Properties

Label 405.2.r.a.152.14
Level $405$
Weight $2$
Character 405.152
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
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] = [405,2,Mod(8,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([2, 27]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.8");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not 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: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 152.14
Character \(\chi\) \(=\) 405.152
Dual form 405.2.r.a.8.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.66533 + 1.16608i) q^{2} +(0.729546 + 2.00441i) q^{4} +(1.48319 + 1.67336i) q^{5} +(1.13512 + 2.43427i) q^{7} +(-0.0700073 + 0.261271i) q^{8} +O(q^{10})\) \(q+(1.66533 + 1.16608i) q^{2} +(0.729546 + 2.00441i) q^{4} +(1.48319 + 1.67336i) q^{5} +(1.13512 + 2.43427i) q^{7} +(-0.0700073 + 0.261271i) q^{8} +(0.518731 + 4.51621i) q^{10} +(-4.08386 - 4.86695i) q^{11} +(1.19516 + 1.70687i) q^{13} +(-0.948196 + 5.37749i) q^{14} +(2.84677 - 2.38873i) q^{16} +(0.174154 + 0.649952i) q^{17} +(-2.70632 + 1.56249i) q^{19} +(-2.27205 + 4.19372i) q^{20} +(-1.12573 - 12.8672i) q^{22} +(0.409999 + 0.191186i) q^{23} +(-0.600292 + 4.96383i) q^{25} +4.23615i q^{26} +(-4.05115 + 4.05115i) q^{28} +(-1.39473 - 7.90988i) q^{29} +(-1.53858 + 0.559998i) q^{31} +(8.06517 - 0.705611i) q^{32} +(-0.467869 + 1.28546i) q^{34} +(-2.38982 + 5.50995i) q^{35} +(2.76163 - 0.739977i) q^{37} +(-6.32889 - 0.553706i) q^{38} +(-0.541035 + 0.270367i) q^{40} +(9.28604 + 1.63738i) q^{41} +(0.307907 - 3.51939i) q^{43} +(6.77601 - 11.7364i) q^{44} +(0.459846 + 0.796477i) q^{46} +(-5.68707 + 2.65193i) q^{47} +(-0.137652 + 0.164047i) q^{49} +(-6.78789 + 7.56643i) q^{50} +(-2.54934 + 3.64084i) q^{52} +(-5.99520 - 5.99520i) q^{53} +(2.08704 - 14.0524i) q^{55} +(-0.715470 + 0.126157i) q^{56} +(6.90084 - 14.7989i) q^{58} +(-6.07856 - 5.10051i) q^{59} +(-1.53937 - 0.560286i) q^{61} +(-3.21525 - 0.861522i) q^{62} +(7.81729 + 4.51332i) q^{64} +(-1.08356 + 4.53156i) q^{65} +(4.38163 - 3.06805i) q^{67} +(-1.17572 + 0.823246i) q^{68} +(-10.4048 + 6.38916i) q^{70} +(-2.05039 - 1.18380i) q^{71} +(-1.33738 - 0.358350i) q^{73} +(5.46189 + 1.98796i) q^{74} +(-5.10626 - 4.28466i) q^{76} +(7.21181 - 15.4658i) q^{77} +(-6.73243 + 1.18711i) q^{79} +(8.21952 + 1.22075i) q^{80} +(13.5550 + 13.5550i) q^{82} +(2.27065 - 3.24283i) q^{83} +(-0.829302 + 1.25543i) q^{85} +(4.61664 - 5.50190i) q^{86} +(1.55749 - 0.726271i) q^{88} +(-0.428822 - 0.742742i) q^{89} +(-2.79833 + 4.84685i) q^{91} +(-0.0841016 + 0.961286i) q^{92} +(-12.5632 - 2.21523i) q^{94} +(-6.62860 - 2.21118i) q^{95} +(-3.88639 - 0.340015i) q^{97} +(-0.420527 + 0.112680i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.66533 + 1.16608i 1.17756 + 0.824540i 0.987560 0.157243i \(-0.0502607\pi\)
0.190005 + 0.981783i \(0.439150\pi\)
\(3\) 0 0
\(4\) 0.729546 + 2.00441i 0.364773 + 1.00221i
\(5\) 1.48319 + 1.67336i 0.663303 + 0.748351i
\(6\) 0 0
\(7\) 1.13512 + 2.43427i 0.429034 + 0.920067i 0.995390 + 0.0959060i \(0.0305748\pi\)
−0.566356 + 0.824160i \(0.691647\pi\)
\(8\) −0.0700073 + 0.261271i −0.0247513 + 0.0923732i
\(9\) 0 0
\(10\) 0.518731 + 4.51621i 0.164037 + 1.42815i
\(11\) −4.08386 4.86695i −1.23133 1.46744i −0.835842 0.548970i \(-0.815020\pi\)
−0.395488 0.918471i \(-0.629424\pi\)
\(12\) 0 0
\(13\) 1.19516 + 1.70687i 0.331479 + 0.473401i 0.949948 0.312408i \(-0.101136\pi\)
−0.618469 + 0.785809i \(0.712247\pi\)
\(14\) −0.948196 + 5.37749i −0.253416 + 1.43719i
\(15\) 0 0
\(16\) 2.84677 2.38873i 0.711694 0.597182i
\(17\) 0.174154 + 0.649952i 0.0422386 + 0.157637i 0.983824 0.179138i \(-0.0573308\pi\)
−0.941585 + 0.336774i \(0.890664\pi\)
\(18\) 0 0
\(19\) −2.70632 + 1.56249i −0.620871 + 0.358460i −0.777208 0.629243i \(-0.783365\pi\)
0.156337 + 0.987704i \(0.450031\pi\)
\(20\) −2.27205 + 4.19372i −0.508046 + 0.937744i
\(21\) 0 0
\(22\) −1.12573 12.8672i −0.240007 2.74329i
\(23\) 0.409999 + 0.191186i 0.0854907 + 0.0398650i 0.464893 0.885367i \(-0.346093\pi\)
−0.379403 + 0.925232i \(0.623870\pi\)
\(24\) 0 0
\(25\) −0.600292 + 4.96383i −0.120058 + 0.992767i
\(26\) 4.23615i 0.830778i
\(27\) 0 0
\(28\) −4.05115 + 4.05115i −0.765596 + 0.765596i
\(29\) −1.39473 7.90988i −0.258994 1.46883i −0.785608 0.618724i \(-0.787650\pi\)
0.526614 0.850104i \(-0.323461\pi\)
\(30\) 0 0
\(31\) −1.53858 + 0.559998i −0.276338 + 0.100579i −0.476472 0.879190i \(-0.658084\pi\)
0.200134 + 0.979769i \(0.435862\pi\)
\(32\) 8.06517 0.705611i 1.42573 0.124735i
\(33\) 0 0
\(34\) −0.467869 + 1.28546i −0.0802389 + 0.220455i
\(35\) −2.38982 + 5.50995i −0.403953 + 0.931351i
\(36\) 0 0
\(37\) 2.76163 0.739977i 0.454009 0.121651i −0.0245656 0.999698i \(-0.507820\pi\)
0.478575 + 0.878047i \(0.341154\pi\)
\(38\) −6.32889 0.553706i −1.02668 0.0898230i
\(39\) 0 0
\(40\) −0.541035 + 0.270367i −0.0855452 + 0.0427487i
\(41\) 9.28604 + 1.63738i 1.45024 + 0.255716i 0.842617 0.538514i \(-0.181014\pi\)
0.607618 + 0.794229i \(0.292125\pi\)
\(42\) 0 0
\(43\) 0.307907 3.51939i 0.0469554 0.536702i −0.935893 0.352285i \(-0.885405\pi\)
0.982848 0.184417i \(-0.0590397\pi\)
\(44\) 6.77601 11.7364i 1.02152 1.76933i
\(45\) 0 0
\(46\) 0.459846 + 0.796477i 0.0678006 + 0.117434i
\(47\) −5.68707 + 2.65193i −0.829545 + 0.386823i −0.790536 0.612416i \(-0.790198\pi\)
−0.0390089 + 0.999239i \(0.512420\pi\)
\(48\) 0 0
\(49\) −0.137652 + 0.164047i −0.0196646 + 0.0234353i
\(50\) −6.78789 + 7.56643i −0.959952 + 1.07005i
\(51\) 0 0
\(52\) −2.54934 + 3.64084i −0.353530 + 0.504894i
\(53\) −5.99520 5.99520i −0.823504 0.823504i 0.163105 0.986609i \(-0.447849\pi\)
−0.986609 + 0.163105i \(0.947849\pi\)
\(54\) 0 0
\(55\) 2.08704 14.0524i 0.281417 1.89483i
\(56\) −0.715470 + 0.126157i −0.0956087 + 0.0168584i
\(57\) 0 0
\(58\) 6.90084 14.7989i 0.906125 1.94319i
\(59\) −6.07856 5.10051i −0.791361 0.664030i 0.154721 0.987958i \(-0.450552\pi\)
−0.946082 + 0.323928i \(0.894997\pi\)
\(60\) 0 0
\(61\) −1.53937 0.560286i −0.197096 0.0717372i 0.241586 0.970379i \(-0.422332\pi\)
−0.438682 + 0.898642i \(0.644555\pi\)
\(62\) −3.21525 0.861522i −0.408337 0.109413i
\(63\) 0 0
\(64\) 7.81729 + 4.51332i 0.977162 + 0.564165i
\(65\) −1.08356 + 4.53156i −0.134399 + 0.562071i
\(66\) 0 0
\(67\) 4.38163 3.06805i 0.535302 0.374822i −0.274444 0.961603i \(-0.588494\pi\)
0.809746 + 0.586781i \(0.199605\pi\)
\(68\) −1.17572 + 0.823246i −0.142577 + 0.0998333i
\(69\) 0 0
