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Properties

Label 1872.4.a.k.1.1
Level $1872$
Weight $4$
Character 1872.1
Self dual yes
Analytic conductor $110.452$
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] = [1872,4,Mod(1,1872)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1872, 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("1872.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1872.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: \(110.451575531\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1872.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+7.00000 q^{5} +13.0000 q^{7} +O(q^{10})\) \(q+7.00000 q^{5} +13.0000 q^{7} -26.0000 q^{11} +13.0000 q^{13} -77.0000 q^{17} +126.000 q^{19} -96.0000 q^{23} -76.0000 q^{25} +82.0000 q^{29} -196.000 q^{31} +91.0000 q^{35} -131.000 q^{37} -336.000 q^{41} +201.000 q^{43} -105.000 q^{47} -174.000 q^{49} +432.000 q^{53} -182.000 q^{55} -294.000 q^{59} -56.0000 q^{61} +91.0000 q^{65} -478.000 q^{67} +9.00000 q^{71} +98.0000 q^{73} -338.000 q^{77} -1304.00 q^{79} -308.000 q^{83} -539.000 q^{85} +1190.00 q^{89} +169.000 q^{91} +882.000 q^{95} +70.0000 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 7.00000 0.626099 0.313050 − 0.949737i \(-0.398649\pi\)
0.313050 + 0.949737i \(0.398649\pi\)
\(6\) 0 0
\(7\) 13.0000 0.701934 0.350967 − 0.936388i \(-0.385853\pi\)
0.350967 + 0.936388i \(0.385853\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −26.0000 −0.712663 −0.356332 − 0.934360i \(-0.615973\pi\)
−0.356332 + 0.934360i \(0.615973\pi\)
\(12\) 0 0
\(13\) 13.0000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −77.0000 −1.09854 −0.549272 − 0.835644i \(-0.685095\pi\)
−0.549272 + 0.835644i \(0.685095\pi\)
\(18\) 0 0
\(19\) 126.000 1.52139 0.760694 − 0.649110i \(-0.224859\pi\)
0.760694 + 0.649110i \(0.224859\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −96.0000 −0.870321 −0.435161 − 0.900353i \(-0.643308\pi\)
−0.435161 + 0.900353i \(0.643308\pi\)
\(24\) 0 0
\(25\) −76.0000 −0.608000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 82.0000 0.525070 0.262535 − 0.964923i \(-0.415442\pi\)
0.262535 + 0.964923i \(0.415442\pi\)
\(30\) 0 0
\(31\) −196.000 −1.13557 −0.567785 − 0.823177i \(-0.692199\pi\)
−0.567785 + 0.823177i \(0.692199\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 91.0000 0.439480
\(36\) 0 0
\(37\) −131.000 −0.582061 −0.291031 − 0.956714i \(-0.593998\pi\)
−0.291031 + 0.956714i \(0.593998\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −336.000 −1.27986 −0.639932 − 0.768432i \(-0.721037\pi\)
−0.639932 + 0.768432i \(0.721037\pi\)
\(42\) 0 0
\(43\) 201.000 0.712842 0.356421 − 0.934325i \(-0.383997\pi\)
0.356421 + 0.934325i \(0.383997\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −105.000 −0.325869 −0.162934 − 0.986637i \(-0.552096\pi\)
−0.162934 + 0.986637i \(0.552096\pi\)
\(48\) 0 0
\(49\) −174.000 −0.507289
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 432.000 1.11962 0.559809 − 0.828622i \(-0.310874\pi\)
0.559809 + 0.828622i \(0.310874\pi\)
\(54\) 0 0
\(55\) −182.000 −0.446198
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −294.000 −0.648738 −0.324369 − 0.945931i \(-0.605152\pi\)
−0.324369 + 0.945931i \(0.605152\pi\)
\(60\) 0 0
\(61\) −56.0000 −0.117542 −0.0587710 − 0.998271i \(-0.518718\pi\)
−0.0587710 + 0.998271i \(0.518718\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 91.0000 0.173649
\(66\) 0 0
\(67\) −478.000 −0.871597 −0.435798 − 0.900044i \(-0.643534\pi\)
−0.435798 + 0.900044i \(0.643534\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 9.00000 0.0150437 0.00752186 − 0.999972i \(-0.497606\pi\)
0.00752186 + 0.999972i \(0.497606\pi\)
\(72\) 0 0
\(73\) 98.0000 0.157124 0.0785619 − 0.996909i \(-0.474967\pi\)
0.0785619 + 0.996909i \(0.474967\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −338.000 −0.500243
\(78\) 0 0
\(79\) −1304.00 −1.85711 −0.928554 − 0.371198i \(-0.878947\pi\)
−0.928554 + 0.371198i \(0.878947\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −308.000 −0.407318 −0.203659 − 0.979042i \(-0.565283\pi\)
−0.203659 + 0.979042i \(0.565283\pi\)
\(84\) 0 0
