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Properties

Label 1440.4.a.p.1.1
Level $1440$
Weight $4$
Character 1440.1
Self dual yes
Analytic conductor $84.963$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1440,4,Mod(1,1440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1440, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1440.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1440.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(84.9627504083\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 480)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.00000 q^{5} +8.00000 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} +8.00000 q^{7} +4.00000 q^{11} -6.00000 q^{13} +2.00000 q^{17} +16.0000 q^{19} -60.0000 q^{23} +25.0000 q^{25} +142.000 q^{29} +176.000 q^{31} +40.0000 q^{35} -214.000 q^{37} +278.000 q^{41} +68.0000 q^{43} +116.000 q^{47} -279.000 q^{49} +350.000 q^{53} +20.0000 q^{55} +684.000 q^{59} -394.000 q^{61} -30.0000 q^{65} -108.000 q^{67} -96.0000 q^{71} -398.000 q^{73} +32.0000 q^{77} -136.000 q^{79} +436.000 q^{83} +10.0000 q^{85} +750.000 q^{89} -48.0000 q^{91} +80.0000 q^{95} +82.0000 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 8.00000 0.431959 0.215980 − 0.976398i \(-0.430705\pi\)
0.215980 + 0.976398i \(0.430705\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.00000 0.109640 0.0548202 − 0.998496i \(-0.482541\pi\)
0.0548202 + 0.998496i \(0.482541\pi\)
\(12\) 0 0
\(13\) −6.00000 −0.128008 −0.0640039 − 0.997950i \(-0.520387\pi\)
−0.0640039 + 0.997950i \(0.520387\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.00000 0.0285336 0.0142668 − 0.999898i \(-0.495459\pi\)
0.0142668 + 0.999898i \(0.495459\pi\)
\(18\) 0 0
\(19\) 16.0000 0.193192 0.0965961 − 0.995324i \(-0.469204\pi\)
0.0965961 + 0.995324i \(0.469204\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −60.0000 −0.543951 −0.271975 − 0.962304i \(-0.587677\pi\)
−0.271975 + 0.962304i \(0.587677\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 142.000 0.909267 0.454633 − 0.890679i \(-0.349770\pi\)
0.454633 + 0.890679i \(0.349770\pi\)
\(30\) 0 0
\(31\) 176.000 1.01969 0.509847 − 0.860265i \(-0.329702\pi\)
0.509847 + 0.860265i \(0.329702\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 40.0000 0.193178
\(36\) 0 0
\(37\) −214.000 −0.950848 −0.475424 − 0.879757i \(-0.657705\pi\)
−0.475424 + 0.879757i \(0.657705\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 278.000 1.05893 0.529467 − 0.848330i \(-0.322392\pi\)
0.529467 + 0.848330i \(0.322392\pi\)
\(42\) 0 0
\(43\) 68.0000 0.241161 0.120580 − 0.992704i \(-0.461524\pi\)
0.120580 + 0.992704i \(0.461524\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 116.000 0.360007 0.180004 − 0.983666i \(-0.442389\pi\)
0.180004 + 0.983666i \(0.442389\pi\)
\(48\) 0 0
\(49\) −279.000 −0.813411
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 350.000 0.907098 0.453549 − 0.891231i \(-0.350158\pi\)
0.453549 + 0.891231i \(0.350158\pi\)
\(54\) 0 0
\(55\) 20.0000 0.0490327
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 684.000 1.50931 0.754654 − 0.656123i \(-0.227805\pi\)
0.754654 + 0.656123i \(0.227805\pi\)
\(60\) 0 0
\(61\) −394.000 −0.826992 −0.413496 − 0.910506i \(-0.635692\pi\)
−0.413496 + 0.910506i \(0.635692\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −30.0000 −0.0572468
\(66\) 0 0
\(67\) −108.000 −0.196930 −0.0984649 − 0.995141i \(-0.531393\pi\)
−0.0984649 + 0.995141i \(0.531393\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −96.0000 −0.160466 −0.0802331 − 0.996776i \(-0.525566\pi\)
−0.0802331 + 0.996776i \(0.525566\pi\)
\(72\) 0 0
\(73\) −398.000 −0.638115 −0.319057 − 0.947735i \(-0.603366\pi\)
−0.319057 + 0.947735i \(0.603366\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 32.0000 0.0473602
\(78\) 0 0
\(79\) −136.000 −0.193686 −0.0968430 − 0.995300i \(-0.530874\pi\)
−0.0968430 + 0.995300i \(0.530874\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 436.000 0.576593 0.288296 − 0.957541i \(-0.406911\pi\)
