Properties

Label 6027.2.a.bn.1.24
Level $6027$
Weight $2$
Character 6027.1
Self dual yes
Analytic conductor $48.126$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6027,2,Mod(1,6027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("6027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6027.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: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.24
Character \(\chi\) \(=\) 6027.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.78139 q^{2} -1.00000 q^{3} +5.73612 q^{4} -0.739443 q^{5} -2.78139 q^{6} +10.3916 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.78139 q^{2} -1.00000 q^{3} +5.73612 q^{4} -0.739443 q^{5} -2.78139 q^{6} +10.3916 q^{8} +1.00000 q^{9} -2.05668 q^{10} +4.44400 q^{11} -5.73612 q^{12} -0.996618 q^{13} +0.739443 q^{15} +17.4308 q^{16} +1.26311 q^{17} +2.78139 q^{18} +1.98029 q^{19} -4.24153 q^{20} +12.3605 q^{22} +0.818638 q^{23} -10.3916 q^{24} -4.45322 q^{25} -2.77198 q^{26} -1.00000 q^{27} -0.261203 q^{29} +2.05668 q^{30} +7.23078 q^{31} +27.6987 q^{32} -4.44400 q^{33} +3.51319 q^{34} +5.73612 q^{36} -7.70796 q^{37} +5.50796 q^{38} +0.996618 q^{39} -7.68399 q^{40} +1.00000 q^{41} -4.72101 q^{43} +25.4913 q^{44} -0.739443 q^{45} +2.27695 q^{46} +8.48773 q^{47} -17.4308 q^{48} -12.3861 q^{50} -1.26311 q^{51} -5.71672 q^{52} -10.1423 q^{53} -2.78139 q^{54} -3.28608 q^{55} -1.98029 q^{57} -0.726506 q^{58} +7.87031 q^{59} +4.24153 q^{60} -6.85524 q^{61} +20.1116 q^{62} +42.1791 q^{64} +0.736942 q^{65} -12.3605 q^{66} +4.70290 q^{67} +7.24534 q^{68} -0.818638 q^{69} -5.60455 q^{71} +10.3916 q^{72} -10.6056 q^{73} -21.4388 q^{74} +4.45322 q^{75} +11.3592 q^{76} +2.77198 q^{78} +1.81828 q^{79} -12.8891 q^{80} +1.00000 q^{81} +2.78139 q^{82} +14.9327 q^{83} -0.933996 q^{85} -13.1310 q^{86} +0.261203 q^{87} +46.1802 q^{88} -11.9846 q^{89} -2.05668 q^{90} +4.69581 q^{92} -7.23078 q^{93} +23.6077 q^{94} -1.46431 q^{95} -27.6987 q^{96} +7.76174 q^{97} +4.44400 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9} + 4 q^{10} + 12 q^{11} - 32 q^{12} + 4 q^{15} + 44 q^{16} - 8 q^{17} + 8 q^{18} + 4 q^{19} - 28 q^{20} + 16 q^{22} + 20 q^{23} - 24 q^{24} + 48 q^{25} - 32 q^{26} - 24 q^{27} + 24 q^{29} - 4 q^{30} + 4 q^{31} + 36 q^{32} - 12 q^{33} - 16 q^{34} + 32 q^{36} + 64 q^{37} - 20 q^{38} + 48 q^{40} + 24 q^{41} + 20 q^{43} + 48 q^{44} - 4 q^{45} + 28 q^{46} - 32 q^{47} - 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} - 8 q^{54} + 24 q^{55} - 4 q^{57} + 28 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} + 4 q^{62} + 48 q^{64} + 28 q^{65} - 16 q^{66} + 44 q^{67} + 32 q^{68} - 20 q^{69} + 20 q^{71} + 24 q^{72} + 16 q^{73} + 44 q^{74} - 48 q^{75} + 16 q^{76} + 32 q^{78} + 4 q^{79} - 44 q^{80} + 24 q^{81} + 8 q^{82} - 8 q^{83} + 28 q^{85} + 56 q^{86} - 24 q^{87} + 60 q^{88} - 60 q^{89} + 4 q^{90} + 60 q^{92} - 4 q^{93} - 24 q^{94} + 28 q^{95} - 36 q^{96} + 48 q^{97} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.78139 1.96674 0.983369 0.181618i \(-0.0581335\pi\)
0.983369 + 0.181618i \(0.0581335\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.73612 2.86806
\(5\) −0.739443 −0.330689 −0.165344 0.986236i \(-0.552874\pi\)
−0.165344 + 0.986236i \(0.552874\pi\)
\(6\) −2.78139 −1.13550
\(7\) 0 0
\(8\) 10.3916 3.67398
\(9\) 1.00000 0.333333
\(10\) −2.05668 −0.650378
\(11\) 4.44400 1.33992 0.669958 0.742399i \(-0.266312\pi\)
0.669958 + 0.742399i \(0.266312\pi\)
\(12\) −5.73612 −1.65587
\(13\) −0.996618 −0.276412 −0.138206 0.990404i \(-0.544134\pi\)
−0.138206 + 0.990404i \(0.544134\pi\)
\(14\) 0 0
\(15\) 0.739443 0.190923
\(16\) 17.4308 4.35770
\(17\) 1.26311 0.306349 0.153174 0.988199i \(-0.451050\pi\)
0.153174 + 0.988199i \(0.451050\pi\)
\(18\) 2.78139 0.655579
\(19\) 1.98029 0.454310 0.227155 0.973859i \(-0.427058\pi\)
0.227155 + 0.973859i \(0.427058\pi\)
\(20\) −4.24153 −0.948435
\(21\) 0 0
\(22\) 12.3605 2.63526
\(23\) 0.818638 0.170698 0.0853490 0.996351i \(-0.472799\pi\)
0.0853490 + 0.996351i \(0.472799\pi\)
\(24\) −10.3916 −2.12118
\(25\) −4.45322 −0.890645
\(26\) −2.77198 −0.543630
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −0.261203 −0.0485042 −0.0242521 0.999706i \(-0.507720\pi\)
−0.0242521 + 0.999706i \(0.507720\pi\)
\(30\) 2.05668 0.375496
\(31\) 7.23078 1.29869 0.649344 0.760495i \(-0.275044\pi\)
0.649344 + 0.760495i \(0.275044\pi\)
\(32\) 27.6987 4.89648
\(33\) −4.44400 −0.773600
\(34\) 3.51319 0.602508
\(35\) 0 0
\(36\) 5.73612 0.956020
\(37\) −7.70796 −1.26718 −0.633591 0.773668i \(-0.718420\pi\)
−0.633591 + 0.773668i \(0.718420\pi\)
\(38\) 5.50796 0.893510
\(39\) 0.996618 0.159587
\(40\) −7.68399 −1.21495
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −4.72101 −0.719947 −0.359974 0.932963i \(-0.617214\pi\)
−0.359974 + 0.932963i \(0.617214\pi\)
\(44\) 25.4913 3.84296
\(45\) −0.739443 −0.110230
\(46\) 2.27695 0.335718
\(47\) 8.48773 1.23806 0.619031 0.785366i \(-0.287525\pi\)
