Properties

Label 324.2.l.a.35.6
Level $324$
Weight $2$
Character 324.35
Analytic conductor $2.587$
Analytic rank $0$
Dimension $96$
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] = [324,2,Mod(35,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 324.l (of order \(18\), degree \(6\), 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: \(2.58715302549\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(16\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 35.6
Character \(\chi\) \(=\) 324.35
Dual form 324.2.l.a.287.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.557089 - 1.29987i) q^{2} +(-1.37930 + 1.44828i) q^{4} +(1.27150 - 3.49343i) q^{5} +(1.63150 + 0.287677i) q^{7} +(2.65097 + 0.986086i) q^{8} +O(q^{10})\) \(q+(-0.557089 - 1.29987i) q^{2} +(-1.37930 + 1.44828i) q^{4} +(1.27150 - 3.49343i) q^{5} +(1.63150 + 0.287677i) q^{7} +(2.65097 + 0.986086i) q^{8} +(-5.24933 + 0.293367i) q^{10} +(0.526615 - 0.191672i) q^{11} +(1.99017 - 1.66995i) q^{13} +(-0.534948 - 2.28099i) q^{14} +(-0.195046 - 3.99524i) q^{16} +(-4.50885 + 2.60318i) q^{17} +(-0.925473 - 0.534322i) q^{19} +(3.30568 + 6.66000i) q^{20} +(-0.542520 - 0.577751i) q^{22} +(-1.54747 - 8.77613i) q^{23} +(-6.75711 - 5.66989i) q^{25} +(-3.27942 - 1.65664i) q^{26} +(-2.66696 + 1.96607i) q^{28} +(0.702597 - 0.837323i) q^{29} +(3.17422 - 0.559701i) q^{31} +(-5.08462 + 2.47924i) q^{32} +(5.89562 + 4.41069i) q^{34} +(3.07943 - 5.33373i) q^{35} +(3.17849 + 5.50530i) q^{37} +(-0.178976 + 1.50066i) q^{38} +(6.81554 - 8.00716i) q^{40} +(0.556211 + 0.662866i) q^{41} +(0.690832 + 1.89805i) q^{43} +(-0.448767 + 1.02706i) q^{44} +(-10.5457 + 6.90059i) q^{46} +(-1.22624 + 6.95438i) q^{47} +(-3.99883 - 1.45545i) q^{49} +(-3.60578 + 11.9420i) q^{50} +(-0.326486 + 5.18570i) q^{52} +6.80497i q^{53} -2.08341i q^{55} +(4.04137 + 2.37142i) q^{56} +(-1.47982 - 0.446819i) q^{58} +(8.57009 + 3.11926i) q^{59} +(0.832127 - 4.71923i) q^{61} +(-2.49586 - 3.81426i) q^{62} +(6.05527 + 5.22817i) q^{64} +(-3.30335 - 9.07588i) q^{65} +(7.06749 + 8.42270i) q^{67} +(2.44892 - 10.1207i) q^{68} +(-8.64866 - 1.03148i) q^{70} +(3.98206 + 6.89713i) q^{71} +(1.92588 - 3.33572i) q^{73} +(5.38545 - 7.19855i) q^{74} +(2.05036 - 0.603355i) q^{76} +(0.914311 - 0.161218i) q^{77} +(6.28979 - 7.49588i) q^{79} +(-14.2051 - 4.39859i) q^{80} +(0.551778 - 1.09228i) q^{82} +(-1.28797 - 1.08073i) q^{83} +(3.36102 + 19.0613i) q^{85} +(2.08235 - 1.95537i) q^{86} +(1.58505 + 0.0111708i) q^{88} +(10.9229 + 6.30632i) q^{89} +(3.72736 - 2.15199i) q^{91} +(14.8448 + 9.86377i) q^{92} +(9.72289 - 2.28026i) q^{94} +(-3.04336 + 2.55368i) q^{95} +(3.74927 - 1.36462i) q^{97} +(0.335809 + 6.00876i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.557089 1.29987i −0.393922 0.919144i
\(3\) 0 0
\(4\) −1.37930 + 1.44828i −0.689652 + 0.724141i
\(5\) 1.27150 3.49343i 0.568634 1.56231i −0.238004 0.971264i \(-0.576493\pi\)
0.806638 0.591045i \(-0.201285\pi\)
\(6\) 0 0
\(7\) 1.63150 + 0.287677i 0.616647 + 0.108732i 0.473242 0.880932i \(-0.343084\pi\)
0.143405 + 0.989664i \(0.454195\pi\)
\(8\) 2.65097 + 0.986086i 0.937259 + 0.348634i
\(9\) 0 0
\(10\) −5.24933 + 0.293367i −1.65998 + 0.0927708i
\(11\) 0.526615 0.191672i 0.158781 0.0577914i −0.261407 0.965229i \(-0.584186\pi\)
0.420188 + 0.907437i \(0.361964\pi\)
\(12\) 0 0
\(13\) 1.99017 1.66995i 0.551974 0.463161i −0.323635 0.946182i \(-0.604905\pi\)
0.875609 + 0.483021i \(0.160460\pi\)
\(14\) −0.534948 2.28099i −0.142971 0.609620i
\(15\) 0 0
\(16\) −0.195046 3.99524i −0.0487616 0.998810i
\(17\) −4.50885 + 2.60318i −1.09356 + 0.631365i −0.934521 0.355908i \(-0.884172\pi\)
−0.159035 + 0.987273i \(0.550838\pi\)
\(18\) 0 0
\(19\) −0.925473 0.534322i −0.212318 0.122582i 0.390070 0.920785i \(-0.372451\pi\)
−0.602388 + 0.798203i \(0.705784\pi\)
\(20\) 3.30568 + 6.66000i 0.739174 + 1.48922i
\(21\) 0 0
\(22\) −0.542520 0.577751i −0.115666 0.123177i
\(23\) −1.54747 8.77613i −0.322670 1.82995i −0.525570 0.850751i \(-0.676148\pi\)
0.202900 0.979199i \(-0.434963\pi\)
\(24\) 0 0
\(25\) −6.75711 5.66989i −1.35142 1.13398i
\(26\) −3.27942 1.65664i −0.643147 0.324895i
\(27\) 0 0
\(28\) −2.66696 + 1.96607i −0.504009 + 0.371553i
\(29\) 0.702597 0.837323i 0.130469 0.155487i −0.696855 0.717212i \(-0.745418\pi\)
0.827324 + 0.561725i \(0.189862\pi\)
\(30\) 0 0
\(31\) 3.17422 0.559701i 0.570107 0.100525i 0.118839 0.992914i \(-0.462083\pi\)
0.451269 + 0.892388i \(0.350972\pi\)
\(32\) −5.08462 + 2.47924i −0.898842 + 0.438272i
\(33\) 0 0
\(34\) 5.89562 + 4.41069i 1.01109 + 0.756427i
\(35\) 3.07943 5.33373i 0.520519 0.901566i
\(36\) 0 0
\(37\) 3.17849 + 5.50530i 0.522540 + 0.905066i 0.999656 + 0.0262257i \(0.00834884\pi\)
−0.477116 + 0.878840i \(0.658318\pi\)
\(38\) −0.178976 + 1.50066i −0.0290337 + 0.243439i
\(39\) 0 0
\(40\) 6.81554 8.00716i 1.07763 1.26604i
\(41\) 0.556211 + 0.662866i 0.0868655 + 0.103522i 0.807726 0.589557i \(-0.200698\pi\)
−0.720861 + 0.693080i \(0.756253\pi\)
\(42\) 0 0
\(43\) 0.690832 + 1.89805i 0.105351 + 0.289449i 0.981156 0.193215i \(-0.0618914\pi\)
−0.875806 + 0.482664i \(0.839669\pi\)
\(44\) −0.448767 + 1.02706i −0.0676541 + 0.154835i
\(45\) 0 0
\(46\) −10.5457 + 6.90059i −1.55488 + 1.01744i
\(47\) −1.22624 + 6.95438i −0.178866 + 1.01440i 0.754720 + 0.656047i \(0.227773\pi\)
−0.933586 + 0.358353i \(0.883338\pi\)
\(48\) 0 0
\(49\) −3.99883 1.45545i −0.571261 0.207922i
\(50\) −3.60578 + 11.9420i −0.509934 + 1.68885i
\(51\) 0 0
\(52\) −0.326486 + 5.18570i −0.0452755 + 0.719127i
\(53\) 6.80497i 0.934734i 0.884063 + 0.467367i \(0.154797\pi\)
−0.884063 + 0.467367i \(0.845203\pi\)
\(54\) 0 0
\(55\) 2.08341i 0.280926i
\(56\) 4.04137 + 2.37142i 0.540051 + 0.316894i
\(57\) 0 0
\(58\) −1.47982 0.446819i −0.194309 0.0586702i
\(59\) 8.57009 + 3.11926i 1.11573 + 0.406093i 0.833093 0.553134i \(-0.186568\pi\)
0.282639 + 0.959226i \(0.408790\pi\)
\(60\) 0 0
\(61\) 0.832127 4.71923i 0.106543 0.604235i −0.884050 0.467393i \(-0.845193\pi\)
0.990593 0.136842i \(-0.0436954\pi\)
\(62\) −2.49586 3.81426i −0.316975 0.484412i
\(63\) 0 0
\(64\) 6.05527 + 5.22817i 0.756909 + 0.653521i
\(65\) −3.30335 9.07588i −0.409730 1.12572i
\(66\) 0 0
\(67\) 7.06749 + 8.42270i 0.863431 + 1.02900i 0.999268 + 0.0382656i \(0.0121833\pi\)
−0.135837 + 0.990731i \(0.543372\pi\)
\(68\) 2.44892 10.1207i 0.296975 1.22731i
\(69\) 0 0
\(70\) −8.64866 1.03148i −1.03371 0.123286i
\(71\) 3.98206 + 6.89713i 0.472583 + 0.818538i 0.999508 0.0313737i \(-0.00998821\pi\)
