Properties

Label 9555.2.a.t.1.1
Level $9555$
Weight $2$
Character 9555.1
Self dual yes
Analytic conductor $76.297$
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] = [9555,2,Mod(1,9555)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9555, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9555.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9555 = 3 \cdot 5 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9555.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: \(76.2970591313\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 195)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9555.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} -1.00000 q^{5} -2.00000 q^{6} +1.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} -1.00000 q^{5} -2.00000 q^{6} +1.00000 q^{9} -2.00000 q^{10} -5.00000 q^{11} -2.00000 q^{12} -1.00000 q^{13} +1.00000 q^{15} -4.00000 q^{16} -5.00000 q^{17} +2.00000 q^{18} -2.00000 q^{19} -2.00000 q^{20} -10.0000 q^{22} -1.00000 q^{23} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} +10.0000 q^{29} +2.00000 q^{30} +2.00000 q^{31} -8.00000 q^{32} +5.00000 q^{33} -10.0000 q^{34} +2.00000 q^{36} -3.00000 q^{37} -4.00000 q^{38} +1.00000 q^{39} +9.00000 q^{41} -4.00000 q^{43} -10.0000 q^{44} -1.00000 q^{45} -2.00000 q^{46} -10.0000 q^{47} +4.00000 q^{48} +2.00000 q^{50} +5.00000 q^{51} -2.00000 q^{52} +9.00000 q^{53} -2.00000 q^{54} +5.00000 q^{55} +2.00000 q^{57} +20.0000 q^{58} +2.00000 q^{60} +11.0000 q^{61} +4.00000 q^{62} -8.00000 q^{64} +1.00000 q^{65} +10.0000 q^{66} -4.00000 q^{67} -10.0000 q^{68} +1.00000 q^{69} +15.0000 q^{71} -6.00000 q^{73} -6.00000 q^{74} -1.00000 q^{75} -4.00000 q^{76} +2.00000 q^{78} -11.0000 q^{79} +4.00000 q^{80} +1.00000 q^{81} +18.0000 q^{82} -8.00000 q^{83} +5.00000 q^{85} -8.00000 q^{86} -10.0000 q^{87} +11.0000 q^{89} -2.00000 q^{90} -2.00000 q^{92} -2.00000 q^{93} -20.0000 q^{94} +2.00000 q^{95} +8.00000 q^{96} +9.00000 q^{97} -5.00000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.00000 1.00000
\(5\) −1.00000 −0.447214
\(6\) −2.00000 −0.816497
\(7\) 0 0
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) −2.00000 −0.632456
\(11\) −5.00000 −1.50756 −0.753778 0.657129i \(-0.771771\pi\)
−0.753778 + 0.657129i \(0.771771\pi\)
\(12\) −2.00000 −0.577350
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) −4.00000 −1.00000
\(17\) −5.00000 −1.21268 −0.606339 0.795206i \(-0.707363\pi\)
−0.606339 + 0.795206i \(0.707363\pi\)
\(18\) 2.00000 0.471405
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) −10.0000 −2.13201
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −2.00000 −0.392232
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 10.0000 1.85695 0.928477 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 2.00000 0.365148
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) −8.00000 −1.41421
\(33\) 5.00000 0.870388
\(34\) −10.0000 −1.71499
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) −3.00000 −0.493197 −0.246598 0.969118i \(-0.579313\pi\)
−0.246598 + 0.969118i \(0.579313\pi\)
\(38\) −4.00000 −0.648886
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −10.0000 −1.50756
\(45\) −1.00000 −0.149071
\(46\) −2.00000 −0.294884
\(47\) −10.0000 −1.45865 −0.729325 0.684167i \(-0.760166\pi\)
−0.729325 + 0.684167i \(0.760166\pi\)
\(48\) 4.00000 0.577350
\(49\) 0 0
\(50\) 2.00000 0.282843
\(51\) 5.00000 0.700140
\(52\) −2.00000 −0.277350
\(53\) 9.00000 1.23625 0.618123 0.786082i \(-0.287894\pi\)
0.618123 + 0.786082i \(0.287894\pi\)
\(54\) −2.00000 −0.272166
\(55\) 5.00000 0.674200
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) 20.0000 2.62613
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 2.00000 0.258199
\(61\) 11.0000 1.40841 0.704203 0.709999i \(-0.251305\pi\)
0.704203 + 0.709999i \(0.251305\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 1.00000 0.124035
\(66\) 10.0000 1.23091
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −10.0000 −1.21268
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 15.0000 1.78017 0.890086 0.455792i \(-0.150644\pi\)
0.890086 + 0.455792i \(0.150644\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −6.00000 −0.697486
\(75\) −1.00000 −0.115470
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 2.00000 0.226455
\(79\) −11.0000 −1.23760 −0.618798 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) 4.00000 0.447214
