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Properties

Label 1008.4.a.q.1.1
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
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] = [1008,4,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, 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("1008.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.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: \(59.4739252858\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 168)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+10.0000 q^{5} +7.00000 q^{7} +O(q^{10})\) \(q+10.0000 q^{5} +7.00000 q^{7} -52.0000 q^{11} -10.0000 q^{13} +54.0000 q^{17} +52.0000 q^{19} +48.0000 q^{23} -25.0000 q^{25} +186.000 q^{29} -224.000 q^{31} +70.0000 q^{35} +94.0000 q^{37} +478.000 q^{41} +316.000 q^{43} +256.000 q^{47} +49.0000 q^{49} +66.0000 q^{53} -520.000 q^{55} +420.000 q^{59} +342.000 q^{61} -100.000 q^{65} -668.000 q^{67} -272.000 q^{71} -86.0000 q^{73} -364.000 q^{77} -1360.00 q^{79} +188.000 q^{83} +540.000 q^{85} +366.000 q^{89} -70.0000 q^{91} +520.000 q^{95} +1554.00 q^{97} +O(q^{100})\)

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 \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −52.0000 −1.42533 −0.712663 − 0.701506i \(-0.752511\pi\)
−0.712663 + 0.701506i \(0.752511\pi\)
\(12\) 0 0
\(13\) −10.0000 −0.213346 −0.106673 − 0.994294i \(-0.534020\pi\)
−0.106673 + 0.994294i \(0.534020\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 54.0000 0.770407 0.385204 − 0.922832i \(-0.374131\pi\)
0.385204 + 0.922832i \(0.374131\pi\)
\(18\) 0 0
\(19\) 52.0000 0.627875 0.313937 − 0.949444i \(-0.398352\pi\)
0.313937 + 0.949444i \(0.398352\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 48.0000 0.435161 0.217580 − 0.976042i \(-0.430184\pi\)
0.217580 + 0.976042i \(0.430184\pi\)
\(24\) 0 0
\(25\) −25.0000 −0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 186.000 1.19101 0.595506 − 0.803351i \(-0.296952\pi\)
0.595506 + 0.803351i \(0.296952\pi\)
\(30\) 0 0
\(31\) −224.000 −1.29779 −0.648897 − 0.760877i \(-0.724769\pi\)
−0.648897 + 0.760877i \(0.724769\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 70.0000 0.338062
\(36\) 0 0
\(37\) 94.0000 0.417662 0.208831 − 0.977952i \(-0.433034\pi\)
0.208831 + 0.977952i \(0.433034\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 478.000 1.82076 0.910379 − 0.413776i \(-0.135790\pi\)
0.910379 + 0.413776i \(0.135790\pi\)
\(42\) 0 0
\(43\) 316.000 1.12069 0.560344 − 0.828260i \(-0.310669\pi\)
0.560344 + 0.828260i \(0.310669\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 256.000 0.794499 0.397249 − 0.917711i \(-0.369965\pi\)
0.397249 + 0.917711i \(0.369965\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 66.0000 0.171053 0.0855264 − 0.996336i \(-0.472743\pi\)
0.0855264 + 0.996336i \(0.472743\pi\)
\(54\) 0 0
\(55\) −520.000 −1.27485
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 420.000 0.926769 0.463384 − 0.886157i \(-0.346635\pi\)
0.463384 + 0.886157i \(0.346635\pi\)
\(60\) 0 0
\(61\) 342.000 0.717846 0.358923 − 0.933367i \(-0.383144\pi\)
0.358923 + 0.933367i \(0.383144\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −100.000 −0.190823
\(66\) 0 0
\(67\) −668.000 −1.21805 −0.609024 − 0.793152i \(-0.708439\pi\)
−0.609024 + 0.793152i \(0.708439\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −272.000 −0.454654 −0.227327 − 0.973818i \(-0.572999\pi\)
−0.227327 + 0.973818i \(0.572999\pi\)
\(72\) 0 0
\(73\) −86.0000 −0.137884 −0.0689420 − 0.997621i \(-0.521962\pi\)
−0.0689420 + 0.997621i \(0.521962\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −364.000 −0.538723
\(78\) 0 0
\(79\) −1360.00 −1.93686 −0.968430 − 0.249285i \(-0.919804\pi\)
−0.968430 + 0.249285i \(0.919804\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 188.000 0.248623 0.124311 − 0.992243i \(-0.460328\pi\)
0.124311 + 0.992243i \(0.460328\pi\)
\(84\) 0 0
\(85\) 540.000 0.689073