0.288296 + 0.957541i \(0.406911\pi\)
\(84\) 0 0
\(85\) 10.0000 0.0127606
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 750.000 0.893257 0.446628 − 0.894720i \(-0.352625\pi\)
0.446628 + 0.894720i \(0.352625\pi\)
\(90\) 0 0
\(91\) −48.0000 −0.0552941
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 80.0000 0.0863982
\(96\) 0 0
\(97\) 82.0000 0.0858334 0.0429167 − 0.999079i \(-0.486335\pi\)
0.0429167 + 0.999079i \(0.486335\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −154.000 −0.151719 −0.0758593 − 0.997119i \(-0.524170\pi\)
−0.0758593 + 0.997119i \(0.524170\pi\)
\(102\) 0 0
\(103\) 1216.00 1.16326 0.581631 − 0.813453i \(-0.302415\pi\)
0.581631 + 0.813453i \(0.302415\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 732.000 0.661356 0.330678 − 0.943744i \(-0.392723\pi\)
0.330678 + 0.943744i \(0.392723\pi\)
\(108\) 0 0
\(109\) −554.000 −0.486822 −0.243411 − 0.969923i \(-0.578266\pi\)
−0.243411 + 0.969923i \(0.578266\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 474.000 0.394603 0.197302 − 0.980343i \(-0.436782\pi\)
0.197302 + 0.980343i \(0.436782\pi\)
\(114\) 0 0
\(115\) −300.000 −0.243262
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 16.0000 0.0123254
\(120\) 0 0
\(121\) −1315.00 −0.987979
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 840.000 0.586913 0.293456 − 0.955972i \(-0.405194\pi\)
0.293456 + 0.955972i \(0.405194\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1484.00 0.989753 0.494877 − 0.868963i \(-0.335213\pi\)
0.494877 + 0.868963i \(0.335213\pi\)
\(132\) 0 0
\(133\) 128.000 0.0834512
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1006.00 −0.627360 −0.313680 − 0.949529i \(-0.601562\pi\)
−0.313680 + 0.949529i \(0.601562\pi\)
\(138\) 0 0
\(139\) −1400.00 −0.854291 −0.427146 − 0.904183i \(-0.640481\pi\)
−0.427146 + 0.904183i \(0.640481\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −24.0000 −0.0140348
\(144\) 0 0
\(145\) 710.000 0.406636
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2.00000 −0.00109964 −0.000549820 − 1.00000i \(-0.500175\pi\)
−0.000549820 1.00000i \(0.500175\pi\)
\(150\) 0 0
\(151\) 2248.00 1.21152 0.605760 − 0.795647i \(-0.292869\pi\)
0.605760 + 0.795647i \(0.292869\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 880.000 0.456021
\(156\) 0 0
\(157\) 2890.00 1.46909 0.734545 − 0.678560i \(-0.237396\pi\)
0.734545 + 0.678560i \(0.237396\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −480.000 −0.234965
\(162\) 0 0
\(163\) 252.000 0.121093 0.0605465 − 0.998165i \(-0.480716\pi\)
0.0605465 + 0.998165i \(0.480716\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −884.000 −0.409617 −0.204808 − 0.978802i \(-0.565657\pi\)
−0.204808 + 0.978802i \(0.565657\pi\)
\(168\) 0 0
\(169\) −2161.00 −0.983614
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1398.00 0.614381 0.307191 − 0.951648i \(-0.400611\pi\)
0.307191 + 0.951648i \(0.400611\pi\)
\(174\) 0 0
\(175\) 200.000 0.0863919
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3612.00 1.50823 0.754116 − 0.656741i \(-0.228066\pi\)
0.754116 + 0.656741i \(0.228066\pi\)
\(180\) 0 0
\(181\) 3150.00 1.29358 0.646789 − 0.762669i \(-0.276111\pi\)
0.646789 + 0.762669i \(0.276111\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1070.00 −0.425232
\(186\) 0 0
\(187\) 8.00000 0.00312844
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3040.00 1.15166 0.575829 − 0.817570i \(-0.304679\pi\)
0.575829 + 0.817570i \(0.304679\pi\)
\(192\) 0 0
\(193\) 1994.00 0.743685 0.371843 − 0.928296i \(-0.378726\pi\)
0.371843 + 0.928296i \(0.378726\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4066.00 −1.47051 −0.735255 − 0.677790i \(-0.762938\pi\)
−0.735255 + 0.677790i \(0.762938\pi\)
\(198\) 0 0
\(199\) 3904.00 1.39069 0.695345 − 0.718676i \(-0.255252\pi\)
0.695345 + 0.718676i \(0.255252\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1136.00 0.392766
\(204\) 0 0
\(205\) 1390.00 0.473570
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 64.0000 0.0211817
