Properties

Label 1600.4.a.bn.1.1
Level $1600$
Weight $4$
Character 1600.1
Self dual yes
Analytic conductor $94.403$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1600,4,Mod(1,1600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1600, 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("1600.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1600.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: \(94.4030560092\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 200)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1600.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.00000 q^{3} -2.00000 q^{7} -2.00000 q^{9} +O(q^{10})\) \(q+5.00000 q^{3} -2.00000 q^{7} -2.00000 q^{9} -39.0000 q^{11} +84.0000 q^{13} +61.0000 q^{17} -151.000 q^{19} -10.0000 q^{21} +58.0000 q^{23} -145.000 q^{27} -192.000 q^{29} -18.0000 q^{31} -195.000 q^{33} -138.000 q^{37} +420.000 q^{39} +229.000 q^{41} -164.000 q^{43} +212.000 q^{47} -339.000 q^{49} +305.000 q^{51} +578.000 q^{53} -755.000 q^{57} +336.000 q^{59} -858.000 q^{61} +4.00000 q^{63} -209.000 q^{67} +290.000 q^{69} -780.000 q^{71} +403.000 q^{73} +78.0000 q^{77} -230.000 q^{79} -671.000 q^{81} -1293.00 q^{83} -960.000 q^{87} -1369.00 q^{89} -168.000 q^{91} -90.0000 q^{93} -382.000 q^{97} +78.0000 q^{99} +O(q^{100})\)

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
\(3\) 5.00000 0.962250 0.481125 0.876652i \(-0.340228\pi\)
0.481125 + 0.876652i \(0.340228\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.00000 −0.107990 −0.0539949 0.998541i \(-0.517195\pi\)
−0.0539949 + 0.998541i \(0.517195\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.0740741
\(10\) 0 0
\(11\) −39.0000 −1.06899 −0.534497 0.845170i \(-0.679499\pi\)
−0.534497 + 0.845170i \(0.679499\pi\)
\(12\) 0 0
\(13\) 84.0000 1.79211 0.896054 0.443945i \(-0.146421\pi\)
0.896054 + 0.443945i \(0.146421\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 61.0000 0.870275 0.435137 0.900364i \(-0.356700\pi\)
0.435137 + 0.900364i \(0.356700\pi\)
\(18\) 0 0
\(19\) −151.000 −1.82325 −0.911626 0.411021i \(-0.865172\pi\)
−0.911626 + 0.411021i \(0.865172\pi\)
\(20\) 0 0
\(21\) −10.0000 −0.103913
\(22\) 0 0
\(23\) 58.0000 0.525819 0.262909 0.964821i \(-0.415318\pi\)
0.262909 + 0.964821i \(0.415318\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −145.000 −1.03353
\(28\) 0 0
\(29\) −192.000 −1.22943 −0.614716 0.788749i \(-0.710729\pi\)
−0.614716 + 0.788749i \(0.710729\pi\)
\(30\) 0 0
\(31\) −18.0000 −0.104287 −0.0521435 0.998640i \(-0.516605\pi\)
−0.0521435 + 0.998640i \(0.516605\pi\)
\(32\) 0 0
\(33\) −195.000 −1.02864
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −138.000 −0.613164 −0.306582 0.951844i \(-0.599185\pi\)
−0.306582 + 0.951844i \(0.599185\pi\)
\(38\) 0 0
\(39\) 420.000 1.72446
\(40\) 0 0
\(41\) 229.000 0.872288 0.436144 0.899877i \(-0.356344\pi\)
0.436144 + 0.899877i \(0.356344\pi\)
\(42\) 0 0
\(43\) −164.000 −0.581622 −0.290811 0.956780i \(-0.593925\pi\)
−0.290811 + 0.956780i \(0.593925\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 212.000 0.657944 0.328972 0.944340i \(-0.393298\pi\)
0.328972 + 0.944340i \(0.393298\pi\)
\(48\) 0 0
\(49\) −339.000 −0.988338
\(50\) 0 0
\(51\) 305.000 0.837422
\(52\) 0 0
\(53\) 578.000 1.49801 0.749004 0.662566i \(-0.230532\pi\)
0.749004 + 0.662566i \(0.230532\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −755.000 −1.75442
\(58\) 0 0
\(59\) 336.000 0.741415 0.370707 0.928750i \(-0.379115\pi\)
0.370707 + 0.928750i \(0.379115\pi\)
\(60\) 0 0
\(61\) −858.000 −1.80091 −0.900456 0.434947i \(-0.856767\pi\)
−0.900456 + 0.434947i \(0.856767\pi\)
\(62\) 0 0
\(63\) 4.00000 0.00799925
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −209.000 −0.381096 −0.190548 0.981678i \(-0.561026\pi\)
−0.190548 + 0.981678i \(0.561026\pi\)
\(68\) 0 0
\(69\) 290.000 0.505970
\(70\) 0 0
\(71\) −780.000 −1.30379 −0.651894 0.758310i \(-0.726025\pi\)
−0.651894 + 0.758310i \(0.726025\pi\)
\(72\) 0 0
\(73\) 403.000 0.646131 0.323066 0.946377i \(-0.395287\pi\)
0.323066 + 0.946377i \(0.395287\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 78.0000 0.115441
\(78\) 0 0
