LMFDB - Embedded newform 81.2.g.a.70.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,2,Mod(4,81)] 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("81.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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: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:	$0.646788256372$
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			70.4
Character	$\chi$	$=$	81.70
Dual form			81.2.g.a.22.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.165895 + 0.175839i) q^{2} +(-1.67219 - 0.451413i) q^{3} +(0.112892 + 1.93827i) q^{4} +(4.21919 + 0.493153i) q^{5} +(0.356785 - 0.219149i) q^{6} +(-1.02960 + 0.517085i) q^{7} +(-0.729927 - 0.612481i) q^{8} +(2.59245 + 1.50970i) q^{9} +(-0.786660 + 0.660086i) q^{10} +(0.782094 - 1.81310i) q^{11} +(0.686186 - 3.29213i) q^{12} +(-3.89722 + 0.923659i) q^{13} +(0.0798824 - 0.266826i) q^{14} +(-6.83269 - 2.72925i) q^{15} +(-3.62807 + 0.424061i) q^{16} +(-0.731666 - 4.14948i) q^{17} +(-0.695540 + 0.205402i) q^{18} +(0.525049 - 2.97770i) q^{19} +(-0.479554 + 8.23363i) q^{20} +(1.95511 - 0.399890i) q^{21} +(0.189067 + 0.438307i) q^{22} +(-1.09019 - 0.547514i) q^{23} +(0.944095 + 1.35368i) q^{24} +(12.6932 + 3.00834i) q^{25} +(0.484116 - 0.838513i) q^{26} +(-3.65358 - 3.69477i) q^{27} +(-1.11849 - 1.93728i) q^{28} +(0.171179 + 0.571777i) q^{29} +(1.61342 - 0.748682i) q^{30} +(1.62541 - 1.06905i) q^{31} +(1.66532 - 2.23691i) q^{32} +(-2.12627 + 2.67880i) q^{33} +(0.851020 + 0.559725i) q^{34} +(-4.59909 + 1.67393i) q^{35} +(-2.63355 + 5.19532i) q^{36} +(-4.95333 - 1.80287i) q^{37} +(0.436492 + 0.586310i) q^{38} +(6.93385 + 0.214723i) q^{39} +(-2.77766 - 2.94414i) q^{40} +(-3.93113 - 4.16676i) q^{41} +(-0.254028 + 0.410124i) q^{42} +(4.35863 + 5.85466i) q^{43} +(3.60257 + 1.31123i) q^{44} +(10.1935 + 7.64819i) q^{45} +(0.277132 - 0.100868i) q^{46} +(0.364825 + 0.239949i) q^{47} +(6.25826 + 0.928649i) q^{48} +(-3.38741 + 4.55008i) q^{49} +(-2.63472 + 1.73288i) q^{50} +(-0.649646 + 7.26902i) q^{51} +(-2.23027 - 7.44961i) q^{52} +(-2.23695 - 3.87450i) q^{53} +(1.25580 - 0.0294951i) q^{54} +(4.19394 - 7.26412i) q^{55} +(1.06824 + 0.253177i) q^{56} +(-2.22216 + 4.74227i) q^{57} +(-0.128938 - 0.0647553i) q^{58} +(3.30053 + 7.65148i) q^{59} +(4.51868 - 13.5517i) q^{60} +(0.613247 - 10.5290i) q^{61} +(-0.0816677 + 0.463161i) q^{62} +(-3.44984 - 0.213870i) q^{63} +(-1.15153 - 6.53063i) q^{64} +(-16.8986 + 1.97517i) q^{65} +(-0.118299 - 0.818281i) q^{66} +(-2.10105 + 7.01801i) q^{67} +(7.96024 - 1.88661i) q^{68} +(1.57585 + 1.40767i) q^{69} +(0.468625 - 1.08640i) q^{70} +(-3.66891 + 3.07858i) q^{71} +(-0.967637 - 2.68980i) q^{72} +(5.52198 + 4.63349i) q^{73} +(1.13875 - 0.571901i) q^{74} +(-19.8674 - 10.7604i) q^{75} +(5.83087 + 0.681531i) q^{76} +(0.132281 + 2.27118i) q^{77} +(-1.18805 + 1.18362i) q^{78} +(-8.64862 + 9.16700i) q^{79} -15.5167 q^{80} +(4.44162 + 7.82765i) q^{81} +1.38483 q^{82} +(7.94414 - 8.42030i) q^{83} +(0.995812 + 3.74440i) q^{84} +(-1.04071 - 17.8683i) q^{85} +(-1.75255 - 0.204844i) q^{86} +(-0.0281361 - 1.03339i) q^{87} +(-1.68136 + 0.844410i) q^{88} +(8.43420 + 7.07713i) q^{89} +(-3.03591 + 0.523622i) q^{90} +(3.53497 - 2.96620i) q^{91} +(0.938159 - 2.17490i) q^{92} +(-3.20058 + 1.05392i) q^{93} +(-0.102715 + 0.0243439i) q^{94} +(3.68374 - 12.3046i) q^{95} +(-3.79451 + 2.98880i) q^{96} +(-6.24523 + 0.729963i) q^{97} +(-0.238125 - 1.35047i) q^{98} +(4.76477 - 3.51964i) 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{20}{27}\right)$

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 $

$2$	−0.165895	+	0.175839i	−0.117306	+	0.124337i	−0.783365	−	0.621562i	$-0.786498\pi$
$2$	−0.165895	+	0.175839i	−0.117306	+	0.124337i	0.666059	+	0.745899i	$0.267980\pi$
$3$	−1.67219	−	0.451413i	−0.965440	−	0.260624i
$3$	−1.67219	−	0.451413i	−0.965440	−	0.260624i
$4$	0.112892	+	1.93827i	0.0564458	+	0.969137i
$5$	4.21919	+	0.493153i	1.88688	+	0.220545i	0.979739	−	0.200280i	$-0.0641851\pi$
$5$	4.21919	+	0.493153i	1.88688	+	0.220545i	0.907142	+	0.420824i	$0.138259\pi$
$6$	0.356785	−	0.219149i	0.145657	−	0.0894672i
$7$	−1.02960	+	0.517085i	−0.389153	+	0.195440i	−0.632608	−	0.774472i	$-0.718015\pi$
$7$	−1.02960	+	0.517085i	−0.389153	+	0.195440i	0.243455	+	0.969912i	$0.421719\pi$
$8$	−0.729927	−	0.612481i	−0.258068	−	0.216545i
$9$	2.59245	+	1.50970i	0.864151	+	0.503233i
$10$	−0.786660	+	0.660086i	−0.248764	+	0.208738i
$11$	0.782094	−	1.81310i	0.235810	−	0.546669i	−0.758684	−	0.651458i	$-0.774157\pi$
$11$	0.782094	−	1.81310i	0.235810	−	0.546669i	0.994494	+	0.104789i	$0.0334167\pi$
$12$	0.686186	−	3.29213i	0.198085	−	0.950356i
$13$	−3.89722	+	0.923659i	−1.08089	+	0.256177i	−0.732221	−	0.681067i	$-0.761516\pi$
$13$	−3.89722	+	0.923659i	−1.08089	+	0.256177i	−0.348674	+	0.937244i	$0.613368\pi$
$14$	0.0798824	−	0.266826i	0.0213495	−	0.0713122i
$15$	−6.83269	−	2.72925i	−1.76419	−	0.704688i
$16$	−3.62807	+	0.424061i	−0.907018	+	0.106015i
$17$	−0.731666	−	4.14948i	−0.177455	−	1.00640i	−0.935272	−	0.353930i	$-0.884845\pi$
$17$	−0.731666	−	4.14948i	−0.177455	−	1.00640i	0.757817	−	0.652467i	$-0.226266\pi$
$18$	−0.695540	+	0.205402i	−0.163940	+	0.0484136i
$19$	0.525049	−	2.97770i	0.120454	−	0.683131i	−0.863450	−	0.504435i	$-0.831701\pi$
$19$	0.525049	−	2.97770i	0.120454	−	0.683131i	0.983904	−	0.178696i	$-0.0571880\pi$
$20$	−0.479554	+	8.23363i	−0.107232	+	1.84110i
$21$	1.95511	−	0.399890i	0.426640	−	0.0872632i
$22$	0.189067	+	0.438307i	0.0403092	+	0.0934473i
$23$	−1.09019	−	0.547514i	−0.227320	−	0.114165i	0.331494	−	0.943457i	$-0.392447\pi$
$23$	−1.09019	−	0.547514i	−0.227320	−	0.114165i	−0.558814	+	0.829293i	$0.688744\pi$
$24$	0.944095	+	1.35368i	0.192713	+	0.276320i
$25$	12.6932	+	3.00834i	2.53863	+	0.601667i
$26$	0.484116	−	0.838513i	0.0949430	−	0.164446i
$27$	−3.65358	−	3.69477i	−0.703132	−	0.711060i
$28$	−1.11849	−	1.93728i	−0.211374	−	0.366111i
$29$	0.171179	+	0.571777i	0.0317871	+	0.106176i	0.972411	−	0.233274i	$-0.0749440\pi$
$29$	0.171179	+	0.571777i	0.0317871	+	0.106176i	−0.940624	+	0.339451i	$0.889759\pi$
$30$	1.61342	−	0.748682i	0.294569	−	0.136690i
$31$	1.62541	−	1.06905i	0.291932	−	0.192007i	−0.395091	−	0.918642i	$-0.629287\pi$
$31$	1.62541	−	1.06905i	0.291932	−	0.192007i	0.687024	+	0.726635i	$0.258917\pi$
$32$	1.66532	−	2.23691i	0.294390	−	0.395434i
$33$	−2.12627	+	2.67880i	−0.370136	+	0.466319i
$34$	0.851020	+	0.559725i	0.145949	+	0.0959920i
$35$	−4.59909	+	1.67393i	−0.777388	+	0.282946i
$36$	−2.63355	+	5.19532i	−0.438924	+	0.865886i
$37$	−4.95333	−	1.80287i	−0.814323	−	0.296389i	−0.0989148	−	0.995096i	$-0.531537\pi$
$37$	−4.95333	−	1.80287i	−0.814323	−	0.296389i	−0.715408	+	0.698706i	$0.753759\pi$
$38$	0.436492	+	0.586310i	0.0708083	+	0.0951121i
$39$	6.93385	+	0.214723i	1.11031	+	0.0343833i
$40$	−2.77766	−	2.94414i	−0.439186	−	0.465510i
$41$	−3.93113	−	4.16676i	−0.613940	−	0.650738i	0.343574	−	0.939126i	$-0.388362\pi$
$41$	−3.93113	−	4.16676i	−0.613940	−	0.650738i	−0.957514	+	0.288387i	$0.906881\pi$
$42$	−0.254028	+	0.410124i	−0.0391973	+	0.0632835i
$43$	4.35863	+	5.85466i	0.664685	+	0.892827i	0.998763	−	0.0497186i	$-0.0158324\pi$
$43$	4.35863	+	5.85466i	0.664685	+	0.892827i	−0.334078	+	0.942545i	$0.608425\pi$
$44$	3.60257	+	1.31123i	0.543108	+	0.197675i
$45$	10.1935	+	7.64819i	1.51956	+	1.14012i
$46$	0.277132	−	0.100868i	0.0408608	−	0.0148721i
$47$	0.364825	+	0.239949i	0.0532152	+	0.0350002i	0.575838	−	0.817564i	$-0.304676\pi$
$47$	0.364825	+	0.239949i	0.0532152	+	0.0350002i	−0.522623	+	0.852564i	$0.675046\pi$
$48$	6.25826	+	0.928649i	0.903302	+	0.134039i
$49$	−3.38741	+	4.55008i	−0.483915	+	0.650011i
$50$	−2.63472	+	1.73288i	−0.372606	+	0.245067i
$51$	−0.649646	+	7.26902i	−0.0909687	+	1.01787i
$52$	−2.23027	−	7.44961i	−0.309282	−	1.03308i
$53$	−2.23695	−	3.87450i	−0.307268	−	0.532204i	0.670496	−	0.741913i	$-0.266081\pi$
$53$	−2.23695	−	3.87450i	−0.307268	−	0.532204i	−0.977764	+	0.209710i	$0.932748\pi$
$54$	1.25580	−	0.0294951i	0.170892	−	0.00401377i
$55$	4.19394	−	7.26412i	0.565511	−	0.979493i
$56$	1.06824	+	0.253177i	0.142749	+	0.0338322i
$57$	−2.22216	+	4.74227i	−0.294332	+	0.628129i
$58$	−0.128938	−	0.0647553i	−0.0169304	−	0.00850279i
$59$	3.30053	+	7.65148i	0.429692	+	0.996138i	0.986240	+	0.165322i	$0.0528664\pi$
$59$	3.30053	+	7.65148i	0.429692	+	0.996138i	−0.556548	+	0.830816i	$0.687874\pi$
$60$	4.51868	−	13.5517i	0.583359	−	1.74952i
$61$	0.613247	−	10.5290i	0.0785182	−	1.34811i	−0.697132	−	0.716943i	$-0.745541\pi$
$61$	0.613247	−	10.5290i	0.0785182	−	1.34811i	0.775650	−	0.631163i	$-0.217422\pi$
$62$	−0.0816677	+	0.463161i	−0.0103718	+	0.0588215i
$63$	−3.44984	−	0.213870i	−0.434638	−	0.0269451i
$64$	−1.15153	−	6.53063i	−0.143941	−	0.816329i
$65$	−16.8986	+	1.97517i	−2.09602	+	0.244989i
$66$	−0.118299	−	0.818281i	−0.0145616	−	0.100723i
$67$	−2.10105	+	7.01801i	−0.256685	+	0.857387i	0.728376	+	0.685178i	$0.240276\pi$
$67$	−2.10105	+	7.01801i	−0.256685	+	0.857387i	−0.985060	+	0.172209i	$0.944910\pi$
$68$	7.96024	−	1.88661i	0.965321	−	0.228785i
$69$	1.57585	+	1.40767i	0.189710	+	0.169464i
$70$	0.468625	−	1.08640i	0.0560115	−	0.129849i
$71$	−3.66891	+	3.07858i	−0.435420	+	0.365361i	−0.833992	−	0.551776i	$-0.813950\pi$
$71$	−3.66891	+	3.07858i	−0.435420	+	0.365361i	0.398572	+	0.917137i	$0.369506\pi$
$72$	−0.967637	−	2.68980i	−0.114037	−	0.316996i
$73$	5.52198	+	4.63349i	0.646298	+	0.542309i	0.905945	−	0.423395i	$-0.139162\pi$
$73$	5.52198	+	4.63349i	0.646298	+	0.542309i	−0.259647	+	0.965704i	$0.583606\pi$
