Properties

Label 156.3.e.c.103.8
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 103.8
Character \(\chi\) \(=\) 156.103
Dual form 156.3.e.c.103.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.31729 + 1.50490i) q^{2} +1.73205i q^{3} +(-0.529474 - 3.96480i) q^{4} +7.41736i q^{5} +(-2.60657 - 2.28162i) q^{6} +13.3843 q^{7} +(6.66412 + 4.42600i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-1.31729 + 1.50490i) q^{2} +1.73205i q^{3} +(-0.529474 - 3.96480i) q^{4} +7.41736i q^{5} +(-2.60657 - 2.28162i) q^{6} +13.3843 q^{7} +(6.66412 + 4.42600i) q^{8} -3.00000 q^{9} +(-11.1624 - 9.77084i) q^{10} -14.6051 q^{11} +(6.86724 - 0.917075i) q^{12} +(9.82465 + 8.51330i) q^{13} +(-17.6310 + 20.1421i) q^{14} -12.8472 q^{15} +(-15.4393 + 4.19852i) q^{16} -3.85621 q^{17} +(3.95188 - 4.51471i) q^{18} -19.0947 q^{19} +(29.4084 - 3.92730i) q^{20} +23.1822i q^{21} +(19.2392 - 21.9792i) q^{22} -2.41298i q^{23} +(-7.66606 + 11.5426i) q^{24} -30.0172 q^{25} +(-25.7537 + 3.57064i) q^{26} -5.19615i q^{27} +(-7.08662 - 53.0660i) q^{28} +18.9541 q^{29} +(16.9236 - 19.3339i) q^{30} -11.2035 q^{31} +(14.0198 - 28.7654i) q^{32} -25.2967i q^{33} +(5.07976 - 5.80322i) q^{34} +99.2760i q^{35} +(1.58842 + 11.8944i) q^{36} +38.0750i q^{37} +(25.1534 - 28.7358i) q^{38} +(-14.7455 + 17.0168i) q^{39} +(-32.8293 + 49.4302i) q^{40} -35.5289i q^{41} +(-34.8871 - 30.5378i) q^{42} -10.1670i q^{43} +(7.73300 + 57.9062i) q^{44} -22.2521i q^{45} +(3.63130 + 3.17860i) q^{46} +52.7193 q^{47} +(-7.27204 - 26.7417i) q^{48} +130.139 q^{49} +(39.5415 - 45.1730i) q^{50} -6.67915i q^{51} +(28.5517 - 43.4604i) q^{52} +56.1801 q^{53} +(7.81971 + 6.84486i) q^{54} -108.331i q^{55} +(89.1944 + 59.2388i) q^{56} -33.0731i q^{57} +(-24.9681 + 28.5241i) q^{58} -22.9260 q^{59} +(6.80228 + 50.9368i) q^{60} -2.26008 q^{61} +(14.7583 - 16.8602i) q^{62} -40.1528 q^{63} +(24.8210 + 58.9908i) q^{64} +(-63.1462 + 72.8729i) q^{65} +(38.0691 + 33.3232i) q^{66} +27.1686 q^{67} +(2.04176 + 15.2891i) q^{68} +4.17941 q^{69} +(-149.401 - 130.776i) q^{70} +25.9461 q^{71} +(-19.9924 - 13.2780i) q^{72} +20.2720i q^{73} +(-57.2993 - 50.1560i) q^{74} -51.9913i q^{75} +(10.1102 + 75.7069i) q^{76} -195.478 q^{77} +(-6.18453 - 44.6066i) q^{78} +14.9255i q^{79} +(-31.1419 - 114.519i) q^{80} +9.00000 q^{81} +(53.4676 + 46.8020i) q^{82} -3.46387 q^{83} +(91.9130 - 12.2744i) q^{84} -28.6029i q^{85} +(15.3004 + 13.3930i) q^{86} +32.8295i q^{87} +(-97.3299 - 64.6421i) q^{88} -147.408i q^{89} +(33.4872 + 29.3125i) q^{90} +(131.496 + 113.944i) q^{91} +(-9.56699 + 1.27761i) q^{92} -19.4050i q^{93} +(-69.4468 + 79.3375i) q^{94} -141.633i q^{95} +(49.8231 + 24.2829i) q^{96} +163.142i q^{97} +(-171.431 + 195.846i) q^{98} +43.8152 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31729 + 1.50490i −0.658647 + 0.752452i
\(3\) 1.73205i 0.577350i
\(4\) −0.529474 3.96480i −0.132368 0.991201i
\(5\) 7.41736i 1.48347i 0.670692 + 0.741736i \(0.265997\pi\)
−0.670692 + 0.741736i \(0.734003\pi\)
\(6\) −2.60657 2.28162i −0.434428 0.380270i
\(7\) 13.3843 1.91204 0.956020 0.293303i \(-0.0947544\pi\)
0.956020 + 0.293303i \(0.0947544\pi\)
\(8\) 6.66412 + 4.42600i 0.833015 + 0.553250i
\(9\) −3.00000 −0.333333
\(10\) −11.1624 9.77084i −1.11624 0.977084i
\(11\) −14.6051 −1.32773 −0.663867 0.747851i \(-0.731086\pi\)
−0.663867 + 0.747851i \(0.731086\pi\)
\(12\) 6.86724 0.917075i 0.572270 0.0764229i
\(13\) 9.82465 + 8.51330i 0.755742 + 0.654869i
\(14\) −17.6310 + 20.1421i −1.25936 + 1.43872i
\(15\) −12.8472 −0.856483
\(16\) −15.4393 + 4.19852i −0.964957 + 0.262407i
\(17\) −3.85621 −0.226836 −0.113418 0.993547i \(-0.536180\pi\)
−0.113418 + 0.993547i \(0.536180\pi\)
\(18\) 3.95188 4.51471i 0.219549 0.250817i
\(19\) −19.0947 −1.00499 −0.502493 0.864581i \(-0.667584\pi\)
−0.502493 + 0.864581i \(0.667584\pi\)
\(20\) 29.4084 3.92730i 1.47042 0.196365i
\(21\) 23.1822i 1.10392i
\(22\) 19.2392 21.9792i 0.874508 0.999056i
\(23\) 2.41298i 0.104912i −0.998623 0.0524561i \(-0.983295\pi\)
0.998623 0.0524561i \(-0.0167050\pi\)
\(24\) −7.66606 + 11.5426i −0.319419 + 0.480941i
\(25\) −30.0172 −1.20069
\(26\) −25.7537 + 3.57064i −0.990525 + 0.137332i
\(27\) 5.19615i 0.192450i
\(28\) −7.08662 53.0660i −0.253094 1.89521i
\(29\) 18.9541 0.653589 0.326795 0.945095i \(-0.394031\pi\)
0.326795 + 0.945095i \(0.394031\pi\)
\(30\) 16.9236 19.3339i 0.564120 0.644462i
\(31\) −11.2035 −0.361403 −0.180702 0.983538i \(-0.557837\pi\)
−0.180702 + 0.983538i \(0.557837\pi\)
\(32\) 14.0198 28.7654i 0.438117 0.898918i
\(33\) 25.2967i 0.766567i
\(34\) 5.07976 5.80322i 0.149405 0.170683i
\(35\) 99.2760i 2.83646i
\(36\) 1.58842 + 11.8944i 0.0441228 + 0.330400i
\(37\) 38.0750i 1.02906i 0.857474 + 0.514528i \(0.172033\pi\)
−0.857474 + 0.514528i \(0.827967\pi\)
\(38\) 25.1534 28.7358i 0.661931 0.756204i
\(39\) −14.7455 + 17.0168i −0.378089 + 0.436328i
\(40\) −32.8293 + 49.4302i −0.820731 + 1.23575i
\(41\) 35.5289i 0.866558i −0.901260 0.433279i \(-0.857356\pi\)
0.901260 0.433279i \(-0.142644\pi\)
\(42\) −34.8871 30.5378i −0.830644 0.727091i
\(43\) 10.1670i 0.236443i −0.992987 0.118221i \(-0.962281\pi\)
0.992987 0.118221i \(-0.0377192\pi\)
\(44\) 7.73300 + 57.9062i 0.175750 + 1.31605i
\(45\) 22.2521i 0.494491i
\(46\) 3.63130 + 3.17860i 0.0789414 + 0.0691001i
\(47\) 52.7193 1.12169 0.560843 0.827922i \(-0.310477\pi\)
0.560843 + 0.827922i \(0.310477\pi\)
\(48\) −7.27204 26.7417i −0.151501 0.557118i
\(49\) 130.139 2.65589
\(50\) 39.5415 45.1730i 0.790830 0.903461i
\(51\) 6.67915i 0.130964i
\(52\) 28.5517 43.4604i 0.549070 0.835776i
\(53\) 56.1801 1.06000 0.530001 0.847997i \(-0.322191\pi\)
0.530001 + 0.847997i \(0.322191\pi\)
\(54\) 7.81971 + 6.84486i 0.144809 + 0.126757i
\(55\) 108.331i 1.96966i
\(56\) 89.1944 + 59.2388i 1.59276 + 1.05784i
\(57\) 33.0731i 0.580229i
\(58\) −24.9681 + 28.5241i −0.430485 + 0.491795i
\(59\) −22.9260 −0.388576 −0.194288 0.980945i \(-0.562240\pi\)
−0.194288 + 0.980945i \(0.562240\pi\)
\(60\) 6.80228 + 50.9368i 0.113371 + 0.848946i
\(61\) −2.26008 −0.0370505 −0.0185252 0.999828i \(-0.505897\pi\)
−0.0185252 + 0.999828i \(0.505897\pi\)
\(62\) 14.7583 16.8602i 0.238037 0.271939i
\(63\) −40.1528 −0.637346
\(64\) 24.8210 + 58.9908i 0.387828 + 0.921732i
\(65\) −63.1462 + 72.8729i −0.971480 + 1.12112i
\(66\) 38.0691 + 33.3232i 0.576805 + 0.504897i
\(67\) 27.1686 0.405501 0.202750 0.979230i \(-0.435012\pi\)
0.202750 + 0.979230i \(0.435012\pi\)
\(68\) 2.04176 + 15.2891i 0.0300259 + 0.224840i
\(69\) 4.17941 0.0605711
\(70\) −149.401 130.776i −2.13430 1.86822i
\(71\) 25.9461 0.365439 0.182719 0.983165i \(-0.441510\pi\)
0.182719 + 0.983165i \(0.441510\pi\)
\(72\) −19.9924 13.2780i −0.277672 0.184417i
