LMFDB - Embedded newform 930.2.br.b.761.11

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			761.11
Character	$\chi$	$=$	930.761
Dual form			930.2.br.b.11.11

$q$-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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{30}\right)$

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	0.851079	+	0.525037i	$0.175949\pi$
$7$	−0.239608	+	2.27972i	−0.0905632	+	0.861652i	−0.941643	+	0.336614i	$0.890718\pi$
$8$	−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	0.476156	−	0.879361i	$-0.342030\pi$
$11$	4.80333	−	2.13858i	1.44826	−	0.644806i	0.972103	+	0.234555i	$0.0753631\pi$
$12$	1.71545	+	0.239219i	0.495208	+	0.0690564i
$13$	0.102539	−	0.482408i	0.0284392	−	0.133796i	−0.961638	−	0.274323i	$-0.911546\pi$
$13$	0.102539	−	0.482408i	0.0284392	−	0.133796i	0.990077	+	0.140527i	$0.0448797\pi$
$14$	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	0.433809	−	0.901005i	$-0.357169\pi$
$17$	0.224735	+	0.100059i	0.0545063	+	0.0242678i	−0.379302	+	0.925273i	$0.623836\pi$
$18$	−2.36007	+	1.85204i	−0.556274	+	0.436530i
$19$	−2.25806	+	0.479966i	−0.518035	+	0.110112i	−0.459507	−	0.888174i	$-0.651974\pi$
$19$	−2.25806	+	0.479966i	−0.518035	+	0.110112i	−0.0585276	+	0.998286i	$0.518641\pi$
$20$	−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	−0.562319	−	0.826920i	$-0.690091\pi$
$23$	0.241527	−	0.175480i	0.0503620	−	0.0365901i	0.612681	+	0.790330i	$0.290091\pi$
$24$	−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	−0.918867	−	0.394567i	$-0.870894\pi$
$29$	0.303900	−	0.935309i	0.0564329	−	0.173683i	0.975300	+	0.220885i	$0.0708945\pi$
$30$	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	−0.126848	−	0.991922i	$-0.540486\pi$
$37$	4.06789	−	2.34860i	0.668757	−	0.386107i	0.795606	+	0.605815i	$0.207153\pi$
$38$	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	0.103252	−	0.994655i	$-0.467075\pi$
$41$	7.06425	−	6.36068i	1.10325	−	0.993372i	0.999999	+	0.00128345i	$0.000408534\pi$
$42$	−0.281196	−	3.96036i	−0.0433896	−	0.611097i
$43$	0.238577	+	1.12242i	0.0363827	+	0.171167i	0.992588	−	0.121531i	$-0.0387803\pi$
$43$	0.238577	+	1.12242i	0.0363827	+	0.171167i	−0.956205	+	0.292698i	$0.905447\pi$
$44$	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	−0.00741320	−	0.999973i	$-0.502360\pi$
$47$	3.93760	−	1.27940i	0.574358	−	0.186620i	0.581772	+	0.813352i	$0.302360\pi$
$48$	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	0.972986	+	0.230865i	$0.0741556\pi$
$53$	0.504232	+	4.79745i	0.0692616	+	0.658980i	−0.903724	+	0.428115i	$0.859178\pi$
$54$	−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	−0.912400	−	0.409300i	$-0.865773\pi$
$59$	−10.8675	−	9.78515i	−1.41483	−	1.27392i	−0.502430	−	0.864618i	$-0.667560\pi$
$60$	−1.36602	−	1.06490i	−0.176352	−	0.137477i
$61$		−	11.6416i		−	1.49056i	−0.666753	−	0.745279i	$-0.732316\pi$
$61$		−	11.6416i		−	1.49056i	0.666753	−	0.745279i	$-0.267684\pi$
$62$	−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	0.388745	+	0.921345i	$0.372909\pi$
$67$	−4.94015	+	8.55660i	−0.603536	+	1.04535i	−0.992281	+	0.124010i	$0.960425\pi$
$68$	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	0.286959	−	0.957943i	$-0.407356\pi$
$71$	6.46130	−	0.679110i	0.766816	−	0.0805956i	0.479856	+	0.877347i	$0.340689\pi$
$72$	−2.99794	+	0.111118i	−0.353311	+	0.0130953i
$73$	−0.845091	−	1.89810i	−0.0989104	−	0.222156i	0.857312	−	0.514797i	$-0.172133\pi$
$73$	−0.845091	−	1.89810i	−0.0989104	−	0.222156i	−0.956222	+	0.292641i	$0.905466\pi$
$74$	−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	−0.977438	−	0.211221i	$-0.932256\pi$
$79$	−1.47932	+	3.32261i	−0.166437	+	0.373823i	0.811002	+	0.585044i	$0.198923\pi$
$80$	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	0.783332	−	0.621603i	$-0.213518\pi$
$83$	0.758476	+	0.842373i	0.0832536	+	0.0924625i	−0.700079	+	0.714066i	$0.746852\pi$