$74$	1.13875	−	0.571901i	0.132377	−	0.0664822i
$75$	−19.8674	−	10.7604i	−2.29409	−	1.24250i
$76$	5.83087	+	0.681531i	0.668847	+	0.0781770i
$77$	0.132281	+	2.27118i	0.0150748	+	0.258825i
$78$	−1.18805	+	1.18362i	−0.134520	+	0.134018i
$79$	−8.64862	+	9.16700i	−0.973046	+	1.03137i	0.0264509	+	0.999650i	$0.491579\pi$
$79$	−8.64862	+	9.16700i	−0.973046	+	1.03137i	−0.999497	+	0.0317183i	$0.989902\pi$
$80$	−15.5167			−1.73482
$81$	4.44162	+	7.82765i	0.493513	+	0.869739i
$82$	1.38483			0.152929
$83$	7.94414	−	8.42030i	0.871983	−	0.924248i	−0.125715	−	0.992066i	$-0.540122\pi$
$83$	7.94414	−	8.42030i	0.871983	−	0.924248i	0.997698	+	0.0678183i	$0.0216038\pi$
$84$	0.995812	+	3.74440i	0.108652	+	0.408547i
$85$	−1.04071	−	17.8683i	−0.112881	−	1.93809i
$86$	−1.75255	−	0.204844i	−0.188983	−	0.0220889i
$87$	−0.0281361	−	1.03339i	−0.00301650	−	0.110791i
$88$	−1.68136	+	0.844410i	−0.179233	+	0.0900144i
$89$	8.43420	+	7.07713i	0.894023	+	0.750174i	0.969013	−	0.247010i	$-0.0794480\pi$
$89$	8.43420	+	7.07713i	0.894023	+	0.750174i	−0.0749899	+	0.997184i	$0.523892\pi$
$90$	−3.03591	+	0.523622i	−0.320013	+	0.0551946i
$91$	3.53497	−	2.96620i	0.370566	−	0.310942i
$92$	0.938159	−	2.17490i	0.0978098	−	0.226749i
$93$	−3.20058	+	1.05392i	−0.331885	+	0.109287i
$94$	−0.102715	+	0.0243439i	−0.0105943	+	0.00251088i
$95$	3.68374	−	12.3046i	0.377944	−	1.26242i
$96$	−3.79451	+	2.98880i	−0.387276	+	0.305043i
$97$	−6.24523	+	0.729963i	−0.634107	+	0.0741165i	−0.427073	−	0.904217i	$-0.640455\pi$
$97$	−6.24523	+	0.729963i	−0.634107	+	0.0741165i	−0.207034	+	0.978334i	$0.566381\pi$
$98$	−0.238125	−	1.35047i	−0.0240543	−	0.136419i
$99$	4.76477	−	3.51964i	0.478878	−	0.353737i
$100$	−4.39803	+	24.9425i	−0.439803	+	2.49425i
$101$	0.235359	−	4.04096i	0.0234191	−	0.402090i	−0.966145	−	0.257999i	$-0.916937\pi$
$101$	0.235359	−	4.04096i	0.0234191	−	0.402090i	0.989564	−	0.144092i	$-0.0460260\pi$
$102$	−1.17040	−	1.32013i	−0.115887	−	0.130712i
$103$	3.28144	+	7.60723i	0.323330	+	0.749563i	0.999913	+	0.0131964i	$0.00420066\pi$
$103$	3.28144	+	7.60723i	0.323330	+	0.749563i	−0.676583	+	0.736366i	$0.736540\pi$
$104$	3.41041	+	1.71277i	0.334418	+	0.167951i
$105$	8.44620	−	0.723045i	0.824264	−	0.0705620i
$106$	1.05239	+	0.249420i	0.102217	+	0.0242258i
$107$	7.95369	−	13.7762i	0.768912	−	1.33179i	−0.169241	−	0.985575i	$-0.554132\pi$
$107$	7.95369	−	13.7762i	0.768912	−	1.33179i	0.938153	−	0.346220i	$-0.112535\pi$
$108$	6.74903	−	7.49875i	0.649426	−	0.721567i
$109$	1.81056	+	3.13598i	0.173420	+	0.300372i	0.939613	−	0.342238i	$-0.111185\pi$
$109$	1.81056	+	3.13598i	0.173420	+	0.300372i	−0.766193	+	0.642610i	$0.777852\pi$
$110$	0.581558	+	1.94254i	0.0554494	+	0.185214i
$111$	7.46909	+	5.25074i	0.708935	+	0.498378i
$112$	3.51619	−	2.31264i	0.332249	−	0.218524i
$113$	−5.67010	+	7.61626i	−0.533398	+	0.716477i	−0.984380	−	0.176055i	$-0.943666\pi$
$113$	−5.67010	+	7.61626i	−0.533398	+	0.716477i	0.450983	+	0.892533i	$0.351074\pi$
$114$	−0.465230	−	1.17746i	−0.0435728	−	0.110279i
$115$	−4.32971	−	2.84770i	−0.403748	−	0.265549i
$116$	−1.08894	+	0.396341i	−0.101105	+	0.0367993i
$117$	−11.4978	−	3.48909i	−1.06297	−	0.322567i
$118$	−1.89297	−	0.688984i	−0.174262	−	0.0634261i
$119$	2.89896	+	3.89398i	0.265747	+	0.356961i
$120$	3.31575	+	6.17704i	0.302685	+	0.563884i
$121$	4.87301	+	5.16509i	0.443001	+	0.469553i
$122$	1.74968	+	1.85455i	0.158409	+	0.167903i
$123$	4.69268	+	8.74219i	0.423125	+	0.788257i
$124$	2.25561	+	3.02981i	0.202560	+	0.272085i
$125$	32.1127	+	11.6881i	2.87225	+	1.04541i
$126$	0.609918	−	0.571135i	0.0543358	−	0.0508807i
$127$	−10.4753	+	3.81269i	−0.929532	+	0.338322i	−0.762024	−	0.647549i	$-0.775794\pi$
$127$	−10.4753	+	3.81269i	−0.929532	+	0.338322i	−0.167508	+	0.985871i	$0.553572\pi$
$128$	5.99929	+	3.94580i	0.530267	+	0.348762i
$129$	−4.64560	−	11.7577i	−0.409022	−	1.03520i
$130$	2.45609	−	3.29911i	0.215414	−	0.289351i
$131$	−10.1355	+	6.66624i	−0.885545	+	0.582432i	−0.908770	−	0.417298i	$-0.862977\pi$
$131$	−10.1355	+	6.66624i	−0.885545	+	0.582432i	0.0232244	+	0.999730i	$0.492607\pi$
$132$	−5.43229	−	3.81888i	−0.472820	−	0.332390i
$133$	0.999133	+	3.33734i	0.0866359	+	0.289384i
$134$	−0.885484	−	1.53370i	−0.0764941	−	0.132492i
$135$	−13.5931	−	17.3907i	−1.16991	−	1.49676i
$136$	−2.00742	+	3.47695i	−0.172135	+	0.298146i
$137$	−0.291152	−	0.0690043i	−0.0248748	−	0.00589543i	0.218160	−	0.975913i	$-0.429995\pi$
$137$	−0.291152	−	0.0690043i	−0.0248748	−	0.00589543i	−0.243034	+	0.970018i	$0.578143\pi$
$138$	−0.508950	+	0.0435692i	−0.0433247	+	0.00370886i
$139$	−5.01291	−	2.51758i	−0.425189	−	0.213538i	0.223319	−	0.974745i	$-0.428311\pi$
$139$	−5.01291	−	2.51758i	−0.425189	−	0.213538i	−0.648509	+	0.761207i	$0.724607\pi$
$140$	−3.76374	−	8.72533i	−0.318094	−	0.737425i
$141$	−0.501741	−	0.565928i	−0.0422542	−	0.0476597i
$142$	0.0673212	−	1.15586i	0.00564947	−	0.0969976i
$143$	−1.37331	+	7.78843i	−0.114842	+	0.651301i
$144$	−10.0458	−	4.37794i	−0.837151	−	0.364829i
$145$	0.440263	+	2.49686i	0.0365619	+	0.207353i
$146$	−1.73082	+	0.202304i	−0.143243	+	0.0167428i
$147$	7.71836	−	6.07948i	0.636600	−	0.501427i
$148$	2.93526	−	9.80445i	0.241277	−	0.805921i
$149$	−13.2590	+	3.14244i	−1.08622	+	0.257438i	−0.734460	−	0.678652i	$-0.762564\pi$
$149$	−13.2590	+	3.14244i	−1.08622	+	0.257438i	−0.351759	+	0.936091i	$0.614416\pi$
$150$	5.18801	−	1.70837i	0.423599	−	0.139487i
$151$	−3.74426	+	8.68017i	−0.304703	+	0.706382i	−0.999923	−	0.0124155i	$-0.996048\pi$
$151$	−3.74426	+	8.68017i	−0.304703	+	0.706382i	0.695219	+	0.718798i	$0.255307\pi$
$152$	−2.20703	+	1.85192i	−0.179014	+	0.150211i
$153$	4.36766	−	11.8619i	0.353105	−	0.958980i
$154$	−0.421306	−	0.353517i	−0.0339498	−	0.0284872i
$155$	7.38513	−	3.70895i	0.593188	−	0.297910i
$156$	0.366581	+	13.4640i	0.0293500	+	1.07798i
$157$	9.06059	+	1.05903i	0.723114	+	0.0845199i	0.469685	−	0.882834i	$-0.344368\pi$
$157$	9.06059	+	1.05903i	0.723114	+	0.0845199i	0.253429	+	0.967354i	$0.418442\pi$
$158$	−0.177149	−	3.04153i	−0.0140932	−	0.241971i
$159$	1.99160	+	7.48870i	0.157944	+	0.593893i
$160$	8.12945	−	8.61672i	0.642690	−	0.681211i
$161$	1.40557			0.110775
$162$	−2.11325	−	0.517562i	−0.166032	−	0.0406635i
$163$	7.94158			0.622033			0.311016	−	0.950405i	$-0.399331\pi$
$163$	7.94158			0.622033			0.311016	+	0.950405i	$0.399331\pi$
$164$	7.63253	−	8.09001i	0.596001	−	0.631724i
$165$	−10.2922	+	10.2538i	−0.801246	+	0.798257i
$166$	0.162719	+	2.79378i	0.0126294	+	0.216839i
$167$	4.41487	+	0.516025i	0.341633	+	0.0399312i	0.285180	−	0.958474i	$-0.407947\pi$
$167$	4.41487	+	0.516025i	0.341633	+	0.0399312i	0.0564535	+	0.998405i	$0.482021\pi$
$168$	−1.67201	−	0.905578i	−0.128999	−	0.0698668i
$169$	2.71797	−	1.36502i	0.209074	−	0.105001i
$170$	3.31459	+	2.78127i	0.254217	+	0.213314i
$171$	5.85659	−	6.92688i	0.447865	−	0.529712i
$172$	−10.8559	+	9.10916i	−0.827753	+	0.694567i
$173$	1.23517	−	2.86344i	0.0939080	−	0.217703i	−0.864787	−	0.502138i	$-0.832547\pi$
$173$	1.23517	−	2.86344i	0.0939080	−	0.217703i	0.958695	+	0.284435i	$0.0918061\pi$
$174$	0.186378	+	0.166488i	0.0141293	+	0.0126214i
$175$	−14.6245	+	3.46606i	−1.10551	+	0.262010i
$176$	−2.06863	+	6.90970i	−0.155929	+	0.520839i
$177$	−2.06513	−	14.2846i	−0.155225	−	1.07370i
$178$	−2.64363	+	0.308996i	−0.198148	+	0.0231602i
$179$	−2.47200	−	14.0194i	−0.184766	−	1.04786i	−0.926255	−	0.376897i	$-0.876991\pi$
$179$	−2.47200	−	14.0194i	−0.184766	−	1.04786i	0.741489	−	0.670965i	$-0.234120\pi$
$180$	−13.6735	+	20.6213i	−1.01916	+	1.53702i
$181$	2.75966	−	15.6508i	0.205124	−	1.16332i	−0.692120	−	0.721783i	$-0.743323\pi$
$181$	2.75966	−	15.6508i	0.205124	−	1.16332i	0.897244	−	0.441535i	$-0.145566\pi$
$182$	−0.0648635	+	1.11366i	−0.00480800	+	0.0825502i
$183$	−5.77842	+	17.3298i	−0.427153	+	1.28105i
$184$	0.460417	+	1.06737i	0.0339424	+	0.0786872i
$185$	−20.0100	−	10.0494i	−1.47116	−	0.738846i
$186$	0.345641	−	0.737628i	0.0253436	−	0.0540855i
$187$	−8.09565	−	1.91870i	−0.592012	−	0.140310i
$188$	−0.423901	+	0.734219i	−0.0309162	+	0.0535484i
$189$	5.67224	+	1.91493i	0.412595	+	0.139291i
$190$	1.55250	+	2.68901i	0.112630	+	0.195082i
$191$	−5.82426	−	19.4544i	−0.421429	−	1.40767i	−0.860607	−	0.509270i	$-0.829915\pi$
$191$	−5.82426	−	19.4544i	−0.421429	−	1.40767i	0.439178	−	0.898400i	$-0.355270\pi$
$192$	−1.02244	+	11.4403i	−0.0737883	+	0.825632i
$193$	2.23280	−	1.46854i	0.160720	−	0.105707i	−0.466601	−	0.884468i	$-0.654522\pi$
$193$	2.23280	−	1.46854i	0.160720	−	0.105707i	0.627321	+	0.778760i	$0.284151\pi$
$194$	0.907699	−	1.21925i	0.0651690	−	0.0875372i
$195$	29.1494	+	4.32541i	2.08743	+	0.309749i
$196$	−9.20171	−	6.05206i	−0.657265	−	0.432290i
$197$	−15.7132	+	5.71915i	−1.11952	+	0.407473i	−0.834478	−	0.551042i	$-0.814230\pi$
$197$	−15.7132	+	5.71915i	−1.11952	+	0.407473i	−0.285044	+	0.958514i	$0.592008\pi$
$198$	−0.171564	+	1.42172i	−0.0121925	+	0.101038i
$199$	−1.83812	−	0.669021i	−0.130301	−	0.0474257i	0.276047	−	0.961144i	$-0.410976\pi$
$199$	−1.83812	−	0.669021i	−0.130301	−	0.0474257i	−0.406348	+	0.913719i	$0.633198\pi$
$200$	−7.42253	−	9.97019i	−0.524852	−	0.704999i
$201$	6.68139	−	10.7870i	0.471269	−	0.760858i
$202$	0.671512	+	0.711761i	0.0472474	+	0.0500794i
$203$	−0.471904	−	0.500189i	−0.0331211	−	0.0351064i
$204$	−14.1627	−	0.438581i	−0.991587	−	0.0307068i
$205$	−14.5314	−	19.5190i	−1.01491	−	1.36327i
$206$	−1.88202	−	0.685000i	−0.131127	−	0.0477262i
$207$	−1.99968	−	3.06526i	−0.138988	−	0.213050i
$208$	13.7477	−	5.00376i	0.953233	−	0.346948i