\(79\) −230.000 −0.327557 −0.163779 0.986497i \(-0.552368\pi\)
−0.163779 + 0.986497i \(0.552368\pi\)
\(80\) 0 0
\(81\) −671.000 −0.920439
\(82\) 0 0
\(83\) −1293.00 −1.70994 −0.854971 0.518676i \(-0.826425\pi\)
−0.854971 + 0.518676i \(0.826425\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −960.000 −1.18302
\(88\) 0 0
\(89\) −1369.00 −1.63049 −0.815246 0.579115i \(-0.803398\pi\)
−0.815246 + 0.579115i \(0.803398\pi\)
\(90\) 0 0
\(91\) −168.000 −0.193530
\(92\) 0 0
\(93\) −90.0000 −0.100350
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −382.000 −0.399858 −0.199929 0.979810i \(-0.564071\pi\)
−0.199929 + 0.979810i \(0.564071\pi\)
\(98\) 0 0
\(99\) 78.0000 0.0791848
\(100\) 0 0
\(101\) 794.000 0.782237 0.391119 0.920340i \(-0.372088\pi\)
0.391119 + 0.920340i \(0.372088\pi\)
\(102\) 0 0
\(103\) 1348.00 1.28954 0.644769 0.764378i \(-0.276954\pi\)
0.644769 + 0.764378i \(0.276954\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −775.000 −0.700206 −0.350103 0.936711i \(-0.613853\pi\)
−0.350103 + 0.936711i \(0.613853\pi\)
\(108\) 0 0
\(109\) −446.000 −0.391918 −0.195959 0.980612i \(-0.562782\pi\)
−0.195959 + 0.980612i \(0.562782\pi\)
\(110\) 0 0
\(111\) −690.000 −0.590017
\(112\) 0 0
\(113\) 231.000 0.192307 0.0961533 0.995367i \(-0.469346\pi\)
0.0961533 + 0.995367i \(0.469346\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −168.000 −0.132749
\(118\) 0 0
\(119\) −122.000 −0.0939809
\(120\) 0 0
\(121\) 190.000 0.142750
\(122\) 0 0
\(123\) 1145.00 0.839359
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −2386.00 −1.66711 −0.833556 0.552435i \(-0.813699\pi\)
−0.833556 + 0.552435i \(0.813699\pi\)
\(128\) 0 0
\(129\) −820.000 −0.559666
\(130\) 0 0
\(131\) −2452.00 −1.63536 −0.817680 0.575673i \(-0.804740\pi\)
−0.817680 + 0.575673i \(0.804740\pi\)
\(132\) 0 0
\(133\) 302.000 0.196893
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1125.00 0.701571 0.350786 0.936456i \(-0.385915\pi\)
0.350786 + 0.936456i \(0.385915\pi\)
\(138\) 0 0
\(139\) 1377.00 0.840256 0.420128 0.907465i \(-0.361985\pi\)
0.420128 + 0.907465i \(0.361985\pi\)
\(140\) 0 0
\(141\) 1060.00 0.633107
\(142\) 0 0
\(143\) −3276.00 −1.91575
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −1695.00 −0.951029
\(148\) 0 0
\(149\) −1920.00 −1.05565 −0.527827 0.849352i \(-0.676993\pi\)
−0.527827 + 0.849352i \(0.676993\pi\)
\(150\) 0 0
\(151\) 1854.00 0.999181 0.499591 0.866262i \(-0.333484\pi\)
0.499591 + 0.866262i \(0.333484\pi\)
\(152\) 0 0
\(153\) −122.000 −0.0644648
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −634.000 −0.322285 −0.161142 0.986931i \(-0.551518\pi\)
−0.161142 + 0.986931i \(0.551518\pi\)
\(158\) 0 0
\(159\) 2890.00 1.44146
\(160\) 0 0
\(161\) −116.000 −0.0567831
\(162\) 0 0
\(163\) 103.000 0.0494944 0.0247472 0.999694i \(-0.492122\pi\)
0.0247472 + 0.999694i \(0.492122\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −44.0000 −0.0203882 −0.0101941 0.999948i \(-0.503245\pi\)
−0.0101941 + 0.999948i \(0.503245\pi\)
\(168\) 0 0
\(169\) 4859.00 2.21165
\(170\) 0 0
\(171\) 302.000 0.135056
\(172\) 0 0
\(173\) −1128.00 −0.495724 −0.247862 0.968795i \(-0.579728\pi\)
−0.247862 + 0.968795i \(0.579728\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1680.00 0.713427
\(178\) 0 0
\(179\) 2245.00 0.937426 0.468713 0.883351i \(-0.344718\pi\)
0.468713 + 0.883351i \(0.344718\pi\)
\(180\) 0 0
\(181\) −3050.00 −1.25251 −0.626256 0.779617i \(-0.715414\pi\)
−0.626256 + 0.779617i \(0.715414\pi\)
\(182\) 0 0
\(183\) −4290.00 −1.73293
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2379.00 −0.930319
\(188\) 0 0
\(189\) 290.000 0.111611
\(190\) 0 0
\(191\) −4222.00 −1.59944 −0.799720 0.600373i \(-0.795019\pi\)
−0.799720 + 0.600373i \(0.795019\pi\)
\(192\) 0 0
\(193\) 3357.00 1.25203 0.626016 0.779810i \(-0.284684\pi\)
0.626016 + 0.779810i \(0.284684\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −166.000 −0.0600356 −0.0300178 0.999549i \(-0.509556\pi\)
−0.0300178 + 0.999549i \(0.509556\pi\)
\(198\) 0 0
\(199\) 3372.00 1.20118 0.600590 0.799557i \(-0.294932\pi\)
0.600590 + 0.799557i \(0.294932\pi\)
\(200\) 0 0
\(201\) −1045.00 −0.366710
\(202\) 0 0
