LMFDB - Embedded newform 930.2.br.b.761.16

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			761.16
Character	$\chi$	$=$	930.761
Dual form			930.2.br.b.11.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(-0.650557 + 1.60523i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.11476 + 1.32564i) q^{6} +(-0.239608 + 2.27972i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.15355 - 2.08859i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(-0.650557 + 1.60523i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.11476 + 1.32564i) q^{6} +(-0.239608 + 2.27972i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.15355 - 2.08859i) q^{9} +(0.669131 + 0.743145i) q^{10} +(-4.80333 + 2.13858i) q^{11} +(-1.46984 + 0.916274i) q^{12} +(0.102539 - 0.482408i) q^{13} +(-0.932352 + 2.09410i) q^{14} +(-1.36602 + 1.06490i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.224735 - 0.100059i) q^{17} +(-1.40274 - 2.65185i) q^{18} +(-2.25806 + 0.479966i) q^{19} +(0.406737 + 0.913545i) q^{20} +(-3.50360 - 1.86771i) q^{21} +(-5.22910 + 0.549600i) q^{22} +(-0.241527 + 0.175480i) q^{23} +(-1.68105 + 0.417222i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.246593 - 0.427111i) q^{26} +(4.75368 - 2.09821i) 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} +(-0.308084 - 9.10174i) q^{33} +(-0.182816 - 0.164608i) q^{34} +(-1.34736 + 1.85449i) q^{35} +(-0.514618 - 2.95553i) q^{36} +(4.06789 - 2.34860i) q^{37} +(-2.29586 - 0.241305i) q^{38} +(0.707670 + 0.478433i) q^{39} +(0.104528 + 0.994522i) q^{40} +(-7.06425 + 6.36068i) q^{41} +(-2.75497 - 2.85897i) q^{42} +(0.238577 + 1.12242i) q^{43} +(-5.14300 - 1.09318i) q^{44} +(-0.820736 - 2.88555i) q^{45} +(-0.283933 + 0.0922553i) q^{46} +(-3.93760 + 1.27940i) q^{47} +(-1.72770 - 0.122671i) q^{48} +(1.70734 + 0.362906i) q^{49} +(0.207912 + 0.978148i) q^{50} +(0.306821 - 0.295659i) q^{51} +(0.366508 - 0.330005i) q^{52} +(-0.504232 - 4.79745i) q^{53} +(5.16941 - 0.526546i) q^{54} +(-5.22910 - 0.549600i) q^{55} +(-1.98517 + 1.14614i) q^{56} +(0.698539 - 3.93696i) q^{57} +(-0.578053 + 0.795622i) q^{58} +(10.8675 + 9.78515i) q^{59} +(-1.73106 + 0.0585945i) 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} +(2.51959 - 8.75147i) q^{66} +(-4.94015 + 8.55660i) q^{67} +(-0.123002 - 0.213045i) q^{68} +(-0.124559 - 0.501868i) q^{69} +(-1.85449 + 1.34736i) q^{70} +(-6.46130 + 0.679110i) q^{71} +(0.423879 - 2.96990i) q^{72} +(-0.845091 - 1.89810i) q^{73} +(4.59455 - 0.976602i) q^{74} +(-1.71545 + 0.239219i) q^{75} +(-2.10893 - 0.938954i) q^{76} +(-3.72444 - 11.4627i) q^{77} +(0.525191 + 0.673699i) q^{78} +(-1.47932 + 3.32261i) q^{79} +(-0.207912 + 0.978148i) q^{80} +(0.275576 + 8.99578i) q^{81} +(-8.68406 + 3.86639i) q^{82} +(-0.758476 - 0.842373i) q^{83} +(-1.73666 - 3.57037i) q^{84} +(-0.144597 - 0.199021i) q^{85} +(-0.119946 + 1.14121i) q^{86} +(-1.30369 - 1.09630i) q^{87} +(-4.55348 - 2.62895i) q^{88} +(11.3890 + 8.27458i) q^{89} +(0.111118 - 2.99794i) q^{90} +(1.07518 + 0.349348i) q^{91} -0.298544 q^{92} +(-7.52246 + 6.03428i) q^{93} -4.14024 q^{94} +(-2.19552 - 0.713368i) q^{95} +(-1.60523 - 0.650557i) q^{96} +(-2.96658 - 2.15535i) q^{97} +(1.51163 + 0.872742i) q^{98} +(14.8108 + 5.42665i) 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
$3$	−0.650557	+	1.60523i	−0.375599	+	0.926782i
$3$	−0.650557	+	1.60523i	−0.375599	+	0.926782i
$4$	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
$6$	−1.11476	+	1.32564i	−0.455099	+	0.541188i
$7$	−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
$9$	−2.15355	−	2.08859i	−0.717851	−	0.696197i
$10$	0.669131	+	0.743145i	0.211598	+	0.235003i
$11$	−4.80333	+	2.13858i	−1.44826	+	0.644806i	−0.972103	−	0.234555i	$-0.924637\pi$
$11$	−4.80333	+	2.13858i	−1.44826	+	0.644806i	−0.476156	+	0.879361i	$0.657970\pi$
$12$	−1.46984	+	0.916274i	−0.424307	+	0.264506i
$13$	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
$15$	−1.36602	+	1.06490i	−0.352704	+	0.274955i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.224735	−	0.100059i	−0.0545063	−	0.0242678i	0.379302	−	0.925273i	$-0.376164\pi$
$17$	−0.224735	−	0.100059i	−0.0545063	−	0.0242678i	−0.433809	+	0.901005i	$0.642831\pi$
$18$	−1.40274	−	2.65185i	−0.330629	−	0.625048i
$19$	−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
$21$	−3.50360	−	1.86771i	−0.764548	−	0.407568i
$22$	−5.22910	+	0.549600i	−1.11485	+	0.117175i
$23$	−0.241527	+	0.175480i	−0.0503620	+	0.0365901i	−0.612681	−	0.790330i	$-0.709909\pi$
$23$	−0.241527	+	0.175480i	−0.0503620	+	0.0365901i	0.562319	+	0.826920i	$0.309909\pi$
$24$	−1.68105	+	0.417222i	−0.343143	+	0.0851650i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	0.246593	−	0.427111i	0.0483608	−	0.0837634i
$27$	4.75368	−	2.09821i	0.914847	−	0.403801i
$28$	−1.53383	+	1.70349i	−0.289867	+	0.321930i
$29$	−0.303900	+	0.935309i	−0.0564329	+	0.173683i	−0.975300	−	0.220885i	$-0.929106\pi$
$29$	−0.303900	+	0.935309i	−0.0564329	+	0.173683i	0.918867	+	0.394567i	$0.129106\pi$
$30$	−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
$33$	−0.308084	−	9.10174i	−0.0536306	−	1.58441i
$34$	−0.182816	−	0.164608i	−0.0313527	−	0.0282301i
$35$	−1.34736	+	1.85449i	−0.227746	+	0.313466i
$36$	−0.514618	−	2.95553i	−0.0857696	−	0.492589i
$37$	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
$39$	0.707670	+	0.478433i	0.113318	+	0.0766105i
$40$	0.104528	+	0.994522i	0.0165274	+	0.157248i
$41$	−7.06425	+	6.36068i	−1.10325	+	0.993372i	−0.999999	−	0.00128345i	$-0.999591\pi$
$41$	−7.06425	+	6.36068i	−1.10325	+	0.993372i	−0.103252	+	0.994655i	$0.532925\pi$
$42$	−2.75497	−	2.85897i	−0.425101	−	0.441149i
$43$	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
$45$	−0.820736	−	2.88555i	−0.122348	−	0.430152i
$46$	−0.283933	+	0.0922553i	−0.0418636	+	0.0136023i
$47$	−3.93760	+	1.27940i	−0.574358	+	0.186620i	−0.581772	−	0.813352i	$-0.697640\pi$
$47$	−3.93760	+	1.27940i	−0.574358	+	0.186620i	0.00741320	+	0.999973i	$0.497640\pi$
$48$	−1.72770	−	0.122671i	−0.249372	−	0.0177061i
$49$	1.70734	+	0.362906i	0.243906	+	0.0518438i
$50$	0.207912	+	0.978148i	0.0294032	+	0.138331i
$51$	0.306821	−	0.295659i	0.0429635	−	0.0414005i
$52$	0.366508	−	0.330005i	0.0508255	−	0.0457635i
$53$	−0.504232	−	4.79745i	−0.0692616	−	0.658980i	−0.972986	−	0.230865i	$-0.925844\pi$
$53$	−0.504232	−	4.79745i	−0.0692616	−	0.658980i	0.903724	−	0.428115i	$-0.140822\pi$
$54$	5.16941	−	0.526546i	0.703467	−	0.0716539i
$55$	−5.22910	−	0.549600i	−0.705091	−	0.0741081i
$56$	−1.98517	+	1.14614i	−0.265279	+	0.153159i
$57$	0.698539	−	3.93696i	0.0925238	−	0.521463i
$58$	−0.578053	+	0.795622i	−0.0759021	+	0.104470i
$59$	10.8675	+	9.78515i	1.41483	+	1.27392i	0.912400	+	0.409300i	$0.134227\pi$
$59$	10.8675	+	9.78515i	1.41483	+	1.27392i	0.502430	+	0.864618i	$0.332440\pi$
$60$	−1.73106	+	0.0585945i	−0.223479	+	0.00756452i
$61$		−	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
$66$	2.51959	−	8.75147i	0.310140	−	1.07723i
$67$	−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
$69$	−0.124559	−	0.501868i	−0.0149952	−	0.0604178i
$70$	−1.85449	+	1.34736i	−0.221654	+	0.161041i
$71$	−6.46130	+	0.679110i	−0.766816	+	0.0805956i	−0.479856	−	0.877347i	$-0.659311\pi$
$71$	−6.46130	+	0.679110i	−0.766816	+	0.0805956i	−0.286959	+	0.957943i	$0.592644\pi$
$72$	0.423879	−	2.96990i	0.0499546	−	0.350006i
$73$	−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
