↑

Properties

Label 576.4.a.h.1.1
Level $576$
Weight $4$
Character 576.1
Self dual yes
Analytic conductor $33.985$
Analytic rank $1$
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] = [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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 32)
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)
 
\(f(q)\) \(=\) \(q-10.0000 q^{5} +16.0000 q^{7} +O(q^{10})\) \(q-10.0000 q^{5} +16.0000 q^{7} -40.0000 q^{11} +50.0000 q^{13} +30.0000 q^{17} -40.0000 q^{19} -48.0000 q^{23} -25.0000 q^{25} -34.0000 q^{29} +320.000 q^{31} -160.000 q^{35} -310.000 q^{37} -410.000 q^{41} -152.000 q^{43} +416.000 q^{47} -87.0000 q^{49} -410.000 q^{53} +400.000 q^{55} -200.000 q^{59} -30.0000 q^{61} -500.000 q^{65} -776.000 q^{67} -400.000 q^{71} -630.000 q^{73} -640.000 q^{77} -1120.00 q^{79} +552.000 q^{83} -300.000 q^{85} +326.000 q^{89} +800.000 q^{91} +400.000 q^{95} -110.000 q^{97} +O(q^{100})\)

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
\(5\) −10.0000 −0.894427 −0.447214 − 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 0 0
\(7\) 16.0000 0.863919 0.431959 − 0.901893i \(-0.357822\pi\)
0.431959 + 0.901893i \(0.357822\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −40.0000 −1.09640 −0.548202 − 0.836346i \(-0.684688\pi\)
−0.548202 + 0.836346i \(0.684688\pi\)
\(12\) 0 0
\(13\) 50.0000 1.06673 0.533366 − 0.845885i \(-0.320927\pi\)
0.533366 + 0.845885i \(0.320927\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 30.0000 0.428004 0.214002 − 0.976833i \(-0.431350\pi\)
0.214002 + 0.976833i \(0.431350\pi\)
\(18\) 0 0
\(19\) −40.0000 −0.482980 −0.241490 − 0.970403i \(-0.577636\pi\)
−0.241490 + 0.970403i \(0.577636\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −48.0000 −0.435161 −0.217580 − 0.976042i \(-0.569816\pi\)
−0.217580 + 0.976042i \(0.569816\pi\)
\(24\) 0 0
\(25\) −25.0000 −0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −34.0000 −0.217712 −0.108856 − 0.994058i \(-0.534719\pi\)
−0.108856 + 0.994058i \(0.534719\pi\)
\(30\) 0 0
\(31\) 320.000 1.85399 0.926995 − 0.375073i \(-0.122383\pi\)
0.926995 + 0.375073i \(0.122383\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −160.000 −0.772712
\(36\) 0 0
\(37\) −310.000 −1.37740 −0.688698 − 0.725048i \(-0.741818\pi\)
−0.688698 + 0.725048i \(0.741818\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −410.000 −1.56174 −0.780869 − 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) −152.000 −0.539065 −0.269532 − 0.962991i \(-0.586869\pi\)
−0.269532 + 0.962991i \(0.586869\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 416.000 1.29106 0.645530 − 0.763735i \(-0.276636\pi\)
0.645530 + 0.763735i \(0.276636\pi\)
\(48\) 0 0
\(49\) −87.0000 −0.253644
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −410.000 −1.06260 −0.531300 − 0.847184i \(-0.678296\pi\)
−0.531300 + 0.847184i \(0.678296\pi\)
\(54\) 0 0
\(55\) 400.000 0.980654
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −200.000 −0.441318 −0.220659 − 0.975351i \(-0.570821\pi\)
−0.220659 + 0.975351i \(0.570821\pi\)
\(60\) 0 0
\(61\) −30.0000 −0.0629690 −0.0314845 − 0.999504i \(-0.510023\pi\)
−0.0314845 + 0.999504i \(0.510023\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −500.000 −0.954113
\(66\) 0 0
\(67\) −776.000 −1.41498 −0.707489 − 0.706725i \(-0.750172\pi\)
−0.707489 + 0.706725i \(0.750172\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −400.000 −0.668609 −0.334305 − 0.942465i \(-0.608501\pi\)
−0.334305 + 0.942465i \(0.608501\pi\)
\(72\) 0 0
\(73\) −630.000 −1.01008 −0.505041 − 0.863096i \(-0.668522\pi\)
−0.505041 + 0.863096i \(0.668522\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −640.000 −0.947205
\(78\) 0 0
\(79\) −1120.00 −1.59506 −0.797531 − 0.603278i \(-0.793861\pi\)
−0.797531 + 0.603278i \(0.793861\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 552.000 0.729998 0.364999 − 0.931008i \(-0.381069\pi\)
0.364999 + 0.931008i \(0.381069\pi\)
\(84\) 0 0
\(85\) −300.000 −0.382818
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 326.000 0.388269 0.194134 − 0.980975i \(-0.437810\pi\)
