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Properties

Label 504.4.a.b.1.1
Level $504$
Weight $4$
Character 504.1
Self dual yes
Analytic conductor $29.737$
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] = [504,4,Mod(1,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, 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("504.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 504.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: \(29.7369626429\)
Analytic rank: \(1\)
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 \(\chi\) \(=\) 504.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000 q^{5} -7.00000 q^{7} +O(q^{10})\) \(q-4.00000 q^{5} -7.00000 q^{7} +26.0000 q^{11} +2.00000 q^{13} +36.0000 q^{17} -76.0000 q^{19} +114.000 q^{23} -109.000 q^{25} -6.00000 q^{29} -256.000 q^{31} +28.0000 q^{35} -86.0000 q^{37} -160.000 q^{41} -220.000 q^{43} -308.000 q^{47} +49.0000 q^{49} -258.000 q^{53} -104.000 q^{55} -264.000 q^{59} +606.000 q^{61} -8.00000 q^{65} -520.000 q^{67} +286.000 q^{71} -530.000 q^{73} -182.000 q^{77} -44.0000 q^{79} -1012.00 q^{83} -144.000 q^{85} -768.000 q^{89} -14.0000 q^{91} +304.000 q^{95} +222.000 q^{97} +O(q^{100})\)

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
\(5\) −4.00000 −0.357771 −0.178885 − 0.983870i \(-0.557249\pi\)
−0.178885 + 0.983870i \(0.557249\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 26.0000 0.712663 0.356332 − 0.934360i \(-0.384027\pi\)
0.356332 + 0.934360i \(0.384027\pi\)
\(12\) 0 0
\(13\) 2.00000 0.0426692 0.0213346 − 0.999772i \(-0.493208\pi\)
0.0213346 + 0.999772i \(0.493208\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 36.0000 0.513605 0.256802 − 0.966464i \(-0.417331\pi\)
0.256802 + 0.966464i \(0.417331\pi\)
\(18\) 0 0
\(19\) −76.0000 −0.917663 −0.458831 − 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 114.000 1.03351 0.516753 − 0.856134i \(-0.327141\pi\)
0.516753 + 0.856134i \(0.327141\pi\)
\(24\) 0 0
\(25\) −109.000 −0.872000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.00000 −0.0384197 −0.0192099 − 0.999815i \(-0.506115\pi\)
−0.0192099 + 0.999815i \(0.506115\pi\)
\(30\) 0 0
\(31\) −256.000 −1.48319 −0.741596 − 0.670847i \(-0.765931\pi\)
−0.741596 + 0.670847i \(0.765931\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 28.0000 0.135225
\(36\) 0 0
\(37\) −86.0000 −0.382117 −0.191058 − 0.981579i \(-0.561192\pi\)
−0.191058 + 0.981579i \(0.561192\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −160.000 −0.609459 −0.304729 − 0.952439i \(-0.598566\pi\)
−0.304729 + 0.952439i \(0.598566\pi\)
\(42\) 0 0
\(43\) −220.000 −0.780225 −0.390113 − 0.920767i \(-0.627564\pi\)
−0.390113 + 0.920767i \(0.627564\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −308.000 −0.955881 −0.477941 − 0.878392i \(-0.658617\pi\)
−0.477941 + 0.878392i \(0.658617\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −258.000 −0.668661 −0.334330 − 0.942456i \(-0.608510\pi\)
−0.334330 + 0.942456i \(0.608510\pi\)
\(54\) 0 0
\(55\) −104.000 −0.254970
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −264.000 −0.582540 −0.291270 − 0.956641i \(-0.594078\pi\)
−0.291270 + 0.956641i \(0.594078\pi\)
\(60\) 0 0
\(61\) 606.000 1.27197 0.635986 − 0.771700i \(-0.280593\pi\)
0.635986 + 0.771700i \(0.280593\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −8.00000 −0.0152658
\(66\) 0 0
\(67\) −520.000 −0.948181 −0.474090 − 0.880476i \(-0.657223\pi\)
−0.474090 + 0.880476i \(0.657223\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 286.000 0.478056 0.239028 − 0.971013i \(-0.423171\pi\)
0.239028 + 0.971013i \(0.423171\pi\)
\(72\) 0 0
\(73\) −530.000 −0.849751 −0.424875 − 0.905252i \(-0.639682\pi\)
−0.424875 + 0.905252i \(0.639682\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −182.000 −0.269361
\(78\) 0 0
\(79\) −44.0000 −0.0626631 −0.0313316 − 0.999509i \(-0.509975\pi\)
−0.0313316 + 0.999509i \(0.509975\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1012.00 −1.33833 −0.669165 − 0.743114i \(-0.733348\pi\)
