LMFDB - Embedded newform 243.2.i.a.4.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(4,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(162)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.i (of order $81$, degree $54$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			4.4
Character	$\chi$	$=$	243.4
Dual form			243.2.i.a.61.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.16400 - 0.0839729i) q^{2} +(-1.61426 + 0.627826i) q^{3} +(2.68184 + 0.208449i) q^{4} +(-2.41283 - 2.99144i) q^{5} +(3.54597 - 1.22306i) q^{6} +(2.23840 - 1.01748i) q^{7} +(-1.48402 - 0.173458i) q^{8} +(2.21167 - 2.02695i) q^{9} +(4.97016 + 6.67608i) q^{10} +(0.0886806 + 4.57235i) q^{11} +(-4.46006 + 1.34724i) q^{12} +(-2.89504 - 0.928257i) q^{13} +(-4.92933 + 2.01385i) q^{14} +(5.77304 + 3.31413i) q^{15} +(-2.11839 - 0.331310i) q^{16} +(-1.47266 - 4.91903i) q^{17} +(-4.95625 + 4.20059i) q^{18} +(-5.12892 + 1.21558i) q^{19} +(-5.84727 - 8.52552i) q^{20} +(-2.97456 + 3.04780i) q^{21} +(0.192049 - 9.90199i) q^{22} +(-1.82161 + 1.30201i) q^{23} +(2.50450 - 0.651704i) q^{24} +(-2.06845 + 9.54903i) q^{25} +(6.18690 + 2.25185i) q^{26} +(-2.29764 + 4.66057i) q^{27} +(6.21512 - 2.26212i) q^{28} +(0.997881 + 7.30578i) q^{29} +(-12.2145 - 7.65653i) q^{30} +(3.46233 + 3.39583i) q^{31} +(7.48860 + 1.47071i) q^{32} +(-3.01379 - 7.32528i) q^{33} +(2.77377 + 10.7684i) q^{34} +(-8.44461 - 4.24104i) q^{35} +(6.35386 - 4.97493i) q^{36} +(-2.63039 - 1.73003i) q^{37} +(11.2010 - 2.19981i) q^{38} +(5.25613 - 0.319134i) q^{39} +(3.06181 + 4.85790i) q^{40} +(-0.0783398 + 0.148724i) q^{41} +(6.69286 - 6.34564i) q^{42} +(-1.16516 + 3.40530i) q^{43} +(-0.715275 + 12.2808i) q^{44} +(-11.3999 - 1.72539i) q^{45} +(4.05128 - 2.66457i) q^{46} +(-4.90220 + 4.80805i) q^{47} +(3.62763 - 0.795160i) q^{48} +(-0.627481 + 0.719013i) q^{49} +(5.27798 - 20.4904i) q^{50} +(5.46555 + 7.01602i) q^{51} +(-7.57054 - 3.09290i) q^{52} +(0.547902 + 0.459744i) q^{53} +(5.36343 - 9.89250i) q^{54} +(13.4639 - 11.2976i) q^{55} +(-3.49833 + 1.12169i) q^{56} +(7.51623 - 5.18232i) q^{57} +(-1.54592 - 15.8935i) q^{58} +(1.40523 - 0.775374i) q^{59} +(14.7916 + 10.0913i) q^{60} +(-3.30815 + 0.257130i) q^{61} +(-7.20732 - 7.63931i) q^{62} +(2.88822 - 6.78744i) q^{63} +(-11.9091 - 2.82251i) q^{64} +(4.20842 + 10.9001i) q^{65} +(5.90671 + 16.1050i) q^{66} +(1.27972 - 9.36919i) q^{67} +(-2.92407 - 13.4990i) q^{68} +(2.12311 - 3.24543i) q^{69} +(17.9180 + 9.88671i) q^{70} +(-3.06574 + 7.10719i) q^{71} +(-3.63376 + 2.62441i) q^{72} +(-9.19271 + 12.3480i) q^{73} +(5.54687 + 3.96467i) q^{74} +(-2.65612 - 16.7132i) q^{75} +(-14.0083 + 2.19086i) q^{76} +(4.85076 + 10.1445i) q^{77} +(-11.4010 + 0.249232i) q^{78} +(4.55127 - 7.22108i) q^{79} +(4.12022 + 7.13644i) q^{80} +(0.782955 - 8.96588i) q^{81} +(0.182016 - 0.315260i) q^{82} +(-7.10092 - 13.4808i) q^{83} +(-8.61260 + 7.55366i) q^{84} +(-11.1617 + 16.2742i) q^{85} +(2.80735 - 7.27122i) q^{86} +(-6.19760 - 11.1669i) q^{87} +(0.661504 - 6.80086i) q^{88} +(-2.29572 - 5.32208i) q^{89} +(24.5244 + 4.69102i) q^{90} +(-7.42473 + 0.867826i) q^{91} +(-5.15666 + 3.11206i) q^{92} +(-7.72110 - 3.30801i) q^{93} +(11.0121 - 9.99294i) q^{94} +(16.0115 + 12.4099i) q^{95} +(-13.0119 + 2.32743i) q^{96} +(5.58072 - 6.91900i) q^{97} +(1.41824 - 1.50325i) q^{98} +(9.46405 + 9.93277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) $ 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{81}\right)$

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 $

$2$	−2.16400	−	0.0839729i	−1.53018	−	0.0593778i	−0.740146	−	0.672446i	$-0.765244\pi$
$2$	−2.16400	−	0.0839729i	−1.53018	−	0.0593778i	−0.790030	+	0.613068i	$0.789935\pi$
$3$	−1.61426	+	0.627826i	−0.931993	+	0.362476i
$3$	−1.61426	+	0.627826i	−0.931993	+	0.362476i
$4$	2.68184	+	0.208449i	1.34092	+	0.104225i
$5$	−2.41283	−	2.99144i	−1.07905	−	1.33781i	−0.937540	−	0.347877i	$-0.886903\pi$
$5$	−2.41283	−	2.99144i	−1.07905	−	1.33781i	−0.141512	−	0.989937i	$-0.545196\pi$
$6$	3.54597	−	1.22306i	1.44764	−	0.499312i
$7$	2.23840	−	1.01748i	0.846035	−	0.384570i	0.0565946	−	0.998397i	$-0.481976\pi$
$7$	2.23840	−	1.01748i	0.846035	−	0.384570i	0.789441	+	0.613827i	$0.210371\pi$
$8$	−1.48402	−	0.173458i	−0.524682	−	0.0613265i
$9$	2.21167	−	2.02695i	0.737223	−	0.675650i
$10$	4.97016	+	6.67608i	1.57170	+	2.11116i
$11$	0.0886806	+	4.57235i	0.0267382	+	1.37861i	0.737579	+	0.675261i	$0.235969\pi$
$11$	0.0886806	+	4.57235i	0.0267382	+	1.37861i	−0.710840	+	0.703353i	$0.751685\pi$
$12$	−4.46006	+	1.34724i	−1.28751	+	0.388914i
$13$	−2.89504	−	0.928257i	−0.802939	−	0.257452i	−0.124606	−	0.992206i	$-0.539767\pi$
$13$	−2.89504	−	0.928257i	−0.802939	−	0.257452i	−0.678333	+	0.734754i	$0.737297\pi$
$14$	−4.92933	+	2.01385i	−1.31742	+	0.538224i
$15$	5.77304	+	3.31413i	1.49059	+	0.855704i
$16$	−2.11839	−	0.331310i	−0.529597	−	0.0828275i
$17$	−1.47266	−	4.91903i	−0.357173	−	1.19304i	−0.928191	−	0.372103i	$-0.878637\pi$
$17$	−1.47266	−	4.91903i	−0.357173	−	1.19304i	0.571019	−	0.820937i	$-0.306548\pi$
$18$	−4.95625	+	4.20059i	−1.16820	+	0.990088i
$19$	−5.12892	+	1.21558i	−1.17665	+	0.278872i	−0.772015	−	0.635604i	$-0.780751\pi$
$19$	−5.12892	+	1.21558i	−1.17665	+	0.278872i	−0.404639	+	0.914476i	$0.632603\pi$
$20$	−5.84727	−	8.52552i	−1.30749	−	1.90637i
$21$	−2.97456	+	3.04780i	−0.649102	+	0.665084i
$22$	0.192049	−	9.90199i	0.0409449	−	2.11111i
$23$	−1.82161	+	1.30201i	−0.379831	+	0.271487i	−0.755342	−	0.655331i	$-0.772529\pi$
$23$	−1.82161	+	1.30201i	−0.379831	+	0.271487i	0.375511	+	0.926818i	$0.377467\pi$
$24$	2.50450	−	0.651704i	0.511229	−	0.133028i
$25$	−2.06845	+	9.54903i	−0.413690	+	1.90981i
$26$	6.18690	+	2.25185i	1.21335	+	0.441624i
$27$	−2.29764	+	4.66057i	−0.442180	+	0.896926i
$28$	6.21512	−	2.26212i	1.17455	−	0.427500i
$29$	0.997881	+	7.30578i	0.185302	+	1.35665i	0.814843	+	0.579682i	$0.196823\pi$
$29$	0.997881	+	7.30578i	0.185302	+	1.35665i	−0.629541	+	0.776967i	$0.716757\pi$
$30$	−12.2145	−	7.65653i	−2.23006	−	1.39789i
$31$	3.46233	+	3.39583i	0.621854	+	0.609910i	0.941250	−	0.337712i	$-0.109653\pi$
$31$	3.46233	+	3.39583i	0.621854	+	0.609910i	−0.319396	+	0.947621i	$0.603480\pi$
$32$	7.48860	+	1.47071i	1.32381	+	0.259988i
$33$	−3.01379	−	7.32528i	−0.524634	−	1.27517i
$34$	2.77377	+	10.7684i	0.475697	+	1.84677i
$35$	−8.44461	−	4.24104i	−1.42740	−	0.716867i
$36$	6.35386	−	4.97493i	1.05898	−	0.829156i
$37$	−2.63039	−	1.73003i	−0.432433	−	0.284416i	0.314572	−	0.949233i	$-0.398139\pi$
$37$	−2.63039	−	1.73003i	−0.432433	−	0.284416i	−0.747006	+	0.664818i	$0.768509\pi$
$38$	11.2010	−	2.19981i	1.81705	−	0.356856i
$39$	5.25613	−	0.319134i	0.841654	−	0.0511023i
$40$	3.06181	+	4.85790i	0.484115	+	0.768101i
$41$	−0.0783398	+	0.148724i	−0.0122346	+	0.0232268i	−0.890803	−	0.454390i	$-0.849857\pi$
$41$	−0.0783398	+	0.148724i	−0.0122346	+	0.0232268i	0.878568	+	0.477617i	$0.158499\pi$
$42$	6.69286	−	6.34564i	1.03273	−	0.979153i
$43$	−1.16516	+	3.40530i	−0.177685	+	0.519304i	−0.998665	−	0.0516530i	$-0.983551\pi$
$43$	−1.16516	+	3.40530i	−0.177685	+	0.519304i	0.820980	+	0.570957i	$0.193428\pi$
$44$	−0.715275	+	12.2808i	−0.107832	+	1.85140i
$45$	−11.3999	−	1.72539i	−1.69940	−	0.257206i
$46$	4.05128	−	2.66457i	0.597329	−	0.392869i
$47$	−4.90220	+	4.80805i	−0.715060	+	0.701326i	−0.963616	−	0.267292i	$-0.913871\pi$
$47$	−4.90220	+	4.80805i	−0.715060	+	0.701326i	0.248556	+	0.968618i	$0.420044\pi$
$48$	3.62763	−	0.795160i	0.523604	−	0.114771i
$49$	−0.627481	+	0.719013i	−0.0896401	+	0.102716i
$50$	5.27798	−	20.4904i	0.746419	−	2.89778i
$51$	5.46555	+	7.01602i	0.765331	+	0.982439i
$52$	−7.57054	−	3.09290i	−1.04984	−	0.428909i
$53$	0.547902	+	0.459744i	0.0752601	+	0.0631508i	0.679642	−	0.733544i	$-0.262135\pi$
$53$	0.547902	+	0.459744i	0.0752601	+	0.0631508i	−0.604382	+	0.796695i	$0.706580\pi$
$54$	5.36343	−	9.89250i	0.729871	−	1.34620i
$55$	13.4639	−	11.2976i	1.81548	−	1.52337i
$56$	−3.49833	+	1.12169i	−0.467484	+	0.149893i
$57$	7.51623	−	5.18232i	0.995549	−	0.686415i
$58$	−1.54592	−	15.8935i	−0.202990	−	2.08691i
$59$	1.40523	−	0.775374i	0.182946	−	0.100945i	−0.388996	−	0.921239i	$-0.627178\pi$
$59$	1.40523	−	0.775374i	0.182946	−	0.100945i	0.571942	+	0.820294i	$0.306190\pi$
$60$	14.7916	+	10.0913i	1.90958	+	1.30279i
$61$	−3.30815	+	0.257130i	−0.423565	+	0.0329221i	−0.287506	−	0.957779i	$-0.592826\pi$
$61$	−3.30815	+	0.257130i	−0.423565	+	0.0329221i	−0.136059	+	0.990701i	$0.543444\pi$
$62$	−7.20732	−	7.63931i	−0.915331	−	0.970194i
$63$	2.88822	−	6.78744i	0.363882	−	0.855137i
$64$	−11.9091	−	2.82251i	−1.48864	−	0.352814i
$65$	4.20842	+	10.9001i	0.521990	+	1.35199i
$66$	5.90671	+	16.1050i	0.727066	+	1.98238i
$67$	1.27972	−	9.36919i	0.156342	−	1.14463i	−0.730619	−	0.682785i	$-0.760769\pi$
$67$	1.27972	−	9.36919i	0.156342	−	1.14463i	0.886962	−	0.461843i	$-0.152812\pi$
$68$	−2.92407	−	13.4990i	−0.354596	−	1.63700i
$69$	2.12311	−	3.24543i	0.255593	−	0.390703i
$70$	17.9180	+	9.88671i	2.14161	+	1.18169i
$71$	−3.06574	+	7.10719i	−0.363837	+	0.843468i	0.633717	+	0.773565i	$0.281528\pi$
$71$	−3.06574	+	7.10719i	−0.363837	+	0.843468i	−0.997554	+	0.0699033i	$0.977731\pi$
$72$	−3.63376	+	2.62441i	−0.428243	+	0.309290i
$73$	−9.19271	+	12.3480i	−1.07593	+	1.44522i	−0.189772	+	0.981828i	$0.560775\pi$
$73$	−9.19271	+	12.3480i	−1.07593	+	1.44522i	−0.886154	+	0.463391i	$0.846633\pi$