0.194134 + 0.980975i \(0.437810\pi\)
\(90\) 0 0
\(91\) 800.000 0.921569
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 400.000 0.431991
\(96\) 0 0
\(97\) −110.000 −0.115142 −0.0575712 − 0.998341i \(-0.518336\pi\)
−0.0575712 + 0.998341i \(0.518336\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1098.00 −1.08173 −0.540867 − 0.841108i \(-0.681904\pi\)
−0.540867 + 0.841108i \(0.681904\pi\)
\(102\) 0 0
\(103\) −48.0000 −0.0459183 −0.0229591 − 0.999736i \(-0.507309\pi\)
−0.0229591 + 0.999736i \(0.507309\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 664.000 0.599919 0.299959 − 0.953952i \(-0.403027\pi\)
0.299959 + 0.953952i \(0.403027\pi\)
\(108\) 0 0
\(109\) 370.000 0.325134 0.162567 − 0.986698i \(-0.448023\pi\)
0.162567 + 0.986698i \(0.448023\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1490.00 −1.24042 −0.620210 − 0.784436i \(-0.712953\pi\)
−0.620210 + 0.784436i \(0.712953\pi\)
\(114\) 0 0
\(115\) 480.000 0.389219
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 480.000 0.369761
\(120\) 0 0
\(121\) 269.000 0.202104
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1500.00 1.07331
\(126\) 0 0
\(127\) −1024.00 −0.715475 −0.357737 − 0.933822i \(-0.616452\pi\)
−0.357737 + 0.933822i \(0.616452\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1160.00 0.773662 0.386831 − 0.922151i \(-0.373570\pi\)
0.386831 + 0.922151i \(0.373570\pi\)
\(132\) 0 0
\(133\) −640.000 −0.417256
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −570.000 −0.355463 −0.177731 − 0.984079i \(-0.556876\pi\)
−0.177731 + 0.984079i \(0.556876\pi\)
\(138\) 0 0
\(139\) 1960.00 1.19601 0.598004 − 0.801493i \(-0.295961\pi\)
0.598004 + 0.801493i \(0.295961\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2000.00 −1.16957
\(144\) 0 0
\(145\) 340.000 0.194727
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2010.00 −1.10514 −0.552569 − 0.833467i \(-0.686352\pi\)
−0.552569 + 0.833467i \(0.686352\pi\)
\(150\) 0 0
\(151\) −720.000 −0.388032 −0.194016 − 0.980998i \(-0.562151\pi\)
−0.194016 + 0.980998i \(0.562151\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3200.00 −1.65826
\(156\) 0 0
\(157\) −1790.00 −0.909921 −0.454960 − 0.890512i \(-0.650347\pi\)
−0.454960 + 0.890512i \(0.650347\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −768.000 −0.375943
\(162\) 0 0
\(163\) 1208.00 0.580478 0.290239 − 0.956954i \(-0.406265\pi\)
0.290239 + 0.956954i \(0.406265\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2896.00 −1.34191 −0.670956 − 0.741497i \(-0.734116\pi\)
−0.670956 + 0.741497i \(0.734116\pi\)
\(168\) 0 0
\(169\) 303.000 0.137915
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 750.000 0.329604 0.164802 − 0.986327i \(-0.447302\pi\)
0.164802 + 0.986327i \(0.447302\pi\)
\(174\) 0 0
\(175\) −400.000 −0.172784
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2280.00 0.952040 0.476020 − 0.879434i \(-0.342079\pi\)
0.476020 + 0.879434i \(0.342079\pi\)
\(180\) 0 0
\(181\) 442.000 0.181512 0.0907558 − 0.995873i \(-0.471072\pi\)
0.0907558 + 0.995873i \(0.471072\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3100.00 1.23198
\(186\) 0 0
\(187\) −1200.00 −0.469266
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1920.00 0.727363 0.363681 − 0.931523i \(-0.381520\pi\)
0.363681 + 0.931523i \(0.381520\pi\)
\(192\) 0 0
\(193\) −5070.00 −1.89091 −0.945457 − 0.325746i \(-0.894385\pi\)
−0.945457 + 0.325746i \(0.894385\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1910.00 0.690771 0.345385 − 0.938461i \(-0.387748\pi\)
0.345385 + 0.938461i \(0.387748\pi\)
\(198\) 0 0
\(199\) 2960.00 1.05442 0.527208 − 0.849736i \(-0.323239\pi\)
0.527208 + 0.849736i \(0.323239\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −544.000 −0.188085
\(204\) 0 0
\(205\) 4100.00 1.39686
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1600.00 0.529542
\(210\) 0 0
\(211\) −40.0000 −0.0130508 −0.00652539 − 0.999979i \(-0.502077\pi\)
−0.00652539 + 0.999979i \(0.502077\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1520.00 0.482154
\(216\) 0 0
\(217\) 5120.00 1.60170
