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −13972.0 −2.00364
\(366\) 0 0
\(367\) −1408.00 −0.200264 −0.100132 − 0.994974i \(-0.531927\pi\)
−0.100132 + 0.994974i \(0.531927\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −3120.00 −0.436610
\(372\) 0 0
\(373\) 1714.00 0.237929 0.118965 − 0.992899i \(-0.462043\pi\)
0.118965 + 0.992899i \(0.462043\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −10212.0 −1.39508
\(378\) 0 0
\(379\) 884.000 0.119810 0.0599051 − 0.998204i \(-0.480920\pi\)
0.0599051 + 0.998204i \(0.480920\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 10368.0 1.38324 0.691619 − 0.722263i \(-0.256898\pi\)
0.691619 + 0.722263i \(0.256898\pi\)
\(384\) 0 0
\(385\) 9408.00 1.24539
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 398.000 0.0518751 0.0259375 − 0.999664i \(-0.491743\pi\)
0.0259375 + 0.999664i \(0.491743\pi\)
\(390\) 0 0
\(391\) −656.000 −0.0848474
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 448.000 0.0570666
\(396\) 0 0
\(397\) 5098.00 0.644487 0.322243 − 0.946657i \(-0.395563\pi\)
0.322243 + 0.946657i \(0.395563\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10002.0 −1.24558 −0.622788 − 0.782391i \(-0.714000\pi\)
−0.622788 + 0.782391i \(0.714000\pi\)
\(402\) 0 0
\(403\) −5920.00 −0.731752
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −840.000 −0.102303
\(408\) 0 0
\(409\) −9270.00 −1.12071 −0.560357 − 0.828251i \(-0.689336\pi\)
−0.560357 + 0.828251i \(0.689336\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −14304.0 −1.70425
\(414\) 0 0
\(415\) 21112.0 2.49722
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6516.00 0.759731 0.379866 − 0.925042i \(-0.375970\pi\)
0.379866 + 0.925042i \(0.375970\pi\)
\(420\) 0 0
\(421\) 2626.00 0.303999 0.151999 − 0.988381i \(-0.451429\pi\)
0.151999 + 0.988381i \(0.451429\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5822.00 −0.664491
\(426\) 0 0
\(427\) 5232.00 0.592961
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4304.00 −0.481012 −0.240506 − 0.970648i \(-0.577313\pi\)
−0.240506 + 0.970648i \(0.577313\pi\)
\(432\) 0 0
\(433\) 11794.0 1.30897 0.654484 − 0.756076i \(-0.272886\pi\)
0.654484 + 0.756076i \(0.272886\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 736.000 0.0805667
\(438\) 0 0
\(439\) 5544.00 0.602735 0.301368 − 0.953508i \(-0.402557\pi\)
0.301368 + 0.953508i \(0.402557\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3788.00 0.406260 0.203130 − 0.979152i \(-0.434889\pi\)
0.203130 + 0.979152i \(0.434889\pi\)
\(444\) 0 0
\(445\) 3444.00 0.366879
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 13342.0 1.40233 0.701167 − 0.712997i \(-0.252663\pi\)
0.701167 + 0.712997i \(0.252663\pi\)
\(450\) 0 0
\(451\) −7896.00 −0.824408
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 24864.0 2.56185
\(456\) 0 0
\(457\) −4390.00 −0.449356 −0.224678 − 0.974433i \(-0.572133\pi\)
−0.224678 + 0.974433i \(0.572133\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5798.00 0.585770 0.292885 − 0.956148i \(-0.405385\pi\)
0.292885 + 0.956148i \(0.405385\pi\)
\(462\) 0 0
\(463\) 14656.0 1.47111 0.735553 − 0.677467i \(-0.236922\pi\)
0.735553 + 0.677467i \(0.236922\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8412.00 −0.833535 −0.416768 − 0.909013i \(-0.636837\pi\)
−0.416768 + 0.909013i \(0.636837\pi\)
\(468\) 0 0
\(469\) −10464.0 −1.03024
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 112.000 0.0108875