$75$	−1.71545	+	0.239219i	−0.198083	+	0.0276226i
$76$	−2.10893	−	0.938954i	−0.241910	−	0.107705i
$77$	−3.72444	−	11.4627i	−0.424439	−	1.30629i
$78$	0.525191	+	0.673699i	0.0594661	+	0.0762814i
$79$	−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
$81$	0.275576	+	8.99578i	0.0306196	+	0.999531i
$82$	−8.68406	+	3.86639i	−0.958994	+	0.426972i
$83$	−0.758476	−	0.842373i	−0.0832536	−	0.0924625i	0.700079	−	0.714066i	$-0.253148\pi$
$83$	−0.758476	−	0.842373i	−0.0832536	−	0.0924625i	−0.783332	+	0.621603i	$0.786482\pi$
$84$	−1.73666	−	3.57037i	−0.189485	−	0.389560i
$85$	−0.144597	−	0.199021i	−0.0156838	−	0.0215869i
$86$	−0.119946	+	1.14121i	−0.0129341	+	0.123060i
$87$	−1.30369	−	1.09630i	−0.139770	−	0.117536i
$88$	−4.55348	−	2.62895i	−0.485402	−	0.280247i
$89$	11.3890	+	8.27458i	1.20723	+	0.877104i	0.994976	−	0.100111i	$-0.0319197\pi$
$89$	11.3890	+	8.27458i	1.20723	+	0.877104i	0.212254	+	0.977215i	$0.431920\pi$
$90$	0.111118	−	2.99794i	0.0117128	−	0.316011i
$91$	1.07518	+	0.349348i	0.112710	+	0.0366217i
$92$	−0.298544			−0.0311254
$93$	−7.52246	+	6.03428i	−0.780043	+	0.625726i
$94$	−4.14024			−0.427033
$95$	−2.19552	−	0.713368i	−0.225256	−	0.0731900i
$96$	−1.60523	−	0.650557i	−0.163834	−	0.0663971i
$97$	−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
$99$	14.8108	+	5.42665i	1.48855	+	0.545399i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	−3.90718	−	5.37777i	−0.388779	−	0.535108i	0.569105	−	0.822265i	$-0.307290\pi$
$101$	−3.90718	−	5.37777i	−0.388779	−	0.535108i	−0.957884	+	0.287157i	$0.907290\pi$
$102$	0.383167	−	0.186376i	0.0379392	−	0.0184539i
$103$	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
$105$	−2.10035	−	3.36928i	−0.204973	−	0.328808i
$106$	1.00294	−	4.71846i	0.0974141	−	0.458297i
$107$	4.02477	−	9.03979i	0.389090	−	0.873910i	−0.607724	−	0.794148i	$-0.707917\pi$
$107$	4.02477	−	9.03979i	0.389090	−	0.873910i	0.996814	−	0.0797616i	$-0.0254159\pi$
$108$	5.07911	+	1.09666i	0.488737	+	0.105526i
$109$	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
$111$	1.12366	+	8.05782i	0.106653	+	0.764814i
$112$	−2.24218	+	0.476590i	−0.211866	+	0.0450336i
$113$	4.07478	+	9.15212i	0.383323	+	0.860959i	0.997424	+	0.0717308i	$0.0228523\pi$
$113$	4.07478	+	9.15212i	0.383323	+	0.860959i	−0.614101	+	0.789228i	$0.710481\pi$
$114$	1.88094	−	3.52841i	0.176166	−	0.330466i
$115$	−0.296909	+	0.0312064i	−0.0276869	+	0.00291001i
$116$	−0.795622	+	0.578053i	−0.0738716	+	0.0536709i
$117$	−1.22838	+	0.824729i	−0.113563	+	0.0762462i
$118$	7.31184	+	12.6645i	0.673109	+	1.16586i
$119$	0.281954	−	0.488358i	0.0258466	−	0.0447677i
$120$	−1.66444	−	0.479200i	−0.151942	−	0.0437448i
$121$	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
$126$	6.38158	−	2.56244i	0.568516	−	0.228281i
$127$	−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
$129$	−1.95695	−	0.347224i	−0.172300	−	0.0305714i
$130$	0.427111	−	0.246593i	0.0374601	−	0.0216276i
$131$	6.90739	+	0.725996i	0.603502	+	0.0634306i	0.401352	−	0.915924i	$-0.368541\pi$
$131$	6.90739	+	0.725996i	0.603502	+	0.0634306i	0.202150	+	0.979355i	$0.435207\pi$
$132$	5.10062	−	7.54455i	0.443952	−	0.656669i
$133$	−0.553136	−	5.26274i	−0.0479630	−	0.456337i
$134$	−7.34250	+	6.61122i	−0.634295	+	0.571122i
$135$	5.16592	+	0.559740i	0.444611	+	0.0481747i
$136$	−0.0511470	−	0.240628i	−0.00438582	−	0.0206337i
$137$	7.24675	+	1.54034i	0.619131	+	0.131600i	0.506790	−	0.862069i	$-0.330832\pi$
$137$	7.24675	+	1.54034i	0.619131	+	0.131600i	0.112341	+	0.993670i	$0.464165\pi$
$138$	0.0366229	−	0.515796i	0.00311755	−	0.0439074i
$139$	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
$141$	0.507889	−	7.15310i	0.0427720	−	0.602400i
$142$	−6.35492	−	1.35078i	−0.533293	−	0.113355i
$143$	0.539140	+	2.53645i	0.0450851	+	0.212109i
$144$	1.32088	−	2.69356i	0.110074	−	0.224463i
$145$	−0.730840	+	0.658051i	−0.0606930	+	0.0546482i
$146$	−0.217182	−	2.06635i	−0.0179741	−	0.171013i
$147$	−1.69327	+	2.50459i	−0.139659	+	0.206575i
$148$	4.67147	+	0.490991i	0.383992	+	0.0403592i
$149$	8.29682	−	4.79017i	0.679702	−	0.392426i	−0.120041	−	0.992769i	$-0.538303\pi$
$149$	8.29682	−	4.79017i	0.679702	−	0.392426i	0.799743	+	0.600343i	$0.204969\pi$
$150$	−1.70541	−	0.302593i	−0.139246	−	0.0247066i
$151$	−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
$153$	0.274998	+	0.684862i	0.0222323	+	0.0553678i
$154$		−	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
$159$	8.02906	+	2.31160i	0.636746	+	0.183322i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−0.342173	−	0.592660i	−0.0269670	−	0.0467082i
$162$	−2.51776	+	8.64065i	−0.197814	+	0.678874i
$163$	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
$165$	4.28406	−	8.03638i	0.333514	−	0.625631i
$166$	−0.461046	−	1.03553i	−0.0357841	−	0.0803724i
$167$	2.27172	−	0.482869i	0.175791	−	0.0373655i	−0.119175	−	0.992873i	$-0.538025\pi$
$167$	2.27172	−	0.482869i	0.175791	−	0.0373655i	0.294966	+	0.955508i	$0.404692\pi$
$168$	−0.548354	−	3.93228i	−0.0423064	−	0.303382i
$169$	11.6539	+	5.18865i	0.896453	+	0.399127i
$170$	−0.0760193	−	0.233963i	−0.00583041	−	0.0179442i
$171$	5.86530	+	3.68253i	0.448531	+	0.281610i
$172$	−0.466728	+	1.04829i	−0.0355877	+	0.0799312i
$173$	3.73588	−	17.5759i	0.284034	−	1.33627i	−0.572382	−	0.819987i	$-0.693980\pi$
$173$	3.73588	−	17.5759i	0.284034	−	1.33627i	0.856416	−	0.516287i	$-0.172686\pi$
$174$	−0.901103	−	1.44551i	−0.0683124	−	0.109584i
$175$	−2.09410	+	0.932352i	−0.158299	+	0.0704792i
$176$	−3.51822	−	3.90738i	−0.265196	−	0.294530i
$177$	−22.7774	+	11.0791i	−1.71205	+	0.832757i
$178$	8.27458	+	11.3890i	0.620206	+	0.853640i
$179$	0.107315	−	1.02103i	0.00802109	−	0.0763156i	−0.989779	−	0.142609i	$-0.954451\pi$
$179$	0.107315	−	1.02103i	0.00802109	−	0.0763156i	0.997800	+	0.0662937i	$0.0211174\pi$
$180$	1.03209	−	2.81687i	0.0769277	−	0.209957i
$181$	−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
$183$	18.6875	+	7.57354i	1.38142	+	0.559852i
$184$	−0.283933	−	0.0922553i	−0.0209318	−	0.00680115i
$185$	4.69720			0.345345
$186$	−9.01898	+	3.41438i	−0.661304	+	0.250354i
$187$	1.29346			0.0945873
$188$	−3.93760	−	1.27940i	−0.287179	−	0.0933102i
$189$	3.64430	+	11.3398i	0.265084	+	0.824849i
$190$	−1.86762	−	1.35691i	−0.135492	−	0.0984403i
$191$	−1.20866	−	0.697818i	−0.0874553	−	0.0504924i	0.455635	−	0.890167i	$-0.349412\pi$
$191$	−1.20866	−	0.697818i	−0.0874553	−	0.0504924i	−0.543090	+	0.839675i	$0.682746\pi$
$192$	−1.32564	−	1.11476i	−0.0956695	−	0.0804509i
$193$	−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
$195$	0.373644	+	0.768170i	0.0267572	+	0.0550098i
$196$	1.16796	+	1.29715i	0.0834255	+	0.0926533i
$197$	20.1991	−	8.99323i	1.43913	−	0.640741i	0.468970	−	0.883214i	$-0.344625\pi$
$197$	20.1991	−	8.99323i	1.43913	−	0.640741i	0.970158	+	0.242473i	$0.0779585\pi$
$198$	12.4090	+	9.73785i	0.881871	+	0.692039i
$199$	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
$201$	−10.5215	−	13.4967i	−0.742129	−	0.951981i
$202$	−2.05412	−	6.32195i	−0.144528	−	0.444811i
$203$	−2.05942	−	0.916914i	−0.144543	−	0.0643547i
$204$	0.422007	−	0.0588486i	0.0295464	−	0.00412023i
$205$	−9.29816	+	1.97639i	−0.649412	+	0.138037i
$206$	2.99845	+	6.73462i	0.208912	+	0.469223i
$207$	0.886648	+	0.126547i	0.0616263	+	0.00879561i
$208$	0.490484	−	0.0515519i	0.0340089	−	0.00357448i
$209$	9.81977	−	7.13448i	0.679248	−	0.493502i