\(73\) 20.2720i 0.277699i 0.990314 + 0.138849i \(0.0443404\pi\)
−0.990314 + 0.138849i \(0.955660\pi\)
\(74\) −57.2993 50.1560i −0.774315 0.677784i
\(75\) 51.9913i 0.693218i
\(76\) 10.1102 + 75.7069i 0.133028 + 0.996143i
\(77\) −195.478 −2.53868
\(78\) −6.18453 44.6066i −0.0792888 0.571880i
\(79\) 14.9255i 0.188931i 0.995528 + 0.0944654i \(0.0301142\pi\)
−0.995528 + 0.0944654i \(0.969886\pi\)
\(80\) −31.1419 114.519i −0.389274 1.43149i
\(81\) 9.00000 0.111111
\(82\) 53.4676 + 46.8020i 0.652044 + 0.570756i
\(83\) −3.46387 −0.0417334 −0.0208667 0.999782i \(-0.506643\pi\)
−0.0208667 + 0.999782i \(0.506643\pi\)
\(84\) 91.9130 12.2744i 1.09420 0.146124i
\(85\) 28.6029i 0.336504i
\(86\) 15.3004 + 13.3930i 0.177912 + 0.155732i
\(87\) 32.8295i 0.377350i
\(88\) −97.3299 64.6421i −1.10602 0.734569i
\(89\) 147.408i 1.65627i −0.560525 0.828137i \(-0.689401\pi\)
0.560525 0.828137i \(-0.310599\pi\)
\(90\) 33.4872 + 29.3125i 0.372080 + 0.325695i
\(91\) 131.496 + 113.944i 1.44501 + 1.25214i
\(92\) −9.56699 + 1.27761i −0.103989 + 0.0138871i
\(93\) 19.4050i 0.208656i
\(94\) −69.4468 + 79.3375i −0.738795 + 0.844015i
\(95\) 141.633i 1.49087i
\(96\) 49.8231 + 24.2829i 0.518990 + 0.252947i
\(97\) 163.142i 1.68187i 0.541135 + 0.840936i \(0.317995\pi\)
−0.541135 + 0.840936i \(0.682005\pi\)
\(98\) −171.431 + 195.846i −1.74930 + 1.99843i
\(99\) 43.8152 0.442578
\(100\) 15.8933 + 119.012i 0.158933 + 1.19012i
\(101\) −45.3731 −0.449238 −0.224619 0.974447i \(-0.572114\pi\)
−0.224619 + 0.974447i \(0.572114\pi\)
\(102\) 10.0515 + 8.79840i 0.0985439 + 0.0862588i
\(103\) 106.266i 1.03171i −0.856677 0.515853i \(-0.827475\pi\)
0.856677 0.515853i \(-0.172525\pi\)
\(104\) 27.7928 + 100.218i 0.267238 + 0.963631i
\(105\) −171.951 −1.63763
\(106\) −74.0057 + 84.5457i −0.698167 + 0.797601i
\(107\) 76.2855i 0.712949i 0.934305 + 0.356474i \(0.116021\pi\)
−0.934305 + 0.356474i \(0.883979\pi\)
\(108\) −20.6017 + 2.75123i −0.190757 + 0.0254743i
\(109\) 137.421i 1.26075i −0.776293 0.630373i \(-0.782902\pi\)
0.776293 0.630373i \(-0.217098\pi\)
\(110\) 163.028 + 142.704i 1.48207 + 1.29731i
\(111\) −65.9479 −0.594125
\(112\) −206.644 + 56.1941i −1.84504 + 0.501733i
\(113\) 168.559 1.49167 0.745837 0.666129i \(-0.232050\pi\)
0.745837 + 0.666129i \(0.232050\pi\)
\(114\) 49.7718 + 43.5669i 0.436595 + 0.382166i
\(115\) 17.8979 0.155634
\(116\) −10.0357 75.1492i −0.0865146 0.647838i
\(117\) −29.4739 25.5399i −0.251914 0.218290i
\(118\) 30.2002 34.5014i 0.255934 0.292385i
\(119\) −51.6125 −0.433719
\(120\) −85.6156 56.8619i −0.713463 0.473849i
\(121\) 92.3080 0.762876
\(122\) 2.97719 3.40120i 0.0244032 0.0278787i
\(123\) 61.5378 0.500308
\(124\) 5.93196 + 44.4197i 0.0478383 + 0.358223i
\(125\) 37.2145i 0.297716i
\(126\) 52.8931 60.4262i 0.419786 0.479573i
\(127\) 124.858i 0.983131i 0.870841 + 0.491565i \(0.163575\pi\)
−0.870841 + 0.491565i \(0.836425\pi\)
\(128\) −121.472 40.3550i −0.949001 0.315274i
\(129\) 17.6098 0.136510
\(130\) −26.4847 191.024i −0.203729 1.46942i
\(131\) 98.6905i 0.753363i −0.926343 0.376681i \(-0.877065\pi\)
0.926343 0.376681i \(-0.122935\pi\)
\(132\) −100.297 + 13.3939i −0.759822 + 0.101469i
\(133\) −255.569 −1.92157
\(134\) −35.7890 + 40.8861i −0.267082 + 0.305120i
\(135\) 38.5417 0.285494
\(136\) −25.6982 17.0676i −0.188958 0.125497i
\(137\) 96.5730i 0.704912i −0.935828 0.352456i \(-0.885347\pi\)
0.935828 0.352456i \(-0.114653\pi\)
\(138\) −5.50550 + 6.28960i −0.0398950 + 0.0455768i
\(139\) 253.423i 1.82318i −0.411096 0.911592i \(-0.634854\pi\)
0.411096 0.911592i \(-0.365146\pi\)
\(140\) 393.610 52.5640i 2.81150 0.375457i
\(141\) 91.3125i 0.647606i
\(142\) −34.1787 + 39.0465i −0.240695 + 0.274975i
\(143\) −143.490 124.337i −1.00342 0.869492i
\(144\) 46.3179 12.5955i 0.321652 0.0874691i
\(145\) 140.589i 0.969582i
\(146\) −30.5074 26.7042i −0.208955 0.182905i
\(147\) 225.407i 1.53338i
\(148\) 150.960 20.1597i 1.02000 0.136214i
\(149\) 86.7895i 0.582480i 0.956650 + 0.291240i \(0.0940677\pi\)
−0.956650 + 0.291240i \(0.905932\pi\)
\(150\) 78.2420 + 68.4879i 0.521613 + 0.456586i
\(151\) 196.093 1.29863 0.649314 0.760520i \(-0.275056\pi\)
0.649314 + 0.760520i \(0.275056\pi\)
\(152\) −127.250 84.5134i −0.837169 0.556009i
\(153\) 11.5686 0.0756119
\(154\) 257.502 294.176i 1.67209 1.91023i
\(155\) 83.1004i 0.536131i
\(156\) 75.2756 + 49.4529i 0.482536 + 0.317006i
\(157\) −92.4509 −0.588859 −0.294430 0.955673i \(-0.595130\pi\)
−0.294430 + 0.955673i \(0.595130\pi\)
\(158\) −22.4615 19.6613i −0.142161 0.124439i
\(159\) 97.3068i 0.611993i
\(160\) 213.363 + 103.990i 1.33352 + 0.649935i
\(161\) 32.2960i 0.200596i
\(162\) −11.8556 + 13.5441i −0.0731830 + 0.0836058i
\(163\) 227.182 1.39375 0.696877 0.717190i \(-0.254572\pi\)
0.696877 + 0.717190i \(0.254572\pi\)
\(164\) −140.865 + 18.8116i −0.858933 + 0.114705i
\(165\) 187.635 1.13718
\(166\) 4.56293 5.21279i 0.0274875 0.0314024i
\(167\) −209.783 −1.25618 −0.628092 0.778139i \(-0.716164\pi\)
−0.628092 + 0.778139i \(0.716164\pi\)
\(168\) −102.605 + 154.489i −0.610742 + 0.919579i
\(169\) 24.0475 + 167.280i 0.142293 + 0.989825i
\(170\) 43.0446 + 37.6784i 0.253203 + 0.221638i
\(171\) 57.2842 0.334995
\(172\) −40.3103 + 5.38318i −0.234362 + 0.0312975i
\(173\) 307.527 1.77761 0.888807 0.458282i \(-0.151535\pi\)
0.888807 + 0.458282i \(0.151535\pi\)
\(174\) −49.4052 43.2460i −0.283938 0.248540i
\(175\) −401.759 −2.29576
\(176\) 225.492 61.3196i 1.28121 0.348407i
\(177\) 39.7089i 0.224344i
\(178\) 221.836 + 194.180i 1.24627 + 1.09090i
\(179\) 319.597i 1.78546i 0.450595 + 0.892729i \(0.351212\pi\)
−0.450595 + 0.892729i \(0.648788\pi\)
\(180\) −88.2251 + 11.7819i −0.490139 + 0.0654549i
\(181\) 237.850 1.31409 0.657044 0.753852i \(-0.271806\pi\)
0.657044 + 0.753852i \(0.271806\pi\)
\(182\) −344.694 + 47.7904i −1.89392 + 0.262585i
\(183\) 3.91457i 0.0213911i
\(184\) 10.6799 16.0804i 0.0580427 0.0873934i
\(185\) −282.416 −1.52657
\(186\) 29.2027 + 25.5621i 0.157004 + 0.137431i
\(187\) 56.3202 0.301177
\(188\) −27.9135 209.021i −0.148476 1.11182i
\(189\) 69.5467i 0.367972i
\(190\) 213.143 + 186.572i 1.12181 + 0.981956i
\(191\) 4.29489i 0.0224864i −0.999937 0.0112432i \(-0.996421\pi\)
0.999937 0.0112432i \(-0.00357889\pi\)
\(192\) −102.175 + 42.9912i −0.532162 + 0.223913i
\(193\) 375.756i 1.94692i −0.228848 0.973462i \(-0.573496\pi\)
0.228848 0.973462i \(-0.426504\pi\)
\(194\) −245.512 214.905i −1.26553 1.10776i
\(195\) −126.220 109.372i −0.647280 0.560884i
\(196\) −68.9051 515.975i −0.351556 2.63252i
\(197\) 54.1267i 0.274755i 0.990519 + 0.137377i \(0.0438673\pi\)
−0.990519 + 0.137377i \(0.956133\pi\)
\(198\) −57.7175 + 65.9377i −0.291503 + 0.333019i
\(199\) 141.950i 0.713317i 0.934235 + 0.356658i \(0.116084\pi\)
−0.934235 + 0.356658i \(0.883916\pi\)