$209$	−4.98822	−	3.28080i	−0.345042	−	0.226938i
$210$	−1.27405	+	1.60512i	−0.0879175	+	0.110764i
$211$	6.18914	−	8.31346i	0.426078	−	0.572322i	−0.536303	−	0.844025i	$-0.680180\pi$
$211$	6.18914	−	8.31346i	0.426078	−	0.572322i	0.962381	+	0.271704i	$0.0875870\pi$
$212$	7.25732	−	4.77321i	0.498435	−	0.327826i
$213$	7.52484	−	3.49179i	0.515593	−	0.239253i
$214$	1.10291	+	3.68397i	0.0753933	+	0.251831i
$215$	15.5027	+	26.8514i	1.05727	+	1.83125i
$216$	0.403865	+	4.93466i	0.0274795	+	0.335761i
$217$	−1.12074	+	1.94117i	−0.0760805	+	0.131775i
$218$	−0.851789	−	0.201878i	−0.0576904	−	0.0136729i
$219$	−7.14219	−	10.2408i	−0.482624	−	0.692008i
$220$	14.5533	+	7.30895i	0.981184	+	0.492769i
$221$	6.68417	+	15.4956i	0.449626	+	1.04235i
$222$	−2.16237	+	0.442282i	−0.145129	+	0.0296840i
$223$	−0.426091	+	7.31569i	−0.0285331	+	0.489895i	0.953525	+	0.301315i	$0.0974256\pi$
$223$	−0.426091	+	7.31569i	−0.0285331	+	0.489895i	−0.982058	+	0.188580i	$0.939611\pi$
$224$	−0.557941	+	3.16424i	−0.0372790	+	0.211420i
$225$	28.3648	+	26.9618i	1.89098	+	1.79746i
$226$	−0.398592	−	2.26052i	−0.0265139	−	0.150368i
$227$	23.1203	−	2.70238i	1.53455	−	0.179363i	0.693554	−	0.720404i	$-0.256044\pi$
$227$	23.1203	−	2.70238i	1.53455	−	0.179363i	0.840996	+	0.541041i	$0.181970\pi$
$228$	−9.44269	−	3.77178i	−0.625357	−	0.249793i
$229$	0.0143156	−	0.0478175i	0.000946003	−	0.00315987i	−0.957515	−	0.288383i	$-0.906882\pi$
$229$	0.0143156	−	0.0478175i	0.000946003	−	0.00315987i	0.958461	+	0.285223i	$0.0920676\pi$
$230$	1.21901	−	0.288912i	0.0803795	−	0.0190503i
$231$	0.804040	−	3.85756i	0.0529019	−	0.253809i
$232$	0.225255	−	0.522199i	0.0147887	−	0.0342841i
$233$	−17.1664	+	14.4043i	−1.12461	+	0.943660i	−0.998828	−	0.0483977i	$-0.984589\pi$
$233$	−17.1664	+	14.4043i	−1.12461	+	0.943660i	−0.125782	+	0.992058i	$0.540144\pi$
$234$	2.52095	−	1.44294i	0.164800	−	0.0943277i
$235$	1.42093	+	1.19231i	0.0926916	+	0.0777775i
$236$	−14.4581	+	7.26111i	−0.941140	+	0.472658i
$237$	18.6003	−	11.4249i	1.20822	−	0.742126i
$238$	−1.16564	−	0.136243i	−0.0755570	−	0.00883135i
$239$	1.19389	+	20.4983i	0.0772265	+	1.32593i	0.785003	+	0.619491i	$0.212661\pi$
$239$	1.19389	+	20.4983i	0.0772265	+	1.32593i	−0.707777	+	0.706436i	$0.750302\pi$
$240$	25.9469	+	7.00443i	1.67486	+	0.452134i
$241$	19.7548	−	20.9389i	1.27252	−	1.34879i	0.363746	−	0.931498i	$-0.381498\pi$
$241$	19.7548	−	20.9389i	1.27252	−	1.34879i	0.908772	−	0.417292i	$-0.137021\pi$
$242$	−1.71663			−0.110349
$243$	−3.89373	−	15.0943i	−0.249783	−	0.968302i
$244$	20.4774			1.31093
$245$	−16.5360	+	17.5272i	−1.05645	+	1.11977i
$246$	−2.31571	−	0.625133i	−0.147644	−	0.0398570i
$247$	0.704146	+	12.0897i	0.0448037	+	0.769251i
$248$	−1.84120	−	0.215206i	−0.116917	−	0.0136656i
$249$	−17.0852	+	10.4943i	−1.08273	+	0.665047i
$250$	−7.38256	+	3.70766i	−0.466914	+	0.234493i
$251$	−7.80826	−	6.55190i	−0.492853	−	0.413553i	0.362195	−	0.932102i	$-0.382028\pi$
$251$	−7.80826	−	6.55190i	−0.492853	−	0.413553i	−0.855047	+	0.518550i	$0.826472\pi$
$252$	0.0250809	−	6.71087i	0.00157995	−	0.422745i
$253$	−1.84533	+	1.54841i	−0.116015	+	0.0973479i
$254$	1.06738	−	2.47447i	0.0669735	−	0.155262i
$255$	−6.32572	+	30.3490i	−0.396132	+	1.90053i
$256$	11.2162	−	2.65828i	0.701011	−	0.166143i
$257$	−1.73817	+	5.80588i	−0.108424	+	0.362161i	−0.994932	−	0.100553i	$-0.967939\pi$
$257$	−1.73817	+	5.80588i	−0.108424	+	0.362161i	0.886508	+	0.462714i	$0.153124\pi$
$258$	2.83813	+	1.13366i	0.176695	+	0.0705788i
$259$	6.03220	−	0.705063i	0.374822	−	0.0438105i
$260$	−5.73613	−	32.5312i	−0.355740	−	2.01750i
$261$	−0.419439	+	1.74073i	−0.0259626	+	0.107749i
$262$	0.509253	−	2.88812i	0.0314618	−	0.178429i
$263$	−0.780181	+	13.3952i	−0.0481080	+	0.825983i	0.884823	+	0.465927i	$0.154279\pi$
$263$	−0.780181	+	13.3952i	−0.0481080	+	0.825983i	−0.932931	+	0.360055i	$0.882758\pi$
$264$	3.19273	−	0.653028i	0.196499	−	0.0401911i
$265$	−7.52738	−	17.4504i	−0.462403	−	1.07197i
$266$	−0.752585	−	0.377962i	−0.0461440	−	0.0231744i
$267$	−10.9089	−	15.6416i	−0.667613	−	0.957252i
$268$	−13.8400	−	3.28015i	−0.845414	−	0.200367i
$269$	1.44120	−	2.49623i	0.0878715	−	0.152198i	−0.818740	−	0.574165i	$-0.805327\pi$
$269$	1.44120	−	2.49623i	0.0878715	−	0.152198i	0.906611	+	0.421967i	$0.138660\pi$
$270$	5.31299	+	0.494855i	0.323339	+	0.0301159i
$271$	−1.60573	−	2.78120i	−0.0975410	−	0.168946i	0.813125	−	0.582089i	$-0.197764\pi$
$271$	−1.60573	−	2.78120i	−0.0975410	−	0.168946i	−0.910666	+	0.413143i	$0.864431\pi$
$272$	4.41417	+	14.7444i	0.267648	+	0.894008i
$273$	−7.25014	+	3.36431i	−0.438798	+	0.203618i
$274$	0.0604344	−	0.0397483i	0.00365098	−	0.00240128i
$275$	15.3817	−	20.6612i	0.927549	−	1.24591i
$276$	−2.55056	+	3.21335i	−0.153526	+	0.193421i
$277$	2.84591	+	1.87178i	0.170994	+	0.112465i	0.632121	−	0.774869i	$-0.282184\pi$
$277$	2.84591	+	1.87178i	0.170994	+	0.112465i	−0.461127	+	0.887334i	$0.652555\pi$
$278$	1.27431	−	0.463810i	0.0764278	−	0.0278174i
$279$	5.82774	−	0.317578i	0.348898	−	0.0190129i
$280$	4.38225	+	1.59501i	0.261889	+	0.0953200i
$281$	−6.85829	−	9.21228i	−0.409131	−	0.549558i	0.549025	−	0.835806i	$-0.314999\pi$
$281$	−6.85829	−	9.21228i	−0.409131	−	0.549558i	−0.958156	+	0.286248i	$0.907592\pi$
$282$	0.182749	+	0.00565924i	0.0108825	+	0.000337003i
$283$	−17.3905	−	18.4328i	−1.03376	−	1.09572i	−0.995337	−	0.0964565i	$-0.969249\pi$
$283$	−17.3905	−	18.4328i	−1.03376	−	1.09572i	−0.0384196	−	0.999262i	$-0.512232\pi$
$284$	−6.38133	−	6.76381i	−0.378662	−	0.401358i
$285$	−11.7144	+	18.9127i	−0.693899	+	1.12029i
$286$	−1.14168	−	1.53355i	−0.0675091	−	0.0906804i
$287$	6.20207	+	2.25737i	0.366097	+	0.133248i
$288$	7.69433	−	3.28496i	0.453393	−	0.193568i
$289$	−0.708104	+	0.257729i	−0.0416532	+	0.0151605i
$290$	−0.512082	−	0.336802i	−0.0300705	−	0.0197777i
$291$	10.7727	+	1.59854i	0.631510	+	0.0937083i
$292$	−8.35759	+	11.2262i	−0.489091	+	0.656963i
$293$	3.35543	−	2.20690i	0.196027	−	0.128929i	−0.447701	−	0.894183i	$-0.647757\pi$
$293$	3.35543	−	2.20690i	0.196027	−	0.128929i	0.643728	+	0.765254i	$0.277387\pi$
$294$	−0.211431	+	2.36575i	−0.0123309	+	0.137973i
$295$	10.1522	+	33.9107i	0.591084	+	1.97436i
$296$	2.51135	+	4.34978i	0.145969	+	0.252826i
$297$	−9.55643	+	3.73463i	−0.554520	+	0.216705i
$298$	1.64704	−	2.85276i	0.0954106	−	0.165256i
$299$	4.75443	+	1.12682i	0.274956	+	0.0651657i
$300$	18.6137	−	39.7233i	1.07466	−	2.29342i
$301$	−7.51501	−	3.77418i	−0.433158	−	0.217540i
$302$	−0.905155	−	2.09839i	−0.0520858	−	0.120749i
$303$	−2.21771	+	6.65101i	−0.127404	+	0.382091i
$304$	−0.642189	+	11.0260i	−0.0368321	+	0.632382i
$305$	7.77984	−	44.1216i	0.445472	−	2.52640i
$306$	1.36121	+	2.73584i	0.0778154	+	0.156398i
$307$	3.45206	+	19.5776i	0.197020	+	1.11735i	0.909513	+	0.415675i	$0.136455\pi$
$307$	3.45206	+	19.5776i	0.197020	+	1.11735i	−0.712493	+	0.701679i	$0.752434\pi$
$308$	−4.38723	+	0.512794i	−0.249986	+	0.0292191i
$309$	−2.05319	−	14.2020i	−0.116802	−	0.807925i
$310$	−0.572981	+	1.91389i	−0.0325431	+	0.108702i
$311$	1.50256	−	0.356114i	0.0852026	−	0.0201934i	−0.187793	−	0.982209i	$-0.560134\pi$
$311$	1.50256	−	0.356114i	0.0852026	−	0.0201934i	0.272996	+	0.962015i	$0.411985\pi$
$312$	−4.92969	−	4.40359i	−0.279089	−	0.249304i
$313$	−6.93106	+	16.0680i	−0.391767	+	0.908218i	0.602181	+	0.798360i	$0.294299\pi$
$313$	−6.93106	+	16.0680i	−0.391767	+	0.908218i	−0.993947	+	0.109858i	$0.964961\pi$
$314$	−1.68933	+	1.41751i	−0.0953343	+	0.0799950i
$315$	−14.4501	−	2.60365i	−0.814168	−	0.146699i
$316$	−18.7445	−	15.7285i	−1.05446	−	0.884799i
$317$	1.75554	−	0.881664i	0.0986008	−	0.0495192i	−0.398815	−	0.917031i	$-0.630579\pi$
$317$	1.75554	−	0.881664i	0.0986008	−	0.0495192i	0.497416	+	0.867512i	$0.334282\pi$
$318$	−1.64720	−	0.892140i	−0.0923705	−	0.0500287i
$319$	1.17057	+	0.136819i	0.0655391	+	0.00766042i
$320$	−1.63791	−	28.1219i	−0.0915622	−	1.57206i
$321$	−19.5188	+	19.4460i	−1.08944	+	1.08537i
$322$	−0.233178	+	0.247154i	−0.0129945	+	0.0137734i
$323$	−12.7401			−0.708877
$324$	−14.6707	+	9.49275i	−0.815039	+	0.527375i
$325$	−52.2468			−2.89813
$326$	−1.31747	+	1.39644i	−0.0729680	+	0.0773416i
$327$	−1.61198	−	6.06126i	−0.0891425	−	0.335189i
$328$	0.317378	+	5.44917i	0.0175243	+	0.300880i
$329$	−0.499698	−	0.0584063i	−0.0275492	−	0.00322005i
$330$	−0.0955888	−	3.51082i	−0.00526199	−	0.193264i
$331$	30.8145	−	15.4756i	1.69372	−	0.850616i	0.703562	−	0.710634i	$-0.251592\pi$
$331$	30.8145	−	15.4756i	1.69372	−	0.850616i	0.990154	−	0.139982i	$-0.0447045\pi$
$332$	17.2177	+	14.4474i	0.944943	+	0.792901i
$333$	−10.1195	−	12.1519i	−0.554545	−	0.665920i
$334$	−0.823144	+	0.690700i	−0.0450405	+	0.0377934i
$335$	−12.3257	+	28.5742i	−0.673426	+	1.56118i
$336$	−6.92370	+	2.27992i	−0.377719	+	0.124380i
$337$	15.7401	−	3.73046i	0.857415	−	0.203211i	0.221681	−	0.975119i	$-0.428846\pi$
$337$	15.7401	−	3.73046i	0.857415	−	0.203211i	0.635734	+	0.771908i	$0.280697\pi$
$338$	−0.210876	+	0.704374i	−0.0114701	+	0.0383129i
$339$	12.9196	−	10.1763i	0.701695	−	0.552700i
$340$	34.5162	−	4.03436i	1.87190	−	0.218794i
$341$	−0.667067	−	3.78313i	−0.0361237	−	0.204868i
$342$	0.246432	+	2.17895i	0.0133255	+	0.117824i
$343$	2.53539	−	14.3789i	0.136898	−	0.776387i
$344$	0.404387	−	6.94305i	0.0218031	−	0.374344i
$345$	5.95462	+	6.71639i	0.320586	+	0.361598i
$346$	0.298595	+	0.692221i	0.0160526	+	0.0372141i
$347$	28.4307	+	14.2785i	1.52624	+	0.766508i	0.996653	−	0.0817463i	$-0.0260497\pi$
$347$	28.4307	+	14.2785i	1.52624	+	0.766508i	0.529589	+	0.848254i	$0.322346\pi$
