LMFDB - Embedded newform 81.2.g.a.40.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(4,81)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("81.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			40.3
Character	$\chi$	$=$	81.40
Dual form			81.2.g.a.79.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0883342 - 1.51664i) q^{2} +(0.961557 + 1.44063i) q^{3} +(-0.305915 + 0.0357564i) q^{4} +(-0.0774602 - 0.0183584i) q^{5} +(2.09997 - 1.58559i) q^{6} +(-0.510276 + 0.685420i) q^{7} +(-0.446364 - 2.53145i) q^{8} +(-1.15082 + 2.77049i) q^{9} +(-0.0210007 + 0.119101i) q^{10} +(-2.74014 - 2.90438i) q^{11} +(-0.345667 - 0.406328i) q^{12} +(-1.81277 + 0.910408i) q^{13} +(1.08461 + 0.713359i) q^{14} +(-0.0480348 - 0.129244i) q^{15} +(-4.39927 + 1.04265i) q^{16} +(-1.92609 + 0.701038i) q^{17} +(4.30349 + 1.50064i) q^{18} +(5.26032 + 1.91460i) q^{19} +(0.0243527 + 0.00284642i) q^{20} +(-1.47810 - 0.0760476i) q^{21} +(-4.16285 + 4.41236i) q^{22} +(4.48100 + 6.01902i) q^{23} +(3.21768 - 3.07718i) q^{24} +(-4.46250 - 2.24115i) q^{25} +(1.54089 + 2.66890i) q^{26} +(-5.09782 + 1.00609i) q^{27} +(0.131593 - 0.227926i) q^{28} +(-0.928490 + 0.610677i) q^{29} +(-0.191773 + 0.0842682i) q^{30} +(2.37351 - 5.50241i) q^{31} +(0.495463 + 1.65496i) q^{32} +(1.54933 - 6.74025i) q^{33} +(1.23336 + 2.85925i) q^{34} +(0.0521094 - 0.0437249i) q^{35} +(0.252989 - 0.888685i) q^{36} +(-0.782274 - 0.656406i) q^{37} +(2.43909 - 8.14713i) q^{38} +(-3.05464 - 1.73612i) q^{39} +(-0.0118980 + 0.204282i) q^{40} +(0.254528 - 4.37008i) q^{41} +(0.0152296 + 2.24845i) q^{42} +(3.44402 - 11.5038i) q^{43} +(0.942101 + 0.790516i) q^{44} +(0.140004 - 0.193476i) q^{45} +(8.73286 - 7.32774i) q^{46} +(2.03795 + 4.72449i) q^{47} +(-5.73221 - 5.33514i) q^{48} +(1.79820 + 6.00642i) q^{49} +(-3.00483 + 6.96597i) q^{50} +(-2.86198 - 2.10068i) q^{51} +(0.522002 - 0.343326i) q^{52} +(-5.16096 + 8.93905i) q^{53} +(1.97619 + 7.64268i) q^{54} +(0.158932 + 0.275278i) q^{55} +(1.96288 + 0.985795i) q^{56} +(2.29987 + 9.41916i) q^{57} +(1.00819 + 1.35424i) q^{58} +(7.51758 - 7.96817i) q^{59} +(0.0193159 + 0.0378202i) q^{60} +(10.5595 + 1.23423i) q^{61} +(-8.55483 - 3.11370i) q^{62} +(-1.31172 - 2.20251i) q^{63} +(-6.03074 + 2.19501i) q^{64} +(0.157131 - 0.0372408i) q^{65} +(-10.3594 - 1.75438i) q^{66} +(3.83910 + 2.52502i) q^{67} +(0.564152 - 0.283328i) q^{68} +(-4.36244 + 12.2431i) q^{69} +(-0.0709180 - 0.0751687i) q^{70} +(-0.963622 + 5.46497i) q^{71} +(7.52705 + 1.67659i) q^{72} +(0.267464 + 1.51686i) q^{73} +(-0.926430 + 1.24441i) q^{74} +(-1.06228 - 8.58380i) q^{75} +(-1.67767 - 0.397615i) q^{76} +(3.38895 - 0.396111i) q^{77} +(-2.36324 + 4.78615i) q^{78} +(-0.793846 - 13.6298i) q^{79} +0.359909 q^{80} +(-6.35125 - 6.37665i) q^{81} -6.65031 q^{82} +(0.365349 + 6.27280i) q^{83} +(0.454891 - 0.0295872i) q^{84} +(0.162065 - 0.0189427i) q^{85} +(-17.7514 - 4.20715i) q^{86} +(-1.77255 - 0.750407i) q^{87} +(-6.12920 + 8.23295i) q^{88} +(-1.79520 - 10.1811i) q^{89} +(-0.305800 - 0.195245i) q^{90} +(0.301002 - 1.70707i) q^{91} +(-1.58602 - 1.68109i) q^{92} +(10.2092 - 1.87154i) q^{93} +(6.98533 - 3.50817i) q^{94} +(-0.372317 - 0.244876i) q^{95} +(-1.90777 + 2.30512i) q^{96} +(-13.3681 + 3.16829i) q^{97} +(8.95073 - 3.25780i) q^{98} +(11.2000 - 4.24913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{27}\right)$

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 $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0883342	−	1.51664i	−0.0624617	−	1.07243i	−0.873309	−	0.487168i	$-0.838030\pi$
$2$	−0.0883342	−	1.51664i	−0.0624617	−	1.07243i	0.810847	−	0.585258i	$-0.199007\pi$
$3$	0.961557	+	1.44063i	0.555155	+	0.831747i
$3$	0.961557	+	1.44063i	0.555155	+	0.831747i
$4$	−0.305915	+	0.0357564i	−0.152958	+	0.0178782i
$5$	−0.0774602	−	0.0183584i	−0.0346413	−	0.00821013i	0.213259	−	0.976996i	$-0.431592\pi$
$5$	−0.0774602	−	0.0183584i	−0.0346413	−	0.00821013i	−0.247900	+	0.968786i	$0.579740\pi$
$6$	2.09997	−	1.58559i	0.857311	−	0.647315i
$7$	−0.510276	+	0.685420i	−0.192866	+	0.259064i	−0.888028	−	0.459789i	$-0.847925\pi$
$7$	−0.510276	+	0.685420i	−0.192866	+	0.259064i	0.695162	+	0.718853i	$0.255333\pi$
$8$	−0.446364	−	2.53145i	−0.157813	−	0.895004i
$9$	−1.15082	+	2.77049i	−0.383605	+	0.923497i
$10$	−0.0210007	+	0.119101i	−0.00664101	+	0.0376630i
$11$	−2.74014	−	2.90438i	−0.826183	−	0.875703i	0.167734	−	0.985832i	$-0.446355\pi$
$11$	−2.74014	−	2.90438i	−0.826183	−	0.875703i	−0.993917	+	0.110129i	$0.964874\pi$
$12$	−0.345667	−	0.406328i	−0.0997854	−	0.117297i
$13$	−1.81277	+	0.910408i	−0.502772	+	0.252502i	−0.682062	−	0.731295i	$-0.738916\pi$
$13$	−1.81277	+	0.910408i	−0.502772	+	0.252502i	0.179289	+	0.983796i	$0.442620\pi$
$14$	1.08461	+	0.713359i	0.289874	+	0.190653i
$15$	−0.0480348	−	0.129244i	−0.0124025	−	0.0333707i
$16$	−4.39927	+	1.04265i	−1.09982	+	0.260661i
$17$	−1.92609	+	0.701038i	−0.467144	+	0.170027i	−0.564858	−	0.825188i	$-0.691069\pi$
$17$	−1.92609	+	0.701038i	−0.467144	+	0.170027i	0.0977140	+	0.995215i	$0.468847\pi$
$18$	4.30349	+	1.50064i	1.01434	+	0.353705i
$19$	5.26032	+	1.91460i	1.20680	+	0.439239i	0.865593	−	0.500749i	$-0.166942\pi$
$19$	5.26032	+	1.91460i	1.20680	+	0.439239i	0.341207	+	0.939988i	$0.389164\pi$
$20$	0.0243527	+	0.00284642i	0.00544543	+	0.000636479i
$21$	−1.47810	−	0.0760476i	−0.322547	−	0.0165949i
$22$	−4.16285	+	4.41236i	−0.887522	+	0.940718i
$23$	4.48100	+	6.01902i	0.934352	+	1.25505i	0.966788	+	0.255579i	$0.0822661\pi$
$23$	4.48100	+	6.01902i	0.934352	+	1.25505i	−0.0324361	+	0.999474i	$0.510327\pi$
$24$	3.21768	−	3.07718i	0.656806	−	0.628127i
$25$	−4.46250	−	2.24115i	−0.892500	−	0.448230i
$26$	1.54089	+	2.66890i	0.302193	+	0.523414i
$27$	−5.09782	+	1.00609i	−0.981076	+	0.193622i
$28$	0.131593	−	0.227926i	0.0248688	−	0.0430740i
$29$	−0.928490	+	0.610677i	−0.172416	+	0.113400i	−0.632784	−	0.774328i	$-0.718088\pi$
$29$	−0.928490	+	0.610677i	−0.172416	+	0.113400i	0.460368	+	0.887728i	$0.347718\pi$
$30$	−0.191773	+	0.0842682i	−0.0350129	+	0.0153852i
$31$	2.37351	−	5.50241i	0.426294	−	0.988262i	−0.560775	−	0.827968i	$-0.689497\pi$
$31$	2.37351	−	5.50241i	0.426294	−	0.988262i	0.987069	−	0.160293i	$-0.0512440\pi$
$32$	0.495463	+	1.65496i	0.0875863	+	0.292559i
$33$	1.54933	−	6.74025i	0.269703	−	1.17333i
$34$	1.23336	+	2.85925i	0.211520	+	0.490357i
$35$	0.0521094	−	0.0437249i	0.00880809	−	0.00739086i
$36$	0.252989	−	0.888685i	0.0421649	−	0.148114i
$37$	−0.782274	−	0.656406i	−0.128605	−	0.107913i	0.576216	−	0.817297i	$-0.304529\pi$
$37$	−0.782274	−	0.656406i	−0.128605	−	0.107913i	−0.704822	+	0.709385i	$0.748973\pi$
$38$	2.43909	−	8.14713i	0.395673	−	1.32164i
$39$	−3.05464	−	1.73612i	−0.489134	−	0.278002i
$40$	−0.0118980	+	0.204282i	−0.00188125	+	0.0322998i
$41$	0.254528	−	4.37008i	0.0397506	−	0.682491i	−0.918299	−	0.395888i	$-0.870437\pi$
$41$	0.254528	−	4.37008i	0.0397506	−	0.682491i	0.958049	−	0.286603i	$-0.0925262\pi$
$42$	0.0152296	+	2.24845i	0.00234997	+	0.346944i
$43$	3.44402	−	11.5038i	0.525208	−	1.75432i	−0.122543	−	0.992463i	$-0.539105\pi$
$43$	3.44402	−	11.5038i	0.525208	−	1.75432i	0.647751	−	0.761852i	$-0.275710\pi$
$44$	0.942101	+	0.790516i	0.142027	+	0.119175i
$45$	0.140004	−	0.193476i	0.0208706	−	0.0288417i
$46$	8.73286	−	7.32774i	1.28759	−	1.08042i
$47$	2.03795	+	4.72449i	0.297265	+	0.689138i	0.999745	−	0.0225650i	$-0.00718327\pi$
$47$	2.03795	+	4.72449i	0.297265	+	0.689138i	−0.702480	+	0.711703i	$0.747924\pi$
$48$	−5.73221	−	5.33514i	−0.827373	−	0.770061i
$49$	1.79820	+	6.00642i	0.256886	+	0.858060i
$50$	−3.00483	+	6.96597i	−0.424947	+	0.985137i
$51$	−2.86198	−	2.10068i	−0.400757	−	0.294155i
$52$	0.522002	−	0.343326i	0.0723886	−	0.0476107i
$53$	−5.16096	+	8.93905i	−0.708913	+	1.22787i	0.256348	+	0.966584i	$0.417481\pi$
$53$	−5.16096	+	8.93905i	−0.708913	+	1.22787i	−0.965261	+	0.261288i	$0.915853\pi$
$54$	1.97619	+	7.64268i	0.268925	+	1.04004i
$55$	0.158932	+	0.275278i	0.0214304	+	0.0371185i
$56$	1.96288	+	0.985795i	0.262301	+	0.131732i
$57$	2.29987	+	9.41916i	0.304626	+	1.24760i
$58$	1.00819	+	1.35424i	0.132382	+	0.177820i
$59$	7.51758	−	7.96817i	0.978705	−	1.03737i	−0.0205882	−	0.999788i	$-0.506554\pi$
$59$	7.51758	−	7.96817i	0.978705	−	1.03737i	0.999294	−	0.0375792i	$-0.0119646\pi$
$60$	0.0193159	+	0.0378202i	0.00249367	+	0.00488256i
$61$	10.5595	+	1.23423i	1.35201	+	0.158027i	0.761060	−	0.648681i	$-0.224679\pi$
$61$	10.5595	+	1.23423i	1.35201	+	0.158027i	0.590950	+	0.806708i	$0.298753\pi$
$62$	−8.55483	−	3.11370i	−1.08646	−	0.395441i
$63$	−1.31172	−	2.20251i	−0.165261	−	0.277490i
$64$	−6.03074	+	2.19501i	−0.753842	+	0.274376i
$65$	0.157131	−	0.0372408i	0.0194897	−	0.00461915i
$66$	−10.3594	−	1.75438i	−1.27515	−	0.215949i
$67$	3.83910	+	2.52502i	0.469021	+	0.308480i	0.761929	−	0.647661i	$-0.224253\pi$
$67$	3.83910	+	2.52502i	0.469021	+	0.308480i	−0.292908	+	0.956141i	$0.594623\pi$
$68$	0.564152	−	0.283328i	0.0684135	−	0.0343586i
$69$	−4.36244	+	12.2431i	−0.525175	+	1.47389i
$70$	−0.0709180	−	0.0751687i	−0.00847632	−	0.00898438i
$71$	−0.963622	+	5.46497i	−0.114361	+	0.648573i	0.872704	+	0.488250i	$0.162365\pi$
$71$	−0.963622	+	5.46497i	−0.114361	+	0.648573i	−0.987065	+	0.160323i	$0.948746\pi$
$72$	7.52705	+	1.67659i	0.887072	+	0.197588i
$73$	0.267464	+	1.51686i	0.0313043	+	0.177536i	0.996451	−	0.0841735i	$-0.0268250\pi$
$73$	0.267464	+	1.51686i	0.0313043	+	0.177536i	−0.965147	+	0.261709i	$0.915714\pi$
$74$	−0.926430	+	1.24441i	−0.107695	+	0.144660i
$75$	−1.06228	−	8.58380i	−0.122662	−	0.991171i
$76$	−1.67767	−	0.397615i	−0.192442	−	0.0456096i
