Properties

Label 483.3.g.a.139.17
Level $483$
Weight $3$
Character 483.139
Analytic conductor $13.161$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [483,3,Mod(139,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.139");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 483.g (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(13.1607967686\)
Analytic rank: \(0\)
Dimension: \(60\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 139.17
Character \(\chi\) \(=\) 483.139
Dual form 483.3.g.a.139.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.01661 q^{2} -1.73205i q^{3} +0.0667068 q^{4} +2.33922i q^{5} +3.49287i q^{6} +(-5.55691 + 4.25685i) q^{7} +7.93191 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-2.01661 q^{2} -1.73205i q^{3} +0.0667068 q^{4} +2.33922i q^{5} +3.49287i q^{6} +(-5.55691 + 4.25685i) q^{7} +7.93191 q^{8} -3.00000 q^{9} -4.71728i q^{10} -12.1330 q^{11} -0.115540i q^{12} -13.3993i q^{13} +(11.2061 - 8.58440i) q^{14} +4.05164 q^{15} -16.2624 q^{16} +0.115332i q^{17} +6.04982 q^{18} +27.1188i q^{19} +0.156042i q^{20} +(7.37308 + 9.62485i) q^{21} +24.4676 q^{22} +4.79583 q^{23} -13.7385i q^{24} +19.5281 q^{25} +27.0211i q^{26} +5.19615i q^{27} +(-0.370684 + 0.283961i) q^{28} +0.360599 q^{29} -8.17058 q^{30} -0.231242i q^{31} +1.06720 q^{32} +21.0150i q^{33} -0.232580i q^{34} +(-9.95770 - 12.9988i) q^{35} -0.200120 q^{36} +66.3104 q^{37} -54.6880i q^{38} -23.2082 q^{39} +18.5545i q^{40} -55.2490i q^{41} +(-14.8686 - 19.4095i) q^{42} -10.0786 q^{43} -0.809355 q^{44} -7.01765i q^{45} -9.67131 q^{46} -60.4153i q^{47} +28.1673i q^{48} +(12.7584 - 47.3099i) q^{49} -39.3804 q^{50} +0.199762 q^{51} -0.893822i q^{52} -34.9684 q^{53} -10.4786i q^{54} -28.3818i q^{55} +(-44.0769 + 33.7650i) q^{56} +46.9711 q^{57} -0.727187 q^{58} -43.3189i q^{59} +0.270272 q^{60} -19.6256i q^{61} +0.466325i q^{62} +(16.6707 - 12.7706i) q^{63} +62.8974 q^{64} +31.3438 q^{65} -42.3791i q^{66} +115.924 q^{67} +0.00769346i q^{68} -8.30662i q^{69} +(20.0808 + 26.2135i) q^{70} +5.79639 q^{71} -23.7957 q^{72} +17.7978i q^{73} -133.722 q^{74} -33.8236i q^{75} +1.80901i q^{76} +(67.4221 - 51.6485i) q^{77} +46.8019 q^{78} +20.5579 q^{79} -38.0412i q^{80} +9.00000 q^{81} +111.416i q^{82} -111.368i q^{83} +(0.491835 + 0.642043i) q^{84} -0.269788 q^{85} +20.3246 q^{86} -0.624576i q^{87} -96.2381 q^{88} -26.8035i q^{89} +14.1519i q^{90} +(57.0387 + 74.4585i) q^{91} +0.319915 q^{92} -0.400524 q^{93} +121.834i q^{94} -63.4368 q^{95} -1.84844i q^{96} -134.649i q^{97} +(-25.7288 + 95.4054i) q^{98} +36.3991 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9} + 28 q^{14} - 48 q^{15} + 192 q^{16} + 48 q^{21} - 8 q^{22} - 292 q^{25} - 128 q^{28} + 136 q^{29} + 96 q^{32} - 88 q^{35} - 384 q^{36} - 200 q^{37} + 48 q^{39} - 60 q^{42} + 72 q^{43} + 352 q^{44} + 132 q^{49} - 376 q^{50} - 112 q^{53} + 260 q^{56} - 240 q^{57} + 32 q^{58} - 216 q^{60} + 48 q^{63} + 536 q^{64} - 8 q^{65} - 408 q^{67} - 112 q^{70} + 456 q^{71} - 72 q^{72} - 120 q^{74} + 104 q^{77} + 48 q^{78} + 192 q^{79} + 540 q^{81} + 24 q^{84} + 488 q^{85} + 72 q^{86} + 432 q^{88} + 88 q^{91} + 48 q^{93} + 880 q^{95} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.01661 −1.00830 −0.504152 0.863615i \(-0.668195\pi\)
−0.504152 + 0.863615i \(0.668195\pi\)
\(3\) 1.73205i 0.577350i
\(4\) 0.0667068 0.0166767
\(5\) 2.33922i 0.467844i 0.972255 + 0.233922i \(0.0751560\pi\)
−0.972255 + 0.233922i \(0.924844\pi\)
\(6\) 3.49287i 0.582145i
\(7\) −5.55691 + 4.25685i −0.793844 + 0.608122i
\(8\) 7.93191 0.991489
\(9\) −3.00000 −0.333333
\(10\) 4.71728i 0.471728i
\(11\) −12.1330 −1.10300 −0.551501 0.834174i \(-0.685945\pi\)
−0.551501 + 0.834174i \(0.685945\pi\)
\(12\) 0.115540i 0.00962830i
\(13\) 13.3993i 1.03071i −0.856976 0.515356i \(-0.827660\pi\)
0.856976 0.515356i \(-0.172340\pi\)
\(14\) 11.2061 8.58440i 0.800436 0.613171i
\(15\) 4.05164 0.270110
\(16\) −16.2624 −1.01640
\(17\) 0.115332i 0.00678426i 0.999994 + 0.00339213i \(0.00107975\pi\)
−0.999994 + 0.00339213i \(0.998920\pi\)
\(18\) 6.04982 0.336101
\(19\) 27.1188i 1.42731i 0.700500 + 0.713653i \(0.252960\pi\)
−0.700500 + 0.713653i \(0.747040\pi\)
\(20\) 0.156042i 0.00780209i
\(21\) 7.37308 + 9.62485i 0.351099 + 0.458326i
\(22\) 24.4676 1.11216
\(23\) 4.79583 0.208514
\(24\) 13.7385i 0.572436i
\(25\) 19.5281 0.781122
\(26\) 27.0211i 1.03927i
\(27\) 5.19615i 0.192450i
\(28\) −0.370684 + 0.283961i −0.0132387 + 0.0101415i
\(29\) 0.360599 0.0124345 0.00621723 0.999981i \(-0.498021\pi\)
0.00621723 + 0.999981i \(0.498021\pi\)
\(30\) −8.17058 −0.272353
\(31\) 0.231242i 0.00745943i −0.999993 0.00372972i \(-0.998813\pi\)
0.999993 0.00372972i \(-0.00118721\pi\)
\(32\) 1.06720 0.0333499
\(33\) 21.0150i 0.636819i
\(34\) 0.232580i 0.00684060i
\(35\) −9.95770 12.9988i −0.284506 0.371395i
\(36\) −0.200120 −0.00555890
\(37\) 66.3104 1.79217 0.896086 0.443880i \(-0.146398\pi\)
0.896086 + 0.443880i \(0.146398\pi\)
\(38\) 54.6880i 1.43916i
\(39\) −23.2082 −0.595082
\(40\) 18.5545i 0.463862i
\(41\) 55.2490i 1.34754i −0.738943 0.673768i \(-0.764675\pi\)
0.738943 0.673768i \(-0.235325\pi\)
\(42\) −14.8686 19.4095i −0.354015 0.462132i
\(43\) −10.0786 −0.234386 −0.117193 0.993109i \(-0.537390\pi\)
−0.117193 + 0.993109i \(0.537390\pi\)
\(44\) −0.809355 −0.0183944
\(45\) 7.01765i 0.155948i
\(46\) −9.67131 −0.210246
\(47\) 60.4153i 1.28543i −0.766104 0.642716i \(-0.777807\pi\)
0.766104 0.642716i \(-0.222193\pi\)
\(48\) 28.1673i 0.586818i
\(49\) 12.7584 47.3099i 0.260376 0.965507i
\(50\) −39.3804 −0.787609
\(51\) 0.199762 0.00391689
\(52\) 0.893822i 0.0171889i
\(53\) −34.9684 −0.659781 −0.329891 0.944019i \(-0.607012\pi\)
−0.329891 + 0.944019i \(0.607012\pi\)
\(54\) 10.4786i 0.194048i