$348$	1.99982	−	0.171197i	0.107202	−	0.00917712i
$349$	−16.8680	−	3.99780i	−0.902925	−	0.213997i	−0.247171	−	0.968972i	$-0.579501\pi$
$349$	−16.8680	−	3.99780i	−0.902925	−	0.213997i	−0.655754	+	0.754975i	$0.727649\pi$
$350$	1.81666	−	3.14655i	0.0971048	−	0.168190i
$351$	17.6515	+	11.0247i	0.942168	+	0.588455i
$352$	−2.75331	−	4.76887i	−0.146752	−	0.254181i
$353$	0.975076	+	3.25698i	0.0518981	+	0.173352i	0.980009	−	0.198951i	$-0.0637535\pi$
$353$	0.975076	+	3.25698i	0.0518981	+	0.173352i	−0.928111	+	0.372303i	$0.878568\pi$
$354$	2.85439	+	2.00663i	0.151709	+	0.106651i
$355$	−16.9981	+	11.1798i	−0.902164	+	0.593362i
$356$	−12.7653	+	17.1467i	−0.676558	+	0.908775i
$357$	−3.08982	−	7.82011i	−0.163531	−	0.413884i
$358$	2.87525	+	1.89108i	0.151962	+	0.0999469i
$359$	9.53489	−	3.47042i	0.503232	−	0.183162i	−0.0779150	−	0.996960i	$-0.524826\pi$
$359$	9.53489	−	3.47042i	0.503232	−	0.183162i	0.581147	+	0.813798i	$0.302604\pi$
$360$	−2.75617	−	11.8260i	−0.145263	−	0.623283i
$361$	9.26314	+	3.37151i	0.487534	+	0.177448i
$362$	2.29421	+	3.08166i	0.120581	+	0.161968i
$363$	−5.81702	−	10.8368i	−0.305314	−	0.568782i
$364$	6.14837	+	6.51689i	0.322262	+	0.341578i
$365$	21.0133	+	22.2728i	1.09988	+	1.16581i
$366$	−2.08863	−	3.89100i	−0.109174	−	0.203386i
$367$	8.87614	+	11.9227i	0.463331	+	0.622362i	0.970968	−	0.239210i	$-0.0768883\pi$
$367$	8.87614	+	11.9227i	0.463331	+	0.622362i	−0.507637	+	0.861571i	$0.669481\pi$
$368$	4.18747	+	1.52411i	0.218287	+	0.0794499i
$369$	−3.90072	−	16.7370i	−0.203064	−	0.871291i
$370$	5.08664	−	1.85138i	0.264442	−	0.0962489i
$371$	4.30661	+	2.83250i	0.223588	+	0.147056i
$372$	−2.40411	−	6.08463i	−0.124647	−	0.315473i
$373$	−12.5886	+	16.9094i	−0.651814	+	0.875538i	−0.998038	−	0.0626138i	$-0.980056\pi$
$373$	−12.5886	+	16.9094i	−0.651814	+	0.875538i	0.346224	+	0.938152i	$0.387464\pi$
$374$	1.68041	−	1.10523i	0.0868921	−	0.0571498i
$375$	−48.4225	−	34.0408i	−2.50052	−	1.75786i
$376$	−0.119331	−	0.398593i	−0.00615403	−	0.0205559i
$377$	−1.19525	−	2.07023i	−0.0615585	−	0.106622i
$378$	−1.27772	+	0.679722i	−0.0657187	+	0.0349611i
$379$	−3.47462	+	6.01822i	−0.178479	+	0.309135i	−0.941360	−	0.337404i	$-0.890451\pi$
$379$	−3.47462	+	6.01822i	−0.178479	+	0.309135i	0.762880	+	0.646540i	$0.223784\pi$
$380$	24.2655	+	5.75103i	1.24479	+	0.295021i
$381$	19.2378	−	1.64687i	0.985582	−	0.0843718i
$382$	4.38706	+	2.20326i	0.224461	+	0.112729i
$383$	−13.9944	−	32.4427i	−0.715081	−	1.65774i	−0.752625	−	0.658450i	$-0.771212\pi$
$383$	−13.9944	−	32.4427i	−0.715081	−	1.65774i	0.0375433	−	0.999295i	$-0.488047\pi$
$384$	−8.25078	−	9.30629i	−0.421046	−	0.474910i
$385$	−0.561918	+	9.64777i	−0.0286380	+	0.491696i
$386$	−0.112186	+	0.636236i	−0.00571010	+	0.0323836i
$387$	2.46077	+	21.7581i	0.125088	+	1.10603i
$388$	−2.11990	−	12.0226i	−0.107622	−	0.610354i
$389$	25.5497	−	2.98633i	1.29542	−	0.151413i	0.559698	−	0.828697i	$-0.310917\pi$
$389$	25.5497	−	2.98633i	1.29542	−	0.151413i	0.735722	+	0.677284i	$0.236843\pi$
$390$	−5.59632	+	4.40803i	−0.283381	+	0.223209i
$391$	−1.47424	+	4.92432i	−0.0745558	+	0.249034i
$392$	5.25940	−	1.24650i	0.265640	−	0.0629578i
$393$	19.9578	−	6.57192i	1.00674	−	0.331510i
$394$	1.60110	−	3.71178i	0.0806625	−	0.186997i
$395$	−41.0109	+	34.4123i	−2.06348	+	1.73147i
$396$	7.35993	+	8.83810i	0.369851	+	0.444131i
$397$	14.2470	+	11.9547i	0.715038	+	0.599988i	0.926008	−	0.377504i	$-0.123218\pi$
$397$	14.2470	+	11.9547i	0.715038	+	0.599988i	−0.210970	+	0.977493i	$0.567662\pi$
$398$	0.422576	−	0.212225i	0.0211818	−	0.0106379i
$399$	−0.164224	−	6.03169i	−0.00822149	−	0.301962i
$400$	−47.3275	−	5.53179i	−2.36637	−	0.276589i
$401$	0.268845	+	4.61589i	0.0134255	+	0.230506i	0.998346	+	0.0574971i	$0.0183120\pi$
$401$	0.268845	+	4.61589i	0.0134255	+	0.230506i	−0.984920	+	0.173009i	$0.944651\pi$
$402$	0.788365	+	2.96436i	0.0393201	+	0.147849i
$403$	−5.34715	+	5.66765i	−0.266361	+	0.282326i
$404$	7.85906			0.391003
$405$	14.8798	+	35.2168i	0.739384	+	1.74993i
$406$	0.166239			0.00825031
$407$	−7.14274	+	7.57087i	−0.354053	+	0.375274i
$408$	4.92633	−	4.90795i	0.243890	−	0.242980i
$409$	0.636048	+	10.9205i	0.0314505	+	0.539985i	0.976830	+	0.214015i	$0.0686540\pi$
$409$	0.636048	+	10.9205i	0.0314505	+	0.539985i	−0.945380	+	0.325971i	$0.894309\pi$
$410$	5.84289	+	0.682936i	0.288560	+	0.0337278i
$411$	0.455713	+	0.246818i	0.0224786	+	0.0121746i
$412$	−14.3745	+	7.21912i	−0.708178	+	0.355661i
$413$	−7.35469	−	6.17132i	−0.361901	−	0.303671i
$414$	0.870730	+	0.156891i	0.0427940	+	0.00771076i
$415$	37.6704	−	31.6092i	1.84917	−	1.55163i
$416$	−4.42398	+	10.2559i	−0.216903	+	0.502839i
$417$	7.24608	+	6.47277i	0.354842	+	0.316973i
$418$	1.40442	−	0.332853i	0.0686922	−	0.0162804i
$419$	9.61972	−	32.1321i	0.469954	−	1.56976i	−0.314304	−	0.949322i	$-0.601771\pi$
$419$	9.61972	−	32.1321i	0.469954	−	1.56976i	0.784259	−	0.620434i	$-0.213044\pi$
$420$	2.35496	+	16.2894i	0.114911	+	0.794842i
$421$	−1.64743	+	0.192557i	−0.0802908	+	0.00938465i	−0.156143	−	0.987734i	$-0.549906\pi$
$421$	−1.64743	+	0.192557i	−0.0802908	+	0.00938465i	0.0758527	+	0.997119i	$0.475832\pi$
$422$	0.435079	+	2.46745i	0.0211793	+	0.120114i
$423$	0.583540	+	1.17283i	0.0283727	+	0.0570250i
$424$	−0.740254	+	4.19819i	−0.0359499	+	0.203882i
$425$	3.19588	−	54.8712i	0.155023	−	2.66164i
$426$	−0.634344	+	1.90243i	−0.0307341	+	0.0921730i
$427$	4.81301	+	11.1578i	0.232918	+	0.539965i
$428$	27.5999	+	13.8612i	1.33409	+	0.670007i
$429$	5.81224	−	12.4038i	0.280618	−	0.598862i
$430$	−7.29334	−	1.72855i	−0.351716	−	0.0833582i
$431$	7.55425	−	13.0843i	0.363876	−	0.630251i	−0.624720	−	0.780849i	$-0.714787\pi$
$431$	7.55425	−	13.0843i	0.363876	−	0.630251i	0.988595	+	0.150598i	$0.0481200\pi$
$432$	14.8223	+	11.8556i	0.713136	+	0.570401i
$433$	−2.46655	−	4.27218i	−0.118535	−	0.205308i	0.800653	−	0.599129i	$-0.204486\pi$
$433$	−2.46655	−	4.27218i	−0.118535	−	0.205308i	−0.919187	+	0.393821i	$0.871153\pi$
$434$	−0.155408	−	0.519100i	−0.00745984	−	0.0249176i
$435$	0.390910	−	4.37396i	0.0187427	−	0.209716i
$436$	−5.87399	+	3.86338i	−0.281313	+	0.185022i
$437$	−2.20273	+	2.95879i	−0.105371	+	0.141538i
$438$	2.98558	+	0.443024i	0.142657	+	0.0211685i
$439$	16.8607	+	11.0894i	0.804716	+	0.529270i	0.883947	−	0.467586i	$-0.154876\pi$
$439$	16.8607	+	11.0894i	0.804716	+	0.529270i	−0.0792316	+	0.996856i	$0.525247\pi$
$440$	−7.51040	+	2.73356i	−0.358044	+	0.130318i
$441$	−15.6509	+	6.68189i	−0.745283	+	0.318185i
$442$	−3.83361	−	1.39532i	−0.182346	−	0.0663686i
$443$	16.8317	+	22.6089i	0.799699	+	1.07418i	0.995614	+	0.0935608i	$0.0298250\pi$
$443$	16.8317	+	22.6089i	0.799699	+	1.07418i	−0.195915	+	0.980621i	$0.562768\pi$
$444$	−9.33418	+	15.0699i	−0.442981	+	0.715186i
$445$	32.0954	+	34.0191i	1.52147	+	1.61266i
$446$	−1.21570	−	1.28856i	−0.0575649	−	0.0610152i
$447$	23.5901	+	0.730524i	1.11577	+	0.0345526i
$448$	4.56251	+	6.12851i	0.215558	+	0.289545i
$449$	−0.407937	−	0.148477i	−0.0192517	−	0.00700706i	0.332376	−	0.943147i	$-0.392150\pi$
$449$	−0.407937	−	0.148477i	−0.0192517	−	0.00700706i	−0.351628	+	0.936140i	$0.614372\pi$
$450$	−9.44652	+	0.514780i	−0.445313	+	0.0242670i
$451$	−10.6293	+	3.86873i	−0.500512	+	0.182171i
$452$	−15.4025	−	10.1304i	−0.724473	−	0.476493i
$453$	10.1795	−	12.8247i	0.478273	−	0.602557i
$454$	−3.36037	+	4.51376i	−0.157710	+	0.211841i
$455$	16.3775	−	10.7717i	0.767790	−	0.504984i
$456$	4.52656	−	2.10048i	0.211976	−	0.0983641i
$457$	−7.77292	−	25.9634i	−0.363602	−	1.21452i	−0.922734	−	0.385437i	$-0.874051\pi$
$457$	−7.77292	−	25.9634i	−0.363602	−	1.21452i	0.559132	−	0.829079i	$-0.311134\pi$
$458$	0.00603328	+	0.0104499i	0.000281917	+	0.000488294i
$459$	−12.6582	+	17.8638i	−0.590834	+	0.833811i
$460$	5.03083	−	8.71365i	0.234564	−	0.406276i
$461$	−41.5746	−	9.85335i	−1.93632	−	0.458916i	−0.991239	−	0.132079i	$-0.957835\pi$
$461$	−41.5746	−	9.85335i	−1.93632	−	0.458916i	−0.945081	−	0.326837i	$-0.894017\pi$
$462$	0.544922	+	0.781332i	0.0253520	+	0.0363509i
$463$	−27.1142	−	13.6173i	−1.26011	−	0.632849i	−0.311782	−	0.950154i	$-0.600926\pi$
$463$	−27.1142	−	13.6173i	−1.26011	−	0.632849i	−0.948324	+	0.317305i	$0.897222\pi$
$464$	−0.863518	−	2.00186i	−0.0400878	−	0.0929340i
$465$	−14.0236	+	2.86833i	−0.650330	+	0.133016i
$466$	0.314988	−	5.40814i	0.0145915	−	0.250527i
$467$	2.33662	−	13.2516i	0.108126	−	0.613212i	−0.881800	−	0.471624i	$-0.843668\pi$
$467$	2.33662	−	13.2516i	0.108126	−	0.613212i	0.989926	−	0.141588i	$-0.0452209\pi$
$468$	5.46481	−	22.6798i	0.252611	−	1.04837i
$469$	−1.46566	−	8.31218i	−0.0676779	−	0.383821i
$470$	−0.445380	+	0.0520575i	−0.0205439	+	0.00240123i
$471$	−14.6730	−	5.86097i	−0.676095	−	0.270059i
$472$	2.27725	−	7.60653i	0.104819	−	0.350119i
$473$	14.0239	−	3.32373i	0.644820	−	0.152825i
$474$	−1.07676	+	5.16598i	−0.0494572	+	0.237281i
$475$	15.6225	−	36.2169i	0.716808	−	1.66175i
$476$	−7.22033	+	6.05858i	−0.330943	+	0.277695i
$477$	0.0501612	−	13.4216i	0.00229672	−	0.614532i
$478$	−3.80246	−	3.19065i	−0.173921	−	0.145937i
$479$	−23.2134	+	11.6582i	−1.06065	+	0.532677i	−0.891550	−	0.452922i	$-0.850382\pi$
$479$	−23.2134	+	11.6582i	−1.06065	+	0.532677i	−0.169098	+	0.985599i	$0.554085\pi$
$480$	−17.4837	+	10.7391i	−0.798018	+	0.490169i
$481$	20.9695	+	2.45098i	0.956126	+	0.111755i
$482$	0.404635	+	6.94732i	0.0184306	+	0.316442i
$483$	−2.35039	−	0.634494i	−0.106946	−	0.0288705i
$484$	−9.46123	+	10.0283i	−0.430056	+	0.455833i
$485$	−26.7098			−1.21283
$486$	3.30012	+	1.81941i	0.149697	+	0.0825301i
