Properties

Label 261.3.s.a.172.3
Level $261$
Weight $3$
Character 261.172
Analytic conductor $7.112$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [261,3,Mod(10,261)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(261, base_ring=CyclotomicField(28))
 
chi = DirichletCharacter(H, H._module([0, 23]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("261.10");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 261.s (of order \(28\), degree \(12\), 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: \(7.11173489980\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{28})\)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 172.3
Character \(\chi\) \(=\) 261.172
Dual form 261.3.s.a.217.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.170607 - 1.51418i) q^{2} +(1.63608 + 0.373424i) q^{4} +(5.91405 - 4.71630i) q^{5} +(-1.42870 - 6.25955i) q^{7} +(2.85762 - 8.16662i) q^{8} +O(q^{10})\) \(q+(0.170607 - 1.51418i) q^{2} +(1.63608 + 0.373424i) q^{4} +(5.91405 - 4.71630i) q^{5} +(-1.42870 - 6.25955i) q^{7} +(2.85762 - 8.16662i) q^{8} +(-6.13235 - 9.75958i) q^{10} +(5.33282 + 15.2403i) q^{11} +(-5.47235 + 11.3635i) q^{13} +(-9.72184 + 1.09539i) q^{14} +(-5.83035 - 2.80775i) q^{16} +(-11.5542 - 11.5542i) q^{17} +(12.1000 - 7.60291i) q^{19} +(11.4370 - 5.50778i) q^{20} +(23.9864 - 5.47475i) q^{22} +(2.84328 - 3.56536i) q^{23} +(7.16951 - 31.4117i) q^{25} +(16.2727 + 10.2248i) q^{26} -10.7746i q^{28} +(-23.5053 + 16.9853i) q^{29} +(-1.32747 + 11.7816i) q^{31} +(13.1667 - 20.9547i) q^{32} +(-19.4664 + 15.5239i) q^{34} +(-37.9713 - 30.2811i) q^{35} +(2.68961 - 7.68647i) q^{37} +(-9.44783 - 19.6186i) q^{38} +(-21.6161 - 61.7752i) q^{40} +(-10.8682 + 10.8682i) q^{41} +(-41.8092 + 4.71076i) q^{43} +(3.03380 + 26.9258i) q^{44} +(-4.91352 - 4.91352i) q^{46} +(28.2097 - 9.87101i) q^{47} +(7.00665 - 3.37423i) q^{49} +(-46.3398 - 16.2150i) q^{50} +(-13.1966 + 16.5480i) q^{52} +(25.1303 + 31.5124i) q^{53} +(103.417 + 64.9809i) q^{55} +(-55.2021 - 6.21978i) q^{56} +(21.7087 + 38.4890i) q^{58} +72.0544 q^{59} +(-36.0211 + 57.3273i) q^{61} +(17.6131 + 4.02006i) q^{62} +(-49.7205 - 39.6508i) q^{64} +(21.2297 + 93.0134i) q^{65} +(-40.9142 - 84.9592i) q^{67} +(-14.5890 - 23.2182i) q^{68} +(-52.3293 + 52.3293i) q^{70} +(-13.8330 + 28.7244i) q^{71} +(14.9474 + 132.662i) q^{73} +(-11.1798 - 5.38392i) q^{74} +(22.6356 - 7.92053i) q^{76} +(87.7787 - 55.1550i) q^{77} +(82.9084 + 29.0109i) q^{79} +(-47.7232 + 10.8925i) q^{80} +(14.6022 + 18.3106i) q^{82} +(14.4328 - 63.2343i) q^{83} +(-122.825 - 13.8391i) q^{85} +64.1103i q^{86} +139.701 q^{88} +(-10.8152 + 95.9875i) q^{89} +(78.9486 + 18.0195i) q^{91} +(5.98322 - 4.77146i) q^{92} +(-10.1337 - 44.3987i) q^{94} +(35.7022 - 102.031i) q^{95} +(63.6202 + 101.251i) q^{97} +(-3.91380 - 11.1850i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/261\mathbb{Z}\right)^\times\).

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{15}{28}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.170607 1.51418i 0.0853036 0.757090i −0.876134 0.482067i \(-0.839886\pi\)
0.961438 0.275023i \(-0.0886854\pi\)
\(3\) 0 0
\(4\) 1.63608 + 0.373424i 0.409019 + 0.0933560i
\(5\) 5.91405 4.71630i 1.18281 0.943260i 0.183600 0.983001i \(-0.441225\pi\)
0.999210 + 0.0397411i \(0.0126533\pi\)
\(6\) 0 0
\(7\) −1.42870 6.25955i −0.204100 0.894222i −0.968408 0.249370i \(-0.919776\pi\)
0.764308 0.644852i \(-0.223081\pi\)
\(8\) 2.85762 8.16662i 0.357203 1.02083i
\(9\) 0 0
\(10\) −6.13235 9.75958i −0.613235 0.975958i
\(11\) 5.33282 + 15.2403i 0.484802 + 1.38548i 0.883512 + 0.468408i \(0.155172\pi\)
−0.398710 + 0.917077i \(0.630542\pi\)
\(12\) 0 0
\(13\) −5.47235 + 11.3635i −0.420950 + 0.874112i 0.577387 + 0.816471i \(0.304072\pi\)
−0.998337 + 0.0576417i \(0.981642\pi\)
\(14\) −9.72184 + 1.09539i −0.694417 + 0.0782420i
\(15\) 0 0
\(16\) −5.83035 2.80775i −0.364397 0.175484i
\(17\) −11.5542 11.5542i −0.679659 0.679659i 0.280264 0.959923i \(-0.409578\pi\)
−0.959923 + 0.280264i \(0.909578\pi\)
\(18\) 0 0
\(19\) 12.1000 7.60291i 0.636840 0.400153i −0.174558 0.984647i \(-0.555850\pi\)
0.811398 + 0.584494i \(0.198707\pi\)
\(20\) 11.4370 5.50778i 0.571851 0.275389i
\(21\) 0 0
\(22\) 23.9864 5.47475i 1.09029 0.248852i
\(23\) 2.84328 3.56536i 0.123621 0.155016i −0.716170 0.697926i \(-0.754106\pi\)
0.839791 + 0.542910i \(0.182678\pi\)
\(24\) 0 0
\(25\) 7.16951 31.4117i 0.286780 1.25647i
\(26\) 16.2727 + 10.2248i 0.625873 + 0.393262i
\(27\) 0 0
\(28\) 10.7746i 0.384808i
\(29\) −23.5053 + 16.9853i −0.810527 + 0.585702i
\(30\) 0 0
\(31\) −1.32747 + 11.7816i −0.0428217 + 0.380053i 0.953963 + 0.299925i \(0.0969616\pi\)
−0.996785 + 0.0801282i \(0.974467\pi\)
\(32\) 13.1667 20.9547i 0.411461 0.654836i
\(33\) 0 0
\(34\) −19.4664 + 15.5239i −0.572541 + 0.456586i
\(35\) −37.9713 30.2811i −1.08490 0.865175i
\(36\) 0 0
\(37\) 2.68961 7.68647i 0.0726922 0.207742i −0.901804 0.432144i \(-0.857757\pi\)
0.974497 + 0.224402i \(0.0720428\pi\)
\(38\) −9.44783 19.6186i −0.248627 0.516280i
\(39\) 0 0
\(40\) −21.6161 61.7752i −0.540402 1.54438i
\(41\) −10.8682 + 10.8682i −0.265077 + 0.265077i −0.827113 0.562036i \(-0.810018\pi\)
0.562036 + 0.827113i \(0.310018\pi\)
\(42\) 0 0
\(43\) −41.8092 + 4.71076i −0.972307 + 0.109553i −0.583804 0.811895i \(-0.698436\pi\)
−0.388503 + 0.921447i \(0.627008\pi\)
\(44\) 3.03380 + 26.9258i 0.0689501 + 0.611949i
\(45\) 0 0
\(46\) −4.91352 4.91352i −0.106816 0.106816i
\(47\) 28.2097 9.87101i 0.600207 0.210022i −0.0130369 0.999915i \(-0.504150\pi\)
0.613244 + 0.789893i \(0.289864\pi\)
\(48\) 0 0
\(49\) 7.00665 3.37423i 0.142993 0.0688618i
\(50\) −46.3398 16.2150i −0.926796 0.324300i
\(51\) 0 0
\(52\) −13.1966 + 16.5480i −0.253780 + 0.318230i
\(53\) 25.1303 + 31.5124i 0.474157 + 0.594574i 0.960184 0.279370i \(-0.0901255\pi\)
−0.486026 + 0.873944i \(0.661554\pi\)
\(54\) 0 0
\(55\) 103.417 + 64.9809i 1.88030 + 1.18147i
\(56\) −55.2021 6.21978i −0.985751 0.111068i
\(57\) 0 0
\(58\) 21.7087 + 38.4890i 0.374288 + 0.663604i
\(59\) 72.0544 1.22126 0.610631 0.791915i \(-0.290916\pi\)
0.610631 + 0.791915i \(0.290916\pi\)
\(60\) 0 0
\(61\) −36.0211 + 57.3273i −0.590510 + 0.939791i 0.409117 + 0.912482i \(0.365837\pi\)
−0.999627 + 0.0273095i \(0.991306\pi\)
\(62\) 17.6131 + 4.02006i 0.284081 + 0.0648397i
\(63\) 0 0