$77$	3.38895	−	0.396111i	0.386206	−	0.0451411i
$78$	−2.36324	+	4.78615i	−0.267584	+	0.541925i
$79$	−0.793846	−	13.6298i	−0.0893146	−	1.53347i	−0.683981	−	0.729500i	$-0.739753\pi$
$79$	−0.793846	−	13.6298i	−0.0893146	−	1.53347i	0.594666	−	0.803973i	$-0.297284\pi$
$80$	0.359909			0.0402391
$81$	−6.35125	−	6.37665i	−0.705694	−	0.708517i
$82$	−6.65031			−0.734404
$83$	0.365349	+	6.27280i	0.0401022	+	0.688529i	0.957122	+	0.289686i	$0.0935510\pi$
$83$	0.365349	+	6.27280i	0.0401022	+	0.688529i	−0.917019	+	0.398843i	$0.869412\pi$
$84$	0.454891	−	0.0295872i	0.0496327	−	0.00322823i
$85$	0.162065	−	0.0189427i	0.0175784	−	0.00205462i
$86$	−17.7514	−	4.20715i	−1.91418	−	0.453669i
$87$	−1.77255	−	0.750407i	−0.190038	−	0.0804521i
$88$	−6.12920	+	8.23295i	−0.653375	+	0.877635i
$89$	−1.79520	−	10.1811i	−0.190291	−	1.07919i	−0.918967	−	0.394334i	$-0.870975\pi$
$89$	−1.79520	−	10.1811i	−0.190291	−	1.07919i	0.728676	−	0.684858i	$-0.240136\pi$
$90$	−0.305800	−	0.195245i	−0.0322342	−	0.0205807i
$91$	0.301002	−	1.70707i	0.0315536	−	0.178950i
$92$	−1.58602	−	1.68109i	−0.165354	−	0.175265i
$93$	10.2092	−	1.87154i	1.05864	−	0.194070i
$94$	6.98533	−	3.50817i	0.720482	−	0.361840i
$95$	−0.372317	−	0.244876i	−0.0381989	−	0.0251238i
$96$	−1.90777	+	2.30512i	−0.194711	+	0.235265i
$97$	−13.3681	+	3.16829i	−1.35732	+	0.321691i	−0.843926	−	0.536460i	$-0.819761\pi$
$97$	−13.3681	+	3.16829i	−1.35732	+	0.321691i	−0.513397	+	0.858151i	$0.671613\pi$
$98$	8.95073	−	3.25780i	0.904160	−	0.329087i
$99$	11.2000	−	4.24913i	1.12564	−	0.427054i
$100$	1.44528	+	0.526040i	0.144528	+	0.0526040i
$101$	8.47927	+	0.991085i	0.843719	+	0.0986166i	0.526961	−	0.849890i	$-0.323331\pi$
$101$	8.47927	+	0.991085i	0.843719	+	0.0986166i	0.316758	+	0.948506i	$0.397406\pi$
$102$	−2.93317	+	4.52615i	−0.290427	+	0.448155i
$103$	−5.64758	+	5.98608i	−0.556472	+	0.589826i	−0.943141	−	0.332393i	$-0.892144\pi$
$103$	−5.64758	+	5.98608i	−0.556472	+	0.589826i	0.386669	+	0.922219i	$0.373626\pi$
$104$	3.11381	+	4.18257i	0.305334	+	0.410135i
$105$	0.113097	+	0.0330261i	0.0110372	+	0.00322302i
$106$	14.0132	+	7.03769i	1.36108	+	0.683561i
$107$	2.93755	+	5.08798i	0.283984	+	0.491874i	0.972362	−	0.233478i	$-0.0750106\pi$
$107$	2.93755	+	5.08798i	0.283984	+	0.491874i	−0.688379	+	0.725352i	$0.741677\pi$
$108$	1.52353	−	0.490058i	0.146601	−	0.0471558i
$109$	−5.21293	+	9.02906i	−0.499308	+	0.864827i	−1.00000		0.000798944i	$-0.999746\pi$
$109$	−5.21293	+	9.02906i	−0.499308	+	0.864827i	0.500692	+	0.865626i	$0.333079\pi$
$110$	0.403459	−	0.265359i	0.0384683	−	0.0253010i
$111$	0.193435	−	1.75814i	0.0183601	−	0.166875i
$112$	1.53019	−	3.54738i	0.144589	−	0.335196i
$113$	0.795419	+	2.65689i	0.0748268	+	0.249939i	0.987217	−	0.159383i	$-0.0509505\pi$
$113$	0.795419	+	2.65689i	0.0748268	+	0.249939i	−0.912390	+	0.409322i	$0.865765\pi$
$114$	14.0823	−	4.32011i	1.31893	−	0.404615i
$115$	−0.236599	−	0.548499i	−0.0220630	−	0.0511478i
$116$	0.262204	−	0.220015i	0.0243450	−	0.0204279i
$117$	−0.436112	−	6.06998i	−0.0403186	−	0.561170i
$118$	−12.7489	−	10.6976i	−1.17363	−	0.984793i
$119$	0.502330	−	1.67790i	0.0460486	−	0.153813i
$120$	−0.305734	+	0.179288i	−0.0279096	+	0.0163667i
$121$	−0.287455	+	4.93541i	−0.0261323	+	0.448674i
$122$	0.939118	−	16.1240i	0.0850238	−	1.45980i
$123$	6.54040	−	3.83540i	0.589728	−	0.345826i
$124$	−0.529346	+	1.76814i	−0.0475367	+	0.158784i
$125$	0.609431	+	0.511373i	0.0545092	+	0.0457386i
$126$	−3.22454	+	2.18396i	−0.287265	+	0.194562i
$127$	−8.52362	+	7.15216i	−0.756349	+	0.634652i	−0.937174	−	0.348863i	$-0.886568\pi$
$127$	−8.52362	+	7.15216i	−0.756349	+	0.634652i	0.180825	+	0.983515i	$0.442123\pi$
$128$	5.23024	+	12.1251i	0.462292	+	1.07171i
$129$	19.8843	−	6.10003i	1.75072	−	0.537078i
$130$	−0.0703610	−	0.235022i	−0.00617106	−	0.0206128i
$131$	3.93336	−	9.11855i	0.343659	−	0.796691i	−0.655480	−	0.755212i	$-0.727534\pi$
$131$	3.93336	−	9.11855i	0.343659	−	0.796691i	0.999139	−	0.0414790i	$-0.0132070\pi$
$132$	−0.232956	+	2.11734i	−0.0202762	+	0.184291i
$133$	−3.99652	+	2.62855i	−0.346542	+	0.227925i
$134$	3.49042	−	6.04558i	0.301526	−	0.522259i
$135$	0.413349	+	0.0156560i	0.0355754	+	0.00134745i
$136$	2.63438	+	4.56288i	0.225896	+	0.391264i
$137$	−14.3691	−	7.21646i	−1.22764	−	0.616543i	−0.287646	−	0.957737i	$-0.592873\pi$
$137$	−14.3691	−	7.21646i	−1.22764	−	0.616543i	−0.939993	+	0.341193i	$0.889169\pi$
$138$	18.9537	+	5.53476i	1.61345	+	0.471150i
$139$	−12.1194	−	16.2791i	−1.02795	−	1.38078i	−0.922344	−	0.386370i	$-0.873729\pi$
$139$	−12.1194	−	16.2791i	−1.02795	−	1.38078i	−0.105607	−	0.994408i	$-0.533679\pi$
$140$	−0.0143776	+	0.0152394i	−0.00121513	+	0.00128796i
$141$	−4.84663	+	7.47880i	−0.408160	+	0.629828i
$142$	8.37351	+	0.978723i	0.702690	+	0.0821326i
$143$	7.61142	+	2.77033i	0.636499	+	0.231667i
$144$	2.17410	−	13.3880i	0.181175	−	1.11567i
$145$	0.0831321	−	0.0302576i	0.00690375	−	0.00251276i
$146$	2.27691	−	0.539638i	0.188438	−	0.0446607i
$147$	−6.92394	+	8.36606i	−0.571077	+	0.690021i
$148$	0.262780	+	0.172833i	0.0216004	+	0.0142068i
$149$	−4.56885	+	2.29456i	−0.374295	+	0.187978i	−0.625995	−	0.779827i	$-0.715307\pi$
$149$	−4.56885	+	2.29456i	−0.374295	+	0.187978i	0.251700	+	0.967805i	$0.419010\pi$
$150$	−12.9247	+	2.36934i	−1.05530	+	0.193456i
$151$	12.1904	+	12.9211i	0.992044	+	1.05150i	0.998672	+	0.0515269i	$0.0164088\pi$
$151$	12.1904	+	12.9211i	0.992044	+	1.05150i	−0.00662782	+	0.999978i	$0.502110\pi$
$152$	2.49871	−	14.1709i	0.202672	−	1.14941i
$153$	0.274350	−	6.14297i	0.0221799	−	0.496629i
$154$	−0.900118	−	5.10482i	−0.0725336	−	0.411358i
$155$	−0.284868	+	0.382644i	−0.0228811	+	0.0307347i
$156$	0.996539	+	0.421882i	0.0797870	+	0.0337776i
$157$	−7.02249	−	1.66436i	−0.560456	−	0.132830i	−0.0593825	−	0.998235i	$-0.518913\pi$
$157$	−7.02249	−	1.66436i	−0.560456	−	0.132830i	−0.501073	+	0.865405i	$0.667061\pi$
$158$	−20.6014	+	2.40796i	−1.63896	+	0.191567i
$159$	−17.8404	+	1.16038i	−1.41484	+	0.0920243i
$160$	−0.00799621	−	0.137290i	−0.000632156	−	0.0108537i
$161$	−6.41210			−0.505345
$162$	−9.11005	+	10.1958i	−0.715753	+	0.801060i
$163$	4.94597			0.387398			0.193699	−	0.981061i	$-0.437951\pi$
$163$	4.94597			0.387398			0.193699	+	0.981061i	$0.437951\pi$
$164$	0.0783941	+	1.34597i	0.00612155	+	0.105103i
$165$	−0.243751	+	0.493658i	−0.0189760	+	0.0384312i
$166$	9.48130	−	1.10820i	0.735891	−	0.0860134i
$167$	−17.4390	−	4.13312i	−1.34947	−	0.319831i	−0.508571	−	0.861020i	$-0.669826\pi$
$167$	−17.4390	−	4.13312i	−1.34947	−	0.319831i	−0.840901	+	0.541190i	$0.817974\pi$
$168$	0.467257	+	3.77567i	0.0360497	+	0.291300i
$169$	−5.30576	+	7.12688i	−0.408136	+	0.548221i
$170$	−0.0430451	−	0.244121i	−0.00330141	−	0.0187232i
$171$	−11.3580	+	12.3703i	−0.868571	+	0.945982i
$172$	−0.642242	+	3.64234i	−0.0489705	+	0.277726i
$173$	−1.18242	−	1.25329i	−0.0898978	−	0.0952861i	0.680863	−	0.732411i	$-0.261605\pi$
$173$	−1.18242	−	1.25329i	−0.0898978	−	0.0952861i	−0.770761	+	0.637125i	$0.780124\pi$
$174$	−0.981519	+	2.75461i	−0.0744088	+	0.208827i
$175$	3.81324	−	1.91508i	0.288254	−	0.144766i
$176$	15.0828	+	9.92014i	1.13691	+	0.747759i
$177$	18.7077	+	3.16818i	1.40616	+	0.238135i
$178$	−15.2824	+	3.62201i	−1.14547	+	0.271481i
$179$	11.6071	−	4.22465i	0.867558	−	0.315765i	0.130380	−	0.991464i	$-0.458380\pi$
$179$	11.6071	−	4.22465i	0.867558	−	0.315765i	0.737178	+	0.675699i	$0.236158\pi$
$180$	−0.0359115	+	0.0641932i	−0.00267668	+	0.00478468i
$181$	−0.0341083	−	0.0124144i	−0.00253525	−	0.000922757i	0.340752	−	0.940153i	$-0.389318\pi$
$181$	−0.0341083	−	0.0124144i	−0.00253525	−	0.000922757i	−0.343287	+	0.939230i	$0.611541\pi$
$182$	−2.61560	−	0.305720i	−0.193881	−	0.0226614i
$183$	8.37553	+	16.3991i	0.619137	+	1.21226i
$184$	13.2367	−	14.0301i	0.975824	−	1.03431i
$185$	0.0485446	+	0.0652067i	0.00356907	+	0.00479409i
$186$	−3.74027	−	15.3183i	−0.274250	−	1.12319i
$187$	7.31382	+	3.67314i	0.534840	+	0.268607i
$188$	−0.792370	−	1.37243i	−0.0577895	−	0.100094i
$189$	1.91170	−	4.00753i	0.139056	−	0.291505i
$190$	−0.338501	+	0.586301i	−0.0245574	+	0.0425347i
$191$	−22.1875	+	14.5930i	−1.60543	+	1.05591i	−0.650325	+	0.759656i	$0.725367\pi$
$191$	−22.1875	+	14.5930i	−1.60543	+	1.05591i	−0.955109	+	0.296255i	$0.904262\pi$
$192$	−8.96109	−	6.57742i	−0.646711	−	0.474684i
$193$	−0.0179151	+	0.0415320i	−0.00128956	+	0.00298954i	−0.918860	−	0.394584i	$-0.870889\pi$
$193$	−0.0179151	+	0.0415320i	−0.00128956	+	0.00298954i	0.917570	+	0.397574i	$0.130148\pi$
$194$	5.98602	+	19.9947i	0.429771	+	1.43553i
$195$	0.204741	+	0.190559i	0.0146618	+	0.0136462i
$196$	−0.764866	−	1.77316i	−0.0546333	−	0.126654i
$197$	9.33211	−	7.83057i	0.664885	−	0.557905i	−0.246661	−	0.969102i	$-0.579334\pi$
$197$	9.33211	−	7.83057i	0.664885	−	0.557905i	0.911547	+	0.411197i	$0.134889\pi$
$198$	−7.43374	−	16.6109i	−0.528293	−	1.18049i
$199$	9.63166	+	8.08192i	0.682770	+	0.572912i	0.916814	−	0.399314i	$-0.130752\pi$
$199$	9.63166	+	8.08192i	0.682770	+	0.572912i	−0.234044	+	0.972226i	$0.575196\pi$
$200$	−3.68148	+	12.2970i	−0.260320	+	0.869528i
$201$	0.0539068	+	7.95867i	0.00380229	+	0.561361i
$202$	0.754109	−	12.9475i	0.0530589	−	0.910986i
$203$	0.0552159	−	0.948020i	0.00387539	−	0.0665379i
$204$	0.950635	+	0.540297i	0.0665577	+	0.0378284i
$205$	−0.0999435	+	0.333834i	−0.00698036	+	0.0233160i
$206$	9.57760	+	8.03656i	0.667303	+	0.559934i
$207$	−21.8324	+	5.48778i	−1.51746	+	0.381427i
$208$	7.02563	−	5.89520i	0.487140	−	0.408759i
$209$	−8.85329	−	20.5242i	−0.612395	−	1.41969i
$210$	0.0400984	−	0.174445i	0.00276705	−	0.0120379i