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1500.00 0.456565
\(222\) 0 0
\(223\) 4288.00 1.28765 0.643824 − 0.765173i \(-0.277347\pi\)
0.643824 + 0.765173i \(0.277347\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6456.00 −1.88766 −0.943832 − 0.330425i \(-0.892808\pi\)
−0.943832 + 0.330425i \(0.892808\pi\)
\(228\) 0 0
\(229\) 1066.00 0.307613 0.153806 − 0.988101i \(-0.450847\pi\)
0.153806 + 0.988101i \(0.450847\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5910.00 1.66170 0.830852 − 0.556494i \(-0.187854\pi\)
0.830852 + 0.556494i \(0.187854\pi\)
\(234\) 0 0
\(235\) −4160.00 −1.15476
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3360.00 0.909374 0.454687 − 0.890651i \(-0.349751\pi\)
0.454687 + 0.890651i \(0.349751\pi\)
\(240\) 0 0
\(241\) 3970.00 1.06112 0.530561 − 0.847647i \(-0.321981\pi\)
0.530561 + 0.847647i \(0.321981\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 870.000 0.226866
\(246\) 0 0
\(247\) −2000.00 −0.515210
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6840.00 1.72007 0.860034 − 0.510237i \(-0.170442\pi\)
0.860034 + 0.510237i \(0.170442\pi\)
\(252\) 0 0
\(253\) 1920.00 0.477112
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4610.00 −1.11893 −0.559463 − 0.828855i \(-0.688993\pi\)
−0.559463 + 0.828855i \(0.688993\pi\)
\(258\) 0 0
\(259\) −4960.00 −1.18996
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4848.00 1.13666 0.568328 − 0.822802i \(-0.307591\pi\)
0.568328 + 0.822802i \(0.307591\pi\)
\(264\) 0 0
\(265\) 4100.00 0.950419
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 5550.00 1.25795 0.628977 − 0.777424i \(-0.283474\pi\)
0.628977 + 0.777424i \(0.283474\pi\)
\(270\) 0 0
\(271\) −480.000 −0.107594 −0.0537969 − 0.998552i \(-0.517132\pi\)
−0.0537969 + 0.998552i \(0.517132\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1000.00 0.219281
\(276\) 0 0
\(277\) −1030.00 −0.223418 −0.111709 − 0.993741i \(-0.535632\pi\)
−0.111709 + 0.993741i \(0.535632\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3270.00 0.694206 0.347103 − 0.937827i \(-0.387165\pi\)
0.347103 + 0.937827i \(0.387165\pi\)
\(282\) 0 0
\(283\) −2168.00 −0.455386 −0.227693 − 0.973733i \(-0.573118\pi\)
−0.227693 + 0.973733i \(0.573118\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6560.00 −1.34921
\(288\) 0 0
\(289\) −4013.00 −0.816813
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2070.00 0.412733 0.206366 − 0.978475i \(-0.433836\pi\)
0.206366 + 0.978475i \(0.433836\pi\)
\(294\) 0 0
\(295\) 2000.00 0.394727
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2400.00 −0.464199
\(300\) 0 0
\(301\) −2432.00 −0.465708
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 300.000 0.0563211
\(306\) 0 0
\(307\) −1896.00 −0.352477 −0.176238 − 0.984347i \(-0.556393\pi\)
−0.176238 + 0.984347i \(0.556393\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1680.00 0.306315 0.153158 − 0.988202i \(-0.451056\pi\)
0.153158 + 0.988202i \(0.451056\pi\)
\(312\) 0 0
\(313\) 970.000 0.175168 0.0875841 − 0.996157i \(-0.472085\pi\)
0.0875841 + 0.996157i \(0.472085\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7230.00 1.28100 0.640500 − 0.767958i \(-0.278727\pi\)
0.640500 + 0.767958i \(0.278727\pi\)
\(318\) 0 0
\(319\) 1360.00 0.238700
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1200.00 −0.206718
\(324\) 0 0
\(325\) −1250.00 −0.213346
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6656.00 1.11537
\(330\) 0 0
\(331\) 5800.00 0.963132 0.481566 − 0.876410i \(-0.340068\pi\)
0.481566 + 0.876410i \(0.340068\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7760.00 1.26559
\(336\) 0 0
\(337\) −1870.00 −0.302271 −0.151136 − 0.988513i \(-0.548293\pi\)
−0.151136 + 0.988513i \(0.548293\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −12800.0 −2.03272
\(342\) 0 0
\(343\) −6880.00 −1.08305
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 376.000 0.0581693 0.0290846 − 0.999577i \(-0.490741\pi\)
0.0290846 + 0.999577i \(0.490741\pi\)
\(348\) 0 0
\(349\) 7586.00 1.16352 0.581761 − 0.813360i \(-0.302364\pi\)