\(64\) −49.7205 39.6508i −0.776883 0.619543i
\(65\) 21.2297 + 93.0134i 0.326611 + 1.43097i
\(66\) 0 0
\(67\) −40.9142 84.9592i −0.610659 1.26805i −0.945454 0.325756i \(-0.894381\pi\)
0.334794 0.942291i \(-0.391333\pi\)
\(68\) −14.5890 23.2182i −0.214543 0.341444i
\(69\) 0 0
\(70\) −52.3293 + 52.3293i −0.747561 + 0.747561i
\(71\) −13.8330 + 28.7244i −0.194830 + 0.404570i −0.975382 0.220522i \(-0.929224\pi\)
0.780552 + 0.625091i \(0.214938\pi\)
\(72\) 0 0
\(73\) 14.9474 + 132.662i 0.204758 + 1.81728i 0.504668 + 0.863313i \(0.331615\pi\)
−0.299910 + 0.953968i \(0.596957\pi\)
\(74\) −11.1798 5.38392i −0.151079 0.0727557i
\(75\) 0 0
\(76\) 22.6356 7.92053i 0.297836 0.104217i
\(77\) 87.7787 55.1550i 1.13998 0.716299i
\(78\) 0 0
\(79\) 82.9084 + 29.0109i 1.04947 + 0.367227i 0.799274 0.600967i \(-0.205218\pi\)
0.250200 + 0.968194i \(0.419504\pi\)
\(80\) −47.7232 + 10.8925i −0.596540 + 0.136156i
\(81\) 0 0
\(82\) 14.6022 + 18.3106i 0.178075 + 0.223300i
\(83\) 14.4328 63.2343i 0.173889 0.761859i −0.810483 0.585762i \(-0.800795\pi\)
0.984373 0.176098i \(-0.0563475\pi\)
\(84\) 0 0
\(85\) −122.825 13.8391i −1.44500 0.162813i
\(86\) 64.1103i 0.745469i
\(87\) 0 0
\(88\) 139.701 1.58751
\(89\) −10.8152 + 95.9875i −0.121519 + 1.07851i 0.773907 + 0.633300i \(0.218300\pi\)
−0.895426 + 0.445211i \(0.853129\pi\)
\(90\) 0 0
\(91\) 78.9486 + 18.0195i 0.867567 + 0.198016i
\(92\) 5.98322 4.77146i 0.0650350 0.0518637i
\(93\) 0 0
\(94\) −10.1337 44.3987i −0.107805 0.472327i
\(95\) 35.7022 102.031i 0.375813 1.07401i
\(96\) 0 0
\(97\) 63.6202 + 101.251i 0.655879 + 1.04382i 0.994685 + 0.102969i \(0.0328341\pi\)
−0.338806 + 0.940856i \(0.610023\pi\)
\(98\) −3.91380 11.1850i −0.0399367 0.114133i
\(99\) 0 0
\(100\) 23.4597 48.7146i 0.234597 0.487146i
\(101\) −44.5062 + 5.01465i −0.440656 + 0.0496500i −0.329505 0.944154i \(-0.606882\pi\)
−0.111150 + 0.993804i \(0.535453\pi\)
\(102\) 0 0
\(103\) −58.9299 28.3791i −0.572135 0.275526i 0.125365 0.992111i \(-0.459990\pi\)
−0.697500 + 0.716585i \(0.745704\pi\)
\(104\) 77.1631 + 77.1631i 0.741953 + 0.741953i
\(105\) 0 0
\(106\) 52.0029 32.6756i 0.490594 0.308260i
\(107\) −73.6724 + 35.4788i −0.688527 + 0.331577i −0.745224 0.666814i \(-0.767657\pi\)
0.0566968 + 0.998391i \(0.481943\pi\)
\(108\) 0 0
\(109\) −70.6783 + 16.1319i −0.648425 + 0.147999i −0.534069 0.845441i \(-0.679338\pi\)
−0.114356 + 0.993440i \(0.536481\pi\)
\(110\) 116.036 145.505i 1.05488 1.32277i
\(111\) 0 0
\(112\) −9.24542 + 40.5068i −0.0825484 + 0.361668i
\(113\) 32.1123 + 20.1775i 0.284180 + 0.178562i 0.666577 0.745436i \(-0.267759\pi\)
−0.382397 + 0.923998i \(0.624901\pi\)
\(114\) 0 0
\(115\) 34.4955i 0.299961i
\(116\) −44.7992 + 19.0119i −0.386200 + 0.163896i
\(117\) 0 0
\(118\) 12.2930 109.103i 0.104178 0.924605i
\(119\) −55.8167 + 88.8317i −0.469048 + 0.746485i
\(120\) 0 0
\(121\) −109.227 + 87.1058i −0.902704 + 0.719882i
\(122\) 80.6584 + 64.3229i 0.661134 + 0.527237i
\(123\) 0 0
\(124\) −6.57139 + 18.7800i −0.0529951 + 0.151451i
\(125\) −23.6947 49.2026i −0.189558 0.393621i
\(126\) 0 0
\(127\) −16.1833 46.2491i −0.127427 0.364166i 0.862441 0.506158i \(-0.168935\pi\)
−0.989868 + 0.141992i \(0.954649\pi\)
\(128\) 1.47690 1.47690i 0.0115383 0.0115383i
\(129\) 0 0
\(130\) 144.461 16.2768i 1.11124 0.125206i
\(131\) 9.85869 + 87.4983i 0.0752572 + 0.667926i 0.973541 + 0.228511i \(0.0733857\pi\)
−0.898284 + 0.439415i \(0.855186\pi\)
\(132\) 0 0
\(133\) −64.8780 64.8780i −0.487805 0.487805i
\(134\) −135.624 + 47.4568i −1.01212 + 0.354155i
\(135\) 0 0
\(136\) −127.376 + 61.3412i −0.936591 + 0.451039i
\(137\) −47.1122 16.4853i −0.343885 0.120330i 0.152811 0.988255i \(-0.451168\pi\)
−0.496695 + 0.867925i \(0.665453\pi\)
\(138\) 0 0
\(139\) 3.30447 4.14367i 0.0237732 0.0298106i −0.769803 0.638282i \(-0.779645\pi\)
0.793576 + 0.608471i \(0.208217\pi\)
\(140\) −50.8163 63.7217i −0.362974 0.455155i
\(141\) 0 0
\(142\) 41.1340 + 25.8462i 0.289676 + 0.182015i
\(143\) −202.366 22.8012i −1.41515 0.159449i
\(144\) 0 0
\(145\) −58.9034 + 211.310i −0.406231 + 1.45731i
\(146\) 203.424 1.39331
\(147\) 0 0
\(148\) 7.27072 11.5713i 0.0491265 0.0781844i
\(149\) −121.378 27.7037i −0.814617 0.185931i −0.205138 0.978733i \(-0.565764\pi\)
−0.609479 + 0.792802i \(0.708621\pi\)
\(150\) 0 0
\(151\) 116.656 + 93.0300i 0.772556 + 0.616093i 0.928355 0.371696i \(-0.121224\pi\)
−0.155798 + 0.987789i \(0.549795\pi\)
\(152\) −27.5129 120.542i −0.181006 0.793039i
\(153\) 0 0
\(154\) −68.5389 142.323i −0.445058 0.924173i
\(155\) 47.7150 + 75.9380i 0.307839 + 0.489923i
\(156\) 0 0
\(157\) 112.055 112.055i 0.713725 0.713725i −0.253587 0.967312i \(-0.581611\pi\)
0.967312 + 0.253587i \(0.0816105\pi\)
\(158\) 58.0725 120.589i 0.367548 0.763221i
\(159\) 0 0
\(160\) −20.9601 186.026i −0.131000 1.16266i
\(161\) −26.3798 12.7038i −0.163850 0.0789058i
\(162\) 0 0
\(163\) −108.237 + 37.8739i −0.664033 + 0.232355i −0.641188 0.767384i \(-0.721558\pi\)
−0.0228453 + 0.999739i \(0.507273\pi\)
\(164\) −21.8396 + 13.7227i −0.133168 + 0.0836752i
\(165\) 0 0
\(166\) −93.2858 32.6421i −0.561963 0.196639i
\(167\) 39.7689 9.07699i 0.238137 0.0543532i −0.101787 0.994806i \(-0.532456\pi\)
0.339924 + 0.940453i \(0.389599\pi\)
\(168\) 0 0
\(169\) 6.18821 + 7.75977i 0.0366166 + 0.0459158i
\(170\) −41.9098 + 183.619i −0.246528 + 1.08011i
\(171\) 0 0
\(172\) −70.1622 7.90538i −0.407919 0.0459615i
\(173\) 92.8408i 0.536652i −0.963328 0.268326i \(-0.913530\pi\)
0.963328 0.268326i \(-0.0864704\pi\)
\(174\) 0 0
\(175\) −206.866 −1.18209
\(176\) 11.6988 103.830i 0.0664705 0.589942i
\(177\) 0 0
\(178\) 143.497 + 32.7523i 0.806164 + 0.184002i
\(179\) 259.613 207.034i 1.45035 1.15662i 0.492153 0.870509i \(-0.336210\pi\)
0.958198 0.286108i \(-0.0923614\pi\)
\(180\) 0 0
\(181\) −5.32646 23.3367i −0.0294279 0.128932i 0.958080 0.286500i \(-0.0924919\pi\)
−0.987508 + 0.157568i \(0.949635\pi\)
\(182\) 40.7539 116.468i 0.223923 0.639935i
\(183\) 0 0
\(184\) −20.9919 33.4085i −0.114087 0.181568i
\(185\) −20.3452 58.1432i −0.109974 0.314288i
\(186\) 0 0
\(187\) 114.473 237.707i 0.612158 1.27116i
\(188\) 49.8394 5.61555i 0.265103 0.0298699i
\(189\) 0 0
\(190\) −148.402 71.4668i −0.781065 0.376141i
\(191\) −80.4392 80.4392i −0.421147 0.421147i 0.464451 0.885599i \(-0.346252\pi\)
−0.885599 + 0.464451i \(0.846252\pi\)
\(192\) 0 0