\(210\) 0 0
\(211\) 560.000 0.182711 0.0913554 − 0.995818i \(-0.470880\pi\)
0.0913554 + 0.995818i \(0.470880\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 340.000 0.107850
\(216\) 0 0
\(217\) 1408.00 0.440467
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −12.0000 −0.00365252
\(222\) 0 0
\(223\) −608.000 −0.182577 −0.0912885 − 0.995824i \(-0.529099\pi\)
−0.0912885 + 0.995824i \(0.529099\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5124.00 1.49820 0.749101 − 0.662456i \(-0.230486\pi\)
0.749101 + 0.662456i \(0.230486\pi\)
\(228\) 0 0
\(229\) 1190.00 0.343395 0.171697 − 0.985150i \(-0.445075\pi\)
0.171697 + 0.985150i \(0.445075\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3862.00 −1.08587 −0.542936 − 0.839774i \(-0.682687\pi\)
−0.542936 + 0.839774i \(0.682687\pi\)
\(234\) 0 0
\(235\) 580.000 0.161000
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1640.00 0.443861 0.221931 − 0.975062i \(-0.428764\pi\)
0.221931 + 0.975062i \(0.428764\pi\)
\(240\) 0 0
\(241\) −2334.00 −0.623843 −0.311921 − 0.950108i \(-0.600973\pi\)
−0.311921 + 0.950108i \(0.600973\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1395.00 −0.363768
\(246\) 0 0
\(247\) −96.0000 −0.0247301
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −772.000 −0.194136 −0.0970681 − 0.995278i \(-0.530946\pi\)
−0.0970681 + 0.995278i \(0.530946\pi\)
\(252\) 0 0
\(253\) −240.000 −0.0596390
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6214.00 −1.50824 −0.754122 − 0.656734i \(-0.771937\pi\)
−0.754122 + 0.656734i \(0.771937\pi\)
\(258\) 0 0
\(259\) −1712.00 −0.410728
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4948.00 1.16010 0.580051 − 0.814580i \(-0.303033\pi\)
0.580051 + 0.814580i \(0.303033\pi\)
\(264\) 0 0
\(265\) 1750.00 0.405667
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7038.00 1.59522 0.797610 − 0.603173i \(-0.206097\pi\)
0.797610 + 0.603173i \(0.206097\pi\)
\(270\) 0 0
\(271\) 728.000 0.163184 0.0815920 − 0.996666i \(-0.474000\pi\)
0.0815920 + 0.996666i \(0.474000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 100.000 0.0219281
\(276\) 0 0
\(277\) 7274.00 1.57781 0.788903 − 0.614518i \(-0.210649\pi\)
0.788903 + 0.614518i \(0.210649\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1714.00 −0.363874 −0.181937 − 0.983310i \(-0.558237\pi\)
−0.181937 + 0.983310i \(0.558237\pi\)
\(282\) 0 0
\(283\) 4316.00 0.906571 0.453285 − 0.891365i \(-0.350252\pi\)
0.453285 + 0.891365i \(0.350252\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2224.00 0.457417
\(288\) 0 0
\(289\) −4909.00 −0.999186
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6078.00 1.21188 0.605940 − 0.795511i \(-0.292797\pi\)
0.605940 + 0.795511i \(0.292797\pi\)
\(294\) 0 0
\(295\) 3420.00 0.674983
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 360.000 0.0696299
\(300\) 0 0
\(301\) 544.000 0.104172
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1970.00 −0.369842
\(306\) 0 0
\(307\) 1564.00 0.290756 0.145378 − 0.989376i \(-0.453560\pi\)
0.145378 + 0.989376i \(0.453560\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5216.00 0.951036 0.475518 − 0.879706i \(-0.342261\pi\)
0.475518 + 0.879706i \(0.342261\pi\)
\(312\) 0 0
\(313\) −5790.00 −1.04559 −0.522796 − 0.852458i \(-0.675111\pi\)
−0.522796 + 0.852458i \(0.675111\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3946.00 −0.699146 −0.349573 − 0.936909i \(-0.613673\pi\)
−0.349573 + 0.936909i \(0.613673\pi\)
\(318\) 0 0
\(319\) 568.000 0.0996925
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 32.0000 0.00551247
\(324\) 0 0
\(325\) −150.000 −0.0256015
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 928.000 0.155508
\(330\) 0 0
\(331\) 9992.00 1.65924 0.829622 − 0.558325i \(-0.188556\pi\)
0.829622 + 0.558325i \(0.188556\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −540.000 −0.0880697
\(336\) 0 0
\(337\) 3274.00 0.529217 0.264609 − 0.964356i \(-0.414757\pi\)
0.264609 + 0.964356i \(0.414757\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 704.000 0.111800