$210$	−0.956386	−	3.85342i	−0.0659969	−	0.265912i
$211$	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
$213$	3.11331	−	10.8137i	0.213321	−	0.740943i
$214$	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
$219$	3.59668	−	0.121744i	0.243041	−	0.00822669i
$220$	−3.90738	−	3.51822i	−0.263436	−	0.237198i
$221$	−0.0713132	+	0.0981542i	−0.00479705	+	0.00660257i
$222$	−1.42134	+	8.01067i	−0.0953942	+	0.537641i
$223$	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
$225$	0.731997	−	2.90933i	0.0487998	−	0.193955i
$226$	1.04719	+	9.96336i	0.0696581	+	0.662753i
$227$	14.3618	−	12.9314i	0.953224	−	0.858286i	−0.0367807	−	0.999323i	$-0.511710\pi$
$227$	14.3618	−	12.9314i	0.953224	−	0.858286i	0.990004	+	0.141037i	$0.0450436\pi$
$228$	2.87922	−	2.77448i	0.190681	−	0.183744i
$229$	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
$231$	20.8232	+	1.47850i	1.37007	+	0.0972783i
$232$	−0.935309	+	0.303900i	−0.0614061	+	0.0199520i
$233$	13.8077	−	4.48638i	0.904570	−	0.293912i	0.180448	−	0.983585i	$-0.442245\pi$
$233$	13.8077	−	4.48638i	0.904570	−	0.293912i	0.724122	+	0.689672i	$0.242245\pi$
$234$	−1.42311	+	0.404775i	−0.0930316	+	0.0264610i
$235$	−4.04977	−	0.860805i	−0.264178	−	0.0561527i
$236$	3.04043	+	14.3041i	0.197915	+	0.931119i
$237$	−4.37119	−	4.53620i	−0.283939	−	0.294658i
$238$	0.419065	−	0.377328i	0.0271639	−	0.0244585i
$239$	0.860790	+	8.18987i	0.0556799	+	0.529758i	0.986439	+	0.164126i	$0.0524805\pi$
$239$	0.860790	+	8.18987i	0.0556799	+	0.529758i	−0.930759	+	0.365632i	$0.880853\pi$
$240$	−1.43490	−	0.970087i	−0.0926222	−	0.0626189i
$241$	−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
$243$	−14.6196	−	5.40990i	−0.937848	−	0.347045i
$244$	6.84278	−	9.41828i	0.438064	−	0.602943i
$245$	1.29715	+	1.16796i	0.0828717	+	0.0746180i
$246$	−0.556993	−	16.4553i	−0.0355126	−	1.04915i
$247$			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	$-0.820390\pi$
$251$	−3.56146	+	3.95540i	−0.224797	+	0.249663i	0.620187	+	0.784454i	$0.287057\pi$
$252$	6.86108	−	0.465013i	0.432207	−	0.0292931i
$253$	0.784858	−	1.35941i	0.0493436	−	0.0854657i
$254$	−2.53084	−	4.38354i	−0.158799	−	0.275048i
$255$	0.413544	−	0.102638i	0.0258971	−	0.00642744i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−28.1552	+	2.95923i	−1.75628	+	0.184592i	−0.927206	−	0.374553i	$-0.877796\pi$
$257$	−28.1552	+	2.95923i	−1.75628	+	0.184592i	−0.829070	+	0.559145i	$0.811130\pi$
$258$	−1.75387	−	0.934961i	−0.109191	−	0.0582082i
$259$	4.37944	+	9.83638i	0.272125	+	0.611203i
$260$	0.482408	−	0.102539i	0.0299177	−	0.00635920i
$261$	2.60794	−	1.37951i	0.161428	−	0.0853898i
$262$	6.34497	+	2.82496i	0.391994	+	0.174527i
$263$	−3.36054	−	10.3427i	−0.207220	−	0.637757i	−0.999615	−	0.0277488i	$-0.991166\pi$
$263$	−3.36054	−	10.3427i	−0.207220	−	0.637757i	0.792395	−	0.610008i	$-0.208834\pi$
$264$	7.18237	−	5.59911i	0.442045	−	0.344602i
$265$	1.96205	−	4.40683i	0.120528	−	0.270709i
$266$	1.10021	−	5.17609i	0.0674584	−	0.317367i
$267$	−20.6918	+	12.8989i	−1.26632	+	0.789400i
$268$	−9.02611	+	4.01868i	−0.551358	+	0.245480i
$269$	−12.1131	−	13.4530i	−0.738549	−	0.820241i	0.250456	−	0.968128i	$-0.419420\pi$
$269$	−12.1131	−	13.4530i	−0.738549	−	0.820241i	−0.989004	+	0.147887i	$0.952753\pi$
$270$	4.74011	+	2.12870i	0.288474	+	0.129549i
$271$	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
$273$	−1.26025	+	1.49865i	−0.0762740	+	0.0907025i
$274$	6.41607	+	3.70432i	0.387609	+	0.223786i
$275$	−4.25373	−	3.09052i	−0.256510	−	0.186365i
$276$	0.194220	−	0.479234i	0.0116907	−	0.0288465i
$277$	−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
$279$	−4.79265	−	16.0010i	−0.286929	−	0.957952i
$280$	−2.29227			−0.136990
$281$	−18.5701	−	6.03378i	−1.10780	−	0.359945i	−0.302699	−	0.953086i	$-0.597888\pi$
$281$	−18.5701	−	6.03378i	−1.10780	−	0.359945i	−0.805099	+	0.593141i	$0.797888\pi$
$282$	2.69346	−	6.64606i	0.160393	−	0.395767i
$283$	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
$285$	2.57343	−	3.06024i	0.152437	−	0.181273i
$286$	−0.271055	+	2.57891i	−0.0160278	+	0.152494i
$287$	−12.8079	−	17.6286i	−0.756026	−	1.04058i
$288$	2.08859	−	2.15355i	0.123071	−	0.126899i
$289$	−11.3347	−	12.5885i	−0.666749	−	0.740499i
$290$	−0.898419	+	0.400002i	−0.0527570	+	0.0234889i
$291$	5.38977	−	3.35988i	0.315954	−	0.196960i
$292$	0.431985	−	2.03233i	0.0252800	−	0.118933i
$293$	9.62081	−	21.6087i	0.562054	−	1.26239i	−0.379394	−	0.925235i	$-0.623868\pi$
$293$	9.62081	−	21.6087i	0.562054	−	1.26239i	0.941448	−	0.337158i	$-0.109466\pi$
$294$	−2.38436	+	1.85876i	−0.139059	+	0.108405i
$295$	4.51897	+	13.9079i	0.263104	+	0.809752i
$296$	4.29110	+	1.91052i	0.249415	+	0.111047i
$297$	−18.3463	+	20.2445i	−1.06456	+	1.17471i
$298$	9.37099	−	1.99186i	0.542847	−	0.115386i
$299$	0.0598870	+	0.134508i	0.00346335	+	0.00777882i
$300$	−1.52844	−	0.814785i	−0.0882444	−	0.0470417i
$301$	−2.61596	+	0.274949i	−0.150781	+	0.0158478i
$302$	−7.05114	+	5.12296i	−0.405748	+	0.294793i
$303$	11.1744	−	2.77339i	0.641954	−	0.159327i
$304$	−1.15425	−	1.99923i	−0.0662010	−	0.114663i
$305$	5.82082	−	10.0819i	0.333299	−	0.577291i
$306$	0.0499046	+	0.736321i	0.00285285	+	0.0420927i
$307$	−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	$0.111575\pi$
$311$			12.1114i			0.686776i	−0.939194	+	0.343388i	$0.888425\pi$
$312$	0.0288980	+	0.853733i	0.00163602	+	0.0483331i
$313$	−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
$315$	6.77489	−	1.17964i	0.381722	−	0.0664654i
$316$	−3.14978	+	1.81853i	−0.177189	+	0.102300i
$317$	30.8863	+	3.24628i	1.73475	+	0.182329i	0.918513	−	0.395390i	$-0.129391\pi$
$317$	30.8863	+	3.24628i	1.73475	+	0.182329i	0.816235	+	0.577719i	$0.196057\pi$
$318$	6.92177	+	4.67958i	0.388153	+	0.262418i
$319$	−0.540500	−	5.14252i	−0.0302622	−	0.287926i
$320$	−0.743145	+	0.669131i	−0.0415431	+	0.0374055i
$321$	11.8926	+	12.3416i	0.663782	+	0.688841i
$322$	−0.142283	−	0.669391i	−0.00792914	−	0.0373037i
$323$	0.555491	+	0.118073i	0.0309083	+	0.00656977i
$324$	−5.06464	+	7.43972i	−0.281369	+	0.413318i
$325$	0.469047	−	0.152403i	0.0260180	−	0.00845378i
$326$	0.869950	−	0.282664i	0.0481821	−	0.0156553i
$327$	−30.0641	−	2.13463i	−1.66255	−	0.118045i
$328$	−9.29816	−	1.97639i	−0.513405	−	0.109128i
$329$	−1.97320	−	9.28317i	−0.108786	−	0.511798i
$330$	6.55776	−	6.31920i	0.360993	−	0.347861i
$331$	−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
$333$	−13.6657	−	3.43833i	−0.748875	−	0.188419i
$334$	2.30975	+	0.242764i	0.126384	+	0.0132835i
$335$	−8.55660	+	4.94015i	−0.467497	+	0.269909i
$336$	0.693627	−	3.90928i	0.0378404	−	0.213268i
$337$	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
$339$	−17.3422	+	0.587014i	−0.941897	+	0.0318822i
$340$		−	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
$345$	0.143062	−	0.496910i	0.00770223	−	0.0267527i
$346$	8.98430	−	15.5613i	0.482999	−	0.836579i
$347$	−6.19451	−	10.7292i	−0.332539	−	0.575974i	0.650470	−	0.759532i	$-0.274572\pi$
$347$	−6.19451	−	10.7292i	−0.332539	−	0.575974i	−0.983009	+	0.183558i	$0.941239\pi$
$348$	−0.410313	−	1.65321i	−0.0219951	−	0.0886216i
$349$	−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
$351$	−0.524755	−	2.50836i	−0.0280093	−	0.133887i
$352$	−2.13858	−	4.80333i	−0.113987	−	0.256018i
$353$	0.519568	−	0.110438i	0.0276538	−	0.00587800i	−0.194064	−	0.980989i	$-0.562167\pi$