\(193\) 185.269 116.412i 0.959941 0.603171i 0.0416731 0.999131i \(-0.486731\pi\)
0.918267 + 0.395961i \(0.129588\pi\)
\(194\) 164.166 79.0584i 0.846218 0.407517i
\(195\) 0 0
\(196\) 12.7234 2.90404i 0.0649155 0.0148165i
\(197\) −156.057 + 195.689i −0.792166 + 0.993345i 0.207719 + 0.978189i \(0.433396\pi\)
−0.999885 + 0.0151563i \(0.995175\pi\)
\(198\) 0 0
\(199\) 68.8429 301.621i 0.345944 1.51568i −0.440349 0.897827i \(-0.645145\pi\)
0.786293 0.617854i \(-0.211998\pi\)
\(200\) −236.039 148.313i −1.18020 0.741567i
\(201\) 0 0
\(202\) 68.2460i 0.337851i
\(203\) 139.903 + 122.866i 0.689176 + 0.605249i
\(204\) 0 0
\(205\) −13.0174 + 115.532i −0.0634994 + 0.563573i
\(206\) −53.0250 + 84.3888i −0.257403 + 0.409654i
\(207\) 0 0
\(208\) 63.8115 50.8880i 0.306786 0.244654i
\(209\) 180.398 + 143.862i 0.863147 + 0.688337i
\(210\) 0 0
\(211\) 15.0592 43.0368i 0.0713708 0.203966i −0.902672 0.430329i \(-0.858398\pi\)
0.974043 + 0.226363i \(0.0726834\pi\)
\(212\) 29.3477 + 60.9410i 0.138432 + 0.287458i
\(213\) 0 0
\(214\) 41.1522 + 117.606i 0.192300 + 0.549562i
\(215\) −225.044 + 225.044i −1.04672 + 1.04672i
\(216\) 0 0
\(217\) 75.6444 8.52307i 0.348592 0.0392768i
\(218\) 12.3683 + 109.772i 0.0567354 + 0.503541i
\(219\) 0 0
\(220\) 144.932 + 144.932i 0.658782 + 0.658782i
\(221\) 194.525 68.0671i 0.880202 0.307996i
\(222\) 0 0
\(223\) −125.985 + 60.6713i −0.564956 + 0.272069i −0.694485 0.719507i \(-0.744368\pi\)
0.129529 + 0.991576i \(0.458654\pi\)
\(224\) −149.979 52.4798i −0.669548 0.234285i
\(225\) 0 0
\(226\) 36.0310 45.1814i 0.159429 0.199918i
\(227\) −18.6570 23.3951i −0.0821894 0.103062i 0.739037 0.673665i \(-0.235281\pi\)
−0.821226 + 0.570603i \(0.806710\pi\)
\(228\) 0 0
\(229\) −251.179 157.826i −1.09685 0.689196i −0.143073 0.989712i \(-0.545698\pi\)
−0.953777 + 0.300516i \(0.902841\pi\)
\(230\) −52.2325 5.88518i −0.227098 0.0255878i
\(231\) 0 0
\(232\) 71.5436 + 240.496i 0.308378 + 1.03662i
\(233\) −102.836 −0.441355 −0.220678 0.975347i \(-0.570827\pi\)
−0.220678 + 0.975347i \(0.570827\pi\)
\(234\) 0 0
\(235\) 120.279 191.423i 0.511826 0.814567i
\(236\) 117.887 + 26.9068i 0.499519 + 0.114012i
\(237\) 0 0
\(238\) 124.985 + 99.6718i 0.525145 + 0.418789i
\(239\) −82.4096 361.060i −0.344810 1.51071i −0.788783 0.614671i \(-0.789289\pi\)
0.443973 0.896040i \(-0.353568\pi\)
\(240\) 0 0
\(241\) −23.2235 48.2241i −0.0963630 0.200100i 0.847215 0.531250i \(-0.178278\pi\)
−0.943578 + 0.331150i \(0.892563\pi\)
\(242\) 113.259 + 180.251i 0.468012 + 0.744837i
\(243\) 0 0
\(244\) −80.3407 + 80.3407i −0.329265 + 0.329265i
\(245\) 25.5238 53.0008i 0.104179 0.216330i
\(246\) 0 0
\(247\) 20.1801 + 179.103i 0.0817007 + 0.725114i
\(248\) 92.4227 + 44.5084i 0.372672 + 0.179470i
\(249\) 0 0
\(250\) −78.5441 + 27.4838i −0.314177 + 0.109935i
\(251\) −309.133 + 194.241i −1.23160 + 0.773868i −0.980960 0.194211i \(-0.937785\pi\)
−0.250644 + 0.968079i \(0.580642\pi\)
\(252\) 0 0
\(253\) 69.5001 + 24.3191i 0.274704 + 0.0961231i
\(254\) −72.7905 + 16.6139i −0.286577 + 0.0654092i
\(255\) 0 0
\(256\) −160.587 201.370i −0.627294 0.786602i
\(257\) 94.8505 415.567i 0.369068 1.61699i −0.360276 0.932846i \(-0.617317\pi\)
0.729344 0.684147i \(-0.239825\pi\)
\(258\) 0 0
\(259\) −51.9565 5.85409i −0.200604 0.0226027i
\(260\) 160.105i 0.615787i
\(261\) 0 0
\(262\) 134.170 0.512100
\(263\) −1.99454 + 17.7021i −0.00758382 + 0.0673083i −0.996934 0.0782461i \(-0.975068\pi\)
0.989350 + 0.145554i \(0.0464966\pi\)
\(264\) 0 0
\(265\) 297.244 + 67.8441i 1.12168 + 0.256015i
\(266\) −109.306 + 87.1684i −0.410924 + 0.327701i
\(267\) 0 0
\(268\) −35.2130 154.278i −0.131392 0.575664i
\(269\) 69.6952 199.177i 0.259090 0.740437i −0.738703 0.674031i \(-0.764561\pi\)
0.997793 0.0664053i \(-0.0211530\pi\)
\(270\) 0 0
\(271\) 168.487 + 268.145i 0.621722 + 0.989464i 0.998016 + 0.0629639i \(0.0200553\pi\)
−0.376294 + 0.926500i \(0.622802\pi\)
\(272\) 34.9238 + 99.8065i 0.128396 + 0.366935i
\(273\) 0 0
\(274\) −32.9993 + 68.5238i −0.120436 + 0.250087i
\(275\) 516.958 58.2472i 1.87985 0.211808i
\(276\) 0 0
\(277\) −486.478 234.275i −1.75624 0.845760i −0.975216 0.221257i \(-0.928984\pi\)
−0.781022 0.624503i \(-0.785302\pi\)
\(278\) −5.71050 5.71050i −0.0205414 0.0205414i
\(279\) 0 0
\(280\) −355.802 + 223.565i −1.27072 + 0.798448i
\(281\) 178.225 85.8285i 0.634252 0.305439i −0.0889921 0.996032i \(-0.528365\pi\)
0.723244 + 0.690593i \(0.242650\pi\)
\(282\) 0 0
\(283\) 155.124 35.4061i 0.548143 0.125110i 0.0605241 0.998167i \(-0.480723\pi\)
0.487619 + 0.873057i \(0.337866\pi\)
\(284\) −33.3582 + 41.8298i −0.117458 + 0.147288i
\(285\) 0 0
\(286\) −69.0502 + 302.529i −0.241434 + 1.05779i
\(287\) 83.5573 + 52.5025i 0.291140 + 0.182936i
\(288\) 0 0
\(289\) 22.0004i 0.0761260i
\(290\) 309.912 + 125.241i 1.06866 + 0.431867i
\(291\) 0 0
\(292\) −25.0839 + 222.626i −0.0859039 + 0.762418i
\(293\) −131.410 + 209.138i −0.448498 + 0.713781i −0.992084 0.125572i \(-0.959923\pi\)
0.543586 + 0.839353i \(0.317066\pi\)
\(294\) 0 0
\(295\) 426.134 339.830i 1.44452 1.15197i
\(296\) −55.0866 43.9301i −0.186103 0.148412i
\(297\) 0 0
\(298\) −62.6564 + 179.062i −0.210256 + 0.600878i
\(299\) 24.9554 + 51.8205i 0.0834630 + 0.173313i
\(300\) 0 0
\(301\) 89.2202 + 254.977i 0.296413 + 0.847098i
\(302\) 160.767 160.767i 0.532340 0.532340i
\(303\) 0 0
\(304\) −91.8941 + 10.3540i −0.302283 + 0.0340591i
\(305\) 57.3418 + 508.923i 0.188006 + 1.66860i
\(306\) 0 0
\(307\) 226.087 + 226.087i 0.736440 + 0.736440i 0.971887 0.235447i \(-0.0756555\pi\)
−0.235447 + 0.971887i \(0.575655\pi\)
\(308\) 164.209 57.4592i 0.533146 0.186556i
\(309\) 0 0
\(310\) 123.124 59.2936i 0.397175 0.191270i
\(311\) −72.3712 25.3238i −0.232705 0.0814269i 0.211408 0.977398i \(-0.432195\pi\)
−0.444112 + 0.895971i \(0.646481\pi\)
\(312\) 0 0
\(313\) −344.367 + 431.823i −1.10022 + 1.37963i −0.182116 + 0.983277i \(0.558294\pi\)
−0.918100 + 0.396349i \(0.870277\pi\)
\(314\) −150.554 188.789i −0.479471 0.601238i
\(315\) 0 0
\(316\) 124.811 + 78.4241i 0.394972 + 0.248177i
\(317\) −7.26544 0.818619i −0.0229194 0.00258239i 0.100497 0.994937i \(-0.467957\pi\)
−0.123417 + 0.992355i \(0.539385\pi\)
\(318\) 0 0
\(319\) −384.212 267.648i −1.20443 0.839023i
\(320\) −481.054 −1.50330
\(321\) 0 0
\(322\) −23.7365 + 37.7764i −0.0737158 + 0.117318i
\(323\) −227.651 51.9599i −0.704802 0.160866i