\(203\) 384.000 0.132766
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −116.000 −0.0389496
\(208\) 0 0
\(209\) 5889.00 1.94905
\(210\) 0 0
\(211\) −5601.00 −1.82743 −0.913717 0.406350i \(-0.866801\pi\)
−0.913717 + 0.406350i \(0.866801\pi\)
\(212\) 0 0
\(213\) −3900.00 −1.25457
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 36.0000 0.0112619
\(218\) 0 0
\(219\) 2015.00 0.621740
\(220\) 0 0
\(221\) 5124.00 1.55963
\(222\) 0 0
\(223\) −828.000 −0.248641 −0.124321 0.992242i \(-0.539675\pi\)
−0.124321 + 0.992242i \(0.539675\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2388.00 −0.698225 −0.349113 0.937081i \(-0.613517\pi\)
−0.349113 + 0.937081i \(0.613517\pi\)
\(228\) 0 0
\(229\) 2844.00 0.820685 0.410342 0.911932i \(-0.365409\pi\)
0.410342 + 0.911932i \(0.365409\pi\)
\(230\) 0 0
\(231\) 390.000 0.111083
\(232\) 0 0
\(233\) −5962.00 −1.67632 −0.838162 0.545421i \(-0.816370\pi\)
−0.838162 + 0.545421i \(0.816370\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1150.00 −0.315192
\(238\) 0 0
\(239\) −4320.00 −1.16919 −0.584597 0.811324i \(-0.698748\pi\)
−0.584597 + 0.811324i \(0.698748\pi\)
\(240\) 0 0
\(241\) 3857.00 1.03092 0.515459 0.856914i \(-0.327621\pi\)
0.515459 + 0.856914i \(0.327621\pi\)
\(242\) 0 0
\(243\) 560.000 0.147835
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −12684.0 −3.26746
\(248\) 0 0
\(249\) −6465.00 −1.64539
\(250\) 0 0
\(251\) 287.000 0.0721724 0.0360862 0.999349i \(-0.488511\pi\)
0.0360862 + 0.999349i \(0.488511\pi\)
\(252\) 0 0
\(253\) −2262.00 −0.562098
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2130.00 −0.516987 −0.258494 0.966013i \(-0.583226\pi\)
−0.258494 + 0.966013i \(0.583226\pi\)
\(258\) 0 0
\(259\) 276.000 0.0662155
\(260\) 0 0
\(261\) 384.000 0.0910690
\(262\) 0 0
\(263\) 3066.00 0.718850 0.359425 0.933174i \(-0.382973\pi\)
0.359425 + 0.933174i \(0.382973\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −6845.00 −1.56894
\(268\) 0 0
\(269\) 3744.00 0.848609 0.424304 0.905520i \(-0.360519\pi\)
0.424304 + 0.905520i \(0.360519\pi\)
\(270\) 0 0
\(271\) −3346.00 −0.750019 −0.375009 0.927021i \(-0.622360\pi\)
−0.375009 + 0.927021i \(0.622360\pi\)
\(272\) 0 0
\(273\) −840.000 −0.186224
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 7040.00 1.52705 0.763525 0.645779i \(-0.223467\pi\)
0.763525 + 0.645779i \(0.223467\pi\)
\(278\) 0 0
\(279\) 36.0000 0.00772496
\(280\) 0 0
\(281\) −3010.00 −0.639009 −0.319505 0.947585i \(-0.603516\pi\)
−0.319505 + 0.947585i \(0.603516\pi\)
\(282\) 0 0
\(283\) −6001.00 −1.26050 −0.630252 0.776391i \(-0.717048\pi\)
−0.630252 + 0.776391i \(0.717048\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −458.000 −0.0941982
\(288\) 0 0
\(289\) −1192.00 −0.242622
\(290\) 0 0
\(291\) −1910.00 −0.384764
\(292\) 0 0
\(293\) 4802.00 0.957460 0.478730 0.877962i \(-0.341097\pi\)
0.478730 + 0.877962i \(0.341097\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 5655.00 1.10484
\(298\) 0 0
\(299\) 4872.00 0.942325
\(300\) 0 0
\(301\) 328.000 0.0628093
\(302\) 0 0
\(303\) 3970.00 0.752708
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 6149.00 1.14313 0.571567 0.820556i \(-0.306336\pi\)
0.571567 + 0.820556i \(0.306336\pi\)
\(308\) 0 0
\(309\) 6740.00 1.24086
\(310\) 0 0
\(311\) −878.000 −0.160086 −0.0800431 0.996791i \(-0.525506\pi\)
−0.0800431 + 0.996791i \(0.525506\pi\)
\(312\) 0 0
\(313\) 4042.00 0.729928 0.364964 0.931022i \(-0.381081\pi\)
0.364964 + 0.931022i \(0.381081\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3844.00 0.681074 0.340537 0.940231i \(-0.389391\pi\)
0.340537 + 0.940231i \(0.389391\pi\)
\(318\) 0 0
\(319\) 7488.00 1.31426
\(320\) 0 0
\(321\) −3875.00 −0.673774
\(322\) 0 0
\(323\) −9211.00 −1.58673
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −2230.00 −0.377123
\(328\) 0 0
\(329\) −424.000 −0.0710513
\(330\) 0 0
\(331\) 2717.00 0.451178 0.225589 0.974223i \(-0.427569\pi\)
0.225589 + 0.974223i \(0.427569\pi\)
\(332\) 0 0
\(333\) 276.000 0.0454195
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1603.00 0.259113 0.129556 0.991572i \(-0.458645\pi\)
0.129556 + 0.991572i \(0.458645\pi\)
\(338\) 0 0