$353$	0.519568	−	0.110438i	0.0276538	−	0.00587800i	0.221718	+	0.975111i	$0.428834\pi$
$354$	−25.0862	+	3.49826i	−1.33332	+	0.185930i
$355$	−5.93521	−	2.64252i	−0.315008	−	0.140251i
$356$	4.35020	+	13.3886i	0.230560	+	0.709592i
$357$	0.600502	+	0.770306i	0.0317819	+	0.0407689i
$358$	0.417579	−	0.937898i	0.0220697	−	0.0495695i
$359$	4.33883	−	20.4126i	0.228995	−	1.07733i	−0.701965	−	0.712212i	$-0.747694\pi$
$359$	4.33883	−	20.4126i	0.228995	−	1.07733i	0.930959	−	0.365123i	$-0.118973\pi$
$360$	1.85204	−	2.36007i	0.0976112	−	0.124387i
$361$	−12.4889	+	5.56041i	−0.657310	+	0.292653i
$362$	−0.0495237	−	0.0550016i	−0.00260291	−	0.00289082i
$363$	12.6109	+	25.9265i	0.661900	+	1.36079i
$364$	0.664500	+	0.914606i	0.0348293	+	0.0479384i
$365$	0.217182	−	2.06635i	0.0113678	−	0.108158i
$366$	15.4326	+	12.9776i	0.806673	+	0.678352i
$367$	−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
$369$	28.4981	+	1.05627i	1.48355	+	0.0549874i
$370$	4.46730	+	1.45151i	0.232244	+	0.0754606i
$371$	11.0576			0.574084
$372$	−9.63266	+	0.460247i	−0.499430	+	0.0238627i
$373$	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
$375$	−1.60523	−	0.650557i	−0.0828939	−	0.0335946i
$376$	−3.34953	−	2.43357i	−0.172739	−	0.125502i
$377$	0.420039	+	0.242510i	0.0216331	+	0.0124899i
$378$	−0.0382541	+	11.9109i	−0.00196758	+	0.612633i
$379$	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
$381$	7.88390	−	3.83479i	0.403905	−	0.196462i
$382$	−0.933863	−	1.03716i	−0.0477806	−	0.0530657i
$383$	−34.4946	+	15.3580i	−1.76259	+	0.784757i	−0.774180	+	0.632965i	$0.781838\pi$
$383$	−34.4946	+	15.3580i	−1.76259	+	0.784757i	−0.988413	+	0.151791i	$0.951496\pi$
$384$	−0.916274	−	1.46984i	−0.0467584	−	0.0750077i
$385$	2.50587	−	11.7892i	0.127711	−	0.600832i
$386$	−6.56569	+	14.7468i	−0.334185	+	0.750592i
$387$	1.83048	−	2.91548i	0.0930487	−	0.148202i
$388$	−1.13313	−	3.48743i	−0.0575261	−	0.177047i
$389$	26.2933	+	11.7065i	1.33312	+	0.593545i	0.944700	−	0.327936i	$-0.106353\pi$
$389$	26.2933	+	11.7065i	1.33312	+	0.593545i	0.388424	+	0.921481i	$0.373020\pi$
$390$	0.117979	+	0.846036i	0.00597410	+	0.0428407i
$391$	0.0718381	−	0.0152697i	0.00363301	−	0.000772219i
$392$	0.709952	+	1.59458i	0.0358580	+	0.0805384i
$393$	−5.65904	+	10.6157i	−0.285461	+	0.535490i
$394$	21.9896	−	2.31120i	1.10782	−	0.116436i
$395$	−2.94244	+	2.13781i	−0.148050	+	0.107565i
$396$	8.79252	+	13.0958i	0.441841	+	0.658091i
$397$	−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
$399$	8.80778	+	2.53580i	0.440940	+	0.126949i
$400$	−0.669131	+	0.743145i	−0.0334565	+	0.0371572i
$401$	5.07464	−	15.6181i	0.253415	−	0.779932i	−0.740723	−	0.671811i	$-0.765517\pi$
$401$	5.07464	−	15.6181i	0.253415	−	0.779932i	0.994138	−	0.108121i	$-0.0344833\pi$
$402$	−5.83584	−	16.0874i	−0.291065	−	0.802367i
$403$	1.80884	−	2.06599i	0.0901045	−	0.102914i
$404$		−	6.64729i		−	0.330715i
$405$	−4.25923	+	7.92836i	−0.211643	+	0.393963i
$406$	−1.67529	−	1.50843i	−0.0831430	−	0.0748623i
$407$	−14.5168	+	19.9806i	−0.719569	+	0.990402i
$408$	0.419538	+	0.0744390i	0.0207702	+	0.00368528i
$409$	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
$411$	−7.18703	+	10.6306i	−0.354510	+	0.524371i
$412$	0.770580	+	7.33157i	0.0379637	+	0.361201i
$413$	−24.9113	+	22.4302i	−1.22581	+	1.10372i
$414$	0.804147	+	0.394342i	0.0395217	+	0.0193809i
$415$	−0.235673	−	1.10875i	−0.0115687	−	0.0544266i
$416$	0.482408	+	0.102539i	0.0236520	+	0.00502739i
$417$	−2.16809	+	30.5353i	−0.106172	+	1.49532i
$418$	11.5438	−	3.75082i	0.564627	−	0.183458i
$419$	5.95487	−	1.93486i	0.290915	−	0.0945239i	−0.159924	−	0.987129i	$-0.551125\pi$
$419$	5.95487	−	1.93486i	0.290915	−	0.0945239i	0.450839	+	0.892605i	$0.351125\pi$
$420$	0.281196	−	3.96036i	0.0137210	−	0.193246i
$421$	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
$423$	11.1520	+	5.46878i	0.542228	+	0.265901i
$424$	3.58484	−	3.22780i	0.174095	−	0.156756i
$425$	−0.0257144	−	0.244656i	−0.00124733	−	0.0118676i
$426$	6.30255	−	9.32238i	0.305360	−	0.451671i
$427$	26.5396	+	2.78943i	1.28434	+	0.134990i
$428$	8.56957	−	4.94764i	0.414226	−	0.239153i
$429$	−4.42234	−	0.784661i	−0.213513	−	0.0378838i
$430$	−0.674480	+	0.928342i	−0.0325263	+	0.0447686i
$431$	18.7969	+	16.9248i	0.905415	+	0.815239i	0.983350	−	0.181719i	$-0.0581662\pi$
$431$	18.7969	+	16.9248i	0.905415	+	0.815239i	−0.0779356	+	0.996958i	$0.524833\pi$
$432$	3.46448	+	3.87264i	0.166685	+	0.186323i
$433$			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
$438$	3.45827	+	0.995650i	0.165242	+	0.0475740i
$439$	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
$441$	−2.91888	−	4.34747i	−0.138994	−	0.207023i
$442$	−0.0981542	+	0.0713132i	−0.00466872	+	0.00339202i
$443$	20.0595	−	2.10834i	0.953054	−	0.100170i	0.384779	−	0.923009i	$-0.374278\pi$
$443$	20.0595	−	2.10834i	0.953054	−	0.100170i	0.568275	+	0.822839i	$0.307611\pi$
$444$	−3.82721	+	7.17938i	−0.181631	+	0.340718i
$445$	5.72586	+	12.8605i	0.271432	+	0.609646i
$446$	10.4762	−	2.22679i	0.496064	−	0.105442i
$447$	2.29179	+	16.4346i	0.108398	+	0.777330i
$448$	−2.09410	−	0.932352i	−0.0989367	−	0.0440495i
$449$	5.05783	+	15.5664i	0.238694	+	0.734624i	0.996610	+	0.0822721i	$0.0262176\pi$
$449$	5.05783	+	15.5664i	0.238694	+	0.734624i	−0.757916	+	0.652352i	$0.773782\pi$
$450$	1.59520	−	2.54073i	0.0751985	−	0.119771i
$451$	20.3291	−	45.6599i	0.957261	−	2.15004i
$452$	−2.08291	+	9.79932i	−0.0979718	+	0.460921i
$453$	−7.98596	−	12.8107i	−0.375213	−	0.601900i
$454$	17.6549	−	7.86045i	0.828584	−	0.368909i
$455$	0.756462	+	0.840137i	0.0354635	+	0.0393862i
$456$	3.59566	−	1.74896i	0.168382	−	0.0819024i
$457$	−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
$459$	−1.27827	−	0.00410538i	−0.0596643	−	0.000191623i
$460$	−0.258547	−	0.149272i	−0.0120548	−	0.00695985i
$461$	20.9266	+	15.2041i	0.974649	+	0.708124i	0.956506	−	0.291711i	$-0.0942246\pi$
$461$	20.9266	+	15.2041i	0.974649	+	0.708124i	0.0181429	+	0.999835i	$0.494225\pi$
$462$	19.3472	+	7.84086i	0.900111	+	0.364790i
$463$	−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
$465$	−9.53178	+	1.46461i	−0.442026	+	0.0679198i
$466$	14.5182			0.672544
$467$	−34.4263	−	11.1858i	−1.59306	−	0.517616i	−0.627681	−	0.778471i	$-0.715996\pi$
$467$	−34.4263	−	11.1858i	−1.59306	−	0.517616i	−0.965378	+	0.260855i	$0.915996\pi$
$468$	−1.47854	−	0.0548016i	−0.0683456	−	0.00253320i
$469$	−18.3229	−	13.3124i	−0.846074	−	0.614708i
$470$	−3.58555	−	2.07012i	−0.165389	−	0.0954875i
$471$	−18.3802	−	15.4564i	−0.846913	−	0.712191i
$472$	−1.52859	+	14.5436i	−0.0703591	+	0.669422i
$473$	−3.54635	−	4.88113i	−0.163061	−	0.224435i
$474$	−2.75548	−	5.66496i	−0.126563	−	0.260200i
$475$	−1.54469	−	1.71556i	−0.0708754	−	0.0787151i
$476$	0.515155	−	0.229362i	0.0236121	−	0.0105128i
$477$	−8.93402	+	11.3847i	−0.409061	+	0.521269i
$478$	−1.71215	+	8.05503i	−0.0783119	+	0.368428i
$479$	10.4039	−	23.3675i	0.475365	−	1.06769i	−0.503652	−	0.863907i	$-0.668010\pi$
$479$	10.4039	−	23.3675i	0.475365	−	1.06769i	0.979017	−	0.203780i	$-0.0653228\pi$
$480$	−1.06490	−	1.36602i	−0.0486056	−	0.0623498i
$481$	−0.715865	−	2.20321i	−0.0326406	−	0.100458i
$482$	−27.8129	−	12.3831i	−1.26684	−	0.564035i
$483$	1.17396	−	0.163708i	0.0534171	−	0.00744898i
$484$	16.2818	−	3.46080i	0.740081	−	0.157309i
$485$	−1.49146	−	3.34988i	−0.0677238	−	0.152110i
$486$	−12.2323	−	9.66283i	−0.554870	−	0.438315i
$487$	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