\(81\) 1.00000 0.111111
\(82\) 18.0000 1.98777
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 0 0
\(85\) 5.00000 0.542326
\(86\) −8.00000 −0.862662
\(87\) −10.0000 −1.07211
\(88\) 0 0
\(89\) 11.0000 1.16600 0.582999 0.812473i \(-0.301879\pi\)
0.582999 + 0.812473i \(0.301879\pi\)
\(90\) −2.00000 −0.210819
\(91\) 0 0
\(92\) −2.00000 −0.208514
\(93\) −2.00000 −0.207390
\(94\) −20.0000 −2.06284
\(95\) 2.00000 0.205196
\(96\) 8.00000 0.816497
\(97\) 9.00000 0.913812 0.456906 0.889515i \(-0.348958\pi\)
0.456906 + 0.889515i \(0.348958\pi\)
\(98\) 0 0
\(99\) −5.00000 −0.502519
\(100\) 2.00000 0.200000
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 10.0000 0.990148
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 18.0000 1.74831
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) −2.00000 −0.192450
\(109\) 16.0000 1.53252 0.766261 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) 10.0000 0.953463
\(111\) 3.00000 0.284747
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 4.00000 0.374634
\(115\) 1.00000 0.0932505
\(116\) 20.0000 1.85695
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 22.0000 1.99179
\(123\) −9.00000 −0.811503
\(124\) 4.00000 0.359211
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 14.0000 1.24230 0.621150 0.783692i \(-0.286666\pi\)
0.621150 + 0.783692i \(0.286666\pi\)
\(128\) 0 0
\(129\) 4.00000 0.352180
\(130\) 2.00000 0.175412
\(131\) −6.00000 −0.524222 −0.262111 0.965038i \(-0.584419\pi\)
−0.262111 + 0.965038i \(0.584419\pi\)
\(132\) 10.0000 0.870388
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 1.00000 0.0860663
\(136\) 0 0
\(137\) 6.00000 0.512615 0.256307 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 2.00000 0.170251
\(139\) 17.0000 1.44192 0.720961 0.692976i \(-0.243701\pi\)
0.720961 + 0.692976i \(0.243701\pi\)
\(140\) 0 0
\(141\) 10.0000 0.842152
\(142\) 30.0000 2.51754
\(143\) 5.00000 0.418121
\(144\) −4.00000 −0.333333
\(145\) −10.0000 −0.830455
\(146\) −12.0000 −0.993127
\(147\) 0 0
\(148\) −6.00000 −0.493197
\(149\) −7.00000 −0.573462 −0.286731 0.958011i \(-0.592569\pi\)
−0.286731 + 0.958011i \(0.592569\pi\)
\(150\) −2.00000 −0.163299
\(151\) −12.0000 −0.976546 −0.488273 0.872691i \(-0.662373\pi\)
−0.488273 + 0.872691i \(0.662373\pi\)
\(152\) 0 0
\(153\) −5.00000 −0.404226
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) 2.00000 0.160128
\(157\) −22.0000 −1.75579 −0.877896 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) −22.0000 −1.75023
\(159\) −9.00000 −0.713746
\(160\) 8.00000 0.632456
\(161\) 0 0
\(162\) 2.00000 0.157135
\(163\) −11.0000 −0.861586 −0.430793 0.902451i \(-0.641766\pi\)
−0.430793 + 0.902451i \(0.641766\pi\)
\(164\) 18.0000 1.40556
\(165\) −5.00000 −0.389249
\(166\) −16.0000 −1.24184
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 10.0000 0.766965
\(171\) −2.00000 −0.152944
\(172\) −8.00000 −0.609994
\(173\) 2.00000 0.152057 0.0760286 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) −20.0000 −1.51620
\(175\) 0 0
\(176\) 20.0000 1.50756
\(177\) 0 0
\(178\) 22.0000 1.64897
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) −2.00000 −0.149071
\(181\) 23.0000 1.70958 0.854788 0.518977i \(-0.173687\pi\)
0.854788 + 0.518977i \(0.173687\pi\)
\(182\) 0 0
\(183\) −11.0000 −0.813143
\(184\) 0 0
\(185\) 3.00000 0.220564
\(186\) −4.00000 −0.293294
\(187\) 25.0000 1.82818
\(188\) −20.0000 −1.45865
\(189\) 0 0
\(190\) 4.00000 0.290191
\(191\) −20.0000 −1.44715 −0.723575 0.690246i \(-0.757502\pi\)
−0.723575 + 0.690246i \(0.757502\pi\)
\(192\) 8.00000 0.577350
\(193\) 13.0000 0.935760 0.467880 0.883792i \(-0.345018\pi\)
0.467880 + 0.883792i \(0.345018\pi\)
\(194\) 18.0000 1.29232
\(195\) −1.00000 −0.0716115
\(196\) 0 0
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) −10.0000 −0.710669
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 0 0
\(201\) 4.00000 0.282138
\(202\) 24.0000 1.68863
\(203\) 0 0
\(204\) 10.0000 0.700140
\(205\) −9.00000 −0.628587
\(206\) −8.00000 −0.557386
\(207\) −1.00000 −0.0695048
\(208\) 4.00000 0.277350
\(209\) 10.0000 0.691714
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 18.0000 1.23625
\(213\) −15.0000 −1.02778
\(214\) 6.00000 0.410152
\(215\) 4.00000 0.272798
\(216\) 0 0
\(217\) 0 0
\(218\) 32.0000 2.16731
\(219\) 6.00000 0.405442
\(220\) 10.0000 0.674200
\(221\) 5.00000 0.336336