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 366.000 0.435909 0.217955 − 0.975959i \(-0.430062\pi\)
0.217955 + 0.975959i \(0.430062\pi\)
\(90\) 0 0
\(91\) −70.0000 −0.0806373
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 520.000 0.561588
\(96\) 0 0
\(97\) 1554.00 1.62665 0.813324 − 0.581811i \(-0.197656\pi\)
0.813324 + 0.581811i \(0.197656\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1690.00 1.66496 0.832482 − 0.554053i \(-0.186919\pi\)
0.832482 + 0.554053i \(0.186919\pi\)
\(102\) 0 0
\(103\) −248.000 −0.237244 −0.118622 − 0.992939i \(-0.537848\pi\)
−0.118622 + 0.992939i \(0.537848\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1620.00 −1.46366 −0.731829 − 0.681489i \(-0.761333\pi\)
−0.731829 + 0.681489i \(0.761333\pi\)
\(108\) 0 0
\(109\) −1066.00 −0.936737 −0.468368 − 0.883533i \(-0.655158\pi\)
−0.468368 + 0.883533i \(0.655158\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1198.00 0.997331 0.498665 − 0.866795i \(-0.333824\pi\)
0.498665 + 0.866795i \(0.333824\pi\)
\(114\) 0 0
\(115\) 480.000 0.389219
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 378.000 0.291187
\(120\) 0 0
\(121\) 1373.00 1.03156
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1500.00 −1.07331
\(126\) 0 0
\(127\) 2528.00 1.76633 0.883164 − 0.469064i \(-0.155409\pi\)
0.883164 + 0.469064i \(0.155409\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2156.00 1.43794 0.718972 − 0.695039i \(-0.244613\pi\)
0.718972 + 0.695039i \(0.244613\pi\)
\(132\) 0 0
\(133\) 364.000 0.237314
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −234.000 −0.145927 −0.0729634 − 0.997335i \(-0.523246\pi\)
−0.0729634 + 0.997335i \(0.523246\pi\)
\(138\) 0 0
\(139\) 2396.00 1.46206 0.731029 − 0.682346i \(-0.239040\pi\)
0.731029 + 0.682346i \(0.239040\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 520.000 0.304088
\(144\) 0 0
\(145\) 1860.00 1.06527
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1602.00 0.880812 0.440406 − 0.897799i \(-0.354835\pi\)
0.440406 + 0.897799i \(0.354835\pi\)
\(150\) 0 0
\(151\) 1320.00 0.711391 0.355696 − 0.934602i \(-0.384244\pi\)
0.355696 + 0.934602i \(0.384244\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2240.00 −1.16078
\(156\) 0 0
\(157\) −1482.00 −0.753353 −0.376677 − 0.926345i \(-0.622933\pi\)
−0.376677 + 0.926345i \(0.622933\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 336.000 0.164475
\(162\) 0 0
\(163\) 2820.00 1.35509 0.677544 − 0.735482i \(-0.263044\pi\)
0.677544 + 0.735482i \(0.263044\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1768.00 0.819233 0.409617 − 0.912258i \(-0.365662\pi\)
0.409617 + 0.912258i \(0.365662\pi\)
\(168\) 0 0
\(169\) −2097.00 −0.954483
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −894.000 −0.392888 −0.196444 − 0.980515i \(-0.562939\pi\)
−0.196444 + 0.980515i \(0.562939\pi\)
\(174\) 0 0
\(175\) −175.000 −0.0755929
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1996.00 −0.833453 −0.416726 − 0.909032i \(-0.636823\pi\)
−0.416726 + 0.909032i \(0.636823\pi\)
\(180\) 0 0
\(181\) 1582.00 0.649664 0.324832 − 0.945772i \(-0.394692\pi\)
0.324832 + 0.945772i \(0.394692\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 940.000 0.373569
\(186\) 0 0
\(187\) −2808.00 −1.09808
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2456.00 0.930418 0.465209 − 0.885201i \(-0.345979\pi\)
0.465209 + 0.885201i \(0.345979\pi\)
\(192\) 0 0
\(193\) −2942.00 −1.09725 −0.548626 − 0.836068i \(-0.684849\pi\)
−0.548626 + 0.836068i \(0.684849\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3666.00 1.32585 0.662923 − 0.748688i \(-0.269316\pi\)
0.662923 + 0.748688i \(0.269316\pi\)
\(198\) 0 0
\(199\) −1224.00 −0.436015 −0.218008 − 0.975947i \(-0.569956\pi\)
−0.218008 + 0.975947i \(0.569956\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1302.00 0.450160
\(204\) 0 0
\(205\) 4780.00 1.62854
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2704.00 −0.894926
\(210\) 0 0
\(211\) 4932.00 1.60916 0.804580 − 0.593844i \(-0.202390\pi\)