0.619031 + 0.785366i \(0.287525\pi\)
\(48\) −17.4308 −2.51592
\(49\) 0 0
\(50\) −12.3861 −1.75167
\(51\) −1.26311 −0.176871
\(52\) −5.71672 −0.792766
\(53\) −10.1423 −1.39316 −0.696579 0.717480i \(-0.745295\pi\)
−0.696579 + 0.717480i \(0.745295\pi\)
\(54\) −2.78139 −0.378499
\(55\) −3.28608 −0.443095
\(56\) 0 0
\(57\) −1.98029 −0.262296
\(58\) −0.726506 −0.0953950
\(59\) 7.87031 1.02463 0.512313 0.858799i \(-0.328789\pi\)
0.512313 + 0.858799i \(0.328789\pi\)
\(60\) 4.24153 0.547579
\(61\) −6.85524 −0.877723 −0.438862 0.898555i \(-0.644618\pi\)
−0.438862 + 0.898555i \(0.644618\pi\)
\(62\) 20.1116 2.55418
\(63\) 0 0
\(64\) 42.1791 5.27239
\(65\) 0.736942 0.0914064
\(66\) −12.3605 −1.52147
\(67\) 4.70290 0.574551 0.287276 0.957848i \(-0.407250\pi\)
0.287276 + 0.957848i \(0.407250\pi\)
\(68\) 7.24534 0.878626
\(69\) −0.818638 −0.0985525
\(70\) 0 0
\(71\) −5.60455 −0.665138 −0.332569 0.943079i \(-0.607915\pi\)
−0.332569 + 0.943079i \(0.607915\pi\)
\(72\) 10.3916 1.22466
\(73\) −10.6056 −1.24129 −0.620643 0.784093i \(-0.713128\pi\)
−0.620643 + 0.784093i \(0.713128\pi\)
\(74\) −21.4388 −2.49221
\(75\) 4.45322 0.514214
\(76\) 11.3592 1.30299
\(77\) 0 0
\(78\) 2.77198 0.313865
\(79\) 1.81828 0.204572 0.102286 0.994755i \(-0.467384\pi\)
0.102286 + 0.994755i \(0.467384\pi\)
\(80\) −12.8891 −1.44104
\(81\) 1.00000 0.111111
\(82\) 2.78139 0.307153
\(83\) 14.9327 1.63907 0.819537 0.573027i \(-0.194231\pi\)
0.819537 + 0.573027i \(0.194231\pi\)
\(84\) 0 0
\(85\) −0.933996 −0.101306
\(86\) −13.1310 −1.41595
\(87\) 0.261203 0.0280039
\(88\) 46.1802 4.92283
\(89\) −11.9846 −1.27036 −0.635181 0.772364i \(-0.719074\pi\)
−0.635181 + 0.772364i \(0.719074\pi\)
\(90\) −2.05668 −0.216793
\(91\) 0 0
\(92\) 4.69581 0.489572
\(93\) −7.23078 −0.749797
\(94\) 23.6077 2.43495
\(95\) −1.46431 −0.150235
\(96\) −27.6987 −2.82698
\(97\) 7.76174 0.788086 0.394043 0.919092i \(-0.371076\pi\)
0.394043 + 0.919092i \(0.371076\pi\)
\(98\) 0 0
\(99\) 4.44400 0.446638
\(100\) −25.5442 −2.55442
\(101\) −1.90481 −0.189536 −0.0947680 0.995499i \(-0.530211\pi\)
−0.0947680 + 0.995499i \(0.530211\pi\)
\(102\) −3.51319 −0.347858
\(103\) 11.9010 1.17264 0.586318 0.810081i \(-0.300577\pi\)
0.586318 + 0.810081i \(0.300577\pi\)
\(104\) −10.3564 −1.01553
\(105\) 0 0
\(106\) −28.2098 −2.73998
\(107\) 20.1914 1.95197 0.975987 0.217828i \(-0.0698973\pi\)
0.975987 + 0.217828i \(0.0698973\pi\)
\(108\) −5.73612 −0.551958
\(109\) 12.9034 1.23592 0.617959 0.786210i \(-0.287960\pi\)
0.617959 + 0.786210i \(0.287960\pi\)
\(110\) −9.13986 −0.871452
\(111\) 7.70796 0.731608
\(112\) 0 0
\(113\) 4.91023 0.461916 0.230958 0.972964i \(-0.425814\pi\)
0.230958 + 0.972964i \(0.425814\pi\)
\(114\) −5.50796 −0.515868
\(115\) −0.605336 −0.0564479
\(116\) −1.49829 −0.139113
\(117\) −0.996618 −0.0921373
\(118\) 21.8904 2.01517
\(119\) 0 0
\(120\) 7.68399 0.701449
\(121\) 8.74910 0.795373
\(122\) −19.0671 −1.72625
\(123\) −1.00000 −0.0901670
\(124\) 41.4766 3.72471
\(125\) 6.99012 0.625215
\(126\) 0 0
\(127\) 13.3656 1.18600 0.593001 0.805201i \(-0.297943\pi\)
0.593001 + 0.805201i \(0.297943\pi\)
\(128\) 61.9191 5.47293
\(129\) 4.72101 0.415662
\(130\) 2.04972 0.179772
\(131\) 6.39618 0.558836 0.279418 0.960169i \(-0.409858\pi\)
0.279418 + 0.960169i \(0.409858\pi\)
\(132\) −25.4913 −2.21873
\(133\) 0 0
\(134\) 13.0806 1.12999
\(135\) 0.739443 0.0636411
\(136\) 13.1257 1.12552
\(137\) −17.7906 −1.51995 −0.759977 0.649950i \(-0.774790\pi\)
−0.759977 + 0.649950i \(0.774790\pi\)
\(138\) −2.27695 −0.193827
\(139\) −17.9649 −1.52376 −0.761881 0.647717i \(-0.775724\pi\)
−0.761881 + 0.647717i \(0.775724\pi\)
\(140\) 0 0
\(141\) −8.48773 −0.714796
\(142\) −15.5884 −1.30815
\(143\) −4.42897 −0.370369
\(144\) 17.4308 1.45257
\(145\) 0.193145 0.0160398
\(146\) −29.4982 −2.44128
\(147\) 0 0
\(148\) −44.2138 −3.63435
\(149\) 9.87073 0.808642 0.404321 0.914617i \(-0.367508\pi\)
0.404321 + 0.914617i \(0.367508\pi\)
\(150\) 12.3861 1.01132
\(151\) 2.97270 0.241915 0.120957 0.992658i \(-0.461404\pi\)
0.120957 + 0.992658i \(0.461404\pi\)
\(152\) 20.5784 1.66913
\(153\) 1.26311 0.102116
\(154\) 0 0
\(155\) −5.34675 −0.429461
\(156\) 5.71672 0.457704
\(157\) −7.59023 −0.605766 −0.302883 0.953028i \(-0.597949\pi\)
−0.302883 + 0.953028i \(0.597949\pi\)
\(158\) 5.05734 0.402340
\(159\) 10.1423 0.804340
\(160\) −20.4816 −1.61921
\(161\) 0 0
\(162\) 2.78139 0.218526
\(163\) 3.51811 0.275560 0.137780 0.990463i \(-0.456003\pi\)
0.137780 + 0.990463i \(0.456003\pi\)
\(164\) 5.73612 0.447916
\(165\) 3.28608 0.255821
\(166\) 41.5335 3.22363
\(167\) −11.7196 −0.906890 −0.453445 0.891284i \(-0.649805\pi\)
−0.453445 + 0.891284i \(0.649805\pi\)
\(168\) 0 0
\(169\) −12.0068 −0.923596
\(170\) −2.59781 −0.199243
\(171\) 1.98029 0.151437
\(172\) −27.0803 −2.06485
\(173\) 1.24977 0.0950180 0.0475090 0.998871i \(-0.484872\pi\)
0.0475090 + 0.998871i \(0.484872\pi\)
\(174\) 0.726506 0.0550763
\(175\) 0 0
\(176\) 77.4625 5.83895
