LMFDB - Embedded newform 900.2.bj.f.163.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(127,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.127"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			163.4
Character	$\chi$	$=$	900.163
Dual form			900.2.bj.f.127.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33300 - 0.472333i) q^{2} +(1.55380 + 1.25924i) q^{4} +(-1.01218 + 1.99386i) q^{5} +(0.189838 + 0.189838i) q^{7} +(-1.47645 - 2.41249i) q^{8} +(2.29101 - 2.17974i) q^{10} +(-2.68290 + 3.69270i) q^{11} +(-1.66631 - 0.263917i) q^{13} +(-0.163389 - 0.342722i) q^{14} +(0.828612 + 3.91323i) q^{16} +(-2.52266 - 4.95101i) q^{17} +(-0.186788 + 0.574876i) q^{19} +(-4.08349 + 1.82349i) q^{20} +(5.32050 - 3.65516i) q^{22} +(3.67098 - 0.581426i) q^{23} +(-2.95097 - 4.03631i) q^{25} +(2.09654 + 1.13886i) q^{26} +(0.0559189 + 0.534025i) q^{28} +(-3.14920 + 1.02324i) q^{29} +(-6.47245 - 2.10303i) q^{31} +(0.743804 - 5.60774i) q^{32} +(1.02420 + 7.79125i) q^{34} +(-0.570663 + 0.186361i) q^{35} +(-0.372643 + 2.35278i) q^{37} +(0.520523 - 0.678086i) q^{38} +(6.30461 - 0.501950i) q^{40} +(9.30874 - 6.76320i) q^{41} +(0.00980686 - 0.00980686i) q^{43} +(-8.81871 + 2.35930i) q^{44} +(-5.16806 - 0.958880i) q^{46} +(1.17702 - 2.31002i) q^{47} -6.92792i q^{49} +(2.02718 + 6.77426i) q^{50} +(-2.25678 - 2.50836i) q^{52} +(4.53201 - 8.89456i) q^{53} +(-4.64714 - 9.08702i) q^{55} +(0.177697 - 0.738270i) q^{56} +(4.68120 + 0.123490i) q^{58} +(-3.15728 + 2.29390i) q^{59} +(-9.40115 - 6.83034i) q^{61} +(7.63448 + 5.86050i) q^{62} +(-3.64021 + 7.12382i) q^{64} +(2.21282 - 3.05526i) q^{65} +(-6.49592 + 3.30984i) q^{67} +(2.31480 - 10.8695i) q^{68} +(0.848721 + 0.0211233i) q^{70} +(-12.6076 + 4.09646i) q^{71} +(-0.770226 - 4.86301i) q^{73} +(1.60803 - 2.96025i) q^{74} +(-1.01414 + 0.658032i) q^{76} +(-1.21033 + 0.191698i) q^{77} +(4.17182 + 12.8395i) q^{79} +(-8.64116 - 2.30877i) q^{80} +(-15.6031 + 4.61855i) q^{82} +(3.42602 + 6.72394i) q^{83} +(12.4250 - 0.0185208i) q^{85} +(-0.0177047 + 0.00844049i) q^{86} +(12.8698 + 1.02040i) q^{88} +(-4.20350 + 5.78562i) q^{89} +(-0.266228 - 0.366431i) q^{91} +(6.43614 + 3.71924i) q^{92} +(-2.66007 + 2.52333i) q^{94} +(-0.957159 - 0.954310i) q^{95} +(-0.917106 - 0.467289i) q^{97} +(-3.27228 + 9.23495i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58}+ \cdots - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−1.33300	−	0.472333i	−0.942577	−	0.333990i
$2$	−1.33300	−	0.472333i	−0.942577	−	0.333990i
$3$		0			0
$3$		0			0
$4$	1.55380	+	1.25924i	0.776902	+	0.629622i
$5$	−1.01218	+	1.99386i	−0.452662	+	0.891682i
$5$	−1.01218	+	1.99386i	−0.452662	+	0.891682i
$6$		0			0
$7$	0.189838	+	0.189838i	0.0717522	+	0.0717522i	0.742072	−	0.670320i	$-0.233843\pi$
$7$	0.189838	+	0.189838i	0.0717522	+	0.0717522i	−0.670320	+	0.742072i	$0.733843\pi$
$8$	−1.47645	−	2.41249i	−0.522003	−	0.852944i
$9$		0			0
$10$	2.29101	−	2.17974i	0.724481	−	0.689295i
$11$	−2.68290	+	3.69270i	−0.808925	+	1.11339i	0.182563	+	0.983194i	$0.441561\pi$
$11$	−2.68290	+	3.69270i	−0.808925	+	1.11339i	−0.991488	+	0.130196i	$0.958439\pi$
$12$		0			0
$13$	−1.66631	−	0.263917i	−0.462151	−	0.0731975i	−0.0789825	−	0.996876i	$-0.525167\pi$
$13$	−1.66631	−	0.263917i	−0.462151	−	0.0731975i	−0.383168	+	0.923678i	$0.625167\pi$
$14$	−0.163389	−	0.342722i	−0.0436675	−	0.0915964i
$15$		0			0
$16$	0.828612	+	3.91323i	0.207153	+	0.978309i
$17$	−2.52266	−	4.95101i	−0.611836	−	1.20080i	−0.964261	−	0.264955i	$-0.914643\pi$
$17$	−2.52266	−	4.95101i	−0.611836	−	1.20080i	0.352425	−	0.935840i	$-0.385357\pi$