\(70\) −10.4048 + 6.38916i −1.24362 + 0.763651i
\(71\) −2.05039 1.18380i −0.243337 0.140491i 0.373372 0.927682i \(-0.378201\pi\)
−0.616710 + 0.787191i \(0.711535\pi\)
\(72\) 0 0
\(73\) −1.33738 0.358350i −0.156529 0.0419417i 0.179704 0.983721i \(-0.442486\pi\)
−0.336232 + 0.941779i \(0.609153\pi\)
\(74\) 5.46189 + 1.98796i 0.634932 + 0.231096i
\(75\) 0 0
\(76\) −5.10626 4.28466i −0.585728 0.491484i
\(77\) 7.21181 15.4658i 0.821861 1.76249i
\(78\) 0 0
\(79\) −6.73243 + 1.18711i −0.757458 + 0.133560i −0.539023 0.842291i \(-0.681206\pi\)
−0.218435 + 0.975851i \(0.570095\pi\)
\(80\) 8.21952 + 1.22075i 0.918970 + 0.136484i
\(81\) 0 0
\(82\) 13.5550 + 13.5550i 1.49690 + 1.49690i
\(83\) 2.27065 3.24283i 0.249236 0.355946i −0.674966 0.737848i \(-0.735842\pi\)
0.924203 + 0.381902i \(0.124731\pi\)
\(84\) 0 0
\(85\) −0.829302 + 1.25543i −0.0899505 + 0.136170i
\(86\) 4.61664 5.50190i 0.497825 0.593285i
\(87\) 0 0
\(88\) 1.55749 0.726271i 0.166029 0.0774208i
\(89\) −0.428822 0.742742i −0.0454551 0.0787305i 0.842403 0.538848i \(-0.181140\pi\)
−0.887858 + 0.460118i \(0.847807\pi\)
\(90\) 0 0
\(91\) −2.79833 + 4.84685i −0.293345 + 0.508088i
\(92\) −0.0841016 + 0.961286i −0.00876820 + 0.100221i
\(93\) 0 0
\(94\) −12.5632 2.21523i −1.29579 0.228483i
\(95\) −6.62860 2.21118i −0.680080 0.226862i
\(96\) 0 0
\(97\) −3.88639 0.340015i −0.394603 0.0345233i −0.111872 0.993723i \(-0.535685\pi\)
−0.282731 + 0.959199i \(0.591240\pi\)
\(98\) −0.420527 + 0.112680i −0.0424797 + 0.0113824i
\(99\) 0 0
\(100\) −10.3875 + 2.41811i −1.03875 + 0.241811i
\(101\) −4.66297 + 12.8114i −0.463983 + 1.27478i 0.458482 + 0.888704i \(0.348393\pi\)
−0.922465 + 0.386080i \(0.873829\pi\)
\(102\) 0 0
\(103\) 6.33428 0.554178i 0.624135 0.0546047i 0.229299 0.973356i \(-0.426357\pi\)
0.394837 + 0.918751i \(0.370801\pi\)
\(104\) −0.529626 + 0.192768i −0.0519341 + 0.0189025i
\(105\) 0 0
\(106\) −2.99312 16.9748i −0.290718 1.64874i
\(107\) 7.42914 7.42914i 0.718202 0.718202i −0.250035 0.968237i \(-0.580442\pi\)
0.968237 + 0.250035i \(0.0804420\pi\)
\(108\) 0 0
\(109\) 2.73749i 0.262204i 0.991369 + 0.131102i \(0.0418515\pi\)
−0.991369 + 0.131102i \(0.958148\pi\)
\(110\) 19.8618 20.9682i 1.89374 1.99924i
\(111\) 0 0
\(112\) 9.04622 + 4.21832i 0.854788 + 0.398594i
\(113\) 1.76514 + 20.1756i 0.166050 + 1.89796i 0.386073 + 0.922468i \(0.373831\pi\)
−0.220022 + 0.975495i \(0.570613\pi\)
\(114\) 0 0
\(115\) 0.288184 + 0.969643i 0.0268733 + 0.0904197i
\(116\) 14.8371 8.56623i 1.37759 0.795354i
\(117\) 0 0
\(118\) −4.17521 15.5821i −0.384359 1.43445i
\(119\) −1.38447 + 1.16171i −0.126914 + 0.106494i
\(120\) 0 0
\(121\) −5.09920 + 28.9190i −0.463564 + 2.62900i
\(122\) −1.91022 2.72808i −0.172944 0.246989i
\(123\) 0 0
\(124\) −2.24493 2.67541i −0.201601 0.240259i
\(125\) −9.19665 + 6.35781i −0.822573 + 0.568659i
\(126\) 0 0
\(127\) −0.371696 + 1.38719i −0.0329827 + 0.123093i −0.980454 0.196747i \(-0.936962\pi\)
0.947472 + 0.319840i \(0.103629\pi\)
\(128\) 0.912480 + 1.95682i 0.0806526 + 0.172960i
\(129\) 0 0
\(130\) −7.08862 + 6.28302i −0.621713 + 0.551057i
\(131\) 6.84812 + 18.8151i 0.598323 + 1.64388i 0.754614 + 0.656168i \(0.227824\pi\)
−0.156291 + 0.987711i \(0.549954\pi\)
\(132\) 0 0
\(133\) −6.87551 4.81428i −0.596182 0.417451i
\(134\) 10.8744 0.939409
\(135\) 0 0
\(136\) −0.182006 −0.0156069
\(137\) 10.7088 + 7.49837i 0.914913 + 0.640629i 0.933260 0.359202i \(-0.116951\pi\)
−0.0183463 + 0.999832i \(0.505840\pi\)
\(138\) 0 0
\(139\) 4.79900 + 13.1851i 0.407046 + 1.11835i 0.958735 + 0.284300i \(0.0917610\pi\)
−0.551690 + 0.834049i \(0.686017\pi\)
\(140\) −12.7877 0.770420i −1.08076 0.0651124i
\(141\) 0 0
\(142\) −2.03418 4.36232i −0.170705 0.366078i
\(143\) 3.42638 12.7874i 0.286528 1.06934i
\(144\) 0 0
\(145\) 11.1675 14.0658i 0.927408 1.16810i
\(146\) −1.80932 2.15626i −0.149740 0.178453i
\(147\) 0 0
\(148\) 3.49795 + 4.99559i 0.287530 + 0.410635i
\(149\) −0.199237 + 1.12993i −0.0163222 + 0.0925675i −0.991881 0.127173i \(-0.959410\pi\)
0.975558 + 0.219740i \(0.0705209\pi\)
\(150\) 0 0
\(151\) 1.20809 1.01370i 0.0983127 0.0824941i −0.592307 0.805713i \(-0.701783\pi\)
0.690619 + 0.723219i \(0.257338\pi\)
\(152\) −0.218772 0.816468i −0.0177447 0.0662243i
\(153\) 0 0
\(154\) 30.0443 17.3461i 2.42104 1.39779i
\(155\) −3.21909 1.74402i −0.258564 0.140083i
\(156\) 0 0
\(157\) −1.15466 13.1978i −0.0921516 1.05330i −0.891679 0.452668i \(-0.850472\pi\)
0.799528 0.600629i \(-0.205083\pi\)
\(158\) −12.5960 5.87360i −1.00208 0.467278i
\(159\) 0 0
\(160\) 13.1429 + 12.4494i 1.03904 + 0.984211i
\(161\) 1.21507i 0.0957606i
\(162\) 0 0
\(163\) −13.2225 + 13.2225i −1.03567 + 1.03567i −0.0363256 + 0.999340i \(0.511565\pi\)
−0.999340 + 0.0363256i \(0.988435\pi\)
\(164\) 3.49261 + 19.8076i 0.272727 + 1.54671i
\(165\) 0 0
\(166\) 7.56276 2.75262i 0.586984 0.213645i
\(167\) −7.51125 + 0.657149i −0.581238 + 0.0508517i −0.373983 0.927435i \(-0.622008\pi\)
−0.207254 + 0.978287i \(0.566453\pi\)
\(168\) 0 0
\(169\) 2.96127 8.13602i 0.227790 0.625848i
\(170\) −2.84498 + 1.12367i −0.218200 + 0.0861813i
\(171\) 0 0
\(172\) 7.27894 1.95039i 0.555014 0.148715i
\(173\) −7.48506 0.654858i −0.569078 0.0497879i −0.201014 0.979588i \(-0.564424\pi\)
−0.368064 + 0.929800i \(0.619979\pi\)
\(174\) 0 0
\(175\) −12.7647 + 4.17326i −0.964921 + 0.315469i
\(176\) −23.2516 4.09989i −1.75266 0.309041i
\(177\) 0 0
\(178\) 0.151963 1.73695i 0.0113901 0.130190i
\(179\) −6.45949 + 11.1882i −0.482805 + 0.836242i −0.999805 0.0197428i \(-0.993715\pi\)
0.517000 + 0.855985i \(0.327049\pi\)
\(180\) 0 0
\(181\) −2.64164 4.57545i −0.196351 0.340091i 0.750991 0.660312i \(-0.229576\pi\)
−0.947343 + 0.320222i \(0.896243\pi\)
\(182\) −10.3119 + 4.80853i −0.764371 + 0.356432i
\(183\) 0 0
\(184\) −0.0786542 + 0.0937365i −0.00579847 + 0.00691034i
\(185\) 5.33427 + 3.52369i 0.392184 + 0.259066i
\(186\) 0 0
\(187\) 2.45207 3.50191i 0.179313 0.256085i
\(188\) −9.46453 9.46453i −0.690272 0.690272i
\(189\) 0 0
\(190\) −8.46039 11.4118i −0.613782 0.827898i
\(191\) −18.3259 + 3.23135i −1.32602 + 0.233812i −0.791408 0.611288i \(-0.790652\pi\)
−0.534607 + 0.845101i \(0.679540\pi\)
\(192\) 0 0
\(193\) −2.42548 + 5.20146i −0.174590 + 0.374410i −0.974058 0.226300i \(-0.927337\pi\)
0.799468 + 0.600709i \(0.205115\pi\)
\(194\) −6.07563 5.09806i −0.436205 0.366020i
\(195\) 0 0
\(196\) −0.429242 0.156231i −0.0306601 0.0111594i
\(197\) −16.4402 4.40513i −1.17131 0.313852i −0.379837 0.925053i \(-0.624020\pi\)