−0.669165 + 0.743114i \(0.733348\pi\)
\(84\) 0 0
\(85\) −144.000 −0.183753
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −768.000 −0.914695 −0.457347 − 0.889288i \(-0.651200\pi\)
−0.457347 + 0.889288i \(0.651200\pi\)
\(90\) 0 0
\(91\) −14.0000 −0.0161275
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 304.000 0.328313
\(96\) 0 0
\(97\) 222.000 0.232378 0.116189 − 0.993227i \(-0.462932\pi\)
0.116189 + 0.993227i \(0.462932\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 320.000 0.315259 0.157630 − 0.987498i \(-0.449615\pi\)
0.157630 + 0.987498i \(0.449615\pi\)
\(102\) 0 0
\(103\) −592.000 −0.566325 −0.283163 − 0.959072i \(-0.591384\pi\)
−0.283163 + 0.959072i \(0.591384\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1782.00 −1.61002 −0.805011 − 0.593259i \(-0.797841\pi\)
−0.805011 + 0.593259i \(0.797841\pi\)
\(108\) 0 0
\(109\) 230.000 0.202110 0.101055 − 0.994881i \(-0.467778\pi\)
0.101055 + 0.994881i \(0.467778\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1718.00 1.43023 0.715114 − 0.699007i \(-0.246375\pi\)
0.715114 + 0.699007i \(0.246375\pi\)
\(114\) 0 0
\(115\) −456.000 −0.369758
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −252.000 −0.194124
\(120\) 0 0
\(121\) −655.000 −0.492111
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 936.000 0.669747
\(126\) 0 0
\(127\) −2444.00 −1.70764 −0.853819 − 0.520571i \(-0.825719\pi\)
−0.853819 + 0.520571i \(0.825719\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1996.00 −1.33123 −0.665616 − 0.746295i \(-0.731831\pi\)
−0.665616 + 0.746295i \(0.731831\pi\)
\(132\) 0 0
\(133\) 532.000 0.346844
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1746.00 1.08884 0.544419 − 0.838813i \(-0.316750\pi\)
0.544419 + 0.838813i \(0.316750\pi\)
\(138\) 0 0
\(139\) 1804.00 1.10081 0.550407 − 0.834896i \(-0.314472\pi\)
0.550407 + 0.834896i \(0.314472\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 52.0000 0.0304088
\(144\) 0 0
\(145\) 24.0000 0.0137455
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2814.00 1.54719 0.773597 − 0.633678i \(-0.218456\pi\)
0.773597 + 0.633678i \(0.218456\pi\)
\(150\) 0 0
\(151\) −792.000 −0.426835 −0.213417 − 0.976961i \(-0.568459\pi\)
−0.213417 + 0.976961i \(0.568459\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1024.00 0.530643
\(156\) 0 0
\(157\) −2778.00 −1.41216 −0.706078 − 0.708134i \(-0.749537\pi\)
−0.706078 + 0.708134i \(0.749537\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −798.000 −0.390629
\(162\) 0 0
\(163\) 2880.00 1.38392 0.691960 − 0.721936i \(-0.256747\pi\)
0.691960 + 0.721936i \(0.256747\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1060.00 0.491169 0.245585 − 0.969375i \(-0.421020\pi\)
0.245585 + 0.969375i \(0.421020\pi\)
\(168\) 0 0
\(169\) −2193.00 −0.998179
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1440.00 0.632839 0.316420 − 0.948619i \(-0.397519\pi\)
0.316420 + 0.948619i \(0.397519\pi\)
\(174\) 0 0
\(175\) 763.000 0.329585
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1210.00 −0.505249 −0.252625 − 0.967564i \(-0.581294\pi\)
−0.252625 + 0.967564i \(0.581294\pi\)
\(180\) 0 0
\(181\) 1618.00 0.664447 0.332224 − 0.943201i \(-0.392201\pi\)
0.332224 + 0.943201i \(0.392201\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 344.000 0.136710
\(186\) 0 0
\(187\) 936.000 0.366027
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4018.00 −1.52216 −0.761079 − 0.648659i \(-0.775330\pi\)
−0.761079 + 0.648659i \(0.775330\pi\)
\(192\) 0 0
\(193\) 3382.00 1.26136 0.630678 − 0.776045i \(-0.282777\pi\)
0.630678 + 0.776045i \(0.282777\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4302.00 1.55586 0.777931 − 0.628350i \(-0.216269\pi\)
0.777931 + 0.628350i \(0.216269\pi\)
\(198\) 0 0
\(199\) −2640.00 −0.940425 −0.470213 − 0.882553i \(-0.655823\pi\)
−0.470213 + 0.882553i \(0.655823\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 42.0000 0.0145213
\(204\) 0 0
\(205\) 640.000 0.218047
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1976.00 −0.653985