$489$	0.381641	+	1.53769i	0.0172584	+	0.0695367i
$490$	0.872742	+	1.51163i	0.0394264	+	0.0682886i
$491$	−12.2452	+	21.2093i	−0.552618	+	0.957162i	0.445467	+	0.895298i	$0.353038\pi$
$491$	−12.2452	+	21.2093i	−0.552618	+	0.957162i	−0.998085	+	0.0618637i	$0.980296\pi$
$492$	4.55522	−	15.8220i	0.205365	−	0.713311i
$493$	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
$498$	1.96220	−	0.0664184i	0.0879282	−	0.00297628i
$499$	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
$501$	−0.702764	+	3.96077i	−0.0313972	+	0.176954i
$502$	−4.60944	+	2.66126i	−0.205729	+	0.118778i
$503$	−37.3797	−	3.92876i	−1.66668	−	0.175175i	−0.776289	−	0.630378i	$-0.782900\pi$
$503$	−37.3797	−	3.92876i	−1.66668	−	0.175175i	−0.890388	+	0.455203i	$0.849567\pi$
$504$	6.66897	+	1.67794i	0.297060	+	0.0747412i
$505$	−0.694831	−	6.61087i	−0.0309196	−	0.294180i
$506$	1.16653	−	1.05035i	0.0518584	−	0.0466936i
$507$	−15.9105	+	15.3317i	−0.706610	+	0.680905i
$508$	−1.05238	−	4.95106i	−0.0466918	−	0.219668i
$509$	−34.9145	−	7.42130i	−1.54756	−	0.328943i	−0.646592	−	0.762836i	$-0.723806\pi$
$509$	−34.9145	−	7.42130i	−1.54756	−	0.328943i	−0.900964	+	0.433893i	$0.857140\pi$
$510$	0.425021	+	0.0301776i	0.0188202	+	0.00133629i
$511$	4.52963	−	1.47177i	0.200379	−	0.0651071i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	−9.72704	+	7.01949i	−0.429459	+	0.309918i
$514$	−27.6917	−	5.88605i	−1.22143	−	0.259622i
$515$	1.53272	+	7.21086i	0.0675396	+	0.317749i
$516$	−1.37911	−	1.43118i	−0.0607121	−	0.0630041i
$517$	16.1775	−	14.5663i	0.711486	−	0.640625i
$518$	1.12549	+	10.7083i	0.0494510	+	0.470495i
$519$	25.7831	+	17.4311i	1.13175	+	0.765141i
$520$	0.490484	+	0.0515519i	0.0215091	+	0.00226070i
$521$	−0.179023	+	0.103359i	−0.00784315	+	0.00452825i	−0.503916	−	0.863752i	$-0.668108\pi$
$521$	−0.179023	+	0.103359i	−0.00784315	+	0.00452825i	0.496073	+	0.868281i	$0.334775\pi$
$522$	2.90660	−	0.506097i	0.127218	−	0.0221513i
$523$	−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
$525$	−0.134315	−	3.96806i	−0.00586197	−	0.173180i
$526$		−	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
$531$	−2.96658	−	43.7706i	−0.128739	−	1.89948i
$532$	2.64586	−	4.58277i	0.114713	−	0.198688i
$533$	2.34408	+	4.06007i	0.101533	+	0.175861i
$534$	−23.6651	+	5.87346i	−1.02409	+	0.254170i
$535$	8.00545	−	5.81630i	0.346106	−	0.251461i
$536$	−9.82618	+	1.03277i	−0.424427	+	0.0446090i
$537$	1.56918	+	0.836505i	0.0677152	+	0.0360979i
$538$	−7.36305	−	16.5377i	−0.317444	−	0.712990i
$539$	−8.97703	+	1.90813i	−0.386668	+	0.0821888i
$540$	3.85031	+	3.48929i	0.165691	+	0.150155i
$541$	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
$543$	0.101102	−	0.0788150i	0.00433868	−	0.00338228i
$544$	0.100059	−	0.224735i	0.00428998	−	0.00963545i
$545$	−3.61792	+	17.0210i	−0.154974	+	0.729098i
$546$	−1.66168	+	1.03586i	−0.0711134	+	0.0443308i
$547$	−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
$549$	−24.3146	+	25.0709i	−1.03772	+	1.07000i
$550$	−3.09052	−	4.25373i	−0.131780	−	0.181380i
$551$	0.237309	−	2.25785i	0.0101097	−	0.0961875i
$552$	0.332806	−	0.395761i	0.0141651	−	0.0168447i
$553$	−7.22015	−	4.16856i	−0.307032	−	0.177265i
$554$	−16.8416	−	12.2362i	−0.715532	−	0.519865i
$555$	−3.05579	+	7.54010i	−0.129711	+	0.320060i
$556$	16.8089	+	5.46155i	0.712857	+	0.231621i
$557$	45.6302			1.93341			0.966707	−	0.255886i	$-0.0823672\pi$
$557$	45.6302			1.93341			0.966707	+	0.255886i	$0.0823672\pi$
$558$	0.386484	−	16.6988i	0.0163612	−	0.706917i
$559$	0.565927			0.0239362
$560$	−2.18008	−	0.708351i	−0.0921253	−	0.0299333i
$561$	−0.841470	+	2.07631i	−0.0355269	+	0.0876618i
$562$	−15.7966	−	11.4769i	−0.666341	−	0.484125i
$563$	−39.2662	−	22.6703i	−1.65487	−	0.955441i	−0.975027	−	0.222085i	$-0.928714\pi$
$563$	−39.2662	−	22.6703i	−1.65487	−	0.955441i	−0.679845	−	0.733356i	$-0.737953\pi$
$564$	4.61538	−	5.48845i	0.194342	−	0.231105i
$565$	−1.04719	+	9.96336i	−0.0440557	+	0.419162i
$566$	7.29076	+	10.0349i	0.306454	+	0.421797i
$567$	−20.5739	−	1.52722i	−0.864021	−	0.0641374i
$568$	−4.34727	−	4.82813i	−0.182407	−	0.202584i
$569$	13.9160	−	6.19581i	0.583390	−	0.259742i	−0.0937505	−	0.995596i	$-0.529886\pi$
$569$	13.9160	−	6.19581i	0.583390	−	0.259742i	0.677140	+	0.735854i	$0.263219\pi$
$570$	3.39315	−	2.11523i	0.142123	−	0.0885970i
$571$	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
$573$	1.90646	−	1.48621i	0.0796435	−	0.0620872i
$574$	−6.73351	−	20.7236i	−0.281051	−	0.864987i
$575$	−0.272734	−	0.121429i	−0.0113738	−	0.00506394i
$576$	2.65185	−	1.40274i	0.110494	−	0.0584475i
$577$	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
$579$	−24.6726	−	13.1526i	−1.02536	−	0.546602i
$580$	−0.978055	+	0.102798i	−0.0406115	+	0.00426844i
$581$	2.10211	−	1.52727i	0.0872102	−	0.0633619i
$582$	6.16423	−	1.52991i	0.255516	−	0.0634167i
$583$	12.6817	+	21.9654i	0.525223	+	0.909714i
$584$	1.03887	−	1.79937i	0.0429886	−	0.0744585i
$585$	−1.47617	+	0.100048i	−0.0610321	+	0.00413648i
$586$	15.8274	−	17.5781i	0.653823	−	0.726144i
$587$	−0.253816	+	0.781166i	−0.0104761	+	0.0322422i	−0.956158	−	0.292852i	$-0.905396\pi$
$587$	−0.253816	+	0.781166i	−0.0104761	+	0.0322422i	0.945682	+	0.325094i	$0.105396\pi$
$588$	−2.84205	+	1.03098i	−0.117204	+	0.0425167i
$589$	−12.2782	−	3.80148i	−0.505914	−	0.156637i
$590$			14.6237i			0.602047i
$591$	1.29557	+	38.2749i	0.0532925	+	1.57442i
$592$	3.49070	+	3.14304i	0.143467	+	0.129178i
$593$	−18.8065	+	25.8850i	−0.772292	+	1.06297i	0.223799	+	0.974635i	$0.428154\pi$
$593$	−18.8065	+	25.8850i	−0.772292	+	1.06297i	−0.996091	+	0.0883335i	$0.971846\pi$
$594$	−23.7043	+	13.5844i	−0.972599	+	0.557373i
$595$	0.488358	−	0.281954i	0.0200207	−	0.0115590i
$596$	9.52786	+	1.00142i	0.390276	+	0.0410197i
$597$	12.1896	+	8.24097i	0.498886	+	0.337281i
$598$	0.0153905	+	0.146431i	0.000629366	+	0.00598801i
$599$	−16.6153	+	14.9605i	−0.678883	+	0.611269i	−0.934692	−	0.355458i	$-0.884325\pi$
$599$	−16.6153	+	14.9605i	−0.678883	+	0.611269i	0.255809	+	0.966727i	$0.417658\pi$
$600$	−1.20185	−	1.24722i	−0.0490653	−	0.0509176i
$601$	−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
$603$	28.5101	−	8.10912i	1.16102	−	0.330229i
$604$	−8.28912	+	2.69330i	−0.337279	+	0.109589i
$605$	15.8308	−	5.14375i	0.643615	−	0.209123i
$606$	11.4845	+	0.815432i	0.466527	+	0.0331247i
$607$	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
$609$	2.81163	−	2.70935i	0.113933	−	0.109788i
$610$	8.65142	−	7.78977i	0.350286	−	0.315399i
$611$	0.213437	+	2.03072i	0.00863475	+	0.0821541i
$612$	−0.180074	+	0.715704i	−0.00727905	+	0.0289306i
$613$	−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
$615$	2.87642	−	16.2115i	0.115988	−	0.653710i
$616$	7.08431	−	9.75071i	0.285435	−	0.392867i
$617$	23.3631	+	21.0362i	0.940563	+	0.846887i	0.988385	−	0.151969i	$-0.0485614\pi$
$617$	23.3631	+	21.0362i	0.940563	+	0.846887i	−0.0478220	+	0.998856i	$0.515228\pi$
$618$	−12.7613	+	0.431957i	−0.513335	+	0.0173758i
$619$			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
$624$	−0.236334	+	0.820878i	−0.00946095	+	0.0328614i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−12.6012	−	21.8259i	−0.503645	−	0.872338i
$627$	5.06419	+	20.4044i	0.202244	+	0.814874i
$628$	−11.2172	+	8.14975i	−0.447614	+	0.325210i
$629$	−1.14920	+	0.120785i	−0.0458215	+	0.00481603i
$630$	6.80783	+	0.971647i	0.271230	+	0.0387113i