\(222\) 6.00000 0.402694
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 4.00000 0.266076
\(227\) 18.0000 1.19470 0.597351 0.801980i \(-0.296220\pi\)
0.597351 + 0.801980i \(0.296220\pi\)
\(228\) 4.00000 0.264906
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 2.00000 0.131876
\(231\) 0 0
\(232\) 0 0
\(233\) −25.0000 −1.63780 −0.818902 0.573933i \(-0.805417\pi\)
−0.818902 + 0.573933i \(0.805417\pi\)
\(234\) −2.00000 −0.130744
\(235\) 10.0000 0.652328
\(236\) 0 0
\(237\) 11.0000 0.714527
\(238\) 0 0
\(239\) 15.0000 0.970269 0.485135 0.874439i \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(240\) −4.00000 −0.258199
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 28.0000 1.79991
\(243\) −1.00000 −0.0641500
\(244\) 22.0000 1.40841
\(245\) 0 0
\(246\) −18.0000 −1.14764
\(247\) 2.00000 0.127257
\(248\) 0 0
\(249\) 8.00000 0.506979
\(250\) −2.00000 −0.126491
\(251\) −20.0000 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 0 0
\(253\) 5.00000 0.314347
\(254\) 28.0000 1.75688
\(255\) −5.00000 −0.313112
\(256\) 16.0000 1.00000
\(257\) −18.0000 −1.12281 −0.561405 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(258\) 8.00000 0.498058
\(259\) 0 0
\(260\) 2.00000 0.124035
\(261\) 10.0000 0.618984
\(262\) −12.0000 −0.741362
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −9.00000 −0.552866
\(266\) 0 0
\(267\) −11.0000 −0.673189
\(268\) −8.00000 −0.488678
\(269\) −32.0000 −1.95107 −0.975537 0.219834i \(-0.929448\pi\)
−0.975537 + 0.219834i \(0.929448\pi\)
\(270\) 2.00000 0.121716
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) 20.0000 1.21268
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) −5.00000 −0.301511
\(276\) 2.00000 0.120386
\(277\) 26.0000 1.56219 0.781094 0.624413i \(-0.214662\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) 34.0000 2.03918
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 20.0000 1.19098
\(283\) 8.00000 0.475551 0.237775 0.971320i \(-0.423582\pi\)
0.237775 + 0.971320i \(0.423582\pi\)
\(284\) 30.0000 1.78017
\(285\) −2.00000 −0.118470
\(286\) 10.0000 0.591312
\(287\) 0 0
\(288\) −8.00000 −0.471405
\(289\) 8.00000 0.470588
\(290\) −20.0000 −1.17444
\(291\) −9.00000 −0.527589
\(292\) −12.0000 −0.702247
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 5.00000 0.290129
\(298\) −14.0000 −0.810998
\(299\) 1.00000 0.0578315
\(300\) −2.00000 −0.115470
\(301\) 0 0
\(302\) −24.0000 −1.38104
\(303\) −12.0000 −0.689382
\(304\) 8.00000 0.458831
\(305\) −11.0000 −0.629858
\(306\) −10.0000 −0.571662
\(307\) 19.0000 1.08439 0.542194 0.840254i \(-0.317594\pi\)
0.542194 + 0.840254i \(0.317594\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) −4.00000 −0.227185
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) 10.0000 0.565233 0.282617 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) −44.0000 −2.48306
\(315\) 0 0
\(316\) −22.0000 −1.23760
\(317\) 12.0000 0.673987 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) −18.0000 −1.00939
\(319\) −50.0000 −2.79946
\(320\) 8.00000 0.447214
\(321\) −3.00000 −0.167444
\(322\) 0 0
\(323\) 10.0000 0.556415
\(324\) 2.00000 0.111111
\(325\) −1.00000 −0.0554700
\(326\) −22.0000 −1.21847
\(327\) −16.0000 −0.884802
\(328\) 0 0
\(329\) 0 0
\(330\) −10.0000 −0.550482
\(331\) 32.0000 1.75888 0.879440 0.476011i \(-0.157918\pi\)
0.879440 + 0.476011i \(0.157918\pi\)
\(332\) −16.0000 −0.878114
\(333\) −3.00000 −0.164399
\(334\) 16.0000 0.875481
\(335\) 4.00000 0.218543
\(336\) 0 0
\(337\) 4.00000 0.217894 0.108947 0.994048i \(-0.465252\pi\)
0.108947 + 0.994048i \(0.465252\pi\)
\(338\) 2.00000 0.108786
\(339\) −2.00000 −0.108625
\(340\) 10.0000 0.542326
\(341\) −10.0000 −0.541530
\(342\) −4.00000 −0.216295
\(343\) 0 0
\(344\) 0 0
\(345\) −1.00000 −0.0538382
\(346\) 4.00000 0.215041
\(347\) −1.00000 −0.0536828 −0.0268414 0.999640i \(-0.508545\pi\)
−0.0268414 + 0.999640i \(0.508545\pi\)
\(348\) −20.0000 −1.07211
\(349\) −20.0000 −1.07058 −0.535288 0.844670i \(-0.679797\pi\)
−0.535288 + 0.844670i \(0.679797\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 40.0000 2.13201
\(353\) 14.0000 0.745145 0.372572 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 0 0
\(355\) −15.0000 −0.796117
\(356\) 22.0000 1.16600
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) 16.0000 0.844448 0.422224 0.906492i \(-0.361250\pi\)