\(324\) 0 0
\(325\) 317.711 + 253.366i 0.977573 + 0.779589i
\(326\) 38.8819 + 170.353i 0.119270 + 0.522554i
\(327\) 0 0
\(328\) 57.6991 + 119.813i 0.175912 + 0.365285i
\(329\) −102.091 162.478i −0.310308 0.493853i
\(330\) 0 0
\(331\) −60.5776 + 60.5776i −0.183014 + 0.183014i −0.792668 0.609654i \(-0.791308\pi\)
0.609654 + 0.792668i \(0.291308\pi\)
\(332\) 47.2264 98.0667i 0.142248 0.295382i
\(333\) 0 0
\(334\) −6.95934 61.7659i −0.0208364 0.184928i
\(335\) −642.661 309.489i −1.91839 0.923849i
\(336\) 0 0
\(337\) 319.145 111.674i 0.947018 0.331376i 0.187796 0.982208i \(-0.439865\pi\)
0.759222 + 0.650832i \(0.225580\pi\)
\(338\) 12.8054 8.04620i 0.0378859 0.0238053i
\(339\) 0 0
\(340\) −195.784 68.5077i −0.575835 0.201493i
\(341\) −186.635 + 42.5983i −0.547318 + 0.124922i
\(342\) 0 0
\(343\) −227.285 285.007i −0.662639 0.830923i
\(344\) −81.0039 + 354.901i −0.235476 + 1.03169i
\(345\) 0 0
\(346\) −140.578 15.8393i −0.406294 0.0457783i
\(347\) 98.3157i 0.283330i −0.989915 0.141665i \(-0.954754\pi\)
0.989915 0.141665i \(-0.0452456\pi\)
\(348\) 0 0
\(349\) −534.702 −1.53210 −0.766049 0.642782i \(-0.777780\pi\)
−0.766049 + 0.642782i \(0.777780\pi\)
\(350\) −35.2929 + 313.233i −0.100837 + 0.894951i
\(351\) 0 0
\(352\) 389.573 + 88.9176i 1.10674 + 0.252607i
\(353\) −263.129 + 209.839i −0.745409 + 0.594444i −0.920791 0.390057i \(-0.872455\pi\)
0.175382 + 0.984500i \(0.443884\pi\)
\(354\) 0 0
\(355\) 53.6642 + 235.118i 0.151167 + 0.662305i
\(356\) −53.5385 + 153.004i −0.150389 + 0.429787i
\(357\) 0 0
\(358\) −269.195 428.422i −0.751943 1.19671i
\(359\) 81.3356 + 232.444i 0.226561 + 0.647475i 0.999909 + 0.0134931i \(0.00429511\pi\)
−0.773348 + 0.633982i \(0.781419\pi\)
\(360\) 0 0
\(361\) −68.0273 + 141.260i −0.188441 + 0.391302i
\(362\) −36.2447 + 4.08380i −0.100124 + 0.0112812i
\(363\) 0 0
\(364\) 122.437 + 58.9625i 0.336365 + 0.161985i
\(365\) 714.071 + 714.071i 1.95636 + 1.95636i
\(366\) 0 0
\(367\) 132.396 83.1898i 0.360752 0.226675i −0.339444 0.940626i \(-0.610239\pi\)
0.700196 + 0.713951i \(0.253096\pi\)
\(368\) −26.5880 + 12.8041i −0.0722500 + 0.0347938i
\(369\) 0 0
\(370\) −91.5103 + 20.8866i −0.247325 + 0.0564504i
\(371\) 161.350 202.327i 0.434906 0.545355i
\(372\) 0 0
\(373\) −130.647 + 572.403i −0.350261 + 1.53459i 0.426318 + 0.904573i \(0.359810\pi\)
−0.776579 + 0.630020i \(0.783047\pi\)
\(374\) −340.401 213.888i −0.910162 0.571893i
\(375\) 0 0
\(376\) 258.586i 0.687728i
\(377\) −64.3831 360.051i −0.170778 0.955043i
\(378\) 0 0
\(379\) −7.44921 + 66.1135i −0.0196549 + 0.174442i −0.999704 0.0243113i \(-0.992261\pi\)
0.980050 + 0.198753i \(0.0636893\pi\)
\(380\) 96.5123 153.598i 0.253980 0.404207i
\(381\) 0 0
\(382\) −135.523 + 108.076i −0.354772 + 0.282921i
\(383\) −21.1423 16.8604i −0.0552018 0.0440220i 0.595500 0.803355i \(-0.296954\pi\)
−0.650702 + 0.759333i \(0.725525\pi\)
\(384\) 0 0
\(385\) 259.000 740.180i 0.672728 1.92255i
\(386\) −144.661 300.391i −0.374768 0.778214i
\(387\) 0 0
\(388\) 66.2780 + 189.412i 0.170820 + 0.488175i
\(389\) 148.329 148.329i 0.381307 0.381307i −0.490266 0.871573i \(-0.663100\pi\)
0.871573 + 0.490266i \(0.163100\pi\)
\(390\) 0 0
\(391\) −74.0469 + 8.34308i −0.189378 + 0.0213378i
\(392\) −7.53364 66.8629i −0.0192185 0.170569i
\(393\) 0 0
\(394\) 269.684 + 269.684i 0.684477 + 0.684477i
\(395\) 627.149 219.449i 1.58772 0.555567i
\(396\) 0 0
\(397\) 625.449 301.201i 1.57544 0.758692i 0.577121 0.816659i \(-0.304176\pi\)
0.998318 + 0.0579674i \(0.0184619\pi\)
\(398\) −444.963 155.699i −1.11800 0.391204i
\(399\) 0 0
\(400\) −129.997 + 163.011i −0.324992 + 0.407527i
\(401\) 475.354 + 596.075i 1.18542 + 1.48647i 0.835324 + 0.549758i \(0.185280\pi\)
0.350097 + 0.936713i \(0.386149\pi\)
\(402\) 0 0
\(403\) −126.616 79.5580i −0.314183 0.197414i
\(404\) −74.6882 8.41534i −0.184872 0.0208300i
\(405\) 0 0
\(406\) 209.909 190.876i 0.517017 0.470138i
\(407\) 131.488 0.323065
\(408\) 0 0
\(409\) 82.4668 131.245i 0.201630 0.320893i −0.730569 0.682839i \(-0.760745\pi\)
0.932199 + 0.361947i \(0.117888\pi\)
\(410\) 172.716 + 39.4213i 0.421259 + 0.0961496i
\(411\) 0 0
\(412\) −85.8164 68.4363i −0.208292 0.166107i
\(413\) −102.944 451.029i −0.249260 1.09208i
\(414\) 0 0
\(415\) −212.876 442.041i −0.512953 1.06516i
\(416\) 166.065 + 264.292i 0.399196 + 0.635316i
\(417\) 0 0
\(418\) 248.611 248.611i 0.594763 0.594763i
\(419\) −149.598 + 310.643i −0.357035 + 0.741390i −0.999693 0.0247624i \(-0.992117\pi\)
0.642659 + 0.766153i \(0.277831\pi\)
\(420\) 0 0
\(421\) −66.7338 592.279i −0.158513 1.40684i −0.781158 0.624334i \(-0.785371\pi\)
0.622645 0.782504i \(-0.286058\pi\)
\(422\) −62.5963 30.1448i −0.148332 0.0714331i
\(423\) 0 0
\(424\) 329.163 115.179i 0.776328 0.271649i
\(425\) −445.775 + 280.099i −1.04888 + 0.659057i
\(426\) 0 0
\(427\) 410.307 + 143.572i 0.960905 + 0.336235i
\(428\) −133.782 + 30.5349i −0.312575 + 0.0713433i
\(429\) 0 0
\(430\) 302.364 + 379.152i 0.703171 + 0.881749i
\(431\) 61.6978 270.316i 0.143150 0.627183i −0.851542 0.524287i \(-0.824332\pi\)
0.994692 0.102896i \(-0.0328109\pi\)
\(432\) 0 0
\(433\) −318.885 35.9297i −0.736454 0.0829785i −0.264233 0.964459i \(-0.585119\pi\)
−0.472221 + 0.881480i \(0.656547\pi\)
\(434\) 115.993i 0.267266i
\(435\) 0 0
\(436\) −121.659 −0.279035
\(437\) 7.29647 64.7580i 0.0166967 0.148188i
\(438\) 0 0
\(439\) −589.295 134.503i −1.34236 0.306384i −0.509785 0.860302i \(-0.670275\pi\)
−0.832572 + 0.553917i \(0.813132\pi\)
\(440\) 826.200 658.873i 1.87773 1.49744i
\(441\) 0 0
\(442\) −69.8786 306.158i −0.158096 0.692665i
\(443\) 286.372 818.404i 0.646438 1.84741i 0.129098 0.991632i \(-0.458792\pi\)
0.517339 0.855781i \(-0.326923\pi\)
\(444\) 0 0
\(445\) 388.744 + 618.683i 0.873582 + 1.39030i
\(446\) 70.3733 + 201.115i 0.157788 + 0.450931i
\(447\) 0 0
\(448\) −177.160 + 367.877i −0.395447 + 0.821154i
\(449\) −583.687 + 65.7657i −1.29997 + 0.146472i −0.734677 0.678417i \(-0.762666\pi\)
−0.565295 + 0.824889i \(0.691238\pi\)
\(450\) 0 0
\(451\) −223.593 107.677i −0.495771 0.238751i
\(452\) 45.0035 + 45.0035i 0.0995652 + 0.0995652i
\(453\) 0 0
\(454\) −38.6075 + 24.2587i −0.0850384 + 0.0534332i
\(455\) 551.891 265.777i 1.21295 0.584125i
\(456\) 0 0
\(457\) 30.9403 7.06192i 0.0677030 0.0154528i −0.188535 0.982066i \(-0.560374\pi\)
0.256238 + 0.966614i \(0.417517\pi\)