$74$	5.54687	+	3.96467i	0.644811	+	0.460883i
$75$	−2.65612	−	16.7132i	−0.306702	−	1.92988i
$76$	−14.0083	+	2.19086i	−1.60686	+	0.251309i
$77$	4.85076	+	10.1445i	0.552795	+	1.15607i
$78$	−11.4010	+	0.249232i	−1.29091	+	0.0282199i
$79$	4.55127	−	7.22108i	0.512058	−	0.812435i	−0.486050	−	0.873931i	$-0.661563\pi$
$79$	4.55127	−	7.22108i	0.512058	−	0.812435i	0.998107	+	0.0614965i	$0.0195873\pi$
$80$	4.12022	+	7.13644i	0.460655	+	0.797878i
$81$	0.782955	−	8.96588i	0.0869950	−	0.996209i
$82$	0.182016	−	0.315260i	0.0201003	−	0.0348147i
$83$	−7.10092	−	13.4808i	−0.779427	−	1.47971i	−0.874915	−	0.484276i	$-0.839083\pi$
$83$	−7.10092	−	13.4808i	−0.779427	−	1.47971i	0.0954879	−	0.995431i	$-0.469559\pi$
$84$	−8.61260	+	7.55366i	−0.939712	+	0.824172i
$85$	−11.1617	+	16.2742i	−1.21066	+	1.76518i
$86$	2.80735	−	7.27122i	0.302724	−	0.784075i
$87$	−6.19760	−	11.1669i	−0.664452	−	1.19722i
$88$	0.661504	−	6.80086i	0.0705166	−	0.724974i
$89$	−2.29572	−	5.32208i	−0.243346	−	0.564139i	0.752145	−	0.658998i	$-0.229019\pi$
$89$	−2.29572	−	5.32208i	−0.243346	−	0.564139i	−0.995491	+	0.0948587i	$0.969760\pi$
$90$	24.5244	+	4.69102i	2.58510	+	0.494477i
$91$	−7.42473	+	0.867826i	−0.778323	+	0.0909729i
$92$	−5.15666	+	3.11206i	−0.537619	+	0.324455i
$93$	−7.72110	−	3.30801i	−0.800641	−	0.343025i
$94$	11.0121	−	9.99294i	1.13581	−	1.03069i
$95$	16.0115	+	12.4099i	1.64275	+	1.27323i
$96$	−13.0119	+	2.32743i	−1.32802	+	0.237542i
$97$	5.58072	−	6.91900i	0.566636	−	0.702518i	−0.411282	−	0.911508i	$-0.634919\pi$
$97$	5.58072	−	6.91900i	0.566636	−	0.702518i	0.977918	+	0.208990i	$0.0670176\pi$
$98$	1.41824	−	1.50325i	0.143264	−	0.151851i
$99$	9.46405	+	9.93277i	0.951173	+	0.998280i
$100$	−7.53774	+	25.1778i	−0.753774	+	2.51778i
$101$	−6.64675	+	13.9005i	−0.661376	+	1.38315i	0.248647	+	0.968594i	$0.420014\pi$
$101$	−6.64675	+	13.9005i	−0.661376	+	1.38315i	−0.910023	+	0.414557i	$0.863937\pi$
$102$	−11.2383	−	15.6416i	−1.11276	−	1.54875i
$103$	−3.27728	−	1.97785i	−0.322920	−	0.194883i	0.345968	−	0.938246i	$-0.387551\pi$
$103$	−3.27728	−	1.97785i	−0.322920	−	0.194883i	−0.668888	+	0.743363i	$0.733230\pi$
$104$	4.13529	+	1.87972i	0.405499	+	0.184322i
$105$	16.2944	+	1.54440i	1.59017	+	0.150718i
$106$	−1.14705	−	1.04089i	−0.111412	−	0.101101i
$107$	1.49493	+	8.47814i	0.144520	+	0.819613i	0.967751	+	0.251907i	$0.0810578\pi$
$107$	1.49493	+	8.47814i	0.144520	+	0.819613i	−0.823232	+	0.567706i	$0.807831\pi$
$108$	−7.13338	+	12.0200i	−0.686410	+	1.15662i
$109$	0.183282	−	1.03944i	0.0175552	−	0.0995604i	−0.974771	−	0.223206i	$-0.928348\pi$
$109$	0.183282	−	1.03944i	0.0175552	−	0.0995604i	0.992326	+	0.123646i	$0.0394587\pi$
$110$	−30.0846	+	23.3173i	−2.86846	+	2.22322i
$111$	5.33229	+	1.14130i	0.506119	+	0.108327i
$112$	−5.07890	+	1.41381i	−0.479911	+	0.133592i
$113$	−2.78607	−	8.14259i	−0.262091	−	0.765990i	−0.996211	−	0.0869702i	$-0.972282\pi$
$113$	−2.78607	−	8.14259i	−0.262091	−	0.765990i	0.734120	−	0.679020i	$-0.237595\pi$
$114$	−16.7003	+	10.5834i	−1.56412	+	0.991223i
$115$	8.29010	+	2.30771i	0.773056	+	0.215195i
$116$	1.15327	+	19.8009i	0.107079	+	1.83847i
$117$	−8.28439	+	3.81510i	−0.765893	+	0.352706i
$118$	−3.10603	+	1.55991i	−0.285933	+	0.143601i
$119$	−8.30140	−	9.51235i	−0.760988	−	0.871996i
$120$	−7.99248	−	5.91962i	−0.729610	−	0.540385i
$121$	−9.90677	+	0.384428i	−0.900615	+	0.0349480i
$122$	7.18041	−	0.278633i	0.650084	−	0.0252262i
$123$	0.0330877	−	0.289263i	0.00298341	−	0.0260820i
$124$	8.57757	+	9.82880i	0.770289	+	0.882653i
$125$	16.3840	−	8.22835i	1.46543	−	0.735966i
$126$	−6.82006	+	14.4455i	−0.607579	+	1.28690i
$127$	1.07426	+	18.4443i	0.0953251	+	1.63667i	0.619456	+	0.785031i	$0.287353\pi$
$127$	1.07426	+	18.4443i	0.0953251	+	1.63667i	−0.524131	+	0.851638i	$0.675610\pi$
$128$	10.8300	+	3.01474i	0.957248	+	0.266468i
$129$	−0.257071	−	6.22856i	−0.0226338	−	0.548394i
$130$	−8.19168	−	23.9411i	−0.718458	−	2.09977i
$131$	18.2849	−	5.08994i	1.59756	−	0.444710i	0.648863	−	0.760905i	$-0.275245\pi$
$131$	18.2849	−	5.08994i	1.59756	−	0.444710i	0.948694	+	0.316195i	$0.102405\pi$
$132$	−6.55556	−	20.2735i	−0.570589	−	1.76458i
$133$	−10.2437	+	7.93950i	−0.888245	+	0.688442i
$134$	−3.55606	+	20.1674i	−0.307197	+	1.74220i
$135$	19.4856	−	4.37192i	1.67706	−	0.376275i
$136$	1.33222	+	7.55540i	0.114237	+	0.647871i
$137$	−2.41185	−	2.18864i	−0.206059	−	0.186988i	0.562443	−	0.826836i	$-0.309862\pi$
$137$	−2.41185	−	2.18864i	−0.206059	−	0.186988i	−0.768502	+	0.639848i	$0.778997\pi$
$138$	−4.86693	+	6.84481i	−0.414301	+	0.582669i
$139$	−13.4445	−	6.11127i	−1.14035	−	0.518351i	−0.247578	−	0.968868i	$-0.579635\pi$
$139$	−13.4445	−	6.11127i	−1.14035	−	0.518351i	−0.892768	+	0.450517i	$0.851240\pi$
$140$	−21.7630	−	13.1341i	−1.83931	−	1.11003i
$141$	4.89481	−	10.8392i	0.412218	−	0.912823i
$142$	7.23106	−	15.1225i	0.606817	−	1.26905i
$143$	3.98758	−	13.3194i	0.333458	−	1.11383i
$144$	−5.35672	+	3.56112i	−0.446394	+	0.296760i
$145$	19.4471	−	20.6127i	1.61499	−	1.71179i
$146$	20.9299	−	25.9490i	1.73217	−	2.14755i
$147$	0.561502	−	1.55462i	0.0463119	−	0.128223i
$148$	−6.69366	−	5.18798i	−0.550215	−	0.426449i
$149$	8.71810	−	7.91125i	0.714214	−	0.648115i	−0.231604	−	0.972810i	$-0.574397\pi$
$149$	8.71810	−	7.91125i	0.714214	−	0.648115i	0.945819	+	0.324695i	$0.105262\pi$
$150$	4.34436	+	36.3904i	0.354716	+	2.97127i
$151$	4.42591	−	2.67105i	0.360176	−	0.217367i	−0.325052	−	0.945696i	$-0.605382\pi$
$151$	4.42591	−	2.67105i	0.360176	−	0.217367i	0.685228	+	0.728329i	$0.259703\pi$
$152$	7.82229	−	0.914294i	0.634471	−	0.0741590i
$153$	−13.2277	−	7.89426i	−1.06939	−	0.638213i
$154$	−9.64516	−	22.3600i	−0.777229	−	1.80182i
$155$	1.80441	−	18.5510i	0.144934	−	1.49005i
$156$	14.1626	+	0.239770i	1.13392	+	0.0191969i
$157$	−6.40651	+	16.5933i	−0.511295	+	1.32429i	0.401497	+	0.915861i	$0.368490\pi$
$157$	−6.40651	+	16.5933i	−0.511295	+	1.32429i	−0.912791	+	0.408426i	$0.866078\pi$
$158$	−10.4553	+	15.2442i	−0.831779	+	1.21276i
$159$	−1.17310	−	0.398160i	−0.0930326	−	0.0315761i
$160$	−13.6692	−	25.9503i	−1.08064	−	2.05155i
$161$	−2.75272	+	4.76785i	−0.216945	+	0.375759i
$162$	−2.44720	+	19.3364i	−0.192270	+	1.51921i
$163$	0.785270	+	1.36013i	0.0615071	+	0.106533i	0.895139	−	0.445787i	$-0.147076\pi$
$163$	0.785270	+	1.36013i	0.0615071	+	0.106533i	−0.833632	+	0.552320i	$0.813743\pi$
$164$	−0.241096	+	0.382525i	−0.0188264	+	0.0298702i
$165$	−14.6414	+	26.6903i	−1.13983	+	2.07783i
$166$	14.2343	+	29.7686i	1.10480	+	2.31049i
$167$	1.56652	−	0.244999i	0.121221	−	0.0189586i	−0.0936173	−	0.995608i	$-0.529843\pi$
$167$	1.56652	−	0.244999i	0.121221	−	0.0189586i	0.214838	+	0.976650i	$0.431078\pi$
$168$	4.94298	−	4.00705i	0.381359	−	0.309150i
$169$	−3.05659	−	2.18472i	−0.235122	−	0.168055i
$170$	25.5205	−	34.2800i	1.95733	−	2.62915i
$171$	−8.87955	+	13.0845i	−0.679036	+	1.00060i
$172$	−3.83460	+	8.88960i	−0.292385	+	0.677826i
$173$	2.99455	+	1.65233i	0.227672	+	0.125624i	0.592848	−	0.805315i	$-0.298004\pi$
$173$	2.99455	+	1.65233i	0.227672	+	0.125624i	−0.365176	+	0.930938i	$0.618991\pi$
$174$	12.4739	+	24.6856i	0.945641	+	1.87141i
$175$	5.08590	+	23.4791i	0.384458	+	1.77486i
$176$	1.32700	−	9.71539i	0.100027	−	0.732325i
$177$	−1.78161	+	2.13390i	−0.133914	+	0.160393i
$178$	4.52102	+	11.7097i	0.338865	+	0.877681i
$179$	−12.6715	−	3.00319i	−0.947110	−	0.224469i	−0.272093	−	0.962271i	$-0.587716\pi$
$179$	−12.6715	−	3.00319i	−0.947110	−	0.224469i	−0.675017	+	0.737802i	$0.735864\pi$
$180$	−30.2130	−	7.00352i	−2.25195	−	0.522012i
$181$	−3.70437	−	3.92641i	−0.275344	−	0.291847i	0.574914	−	0.818214i	$-0.305036\pi$
$181$	−3.70437	−	3.92641i	−0.275344	−	0.291847i	−0.850258	+	0.526366i	$0.823554\pi$
$182$	16.1400	−	1.25450i	1.19637	−	0.0929895i
$183$	5.17878	−	2.49202i	0.382826	−	0.184215i
$184$	2.92915	−	1.61624i	0.215940	−	0.119151i
$185$	1.17139	+	12.0429i	0.0861223	+	0.885415i
$186$	16.4306	+	7.80689i	1.20475	+	0.572429i
$187$	22.3609	−	7.16974i	1.63519	−	0.524303i
$188$	−14.1492	+	11.8726i	−1.03193	+	0.865895i
$189$	−0.401005	+	12.7700i	−0.0291689	+	0.928880i
$190$	−33.6068	−	28.1995i	−2.43809	−	2.04580i
$191$	−5.32130	−	2.17399i	−0.385036	−	0.157304i	0.177413	−	0.984136i	$-0.443227\pi$
$191$	−5.32130	−	2.17399i	−0.385036	−	0.157304i	−0.562449	+	0.826832i	$0.690141\pi$
$192$	20.9965	−	2.92059i	1.51529	−	0.210775i
$193$	4.31355	−	16.7462i	0.310496	−	1.20542i	−0.602723	−	0.797950i	$-0.705918\pi$
$193$	4.31355	−	16.7462i	0.310496	−	1.20542i	0.913219	−	0.407469i	$-0.133589\pi$
$194$	−12.6577	+	14.5041i	−0.908766	+	1.04133i
$195$	−13.6368	−	14.9534i	−0.976553	−	1.07083i
$196$	−1.83268	+	1.79748i	−0.130906	+	0.128391i
$197$	−13.5604	+	8.91883i	−0.966140	+	0.635440i	−0.931416	−	0.363957i	$-0.881426\pi$
$197$	−13.5604	+	8.91883i	−0.966140	+	0.635440i	−0.0347240	+	0.999397i	$0.511055\pi$
$198$	−19.6461	−	22.2892i	−1.39619	−	1.58402i
$199$	0.0611879	−	1.05056i	0.00433750	−	0.0744720i	−0.995445	−	0.0953403i	$-0.969606\pi$
$199$	0.0611879	−	1.05056i	0.00433750	−	0.0744720i	0.999782	+	0.0208684i	$0.00664310\pi$
$200$	4.72598	−	13.8122i	0.334177	−	0.976671i
$201$	3.81643	+	15.9277i	0.269190	+	1.12346i
$202$	15.5508	−	29.5225i	1.09415	−	2.07719i
$203$	9.66712	+	15.3379i	0.678499	+	1.07651i
$204$	13.1953	+	19.9551i	0.923853	+	1.39714i
$205$	0.633921	−	0.124498i	0.0442750	−	0.00869532i
$206$	6.92594	+	4.55526i	0.482553	+	0.317380i
