Properties

Label 156.3.e.c.103.15
Level $156$
Weight $3$
Character 156.103
Analytic conductor $4.251$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [156,3,Mod(103,156)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(156, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("156.103");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 156.e (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: \(4.25069212402\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 103.15
Character \(\chi\) \(=\) 156.103
Dual form 156.3.e.c.103.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.570481 - 1.91691i) q^{2} +1.73205i q^{3} +(-3.34910 - 2.18712i) q^{4} +7.79890i q^{5} +(3.32019 + 0.988102i) q^{6} -7.84779 q^{7} +(-6.10312 + 5.17222i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(0.570481 - 1.91691i) q^{2} +1.73205i q^{3} +(-3.34910 - 2.18712i) q^{4} +7.79890i q^{5} +(3.32019 + 0.988102i) q^{6} -7.84779 q^{7} +(-6.10312 + 5.17222i) q^{8} -3.00000 q^{9} +(14.9498 + 4.44912i) q^{10} -13.1778 q^{11} +(3.78821 - 5.80082i) q^{12} +(-10.3889 + 7.81476i) q^{13} +(-4.47702 + 15.0435i) q^{14} -13.5081 q^{15} +(6.43298 + 14.6498i) q^{16} +22.5790 q^{17} +(-1.71144 + 5.75074i) q^{18} +26.2312 q^{19} +(17.0572 - 26.1193i) q^{20} -13.5928i q^{21} +(-7.51768 + 25.2607i) q^{22} -10.4194i q^{23} +(-8.95855 - 10.5709i) q^{24} -35.8228 q^{25} +(9.05354 + 24.3728i) q^{26} -5.19615i q^{27} +(26.2831 + 17.1641i) q^{28} +37.2030 q^{29} +(-7.70611 + 25.8938i) q^{30} -49.6331 q^{31} +(31.7523 - 3.97401i) q^{32} -22.8246i q^{33} +(12.8809 - 43.2820i) q^{34} -61.2042i q^{35} +(10.0473 + 6.56137i) q^{36} +38.6578i q^{37} +(14.9644 - 50.2829i) q^{38} +(-13.5356 - 17.9941i) q^{39} +(-40.3376 - 47.5976i) q^{40} +11.4818i q^{41} +(-26.0562 - 7.75442i) q^{42} +67.3590i q^{43} +(44.1337 + 28.8214i) q^{44} -23.3967i q^{45} +(-19.9730 - 5.94405i) q^{46} -10.7509 q^{47} +(-25.3742 + 11.1422i) q^{48} +12.5879 q^{49} +(-20.4362 + 68.6692i) q^{50} +39.1080i q^{51} +(51.8854 - 3.45061i) q^{52} -57.9959 q^{53} +(-9.96057 - 2.96431i) q^{54} -102.772i q^{55} +(47.8961 - 40.5905i) q^{56} +45.4338i q^{57} +(21.2236 - 71.3150i) q^{58} +16.0034 q^{59} +(45.2400 + 29.5439i) q^{60} -55.0061 q^{61} +(-28.3148 + 95.1423i) q^{62} +23.5434 q^{63} +(10.4962 - 63.1334i) q^{64} +(-60.9466 - 81.0221i) q^{65} +(-43.7527 - 13.0210i) q^{66} +36.6889 q^{67} +(-75.6194 - 49.3831i) q^{68} +18.0469 q^{69} +(-117.323 - 34.9158i) q^{70} +56.5184 q^{71} +(18.3094 - 15.5167i) q^{72} -37.3642i q^{73} +(74.1036 + 22.0535i) q^{74} -62.0470i q^{75} +(-87.8510 - 57.3709i) q^{76} +103.417 q^{77} +(-42.2149 + 15.6812i) q^{78} +57.2222i q^{79} +(-114.252 + 50.1701i) q^{80} +9.00000 q^{81} +(22.0097 + 6.55017i) q^{82} +14.2141 q^{83} +(-29.7291 + 45.5236i) q^{84} +176.091i q^{85} +(129.121 + 38.4270i) q^{86} +64.4376i q^{87} +(80.4256 - 68.1584i) q^{88} +10.3684i q^{89} +(-44.8494 - 13.3474i) q^{90} +(81.5300 - 61.3287i) q^{91} +(-22.7884 + 34.8955i) q^{92} -85.9671i q^{93} +(-6.13316 + 20.6085i) q^{94} +204.575i q^{95} +(6.88320 + 54.9966i) q^{96} -30.8813i q^{97} +(7.18114 - 24.1298i) q^{98} +39.5334 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 8 q^{4} - 72 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 8 q^{4} - 72 q^{9} + 28 q^{10} + 36 q^{12} + 48 q^{13} - 40 q^{14} + 100 q^{16} + 32 q^{17} + 84 q^{22} - 312 q^{25} - 16 q^{26} - 80 q^{29} + 60 q^{30} - 24 q^{36} + 120 q^{38} - 204 q^{40} - 96 q^{42} - 144 q^{48} + 392 q^{49} + 28 q^{52} - 224 q^{53} + 800 q^{56} - 96 q^{61} - 352 q^{62} - 184 q^{64} - 112 q^{65} + 252 q^{66} - 344 q^{68} + 144 q^{69} + 232 q^{74} - 16 q^{77} - 168 q^{78} + 216 q^{81} + 20 q^{82} - 92 q^{88} - 84 q^{90} - 616 q^{92} - 684 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/156\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(79\) \(145\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.570481 1.91691i 0.285241 0.958456i
\(3\) 1.73205i 0.577350i
\(4\) −3.34910 2.18712i −0.837276 0.546781i
\(5\) 7.79890i 1.55978i 0.625917 + 0.779890i \(0.284725\pi\)
−0.625917 + 0.779890i \(0.715275\pi\)
\(6\) 3.32019 + 0.988102i 0.553365 + 0.164684i
\(7\) −7.84779 −1.12111 −0.560557 0.828116i \(-0.689413\pi\)
−0.560557 + 0.828116i \(0.689413\pi\)
\(8\) −6.10312 + 5.17222i −0.762890 + 0.646528i
\(9\) −3.00000 −0.333333
\(10\) 14.9498 + 4.44912i 1.49498 + 0.444912i
\(11\) −13.1778 −1.19798 −0.598990 0.800756i \(-0.704431\pi\)
−0.598990 + 0.800756i \(0.704431\pi\)
\(12\) 3.78821 5.80082i 0.315684 0.483401i
\(13\) −10.3889 + 7.81476i −0.799147 + 0.601136i
\(14\) −4.47702 + 15.0435i −0.319787 + 1.07454i
\(15\) −13.5081 −0.900539
\(16\) 6.43298 + 14.6498i 0.402061 + 0.915613i
\(17\) 22.5790 1.32818 0.664089 0.747654i \(-0.268820\pi\)
0.664089 + 0.747654i \(0.268820\pi\)
\(18\) −1.71144 + 5.75074i −0.0950802 + 0.319485i
\(19\) 26.2312 1.38059 0.690295 0.723528i \(-0.257481\pi\)
0.690295 + 0.723528i \(0.257481\pi\)
\(20\) 17.0572 26.1193i 0.852858 1.30597i
\(21\) 13.5928i 0.647275i
\(22\) −7.51768 + 25.2607i −0.341713 + 1.14821i
\(23\) 10.4194i 0.453016i −0.974009 0.226508i \(-0.927269\pi\)
0.974009 0.226508i \(-0.0727309\pi\)
\(24\) −8.95855 10.5709i −0.373273 0.440455i
\(25\) −35.8228 −1.43291
\(26\) 9.05354 + 24.3728i 0.348213 + 0.937415i
\(27\) 5.19615i 0.192450i
\(28\) 26.2831 + 17.1641i 0.938681 + 0.613004i
\(29\) 37.2030 1.28286 0.641432 0.767180i \(-0.278341\pi\)
0.641432 + 0.767180i \(0.278341\pi\)
\(30\) −7.70611 + 25.8938i −0.256870 + 0.863127i
\(31\) −49.6331 −1.60107 −0.800534 0.599287i \(-0.795451\pi\)
−0.800534 + 0.599287i \(0.795451\pi\)
\(32\) 31.7523 3.97401i 0.992259 0.124188i
\(33\) 22.8246i 0.691654i
\(34\) 12.8809 43.2820i 0.378850 1.27300i
\(35\) 61.2042i 1.74869i
\(36\) 10.0473 + 6.56137i 0.279092 + 0.182260i
\(37\) 38.6578i 1.04481i 0.852699 + 0.522403i \(0.174964\pi\)
−0.852699 + 0.522403i \(0.825036\pi\)
\(38\) 14.9644 50.2829i 0.393800 1.32323i
\(39\) −13.5356 17.9941i −0.347066 0.461388i
\(40\) −40.3376 47.5976i −1.00844 1.18994i
\(41\) 11.4818i 0.280045i 0.990148 + 0.140022i \(0.0447175\pi\)
−0.990148 + 0.140022i \(0.955283\pi\)
\(42\) −26.0562 7.75442i −0.620385 0.184629i
\(43\) 67.3590i 1.56649i 0.621714 + 0.783244i \(0.286436\pi\)
−0.621714 + 0.783244i \(0.713564\pi\)
\(44\) 44.1337 + 28.8214i 1.00304 + 0.655033i
\(45\) 23.3967i 0.519927i
\(46\) −19.9730 5.94405i −0.434196 0.129218i
\(47\) −10.7509 −0.228742 −0.114371 0.993438i \(-0.536485\pi\)
−0.114371 + 0.993438i \(0.536485\pi\)
\(48\) −25.3742 + 11.1422i −0.528629 + 0.232130i
\(49\) 12.5879 0.256895
\(50\) −20.4362 + 68.6692i −0.408725 + 1.37338i
\(51\) 39.1080i 0.766824i
\(52\) 51.8854 3.45061i 0.997796 0.0663579i
\(53\) −57.9959 −1.09426 −0.547131 0.837047i \(-0.684280\pi\)
−0.547131 + 0.837047i \(0.684280\pi\)
\(54\) −9.96057 2.96431i −0.184455 0.0548946i