$18$		0			0
$19$	−0.186788	+	0.574876i	−0.0428522	+	0.131886i	−0.970194	−	0.242331i	$-0.922088\pi$
$19$	−0.186788	+	0.574876i	−0.0428522	+	0.131886i	0.927342	+	0.374216i	$0.122088\pi$
$20$	−4.08349	+	1.82349i	−0.913096	+	0.407744i
$21$		0			0
$22$	5.32050	−	3.65516i	1.13434	−	0.779283i
$23$	3.67098	−	0.581426i	0.765452	−	0.121236i	0.238514	−	0.971139i	$-0.423340\pi$
$23$	3.67098	−	0.581426i	0.765452	−	0.121236i	0.526939	+	0.849903i	$0.323340\pi$
$24$		0			0
$25$	−2.95097	−	4.03631i	−0.590194	−	0.807261i
$26$	2.09654	+	1.13886i	0.411165	+	0.223348i
$27$		0			0
$28$	0.0559189	+	0.534025i	0.0105677	+	0.100921i
$29$	−3.14920	+	1.02324i	−0.584791	+	0.190010i	−0.586446	−	0.809988i	$-0.699473\pi$
$29$	−3.14920	+	1.02324i	−0.584791	+	0.190010i	0.00165467	+	0.999999i	$0.499473\pi$
$30$		0			0
$31$	−6.47245	−	2.10303i	−1.16249	−	0.377715i	−0.336653	−	0.941629i	$-0.609295\pi$
$31$	−6.47245	−	2.10303i	−1.16249	−	0.377715i	−0.825834	+	0.563914i	$0.809295\pi$
$32$	0.743804	−	5.60774i	0.131487	−	0.991318i
$33$		0			0
$34$	1.02420	+	7.79125i	0.175649	+	1.33619i
$35$	−0.570663	+	0.186361i	−0.0964596	+	0.0315007i
$36$		0			0
$37$	−0.372643	+	2.35278i	−0.0612621	+	0.386794i	0.937938	+	0.346803i	$0.112733\pi$
$37$	−0.372643	+	2.35278i	−0.0612621	+	0.386794i	−0.999200	+	0.0399907i	$0.987267\pi$
$38$	0.520523	−	0.678086i	0.0844399	−	0.110000i
$39$		0			0
$40$	6.30461	−	0.501950i	0.996846	−	0.0793652i
$41$	9.30874	−	6.76320i	1.45378	−	1.05623i	0.468852	−	0.883277i	$-0.344668\pi$
$41$	9.30874	−	6.76320i	1.45378	−	1.05623i	0.984929	−	0.172957i	$-0.0553323\pi$
$42$		0			0
$43$	0.00980686	−	0.00980686i	0.00149553	−	0.00149553i	−0.706359	−	0.707854i	$-0.749663\pi$
$43$	0.00980686	−	0.00980686i	0.00149553	−	0.00149553i	0.707854	+	0.706359i	$0.249663\pi$
$44$	−8.81871	+	2.35930i	−1.32947	+	0.355678i
$45$		0			0
$46$	−5.16806	−	0.958880i	−0.761989	−	0.141379i
$47$	1.17702	−	2.31002i	0.171685	−	0.336952i	−0.789091	−	0.614277i	$-0.789448\pi$
$47$	1.17702	−	2.31002i	0.171685	−	0.336952i	0.960776	+	0.277325i	$0.0894479\pi$
$48$		0			0
$49$		−	6.92792i		−	0.989703i
$50$	2.02718	+	6.77426i	0.286687	+	0.958024i
$51$		0			0
$52$	−2.25678	−	2.50836i	−0.312959	−	0.347848i
$53$	4.53201	−	8.89456i	0.622519	−	1.22176i	−0.337368	−	0.941373i	$-0.609537\pi$
$53$	4.53201	−	8.89456i	0.622519	−	1.22176i	0.959886	−	0.280389i	$-0.0904634\pi$
$54$		0			0
$55$	−4.64714	−	9.08702i	−0.626621	−	1.22529i
$56$	0.177697	−	0.738270i	0.0237458	−	0.0986554i
$57$		0			0
$58$	4.68120	+	0.123490i	0.614672	+	0.0162150i
$59$	−3.15728	+	2.29390i	−0.411043	+	0.298640i	−0.774024	−	0.633156i	$-0.781759\pi$
$59$	−3.15728	+	2.29390i	−0.411043	+	0.298640i	0.362981	+	0.931797i	$0.381759\pi$
$60$		0			0
$61$	−9.40115	−	6.83034i	−1.20369	−	0.874535i	−0.209051	−	0.977905i	$-0.567038\pi$
$61$	−9.40115	−	6.83034i	−1.20369	−	0.874535i	−0.994643	+	0.103369i	$0.967038\pi$
$62$	7.63448	+	5.86050i	0.969581	+	0.744284i
$63$		0			0
$64$	−3.64021	+	7.12382i	−0.455027	+	0.890478i
$65$	2.21282	−	3.05526i	0.274467	−	0.378958i
$66$		0			0
$67$	−6.49592	+	3.30984i	−0.793603	+	0.404361i	−0.803287	−	0.595592i	$-0.796917\pi$
$67$	−6.49592	+	3.30984i	−0.793603	+	0.404361i	0.00968402	+	0.999953i	$0.496917\pi$
$68$	2.31480	−	10.8695i	0.280710	−	1.31813i
$69$		0			0
$70$	0.848721	+	0.0211233i	0.101442	+	0.00252471i
$71$	−12.6076	+	4.09646i	−1.49625	+	0.486160i	−0.938921	−	0.344134i	$-0.888173\pi$
$71$	−12.6076	+	4.09646i	−1.49625	+	0.486160i	−0.557326	+	0.830294i	$0.688173\pi$
$72$		0			0
