LMFDB - Embedded newform 930.2.br.b.11.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.11
Character	$\chi$	$=$	930.11
Dual form			930.2.br.b.761.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(1.52844 + 0.814785i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.70541 - 0.302593i) q^{6} +(-0.239608 - 2.27972i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(1.67225 + 2.49070i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(1.52844 + 0.814785i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.70541 - 0.302593i) q^{6} +(-0.239608 - 2.27972i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(1.67225 + 2.49070i) q^{9} +(0.669131 - 0.743145i) q^{10} +(4.80333 + 2.13858i) q^{11} +(1.71545 - 0.239219i) q^{12} +(0.102539 + 0.482408i) q^{13} +(0.932352 + 2.09410i) q^{14} +(-1.73106 + 0.0585945i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.224735 - 0.100059i) q^{17} +(-2.36007 - 1.85204i) q^{18} +(-2.25806 - 0.479966i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(1.49125 - 3.67963i) q^{21} +(-5.22910 - 0.549600i) q^{22} +(0.241527 + 0.175480i) q^{23} +(-1.55757 + 0.757614i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.246593 - 0.427111i) q^{26} +(0.526546 + 5.16941i) q^{27} +(-1.53383 - 1.70349i) q^{28} +(0.303900 + 0.935309i) q^{29} +(1.62823 - 0.590653i) q^{30} +(4.86007 - 2.71656i) q^{31} +1.00000i q^{32} +(5.59911 + 7.18237i) q^{33} +(-0.182816 + 0.164608i) q^{34} +(1.34736 + 1.85449i) q^{35} +(2.81687 + 1.03209i) q^{36} +(4.06789 + 2.34860i) q^{37} +(2.29586 - 0.241305i) q^{38} +(-0.236334 + 0.820878i) q^{39} +(0.104528 - 0.994522i) q^{40} +(7.06425 + 6.36068i) q^{41} +(-0.281196 + 3.96036i) q^{42} +(0.238577 - 1.12242i) q^{43} +(5.14300 - 1.09318i) q^{44} +(-2.69356 - 1.32088i) q^{45} +(-0.283933 - 0.0922553i) q^{46} +(3.93760 + 1.27940i) q^{47} +(1.24722 - 1.20185i) q^{48} +(1.70734 - 0.362906i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(0.425021 + 0.0301776i) q^{51} +(0.366508 + 0.330005i) q^{52} +(0.504232 - 4.79745i) q^{53} +(-2.09821 - 4.75368i) q^{54} +(-5.22910 + 0.549600i) q^{55} +(1.98517 + 1.14614i) q^{56} +(-3.06024 - 2.57343i) q^{57} +(-0.578053 - 0.795622i) q^{58} +(-10.8675 + 9.78515i) q^{59} +(-1.36602 + 1.06490i) q^{60} +11.6416i q^{61} +(-3.78274 + 4.08544i) q^{62} +(5.27740 - 4.40905i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.330005 - 0.366508i) q^{65} +(-7.54455 - 5.10062i) q^{66} +(-4.94015 - 8.55660i) q^{67} +(0.123002 - 0.213045i) q^{68} +(0.226181 + 0.465003i) q^{69} +(-1.85449 - 1.34736i) q^{70} +(6.46130 + 0.679110i) q^{71} +(-2.99794 - 0.111118i) q^{72} +(-0.845091 + 1.89810i) q^{73} +(-4.59455 - 0.976602i) q^{74} +(1.46984 - 0.916274i) q^{75} +(-2.10893 + 0.938954i) q^{76} +(3.72444 - 11.4627i) q^{77} +(-0.0288980 - 0.853733i) q^{78} +(-1.47932 - 3.32261i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-3.40716 + 8.33014i) q^{81} +(-8.68406 - 3.86639i) q^{82} +(0.758476 - 0.842373i) q^{83} +(-0.956386 - 3.85342i) q^{84} +(-0.144597 + 0.199021i) q^{85} +(0.119946 + 1.14121i) q^{86} +(-0.297583 + 1.67718i) q^{87} +(-4.55348 + 2.62895i) q^{88} +(-11.3890 + 8.27458i) q^{89} +(2.96990 + 0.423879i) q^{90} +(1.07518 - 0.349348i) q^{91} +0.298544 q^{92} +(9.64174 - 0.192172i) q^{93} -4.14024 q^{94} +(2.19552 - 0.713368i) q^{95} +(-0.814785 + 1.52844i) q^{96} +(-2.96658 + 2.15535i) q^{97} +(-1.51163 + 0.872742i) q^{98} +(2.70581 + 15.5399i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

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 $

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$	1.52844	+	0.814785i	0.882444	+	0.470417i
$3$	1.52844	+	0.814785i	0.882444	+	0.470417i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−1.70541	−	0.302593i	−0.696232	−	0.123533i
$7$	−0.239608	−	2.27972i	−0.0905632	−	0.861652i	−0.941643	−	0.336614i	$-0.890718\pi$
$7$	−0.239608	−	2.27972i	−0.0905632	−	0.861652i	0.851079	−	0.525037i	$-0.175949\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	1.67225	+	2.49070i	0.557417	+	0.830233i
$10$	0.669131	−	0.743145i	0.211598	−	0.235003i
$11$	4.80333	+	2.13858i	1.44826	+	0.644806i	0.972103	−	0.234555i	$-0.0753631\pi$
$11$	4.80333	+	2.13858i	1.44826	+	0.644806i	0.476156	+	0.879361i	$0.342030\pi$
$12$	1.71545	−	0.239219i	0.495208	−	0.0690564i
$13$	0.102539	+	0.482408i	0.0284392	+	0.133796i	0.990077	−	0.140527i	$-0.0448797\pi$
$13$	0.102539	+	0.482408i	0.0284392	+	0.133796i	−0.961638	+	0.274323i	$0.911546\pi$
$14$	0.932352	+	2.09410i	0.249181	+	0.559671i
$15$	−1.73106	+	0.0585945i	−0.446958	+	0.0151290i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	0.224735	−	0.100059i	0.0545063	−	0.0242678i	−0.379302	−	0.925273i	$-0.623836\pi$
$17$	0.224735	−	0.100059i	0.0545063	−	0.0242678i	0.433809	+	0.901005i	$0.357169\pi$
$18$	−2.36007	−	1.85204i	−0.556274	−	0.436530i
$19$	−2.25806	−	0.479966i	−0.518035	−	0.110112i	−0.0585276	−	0.998286i	$-0.518641\pi$
$19$	−2.25806	−	0.479966i	−0.518035	−	0.110112i	−0.459507	+	0.888174i	$0.651974\pi$
$20$	−0.406737	+	0.913545i	−0.0909491	+	0.204275i
$21$	1.49125	−	3.67963i	0.325418	−	0.802962i
$22$	−5.22910	−	0.549600i	−1.11485	−	0.117175i
$23$	0.241527	+	0.175480i	0.0503620	+	0.0365901i	0.612681	−	0.790330i	$-0.290091\pi$
$23$	0.241527	+	0.175480i	0.0503620	+	0.0365901i	−0.562319	+	0.826920i	$0.690091\pi$
$24$	−1.55757	+	0.757614i	−0.317937	+	0.154647i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−0.246593	−	0.427111i	−0.0483608	−	0.0837634i
$27$	0.526546	+	5.16941i	0.101334	+	0.994852i
$28$	−1.53383	−	1.70349i	−0.289867	−	0.321930i
$29$	0.303900	+	0.935309i	0.0564329	+	0.173683i	0.975300	−	0.220885i	$-0.0708945\pi$
$29$	0.303900	+	0.935309i	0.0564329	+	0.173683i	−0.918867	+	0.394567i	$0.870894\pi$
$30$	1.62823	−	0.590653i	0.297273	−	0.107838i
$31$	4.86007	−	2.71656i	0.872895	−	0.487908i
$31$	4.86007	−	2.71656i	0.872895	−	0.487908i
$32$			1.00000i			0.176777i
$33$	5.59911	+	7.18237i	0.974680	+	1.25029i
$34$	−0.182816	+	0.164608i	−0.0313527	+	0.0282301i
$35$	1.34736	+	1.85449i	0.227746	+	0.313466i
$36$	2.81687	+	1.03209i	0.469479	+	0.172016i
$37$	4.06789	+	2.34860i	0.668757	+	0.386107i	0.795606	−	0.605815i	$-0.207153\pi$
$37$	4.06789	+	2.34860i	0.668757	+	0.386107i	−0.126848	+	0.991922i	$0.540486\pi$
$38$	2.29586	−	0.241305i	0.372438	−	0.0391448i
$39$	−0.236334	+	0.820878i	−0.0378438	+	0.131446i
$40$	0.104528	−	0.994522i	0.0165274	−	0.157248i
$41$	7.06425	+	6.36068i	1.10325	+	0.993372i	0.999999	−	0.00128345i	$-0.000408534\pi$
$41$	7.06425	+	6.36068i	1.10325	+	0.993372i	0.103252	+	0.994655i	$0.467075\pi$
$42$	−0.281196	+	3.96036i	−0.0433896	+	0.611097i
$43$	0.238577	−	1.12242i	0.0363827	−	0.171167i	−0.956205	−	0.292698i	$-0.905447\pi$
$43$	0.238577	−	1.12242i	0.0363827	−	0.171167i	0.992588	+	0.121531i	$0.0387803\pi$
$44$	5.14300	−	1.09318i	0.775337	−	0.164803i
$45$	−2.69356	−	1.32088i	−0.401532	−	0.196906i
$46$	−0.283933	−	0.0922553i	−0.0418636	−	0.0136023i
$47$	3.93760	+	1.27940i	0.574358	+	0.186620i	0.581772	−	0.813352i	$-0.302360\pi$
$47$	3.93760	+	1.27940i	0.574358	+	0.186620i	−0.00741320	+	0.999973i	$0.502360\pi$
$48$	1.24722	−	1.20185i	0.180021	−	0.173472i
$49$	1.70734	−	0.362906i	0.243906	−	0.0518438i
$50$	−0.207912	+	0.978148i	−0.0294032	+	0.138331i
$51$	0.425021	+	0.0301776i	0.0595148	+	0.00422571i
$52$	0.366508	+	0.330005i	0.0508255	+	0.0457635i
$53$	0.504232	−	4.79745i	0.0692616	−	0.658980i	−0.903724	−	0.428115i	$-0.859178\pi$
$53$	0.504232	−	4.79745i	0.0692616	−	0.658980i	0.972986	−	0.230865i	$-0.0741556\pi$
$54$	−2.09821	−	4.75368i	−0.285530	−	0.646895i
$55$	−5.22910	+	0.549600i	−0.705091	+	0.0741081i
$56$	1.98517	+	1.14614i	0.265279	+	0.153159i
$57$	−3.06024	−	2.57343i	−0.405338	−	0.340860i
$58$	−0.578053	−	0.795622i	−0.0759021	−	0.104470i
$59$	−10.8675	+	9.78515i	−1.41483	+	1.27392i	−0.502430	+	0.864618i	$0.667560\pi$
$59$	−10.8675	+	9.78515i	−1.41483	+	1.27392i	−0.912400	+	0.409300i	$0.865773\pi$
$60$	−1.36602	+	1.06490i	−0.176352	+	0.137477i
$61$			11.6416i			1.49056i	0.666753	+	0.745279i	$0.267684\pi$
$61$			11.6416i			1.49056i	−0.666753	+	0.745279i	$0.732316\pi$
$62$	−3.78274	+	4.08544i	−0.480409	+	0.518852i
$63$	5.27740	−	4.40905i	0.664890	−	0.555487i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−0.330005	−	0.366508i	−0.0409321	−	0.0454597i
$66$	−7.54455	−	5.10062i	−0.928670	−	0.627843i
$67$	−4.94015	−	8.55660i	−0.603536	−	1.04535i	−0.992281	−	0.124010i	$-0.960425\pi$
$67$	−4.94015	−	8.55660i	−0.603536	−	1.04535i	0.388745	−	0.921345i	$-0.372909\pi$
$68$	0.123002	−	0.213045i	0.0149162	−	0.0258355i
$69$	0.226181	+	0.465003i	0.0272290	+	0.0559798i
$70$	−1.85449	−	1.34736i	−0.221654	−	0.161041i
$71$	6.46130	+	0.679110i	0.766816	+	0.0805956i	0.479856	−	0.877347i	$-0.340689\pi$
$71$	6.46130	+	0.679110i	0.766816	+	0.0805956i	0.286959	+	0.957943i	$0.407356\pi$
$72$	−2.99794	−	0.111118i	−0.353311	−	0.0130953i
$73$	−0.845091	+	1.89810i	−0.0989104	+	0.222156i	−0.956222	−	0.292641i	$-0.905466\pi$
$73$	−0.845091	+	1.89810i	−0.0989104	+	0.222156i	0.857312	+	0.514797i	$0.172133\pi$
$74$	−4.59455	−	0.976602i	−0.534106	−	0.113528i
$75$	1.46984	−	0.916274i	0.169723	−	0.105802i
$76$	−2.10893	+	0.938954i	−0.241910	+	0.107705i
$77$	3.72444	−	11.4627i	0.424439	−	1.30629i
$78$	−0.0288980	−	0.853733i	−0.00327205	−	0.0966662i
$79$	−1.47932	−	3.32261i	−0.166437	−	0.373823i	0.811002	−	0.585044i	$-0.198923\pi$
