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Properties

Label 784.4.a.j.1.1
Level $784$
Weight $4$
Character 784.1
Self dual yes
Analytic conductor $46.257$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [784,4,Mod(1,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.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: \(46.2574974445\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 784.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} -7.00000 q^{5} -26.0000 q^{9} -35.0000 q^{11} -66.0000 q^{13} +7.00000 q^{15} -59.0000 q^{17} +137.000 q^{19} +7.00000 q^{23} -76.0000 q^{25} +53.0000 q^{27} +106.000 q^{29} +75.0000 q^{31} +35.0000 q^{33} +11.0000 q^{37} +66.0000 q^{39} +498.000 q^{41} -260.000 q^{43} +182.000 q^{45} -171.000 q^{47} +59.0000 q^{51} -417.000 q^{53} +245.000 q^{55} -137.000 q^{57} -17.0000 q^{59} -51.0000 q^{61} +462.000 q^{65} -439.000 q^{67} -7.00000 q^{69} +784.000 q^{71} -295.000 q^{73} +76.0000 q^{75} +495.000 q^{79} +649.000 q^{81} +932.000 q^{83} +413.000 q^{85} -106.000 q^{87} +873.000 q^{89} -75.0000 q^{93} -959.000 q^{95} +290.000 q^{97} +910.000 q^{99} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.192450 −0.0962250 − 0.995360i \(-0.530677\pi\)
−0.0962250 + 0.995360i \(0.530677\pi\)
\(4\) 0 0
\(5\) −7.00000 −0.626099 −0.313050 − 0.949737i \(-0.601351\pi\)
−0.313050 + 0.949737i \(0.601351\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −26.0000 −0.962963
\(10\) 0 0
\(11\) −35.0000 −0.959354 −0.479677 − 0.877445i \(-0.659246\pi\)
−0.479677 + 0.877445i \(0.659246\pi\)
\(12\) 0 0
\(13\) −66.0000 −1.40809 −0.704043 − 0.710158i \(-0.748624\pi\)
−0.704043 + 0.710158i \(0.748624\pi\)
\(14\) 0 0
\(15\) 7.00000 0.120493
\(16\) 0 0
\(17\) −59.0000 −0.841741 −0.420871 − 0.907121i \(-0.638275\pi\)
−0.420871 + 0.907121i \(0.638275\pi\)
\(18\) 0 0
\(19\) 137.000 1.65421 0.827104 − 0.562049i \(-0.189987\pi\)
0.827104 + 0.562049i \(0.189987\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.00000 0.0634609 0.0317305 − 0.999496i \(-0.489898\pi\)
0.0317305 + 0.999496i \(0.489898\pi\)
\(24\) 0 0
\(25\) −76.0000 −0.608000
\(26\) 0 0
\(27\) 53.0000 0.377772
\(28\) 0 0
\(29\) 106.000 0.678748 0.339374 − 0.940651i \(-0.389785\pi\)
0.339374 + 0.940651i \(0.389785\pi\)
\(30\) 0 0
\(31\) 75.0000 0.434529 0.217264 − 0.976113i \(-0.430287\pi\)
0.217264 + 0.976113i \(0.430287\pi\)
\(32\) 0 0
\(33\) 35.0000 0.184628
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 11.0000 0.0488754 0.0244377 − 0.999701i \(-0.492220\pi\)
0.0244377 + 0.999701i \(0.492220\pi\)
\(38\) 0 0
\(39\) 66.0000 0.270986
\(40\) 0 0
\(41\) 498.000 1.89694 0.948470 − 0.316867i \(-0.102631\pi\)
0.948470 + 0.316867i \(0.102631\pi\)
\(42\) 0 0
\(43\) −260.000 −0.922084 −0.461042 − 0.887378i \(-0.652524\pi\)
−0.461042 + 0.887378i \(0.652524\pi\)
\(44\) 0 0
\(45\) 182.000 0.602910
\(46\) 0 0
\(47\) −171.000 −0.530700 −0.265350 − 0.964152i \(-0.585488\pi\)
−0.265350 + 0.964152i \(0.585488\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 59.0000 0.161993
\(52\) 0 0
\(53\) −417.000 −1.08074 −0.540371 − 0.841427i \(-0.681716\pi\)
−0.540371 + 0.841427i \(0.681716\pi\)
\(54\) 0 0
\(55\) 245.000 0.600651
\(56\) 0 0
\(57\) −137.000 −0.318353
\(58\) 0 0
\(59\) −17.0000 −0.0375121 −0.0187560 − 0.999824i \(-0.505971\pi\)
−0.0187560 + 0.999824i \(0.505971\pi\)
\(60\) 0 0
\(61\) −51.0000 −0.107047 −0.0535236 − 0.998567i \(-0.517045\pi\)
−0.0535236 + 0.998567i \(0.517045\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 462.000 0.881601
\(66\) 0 0
\(67\) −439.000 −0.800483 −0.400242 − 0.916410i \(-0.631074\pi\)
−0.400242 + 0.916410i \(0.631074\pi\)
\(68\) 0 0
\(69\) −7.00000 −0.0122131
\(70\) 0 0
\(71\) 784.000 1.31047 0.655237 − 0.755423i \(-0.272569\pi\)
0.655237 + 0.755423i \(0.272569\pi\)
\(72\) 0 0
\(73\) −295.000 −0.472974 −0.236487 − 0.971635i \(-0.575996\pi\)
−0.236487 + 0.971635i \(0.575996\pi\)
\(74\) 0 0
\(75\) 76.0000 0.117010
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 495.000 0.704960 0.352480 − 0.935819i \(-0.385338\pi\)
0.352480 + 0.935819i \(0.385338\pi\)
\(80\) 0 0
\(81\) 649.000 0.890261
\(82\) 0 0
\(83\) 932.000 1.23253 0.616267 − 0.787537i \(-0.288644\pi\)
0.616267 + 0.787537i \(0.288644\pi\)
\(84\) 0 0
\(85\) 413.000 0.527013
\(86\) 0 0