$73$	−0.770226	−	4.86301i	−0.0901481	−	0.569173i	−0.990875	−	0.134786i	$-0.956965\pi$
$73$	−0.770226	−	4.86301i	−0.0901481	−	0.569173i	0.900727	−	0.434386i	$-0.143035\pi$
$74$	1.60803	−	2.96025i	0.186929	−	0.344122i
$75$		0			0
$76$	−1.01414	+	0.658032i	−0.116330	+	0.0754814i
$77$	−1.21033	+	0.191698i	−0.137930	+	0.0218460i
$78$		0			0
$79$	4.17182	+	12.8395i	0.469366	+	1.44456i	0.853408	+	0.521244i	$0.174532\pi$
$79$	4.17182	+	12.8395i	0.469366	+	1.44456i	−0.384042	+	0.923316i	$0.625468\pi$
$80$	−8.64116	−	2.30877i	−0.966111	−	0.258128i
$81$		0			0
$82$	−15.6031	+	4.61855i	−1.72307	+	0.510034i
$83$	3.42602	+	6.72394i	0.376054	+	0.738048i	0.999023	−	0.0441989i	$-0.0140735\pi$
$83$	3.42602	+	6.72394i	0.376054	+	0.738048i	−0.622969	+	0.782247i	$0.714074\pi$
$84$		0			0
$85$	12.4250	−	0.0185208i	1.34768	−	0.00200886i
$86$	−0.0177047	+	0.00844049i	−0.00190915	+	0.000910161i
$87$		0			0
$88$	12.8698	+	1.02040i	1.37192	+	0.108775i
$89$	−4.20350	+	5.78562i	−0.445570	+	0.613274i	−0.971438	−	0.237292i	$-0.923740\pi$
$89$	−4.20350	+	5.78562i	−0.445570	+	0.613274i	0.525869	+	0.850566i	$0.323740\pi$
$90$		0			0
$91$	−0.266228	−	0.366431i	−0.0279083	−	0.0384124i
$92$	6.43614	+	3.71924i	0.671014	+	0.387757i
$93$		0			0
$94$	−2.66007	+	2.52333i	−0.274365	+	0.260262i
$95$	−0.957159	−	0.954310i	−0.0982024	−	0.0979101i
$96$		0			0
$97$	−0.917106	−	0.467289i	−0.0931180	−	0.0474460i	0.406811	−	0.913512i	$-0.366641\pi$
$97$	−0.917106	−	0.467289i	−0.0931180	−	0.0474460i	−0.499929	+	0.866066i	$0.666641\pi$
$98$	−3.27228	+	9.23495i	−0.330551	+	0.932871i
$99$		0			0
$100$	0.497459	−	9.98762i	0.0497459	−	0.998762i
$101$	−6.65959			−0.662654			−0.331327	−	0.943516i	$-0.607496\pi$
$101$	−6.65959			−0.662654			−0.331327	+	0.943516i	$0.607496\pi$
$102$		0			0
$103$	−13.3848	−	6.81989i	−1.31884	−	0.671984i	−0.354107	−	0.935205i	$-0.615215\pi$
$103$	−13.3848	−	6.81989i	−1.31884	−	0.671984i	−0.964736	+	0.263221i	$0.915215\pi$
$104$	1.82352	+	4.40961i	0.178811	+	0.432398i
$105$		0			0
$106$	−10.2424	+	9.71588i	−0.994828	+	0.943690i
$107$	−11.3660	−	11.3660i	−1.09880	−	1.09880i	−0.994552	−	0.104243i	$-0.966758\pi$
$107$	−11.3660	−	11.3660i	−1.09880	−	1.09880i	−0.104243	−	0.994552i	$-0.533242\pi$
$108$		0			0
$109$	3.89523	+	5.36133i	0.373095	+	0.513522i	0.953739	−	0.300636i	$-0.0971990\pi$
$109$	3.89523	+	5.36133i	0.373095	+	0.513522i	−0.580643	+	0.814158i	$0.697199\pi$
$110$	1.90257	+	14.3080i	0.181403	+	1.36422i
$111$		0			0
$112$	−0.585580	+	0.900185i	−0.0553321	+	0.0850595i
$113$	−16.3189	−	2.58466i	−1.53515	−	0.243144i	−0.669129	−	0.743146i	$-0.733333\pi$
$113$	−16.3189	−	2.58466i	−1.53515	−	0.243144i	−0.866024	+	0.500002i	$0.833333\pi$
$114$		0			0
$115$	−2.55642	+	7.90794i	−0.238387	+	0.737419i
$116$	−6.18174	−	2.37570i	−0.573960	−	0.220578i
$117$		0			0
$118$	5.29216	−	1.56649i	0.487183	−	0.144207i
$119$	0.460993	−	1.41879i	0.0422591	−	0.130060i
$120$		0			0
$121$	−3.03887	−	9.35268i	−0.276261	−	0.850243i
$122$	9.30559	+	13.5453i	0.842489	+	1.22634i
$123$		0			0
$124$	−7.40870	−	11.4181i	−0.665321	−	1.02537i
$125$	11.0348	−	1.79835i	0.986979	−	0.160850i
$126$		0			0
$127$	0.216773	+	1.36865i	0.0192355	+	0.121448i	0.995438	−	0.0954145i	$-0.0304176\pi$
$127$	0.216773	+	1.36865i	0.0192355	+	0.121448i	−0.976202	+	0.216863i	$0.930418\pi$
$128$	8.21724	−	7.77670i	0.726308	−	0.687369i
$129$		0			0
$130$	−4.39280	+	3.02748i	−0.385274	+	0.265528i
$131$	−18.9066	−	6.14313i	−1.65188	−	0.536728i	−0.672732	−	0.739886i	$-0.734880\pi$
$131$	−18.9066	−	6.14313i	−1.65188	−	0.536728i	−0.979146	+	0.203158i	$0.934880\pi$