\(177\) −7.87031 −0.591569
\(178\) −33.3337 −2.49847
\(179\) −22.2805 −1.66532 −0.832661 0.553783i \(-0.813184\pi\)
−0.832661 + 0.553783i \(0.813184\pi\)
\(180\) −4.24153 −0.316145
\(181\) −22.0862 −1.64166 −0.820828 0.571175i \(-0.806488\pi\)
−0.820828 + 0.571175i \(0.806488\pi\)
\(182\) 0 0
\(183\) 6.85524 0.506754
\(184\) 8.50696 0.627141
\(185\) 5.69960 0.419043
\(186\) −20.1116 −1.47466
\(187\) 5.61325 0.410481
\(188\) 48.6866 3.55084
\(189\) 0 0
\(190\) −4.07282 −0.295474
\(191\) −10.3978 −0.752362 −0.376181 0.926546i \(-0.622763\pi\)
−0.376181 + 0.926546i \(0.622763\pi\)
\(192\) −42.1791 −3.04402
\(193\) 7.05716 0.507985 0.253993 0.967206i \(-0.418256\pi\)
0.253993 + 0.967206i \(0.418256\pi\)
\(194\) 21.5884 1.54996
\(195\) −0.736942 −0.0527735
\(196\) 0 0
\(197\) 14.0301 0.999604 0.499802 0.866140i \(-0.333406\pi\)
0.499802 + 0.866140i \(0.333406\pi\)
\(198\) 12.3605 0.878421
\(199\) −18.5358 −1.31397 −0.656984 0.753904i \(-0.728168\pi\)
−0.656984 + 0.753904i \(0.728168\pi\)
\(200\) −46.2761 −3.27221
\(201\) −4.70290 −0.331717
\(202\) −5.29802 −0.372768
\(203\) 0 0
\(204\) −7.24534 −0.507275
\(205\) −0.739443 −0.0516449
\(206\) 33.1012 2.30627
\(207\) 0.818638 0.0568993
\(208\) −17.3719 −1.20452
\(209\) 8.80041 0.608737
\(210\) 0 0
\(211\) −4.96301 −0.341668 −0.170834 0.985300i \(-0.554646\pi\)
−0.170834 + 0.985300i \(0.554646\pi\)
\(212\) −58.1777 −3.99566
\(213\) 5.60455 0.384018
\(214\) 56.1601 3.83902
\(215\) 3.49092 0.238078
\(216\) −10.3916 −0.707058
\(217\) 0 0
\(218\) 35.8893 2.43073
\(219\) 10.6056 0.716657
\(220\) −18.8493 −1.27082
\(221\) −1.25884 −0.0846785
\(222\) 21.4388 1.43888
\(223\) −28.3618 −1.89924 −0.949622 0.313398i \(-0.898533\pi\)
−0.949622 + 0.313398i \(0.898533\pi\)
\(224\) 0 0
\(225\) −4.45322 −0.296882
\(226\) 13.6573 0.908468
\(227\) −12.3166 −0.817482 −0.408741 0.912650i \(-0.634032\pi\)
−0.408741 + 0.912650i \(0.634032\pi\)
\(228\) −11.3592 −0.752281
\(229\) 28.5546 1.88694 0.943470 0.331459i \(-0.107541\pi\)
0.943470 + 0.331459i \(0.107541\pi\)
\(230\) −1.68367 −0.111018
\(231\) 0 0
\(232\) −2.71431 −0.178203
\(233\) 4.44452 0.291170 0.145585 0.989346i \(-0.453493\pi\)
0.145585 + 0.989346i \(0.453493\pi\)
\(234\) −2.77198 −0.181210
\(235\) −6.27619 −0.409413
\(236\) 45.1450 2.93869
\(237\) −1.81828 −0.118110
\(238\) 0 0
\(239\) 6.27584 0.405950 0.202975 0.979184i \(-0.434939\pi\)
0.202975 + 0.979184i \(0.434939\pi\)
\(240\) 12.8891 0.831987
\(241\) 1.02263 0.0658735 0.0329367 0.999457i \(-0.489514\pi\)
0.0329367 + 0.999457i \(0.489514\pi\)
\(242\) 24.3347 1.56429
\(243\) −1.00000 −0.0641500
\(244\) −39.3224 −2.51736
\(245\) 0 0
\(246\) −2.78139 −0.177335
\(247\) −1.97360 −0.125577
\(248\) 75.1394 4.77135
\(249\) −14.9327 −0.946319
\(250\) 19.4422 1.22963
\(251\) −14.9031 −0.940675 −0.470338 0.882486i \(-0.655868\pi\)
−0.470338 + 0.882486i \(0.655868\pi\)
\(252\) 0 0
\(253\) 3.63803 0.228721
\(254\) 37.1748 2.33256
\(255\) 0.933996 0.0584891
\(256\) 87.8629 5.49143
\(257\) 12.2433 0.763716 0.381858 0.924221i \(-0.375284\pi\)
0.381858 + 0.924221i \(0.375284\pi\)
\(258\) 13.1310 0.817498
\(259\) 0 0
\(260\) 4.22718 0.262159
\(261\) −0.261203 −0.0161681
\(262\) 17.7902 1.09908
\(263\) 14.3878 0.887190 0.443595 0.896227i \(-0.353703\pi\)
0.443595 + 0.896227i \(0.353703\pi\)
\(264\) −46.1802 −2.84220
\(265\) 7.49968 0.460702
\(266\) 0 0
\(267\) 11.9846 0.733443
\(268\) 26.9764 1.64785
\(269\) 15.4040 0.939200 0.469600 0.882879i \(-0.344398\pi\)
0.469600 + 0.882879i \(0.344398\pi\)
\(270\) 2.05668 0.125165
\(271\) 23.6110 1.43427 0.717134 0.696936i \(-0.245454\pi\)
0.717134 + 0.696936i \(0.245454\pi\)
\(272\) 22.0170 1.33498
\(273\) 0 0
\(274\) −49.4826 −2.98935
\(275\) −19.7901 −1.19339
\(276\) −4.69581 −0.282654
\(277\) −22.5841 −1.35695 −0.678473 0.734626i \(-0.737358\pi\)
−0.678473 + 0.734626i \(0.737358\pi\)
\(278\) −49.9673 −2.99684
\(279\) 7.23078 0.432896
\(280\) 0 0
\(281\) −16.9736 −1.01256 −0.506280 0.862369i \(-0.668980\pi\)
−0.506280 + 0.862369i \(0.668980\pi\)
\(282\) −23.6077 −1.40582
\(283\) 21.2050 1.26051 0.630254 0.776389i \(-0.282951\pi\)
0.630254 + 0.776389i \(0.282951\pi\)
\(284\) −32.1484 −1.90766
\(285\) 1.46431 0.0867384
\(286\) −12.3187 −0.728418
\(287\) 0 0
\(288\) 27.6987 1.63216
\(289\) −15.4046 −0.906150
\(290\) 0.537210 0.0315460
\(291\) −7.76174 −0.455001
\(292\) −60.8347 −3.56008
\(293\) −2.59209 −0.151431 −0.0757156 0.997129i \(-0.524124\pi\)
−0.0757156 + 0.997129i \(0.524124\pi\)
\(294\) 0 0
\(295\) −5.81964 −0.338833
\(296\) −80.0980 −4.65560
\(297\) −4.44400 −0.257867
\(298\) 27.4543 1.59039
\(299\) −0.815870 −0.0471830
\(300\) 25.5442 1.47480
\(301\) 0 0
\(302\) 8.26822 0.475783
\(303\) 1.90481 0.109429
\(304\) 34.5181 1.97975
\(305\) 5.06905 0.290253
\(306\) 3.51319 0.200836
\(307\) −6.79604 −0.387871 −0.193935 0.981014i \(-0.562125\pi\)
−0.193935 + 0.981014i \(0.562125\pi\)
\(308\) 0 0
\(309\) −11.9010 −0.677022
\(310\) −14.8714 −0.844638