\(85\) −539.000 −0.687797
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1190.00 1.41730 0.708650 − 0.705560i \(-0.249304\pi\)
0.708650 + 0.705560i \(0.249304\pi\)
\(90\) 0 0
\(91\) 169.000 0.194681
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 882.000 0.952540
\(96\) 0 0
\(97\) 70.0000 0.0732724 0.0366362 − 0.999329i \(-0.488336\pi\)
0.0366362 + 0.999329i \(0.488336\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −420.000 −0.413778 −0.206889 − 0.978364i \(-0.566334\pi\)
−0.206889 + 0.978364i \(0.566334\pi\)
\(102\) 0 0
\(103\) −588.000 −0.562499 −0.281249 − 0.959635i \(-0.590749\pi\)
−0.281249 + 0.959635i \(0.590749\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −684.000 −0.617989 −0.308994 − 0.951064i \(-0.599992\pi\)
−0.308994 + 0.951064i \(0.599992\pi\)
\(108\) 0 0
\(109\) 373.000 0.327770 0.163885 − 0.986479i \(-0.447597\pi\)
0.163885 + 0.986479i \(0.447597\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1734.00 1.44355 0.721774 − 0.692128i \(-0.243327\pi\)
0.721774 + 0.692128i \(0.243327\pi\)
\(114\) 0 0
\(115\) −672.000 −0.544907
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1001.00 −0.771105
\(120\) 0 0
\(121\) −655.000 −0.492111
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1407.00 −1.00677
\(126\) 0 0
\(127\) −1892.00 −1.32195 −0.660976 − 0.750407i \(-0.729857\pi\)
−0.660976 + 0.750407i \(0.729857\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1435.00 0.957073 0.478536 − 0.878068i \(-0.341167\pi\)
0.478536 + 0.878068i \(0.341167\pi\)
\(132\) 0 0
\(133\) 1638.00 1.06791
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1776.00 1.10755 0.553773 − 0.832667i \(-0.313187\pi\)
0.553773 + 0.832667i \(0.313187\pi\)
\(138\) 0 0
\(139\) 1869.00 1.14048 0.570239 − 0.821479i \(-0.306850\pi\)
0.570239 + 0.821479i \(0.306850\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −338.000 −0.197657
\(144\) 0 0
\(145\) 574.000 0.328746
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2466.00 −1.35586 −0.677928 − 0.735128i \(-0.737122\pi\)
−0.677928 + 0.735128i \(0.737122\pi\)
\(150\) 0 0
\(151\) 3323.00 1.79087 0.895437 − 0.445189i \(-0.146863\pi\)
0.895437 + 0.445189i \(0.146863\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1372.00 −0.710979
\(156\) 0 0
\(157\) −2730.00 −1.38776 −0.693878 − 0.720092i \(-0.744099\pi\)
−0.693878 + 0.720092i \(0.744099\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1248.00 −0.610908
\(162\) 0 0
\(163\) 544.000 0.261407 0.130704 − 0.991421i \(-0.458276\pi\)
0.130704 + 0.991421i \(0.458276\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1624.00 0.752508 0.376254 − 0.926516i \(-0.377212\pi\)
0.376254 + 0.926516i \(0.377212\pi\)
\(168\) 0 0
\(169\) 169.000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 336.000 0.147662 0.0738312 − 0.997271i \(-0.476477\pi\)
0.0738312 + 0.997271i \(0.476477\pi\)
\(174\) 0 0
\(175\) −988.000 −0.426776
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3029.00 −1.26479 −0.632397 − 0.774645i \(-0.717929\pi\)
−0.632397 + 0.774645i \(0.717929\pi\)
\(180\) 0 0
\(181\) −28.0000 −0.0114985 −0.00574924 − 0.999983i \(-0.501830\pi\)
−0.00574924 + 0.999983i \(0.501830\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −917.000 −0.364428
\(186\) 0 0
\(187\) 2002.00 0.782892
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 422.000 0.159868 0.0799342 − 0.996800i \(-0.474529\pi\)
0.0799342 + 0.996800i \(0.474529\pi\)
\(192\) 0 0
\(193\) 492.000 0.183497 0.0917485 − 0.995782i \(-0.470754\pi\)
0.0917485 + 0.995782i \(0.470754\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2991.00 −1.08173 −0.540863 − 0.841111i \(-0.681902\pi\)
−0.540863 + 0.841111i \(0.681902\pi\)
\(198\) 0 0
\(199\) 70.0000 0.0249355 0.0124678 − 0.999922i \(-0.496031\pi\)
0.0124678 + 0.999922i \(0.496031\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1066.00 0.368564
\(204\) 0 0
\(205\) −2352.00 −0.801321
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −3276.00 −1.08424
\(210\) 0 0
\(211\) −2851.00 −0.930194 −0.465097 − 0.885260i \(-0.653981\pi\)
−0.465097 + 0.885260i \(0.653981\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1407.00 0.446310
