Properties

Label 8027.2.a.d.1.12
Level $8027$
Weight $2$
Character 8027.1
Self dual yes
Analytic conductor $64.096$
Analytic rank $1$
Dimension $149$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8027,2,Mod(1,8027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("8027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8027 = 23 \cdot 349 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8027.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: \(64.0959177025\)
Analytic rank: \(1\)
Dimension: \(149\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 8027.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.37150 q^{2} +0.0708005 q^{3} +3.62401 q^{4} +3.28290 q^{5} -0.167903 q^{6} -0.427363 q^{7} -3.85135 q^{8} -2.99499 q^{9} +O(q^{10})\) \(q-2.37150 q^{2} +0.0708005 q^{3} +3.62401 q^{4} +3.28290 q^{5} -0.167903 q^{6} -0.427363 q^{7} -3.85135 q^{8} -2.99499 q^{9} -7.78539 q^{10} -1.35871 q^{11} +0.256582 q^{12} +0.448163 q^{13} +1.01349 q^{14} +0.232431 q^{15} +1.88545 q^{16} +2.46900 q^{17} +7.10261 q^{18} -2.99998 q^{19} +11.8973 q^{20} -0.0302575 q^{21} +3.22218 q^{22} -1.00000 q^{23} -0.272678 q^{24} +5.77741 q^{25} -1.06282 q^{26} -0.424448 q^{27} -1.54877 q^{28} -4.84023 q^{29} -0.551209 q^{30} +3.26639 q^{31} +3.23135 q^{32} -0.0961972 q^{33} -5.85523 q^{34} -1.40299 q^{35} -10.8539 q^{36} -3.58915 q^{37} +7.11445 q^{38} +0.0317301 q^{39} -12.6436 q^{40} -0.627600 q^{41} +0.0717557 q^{42} +4.02417 q^{43} -4.92398 q^{44} -9.83223 q^{45} +2.37150 q^{46} +1.73579 q^{47} +0.133491 q^{48} -6.81736 q^{49} -13.7011 q^{50} +0.174806 q^{51} +1.62415 q^{52} -0.795557 q^{53} +1.00658 q^{54} -4.46050 q^{55} +1.64593 q^{56} -0.212400 q^{57} +11.4786 q^{58} -8.98326 q^{59} +0.842332 q^{60} +1.00698 q^{61} -7.74624 q^{62} +1.27995 q^{63} -11.4341 q^{64} +1.47127 q^{65} +0.228132 q^{66} +11.1909 q^{67} +8.94768 q^{68} -0.0708005 q^{69} +3.32719 q^{70} +15.5165 q^{71} +11.5347 q^{72} +6.40922 q^{73} +8.51166 q^{74} +0.409043 q^{75} -10.8720 q^{76} +0.580662 q^{77} -0.0752480 q^{78} +10.7771 q^{79} +6.18975 q^{80} +8.95491 q^{81} +1.48835 q^{82} +0.837580 q^{83} -0.109654 q^{84} +8.10546 q^{85} -9.54333 q^{86} -0.342691 q^{87} +5.23287 q^{88} +5.96724 q^{89} +23.3171 q^{90} -0.191528 q^{91} -3.62401 q^{92} +0.231262 q^{93} -4.11643 q^{94} -9.84862 q^{95} +0.228781 q^{96} -11.5225 q^{97} +16.1674 q^{98} +4.06932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37150 −1.67690 −0.838452 0.544975i \(-0.816539\pi\)
−0.838452 + 0.544975i \(0.816539\pi\)
\(3\) 0.0708005 0.0408767 0.0204383 0.999791i \(-0.493494\pi\)
0.0204383 + 0.999791i \(0.493494\pi\)
\(4\) 3.62401 1.81201
\(5\) 3.28290 1.46816 0.734078 0.679065i \(-0.237615\pi\)
0.734078 + 0.679065i \(0.237615\pi\)
\(6\) −0.167903 −0.0685463
\(7\) −0.427363 −0.161528 −0.0807640 0.996733i \(-0.525736\pi\)
−0.0807640 + 0.996733i \(0.525736\pi\)
\(8\) −3.85135 −1.36166
\(9\) −2.99499 −0.998329
\(10\) −7.78539 −2.46196
\(11\) −1.35871 −0.409666 −0.204833 0.978797i \(-0.565665\pi\)
−0.204833 + 0.978797i \(0.565665\pi\)
\(12\) 0.256582 0.0740688
\(13\) 0.448163 0.124298 0.0621490 0.998067i \(-0.480205\pi\)
0.0621490 + 0.998067i \(0.480205\pi\)
\(14\) 1.01349 0.270867
\(15\) 0.232431 0.0600133
\(16\) 1.88545 0.471363
\(17\) 2.46900 0.598820 0.299410 0.954125i \(-0.403210\pi\)
0.299410 + 0.954125i \(0.403210\pi\)
\(18\) 7.10261 1.67410
\(19\) −2.99998 −0.688242 −0.344121 0.938925i \(-0.611823\pi\)
−0.344121 + 0.938925i \(0.611823\pi\)
\(20\) 11.8973 2.66031
\(21\) −0.0302575 −0.00660273
\(22\) 3.22218 0.686971
\(23\) −1.00000 −0.208514
\(24\) −0.272678 −0.0556601
\(25\) 5.77741 1.15548
\(26\) −1.06282 −0.208436
\(27\) −0.424448 −0.0816850
\(28\) −1.54877 −0.292690
\(29\) −4.84023 −0.898808 −0.449404 0.893329i \(-0.648364\pi\)
−0.449404 + 0.893329i \(0.648364\pi\)
\(30\) −0.551209 −0.100637
\(31\) 3.26639 0.586661 0.293330 0.956011i \(-0.405236\pi\)
0.293330 + 0.956011i \(0.405236\pi\)
\(32\) 3.23135 0.571227
\(33\) −0.0961972 −0.0167458
\(34\) −5.85523 −1.00416
\(35\) −1.40299 −0.237148
\(36\) −10.8539 −1.80898
\(37\) −3.58915 −0.590052 −0.295026 0.955489i \(-0.595328\pi\)
−0.295026 + 0.955489i \(0.595328\pi\)
\(38\) 7.11445 1.15412
\(39\) 0.0317301 0.00508089
\(40\) −12.6436 −1.99913
\(41\) −0.627600 −0.0980147 −0.0490073 0.998798i \(-0.515606\pi\)
−0.0490073 + 0.998798i \(0.515606\pi\)
\(42\) 0.0717557 0.0110721
\(43\) 4.02417 0.613681 0.306840 0.951761i \(-0.400728\pi\)
0.306840 + 0.951761i \(0.400728\pi\)
\(44\) −4.92398 −0.742318
\(45\) −9.83223 −1.46570
\(46\) 2.37150 0.349659
\(47\) 1.73579 0.253191 0.126595 0.991954i \(-0.459595\pi\)
0.126595 + 0.991954i \(0.459595\pi\)
\(48\) 0.133491 0.0192678
\(49\) −6.81736 −0.973909
\(50\) −13.7011 −1.93763
\(51\) 0.174806 0.0244778
\(52\) 1.62415 0.225229
\(53\) −0.795557 −0.109278 −0.0546390 0.998506i \(-0.517401\pi\)
−0.0546390 + 0.998506i \(0.517401\pi\)
\(54\) 1.00658 0.136978
\(55\) −4.46050 −0.601454
\(56\) 1.64593 0.219946
\(57\) −0.212400 −0.0281331
\(58\) 11.4786 1.50722
\(59\) −8.98326 −1.16952 −0.584761 0.811206i \(-0.698812\pi\)
−0.584761 + 0.811206i \(0.698812\pi\)
\(60\) 0.842332 0.108745
\(61\) 1.00698 0.128931 0.0644656 0.997920i \(-0.479466\pi\)