\(311\) −30.4275 −1.72538 −0.862692 0.505730i \(-0.831223\pi\)
−0.862692 + 0.505730i \(0.831223\pi\)
\(312\) 10.3564 0.586318
\(313\) −17.2644 −0.975841 −0.487921 0.872888i \(-0.662244\pi\)
−0.487921 + 0.872888i \(0.662244\pi\)
\(314\) −21.1114 −1.19138
\(315\) 0 0
\(316\) 10.4299 0.586725
\(317\) 34.1992 1.92082 0.960409 0.278593i \(-0.0898679\pi\)
0.960409 + 0.278593i \(0.0898679\pi\)
\(318\) 28.2098 1.58193
\(319\) −1.16078 −0.0649915
\(320\) −31.1890 −1.74352
\(321\) −20.1914 −1.12697
\(322\) 0 0
\(323\) 2.50132 0.139177
\(324\) 5.73612 0.318673
\(325\) 4.43816 0.246185
\(326\) 9.78524 0.541954
\(327\) −12.9034 −0.713558
\(328\) 10.3916 0.573780
\(329\) 0 0
\(330\) 9.13986 0.503133
\(331\) −9.26778 −0.509403 −0.254702 0.967020i \(-0.581977\pi\)
−0.254702 + 0.967020i \(0.581977\pi\)
\(332\) 85.6555 4.70096
\(333\) −7.70796 −0.422394
\(334\) −32.5968 −1.78362
\(335\) −3.47753 −0.189998
\(336\) 0 0
\(337\) 6.87332 0.374414 0.187207 0.982321i \(-0.440057\pi\)
0.187207 + 0.982321i \(0.440057\pi\)
\(338\) −33.3954 −1.81647
\(339\) −4.91023 −0.266687
\(340\) −5.35751 −0.290552
\(341\) 32.1336 1.74013
\(342\) 5.50796 0.297837
\(343\) 0 0
\(344\) −49.0588 −2.64507
\(345\) 0.605336 0.0325902
\(346\) 3.47609 0.186876
\(347\) −24.8500 −1.33402 −0.667008 0.745050i \(-0.732425\pi\)
−0.667008 + 0.745050i \(0.732425\pi\)
\(348\) 1.49829 0.0803168
\(349\) −9.14773 −0.489667 −0.244833 0.969565i \(-0.578733\pi\)
−0.244833 + 0.969565i \(0.578733\pi\)
\(350\) 0 0
\(351\) 0.996618 0.0531955
\(352\) 123.093 6.56087
\(353\) −13.1852 −0.701775 −0.350887 0.936418i \(-0.614120\pi\)
−0.350887 + 0.936418i \(0.614120\pi\)
\(354\) −21.8904 −1.16346
\(355\) 4.14425 0.219954
\(356\) −68.7449 −3.64347
\(357\) 0 0
\(358\) −61.9707 −3.27525
\(359\) 19.9471 1.05277 0.526383 0.850247i \(-0.323548\pi\)
0.526383 + 0.850247i \(0.323548\pi\)
\(360\) −7.68399 −0.404982
\(361\) −15.0784 −0.793602
\(362\) −61.4304 −3.22871
\(363\) −8.74910 −0.459209
\(364\) 0 0
\(365\) 7.84220 0.410479
\(366\) 19.0671 0.996652
\(367\) 12.8609 0.671332 0.335666 0.941981i \(-0.391039\pi\)
0.335666 + 0.941981i \(0.391039\pi\)
\(368\) 14.2695 0.743851
\(369\) 1.00000 0.0520579
\(370\) 15.8528 0.824147
\(371\) 0 0
\(372\) −41.4766 −2.15046
\(373\) 24.4376 1.26533 0.632666 0.774425i \(-0.281961\pi\)
0.632666 + 0.774425i \(0.281961\pi\)
\(374\) 15.6126 0.807309
\(375\) −6.99012 −0.360968
\(376\) 88.2010 4.54862
\(377\) 0.260319 0.0134071
\(378\) 0 0
\(379\) −12.0687 −0.619929 −0.309965 0.950748i \(-0.600317\pi\)
−0.309965 + 0.950748i \(0.600317\pi\)
\(380\) −8.39947 −0.430884
\(381\) −13.3656 −0.684739
\(382\) −28.9204 −1.47970
\(383\) −22.0469 −1.12654 −0.563272 0.826272i \(-0.690458\pi\)
−0.563272 + 0.826272i \(0.690458\pi\)
\(384\) −61.9191 −3.15980
\(385\) 0 0
\(386\) 19.6287 0.999074
\(387\) −4.72101 −0.239982
\(388\) 44.5223 2.26028
\(389\) −25.3972 −1.28769 −0.643844 0.765157i \(-0.722662\pi\)
−0.643844 + 0.765157i \(0.722662\pi\)
\(390\) −2.04972 −0.103792
\(391\) 1.03403 0.0522931
\(392\) 0 0
\(393\) −6.39618 −0.322644
\(394\) 39.0232 1.96596
\(395\) −1.34451 −0.0676498
\(396\) 25.4913 1.28099
\(397\) −8.21500 −0.412299 −0.206149 0.978521i \(-0.566093\pi\)
−0.206149 + 0.978521i \(0.566093\pi\)
\(398\) −51.5553 −2.58423
\(399\) 0 0
\(400\) −77.6233 −3.88117
\(401\) −17.4105 −0.869438 −0.434719 0.900566i \(-0.643152\pi\)
−0.434719 + 0.900566i \(0.643152\pi\)
\(402\) −13.0806 −0.652401
\(403\) −7.20633 −0.358973
\(404\) −10.9262 −0.543600
\(405\) −0.739443 −0.0367432
\(406\) 0 0
\(407\) −34.2542 −1.69792
\(408\) −13.1257 −0.649819
\(409\) 32.4066 1.60241 0.801203 0.598393i \(-0.204194\pi\)
0.801203 + 0.598393i \(0.204194\pi\)
\(410\) −2.05668 −0.101572
\(411\) 17.7906 0.877546
\(412\) 68.2653 3.36319
\(413\) 0 0
\(414\) 2.27695 0.111906
\(415\) −11.0419 −0.542023
\(416\) −27.6050 −1.35345
\(417\) 17.9649 0.879745
\(418\) 24.4774 1.19723
\(419\) −30.3528 −1.48283 −0.741417 0.671045i \(-0.765846\pi\)
−0.741417 + 0.671045i \(0.765846\pi\)
\(420\) 0 0
\(421\) −11.4240 −0.556772 −0.278386 0.960469i \(-0.589799\pi\)
−0.278386 + 0.960469i \(0.589799\pi\)
\(422\) −13.8041 −0.671971
\(423\) 8.48773 0.412688
\(424\) −105.395 −5.11844
\(425\) −5.62490 −0.272848
\(426\) 15.5884 0.755262
\(427\) 0 0
\(428\) 115.820 5.59838
\(429\) 4.42897 0.213832
\(430\) 9.70959 0.468238
\(431\) −20.2073 −0.973353 −0.486677 0.873582i \(-0.661791\pi\)
−0.486677 + 0.873582i \(0.661791\pi\)
\(432\) −17.4308 −0.838641
\(433\) 6.32439 0.303931 0.151965 0.988386i \(-0.451440\pi\)
0.151965 + 0.988386i \(0.451440\pi\)
\(434\) 0 0
\(435\) −0.193145 −0.00926057
\(436\) 74.0153 3.54469
\(437\) 1.62114 0.0775498
\(438\) 29.4982 1.40948
\(439\) −24.0627 −1.14845 −0.574226 0.818697i \(-0.694697\pi\)
−0.574226 + 0.818697i \(0.694697\pi\)
\(440\) −34.1476 −1.62792
\(441\) 0 0
\(442\) −3.50131 −0.166540
\(443\) 15.6018 0.741263 0.370631 0.928780i \(-0.379141\pi\)
0.370631 + 0.928780i \(0.379141\pi\)