0.581761 + 0.813360i \(0.302364\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2530.00 −0.381468 −0.190734 − 0.981642i \(-0.561087\pi\)
−0.190734 + 0.981642i \(0.561087\pi\)
\(354\) 0 0
\(355\) 4000.00 0.598022
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9680.00 −1.42309 −0.711547 − 0.702638i \(-0.752005\pi\)
−0.711547 + 0.702638i \(0.752005\pi\)
\(360\) 0 0
\(361\) −5259.00 −0.766730
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 6300.00 0.903444
\(366\) 0 0
\(367\) 2784.00 0.395977 0.197989 − 0.980204i \(-0.436559\pi\)
0.197989 + 0.980204i \(0.436559\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −6560.00 −0.918001
\(372\) 0 0
\(373\) −7910.00 −1.09803 −0.549014 − 0.835813i \(-0.684997\pi\)
−0.549014 + 0.835813i \(0.684997\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1700.00 −0.232240
\(378\) 0 0
\(379\) −1720.00 −0.233115 −0.116557 − 0.993184i \(-0.537186\pi\)
−0.116557 + 0.993184i \(0.537186\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −11008.0 −1.46862 −0.734311 − 0.678813i \(-0.762495\pi\)
−0.734311 + 0.678813i \(0.762495\pi\)
\(384\) 0 0
\(385\) 6400.00 0.847206
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −12330.0 −1.60708 −0.803542 − 0.595248i \(-0.797054\pi\)
−0.803542 + 0.595248i \(0.797054\pi\)
\(390\) 0 0
\(391\) −1440.00 −0.186250
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 11200.0 1.42667
\(396\) 0 0
\(397\) 4370.00 0.552453 0.276227 − 0.961093i \(-0.410916\pi\)
0.276227 + 0.961093i \(0.410916\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3298.00 −0.410709 −0.205354 − 0.978688i \(-0.565835\pi\)
−0.205354 + 0.978688i \(0.565835\pi\)
\(402\) 0 0
\(403\) 16000.0 1.97771
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 12400.0 1.51018
\(408\) 0 0
\(409\) −9110.00 −1.10137 −0.550685 − 0.834713i \(-0.685634\pi\)
−0.550685 + 0.834713i \(0.685634\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3200.00 −0.381263
\(414\) 0 0
\(415\) −5520.00 −0.652930
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7880.00 0.918767 0.459383 − 0.888238i \(-0.348070\pi\)
0.459383 + 0.888238i \(0.348070\pi\)
\(420\) 0 0
\(421\) 5290.00 0.612396 0.306198 − 0.951968i \(-0.400943\pi\)
0.306198 + 0.951968i \(0.400943\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −750.000 −0.0856008
\(426\) 0 0
\(427\) −480.000 −0.0544001
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −13920.0 −1.55569 −0.777845 − 0.628456i \(-0.783687\pi\)
−0.777845 + 0.628456i \(0.783687\pi\)
\(432\) 0 0
\(433\) 4930.00 0.547161 0.273580 − 0.961849i \(-0.411792\pi\)
0.273580 + 0.961849i \(0.411792\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1920.00 0.210174
\(438\) 0 0
\(439\) −10640.0 −1.15676 −0.578382 − 0.815766i \(-0.696316\pi\)
−0.578382 + 0.815766i \(0.696316\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9288.00 −0.996131 −0.498066 − 0.867139i \(-0.665956\pi\)
−0.498066 + 0.867139i \(0.665956\pi\)
\(444\) 0 0
\(445\) −3260.00 −0.347278
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −12850.0 −1.35062 −0.675311 − 0.737533i \(-0.735990\pi\)
−0.675311 + 0.737533i \(0.735990\pi\)
\(450\) 0 0
\(451\) 16400.0 1.71230
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −8000.00 −0.824276
\(456\) 0 0
\(457\) 10490.0 1.07375 0.536873 − 0.843663i \(-0.319606\pi\)
0.536873 + 0.843663i \(0.319606\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11118.0 1.12325 0.561624 − 0.827393i \(-0.310177\pi\)
0.561624 + 0.827393i \(0.310177\pi\)
\(462\) 0 0
\(463\) 5792.00 0.581376 0.290688 − 0.956818i \(-0.406116\pi\)
0.290688 + 0.956818i \(0.406116\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2216.00 0.219581 0.109790 − 0.993955i \(-0.464982\pi\)
0.109790 + 0.993955i \(0.464982\pi\)
\(468\) 0 0
\(469\) −12416.0 −1.22243
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 6080.00 0.591033
\(474\) 0 0
\(475\) 1000.00 0.0965961
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 10560.0 1.00730 0.503652 − 0.863907i \(-0.331989\pi\)
0.503652 + 0.863907i \(0.331989\pi\)
\(480\) 0 0
\(481\) −15500.0 −1.46931
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1100.00 0.102986
\(486\) 0 0