\(87\) −106.000 −0.130625
\(88\) 0 0
\(89\) 873.000 1.03975 0.519875 − 0.854242i \(-0.325978\pi\)
0.519875 + 0.854242i \(0.325978\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −75.0000 −0.0836251
\(94\) 0 0
\(95\) −959.000 −1.03570
\(96\) 0 0
\(97\) 290.000 0.303557 0.151779 − 0.988415i \(-0.451500\pi\)
0.151779 + 0.988415i \(0.451500\pi\)
\(98\) 0 0
\(99\) 910.000 0.923823
\(100\) 0 0
\(101\) 1085.00 1.06893 0.534463 − 0.845192i \(-0.320514\pi\)
0.534463 + 0.845192i \(0.320514\pi\)
\(102\) 0 0
\(103\) 1553.00 1.48565 0.742823 − 0.669487i \(-0.233486\pi\)
0.742823 + 0.669487i \(0.233486\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −129.000 −0.116550 −0.0582752 − 0.998301i \(-0.518560\pi\)
−0.0582752 + 0.998301i \(0.518560\pi\)
\(108\) 0 0
\(109\) −965.000 −0.847984 −0.423992 − 0.905666i \(-0.639372\pi\)
−0.423992 + 0.905666i \(0.639372\pi\)
\(110\) 0 0
\(111\) −11.0000 −0.00940607
\(112\) 0 0
\(113\) −50.0000 −0.0416248 −0.0208124 − 0.999783i \(-0.506625\pi\)
−0.0208124 + 0.999783i \(0.506625\pi\)
\(114\) 0 0
\(115\) −49.0000 −0.0397328
\(116\) 0 0
\(117\) 1716.00 1.35593
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −106.000 −0.0796394
\(122\) 0 0
\(123\) −498.000 −0.365066
\(124\) 0 0
\(125\) 1407.00 1.00677
\(126\) 0 0
\(127\) −936.000 −0.653989 −0.326994 − 0.945026i \(-0.606036\pi\)
−0.326994 + 0.945026i \(0.606036\pi\)
\(128\) 0 0
\(129\) 260.000 0.177455
\(130\) 0 0
\(131\) −755.000 −0.503547 −0.251773 − 0.967786i \(-0.581014\pi\)
−0.251773 + 0.967786i \(0.581014\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −371.000 −0.236523
\(136\) 0 0
\(137\) −2357.00 −1.46987 −0.734935 − 0.678138i \(-0.762787\pi\)
−0.734935 + 0.678138i \(0.762787\pi\)
\(138\) 0 0
\(139\) 28.0000 0.0170858 0.00854291 − 0.999964i \(-0.497281\pi\)
0.00854291 + 0.999964i \(0.497281\pi\)
\(140\) 0 0
\(141\) 171.000 0.102133
\(142\) 0 0
\(143\) 2310.00 1.35085
\(144\) 0 0
\(145\) −742.000 −0.424964
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2295.00 1.26184 0.630919 − 0.775849i \(-0.282678\pi\)
0.630919 + 0.775849i \(0.282678\pi\)
\(150\) 0 0
\(151\) 1109.00 0.597676 0.298838 − 0.954304i \(-0.403401\pi\)
0.298838 + 0.954304i \(0.403401\pi\)
\(152\) 0 0
\(153\) 1534.00 0.810566
\(154\) 0 0
\(155\) −525.000 −0.272058
\(156\) 0 0
\(157\) −1559.00 −0.792495 −0.396248 − 0.918144i \(-0.629688\pi\)
−0.396248 + 0.918144i \(0.629688\pi\)
\(158\) 0 0
\(159\) 417.000 0.207989
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2251.00 1.08167 0.540834 − 0.841129i \(-0.318109\pi\)
0.540834 + 0.841129i \(0.318109\pi\)
\(164\) 0 0
\(165\) −245.000 −0.115595
\(166\) 0 0
\(167\) 2788.00 1.29187 0.645934 − 0.763393i \(-0.276468\pi\)
0.645934 + 0.763393i \(0.276468\pi\)
\(168\) 0 0
\(169\) 2159.00 0.982704
\(170\) 0 0
\(171\) −3562.00 −1.59294
\(172\) 0 0
\(173\) −1579.00 −0.693926 −0.346963 − 0.937879i \(-0.612787\pi\)
−0.346963 + 0.937879i \(0.612787\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 17.0000 0.00721920
\(178\) 0 0
\(179\) −2451.00 −1.02344 −0.511722 − 0.859151i \(-0.670992\pi\)
−0.511722 + 0.859151i \(0.670992\pi\)
\(180\) 0 0
\(181\) 1170.00 0.480472 0.240236 − 0.970715i \(-0.422775\pi\)
0.240236 + 0.970715i \(0.422775\pi\)
\(182\) 0 0
\(183\) 51.0000 0.0206012
\(184\) 0 0
\(185\) −77.0000 −0.0306008
\(186\) 0 0
\(187\) 2065.00 0.807528
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1275.00 0.483014 0.241507 − 0.970399i \(-0.422358\pi\)
0.241507 + 0.970399i \(0.422358\pi\)
\(192\) 0 0
\(193\) 35.0000 0.0130537 0.00652683 − 0.999979i \(-0.497922\pi\)
0.00652683 + 0.999979i \(0.497922\pi\)
\(194\) 0 0
\(195\) −462.000 −0.169664
\(196\) 0 0
\(197\) −2734.00 −0.988779 −0.494389 − 0.869241i \(-0.664608\pi\)
−0.494389 + 0.869241i \(0.664608\pi\)
\(198\) 0 0
\(199\) 2243.00 0.799005 0.399503 − 0.916732i \(-0.369183\pi\)
0.399503 + 0.916732i \(0.369183\pi\)
\(200\) 0 0
\(201\) 439.000 0.154053
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −3486.00 −1.18767
\(206\) 0 0
\(207\) −182.000 −0.0611105
\(208\) 0 0
\(209\) −4795.00 −1.58697
\(210\) 0 0
\(211\) −1172.00 −0.382388 −0.191194 − 0.981552i \(-0.561236\pi\)
−0.191194 + 0.981552i \(0.561236\pi\)
\(212\) 0 0
\(213\) −784.000 −0.252201
\(214\) 0 0
\(215\) 1820.00 0.577316