\(210\) 0 0
\(211\) 3396.00 1.10801 0.554005 − 0.832513i \(-0.313099\pi\)
0.554005 + 0.832513i \(0.313099\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 880.000 0.279142
\(216\) 0 0
\(217\) 1792.00 0.560594
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 72.0000 0.0219151
\(222\) 0 0
\(223\) 3480.00 1.04501 0.522507 − 0.852635i \(-0.324997\pi\)
0.522507 + 0.852635i \(0.324997\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1504.00 0.439753 0.219877 − 0.975528i \(-0.429435\pi\)
0.219877 + 0.975528i \(0.429435\pi\)
\(228\) 0 0
\(229\) 5122.00 1.47804 0.739020 − 0.673683i \(-0.235289\pi\)
0.739020 + 0.673683i \(0.235289\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1630.00 −0.458304 −0.229152 − 0.973391i \(-0.573595\pi\)
−0.229152 + 0.973391i \(0.573595\pi\)
\(234\) 0 0
\(235\) 1232.00 0.341986
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2522.00 0.682572 0.341286 − 0.939960i \(-0.389138\pi\)
0.341286 + 0.939960i \(0.389138\pi\)
\(240\) 0 0
\(241\) 3022.00 0.807735 0.403867 − 0.914817i \(-0.367666\pi\)
0.403867 + 0.914817i \(0.367666\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −196.000 −0.0511101
\(246\) 0 0
\(247\) −152.000 −0.0391560
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −3480.00 −0.875122 −0.437561 − 0.899189i \(-0.644158\pi\)
−0.437561 + 0.899189i \(0.644158\pi\)
\(252\) 0 0
\(253\) 2964.00 0.736542
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3496.00 −0.848539 −0.424269 − 0.905536i \(-0.639469\pi\)
−0.424269 + 0.905536i \(0.639469\pi\)
\(258\) 0 0
\(259\) 602.000 0.144426
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 5058.00 1.18589 0.592946 − 0.805242i \(-0.297965\pi\)
0.592946 + 0.805242i \(0.297965\pi\)
\(264\) 0 0
\(265\) 1032.00 0.239227
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3596.00 −0.815063 −0.407532 − 0.913191i \(-0.633610\pi\)
−0.407532 + 0.913191i \(0.633610\pi\)
\(270\) 0 0
\(271\) −2424.00 −0.543349 −0.271674 − 0.962389i \(-0.587577\pi\)
−0.271674 + 0.962389i \(0.587577\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2834.00 −0.621442
\(276\) 0 0
\(277\) 3634.00 0.788252 0.394126 − 0.919056i \(-0.371047\pi\)
0.394126 + 0.919056i \(0.371047\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2970.00 0.630517 0.315259 − 0.949006i \(-0.397909\pi\)
0.315259 + 0.949006i \(0.397909\pi\)
\(282\) 0 0
\(283\) −7028.00 −1.47622 −0.738112 − 0.674679i \(-0.764282\pi\)
−0.738112 + 0.674679i \(0.764282\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1120.00 0.230354
\(288\) 0 0
\(289\) −3617.00 −0.736210
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 528.000 0.105277 0.0526384 − 0.998614i \(-0.483237\pi\)
0.0526384 + 0.998614i \(0.483237\pi\)
\(294\) 0 0
\(295\) 1056.00 0.208416
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 228.000 0.0440989
\(300\) 0 0
\(301\) 1540.00 0.294897
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2424.00 −0.455075
\(306\) 0 0
\(307\) 4300.00 0.799394 0.399697 − 0.916647i \(-0.369115\pi\)
0.399697 + 0.916647i \(0.369115\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4580.00 0.835074 0.417537 − 0.908660i \(-0.362893\pi\)
0.417537 + 0.908660i \(0.362893\pi\)
\(312\) 0 0
\(313\) 2266.00 0.409207 0.204604 − 0.978845i \(-0.434409\pi\)
0.204604 + 0.978845i \(0.434409\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7926.00 1.40432 0.702159 − 0.712021i \(-0.252220\pi\)
0.702159 + 0.712021i \(0.252220\pi\)
\(318\) 0 0
\(319\) −156.000 −0.0273803
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2736.00 −0.471316
\(324\) 0 0
\(325\) −218.000 −0.0372076
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2156.00 0.361289
\(330\) 0 0
\(331\) −4132.00 −0.686149 −0.343074 − 0.939308i \(-0.611468\pi\)
−0.343074 + 0.939308i \(0.611468\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2080.00 0.339231
\(336\) 0 0
\(337\) −3622.00 −0.585469 −0.292734 − 0.956194i \(-0.594565\pi\)
−0.292734 + 0.956194i \(0.594565\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6656.00 −1.05702