\(487\) 13264.0 1.23419 0.617094 − 0.786890i \(-0.288310\pi\)
0.617094 + 0.786890i \(0.288310\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4840.00 −0.444860 −0.222430 − 0.974949i \(-0.571399\pi\)
−0.222430 + 0.974949i \(0.571399\pi\)
\(492\) 0 0
\(493\) −1020.00 −0.0931815
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6400.00 −0.577624
\(498\) 0 0
\(499\) −19560.0 −1.75476 −0.877381 − 0.479795i \(-0.840711\pi\)
−0.877381 + 0.479795i \(0.840711\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 528.000 0.0468039 0.0234019 − 0.999726i \(-0.492550\pi\)
0.0234019 + 0.999726i \(0.492550\pi\)
\(504\) 0 0
\(505\) 10980.0 0.967532
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −19554.0 −1.70278 −0.851391 − 0.524532i \(-0.824240\pi\)
−0.851391 + 0.524532i \(0.824240\pi\)
\(510\) 0 0
\(511\) −10080.0 −0.872628
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 480.000 0.0410705
\(516\) 0 0
\(517\) −16640.0 −1.41552
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −15162.0 −1.27497 −0.637485 − 0.770463i \(-0.720025\pi\)
−0.637485 + 0.770463i \(0.720025\pi\)
\(522\) 0 0
\(523\) −10968.0 −0.917012 −0.458506 − 0.888691i \(-0.651615\pi\)
−0.458506 + 0.888691i \(0.651615\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 9600.00 0.793515
\(528\) 0 0
\(529\) −9863.00 −0.810635
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −20500.0 −1.66595
\(534\) 0 0
\(535\) −6640.00 −0.536584
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3480.00 0.278097
\(540\) 0 0
\(541\) 6722.00 0.534198 0.267099 − 0.963669i \(-0.413935\pi\)
0.267099 + 0.963669i \(0.413935\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3700.00 −0.290808
\(546\) 0 0
\(547\) −20424.0 −1.59647 −0.798233 − 0.602348i \(-0.794232\pi\)
−0.798233 + 0.602348i \(0.794232\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1360.00 0.105151
\(552\) 0 0
\(553\) −17920.0 −1.37800
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6610.00 −0.502827 −0.251414 − 0.967880i \(-0.580895\pi\)
−0.251414 + 0.967880i \(0.580895\pi\)
\(558\) 0 0
\(559\) −7600.00 −0.575037
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −2712.00 −0.203015 −0.101507 − 0.994835i \(-0.532367\pi\)
−0.101507 + 0.994835i \(0.532367\pi\)
\(564\) 0 0
\(565\) 14900.0 1.10946
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −3530.00 −0.260080 −0.130040 − 0.991509i \(-0.541511\pi\)
−0.130040 + 0.991509i \(0.541511\pi\)
\(570\) 0 0
\(571\) 13640.0 0.999678 0.499839 − 0.866118i \(-0.333392\pi\)
0.499839 + 0.866118i \(0.333392\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1200.00 0.0870321
\(576\) 0 0
\(577\) −6270.00 −0.452380 −0.226190 − 0.974083i \(-0.572627\pi\)
−0.226190 + 0.974083i \(0.572627\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 8832.00 0.630659
\(582\) 0 0
\(583\) 16400.0 1.16504
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8616.00 −0.605827 −0.302913 − 0.953018i \(-0.597959\pi\)
−0.302913 + 0.953018i \(0.597959\pi\)
\(588\) 0 0
\(589\) −12800.0 −0.895441
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −5490.00 −0.380181 −0.190090 − 0.981767i \(-0.560878\pi\)
−0.190090 + 0.981767i \(0.560878\pi\)
\(594\) 0 0
\(595\) −4800.00 −0.330724
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 15440.0 1.05319 0.526595 − 0.850116i \(-0.323468\pi\)
0.526595 + 0.850116i \(0.323468\pi\)
\(600\) 0 0
\(601\) 8890.00 0.603379 0.301689 − 0.953406i \(-0.402449\pi\)
0.301689 + 0.953406i \(0.402449\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2690.00 −0.180767
\(606\) 0 0
\(607\) 23744.0 1.58771 0.793854 − 0.608108i \(-0.208071\pi\)
0.793854 + 0.608108i \(0.208071\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 20800.0 1.37721
\(612\) 0 0
\(613\) 15210.0 1.00216 0.501082 − 0.865400i \(-0.332936\pi\)
0.501082 + 0.865400i \(0.332936\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12630.0 0.824092 0.412046 − 0.911163i \(-0.364814\pi\)
0.412046 + 0.911163i \(0.364814\pi\)
\(618\) 0 0
\(619\) −11160.0 −0.724650 −0.362325 − 0.932052i \(-0.618017\pi\)
−0.362325 + 0.932052i \(0.618017\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5216.00 0.335433