0.422224 + 0.906492i \(0.361250\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 46.0000 2.41771
\(363\) −14.0000 −0.734809
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) −22.0000 −1.14996
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 4.00000 0.208514
\(369\) 9.00000 0.468521
\(370\) 6.00000 0.311925
\(371\) 0 0
\(372\) −4.00000 −0.207390
\(373\) 16.0000 0.828449 0.414224 0.910175i \(-0.364053\pi\)
0.414224 + 0.910175i \(0.364053\pi\)
\(374\) 50.0000 2.58544
\(375\) 1.00000 0.0516398
\(376\) 0 0
\(377\) −10.0000 −0.515026
\(378\) 0 0
\(379\) 6.00000 0.308199 0.154100 0.988055i \(-0.450752\pi\)
0.154100 + 0.988055i \(0.450752\pi\)
\(380\) 4.00000 0.205196
\(381\) −14.0000 −0.717242
\(382\) −40.0000 −2.04658
\(383\) 18.0000 0.919757 0.459879 0.887982i \(-0.347893\pi\)
0.459879 + 0.887982i \(0.347893\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 26.0000 1.32337
\(387\) −4.00000 −0.203331
\(388\) 18.0000 0.913812
\(389\) −24.0000 −1.21685 −0.608424 0.793612i \(-0.708198\pi\)
−0.608424 + 0.793612i \(0.708198\pi\)
\(390\) −2.00000 −0.101274
\(391\) 5.00000 0.252861
\(392\) 0 0
\(393\) 6.00000 0.302660
\(394\) −24.0000 −1.20910
\(395\) 11.0000 0.553470
\(396\) −10.0000 −0.502519
\(397\) 19.0000 0.953583 0.476791 0.879017i \(-0.341800\pi\)
0.476791 + 0.879017i \(0.341800\pi\)
\(398\) −8.00000 −0.401004
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 8.00000 0.399004
\(403\) −2.00000 −0.0996271
\(404\) 24.0000 1.19404
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 15.0000 0.743522
\(408\) 0 0
\(409\) 26.0000 1.28562 0.642809 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) −18.0000 −0.888957
\(411\) −6.00000 −0.295958
\(412\) −8.00000 −0.394132
\(413\) 0 0
\(414\) −2.00000 −0.0982946
\(415\) 8.00000 0.392705
\(416\) 8.00000 0.392232
\(417\) −17.0000 −0.832494
\(418\) 20.0000 0.978232
\(419\) −26.0000 −1.27018 −0.635092 0.772437i \(-0.719038\pi\)
−0.635092 + 0.772437i \(0.719038\pi\)
\(420\) 0 0
\(421\) 32.0000 1.55958 0.779792 0.626038i \(-0.215325\pi\)
0.779792 + 0.626038i \(0.215325\pi\)
\(422\) −8.00000 −0.389434
\(423\) −10.0000 −0.486217
\(424\) 0 0
\(425\) −5.00000 −0.242536
\(426\) −30.0000 −1.45350
\(427\) 0 0
\(428\) 6.00000 0.290021
\(429\) −5.00000 −0.241402
\(430\) 8.00000 0.385794
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 4.00000 0.192450
\(433\) −24.0000 −1.15337 −0.576683 0.816968i \(-0.695653\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(434\) 0 0
\(435\) 10.0000 0.479463
\(436\) 32.0000 1.53252
\(437\) 2.00000 0.0956730
\(438\) 12.0000 0.573382
\(439\) 33.0000 1.57500 0.787502 0.616312i \(-0.211374\pi\)
0.787502 + 0.616312i \(0.211374\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 10.0000 0.475651
\(443\) 35.0000 1.66290 0.831450 0.555599i \(-0.187511\pi\)
0.831450 + 0.555599i \(0.187511\pi\)
\(444\) 6.00000 0.284747
\(445\) −11.0000 −0.521450
\(446\) 0 0
\(447\) 7.00000 0.331089
\(448\) 0 0
\(449\) 15.0000 0.707894 0.353947 0.935266i \(-0.384839\pi\)
0.353947 + 0.935266i \(0.384839\pi\)
\(450\) 2.00000 0.0942809
\(451\) −45.0000 −2.11897
\(452\) 4.00000 0.188144
\(453\) 12.0000 0.563809
\(454\) 36.0000 1.68956
\(455\) 0 0
\(456\) 0 0
\(457\) −13.0000 −0.608114 −0.304057 0.952654i \(-0.598341\pi\)
−0.304057 + 0.952654i \(0.598341\pi\)
\(458\) 28.0000 1.30835
\(459\) 5.00000 0.233380
\(460\) 2.00000 0.0932505
\(461\) −3.00000 −0.139724 −0.0698620 0.997557i \(-0.522256\pi\)
−0.0698620 + 0.997557i \(0.522256\pi\)
\(462\) 0 0
\(463\) 5.00000 0.232370 0.116185 0.993228i \(-0.462933\pi\)
0.116185 + 0.993228i \(0.462933\pi\)
\(464\) −40.0000 −1.85695
\(465\) 2.00000 0.0927478
\(466\) −50.0000 −2.31621
\(467\) 29.0000 1.34196 0.670980 0.741475i \(-0.265874\pi\)
0.670980 + 0.741475i \(0.265874\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) 20.0000 0.922531
\(471\) 22.0000 1.01371
\(472\) 0 0
\(473\) 20.0000 0.919601
\(474\) 22.0000 1.01049
\(475\) −2.00000 −0.0917663
\(476\) 0 0
\(477\) 9.00000 0.412082
\(478\) 30.0000 1.37217
\(479\) −5.00000 −0.228456 −0.114228 0.993455i \(-0.536439\pi\)
−0.114228 + 0.993455i \(0.536439\pi\)
\(480\) −8.00000 −0.365148
\(481\) 3.00000 0.136788
\(482\) 28.0000 1.27537
\(483\) 0 0
\(484\) 28.0000 1.27273
\(485\) −9.00000 −0.408669
\(486\) −2.00000 −0.0907218
\(487\) 7.00000 0.317200 0.158600 0.987343i \(-0.449302\pi\)
0.158600 + 0.987343i \(0.449302\pi\)
\(488\) 0 0
\(489\) 11.0000 0.497437