$84$	−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	−0.212254	−	0.977215i	$-0.568080\pi$
$89$	−11.3890	−	8.27458i	−1.20723	−	0.877104i	−0.994976	+	0.100111i	$0.968080\pi$
$90$	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	0.426905	−	0.904296i	$-0.359604\pi$
$97$	−2.96658	−	2.15535i	−0.301211	−	0.218842i	−0.728116	+	0.685454i	$0.759604\pi$
$98$	−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	0.957884	−	0.287157i	$-0.0927101\pi$
$101$	3.90718	+	5.37777i	0.388779	+	0.535108i	−0.569105	+	0.822265i	$0.692710\pi$
$102$	−0.413544	−	0.102638i	−0.0409470	−	0.0101627i
$103$	4.93280	+	5.47843i	0.486044	+	0.539806i	0.935421	−	0.353536i	$-0.115021\pi$
$103$	4.93280	+	5.47843i	0.486044	+	0.539806i	−0.449377	+	0.893342i	$0.648354\pi$
$104$	−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	0.607724	+	0.794148i	$0.292083\pi$
$107$	−4.02477	+	9.03979i	−0.389090	+	0.873910i	−0.996814	+	0.0797616i	$0.974584\pi$
$108$	3.46448	−	3.87264i	0.333370	−	0.372645i
$109$	5.37727	+	16.5495i	0.515049	+	1.58516i	0.783193	+	0.621779i	$0.213590\pi$
$109$	5.37727	+	16.5495i	0.515049	+	1.58516i	−0.268144	+	0.963379i	$0.586410\pi$
$110$	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	−0.997424	−	0.0717308i	$-0.977148\pi$
$113$	−4.07478	−	9.15212i	−0.383323	−	0.860959i	0.614101	−	0.789228i	$-0.289519\pi$
$114$	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	0.485147	−	0.874433i	$-0.338766\pi$
$127$	−3.76156	−	3.38692i	−0.333784	−	0.300540i	−0.818931	+	0.573892i	$0.805433\pi$
$128$	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	−0.202150	−	0.979355i	$-0.564793\pi$
$131$	−6.90739	−	0.725996i	−0.603502	−	0.0634306i	−0.401352	+	0.915924i	$0.631459\pi$
$132$	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	−0.112341	−	0.993670i	$-0.535835\pi$
$137$	−7.24675	−	1.54034i	−0.619131	−	0.131600i	−0.506790	+	0.862069i	$0.669168\pi$
$138$	−0.358805	+	0.372351i	−0.0305435	+	0.0316966i
$139$	16.8089	−	5.46155i	1.42571	−	0.463242i	0.508301	−	0.861180i	$-0.330274\pi$
$139$	16.8089	−	5.46155i	1.42571	−	0.463242i	0.917413	+	0.397937i	$0.130274\pi$
$140$	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	−0.799743	−	0.600343i	$-0.795031\pi$
$149$	−8.29682	+	4.79017i	−0.679702	+	0.392426i	0.120041	+	0.992769i	$0.461697\pi$
$150$	−1.11476	−	1.32564i	−0.0910198	−	0.108238i
$151$	−5.12296	+	7.05114i	−0.416900	+	0.573814i	−0.964884	−	0.262675i	$-0.915395\pi$
$151$	−5.12296	+	7.05114i	−0.416900	+	0.573814i	0.547984	+	0.836489i	$0.315395\pi$
$152$	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	0.621252	+	0.783611i	$0.286624\pi$
$157$	−4.28458	+	13.1866i	−0.341946	+	1.05240i	−0.963198	+	0.268792i	$0.913376\pi$
$158$	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	−0.558426	−	0.829554i	$-0.688595\pi$
$163$	0.740024	−	0.537659i	0.0579631	−	0.0421127i	0.616390	+	0.787441i	$0.288595\pi$
$164$	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	−0.294966	−	0.955508i	$-0.595308\pi$
$167$	−2.27172	+	0.482869i	−0.175791	+	0.0373655i	0.119175	+	0.992873i	$0.461975\pi$
$168$	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	0.572382	+	0.819987i	$0.306020\pi$
$173$	−3.73588	+	17.5759i	−0.284034	+	1.33627i	−0.856416	+	0.516287i	$0.827314\pi$
$174$	−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	−0.997800	−	0.0662937i	$-0.978883\pi$
$179$	−0.107315	+	1.02103i	−0.00802109	+	0.0763156i	0.989779	+	0.142609i	$0.0455492\pi$
$180$	−2.95553	−	0.514618i	−0.220292	−	0.0383573i
$181$	−0.0640963	−	0.0370060i	−0.00476424	−	0.00275063i	0.497616	−	0.867397i	$-0.334209\pi$
$181$	−0.0640963	−	0.0370060i	−0.00476424	−	0.00275063i	−0.502380	+	0.864647i	$0.667542\pi$
$182$	−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	0.543090	−	0.839675i	$-0.317254\pi$
$191$	1.20866	+	0.697818i	0.0874553	+	0.0504924i	−0.455635	+	0.890167i	$0.650588\pi$