\(342\) 0 0
\(343\) −4976.00 −0.783320
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5580.00 −0.863257 −0.431628 − 0.902052i \(-0.642061\pi\)
−0.431628 + 0.902052i \(0.642061\pi\)
\(348\) 0 0
\(349\) −4154.00 −0.637130 −0.318565 − 0.947901i \(-0.603201\pi\)
−0.318565 + 0.947901i \(0.603201\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2802.00 0.422480 0.211240 − 0.977434i \(-0.432250\pi\)
0.211240 + 0.977434i \(0.432250\pi\)
\(354\) 0 0
\(355\) −480.000 −0.0717627
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −11296.0 −1.66067 −0.830334 − 0.557265i \(-0.811851\pi\)
−0.830334 + 0.557265i \(0.811851\pi\)
\(360\) 0 0
\(361\) −6603.00 −0.962677
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1990.00 −0.285374
\(366\) 0 0
\(367\) −10536.0 −1.49857 −0.749284 − 0.662248i \(-0.769602\pi\)
−0.749284 + 0.662248i \(0.769602\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2800.00 0.391830
\(372\) 0 0
\(373\) −2222.00 −0.308447 −0.154224 − 0.988036i \(-0.549288\pi\)
−0.154224 + 0.988036i \(0.549288\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −852.000 −0.116393
\(378\) 0 0
\(379\) 1512.00 0.204924 0.102462 − 0.994737i \(-0.467328\pi\)
0.102462 + 0.994737i \(0.467328\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 7916.00 1.05611 0.528053 − 0.849211i \(-0.322922\pi\)
0.528053 + 0.849211i \(0.322922\pi\)
\(384\) 0 0
\(385\) 160.000 0.0211801
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 9950.00 1.29688 0.648438 − 0.761267i \(-0.275422\pi\)
0.648438 + 0.761267i \(0.275422\pi\)
\(390\) 0 0
\(391\) −120.000 −0.0155209
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −680.000 −0.0866190
\(396\) 0 0
\(397\) 9554.00 1.20781 0.603906 − 0.797055i \(-0.293610\pi\)
0.603906 + 0.797055i \(0.293610\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6390.00 0.795764 0.397882 − 0.917437i \(-0.369745\pi\)
0.397882 + 0.917437i \(0.369745\pi\)
\(402\) 0 0
\(403\) −1056.00 −0.130529
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −856.000 −0.104251
\(408\) 0 0
\(409\) −13030.0 −1.57529 −0.787643 − 0.616132i \(-0.788699\pi\)
−0.787643 + 0.616132i \(0.788699\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5472.00 0.651960
\(414\) 0 0
\(415\) 2180.00 0.257860
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2100.00 0.244849 0.122424 − 0.992478i \(-0.460933\pi\)
0.122424 + 0.992478i \(0.460933\pi\)
\(420\) 0 0
\(421\) 3478.00 0.402630 0.201315 − 0.979527i \(-0.435478\pi\)
0.201315 + 0.979527i \(0.435478\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 50.0000 0.00570672
\(426\) 0 0
\(427\) −3152.00 −0.357227
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 8504.00 0.950402 0.475201 − 0.879877i \(-0.342375\pi\)
0.475201 + 0.879877i \(0.342375\pi\)
\(432\) 0 0
\(433\) −16102.0 −1.78710 −0.893548 − 0.448967i \(-0.851792\pi\)
−0.893548 + 0.448967i \(0.851792\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −960.000 −0.105087
\(438\) 0 0
\(439\) 1072.00 0.116546 0.0582731 − 0.998301i \(-0.481441\pi\)
0.0582731 + 0.998301i \(0.481441\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −11076.0 −1.18789 −0.593947 − 0.804505i \(-0.702431\pi\)
−0.593947 + 0.804505i \(0.702431\pi\)
\(444\) 0 0
\(445\) 3750.00 0.399477
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 9910.00 1.04161 0.520804 − 0.853676i \(-0.325632\pi\)
0.520804 + 0.853676i \(0.325632\pi\)
\(450\) 0 0
\(451\) 1112.00 0.116102
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −240.000 −0.0247283
\(456\) 0 0
\(457\) −3798.00 −0.388759 −0.194380 − 0.980926i \(-0.562269\pi\)
−0.194380 + 0.980926i \(0.562269\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 8406.00 0.849255 0.424627 − 0.905368i \(-0.360405\pi\)
0.424627 + 0.905368i \(0.360405\pi\)
\(462\) 0 0
\(463\) −18040.0 −1.81078 −0.905389 − 0.424584i \(-0.860420\pi\)
−0.905389 + 0.424584i \(0.860420\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8484.00 −0.840670 −0.420335 − 0.907369i \(-0.638087\pi\)