$207$	−1.38969	+	6.57191i	−0.0965901	+	0.456779i
$208$	5.82528	+	2.92556i	0.403910	+	0.202851i
$209$	−6.01287	−	23.3434i	−0.415919	−	1.61470i
$210$	−35.1314	−	4.71035i	−2.42430	−	0.325045i
$211$	−0.450806	−	0.0885354i	−0.0310348	−	0.00609503i	0.177171	−	0.984180i	$-0.443306\pi$
$211$	−0.450806	−	0.0885354i	−0.0310348	−	0.00609503i	−0.208206	+	0.978085i	$0.566762\pi$
$212$	1.37355	+	1.34717i	0.0943360	+	0.0925241i
$213$	0.486824	−	13.3976i	0.0333566	−	0.917988i
$214$	−2.52308	−	18.4722i	−0.172474	−	1.26273i
$215$	12.9981	−	4.73092i	0.886463	−	0.322646i
$216$	4.21816	−	6.51785i	0.287009	−	0.443483i
$217$	11.2053	+	4.07838i	0.760663	+	0.276859i
$218$	−0.483905	+	2.23396i	−0.0327742	+	0.151303i
$219$	7.08706	−	25.7042i	0.478899	−	1.73693i
$220$	38.4631	−	27.4918i	2.59318	−	1.85350i
$221$	−0.302713	+	15.6078i	−0.0203627	+	1.04989i
$222$	−11.4432	−	2.91753i	−0.768019	−	0.195812i
$223$	2.80912	+	4.09579i	0.188112	+	0.274274i	0.907249	−	0.420594i	$-0.138178\pi$
$223$	2.80912	+	4.09579i	0.188112	+	0.274274i	−0.719136	+	0.694869i	$0.755462\pi$
$224$	18.2589	−	4.32744i	1.21997	−	0.289139i
$225$	14.7807	+	25.3119i	0.985378	+	1.68746i
$226$	5.34528	+	17.8545i	0.355563	+	1.18766i
$227$	−10.4903	−	1.64066i	−0.696268	−	0.108894i	−0.203526	−	0.979070i	$-0.565240\pi$
$227$	−10.4903	−	1.64066i	−0.696268	−	0.108894i	−0.492742	+	0.870175i	$0.664005\pi$
$228$	21.2376	−	12.3314i	1.40649	−	0.816668i
$229$	16.3712	−	6.68835i	1.08184	−	0.441979i	0.234000	−	0.972237i	$-0.424819\pi$
$229$	16.3712	−	6.68835i	1.08184	−	0.441979i	0.847836	+	0.530258i	$0.177905\pi$
$230$	−17.7460	−	5.69001i	−1.17013	−	0.375188i
$231$	−14.1994	−	13.3304i	−0.934250	−	0.877078i
$232$	−0.213636	−	11.0150i	−0.0140259	−	0.723173i
$233$	−5.99906	−	8.05814i	−0.393012	−	0.527906i	0.560944	−	0.827854i	$-0.310438\pi$
$233$	−5.99906	−	8.05814i	−0.393012	−	0.527906i	−0.953956	+	0.299947i	$0.903031\pi$
$234$	18.2478	−	7.56019i	1.19289	−	0.494225i
$235$	26.2112	+	3.06365i	1.70983	+	0.199851i
$236$	3.93023	−	1.78651i	0.255836	−	0.116292i
$237$	−2.81335	+	14.5141i	−0.182746	+	0.942792i
$238$	17.1654	+	21.2818i	1.11267	+	1.37949i
$239$	−16.9084	−	1.31422i	−1.09371	−	0.0850099i	−0.482060	−	0.876138i	$-0.660111\pi$
$239$	−16.9084	−	1.31422i	−1.09371	−	0.0850099i	−0.611650	+	0.791128i	$0.709494\pi$
$240$	−11.1316	−	8.93328i	−0.718539	−	0.576640i
$241$	−0.148667	−	0.00576895i	−0.00957648	−	0.000371611i	0.0339867	−	0.999422i	$-0.489180\pi$
$241$	−0.148667	−	0.00576895i	−0.00957648	−	0.000371611i	−0.0435632	+	0.999051i	$0.513871\pi$
$242$	21.4705			1.38018
$243$	4.36512	+	14.9648i	0.280023	+	0.959993i
$244$	−8.92552			−0.571398
$245$	3.66489	+	0.142215i	0.234141	+	0.00908575i
$246$	−0.0958918	+	0.623186i	−0.00611384	+	0.0397329i
$247$	15.9768	+	1.24181i	1.01658	+	0.0790147i
$248$	−4.54916	−	5.64007i	−0.288872	−	0.358145i
$249$	19.9263	+	17.3033i	1.26278	+	1.09655i
$250$	−36.1459	+	16.4303i	−2.28606	+	1.03914i
$251$	−6.60999	−	0.772597i	−0.417219	−	0.0487659i	−0.0951060	−	0.995467i	$-0.530319\pi$
$251$	−6.60999	−	0.772597i	−0.417219	−	0.0487659i	−0.322113	+	0.946701i	$0.604393\pi$
$252$	9.16058	−	17.6008i	0.577063	−	1.10875i
$253$	−6.11476	−	8.21355i	−0.384432	−	0.516382i
$254$	−0.775870	−	40.0036i	−0.0486824	−	2.51005i
$255$	7.80055	−	33.2784i	0.488489	−	2.08397i
$256$	0.126181	+	0.0404583i	0.00788630	+	0.00252864i
$257$	−20.0693	+	8.19921i	−1.25189	+	0.511453i	−0.904582	−	0.426299i	$-0.859817\pi$
$257$	−20.0693	+	8.19921i	−1.25189	+	0.511453i	−0.347307	+	0.937752i	$0.612904\pi$
$258$	0.0332701	+	13.5002i	0.00207130	+	0.840483i
$259$	−7.64813	−	1.19615i	−0.475232	−	0.0743249i
$260$	9.01419	+	30.1095i	0.559036	+	1.86731i
$261$	17.0154	+	14.1353i	1.05323	+	0.874954i
$262$	−39.9958	+	9.47918i	−2.47095	+	0.585626i
$263$	−8.18091	−	11.9281i	−0.504456	−	0.735515i	0.485907	−	0.874011i	$-0.338489\pi$
$263$	−8.18091	−	11.9281i	−0.504456	−	0.735515i	−0.990363	+	0.138495i	$0.955773\pi$
$264$	3.20192	+	11.3937i	0.197064	+	0.701231i
$265$	0.0533033	−	2.74830i	0.00327440	−	0.168827i
$266$	22.8341	−	16.3208i	1.40005	−	1.00069i
$267$	7.04723	+	7.14990i	0.431283	+	0.437567i
$268$	5.38499	−	24.8599i	0.328941	−	1.51856i
$269$	−22.3335	−	8.12875i	−1.36170	−	0.495618i	−0.445121	−	0.895471i	$-0.646839\pi$
$269$	−22.3335	−	8.12875i	−1.36170	−	0.495618i	−0.916580	+	0.399852i	$0.869061\pi$
$270$	−42.5339	+	7.82455i	−2.58853	+	0.476187i
$271$	5.73169	−	2.08616i	0.348175	−	0.126725i	−0.162012	−	0.986789i	$-0.551798\pi$
$271$	5.73169	−	2.08616i	0.348175	−	0.126725i	0.510187	+	0.860063i	$0.329576\pi$
$272$	1.48995	+	10.9083i	0.0903412	+	0.661415i
$273$	11.4406	−	6.06234i	0.692416	−	0.366909i
$274$	5.03546	+	4.93874i	0.304203	+	0.298360i
$275$	−43.8449	−	8.61086i	−2.64395	−	0.519255i
$276$	6.37035	−	8.26115i	0.383450	−	0.497263i
$277$	1.50359	+	5.83731i	0.0903421	+	0.350730i	0.997550	−	0.0699522i	$-0.0222847\pi$
$277$	1.50359	+	5.83731i	0.0903421	+	0.350730i	−0.907208	+	0.420682i	$0.861791\pi$
$278$	28.5806	+	14.3537i	1.71415	+	0.860880i
$279$	14.5407	+	0.492483i	0.870530	+	0.0294842i
$280$	11.7964	+	7.75859i	0.704967	+	0.463664i
$281$	12.7212	−	2.49836i	0.758881	−	0.149039i	0.201719	−	0.979443i	$-0.435347\pi$
$281$	12.7212	−	2.49836i	0.758881	−	0.149039i	0.557162	+	0.830404i	$0.311890\pi$
$282$	−11.5025	+	23.0449i	−0.684967	+	1.37230i
$283$	1.51035	+	2.39634i	0.0897811	+	0.142447i	0.887873	−	0.460088i	$-0.152182\pi$
$283$	1.51035	+	2.39634i	0.0897811	+	0.142447i	−0.798092	+	0.602535i	$0.794157\pi$
$284$	−9.70332	+	18.4213i	−0.575786	+	1.09310i
$285$	−33.6380	−	9.98030i	−1.99255	−	0.591182i
$286$	−9.74757	+	28.4884i	−0.576386	+	1.68455i
$287$	−0.0240320	+	0.412613i	−0.00141856	+	0.0243558i
$288$	19.5434	−	11.9263i	1.15160	−	0.702763i
$289$	−7.82484	+	5.14648i	−0.460285	+	0.302734i
$290$	−43.8144	+	42.9728i	−2.57287	+	2.52345i
$291$	−4.66479	+	14.6728i	−0.273455	+	0.860134i
$292$	−27.2273	+	31.1990i	−1.59336	+	1.82579i
$293$	7.21374	−	28.0055i	0.421431	−	1.63610i	−0.307528	−	0.951539i	$-0.599502\pi$
$293$	7.21374	−	28.0055i	0.421431	−	1.63610i	0.728959	−	0.684557i	$-0.240004\pi$
$294$	−1.34563	+	3.31705i	−0.0784789	+	0.193454i
$295$	−5.71008	−	2.33282i	−0.332454	−	0.135822i
$296$	3.60347	+	3.02367i	0.209448	+	0.175747i
$297$	−21.5135	−	10.0923i	−1.24834	−	0.585614i
$298$	−19.5303	+	16.3878i	−1.13136	+	0.949322i
$299$	6.48221	−	2.07844i	0.374876	−	0.120199i
$300$	−3.63942	−	45.3759i	−0.210122	−	2.61978i
$301$	0.856729	+	8.80794i	0.0493810	+	0.507681i
$302$	−9.80195	+	5.40849i	−0.564039	+	0.311224i
$303$	2.00248	−	26.6120i	0.115040	−	1.52882i
$304$	11.2678	−	0.875801i	0.646251	−	0.0502306i
$305$	8.75120	+	9.27573i	0.501092	+	0.531126i
$306$	27.9617	+	18.1939i	1.59846	+	1.04008i
$307$	6.37708	+	1.51140i	0.363959	+	0.0862599i	0.408526	−	0.912746i	$-0.366043\pi$
$307$	6.37708	+	1.51140i	0.363959	+	0.0862599i	−0.0445673	+	0.999006i	$0.514191\pi$
$308$	10.8944	+	28.2171i	0.620763	+	1.60782i
$309$	6.53213	+	1.13520i	0.371600	+	0.0645792i
$310$	−5.46251	+	39.9927i	−0.310250	+	2.27143i
$311$	1.36997	+	6.32447i	0.0776837	+	0.358628i	0.999585	−	0.0287963i	$-0.00916740\pi$
$311$	1.36997	+	6.32447i	0.0776837	+	0.358628i	−0.921902	+	0.387424i	$0.873365\pi$
$312$	−7.85558	−	0.438113i	−0.444734	−	0.0248033i
$313$	−21.5024	−	11.8645i	−1.21539	−	0.670623i	−0.259896	−	0.965637i	$-0.583688\pi$
$313$	−21.5024	−	11.8645i	−1.21539	−	0.670623i	−0.955493	+	0.295013i	$0.904676\pi$
$314$	15.2570	−	35.3698i	0.861004	−	1.99603i
$315$	−27.2730	+	7.73701i	−1.53666	+	0.435931i
$316$	13.7110	−	18.4171i	0.771304	−	1.03604i
$317$	24.6586	+	17.6249i	1.38497	+	0.989915i	0.997689	+	0.0679525i	$0.0216466\pi$
$317$	24.6586	+	17.6249i	1.38497	+	0.989915i	0.387279	+	0.921963i	$0.373415\pi$
$318$	2.50514	+	0.960124i	0.140481	+	0.0538411i
$319$	−33.3161	+	5.21054i	−1.86534	+	0.291734i
$320$	20.2913	+	42.4357i	1.13432	+	2.37223i
$321$	−7.73600	−	12.7474i	−0.431781	−	0.711489i
$322$	6.35724	−	10.0865i	0.354275	−	0.562096i
$323$	13.5326	+	23.4392i	0.752975	+	1.30419i
$324$	3.96869	−	23.8818i	0.220483	−	1.32677i
$325$	14.8522	−	25.7248i	0.823852	−	1.42695i
$326$	−1.58511	−	3.00925i	−0.0877910	−	0.166667i
$327$	0.356724	+	1.79300i	0.0197269	+	0.0991530i
$328$	0.142055	−	0.207122i	0.00784370	−	0.0114364i
$329$	−6.08101	+	15.7502i	−0.335257	+	0.868337i
$330$	33.9251	−	56.5281i	1.86752	−	3.11177i
$331$	−1.89508	+	19.4831i	−0.104163	+	1.07089i	0.786923	+	0.617052i	$0.211673\pi$
$331$	−1.89508	+	19.4831i	−0.104163	+	1.07089i	−0.891085	+	0.453836i	$0.850055\pi$
$332$	−16.2335	−	37.6334i	−0.890928	−	2.06540i
$333$	−9.32424	+	1.50540i	−0.510965	+	0.0824956i
$334$	−3.41051	+	0.398632i	−0.186615	+	0.0218122i
$335$	−31.1151	+	18.7781i	−1.70000	+	1.02596i
$336$	7.31104	−	5.47092i	0.398850	−	0.298463i
$337$	−7.81849	+	7.09490i	−0.425900	+	0.386484i	−0.856574	−	0.516024i	$-0.827412\pi$
$337$	−7.81849	+	7.09490i	−0.425900	+	0.386484i	0.430674	+	0.902507i	$0.358276\pi$
$338$	6.43099	+	4.98439i	0.349800	+	0.271115i
$339$	9.60956	+	11.3951i	0.521920	+	0.618896i
$340$	−33.3263	+	41.3181i	−1.80737	+	2.24079i
$341$	−15.2199	+	16.1321i	−0.824203	+	0.873604i
$342$	20.3141	−	27.5692i	1.09846	−	1.49077i
$343$	−5.60931	+	18.7364i	−0.302874	+	1.01167i
$344$	2.31980	−	4.85144i	0.125075	−	0.261572i
$345$	−14.8312	+	1.47950i	−0.798486	+	0.0796539i
$346$	−6.34145	−	3.82709i	−0.340919	−	0.205745i