\(200\) −200.038 132.856i −1.00019 0.664281i
\(201\) 47.0573i 0.234116i
\(202\) 59.7697 68.2821i 0.295889 0.338030i
\(203\) 253.687 1.24969
\(204\) −26.4815 + 3.53643i −0.129811 + 0.0173355i
\(205\) 263.531 1.28551
\(206\) 159.920 + 139.983i 0.776309 + 0.679530i
\(207\) 7.23894i 0.0349707i
\(208\) −187.429 90.1906i −0.901101 0.433609i
\(209\) 278.880 1.33435
\(210\) 226.510 258.770i 1.07862 1.23224i
\(211\) 80.1749i 0.379976i 0.981786 + 0.189988i \(0.0608449\pi\)
−0.981786 + 0.189988i \(0.939155\pi\)
\(212\) −29.7459 222.743i −0.140311 1.05067i
\(213\) 44.9400i 0.210986i
\(214\) −114.802 100.490i −0.536460 0.469582i
\(215\) 75.4125 0.350756
\(216\) 22.9982 34.6278i 0.106473 0.160314i
\(217\) −149.951 −0.691017
\(218\) 206.806 + 181.024i 0.948650 + 0.830386i
\(219\) −35.1121 −0.160329
\(220\) −429.511 + 57.3584i −1.95232 + 0.260720i
\(221\) −37.8859 32.8291i −0.171429 0.148548i
\(222\) 86.8728 99.2453i 0.391319 0.447051i
\(223\) −274.866 −1.23258 −0.616291 0.787519i \(-0.711365\pi\)
−0.616291 + 0.787519i \(0.711365\pi\)
\(224\) 187.644 385.004i 0.837697 1.71877i
\(225\) 90.0516 0.400230
\(226\) −222.042 + 253.665i −0.982486 + 1.12241i
\(227\) −265.324 −1.16883 −0.584414 0.811456i \(-0.698675\pi\)
−0.584414 + 0.811456i \(0.698675\pi\)
\(228\) −131.128 + 17.5113i −0.575123 + 0.0768040i
\(229\) 239.829i 1.04729i −0.851937 0.523644i \(-0.824572\pi\)
0.851937 0.523644i \(-0.175428\pi\)
\(230\) −23.5769 + 26.9347i −0.102508 + 0.117107i
\(231\) 338.578i 1.46571i
\(232\) 126.312 + 83.8909i 0.544450 + 0.361599i
\(233\) −28.7181 −0.123254 −0.0616268 0.998099i \(-0.519629\pi\)
−0.0616268 + 0.998099i \(0.519629\pi\)
\(234\) 77.2610 10.7119i 0.330175 0.0457774i
\(235\) 391.038i 1.66399i
\(236\) 12.1387 + 90.8969i 0.0514351 + 0.385157i
\(237\) −25.8518 −0.109079
\(238\) 67.9889 77.6719i 0.285668 0.326353i
\(239\) 53.5722 0.224151 0.112076 0.993700i \(-0.464250\pi\)
0.112076 + 0.993700i \(0.464250\pi\)
\(240\) 198.353 53.9394i 0.826469 0.224747i
\(241\) 56.8926i 0.236069i −0.993009 0.118034i \(-0.962341\pi\)
0.993009 0.118034i \(-0.0376593\pi\)
\(242\) −121.597 + 138.915i −0.502466 + 0.574028i
\(243\) 15.5885i 0.0641500i
\(244\) 1.19665 + 8.96077i 0.00490431 + 0.0367245i
\(245\) 965.286i 3.93994i
\(246\) −81.0634 + 92.6086i −0.329526 + 0.376458i
\(247\) −187.599 162.559i −0.759511 0.658135i
\(248\) −74.6615 49.5867i −0.301054 0.199946i
\(249\) 5.99960i 0.0240948i
\(250\) 56.0042 + 49.0224i 0.224017 + 0.196090i
\(251\) 0.708529i 0.00282283i 0.999999 + 0.00141141i \(0.000449267\pi\)
−0.999999 + 0.00141141i \(0.999551\pi\)
\(252\) 21.2599 + 159.198i 0.0843645 + 0.631738i
\(253\) 35.2418i 0.139295i
\(254\) −187.899 164.474i −0.739759 0.647536i
\(255\) 49.5416 0.194281
\(256\) 220.745 129.644i 0.862285 0.506424i
\(257\) −151.217 −0.588395 −0.294197 0.955745i \(-0.595052\pi\)
−0.294197 + 0.955745i \(0.595052\pi\)
\(258\) −23.1973 + 26.5011i −0.0899120 + 0.102717i
\(259\) 509.607i 1.96759i
\(260\) 322.361 + 211.778i 1.23985 + 0.814530i
\(261\) −56.8623 −0.217863
\(262\) 148.520 + 130.004i 0.566869 + 0.496200i
\(263\) 215.466i 0.819262i 0.912251 + 0.409631i \(0.134342\pi\)
−0.912251 + 0.409631i \(0.865658\pi\)
\(264\) 111.963 168.580i 0.424104 0.638562i
\(265\) 416.708i 1.57248i
\(266\) 336.660 384.607i 1.26564 1.44589i
\(267\) 255.319 0.956251
\(268\) −14.3850 107.718i −0.0536755 0.401933i
\(269\) −296.034 −1.10050 −0.550249 0.835000i \(-0.685467\pi\)
−0.550249 + 0.835000i \(0.685467\pi\)
\(270\) −50.7708 + 58.0016i −0.188040 + 0.214821i
\(271\) −226.738 −0.836673 −0.418336 0.908292i \(-0.637387\pi\)
−0.418336 + 0.908292i \(0.637387\pi\)
\(272\) 59.5372 16.1904i 0.218887 0.0595233i
\(273\) −197.357 + 227.757i −0.722921 + 0.834276i
\(274\) 145.333 + 127.215i 0.530413 + 0.464288i
\(275\) 438.403 1.59419
\(276\) −2.21288 16.5705i −0.00801770 0.0600381i
\(277\) −57.2551 −0.206697 −0.103349 0.994645i \(-0.532956\pi\)
−0.103349 + 0.994645i \(0.532956\pi\)
\(278\) 381.377 + 333.832i 1.37186 + 1.20083i
\(279\) 33.6105 0.120468
\(280\) −439.396 + 661.587i −1.56927 + 2.36281i
\(281\) 169.616i 0.603615i −0.953369 0.301808i \(-0.902410\pi\)
0.953369 0.301808i \(-0.0975901\pi\)
\(282\) −137.417 120.285i −0.487293 0.426544i
\(283\) 355.164i 1.25500i −0.778618 0.627498i \(-0.784079\pi\)
0.778618 0.627498i \(-0.215921\pi\)
\(284\) −13.7378 102.871i −0.0483725 0.362223i
\(285\) 245.315 0.860753
\(286\) 376.134 52.1494i 1.31515 0.182341i
\(287\) 475.528i 1.65689i
\(288\) −42.0593 + 86.2961i −0.146039 + 0.299639i
\(289\) −274.130 −0.948546
\(290\) −211.573 185.197i −0.729564 0.638612i
\(291\) −282.569 −0.971029
\(292\) 80.3745 10.7335i 0.275255 0.0367585i
\(293\) 484.480i 1.65351i −0.562559 0.826757i \(-0.690183\pi\)
0.562559 0.826757i \(-0.309817\pi\)
\(294\) −339.216 296.927i −1.15380 1.00996i
\(295\) 170.050i 0.576441i
\(296\) −168.520 + 253.737i −0.569325 + 0.857218i
\(297\) 75.8902i 0.255522i
\(298\) −130.610 114.327i −0.438288 0.383648i
\(299\) 20.5424 23.7067i 0.0687038 0.0792866i
\(300\) −206.135 + 27.5280i −0.687118 + 0.0917601i
\(301\) 136.078i 0.452088i
\(302\) −258.312 + 295.101i −0.855338 + 0.977156i
\(303\) 78.5885i 0.259368i
\(304\) 294.810 80.1696i 0.969769 0.263716i
\(305\) 16.7638i 0.0549633i
\(306\) −15.2393 + 17.4097i −0.0498016 + 0.0568944i
\(307\) −179.917 −0.586047 −0.293024 0.956105i \(-0.594661\pi\)
−0.293024 + 0.956105i \(0.594661\pi\)
\(308\) 103.501 + 775.033i 0.336041 + 2.51634i
\(309\) 184.058 0.595656
\(310\) 125.058 + 109.468i 0.403413 + 0.353121i
\(311\) 9.50603i 0.0305660i −0.999883 0.0152830i \(-0.995135\pi\)
0.999883 0.0152830i \(-0.00486492\pi\)
\(312\) −173.582 + 48.1385i −0.556352 + 0.154290i
\(313\) −67.4047 −0.215350 −0.107675 0.994186i \(-0.534341\pi\)
−0.107675 + 0.994186i \(0.534341\pi\)
\(314\) 121.785 139.130i 0.387850 0.443088i
\(315\) 297.828i 0.945485i
\(316\) 59.1768 7.90267i 0.187268 0.0250085i
\(317\) 355.562i 1.12165i −0.827936 0.560823i \(-0.810485\pi\)
0.827936 0.560823i \(-0.189515\pi\)
\(318\) −146.437 128.182i −0.460495 0.403087i
\(319\) −276.826 −0.867793
\(320\) −437.556 + 184.106i −1.36736 + 0.575332i
\(321\) −132.130 −0.411621
\(322\) 48.6024 + 42.5433i 0.150939 + 0.132122i
\(323\) 73.6333 0.227967
\(324\) −4.76526 35.6832i −0.0147076 0.110133i
\(325\) −294.909 255.546i −0.907411 0.786294i
\(326\) −299.266 + 341.887i −0.917992 + 1.04873i
\(327\) 238.021 0.727891
\(328\) 157.251 236.769i 0.479424 0.721856i
\(329\) 705.609 2.14471
\(330\) −247.170 + 282.373i −0.749001 + 0.855674i
\(331\) −332.355 −1.00409 −0.502047 0.864840i \(-0.667420\pi\)
−0.502047 + 0.864840i \(0.667420\pi\)
\(332\) 1.83403 + 13.7336i 0.00552418 + 0.0413661i
\(333\) 114.225i 0.343018i