\(216\) 0 0
\(217\) −2548.00 −0.797095
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1001.00 −0.304681
\(222\) 0 0
\(223\) −217.000 −0.0651632 −0.0325816 − 0.999469i \(-0.510373\pi\)
−0.0325816 + 0.999469i \(0.510373\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2576.00 −0.753194 −0.376597 − 0.926377i \(-0.622906\pi\)
−0.376597 + 0.926377i \(0.622906\pi\)
\(228\) 0 0
\(229\) 455.000 0.131298 0.0656490 − 0.997843i \(-0.479088\pi\)
0.0656490 + 0.997843i \(0.479088\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3061.00 −0.860656 −0.430328 − 0.902673i \(-0.641602\pi\)
−0.430328 + 0.902673i \(0.641602\pi\)
\(234\) 0 0
\(235\) −735.000 −0.204026
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3477.00 −0.941039 −0.470520 − 0.882389i \(-0.655934\pi\)
−0.470520 + 0.882389i \(0.655934\pi\)
\(240\) 0 0
\(241\) −1610.00 −0.430329 −0.215164 − 0.976578i \(-0.569029\pi\)
−0.215164 + 0.976578i \(0.569029\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1218.00 −0.317613
\(246\) 0 0
\(247\) 1638.00 0.421957
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1008.00 0.253484 0.126742 − 0.991936i \(-0.459548\pi\)
0.126742 + 0.991936i \(0.459548\pi\)
\(252\) 0 0
\(253\) 2496.00 0.620246
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6041.00 −1.46625 −0.733127 − 0.680092i \(-0.761940\pi\)
−0.733127 + 0.680092i \(0.761940\pi\)
\(258\) 0 0
\(259\) −1703.00 −0.408569
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3708.00 −0.869373 −0.434686 − 0.900582i \(-0.643141\pi\)
−0.434686 + 0.900582i \(0.643141\pi\)
\(264\) 0 0
\(265\) 3024.00 0.700992
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −8344.00 −1.89124 −0.945618 − 0.325278i \(-0.894542\pi\)
−0.945618 + 0.325278i \(0.894542\pi\)
\(270\) 0 0
\(271\) 1617.00 0.362457 0.181228 − 0.983441i \(-0.441993\pi\)
0.181228 + 0.983441i \(0.441993\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1976.00 0.433299
\(276\) 0 0
\(277\) −3820.00 −0.828598 −0.414299 − 0.910141i \(-0.635973\pi\)
−0.414299 + 0.910141i \(0.635973\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6214.00 1.31920 0.659602 − 0.751615i \(-0.270725\pi\)
0.659602 + 0.751615i \(0.270725\pi\)
\(282\) 0 0
\(283\) 5292.00 1.11158 0.555789 − 0.831323i \(-0.312416\pi\)
0.555789 + 0.831323i \(0.312416\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4368.00 −0.898379
\(288\) 0 0
\(289\) 1016.00 0.206798
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 903.000 0.180047 0.0900236 − 0.995940i \(-0.471306\pi\)
0.0900236 + 0.995940i \(0.471306\pi\)
\(294\) 0 0
\(295\) −2058.00 −0.406174
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1248.00 −0.241384
\(300\) 0 0
\(301\) 2613.00 0.500368
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −392.000 −0.0735930
\(306\) 0 0
\(307\) −2114.00 −0.393004 −0.196502 − 0.980503i \(-0.562958\pi\)
−0.196502 + 0.980503i \(0.562958\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3402.00 0.620288 0.310144 − 0.950690i \(-0.399623\pi\)
0.310144 + 0.950690i \(0.399623\pi\)
\(312\) 0 0
\(313\) −10689.0 −1.93028 −0.965141 − 0.261732i \(-0.915706\pi\)
−0.965141 + 0.261732i \(0.915706\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7054.00 1.24982 0.624909 − 0.780698i \(-0.285136\pi\)
0.624909 + 0.780698i \(0.285136\pi\)
\(318\) 0 0
\(319\) −2132.00 −0.374198
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −9702.00 −1.67131
\(324\) 0 0
\(325\) −988.000 −0.168629
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1365.00 −0.228738
\(330\) 0 0
\(331\) −9704.00 −1.61142 −0.805710 − 0.592310i \(-0.798216\pi\)
−0.805710 + 0.592310i \(0.798216\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3346.00 −0.545706
\(336\) 0 0
\(337\) −10449.0 −1.68900 −0.844500 − 0.535555i \(-0.820103\pi\)
−0.844500 + 0.535555i \(0.820103\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 5096.00 0.809278
\(342\) 0 0
\(343\) −6721.00 −1.05802
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −621.000 −0.0960721 −0.0480361 − 0.998846i \(-0.515296\pi\)
−0.0480361 + 0.998846i \(0.515296\pi\)
\(348\) 0 0
\(349\) 12481.0 1.91431 0.957153 − 0.289584i \(-0.0935168\pi\)