0.0644656 + 0.997920i \(0.479466\pi\)
\(62\) −7.74624 −0.983774
\(63\) 1.27995 0.161258
\(64\) −11.4341 −1.42926
\(65\) 1.47127 0.182489
\(66\) 0.228132 0.0280811
\(67\) 11.1909 1.36719 0.683594 0.729862i \(-0.260416\pi\)
0.683594 + 0.729862i \(0.260416\pi\)
\(68\) 8.94768 1.08507
\(69\) −0.0708005 −0.00852338
\(70\) 3.32719 0.397675
\(71\) 15.5165 1.84147 0.920736 0.390186i \(-0.127589\pi\)
0.920736 + 0.390186i \(0.127589\pi\)
\(72\) 11.5347 1.35938
\(73\) 6.40922 0.750142 0.375071 0.926996i \(-0.377618\pi\)
0.375071 + 0.926996i \(0.377618\pi\)
\(74\) 8.51166 0.989461
\(75\) 0.409043 0.0472322
\(76\) −10.8720 −1.24710
\(77\) 0.580662 0.0661726
\(78\) −0.0752480 −0.00852016
\(79\) 10.7771 1.21252 0.606259 0.795267i \(-0.292669\pi\)
0.606259 + 0.795267i \(0.292669\pi\)
\(80\) 6.18975 0.692035
\(81\) 8.95491 0.994990
\(82\) 1.48835 0.164361
\(83\) 0.837580 0.0919364 0.0459682 0.998943i \(-0.485363\pi\)
0.0459682 + 0.998943i \(0.485363\pi\)
\(84\) −0.109654 −0.0119642
\(85\) 8.10546 0.879160
\(86\) −9.54333 −1.02908
\(87\) −0.342691 −0.0367403
\(88\) 5.23287 0.557825
\(89\) 5.96724 0.632526 0.316263 0.948672i \(-0.397572\pi\)
0.316263 + 0.948672i \(0.397572\pi\)
\(90\) 23.3171 2.45784
\(91\) −0.191528 −0.0200776
\(92\) −3.62401 −0.377830
\(93\) 0.231262 0.0239807
\(94\) −4.11643 −0.424577
\(95\) −9.84862 −1.01045
\(96\) 0.228781 0.0233499
\(97\) −11.5225 −1.16994 −0.584968 0.811056i \(-0.698893\pi\)
−0.584968 + 0.811056i \(0.698893\pi\)
\(98\) 16.1674 1.63315
\(99\) 4.06932 0.408982
\(100\) 20.9374 2.09374
\(101\) −11.1059 −1.10508 −0.552539 0.833487i \(-0.686341\pi\)
−0.552539 + 0.833487i \(0.686341\pi\)
\(102\) −0.414553 −0.0410468
\(103\) 5.32715 0.524900 0.262450 0.964946i \(-0.415470\pi\)
0.262450 + 0.964946i \(0.415470\pi\)
\(104\) −1.72603 −0.169251
\(105\) −0.0993323 −0.00969384
\(106\) 1.88666 0.183249
\(107\) −20.5489 −1.98654 −0.993269 0.115830i \(-0.963047\pi\)
−0.993269 + 0.115830i \(0.963047\pi\)
\(108\) −1.53821 −0.148014
\(109\) 12.8758 1.23328 0.616640 0.787245i \(-0.288493\pi\)
0.616640 + 0.787245i \(0.288493\pi\)
\(110\) 10.5781 1.00858
\(111\) −0.254113 −0.0241194
\(112\) −0.805773 −0.0761384
\(113\) 8.14394 0.766117 0.383059 0.923724i \(-0.374871\pi\)
0.383059 + 0.923724i \(0.374871\pi\)
\(114\) 0.503706 0.0471764
\(115\) −3.28290 −0.306132
\(116\) −17.5411 −1.62865
\(117\) −1.34224 −0.124090
\(118\) 21.3038 1.96118
\(119\) −1.05516 −0.0967262
\(120\) −0.895172 −0.0817176
\(121\) −9.15391 −0.832174
\(122\) −2.38806 −0.216205
\(123\) −0.0444344 −0.00400651
\(124\) 11.8374 1.06303
\(125\) 2.55214 0.228271
\(126\) −3.03540 −0.270415
\(127\) −12.3627 −1.09702 −0.548508 0.836145i \(-0.684804\pi\)
−0.548508 + 0.836145i \(0.684804\pi\)
\(128\) 20.6532 1.82550
\(129\) 0.284913 0.0250852
\(130\) −3.48912 −0.306016
\(131\) −15.5315 −1.35699 −0.678495 0.734605i \(-0.737367\pi\)
−0.678495 + 0.734605i \(0.737367\pi\)
\(132\) −0.348620 −0.0303435
\(133\) 1.28208 0.111170
\(134\) −26.5393 −2.29264
\(135\) −1.39342 −0.119926
\(136\) −9.50897 −0.815388
\(137\) −11.8098 −1.00898 −0.504490 0.863417i \(-0.668320\pi\)
−0.504490 + 0.863417i \(0.668320\pi\)
\(138\) 0.167903 0.0142929
\(139\) −14.9424 −1.26739 −0.633697 0.773581i \(-0.718464\pi\)
−0.633697 + 0.773581i \(0.718464\pi\)
\(140\) −5.08445 −0.429715
\(141\) 0.122895 0.0103496
\(142\) −36.7974 −3.08797
\(143\) −0.608923 −0.0509207
\(144\) −5.64691 −0.470576
\(145\) −15.8900 −1.31959
\(146\) −15.1995 −1.25792
\(147\) −0.482672 −0.0398101
\(148\) −13.0071 −1.06918
\(149\) 20.4166 1.67259 0.836297 0.548276i \(-0.184716\pi\)
0.836297 + 0.548276i \(0.184716\pi\)
\(150\) −0.970046 −0.0792039
\(151\) 4.48504 0.364987 0.182494 0.983207i \(-0.441583\pi\)
0.182494 + 0.983207i \(0.441583\pi\)
\(152\) 11.5540 0.937151
\(153\) −7.39461 −0.597819
\(154\) −1.37704 −0.110965
\(155\) 10.7232 0.861309
\(156\) 0.114990 0.00920660
\(157\) 11.0909 0.885149 0.442574 0.896732i \(-0.354065\pi\)
0.442574 + 0.896732i \(0.354065\pi\)
\(158\) −25.5579 −2.03328
\(159\) −0.0563258 −0.00446692
\(160\) 10.6082 0.838651
\(161\) 0.427363 0.0336809
\(162\) −21.2366 −1.66850
\(163\) −4.63888 −0.363345 −0.181673 0.983359i \(-0.558151\pi\)
−0.181673 + 0.983359i \(0.558151\pi\)
\(164\) −2.27443 −0.177603
\(165\) −0.315806 −0.0245854
\(166\) −1.98632 −0.154168
\(167\) 14.2776 1.10484 0.552418 0.833567i \(-0.313705\pi\)
0.552418 + 0.833567i \(0.313705\pi\)
\(168\) 0.116532 0.00899066
\(169\) −12.7992 −0.984550
\(170\) −19.2221 −1.47427
\(171\) 8.98490 0.687092
\(172\) 14.5837 1.11199
\(173\) 2.25904 0.171752 0.0858759 0.996306i \(-0.472631\pi\)
0.0858759 + 0.996306i \(0.472631\pi\)
\(174\) 0.812691 0.0616099
\(175\) −2.46905 −0.186643
\(176\) −2.56178 −0.193102
\(177\) −0.636019 −0.0478061
\(178\) −14.1513 −1.06069
\(179\) −17.2344 −1.28816 −0.644078 0.764960i \(-0.722759\pi\)
−0.644078 + 0.764960i \(0.722759\pi\)
\(180\) −35.6322 −2.65586
\(181\) −14.5030 −1.07800 −0.539000 0.842306i \(-0.681198\pi\)
−0.539000 + 0.842306i \(0.681198\pi\)
\(182\) 0.454209 0.0336682
\(183\) 0.0712950 0.00527028
\(184\) 3.85135 0.283925
\(185\) −11.7828 −0.866288
\(186\) −0.548438 −0.0402134
\(187\) −3.35465 −0.245316
\(188\) 6.29053 0.458784