\(334\) 276.345 315.703i 0.827381 0.945218i
\(335\) 201.519i 0.601549i
\(336\) −97.3310 357.918i −0.289676 1.06523i
\(337\) −419.712 −1.24544 −0.622718 0.782446i \(-0.713972\pi\)
−0.622718 + 0.782446i \(0.713972\pi\)
\(338\) −283.419 184.168i −0.838516 0.544877i
\(339\) 291.953i 0.861218i
\(340\) −113.405 + 15.1445i −0.333543 + 0.0445426i
\(341\) 163.628 0.479847
\(342\) −75.4601 + 86.2073i −0.220644 + 0.252068i
\(343\) 1085.98 3.16613
\(344\) 44.9993 67.7543i 0.130812 0.196960i
\(345\) 31.0001i 0.0898555i
\(346\) −405.104 + 462.799i −1.17082 + 1.33757i
\(347\) 338.651i 0.975938i 0.872861 + 0.487969i \(0.162262\pi\)
−0.872861 + 0.487969i \(0.837738\pi\)
\(348\) 130.162 17.3823i 0.374030 0.0499492i
\(349\) 201.723i 0.578004i 0.957329 + 0.289002i \(0.0933234\pi\)
−0.957329 + 0.289002i \(0.906677\pi\)
\(350\) 529.234 604.608i 1.51210 1.72745i
\(351\) 44.2364 51.0504i 0.126030 0.145443i
\(352\) −204.759 + 420.120i −0.581703 + 1.19352i
\(353\) 214.052i 0.606378i 0.952930 + 0.303189i \(0.0980514\pi\)
−0.952930 + 0.303189i \(0.901949\pi\)
\(354\) 59.7582 + 52.3083i 0.168808 + 0.147764i
\(355\) 192.452i 0.542118i
\(356\) −584.445 + 78.0489i −1.64170 + 0.219238i
\(357\) 89.3956i 0.250408i
\(358\) −480.963 421.003i −1.34347 1.17599i
\(359\) −44.1415 −0.122957 −0.0614784 0.998108i \(-0.519582\pi\)
−0.0614784 + 0.998108i \(0.519582\pi\)
\(360\) 98.4878 148.291i 0.273577 0.411918i
\(361\) 3.60902 0.00999730
\(362\) −313.318 + 357.942i −0.865521 + 0.988789i
\(363\) 159.882i 0.440447i
\(364\) 382.143 581.685i 1.04984 1.59804i
\(365\) −150.365 −0.411958
\(366\) 5.89106 + 5.15664i 0.0160958 + 0.0140892i
\(367\) 520.972i 1.41954i −0.704432 0.709772i \(-0.748798\pi\)
0.704432 0.709772i \(-0.251202\pi\)
\(368\) 10.1309 + 37.2548i 0.0275297 + 0.101236i
\(369\) 106.587i 0.288853i
\(370\) 372.025 425.009i 1.00547 1.14867i
\(371\) 751.930 2.02677
\(372\) −76.9371 + 10.2744i −0.206820 + 0.0276195i
\(373\) 42.1017 0.112873 0.0564367 0.998406i \(-0.482026\pi\)
0.0564367 + 0.998406i \(0.482026\pi\)
\(374\) −74.1902 + 84.7565i −0.198370 + 0.226622i
\(375\) 64.4574 0.171886
\(376\) 351.328 + 233.336i 0.934382 + 0.620574i
\(377\) 186.217 + 161.362i 0.493945 + 0.428016i
\(378\) 104.661 + 91.6135i 0.276881 + 0.242364i
\(379\) −306.632 −0.809056 −0.404528 0.914526i \(-0.632564\pi\)
−0.404528 + 0.914526i \(0.632564\pi\)
\(380\) −561.545 + 74.9907i −1.47775 + 0.197344i
\(381\) −216.260 −0.567611
\(382\) 6.46340 + 5.65764i 0.0169199 + 0.0148106i
\(383\) 362.077 0.945372 0.472686 0.881231i \(-0.343285\pi\)
0.472686 + 0.881231i \(0.343285\pi\)
\(384\) 69.8970 210.396i 0.182023 0.547906i
\(385\) 1449.93i 3.76606i
\(386\) 565.477 + 494.982i 1.46497 + 1.28234i
\(387\) 30.5011i 0.0788142i
\(388\) 646.824 86.3791i 1.66707 0.222627i
\(389\) −216.745 −0.557184 −0.278592 0.960409i \(-0.589868\pi\)
−0.278592 + 0.960409i \(0.589868\pi\)
\(390\) 330.863 45.8729i 0.848368 0.117623i
\(391\) 9.30496i 0.0237978i
\(392\) 867.261 + 575.995i 2.21240 + 1.46937i
\(393\) 170.937 0.434954
\(394\) −81.4555 71.3008i −0.206740 0.180966i
\(395\) −110.708 −0.280273
\(396\) −23.1990 173.719i −0.0585833 0.438683i
\(397\) 187.791i 0.473025i 0.971628 + 0.236513i \(0.0760045\pi\)
−0.971628 + 0.236513i \(0.923996\pi\)
\(398\) −213.621 186.990i −0.536737 0.469824i
\(399\) 442.659i 1.10942i
\(400\) 463.445 126.028i 1.15861 0.315069i
\(401\) 261.183i 0.651329i −0.945485 0.325665i \(-0.894412\pi\)
0.945485 0.325665i \(-0.105588\pi\)
\(402\) −70.8168 61.9883i −0.176161 0.154200i
\(403\) −110.070 95.3787i −0.273128 0.236672i
\(404\) 24.0238 + 179.895i 0.0594650 + 0.445285i
\(405\) 66.7562i 0.164830i
\(406\) −334.180 + 381.774i −0.823104 + 0.940331i
\(407\) 556.089i 1.36631i
\(408\) 29.5619 44.5106i 0.0724557 0.109095i
\(409\) 461.162i 1.12754i 0.825933 + 0.563768i \(0.190649\pi\)
−0.825933 + 0.563768i \(0.809351\pi\)
\(410\) −347.147 + 396.588i −0.846700 + 0.967288i
\(411\) 167.269 0.406981
\(412\) −421.322 + 56.2649i −1.02263 + 0.136565i
\(413\) −306.847 −0.742972
\(414\) −10.8939 9.53581i −0.0263138 0.0230334i
\(415\) 25.6928i 0.0619103i
\(416\) 382.627 163.255i 0.919777 0.392441i
\(417\) 438.941 1.05262
\(418\) −367.367 + 419.688i −0.878868 + 1.00404i
\(419\) 303.528i 0.724411i −0.932098 0.362205i \(-0.882024\pi\)
0.932098 0.362205i \(-0.117976\pi\)
\(420\) 91.0435 + 681.752i 0.216770 + 1.62322i
\(421\) 463.284i 1.10044i −0.835021 0.550219i \(-0.814544\pi\)
0.835021 0.550219i \(-0.185456\pi\)
\(422\) −120.656 105.614i −0.285914 0.250270i
\(423\) −158.158 −0.373896
\(424\) 374.391 + 248.653i 0.882998 + 0.586447i
\(425\) 115.753 0.272359
\(426\) −67.6304 59.1992i −0.158757 0.138965i
\(427\) −30.2495 −0.0708420
\(428\) 302.457 40.3912i 0.706675 0.0943719i
\(429\) 215.359 248.531i 0.502001 0.579327i
\(430\) −99.3405 + 113.489i −0.231024 + 0.263927i
\(431\) −435.301 −1.00998 −0.504990 0.863125i \(-0.668504\pi\)
−0.504990 + 0.863125i \(0.668504\pi\)
\(432\) 21.8161 + 80.2250i 0.0505003 + 0.185706i
\(433\) −262.026 −0.605142 −0.302571 0.953127i \(-0.597845\pi\)
−0.302571 + 0.953127i \(0.597845\pi\)
\(434\) 197.529 225.661i 0.455136 0.519957i
\(435\) −243.508 −0.559788
\(436\) −544.848 + 72.7609i −1.24965 + 0.166883i
\(437\) 46.0752i 0.105435i
\(438\) 46.2530 52.8404i 0.105600 0.120640i
\(439\) 108.928i 0.248127i −0.992274 0.124063i \(-0.960407\pi\)
0.992274 0.124063i \(-0.0395926\pi\)
\(440\) 479.474 721.931i 1.08971 1.64075i
\(441\) −390.416 −0.885298
\(442\) 99.3114 13.7691i 0.224687 0.0311519i
\(443\) 156.345i 0.352923i −0.984308 0.176462i \(-0.943535\pi\)
0.984308 0.176462i \(-0.0564652\pi\)
\(444\) 34.9177 + 261.470i 0.0786434 + 0.588897i
\(445\) 1093.38 2.45704
\(446\) 362.079 413.647i 0.811836 0.927459i
\(447\) −150.324 −0.336295
\(448\) 332.211 + 789.549i 0.741542 + 1.76239i
\(449\) 6.51043i 0.0144998i 0.999974 + 0.00724992i \(0.00230774\pi\)
−0.999974 + 0.00724992i \(0.997692\pi\)
\(450\) −118.624 + 135.519i −0.263610 + 0.301154i
\(451\) 518.902i 1.15056i
\(452\) −89.2476 668.303i −0.197450 1.47855i
\(453\) 339.643i 0.749764i
\(454\) 349.509 399.287i 0.769844 0.879487i
\(455\) −845.166 + 975.352i −1.85751 + 2.14363i
\(456\) 146.381 220.403i 0.321012 0.483340i
\(457\) 114.069i 0.249603i 0.992182 + 0.124802i \(0.0398294\pi\)
−0.992182 + 0.124802i \(0.960171\pi\)
\(458\) 360.920 + 315.925i 0.788034 + 0.689793i
\(459\) 20.0374i 0.0436546i
\(460\) −9.47649 70.9618i −0.0206011 0.154265i
\(461\) 346.907i 0.752510i 0.926516 + 0.376255i \(0.122788\pi\)
−0.926516 + 0.376255i \(0.877212\pi\)
\(462\) 509.528 + 446.007i 1.10287 + 0.965383i
\(463\) 558.360 1.20596 0.602980 0.797756i \(-0.293980\pi\)
0.602980 + 0.797756i \(0.293980\pi\)
\(464\) −292.638 + 79.5791i −0.630686 + 0.171507i