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 295.000 0.0910240
\(220\) 0 0
\(221\) 3894.00 1.18524
\(222\) 0 0
\(223\) 2024.00 0.607790 0.303895 − 0.952706i \(-0.401713\pi\)
0.303895 + 0.952706i \(0.401713\pi\)
\(224\) 0 0
\(225\) 1976.00 0.585481
\(226\) 0 0
\(227\) 2571.00 0.751732 0.375866 − 0.926674i \(-0.377345\pi\)
0.375866 + 0.926674i \(0.377345\pi\)
\(228\) 0 0
\(229\) −895.000 −0.258268 −0.129134 − 0.991627i \(-0.541220\pi\)
−0.129134 + 0.991627i \(0.541220\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1787.00 0.502447 0.251224 − 0.967929i \(-0.419167\pi\)
0.251224 + 0.967929i \(0.419167\pi\)
\(234\) 0 0
\(235\) 1197.00 0.332271
\(236\) 0 0
\(237\) −495.000 −0.135670
\(238\) 0 0
\(239\) 5100.00 1.38030 0.690150 − 0.723667i \(-0.257545\pi\)
0.690150 + 0.723667i \(0.257545\pi\)
\(240\) 0 0
\(241\) 4177.00 1.11645 0.558225 − 0.829690i \(-0.311483\pi\)
0.558225 + 0.829690i \(0.311483\pi\)
\(242\) 0 0
\(243\) −2080.00 −0.549103
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −9042.00 −2.32927
\(248\) 0 0
\(249\) −932.000 −0.237201
\(250\) 0 0
\(251\) −4680.00 −1.17689 −0.588444 − 0.808538i \(-0.700259\pi\)
−0.588444 + 0.808538i \(0.700259\pi\)
\(252\) 0 0
\(253\) −245.000 −0.0608815
\(254\) 0 0
\(255\) −413.000 −0.101424
\(256\) 0 0
\(257\) 1749.00 0.424512 0.212256 − 0.977214i \(-0.431919\pi\)
0.212256 + 0.977214i \(0.431919\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −2756.00 −0.653610
\(262\) 0 0
\(263\) 4473.00 1.04873 0.524367 − 0.851492i \(-0.324302\pi\)
0.524367 + 0.851492i \(0.324302\pi\)
\(264\) 0 0
\(265\) 2919.00 0.676652
\(266\) 0 0
\(267\) −873.000 −0.200100
\(268\) 0 0
\(269\) −1975.00 −0.447650 −0.223825 − 0.974629i \(-0.571854\pi\)
−0.223825 + 0.974629i \(0.571854\pi\)
\(270\) 0 0
\(271\) −8439.00 −1.89163 −0.945817 − 0.324701i \(-0.894736\pi\)
−0.945817 + 0.324701i \(0.894736\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2660.00 0.583287
\(276\) 0 0
\(277\) 527.000 0.114312 0.0571559 − 0.998365i \(-0.481797\pi\)
0.0571559 + 0.998365i \(0.481797\pi\)
\(278\) 0 0
\(279\) −1950.00 −0.418435
\(280\) 0 0
\(281\) −202.000 −0.0428837 −0.0214418 − 0.999770i \(-0.506826\pi\)
−0.0214418 + 0.999770i \(0.506826\pi\)
\(282\) 0 0
\(283\) −7949.00 −1.66968 −0.834839 − 0.550494i \(-0.814439\pi\)
−0.834839 + 0.550494i \(0.814439\pi\)
\(284\) 0 0
\(285\) 959.000 0.199320
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1432.00 −0.291472
\(290\) 0 0
\(291\) −290.000 −0.0584196
\(292\) 0 0
\(293\) −318.000 −0.0634053 −0.0317027 − 0.999497i \(-0.510093\pi\)
−0.0317027 + 0.999497i \(0.510093\pi\)
\(294\) 0 0
\(295\) 119.000 0.0234863
\(296\) 0 0
\(297\) −1855.00 −0.362418
\(298\) 0 0
\(299\) −462.000 −0.0893584
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −1085.00 −0.205715
\(304\) 0 0
\(305\) 357.000 0.0670222
\(306\) 0 0
\(307\) −8132.00 −1.51178 −0.755892 − 0.654696i \(-0.772797\pi\)
−0.755892 + 0.654696i \(0.772797\pi\)
\(308\) 0 0
\(309\) −1553.00 −0.285913
\(310\) 0 0
\(311\) −929.000 −0.169385 −0.0846925 − 0.996407i \(-0.526991\pi\)
−0.0846925 + 0.996407i \(0.526991\pi\)
\(312\) 0 0
\(313\) 209.000 0.0377424 0.0188712 − 0.999822i \(-0.493993\pi\)
0.0188712 + 0.999822i \(0.493993\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7131.00 1.26346 0.631730 − 0.775188i \(-0.282345\pi\)
0.631730 + 0.775188i \(0.282345\pi\)
\(318\) 0 0
\(319\) −3710.00 −0.651160
\(320\) 0 0
\(321\) 129.000 0.0224301
\(322\) 0 0
\(323\) −8083.00 −1.39242
\(324\) 0 0
\(325\) 5016.00 0.856116
\(326\) 0 0
\(327\) 965.000 0.163195
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 6571.00 1.09116 0.545581 − 0.838058i \(-0.316309\pi\)
0.545581 + 0.838058i \(0.316309\pi\)
\(332\) 0 0
\(333\) −286.000 −0.0470652
\(334\) 0 0
\(335\) 3073.00 0.501182
\(336\) 0 0
\(337\) −11466.0 −1.85339 −0.926696 − 0.375813i \(-0.877364\pi\)
−0.926696 + 0.375813i \(0.877364\pi\)
\(338\) 0 0
\(339\) 50.0000 0.00801070
\(340\) 0 0
\(341\) −2625.00 −0.416867
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 49.0000 0.00764658
\(346\) 0 0
\(347\) 9777.00 1.51256 0.756278 − 0.654251i \(-0.227016\pi\)
0.756278 + 0.654251i \(0.227016\pi\)
\(348\) 0 0
\(349\) −11914.0 −1.82734 −0.913670 − 0.406456i \(-0.866764\pi\)
−0.913670 + 0.406456i \(0.866764\pi\)
\(350\) 0 0
\(351\) −3498.00 −0.531936