$487$	2.70578			0.122611			0.0613053	−	0.998119i	$-0.480474\pi$
$487$	2.70578			0.122611			0.0613053	+	0.998119i	$0.480474\pi$
$488$	−6.89647	+	7.30983i	−0.312188	+	0.330900i
$489$	−13.2799	−	3.58494i	−0.600536	−	0.162116i
$490$	−0.338705	−	5.81535i	−0.0153012	−	0.262711i
$491$	−39.5384	−	4.62138i	−1.78435	−	0.208560i	−0.841151	−	0.540801i	$-0.818121\pi$
$491$	−39.5384	−	4.62138i	−1.78435	−	0.208560i	−0.943195	+	0.332241i	$0.892195\pi$
$492$	−16.4150	+	10.0826i	−0.740045	+	0.454560i
$493$	2.24733	−	1.12865i	0.101215	−	0.0508320i
$494$	−2.24266	−	1.88181i	−0.100902	−	0.0846667i
$495$	21.8392	−	12.5003i	0.981600	−	0.561846i
$496$	−5.44377	+	4.56786i	−0.244432	+	0.205103i
$497$	2.18563	−	5.06685i	0.0980388	−	0.227279i
$498$	0.989051	−	4.74519i	0.0443204	−	0.212637i
$499$	2.41838	−	0.573166i	0.108261	−	0.0256584i	−0.176128	−	0.984367i	$-0.556357\pi$
$499$	2.41838	−	0.573166i	0.108261	−	0.0256584i	0.284389	+	0.958709i	$0.408209\pi$
$500$	−19.0294	+	63.5627i	−0.851022	+	2.84261i
$501$	−7.14958	−	2.85583i	−0.319420	−	0.127589i
$502$	2.44743	−	0.286064i	0.109234	−	0.0127677i
$503$	−2.56729	−	14.5598i	−0.114470	−	0.649191i	−0.987011	−	0.160651i	$-0.948641\pi$
$503$	−2.56729	−	14.5598i	−0.114470	−	0.649191i	0.872541	−	0.488540i	$-0.162470\pi$
$504$	2.38714	+	2.26907i	0.106331	+	0.101072i
$505$	2.98584	−	16.9335i	0.132868	−	0.753532i
$506$	0.0338600	−	0.581354i	0.00150526	−	0.0258444i
$507$	−5.16115	+	1.05564i	−0.229215	+	0.0468826i
$508$	−8.57262	−	19.8736i	−0.380349	−	0.881747i
$509$	−21.4552	−	10.7752i	−0.950983	−	0.477602i	−0.0954985	−	0.995430i	$-0.530444\pi$
$509$	−21.4552	−	10.7752i	−0.950983	−	0.477602i	−0.855485	+	0.517828i	$0.826741\pi$
$510$	−4.28713	−	6.14707i	−0.189837	−	0.272197i
$511$	−8.08134	−	1.91531i	−0.357498	−	0.0847285i
$512$	−8.57387	+	14.8504i	−0.378915	+	0.656300i
$513$	−12.9202	+	8.93932i	−0.570442	+	0.394681i
$514$	−0.732546	−	1.26881i	−0.0323112	−	0.0559646i
$515$	10.0935	+	33.7146i	0.444773	+	1.48564i
$516$	22.2651	−	10.3318i	0.980167	−	0.454831i
$517$	0.720378	−	0.473800i	0.0316822	−	0.0208377i
$518$	−0.876736	+	1.17766i	−0.0385216	+	0.0517434i
$519$	−3.35803	+	4.23065i	−0.147401	+	0.185705i
$520$	13.5445	+	8.90837i	0.593966	+	0.390658i
$521$	18.5919	−	6.76690i	0.814526	−	0.296463i	0.0990342	−	0.995084i	$-0.468425\pi$
$521$	18.5919	−	6.76690i	0.814526	−	0.296463i	0.715492	+	0.698621i	$0.246202\pi$
$522$	−0.236506	−	0.362533i	−0.0103516	−	0.0158676i
$523$	32.2975	+	11.7553i	1.41227	+	0.514025i	0.931796	−	0.362982i	$-0.118241\pi$
$523$	32.2975	+	11.7553i	1.41227	+	0.514025i	0.480477	+	0.877007i	$0.340464\pi$
$524$	−14.0652	−	18.8929i	−0.614442	−	0.825339i
$525$	26.0196	+	0.805757i	1.13559	+	0.0351661i
$526$	−2.22597	−	2.35939i	−0.0970567	−	0.102874i
$527$	−5.62526	−	5.96243i	−0.245040	−	0.259728i
$528$	6.57828	−	10.6205i	0.286283	−	0.462200i
$529$	−12.8459	−	17.2550i	−0.558518	−	0.750219i
$530$	4.31722	+	1.57134i	0.187528	+	0.0682547i
$531$	−2.99498	+	24.8189i	−0.129971	+	1.07705i
$532$	−6.35588	+	2.31335i	−0.275563	+	0.100297i
$533$	19.1692	+	12.6078i	0.830309	+	0.546103i
$534$	4.56014	+	0.676669i	0.197337	+	0.0292823i
$535$	40.3519	−	54.2020i	1.74457	−	2.34336i
$536$	5.83202	−	3.83578i	0.251905	−	0.165680i
$537$	−2.19489	+	24.5591i	−0.0947166	+	1.05980i
$538$	0.199846	+	0.667532i	0.00861597	+	0.0287794i
$539$	5.60046	+	9.70029i	0.241229	+	0.417821i
$540$	32.1735	−	28.3104i	1.38453	−	1.21828i
$541$	−18.0270	+	31.2237i	−0.775042	+	1.34241i	0.159728	+	0.987161i	$0.448938\pi$
$541$	−18.0270	+	31.2237i	−0.775042	+	1.34241i	−0.934771	+	0.355252i	$0.884395\pi$
$542$	0.755426	+	0.179039i	0.0324483	+	0.00769040i
$543$	−11.6797	+	24.9255i	−0.501223	+	1.06965i
$544$	−10.5005	−	5.27355i	−0.450205	−	0.226102i
$545$	6.09257	+	14.1242i	0.260977	+	0.605013i
$546$	0.611187	−	1.83298i	0.0261564	−	0.0784443i
$547$	−0.502380	+	8.62553i	−0.0214802	+	0.368801i	0.970390	+	0.241545i	$0.0776541\pi$
$547$	−0.502380	+	8.62553i	−0.0214802	+	0.368801i	−0.991870	+	0.127256i	$0.959383\pi$
$548$	0.100881	−	0.572123i	0.00430941	−	0.0244399i
$549$	17.4855	−	26.3702i	0.746263	−	1.12545i
$550$	1.08129	+	6.13228i	0.0461062	+	0.261481i
$551$	1.79246	−	0.209508i	0.0763613	−	0.00892535i
$552$	−0.288082	−	1.99268i	−0.0122616	−	0.0848140i
$553$	4.16451	−	13.9104i	0.177093	−	0.591532i
$554$	−0.801255	+	0.189901i	−0.0340421	+	0.00806812i
$555$	28.9241	+	25.8373i	1.22776	+	1.09673i
$556$	4.31384	−	10.0006i	0.182948	−	0.424120i
$557$	16.3664	−	13.7330i	0.693466	−	0.581887i	−0.226441	−	0.974025i	$-0.572709\pi$
$557$	16.3664	−	13.7330i	0.693466	−	0.581887i	0.919906	+	0.392138i	$0.128264\pi$
$558$	−0.910953	+	1.07743i	−0.0385637	+	0.0456112i
$559$	−22.3943	−	18.7910i	−0.947176	−	0.794775i
$560$	15.9760	−	8.02344i	0.675109	−	0.339052i
$561$	12.6713	+	6.86292i	0.534985	+	0.289753i
$562$	2.75763	+	0.322321i	0.116324	+	0.0135963i
$563$	−1.60839	−	27.6150i	−0.0677856	−	1.16383i	−0.845060	−	0.534672i	$-0.820435\pi$
$563$	−1.60839	−	27.6150i	−0.0677856	−	1.16383i	0.777274	−	0.629162i	$-0.216602\pi$
$564$	1.04028	−	1.03640i	0.0438037	−	0.0436403i
$565$	−27.6792	+	29.3383i	−1.16447	+	1.23427i
$566$	6.12621			0.257504
$567$	−8.62065	−	5.76266i	−0.362033	−	0.242009i
$568$	4.56361			0.191485
$569$	−15.1704	+	16.0796i	−0.635975	+	0.674094i	−0.962558	−	0.271075i	$-0.912621\pi$
$569$	−15.1704	+	16.0796i	−0.635975	+	0.674094i	0.326584	+	0.945168i	$0.394102\pi$
$570$	−1.38223	−	5.19737i	−0.0578951	−	0.217694i
$571$	−0.123744	−	2.12459i	−0.00517851	−	0.0889115i	0.994729	−	0.102543i	$-0.0326979\pi$
$571$	−0.123744	−	2.12459i	−0.00517851	−	0.0889115i	−0.999907	+	0.0136314i	$0.995661\pi$
$572$	−15.2511	−	1.78260i	−0.637683	−	0.0745344i
$573$	0.957314	+	35.1606i	0.0399924	+	1.46886i
$574$	−1.42583	+	0.716078i	−0.0595129	+	0.0298885i
$575$	−12.1909	−	10.2293i	−0.508394	−	0.426593i
$576$	6.87402	−	18.6688i	0.286417	−	0.777867i
$577$	−15.8954	+	13.3378i	−0.661733	+	0.555260i	−0.910606	−	0.413276i	$-0.864384\pi$
$577$	−15.8954	+	13.3378i	−0.661733	+	0.555260i	0.248872	+	0.968536i	$0.419940\pi$
$578$	0.0721525	−	0.167268i	0.00300115	−	0.00695744i
$579$	−4.39659	+	1.44776i	−0.182716	+	0.0601668i
$580$	−4.78989	+	1.13523i	−0.198889	+	0.0471377i
$581$	−3.82529	+	12.7774i	−0.158700	+	0.530094i
$582$	−2.06823	+	1.62908i	−0.0857311	+	0.0675274i
$583$	−8.77435	+	1.02557i	−0.363396	+	0.0424750i
$584$	−1.19271	−	6.76421i	−0.0493548	−	0.279905i
$585$	−46.7908	−	20.3913i	−1.93456	−	0.843078i
$586$	−0.168592	+	0.956131i	−0.00696446	+	0.0394974i
$587$	−0.682898	+	11.7249i	−0.0281862	+	0.483939i	0.954447	+	0.298380i	$0.0964464\pi$
$587$	−0.682898	+	11.7249i	−0.0281862	+	0.483939i	−0.982633	+	0.185558i	$0.940591\pi$
$588$	12.6550	+	14.2740i	0.521885	+	0.588649i
$589$	−2.32989	−	5.40129i	−0.0960014	−	0.222556i
$590$	−7.64703	−	3.84048i	−0.314823	−	0.158110i
$591$	28.8572	−	2.47035i	1.18703	−	0.101617i
$592$	18.7356	+	4.44042i	0.770028	+	0.182500i
$593$	10.8840	−	18.8516i	0.446952	−	0.774144i	−0.551234	−	0.834351i	$-0.685843\pi$
$593$	10.8840	−	18.8516i	0.446952	−	0.774144i	0.998186	+	0.0602070i	$0.0191761\pi$
$594$	0.928673	−	2.29995i	0.0381039	−	0.0943681i
$595$	10.3109	+	17.8591i	0.422708	+	0.732151i
$596$	−7.58774	−	25.3448i	−0.310806	−	1.03816i
$597$	2.77169	+	1.94848i	0.113438	+	0.0797461i
$598$	−0.986876	+	0.649078i	−0.0403564	+	0.0265428i
$599$	6.11729	−	8.21695i	0.249946	−	0.335736i	−0.659388	−	0.751803i	$-0.729185\pi$
$599$	6.11729	−	8.21695i	0.249946	−	0.335736i	0.909334	+	0.416067i	$0.136592\pi$
$600$	7.91122	+	20.0227i	0.322974	+	0.817424i
$601$	−2.35821	−	1.55102i	−0.0961935	−	0.0632674i	0.500501	−	0.865736i	$-0.333149\pi$
$601$	−2.35821	−	1.55102i	−0.0961935	−	0.0632674i	−0.596694	+	0.802469i	$0.703520\pi$
$602$	1.91035	−	0.695311i	0.0778601	−	0.0283388i
$603$	−16.0420	+	15.0219i	−0.653280	+	0.611739i
$604$	−17.2472	−	6.27748i	−0.701780	−	0.255427i
$605$	18.0130	+	24.1956i	0.732332	+	0.983693i
$606$	−0.801599	−	1.49333i	−0.0325627	−	0.0606624i
$607$	−9.33562	−	9.89518i	−0.378921	−	0.401633i	0.509643	−	0.860386i	$-0.329778\pi$
$607$	−9.33562	−	9.89518i	−0.378921	−	0.401633i	−0.888564	+	0.458753i	$0.848296\pi$
$608$	−5.78648	−	6.13331i	−0.234673	−	0.248739i
$609$	0.563322	+	1.04943i	0.0228269	+	0.0425252i
$610$	6.46766	+	8.68757i	0.261868	+	0.351750i
$611$	−1.64343	−	0.598161i	−0.0664862	−	0.0241990i
$612$	23.4848	+	7.12662i	0.949315	+	0.288077i
$613$	15.3111	−	5.57278i	0.618410	−	0.225083i	−0.0137693	−	0.999905i	$-0.504383\pi$
$613$	15.3111	−	5.57278i	0.618410	−	0.225083i	0.632179	+	0.774823i	$0.282161\pi$
$614$	−4.01519	−	2.64083i	−0.162040	−	0.106575i
$615$	15.4881	+	39.1992i	0.624540	+	1.58066i
$616$	1.29450	−	1.73881i	0.0521568	−	0.0700587i
$617$	6.48426	−	4.26476i	0.261046	−	0.171693i	−0.412239	−	0.911076i	$-0.635253\pi$
$617$	6.48426	−	4.26476i	0.261046	−	0.171693i	0.673285	+	0.739383i	$0.264883\pi$
$618$	2.83788	+	1.99502i	0.114156	+	0.0802515i
$619$	−12.5687	−	41.9823i	−0.505178	−	1.68741i	−0.706356	−	0.707857i	$-0.749662\pi$
$619$	−12.5687	−	41.9823i	−0.505178	−	1.68741i	0.201178	−	0.979555i	$-0.435523\pi$
$620$	8.02269	+	13.8957i	0.322199	+	0.558065i
$621$	1.96015	+	6.02839i	0.0786583	+	0.241911i
$622$	−0.186650	+	0.323287i	−0.00748397	+	0.0129626i
$623$	−12.3433	−	2.92543i	−0.494525	−	0.117205i
$624$	−25.2476	+	2.16135i	−1.01071	+	0.0865230i
$625$	71.4394	+	35.8782i	2.85758	+	1.43513i
$626$	−1.67555	−	3.88436i	−0.0669684	−	0.155250i
$627$	6.86026	+	7.73788i	0.273973	+	0.309021i