\(444\) 44.2138 2.09829
\(445\) 8.86190 0.420094
\(446\) −78.8850 −3.73531
\(447\) −9.87073 −0.466870
\(448\) 0 0
\(449\) −36.0234 −1.70005 −0.850025 0.526742i \(-0.823413\pi\)
−0.850025 + 0.526742i \(0.823413\pi\)
\(450\) −12.3861 −0.583888
\(451\) 4.44400 0.209260
\(452\) 28.1657 1.32480
\(453\) −2.97270 −0.139669
\(454\) −34.2573 −1.60777
\(455\) 0 0
\(456\) −20.5784 −0.963672
\(457\) 26.2316 1.22706 0.613532 0.789670i \(-0.289748\pi\)
0.613532 + 0.789670i \(0.289748\pi\)
\(458\) 79.4213 3.71112
\(459\) −1.26311 −0.0589568
\(460\) −3.47228 −0.161896
\(461\) −28.3632 −1.32101 −0.660503 0.750823i \(-0.729657\pi\)
−0.660503 + 0.750823i \(0.729657\pi\)
\(462\) 0 0
\(463\) 15.1426 0.703737 0.351869 0.936049i \(-0.385546\pi\)
0.351869 + 0.936049i \(0.385546\pi\)
\(464\) −4.55298 −0.211367
\(465\) 5.34675 0.247950
\(466\) 12.3619 0.572656
\(467\) 32.0316 1.48225 0.741124 0.671369i \(-0.234293\pi\)
0.741124 + 0.671369i \(0.234293\pi\)
\(468\) −5.71672 −0.264255
\(469\) 0 0
\(470\) −17.4565 −0.805209
\(471\) 7.59023 0.349739
\(472\) 81.7850 3.76446
\(473\) −20.9801 −0.964668
\(474\) −5.05734 −0.232291
\(475\) −8.81869 −0.404629
\(476\) 0 0
\(477\) −10.1423 −0.464386
\(478\) 17.4555 0.798398
\(479\) 1.91570 0.0875304 0.0437652 0.999042i \(-0.486065\pi\)
0.0437652 + 0.999042i \(0.486065\pi\)
\(480\) 20.4816 0.934852
\(481\) 7.68189 0.350264
\(482\) 2.84434 0.129556
\(483\) 0 0
\(484\) 50.1859 2.28118
\(485\) −5.73936 −0.260611
\(486\) −2.78139 −0.126166
\(487\) 3.36168 0.152332 0.0761661 0.997095i \(-0.475732\pi\)
0.0761661 + 0.997095i \(0.475732\pi\)
\(488\) −71.2368 −3.22474
\(489\) −3.51811 −0.159095
\(490\) 0 0
\(491\) 32.9652 1.48770 0.743848 0.668348i \(-0.232998\pi\)
0.743848 + 0.668348i \(0.232998\pi\)
\(492\) −5.73612 −0.258604
\(493\) −0.329927 −0.0148592
\(494\) −5.48933 −0.246977
\(495\) −3.28608 −0.147698
\(496\) 126.038 5.65929
\(497\) 0 0
\(498\) −41.5335 −1.86116
\(499\) −41.8130 −1.87180 −0.935902 0.352259i \(-0.885414\pi\)
−0.935902 + 0.352259i \(0.885414\pi\)
\(500\) 40.0961 1.79315
\(501\) 11.7196 0.523593
\(502\) −41.4513 −1.85006
\(503\) 25.0498 1.11692 0.558458 0.829533i \(-0.311393\pi\)
0.558458 + 0.829533i \(0.311393\pi\)
\(504\) 0 0
\(505\) 1.40850 0.0626774
\(506\) 10.1188 0.449834
\(507\) 12.0068 0.533239
\(508\) 76.6665 3.40153
\(509\) −30.3007 −1.34306 −0.671529 0.740979i \(-0.734362\pi\)
−0.671529 + 0.740979i \(0.734362\pi\)
\(510\) 2.59781 0.115033
\(511\) 0 0
\(512\) 120.543 5.32728
\(513\) −1.98029 −0.0874321
\(514\) 34.0534 1.50203
\(515\) −8.80008 −0.387778
\(516\) 27.0803 1.19214
\(517\) 37.7194 1.65890
\(518\) 0 0
\(519\) −1.24977 −0.0548587
\(520\) 7.65800 0.335825
\(521\) −24.0337 −1.05293 −0.526467 0.850195i \(-0.676484\pi\)
−0.526467 + 0.850195i \(0.676484\pi\)
\(522\) −0.726506 −0.0317983
\(523\) −0.910581 −0.0398169 −0.0199085 0.999802i \(-0.506337\pi\)
−0.0199085 + 0.999802i \(0.506337\pi\)
\(524\) 36.6892 1.60278
\(525\) 0 0
\(526\) 40.0181 1.74487
\(527\) 9.13326 0.397851
\(528\) −77.4625 −3.37112
\(529\) −22.3298 −0.970862
\(530\) 20.8595 0.906080
\(531\) 7.87031 0.341542
\(532\) 0 0
\(533\) −0.996618 −0.0431683
\(534\) 33.3337 1.44249
\(535\) −14.9304 −0.645496
\(536\) 48.8707 2.11089
\(537\) 22.2805 0.961475
\(538\) 42.8446 1.84716
\(539\) 0 0
\(540\) 4.24153 0.182526
\(541\) −19.6023 −0.842769 −0.421385 0.906882i \(-0.638456\pi\)
−0.421385 + 0.906882i \(0.638456\pi\)
\(542\) 65.6714 2.82083
\(543\) 22.0862 0.947811
\(544\) 34.9864 1.50003
\(545\) −9.54130 −0.408705
\(546\) 0 0
\(547\) −1.48929 −0.0636774 −0.0318387 0.999493i \(-0.510136\pi\)
−0.0318387 + 0.999493i \(0.510136\pi\)
\(548\) −102.049 −4.35932
\(549\) −6.85524 −0.292574
\(550\) −55.0440 −2.34708
\(551\) −0.517258 −0.0220359
\(552\) −8.50696 −0.362080
\(553\) 0 0
\(554\) −62.8151 −2.66876
\(555\) −5.69960 −0.241934
\(556\) −103.049 −4.37024
\(557\) 3.84524 0.162928 0.0814641 0.996676i \(-0.474040\pi\)
0.0814641 + 0.996676i \(0.474040\pi\)
\(558\) 20.1116 0.851392
\(559\) 4.70504 0.199002
\(560\) 0 0
\(561\) −5.61325 −0.236992
\(562\) −47.2102 −1.99144
\(563\) −33.2100 −1.39963 −0.699817 0.714322i \(-0.746735\pi\)
−0.699817 + 0.714322i \(0.746735\pi\)
\(564\) −48.6866 −2.05008
\(565\) −3.63084 −0.152750
\(566\) 58.9794 2.47909
\(567\) 0 0
\(568\) −58.2402 −2.44371
\(569\) −23.5829 −0.988648 −0.494324 0.869278i \(-0.664584\pi\)
−0.494324 + 0.869278i \(0.664584\pi\)
\(570\) 4.07282 0.170592
\(571\) 12.4917 0.522763 0.261381 0.965236i \(-0.415822\pi\)
0.261381 + 0.965236i \(0.415822\pi\)
\(572\) −25.4051 −1.06224
\(573\) 10.3978 0.434376
\(574\) 0 0
\(575\) −3.64558 −0.152031
\(576\) 42.1791 1.75746
\(577\) 0.650901 0.0270973 0.0135487 0.999908i \(-0.495687\pi\)
0.0135487 + 0.999908i \(0.495687\pi\)
\(578\) −42.8460 −1.78216
\(579\) −7.05716 −0.293285
\(580\) 1.10790 0.0460030
\(581\) 0 0
\(582\) −21.5884 −0.894869
\(583\) −45.0725 −1.86671
\(584\) −110.209 −4.56046
\(585\) 0.736942 0.0304688