$132$		0			0
$133$	−0.144593	+	0.0736739i	−0.0125378	+	0.00638834i
$134$	10.2224	−	1.34379i	0.883084	−	0.116086i
$135$		0			0
$136$	−8.21967	+	13.3958i	−0.704831	+	1.14868i
$137$	0.600835	−	3.79353i	0.0513328	−	0.324103i	−0.948637	−	0.316366i	$-0.897537\pi$
$137$	0.600835	−	3.79353i	0.0513328	−	0.324103i	0.999970	−	0.00773685i	$-0.00246274\pi$
$138$		0			0
$139$	14.9655	+	10.8731i	1.26936	+	0.922243i	0.999177	−	0.0405660i	$-0.0129161\pi$
$139$	14.9655	+	10.8731i	1.26936	+	0.922243i	0.270182	+	0.962809i	$0.412916\pi$
$140$	−1.12137	−	0.429036i	−0.0947732	−	0.0362601i
$141$		0			0
$142$	18.7409	+	0.494383i	1.57270	+	0.0414877i
$143$	5.44511	−	5.44511i	0.455343	−	0.455343i
$144$		0			0
$145$	1.14737	−	7.31477i	0.0952840	−	0.607458i
$146$	−1.27025	+	6.84622i	−0.105126	+	0.566597i
$147$		0			0
$148$	−3.54173	+	3.18650i	−0.291129	+	0.261929i
$149$			19.1283i			1.56705i	0.621359	+	0.783526i	$0.286581\pi$
$149$			19.1283i			1.56705i	−0.621359	+	0.783526i	$0.713419\pi$
$150$		0			0
$151$			0.789590i			0.0642559i	0.999484	+	0.0321280i	$0.0102284\pi$
$151$			0.789590i			0.0642559i	−0.999484	+	0.0321280i	$0.989772\pi$
$152$	1.66267	−	0.398148i	0.134860	−	0.0322941i
$153$		0			0
$154$	1.70393	+	0.316146i	0.137306	+	0.0254758i
$155$	10.7445	−	10.7765i	0.863015	−	0.865592i
$156$		0			0
$157$	0.986707	−	0.986707i	0.0787478	−	0.0787478i	−0.666636	−	0.745384i	$-0.732266\pi$
$157$	0.986707	−	0.986707i	0.0787478	−	0.0787478i	0.745384	+	0.666636i	$0.232266\pi$
$158$	0.503478	−	19.0856i	0.0400546	−	1.51837i
$159$		0			0
$160$	10.4282	+	7.15910i	0.824421	+	0.565977i
$161$	0.807270	+	0.586516i	0.0636218	+	0.0462240i
$162$		0			0
$163$	1.18009	−	7.45082i	0.0924320	−	0.583593i	−0.897385	−	0.441248i	$-0.854536\pi$
$163$	1.18009	−	7.45082i	0.0924320	−	0.583593i	0.989817	−	0.142345i	$-0.0454641\pi$
$164$	22.9805	+	1.21329i	1.79447	+	0.0947421i
$165$		0			0
$166$	−1.39096	−	10.5813i	−0.107960	−	0.821265i
$167$	17.5211	−	8.92744i	1.35582	−	0.690826i	0.383298	−	0.923625i	$-0.374788\pi$
$167$	17.5211	−	8.92744i	1.35582	−	0.690826i	0.972525	+	0.232799i	$0.0747883\pi$
$168$		0			0
$169$	−9.65680	−	3.13769i	−0.742831	−	0.241360i
$170$	−16.5714	−	5.84405i	−1.27097	−	0.448218i
$171$		0			0
$172$	0.0275871	−	0.00288871i	0.00210350	−	0.000220262i
$173$	2.63941	+	16.6646i	0.200670	+	1.26698i	0.858106	+	0.513473i	$0.171641\pi$
$173$	2.63941	+	16.6646i	0.200670	+	1.26698i	−0.657435	+	0.753511i	$0.728359\pi$
$174$		0			0
$175$	0.206038	−	1.32645i	0.0155750	−	0.100271i
$176$	−16.6735	−	7.43901i	−1.25681	−	0.560736i
$177$		0			0
$178$	8.33602	−	5.72681i	0.624811	−	0.429242i
$179$	0.708606	+	2.18087i	0.0529637	+	0.163006i	0.974040	−	0.226377i	$-0.0726883\pi$
$179$	0.708606	+	2.18087i	0.0529637	+	0.163006i	−0.921076	+	0.389383i	$0.872688\pi$
$180$		0			0
$181$	4.25840	−	13.1060i	0.316525	−	0.974163i	−0.658598	−	0.752495i	$-0.728850\pi$
$181$	4.25840	−	13.1060i	0.316525	−	0.974163i	0.975122	−	0.221667i	$-0.0711499\pi$
$182$	0.181806	+	0.614203i	0.0134763	+	0.0455277i
$183$		0			0
$184$	−6.82269	−	7.99776i	−0.502975	−	0.589603i
$185$	−4.31393	−	3.12444i	−0.317166	−	0.229713i
$186$		0			0
$187$	25.0506	+	3.96763i	1.83188	+	0.290142i
$188$	4.73774	−	2.10717i	0.345535	−	0.153682i
$189$		0			0
$190$	0.825146	+	1.72420i	0.0598624	+	0.125086i
$191$	15.6587	+	21.5523i	1.13302	+	1.55947i	0.782200	+	0.623027i	$0.214097\pi$
$191$	15.6587	+	21.5523i	1.13302	+	1.55947i	0.350821	+	0.936443i	$0.385903\pi$
$192$		0			0
$193$	6.53786	+	6.53786i	0.470605	+	0.470605i	0.902110	−	0.431505i	$-0.142017\pi$