\(55\) 28.3818i 0.516033i
\(56\) −44.0769 + 33.7650i −0.787087 + 0.602946i
\(57\) 46.9711 0.824055
\(58\) −0.727187 −0.0125377
\(59\) 43.3189i 0.734218i −0.930178 0.367109i \(-0.880348\pi\)
0.930178 0.367109i \(-0.119652\pi\)
\(60\) 0.270272 0.00450454
\(61\) 19.6256i 0.321732i −0.986976 0.160866i \(-0.948571\pi\)
0.986976 0.160866i \(-0.0514286\pi\)
\(62\) 0.466325i 0.00752137i
\(63\) 16.6707 12.7706i 0.264615 0.202707i
\(64\) 62.8974 0.982772
\(65\) 31.3438 0.482212
\(66\) 42.3791i 0.642107i
\(67\) 115.924 1.73021 0.865107 0.501587i \(-0.167250\pi\)
0.865107 + 0.501587i \(0.167250\pi\)
\(68\) 0.00769346i 0.000113139i
\(69\) 8.30662i 0.120386i
\(70\) 20.0808 + 26.2135i 0.286868 + 0.374479i
\(71\) 5.79639 0.0816392 0.0408196 0.999167i \(-0.487003\pi\)
0.0408196 + 0.999167i \(0.487003\pi\)
\(72\) −23.7957 −0.330496
\(73\) 17.7978i 0.243806i 0.992542 + 0.121903i \(0.0388997\pi\)
−0.992542 + 0.121903i \(0.961100\pi\)
\(74\) −133.722 −1.80705
\(75\) 33.8236i 0.450981i
\(76\) 1.80901i 0.0238027i
\(77\) 67.4221 51.6485i 0.875612 0.670760i
\(78\) 46.8019 0.600024
\(79\) 20.5579 0.260226 0.130113 0.991499i \(-0.458466\pi\)
0.130113 + 0.991499i \(0.458466\pi\)
\(80\) 38.0412i 0.475516i
\(81\) 9.00000 0.111111
\(82\) 111.416i 1.35873i
\(83\) 111.368i 1.34179i −0.741553 0.670894i \(-0.765910\pi\)
0.741553 0.670894i \(-0.234090\pi\)
\(84\) 0.491835 + 0.642043i 0.00585518 + 0.00764336i
\(85\) −0.269788 −0.00317397
\(86\) 20.3246 0.236333
\(87\) 0.624576i 0.00717903i
\(88\) −96.2381 −1.09361
\(89\) 26.8035i 0.301163i −0.988598 0.150581i \(-0.951885\pi\)
0.988598 0.150581i \(-0.0481145\pi\)
\(90\) 14.1519i 0.157243i
\(91\) 57.0387 + 74.4585i 0.626799 + 0.818225i
\(92\) 0.319915 0.00347733
\(93\) −0.400524 −0.00430671
\(94\) 121.834i 1.29611i
\(95\) −63.4368 −0.667756
\(96\) 1.84844i 0.0192546i
\(97\) 134.649i 1.38814i −0.719908 0.694069i \(-0.755816\pi\)
0.719908 0.694069i \(-0.244184\pi\)
\(98\) −25.7288 + 95.4054i −0.262538 + 0.973525i
\(99\) 36.3991 0.367667
\(100\) 1.30265 0.0130265
\(101\) 54.2885i 0.537510i −0.963209 0.268755i \(-0.913388\pi\)
0.963209 0.268755i \(-0.0866122\pi\)
\(102\) −0.402841 −0.00394942
\(103\) 159.943i 1.55284i 0.630216 + 0.776420i \(0.282966\pi\)
−0.630216 + 0.776420i \(0.717034\pi\)
\(104\) 106.282i 1.02194i
\(105\) −22.5146 + 17.2472i −0.214425 + 0.164259i
\(106\) 70.5176 0.665260
\(107\) 105.832 0.989089 0.494544 0.869152i \(-0.335335\pi\)
0.494544 + 0.869152i \(0.335335\pi\)
\(108\) 0.346619i 0.00320943i
\(109\) 199.718 1.83228 0.916140 0.400859i \(-0.131288\pi\)
0.916140 + 0.400859i \(0.131288\pi\)
\(110\) 57.2349i 0.520318i
\(111\) 114.853i 1.03471i
\(112\) 90.3685 69.2265i 0.806862 0.618094i
\(113\) −41.4735 −0.367022 −0.183511 0.983018i \(-0.558746\pi\)
−0.183511 + 0.983018i \(0.558746\pi\)
\(114\) −94.7224 −0.830898
\(115\) 11.2185i 0.0975521i
\(116\) 0.0240544 0.000207366
\(117\) 40.1978i 0.343571i
\(118\) 87.3571i 0.740315i
\(119\) −0.490953 0.640892i −0.00412566 0.00538564i
\(120\) 32.1373 0.267811
\(121\) 26.2104 0.216614
\(122\) 39.5772i 0.324403i
\(123\) −95.6941 −0.778001
\(124\) 0.0154254i 0.000124399i
\(125\) 104.161i 0.833287i
\(126\) −33.6183 + 25.7532i −0.266812 + 0.204390i
\(127\) 94.5345 0.744366 0.372183 0.928159i \(-0.378609\pi\)
0.372183 + 0.928159i \(0.378609\pi\)
\(128\) −131.108 −1.02428
\(129\) 17.4567i 0.135323i
\(130\) −63.2082 −0.486217
\(131\) 159.966i 1.22112i 0.791972 + 0.610558i \(0.209055\pi\)
−0.791972 + 0.610558i \(0.790945\pi\)
\(132\) 1.40184i 0.0106200i
\(133\) −115.441 150.697i −0.867975 1.13306i
\(134\) −233.774 −1.74458
\(135\) −12.1549 −0.0900365
\(136\) 0.914806i 0.00672652i
\(137\) 109.920 0.802338 0.401169 0.916004i \(-0.368604\pi\)
0.401169 + 0.916004i \(0.368604\pi\)
\(138\) 16.7512i 0.121386i
\(139\) 114.111i 0.820939i 0.911874 + 0.410470i \(0.134635\pi\)
−0.911874 + 0.410470i \(0.865365\pi\)
\(140\) −0.664246 0.867109i −0.00474462 0.00619364i
\(141\) −104.642 −0.742145
\(142\) −11.6890 −0.0823172
\(143\) 162.574i 1.13688i
\(144\) 48.7871 0.338800
\(145\) 0.843520i 0.00581738i
\(146\) 35.8913i 0.245831i
\(147\) −81.9431 22.0983i −0.557436 0.150328i
\(148\) 4.42335 0.0298875
\(149\) −138.972 −0.932701 −0.466350 0.884600i \(-0.654431\pi\)
−0.466350 + 0.884600i \(0.654431\pi\)
\(150\) 68.2089i 0.454726i
\(151\) −220.090 −1.45755 −0.728775 0.684753i \(-0.759910\pi\)
−0.728775 + 0.684753i \(0.759910\pi\)
\(152\) 215.104i 1.41516i
\(153\) 0.345997i 0.00226142i
\(154\) −135.964 + 104.155i −0.882883 + 0.676330i
\(155\) 0.540926 0.00348985
\(156\) −1.54815 −0.00992401
\(157\) 137.787i 0.877622i −0.898579 0.438811i \(-0.855400\pi\)
0.898579 0.438811i \(-0.144600\pi\)
\(158\) −41.4571 −0.262387
\(159\) 60.5671i 0.380925i
\(160\) 2.49641i 0.0156026i
\(161\) −26.6500 + 20.4151i −0.165528 + 0.126802i
\(162\) −18.1495 −0.112034
\(163\) −147.893 −0.907318 −0.453659 0.891175i \(-0.649882\pi\)
−0.453659 + 0.891175i \(0.649882\pi\)
\(164\) 3.68548i 0.0224725i
\(165\) −49.1587 −0.297932
\(166\) 224.586i 1.35293i
\(167\) 99.2846i 0.594519i 0.954797 + 0.297259i \(0.0960726\pi\)
−0.954797 + 0.297259i \(0.903927\pi\)
\(168\) 58.4826 + 76.3434i 0.348111 + 0.454425i
\(169\) −10.5404 −0.0623692
\(170\) 0.544056 0.00320033
\(171\) 81.3564i 0.475768i
\(172\) −0.672312 −0.00390879
\(173\) 51.9594i 0.300343i −0.988660 0.150172i \(-0.952017\pi\)
0.988660 0.150172i \(-0.0479826\pi\)
\(174\) 1.25952i 0.00723865i
\(175\) −108.516 + 83.1281i −0.620089 + 0.475017i
\(176\) 197.312 1.12109
\(177\) −75.0305 −0.423901
\(178\) 54.0521i 0.303663i
\(179\) 305.827 1.70853 0.854265 0.519838i \(-0.174008\pi\)
0.854265 + 0.519838i \(0.174008\pi\)
\(180\) 0.468125i 0.00260070i
\(181\) 83.0452i 0.458813i −0.973331 0.229407i \(-0.926321\pi\)
0.973331 0.229407i \(-0.0736786\pi\)