−0.791475 + 0.611201i \(0.790687\pi\)
\(198\) 0 0
\(199\) −20.0824 11.5946i −1.42361 0.821920i −0.427002 0.904251i \(-0.640430\pi\)
−0.996605 + 0.0823307i \(0.973764\pi\)
\(200\) −1.25488 0.504344i −0.0887335 0.0356625i
\(201\) 0 0
\(202\) −22.7045 + 15.8978i −1.59748 + 1.11857i
\(203\) 17.6716 12.3738i 1.24030 0.868469i
\(204\) 0 0
\(205\) 11.0330 + 17.9675i 0.770580 + 1.25490i
\(206\) 11.1949 + 6.46336i 0.779983 + 0.450324i
\(207\) 0 0
\(208\) 7.47961 + 2.00416i 0.518618 + 0.138963i
\(209\) 18.6568 + 6.79052i 1.29052 + 0.469710i
\(210\) 0 0
\(211\) −1.99032 1.67007i −0.137019 0.114973i 0.571702 0.820461i \(-0.306283\pi\)
−0.708721 + 0.705488i \(0.750728\pi\)
\(212\) 7.64307 16.3906i 0.524928 1.12571i
\(213\) 0 0
\(214\) 21.0349 3.70902i 1.43792 0.253543i
\(215\) 6.34591 4.70469i 0.432787 0.320857i
\(216\) 0 0
\(217\) −3.10966 3.10966i −0.211097 0.211097i
\(218\) −3.19212 + 4.55882i −0.216198 + 0.308762i
\(219\) 0 0
\(220\) 29.6894 6.06858i 2.00166 0.409143i
\(221\) −0.901242 + 1.07406i −0.0606241 + 0.0722490i
\(222\) 0 0
\(223\) 4.57405 2.13291i 0.306301 0.142831i −0.263390 0.964689i \(-0.584841\pi\)
0.569691 + 0.821859i \(0.307063\pi\)
\(224\) 10.8726 + 18.8318i 0.726453 + 1.25825i
\(225\) 0 0
\(226\) −20.5868 + 35.6573i −1.36941 + 2.37189i
\(227\) 1.72288 19.6926i 0.114352 1.30705i −0.694696 0.719304i \(-0.744461\pi\)
0.809048 0.587743i \(-0.199983\pi\)
\(228\) 0 0
\(229\) 24.6362 + 4.34402i 1.62800 + 0.287061i 0.911740 0.410768i \(-0.134739\pi\)
0.716264 + 0.697829i \(0.245850\pi\)
\(230\) −0.650756 + 1.95082i −0.0429096 + 0.128633i
\(231\) 0 0
\(232\) 2.16426 + 0.189349i 0.142091 + 0.0124313i
\(233\) −7.90321 + 2.11766i −0.517756 + 0.138732i −0.508229 0.861222i \(-0.669699\pi\)
−0.00952771 + 0.999955i \(0.503033\pi\)
\(234\) 0 0
\(235\) −12.8726 5.58323i −0.839719 0.364210i
\(236\) 5.78894 15.9050i 0.376828 1.03533i
\(237\) 0 0
\(238\) −3.66024 + 0.320230i −0.237258 + 0.0207574i
\(239\) −15.0785 + 5.48812i −0.975347 + 0.354997i −0.780029 0.625743i \(-0.784796\pi\)
−0.195317 + 0.980740i \(0.562574\pi\)
\(240\) 0 0
\(241\) 2.00152 + 11.3512i 0.128929 + 0.731194i 0.978896 + 0.204358i \(0.0655107\pi\)
−0.849967 + 0.526836i \(0.823378\pi\)
\(242\) −42.2136 + 42.2136i −2.71359 + 2.71359i
\(243\) 0 0
\(244\) 3.49429i 0.223699i
\(245\) −0.478675 + 0.0129715i −0.0305814 + 0.000828719i
\(246\) 0 0
\(247\) −5.90147 2.75190i −0.375501 0.175099i
\(248\) −0.0385992 0.441191i −0.00245105 0.0280157i
\(249\) 0 0
\(250\) −22.7291 0.136151i −1.43752 0.00861094i
\(251\) −0.521180 + 0.300903i −0.0328966 + 0.0189928i −0.516358 0.856373i \(-0.672713\pi\)
0.483462 + 0.875366i \(0.339379\pi\)
\(252\) 0 0
\(253\) −0.743887 2.77622i −0.0467677 0.174540i
\(254\) −2.23656 + 1.87670i −0.140334 + 0.117755i
\(255\) 0 0
\(256\) 2.37270 13.4562i 0.148294 0.841014i
\(257\) 5.05815 + 7.22379i 0.315519 + 0.450608i 0.945318 0.326151i \(-0.105752\pi\)
−0.629799 + 0.776758i \(0.716863\pi\)
\(258\) 0 0
\(259\) 4.93607 + 5.88259i 0.306713 + 0.365526i
\(260\) −9.87361 + 1.13408i −0.612336 + 0.0703327i
\(261\) 0 0
\(262\) −10.5354 + 39.3187i −0.650880 + 2.42912i
\(263\) −5.05420 10.8388i −0.311656 0.668347i 0.686622 0.727015i \(-0.259093\pi\)
−0.998278 + 0.0586671i \(0.981315\pi\)
\(264\) 0 0
\(265\) 1.14013 18.9242i 0.0700374 1.16250i
\(266\) −5.83616 16.0347i −0.357838 0.983152i
\(267\) 0 0
\(268\) 9.34624 + 6.54431i 0.570913 + 0.399757i
\(269\) 15.6712 0.955492 0.477746 0.878498i \(-0.341454\pi\)
0.477746 + 0.878498i \(0.341454\pi\)
\(270\) 0 0
\(271\) 15.3544 0.932711 0.466355 0.884597i \(-0.345567\pi\)
0.466355 + 0.884597i \(0.345567\pi\)
\(272\) 2.04834 + 1.43426i 0.124199 + 0.0869648i
\(273\) 0 0
\(274\) 9.08998 + 24.9745i 0.549146 + 1.50876i
\(275\) 26.6103 17.3500i 1.60466 1.04624i
\(276\) 0 0
\(277\) 1.83097 + 3.92654i 0.110013 + 0.235923i 0.953605 0.301062i \(-0.0973411\pi\)
−0.843592 + 0.536985i \(0.819563\pi\)
\(278\) −7.38296 + 27.5536i −0.442800 + 1.65255i
\(279\) 0 0
\(280\) −1.27228 1.01013i −0.0760335 0.0603666i
\(281\) 11.4406 + 13.6344i 0.682490 + 0.813360i 0.990426 0.138047i \(-0.0440825\pi\)
−0.307935 + 0.951407i \(0.599638\pi\)
\(282\) 0 0
\(283\) −11.3847 16.2591i −0.676752 0.966501i −0.999798 0.0201182i \(-0.993596\pi\)
0.323046 0.946383i \(-0.395293\pi\)
\(284\) 0.876956 4.97347i 0.0520378 0.295121i
\(285\) 0 0
\(286\) 20.6172 17.2998i 1.21912 1.02296i
\(287\) 6.55492 + 24.4633i 0.386925 + 1.44402i
\(288\) 0 0
\(289\) 14.3303 8.27362i 0.842960 0.486683i
\(290\) 34.9992 10.4020i 2.05523 0.610825i
\(291\) 0 0
\(292\) −0.257400 2.94209i −0.0150632 0.172173i
\(293\) 14.9126 + 6.95384i 0.871201 + 0.406248i 0.806204 0.591638i \(-0.201518\pi\)
0.0649974 + 0.997885i \(0.479296\pi\)
\(294\) 0 0
\(295\) −0.480642 17.7367i −0.0279840 1.03267i
\(296\) 0.773337i 0.0449493i
\(297\) 0 0
\(298\) −1.64938 + 1.64938i −0.0955460 + 0.0955460i
\(299\) 0.163687 + 0.928314i 0.00946626 + 0.0536858i
\(300\) 0 0
\(301\) 8.91665 3.24540i 0.513947 0.187061i
\(302\) 3.19392 0.279431i 0.183789 0.0160795i
\(303\) 0 0
\(304\) −3.97190 + 10.9127i −0.227804 + 0.625887i
\(305\) −1.34562 3.40694i −0.0770500 0.195081i
\(306\) 0 0
\(307\) −2.83491 + 0.759611i −0.161797 + 0.0433533i −0.338808 0.940856i \(-0.610024\pi\)
0.177011 + 0.984209i \(0.443357\pi\)
\(308\) 36.2611 + 3.17243i 2.06617 + 0.180766i
\(309\) 0 0
\(310\) −3.32718 6.65808i −0.188971 0.378153i
\(311\) 3.75166 + 0.661519i 0.212737 + 0.0375113i 0.279001 0.960291i \(-0.409997\pi\)
−0.0662637 + 0.997802i \(0.521108\pi\)
\(312\) 0 0
\(313\) 0.0495580 0.566450i 0.00280118 0.0320177i −0.994665 0.103153i \(-0.967107\pi\)
0.997467 + 0.0711357i \(0.0226623\pi\)
\(314\) 13.4667 23.3250i 0.759971 1.31631i
\(315\) 0 0
\(316\) −7.29107 12.6285i −0.410155 0.710409i
\(317\) 10.3800 4.84025i 0.582997 0.271856i −0.108664 0.994079i \(-0.534657\pi\)
0.691661 + 0.722223i \(0.256879\pi\)
\(318\) 0 0
\(319\) −32.8012 + 39.0909i −1.83651 + 2.18867i
\(320\) 4.04212 + 19.7753i 0.225961 + 1.10547i
\(321\) 0 0
\(322\) −1.41686 + 2.02348i −0.0789584 + 0.112764i
\(323\) −1.48686 1.48686i −0.0827312 0.0827312i
\(324\) 0 0
\(325\) −9.19007 + 4.90798i −0.509774 + 0.272246i
\(326\) −37.4382 + 6.60137i −2.07351 + 0.365616i
\(327\) 0 0
\(328\) −1.07789 + 2.31154i −0.0595165 + 0.127634i
\(329\) −12.9110 10.8336i −0.711806 0.597276i
\(330\) 0 0
\(331\) 24.0043 + 8.73685i 1.31940 + 0.480221i 0.903265 0.429084i \(-0.141164\pi\)
0.416131 + 0.909305i \(0.363386\pi\)