\(189\) 0.181393 0.0131944
\(190\) 23.3560 1.69442
\(191\) −3.71005 −0.268450 −0.134225 0.990951i \(-0.542855\pi\)
−0.134225 + 0.990951i \(0.542855\pi\)
\(192\) −0.809537 −0.0584233
\(193\) −9.17138 −0.660171 −0.330085 0.943951i \(-0.607078\pi\)
−0.330085 + 0.943951i \(0.607078\pi\)
\(194\) 27.3257 1.96187
\(195\) 0.104167 0.00745953
\(196\) −24.7062 −1.76473
\(197\) −4.71946 −0.336247 −0.168124 0.985766i \(-0.553771\pi\)
−0.168124 + 0.985766i \(0.553771\pi\)
\(198\) −9.65039 −0.685823
\(199\) −21.5208 −1.52557 −0.762783 0.646654i \(-0.776168\pi\)
−0.762783 + 0.646654i \(0.776168\pi\)
\(200\) −22.2508 −1.57337
\(201\) 0.792322 0.0558861
\(202\) 26.3376 1.85311
\(203\) 2.06854 0.145183
\(204\) 0.633500 0.0443539
\(205\) −2.06035 −0.143901
\(206\) −12.6333 −0.880206
\(207\) 2.99499 0.208166
\(208\) 0.844990 0.0585895
\(209\) 4.07610 0.281950
\(210\) 0.235567 0.0162556
\(211\) −21.8699 −1.50559 −0.752794 0.658256i \(-0.771295\pi\)
−0.752794 + 0.658256i \(0.771295\pi\)
\(212\) −2.88311 −0.198013
\(213\) 1.09858 0.0752733
\(214\) 48.7318 3.33123
\(215\) 13.2109 0.900979
\(216\) 1.63470 0.111227
\(217\) −1.39593 −0.0947622
\(218\) −30.5350 −2.06809
\(219\) 0.453776 0.0306633
\(220\) −16.1649 −1.08984
\(221\) 1.10651 0.0744320
\(222\) 0.602630 0.0404459
\(223\) −8.55830 −0.573106 −0.286553 0.958064i \(-0.592509\pi\)
−0.286553 + 0.958064i \(0.592509\pi\)
\(224\) −1.38096 −0.0922693
\(225\) −17.3033 −1.15355
\(226\) −19.3133 −1.28470
\(227\) −8.33166 −0.552992 −0.276496 0.961015i \(-0.589173\pi\)
−0.276496 + 0.961015i \(0.589173\pi\)
\(228\) −0.769740 −0.0509773
\(229\) −7.47362 −0.493871 −0.246935 0.969032i \(-0.579424\pi\)
−0.246935 + 0.969032i \(0.579424\pi\)
\(230\) 7.78539 0.513353
\(231\) 0.0411112 0.00270492
\(232\) 18.6414 1.22387
\(233\) −4.98420 −0.326526 −0.163263 0.986583i \(-0.552202\pi\)
−0.163263 + 0.986583i \(0.552202\pi\)
\(234\) 3.18313 0.208087
\(235\) 5.69842 0.371724
\(236\) −32.5555 −2.11918
\(237\) 0.763024 0.0495637
\(238\) 2.50231 0.162201
\(239\) −1.14546 −0.0740934 −0.0370467 0.999314i \(-0.511795\pi\)
−0.0370467 + 0.999314i \(0.511795\pi\)
\(240\) 0.438237 0.0282881
\(241\) 5.66505 0.364918 0.182459 0.983213i \(-0.441594\pi\)
0.182459 + 0.983213i \(0.441594\pi\)
\(242\) 21.7085 1.39548
\(243\) 1.90736 0.122357
\(244\) 3.64933 0.233624
\(245\) −22.3807 −1.42985
\(246\) 0.105376 0.00671854
\(247\) −1.34448 −0.0855471
\(248\) −12.5800 −0.798831
\(249\) 0.0593011 0.00375805
\(250\) −6.05241 −0.382788
\(251\) −16.2542 −1.02595 −0.512977 0.858402i \(-0.671457\pi\)
−0.512977 + 0.858402i \(0.671457\pi\)
\(252\) 4.63855 0.292201
\(253\) 1.35871 0.0854213
\(254\) 29.3183 1.83959
\(255\) 0.573870 0.0359371
\(256\) −26.1109 −1.63193
\(257\) 16.0377 1.00041 0.500203 0.865908i \(-0.333259\pi\)
0.500203 + 0.865908i \(0.333259\pi\)
\(258\) −0.675672 −0.0420655
\(259\) 1.53387 0.0953100
\(260\) 5.33191 0.330671
\(261\) 14.4964 0.897306
\(262\) 36.8328 2.27554
\(263\) 0.228052 0.0140623 0.00703115 0.999975i \(-0.497762\pi\)
0.00703115 + 0.999975i \(0.497762\pi\)
\(264\) 0.370489 0.0228020
\(265\) −2.61173 −0.160437
\(266\) −3.04045 −0.186422
\(267\) 0.422483 0.0258556
\(268\) 40.5561 2.47736
\(269\) −19.5438 −1.19161 −0.595803 0.803131i \(-0.703166\pi\)
−0.595803 + 0.803131i \(0.703166\pi\)
\(270\) 3.30449 0.201105
\(271\) −3.59548 −0.218410 −0.109205 0.994019i \(-0.534830\pi\)
−0.109205 + 0.994019i \(0.534830\pi\)
\(272\) 4.65518 0.282262
\(273\) −0.0135603 −0.000820706 0
\(274\) 28.0070 1.69196
\(275\) −7.84981 −0.473362
\(276\) −0.256582 −0.0154444
\(277\) −17.6664 −1.06147 −0.530736 0.847537i \(-0.678085\pi\)
−0.530736 + 0.847537i \(0.678085\pi\)
\(278\) 35.4358 2.12530
\(279\) −9.78279 −0.585680
\(280\) 5.40340 0.322915
\(281\) −0.521324 −0.0310996 −0.0155498 0.999879i \(-0.504950\pi\)
−0.0155498 + 0.999879i \(0.504950\pi\)
\(282\) −0.291445 −0.0173553
\(283\) 3.94745 0.234652 0.117326 0.993093i \(-0.462568\pi\)
0.117326 + 0.993093i \(0.462568\pi\)
\(284\) 56.2321 3.33676
\(285\) −0.697287 −0.0413037
\(286\) 1.44406 0.0853891
\(287\) 0.268213 0.0158321
\(288\) −9.67785 −0.570273
\(289\) −10.9041 −0.641415
\(290\) 37.6831 2.21283
\(291\) −0.815801 −0.0478231
\(292\) 23.2271 1.35926
\(293\) −27.8062 −1.62445 −0.812227 0.583341i \(-0.801745\pi\)
−0.812227 + 0.583341i \(0.801745\pi\)
\(294\) 1.14466 0.0667578
\(295\) −29.4911 −1.71704
\(296\) 13.8231 0.803449
\(297\) 0.576701 0.0334636
\(298\) −48.4180 −2.80478
\(299\) −0.448163 −0.0259179
\(300\) 1.48238 0.0855851
\(301\) −1.71978 −0.0991267
\(302\) −10.6363 −0.612049
\(303\) −0.786302 −0.0451719
\(304\) −5.65632 −0.324412
\(305\) 3.30583 0.189291
\(306\) 17.5363 1.00249
\(307\) 15.1753 0.866103 0.433051 0.901369i \(-0.357437\pi\)
0.433051 + 0.901369i \(0.357437\pi\)
\(308\) 2.10433 0.119905
\(309\) 0.377165 0.0214561
\(310\) −25.4301 −1.44433
\(311\) −8.00813 −0.454099 −0.227050 0.973883i \(-0.572908\pi\)
−0.227050 + 0.973883i \(0.572908\pi\)
\(312\) −0.122204 −0.00691843
\(313\) 32.1945 1.81974 0.909871 0.414890i \(-0.136180\pi\)
0.909871 + 0.414890i \(0.136180\pi\)
\(314\) −26.3020 −1.48431
\(315\) 4.20193 0.236752
\(316\) 39.0564 2.19709
\(317\) 1.53520 0.0862256 0.0431128 0.999070i \(-0.486273\pi\)