\(465\) 143.934 0.309536
\(466\) 37.8301 43.2179i 0.0811806 0.0927424i
\(467\) 470.970i 1.00850i −0.863558 0.504250i \(-0.831769\pi\)
0.863558 0.504250i \(-0.168231\pi\)
\(468\) −85.6550 + 130.381i −0.183023 + 0.278592i
\(469\) 363.631 0.775334
\(470\) −588.474 515.112i −1.25207 1.09598i
\(471\) 160.130i 0.339978i
\(472\) −152.781 101.470i −0.323689 0.214980i
\(473\) 148.490i 0.313933i
\(474\) 34.0544 38.9044i 0.0718447 0.0820769i
\(475\) 573.171 1.20668
\(476\) 27.3275 + 204.634i 0.0574107 + 0.429902i
\(477\) −168.540 −0.353334
\(478\) −70.5703 + 80.6210i −0.147637 + 0.168663i
\(479\) 198.543 0.414495 0.207248 0.978289i \(-0.433549\pi\)
0.207248 + 0.978289i \(0.433549\pi\)
\(480\) −180.115 + 369.556i −0.375240 + 0.769908i
\(481\) −324.144 + 374.074i −0.673897 + 0.777700i
\(482\) 85.6180 + 74.9443i 0.177631 + 0.155486i
\(483\) 55.9383 0.115814
\(484\) −48.8747 365.983i −0.100981 0.756164i
\(485\) −1210.08 −2.49501
\(486\) −23.4591 20.5346i −0.0482698 0.0422522i
\(487\) 42.2257 0.0867057 0.0433528 0.999060i \(-0.486196\pi\)
0.0433528 + 0.999060i \(0.486196\pi\)
\(488\) −15.0614 10.0031i −0.0308636 0.0204982i
\(489\) 393.491i 0.804685i
\(490\) −1452.66 1271.57i −2.96462 2.59503i
\(491\) 159.084i 0.324000i −0.986791 0.162000i \(-0.948206\pi\)
0.986791 0.162000i \(-0.0517944\pi\)
\(492\) −32.5827 243.985i −0.0662249 0.495905i
\(493\) −73.0909 −0.148257
\(494\) 491.759 68.1804i 0.995464 0.138017i
\(495\) 324.993i 0.656552i
\(496\) 172.974 47.0381i 0.348739 0.0948348i
\(497\) 347.270 0.698733
\(498\) 9.02882 + 7.90323i 0.0181302 + 0.0158699i
\(499\) −47.8199 −0.0958315 −0.0479158 0.998851i \(-0.515258\pi\)
−0.0479158 + 0.998851i \(0.515258\pi\)
\(500\) −147.548 + 19.7041i −0.295096 + 0.0394082i
\(501\) 363.354i 0.725258i
\(502\) −1.06627 0.933342i −0.00212404 0.00185925i
\(503\) 656.485i 1.30514i 0.757729 + 0.652569i \(0.226309\pi\)
−0.757729 + 0.652569i \(0.773691\pi\)
\(504\) −267.583 177.717i −0.530919 0.352612i
\(505\) 336.548i 0.666432i
\(506\) −53.0355 46.4237i −0.104813 0.0917465i
\(507\) −289.738 + 41.6514i −0.571476 + 0.0821527i
\(508\) 495.036 66.1088i 0.974480 0.130135i
\(509\) 287.339i 0.564517i 0.959338 + 0.282258i \(0.0910835\pi\)
−0.959338 + 0.282258i \(0.908916\pi\)
\(510\) −65.2609 + 74.5554i −0.127963 + 0.146187i
\(511\) 271.326i 0.530971i
\(512\) −95.6835 + 502.980i −0.186882 + 0.982382i
\(513\) 99.2192i 0.193410i
\(514\) 199.198 227.568i 0.387544 0.442739i
\(515\) 788.211 1.53051
\(516\) −9.32393 69.8195i −0.0180696 0.135309i
\(517\) −769.969 −1.48930
\(518\) −766.909 671.302i −1.48052 1.29595i
\(519\) 532.653i 1.02631i
\(520\) −743.350 + 206.149i −1.42952 + 0.396440i
\(521\) −574.903 −1.10346 −0.551730 0.834023i \(-0.686032\pi\)
−0.551730 + 0.834023i \(0.686032\pi\)
\(522\) 74.9043 85.5723i 0.143495 0.163932i
\(523\) 468.034i 0.894903i 0.894308 + 0.447452i \(0.147668\pi\)
−0.894308 + 0.447452i \(0.852332\pi\)
\(524\) −391.288 + 52.2540i −0.746733 + 0.0997214i
\(525\) 695.866i 1.32546i
\(526\) −324.255 283.832i −0.616455 0.539604i
\(527\) 43.2030 0.0819792
\(528\) 106.209 + 390.564i 0.201153 + 0.739705i
\(529\) 523.178 0.988993
\(530\) −627.106 548.927i −1.18322 1.03571i
\(531\) 68.7779 0.129525
\(532\) 135.317 + 1013.28i 0.254356 + 1.90466i
\(533\) 302.468 349.059i 0.567482 0.654895i
\(534\) −336.330 + 384.231i −0.629832 + 0.719533i
\(535\) −565.837 −1.05764
\(536\) 181.055 + 120.248i 0.337788 + 0.224344i
\(537\) −553.558 −1.03083
\(538\) 389.964 445.503i 0.724840 0.828072i
\(539\) −1900.69 −3.52632
\(540\) −20.4068 152.810i −0.0377904 0.282982i
\(541\) 670.174i 1.23877i 0.785088 + 0.619384i \(0.212618\pi\)
−0.785088 + 0.619384i \(0.787382\pi\)
\(542\) 298.681 341.219i 0.551072 0.629556i
\(543\) 411.968i 0.758690i
\(544\) −54.0631 + 110.925i −0.0993807 + 0.203907i
\(545\) 1019.30 1.87028
\(546\) −82.7754 597.027i −0.151603 1.09346i
\(547\) 453.519i 0.829102i −0.910026 0.414551i \(-0.863939\pi\)
0.910026 0.414551i \(-0.136061\pi\)
\(548\) −382.893 + 51.1328i −0.698709 + 0.0933081i
\(549\) 6.78024 0.0123502
\(550\) −577.506 + 659.755i −1.05001 + 1.19955i
\(551\) −361.923 −0.656848
\(552\) 27.8521 + 18.4981i 0.0504566 + 0.0335110i
\(553\) 199.767i 0.361243i
\(554\) 75.4218 86.1635i 0.136141 0.155530i
\(555\) 489.159i 0.881368i
\(556\) −1004.77 + 134.181i −1.80714 + 0.241332i
\(557\) 146.356i 0.262758i 0.991332 + 0.131379i \(0.0419404\pi\)
−0.991332 + 0.131379i \(0.958060\pi\)
\(558\) −44.2749 + 50.5806i −0.0793457 + 0.0906462i
\(559\) 86.5550 99.8875i 0.154839 0.178690i
\(560\) −416.812 1532.75i −0.744307 2.73706i
\(561\) 97.5494i 0.173885i
\(562\) 255.256 + 223.434i 0.454192 + 0.397570i
\(563\) 273.083i 0.485050i −0.970145 0.242525i \(-0.922024\pi\)
0.970145 0.242525i \(-0.0779757\pi\)
\(564\) 362.036 48.3475i 0.641908 0.0857226i
\(565\) 1250.26i 2.21285i
\(566\) 534.487 + 467.855i 0.944324 + 0.826599i
\(567\) 120.458 0.212449
\(568\) 172.908 + 114.838i 0.304416 + 0.202179i
\(569\) 787.692 1.38435 0.692173 0.721732i \(-0.256654\pi\)
0.692173 + 0.721732i \(0.256654\pi\)
\(570\) −323.152 + 369.175i −0.566933 + 0.647676i
\(571\) 552.730i 0.968004i −0.875067 0.484002i \(-0.839183\pi\)
0.875067 0.484002i \(-0.160817\pi\)
\(572\) −416.999 + 634.742i −0.729019 + 1.10969i
\(573\) 7.43897 0.0129825
\(574\) 715.625 + 626.411i 1.24673 + 1.09131i
\(575\) 72.4310i 0.125967i
\(576\) −74.4630 176.972i −0.129276 0.307244i
\(577\) 961.217i 1.66589i 0.553357 + 0.832944i \(0.313346\pi\)
−0.553357 + 0.832944i \(0.686654\pi\)
\(578\) 361.109 412.539i 0.624757 0.713735i
\(579\) 650.829 1.12406
\(580\) 557.409 74.4383i 0.961050 0.128342i
\(581\) −46.3614 −0.0797958
\(582\) 372.227 425.240i 0.639565 0.730653i
\(583\) −820.515 −1.40740
\(584\) −89.7240 + 135.095i −0.153637 + 0.231327i
\(585\) 189.439 218.619i 0.323827 0.373707i
\(586\) 729.095 + 638.202i 1.24419 + 1.08908i
\(587\) 416.312 0.709220 0.354610 0.935014i \(-0.384614\pi\)
0.354610 + 0.935014i \(0.384614\pi\)
\(588\) 893.694 119.347i 1.51989 0.202971i
\(589\) 213.928 0.363205
\(590\) 255.909 + 224.006i 0.433744 + 0.379671i
\(591\) −93.7502 −0.158630
\(592\) −159.859 587.853i −0.270032 0.992994i
\(593\) 956.542i 1.61306i −0.591196 0.806528i \(-0.701344\pi\)
0.591196 0.806528i \(-0.298656\pi\)
\(594\) −114.207 99.9697i −0.192268 0.168299i
\(595\) 382.829i 0.643410i
\(596\) 344.103 45.9527i 0.577354 0.0771019i
\(597\) −245.865 −0.411834
\(598\) 8.61588 + 62.1431i 0.0144078 + 0.103918i
\(599\) 80.3454i 0.134132i 0.997749 + 0.0670662i \(0.0213639\pi\)
−0.997749 + 0.0670662i \(0.978636\pi\)
\(600\) 230.114 346.477i 0.383523 0.577461i
\(601\) 337.707 0.561908 0.280954 0.959721i \(-0.409349\pi\)
0.280954 + 0.959721i \(0.409349\pi\)
\(602\) 204.785 + 179.255i 0.340174 + 0.297766i