−0.420335 + 0.907369i \(0.638087\pi\)
\(468\) 0 0
\(469\) −864.000 −0.0850657
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 272.000 0.0264410
\(474\) 0 0
\(475\) 400.000 0.0386384
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2136.00 −0.203750 −0.101875 − 0.994797i \(-0.532484\pi\)
−0.101875 + 0.994797i \(0.532484\pi\)
\(480\) 0 0
\(481\) 1284.00 0.121716
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 410.000 0.0383859
\(486\) 0 0
\(487\) −3152.00 −0.293287 −0.146643 − 0.989189i \(-0.546847\pi\)
−0.146643 + 0.989189i \(0.546847\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −11812.0 −1.08568 −0.542839 − 0.839837i \(-0.682651\pi\)
−0.542839 + 0.839837i \(0.682651\pi\)
\(492\) 0 0
\(493\) 284.000 0.0259447
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −768.000 −0.0693149
\(498\) 0 0
\(499\) −10352.0 −0.928696 −0.464348 − 0.885653i \(-0.653711\pi\)
−0.464348 + 0.885653i \(0.653711\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1300.00 −0.115237 −0.0576184 − 0.998339i \(-0.518351\pi\)
−0.0576184 + 0.998339i \(0.518351\pi\)
\(504\) 0 0
\(505\) −770.000 −0.0678506
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4398.00 0.382982 0.191491 − 0.981494i \(-0.438668\pi\)
0.191491 + 0.981494i \(0.438668\pi\)
\(510\) 0 0
\(511\) −3184.00 −0.275640
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6080.00 0.520227
\(516\) 0 0
\(517\) 464.000 0.0394714
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1650.00 −0.138748 −0.0693741 − 0.997591i \(-0.522100\pi\)
−0.0693741 + 0.997591i \(0.522100\pi\)
\(522\) 0 0
\(523\) 17276.0 1.44441 0.722205 − 0.691679i \(-0.243129\pi\)
0.722205 + 0.691679i \(0.243129\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 352.000 0.0290956
\(528\) 0 0
\(529\) −8567.00 −0.704118
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1668.00 −0.135552
\(534\) 0 0
\(535\) 3660.00 0.295767
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1116.00 −0.0891828
\(540\) 0 0
\(541\) 3878.00 0.308185 0.154093 − 0.988056i \(-0.450755\pi\)
0.154093 + 0.988056i \(0.450755\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2770.00 −0.217713
\(546\) 0 0
\(547\) −9604.00 −0.750708 −0.375354 − 0.926881i \(-0.622479\pi\)
−0.375354 + 0.926881i \(0.622479\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2272.00 0.175663
\(552\) 0 0
\(553\) −1088.00 −0.0836645
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −13546.0 −1.03045 −0.515227 − 0.857054i \(-0.672292\pi\)
−0.515227 + 0.857054i \(0.672292\pi\)
\(558\) 0 0
\(559\) −408.000 −0.0308704
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −16884.0 −1.26390 −0.631950 − 0.775009i \(-0.717745\pi\)
−0.631950 + 0.775009i \(0.717745\pi\)
\(564\) 0 0
\(565\) 2370.00 0.176472
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −13746.0 −1.01276 −0.506382 − 0.862309i \(-0.669017\pi\)
−0.506382 + 0.862309i \(0.669017\pi\)
\(570\) 0 0
\(571\) 15176.0 1.11225 0.556126 − 0.831098i \(-0.312287\pi\)
0.556126 + 0.831098i \(0.312287\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1500.00 −0.108790
\(576\) 0 0
\(577\) 15106.0 1.08990 0.544949 − 0.838469i \(-0.316549\pi\)
0.544949 + 0.838469i \(0.316549\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3488.00 0.249065
\(582\) 0 0
\(583\) 1400.00 0.0994547
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17332.0 −1.21869 −0.609343 − 0.792907i \(-0.708567\pi\)
−0.609343 + 0.792907i \(0.708567\pi\)
\(588\) 0 0
\(589\) 2816.00 0.196997
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1290.00 0.0893321 0.0446661 − 0.999002i \(-0.485778\pi\)
0.0446661 + 0.999002i \(0.485778\pi\)
\(594\) 0 0
\(595\) 80.0000 0.00551207
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −20544.0 −1.40134 −0.700672 − 0.713484i \(-0.747116\pi\)
−0.700672 + 0.713484i \(0.747116\pi\)
\(600\) 0 0
\(601\) −2630.00 −0.178502 −0.0892512 − 0.996009i \(-0.528447\pi\)
−0.0892512 + 0.996009i \(0.528447\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6575.00 −0.441838
\(606\) 0 0