$628$	−1.02983	+	17.6815i	−0.0410946	+	0.705567i
$629$	−3.85678	+	21.8729i	−0.153780	+	0.872129i
$630$	2.85502	−	2.10895i	0.113747	−	0.0840224i
$631$	3.55734	+	20.1747i	0.141615	+	0.803141i	0.970023	+	0.243015i	$0.0781363\pi$
$631$	3.55734	+	20.1747i	0.141615	+	0.803141i	−0.828407	+	0.560126i	$0.810753\pi$
$632$	11.9275	−	1.39412i	0.474450	−	0.0554552i
$633$	−14.1022	+	11.1078i	−0.560513	+	0.441497i
$634$	−0.136205	+	0.454956i	−0.00540938	+	0.0180686i
$635$	−46.0775	+	10.9206i	−1.82853	+	0.433370i
$636$	−14.2903	+	4.70568i	−0.566648	+	0.186592i
$637$	8.99876	−	20.8615i	0.356544	−	0.826562i
$638$	−0.218250	+	0.183133i	−0.00864058	+	0.00725031i
$639$	−14.1592	+	2.44212i	−0.560130	+	0.0966089i
$640$	23.3663	+	19.6066i	0.923634	+	0.775021i
$641$	30.8827	−	15.5099i	1.21979	−	0.612603i	0.281872	−	0.959452i	$-0.409045\pi$
$641$	30.8827	−	15.5099i	1.21979	−	0.612603i	0.937921	+	0.346849i	$0.112748\pi$
$642$	−0.181281	−	6.65818i	−0.00715461	−	0.262777i
$643$	−29.5404	−	3.45278i	−1.16496	−	0.136164i	−0.488446	−	0.872594i	$-0.662436\pi$
$643$	−29.5404	−	3.45278i	−1.16496	−	0.136164i	−0.676514	+	0.736430i	$0.736510\pi$
$644$	0.158677	+	2.72438i	0.00625276	+	0.107356i
$645$	−13.8024	−	51.8988i	−0.543467	−	2.04351i
$646$	2.11352	−	2.24020i	0.0831553	−	0.0881395i
$647$	43.1443			1.69618			0.848089	−	0.529853i	$-0.177753\pi$
$647$	43.1443			1.69618			0.848089	+	0.529853i	$0.177753\pi$
$648$	1.55223	−	8.43401i	0.0609775	−	0.331319i
$649$	16.4542			0.645884
$650$	8.66750	−	9.18701i	0.339967	−	0.360344i
$651$	2.75036	−	2.74010i	0.107795	−	0.107393i
$652$	0.896538	+	15.3930i	0.0351111	+	0.602835i
$653$	30.9788	+	3.62090i	1.21229	+	0.141697i	0.698114	−	0.715987i	$-0.254023\pi$
$653$	30.9788	+	3.62090i	1.21229	+	0.141697i	0.514178	+	0.857683i	$0.328097\pi$
$654$	1.33322	+	0.722087i	0.0521332	+	0.0282358i
$655$	−46.0512	+	23.1278i	−1.79937	+	0.903678i
$656$	16.0294	+	13.4503i	0.625843	+	0.525145i
$657$	7.32028	+	20.3486i	0.285592	+	0.793875i
$658$	0.0931677	−	0.0781770i	0.00363205	−	0.00304766i
$659$	16.1073	−	37.3409i	0.627452	−	1.45460i	−0.246772	−	0.969073i	$-0.579370\pi$
$659$	16.1073	−	37.3409i	0.627452	−	1.45460i	0.874224	−	0.485523i	$-0.161371\pi$
$660$	−21.0366	−	18.7915i	−0.818848	−	0.731459i
$661$	16.8947	−	4.00411i	0.657126	−	0.155742i	0.111492	−	0.993765i	$-0.464437\pi$
$661$	16.8947	−	4.00411i	0.657126	−	0.155742i	0.545634	+	0.838024i	$0.316289\pi$
$662$	−2.39076	+	7.98571i	−0.0929197	+	0.310373i
$663$	−4.18227	−	28.9290i	−0.162426	−	1.12351i
$664$	−10.9559	+	1.28056i	−0.425172	+	0.0496955i
$665$	2.56972	+	14.5736i	0.0996494	+	0.565140i
$666$	3.81555	+	0.236542i	0.147850	+	0.00916582i
$667$	0.126439	−	0.717068i	0.00489572	−	0.0277650i
$668$	−0.501795	+	8.61550i	−0.0194150	+	0.333344i
$669$	4.01491	−	12.0409i	0.155225	−	0.465528i
$670$	−2.97968	−	6.90767i	−0.115115	−	0.266866i
$671$	−18.6106	−	9.34658i	−0.718453	−	0.360821i
$672$	2.36137	−	5.03936i	0.0910917	−	0.194398i
$673$	42.9001	+	10.1675i	1.65368	+	0.391928i	0.948418	−	0.317023i	$-0.102683\pi$
$673$	42.9001	+	10.1675i	1.65368	+	0.391928i	0.705258	+	0.708951i	$0.250831\pi$
$674$	−1.95524	+	3.38658i	−0.0753131	+	0.130446i
$675$	−35.2604	−	57.8896i	−1.35717	−	2.22817i
$676$	2.95261	+	5.11407i	0.113562	+	0.196695i
$677$	−9.95022	−	33.2361i	−0.382418	−	1.27737i	−0.905232	−	0.424918i	$-0.860303\pi$
$677$	−9.95022	−	33.2361i	−0.382418	−	1.27737i	0.522814	−	0.852447i	$-0.324882\pi$
$678$	−0.353909	+	3.95996i	−0.0135918	+	0.152081i
$679$	6.05265	−	3.98089i	0.232279	−	0.152772i
$680$	−10.1844	+	13.6800i	−0.390552	+	0.524603i
$681$	−39.8815	−	5.91793i	−1.52826	−	0.226776i
$682$	0.775884	+	0.510307i	0.0297101	+	0.0195407i
$683$	−40.1564	+	14.6157i	−1.53654	+	0.559256i	−0.965213	−	0.261465i	$-0.915794\pi$
$683$	−40.1564	+	14.6157i	−1.53654	+	0.559256i	−0.571329	+	0.820721i	$0.693572\pi$
$684$	14.0874	+	10.5697i	0.538643	+	0.404143i
$685$	−1.19440	−	0.434725i	−0.0456356	−	0.0166100i
$686$	2.10776	+	2.83121i	0.0804746	+	0.108096i
$687$	−0.0455239	+	0.0734978i	−0.00173685	+	0.00280412i
$688$	−18.2962	−	19.3928i	−0.697535	−	0.739343i
$689$	12.2966	+	13.0336i	0.468463	+	0.496542i
$690$	−2.16885	−	0.0671635i	−0.0825665	−	0.00255687i
$691$	−9.57368	−	12.8597i	−0.364200	−	0.489205i	0.581818	−	0.813319i	$-0.302341\pi$
$691$	−9.57368	−	12.8597i	−0.364200	−	0.489205i	−0.946018	+	0.324113i	$0.894934\pi$
$692$	5.68957	+	2.07083i	0.216285	+	0.0787213i
$693$	−3.08586	+	6.08762i	−0.117222	+	0.231250i
$694$	−7.22724	+	2.63050i	−0.274342	+	0.0998524i
$695$	−19.9089	−	13.0943i	−0.755187	−	0.496694i
$696$	−0.612397	+	0.771534i	−0.0232128	+	0.0292449i
$697$	−14.4136	+	19.3609i	−0.545955	+	0.733345i
$698$	3.50129	−	2.30284i	0.132526	−	0.0871637i
$699$	35.2079	−	16.3377i	1.33168	−	0.617948i
$700$	−8.36916	−	27.9550i	−0.316325	−	1.05660i
$701$	20.8919	+	36.1858i	0.789075	+	1.36672i	0.926534	+	0.376211i	$0.122773\pi$
$701$	20.8919	+	36.1858i	0.789075	+	1.36672i	−0.137459	+	0.990507i	$0.543894\pi$
$702$	−4.86687	+	1.27488i	−0.183688	+	0.0481171i
$703$	−7.96914	+	13.8029i	−0.300562	+	0.520588i
$704$	−12.7413	−	3.01974i	−0.480205	−	0.113811i
$705$	−1.83785	−	2.63519i	−0.0692175	−	0.0992471i
$706$	−0.734464	−	0.368862i	−0.0276419	−	0.0138823i
$707$	1.84719	+	4.28228i	0.0694709	+	0.161052i
$708$	27.4544	−	5.61541i	1.03180	−	0.211040i
$709$	0.982391	−	16.8670i	0.0368945	−	0.633453i	−0.928286	−	0.371868i	$-0.878718\pi$
$709$	0.982391	−	16.8670i	0.0368945	−	0.633453i	0.965180	−	0.261586i	$-0.0842454\pi$
$710$	0.854057	−	4.84360i	0.0320522	−	0.181777i
$711$	−36.2606	+	10.7082i	−1.35988	+	0.401589i
$712$	−1.82174	−	10.3316i	−0.0682724	−	0.387192i
$713$	−2.35733	+	0.275532i	−0.0882825	+	0.0103187i
$714$	1.88767	+	0.754009i	0.0706441	+	0.0282181i
$715$	−9.63515	+	32.1836i	−0.360334	+	1.20360i
$716$	26.8944	−	6.37410i	1.00509	−	0.238211i
$717$	7.25681	−	34.8161i	0.271010	−	1.30023i
$718$	−0.971560	+	2.25233i	−0.0362583	+	0.0840562i
$719$	−12.7933	+	10.7349i	−0.477111	+	0.400344i	−0.849381	−	0.527781i	$-0.823024\pi$
$719$	−12.7933	+	10.7349i	−0.477111	+	0.400344i	0.372269	+	0.928125i	$0.378580\pi$
$720$	−40.2262	−	23.4255i	−1.49914	−	0.873017i
$721$	−7.31216	−	6.13563i	−0.272319	−	0.228503i
$722$	−2.12955	+	1.06950i	−0.0792538	+	0.0398028i
$723$	−42.4859	+	26.0962i	−1.58007	+	0.970529i
$724$	30.6472	+	3.58214i	1.13899	+	0.133129i
$725$	0.452704	+	7.77263i	0.0168130	+	0.288668i
$726$	2.87054	+	0.774910i	0.106536	+	0.0287596i
$727$	−15.1791	+	16.0889i	−0.562963	+	0.596706i	−0.944850	−	0.327503i	$-0.893793\pi$
$727$	−15.1791	+	16.0889i	−0.562963	+	0.596706i	0.381887	+	0.924209i	$0.375274\pi$
$728$	−4.39701			−0.162964
$729$	−0.302718	+	26.9983i	−0.0112118	+	0.999937i
$730$	−7.40242			−0.273976
$731$	21.1047	−	22.3697i	0.780587	−	0.827374i
$732$	−34.2422	−	9.24377i	−1.26563	−	0.341660i
$733$	0.763834	+	13.1145i	0.0282128	+	0.484396i	0.982589	+	0.185790i	$0.0594845\pi$
$733$	0.763834	+	13.1145i	0.0282128	+	0.484396i	−0.954377	+	0.298606i	$0.903479\pi$
$734$	−3.56899	−	0.417155i	−0.131734	−	0.0153975i
$735$	35.5634	−	21.8442i	1.31178	−	0.805735i
$736$	−3.04026	+	1.52687i	−0.112065	+	0.0562813i
$737$	11.0811	+	9.29816i	0.408178	+	0.342502i
$738$	3.59012	+	2.09068i	0.132154	+	0.0769592i
$739$	−34.4177	+	28.8799i	−1.26608	+	1.06236i	−0.271070	+	0.962560i	$0.587378\pi$
$739$	−34.4177	+	28.8799i	−1.26608	+	1.06236i	−0.995007	+	0.0998052i	$0.968178\pi$
$740$	17.2195	−	39.9193i	0.633002	−	1.46746i
$741$	4.27999	−	20.5342i	0.157229	−	0.754343i
$742$	−1.21251	+	0.287370i	−0.0445127	+	0.0105497i
$743$	6.41571	−	21.4300i	0.235370	−	0.786189i	−0.755940	−	0.654641i	$-0.772820\pi$
$743$	6.41571	−	21.4300i	0.235370	−	0.786189i	0.991310	−	0.131548i	$-0.0419949\pi$
$744$	2.98170	+	1.19101i	0.109314	+	0.0436645i
$745$	−57.4919	+	6.71984i	−2.10634	+	0.246196i
$746$	−0.884944	−	5.01877i	−0.0324001	−	0.183750i
$747$	33.3069	−	9.83596i	1.21864	−	0.359879i
$748$	2.80504	−	15.9082i	0.102563	−	0.581661i
$749$	−1.06566	+	18.2967i	−0.0389385	+	0.668547i
$750$	14.0188	−	2.86734i	0.511893	−	0.104700i
$751$	4.70782	+	10.9140i	0.171791	+	0.398256i	0.982260	−	0.187526i	$-0.0600469\pi$
$751$	4.70782	+	10.9140i	0.171791	+	0.398256i	−0.810469	+	0.585782i	$0.800788\pi$
$752$	−1.42536	−	0.715845i	−0.0519777	−	0.0261042i
$753$	10.0993	+	14.4808i	0.368038	+	0.527709i
$754$	0.562313	+	0.133271i	0.0204782	+	0.00485343i
$755$	−20.0784	+	34.7768i	−0.730728	+	1.26566i
$756$	−3.07132	+	11.2105i	−0.111703	+	0.407724i
$757$	−2.60890	−	4.51875i	−0.0948221	−	0.164237i	0.814712	−	0.579865i	$-0.196895\pi$
$757$	−2.60890	−	4.51875i	−0.0948221	−	0.164237i	−0.909534	+	0.415629i	$0.863562\pi$
$758$	−0.481813	−	1.60937i	−0.0175003	−	0.0584549i
$759$	3.78471	−	1.75624i	0.137376	−	0.0637474i
$760$	−10.2252	+	6.72520i	−0.370906	+	0.243949i
$761$	−0.417060	+	0.560209i	−0.0151184	+	0.0203075i	−0.809618	−	0.586957i	$-0.800326\pi$
$761$	−0.417060	+	0.560209i	−0.0151184	+	0.0203075i	0.794500	+	0.607265i	$0.207733\pi$
$762$	−2.90188	+	3.65596i	−0.105124	+	0.132441i
$763$	−3.48572	−	2.29259i	−0.126191	−	0.0829974i
$764$	37.0505	−	13.4853i	1.34044	−	0.487880i
$765$	24.2778	−	47.8939i	0.877765	−	1.73161i
$766$	8.02630	+	2.92133i	0.290002	+	0.105552i
$767$	−19.9302	−	26.7710i	−0.719639	−	0.966643i
$768$	−19.9556	−	0.617973i	−0.720085	−	0.0222992i
$769$	−7.63552	−	8.09318i	−0.275344	−	0.291848i	0.574914	−	0.818214i	$-0.305036\pi$
$769$	−7.63552	−	8.09318i	−0.275344	−	0.291848i	−0.850258	+	0.526366i	$0.823554\pi$
$770$	−1.60323	−	1.69933i	−0.0577765	−	0.0612395i