\(474\) 0 0
\(475\) 6532.00 0.630966
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 14848.0 1.41633 0.708165 − 0.706047i \(-0.249523\pi\)
0.708165 + 0.706047i \(0.249523\pi\)
\(480\) 0 0
\(481\) −2220.00 −0.210443
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12124.0 1.13510
\(486\) 0 0
\(487\) −18568.0 −1.72771 −0.863857 − 0.503738i \(-0.831958\pi\)
−0.863857 + 0.503738i \(0.831958\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 14364.0 1.32024 0.660120 − 0.751160i \(-0.270505\pi\)
0.660120 + 0.751160i \(0.270505\pi\)
\(492\) 0 0
\(493\) 11316.0 1.03377
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 20544.0 1.85417
\(498\) 0 0
\(499\) 21660.0 1.94316 0.971578 − 0.236720i \(-0.0760724\pi\)
0.971578 + 0.236720i \(0.0760724\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −17112.0 −1.51687 −0.758436 − 0.651748i \(-0.774036\pi\)
−0.758436 + 0.651748i \(0.774036\pi\)
\(504\) 0 0
\(505\) 3780.00 0.333085
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 11478.0 0.999516 0.499758 − 0.866165i \(-0.333422\pi\)
0.499758 + 0.866165i \(0.333422\pi\)
\(510\) 0 0
\(511\) −23952.0 −2.07353
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 20944.0 1.79204
\(516\) 0 0
\(517\) 6720.00 0.571654
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −13114.0 −1.10275 −0.551377 − 0.834256i \(-0.685897\pi\)
−0.551377 + 0.834256i \(0.685897\pi\)
\(522\) 0 0
\(523\) −4508.00 −0.376905 −0.188452 − 0.982082i \(-0.560347\pi\)
−0.188452 + 0.982082i \(0.560347\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6560.00 0.542235
\(528\) 0 0
\(529\) −12103.0 −0.994740
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −20868.0 −1.69586
\(534\) 0 0
\(535\) 23688.0 1.91425
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 6524.00 0.521352
\(540\) 0 0
\(541\) −22950.0 −1.82384 −0.911920 − 0.410368i \(-0.865400\pi\)
−0.911920 + 0.410368i \(0.865400\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5684.00 −0.446745
\(546\) 0 0
\(547\) −6580.00 −0.514334 −0.257167 − 0.966367i \(-0.582789\pi\)
−0.257167 + 0.966367i \(0.582789\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −12696.0 −0.981611
\(552\) 0 0
\(553\) 768.000 0.0590573
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7046.00 0.535994 0.267997 − 0.963420i \(-0.413638\pi\)
0.267997 + 0.963420i \(0.413638\pi\)
\(558\) 0 0
\(559\) 296.000 0.0223962
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −8252.00 −0.617727 −0.308864 − 0.951106i \(-0.599949\pi\)
−0.308864 + 0.951106i \(0.599949\pi\)
\(564\) 0 0
\(565\) −11004.0 −0.819366
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 6838.00 0.503803 0.251901 − 0.967753i \(-0.418944\pi\)
0.251901 + 0.967753i \(0.418944\pi\)
\(570\) 0 0
\(571\) 23316.0 1.70883 0.854417 − 0.519588i \(-0.173915\pi\)
0.854417 + 0.519588i \(0.173915\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 568.000 0.0411952
\(576\) 0 0
\(577\) −10558.0 −0.761760 −0.380880 − 0.924625i \(-0.624379\pi\)
−0.380880 + 0.924625i \(0.624379\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 36192.0 2.58433
\(582\) 0 0
\(583\) −3640.00 −0.258582
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1028.00 −0.0722830 −0.0361415 − 0.999347i \(-0.511507\pi\)
−0.0361415 + 0.999347i \(0.511507\pi\)
\(588\) 0 0
\(589\) −7360.00 −0.514879
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1202.00 −0.0832382 −0.0416191 − 0.999134i \(-0.513252\pi\)