\(586\) −7.20960 −0.297826
\(587\) −7.71470 −0.318420 −0.159210 0.987245i \(-0.550895\pi\)
−0.159210 + 0.987245i \(0.550895\pi\)
\(588\) 0 0
\(589\) 14.3191 0.590007
\(590\) −16.1867 −0.666395
\(591\) −14.0301 −0.577122
\(592\) −134.356 −5.52200
\(593\) −4.01641 −0.164934 −0.0824671 0.996594i \(-0.526280\pi\)
−0.0824671 + 0.996594i \(0.526280\pi\)
\(594\) −12.3605 −0.507157
\(595\) 0 0
\(596\) 56.6197 2.31923
\(597\) 18.5358 0.758620
\(598\) −2.26925 −0.0927965
\(599\) −6.86492 −0.280493 −0.140247 0.990117i \(-0.544790\pi\)
−0.140247 + 0.990117i \(0.544790\pi\)
\(600\) 46.2761 1.88921
\(601\) −13.0763 −0.533393 −0.266697 0.963781i \(-0.585932\pi\)
−0.266697 + 0.963781i \(0.585932\pi\)
\(602\) 0 0
\(603\) 4.70290 0.191517
\(604\) 17.0517 0.693825
\(605\) −6.46946 −0.263021
\(606\) 5.29802 0.215218
\(607\) 43.1382 1.75093 0.875463 0.483285i \(-0.160556\pi\)
0.875463 + 0.483285i \(0.160556\pi\)
\(608\) 54.8515 2.22452
\(609\) 0 0
\(610\) 14.0990 0.570852
\(611\) −8.45902 −0.342215
\(612\) 7.24534 0.292875
\(613\) 12.2221 0.493646 0.246823 0.969061i \(-0.420613\pi\)
0.246823 + 0.969061i \(0.420613\pi\)
\(614\) −18.9024 −0.762840
\(615\) 0.739443 0.0298172
\(616\) 0 0
\(617\) 1.82789 0.0735882 0.0367941 0.999323i \(-0.488285\pi\)
0.0367941 + 0.999323i \(0.488285\pi\)
\(618\) −33.1012 −1.33152
\(619\) 27.7081 1.11368 0.556842 0.830618i \(-0.312013\pi\)
0.556842 + 0.830618i \(0.312013\pi\)
\(620\) −30.6696 −1.23172
\(621\) −0.818638 −0.0328508
\(622\) −84.6306 −3.39338
\(623\) 0 0
\(624\) 17.3719 0.695431
\(625\) 17.0973 0.683893
\(626\) −48.0190 −1.91922
\(627\) −8.80041 −0.351455
\(628\) −43.5385 −1.73737
\(629\) −9.73599 −0.388200
\(630\) 0 0
\(631\) 13.4494 0.535413 0.267707 0.963501i \(-0.413734\pi\)
0.267707 + 0.963501i \(0.413734\pi\)
\(632\) 18.8948 0.751595
\(633\) 4.96301 0.197262
\(634\) 95.1213 3.77775
\(635\) −9.88308 −0.392198
\(636\) 58.1777 2.30690
\(637\) 0 0
\(638\) −3.22859 −0.127821
\(639\) −5.60455 −0.221713
\(640\) −45.7857 −1.80984
\(641\) −20.7826 −0.820863 −0.410432 0.911891i \(-0.634622\pi\)
−0.410432 + 0.911891i \(0.634622\pi\)
\(642\) −56.1601 −2.21646
\(643\) −43.3748 −1.71054 −0.855268 0.518186i \(-0.826607\pi\)
−0.855268 + 0.518186i \(0.826607\pi\)
\(644\) 0 0
\(645\) −3.49092 −0.137455
\(646\) 6.95715 0.273726
\(647\) 22.5713 0.887369 0.443685 0.896183i \(-0.353671\pi\)
0.443685 + 0.896183i \(0.353671\pi\)
\(648\) 10.3916 0.408220
\(649\) 34.9756 1.37291
\(650\) 12.3443 0.484181
\(651\) 0 0
\(652\) 20.1803 0.790322
\(653\) −38.7485 −1.51635 −0.758173 0.652053i \(-0.773908\pi\)
−0.758173 + 0.652053i \(0.773908\pi\)
\(654\) −35.8893 −1.40338
\(655\) −4.72960 −0.184801
\(656\) 17.4308 0.680559
\(657\) −10.6056 −0.413762
\(658\) 0 0
\(659\) 36.1448 1.40800 0.704001 0.710199i \(-0.251395\pi\)
0.704001 + 0.710199i \(0.251395\pi\)
\(660\) 18.8493 0.733710
\(661\) −22.4151 −0.871846 −0.435923 0.899984i \(-0.643578\pi\)
−0.435923 + 0.899984i \(0.643578\pi\)
\(662\) −25.7773 −1.00186
\(663\) 1.25884 0.0488891
\(664\) 155.174 6.02193
\(665\) 0 0
\(666\) −21.4388 −0.830738
\(667\) −0.213831 −0.00827956
\(668\) −67.2250 −2.60101
\(669\) 28.3618 1.09653
\(670\) −9.67235 −0.373676
\(671\) −30.4646 −1.17607
\(672\) 0 0
\(673\) 38.9476 1.50132 0.750660 0.660688i \(-0.229735\pi\)
0.750660 + 0.660688i \(0.229735\pi\)
\(674\) 19.1174 0.736374
\(675\) 4.45322 0.171405
\(676\) −68.8722 −2.64893
\(677\) 46.3643 1.78192 0.890962 0.454077i \(-0.150031\pi\)
0.890962 + 0.454077i \(0.150031\pi\)
\(678\) −13.6573 −0.524504
\(679\) 0 0
\(680\) −9.70571 −0.372197
\(681\) 12.3166 0.471974
\(682\) 89.3759 3.42238
\(683\) −25.7755 −0.986271 −0.493135 0.869953i \(-0.664149\pi\)
−0.493135 + 0.869953i \(0.664149\pi\)
\(684\) 11.3592 0.434330
\(685\) 13.1551 0.502632
\(686\) 0 0
\(687\) −28.5546 −1.08942
\(688\) −82.2910 −3.13732
\(689\) 10.1080 0.385086
\(690\) 1.68367 0.0640964
\(691\) 43.5702 1.65749 0.828744 0.559628i \(-0.189056\pi\)
0.828744 + 0.559628i \(0.189056\pi\)
\(692\) 7.16881 0.272517
\(693\) 0 0
\(694\) −69.1174 −2.62366
\(695\) 13.2840 0.503891
\(696\) 2.71431 0.102886
\(697\) 1.26311 0.0478436
\(698\) −25.4434 −0.963047
\(699\) −4.44452 −0.168107
\(700\) 0 0
\(701\) 26.0873 0.985305 0.492652 0.870226i \(-0.336027\pi\)
0.492652 + 0.870226i \(0.336027\pi\)
\(702\) 2.77198 0.104622
\(703\) −15.2640 −0.575694
\(704\) 187.444 7.06456
\(705\) 6.27619 0.236375
\(706\) −36.6730 −1.38021
\(707\) 0 0
\(708\) −45.1450 −1.69665
\(709\) −5.54993 −0.208432 −0.104216 0.994555i \(-0.533233\pi\)
−0.104216 + 0.994555i \(0.533233\pi\)
\(710\) 11.5268 0.432591
\(711\) 1.81828 0.0681908
\(712\) −124.539 −4.66729
\(713\) 5.91940 0.221683
\(714\) 0 0
\(715\) 3.27497 0.122477
\(716\) −127.804 −4.77624
\(717\) −6.27584 −0.234375
\(718\) 55.4806 2.07052
\(719\) −12.7308 −0.474777 −0.237388 0.971415i \(-0.576291\pi\)
−0.237388 + 0.971415i \(0.576291\pi\)
\(720\) −12.8891 −0.480348
\(721\) 0 0
\(722\) −41.9390 −1.56081
\(723\) −1.02263 −0.0380321