0.804580 + 0.593844i \(0.202390\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3160.00 1.00237
\(216\) 0 0
\(217\) −1568.00 −0.490520
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −540.000 −0.164363
\(222\) 0 0
\(223\) 816.000 0.245038 0.122519 − 0.992466i \(-0.460903\pi\)
0.122519 + 0.992466i \(0.460903\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1316.00 −0.384784 −0.192392 − 0.981318i \(-0.561625\pi\)
−0.192392 + 0.981318i \(0.561625\pi\)
\(228\) 0 0
\(229\) −2786.00 −0.803948 −0.401974 − 0.915651i \(-0.631676\pi\)
−0.401974 + 0.915651i \(0.631676\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5162.00 −1.45139 −0.725695 − 0.688017i \(-0.758482\pi\)
−0.725695 + 0.688017i \(0.758482\pi\)
\(234\) 0 0
\(235\) 2560.00 0.710621
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3320.00 0.898548 0.449274 − 0.893394i \(-0.351683\pi\)
0.449274 + 0.893394i \(0.351683\pi\)
\(240\) 0 0
\(241\) 4066.00 1.08678 0.543390 − 0.839480i \(-0.317140\pi\)
0.543390 + 0.839480i \(0.317140\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 490.000 0.127775
\(246\) 0 0
\(247\) −520.000 −0.133955
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1116.00 −0.280643 −0.140321 − 0.990106i \(-0.544814\pi\)
−0.140321 + 0.990106i \(0.544814\pi\)
\(252\) 0 0
\(253\) −2496.00 −0.620246
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −650.000 −0.157766 −0.0788830 − 0.996884i \(-0.525135\pi\)
−0.0788830 + 0.996884i \(0.525135\pi\)
\(258\) 0 0
\(259\) 658.000 0.157862
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3648.00 0.855305 0.427653 − 0.903943i \(-0.359341\pi\)
0.427653 + 0.903943i \(0.359341\pi\)
\(264\) 0 0
\(265\) 660.000 0.152994
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7058.00 1.59975 0.799877 − 0.600164i \(-0.204898\pi\)
0.799877 + 0.600164i \(0.204898\pi\)
\(270\) 0 0
\(271\) −6960.00 −1.56011 −0.780055 − 0.625711i \(-0.784809\pi\)
−0.780055 + 0.625711i \(0.784809\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1300.00 0.285065
\(276\) 0 0
\(277\) −5330.00 −1.15613 −0.578066 − 0.815990i \(-0.696192\pi\)
−0.578066 + 0.815990i \(0.696192\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −5754.00 −1.22155 −0.610774 − 0.791805i \(-0.709142\pi\)
−0.610774 + 0.791805i \(0.709142\pi\)
\(282\) 0 0
\(283\) −3076.00 −0.646110 −0.323055 − 0.946380i \(-0.604710\pi\)
−0.323055 + 0.946380i \(0.604710\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3346.00 0.688182
\(288\) 0 0
\(289\) −1997.00 −0.406473
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2982.00 −0.594574 −0.297287 − 0.954788i \(-0.596082\pi\)
−0.297287 + 0.954788i \(0.596082\pi\)
\(294\) 0 0
\(295\) 4200.00 0.828927
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −480.000 −0.0928399
\(300\) 0 0
\(301\) 2212.00 0.423580
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3420.00 0.642061
\(306\) 0 0
\(307\) 1460.00 0.271422 0.135711 − 0.990748i \(-0.456668\pi\)
0.135711 + 0.990748i \(0.456668\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1496.00 0.272766 0.136383 − 0.990656i \(-0.456452\pi\)
0.136383 + 0.990656i \(0.456452\pi\)
\(312\) 0 0
\(313\) −9494.00 −1.71448 −0.857241 − 0.514916i \(-0.827823\pi\)
−0.857241 + 0.514916i \(0.827823\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1974.00 −0.349750 −0.174875 − 0.984591i \(-0.555952\pi\)
−0.174875 + 0.984591i \(0.555952\pi\)
\(318\) 0 0
\(319\) −9672.00 −1.69758
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2808.00 0.483719
\(324\) 0 0
\(325\) 250.000 0.0426692
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1792.00 0.300292
\(330\) 0 0
\(331\) 5884.00 0.977081 0.488541 − 0.872541i \(-0.337529\pi\)
0.488541 + 0.872541i \(0.337529\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −6680.00 −1.08945
\(336\) 0 0
\(337\) −10030.0 −1.62127 −0.810636 − 0.585550i \(-0.800879\pi\)
−0.810636 + 0.585550i \(0.800879\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 11648.0 1.84978