$79$	−1.47932	−	3.32261i	−0.166437	−	0.373823i	−0.977438	+	0.211221i	$0.932256\pi$
$80$	0.207912	+	0.978148i	0.0232452	+	0.109360i
$81$	−3.40716	+	8.33014i	−0.378574	+	0.925571i
$82$	−8.68406	−	3.86639i	−0.958994	−	0.426972i
$83$	0.758476	−	0.842373i	0.0832536	−	0.0924625i	−0.700079	−	0.714066i	$-0.746852\pi$
$83$	0.758476	−	0.842373i	0.0832536	−	0.0924625i	0.783332	+	0.621603i	$0.213518\pi$
$84$	−0.956386	−	3.85342i	−0.104350	−	0.420443i
$85$	−0.144597	+	0.199021i	−0.0156838	+	0.0215869i
$86$	0.119946	+	1.14121i	0.0129341	+	0.123060i
$87$	−0.297583	+	1.67718i	−0.0319043	+	0.179812i
$88$	−4.55348	+	2.62895i	−0.485402	+	0.280247i
$89$	−11.3890	+	8.27458i	−1.20723	+	0.877104i	−0.994976	−	0.100111i	$-0.968080\pi$
$89$	−11.3890	+	8.27458i	−1.20723	+	0.877104i	−0.212254	+	0.977215i	$0.568080\pi$
$90$	2.96990	+	0.423879i	0.313055	+	0.0446808i
$91$	1.07518	−	0.349348i	0.112710	−	0.0366217i
$92$	0.298544			0.0311254
$93$	9.64174	−	0.192172i	0.999801	−	0.0199273i
$94$	−4.14024			−0.427033
$95$	2.19552	−	0.713368i	0.225256	−	0.0731900i
$96$	−0.814785	+	1.52844i	−0.0831587	+	0.155996i
$97$	−2.96658	+	2.15535i	−0.301211	+	0.218842i	−0.728116	−	0.685454i	$-0.759604\pi$
$97$	−2.96658	+	2.15535i	−0.301211	+	0.218842i	0.426905	+	0.904296i	$0.359604\pi$
$98$	−1.51163	+	0.872742i	−0.152698	+	0.0881602i
$99$	2.70581	+	15.5399i	0.271944	+	1.56182i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	3.90718	−	5.37777i	0.388779	−	0.535108i	−0.569105	−	0.822265i	$-0.692710\pi$
$101$	3.90718	−	5.37777i	0.388779	−	0.535108i	0.957884	+	0.287157i	$0.0927101\pi$
$102$	−0.413544	+	0.102638i	−0.0409470	+	0.0101627i
$103$	4.93280	−	5.47843i	0.486044	−	0.539806i	−0.449377	−	0.893342i	$-0.648354\pi$
$103$	4.93280	−	5.47843i	0.486044	−	0.539806i	0.935421	+	0.353536i	$0.115021\pi$
$104$	−0.450547	−	0.200597i	−0.0441798	−	0.0196701i
$105$	0.548354	+	3.93228i	0.0535139	+	0.383752i
$106$	1.00294	+	4.71846i	0.0974141	+	0.458297i
$107$	−4.02477	−	9.03979i	−0.389090	−	0.873910i	−0.996814	−	0.0797616i	$-0.974584\pi$
$107$	−4.02477	−	9.03979i	−0.389090	−	0.873910i	0.607724	−	0.794148i	$-0.292083\pi$
$108$	3.46448	+	3.87264i	0.333370	+	0.372645i
$109$	5.37727	−	16.5495i	0.515049	−	1.58516i	−0.268144	−	0.963379i	$-0.586410\pi$
$109$	5.37727	−	16.5495i	0.515049	−	1.58516i	0.783193	−	0.621779i	$-0.213590\pi$
$110$	4.80333	−	2.13858i	0.457980	−	0.203906i
$111$	4.30392	+	6.90415i	0.408510	+	0.655313i
$112$	−2.24218	−	0.476590i	−0.211866	−	0.0450336i
$113$	−4.07478	+	9.15212i	−0.383323	+	0.860959i	0.614101	+	0.789228i	$0.289519\pi$
$113$	−4.07478	+	9.15212i	−0.383323	+	0.860959i	−0.997424	+	0.0717308i	$0.977148\pi$
$114$	3.70569	+	1.50181i	0.347070	+	0.140658i
$115$	−0.296909	−	0.0312064i	−0.0276869	−	0.00291001i
$116$	0.795622	+	0.578053i	0.0738716	+	0.0536709i
$117$	−1.03006	+	1.06210i	−0.0952293	+	0.0981912i
$118$	7.31184	−	12.6645i	0.673109	−	1.16586i
$119$	−0.281954	−	0.488358i	−0.0258466	−	0.0447677i
$120$	0.970087	−	1.43490i	0.0885564	−	0.130988i
$121$	11.1380	+	12.3700i	1.01255	+	1.12455i
$122$	−3.59746	−	11.0718i	−0.325699	−	1.00240i
$123$	5.61469	+	15.4778i	0.506259	+	1.39558i
$124$	2.33513	−	5.05442i	0.209701	−	0.453900i
$125$			1.00000i			0.0894427i
$126$	−3.65664	+	5.82406i	−0.325759	+	0.518848i
$127$	−3.76156	+	3.38692i	−0.333784	+	0.300540i	−0.818931	−	0.573892i	$-0.805433\pi$
$127$	−3.76156	+	3.38692i	−0.333784	+	0.300540i	0.485147	+	0.874433i	$0.338766\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	1.27918	−	1.52116i	0.112626	−	0.133931i
$130$	0.427111	+	0.246593i	0.0374601	+	0.0216276i
$131$	−6.90739	+	0.725996i	−0.603502	+	0.0634306i	−0.401352	−	0.915924i	$-0.631459\pi$
$131$	−6.90739	+	0.725996i	−0.603502	+	0.0634306i	−0.202150	+	0.979355i	$0.564793\pi$
$132$	8.75147	+	2.51959i	0.761718	+	0.219302i
$133$	−0.553136	+	5.26274i	−0.0479630	+	0.456337i
$134$	7.34250	+	6.61122i	0.634295	+	0.571122i
$135$	−3.04070	−	4.21356i	−0.261702	−	0.362646i
$136$	−0.0511470	+	0.240628i	−0.00438582	+	0.0206337i
$137$	−7.24675	+	1.54034i	−0.619131	+	0.131600i	−0.506790	−	0.862069i	$-0.669168\pi$
$137$	−7.24675	+	1.54034i	−0.619131	+	0.131600i	−0.112341	+	0.993670i	$0.535835\pi$
$138$	−0.358805	−	0.372351i	−0.0305435	−	0.0316966i
$139$	16.8089	+	5.46155i	1.42571	+	0.463242i	0.917413	−	0.397937i	$-0.130274\pi$
$139$	16.8089	+	5.46155i	1.42571	+	0.463242i	0.508301	+	0.861180i	$0.330274\pi$
$140$	2.18008	+	0.708351i	0.184251	+	0.0598666i
$141$	4.97595	+	5.16379i	0.419050	+	0.434870i
$142$	−6.35492	+	1.35078i	−0.533293	+	0.113355i
$143$	−0.539140	+	2.53645i	−0.0450851	+	0.212109i
$144$	2.88555	−	0.820736i	0.240462	−	0.0683946i
$145$	−0.730840	−	0.658051i	−0.0606930	−	0.0546482i
$146$	0.217182	−	2.06635i	0.0179741	−	0.171013i
$147$	2.90526	+	0.836436i	0.239621	+	0.0689881i
$148$	4.67147	−	0.490991i	0.383992	−	0.0403592i
$149$	−8.29682	−	4.79017i	−0.679702	−	0.392426i	0.120041	−	0.992769i	$-0.461697\pi$
$149$	−8.29682	−	4.79017i	−0.679702	−	0.392426i	−0.799743	+	0.600343i	$0.795031\pi$
$150$	−1.11476	+	1.32564i	−0.0910198	+	0.108238i
$151$	−5.12296	−	7.05114i	−0.416900	−	0.573814i	0.547984	−	0.836489i	$-0.315395\pi$
$151$	−5.12296	−	7.05114i	−0.416900	−	0.573814i	−0.964884	+	0.262675i	$0.915395\pi$
$152$	1.71556	−	1.54469i	0.139150	−	0.125291i
$153$	0.625030	+	0.392425i	0.0505306	+	0.0317257i
$154$			12.0525i			0.971222i
$155$	−2.85067	+	4.78264i	−0.228971	+	0.384151i
$156$	0.291302	+	0.803018i	0.0233228	+	0.0642929i
$157$	−4.28458	−	13.1866i	−0.341946	−	1.05240i	−0.963198	−	0.268792i	$-0.913376\pi$
$157$	−4.28458	−	13.1866i	−0.341946	−	1.05240i	0.621252	−	0.783611i	$-0.286624\pi$
$158$	2.43366	+	2.70286i	0.193612	+	0.215028i
$159$	4.67958	−	6.92177i	0.371115	−	0.548932i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	0.342173	−	0.592660i	0.0269670	−	0.0467082i
$162$	0.666249	−	8.97531i	0.0523454	−	0.705167i
$163$	0.740024	+	0.537659i	0.0579631	+	0.0421127i	0.616390	−	0.787441i	$-0.288595\pi$
$163$	0.740024	+	0.537659i	0.0579631	+	0.0421127i	−0.558426	+	0.829554i	$0.688595\pi$
$164$	9.45382	+	0.993636i	0.738219	+	0.0775900i
$165$	−8.44016	−	3.42056i	−0.657066	−	0.266290i
$166$	−0.461046	+	1.03553i	−0.0357841	+	0.0803724i
$167$	−2.27172	−	0.482869i	−0.175791	−	0.0373655i	0.119175	−	0.992873i	$-0.461975\pi$
$167$	−2.27172	−	0.482869i	−0.175791	−	0.0373655i	−0.294966	+	0.955508i	$0.595308\pi$
$168$	2.10035	+	3.36928i	0.162046	+	0.259946i
$169$	11.6539	−	5.18865i	0.896453	−	0.399127i
$170$	0.0760193	−	0.233963i	0.00583041	−	0.0179442i
$171$	−2.58059	−	6.42677i	−0.197343	−	0.491468i
$172$	−0.466728	−	1.04829i	−0.0355877	−	0.0799312i
$173$	−3.73588	−	17.5759i	−0.284034	−	1.33627i	−0.856416	−	0.516287i	$-0.827314\pi$
$173$	−3.73588	−	17.5759i	−0.284034	−	1.33627i	0.572382	−	0.819987i	$-0.306020\pi$
$174$	−0.235258	−	1.68705i	−0.0178348	−	0.127895i
$175$	−2.09410	−	0.932352i	−0.158299	−	0.0704792i
$176$	3.51822	−	3.90738i	0.265196	−	0.294530i
$177$	−24.5831	+	6.10131i	−1.84778	+	0.458603i
$178$	8.27458	−	11.3890i	0.620206	−	0.853640i
$179$	−0.107315	−	1.02103i	−0.00802109	−	0.0763156i	0.989779	−	0.142609i	$-0.0455492\pi$
$179$	−0.107315	−	1.02103i	−0.00802109	−	0.0763156i	−0.997800	+	0.0662937i	$0.978883\pi$
$180$	−2.95553	+	0.514618i	−0.220292	+	0.0383573i
$181$	−0.0640963	+	0.0370060i	−0.00476424	+	0.00275063i	−0.502380	−	0.864647i	$-0.667542\pi$
$181$	−0.0640963	+	0.0370060i	−0.00476424	+	0.00275063i	0.497616	+	0.867397i	$0.334209\pi$
$182$	−0.914606	+	0.664500i	−0.0677951	+	0.0492560i
$183$	−9.48543	+	17.7935i	−0.701183	+	1.31533i
$184$	−0.283933	+	0.0922553i	−0.0209318	+	0.00680115i
$185$	−4.69720			−0.345345
$186$	−9.11045	+	3.16223i	−0.668011	+	0.231866i
$187$	1.29346			0.0945873
$188$	3.93760	−	1.27940i	0.287179	−	0.0933102i
$189$	11.6586	−	2.43901i	0.848039	−	0.177412i
$190$	−1.86762	+	1.35691i	−0.135492	+	0.0984403i
$191$	1.20866	−	0.697818i	0.0874553	−	0.0504924i	−0.455635	−	0.890167i	$-0.650588\pi$
$191$	1.20866	−	0.697818i	0.0874553	−	0.0504924i	0.543090	+	0.839675i	$0.317254\pi$
$192$	0.302593	−	1.70541i	0.0218378	−	0.123078i
$193$	−1.68734	−	16.0539i	−0.121457	−	1.15559i	−0.870190	−	0.492716i	$-0.836004\pi$
$193$	−1.68734	−	16.0539i	−0.121457	−	1.15559i	0.748733	−	0.662872i	$-0.230663\pi$
$194$	2.15535	−	2.96658i	0.154745	−	0.212988i
$195$	−0.205768	−	0.829069i	−0.0147353	−	0.0593708i
$196$	1.16796	−	1.29715i	0.0834255	−	0.0926533i
$197$	−20.1991	−	8.99323i	−1.43913	−	0.640741i	−0.468970	−	0.883214i	$-0.655375\pi$
$197$	−20.1991	−	8.99323i	−1.43913	−	0.640741i	−0.970158	+	0.242473i	$0.922041\pi$
$198$	−7.37547	−	13.9432i	−0.524152	−	0.990898i
$199$	1.76623	+	8.30945i	0.125205	+	0.589041i	0.995356	+	0.0962575i	$0.0306872\pi$
$199$	1.76623	+	8.30945i	0.125205	+	0.589041i	−0.870152	+	0.492784i	$0.835979\pi$
$200$	0.406737	+	0.913545i	0.0287606	+	0.0645974i
$201$	−0.578932	−	17.1034i	−0.0408347	−	1.20638i
$202$	−2.05412	+	6.32195i	−0.144528	+	0.444811i
$203$	2.05942	−	0.916914i	0.144543	−	0.0643547i
$204$	0.361587	−	0.225407i	0.0253161	−	0.0157816i
$205$	−9.29816	−	1.97639i	−0.649412	−	0.138037i
$206$	−2.99845	+	6.73462i	−0.208912	+	0.469223i
$207$	−0.0331736	+	0.895019i	−0.00230572	+	0.0622081i
$208$	0.490484	+	0.0515519i	0.0340089	+	0.00357448i
$209$	−9.81977	−	7.13448i	−0.679248	−	0.493502i
$210$	−1.73666	−	3.57037i	−0.119841	−	0.246379i
$211$	7.90836	−	13.6977i	0.544434	−	0.942988i	−0.454208	−	0.890896i	$-0.650078\pi$