\(55\) 102.772i 1.86859i
\(56\) 47.8961 40.5905i 0.855287 0.724831i
\(57\) 45.4338i 0.797084i
\(58\) 21.2236 71.3150i 0.365925 1.22957i
\(59\) 16.0034 0.271244 0.135622 0.990761i \(-0.456697\pi\)
0.135622 + 0.990761i \(0.456697\pi\)
\(60\) 45.2400 + 29.5439i 0.754000 + 0.492398i
\(61\) −55.0061 −0.901739 −0.450870 0.892590i \(-0.648886\pi\)
−0.450870 + 0.892590i \(0.648886\pi\)
\(62\) −28.3148 + 95.1423i −0.456690 + 1.53455i
\(63\) 23.5434 0.373704
\(64\) 10.4962 63.1334i 0.164004 0.986460i
\(65\) −60.9466 81.0221i −0.937639 1.24649i
\(66\) −43.7527 13.0210i −0.662920 0.197288i
\(67\) 36.6889 0.547596 0.273798 0.961787i \(-0.411720\pi\)
0.273798 + 0.961787i \(0.411720\pi\)
\(68\) −75.6194 49.3831i −1.11205 0.726222i
\(69\) 18.0469 0.261549
\(70\) −117.323 34.9158i −1.67604 0.498797i
\(71\) 56.5184 0.796033 0.398017 0.917378i \(-0.369699\pi\)
0.398017 + 0.917378i \(0.369699\pi\)
\(72\) 18.3094 15.5167i 0.254297 0.215509i
\(73\) 37.3642i 0.511839i −0.966698 0.255919i \(-0.917622\pi\)
0.966698 0.255919i \(-0.0823782\pi\)
\(74\) 74.1036 + 22.0535i 1.00140 + 0.298021i
\(75\) 62.0470i 0.827293i
\(76\) −87.8510 57.3709i −1.15593 0.754880i
\(77\) 103.417 1.34307
\(78\) −42.2149 + 15.6812i −0.541217 + 0.201041i
\(79\) 57.2222i 0.724332i 0.932114 + 0.362166i \(0.117963\pi\)
−0.932114 + 0.362166i \(0.882037\pi\)
\(80\) −114.252 + 50.1701i −1.42815 + 0.627127i
\(81\) 9.00000 0.111111
\(82\) 22.0097 + 6.55017i 0.268411 + 0.0798801i
\(83\) 14.2141 0.171255 0.0856273 0.996327i \(-0.472711\pi\)
0.0856273 + 0.996327i \(0.472711\pi\)
\(84\) −29.7291 + 45.5236i −0.353918 + 0.541948i
\(85\) 176.091i 2.07166i
\(86\) 129.121 + 38.4270i 1.50141 + 0.446826i
\(87\) 64.4376i 0.740662i
\(88\) 80.4256 68.1584i 0.913928 0.774528i
\(89\) 10.3684i 0.116498i 0.998302 + 0.0582492i \(0.0185518\pi\)
−0.998302 + 0.0582492i \(0.981448\pi\)
\(90\) −44.8494 13.3474i −0.498327 0.148304i
\(91\) 81.5300 61.3287i 0.895934 0.673941i
\(92\) −22.7884 + 34.8955i −0.247700 + 0.379299i
\(93\) 85.9671i 0.924377i
\(94\) −6.13316 + 20.6085i −0.0652464 + 0.219239i
\(95\) 204.575i 2.15342i
\(96\) 6.88320 + 54.9966i 0.0717000 + 0.572881i
\(97\) 30.8813i 0.318364i −0.987249 0.159182i \(-0.949114\pi\)
0.987249 0.159182i \(-0.0508856\pi\)
\(98\) 7.18114 24.1298i 0.0732770 0.246223i
\(99\) 39.5334 0.399327
\(100\) 119.974 + 78.3490i 1.19974 + 0.783490i
\(101\) 136.133 1.34785 0.673925 0.738799i \(-0.264607\pi\)
0.673925 + 0.738799i \(0.264607\pi\)
\(102\) 74.9666 + 22.3104i 0.734967 + 0.218729i
\(103\) 124.738i 1.21105i 0.795825 + 0.605526i \(0.207037\pi\)
−0.795825 + 0.605526i \(0.792963\pi\)
\(104\) 22.9851 101.428i 0.221011 0.975271i
\(105\) 106.009 1.00961
\(106\) −33.0856 + 111.173i −0.312128 + 1.04880i
\(107\) 53.3555i 0.498650i 0.968420 + 0.249325i \(0.0802087\pi\)
−0.968420 + 0.249325i \(0.919791\pi\)
\(108\) −11.3646 + 17.4024i −0.105228 + 0.161134i
\(109\) 50.9829i 0.467733i −0.972269 0.233867i \(-0.924862\pi\)
0.972269 0.233867i \(-0.0751379\pi\)
\(110\) −197.005 58.6296i −1.79096 0.532996i
\(111\) −66.9573 −0.603219
\(112\) −50.4847 114.969i −0.450756 1.02651i
\(113\) −33.1089 −0.293000 −0.146500 0.989211i \(-0.546801\pi\)
−0.146500 + 0.989211i \(0.546801\pi\)
\(114\) 87.0926 + 25.9191i 0.763970 + 0.227361i
\(115\) 81.2595 0.706605
\(116\) −124.597 81.3677i −1.07411 0.701446i
\(117\) 31.1667 23.4443i 0.266382 0.200379i
\(118\) 9.12964 30.6771i 0.0773698 0.259976i
\(119\) −177.195 −1.48904
\(120\) 82.4415 69.8668i 0.687013 0.582224i
\(121\) 52.6540 0.435157
\(122\) −31.3799 + 105.442i −0.257213 + 0.864277i
\(123\) −19.8871 −0.161684
\(124\) 166.226 + 108.554i 1.34054 + 0.875434i
\(125\) 84.4062i 0.675250i
\(126\) 13.4311 45.1306i 0.106596 0.358179i
\(127\) 184.395i 1.45193i 0.687733 + 0.725963i \(0.258606\pi\)
−0.687733 + 0.725963i \(0.741394\pi\)
\(128\) −115.033 56.1368i −0.898698 0.438569i
\(129\) −116.669 −0.904412
\(130\) −190.081 + 70.6076i −1.46216 + 0.543136i
\(131\) 9.22179i 0.0703953i 0.999380 + 0.0351977i \(0.0112061\pi\)
−0.999380 + 0.0351977i \(0.988794\pi\)
\(132\) −49.9202 + 76.4419i −0.378183 + 0.579105i
\(133\) −205.857 −1.54780
\(134\) 20.9303 70.3295i 0.156197 0.524847i
\(135\) 40.5243 0.300180
\(136\) −137.803 + 116.784i −1.01325 + 0.858704i
\(137\) 25.1044i 0.183244i −0.995794 0.0916218i \(-0.970795\pi\)
0.995794 0.0916218i \(-0.0292051\pi\)
\(138\) 10.2954 34.5942i 0.0746043 0.250683i
\(139\) 122.678i 0.882578i −0.897365 0.441289i \(-0.854521\pi\)
0.897365 0.441289i \(-0.145479\pi\)
\(140\) −133.861 + 204.979i −0.956151 + 1.46414i
\(141\) 18.6210i 0.132064i
\(142\) 32.2427 108.341i 0.227061 0.762963i
\(143\) 136.903 102.981i 0.957362 0.720149i
\(144\) −19.2989 43.9494i −0.134020 0.305204i
\(145\) 290.143i 2.00099i
\(146\) −71.6239 21.3156i −0.490575 0.145997i
\(147\) 21.8028i 0.148319i
\(148\) 84.5494 129.469i 0.571280 0.874790i
\(149\) 24.4303i 0.163962i −0.996634 0.0819809i \(-0.973875\pi\)
0.996634 0.0819809i \(-0.0261246\pi\)
\(150\) −118.939 35.3966i −0.792924 0.235977i
\(151\) −163.895 −1.08540 −0.542700 0.839927i \(-0.682598\pi\)
−0.542700 + 0.839927i \(0.682598\pi\)
\(152\) −160.092 + 135.674i −1.05324 + 0.892590i
\(153\) −67.7371 −0.442726
\(154\) 58.9972 198.240i 0.383099 1.28728i
\(155\) 387.084i 2.49731i
\(156\) 5.97663 + 89.8681i 0.0383118 + 0.576078i
\(157\) 148.220 0.944077 0.472039 0.881578i \(-0.343518\pi\)
0.472039 + 0.881578i \(0.343518\pi\)
\(158\) 109.690 + 32.6442i 0.694240 + 0.206609i
\(159\) 100.452i 0.631773i
\(160\) 30.9929 + 247.633i 0.193706 + 1.54771i
\(161\) 81.7690i 0.507882i
\(162\) 5.13433 17.2522i 0.0316934 0.106495i
\(163\) 67.4230 0.413638 0.206819 0.978379i \(-0.433689\pi\)
0.206819 + 0.978379i \(0.433689\pi\)
\(164\) 25.1122 38.4539i 0.153123 0.234475i
\(165\) 178.007 1.07883
\(166\) 8.10889 27.2472i 0.0488487 0.164140i
\(167\) 148.240 0.887668 0.443834 0.896109i \(-0.353618\pi\)
0.443834 + 0.896109i \(0.353618\pi\)
\(168\) 70.3049 + 82.9584i 0.418481 + 0.493800i
\(169\) 46.8589 162.374i 0.277272 0.960792i
\(170\) 337.552 + 100.457i 1.98560 + 0.590923i
\(171\) −78.6936 −0.460197
\(172\) 147.322 225.592i 0.856526 1.31158i
\(173\) 23.5907 0.136362 0.0681811 0.997673i \(-0.478280\pi\)
0.0681811 + 0.997673i \(0.478280\pi\)
\(174\) 123.521 + 36.7604i 0.709892 + 0.211267i
\(175\) 281.130 1.60646
\(176\) −84.7724 193.052i −0.481661 1.09689i
\(177\) 27.7187i 0.156603i
\(178\) 19.8752 + 5.91496i 0.111659 + 0.0332301i
\(179\) 87.8770i 0.490933i 0.969405 + 0.245466i \(0.0789411\pi\)
−0.969405 + 0.245466i \(0.921059\pi\)
\(180\) −51.1715 + 78.3579i −0.284286 + 0.435322i
\(181\) −156.626 −0.865338 −0.432669 0.901553i \(-0.642428\pi\)
−0.432669 + 0.901553i \(0.642428\pi\)
\(182\) −71.0503 191.273i −0.390386 1.05095i
\(183\) 95.2734i 0.520619i
\(184\) 53.8912 + 63.5906i 0.292887 + 0.345601i
\(185\) −301.488 −1.62967