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 972.000 0.150374 0.0751869 − 0.997169i \(-0.476045\pi\)
0.0751869 + 0.997169i \(0.476045\pi\)
\(348\) 0 0
\(349\) −4362.00 −0.669033 −0.334516 − 0.942390i \(-0.608573\pi\)
−0.334516 + 0.942390i \(0.608573\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3686.00 0.555768 0.277884 − 0.960615i \(-0.410367\pi\)
0.277884 + 0.960615i \(0.410367\pi\)
\(354\) 0 0
\(355\) −2720.00 −0.406655
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −11280.0 −1.65832 −0.829158 − 0.559014i \(-0.811180\pi\)
−0.829158 + 0.559014i \(0.811180\pi\)
\(360\) 0 0
\(361\) −4155.00 −0.605773
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −860.000 −0.123327
\(366\) 0 0
\(367\) −6496.00 −0.923947 −0.461973 − 0.886894i \(-0.652858\pi\)
−0.461973 + 0.886894i \(0.652858\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 462.000 0.0646519
\(372\) 0 0
\(373\) 13582.0 1.88539 0.942693 − 0.333660i \(-0.108284\pi\)
0.942693 + 0.333660i \(0.108284\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1860.00 −0.254098
\(378\) 0 0
\(379\) −6068.00 −0.822407 −0.411203 − 0.911544i \(-0.634891\pi\)
−0.411203 + 0.911544i \(0.634891\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8736.00 −1.16551 −0.582753 − 0.812649i \(-0.698024\pi\)
−0.582753 + 0.812649i \(0.698024\pi\)
\(384\) 0 0
\(385\) −3640.00 −0.481848
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2206.00 −0.287529 −0.143764 − 0.989612i \(-0.545921\pi\)
−0.143764 + 0.989612i \(0.545921\pi\)
\(390\) 0 0
\(391\) 2592.00 0.335251
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −13600.0 −1.73238
\(396\) 0 0
\(397\) 11974.0 1.51375 0.756874 − 0.653561i \(-0.226726\pi\)
0.756874 + 0.653561i \(0.226726\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12642.0 −1.57434 −0.787171 − 0.616734i \(-0.788455\pi\)
−0.787171 + 0.616734i \(0.788455\pi\)
\(402\) 0 0
\(403\) 2240.00 0.276879
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4888.00 −0.595305
\(408\) 0 0
\(409\) 14170.0 1.71311 0.856554 − 0.516057i \(-0.172601\pi\)
0.856554 + 0.516057i \(0.172601\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2940.00 0.350286
\(414\) 0 0
\(415\) 1880.00 0.222375
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4604.00 0.536802 0.268401 − 0.963307i \(-0.413505\pi\)
0.268401 + 0.963307i \(0.413505\pi\)
\(420\) 0 0
\(421\) 11998.0 1.38895 0.694474 − 0.719518i \(-0.255637\pi\)
0.694474 + 0.719518i \(0.255637\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1350.00 −0.154081
\(426\) 0 0
\(427\) 2394.00 0.271320
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 712.000 0.0795727 0.0397863 − 0.999208i \(-0.487332\pi\)
0.0397863 + 0.999208i \(0.487332\pi\)
\(432\) 0 0
\(433\) −10574.0 −1.17357 −0.586783 − 0.809744i \(-0.699606\pi\)
−0.586783 + 0.809744i \(0.699606\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2496.00 0.273226
\(438\) 0 0
\(439\) 10536.0 1.14546 0.572729 − 0.819745i \(-0.305885\pi\)
0.572729 + 0.819745i \(0.305885\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −7956.00 −0.853275 −0.426638 − 0.904423i \(-0.640302\pi\)
−0.426638 + 0.904423i \(0.640302\pi\)
\(444\) 0 0
\(445\) 3660.00 0.389889
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −6178.00 −0.649349 −0.324675 − 0.945826i \(-0.605255\pi\)
−0.324675 + 0.945826i \(0.605255\pi\)
\(450\) 0 0
\(451\) −24856.0 −2.59517
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −700.000 −0.0721242
\(456\) 0 0
\(457\) 10330.0 1.05737 0.528684 − 0.848819i \(-0.322686\pi\)
0.528684 + 0.848819i \(0.322686\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −14142.0 −1.42876 −0.714380 − 0.699758i \(-0.753291\pi\)
−0.714380 + 0.699758i \(0.753291\pi\)
\(462\) 0 0
\(463\) 1936.00 0.194327 0.0971637 − 0.995268i \(-0.469023\pi\)
0.0971637 + 0.995268i \(0.469023\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5204.00 −0.515658 −0.257829 − 0.966191i \(-0.583007\pi\)
−0.257829 + 0.966191i \(0.583007\pi\)
\(468\) 0 0
\(469\) −4676.00 −0.460379