$211$	7.90836	−	13.6977i	0.544434	−	0.942988i	0.998642	−	0.0520920i	$-0.0165889\pi$
$212$	−2.41194	−	4.17760i	−0.165653	−	0.286919i
$213$	9.32238	+	6.30255i	0.638759	+	0.431844i
$214$	6.62124	+	7.35363i	0.452618	+	0.502684i
$215$	0.354595	+	1.09133i	0.0241832	+	0.0744282i
$216$	−4.49163	−	2.61252i	−0.305617	−	0.177759i
$217$	−7.35749	−	10.4287i	−0.499459	−	0.707945i
$218$			17.4012i			1.17856i
$219$	−2.83822	+	2.21257i	−0.191789	+	0.149512i
$220$	−3.90738	+	3.51822i	−0.263436	+	0.237198i
$221$	0.0713132	+	0.0981542i	0.00479705	+	0.00660257i
$222$	−6.22677	−	5.23625i	−0.417914	−	0.351434i
$223$	9.27537	+	5.35514i	0.621125	+	0.358607i	0.777307	−	0.629122i	$-0.216585\pi$
$223$	9.27537	+	5.35514i	0.621125	+	0.358607i	−0.156182	+	0.987728i	$0.549919\pi$
$224$	2.27972	−	0.239608i	0.152320	−	0.0160095i
$225$	2.99313	−	0.202861i	0.199542	−	0.0135241i
$226$	1.04719	−	9.96336i	0.0696581	−	0.662753i
$227$	−14.3618	−	12.9314i	−0.953224	−	0.858286i	0.0367807	−	0.999323i	$-0.488290\pi$
$227$	−14.3618	−	12.9314i	−0.953224	−	0.858286i	−0.990004	+	0.141037i	$0.954956\pi$
$228$	−3.98841	−	0.283188i	−0.264139	−	0.0187546i
$229$	4.20055	−	19.7621i	0.277580	−	1.30591i	−0.589509	−	0.807762i	$-0.700679\pi$
$229$	4.20055	−	19.7621i	0.277580	−	1.30591i	0.867090	−	0.498152i	$-0.165988\pi$
$230$	0.292020	−	0.0620709i	0.0192553	−	0.00409283i
$231$	15.0322	−	14.4853i	0.989045	−	0.953065i
$232$	−0.935309	−	0.303900i	−0.0614061	−	0.0199520i
$233$	−13.8077	−	4.48638i	−0.904570	−	0.293912i	−0.180448	−	0.983585i	$-0.557755\pi$
$233$	−13.8077	−	4.48638i	−0.904570	−	0.293912i	−0.724122	+	0.689672i	$0.757755\pi$
$234$	0.651440	−	1.32842i	0.0425860	−	0.0868418i
$235$	−4.04977	+	0.860805i	−0.264178	+	0.0561527i
$236$	−3.04043	+	14.3041i	−0.197915	+	0.931119i
$237$	0.446162	−	6.28374i	0.0289814	−	0.408173i
$238$	0.419065	+	0.377328i	0.0271639	+	0.0244585i
$239$	−0.860790	+	8.18987i	−0.0556799	+	0.529758i	0.930759	+	0.365632i	$0.119147\pi$
$239$	−0.860790	+	8.18987i	−0.0556799	+	0.529758i	−0.986439	+	0.164126i	$0.947520\pi$
$240$	−0.479200	+	1.66444i	−0.0309322	+	0.107439i
$241$	−30.2783	+	3.18237i	−1.95039	+	0.204995i	−0.995703	−	0.0926038i	$-0.970481\pi$
$241$	−30.2783	+	3.18237i	−1.95039	+	0.204995i	−0.954691	+	0.297598i	$0.903814\pi$
$242$	−14.4154	−	8.32276i	−0.926660	−	0.535007i
$243$	−11.9949	+	9.95600i	−0.769474	+	0.638678i
$244$	6.84278	+	9.41828i	0.438064	+	0.602943i
$245$	−1.29715	+	1.16796i	−0.0828717	+	0.0746180i
$246$	−10.1228	−	12.9852i	−0.645405	−	0.827906i
$247$		−	1.13852i		−	0.0724424i
$248$	−0.658940	+	5.52863i	−0.0418428	+	0.351069i
$249$	1.84564	−	0.669520i	0.116963	−	0.0424291i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	3.56146	+	3.95540i	0.224797	+	0.249663i	0.844984	−	0.534791i	$-0.179610\pi$
$251$	3.56146	+	3.95540i	0.224797	+	0.249663i	−0.620187	+	0.784454i	$0.712943\pi$
$252$	1.67794	−	6.66897i	0.105700	−	0.420106i
$253$	0.784858	+	1.35941i	0.0493436	+	0.0854657i
$254$	2.53084	−	4.38354i	0.158799	−	0.275048i
$255$	−0.383167	+	0.186376i	−0.0239949	+	0.0116713i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	28.1552	+	2.95923i	1.75628	+	0.184592i	0.927206	−	0.374553i	$-0.122204\pi$
$257$	28.1552	+	2.95923i	1.75628	+	0.184592i	0.829070	+	0.559145i	$0.188870\pi$
$258$	−0.746510	+	1.84200i	−0.0464757	+	0.114678i
$259$	4.37944	−	9.83638i	0.272125	−	0.611203i
$260$	−0.482408	−	0.102539i	−0.0299177	−	0.00635920i
$261$	−1.82138	+	2.32100i	−0.112740	+	0.143666i
$262$	6.34497	−	2.82496i	0.391994	−	0.174527i
$263$	3.36054	−	10.3427i	0.207220	−	0.637757i	−0.792395	−	0.610008i	$-0.791166\pi$
$263$	3.36054	−	10.3427i	0.207220	−	0.637757i	0.999615	−	0.0277488i	$-0.00883384\pi$
$264$	−9.10174	+	0.308084i	−0.560173	+	0.0189613i
$265$	1.96205	+	4.40683i	0.120528	+	0.270709i
$266$	−1.10021	−	5.17609i	−0.0674584	−	0.317367i
$267$	−24.1494	+	3.36761i	−1.47792	+	0.206095i
$268$	−9.02611	−	4.01868i	−0.551358	−	0.245480i
$269$	12.1131	−	13.4530i	0.738549	−	0.820241i	−0.250456	−	0.968128i	$-0.580580\pi$
$269$	12.1131	−	13.4530i	0.738549	−	0.820241i	0.989004	+	0.147887i	$0.0472471\pi$
$270$	4.19394	+	3.06771i	0.255235	+	0.186695i
$271$	7.34577	−	10.1106i	0.446223	−	0.614174i	−0.525357	−	0.850882i	$-0.676068\pi$
$271$	7.34577	−	10.1106i	0.446223	−	0.614174i	0.971581	+	0.236708i	$0.0760684\pi$
$272$	−0.0257144	−	0.244656i	−0.00155916	−	0.0148344i
$273$	1.92800	+	0.342086i	0.116688	+	0.0207040i
$274$	6.41607	−	3.70432i	0.387609	−	0.223786i
$275$	4.25373	−	3.09052i	0.256510	−	0.186365i
$276$	0.456307	+	0.243250i	0.0274664	+	0.0146419i
$277$	−19.7985	+	6.43293i	−1.18958	+	0.386517i	−0.835917	−	0.548856i	$-0.815063\pi$
$277$	−19.7985	+	6.43293i	−1.18958	+	0.386517i	−0.353661	+	0.935374i	$0.615063\pi$
$278$	−17.6739			−1.06001
$279$	14.8934	+	7.56222i	0.891643	+	0.452738i
$280$	−2.29227			−0.136990
$281$	18.5701	−	6.03378i	1.10780	−	0.359945i	0.302699	−	0.953086i	$-0.402112\pi$
$281$	18.5701	−	6.03378i	1.10780	−	0.359945i	0.805099	+	0.593141i	$0.202112\pi$
$282$	−6.32811	−	3.37341i	−0.376833	−	0.200884i
$283$	10.0349	−	7.29076i	0.596511	−	0.433391i	−0.248128	−	0.968727i	$-0.579815\pi$
$283$	10.0349	−	7.29076i	0.596511	−	0.433391i	0.844639	+	0.535337i	$0.179815\pi$
$284$	5.62647	−	3.24845i	0.333870	−	0.192760i
$285$	3.93696	+	0.698539i	0.233205	+	0.0413779i
$286$	−0.271055	−	2.57891i	−0.0160278	−	0.152494i
$287$	12.8079	−	17.6286i	0.756026	−	1.04058i
$288$	−2.49070	+	1.67225i	−0.146766	+	0.0985383i
$289$	−11.3347	+	12.5885i	−0.666749	+	0.740499i
$290$	0.898419	+	0.400002i	0.0527570	+	0.0234889i
$291$	−6.29038	+	0.877190i	−0.368749	+	0.0514218i
$292$	0.431985	+	2.03233i	0.0252800	+	0.118933i
$293$	−9.62081	−	21.6087i	−0.562054	−	1.26239i	−0.941448	−	0.337158i	$-0.890534\pi$
$293$	−9.62081	−	21.6087i	−0.562054	−	1.26239i	0.379394	−	0.925235i	$-0.376132\pi$
$294$	−3.02154	+	0.102276i	−0.176220	+	0.00596485i
$295$	4.51897	−	13.9079i	0.263104	−	0.809752i
$296$	−4.29110	+	1.91052i	−0.249415	+	0.111047i
$297$	−8.52602	+	25.9564i	−0.494730	+	1.50614i
$298$	9.37099	+	1.99186i	0.542847	+	0.115386i
$299$	−0.0598870	+	0.134508i	−0.00346335	+	0.00777882i
$300$	0.650557	−	1.60523i	0.0375599	−	0.0926782i
$301$	−2.61596	−	0.274949i	−0.150781	−	0.0158478i
$302$	7.05114	+	5.12296i	0.405748	+	0.294793i
$303$	10.3536	−	5.03608i	0.594799	−	0.289315i
$304$	−1.15425	+	1.99923i	−0.0662010	+	0.114663i
$305$	−5.82082	−	10.0819i	−0.333299	−	0.577291i
$306$	−0.715704	−	0.180074i	−0.0409141	−	0.0102941i
$307$	−1.65859	−	1.84205i	−0.0946605	−	0.105131i	0.693953	−	0.720020i	$-0.255867\pi$
$307$	−1.65859	−	1.84205i	−0.0946605	−	0.105131i	−0.788614	+	0.614889i	$0.789201\pi$
$308$	−3.72444	−	11.4627i	−0.212220	−	0.653145i
$309$	12.0032	−	4.35427i	0.682840	−	0.247706i
$310$	1.23323	−	5.42947i	0.0700428	−	0.308373i
$311$			12.1114i			0.686776i	0.939194	+	0.343388i	$0.111575\pi$
$311$			12.1114i			0.686776i	−0.939194	+	0.343388i	$0.888425\pi$
$312$	−0.525191	−	0.673699i	−0.0297331	−	0.0381407i
$313$	−18.7290	+	16.8637i	−1.05863	+	0.953191i	−0.998986	−	0.0450286i	$-0.985662\pi$
$313$	−18.7290	+	16.8637i	−1.05863	+	0.953191i	−0.0596405	+	0.998220i	$0.518995\pi$
$314$	8.14975	+	11.2172i	0.459917	+	0.633021i
$315$	−2.36584	+	6.45705i	−0.133300	+	0.363813i
$316$	−3.14978	−	1.81853i	−0.177189	−	0.102300i
$317$	−30.8863	+	3.24628i	−1.73475	+	0.182329i	−0.918513	−	0.395390i	$-0.870609\pi$
$317$	−30.8863	+	3.24628i	−1.73475	+	0.182329i	−0.816235	+	0.577719i	$0.803943\pi$
$318$	−2.31160	+	8.02906i	−0.129628	+	0.450247i
$319$	−0.540500	+	5.14252i	−0.0302622	+	0.287926i
$320$	0.743145	+	0.669131i	0.0415431	+	0.0374055i
$321$	1.21387	−	17.0961i	0.0677515	−	0.954211i
$322$	−0.142283	+	0.669391i	−0.00792914	+	0.0373037i
$323$	−0.555491	+	0.118073i	−0.0309083	+	0.00656977i
$324$	2.13988	+	8.74191i	0.118882	+	0.485661i
$325$	0.469047	+	0.152403i	0.0260180	+	0.00845378i
$326$	−0.869950	−	0.282664i	−0.0481821	−	0.0156553i
$327$	21.7031	−	20.9136i	1.20019	−	1.15653i
$328$	−9.29816	+	1.97639i	−0.513405	+	0.109128i
$329$	1.97320	−	9.28317i	0.108786	−	0.511798i
$330$	9.08408	+	0.644994i	0.500062	+	0.0355058i
$331$	−8.47772	−	7.63337i	−0.465978	−	0.419568i	0.402406	−	0.915461i	$-0.368174\pi$
$331$	−8.47772	−	7.63337i	−0.465978	−	0.419568i	−0.868384	+	0.495893i	$0.834841\pi$
$332$	0.118486	−	1.12732i	0.00650274	−	0.0618695i
$333$	0.952879	+	14.0593i	0.0522175	+	0.770447i
$334$	2.30975	−	0.242764i	0.126384	−	0.0132835i
$335$	8.55660	+	4.94015i	0.467497	+	0.269909i
$336$	−3.03872	−	2.55534i	−0.165776	−	0.139405i
$337$	15.0019	+	20.6484i	0.817206	+	1.12479i	0.990171	+	0.139860i	$0.0446651\pi$
$337$	15.0019	+	20.6484i	0.817206	+	1.12479i	−0.172965	+	0.984928i	$0.555335\pi$
$338$	−9.48013	+	8.53594i	−0.515651	+	0.464294i
$339$	−13.6851	+	10.6684i	−0.743271	+	0.579426i
$340$			0.246003i			0.0133414i
$341$	29.1541	−	2.65486i	1.57878	−	0.143768i
$342$	4.44027	+	5.31478i	0.240102	+	0.287390i
$343$	−6.19488	−	19.0659i	−0.334492	−	1.02946i
$344$	0.767823	+	0.852754i	0.0413983	+	0.0459774i
$345$	−0.428381	−	0.289614i	−0.0230632	−	0.0155923i
$346$	8.98430	+	15.5613i	0.482999	+	0.836579i
$347$	6.19451	−	10.7292i	0.332539	−	0.575974i	−0.650470	−	0.759532i	$-0.725428\pi$
$347$	6.19451	−	10.7292i	0.332539	−	0.575974i	0.983009	+	0.183558i	$0.0587614\pi$
$348$	0.745070	+	1.53178i	0.0399399	+	0.0821120i