0.0431128 + 0.999070i \(0.486273\pi\)
\(318\) 0.133577 0.00749060
\(319\) 6.57647 0.368211
\(320\) −37.5368 −2.09837
\(321\) −1.45487 −0.0812031
\(322\) −1.01349 −0.0564797
\(323\) −7.40694 −0.412133
\(324\) 32.4527 1.80293
\(325\) 2.58922 0.143624
\(326\) 11.0011 0.609295
\(327\) 0.911615 0.0504124
\(328\) 2.41711 0.133463
\(329\) −0.741813 −0.0408974
\(330\) 0.748933 0.0412274
\(331\) −20.1527 −1.10769 −0.553846 0.832619i \(-0.686840\pi\)
−0.553846 + 0.832619i \(0.686840\pi\)
\(332\) 3.03540 0.166589
\(333\) 10.7494 0.589066
\(334\) −33.8594 −1.85271
\(335\) 36.7386 2.00725
\(336\) −0.0570491 −0.00311228
\(337\) −26.1121 −1.42242 −0.711208 0.702982i \(-0.751851\pi\)
−0.711208 + 0.702982i \(0.751851\pi\)
\(338\) 30.3532 1.65100
\(339\) 0.576595 0.0313163
\(340\) 29.3743 1.59305
\(341\) −4.43807 −0.240335
\(342\) −21.3077 −1.15219
\(343\) 5.90503 0.318842
\(344\) −15.4985 −0.835624
\(345\) −0.232431 −0.0125136
\(346\) −5.35732 −0.288011
\(347\) 1.81219 0.0972835 0.0486417 0.998816i \(-0.484511\pi\)
0.0486417 + 0.998816i \(0.484511\pi\)
\(348\) −1.24192 −0.0665737
\(349\) −1.00000 −0.0535288
\(350\) 5.85535 0.312982
\(351\) −0.190222 −0.0101533
\(352\) −4.39047 −0.234013
\(353\) −6.41239 −0.341297 −0.170649 0.985332i \(-0.554586\pi\)
−0.170649 + 0.985332i \(0.554586\pi\)
\(354\) 1.50832 0.0801663
\(355\) 50.9391 2.70357
\(356\) 21.6254 1.14614
\(357\) −0.0747057 −0.00395384
\(358\) 40.8713 2.16012
\(359\) 12.1824 0.642961 0.321481 0.946916i \(-0.395820\pi\)
0.321481 + 0.946916i \(0.395820\pi\)
\(360\) 37.8674 1.99579
\(361\) −10.0001 −0.526323
\(362\) 34.3939 1.80770
\(363\) −0.648101 −0.0340165
\(364\) −0.694101 −0.0363808
\(365\) 21.0408 1.10133
\(366\) −0.169076 −0.00883775
\(367\) 10.7597 0.561650 0.280825 0.959759i \(-0.409392\pi\)
0.280825 + 0.959759i \(0.409392\pi\)
\(368\) −1.88545 −0.0982860
\(369\) 1.87965 0.0978509
\(370\) 27.9429 1.45268
\(371\) 0.339992 0.0176515
\(372\) 0.838096 0.0434533
\(373\) −27.2837 −1.41269 −0.706347 0.707865i \(-0.749658\pi\)
−0.706347 + 0.707865i \(0.749658\pi\)
\(374\) 7.95555 0.411372
\(375\) 0.180693 0.00933094
\(376\) −6.68514 −0.344760
\(377\) −2.16921 −0.111720
\(378\) −0.430175 −0.0221258
\(379\) −27.0044 −1.38712 −0.693562 0.720397i \(-0.743960\pi\)
−0.693562 + 0.720397i \(0.743960\pi\)
\(380\) −35.6915 −1.83094
\(381\) −0.875288 −0.0448424
\(382\) 8.79840 0.450165
\(383\) 4.44985 0.227377 0.113688 0.993516i \(-0.463733\pi\)
0.113688 + 0.993516i \(0.463733\pi\)
\(384\) 1.46225 0.0746203
\(385\) 1.90625 0.0971517
\(386\) 21.7499 1.10704
\(387\) −12.0524 −0.612656
\(388\) −41.7578 −2.11993
\(389\) −9.66647 −0.490109 −0.245055 0.969509i \(-0.578806\pi\)
−0.245055 + 0.969509i \(0.578806\pi\)
\(390\) −0.247031 −0.0125089
\(391\) −2.46900 −0.124863
\(392\) 26.2561 1.32613
\(393\) −1.09963 −0.0554692
\(394\) 11.1922 0.563855
\(395\) 35.3801 1.78017
\(396\) 14.7473 0.741078
\(397\) −14.1734 −0.711342 −0.355671 0.934611i \(-0.615748\pi\)
−0.355671 + 0.934611i \(0.615748\pi\)
\(398\) 51.0365 2.55823
\(399\) 0.0907719 0.00454428
\(400\) 10.8930 0.544651
\(401\) 29.4412 1.47022 0.735111 0.677947i \(-0.237130\pi\)
0.735111 + 0.677947i \(0.237130\pi\)
\(402\) −1.87899 −0.0937156
\(403\) 1.46387 0.0729207
\(404\) −40.2479 −2.00241
\(405\) 29.3980 1.46080
\(406\) −4.90553 −0.243458
\(407\) 4.87661 0.241724
\(408\) −0.673240 −0.0333303
\(409\) 8.84877 0.437544 0.218772 0.975776i \(-0.429795\pi\)
0.218772 + 0.975776i \(0.429795\pi\)
\(410\) 4.88611 0.241308
\(411\) −0.836140 −0.0412438
\(412\) 19.3057 0.951122
\(413\) 3.83912 0.188911
\(414\) −7.10261 −0.349074
\(415\) 2.74969 0.134977
\(416\) 1.44817 0.0710024
\(417\) −1.05793 −0.0518069
\(418\) −9.66647 −0.472802
\(419\) 1.89585 0.0926185 0.0463092 0.998927i \(-0.485254\pi\)
0.0463092 + 0.998927i \(0.485254\pi\)
\(420\) −0.359982 −0.0175653
\(421\) 7.76042 0.378220 0.189110 0.981956i \(-0.439440\pi\)
0.189110 + 0.981956i \(0.439440\pi\)
\(422\) 51.8646 2.52473
\(423\) −5.19867 −0.252768
\(424\) 3.06397 0.148799
\(425\) 14.2644 0.691925
\(426\) −2.60528 −0.126226
\(427\) −0.430348 −0.0208260
\(428\) −74.4696 −3.59962
\(429\) −0.0431120 −0.00208147
\(430\) −31.3298 −1.51086
\(431\) 35.5311 1.71147 0.855737 0.517411i \(-0.173104\pi\)
0.855737 + 0.517411i \(0.173104\pi\)
\(432\) −0.800277 −0.0385033
\(433\) −1.94044 −0.0932517 −0.0466258 0.998912i \(-0.514847\pi\)
−0.0466258 + 0.998912i \(0.514847\pi\)
\(434\) 3.31046 0.158907
\(435\) −1.12502 −0.0539405
\(436\) 46.6622 2.23471
\(437\) 2.99998 0.143508
\(438\) −1.07613 −0.0514194
\(439\) 38.8947 1.85635 0.928173 0.372150i \(-0.121379\pi\)
0.928173 + 0.372150i \(0.121379\pi\)
\(440\) 17.1790 0.818975
\(441\) 20.4179 0.972281
\(442\) −2.62409 −0.124815
\(443\) 25.9508 1.23296 0.616479 0.787371i \(-0.288559\pi\)
0.616479 + 0.787371i \(0.288559\pi\)
\(444\) −0.920910 −0.0437045
\(445\) 19.5898 0.928647
\(446\) 20.2960 0.961044
\(447\) 1.44551 0.0683701
\(448\) 4.88649 0.230865
\(449\) 9.62968 0.454453 0.227226 0.973842i \(-0.427034\pi\)
0.227226 + 0.973842i \(0.427034\pi\)
\(450\) 41.0347 1.93439
\(451\) 0.852726 0.0401533
\(452\) 29.5137 1.38821
\(453\) 0.317543 0.0149195
\(454\) 19.7585 0.927314
\(455\) −0.628767 −0.0294771