\(332\) 8.15650 + 2.18553i 0.447646 + 0.119946i
\(333\) 0 0
\(334\) −13.2750 7.66431i −0.726374 0.419372i
\(335\) 11.6328 + 2.78156i 0.635566 + 0.151973i
\(336\) 0 0
\(337\) 14.4868 10.1438i 0.789147 0.552566i −0.108077 0.994143i \(-0.534469\pi\)
0.897224 + 0.441576i \(0.145580\pi\)
\(338\) 14.4187 10.0961i 0.784274 0.549154i
\(339\) 0 0
\(340\) −3.12140 0.746372i −0.169282 0.0404777i
\(341\) 9.00884 + 5.20126i 0.487856 + 0.281664i
\(342\) 0 0
\(343\) 17.6052 + 4.71730i 0.950591 + 0.254710i
\(344\) 0.897959 + 0.326830i 0.0484147 + 0.0176215i
\(345\) 0 0
\(346\) −11.7015 9.81869i −0.629075 0.527856i
\(347\) −0.943762 + 2.02390i −0.0506638 + 0.108649i −0.930010 0.367534i \(-0.880202\pi\)
0.879346 + 0.476183i \(0.157980\pi\)
\(348\) 0 0
\(349\) −18.9031 + 3.33312i −1.01186 + 0.178418i −0.654910 0.755707i \(-0.727294\pi\)
−0.356948 + 0.934124i \(0.616183\pi\)
\(350\) −26.1238 7.93475i −1.39637 0.424130i
\(351\) 0 0
\(352\) −36.3712 36.3712i −1.93859 1.93859i
\(353\) −17.0436 + 24.3407i −0.907137 + 1.29553i 0.0478427 + 0.998855i \(0.484765\pi\)
−0.954980 + 0.296671i \(0.904124\pi\)
\(354\) 0 0
\(355\) −1.06020 5.18685i −0.0562698 0.275289i
\(356\) 1.17591 1.40140i 0.0623233 0.0742741i
\(357\) 0 0
\(358\) −23.8034 + 11.0997i −1.25805 + 0.586638i
\(359\) −14.0984 24.4191i −0.744085 1.28879i −0.950621 0.310354i \(-0.899552\pi\)
0.206536 0.978439i \(-0.433781\pi\)
\(360\) 0 0
\(361\) −4.61724 + 7.99729i −0.243012 + 0.420910i
\(362\) 0.936127 10.7000i 0.0492017 0.562378i
\(363\) 0 0
\(364\) −11.7566 2.07300i −0.616212 0.108655i
\(365\) −1.38394 2.76943i −0.0724388 0.144958i
\(366\) 0 0
\(367\) 23.9655 + 2.09671i 1.25099 + 0.109447i 0.693328 0.720622i \(-0.256144\pi\)
0.557660 + 0.830069i \(0.311699\pi\)
\(368\) 1.62387 0.435114i 0.0846499 0.0226819i
\(369\) 0 0
\(370\) 4.77443 + 12.0883i 0.248211 + 0.628438i
\(371\) 7.78866 21.3992i 0.404367 1.11099i
\(372\) 0 0
\(373\) 7.15282 0.625791i 0.370359 0.0324022i 0.0995428 0.995033i \(-0.468262\pi\)
0.270816 + 0.962631i \(0.412706\pi\)
\(374\) 8.16699 2.97254i 0.422305 0.153706i
\(375\) 0 0
\(376\) −0.294734 1.67152i −0.0151998 0.0862021i
\(377\) 11.8342 11.8342i 0.609494 0.609494i
\(378\) 0 0
\(379\) 6.61098i 0.339583i −0.985480 0.169792i \(-0.945691\pi\)
0.985480 0.169792i \(-0.0543094\pi\)
\(380\) −0.403760 14.8996i −0.0207125 0.764333i
\(381\) 0 0
\(382\) −34.2866 15.9881i −1.75426 0.818023i
\(383\) −0.852747 9.74694i −0.0435733 0.498046i −0.986355 0.164634i \(-0.947356\pi\)
0.942781 0.333412i \(-0.108200\pi\)
\(384\) 0 0
\(385\) 36.5763 10.8707i 1.86410 0.554022i
\(386\) −10.1045 + 5.83385i −0.514307 + 0.296935i
\(387\) 0 0
\(388\) −2.15377 8.03798i −0.109341 0.408067i
\(389\) −7.47118 + 6.26906i −0.378804 + 0.317854i −0.812233 0.583334i \(-0.801748\pi\)
0.433429 + 0.901188i \(0.357304\pi\)
\(390\) 0 0
\(391\) −0.0528585 + 0.299776i −0.00267317 + 0.0151603i
\(392\) −0.0332242 0.0474490i −0.00167807 0.00239654i
\(393\) 0 0
\(394\) −22.2415 26.5064i −1.12051 1.33538i
\(395\) −11.9719 9.50510i −0.602374 0.478253i
\(396\) 0 0
\(397\) −5.87091 + 21.9105i −0.294653 + 1.09966i 0.646840 + 0.762626i \(0.276090\pi\)
−0.941493 + 0.337033i \(0.890577\pi\)
\(398\) −19.9237 42.7265i −0.998684 2.14168i
\(399\) 0 0
\(400\) 10.1484 + 15.5648i 0.507418 + 0.778242i
\(401\) −10.7416 29.5124i −0.536411 1.47378i −0.851316 0.524654i \(-0.824195\pi\)
0.314905 0.949123i \(-0.398027\pi\)
\(402\) 0 0
\(403\) −2.79470 1.95687i −0.139214 0.0974788i
\(404\) −29.0812 −1.44684
\(405\) 0 0
\(406\) 43.8578 2.17662
\(407\) −14.8795 10.4188i −0.737551 0.516439i
\(408\) 0 0
\(409\) −9.77070 26.8448i −0.483130 1.32739i −0.906796 0.421570i \(-0.861479\pi\)
0.423666 0.905818i \(-0.360743\pi\)
\(410\) −2.57779 + 42.7871i −0.127308 + 2.11310i
\(411\) 0 0
\(412\) 5.73195 + 12.2922i 0.282393 + 0.605593i
\(413\) 5.51614 20.5865i 0.271432 1.01300i
\(414\) 0 0
\(415\) 8.79424 1.01010i 0.431692 0.0495840i
\(416\) 10.8436 + 12.9229i 0.531650 + 0.633596i
\(417\) 0 0
\(418\) 23.1514 + 33.0637i 1.13237 + 1.61720i
\(419\) −0.704690 + 3.99650i −0.0344264 + 0.195242i −0.997171 0.0751721i \(-0.976049\pi\)
0.962744 + 0.270414i \(0.0871605\pi\)
\(420\) 0 0
\(421\) −7.52582 + 6.31491i −0.366786 + 0.307770i −0.807489 0.589883i \(-0.799174\pi\)
0.440703 + 0.897653i \(0.354729\pi\)
\(422\) −1.36710 5.10208i −0.0665493 0.248366i
\(423\) 0 0
\(424\) 1.98608 1.14666i 0.0964525 0.0556869i
\(425\) −3.33080 + 0.474311i −0.161567 + 0.0230075i
\(426\) 0 0
\(427\) −0.383483 4.38323i −0.0185581 0.212119i
\(428\) 20.3110 + 9.47115i 0.981767 + 0.457805i
\(429\) 0 0
\(430\) 16.0540 0.435044i 0.774194 0.0209797i
\(431\) 3.57709i 0.172302i 0.996282 + 0.0861512i \(0.0274568\pi\)
−0.996282 + 0.0861512i \(0.972543\pi\)
\(432\) 0 0
\(433\) 0.671243 0.671243i 0.0322579 0.0322579i −0.690794 0.723052i \(-0.742739\pi\)
0.723052 + 0.690794i \(0.242739\pi\)
\(434\) −1.55251 8.80470i −0.0745227 0.422639i
\(435\) 0 0
\(436\) −5.48705 + 1.99712i −0.262782 + 0.0956449i
\(437\) −1.40831 + 0.123211i −0.0673688 + 0.00589400i
\(438\) 0 0
\(439\) 11.2524 30.9157i 0.537048 1.47553i −0.313479 0.949595i \(-0.601495\pi\)
0.850527 0.525932i \(-0.176283\pi\)
\(440\) 3.52537 + 1.52905i 0.168066 + 0.0728948i
\(441\) 0 0
\(442\) −2.75330 + 0.737744i −0.130961 + 0.0350909i
\(443\) 22.3331 + 1.95389i 1.06108 + 0.0928322i 0.604306 0.796752i \(-0.293450\pi\)
0.456771 + 0.889585i \(0.349006\pi\)
\(444\) 0 0
\(445\) 0.606852 1.81920i 0.0287676 0.0862385i
\(446\) 10.1044 + 1.78168i 0.478459 + 0.0843652i
\(447\) 0 0
\(448\) −2.11307 + 24.1525i −0.0998333 + 1.14110i
\(449\) −4.96273 + 8.59571i −0.234206 + 0.405656i −0.959042 0.283265i \(-0.908582\pi\)
0.724836 + 0.688922i \(0.241916\pi\)
\(450\) 0 0
\(451\) −29.9538 51.8815i −1.41047 2.44301i
\(452\) −39.1525 + 18.2571i −1.84158 + 0.858742i
\(453\) 0 0
\(454\) 25.8323 30.7857i 1.21237 1.44484i
\(455\) −12.2610 + 2.50618i −0.574804 + 0.117491i
\(456\) 0 0
\(457\) 19.8172 28.3019i 0.927010 1.32391i −0.0190173 0.999819i \(-0.506054\pi\)
0.946027 0.324088i \(-0.105057\pi\)
\(458\) 35.9619 + 35.9619i 1.68039 + 1.68039i
\(459\) 0 0
\(460\) −1.73332 + 1.28504i −0.0808164 + 0.0599152i
\(461\) 10.2855 1.81362i 0.479046 0.0844687i 0.0710890 0.997470i \(-0.477353\pi\)
0.407957 + 0.913001i \(0.366241\pi\)
\(462\) 0 0
\(463\) −7.80727 + 16.7427i −0.362835 + 0.778101i 0.637138 + 0.770749i \(0.280118\pi\)
−0.999973 + 0.00735185i \(0.997660\pi\)
\(464\) −22.8650 19.1860i −1.06148 0.890689i