\(724\) −126.689 −4.70837
\(725\) 1.16319 0.0432000
\(726\) −24.3347 −0.903144
\(727\) 8.95982 0.332301 0.166151 0.986100i \(-0.446866\pi\)
0.166151 + 0.986100i \(0.446866\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 21.8122 0.807306
\(731\) −5.96315 −0.220555
\(732\) 39.3224 1.45340
\(733\) −22.4833 −0.830438 −0.415219 0.909721i \(-0.636295\pi\)
−0.415219 + 0.909721i \(0.636295\pi\)
\(734\) 35.7711 1.32033
\(735\) 0 0
\(736\) 22.6752 0.835819
\(737\) 20.8997 0.769850
\(738\) 2.78139 0.102384
\(739\) −41.6105 −1.53067 −0.765334 0.643633i \(-0.777426\pi\)
−0.765334 + 0.643633i \(0.777426\pi\)
\(740\) 32.6936 1.20184
\(741\) 1.97360 0.0725018
\(742\) 0 0
\(743\) −5.94361 −0.218050 −0.109025 0.994039i \(-0.534773\pi\)
−0.109025 + 0.994039i \(0.534773\pi\)
\(744\) −75.1394 −2.75474
\(745\) −7.29884 −0.267409
\(746\) 67.9705 2.48858
\(747\) 14.9327 0.546358
\(748\) 32.1983 1.17728
\(749\) 0 0
\(750\) −19.4422 −0.709930
\(751\) −33.6224 −1.22690 −0.613450 0.789734i \(-0.710219\pi\)
−0.613450 + 0.789734i \(0.710219\pi\)
\(752\) 147.948 5.39511
\(753\) 14.9031 0.543099
\(754\) 0.724049 0.0263683
\(755\) −2.19814 −0.0799984
\(756\) 0 0
\(757\) −0.503440 −0.0182978 −0.00914892 0.999958i \(-0.502912\pi\)
−0.00914892 + 0.999958i \(0.502912\pi\)
\(758\) −33.5678 −1.21924
\(759\) −3.63803 −0.132052
\(760\) −15.2165 −0.551962
\(761\) −33.1318 −1.20103 −0.600513 0.799615i \(-0.705037\pi\)
−0.600513 + 0.799615i \(0.705037\pi\)
\(762\) −37.1748 −1.34670
\(763\) 0 0
\(764\) −59.6433 −2.15782
\(765\) −0.933996 −0.0337687
\(766\) −61.3210 −2.21562
\(767\) −7.84369 −0.283219
\(768\) −87.8629 −3.17048
\(769\) 17.7871 0.641419 0.320710 0.947178i \(-0.396079\pi\)
0.320710 + 0.947178i \(0.396079\pi\)
\(770\) 0 0
\(771\) −12.2433 −0.440932
\(772\) 40.4807 1.45693
\(773\) −9.30219 −0.334577 −0.167288 0.985908i \(-0.553501\pi\)
−0.167288 + 0.985908i \(0.553501\pi\)
\(774\) −13.1310 −0.471983
\(775\) −32.2003 −1.15667
\(776\) 80.6569 2.89541
\(777\) 0 0
\(778\) −70.6394 −2.53255
\(779\) 1.98029 0.0709514
\(780\) −4.22718 −0.151357
\(781\) −24.9066 −0.891229
\(782\) 2.87604 0.102847
\(783\) 0.261203 0.00933463
\(784\) 0 0
\(785\) 5.61254 0.200320
\(786\) −17.7902 −0.634557
\(787\) 1.42985 0.0509687 0.0254844 0.999675i \(-0.491887\pi\)
0.0254844 + 0.999675i \(0.491887\pi\)
\(788\) 80.4784 2.86692
\(789\) −14.3878 −0.512219
\(790\) −3.73961 −0.133049
\(791\) 0 0
\(792\) 46.1802 1.64094
\(793\) 6.83205 0.242613
\(794\) −22.8491 −0.810884
\(795\) −7.49968 −0.265986
\(796\) −106.324 −3.76854
\(797\) −22.3072 −0.790163 −0.395081 0.918646i \(-0.629284\pi\)
−0.395081 + 0.918646i \(0.629284\pi\)
\(798\) 0 0
\(799\) 10.7209 0.379279
\(800\) −123.348 −4.36102
\(801\) −11.9846 −0.423454
\(802\) −48.4253 −1.70996
\(803\) −47.1310 −1.66322
\(804\) −26.9764 −0.951385
\(805\) 0 0
\(806\) −20.0436 −0.706005
\(807\) −15.4040 −0.542247
\(808\) −19.7940 −0.696352
\(809\) −13.6353 −0.479392 −0.239696 0.970848i \(-0.577048\pi\)
−0.239696 + 0.970848i \(0.577048\pi\)
\(810\) −2.05668 −0.0722643
\(811\) 13.4034 0.470659 0.235329 0.971916i \(-0.424383\pi\)
0.235329 + 0.971916i \(0.424383\pi\)
\(812\) 0 0
\(813\) −23.6110 −0.828074
\(814\) −95.2741 −3.33936
\(815\) −2.60144 −0.0911246
\(816\) −22.0170 −0.770749
\(817\) −9.34898 −0.327079
\(818\) 90.1355 3.15151
\(819\) 0 0
\(820\) −4.24153 −0.148121
\(821\) 50.9993 1.77989 0.889944 0.456070i \(-0.150743\pi\)
0.889944 + 0.456070i \(0.150743\pi\)
\(822\) 49.4826 1.72590
\(823\) −46.0488 −1.60516 −0.802580 0.596545i \(-0.796540\pi\)
−0.802580 + 0.596545i \(0.796540\pi\)
\(824\) 123.670 4.30825
\(825\) 19.7901 0.689003
\(826\) 0 0
\(827\) −33.3779 −1.16066 −0.580332 0.814380i \(-0.697077\pi\)
−0.580332 + 0.814380i \(0.697077\pi\)
\(828\) 4.69581 0.163191
\(829\) 13.5451 0.470440 0.235220 0.971942i \(-0.424419\pi\)
0.235220 + 0.971942i \(0.424419\pi\)
\(830\) −30.7117 −1.06602
\(831\) 22.5841 0.783433
\(832\) −42.0365 −1.45735
\(833\) 0 0
\(834\) 49.9673 1.73023
\(835\) 8.66597 0.299898
\(836\) 50.4802 1.74589
\(837\) −7.23078 −0.249932
\(838\) −84.4230 −2.91634
\(839\) −37.2031 −1.28439 −0.642196 0.766540i \(-0.721977\pi\)
−0.642196 + 0.766540i \(0.721977\pi\)
\(840\) 0 0
\(841\) −28.9318 −0.997647
\(842\) −31.7746 −1.09503
\(843\) 16.9736 0.584602
\(844\) −28.4684 −0.979923
\(845\) 8.87831 0.305423
\(846\) 23.6077 0.811648
\(847\) 0 0
\(848\) −176.789 −6.07097
\(849\) −21.2050 −0.727755
\(850\) −15.6450 −0.536621
\(851\) −6.31004 −0.216305
\(852\) 32.1484 1.10139
\(853\) 6.70239 0.229486 0.114743 0.993395i \(-0.463396\pi\)
0.114743 + 0.993395i \(0.463396\pi\)
\(854\) 0 0
\(855\) −1.46431 −0.0500785
\(856\) 209.821 7.17152
\(857\) −35.3173 −1.20642 −0.603208 0.797584i \(-0.706111\pi\)
−0.603208 + 0.797584i \(0.706111\pi\)
\(858\) 12.3187 0.420552
\(859\) 48.0851 1.64064 0.820322 0.571902i \(-0.193794\pi\)
0.820322 + 0.571902i \(0.193794\pi\)
\(860\) 20.0243 0.682823
\(861\) 0 0
\(862\) −56.2044 −1.91433