\(490\) 0 0
\(491\) 16.0000 0.722070 0.361035 0.932552i \(-0.382424\pi\)
0.361035 + 0.932552i \(0.382424\pi\)
\(492\) −18.0000 −0.811503
\(493\) −50.0000 −2.25189
\(494\) 4.00000 0.179969
\(495\) 5.00000 0.224733
\(496\) −8.00000 −0.359211
\(497\) 0 0
\(498\) 16.0000 0.716977
\(499\) 34.0000 1.52205 0.761025 0.648723i \(-0.224697\pi\)
0.761025 + 0.648723i \(0.224697\pi\)
\(500\) −2.00000 −0.0894427
\(501\) −8.00000 −0.357414
\(502\) −40.0000 −1.78529
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) 10.0000 0.444554
\(507\) −1.00000 −0.0444116
\(508\) 28.0000 1.24230
\(509\) −21.0000 −0.930809 −0.465404 0.885098i \(-0.654091\pi\)
−0.465404 + 0.885098i \(0.654091\pi\)
\(510\) −10.0000 −0.442807
\(511\) 0 0
\(512\) 32.0000 1.41421
\(513\) 2.00000 0.0883022
\(514\) −36.0000 −1.58789
\(515\) 4.00000 0.176261
\(516\) 8.00000 0.352180
\(517\) 50.0000 2.19900
\(518\) 0 0
\(519\) −2.00000 −0.0877903
\(520\) 0 0
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) 20.0000 0.875376
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 0 0
\(527\) −10.0000 −0.435607
\(528\) −20.0000 −0.870388
\(529\) −22.0000 −0.956522
\(530\) −18.0000 −0.781870
\(531\) 0 0
\(532\) 0 0
\(533\) −9.00000 −0.389833
\(534\) −22.0000 −0.952033
\(535\) −3.00000 −0.129701
\(536\) 0 0
\(537\) 6.00000 0.258919
\(538\) −64.0000 −2.75924
\(539\) 0 0
\(540\) 2.00000 0.0860663
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) 4.00000 0.171815
\(543\) −23.0000 −0.987024
\(544\) 40.0000 1.71499
\(545\) −16.0000 −0.685365
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 12.0000 0.512615
\(549\) 11.0000 0.469469
\(550\) −10.0000 −0.426401
\(551\) −20.0000 −0.852029
\(552\) 0 0
\(553\) 0 0
\(554\) 52.0000 2.20927
\(555\) −3.00000 −0.127343
\(556\) 34.0000 1.44192
\(557\) −30.0000 −1.27114 −0.635570 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 4.00000 0.169334
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) −25.0000 −1.05550
\(562\) −20.0000 −0.843649
\(563\) 41.0000 1.72794 0.863972 0.503540i \(-0.167969\pi\)
0.863972 + 0.503540i \(0.167969\pi\)
\(564\) 20.0000 0.842152
\(565\) −2.00000 −0.0841406
\(566\) 16.0000 0.672530
\(567\) 0 0
\(568\) 0 0
\(569\) 16.0000 0.670755 0.335377 0.942084i \(-0.391136\pi\)
0.335377 + 0.942084i \(0.391136\pi\)
\(570\) −4.00000 −0.167542
\(571\) 17.0000 0.711428 0.355714 0.934595i \(-0.384238\pi\)
0.355714 + 0.934595i \(0.384238\pi\)
\(572\) 10.0000 0.418121
\(573\) 20.0000 0.835512
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) −8.00000 −0.333333
\(577\) 21.0000 0.874241 0.437121 0.899403i \(-0.355998\pi\)
0.437121 + 0.899403i \(0.355998\pi\)
\(578\) 16.0000 0.665512
\(579\) −13.0000 −0.540262
\(580\) −20.0000 −0.830455
\(581\) 0 0
\(582\) −18.0000 −0.746124
\(583\) −45.0000 −1.86371
\(584\) 0 0
\(585\) 1.00000 0.0413449
\(586\) −48.0000 −1.98286
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 0 0
\(589\) −4.00000 −0.164817
\(590\) 0 0
\(591\) 12.0000 0.493614
\(592\) 12.0000 0.493197
\(593\) 36.0000 1.47834 0.739171 0.673517i \(-0.235217\pi\)
0.739171 + 0.673517i \(0.235217\pi\)
\(594\) 10.0000 0.410305
\(595\) 0 0
\(596\) −14.0000 −0.573462
\(597\) 4.00000 0.163709
\(598\) 2.00000 0.0817861
\(599\) 4.00000 0.163436 0.0817178 0.996656i \(-0.473959\pi\)
0.0817178 + 0.996656i \(0.473959\pi\)
\(600\) 0 0
\(601\) 5.00000 0.203954 0.101977 0.994787i \(-0.467483\pi\)
0.101977 + 0.994787i \(0.467483\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) −24.0000 −0.976546
\(605\) −14.0000 −0.569181
\(606\) −24.0000 −0.974933
\(607\) 40.0000 1.62355 0.811775 0.583970i \(-0.198502\pi\)
0.811775 + 0.583970i \(0.198502\pi\)
\(608\) 16.0000 0.648886
\(609\) 0 0
\(610\) −22.0000 −0.890754
\(611\) 10.0000 0.404557
\(612\) −10.0000 −0.404226
\(613\) 3.00000 0.121169 0.0605844 0.998163i \(-0.480704\pi\)
0.0605844 + 0.998163i \(0.480704\pi\)
\(614\) 38.0000 1.53356
\(615\) 9.00000 0.362915
\(616\) 0 0
\(617\) 22.0000 0.885687 0.442843 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(618\) 8.00000 0.321807
\(619\) 2.00000 0.0803868 0.0401934 0.999192i \(-0.487203\pi\)
0.0401934 + 0.999192i \(0.487203\pi\)
\(620\) −4.00000 −0.160644
\(621\) 1.00000 0.0401286
\(622\) −48.0000 −1.92462
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 1.00000 0.0400000
\(626\) 20.0000 0.799361
\(627\) −10.0000 −0.399362
\(628\) −44.0000 −1.75579
\(629\) 15.0000 0.598089