$347$	−20.8086	−	9.45868i	−1.11707	−	0.507769i	−0.231758	−	0.972774i	$-0.574448\pi$
$347$	−20.8086	−	9.45868i	−1.11707	−	0.507769i	−0.885308	+	0.465005i	$0.846053\pi$
$348$	−14.2932	−	31.2398i	−0.766198	−	1.67463i
$349$	9.48806	+	8.60995i	0.507884	+	0.460880i	0.885204	−	0.465203i	$-0.154019\pi$
$349$	9.48806	+	8.60995i	0.507884	+	0.460880i	−0.377320	+	0.926083i	$0.623154\pi$
$350$	−9.03426	−	51.2358i	−0.482902	−	2.73867i
$351$	10.9779	−	11.3597i	0.585959	−	0.606337i
$352$	−6.06052	+	34.3709i	−0.323027	+	1.83198i
$353$	10.3697	−	8.03711i	0.551923	−	0.427772i	−0.298088	−	0.954539i	$-0.596349\pi$
$353$	10.3697	−	8.03711i	0.551923	−	0.427772i	0.850010	+	0.526766i	$0.176596\pi$
$354$	4.03458	−	4.46814i	0.214436	−	0.237479i
$355$	28.6579	−	7.97746i	1.52100	−	0.423400i
$356$	−5.04737	−	14.7515i	−0.267510	−	0.781828i
$357$	19.3727	+	10.1436i	1.02531	+	0.536855i
$358$	27.1688	+	7.56296i	1.43592	+	0.399715i
$359$	−1.08524	−	18.6328i	−0.0572767	−	0.983403i	−0.897459	−	0.441098i	$-0.854589\pi$
$359$	−1.08524	−	18.6328i	−0.0572767	−	0.983403i	0.840182	−	0.542304i	$-0.182448\pi$
$360$	16.6184	+	4.53792i	0.875868	+	0.239169i
$361$	7.84914	−	3.94199i	0.413113	−	0.207473i
$362$	7.68654	+	8.80779i	0.403995	+	0.462927i
$363$	15.7507	−	6.84030i	0.826700	−	0.359022i
$364$	−20.0928	+	0.779694i	−1.05315	+	0.0408670i
$365$	59.1187	−	2.29407i	3.09441	−	0.120077i
$366$	−11.4161	+	4.95783i	−0.596730	+	0.259150i
$367$	2.96510	+	3.39762i	0.154777	+	0.177354i	0.825588	−	0.564274i	$-0.190844\pi$
$367$	2.96510	+	3.39762i	0.154777	+	0.177354i	−0.670811	+	0.741629i	$0.734054\pi$
$368$	4.29024	−	2.15464i	0.223644	−	0.112318i
$369$	0.128195	+	0.487720i	0.00667357	+	0.0253897i
$370$	−1.52360	−	26.1592i	−0.0792083	−	1.35995i
$371$	1.69420	+	0.471614i	0.0879586	+	0.0244850i
$372$	−20.0172	−	10.4810i	−1.03784	−	0.543416i
$373$	−6.41113	−	18.7372i	−0.331956	−	0.970177i	−0.978311	−	0.207141i	$-0.933584\pi$
$373$	−6.41113	−	18.7372i	−0.331956	−	0.970177i	0.646356	−	0.763036i	$-0.276292\pi$
$374$	−48.9910	+	13.6376i	−2.53326	+	0.705182i
$375$	−21.2820	+	23.5690i	−1.09900	+	1.21710i
$376$	8.10898	−	6.28494i	0.418189	−	0.324121i
$377$	3.89274	−	22.0768i	0.200486	−	1.13701i
$378$	1.94011	−	27.6005i	0.0997884	−	1.41962i
$379$	−2.86003	−	16.2201i	−0.146910	−	0.833169i	−0.965814	−	0.259237i	$-0.916529\pi$
$379$	−2.86003	−	16.2201i	−0.146910	−	0.833169i	0.818904	−	0.573931i	$-0.194582\pi$
$380$	40.3536	+	36.6189i	2.07009	+	1.87851i
$381$	−13.3140	−	29.0995i	−0.682095	−	1.49081i
$382$	11.3327	+	5.15135i	0.579832	+	0.263566i
$383$	11.0963	+	6.69666i	0.566995	+	0.342183i	0.771049	−	0.636776i	$-0.219733\pi$
$383$	11.0963	+	6.69666i	0.566995	+	0.342183i	−0.204053	+	0.978960i	$0.565412\pi$
$384$	−19.3752	+	1.93280i	−0.988737	+	0.0986326i
$385$	18.6426	−	38.9878i	0.950117	−	1.98700i
$386$	−10.7407	+	35.8765i	−0.546689	+	1.82607i
$387$	4.32543	+	9.89311i	0.219874	+	0.502895i
$388$	16.4088	−	17.3924i	0.833033	−	0.882963i
$389$	−11.3821	+	14.1116i	−0.577097	+	0.715488i	−0.979831	−	0.199829i	$-0.935961\pi$
$389$	−11.3821	+	14.1116i	−0.577097	+	0.715488i	0.402733	+	0.915317i	$0.368060\pi$
$390$	28.2544	+	33.5042i	1.43071	+	1.69655i
$391$	9.08721	+	7.04312i	0.459560	+	0.356186i
$392$	1.05591	−	0.958192i	0.0533318	−	0.0483960i
$393$	−26.3209	+	19.6962i	−1.32772	+	0.993543i
$394$	30.0936	−	18.1616i	1.51610	−	0.914968i
$395$	−32.5829	+	3.80839i	−1.63942	+	0.191621i
$396$	23.3106	+	28.6109i	1.17140	+	1.43775i
$397$	−11.4404	−	26.5218i	−0.574176	−	1.33109i	−0.919679	−	0.392671i	$-0.871551\pi$
$397$	−11.4404	−	26.5218i	−0.574176	−	1.33109i	0.345503	−	0.938418i	$-0.387708\pi$
$398$	−0.220629	+	2.26826i	−0.0110591	+	0.113698i
$399$	11.5514	−	19.2477i	0.578295	−	0.963590i
$400$	7.54547	−	19.5433i	0.377274	−	0.977163i
$401$	13.8126	−	20.1393i	0.689770	−	1.00571i	−0.308740	−	0.951146i	$-0.599907\pi$
$401$	13.8126	−	20.1393i	0.689770	−	1.00571i	0.998510	−	0.0545628i	$-0.0173765\pi$
$402$	−6.92123	−	34.7880i	−0.345200	−	1.73507i
$403$	−6.87139	−	13.0450i	−0.342288	−	0.649818i
$404$	−20.7231	+	35.8934i	−1.03101	+	1.78576i
$405$	−28.7101	+	19.2910i	−1.42661	+	0.958578i
$406$	−19.6316	−	34.0030i	−0.974301	−	1.68754i
$407$	7.67705	−	12.1805i	0.380537	−	0.603764i
$408$	−6.89403	−	11.3600i	−0.341305	−	0.562403i
$409$	−9.33332	−	19.5190i	−0.461503	−	0.965151i	−0.993003	−	0.118093i	$-0.962322\pi$
$409$	−9.33332	−	19.5190i	−0.461503	−	0.965151i	0.531500	−	0.847059i	$-0.321629\pi$
$410$	−1.38226	+	0.216181i	−0.0682648	+	0.0106764i
$411$	5.26745	+	2.01881i	0.259824	+	0.0995805i
$412$	−8.37686	−	5.98742i	−0.412698	−	0.294979i
$413$	2.35654	−	3.16539i	0.115958	−	0.155759i
$414$	3.55914	−	14.1049i	0.174922	−	0.693217i
$415$	−23.1936	+	53.7688i	−1.13853	+	2.63941i
$416$	−20.3146	−	11.2091i	−0.996005	−	0.549572i
$417$	25.5397	+	1.42437i	1.25068	+	0.0697519i
$418$	11.0516	+	51.0199i	0.540552	+	2.49547i
$419$	−2.31927	+	16.9801i	−0.113304	+	0.829532i	0.843156	+	0.537669i	$0.180695\pi$
$419$	−2.31927	+	16.9801i	−0.113304	+	0.829532i	−0.956460	+	0.291863i	$0.905725\pi$
$420$	43.3771	+	7.53838i	2.11659	+	0.367835i
$421$	3.71722	+	9.62783i	0.181166	+	0.469232i	0.993482	−	0.113985i	$-0.0363616\pi$
$421$	3.71722	+	9.62783i	0.181166	+	0.469232i	−0.812316	+	0.583217i	$0.801794\pi$
$422$	0.968108	+	0.229446i	0.0471268	+	0.0111692i
$423$	−1.09638	+	20.5703i	−0.0533079	+	1.00016i
$424$	−0.733354	−	0.777310i	−0.0356148	−	0.0377495i
$425$	50.0181	−	3.88772i	2.42624	−	0.188582i
$426$	−2.17852	+	28.9515i	−0.105550	+	1.40270i
$427$	−7.14333	+	3.94152i	−0.345690	+	0.190744i
$428$	2.24189	+	23.0486i	0.108366	+	1.11410i
$429$	1.92531	+	24.0045i	0.0929547	+	1.15895i
$430$	−28.5251	+	9.14620i	−1.37560	+	0.441069i
$431$	20.0741	−	16.8442i	0.966936	−	0.811356i	−0.0151314	−	0.999886i	$-0.504817\pi$
$431$	20.0741	−	16.8442i	0.966936	−	0.811356i	0.982067	+	0.188530i	$0.0603722\pi$
$432$	6.41138	−	9.11166i	0.308468	−	0.438385i
$433$	22.4849	+	18.8671i	1.08055	+	0.906693i	0.995967	−	0.0897232i	$-0.0285982\pi$
$433$	22.4849	+	18.8671i	1.08055	+	0.906693i	0.0845877	+	0.996416i	$0.473043\pi$
$434$	−23.9057	−	9.76654i	−1.14751	−	0.468809i
$435$	−18.4515	+	45.4837i	−0.884680	+	2.18078i
$436$	0.708202	−	2.74941i	0.0339167	−	0.131673i
$437$	7.76018	−	8.89218i	0.371220	−	0.425370i
$438$	−17.4948	+	55.0287i	−0.835935	+	2.62938i
$439$	−16.6032	+	16.2843i	−0.792430	+	0.777209i	−0.978701	−	0.205289i	$-0.934187\pi$
$439$	−16.6032	+	16.2843i	−0.792430	+	0.777209i	0.186272	+	0.982498i	$0.440359\pi$
$440$	−21.9405	+	14.4305i	−1.04597	+	0.687946i
$441$	0.0696237	+	2.86209i	0.00331542	+	0.136290i
$442$	1.96570	−	33.7498i	0.0934988	−	1.60531i
$443$	3.80064	−	11.1078i	0.180574	−	0.527747i	−0.818320	−	0.574762i	$-0.805094\pi$
$443$	3.80064	−	11.1078i	0.180574	−	0.527747i	0.998894	+	0.0470156i	$0.0149710\pi$
$444$	14.0625	+	4.17229i	0.667374	+	0.198008i
$445$	−10.3815	+	19.7088i	−0.492130	+	0.934287i
$446$	−5.73498	−	9.09916i	−0.271559	−	0.430858i
$447$	−9.10638	+	18.2443i	−0.430717	+	0.862924i
$448$	−29.5292	+	5.79934i	−1.39512	+	0.273993i
$449$	−17.2752	−	11.3621i	−0.815268	−	0.536210i	0.0720326	−	0.997402i	$-0.477051\pi$
$449$	−17.2752	−	11.3621i	−0.815268	−	0.536210i	−0.887300	+	0.461192i	$0.847422\pi$
$450$	−29.8598	−	56.0161i	−1.40760	−	2.64062i
$451$	−0.686967	−	0.345008i	−0.0323480	−	0.0162458i
$452$	−5.77447	−	22.4179i	−0.271608	−	1.05445i
$453$	−5.46762	+	7.09048i	−0.256891	+	0.333140i
$454$	22.5633	+	4.43128i	1.05895	+	0.207970i
$455$	20.5107	+	20.1167i	0.961556	+	0.943087i
$456$	−12.0532	+	6.38694i	−0.564442	+	0.299096i
$457$	2.03134	+	14.8720i	0.0950219	+	0.695683i	0.975246	+	0.221124i	$0.0709726\pi$
$457$	2.03134	+	14.8720i	0.0950219	+	0.695683i	−0.880224	+	0.474559i	$0.842608\pi$
$458$	−35.9887	+	13.0988i	−1.68164	+	0.612068i
$459$	26.3091	+	4.43871i	1.22800	+	0.207181i
$460$	21.7517	+	7.91697i	1.01418	+	0.369131i
$461$	2.03338	−	9.38713i	0.0947040	−	0.437202i	−0.905221	−	0.424941i	$-0.860295\pi$
$461$	2.03338	−	9.38713i	0.0947040	−	0.437202i	0.999925	−	0.0122608i	$-0.00390283\pi$
$462$	29.6080	+	30.0394i	1.37749	+	1.39756i
$463$	−29.3654	+	20.9892i	−1.36473	+	0.975449i	−0.365729	+	0.930722i	$0.619180\pi$
$463$	−29.3654	+	20.9892i	−1.36473	+	0.975449i	−0.998999	+	0.0447273i	$0.985758\pi$
$464$	0.306578	−	15.8071i	0.0142325	−	0.733826i
$465$	8.73399	+	31.0789i	0.405029	+	1.44125i
$466$	12.3053	+	17.9415i	0.570031	+	0.831126i
$467$	1.82979	−	0.433668i	0.0846725	−	0.0200678i	−0.188061	−	0.982157i	$-0.560220\pi$
$467$	1.82979	−	0.433668i	0.0846725	−	0.0200678i	0.272734	+	0.962090i	$0.412072\pi$
$468$	−23.0127	+	8.50461i	−1.06376	+	0.393126i
$469$	−6.66841	−	22.2741i	−0.307919	−	1.02852i
$470$	−56.4637	−	8.83076i	−2.60447	−	0.407332i
$471$	−0.0759239	−	30.8080i	−0.00349839	−	1.41956i
$472$	−2.21989	+	0.906926i	−0.102179	+	0.0417446i
$473$	−15.6735	−	5.02552i	−0.720671	−	0.231074i
$474$	7.30686	−	31.1722i	0.335615	−	1.43179i
$475$	−0.998658	−	51.4906i	−0.0458216	−	2.36255i
$476$	−20.2802	−	27.2410i	−0.929541	−	1.24859i
$477$	2.14366	−	0.0937674i	0.0981513	−	0.00429331i
$478$	36.4792	+	4.26381i	1.66852	+	0.195022i
$479$	29.8962	−	13.5895i	1.36599	−	0.620919i	0.409400	−	0.912355i	$-0.365738\pi$
$479$	29.8962	−	13.5895i	1.36599	−	0.620919i	0.956590	+	0.291436i	$0.0941331\pi$
$480$	38.3579	+	33.3087i	1.75079	+	1.52033i