−0.0416191 + 0.999134i \(0.513252\pi\)
\(594\) 0 0
\(595\) −27552.0 −1.89836
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3576.00 −0.243926 −0.121963 − 0.992535i \(-0.538919\pi\)
−0.121963 + 0.992535i \(0.538919\pi\)
\(600\) 0 0
\(601\) 8650.00 0.587090 0.293545 − 0.955945i \(-0.405165\pi\)
0.293545 + 0.955945i \(0.405165\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7658.00 −0.514615
\(606\) 0 0
\(607\) −12656.0 −0.846279 −0.423139 − 0.906065i \(-0.639072\pi\)
−0.423139 + 0.906065i \(0.639072\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 17760.0 1.17593
\(612\) 0 0
\(613\) 3298.00 0.217300 0.108650 − 0.994080i \(-0.465347\pi\)
0.108650 + 0.994080i \(0.465347\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5370.00 −0.350386 −0.175193 − 0.984534i \(-0.556055\pi\)
−0.175193 + 0.984534i \(0.556055\pi\)
\(618\) 0 0
\(619\) −16220.0 −1.05321 −0.526605 − 0.850110i \(-0.676535\pi\)
−0.526605 + 0.850110i \(0.676535\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5904.00 0.379677
\(624\) 0 0
\(625\) −19459.0 −1.24538
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2460.00 0.155941
\(630\) 0 0
\(631\) 20360.0 1.28450 0.642249 − 0.766496i \(-0.278001\pi\)
0.642249 + 0.766496i \(0.278001\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −24416.0 −1.52586
\(636\) 0 0
\(637\) 17242.0 1.07245
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −14498.0 −0.893349 −0.446674 − 0.894697i \(-0.647392\pi\)
−0.446674 + 0.894697i \(0.647392\pi\)
\(642\) 0 0
\(643\) 21612.0 1.32550 0.662748 − 0.748842i \(-0.269390\pi\)
0.662748 + 0.748842i \(0.269390\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12184.0 0.740344 0.370172 − 0.928963i \(-0.379299\pi\)
0.370172 + 0.928963i \(0.379299\pi\)
\(648\) 0 0
\(649\) −16688.0 −1.00934
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −28122.0 −1.68530 −0.842648 − 0.538464i \(-0.819005\pi\)
−0.842648 + 0.538464i \(0.819005\pi\)
\(654\) 0 0
\(655\) −9128.00 −0.544520
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 5700.00 0.336935 0.168468 − 0.985707i \(-0.446118\pi\)
0.168468 + 0.985707i \(0.446118\pi\)
\(660\) 0 0
\(661\) 29458.0 1.73341 0.866705 − 0.498822i \(-0.166234\pi\)
0.866705 + 0.498822i \(0.166234\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 30912.0 1.80258
\(666\) 0 0
\(667\) −1104.00 −0.0640885
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6104.00 0.351181
\(672\) 0 0
\(673\) 19810.0 1.13465 0.567325 − 0.823494i \(-0.307978\pi\)
0.567325 + 0.823494i \(0.307978\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −10450.0 −0.593244 −0.296622 − 0.954995i \(-0.595860\pi\)
−0.296622 + 0.954995i \(0.595860\pi\)
\(678\) 0 0
\(679\) 20784.0 1.17469
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −23300.0 −1.30534 −0.652672 − 0.757641i \(-0.726352\pi\)
−0.652672 + 0.757641i \(0.726352\pi\)
\(684\) 0 0
\(685\) −21420.0 −1.19477
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −9620.00 −0.531920
\(690\) 0 0
\(691\) −14212.0 −0.782417 −0.391208 − 0.920302i \(-0.627943\pi\)
−0.391208 + 0.920302i \(0.627943\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 7224.00 0.394276
\(696\) 0 0
\(697\) 23124.0 1.25665
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −15978.0 −0.860885 −0.430443 − 0.902618i \(-0.641643\pi\)
−0.430443 + 0.902618i \(0.641643\pi\)
\(702\) 0 0
\(703\) −2760.00 −0.148073