\(456\) 0.818027 0.0383076
\(457\) −5.82946 −0.272691 −0.136345 0.990661i \(-0.543536\pi\)
−0.136345 + 0.990661i \(0.543536\pi\)
\(458\) 17.7237 0.828174
\(459\) −1.04796 −0.0489146
\(460\) −11.8973 −0.554713
\(461\) −11.5466 −0.537780 −0.268890 0.963171i \(-0.586657\pi\)
−0.268890 + 0.963171i \(0.586657\pi\)
\(462\) −0.0974951 −0.00453588
\(463\) −14.7008 −0.683203 −0.341602 0.939845i \(-0.610969\pi\)
−0.341602 + 0.939845i \(0.610969\pi\)
\(464\) −9.12603 −0.423665
\(465\) 0.759209 0.0352075
\(466\) 11.8200 0.547553
\(467\) 5.68488 0.263065 0.131533 0.991312i \(-0.458010\pi\)
0.131533 + 0.991312i \(0.458010\pi\)
\(468\) −4.86430 −0.224852
\(469\) −4.78259 −0.220839
\(470\) −13.5138 −0.623345
\(471\) 0.785240 0.0361819
\(472\) 34.5977 1.59249
\(473\) −5.46768 −0.251404
\(474\) −1.80951 −0.0831136
\(475\) −17.3321 −0.795251
\(476\) −3.82391 −0.175269
\(477\) 2.38268 0.109095
\(478\) 2.71645 0.124247
\(479\) 25.5967 1.16954 0.584772 0.811198i \(-0.301184\pi\)
0.584772 + 0.811198i \(0.301184\pi\)
\(480\) 0.751065 0.0342813
\(481\) −1.60852 −0.0733423
\(482\) −13.4347 −0.611933
\(483\) 0.0302575 0.00137676
\(484\) −33.1739 −1.50790
\(485\) −37.8273 −1.71765
\(486\) −4.52330 −0.205181
\(487\) −16.9416 −0.767698 −0.383849 0.923396i \(-0.625402\pi\)
−0.383849 + 0.923396i \(0.625402\pi\)
\(488\) −3.87825 −0.175560
\(489\) −0.328435 −0.0148523
\(490\) 53.0758 2.39772
\(491\) 34.5459 1.55903 0.779517 0.626382i \(-0.215465\pi\)
0.779517 + 0.626382i \(0.215465\pi\)
\(492\) −0.161031 −0.00725983
\(493\) −11.9505 −0.538224
\(494\) 3.18843 0.143454
\(495\) 13.3591 0.600449
\(496\) 6.15862 0.276530
\(497\) −6.63119 −0.297449
\(498\) −0.140633 −0.00630190
\(499\) −28.7286 −1.28607 −0.643034 0.765837i \(-0.722325\pi\)
−0.643034 + 0.765837i \(0.722325\pi\)
\(500\) 9.24901 0.413628
\(501\) 1.01086 0.0451620
\(502\) 38.5468 1.72043
\(503\) 25.7974 1.15025 0.575125 0.818065i \(-0.304953\pi\)
0.575125 + 0.818065i \(0.304953\pi\)
\(504\) −4.92953 −0.219579
\(505\) −36.4595 −1.62243
\(506\) −3.22218 −0.143243
\(507\) −0.906186 −0.0402451
\(508\) −44.8028 −1.98780
\(509\) −38.7204 −1.71625 −0.858126 0.513439i \(-0.828371\pi\)
−0.858126 + 0.513439i \(0.828371\pi\)
\(510\) −1.36093 −0.0602632
\(511\) −2.73906 −0.121169
\(512\) 20.6156 0.911091
\(513\) 1.27333 0.0562191
\(514\) −38.0335 −1.67759
\(515\) 17.4885 0.770634
\(516\) 1.03253 0.0454546
\(517\) −2.35843 −0.103724
\(518\) −3.63757 −0.159826
\(519\) 0.159941 0.00702064
\(520\) −5.66638 −0.248487
\(521\) −23.6813 −1.03750 −0.518749 0.854926i \(-0.673602\pi\)
−0.518749 + 0.854926i \(0.673602\pi\)
\(522\) −34.3783 −1.50470
\(523\) −7.47918 −0.327042 −0.163521 0.986540i \(-0.552285\pi\)
−0.163521 + 0.986540i \(0.552285\pi\)
\(524\) −56.2862 −2.45887
\(525\) −0.174810 −0.00762933
\(526\) −0.540826 −0.0235811
\(527\) 8.06470 0.351304
\(528\) −0.181375 −0.00789335
\(529\) 1.00000 0.0434783
\(530\) 6.19372 0.269038
\(531\) 26.9048 1.16757
\(532\) 4.64628 0.201442
\(533\) −0.281267 −0.0121830
\(534\) −1.00192 −0.0433573
\(535\) −67.4599 −2.91655
\(536\) −43.1002 −1.86164
\(537\) −1.22020 −0.0526556
\(538\) 46.3481 1.99821
\(539\) 9.26281 0.398977
\(540\) −5.04977 −0.217307
\(541\) −10.6869 −0.459464 −0.229732 0.973254i \(-0.573785\pi\)
−0.229732 + 0.973254i \(0.573785\pi\)
\(542\) 8.52668 0.366252
\(543\) −1.02682 −0.0440650
\(544\) 7.97819 0.342062
\(545\) 42.2700 1.81065
\(546\) 0.0321582 0.00137625
\(547\) −21.0523 −0.900129 −0.450065 0.892996i \(-0.648599\pi\)
−0.450065 + 0.892996i \(0.648599\pi\)
\(548\) −42.7989 −1.82828
\(549\) −3.01591 −0.128716
\(550\) 18.6158 0.793782
\(551\) 14.5206 0.618598
\(552\) 0.272678 0.0116059
\(553\) −4.60573 −0.195856
\(554\) 41.8959 1.77999
\(555\) −0.834227 −0.0354110
\(556\) −54.1514 −2.29653
\(557\) −26.6241 −1.12810 −0.564049 0.825741i \(-0.690757\pi\)
−0.564049 + 0.825741i \(0.690757\pi\)
\(558\) 23.1999 0.982130
\(559\) 1.80348 0.0762793
\(560\) −2.64527 −0.111783
\(561\) −0.237511 −0.0100277
\(562\) 1.23632 0.0521511
\(563\) −12.9520 −0.545863 −0.272932 0.962033i \(-0.587993\pi\)
−0.272932 + 0.962033i \(0.587993\pi\)
\(564\) 0.445372 0.0187536
\(565\) 26.7357 1.12478
\(566\) −9.36139 −0.393488
\(567\) −3.82700 −0.160719
\(568\) −59.7596 −2.50746
\(569\) 1.54625 0.0648223 0.0324111 0.999475i \(-0.489681\pi\)
0.0324111 + 0.999475i \(0.489681\pi\)
\(570\) 1.65362 0.0692623
\(571\) 9.90623 0.414563 0.207281 0.978281i \(-0.433538\pi\)
0.207281 + 0.978281i \(0.433538\pi\)
\(572\) −2.20674 −0.0922686
\(573\) −0.262674 −0.0109733
\(574\) −0.636068 −0.0265489
\(575\) −5.77741 −0.240934
\(576\) 34.2449 1.42687
\(577\) −38.2024 −1.59039 −0.795193 0.606356i \(-0.792631\pi\)
−0.795193 + 0.606356i \(0.792631\pi\)
\(578\) 25.8590 1.07559
\(579\) −0.649338 −0.0269856
\(580\) −57.5855 −2.39111
\(581\) −0.357951 −0.0148503
\(582\) 1.93467 0.0801947
\(583\) 1.08093 0.0447675
\(584\) −24.6842 −1.02144
\(585\) −4.40644 −0.182184
\(586\) 65.9424 2.72406
\(587\) −15.5300 −0.640991 −0.320496 0.947250i \(-0.603849\pi\)
−0.320496 + 0.947250i \(0.603849\pi\)
\(588\) −1.74921 −0.0721363
\(589\) −9.79909 −0.403765
\(590\) 69.9382 2.87931
\(591\) −0.334140 −0.0137447
\(592\) −6.76717 −0.278129