$481$	6.00916	+	7.45019i	0.273994	+	0.339699i
$482$	0.321230	+	0.0249680i	0.0146316	+	0.00113726i
$483$	1.45022	−	9.42477i	0.0659874	−	0.428842i
$484$	−26.6485	−	1.03408i	−1.21130	−	0.0470038i
$485$	−34.1631			−1.55127
$486$	−8.18947	−	32.7503i	−0.371482	−	1.48559i
$487$	−2.03399			−0.0921691			−0.0460845	−	0.998938i	$-0.514674\pi$
$487$	−2.03399			−0.0921691			−0.0460845	+	0.998938i	$0.514674\pi$
$488$	4.95397	+	0.192237i	0.224256	+	0.00870215i
$489$	−2.12155	−	1.70259i	−0.0959400	−	0.0769936i
$490$	−7.91887	−	0.615503i	−0.357738	−	0.0278056i
$491$	−15.8613	−	19.6649i	−0.715811	−	0.887466i	0.281589	−	0.959535i	$-0.409138\pi$
$491$	−15.8613	−	19.6649i	−0.715811	−	0.887466i	−0.997400	+	0.0720693i	$0.977040\pi$
$492$	0.149033	−	0.768861i	0.00671890	−	0.0346629i
$493$	34.4678	−	15.6675i	1.55235	−	0.705631i
$494$	−34.4694	−	4.02889i	−1.55085	−	0.181269i
$495$	6.87814	−	52.2773i	0.309149	−	2.34969i
$496$	−6.20950	−	8.34080i	−0.278815	−	0.374513i
$497$	0.369048	+	19.0280i	0.0165541	+	0.853524i
$498$	−41.6674	−	39.1176i	−1.86716	−	1.75290i
$499$	−20.4145	−	6.54564i	−0.913878	−	0.293023i	−0.189062	−	0.981965i	$-0.560545\pi$
$499$	−20.4145	−	6.54564i	−0.913878	−	0.293023i	−0.724817	+	0.688942i	$0.758076\pi$
$500$	45.6544	−	18.6519i	2.04173	−	0.834138i
$501$	−2.37495	+	1.37899i	−0.106105	+	0.0616089i
$502$	14.2391	+	2.22696i	0.635523	+	0.0993939i
$503$	7.47943	+	24.9830i	0.333491	+	1.11394i	0.946187	+	0.323619i	$0.104900\pi$
$503$	7.47943	+	24.9830i	0.333491	+	1.11394i	−0.612696	+	0.790318i	$0.709915\pi$
$504$	−5.46352	+	9.57174i	−0.243365	+	0.426359i
$505$	57.6200	−	13.6562i	2.56406	−	0.607693i
$506$	12.5426	+	18.2876i	0.557587	+	0.812981i
$507$	6.30575	+	1.60770i	0.280048	+	0.0714003i
$508$	−0.963710	+	49.6887i	−0.0427577	+	2.20458i
$509$	−21.2141	+	15.1629i	−0.940297	+	0.672084i	−0.944710	−	0.327907i	$-0.893657\pi$
$509$	−21.2141	+	15.1629i	−0.940297	+	0.672084i	0.00441360	+	0.999990i	$0.498595\pi$
$510$	−19.6748	+	71.3592i	−0.871217	+	3.15984i
$511$	−8.01320	+	36.9930i	−0.354483	+	1.63648i
$512$	−21.3973	−	7.78800i	−0.945638	−	0.344184i
$513$	6.11911	−	26.6966i	0.270165	−	1.17868i
$514$	44.1184	−	16.0578i	1.94598	−	0.708279i
$515$	1.99091	+	14.5760i	0.0877298	+	0.642296i
$516$	0.608915	−	16.7576i	0.0268060	−	0.737711i
$517$	−22.4188	−	21.9882i	−0.985978	−	0.967040i
$518$	16.4501	+	3.23069i	0.722775	+	0.141948i
$519$	−5.87136	−	0.787222i	−0.257724	−	0.0345552i
$520$	−4.35469	−	16.9059i	−0.190966	−	0.741375i
$521$	5.14125	+	2.58203i	0.225242	+	0.113121i	0.557842	−	0.829947i	$-0.311630\pi$
$521$	5.14125	+	2.58203i	0.225242	+	0.113121i	−0.332600	+	0.943068i	$0.607926\pi$
$522$	−35.6343	−	32.0176i	−1.55967	−	1.40137i
$523$	19.7381	+	12.9819i	0.863086	+	0.567661i	0.902075	−	0.431579i	$-0.142043\pi$
$523$	19.7381	+	12.9819i	0.863086	+	0.567661i	−0.0389890	+	0.999240i	$0.512414\pi$
$524$	50.0981	−	9.83895i	2.18855	−	0.429817i
$525$	−22.9508	−	34.7084i	−1.00165	−	1.51480i
$526$	16.7018	+	26.4992i	0.728234	+	1.15542i
$527$	11.6054	−	22.0322i	0.505538	−	0.959740i
$528$	3.95745	+	16.5163i	0.172226	+	0.718779i
$529$	−5.82285	+	17.0179i	−0.253167	+	0.739910i
$530$	−0.346131	+	5.94284i	−0.0150350	+	0.258141i
$531$	1.53626	−	4.56320i	0.0666681	−	0.198026i
$532$	−29.1271	+	19.1572i	−1.26282	+	0.830568i
$533$	0.364851	−	0.357843i	0.0158034	−	0.0154999i
$534$	−14.6498	−	16.0641i	−0.633958	−	0.695163i
$535$	21.7549	−	24.9283i	0.940545	−	1.07775i
$536$	−3.52429	+	13.6821i	−0.152226	+	0.590978i
$537$	22.3405	−	3.10755i	0.964065	−	0.134101i
$538$	47.6471	+	19.4660i	2.05421	+	0.839238i
$539$	−3.34322	−	2.80530i	−0.144003	−	0.120833i
$540$	53.1687	−	7.66303i	2.28801	−	0.329764i
$541$	0.491299	−	0.412249i	0.0211226	−	0.0177240i	−0.632165	−	0.774834i	$-0.717834\pi$
$541$	0.491299	−	0.412249i	0.0211226	−	0.0177240i	0.653288	+	0.757110i	$0.273389\pi$
$542$	−12.5785	+	4.03314i	−0.540294	+	0.173238i
$543$	8.44492	+	4.01254i	0.362406	+	0.172194i
$544$	−3.79369	−	39.0025i	−0.162653	−	1.67222i
$545$	−3.55166	+	1.95972i	−0.152136	+	0.0839452i
$546$	−25.2665	+	12.1582i	−1.08131	+	0.520322i
$547$	23.1361	−	1.79828i	0.989230	−	0.0768890i	0.427331	−	0.904095i	$-0.359454\pi$
$547$	23.1361	−	1.79828i	0.989230	−	0.0768890i	0.561899	+	0.827206i	$0.310071\pi$
$548$	−6.01199	−	6.37234i	−0.256819	−	0.272213i
$549$	−6.79534	+	7.27413i	−0.290018	+	0.310452i
$550$	94.1572	+	22.3157i	4.01487	+	0.951543i
$551$	−13.9988	−	36.2577i	−0.596368	−	1.54463i
$552$	−3.71369	+	4.44802i	−0.158065	+	0.189320i
$553$	2.84027	−	20.7945i	0.120781	−	0.884270i
$554$	−2.76359	−	12.7582i	−0.117414	−	0.542042i
$555$	−9.45180	−	18.7050i	−0.401207	−	0.793983i
$556$	−34.7821	−	19.1919i	−1.47509	−	0.813919i
$557$	9.14218	−	21.1940i	0.387367	−	0.898017i	−0.607261	−	0.794502i	$-0.707732\pi$
$557$	9.14218	−	21.1940i	0.387367	−	0.898017i	0.994628	−	0.103515i	$-0.0330089\pi$
$558$	−31.4247	−	2.28676i	−1.33031	−	0.0968061i
$559$	6.53417	−	8.77691i	0.276366	−	0.371224i
$560$	16.4839	+	11.7820i	0.696570	+	0.497878i
$561$	−31.5950	+	25.6126i	−1.33394	+	1.08136i
$562$	−27.7383	+	4.33820i	−1.17007	+	0.182996i
$563$	19.2877	+	40.3368i	0.812879	+	1.69999i	0.708785	+	0.705424i	$0.249243\pi$
$563$	19.2877	+	40.3368i	0.812879	+	1.69999i	0.104093	+	0.994568i	$0.466806\pi$
$564$	15.3865	−	28.0486i	0.647889	−	1.18106i
$565$	−17.6358	+	27.9811i	−0.741943	+	1.17717i
$566$	−3.06717	−	5.31249i	−0.128923	−	0.223301i
$567$	−7.37001	−	20.8658i	−0.309511	−	0.876283i
$568$	5.78243	−	10.0155i	0.242625	−	0.420239i
$569$	−10.5512	−	20.0309i	−0.442328	−	0.839739i	−0.999953	−	0.00964629i	$-0.996929\pi$
$569$	−10.5512	−	20.0309i	−0.442328	−	0.839739i	0.557626	−	0.830093i	$-0.311713\pi$
$570$	71.9545	+	24.4220i	3.01384	+	1.02293i
$571$	1.72995	−	2.52233i	0.0723962	−	0.105556i	−0.786786	−	0.617225i	$-0.788257\pi$
$571$	1.72995	−	2.52233i	0.0723962	−	0.105556i	0.859182	+	0.511669i	$0.170973\pi$
$572$	13.4705	−	34.8894i	0.563229	−	1.45880i
$573$	9.95484	+	0.168533i	0.415870	+	0.00704057i
$574$	0.0866534	−	0.890875i	0.00361684	−	0.0371844i
$575$	−8.66499	−	20.0877i	−0.361355	−	0.837715i
$576$	−32.0601	+	17.8967i	−1.33584	+	0.745696i
$577$	−23.2241	+	2.71450i	−0.966830	+	0.113006i	−0.584830	−	0.811156i	$-0.698839\pi$
$577$	−23.2241	+	2.71450i	−0.966830	+	0.113006i	−0.382000	+	0.924162i	$0.624765\pi$
$578$	17.3651	−	10.4799i	0.722293	−	0.435906i
$579$	3.55053	+	29.7409i	0.147555	+	1.23599i
$580$	56.4507	−	51.2263i	2.34399	−	2.12706i
$581$	−29.6111	−	22.9503i	−1.22847	−	0.952139i
$582$	11.3267	−	31.3601i	0.469507	−	1.29992i
$583$	−2.05352	+	2.54597i	−0.0850482	+	0.105443i
$584$	15.7841	−	16.7301i	0.653149	−	0.692297i
$585$	31.4015	+	15.5771i	1.29829	+	0.644034i
$586$	−17.9622	+	59.9979i	−0.742012	+	2.47849i
$587$	−11.1584	+	23.3359i	−0.460557	+	0.963174i	0.532597	+	0.846369i	$0.321216\pi$
$587$	−11.1584	+	23.3359i	−0.460557	+	0.963174i	−0.993155	+	0.116805i	$0.962735\pi$
$588$	1.82992	−	4.05221i	0.0754645	−	0.167110i
$589$	−21.8859	−	13.2082i	−0.901794	−	0.544235i
$590$	12.1607	+	5.52771i	0.500648	+	0.227572i
$591$	16.2906	−	22.9109i	0.670104	−	0.942428i
$592$	4.99901	+	4.53636i	0.205458	+	0.186443i
$593$	5.42563	+	30.7703i	0.222804	+	1.26358i	0.866839	+	0.498588i	$0.166148\pi$
$593$	5.42563	+	30.7703i	0.222804	+	1.26358i	−0.644035	+	0.764996i	$0.722741\pi$
$594$	45.7076	+	23.6462i	1.87541	+	0.970216i
$595$	−8.42577	+	47.7849i	−0.345423	+	1.95899i
$596$	25.0296	−	19.3994i	1.02525	−	0.794632i
$597$	0.560793	+	1.73429i	0.0229517	+	0.0709796i
$598$	−14.2020	+	3.95340i	−0.580764	+	0.161667i
$599$	14.6852	+	42.9192i	0.600022	+	1.75363i	0.655525	+	0.755173i	$0.272447\pi$
$599$	14.6852	+	42.9192i	0.600022	+	1.75363i	−0.0555026	+	0.998459i	$0.517676\pi$
$600$	1.04270	+	25.2636i	0.0425681	+	1.03138i
$601$	−26.7554	−	7.44786i	−1.09137	−	0.303805i	−0.324684	−	0.945823i	$-0.605258\pi$
$601$	−26.7554	−	7.44786i	−1.09137	−	0.303805i	−0.766690	+	0.642018i	$0.778097\pi$
$602$	−1.11433	−	19.1323i	−0.0454167	−	0.779774i
$603$	−16.1606	−	23.3155i	−0.658109	−	0.949479i
$604$	12.4264	−	6.24076i	0.505622	−	0.253933i
$605$	25.0534	+	28.7080i	1.01856	+	1.16715i
$606$	−6.56805	+	57.4201i	−0.266809	+	2.33253i
$607$	43.0586	−	1.67087i	1.74770	−	0.0678186i	0.855041	−	0.518560i	$-0.173532\pi$
$607$	43.0586	−	1.67087i	1.74770	−	0.0678186i	0.892655	+	0.450742i	$0.148840\pi$
$608$	−40.1962	+	1.55979i	−1.63017	+	0.0632580i
$609$	−25.2348	−	18.6901i	−1.02257	−	0.757362i
$610$	−18.1586	−	20.8075i	−0.735222	−	0.842471i
$611$	18.6552	−	9.36898i	0.754708	−	0.379028i
$612$	−33.8289	−	23.9284i	−1.36745	−	0.967249i
$613$	−1.55331	−	26.6692i	−0.0627375	−	1.07716i	−0.871934	−	0.489623i	$-0.837134\pi$
$613$	−1.55331	−	26.6692i	−0.0627375	−	1.07716i	0.809197	−	0.587538i	$-0.199903\pi$
$614$	−13.6731	−	3.80616i	−0.551800	−	0.153604i
$615$	−0.945150	+	0.598965i	−0.0381121	+	0.0241526i
$616$	−5.43900	−	15.8961i	−0.219144	−	0.640472i
$617$	−27.6634	+	7.70064i	−1.11369	+	0.310016i	−0.775680	−	0.631127i	$-0.782593\pi$
$617$	−27.6634	+	7.70064i	−1.11369	+	0.310016i	−0.338008	+	0.941143i	$0.609753\pi$
$618$	−14.0402	−	3.00509i	−0.564778	−	0.120882i
$619$	12.7334	−	9.86911i	0.511798	−	0.396673i	−0.323706	−	0.946158i	$-0.604929\pi$
$619$	12.7334	−	9.86911i	0.511798	−	0.396673i	0.835504	+	0.549484i	$0.185176\pi$
$620$	8.70607	−	49.3746i	0.349644	−	1.98293i
$621$	−1.88270	−	11.4812i	−0.0755500	−	0.460727i