\(352\) 0 0
\(353\) −9123.00 −1.37555 −0.687774 − 0.725925i \(-0.741412\pi\)
−0.687774 + 0.725925i \(0.741412\pi\)
\(354\) 0 0
\(355\) −5488.00 −0.820487
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8149.00 −1.19802 −0.599008 − 0.800743i \(-0.704438\pi\)
−0.599008 + 0.800743i \(0.704438\pi\)
\(360\) 0 0
\(361\) 11910.0 1.73640
\(362\) 0 0
\(363\) 106.000 0.0153266
\(364\) 0 0
\(365\) 2065.00 0.296129
\(366\) 0 0
\(367\) 9671.00 1.37554 0.687769 − 0.725930i \(-0.258590\pi\)
0.687769 + 0.725930i \(0.258590\pi\)
\(368\) 0 0
\(369\) −12948.0 −1.82668
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −4109.00 −0.570391 −0.285196 − 0.958469i \(-0.592059\pi\)
−0.285196 + 0.958469i \(0.592059\pi\)
\(374\) 0 0
\(375\) −1407.00 −0.193752
\(376\) 0 0
\(377\) −6996.00 −0.955736
\(378\) 0 0
\(379\) 3488.00 0.472735 0.236367 − 0.971664i \(-0.424043\pi\)
0.236367 + 0.971664i \(0.424043\pi\)
\(380\) 0 0
\(381\) 936.000 0.125860
\(382\) 0 0
\(383\) 8717.00 1.16297 0.581485 − 0.813557i \(-0.302472\pi\)
0.581485 + 0.813557i \(0.302472\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 6760.00 0.887933
\(388\) 0 0
\(389\) 163.000 0.0212453 0.0106227 − 0.999944i \(-0.496619\pi\)
0.0106227 + 0.999944i \(0.496619\pi\)
\(390\) 0 0
\(391\) −413.000 −0.0534177
\(392\) 0 0
\(393\) 755.000 0.0969077
\(394\) 0 0
\(395\) −3465.00 −0.441375
\(396\) 0 0
\(397\) −999.000 −0.126293 −0.0631466 − 0.998004i \(-0.520114\pi\)
−0.0631466 + 0.998004i \(0.520114\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −14757.0 −1.83773 −0.918865 − 0.394573i \(-0.870893\pi\)
−0.918865 + 0.394573i \(0.870893\pi\)
\(402\) 0 0
\(403\) −4950.00 −0.611854
\(404\) 0 0
\(405\) −4543.00 −0.557391
\(406\) 0 0
\(407\) −385.000 −0.0468888
\(408\) 0 0
\(409\) 133.000 0.0160793 0.00803964 − 0.999968i \(-0.497441\pi\)
0.00803964 + 0.999968i \(0.497441\pi\)
\(410\) 0 0
\(411\) 2357.00 0.282876
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −6524.00 −0.771688
\(416\) 0 0
\(417\) −28.0000 −0.00328817
\(418\) 0 0
\(419\) −6420.00 −0.748538 −0.374269 − 0.927320i \(-0.622106\pi\)
−0.374269 + 0.927320i \(0.622106\pi\)
\(420\) 0 0
\(421\) 10266.0 1.18844 0.594221 − 0.804302i \(-0.297460\pi\)
0.594221 + 0.804302i \(0.297460\pi\)
\(422\) 0 0
\(423\) 4446.00 0.511045
\(424\) 0 0
\(425\) 4484.00 0.511779
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −2310.00 −0.259972
\(430\) 0 0
\(431\) 15213.0 1.70020 0.850098 − 0.526625i \(-0.176543\pi\)
0.850098 + 0.526625i \(0.176543\pi\)
\(432\) 0 0
\(433\) 1378.00 0.152939 0.0764693 − 0.997072i \(-0.475635\pi\)
0.0764693 + 0.997072i \(0.475635\pi\)
\(434\) 0 0
\(435\) 742.000 0.0817843
\(436\) 0 0
\(437\) 959.000 0.104978
\(438\) 0 0
\(439\) −2763.00 −0.300389 −0.150195 − 0.988656i \(-0.547990\pi\)
−0.150195 + 0.988656i \(0.547990\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5849.00 −0.627301 −0.313651 − 0.949538i \(-0.601552\pi\)
−0.313651 + 0.949538i \(0.601552\pi\)
\(444\) 0 0
\(445\) −6111.00 −0.650987
\(446\) 0 0
\(447\) −2295.00 −0.242841
\(448\) 0 0
\(449\) 4582.00 0.481599 0.240799 − 0.970575i \(-0.422590\pi\)
0.240799 + 0.970575i \(0.422590\pi\)
\(450\) 0 0
\(451\) −17430.0 −1.81984
\(452\) 0 0
\(453\) −1109.00 −0.115023
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 11551.0 1.18235 0.591174 − 0.806544i \(-0.298665\pi\)
0.591174 + 0.806544i \(0.298665\pi\)
\(458\) 0 0
\(459\) −3127.00 −0.317987
\(460\) 0 0
\(461\) 9494.00 0.959175 0.479587 − 0.877494i \(-0.340786\pi\)
0.479587 + 0.877494i \(0.340786\pi\)
\(462\) 0 0
\(463\) 10160.0 1.01982 0.509908 − 0.860229i \(-0.329679\pi\)
0.509908 + 0.860229i \(0.329679\pi\)
\(464\) 0 0
\(465\) 525.000 0.0523576
\(466\) 0 0
\(467\) −1307.00 −0.129509 −0.0647545 − 0.997901i \(-0.520626\pi\)
−0.0647545 + 0.997901i \(0.520626\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 1559.00 0.152516
\(472\) 0 0
\(473\) 9100.00 0.884606
\(474\) 0 0
\(475\) −10412.0 −1.00576
\(476\) 0 0
\(477\) 10842.0 1.04072
\(478\) 0 0
\(479\) 18287.0 1.74437 0.872186 − 0.489174i \(-0.162702\pi\)
0.872186 + 0.489174i \(0.162702\pi\)
\(480\) 0 0
\(481\) −726.000 −0.0688207
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2030.00 −0.190057
\(486\) 0 0
\(487\) 14953.0 1.39135 0.695673 − 0.718359i \(-0.255106\pi\)