$192$	0.302593	+	1.70541i	0.0218378	+	0.123078i
$193$	−1.68734	+	16.0539i	−0.121457	+	1.15559i	0.748733	+	0.662872i	$0.230663\pi$
$193$	−1.68734	+	16.0539i	−0.121457	+	1.15559i	−0.870190	+	0.492716i	$0.836004\pi$
$194$	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	−0.970158	−	0.242473i	$-0.922041\pi$
$197$	−20.1991	+	8.99323i	−1.43913	+	0.640741i	−0.468970	+	0.883214i	$0.655375\pi$
$198$	−7.37547	+	13.9432i	−0.524152	+	0.990898i
$199$	1.76623	−	8.30945i	0.125205	−	0.589041i	−0.870152	−	0.492784i	$-0.835979\pi$
$199$	1.76623	−	8.30945i	0.125205	−	0.589041i	0.995356	−	0.0962575i	$-0.0306872\pi$
$200$	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	0.998642	+	0.0520920i	$0.0165889\pi$
$211$	7.90836	+	13.6977i	0.544434	+	0.942988i	−0.454208	+	0.890896i	$0.650078\pi$
$212$	−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	−0.156182	−	0.987728i	$-0.549919\pi$
$223$	9.27537	−	5.35514i	0.621125	−	0.358607i	0.777307	+	0.629122i	$0.216585\pi$
$224$	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	−0.990004	−	0.141037i	$-0.954956\pi$
$227$	−14.3618	+	12.9314i	−0.953224	+	0.858286i	0.0367807	+	0.999323i	$0.488290\pi$
$228$	−3.98841	+	0.283188i	−0.264139	+	0.0187546i
$229$	4.20055	+	19.7621i	0.277580	+	1.30591i	0.867090	+	0.498152i	$0.165988\pi$
$229$	4.20055	+	19.7621i	0.277580	+	1.30591i	−0.589509	+	0.807762i	$0.700679\pi$
$230$	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	−0.724122	−	0.689672i	$-0.757755\pi$
$233$	−13.8077	+	4.48638i	−0.904570	+	0.293912i	−0.180448	+	0.983585i	$0.557755\pi$
$234$	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	−0.986439	−	0.164126i	$-0.947520\pi$
$239$	−0.860790	−	8.18987i	−0.0556799	−	0.529758i	0.930759	−	0.365632i	$-0.119147\pi$
$240$	−0.479200	−	1.66444i	−0.0309322	−	0.107439i
$241$	−30.2783	−	3.18237i	−1.95039	−	0.204995i	−0.954691	−	0.297598i	$-0.903814\pi$
$241$	−30.2783	−	3.18237i	−1.95039	−	0.204995i	−0.995703	+	0.0926038i	$0.970481\pi$
$242$	−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	−0.620187	−	0.784454i	$-0.712943\pi$
$251$	3.56146	−	3.95540i	0.224797	−	0.249663i	0.844984	+	0.534791i	$0.179610\pi$
$252$	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	0.829070	−	0.559145i	$-0.188870\pi$
$257$	28.1552	−	2.95923i	1.75628	−	0.184592i	0.927206	+	0.374553i	$0.122204\pi$
$258$	−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	0.999615	+	0.0277488i	$0.00883384\pi$
$263$	3.36054	+	10.3427i	0.207220	+	0.637757i	−0.792395	+	0.610008i	$0.791166\pi$
$264$	−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	0.989004	−	0.147887i	$-0.0472471\pi$
$269$	12.1131	+	13.4530i	0.738549	+	0.820241i	−0.250456	+	0.968128i	$0.580580\pi$
$270$	4.19394	−	3.06771i	0.255235	−	0.186695i
$271$	7.34577	+	10.1106i	0.446223	+	0.614174i	0.971581	−	0.236708i	$-0.0760684\pi$
$271$	7.34577	+	10.1106i	0.446223	+	0.614174i	−0.525357	+	0.850882i	$0.676068\pi$
$272$	−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	−0.353661	−	0.935374i	$-0.615063\pi$
$277$	−19.7985	−	6.43293i	−1.18958	−	0.386517i	−0.835917	+	0.548856i	$0.815063\pi$
$278$	−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	0.805099	−	0.593141i	$-0.202112\pi$
$281$	18.5701	+	6.03378i	1.10780	+	0.359945i	0.302699	+	0.953086i	$0.402112\pi$
$282$	−6.32811	+	3.37341i	−0.376833	+	0.200884i
$283$	10.0349	+	7.29076i	0.596511	+	0.433391i	0.844639	−	0.535337i	$-0.179815\pi$
$283$	10.0349	+	7.29076i	0.596511	+	0.433391i	−0.248128	+	0.968727i	$0.579815\pi$
$284$	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	0.379394	+	0.925235i	$0.376132\pi$
$293$	−9.62081	+	21.6087i	−0.562054	+	1.26239i	−0.941448	+	0.337158i	$0.890534\pi$
$294$	−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	−0.788614	−	0.614889i	$-0.789201\pi$
$307$	−1.65859	+	1.84205i	−0.0946605	+	0.105131i	0.693953	+	0.720020i	$0.255867\pi$