$211$	−3.93645	−	13.1487i	−0.270997	−	0.905192i	−0.979833	−	0.199819i	$-0.935965\pi$
$211$	−3.93645	−	13.1487i	−0.270997	−	0.905192i	0.708836	−	0.705373i	$-0.249221\pi$
$212$	1.25919	−	2.91913i	0.0864815	−	0.200487i
$213$	−8.79957	+	3.86666i	−0.602936	+	0.264939i
$214$	7.45715	−	4.90464i	0.509760	−	0.335275i
$215$	−0.477966	+	0.827862i	−0.0325970	+	0.0564597i
$216$	4.82235	+	12.4558i	0.328119	+	0.847511i
$217$	2.56032	+	4.43460i	0.173806	+	0.301040i
$218$	14.1543	+	7.10856i	0.958650	+	0.481452i
$219$	−1.92806	+	1.84387i	−0.130286	+	0.124597i
$220$	−0.0584627	−	0.0785291i	−0.00394156	−	0.00529443i
$221$	2.85332	−	3.02434i	0.191935	−	0.203439i
$222$	−2.68355	−	0.138068i	−0.180108	−	0.00926651i
$223$	2.91741	+	0.340996i	0.195364	+	0.0228348i	0.213212	−	0.977006i	$-0.431607\pi$
$223$	2.91741	+	0.340996i	0.195364	+	0.0228348i	−0.0178480	+	0.999841i	$0.505681\pi$
$224$	−1.38717	−	0.504888i	−0.0926840	−	0.0337342i
$225$	11.3446	−	9.78417i	0.756307	−	0.652278i
$226$	3.95927	−	1.44106i	0.263367	−	0.0958578i
$227$	3.85911	−	0.914626i	0.256138	−	0.0607059i	−0.100541	−	0.994933i	$-0.532057\pi$
$227$	3.85911	−	0.914626i	0.256138	−	0.0607059i	0.356679	+	0.934227i	$0.383909\pi$
$228$	−1.04036	−	2.79923i	−0.0688996	−	0.185383i
$229$	8.53681	+	5.61475i	0.564128	+	0.371033i	0.799310	−	0.600918i	$-0.205198\pi$
$229$	8.53681	+	5.61475i	0.564128	+	0.371033i	−0.235182	+	0.971951i	$0.575569\pi$
$230$	−0.810975	+	0.407287i	−0.0534741	+	0.0268557i
$231$	3.82932	+	4.50133i	0.251950	+	0.296166i
$232$	1.96035	+	2.07785i	0.128703	+	0.136417i
$233$	0.443423	−	2.51478i	0.0290496	−	0.164748i	−0.966832	−	0.255414i	$-0.917788\pi$
$233$	0.443423	−	2.51478i	0.0290496	−	0.164748i	0.995881	+	0.0906654i	$0.0288994\pi$
$234$	−9.16745	+	1.19761i	−0.599295	+	0.0782903i
$235$	−0.0711257	−	0.403374i	−0.00463973	−	0.0263132i
$236$	−2.01483	+	2.70639i	−0.131154	+	0.176171i
$237$	18.8721	−	14.2495i	1.22588	−	0.925603i
$238$	−2.58914	−	0.613638i	−0.167829	−	0.0397763i
$239$	4.63024	−	0.541197i	0.299505	−	0.0350071i	0.0349867	−	0.999388i	$-0.488861\pi$
$239$	4.63024	−	0.541197i	0.299505	−	0.0350071i	0.264518	+	0.964381i	$0.414787\pi$
$240$	0.346074	+	0.518495i	0.0223389	+	0.0334687i
$241$	−0.0882797	−	1.51570i	−0.00568660	−	0.0976351i	0.994271	−	0.106893i	$-0.0340902\pi$
$241$	−0.0882797	−	1.51570i	−0.00568660	−	0.0976351i	−0.999957	+	0.00925773i	$0.997053\pi$
$242$	7.51064			0.482802
$243$	3.07929	−	15.2813i	0.197537	−	0.980296i
$244$	−3.27446			−0.209626
$245$	−0.0290210	−	0.498271i	−0.00185408	−	0.0318334i
$246$	−6.39466	−	9.58063i	−0.407708	−	0.610838i
$247$	−11.2788	+	1.31831i	−0.717654	+	0.0838818i
$248$	−14.9885	−	3.55235i	−0.951773	−	0.225574i
$249$	−8.68546	+	6.55798i	−0.550419	+	0.415595i
$250$	0.721735	−	0.969459i	0.0456466	−	0.0613140i
$251$	3.80000	+	21.5509i	0.239854	+	1.36028i	0.832146	+	0.554556i	$0.187112\pi$
$251$	3.80000	+	21.5509i	0.239854	+	1.36028i	−0.592293	+	0.805723i	$0.701777\pi$
$252$	0.480028	+	0.626879i	0.0302389	+	0.0394897i
$253$	5.20296	−	29.5075i	0.327107	−	1.85512i
$254$	11.6002	+	12.2955i	0.727860	+	0.771486i
$255$	0.183124	+	0.215261i	0.0114677	+	0.0134802i
$256$	6.45707	−	3.24286i	0.403567	−	0.202679i
$257$	5.94694	+	3.91136i	0.370960	+	0.243984i	0.721277	−	0.692647i	$-0.243556\pi$
$257$	5.94694	+	3.91136i	0.370960	+	0.243984i	−0.350317	+	0.936631i	$0.613926\pi$
$258$	−11.0080	−	29.6185i	−0.685329	−	1.84397i
$259$	0.849090	−	0.201238i	0.0527599	−	0.0125043i
$260$	−0.0467373	+	0.0170110i	−0.00289852	+	0.00105498i
$261$	−0.623356	−	3.27515i	−0.0385848	−	0.202727i
$262$	−14.1770	−	5.16001i	−0.875858	−	0.318786i
$263$	16.6763	+	1.94919i	1.02831	+	0.120192i	0.613482	−	0.789709i	$-0.289768\pi$
$263$	16.6763	+	1.94919i	1.02831	+	0.120192i	0.414826	+	0.909901i	$0.363843\pi$
$264$	−17.7542	−	0.913448i	−1.09269	−	0.0562188i
$265$	0.563876	−	0.597674i	0.0346386	−	0.0367148i
$266$	4.33960	+	5.82909i	0.266078	+	0.357405i
$267$	12.9410	−	12.3759i	0.791974	−	0.757393i
$268$	−1.26473	−	0.635169i	−0.0772554	−	0.0387991i
$269$	−10.3000	−	17.8402i	−0.628003	−	1.08773i	−0.987952	−	0.154762i	$-0.950539\pi$
$269$	−10.3000	−	17.8402i	−0.628003	−	1.08773i	0.359948	−	0.932972i	$-0.382794\pi$
$270$	−0.0127683	−	0.628284i	−0.000777054	−	0.0382361i
$271$	−1.75375	+	3.03758i	−0.106533	+	0.184520i	−0.914363	−	0.404895i	$-0.867308\pi$
$271$	−1.75375	+	3.03758i	−0.106533	+	0.184520i	0.807831	+	0.589414i	$0.200641\pi$
$272$	7.74243	−	5.09227i	0.469454	−	0.308764i
$273$	2.74868	−	1.20781i	0.166358	−	0.0731001i
$274$	−9.67548	+	22.4303i	−0.584517	+	1.35506i
$275$	5.71872	+	19.1019i	0.344852	+	1.15189i
$276$	0.896767	−	3.90133i	0.0539791	−	0.234832i
$277$	−6.43374	−	14.9151i	−0.386566	−	0.896160i	−0.994747	−	0.102362i	$-0.967360\pi$
$277$	−6.43374	−	14.9151i	−0.386566	−	0.896160i	0.608181	−	0.793798i	$-0.291899\pi$
$278$	−23.6190	+	19.8187i	−1.41657	+	1.18865i
$279$	12.5129	+	12.9080i	0.749128	+	0.772784i
$280$	−0.133947	−	0.112395i	−0.00800489	−	0.00671690i
$281$	0.116738	−	0.389931i	0.00696398	−	0.0232613i	−0.954437	−	0.298413i	$-0.903543\pi$
$281$	0.116738	−	0.389931i	0.00696398	−	0.0232613i	0.961401	+	0.275151i	$0.0887280\pi$
$282$	11.7708	+	6.68996i	0.700939	+	0.398381i
$283$	−1.08676	+	18.6589i	−0.0646011	+	1.10916i	0.797797	+	0.602927i	$0.205999\pi$
$283$	−1.08676	+	18.6589i	−0.0646011	+	1.10916i	−0.862398	+	0.506231i	$0.831038\pi$
$284$	0.0993791	−	1.70627i	0.00589707	−	0.101249i
$285$	−0.00522788	−	0.771832i	−0.000309673	−	0.0457194i
$286$	3.52924	−	11.7885i	0.208688	−	0.697068i
$287$	2.86546	+	2.40441i	0.169143	+	0.141928i
$288$	−5.15525	−	0.531880i	−0.303776	−	0.0313413i
$289$	−9.80441	+	8.22687i	−0.576730	+	0.483934i
$290$	−0.0532333	−	0.123409i	−0.00312597	−	0.00724681i
$291$	−17.4185	−	16.2119i	−1.02109	−	0.950360i
$292$	−0.136059	−	0.454469i	−0.00796225	−	0.0265958i
$293$	5.10071	−	11.8248i	0.297987	−	0.690810i	−0.701781	−	0.712393i	$-0.747611\pi$
$293$	5.10071	−	11.8248i	0.297987	−	0.690810i	0.999767	+	0.0215828i	$0.00687056\pi$
$294$	13.2999	+	9.76211i	0.775667	+	0.569338i
$295$	−0.728596	+	0.479205i	−0.0424205	+	0.0279004i
$296$	−1.31248	+	2.27329i	−0.0762865	+	0.132132i
$297$	16.8908	+	12.0492i	0.980104	+	0.699164i
$298$	3.88361	+	6.72661i	0.224972	+	0.389662i
$299$	−13.6028	−	6.83158i	−0.786669	−	0.395080i
$300$	0.631894	+	2.58793i	0.0364824	+	0.149414i
$301$	6.12755	+	8.23072i	0.353186	+	0.474411i
$302$	18.5198	−	19.6299i	1.06570	−	1.12957i
$303$	6.72552	+	13.1685i	0.386371	+	0.756508i
$304$	−25.1378	−	2.93819i	−1.44175	−	0.168517i
$305$	−0.795286	−	0.289460i	−0.0455379	−	0.0165745i
$306$	−9.34090	+	0.126544i	−0.533984	+	0.00723404i
$307$	8.20971	−	2.98809i	0.468553	−	0.170539i	−0.0969439	−	0.995290i	$-0.530907\pi$
$307$	8.20971	−	2.98809i	0.468553	−	0.170539i	0.565497	+	0.824751i	$0.308685\pi$
$308$	−1.02257	+	0.242353i	−0.0582662	+	0.0138093i
$309$	−14.0542	−	2.38009i	−0.799514	−	0.135399i
$310$	0.605497	+	0.398241i	0.0343899	+	0.0226186i
$311$	−16.6117	+	8.34269i	−0.941961	+	0.473071i	−0.852388	−	0.522909i	$-0.824847\pi$
$311$	−16.6117	+	8.34269i	−0.941961	+	0.473071i	−0.0895731	+	0.995980i	$0.528550\pi$
$312$	−3.03142	+	8.50763i	−0.171621	+	0.481650i
$313$	14.4377	+	15.3030i	0.816065	+	0.864979i	0.992862	−	0.119269i	$-0.0380550\pi$
$313$	14.4377	+	15.3030i	0.816065	+	0.864979i	−0.176797	+	0.984247i	$0.556574\pi$
$314$	−1.90391	+	10.7976i	−0.107444	+	0.609344i
$315$	0.0611713	+	0.194688i	0.00344661	+	0.0109694i
$316$	0.730202	+	4.14118i	0.0410771	+	0.232960i
$317$	9.67477	−	12.9955i	0.543389	−	0.729898i	−0.442598	−	0.896720i	$-0.645943\pi$
$317$	9.67477	−	12.9955i	0.543389	−	0.729898i	0.985987	+	0.166822i	$0.0533505\pi$
$318$	3.33580	+	26.9549i	0.187062	+	1.51156i
$319$	4.31783	+	1.02334i	0.241752	+	0.0572963i
$320$	0.507439	−	0.0593111i	0.0283667	−	0.00331559i
$321$	−4.50527	+	9.12430i	−0.251460	+	0.509269i
$322$	0.566408	+	9.72485i	0.0315647	+	0.541945i
$323$	−11.4740			−0.638432
$324$	2.17095	+	1.72362i	0.120608	+	0.0957565i
$325$	10.1299			0.561903
$326$	−0.436898	−	7.50125i	−0.0241976	−	0.415456i
$327$	−18.0200	+	1.17207i	−0.996510	+	0.0648154i
$328$	−11.1763	+	1.30632i	−0.617106	+	0.0721293i
$329$	−4.27818	−	1.01395i	−0.235864	−	0.0559007i
$330$	0.770233	+	0.326076i	0.0423999	+	0.0179499i
$331$	11.3784	−	15.2839i	0.625414	−	0.840077i	−0.370645	−	0.928775i	$-0.620863\pi$
$331$	11.3784	−	15.2839i	0.625414	−	0.840077i	0.996059	+	0.0886981i	$0.0282706\pi$
$332$	−0.336058	−	1.90588i	−0.0184436	−	0.104599i
$333$	2.71882	−	1.41188i	0.148990	−	0.0773707i
$334$	−4.72799	+	26.8138i	−0.258704	+	1.46719i
$335$	−0.251023	−	0.266068i	−0.0137148	−	0.0145369i
$336$	6.58182	−	1.20657i	0.359068	−	0.0658241i
$337$	−9.76843	+	4.90589i	−0.532120	+	0.267241i	−0.694507	−	0.719486i	$-0.744377\pi$
$337$	−9.76843	+	4.90589i	−0.532120	+	0.267241i	0.162386	+	0.986727i	$0.448081\pi$
$338$	11.2776	+	7.41738i	0.613420	+	0.403453i
$339$	−3.06274	+	3.70065i	−0.166345	+	0.200992i
$340$	−0.0489008	+	0.0115897i	−0.00265202	+	0.000628540i
$341$	−22.4848	+	8.18380i	−1.21762	+	0.443178i
$342$	19.7646	+	16.1333i	1.06875	+	0.872390i
$343$	−10.6553	−	3.87822i	−0.575333	−	0.209404i
$344$	−30.6587	−	3.58348i	−1.65300	−	0.193208i
$345$	0.562679	−	0.868264i	0.0302936	−	0.0467458i
$346$	−1.79635	+	1.90401i	−0.0965721	+	0.102360i
$347$	−13.3267	−	17.9008i	−0.715413	−	0.960966i	−0.999997	−	0.00231546i	$-0.999263\pi$
$347$	−13.3267	−	17.9008i	−0.715413	−	0.960966i	0.284584	−	0.958651i	$-0.408144\pi$
$348$	0.569083	+	0.166181i	0.0305061	+	0.00890823i
$349$	−20.8909	−	10.4918i	−1.11826	−	0.561613i	−0.209034	−	0.977908i	$-0.567032\pi$