$349$	−7.18740	−	5.22195i	−0.384733	−	0.279525i	0.378561	−	0.925576i	$-0.376419\pi$
$349$	−7.18740	−	5.22195i	−0.384733	−	0.279525i	−0.763294	+	0.646052i	$0.776419\pi$
$350$	2.27972	+	0.239608i	0.121856	+	0.0128076i
$351$	−2.43977	+	0.784076i	−0.130225	+	0.0418509i
$352$	−2.13858	+	4.80333i	−0.113987	+	0.256018i
$353$	−0.519568	−	0.110438i	−0.0276538	−	0.00587800i	0.194064	−	0.980989i	$-0.437833\pi$
$353$	−0.519568	−	0.110438i	−0.0276538	−	0.00587800i	−0.221718	+	0.975111i	$0.571166\pi$
$354$	21.4945	−	13.3993i	1.14242	−	0.712165i
$355$	−5.93521	+	2.64252i	−0.315008	+	0.140251i
$356$	−4.35020	+	13.3886i	−0.230560	+	0.709592i
$357$	−0.0330419	−	0.976157i	−0.00174876	−	0.0516637i
$358$	0.417579	+	0.937898i	0.0220697	+	0.0495695i
$359$	−4.33883	−	20.4126i	−0.228995	−	1.07733i	−0.930959	−	0.365123i	$-0.881027\pi$
$359$	−4.33883	−	20.4126i	−0.228995	−	1.07733i	0.701965	−	0.712212i	$-0.252306\pi$
$360$	2.65185	−	1.40274i	0.139765	−	0.0739309i
$361$	−12.4889	−	5.56041i	−0.657310	−	0.292653i
$362$	0.0495237	−	0.0550016i	0.00260291	−	0.00289082i
$363$	6.94487	+	27.9819i	0.364511	+	1.46867i
$364$	0.664500	−	0.914606i	0.0348293	−	0.0479384i
$365$	−0.217182	−	2.06635i	−0.0113678	−	0.108158i
$366$	3.52268	−	19.8538i	0.184133	−	1.03777i
$367$	−10.5070	+	6.06625i	−0.548463	+	0.316656i	−0.748502	−	0.663132i	$-0.769227\pi$
$367$	−10.5070	+	6.06625i	−0.548463	+	0.316656i	0.200039	+	0.979788i	$0.435893\pi$
$368$	0.241527	−	0.175480i	0.0125905	−	0.00914753i
$369$	−4.02935	+	28.2316i	−0.209760	+	1.46968i
$370$	4.46730	−	1.45151i	0.232244	−	0.0754606i
$371$	−11.0576			−0.574084
$372$	7.68737	−	5.82274i	0.398572	−	0.301895i
$373$	3.98423			0.206296			0.103148	−	0.994666i	$-0.467109\pi$
$373$	3.98423			0.206296			0.103148	+	0.994666i	$0.467109\pi$
$374$	−1.23016	+	0.399702i	−0.0636098	+	0.0206681i
$375$	−0.814785	+	1.52844i	−0.0420753	+	0.0789282i
$376$	−3.34953	+	2.43357i	−0.172739	+	0.125502i
$377$	−0.420039	+	0.242510i	−0.0216331	+	0.0124899i
$378$	−10.3343	+	5.92234i	−0.531539	+	0.304612i
$379$	2.74802	+	26.1456i	0.141156	+	1.34301i	0.804168	+	0.594402i	$0.202611\pi$
$379$	2.74802	+	26.1456i	0.141156	+	1.34301i	−0.663012	+	0.748609i	$0.730722\pi$
$380$	1.35691	−	1.86762i	0.0696078	−	0.0958070i
$381$	−8.50892	+	2.11184i	−0.435925	+	0.108193i
$382$	−0.933863	+	1.03716i	−0.0477806	+	0.0530657i
$383$	34.4946	+	15.3580i	1.76259	+	0.784757i	0.988413	+	0.151791i	$0.0485042\pi$
$383$	34.4946	+	15.3580i	1.76259	+	0.784757i	0.774180	+	0.632965i	$0.218162\pi$
$384$	0.239219	+	1.71545i	0.0122076	+	0.0875413i
$385$	2.50587	+	11.7892i	0.127711	+	0.600832i
$386$	6.56569	+	14.7468i	0.334185	+	0.750592i
$387$	3.19457	−	1.28274i	0.162389	−	0.0652053i
$388$	−1.13313	+	3.48743i	−0.0575261	+	0.177047i
$389$	−26.2933	+	11.7065i	−1.33312	+	0.593545i	−0.944700	−	0.327936i	$-0.893647\pi$
$389$	−26.2933	+	11.7065i	−1.33312	+	0.593545i	−0.388424	+	0.921481i	$0.626980\pi$
$390$	0.451893	+	0.724905i	0.0228825	+	0.0367070i
$391$	0.0718381	+	0.0152697i	0.00363301	+	0.000772219i
$392$	−0.709952	+	1.59458i	−0.0358580	+	0.0805384i
$393$	−11.1491	−	4.51840i	−0.562395	−	0.227923i
$394$	21.9896	+	2.31120i	1.10782	+	0.116436i
$395$	2.94244	+	2.13781i	0.148050	+	0.107565i
$396$	11.3232	+	10.9816i	0.569010	+	0.551846i
$397$	−13.9943	+	24.2388i	−0.702353	+	1.21651i	0.265285	+	0.964170i	$0.414534\pi$
$397$	−13.9943	+	24.2388i	−0.702353	+	1.21651i	−0.967638	+	0.252342i	$0.918799\pi$
$398$	−4.24754	−	7.35696i	−0.212910	−	0.368771i
$399$	−5.13344	+	7.59309i	−0.256993	+	0.380130i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	−5.07464	−	15.6181i	−0.253415	−	0.779932i	−0.994138	−	0.108121i	$-0.965517\pi$
$401$	−5.07464	−	15.6181i	−0.253415	−	0.779932i	0.740723	−	0.671811i	$-0.234483\pi$
$402$	5.83584	+	16.0874i	0.291065	+	0.802367i
$403$	1.80884	+	2.06599i	0.0901045	+	0.102914i
$404$		−	6.64729i		−	0.330715i
$405$	−1.21438	−	8.91769i	−0.0603431	−	0.443124i
$406$	−1.67529	+	1.50843i	−0.0831430	+	0.0748623i
$407$	14.5168	+	19.9806i	0.719569	+	0.990402i
$408$	−0.274235	+	0.326111i	−0.0135767	+	0.0161449i
$409$	4.78834	+	2.76455i	0.236768	+	0.136698i	0.613690	−	0.789547i	$-0.289684\pi$
$409$	4.78834	+	2.76455i	0.236768	+	0.136698i	−0.376922	+	0.926245i	$0.623018\pi$
$410$	9.45382	−	0.993636i	0.466891	−	0.0490722i
$411$	−12.3313	−	3.55022i	−0.608256	−	0.175120i
$412$	0.770580	−	7.33157i	0.0379637	−	0.361201i
$413$	24.9113	+	22.4302i	1.22581	+	1.10372i
$414$	−0.245026	−	0.861464i	−0.0120424	−	0.0423387i
$415$	−0.235673	+	1.10875i	−0.0115687	+	0.0544266i
$416$	−0.482408	+	0.102539i	−0.0236520	+	0.00502739i
$417$	21.2414	+	22.0433i	1.04020	+	1.07946i
$418$	11.5438	+	3.75082i	0.564627	+	0.183458i
$419$	−5.95487	−	1.93486i	−0.290915	−	0.0945239i	0.159924	−	0.987129i	$-0.448875\pi$
$419$	−5.95487	−	1.93486i	−0.290915	−	0.0945239i	−0.450839	+	0.892605i	$0.648875\pi$
$420$	2.75497	+	2.85897i	0.134429	+	0.139503i
$421$	7.31970	−	1.55585i	0.356741	−	0.0758275i	−0.0260553	−	0.999661i	$-0.508295\pi$
$421$	7.31970	−	1.55585i	0.356741	−	0.0758275i	0.382796	+	0.923833i	$0.374961\pi$
$422$	−3.28848	+	15.4711i	−0.160081	+	0.753121i
$423$	3.39804	+	11.9469i	0.165219	+	0.580877i
$424$	3.58484	+	3.22780i	0.174095	+	0.156756i
$425$	0.0257144	−	0.244656i	0.00124733	−	0.0118676i
$426$	−10.8137	−	3.11331i	−0.523926	−	0.150840i
$427$	26.5396	−	2.78943i	1.28434	−	0.134990i
$428$	−8.56957	−	4.94764i	−0.414226	−	0.239153i
$429$	−2.89071	+	3.43753i	−0.139565	+	0.165966i
$430$	−0.674480	−	0.928342i	−0.0325263	−	0.0447686i
$431$	−18.7969	+	16.9248i	−0.905415	+	0.815239i	−0.983350	−	0.181719i	$-0.941834\pi$
$431$	−18.7969	+	16.9248i	−0.905415	+	0.815239i	0.0779356	+	0.996958i	$0.475167\pi$
$432$	5.07911	+	1.09666i	0.244369	+	0.0527630i
$433$		−	22.8130i		−	1.09632i	−0.836372	−	0.548162i	$-0.815328\pi$
$433$		−	22.8130i		−	1.09632i	0.836372	−	0.548162i	$-0.184672\pi$
$434$	10.2200	+	7.64468i	0.490577	+	0.366956i
$435$	−0.580874	−	1.60127i	−0.0278508	−	0.0767750i
$436$	−5.37727	−	16.5495i	−0.257525	−	0.792579i
$437$	−0.461159	−	0.512169i	−0.0220602	−	0.0245004i
$438$	2.01558	−	2.98134i	0.0963083	−	0.142454i
$439$	3.60601	+	6.24579i	0.172105	+	0.298095i	0.939156	−	0.343492i	$-0.111610\pi$
$439$	3.60601	+	6.24579i	0.172105	+	0.298095i	−0.767050	+	0.641587i	$0.778276\pi$
$440$	2.62895	−	4.55348i	0.125330	−	0.217078i
$441$	3.75899	+	3.64560i	0.179000	+	0.173600i
$442$	−0.0981542	−	0.0713132i	−0.00466872	−	0.00339202i
$443$	−20.0595	−	2.10834i	−0.953054	−	0.100170i	−0.384779	−	0.923009i	$-0.625722\pi$
$443$	−20.0595	−	2.10834i	−0.953054	−	0.100170i	−0.568275	+	0.822839i	$0.692389\pi$
$444$	7.54010	+	3.05579i	0.357837	+	0.145022i
$445$	5.72586	−	12.8605i	0.271432	−	0.609646i
$446$	−10.4762	−	2.22679i	−0.496064	−	0.105442i
$447$	−8.77822	−	14.0816i	−0.415195	−	0.666037i
$448$	−2.09410	+	0.932352i	−0.0989367	+	0.0440495i
$449$	−5.05783	+	15.5664i	−0.238694	+	0.734624i	0.757916	+	0.652352i	$0.226218\pi$
$449$	−5.05783	+	15.5664i	−0.238694	+	0.734624i	−0.996610	+	0.0822721i	$0.973782\pi$
$450$	−2.78395	+	1.11786i	−0.131237	+	0.0526965i
$451$	20.3291	+	45.6599i	0.957261	+	2.15004i
$452$	2.08291	+	9.79932i	0.0979718	+	0.460921i
$453$	−2.08496	−	14.9513i	−0.0979597	−	0.702476i
$454$	17.6549	+	7.86045i	0.828584	+	0.368909i
$455$	−0.756462	+	0.840137i	−0.0354635	+	0.0393862i
$456$	3.88071	−	0.963159i	0.181731	−	0.0451041i
$457$	−16.5597	+	22.7924i	−0.774628	+	1.06618i	0.221227	+	0.975222i	$0.428994\pi$
$457$	−16.5597	+	22.7924i	−0.774628	+	1.06618i	−0.995854	+	0.0909613i	$0.971006\pi$
$458$	2.11185	+	20.0929i	0.0986801	+	0.938878i
$459$	0.635577	+	1.10906i	0.0296662	+	0.0517666i
$460$	−0.258547	+	0.149272i	−0.0120548	+	0.00695985i
$461$	−20.9266	+	15.2041i	−0.974649	+	0.708124i	−0.956506	−	0.291711i	$-0.905775\pi$
$461$	−20.9266	+	15.2041i	−0.974649	+	0.708124i	−0.0181429	+	0.999835i	$0.505775\pi$
$462$	−9.82024	+	18.4216i	−0.456879	+	0.857049i
$463$	−14.8293	+	4.81833i	−0.689176	+	0.223927i	−0.632609	−	0.774472i	$-0.718016\pi$
$463$	−14.8293	+	4.81833i	−0.689176	+	0.223927i	−0.0565680	+	0.998399i	$0.518016\pi$
$464$	0.983442			0.0456552
$465$	−8.25390	+	4.98729i	−0.382766	+	0.231280i
$466$	14.5182			0.672544
$467$	34.4263	−	11.1858i	1.59306	−	0.517616i	0.627681	−	0.778471i	$-0.284004\pi$
$467$	34.4263	−	11.1858i	1.59306	−	0.517616i	0.965378	+	0.260855i	$0.0840044\pi$
$468$	−0.209051	+	1.46471i	−0.00966338	+	0.0677064i
$469$	−18.3229	+	13.3124i	−0.846074	+	0.614708i
$470$	3.58555	−	2.07012i	0.165389	−	0.0954875i
$471$	4.19551	−	23.6459i	0.193319	−	1.08954i
$472$	−1.52859	−	14.5436i	−0.0703591	−	0.669422i
$473$	3.54635	−	4.88113i	0.163061	−	0.224435i
$474$	1.51746	+	6.11406i	0.0696991	+	0.280828i
$475$	−1.54469	+	1.71556i	−0.0708754	+	0.0787151i
$476$	−0.515155	−	0.229362i	−0.0236121	−	0.0105128i
$477$	12.7922	−	6.76664i	0.585715	−	0.309823i
$478$	−1.71215	−	8.05503i	−0.0783119	−	0.368428i
$479$	−10.4039	−	23.3675i	−0.475365	−	1.06769i	−0.979017	−	0.203780i	$-0.934677\pi$
$479$	−10.4039	−	23.3675i	−0.475365	−	1.06769i	0.503652	−	0.863907i	$-0.331990\pi$
$480$	−0.0585945	−	1.73106i	−0.00267446	−	0.0790117i
$481$	−0.715865	+	2.20321i	−0.0326406	+	0.100458i
$482$	27.8129	−	12.3831i	1.26684	−	0.564035i
$483$	1.00588	−	0.627048i	0.0457692	−	0.0285317i
$484$	16.2818	+	3.46080i	0.740081	+	0.157309i
$485$	1.49146	−	3.34988i	0.0677238	−	0.152110i
$486$	8.33127	−	13.1754i	0.377914	−	0.597646i