\(182\) −115.025 150.154i −0.632004 0.825020i
\(183\) −33.9926 −0.185752
\(184\) 38.0401 0.206740
\(185\) 155.114i 0.838456i
\(186\) 0.807699 0.00434247
\(187\) 1.39933i 0.00748306i
\(188\) 4.03011i 0.0214368i
\(189\) −22.1192 28.8745i −0.117033 0.152775i
\(190\) 127.927 0.673300
\(191\) 108.802 0.569646 0.284823 0.958580i \(-0.408065\pi\)
0.284823 + 0.958580i \(0.408065\pi\)
\(192\) 108.941i 0.567404i
\(193\) −17.5365 −0.0908628 −0.0454314 0.998967i \(-0.514466\pi\)
−0.0454314 + 0.998967i \(0.514466\pi\)
\(194\) 271.535i 1.39967i
\(195\) 54.2891i 0.278405i
\(196\) 0.851074 3.15589i 0.00434222 0.0161015i
\(197\) −344.079 −1.74659 −0.873297 0.487189i \(-0.838022\pi\)
−0.873297 + 0.487189i \(0.838022\pi\)
\(198\) −73.4027 −0.370721
\(199\) 131.485i 0.660730i −0.943853 0.330365i \(-0.892828\pi\)
0.943853 0.330365i \(-0.107172\pi\)
\(200\) 154.895 0.774474
\(201\) 200.787i 0.998940i
\(202\) 109.479i 0.541973i
\(203\) −2.00382 + 1.53502i −0.00987101 + 0.00756166i
\(204\) 0.0133255 6.53209e−5
\(205\) 129.239 0.630436
\(206\) 322.541i 1.56573i
\(207\) −14.3875 −0.0695048
\(208\) 217.904i 1.04762i
\(209\) 329.033i 1.57432i
\(210\) 45.4031 34.7809i 0.216205 0.165623i
\(211\) 159.966 0.758132 0.379066 0.925370i \(-0.376245\pi\)
0.379066 + 0.925370i \(0.376245\pi\)
\(212\) −2.33263 −0.0110030
\(213\) 10.0396i 0.0471344i
\(214\) −213.423 −0.997302
\(215\) 23.5761i 0.109656i
\(216\) 41.2154i 0.190812i
\(217\) 0.984365 + 1.28499i 0.00453624 + 0.00592162i
\(218\) −402.754 −1.84749
\(219\) 30.8268 0.140762
\(220\) 1.89326i 0.00860572i
\(221\) 1.54537 0.00699263
\(222\) 231.613i 1.04330i
\(223\) 374.032i 1.67727i 0.544691 + 0.838637i \(0.316647\pi\)
−0.544691 + 0.838637i \(0.683353\pi\)
\(224\) −5.93032 + 4.54290i −0.0264746 + 0.0202808i
\(225\) −58.5842 −0.260374
\(226\) 83.6359 0.370070
\(227\) 31.6312i 0.139345i 0.997570 + 0.0696723i \(0.0221954\pi\)
−0.997570 + 0.0696723i \(0.977805\pi\)
\(228\) 3.13329 0.0137425
\(229\) 376.510i 1.64415i 0.569381 + 0.822074i \(0.307183\pi\)
−0.569381 + 0.822074i \(0.692817\pi\)
\(230\) 22.6233i 0.0983622i
\(231\) −89.4578 116.779i −0.387263 0.505535i
\(232\) 2.86024 0.0123286
\(233\) 2.64982 0.0113726 0.00568632 0.999984i \(-0.498190\pi\)
0.00568632 + 0.999984i \(0.498190\pi\)
\(234\) 81.0632i 0.346424i
\(235\) 141.325 0.601381
\(236\) 2.88966i 0.0122443i
\(237\) 35.6073i 0.150242i
\(238\) 0.990060 + 1.29243i 0.00415991 + 0.00543037i
\(239\) 153.415 0.641904 0.320952 0.947096i \(-0.395997\pi\)
0.320952 + 0.947096i \(0.395997\pi\)
\(240\) −65.8894 −0.274539
\(241\) 155.790i 0.646431i −0.946325 0.323216i \(-0.895236\pi\)
0.946325 0.323216i \(-0.104764\pi\)
\(242\) −52.8560 −0.218413
\(243\) 15.5885i 0.0641500i
\(244\) 1.30916i 0.00536542i
\(245\) 110.668 + 29.8448i 0.451706 + 0.121815i
\(246\) 192.977 0.784461
\(247\) 363.372 1.47114
\(248\) 1.83419i 0.00739594i
\(249\) −192.896 −0.774682
\(250\) 210.052i 0.840206i
\(251\) 313.684i 1.24974i −0.780729 0.624869i \(-0.785152\pi\)
0.780729 0.624869i \(-0.214848\pi\)
\(252\) 1.11205 0.851883i 0.00441290 0.00338049i
\(253\) −58.1880 −0.229992
\(254\) −190.639 −0.750547
\(255\) 0.467286i 0.00183249i
\(256\) 12.8042 0.0500163
\(257\) 322.328i 1.25419i 0.778942 + 0.627097i \(0.215757\pi\)
−0.778942 + 0.627097i \(0.784243\pi\)
\(258\) 35.2032i 0.136447i
\(259\) −368.481 + 282.273i −1.42271 + 1.08986i
\(260\) 2.09085 0.00804171
\(261\) −1.08180 −0.00414482
\(262\) 322.589i 1.23126i
\(263\) 289.840 1.10205 0.551026 0.834488i \(-0.314236\pi\)
0.551026 + 0.834488i \(0.314236\pi\)
\(264\) 166.689i 0.631399i
\(265\) 81.7987i 0.308674i
\(266\) 232.799 + 303.896i 0.875183 + 1.14247i
\(267\) −46.4250 −0.173876
\(268\) 7.73294 0.0288543
\(269\) 221.588i 0.823749i −0.911241 0.411874i \(-0.864874\pi\)
0.911241 0.411874i \(-0.135126\pi\)
\(270\) 24.5117 0.0907842
\(271\) 321.439i 1.18612i −0.805157 0.593062i \(-0.797919\pi\)
0.805157 0.593062i \(-0.202081\pi\)
\(272\) 1.87558i 0.00689551i
\(273\) 128.966 98.7939i 0.472403 0.361882i
\(274\) −221.666 −0.809000
\(275\) −236.934 −0.861580
\(276\) 0.554108i 0.00200764i
\(277\) 168.521 0.608379 0.304190 0.952611i \(-0.401614\pi\)
0.304190 + 0.952611i \(0.401614\pi\)
\(278\) 230.116i 0.827756i
\(279\) 0.693727i 0.00248648i
\(280\) −78.9836 103.105i −0.282084 0.368234i
\(281\) 315.524 1.12286 0.561431 0.827524i \(-0.310251\pi\)
0.561431 + 0.827524i \(0.310251\pi\)
\(282\) 211.023 0.748307
\(283\) 330.149i 1.16661i −0.812255 0.583303i \(-0.801760\pi\)
0.812255 0.583303i \(-0.198240\pi\)
\(284\) 0.386658 0.00136147
\(285\) 109.876i 0.385529i
\(286\) 327.847i 1.14632i
\(287\) 235.187 + 307.014i 0.819466 + 1.06973i
\(288\) −3.20159 −0.0111166
\(289\) 288.987 0.999954
\(290\) 1.70105i 0.00586569i
\(291\) −233.220 −0.801442
\(292\) 1.18724i 0.00406588i
\(293\) 359.896i 1.22831i −0.789184 0.614157i \(-0.789496\pi\)
0.789184 0.614157i \(-0.210504\pi\)
\(294\) 165.247 + 44.5635i 0.562065 + 0.151577i
\(295\) 101.332 0.343499
\(296\) 525.968 1.77692
\(297\) 63.0451i 0.212273i
\(298\) 280.253 0.940446
\(299\) 64.2606i 0.214919i
\(300\) 2.25626i 0.00752088i
\(301\) 56.0059 42.9031i 0.186066 0.142535i
\(302\) 443.835 1.46965
\(303\) −94.0304 −0.310331
\(304\) 441.016i 1.45071i
\(305\) 45.9086 0.150520
\(306\) 0.697741i 0.00228020i
\(307\) 192.798i 0.628005i 0.949422 + 0.314003i \(0.101670\pi\)
−0.949422 + 0.314003i \(0.898330\pi\)
\(308\) 4.49751 3.44531i 0.0146023 0.0111861i
\(309\) 277.029 0.896533
\(310\) −1.09084 −0.00351883
\(311\) 481.302i 1.54759i −0.633434 0.773797i \(-0.718355\pi\)
0.633434 0.773797i \(-0.281645\pi\)
\(312\) −184.085 −0.590017
\(313\) 376.244i 1.20206i 0.799227 + 0.601029i \(0.205242\pi\)
−0.799227 + 0.601029i \(0.794758\pi\)
\(314\) 277.862i 0.884909i