\(603\) −81.5057 −0.135167
\(604\) −103.826 777.470i −0.171897 1.28720i
\(605\) 684.682i 1.13171i
\(606\) 118.268 + 103.524i 0.195162 + 0.170832i
\(607\) 519.206i 0.855365i 0.903929 + 0.427682i \(0.140670\pi\)
−0.903929 + 0.427682i \(0.859330\pi\)
\(608\) −267.703 + 549.267i −0.440302 + 0.903400i
\(609\) 439.398i 0.721508i
\(610\) 25.2279 + 22.0829i 0.0413573 + 0.0362014i
\(611\) 517.948 + 448.815i 0.847706 + 0.734558i
\(612\) −6.12528 45.8673i −0.0100086 0.0749466i
\(613\) 538.029i 0.877698i −0.898561 0.438849i \(-0.855386\pi\)
0.898561 0.438849i \(-0.144614\pi\)
\(614\) 237.003 270.757i 0.385998 0.440973i
\(615\) 456.448i 0.742192i
\(616\) −1302.69 865.187i −2.11476 1.40452i
\(617\) 136.853i 0.221803i 0.993831 + 0.110902i \(0.0353739\pi\)
−0.993831 + 0.110902i \(0.964626\pi\)
\(618\) −242.458 + 276.989i −0.392327 + 0.448202i
\(619\) −734.349 −1.18635 −0.593174 0.805074i \(-0.702125\pi\)
−0.593174 + 0.805074i \(0.702125\pi\)
\(620\) −329.476 + 43.9994i −0.531414 + 0.0709668i
\(621\) −12.5382 −0.0201904
\(622\) 14.3057 + 12.5222i 0.0229995 + 0.0201322i
\(623\) 1972.96i 3.16686i
\(624\) 156.215 324.637i 0.250344 0.520251i
\(625\) −474.397 −0.759036
\(626\) 88.7918 101.438i 0.141840 0.162041i
\(627\) 483.034i 0.770390i
\(628\) 48.9503 + 366.549i 0.0779463 + 0.583677i
\(629\) 146.825i 0.233427i
\(630\) 448.202 + 392.327i 0.711433 + 0.622741i
\(631\) 535.698 0.848967 0.424484 0.905436i \(-0.360456\pi\)
0.424484 + 0.905436i \(0.360456\pi\)
\(632\) −66.0604 + 99.4655i −0.104526 + 0.157382i
\(633\) −138.867 −0.219379
\(634\) 535.086 + 468.379i 0.843985 + 0.738768i
\(635\) −926.114 −1.45845
\(636\) 385.802 51.5214i 0.606607 0.0810085i
\(637\) 1278.57 + 1107.91i 2.00717 + 1.73926i
\(638\) 364.661 416.596i 0.571569 0.652972i
\(639\) −77.8384 −0.121813
\(640\) 299.328 901.002i 0.467700 1.40782i
\(641\) −635.460 −0.991358 −0.495679 0.868506i \(-0.665081\pi\)
−0.495679 + 0.868506i \(0.665081\pi\)
\(642\) 174.055 198.844i 0.271113 0.309725i
\(643\) 690.793 1.07433 0.537164 0.843478i \(-0.319495\pi\)
0.537164 + 0.843478i \(0.319495\pi\)
\(644\) −128.047 + 17.0999i −0.198831 + 0.0265526i
\(645\) 130.618i 0.202509i
\(646\) −96.9967 + 110.811i −0.150150 + 0.171534i
\(647\) 1203.66i 1.86036i 0.367099 + 0.930182i \(0.380351\pi\)
−0.367099 + 0.930182i \(0.619649\pi\)
\(648\) 59.9771 + 39.8340i 0.0925572 + 0.0614723i
\(649\) 334.835 0.515925
\(650\) 773.053 107.181i 1.18931 0.164893i
\(651\) 259.722i 0.398959i
\(652\) −120.287 900.732i −0.184489 1.38149i
\(653\) −1145.08 −1.75357 −0.876784 0.480884i \(-0.840316\pi\)
−0.876784 + 0.480884i \(0.840316\pi\)
\(654\) −313.543 + 358.198i −0.479424 + 0.547703i
\(655\) 732.023 1.11759
\(656\) 149.169 + 548.542i 0.227391 + 0.836192i
\(657\) 60.8160i 0.0925662i
\(658\) −929.495 + 1061.87i −1.41261 + 1.61379i
\(659\) 462.567i 0.701922i −0.936390 0.350961i \(-0.885855\pi\)
0.936390 0.350961i \(-0.114145\pi\)
\(660\) −99.3477 743.935i −0.150527 1.12717i
\(661\) 225.809i 0.341617i −0.985304 0.170808i \(-0.945362\pi\)
0.985304 0.170808i \(-0.0546379\pi\)
\(662\) 437.809 500.162i 0.661343 0.755532i
\(663\) 56.8616 65.6203i 0.0857641 0.0989748i
\(664\) −23.0836 15.3311i −0.0347645 0.0230890i
\(665\) 1895.65i 2.85060i
\(666\) 171.898 + 150.468i 0.258105 + 0.225928i
\(667\) 45.7359i 0.0685695i
\(668\) 111.074 + 831.746i 0.166279 + 1.24513i
\(669\) 476.081i 0.711632i
\(670\) −303.267 265.460i −0.452637 0.396209i
\(671\) 33.0086 0.0491932
\(672\) 666.846 + 325.009i 0.992330 + 0.483645i
\(673\) −320.086 −0.475611 −0.237805 0.971313i \(-0.576428\pi\)
−0.237805 + 0.971313i \(0.576428\pi\)
\(674\) 552.884 631.626i 0.820303 0.937131i
\(675\) 155.974i 0.231073i
\(676\) 650.501 183.914i 0.962280 0.272062i
\(677\) 401.560 0.593146 0.296573 0.955010i \(-0.404156\pi\)
0.296573 + 0.955010i \(0.404156\pi\)
\(678\) −439.361 384.588i −0.648025 0.567239i
\(679\) 2183.53i 3.21580i
\(680\) 126.596 190.613i 0.186171 0.280313i
\(681\) 459.554i 0.674823i
\(682\) −215.546 + 246.244i −0.316050 + 0.361062i
\(683\) −1349.93 −1.97647 −0.988233 0.152954i \(-0.951121\pi\)
−0.988233 + 0.152954i \(0.951121\pi\)
\(684\) −30.3305 227.121i −0.0443428 0.332048i
\(685\) 716.316 1.04572
\(686\) −1430.56 + 1634.30i −2.08536 + 2.38236i
\(687\) 415.396 0.604652
\(688\) 42.6865 + 156.972i 0.0620443 + 0.228157i
\(689\) 551.950 + 478.278i 0.801089 + 0.694163i
\(690\) −46.6523 40.8363i −0.0676120 0.0591831i
\(691\) 357.059 0.516728 0.258364 0.966048i \(-0.416817\pi\)
0.258364 + 0.966048i \(0.416817\pi\)
\(692\) −162.827 1219.28i −0.235300 1.76197i
\(693\) 586.435 0.846226
\(694\) −509.637 446.102i −0.734347 0.642799i
\(695\) 1879.73 2.70464
\(696\) −145.303 + 218.779i −0.208769 + 0.314338i
\(697\) 137.007i 0.196566i
\(698\) −303.574 265.729i −0.434920 0.380700i
\(699\) 49.7412i 0.0711605i
\(700\) 212.721 + 1592.89i 0.303887 + 2.27556i
\(701\) 878.148 1.25271 0.626354 0.779539i \(-0.284546\pi\)
0.626354 + 0.779539i \(0.284546\pi\)
\(702\) 18.5536 + 133.820i 0.0264296 + 0.190627i
\(703\) 727.033i 1.03419i
\(704\) −362.512 861.565i −0.514932 1.22381i
\(705\) −677.297 −0.960705
\(706\) −322.127 281.969i −0.456271 0.399389i
\(707\) −607.286 −0.858961
\(708\) −157.438 + 21.0248i −0.222370 + 0.0296961i
\(709\) 939.736i 1.32544i −0.748868 0.662719i \(-0.769402\pi\)
0.748868 0.662719i \(-0.230598\pi\)
\(710\) −289.622 253.516i −0.407918 0.357064i
\(711\) 44.7766i 0.0629769i
\(712\) 652.430 982.348i 0.916335 1.37970i
\(713\) 27.0338i 0.0379156i
\(714\) 134.532 + 117.760i 0.188420 + 0.164930i
\(715\) 922.255 1064.31i 1.28987 1.48855i
\(716\) 1267.14 169.218i 1.76975 0.236338i
\(717\) 92.7897i 0.129414i
\(718\) 58.1473 66.4287i 0.0809851 0.0925191i
\(719\) 570.999i 0.794157i −0.917785 0.397078i \(-0.870024\pi\)
0.917785 0.397078i \(-0.129976\pi\)
\(720\) 93.4257 + 343.557i 0.129758 + 0.477162i
\(721\) 1422.29i 1.97266i
\(722\) −4.75415 + 5.43124i −0.00658469 + 0.00752249i
\(723\) 98.5409 0.136294
\(724\) −125.935 943.029i −0.173944 1.30253i
\(725\) −568.949 −0.784757
\(726\) −240.607 210.612i −0.331415 0.290099i
\(727\) 754.407i 1.03770i 0.854866 + 0.518849i \(0.173639\pi\)
−0.854866 + 0.518849i \(0.826361\pi\)
\(728\) 371.986 + 1341.34i 0.510970 + 1.84250i
\(729\) −27.0000 −0.0370370
\(730\) 198.075 226.285i 0.271335 0.309979i
\(731\) 39.2062i 0.0536337i
\(732\) −15.5205 + 2.07266i −0.0212029 + 0.00283151i
\(733\) 360.331i 0.491584i −0.969323 0.245792i \(-0.920952\pi\)
0.969323 0.245792i \(-0.0790480\pi\)
\(734\) 784.014 + 686.274i 1.06814 + 0.934978i
\(735\) −1671.92 −2.27473
\(736\) −69.4103 33.8294i −0.0943075 0.0459638i
\(737\) −396.799 −0.538397
\(738\) −160.403 140.406i −0.217348 0.190252i