\(624\) 0 0
\(625\) −11875.0 −0.760000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −9300.00 −0.589531
\(630\) 0 0
\(631\) 13040.0 0.822685 0.411342 − 0.911481i \(-0.365060\pi\)
0.411342 + 0.911481i \(0.365060\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 10240.0 0.639940
\(636\) 0 0
\(637\) −4350.00 −0.270570
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 16910.0 1.04197 0.520987 − 0.853565i \(-0.325564\pi\)
0.520987 + 0.853565i \(0.325564\pi\)
\(642\) 0 0
\(643\) −4488.00 −0.275256 −0.137628 − 0.990484i \(-0.543948\pi\)
−0.137628 + 0.990484i \(0.543948\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2064.00 −0.125416 −0.0627080 − 0.998032i \(-0.519974\pi\)
−0.0627080 + 0.998032i \(0.519974\pi\)
\(648\) 0 0
\(649\) 8000.00 0.483864
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4270.00 0.255893 0.127946 − 0.991781i \(-0.459161\pi\)
0.127946 + 0.991781i \(0.459161\pi\)
\(654\) 0 0
\(655\) −11600.0 −0.691984
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −19800.0 −1.17041 −0.585204 − 0.810886i \(-0.698985\pi\)
−0.585204 + 0.810886i \(0.698985\pi\)
\(660\) 0 0
\(661\) −27110.0 −1.59524 −0.797622 − 0.603157i \(-0.793909\pi\)
−0.797622 + 0.603157i \(0.793909\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 6400.00 0.373205
\(666\) 0 0
\(667\) 1632.00 0.0947396
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1200.00 0.0690395
\(672\) 0 0
\(673\) 32210.0 1.84488 0.922440 − 0.386140i \(-0.126192\pi\)
0.922440 + 0.386140i \(0.126192\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 27190.0 1.54357 0.771785 − 0.635884i \(-0.219364\pi\)
0.771785 + 0.635884i \(0.219364\pi\)
\(678\) 0 0
\(679\) −1760.00 −0.0994736
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −20328.0 −1.13884 −0.569421 − 0.822046i \(-0.692833\pi\)
−0.569421 + 0.822046i \(0.692833\pi\)
\(684\) 0 0
\(685\) 5700.00 0.317935
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −20500.0 −1.13351
\(690\) 0 0
\(691\) −12520.0 −0.689267 −0.344633 − 0.938737i \(-0.611997\pi\)
−0.344633 + 0.938737i \(0.611997\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −19600.0 −1.06974
\(696\) 0 0
\(697\) −12300.0 −0.668430
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 11550.0 0.622307 0.311154 − 0.950360i \(-0.399285\pi\)
0.311154 + 0.950360i \(0.399285\pi\)
\(702\) 0 0
\(703\) 12400.0 0.665256
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −17568.0 −0.934530
\(708\) 0 0
\(709\) 34154.0 1.80914 0.904570 − 0.426325i \(-0.140192\pi\)
0.904570 + 0.426325i \(0.140192\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −15360.0 −0.806783
\(714\) 0 0
\(715\) 20000.0 1.04609
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 22880.0 1.18676 0.593380 − 0.804923i \(-0.297793\pi\)
0.593380 + 0.804923i \(0.297793\pi\)
\(720\) 0 0
\(721\) −768.000 −0.0396696
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 850.000 0.0435424
\(726\) 0 0
\(727\) 10416.0 0.531373 0.265686 − 0.964060i \(-0.414401\pi\)
0.265686 + 0.964060i \(0.414401\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4560.00 −0.230722
\(732\) 0 0
\(733\) −14750.0 −0.743252 −0.371626 − 0.928383i \(-0.621200\pi\)
−0.371626 + 0.928383i \(0.621200\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 31040.0 1.55139
\(738\) 0 0
\(739\) 2360.00 0.117475 0.0587375 − 0.998273i \(-0.481293\pi\)
0.0587375 + 0.998273i \(0.481293\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −32208.0 −1.59031 −0.795153 − 0.606409i \(-0.792609\pi\)
−0.795153 + 0.606409i \(0.792609\pi\)
\(744\) 0 0
\(745\) 20100.0 0.988466
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 10624.0 0.518281
\(750\) 0 0
\(751\) −36640.0 −1.78031 −0.890155 − 0.455658i \(-0.849404\pi\)
−0.890155 + 0.455658i \(0.849404\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 7200.00 0.347066
\(756\) 0 0
\(757\) 12090.0 0.580474 0.290237 − 0.956955i \(-0.406266\pi\)
0.290237 + 0.956955i \(0.406266\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 3318.00 0.158052 0.0790259 − 0.996873i \(-0.474819\pi\)