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6480.00 0.344704
\(708\) 0 0
\(709\) 8866.00 0.469633 0.234816 − 0.972040i \(-0.424551\pi\)
0.234816 + 0.972040i \(0.424551\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −640.000 −0.0336160
\(714\) 0 0
\(715\) 29008.0 1.51726
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 7760.00 0.402502 0.201251 − 0.979540i \(-0.435499\pi\)
0.201251 + 0.979540i \(0.435499\pi\)
\(720\) 0 0
\(721\) 35904.0 1.85456
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −9798.00 −0.501915
\(726\) 0 0
\(727\) −13080.0 −0.667277 −0.333638 − 0.942701i \(-0.608276\pi\)
−0.333638 + 0.942701i \(0.608276\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −328.000 −0.0165958
\(732\) 0 0
\(733\) −16934.0 −0.853304 −0.426652 − 0.904416i \(-0.640307\pi\)
−0.426652 + 0.904416i \(0.640307\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −12208.0 −0.610159
\(738\) 0 0
\(739\) −7060.00 −0.351429 −0.175715 − 0.984441i \(-0.556224\pi\)
−0.175715 + 0.984441i \(0.556224\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −12520.0 −0.618189 −0.309094 − 0.951031i \(-0.600026\pi\)
−0.309094 + 0.951031i \(0.600026\pi\)
\(744\) 0 0
\(745\) 18788.0 0.923945
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 40608.0 1.98102
\(750\) 0 0
\(751\) 9792.00 0.475786 0.237893 − 0.971291i \(-0.423543\pi\)
0.237893 + 0.971291i \(0.423543\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5936.00 0.286137
\(756\) 0 0
\(757\) −13166.0 −0.632135 −0.316068 − 0.948737i \(-0.602363\pi\)
−0.316068 + 0.948737i \(0.602363\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 23222.0 1.10617 0.553086 − 0.833124i \(-0.313450\pi\)
0.553086 + 0.833124i \(0.313450\pi\)
\(762\) 0 0
\(763\) −9744.00 −0.462328
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −44104.0 −2.07628
\(768\) 0 0
\(769\) −39934.0 −1.87264 −0.936318 − 0.351154i \(-0.885789\pi\)
−0.936318 + 0.351154i \(0.885789\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −17106.0 −0.795938 −0.397969 − 0.917399i \(-0.630285\pi\)
−0.397969 + 0.917399i \(0.630285\pi\)
\(774\) 0 0
\(775\) −5680.00 −0.263267
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −25944.0 −1.19325
\(780\) 0 0
\(781\) 23968.0 1.09813
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3668.00 −0.166773
\(786\) 0 0
\(787\) −9956.00 −0.450944 −0.225472 − 0.974250i \(-0.572392\pi\)
−0.225472 + 0.974250i \(0.572392\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −18864.0 −0.847948
\(792\) 0 0
\(793\) 16132.0 0.722401
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −9130.00 −0.405773 −0.202887 − 0.979202i \(-0.565032\pi\)
−0.202887 + 0.979202i \(0.565032\pi\)
\(798\) 0 0
\(799\) −19680.0 −0.871375
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −27944.0 −1.22805
\(804\) 0 0
\(805\) 2688.00 0.117689
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −11482.0 −0.498993 −0.249497 − 0.968376i \(-0.580265\pi\)
−0.249497 + 0.968376i \(0.580265\pi\)
\(810\) 0 0
\(811\) 4612.00 0.199691 0.0998454 − 0.995003i \(-0.468165\pi\)
0.0998454 + 0.995003i \(0.468165\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −32088.0 −1.37913
\(816\) 0 0
\(817\) 368.000 0.0157585
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −35010.0 −1.48826 −0.744128 − 0.668038i \(-0.767135\pi\)
−0.744128 + 0.668038i \(0.767135\pi\)
\(822\) 0 0
\(823\) −13688.0 −0.579749 −0.289875 − 0.957065i \(-0.593614\pi\)