\(315\) 29.8731 + 38.9964i 0.0948353 + 0.123798i
\(316\) 1.37135 0.00433971
\(317\) −223.316 −0.704466 −0.352233 0.935912i \(-0.614578\pi\)
−0.352233 + 0.935912i \(0.614578\pi\)
\(318\) 122.140i 0.384088i
\(319\) −4.37516 −0.0137152
\(320\) 147.131i 0.459783i
\(321\) 183.307i 0.571051i
\(322\) 53.7426 41.1693i 0.166902 0.127855i
\(323\) −3.12768 −0.00968321
\(324\) 0.600361 0.00185297
\(325\) 261.662i 0.805113i
\(326\) 298.242 0.914853
\(327\) 345.923i 1.05787i
\(328\) 438.230i 1.33607i
\(329\) 257.179 + 335.722i 0.781699 + 1.02043i
\(330\) 99.1338 0.300406
\(331\) −81.3038 −0.245631 −0.122815 0.992430i \(-0.539192\pi\)
−0.122815 + 0.992430i \(0.539192\pi\)
\(332\) 7.42903i 0.0223766i
\(333\) −198.931 −0.597391
\(334\) 200.218i 0.599455i
\(335\) 271.172i 0.809470i
\(336\) −119.904 156.523i −0.356857 0.465842i
\(337\) −486.946 −1.44494 −0.722472 0.691400i \(-0.756994\pi\)
−0.722472 + 0.691400i \(0.756994\pi\)
\(338\) 21.2559 0.0628871
\(339\) 71.8343i 0.211901i
\(340\) −0.0179967 −5.29314e−5
\(341\) 2.80567i 0.00822777i
\(342\) 164.064i 0.479719i
\(343\) 130.494 + 317.207i 0.380448 + 0.924802i
\(344\) −79.9426 −0.232391
\(345\) 19.4310 0.0563217
\(346\) 104.782i 0.302837i
\(347\) 28.4035 0.0818544 0.0409272 0.999162i \(-0.486969\pi\)
0.0409272 + 0.999162i \(0.486969\pi\)
\(348\) 0.0416635i 0.000119723i
\(349\) 687.696i 1.97048i −0.171187 0.985239i \(-0.554760\pi\)
0.171187 0.985239i \(-0.445240\pi\)
\(350\) 218.833 167.637i 0.625238 0.478962i
\(351\) 69.6246 0.198361
\(352\) −12.9483 −0.0367851
\(353\) 3.12789i 0.00886088i −0.999990 0.00443044i \(-0.998590\pi\)
0.999990 0.00443044i \(-0.00141026\pi\)
\(354\) 151.307 0.427421
\(355\) 13.5590i 0.0381944i
\(356\) 1.78797i 0.00502240i
\(357\) −1.11006 + 0.850356i −0.00310940 + 0.00238195i
\(358\) −616.733 −1.72272
\(359\) −464.707 −1.29445 −0.647224 0.762300i \(-0.724070\pi\)
−0.647224 + 0.762300i \(0.724070\pi\)
\(360\) 55.6634i 0.154621i
\(361\) −374.429 −1.03720
\(362\) 167.470i 0.462623i
\(363\) 45.3977i 0.125062i
\(364\) 3.80487 + 4.96689i 0.0104529 + 0.0136453i
\(365\) −41.6330 −0.114063
\(366\) 68.5497 0.187294
\(367\) 282.058i 0.768550i 0.923219 + 0.384275i \(0.125549\pi\)
−0.923219 + 0.384275i \(0.874451\pi\)
\(368\) −77.9916 −0.211934
\(369\) 165.747i 0.449179i
\(370\) 312.805i 0.845419i
\(371\) 194.316 148.855i 0.523763 0.401227i
\(372\) −0.0267176 −7.18216e−5
\(373\) 193.560 0.518928 0.259464 0.965753i \(-0.416454\pi\)
0.259464 + 0.965753i \(0.416454\pi\)
\(374\) 2.82190i 0.00754519i
\(375\) 180.412 0.481098
\(376\) 479.209i 1.27449i
\(377\) 4.83176i 0.0128164i
\(378\) 44.6058 + 58.2286i 0.118005 + 0.154044i
\(379\) −170.530 −0.449948 −0.224974 0.974365i \(-0.572230\pi\)
−0.224974 + 0.974365i \(0.572230\pi\)
\(380\) −4.23166 −0.0111360
\(381\) 163.739i 0.429760i
\(382\) −219.412 −0.574376
\(383\) 513.611i 1.34102i 0.741900 + 0.670510i \(0.233925\pi\)
−0.741900 + 0.670510i \(0.766075\pi\)
\(384\) 227.086i 0.591370i
\(385\) 120.817 + 157.715i 0.313811 + 0.409649i
\(386\) 35.3643 0.0916173
\(387\) 30.2358 0.0781287
\(388\) 8.98203i 0.0231496i
\(389\) 486.118 1.24966 0.624830 0.780761i \(-0.285168\pi\)
0.624830 + 0.780761i \(0.285168\pi\)
\(390\) 109.480i 0.280717i
\(391\) 0.553115i 0.00141462i
\(392\) 101.199 375.257i 0.258160 0.957290i
\(393\) 277.069 0.705011
\(394\) 693.872 1.76110
\(395\) 48.0893i 0.121745i
\(396\) 2.42807 0.00613148
\(397\) 77.1778i 0.194402i −0.995265 0.0972012i \(-0.969011\pi\)
0.995265 0.0972012i \(-0.0309890\pi\)
\(398\) 265.154i 0.666217i
\(399\) −261.014 + 199.949i −0.654171 + 0.501126i
\(400\) −317.573 −0.793932
\(401\) −455.348 −1.13553 −0.567766 0.823190i \(-0.692192\pi\)
−0.567766 + 0.823190i \(0.692192\pi\)
\(402\) 404.908i 1.00723i
\(403\) −3.09848 −0.00768853
\(404\) 3.62141i 0.00896389i
\(405\) 21.0530i 0.0519826i
\(406\) 4.04091 3.09553i 0.00995298 0.00762445i
\(407\) −804.546 −1.97677
\(408\) 1.58449 0.00388356
\(409\) 354.597i 0.866986i −0.901157 0.433493i \(-0.857281\pi\)
0.901157 0.433493i \(-0.142719\pi\)
\(410\) −260.625 −0.635671
\(411\) 190.387i 0.463230i
\(412\) 10.6693i 0.0258963i
\(413\) 184.402 + 240.719i 0.446494 + 0.582854i
\(414\) 29.0139 0.0700820
\(415\) 260.515 0.627747
\(416\) 14.2997i 0.0343742i
\(417\) 197.645 0.473970
\(418\) 663.531i 1.58739i
\(419\) 238.372i 0.568908i −0.958690 0.284454i \(-0.908188\pi\)
0.958690 0.284454i \(-0.0918122\pi\)
\(420\) −1.50188 + 1.15051i −0.00357590 + 0.00273931i
\(421\) −81.3807 −0.193303 −0.0966517 0.995318i \(-0.530813\pi\)
−0.0966517 + 0.995318i \(0.530813\pi\)
\(422\) −322.589 −0.764428
\(423\) 181.246i 0.428477i
\(424\) −277.366 −0.654166
\(425\) 2.25222i 0.00529934i
\(426\) 20.2460i 0.0475258i
\(427\) 83.5434 + 109.058i 0.195652 + 0.255405i
\(428\) 7.05975 0.0164947
\(429\) 281.586 0.656377
\(430\) 47.5437i 0.110567i
\(431\) 256.291 0.594642 0.297321 0.954778i \(-0.403907\pi\)
0.297321 + 0.954778i \(0.403907\pi\)
\(432\) 84.5018i 0.195606i
\(433\) 23.6575i 0.0546362i −0.999627 0.0273181i \(-0.991303\pi\)
0.999627 0.0273181i \(-0.00869670\pi\)
\(434\) −1.98508 2.59133i −0.00457391 0.00597080i
\(435\) 1.46102 0.00335867
\(436\) 13.3226 0.0305564
\(437\) 130.057i 0.297614i
\(438\) −62.1655 −0.141930
\(439\) 415.759i 0.947059i −0.880778 0.473529i \(-0.842980\pi\)
0.880778 0.473529i \(-0.157020\pi\)
\(440\) 225.122i 0.511640i
\(441\) −38.2753 + 141.930i −0.0867921 + 0.321836i
\(442\) −3.11641 −0.00705069
\(443\) −842.902 −1.90271 −0.951357 0.308091i \(-0.900310\pi\)
−0.951357 + 0.308091i \(0.900310\pi\)
\(444\) 7.66147i 0.0172556i
\(445\) 62.6992 0.140897
\(446\) 754.276i 1.69120i
\(447\) 240.707i 0.538495i
\(448\) −349.515 + 267.745i −0.780167 + 0.597645i
\(449\) −214.674 −0.478116 −0.239058 0.971005i \(-0.576839\pi\)