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 10254.0 1.58635 0.793175 − 0.608994i \(-0.208426\pi\)
0.793175 + 0.608994i \(0.208426\pi\)
\(348\) 0 0
\(349\) −8178.00 −1.25432 −0.627161 − 0.778890i \(-0.715783\pi\)
−0.627161 + 0.778890i \(0.715783\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9932.00 −1.49753 −0.748763 − 0.662837i \(-0.769352\pi\)
−0.748763 + 0.662837i \(0.769352\pi\)
\(354\) 0 0
\(355\) −1144.00 −0.171034
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6546.00 −0.962353 −0.481176 − 0.876624i \(-0.659790\pi\)
−0.481176 + 0.876624i \(0.659790\pi\)
\(360\) 0 0
\(361\) −1083.00 −0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2120.00 0.304016
\(366\) 0 0
\(367\) −12176.0 −1.73183 −0.865916 − 0.500190i \(-0.833263\pi\)
−0.865916 + 0.500190i \(0.833263\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1806.00 0.252730
\(372\) 0 0
\(373\) −8210.00 −1.13967 −0.569836 − 0.821758i \(-0.692993\pi\)
−0.569836 + 0.821758i \(0.692993\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.0000 −0.00163934
\(378\) 0 0
\(379\) 6908.00 0.936254 0.468127 − 0.883661i \(-0.344929\pi\)
0.468127 + 0.883661i \(0.344929\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 10248.0 1.36723 0.683614 − 0.729844i \(-0.260407\pi\)
0.683614 + 0.729844i \(0.260407\pi\)
\(384\) 0 0
\(385\) 728.000 0.0963697
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 274.000 0.0357130 0.0178565 − 0.999841i \(-0.494316\pi\)
0.0178565 + 0.999841i \(0.494316\pi\)
\(390\) 0 0
\(391\) 4104.00 0.530814
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 176.000 0.0224190
\(396\) 0 0
\(397\) −10010.0 −1.26546 −0.632730 − 0.774373i \(-0.718066\pi\)
−0.632730 + 0.774373i \(0.718066\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1998.00 −0.248816 −0.124408 − 0.992231i \(-0.539703\pi\)
−0.124408 + 0.992231i \(0.539703\pi\)
\(402\) 0 0
\(403\) −512.000 −0.0632867
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2236.00 −0.272320
\(408\) 0 0
\(409\) −12842.0 −1.55256 −0.776279 − 0.630390i \(-0.782895\pi\)
−0.776279 + 0.630390i \(0.782895\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1848.00 0.220180
\(414\) 0 0
\(415\) 4048.00 0.478816
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10400.0 1.21259 0.606293 − 0.795242i \(-0.292656\pi\)
0.606293 + 0.795242i \(0.292656\pi\)
\(420\) 0 0
\(421\) 15586.0 1.80431 0.902156 − 0.431410i \(-0.141984\pi\)
0.902156 + 0.431410i \(0.141984\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3924.00 −0.447863
\(426\) 0 0
\(427\) −4242.00 −0.480761
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8066.00 −0.901451 −0.450726 − 0.892663i \(-0.648835\pi\)
−0.450726 + 0.892663i \(0.648835\pi\)
\(432\) 0 0
\(433\) −5222.00 −0.579569 −0.289784 − 0.957092i \(-0.593584\pi\)
−0.289784 + 0.957092i \(0.593584\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −8664.00 −0.948410
\(438\) 0 0
\(439\) −10920.0 −1.18721 −0.593603 − 0.804758i \(-0.702295\pi\)
−0.593603 + 0.804758i \(0.702295\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1650.00 −0.176961 −0.0884807 − 0.996078i \(-0.528201\pi\)
−0.0884807 + 0.996078i \(0.528201\pi\)
\(444\) 0 0
\(445\) 3072.00 0.327251
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −11858.0 −1.24636 −0.623178 − 0.782080i \(-0.714159\pi\)
−0.623178 + 0.782080i \(0.714159\pi\)
\(450\) 0 0
\(451\) −4160.00 −0.434339
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 56.0000 0.00576994
\(456\) 0 0
\(457\) −17894.0 −1.83161 −0.915805 − 0.401623i \(-0.868446\pi\)
−0.915805 + 0.401623i \(0.868446\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2088.00 0.210950 0.105475 − 0.994422i \(-0.466364\pi\)
0.105475 + 0.994422i \(0.466364\pi\)
\(462\) 0 0
\(463\) 13532.0 1.35828 0.679142 − 0.734007i \(-0.262352\pi\)
0.679142 + 0.734007i \(0.262352\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6344.00 −0.628620 −0.314310 − 0.949320i \(-0.601773\pi\)
−0.314310 + 0.949320i \(0.601773\pi\)