0.695673 + 0.718359i \(0.255106\pi\)
\(488\) 0 0
\(489\) −2251.00 −0.208167
\(490\) 0 0
\(491\) −14352.0 −1.31914 −0.659569 − 0.751644i \(-0.729261\pi\)
−0.659569 + 0.751644i \(0.729261\pi\)
\(492\) 0 0
\(493\) −6254.00 −0.571331
\(494\) 0 0
\(495\) −6370.00 −0.578404
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 5531.00 0.496196 0.248098 − 0.968735i \(-0.420195\pi\)
0.248098 + 0.968735i \(0.420195\pi\)
\(500\) 0 0
\(501\) −2788.00 −0.248620
\(502\) 0 0
\(503\) 8400.00 0.744607 0.372304 − 0.928111i \(-0.378568\pi\)
0.372304 + 0.928111i \(0.378568\pi\)
\(504\) 0 0
\(505\) −7595.00 −0.669254
\(506\) 0 0
\(507\) −2159.00 −0.189121
\(508\) 0 0
\(509\) 2385.00 0.207688 0.103844 − 0.994594i \(-0.466886\pi\)
0.103844 + 0.994594i \(0.466886\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 7261.00 0.624914
\(514\) 0 0
\(515\) −10871.0 −0.930162
\(516\) 0 0
\(517\) 5985.00 0.509130
\(518\) 0 0
\(519\) 1579.00 0.133546
\(520\) 0 0
\(521\) 9153.00 0.769674 0.384837 − 0.922985i \(-0.374258\pi\)
0.384837 + 0.922985i \(0.374258\pi\)
\(522\) 0 0
\(523\) −13807.0 −1.15437 −0.577187 − 0.816612i \(-0.695850\pi\)
−0.577187 + 0.816612i \(0.695850\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4425.00 −0.365761
\(528\) 0 0
\(529\) −12118.0 −0.995973
\(530\) 0 0
\(531\) 442.000 0.0361227
\(532\) 0 0
\(533\) −32868.0 −2.67105
\(534\) 0 0
\(535\) 903.000 0.0729721
\(536\) 0 0
\(537\) 2451.00 0.196962
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 8175.00 0.649669 0.324834 − 0.945771i \(-0.394691\pi\)
0.324834 + 0.945771i \(0.394691\pi\)
\(542\) 0 0
\(543\) −1170.00 −0.0924669
\(544\) 0 0
\(545\) 6755.00 0.530922
\(546\) 0 0
\(547\) −4656.00 −0.363942 −0.181971 − 0.983304i \(-0.558248\pi\)
−0.181971 + 0.983304i \(0.558248\pi\)
\(548\) 0 0
\(549\) 1326.00 0.103083
\(550\) 0 0
\(551\) 14522.0 1.12279
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 77.0000 0.00588913
\(556\) 0 0
\(557\) 7003.00 0.532723 0.266361 − 0.963873i \(-0.414179\pi\)
0.266361 + 0.963873i \(0.414179\pi\)
\(558\) 0 0
\(559\) 17160.0 1.29837
\(560\) 0 0
\(561\) −2065.00 −0.155409
\(562\) 0 0
\(563\) −19753.0 −1.47867 −0.739334 − 0.673339i \(-0.764859\pi\)
−0.739334 + 0.673339i \(0.764859\pi\)
\(564\) 0 0
\(565\) 350.000 0.0260613
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6897.00 −0.508150 −0.254075 − 0.967185i \(-0.581771\pi\)
−0.254075 + 0.967185i \(0.581771\pi\)
\(570\) 0 0
\(571\) −24915.0 −1.82603 −0.913013 − 0.407932i \(-0.866250\pi\)
−0.913013 + 0.407932i \(0.866250\pi\)
\(572\) 0 0
\(573\) −1275.00 −0.0929562
\(574\) 0 0
\(575\) −532.000 −0.0385842
\(576\) 0 0
\(577\) −127.000 −0.00916305 −0.00458152 − 0.999990i \(-0.501458\pi\)
−0.00458152 + 0.999990i \(0.501458\pi\)
\(578\) 0 0
\(579\) −35.0000 −0.00251218
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 14595.0 1.03681
\(584\) 0 0
\(585\) −12012.0 −0.848949
\(586\) 0 0
\(587\) 9044.00 0.635921 0.317961 − 0.948104i \(-0.397002\pi\)
0.317961 + 0.948104i \(0.397002\pi\)
\(588\) 0 0
\(589\) 10275.0 0.718801
\(590\) 0 0
\(591\) 2734.00 0.190291
\(592\) 0 0
\(593\) 10701.0 0.741041 0.370521 − 0.928824i \(-0.379179\pi\)
0.370521 + 0.928824i \(0.379179\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2243.00 −0.153769
\(598\) 0 0
\(599\) −20799.0 −1.41874 −0.709369 − 0.704837i \(-0.751020\pi\)
−0.709369 + 0.704837i \(0.751020\pi\)
\(600\) 0 0
\(601\) 1402.00 0.0951560 0.0475780 − 0.998868i \(-0.484850\pi\)
0.0475780 + 0.998868i \(0.484850\pi\)
\(602\) 0 0
\(603\) 11414.0 0.770836
\(604\) 0 0
\(605\) 742.000 0.0498621
\(606\) 0 0
\(607\) 6525.00 0.436312 0.218156 − 0.975914i \(-0.429996\pi\)
0.218156 + 0.975914i \(0.429996\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 11286.0 0.747271
\(612\) 0 0
\(613\) 15051.0 0.991687 0.495844 − 0.868412i \(-0.334859\pi\)
0.495844 + 0.868412i \(0.334859\pi\)
\(614\) 0 0
\(615\) 3486.00 0.228568
\(616\) 0 0
\(617\) 11150.0 0.727524 0.363762 − 0.931492i \(-0.381492\pi\)
0.363762 + 0.931492i \(0.381492\pi\)
\(618\) 0 0
\(619\) 3415.00 0.221745 0.110873 − 0.993835i \(-0.464635\pi\)
0.110873 + 0.993835i \(0.464635\pi\)
\(620\) 0 0
\(621\) 371.000 0.0239738
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −349.000 −0.0223360
\(626\) 0 0
\(627\) 4795.00 0.305413
\(628\) 0 0
\(629\) −649.000 −0.0411404