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 4.00000 0.158986
\(634\) 24.0000 0.953162
\(635\) −14.0000 −0.555573
\(636\) −18.0000 −0.713746
\(637\) 0 0
\(638\) −100.000 −3.95904
\(639\) 15.0000 0.593391
\(640\) 0 0
\(641\) −36.0000 −1.42191 −0.710957 0.703235i \(-0.751738\pi\)
−0.710957 + 0.703235i \(0.751738\pi\)
\(642\) −6.00000 −0.236801
\(643\) −1.00000 −0.0394362 −0.0197181 0.999806i \(-0.506277\pi\)
−0.0197181 + 0.999806i \(0.506277\pi\)
\(644\) 0 0
\(645\) −4.00000 −0.157500
\(646\) 20.0000 0.786889
\(647\) −21.0000 −0.825595 −0.412798 0.910823i \(-0.635448\pi\)
−0.412798 + 0.910823i \(0.635448\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) −22.0000 −0.861586
\(653\) −30.0000 −1.17399 −0.586995 0.809590i \(-0.699689\pi\)
−0.586995 + 0.809590i \(0.699689\pi\)
\(654\) −32.0000 −1.25130
\(655\) 6.00000 0.234439
\(656\) −36.0000 −1.40556
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) −10.0000 −0.389249
\(661\) 16.0000 0.622328 0.311164 0.950356i \(-0.399281\pi\)
0.311164 + 0.950356i \(0.399281\pi\)
\(662\) 64.0000 2.48743
\(663\) −5.00000 −0.194184
\(664\) 0 0
\(665\) 0 0
\(666\) −6.00000 −0.232495
\(667\) −10.0000 −0.387202
\(668\) 16.0000 0.619059
\(669\) 0 0
\(670\) 8.00000 0.309067
\(671\) −55.0000 −2.12325
\(672\) 0 0
\(673\) 22.0000 0.848038 0.424019 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(674\) 8.00000 0.308148
\(675\) −1.00000 −0.0384900
\(676\) 2.00000 0.0769231
\(677\) 7.00000 0.269032 0.134516 0.990911i \(-0.457052\pi\)
0.134516 + 0.990911i \(0.457052\pi\)
\(678\) −4.00000 −0.153619
\(679\) 0 0
\(680\) 0 0
\(681\) −18.0000 −0.689761
\(682\) −20.0000 −0.765840
\(683\) 4.00000 0.153056 0.0765279 0.997067i \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) −4.00000 −0.152944
\(685\) −6.00000 −0.229248
\(686\) 0 0
\(687\) −14.0000 −0.534133
\(688\) 16.0000 0.609994
\(689\) −9.00000 −0.342873
\(690\) −2.00000 −0.0761387
\(691\) −6.00000 −0.228251 −0.114125 0.993466i \(-0.536407\pi\)
−0.114125 + 0.993466i \(0.536407\pi\)
\(692\) 4.00000 0.152057
\(693\) 0 0
\(694\) −2.00000 −0.0759190
\(695\) −17.0000 −0.644847
\(696\) 0 0
\(697\) −45.0000 −1.70450
\(698\) −40.0000 −1.51402
\(699\) 25.0000 0.945587
\(700\) 0 0
\(701\) −4.00000 −0.151078 −0.0755390 0.997143i \(-0.524068\pi\)
−0.0755390 + 0.997143i \(0.524068\pi\)
\(702\) 2.00000 0.0754851
\(703\) 6.00000 0.226294
\(704\) 40.0000 1.50756
\(705\) −10.0000 −0.376622
\(706\) 28.0000 1.05379
\(707\) 0 0
\(708\) 0 0
\(709\) 20.0000 0.751116 0.375558 0.926799i \(-0.377451\pi\)
0.375558 + 0.926799i \(0.377451\pi\)
\(710\) −30.0000 −1.12588
\(711\) −11.0000 −0.412532
\(712\) 0 0
\(713\) −2.00000 −0.0749006
\(714\) 0 0
\(715\) −5.00000 −0.186989
\(716\) −12.0000 −0.448461
\(717\) −15.0000 −0.560185
\(718\) 32.0000 1.19423
\(719\) −12.0000 −0.447524 −0.223762 0.974644i \(-0.571834\pi\)
−0.223762 + 0.974644i \(0.571834\pi\)
\(720\) 4.00000 0.149071
\(721\) 0 0
\(722\) −30.0000 −1.11648
\(723\) −14.0000 −0.520666
\(724\) 46.0000 1.70958
\(725\) 10.0000 0.371391
\(726\) −28.0000 −1.03918
\(727\) −6.00000 −0.222528 −0.111264 0.993791i \(-0.535490\pi\)
−0.111264 + 0.993791i \(0.535490\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 12.0000 0.444140
\(731\) 20.0000 0.739727
\(732\) −22.0000 −0.813143
\(733\) 15.0000 0.554038 0.277019 0.960864i \(-0.410654\pi\)
0.277019 + 0.960864i \(0.410654\pi\)
\(734\) −16.0000 −0.590571
\(735\) 0 0
\(736\) 8.00000 0.294884
\(737\) 20.0000 0.736709
\(738\) 18.0000 0.662589
\(739\) 38.0000 1.39785 0.698926 0.715194i \(-0.253662\pi\)
0.698926 + 0.715194i \(0.253662\pi\)
\(740\) 6.00000 0.220564
\(741\) −2.00000 −0.0734718
\(742\) 0 0
\(743\) 6.00000 0.220119 0.110059 0.993925i \(-0.464896\pi\)
0.110059 + 0.993925i \(0.464896\pi\)
\(744\) 0 0
\(745\) 7.00000 0.256460
\(746\) 32.0000 1.17160
\(747\) −8.00000 −0.292705
\(748\) 50.0000 1.82818
\(749\) 0 0
\(750\) 2.00000 0.0730297
\(751\) −45.0000 −1.64207 −0.821037 0.570875i \(-0.806604\pi\)
−0.821037 + 0.570875i \(0.806604\pi\)
\(752\) 40.0000 1.45865
\(753\) 20.0000 0.728841
\(754\) −20.0000 −0.728357
\(755\) 12.0000 0.436725
\(756\) 0 0
\(757\) 36.0000 1.30844 0.654221 0.756303i \(-0.272997\pi\)
0.654221 + 0.756303i \(0.272997\pi\)
\(758\) 12.0000 0.435860
\(759\) −5.00000 −0.181489
\(760\) 0 0
\(761\) 14.0000 0.507500 0.253750 0.967270i \(-0.418336\pi\)
0.253750 + 0.967270i \(0.418336\pi\)