−0.526924 + 0.849912i \(0.676655\pi\)
\(72\) 0 0
\(73\) 1.92588 3.33572i 0.225407 0.390416i −0.731035 0.682340i \(-0.760962\pi\)
0.956441 + 0.291924i \(0.0942955\pi\)
\(74\) 5.38545 7.19855i 0.626046 0.836815i
\(75\) 0 0
\(76\) 2.05036 0.603355i 0.235192 0.0692095i
\(77\) 0.914311 0.161218i 0.104195 0.0183725i
\(78\) 0 0
\(79\) 6.28979 7.49588i 0.707657 0.843353i −0.285713 0.958315i \(-0.592230\pi\)
0.993370 + 0.114963i \(0.0366748\pi\)
\(80\) −14.2051 4.39859i −1.58818 0.491777i
\(81\) 0 0
\(82\) 0.551778 1.09228i 0.0609337 0.120622i
\(83\) −1.28797 1.08073i −0.141373 0.118626i 0.569359 0.822089i \(-0.307191\pi\)
−0.710732 + 0.703463i \(0.751636\pi\)
\(84\) 0 0
\(85\) 3.36102 + 19.0613i 0.364554 + 2.06749i
\(86\) 2.08235 1.95537i 0.224546 0.210853i
\(87\) 0 0
\(88\) 1.58505 + 0.0111708i 0.168967 + 0.00119081i
\(89\) 10.9229 + 6.30632i 1.15782 + 0.668469i 0.950781 0.309864i \(-0.100283\pi\)
0.207041 + 0.978332i \(0.433617\pi\)
\(90\) 0 0
\(91\) 3.72736 2.15199i 0.390734 0.225590i
\(92\) 14.8448 + 9.86377i 1.54767 + 1.02837i
\(93\) 0 0
\(94\) 9.72289 2.28026i 1.00284 0.235190i
\(95\) −3.04336 + 2.55368i −0.312242 + 0.262002i
\(96\) 0 0
\(97\) 3.74927 1.36462i 0.380681 0.138556i −0.144590 0.989492i \(-0.546186\pi\)
0.525271 + 0.850935i \(0.323964\pi\)
\(98\) 0.335809 + 6.00876i 0.0339218 + 0.606976i
\(99\) 0 0
\(100\) 17.5317 1.96571i 1.75317 0.196571i
\(101\) −7.58285 1.33706i −0.754522 0.133043i −0.216860 0.976203i \(-0.569581\pi\)
−0.537662 + 0.843160i \(0.680693\pi\)
\(102\) 0 0
\(103\) −1.02587 + 2.81855i −0.101082 + 0.277720i −0.979917 0.199405i \(-0.936099\pi\)
0.878835 + 0.477125i \(0.158321\pi\)
\(104\) 6.92260 2.46451i 0.678817 0.241665i
\(105\) 0 0
\(106\) 8.84555 3.79098i 0.859156 0.368212i
\(107\) −11.8919 −1.14963 −0.574815 0.818283i \(-0.694926\pi\)
−0.574815 + 0.818283i \(0.694926\pi\)
\(108\) 0 0
\(109\) 9.26570 0.887493 0.443747 0.896152i \(-0.353649\pi\)
0.443747 + 0.896152i \(0.353649\pi\)
\(110\) −2.70815 + 1.16064i −0.258212 + 0.110663i
\(111\) 0 0
\(112\) 0.831121 6.57433i 0.0785335 0.621216i
\(113\) 1.92797 5.29705i 0.181368 0.498304i −0.815376 0.578931i \(-0.803470\pi\)
0.996744 + 0.0806268i \(0.0256922\pi\)
\(114\) 0 0
\(115\) −32.6264 5.75292i −3.04243 0.536462i
\(116\) 0.243586 + 2.17248i 0.0226164 + 0.201710i
\(117\) 0 0
\(118\) −0.719689 12.8777i −0.0662527 1.18549i
\(119\) −8.10504 + 2.94999i −0.742988 + 0.270426i
\(120\) 0 0
\(121\) −8.18590 + 6.86879i −0.744173 + 0.624435i
\(122\) −6.59793 + 1.54738i −0.597349 + 0.140093i
\(123\) 0 0
\(124\) −3.56761 + 5.36917i −0.320381 + 0.482166i
\(125\) −12.3012 + 7.10212i −1.10026 + 0.635233i
\(126\) 0 0
\(127\) −7.01988 4.05293i −0.622914 0.359639i 0.155089 0.987901i \(-0.450434\pi\)
−0.778002 + 0.628261i \(0.783767\pi\)
\(128\) 3.42259 10.7836i 0.302517 0.953144i
\(129\) 0 0
\(130\) −9.95716 + 9.34998i −0.873301 + 0.820048i
\(131\) 1.61022 + 9.13203i 0.140686 + 0.797869i 0.970730 + 0.240172i \(0.0772039\pi\)
−0.830044 + 0.557697i \(0.811685\pi\)
\(132\) 0 0
\(133\) −1.35619 1.13798i −0.117597 0.0986755i
\(134\) 7.01116 13.8790i 0.605672 1.19896i
\(135\) 0 0
\(136\) −14.5198 + 2.45485i −1.24506 + 0.210501i
\(137\) 2.22025 2.64599i 0.189689 0.226062i −0.662815 0.748783i \(-0.730638\pi\)
0.852504 + 0.522721i \(0.175083\pi\)
\(138\) 0 0
\(139\) −5.28870 + 0.932540i −0.448581 + 0.0790970i −0.393375 0.919378i \(-0.628693\pi\)
−0.0552061 + 0.998475i \(0.517582\pi\)
\(140\) 3.47728 + 11.8167i 0.293884 + 0.998696i
\(141\) 0 0
\(142\) 6.74698 9.01846i 0.566194 0.756812i
\(143\) 0.727971 1.26088i 0.0608760 0.105440i
\(144\) 0 0
\(145\) −2.03177 3.51913i −0.168730 0.292248i
\(146\) −5.40887 0.645090i −0.447641 0.0533880i
\(147\) 0 0
\(148\) −12.3573 2.99013i −1.01577 0.245787i
\(149\) 7.36478 + 8.77701i 0.603346 + 0.719040i 0.978112 0.208079i \(-0.0667212\pi\)
−0.374766 + 0.927120i \(0.622277\pi\)
\(150\) 0 0
\(151\) 7.80528 + 21.4448i 0.635185 + 1.74516i 0.666348 + 0.745641i \(0.267857\pi\)
−0.0311634 + 0.999514i \(0.509921\pi\)
\(152\) −1.92651 2.32907i −0.156261 0.188912i
\(153\) 0 0
\(154\) −0.718914 1.09867i −0.0579317 0.0885332i
\(155\) 2.08076 11.8006i 0.167131 0.947846i
\(156\) 0 0
\(157\) −7.79694 2.83786i −0.622264 0.226485i 0.0115969 0.999933i \(-0.496309\pi\)
−0.633861 + 0.773447i \(0.718531\pi\)
\(158\) −13.2476 4.00001i −1.05392 0.318224i
\(159\) 0 0
\(160\) 2.19594 + 20.9151i 0.173604 + 1.65349i
\(161\) 14.7634i 1.16352i
\(162\) 0 0
\(163\) 8.81551i 0.690484i −0.938514 0.345242i \(-0.887797\pi\)
0.938514 0.345242i \(-0.112203\pi\)
\(164\) −1.72720 0.108743i −0.134872 0.00849139i
\(165\) 0 0
\(166\) −0.687294 + 2.27625i −0.0533444 + 0.176671i
\(167\) −21.1905 7.71271i −1.63977 0.596828i −0.652772 0.757555i \(-0.726394\pi\)
−0.986999 + 0.160727i \(0.948616\pi\)
\(168\) 0 0
\(169\) −1.08538 + 6.15552i −0.0834911 + 0.473502i
\(170\) 22.9048 14.9877i 1.75671 1.14951i
\(171\) 0 0
\(172\) −3.70177 1.61746i −0.282258 0.123330i
\(173\) 3.50842 + 9.63931i 0.266740 + 0.732863i 0.998674 + 0.0514871i \(0.0163961\pi\)
−0.731933 + 0.681376i \(0.761382\pi\)
\(174\) 0 0
\(175\) −9.39310 11.1943i −0.710052 0.846207i
\(176\) −0.868492 2.06657i −0.0654650 0.155774i
\(177\) 0 0
\(178\) 2.11236 17.7114i 0.158328 1.32753i
\(179\) 7.25044 + 12.5581i 0.541923 + 0.938639i 0.998794 + 0.0491053i \(0.0156370\pi\)
−0.456870 + 0.889533i \(0.651030\pi\)
\(180\) 0 0
\(181\) −2.64382 + 4.57923i −0.196513 + 0.340371i −0.947396 0.320065i \(-0.896295\pi\)
0.750882 + 0.660436i \(0.229629\pi\)
\(182\) −4.87378 3.64622i −0.361268 0.270276i
\(183\) 0 0
\(184\) 4.55173 24.7912i 0.335558 1.82763i
\(185\) 23.2738 4.10381i 1.71113 0.301718i
\(186\) 0 0
\(187\) −1.87547 + 2.23510i −0.137148 + 0.163447i
\(188\) −8.38054 11.3681i −0.611214 0.829107i
\(189\) 0 0
\(190\) 5.01487 + 2.53333i 0.363817 + 0.183787i
\(191\) 8.98845 + 7.54221i 0.650381 + 0.545735i 0.907187 0.420728i \(-0.138225\pi\)
−0.256805 + 0.966463i \(0.582670\pi\)
\(192\) 0 0
\(193\) −4.02043 22.8010i −0.289397 1.64125i −0.689144 0.724624i \(-0.742013\pi\)
0.399748 0.916625i \(-0.369098\pi\)
\(194\) −3.86251 4.11333i −0.277312 0.295320i
\(195\) 0 0
\(196\) 7.62350 3.78392i 0.544536 0.270280i
\(197\) 0.386490 + 0.223140i 0.0275363 + 0.0158981i 0.513705 0.857967i \(-0.328273\pi\)
−0.486169 + 0.873865i \(0.661606\pi\)
\(198\) 0 0
\(199\) −9.88191 + 5.70532i −0.700510 + 0.404440i −0.807537 0.589816i \(-0.799200\pi\)
0.107027 + 0.994256i \(0.465867\pi\)
\(200\) −12.3219 21.6938i −0.871289 1.53398i
\(201\) 0 0