$349$	−20.8909	−	10.4918i	−1.11826	−	0.561613i	−0.909229	+	0.416295i	$0.863328\pi$
$350$	−3.24133	−	5.61414i	−0.173256	−	0.300088i
$351$	8.32523	−	6.46491i	0.444368	−	0.345071i
$352$	3.44900	−	5.97384i	0.183832	−	0.318407i
$353$	26.6369	−	17.5193i	1.41774	−	0.932461i	0.418026	−	0.908435i	$-0.362722\pi$
$353$	26.6369	−	17.5193i	1.41774	−	0.932461i	0.999711	−	0.0240257i	$-0.00764835\pi$
$354$	3.15246	−	28.6528i	0.167551	−	1.52288i
$355$	0.174971	−	0.405627i	0.00928648	−	0.0215285i
$356$	0.913217	+	3.05036i	0.0484004	+	0.161669i
$357$	2.90025	−	0.889726i	0.153497	−	0.0470893i
$358$	−7.43258	−	17.2307i	−0.392824	−	0.910669i
$359$	8.66761	−	7.27299i	0.457459	−	0.383854i	−0.384736	−	0.923027i	$-0.625708\pi$
$359$	8.66761	−	7.27299i	0.457459	−	0.383854i	0.842195	+	0.539173i	$0.181263\pi$
$360$	−0.552268	−	0.268054i	−0.0291071	−	0.0141277i
$361$	9.45042	+	7.92984i	0.497391	+	0.417360i
$362$	−0.0158153	+	0.0528267i	−0.000831232	+	0.00277651i
$363$	−7.38650	+	4.33157i	−0.387691	+	0.227348i
$364$	−0.0310426	+	0.532981i	−0.00162708	+	0.0279358i
$365$	0.00712939	−	0.122407i	0.000373169	−	0.00640707i
$366$	24.1317	−	14.1513i	1.26139	−	0.739698i
$367$	0.194561	−	0.649881i	0.0101560	−	0.0339235i	−0.952761	−	0.303720i	$-0.901771\pi$
$367$	0.194561	−	0.649881i	0.0101560	−	0.0339235i	0.962917	+	0.269797i	$0.0869564\pi$
$368$	−25.9888	−	21.8072i	−1.35476	−	1.13678i
$369$	11.8143	+	5.73432i	0.615030	+	0.298517i
$370$	0.0946069	−	0.0793846i	0.00491838	−	0.00412701i
$371$	−3.49349	−	8.09881i	−0.181373	−	0.420469i
$372$	−3.05623	+	0.937576i	−0.158458	+	0.0486110i
$373$	3.19886	+	10.6849i	0.165630	+	0.553244i	0.999998	+	0.00203573i	$0.000647993\pi$
$373$	3.19886	+	10.6849i	0.165630	+	0.553244i	−0.834367	+	0.551209i	$0.814167\pi$
$374$	4.92477	−	11.4169i	0.254654	−	0.590353i
$375$	−0.150696	+	1.36968i	−0.00778190	+	0.0707299i
$376$	11.0502	−	7.26782i	0.569869	−	0.374809i
$377$	1.12717	−	1.95232i	0.0580524	−	0.100550i
$378$	−6.24685	−	2.54536i	−0.321303	−	0.130919i
$379$	−9.99112	−	17.3051i	−0.513209	−	0.888905i	−0.999883	−	0.0153206i	$-0.995123\pi$
$379$	−9.99112	−	17.3051i	−0.513209	−	0.888905i	0.486673	−	0.873584i	$-0.338210\pi$
$380$	0.122653	+	0.0615988i	0.00629198	+	0.00315995i
$381$	−18.4995	−	5.40214i	−0.947761	−	0.276760i
$382$	24.0922	+	32.3614i	1.23266	+	1.65576i
$383$	16.1583	−	17.1268i	0.825651	−	0.875139i	−0.168212	−	0.985751i	$-0.553799\pi$
$383$	16.1583	−	17.1268i	0.825651	−	0.875139i	0.993864	+	0.110611i	$0.0352809\pi$
$384$	−12.4385	+	19.1938i	−0.634751	+	0.979478i
$385$	−0.269781	−	0.0315328i	−0.0137493	−	0.00160706i
$386$	0.0645715	+	0.0235021i	0.00328660	+	0.00119623i
$387$	27.9078	+	22.7804i	1.41863	+	1.15799i
$388$	3.97621	−	1.44722i	0.201862	−	0.0734716i
$389$	−6.07680	+	1.44023i	−0.308106	+	0.0730225i	−0.381760	−	0.924261i	$-0.624682\pi$
$389$	−6.07680	+	1.44023i	−0.308106	+	0.0730225i	0.0736542	+	0.997284i	$0.476534\pi$
$390$	0.270923	−	0.327351i	0.0137187	−	0.0165761i
$391$	−12.8503	−	8.45180i	−0.649870	−	0.427426i
$392$	14.4023	−	7.23312i	0.727427	−	0.365328i
$393$	16.9186	−	3.10150i	0.853429	−	0.156450i
$394$	−12.7005	−	13.4617i	−0.639842	−	0.678192i
$395$	−0.188730	+	1.07034i	−0.00949604	+	0.0538547i
$396$	−3.27430	+	1.70034i	−0.164540	+	0.0854455i
$397$	−0.194836	−	1.10497i	−0.00977853	−	0.0554568i	0.979528	−	0.201308i	$-0.0645191\pi$
$397$	−0.194836	−	1.10497i	−0.00977853	−	0.0554568i	−0.989307	+	0.145851i	$0.953408\pi$
$398$	11.4066	−	15.3217i	0.571759	−	0.768006i
$399$	−7.62965	−	3.22999i	−0.381960	−	0.161702i
$400$	21.9684	+	5.20662i	1.09842	+	0.260331i
$401$	−4.20990	+	0.492067i	−0.210232	+	0.0245726i	−0.220557	−	0.975374i	$-0.570788\pi$
$401$	−4.20990	+	0.492067i	−0.210232	+	0.0245726i	0.0103248	+	0.999947i	$0.496713\pi$
$402$	12.0657	−	0.784780i	0.601781	−	0.0391412i
$403$	0.706810	+	12.1355i	0.0352087	+	0.604511i
$404$	−2.62938			−0.130816
$405$	0.374904	+	0.610536i	0.0186291	+	0.0303378i
$406$	−1.44268			−0.0715991
$407$	0.237089	+	4.07067i	0.0117521	+	0.201775i
$408$	−4.04030	+	8.18263i	−0.200025	+	0.405100i
$409$	1.89802	−	0.221846i	0.0938509	−	0.0109696i	−0.0690378	−	0.997614i	$-0.521993\pi$
$409$	1.89802	−	0.221846i	0.0938509	−	0.0109696i	0.162889	+	0.986644i	$0.447919\pi$
$410$	0.515135	+	0.122089i	0.0254407	+	0.00602956i
$411$	−3.42053	−	27.6396i	−0.168722	−	1.36336i
$412$	1.51364	−	2.03317i	0.0745717	−	0.100167i
$413$	1.62550	+	9.21867i	0.0799856	+	0.453621i
$414$	10.2515	+	32.6272i	0.503835	+	1.60354i
$415$	0.0868586	−	0.492600i	0.00426372	−	0.0241808i
$416$	−2.40485	−	2.54899i	−0.117908	−	0.124975i
$417$	11.7987	−	33.1128i	0.577785	−	1.62154i
$418$	−30.3458	+	15.2402i	−1.48426	+	0.745424i
$419$	−2.07357	−	1.36381i	−0.101300	−	0.0666263i	0.497848	−	0.867264i	$-0.334124\pi$
$419$	−2.07357	−	1.36381i	−0.101300	−	0.0666263i	−0.599148	+	0.800638i	$0.704494\pi$
$420$	−0.0357791	−	0.00605925i	−0.00174584	−	0.000295661i
$421$	16.9944	−	4.02774i	0.828255	−	0.196300i	0.205440	−	0.978670i	$-0.434137\pi$
$421$	16.9944	−	4.02774i	0.828255	−	0.196300i	0.622814	+	0.782370i	$0.285989\pi$
$422$	−19.5941	+	7.13166i	−0.953825	+	0.347164i
$423$	−15.4345	+	0.209096i	−0.750450	+	0.0101666i
$424$	24.9325	+	9.07467i	1.21083	+	0.440705i
$425$	10.1663	+	1.18827i	0.493137	+	0.0576395i
$426$	6.64164	+	13.0042i	0.321788	+	0.630056i
$427$	−6.23425	+	6.60792i	−0.301697	+	0.319780i
$428$	−1.08057	−	1.45146i	−0.0522313	−	0.0701588i
$429$	3.32780	+	13.6290i	0.160668	+	0.658016i
$430$	1.29779	+	0.651774i	0.0625849	+	0.0314313i
$431$	11.6850	+	20.2390i	0.562845	+	0.974877i	0.997247	+	0.0741572i	$0.0236267\pi$
$431$	11.6850	+	20.2390i	0.562845	+	0.974877i	−0.434401	+	0.900719i	$0.643040\pi$
$432$	21.3777	−	9.74127i	1.02853	−	0.468677i
$433$	15.2874	−	26.4785i	0.734664	−	1.27247i	−0.220207	−	0.975453i	$-0.570673\pi$
$433$	15.2874	−	26.4785i	0.734664	−	1.27247i	0.954871	−	0.297021i	$-0.0959933\pi$
$434$	6.49952	−	4.27480i	0.311987	−	0.205197i
$435$	0.123526	+	0.0906680i	0.00592263	+	0.00434720i
$436$	1.27187	−	2.94852i	0.0609114	−	0.141209i
$437$	12.0474	+	40.2413i	0.576308	+	1.92500i
$438$	2.96680	+	2.76129i	0.141759	+	0.131939i
$439$	4.91463	+	11.3934i	0.234563	+	0.543777i	0.994320	−	0.106429i	$-0.0339417\pi$
$439$	4.91463	+	11.3934i	0.234563	+	0.543777i	−0.759758	+	0.650206i	$0.774682\pi$
$440$	0.625913	−	0.525204i	0.0298392	−	0.0250381i
$441$	−18.7101	−	1.93037i	−0.890959	−	0.0919225i
$442$	−4.83889	−	4.06031i	−0.230162	−	0.193129i
$443$	−0.994767	+	3.32275i	−0.0472628	+	0.157869i	−0.978363	−	0.206894i	$-0.933665\pi$
$443$	−0.994767	+	3.32275i	−0.0472628	+	0.157869i	0.931101	+	0.364762i	$0.118850\pi$
$444$	0.00368983	+	0.544758i	0.000175112	+	0.0258531i
$445$	−0.0478519	+	0.821586i	−0.00226840	+	0.0389469i
$446$	0.259462	−	4.45478i	0.0122859	−	0.210940i
$447$	−7.69882	−	4.37566i	−0.364142	−	0.206962i
$448$	1.57284	−	5.25365i	0.0743097	−	0.248212i
$449$	2.37761	+	1.99505i	0.112206	+	0.0941523i	0.697165	−	0.716911i	$-0.254445\pi$
$449$	2.37761	+	1.99505i	0.112206	+	0.0941523i	−0.584958	+	0.811063i	$0.698889\pi$
$450$	−15.8412	−	16.3414i	−0.746760	−	0.770341i
$451$	−13.3898	+	11.2354i	−0.630501	+	0.529053i
$452$	−0.338331	−	0.784341i	−0.0159138	−	0.0368923i
$453$	−6.89270	+	29.9863i	−0.323847	+	1.40888i
$454$	−1.72805	−	5.77209i	−0.0811014	−	0.270897i
$455$	−0.0546548	+	0.126704i	−0.00256226	+	0.00593998i
$456$	22.8176	−	10.0264i	1.06853	−	0.469529i
$457$	−29.6424	+	19.4961i	−1.38662	+	0.911991i	−0.999948	−	0.0102280i	$-0.996744\pi$
$457$	−29.6424	+	19.4961i	−1.38662	+	0.911991i	−0.386668	+	0.922219i	$0.626374\pi$
$458$	7.76145	−	13.4432i	0.362669	−	0.628161i
$459$	9.11353	−	5.51158i	0.425383	−	0.257258i
$460$	0.0919917	+	0.159334i	0.00428913	+	0.00742900i
$461$	22.7764	+	11.4387i	1.06080	+	0.532754i	0.891598	−	0.452827i	$-0.149584\pi$
$461$	22.7764	+	11.4387i	1.06080	+	0.532754i	0.169203	+	0.985581i	$0.445881\pi$
$462$	6.48863	−	6.20531i	0.301878	−	0.288697i
$463$	−5.56359	−	7.47319i	−0.258562	−	0.347309i	0.653819	−	0.756651i	$-0.273166\pi$
$463$	−5.56359	−	7.47319i	−0.258562	−	0.347309i	−0.912381	+	0.409342i	$0.865758\pi$
$464$	3.44795	−	3.65462i	0.160067	−	0.169661i
$465$	−0.825164	−	0.0424545i	−0.0382661	−	0.00196878i
$466$	−3.85318	−	0.450372i	−0.178495	−	0.0208631i
$467$	11.6612	+	4.24434i	0.539617	+	0.196404i	0.597427	−	0.801923i	$-0.296190\pi$
$467$	11.6612	+	4.24434i	0.539617	+	0.196404i	−0.0578105	+	0.998328i	$0.518412\pi$
$468$	0.350454	+	1.84131i	0.0161997	+	0.0851144i
$469$	−3.68970	+	1.34294i	−0.170375	+	0.0620113i
$470$	−0.605490	+	0.143504i	−0.0279292	+	0.00661934i
$471$	−4.35480	−	11.7172i	−0.200659	−	0.539899i
$472$	−23.5266	−	15.4737i	−1.08290	−	0.712235i
$473$	−42.8485	+	21.5193i	−1.97018	+	0.989460i
$474$	−23.2784	−	27.3635i	−1.06921	−	1.25685i
$475$	−19.1833	−	20.3331i	−0.880189	−	0.932945i
$476$	−0.0936749	+	0.531257i	−0.00429358	+	0.0243501i
$477$	−18.8262	−	24.5856i	−0.861994	−	1.12570i
$478$	−1.22981	−	6.97459i	−0.0562501	−	0.319010i
$479$	−20.7600	+	27.8855i	−0.948548	+	1.27412i	0.0131220	+	0.999914i	$0.495823\pi$
$479$	−20.7600	+	27.8855i	−0.948548	+	1.27412i	−0.961670	+	0.274208i	$0.911584\pi$
$480$	0.190094	−	0.143531i	0.00867659	−	0.00655128i
$481$	2.01568	+	0.477725i	0.0919072	+	0.0217824i
$482$	−2.29098	+	0.267777i	−0.104351	+	0.0121969i
$483$	−6.16561	−	9.23746i	−0.280545	−	0.420319i
$484$	−0.0885356	−	1.52010i	−0.00402434	−	0.0690953i
$485$	1.09366			0.0496605
$486$	−23.4482	−	3.32031i	−1.06363	−	0.150612i
$487$	4.53564			0.205529			0.102765	−	0.994706i	$-0.467231\pi$