−0.239058 + 0.971005i \(0.576839\pi\)
\(450\) 118.141 0.262536
\(451\) 670.338i 1.48634i
\(452\) −2.76657 −0.00612072
\(453\) 381.207i 0.841517i
\(454\) 63.7878i 0.140502i
\(455\) −174.175 + 133.426i −0.382801 + 0.293244i
\(456\) 372.571 0.817041
\(457\) −481.061 −1.05265 −0.526325 0.850283i \(-0.676431\pi\)
−0.526325 + 0.850283i \(0.676431\pi\)
\(458\) 759.273i 1.65780i
\(459\) −0.599285 −0.00130563
\(460\) 0.748350i 0.00162685i
\(461\) 422.982i 0.917530i 0.888558 + 0.458765i \(0.151708\pi\)
−0.888558 + 0.458765i \(0.848292\pi\)
\(462\) 180.401 + 235.496i 0.390479 + 0.509733i
\(463\) 642.954 1.38867 0.694335 0.719652i \(-0.255699\pi\)
0.694335 + 0.719652i \(0.255699\pi\)
\(464\) −5.86420 −0.0126384
\(465\) 0.936912i 0.00201486i
\(466\) −5.34366 −0.0114671
\(467\) 10.6389i 0.0227814i −0.999935 0.0113907i \(-0.996374\pi\)
0.999935 0.0113907i \(-0.00362585\pi\)
\(468\) 2.68147i 0.00572963i
\(469\) −644.181 + 493.473i −1.37352 + 1.05218i
\(470\) −284.996 −0.606375
\(471\) −238.653 −0.506695
\(472\) 343.601i 0.727969i
\(473\) 122.284 0.258529
\(474\) 71.8059i 0.151489i
\(475\) 529.578i 1.11490i
\(476\) −0.0327499 0.0427518i −6.88023e−5 8.98148e-5i
\(477\) 104.905 0.219927
\(478\) −309.378 −0.647234
\(479\) 201.028i 0.419682i −0.977736 0.209841i \(-0.932705\pi\)
0.977736 0.209841i \(-0.0672946\pi\)
\(480\) 4.32391 0.00900814
\(481\) 888.511i 1.84722i
\(482\) 314.167i 0.651799i
\(483\) 35.3601 + 46.1591i 0.0732092 + 0.0955676i
\(484\) 1.74841 0.00361241
\(485\) 314.974 0.649432
\(486\) 31.4358i 0.0646827i
\(487\) 326.372 0.670169 0.335085 0.942188i \(-0.391235\pi\)
0.335085 + 0.942188i \(0.391235\pi\)
\(488\) 155.669i 0.318993i
\(489\) 256.158i 0.523840i
\(490\) −223.174 60.1852i −0.455457 0.122827i
\(491\) 334.331 0.680918 0.340459 0.940259i \(-0.389417\pi\)
0.340459 + 0.940259i \(0.389417\pi\)
\(492\) −6.38345 −0.0129745
\(493\) 0.0415888i 8.43586e-5i
\(494\) −732.779 −1.48336
\(495\) 85.1454i 0.172011i
\(496\) 3.76055i 0.00758176i
\(497\) −32.2100 + 24.6744i −0.0648088 + 0.0496466i
\(498\) 388.995 0.781115
\(499\) −492.699 −0.987373 −0.493687 0.869640i \(-0.664351\pi\)
−0.493687 + 0.869640i \(0.664351\pi\)
\(500\) 6.94824i 0.0138965i
\(501\) 171.966 0.343246
\(502\) 632.578i 1.26012i
\(503\) 671.425i 1.33484i 0.744681 + 0.667421i \(0.232602\pi\)
−0.744681 + 0.667421i \(0.767398\pi\)
\(504\) 132.231 101.295i 0.262362 0.200982i
\(505\) 126.993 0.251471
\(506\) 117.342 0.231902
\(507\) 18.2565i 0.0360089i
\(508\) 6.30609 0.0124136
\(509\) 714.776i 1.40428i −0.712041 0.702138i \(-0.752229\pi\)
0.712041 0.702138i \(-0.247771\pi\)
\(510\) 0.942332i 0.00184771i
\(511\) −75.7628 98.9010i −0.148264 0.193544i
\(512\) 498.612 0.973851
\(513\) −140.913 −0.274685
\(514\) 650.008i 1.26461i
\(515\) −374.140 −0.726486
\(516\) 1.16448i 0.00225674i
\(517\) 733.021i 1.41784i
\(518\) 743.081 569.235i 1.43452 1.09891i
\(519\) −89.9963 −0.173403
\(520\) 248.616 0.478108
\(521\) 662.096i 1.27082i −0.772176 0.635409i \(-0.780832\pi\)
0.772176 0.635409i \(-0.219168\pi\)
\(522\) 2.18156 0.00417924
\(523\) 99.8558i 0.190929i 0.995433 + 0.0954644i \(0.0304336\pi\)
−0.995433 + 0.0954644i \(0.969566\pi\)
\(524\) 10.6708i 0.0203642i
\(525\) 143.982 + 187.955i 0.274251 + 0.358009i
\(526\) −584.493 −1.11120
\(527\) 0.0266697 5.06067e−5
\(528\) 341.754i 0.647262i
\(529\) 23.0000 0.0434783
\(530\) 164.956i 0.311238i
\(531\) 129.957i 0.244739i
\(532\) −7.70068 10.0525i −0.0144750 0.0188957i
\(533\) −740.296 −1.38892
\(534\) 93.6210 0.175320
\(535\) 247.565i 0.462739i
\(536\) 919.502 1.71549
\(537\) 529.708i 0.986420i
\(538\) 446.857i 0.830589i
\(539\) −154.798 + 574.012i −0.287196 + 1.06496i
\(540\) −0.810817 −0.00150151
\(541\) 1011.80 1.87024 0.935122 0.354327i \(-0.115290\pi\)
0.935122 + 0.354327i \(0.115290\pi\)
\(542\) 648.217i 1.19597i
\(543\) −143.839 −0.264896
\(544\) 0.123083i 0.000226255i
\(545\) 467.185i 0.857220i
\(546\) −260.074 + 199.229i −0.476325 + 0.364888i
\(547\) −191.473 −0.350042 −0.175021 0.984565i \(-0.555999\pi\)
−0.175021 + 0.984565i \(0.555999\pi\)
\(548\) 7.33243 0.0133803
\(549\) 58.8769i 0.107244i
\(550\) 477.804 0.868734
\(551\) 9.77902i 0.0177478i
\(552\) 65.8874i 0.119361i
\(553\) −114.238 + 87.5118i −0.206579 + 0.158249i
\(554\) −339.841 −0.613431
\(555\) 268.666 0.484083
\(556\) 7.61195i 0.0136906i
\(557\) −108.847 −0.195417 −0.0977086 0.995215i \(-0.531151\pi\)
−0.0977086 + 0.995215i \(0.531151\pi\)
\(558\) 1.39898i 0.00250712i
\(559\) 135.046i 0.241585i
\(560\) 161.936 + 211.392i 0.289171 + 0.377485i
\(561\) −2.42371 −0.00432034
\(562\) −636.288 −1.13219
\(563\) 969.946i 1.72282i 0.507913 + 0.861409i \(0.330417\pi\)
−0.507913 + 0.861409i \(0.669583\pi\)
\(564\) −6.98036 −0.0123765
\(565\) 97.0156i 0.171709i
\(566\) 665.782i 1.17629i
\(567\) −50.0122 + 38.3117i −0.0882049 + 0.0675691i
\(568\) 45.9764 0.0809444
\(569\) −122.881 −0.215959 −0.107979 0.994153i \(-0.534438\pi\)
−0.107979 + 0.994153i \(0.534438\pi\)
\(570\) 221.576i 0.388730i
\(571\) −752.698 −1.31821 −0.659105 0.752051i \(-0.729065\pi\)
−0.659105 + 0.752051i \(0.729065\pi\)
\(572\) 10.8448i 0.0189594i
\(573\) 188.451i 0.328885i
\(574\) −474.279 619.126i −0.826271 1.07862i
\(575\) 93.6533 0.162875
\(576\) −188.692 −0.327591
\(577\) 431.303i 0.747493i 0.927531 + 0.373746i \(0.121927\pi\)
−0.927531 + 0.373746i \(0.878073\pi\)
\(578\) −582.773 −1.00826
\(579\) 30.3741i 0.0524596i
\(580\) 0.0562685i 9.70147e-5i
\(581\) 474.079 + 618.864i 0.815971 + 1.06517i
\(582\) 470.312 0.808097
\(583\) 424.273 0.727740
\(584\) 141.171i 0.241731i
\(585\) −94.0314 −0.160737
\(586\) 725.769i 1.23851i
\(587\) 1045.67i 1.78139i −0.454604 0.890694i \(-0.650219\pi\)
0.454604 0.890694i \(-0.349781\pi\)
\(588\) −5.46616 1.47410i −0.00929619 0.00250698i