\(465\) 0 0
\(466\) −15.6308 5.68914i −0.724082 0.263544i
\(467\) 37.1950 + 9.96636i 1.72118 + 0.461188i 0.978120 0.208040i \(-0.0667084\pi\)
0.743057 + 0.669228i \(0.233375\pi\)
\(468\) 0 0
\(469\) 12.4421 + 7.18347i 0.574524 + 0.331702i
\(470\) −14.9267 24.3084i −0.688518 1.12126i
\(471\) 0 0
\(472\) 1.75816 1.23108i 0.0809259 0.0566649i
\(473\) −18.3862 + 12.8741i −0.845397 + 0.591953i
\(474\) 0 0
\(475\) −6.13137 14.3717i −0.281327 0.659417i
\(476\) −3.33858 1.92753i −0.153024 0.0883482i
\(477\) 0 0
\(478\) −31.5102 8.44313i −1.44124 0.386180i
\(479\) −13.8251 5.03191i −0.631684 0.229914i 0.00628038 0.999980i \(-0.498001\pi\)
−0.637964 + 0.770066i \(0.720223\pi\)
\(480\) 0 0
\(481\) 4.56365 + 3.82935i 0.208084 + 0.174604i
\(482\) −9.90315 + 21.2374i −0.451076 + 0.967336i
\(483\) 0 0
\(484\) −61.6857 + 10.8768i −2.80389 + 0.494402i
\(485\) −5.19529 7.00765i −0.235906 0.318201i
\(486\) 0 0
\(487\) 3.40980 + 3.40980i 0.154513 + 0.154513i 0.780130 0.625617i \(-0.215153\pi\)
−0.625617 + 0.780130i \(0.715153\pi\)
\(488\) 0.254154 0.362969i 0.0115050 0.0164308i
\(489\) 0 0
\(490\) −0.812277 0.536569i −0.0366949 0.0242397i
\(491\) 4.15599 4.95292i 0.187557 0.223522i −0.664069 0.747671i \(-0.731172\pi\)
0.851627 + 0.524149i \(0.175617\pi\)
\(492\) 0 0
\(493\) 4.89815 2.28404i 0.220602 0.102868i
\(494\) −6.61896 11.4644i −0.297801 0.515806i
\(495\) 0 0
\(496\) −3.04231 + 5.26944i −0.136604 + 0.236605i
\(497\) 0.554237 6.33496i 0.0248609 0.284162i
\(498\) 0 0
\(499\) −24.8022 4.37330i −1.11030 0.195776i −0.411722 0.911309i \(-0.635073\pi\)
−0.698578 + 0.715534i \(0.746184\pi\)
\(500\) −19.4530 13.7955i −0.869966 0.616956i
\(501\) 0 0
\(502\) −1.21881 0.106632i −0.0543982 0.00475922i
\(503\) 37.5360 10.0577i 1.67365 0.448452i 0.707556 0.706657i \(-0.249798\pi\)
0.966090 + 0.258205i \(0.0831310\pi\)
\(504\) 0 0
\(505\) −28.3542 + 11.1989i −1.26175 + 0.498345i
\(506\) 1.99847 5.49075i 0.0888428 0.244094i
\(507\) 0 0
\(508\) −3.05166 + 0.266986i −0.135396 + 0.0118456i
\(509\) −5.50573 + 2.00392i −0.244037 + 0.0888223i −0.461143 0.887326i \(-0.652561\pi\)
0.217106 + 0.976148i \(0.430338\pi\)
\(510\) 0 0
\(511\) −0.645765 3.66231i −0.0285669 0.162011i
\(512\) 22.6957 22.6957i 1.00302 1.00302i
\(513\) 0 0
\(514\) 17.9282i 0.790777i
\(515\) 10.3223 + 9.77760i 0.454854 + 0.430853i
\(516\) 0 0
\(517\) 36.1320 + 16.8486i 1.58908 + 0.741002i
\(518\) 1.36065 + 15.5523i 0.0597834 + 0.683327i
\(519\) 0 0
\(520\) −1.10811 0.600345i −0.0485937 0.0263269i
\(521\) −16.6908 + 9.63645i −0.731238 + 0.422180i −0.818875 0.573972i \(-0.805402\pi\)
0.0876370 + 0.996152i \(0.472068\pi\)
\(522\) 0 0
\(523\) 5.63988 + 21.0483i 0.246615 + 0.920379i 0.972565 + 0.232631i \(0.0747336\pi\)
−0.725950 + 0.687747i \(0.758600\pi\)
\(524\) −32.7171 + 27.4529i −1.42925 + 1.19929i
\(525\) 0 0
\(526\) 4.22192 23.9437i 0.184084 1.04399i
\(527\) −0.631923 0.902479i −0.0275270 0.0393126i
\(528\) 0 0
\(529\) −14.6526 17.4623i −0.637068 0.759228i
\(530\) 23.9657 30.1855i 1.04100 1.31117i
\(531\) 0 0
\(532\) 4.63380 17.2936i 0.200901 0.749772i
\(533\) 8.30354 + 17.8070i 0.359666 + 0.771307i
\(534\) 0 0
\(535\) 23.4505 + 1.41282i 1.01385 + 0.0610817i
\(536\) 0.494847 + 1.35958i 0.0213741 + 0.0587249i
\(537\) 0 0
\(538\) 26.0978 + 18.2738i 1.12515 + 0.787841i
\(539\) 1.36056 0.0586036
\(540\) 0 0
\(541\) 17.4882 0.751877 0.375938 0.926645i \(-0.377320\pi\)
0.375938 + 0.926645i \(0.377320\pi\)
\(542\) 25.5700 + 17.9043i 1.09833 + 0.769057i
\(543\) 0 0
\(544\) 1.86319 + 5.11909i 0.0798838 + 0.219479i
\(545\) −4.58081 + 4.06022i −0.196221 + 0.173921i
\(546\) 0 0
\(547\) −15.2727 32.7524i −0.653013 1.40039i −0.901937 0.431868i \(-0.857855\pi\)
0.248924 0.968523i \(-0.419923\pi\)
\(548\) −7.21727 + 26.9352i −0.308306 + 1.15062i
\(549\) 0 0
\(550\) 64.5462 + 2.13611i 2.75226 + 0.0910841i
\(551\) 16.1337 + 19.2274i 0.687319 + 0.819115i
\(552\) 0 0
\(553\) −10.5318 15.0410i −0.447859 0.639610i
\(554\) −1.52946 + 8.67402i −0.0649807 + 0.368524i
\(555\) 0 0
\(556\) −22.9273 + 19.2383i −0.972336 + 0.815887i
\(557\) 0.942784 + 3.51852i 0.0399470 + 0.149084i 0.983019 0.183505i \(-0.0587444\pi\)
−0.943072 + 0.332589i \(0.892078\pi\)
\(558\) 0 0
\(559\) 6.37515 3.68069i 0.269640 0.155677i
\(560\) 6.35848 + 21.3942i 0.268695 + 0.904070i
\(561\) 0 0
\(562\) 3.15365 + 36.0464i 0.133029 + 1.52053i
\(563\) −7.85254 3.66170i −0.330945 0.154322i 0.250042 0.968235i \(-0.419556\pi\)
−0.580987 + 0.813913i \(0.697333\pi\)
\(564\) 0 0
\(565\) −31.1431 + 32.8780i −1.31020 + 1.38319i
\(566\) 40.3521i 1.69613i
\(567\) 0 0
\(568\) 0.452834 0.452834i 0.0190005 0.0190005i
\(569\) 6.84317 + 38.8095i 0.286881 + 1.62698i 0.698490 + 0.715620i \(0.253856\pi\)
−0.411609 + 0.911361i \(0.635033\pi\)
\(570\) 0 0
\(571\) −4.05495 + 1.47588i −0.169694 + 0.0617636i −0.425470 0.904972i \(-0.639891\pi\)
0.255776 + 0.966736i \(0.417669\pi\)
\(572\) 28.1310 2.46114i 1.17621 0.102905i
\(573\) 0 0
\(574\) −17.6100 + 48.3830i −0.735026 + 2.01947i
\(575\) −1.19513 + 1.92040i −0.0498405 + 0.0800863i
\(576\) 0 0
\(577\) 29.3682 7.86919i 1.22261 0.327598i 0.410915 0.911674i \(-0.365209\pi\)
0.811699 + 0.584075i \(0.198543\pi\)
\(578\) 33.5123 + 2.93195i 1.39393 + 0.121953i
\(579\) 0 0
\(580\) 36.3407 + 12.1226i 1.50897 + 0.503363i
\(581\) 10.4714 + 1.84638i 0.434425 + 0.0766009i
\(582\) 0 0
\(583\) −4.69481 + 53.6619i −0.194439 + 2.22245i
\(584\) 0.187253 0.324332i 0.00774858 0.0134209i
\(585\) 0 0
\(586\) 16.7256 + 28.9696i 0.690929 + 1.19672i
\(587\) −17.8591 + 8.32785i −0.737126 + 0.343727i −0.754657 0.656119i \(-0.772197\pi\)
0.0175318 + 0.999846i \(0.494419\pi\)
\(588\) 0 0
\(589\) 3.28890 3.91956i 0.135517 0.161503i
\(590\) 19.8819 30.0978i 0.818524 1.23911i
\(591\) 0 0
\(592\) 6.09413 8.70333i 0.250467 0.357705i
\(593\) 1.60584 + 1.60584i 0.0659438 + 0.0659438i 0.739310 0.673366i \(-0.235152\pi\)
−0.673366 + 0.739310i \(0.735152\pi\)
\(594\) 0 0
\(595\) −3.99740 0.593688i −0.163877 0.0243388i
\(596\) −2.41020 + 0.424983i −0.0987255 + 0.0174080i
\(597\) 0 0
\(598\) −0.809892 + 1.73682i −0.0331190 + 0.0710238i
\(599\) 16.1072 + 13.5155i 0.658122 + 0.552230i 0.909523 0.415653i \(-0.136447\pi\)
−0.251401 + 0.967883i \(0.580891\pi\)
\(600\) 0 0
\(601\) −25.6301 9.32859i −1.04547 0.380521i −0.238521 0.971137i \(-0.576662\pi\)
−0.806952 + 0.590616i \(0.798885\pi\)
\(602\) 18.6335 + 4.99284i 0.759446 + 0.203493i
\(603\) 0 0