\(630\) 0 0
\(631\) 21184.0 1.33648 0.668242 − 0.743944i \(-0.267047\pi\)
0.668242 + 0.743944i \(0.267047\pi\)
\(632\) 0 0
\(633\) 1172.00 0.0735905
\(634\) 0 0
\(635\) 6552.00 0.409462
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −20384.0 −1.26194
\(640\) 0 0
\(641\) −10705.0 −0.659629 −0.329814 − 0.944046i \(-0.606986\pi\)
−0.329814 + 0.944046i \(0.606986\pi\)
\(642\) 0 0
\(643\) 6860.00 0.420734 0.210367 − 0.977622i \(-0.432534\pi\)
0.210367 + 0.977622i \(0.432534\pi\)
\(644\) 0 0
\(645\) −1820.00 −0.111105
\(646\) 0 0
\(647\) 14463.0 0.878824 0.439412 − 0.898286i \(-0.355187\pi\)
0.439412 + 0.898286i \(0.355187\pi\)
\(648\) 0 0
\(649\) 595.000 0.0359874
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5979.00 0.358310 0.179155 − 0.983821i \(-0.442664\pi\)
0.179155 + 0.983821i \(0.442664\pi\)
\(654\) 0 0
\(655\) 5285.00 0.315270
\(656\) 0 0
\(657\) 7670.00 0.455457
\(658\) 0 0
\(659\) 6940.00 0.410234 0.205117 − 0.978737i \(-0.434243\pi\)
0.205117 + 0.978737i \(0.434243\pi\)
\(660\) 0 0
\(661\) −13399.0 −0.788443 −0.394221 − 0.919015i \(-0.628986\pi\)
−0.394221 + 0.919015i \(0.628986\pi\)
\(662\) 0 0
\(663\) −3894.00 −0.228100
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 742.000 0.0430740
\(668\) 0 0
\(669\) −2024.00 −0.116969
\(670\) 0 0
\(671\) 1785.00 0.102696
\(672\) 0 0
\(673\) 29510.0 1.69023 0.845117 − 0.534582i \(-0.179531\pi\)
0.845117 + 0.534582i \(0.179531\pi\)
\(674\) 0 0
\(675\) −4028.00 −0.229686
\(676\) 0 0
\(677\) 26001.0 1.47607 0.738035 − 0.674762i \(-0.235754\pi\)
0.738035 + 0.674762i \(0.235754\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −2571.00 −0.144671
\(682\) 0 0
\(683\) 8805.00 0.493285 0.246643 − 0.969106i \(-0.420673\pi\)
0.246643 + 0.969106i \(0.420673\pi\)
\(684\) 0 0
\(685\) 16499.0 0.920284
\(686\) 0 0
\(687\) 895.000 0.0497036
\(688\) 0 0
\(689\) 27522.0 1.52178
\(690\) 0 0
\(691\) 28685.0 1.57920 0.789601 − 0.613620i \(-0.210287\pi\)
0.789601 + 0.613620i \(0.210287\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −196.000 −0.0106974
\(696\) 0 0
\(697\) −29382.0 −1.59673
\(698\) 0 0
\(699\) −1787.00 −0.0966961
\(700\) 0 0
\(701\) −3146.00 −0.169505 −0.0847523 − 0.996402i \(-0.527010\pi\)
−0.0847523 + 0.996402i \(0.527010\pi\)
\(702\) 0 0
\(703\) 1507.00 0.0808500
\(704\) 0 0
\(705\) −1197.00 −0.0639456
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1259.00 0.0666893 0.0333447 − 0.999444i \(-0.489384\pi\)
0.0333447 + 0.999444i \(0.489384\pi\)
\(710\) 0 0
\(711\) −12870.0 −0.678851
\(712\) 0 0
\(713\) 525.000 0.0275756
\(714\) 0 0
\(715\) −16170.0 −0.845767
\(716\) 0 0
\(717\) −5100.00 −0.265639
\(718\) 0 0
\(719\) 16425.0 0.851946 0.425973 − 0.904736i \(-0.359932\pi\)
0.425973 + 0.904736i \(0.359932\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −4177.00 −0.214861
\(724\) 0 0
\(725\) −8056.00 −0.412679
\(726\) 0 0
\(727\) −6032.00 −0.307723 −0.153861 − 0.988092i \(-0.549171\pi\)
−0.153861 + 0.988092i \(0.549171\pi\)
\(728\) 0 0
\(729\) −15443.0 −0.784586
\(730\) 0 0
\(731\) 15340.0 0.776156
\(732\) 0 0
\(733\) −15243.0 −0.768094 −0.384047 − 0.923314i \(-0.625470\pi\)
−0.384047 + 0.923314i \(0.625470\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 15365.0 0.767947
\(738\) 0 0
\(739\) 10053.0 0.500414 0.250207 − 0.968192i \(-0.419501\pi\)
0.250207 + 0.968192i \(0.419501\pi\)
\(740\) 0 0
\(741\) 9042.00 0.448267
\(742\) 0 0
\(743\) −24384.0 −1.20399 −0.601993 − 0.798501i \(-0.705627\pi\)
−0.601993 + 0.798501i \(0.705627\pi\)
\(744\) 0 0
\(745\) −16065.0 −0.790035
\(746\) 0 0
\(747\) −24232.0 −1.18688
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −11589.0 −0.563101 −0.281550 − 0.959546i \(-0.590849\pi\)
−0.281550 + 0.959546i \(0.590849\pi\)
\(752\) 0 0
\(753\) 4680.00 0.226492
\(754\) 0 0
\(755\) −7763.00 −0.374205
\(756\) 0 0
\(757\) 14562.0 0.699161 0.349581 − 0.936906i \(-0.386324\pi\)
0.349581 + 0.936906i \(0.386324\pi\)
\(758\) 0 0
\(759\) 245.000 0.0117166
\(760\) 0 0
\(761\) 22765.0 1.08440 0.542201 − 0.840249i \(-0.317591\pi\)
0.542201 + 0.840249i \(0.317591\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −10738.0 −0.507494
\(766\) 0 0
\(767\) 1122.00 0.0528202
\(768\) 0 0
\(769\) −3766.00 −0.176600 −0.0883000 − 0.996094i \(-0.528143\pi\)