\(458\) −281.830 + 353.403i −0.615349 + 0.771623i
\(459\) 0 0
\(460\) 12.8815 56.4373i 0.0280032 0.122690i
\(461\) 26.3626 + 16.5647i 0.0571858 + 0.0359322i 0.560322 0.828275i \(-0.310678\pi\)
−0.503136 + 0.864207i \(0.667820\pi\)
\(462\) 0 0
\(463\) 492.788i 1.06434i −0.846638 0.532169i \(-0.821377\pi\)
0.846638 0.532169i \(-0.178623\pi\)
\(464\) 184.735 33.0336i 0.398135 0.0711932i
\(465\) 0 0
\(466\) −17.5445 + 155.712i −0.0376492 + 0.334146i
\(467\) −70.6660 + 112.464i −0.151319 + 0.240823i −0.913778 0.406214i \(-0.866849\pi\)
0.762459 + 0.647036i \(0.223992\pi\)
\(468\) 0 0
\(469\) −473.352 + 377.486i −1.00928 + 0.804874i
\(470\) −269.329 214.783i −0.573040 0.456984i
\(471\) 0 0
\(472\) 205.904 588.441i 0.436238 1.24670i
\(473\) −294.755 612.064i −0.623160 1.29401i
\(474\) 0 0
\(475\) −152.069 434.589i −0.320146 0.914924i
\(476\) −124.492 + 124.492i −0.261538 + 0.261538i
\(477\) 0 0
\(478\) −560.770 + 63.1836i −1.17316 + 0.132183i
\(479\) −20.8876 185.382i −0.0436066 0.387020i −0.996492 0.0836888i \(-0.973330\pi\)
0.952885 0.303331i \(-0.0980987\pi\)
\(480\) 0 0
\(481\) 72.6264 + 72.6264i 0.150990 + 0.150990i
\(482\) −76.9820 + 26.9372i −0.159714 + 0.0558863i
\(483\) 0 0
\(484\) −211.231 + 101.724i −0.436429 + 0.210173i
\(485\) 853.784 + 298.752i 1.76038 + 0.615983i
\(486\) 0 0
\(487\) 348.899 437.506i 0.716426 0.898369i −0.281704 0.959501i \(-0.590900\pi\)
0.998130 + 0.0611319i \(0.0194710\pi\)
\(488\) 365.235 + 457.990i 0.748433 + 0.938505i
\(489\) 0 0
\(490\) −75.8982 47.6900i −0.154894 0.0973266i
\(491\) −244.577 27.5572i −0.498121 0.0561247i −0.140670 0.990057i \(-0.544926\pi\)
−0.357451 + 0.933932i \(0.616354\pi\)
\(492\) 0 0
\(493\) 467.837 + 75.3326i 0.948960 + 0.152805i
\(494\) 274.637 0.555946
\(495\) 0 0
\(496\) 40.8195 64.9639i 0.0822974 0.130976i
\(497\) 199.565 + 45.5495i 0.401540 + 0.0916489i
\(498\) 0 0
\(499\) −414.297 330.391i −0.830254 0.662106i 0.113213 0.993571i \(-0.463886\pi\)
−0.943468 + 0.331465i \(0.892457\pi\)
\(500\) −20.3930 89.3475i −0.0407859 0.178695i
\(501\) 0 0
\(502\) 241.376 + 501.221i 0.480828 + 0.998449i
\(503\) 337.253 + 536.736i 0.670484 + 1.06707i 0.992724 + 0.120411i \(0.0384212\pi\)
−0.322240 + 0.946658i \(0.604436\pi\)
\(504\) 0 0
\(505\) −239.562 + 239.562i −0.474379 + 0.474379i
\(506\) 48.6808 101.087i 0.0962070 0.199776i
\(507\) 0 0
\(508\) −9.20654 81.7103i −0.0181231 0.160847i
\(509\) −480.177 231.241i −0.943374 0.454305i −0.102016 0.994783i \(-0.532529\pi\)
−0.841358 + 0.540478i \(0.818244\pi\)
\(510\) 0 0
\(511\) 809.047 283.098i 1.58326 0.554007i
\(512\) −325.234 + 204.358i −0.635223 + 0.399137i
\(513\) 0 0
\(514\) −613.062 214.520i −1.19273 0.417353i
\(515\) −482.359 + 110.095i −0.936619 + 0.213777i
\(516\) 0 0
\(517\) 300.875 + 377.285i 0.581964 + 0.729759i
\(518\) −17.7283 + 77.6728i −0.0342245 + 0.149947i
\(519\) 0 0
\(520\) 820.271 + 92.4223i 1.57744 + 0.177735i
\(521\) 491.340i 0.943071i −0.881847 0.471535i \(-0.843700\pi\)
0.881847 0.471535i \(-0.156300\pi\)
\(522\) 0 0
\(523\) −633.523 −1.21133 −0.605663 0.795721i \(-0.707092\pi\)
−0.605663 + 0.795721i \(0.707092\pi\)
\(524\) −16.5444 + 146.835i −0.0315732 + 0.280220i
\(525\) 0 0
\(526\) 26.4638 + 6.04020i 0.0503115 + 0.0114833i
\(527\) 151.465 120.790i 0.287411 0.229202i
\(528\) 0 0
\(529\) 113.086 + 495.462i 0.213773 + 0.936601i
\(530\) 153.440 438.507i 0.289510 0.827371i
\(531\) 0 0
\(532\) −81.9184 130.372i −0.153982 0.245061i
\(533\) −64.0256 182.975i −0.120123 0.343292i
\(534\) 0 0
\(535\) −268.374 + 557.284i −0.501634 + 1.04165i
\(536\) −810.746 + 91.3492i −1.51259 + 0.170428i
\(537\) 0 0
\(538\) −289.700 139.512i −0.538476 0.259316i
\(539\) 88.7896 + 88.7896i 0.164730 + 0.164730i
\(540\) 0 0
\(541\) −450.657 + 283.166i −0.833007 + 0.523413i −0.879718 0.475496i \(-0.842269\pi\)
0.0467114 + 0.998908i \(0.485126\pi\)
\(542\) 434.765 209.372i 0.802149 0.386294i
\(543\) 0 0
\(544\) −394.247 + 89.9843i −0.724719 + 0.165412i
\(545\) −341.913 + 428.745i −0.627362 + 0.786688i
\(546\) 0 0
\(547\) 93.5855 410.025i 0.171089 0.749588i −0.814463 0.580215i \(-0.802969\pi\)
0.985552 0.169373i \(-0.0541743\pi\)
\(548\) −70.9231 44.5640i −0.129422 0.0813211i
\(549\) 0 0
\(550\) 792.705i 1.44128i
\(551\) −155.275 + 384.230i −0.281805 + 0.697333i
\(552\) 0 0
\(553\) 63.1439 560.418i 0.114184 1.01341i
\(554\) −437.732 + 696.646i −0.790130 + 1.25748i
\(555\) 0 0
\(556\) 6.95371 5.54540i 0.0125067 0.00997374i
\(557\) −436.339 347.969i −0.783374 0.624720i 0.147915 0.989000i \(-0.452744\pi\)
−0.931289 + 0.364280i \(0.881315\pi\)
\(558\) 0 0
\(559\) 175.264 500.876i 0.313531 0.896022i
\(560\) 136.364 + 283.164i 0.243508 + 0.505650i
\(561\) 0 0
\(562\) −99.5534 284.507i −0.177141 0.506241i
\(563\) 624.348 624.348i 1.10897 1.10897i 0.115679 0.993287i \(-0.463096\pi\)
0.993287 0.115679i \(-0.0369044\pi\)
\(564\) 0 0
\(565\) 285.077 32.1205i 0.504561 0.0568504i
\(566\) −27.1459 240.927i −0.0479610 0.425666i
\(567\) 0 0
\(568\) 195.052 + 195.052i 0.343402 + 0.343402i
\(569\) −994.025 + 347.824i −1.74697 + 0.611290i −0.998645 0.0520443i \(-0.983426\pi\)
−0.748323 + 0.663335i \(0.769141\pi\)
\(570\) 0 0
\(571\) 383.661 184.761i 0.671911 0.323575i −0.0666361 0.997777i \(-0.521227\pi\)
0.738547 + 0.674202i \(0.235512\pi\)
\(572\) −322.572 112.873i −0.563937 0.197330i
\(573\) 0 0
\(574\) 93.7538 117.563i 0.163334 0.204814i
\(575\) −91.6092 114.874i −0.159320 0.199781i
\(576\) 0 0
\(577\) 174.128 + 109.412i 0.301782 + 0.189622i 0.674407 0.738360i \(-0.264399\pi\)
−0.372625 + 0.927982i \(0.621542\pi\)
\(578\) −33.3126 3.75343i −0.0576343 0.00649382i
\(579\) 0 0
\(580\) −175.279 + 323.724i −0.302205 + 0.558144i
\(581\) −416.439 −0.716762
\(582\) 0 0
\(583\) −346.245 + 551.045i −0.593901 + 0.945189i
\(584\) 1126.11 + 257.027i 1.92827 + 0.440115i
\(585\) 0 0
\(586\) 294.253 + 234.659i 0.502138 + 0.400442i
\(587\) 110.905 + 485.906i 0.188935 + 0.827778i 0.977179 + 0.212416i \(0.0681331\pi\)
−0.788244 + 0.615362i \(0.789010\pi\)
\(588\) 0 0
\(589\) 73.5124 + 152.650i 0.124809 + 0.259168i
\(590\) −441.863 703.221i −0.748920 1.19190i
\(591\) 0 0
\(592\) −37.2631 + 37.2631i −0.0629444 + 0.0629444i
\(593\) −27.9471 + 58.0328i −0.0471283 + 0.0978630i −0.923203 0.384312i \(-0.874439\pi\)
0.876075 + 0.482175i \(0.160153\pi\)
\(594\) 0 0