\(593\) 18.0864 0.742719 0.371360 0.928489i \(-0.378892\pi\)
0.371360 + 0.928489i \(0.378892\pi\)
\(594\) −1.36765 −0.0561153
\(595\) −3.46397 −0.142009
\(596\) 73.9901 3.03075
\(597\) −1.52368 −0.0623601
\(598\) 1.06282 0.0434619
\(599\) 41.4872 1.69512 0.847561 0.530698i \(-0.178070\pi\)
0.847561 + 0.530698i \(0.178070\pi\)
\(600\) −1.57537 −0.0643142
\(601\) 5.38795 0.219779 0.109889 0.993944i \(-0.464950\pi\)
0.109889 + 0.993944i \(0.464950\pi\)
\(602\) 4.07847 0.166226
\(603\) −33.5167 −1.36490
\(604\) 16.2538 0.661360
\(605\) −30.0513 −1.22176
\(606\) 1.86472 0.0757489
\(607\) 35.2111 1.42917 0.714587 0.699546i \(-0.246614\pi\)
0.714587 + 0.699546i \(0.246614\pi\)
\(608\) −9.69398 −0.393143
\(609\) 0.146453 0.00593459
\(610\) −7.83977 −0.317423
\(611\) 0.777916 0.0314711
\(612\) −26.7982 −1.08325
\(613\) −24.5858 −0.993010 −0.496505 0.868034i \(-0.665384\pi\)
−0.496505 + 0.868034i \(0.665384\pi\)
\(614\) −35.9883 −1.45237
\(615\) −0.145873 −0.00588219
\(616\) −2.23633 −0.0901045
\(617\) −24.0060 −0.966447 −0.483223 0.875497i \(-0.660534\pi\)
−0.483223 + 0.875497i \(0.660534\pi\)
\(618\) −0.894446 −0.0359799
\(619\) −6.83191 −0.274598 −0.137299 0.990530i \(-0.543842\pi\)
−0.137299 + 0.990530i \(0.543842\pi\)
\(620\) 38.8611 1.56070
\(621\) 0.424448 0.0170325
\(622\) 18.9913 0.761481
\(623\) −2.55018 −0.102171
\(624\) 0.0598257 0.00239494
\(625\) −20.5086 −0.820344
\(626\) −76.3494 −3.05153
\(627\) 0.288590 0.0115252
\(628\) 40.1935 1.60390
\(629\) −8.86159 −0.353335
\(630\) −9.96489 −0.397011
\(631\) 17.4275 0.693779 0.346890 0.937906i \(-0.387238\pi\)
0.346890 + 0.937906i \(0.387238\pi\)
\(632\) −41.5064 −1.65104
\(633\) −1.54840 −0.0615435
\(634\) −3.64074 −0.144592
\(635\) −40.5856 −1.61059
\(636\) −0.204125 −0.00809410
\(637\) −3.05529 −0.121055
\(638\) −15.5961 −0.617455
\(639\) −46.4718 −1.83840
\(640\) 67.8022 2.68012
\(641\) −40.2322 −1.58907 −0.794537 0.607215i \(-0.792287\pi\)
−0.794537 + 0.607215i \(0.792287\pi\)
\(642\) 3.45023 0.136170
\(643\) 30.0436 1.18480 0.592402 0.805642i \(-0.298180\pi\)
0.592402 + 0.805642i \(0.298180\pi\)
\(644\) 1.54877 0.0610301
\(645\) 0.935341 0.0368290
\(646\) 17.5656 0.691107
\(647\) 30.3655 1.19379 0.596895 0.802320i \(-0.296401\pi\)
0.596895 + 0.802320i \(0.296401\pi\)
\(648\) −34.4885 −1.35484
\(649\) 12.2056 0.479113
\(650\) −6.14033 −0.240844
\(651\) −0.0988328 −0.00387356
\(652\) −16.8114 −0.658384
\(653\) −49.1340 −1.92276 −0.961382 0.275218i \(-0.911250\pi\)
−0.961382 + 0.275218i \(0.911250\pi\)
\(654\) −2.16189 −0.0845368
\(655\) −50.9881 −1.99227
\(656\) −1.18331 −0.0462005
\(657\) −19.1955 −0.748889
\(658\) 1.75921 0.0685811
\(659\) 42.0950 1.63979 0.819894 0.572516i \(-0.194032\pi\)
0.819894 + 0.572516i \(0.194032\pi\)
\(660\) −1.14448 −0.0445490
\(661\) 16.7546 0.651679 0.325840 0.945425i \(-0.394353\pi\)
0.325840 + 0.945425i \(0.394353\pi\)
\(662\) 47.7921 1.85749
\(663\) 0.0783416 0.00304253
\(664\) −3.22582 −0.125186
\(665\) 4.20894 0.163216
\(666\) −25.4923 −0.987807
\(667\) 4.84023 0.187414
\(668\) 51.7424 2.00197
\(669\) −0.605931 −0.0234267
\(670\) −87.1257 −3.36596
\(671\) −1.36820 −0.0528187
\(672\) −0.0977726 −0.00377166
\(673\) −42.0184 −1.61969 −0.809845 0.586644i \(-0.800449\pi\)
−0.809845 + 0.586644i \(0.800449\pi\)
\(674\) 61.9248 2.38525
\(675\) −2.45221 −0.0943855
\(676\) −46.3843 −1.78401
\(677\) −10.7287 −0.412339 −0.206169 0.978516i \(-0.566100\pi\)
−0.206169 + 0.978516i \(0.566100\pi\)
\(678\) −1.36739 −0.0525145
\(679\) 4.92431 0.188977
\(680\) −31.2170 −1.19712
\(681\) −0.589886 −0.0226045
\(682\) 10.5249 0.403019
\(683\) −41.2719 −1.57922 −0.789612 0.613606i \(-0.789718\pi\)
−0.789612 + 0.613606i \(0.789718\pi\)
\(684\) 32.5614 1.24502
\(685\) −38.7704 −1.48134
\(686\) −14.0038 −0.534667
\(687\) −0.529136 −0.0201878
\(688\) 7.58739 0.289267
\(689\) −0.356539 −0.0135830
\(690\) 0.551209 0.0209842
\(691\) 9.22467 0.350923 0.175462 0.984486i \(-0.443858\pi\)
0.175462 + 0.984486i \(0.443858\pi\)
\(692\) 8.18681 0.311216
\(693\) −1.73908 −0.0660620
\(694\) −4.29761 −0.163135
\(695\) −49.0542 −1.86073
\(696\) 1.31982 0.0500277
\(697\) −1.54954 −0.0586931
\(698\) 2.37150 0.0897626
\(699\) −0.352884 −0.0133473
\(700\) −8.94787 −0.338198
\(701\) −18.5219 −0.699564 −0.349782 0.936831i \(-0.613744\pi\)
−0.349782 + 0.936831i \(0.613744\pi\)
\(702\) 0.451111 0.0170261
\(703\) 10.7674 0.406099
\(704\) 15.5356 0.585518
\(705\) 0.403451 0.0151948
\(706\) 15.2070 0.572323
\(707\) 4.74625 0.178501
\(708\) −2.30494 −0.0866251
\(709\) 28.7336 1.07911 0.539556 0.841950i \(-0.318592\pi\)
0.539556 + 0.841950i \(0.318592\pi\)
\(710\) −120.802 −4.53362
\(711\) −32.2773 −1.21049
\(712\) −22.9819 −0.861285
\(713\) −3.26639 −0.122327
\(714\) 0.177165 0.00663022
\(715\) −1.99903 −0.0747595
\(716\) −62.4576 −2.33415
\(717\) −0.0810988 −0.00302869
\(718\) −28.8905 −1.07818
\(719\) 45.3951 1.69295 0.846476 0.532427i \(-0.178720\pi\)
0.846476 + 0.532427i \(0.178720\pi\)
\(720\) −18.5382 −0.690878
\(721\) −2.27663 −0.0847860
\(722\) 23.7153 0.882593
\(723\) 0.401088 0.0149166
\(724\) −52.5591 −1.95334
\(725\) −27.9640 −1.03856
\(726\) 1.53697 0.0570424
\(727\) −25.2832 −0.937701 −0.468851 0.883277i \(-0.655332\pi\)