$308$	−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	$-0.888425\pi$
$311$		−	12.1114i		−	0.686776i	0.939194	−	0.343388i	$-0.111575\pi$
$312$	−0.525191	+	0.673699i	−0.0297331	+	0.0381407i
$313$	−18.7290	−	16.8637i	−1.05863	−	0.953191i	−0.0596405	−	0.998220i	$-0.518995\pi$
$313$	−18.7290	−	16.8637i	−1.05863	−	0.953191i	−0.998986	+	0.0450286i	$0.985662\pi$
$314$	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	−0.816235	−	0.577719i	$-0.803943\pi$
$317$	−30.8863	−	3.24628i	−1.73475	−	0.182329i	−0.918513	+	0.395390i	$0.870609\pi$
$318$	−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	−0.868384	−	0.495893i	$-0.834841\pi$
$331$	−8.47772	+	7.63337i	−0.465978	+	0.419568i	0.402406	+	0.915461i	$0.368174\pi$
$332$	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	−0.172965	−	0.984928i	$-0.555335\pi$
$337$	15.0019	−	20.6484i	0.817206	−	1.12479i	0.990171	−	0.139860i	$-0.0446651\pi$
$338$	−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	0.983009	−	0.183558i	$-0.0587614\pi$
$347$	6.19451	+	10.7292i	0.332539	+	0.575974i	−0.650470	+	0.759532i	$0.725428\pi$
$348$	0.745070	−	1.53178i	0.0399399	−	0.0821120i
$349$	−7.18740	+	5.22195i	−0.384733	+	0.279525i	−0.763294	−	0.646052i	$-0.776419\pi$
$349$	−7.18740	+	5.22195i	−0.384733	+	0.279525i	0.378561	+	0.925576i	$0.376419\pi$
$350$	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	−0.221718	−	0.975111i	$-0.571166\pi$
$353$	−0.519568	+	0.110438i	−0.0276538	+	0.00587800i	0.194064	+	0.980989i	$0.437833\pi$
$354$	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	0.701965	+	0.712212i	$0.252306\pi$
$359$	−4.33883	+	20.4126i	−0.228995	+	1.07733i	−0.930959	+	0.365123i	$0.881027\pi$
$360$	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	0.200039	−	0.979788i	$-0.435893\pi$
$367$	−10.5070	−	6.06625i	−0.548463	−	0.316656i	−0.748502	+	0.663132i	$0.769227\pi$
$368$	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	−0.663012	−	0.748609i	$-0.730722\pi$
$379$	2.74802	−	26.1456i	0.141156	−	1.34301i	0.804168	−	0.594402i	$-0.202611\pi$
$380$	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	0.774180	−	0.632965i	$-0.218162\pi$
$383$	34.4946	−	15.3580i	1.76259	−	0.784757i	0.988413	−	0.151791i	$-0.0485042\pi$
$384$	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	−0.388424	−	0.921481i	$-0.626980\pi$
$389$	−26.2933	−	11.7065i	−1.33312	−	0.593545i	−0.944700	+	0.327936i	$0.893647\pi$
$390$	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	−0.967638	−	0.252342i	$-0.918799\pi$
$397$	−13.9943	−	24.2388i	−0.702353	−	1.21651i	0.265285	−	0.964170i	$-0.414534\pi$
$398$	−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	0.740723	+	0.671811i	$0.234483\pi$
$401$	−5.07464	+	15.6181i	−0.253415	+	0.779932i	−0.994138	+	0.108121i	$0.965517\pi$
$402$	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	−0.376922	−	0.926245i	$-0.623018\pi$
$409$	4.78834	−	2.76455i	0.236768	−	0.136698i	0.613690	+	0.789547i	$0.289684\pi$
$410$	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	−0.450839	−	0.892605i	$-0.648875\pi$
$419$	−5.95487	+	1.93486i	−0.290915	+	0.0945239i	0.159924	+	0.987129i	$0.448875\pi$
$420$	2.75497	−	2.85897i	0.134429	−	0.139503i
$421$	7.31970	+	1.55585i	0.356741	+	0.0758275i	0.382796	−	0.923833i	$-0.374961\pi$
$421$	7.31970	+	1.55585i	0.356741	+	0.0758275i	−0.0260553	+	0.999661i	$0.508295\pi$
$422$	−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	0.0779356	−	0.996958i	$-0.475167\pi$
$431$	−18.7969	−	16.9248i	−0.905415	−	0.815239i	−0.983350	+	0.181719i	$0.941834\pi$
$432$	5.07911	−	1.09666i	0.244369	−	0.0527630i
$433$			22.8130i			1.09632i	0.836372	+	0.548162i	$0.184672\pi$
$433$			22.8130i			1.09632i	−0.836372	+	0.548162i	$0.815328\pi$
$434$	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	−0.767050	−	0.641587i	$-0.778276\pi$
$439$	3.60601	−	6.24579i	0.172105	−	0.298095i	0.939156	+	0.343492i	$0.111610\pi$