$771$	5.52740	−	8.92392i	0.199065	−	0.321387i
$772$	3.09849	+	4.16199i	0.111517	+	0.149793i
$773$	−14.5554	−	5.29774i	−0.523522	−	0.190546i	0.0667217	−	0.997772i	$-0.478746\pi$
$773$	−14.5554	−	5.29774i	−0.523522	−	0.190546i	−0.590243	+	0.807225i	$0.700968\pi$
$774$	−4.23415	−	3.17688i	−0.152194	−	0.114190i
$775$	23.8477	−	8.67985i	0.856634	−	0.311789i
$776$	5.00565	+	3.29227i	0.179692	+	0.118186i
$777$	−10.4053	−	1.54401i	−0.373287	−	0.0553912i
$778$	−3.71346	+	4.98804i	−0.133134	+	0.178830i
$779$	−14.4714	+	9.51799i	−0.518491	+	0.341017i
$780$	−5.09311	+	56.9878i	−0.182363	+	2.04049i
$781$	2.71234	+	9.05983i	0.0970550	+	0.324186i
$782$	−0.621316	−	1.07615i	−0.0222182	−	0.0384831i
$783$	1.48717	−	2.72150i	0.0531472	−	0.0972585i
$784$	10.3603	−	17.9445i	0.370009	−	0.640875i
$785$	37.7061	+	8.93651i	1.34579	+	0.318958i
$786$	−2.15530	+	4.59960i	−0.0768771	+	0.164062i
$787$	−31.4879	−	15.8138i	−1.12242	−	0.563702i	−0.211954	−	0.977280i	$-0.567983\pi$
$787$	−31.4879	−	15.8138i	−1.12242	−	0.563702i	−0.910469	+	0.413578i	$0.864279\pi$
$788$	−12.8592	−	29.8109i	−0.458089	−	1.06197i
$789$	7.35138	−	22.0471i	0.261716	−	0.784899i
$790$	0.752513	−	12.9202i	0.0267732	−	0.459678i
$791$	1.89968	−	10.7736i	0.0675449	−	0.383066i
$792$	−5.63365	−	0.349254i	−0.200183	−	0.0124102i
$793$	7.33528	+	41.6004i	0.260483	+	1.47728i
$794$	−4.46561	+	0.521955i	−0.158479	+	0.0185235i
$795$	4.70987	+	32.5784i	0.167042	+	1.15544i
$796$	1.08924	−	3.63831i	0.0386070	−	0.128956i
$797$	−25.7981	+	6.11427i	−0.913816	+	0.216578i	−0.660518	−	0.750810i	$-0.729663\pi$
$797$	−25.7981	+	6.11427i	−0.913816	+	0.216578i	−0.253298	+	0.967388i	$0.581515\pi$
$798$	1.08785	+	0.971753i	0.0385095	+	0.0343997i
$799$	0.728735	−	1.68940i	0.0257808	−	0.0597666i
$800$	27.8676	−	23.3837i	0.985268	−	0.826738i
$801$	11.1809	+	31.0802i	0.395058	+	1.09817i
$802$	−0.856252	−	0.718481i	−0.0302353	−	0.0253704i
$803$	12.7197	−	6.38806i	0.448867	−	0.225430i
$804$	21.6625	+	11.7326i	0.763977	+	0.413777i
$805$	5.93038	+	0.693162i	0.209018	+	0.0244308i
$806$	−0.109525	−	1.88047i	−0.00385786	−	0.0662368i
$807$	−3.53680	+	3.52360i	−0.124501	+	0.124037i
$808$	−2.64681	+	2.80545i	−0.0931143	+	0.0986954i
$809$	−4.72350			−0.166070			−0.0830348	−	0.996547i	$-0.526461\pi$
$809$	−4.72350			−0.166070			−0.0830348	+	0.996547i	$0.526461\pi$
$810$	−8.66096	−	3.22585i	−0.304315	−	0.113345i
$811$	−14.2884			−0.501733			−0.250866	−	0.968022i	$-0.580716\pi$
$811$	−14.2884			−0.501733			−0.250866	+	0.968022i	$0.580716\pi$
$812$	0.916229	−	0.971146i	0.0321533	−	0.0340805i
$813$	1.42961	+	5.37555i	0.0501388	+	0.188529i
$814$	−0.146304	−	2.51194i	−0.00512795	−	0.0880436i
$815$	33.5071	+	3.91642i	1.17370	+	0.137186i
$816$	−0.725542	−	26.6480i	−0.0253991	−	0.932867i
$817$	19.7219	−	9.90471i	0.689982	−	0.346522i
$818$	−2.02577	−	1.69982i	−0.0708294	−	0.0594329i
$819$	13.6423	−	2.35297i	0.476701	−	0.0822195i
$820$	36.1927	−	30.3693i	1.26391	−	1.06054i
$821$	−8.66239	+	20.0817i	−0.302319	+	0.700855i	−0.999877	−	0.0156735i	$-0.995011\pi$
$821$	−8.66239	+	20.0817i	−0.302319	+	0.700855i	0.697558	+	0.716528i	$0.254270\pi$
$822$	−0.119001	+	0.0391859i	−0.00415063	+	0.00136677i
$823$	22.8742	−	5.42129i	0.797346	−	0.188974i	0.188302	−	0.982111i	$-0.439702\pi$
$823$	22.8742	−	5.42129i	0.797346	−	0.188974i	0.609044	+	0.793137i	$0.291553\pi$
$824$	2.26408	−	7.56254i	0.0788728	−	0.263454i
$825$	−35.0478	+	27.6059i	−1.22021	+	0.961115i
$826$	2.30527	−	0.269447i	0.0802105	−	0.00937526i
$827$	3.09330	+	17.5430i	0.107565	+	0.610030i	0.990165	+	0.139905i	$0.0446799\pi$
$827$	3.09330	+	17.5430i	0.107565	+	0.610030i	−0.882600	+	0.470124i	$0.844209\pi$
$828$	5.71557	−	4.22198i	0.198630	−	0.146724i
$829$	−9.35023	+	53.0278i	−0.324747	+	1.84173i	0.186700	+	0.982417i	$0.440221\pi$
$829$	−9.35023	+	53.0278i	−0.324747	+	1.84173i	−0.511447	+	0.859315i	$0.670890\pi$
$830$	−0.691217	+	11.8677i	−0.0239925	+	0.411935i
$831$	−3.91396	−	4.41466i	−0.135774	−	0.153143i
$832$	10.5198	+	24.3877i	0.364710	+	0.845492i
$833$	21.3589	+	10.7269i	0.740043	+	0.371664i
$834$	−2.34025	+	0.200340i	−0.0810364	+	0.00693720i
$835$	18.3727	+	4.35442i	0.635815	+	0.150691i
$836$	5.79597	−	10.0389i	0.200458	−	0.347203i
$837$	−9.88847	−	2.09967i	−0.341795	−	0.0725752i
$838$	4.05420	+	7.02209i	0.140050	+	0.242574i
$839$	14.9376	+	49.8951i	0.515703	+	1.72257i	0.677295	+	0.735712i	$0.263152\pi$
$839$	14.9376	+	49.8951i	0.515703	+	1.72257i	−0.161591	+	0.986858i	$0.551663\pi$
$840$	−6.60795	−	4.64537i	−0.227996	−	0.160280i
$841$	23.9315	−	15.7400i	0.825225	−	0.542759i
$842$	0.239442	−	0.321626i	0.00825171	−	0.0110840i
$843$	7.30983	+	18.5006i	0.251764	+	0.637195i
$844$	16.8125	+	11.0577i	0.578709	+	0.380623i
$845$	12.1408	−	4.41889i	0.417656	−	0.152014i
$846$	−0.303036	−	0.0919584i	−0.0104186	−	0.00316160i
$847$	−7.68804	−	2.79822i	−0.264164	−	0.0961480i
$848$	9.75883	+	13.1084i	0.335119	+	0.450144i
$849$	20.7594	+	38.6735i	0.712461	+	1.32727i
$850$	9.11831	+	9.66484i	0.312755	+	0.331501i
$851$	4.41298	+	4.67749i	0.151275	+	0.160342i
$852$	7.61753	+	14.1910i	0.260972	+	0.486176i
$853$	28.9997	+	38.9533i	0.992930	+	1.33374i	0.942210	+	0.335024i	$0.108744\pi$
$853$	28.9997	+	38.9533i	0.992930	+	1.33374i	0.0507205	+	0.998713i	$0.483848\pi$
$854$	−2.76043	−	1.00472i	−0.0944601	−	0.0343807i
$855$	28.1261	−	26.3376i	0.961893	−	0.900728i
$856$	−14.2433	+	5.18412i	−0.486825	+	0.177190i
$857$	−36.4270	−	23.9584i	−1.24432	−	0.818403i	−0.255399	−	0.966836i	$-0.582207\pi$
$857$	−36.4270	−	23.9584i	−1.24432	−	0.818403i	−0.988922	+	0.148433i	$0.952577\pi$
$858$	1.21685	+	3.07975i	0.0415425	+	0.105141i
$859$	9.73608	−	13.0778i	0.332191	−	0.446209i	−0.604376	−	0.796699i	$-0.706577\pi$
$859$	9.73608	−	13.0778i	0.332191	−	0.446209i	0.936567	+	0.350490i	$0.113985\pi$
$860$	−50.2953	+	33.0797i	−1.71505	+	1.12801i
$861$	−9.35205	−	6.57445i	−0.318717	−	0.224057i
$862$	1.04752	+	3.49896i	0.0356787	+	0.119175i
$863$	−25.0920	−	43.4607i	−0.854142	−	1.47942i	−0.877439	−	0.479689i	$-0.840749\pi$
$863$	−25.0920	−	43.4607i	−0.854142	−	1.47942i	0.0232963	−	0.999729i	$-0.492584\pi$
$864$	−14.3493	+	2.01976i	−0.488172	+	0.0687136i
$865$	6.62352	−	11.4723i	0.225207	−	0.390069i
$866$	1.16040	+	0.275021i	0.0394322	+	0.00934559i
$867$	1.30043	−	0.111324i	0.0441649	−	0.00378078i
$868$	−3.88904	−	1.95315i	−0.132003	−	0.0662943i
$869$	9.85663	+	22.8502i	0.334363	+	0.775142i
$870$	0.704262	+	0.794357i	0.0238767	+	0.0269312i
$871$	1.70603	−	29.2914i	0.0578066	−	0.992501i
$872$	0.599153	−	3.39796i	0.0202899	−	0.115070i
$873$	−17.2925	−	7.53603i	−0.585262	−	0.255056i
$874$	−0.154846	−	0.878175i	−0.00523774	−	0.0297047i
$875$	−39.1070	+	4.57095i	−1.32206	+	0.154526i
$876$	19.0431	−	14.9996i	0.643408	−	0.506790i
$877$	12.8676	−	42.9809i	0.434509	−	1.45136i	−0.408151	−	0.912914i	$-0.633826\pi$
$877$	12.8676	−	42.9809i	0.434509	−	1.45136i	0.842660	−	0.538446i	$-0.180988\pi$
$878$	−4.74706	+	1.12507i	−0.160206	+	0.0379694i
$879$	−6.60716	+	2.17568i	−0.222854	+	0.0733838i
$880$	−12.1355	+	28.1332i	−0.409087	+	0.948371i
$881$	13.9661	−	11.7190i	0.470531	−	0.394822i	−0.376457	−	0.926434i	$-0.622858\pi$
$881$	13.9661	−	11.7190i	0.470531	−	0.394822i	0.846988	+	0.531612i	$0.178413\pi$
$882$	1.42148	−	3.86054i	0.0478638	−	0.129991i
$883$	−13.4700	−	11.3026i	−0.453300	−	0.380364i	0.387359	−	0.921929i	$-0.373388\pi$
$883$	−13.4700	−	11.3026i	−0.453300	−	0.380364i	−0.840659	+	0.541565i	$0.817832\pi$
$884$	−29.2802	+	14.7051i	−0.984801	+	0.494586i
$885$	−1.66868	−	61.2881i	−0.0560922	−	2.06018i
$886$	−6.76783	−	0.791045i	−0.227370	−	0.0265757i
$887$	1.91686	+	32.9112i	0.0643618	+	1.10505i	0.863647	+	0.504097i	$0.168175\pi$
$887$	1.91686	+	32.9112i	0.0643618	+	1.10505i	−0.799285	+	0.600952i	$0.794788\pi$
$888$	−2.23591	−	8.40733i	−0.0750321	−	0.282132i
$889$	8.81389	−	9.34217i	0.295608	−	0.313326i
$890$	−11.3064			−0.378990
$891$	17.6660	−	1.93113i	0.591835	−	0.0646952i
$892$	−14.2279			−0.476386
$893$	0.906047	−	0.960353i	0.0303197	−	0.0321370i
$894$	−4.04194	+	4.02687i	−0.135183	+	0.134679i
$895$	−3.51614	−	60.3698i	−0.117532	−	2.01794i
$896$	−8.21719	−	0.960452i	−0.274517	−	0.0320864i
$897$	−7.44165	−	4.03047i	−0.248470	−	0.134573i
$898$	0.0937829	−	0.0470995i	0.00312957	−	0.00157173i
$899$	0.889494	+	0.746374i	0.0296663	+	0.0248930i
$900$	−49.0573	+	58.0225i	−1.63524	+	1.93408i
$901$	−14.4405	+	12.1170i	−0.481082	+	0.403676i
$902$	1.08307	−	2.51084i	0.0360623	−	0.0836018i
$903$	10.8628	+	9.70352i	0.361492	+	0.322913i
$904$	8.80357	−	2.08648i	0.292802	−	0.0693954i
$905$	19.3618	−	64.6730i	0.643609	−	2.14980i
$906$	0.566354	+	3.91750i	0.0188159	+	0.130150i
$907$	38.9906	−	4.55734i	1.29466	−	0.151324i	0.559280	−	0.828979i	$-0.311078\pi$
$907$	38.9906	−	4.55734i	1.29466	−	0.151324i	0.735380	+	0.677655i	$0.237004\pi$
$908$	7.84805	+	44.5085i	0.260447	+	1.47707i
$909$	6.71079	−	10.1207i	0.222583	−	0.335681i
$910$	−0.822878	+	4.66678i	−0.0272782	+	0.154702i
$911$	−0.885525	+	15.2039i	−0.0293388	+	0.503727i	0.951345	+	0.308127i	$0.0997023\pi$
$911$	−0.885525	+	15.2039i	−0.0293388	+	0.503727i	−0.980684	+	0.195600i	$0.937335\pi$
$912$	6.05113	−	18.1476i	0.200373	−	0.600928i
$913$	−9.05376	−	20.9890i	−0.299636	−	0.694634i
$914$	5.85486	+	2.94042i	0.193662	+	0.0972605i
$915$	−32.9265	+	70.2679i	−1.08852	+	2.32299i
$916$	0.0942996	+	0.0223494i	0.00311575	+	0.000738445i
$917$	6.98854	−	12.1045i	0.230782	−	0.399726i
$918$	−1.04121	−	5.18933i	−0.0343651	−	0.171273i