\(202\) 2.48633 + 10.6016i 0.174937 + 0.745923i
\(203\) 1.38716 1.16397i 0.0973597 0.0816945i
\(204\) 0 0
\(205\) 3.02290 1.10025i 0.211129 0.0768445i
\(206\) 4.23523 0.236693i 0.295083 0.0164912i
\(207\) 0 0
\(208\) −7.06004 7.62550i −0.489526 0.528733i
\(209\) −0.589783 0.103995i −0.0407962 0.00719346i
\(210\) 0 0
\(211\) 1.98697 5.45916i 0.136789 0.375824i −0.852318 0.523024i \(-0.824804\pi\)
0.989107 + 0.147200i \(0.0470261\pi\)
\(212\) −9.85552 9.38611i −0.676880 0.644641i
\(213\) 0 0
\(214\) 6.62483 + 15.4578i 0.452864 + 1.05668i
\(215\) 7.50908 0.512115
\(216\) 0 0
\(217\) 5.33975 0.362486
\(218\) −5.16182 12.0442i −0.349603 0.815734i
\(219\) 0 0
\(220\) 3.01736 + 2.87365i 0.203431 + 0.193741i
\(221\) −4.62619 + 12.7103i −0.311191 + 0.854990i
\(222\) 0 0
\(223\) 3.66426 + 0.646109i 0.245377 + 0.0432666i 0.294984 0.955502i \(-0.404686\pi\)
−0.0496067 + 0.998769i \(0.515797\pi\)
\(224\) −9.00876 + 2.58214i −0.601923 + 0.172527i
\(225\) 0 0
\(226\) −7.95950 + 0.444829i −0.529458 + 0.0295896i
\(227\) −6.21679 + 2.26273i −0.412623 + 0.150183i −0.539987 0.841674i \(-0.681571\pi\)
0.127364 + 0.991856i \(0.459348\pi\)
\(228\) 0 0
\(229\) 0.885467 0.742995i 0.0585133 0.0490985i −0.613062 0.790035i \(-0.710062\pi\)
0.671575 + 0.740936i \(0.265618\pi\)
\(230\) 10.6978 + 45.6149i 0.705393 + 3.00775i
\(231\) 0 0
\(232\) 2.68824 1.52689i 0.176491 0.100246i
\(233\) 14.7446 8.51281i 0.965953 0.557693i 0.0679527 0.997689i \(-0.478353\pi\)
0.898000 + 0.439996i \(0.145020\pi\)
\(234\) 0 0
\(235\) 22.7355 + 13.1263i 1.48310 + 0.856267i
\(236\) −16.3383 + 8.10952i −1.06353 + 0.527885i
\(237\) 0 0
\(238\) 8.34983 + 8.89206i 0.541239 + 0.576387i
\(239\) −0.209499 1.18813i −0.0135514 0.0768536i 0.977282 0.211943i \(-0.0679790\pi\)
−0.990833 + 0.135089i \(0.956868\pi\)
\(240\) 0 0
\(241\) −7.65607 6.42420i −0.493171 0.413819i 0.361990 0.932182i \(-0.382097\pi\)
−0.855161 + 0.518363i \(0.826542\pi\)
\(242\) 13.4888 + 6.81405i 0.867092 + 0.438024i
\(243\) 0 0
\(244\) 5.68702 + 7.71440i 0.364074 + 0.493864i
\(245\) −10.1691 + 12.1190i −0.649677 + 0.774255i
\(246\) 0 0
\(247\) −2.73414 + 0.482103i −0.173969 + 0.0306755i
\(248\) 8.96668 + 1.64631i 0.569385 + 0.104541i
\(249\) 0 0
\(250\) 16.0847 + 12.0334i 1.01729 + 0.761062i
\(251\) 6.65375 11.5246i 0.419981 0.727429i −0.575956 0.817481i \(-0.695370\pi\)
0.995937 + 0.0900521i \(0.0287034\pi\)
\(252\) 0 0
\(253\) −2.49706 4.32504i −0.156989 0.271913i
\(254\) −1.35756 + 11.3827i −0.0851812 + 0.714217i
\(255\) 0 0
\(256\) −15.9239 + 1.55852i −0.995245 + 0.0974072i
\(257\) −8.91483 10.6243i −0.556092 0.662725i 0.412623 0.910902i \(-0.364613\pi\)
−0.968715 + 0.248178i \(0.920168\pi\)
\(258\) 0 0
\(259\) 3.60194 + 9.89625i 0.223814 + 0.614923i
\(260\) 17.7008 + 7.73420i 1.09775 + 0.479655i
\(261\) 0 0
\(262\) 10.9734 7.18043i 0.677938 0.443609i
\(263\) −0.425181 + 2.41132i −0.0262178 + 0.148688i −0.995106 0.0988085i \(-0.968497\pi\)
0.968889 + 0.247497i \(0.0796080\pi\)
\(264\) 0 0
\(265\) 23.7727 + 8.65255i 1.46034 + 0.531522i
\(266\) −0.723702 + 2.39683i −0.0443730 + 0.146959i
\(267\) 0 0
\(268\) −21.9467 1.38174i −1.34061 0.0844032i
\(269\) 4.12106i 0.251266i −0.992077 0.125633i \(-0.959904\pi\)
0.992077 0.125633i \(-0.0400961\pi\)
\(270\) 0 0
\(271\) 11.9859i 0.728089i 0.931382 + 0.364044i \(0.118604\pi\)
−0.931382 + 0.364044i \(0.881396\pi\)
\(272\) 11.2798 + 17.5062i 0.683938 + 1.06147i
\(273\) 0 0
\(274\) −4.67632 1.41198i −0.282507 0.0853006i
\(275\) −4.64516 1.69070i −0.280114 0.101953i
\(276\) 0 0
\(277\) −5.21533 + 29.5776i −0.313359 + 1.77715i 0.267921 + 0.963441i \(0.413664\pi\)
−0.581279 + 0.813704i \(0.697448\pi\)
\(278\) 4.15845 + 6.35509i 0.249407 + 0.381153i
\(279\) 0 0
\(280\) 13.4230 11.1030i 0.802178 0.663530i
\(281\) −2.37006 6.51169i −0.141386 0.388455i 0.848708 0.528862i \(-0.177381\pi\)
−0.990094 + 0.140407i \(0.955159\pi\)
\(282\) 0 0
\(283\) −12.1288 14.4545i −0.720981 0.859232i 0.273745 0.961802i \(-0.411738\pi\)
−0.994726 + 0.102571i \(0.967293\pi\)
\(284\) −15.4815 3.74608i −0.918655 0.222289i
\(285\) 0 0
\(286\) −2.04452 0.243841i −0.120895 0.0144186i
\(287\) 0.716765 + 1.24147i 0.0423093 + 0.0732818i
\(288\) 0 0
\(289\) 5.05314 8.75230i 0.297244 0.514841i
\(290\) −3.44252 + 4.60150i −0.202152 + 0.270210i
\(291\) 0 0
\(292\) 2.17469 + 7.39018i 0.127264 + 0.432477i
\(293\) −20.8109 + 3.66952i −1.21578 + 0.214375i −0.744510 0.667612i \(-0.767317\pi\)
−0.471274 + 0.881987i \(0.656206\pi\)
\(294\) 0 0
\(295\) 21.7938 25.9729i 1.26889 1.51220i
\(296\) 2.99737 + 17.7286i 0.174218 + 1.03046i
\(297\) 0 0
\(298\) 7.30609 14.4628i 0.423230 0.837808i
\(299\) −17.7354 14.8818i −1.02567 0.860637i
\(300\) 0 0
\(301\) 0.581066 + 3.29539i 0.0334921 + 0.189943i
\(302\) 23.5272 22.0925i 1.35384 1.27128i
\(303\) 0 0
\(304\) −1.95424 + 3.80171i −0.112083 + 0.218043i
\(305\) −15.4282 8.90750i −0.883418 0.510042i
\(306\) 0 0
\(307\) 17.4037 10.0480i 0.993279 0.573470i 0.0870262 0.996206i \(-0.472264\pi\)
0.906253 + 0.422736i \(0.138930\pi\)
\(308\) −1.02762 + 1.54655i −0.0585542 + 0.0881228i
\(309\) 0 0
\(310\) −16.4984 + 3.86927i −0.937044 + 0.219760i
\(311\) 19.9629 16.7508i 1.13199 0.949853i 0.132844 0.991137i \(-0.457589\pi\)
0.999147 + 0.0412837i \(0.0131448\pi\)
\(312\) 0 0
\(313\) 22.8210 8.30617i 1.28992 0.469493i 0.396219 0.918156i \(-0.370322\pi\)
0.893701 + 0.448663i \(0.148100\pi\)
\(314\) 0.654762 + 11.7159i 0.0369504 + 0.661168i
\(315\) 0 0
\(316\) 2.18063 + 19.4485i 0.122670 + 1.09406i
\(317\) −6.07999 1.07207i −0.341486 0.0602132i 0.000275215 1.00000i \(-0.499912\pi\)
−0.341762 + 0.939787i \(0.611024\pi\)
\(318\) 0 0
\(319\) 0.209507 0.575616i 0.0117301 0.0322283i
\(320\) 25.9635 14.5060i 1.45141 0.810911i
\(321\) 0 0
\(322\) −19.1904 + 8.22453i −1.06944 + 0.458335i
\(323\) 5.56376 0.309576
\(324\) 0 0
\(325\) −22.9162 −1.27116
\(326\) −11.4590 + 4.91103i −0.634654 + 0.271997i
\(327\) 0 0
\(328\) 0.820854 + 2.30571i 0.0453241 + 0.127312i
\(329\) −4.00123 + 10.9933i −0.220595 + 0.606079i
\(330\) 0 0
\(331\) 14.1356 + 2.49248i 0.776962 + 0.136999i 0.548047 0.836447i \(-0.315371\pi\)
0.228914 + 0.973447i \(0.426482\pi\)
\(332\) 3.34170 0.374682i 0.183400 0.0205634i
\(333\) 0 0
\(334\) 1.77951 + 31.8415i 0.0973705 + 1.74229i
\(335\) 38.4105 13.9803i 2.09859 0.763823i
\(336\) 0 0
\(337\) −14.7441 + 12.3718i −0.803163 + 0.673934i −0.948966 0.315380i \(-0.897868\pi\)
0.145802 + 0.989314i \(0.453424\pi\)
\(338\) 8.60601 2.01832i 0.468105 0.109782i