\(468\) 0 0
\(469\) 3640.00 0.358379
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5720.00 −0.556038
\(474\) 0 0
\(475\) 8284.00 0.800202
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9948.00 −0.948926 −0.474463 − 0.880275i \(-0.657358\pi\)
−0.474463 + 0.880275i \(0.657358\pi\)
\(480\) 0 0
\(481\) −172.000 −0.0163046
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −888.000 −0.0831382
\(486\) 0 0
\(487\) 20144.0 1.87436 0.937178 − 0.348850i \(-0.113428\pi\)
0.937178 + 0.348850i \(0.113428\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −10530.0 −0.967846 −0.483923 − 0.875111i \(-0.660788\pi\)
−0.483923 + 0.875111i \(0.660788\pi\)
\(492\) 0 0
\(493\) −216.000 −0.0197326
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2002.00 −0.180688
\(498\) 0 0
\(499\) −5548.00 −0.497721 −0.248860 − 0.968539i \(-0.580056\pi\)
−0.248860 + 0.968539i \(0.580056\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2152.00 0.190761 0.0953807 − 0.995441i \(-0.469593\pi\)
0.0953807 + 0.995441i \(0.469593\pi\)
\(504\) 0 0
\(505\) −1280.00 −0.112791
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 19780.0 1.72246 0.861231 − 0.508214i \(-0.169694\pi\)
0.861231 + 0.508214i \(0.169694\pi\)
\(510\) 0 0
\(511\) 3710.00 0.321176
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2368.00 0.202615
\(516\) 0 0
\(517\) −8008.00 −0.681221
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −23052.0 −1.93844 −0.969219 − 0.246199i \(-0.920818\pi\)
−0.969219 + 0.246199i \(0.920818\pi\)
\(522\) 0 0
\(523\) −13364.0 −1.11734 −0.558668 − 0.829391i \(-0.688687\pi\)
−0.558668 + 0.829391i \(0.688687\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −9216.00 −0.761775
\(528\) 0 0
\(529\) 829.000 0.0681351
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −320.000 −0.0260051
\(534\) 0 0
\(535\) 7128.00 0.576019
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1274.00 0.101809
\(540\) 0 0
\(541\) −9766.00 −0.776106 −0.388053 − 0.921637i \(-0.626852\pi\)
−0.388053 + 0.921637i \(0.626852\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −920.000 −0.0723091
\(546\) 0 0
\(547\) 3768.00 0.294530 0.147265 − 0.989097i \(-0.452953\pi\)
0.147265 + 0.989097i \(0.452953\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 456.000 0.0352564
\(552\) 0 0
\(553\) 308.000 0.0236844
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1618.00 −0.123082 −0.0615412 − 0.998105i \(-0.519602\pi\)
−0.0615412 + 0.998105i \(0.519602\pi\)
\(558\) 0 0
\(559\) −440.000 −0.0332916
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5768.00 0.431780 0.215890 − 0.976418i \(-0.430735\pi\)
0.215890 + 0.976418i \(0.430735\pi\)
\(564\) 0 0
\(565\) −6872.00 −0.511694
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8114.00 0.597815 0.298907 − 0.954282i \(-0.403378\pi\)
0.298907 + 0.954282i \(0.403378\pi\)
\(570\) 0 0
\(571\) 7816.00 0.572836 0.286418 − 0.958105i \(-0.407535\pi\)
0.286418 + 0.958105i \(0.407535\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −12426.0 −0.901217
\(576\) 0 0
\(577\) −18278.0 −1.31876 −0.659379 − 0.751811i \(-0.729181\pi\)
−0.659379 + 0.751811i \(0.729181\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7084.00 0.505841
\(582\) 0 0
\(583\) −6708.00 −0.476530
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 24960.0 1.75504 0.877521 − 0.479539i \(-0.159196\pi\)
0.877521 + 0.479539i \(0.159196\pi\)
\(588\) 0 0
\(589\) 19456.0 1.36107
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −10892.0 −0.754268 −0.377134 − 0.926159i \(-0.623090\pi\)
−0.377134 + 0.926159i \(0.623090\pi\)
\(594\) 0 0
\(595\) 1008.00 0.0694521
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 20022.0 1.36574 0.682869 − 0.730541i \(-0.260732\pi\)
0.682869 + 0.730541i \(0.260732\pi\)
\(600\) 0 0
\(601\) 10370.0 0.703829 0.351914 − 0.936032i \(-0.385531\pi\)
0.351914 + 0.936032i \(0.385531\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2620.00 0.176063
\(606\) 0 0
\(607\) −8992.00 −0.601275 −0.300638 − 0.953738i \(-0.597199\pi\)