$631$	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
$633$	−27.1328	+	3.78365i	−1.07843	+	0.150387i
$634$	28.3715	+	12.6318i	1.12678	+	0.501673i
$635$	−1.56414	−	4.81394i	−0.0620711	−	0.191035i
$636$	5.13692	+	6.58949i	0.203692	+	0.261290i
$637$	0.350138	−	0.786423i	0.0138730	−	0.0311592i
$638$	1.07508	−	5.05785i	0.0425628	−	0.200242i
$639$	15.3331	+	12.0325i	0.606570	+	0.475999i
$640$	−0.913545	+	0.406737i	−0.0361111	+	0.0160777i
$641$	−10.2974	−	11.4364i	−0.406723	−	0.451711i	0.504631	−	0.863335i	$-0.331628\pi$
$641$	−10.2974	−	11.4364i	−0.406723	−	0.451711i	−0.911354	+	0.411624i	$0.864962\pi$
$642$	7.49681	+	15.4126i	0.295875	+	0.608286i
$643$	−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
$645$	−1.52116	−	1.27918i	−0.0598956	−	0.0503677i
$646$	0.491817	+	0.283950i	0.0193503	+	0.0111719i
$647$	9.04964	+	6.57495i	0.355778	+	0.258488i	0.751289	−	0.659973i	$-0.229432\pi$
$647$	9.04964	+	6.57495i	0.355778	+	0.258488i	−0.395511	+	0.918461i	$0.629432\pi$
$648$	−7.11576	+	5.51053i	−0.279533	+	0.216474i
$649$	−73.1266	−	23.7603i	−2.87047	−	0.932672i
$650$	0.493185			0.0193443
$651$	−11.9540	−	18.5949i	−0.468515	−	0.728793i
$652$	0.914720			0.0358232
$653$	30.2394	+	9.82539i	1.18336	+	0.384497i	0.833614	−	0.552347i	$-0.186268\pi$
$653$	30.2394	+	9.82539i	1.18336	+	0.384497i	0.349746	+	0.936844i	$0.386268\pi$
$654$	−27.9330	−	11.3205i	−1.09227	−	0.442665i
$655$	5.61898	+	4.08243i	0.219552	+	0.159514i
$656$	−8.23234	−	4.75295i	−0.321419	−	0.185571i
$657$	−2.14442	+	5.85272i	−0.0836617	+	0.228336i
$658$	0.992034	−	9.43857i	0.0386735	−	0.367954i
$659$	15.4621	+	21.2818i	0.602320	+	0.829022i	0.995918	−	0.0902606i	$-0.0287700\pi$
$659$	15.4621	+	21.2818i	0.602320	+	0.829022i	−0.393599	+	0.919282i	$0.628770\pi$
$660$	8.18954	−	3.98346i	0.318778	−	0.155056i
$661$	−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
$663$	−0.111167	−	0.178329i	−0.00431738	−	0.00692574i
$664$	0.235673	−	1.10875i	0.00914589	−	0.0430280i
$665$	2.15234	−	4.83424i	0.0834642	−	0.187464i
$666$	−11.9343	−	7.49298i	−0.462446	−	0.290347i
$667$	−0.0907278	−	0.279231i	−0.00351299	−	0.0108119i
$668$	2.12168	+	0.944634i	0.0820904	+	0.0365490i
$669$	2.56210	+	18.3730i	0.0990564	+	0.710340i
$670$	−9.66440	+	2.05423i	−0.373368	+	0.0793619i
$671$	24.8966	+	55.9186i	0.961121	+	2.15871i
$672$	1.86771	−	3.50360i	0.0720485	−	0.135154i
$673$	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
$675$	4.19394	+	3.06771i	0.161425	+	0.118076i
$676$	6.37838	+	11.0477i	0.245322	+	0.424911i
$677$	13.3581	−	23.1369i	0.513394	−	0.889224i	−0.486486	−	0.873689i	$-0.661721\pi$
$677$	13.3581	−	23.1369i	0.513394	−	0.889224i	0.999879	−	0.0155355i	$-0.00494531\pi$
$678$	−16.6748	−	4.80074i	−0.640391	−	0.184371i
$679$	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	$-0.219823\pi$
$684$	2.58059	+	6.42677i	0.0986714	+	0.245734i
$685$	5.50569	+	4.95735i	0.210362	+	0.189411i
$686$	−11.7834	+	16.2184i	−0.449891	+	0.619221i
$687$	−34.4554	−	6.11346i	−1.31456	−	0.233243i
$688$	−0.993759	+	0.573747i	−0.0378867	+	0.0218739i
$689$	−2.36603	−	0.248680i	−0.0901386	−	0.00947395i
$690$	0.289614	−	0.428381i	0.0110254	−	0.0163082i
$691$	−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
$693$	−15.9200	+	32.4643i	−0.604751	+	1.23322i
$694$	−2.57582	−	12.1183i	−0.0977769	−	0.460004i
$695$	17.2877	+	3.67462i	0.655761	+	0.139386i
$696$	0.120640	−	1.69909i	0.00457286	−	0.0644040i
$697$	2.22403	−	0.722631i	0.0842411	−	0.0273716i
$698$	−8.44929	+	2.74534i	−0.319810	+	0.103913i
$699$	−1.78097	+	25.0832i	−0.0673625	+	0.948732i
$700$	−2.24218	−	0.476590i	−0.0847465	−	0.0180134i
$701$	0.149227	+	0.702060i	0.00563624	+	0.0265164i	0.980876	−	0.194634i	$-0.0623520\pi$
$701$	0.149227	+	0.702060i	0.00563624	+	0.0265164i	−0.975240	+	0.221151i	$0.929019\pi$
$702$	0.276055	−	2.54775i	0.0104190	−	0.0961588i
$703$	−8.05830	+	7.25573i	−0.303925	+	0.273655i
$704$	−0.549600	−	5.22910i	−0.0207138	−	0.197079i
$705$	4.01640	−	5.94082i	0.151266	−	0.223744i
$706$	0.528266	+	0.0555230i	0.0198815	+	0.00208963i
$707$	13.1960	−	7.61870i	0.496286	−	0.286531i
$708$	−24.9394	−	4.42503i	−0.937281	−	0.166303i
$709$	−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
$711$	10.1254	−	4.06572i	0.379731	−	0.152476i
$712$			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
$717$	−13.7066	−	3.94620i	−0.511884	−	0.147374i
$718$	10.4343	−	18.0727i	0.389405	−	0.674469i
$719$	−5.47011	−	9.47450i	−0.204001	−	0.353339i	0.745813	−	0.666155i	$-0.232061\pi$
$719$	−5.47011	−	9.47450i	−0.204001	−	0.353339i	−0.949814	+	0.312816i	$0.898728\pi$
$720$	2.49070	−	1.67225i	0.0928229	−	0.0623211i
$721$	−13.6712	+	9.93272i	−0.509142	+	0.369914i
$722$	−13.5959	+	1.42899i	−0.505987	+	0.0531814i
$723$	24.8062	−	46.5334i	0.922552	−	1.73059i
$724$	−0.0301034	−	0.0676133i	−0.00111878	−	0.00251283i
$725$	−0.961952	+	0.204469i	−0.0357260	+	0.00759379i
$726$	3.98192	+	28.5546i	0.147783	+	1.05976i
$727$	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
$729$	18.1950	−	19.9484i	0.673890	−	0.738831i
$730$	0.845091	−	1.89810i	0.0312782	−	0.0702520i
$731$	0.0586909	−	0.276119i	0.00217076	−	0.0102126i
$732$	10.6669	+	17.1114i	0.394261	+	0.632455i
$733$	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
$735$	−2.71871	+	1.32240i	−0.100281	+	0.0487776i
$736$	−0.175480	−	0.241527i	−0.00646828	−	0.00890282i
$737$	5.43022	−	51.6651i	0.200025	−	1.90311i
$738$	26.7769	+	9.81097i	0.985671	+	0.361147i
$739$	−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
$741$	−1.82759	−	0.740673i	−0.0671383	−	0.0272093i
$742$	10.5164	+	3.41700i	0.386071	+	0.125442i
$743$	22.1651			0.813159			0.406579	−	0.913615i	$-0.366721\pi$
$743$	22.1651			0.813159			0.406579	+	0.913615i	$0.366721\pi$
$744$	−9.30343	−	2.53894i	−0.341080	−	0.0930819i
$745$	9.58034			0.350996
$746$	3.78923	+	1.23120i	0.138734	+	0.0450773i
$747$	−0.125955	+	3.39824i	−0.00460844	+	0.124335i
$748$	1.04643	+	0.760278i	0.0382614	+	0.0277985i
$749$	19.6438	+	11.3413i	0.717768	+	0.414404i
$750$	−1.32564	−	1.11476i	−0.0484054	−	0.0407053i
$751$	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
$753$	−4.03242	−	8.29019i	−0.146949	−	0.302111i
$754$	0.324541	+	0.360440i	0.0118191	+	0.0131264i
$755$	−7.96218	+	3.54499i	−0.289773	+	0.129015i
$756$	−3.71706	+	11.3162i	−0.135188	+	0.411565i
$757$	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
$759$	1.67158	+	2.14426i	0.0606746	+	0.0778316i
$760$	−0.713368	−	2.19552i	−0.0258766	−	0.0796399i
$761$	−24.3098	−	10.8234i	−0.881229	−	0.392348i	−0.0843135	−	0.996439i	$-0.526870\pi$
$761$	−24.3098	−	10.8234i	−0.881229	−	0.392348i	−0.796915	+	0.604091i	$0.793536\pi$
$762$	8.68305	−	1.21085i	0.314554	−	0.0438643i
$763$	−39.0167	+	8.29325i	−1.41250	+	0.300236i
$764$	−0.567656	−	1.27498i	−0.0205371	−	0.0461271i
$765$	−0.104276	+	0.730607i	−0.00377010	+	0.0264151i
$766$	−37.5522	+	3.94690i	−1.35682	+	0.142607i
$767$	5.83478	−	4.23922i	0.210682	−	0.153069i
$768$	−0.417222	−	1.68105i	−0.0150552	−	0.0606596i
$769$	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
$771$	13.5663	−	47.1209i	0.488579	−	1.69702i
$772$	−10.8014	+	11.9961i	−0.388749	+	0.431750i
$773$	6.01898	−	18.5245i	0.216488	−	0.666280i	−0.782557	−	0.622579i	$-0.786085\pi$
$773$	6.01898	−	18.5245i	0.216488	−	0.666280i	0.999045	−	0.0437014i	$-0.0139150\pi$
$774$	2.64183	−	2.20713i	0.0949585	−	0.0793338i