$487$	29.7680	+	3.12874i	1.34892	+	0.141777i	0.751276	−	0.659988i	$-0.229439\pi$
$487$	29.7680	+	3.12874i	1.34892	+	0.141777i	0.597640	+	0.801765i	$0.296105\pi$
$488$	−9.41828	−	6.84278i	−0.426345	−	0.309758i
$489$	0.693005	+	1.42474i	0.0313388	+	0.0644289i
$490$	0.872742	−	1.51163i	0.0394264	−	0.0682886i
$491$	12.2452	+	21.2093i	0.552618	+	0.957162i	0.998085	+	0.0618637i	$0.0197044\pi$
$491$	12.2452	+	21.2093i	0.552618	+	0.957162i	−0.445467	+	0.895298i	$0.646962\pi$
$492$	13.6400	+	9.22154i	0.614938	+	0.415739i
$493$	0.161883	+	0.179789i	0.00729084	+	0.00809730i
$494$	0.351823	+	1.08280i	0.0158292	+	0.0487174i
$495$	−10.1132	−	12.1050i	−0.454557	−	0.544081i
$496$	−1.08175	−	5.46167i	−0.0485721	−	0.245236i
$497$		−	14.8927i		−	0.668027i
$498$	−1.54841	+	1.20709i	−0.0693860	+	0.0540908i
$499$	13.2301	−	11.9125i	0.592263	−	0.533276i	−0.317579	−	0.948232i	$-0.602870\pi$
$499$	13.2301	−	11.9125i	0.592263	−	0.533276i	0.909841	+	0.414956i	$0.136203\pi$
$500$	0.587785	+	0.809017i	0.0262866	+	0.0361803i
$501$	−3.07875	−	2.58900i	−0.137548	−	0.115668i
$502$	−4.60944	−	2.66126i	−0.205729	−	0.118778i
$503$	37.3797	−	3.92876i	1.66668	−	0.175175i	0.776289	−	0.630378i	$-0.217100\pi$
$503$	37.3797	−	3.92876i	1.66668	−	0.175175i	0.890388	+	0.455203i	$0.150433\pi$
$504$	0.465013	+	6.86108i	0.0207133	+	0.305617i
$505$	−0.694831	+	6.61087i	−0.0309196	+	0.294180i
$506$	−1.16653	−	1.05035i	−0.0518584	−	0.0466936i
$507$	22.0399	+	1.56489i	0.978826	+	0.0694992i
$508$	−1.05238	+	4.95106i	−0.0466918	+	0.219668i
$509$	34.9145	−	7.42130i	1.54756	−	0.328943i	0.646592	−	0.762836i	$-0.276194\pi$
$509$	34.9145	−	7.42130i	1.54756	−	0.328943i	0.900964	+	0.433893i	$0.142860\pi$
$510$	0.306821	−	0.295659i	0.0135862	−	0.0130920i
$511$	4.52963	+	1.47177i	0.200379	+	0.0651071i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	1.29216	−	11.9256i	0.0570504	−	0.526526i
$514$	−27.6917	+	5.88605i	−1.22143	+	0.259622i
$515$	−1.53272	+	7.21086i	−0.0675396	+	0.317749i
$516$	0.140765	−	1.98253i	0.00619682	−	0.0872759i
$517$	16.1775	+	14.5663i	0.711486	+	0.640625i
$518$	−1.12549	+	10.7083i	−0.0494510	+	0.470495i
$519$	8.61056	−	29.9077i	0.377961	−	1.31280i
$520$	0.490484	−	0.0515519i	0.0215091	−	0.00226070i
$521$	0.179023	+	0.103359i	0.00784315	+	0.00452825i	0.503916	−	0.863752i	$-0.331892\pi$
$521$	0.179023	+	0.103359i	0.00784315	+	0.00452825i	−0.496073	+	0.868281i	$0.665225\pi$
$522$	1.01500	−	2.77023i	0.0444256	−	0.121250i
$523$	−1.27828	−	1.75941i	−0.0558954	−	0.0769335i	0.780154	−	0.625587i	$-0.215141\pi$
$523$	−1.27828	−	1.75941i	−0.0558954	−	0.0769335i	−0.836050	+	0.548654i	$0.815141\pi$
$524$	−5.16147	+	4.64741i	−0.225480	+	0.203023i
$525$	−2.44103	−	3.13128i	−0.106535	−	0.136660i
$526$			10.8749i			0.474170i
$527$	0.820416	−	1.09680i	0.0357379	−	0.0477773i
$528$	8.56106	−	3.10560i	0.372573	−	0.135154i
$529$	−7.07985	−	21.7895i	−0.307820	−	0.947371i
$530$	−3.22780	−	3.58484i	−0.140207	−	0.155715i
$531$	−42.5451	−	10.7045i	−1.84630	−	0.464535i
$532$	2.64586	+	4.58277i	0.114713	+	0.198688i
$533$	−2.34408	+	4.06007i	−0.101533	+	0.175861i
$534$	21.9268	−	10.6654i	0.948864	−	0.461535i
$535$	8.00545	+	5.81630i	0.346106	+	0.251461i
$536$	9.82618	+	1.03277i	0.424427	+	0.0446090i
$537$	0.667899	−	1.64803i	0.0288220	−	0.0711175i
$538$	−7.36305	+	16.5377i	−0.317444	+	0.712990i
$539$	8.97703	+	1.90813i	0.386668	+	0.0821888i
$540$	−4.93665	−	1.62156i	−0.212440	−	0.0697809i
$541$	3.45918	−	1.54013i	0.148722	−	0.0662152i	−0.331026	−	0.943622i	$-0.607395\pi$
$541$	3.45918	−	1.54013i	0.148722	−	0.0662152i	0.479748	+	0.877406i	$0.340728\pi$
$542$	−3.86190	+	11.8857i	−0.165883	+	0.510534i
$543$	−0.128119	+	0.00433670i	−0.00549812	+	0.000186106i
$544$	0.100059	+	0.224735i	0.00428998	+	0.00963545i
$545$	3.61792	+	17.0210i	0.154974	+	0.729098i
$546$	−1.93934	+	0.270440i	−0.0829963	+	0.0115738i
$547$	−20.6667	−	9.20141i	−0.883644	−	0.393424i	−0.0858177	−	0.996311i	$-0.527350\pi$
$547$	−20.6667	−	9.20141i	−0.883644	−	0.393424i	−0.797826	+	0.602887i	$0.794017\pi$
$548$	−4.95735	+	5.50569i	−0.211767	+	0.235192i
$549$	−28.9958	+	19.4677i	−1.23751	+	0.830862i
$550$	−3.09052	+	4.25373i	−0.131780	+	0.181380i
$551$	−0.237309	−	2.25785i	−0.0101097	−	0.0961875i
$552$	−0.509142	−	0.0903376i	−0.0216705	−	0.00384502i
$553$	−7.22015	+	4.16856i	−0.307032	+	0.177265i
$554$	16.8416	−	12.2362i	0.715532	−	0.519865i
$555$	−7.17938	−	3.82721i	−0.304748	−	0.162456i
$556$	16.8089	−	5.46155i	0.712857	−	0.231621i
$557$	−45.6302			−1.93341			−0.966707	−	0.255886i	$-0.917633\pi$
$557$	−45.6302			−1.93341			−0.966707	+	0.255886i	$0.917633\pi$
$558$	−16.5013	−	2.58979i	−0.698556	−	0.109635i
$559$	0.565927			0.0239362
$560$	2.18008	−	0.708351i	0.0921253	−	0.0299333i
$561$	1.97698	+	1.05389i	0.0834680	+	0.0444954i
$562$	−15.7966	+	11.4769i	−0.666341	+	0.484125i
$563$	39.2662	−	22.6703i	1.65487	−	0.955441i	0.679845	−	0.733356i	$-0.262047\pi$
$563$	39.2662	−	22.6703i	1.65487	−	0.955441i	0.975027	−	0.222085i	$-0.0712861\pi$
$564$	7.06083	+	1.25281i	0.297314	+	0.0527528i
$565$	−1.04719	−	9.96336i	−0.0440557	−	0.419162i
$566$	−7.29076	+	10.0349i	−0.306454	+	0.421797i
$567$	19.8067	+	5.77139i	0.831805	+	0.242376i
$568$	−4.34727	+	4.82813i	−0.182407	+	0.202584i
$569$	−13.9160	−	6.19581i	−0.583390	−	0.259742i	0.0937505	−	0.995596i	$-0.470114\pi$
$569$	−13.9160	−	6.19581i	−0.583390	−	0.259742i	−0.677140	+	0.735854i	$0.736781\pi$
$570$	−3.96013	+	0.552238i	−0.165872	+	0.0231307i
$571$	6.66608	+	31.3614i	0.278967	+	1.31243i	0.864846	+	0.502037i	$0.167416\pi$
$571$	6.66608	+	31.3614i	0.278967	+	1.31243i	−0.585880	+	0.810398i	$0.699251\pi$
$572$	1.05472	+	2.36893i	0.0440999	+	0.0990500i
$573$	2.41593	−	0.0817767i	0.100927	−	0.00341627i
$574$	−6.73351	+	20.7236i	−0.281051	+	0.864987i
$575$	0.272734	−	0.121429i	0.0113738	−	0.00506394i
$576$	1.85204	−	2.36007i	0.0771684	−	0.0983363i
$577$	2.48441	+	0.528077i	0.103427	+	0.0219841i	0.259335	−	0.965788i	$-0.416497\pi$
$577$	2.48441	+	0.528077i	0.103427	+	0.0219841i	−0.155907	+	0.987772i	$0.549830\pi$
$578$	6.88991	−	15.4750i	0.286582	−	0.643675i
$579$	10.5015	−	25.9123i	0.436428	−	1.07688i
$580$	−0.978055	−	0.102798i	−0.0406115	−	0.00426844i
$581$	−2.10211	−	1.52727i	−0.0872102	−	0.0633619i
$582$	5.71144	−	2.77809i	0.236747	−	0.115156i
$583$	12.6817	−	21.9654i	0.525223	−	0.909714i
$584$	−1.03887	−	1.79937i	−0.0429886	−	0.0744585i
$585$	0.361010	−	1.43484i	0.0149259	−	0.0593232i
$586$	15.8274	+	17.5781i	0.653823	+	0.726144i
$587$	0.253816	+	0.781166i	0.0104761	+	0.0322422i	0.956158	−	0.292852i	$-0.0946042\pi$
$587$	0.253816	+	0.781166i	0.0104761	+	0.0322422i	−0.945682	+	0.325094i	$0.894604\pi$
$588$	2.84205	−	1.03098i	0.117204	−	0.0425167i
$589$	−12.2782	+	3.80148i	−0.505914	+	0.156637i
$590$			14.6237i			0.602047i
$591$	−23.5456	−	30.2036i	−0.968536	−	1.24241i
$592$	3.49070	−	3.14304i	0.143467	−	0.129178i
$593$	18.8065	+	25.8850i	0.772292	+	1.06297i	0.996091	+	0.0883335i	$0.0281541\pi$
$593$	18.8065	+	25.8850i	0.772292	+	1.06297i	−0.223799	+	0.974635i	$0.571846\pi$
$594$	0.0877454	−	27.3207i	0.00360024	−	1.12098i
$595$	0.488358	+	0.281954i	0.0200207	+	0.0115590i
$596$	−9.52786	+	1.00142i	−0.390276	+	0.0410197i
$597$	−4.07085	+	14.1396i	−0.166609	+	0.578694i
$598$	0.0153905	−	0.146431i	0.000629366	−	0.00598801i
$599$	16.6153	+	14.9605i	0.678883	+	0.611269i	0.934692	−	0.355458i	$-0.115675\pi$
$599$	16.6153	+	14.9605i	0.678883	+	0.611269i	−0.255809	+	0.966727i	$0.582342\pi$
$600$	−0.122671	+	1.72770i	−0.00500804	+	0.0705331i
$601$	−2.67919	+	12.6046i	−0.109287	+	0.514153i	0.889118	+	0.457679i	$0.151319\pi$
$601$	−2.67919	+	12.6046i	−0.109287	+	0.514153i	−0.998404	+	0.0564739i	$0.982014\pi$
$602$	2.57289	−	0.546885i	0.104863	−	0.0222894i
$603$	13.0507	−	26.6132i	0.531467	−	1.08377i
$604$	−8.28912	−	2.69330i	−0.337279	−	0.109589i
$605$	−15.8308	−	5.14375i	−0.643615	−	0.209123i
$606$	−8.29063	+	7.98904i	−0.336784	+	0.324532i
$607$	9.52421	−	2.02443i	0.386576	−	0.0821692i	−0.0105241	−	0.999945i	$-0.503350\pi$
$607$	9.52421	−	2.02443i	0.386576	−	0.0821692i	0.397100	+	0.917775i	$0.370017\pi$
$608$	0.479966	−	2.25806i	0.0194652	−	0.0915765i
$609$	3.89479	+	0.276540i	0.157825	+	0.0112060i
$610$	8.65142	+	7.78977i	0.350286	+	0.315399i
$611$	−0.213437	+	2.03072i	−0.00863475	+	0.0821541i
$612$	0.736321	−	0.0499046i	0.0297640	−	0.00201727i
$613$	−23.9041	+	2.51242i	−0.965478	+	0.101476i	−0.574128	−	0.818766i	$-0.694659\pi$
$613$	−23.9041	+	2.51242i	−0.965478	+	0.101476i	−0.391351	+	0.920242i	$0.627992\pi$
$614$	2.14663	+	1.23936i	0.0866311	+	0.0500165i
$615$	−12.6013	−	10.5968i	−0.508135	−	0.427304i
$616$	7.08431	+	9.75071i	0.285435	+	0.392867i
$617$	−23.3631	+	21.0362i	−0.940563	+	0.846887i	−0.988385	−	0.151969i	$-0.951439\pi$
$617$	−23.3631	+	21.0362i	−0.940563	+	0.846887i	0.0478220	+	0.998856i	$0.484772\pi$
$618$	−10.0702	+	7.85036i	−0.405083	+	0.315788i
$619$		−	19.2249i		−	0.772714i	−0.922349	−	0.386357i	$-0.873733\pi$
$619$		−	19.2249i		−	0.772714i	0.922349	−	0.386357i	$-0.126267\pi$
$620$	0.504927	+	5.54482i	0.0202783	+	0.222685i
$621$	−0.779952	+	1.34095i	−0.0312984	+	0.0538105i
$622$	−3.74264	−	11.5187i	−0.150066	−	0.461856i
$623$	21.5926	+	23.9810i	0.865089	+	0.960778i
$624$	0.707670	+	0.478433i	0.0283295	+	0.0191526i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	12.6012	−	21.8259i	0.503645	−	0.872338i
$627$	−9.19584	−	18.9056i	−0.367247	−	0.755018i