−0.300638 + 0.953738i \(0.597199\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −616.000 −0.0407867
\(612\) 0 0
\(613\) 12318.0 0.811614 0.405807 − 0.913959i \(-0.366991\pi\)
0.405807 + 0.913959i \(0.366991\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 26026.0 1.69816 0.849082 − 0.528261i \(-0.177156\pi\)
0.849082 + 0.528261i \(0.177156\pi\)
\(618\) 0 0
\(619\) −18332.0 −1.19035 −0.595174 − 0.803597i \(-0.702917\pi\)
−0.595174 + 0.803597i \(0.702917\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5376.00 0.345722
\(624\) 0 0
\(625\) 9881.00 0.632384
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3096.00 −0.196257
\(630\) 0 0
\(631\) 10572.0 0.666980 0.333490 − 0.942754i \(-0.391774\pi\)
0.333490 + 0.942754i \(0.391774\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 9776.00 0.610943
\(636\) 0 0
\(637\) 98.0000 0.00609561
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −24822.0 −1.52950 −0.764750 − 0.644327i \(-0.777138\pi\)
−0.764750 + 0.644327i \(0.777138\pi\)
\(642\) 0 0
\(643\) −6620.00 −0.406014 −0.203007 − 0.979177i \(-0.565071\pi\)
−0.203007 + 0.979177i \(0.565071\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15956.0 −0.969544 −0.484772 − 0.874641i \(-0.661097\pi\)
−0.484772 + 0.874641i \(0.661097\pi\)
\(648\) 0 0
\(649\) −6864.00 −0.415155
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 30802.0 1.84590 0.922952 − 0.384915i \(-0.125769\pi\)
0.922952 + 0.384915i \(0.125769\pi\)
\(654\) 0 0
\(655\) 7984.00 0.476276
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 12714.0 0.751543 0.375772 − 0.926712i \(-0.377378\pi\)
0.375772 + 0.926712i \(0.377378\pi\)
\(660\) 0 0
\(661\) 5822.00 0.342586 0.171293 − 0.985220i \(-0.445205\pi\)
0.171293 + 0.985220i \(0.445205\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2128.00 −0.124091
\(666\) 0 0
\(667\) −684.000 −0.0397070
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 15756.0 0.906488
\(672\) 0 0
\(673\) 28510.0 1.63296 0.816478 − 0.577376i \(-0.195923\pi\)
0.816478 + 0.577376i \(0.195923\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 21864.0 1.24121 0.620607 − 0.784122i \(-0.286886\pi\)
0.620607 + 0.784122i \(0.286886\pi\)
\(678\) 0 0
\(679\) −1554.00 −0.0878307
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 17862.0 1.00069 0.500344 − 0.865826i \(-0.333207\pi\)
0.500344 + 0.865826i \(0.333207\pi\)
\(684\) 0 0
\(685\) −6984.00 −0.389555
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −516.000 −0.0285313
\(690\) 0 0
\(691\) −6068.00 −0.334063 −0.167032 − 0.985952i \(-0.553418\pi\)
−0.167032 + 0.985952i \(0.553418\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7216.00 −0.393840
\(696\) 0 0
\(697\) −5760.00 −0.313021
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −7734.00 −0.416703 −0.208352 − 0.978054i \(-0.566810\pi\)
−0.208352 + 0.978054i \(0.566810\pi\)
\(702\) 0 0
\(703\) 6536.00 0.350654
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2240.00 −0.119157
\(708\) 0 0
\(709\) 19902.0 1.05421 0.527105 − 0.849800i \(-0.323277\pi\)
0.527105 + 0.849800i \(0.323277\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −29184.0 −1.53289
\(714\) 0 0
\(715\) −208.000 −0.0108794
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −12160.0 −0.630725 −0.315363 − 0.948971i \(-0.602126\pi\)
−0.315363 + 0.948971i \(0.602126\pi\)
\(720\) 0 0
\(721\) 4144.00 0.214051
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 654.000 0.0335020
\(726\) 0 0
\(727\) 3088.00 0.157534 0.0787672 − 0.996893i \(-0.474902\pi\)
0.0787672 + 0.996893i \(0.474902\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −7920.00 −0.400727
\(732\) 0 0
\(733\) 10178.0 0.512869 0.256435 − 0.966562i \(-0.417452\pi\)
0.256435 + 0.966562i \(0.417452\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −13520.0 −0.675734
\(738\) 0 0
\(739\) −5840.00 −0.290701 −0.145350 − 0.989380i \(-0.546431\pi\)
−0.145350 + 0.989380i \(0.546431\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14414.0 0.711707 0.355854 − 0.934542i \(-0.384190\pi\)