0.957153 + 0.289584i \(0.0935168\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1400.00 0.211089 0.105545 − 0.994415i \(-0.466341\pi\)
0.105545 + 0.994415i \(0.466341\pi\)
\(354\) 0 0
\(355\) 63.0000 0.00941885
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4968.00 −0.730365 −0.365182 − 0.930936i \(-0.618993\pi\)
−0.365182 + 0.930936i \(0.618993\pi\)
\(360\) 0 0
\(361\) 9017.00 1.31462
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 686.000 0.0983750
\(366\) 0 0
\(367\) −8722.00 −1.24056 −0.620279 − 0.784381i \(-0.712981\pi\)
−0.620279 + 0.784381i \(0.712981\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 5616.00 0.785898
\(372\) 0 0
\(373\) 10012.0 1.38982 0.694908 − 0.719098i \(-0.255445\pi\)
0.694908 + 0.719098i \(0.255445\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1066.00 0.145628
\(378\) 0 0
\(379\) 3372.00 0.457013 0.228507 − 0.973542i \(-0.426616\pi\)
0.228507 + 0.973542i \(0.426616\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −847.000 −0.113002 −0.0565009 − 0.998403i \(-0.517994\pi\)
−0.0565009 + 0.998403i \(0.517994\pi\)
\(384\) 0 0
\(385\) −2366.00 −0.313201
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −11314.0 −1.47466 −0.737330 − 0.675533i \(-0.763914\pi\)
−0.737330 + 0.675533i \(0.763914\pi\)
\(390\) 0 0
\(391\) 7392.00 0.956086
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −9128.00 −1.16273
\(396\) 0 0
\(397\) 1862.00 0.235393 0.117697 − 0.993050i \(-0.462449\pi\)
0.117697 + 0.993050i \(0.462449\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6820.00 −0.849313 −0.424657 − 0.905355i \(-0.639605\pi\)
−0.424657 + 0.905355i \(0.639605\pi\)
\(402\) 0 0
\(403\) −2548.00 −0.314950
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3406.00 0.414814
\(408\) 0 0
\(409\) −12992.0 −1.57069 −0.785346 − 0.619057i \(-0.787515\pi\)
−0.785346 + 0.619057i \(0.787515\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3822.00 −0.455371
\(414\) 0 0
\(415\) −2156.00 −0.255021
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7343.00 −0.856155 −0.428078 − 0.903742i \(-0.640809\pi\)
−0.428078 + 0.903742i \(0.640809\pi\)
\(420\) 0 0
\(421\) −5059.00 −0.585655 −0.292827 − 0.956165i \(-0.594596\pi\)
−0.292827 + 0.956165i \(0.594596\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5852.00 0.667915
\(426\) 0 0
\(427\) −728.000 −0.0825068
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3243.00 0.362436 0.181218 − 0.983443i \(-0.441996\pi\)
0.181218 + 0.983443i \(0.441996\pi\)
\(432\) 0 0
\(433\) 11599.0 1.28733 0.643663 − 0.765309i \(-0.277414\pi\)
0.643663 + 0.765309i \(0.277414\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −12096.0 −1.32410
\(438\) 0 0
\(439\) 17374.0 1.88887 0.944437 − 0.328692i \(-0.106608\pi\)
0.944437 + 0.328692i \(0.106608\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 989.000 0.106070 0.0530348 − 0.998593i \(-0.483111\pi\)
0.0530348 + 0.998593i \(0.483111\pi\)
\(444\) 0 0
\(445\) 8330.00 0.887370
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 14474.0 1.52131 0.760657 − 0.649154i \(-0.224877\pi\)
0.760657 + 0.649154i \(0.224877\pi\)
\(450\) 0 0
\(451\) 8736.00 0.912111
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1183.00 0.121890
\(456\) 0 0
\(457\) −1594.00 −0.163160 −0.0815801 − 0.996667i \(-0.525997\pi\)
−0.0815801 + 0.996667i \(0.525997\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5915.00 0.597590 0.298795 − 0.954317i \(-0.403415\pi\)
0.298795 + 0.954317i \(0.403415\pi\)
\(462\) 0 0
\(463\) 11072.0 1.11136 0.555680 − 0.831396i \(-0.312458\pi\)
0.555680 + 0.831396i \(0.312458\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1260.00 0.124852 0.0624260 − 0.998050i \(-0.480116\pi\)
0.0624260 + 0.998050i \(0.480116\pi\)
\(468\) 0 0
\(469\) −6214.00 −0.611804
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5226.00 −0.508016
\(474\) 0 0
\(475\) −9576.00 −0.925004
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12033.0 −1.14781 −0.573906 − 0.818921i \(-0.694572\pi\)
−0.573906 + 0.818921i \(0.694572\pi\)
\(480\) 0 0
\(481\) −1703.00 −0.161435