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −16432.0 −1.59734
\(474\) 0 0
\(475\) −1300.00 −0.125575
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8016.00 0.764635 0.382318 − 0.924031i \(-0.375126\pi\)
0.382318 + 0.924031i \(0.375126\pi\)
\(480\) 0 0
\(481\) −940.000 −0.0891067
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 15540.0 1.45492
\(486\) 0 0
\(487\) 9112.00 0.847852 0.423926 − 0.905697i \(-0.360652\pi\)
0.423926 + 0.905697i \(0.360652\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 17340.0 1.59377 0.796887 − 0.604128i \(-0.206478\pi\)
0.796887 + 0.604128i \(0.206478\pi\)
\(492\) 0 0
\(493\) 10044.0 0.917564
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1904.00 −0.171843
\(498\) 0 0
\(499\) −2108.00 −0.189112 −0.0945562 − 0.995520i \(-0.530143\pi\)
−0.0945562 + 0.995520i \(0.530143\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −18872.0 −1.67288 −0.836442 − 0.548055i \(-0.815368\pi\)
−0.836442 + 0.548055i \(0.815368\pi\)
\(504\) 0 0
\(505\) 16900.0 1.48919
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1346.00 0.117211 0.0586055 − 0.998281i \(-0.481335\pi\)
0.0586055 + 0.998281i \(0.481335\pi\)
\(510\) 0 0
\(511\) −602.000 −0.0521153
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2480.00 −0.212198
\(516\) 0 0
\(517\) −13312.0 −1.13242
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −22674.0 −1.90665 −0.953326 − 0.301942i \(-0.902365\pi\)
−0.953326 + 0.301942i \(0.902365\pi\)
\(522\) 0 0
\(523\) −16228.0 −1.35679 −0.678395 − 0.734698i \(-0.737324\pi\)
−0.678395 + 0.734698i \(0.737324\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −12096.0 −0.999829
\(528\) 0 0
\(529\) −9863.00 −0.810635
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4780.00 −0.388452
\(534\) 0 0
\(535\) −16200.0 −1.30913
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2548.00 −0.203618
\(540\) 0 0
\(541\) 11846.0 0.941404 0.470702 − 0.882292i \(-0.344001\pi\)
0.470702 + 0.882292i \(0.344001\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −10660.0 −0.837843
\(546\) 0 0
\(547\) 10692.0 0.835753 0.417877 − 0.908504i \(-0.362774\pi\)
0.417877 + 0.908504i \(0.362774\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 9672.00 0.747806
\(552\) 0 0
\(553\) −9520.00 −0.732064
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2458.00 0.186982 0.0934908 − 0.995620i \(-0.470197\pi\)
0.0934908 + 0.995620i \(0.470197\pi\)
\(558\) 0 0
\(559\) −3160.00 −0.239094
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1196.00 0.0895300 0.0447650 − 0.998998i \(-0.485746\pi\)
0.0447650 + 0.998998i \(0.485746\pi\)
\(564\) 0 0
\(565\) 11980.0 0.892040
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 19174.0 1.41268 0.706341 − 0.707872i \(-0.250345\pi\)
0.706341 + 0.707872i \(0.250345\pi\)
\(570\) 0 0
\(571\) −9892.00 −0.724987 −0.362493 − 0.931986i \(-0.618074\pi\)
−0.362493 + 0.931986i \(0.618074\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1200.00 −0.0870321
\(576\) 0 0
\(577\) −11870.0 −0.856420 −0.428210 − 0.903679i \(-0.640856\pi\)
−0.428210 + 0.903679i \(0.640856\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1316.00 0.0939705
\(582\) 0 0
\(583\) −3432.00 −0.243806
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −26892.0 −1.89089 −0.945444 − 0.325784i \(-0.894372\pi\)
−0.945444 + 0.325784i \(0.894372\pi\)
\(588\) 0 0
\(589\) −11648.0 −0.814851
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 16790.0 1.16270 0.581351 − 0.813653i \(-0.302524\pi\)
0.581351 + 0.813653i \(0.302524\pi\)
\(594\) 0 0
\(595\) 3780.00 0.260445
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 3264.00 0.222643 0.111322 − 0.993784i \(-0.464492\pi\)
0.111322 + 0.993784i \(0.464492\pi\)
\(600\) 0 0
\(601\) 5162.00 0.350353 0.175177 − 0.984537i \(-0.443950\pi\)
0.175177 + 0.984537i \(0.443950\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 13730.0 0.922651
\(606\) 0 0
\(607\) 27088.0 1.81131 0.905657 − 0.424010i \(-0.139378\pi\)