0.355854 + 0.934542i \(0.384190\pi\)
\(744\) 0 0
\(745\) −11256.0 −0.553541
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 12474.0 0.608531
\(750\) 0 0
\(751\) −12608.0 −0.612613 −0.306307 − 0.951933i \(-0.599093\pi\)
−0.306307 + 0.951933i \(0.599093\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3168.00 0.152709
\(756\) 0 0
\(757\) 22606.0 1.08538 0.542688 − 0.839935i \(-0.317407\pi\)
0.542688 + 0.839935i \(0.317407\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −5952.00 −0.283521 −0.141761 − 0.989901i \(-0.545276\pi\)
−0.141761 + 0.989901i \(0.545276\pi\)
\(762\) 0 0
\(763\) −1610.00 −0.0763905
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −528.000 −0.0248566
\(768\) 0 0
\(769\) 14138.0 0.662977 0.331489 − 0.943459i \(-0.392449\pi\)
0.331489 + 0.943459i \(0.392449\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −12616.0 −0.587019 −0.293510 − 0.955956i \(-0.594823\pi\)
−0.293510 + 0.955956i \(0.594823\pi\)
\(774\) 0 0
\(775\) 27904.0 1.29334
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 12160.0 0.559278
\(780\) 0 0
\(781\) 7436.00 0.340693
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 11112.0 0.505228
\(786\) 0 0
\(787\) −12292.0 −0.556750 −0.278375 − 0.960472i \(-0.589796\pi\)
−0.278375 + 0.960472i \(0.589796\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −12026.0 −0.540576
\(792\) 0 0
\(793\) 1212.00 0.0542741
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 20784.0 0.923723 0.461861 − 0.886952i \(-0.347182\pi\)
0.461861 + 0.886952i \(0.347182\pi\)
\(798\) 0 0
\(799\) −11088.0 −0.490945
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −13780.0 −0.605586
\(804\) 0 0
\(805\) 3192.00 0.139756
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 13574.0 0.589909 0.294955 − 0.955511i \(-0.404695\pi\)
0.294955 + 0.955511i \(0.404695\pi\)
\(810\) 0 0
\(811\) 32308.0 1.39887 0.699437 − 0.714694i \(-0.253434\pi\)
0.699437 + 0.714694i \(0.253434\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −11520.0 −0.495126
\(816\) 0 0
\(817\) 16720.0 0.715984
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2390.00 0.101598 0.0507988 − 0.998709i \(-0.483823\pi\)
0.0507988 + 0.998709i \(0.483823\pi\)
\(822\) 0 0
\(823\) 28020.0 1.18677 0.593387 − 0.804917i \(-0.297790\pi\)
0.593387 + 0.804917i \(0.297790\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −34006.0 −1.42987 −0.714936 − 0.699190i \(-0.753544\pi\)
−0.714936 + 0.699190i \(0.753544\pi\)
\(828\) 0 0
\(829\) −6310.00 −0.264361 −0.132181 − 0.991226i \(-0.542198\pi\)
−0.132181 + 0.991226i \(0.542198\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1764.00 0.0733721
\(834\) 0 0
\(835\) −4240.00 −0.175726
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 16524.0 0.679943 0.339971 − 0.940436i \(-0.389583\pi\)
0.339971 + 0.940436i \(0.389583\pi\)
\(840\) 0 0
\(841\) −24353.0 −0.998524
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 8772.00 0.357119
\(846\) 0 0
\(847\) 4585.00 0.186001
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −9804.00 −0.394920
\(852\) 0 0
\(853\) 36662.0 1.47161 0.735805 − 0.677194i \(-0.236804\pi\)
0.735805 + 0.677194i \(0.236804\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 42000.0 1.67409 0.837044 − 0.547136i \(-0.184282\pi\)
0.837044 + 0.547136i \(0.184282\pi\)
\(858\) 0 0
\(859\) 28388.0 1.12757 0.563787 − 0.825920i \(-0.309344\pi\)
0.563787 + 0.825920i \(0.309344\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −23918.0 −0.943428 −0.471714 − 0.881752i \(-0.656364\pi\)
−0.471714 + 0.881752i \(0.656364\pi\)
\(864\) 0 0
\(865\) −5760.00 −0.226411
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −1144.00 −0.0446577
\(870\) 0 0
\(871\) −1040.00 −0.0404582
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −6552.00 −0.253141
\(876\) 0 0
\(877\) −2346.00 −0.0903293 −0.0451646 − 0.998980i \(-0.514381\pi\)
−0.0451646 + 0.998980i \(0.514381\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −51876.0 −1.98382 −0.991911 − 0.126937i \(-0.959485\pi\)