$193$	6.53786	+	6.53786i	0.470605	+	0.470605i	−0.431505	+	0.902110i	$0.642017\pi$
$194$	1.00179	+	1.05608i	0.0719244	+	0.0758219i
$195$		0			0
$196$	8.72394	−	10.7646i	0.623139	−	0.768902i
$197$	−12.1115	−	6.17110i	−0.862906	−	0.439673i	−0.0342384	−	0.999414i	$-0.510901\pi$
$197$	−12.1115	−	6.17110i	−0.862906	−	0.439673i	−0.828668	+	0.559741i	$0.810901\pi$
$198$		0			0
$199$	7.41416			0.525576			0.262788	−	0.964854i	$-0.415358\pi$
$199$	7.41416			0.525576			0.262788	+	0.964854i	$0.415358\pi$
$200$	−5.38059	+	13.0786i	−0.380465	+	0.924795i
$201$		0			0
$202$	8.87726	+	3.14554i	0.624602	+	0.221319i
$203$	−0.792088	−	0.403589i	−0.0555937	−	0.0283264i
$204$		0			0
$205$	4.06274	+	25.4059i	0.283754	+	1.77443i
$206$	14.6207	+	15.4130i	1.01867	+	1.07388i
$207$		0			0
$208$	−0.347953	−	6.73934i	−0.0241262	−	0.467289i
$209$	−1.62171	−	2.23209i	−0.112176	−	0.154397i
$210$		0			0
$211$	4.85618	−	6.68396i	0.334313	−	0.460142i	−0.608457	−	0.793587i	$-0.708211\pi$
$211$	4.85618	−	6.68396i	0.334313	−	0.460142i	0.942770	+	0.333445i	$0.108211\pi$
$212$	18.2423	−	8.11350i	1.25288	−	0.557238i
$213$		0			0
$214$	9.78242	+	20.5195i	0.668713	+	1.40268i
$215$	0.00962719	+	0.0294799i	0.000656569	+	0.00201051i
$216$		0			0
$217$	−0.829485	−	1.62796i	−0.0563091	−	0.110513i
$218$	−2.66003	−	8.98652i	−0.180160	−	0.608644i
$219$		0			0
$220$	4.22202	−	19.9713i	0.284649	−	1.34647i
$221$	2.89688	+	8.91568i	0.194865	+	0.599733i
$222$		0			0
$223$	−4.16161	+	0.659135i	−0.278682	+	0.0441389i	−0.294211	−	0.955741i	$-0.595057\pi$
$223$	−4.16161	+	0.659135i	−0.278682	+	0.0441389i	0.0155288	+	0.999879i	$0.495057\pi$
$224$	1.20577	−	0.923362i	0.0805637	−	0.0616947i
$225$		0			0
$226$	20.5324	+	11.1533i	1.36579	+	0.741907i
$227$	1.61847	+	10.2186i	0.107421	+	0.678232i	0.981358	+	0.192191i	$0.0615594\pi$
$227$	1.61847	+	10.2186i	0.107421	+	0.678232i	−0.873936	+	0.486041i	$0.838441\pi$
$228$		0			0
$229$	−1.55021	+	0.503695i	−0.102441	+	0.0332851i	−0.359789	−	0.933034i	$-0.617151\pi$
$229$	−1.55021	+	0.503695i	−0.102441	+	0.0332851i	0.257348	+	0.966319i	$0.417151\pi$
$230$	7.14290	−	9.33384i	0.470989	−	0.615455i
$231$		0			0
$232$	7.11817	+	6.08665i	0.467330	+	0.399608i
$233$	−2.66801	+	1.35942i	−0.174787	+	0.0890586i	−0.539195	−	0.842181i	$-0.681271\pi$
$233$	−2.66801	+	1.35942i	−0.174787	+	0.0890586i	0.364408	+	0.931240i	$0.381271\pi$
$234$		0			0
$235$	3.41451	+	4.68497i	0.222738	+	0.305614i
$236$	−7.79438	−	0.411517i	−0.507371	−	0.0267875i
$237$		0			0
$238$	−1.28465	+	1.67351i	−0.0832713	+	0.108478i
$239$	17.9159	+	13.0167i	1.15888	+	0.841979i	0.989637	−	0.143595i	$-0.0458662\pi$
$239$	17.9159	+	13.0167i	1.15888	+	0.841979i	0.169248	+	0.985574i	$0.445866\pi$
$240$		0			0
$241$	−0.0614146	+	0.0446203i	−0.00395606	+	0.00287425i	−0.589762	−	0.807577i	$-0.700778\pi$
$241$	−0.0614146	+	0.0446203i	−0.00395606	+	0.00287425i	0.585805	+	0.810452i	$0.300778\pi$
$242$	−0.366748	+	13.9025i	−0.0235754	+	0.893688i
$243$		0			0
$244$	−6.00649	−	22.4513i	−0.384526	−	1.43730i
$245$	13.8133	+	7.01232i	0.882501	+	0.448001i
$246$		0			0
$247$	0.462967	−	0.908624i	0.0294579	−	0.0578144i
$248$	4.48270	+	18.7197i	0.284652	+	1.18870i
$249$		0			0
$250$	−15.5588	−	2.81486i	−0.984025	−	0.178028i
$251$		−	29.9398i		−	1.88979i	−0.327379	−	0.944893i	$-0.606165\pi$
$251$		−	29.9398i		−	1.88979i	0.327379	−	0.944893i	$-0.393835\pi$
$252$		0			0
$253$	−7.70185	+	15.1157i	−0.484211	+	0.950318i
$254$	0.357499	−	1.92681i	0.0224315	−	0.120899i
$255$		0			0
$256$	−14.6268	+	6.48511i	−0.914175	+	0.405319i