0.0790259 + 0.996873i \(0.474819\pi\)
\(762\) 0 0
\(763\) 5920.00 0.280889
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −10000.0 −0.470768
\(768\) 0 0
\(769\) 11506.0 0.539554 0.269777 − 0.962923i \(-0.413050\pi\)
0.269777 + 0.962923i \(0.413050\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 22230.0 1.03436 0.517178 − 0.855878i \(-0.326982\pi\)
0.517178 + 0.855878i \(0.326982\pi\)
\(774\) 0 0
\(775\) −8000.00 −0.370798
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 16400.0 0.754289
\(780\) 0 0
\(781\) 16000.0 0.733067
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 17900.0 0.813858
\(786\) 0 0
\(787\) 21336.0 0.966387 0.483193 − 0.875514i \(-0.339477\pi\)
0.483193 + 0.875514i \(0.339477\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −23840.0 −1.07162
\(792\) 0 0
\(793\) −1500.00 −0.0671709
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −7170.00 −0.318663 −0.159332 − 0.987225i \(-0.550934\pi\)
−0.159332 + 0.987225i \(0.550934\pi\)
\(798\) 0 0
\(799\) 12480.0 0.552579
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 25200.0 1.10746
\(804\) 0 0
\(805\) 7680.00 0.336254
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 23654.0 1.02797 0.513987 − 0.857798i \(-0.328168\pi\)
0.513987 + 0.857798i \(0.328168\pi\)
\(810\) 0 0
\(811\) 30440.0 1.31799 0.658997 − 0.752146i \(-0.270981\pi\)
0.658997 + 0.752146i \(0.270981\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −12080.0 −0.519195
\(816\) 0 0
\(817\) 6080.00 0.260358
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −19930.0 −0.847213 −0.423606 − 0.905846i \(-0.639236\pi\)
−0.423606 + 0.905846i \(0.639236\pi\)
\(822\) 0 0
\(823\) −9872.00 −0.418124 −0.209062 − 0.977902i \(-0.567041\pi\)
−0.209062 + 0.977902i \(0.567041\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −5704.00 −0.239840 −0.119920 − 0.992784i \(-0.538264\pi\)
−0.119920 + 0.992784i \(0.538264\pi\)
\(828\) 0 0
\(829\) −27230.0 −1.14082 −0.570408 − 0.821361i \(-0.693215\pi\)
−0.570408 + 0.821361i \(0.693215\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2610.00 −0.108561
\(834\) 0 0
\(835\) 28960.0 1.20024
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 18800.0 0.773597 0.386799 − 0.922164i \(-0.373581\pi\)
0.386799 + 0.922164i \(0.373581\pi\)
\(840\) 0 0
\(841\) −23233.0 −0.952602
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3030.00 −0.123355
\(846\) 0 0
\(847\) 4304.00 0.174601
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 14880.0 0.599389
\(852\) 0 0
\(853\) 12090.0 0.485292 0.242646 − 0.970115i \(-0.421985\pi\)
0.242646 + 0.970115i \(0.421985\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 470.000 0.0187338 0.00936692 − 0.999956i \(-0.497018\pi\)
0.00936692 + 0.999956i \(0.497018\pi\)
\(858\) 0 0
\(859\) −24440.0 −0.970759 −0.485380 − 0.874304i \(-0.661319\pi\)
−0.485380 + 0.874304i \(0.661319\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 22592.0 0.891125 0.445562 − 0.895251i \(-0.353004\pi\)
0.445562 + 0.895251i \(0.353004\pi\)
\(864\) 0 0
\(865\) −7500.00 −0.294807
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 44800.0 1.74883
\(870\) 0 0
\(871\) −38800.0 −1.50940
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 24000.0 0.927255
\(876\) 0 0
\(877\) 17330.0 0.667266 0.333633 − 0.942703i \(-0.391725\pi\)
0.333633 + 0.942703i \(0.391725\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 31470.0 1.20346 0.601732 − 0.798698i \(-0.294478\pi\)
0.601732 + 0.798698i \(0.294478\pi\)
\(882\) 0 0
\(883\) 3352.00 0.127751 0.0638753 − 0.997958i \(-0.479654\pi\)
0.0638753 + 0.997958i \(0.479654\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 48144.0 1.82245 0.911227 − 0.411904i \(-0.135136\pi\)
0.911227 + 0.411904i \(0.135136\pi\)
\(888\) 0 0
\(889\) −16384.0 −0.618112
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −16640.0 −0.623557
\(894\) 0 0
\(895\) −22800.0 −0.851531
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −10880.0 −0.403636
\(900\) 0 0
\(901\) −12300.0 −0.454797
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −4420.00 −0.162349
\(906\) 0 0