$440$	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	−0.568275	−	0.822839i	$-0.692389\pi$
$443$	−20.0595	+	2.10834i	−0.953054	+	0.100170i	−0.384779	+	0.923009i	$0.625722\pi$
$444$	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	−0.996610	−	0.0822721i	$-0.973782\pi$
$449$	−5.05783	−	15.5664i	−0.238694	−	0.734624i	0.757916	−	0.652352i	$-0.226218\pi$
$450$	−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	−0.995854	−	0.0909613i	$-0.971006\pi$
$457$	−16.5597	−	22.7924i	−0.774628	−	1.06618i	0.221227	−	0.975222i	$-0.428994\pi$
$458$	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	−0.0181429	−	0.999835i	$-0.505775\pi$
$461$	−20.9266	−	15.2041i	−0.974649	−	0.708124i	−0.956506	+	0.291711i	$0.905775\pi$
$462$	−9.82024	−	18.4216i	−0.456879	−	0.857049i
$463$	−14.8293	−	4.81833i	−0.689176	−	0.223927i	−0.0565680	−	0.998399i	$-0.518016\pi$
$463$	−14.8293	−	4.81833i	−0.689176	−	0.223927i	−0.632609	+	0.774472i	$0.718016\pi$
$464$	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	0.965378	−	0.260855i	$-0.0840044\pi$
$467$	34.4263	+	11.1858i	1.59306	+	0.517616i	0.627681	+	0.778471i	$0.284004\pi$
$468$	−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	0.503652	+	0.863907i	$0.331990\pi$
$479$	−10.4039	+	23.3675i	−0.475365	+	1.06769i	−0.979017	+	0.203780i	$0.934677\pi$
$480$	−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	0.597640	−	0.801765i	$-0.296105\pi$
$487$	29.7680	−	3.12874i	1.34892	−	0.141777i	0.751276	+	0.659988i	$0.229439\pi$
$488$	−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	−0.445467	−	0.895298i	$-0.646962\pi$
$491$	12.2452	−	21.2093i	0.552618	−	0.957162i	0.998085	−	0.0618637i	$-0.0197044\pi$
$492$	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	0.909841	−	0.414956i	$-0.136203\pi$
$499$	13.2301	+	11.9125i	0.592263	+	0.533276i	−0.317579	+	0.948232i	$0.602870\pi$
$500$	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	0.890388	−	0.455203i	$-0.150433\pi$
$503$	37.3797	+	3.92876i	1.66668	+	0.175175i	0.776289	+	0.630378i	$0.217100\pi$
$504$	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	0.900964	−	0.433893i	$-0.142860\pi$
$509$	34.9145	+	7.42130i	1.54756	+	0.328943i	0.646592	+	0.762836i	$0.276194\pi$
$510$	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	−0.496073	−	0.868281i	$-0.665225\pi$
$521$	0.179023	−	0.103359i	0.00784315	−	0.00452825i	0.503916	+	0.863752i	$0.331892\pi$
$522$	1.01500	+	2.77023i	0.0444256	+	0.121250i
$523$	−1.27828	+	1.75941i	−0.0558954	+	0.0769335i	−0.836050	−	0.548654i	$-0.815141\pi$
$523$	−1.27828	+	1.75941i	−0.0558954	+	0.0769335i	0.780154	+	0.625587i	$0.215141\pi$
$524$	−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	0.479748	−	0.877406i	$-0.340728\pi$
$541$	3.45918	+	1.54013i	0.148722	+	0.0662152i	−0.331026	+	0.943622i	$0.607395\pi$
$542$	−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	−0.797826	−	0.602887i	$-0.794017\pi$
$547$	−20.6667	+	9.20141i	−0.883644	+	0.393424i	−0.0858177	+	0.996311i	$0.527350\pi$
$548$	−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	0.975027	+	0.222085i	$0.0712861\pi$
$563$	39.2662	+	22.6703i	1.65487	+	0.955441i	0.679845	+	0.733356i	$0.262047\pi$
$564$	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	−0.677140	−	0.735854i	$-0.736781\pi$
$569$	−13.9160	+	6.19581i	−0.583390	+	0.259742i	0.0937505	+	0.995596i	$0.470114\pi$
$570$	−3.96013	−	0.552238i	−0.165872	−	0.0231307i
$571$	6.66608	−	31.3614i	0.278967	−	1.31243i	−0.585880	−	0.810398i	$-0.699251\pi$
$571$	6.66608	−	31.3614i	0.278967	−	1.31243i	0.864846	−	0.502037i	$-0.167416\pi$
$572$	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	−0.155907	−	0.987772i	$-0.549830\pi$
$577$	2.48441	−	0.528077i	0.103427	−	0.0219841i	0.259335	+	0.965788i	$0.416497\pi$
$578$	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	−0.945682	−	0.325094i	$-0.894604\pi$