\(739\) −112.666 −0.152458 −0.0762290 0.997090i \(-0.524288\pi\)
−0.0762290 + 0.997090i \(0.524288\pi\)
\(740\) 149.532 + 1119.72i 0.202070 + 1.51314i
\(741\) 281.561 324.931i 0.379974 0.438504i
\(742\) −990.513 + 1131.58i −1.33492 + 1.52504i
\(743\) −553.113 −0.744431 −0.372216 0.928146i \(-0.621402\pi\)
−0.372216 + 0.928146i \(0.621402\pi\)
\(744\) 85.8867 129.317i 0.115439 0.173814i
\(745\) −643.749 −0.864092
\(746\) −55.4604 + 63.3591i −0.0743437 + 0.0849318i
\(747\) 10.3916 0.0139111
\(748\) −29.8200 223.298i −0.0398664 0.298527i
\(749\) 1021.03i 1.36319i
\(750\) −84.9093 + 97.0021i −0.113212 + 0.129336i
\(751\) 871.208i 1.16006i −0.814594 0.580032i \(-0.803040\pi\)
0.814594 0.580032i \(-0.196960\pi\)
\(752\) −813.949 + 221.343i −1.08238 + 0.294339i
\(753\) −1.22721 −0.00162976
\(754\) −488.137 + 67.6782i −0.647397 + 0.0897589i
\(755\) 1454.49i 1.92648i
\(756\) −275.739 + 36.8232i −0.364734 + 0.0487079i
\(757\) 360.627 0.476390 0.238195 0.971217i \(-0.423444\pi\)
0.238195 + 0.971217i \(0.423444\pi\)
\(758\) 403.925 461.452i 0.532882 0.608776i
\(759\) −61.0405 −0.0804223
\(760\) 626.866 943.856i 0.824824 1.24192i
\(761\) 925.537i 1.21621i −0.793856 0.608106i \(-0.791930\pi\)
0.793856 0.608106i \(-0.208070\pi\)
\(762\) 284.878 325.450i 0.373855 0.427100i
\(763\) 1839.28i 2.41059i
\(764\) −17.0284 + 2.27403i −0.0222885 + 0.00297648i
\(765\) 85.8086i 0.112168i
\(766\) −476.962 + 544.892i −0.622666 + 0.711347i
\(767\) −225.240 195.176i −0.293663 0.254466i
\(768\) 224.551 + 382.341i 0.292384 + 0.497840i
\(769\) 106.770i 0.138842i 0.997587 + 0.0694211i \(0.0221152\pi\)
−0.997587 + 0.0694211i \(0.977885\pi\)
\(770\) 2182.01 + 1909.99i 2.83378 + 2.48050i
\(771\) 261.916i 0.339710i
\(772\) −1489.80 + 198.953i −1.92979 + 0.257711i
\(773\) 118.583i 0.153406i −0.997054 0.0767032i \(-0.975561\pi\)
0.997054 0.0767032i \(-0.0244394\pi\)
\(774\) −45.9012 40.1789i −0.0593039 0.0519107i
\(775\) 336.298 0.433933
\(776\) −722.065 + 1087.19i −0.930496 + 1.40102i
\(777\) −882.665 −1.13599
\(778\) 285.516 326.180i 0.366988 0.419255i
\(779\) 678.415i 0.870879i
\(780\) −366.810 + 558.346i −0.470269 + 0.715828i
\(781\) −378.945 −0.485205
\(782\) −14.0031 12.2574i −0.0179067 0.0156744i
\(783\) 98.4884i 0.125783i
\(784\) −2009.25 + 546.390i −2.56282 + 0.696926i
\(785\) 685.741i 0.873556i
\(786\) −225.174 + 257.244i −0.286481 + 0.327282i
\(787\) 1328.64 1.68823 0.844117 0.536160i \(-0.180126\pi\)
0.844117 + 0.536160i \(0.180126\pi\)
\(788\) 214.602 28.6587i 0.272337 0.0363689i
\(789\) −373.198 −0.473001
\(790\) 145.835 166.605i 0.184601 0.210892i
\(791\) 2256.04 2.85214
\(792\) 291.990 + 193.926i 0.368674 + 0.244856i
\(793\) −22.2045 19.2407i −0.0280006 0.0242632i
\(794\) −282.608 247.376i −0.355929 0.311557i
\(795\) −721.760 −0.907874
\(796\) 562.804 75.1588i 0.707040 0.0944206i
\(797\) −1194.46 −1.49869 −0.749347 0.662178i \(-0.769632\pi\)
−0.749347 + 0.662178i \(0.769632\pi\)
\(798\) 666.159 + 583.112i 0.834786 + 0.730717i
\(799\) −203.296 −0.254439
\(800\) −420.834 + 863.456i −0.526042 + 1.07932i
\(801\) 442.225i 0.552092i
\(802\) 393.056 + 344.055i 0.490094 + 0.428996i
\(803\) 296.074i 0.368710i
\(804\) 186.573 24.9156i 0.232056 0.0309896i
\(805\) 239.551 0.297579
\(806\) 288.531 40.0036i 0.357979 0.0496323i
\(807\) 512.746i 0.635373i
\(808\) −302.372 200.821i −0.374222 0.248541i
\(809\) 466.988 0.577241 0.288621 0.957444i \(-0.406803\pi\)
0.288621 + 0.957444i \(0.406803\pi\)
\(810\) −100.462 87.9376i −0.124027 0.108565i
\(811\) −1484.79 −1.83081 −0.915407 0.402530i \(-0.868131\pi\)
−0.915407 + 0.402530i \(0.868131\pi\)
\(812\) −134.320 1005.82i −0.165419 1.23869i
\(813\) 392.722i 0.483053i
\(814\) 836.860 + 732.532i 1.02808 + 0.899917i
\(815\) 1685.09i 2.06760i
\(816\) 28.0425 + 103.121i 0.0343658 + 0.126374i
\(817\) 194.137i 0.237622i
\(818\) −694.005 607.486i −0.848416 0.742648i
\(819\) −394.487 341.833i −0.481670 0.417379i
\(820\) −139.532 1044.85i −0.170162 1.27420i
\(821\) 1560.92i 1.90124i 0.310357 + 0.950620i \(0.399551\pi\)
−0.310357 + 0.950620i \(0.600449\pi\)
\(822\) −220.343 + 251.724i −0.268057 + 0.306234i
\(823\) 800.989i 0.973255i −0.873610 0.486627i \(-0.838227\pi\)
0.873610 0.486627i \(-0.161773\pi\)
\(824\) 470.332 708.167i 0.570792 0.859426i
\(825\) 759.337i 0.920409i
\(826\) 404.208 461.776i 0.489356 0.559051i
\(827\) 324.850 0.392805 0.196402 0.980523i \(-0.437074\pi\)
0.196402 + 0.980523i \(0.437074\pi\)
\(828\) 28.7010 3.83283i 0.0346630 0.00462902i
\(829\) −1114.31 −1.34416 −0.672078 0.740480i \(-0.734598\pi\)
−0.672078 + 0.740480i \(0.734598\pi\)
\(830\) 38.6651 + 33.8449i 0.0465845 + 0.0407770i
\(831\) 99.1688i 0.119337i
\(832\) −258.349 + 790.873i −0.310516 + 0.950568i
\(833\) −501.842 −0.602452
\(834\) −578.214 + 660.564i −0.693302 + 0.792043i
\(835\) 1556.03i 1.86351i
\(836\) −147.660 1105.70i −0.176626 1.32261i
\(837\) 58.2151i 0.0695521i
\(838\) 456.781 + 399.836i 0.545085 + 0.477131i
\(839\) 362.224 0.431733 0.215867 0.976423i \(-0.430742\pi\)
0.215867 + 0.976423i \(0.430742\pi\)
\(840\) −1145.90 761.056i −1.36417 0.906019i
\(841\) −481.742 −0.572821
\(842\) 697.198 + 610.281i 0.828026 + 0.724800i
\(843\) 293.783 0.348498
\(844\) 317.878 42.4505i 0.376632 0.0502968i
\(845\) −1240.78 + 178.369i −1.46838 + 0.211087i
\(846\) 208.340 238.012i 0.246265 0.281338i
\(847\) 1235.48 1.45865
\(848\) −867.383 + 235.873i −1.02286 + 0.278152i
\(849\) 615.161 0.724572
\(850\) −152.480 + 174.197i −0.179388 + 0.204937i
\(851\) 91.8743 0.107960
\(852\) 178.178 23.7946i 0.209129 0.0279279i
\(853\) 433.461i 0.508160i −0.967183 0.254080i \(-0.918227\pi\)
0.967183 0.254080i \(-0.0817727\pi\)
\(854\) 39.8475 45.5226i 0.0466599 0.0533052i
\(855\) 424.898i 0.496956i
\(856\) −337.640 + 508.376i −0.394439 + 0.593897i
\(857\) 287.654 0.335653 0.167826 0.985817i \(-0.446325\pi\)
0.167826 + 0.985817i \(0.446325\pi\)
\(858\) 90.3255 + 651.483i 0.105274 + 0.759304i
\(859\) 385.620i 0.448917i −0.974484 0.224459i \(-0.927939\pi\)
0.974484 0.224459i \(-0.0720614\pi\)
\(860\) −39.9289 298.996i −0.0464290 0.347670i
\(861\) 823.639 0.956608
\(862\) 573.420 655.087i 0.665220 0.759961i
\(863\) 1384.23 1.60397 0.801985 0.597344i \(-0.203777\pi\)
0.801985 + 0.597344i \(0.203777\pi\)
\(864\) −149.469 72.8488i −0.172997 0.0843157i
\(865\) 2281.04i 2.63704i
\(866\) 345.166 394.325i 0.398575 0.455340i
\(867\) 474.806i 0.547643i
\(868\) 79.3949 + 594.525i 0.0914688 + 0.684936i
\(869\) 217.988i 0.250850i
\(870\) 320.771 366.456i 0.368703 0.421214i
\(871\) 266.922 + 231.294i 0.306454 + 0.265550i
\(872\) 608.227 915.791i 0.697508 1.05022i
\(873\) 489.425i 0.560624i
\(874\) −69.3388 60.6946i −0.0793350 0.0694447i
\(875\) 498.089i 0.569244i