\(907\) −16216.0 −0.593653 −0.296827 − 0.954931i \(-0.595928\pi\)
−0.296827 + 0.954931i \(0.595928\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −49440.0 −1.79805 −0.899023 − 0.437901i \(-0.855722\pi\)
−0.899023 + 0.437901i \(0.855722\pi\)
\(912\) 0 0
\(913\) −22080.0 −0.800374
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 18560.0 0.668381
\(918\) 0 0
\(919\) −16080.0 −0.577182 −0.288591 − 0.957452i \(-0.593187\pi\)
−0.288591 + 0.957452i \(0.593187\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −20000.0 −0.713226
\(924\) 0 0
\(925\) 7750.00 0.275479
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 11310.0 0.399428 0.199714 − 0.979854i \(-0.435999\pi\)
0.199714 + 0.979854i \(0.435999\pi\)
\(930\) 0 0
\(931\) 3480.00 0.122505
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 12000.0 0.419724
\(936\) 0 0
\(937\) 25130.0 0.876159 0.438080 − 0.898936i \(-0.355659\pi\)
0.438080 + 0.898936i \(0.355659\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −22322.0 −0.773301 −0.386651 − 0.922226i \(-0.626368\pi\)
−0.386651 + 0.922226i \(0.626368\pi\)
\(942\) 0 0
\(943\) 19680.0 0.679607
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 36456.0 1.25096 0.625481 − 0.780239i \(-0.284903\pi\)
0.625481 + 0.780239i \(0.284903\pi\)
\(948\) 0 0
\(949\) −31500.0 −1.07749
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −40650.0 −1.38172 −0.690862 − 0.722987i \(-0.742769\pi\)
−0.690862 + 0.722987i \(0.742769\pi\)
\(954\) 0 0
\(955\) −19200.0 −0.650573
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −9120.00 −0.307091
\(960\) 0 0
\(961\) 72609.0 2.43728
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 50700.0 1.69129
\(966\) 0 0
\(967\) 34704.0 1.15409 0.577045 − 0.816712i \(-0.304206\pi\)
0.577045 + 0.816712i \(0.304206\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −30760.0 −1.01662 −0.508309 − 0.861175i \(-0.669729\pi\)
−0.508309 + 0.861175i \(0.669729\pi\)
\(972\) 0 0
\(973\) 31360.0 1.03325
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 38110.0 1.24795 0.623975 − 0.781444i \(-0.285517\pi\)
0.623975 + 0.781444i \(0.285517\pi\)
\(978\) 0 0
\(979\) −13040.0 −0.425700
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −19632.0 −0.636992 −0.318496 − 0.947924i \(-0.603178\pi\)
−0.318496 + 0.947924i \(0.603178\pi\)
\(984\) 0 0
\(985\) −19100.0 −0.617844
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 7296.00 0.234580
\(990\) 0 0
\(991\) −47680.0 −1.52836 −0.764180 − 0.645003i \(-0.776856\pi\)
−0.764180 + 0.645003i \(0.776856\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −29600.0 −0.943099
\(996\) 0 0
\(997\) 39690.0 1.26078 0.630389 − 0.776280i \(-0.282896\pi\)
0.630389 + 0.776280i \(0.282896\pi\)
\(998\) 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.h.1.1 1
3.2 odd 2 64.4.a.a.1.1 1
4.3 odd 2 576.4.a.g.1.1 1
8.3 odd 2 288.4.a.h.1.1 1
8.5 even 2 288.4.a.i.1.1 1
12.11 even 2 64.4.a.e.1.1 1
15.14 odd 2 1600.4.a.bw.1.1 1
24.5 odd 2 32.4.a.c.1.1 yes 1
24.11 even 2 32.4.a.a.1.1 ✓ 1
48.5 odd 4 256.4.b.c.129.2 2
48.11 even 4 256.4.b.e.129.1 2
48.29 odd 4 256.4.b.c.129.1 2
48.35 even 4 256.4.b.e.129.2 2
60.59 even 2 1600.4.a.e.1.1 1
120.29 odd 2 800.4.a.a.1.1 1
120.53 even 4 800.4.c.a.449.2 2
120.59 even 2 800.4.a.k.1.1 1
120.77 even 4 800.4.c.a.449.1 2
120.83 odd 4 800.4.c.b.449.1 2
120.107 odd 4 800.4.c.b.449.2 2
168.83 odd 2 1568.4.a.o.1.1 1
168.125 even 2 1568.4.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.4.a.a.1.1 ✓ 1 24.11 even 2
32.4.a.c.1.1 yes 1 24.5 odd 2
64.4.a.a.1.1 1 3.2 odd 2
64.4.a.e.1.1 1 12.11 even 2
256.4.b.c.129.1 2 48.29 odd 4
256.4.b.c.129.2 2 48.5 odd 4
256.4.b.e.129.1 2 48.11 even 4
256.4.b.e.129.2 2 48.35 even 4
288.4.a.h.1.1 1 8.3 odd 2
288.4.a.i.1.1 1 8.5 even 2
576.4.a.g.1.1 1 4.3 odd 2
576.4.a.h.1.1 1 1.1 even 1 trivial
800.4.a.a.1.1 1 120.29 odd 2
800.4.a.k.1.1 1 120.59 even 2
800.4.c.a.449.1 2 120.77 even 4
800.4.c.a.449.2 2 120.53 even 4
800.4.c.b.449.1 2 120.83 odd 4
800.4.c.b.449.2 2 120.107 odd 4
1568.4.a.c.1.1 1 168.125 even 2
1568.4.a.o.1.1 1 168.83 odd 2
1600.4.a.e.1.1 1 60.59 even 2
1600.4.a.bw.1.1 1 15.14 odd 2