\(339\) 1155.00 0.185047
\(340\) 0 0
\(341\) 702.000 0.111482
\(342\) 0 0
\(343\) 1364.00 0.214720
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −11607.0 −1.79567 −0.897833 0.440335i \(-0.854860\pi\)
−0.897833 + 0.440335i \(0.854860\pi\)
\(348\) 0 0
\(349\) −4030.00 −0.618112 −0.309056 0.951044i \(-0.600013\pi\)
−0.309056 + 0.951044i \(0.600013\pi\)
\(350\) 0 0
\(351\) −12180.0 −1.85219
\(352\) 0 0
\(353\) −2106.00 −0.317538 −0.158769 0.987316i \(-0.550753\pi\)
−0.158769 + 0.987316i \(0.550753\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −610.000 −0.0904331
\(358\) 0 0
\(359\) 7394.00 1.08702 0.543510 0.839402i \(-0.317095\pi\)
0.543510 + 0.839402i \(0.317095\pi\)
\(360\) 0 0
\(361\) 15942.0 2.32425
\(362\) 0 0
\(363\) 950.000 0.137361
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 6940.00 0.987098 0.493549 0.869718i \(-0.335699\pi\)
0.493549 + 0.869718i \(0.335699\pi\)
\(368\) 0 0
\(369\) −458.000 −0.0646139
\(370\) 0 0
\(371\) −1156.00 −0.161770
\(372\) 0 0
\(373\) 7486.00 1.03917 0.519585 0.854419i \(-0.326087\pi\)
0.519585 + 0.854419i \(0.326087\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −16128.0 −2.20327
\(378\) 0 0
\(379\) −1285.00 −0.174158 −0.0870792 0.996201i \(-0.527753\pi\)
−0.0870792 + 0.996201i \(0.527753\pi\)
\(380\) 0 0
\(381\) −11930.0 −1.60418
\(382\) 0 0
\(383\) −9622.00 −1.28371 −0.641855 0.766826i \(-0.721835\pi\)
−0.641855 + 0.766826i \(0.721835\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 328.000 0.0430831
\(388\) 0 0
\(389\) −1974.00 −0.257290 −0.128645 0.991691i \(-0.541063\pi\)
−0.128645 + 0.991691i \(0.541063\pi\)
\(390\) 0 0
\(391\) 3538.00 0.457607
\(392\) 0 0
\(393\) −12260.0 −1.57363
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −8084.00 −1.02198 −0.510988 0.859588i \(-0.670720\pi\)
−0.510988 + 0.859588i \(0.670720\pi\)
\(398\) 0 0
\(399\) 1510.00 0.189460
\(400\) 0 0
\(401\) −5667.00 −0.705727 −0.352863 0.935675i \(-0.614792\pi\)
−0.352863 + 0.935675i \(0.614792\pi\)
\(402\) 0 0
\(403\) −1512.00 −0.186894
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5382.00 0.655469
\(408\) 0 0
\(409\) −4835.00 −0.584536 −0.292268 0.956336i \(-0.594410\pi\)
−0.292268 + 0.956336i \(0.594410\pi\)
\(410\) 0 0
\(411\) 5625.00 0.675087
\(412\) 0 0
\(413\) −672.000 −0.0800653
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 6885.00 0.808537
\(418\) 0 0
\(419\) −4619.00 −0.538551 −0.269276 0.963063i \(-0.586784\pi\)
−0.269276 + 0.963063i \(0.586784\pi\)
\(420\) 0 0
\(421\) −7476.00 −0.865458 −0.432729 0.901524i \(-0.642449\pi\)
−0.432729 + 0.901524i \(0.642449\pi\)
\(422\) 0 0
\(423\) −424.000 −0.0487366
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1716.00 0.194480
\(428\) 0 0
\(429\) −16380.0 −1.84344
\(430\) 0 0
\(431\) 7810.00 0.872841 0.436420 0.899743i \(-0.356246\pi\)
0.436420 + 0.899743i \(0.356246\pi\)
\(432\) 0 0
\(433\) 2029.00 0.225191 0.112595 0.993641i \(-0.464084\pi\)
0.112595 + 0.993641i \(0.464084\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −8758.00 −0.958700
\(438\) 0 0
\(439\) 3208.00 0.348769 0.174384 0.984678i \(-0.444206\pi\)
0.174384 + 0.984678i \(0.444206\pi\)
\(440\) 0 0
\(441\) 678.000 0.0732102
\(442\) 0 0
\(443\) 13227.0 1.41859 0.709293 0.704914i \(-0.249014\pi\)
0.709293 + 0.704914i \(0.249014\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −9600.00 −1.01580
\(448\) 0 0
\(449\) 3617.00 0.380171 0.190086 0.981768i \(-0.439123\pi\)
0.190086 + 0.981768i \(0.439123\pi\)
\(450\) 0 0
\(451\) −8931.00 −0.932471
\(452\) 0 0
\(453\) 9270.00 0.961463
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −6215.00 −0.636161 −0.318080 0.948064i \(-0.603038\pi\)
−0.318080 + 0.948064i \(0.603038\pi\)
\(458\) 0 0
\(459\) −8845.00 −0.899454
\(460\) 0 0
\(461\) 7108.00 0.718118 0.359059 0.933315i \(-0.383098\pi\)
0.359059 + 0.933315i \(0.383098\pi\)
\(462\) 0 0
\(463\) 3364.00 0.337664 0.168832 0.985645i \(-0.446000\pi\)
0.168832 + 0.985645i \(0.446000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18964.0 −1.87912 −0.939560 0.342384i \(-0.888766\pi\)
−0.939560 + 0.342384i \(0.888766\pi\)
\(468\) 0 0
\(469\) 418.000 0.0411545