\(604\) 2.91323 + 1.68196i 0.118538 + 0.0684378i
\(605\) −55.9551 + 34.3596i −2.27490 + 1.39692i
\(606\) 0 0
\(607\) −27.5055 + 19.2596i −1.11641 + 0.781721i −0.977990 0.208652i \(-0.933092\pi\)
−0.138424 + 0.990373i \(0.544204\pi\)
\(608\) −20.7244 + 14.5114i −0.840484 + 0.588513i
\(609\) 0 0
\(610\) 1.73185 7.24277i 0.0701205 0.293251i
\(611\) −11.3235 6.53761i −0.458099 0.264484i
\(612\) 0 0
\(613\) 42.7632 + 11.4584i 1.72719 + 0.462799i 0.979532 0.201288i \(-0.0645126\pi\)
0.747656 + 0.664086i \(0.231179\pi\)
\(614\) −5.60681 2.04071i −0.226272 0.0823564i
\(615\) 0 0
\(616\) 3.53588 + 2.96695i 0.142464 + 0.119542i
\(617\) −5.99691 + 12.8604i −0.241427 + 0.517741i −0.989264 0.146141i \(-0.953315\pi\)
0.747837 + 0.663882i \(0.231092\pi\)
\(618\) 0 0
\(619\) 21.7592 3.83673i 0.874576 0.154211i 0.281697 0.959503i \(-0.409103\pi\)
0.592878 + 0.805292i \(0.297991\pi\)
\(620\) 1.14727 7.72473i 0.0460753 0.310233i
\(621\) 0 0
\(622\) 5.47637 + 5.47637i 0.219582 + 0.219582i
\(623\) 1.32127 1.88697i 0.0529355 0.0755998i
\(624\) 0 0
\(625\) −24.2793 5.95950i −0.971172 0.238380i
\(626\) 0.743054 0.885537i 0.0296984 0.0353932i
\(627\) 0 0
\(628\) 25.6114 11.9428i 1.02201 0.476569i
\(629\) 0.961899 + 1.66606i 0.0383534 + 0.0664301i
\(630\) 0 0
\(631\) 6.92272 11.9905i 0.275589 0.477334i −0.694694 0.719305i \(-0.744460\pi\)
0.970284 + 0.241971i \(0.0777937\pi\)
\(632\) 0.161162 1.84210i 0.00641070 0.0732746i
\(633\) 0 0
\(634\) 22.9301 + 4.04320i 0.910672 + 0.160576i
\(635\) −2.87257 + 1.43548i −0.113994 + 0.0569654i
\(636\) 0 0
\(637\) −0.444525 0.0388909i −0.0176127 0.00154091i
\(638\) −100.208 + 26.8506i −3.96726 + 1.06302i
\(639\) 0 0
\(640\) −1.92109 + 4.42925i −0.0759377 + 0.175081i
\(641\) 7.88689 21.6691i 0.311513 0.855876i −0.680838 0.732434i \(-0.738384\pi\)
0.992352 0.123442i \(-0.0393934\pi\)
\(642\) 0 0
\(643\) 7.31553 0.640026i 0.288496 0.0252402i 0.0580110 0.998316i \(-0.481524\pi\)
0.230485 + 0.973076i \(0.425969\pi\)
\(644\) −2.43549 + 0.886446i −0.0959718 + 0.0349309i
\(645\) 0 0
\(646\) −0.742320 4.20990i −0.0292062 0.165636i
\(647\) 24.4108 24.4108i 0.959686 0.959686i −0.0395324 0.999218i \(-0.512587\pi\)
0.999218 + 0.0395324i \(0.0125868\pi\)
\(648\) 0 0
\(649\) 50.4138i 1.97892i
\(650\) −21.0276 2.54293i −0.824769 0.0997418i
\(651\) 0 0
\(652\) −36.1497 16.8569i −1.41573 0.660167i
\(653\) 0.801061 + 9.15617i 0.0313480 + 0.358309i 0.995627 + 0.0934196i \(0.0297798\pi\)
−0.964279 + 0.264889i \(0.914665\pi\)
\(654\) 0 0
\(655\) −21.3274 + 39.3657i −0.833329 + 1.53815i
\(656\) 30.3465 17.5206i 1.18483 0.684063i
\(657\) 0 0
\(658\) −8.86823 33.0967i −0.345720 1.29024i
\(659\) 23.2374 19.4985i 0.905199 0.759552i −0.0660005 0.997820i \(-0.521024\pi\)
0.971200 + 0.238267i \(0.0765795\pi\)
\(660\) 0 0
\(661\) 1.43027 8.11147i 0.0556311 0.315500i −0.944276 0.329156i \(-0.893236\pi\)
0.999907 + 0.0136561i \(0.00434700\pi\)
\(662\) 29.7872 + 42.5405i 1.15771 + 1.65338i
\(663\) 0 0
\(664\) 0.688294 + 0.820277i 0.0267110 + 0.0318329i
\(665\) −2.14164 18.6457i −0.0830494 0.723050i
\(666\) 0 0
\(667\) 0.940421 3.50970i 0.0364132 0.135896i
\(668\) −6.79699 14.5762i −0.262984 0.563970i
\(669\) 0 0
\(670\) 16.1289 + 18.1969i 0.623112 + 0.703007i
\(671\) 3.55969 + 9.78018i 0.137420 + 0.377560i
\(672\) 0 0
\(673\) −8.54498 5.98326i −0.329385 0.230638i 0.397172 0.917744i \(-0.369992\pi\)
−0.726557 + 0.687107i \(0.758881\pi\)
\(674\) 35.9537 1.38488
\(675\) 0 0
\(676\) 18.4683 0.710319
\(677\) −32.5175 22.7690i −1.24975 0.875083i −0.254000 0.967204i \(-0.581746\pi\)
−0.995748 + 0.0921212i \(0.970635\pi\)
\(678\) 0 0
\(679\) −3.58382 9.84647i −0.137535 0.377873i
\(680\) −0.269949 0.304562i −0.0103521 0.0116794i
\(681\) 0 0
\(682\) 8.93762 + 19.1668i 0.342239 + 0.733934i
\(683\) −0.244148 + 0.911173i −0.00934207 + 0.0348651i −0.970440 0.241344i \(-0.922412\pi\)
0.961097 + 0.276209i \(0.0890783\pi\)
\(684\) 0 0
\(685\) 3.33567 + 29.0412i 0.127449 + 1.10961i
\(686\) 23.8177 + 28.3848i 0.909364 + 1.08374i
\(687\) 0 0
\(688\) −7.53032 10.7544i −0.287091 0.410008i
\(689\) 3.06779 17.3983i 0.116873 0.662822i
\(690\) 0 0
\(691\) −8.89879 + 7.46697i −0.338526 + 0.284057i −0.796163 0.605082i \(-0.793140\pi\)
0.457637 + 0.889139i \(0.348696\pi\)
\(692\) −4.14809 15.4809i −0.157687 0.588495i
\(693\) 0 0
\(694\) −3.93170 + 2.26997i −0.149245 + 0.0861668i
\(695\) −14.9457 + 27.5865i −0.566923 + 1.04642i
\(696\) 0 0
\(697\) 0.552984 + 6.32063i 0.0209458 + 0.239411i
\(698\) −35.3665 16.4917i −1.33864 0.624219i
\(699\) 0 0
\(700\) −17.6774 22.5411i −0.668142 0.851974i
\(701\) 27.3341i 1.03240i 0.856469 + 0.516198i \(0.172653\pi\)
−0.856469 + 0.516198i \(0.827347\pi\)
\(702\) 0 0
\(703\) −6.31764 + 6.31764i −0.238274 + 0.238274i
\(704\) −9.95862 56.4781i −0.375330 2.12860i
\(705\) 0 0
\(706\) −56.7662 + 20.6612i −2.13643 + 0.777595i
\(707\) −36.4794 + 3.19154i −1.37195 + 0.120030i
\(708\) 0 0
\(709\) 10.1733 27.9510i 0.382068 1.04972i −0.588417 0.808558i \(-0.700249\pi\)
0.970484 0.241164i \(-0.0775292\pi\)
\(710\) 4.28267 9.87409i 0.160726 0.370568i
\(711\) 0 0
\(712\) 0.224078 0.0600414i 0.00839766 0.00225015i
\(713\) −0.737882 0.0645563i −0.0276339 0.00241765i
\(714\) 0 0
\(715\) 26.4800 13.2326i 0.990296 0.494872i
\(716\) −27.1382 4.78519i −1.01420 0.178831i
\(717\) 0 0
\(718\) 4.99610 57.1057i 0.186453 2.13116i
\(719\) −4.04581 + 7.00756i −0.150883 + 0.261338i −0.931552 0.363607i \(-0.881545\pi\)
0.780669 + 0.624945i \(0.214878\pi\)
\(720\) 0 0
\(721\) 8.53917 + 14.7903i 0.318015 + 0.550819i
\(722\) −17.0147 + 7.93406i −0.633220 + 0.295275i
\(723\) 0 0
\(724\) 7.24389 8.63293i 0.269217 0.320840i
\(725\) 40.1006 2.17495i 1.48930 0.0807756i
\(726\) 0 0
\(727\) −26.0879 + 37.2574i −0.967546 + 1.38180i −0.0436958 + 0.999045i \(0.513913\pi\)
−0.923850 + 0.382754i \(0.874976\pi\)
\(728\) −1.07044 1.07044i −0.0396730 0.0396730i
\(729\) 0 0
\(730\) 0.924644 6.22578i 0.0342226 0.230427i
\(731\) 2.34106 0.412792i 0.0865872 0.0152677i
\(732\) 0 0
\(733\) 11.4484 24.5512i 0.422857 0.906819i −0.573309 0.819339i \(-0.694341\pi\)
0.996166 0.0874805i \(-0.0278815\pi\)
\(734\) 37.4655 + 31.4373i 1.38288 + 1.16037i
\(735\) 0 0
\(736\) 3.44161 + 1.25265i 0.126860 + 0.0461731i
\(737\) −32.8260 8.79571i −1.20916 0.323994i
\(738\) 0 0
\(739\) −13.2893 7.67257i −0.488854 0.282240i 0.235245 0.971936i \(-0.424411\pi\)
−0.724099 + 0.689696i \(0.757744\pi\)
\(740\) −3.17131 + 13.2628i −0.116580 + 0.487549i