\(762\) −28.0000 −1.01433
\(763\) 0 0
\(764\) −40.0000 −1.44715
\(765\) 5.00000 0.180775
\(766\) 36.0000 1.30073
\(767\) 0 0
\(768\) −16.0000 −0.577350
\(769\) 12.0000 0.432731 0.216366 0.976312i \(-0.430580\pi\)
0.216366 + 0.976312i \(0.430580\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 26.0000 0.935760
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) −8.00000 −0.287554
\(775\) 2.00000 0.0718421
\(776\) 0 0
\(777\) 0 0
\(778\) −48.0000 −1.72088
\(779\) −18.0000 −0.644917
\(780\) −2.00000 −0.0716115
\(781\) −75.0000 −2.68371
\(782\) 10.0000 0.357599
\(783\) −10.0000 −0.357371
\(784\) 0 0
\(785\) 22.0000 0.785214
\(786\) 12.0000 0.428026
\(787\) −44.0000 −1.56843 −0.784215 0.620489i \(-0.786934\pi\)
−0.784215 + 0.620489i \(0.786934\pi\)
\(788\) −24.0000 −0.854965
\(789\) 0 0
\(790\) 22.0000 0.782725
\(791\) 0 0
\(792\) 0 0
\(793\) −11.0000 −0.390621
\(794\) 38.0000 1.34857
\(795\) 9.00000 0.319197
\(796\) −8.00000 −0.283552
\(797\) 5.00000 0.177109 0.0885545 0.996071i \(-0.471775\pi\)
0.0885545 + 0.996071i \(0.471775\pi\)
\(798\) 0 0
\(799\) 50.0000 1.76887
\(800\) −8.00000 −0.282843
\(801\) 11.0000 0.388666
\(802\) −36.0000 −1.27120
\(803\) 30.0000 1.05868
\(804\) 8.00000 0.282138
\(805\) 0 0
\(806\) −4.00000 −0.140894
\(807\) 32.0000 1.12645
\(808\) 0 0
\(809\) −6.00000 −0.210949 −0.105474 0.994422i \(-0.533636\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(810\) −2.00000 −0.0702728
\(811\) 4.00000 0.140459 0.0702295 0.997531i \(-0.477627\pi\)
0.0702295 + 0.997531i \(0.477627\pi\)
\(812\) 0 0
\(813\) −2.00000 −0.0701431
\(814\) 30.0000 1.05150
\(815\) 11.0000 0.385313
\(816\) −20.0000 −0.700140
\(817\) 8.00000 0.279885
\(818\) 52.0000 1.81814
\(819\) 0 0
\(820\) −18.0000 −0.628587
\(821\) −41.0000 −1.43091 −0.715455 0.698659i \(-0.753781\pi\)
−0.715455 + 0.698659i \(0.753781\pi\)
\(822\) −12.0000 −0.418548
\(823\) −48.0000 −1.67317 −0.836587 0.547833i \(-0.815453\pi\)
−0.836587 + 0.547833i \(0.815453\pi\)
\(824\) 0 0
\(825\) 5.00000 0.174078
\(826\) 0 0
\(827\) −42.0000 −1.46048 −0.730242 0.683189i \(-0.760592\pi\)
−0.730242 + 0.683189i \(0.760592\pi\)
\(828\) −2.00000 −0.0695048
\(829\) −14.0000 −0.486240 −0.243120 0.969996i \(-0.578171\pi\)
−0.243120 + 0.969996i \(0.578171\pi\)
\(830\) 16.0000 0.555368
\(831\) −26.0000 −0.901930
\(832\) 8.00000 0.277350
\(833\) 0 0
\(834\) −34.0000 −1.17732
\(835\) −8.00000 −0.276851
\(836\) 20.0000 0.691714
\(837\) −2.00000 −0.0691301
\(838\) −52.0000 −1.79631
\(839\) −7.00000 −0.241667 −0.120833 0.992673i \(-0.538557\pi\)
−0.120833 + 0.992673i \(0.538557\pi\)
\(840\) 0 0
\(841\) 71.0000 2.44828
\(842\) 64.0000 2.20559
\(843\) 10.0000 0.344418
\(844\) −8.00000 −0.275371
\(845\) −1.00000 −0.0344010
\(846\) −20.0000 −0.687614
\(847\) 0 0
\(848\) −36.0000 −1.23625
\(849\) −8.00000 −0.274559
\(850\) −10.0000 −0.342997
\(851\) 3.00000 0.102839
\(852\) −30.0000 −1.02778
\(853\) −51.0000 −1.74621 −0.873103 0.487535i \(-0.837896\pi\)
−0.873103 + 0.487535i \(0.837896\pi\)
\(854\) 0 0
\(855\) 2.00000 0.0683986
\(856\) 0 0
\(857\) 17.0000 0.580709 0.290354 0.956919i \(-0.406227\pi\)
0.290354 + 0.956919i \(0.406227\pi\)
\(858\) −10.0000 −0.341394
\(859\) −35.0000 −1.19418 −0.597092 0.802173i \(-0.703677\pi\)
−0.597092 + 0.802173i \(0.703677\pi\)
\(860\) 8.00000 0.272798
\(861\) 0 0
\(862\) −32.0000 −1.08992
\(863\) −22.0000 −0.748889 −0.374444 0.927249i \(-0.622167\pi\)
−0.374444 + 0.927249i \(0.622167\pi\)
\(864\) 8.00000 0.272166
\(865\) −2.00000 −0.0680020
\(866\) −48.0000 −1.63111
\(867\) −8.00000 −0.271694
\(868\) 0 0
\(869\) 55.0000 1.86575
\(870\) 20.0000 0.678064
\(871\) 4.00000 0.135535
\(872\) 0 0
\(873\) 9.00000 0.304604
\(874\) 4.00000 0.135302
\(875\) 0 0
\(876\) 12.0000 0.405442
\(877\) 22.0000 0.742887 0.371444 0.928456i \(-0.378863\pi\)
0.371444 + 0.928456i \(0.378863\pi\)
\(878\) 66.0000 2.22739
\(879\) 24.0000 0.809500
\(880\) −20.0000 −0.674200
\(881\) 14.0000 0.471672 0.235836 0.971793i \(-0.424217\pi\)
0.235836 + 0.971793i \(0.424217\pi\)
\(882\) 0 0
\(883\) 12.0000 0.403832 0.201916 0.979403i \(-0.435283\pi\)
0.201916 + 0.979403i \(0.435283\pi\)
\(884\) 10.0000 0.336336
\(885\) 0 0
\(886\) 70.0000 2.35170
\(887\) 15.0000 0.503651 0.251825 0.967773i \(-0.418969\pi\)
0.251825 + 0.967773i \(0.418969\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −22.0000 −0.737442