\(589\) 6.27102 0.0106469
\(590\) −204.347 −0.346351
\(591\) 595.962i 1.00840i
\(592\) −1078.36 −1.82156
\(593\) 569.615i 0.960564i −0.877114 0.480282i \(-0.840534\pi\)
0.877114 0.480282i \(-0.159466\pi\)
\(594\) 127.137i 0.214036i
\(595\) 1.49919 1.14845i 0.00251964 0.00193016i
\(596\) −9.27040 −0.0155544
\(597\) −227.739 −0.381473
\(598\) 129.588i 0.216703i
\(599\) 297.266 0.496270 0.248135 0.968725i \(-0.420182\pi\)
0.248135 + 0.968725i \(0.420182\pi\)
\(600\) 268.286i 0.447143i
\(601\) 436.954i 0.727045i −0.931585 0.363523i \(-0.881574\pi\)
0.931585 0.363523i \(-0.118426\pi\)
\(602\) −112.942 + 86.5188i −0.187611 + 0.143719i
\(603\) −347.773 −0.576738
\(604\) −14.6815 −0.0243071
\(605\) 61.3117i 0.101342i
\(606\) 189.623 0.312908
\(607\) 438.780i 0.722867i −0.932398 0.361433i \(-0.882287\pi\)
0.932398 0.361433i \(-0.117713\pi\)
\(608\) 28.9411i 0.0476005i
\(609\) 2.65873 + 3.47071i 0.00436573 + 0.00569903i
\(610\) −92.5797 −0.151770
\(611\) −809.521 −1.32491
\(612\) 0.0230804i 3.77130e-5i
\(613\) 466.673 0.761294 0.380647 0.924720i \(-0.375701\pi\)
0.380647 + 0.924720i \(0.375701\pi\)
\(614\) 388.797i 0.633220i
\(615\) 223.849i 0.363983i
\(616\) 534.786 409.671i 0.868159 0.665051i
\(617\) 1071.16 1.73608 0.868040 0.496494i \(-0.165380\pi\)
0.868040 + 0.496494i \(0.165380\pi\)
\(618\) −558.658 −0.903977
\(619\) 797.671i 1.28864i −0.764754 0.644322i \(-0.777140\pi\)
0.764754 0.644322i \(-0.222860\pi\)
\(620\) 0.0360835 5.81991e−5
\(621\) 24.9199i 0.0401286i
\(622\) 970.597i 1.56044i
\(623\) 114.098 + 148.944i 0.183144 + 0.239076i
\(624\) 377.421 0.604841
\(625\) 244.547 0.391275
\(626\) 758.737i 1.21204i
\(627\) −569.902 −0.908935
\(628\) 9.19130i 0.0146358i
\(629\) 7.64774i 0.0121586i
\(630\) −60.2423 78.6405i −0.0956228 0.124826i
\(631\) 172.064 0.272684 0.136342 0.990662i \(-0.456465\pi\)
0.136342 + 0.990662i \(0.456465\pi\)
\(632\) 163.063 0.258011
\(633\) 277.069i 0.437708i
\(634\) 450.340 0.710316
\(635\) 221.137i 0.348247i
\(636\) 4.04023i 0.00635257i
\(637\) −633.917 170.954i −0.995161 0.268373i
\(638\) 8.82298 0.0138291
\(639\) −17.3892 −0.0272131
\(640\) 306.691i 0.479204i
\(641\) 865.373 1.35004 0.675018 0.737801i \(-0.264136\pi\)
0.675018 + 0.737801i \(0.264136\pi\)
\(642\) 369.659i 0.575793i
\(643\) 542.527i 0.843744i −0.906655 0.421872i \(-0.861373\pi\)
0.906655 0.421872i \(-0.138627\pi\)
\(644\) −1.77774 + 1.36183i −0.00276046 + 0.00211464i
\(645\) −40.8349 −0.0633100
\(646\) 6.30730 0.00976362
\(647\) 788.734i 1.21906i −0.792762 0.609531i \(-0.791358\pi\)
0.792762 0.609531i \(-0.208642\pi\)
\(648\) 71.3872 0.110165
\(649\) 525.589i 0.809844i
\(650\) 527.669i 0.811799i
\(651\) 2.22567 1.70497i 0.00341885 0.00261900i
\(652\) −9.86546 −0.0151311
\(653\) 267.720 0.409985 0.204992 0.978764i \(-0.434283\pi\)
0.204992 + 0.978764i \(0.434283\pi\)
\(654\) 697.590i 1.06665i
\(655\) −374.196 −0.571291
\(656\) 898.480i 1.36963i
\(657\) 53.3935i 0.0812687i
\(658\) −518.629 677.020i −0.788190 1.02891i
\(659\) −939.789 −1.42608 −0.713042 0.701122i \(-0.752683\pi\)
−0.713042 + 0.701122i \(0.752683\pi\)
\(660\) −3.27922 −0.00496852
\(661\) 220.558i 0.333674i −0.985984 0.166837i \(-0.946645\pi\)
0.985984 0.166837i \(-0.0533553\pi\)
\(662\) 163.958 0.247671
\(663\) 2.67666i 0.00403719i
\(664\) 883.365i 1.33037i
\(665\) 352.512 270.041i 0.530094 0.406077i
\(666\) 401.166 0.602351
\(667\) 1.72937 0.00259276
\(668\) 6.62296i 0.00991461i
\(669\) 647.843 0.968375
\(670\) 546.848i 0.816191i
\(671\) 238.118i 0.354871i
\(672\) 7.86854 + 10.2716i 0.0117091 + 0.0152851i
\(673\) 227.275 0.337704 0.168852 0.985641i \(-0.445994\pi\)
0.168852 + 0.985641i \(0.445994\pi\)
\(674\) 981.979 1.45694
\(675\) 101.471i 0.150327i
\(676\) −0.703116 −0.00104011
\(677\) 808.648i 1.19446i −0.802071 0.597229i \(-0.796268\pi\)
0.802071 0.597229i \(-0.203732\pi\)
\(678\) 144.862i 0.213660i
\(679\) 573.183 + 748.234i 0.844157 + 1.10197i
\(680\) −2.13993 −0.00314696
\(681\) 54.7869 0.0804507
\(682\) 5.65794i 0.00829610i
\(683\) −799.836 −1.17106 −0.585532 0.810650i \(-0.699114\pi\)
−0.585532 + 0.810650i \(0.699114\pi\)
\(684\) 5.42702i 0.00793425i
\(685\) 257.127i 0.375369i
\(686\) −263.154 639.683i −0.383607 0.932482i
\(687\) 652.134 0.949249
\(688\) 163.902 0.238230
\(689\) 468.551i 0.680045i
\(690\) −39.1847 −0.0567894
\(691\) 497.520i 0.719999i −0.932952 0.360000i \(-0.882777\pi\)
0.932952 0.360000i \(-0.117223\pi\)
\(692\) 3.46605i 0.00500874i
\(693\) −202.266 + 154.945i −0.291871 + 0.223587i
\(694\) −57.2787 −0.0825341
\(695\) −266.929 −0.384071
\(696\) 4.95408i 0.00711793i
\(697\) 6.37200 0.00914204
\(698\) 1386.81i 1.98684i
\(699\) 4.58963i 0.00656599i
\(700\) −7.23873 + 5.54521i −0.0103410 + 0.00792172i
\(701\) 141.312 0.201586 0.100793 0.994907i \(-0.467862\pi\)
0.100793 + 0.994907i \(0.467862\pi\)
\(702\) −140.406 −0.200008
\(703\) 1798.26i 2.55798i
\(704\) −763.136 −1.08400
\(705\) 244.781i 0.347208i
\(706\) 6.30773i 0.00893446i
\(707\) 231.098 + 301.676i 0.326871 + 0.426699i
\(708\) −5.00504 −0.00706927
\(709\) 460.837 0.649982 0.324991 0.945717i \(-0.394639\pi\)
0.324991 + 0.945717i \(0.394639\pi\)
\(710\) 27.3432i 0.0385115i
\(711\) −61.6736 −0.0867420
\(712\) 212.603i 0.298599i
\(713\) 1.10900i 0.00155540i
\(714\) 2.23855 1.71483i 0.00313522 0.00240173i
\(715\) −380.295 −0.531881
\(716\) 20.4007 0.0284926
\(717\) 265.723i 0.370603i
\(718\) 937.132 1.30520
\(719\) 1300.87i 1.80928i −0.426178 0.904639i \(-0.640140\pi\)
0.426178 0.904639i \(-0.359860\pi\)
\(720\) 114.124i 0.158505i
\(721\) −680.852 888.786i −0.944316 1.23271i
\(722\) 755.077 1.04581
\(723\) −269.836 −0.373217
\(724\) 5.53968i 0.00765149i
\(725\) 7.04180 0.00971283
\(726\) 91.5493i 0.126101i