0.905657 + 0.424010i \(0.139378\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2560.00 −0.169503
\(612\) 0 0
\(613\) −26178.0 −1.72483 −0.862414 − 0.506204i \(-0.831048\pi\)
−0.862414 + 0.506204i \(0.831048\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −28330.0 −1.84850 −0.924249 − 0.381791i \(-0.875307\pi\)
−0.924249 + 0.381791i \(0.875307\pi\)
\(618\) 0 0
\(619\) −17956.0 −1.16593 −0.582967 − 0.812496i \(-0.698108\pi\)
−0.582967 + 0.812496i \(0.698108\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2562.00 0.164758
\(624\) 0 0
\(625\) −11875.0 −0.760000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5076.00 0.321770
\(630\) 0 0
\(631\) −6792.00 −0.428503 −0.214251 − 0.976779i \(-0.568731\pi\)
−0.214251 + 0.976779i \(0.568731\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 25280.0 1.57985
\(636\) 0 0
\(637\) −490.000 −0.0304780
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −10098.0 −0.622226 −0.311113 − 0.950373i \(-0.600702\pi\)
−0.311113 + 0.950373i \(0.600702\pi\)
\(642\) 0 0
\(643\) 16292.0 0.999213 0.499606 − 0.866253i \(-0.333478\pi\)
0.499606 + 0.866253i \(0.333478\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −31544.0 −1.91673 −0.958364 − 0.285550i \(-0.907824\pi\)
−0.958364 + 0.285550i \(0.907824\pi\)
\(648\) 0 0
\(649\) −21840.0 −1.32095
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 170.000 0.0101878 0.00509389 − 0.999987i \(-0.498379\pi\)
0.00509389 + 0.999987i \(0.498379\pi\)
\(654\) 0 0
\(655\) 21560.0 1.28614
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 29220.0 1.72724 0.863619 − 0.504145i \(-0.168192\pi\)
0.863619 + 0.504145i \(0.168192\pi\)
\(660\) 0 0
\(661\) −10402.0 −0.612089 −0.306045 − 0.952017i \(-0.599006\pi\)
−0.306045 + 0.952017i \(0.599006\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3640.00 0.212260
\(666\) 0 0
\(667\) 8928.00 0.518281
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −17784.0 −1.02316
\(672\) 0 0
\(673\) 2338.00 0.133913 0.0669564 − 0.997756i \(-0.478671\pi\)
0.0669564 + 0.997756i \(0.478671\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 18330.0 1.04059 0.520295 − 0.853987i \(-0.325822\pi\)
0.520295 + 0.853987i \(0.325822\pi\)
\(678\) 0 0
\(679\) 10878.0 0.614815
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4956.00 0.277652 0.138826 − 0.990317i \(-0.455667\pi\)
0.138826 + 0.990317i \(0.455667\pi\)
\(684\) 0 0
\(685\) −2340.00 −0.130521
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −660.000 −0.0364935
\(690\) 0 0
\(691\) 6692.00 0.368416 0.184208 − 0.982887i \(-0.441028\pi\)
0.184208 + 0.982887i \(0.441028\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 23960.0 1.30770
\(696\) 0 0
\(697\) 25812.0 1.40272
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 33306.0 1.79451 0.897254 − 0.441515i \(-0.145559\pi\)
0.897254 + 0.441515i \(0.145559\pi\)
\(702\) 0 0
\(703\) 4888.00 0.262240
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 11830.0 0.629297
\(708\) 0 0
\(709\) −13218.0 −0.700159 −0.350079 − 0.936720i \(-0.613845\pi\)
−0.350079 + 0.936720i \(0.613845\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −10752.0 −0.564748
\(714\) 0 0
\(715\) 5200.00 0.271985
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −6640.00 −0.344409 −0.172205 − 0.985061i \(-0.555089\pi\)
−0.172205 + 0.985061i \(0.555089\pi\)
\(720\) 0 0
\(721\) −1736.00 −0.0896699
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4650.00 −0.238202
\(726\) 0 0
\(727\) 1304.00 0.0665236 0.0332618 − 0.999447i \(-0.489410\pi\)
0.0332618 + 0.999447i \(0.489410\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 17064.0 0.863386
\(732\) 0 0
\(733\) 8294.00 0.417934 0.208967 − 0.977923i \(-0.432990\pi\)
0.208967 + 0.977923i \(0.432990\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 34736.0 1.73612
\(738\) 0 0
\(739\) 8420.00 0.419127 0.209563 − 0.977795i \(-0.432796\pi\)
0.209563 + 0.977795i \(0.432796\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 22352.0 1.10365 0.551827 − 0.833958i \(-0.313931\pi\)