\(186\) −164.791 49.0426i −0.885975 0.263670i
\(187\) −297.541 −1.59113
\(188\) 36.0057 + 23.5135i 0.191520 + 0.125072i
\(189\) 40.7783i 0.215758i
\(190\) 392.151 + 116.706i 2.06395 + 0.614242i
\(191\) 365.952i 1.91598i 0.286800 + 0.957990i \(0.407409\pi\)
−0.286800 + 0.957990i \(0.592591\pi\)
\(192\) 109.350 + 18.1800i 0.569533 + 0.0946876i
\(193\) 28.6209i 0.148295i −0.997247 0.0741473i \(-0.976377\pi\)
0.997247 0.0741473i \(-0.0236235\pi\)
\(194\) −59.1967 17.6172i −0.305138 0.0908103i
\(195\) 140.334 105.563i 0.719663 0.541346i
\(196\) −42.1581 27.5312i −0.215092 0.140465i
\(197\) 312.113i 1.58433i −0.610307 0.792165i \(-0.708954\pi\)
0.610307 0.792165i \(-0.291046\pi\)
\(198\) 22.5530 75.7820i 0.113904 0.382737i
\(199\) 155.166i 0.779729i −0.920872 0.389865i \(-0.872522\pi\)
0.920872 0.389865i \(-0.127478\pi\)
\(200\) 218.631 185.284i 1.09316 0.926418i
\(201\) 63.5471i 0.316155i
\(202\) 77.6613 260.955i 0.384462 1.29186i
\(203\) −291.962 −1.43824
\(204\) 85.5341 130.977i 0.419285 0.642043i
\(205\) −89.5457 −0.436808
\(206\) 239.113 + 71.1609i 1.16074 + 0.345441i
\(207\) 31.2581i 0.151005i
\(208\) −181.316 101.923i −0.871713 0.490016i
\(209\) −345.669 −1.65392
\(210\) 60.4760 203.209i 0.287981 0.967664i
\(211\) 294.581i 1.39612i −0.716040 0.698059i \(-0.754047\pi\)
0.716040 0.698059i \(-0.245953\pi\)
\(212\) 194.234 + 126.844i 0.916200 + 0.598322i
\(213\) 97.8927i 0.459590i
\(214\) 102.278 + 30.4383i 0.477934 + 0.142235i
\(215\) −525.326 −2.44338
\(216\) 26.8757 + 31.7128i 0.124424 + 0.146818i
\(217\) 389.511 1.79498
\(218\) −97.7297 29.0848i −0.448301 0.133416i
\(219\) 64.7167 0.295510
\(220\) −224.776 + 344.195i −1.02171 + 1.56452i
\(221\) −234.571 + 176.450i −1.06141 + 0.798415i
\(222\) −38.1979 + 128.351i −0.172062 + 0.578159i
\(223\) 130.127 0.583529 0.291765 0.956490i \(-0.405758\pi\)
0.291765 + 0.956490i \(0.405758\pi\)
\(224\) −249.185 + 31.1873i −1.11243 + 0.139229i
\(225\) 107.469 0.477638
\(226\) −18.8880 + 63.4669i −0.0835753 + 0.280827i
\(227\) 129.292 0.569567 0.284783 0.958592i \(-0.408078\pi\)
0.284783 + 0.958592i \(0.408078\pi\)
\(228\) 99.3693 152.162i 0.435830 0.667379i
\(229\) 163.279i 0.713007i 0.934294 + 0.356504i \(0.116031\pi\)
−0.934294 + 0.356504i \(0.883969\pi\)
\(230\) 46.3570 155.767i 0.201552 0.677250i
\(231\) 179.123i 0.775423i
\(232\) −227.055 + 192.422i −0.978685 + 0.829407i
\(233\) 419.074 1.79860 0.899301 0.437330i \(-0.144076\pi\)
0.899301 + 0.437330i \(0.144076\pi\)
\(234\) −27.1606 73.1184i −0.116071 0.312472i
\(235\) 83.8449i 0.356787i
\(236\) −53.5971 35.0014i −0.227106 0.148311i
\(237\) −99.1118 −0.418193
\(238\) −101.087 + 339.668i −0.424734 + 1.42718i
\(239\) −11.5936 −0.0485089 −0.0242545 0.999706i \(-0.507721\pi\)
−0.0242545 + 0.999706i \(0.507721\pi\)
\(240\) −86.8972 197.891i −0.362072 0.824545i
\(241\) 183.134i 0.759892i −0.925009 0.379946i \(-0.875943\pi\)
0.925009 0.379946i \(-0.124057\pi\)
\(242\) 30.0381 100.933i 0.124124 0.417079i
\(243\) 15.5885i 0.0641500i
\(244\) 184.221 + 120.305i 0.755004 + 0.493054i
\(245\) 98.1715i 0.400700i
\(246\) −11.3452 + 38.1219i −0.0461188 + 0.154967i
\(247\) −272.514 + 204.991i −1.10329 + 0.829922i
\(248\) 302.917 256.714i 1.22144 1.03514i
\(249\) 24.6196i 0.0988738i
\(250\) −161.799 48.1521i −0.647197 0.192609i
\(251\) 192.907i 0.768555i −0.923218 0.384278i \(-0.874451\pi\)
0.923218 0.384278i \(-0.125549\pi\)
\(252\) −78.8492 51.4923i −0.312894 0.204335i
\(253\) 137.304i 0.542704i
\(254\) 353.468 + 105.194i 1.39161 + 0.414148i
\(255\) −304.999 −1.19608
\(256\) −173.234 + 188.484i −0.676694 + 0.736265i
\(257\) 192.474 0.748925 0.374462 0.927242i \(-0.377827\pi\)
0.374462 + 0.927242i \(0.377827\pi\)
\(258\) −66.5576 + 223.645i −0.257975 + 0.866839i
\(259\) 303.378i 1.17135i
\(260\) 26.9110 + 404.649i 0.103504 + 1.55634i
\(261\) −111.609 −0.427621
\(262\) 17.6774 + 5.26086i 0.0674708 + 0.0200796i
\(263\) 38.1415i 0.145025i −0.997368 0.0725124i \(-0.976898\pi\)
0.997368 0.0725124i \(-0.0231017\pi\)
\(264\) 118.054 + 139.301i 0.447174 + 0.527656i
\(265\) 452.304i 1.70681i
\(266\) −117.438 + 394.610i −0.441495 + 1.48350i
\(267\) −17.9585 −0.0672604
\(268\) −122.875 80.2433i −0.458489 0.299415i
\(269\) −80.2898 −0.298475 −0.149238 0.988801i \(-0.547682\pi\)
−0.149238 + 0.988801i \(0.547682\pi\)
\(270\) 23.1183 77.6815i 0.0856234 0.287709i
\(271\) −241.183 −0.889975 −0.444987 0.895537i \(-0.646792\pi\)
−0.444987 + 0.895537i \(0.646792\pi\)
\(272\) 145.250 + 330.778i 0.534009 + 1.21610i
\(273\) 106.224 + 141.214i 0.389100 + 0.517268i
\(274\) −48.1229 14.3216i −0.175631 0.0522685i
\(275\) 472.066 1.71660
\(276\) −60.4408 39.4707i −0.218988 0.143010i
\(277\) 115.454 0.416800 0.208400 0.978044i \(-0.433174\pi\)
0.208400 + 0.978044i \(0.433174\pi\)
\(278\) −235.164 69.9857i −0.845912 0.251747i
\(279\) 148.899 0.533690
\(280\) 316.561 + 373.537i 1.13058 + 1.33406i
\(281\) 362.576i 1.29031i 0.764053 + 0.645153i \(0.223206\pi\)
−0.764053 + 0.645153i \(0.776794\pi\)
\(282\) −35.6949 10.6229i −0.126578 0.0376700i
\(283\) 239.084i 0.844820i 0.906405 + 0.422410i \(0.138816\pi\)
−0.906405 + 0.422410i \(0.861184\pi\)
\(284\) −189.286 123.613i −0.666499 0.435256i
\(285\) −354.333 −1.24328
\(286\) −119.306 321.180i −0.417152 1.12301i
\(287\) 90.1071i 0.313962i
\(288\) −95.2568 + 11.9220i −0.330753 + 0.0413960i
\(289\) 220.812 0.764056
\(290\) 556.178 + 165.521i 1.91786 + 0.570762i
\(291\) 53.4880 0.183807
\(292\) −81.7202 + 125.137i −0.279864 + 0.428550i
\(293\) 439.949i 1.50153i 0.660569 + 0.750766i \(0.270315\pi\)
−0.660569 + 0.750766i \(0.729685\pi\)
\(294\) 41.7941 + 12.4381i 0.142157 + 0.0423065i
\(295\) 124.809i 0.423081i
\(296\) −199.947 235.933i −0.675496 0.797072i
\(297\) 68.4738i 0.230551i
\(298\) −46.8307 13.9370i −0.157150 0.0467685i
\(299\) 81.4248 + 108.246i 0.272324 + 0.362026i
\(300\) −135.704 + 207.802i −0.452348 + 0.692672i
\(301\) 528.619i 1.75621i
\(302\) −93.4992 + 314.173i −0.309600 + 1.04031i
\(303\) 235.789i 0.778182i
\(304\) 168.745 + 384.282i 0.555081 + 1.26409i
\(305\) 428.987i 1.40651i
\(306\) −38.6427 + 129.846i −0.126283 + 0.424333i
\(307\) −409.415 −1.33360 −0.666800 0.745237i \(-0.732336\pi\)
−0.666800 + 0.745237i \(0.732336\pi\)
\(308\) −346.353 226.185i −1.12452 0.734366i
\(309\) −216.053 −0.699202
\(310\) −742.006 220.824i −2.39357 0.712335i
\(311\) 298.658i 0.960315i −0.877182 0.480157i \(-0.840580\pi\)
0.877182 0.480157i \(-0.159420\pi\)
\(312\) 175.679 + 39.8114i 0.563073 + 0.127601i
\(313\) 20.3892 0.0651412 0.0325706 0.999469i \(-0.489631\pi\)
0.0325706 + 0.999469i \(0.489631\pi\)
\(314\) 84.5568 284.125i 0.269289 0.904856i
\(315\) 183.612i 0.582897i
\(316\) 125.152 191.643i 0.396051 0.606465i
\(317\) 514.348i 1.62255i 0.584665 + 0.811275i \(0.301226\pi\)
−0.584665 + 0.811275i \(0.698774\pi\)