\(607\) −20320.0 −1.35875 −0.679377 − 0.733790i \(-0.737750\pi\)
−0.679377 + 0.733790i \(0.737750\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −696.000 −0.0460837
\(612\) 0 0
\(613\) 15386.0 1.01376 0.506880 − 0.862017i \(-0.330799\pi\)
0.506880 + 0.862017i \(0.330799\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8934.00 −0.582932 −0.291466 − 0.956581i \(-0.594143\pi\)
−0.291466 + 0.956581i \(0.594143\pi\)
\(618\) 0 0
\(619\) −20408.0 −1.32515 −0.662574 − 0.748996i \(-0.730536\pi\)
−0.662574 + 0.748996i \(0.730536\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6000.00 0.385851
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −428.000 −0.0271311
\(630\) 0 0
\(631\) 24000.0 1.51414 0.757072 − 0.653331i \(-0.226629\pi\)
0.757072 + 0.653331i \(0.226629\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4200.00 0.262475
\(636\) 0 0
\(637\) 1674.00 0.104123
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −15810.0 −0.974193 −0.487096 − 0.873348i \(-0.661944\pi\)
−0.487096 + 0.873348i \(0.661944\pi\)
\(642\) 0 0
\(643\) −7716.00 −0.473234 −0.236617 − 0.971603i \(-0.576039\pi\)
−0.236617 + 0.971603i \(0.576039\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −27324.0 −1.66030 −0.830152 − 0.557536i \(-0.811747\pi\)
−0.830152 + 0.557536i \(0.811747\pi\)
\(648\) 0 0
\(649\) 2736.00 0.165481
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9450.00 −0.566320 −0.283160 − 0.959073i \(-0.591383\pi\)
−0.283160 + 0.959073i \(0.591383\pi\)
\(654\) 0 0
\(655\) 7420.00 0.442631
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 10804.0 0.638640 0.319320 − 0.947647i \(-0.396545\pi\)
0.319320 + 0.947647i \(0.396545\pi\)
\(660\) 0 0
\(661\) 1534.00 0.0902658 0.0451329 − 0.998981i \(-0.485629\pi\)
0.0451329 + 0.998981i \(0.485629\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 640.000 0.0373205
\(666\) 0 0
\(667\) −8520.00 −0.494596
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1576.00 −0.0906718
\(672\) 0 0
\(673\) 1306.00 0.0748033 0.0374016 − 0.999300i \(-0.488092\pi\)
0.0374016 + 0.999300i \(0.488092\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6398.00 0.363213 0.181606 − 0.983371i \(-0.441870\pi\)
0.181606 + 0.983371i \(0.441870\pi\)
\(678\) 0 0
\(679\) 656.000 0.0370765
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −20396.0 −1.14265 −0.571326 − 0.820723i \(-0.693571\pi\)
−0.571326 + 0.820723i \(0.693571\pi\)
\(684\) 0 0
\(685\) −5030.00 −0.280564
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2100.00 −0.116116
\(690\) 0 0
\(691\) 11592.0 0.638177 0.319089 − 0.947725i \(-0.396623\pi\)
0.319089 + 0.947725i \(0.396623\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7000.00 −0.382051
\(696\) 0 0
\(697\) 556.000 0.0302152
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −3618.00 −0.194936 −0.0974679 − 0.995239i \(-0.531074\pi\)
−0.0974679 + 0.995239i \(0.531074\pi\)
\(702\) 0 0
\(703\) −3424.00 −0.183696
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1232.00 −0.0655362
\(708\) 0 0
\(709\) 30518.0 1.61654 0.808270 − 0.588811i \(-0.200404\pi\)
0.808270 + 0.588811i \(0.200404\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −10560.0 −0.554664
\(714\) 0 0
\(715\) −120.000 −0.00627657
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −13088.0 −0.678860 −0.339430 − 0.940631i \(-0.610234\pi\)
−0.339430 + 0.940631i \(0.610234\pi\)
\(720\) 0 0
\(721\) 9728.00 0.502482
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3550.00 0.181853
\(726\) 0 0
\(727\) −6064.00 −0.309355 −0.154678 − 0.987965i \(-0.549434\pi\)
−0.154678 + 0.987965i \(0.549434\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 136.000 0.00688118
\(732\) 0 0
\(733\) 3522.00 0.177473 0.0887367 − 0.996055i \(-0.471717\pi\)
0.0887367 + 0.996055i \(0.471717\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −432.000 −0.0215915
\(738\) 0 0
\(739\) −39040.0 −1.94331 −0.971657 − 0.236394i \(-0.924035\pi\)
−0.971657 + 0.236394i \(0.924035\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −14868.0 −0.734124 −0.367062 − 0.930197i \(-0.619636\pi\)