$775$	0.0774309	+	5.56723i	0.00278140	+	0.199981i
$776$		−	3.66690i		−	0.131634i
$777$	−18.6388	+	0.630903i	−0.668662	+	0.0226335i
$778$	21.3889	+	19.2587i	0.766830	+	0.690457i
$779$	12.8986	−	17.7534i	0.462141	−	0.636082i
$780$	−0.149235	+	0.841085i	−0.00534346	+	0.0301157i
$781$	29.5834	−	17.0800i	1.05858	−	0.611171i
$782$	0.0730406	+	0.00767688i	0.00261193	+	0.000274525i
$783$	0.517828	+	5.08381i	0.0185057	+	0.181681i
$784$	0.182453	+	1.73592i	0.00651617	+	0.0619972i
$785$	−10.3038	+	9.27761i	−0.367760	+	0.331132i
$786$	−8.66249	+	8.34737i	−0.308981	+	0.297741i
$787$	−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
$789$	18.7886	+	1.33404i	0.668893	+	0.0474932i
$790$	−3.45904	+	1.12391i	−0.123067	+	0.0399869i
$791$	−21.8406	+	7.09643i	−0.776561	+	0.252320i
$792$	4.31535	+	15.1719i	0.153339	+	0.539111i
$793$	−5.61602	−	1.19372i	−0.199431	−	0.0423903i
$794$	−5.81915	−	27.3770i	−0.206514	−	0.971572i
$795$	5.79757	+	6.01643i	0.205619	+	0.213381i
$796$	6.31308	−	5.68432i	0.223761	−	0.201475i
$797$	4.38422	+	41.7131i	0.155297	+	1.47755i	0.743444	+	0.668798i	$0.233191\pi$
$797$	4.38422	+	41.7131i	0.155297	+	1.47755i	−0.588147	+	0.808754i	$0.700142\pi$
$798$	7.59309	+	5.13344i	0.268792	+	0.181722i
$799$	1.01293	+	0.106464i	0.0358350	+	0.00376641i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	−7.24456	−	41.6067i	−0.255974	−	1.47010i
$802$	9.65253	−	13.2856i	0.340843	−	0.469130i
$803$	8.11850	+	7.30993i	0.286496	+	0.257962i
$804$	−0.578932	−	17.1034i	−0.0204174	−	0.603191i
$805$		−	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	$0.478127\pi$
$809$	−26.4716	+	29.3997i	−0.930691	+	1.03364i	−0.999352	+	0.0359968i	$0.988539\pi$
$810$	−6.50077	+	6.22414i	−0.228414	+	0.218694i
$811$	−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
$813$	−21.0087	+	5.21417i	−0.736807	+	0.182869i
$814$	−19.9806	+	14.5168i	−0.700320	+	0.508812i
$815$	0.909709	−	0.0956143i	0.0318657	−	0.00334922i
$816$	0.376001	+	0.200440i	0.0131627	+	0.00701680i
$817$	−1.07744	−	2.41998i	−0.0376950	−	0.0846644i
$818$	5.40827	−	1.14956i	0.189096	−	0.0401936i
$819$	−1.58582	−	2.99796i	−0.0554130	−	0.104757i
$820$	−8.68406	−	3.86639i	−0.303261	−	0.135020i
$821$	−7.94002	−	24.4369i	−0.277109	−	0.852853i	−0.988654	−	0.150212i	$-0.952004\pi$
$821$	−7.94002	−	24.4369i	−0.277109	−	0.852853i	0.711545	−	0.702640i	$-0.247996\pi$
$822$	−10.1203	+	7.88943i	−0.352987	+	0.275175i
$823$	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
$825$	7.72829	−	4.81768i	0.269065	−	0.167730i
$826$	−30.6234	+	13.6344i	−1.06552	+	0.474402i
$827$	−4.15360	−	4.61304i	−0.144435	−	0.160411i	0.666587	−	0.745428i	$-0.267755\pi$
$827$	−4.15360	−	4.61304i	−0.144435	−	0.160411i	−0.811021	+	0.585016i	$0.801088\pi$
$828$	0.642931	+	0.623537i	0.0223434	+	0.0216694i
$829$	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
$831$	23.2064	−	27.5963i	0.805022	−	0.957305i
$832$	0.427111	+	0.246593i	0.0148074	+	0.00854906i
$833$	−0.347388	−	0.252392i	−0.0120363	−	0.00874487i
$834$	−11.4979	+	28.3708i	−0.398140	+	0.982401i
$835$	2.20880	+	0.717683i	0.0764387	+	0.0248364i
$836$	12.1379			0.419798
$837$	28.8032	+	2.71620i	0.995583	+	0.0938855i
$838$	6.26133			0.216294
$839$	46.3048	+	15.0454i	1.59862	+	0.519423i	0.966766	−	0.255664i	$-0.0822940\pi$
$839$	46.3048	+	15.0454i	1.59862	+	0.519423i	0.631854	+	0.775087i	$0.282294\pi$
$840$	1.49125	−	3.67963i	0.0514531	−	0.126959i
$841$	22.6790	+	16.4773i	0.782036	+	0.568182i
$842$	6.48067	+	3.74161i	0.223339	+	0.128945i
$843$	21.7665	−	25.8840i	0.749678	−	0.891492i
$844$	−1.65330	+	15.7301i	−0.0569089	+	0.541452i
$845$	7.49824	+	10.3204i	0.257947	+	0.355034i
$846$	8.91623	+	8.64727i	0.306546	+	0.297299i
$847$	25.5314	+	28.3555i	0.877269	+	0.974306i
$848$	4.40683	−	1.96205i	0.151331	−	0.0673770i
$849$	−18.2316	+	11.3653i	−0.625708	+	0.390055i
$850$	0.0511470	−	0.240628i	0.00175433	−	0.00825346i
$851$	−0.570376	+	1.28109i	−0.0195522	+	0.0439150i
$852$	8.87486	−	6.91851i	0.304048	−	0.237024i
$853$	−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
$855$	3.23824	+	6.12182i	0.110745	+	0.209362i
$856$	9.67905	−	2.05735i	0.330823	−	0.0703186i
$857$	5.20493	+	11.6905i	0.177797	+	0.399339i	0.980357	−	0.197233i	$-0.0631956\pi$
$857$	5.20493	+	11.6905i	0.177797	+	0.399339i	−0.802559	+	0.596572i	$0.796529\pi$
$858$	−3.96342	−	2.11284i	−0.135309	−	0.0721310i
$859$	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
$861$	36.6302	−	9.09130i	1.24835	−	0.309831i
$862$	12.6469	+	21.9050i	0.430754	+	0.746088i
$863$	2.23790	−	3.87616i	0.0761790	−	0.131946i	−0.825419	−	0.564520i	$-0.809061\pi$
$863$	2.23790	−	3.87616i	0.0761790	−	0.131946i	0.901598	+	0.432574i	$0.142395\pi$
$864$	2.09821	+	4.75368i	0.0713825	+	0.161724i
$865$	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
$870$	−0.0576244	−	1.70240i	−0.00195365	−	0.0577167i
$871$	3.62121	+	3.26056i	0.122700	+	0.110480i
$872$	−10.2282	+	14.0779i	−0.346370	+	0.476737i
$873$	1.88705	+	10.8376i	0.0638669	+	0.366798i
$874$	0.596858	−	0.344596i	0.0201890	−	0.0116561i
$875$	−2.27972	−	0.239608i	−0.0770685	−	0.00810022i
$876$	2.98134	+	2.01558i	0.100730	+	0.0681003i
$877$	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
$879$	28.4281	+	29.5013i	0.958857	+	0.995055i
$880$	−1.09318	−	5.14300i	−0.0368511	−	0.173371i
$881$	−36.4811	−	7.75430i	−1.22908	−	0.261249i	−0.452786	−	0.891619i	$-0.649570\pi$
$881$	−36.4811	−	7.75430i	−1.22908	−	0.261249i	−0.776294	+	0.630370i	$0.782903\pi$
$882$	−1.43258	−	5.03668i	−0.0482375	−	0.169594i
$883$	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
$885$	−25.2654	−	1.79391i	−0.849285	−	0.0603015i
$886$	19.7292	+	4.19357i	0.662815	+	0.140886i
$887$	1.18091	+	5.55576i	0.0396512	+	0.186544i	0.993516	−	0.113692i	$-0.0362678\pi$
$887$	1.18091	+	5.55576i	0.0396512	+	0.186544i	−0.953865	+	0.300236i	$0.902934\pi$
$888$	−5.85844	+	5.64532i	−0.196596	+	0.189445i
$889$	8.62251	−	7.76374i	0.289190	−	0.260388i
$890$	1.47151	+	14.0004i	0.0493250	+	0.469296i
$891$	−20.5619	−	42.6204i	−0.688849	−	1.42784i
$892$	10.6516	+	1.11953i	0.356642	+	0.0374846i
$893$	8.27728	−	4.77889i	0.276989	−	0.159919i
$894$	−2.89895	+	16.3384i	−0.0969553	+	0.546439i
$895$	0.603454	−	0.830583i	0.0201712	−	0.0277633i
$896$	−1.70349	−	1.53383i	−0.0569096	−	0.0512417i
$897$	−0.254877	+	0.00862733i	−0.00851010	+	0.000288058i
$898$			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
$903$	1.26047	−	4.37810i	0.0419459	−	0.145694i
$904$	−5.00912	+	8.67605i	−0.166601	+	0.288561i
$905$	−0.0370060	−	0.0640963i	−0.00123012	−	0.00213063i
$906$	−3.63637	−	14.6515i	−0.120810	−	0.486764i
$907$	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
$909$	−2.81765	+	19.7418i	−0.0934554	+	0.654794i
$910$	0.459822	+	1.03278i	0.0152430	+	0.0342362i
$911$	12.8223	−	2.72546i	0.424822	−	0.0902987i	0.00946067	−	0.999955i	$-0.496989\pi$
$911$	12.8223	−	2.72546i	0.424822	−	0.0902987i	0.415361	+	0.909657i	$0.363655\pi$
$912$	3.96013	−	0.552238i	0.131133	−	0.0182864i
$913$	5.44470	+	2.42413i	0.180193	+	0.0802272i
$914$	−8.70592	−	26.7941i	−0.287966	−	0.886269i
$915$	12.3971	+	15.9026i	0.409836	+	0.525725i
$916$	−8.21752	+	18.4569i	−0.271515	+	0.609832i
$917$	−3.31013	+	15.5729i	−0.109310	+	0.514264i
$918$	−1.21443	−	0.398910i	−0.0400823	−	0.0131660i
$919$	−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