$487$	4.53564			0.205529			0.102765	+	0.994706i	$0.467231\pi$
$488$	−1.58899	−	27.2819i	−0.0719302	−	1.23499i
$489$	4.75583	+	7.12530i	0.215066	+	0.322217i
$490$	−0.753134	+	0.0880287i	−0.0340231	+	0.00397673i
$491$	29.1460	+	6.90774i	1.31534	+	0.311742i	0.827636	−	0.561266i	$-0.189685\pi$
$491$	29.1460	+	6.90774i	1.31534	+	0.311742i	0.487707	+	0.873008i	$0.337834\pi$
$492$	−1.86367	+	1.40717i	−0.0840206	+	0.0634400i
$493$	1.36024	−	1.82712i	0.0612622	−	0.0822895i
$494$	2.99570	+	16.9895i	0.134783	+	0.764392i
$495$	−0.945558	+	0.123525i	−0.0424997	+	0.00555205i
$496$	−4.70463	+	26.6813i	−0.211244	+	1.19802i
$497$	−3.25409	−	3.44913i	−0.145966	−	0.154715i
$498$	10.7133	+	12.5934i	0.480075	+	0.564324i
$499$	6.09867	−	3.06287i	0.273014	−	0.137113i	−0.307025	−	0.951701i	$-0.599334\pi$
$499$	6.09867	−	3.06287i	0.273014	−	0.137113i	0.580039	+	0.814589i	$0.303037\pi$
$500$	−0.204719	−	0.134646i	−0.00915532	−	0.00602155i
$501$	−10.8143	−	29.0974i	−0.483148	−	1.29997i
$502$	32.3492	−	7.66691i	1.44382	−	0.342191i
$503$	−5.01364	+	1.82482i	−0.223547	+	0.0813646i	−0.451366	−	0.892339i	$-0.649063\pi$
$503$	−5.01364	+	1.82482i	−0.223547	+	0.0813646i	0.227818	+	0.973704i	$0.426841\pi$
$504$	−4.99005	+	4.30367i	−0.222274	+	0.191701i
$505$	−0.638612	−	0.232436i	−0.0284179	−	0.0103433i
$506$	−45.2118	−	5.28450i	−2.00991	−	0.234925i
$507$	−15.3690	−	0.790730i	−0.682560	−	0.0351175i
$508$	2.35177	−	2.49273i	0.104343	−	0.110597i
$509$	26.6991	+	35.8631i	1.18342	+	1.58960i	0.699839	+	0.714301i	$0.253255\pi$
$509$	26.6991	+	35.8631i	1.18342	+	1.58960i	0.483577	+	0.875302i	$0.339337\pi$
$510$	0.310297	−	0.296748i	0.0137402	−	0.0131402i
$511$	−1.17617	−	0.590695i	−0.0520307	−	0.0261308i
$512$	7.71639	+	13.3652i	0.341019	+	0.590663i
$513$	−28.7424	−	4.46794i	−1.26901	−	0.197264i
$514$	5.40681	−	9.36487i	0.238484	−	0.413067i
$515$	0.547358	−	0.360003i	0.0241195	−	0.0158636i
$516$	−5.86481	+	2.57708i	−0.258184	+	0.113450i
$517$	8.13746	−	18.8647i	0.357885	−	0.829671i
$518$	−0.380209	−	1.26999i	−0.0167054	−	0.0558000i
$519$	0.668563	−	2.90854i	0.0293467	−	0.127671i
$520$	−0.164411	−	0.381148i	−0.00720991	−	0.0167144i
$521$	7.56500	−	6.34779i	0.331429	−	0.278102i	−0.461853	−	0.886956i	$-0.652815\pi$
$521$	7.56500	−	6.34779i	0.331429	−	0.278102i	0.793282	+	0.608855i	$0.208371\pi$
$522$	−4.91216	+	1.23471i	−0.214999	+	0.0540420i
$523$	29.0347	+	24.3630i	1.26960	+	1.06532i	0.994590	+	0.103880i	$0.0331258\pi$
$523$	29.0347	+	24.3630i	1.26960	+	1.06532i	0.275010	+	0.961441i	$0.411319\pi$
$524$	−0.877228	+	2.93015i	−0.0383219	+	0.128004i
$525$	6.42557	+	3.65200i	0.280435	+	0.159386i
$526$	1.48312	−	25.4642i	0.0646671	−	1.11029i
$527$	−0.714181	+	12.2620i	−0.0311102	+	0.534142i
$528$	0.211786	+	31.2675i	0.00921679	+	1.36074i
$529$	−9.55282	+	31.9087i	−0.415340	+	1.38733i
$530$	−0.956265	−	0.802402i	−0.0415375	−	0.0348541i
$531$	13.4244	+	29.9973i	0.582569	+	1.30177i
$532$	1.12861	−	0.947016i	0.0489314	−	0.0410583i
$533$	3.51715	+	8.15367i	0.152345	+	0.353175i
$534$	−19.9129	−	18.5335i	−0.861716	−	0.802025i
$535$	−0.134136	−	0.448045i	−0.00579920	−	0.0193707i
$536$	4.67833	−	10.8456i	0.202073	−	0.468458i
$537$	17.2471	+	12.6593i	0.744266	+	0.546290i
$538$	−26.1472	+	17.1973i	−1.12729	+	0.741429i
$539$	12.5176	−	21.6811i	0.539171	−	0.933871i
$540$	−0.127009	+	0.00999044i	−0.00546562	+	0.000429920i
$541$	−22.1922	−	38.4380i	−0.954116	−	1.65258i	−0.736378	−	0.676570i	$-0.763466\pi$
$541$	−22.1922	−	38.4380i	−0.954116	−	1.65258i	−0.217737	−	0.976007i	$-0.569868\pi$
$542$	4.76183	+	2.39148i	0.204538	+	0.102723i
$543$	−0.0149126	−	0.0610746i	−0.000639959	−	0.00262096i
$544$	−2.11449	−	2.84026i	−0.0906582	−	0.121775i
$545$	0.569554	−	0.603692i	0.0243970	−	0.0258593i
$546$	−2.07462	−	4.06207i	−0.0887855	−	0.173841i
$547$	−3.16949	−	0.370461i	−0.135518	−	0.0158398i	0.0480635	−	0.998844i	$-0.484695\pi$
$547$	−3.16949	−	0.370461i	−0.135518	−	0.0158398i	−0.183581	+	0.983005i	$0.558769\pi$
$548$	4.65378	+	1.69384i	0.198799	+	0.0723571i
$549$	−15.5715	+	27.8347i	−0.664576	+	1.18796i
$550$	28.4655	−	10.3606i	1.21377	−	0.441777i
$551$	−6.05335	+	1.43467i	−0.257882	+	0.0611191i
$552$	32.9400	+	5.57844i	1.40202	+	0.237434i
$553$	9.74723	+	6.41085i	0.414494	+	0.272617i
$554$	−22.0525	+	11.0752i	−0.936920	+	0.470539i
$555$	−0.0472602	+	0.132635i	−0.00200608	+	0.00563003i
$556$	4.28958	+	4.54669i	0.181919	+	0.192823i
$557$	−4.44633	+	25.2164i	−0.188397	+	1.06845i	0.733116	+	0.680104i	$0.238065\pi$
$557$	−4.44633	+	25.2164i	−0.188397	+	1.06845i	−0.921513	+	0.388348i	$0.873046\pi$
$558$	18.4715	−	20.1178i	0.781962	−	0.851654i
$559$	4.22995	+	23.9892i	0.178908	+	1.01464i
$560$	−0.183653	+	0.246689i	−0.00776077	+	0.0104245i
$561$	1.74103	+	14.0684i	0.0735064	+	0.593969i
$562$	−0.601696	−	0.142605i	−0.0253810	−	0.00601541i
$563$	−15.1734	+	1.77351i	−0.639481	+	0.0747446i	−0.429653	−	0.902994i	$-0.641364\pi$
$563$	−15.1734	+	1.77351i	−0.639481	+	0.0747446i	−0.209827	+	0.977738i	$0.567290\pi$
$564$	1.21524	−	2.46118i	0.0511710	−	0.103634i
$565$	−0.0128372	−	0.220406i	−0.000540064	−	0.00927253i
$566$	28.3949			1.19352
$567$	7.61158	−	1.09942i	0.319656	−	0.0461712i
$568$	14.2645			0.598523
$569$	0.935369	+	16.0597i	0.0392127	+	0.673256i	0.959447	+	0.281889i	$0.0909609\pi$
$569$	0.935369	+	16.0597i	0.0392127	+	0.673256i	−0.920234	+	0.391368i	$0.872002\pi$
$570$	−1.17013	+	0.0761080i	−0.0490113	+	0.00318781i
$571$	18.1635	−	2.12301i	0.760119	−	0.0888451i	0.272802	−	0.962070i	$-0.412050\pi$
$571$	18.1635	−	2.12301i	0.760119	−	0.0888451i	0.487317	+	0.873225i	$0.337976\pi$
$572$	−2.42751	−	0.575329i	−0.101499	−	0.0240557i
$573$	−42.3576	−	17.9320i	−1.76952	−	0.749120i
$574$	3.39350	−	4.55826i	0.141642	−	0.190258i
$575$	−6.50690	−	36.9025i	−0.271357	−	1.53894i
$576$	0.859013	−	19.2342i	0.0357922	−	0.801423i
$577$	1.90472	−	10.8022i	0.0792945	−	0.449702i	−0.919148	−	0.393912i	$-0.871121\pi$
$577$	1.90472	−	10.8022i	0.0792945	−	0.449702i	0.998443	−	0.0557894i	$-0.0177675\pi$
$578$	13.3433	+	14.1430i	0.555007	+	0.588273i
$579$	−0.0770585	+	0.0141263i	−0.00320244	+	0.000587069i
$580$	−0.0243495	+	0.0122288i	−0.00101106	+	0.000507772i
$581$	−4.48593	−	2.95044i	−0.186108	−	0.122405i
$582$	−23.0490	+	27.8497i	−0.955412	+	1.15441i
$583$	40.1041	−	9.50485i	1.66094	−	0.393651i
$584$	3.72049	−	1.35415i	0.153955	−	0.0560350i
$585$	−0.0776539	+	0.478188i	−0.00321059	+	0.0197707i
$586$	−18.3845	−	6.69140i	−0.759456	−	0.276419i
$587$	15.5791	+	1.82094i	0.643019	+	0.0751581i	0.431352	−	0.902184i	$-0.358037\pi$
$587$	15.5791	+	1.82094i	0.643019	+	0.0751581i	0.211667	+	0.977342i	$0.432111\pi$
$588$	1.81900	−	2.80688i	0.0750142	−	0.115754i
$589$	23.0203	−	24.4001i	0.948535	−	1.00539i
$590$	0.791142	+	1.06269i	0.0325708	+	0.0437502i
$591$	20.2543	+	5.91455i	0.833150	+	0.243292i
$592$	4.12583	+	2.07207i	0.169571	+	0.0851616i
$593$	−20.4416	−	35.4058i	−0.839434	−	1.45394i	−0.890369	−	0.455240i	$-0.849553\pi$
$593$	−20.4416	−	35.4058i	−0.839434	−	1.45394i	0.0509346	−	0.998702i	$-0.483780\pi$
$594$	16.7822	−	26.6816i	0.688583	−	1.09476i
$595$	−0.0697142	+	0.120749i	−0.00285800	+	0.00495021i
$596$	1.31564	−	0.865308i	0.0538906	−	0.0354444i
$597$	−2.38165	+	21.6469i	−0.0974744	+	0.885947i
$598$	−9.15945	+	21.2340i	−0.374558	+	0.868322i
$599$	−7.75749	−	25.9118i	−0.316962	−	1.05873i	−0.956928	−	0.290325i	$-0.906237\pi$
$599$	−7.75749	−	25.9118i	−0.316962	−	1.05873i	0.639966	−	0.768403i	$-0.278948\pi$
$600$	−21.2553	+	6.52062i	−0.867745	+	0.266203i
$601$	6.61392	+	15.3328i	0.269788	+	0.625438i	0.998217	−	0.0596825i	$-0.0190088\pi$
$601$	6.61392	+	15.3328i	0.269788	+	0.625438i	−0.728430	+	0.685120i	$0.759750\pi$
$602$	11.9418	−	10.0203i	0.486710	−	0.408398i
$603$	−11.4136	+	7.73037i	−0.464799	+	0.314805i
$604$	−4.19125	−	3.51688i	−0.170540	−	0.143100i
$605$	0.112873	−	0.377021i	0.00458893	−	0.0153281i
$606$	19.3777	−	11.3634i	0.787166	−	0.461607i
$607$	2.65408	−	45.5688i	0.107726	−	1.84958i	−0.322143	−	0.946691i	$-0.604403\pi$
$607$	2.65408	−	45.5688i	0.107726	−	1.84958i	0.429869	−	0.902891i	$-0.358560\pi$
$608$	−0.562296	+	9.65424i	−0.0228041	+	0.391531i
$609$	1.41884	−	0.832030i	0.0574942	−	0.0337155i
$610$	−0.368756	+	1.23173i	−0.0149305	+	0.0498713i
$611$	−7.99555	−	6.70906i	−0.323465	−	0.271420i
$612$	0.135722	+	1.88904i	0.00548625	+	0.0763598i
$613$	30.0949	−	25.2526i	1.21552	−	1.01994i	0.216476	−	0.976288i	$-0.430544\pi$
$613$	30.0949	−	25.2526i	1.21552	−	1.01994i	0.999047	−	0.0436562i	$-0.0139006\pi$
$614$	−5.25705	−	12.1872i	−0.212157	−	0.491836i
$615$	−0.577033	+	0.177020i	−0.0232682	+	0.00713812i
$616$	−2.51544	−	8.40216i	−0.101350	−	0.338533i
$617$	−1.00511	+	2.33010i	−0.0404640	+	0.0938061i	−0.937249	−	0.348660i	$-0.886637\pi$
$617$	−1.00511	+	2.33010i	−0.0404640	+	0.0938061i	0.896785	+	0.442466i	$0.145896\pi$
$618$	−2.36828	+	21.5254i	−0.0952662	+	0.865877i
$619$	10.2465	−	6.73923i	0.411841	−	0.270872i	−0.326637	−	0.945150i	$-0.605915\pi$
$619$	10.2465	−	6.73923i	0.411841	−	0.270872i	0.738478	+	0.674278i	$0.235545\pi$
$620$	0.0734635	−	0.127242i	0.00295036	−	0.00511018i
$621$	−28.8990	−	26.1756i	−1.15968	−	1.05039i
$622$	14.1202	+	24.4570i	0.566170	+	0.980635i
$623$	7.89436	+	3.96470i	0.316281	+	0.158842i
$624$	15.2483	+	4.45274i	0.610422	+	0.178252i
$625$	14.8722	+	19.9769i	0.594889	+	0.799075i
$626$	21.9338	−	23.2485i	0.876653	−	0.929198i
$627$	21.0548	−	32.4895i	0.840849	−	1.29751i
$628$	2.20780	+	0.258055i	0.0881008	+	0.0102975i
$629$	1.96689	+	0.715890i	0.0784251	+	0.0285444i