\(470\) 0 0
\(471\) −3170.00 −0.310119
\(472\) 0 0
\(473\) 6396.00 0.621751
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1156.00 −0.110964
\(478\) 0 0
\(479\) −10926.0 −1.04222 −0.521108 0.853491i \(-0.674481\pi\)
−0.521108 + 0.853491i \(0.674481\pi\)
\(480\) 0 0
\(481\) −11592.0 −1.09886
\(482\) 0 0
\(483\) −580.000 −0.0546396
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 4350.00 0.404758 0.202379 0.979307i \(-0.435133\pi\)
0.202379 + 0.979307i \(0.435133\pi\)
\(488\) 0 0
\(489\) 515.000 0.0476260
\(490\) 0 0
\(491\) 1324.00 0.121693 0.0608465 0.998147i \(-0.480620\pi\)
0.0608465 + 0.998147i \(0.480620\pi\)
\(492\) 0 0
\(493\) −11712.0 −1.06994
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1560.00 0.140796
\(498\) 0 0
\(499\) −9068.00 −0.813506 −0.406753 0.913538i \(-0.633339\pi\)
−0.406753 + 0.913538i \(0.633339\pi\)
\(500\) 0 0
\(501\) −220.000 −0.0196185
\(502\) 0 0
\(503\) 19836.0 1.75834 0.879169 0.476511i \(-0.158099\pi\)
0.879169 + 0.476511i \(0.158099\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 24295.0 2.12816
\(508\) 0 0
\(509\) −2682.00 −0.233551 −0.116776 0.993158i \(-0.537256\pi\)
−0.116776 + 0.993158i \(0.537256\pi\)
\(510\) 0 0
\(511\) −806.000 −0.0697756
\(512\) 0 0
\(513\) 21895.0 1.88438
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −8268.00 −0.703339
\(518\) 0 0
\(519\) −5640.00 −0.477011
\(520\) 0 0
\(521\) −3035.00 −0.255213 −0.127606 0.991825i \(-0.540729\pi\)
−0.127606 + 0.991825i \(0.540729\pi\)
\(522\) 0 0
\(523\) 7701.00 0.643865 0.321932 0.946763i \(-0.395668\pi\)
0.321932 + 0.946763i \(0.395668\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1098.00 −0.0907583
\(528\) 0 0
\(529\) −8803.00 −0.723514
\(530\) 0 0
\(531\) −672.000 −0.0549196
\(532\) 0 0
\(533\) 19236.0 1.56323
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 11225.0 0.902038
\(538\) 0 0
\(539\) 13221.0 1.05653
\(540\) 0 0
\(541\) 18112.0 1.43936 0.719682 0.694304i \(-0.244288\pi\)
0.719682 + 0.694304i \(0.244288\pi\)
\(542\) 0 0
\(543\) −15250.0 −1.20523
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 19541.0 1.52745 0.763723 0.645544i \(-0.223369\pi\)
0.763723 + 0.645544i \(0.223369\pi\)
\(548\) 0 0
\(549\) 1716.00 0.133401
\(550\) 0 0
\(551\) 28992.0 2.24156
\(552\) 0 0
\(553\) 460.000 0.0353729
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 13508.0 1.02756 0.513781 0.857921i \(-0.328244\pi\)
0.513781 + 0.857921i \(0.328244\pi\)
\(558\) 0 0
\(559\) −13776.0 −1.04233
\(560\) 0 0
\(561\) −11895.0 −0.895200
\(562\) 0 0
\(563\) −8712.00 −0.652162 −0.326081 0.945342i \(-0.605728\pi\)
−0.326081 + 0.945342i \(0.605728\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1342.00 0.0993981
\(568\) 0 0
\(569\) −9623.00 −0.708993 −0.354497 0.935057i \(-0.615348\pi\)
−0.354497 + 0.935057i \(0.615348\pi\)
\(570\) 0 0
\(571\) −604.000 −0.0442673 −0.0221336 0.999755i \(-0.507046\pi\)
−0.0221336 + 0.999755i \(0.507046\pi\)
\(572\) 0 0
\(573\) −21110.0 −1.53906
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −3629.00 −0.261832 −0.130916 0.991393i \(-0.541792\pi\)
−0.130916 + 0.991393i \(0.541792\pi\)
\(578\) 0 0
\(579\) 16785.0 1.20477
\(580\) 0 0
\(581\) 2586.00 0.184656
\(582\) 0 0
\(583\) −22542.0 −1.60136
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9219.00 0.648226 0.324113 0.946018i \(-0.394934\pi\)
0.324113 + 0.946018i \(0.394934\pi\)
\(588\) 0 0
\(589\) 2718.00 0.190141
\(590\) 0 0
\(591\) −830.000 −0.0577693
\(592\) 0 0
\(593\) 19111.0 1.32343 0.661716 0.749755i \(-0.269829\pi\)
0.661716 + 0.749755i \(0.269829\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 16860.0 1.15584
\(598\) 0 0
\(599\) −17086.0 −1.16547 −0.582734 0.812663i \(-0.698017\pi\)
−0.582734 + 0.812663i \(0.698017\pi\)
\(600\) 0 0
\(601\) 9035.00 0.613220 0.306610 0.951835i \(-0.400805\pi\)
0.306610 + 0.951835i \(0.400805\pi\)
\(602\) 0 0
\(603\) 418.000 0.0282293
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 14784.0 0.988573 0.494287 0.869299i \(-0.335429\pi\)
0.494287 + 0.869299i \(0.335429\pi\)
\(608\) 0 0
\(609\) 1920.00 0.127754
\(610\) 0 0
\(611\) 17808.0 1.17911
\(612\) 0 0