$622$	−2.43352	−	13.8012i	−0.0975752	−	0.553376i
$623$	−10.5538	−	9.57709i	−0.422830	−	0.383698i
$624$	−11.2403	−	1.06536i	−0.449970	−	0.0426485i
$625$	−19.6730	−	8.94248i	−0.786920	−	0.357699i
$626$	45.5349	+	27.4804i	1.81994	+	1.09834i
$627$	24.3619	+	33.9073i	0.972922	+	1.35413i
$628$	−20.6401	+	43.1651i	−0.823629	+	1.72247i
$629$	−4.63642	+	15.4867i	−0.184866	+	0.617496i
$630$	59.6684	−	14.4527i	2.37725	−	0.575808i
$631$	−16.4456	+	17.4313i	−0.654688	+	0.693929i	−0.966631	−	0.256172i	$-0.917539\pi$
$631$	−16.4456	+	17.4313i	−0.654688	+	0.693929i	0.311943	+	0.950101i	$0.399020\pi$
$632$	−8.00674	+	9.92680i	−0.318491	+	0.394867i
$633$	0.783303	−	0.140109i	0.0311335	−	0.00556882i
$634$	−51.8812	−	40.2109i	−2.06046	−	1.59698i
$635$	52.5831	−	47.7167i	2.08670	−	1.89358i
$636$	−3.06306	−	1.31233i	−0.121458	−	0.0520373i
$637$	2.48401	−	1.49911i	0.0984201	−	0.0593968i
$638$	72.5334	−	8.47793i	2.87162	−	0.335645i
$639$	7.62550	+	21.9328i	0.301660	+	0.867650i
$640$	−17.1126	−	39.6715i	−0.676435	−	1.56815i
$641$	−1.33058	+	13.6796i	−0.0525548	+	0.540311i	0.931660	+	0.363332i	$0.118361\pi$
$641$	−1.33058	+	13.6796i	−0.0525548	+	0.540311i	−0.984215	+	0.176979i	$0.943368\pi$
$642$	15.6702	+	28.2349i	0.618455	+	1.11434i
$643$	−3.69430	+	9.56848i	−0.145689	+	0.377344i	−0.986450	−	0.164063i	$-0.947540\pi$
$643$	−3.69430	+	9.56848i	−0.145689	+	0.377344i	0.840761	+	0.541407i	$0.182108\pi$
$644$	−8.37621	+	12.2128i	−0.330069	+	0.481252i
$645$	−18.0121	+	15.7975i	−0.709226	+	0.622025i
$646$	−27.3163	−	51.8586i	−1.07474	−	2.04035i
$647$	−18.0255	+	31.2211i	−0.708655	+	1.22743i	0.256701	+	0.966491i	$0.417364\pi$
$647$	−18.0255	+	31.2211i	−0.708655	+	1.22743i	−0.965356	+	0.260936i	$0.915969\pi$
$648$	−2.71712	+	13.1698i	−0.106739	+	0.517357i
$649$	3.66990	+	6.35645i	0.144056	+	0.249512i
$650$	−34.3003	+	54.4211i	−1.34537	+	2.13457i
$651$	−20.6487	+	0.451390i	−0.809287	+	0.0176914i
$652$	1.82245	+	3.81133i	0.0713727	+	0.149263i
$653$	13.0833	−	2.04620i	0.511991	−	0.0800739i	0.106754	−	0.994285i	$-0.465954\pi$
$653$	13.0833	−	2.04620i	0.511991	−	0.0800739i	0.405237	+	0.914212i	$0.367189\pi$
$654$	−0.621387	−	3.90999i	−0.0242982	−	0.152893i
$655$	−59.3446	−	42.4170i	−2.31879	−	1.65737i
$656$	0.215228	−	0.289101i	0.00840324	−	0.0112875i
$657$	4.69745	+	45.9428i	0.183265	+	1.79240i
$658$	14.4819	−	33.5727i	0.564562	−	1.30880i
$659$	15.5025	+	8.55390i	0.603890	+	0.333213i	0.755421	−	0.655240i	$-0.227433\pi$
$659$	15.5025	+	8.55390i	0.603890	+	0.333213i	−0.151531	+	0.988453i	$0.548420\pi$
$660$	−44.8294	+	68.5270i	−1.74498	+	2.66741i
$661$	8.28664	+	38.2554i	0.322313	+	1.48796i	0.794934	+	0.606696i	$0.207505\pi$
$661$	8.28664	+	38.2554i	0.322313	+	1.48796i	−0.472621	+	0.881266i	$0.656692\pi$
$662$	5.73699	−	42.0022i	0.222974	−	1.63246i
$663$	−9.31032	−	25.3851i	−0.361583	−	0.985875i
$664$	8.19960	+	21.2375i	0.318206	+	0.824174i
$665$	48.4670	+	11.4869i	1.87947	+	0.445442i
$666$	20.3040	−	2.47470i	0.786765	−	0.0958928i
$667$	−11.3299	−	12.0090i	−0.438696	−	0.464990i
$668$	4.25222	−	0.330509i	0.164523	−	0.0127878i
$669$	−7.10609	−	4.84803i	−0.274737	−	0.187436i
$670$	68.9099	−	38.0229i	2.66222	−	1.46895i
$671$	−1.46905	−	15.1032i	−0.0567122	−	0.583053i
$672$	−26.7577	+	18.4490i	−1.03220	+	0.711686i
$673$	−19.2458	+	6.17090i	−0.741869	+	0.237871i	−0.652143	−	0.758096i	$-0.726130\pi$
$673$	−19.2458	+	6.17090i	−0.741869	+	0.237871i	−0.0897259	+	0.995966i	$0.528599\pi$
$674$	17.5150	−	14.6968i	0.674651	−	0.566099i
$675$	−39.7514	−	31.5804i	−1.53003	−	1.21553i
$676$	−7.74188	−	6.49621i	−0.297765	−	0.249854i
$677$	−41.0992	−	16.7909i	−1.57957	−	0.645325i	−0.592494	−	0.805575i	$-0.701856\pi$
$677$	−41.0992	−	16.7909i	−1.57957	−	0.645325i	−0.987076	+	0.160250i	$0.948770\pi$
$678$	−19.8382	−	25.4659i	−0.761881	−	0.978010i
$679$	5.45194	−	21.1657i	0.209226	−	0.812266i
$680$	19.3871	−	22.2152i	0.743463	−	0.851914i
$681$	17.9642	−	3.93766i	0.688389	−	0.150891i
$682$	34.2904	−	33.6318i	1.31305	−	1.28783i
$683$	−17.2751	+	11.3620i	−0.661015	+	0.434756i	−0.835192	−	0.549958i	$-0.814644\pi$
$683$	−17.2751	+	11.3620i	−0.661015	+	0.434756i	0.174178	+	0.984714i	$0.444273\pi$
$684$	−26.5410	+	33.2396i	−1.01482	+	1.27095i
$685$	−0.727795	+	12.4958i	−0.0278076	+	0.477438i
$686$	13.7119	−	40.0745i	0.523522	−	1.53005i
$687$	−22.2282	+	21.0750i	−0.848057	+	0.804060i
$688$	3.59647	−	6.82773i	0.137114	−	0.260305i
$689$	−1.15944	−	1.83957i	−0.0441710	−	0.0700821i
$690$	32.2189	−	1.95622i	1.22655	−	0.0744721i
$691$	26.6873	−	5.24121i	1.01523	−	0.199385i	0.342693	−	0.939447i	$-0.388661\pi$
$691$	26.6873	−	5.24121i	1.01523	−	0.199385i	0.672538	+	0.740063i	$0.265204\pi$
$692$	7.68649	+	5.05548i	0.292196	+	0.192181i
$693$	31.2907	+	12.6040i	1.18863	+	0.478788i
$694$	44.2355	+	22.2159i	1.67916	+	0.843304i
$695$	14.1578	+	54.9639i	0.537035	+	2.08490i
$696$	7.26040	+	17.6470i	0.275205	+	0.668908i
$697$	0.846948	+	0.166335i	0.0320804	+	0.00630039i
$698$	−19.8091	−	19.4286i	−0.749786	−	0.735385i
$699$	14.7432	+	9.24156i	0.557638	+	0.349548i
$700$	8.74537	+	64.0275i	0.330544	+	2.42001i
$701$	21.9153	−	7.97653i	0.827731	−	0.301269i	0.106804	−	0.994280i	$-0.465938\pi$
$701$	21.9153	−	7.97653i	0.827731	−	0.301269i	0.720927	+	0.693011i	$0.243716\pi$
$702$	−24.7101	+	23.6605i	−0.932624	+	0.893009i
$703$	15.5940	+	5.67576i	0.588140	+	0.214065i
$704$	11.8494	−	54.7029i	0.446591	−	2.06169i
$705$	−44.2351	+	11.5106i	−1.66599	+	0.433513i
$706$	−23.1149	+	16.5215i	−0.869939	+	0.621795i
$707$	−0.734638	+	37.8778i	−0.0276289	+	1.42454i
$708$	−5.22280	+	5.35139i	−0.196285	+	0.201118i
$709$	−9.01069	−	13.1379i	−0.338404	−	0.493405i	0.617708	−	0.786408i	$-0.288061\pi$
$709$	−9.01069	−	13.1379i	−0.338404	−	0.493405i	−0.956111	+	0.293003i	$0.905345\pi$
$710$	−62.6854	+	14.8567i	−2.35254	+	0.557563i
$711$	−4.57086	−	25.1958i	−0.171421	−	0.944917i
$712$	2.48375	+	8.29630i	0.0930824	+	0.310917i
$713$	−10.7284	−	1.67789i	−0.401782	−	0.0628375i
$714$	−41.0707	−	23.5774i	−1.53703	−	0.882363i
$715$	−49.4657	+	20.2090i	−1.84991	+	0.755772i
$716$	−33.3568	−	10.6954i	−1.24660	−	0.399707i
$717$	28.1196	−	8.49401i	1.05014	−	0.317215i
$718$	0.783799	+	40.4125i	0.0292511	+	1.50818i
$719$	18.6116	+	24.9997i	0.694095	+	0.932332i	0.999804	−	0.0197932i	$-0.00630078\pi$
$719$	18.6116	+	24.9997i	0.694095	+	0.932332i	−0.305709	+	0.952125i	$0.598893\pi$
$720$	23.5778	+	7.43195i	0.878691	+	0.276972i
$721$	−9.34828	−	1.09266i	−0.348148	−	0.0406927i
$722$	−17.3165	+	7.87133i	−0.644454	+	0.292940i
$723$	0.243609	−	0.0840244i	0.00905991	−	0.00312490i
$724$	−9.11608	−	11.3022i	−0.338796	−	0.420042i
$725$	−71.8272	−	5.58285i	−2.66760	−	0.207342i
$726$	−34.6589	+	13.4797i	−1.28631	+	0.500280i
$727$	−26.9470	−	1.04567i	−0.999410	−	0.0387816i	−0.466126	−	0.884718i	$-0.654351\pi$
$727$	−26.9470	−	1.04567i	−0.999410	−	0.0387816i	−0.533283	+	0.845937i	$0.679042\pi$
$728$	11.1690			0.413951
$729$	−16.4417	−	21.4166i	−0.608953	−	0.793206i
$730$	−128.125			−4.74213
$731$	18.4667	+	0.716591i	0.683014	+	0.0265041i
$732$	14.4081	−	5.60368i	0.532539	−	0.207118i
$733$	−7.15886	−	0.556431i	−0.264419	−	0.0205522i	−0.0554012	−	0.998464i	$-0.517644\pi$
$733$	−7.15886	−	0.556431i	−0.264419	−	0.0205522i	−0.209017	+	0.977912i	$0.567027\pi$
$734$	−6.13115	−	7.60143i	−0.226305	−	0.280574i
$735$	−6.00538	+	2.07135i	−0.221512	+	0.0764027i
$736$	−15.5562	+	7.07114i	−0.573408	+	0.260646i
$737$	42.9527	+	5.02045i	1.58218	+	0.184930i
$738$	−0.236458	−	1.06619i	−0.00870416	−	0.0392469i
$739$	−24.6330	−	33.0879i	−0.906141	−	1.21716i	−0.975596	−	0.219574i	$-0.929533\pi$
$739$	−24.6330	−	33.0879i	−0.906141	−	1.21716i	0.0694545	−	0.997585i	$-0.477874\pi$
$740$	0.631140	+	32.5414i	0.0232012	+	1.19625i
$741$	−26.5703	+	8.02603i	−0.976085	+	0.294844i
$742$	−3.62664	−	1.16284i	−0.133138	−	0.0426891i
$743$	−18.7004	+	7.63996i	−0.686052	+	0.280283i	−0.694303	−	0.719683i	$-0.744287\pi$
$743$	−18.7004	+	7.63996i	−0.686052	+	0.280283i	0.00825087	+	0.999966i	$0.497374\pi$
$744$	10.8845	+	6.24845i	0.399045	+	0.229079i
$745$	−44.7014	−	6.99117i	−1.63773	−	0.256137i
$746$	12.3002	+	41.0856i	0.450344	+	1.50425i
$747$	−43.0297	−	15.4218i	−1.57437	−	0.564253i
$748$	61.4629	−	14.5670i	2.24731	−	0.532622i
$749$	11.9726	+	17.4564i	0.437468	+	0.637843i
$750$	48.0334	−	49.2161i	1.75393	−	1.79712i
$751$	−0.0180183	+	0.929018i	−0.000657496	+	0.0339003i	−0.999997	−	0.00243838i	$-0.999224\pi$
$751$	−0.0180183	+	0.929018i	−0.000657496	+	0.0339003i	0.999340	+	0.0363387i	$0.0115695\pi$
$752$	11.9777	−	8.56117i	0.436783	−	0.312194i
$753$	11.1553	−	2.90275i	0.406522	−	0.105782i
$754$	−10.2777	+	47.4472i	−0.374292	+	1.72793i
$755$	−18.6693	−	6.79507i	−0.679445	−	0.247298i
$756$	−3.73733	+	34.1635i	−0.135925	+	1.24251i
$757$	2.92806	−	1.06573i	0.106422	−	0.0387345i	−0.288260	−	0.957552i	$-0.593077\pi$
$757$	2.92806	−	1.06573i	0.106422	−	0.0387345i	0.394682	+	0.918818i	$0.370855\pi$
$758$	4.82706	+	35.3403i	0.175327	+	1.28362i
$759$	15.0275	+	9.41980i	0.545464	+	0.341917i
$760$	−21.6089	−	21.1939i	−0.783838	−	0.768783i
$761$	45.6842	+	8.97208i	1.65605	+	0.325238i	0.931433	−	0.363913i	$-0.118560\pi$
$761$	45.6842	+	8.97208i	1.65605	+	0.325238i	0.724618	+	0.689151i	$0.242016\pi$
$762$	26.3678	+	64.0892i	0.955204	+	2.32171i
$763$	−0.647350	−	2.51317i	−0.0234357	−	0.0909828i