\(318\) −192.557 57.3059i −0.605526 0.180207i
\(319\) −490.254 −1.53685
\(320\) 492.371 + 81.8591i 1.53866 + 0.255810i
\(321\) −92.4145 −0.287896
\(322\) 156.744 + 46.6477i 0.486782 + 0.144869i
\(323\) 592.275 1.83367
\(324\) −30.1419 19.6841i −0.0930306 0.0607534i
\(325\) 372.160 279.947i 1.14511 0.861375i
\(326\) 38.4635 129.244i 0.117986 0.396454i
\(327\) 88.3050 0.270046
\(328\) −59.3866 70.0751i −0.181057 0.213644i
\(329\) 84.3705 0.256445
\(330\) 101.549 341.223i 0.307726 1.03401i
\(331\) 456.718 1.37981 0.689906 0.723899i \(-0.257652\pi\)
0.689906 + 0.723899i \(0.257652\pi\)
\(332\) −47.6046 31.0881i −0.143387 0.0936387i
\(333\) 115.973i 0.348269i
\(334\) 84.5684 284.164i 0.253199 0.850790i
\(335\) 286.133i 0.854130i
\(336\) 199.132 87.4420i 0.592653 0.260244i
\(337\) −597.668 −1.77349 −0.886747 0.462254i \(-0.847041\pi\)
−0.886747 + 0.462254i \(0.847041\pi\)
\(338\) −284.524 182.456i −0.841787 0.539809i
\(339\) 57.3464i 0.169163i
\(340\) 385.134 589.748i 1.13275 1.73455i
\(341\) 654.055 1.91805
\(342\) −44.8932 + 150.849i −0.131267 + 0.441078i
\(343\) 285.755 0.833105
\(344\) −348.396 411.100i −1.01278 1.19506i
\(345\) 140.746i 0.407958i
\(346\) 13.4580 45.2212i 0.0388960 0.130697i
\(347\) 354.809i 1.02251i 0.859430 + 0.511253i \(0.170818\pi\)
−0.859430 + 0.511253i \(0.829182\pi\)
\(348\) 140.933 215.808i 0.404980 0.620138i
\(349\) 443.875i 1.27185i −0.771752 0.635923i \(-0.780619\pi\)
0.771752 0.635923i \(-0.219381\pi\)
\(350\) 160.379 538.902i 0.458227 1.53972i
\(351\) 40.6067 + 53.9824i 0.115689 + 0.153796i
\(352\) −418.425 + 52.3687i −1.18871 + 0.148775i
\(353\) 138.241i 0.391617i 0.980642 + 0.195808i \(0.0627331\pi\)
−0.980642 + 0.195808i \(0.937267\pi\)
\(354\) 53.1343 + 15.8130i 0.150097 + 0.0446695i
\(355\) 440.781i 1.24164i
\(356\) 22.6769 34.7247i 0.0636992 0.0975414i
\(357\) 306.912i 0.859696i
\(358\) 168.452 + 50.1322i 0.470538 + 0.140034i
\(359\) −245.747 −0.684533 −0.342266 0.939603i \(-0.611194\pi\)
−0.342266 + 0.939603i \(0.611194\pi\)
\(360\) 121.013 + 142.793i 0.336147 + 0.396647i
\(361\) 327.076 0.906028
\(362\) −89.3523 + 300.239i −0.246829 + 0.829388i
\(363\) 91.1994i 0.251238i
\(364\) −407.186 + 27.0797i −1.11864 + 0.0743948i
\(365\) 291.400 0.798356
\(366\) −182.631 54.3516i −0.498991 0.148502i
\(367\) 458.704i 1.24988i 0.780674 + 0.624938i \(0.214876\pi\)
−0.780674 + 0.624938i \(0.785124\pi\)
\(368\) 152.642 67.0275i 0.414787 0.182140i
\(369\) 34.4455i 0.0933483i
\(370\) −171.993 + 577.927i −0.464847 + 1.56196i
\(371\) 455.140 1.22679
\(372\) −188.021 + 287.913i −0.505432 + 0.773959i
\(373\) −269.970 −0.723780 −0.361890 0.932221i \(-0.617868\pi\)
−0.361890 + 0.932221i \(0.617868\pi\)
\(374\) −169.742 + 570.361i −0.453855 + 1.52503i
\(375\) 146.196 0.389856
\(376\) 65.6138 55.6058i 0.174505 0.147888i
\(377\) −386.499 + 290.733i −1.02520 + 0.771175i
\(378\) 78.1685 + 23.2633i 0.206795 + 0.0615430i
\(379\) 474.173 1.25112 0.625559 0.780177i \(-0.284871\pi\)
0.625559 + 0.780177i \(0.284871\pi\)
\(380\) 447.430 685.141i 1.17745 1.80300i
\(381\) −319.381 −0.838270
\(382\) 701.498 + 208.769i 1.83638 + 0.546515i
\(383\) 237.625 0.620431 0.310215 0.950666i \(-0.399599\pi\)
0.310215 + 0.950666i \(0.399599\pi\)
\(384\) 97.2318 199.244i 0.253208 0.518863i
\(385\) 806.535i 2.09490i
\(386\) −54.8637 16.3277i −0.142134 0.0422996i
\(387\) 202.077i 0.522163i
\(388\) −67.5412 + 103.425i −0.174075 + 0.266558i
\(389\) 94.1823 0.242114 0.121057 0.992646i \(-0.461372\pi\)
0.121057 + 0.992646i \(0.461372\pi\)
\(390\) −122.296 329.230i −0.313579 0.844179i
\(391\) 235.259i 0.601685i
\(392\) −76.8253 + 65.1073i −0.195983 + 0.166090i
\(393\) −15.9726 −0.0406428
\(394\) −598.293 178.054i −1.51851 0.451915i
\(395\) −446.270 −1.12980
\(396\) −132.401 86.4643i −0.334347 0.218344i
\(397\) 418.475i 1.05409i −0.849836 0.527047i \(-0.823299\pi\)
0.849836 0.527047i \(-0.176701\pi\)
\(398\) −297.440 88.5193i −0.747336 0.222410i
\(399\) 356.555i 0.893621i
\(400\) −230.447 524.798i −0.576119 1.31199i
\(401\) 673.251i 1.67893i −0.543413 0.839465i \(-0.682868\pi\)
0.543413 0.839465i \(-0.317132\pi\)
\(402\) 121.814 + 36.2524i 0.303020 + 0.0901802i
\(403\) 515.634 387.871i 1.27949 0.962460i
\(404\) −455.923 297.740i −1.12852 0.736979i
\(405\) 70.1901i 0.173309i
\(406\) −166.559 + 559.665i −0.410243 + 1.37849i
\(407\) 509.424i 1.25166i
\(408\) −202.275 238.681i −0.495773 0.585002i
\(409\) 159.073i 0.388932i 0.980909 + 0.194466i \(0.0622973\pi\)
−0.980909 + 0.194466i \(0.937703\pi\)
\(410\) −51.0841 + 171.651i −0.124595 + 0.418662i
\(411\) 43.4821 0.105796
\(412\) 272.818 417.762i 0.662181 1.01398i
\(413\) −125.591 −0.304095
\(414\) 59.9190 + 17.8321i 0.144732 + 0.0430728i
\(415\) 110.855i 0.267119i
\(416\) −298.816 + 289.422i −0.718307 + 0.695727i
\(417\) 212.485 0.509557
\(418\) −197.198 + 662.617i −0.471765 + 1.58521i
\(419\) 706.798i 1.68687i −0.537232 0.843435i \(-0.680530\pi\)
0.537232 0.843435i \(-0.319470\pi\)
\(420\) −355.034 231.854i −0.845319 0.552034i
\(421\) 181.323i 0.430696i −0.976537 0.215348i \(-0.930911\pi\)
0.976537 0.215348i \(-0.0690885\pi\)
\(422\) −564.686 168.053i −1.33812 0.398229i
\(423\) 32.2526 0.0762472
\(424\) 353.956 299.968i 0.834803 0.707471i
\(425\) −808.844 −1.90316
\(426\) 187.652 + 55.8459i 0.440497 + 0.131094i
\(427\) 431.676 1.01095
\(428\) 116.695 178.693i 0.272652 0.417507i
\(429\) 178.369 + 237.123i 0.415778 + 0.552733i
\(430\) −299.689 + 1007.00i −0.696950 + 2.34187i
\(431\) −430.786 −0.999505 −0.499752 0.866168i \(-0.666576\pi\)
−0.499752 + 0.866168i \(0.666576\pi\)
\(432\) 76.1226 33.4267i 0.176210 0.0773767i
\(433\) 12.3174 0.0284467 0.0142233 0.999899i \(-0.495472\pi\)
0.0142233 + 0.999899i \(0.495472\pi\)
\(434\) 222.208 746.658i 0.512001 1.72041i
\(435\) −502.542 −1.15527
\(436\) −111.506 + 170.747i −0.255748 + 0.391621i
\(437\) 273.312i 0.625429i
\(438\) 36.9197 124.056i 0.0842915 0.283234i
\(439\) 499.229i 1.13719i −0.822616 0.568597i \(-0.807486\pi\)
0.822616 0.568597i \(-0.192514\pi\)
\(440\) 531.561 + 627.231i 1.20809 + 1.42553i
\(441\) −37.7636 −0.0856318
\(442\) 204.420 + 550.314i 0.462489 + 1.24505i
\(443\) 417.285i 0.941953i 0.882146 + 0.470976i \(0.156098\pi\)
−0.882146 + 0.470976i \(0.843902\pi\)
\(444\) 224.247 + 146.444i 0.505060 + 0.329829i
\(445\) −80.8618 −0.181712
\(446\) 74.2350 249.442i 0.166446 0.559287i
\(447\) 42.3145 0.0946634
\(448\) −82.3723 + 495.458i −0.183867 + 1.10593i
\(449\) 290.199i 0.646323i −0.946344 0.323161i \(-0.895254\pi\)
0.946344 0.323161i \(-0.104746\pi\)
\(450\) 61.3087 206.008i 0.136242 0.457795i
\(451\) 151.305i 0.335488i
\(452\) 110.885 + 72.4134i 0.245321 + 0.160207i
\(453\) 283.875i 0.626656i
\(454\) 73.7584 247.841i 0.162464 0.545905i
\(455\) 478.296 + 635.845i 1.05120 + 1.39746i
\(456\) −234.994 277.288i −0.515337 0.608088i