\(339\) 0 0
\(340\) −32.2420 21.4236i −1.74857 1.16186i
\(341\) 1.56432 0.903158i 0.0847125 0.0489088i
\(342\) 0 0
\(343\) −16.1484 9.32326i −0.871930 0.503409i
\(344\) −0.0402623 + 5.71288i −0.00217080 + 0.308018i
\(345\) 0 0
\(346\) 10.5753 9.93044i 0.568532 0.533864i
\(347\) 5.51709 + 31.2889i 0.296173 + 1.67968i 0.662398 + 0.749152i \(0.269539\pi\)
−0.366225 + 0.930526i \(0.619350\pi\)
\(348\) 0 0
\(349\) 13.2668 + 11.1322i 0.710158 + 0.595893i 0.924643 0.380834i \(-0.124363\pi\)
−0.214485 + 0.976727i \(0.568807\pi\)
\(350\) −9.31824 + 18.4460i −0.498081 + 0.985979i
\(351\) 0 0
\(352\) −2.20244 + 2.28019i −0.117390 + 0.121534i
\(353\) 2.57802 3.07236i 0.137214 0.163525i −0.693061 0.720878i \(-0.743739\pi\)
0.830276 + 0.557353i \(0.188183\pi\)
\(354\) 0 0
\(355\) 29.1578 5.14131i 1.54754 0.272873i
\(356\) −24.1993 + 7.12107i −1.28256 + 0.377416i
\(357\) 0 0
\(358\) 12.2847 16.4206i 0.649269 0.867856i
\(359\) −6.05065 + 10.4800i −0.319341 + 0.553115i −0.980351 0.197262i \(-0.936795\pi\)
0.661010 + 0.750377i \(0.270128\pi\)
\(360\) 0 0
\(361\) −8.92900 15.4655i −0.469947 0.813973i
\(362\) 7.42522 + 0.885570i 0.390261 + 0.0465445i
\(363\) 0 0
\(364\) −2.02447 + 8.36653i −0.106111 + 0.438525i
\(365\) −9.20433 10.9693i −0.481777 0.574159i
\(366\) 0 0
\(367\) −1.17616 3.23148i −0.0613952 0.168682i 0.905202 0.424981i \(-0.139719\pi\)
−0.966598 + 0.256299i \(0.917497\pi\)
\(368\) −34.7609 + 7.89427i −1.81204 + 0.411517i
\(369\) 0 0
\(370\) −18.3000 27.9667i −0.951372 1.45392i
\(371\) −1.95763 + 11.1023i −0.101635 + 0.576402i
\(372\) 0 0
\(373\) −5.38991 1.96177i −0.279079 0.101576i 0.198689 0.980063i \(-0.436332\pi\)
−0.477768 + 0.878486i \(0.658554\pi\)
\(374\) 3.95013 + 1.19271i 0.204257 + 0.0616736i
\(375\) 0 0
\(376\) −10.1084 + 17.2267i −0.521298 + 0.888397i
\(377\) 2.83972i 0.146253i
\(378\) 0 0
\(379\) 25.2439i 1.29669i 0.761346 + 0.648346i \(0.224539\pi\)
−0.761346 + 0.648346i \(0.775461\pi\)
\(380\) 0.499261 7.92995i 0.0256116 0.406798i
\(381\) 0 0
\(382\) 4.79649 15.8855i 0.245410 0.812771i
\(383\) 9.14102 + 3.32706i 0.467084 + 0.170005i 0.564831 0.825206i \(-0.308941\pi\)
−0.0977467 + 0.995211i \(0.531164\pi\)
\(384\) 0 0
\(385\) 0.599348 3.39907i 0.0305456 0.173233i
\(386\) −27.3985 + 17.9282i −1.39454 + 0.912521i
\(387\) 0 0
\(388\) −3.19502 + 7.31223i −0.162203 + 0.371222i
\(389\) 3.05382 + 8.39029i 0.154835 + 0.425405i 0.992721 0.120441i \(-0.0384308\pi\)
−0.837886 + 0.545845i \(0.816209\pi\)
\(390\) 0 0
\(391\) 29.8232 + 35.5419i 1.50822 + 1.79743i
\(392\) −9.16556 7.80155i −0.462931 0.394038i
\(393\) 0 0
\(394\) 0.0747428 0.626695i 0.00376549 0.0315724i
\(395\) −18.1888 31.5040i −0.915180 1.58514i
\(396\) 0 0
\(397\) −1.03466 + 1.79209i −0.0519283 + 0.0899424i −0.890821 0.454354i \(-0.849870\pi\)
0.838893 + 0.544297i \(0.183203\pi\)
\(398\) 12.9213 + 9.66678i 0.647684 + 0.484552i
\(399\) 0 0
\(400\) −21.3346 + 28.1022i −1.06673 + 1.40511i
\(401\) −30.0242 + 5.29408i −1.49934 + 0.264374i −0.862276 0.506439i \(-0.830961\pi\)
−0.637062 + 0.770813i \(0.719850\pi\)
\(402\) 0 0
\(403\) 5.38257 6.41470i 0.268125 0.319539i
\(404\) 12.3955 9.13790i 0.616699 0.454628i
\(405\) 0 0
\(406\) −2.28578 1.15469i −0.113441 0.0573064i
\(407\) 2.72905 + 2.28995i 0.135274 + 0.113509i
\(408\) 0 0
\(409\) −6.17283 35.0079i −0.305227 1.73103i −0.622434 0.782672i \(-0.713856\pi\)
0.317207 0.948356i \(-0.397255\pi\)
\(410\) −3.11420 3.31643i −0.153799 0.163787i
\(411\) 0 0
\(412\) −2.66707 5.37338i −0.131397 0.264727i
\(413\) 13.0847 + 7.55447i 0.643858 + 0.371731i
\(414\) 0 0
\(415\) −5.41311 + 3.12526i −0.265719 + 0.153413i
\(416\) −5.97905 + 13.4252i −0.293147 + 0.658224i
\(417\) 0 0
\(418\) 0.193383 + 0.824573i 0.00945866 + 0.0403312i
\(419\) −9.43828 + 7.91966i −0.461090 + 0.386901i −0.843532 0.537079i \(-0.819528\pi\)
0.382442 + 0.923980i \(0.375083\pi\)
\(420\) 0 0
\(421\) 16.3519 5.95160i 0.796943 0.290063i 0.0887237 0.996056i \(-0.471721\pi\)
0.708219 + 0.705993i \(0.249499\pi\)
\(422\) −8.20309 + 0.458443i −0.399320 + 0.0223166i
\(423\) 0 0
\(424\) −6.71029 + 18.0398i −0.325880 + 0.876088i
\(425\) 45.2265 + 7.97466i 2.19381 + 0.386828i
\(426\) 0 0
\(427\) 2.71522 7.46001i 0.131399 0.361015i
\(428\) 16.4025 17.2228i 0.792844 0.832495i
\(429\) 0 0
\(430\) −4.18323 9.76080i −0.201733 0.470708i
\(431\) −19.0526 −0.917729 −0.458865 0.888506i \(-0.651744\pi\)
−0.458865 + 0.888506i \(0.651744\pi\)
\(432\) 0 0
\(433\) −37.4918 −1.80174 −0.900870 0.434088i \(-0.857071\pi\)
−0.900870 + 0.434088i \(0.857071\pi\)
\(434\) −2.97472 6.94095i −0.142791 0.333176i
\(435\) 0 0
\(436\) −12.7802 + 13.4194i −0.612061 + 0.642671i
\(437\) −3.25714 + 8.94892i −0.155810 + 0.428085i
\(438\) 0 0
\(439\) −22.1128 3.89909i −1.05539 0.186093i −0.381079 0.924543i \(-0.624447\pi\)
−0.674309 + 0.738449i \(0.735558\pi\)
\(440\) 2.05442 5.52305i 0.0979406 0.263301i
\(441\) 0 0
\(442\) 19.0989 1.06737i 0.908444 0.0507698i
\(443\) −9.66840 + 3.51901i −0.459359 + 0.167193i −0.561326 0.827595i \(-0.689709\pi\)
0.101967 + 0.994788i \(0.467486\pi\)
\(444\) 0 0
\(445\) 35.9192 30.1398i 1.70273 1.42876i
\(446\) −1.20147 5.12299i −0.0568911 0.242581i
\(447\) 0 0
\(448\) 8.37512 + 10.2717i 0.395687 + 0.485292i
\(449\) 7.77889 4.49114i 0.367109 0.211950i −0.305086 0.952325i \(-0.598685\pi\)
0.672194 + 0.740375i \(0.265352\pi\)
\(450\) 0 0
\(451\) 0.419962 + 0.242465i 0.0197753 + 0.0114172i
\(452\) 5.01237 + 10.0985i 0.235762 + 0.474992i
\(453\) 0 0
\(454\) 6.40455 + 6.82046i 0.300580 + 0.320100i
\(455\) −2.77848 15.7576i −0.130257 0.738725i
\(456\) 0 0
\(457\) −3.65475 3.06670i −0.170962 0.143454i 0.553292 0.832987i \(-0.313371\pi\)
−0.724254 + 0.689533i \(0.757816\pi\)
\(458\) −1.45908 0.737074i −0.0681782 0.0344412i
\(459\) 0 0
\(460\) 53.3336 39.3173i 2.48669 1.83318i
\(461\) 18.3723 21.8953i 0.855684 1.01976i −0.143861 0.989598i \(-0.545952\pi\)
0.999545 0.0301663i \(-0.00960370\pi\)
\(462\) 0 0
\(463\) −41.7768 + 7.36638i −1.94153 + 0.342345i −0.941548 + 0.336878i \(0.890629\pi\)
−0.999985 + 0.00546674i \(0.998260\pi\)
\(464\) −3.48235 2.64373i −0.161664 0.122732i
\(465\) 0 0
\(466\) −19.2796 14.4236i −0.893110 0.668162i
\(467\) 3.22767 5.59048i 0.149359 0.258697i −0.781632 0.623740i \(-0.785612\pi\)
0.930991 + 0.365043i \(0.118946\pi\)
\(468\) 0 0
\(469\) 9.10756 + 15.7748i 0.420548 + 0.728410i
\(470\) 4.39678 36.8656i 0.202808 1.70048i
\(471\) 0 0
\(472\) 19.6432 + 16.7199i 0.904151 + 0.769596i
\(473\) 0.727606 + 0.867127i 0.0334553 + 0.0398705i