$764$	−13.8177	−	6.93951i	−0.499907	−	0.251063i
$765$	8.30092	+	58.6173i	0.300120	+	2.11931i
$766$	−23.4500	−	15.4233i	−0.847284	−	0.557268i
$767$	−4.78795	+	0.940322i	−0.172883	+	0.0339531i
$768$	−0.229089	+	0.0139095i	−0.00826655	+	0.000501916i
$769$	23.3086	+	36.9817i	0.840531	+	1.33359i	0.940914	+	0.338645i	$0.109968\pi$
$769$	23.3086	+	36.9817i	0.840531	+	1.33359i	−0.100383	+	0.994949i	$0.532007\pi$
$770$	−43.6165	+	82.8039i	−1.57183	+	2.98404i
$771$	27.2494	−	25.8357i	0.981363	−	0.930450i
$772$	15.0590	−	44.0115i	0.541985	−	1.58401i
$773$	2.76085	−	47.4019i	0.0993008	−	1.70493i	−0.469892	−	0.882724i	$-0.655707\pi$
$773$	2.76085	−	47.4019i	0.0993008	−	1.70493i	0.569193	−	0.822204i	$-0.307256\pi$
$774$	−8.52946	−	21.7719i	−0.306585	−	0.782574i
$775$	−39.5886	+	26.0378i	−1.42206	+	0.935307i
$776$	−9.48207	+	9.29995i	−0.340386	+	0.333849i
$777$	13.0970	−	2.87081i	0.469854	−	0.102990i
$778$	25.8159	−	29.5817i	0.925545	−	1.06056i
$779$	0.221012	−	0.858023i	0.00791859	−	0.0307419i
$780$	−33.4548	−	42.9452i	−1.19787	−	1.53768i
$781$	−32.7684	−	13.3874i	−1.17255	−	0.479038i
$782$	−19.0733	−	16.0044i	−0.682058	−	0.572315i
$783$	−36.3418	−	12.1353i	−1.29875	−	0.433681i
$784$	1.56746	−	1.31526i	0.0559809	−	0.0469735i
$785$	65.0956	−	20.8721i	2.32336	−	0.744956i
$786$	58.6124	−	40.4123i	2.09063	−	1.44146i
$787$	1.63903	+	16.8507i	0.0584250	+	0.600662i	0.978122	+	0.208033i	$0.0667060\pi$
$787$	1.63903	+	16.8507i	0.0584250	+	0.600662i	−0.919697	+	0.392629i	$0.871566\pi$
$788$	−38.2260	+	21.0922i	−1.36174	+	0.751379i
$789$	20.6949	+	14.1188i	0.736756	+	0.502642i
$790$	70.8290	−	5.50527i	2.51998	−	0.195869i
$791$	−14.5212	−	15.3916i	−0.516315	−	0.547262i
$792$	−12.3220	−	16.3821i	−0.437842	−	0.582112i
$793$	9.81590	+	2.32641i	0.348573	+	0.0826133i
$794$	22.5298	+	58.3536i	0.799553	+	2.07089i
$795$	1.63941	+	4.46994i	0.0581440	+	0.158533i
$796$	0.383084	−	2.80467i	0.0135780	−	0.0994089i
$797$	0.718409	+	3.31655i	0.0254474	+	0.117478i	0.988291	−	0.152582i	$-0.0487589\pi$
$797$	0.718409	+	3.31655i	0.0254474	+	0.117478i	−0.962843	+	0.270060i	$0.912956\pi$
$798$	−26.6135	+	40.6819i	−0.942109	+	1.44012i
$799$	30.8702	+	17.0335i	1.09211	+	0.602601i
$800$	−29.5337	+	68.4668i	−1.04417	+	2.42067i
$801$	−15.8650	−	7.11736i	−0.560561	−	0.251480i
$802$	−31.5816	+	42.4215i	−1.11519	+	1.49796i
$803$	−57.2744	−	40.9373i	−2.02117	−	1.44464i
$804$	6.91492	+	43.5112i	0.243870	+	1.53452i
$805$	20.9046	−	3.26942i	0.736790	−	0.115232i
$806$	13.7742	+	28.8063i	0.485176	+	1.01466i
$807$	41.1556	−	0.899679i	1.44874	−	0.0316702i
$808$	12.2751	−	19.4757i	0.431836	−	0.685154i
$809$	22.0049	+	38.1136i	0.773652	+	1.34000i	0.935549	+	0.353196i	$0.114905\pi$
$809$	22.0049	+	38.1136i	0.773652	+	1.34000i	−0.161898	+	0.986808i	$0.551761\pi$
$810$	63.7484	−	39.3348i	2.23989	−	1.38208i
$811$	26.8147	−	46.4444i	0.941591	−	1.63088i	0.179153	−	0.983821i	$-0.442664\pi$
$811$	26.8147	−	46.4444i	0.941591	−	1.63088i	0.762437	−	0.647062i	$-0.224002\pi$
$812$	22.7285	+	43.1490i	0.797613	+	1.51423i
$813$	−7.94269	+	6.96612i	−0.278562	+	0.244312i
$814$	−17.6359	+	25.7138i	−0.618139	+	0.901269i
$815$	2.17402	−	5.63085i	0.0761526	−	0.197240i
$816$	−9.25369	−	16.6734i	−0.323944	−	0.583687i
$817$	1.83659	−	18.8818i	0.0642543	−	0.660592i
$818$	18.5582	+	43.0227i	0.648872	+	1.50425i
$819$	−14.6620	+	16.9689i	−0.512332	+	0.592941i
$820$	1.72603	−	0.201744i	0.0602755	−	0.00704519i
$821$	5.03055	−	3.03595i	0.175568	−	0.105956i	−0.426193	−	0.904632i	$-0.640145\pi$
$821$	5.03055	−	3.03595i	0.175568	−	0.105956i	0.601760	+	0.798677i	$0.294466\pi$
$822$	−11.2292	−	4.81102i	−0.391664	−	0.167804i
$823$	15.7053	−	14.2518i	0.547453	−	0.496787i	−0.350690	−	0.936492i	$-0.614053\pi$
$823$	15.7053	−	14.2518i	0.547453	−	0.496787i	0.898142	+	0.439705i	$0.144917\pi$
$824$	4.52049	+	3.50364i	0.157479	+	0.122055i
$825$	76.1832	−	13.6268i	2.65236	−	0.474425i
$826$	−5.36536	+	6.65200i	−0.186685	+	0.231453i
$827$	6.36098	−	6.74224i	0.221193	−	0.234451i	−0.607269	−	0.794496i	$-0.707735\pi$
$827$	6.36098	−	6.74224i	0.221193	−	0.234451i	0.828462	+	0.560046i	$0.189216\pi$
$828$	−5.09683	+	17.3351i	−0.177127	+	0.602437i
$829$	10.8455	−	36.2265i	0.376680	−	1.25820i	−0.534140	−	0.845396i	$-0.679364\pi$
$829$	10.8455	−	36.2265i	0.376680	−	1.25820i	0.910820	−	0.412804i	$-0.135450\pi$
$830$	54.7060	−	114.408i	1.89887	−	3.97116i
$831$	−6.09200	−	8.47893i	−0.211329	−	0.294131i
$832$	31.8573	+	19.2260i	1.10445	+	0.666542i
$833$	4.46092	+	2.02773i	0.154562	+	0.0702568i
$834$	−55.1482	−	5.22698i	−1.90963	−	0.180996i
$835$	−4.51265	−	4.09501i	−0.156167	−	0.141714i
$836$	−11.2596	−	63.8566i	−0.389423	−	2.20853i
$837$	−23.7817	+	8.33405i	−0.822015	+	0.288067i
$838$	6.44477	−	36.5501i	0.222631	−	1.26260i
$839$	−5.46088	+	4.23250i	−0.188531	+	0.146122i	−0.702493	−	0.711690i	$-0.747930\pi$
$839$	−5.46088	+	4.23250i	−0.188531	+	0.146122i	0.513963	+	0.857812i	$0.328177\pi$
$840$	−23.9134	−	5.11831i	−0.825092	−	0.176598i
$841$	−24.4409	+	6.80358i	−0.842789	+	0.234606i
$842$	−7.23557	−	21.1467i	−0.249354	−	0.728765i
$843$	−18.9667	+	12.0197i	−0.653249	+	0.413980i
$844$	−1.19053	−	0.331408i	−0.0409799	−	0.0114075i
$845$	0.839577	+	14.4150i	0.0288823	+	0.495890i
$846$	4.09992	−	44.4220i	0.140958	−	1.52726i
$847$	−21.7842	+	10.9404i	−0.748512	+	0.375917i
$848$	−1.00835	−	1.15544i	−0.0346269	−	0.0396781i
$849$	−3.94258	−	2.92007i	−0.135309	−	0.100217i
$850$	−108.565	+	4.21283i	−3.72376	+	0.144499i
$851$	7.04405	−	0.273341i	0.241467	−	0.00937001i
$852$	4.09830	−	35.8287i	0.140406	−	1.22747i
$853$	−10.2678	−	11.7656i	−0.351564	−	0.402847i	0.550231	−	0.835013i	$-0.314540\pi$
$853$	−10.2678	−	11.7656i	−0.351564	−	0.402847i	−0.901794	+	0.432165i	$0.857750\pi$
$854$	15.7891	−	7.92959i	0.540292	−	0.271345i
$855$	60.5664	−	5.00804i	2.07133	−	0.171271i
$856$	−0.747907	−	12.8411i	−0.0255629	−	0.438899i
$857$	35.8339	+	9.97504i	1.22406	+	0.340741i	0.819131	−	0.573607i	$-0.194456\pi$
$857$	35.8339	+	9.97504i	1.22406	+	0.340741i	0.404931	+	0.914347i	$0.367296\pi$
$858$	−2.15062	−	52.1074i	−0.0734211	−	1.77892i
$859$	5.67935	+	16.5985i	0.193777	+	0.566334i	0.999669	−	0.0257280i	$-0.00819039\pi$
$859$	5.67935	+	16.5985i	0.193777	+	0.566334i	−0.805892	+	0.592063i	$0.798314\pi$
$860$	35.8450	−	9.97813i	1.22230	−	0.340251i
$861$	−0.220256	−	0.681153i	−0.00750629	−	0.0232136i
$862$	−44.8548	+	34.7651i	−1.52776	+	1.18410i
$863$	−8.02572	+	45.5161i	−0.273199	+	1.54939i	0.471427	+	0.881905i	$0.343739\pi$
$863$	−8.02572	+	45.5161i	−0.273199	+	1.54939i	−0.744626	+	0.667482i	$0.767372\pi$
$864$	−24.0604	+	31.5220i	−0.818553	+	1.07240i
$865$	−2.28252	−	12.9448i	−0.0776081	−	0.440137i
$866$	−47.0729	−	42.7163i	−1.59960	−	1.45156i
$867$	9.40023	−	13.2204i	0.319249	−	0.448988i
$868$	29.2006	+	13.2733i	0.991133	+	0.450525i
$869$	33.4209	+	20.1696i	1.13373	+	0.684207i
$870$	43.7483	−	96.8771i	1.48321	−	3.28444i
$871$	−12.4018	+	25.9362i	−0.420220	+	0.878816i
$872$	−0.452293	+	1.51076i	−0.0153166	+	0.0511609i
$873$	−1.68177	−	26.6144i	−0.0569193	−	0.900760i
$874$	−17.5397	+	18.5910i	−0.593289	+	0.628849i
$875$	28.3018	−	35.0887i	0.956774	−	1.18621i
$876$	24.3644	−	67.4574i	0.823196	−	2.27917i
$877$	−6.66238	−	5.16373i	−0.224973	−	0.174367i	0.493879	−	0.869531i	$-0.335579\pi$
$877$	−6.66238	−	5.16373i	−0.224973	−	0.174367i	−0.718851	+	0.695164i	$0.755332\pi$
$878$	37.2968	−	33.8450i	1.25871	−	1.14221i
$879$	5.93771	+	49.7370i	0.200274	+	1.67759i
$880$	−32.2649	+	19.4720i	−1.08765	+	0.656399i
$881$	−25.7913	+	3.01457i	−0.868929	+	0.101563i	−0.538862	−	0.842394i	$-0.681146\pi$
$881$	−25.7913	+	3.01457i	−0.868929	+	0.101563i	−0.330067	+	0.943957i	$0.607072\pi$
$882$	0.0896726	−	6.19940i	0.00301943	−	0.208745i
$883$	−6.40950	−	14.8589i	−0.215697	−	0.500041i	0.775673	−	0.631135i	$-0.217411\pi$
$883$	−6.40950	−	14.8589i	−0.215697	−	0.500041i	−0.991370	+	0.131093i	$0.958151\pi$
$884$	−4.06526	+	41.7945i	−0.136729	+	1.40570i
$885$	10.6822	+	0.180846i	0.359077	+	0.00607908i
$886$	−9.15732	+	23.7180i	−0.307646	+	0.796823i
$887$	13.2360	−	19.2986i	0.444422	−	0.647983i	−0.536155	−	0.844120i	$-0.680124\pi$
$887$	13.2360	−	19.2986i	0.444422	−	0.647983i	0.980576	+	0.196137i	$0.0628397\pi$
$888$	−7.71528	−	2.61864i	−0.258908	−	0.0878757i
$889$	21.1713	+	40.1927i	0.710062	+	1.34802i
$890$	24.1205	−	41.7780i	0.808522	−	1.40040i
$891$	41.0645	+	2.78484i	1.37571	+	0.0932957i
$892$	6.67984	+	11.5698i	0.223657	+	0.387386i
$893$	19.2985	−	30.6191i	0.645798	−	1.02463i
$894$	21.2382	−	38.7158i	0.710312	−	1.29485i
$895$	21.5903	+	45.1522i	0.721683	+	1.50927i
$896$	27.3094	−	4.27111i	0.912342	−	0.142688i
$897$	−9.15908	+	7.42484i	−0.305813	+	0.247908i
$898$	36.4294	+	26.0382i	1.21566	+	0.868904i
$899$	−21.3542	+	28.6837i	−0.712203	+	0.956655i
$900$	34.3632	+	70.9636i	1.14544	+	2.36545i
$901$	1.45462	−	3.37220i	0.0484605	−	0.112344i
$902$	1.45762	+	0.804282i	0.0485335	+	0.0267796i
$903$	−6.91284	−	13.6804i	−0.230045	−	0.455256i
$904$	2.72220	+	12.5671i	0.0905389	+	0.417974i
$905$	−2.80759	+	20.5552i	−0.0933274	+	0.683277i
$906$	12.4273	−	14.8846i	0.412870	−	0.494509i
$907$	−14.6134	−	37.8497i	−0.485231	−	1.25678i	−0.932107	−	0.362183i	$-0.882031\pi$
$907$	−14.6134	−	37.8497i	−0.485231	−	1.25678i	0.446876	−	0.894596i	$-0.352536\pi$
$908$	−27.7914	−	6.58668i	−0.922290	−	0.218587i