\(741\) 0 0
\(742\) 37.9237 26.5545i 1.39222 0.974846i
\(743\) −31.3637 + 21.9611i −1.15062 + 0.805674i −0.983615 0.180282i \(-0.942299\pi\)
−0.167007 + 0.985956i \(0.553410\pi\)
\(744\) 0 0
\(745\) −2.18629 + 1.34251i −0.0800995 + 0.0491856i
\(746\) 12.6415 + 7.29858i 0.462839 + 0.267220i
\(747\) 0 0
\(748\) 8.80816 + 2.36014i 0.322058 + 0.0862953i
\(749\) 26.5175 + 9.65157i 0.968927 + 0.352661i
\(750\) 0 0
\(751\) −6.83954 5.73906i −0.249578 0.209421i 0.509412 0.860523i \(-0.329863\pi\)
−0.758991 + 0.651101i \(0.774307\pi\)
\(752\) −9.85508 + 21.1343i −0.359378 + 0.770688i
\(753\) 0 0
\(754\) 33.5075 5.90827i 1.22027 0.215167i
\(755\) 3.48812 + 0.518050i 0.126946 + 0.0188538i
\(756\) 0 0
\(757\) −12.0849 12.0849i −0.439232 0.439232i 0.452522 0.891753i \(-0.350525\pi\)
−0.891753 + 0.452522i \(0.850525\pi\)
\(758\) 7.70890 11.0094i 0.280000 0.399881i
\(759\) 0 0
\(760\) 1.04177 1.57706i 0.0377889 0.0572060i
\(761\) 28.7638 34.2794i 1.04269 1.24263i 0.0732447 0.997314i \(-0.476665\pi\)
0.969444 0.245314i \(-0.0788910\pi\)
\(762\) 0 0
\(763\) −6.66378 + 3.10737i −0.241245 + 0.112494i
\(764\) −19.8465 34.3752i −0.718022 1.24365i
\(765\) 0 0
\(766\) 9.94557 17.2262i 0.359348 0.622409i
\(767\) 1.44105 16.4713i 0.0520333 0.594743i
\(768\) 0 0
\(769\) 22.4692 + 3.96193i 0.810262 + 0.142871i 0.563405 0.826181i \(-0.309491\pi\)
0.246857 + 0.969052i \(0.420602\pi\)
\(770\) 73.5877 + 24.5475i 2.65191 + 0.884629i
\(771\) 0 0
\(772\) −12.1954 1.06696i −0.438921 0.0384006i
\(773\) 40.1817 10.7667i 1.44524 0.387250i 0.550872 0.834589i \(-0.314295\pi\)
0.894364 + 0.447339i \(0.147628\pi\)
\(774\) 0 0
\(775\) −1.85614 7.97343i −0.0666745 0.286414i
\(776\) 0.360912 0.991598i 0.0129560 0.0355963i
\(777\) 0 0
\(778\) −19.7522 + 1.72809i −0.708149 + 0.0619550i
\(779\) −27.6893 + 10.0781i −0.992074 + 0.361085i
\(780\) 0 0
\(781\) 2.61204 + 14.8136i 0.0934662 + 0.530073i
\(782\) −0.437588 + 0.437588i −0.0156481 + 0.0156481i
\(783\) 0 0
\(784\) 0.795819i 0.0284221i
\(785\) 20.3721 21.5070i 0.727112 0.767617i
\(786\) 0 0
\(787\) −0.509559 0.237611i −0.0181638 0.00846992i 0.413515 0.910497i \(-0.364301\pi\)
−0.431679 + 0.902027i \(0.642079\pi\)
\(788\) −3.16416 36.1666i −0.112719 1.28838i
\(789\) 0 0
\(790\) −8.85356 29.7893i −0.314995 1.05986i
\(791\) −47.1092 + 27.1985i −1.67501 + 0.967068i
\(792\) 0 0
\(793\) −0.883467 3.29714i −0.0313728 0.117085i
\(794\) −35.3263 + 29.6423i −1.25368 + 1.05197i
\(795\) 0 0
\(796\) 8.58929 48.7123i 0.304439 1.72656i
\(797\) −29.3985 41.9854i −1.04135 1.48720i −0.864288 0.502998i \(-0.832230\pi\)
−0.177060 0.984200i \(-0.556659\pi\)
\(798\) 0 0
\(799\) −2.71405 3.23448i −0.0960162 0.114428i
\(800\) −1.33892 + 40.4577i −0.0473379 + 1.43040i
\(801\) 0 0
\(802\) 16.5253 61.6733i 0.583529 2.17776i
\(803\) 3.71760 + 7.97242i 0.131191 + 0.281341i
\(804\) 0 0
\(805\) −2.03325 + 1.80217i −0.0716626 + 0.0635183i
\(806\) −2.37224 6.51767i −0.0835585 0.229575i
\(807\) 0 0
\(808\) −3.02081 2.11519i −0.106272 0.0744122i
\(809\) −10.4010 −0.365681 −0.182841 0.983143i \(-0.558529\pi\)
−0.182841 + 0.983143i \(0.558529\pi\)
\(810\) 0 0
\(811\) 3.01122 0.105738 0.0528692 0.998601i \(-0.483163\pi\)
0.0528692 + 0.998601i \(0.483163\pi\)
\(812\) 37.6944 + 26.3939i 1.32281 + 0.926244i
\(813\) 0 0
\(814\) −12.6302 34.7013i −0.442690 1.21628i
\(815\) −41.7375 2.51456i −1.46200 0.0880813i
\(816\) 0 0
\(817\) 4.66573 + 10.0057i 0.163233 + 0.350055i
\(818\) 15.0316 56.0987i 0.525568 1.96145i
\(819\) 0 0
\(820\) −27.9651 + 35.2228i −0.976582 + 1.23003i
\(821\) −23.3489 27.8262i −0.814883 0.971140i 0.185050 0.982729i \(-0.440755\pi\)
−0.999933 + 0.0115894i \(0.996311\pi\)
\(822\) 0 0
\(823\) −4.70013 6.71249i −0.163836 0.233983i 0.728836 0.684688i \(-0.240061\pi\)
−0.892673 + 0.450705i \(0.851173\pi\)
\(824\) −0.298656 + 1.69376i −0.0104042 + 0.0590049i
\(825\) 0 0
\(826\) 33.1916 27.8511i 1.15488 0.969063i
\(827\) −2.16528 8.08092i −0.0752940 0.281001i 0.918006 0.396567i \(-0.129799\pi\)
−0.993300 + 0.115566i \(0.963132\pi\)
\(828\) 0 0
\(829\) −24.2355 + 13.9924i −0.841734 + 0.485975i −0.857853 0.513895i \(-0.828202\pi\)
0.0161192 + 0.999870i \(0.494869\pi\)
\(830\) 15.8231 + 8.57259i 0.549229 + 0.297559i
\(831\) 0 0
\(832\) 1.63930 + 18.7373i 0.0568325 + 0.649598i
\(833\) −0.130596 0.0608977i −0.00452487 0.00210998i
\(834\) 0 0
\(835\) −12.2403 11.5944i −0.423592 0.401240i
\(836\) 42.3499i 1.46470i
\(837\) 0 0
\(838\) −5.83376 + 5.83376i −0.201524 + 0.201524i
\(839\) −4.76834 27.0426i −0.164621 0.933615i −0.949454 0.313907i \(-0.898362\pi\)
0.784832 0.619708i \(-0.212749\pi\)
\(840\) 0 0
\(841\) −33.3699 + 12.1457i −1.15069 + 0.418816i
\(842\) −19.8966 + 1.74073i −0.685683 + 0.0599895i
\(843\) 0 0
\(844\) 1.89549 5.20781i 0.0652454 0.179260i
\(845\) 18.0066 7.11199i 0.619448 0.244660i
\(846\) 0 0
\(847\) −76.1848 + 20.4137i −2.61774 + 0.701421i
\(848\) −31.3879 2.74608i −1.07786 0.0943009i
\(849\) 0 0
\(850\) −6.09995 3.09408i −0.209227 0.106126i
\(851\) 1.27374 + 0.224595i 0.0436632 + 0.00769900i
\(852\) 0 0
\(853\) 1.45086 16.5834i 0.0496766 0.567806i −0.930045 0.367444i \(-0.880233\pi\)
0.979722 0.200361i \(-0.0642116\pi\)
\(854\) 4.47255 7.74669i 0.153048 0.265086i
\(855\) 0 0
\(856\) 1.42092 + 2.46111i 0.0485662 + 0.0841191i
\(857\) −9.84971 + 4.59299i −0.336460 + 0.156894i −0.583504 0.812111i \(-0.698319\pi\)
0.247044 + 0.969004i \(0.420541\pi\)
\(858\) 0 0
\(859\) 0.275808 0.328695i 0.00941045 0.0112149i −0.761319 0.648378i \(-0.775448\pi\)
0.770729 + 0.637163i \(0.219892\pi\)
\(860\) 14.0598 + 9.28752i 0.479434 + 0.316702i
\(861\) 0 0
\(862\) −4.17115 + 5.95703i −0.142070 + 0.202897i
\(863\) 7.52083 + 7.52083i 0.256012 + 0.256012i 0.823430 0.567418i \(-0.192058\pi\)
−0.567418 + 0.823430i \(0.692058\pi\)
\(864\) 0 0
\(865\) −10.0060 13.4965i −0.340213 0.458895i
\(866\) 1.90056 0.335120i 0.0645837 0.0113878i
\(867\) 0 0
\(868\) 3.96439 8.50167i 0.134560 0.288565i
\(869\) 33.2719 + 27.9184i 1.12867 + 0.947068i
\(870\) 0 0
\(871\) 10.4735 + 3.81206i 0.354883 + 0.129167i
\(872\) −0.715226 0.191644i −0.0242206 0.00648989i
\(873\) 0 0
\(874\) −2.48898 1.43701i −0.0841909 0.0486077i
\(875\) −25.9159 15.1702i −0.876116 0.512848i
\(876\) 0 0
\(877\) 4.01504 2.81136i 0.135578 0.0949330i −0.503820 0.863809i \(-0.668072\pi\)
0.639398 + 0.768876i \(0.279184\pi\)
\(878\) 54.7890 38.3637i 1.84904 1.29471i
\(879\) 0 0
\(880\) −27.6260 44.9894i −0.931273 1.51659i