\(474\) 0 0
\(475\) 3.22398 + 8.85780i 0.147926 + 0.406424i
\(476\) 6.90688 15.8073i 0.316577 0.724528i
\(477\) 0 0
\(478\) −1.42770 + 0.934214i −0.0653014 + 0.0427300i
\(479\) 6.20075 35.1662i 0.283319 1.60678i −0.427909 0.903822i \(-0.640750\pi\)
0.711228 0.702961i \(-0.248139\pi\)
\(480\) 0 0
\(481\) 15.5193 + 5.64857i 0.707620 + 0.257553i
\(482\) −4.08549 + 13.5307i −0.186089 + 0.616307i
\(483\) 0 0
\(484\) 1.34289 21.3296i 0.0610406 0.969529i
\(485\) 14.8329i 0.673529i
\(486\) 0 0
\(487\) 40.6600i 1.84248i −0.388993 0.921241i \(-0.627177\pi\)
0.388993 0.921241i \(-0.372823\pi\)
\(488\) 6.85951 11.6900i 0.310515 0.529180i
\(489\) 0 0
\(490\) 21.4182 + 6.46704i 0.967574 + 0.292151i
\(491\) 26.4253 + 9.61801i 1.19256 + 0.434055i 0.860620 0.509247i \(-0.170076\pi\)
0.331935 + 0.943302i \(0.392298\pi\)
\(492\) 0 0
\(493\) −0.988198 + 5.60435i −0.0445062 + 0.252407i
\(494\) 2.14983 + 3.28544i 0.0967254 + 0.147819i
\(495\) 0 0
\(496\) −2.85526 12.5726i −0.128205 0.564527i
\(497\) 4.51257 + 12.3982i 0.202416 + 0.556134i
\(498\) 0 0
\(499\) −21.2879 25.3699i −0.952977 1.13571i −0.990651 0.136423i \(-0.956439\pi\)
0.0376739 0.999290i \(-0.488005\pi\)
\(500\) 6.68125 27.6116i 0.298795 1.23483i
\(501\) 0 0
\(502\) −18.6872 2.22873i −0.834051 0.0994733i
\(503\) −13.4484 23.2932i −0.599633 1.03859i −0.992875 0.119159i \(-0.961980\pi\)
0.393242 0.919435i \(-0.371353\pi\)
\(504\) 0 0
\(505\) −14.3126 + 24.7901i −0.636901 + 1.10314i
\(506\) −4.23089 + 5.65528i −0.188086 + 0.251408i
\(507\) 0 0
\(508\) 15.5523 4.57655i 0.690023 0.203052i
\(509\) 9.32093 1.64353i 0.413143 0.0728482i 0.0367864 0.999323i \(-0.488288\pi\)
0.376357 + 0.926475i \(0.377177\pi\)
\(510\) 0 0
\(511\) 4.10167 4.88818i 0.181447 0.216240i
\(512\) 10.8969 + 19.8307i 0.481580 + 0.876402i
\(513\) 0 0
\(514\) −8.84379 + 17.5068i −0.390083 + 0.772190i
\(515\) 8.54200 + 7.16759i 0.376406 + 0.315842i
\(516\) 0 0
\(517\) 0.687203 + 3.89732i 0.0302231 + 0.171404i
\(518\) 10.8572 10.1951i 0.477038 0.447949i
\(519\) 0 0
\(520\) 0.192522 27.3172i 0.00844265 1.19794i
\(521\) −15.6963 9.06226i −0.687667 0.397025i 0.115070 0.993357i \(-0.463291\pi\)
−0.802737 + 0.596333i \(0.796624\pi\)
\(522\) 0 0
\(523\) −31.7246 + 18.3162i −1.38722 + 0.800912i −0.993001 0.118105i \(-0.962318\pi\)
−0.394219 + 0.919017i \(0.628985\pi\)
\(524\) −15.4468 10.2638i −0.674794 0.448375i
\(525\) 0 0
\(526\) 3.37126 0.790643i 0.146994 0.0344737i
\(527\) −12.8551 + 10.7867i −0.559976 + 0.469876i
\(528\) 0 0
\(529\) −53.0129 + 19.2951i −2.30491 + 0.838918i
\(530\) −1.99635 35.7215i −0.0867161 1.55164i
\(531\) 0 0
\(532\) 3.51872 0.394530i 0.152556 0.0171051i
\(533\) 2.21391 + 0.390372i 0.0958951 + 0.0169089i
\(534\) 0 0
\(535\) −15.1206 + 41.5434i −0.653719 + 1.79608i
\(536\) 10.4302 + 29.2975i 0.450515 + 1.26546i
\(537\) 0 0
\(538\) −5.35683 + 2.29580i −0.230949 + 0.0989790i
\(539\) −2.38481 −0.102721
\(540\) 0 0
\(541\) 31.5175 1.35504 0.677521 0.735504i \(-0.263054\pi\)
0.677521 + 0.735504i \(0.263054\pi\)
\(542\) 15.5800 6.67719i 0.669219 0.286810i
\(543\) 0 0
\(544\) 16.4719 24.4147i 0.706225 1.04677i
\(545\) 11.7814 32.3691i 0.504659 1.38654i
\(546\) 0 0
\(547\) −31.0212 5.46987i −1.32637 0.233875i −0.534813 0.844970i \(-0.679618\pi\)
−0.791557 + 0.611095i \(0.790729\pi\)
\(548\) 0.769746 + 6.86518i 0.0328819 + 0.293266i
\(549\) 0 0
\(550\) 0.390085 + 6.97995i 0.0166333 + 0.297626i
\(551\) −1.09763 + 0.399506i −0.0467608 + 0.0170195i
\(552\) 0 0
\(553\) 12.4182 10.4201i 0.528074 0.443107i
\(554\) 41.3523 9.69813i 1.75689 0.412034i
\(555\) 0 0
\(556\) 5.94413 8.94578i 0.252087 0.379386i
\(557\) 13.9805 8.07165i 0.592373 0.342007i −0.173662 0.984805i \(-0.555560\pi\)
0.766035 + 0.642799i \(0.222227\pi\)
\(558\) 0 0
\(559\) 4.54452 + 2.62378i 0.192213 + 0.110974i
\(560\) −21.9102 11.2628i −0.925875 0.475938i
\(561\) 0 0
\(562\) −7.14399 + 6.70835i −0.301351 + 0.282975i
\(563\) −5.14604 29.1846i −0.216880 1.22999i −0.877615 0.479366i \(-0.840867\pi\)
0.660735 0.750619i \(-0.270245\pi\)
\(564\) 0 0
\(565\) −16.0534 13.4704i −0.675374 0.566706i
\(566\) −12.0321 + 23.8182i −0.505748 + 1.00116i
\(567\) 0 0
\(568\) 3.75515 + 22.2107i 0.157563 + 0.931941i
\(569\) −23.6512 + 28.1864i −0.991509 + 1.18163i −0.00814907 + 0.999967i \(0.502594\pi\)
−0.983360 + 0.181668i \(0.941850\pi\)
\(570\) 0 0
\(571\) 0.987914 0.174196i 0.0413429 0.00728987i −0.152938 0.988236i \(-0.548874\pi\)
0.194281 + 0.980946i \(0.437763\pi\)
\(572\) 0.822023 + 2.79345i 0.0343705 + 0.116800i
\(573\) 0 0
\(574\) 1.21445 1.62331i 0.0506900 0.0677556i
\(575\) −39.3033 + 68.0753i −1.63906 + 2.83893i
\(576\) 0 0
\(577\) 10.1847 + 17.6404i 0.423994 + 0.734379i 0.996326 0.0856433i \(-0.0272945\pi\)
−0.572332 + 0.820022i \(0.693961\pi\)
\(578\) −14.1919 1.69260i −0.590304 0.0704027i
\(579\) 0 0
\(580\) 7.89913 + 1.91137i 0.327994 + 0.0793653i
\(581\) −1.79041 2.13373i −0.0742787 0.0885219i
\(582\) 0 0
\(583\) 1.30432 + 3.58360i 0.0540196 + 0.148418i
\(584\) 8.39474 6.94380i 0.347377 0.287336i
\(585\) 0 0
\(586\) 16.3634 + 25.0071i 0.675965 + 1.03303i
\(587\) −4.50124 + 25.5278i −0.185786 + 1.05364i 0.739155 + 0.673535i \(0.235225\pi\)
−0.924941 + 0.380110i \(0.875886\pi\)
\(588\) 0 0
\(589\) −3.23672 1.17807i −0.133367 0.0485415i
\(590\) −45.9024 13.8598i −1.88977 0.570601i
\(591\) 0 0
\(592\) 21.3751 13.7726i 0.878509 0.566051i
\(593\) 41.3947i 1.69988i 0.526881 + 0.849939i \(0.323361\pi\)
−0.526881 + 0.849939i \(0.676639\pi\)
\(594\) 0 0
\(595\) 32.0653i 1.31455i
\(596\) −22.8699 1.43986i −0.936786 0.0589791i
\(597\) 0 0
\(598\) −9.46413 + 31.3442i −0.387017 + 1.28176i
\(599\) 20.6951 + 7.53238i 0.845577 + 0.307765i 0.728236 0.685327i \(-0.240341\pi\)
0.117341 + 0.993092i \(0.462563\pi\)
\(600\) 0 0
\(601\) 1.14732 6.50676i 0.0468001 0.265416i −0.952425 0.304773i \(-0.901420\pi\)
0.999225 + 0.0393561i \(0.0125307\pi\)
\(602\) 3.95986 2.59113i 0.161392 0.105607i
\(603\) 0 0
\(604\) −41.8240 18.2747i −1.70180 0.743585i
\(605\) 13.5872 + 37.3306i 0.552399 + 1.51770i
\(606\) 0 0
\(607\) −4.01395 4.78364i −0.162921 0.194162i 0.678407 0.734686i \(-0.262670\pi\)
−0.841329 + 0.540524i \(0.818226\pi\)
\(608\) 6.03039 + 0.422355i 0.244565 + 0.0171287i
\(609\) 0 0
\(610\) −2.98365 + 25.0169i −0.120804 + 1.01291i
\(611\) 9.17304 + 15.8882i 0.371101 + 0.642767i
\(612\) 0 0
\(613\) −1.30807 + 2.26564i −0.0528323 + 0.0915083i −0.891232 0.453548i \(-0.850158\pi\)
0.838400 + 0.545056i \(0.183492\pi\)