$630$	0.289868	−	0.109972i	0.0115486	−	0.00438141i
$631$	−38.1004	+	13.8674i	−1.51675	+	0.552053i	−0.960335	−	0.278848i	$-0.910047\pi$
$631$	−38.1004	+	13.8674i	−1.51675	+	0.552053i	−0.556419	+	0.830902i	$0.687825\pi$
$632$	−34.1489	+	8.09344i	−1.35837	+	0.321940i
$633$	15.1572	−	18.3142i	0.602445	−	0.727923i
$634$	−20.5641	−	13.5252i	−0.816703	−	0.537154i
$635$	0.791544	−	0.397528i	0.0314115	−	0.0157754i
$636$	5.41616	−	0.992886i	0.214765	−	0.0393705i
$637$	−8.72802	−	9.25117i	−0.345817	−	0.366545i
$638$	1.17063	−	6.63899i	0.0463458	−	0.262840i
$639$	−14.0317	−	8.95888i	−0.555086	−	0.354408i
$640$	−0.182539	−	1.03523i	−0.00721548	−	0.0409210i
$641$	−18.0299	+	24.2184i	−0.712140	+	0.956570i	−0.999999	−	0.00110272i	$-0.999649\pi$
$641$	−18.0299	+	24.2184i	−0.712140	+	0.956570i	0.287859	+	0.957673i	$0.407056\pi$
$642$	14.2362	+	6.02688i	0.561860	+	0.237862i
$643$	−0.432548	−	0.102516i	−0.0170580	−	0.00404283i	0.222078	−	0.975029i	$-0.428716\pi$
$643$	−0.432548	−	0.102516i	−0.0170580	−	0.00404283i	−0.239136	+	0.970986i	$0.576864\pi$
$644$	1.96156	−	0.229274i	0.0772963	−	0.00903464i
$645$	−1.65223	+	0.107465i	−0.0650566	+	0.00423143i
$646$	1.01355	+	17.4020i	0.0398775	+	0.684671i
$647$	38.0107			1.49436			0.747178	−	0.664624i	$-0.231408\pi$
$647$	38.0107			1.49436			0.747178	+	0.664624i	$0.231408\pi$
$648$	−13.3072	+	18.9242i	−0.522757	+	0.743413i
$649$	−43.7418			−1.71702
$650$	−0.894812	−	15.3633i	−0.0350974	−	0.602600i
$651$	−3.92671	+	7.95258i	−0.153900	+	0.311686i
$652$	−1.51305	+	0.176850i	−0.0592555	+	0.00692598i
$653$	−13.1542	−	3.11759i	−0.514762	−	0.122001i	−0.0349790	−	0.999388i	$-0.511136\pi$
$653$	−13.1542	−	3.11759i	−0.514762	−	0.122001i	−0.479783	+	0.877387i	$0.659285\pi$
$654$	3.36939	+	27.2264i	0.131753	+	1.06463i
$655$	−0.472081	+	0.634115i	−0.0184457	+	0.0247769i
$656$	3.43670	+	19.4905i	0.134181	+	0.760977i
$657$	−4.51026	−	1.00462i	−0.175962	−	0.0391941i
$658$	−1.15988	+	6.57802i	−0.0452169	+	0.256438i
$659$	−17.8731	−	18.9443i	−0.696235	−	0.737966i	0.278719	−	0.960373i	$-0.410090\pi$
$659$	−17.8731	−	18.9443i	−0.696235	−	0.737966i	−0.974954	+	0.222407i	$0.928609\pi$
$660$	0.0569159	−	0.159733i	0.00221545	−	0.00621761i
$661$	2.14977	−	1.07965i	0.0836162	−	0.0419936i	−0.406500	−	0.913651i	$-0.633251\pi$
$661$	2.14977	−	1.07965i	0.0836162	−	0.0419936i	0.490116	+	0.871657i	$0.336954\pi$
$662$	−24.1852	−	15.9069i	−0.939984	−	0.618237i
$663$	7.10059	+	1.20249i	0.275764	+	0.0467010i
$664$	15.7162	−	3.72481i	0.609908	−	0.144551i
$665$	0.357828	−	0.130239i	0.0138760	−	0.00505044i
$666$	−2.38148	−	3.99875i	−0.0922805	−	0.154949i
$667$	−7.83624	−	2.85216i	−0.303420	−	0.110436i
$668$	5.48265	+	0.640829i	0.212130	+	0.0247944i
$669$	2.31401	+	4.53079i	0.0894647	+	0.175170i
$670$	−0.381356	+	0.404214i	−0.0147331	+	0.0156161i
$671$	−25.3499	−	34.0509i	−0.978623	−	1.31452i
$672$	−0.606486	−	2.48387i	−0.0233957	−	0.0958174i
$673$	−11.7838	−	5.91802i	−0.454230	−	0.228123i	0.206948	−	0.978352i	$-0.433647\pi$
$673$	−11.7838	−	5.91802i	−0.454230	−	0.228123i	−0.661178	+	0.750229i	$0.729943\pi$
$674$	8.30335	+	14.3818i	0.319833	+	0.553967i
$675$	25.0038	+	6.93532i	0.962398	+	0.266941i
$676$	1.36828	−	2.36994i	0.0526263	−	0.0911514i
$677$	9.64188	−	6.34156i	0.370568	−	0.243726i	−0.350542	−	0.936547i	$-0.614003\pi$
$677$	9.64188	−	6.34156i	0.370568	−	0.243726i	0.721110	+	0.692821i	$0.243632\pi$
$678$	5.88310	+	4.31818i	0.225939	+	0.165839i
$679$	4.64980	−	10.7795i	0.178443	−	0.413678i
$680$	−0.120292	−	0.401805i	−0.00461300	−	0.0154085i
$681$	5.02839	+	4.68008i	0.192688	+	0.179341i
$682$	14.3981	+	33.3784i	0.551330	+	1.27813i
$683$	−7.16633	+	6.01327i	−0.274212	+	0.230091i	−0.769514	−	0.638629i	$-0.779502\pi$
$683$	−7.16633	+	6.01327i	−0.274212	+	0.230091i	0.495302	+	0.868721i	$0.335057\pi$
$684$	3.03228	−	4.19039i	0.115942	−	0.160224i
$685$	0.980555	+	0.822783i	0.0374651	+	0.0314369i
$686$	−4.94063	+	16.5029i	−0.188634	+	0.630082i
$687$	0.119870	+	17.6973i	0.00457331	+	0.675193i
$688$	−3.15674	+	54.1992i	−0.120350	+	2.06633i
$689$	1.21746	−	20.9030i	0.0463816	−	0.796342i
$690$	−1.36655	−	0.776683i	−0.0520236	−	0.0295678i
$691$	−4.30869	+	14.3920i	−0.163910	+	0.547498i	−0.999999	−	0.00109520i	$-0.999651\pi$
$691$	−4.30869	+	14.3920i	−0.163910	+	0.547498i	0.836089	+	0.548594i	$0.184837\pi$
$692$	0.406534	+	0.341122i	0.0154541	+	0.0129675i
$693$	−2.80263	+	9.84490i	−0.106463	+	0.373977i
$694$	−25.9719	+	21.7930i	−0.985880	+	0.827251i
$695$	0.639910	+	1.48348i	0.0242732	+	0.0562715i
$696$	−1.10842	+	4.82210i	−0.0420144	+	0.182781i
$697$	2.57335	+	8.59557i	0.0974724	+	0.325581i
$698$	−14.0669	+	32.6107i	−0.532440	+	1.23433i
$699$	4.04923	−	1.77929i	0.153156	−	0.0672991i
$700$	−1.09805	+	0.722200i	−0.0415025	+	0.0272966i
$701$	−8.41328	+	14.5722i	−0.317765	+	0.550385i	−0.980021	−	0.198892i	$-0.936266\pi$
$701$	−8.41328	+	14.5722i	−0.317765	+	0.550385i	0.662256	+	0.749277i	$0.269599\pi$
$702$	−10.5403	−	12.0553i	−0.397819	−	0.454998i
$703$	−2.85826	−	4.95065i	−0.107801	−	0.186717i
$704$	22.9002	+	11.5009i	0.863084	+	0.433457i
$705$	0.512720	−	0.490333i	0.0193102	−	0.0184670i
$706$	−28.9235	−	38.8510i	−1.08855	−	1.46218i
$707$	−5.00608	+	5.30614i	−0.188273	+	0.199558i
$708$	−5.83627	−	0.300274i	−0.219340	−	0.0112850i
$709$	−9.55304	−	1.11659i	−0.358772	−	0.0419344i	−0.0652022	−	0.997872i	$-0.520769\pi$
$709$	−9.55304	−	1.11659i	−0.358772	−	0.0419344i	−0.293570	+	0.955938i	$0.594843\pi$
$710$	−0.630647	−	0.229537i	−0.0236677	−	0.00861435i
$711$	38.6748	+	13.4861i	1.45042	+	0.505766i
$712$	−24.9716	+	9.08893i	−0.935851	+	0.340622i
$713$	43.7548	−	10.3701i	1.63863	−	0.388362i
$714$	−1.60558	−	4.32004i	−0.0600875	−	0.161673i
$715$	−0.538723	−	0.354324i	−0.0201471	−	0.0132510i
$716$	−3.39974	+	1.70741i	−0.127054	+	0.0638091i
$717$	5.23190	+	6.15005i	0.195389	+	0.229678i
$718$	−11.7961	−	12.5032i	−0.440228	−	0.466615i
$719$	3.87901	−	21.9989i	0.144663	−	0.820422i	−0.822975	−	0.568078i	$-0.807687\pi$
$719$	3.87901	−	21.9989i	0.144663	−	0.820422i	0.967638	−	0.252344i	$-0.0812016\pi$
$720$	−0.414189	+	0.997126i	−0.0154359	+	0.0371607i
$721$	−1.22116	−	6.92552i	−0.0454782	−	0.257920i
$722$	11.1919	−	15.0334i	0.416520	−	0.559484i
$723$	2.09868	−	1.58461i	0.0780507	−	0.0589324i
$724$	0.0108782	+	0.00257817i	0.000404283	+	9.58169e-5i
$725$	5.51201	−	0.644261i	0.204711	−	0.0239273i
$726$	7.22191	+	10.8200i	0.268030	+	0.401569i
$727$	2.37548	+	40.7855i	0.0881018	+	1.51265i	0.695658	+	0.718373i	$0.255113\pi$
$727$	2.37548	+	40.7855i	0.0881018	+	1.51265i	−0.607556	+	0.794277i	$0.707850\pi$
$728$	−4.45573			−0.165140
$729$	24.9756	−	10.2577i	0.925021	−	0.379916i
$730$	−0.186277			−0.00689442
$731$	1.43114	+	24.5717i	0.0529326	+	0.908818i
$732$	−3.14858	−	4.71727i	−0.116375	−	0.174355i
$733$	27.1610	−	3.17467i	1.00321	−	0.117259i	0.401407	−	0.915900i	$-0.368521\pi$
$733$	27.1610	−	3.17467i	1.00321	−	0.117259i	0.601808	+	0.798641i	$0.294447\pi$
$734$	−1.00282	−	0.237673i	−0.0370148	−	0.00877267i
$735$	0.689917	−	0.520924i	0.0254480	−	0.0192146i
$736$	−7.74108	+	10.3981i	−0.285340	+	0.383278i
$737$	−3.18607	−	18.0691i	−0.117360	−	0.665584i
$738$	7.65329	−	18.4246i	0.281721	−	0.678220i
$739$	−1.54918	+	8.78585i	−0.0569876	+	0.323193i	−0.999953	−	0.00969806i	$-0.996913\pi$
$739$	−1.54918	+	8.78585i	−0.0569876	+	0.323193i	0.942965	+	0.332891i	$0.108024\pi$
$740$	−0.0171821	−	0.0182119i	−0.000631626	−	0.000669485i
$741$	−12.7444	−	14.9810i	−0.468178	−	0.550339i
$742$	−11.9744	+	6.01376i	−0.439593	+	0.220772i
$743$	−12.8882	−	8.47670i	−0.472822	−	0.310980i	0.290640	−	0.956832i	$-0.406132\pi$
$743$	−12.8882	−	8.47670i	−0.472822	−	0.310980i	−0.763462	+	0.645852i	$0.776502\pi$
$744$	−9.29473	−	25.0087i	−0.340761	−	0.916863i
$745$	0.396029	−	0.0938606i	0.0145094	−	0.00343879i
$746$	15.9226	−	5.79536i	0.582968	−	0.212183i
$747$	−17.7992	−	6.20664i	−0.651238	−	0.227089i
$748$	−2.36875	−	0.862154i	−0.0866100	−	0.0315235i
$749$	−4.98637	−	0.582823i	−0.182198	−	0.0212959i
$750$	2.09062	+	0.107562i	0.0763386	+	0.00392760i
$751$	−20.0965	+	21.3010i	−0.733332	+	0.777286i	−0.981506	−	0.191429i	$-0.938688\pi$
$751$	−20.0965	+	21.3010i	−0.733332	+	0.777286i	0.248175	+	0.968715i	$0.420169\pi$
$752$	−13.8914	−	18.6594i	−0.506569	−	0.680440i
$753$	−27.3929	+	26.1968i	−0.998251	+	0.954664i
$754$	−3.06054	−	1.53706i	−0.111458	−	0.0559764i
$755$	−0.707063	−	1.22467i	−0.0257327	−	0.0445703i
$756$	−0.441525	+	1.29432i	−0.0160581	+	0.0470740i
$757$	−16.6330	+	28.8091i	−0.604536	+	1.04709i	0.387589	+	0.921832i	$0.373308\pi$
$757$	−16.6330	+	28.8091i	−0.604536	+	1.04709i	−0.992125	+	0.125254i	$0.960025\pi$
$758$	−25.3631	+	16.6816i	−0.921228	+	0.605901i
$759$	47.5122	−	20.8776i	1.72458	−	0.757808i
$760$	−0.453705	+	1.05181i	−0.0164576	+	0.0381530i
$761$	−0.0917864	−	0.306588i	−0.00332726	−	0.0111138i	0.956310	−	0.292355i	$-0.0944390\pi$
$761$	−0.0917864	−	0.306588i	−0.00332726	−	0.0111138i	−0.959637	+	0.281242i	$0.909254\pi$
$762$	−6.55896	+	28.5343i	−0.237606	+	1.03369i
$763$	−3.52866	−	8.18036i	−0.127746	−	0.296149i
$764$	6.26572	−	5.25756i	0.226686	−	0.190212i
$765$	−0.134026	+	0.470799i	−0.00484573	+	0.0170218i
$766$	−27.4025	−	22.9935i	−0.990094	−	0.830787i
$767$	−6.37337	+	21.2885i	−0.230129	+	0.768684i
$768$	10.8806	+	6.18404i	0.392620	+	0.223147i
$769$	−0.120845	+	2.07483i	−0.00435778	+	0.0748202i	−0.999786	−	0.0206939i	$-0.993412\pi$
$769$	−0.120845	+	2.07483i	−0.00435778	+	0.0748202i	0.995428	+	0.0955141i	$0.0304495\pi$
$770$	−0.0239931	+	0.411945i	−0.000864651	+	0.0148455i