\(863\) 0.553632 0.0188458 0.00942292 0.999956i \(-0.497001\pi\)
0.00942292 + 0.999956i \(0.497001\pi\)
\(864\) −27.6987 −0.942328
\(865\) −0.924131 −0.0314214
\(866\) 17.5906 0.597752
\(867\) 15.4046 0.523166
\(868\) 0 0
\(869\) 8.08042 0.274110
\(870\) −0.537210 −0.0182131
\(871\) −4.68700 −0.158813
\(872\) 134.087 4.54075
\(873\) 7.76174 0.262695
\(874\) 4.50903 0.152520
\(875\) 0 0
\(876\) 60.8347 2.05541
\(877\) −13.8660 −0.468222 −0.234111 0.972210i \(-0.575218\pi\)
−0.234111 + 0.972210i \(0.575218\pi\)
\(878\) −66.9278 −2.25870
\(879\) 2.59209 0.0874289
\(880\) −57.2791 −1.93088
\(881\) 8.62496 0.290582 0.145291 0.989389i \(-0.453588\pi\)
0.145291 + 0.989389i \(0.453588\pi\)
\(882\) 0 0
\(883\) 28.1227 0.946404 0.473202 0.880954i \(-0.343098\pi\)
0.473202 + 0.880954i \(0.343098\pi\)
\(884\) −7.22083 −0.242863
\(885\) 5.81964 0.195625
\(886\) 43.3946 1.45787
\(887\) 28.6430 0.961737 0.480869 0.876793i \(-0.340321\pi\)
0.480869 + 0.876793i \(0.340321\pi\)
\(888\) 80.0980 2.68791
\(889\) 0 0
\(890\) 24.6484 0.826215
\(891\) 4.44400 0.148879
\(892\) −162.686 −5.44714
\(893\) 16.8082 0.562465
\(894\) −27.4543 −0.918210
\(895\) 16.4752 0.550704
\(896\) 0 0
\(897\) 0.815870 0.0272411
\(898\) −100.195 −3.34355
\(899\) −1.88870 −0.0629917
\(900\) −25.5442 −0.851474
\(901\) −12.8109 −0.426792
\(902\) 12.3605 0.411559
\(903\) 0 0
\(904\) 51.0252 1.69707
\(905\) 16.3315 0.542878
\(906\) −8.26822 −0.274693
\(907\) 15.9653 0.530119 0.265060 0.964232i \(-0.414608\pi\)
0.265060 + 0.964232i \(0.414608\pi\)
\(908\) −70.6495 −2.34459
\(909\) −1.90481 −0.0631787
\(910\) 0 0
\(911\) 5.29604 0.175466 0.0877328 0.996144i \(-0.472038\pi\)
0.0877328 + 0.996144i \(0.472038\pi\)
\(912\) −34.5181 −1.14301
\(913\) 66.3607 2.19622
\(914\) 72.9604 2.41332
\(915\) −5.06905 −0.167578
\(916\) 163.792 5.41185
\(917\) 0 0
\(918\) −3.51319 −0.115953
\(919\) 37.9280 1.25113 0.625564 0.780173i \(-0.284869\pi\)
0.625564 + 0.780173i \(0.284869\pi\)
\(920\) −6.29041 −0.207389
\(921\) 6.79604 0.223937
\(922\) −78.8891 −2.59807
\(923\) 5.58560 0.183852
\(924\) 0 0
\(925\) 34.3253 1.12861
\(926\) 42.1175 1.38407
\(927\) 11.9010 0.390879
\(928\) −7.23497 −0.237500
\(929\) −48.1695 −1.58039 −0.790195 0.612855i \(-0.790021\pi\)
−0.790195 + 0.612855i \(0.790021\pi\)
\(930\) 14.8714 0.487652
\(931\) 0 0
\(932\) 25.4943 0.835094
\(933\) 30.4275 0.996150
\(934\) 89.0924 2.91519
\(935\) −4.15068 −0.135742
\(936\) −10.3564 −0.338511
\(937\) −57.1372 −1.86659 −0.933295 0.359111i \(-0.883080\pi\)
−0.933295 + 0.359111i \(0.883080\pi\)
\(938\) 0 0
\(939\) 17.2644 0.563402
\(940\) −36.0010 −1.17422
\(941\) 47.0404 1.53347 0.766736 0.641962i \(-0.221879\pi\)
0.766736 + 0.641962i \(0.221879\pi\)
\(942\) 21.1114 0.687846
\(943\) 0.818638 0.0266585
\(944\) 137.186 4.46502
\(945\) 0 0
\(946\) −58.3539 −1.89725
\(947\) −2.12620 −0.0690922 −0.0345461 0.999403i \(-0.510999\pi\)
−0.0345461 + 0.999403i \(0.510999\pi\)
\(948\) −10.4299 −0.338746
\(949\) 10.5697 0.343106
\(950\) −24.5282 −0.795800
\(951\) −34.1992 −1.10899
\(952\) 0 0
\(953\) 36.1574 1.17125 0.585627 0.810581i \(-0.300848\pi\)
0.585627 + 0.810581i \(0.300848\pi\)
\(954\) −28.2098 −0.913326
\(955\) 7.68861 0.248798
\(956\) 35.9989 1.16429
\(957\) 1.16078 0.0375228
\(958\) 5.32829 0.172149
\(959\) 0 0
\(960\) 31.1890 1.00662
\(961\) 21.2842 0.686588
\(962\) 21.3663 0.688878
\(963\) 20.1914 0.650658
\(964\) 5.86594 0.188929
\(965\) −5.21836 −0.167985
\(966\) 0 0
\(967\) 42.8312 1.37736 0.688679 0.725066i \(-0.258191\pi\)
0.688679 + 0.725066i \(0.258191\pi\)
\(968\) 90.9171 2.92219
\(969\) −2.50132 −0.0803541
\(970\) −15.9634 −0.512554
\(971\) 7.63406 0.244988 0.122494 0.992469i \(-0.460911\pi\)
0.122494 + 0.992469i \(0.460911\pi\)
\(972\) −5.73612 −0.183986
\(973\) 0 0
\(974\) 9.35013 0.299597
\(975\) −4.43816 −0.142135
\(976\) −119.492 −3.82486
\(977\) 31.7537 1.01589 0.507945 0.861390i \(-0.330405\pi\)
0.507945 + 0.861390i \(0.330405\pi\)
\(978\) −9.78524 −0.312897
\(979\) −53.2594 −1.70218
\(980\) 0 0
\(981\) 12.9034 0.411973
\(982\) 91.6889 2.92591
\(983\) 17.8060 0.567924 0.283962 0.958836i \(-0.408351\pi\)
0.283962 + 0.958836i \(0.408351\pi\)
\(984\) −10.3916 −0.331272
\(985\) −10.3745 −0.330558
\(986\) −0.917656 −0.0292241
\(987\) 0 0
\(988\) −11.3208 −0.360162
\(989\) −3.86480 −0.122893
\(990\) −9.13986 −0.290484
\(991\) 37.4634 1.19007 0.595033 0.803702i \(-0.297139\pi\)
0.595033 + 0.803702i \(0.297139\pi\)
\(992\) 200.283 6.35899
\(993\) 9.26778 0.294104
\(994\) 0 0
\(995\) 13.7062 0.434515
\(996\) −85.6555 −2.71410
\(997\) 24.7442 0.783657 0.391829 0.920038i \(-0.371843\pi\)
0.391829 + 0.920038i \(0.371843\pi\)
\(998\) −116.298 −3.68135
\(999\) 7.70796 0.243869
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 6027.2.a.bn.1.24 24
7.6 odd 2 6027.2.a.bo.1.24 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6027.2.a.bn.1.24 24 1.1 even 1 trivial
6027.2.a.bo.1.24 yes 24 7.6 odd 2