−0.468851 + 0.883277i \(0.655332\pi\)
\(728\) 0.737642 0.0273388
\(729\) −26.7297 −0.989989
\(730\) −49.8983 −1.84682
\(731\) 9.93567 0.367484
\(732\) 0.258374 0.00954978
\(733\) −1.59212 −0.0588064 −0.0294032 0.999568i \(-0.509361\pi\)
−0.0294032 + 0.999568i \(0.509361\pi\)
\(734\) −25.5166 −0.941833
\(735\) −1.58456 −0.0584475
\(736\) −3.23135 −0.119109
\(737\) −15.2052 −0.560091
\(738\) −4.45760 −0.164087
\(739\) 9.43878 0.347211 0.173606 0.984815i \(-0.444458\pi\)
0.173606 + 0.984815i \(0.444458\pi\)
\(740\) −42.7010 −1.56972
\(741\) −0.0951897 −0.00349688
\(742\) −0.806290 −0.0295998
\(743\) −50.9796 −1.87026 −0.935131 0.354302i \(-0.884718\pi\)
−0.935131 + 0.354302i \(0.884718\pi\)
\(744\) −0.890671 −0.0326536
\(745\) 67.0256 2.45563
\(746\) 64.7032 2.36895
\(747\) −2.50854 −0.0917828
\(748\) −12.1573 −0.444515
\(749\) 8.78185 0.320882
\(750\) −0.428513 −0.0156471
\(751\) 12.3512 0.450701 0.225350 0.974278i \(-0.427647\pi\)
0.225350 + 0.974278i \(0.427647\pi\)
\(752\) 3.27275 0.119345
\(753\) −1.15080 −0.0419376
\(754\) 5.14428 0.187344
\(755\) 14.7239 0.535858
\(756\) 0.657372 0.0239084
\(757\) −36.7649 −1.33624 −0.668121 0.744053i \(-0.732901\pi\)
−0.668121 + 0.744053i \(0.732901\pi\)
\(758\) 64.0410 2.32608
\(759\) 0.0961972 0.00349174
\(760\) 37.9305 1.37588
\(761\) 20.7152 0.750926 0.375463 0.926837i \(-0.377484\pi\)
0.375463 + 0.926837i \(0.377484\pi\)
\(762\) 2.07575 0.0751964
\(763\) −5.50265 −0.199209
\(764\) −13.4453 −0.486434
\(765\) −24.2757 −0.877691
\(766\) −10.5528 −0.381289
\(767\) −4.02596 −0.145369
\(768\) −1.84866 −0.0667079
\(769\) 35.8345 1.29222 0.646112 0.763243i \(-0.276394\pi\)
0.646112 + 0.763243i \(0.276394\pi\)
\(770\) −4.52068 −0.162914
\(771\) 1.13548 0.0408933
\(772\) −33.2372 −1.19623
\(773\) −12.5653 −0.451942 −0.225971 0.974134i \(-0.572556\pi\)
−0.225971 + 0.974134i \(0.572556\pi\)
\(774\) 28.5822 1.02736
\(775\) 18.8713 0.677875
\(776\) 44.3773 1.59305
\(777\) 0.108599 0.00389595
\(778\) 22.9240 0.821867
\(779\) 1.88279 0.0674578
\(780\) 0.377502 0.0135167
\(781\) −21.0824 −0.754389
\(782\) 5.85523 0.209382
\(783\) 2.05443 0.0734192
\(784\) −12.8538 −0.459065
\(785\) 36.4102 1.29954
\(786\) 2.60778 0.0930165
\(787\) −43.6081 −1.55446 −0.777231 0.629216i \(-0.783376\pi\)
−0.777231 + 0.629216i \(0.783376\pi\)
\(788\) −17.1034 −0.609283
\(789\) 0.0161462 0.000574820 0
\(790\) −83.9039 −2.98517
\(791\) −3.48042 −0.123749
\(792\) −15.6724 −0.556893
\(793\) 0.451293 0.0160259
\(794\) 33.6122 1.19285
\(795\) −0.184912 −0.00655814
\(796\) −77.9916 −2.76434
\(797\) −22.1270 −0.783779 −0.391889 0.920012i \(-0.628178\pi\)
−0.391889 + 0.920012i \(0.628178\pi\)
\(798\) −0.215266 −0.00762032
\(799\) 4.28566 0.151616
\(800\) 18.6688 0.660043
\(801\) −17.8718 −0.631469
\(802\) −69.8198 −2.46542
\(803\) −8.70826 −0.307308
\(804\) 2.87139 0.101266
\(805\) 1.40299 0.0494489
\(806\) −3.47158 −0.122281
\(807\) −1.38371 −0.0487089
\(808\) 42.7727 1.50474
\(809\) −1.43560 −0.0504731 −0.0252366 0.999682i \(-0.508034\pi\)
−0.0252366 + 0.999682i \(0.508034\pi\)
\(810\) −69.7175 −2.44962
\(811\) −22.2219 −0.780318 −0.390159 0.920748i \(-0.627580\pi\)
−0.390159 + 0.920748i \(0.627580\pi\)
\(812\) 7.49640 0.263072
\(813\) −0.254562 −0.00892787
\(814\) −11.5649 −0.405349
\(815\) −15.2290 −0.533448
\(816\) 0.329589 0.0115379
\(817\) −12.0724 −0.422361
\(818\) −20.9849 −0.733719
\(819\) 0.573624 0.0200441
\(820\) −7.46672 −0.260749
\(821\) 20.9555 0.731351 0.365675 0.930742i \(-0.380838\pi\)
0.365675 + 0.930742i \(0.380838\pi\)
\(822\) 1.98291 0.0691618
\(823\) 26.3829 0.919649 0.459824 0.888010i \(-0.347912\pi\)
0.459824 + 0.888010i \(0.347912\pi\)
\(824\) −20.5167 −0.714734
\(825\) −0.555771 −0.0193494
\(826\) −9.10446 −0.316785
\(827\) 36.4958 1.26908 0.634542 0.772888i \(-0.281189\pi\)
0.634542 + 0.772888i \(0.281189\pi\)
\(828\) 10.8539 0.377198
\(829\) −36.8024 −1.27820 −0.639100 0.769124i \(-0.720693\pi\)
−0.639100 + 0.769124i \(0.720693\pi\)
\(830\) −6.52089 −0.226343
\(831\) −1.25079 −0.0433895
\(832\) −5.12432 −0.177654
\(833\) −16.8320 −0.583196
\(834\) 2.50887 0.0868752
\(835\) 46.8720 1.62207
\(836\) 14.7718 0.510895
\(837\) −1.38641 −0.0479214
\(838\) −4.49602 −0.155312
\(839\) 8.80000 0.303810 0.151905 0.988395i \(-0.451459\pi\)
0.151905 + 0.988395i \(0.451459\pi\)
\(840\) 0.382563 0.0131997
\(841\) −5.57217 −0.192144
\(842\) −18.4038 −0.634238
\(843\) −0.0369100 −0.00127125
\(844\) −79.2570 −2.72814
\(845\) −42.0183 −1.44547
\(846\) 12.3286 0.423868
\(847\) 3.91204 0.134419
\(848\) −1.49998 −0.0515097
\(849\) 0.279482 0.00959178
\(850\) −33.8280 −1.16029
\(851\) 3.58915 0.123034
\(852\) 3.98126 0.136396
\(853\) 36.2770 1.24210 0.621051 0.783770i \(-0.286706\pi\)
0.621051 + 0.783770i \(0.286706\pi\)
\(854\) 1.02057 0.0349232
\(855\) 29.4965 1.00876
\(856\) 79.1411 2.70499
\(857\) 10.2509 0.350165 0.175082 0.984554i \(-0.443981\pi\)
0.175082 + 0.984554i \(0.443981\pi\)
\(858\) 0.102240 0.00349042
\(859\) 35.5395 1.21259 0.606295 0.795239i \(-0.292655\pi\)
0.606295 + 0.795239i \(0.292655\pi\)
\(860\) 47.8767 1.63258
\(861\) 0.0189896 0.000647164 0
\(862\) −84.2621 −2.86998
\(863\) 38.5309 1.31161 0.655804 0.754931i \(-0.272330\pi\)