$257$	−14.7898	+	14.7898i	−0.922565	+	0.922565i	−0.997210	−	0.0746451i	$-0.976218\pi$
$257$	−14.7898	+	14.7898i	−0.922565	+	0.922565i	0.0746451	+	0.997210i	$0.476218\pi$
$258$		0			0
$259$	−0.517389	+	0.375905i	−0.0321490	+	0.0233576i
$260$	7.28561	−	1.96079i	0.451834	−	0.121603i
$261$		0			0
$262$	22.3010	+	17.1190i	1.37776	+	1.05762i
$263$	−4.13096	+	26.0818i	−0.254726	+	1.60827i	0.446128	+	0.894969i	$0.352803\pi$
$263$	−4.13096	+	26.0818i	−0.254726	+	1.60827i	−0.700854	+	0.713305i	$0.747197\pi$
$264$		0			0
$265$	13.1473	+	18.0391i	0.807633	+	1.10813i
$266$	0.227542	−	0.0299116i	0.0139515	−	0.00183400i
$267$		0			0
$268$	−14.2613	−	3.03711i	−0.871146	−	0.185521i
$269$	14.2213	+	4.62080i	0.867091	+	0.281735i	0.708587	−	0.705623i	$-0.249333\pi$
$269$	14.2213	+	4.62080i	0.867091	+	0.281735i	0.158504	+	0.987358i	$0.449333\pi$
$270$		0			0
$271$	−8.37925	+	2.72258i	−0.509003	+	0.165385i	−0.552249	−	0.833679i	$-0.686230\pi$
$271$	−8.37925	+	2.72258i	−0.509003	+	0.165385i	0.0432457	+	0.999064i	$0.486230\pi$
$272$	17.2841	−	13.9742i	1.04800	−	0.847313i
$273$		0			0
$274$	−2.59272	+	4.77299i	−0.156632	+	0.288347i
$275$	22.8220	−	0.0680375i	1.37622	−	0.00410281i
$276$		0			0
$277$	−8.96925	+	1.42059i	−0.538910	+	0.0853549i	−0.419955	−	0.907545i	$-0.637954\pi$
$277$	−8.96925	+	1.42059i	−0.538910	+	0.0853549i	−0.118955	+	0.992900i	$0.537954\pi$
$278$	−14.8134	−	21.5626i	−0.888449	−	1.29324i
$279$		0			0
$280$	1.29215	+	1.10157i	0.0772205	+	0.0658312i
$281$	8.89363	−	27.3718i	0.530549	−	1.63286i	−0.222525	−	0.974927i	$-0.571430\pi$
$281$	8.89363	−	27.3718i	0.530549	−	1.63286i	0.753074	−	0.657936i	$-0.228570\pi$
$282$		0			0
$283$	−8.13832	−	15.9724i	−0.483773	−	0.949458i	−0.995892	−	0.0905436i	$-0.971140\pi$
$283$	−8.13832	−	15.9724i	−0.483773	−	0.949458i	0.512120	−	0.858914i	$-0.328860\pi$
$284$	−24.7482	−	9.51094i	−1.46853	−	0.564371i
$285$		0			0
$286$	−9.83026	+	4.68646i	−0.581276	+	0.277116i
$287$	3.05107	+	0.483242i	0.180099	+	0.0285249i
$288$		0			0
$289$	−8.15628	+	11.2262i	−0.479781	+	0.660362i
$290$	−4.98445	+	9.20868i	−0.292697	+	0.540752i
$291$		0			0
$292$	4.92694	−	8.52607i	0.288327	−	0.498950i
$293$	1.24037	+	1.24037i	0.0724632	+	0.0724632i	0.742410	−	0.669946i	$-0.233683\pi$
$293$	1.24037	+	1.24037i	0.0724632	+	0.0724632i	−0.669946	+	0.742410i	$0.733683\pi$
$294$		0			0
$295$	−1.37797	−	8.61703i	−0.0802287	−	0.501703i
$296$	6.22624	−	2.57475i	0.361893	−	0.149654i
$297$		0			0
$298$	9.03492	−	25.4981i	0.523379	−	1.47707i
$299$	−6.27044			−0.362629
$300$		0			0
$301$	0.00372344			0.000214615
$302$	0.372949	−	1.05253i	0.0214608	−	0.0605661i
$303$		0			0
$304$	−2.40440	−	0.254598i	−0.137902	−	0.0146022i
$305$	23.1344	−	11.8311i	1.32467	−	0.677444i
$306$		0			0
$307$	11.6840	+	11.6840i	0.666844	+	0.666844i	0.956984	−	0.290140i	$-0.0937020\pi$
$307$	11.6840	+	11.6840i	0.666844	+	0.666844i	−0.290140	+	0.956984i	$0.593702\pi$
$308$	−2.12202	−	1.22624i	−0.120913	−	0.0698717i
$309$		0			0
$310$	−19.4125	+	9.29022i	−1.10256	+	0.527649i
$311$	−3.31285	+	4.55974i	−0.187854	+	0.258559i	−0.892548	−	0.450952i	$-0.851084\pi$
$311$	−3.31285	+	4.55974i	−0.187854	+	0.258559i	0.704694	+	0.709512i	$0.251084\pi$
$312$		0			0
$313$	−17.7167	−	2.80604i	−1.00141	−	0.158607i	−0.365859	−	0.930670i	$-0.619225\pi$
$313$	−17.7167	−	2.80604i	−1.00141	−	0.158607i	−0.635546	+	0.772063i	$0.719225\pi$
$314$	−1.78134	+	0.849231i	−0.100527	+	0.0479249i
$315$		0			0
$316$	−9.68591	+	25.2034i	−0.544875	+	1.41780i
$317$	−4.15260	−	8.14994i	−0.233233	−	0.457746i	0.744493	−	0.667630i	$-0.232691\pi$