\(614\) −22.7565 17.0248i −0.918376 0.687064i
\(615\) 0 0
\(616\) 2.58278 + 0.474206i 0.104063 + 0.0191063i
\(617\) −13.1781 + 2.32365i −0.530528 + 0.0935465i −0.432494 0.901637i \(-0.642366\pi\)
−0.0980339 + 0.995183i \(0.531255\pi\)
\(618\) 0 0
\(619\) 17.2591 20.5686i 0.693703 0.826723i −0.298095 0.954536i \(-0.596351\pi\)
0.991798 + 0.127813i \(0.0407957\pi\)
\(620\) 14.2206 + 19.2901i 0.571113 + 0.774710i
\(621\) 0 0
\(622\) −32.8950 16.6174i −1.31897 0.666295i
\(623\) 16.0064 + 13.4310i 0.641284 + 0.538101i
\(624\) 0 0
\(625\) 1.51113 + 8.57003i 0.0604451 + 0.342801i
\(626\) −23.5103 25.0370i −0.939659 1.00068i
\(627\) 0 0
\(628\) 14.8644 7.37792i 0.593153 0.294411i
\(629\) −28.6626 16.5484i −1.14285 0.659827i
\(630\) 0 0
\(631\) 24.9119 14.3829i 0.991726 0.572573i 0.0859365 0.996301i \(-0.472612\pi\)
0.905790 + 0.423727i \(0.139278\pi\)
\(632\) 24.0656 13.6691i 0.957279 0.543726i
\(633\) 0 0
\(634\) 1.99356 + 8.50041i 0.0791742 + 0.337594i
\(635\) −23.0844 + 19.3701i −0.916078 + 0.768681i
\(636\) 0 0
\(637\) −10.3889 + 3.78125i −0.411623 + 0.149818i
\(638\) −0.864937 + 0.0483383i −0.0342432 + 0.00191373i
\(639\) 0 0
\(640\) −33.3199 25.6680i −1.31708 1.01462i
\(641\) −1.94287 0.342580i −0.0767386 0.0135311i 0.135147 0.990826i \(-0.456849\pi\)
−0.211886 + 0.977294i \(0.567960\pi\)
\(642\) 0 0
\(643\) 13.0375 35.8203i 0.514150 1.41262i −0.362724 0.931897i \(-0.618153\pi\)
0.876874 0.480720i \(-0.159625\pi\)
\(644\) 21.3816 + 20.3632i 0.842552 + 0.802422i
\(645\) 0 0
\(646\) −3.09951 7.23214i −0.121949 0.284545i
\(647\) 7.03763 0.276678 0.138339 0.990385i \(-0.455824\pi\)
0.138339 + 0.990385i \(0.455824\pi\)
\(648\) 0 0
\(649\) 5.11102 0.200625
\(650\) 12.7664 + 29.7880i 0.500739 + 1.16838i
\(651\) 0 0
\(652\) 12.7674 + 12.1593i 0.500008 + 0.476194i
\(653\) 3.81006 10.4681i 0.149099 0.409647i −0.842549 0.538620i \(-0.818946\pi\)
0.991648 + 0.128973i \(0.0411681\pi\)
\(654\) 0 0
\(655\) 33.9495 + 5.98622i 1.32652 + 0.233901i
\(656\) 2.53982 2.35149i 0.0991635 0.0918101i
\(657\) 0 0
\(658\) 16.5188 0.923180i 0.643971 0.0359893i
\(659\) −35.1305 + 12.7864i −1.36849 + 0.498089i −0.918668 0.395030i \(-0.870734\pi\)
−0.449821 + 0.893119i \(0.648512\pi\)
\(660\) 0 0
\(661\) 4.29644 3.60514i 0.167112 0.140224i −0.555396 0.831586i \(-0.687433\pi\)
0.722509 + 0.691362i \(0.242989\pi\)
\(662\) −4.63489 19.7629i −0.180140 0.768107i
\(663\) 0 0
\(664\) −2.34866 4.13503i −0.0911457 0.160470i
\(665\) −5.69986 + 3.29082i −0.221031 + 0.127612i
\(666\) 0 0
\(667\) −8.43570 4.87036i −0.326632 0.188581i
\(668\) 40.3983 20.0517i 1.56306 0.775823i
\(669\) 0 0
\(670\) −39.5705 42.1402i −1.52874 1.62802i
\(671\) −0.466334 2.64471i −0.0180026 0.102098i
\(672\) 0 0
\(673\) 29.0189 + 24.3497i 1.11860 + 0.938613i 0.998533 0.0541531i \(-0.0172459\pi\)
0.120063 + 0.992766i \(0.461690\pi\)
\(674\) 24.2955 + 12.2732i 0.935826 + 0.472746i
\(675\) 0 0
\(676\) −7.41786 10.0623i −0.285302 0.387010i
\(677\) 24.2754 28.9303i 0.932980 1.11188i −0.0605328 0.998166i \(-0.519280\pi\)
0.993513 0.113717i \(-0.0362756\pi\)
\(678\) 0 0
\(679\) 6.50949 1.14780i 0.249811 0.0440485i
\(680\) −9.88613 + 53.8452i −0.379116 + 2.06487i
\(681\) 0 0
\(682\) −2.04545 1.53026i −0.0783243 0.0585967i
\(683\) 13.9252 24.1192i 0.532834 0.922895i −0.466431 0.884558i \(-0.654460\pi\)
0.999265 0.0383376i \(-0.0122062\pi\)
\(684\) 0 0
\(685\) −6.42053 11.1207i −0.245316 0.424900i
\(686\) −3.12291 + 26.1846i −0.119233 + 0.999733i
\(687\) 0 0
\(688\) 7.44841 3.13025i 0.283968 0.119340i
\(689\) 11.3640 + 13.5431i 0.432933 + 0.515949i
\(690\) 0 0
\(691\) 1.46193 + 4.01662i 0.0556145 + 0.152800i 0.964389 0.264488i \(-0.0852030\pi\)
−0.908774 + 0.417288i \(0.862981\pi\)
\(692\) −18.7996 8.21435i −0.714655 0.312263i
\(693\) 0 0
\(694\) 37.5979 24.6022i 1.42720 0.933887i
\(695\) −3.46684 + 19.6614i −0.131505 + 0.745800i
\(696\) 0 0
\(697\) −4.23343 1.54084i −0.160353 0.0583636i
\(698\) 7.07956 23.4468i 0.267965 0.887473i
\(699\) 0 0
\(700\) 29.1684 + 1.83641i 1.10246 + 0.0694098i
\(701\) 20.9584i 0.791586i 0.918340 + 0.395793i \(0.129530\pi\)
−0.918340 + 0.395793i \(0.870470\pi\)
\(702\) 0 0
\(703\) 6.79334i 0.256216i
\(704\) 4.19089 + 1.59261i 0.157950 + 0.0600236i
\(705\) 0 0
\(706\) −5.42985 1.63950i −0.204355 0.0617033i
\(707\) −11.9868 4.36282i −0.450808 0.164081i
\(708\) 0 0
\(709\) −1.39089 + 7.88813i −0.0522360 + 0.296245i −0.999723 0.0235502i \(-0.992503\pi\)
0.947487 + 0.319795i \(0.103614\pi\)
\(710\) −22.9265 35.0371i −0.860418 1.31492i
\(711\) 0 0
\(712\) 22.7376 + 27.4887i 0.852128 + 1.03018i
\(713\) −9.82403 26.9913i −0.367913 1.01083i
\(714\) 0 0
\(715\) −3.47919 4.14634i −0.130114 0.155064i
\(716\) −28.1883 6.82078i −1.05345 0.254904i
\(717\) 0 0
\(718\) 16.9934 + 2.02672i 0.634188 + 0.0756365i
\(719\) 4.27525 + 7.40496i 0.159440 + 0.276158i 0.934667 0.355525i \(-0.115698\pi\)
−0.775227 + 0.631683i \(0.782364\pi\)
\(720\) 0 0
\(721\) −2.48453 + 4.30333i −0.0925287 + 0.160264i
\(722\) −15.1288 + 20.2222i −0.563036 + 0.752591i
\(723\) 0 0
\(724\) −2.98539 10.1451i −0.110951 0.377041i
\(725\) −9.49505 + 1.67423i −0.352637 + 0.0621795i
\(726\) 0 0
\(727\) −16.9742 + 20.2291i −0.629538 + 0.750255i −0.982679 0.185316i \(-0.940669\pi\)
0.353141 + 0.935570i \(0.385114\pi\)
\(728\) 12.0032 2.02937i 0.444867 0.0752134i
\(729\) 0 0
\(730\) −9.13098 + 18.0753i −0.337953 + 0.668996i
\(731\) −8.05582 6.75964i −0.297955 0.250014i
\(732\) 0 0
\(733\) 6.75770 + 38.3248i 0.249601 + 1.41556i 0.809559 + 0.587039i \(0.199706\pi\)
−0.559957 + 0.828521i \(0.689182\pi\)
\(734\) −3.54527 + 3.32908i −0.130858 + 0.122879i
\(735\) 0 0
\(736\) 29.6264 + 40.7868i 1.09204 + 1.50342i
\(737\) 5.33625 + 3.08088i 0.196563 + 0.113486i
\(738\) 0 0
\(739\) −10.6334 + 6.13920i −0.391156 + 0.225834i −0.682661 0.730735i \(-0.739177\pi\)
0.291505 + 0.956569i \(0.405844\pi\)
\(740\) −26.1582 + 39.3675i −0.961595 + 1.44718i
\(741\) 0 0
\(742\) 15.5221 3.64030i 0.569832 0.133640i
\(743\) −14.9811 + 12.5706i −0.549603 + 0.461172i −0.874807 0.484472i \(-0.839012\pi\)
0.325204 + 0.945644i \(0.394567\pi\)
\(744\) 0 0
\(745\) 40.0262 14.5683i 1.46645 0.533743i
\(746\) 0.452627 + 8.09904i 0.0165719 + 0.296527i
\(747\) 0 0
\(748\) −0.650213 5.79909i −0.0237741 0.212036i
\(749\) −19.4015 3.42101i −0.708917 0.125001i
\(750\) 0 0
\(751\) −0.401897 + 1.10420i −0.0146654 + 0.0402929i −0.946809 0.321795i \(-0.895714\pi\)
0.932144 + 0.362088i \(0.117936\pi\)
\(752\) 28.0236 + 3.54272i 1.02192 + 0.129190i