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 490.000 0.0458758
\(486\) 0 0
\(487\) 2280.00 0.212149 0.106075 − 0.994358i \(-0.466172\pi\)
0.106075 + 0.994358i \(0.466172\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 16767.0 1.54111 0.770554 − 0.637375i \(-0.219980\pi\)
0.770554 + 0.637375i \(0.219980\pi\)
\(492\) 0 0
\(493\) −6314.00 −0.576812
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 117.000 0.0105597
\(498\) 0 0
\(499\) −12840.0 −1.15190 −0.575949 − 0.817485i \(-0.695367\pi\)
−0.575949 + 0.817485i \(0.695367\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2198.00 −0.194839 −0.0974195 − 0.995243i \(-0.531059\pi\)
−0.0974195 + 0.995243i \(0.531059\pi\)
\(504\) 0 0
\(505\) −2940.00 −0.259066
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 17066.0 1.48612 0.743062 − 0.669223i \(-0.233373\pi\)
0.743062 + 0.669223i \(0.233373\pi\)
\(510\) 0 0
\(511\) 1274.00 0.110290
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4116.00 −0.352180
\(516\) 0 0
\(517\) 2730.00 0.232235
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −2583.00 −0.217204 −0.108602 − 0.994085i \(-0.534637\pi\)
−0.108602 + 0.994085i \(0.534637\pi\)
\(522\) 0 0
\(523\) −18620.0 −1.55678 −0.778390 − 0.627781i \(-0.783963\pi\)
−0.778390 + 0.627781i \(0.783963\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 15092.0 1.24747
\(528\) 0 0
\(529\) −2951.00 −0.242541
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4368.00 −0.354970
\(534\) 0 0
\(535\) −4788.00 −0.386922
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4524.00 0.361526
\(540\) 0 0
\(541\) −16833.0 −1.33772 −0.668861 − 0.743388i \(-0.733218\pi\)
−0.668861 + 0.743388i \(0.733218\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2611.00 0.205216
\(546\) 0 0
\(547\) 8615.00 0.673402 0.336701 − 0.941612i \(-0.390689\pi\)
0.336701 + 0.941612i \(0.390689\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 10332.0 0.798835
\(552\) 0 0
\(553\) −16952.0 −1.30357
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8535.00 −0.649263 −0.324632 − 0.945841i \(-0.605240\pi\)
−0.324632 + 0.945841i \(0.605240\pi\)
\(558\) 0 0
\(559\) 2613.00 0.197707
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4641.00 −0.347415 −0.173708 − 0.984797i \(-0.555575\pi\)
−0.173708 + 0.984797i \(0.555575\pi\)
\(564\) 0 0
\(565\) 12138.0 0.903804
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4793.00 0.353134 0.176567 − 0.984289i \(-0.443501\pi\)
0.176567 + 0.984289i \(0.443501\pi\)
\(570\) 0 0
\(571\) 5563.00 0.407713 0.203857 − 0.979001i \(-0.434652\pi\)
0.203857 + 0.979001i \(0.434652\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 7296.00 0.529155
\(576\) 0 0
\(577\) 24038.0 1.73434 0.867171 − 0.498011i \(-0.165936\pi\)
0.867171 + 0.498011i \(0.165936\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4004.00 −0.285910
\(582\) 0 0
\(583\) −11232.0 −0.797911
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −21224.0 −1.49235 −0.746174 − 0.665751i \(-0.768111\pi\)
−0.746174 + 0.665751i \(0.768111\pi\)
\(588\) 0 0
\(589\) −24696.0 −1.72764
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −4354.00 −0.301513 −0.150757 − 0.988571i \(-0.548171\pi\)
−0.150757 + 0.988571i \(0.548171\pi\)
\(594\) 0 0
\(595\) −7007.00 −0.482788
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 7310.00 0.498629 0.249314 − 0.968423i \(-0.419795\pi\)
0.249314 + 0.968423i \(0.419795\pi\)
\(600\) 0 0
\(601\) −7595.00 −0.515485 −0.257743 − 0.966214i \(-0.582979\pi\)
−0.257743 + 0.966214i \(0.582979\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4585.00 −0.308110
\(606\) 0 0
\(607\) 826.000 0.0552328 0.0276164 − 0.999619i \(-0.491208\pi\)
0.0276164 + 0.999619i \(0.491208\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1365.00 −0.0903797
\(612\) 0 0
\(613\) 14590.0 0.961312 0.480656 − 0.876909i \(-0.340398\pi\)
0.480656 + 0.876909i \(0.340398\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4888.00 −0.318936 −0.159468 − 0.987203i \(-0.550978\pi\)
−0.159468 + 0.987203i \(0.550978\pi\)
\(618\) 0 0
\(619\) 11004.0 0.714520 0.357260 − 0.934005i \(-0.383711\pi\)