$628$	−11.2172	−	8.14975i	−0.447614	−	0.325210i
$629$	1.14920	+	0.120785i	0.0458215	+	0.00481603i
$630$	0.254712	−	6.87210i	0.0101480	−	0.273791i
$631$	2.78533	−	6.25596i	0.110882	−	0.249046i	−0.849578	−	0.527463i	$-0.823143\pi$
$631$	2.78533	−	6.25596i	0.110882	−	0.249046i	0.960460	+	0.278417i	$0.0898099\pi$
$632$	3.55757	+	0.756185i	0.141513	+	0.0300794i
$633$	23.2481	−	14.4925i	0.924030	−	0.576023i
$634$	28.3715	−	12.6318i	1.12678	−	0.501673i
$635$	1.56414	−	4.81394i	0.0620711	−	0.191035i
$636$	−0.282653	−	8.35041i	−0.0112079	−	0.331115i
$637$	0.350138	+	0.786423i	0.0138730	+	0.0311592i
$638$	−1.07508	−	5.05785i	−0.0425628	−	0.200242i
$639$	9.11345	+	17.2288i	0.360523	+	0.681561i
$640$	−0.913545	−	0.406737i	−0.0361111	−	0.0160777i
$641$	10.2974	−	11.4364i	0.406723	−	0.451711i	−0.504631	−	0.863335i	$-0.668372\pi$
$641$	10.2974	−	11.4364i	0.406723	−	0.451711i	0.911354	+	0.411624i	$0.135038\pi$
$642$	4.12853	+	16.6345i	0.162940	+	0.656510i
$643$	−17.7966	+	24.4949i	−0.701829	+	0.965984i	0.298106	+	0.954533i	$0.403645\pi$
$643$	−17.7966	+	24.4949i	−0.701829	+	0.965984i	−0.999934	+	0.0114514i	$0.996355\pi$
$644$	−0.0715336	−	0.680596i	−0.00281882	−	0.0268193i
$645$	−0.347224	+	1.95695i	−0.0136719	+	0.0770549i
$646$	0.491817	−	0.283950i	0.0193503	−	0.0111719i
$647$	−9.04964	+	6.57495i	−0.355778	+	0.258488i	−0.751289	−	0.659973i	$-0.770568\pi$
$647$	−9.04964	+	6.57495i	−0.355778	+	0.258488i	0.395511	+	0.918461i	$0.370568\pi$
$648$	−4.73655	−	7.65279i	−0.186069	−	0.300630i
$649$	−73.1266	+	23.7603i	−2.87047	+	0.932672i
$650$	−0.493185			−0.0193443
$651$	−2.74833	−	21.9344i	−0.107716	−	0.859676i
$652$	0.914720			0.0358232
$653$	−30.2394	+	9.82539i	−1.18336	+	0.384497i	−0.833614	−	0.552347i	$-0.813732\pi$
$653$	−30.2394	+	9.82539i	−1.18336	+	0.384497i	−0.349746	+	0.936844i	$0.613732\pi$
$654$	−14.1783	+	26.5967i	−0.554414	+	1.04001i
$655$	5.61898	−	4.08243i	0.219552	−	0.159514i
$656$	8.23234	−	4.75295i	0.321419	−	0.185571i
$657$	−6.14081	+	1.06924i	−0.239576	+	0.0417150i
$658$	0.992034	+	9.43857i	0.0386735	+	0.367954i
$659$	−15.4621	+	21.2818i	−0.602320	+	0.829022i	−0.995918	−	0.0902606i	$-0.971230\pi$
$659$	−15.4621	+	21.2818i	−0.602320	+	0.829022i	0.393599	+	0.919282i	$0.371230\pi$
$660$	−8.83879	+	2.19371i	−0.344049	+	0.0853900i
$661$	−15.7873	+	17.5336i	−0.614055	+	0.681977i	−0.967324	−	0.253545i	$-0.918403\pi$
$661$	−15.7873	+	17.5336i	−0.614055	+	0.681977i	0.353269	+	0.935522i	$0.385070\pi$
$662$	10.4216	+	4.64001i	0.405048	+	0.180339i
$663$	0.0290233	+	0.208128i	0.00112717	+	0.00808301i
$664$	0.235673	+	1.10875i	0.00914589	+	0.0430280i
$665$	−2.15234	−	4.83424i	−0.0834642	−	0.187464i
$666$	−5.25082	−	13.0768i	−0.203465	−	0.506715i
$667$	−0.0907278	+	0.279231i	−0.00351299	+	0.0108119i
$668$	−2.12168	+	0.944634i	−0.0820904	+	0.0365490i
$669$	9.81355	+	15.7424i	0.379414	+	0.608638i
$670$	−9.66440	−	2.05423i	−0.373368	−	0.0793619i
$671$	−24.8966	+	55.9186i	−0.961121	+	2.15871i
$672$	3.67963	+	1.49125i	0.141945	+	0.0575263i
$673$	30.6609	+	3.22259i	1.18189	+	0.124222i	0.675020	−	0.737799i	$-0.264135\pi$
$673$	30.6609	+	3.22259i	1.18189	+	0.124222i	0.506872	+	0.862021i	$0.330802\pi$
$674$	−20.6484	−	15.0019i	−0.795345	−	0.577852i
$675$	4.74011	+	2.12870i	0.182447	+	0.0819337i
$676$	6.37838	−	11.0477i	0.245322	−	0.424911i
$677$	−13.3581	−	23.1369i	−0.513394	−	0.889224i	−0.999879	−	0.0155355i	$-0.995055\pi$
$677$	−13.3581	−	23.1369i	−0.513394	−	0.889224i	0.486486	−	0.873689i	$-0.338279\pi$
$678$	9.71856	−	14.3751i	0.373239	−	0.552074i
$679$	5.62440	+	6.24652i	0.215845	+	0.239720i
$680$	−0.0760193	−	0.233963i	−0.00291521	−	0.00897208i
$681$	−11.4148	−	31.4666i	−0.437415	−	1.20580i
$682$	−26.9068	+	11.5340i	−1.03032	+	0.441661i
$683$		−	33.2948i		−	1.27399i	−0.770868	−	0.636995i	$-0.780177\pi$
$683$		−	33.2948i		−	1.27399i	0.770868	−	0.636995i	$-0.219823\pi$
$684$	−5.86530	−	3.68253i	−0.224266	−	0.140805i
$685$	5.50569	−	4.95735i	0.210362	−	0.189411i
$686$	11.7834	+	16.2184i	0.449891	+	0.619221i
$687$	22.5221	−	26.7825i	0.859273	−	1.02182i
$688$	−0.993759	−	0.573747i	−0.0378867	−	0.0218739i
$689$	2.36603	−	0.248680i	0.0901386	−	0.00947395i
$690$	0.496910	+	0.143062i	0.0189170	+	0.00544630i
$691$	−0.918469	+	8.73865i	−0.0349402	+	0.332434i	0.963063	+	0.269275i	$0.0867841\pi$
$691$	−0.918469	+	8.73865i	−0.0349402	+	0.332434i	−0.998003	+	0.0631587i	$0.979883\pi$
$692$	−13.3533	−	12.0233i	−0.507615	−	0.457059i
$693$	34.7782	−	9.89195i	1.32111	−	0.375764i
$694$	−2.57582	+	12.1183i	−0.0977769	+	0.460004i
$695$	−17.2877	+	3.67462i	−0.655761	+	0.139386i
$696$	−1.18195	−	1.22657i	−0.0448017	−	0.0464930i
$697$	2.22403	+	0.722631i	0.0842411	+	0.0273716i
$698$	8.44929	+	2.74534i	0.319810	+	0.103913i
$699$	−17.4487	−	18.1074i	−0.659971	−	0.684886i
$700$	−2.24218	+	0.476590i	−0.0847465	+	0.0180134i
$701$	−0.149227	+	0.702060i	−0.00563624	+	0.0265164i	−0.980876	−	0.194634i	$-0.937648\pi$
$701$	−0.149227	+	0.702060i	−0.00563624	+	0.0265164i	0.975240	+	0.221151i	$0.0709813\pi$
$702$	2.07807	−	1.49963i	0.0784316	−	0.0565999i
$703$	−8.05830	−	7.25573i	−0.303925	−	0.273655i
$704$	0.549600	−	5.22910i	0.0207138	−	0.197079i
$705$	−6.89119	−	1.98400i	−0.259537	−	0.0747219i
$706$	0.528266	−	0.0555230i	0.0198815	−	0.00208963i
$707$	−13.1960	−	7.61870i	−0.496286	−	0.286531i
$708$	−16.3019	+	19.3857i	−0.612663	+	0.728558i
$709$	−16.2152	−	22.3182i	−0.608973	−	0.838179i	0.387520	−	0.921861i	$-0.373332\pi$
$709$	−16.2152	−	22.3182i	−0.608973	−	0.838179i	−0.996492	+	0.0836823i	$0.973332\pi$
$710$	4.82813	−	4.34727i	0.181197	−	0.163150i
$711$	5.80183	−	9.24078i	0.217586	−	0.346556i
$712$		−	14.0776i		−	0.527579i
$713$	1.65054	+	0.196723i	0.0618133	+	0.00736733i
$714$	0.333074	+	0.918170i	0.0124650	+	0.0343616i
$715$	−0.801318	−	2.46620i	−0.0299676	−	0.0922308i
$716$	−0.686968	−	0.762955i	−0.0256732	−	0.0285130i
$717$	−7.98865	+	11.8164i	−0.298342	+	0.441290i
$718$	10.4343	+	18.0727i	0.389405	+	0.674469i
$719$	5.47011	−	9.47450i	0.204001	−	0.353339i	−0.745813	−	0.666155i	$-0.767939\pi$
$719$	5.47011	−	9.47450i	0.204001	−	0.353339i	0.949814	+	0.312816i	$0.101272\pi$
$720$	−2.08859	+	2.15355i	−0.0778372	+	0.0802582i
$721$	−13.6712	−	9.93272i	−0.509142	−	0.369914i
$722$	13.5959	+	1.42899i	0.505987	+	0.0531814i
$723$	−48.8714	−	19.8062i	−1.81755	−	0.736601i
$724$	−0.0301034	+	0.0676133i	−0.00111878	+	0.00251283i
$725$	0.961952	+	0.204469i	0.0357260	+	0.00759379i
$726$	−15.2519	−	24.4663i	−0.566050	−	0.908030i
$727$	20.0221	−	8.91442i	0.742579	−	0.330617i	−0.000339107	−	1.00000i	$-0.500108\pi$
$727$	20.0221	−	8.91442i	0.742579	−	0.330617i	0.742918	+	0.669383i	$0.233441\pi$
$728$	−0.349348	+	1.07518i	−0.0129477	+	0.0398490i
$729$	−26.4455	+	5.44386i	−0.979463	+	0.201624i
$730$	0.845091	+	1.89810i	0.0312782	+	0.0702520i
$731$	−0.0586909	−	0.276119i	−0.00217076	−	0.0102126i
$732$	2.78489	+	19.9707i	0.102933	+	0.738137i
$733$	16.2709	+	7.24425i	0.600978	+	0.267572i	0.684593	−	0.728926i	$-0.259980\pi$
$733$	16.2709	+	7.24425i	0.600978	+	0.267572i	−0.0836153	+	0.996498i	$0.526647\pi$
$734$	8.11822	−	9.01620i	0.299649	−	0.332794i
$735$	−2.93424	+	0.728253i	−0.108231	+	0.0268620i
$736$	−0.175480	+	0.241527i	−0.00646828	+	0.00890282i
$737$	−5.43022	−	51.6651i	−0.200025	−	1.90311i
$738$	−4.89190	−	28.0950i	−0.180073	−	1.03419i
$739$	−14.7512	+	8.51661i	−0.542632	+	0.313288i	−0.746145	−	0.665784i	$-0.768097\pi$
$739$	−14.7512	+	8.51661i	−0.542632	+	0.313288i	0.203513	+	0.979072i	$0.434764\pi$
$740$	−3.80011	+	2.76094i	−0.139695	+	0.101494i
$741$	0.927651	−	1.74016i	0.0340781	−	0.0639264i
$742$	10.5164	−	3.41700i	0.386071	−	0.125442i
$743$	−22.1651			−0.813159			−0.406579	−	0.913615i	$-0.633279\pi$
$743$	−22.1651			−0.813159			−0.406579	+	0.913615i	$0.633279\pi$
$744$	−5.51180	+	7.91328i	−0.202072	+	0.290115i
$745$	9.58034			0.350996
$746$	−3.78923	+	1.23120i	−0.138734	+	0.0450773i
$747$	3.36646	+	0.480478i	0.123172	+	0.0175798i
$748$	1.04643	−	0.760278i	0.0382614	−	0.0277985i
$749$	−19.6438	+	11.3413i	−0.717768	+	0.414404i
$750$	0.302593	−	1.70541i	0.0110491	−	0.0622729i
$751$	2.67632	+	25.4635i	0.0976602	+	0.929175i	0.928166	+	0.372165i	$0.121385\pi$
$751$	2.67632	+	25.4635i	0.0976602	+	0.929175i	−0.830506	+	0.557009i	$0.811949\pi$
$752$	2.43357	−	3.34953i	0.0887433	−	0.122145i
$753$	2.22067	+	8.94742i	0.0809257	+	0.326062i
$754$	0.324541	−	0.360440i	0.0118191	−	0.0131264i
$755$	7.96218	+	3.54499i	0.289773	+	0.129015i
$756$	7.99840	−	8.82596i	0.290899	−	0.320997i
$757$	5.87000	+	27.6162i	0.213349	+	1.00373i	0.946261	+	0.323403i	$0.104827\pi$
$757$	5.87000	+	27.6162i	0.213349	+	1.00373i	−0.732913	+	0.680323i	$0.761840\pi$
$758$	−10.6930	−	24.0168i	−0.388386	−	0.872329i
$759$	0.0919768	+	2.71727i	0.00333855	+	0.0986308i
$760$	−0.713368	+	2.19552i	−0.0258766	+	0.0796399i
$761$	24.3098	−	10.8234i	0.881229	−	0.392348i	0.0843135	−	0.996439i	$-0.473130\pi$
$761$	24.3098	−	10.8234i	0.881229	−	0.392348i	0.796915	+	0.604091i	$0.206464\pi$
$762$	7.43987	−	4.63788i	0.269518	−	0.168013i
$763$	−39.0167	−	8.29325i	−1.41250	−	0.300236i
$764$	0.567656	−	1.27498i	0.0205371	−	0.0461271i
$765$	−0.737504	−	0.0273353i	−0.0266645	−	0.000988311i
$766$	−37.5522	−	3.94690i	−1.35682	−	0.142607i
$767$	−5.83478	−	4.23922i	−0.210682	−	0.153069i
$768$	−0.757614	−	1.55757i	−0.0273380	−	0.0562039i
$769$	22.4723	−	38.9232i	0.810372	−	1.40360i	−0.102232	−	0.994761i	$-0.532599\pi$