0.551827 + 0.833958i \(0.313931\pi\)
\(744\) 0 0
\(745\) 16020.0 0.787822
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −11340.0 −0.553210
\(750\) 0 0
\(751\) −24160.0 −1.17392 −0.586958 − 0.809617i \(-0.699675\pi\)
−0.586958 + 0.809617i \(0.699675\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 13200.0 0.636288
\(756\) 0 0
\(757\) −35858.0 −1.72164 −0.860820 − 0.508910i \(-0.830049\pi\)
−0.860820 + 0.508910i \(0.830049\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −10770.0 −0.513025 −0.256513 − 0.966541i \(-0.582574\pi\)
−0.256513 + 0.966541i \(0.582574\pi\)
\(762\) 0 0
\(763\) −7462.00 −0.354053
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4200.00 −0.197723
\(768\) 0 0
\(769\) −36190.0 −1.69707 −0.848534 − 0.529141i \(-0.822514\pi\)
−0.848534 + 0.529141i \(0.822514\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 8026.00 0.373448 0.186724 − 0.982412i \(-0.440213\pi\)
0.186724 + 0.982412i \(0.440213\pi\)
\(774\) 0 0
\(775\) 5600.00 0.259559
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 24856.0 1.14321
\(780\) 0 0
\(781\) 14144.0 0.648031
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −14820.0 −0.673820
\(786\) 0 0
\(787\) −9308.00 −0.421594 −0.210797 − 0.977530i \(-0.567606\pi\)
−0.210797 + 0.977530i \(0.567606\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 8386.00 0.376956
\(792\) 0 0
\(793\) −3420.00 −0.153150
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −22734.0 −1.01039 −0.505194 − 0.863006i \(-0.668579\pi\)
−0.505194 + 0.863006i \(0.668579\pi\)
\(798\) 0 0
\(799\) 13824.0 0.612088
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4472.00 0.196530
\(804\) 0 0
\(805\) 3360.00 0.147111
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −21818.0 −0.948183 −0.474091 − 0.880476i \(-0.657223\pi\)
−0.474091 + 0.880476i \(0.657223\pi\)
\(810\) 0 0
\(811\) −25252.0 −1.09336 −0.546682 − 0.837341i \(-0.684109\pi\)
−0.546682 + 0.837341i \(0.684109\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 28200.0 1.21203
\(816\) 0 0
\(817\) 16432.0 0.703651
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 4642.00 0.197329 0.0986644 − 0.995121i \(-0.468543\pi\)
0.0986644 + 0.995121i \(0.468543\pi\)
\(822\) 0 0
\(823\) 19512.0 0.826422 0.413211 − 0.910635i \(-0.364407\pi\)
0.413211 + 0.910635i \(0.364407\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −12484.0 −0.524923 −0.262461 − 0.964942i \(-0.584534\pi\)
−0.262461 + 0.964942i \(0.584534\pi\)
\(828\) 0 0
\(829\) 24902.0 1.04328 0.521642 − 0.853165i \(-0.325320\pi\)
0.521642 + 0.853165i \(0.325320\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2646.00 0.110058
\(834\) 0 0
\(835\) 17680.0 0.732744
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 14376.0 0.591555 0.295777 − 0.955257i \(-0.404421\pi\)
0.295777 + 0.955257i \(0.404421\pi\)
\(840\) 0 0
\(841\) 10207.0 0.418508
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −20970.0 −0.853716
\(846\) 0 0
\(847\) 9611.00 0.389891
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4512.00 0.181750
\(852\) 0 0
\(853\) 6878.00 0.276082 0.138041 − 0.990426i \(-0.455919\pi\)
0.138041 + 0.990426i \(0.455919\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 9870.00 0.393410 0.196705 − 0.980463i \(-0.436976\pi\)
0.196705 + 0.980463i \(0.436976\pi\)
\(858\) 0 0
\(859\) −26660.0 −1.05894 −0.529469 − 0.848329i \(-0.677609\pi\)
−0.529469 + 0.848329i \(0.677609\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 33544.0 1.32312 0.661559 − 0.749893i \(-0.269895\pi\)
0.661559 + 0.749893i \(0.269895\pi\)
\(864\) 0 0
\(865\) −8940.00 −0.351409
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 70720.0 2.76066
\(870\) 0 0
\(871\) 6680.00 0.259866
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −10500.0 −0.405674
\(876\) 0 0
\(877\) 49494.0 1.90569 0.952847 − 0.303451i \(-0.0981389\pi\)
0.952847 + 0.303451i \(0.0981389\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 3798.00 0.145242 0.0726208 − 0.997360i \(-0.476864\pi\)