$587$	0.253816	−	0.781166i	0.0104761	−	0.0322422i	0.956158	+	0.292852i	$0.0946042\pi$
$588$	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	−0.223799	−	0.974635i	$-0.571846\pi$
$593$	18.8065	−	25.8850i	0.772292	−	1.06297i	0.996091	−	0.0883335i	$-0.0281541\pi$
$594$	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	−0.255809	−	0.966727i	$-0.582342\pi$
$599$	16.6153	−	14.9605i	0.678883	−	0.611269i	0.934692	+	0.355458i	$0.115675\pi$
$600$	−0.122671	−	1.72770i	−0.00500804	−	0.0705331i
$601$	−2.67919	−	12.6046i	−0.109287	−	0.514153i	−0.998404	−	0.0564739i	$-0.982014\pi$
$601$	−2.67919	−	12.6046i	−0.109287	−	0.514153i	0.889118	−	0.457679i	$-0.151319\pi$
$602$	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	0.397100	−	0.917775i	$-0.370017\pi$
$607$	9.52421	+	2.02443i	0.386576	+	0.0821692i	−0.0105241	+	0.999945i	$0.503350\pi$
$608$	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	−0.391351	−	0.920242i	$-0.627992\pi$
$613$	−23.9041	−	2.51242i	−0.965478	−	0.101476i	−0.574128	+	0.818766i	$0.694659\pi$
$614$	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	0.0478220	−	0.998856i	$-0.484772\pi$
$617$	−23.3631	−	21.0362i	−0.940563	−	0.846887i	−0.988385	+	0.151969i	$0.951439\pi$
$618$	−10.0702	−	7.85036i	−0.405083	−	0.315788i
$619$			19.2249i			0.772714i	0.922349	+	0.386357i	$0.126267\pi$
$619$			19.2249i			0.772714i	−0.922349	+	0.386357i	$0.873733\pi$
$620$	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	0.960460	−	0.278417i	$-0.0898099\pi$
$631$	2.78533	+	6.25596i	0.110882	+	0.249046i	−0.849578	+	0.527463i	$0.823143\pi$
$632$	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	0.911354	−	0.411624i	$-0.135038\pi$
$641$	10.2974	+	11.4364i	0.406723	+	0.451711i	−0.504631	+	0.863335i	$0.668372\pi$
$642$	4.12853	−	16.6345i	0.162940	−	0.656510i
$643$	−17.7966	−	24.4949i	−0.701829	−	0.965984i	−0.999934	−	0.0114514i	$-0.996355\pi$
$643$	−17.7966	−	24.4949i	−0.701829	−	0.965984i	0.298106	−	0.954533i	$-0.403645\pi$
$644$	−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	0.395511	−	0.918461i	$-0.370568\pi$
$647$	−9.04964	−	6.57495i	−0.355778	−	0.258488i	−0.751289	+	0.659973i	$0.770568\pi$
$648$	−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	−0.349746	−	0.936844i	$-0.613732\pi$
$653$	−30.2394	−	9.82539i	−1.18336	−	0.384497i	−0.833614	+	0.552347i	$0.813732\pi$
$654$	−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	0.393599	−	0.919282i	$-0.371230\pi$
$659$	−15.4621	−	21.2818i	−0.602320	−	0.829022i	−0.995918	+	0.0902606i	$0.971230\pi$
$660$	−8.83879	−	2.19371i	−0.344049	−	0.0853900i
$661$	−15.7873	−	17.5336i	−0.614055	−	0.681977i	0.353269	−	0.935522i	$-0.385070\pi$
$661$	−15.7873	−	17.5336i	−0.614055	−	0.681977i	−0.967324	+	0.253545i	$0.918403\pi$
$662$	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	0.506872	−	0.862021i	$-0.330802\pi$
$673$	30.6609	−	3.22259i	1.18189	−	0.124222i	0.675020	+	0.737799i	$0.264135\pi$
$674$	−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	0.486486	+	0.873689i	$0.338279\pi$
$677$	−13.3581	+	23.1369i	−0.513394	+	0.889224i	−0.999879	+	0.0155355i	$0.995055\pi$
$678$	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	$0.219823\pi$
$683$			33.2948i			1.27399i	−0.770868	+	0.636995i	$0.780177\pi$
$684$	−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	−0.998003	−	0.0631587i	$-0.979883\pi$
$691$	−0.918469	−	8.73865i	−0.0349402	−	0.332434i	0.963063	−	0.269275i	$-0.0867841\pi$
$692$	−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	0.975240	−	0.221151i	$-0.0709813\pi$
$701$	−0.149227	−	0.702060i	−0.00563624	−	0.0265164i	−0.980876	+	0.194634i	$0.937648\pi$
$702$	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	−0.996492	−	0.0836823i	$-0.973332\pi$
$709$	−16.2152	+	22.3182i	−0.608973	+	0.838179i	0.387520	+	0.921861i	$0.373332\pi$