−0.0883000 + 0.996094i \(0.528143\pi\)
\(770\) 0 0
\(771\) −1749.00 −0.0816974
\(772\) 0 0
\(773\) 26861.0 1.24984 0.624918 − 0.780691i \(-0.285132\pi\)
0.624918 + 0.780691i \(0.285132\pi\)
\(774\) 0 0
\(775\) −5700.00 −0.264194
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 68226.0 3.13793
\(780\) 0 0
\(781\) −27440.0 −1.25721
\(782\) 0 0
\(783\) 5618.00 0.256412
\(784\) 0 0
\(785\) 10913.0 0.496180
\(786\) 0 0
\(787\) −2097.00 −0.0949809 −0.0474905 − 0.998872i \(-0.515122\pi\)
−0.0474905 + 0.998872i \(0.515122\pi\)
\(788\) 0 0
\(789\) −4473.00 −0.201829
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 3366.00 0.150732
\(794\) 0 0
\(795\) −2919.00 −0.130222
\(796\) 0 0
\(797\) 35334.0 1.57038 0.785191 − 0.619254i \(-0.212565\pi\)
0.785191 + 0.619254i \(0.212565\pi\)
\(798\) 0 0
\(799\) 10089.0 0.446712
\(800\) 0 0
\(801\) −22698.0 −1.00124
\(802\) 0 0
\(803\) 10325.0 0.453750
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1975.00 0.0861503
\(808\) 0 0
\(809\) 42535.0 1.84852 0.924259 − 0.381766i \(-0.124684\pi\)
0.924259 + 0.381766i \(0.124684\pi\)
\(810\) 0 0
\(811\) 30676.0 1.32821 0.664106 − 0.747638i \(-0.268812\pi\)
0.664106 + 0.747638i \(0.268812\pi\)
\(812\) 0 0
\(813\) 8439.00 0.364045
\(814\) 0 0
\(815\) −15757.0 −0.677231
\(816\) 0 0
\(817\) −35620.0 −1.52532
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 37343.0 1.58743 0.793715 − 0.608290i \(-0.208144\pi\)
0.793715 + 0.608290i \(0.208144\pi\)
\(822\) 0 0
\(823\) −2815.00 −0.119228 −0.0596141 − 0.998222i \(-0.518987\pi\)
−0.0596141 + 0.998222i \(0.518987\pi\)
\(824\) 0 0
\(825\) −2660.00 −0.112254
\(826\) 0 0
\(827\) 9276.00 0.390034 0.195017 − 0.980800i \(-0.437524\pi\)
0.195017 + 0.980800i \(0.437524\pi\)
\(828\) 0 0
\(829\) −18571.0 −0.778043 −0.389021 − 0.921229i \(-0.627187\pi\)
−0.389021 + 0.921229i \(0.627187\pi\)
\(830\) 0 0
\(831\) −527.000 −0.0219993
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −19516.0 −0.808837
\(836\) 0 0
\(837\) 3975.00 0.164153
\(838\) 0 0
\(839\) 29048.0 1.19529 0.597645 − 0.801761i \(-0.296103\pi\)
0.597645 + 0.801761i \(0.296103\pi\)
\(840\) 0 0
\(841\) −13153.0 −0.539301
\(842\) 0 0
\(843\) 202.000 0.00825297
\(844\) 0 0
\(845\) −15113.0 −0.615270
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 7949.00 0.321330
\(850\) 0 0
\(851\) 77.0000 0.00310168
\(852\) 0 0
\(853\) −32090.0 −1.28809 −0.644045 − 0.764988i \(-0.722745\pi\)
−0.644045 + 0.764988i \(0.722745\pi\)
\(854\) 0 0
\(855\) 24934.0 0.997339
\(856\) 0 0
\(857\) 24537.0 0.978026 0.489013 − 0.872277i \(-0.337357\pi\)
0.489013 + 0.872277i \(0.337357\pi\)
\(858\) 0 0
\(859\) 20825.0 0.827171 0.413585 − 0.910465i \(-0.364276\pi\)
0.413585 + 0.910465i \(0.364276\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 22847.0 0.901183 0.450591 − 0.892730i \(-0.351213\pi\)
0.450591 + 0.892730i \(0.351213\pi\)
\(864\) 0 0
\(865\) 11053.0 0.434466
\(866\) 0 0
\(867\) 1432.00 0.0560937
\(868\) 0 0
\(869\) −17325.0 −0.676307
\(870\) 0 0
\(871\) 28974.0 1.12715
\(872\) 0 0
\(873\) −7540.00 −0.292314
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −42737.0 −1.64553 −0.822763 − 0.568385i \(-0.807568\pi\)
−0.822763 + 0.568385i \(0.807568\pi\)
\(878\) 0 0
\(879\) 318.000 0.0122024
\(880\) 0 0
\(881\) −6162.00 −0.235645 −0.117822 − 0.993035i \(-0.537591\pi\)
−0.117822 + 0.993035i \(0.537591\pi\)
\(882\) 0 0
\(883\) −7748.00 −0.295290 −0.147645 − 0.989040i \(-0.547169\pi\)
−0.147645 + 0.989040i \(0.547169\pi\)
\(884\) 0 0
\(885\) −119.000 −0.00451993
\(886\) 0 0
\(887\) −25923.0 −0.981296 −0.490648 − 0.871358i \(-0.663240\pi\)
−0.490648 + 0.871358i \(0.663240\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −22715.0 −0.854075
\(892\) 0 0
\(893\) −23427.0 −0.877889
\(894\) 0 0
\(895\) 17157.0 0.640777
\(896\) 0 0
\(897\) 462.000 0.0171970
\(898\) 0 0
\(899\) 7950.00 0.294936
\(900\) 0 0
\(901\) 24603.0 0.909706
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −8190.00 −0.300823
\(906\) 0 0
\(907\) −31935.0 −1.16911 −0.584556 − 0.811353i \(-0.698731\pi\)
−0.584556 + 0.811353i \(0.698731\pi\)
\(908\) 0 0
\(909\) −28210.0 −1.02934
\(910\) 0 0
\(911\) −3408.00 −0.123943 −0.0619715 − 0.998078i \(-0.519739\pi\)
−0.0619715 + 0.998078i \(0.519739\pi\)
\(912\) 0 0
\(913\) −32620.0 −1.18244
\(914\) 0 0