0.655804 + 0.754931i \(0.272330\pi\)
\(864\) −1.37154 −0.0466607
\(865\) 7.41620 0.252158
\(866\) 4.60176 0.156374
\(867\) −0.772012 −0.0262189
\(868\) −5.05889 −0.171710
\(869\) −14.6429 −0.496728
\(870\) 2.66798 0.0904530
\(871\) 5.01535 0.169939
\(872\) −49.5893 −1.67931
\(873\) 34.5098 1.16798
\(874\) −7.11445 −0.240650
\(875\) −1.09069 −0.0368721
\(876\) 1.64449 0.0555622
\(877\) −13.1817 −0.445116 −0.222558 0.974919i \(-0.571441\pi\)
−0.222558 + 0.974919i \(0.571441\pi\)
\(878\) −92.2389 −3.11291
\(879\) −1.96869 −0.0664023
\(880\) −8.41006 −0.283503
\(881\) 52.2107 1.75902 0.879511 0.475878i \(-0.157870\pi\)
0.879511 + 0.475878i \(0.157870\pi\)
\(882\) −48.4211 −1.63042
\(883\) 1.13890 0.0383269 0.0191635 0.999816i \(-0.493900\pi\)
0.0191635 + 0.999816i \(0.493900\pi\)
\(884\) 4.01002 0.134871
\(885\) −2.08799 −0.0701869
\(886\) −61.5422 −2.06755
\(887\) −39.3793 −1.32223 −0.661113 0.750286i \(-0.729916\pi\)
−0.661113 + 0.750286i \(0.729916\pi\)
\(888\) 0.978679 0.0328423
\(889\) 5.28338 0.177199
\(890\) −46.4573 −1.55725
\(891\) −12.1671 −0.407614
\(892\) −31.0154 −1.03847
\(893\) −5.20733 −0.174257
\(894\) −3.42802 −0.114650
\(895\) −56.5786 −1.89121
\(896\) −8.82640 −0.294869
\(897\) −0.0317301 −0.00105944
\(898\) −22.8368 −0.762073
\(899\) −15.8101 −0.527295
\(900\) −62.7073 −2.09024
\(901\) −1.96423 −0.0654379
\(902\) −2.02224 −0.0673332
\(903\) −0.121762 −0.00405197
\(904\) −31.3652 −1.04319
\(905\) −47.6118 −1.58267
\(906\) −0.753053 −0.0250185
\(907\) 23.4040 0.777115 0.388558 0.921424i \(-0.372973\pi\)
0.388558 + 0.921424i \(0.372973\pi\)
\(908\) −30.1941 −1.00203
\(909\) 33.2620 1.10323
\(910\) 1.49112 0.0494302
\(911\) 43.5934 1.44431 0.722157 0.691729i \(-0.243151\pi\)
0.722157 + 0.691729i \(0.243151\pi\)
\(912\) −0.400470 −0.0132609
\(913\) −1.13803 −0.0376632
\(914\) 13.8246 0.457276
\(915\) 0.234054 0.00773759
\(916\) −27.0845 −0.894898
\(917\) 6.63757 0.219192
\(918\) 2.48524 0.0820251
\(919\) 9.27019 0.305795 0.152898 0.988242i \(-0.451140\pi\)
0.152898 + 0.988242i \(0.451140\pi\)
\(920\) 12.6436 0.416847
\(921\) 1.07442 0.0354034
\(922\) 27.3828 0.901805
\(923\) 6.95393 0.228891
\(924\) 0.148987 0.00490133
\(925\) −20.7360 −0.681794
\(926\) 34.8629 1.14567
\(927\) −15.9547 −0.524023
\(928\) −15.6405 −0.513424
\(929\) 37.3546 1.22557 0.612783 0.790251i \(-0.290050\pi\)
0.612783 + 0.790251i \(0.290050\pi\)
\(930\) −1.80046 −0.0590395
\(931\) 20.4519 0.670285
\(932\) −18.0628 −0.591667
\(933\) −0.566979 −0.0185621
\(934\) −13.4817 −0.441135
\(935\) −11.0130 −0.360162
\(936\) 5.16944 0.168969
\(937\) −34.9379 −1.14137 −0.570686 0.821168i \(-0.693323\pi\)
−0.570686 + 0.821168i \(0.693323\pi\)
\(938\) 11.3419 0.370326
\(939\) 2.27939 0.0743850
\(940\) 20.6511 0.673566
\(941\) 32.4318 1.05724 0.528622 0.848857i \(-0.322709\pi\)
0.528622 + 0.848857i \(0.322709\pi\)
\(942\) −1.86220 −0.0606736
\(943\) 0.627600 0.0204375
\(944\) −16.9375 −0.551269
\(945\) 0.595496 0.0193715
\(946\) 12.9666 0.421581
\(947\) −43.1450 −1.40202 −0.701012 0.713150i \(-0.747268\pi\)
−0.701012 + 0.713150i \(0.747268\pi\)
\(948\) 2.76521 0.0898098
\(949\) 2.87237 0.0932411
\(950\) 41.1031 1.33356
\(951\) 0.108693 0.00352462
\(952\) 4.06378 0.131708
\(953\) 52.6746 1.70630 0.853148 0.521669i \(-0.174690\pi\)
0.853148 + 0.521669i \(0.174690\pi\)
\(954\) −5.65053 −0.182943
\(955\) −12.1797 −0.394127
\(956\) −4.15115 −0.134258
\(957\) 0.465617 0.0150513
\(958\) −60.7027 −1.96121
\(959\) 5.04708 0.162979
\(960\) −2.65762 −0.0857745
\(961\) −20.3307 −0.655829
\(962\) 3.81461 0.122988
\(963\) 61.5437 1.98322
\(964\) 20.5302 0.661234
\(965\) −30.1087 −0.969233
\(966\) −0.0717557 −0.00230870
\(967\) −2.45234 −0.0788620 −0.0394310 0.999222i \(-0.512555\pi\)
−0.0394310 + 0.999222i \(0.512555\pi\)
\(968\) 35.2549 1.13314
\(969\) −0.524415 −0.0168466
\(970\) 89.7074 2.88033
\(971\) −32.5981 −1.04612 −0.523062 0.852295i \(-0.675210\pi\)
−0.523062 + 0.852295i \(0.675210\pi\)
\(972\) 6.91229 0.221712
\(973\) 6.38582 0.204720
\(974\) 40.1770 1.28736
\(975\) 0.183318 0.00587087
\(976\) 1.89862 0.0607734
\(977\) 18.3561 0.587263 0.293632 0.955919i \(-0.405136\pi\)
0.293632 + 0.955919i \(0.405136\pi\)
\(978\) 0.778884 0.0249060
\(979\) −8.10774 −0.259125
\(980\) −81.1079 −2.59090
\(981\) −38.5629 −1.23122
\(982\) −81.9255 −2.61435
\(983\) −20.6927 −0.659994 −0.329997 0.943982i \(-0.607048\pi\)
−0.329997 + 0.943982i \(0.607048\pi\)
\(984\) 0.171132 0.00545550
\(985\) −15.4935 −0.493663
\(986\) 28.3406 0.902550
\(987\) −0.0525207 −0.00167175
\(988\) −4.87241 −0.155012
\(989\) −4.02417 −0.127961
\(990\) −31.6812 −1.00690
\(991\) −3.84181 −0.122039 −0.0610196 0.998137i \(-0.519435\pi\)
−0.0610196 + 0.998137i \(0.519435\pi\)
\(992\) 10.5548 0.335117
\(993\) −1.42682 −0.0452787
\(994\) 15.7259 0.498794
\(995\) −70.6504 −2.23977
\(996\) 0.214908 0.00680962
\(997\) −8.35678 −0.264662 −0.132331 0.991206i \(-0.542246\pi\)
−0.132331 + 0.991206i \(0.542246\pi\)
\(998\) 68.1299 2.15661
\(999\) 1.52341 0.0481984
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 8027.2.a.d.1.12 149
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8027.2.a.d.1.12 149 1.1 even 1 trivial