\(727\) 327.305i 0.450214i 0.974334 + 0.225107i \(0.0722731\pi\)
−0.974334 + 0.225107i \(0.927727\pi\)
\(728\) 452.426 + 590.598i 0.621464 + 0.811261i
\(729\) −27.0000 −0.0370370
\(730\) 83.9575 0.115010
\(731\) 1.16239i 0.00159014i
\(732\) −2.26754 −0.00309773
\(733\) 1217.68i 1.66123i −0.556850 0.830613i \(-0.687990\pi\)
0.556850 0.830613i \(-0.312010\pi\)
\(734\) 568.800i 0.774932i
\(735\) 51.6926 191.683i 0.0703301 0.260793i
\(736\) 5.11810 0.00695394
\(737\) −1406.51 −1.90843
\(738\) 334.247i 0.452909i
\(739\) 73.9055 0.100007 0.0500037 0.998749i \(-0.484077\pi\)
0.0500037 + 0.998749i \(0.484077\pi\)
\(740\) 10.3472i 0.0139827i
\(741\) 629.379i 0.849364i
\(742\) −391.860 + 300.183i −0.528113 + 0.404559i
\(743\) −923.482 −1.24291 −0.621455 0.783450i \(-0.713458\pi\)
−0.621455 + 0.783450i \(0.713458\pi\)
\(744\) −3.17692 −0.00427005
\(745\) 325.087i 0.436358i
\(746\) −390.335 −0.523237
\(747\) 334.105i 0.447263i
\(748\) 0.0933449i 0.000124793i
\(749\) −588.101 + 450.513i −0.785182 + 0.601486i
\(750\) −363.820 −0.485093
\(751\) 484.296 0.644868 0.322434 0.946592i \(-0.395499\pi\)
0.322434 + 0.946592i \(0.395499\pi\)
\(752\) 982.497i 1.30651i
\(753\) −543.317 −0.721537
\(754\) 9.74377i 0.0129228i
\(755\) 514.839i 0.681906i
\(756\) −1.47550 1.92613i −0.00195173 0.00254779i
\(757\) 1119.03 1.47824 0.739121 0.673573i \(-0.235241\pi\)
0.739121 + 0.673573i \(0.235241\pi\)
\(758\) 343.893 0.453684
\(759\) 100.784i 0.132786i
\(760\) −503.175 −0.662072
\(761\) 762.609i 1.00211i 0.865414 + 0.501057i \(0.167055\pi\)
−0.865414 + 0.501057i \(0.832945\pi\)
\(762\) 330.196i 0.433329i
\(763\) −1109.82 + 850.172i −1.45454 + 1.11425i
\(764\) 7.25785 0.00949981
\(765\) 0.809363 0.00105799
\(766\) 1035.75i 1.35216i
\(767\) −580.441 −0.756768
\(768\) 22.1775i 0.0288769i
\(769\) 80.1758i 0.104260i −0.998640 0.0521299i \(-0.983399\pi\)
0.998640 0.0521299i \(-0.0166010\pi\)
\(770\) −243.641 318.049i −0.316416 0.413051i
\(771\) 558.288 0.724109
\(772\) −1.16980 −0.00151529
\(773\) 698.654i 0.903822i −0.892063 0.451911i \(-0.850743\pi\)
0.892063 0.451911i \(-0.149257\pi\)
\(774\) −60.9738 −0.0787775
\(775\) 4.51572i 0.00582673i
\(776\) 1068.03i 1.37632i
\(777\) 488.912 + 638.227i 0.629230 + 0.821399i
\(778\) −980.309 −1.26004
\(779\) 1498.29 1.92335
\(780\) 3.62145i 0.00464288i
\(781\) −70.3277 −0.0900483
\(782\) 1.11542i 0.00142636i
\(783\) 1.87373i 0.00239301i
\(784\) −207.482 + 769.371i −0.264646 + 0.981340i
\(785\) 322.313 0.410590
\(786\) −558.740 −0.710866
\(787\) 1245.34i 1.58239i 0.611562 + 0.791197i \(0.290542\pi\)
−0.611562 + 0.791197i \(0.709458\pi\)
\(788\) −22.9524 −0.0291274
\(789\) 502.017i 0.636270i
\(790\) 96.9773i 0.122756i
\(791\) 230.465 176.547i 0.291359 0.223194i
\(792\) 288.714 0.364538
\(793\) −262.969 −0.331613
\(794\) 155.637i 0.196017i
\(795\) −141.680 −0.178213
\(796\) 8.77096i 0.0110188i
\(797\) 91.7211i 0.115083i −0.998343 0.0575415i \(-0.981674\pi\)
0.998343 0.0575415i \(-0.0183261\pi\)
\(798\) 526.363 403.219i 0.659603 0.505287i
\(799\) 6.96785 0.00872071
\(800\) 20.8403 0.0260504
\(801\) 80.4104i 0.100388i
\(802\) 918.259 1.14496
\(803\) 215.942i 0.268919i
\(804\) 13.3939i 0.0166590i
\(805\) −47.7555 62.3401i −0.0593236 0.0774412i
\(806\) 6.24842 0.00775238
\(807\) −383.802 −0.475592
\(808\) 430.611i 0.532935i
\(809\) 480.075 0.593418 0.296709 0.954968i \(-0.404111\pi\)
0.296709 + 0.954968i \(0.404111\pi\)
\(810\) 42.4556i 0.0524143i
\(811\) 324.813i 0.400510i 0.979744 + 0.200255i \(0.0641770\pi\)
−0.979744 + 0.200255i \(0.935823\pi\)
\(812\) −0.133668 + 0.102396i −0.000164616 + 0.000126104i
\(813\) −556.750 −0.684809
\(814\) 1622.45 1.99319
\(815\) 345.954i 0.424483i
\(816\) −3.24860 −0.00398113
\(817\) 273.320i 0.334541i
\(818\) 715.084i 0.874185i
\(819\) −171.116 223.375i −0.208933 0.272742i
\(820\) 8.62115 0.0105136
\(821\) 623.212 0.759089 0.379544 0.925174i \(-0.376081\pi\)
0.379544 + 0.925174i \(0.376081\pi\)
\(822\) 383.937i 0.467077i
\(823\) 173.202 0.210452 0.105226 0.994448i \(-0.466443\pi\)
0.105226 + 0.994448i \(0.466443\pi\)
\(824\) 1268.65i 1.53962i
\(825\) 410.383i 0.497433i
\(826\) −371.866 485.435i −0.450201 0.587694i
\(827\) −1124.73 −1.36001 −0.680006 0.733206i \(-0.738023\pi\)
−0.680006 + 0.733206i \(0.738023\pi\)
\(828\) −0.959744 −0.00115911
\(829\) 1439.63i 1.73659i 0.496051 + 0.868293i \(0.334783\pi\)
−0.496051 + 0.868293i \(0.665217\pi\)
\(830\) −525.357 −0.632960
\(831\) 291.887i 0.351248i
\(832\) 842.779i 1.01296i
\(833\) 5.45636 + 1.47146i 0.00655025 + 0.00176646i
\(834\) −398.573 −0.477905
\(835\) −232.248 −0.278142
\(836\) 21.9487i 0.0262545i
\(837\) 1.20157 0.00143557
\(838\) 480.703i 0.573632i
\(839\) 1342.90i 1.60060i 0.599602 + 0.800298i \(0.295326\pi\)
−0.599602 + 0.800298i \(0.704674\pi\)
\(840\) −178.584 + 136.804i −0.212600 + 0.162861i
\(841\) −840.870 −0.999845
\(842\) 164.113 0.194908
\(843\) 546.504i 0.648284i
\(844\) 10.6708 0.0126431
\(845\) 24.6563i 0.0291790i
\(846\) 365.502i 0.432035i
\(847\) −145.648 + 111.574i −0.171958 + 0.131728i
\(848\) 568.669 0.670601
\(849\) −571.835 −0.673540
\(850\) 4.54184i 0.00534334i
\(851\) 318.013 0.373694
\(852\) 0.669712i 0.000786047i
\(853\) 58.2855i 0.0683301i 0.999416 + 0.0341650i \(0.0108772\pi\)
−0.999416 + 0.0341650i \(0.989123\pi\)
\(854\) −168.474 219.927i −0.197277 0.257526i
\(855\) 190.310 0.222585
\(856\) 839.454 0.980670
\(857\) 325.688i 0.380032i 0.981781 + 0.190016i \(0.0608540\pi\)
−0.981781 + 0.190016i \(0.939146\pi\)
\(858\) −567.848 −0.661828
\(859\) 389.076i 0.452940i 0.974018 + 0.226470i \(0.0727186\pi\)
−0.974018 + 0.226470i \(0.927281\pi\)
\(860\) 1.57268i 0.00182870i
\(861\) 531.763 407.355i 0.617611 0.473119i
\(862\) −516.838 −0.599580
\(863\) −757.604 −0.877872 −0.438936 0.898518i \(-0.644645\pi\)