\(613\) −17846.0 −1.17585 −0.587923 0.808917i \(-0.700054\pi\)
−0.587923 + 0.808917i \(0.700054\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −11618.0 −0.758060 −0.379030 0.925384i \(-0.623742\pi\)
−0.379030 + 0.925384i \(0.623742\pi\)
\(618\) 0 0
\(619\) 9556.00 0.620498 0.310249 0.950655i \(-0.399588\pi\)
0.310249 + 0.950655i \(0.399588\pi\)
\(620\) 0 0
\(621\) −8410.00 −0.543449
\(622\) 0 0
\(623\) 2738.00 0.176076
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 29445.0 1.87547
\(628\) 0 0
\(629\) −8418.00 −0.533621
\(630\) 0 0
\(631\) −19394.0 −1.22355 −0.611777 0.791030i \(-0.709545\pi\)
−0.611777 + 0.791030i \(0.709545\pi\)
\(632\) 0 0
\(633\) −28005.0 −1.75845
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −28476.0 −1.77121
\(638\) 0 0
\(639\) 1560.00 0.0965769
\(640\) 0 0
\(641\) 12138.0 0.747929 0.373964 0.927443i \(-0.377998\pi\)
0.373964 + 0.927443i \(0.377998\pi\)
\(642\) 0 0
\(643\) 27036.0 1.65816 0.829079 0.559131i \(-0.188865\pi\)
0.829079 + 0.559131i \(0.188865\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17556.0 1.06677 0.533383 0.845874i \(-0.320920\pi\)
0.533383 + 0.845874i \(0.320920\pi\)
\(648\) 0 0
\(649\) −13104.0 −0.792569
\(650\) 0 0
\(651\) 180.000 0.0108368
\(652\) 0 0
\(653\) −17262.0 −1.03448 −0.517239 0.855841i \(-0.673040\pi\)
−0.517239 + 0.855841i \(0.673040\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −806.000 −0.0478616
\(658\) 0 0
\(659\) −10517.0 −0.621675 −0.310838 0.950463i \(-0.600610\pi\)
−0.310838 + 0.950463i \(0.600610\pi\)
\(660\) 0 0
\(661\) −1408.00 −0.0828515 −0.0414258 0.999142i \(-0.513190\pi\)
−0.0414258 + 0.999142i \(0.513190\pi\)
\(662\) 0 0
\(663\) 25620.0 1.50075
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −11136.0 −0.646458
\(668\) 0 0
\(669\) −4140.00 −0.239255
\(670\) 0 0
\(671\) 33462.0 1.92517
\(672\) 0 0
\(673\) 9626.00 0.551345 0.275672 0.961252i \(-0.411100\pi\)
0.275672 + 0.961252i \(0.411100\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 28464.0 1.61589 0.807947 0.589255i \(-0.200579\pi\)
0.807947 + 0.589255i \(0.200579\pi\)
\(678\) 0 0
\(679\) 764.000 0.0431806
\(680\) 0 0
\(681\) −11940.0 −0.671868
\(682\) 0 0
\(683\) −3963.00 −0.222020 −0.111010 0.993819i \(-0.535409\pi\)
−0.111010 + 0.993819i \(0.535409\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 14220.0 0.789704
\(688\) 0 0
\(689\) 48552.0 2.68459
\(690\) 0 0
\(691\) 31781.0 1.74965 0.874824 0.484442i \(-0.160977\pi\)
0.874824 + 0.484442i \(0.160977\pi\)
\(692\) 0 0
\(693\) −156.000 −0.00855115
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 13969.0 0.759130
\(698\) 0 0
\(699\) −29810.0 −1.61304
\(700\) 0 0
\(701\) 28004.0 1.50884 0.754420 0.656392i \(-0.227918\pi\)
0.754420 + 0.656392i \(0.227918\pi\)
\(702\) 0 0
\(703\) 20838.0 1.11795
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1588.00 −0.0844737
\(708\) 0 0
\(709\) 35228.0 1.86603 0.933015 0.359837i \(-0.117168\pi\)
0.933015 + 0.359837i \(0.117168\pi\)
\(710\) 0 0
\(711\) 460.000 0.0242635
\(712\) 0 0
\(713\) −1044.00 −0.0548361
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −21600.0 −1.12506
\(718\) 0 0
\(719\) −8658.00 −0.449081 −0.224540 0.974465i \(-0.572088\pi\)
−0.224540 + 0.974465i \(0.572088\pi\)
\(720\) 0 0
\(721\) −2696.00 −0.139257
\(722\) 0 0
\(723\) 19285.0 0.992001
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −5728.00 −0.292214 −0.146107 0.989269i \(-0.546674\pi\)
−0.146107 + 0.989269i \(0.546674\pi\)
\(728\) 0 0
\(729\) 20917.0 1.06269
\(730\) 0 0
\(731\) −10004.0 −0.506171
\(732\) 0 0
\(733\) 21460.0 1.08137 0.540684 0.841226i \(-0.318165\pi\)
0.540684 + 0.841226i \(0.318165\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8151.00 0.407389
\(738\) 0 0
\(739\) −29164.0 −1.45171 −0.725856 0.687847i \(-0.758556\pi\)
−0.725856 + 0.687847i \(0.758556\pi\)
\(740\) 0 0
\(741\) −63420.0 −3.14412
\(742\) 0 0
\(743\) −29478.0 −1.45551 −0.727754 0.685838i \(-0.759436\pi\)
−0.727754 + 0.685838i \(0.759436\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 2586.00 0.126662
\(748\) 0 0
\(749\) 1550.00 0.0756152
\(750\) 0 0
\(751\) 576.000 0.0279874 0.0139937 0.999902i \(-0.495546\pi\)