\(457\) 561.395i 1.22844i 0.789137 + 0.614218i \(0.210528\pi\)
−0.789137 + 0.614218i \(0.789472\pi\)
\(458\) 312.991 + 93.1474i 0.683386 + 0.203379i
\(459\) 117.324i 0.255608i
\(460\) −272.147 177.725i −0.591623 0.386358i
\(461\) 381.251i 0.827009i 0.910502 + 0.413505i \(0.135695\pi\)
−0.910502 + 0.413505i \(0.864305\pi\)
\(462\) 343.362 + 102.186i 0.743209 + 0.221182i
\(463\) 24.2335 0.0523401 0.0261700 0.999658i \(-0.491669\pi\)
0.0261700 + 0.999658i \(0.491669\pi\)
\(464\) 239.326 + 545.017i 0.515790 + 1.17461i
\(465\) 670.449 1.44183
\(466\) 239.074 803.329i 0.513034 1.72388i
\(467\) 813.014i 1.74093i 0.492230 + 0.870465i \(0.336182\pi\)
−0.492230 + 0.870465i \(0.663818\pi\)
\(468\) −155.656 + 10.3518i −0.332599 + 0.0221193i
\(469\) −287.927 −0.613917
\(470\) −160.723 47.8319i −0.341964 0.101770i
\(471\) 256.725i 0.545063i
\(472\) −97.6708 + 82.7732i −0.206930 + 0.175367i
\(473\) 887.642i 1.87662i
\(474\) −56.5414 + 189.989i −0.119286 + 0.400820i
\(475\) −939.676 −1.97827
\(476\) 593.446 + 387.548i 1.24673 + 0.814177i
\(477\) 173.988 0.364754
\(478\) −6.61395 + 22.2240i −0.0138367 + 0.0464936i
\(479\) −10.7399 −0.0224214 −0.0112107 0.999937i \(-0.503569\pi\)
−0.0112107 + 0.999937i \(0.503569\pi\)
\(480\) −428.913 + 53.6814i −0.893568 + 0.111836i
\(481\) −302.102 401.612i −0.628070 0.834953i
\(482\) −351.052 104.474i −0.728323 0.216752i
\(483\) −141.628 −0.293226
\(484\) −176.344 115.161i −0.364346 0.237935i
\(485\) 240.840 0.496577
\(486\) 29.8817 + 8.89292i 0.0614850 + 0.0182982i
\(487\) 561.520 1.15302 0.576509 0.817091i \(-0.304414\pi\)
0.576509 + 0.817091i \(0.304414\pi\)
\(488\) 335.709 284.504i 0.687928 0.582999i
\(489\) 116.780i 0.238814i
\(490\) 188.186 + 56.0050i 0.384053 + 0.114296i
\(491\) 573.500i 1.16803i −0.811745 0.584013i \(-0.801482\pi\)
0.811745 0.584013i \(-0.198518\pi\)
\(492\) 66.6040 + 43.4956i 0.135374 + 0.0884057i
\(493\) 840.008 1.70387
\(494\) 237.485 + 639.328i 0.480739 + 1.29419i
\(495\) 308.317i 0.622862i
\(496\) −319.289 727.116i −0.643727 1.46596i
\(497\) −443.545 −0.892444
\(498\) 47.1936 + 14.0450i 0.0947662 + 0.0282028i
\(499\) −700.846 −1.40450 −0.702250 0.711930i \(-0.747821\pi\)
−0.702250 + 0.711930i \(0.747821\pi\)
\(500\) −184.607 + 282.685i −0.369214 + 0.565370i
\(501\) 256.760i 0.512495i
\(502\) −369.786 110.050i −0.736626 0.219223i
\(503\) 220.983i 0.439330i −0.975575 0.219665i \(-0.929504\pi\)
0.975575 0.219665i \(-0.0704964\pi\)
\(504\) −143.688 + 121.772i −0.285096 + 0.241610i
\(505\) 1061.69i 2.10235i
\(506\) 263.200 + 78.3294i 0.520158 + 0.154801i
\(507\) 281.240 + 81.1620i 0.554713 + 0.160083i
\(508\) 403.294 617.557i 0.793886 1.21566i
\(509\) 686.143i 1.34802i 0.738721 + 0.674011i \(0.235430\pi\)
−0.738721 + 0.674011i \(0.764570\pi\)
\(510\) −173.996 + 584.657i −0.341169 + 1.14639i
\(511\) 293.227i 0.573829i
\(512\) 262.480 + 439.600i 0.512657 + 0.858594i
\(513\) 136.301i 0.265695i
\(514\) 109.803 368.955i 0.213624 0.717811i
\(515\) −972.823 −1.88898
\(516\) 390.737 + 255.170i 0.757242 + 0.494515i
\(517\) 141.673 0.274028
\(518\) −581.550 173.072i −1.12268 0.334115i
\(519\) 40.8602i 0.0787288i
\(520\) 791.029 + 179.259i 1.52121 + 0.344728i
\(521\) 384.581 0.738160 0.369080 0.929398i \(-0.379673\pi\)
0.369080 + 0.929398i \(0.379673\pi\)
\(522\) −63.6709 + 213.945i −0.121975 + 0.409856i
\(523\) 367.884i 0.703411i 0.936111 + 0.351706i \(0.114398\pi\)
−0.936111 + 0.351706i \(0.885602\pi\)
\(524\) 20.1692 30.8847i 0.0384908 0.0589403i
\(525\) 486.932i 0.927489i
\(526\) −73.1139 21.7590i −0.139000 0.0413670i
\(527\) −1120.67 −2.12650
\(528\) 334.376 146.830i 0.633288 0.278087i
\(529\) 420.437 0.794777
\(530\) −867.028 258.031i −1.63590 0.486851i
\(531\) −48.0102 −0.0904147
\(532\) 689.437 + 450.235i 1.29593 + 0.846306i
\(533\) −89.7279 119.284i −0.168345 0.223797i
\(534\) −10.2450 + 34.4249i −0.0191854 + 0.0644662i
\(535\) −416.114 −0.777784
\(536\) −223.917 + 189.763i −0.417756 + 0.354036i
\(537\) −152.207 −0.283440
\(538\) −45.8038 + 153.909i −0.0851372 + 0.286075i
\(539\) −165.880 −0.307756
\(540\) −135.720 88.6316i −0.251333 0.164133i
\(541\) 235.088i 0.434544i 0.976111 + 0.217272i \(0.0697158\pi\)
−0.976111 + 0.217272i \(0.930284\pi\)
\(542\) −137.590 + 462.327i −0.253857 + 0.853001i
\(543\) 271.285i 0.499603i
\(544\) 716.935 89.7294i 1.31790 0.164944i
\(545\) 397.610 0.729561
\(546\) 331.294 123.063i 0.606766 0.225390i
\(547\) 230.496i 0.421382i 0.977553 + 0.210691i \(0.0675714\pi\)
−0.977553 + 0.210691i \(0.932429\pi\)
\(548\) −54.9064 + 84.0771i −0.100194 + 0.153425i
\(549\) 165.018 0.300580
\(550\) 269.304 904.908i 0.489644 1.64529i
\(551\) 975.881 1.77111
\(552\) −110.142 + 93.3424i −0.199533 + 0.169099i
\(553\) 449.068i 0.812058i
\(554\) 65.8641 221.315i 0.118888 0.399485i
\(555\) 522.193i 0.940888i
\(556\) −268.313 + 410.862i −0.482577 + 0.738961i
\(557\) 497.920i 0.893933i −0.894551 0.446966i \(-0.852504\pi\)
0.894551 0.446966i \(-0.147496\pi\)
\(558\) 84.9443 285.427i 0.152230 0.511518i
\(559\) −526.395 699.787i −0.941672 1.25185i
\(560\) 896.629 393.725i 1.60112 0.703080i
\(561\) 515.357i 0.918640i
\(562\) 695.026 + 206.843i 1.23670 + 0.368048i
\(563\) 10.9662i 0.0194782i 0.999953 + 0.00973912i \(0.00310011\pi\)
−0.999953 + 0.00973912i \(0.996900\pi\)
\(564\) −40.7265 + 62.3638i −0.0722101 + 0.110574i
\(565\) 258.213i 0.457015i
\(566\) 458.303 + 136.393i 0.809723 + 0.240977i
\(567\) −70.6301 −0.124568
\(568\) −344.939 + 292.326i −0.607286 + 0.514658i
\(569\) −1049.19 −1.84393 −0.921964 0.387276i \(-0.873416\pi\)
−0.921964 + 0.387276i \(0.873416\pi\)
\(570\) −202.141 + 679.226i −0.354633 + 1.19162i
\(571\) 1062.00i 1.85989i 0.367703 + 0.929943i \(0.380144\pi\)
−0.367703 + 0.929943i \(0.619856\pi\)
\(572\) −683.734 + 45.4714i −1.19534 + 0.0794955i
\(573\) −633.848 −1.10619
\(574\) −172.727 51.4044i −0.300919 0.0895547i
\(575\) 373.251i 0.649132i
\(576\) −31.4887 + 189.400i −0.0546679 + 0.328820i
\(577\) 634.074i 1.09892i 0.835521 + 0.549458i \(0.185166\pi\)
−0.835521 + 0.549458i \(0.814834\pi\)
\(578\) 125.969 423.277i 0.217940 0.732314i
\(579\) 49.5728 0.0856179
\(580\) 634.578 971.718i 1.09410 1.67538i
\(581\) −111.550 −0.191996
\(582\) 30.5139 102.532i 0.0524293 0.176171i
\(583\) 764.258 1.31091
\(584\) 193.256 + 228.038i 0.330918 + 0.390477i
\(585\) 182.840 + 243.066i 0.312546 + 0.415498i
\(586\) 843.343 + 250.982i 1.43915 + 0.428298i
\(587\) 64.5958 0.110044 0.0550220 0.998485i \(-0.482477\pi\)
0.0550220 + 0.998485i \(0.482477\pi\)
\(588\) 47.6855 73.0199i 0.0810978 0.124184i
\(589\) −1301.94 −2.21042
\(590\) 239.248 + 71.2011i 0.405505 + 0.120680i
\(591\) 540.595 0.914713
\(592\) −566.329 + 248.685i −0.956637 + 0.420076i
\(593\) 146.523i 0.247087i −0.992339 0.123544i \(-0.960574\pi\)
0.992339 0.123544i \(-0.0394259\pi\)
\(594\) 131.258 + 39.0630i 0.220973 + 0.0657626i
\(595\) 1381.93i 2.32257i