−0.289875 + 0.957065i \(0.593614\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −11668.0 −0.490612 −0.245306 − 0.969446i \(-0.578888\pi\)
−0.245306 + 0.969446i \(0.578888\pi\)
\(828\) 0 0
\(829\) 29306.0 1.22779 0.613896 − 0.789387i \(-0.289601\pi\)
0.613896 + 0.789387i \(0.289601\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −19106.0 −0.794698
\(834\) 0 0
\(835\) −26544.0 −1.10011
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −2664.00 −0.109620 −0.0548102 − 0.998497i \(-0.517455\pi\)
−0.0548102 + 0.998497i \(0.517455\pi\)
\(840\) 0 0
\(841\) −5345.00 −0.219156
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 45906.0 1.86889
\(846\) 0 0
\(847\) −13128.0 −0.532566
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −240.000 −0.00966756
\(852\) 0 0
\(853\) −26030.0 −1.04484 −0.522421 − 0.852688i \(-0.674971\pi\)
−0.522421 + 0.852688i \(0.674971\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −44202.0 −1.76186 −0.880929 − 0.473249i \(-0.843081\pi\)
−0.880929 + 0.473249i \(0.843081\pi\)
\(858\) 0 0
\(859\) −32748.0 −1.30075 −0.650377 − 0.759612i \(-0.725389\pi\)
−0.650377 + 0.759612i \(0.725389\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 45344.0 1.78856 0.894280 − 0.447507i \(-0.147688\pi\)
0.894280 + 0.447507i \(0.147688\pi\)
\(864\) 0 0
\(865\) −40236.0 −1.58158
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 896.000 0.0349767
\(870\) 0 0
\(871\) −32264.0 −1.25514
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −18144.0 −0.701005
\(876\) 0 0
\(877\) 8778.00 0.337984 0.168992 − 0.985617i \(-0.445949\pi\)
0.168992 + 0.985617i \(0.445949\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 4142.00 0.158397 0.0791984 − 0.996859i \(-0.474764\pi\)
0.0791984 + 0.996859i \(0.474764\pi\)
\(882\) 0 0
\(883\) 22076.0 0.841355 0.420678 − 0.907210i \(-0.361792\pi\)
0.420678 + 0.907210i \(0.361792\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −40376.0 −1.52840 −0.764201 − 0.644978i \(-0.776867\pi\)
−0.764201 + 0.644978i \(0.776867\pi\)
\(888\) 0 0
\(889\) −41856.0 −1.57908
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 22080.0 0.827412
\(894\) 0 0
\(895\) 16632.0 0.621169
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 11040.0 0.409571
\(900\) 0 0
\(901\) 10660.0 0.394158
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 48636.0 1.78643
\(906\) 0 0
\(907\) −26396.0 −0.966334 −0.483167 − 0.875528i \(-0.660514\pi\)
−0.483167 + 0.875528i \(0.660514\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 24368.0 0.886222 0.443111 − 0.896467i \(-0.353875\pi\)
0.443111 + 0.896467i \(0.353875\pi\)
\(912\) 0 0
\(913\) 42224.0 1.53057
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −15648.0 −0.563514
\(918\) 0 0
\(919\) 5096.00 0.182918 0.0914589 − 0.995809i \(-0.470847\pi\)
0.0914589 + 0.995809i \(0.470847\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 63344.0 2.25893
\(924\) 0 0
\(925\) −2130.00 −0.0757124
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 18494.0 0.653142 0.326571 − 0.945173i \(-0.394107\pi\)
0.326571 + 0.945173i \(0.394107\pi\)
\(930\) 0 0
\(931\) 21436.0 0.754604
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −32144.0 −1.12430
\(936\) 0 0
\(937\) −33222.0 −1.15829 −0.579144 − 0.815225i \(-0.696613\pi\)
−0.579144 + 0.815225i \(0.696613\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 27846.0 0.964669 0.482335 − 0.875987i \(-0.339789\pi\)