$710$	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	0.949814	−	0.312816i	$-0.101272\pi$
$719$	5.47011	+	9.47450i	0.204001	+	0.353339i	−0.745813	+	0.666155i	$0.767939\pi$
$720$	−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	0.742918	−	0.669383i	$-0.233441\pi$
$727$	20.0221	+	8.91442i	0.742579	+	0.330617i	−0.000339107		1.00000i	$0.500108\pi$
$728$	−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	−0.0836153	−	0.996498i	$-0.526647\pi$
$733$	16.2709	−	7.24425i	0.600978	−	0.267572i	0.684593	+	0.728926i	$0.259980\pi$
$734$	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	0.203513	−	0.979072i	$-0.434764\pi$
$739$	−14.7512	−	8.51661i	−0.542632	−	0.313288i	−0.746145	+	0.665784i	$0.768097\pi$
$740$	−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	−0.830506	−	0.557009i	$-0.811949\pi$
$751$	2.67632	−	25.4635i	0.0976602	−	0.929175i	0.928166	−	0.372165i	$-0.121385\pi$
$752$	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	−0.732913	−	0.680323i	$-0.761840\pi$
$757$	5.87000	−	27.6162i	0.213349	−	1.00373i	0.946261	−	0.323403i	$-0.104827\pi$
$758$	−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	0.796915	−	0.604091i	$-0.206464\pi$
$761$	24.3098	+	10.8234i	0.881229	+	0.392348i	0.0843135	+	0.996439i	$0.473130\pi$
$762$	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	0.912604	+	0.408844i	$0.134068\pi$
$769$	22.4723	+	38.9232i	0.810372	+	1.40360i	−0.102232	+	0.994761i	$0.532599\pi$
$770$	−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	0.782557	+	0.622579i	$0.213915\pi$
$773$	−6.01898	+	18.5245i	−0.216488	+	0.666280i	−0.999045	+	0.0437014i	$0.986085\pi$
$774$	−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	−0.961477	−	0.274887i	$-0.911360\pi$
$787$	−5.46849	−	25.7272i	−0.194931	−	0.917077i	0.766546	−	0.642190i	$-0.221974\pi$
$788$	−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	−0.743444	−	0.668798i	$-0.766809\pi$
$797$	−4.38422	−	41.7131i	−0.155297	−	1.47755i	0.588147	−	0.808754i	$-0.299858\pi$
$798$	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	−0.0686611	−	0.997640i	$-0.521873\pi$
$809$	26.4716	−	29.3997i	0.930691	−	1.03364i	0.999352	−	0.0359968i	$-0.0114606\pi$
$810$	3.91066	−	8.10597i	0.137407	−	0.284815i
$811$	−14.5537	+	25.2078i	−0.511050	+	0.885165i	0.488868	+	0.872358i	$0.337410\pi$
$811$	−14.5537	+	25.2078i	−0.511050	+	0.885165i	−0.999918	+	0.0128073i	$0.995923\pi$
$812$	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	0.988654	+	0.150212i	$0.0479957\pi$
$821$	7.94002	+	24.4369i	0.277109	+	0.852853i	−0.711545	+	0.702640i	$0.752004\pi$
$822$	12.8248	+	0.434106i	0.447316	+	0.0151412i
$823$	15.1418	−	34.0091i	0.527811	−	1.18548i	−0.431236	−	0.902239i	$-0.641922\pi$
$823$	15.1418	−	34.0091i	0.527811	−	1.18548i	0.959048	−	0.283245i	$-0.0914108\pi$
$824$	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	0.811021	−	0.585016i	$-0.198912\pi$
$827$	4.15360	+	4.61304i	0.144435	+	0.160411i	−0.666587	+	0.745428i	$0.732245\pi$
$828$	0.499241	−	0.743584i	0.0173498	−	0.0258413i
$829$	5.37154	+	7.39329i	0.186561	+	0.256779i	0.892045	−	0.451947i	$-0.149270\pi$
$829$	5.37154	+	7.39329i	0.186561	+	0.256779i	−0.705484	+	0.708726i	$0.749270\pi$
$830$	−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	−0.631854	−	0.775087i	$-0.717706\pi$
$839$	−46.3048	−	15.0454i	−1.59862	−	0.519423i	−0.966766	+	0.255664i	$0.917706\pi$
$840$	−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	−0.984478	−	0.175508i	$-0.943843\pi$
$853$	−8.50423	−	26.1733i	−0.291179	−	0.896158i	0.693299	−	0.720650i	$-0.256157\pi$
$854$	−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	0.802559	−	0.596572i	$-0.203471\pi$
$857$	−5.20493	−	11.6905i	−0.177797	−	0.399339i	−0.980357	+	0.197233i	$0.936804\pi$
$858$	1.68697	+	4.16256i	0.0575922	+	0.142108i
$859$	8.89673	−	0.935084i	0.303552	−	0.0319046i	0.0484722	−	0.998825i	$-0.484565\pi$