$769$	22.4723	−	38.9232i	0.810372	−	1.40360i	0.912604	−	0.408844i	$-0.134068\pi$
$770$	−6.02627	−	10.4378i	−0.217172	−	0.376153i
$771$	40.6224	+	27.4635i	1.46298	+	0.989073i
$772$	−10.8014	−	11.9961i	−0.388749	−	0.431750i
$773$	−6.01898	−	18.5245i	−0.216488	−	0.666280i	−0.999045	−	0.0437014i	$-0.986085\pi$
$773$	−6.01898	−	18.5245i	−0.216488	−	0.666280i	0.782557	−	0.622579i	$-0.213915\pi$
$774$	−2.64183	+	2.20713i	−0.0949585	+	0.0793338i
$775$	0.0774309	−	5.56723i	0.00278140	−	0.199981i
$776$		−	3.66690i		−	0.131634i
$777$	14.7082	−	11.4660i	0.527655	−	0.411341i
$778$	21.3889	−	19.2587i	0.766830	−	0.690457i
$779$	−12.8986	−	17.7534i	−0.462141	−	0.636082i
$780$	−0.653784	−	0.549784i	−0.0234092	−	0.0196854i
$781$	29.5834	+	17.0800i	1.05858	+	0.611171i
$782$	−0.0730406	+	0.00767688i	−0.00261193	+	0.000274525i
$783$	−4.67497	+	2.06347i	−0.167070	+	0.0737423i
$784$	0.182453	−	1.73592i	0.00651617	−	0.0619972i
$785$	10.3038	+	9.27761i	0.367760	+	0.331132i
$786$	11.9996	+	0.852007i	0.428013	+	0.0303901i
$787$	−5.46849	+	25.7272i	−0.194931	+	0.917077i	0.766546	+	0.642190i	$0.221974\pi$
$787$	−5.46849	+	25.7272i	−0.194931	+	0.917077i	−0.961477	+	0.274887i	$0.911360\pi$
$788$	−21.6275	+	4.59707i	−0.770449	+	0.163764i
$789$	13.5634	−	13.0700i	0.482871	−	0.465305i
$790$	−3.45904	−	1.12391i	−0.123067	−	0.0399869i
$791$	21.8406	+	7.09643i	0.776561	+	0.252320i
$792$	−14.1625	−	6.94508i	−0.503242	−	0.246782i
$793$	−5.61602	+	1.19372i	−0.199431	+	0.0423903i
$794$	5.81915	−	27.3770i	0.206514	−	0.971572i
$795$	−0.591752	+	8.33421i	−0.0209873	+	0.295584i
$796$	6.31308	+	5.68432i	0.223761	+	0.201475i
$797$	−4.38422	+	41.7131i	−0.155297	+	1.47755i	0.588147	+	0.808754i	$0.299858\pi$
$797$	−4.38422	+	41.7131i	−0.155297	+	1.47755i	−0.743444	+	0.668798i	$0.766809\pi$
$798$	2.53580	−	8.80778i	0.0897662	−	0.311792i
$799$	1.01293	−	0.106464i	0.0358350	−	0.00376641i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	−39.6547	−	14.5294i	−1.40113	−	0.513370i
$802$	9.65253	+	13.2856i	0.340843	+	0.469130i
$803$	−8.11850	+	7.30993i	−0.286496	+	0.257962i
$804$	−10.5215	−	13.4967i	−0.371064	−	0.475990i
$805$			0.684345i			0.0241200i
$806$	−2.35873	−	1.40591i	−0.0830827	−	0.0495210i
$807$	29.4754	−	10.6924i	1.03758	−	0.376392i
$808$	2.05412	+	6.32195i	0.0722639	+	0.222405i
$809$	26.4716	+	29.3997i	0.930691	+	1.03364i	0.999352	+	0.0359968i	$0.0114606\pi$
$809$	26.4716	+	29.3997i	0.930691	+	1.03364i	−0.0686611	+	0.997640i	$0.521873\pi$
$810$	3.91066	+	8.10597i	0.137407	+	0.284815i
$811$	−14.5537	−	25.2078i	−0.511050	−	0.885165i	−0.999918	−	0.0128073i	$-0.995923\pi$
$811$	−14.5537	−	25.2078i	−0.511050	−	0.885165i	0.488868	−	0.872358i	$-0.337410\pi$
$812$	1.12716	−	1.95230i	0.0395555	−	0.0685122i
$813$	19.4655	−	9.46818i	0.682685	−	0.332064i
$814$	−19.9806	−	14.5168i	−0.700320	−	0.508812i
$815$	−0.909709	−	0.0956143i	−0.0318657	−	0.00334922i
$816$	0.160039	−	0.394893i	0.00560249	−	0.0138240i
$817$	−1.07744	+	2.41998i	−0.0376950	+	0.0846644i
$818$	−5.40827	−	1.14956i	−0.189096	−	0.0401936i
$819$	2.66810	+	2.09376i	0.0932309	+	0.0731620i
$820$	−8.68406	+	3.86639i	−0.303261	+	0.135020i
$821$	7.94002	−	24.4369i	0.277109	−	0.852853i	−0.711545	−	0.702640i	$-0.752004\pi$
$821$	7.94002	−	24.4369i	0.277109	−	0.852853i	0.988654	−	0.150212i	$-0.0479957\pi$
$822$	12.8248	−	0.434106i	0.447316	−	0.0151412i
$823$	15.1418	+	34.0091i	0.527811	+	1.18548i	0.959048	+	0.283245i	$0.0914108\pi$
$823$	15.1418	+	34.0091i	0.527811	+	1.18548i	−0.431236	+	0.902239i	$0.641922\pi$
$824$	1.53272	+	7.21086i	0.0533947	+	0.251202i
$825$	9.01967	−	1.25779i	0.314025	−	0.0437905i
$826$	−30.6234	−	13.6344i	−1.06552	−	0.474402i
$827$	4.15360	−	4.61304i	0.144435	−	0.160411i	−0.666587	−	0.745428i	$-0.732245\pi$
$827$	4.15360	−	4.61304i	0.144435	−	0.160411i	0.811021	+	0.585016i	$0.198912\pi$
$828$	0.499241	+	0.743584i	0.0173498	+	0.0258413i
$829$	5.37154	−	7.39329i	0.186561	−	0.256779i	−0.705484	−	0.708726i	$-0.749270\pi$
$829$	5.37154	−	7.39329i	0.186561	−	0.256779i	0.892045	+	0.451947i	$0.149270\pi$
$830$	−0.118486	−	1.12732i	−0.00411270	−	0.0391297i
$831$	−35.5023	−	6.29921i	−1.23156	−	0.218517i
$832$	0.427111	−	0.246593i	0.0148074	−	0.00854906i
$833$	0.347388	−	0.252392i	0.0120363	−	0.00874487i
$834$	−27.0135	−	14.4005i	−0.935402	−	0.498647i
$835$	2.20880	−	0.717683i	0.0764387	−	0.0248364i
$836$	−12.1379			−0.419798
$837$	16.6020	+	23.6933i	0.573850	+	0.818960i
$838$	6.26133			0.216294
$839$	−46.3048	+	15.0454i	−1.59862	+	0.519423i	−0.966766	−	0.255664i	$-0.917706\pi$
$839$	−46.3048	+	15.0454i	−1.59862	+	0.519423i	−0.631854	+	0.775087i	$0.717706\pi$
$840$	−3.50360	−	1.86771i	−0.120886	−	0.0644421i
$841$	22.6790	−	16.4773i	0.782036	−	0.568182i
$842$	−6.48067	+	3.74161i	−0.223339	+	0.128945i
$843$	33.2995	+	5.90836i	1.14689	+	0.203495i
$844$	−1.65330	−	15.7301i	−0.0569089	−	0.541452i
$845$	−7.49824	+	10.3204i	−0.257947	+	0.355034i
$846$	−6.92352	−	10.3121i	−0.238035	−	0.354537i
$847$	25.5314	−	28.3555i	0.877269	−	0.974306i
$848$	−4.40683	−	1.96205i	−0.151331	−	0.0673770i
$849$	21.2781	−	2.96721i	0.730262	−	0.101835i
$850$	0.0511470	+	0.240628i	0.00175433	+	0.00825346i
$851$	0.570376	+	1.28109i	0.0195522	+	0.0439150i
$852$	11.2465	−	0.380682i	0.385299	−	0.0130420i
$853$	−8.50423	+	26.1733i	−0.291179	+	0.896158i	0.693299	+	0.720650i	$0.256157\pi$
$853$	−8.50423	+	26.1733i	−0.291179	+	0.896158i	−0.984478	+	0.175508i	$0.943843\pi$
$854$	−24.3787	+	10.8541i	−0.834222	+	0.371419i
$855$	5.44824	+	4.27545i	0.186326	+	0.146217i
$856$	9.67905	+	2.05735i	0.330823	+	0.0703186i
$857$	−5.20493	+	11.6905i	−0.177797	+	0.399339i	−0.980357	−	0.197233i	$-0.936804\pi$
$857$	−5.20493	+	11.6905i	−0.177797	+	0.399339i	0.802559	+	0.596572i	$0.203471\pi$
$858$	1.68697	−	4.16256i	0.0575922	−	0.142108i
$859$	8.89673	+	0.935084i	0.303552	+	0.0319046i	0.255080	−	0.966920i	$-0.417898\pi$
$859$	8.89673	+	0.935084i	0.303552	+	0.0319046i	0.0484722	+	0.998825i	$0.484565\pi$
$860$	0.928342	+	0.674480i	0.0316562	+	0.0229996i
$861$	33.9396	−	16.5085i	1.15666	−	0.562608i
$862$	12.6469	−	21.9050i	0.430754	−	0.746088i
$863$	−2.23790	−	3.87616i	−0.0761790	−	0.131946i	0.825419	−	0.564520i	$-0.190939\pi$
$863$	−2.23790	−	3.87616i	−0.0761790	−	0.131946i	−0.901598	+	0.432574i	$0.857605\pi$
$864$	−5.16941	+	0.526546i	−0.175867	+	0.0179135i
$865$	12.0233	+	13.3533i	0.408806	+	0.454025i
$866$	7.04961	+	21.6965i	0.239556	+	0.737276i
$867$	−27.5813	+	10.0054i	−0.936712	+	0.339800i
$868$	−12.0822	−	4.11236i	−0.410095	−	0.139583i
$869$		−	19.1233i		−	0.648712i
$870$	1.04726	+	1.34340i	0.0355055	+	0.0455454i
$871$	3.62121	−	3.26056i	0.122700	−	0.110480i
$872$	10.2282	+	14.0779i	0.346370	+	0.476737i
$873$	−10.3292	−	3.78458i	−0.349590	−	0.128089i
$874$	0.596858	+	0.344596i	0.0201890	+	0.0116561i
$875$	2.27972	−	0.239608i	0.0770685	−	0.00810022i
$876$	−0.995650	+	3.45827i	−0.0336399	+	0.116844i
$877$	5.70869	−	54.3146i	0.192769	−	1.83407i	−0.288476	−	0.957487i	$-0.593149\pi$
$877$	5.70869	−	54.3146i	0.192769	−	1.83407i	0.481245	−	0.876586i	$-0.340185\pi$
$878$	−5.35957	−	4.82578i	−0.180877	−	0.162862i
$879$	2.90163	−	40.8665i	0.0978695	−	1.37839i
$880$	−1.09318	+	5.14300i	−0.0368511	+	0.173371i
$881$	36.4811	−	7.75430i	1.22908	−	0.261249i	0.452786	−	0.891619i	$-0.350430\pi$
$881$	36.4811	−	7.75430i	1.22908	−	0.261249i	0.776294	+	0.630370i	$0.217097\pi$
$882$	−4.70156	−	2.30558i	−0.158310	−	0.0776329i
$883$	16.5694	+	5.38372i	0.557605	+	0.181177i	0.574243	−	0.818685i	$-0.305296\pi$
$883$	16.5694	+	5.38372i	0.557605	+	0.181177i	−0.0166384	+	0.999862i	$0.505296\pi$
$884$	0.115387	+	0.0374916i	0.00388089	+	0.00126098i
$885$	18.2390	−	17.5755i	0.613096	−	0.590792i
$886$	19.7292	−	4.19357i	0.662815	−	0.140886i
$887$	−1.18091	+	5.55576i	−0.0396512	+	0.186544i	−0.993516	−	0.113692i	$-0.963732\pi$
$887$	−1.18091	+	5.55576i	−0.0396512	+	0.186544i	0.953865	+	0.300236i	$0.0970655\pi$
$888$	−8.11536	−	0.576212i	−0.272333	−	0.0193364i
$889$	8.62251	+	7.76374i	0.289190	+	0.260388i
$890$	−1.47151	+	14.0004i	−0.0493250	+	0.469296i
$891$	−34.1804	+	32.7259i	−1.14509	+	1.09636i
$892$	10.6516	−	1.11953i	0.356642	−	0.0374846i
$893$	−8.27728	−	4.77889i	−0.276989	−	0.159919i
$894$	12.7000	+	10.6798i	0.424753	+	0.357185i
$895$	0.603454	+	0.830583i	0.0201712	+	0.0277633i
$896$	1.70349	−	1.53383i	0.0569096	−	0.0512417i
$897$	−0.201129	+	0.156793i	−0.00671550	+	0.00523516i
$898$		−	16.3675i		−	0.546190i
$899$	4.01780	+	3.72011i	0.134001	+	0.124073i
$900$	2.30226	−	1.92344i	0.0767419	−	0.0641146i
$901$	−0.366707	−	1.12861i	−0.0122168	−	0.0375994i
$902$	−33.4438	−	37.1431i	−1.11356	−	1.23673i
$903$	−3.77431	−	2.55169i	−0.125601	−	0.0849149i
$904$	−5.00912	−	8.67605i	−0.166601	−	0.288561i
$905$	0.0370060	−	0.0640963i	0.00123012	−	0.00213063i
$906$	6.60313	+	13.5753i	0.219374	+	0.451009i
$907$	43.1516	+	31.3514i	1.43282	+	1.04101i	0.989482	+	0.144655i	$0.0462071\pi$
$907$	43.1516	+	31.3514i	1.43282	+	1.04101i	0.443342	+	0.896353i	$0.353793\pi$
$908$	−19.2198	−	2.02008i	−0.637831	−	0.0670388i
$909$	19.9282	+	0.738631i	0.660976	+	0.0244988i
$910$	0.459822	−	1.03278i	0.0152430	−	0.0342362i
$911$	−12.8223	−	2.72546i	−0.424822	−	0.0902987i	−0.00946067	−	0.999955i	$-0.503011\pi$
$911$	−12.8223	−	2.72546i	−0.424822	−	0.0902987i	−0.415361	+	0.909657i	$0.636345\pi$
$912$	−3.39315	+	2.11523i	−0.112358	+	0.0700421i