0.482335 + 0.875987i \(0.339789\pi\)
\(942\) 0 0
\(943\) −2256.00 −0.0779061
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −41052.0 −1.40867 −0.704335 − 0.709868i \(-0.748755\pi\)
−0.704335 + 0.709868i \(0.748755\pi\)
\(948\) 0 0
\(949\) −73852.0 −2.52617
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −5706.00 −0.193951 −0.0969756 − 0.995287i \(-0.530917\pi\)
−0.0969756 + 0.995287i \(0.530917\pi\)
\(954\) 0 0
\(955\) 2688.00 0.0910802
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −36720.0 −1.23644
\(960\) 0 0
\(961\) −23391.0 −0.785170
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 67228.0 2.24264
\(966\) 0 0
\(967\) 39352.0 1.30866 0.654330 − 0.756209i \(-0.272951\pi\)
0.654330 + 0.756209i \(0.272951\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 33180.0 1.09660 0.548299 − 0.836282i \(-0.315276\pi\)
0.548299 + 0.836282i \(0.315276\pi\)
\(972\) 0 0
\(973\) 12384.0 0.408030
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4014.00 0.131442 0.0657212 − 0.997838i \(-0.479065\pi\)
0.0657212 + 0.997838i \(0.479065\pi\)
\(978\) 0 0
\(979\) 6888.00 0.224864
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 20328.0 0.659575 0.329788 − 0.944055i \(-0.393023\pi\)
0.329788 + 0.944055i \(0.393023\pi\)
\(984\) 0 0
\(985\) 21252.0 0.687457
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 32.0000 0.00102886
\(990\) 0 0
\(991\) −11728.0 −0.375936 −0.187968 − 0.982175i \(-0.560190\pi\)
−0.187968 + 0.982175i \(0.560190\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −71792.0 −2.28740
\(996\) 0 0
\(997\) −50974.0 −1.61922 −0.809610 − 0.586968i \(-0.800321\pi\)
−0.809610 + 0.586968i \(0.800321\pi\)
\(998\) 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 576.4.a.v.1.1 1
3.2 odd 2 192.4.a.g.1.1 1
4.3 odd 2 576.4.a.u.1.1 1
8.3 odd 2 72.4.a.b.1.1 1
8.5 even 2 144.4.a.b.1.1 1
12.11 even 2 192.4.a.a.1.1 1
24.5 odd 2 48.4.a.b.1.1 1
24.11 even 2 24.4.a.a.1.1 ✓ 1
40.3 even 4 1800.4.f.q.649.2 2
40.19 odd 2 1800.4.a.bg.1.1 1
40.27 even 4 1800.4.f.q.649.1 2
48.5 odd 4 768.4.d.b.385.1 2
48.11 even 4 768.4.d.o.385.2 2
48.29 odd 4 768.4.d.b.385.2 2
48.35 even 4 768.4.d.o.385.1 2
72.11 even 6 648.4.i.b.433.1 2
72.43 odd 6 648.4.i.k.433.1 2
72.59 even 6 648.4.i.b.217.1 2
72.67 odd 6 648.4.i.k.217.1 2
120.29 odd 2 1200.4.a.u.1.1 1
120.53 even 4 1200.4.f.p.49.1 2
120.59 even 2 600.4.a.h.1.1 1
120.77 even 4 1200.4.f.p.49.2 2
120.83 odd 4 600.4.f.b.49.2 2
120.107 odd 4 600.4.f.b.49.1 2
168.83 odd 2 1176.4.a.a.1.1 1
168.125 even 2 2352.4.a.w.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
24.4.a.a.1.1 ✓ 1 24.11 even 2
48.4.a.b.1.1 1 24.5 odd 2
72.4.a.b.1.1 1 8.3 odd 2
144.4.a.b.1.1 1 8.5 even 2
192.4.a.a.1.1 1 12.11 even 2
192.4.a.g.1.1 1 3.2 odd 2
576.4.a.u.1.1 1 4.3 odd 2
576.4.a.v.1.1 1 1.1 even 1 trivial
600.4.a.h.1.1 1 120.59 even 2
600.4.f.b.49.1 2 120.107 odd 4
600.4.f.b.49.2 2 120.83 odd 4
648.4.i.b.217.1 2 72.59 even 6
648.4.i.b.433.1 2 72.11 even 6
648.4.i.k.217.1 2 72.67 odd 6
648.4.i.k.433.1 2 72.43 odd 6
768.4.d.b.385.1 2 48.5 odd 4
768.4.d.b.385.2 2 48.29 odd 4
768.4.d.o.385.1 2 48.35 even 4
768.4.d.o.385.2 2 48.11 even 4
1176.4.a.a.1.1 1 168.83 odd 2
1200.4.a.u.1.1 1 120.29 odd 2
1200.4.f.p.49.1 2 120.53 even 4
1200.4.f.p.49.2 2 120.77 even 4
1800.4.a.bg.1.1 1 40.19 odd 2
1800.4.f.q.649.1 2 40.27 even 4
1800.4.f.q.649.2 2 40.3 even 4
2352.4.a.w.1.1 1 168.125 even 2