\(596\) −53.4321 + 81.8196i −0.0896512 + 0.137281i
\(597\) 268.756 0.450177
\(598\) 253.949 94.3321i 0.424664 0.157746i
\(599\) 469.062i 0.783074i −0.920162 0.391537i \(-0.871943\pi\)
0.920162 0.391537i \(-0.128057\pi\)
\(600\) 320.921 + 378.680i 0.534868 + 0.631134i
\(601\) 287.117 0.477732 0.238866 0.971052i \(-0.423224\pi\)
0.238866 + 0.971052i \(0.423224\pi\)
\(602\) −1013.32 301.567i −1.68325 0.500943i
\(603\) −110.067 −0.182532
\(604\) 548.902 + 358.459i 0.908778 + 0.593476i
\(605\) 410.643i 0.678749i
\(606\) 451.987 + 134.513i 0.745853 + 0.221969i
\(607\) 534.181i 0.880035i −0.897989 0.440017i \(-0.854972\pi\)
0.897989 0.440017i \(-0.145028\pi\)
\(608\) 832.901 104.243i 1.36990 0.171453i
\(609\) 505.693i 0.830366i
\(610\) −822.330 244.729i −1.34808 0.401195i
\(611\) 111.690 84.0154i 0.182798 0.137505i
\(612\) 226.858 + 148.149i 0.370684 + 0.242074i
\(613\) 845.316i 1.37898i 0.724294 + 0.689491i \(0.242166\pi\)
−0.724294 + 0.689491i \(0.757834\pi\)
\(614\) −233.564 + 784.813i −0.380397 + 1.27820i
\(615\) 155.098i 0.252191i
\(616\) −631.164 + 534.893i −1.02462 + 0.868333i
\(617\) 30.9449i 0.0501538i 0.999686 + 0.0250769i \(0.00798305\pi\)
−0.999686 + 0.0250769i \(0.992017\pi\)
\(618\) −123.254 + 414.155i −0.199441 + 0.670154i
\(619\) −637.250 −1.02948 −0.514741 0.857346i \(-0.672112\pi\)
−0.514741 + 0.857346i \(0.672112\pi\)
\(620\) −846.600 + 1296.38i −1.36548 + 2.09094i
\(621\) −54.1406 −0.0871829
\(622\) −572.501 170.379i −0.920419 0.273921i
\(623\) 81.3688i 0.130608i
\(624\) 176.536 314.049i 0.282911 0.503284i
\(625\) −237.295 −0.379673
\(626\) 11.6316 39.0843i 0.0185809 0.0624349i
\(627\) 598.716i 0.954891i
\(628\) −496.404 324.176i −0.790453 0.516203i
\(629\) 872.855i 1.38769i
\(630\) 351.969 + 104.747i 0.558681 + 0.166266i
\(631\) 440.047 0.697380 0.348690 0.937238i \(-0.386627\pi\)
0.348690 + 0.937238i \(0.386627\pi\)
\(632\) −295.966 349.234i −0.468301 0.552586i
\(633\) 510.229 0.806049
\(634\) 985.960 + 293.426i 1.55514 + 0.462817i
\(635\) −1438.08 −2.26469
\(636\) −219.701 + 336.424i −0.345441 + 0.528968i
\(637\) −130.774 + 98.3712i −0.205297 + 0.154429i
\(638\) −279.680 + 939.773i −0.438371 + 1.47300i
\(639\) −169.555 −0.265344
\(640\) 437.805 897.133i 0.684071 1.40177i
\(641\) 203.080 0.316817 0.158408 0.987374i \(-0.449364\pi\)
0.158408 + 0.987374i \(0.449364\pi\)
\(642\) −52.7207 + 177.150i −0.0821195 + 0.275935i
\(643\) −130.355 −0.202729 −0.101365 0.994849i \(-0.532321\pi\)
−0.101365 + 0.994849i \(0.532321\pi\)
\(644\) 178.839 273.853i 0.277700 0.425237i
\(645\) 909.891i 1.41068i
\(646\) 337.882 1135.34i 0.523036 1.75749i
\(647\) 423.596i 0.654709i 0.944902 + 0.327354i \(0.106157\pi\)
−0.944902 + 0.327354i \(0.893843\pi\)
\(648\) −54.9281 + 46.5500i −0.0847656 + 0.0718364i
\(649\) −210.889 −0.324945
\(650\) −324.323 873.103i −0.498959 1.34324i
\(651\) 674.652i 1.03633i
\(652\) −225.807 147.462i −0.346329 0.226169i
\(653\) 149.879 0.229524 0.114762 0.993393i \(-0.463389\pi\)
0.114762 + 0.993393i \(0.463389\pi\)
\(654\) 50.3763 169.273i 0.0770280 0.258827i
\(655\) −71.9198 −0.109801
\(656\) −168.207 + 73.8624i −0.256413 + 0.112595i
\(657\) 112.093i 0.170613i
\(658\) 48.1318 161.731i 0.0731486 0.245792i
\(659\) 590.762i 0.896452i −0.893920 0.448226i \(-0.852056\pi\)
0.893920 0.448226i \(-0.147944\pi\)
\(660\) −596.163 389.323i −0.903277 0.589883i
\(661\) 668.639i 1.01156i 0.862664 + 0.505778i \(0.168795\pi\)
−0.862664 + 0.505778i \(0.831205\pi\)
\(662\) 260.549 875.487i 0.393578 1.32249i
\(663\) −305.620 406.290i −0.460965 0.612805i
\(664\) −86.7506 + 73.5186i −0.130648 + 0.110721i
\(665\) 1605.46i 2.41422i
\(666\) −222.311 66.1606i −0.333800 0.0993403i
\(667\) 387.632i 0.581157i
\(668\) −496.473 324.220i −0.743223 0.485360i
\(669\) 225.387i 0.336901i
\(670\) 548.493 + 163.234i 0.818646 + 0.243632i
\(671\) 724.858 1.08027
\(672\) −54.0179 431.602i −0.0803838 0.642264i
\(673\) −1223.15 −1.81746 −0.908729 0.417388i \(-0.862946\pi\)
−0.908729 + 0.417388i \(0.862946\pi\)
\(674\) −340.958 + 1145.68i −0.505873 + 1.69982i
\(675\) 186.141i 0.275764i
\(676\) −512.067 + 441.320i −0.757495 + 0.652840i
\(677\) 1157.62 1.70992 0.854961 0.518692i \(-0.173581\pi\)
0.854961 + 0.518692i \(0.173581\pi\)
\(678\) −109.928 32.7150i −0.162136 0.0482522i
\(679\) 242.350i 0.356922i
\(680\) −910.784 1074.71i −1.33939 1.58045i
\(681\) 223.940i 0.328839i
\(682\) 373.126 1253.77i 0.547105 1.83837i
\(683\) 1000.21 1.46443 0.732217 0.681072i \(-0.238486\pi\)
0.732217 + 0.681072i \(0.238486\pi\)
\(684\) 263.553 + 172.113i 0.385311 + 0.251627i
\(685\) 195.787 0.285820
\(686\) 163.018 547.767i 0.237635 0.798494i
\(687\) −282.807 −0.411655
\(688\) −986.796 + 433.319i −1.43430 + 0.629824i
\(689\) 602.514 453.224i 0.874477 0.657800i
\(690\) 269.797 + 80.2927i 0.391010 + 0.116366i
\(691\) 120.026 0.173699 0.0868496 0.996221i \(-0.472320\pi\)
0.0868496 + 0.996221i \(0.472320\pi\)
\(692\) −79.0076 51.5957i −0.114173 0.0745603i
\(693\) −310.250 −0.447691
\(694\) 680.138 + 202.412i 0.980027 + 0.291660i
\(695\) 956.756 1.37663
\(696\) −333.285 393.270i −0.478858 0.565044i
\(697\) 259.249i 0.371949i
\(698\) −850.868 253.222i −1.21901 0.362782i
\(699\) 725.858i 1.03842i
\(700\) −941.534 614.867i −1.34505 0.878381i
\(701\) 882.073 1.25831 0.629153 0.777281i \(-0.283402\pi\)
0.629153 + 0.777281i \(0.283402\pi\)
\(702\) 126.645 47.0436i 0.180406 0.0670136i
\(703\) 1014.04i 1.44245i
\(704\) −138.317 + 831.959i −0.196473 + 1.18176i
\(705\) 145.224 0.205991
\(706\) 264.995 + 78.8637i 0.375348 + 0.111705i
\(707\) −1068.34 −1.51109
\(708\) 60.6243 92.8328i 0.0856275 0.131120i
\(709\) 285.806i 0.403112i 0.979477 + 0.201556i \(0.0645998\pi\)
−0.979477 + 0.201556i \(0.935400\pi\)
\(710\) 844.939 + 251.457i 1.19005 + 0.354165i
\(711\) 171.667i 0.241444i
\(712\) −53.6275 63.2794i −0.0753195 0.0888756i
\(713\) 517.146i 0.725309i
\(714\) −588.322 175.087i −0.823981 0.245220i
\(715\) 803.141 + 1067.69i 1.12327 + 1.49327i
\(716\) 192.198 294.309i 0.268433 0.411046i
\(717\) 20.0808i 0.0280066i
\(718\) −140.194 + 471.076i −0.195256 + 0.656094i
\(719\) 984.643i 1.36946i −0.728796 0.684731i \(-0.759920\pi\)
0.728796 0.684731i \(-0.240080\pi\)
\(720\) 342.757 150.510i 0.476052 0.209042i
\(721\) 978.922i 1.35773i
\(722\) 186.591 626.976i 0.258436 0.868388i
\(723\) 317.197 0.438724
\(724\) 524.557 + 342.561i 0.724526 + 0.473150i
\(725\) −1332.72 −1.83823
\(726\) 174.821 + 52.0275i 0.240800 + 0.0716632i
\(727\) 566.297i 0.778950i −0.921037 0.389475i \(-0.872656\pi\)
0.921037 0.389475i \(-0.127344\pi\)
\(728\) −180.382 + 795.988i −0.247778 + 1.09339i
\(729\) −27.0000 −0.0370370
\(730\) 166.238 558.588i 0.227723 0.765189i
\(731\) 1520.90i 2.08057i
\(732\) −208.375 + 319.080i −0.284665 + 0.435902i
\(733\) 1398.80i 1.90832i −0.299303 0.954158i \(-0.596754\pi\)