$317$	−4.15260	−	8.14994i	−0.233233	−	0.457746i	−0.977726	+	0.209884i	$0.932691\pi$
$318$		0			0
$319$	4.67049	−	14.3743i	0.261497	−	0.804805i
$320$	−10.5194	−	14.4687i	−0.588050	−	0.808825i
$321$		0			0
$322$	−0.799064	−	1.16313i	−0.0445301	−	0.0648186i
$323$	3.31742	−	0.525427i	0.184586	−	0.0292356i
$324$		0			0
$325$	3.85198	+	7.50454i	0.213669	+	0.416277i
$326$	−5.09233	+	9.37458i	−0.282038	+	0.519210i
$327$		0			0
$328$	−30.0600	−	12.4718i	−1.65979	−	0.688637i
$329$	0.661974	−	0.215089i	0.0364958	−	0.0118582i
$330$		0			0
$331$	−7.07411	−	2.29852i	−0.388828	−	0.126338i	0.108077	−	0.994142i	$-0.465531\pi$
$331$	−7.07411	−	2.29852i	−0.388828	−	0.126338i	−0.496906	+	0.867804i	$0.665531\pi$
$332$	−3.14371	+	14.7619i	−0.172534	+	0.810163i
$333$		0			0
$334$	−27.5724	+	3.62454i	−1.50870	+	0.198326i
$335$	−0.0243001	−	16.3021i	−0.00132765	−	0.890680i
$336$		0			0
$337$	1.87071	−	11.8112i	0.101904	−	0.643398i	−0.882878	−	0.469603i	$-0.844397\pi$
$337$	1.87071	−	11.8112i	0.101904	−	0.643398i	0.984782	−	0.173795i	$-0.0556030\pi$
$338$	11.3905	+	8.74377i	0.619563	+	0.475599i
$339$		0			0
$340$	19.3294	+	15.6173i	1.04828	+	0.846969i
$341$	25.1308	−	18.2586i	1.36091	−	0.988759i
$342$		0			0
$343$	2.64406	−	2.64406i	0.142766	−	0.142766i
$344$	−0.0381382	−	0.00917964i	−0.00205628	−	0.000494933i
$345$		0			0
$346$	4.35287	−	23.4606i	0.234012	−	1.26125i
$347$	−15.3433	+	30.1129i	−0.823672	+	1.61655i	−0.0368882	+	0.999319i	$0.511745\pi$
$347$	−15.3433	+	30.1129i	−0.823672	+	1.61655i	−0.786784	+	0.617228i	$0.788255\pi$
$348$		0			0
$349$			27.4462i			1.46916i	0.678523	+	0.734579i	$0.262620\pi$
$349$			27.4462i			1.46916i	−0.678523	+	0.734579i	$0.737380\pi$
$350$	−0.901177	+	1.67085i	−0.0481699	+	0.0893108i
$351$		0			0
$352$	18.7121	+	17.7917i	0.997360	+	0.948299i
$353$	−4.86385	+	9.54584i	−0.258876	+	0.508074i	−0.983463	−	0.181110i	$-0.942031\pi$
$353$	−4.86385	+	9.54584i	−0.258876	+	0.508074i	0.724586	+	0.689184i	$0.242031\pi$
$354$		0			0
$355$	4.59342	−	29.2842i	0.243794	−	1.55424i
$356$	−13.8169	+	3.69649i	−0.732295	+	0.195913i
$357$		0			0
$358$	0.0855185	−	3.24180i	0.00451980	−	0.171335i
$359$	10.7538	−	7.81307i	0.567562	−	0.412358i	−0.266657	−	0.963792i	$-0.585919\pi$
$359$	10.7538	−	7.81307i	0.567562	−	0.412358i	0.834219	+	0.551434i	$0.185919\pi$
$360$		0			0
$361$	15.0757	+	10.9532i	0.793460	+	0.576482i
$362$	−11.8669	+	15.4590i	−0.623709	+	0.812507i
$363$		0			0
$364$	0.0477602	−	0.904608i	0.00250332	−	0.0474143i
$365$	10.4758	+	3.38653i	0.548328	+	0.177259i
$366$		0			0
$367$	−23.2351	+	11.8389i	−1.21286	+	0.617983i	−0.939043	−	0.343799i	$-0.888286\pi$
$367$	−23.2351	+	11.8389i	−1.21286	+	0.617983i	−0.273817	+	0.961782i	$0.588286\pi$
$368$	5.31708	+	13.8836i	0.277172	+	0.723734i
$369$		0			0
$370$	4.27471	+	6.20250i	0.222232	+	0.322453i
$371$	2.54888	−	0.828181i	0.132331	−	0.0429970i
$372$		0			0
$373$	−4.62618	−	29.2086i	−0.239535	−	1.51236i	−0.755156	−	0.655545i	$-0.772439\pi$
$373$	−4.62618	−	29.2086i	−0.239535	−	1.51236i	0.515621	−	0.856817i	$-0.327561\pi$
$374$	−31.5186	−	17.1211i	−1.62979	−	0.885311i
$375$		0			0
$376$	−7.31071	+	0.571087i	−0.377021	+	0.0294516i
$377$	5.51758	−	0.873899i	0.284170	−	0.0450081i
$378$		0			0
$379$	−5.98387	−	18.4165i	−0.307371	−	0.945990i	−0.978782	−	0.204905i	$-0.934311\pi$
$379$	−5.98387	−	18.4165i	−0.307371	−	0.945990i	0.671411	−	0.741085i	$-0.265689\pi$
$380$	−0.285529	−	2.68811i	−0.0146473	−	0.137897i
$381$		0			0
$382$	−10.6932	−	36.1254i	−0.547113	−	1.84834i