$913$	5.44470	−	2.42413i	0.180193	−	0.0802272i
$914$	8.70592	−	26.7941i	0.287966	−	0.886269i
$915$	−0.682136	−	20.1524i	−0.0225507	−	0.666216i
$916$	−8.21752	−	18.4569i	−0.271515	−	0.609832i
$917$	3.31013	+	15.5729i	0.109310	+	0.514264i
$918$	−0.947189	−	0.858377i	−0.0312619	−	0.0283307i
$919$	−11.7942	−	5.25111i	−0.389054	−	0.173218i	0.202881	−	0.979203i	$-0.434969\pi$
$919$	−11.7942	−	5.25111i	−0.389054	−	0.173218i	−0.591936	+	0.805985i	$0.701636\pi$
$920$	0.199765	−	0.221862i	0.00658606	−	0.00731456i
$921$	−1.03418	−	4.16685i	−0.0340772	−	0.137302i
$922$	15.2041	−	20.9266i	0.500719	−	0.689181i
$923$	0.334927	+	3.18662i	0.0110243	+	0.104889i
$924$	3.64702	−	20.5546i	0.119978	−	0.676196i
$925$	4.06789	−	2.34860i	0.133751	−	0.0772215i
$926$	12.6146	−	9.16502i	0.414540	−	0.301181i
$927$	21.8940	+	3.12482i	0.719094	+	0.102633i
$928$	−0.935309	+	0.303900i	−0.0307030	+	0.00997602i
$929$	−56.9658			−1.86899			−0.934493	−	0.355980i	$-0.884147\pi$
$929$	−56.9658			−1.86899			−0.934493	+	0.355980i	$0.884147\pi$
$930$	6.30877	−	7.29379i	0.206873	−	0.239173i
$931$	−4.02946			−0.132060
$932$	−13.8077	+	4.48638i	−0.452285	+	0.146956i
$933$	−9.86821	+	18.5116i	−0.323071	+	0.606042i
$934$	−29.2848	+	21.2766i	−0.958226	+	0.696192i
$935$	−1.12017	+	0.646731i	−0.0366335	+	0.0211504i
$936$	−0.253802	−	1.45762i	−0.00829577	−	0.0476440i
$937$	2.03897	+	19.3996i	0.0666104	+	0.633756i	0.975994	+	0.217797i	$0.0698872\pi$
$937$	2.03897	+	19.3996i	0.0666104	+	0.633756i	−0.909384	+	0.415958i	$0.863446\pi$
$938$	13.3124	−	18.3229i	0.434665	−	0.598264i
$939$	−42.3664	+	10.5150i	−1.38258	+	0.343143i
$940$	−2.77036	+	3.07680i	−0.0903593	+	0.100354i
$941$	−2.61682	−	1.16508i	−0.0853059	−	0.0379806i	0.363640	−	0.931540i	$-0.381534\pi$
$941$	−2.61682	−	1.16508i	−0.0853059	−	0.0379806i	−0.448946	+	0.893559i	$0.648200\pi$
$942$	3.31681	+	23.7850i	0.108067	+	0.774959i
$943$	0.590039	+	2.77592i	0.0192143	+	0.0903962i
$944$	5.94799	+	13.3594i	0.193590	+	0.434811i
$945$	−8.87715	+	7.94155i	−0.288774	+	0.258339i
$946$	−1.86443	+	5.73811i	−0.0606177	+	0.186562i
$947$	40.8152	−	18.1721i	1.32632	−	0.590514i	0.383411	−	0.923578i	$-0.374749\pi$
$947$	40.8152	−	18.1721i	1.32632	−	0.590514i	0.942904	+	0.333064i	$0.108083\pi$
$948$	−3.33254	−	5.34590i	−0.108236	−	0.173627i
$949$	−1.00232	−	0.213049i	−0.0325365	−	0.00691586i
$950$	0.938954	−	2.10893i	0.0304637	−	0.0684226i
$951$	−49.8529	−	20.2040i	−1.61659	−	0.655159i
$952$	0.560818	+	0.0589444i	0.0181762	+	0.00191040i
$953$	−19.5581	−	14.2098i	−0.633548	−	0.460300i	0.224080	−	0.974571i	$-0.428062\pi$
$953$	−19.5581	−	14.2098i	−0.633548	−	0.460300i	−0.857628	+	0.514271i	$0.828062\pi$
$954$	−10.0751	+	10.3885i	−0.326193	+	0.336339i
$955$	−0.697818	+	1.20866i	−0.0225809	+	0.0391112i
$956$	4.11749	+	7.13170i	0.133169	+	0.230656i
$957$	−5.01617	+	7.41963i	−0.162150	+	0.239843i
$958$	17.1156	+	19.0088i	0.552980	+	0.614147i
$959$	5.24792	+	16.1514i	0.169464	+	0.521557i
$960$	0.590653	+	1.62823i	0.0190633	+	0.0525509i
$961$	16.2406	−	26.4053i	0.523892	−	0.851785i
$962$		−	2.31659i		−	0.0746898i
$963$	15.7850	−	25.1413i	0.508664	−	0.810167i
$964$	−22.6251	+	20.3717i	−0.728705	+	0.656129i
$965$	9.48825	+	13.0595i	0.305437	+	0.420399i
$966$	−0.762881	+	0.907192i	−0.0245453	+	0.0291884i
$967$	33.7267	+	19.4721i	1.08458	+	0.626182i	0.932128	−	0.362129i	$-0.117950\pi$
$967$	33.7267	+	19.4721i	1.08458	+	0.626182i	0.152451	+	0.988311i	$0.451283\pi$
$968$	−16.5543	+	1.73993i	−0.532076	+	0.0559235i
$969$	−0.945238	−	0.272138i	−0.0303654	−	0.00874234i
$970$	−0.383295	+	3.64681i	−0.0123069	+	0.117092i
$971$	36.7171	+	33.0602i	1.17831	+	1.06095i	0.996990	+	0.0775274i	$0.0247025\pi$
$971$	36.7171	+	33.0602i	1.17831	+	1.06095i	0.181317	+	0.983425i	$0.441964\pi$
$972$	−3.85210	+	15.1050i	−0.123556	+	0.484493i
$973$	8.42323	−	39.6282i	0.270036	−	1.27042i
$974$	−29.2779	+	6.22320i	−0.938124	+	0.199404i
$975$	0.592734	+	0.615111i	0.0189827	+	0.0196993i
$976$	11.0718	+	3.59746i	0.354401	+	0.115152i
$977$	17.8663	+	5.80511i	0.571593	+	0.185722i	0.580531	−	0.814238i	$-0.302845\pi$
$977$	17.8663	+	5.80511i	0.571593	+	0.185722i	−0.00893793	+	0.999960i	$0.502845\pi$
$978$	−1.09936	−	1.14086i	−0.0351535	−	0.0364806i
$979$	−72.4009	+	15.3893i	−2.31394	+	0.491844i
$980$	−0.362906	+	1.70734i	−0.0115926	+	0.0545390i
$981$	50.2121	−	14.2818i	1.60315	−	0.455983i
$982$	−18.1999	−	16.3873i	−0.580782	−	0.522939i
$983$	−4.54950	+	43.2856i	−0.145106	+	1.38059i	0.643382	+	0.765545i	$0.277531\pi$
$983$	−4.54950	+	43.2856i	−0.145106	+	1.38059i	−0.788488	+	0.615050i	$0.789136\pi$
$984$	−15.8220	−	4.55522i	−0.504387	−	0.145215i
$985$	21.9896	−	2.31120i	0.700646	−	0.0736409i
$986$	−0.209518	−	0.120965i	−0.00667240	−	0.00385231i
$987$	10.5797	−	12.5810i	0.336756	−	0.400458i
$988$	−0.669206	−	0.921083i	−0.0212903	−	0.0293036i
$989$	0.254585	−	0.229229i	0.00809533	−	0.00728907i
$990$	13.3589	+	8.38741i	0.424575	+	0.266569i
$991$		−	31.6454i		−	1.00525i	−0.864504	−	0.502625i	$-0.832368\pi$
$991$		−	31.6454i		−	1.00525i	0.864504	−	0.502625i	$-0.167632\pi$
$992$	2.71656	+	4.86007i	0.0862507	+	0.154308i
$993$	−6.73812	−	18.5747i	−0.213828	−	0.589449i
$994$	4.60208	+	14.1638i	0.145969	+	0.449247i
$995$	−5.68432	−	6.31308i	−0.180205	−	0.200138i
$996$	1.09962	−	1.62649i	0.0348427	−	0.0515374i
$997$	27.4671	+	47.5744i	0.869892	+	1.50670i	0.862106	+	0.506727i	$0.169145\pi$
$997$	27.4671	+	47.5744i	0.869892	+	1.50670i	0.00778552	+	0.999970i	$0.497522\pi$
$998$	−8.90146	+	15.4178i	−0.281771	+	0.488041i
$999$	−9.99893	+	22.2652i	−0.316352	+	0.704441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.b.11.11	✓	176
3.2	odd	2	inner	930.2.br.b.11.16	yes	176
31.17	odd	30	inner	930.2.br.b.761.16	yes	176
93.17	even	30	inner	930.2.br.b.761.11	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.11	✓	176	1.1	even	1	trivial
930.2.br.b.11.16	yes	176	3.2	odd	2	inner
930.2.br.b.761.11	yes	176	93.17	even	30	inner
930.2.br.b.761.16	yes	176	31.17	odd	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(1.52844 + 0.814785i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.70541 - 0.302593i) q^{6} +(-0.239608 - 2.27972i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(1.67225 + 2.49070i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(1.52844 + 0.814785i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.70541 - 0.302593i) q^{6} +(-0.239608 - 2.27972i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(1.67225 + 2.49070i) q^{9} +(0.669131 - 0.743145i) q^{10} +(4.80333 + 2.13858i) q^{11} +(1.71545 - 0.239219i) q^{12} +(0.102539 + 0.482408i) q^{13} +(0.932352 + 2.09410i) q^{14} +(-1.73106 + 0.0585945i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.224735 - 0.100059i) q^{17} +(-2.36007 - 1.85204i) q^{18} +(-2.25806 - 0.479966i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(1.49125 - 3.67963i) q^{21} +(-5.22910 - 0.549600i) q^{22} +(0.241527 + 0.175480i) q^{23} +(-1.55757 + 0.757614i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.246593 - 0.427111i) q^{26} +(0.526546 + 5.16941i) q^{27} +(-1.53383 - 1.70349i) q^{28} +(0.303900 + 0.935309i) q^{29} +(1.62823 - 0.590653i) q^{30} +(4.86007 - 2.71656i) q^{31} +1.00000i q^{32} +(5.59911 + 7.18237i) q^{33} +(-0.182816 + 0.164608i) q^{34} +(1.34736 + 1.85449i) q^{35} +(2.81687 + 1.03209i) q^{36} +(4.06789 + 2.34860i) q^{37} +(2.29586 - 0.241305i) q^{38} +(-0.236334 + 0.820878i) q^{39} +(0.104528 - 0.994522i) q^{40} +(7.06425 + 6.36068i) q^{41} +(-0.281196 + 3.96036i) q^{42} +(0.238577 - 1.12242i) q^{43} +(5.14300 - 1.09318i) q^{44} +(-2.69356 - 1.32088i) q^{45} +(-0.283933 - 0.0922553i) q^{46} +(3.93760 + 1.27940i) q^{47} +(1.24722 - 1.20185i) q^{48} +(1.70734 - 0.362906i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(0.425021 + 0.0301776i) q^{51} +(0.366508 + 0.330005i) q^{52} +(0.504232 - 4.79745i) q^{53} +(-2.09821 - 4.75368i) q^{54} +(-5.22910 + 0.549600i) q^{55} +(1.98517 + 1.14614i) q^{56} +(-3.06024 - 2.57343i) q^{57} +(-0.578053 - 0.795622i) q^{58} +(-10.8675 + 9.78515i) q^{59} +(-1.36602 + 1.06490i) q^{60} +11.6416i q^{61} +(-3.78274 + 4.08544i) q^{62} +(5.27740 - 4.40905i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.330005 - 0.366508i) q^{65} +(-7.54455 - 5.10062i) q^{66} +(-4.94015 - 8.55660i) q^{67} +(0.123002 - 0.213045i) q^{68} +(0.226181 + 0.465003i) q^{69} +(-1.85449 - 1.34736i) q^{70} +(6.46130 + 0.679110i) q^{71} +(-2.99794 - 0.111118i) q^{72} +(-0.845091 + 1.89810i) q^{73} +(-4.59455 - 0.976602i) q^{74} +(1.46984 - 0.916274i) q^{75} +(-2.10893 + 0.938954i) q^{76} +(3.72444 - 11.4627i) q^{77} +(-0.0288980 - 0.853733i) q^{78} +(-1.47932 - 3.32261i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-3.40716 + 8.33014i) q^{81} +(-8.68406 - 3.86639i) q^{82} +(0.758476 - 0.842373i) q^{83} +(-0.956386 - 3.85342i) q^{84} +(-0.144597 + 0.199021i) q^{85} +(0.119946 + 1.14121i) q^{86} +(-0.297583 + 1.67718i) q^{87} +(-4.55348 + 2.62895i) q^{88} +(-11.3890 + 8.27458i) q^{89} +(2.96990 + 0.423879i) q^{90} +(1.07518 - 0.349348i) q^{91} +0.298544 q^{92} +(9.64174 - 0.192172i) q^{93} -4.14024 q^{94} +(2.19552 - 0.713368i) q^{95} +(-0.814785 + 1.52844i) q^{96} +(-2.96658 + 2.15535i) q^{97} +(-1.51163 + 0.872742i) q^{98} +(2.70581 + 15.5399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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