0.299303 0.954158i \(-0.403246\pi\)
\(734\) 879.296 + 261.682i 1.19795 + 0.356515i
\(735\) −170.038 −0.231344
\(736\) −41.4067 330.838i −0.0562591 0.449509i
\(737\) −483.479 −0.656009
\(738\) −66.0290 19.6505i −0.0894702 0.0266267i
\(739\) 500.468 0.677223 0.338611 0.940926i \(-0.390043\pi\)
0.338611 + 0.940926i \(0.390043\pi\)
\(740\) 1009.72 + 659.392i 1.36448 + 0.891071i
\(741\) −355.054 472.007i −0.479156 0.636987i
\(742\) 259.649 872.463i 0.349931 1.17583i
\(743\) 349.050 0.469784 0.234892 0.972021i \(-0.424526\pi\)
0.234892 + 0.972021i \(0.424526\pi\)
\(744\) 444.641 + 524.668i 0.597636 + 0.705199i
\(745\) 190.529 0.255744
\(746\) −154.013 + 517.509i −0.206451 + 0.693711i
\(747\) −42.6424 −0.0570848
\(748\) 996.497 + 650.760i 1.33221 + 0.870000i
\(749\) 418.723i 0.559043i
\(750\) 83.4019 280.245i 0.111203 0.373659i
\(751\) 25.5035i 0.0339594i 0.999856 + 0.0169797i \(0.00540507\pi\)
−0.999856 + 0.0169797i \(0.994595\pi\)
\(752\) −69.1601 157.498i −0.0919682 0.209439i
\(753\) 334.125 0.443725
\(754\) 336.819 + 906.743i 0.446710 + 1.20258i
\(755\) 1278.20i 1.69298i
\(756\) 89.1873 136.571i 0.117973 0.180649i
\(757\) 371.325 0.490522 0.245261 0.969457i \(-0.421126\pi\)
0.245261 + 0.969457i \(0.421126\pi\)
\(758\) 270.507 908.949i 0.356869 1.19914i
\(759\) −237.818 −0.313330
\(760\) −1058.10 1248.54i −1.39224 1.64282i
\(761\) 30.6207i 0.0402374i 0.999798 + 0.0201187i \(0.00640441\pi\)
−0.999798 + 0.0201187i \(0.993596\pi\)
\(762\) −182.201 + 612.225i −0.239109 + 0.803445i
\(763\) 400.103i 0.524382i
\(764\) 800.383 1225.61i 1.04762 1.60420i
\(765\) 528.274i 0.690555i
\(766\) 135.561 455.506i 0.176972 0.594655i
\(767\) −166.258 + 125.063i −0.216764 + 0.163055i
\(768\) −326.463 300.049i −0.425083 0.390689i
\(769\) 563.426i 0.732674i 0.930482 + 0.366337i \(0.119388\pi\)
−0.930482 + 0.366337i \(0.880612\pi\)
\(770\) 1546.06 + 460.113i 2.00787 + 0.597549i
\(771\) 333.374i 0.432392i
\(772\) −62.5974 + 95.8542i −0.0810847 + 0.124163i
\(773\) 1408.83i 1.82255i −0.411800 0.911274i \(-0.635100\pi\)
0.411800 0.911274i \(-0.364900\pi\)
\(774\) −387.364 115.281i −0.500470 0.148942i
\(775\) 1778.00 2.29419
\(776\) 159.725 + 188.472i 0.205831 + 0.242877i
\(777\) 525.467 0.676277
\(778\) 53.7292 180.539i 0.0690607 0.232055i
\(779\) 301.182i 0.386627i
\(780\) −700.872 + 46.6112i −0.898554 + 0.0597579i
\(781\) −744.787 −0.953632
\(782\) −450.971 134.211i −0.576689 0.171625i
\(783\) 193.313i 0.246887i
\(784\) 80.9775 + 184.410i 0.103288 + 0.235217i
\(785\) 1155.95i 1.47255i
\(786\) −9.11207 + 30.6181i −0.0115930 + 0.0389543i
\(787\) 740.379 0.940761 0.470381 0.882464i \(-0.344117\pi\)
0.470381 + 0.882464i \(0.344117\pi\)
\(788\) −682.630 + 1045.30i −0.866281 + 1.32652i
\(789\) 66.0631 0.0837301
\(790\) −254.589 + 855.461i −0.322264 + 1.08286i
\(791\) 259.832 0.328486
\(792\) −241.277 + 204.475i −0.304643 + 0.258176i
\(793\) 571.453 429.860i 0.720622 0.542068i
\(794\) −802.180 238.732i −1.01030 0.300670i
\(795\) 783.414 0.985427
\(796\) −339.367 + 519.667i −0.426341 + 0.652848i
\(797\) 1439.36 1.80597 0.902985 0.429673i \(-0.141371\pi\)
0.902985 + 0.429673i \(0.141371\pi\)
\(798\) −683.484 203.408i −0.856497 0.254897i
\(799\) −242.744 −0.303810
\(800\) −1137.46 + 142.360i −1.42182 + 0.177951i
\(801\) 31.1051i 0.0388328i
\(802\) −1290.56 384.077i −1.60918 0.478899i
\(803\) 492.378i 0.613173i
\(804\) 138.985 212.826i 0.172867 0.264709i
\(805\) −637.708 −0.792184
\(806\) −449.355 1209.70i −0.557513 1.50087i
\(807\) 139.066i 0.172325i
\(808\) −830.836 + 704.110i −1.02826 + 0.871423i
\(809\) −676.465 −0.836174 −0.418087 0.908407i \(-0.637299\pi\)
−0.418087 + 0.908407i \(0.637299\pi\)
\(810\) 134.548 + 40.0421i 0.166109 + 0.0494347i
\(811\) −839.069 −1.03461 −0.517305 0.855801i \(-0.673065\pi\)
−0.517305 + 0.855801i \(0.673065\pi\)
\(812\) 977.810 + 638.557i 1.20420 + 0.786400i
\(813\) 417.741i 0.513827i
\(814\) −976.521 290.617i −1.19966 0.357023i
\(815\) 525.825i 0.645184i
\(816\) −572.925 + 251.581i −0.702114 + 0.308310i
\(817\) 1766.91i 2.16268i
\(818\) 304.929 + 90.7481i 0.372774 + 0.110939i
\(819\) −244.590 + 183.986i −0.298645 + 0.224647i
\(820\) 299.898 + 195.848i 0.365729 + 0.238838i
\(821\) 1228.30i 1.49611i 0.663638 + 0.748054i \(0.269012\pi\)
−0.663638 + 0.748054i \(0.730988\pi\)
\(822\) 24.8057 83.3513i 0.0301772 0.101401i
\(823\) 1171.99i 1.42405i −0.702154 0.712025i \(-0.747778\pi\)
0.702154 0.712025i \(-0.252222\pi\)
\(824\) −645.175 761.294i −0.782979 0.923901i
\(825\) 817.642i 0.991081i
\(826\) −71.6475 + 240.748i −0.0867404 + 0.291462i
\(827\) 750.467 0.907457 0.453729 0.891140i \(-0.350094\pi\)
0.453729 + 0.891140i \(0.350094\pi\)
\(828\) 68.3653 104.687i 0.0825668 0.126433i
\(829\) 766.089 0.924113 0.462056 0.886851i \(-0.347112\pi\)
0.462056 + 0.886851i \(0.347112\pi\)
\(830\) 212.498 + 63.2404i 0.256022 + 0.0761933i
\(831\) 199.972i 0.240640i
\(832\) 384.328 + 737.913i 0.461933 + 0.886915i
\(833\) 284.222 0.341203
\(834\) 121.219 407.315i 0.145346 0.488388i
\(835\) 1156.11i 1.38457i
\(836\) 1157.68 + 756.021i 1.38479 + 0.904332i
\(837\) 257.901i 0.308126i
\(838\) −1354.87 403.215i −1.61679 0.481163i
\(839\) −180.988 −0.215719 −0.107859 0.994166i \(-0.534400\pi\)
−0.107859 + 0.994166i \(0.534400\pi\)
\(840\) −646.984 + 548.301i −0.770219 + 0.652739i
\(841\) 543.067 0.645739
\(842\) −347.580 103.441i −0.412803 0.122852i
\(843\) −628.000 −0.744959
\(844\) −644.285 + 986.581i −0.763371 + 1.16894i
\(845\) 1266.34 + 365.448i 1.49862 + 0.432483i
\(846\) 18.3995 61.8254i 0.0217488 0.0730796i
\(847\) −413.218 −0.487860
\(848\) −373.086 849.629i −0.439960 1.00192i
\(849\) −414.106 −0.487757
\(850\) −461.430 + 1550.48i −0.542859 + 1.82410i
\(851\) 402.790 0.473313
\(852\) 214.103 327.853i 0.251295 0.384804i
\(853\) 984.643i 1.15433i 0.816628 + 0.577165i \(0.195841\pi\)
−0.816628 + 0.577165i \(0.804159\pi\)
\(854\) 246.263 827.486i 0.288364 0.968953i
\(855\) 613.724i 0.717805i
\(856\) −275.967 325.635i −0.322391 0.380415i
\(857\) −1513.36 −1.76588 −0.882939 0.469488i \(-0.844439\pi\)
−0.882939 + 0.469488i \(0.844439\pi\)
\(858\) 556.299 206.643i 0.648367 0.240843i
\(859\) 107.816i 0.125513i −0.998029 0.0627564i \(-0.980011\pi\)
0.998029 0.0627564i \(-0.0199891\pi\)
\(860\) 1759.37 + 1148.95i 2.04578 + 1.33599i
\(861\) 156.070 0.181266
\(862\) −245.756 + 825.780i −0.285099 + 0.957981i
\(863\) 642.697 0.744725 0.372362 0.928087i \(-0.378548\pi\)
0.372362 + 0.928087i \(0.378548\pi\)
\(864\) −20.6496 164.990i −0.0239000 0.190960i
\(865\) 183.981i 0.212695i
\(866\) 7.02685 23.6114i 0.00811414 0.0272649i
\(867\) 382.458i 0.441128i
\(868\) −1304.51 851.908i −1.50289 0.981461i
\(869\) 754.062i 0.867735i
\(870\) −286.691 + 963.329i −0.329530 + 1.10727i
\(871\) −381.158 + 286.715i −0.437610 + 0.329180i
\(872\) 263.695 + 311.155i 0.302402 + 0.356829i