$919$	−7.39953	−	12.8164i	−0.244088	−	0.422773i	0.717787	−	0.696263i	$-0.245155\pi$
$919$	−7.39953	−	12.8164i	−0.244088	−	0.422773i	−0.961875	+	0.273490i	$0.911822\pi$
$920$	1.41621	+	4.73048i	0.0466911	+	0.155959i
$921$	3.06509	−	34.2959i	0.100998	−	1.13009i
$922$	8.62963	−	5.67579i	0.284202	−	0.186922i
$923$	11.4550	−	15.3867i	0.377046	−	0.506461i
$924$	7.56777	+	1.12296i	0.248961	+	0.0369428i
$925$	−57.4499	−	37.7854i	−1.88894	−	1.24238i
$926$	6.89258	−	2.50869i	0.226504	−	0.0824407i
$927$	−2.97766	+	24.6754i	−0.0977991	+	0.810445i
$928$	1.56408	+	0.569280i	0.0513436	+	0.0186875i
$929$	18.2773	+	24.5506i	0.599658	+	0.805480i	0.993516	−	0.113691i	$-0.0362673\pi$
$929$	18.2773	+	24.5506i	0.599658	+	0.805480i	−0.393858	+	0.919171i	$0.628860\pi$
$930$	1.82209	−	2.94174i	0.0597487	−	0.0964635i
$931$	11.7702	+	12.4757i	0.385753	+	0.408874i
$932$	−29.8575	−	31.6471i	−0.978016	−	1.03664i
$933$	−2.67333	−	0.0827860i	−0.0875209	−	0.00271029i
$934$	1.94252	+	2.60925i	0.0635610	+	0.0853773i
$935$	−33.2109	−	12.0878i	−1.08611	−	0.395313i
$936$	6.25555	+	9.58897i	0.204469	+	0.313425i
$937$	3.22880	−	1.17519i	0.105480	−	0.0383917i	−0.288741	−	0.957407i	$-0.593237\pi$
$937$	3.22880	−	1.17519i	0.105480	−	0.0383917i	0.394221	+	0.919016i	$0.371014\pi$
$938$	1.70475	+	1.12123i	0.0556621	+	0.0366095i
$939$	18.8434	−	23.7400i	0.614930	−	0.774726i
$940$	−2.15060	+	2.88876i	−0.0701450	+	0.0942211i
$941$	16.1846	−	10.6448i	0.527603	−	0.347010i	−0.257596	−	0.966253i	$-0.582931\pi$
$941$	16.1846	−	10.6448i	0.527603	−	0.347010i	0.785200	+	0.619242i	$0.212560\pi$
$942$	3.46477	−	1.60777i	0.112888	−	0.0523840i
$943$	2.00432	+	6.69491i	0.0652698	+	0.218016i
$944$	−15.2192	−	26.3605i	−0.495344	−	0.857961i
$945$	22.9879	+	10.8768i	0.747798	+	0.353821i
$946$	−1.74206	+	3.01734i	−0.0566393	+	0.0981022i
$947$	13.4174	+	3.17998i	0.436006	+	0.103335i	0.442757	−	0.896642i	$-0.354001\pi$
$947$	13.4174	+	3.17998i	0.436006	+	0.103335i	−0.00675038	+	0.999977i	$0.502149\pi$
$948$	24.2444	+	34.7626i	0.787421	+	1.12904i
$949$	−25.8001	−	12.9573i	−0.837508	−	0.420612i
$950$	3.77665	+	8.75525i	0.122531	+	0.284058i
$951$	−3.33359	+	0.681839i	−0.108099	+	0.0221101i
$952$	0.268961	−	4.61788i	0.00871707	−	0.149666i
$953$	−6.51937	+	36.9732i	−0.211183	+	1.19768i	0.676225	+	0.736695i	$0.263615\pi$
$953$	−6.51937	+	36.9732i	−0.211183	+	1.19768i	−0.887408	+	0.460984i	$0.847497\pi$
$954$	2.35171	+	2.23540i	0.0761395	+	0.0723737i
$955$	−14.9797	−	84.9541i	−0.484732	−	2.74905i
$956$	−39.5966	+	4.62818i	−1.28065	+	0.149686i
$957$	−1.89565	−	0.757197i	−0.0612776	−	0.0244767i
$958$	1.80103	−	6.01586i	0.0581887	−	0.194364i
$959$	0.335452	−	0.0795035i	0.0108323	−	0.00256730i
$960$	−9.95569	+	47.7646i	−0.321319	+	1.54160i
$961$	−10.7794	+	24.9894i	−0.347722	+	0.806110i
$962$	−3.90972	+	3.28064i	−0.126054	+	0.105772i
$963$	41.4175	−	23.7064i	1.33466	−	0.763929i
$964$	42.8154	+	35.9264i	1.37899	+	1.15711i
$965$	10.1448	−	5.09492i	0.326574	−	0.164011i
$966$	0.501487	−	0.308029i	0.0161351	−	0.00991069i
$967$	−24.4158	−	2.85380i	−0.785160	−	0.0917720i	−0.285940	−	0.958248i	$-0.592306\pi$
$967$	−24.4158	−	2.85380i	−0.785160	−	0.0917720i	−0.499220	+	0.866475i	$0.666380\pi$
$968$	−0.393420	−	6.75476i	−0.0126450	−	0.217106i
$969$	21.3039	+	5.75104i	0.684378	+	0.184750i
$970$	4.43104	−	4.69663i	0.142272	−	0.150800i
$971$	13.0415			0.418522			0.209261	−	0.977860i	$-0.432894\pi$
$971$	13.0415			0.418522			0.209261	+	0.977860i	$0.432894\pi$
$972$	28.8174	−	9.25114i	0.924318	−	0.296731i
$973$	6.46310			0.207197
$974$	−0.448877	+	0.475782i	−0.0143829	+	0.0152450i
$975$	87.3667	+	23.5849i	2.79797	+	0.755321i
$976$	2.24005	+	38.4602i	0.0717023	+	1.23108i
$977$	−48.1120	−	5.62348i	−1.53924	−	0.179911i	−0.696233	−	0.717816i	$-0.745142\pi$
$977$	−48.1120	−	5.62348i	−1.53924	−	0.179911i	−0.843006	+	0.537905i	$0.819216\pi$
$978$	2.83344	−	1.74039i	0.0906033	−	0.0556515i
$979$	19.4279	−	9.75704i	0.620917	−	0.311836i
$980$	−35.8392	−	30.0727i	−1.14484	−	0.960636i
$981$	−0.0405998	+	10.8633i	−0.00129625	+	0.346837i
$982$	7.37186	−	6.18573i	0.235246	−	0.197394i
$983$	−13.1111	+	30.3950i	−0.418179	+	0.969449i	0.570759	+	0.821118i	$0.306649\pi$
$983$	−13.1111	+	30.3950i	−0.418179	+	0.969449i	−0.988938	+	0.148331i	$0.952610\pi$
$984$	1.92911	−	9.25533i	0.0614979	−	0.295049i
$985$	−69.1176	+	16.3812i	−2.20227	+	0.521948i
$986$	−0.174361	+	0.582407i	−0.00555279	+	0.0185476i
$987$	0.809226	+	0.323237i	0.0257579	+	0.0102887i
$988$	−23.3537	+	2.72966i	−0.742980	+	0.0868420i
$989$	−1.54623	−	8.76910i	−0.0491672	−	0.278841i
$990$	−1.42499	+	5.91392i	−0.0452891	+	0.187957i
$991$	−3.02007	+	17.1276i	−0.0959355	+	0.544078i	0.898521	+	0.438930i	$0.144642\pi$
$991$	−3.02007	+	17.1276i	−0.0959355	+	0.544078i	−0.994457	+	0.105147i	$0.966469\pi$
$992$	0.315459	−	5.41622i	0.0100158	−	0.171965i
$993$	−58.5136	+	11.9681i	−1.85687	+	0.379797i
$994$	0.528364	+	1.22489i	0.0167587	+	0.0388510i
$995$	−7.42546	−	3.72921i	−0.235403	−	0.118224i
$996$	−22.2695	−	31.9310i	−0.705638	−	1.01177i
$997$	−16.8175	−	3.98582i	−0.532615	−	0.126232i	−0.0444969	−	0.999010i	$-0.514168\pi$
$997$	−16.8175	−	3.98582i	−0.532615	−	0.126232i	−0.488119	+	0.872777i	$0.662317\pi$
$998$	−0.300413	+	0.520330i	−0.00950940	+	0.0164708i
$999$	11.4362	+	24.8884i	0.361826	+	0.787433i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.70.4	yes	144
3.2	odd	2		243.2.g.a.127.5		144
9.2	odd	6		729.2.g.b.136.4		144
9.4	even	3		729.2.g.d.379.4		144
9.5	odd	6		729.2.g.a.379.5		144
9.7	even	3		729.2.g.c.136.5		144
81.5	odd	54		729.2.g.a.352.5		144
81.22	even	27	inner	81.2.g.a.22.4	✓	144
81.32	odd	54		729.2.g.b.595.4		144
81.34	even	27		6561.2.a.c.1.41		72
81.47	odd	54		6561.2.a.d.1.32		72
81.49	even	27		729.2.g.c.595.5		144
81.59	odd	54		243.2.g.a.199.5		144
81.76	even	27		729.2.g.d.352.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.22.4	✓	144	81.22	even	27	inner
81.2.g.a.70.4	yes	144	1.1	even	1	trivial
243.2.g.a.127.5		144	3.2	odd	2
243.2.g.a.199.5		144	81.59	odd	54
729.2.g.a.352.5		144	81.5	odd	54
729.2.g.a.379.5		144	9.5	odd	6
729.2.g.b.136.4		144	9.2	odd	6
729.2.g.b.595.4		144	81.32	odd	54
729.2.g.c.136.5		144	9.7	even	3
729.2.g.c.595.5		144	81.49	even	27
729.2.g.d.352.4		144	81.76	even	27
729.2.g.d.379.4		144	9.4	even	3
6561.2.a.c.1.41		72	81.34	even	27
6561.2.a.d.1.32		72	81.47	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.165895 + 0.175839i) q^{2} +(-1.67219 - 0.451413i) q^{3} +(0.112892 + 1.93827i) q^{4} +(4.21919 + 0.493153i) q^{5} +(0.356785 - 0.219149i) q^{6} +(-1.02960 + 0.517085i) q^{7} +(-0.729927 - 0.612481i) q^{8} +(2.59245 + 1.50970i) q^{9} +(-0.786660 + 0.660086i) q^{10} +(0.782094 - 1.81310i) q^{11} +(0.686186 - 3.29213i) q^{12} +(-3.89722 + 0.923659i) q^{13} +(0.0798824 - 0.266826i) q^{14} +(-6.83269 - 2.72925i) q^{15} +(-3.62807 + 0.424061i) q^{16} +(-0.731666 - 4.14948i) q^{17} +(-0.695540 + 0.205402i) q^{18} +(0.525049 - 2.97770i) q^{19} +(-0.479554 + 8.23363i) q^{20} +(1.95511 - 0.399890i) q^{21} +(0.189067 + 0.438307i) q^{22} +(-1.09019 - 0.547514i) q^{23} +(0.944095 + 1.35368i) q^{24} +(12.6932 + 3.00834i) q^{25} +(0.484116 - 0.838513i) q^{26} +(-3.65358 - 3.69477i) q^{27} +(-1.11849 - 1.93728i) q^{28} +(0.171179 + 0.571777i) q^{29} +(1.61342 - 0.748682i) q^{30} +(1.62541 - 1.06905i) q^{31} +(1.66532 - 2.23691i) q^{32} +(-2.12627 + 2.67880i) q^{33} +(0.851020 + 0.559725i) q^{34} +(-4.59909 + 1.67393i) q^{35} +(-2.63355 + 5.19532i) q^{36} +(-4.95333 - 1.80287i) q^{37} +(0.436492 + 0.586310i) q^{38} +(6.93385 + 0.214723i) q^{39} +(-2.77766 - 2.94414i) q^{40} +(-3.93113 - 4.16676i) q^{41} +(-0.254028 + 0.410124i) q^{42} +(4.35863 + 5.85466i) q^{43} +(3.60257 + 1.31123i) q^{44} +(10.1935 + 7.64819i) q^{45} +(0.277132 - 0.100868i) q^{46} +(0.364825 + 0.239949i) q^{47} +(6.25826 + 0.928649i) q^{48} +(-3.38741 + 4.55008i) q^{49} +(-2.63472 + 1.73288i) q^{50} +(-0.649646 + 7.26902i) q^{51} +(-2.23027 - 7.44961i) q^{52} +(-2.23695 - 3.87450i) q^{53} +(1.25580 - 0.0294951i) q^{54} +(4.19394 - 7.26412i) q^{55} +(1.06824 + 0.253177i) q^{56} +(-2.22216 + 4.74227i) q^{57} +(-0.128938 - 0.0647553i) q^{58} +(3.30053 + 7.65148i) q^{59} +(4.51868 - 13.5517i) q^{60} +(0.613247 - 10.5290i) q^{61} +(-0.0816677 + 0.463161i) q^{62} +(-3.44984 - 0.213870i) q^{63} +(-1.15153 - 6.53063i) q^{64} +(-16.8986 + 1.97517i) q^{65} +(-0.118299 - 0.818281i) q^{66} +(-2.10105 + 7.01801i) q^{67} +(7.96024 - 1.88661i) q^{68} +(1.57585 + 1.40767i) q^{69} +(0.468625 - 1.08640i) q^{70} +(-3.66891 + 3.07858i) q^{71} +(-0.967637 - 2.68980i) q^{72} +(5.52198 + 4.63349i) q^{73} +(1.13875 - 0.571901i) q^{74} +(-19.8674 - 10.7604i) q^{75} +(5.83087 + 0.681531i) q^{76} +(0.132281 + 2.27118i) q^{77} +(-1.18805 + 1.18362i) q^{78} +(-8.64862 + 9.16700i) q^{79} -15.5167 q^{80} +(4.44162 + 7.82765i) q^{81} +1.38483 q^{82} +(7.94414 - 8.42030i) q^{83} +(0.995812 + 3.74440i) q^{84} +(-1.04071 - 17.8683i) q^{85} +(-1.75255 - 0.204844i) q^{86} +(-0.0281361 - 1.03339i) q^{87} +(-1.68136 + 0.844410i) q^{88} +(8.43420 + 7.07713i) q^{89} +(-3.03591 + 0.523622i) q^{90} +(3.53497 - 2.96620i) q^{91} +(0.938159 - 2.17490i) q^{92} +(-3.20058 + 1.05392i) q^{93} +(-0.102715 + 0.0243439i) q^{94} +(3.68374 - 12.3046i) q^{95} +(-3.79451 + 2.98880i) q^{96} +(-6.24523 + 0.729963i) q^{97} +(-0.238125 - 1.35047i) q^{98} +(4.76477 - 3.51964i) 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

Properties

Related objects

Downloads

Learn more