\(595\) 88.8543 + 788.604i 0.149335 + 1.32538i
\(596\) −188.238 90.6509i −0.315836 0.152099i
\(597\) 0 0
\(598\) 82.7231 28.9461i 0.138333 0.0484048i
\(599\) 693.663 435.857i 1.15803 0.727641i 0.190826 0.981624i \(-0.438883\pi\)
0.967209 + 0.253983i \(0.0817406\pi\)
\(600\) 0 0
\(601\) −311.390 108.960i −0.518119 0.181298i 0.0585361 0.998285i \(-0.481357\pi\)
−0.576655 + 0.816988i \(0.695642\pi\)
\(602\) 401.302 91.5946i 0.666615 0.152150i
\(603\) 0 0
\(604\) 156.118 + 195.766i 0.258474 + 0.324116i
\(605\) −235.158 + 1030.30i −0.388692 + 1.70297i
\(606\) 0 0
\(607\) −344.589 38.8258i −0.567692 0.0639635i −0.176546 0.984292i \(-0.556492\pi\)
−0.391145 + 0.920329i \(0.627921\pi\)
\(608\) 353.657i 0.581673i
\(609\) 0 0
\(610\) 780.384 1.27932
\(611\) −42.2048 + 374.578i −0.0690750 + 0.613057i
\(612\) 0 0
\(613\) −869.396 198.434i −1.41826 0.323710i −0.556428 0.830896i \(-0.687829\pi\)
−0.861837 + 0.507186i \(0.830686\pi\)
\(614\) 380.909 303.764i 0.620372 0.494730i
\(615\) 0 0
\(616\) −199.591 874.467i −0.324012 1.41959i
\(617\) −130.369 + 372.572i −0.211294 + 0.603845i −0.999939 0.0110041i \(-0.996497\pi\)
0.788645 + 0.614849i \(0.210783\pi\)
\(618\) 0 0
\(619\) 547.850 + 871.898i 0.885057 + 1.40856i 0.912562 + 0.408938i \(0.134101\pi\)
−0.0275057 + 0.999622i \(0.508756\pi\)
\(620\) 49.7083 + 142.058i 0.0801748 + 0.229126i
\(621\) 0 0
\(622\) −50.6918 + 105.263i −0.0814980 + 0.169232i
\(623\) 616.290 69.4393i 0.989230 0.111459i
\(624\) 0 0
\(625\) 353.533 + 170.252i 0.565652 + 0.272404i
\(626\) 595.106 + 595.106i 0.950649 + 0.950649i
\(627\) 0 0
\(628\) 225.174 141.486i 0.358558 0.225297i
\(629\) −119.887 + 57.7347i −0.190600 + 0.0917881i
\(630\) 0 0
\(631\) −75.0733 + 17.1350i −0.118975 + 0.0271553i −0.281594 0.959534i \(-0.590863\pi\)
0.162619 + 0.986689i \(0.448006\pi\)
\(632\) 473.842 594.179i 0.749750 0.940157i
\(633\) 0 0
\(634\) −2.47907 + 10.8615i −0.00391021 + 0.0171317i
\(635\) −313.833 197.194i −0.494226 0.310542i
\(636\) 0 0
\(637\) 98.0848i 0.153979i
\(638\) −470.817 + 536.103i −0.737958 + 0.840287i
\(639\) 0 0
\(640\) 1.76896 15.7000i 0.00276400 0.0245312i
\(641\) 57.7855 91.9651i 0.0901490 0.143471i −0.798605 0.601855i \(-0.794429\pi\)
0.888754 + 0.458384i \(0.151571\pi\)
\(642\) 0 0
\(643\) 353.051 281.549i 0.549069 0.437868i −0.309253 0.950980i \(-0.600079\pi\)
0.858322 + 0.513112i \(0.171508\pi\)
\(644\) −38.4155 30.6353i −0.0596513 0.0475703i
\(645\) 0 0
\(646\) −117.515 + 335.840i −0.181913 + 0.519876i
\(647\) 353.316 + 733.668i 0.546084 + 1.13395i 0.973243 + 0.229778i \(0.0738000\pi\)
−0.427160 + 0.904176i \(0.640486\pi\)
\(648\) 0 0
\(649\) 384.254 + 1098.13i 0.592070 + 1.69204i
\(650\) 437.846 437.846i 0.673609 0.673609i
\(651\) 0 0
\(652\) −191.228 + 21.5462i −0.293294 + 0.0330463i
\(653\) 41.8389 + 371.331i 0.0640719 + 0.568653i 0.984203 + 0.177043i \(0.0566533\pi\)
−0.920131 + 0.391610i \(0.871918\pi\)
\(654\) 0 0
\(655\) 470.973 + 470.973i 0.719043 + 0.719043i
\(656\) 93.8804 32.8502i 0.143110 0.0500765i
\(657\) 0 0
\(658\) −263.438 + 126.865i −0.400362 + 0.192804i
\(659\) −874.680 306.064i −1.32728 0.464436i −0.428782 0.903408i \(-0.641057\pi\)
−0.898501 + 0.438971i \(0.855343\pi\)
\(660\) 0 0
\(661\) −560.439 + 702.769i −0.847866 + 1.06319i 0.149362 + 0.988783i \(0.452278\pi\)
−0.997228 + 0.0744073i \(0.976293\pi\)
\(662\) 81.3904 + 102.060i 0.122946 + 0.154170i
\(663\) 0 0
\(664\) −475.167 298.567i −0.715613 0.449650i
\(665\) −689.676 77.7079i −1.03711 0.116854i
\(666\) 0 0
\(667\) −6.27320 + 132.099i −0.00940510 + 0.198050i
\(668\) 68.4545 0.102477
\(669\) 0 0
\(670\) −578.265 + 920.304i −0.863083 + 1.37359i
\(671\) −1065.78 243.258i −1.58835 0.362530i
\(672\) 0 0
\(673\) −481.293 383.819i −0.715146 0.570310i 0.196887 0.980426i \(-0.436917\pi\)
−0.912033 + 0.410116i \(0.865488\pi\)
\(674\) −114.646 502.296i −0.170097 0.745246i
\(675\) 0 0
\(676\) 7.22671 + 15.0064i 0.0106904 + 0.0221988i
\(677\) 421.002 + 670.021i 0.621864 + 0.989692i 0.998005 + 0.0631292i \(0.0201080\pi\)
−0.376141 + 0.926562i \(0.622749\pi\)
\(678\) 0 0
\(679\) 542.892 542.892i 0.799546 0.799546i
\(680\) −464.007 + 963.521i −0.682363 + 1.41694i
\(681\) 0 0
\(682\) 32.6602 + 289.867i 0.0478888 + 0.425025i
\(683\) −241.679 116.387i −0.353849 0.170405i 0.248511 0.968629i \(-0.420059\pi\)
−0.602361 + 0.798224i \(0.705773\pi\)
\(684\) 0 0
\(685\) −356.373 + 124.700i −0.520253 + 0.182044i
\(686\) −470.328 + 295.527i −0.685609 + 0.430797i
\(687\) 0 0
\(688\) 256.989 + 89.9243i 0.373530 + 0.130704i
\(689\) −495.612 + 113.120i −0.719321 + 0.164180i
\(690\) 0 0
\(691\) 10.6882 + 13.4026i 0.0154677 + 0.0193959i 0.789505 0.613744i \(-0.210337\pi\)
−0.774037 + 0.633140i \(0.781766\pi\)
\(692\) 34.6689 151.895i 0.0500996 0.219501i
\(693\) 0 0
\(694\) −148.868 16.7734i −0.214507 0.0241691i
\(695\) 40.0908i 0.0576845i
\(696\) 0 0
\(697\) 251.146 0.360325
\(698\) −91.2241 + 809.636i −0.130693 + 1.15994i
\(699\) 0 0
\(700\) −338.449 77.2488i −0.483498 0.110355i
\(701\) 554.998 442.596i 0.791723 0.631378i −0.141800 0.989895i \(-0.545289\pi\)
0.933523 + 0.358517i \(0.116718\pi\)
\(702\) 0 0
\(703\) −25.8953 113.455i −0.0368354 0.161387i
\(704\) 339.140 969.207i 0.481733 1.37672i
\(705\) 0 0
\(706\) 272.842 + 434.225i 0.386461 + 0.615050i
\(707\) 94.9756 + 271.425i 0.134336 + 0.383910i
\(708\) 0 0
\(709\) 397.216 824.828i 0.560249 1.16337i −0.407908 0.913023i \(-0.633742\pi\)
0.968157 0.250345i \(-0.0805442\pi\)
\(710\) 365.167 41.1444i 0.514320 0.0579499i
\(711\) 0 0
\(712\) 752.987 + 362.620i 1.05757 + 0.509297i
\(713\) 38.2315 + 38.2315i 0.0536206 + 0.0536206i
\(714\) 0 0
\(715\) −1304.34 + 819.571i −1.82425 + 1.14625i
\(716\) 502.058 241.778i 0.701198 0.337679i
\(717\) 0 0
\(718\) 365.838 83.5002i 0.509524 0.116295i
\(719\) 98.7345 123.809i 0.137322 0.172196i −0.708415 0.705796i \(-0.750590\pi\)
0.845737 + 0.533600i \(0.179161\pi\)
\(720\) 0 0
\(721\) −93.4475 + 409.420i −0.129608 + 0.567851i
\(722\) 202.287 + 127.106i 0.280176 + 0.176046i
\(723\) 0 0
\(724\) 40.1697i 0.0554830i
\(725\) 365.017 + 860.117i 0.503472 + 1.18637i
\(726\) 0 0
\(727\) −85.2122 + 756.279i −0.117211 + 1.04027i 0.788107 + 0.615538i \(0.211061\pi\)
−0.905318 + 0.424735i \(0.860367\pi\)
\(728\) 372.764 593.250i 0.512038 0.814903i
\(729\) 0 0
\(730\) 1203.06 959.406i 1.64802 1.31426i