−0.367062 + 0.930197i \(0.619636\pi\)
\(744\) 0 0
\(745\) −10.0000 −0.000491774 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5856.00 0.285679
\(750\) 0 0
\(751\) 4016.00 0.195134 0.0975672 − 0.995229i \(-0.468894\pi\)
0.0975672 + 0.995229i \(0.468894\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 11240.0 0.541809
\(756\) 0 0
\(757\) −7958.00 −0.382085 −0.191043 − 0.981582i \(-0.561187\pi\)
−0.191043 + 0.981582i \(0.561187\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −15890.0 −0.756915 −0.378457 − 0.925619i \(-0.623545\pi\)
−0.378457 + 0.925619i \(0.623545\pi\)
\(762\) 0 0
\(763\) −4432.00 −0.210287
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4104.00 −0.193203
\(768\) 0 0
\(769\) 6834.00 0.320469 0.160234 − 0.987079i \(-0.448775\pi\)
0.160234 + 0.987079i \(0.448775\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 3694.00 0.171881 0.0859405 − 0.996300i \(-0.472611\pi\)
0.0859405 + 0.996300i \(0.472611\pi\)
\(774\) 0 0
\(775\) 4400.00 0.203939
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4448.00 0.204578
\(780\) 0 0
\(781\) −384.000 −0.0175936
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 14450.0 0.656997
\(786\) 0 0
\(787\) −38284.0 −1.73402 −0.867012 − 0.498287i \(-0.833963\pi\)
−0.867012 + 0.498287i \(0.833963\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3792.00 0.170453
\(792\) 0 0
\(793\) 2364.00 0.105861
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −3258.00 −0.144798 −0.0723992 − 0.997376i \(-0.523066\pi\)
−0.0723992 + 0.997376i \(0.523066\pi\)
\(798\) 0 0
\(799\) 232.000 0.0102723
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1592.00 −0.0699632
\(804\) 0 0
\(805\) −2400.00 −0.105079
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −29754.0 −1.29307 −0.646536 − 0.762884i \(-0.723783\pi\)
−0.646536 + 0.762884i \(0.723783\pi\)
\(810\) 0 0
\(811\) 42848.0 1.85524 0.927618 − 0.373530i \(-0.121853\pi\)
0.927618 + 0.373530i \(0.121853\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1260.00 0.0541544
\(816\) 0 0
\(817\) 1088.00 0.0465903
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 6454.00 0.274356 0.137178 − 0.990546i \(-0.456197\pi\)
0.137178 + 0.990546i \(0.456197\pi\)
\(822\) 0 0
\(823\) −19128.0 −0.810158 −0.405079 − 0.914282i \(-0.632756\pi\)
−0.405079 + 0.914282i \(0.632756\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 7060.00 0.296856 0.148428 − 0.988923i \(-0.452579\pi\)
0.148428 + 0.988923i \(0.452579\pi\)
\(828\) 0 0
\(829\) −4666.00 −0.195485 −0.0977424 − 0.995212i \(-0.531162\pi\)
−0.0977424 + 0.995212i \(0.531162\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −558.000 −0.0232095
\(834\) 0 0
\(835\) −4420.00 −0.183186
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −33792.0 −1.39050 −0.695250 − 0.718768i \(-0.744706\pi\)
−0.695250 + 0.718768i \(0.744706\pi\)
\(840\) 0 0
\(841\) −4225.00 −0.173234
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −10805.0 −0.439886
\(846\) 0 0
\(847\) −10520.0 −0.426767
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 12840.0 0.517214
\(852\) 0 0
\(853\) 23146.0 0.929078 0.464539 − 0.885553i \(-0.346220\pi\)
0.464539 + 0.885553i \(0.346220\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 40698.0 1.62219 0.811095 − 0.584914i \(-0.198872\pi\)
0.811095 + 0.584914i \(0.198872\pi\)
\(858\) 0 0
\(859\) −40136.0 −1.59421 −0.797103 − 0.603844i \(-0.793635\pi\)
−0.797103 + 0.603844i \(0.793635\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1396.00 0.0550642 0.0275321 − 0.999621i \(-0.491235\pi\)
0.0275321 + 0.999621i \(0.491235\pi\)
\(864\) 0 0
\(865\) 6990.00 0.274760
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −544.000 −0.0212358
\(870\) 0 0
\(871\) 648.000 0.0252085
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1000.00 0.0386356
\(876\) 0 0
\(877\) −34646.0 −1.33399 −0.666997 − 0.745061i \(-0.732421\pi\)