\(915\) −357.000 −0.0128984
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −13909.0 −0.499255 −0.249628 − 0.968342i \(-0.580308\pi\)
−0.249628 + 0.968342i \(0.580308\pi\)
\(920\) 0 0
\(921\) 8132.00 0.290943
\(922\) 0 0
\(923\) −51744.0 −1.84526
\(924\) 0 0
\(925\) −836.000 −0.0297162
\(926\) 0 0
\(927\) −40378.0 −1.43062
\(928\) 0 0
\(929\) 24537.0 0.866559 0.433279 − 0.901260i \(-0.357356\pi\)
0.433279 + 0.901260i \(0.357356\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 929.000 0.0325982
\(934\) 0 0
\(935\) −14455.0 −0.505593
\(936\) 0 0
\(937\) 32758.0 1.14211 0.571055 − 0.820912i \(-0.306534\pi\)
0.571055 + 0.820912i \(0.306534\pi\)
\(938\) 0 0
\(939\) −209.000 −0.00726353
\(940\) 0 0
\(941\) 38561.0 1.33587 0.667934 − 0.744220i \(-0.267179\pi\)
0.667934 + 0.744220i \(0.267179\pi\)
\(942\) 0 0
\(943\) 3486.00 0.120382
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −39661.0 −1.36094 −0.680470 − 0.732776i \(-0.738224\pi\)
−0.680470 + 0.732776i \(0.738224\pi\)
\(948\) 0 0
\(949\) 19470.0 0.665988
\(950\) 0 0
\(951\) −7131.00 −0.243153
\(952\) 0 0
\(953\) −46618.0 −1.58458 −0.792290 − 0.610144i \(-0.791111\pi\)
−0.792290 + 0.610144i \(0.791111\pi\)
\(954\) 0 0
\(955\) −8925.00 −0.302415
\(956\) 0 0
\(957\) 3710.00 0.125316
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −24166.0 −0.811185
\(962\) 0 0
\(963\) 3354.00 0.112234
\(964\) 0 0
\(965\) −245.000 −0.00817288
\(966\) 0 0
\(967\) −14816.0 −0.492710 −0.246355 − 0.969180i \(-0.579233\pi\)
−0.246355 + 0.969180i \(0.579233\pi\)
\(968\) 0 0
\(969\) 8083.00 0.267970
\(970\) 0 0
\(971\) −16875.0 −0.557718 −0.278859 − 0.960332i \(-0.589956\pi\)
−0.278859 + 0.960332i \(0.589956\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −5016.00 −0.164760
\(976\) 0 0
\(977\) −15837.0 −0.518598 −0.259299 − 0.965797i \(-0.583492\pi\)
−0.259299 + 0.965797i \(0.583492\pi\)
\(978\) 0 0
\(979\) −30555.0 −0.997489
\(980\) 0 0
\(981\) 25090.0 0.816577
\(982\) 0 0
\(983\) 9915.00 0.321708 0.160854 − 0.986978i \(-0.448575\pi\)
0.160854 + 0.986978i \(0.448575\pi\)
\(984\) 0 0
\(985\) 19138.0 0.619073
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1820.00 −0.0585163
\(990\) 0 0
\(991\) 43681.0 1.40017 0.700087 − 0.714057i \(-0.253144\pi\)
0.700087 + 0.714057i \(0.253144\pi\)
\(992\) 0 0
\(993\) −6571.00 −0.209994
\(994\) 0 0
\(995\) −15701.0 −0.500256
\(996\) 0 0
\(997\) 47113.0 1.49657 0.748287 − 0.663375i \(-0.230877\pi\)
0.748287 + 0.663375i \(0.230877\pi\)
\(998\) 0 0
\(999\) 583.000 0.0184638
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 784.4.a.j.1.1 1
4.3 odd 2 98.4.a.c.1.1 1
7.3 odd 6 112.4.i.b.65.1 2
7.5 odd 6 112.4.i.b.81.1 2
7.6 odd 2 784.4.a.l.1.1 1
12.11 even 2 882.4.a.p.1.1 1
20.19 odd 2 2450.4.a.bf.1.1 1
28.3 even 6 14.4.c.b.9.1 ✓ 2
28.11 odd 6 98.4.c.e.79.1 2
28.19 even 6 14.4.c.b.11.1 yes 2
28.23 odd 6 98.4.c.e.67.1 2
28.27 even 2 98.4.a.b.1.1 1
56.3 even 6 448.4.i.c.65.1 2
56.5 odd 6 448.4.i.d.193.1 2
56.19 even 6 448.4.i.c.193.1 2
56.45 odd 6 448.4.i.d.65.1 2
84.11 even 6 882.4.g.d.667.1 2
84.23 even 6 882.4.g.d.361.1 2
84.47 odd 6 126.4.g.c.109.1 2
84.59 odd 6 126.4.g.c.37.1 2
84.83 odd 2 882.4.a.k.1.1 1
140.3 odd 12 350.4.j.d.149.1 4
140.19 even 6 350.4.e.b.151.1 2
140.47 odd 12 350.4.j.d.249.1 4
140.59 even 6 350.4.e.b.51.1 2
140.87 odd 12 350.4.j.d.149.2 4
140.103 odd 12 350.4.j.d.249.2 4
140.139 even 2 2450.4.a.bh.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.4.c.b.9.1 ✓ 2 28.3 even 6
14.4.c.b.11.1 yes 2 28.19 even 6
98.4.a.b.1.1 1 28.27 even 2
98.4.a.c.1.1 1 4.3 odd 2
98.4.c.e.67.1 2 28.23 odd 6
98.4.c.e.79.1 2 28.11 odd 6
112.4.i.b.65.1 2 7.3 odd 6
112.4.i.b.81.1 2 7.5 odd 6
126.4.g.c.37.1 2 84.59 odd 6
126.4.g.c.109.1 2 84.47 odd 6
350.4.e.b.51.1 2 140.59 even 6
350.4.e.b.151.1 2 140.19 even 6
350.4.j.d.149.1 4 140.3 odd 12
350.4.j.d.149.2 4 140.87 odd 12
350.4.j.d.249.1 4 140.47 odd 12
350.4.j.d.249.2 4 140.103 odd 12
448.4.i.c.65.1 2 56.3 even 6
448.4.i.c.193.1 2 56.19 even 6
448.4.i.d.65.1 2 56.45 odd 6
448.4.i.d.193.1 2 56.5 odd 6
784.4.a.j.1.1 1 1.1 even 1 trivial
784.4.a.l.1.1 1 7.6 odd 2
882.4.a.k.1.1 1 84.83 odd 2
882.4.a.p.1.1 1 12.11 even 2
882.4.g.d.361.1 2 84.23 even 6
882.4.g.d.667.1 2 84.11 even 6
2450.4.a.bf.1.1 1 20.19 odd 2
2450.4.a.bh.1.1 1 140.139 even 2