$921$	−1.87791	−	3.86078i	−0.0618793	−	0.127217i
$922$	15.2041	+	20.9266i	0.500719	+	0.689181i
$923$	−0.334927	+	3.18662i	−0.0110243	+	0.104889i
$924$	15.9773	+	13.4357i	0.525614	+	0.442002i
$925$	4.06789	+	2.34860i	0.133751	+	0.0772215i
$926$	−12.6146	−	9.16502i	−0.414540	−	0.301181i
$927$	0.819155	−	22.1007i	0.0269046	−	0.725882i
$928$	−0.935309	−	0.303900i	−0.0307030	−	0.00997602i
$929$	56.9658			1.86899			0.934493	−	0.355980i	$-0.115853\pi$
$929$	56.9658			1.86899			0.934493	+	0.355980i	$0.115853\pi$
$930$	−9.51786	−	1.55255i	−0.312103	−	0.0509102i
$931$	−4.02946			−0.132060
$932$	13.8077	+	4.48638i	0.452285	+	0.146956i
$933$	−19.4417	−	7.87917i	−0.636492	−	0.257952i
$934$	−29.2848	−	21.2766i	−0.958226	−	0.696192i
$935$	1.12017	+	0.646731i	0.0366335	+	0.0211504i
$936$	−1.38924	−	0.509014i	−0.0454088	−	0.0166376i
$937$	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
$939$	39.2544	−	19.0937i	1.28102	−	0.623098i
$940$	−2.77036	−	3.07680i	−0.0903593	−	0.100354i
$941$	2.61682	−	1.16508i	0.0853059	−	0.0379806i	−0.363640	−	0.931540i	$-0.618466\pi$
$941$	2.61682	−	1.16508i	0.0853059	−	0.0379806i	0.448946	+	0.893559i	$0.351800\pi$
$942$	−12.7043	−	20.3797i	−0.413929	−	0.664005i
$943$	0.590039	−	2.77592i	0.0192143	−	0.0903962i
$944$	−5.94799	+	13.3594i	−0.193590	+	0.434811i
$945$	−2.51384	+	11.6427i	−0.0817753	+	0.378737i
$946$	−1.86443	−	5.73811i	−0.0606177	−	0.186562i
$947$	−40.8152	−	18.1721i	−1.32632	−	0.590514i	−0.383411	−	0.923578i	$-0.625251\pi$
$947$	−40.8152	−	18.1721i	−1.32632	−	0.590514i	−0.942904	+	0.333064i	$0.891917\pi$
$948$	−0.870050	−	6.23919i	−0.0282579	−	0.202639i
$949$	−1.00232	+	0.213049i	−0.0325365	+	0.00691586i
$950$	−0.938954	−	2.10893i	−0.0304637	−	0.0684226i
$951$	−25.3043	+	47.4679i	−0.820550	+	1.53925i
$952$	0.560818	−	0.0589444i	0.0181762	−	0.00191040i
$953$	19.5581	−	14.2098i	0.633548	−	0.460300i	−0.224080	−	0.974571i	$-0.571938\pi$
$953$	19.5581	−	14.2098i	0.633548	−	0.460300i	0.857628	+	0.514271i	$0.171938\pi$
$954$	−12.0148	+	8.06672i	−0.388994	+	0.261170i
$955$	−0.697818	−	1.20866i	−0.0225809	−	0.0391112i
$956$	−4.11749	+	7.13170i	−0.133169	+	0.230656i
$957$	8.60657	+	2.47787i	0.278211	+	0.0800981i
$958$	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
$963$	−27.5480	+	11.0616i	−0.887722	+	0.356454i
$964$	−22.6251	−	20.3717i	−0.728705	−	0.656129i
$965$	−9.48825	+	13.0595i	−0.305437	+	0.420399i
$966$	1.16709	+	0.207078i	0.0375506	+	0.00666264i
$967$	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
$969$	−0.550913	+	0.814879i	−0.0176979	+	0.0261777i
$970$	−0.383295	−	3.64681i	−0.0123069	−	0.117092i
$971$	−36.7171	+	33.0602i	−1.17831	+	1.06095i	−0.181317	+	0.983425i	$0.558036\pi$
$971$	−36.7171	+	33.0602i	−1.17831	+	1.06095i	−0.996990	+	0.0775274i	$0.975297\pi$
$972$	−8.64765	−	12.9699i	−0.277374	−	0.416009i
$973$	8.42323	+	39.6282i	0.270036	+	1.27042i
$974$	29.2779	+	6.22320i	0.938124	+	0.199404i
$975$	−0.0604997	+	0.852077i	−0.00193754	+	0.0272883i
$976$	11.0718	−	3.59746i	0.354401	−	0.115152i
$977$	−17.8663	+	5.80511i	−0.571593	+	0.185722i	−0.580531	−	0.814238i	$-0.697155\pi$
$977$	−17.8663	+	5.80511i	−0.571593	+	0.185722i	0.00893793	+	0.999960i	$0.497155\pi$
$978$	−0.112210	+	1.58036i	−0.00358808	+	0.0505344i
$979$	−72.4009	−	15.3893i	−2.31394	−	0.491844i
$980$	0.362906	+	1.70734i	0.0115926	+	0.0545390i
$981$	22.9850	−	46.8712i	0.733854	−	1.49648i
$982$	−18.1999	+	16.3873i	−0.580782	+	0.522939i
$983$	4.54950	+	43.2856i	0.145106	+	1.38059i	0.788488	+	0.615050i	$0.210864\pi$
$983$	4.54950	+	43.2856i	0.145106	+	1.38059i	−0.643382	+	0.765545i	$0.722469\pi$
$984$	9.22154	−	13.6400i	0.293972	−	0.434827i
$985$	21.9896	+	2.31120i	0.700646	+	0.0736409i
$986$	0.209518	−	0.120965i	0.00667240	−	0.00385231i
$987$	16.1853	+	2.87178i	0.515185	+	0.0914098i
$988$	−0.669206	+	0.921083i	−0.0212903	+	0.0293036i
$989$	−0.254585	−	0.229229i	−0.00809533	−	0.00728907i
$990$	5.87761	+	14.6377i	0.186803	+	0.465218i
$991$			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
$996$	1.88669	+	0.543185i	0.0597820	+	0.0172115i
$997$	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
$999$	14.4096	−	19.6998i	0.455900	−	0.623274i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.650557 + 1.60523i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.11476 + 1.32564i) q^{6} +(-0.239608 + 2.27972i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.15355 - 2.08859i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.650557 + 1.60523i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.11476 + 1.32564i) q^{6} +(-0.239608 + 2.27972i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.15355 - 2.08859i) q^{9} +(0.669131 + 0.743145i) q^{10} +(-4.80333 + 2.13858i) q^{11} +(-1.46984 + 0.916274i) q^{12} +(0.102539 - 0.482408i) q^{13} +(-0.932352 + 2.09410i) q^{14} +(-1.36602 + 1.06490i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.224735 - 0.100059i) q^{17} +(-1.40274 - 2.65185i) q^{18} +(-2.25806 + 0.479966i) q^{19} +(0.406737 + 0.913545i) q^{20} +(-3.50360 - 1.86771i) q^{21} +(-5.22910 + 0.549600i) q^{22} +(-0.241527 + 0.175480i) q^{23} +(-1.68105 + 0.417222i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.246593 - 0.427111i) q^{26} +(4.75368 - 2.09821i) 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} +(-0.308084 - 9.10174i) q^{33} +(-0.182816 - 0.164608i) q^{34} +(-1.34736 + 1.85449i) q^{35} +(-0.514618 - 2.95553i) q^{36} +(4.06789 - 2.34860i) q^{37} +(-2.29586 - 0.241305i) q^{38} +(0.707670 + 0.478433i) q^{39} +(0.104528 + 0.994522i) q^{40} +(-7.06425 + 6.36068i) q^{41} +(-2.75497 - 2.85897i) q^{42} +(0.238577 + 1.12242i) q^{43} +(-5.14300 - 1.09318i) q^{44} +(-0.820736 - 2.88555i) q^{45} +(-0.283933 + 0.0922553i) q^{46} +(-3.93760 + 1.27940i) q^{47} +(-1.72770 - 0.122671i) q^{48} +(1.70734 + 0.362906i) q^{49} +(0.207912 + 0.978148i) q^{50} +(0.306821 - 0.295659i) q^{51} +(0.366508 - 0.330005i) q^{52} +(-0.504232 - 4.79745i) q^{53} +(5.16941 - 0.526546i) q^{54} +(-5.22910 - 0.549600i) q^{55} +(-1.98517 + 1.14614i) q^{56} +(0.698539 - 3.93696i) q^{57} +(-0.578053 + 0.795622i) q^{58} +(10.8675 + 9.78515i) q^{59} +(-1.73106 + 0.0585945i) 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} +(2.51959 - 8.75147i) q^{66} +(-4.94015 + 8.55660i) q^{67} +(-0.123002 - 0.213045i) q^{68} +(-0.124559 - 0.501868i) q^{69} +(-1.85449 + 1.34736i) q^{70} +(-6.46130 + 0.679110i) q^{71} +(0.423879 - 2.96990i) q^{72} +(-0.845091 - 1.89810i) q^{73} +(4.59455 - 0.976602i) q^{74} +(-1.71545 + 0.239219i) q^{75} +(-2.10893 - 0.938954i) q^{76} +(-3.72444 - 11.4627i) q^{77} +(0.525191 + 0.673699i) q^{78} +(-1.47932 + 3.32261i) q^{79} +(-0.207912 + 0.978148i) q^{80} +(0.275576 + 8.99578i) q^{81} +(-8.68406 + 3.86639i) q^{82} +(-0.758476 - 0.842373i) q^{83} +(-1.73666 - 3.57037i) q^{84} +(-0.144597 - 0.199021i) q^{85} +(-0.119946 + 1.14121i) q^{86} +(-1.30369 - 1.09630i) q^{87} +(-4.55348 - 2.62895i) q^{88} +(11.3890 + 8.27458i) q^{89} +(0.111118 - 2.99794i) q^{90} +(1.07518 + 0.349348i) q^{91} -0.298544 q^{92} +(-7.52246 + 6.03428i) q^{93} -4.14024 q^{94} +(-2.19552 - 0.713368i) q^{95} +(-1.60523 - 0.650557i) q^{96} +(-2.96658 - 2.15535i) q^{97} +(1.51163 + 0.872742i) q^{98} +(14.8108 + 5.42665i) 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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