−0.666997 + 0.745061i \(0.732421\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 15302.0 0.585173 0.292587 − 0.956239i \(-0.405484\pi\)
0.292587 + 0.956239i \(0.405484\pi\)
\(882\) 0 0
\(883\) 26300.0 1.00234 0.501170 − 0.865349i \(-0.332903\pi\)
0.501170 + 0.865349i \(0.332903\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −12052.0 −0.456219 −0.228110 − 0.973635i \(-0.573254\pi\)
−0.228110 + 0.973635i \(0.573254\pi\)
\(888\) 0 0
\(889\) 6720.00 0.253523
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1856.00 0.0695506
\(894\) 0 0
\(895\) 18060.0 0.674502
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 24992.0 0.927174
\(900\) 0 0
\(901\) 700.000 0.0258828
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 15750.0 0.578506
\(906\) 0 0
\(907\) −18260.0 −0.668482 −0.334241 − 0.942488i \(-0.608480\pi\)
−0.334241 + 0.942488i \(0.608480\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −10280.0 −0.373866 −0.186933 − 0.982373i \(-0.559855\pi\)
−0.186933 + 0.982373i \(0.559855\pi\)
\(912\) 0 0
\(913\) 1744.00 0.0632179
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 11872.0 0.427533
\(918\) 0 0
\(919\) 34504.0 1.23850 0.619250 − 0.785194i \(-0.287437\pi\)
0.619250 + 0.785194i \(0.287437\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 576.000 0.0205409
\(924\) 0 0
\(925\) −5350.00 −0.190170
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −28266.0 −0.998253 −0.499127 − 0.866529i \(-0.666346\pi\)
−0.499127 + 0.866529i \(0.666346\pi\)
\(930\) 0 0
\(931\) −4464.00 −0.157145
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 40.0000 0.00139908
\(936\) 0 0
\(937\) −51494.0 −1.79534 −0.897671 − 0.440666i \(-0.854742\pi\)
−0.897671 + 0.440666i \(0.854742\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −5338.00 −0.184924 −0.0924622 − 0.995716i \(-0.529474\pi\)
−0.0924622 + 0.995716i \(0.529474\pi\)
\(942\) 0 0
\(943\) −16680.0 −0.576008
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −47644.0 −1.63487 −0.817435 − 0.576021i \(-0.804605\pi\)
−0.817435 + 0.576021i \(0.804605\pi\)
\(948\) 0 0
\(949\) 2388.00 0.0816836
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 13906.0 0.472675 0.236338 − 0.971671i \(-0.424053\pi\)
0.236338 + 0.971671i \(0.424053\pi\)
\(954\) 0 0
\(955\) 15200.0 0.515037
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −8048.00 −0.270994
\(960\) 0 0
\(961\) 1185.00 0.0397771
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 9970.00 0.332586
\(966\) 0 0
\(967\) −8536.00 −0.283867 −0.141933 − 0.989876i \(-0.545332\pi\)
−0.141933 + 0.989876i \(0.545332\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 22572.0 0.746004 0.373002 − 0.927831i \(-0.378328\pi\)
0.373002 + 0.927831i \(0.378328\pi\)
\(972\) 0 0
\(973\) −11200.0 −0.369019
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 51474.0 1.68557 0.842784 − 0.538253i \(-0.180915\pi\)
0.842784 + 0.538253i \(0.180915\pi\)
\(978\) 0 0
\(979\) 3000.00 0.0979371
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 6412.00 0.208048 0.104024 − 0.994575i \(-0.466828\pi\)
0.104024 + 0.994575i \(0.466828\pi\)
\(984\) 0 0
\(985\) −20330.0 −0.657632
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4080.00 −0.131179
\(990\) 0 0
\(991\) 54008.0 1.73120 0.865601 − 0.500735i \(-0.166937\pi\)
0.865601 + 0.500735i \(0.166937\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 19520.0 0.621935
\(996\) 0 0
\(997\) −30846.0 −0.979842 −0.489921 − 0.871767i \(-0.662974\pi\)
−0.489921 + 0.871767i \(0.662974\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1440.4.a.p.1.1 1
3.2 odd 2 480.4.a.b.1.1 ✓ 1
4.3 odd 2 1440.4.a.m.1.1 1
12.11 even 2 480.4.a.g.1.1 yes 1
15.14 odd 2 2400.4.a.q.1.1 1
24.5 odd 2 960.4.a.bh.1.1 1
24.11 even 2 960.4.a.m.1.1 1
60.59 even 2 2400.4.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
480.4.a.b.1.1 ✓ 1 3.2 odd 2
480.4.a.g.1.1 yes 1 12.11 even 2
960.4.a.m.1.1 1 24.11 even 2
960.4.a.bh.1.1 1 24.5 odd 2
1440.4.a.m.1.1 1 4.3 odd 2
1440.4.a.p.1.1 1 1.1 even 1 trivial
2400.4.a.f.1.1 1 60.59 even 2
2400.4.a.q.1.1 1 15.14 odd 2