$859$	8.89673	−	0.935084i	0.303552	−	0.0319046i	0.255080	+	0.966920i	$0.417898\pi$
$860$	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	−0.901598	−	0.432574i	$-0.857605\pi$
$863$	−2.23790	+	3.87616i	−0.0761790	+	0.131946i	0.825419	+	0.564520i	$0.190939\pi$
$864$	−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	0.481245	+	0.876586i	$0.340185\pi$
$877$	5.70869	+	54.3146i	0.192769	+	1.83407i	−0.288476	+	0.957487i	$0.593149\pi$
$878$	−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	0.776294	−	0.630370i	$-0.217097\pi$
$881$	36.4811	+	7.75430i	1.22908	+	0.261249i	0.452786	+	0.891619i	$0.350430\pi$
$882$	−4.70156	+	2.30558i	−0.158310	+	0.0776329i
$883$	16.5694	−	5.38372i	0.557605	−	0.181177i	−0.0166384	−	0.999862i	$-0.505296\pi$
$883$	16.5694	−	5.38372i	0.557605	−	0.181177i	0.574243	+	0.818685i	$0.305296\pi$
$884$	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	0.953865	−	0.300236i	$-0.0970655\pi$
$887$	−1.18091	−	5.55576i	−0.0396512	−	0.186544i	−0.993516	+	0.113692i	$0.963732\pi$
$888$	−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	0.443342	−	0.896353i	$-0.353793\pi$
$907$	43.1516	−	31.3514i	1.43282	−	1.04101i	0.989482	−	0.144655i	$-0.0462071\pi$
$908$	−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	−0.415361	−	0.909657i	$-0.636345\pi$
$911$	−12.8223	+	2.72546i	−0.424822	+	0.0902987i	−0.00946067	+	0.999955i	$0.503011\pi$
$912$	−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	−0.591936	−	0.805985i	$-0.701636\pi$
$919$	−11.7942	+	5.25111i	−0.389054	+	0.173218i	0.202881	+	0.979203i	$0.434969\pi$
$920$	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	−0.909384	−	0.415958i	$-0.863446\pi$
$937$	2.03897	−	19.3996i	0.0666104	−	0.633756i	0.975994	−	0.217797i	$-0.0698872\pi$
$938$	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	−0.448946	−	0.893559i	$-0.648200\pi$
$941$	−2.61682	+	1.16508i	−0.0853059	+	0.0379806i	0.363640	+	0.931540i	$0.381534\pi$
$942$	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	0.942904	−	0.333064i	$-0.108083\pi$
$947$	40.8152	+	18.1721i	1.32632	+	0.590514i	0.383411	+	0.923578i	$0.374749\pi$
$948$	−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	−0.857628	−	0.514271i	$-0.828062\pi$
$953$	−19.5581	+	14.2098i	−0.633548	+	0.460300i	0.224080	+	0.974571i	$0.428062\pi$
$954$	−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	0.152451	−	0.988311i	$-0.451283\pi$
$967$	33.7267	−	19.4721i	1.08458	−	0.626182i	0.932128	+	0.362129i	$0.117950\pi$
$968$	−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	0.181317	−	0.983425i	$-0.441964\pi$
$971$	36.7171	−	33.0602i	1.17831	−	1.06095i	0.996990	−	0.0775274i	$-0.0247025\pi$
$972$	−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	−0.00893793	−	0.999960i	$-0.502845\pi$
$977$	17.8663	−	5.80511i	0.571593	−	0.185722i	0.580531	+	0.814238i	$0.302845\pi$
$978$	−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	−0.788488	−	0.615050i	$-0.789136\pi$
$983$	−4.54950	−	43.2856i	−0.145106	−	1.38059i	0.643382	−	0.765545i	$-0.277531\pi$
$984$	−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	$0.167632\pi$
$991$			31.6454i			1.00525i	−0.864504	+	0.502625i	$0.832368\pi$
$992$	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	0.00778552	−	0.999970i	$-0.497522\pi$
$997$	27.4671	−	47.5744i	0.869892	−	1.50670i	0.862106	−	0.506727i	$-0.169145\pi$
$998$	−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.761.11	yes	176
3.2	odd	2	inner	930.2.br.b.761.16	yes	176
31.11	odd	30	inner	930.2.br.b.11.16	yes	176
93.11	even	30	inner	930.2.br.b.11.11	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.11	✓	176	93.11	even	30	inner
930.2.br.b.11.16	yes	176	31.11	odd	30	inner
930.2.br.b.761.11	yes	176	1.1	even	1	trivial
930.2.br.b.761.16	yes	176	3.2	odd	2	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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