0.0139937 + 0.999902i \(0.495546\pi\)
\(752\) 0 0
\(753\) 1435.00 0.0694480
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 2880.00 0.138277 0.0691383 0.997607i \(-0.477975\pi\)
0.0691383 + 0.997607i \(0.477975\pi\)
\(758\) 0 0
\(759\) −11310.0 −0.540879
\(760\) 0 0
\(761\) 20789.0 0.990277 0.495138 0.868814i \(-0.335117\pi\)
0.495138 + 0.868814i \(0.335117\pi\)
\(762\) 0 0
\(763\) 892.000 0.0423232
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 28224.0 1.32870
\(768\) 0 0
\(769\) 26421.0 1.23897 0.619484 0.785010i \(-0.287342\pi\)
0.619484 + 0.785010i \(0.287342\pi\)
\(770\) 0 0
\(771\) −10650.0 −0.497471
\(772\) 0 0
\(773\) 32504.0 1.51240 0.756202 0.654339i \(-0.227053\pi\)
0.756202 + 0.654339i \(0.227053\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1380.00 0.0637159
\(778\) 0 0
\(779\) −34579.0 −1.59040
\(780\) 0 0
\(781\) 30420.0 1.39374
\(782\) 0 0
\(783\) 27840.0 1.27065
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 996.000 0.0451125 0.0225563 0.999746i \(-0.492820\pi\)
0.0225563 + 0.999746i \(0.492820\pi\)
\(788\) 0 0
\(789\) 15330.0 0.691714
\(790\) 0 0
\(791\) −462.000 −0.0207672
\(792\) 0 0
\(793\) −72072.0 −3.22743
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 15134.0 0.672615 0.336307 0.941752i \(-0.390822\pi\)
0.336307 + 0.941752i \(0.390822\pi\)
\(798\) 0 0
\(799\) 12932.0 0.572592
\(800\) 0 0
\(801\) 2738.00 0.120777
\(802\) 0 0
\(803\) −15717.0 −0.690711
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 18720.0 0.816574
\(808\) 0 0
\(809\) −36942.0 −1.60545 −0.802727 0.596347i \(-0.796618\pi\)
−0.802727 + 0.596347i \(0.796618\pi\)
\(810\) 0 0
\(811\) 11748.0 0.508666 0.254333 0.967117i \(-0.418144\pi\)
0.254333 + 0.967117i \(0.418144\pi\)
\(812\) 0 0
\(813\) −16730.0 −0.721706
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 24764.0 1.06044
\(818\) 0 0
\(819\) 336.000 0.0143355
\(820\) 0 0
\(821\) 1198.00 0.0509263 0.0254631 0.999676i \(-0.491894\pi\)
0.0254631 + 0.999676i \(0.491894\pi\)
\(822\) 0 0
\(823\) 6788.00 0.287503 0.143751 0.989614i \(-0.454083\pi\)
0.143751 + 0.989614i \(0.454083\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 33011.0 1.38803 0.694017 0.719958i \(-0.255839\pi\)
0.694017 + 0.719958i \(0.255839\pi\)
\(828\) 0 0
\(829\) −17732.0 −0.742892 −0.371446 0.928454i \(-0.621138\pi\)
−0.371446 + 0.928454i \(0.621138\pi\)
\(830\) 0 0
\(831\) 35200.0 1.46940
\(832\) 0 0
\(833\) −20679.0 −0.860126
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 2610.00 0.107784
\(838\) 0 0
\(839\) 8480.00 0.348942 0.174471 0.984662i \(-0.444179\pi\)
0.174471 + 0.984662i \(0.444179\pi\)
\(840\) 0 0
\(841\) 12475.0 0.511501
\(842\) 0 0
\(843\) −15050.0 −0.614887
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −380.000 −0.0154155
\(848\) 0 0
\(849\) −30005.0 −1.21292
\(850\) 0 0
\(851\) −8004.00 −0.322413
\(852\) 0 0
\(853\) 30014.0 1.20476 0.602380 0.798210i \(-0.294219\pi\)
0.602380 + 0.798210i \(0.294219\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −21643.0 −0.862673 −0.431337 0.902191i \(-0.641958\pi\)
−0.431337 + 0.902191i \(0.641958\pi\)
\(858\) 0 0
\(859\) −2799.00 −0.111177 −0.0555883 0.998454i \(-0.517703\pi\)
−0.0555883 + 0.998454i \(0.517703\pi\)
\(860\) 0 0
\(861\) −2290.00 −0.0906423
\(862\) 0 0
\(863\) 19384.0 0.764588 0.382294 0.924041i \(-0.375134\pi\)
0.382294 + 0.924041i \(0.375134\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −5960.00 −0.233463
\(868\) 0 0
\(869\) 8970.00 0.350157
\(870\) 0 0
\(871\) −17556.0 −0.682965
\(872\) 0 0
\(873\) 764.000 0.0296191
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 5132.00 0.197600 0.0988001 0.995107i \(-0.468500\pi\)
0.0988001 + 0.995107i \(0.468500\pi\)
\(878\) 0 0
\(879\) 24010.0 0.921316
\(880\) 0 0
\(881\) 4430.00 0.169410 0.0847052 0.996406i \(-0.473005\pi\)
0.0847052 + 0.996406i \(0.473005\pi\)
\(882\) 0 0
\(883\) 24317.0 0.926764 0.463382 0.886159i \(-0.346636\pi\)
0.463382 + 0.886159i \(0.346636\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 26100.0 0.987996 0.493998 0.869463i \(-0.335535\pi\)
0.493998 + 0.869463i \(0.335535\pi\)
\(888\) 0 0
\(889\) 4772.00 0.180031