\(881\) 0.734747 + 0.424206i 0.0247542 + 0.0142919i 0.512326 0.858791i \(-0.328784\pi\)
−0.487572 + 0.873083i \(0.662117\pi\)
\(882\) 0 0
\(883\) 33.9530 + 9.09767i 1.14261 + 0.306161i 0.779999 0.625781i \(-0.215219\pi\)
0.362609 + 0.931941i \(0.381886\pi\)
\(884\) −2.81035 1.02288i −0.0945223 0.0344033i
\(885\) 0 0
\(886\) 34.9135 + 29.2959i 1.17294 + 0.984216i
\(887\) −9.41211 + 20.1843i −0.316028 + 0.677724i −0.998589 0.0531048i \(-0.983088\pi\)
0.682561 + 0.730828i \(0.260866\pi\)
\(888\) 0 0
\(889\) −3.79871 + 0.669814i −0.127405 + 0.0224649i
\(890\) 3.13194 2.32194i 0.104983 0.0778314i
\(891\) 0 0
\(892\) 7.61222 + 7.61222i 0.254876 + 0.254876i
\(893\) 11.2474 16.0630i 0.376380 0.537526i
\(894\) 0 0
\(895\) −28.3025 + 5.78510i −0.946049 + 0.193375i
\(896\) −3.72765 + 4.44244i −0.124532 + 0.148412i
\(897\) 0 0
\(898\) −18.2878 + 8.52775i −0.610272 + 0.284575i
\(899\) 6.57542 + 11.3890i 0.219303 + 0.379843i
\(900\) 0 0
\(901\) 2.85250 4.94068i 0.0950307 0.164598i
\(902\) 10.6148 121.328i 0.353435 4.03979i
\(903\) 0 0
\(904\) −5.39488 0.951262i −0.179431 0.0316385i
\(905\) 3.73834 11.2067i 0.124267 0.372523i
\(906\) 0 0
\(907\) 50.6679 + 4.43286i 1.68240 + 0.147191i 0.887888 0.460060i \(-0.152172\pi\)
0.794511 + 0.607250i \(0.207727\pi\)
\(908\) 40.7291 10.9133i 1.35164 0.362171i
\(909\) 0 0
\(910\) −23.3410 10.1236i −0.773746 0.335595i
\(911\) 1.01302 2.78325i 0.0335629 0.0922132i −0.921779 0.387715i \(-0.873265\pi\)
0.955342 + 0.295502i \(0.0954868\pi\)
\(912\) 0 0
\(913\) −25.0557 + 2.19209i −0.829223 + 0.0725476i
\(914\) 66.0043 24.0236i 2.18323 0.794630i
\(915\) 0 0
\(916\) 9.26601 + 52.5502i 0.306158 + 1.73631i
\(917\) −38.0275 + 38.0275i −1.25578 + 1.25578i
\(918\) 0 0
\(919\) 4.33194i 0.142897i −0.997444 0.0714487i \(-0.977238\pi\)
0.997444 0.0714487i \(-0.0227622\pi\)
\(920\) −0.273514 + 0.00741190i −0.00901750 + 0.000244363i
\(921\) 0 0
\(922\) 19.2436 + 8.97345i 0.633755 + 0.295525i
\(923\) −0.429971 4.91459i −0.0141527 0.161766i
\(924\) 0 0
\(925\) 2.01534 + 14.1525i 0.0662639 + 0.465331i
\(926\) −32.5250 + 18.7783i −1.06884 + 0.617093i
\(927\) 0 0
\(928\) −16.8300 62.8104i −0.552472 2.06185i
\(929\) 24.5535 20.6028i 0.805574 0.675957i −0.143973 0.989582i \(-0.545988\pi\)
0.949547 + 0.313625i \(0.101543\pi\)
\(930\) 0 0
\(931\) 0.116207 0.659044i 0.00380854 0.0215993i
\(932\) −10.0104 14.2963i −0.327902 0.468292i
\(933\) 0 0
\(934\) 50.3203 + 59.9694i 1.64653 + 1.96226i
\(935\) 9.49685 1.09081i 0.310580 0.0356732i
\(936\) 0 0
\(937\) −3.81043 + 14.2207i −0.124481 + 0.464571i −0.999821 0.0189383i \(-0.993971\pi\)
0.875339 + 0.483509i \(0.160638\pi\)
\(938\) 12.3438 + 26.4713i 0.403038 + 0.864318i
\(939\) 0 0
\(940\) 1.79990 29.8753i 0.0587062 0.974425i
\(941\) 0.647073 + 1.77782i 0.0210940 + 0.0579552i 0.949793 0.312880i \(-0.101294\pi\)
−0.928699 + 0.370835i \(0.879072\pi\)
\(942\) 0 0
\(943\) 3.49422 + 2.44668i 0.113788 + 0.0796749i
\(944\) −29.4880 −0.959753
\(945\) 0 0
\(946\) −45.6312 −1.48360
\(947\) 27.3760 + 19.1689i 0.889601 + 0.622906i 0.926451 0.376415i \(-0.122843\pi\)
−0.0368497 + 0.999321i \(0.511732\pi\)
\(948\) 0 0
\(949\) −0.986732 2.71103i −0.0320307 0.0880036i
\(950\) 6.54768 31.0832i 0.212435 1.00847i
\(951\) 0 0
\(952\) −0.206598 0.443050i −0.00669587 0.0143593i
\(953\) −4.71015 + 17.5785i −0.152577 + 0.569424i 0.846724 + 0.532032i \(0.178572\pi\)
−0.999301 + 0.0373915i \(0.988095\pi\)
\(954\) 0 0
\(955\) −32.5880 25.8732i −1.05452 0.837236i
\(956\) −22.0009 26.2197i −0.711560 0.848004i
\(957\) 0 0
\(958\) −17.1557 24.5009i −0.554275 0.791587i
\(959\) −6.09731 + 34.5796i −0.196893 + 1.11663i
\(960\) 0 0
\(961\) −21.6937 + 18.2032i −0.699798 + 0.587200i
\(962\) 3.13465 + 11.6987i 0.101065 + 0.377181i
\(963\) 0 0
\(964\) −21.2922 + 12.2931i −0.685777 + 0.395934i
\(965\) −12.3014 + 3.65605i −0.395996 + 0.117692i
\(966\) 0 0
\(967\) 3.69964 + 42.2870i 0.118972 + 1.35986i 0.787566 + 0.616231i \(0.211341\pi\)
−0.668593 + 0.743628i \(0.733103\pi\)
\(968\) −7.19871 3.35682i −0.231375 0.107892i
\(969\) 0 0
\(970\) −0.480411 17.7281i −0.0154251 0.569216i
\(971\) 8.10739i 0.260179i 0.991502 + 0.130089i \(0.0415264\pi\)
−0.991502 + 0.130089i \(0.958474\pi\)
\(972\) 0 0
\(973\) −26.6487 + 26.6487i −0.854319 + 0.854319i
\(974\) 1.70235 + 9.65451i 0.0545468 + 0.309350i
\(975\) 0 0
\(976\) −5.72061 + 2.08213i −0.183112 + 0.0666475i
\(977\) 42.0388 3.67792i 1.34494 0.117667i 0.608168 0.793808i \(-0.291905\pi\)
0.736772 + 0.676141i \(0.236349\pi\)
\(978\) 0 0
\(979\) −1.86364 + 5.12031i −0.0595622 + 0.163646i
\(980\) −0.375216 0.949998i −0.0119858 0.0303466i
\(981\) 0 0
\(982\) 12.6966 3.40203i 0.405163 0.108563i
\(983\) −14.2769 1.24906i −0.455362 0.0398390i −0.142832 0.989747i \(-0.545621\pi\)
−0.312530 + 0.949908i \(0.601176\pi\)
\(984\) 0 0
\(985\) −17.0125 34.0440i −0.542064 1.08473i
\(986\) 10.8204 + 1.90793i 0.344592 + 0.0607608i
\(987\) 0 0
\(988\) 1.21055 13.8366i 0.0385126 0.440201i
\(989\) 0.799099 1.38408i 0.0254099 0.0440112i
\(990\) 0 0
\(991\) 15.7989 + 27.3646i 0.501870 + 0.869265i 0.999998 + 0.00216080i \(0.000687805\pi\)
−0.498128 + 0.867104i \(0.665979\pi\)
\(992\) −12.0138 + 5.60212i −0.381438 + 0.177867i
\(993\) 0 0
\(994\) 8.31002 9.90350i 0.263578 0.314120i
\(995\) −10.3841 50.8023i −0.329198 1.61054i
\(996\) 0 0
\(997\) 7.09629 10.1346i 0.224742 0.320965i −0.690907 0.722944i \(-0.742789\pi\)
0.915649 + 0.401979i \(0.131678\pi\)
\(998\) −36.2043 36.2043i −1.14603 1.14603i
\(999\) 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 405.2.r.a.152.14 192
3.2 odd 2 135.2.q.a.122.3 yes 192
5.3 odd 4 inner 405.2.r.a.233.14 192
15.2 even 4 675.2.ba.b.68.14 192
15.8 even 4 135.2.q.a.68.3 yes 192
15.14 odd 2 675.2.ba.b.257.14 192
27.2 odd 18 inner 405.2.r.a.332.14 192
27.25 even 9 135.2.q.a.2.3 192
135.52 odd 36 675.2.ba.b.218.14 192
135.79 even 18 675.2.ba.b.407.14 192
135.83 even 36 inner 405.2.r.a.8.14 192
135.133 odd 36 135.2.q.a.83.3 yes 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
135.2.q.a.2.3 192 27.25 even 9
135.2.q.a.68.3 yes 192 15.8 even 4
135.2.q.a.83.3 yes 192 135.133 odd 36
135.2.q.a.122.3 yes 192 3.2 odd 2
405.2.r.a.8.14 192 135.83 even 36 inner
405.2.r.a.152.14 192 1.1 even 1 trivial
405.2.r.a.233.14 192 5.3 odd 4 inner
405.2.r.a.332.14 192 27.2 odd 18 inner
675.2.ba.b.68.14 192 15.2 even 4
675.2.ba.b.218.14 192 135.52 odd 36
675.2.ba.b.257.14 192 15.14 odd 2
675.2.ba.b.407.14 192 135.79 even 18