\(753\) 0 0
\(754\) −3.69125 + 1.58198i −0.134428 + 0.0576122i
\(755\) 84.8405 3.08766
\(756\) 0 0
\(757\) −15.1258 −0.549756 −0.274878 0.961479i \(-0.588638\pi\)
−0.274878 + 0.961479i \(0.588638\pi\)
\(758\) 32.8137 14.0631i 1.19185 0.510795i
\(759\) 0 0
\(760\) −10.5860 + 3.76872i −0.383995 + 0.136706i
\(761\) −4.81963 + 13.2418i −0.174711 + 0.480016i −0.995881 0.0906683i \(-0.971100\pi\)
0.821170 + 0.570684i \(0.193322\pi\)
\(762\) 0 0
\(763\) 15.1170 + 2.66553i 0.547271 + 0.0964986i
\(764\) −23.3210 + 2.61483i −0.843726 + 0.0946013i
\(765\) 0 0
\(766\) −0.767634 13.7356i −0.0277357 0.496286i
\(767\) 22.2650 8.10379i 0.803941 0.292611i
\(768\) 0 0
\(769\) −19.1139 + 16.0385i −0.689265 + 0.578362i −0.918697 0.394962i \(-0.870758\pi\)
0.229432 + 0.973325i \(0.426313\pi\)
\(770\) −4.75222 + 1.11451i −0.171258 + 0.0401643i
\(771\) 0 0
\(772\) 38.5676 + 25.6267i 1.38808 + 0.922326i
\(773\) 12.7170 7.34218i 0.457400 0.264080i −0.253550 0.967322i \(-0.581598\pi\)
0.710950 + 0.703242i \(0.248265\pi\)
\(774\) 0 0
\(775\) −24.6220 14.2155i −0.884449 0.510637i
\(776\) 11.2848 + 0.0795314i 0.405102 + 0.00285501i
\(777\) 0 0
\(778\) 9.20500 8.64369i 0.330015 0.309891i
\(779\) −0.160574 0.910661i −0.00575316 0.0326278i
\(780\) 0 0
\(781\) 3.41900 + 2.86888i 0.122342 + 0.102657i
\(782\) 29.5855 58.5662i 1.05798 2.09432i
\(783\) 0 0
\(784\) −5.03493 + 16.2602i −0.179819 + 0.580720i
\(785\) −19.8277 + 23.6297i −0.707681 + 0.843381i
\(786\) 0 0
\(787\) −6.40180 + 1.12881i −0.228199 + 0.0402377i −0.286578 0.958057i \(-0.592518\pi\)
0.0583791 + 0.998294i \(0.481407\pi\)
\(788\) −0.856257 + 0.251969i −0.0305029 + 0.00897603i
\(789\) 0 0
\(790\) −30.8182 + 41.1936i −1.09646 + 1.46560i
\(791\) 4.66931 8.08748i 0.166021 0.287558i
\(792\) 0 0
\(793\) −6.22481 10.7817i −0.221049 0.382869i
\(794\) 2.90588 + 0.346570i 0.103126 + 0.0122993i
\(795\) 0 0
\(796\) 5.36723 22.1812i 0.190236 0.786191i
\(797\) 16.1321 + 19.2255i 0.571427 + 0.681001i 0.971923 0.235298i \(-0.0756066\pi\)
−0.400496 + 0.916299i \(0.631162\pi\)
\(798\) 0 0
\(799\) −12.5746 34.5484i −0.444857 1.22223i
\(800\) 48.4143 + 12.0767i 1.71171 + 0.426977i
\(801\) 0 0
\(802\) 23.6078 + 36.0782i 0.833619 + 1.27396i
\(803\) 0.374832 2.12578i 0.0132275 0.0750170i
\(804\) 0 0
\(805\) −51.5749 18.7717i −1.81778 0.661616i
\(806\) −11.3368 3.42306i −0.399323 0.120572i
\(807\) 0 0
\(808\) −18.7834 11.0219i −0.660799 0.387748i
\(809\) 18.1165i 0.636944i −0.947932 0.318472i \(-0.896830\pi\)
0.947932 0.318472i \(-0.103170\pi\)
\(810\) 0 0
\(811\) 6.98634i 0.245324i 0.992449 + 0.122662i \(0.0391430\pi\)
−0.992449 + 0.122662i \(0.960857\pi\)
\(812\) −0.227563 + 3.61447i −0.00798590 + 0.126843i
\(813\) 0 0
\(814\) 1.45630 4.82311i 0.0510433 0.169050i
\(815\) −30.7964 11.2090i −1.07875 0.392633i
\(816\) 0 0
\(817\) 0.374821 2.12572i 0.0131133 0.0743694i
\(818\) −42.0667 + 27.5264i −1.47083 + 0.962437i
\(819\) 0 0
\(820\) −2.57603 + 5.89559i −0.0899589 + 0.205883i
\(821\) −12.3202 33.8494i −0.429977 1.18135i −0.945826 0.324673i \(-0.894746\pi\)
0.515849 0.856679i \(-0.327477\pi\)
\(822\) 0 0
\(823\) 14.6929 + 17.5103i 0.512161 + 0.610369i 0.958709 0.284390i \(-0.0917912\pi\)
−0.446548 + 0.894760i \(0.647347\pi\)
\(824\) −5.49887 + 6.46029i −0.191562 + 0.225055i
\(825\) 0 0
\(826\) 2.53044 21.2169i 0.0880452 0.738231i
\(827\) −17.2618 29.8984i −0.600253 1.03967i −0.992782 0.119929i \(-0.961733\pi\)
0.392530 0.919739i \(-0.371600\pi\)
\(828\) 0 0
\(829\) 11.3276 19.6199i 0.393423 0.681429i −0.599475 0.800393i \(-0.704624\pi\)
0.992899 + 0.118964i \(0.0379574\pi\)
\(830\) 7.07801 + 5.29527i 0.245681 + 0.183802i
\(831\) 0 0
\(832\) 20.7818 + 0.292940i 0.720480 + 0.0101559i
\(833\) 21.8189 3.84726i 0.755981 0.133300i
\(834\) 0 0
\(835\) −53.8877 + 64.2208i −1.86486 + 2.22245i
\(836\) 0.964103 0.710733i 0.0333442 0.0245812i
\(837\) 0 0
\(838\) 15.5525 + 7.85655i 0.537251 + 0.271400i
\(839\) 8.27145 + 6.94057i 0.285562 + 0.239615i 0.774305 0.632813i \(-0.218100\pi\)
−0.488743 + 0.872428i \(0.662544\pi\)
\(840\) 0 0
\(841\) 4.82833 + 27.3828i 0.166494 + 0.944235i
\(842\) −16.8458 17.9397i −0.580543 0.618243i
\(843\) 0 0
\(844\) 5.16577 + 10.4075i 0.177813 + 0.358242i
\(845\) 20.1238 + 11.6185i 0.692280 + 0.399688i
\(846\) 0 0
\(847\) −15.3313 + 8.85151i −0.526788 + 0.304141i
\(848\) 27.1875 1.32728i 0.933623 0.0455792i
\(849\) 0 0
\(850\) −14.8292 63.2310i −0.508639 2.16881i
\(851\) 43.3966 36.4141i 1.48762 1.24826i
\(852\) 0 0
\(853\) 16.8556 6.13495i 0.577126 0.210057i −0.0369315 0.999318i \(-0.511758\pi\)
0.614058 + 0.789261i \(0.289536\pi\)
\(854\) −11.2096 + 0.626468i −0.383586 + 0.0214373i
\(855\) 0 0
\(856\) −31.5250 11.7264i −1.07750 0.400800i
\(857\) −5.62708 0.992207i −0.192218 0.0338931i 0.0767105 0.997053i \(-0.475558\pi\)
−0.268928 + 0.963160i \(0.586669\pi\)
\(858\) 0 0
\(859\) 6.53894 17.9656i 0.223106 0.612978i −0.776753 0.629806i \(-0.783134\pi\)
0.999858 + 0.0168277i \(0.00535669\pi\)
\(860\) −10.3573 + 10.8753i −0.353181 + 0.370844i
\(861\) 0 0
\(862\) 10.6140 + 24.7658i 0.361513 + 0.843525i
\(863\) −42.9009 −1.46036 −0.730181 0.683254i \(-0.760564\pi\)
−0.730181 + 0.683254i \(0.760564\pi\)
\(864\) 0 0
\(865\) 38.1352 1.29664
\(866\) 20.8863 + 48.7343i 0.709745 + 1.65606i
\(867\) 0 0
\(868\) −7.36513 + 7.73346i −0.249989 + 0.262491i
\(869\) 1.87555 5.15303i 0.0636236 0.174804i
\(870\) 0 0
\(871\) 28.1310 + 4.96026i 0.953183 + 0.168072i
\(872\) 24.5631 + 9.13678i 0.831811 + 0.309410i
\(873\) 0 0
\(874\) 13.4469 0.751502i 0.454849 0.0254199i
\(875\) −22.1125 + 8.04830i −0.747540 + 0.272082i
\(876\) 0 0
\(877\) −20.7445 + 17.4067i −0.700491 + 0.587781i −0.921913 0.387397i \(-0.873374\pi\)
0.221423 + 0.975178i \(0.428930\pi\)
\(878\) 7.25053 + 30.9159i 0.244694 + 1.04336i
\(879\) 0 0
\(880\) −8.32371 + 0.406361i −0.280592 + 0.0136984i
\(881\) −6.75989 + 3.90282i −0.227746 + 0.131489i −0.609532 0.792761i \(-0.708643\pi\)
0.381786 + 0.924251i \(0.375309\pi\)
\(882\) 0 0
\(883\) 43.9985 + 25.4025i 1.48067 + 0.854864i 0.999760 0.0219080i \(-0.00697411\pi\)
0.480907 + 0.876772i \(0.340307\pi\)
\(884\) −12.0273 24.2314i −0.404521 0.814992i
\(885\) 0 0
\(886\) 9.96040 + 10.6072i 0.334626 + 0.356356i
\(887\) −0.849885 4.81994i −0.0285363 0.161838i 0.967210 0.253980i \(-0.0817397\pi\)
−0.995746 + 0.0921422i \(0.970629\pi\)
\(888\) 0 0
\(889\) −10.2870 8.63179i −0.345014 0.289501i
\(890\) −59.1878 29.8996i −1.98398 1.00224i
\(891\) 0 0