0.357260 + 0.934005i \(0.383711\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 15470.0 0.994851
\(624\) 0 0
\(625\) −349.000 −0.0223360
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 10087.0 0.639420
\(630\) 0 0
\(631\) 4975.00 0.313869 0.156935 − 0.987609i \(-0.449839\pi\)
0.156935 + 0.987609i \(0.449839\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −13244.0 −0.827673
\(636\) 0 0
\(637\) −2262.00 −0.140697
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −3950.00 −0.243394 −0.121697 − 0.992567i \(-0.538834\pi\)
−0.121697 + 0.992567i \(0.538834\pi\)
\(642\) 0 0
\(643\) 3682.00 0.225823 0.112911 − 0.993605i \(-0.463982\pi\)
0.112911 + 0.993605i \(0.463982\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 10402.0 0.632063 0.316032 − 0.948749i \(-0.397649\pi\)
0.316032 + 0.948749i \(0.397649\pi\)
\(648\) 0 0
\(649\) 7644.00 0.462332
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 31680.0 1.89852 0.949260 − 0.314491i \(-0.101834\pi\)
0.949260 + 0.314491i \(0.101834\pi\)
\(654\) 0 0
\(655\) 10045.0 0.599222
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 21940.0 1.29691 0.648453 − 0.761255i \(-0.275416\pi\)
0.648453 + 0.761255i \(0.275416\pi\)
\(660\) 0 0
\(661\) −31374.0 −1.84615 −0.923077 − 0.384616i \(-0.874334\pi\)
−0.923077 + 0.384616i \(0.874334\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 11466.0 0.668620
\(666\) 0 0
\(667\) −7872.00 −0.456979
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1456.00 0.0837679
\(672\) 0 0
\(673\) 18013.0 1.03172 0.515862 − 0.856672i \(-0.327472\pi\)
0.515862 + 0.856672i \(0.327472\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10640.0 0.604030 0.302015 − 0.953303i \(-0.402341\pi\)
0.302015 + 0.953303i \(0.402341\pi\)
\(678\) 0 0
\(679\) 910.000 0.0514324
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9336.00 −0.523034 −0.261517 − 0.965199i \(-0.584223\pi\)
−0.261517 + 0.965199i \(0.584223\pi\)
\(684\) 0 0
\(685\) 12432.0 0.693434
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 5616.00 0.310526
\(690\) 0 0
\(691\) −4200.00 −0.231224 −0.115612 − 0.993294i \(-0.536883\pi\)
−0.115612 + 0.993294i \(0.536883\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 13083.0 0.714052
\(696\) 0 0
\(697\) 25872.0 1.40599
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −9872.00 −0.531898 −0.265949 − 0.963987i \(-0.585685\pi\)
−0.265949 + 0.963987i \(0.585685\pi\)
\(702\) 0 0
\(703\) −16506.0 −0.885541
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5460.00 −0.290445
\(708\) 0 0
\(709\) 28450.0 1.50700 0.753499 − 0.657449i \(-0.228364\pi\)
0.753499 + 0.657449i \(0.228364\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 18816.0 0.988310
\(714\) 0 0
\(715\) −2366.00 −0.123753
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 32718.0 1.69705 0.848523 − 0.529159i \(-0.177493\pi\)
0.848523 + 0.529159i \(0.177493\pi\)
\(720\) 0 0
\(721\) −7644.00 −0.394837
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6232.00 −0.319242
\(726\) 0 0
\(727\) 22834.0 1.16488 0.582439 − 0.812874i \(-0.302099\pi\)
0.582439 + 0.812874i \(0.302099\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −15477.0 −0.783088
\(732\) 0 0
\(733\) 7875.00 0.396821 0.198410 − 0.980119i \(-0.436422\pi\)
0.198410 + 0.980119i \(0.436422\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 12428.0 0.621155
\(738\) 0 0
\(739\) 2140.00 0.106524 0.0532620 − 0.998581i \(-0.483038\pi\)
0.0532620 + 0.998581i \(0.483038\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 31971.0 1.57860 0.789302 − 0.614006i \(-0.210443\pi\)
0.789302 + 0.614006i \(0.210443\pi\)
\(744\) 0 0
\(745\) −17262.0 −0.848900
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −8892.00 −0.433787
\(750\) 0 0
\(751\) 7432.00 0.361115 0.180558 − 0.983564i \(-0.442210\pi\)
0.180558 + 0.983564i \(0.442210\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 23261.0 1.12126
\(756\) 0 0
\(757\) 20176.0 0.968704 0.484352 − 0.874873i \(-0.339055\pi\)
0.484352 + 0.874873i \(0.339055\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 9478.00 0.451481 0.225741 − 0.974187i \(-0.427520\pi\)
0.225741 + 0.974187i \(0.427520\pi\)
\(762\) 0 0