$771$	0.0835039	+	12.3283i	0.00300732	+	0.443994i
$772$	0.00399548	−	0.0133458i	0.000143801	−	0.000480327i
$773$	5.06191	+	4.24745i	0.182064	+	0.152770i	0.729265	−	0.684231i	$-0.239862\pi$
$773$	5.06191	+	4.24745i	0.182064	+	0.152770i	−0.547201	+	0.837001i	$0.684307\pi$
$774$	32.0844	−	44.3383i	1.15325	−	1.59371i
$775$	−22.9235	+	19.2351i	−0.823437	+	0.690945i
$776$	13.9874	+	32.4265i	0.502119	+	1.16404i
$777$	1.10636	+	1.02972i	0.0396904	+	0.0369410i
$778$	2.72110	+	9.08910i	0.0975561	+	0.325860i
$779$	9.70585	−	22.5007i	0.347748	−	0.806171i
$780$	−0.0694471	−	0.0509740i	−0.00248660	−	0.00182516i
$781$	18.5128	−	12.1761i	0.662440	−	0.435694i
$782$	−11.6832	+	20.2359i	−0.417791	+	0.723635i
$783$	4.11888	−	4.04727i	0.147197	−	0.144638i
$784$	−14.1733	−	24.5489i	−0.506191	−	0.876748i
$785$	0.513409	+	0.257844i	0.0183243	+	0.00920283i
$786$	−6.19835	−	25.3854i	−0.221088	−	0.905468i
$787$	1.88656	+	2.53409i	0.0672487	+	0.0903306i	0.834475	−	0.551046i	$-0.185771\pi$
$787$	1.88656	+	2.53409i	0.0672487	+	0.0903306i	−0.767226	+	0.641377i	$0.778364\pi$
$788$	−2.57484	+	2.72917i	−0.0917249	+	0.0972228i
$789$	13.2272	+	25.8987i	0.470901	+	0.922017i
$790$	1.63999	+	0.191688i	0.0583484	+	0.00681995i
$791$	−2.22697	−	0.810550i	−0.0791818	−	0.0288198i
$792$	−15.7557	−	26.4555i	−0.559855	−	0.940055i
$793$	−20.2657	+	7.37611i	−0.719656	+	0.261933i
$794$	−1.65863	+	0.393102i	−0.0588626	+	0.0139507i
$795$	1.40322	+	0.237638i	0.0497672	+	0.00842815i
$796$	−3.23545	−	2.12799i	−0.114678	−	0.0754246i
$797$	41.8410	−	21.0134i	1.48209	−	0.744331i	0.490217	−	0.871600i	$-0.336918\pi$
$797$	41.8410	−	21.0134i	1.48209	−	0.744331i	0.991868	+	0.127269i	$0.0406213\pi$
$798$	−4.22478	+	11.8567i	−0.149556	+	0.419724i
$799$	−7.23731	−	7.67110i	−0.256038	−	0.271384i
$800$	1.49802	−	8.49568i	0.0529629	−	0.300368i
$801$	30.2725	+	6.74296i	1.06963	+	0.238251i
$802$	1.11817	+	6.34143i	0.0394838	+	0.223924i
$803$	3.67266	−	4.93324i	0.129605	−	0.174090i
$804$	−0.301064	−	2.43275i	−0.0106177	−	0.0857965i
$805$	0.496683	+	0.117716i	0.0175058	+	0.00414895i
$806$	18.3427	−	2.14395i	0.646094	−	0.0755175i
$807$	15.7970	−	31.9928i	0.556080	−	1.12620i
$808$	−1.27595	−	21.9073i	−0.0448879	−	0.770695i
$809$	−47.8251			−1.68144			−0.840721	−	0.541468i	$-0.817869\pi$
$809$	−47.8251			−1.68144			−0.840721	+	0.541468i	$0.817869\pi$
$810$	0.892846	−	0.622525i	0.0313714	−	0.0218733i
$811$	11.3948			0.400124			0.200062	−	0.979783i	$-0.435886\pi$
$811$	11.3948			0.400124			0.200062	+	0.979783i	$0.435886\pi$
$812$	0.0170064	+	0.291988i	0.000596807	+	0.0102468i
$813$	−6.06235	+	0.394309i	−0.212616	+	0.0138290i
$814$	6.15279	−	0.719158i	0.215655	−	0.0252065i
$815$	−0.383116	−	0.0908002i	−0.0134200	−	0.00318059i
$816$	14.7809	+	6.25744i	0.517433	+	0.219054i
$817$	40.1418	−	53.9198i	1.40438	−	1.88642i
$818$	−0.504121	−	2.85901i	−0.0176262	−	0.0999630i
$819$	4.38302	+	2.79845i	0.153155	+	0.0977857i
$820$	0.0186375	−	0.105699i	0.000650851	−	0.00369116i
$821$	10.9406	+	11.5964i	0.381830	+	0.404716i	0.889573	−	0.456792i	$-0.151002\pi$
$821$	10.9406	+	11.5964i	0.381830	+	0.404716i	−0.507744	+	0.861508i	$0.669520\pi$
$822$	−41.6172	+	7.62923i	−1.45157	+	0.266100i
$823$	34.5077	−	17.3304i	1.20286	−	0.604100i	0.269488	−	0.963004i	$-0.413146\pi$
$823$	34.5077	−	17.3304i	1.20286	−	0.604100i	0.933375	+	0.358904i	$0.116849\pi$
$824$	17.6744	+	11.6246i	0.615716	+	0.404963i
$825$	−22.0198	+	26.6061i	−0.766631	+	0.926305i
$826$	13.8378	−	3.27962i	0.481479	−	0.114113i
$827$	−32.7798	+	11.9309i	−1.13986	+	0.414877i	−0.841865	−	0.539689i	$-0.818542\pi$
$827$	−32.7798	+	11.9309i	−1.13986	+	0.414877i	−0.298000	+	0.954566i	$0.596320\pi$
$828$	6.48266	−	2.45944i	0.225288	−	0.0854716i
$829$	25.8256	+	9.39976i	0.896961	+	0.326467i	0.749034	−	0.662531i	$-0.230518\pi$
$829$	25.8256	+	9.39976i	0.896961	+	0.326467i	0.147927	+	0.988998i	$0.452740\pi$
$830$	−0.754768	−	0.0882198i	−0.0261984	−	0.00306215i
$831$	15.3007	−	23.6103i	0.530774	−	0.819033i
$832$	8.93399	−	9.46948i	0.309730	−	0.328295i
$833$	−7.67422	−	10.3083i	−0.265896	−	0.357160i
$834$	−51.2624	−	14.9694i	−1.77507	−	0.518348i
$835$	1.27495	+	0.640305i	0.0441216	+	0.0221587i
$836$	3.44223	+	5.96211i	0.119052	+	0.206204i
$837$	−6.56380	+	30.4383i	−0.226878	+	1.05210i
$838$	−1.88524	+	3.26532i	−0.0651244	+	0.112799i
$839$	19.1139	−	12.5714i	0.659884	−	0.434013i	−0.174903	−	0.984586i	$-0.555961\pi$
$839$	19.1139	−	12.5714i	0.659884	−	0.434013i	0.834787	+	0.550573i	$0.185591\pi$
$840$	0.0331216	−	0.301043i	0.00114280	−	0.0103870i
$841$	−10.9971	+	25.4943i	−0.379212	+	0.879112i
$842$	−7.60981	−	25.4185i	−0.262251	−	0.875981i
$843$	0.673995	−	0.206765i	0.0232136	−	0.00712138i
$844$	1.67437	+	3.88163i	0.0576342	+	0.133611i
$845$	0.541824	−	0.454644i	0.0186393	−	0.0156402i
$846$	1.68051	+	23.3901i	0.0577773	+	0.804167i
$847$	−3.23615	−	2.71545i	−0.111195	−	0.0933041i
$848$	13.3842	−	44.7063i	0.459615	−	1.53522i
$849$	−27.9255	+	16.3760i	−0.958402	+	0.562023i
$850$	0.904144	−	15.5236i	0.0310119	−	0.532454i
$851$	0.445555	−	7.64988i	0.0152734	−	0.262234i
$852$	2.55366	−	1.49751i	0.0874871	−	0.0513039i
$853$	−15.1823	+	50.7124i	−0.519832	+	1.73636i	0.145064	+	0.989422i	$0.453661\pi$
$853$	−15.1823	+	50.7124i	−0.519832	+	1.73636i	−0.664896	+	0.746936i	$0.731524\pi$
$854$	10.5725	+	8.87141i	0.361785	+	0.303573i
$855$	1.10690	−	0.749692i	0.0378550	−	0.0256389i
$856$	11.5688	−	9.70736i	0.395413	−	0.331791i
$857$	−6.23293	−	14.4496i	−0.212913	−	0.493588i	0.777972	−	0.628299i	$-0.216249\pi$
$857$	−6.23293	−	14.4496i	−0.212913	−	0.493588i	−0.990885	+	0.134711i	$0.956989\pi$
$858$	20.3764	−	6.25098i	0.695638	−	0.213405i
$859$	5.14494	+	17.1853i	0.175543	+	0.586355i	0.999797	+	0.0201350i	$0.00640959\pi$
$859$	5.14494	+	17.1853i	0.175543	+	0.586355i	−0.824254	+	0.566220i	$0.808405\pi$
$860$	0.116616	−	0.270346i	0.00397657	−	0.00921872i
$861$	−0.708550	+	6.44003i	−0.0241473	+	0.219476i
$862$	29.6630	−	19.5097i	1.01033	−	0.664502i
$863$	24.9816	−	43.2695i	0.850385	−	1.47291i	−0.0304761	−	0.999535i	$-0.509702\pi$
$863$	24.9816	−	43.2695i	0.850385	−	1.47291i	0.880861	−	0.473375i	$-0.156964\pi$
$864$	−4.19082	−	7.93822i	−0.142575	−	0.270064i
$865$	0.0685821	+	0.118788i	0.00233186	+	0.00403890i
$866$	−41.5087	−	20.8465i	−1.41052	−	0.708391i
$867$	−21.2794	−	6.21389i	−0.722685	−	0.211035i
$868$	−0.941805	−	1.26506i	−0.0319669	−	0.0429391i
$869$	−37.4109	+	39.6532i	−1.26908	+	1.34514i
$870$	0.126599	−	0.195354i	0.00429211	−	0.00662311i
$871$	−9.25821	−	1.08213i	−0.313703	−	0.0366666i
$872$	25.1835	+	9.16605i	0.852821	+	0.310401i
$873$	6.60647	−	40.6823i	0.223595	−	1.37689i
$874$	59.9673	−	21.8263i	2.02842	−	0.738286i
$875$	−0.661484	+	0.156775i	−0.0223622	+	0.00529995i
$876$	0.523892	−	0.633008i	0.0177007	−	0.0213874i
$877$	6.84275	+	4.50055i	0.231063	+	0.151973i	0.659762	−	0.751475i	$-0.270657\pi$
$877$	6.84275	+	4.50055i	0.231063	+	0.151973i	−0.428698	+	0.903448i	$0.641028\pi$
$878$	16.8455	−	8.46015i	0.568510	−	0.285516i
$879$	21.9397	−	4.02197i	0.740008	−	0.135658i
$880$	−0.986202	−	1.04531i	−0.0332449	−	0.0352375i
$881$	−2.64591	+	15.0057i	−0.0891429	+	0.505555i	0.907243	+	0.420608i	$0.138183\pi$
$881$	−2.64591	+	15.0057i	−0.0891429	+	0.505555i	−0.996385	+	0.0849468i	$0.972928\pi$
$882$	−1.27493	+	28.5470i	−0.0429293	+	0.961229i
$883$	−5.32760	−	30.2143i	−0.179288	−	1.01679i	−0.933077	−	0.359677i	$-0.882887\pi$
$883$	−5.32760	−	30.2143i	−0.179288	−	1.01679i	0.753789	−	0.657117i	$-0.228224\pi$
$884$	−0.764735	+	1.02722i	−0.0257208	+	0.0345491i
$885$	−1.39094	−	0.588853i	−0.0467561	−	0.0197941i
$886$	5.12729	+	1.21519i	0.172255	+	0.0408251i
$887$	−23.6129	+	2.75996i	−0.792845	+	0.0926702i	−0.502868	−	0.864363i	$-0.667722\pi$
$887$	−23.6129	+	2.75996i	−0.792845	+	0.0926702i	−0.289977	+	0.957034i	$0.593648\pi$
$888$	−4.53699	+	0.295096i	−0.152251	+	0.00990279i
$889$	−0.552837	−	9.49184i	−0.0185415	−	0.318346i
$890$	1.25028			0.0419094
$891$	−1.11690	+	35.9193i	−0.0374176	+	1.20334i
$892$	−0.904673			−0.0302907
$893$	1.67474	+	28.7542i	0.0560431	+	0.962223i
$894$	−5.95623	+	12.0629i	−0.199206	+	0.403442i
$895$	−0.976650	+	0.114154i	−0.0326458	+	0.00381575i
$896$	−10.9796	−	2.60222i	−0.366804	−	0.0869341i
$897$	−3.23810	−	26.1655i	−0.108117	−	0.873641i
$898$	2.81575	−	3.78221i	0.0939628	−	0.126214i
$899$	1.15642	+	6.55838i	0.0385687	+	0.218734i
$900$	−3.12064	+	3.39877i	−0.104021	+	0.113292i
$901$	3.67384	−	20.8354i	0.122393	−	0.694128i
$902$	18.2228	+	19.3150i	0.606753	+	0.643120i
$903$	−5.96542	+	16.7418i	−0.198517	+	0.557133i
$904$	6.37074	−	3.19950i	0.211888	−	0.106414i
$905$	0.00241413	+	0.00158780i	8.02484e−5	+	5.27802e-5i
$906$	46.0872	+	7.80493i	1.53115	+	0.259302i
$907$	−33.6177	+	7.96755i	−1.11626	+	0.264558i	−0.747037	−	0.664783i	$-0.768524\pi$
$907$	−33.6177	+	7.96755i	−1.11626	+	0.264558i	−0.369222	+	0.929341i	$0.620376\pi$
$908$	−1.14786	+	0.417786i	−0.0380930	+	0.0138647i
$909$	−12.5039	+	22.3512i	−0.414727	+	0.741343i
$910$	0.196992	+	0.0716993i	0.00653023	+	0.00237681i
$911$	49.7468	+	5.81456i	1.64818	+	0.192645i	0.888896	−	0.458110i	$-0.151473\pi$
$911$	49.7468	+	5.81456i	1.64818	+	0.192645i	0.759288	+	0.650755i	$0.225547\pi$
$912$	−19.9386	−	39.0394i	−0.660233	−	1.29272i
$913$	17.2175	−	18.2494i	0.569815	−	0.603969i
$914$	32.1871	+	43.2347i	1.06465	+	1.43008i
$915$	−0.347708	−	1.42404i	−0.0114949	−	0.0470774i
$916$	−2.81230	−	1.41239i	−0.0929211	−	0.0466667i
$917$	4.24294	+	7.34898i	0.140114	+	0.242685i
$918$	−9.16411	−	13.3351i	−0.302461	−	0.440123i