\(731\) 537.501 + 428.643i 0.735296 + 0.586379i
\(732\) 0 0
\(733\) 268.707 767.920i 0.366585 1.04764i −0.601901 0.798571i \(-0.705590\pi\)
0.968486 0.249069i \(-0.0801245\pi\)
\(734\) −103.377 214.664i −0.140840 0.292458i
\(735\) 0 0
\(736\) −37.2745 106.525i −0.0506448 0.144734i
\(737\) 1076.62 1076.62i 1.46081 1.46081i
\(738\) 0 0
\(739\) 1094.54 123.325i 1.48111 0.166881i 0.665900 0.746041i \(-0.268048\pi\)
0.815214 + 0.579160i \(0.196619\pi\)
\(740\) −11.5742 102.724i −0.0156408 0.138816i
\(741\) 0 0
\(742\) −278.831 278.831i −0.375784 0.375784i
\(743\) 786.175 275.095i 1.05811 0.370248i 0.255534 0.966800i \(-0.417749\pi\)
0.802575 + 0.596552i \(0.203463\pi\)
\(744\) 0 0
\(745\) −848.495 + 408.614i −1.13892 + 0.548475i
\(746\) 844.433 + 295.480i 1.13195 + 0.396085i
\(747\) 0 0
\(748\) 276.053 346.159i 0.369054 0.462780i
\(749\) 327.337 + 410.468i 0.437032 + 0.548021i
\(750\) 0 0
\(751\) −163.686 102.851i −0.217958 0.136952i 0.418628 0.908158i \(-0.362511\pi\)
−0.636586 + 0.771206i \(0.719654\pi\)
\(752\) −192.188 21.6544i −0.255569 0.0287957i
\(753\) 0 0
\(754\) −556.166 + 36.0604i −0.737621 + 0.0478254i
\(755\) 1128.67 1.49492
\(756\) 0 0
\(757\) 39.3932 62.6939i 0.0520386 0.0828189i −0.819692 0.572805i \(-0.805855\pi\)
0.871730 + 0.489986i \(0.162998\pi\)
\(758\) 98.8369 + 22.5589i 0.130392 + 0.0297611i
\(759\) 0 0
\(760\) −731.225 583.132i −0.962138 0.767279i
\(761\) −158.627 694.991i −0.208446 0.913261i −0.965602 0.260026i \(-0.916269\pi\)
0.757156 0.653234i \(-0.226588\pi\)
\(762\) 0 0
\(763\) 201.957 + 419.367i 0.264687 + 0.549629i
\(764\) −101.567 161.643i −0.132941 0.211574i
\(765\) 0 0
\(766\) −29.1367 + 29.1367i −0.0380375 + 0.0380375i
\(767\) −394.307 + 818.788i −0.514090 + 1.06752i
\(768\) 0 0
\(769\) 54.5870 + 484.473i 0.0709845 + 0.630004i 0.977956 + 0.208812i \(0.0669597\pi\)
−0.906971 + 0.421192i \(0.861612\pi\)
\(770\) −1076.58 518.453i −1.39815 0.673316i
\(771\) 0 0
\(772\) 346.585 121.275i 0.448944 0.157092i
\(773\) −929.493 + 584.039i −1.20245 + 0.755549i −0.975851 0.218439i \(-0.929903\pi\)
−0.226599 + 0.973988i \(0.572761\pi\)
\(774\) 0 0
\(775\) 360.564 + 126.167i 0.465244 + 0.162796i
\(776\) 1008.68 230.225i 1.29985 0.296682i
\(777\) 0 0
\(778\) −199.290 249.902i −0.256157 0.321211i
\(779\) −48.8747 + 214.134i −0.0627403 + 0.274883i
\(780\) 0 0
\(781\) −511.539 57.6366i −0.654979 0.0737984i
\(782\) 113.544i 0.145197i
\(783\) 0 0
\(784\) −50.3252 −0.0641903
\(785\) 134.214 1191.18i 0.170973 1.51743i
\(786\) 0 0
\(787\) 600.614 + 137.086i 0.763169 + 0.174188i 0.586353 0.810056i \(-0.300563\pi\)
0.176816 + 0.984244i \(0.443420\pi\)
\(788\) −328.396 + 261.887i −0.416746 + 0.332344i
\(789\) 0 0
\(790\) −225.289 987.056i −0.285176 1.24944i
\(791\) 80.4233 229.836i 0.101673 0.290564i
\(792\) 0 0
\(793\) −454.316 723.040i −0.572908 0.911778i
\(794\) −349.366 998.430i −0.440007 1.25747i
\(795\) 0 0
\(796\) 225.265 467.767i 0.282996 0.587647i
\(797\) 1072.38 120.828i 1.34552 0.151604i 0.590359 0.807141i \(-0.298986\pi\)
0.755163 + 0.655537i \(0.227558\pi\)
\(798\) 0 0
\(799\) −439.993 211.889i −0.550680 0.265193i
\(800\) −563.825 563.825i −0.704781 0.704781i
\(801\) 0 0
\(802\) 983.664 618.077i 1.22651 0.770669i
\(803\) −1942.09 + 935.263i −2.41855 + 1.16471i
\(804\) 0 0
\(805\) −215.927 + 49.2838i −0.268232 + 0.0612222i
\(806\) −142.067 + 178.146i −0.176261 + 0.221025i
\(807\) 0 0
\(808\) −86.2293 + 377.795i −0.106719 + 0.467568i
\(809\) 188.811 + 118.638i 0.233388 + 0.146648i 0.643649 0.765321i \(-0.277420\pi\)
−0.410261 + 0.911968i \(0.634562\pi\)
\(810\) 0 0
\(811\) 697.499i 0.860048i 0.902817 + 0.430024i \(0.141495\pi\)
−0.902817 + 0.430024i \(0.858505\pi\)
\(812\) 183.011 + 253.260i 0.225383 + 0.311897i
\(813\) 0 0
\(814\) 22.4327 199.096i 0.0275586 0.244590i
\(815\) −461.497 + 734.469i −0.566254 + 0.901188i
\(816\) 0 0
\(817\) −470.074 + 374.871i −0.575366 + 0.458839i
\(818\) −184.659 147.261i −0.225745 0.180026i
\(819\) 0 0
\(820\) −64.4400 + 184.159i −0.0785854 + 0.224584i
\(821\) −505.781 1050.27i −0.616055 1.27925i −0.942554 0.334054i \(-0.891583\pi\)
0.326499 0.945198i \(-0.394131\pi\)
\(822\) 0 0
\(823\) −240.718 687.933i −0.292489 0.835885i −0.992554 0.121806i \(-0.961131\pi\)
0.700065 0.714079i \(-0.253154\pi\)
\(824\) −400.161 + 400.161i −0.485632 + 0.485632i
\(825\) 0 0
\(826\) −700.502 + 78.9276i −0.848065 + 0.0955540i
\(827\) −88.9721 789.649i −0.107584 0.954836i −0.925306 0.379222i \(-0.876192\pi\)
0.817722 0.575614i \(-0.195237\pi\)
\(828\) 0 0
\(829\) 18.8713 + 18.8713i 0.0227640 + 0.0227640i 0.718397 0.695633i \(-0.244876\pi\)
−0.695633 + 0.718397i \(0.744876\pi\)
\(830\) −705.647 + 246.917i −0.850178 + 0.297490i
\(831\) 0 0
\(832\) 722.658 348.014i 0.868579 0.418286i
\(833\) −119.943 41.9698i −0.143989 0.0503839i
\(834\) 0 0
\(835\) 192.385 241.244i 0.230402 0.288915i
\(836\) 241.423 + 302.735i 0.288783 + 0.362123i
\(837\) 0 0
\(838\) 444.846 + 279.516i 0.530843 + 0.333551i
\(839\) −1184.37 133.446i −1.41164 0.159054i −0.627008 0.779013i \(-0.715721\pi\)
−0.784634 + 0.619959i \(0.787149\pi\)
\(840\) 0 0
\(841\) 263.996 798.491i 0.313907 0.949454i
\(842\) −908.202 −1.07862
\(843\) 0 0
\(844\) 40.7090 64.7881i 0.0482335 0.0767631i
\(845\) 73.1948 + 16.7062i 0.0866211 + 0.0197707i
\(846\) 0 0
\(847\) 701.296 + 559.265i 0.827977 + 0.660290i
\(848\) −58.0397 254.288i −0.0684430 0.299868i
\(849\) 0 0
\(850\) 348.068 + 722.771i 0.409492 + 0.850319i
\(851\) −19.7577 31.4443i −0.0232171 0.0369498i
\(852\) 0 0
\(853\) 723.120 723.120i 0.847738 0.847738i −0.142113 0.989850i \(-0.545390\pi\)
0.989850 + 0.142113i \(0.0453896\pi\)
\(854\) 287.396 596.784i 0.336529 0.698810i
\(855\) 0 0
\(856\) 79.2135 + 703.039i 0.0925391 + 0.821308i
\(857\) −274.867 132.369i −0.320731 0.154456i 0.266590 0.963810i \(-0.414103\pi\)
−0.587321 + 0.809354i \(0.699817\pi\)
\(858\) 0 0
\(859\) −1406.36 + 492.106i −1.63720 + 0.572882i −0.983027 0.183460i \(-0.941270\pi\)
−0.654176 + 0.756342i \(0.726985\pi\)
\(860\) −452.227 + 284.153i −0.525845 + 0.330410i
\(861\) 0 0
\(862\) −398.781 139.539i −0.462623 0.161879i
\(863\) 1181.05 269.567i 1.36854 0.312360i 0.525766 0.850629i \(-0.323779\pi\)
0.842773 + 0.538270i \(0.180922\pi\)
\(864\) 0 0
\(865\) −437.865 549.065i −0.506202 0.634757i
\(866\) −108.808 + 476.719i −0.125644 + 0.550484i