\(876\) 18.5910 + 139.213i 0.0212225 + 0.158919i
\(877\) 983.819i 1.12180i −0.827883 0.560900i \(-0.810455\pi\)
0.827883 0.560900i \(-0.189545\pi\)
\(878\) 163.926 + 143.490i 0.186704 + 0.163428i
\(879\) 839.143 0.954657
\(880\) 454.830 + 1672.56i 0.516852 + 1.90063i
\(881\) 762.632 0.865644 0.432822 0.901479i \(-0.357518\pi\)
0.432822 + 0.901479i \(0.357518\pi\)
\(882\) 514.293 587.539i 0.583099 0.666144i
\(883\) 1129.18i 1.27879i 0.768877 + 0.639397i \(0.220816\pi\)
−0.768877 + 0.639397i \(0.779184\pi\)
\(884\) −110.101 + 167.592i −0.124549 + 0.189584i
\(885\) 294.535 0.332808
\(886\) 235.284 + 205.952i 0.265558 + 0.232452i
\(887\) 1424.54i 1.60602i −0.595963 0.803012i \(-0.703229\pi\)
0.595963 0.803012i \(-0.296771\pi\)
\(888\) −439.485 291.886i −0.494915 0.328700i
\(889\) 1671.13i 1.87978i
\(890\) −1440.30 + 1645.43i −1.61832 + 1.84880i
\(891\) −131.446 −0.147526
\(892\) 145.534 + 1089.79i 0.163155 + 1.22174i
\(893\) −1006.66 −1.12728
\(894\) 198.021 226.223i 0.221500 0.253046i
\(895\) −2370.56 −2.64868
\(896\) −1625.82 540.123i −1.81453 0.602816i
\(897\) 41.0612 + 35.5805i 0.0457761 + 0.0396661i
\(898\) −9.79757 8.57615i −0.0109104 0.00955028i
\(899\) −212.352 −0.236209
\(900\) −47.6800 357.037i −0.0529777 0.396708i
\(901\) −216.642 −0.240446
\(902\) −780.898 683.546i −0.865740 0.757812i
\(903\) 235.695 0.261013
\(904\) 1123.30 + 746.043i 1.24259 + 0.825269i
\(905\) 1764.22i 1.94941i
\(906\) −511.130 447.410i −0.564161 0.493830i
\(907\) 844.091i 0.930641i 0.885142 + 0.465320i \(0.154061\pi\)
−0.885142 + 0.465320i \(0.845939\pi\)
\(908\) 140.482 + 1051.96i 0.154716 + 1.15854i
\(909\) 136.119 0.149746
\(910\) −354.479 2556.72i −0.389537 2.80958i
\(911\) 1205.50i 1.32327i 0.749826 + 0.661635i \(0.230137\pi\)
−0.749826 + 0.661635i \(0.769863\pi\)
\(912\) 138.858 + 510.625i 0.152256 + 0.559896i
\(913\) 50.5900 0.0554108
\(914\) −171.662 150.262i −0.187814 0.164400i
\(915\) 29.0358 0.0317331
\(916\) −950.874 + 126.983i −1.03807 + 0.138628i
\(917\) 1320.90i 1.44046i
\(918\) −30.1544 26.3952i −0.0328480 0.0287529i
\(919\) 38.0600i 0.0414146i −0.999786 0.0207073i \(-0.993408\pi\)
0.999786 0.0207073i \(-0.00659181\pi\)
\(920\) 119.274 + 79.2164i 0.129646 + 0.0861047i
\(921\) 311.625i 0.338355i
\(922\) −522.062 456.979i −0.566228 0.495638i
\(923\) 254.912 + 220.887i 0.276177 + 0.239314i
\(924\) −1342.40 + 179.268i −1.45281 + 0.194013i
\(925\) 1142.91i 1.23557i
\(926\) −735.524 + 840.278i −0.794302 + 0.907428i
\(927\) 318.797i 0.343902i
\(928\) 265.732 545.222i 0.286349 0.587523i
\(929\) 160.346i 0.172601i 0.996269 + 0.0863005i \(0.0275045\pi\)
−0.996269 + 0.0863005i \(0.972495\pi\)
\(930\) −189.603 + 216.607i −0.203875 + 0.232911i
\(931\) −2484.97 −2.66914
\(932\) 15.2055 + 113.861i 0.0163149 + 0.122169i
\(933\) 16.4649 0.0176473
\(934\) 708.764 + 620.405i 0.758848 + 0.664246i
\(935\) 417.747i 0.446788i
\(936\) −83.3783 300.653i −0.0890793 0.321210i
\(937\) 1656.50 1.76787 0.883937 0.467605i \(-0.154883\pi\)
0.883937 + 0.467605i \(0.154883\pi\)
\(938\) −479.010 + 547.231i −0.510671 + 0.583401i
\(939\) 116.748i 0.124333i
\(940\) 1550.39 207.044i 1.64935 0.220260i
\(941\) 561.474i 0.596678i −0.954460 0.298339i \(-0.903567\pi\)
0.954460 0.298339i \(-0.0964326\pi\)
\(942\) 240.980 + 210.938i 0.255817 + 0.223925i
\(943\) −85.7305 −0.0909125
\(944\) 353.961 96.2550i 0.374959 0.101965i
\(945\) 515.853 0.545876
\(946\) −223.464 195.605i −0.236219 0.206771i
\(947\) −221.394 −0.233785 −0.116892 0.993145i \(-0.537293\pi\)
−0.116892 + 0.993145i \(0.537293\pi\)
\(948\) 13.6878 + 102.497i 0.0144386 + 0.108119i
\(949\) −172.582 + 199.165i −0.181856 + 0.209869i
\(950\) −755.034 + 862.567i −0.794773 + 0.907965i
\(951\) 615.851 0.647582
\(952\) −343.952 228.437i −0.361294 0.239955i
\(953\) 1070.55 1.12335 0.561673 0.827360i \(-0.310158\pi\)
0.561673 + 0.827360i \(0.310158\pi\)
\(954\) 222.017 253.637i 0.232722 0.265867i
\(955\) 31.8568 0.0333579
\(956\) −28.3651 212.403i −0.0296706 0.222179i
\(957\) 479.476i 0.501020i
\(958\) −261.540 + 298.789i −0.273006 + 0.311888i
\(959\) 1292.56i 1.34782i
\(960\) −318.881 757.870i −0.332168 0.789447i
\(961\) −835.482 −0.869388
\(962\) −135.952 980.571i −0.141322 1.01930i
\(963\) 228.857i 0.237650i
\(964\) −225.568 + 30.1231i −0.233992 + 0.0312481i
\(965\) 2787.12 2.88821
\(966\) −73.6872 + 84.1818i −0.0762807 + 0.0871447i
\(967\) 856.229 0.885449 0.442724 0.896658i \(-0.354012\pi\)
0.442724 + 0.896658i \(0.354012\pi\)
\(968\) 615.152 + 408.556i 0.635488 + 0.422062i
\(969\) 127.537i 0.131617i
\(970\) 1594.03 1821.05i 1.64333 1.87738i
\(971\) 505.753i 0.520858i −0.965493 0.260429i \(-0.916136\pi\)
0.965493 0.260429i \(-0.0838640\pi\)
\(972\) 61.8052 8.25368i 0.0635855 0.00849144i
\(973\) 3391.88i 3.48600i
\(974\) −55.6236 + 63.5456i −0.0571084 + 0.0652419i
\(975\) 442.618 510.797i 0.453967 0.523894i
\(976\) 34.8941 9.48898i 0.0357521 0.00972232i
\(977\) 1308.46i 1.33927i 0.742693 + 0.669633i \(0.233548\pi\)
−0.742693 + 0.669633i \(0.766452\pi\)
\(978\) −592.166 518.343i −0.605487 0.530003i
\(979\) 2152.91i 2.19909i
\(980\) 3827.17 511.094i 3.90527 0.521524i
\(981\) 412.264i 0.420248i
\(982\) 239.406 + 209.560i 0.243794 + 0.213401i
\(983\) 99.6372 0.101360 0.0506802 0.998715i \(-0.483861\pi\)
0.0506802 + 0.998715i \(0.483861\pi\)
\(984\) 410.096 + 272.367i 0.416764 + 0.276795i
\(985\) −401.477 −0.407591
\(986\) 96.2822 109.995i 0.0976493 0.111557i
\(987\) 1222.15i 1.23825i
\(988\) −545.186 + 829.864i −0.551808 + 0.839944i
\(989\) −24.5329 −0.0248057
\(990\) −489.084 428.111i −0.494024 0.432436i
\(991\) 1381.79i 1.39434i −0.716906 0.697170i \(-0.754442\pi\)
0.716906 0.697170i \(-0.245558\pi\)
\(992\) −157.070 + 322.273i −0.158337 + 0.324872i
\(993\) 575.656i 0.579714i
\(994\) −457.457 + 522.608i −0.460218 + 0.525763i
\(995\) −1052.89 −1.05819
\(996\) −23.7872 + 3.17663i −0.0238827 + 0.00318938i
\(997\) −1498.53 −1.50304 −0.751518 0.659713i \(-0.770678\pi\)
−0.751518 + 0.659713i \(0.770678\pi\)
\(998\) 62.9929 71.9644i 0.0631191 0.0721086i
\(999\) 197.844 0.198042
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.103.8 yes 24
3.2 odd 2 468.3.e.m.415.17 24
4.3 odd 2 inner 156.3.e.c.103.18 yes 24
12.11 even 2 468.3.e.m.415.7 24
13.12 even 2 inner 156.3.e.c.103.17 yes 24
39.38 odd 2 468.3.e.m.415.8 24
52.51 odd 2 inner 156.3.e.c.103.7 24
156.155 even 2 468.3.e.m.415.18 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
156.3.e.c.103.7 24 52.51 odd 2 inner
156.3.e.c.103.8 yes 24 1.1 even 1 trivial
156.3.e.c.103.17 yes 24 13.12 even 2 inner
156.3.e.c.103.18 yes 24 4.3 odd 2 inner
468.3.e.m.415.7 24 12.11 even 2
468.3.e.m.415.8 24 39.38 odd 2
468.3.e.m.415.17 24 3.2 odd 2
468.3.e.m.415.18 24 156.155 even 2