0.0726208 + 0.997360i \(0.476864\pi\)
\(882\) 0 0
\(883\) 31268.0 1.19168 0.595839 − 0.803104i \(-0.296820\pi\)
0.595839 + 0.803104i \(0.296820\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −6184.00 −0.234091 −0.117045 − 0.993127i \(-0.537342\pi\)
−0.117045 + 0.993127i \(0.537342\pi\)
\(888\) 0 0
\(889\) 17696.0 0.667609
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 13312.0 0.498846
\(894\) 0 0
\(895\) −19960.0 −0.745463
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −41664.0 −1.54569
\(900\) 0 0
\(901\) 3564.00 0.131780
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 15820.0 0.581077
\(906\) 0 0
\(907\) 23452.0 0.858557 0.429278 − 0.903172i \(-0.358768\pi\)
0.429278 + 0.903172i \(0.358768\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −16632.0 −0.604877 −0.302438 − 0.953169i \(-0.597801\pi\)
−0.302438 + 0.953169i \(0.597801\pi\)
\(912\) 0 0
\(913\) −9776.00 −0.354368
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 15092.0 0.543492
\(918\) 0 0
\(919\) −34232.0 −1.22874 −0.614369 − 0.789019i \(-0.710589\pi\)
−0.614369 + 0.789019i \(0.710589\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2720.00 0.0969988
\(924\) 0 0
\(925\) −2350.00 −0.0835325
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 31958.0 1.12864 0.564321 − 0.825556i \(-0.309138\pi\)
0.564321 + 0.825556i \(0.309138\pi\)
\(930\) 0 0
\(931\) 2548.00 0.0896964
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −28080.0 −0.982154
\(936\) 0 0
\(937\) −40262.0 −1.40374 −0.701869 − 0.712306i \(-0.747651\pi\)
−0.701869 + 0.712306i \(0.747651\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −22830.0 −0.790900 −0.395450 − 0.918488i \(-0.629411\pi\)
−0.395450 + 0.918488i \(0.629411\pi\)
\(942\) 0 0
\(943\) 22944.0 0.792322
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 46852.0 1.60769 0.803847 − 0.594837i \(-0.202783\pi\)
0.803847 + 0.594837i \(0.202783\pi\)
\(948\) 0 0
\(949\) 860.000 0.0294171
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2934.00 0.0997288 0.0498644 − 0.998756i \(-0.484121\pi\)
0.0498644 + 0.998756i \(0.484121\pi\)
\(954\) 0 0
\(955\) 24560.0 0.832192
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1638.00 −0.0551551
\(960\) 0 0
\(961\) 20385.0 0.684267
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −29420.0 −0.981413
\(966\) 0 0
\(967\) 6376.00 0.212036 0.106018 − 0.994364i \(-0.466190\pi\)
0.106018 + 0.994364i \(0.466190\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −28476.0 −0.941131 −0.470566 − 0.882365i \(-0.655950\pi\)
−0.470566 + 0.882365i \(0.655950\pi\)
\(972\) 0 0
\(973\) 16772.0 0.552606
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −19682.0 −0.644507 −0.322253 − 0.946653i \(-0.604440\pi\)
−0.322253 + 0.946653i \(0.604440\pi\)
\(978\) 0 0
\(979\) −19032.0 −0.621313
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −15960.0 −0.517848 −0.258924 − 0.965898i \(-0.583368\pi\)
−0.258924 + 0.965898i \(0.583368\pi\)
\(984\) 0 0
\(985\) 36660.0 1.18587
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 15168.0 0.487679
\(990\) 0 0
\(991\) −52592.0 −1.68581 −0.842906 − 0.538061i \(-0.819157\pi\)
−0.842906 + 0.538061i \(0.819157\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −12240.0 −0.389984
\(996\) 0 0
\(997\) 41806.0 1.32799 0.663997 − 0.747736i \(-0.268859\pi\)
0.663997 + 0.747736i \(0.268859\pi\)
\(998\) 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 1008.4.a.q.1.1 1
3.2 odd 2 336.4.a.b.1.1 1
4.3 odd 2 504.4.a.e.1.1 1
12.11 even 2 168.4.a.e.1.1 ✓ 1
21.20 even 2 2352.4.a.bh.1.1 1
24.5 odd 2 1344.4.a.x.1.1 1
24.11 even 2 1344.4.a.k.1.1 1
84.83 odd 2 1176.4.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.4.a.e.1.1 ✓ 1 12.11 even 2
336.4.a.b.1.1 1 3.2 odd 2
504.4.a.e.1.1 1 4.3 odd 2
1008.4.a.q.1.1 1 1.1 even 1 trivial
1176.4.a.g.1.1 1 84.83 odd 2
1344.4.a.k.1.1 1 24.11 even 2
1344.4.a.x.1.1 1 24.5 odd 2
2352.4.a.bh.1.1 1 21.20 even 2