\(892\) −5.98988 + 4.41571i −0.200556 + 0.147849i
\(893\) 4.85073 5.78088i 0.162324 0.193450i
\(894\) 0 0
\(895\) 53.0899 9.36118i 1.77460 0.312910i
\(896\) 8.68613 16.6088i 0.290183 0.554861i
\(897\) 0 0
\(898\) −10.1714 7.60955i −0.339425 0.253934i
\(899\) 1.76155 3.05109i 0.0587510 0.101760i
\(900\) 0 0
\(901\) −17.7146 30.6826i −0.590159 1.02218i
\(902\) 0.0812160 0.680970i 0.00270420 0.0226738i
\(903\) 0 0
\(904\) 10.3343 12.1412i 0.343715 0.403809i
\(905\) 12.6356 + 15.0585i 0.420021 + 0.500561i
\(906\) 0 0
\(907\) −8.73803 24.0076i −0.290142 0.797158i −0.996045 0.0888495i \(-0.971681\pi\)
0.705903 0.708308i \(-0.250541\pi\)
\(908\) 5.29777 12.1247i 0.175813 0.402371i
\(909\) 0 0
\(910\) −18.9348 + 12.3900i −0.627684 + 0.410725i
\(911\) 7.53014 42.7055i 0.249485 1.41490i −0.560358 0.828250i \(-0.689337\pi\)
0.809843 0.586647i \(-0.199552\pi\)
\(912\) 0 0
\(913\) −0.885409 0.322262i −0.0293028 0.0106653i
\(914\) −1.95028 + 6.45911i −0.0645094 + 0.213648i
\(915\) 0 0
\(916\) −0.145260 + 2.30722i −0.00479953 + 0.0762327i
\(917\) 15.3621i 0.507301i
\(918\) 0 0
\(919\) 31.6571i 1.04427i −0.852862 0.522136i \(-0.825135\pi\)
0.852862 0.522136i \(-0.174865\pi\)
\(920\) −80.8187 47.4233i −2.66451 1.56350i
\(921\) 0 0
\(922\) −38.6959 11.6839i −1.27438 0.384789i
\(923\) 19.4429 + 7.07662i 0.639969 + 0.232930i
\(924\) 0 0
\(925\) 9.73706 55.2216i 0.320152 1.81567i
\(926\) 32.8487 + 50.2005i 1.07948 + 1.64969i
\(927\) 0 0
\(928\) −1.49652 + 5.99938i −0.0491255 + 0.196939i
\(929\) −16.4439 45.1792i −0.539507 1.48228i −0.847449 0.530877i \(-0.821863\pi\)
0.307942 0.951405i \(-0.400360\pi\)
\(930\) 0 0
\(931\) 2.92313 + 3.48365i 0.0958016 + 0.114172i
\(932\) −8.00835 + 33.0961i −0.262322 + 1.08410i
\(933\) 0 0
\(934\) −9.06498 1.08114i −0.296615 0.0353759i
\(935\) 5.42349 + 9.39376i 0.177367 + 0.307209i
\(936\) 0 0
\(937\) 28.1506 48.7583i 0.919641 1.59287i 0.119681 0.992812i \(-0.461813\pi\)
0.799961 0.600053i \(-0.204854\pi\)
\(938\) 15.4313 20.6266i 0.503851 0.673481i
\(939\) 0 0
\(940\) −50.3697 + 14.8222i −1.64288 + 0.483447i
\(941\) 54.1362 9.54567i 1.76479 0.311180i 0.805288 0.592884i \(-0.202011\pi\)
0.959501 + 0.281704i \(0.0908997\pi\)
\(942\) 0 0
\(943\) 4.95668 5.90715i 0.161412 0.192363i
\(944\) 10.7906 34.8480i 0.351205 1.13421i
\(945\) 0 0
\(946\) 0.721807 1.42886i 0.0234680 0.0464561i
\(947\) −36.2498 30.4172i −1.17796 0.988427i −0.999990 0.00439122i \(-0.998602\pi\)
−0.177971 0.984036i \(-0.556953\pi\)
\(948\) 0 0
\(949\) −1.73766 9.85477i −0.0564069 0.319899i
\(950\) 9.71791 9.12532i 0.315291 0.296065i
\(951\) 0 0
\(952\) −24.3952 0.171928i −0.790652 0.00557223i
\(953\) 29.6972 + 17.1457i 0.961985 + 0.555402i 0.896783 0.442470i \(-0.145898\pi\)
0.0652018 + 0.997872i \(0.479231\pi\)
\(954\) 0 0
\(955\) 37.7770 21.8106i 1.22244 0.705774i
\(956\) 2.00971 + 1.33537i 0.0649986 + 0.0431891i
\(957\) 0 0
\(958\) −49.1657 + 11.5306i −1.58847 + 0.372536i
\(959\) 4.38352 3.67821i 0.141551 0.118776i
\(960\) 0 0
\(961\) −19.3680 + 7.04939i −0.624775 + 0.227400i
\(962\) −1.30326 23.3198i −0.0420189 0.751861i
\(963\) 0 0
\(964\) 19.8641 2.22723i 0.639779 0.0717342i
\(965\) −84.7656 14.9465i −2.72870 0.481143i
\(966\) 0 0
\(967\) −8.31365 + 22.8416i −0.267349 + 0.734535i 0.731275 + 0.682083i \(0.238926\pi\)
−0.998623 + 0.0524519i \(0.983296\pi\)
\(968\) −28.4738 + 10.1369i −0.915182 + 0.325813i
\(969\) 0 0
\(970\) −19.2808 + 8.26327i −0.619070 + 0.265318i
\(971\) 39.8444 1.27867 0.639334 0.768929i \(-0.279210\pi\)
0.639334 + 0.768929i \(0.279210\pi\)
\(972\) 0 0
\(973\) −8.89676 −0.285217
\(974\) −52.8526 + 22.6513i −1.69351 + 0.725793i
\(975\) 0 0
\(976\) −19.0168 2.40408i −0.608711 0.0769527i
\(977\) −15.9360 + 43.7837i −0.509836 + 1.40076i 0.371570 + 0.928405i \(0.378820\pi\)
−0.881406 + 0.472359i \(0.843403\pi\)
\(978\) 0 0
\(979\) 6.96090 + 1.22739i 0.222471 + 0.0392277i
\(980\) −3.52554 31.4435i −0.112619 1.00442i
\(981\) 0 0
\(982\) −2.21911 39.7074i −0.0708146 1.26711i
\(983\) 9.94420 3.61939i 0.317171 0.115441i −0.178529 0.983935i \(-0.557134\pi\)
0.495700 + 0.868494i \(0.334912\pi\)
\(984\) 0 0
\(985\) 1.27095 1.06645i 0.0404958 0.0339800i
\(986\) 7.83542 1.83760i 0.249531 0.0585211i
\(987\) 0 0
\(988\) 3.07299 4.62478i 0.0977648 0.147134i
\(989\) 15.5885 9.00000i 0.495684 0.286183i
\(990\) 0 0
\(991\) 20.1628 + 11.6410i 0.640492 + 0.369788i 0.784804 0.619744i \(-0.212764\pi\)
−0.144312 + 0.989532i \(0.546097\pi\)
\(992\) −14.7521 + 10.7155i −0.468379 + 0.340219i
\(993\) 0 0
\(994\) 13.6021 12.7726i 0.431431 0.405123i
\(995\) 7.36626 + 41.7761i 0.233526 + 1.32439i
\(996\) 0 0
\(997\) −43.9556 36.8831i −1.39209 1.16810i −0.964486 0.264134i \(-0.914914\pi\)
−0.427602 0.903967i \(-0.640642\pi\)
\(998\) −21.1182 + 41.8047i −0.668486 + 1.32330i
\(999\) 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 324.2.l.a.35.6 96
3.2 odd 2 108.2.l.a.11.11 yes 96
4.3 odd 2 inner 324.2.l.a.35.16 96
9.2 odd 6 972.2.l.d.755.12 96
9.4 even 3 972.2.l.b.431.15 96
9.5 odd 6 972.2.l.c.431.2 96
9.7 even 3 972.2.l.a.755.5 96
12.11 even 2 108.2.l.a.11.1 96
27.4 even 9 972.2.l.d.215.10 96
27.5 odd 18 inner 324.2.l.a.287.16 96
27.13 even 9 972.2.l.c.539.12 96
27.14 odd 18 972.2.l.b.539.5 96
27.22 even 9 108.2.l.a.59.1 yes 96
27.23 odd 18 972.2.l.a.215.7 96
36.7 odd 6 972.2.l.a.755.7 96
36.11 even 6 972.2.l.d.755.10 96
36.23 even 6 972.2.l.c.431.12 96
36.31 odd 6 972.2.l.b.431.5 96
108.23 even 18 972.2.l.a.215.5 96
108.31 odd 18 972.2.l.d.215.12 96
108.59 even 18 inner 324.2.l.a.287.6 96
108.67 odd 18 972.2.l.c.539.2 96
108.95 even 18 972.2.l.b.539.15 96
108.103 odd 18 108.2.l.a.59.11 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.2.l.a.11.1 96 12.11 even 2
108.2.l.a.11.11 yes 96 3.2 odd 2
108.2.l.a.59.1 yes 96 27.22 even 9
108.2.l.a.59.11 yes 96 108.103 odd 18
324.2.l.a.35.6 96 1.1 even 1 trivial
324.2.l.a.35.16 96 4.3 odd 2 inner
324.2.l.a.287.6 96 108.59 even 18 inner
324.2.l.a.287.16 96 27.5 odd 18 inner
972.2.l.a.215.5 96 108.23 even 18
972.2.l.a.215.7 96 27.23 odd 18
972.2.l.a.755.5 96 9.7 even 3
972.2.l.a.755.7 96 36.7 odd 6
972.2.l.b.431.5 96 36.31 odd 6
972.2.l.b.431.15 96 9.4 even 3
972.2.l.b.539.5 96 27.14 odd 18
972.2.l.b.539.15 96 108.95 even 18
972.2.l.c.431.2 96 9.5 odd 6
972.2.l.c.431.12 96 36.23 even 6
972.2.l.c.539.2 96 108.67 odd 18
972.2.l.c.539.12 96 27.13 even 9
972.2.l.d.215.10 96 27.4 even 9
972.2.l.d.215.12 96 108.31 odd 18
972.2.l.d.755.10 96 36.11 even 6
972.2.l.d.755.12 96 9.2 odd 6