\(763\) 4849.00 0.230073
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3822.00 −0.179928
\(768\) 0 0
\(769\) −12096.0 −0.567221 −0.283610 − 0.958940i \(-0.591532\pi\)
−0.283610 + 0.958940i \(0.591532\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −17941.0 −0.834790 −0.417395 − 0.908725i \(-0.637057\pi\)
−0.417395 + 0.908725i \(0.637057\pi\)
\(774\) 0 0
\(775\) 14896.0 0.690426
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −42336.0 −1.94717
\(780\) 0 0
\(781\) −234.000 −0.0107211
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −19110.0 −0.868873
\(786\) 0 0
\(787\) −6664.00 −0.301837 −0.150919 − 0.988546i \(-0.548223\pi\)
−0.150919 + 0.988546i \(0.548223\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 22542.0 1.01328
\(792\) 0 0
\(793\) −728.000 −0.0326003
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1442.00 0.0640882 0.0320441 − 0.999486i \(-0.489798\pi\)
0.0320441 + 0.999486i \(0.489798\pi\)
\(798\) 0 0
\(799\) 8085.00 0.357981
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2548.00 −0.111976
\(804\) 0 0
\(805\) −8736.00 −0.382489
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −30207.0 −1.31276 −0.656379 − 0.754431i \(-0.727913\pi\)
−0.656379 + 0.754431i \(0.727913\pi\)
\(810\) 0 0
\(811\) −21140.0 −0.915322 −0.457661 − 0.889127i \(-0.651313\pi\)
−0.457661 + 0.889127i \(0.651313\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 3808.00 0.163667
\(816\) 0 0
\(817\) 25326.0 1.08451
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −569.000 −0.0241879 −0.0120939 − 0.999927i \(-0.503850\pi\)
−0.0120939 + 0.999927i \(0.503850\pi\)
\(822\) 0 0
\(823\) 8538.00 0.361623 0.180812 − 0.983518i \(-0.442128\pi\)
0.180812 + 0.983518i \(0.442128\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −32702.0 −1.37504 −0.687521 − 0.726164i \(-0.741301\pi\)
−0.687521 + 0.726164i \(0.741301\pi\)
\(828\) 0 0
\(829\) −21154.0 −0.886259 −0.443130 − 0.896458i \(-0.646132\pi\)
−0.443130 + 0.896458i \(0.646132\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 13398.0 0.557279
\(834\) 0 0
\(835\) 11368.0 0.471145
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −2184.00 −0.0898690 −0.0449345 − 0.998990i \(-0.514308\pi\)
−0.0449345 + 0.998990i \(0.514308\pi\)
\(840\) 0 0
\(841\) −17665.0 −0.724302
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1183.00 0.0481615
\(846\) 0 0
\(847\) −8515.00 −0.345430
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 12576.0 0.506580
\(852\) 0 0
\(853\) 36687.0 1.47261 0.736307 − 0.676648i \(-0.236568\pi\)
0.736307 + 0.676648i \(0.236568\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −36806.0 −1.46706 −0.733529 − 0.679658i \(-0.762128\pi\)
−0.733529 + 0.679658i \(0.762128\pi\)
\(858\) 0 0
\(859\) −4900.00 −0.194628 −0.0973142 − 0.995254i \(-0.531025\pi\)
−0.0973142 + 0.995254i \(0.531025\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −13697.0 −0.540268 −0.270134 − 0.962823i \(-0.587068\pi\)
−0.270134 + 0.962823i \(0.587068\pi\)
\(864\) 0 0
\(865\) 2352.00 0.0924513
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 33904.0 1.32349
\(870\) 0 0
\(871\) −6214.00 −0.241737
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −18291.0 −0.706684
\(876\) 0 0
\(877\) 6239.00 0.240224 0.120112 − 0.992760i \(-0.461675\pi\)
0.120112 + 0.992760i \(0.461675\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −133.000 −0.00508613 −0.00254307 − 0.999997i \(-0.500809\pi\)
−0.00254307 + 0.999997i \(0.500809\pi\)
\(882\) 0 0
\(883\) 26003.0 0.991020 0.495510 − 0.868602i \(-0.334981\pi\)
0.495510 + 0.868602i \(0.334981\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −31248.0 −1.18287 −0.591435 − 0.806353i \(-0.701438\pi\)
−0.591435 + 0.806353i \(0.701438\pi\)
\(888\) 0 0
\(889\) −24596.0 −0.927923
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −13230.0 −0.495773
\(894\) 0 0
\(895\) −21203.0 −0.791886
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −16072.0 −0.596253
\(900\) 0 0
\(901\) −33264.0 −1.22995
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −196.000 −0.00719918
\(906\) 0 0
\(907\) 38253.0 1.40041 0.700204 − 0.713943i \(-0.253092\pi\)