$909$	13.4752	+	44.2159i	0.446944	+	1.46655i
$910$	−42.6958	−	45.2549i	−1.41535	−	1.50018i
$911$	−45.2508	+	3.51717i	−1.49923	+	0.116529i	−0.800704	−	0.599060i	$-0.795541\pi$
$911$	−45.2508	+	3.51717i	−1.49923	+	0.116529i	−0.698522	+	0.715589i	$0.746159\pi$
$912$	−17.6393	+	8.48797i	−0.584094	+	0.281065i
$913$	61.0090	−	33.6634i	2.01910	−	1.11409i
$914$	−3.14696	−	32.3535i	−0.104092	−	1.07016i
$915$	−19.9502	−	9.47920i	−0.659535	−	0.313373i
$916$	45.2990	−	14.5245i	1.49672	−	0.479904i
$917$	35.7499	−	29.9978i	1.18057	−	0.990614i
$918$	−56.5601	−	11.8146i	−1.86676	−	0.389940i
$919$	−3.96779	−	3.32937i	−0.130885	−	0.109826i	0.574995	−	0.818157i	$-0.305004\pi$
$919$	−3.96779	−	3.32937i	−0.130885	−	0.109826i	−0.705880	+	0.708331i	$0.749448\pi$
$920$	−11.9024	−	4.86268i	−0.392411	−	0.160318i
$921$	−11.2432	+	1.56391i	−0.370475	+	0.0515327i
$922$	−5.18849	+	20.1430i	−0.170874	+	0.663373i
$923$	15.4727	−	17.7298i	0.509291	−	0.583583i
$924$	−35.3017	−	38.7099i	−1.16134	−	1.27346i
$925$	21.9610	−	21.5392i	0.722073	−	0.708204i
$926$	65.3092	−	42.9545i	2.14619	−	1.41157i
$927$	−11.2573	+	2.26853i	−0.369737	+	0.0745085i
$928$	−3.27198	+	56.1777i	−0.107408	+	1.84412i
$929$	9.27840	−	27.1171i	0.304414	−	0.889684i	−0.682845	−	0.730563i	$-0.739258\pi$
$929$	9.27840	−	27.1171i	0.304414	−	0.889684i	0.987259	−	0.159121i	$-0.0508660\pi$
$930$	−16.2905	−	67.9881i	−0.534188	−	2.22942i
$931$	2.34428	−	4.45051i	0.0768307	−	0.145860i
$932$	−14.4088	−	22.8611i	−0.471977	−	0.748842i
$933$	−6.18215	−	9.34924i	−0.202395	−	0.306080i
$934$	−3.99607	+	0.784803i	−0.130755	+	0.0256795i
$935$	−75.4010	−	49.5920i	−2.46588	−	1.62183i
$936$	12.9560	−	4.22471i	0.423480	−	0.138089i
$937$	−39.3633	−	19.7690i	−1.28594	−	0.645825i	−0.331286	−	0.943530i	$-0.607483\pi$
$937$	−39.3633	−	19.7690i	−1.28594	−	0.645825i	−0.954658	+	0.297705i	$0.903779\pi$
$938$	12.5600	+	48.7609i	0.410099	+	1.59210i
$939$	42.1594	+	5.65266i	1.37582	+	0.184467i
$940$	69.6556	+	13.6799i	2.27192	+	0.446190i
$941$	6.95481	+	6.82123i	0.226720	+	0.222366i	0.804694	−	0.593689i	$-0.202329\pi$
$941$	6.95481	+	6.82123i	0.226720	+	0.222366i	−0.577974	+	0.816055i	$0.696156\pi$
$942$	−2.42274	+	66.6748i	−0.0789371	+	2.17238i
$943$	−0.0509358	−	0.372916i	−0.00165870	−	0.0121438i
$944$	−3.23372	+	1.17698i	−0.105249	+	0.0383073i
$945$	39.1683	−	29.6123i	1.27414	−	0.963287i
$946$	33.4955	+	12.1914i	1.08903	+	0.396375i
$947$	1.40801	−	6.50011i	0.0457542	−	0.211225i	−0.948734	−	0.316077i	$-0.897634\pi$
$947$	1.40801	−	6.50011i	0.0457542	−	0.211225i	0.994488	+	0.104852i	$0.0334368\pi$
$948$	−10.5704	+	38.3381i	−0.343310	+	1.24516i
$949$	38.0753	−	27.2146i	1.23598	−	0.883424i
$950$	−2.16272	+	111.509i	−0.0701679	+	3.61784i
$951$	−50.8709	−	12.9699i	−1.64960	−	0.420577i
$952$	10.6695	+	15.5565i	0.345800	+	0.504189i
$953$	11.8587	−	2.81057i	0.384142	−	0.0910432i	−0.0340077	−	0.999422i	$-0.510827\pi$
$953$	11.8587	−	2.81057i	0.384142	−	0.0910432i	0.418149	+	0.908378i	$0.362679\pi$
$954$	−4.64674	+	0.0229032i	−0.150444	+	0.000741517i
$955$	6.33604	+	21.1638i	0.205029	+	0.684846i
$956$	−45.0715	−	7.04906i	−1.45772	−	0.227983i
$957$	50.5095	−	29.3279i	1.63274	−	0.948035i
$958$	−65.8363	+	26.8971i	−2.12707	+	0.869006i
$959$	−7.62558	−	2.44505i	−0.246243	−	0.0789546i
$960$	−59.3977	−	55.7628i	−1.91705	−	1.79974i
$961$	−0.145058	−	7.47914i	−0.00467928	−	0.241263i
$962$	−12.3782	−	16.6268i	−0.399089	−	0.536069i
$963$	20.4910	+	15.7207i	0.660315	+	0.506593i
$964$	−0.397498	−	0.0464609i	−0.0128026	−	0.00149641i
$965$	−60.5032	+	27.5021i	−1.94767	+	0.885324i
$966$	−3.92970	+	20.2734i	−0.126436	+	0.652286i
$967$	5.92283	+	7.34316i	0.190465	+	0.236140i	0.864590	−	0.502477i	$-0.167578\pi$
$967$	5.92283	+	7.34316i	0.190465	+	0.236140i	−0.674125	+	0.738617i	$0.735479\pi$
$968$	14.7686	+	1.14790i	0.474680	+	0.0368950i
$969$	−36.5609	−	29.3408i	−1.17450	−	0.942562i
$970$	73.9289	+	2.86878i	2.37371	+	0.0921109i
$971$	12.8990			0.413948			0.206974	−	0.978346i	$-0.433638\pi$
$971$	12.8990			0.413948			0.206974	+	0.978346i	$0.433638\pi$
$972$	8.58716	+	41.0431i	0.275433	+	1.31646i
$973$	−36.3122			−1.16412
$974$	4.40155	+	0.170800i	0.141035	+	0.00547280i
$975$	−7.82463	+	50.8511i	−0.250589	+	1.62854i
$976$	7.09313	+	0.551322i	0.227046	+	0.0176474i
$977$	5.78969	+	7.17809i	0.185228	+	0.229647i	0.862463	−	0.506120i	$-0.168921\pi$
$977$	5.78969	+	7.17809i	0.185228	+	0.229647i	−0.677235	+	0.735767i	$0.736822\pi$
$978$	4.44806	+	3.86254i	0.142233	+	0.123510i
$979$	24.1308	−	10.9688i	0.771224	−	0.350564i
$980$	9.79901	+	1.14534i	0.313018	+	0.0365866i
$981$	−1.70154	−	2.67040i	−0.0543259	−	0.0852594i
$982$	32.6725	+	43.8867i	1.04262	+	1.40048i
$983$	0.549338	+	28.3237i	0.0175211	+	0.903386i	0.900723	+	0.434393i	$0.143037\pi$
$983$	0.549338	+	28.3237i	0.0175211	+	0.903386i	−0.883202	+	0.468992i	$0.844617\pi$
$984$	−0.0992778	+	0.423535i	−0.00316486	+	0.0135018i
$985$	59.3992	+	19.0456i	1.89262	+	0.606843i
$986$	−75.9038	+	31.0101i	−2.41727	+	0.987564i
$987$	−0.0720664	−	29.2427i	−0.00229390	−	0.930807i
$988$	42.5883	+	6.66069i	1.35491	+	0.211905i
$989$	−2.31126	−	7.72016i	−0.0734939	−	0.245487i
$990$	−19.2741	+	112.550i	−0.612572	+	3.57708i
$991$	37.2046	−	8.81765i	1.18184	−	0.280102i	0.407702	−	0.913115i	$-0.366330\pi$
$991$	37.2046	−	8.81765i	1.18184	−	0.280102i	0.774141	+	0.633013i	$0.218182\pi$
$992$	20.9338	+	30.5222i	0.664647	+	0.969079i
$993$	−9.17285	−	32.6405i	−0.291092	−	1.03582i
$994$	0.799220	−	41.2076i	0.0253497	−	1.30703i
$995$	−3.29032	+	2.35178i	−0.104310	+	0.0745563i
$996$	49.8323	+	50.5583i	1.57900	+	1.60200i
$997$	10.1347	−	46.7868i	0.320968	−	1.48175i	−0.476919	−	0.878947i	$-0.658246\pi$
$997$	10.1347	−	46.7868i	0.320968	−	1.48175i	0.797887	−	0.602807i	$-0.205951\pi$
$998$	43.6272	+	15.8790i	1.38100	+	0.502641i
$999$	14.1066	−	8.28411i	0.446313	−	0.262098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.4.4	✓	1404
3.2	odd	2		729.2.i.a.64.23		1404
243.61	even	81	inner	243.2.i.a.61.4	yes	1404
243.182	odd	162		729.2.i.a.262.23		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.4.4	✓	1404	1.1	even	1	trivial
243.2.i.a.61.4	yes	1404	243.61	even	81	inner
729.2.i.a.64.23		1404	3.2	odd	2
729.2.i.a.262.23		1404	243.182	odd	162

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.16400 - 0.0839729i) q^{2} +(-1.61426 + 0.627826i) q^{3} +(2.68184 + 0.208449i) q^{4} +(-2.41283 - 2.99144i) q^{5} +(3.54597 - 1.22306i) q^{6} +(2.23840 - 1.01748i) q^{7} +(-1.48402 - 0.173458i) q^{8} +(2.21167 - 2.02695i) q^{9} +(4.97016 + 6.67608i) q^{10} +(0.0886806 + 4.57235i) q^{11} +(-4.46006 + 1.34724i) q^{12} +(-2.89504 - 0.928257i) q^{13} +(-4.92933 + 2.01385i) q^{14} +(5.77304 + 3.31413i) q^{15} +(-2.11839 - 0.331310i) q^{16} +(-1.47266 - 4.91903i) q^{17} +(-4.95625 + 4.20059i) q^{18} +(-5.12892 + 1.21558i) q^{19} +(-5.84727 - 8.52552i) q^{20} +(-2.97456 + 3.04780i) q^{21} +(0.192049 - 9.90199i) q^{22} +(-1.82161 + 1.30201i) q^{23} +(2.50450 - 0.651704i) q^{24} +(-2.06845 + 9.54903i) q^{25} +(6.18690 + 2.25185i) q^{26} +(-2.29764 + 4.66057i) q^{27} +(6.21512 - 2.26212i) q^{28} +(0.997881 + 7.30578i) q^{29} +(-12.2145 - 7.65653i) q^{30} +(3.46233 + 3.39583i) q^{31} +(7.48860 + 1.47071i) q^{32} +(-3.01379 - 7.32528i) q^{33} +(2.77377 + 10.7684i) q^{34} +(-8.44461 - 4.24104i) q^{35} +(6.35386 - 4.97493i) q^{36} +(-2.63039 - 1.73003i) q^{37} +(11.2010 - 2.19981i) q^{38} +(5.25613 - 0.319134i) q^{39} +(3.06181 + 4.85790i) q^{40} +(-0.0783398 + 0.148724i) q^{41} +(6.69286 - 6.34564i) q^{42} +(-1.16516 + 3.40530i) q^{43} +(-0.715275 + 12.2808i) q^{44} +(-11.3999 - 1.72539i) q^{45} +(4.05128 - 2.66457i) q^{46} +(-4.90220 + 4.80805i) q^{47} +(3.62763 - 0.795160i) q^{48} +(-0.627481 + 0.719013i) q^{49} +(5.27798 - 20.4904i) q^{50} +(5.46555 + 7.01602i) q^{51} +(-7.57054 - 3.09290i) q^{52} +(0.547902 + 0.459744i) q^{53} +(5.36343 - 9.89250i) q^{54} +(13.4639 - 11.2976i) q^{55} +(-3.49833 + 1.12169i) q^{56} +(7.51623 - 5.18232i) q^{57} +(-1.54592 - 15.8935i) q^{58} +(1.40523 - 0.775374i) q^{59} +(14.7916 + 10.0913i) q^{60} +(-3.30815 + 0.257130i) q^{61} +(-7.20732 - 7.63931i) q^{62} +(2.88822 - 6.78744i) q^{63} +(-11.9091 - 2.82251i) q^{64} +(4.20842 + 10.9001i) q^{65} +(5.90671 + 16.1050i) q^{66} +(1.27972 - 9.36919i) q^{67} +(-2.92407 - 13.4990i) q^{68} +(2.12311 - 3.24543i) q^{69} +(17.9180 + 9.88671i) q^{70} +(-3.06574 + 7.10719i) q^{71} +(-3.63376 + 2.62441i) q^{72} +(-9.19271 + 12.3480i) q^{73} +(5.54687 + 3.96467i) q^{74} +(-2.65612 - 16.7132i) q^{75} +(-14.0083 + 2.19086i) q^{76} +(4.85076 + 10.1445i) q^{77} +(-11.4010 + 0.249232i) q^{78} +(4.55127 - 7.22108i) q^{79} +(4.12022 + 7.13644i) q^{80} +(0.782955 - 8.96588i) q^{81} +(0.182016 - 0.315260i) q^{82} +(-7.10092 - 13.4808i) q^{83} +(-8.61260 + 7.55366i) q^{84} +(-11.1617 + 16.2742i) q^{85} +(2.80735 - 7.27122i) q^{86} +(-6.19760 - 11.1669i) q^{87} +(0.661504 - 6.80086i) q^{88} +(-2.29572 - 5.32208i) q^{89} +(24.5244 + 4.69102i) q^{90} +(-7.42473 + 0.867826i) q^{91} +(-5.15666 + 3.11206i) q^{92} +(-7.72110 - 3.30801i) q^{93} +(11.0121 - 9.99294i) q^{94} +(16.0115 + 12.4099i) q^{95} +(-13.0119 + 2.32743i) q^{96} +(5.58072 - 6.91900i) q^{97} +(1.41824 - 1.50325i) q^{98} +(9.46405 + 9.93277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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