\(867\) 0 0
\(868\) 126.943 + 14.3030i 0.146247 + 0.0164781i
\(869\) 1418.26i 1.63206i
\(870\) 0 0
\(871\) 1189.33 1.36547
\(872\) −70.2292 + 623.302i −0.0805381 + 0.714795i
\(873\) 0 0
\(874\) −96.8104 22.0963i −0.110767 0.0252819i
\(875\) −274.134 + 218.614i −0.313296 + 0.249845i
\(876\) 0 0
\(877\) 155.507 + 681.320i 0.177317 + 0.776876i 0.982862 + 0.184342i \(0.0590154\pi\)
−0.805545 + 0.592534i \(0.798127\pi\)
\(878\) −304.199 + 869.351i −0.346468 + 0.990150i
\(879\) 0 0
\(880\) −420.505 669.230i −0.477846 0.760488i
\(881\) 290.040 + 828.888i 0.329217 + 0.940849i 0.982910 + 0.184089i \(0.0589333\pi\)
−0.653692 + 0.756760i \(0.726781\pi\)
\(882\) 0 0
\(883\) −303.884 + 631.021i −0.344149 + 0.714634i −0.999160 0.0409863i \(-0.986950\pi\)
0.655010 + 0.755620i \(0.272664\pi\)
\(884\) 343.675 38.7229i 0.388773 0.0438041i
\(885\) 0 0
\(886\) −1190.35 573.244i −1.34351 0.647002i
\(887\) 505.923 + 505.923i 0.570376 + 0.570376i 0.932233 0.361858i \(-0.117857\pi\)
−0.361858 + 0.932233i \(0.617857\pi\)
\(888\) 0 0
\(889\) −266.378 + 167.376i −0.299637 + 0.188275i
\(890\) 1003.12 483.077i 1.12710 0.542783i
\(891\) 0 0
\(892\) −228.778 + 52.2170i −0.256477 + 0.0585392i
\(893\) 266.288 333.915i 0.298195 0.373925i
\(894\) 0 0
\(895\) 558.928 2448.82i 0.624500 2.73612i
\(896\) −11.3548 7.13468i −0.0126727 0.00796281i
\(897\) 0 0
\(898\) 895.028i 0.996690i
\(899\) −168.913 299.478i −0.187890 0.333124i
\(900\) 0 0
\(901\) 73.7402 654.463i 0.0818426 0.726374i
\(902\) −201.188 + 320.189i −0.223047 + 0.354977i
\(903\) 0 0
\(904\) 256.547 204.589i 0.283791 0.226316i
\(905\) −141.564 112.893i −0.156424 0.124744i
\(906\) 0 0
\(907\) −438.151 + 1252.16i −0.483077 + 1.38056i 0.402225 + 0.915541i \(0.368237\pi\)
−0.885303 + 0.465015i \(0.846049\pi\)
\(908\) −21.7880 45.2432i −0.0239956 0.0498273i
\(909\) 0 0
\(910\) −308.277 881.006i −0.338766 0.968139i
\(911\) 635.324 635.324i 0.697392 0.697392i −0.266455 0.963847i \(-0.585852\pi\)
0.963847 + 0.266455i \(0.0858524\pi\)
\(912\) 0 0
\(913\) 1040.68 117.256i 1.13985 0.128430i
\(914\) −5.41438 48.0540i −0.00592383 0.0525755i
\(915\) 0 0
\(916\) −352.011 352.011i −0.384292 0.384292i
\(917\) 533.615 186.720i 0.581914 0.203621i
\(918\) 0 0
\(919\) 507.688 244.490i 0.552435 0.266039i −0.136773 0.990602i \(-0.543673\pi\)
0.689208 + 0.724564i \(0.257959\pi\)
\(920\) −281.712 98.5752i −0.306208 0.107147i
\(921\) 0 0
\(922\) 29.5797 37.0917i 0.0320821 0.0402297i
\(923\) −250.710 314.381i −0.271625 0.340607i
\(924\) 0 0
\(925\) −222.162 139.593i −0.240175 0.150912i
\(926\) −746.170 84.0732i −0.805799 0.0907918i
\(927\) 0 0
\(928\) 46.4358 + 716.189i 0.0500386 + 0.771755i
\(929\) 1219.83 1.31306 0.656528 0.754301i \(-0.272024\pi\)
0.656528 + 0.754301i \(0.272024\pi\)
\(930\) 0 0
\(931\) 59.1263 94.0989i 0.0635083 0.101073i
\(932\) −168.247 38.4013i −0.180523 0.0412031i
\(933\) 0 0
\(934\) 158.235 + 126.188i 0.169416 + 0.135105i
\(935\) −444.093 1945.70i −0.474966 2.08096i
\(936\) 0 0
\(937\) −446.623 927.423i −0.476652 0.989779i −0.991207 0.132321i \(-0.957757\pi\)
0.514555 0.857458i \(-0.327957\pi\)
\(938\) 490.824 + 781.143i 0.523267 + 0.832775i
\(939\) 0 0
\(940\) 268.268 268.268i 0.285391 0.285391i
\(941\) 640.029 1329.03i 0.680159 1.41236i −0.219431 0.975628i \(-0.570420\pi\)
0.899590 0.436736i \(-0.143866\pi\)
\(942\) 0 0
\(943\) 7.84770 + 69.6503i 0.00832206 + 0.0738603i
\(944\) −420.103 202.311i −0.445024 0.214312i
\(945\) 0 0
\(946\) −977.063 + 341.889i −1.03284 + 0.361405i
\(947\) −1469.18 + 923.149i −1.55141 + 0.974814i −0.562413 + 0.826856i \(0.690127\pi\)
−0.988994 + 0.147957i \(0.952730\pi\)
\(948\) 0 0
\(949\) −1589.29 556.117i −1.67470 0.586003i
\(950\) −683.990 + 156.116i −0.719990 + 0.164333i
\(951\) 0 0
\(952\) 565.952 + 709.681i 0.594487 + 0.745463i
\(953\) −36.8085 + 161.269i −0.0386239 + 0.169222i −0.990561 0.137070i \(-0.956231\pi\)
0.951937 + 0.306292i \(0.0990885\pi\)
\(954\) 0 0
\(955\) −855.097 96.3462i −0.895389 0.100886i
\(956\) 621.495i 0.650100i
\(957\) 0 0
\(958\) −284.266 −0.296728
\(959\) −35.8811 + 318.454i −0.0374151 + 0.332069i
\(960\) 0 0
\(961\) 799.861 + 182.563i 0.832321 + 0.189972i
\(962\) 122.360 97.5788i 0.127193 0.101433i
\(963\) 0 0
\(964\) −19.9874 87.5705i −0.0207338 0.0908407i
\(965\) 546.654 1562.25i 0.566481 1.61891i
\(966\) 0 0
\(967\) −727.782 1158.26i −0.752618 1.19779i −0.974865 0.222795i \(-0.928482\pi\)
0.222247 0.974990i \(-0.428661\pi\)
\(968\) 399.229 + 1140.93i 0.412427 + 1.17865i
\(969\) 0 0
\(970\) 598.026 1241.81i 0.616521 1.28022i
\(971\) −138.857 + 15.6455i −0.143004 + 0.0161127i −0.183177 0.983080i \(-0.558638\pi\)
0.0401720 + 0.999193i \(0.487209\pi\)
\(972\) 0 0
\(973\) −30.6586 14.7644i −0.0315094 0.0151741i
\(974\) −602.938 602.938i −0.619033 0.619033i
\(975\) 0 0
\(976\) 370.976 233.100i 0.380099 0.238832i
\(977\) 1183.23 569.814i 1.21109 0.583228i 0.284270 0.958744i \(-0.408249\pi\)
0.926816 + 0.375516i \(0.122534\pi\)
\(978\) 0 0
\(979\) −1520.56 + 347.057i −1.55317 + 0.354502i
\(980\) 61.5507 77.1822i 0.0628069 0.0787573i
\(981\) 0 0
\(982\) −83.4533 + 365.633i −0.0849830 + 0.372335i
\(983\) 197.408 + 124.040i 0.200822 + 0.126185i 0.628689 0.777657i \(-0.283592\pi\)
−0.427867 + 0.903842i \(0.640735\pi\)
\(984\) 0 0
\(985\) 1893.32i 1.92216i
\(986\) 193.884 695.538i 0.196636 0.705413i
\(987\) 0 0
\(988\) −33.8652 + 300.562i −0.0342765 + 0.304213i
\(989\) −102.080 + 162.459i −0.103215 + 0.164266i
\(990\) 0 0
\(991\) 757.063 603.738i 0.763939 0.609221i −0.162045 0.986783i \(-0.551809\pi\)
0.925984 + 0.377563i \(0.123238\pi\)
\(992\) 229.403 + 182.943i 0.231253 + 0.184418i
\(993\) 0 0
\(994\) 103.017 294.407i 0.103639 0.296184i
\(995\) −1015.39 2108.48i −1.02049 2.11908i
\(996\) 0 0
\(997\) 277.571 + 793.254i 0.278407 + 0.795640i 0.995156 + 0.0983095i \(0.0313435\pi\)
−0.716749 + 0.697331i \(0.754371\pi\)
\(998\) −570.953 + 570.953i −0.572097 + 0.572097i
\(999\) 0 0
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 261.3.s.a.172.3 48
3.2 odd 2 29.3.f.a.27.2 yes 48
29.14 odd 28 inner 261.3.s.a.217.3 48
87.14 even 28 29.3.f.a.14.2 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.3.f.a.14.2 48 87.14 even 28
29.3.f.a.27.2 yes 48 3.2 odd 2
261.3.s.a.172.3 48 1.1 even 1 trivial
261.3.s.a.217.3 48 29.14 odd 28 inner