−0.991911 + 0.126937i \(0.959485\pi\)
\(882\) 0 0
\(883\) −11372.0 −0.433407 −0.216703 − 0.976237i \(-0.569530\pi\)
−0.216703 + 0.976237i \(0.569530\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −38764.0 −1.46738 −0.733691 − 0.679483i \(-0.762204\pi\)
−0.733691 + 0.679483i \(0.762204\pi\)
\(888\) 0 0
\(889\) 17108.0 0.645426
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 23408.0 0.877177
\(894\) 0 0
\(895\) 4840.00 0.180764
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1536.00 0.0569838
\(900\) 0 0
\(901\) −9288.00 −0.343427
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −6472.00 −0.237720
\(906\) 0 0
\(907\) −11212.0 −0.410461 −0.205231 − 0.978714i \(-0.565794\pi\)
−0.205231 + 0.978714i \(0.565794\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −1458.00 −0.0530249 −0.0265125 − 0.999648i \(-0.508440\pi\)
−0.0265125 + 0.999648i \(0.508440\pi\)
\(912\) 0 0
\(913\) −26312.0 −0.953779
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 13972.0 0.503158
\(918\) 0 0
\(919\) −38608.0 −1.38581 −0.692906 − 0.721028i \(-0.743670\pi\)
−0.692906 + 0.721028i \(0.743670\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 572.000 0.0203983
\(924\) 0 0
\(925\) 9374.00 0.333206
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −7376.00 −0.260494 −0.130247 − 0.991482i \(-0.541577\pi\)
−0.130247 + 0.991482i \(0.541577\pi\)
\(930\) 0 0
\(931\) −3724.00 −0.131095
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −3744.00 −0.130954
\(936\) 0 0
\(937\) −24878.0 −0.867373 −0.433687 − 0.901064i \(-0.642788\pi\)
−0.433687 + 0.901064i \(0.642788\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 26148.0 0.905845 0.452923 − 0.891550i \(-0.350381\pi\)
0.452923 + 0.891550i \(0.350381\pi\)
\(942\) 0 0
\(943\) −18240.0 −0.629879
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −18350.0 −0.629667 −0.314834 − 0.949147i \(-0.601949\pi\)
−0.314834 + 0.949147i \(0.601949\pi\)
\(948\) 0 0
\(949\) −1060.00 −0.0362582
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 57510.0 1.95481 0.977404 − 0.211381i \(-0.0677960\pi\)
0.977404 + 0.211381i \(0.0677960\pi\)
\(954\) 0 0
\(955\) 16072.0 0.544584
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −12222.0 −0.411542
\(960\) 0 0
\(961\) 35745.0 1.19986
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −13528.0 −0.451276
\(966\) 0 0
\(967\) −33364.0 −1.10953 −0.554764 − 0.832008i \(-0.687192\pi\)
−0.554764 + 0.832008i \(0.687192\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −26892.0 −0.888780 −0.444390 − 0.895833i \(-0.646580\pi\)
−0.444390 + 0.895833i \(0.646580\pi\)
\(972\) 0 0
\(973\) −12628.0 −0.416069
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 31970.0 1.04689 0.523445 − 0.852060i \(-0.324647\pi\)
0.523445 + 0.852060i \(0.324647\pi\)
\(978\) 0 0
\(979\) −19968.0 −0.651869
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 19728.0 0.640107 0.320054 − 0.947399i \(-0.396299\pi\)
0.320054 + 0.947399i \(0.396299\pi\)
\(984\) 0 0
\(985\) −17208.0 −0.556642
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −25080.0 −0.806368
\(990\) 0 0
\(991\) −21400.0 −0.685967 −0.342984 − 0.939341i \(-0.611438\pi\)
−0.342984 + 0.939341i \(0.611438\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 10560.0 0.336457
\(996\) 0 0
\(997\) −4754.00 −0.151014 −0.0755069 − 0.997145i \(-0.524057\pi\)
−0.0755069 + 0.997145i \(0.524057\pi\)
\(998\) 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 504.4.a.b.1.1 1
3.2 odd 2 168.4.a.c.1.1 ✓ 1
4.3 odd 2 1008.4.a.i.1.1 1
12.11 even 2 336.4.a.j.1.1 1
21.20 even 2 1176.4.a.j.1.1 1
24.5 odd 2 1344.4.a.s.1.1 1
24.11 even 2 1344.4.a.e.1.1 1
84.83 odd 2 2352.4.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.4.a.c.1.1 ✓ 1 3.2 odd 2
336.4.a.j.1.1 1 12.11 even 2
504.4.a.b.1.1 1 1.1 even 1 trivial
1008.4.a.i.1.1 1 4.3 odd 2
1176.4.a.j.1.1 1 21.20 even 2
1344.4.a.e.1.1 1 24.11 even 2
1344.4.a.s.1.1 1 24.5 odd 2
2352.4.a.h.1.1 1 84.83 odd 2