\(873\) 92.6439i 0.106121i
\(874\) −523.916 155.920i −0.599446 0.178398i
\(875\) 662.402i 0.757031i
\(876\) −216.743 141.544i −0.247424 0.161579i
\(877\) 235.180i 0.268164i 0.990970 + 0.134082i \(0.0428085\pi\)
−0.990970 + 0.134082i \(0.957191\pi\)
\(878\) −956.977 284.800i −1.08995 0.324374i
\(879\) −762.013 −0.866909
\(880\) 1505.59 661.131i 1.71090 0.751286i
\(881\) 370.037 0.420019 0.210010 0.977699i \(-0.432650\pi\)
0.210010 + 0.977699i \(0.432650\pi\)
\(882\) −21.5434 + 72.3895i −0.0244257 + 0.0820743i
\(883\) 1004.78i 1.13792i 0.822367 + 0.568958i \(0.192653\pi\)
−0.822367 + 0.568958i \(0.807347\pi\)
\(884\) 1171.52 77.9114i 1.32525 0.0881351i
\(885\) −216.175 −0.244266
\(886\) 799.899 + 238.053i 0.902820 + 0.268683i
\(887\) 301.209i 0.339582i −0.985480 0.169791i \(-0.945691\pi\)
0.985480 0.169791i \(-0.0543093\pi\)
\(888\) 408.649 346.318i 0.460190 0.389998i
\(889\) 1447.09i 1.62777i
\(890\) −46.1302 + 155.005i −0.0518316 + 0.174163i
\(891\) −118.600 −0.133109
\(892\) −435.809 284.604i −0.488575 0.319063i
\(893\) −282.008 −0.315798
\(894\) 24.1396 81.1132i 0.0270018 0.0907307i
\(895\) −685.344 −0.765747
\(896\) 902.758 + 440.550i 1.00754 + 0.491685i
\(897\) −187.487 + 141.032i −0.209016 + 0.157226i
\(898\) −556.286 165.553i −0.619472 0.184357i
\(899\) −1846.50 −2.05395
\(900\) −359.923 235.047i −0.399914 0.261163i
\(901\) −1309.49 −1.45338
\(902\) −290.039 86.3167i −0.321551 0.0956948i
\(903\) 915.596 1.01395
\(904\) 202.068 171.247i 0.223527 0.189432i
\(905\) 1221.51i 1.34974i
\(906\) −544.163 161.945i −0.600622 0.178748i
\(907\) 446.087i 0.491827i 0.969292 + 0.245914i \(0.0790879\pi\)
−0.969292 + 0.245914i \(0.920912\pi\)
\(908\) −433.011 282.777i −0.476884 0.311428i
\(909\) −408.399 −0.449284
\(910\) 1491.72 554.114i 1.63925 0.608917i
\(911\) 12.3523i 0.0135591i 0.999977 + 0.00677954i \(0.00215801\pi\)
−0.999977 + 0.00677954i \(0.997842\pi\)
\(912\) −665.596 + 292.274i −0.729820 + 0.320476i
\(913\) −187.311 −0.205160
\(914\) 1076.14 + 320.265i 1.17740 + 0.350399i
\(915\) 743.027 0.812052
\(916\) 357.111 546.837i 0.389859 0.596984i
\(917\) 72.3707i 0.0789212i
\(918\) −224.900 66.9311i −0.244989 0.0729097i
\(919\) 1314.71i 1.43059i 0.698822 + 0.715295i \(0.253708\pi\)
−0.698822 + 0.715295i \(0.746292\pi\)
\(920\) −495.937 + 420.292i −0.539062 + 0.456840i
\(921\) 709.128i 0.769954i
\(922\) 730.825 + 217.497i 0.792652 + 0.235897i
\(923\) −587.164 + 441.678i −0.636148 + 0.478524i
\(924\) 391.764 599.900i 0.423986 0.649243i
\(925\) 1384.83i 1.49712i
\(926\) 13.8247 46.4534i 0.0149295 0.0501657i
\(927\) 374.215i 0.403684i
\(928\) 1181.28 147.845i 1.27293 0.159316i
\(929\) 1683.34i 1.81199i 0.423292 + 0.905993i \(0.360874\pi\)
−0.423292 + 0.905993i \(0.639126\pi\)
\(930\) 382.478 1285.19i 0.411267 1.38193i
\(931\) 330.195 0.354667
\(932\) −1403.52 916.568i −1.50593 0.983442i
\(933\) 517.291 0.554438
\(934\) 1558.48 + 463.809i 1.66860 + 0.496584i
\(935\) 2320.50i 2.48181i
\(936\) −68.9553 + 304.285i −0.0736702 + 0.325090i
\(937\) −652.570 −0.696447 −0.348223 0.937412i \(-0.613215\pi\)
−0.348223 + 0.937412i \(0.613215\pi\)
\(938\) −164.257 + 551.931i −0.175114 + 0.588413i
\(939\) 35.3151i 0.0376093i
\(940\) −183.379 + 280.805i −0.195084 + 0.298729i
\(941\) 857.642i 0.911416i 0.890129 + 0.455708i \(0.150614\pi\)
−0.890129 + 0.455708i \(0.849386\pi\)
\(942\) 492.119 + 146.457i 0.522419 + 0.155474i
\(943\) 119.633 0.126865
\(944\) 102.950 + 234.447i 0.109057 + 0.248355i
\(945\) −318.026 −0.336536
\(946\) −1701.53 506.383i −1.79866 0.535289i
\(947\) 1477.66 1.56036 0.780181 0.625554i \(-0.215127\pi\)
0.780181 + 0.625554i \(0.215127\pi\)
\(948\) 331.936 + 216.770i 0.350143 + 0.228660i
\(949\) 291.993 + 388.174i 0.307685 + 0.409034i
\(950\) −536.067 + 1801.28i −0.564281 + 1.89608i
\(951\) −890.877 −0.936780
\(952\) 1081.45 916.494i 1.13597 0.962704i
\(953\) 589.275 0.618337 0.309169 0.951007i \(-0.399949\pi\)
0.309169 + 0.951007i \(0.399949\pi\)
\(954\) 99.2567 333.519i 0.104043 0.349601i
\(955\) −2854.03 −2.98851
\(956\) 38.8282 + 25.3567i 0.0406153 + 0.0265237i
\(957\) 849.144i 0.887298i
\(958\) −6.12688 + 20.5874i −0.00639549 + 0.0214899i
\(959\) 197.014i 0.205437i
\(960\) −141.784 + 852.812i −0.147692 + 0.888346i
\(961\) 1502.45 1.56342
\(962\) −942.199 + 349.990i −0.979417 + 0.363815i
\(963\) 160.067i 0.166217i
\(964\) −400.537 + 613.334i −0.415494 + 0.636239i
\(965\) 223.211 0.231307
\(966\) −80.7961 + 271.489i −0.0836399 + 0.281044i
\(967\) 834.227 0.862696 0.431348 0.902186i \(-0.358038\pi\)
0.431348 + 0.902186i \(0.358038\pi\)
\(968\) −321.354 + 272.338i −0.331977 + 0.281341i
\(969\) 1025.85i 1.05867i
\(970\) 137.395 461.669i 0.141644 0.475948i
\(971\) 489.291i 0.503905i 0.967740 + 0.251952i \(0.0810726\pi\)
−0.967740 + 0.251952i \(0.918927\pi\)
\(972\) 34.0939 52.2073i 0.0350760 0.0537113i
\(973\) 962.754i 0.989470i
\(974\) 320.337 1076.38i 0.328888 1.10512i
\(975\) 484.882 + 644.600i 0.497315 + 0.661129i
\(976\) −353.853 805.829i −0.362554 0.825644i
\(977\) 665.403i 0.681068i −0.940232 0.340534i \(-0.889392\pi\)
0.940232 0.340534i \(-0.110608\pi\)
\(978\) 223.857 + 66.6208i 0.228893 + 0.0681194i
\(979\) 136.632i 0.139563i
\(980\) 214.713 328.787i 0.219095 0.335496i
\(981\) 152.949i 0.155911i
\(982\) −1099.35 327.171i −1.11950 0.333168i
\(983\) −1117.01 −1.13633 −0.568164 0.822915i \(-0.692346\pi\)
−0.568164 + 0.822915i \(0.692346\pi\)
\(984\) 121.374 102.861i 0.123347 0.104533i
\(985\) 2434.14 2.47121
\(986\) 479.209 1610.22i 0.486013 1.63309i
\(987\) 146.134i 0.148059i
\(988\) 1361.02 90.5137i 1.37755 0.0916131i
\(989\) 701.838 0.709644
\(990\) 591.016 + 175.889i 0.596986 + 0.177665i
\(991\) 1643.98i 1.65891i −0.558575 0.829454i \(-0.688652\pi\)
0.558575 0.829454i \(-0.311348\pi\)
\(992\) −1575.97 + 197.243i −1.58867 + 0.198833i
\(993\) 791.058i 0.796635i
\(994\) −253.034 + 850.236i −0.254561 + 0.855368i
\(995\) 1210.12 1.21621
\(996\) 53.8461 82.4535i 0.0540623 0.0827847i
\(997\) −1794.73 −1.80013 −0.900066 0.435754i \(-0.856482\pi\)
−0.900066 + 0.435754i \(0.856482\pi\)
\(998\) −399.819 + 1343.46i −0.400621 + 1.34615i
\(999\) 200.872 0.201073
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 156.3.e.c.103.15 yes 24
3.2 odd 2 468.3.e.m.415.10 24
4.3 odd 2 inner 156.3.e.c.103.9 24
12.11 even 2 468.3.e.m.415.16 24
13.12 even 2 inner 156.3.e.c.103.10 yes 24
39.38 odd 2 468.3.e.m.415.15 24
52.51 odd 2 inner 156.3.e.c.103.16 yes 24
156.155 even 2 468.3.e.m.415.9 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
156.3.e.c.103.9 24 4.3 odd 2 inner
156.3.e.c.103.10 yes 24 13.12 even 2 inner
156.3.e.c.103.15 yes 24 1.1 even 1 trivial
156.3.e.c.103.16 yes 24 52.51 odd 2 inner
468.3.e.m.415.9 24 156.155 even 2
468.3.e.m.415.10 24 3.2 odd 2
468.3.e.m.415.15 24 39.38 odd 2
468.3.e.m.415.16 24 12.11 even 2