0.700204 + 0.713943i \(0.253092\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 36374.0 1.32286 0.661429 − 0.750007i \(-0.269950\pi\)
0.661429 + 0.750007i \(0.269950\pi\)
\(912\) 0 0
\(913\) 8008.00 0.290281
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 18655.0 0.671802
\(918\) 0 0
\(919\) 27648.0 0.992408 0.496204 − 0.868206i \(-0.334727\pi\)
0.496204 + 0.868206i \(0.334727\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 117.000 0.00417237
\(924\) 0 0
\(925\) 9956.00 0.353893
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −756.000 −0.0266992 −0.0133496 − 0.999911i \(-0.504249\pi\)
−0.0133496 + 0.999911i \(0.504249\pi\)
\(930\) 0 0
\(931\) −21924.0 −0.771783
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 14014.0 0.490168
\(936\) 0 0
\(937\) 20846.0 0.726797 0.363399 − 0.931634i \(-0.381616\pi\)
0.363399 + 0.931634i \(0.381616\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 41321.0 1.43148 0.715742 − 0.698365i \(-0.246089\pi\)
0.715742 + 0.698365i \(0.246089\pi\)
\(942\) 0 0
\(943\) 32256.0 1.11389
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 54966.0 1.88612 0.943060 − 0.332624i \(-0.107934\pi\)
0.943060 + 0.332624i \(0.107934\pi\)
\(948\) 0 0
\(949\) 1274.00 0.0435783
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 44553.0 1.51439 0.757195 − 0.653189i \(-0.226569\pi\)
0.757195 + 0.653189i \(0.226569\pi\)
\(954\) 0 0
\(955\) 2954.00 0.100093
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 23088.0 0.777425
\(960\) 0 0
\(961\) 8625.00 0.289517
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 3444.00 0.114887
\(966\) 0 0
\(967\) 27907.0 0.928054 0.464027 − 0.885821i \(-0.346404\pi\)
0.464027 + 0.885821i \(0.346404\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −16443.0 −0.543441 −0.271720 − 0.962376i \(-0.587593\pi\)
−0.271720 + 0.962376i \(0.587593\pi\)
\(972\) 0 0
\(973\) 24297.0 0.800541
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 45414.0 1.48713 0.743563 − 0.668666i \(-0.233134\pi\)
0.743563 + 0.668666i \(0.233134\pi\)
\(978\) 0 0
\(979\) −30940.0 −1.01006
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −8981.00 −0.291403 −0.145702 − 0.989329i \(-0.546544\pi\)
−0.145702 + 0.989329i \(0.546544\pi\)
\(984\) 0 0
\(985\) −20937.0 −0.677267
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −19296.0 −0.620402
\(990\) 0 0
\(991\) 17414.0 0.558198 0.279099 − 0.960262i \(-0.409964\pi\)
0.279099 + 0.960262i \(0.409964\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 490.000 0.0156121
\(996\) 0 0
\(997\) −23702.0 −0.752909 −0.376454 − 0.926435i \(-0.622857\pi\)
−0.376454 + 0.926435i \(0.622857\pi\)
\(998\) 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 1872.4.a.k.1.1 1
3.2 odd 2 208.4.a.g.1.1 1
4.3 odd 2 117.4.a.b.1.1 1
12.11 even 2 13.4.a.a.1.1 ✓ 1
24.5 odd 2 832.4.a.a.1.1 1
24.11 even 2 832.4.a.r.1.1 1
52.51 odd 2 1521.4.a.a.1.1 1
60.23 odd 4 325.4.b.b.274.2 2
60.47 odd 4 325.4.b.b.274.1 2
60.59 even 2 325.4.a.d.1.1 1
84.83 odd 2 637.4.a.a.1.1 1
132.131 odd 2 1573.4.a.a.1.1 1
156.11 odd 12 169.4.e.e.147.2 4
156.23 even 6 169.4.c.a.22.1 2
156.35 even 6 169.4.c.e.146.1 2
156.47 odd 4 169.4.b.a.168.1 2
156.59 odd 12 169.4.e.e.23.1 4
156.71 odd 12 169.4.e.e.23.2 4
156.83 odd 4 169.4.b.a.168.2 2
156.95 even 6 169.4.c.a.146.1 2
156.107 even 6 169.4.c.e.22.1 2
156.119 odd 12 169.4.e.e.147.1 4
156.155 even 2 169.4.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.4.a.a.1.1 ✓ 1 12.11 even 2
117.4.a.b.1.1 1 4.3 odd 2
169.4.a.e.1.1 1 156.155 even 2
169.4.b.a.168.1 2 156.47 odd 4
169.4.b.a.168.2 2 156.83 odd 4
169.4.c.a.22.1 2 156.23 even 6
169.4.c.a.146.1 2 156.95 even 6
169.4.c.e.22.1 2 156.107 even 6
169.4.c.e.146.1 2 156.35 even 6
169.4.e.e.23.1 4 156.59 odd 12
169.4.e.e.23.2 4 156.71 odd 12
169.4.e.e.147.1 4 156.119 odd 12
169.4.e.e.147.2 4 156.11 odd 12
208.4.a.g.1.1 1 3.2 odd 2
325.4.a.d.1.1 1 60.59 even 2
325.4.b.b.274.1 2 60.47 odd 4
325.4.b.b.274.2 2 60.23 odd 4
637.4.a.a.1.1 1 84.83 odd 2
832.4.a.a.1.1 1 24.5 odd 2
832.4.a.r.1.1 1 24.11 even 2
1521.4.a.a.1.1 1 52.51 odd 2
1573.4.a.a.1.1 1 132.131 odd 2
1872.4.a.k.1.1 1 1.1 even 1 trivial