$919$	1.41443	−	2.44986i	0.0466577	−	0.0808136i	−0.841753	−	0.539862i	$-0.818476\pi$
$919$	1.41443	−	2.44986i	0.0466577	−	0.0808136i	0.888411	+	0.459049i	$0.151810\pi$
$920$	−1.28289	+	0.843770i	−0.0422956	+	0.0278183i
$921$	12.1988	+	8.95391i	0.401965	+	0.295041i
$922$	15.3365	−	35.5540i	0.505080	−	1.17091i
$923$	−3.22853	−	10.7840i	−0.106268	−	0.354961i
$924$	−1.33240	−	1.24010i	−0.0438327	−	0.0407964i
$925$	2.01979	+	4.68241i	0.0664104	+	0.153957i
$926$	−10.8427	+	9.09809i	−0.356313	+	0.298982i
$927$	−10.0851	−	22.5354i	−0.331237	−	0.740161i
$928$	−1.47068	−	1.23405i	−0.0482774	−	0.0405096i
$929$	−3.54186	+	11.8306i	−0.116205	+	0.388150i	−0.996227	−	0.0867811i	$-0.972342\pi$
$929$	−3.54186	+	11.8306i	−0.116205	+	0.388150i	0.880023	+	0.474931i	$0.157527\pi$
$930$	0.00850208	+	1.25523i	0.000278794	+	0.0411605i
$931$	−2.04076	+	35.0385i	−0.0668833	+	1.14834i
$932$	−0.0457306	+	0.785164i	−0.00149795	+	0.0257189i
$933$	−27.9918	−	15.9093i	−0.916410	−	0.520846i
$934$	5.40704	−	18.0608i	0.176924	−	0.590967i
$935$	−0.499097	−	0.418792i	−0.0163222	−	0.0136960i
$936$	−15.1712	+	3.81342i	−0.495887	+	0.124645i
$937$	−4.94841	+	4.15221i	−0.161658	+	0.135647i	−0.720028	−	0.693945i	$-0.755871\pi$
$937$	−4.94841	+	4.15221i	−0.161658	+	0.135647i	0.558371	+	0.829592i	$0.311427\pi$
$938$	2.36269	+	5.47732i	0.0771444	+	0.178841i
$939$	−8.16333	+	35.5140i	−0.266400	+	1.15896i
$940$	0.0361816	+	0.120855i	0.00118011	+	0.00394186i
$941$	−4.95563	+	11.4885i	−0.161549	+	0.374513i	−0.979694	−	0.200500i	$-0.935743\pi$
$941$	−4.95563	+	11.4885i	−0.161549	+	0.374513i	0.818145	+	0.575012i	$0.195003\pi$
$942$	−17.3860	+	7.63969i	−0.566468	+	0.248915i
$943$	27.4441	−	18.0503i	0.893704	−	0.587798i
$944$	−24.7639	+	42.8923i	−0.805995	+	1.39602i
$945$	−0.221653	+	0.275329i	−0.00721037	+	0.00895644i
$946$	36.4221	+	63.0849i	1.18418	+	2.05107i
$947$	−43.0350	−	21.6130i	−1.39845	−	0.702328i	−0.419752	−	0.907639i	$-0.637883\pi$
$947$	−43.0350	−	21.6130i	−1.39845	−	0.702328i	−0.978697	+	0.205311i	$0.934179\pi$
$948$	−5.26377	+	5.03393i	−0.170959	+	0.163494i
$949$	−1.86582	−	2.50623i	−0.0605670	−	0.0813556i
$950$	−29.1434	+	30.8902i	−0.945537	+	1.00221i
$951$	28.0245	+	1.44185i	0.908756	+	0.0467552i
$952$	−4.47175	−	0.522673i	−0.144930	−	0.0169399i
$953$	−23.6434	−	8.60549i	−0.765884	−	0.278759i	−0.0706105	−	0.997504i	$-0.522495\pi$
$953$	−23.6434	−	8.60549i	−0.765884	−	0.278759i	−0.695274	+	0.718745i	$0.744717\pi$
$954$	−35.6245	+	30.7244i	−1.15339	+	0.994738i
$955$	1.98656	−	0.723047i	0.0642834	−	0.0233973i
$956$	−1.39711	+	0.331121i	−0.0451857	+	0.0107092i
$957$	2.67758	+	7.20439i	0.0865539	+	0.232885i
$958$	44.1261	+	29.0222i	1.42565	+	0.937664i
$959$	12.2785	−	6.16651i	0.396495	−	0.199127i
$960$	0.573377	+	0.674000i	0.0185057	+	0.0217533i
$961$	−3.36946	−	3.57142i	−0.108692	−	0.115207i
$962$	0.546484	−	3.09926i	0.0176193	−	0.0999242i
$963$	−17.4768	+	2.28312i	−0.563182	+	0.0735726i
$964$	0.0812022	+	0.460520i	0.00261535	+	0.0148324i
$965$	0.00215017	−	0.00288818i	6.92165e−5	−	9.29739e-5i
$966$	−13.4653	+	10.1670i	−0.433237	+	0.327117i
$967$	−45.8988	−	10.8782i	−1.47601	−	0.349820i	−0.587704	−	0.809076i	$-0.699968\pi$
$967$	−45.8988	−	10.8782i	−1.47601	−	0.349820i	−0.888304	+	0.459256i	$0.848116\pi$
$968$	12.6221	−	1.47531i	0.405689	−	0.0474183i
$969$	−11.0329	−	16.5298i	−0.354429	−	0.531014i
$970$	−0.0966075	−	1.65869i	−0.00310188	−	0.0532572i
$971$	−26.3271			−0.844876			−0.422438	−	0.906392i	$-0.638826\pi$
$971$	−26.3271			−0.844876			−0.422438	+	0.906392i	$0.638826\pi$
$972$	−0.395599	+	4.78489i	−0.0126888	+	0.153475i
$973$	17.3423			0.555968
$974$	−0.400652	−	6.87893i	−0.0128377	−	0.220415i
$975$	9.74043	+	14.5933i	0.311944	+	0.467361i
$976$	−47.7411	+	5.58013i	−1.52815	+	0.178616i
$977$	17.0061	+	4.03051i	0.544072	+	0.128947i	0.493456	−	0.869771i	$-0.335733\pi$
$977$	17.0061	+	4.03051i	0.544072	+	0.128947i	0.0506160	+	0.998718i	$0.483882\pi$
$978$	10.3864	−	7.84229i	0.332121	−	0.250769i
$979$	−24.6506	+	33.1115i	−0.787837	+	1.05825i
$980$	0.0266943	+	0.151391i	0.000852719	+	0.00483601i
$981$	−19.0158	−	24.8332i	−0.607128	−	0.792862i
$982$	7.90196	−	44.8142i	0.252162	−	1.43008i
$983$	−27.2676	−	28.9020i	−0.869701	−	0.921830i	0.127848	−	0.991794i	$-0.459193\pi$
$983$	−27.2676	−	28.9020i	−0.869701	−	0.921830i	−0.997550	+	0.0699641i	$0.977712\pi$
$984$	−12.6285	−	14.8447i	−0.402583	−	0.473233i
$985$	−0.866624	+	0.435235i	−0.0276129	+	0.0138677i
$986$	−2.89124	−	1.90160i	−0.0920759	−	0.0605593i
$987$	−2.65299	−	7.13823i	−0.0844458	−	0.227212i
$988$	3.40323	−	0.806579i	0.108271	−	0.0256607i
$989$	84.6743	−	30.8189i	2.69249	−	0.979985i
$990$	0.270868	+	1.42316i	0.00860876	+	0.0452310i
$991$	−11.5059	−	4.18780i	−0.365497	−	0.133030i	0.152742	−	0.988266i	$-0.451190\pi$
$991$	−11.5059	−	4.18780i	−0.365497	−	0.133030i	−0.518238	+	0.855236i	$0.673412\pi$
$992$	10.2823	+	1.20182i	0.326462	+	0.0381580i
$993$	32.9593	+	1.69575i	1.04593	+	0.0538130i
$994$	−4.94364	+	5.23995i	−0.156803	+	0.166201i
$995$	−0.597699	−	0.802850i	−0.0189483	−	0.0254520i
$996$	2.42252	−	2.31675i	0.0767606	−	0.0734090i
$997$	−7.48521	−	3.75921i	−0.237059	−	0.119056i	0.326304	−	0.945265i	$-0.394197\pi$
$997$	−7.48521	−	3.75921i	−0.237059	−	0.119056i	−0.563363	+	0.826209i	$0.690493\pi$
$998$	−5.18398	−	8.97892i	−0.164096	−	0.284223i
$999$	4.64830	+	2.55920i	0.147066	+	0.0809696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.40.3	✓	144
3.2	odd	2		243.2.g.a.91.6		144
9.2	odd	6		729.2.g.a.28.6		144
9.4	even	3		729.2.g.c.271.6		144
9.5	odd	6		729.2.g.b.271.3		144
9.7	even	3		729.2.g.d.28.3		144
81.2	odd	54		243.2.g.a.235.6		144
81.22	even	27		6561.2.a.c.1.55		72
81.25	even	27		729.2.g.d.703.3		144
81.29	odd	54		729.2.g.b.460.3		144
81.52	even	27		729.2.g.c.460.6		144
81.56	odd	54		729.2.g.a.703.6		144
81.59	odd	54		6561.2.a.d.1.18		72
81.79	even	27	inner	81.2.g.a.79.3	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.40.3	✓	144	1.1	even	1	trivial
81.2.g.a.79.3	yes	144	81.79	even	27	inner
243.2.g.a.91.6		144	3.2	odd	2
243.2.g.a.235.6		144	81.2	odd	54
729.2.g.a.28.6		144	9.2	odd	6
729.2.g.a.703.6		144	81.56	odd	54
729.2.g.b.271.3		144	9.5	odd	6
729.2.g.b.460.3		144	81.29	odd	54
729.2.g.c.271.6		144	9.4	even	3
729.2.g.c.460.6		144	81.52	even	27
729.2.g.d.28.3		144	9.7	even	3
729.2.g.d.703.3		144	81.25	even	27
6561.2.a.c.1.55		72	81.22	even	27
6561.2.a.d.1.18		72	81.59	odd	54

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0883342 - 1.51664i) q^{2} +(0.961557 + 1.44063i) q^{3} +(-0.305915 + 0.0357564i) q^{4} +(-0.0774602 - 0.0183584i) q^{5} +(2.09997 - 1.58559i) q^{6} +(-0.510276 + 0.685420i) q^{7} +(-0.446364 - 2.53145i) q^{8} +(-1.15082 + 2.77049i) q^{9} +(-0.0210007 + 0.119101i) q^{10} +(-2.74014 - 2.90438i) q^{11} +(-0.345667 - 0.406328i) q^{12} +(-1.81277 + 0.910408i) q^{13} +(1.08461 + 0.713359i) q^{14} +(-0.0480348 - 0.129244i) q^{15} +(-4.39927 + 1.04265i) q^{16} +(-1.92609 + 0.701038i) q^{17} +(4.30349 + 1.50064i) q^{18} +(5.26032 + 1.91460i) q^{19} +(0.0243527 + 0.00284642i) q^{20} +(-1.47810 - 0.0760476i) q^{21} +(-4.16285 + 4.41236i) q^{22} +(4.48100 + 6.01902i) q^{23} +(3.21768 - 3.07718i) q^{24} +(-4.46250 - 2.24115i) q^{25} +(1.54089 + 2.66890i) q^{26} +(-5.09782 + 1.00609i) q^{27} +(0.131593 - 0.227926i) q^{28} +(-0.928490 + 0.610677i) q^{29} +(-0.191773 + 0.0842682i) q^{30} +(2.37351 - 5.50241i) q^{31} +(0.495463 + 1.65496i) q^{32} +(1.54933 - 6.74025i) q^{33} +(1.23336 + 2.85925i) q^{34} +(0.0521094 - 0.0437249i) q^{35} +(0.252989 - 0.888685i) q^{36} +(-0.782274 - 0.656406i) q^{37} +(2.43909 - 8.14713i) q^{38} +(-3.05464 - 1.73612i) q^{39} +(-0.0118980 + 0.204282i) q^{40} +(0.254528 - 4.37008i) q^{41} +(0.0152296 + 2.24845i) q^{42} +(3.44402 - 11.5038i) q^{43} +(0.942101 + 0.790516i) q^{44} +(0.140004 - 0.193476i) q^{45} +(8.73286 - 7.32774i) q^{46} +(2.03795 + 4.72449i) q^{47} +(-5.73221 - 5.33514i) q^{48} +(1.79820 + 6.00642i) q^{49} +(-3.00483 + 6.96597i) q^{50} +(-2.86198 - 2.10068i) q^{51} +(0.522002 - 0.343326i) q^{52} +(-5.16096 + 8.93905i) q^{53} +(1.97619 + 7.64268i) q^{54} +(0.158932 + 0.275278i) q^{55} +(1.96288 + 0.985795i) q^{56} +(2.29987 + 9.41916i) q^{57} +(1.00819 + 1.35424i) q^{58} +(7.51758 - 7.96817i) q^{59} +(0.0193159 + 0.0378202i) q^{60} +(10.5595 + 1.23423i) q^{61} +(-8.55483 - 3.11370i) q^{62} +(-1.31172 - 2.20251i) q^{63} +(-6.03074 + 2.19501i) q^{64} +(0.157131 - 0.0372408i) q^{65} +(-10.3594 - 1.75438i) q^{66} +(3.83910 + 2.52502i) q^{67} +(0.564152 - 0.283328i) q^{68} +(-4.36244 + 12.2431i) q^{69} +(-0.0709180 - 0.0751687i) q^{70} +(-0.963622 + 5.46497i) q^{71} +(7.52705 + 1.67659i) q^{72} +(0.267464 + 1.51686i) q^{73} +(-0.926430 + 1.24441i) q^{74} +(-1.06228 - 8.58380i) q^{75} +(-1.67767 - 0.397615i) q^{76} +(3.38895 - 0.396111i) q^{77} +(-2.36324 + 4.78615i) q^{78} +(-0.793846 - 13.6298i) q^{79} +0.359909 q^{80} +(-6.35125 - 6.37665i) q^{81} -6.65031 q^{82} +(0.365349 + 6.27280i) q^{83} +(0.454891 - 0.0295872i) q^{84} +(0.162065 - 0.0189427i) q^{85} +(-17.7514 - 4.20715i) q^{86} +(-1.77255 - 0.750407i) q^{87} +(-6.12920 + 8.23295i) q^{88} +(-1.79520 - 10.1811i) q^{89} +(-0.305800 - 0.195245i) q^{90} +(0.301002 - 1.70707i) q^{91} +(-1.58602 - 1.68109i) q^{92} +(10.2092 - 1.87154i) q^{93} +(6.98533 - 3.50817i) q^{94} +(-0.372317 - 0.244876i) q^{95} +(-1.90777 + 2.30512i) q^{96} +(-13.3681 + 3.16829i) q^{97} +(8.95073 - 3.25780i) q^{98} +(11.2000 - 4.24913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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