\(890\) 0 0
\(891\) 26169.0 0.983944
\(892\) 0 0
\(893\) −32012.0 −1.19960
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 24360.0 0.906752
\(898\) 0 0
\(899\) 3456.00 0.128214
\(900\) 0 0
\(901\) 35258.0 1.30368
\(902\) 0 0
\(903\) 1640.00 0.0604383
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 24356.0 0.891651 0.445826 0.895120i \(-0.352910\pi\)
0.445826 + 0.895120i \(0.352910\pi\)
\(908\) 0 0
\(909\) −1588.00 −0.0579435
\(910\) 0 0
\(911\) −29900.0 −1.08741 −0.543705 0.839276i \(-0.682979\pi\)
−0.543705 + 0.839276i \(0.682979\pi\)
\(912\) 0 0
\(913\) 50427.0 1.82792
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 4904.00 0.176602
\(918\) 0 0
\(919\) −34838.0 −1.25049 −0.625245 0.780429i \(-0.715001\pi\)
−0.625245 + 0.780429i \(0.715001\pi\)
\(920\) 0 0
\(921\) 30745.0 1.09998
\(922\) 0 0
\(923\) −65520.0 −2.33653
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −2696.00 −0.0955213
\(928\) 0 0
\(929\) 26334.0 0.930022 0.465011 0.885305i \(-0.346050\pi\)
0.465011 + 0.885305i \(0.346050\pi\)
\(930\) 0 0
\(931\) 51189.0 1.80199
\(932\) 0 0
\(933\) −4390.00 −0.154043
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −30949.0 −1.07904 −0.539520 0.841973i \(-0.681394\pi\)
−0.539520 + 0.841973i \(0.681394\pi\)
\(938\) 0 0
\(939\) 20210.0 0.702373
\(940\) 0 0
\(941\) −25276.0 −0.875637 −0.437818 0.899063i \(-0.644249\pi\)
−0.437818 + 0.899063i \(0.644249\pi\)
\(942\) 0 0
\(943\) 13282.0 0.458665
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1216.00 −0.0417262 −0.0208631 0.999782i \(-0.506641\pi\)
−0.0208631 + 0.999782i \(0.506641\pi\)
\(948\) 0 0
\(949\) 33852.0 1.15794
\(950\) 0 0
\(951\) 19220.0 0.655364
\(952\) 0 0
\(953\) 6033.00 0.205066 0.102533 0.994730i \(-0.467305\pi\)
0.102533 + 0.994730i \(0.467305\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 37440.0 1.26464
\(958\) 0 0
\(959\) −2250.00 −0.0757626
\(960\) 0 0
\(961\) −29467.0 −0.989124
\(962\) 0 0
\(963\) 1550.00 0.0518671
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 41792.0 1.38980 0.694902 0.719105i \(-0.255448\pi\)
0.694902 + 0.719105i \(0.255448\pi\)
\(968\) 0 0
\(969\) −46055.0 −1.52683
\(970\) 0 0
\(971\) 2105.00 0.0695702 0.0347851 0.999395i \(-0.488925\pi\)
0.0347851 + 0.999395i \(0.488925\pi\)
\(972\) 0 0
\(973\) −2754.00 −0.0907391
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −30119.0 −0.986277 −0.493138 0.869951i \(-0.664150\pi\)
−0.493138 + 0.869951i \(0.664150\pi\)
\(978\) 0 0
\(979\) 53391.0 1.74299
\(980\) 0 0
\(981\) 892.000 0.0290310
\(982\) 0 0
\(983\) −18438.0 −0.598251 −0.299126 0.954214i \(-0.596695\pi\)
−0.299126 + 0.954214i \(0.596695\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −2120.00 −0.0683691
\(988\) 0 0
\(989\) −9512.00 −0.305828
\(990\) 0 0
\(991\) −2230.00 −0.0714816 −0.0357408 0.999361i \(-0.511379\pi\)
−0.0357408 + 0.999361i \(0.511379\pi\)
\(992\) 0 0
\(993\) 13585.0 0.434146
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −6804.00 −0.216133 −0.108067 0.994144i \(-0.534466\pi\)
−0.108067 + 0.994144i \(0.534466\pi\)
\(998\) 0 0
\(999\) 20010.0 0.633722
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 1600.4.a.bn.1.1 1
4.3 odd 2 1600.4.a.n.1.1 1
5.4 even 2 1600.4.a.m.1.1 1
8.3 odd 2 400.4.a.q.1.1 1
8.5 even 2 200.4.a.c.1.1 1
20.19 odd 2 1600.4.a.bo.1.1 1
24.5 odd 2 1800.4.a.p.1.1 1
40.3 even 4 400.4.c.g.49.2 2
40.13 odd 4 200.4.c.d.49.1 2
40.19 odd 2 400.4.a.f.1.1 1
40.27 even 4 400.4.c.g.49.1 2
40.29 even 2 200.4.a.h.1.1 yes 1
40.37 odd 4 200.4.c.d.49.2 2
120.29 odd 2 1800.4.a.t.1.1 1
120.53 even 4 1800.4.f.c.649.2 2
120.77 even 4 1800.4.f.c.649.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
200.4.a.c.1.1 1 8.5 even 2
200.4.a.h.1.1 yes 1 40.29 even 2
200.4.c.d.49.1 2 40.13 odd 4
200.4.c.d.49.2 2 40.37 odd 4
400.4.a.f.1.1 1 40.19 odd 2
400.4.a.q.1.1 1 8.3 odd 2
400.4.c.g.49.1 2 40.27 even 4
400.4.c.g.49.2 2 40.3 even 4
1600.4.a.m.1.1 1 5.4 even 2
1600.4.a.n.1.1 1 4.3 odd 2
1600.4.a.bn.1.1 1 1.1 even 1 trivial
1600.4.a.bo.1.1 1 20.19 odd 2
1800.4.a.p.1.1 1 24.5 odd 2
1800.4.a.t.1.1 1 120.29 odd 2
1800.4.f.c.649.1 2 120.77 even 4
1800.4.f.c.649.2 2 120.53 even 4