−0.438936 + 0.898518i \(0.644645\pi\)
\(864\) 5.54532i 0.00641820i
\(865\) 121.544 0.140514
\(866\) 47.7078i 0.0550898i
\(867\) 500.540i 0.577324i
\(868\) 0.0656638 + 0.0857177i 7.56496e−5 + 9.87532e-5i
\(869\) −249.429 −0.287030
\(870\) −2.94630 −0.00338656
\(871\) 1553.30i 1.78335i
\(872\) 1584.15 1.81668
\(873\) 403.948i 0.462713i
\(874\) 262.274i 0.300085i
\(875\) −443.397 578.812i −0.506740 0.661499i
\(876\) 2.05636 0.00234744
\(877\) 1016.23 1.15875 0.579377 0.815060i \(-0.303296\pi\)
0.579377 + 0.815060i \(0.303296\pi\)
\(878\) 838.422i 0.954923i
\(879\) −623.358 −0.709167
\(880\) 461.555i 0.524495i
\(881\) 671.812i 0.762556i 0.924460 + 0.381278i \(0.124516\pi\)
−0.924460 + 0.381278i \(0.875484\pi\)
\(882\) 77.1863 286.216i 0.0875128 0.324508i
\(883\) 1262.79 1.43012 0.715058 0.699065i \(-0.246400\pi\)
0.715058 + 0.699065i \(0.246400\pi\)
\(884\) 0.103087 0.000116614
\(885\) 175.513i 0.198319i
\(886\) 1699.80 1.91851
\(887\) 1304.28i 1.47044i −0.677829 0.735219i \(-0.737079\pi\)
0.677829 0.735219i \(-0.262921\pi\)
\(888\) 911.003i 1.02590i
\(889\) −525.319 + 402.419i −0.590911 + 0.452665i
\(890\) −126.440 −0.142067
\(891\) −109.197 −0.122556
\(892\) 24.9505i 0.0279714i
\(893\) 1638.39 1.83470
\(894\) 485.412i 0.542967i
\(895\) 715.395i 0.799325i
\(896\) 728.556 558.108i 0.813120 0.622888i
\(897\) −111.303 −0.124083
\(898\) 432.914 0.482087
\(899\) 0.0833858i 9.27540e-5i
\(900\) −3.90796 −0.00434218
\(901\) 4.03299i 0.00447613i
\(902\) 1351.81i 1.49868i
\(903\) −74.3104 97.0050i −0.0822928 0.107425i
\(904\) −328.964 −0.363899
\(905\) 194.261 0.214653
\(906\) 768.746i 0.848505i
\(907\) −1536.55 −1.69410 −0.847051 0.531512i \(-0.821624\pi\)
−0.847051 + 0.531512i \(0.821624\pi\)
\(908\) 2.11002i 0.00232381i
\(909\) 162.865i 0.179170i
\(910\) 351.242 269.068i 0.385980 0.295679i
\(911\) 1717.65 1.88546 0.942728 0.333561i \(-0.108250\pi\)
0.942728 + 0.333561i \(0.108250\pi\)
\(912\) −763.862 −0.837568
\(913\) 1351.24i 1.48000i
\(914\) 970.112 1.06139
\(915\) 79.5161i 0.0869028i
\(916\) 25.1158i 0.0274190i
\(917\) −680.952 888.917i −0.742587 0.969375i
\(918\) 1.20852 0.00131647
\(919\) 600.919 0.653883 0.326942 0.945044i \(-0.393982\pi\)
0.326942 + 0.945044i \(0.393982\pi\)
\(920\) 88.9841i 0.0967218i
\(921\) 333.935 0.362579
\(922\) 852.988i 0.925150i
\(923\) 77.6673i 0.0841466i
\(924\) −5.96744 7.78992i −0.00645827 0.00843065i
\(925\) 1294.91 1.39991
\(926\) −1296.59 −1.40020
\(927\) 479.828i 0.517613i
\(928\) 0.384831 0.000414688
\(929\) 145.356i 0.156465i −0.996935 0.0782323i \(-0.975072\pi\)
0.996935 0.0782323i \(-0.0249276\pi\)
\(930\) 1.88938i 0.00203160i
\(931\) 1282.99 + 345.993i 1.37807 + 0.371636i
\(932\) 0.176761 0.000189658
\(933\) −833.639 −0.893504
\(934\) 21.4545i 0.0229705i
\(935\) 3.27334 0.00350090
\(936\) 318.845i 0.340647i
\(937\) 55.3524i 0.0590741i −0.999564 0.0295370i \(-0.990597\pi\)
0.999564 0.0295370i \(-0.00940330\pi\)
\(938\) 1299.06 995.141i 1.38493 1.06092i
\(939\) 651.674 0.694008
\(940\) 9.42731 0.0100291
\(941\) 748.881i 0.795836i −0.917421 0.397918i \(-0.869733\pi\)
0.917421 0.397918i \(-0.130267\pi\)
\(942\) 481.270 0.510903
\(943\) 264.965i 0.280981i
\(944\) 704.468i 0.746258i
\(945\) 67.5438 51.7417i 0.0714749 0.0547532i
\(946\) −246.599 −0.260675
\(947\) 323.543 0.341650 0.170825 0.985301i \(-0.445357\pi\)
0.170825 + 0.985301i \(0.445357\pi\)
\(948\) 2.37525i 0.00250553i
\(949\) 238.478 0.251294
\(950\) 1067.95i 1.12416i
\(951\) 386.794i 0.406724i
\(952\) −3.89419 5.08349i −0.00409054 0.00533980i
\(953\) 848.969 0.890839 0.445419 0.895322i \(-0.353055\pi\)
0.445419 + 0.895322i \(0.353055\pi\)
\(954\) −211.553 −0.221753
\(955\) 254.512i 0.266505i
\(956\) 10.2338 0.0107048
\(957\) 7.57800i 0.00791849i
\(958\) 405.394i 0.423167i
\(959\) −610.817 + 467.914i −0.636931 + 0.487919i
\(960\) 254.838 0.265456
\(961\) 960.947 0.999944
\(962\) 1791.78i 1.86255i
\(963\) −317.497 −0.329696
\(964\) 10.3922i 0.0107803i
\(965\) 41.0217i 0.0425096i
\(966\) −71.3074 93.0849i −0.0738172 0.0963612i
\(967\) −78.0643 −0.0807283 −0.0403642 0.999185i \(-0.512852\pi\)
−0.0403642 + 0.999185i \(0.512852\pi\)
\(968\) 207.898 0.214771
\(969\) 5.41730i 0.00559060i
\(970\) −635.180 −0.654824
\(971\) 22.2874i 0.0229530i −0.999934 0.0114765i \(-0.996347\pi\)
0.999934 0.0114765i \(-0.00365317\pi\)
\(972\) 1.03986i 0.00106981i
\(973\) −485.752 634.102i −0.499231 0.651698i
\(974\) −658.165 −0.675734
\(975\) −453.211 −0.464832
\(976\) 319.159i 0.327008i
\(977\) −1163.05 −1.19043 −0.595216 0.803566i \(-0.702934\pi\)
−0.595216 + 0.803566i \(0.702934\pi\)
\(978\) 516.570i 0.528190i
\(979\) 325.207i 0.332183i
\(980\) 7.38231 + 1.99085i 0.00753297 + 0.00203148i
\(981\) −599.155 −0.610760
\(982\) −674.214 −0.686573
\(983\) 694.119i 0.706123i 0.935600 + 0.353062i \(0.114859\pi\)
−0.935600 + 0.353062i \(0.885141\pi\)
\(984\) −759.037 −0.771379
\(985\) 804.875i 0.817132i
\(986\) 0.0838682i 8.50591e-5i
\(987\) 581.488 445.447i 0.589147 0.451314i
\(988\) 24.2394 0.0245338
\(989\) −48.3353 −0.0488729
\(990\) 171.705i 0.173439i
\(991\) −161.169 −0.162632 −0.0813162 0.996688i \(-0.525912\pi\)
−0.0813162 + 0.996688i \(0.525912\pi\)
\(992\) 0.246781i 0.000248772i
\(993\) 140.822i 0.141815i
\(994\) 64.9549 49.7585i 0.0653470 0.0500588i
\(995\) 307.573 0.309118
\(996\) −12.8675 −0.0129191
\(997\) 1338.45i 1.34248i 0.741241 + 0.671239i \(0.234238\pi\)
−0.741241 + 0.671239i \(0.765762\pi\)
\(998\) 993.581 0.995572
\(999\) 344.559i 0.344904i
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 483.3.g.a.139.17 60
7.6 odd 2 inner 483.3.g.a.139.18 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.3.g.a.139.17 60 1.1 even 1 trivial
483.3.g.a.139.18 yes 60 7.6 odd 2 inner