\(891\) −5.00000 −0.167506
\(892\) 0 0
\(893\) 20.0000 0.669274
\(894\) 14.0000 0.468230
\(895\) 6.00000 0.200558
\(896\) 0 0
\(897\) −1.00000 −0.0333890
\(898\) 30.0000 1.00111
\(899\) 20.0000 0.667037
\(900\) 2.00000 0.0666667
\(901\) −45.0000 −1.49917
\(902\) −90.0000 −2.99667
\(903\) 0 0
\(904\) 0 0
\(905\) −23.0000 −0.764546
\(906\) 24.0000 0.797347
\(907\) 2.00000 0.0664089 0.0332045 0.999449i \(-0.489429\pi\)
0.0332045 + 0.999449i \(0.489429\pi\)
\(908\) 36.0000 1.19470
\(909\) 12.0000 0.398015
\(910\) 0 0
\(911\) 8.00000 0.265052 0.132526 0.991180i \(-0.457691\pi\)
0.132526 + 0.991180i \(0.457691\pi\)
\(912\) −8.00000 −0.264906
\(913\) 40.0000 1.32381
\(914\) −26.0000 −0.860004
\(915\) 11.0000 0.363649
\(916\) 28.0000 0.925146
\(917\) 0 0
\(918\) 10.0000 0.330049
\(919\) 29.0000 0.956622 0.478311 0.878191i \(-0.341249\pi\)
0.478311 + 0.878191i \(0.341249\pi\)
\(920\) 0 0
\(921\) −19.0000 −0.626071
\(922\) −6.00000 −0.197599
\(923\) −15.0000 −0.493731
\(924\) 0 0
\(925\) −3.00000 −0.0986394
\(926\) 10.0000 0.328620
\(927\) −4.00000 −0.131377
\(928\) −80.0000 −2.62613
\(929\) −21.0000 −0.688988 −0.344494 0.938789i \(-0.611949\pi\)
−0.344494 + 0.938789i \(0.611949\pi\)
\(930\) 4.00000 0.131165
\(931\) 0 0
\(932\) −50.0000 −1.63780
\(933\) 24.0000 0.785725
\(934\) 58.0000 1.89782
\(935\) −25.0000 −0.817587
\(936\) 0 0
\(937\) −2.00000 −0.0653372 −0.0326686 0.999466i \(-0.510401\pi\)
−0.0326686 + 0.999466i \(0.510401\pi\)
\(938\) 0 0
\(939\) −10.0000 −0.326338
\(940\) 20.0000 0.652328
\(941\) 23.0000 0.749779 0.374889 0.927070i \(-0.377681\pi\)
0.374889 + 0.927070i \(0.377681\pi\)
\(942\) 44.0000 1.43360
\(943\) −9.00000 −0.293080
\(944\) 0 0
\(945\) 0 0
\(946\) 40.0000 1.30051
\(947\) 36.0000 1.16984 0.584921 0.811090i \(-0.301125\pi\)
0.584921 + 0.811090i \(0.301125\pi\)
\(948\) 22.0000 0.714527
\(949\) 6.00000 0.194768
\(950\) −4.00000 −0.129777
\(951\) −12.0000 −0.389127
\(952\) 0 0
\(953\) −11.0000 −0.356325 −0.178162 0.984001i \(-0.557015\pi\)
−0.178162 + 0.984001i \(0.557015\pi\)
\(954\) 18.0000 0.582772
\(955\) 20.0000 0.647185
\(956\) 30.0000 0.970269
\(957\) 50.0000 1.61627
\(958\) −10.0000 −0.323085
\(959\) 0 0
\(960\) −8.00000 −0.258199
\(961\) −27.0000 −0.870968
\(962\) 6.00000 0.193448
\(963\) 3.00000 0.0966736
\(964\) 28.0000 0.901819
\(965\) −13.0000 −0.418485
\(966\) 0 0
\(967\) −40.0000 −1.28631 −0.643157 0.765735i \(-0.722376\pi\)
−0.643157 + 0.765735i \(0.722376\pi\)
\(968\) 0 0
\(969\) −10.0000 −0.321246
\(970\) −18.0000 −0.577945
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) −2.00000 −0.0641500
\(973\) 0 0
\(974\) 14.0000 0.448589
\(975\) 1.00000 0.0320256
\(976\) −44.0000 −1.40841
\(977\) 12.0000 0.383914 0.191957 0.981403i \(-0.438517\pi\)
0.191957 + 0.981403i \(0.438517\pi\)
\(978\) 22.0000 0.703482
\(979\) −55.0000 −1.75781
\(980\) 0 0
\(981\) 16.0000 0.510841
\(982\) 32.0000 1.02116
\(983\) −36.0000 −1.14822 −0.574111 0.818778i \(-0.694652\pi\)
−0.574111 + 0.818778i \(0.694652\pi\)
\(984\) 0 0
\(985\) 12.0000 0.382352
\(986\) −100.000 −3.18465
\(987\) 0 0
\(988\) 4.00000 0.127257
\(989\) 4.00000 0.127193
\(990\) 10.0000 0.317821
\(991\) 39.0000 1.23888 0.619438 0.785046i \(-0.287361\pi\)
0.619438 + 0.785046i \(0.287361\pi\)
\(992\) −16.0000 −0.508001
\(993\) −32.0000 −1.01549
\(994\) 0 0
\(995\) 4.00000 0.126809
\(996\) 16.0000 0.506979
\(997\) 16.0000 0.506725 0.253363 0.967371i \(-0.418463\pi\)
0.253363 + 0.967371i \(0.418463\pi\)
\(998\) 68.0000 2.15250
\(999\) 3.00000 0.0949158
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 9555.2.a.t.1.1 1
7.6 odd 2 195.2.a.d.1.1 1
21.20 even 2 585.2.a.a.1.1 1
28.27 even 2 3120.2.a.n.1.1 1
35.13 even 4 975.2.c.b.274.1 2
35.27 even 4 975.2.c.b.274.2 2
35.34 odd 2 975.2.a.b.1.1 1
84.83 odd 2 9360.2.a.w.1.1 1
91.90 odd 2 2535.2.a.b.1.1 1
105.62 odd 4 2925.2.c.d.2224.1 2
105.83 odd 4 2925.2.c.d.2224.2 2
105.104 even 2 2925.2.a.t.1.1 1
273.272 even 2 7605.2.a.v.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.d.1.1 1 7.6 odd 2
585.2.a.a.1.1 1 21.20 even 2
975.2.a.b.1.1 1 35.34 odd 2
975.2.c.b.274.1 2 35.13 even 4
975.2.c.b.274.2 2 35.27 even 4
2535.2.a.b.1.1 1 91.90 odd 2
2925.2.a.t.1.1 1 105.104 even 2
2925.2.c.d.2224.1 2 105.62 odd 4
2925.2.c.d.2224.2 2 105.83 odd 4
3120.2.a.n.1.1 1 28.27 even 2
7605.2.a.v.1.1 1 273.272 even 2
9360.2.a.w.1.1 1 84.83 odd 2
9555.2.a.t.1.1 1 1.1 even 1 trivial