$383$	−4.35881	−	8.55465i	−0.222725	−	0.437122i	0.752422	−	0.658681i	$-0.228885\pi$
$383$	−4.35881	−	8.55465i	−0.222725	−	0.437122i	−0.975147	+	0.221559i	$0.928885\pi$
$384$		0			0
$385$	0.842860	−	2.60727i	0.0429561	−	0.132879i
$386$	−5.62695	−	11.8030i	−0.286404	−	0.600759i
$387$		0			0
$388$	−0.836572	−	1.88093i	−0.0424705	−	0.0954900i
$389$	−11.3570	+	15.6316i	−0.575825	+	0.792555i	−0.993230	−	0.116166i	$-0.962940\pi$
$389$	−11.3570	+	15.6316i	−0.575825	+	0.792555i	0.417405	+	0.908721i	$0.362940\pi$
$390$		0			0
$391$	−12.1393	−	16.7083i	−0.613910	−	0.844975i
$392$	−16.7135	+	10.2287i	−0.844161	+	0.516628i
$393$		0			0
$394$	13.2298	+	13.9467i	0.666509	+	0.702627i
$395$	−29.8229	−	4.67792i	−1.50055	−	0.235372i
$396$		0			0
$397$	17.5405	+	8.93731i	0.880331	+	0.448551i	0.834890	−	0.550416i	$-0.185531\pi$
$397$	17.5405	+	8.93731i	0.880331	+	0.448551i	0.0454402	+	0.998967i	$0.485531\pi$
$398$	−9.88311	−	3.50195i	−0.495395	−	0.175537i
$399$		0			0
$400$	13.3498	−	14.8924i	0.667490	−	0.744619i
$401$	−33.9482			−1.69529			−0.847645	−	0.530564i	$-0.821980\pi$
$401$	−33.9482			−1.69529			−0.847645	+	0.530564i	$0.821980\pi$
$402$		0			0
$403$	10.2301	+	5.21249i	0.509597	+	0.259652i
$404$	−10.3477	−	8.38604i	−0.514817	−	0.417221i
$405$		0			0
$406$	0.865229	+	0.912115i	0.0429406	+	0.0452675i
$407$	−7.68833	−	7.68833i	−0.381096	−	0.381096i
$408$		0			0
$409$	8.02687	+	11.0480i	0.396903	+	0.546291i	0.959963	−	0.280125i	$-0.0903760\pi$
$409$	8.02687	+	11.0480i	0.396903	+	0.546291i	−0.563060	+	0.826416i	$0.690376\pi$
$410$	6.58441	−	35.7852i	0.325181	−	1.76731i
$411$		0			0
$412$	−12.2094	−	27.4515i	−0.601516	−	1.35244i
$413$	−1.03484	−	0.163903i	−0.0509214	−	0.00806515i
$414$		0			0
$415$	−16.8744	+	0.0251530i	−0.828330	+	0.00123471i
$416$	−2.71939	+	9.14792i	−0.133329	+	0.448514i
$417$		0			0
$418$	1.10746	+	3.74137i	0.0541674	+	0.182996i
$419$	2.10539	−	6.47973i	0.102855	−	0.316555i	−0.886366	−	0.462985i	$-0.846778\pi$
$419$	2.10539	−	6.47973i	0.102855	−	0.316555i	0.989221	+	0.146430i	$0.0467783\pi$
$420$		0			0
$421$	3.96818	+	12.2128i	0.193397	+	0.595215i	0.999992	+	0.00410979i	$0.00130819\pi$
$421$	3.96818	+	12.2128i	0.193397	+	0.595215i	−0.806594	+	0.591105i	$0.798692\pi$
$422$	−9.63036	+	6.61601i	−0.468799	+	0.322062i
$423$		0			0
$424$	−28.1493	+	2.19892i	−1.36705	+	0.106789i
$425$	−12.5395	+	24.7925i	−0.608253	+	1.20261i
$426$		0			0
$427$	−0.488040	−	3.08136i	−0.0236179	−	0.149118i
$428$	−3.34798	−	31.9732i	−0.161831	−	1.54548i
$429$		0			0
$430$	0.00109121	−	0.0438440i	5.26226e−5	−	0.00211435i
$431$	−3.23293	−	1.05044i	−0.155725	−	0.0505981i	0.230117	−	0.973163i	$-0.426089\pi$
$431$	−3.23293	−	1.05044i	−0.155725	−	0.0505981i	−0.385842	+	0.922565i	$0.626089\pi$
$432$		0			0
$433$	3.04817	−	1.55312i	0.146486	−	0.0746383i	−0.379211	−	0.925310i	$-0.623805\pi$
$433$	3.04817	−	1.55312i	0.146486	−	0.0746383i	0.525697	+	0.850672i	$0.323805\pi$
$434$	0.336771	+	2.56187i	0.0161655	+	0.122974i
$435$		0			0
$436$	−0.698789	+	13.2355i	−0.0334659	+	0.633865i
$437$	−0.351449	+	2.21896i	−0.0168121	+	0.106147i
$438$		0			0
$439$	16.2122	+	11.7788i	0.773766	+	0.562174i	0.903102	−	0.429427i	$-0.141285\pi$
$439$	16.2122	+	11.7788i	0.773766	+	0.562174i	−0.129336	+	0.991601i	$0.541285\pi$
$440$	−15.0611	+	24.6277i	−0.718009	+	1.17408i
$441$		0			0
$442$	0.349612	−	13.2529i	0.0166293	−	0.630378i
$443$	−10.2267	+	10.2267i	−0.485887	+	0.485887i	−0.907006	−	0.421119i	$-0.861638\pi$
$443$	−10.2267	+	10.2267i	−0.485887	+	0.485887i	0.421119	+	0.907006i	$0.361638\pi$
$444$		0			0
$445$	−7.28102	−	14.2373i	−0.345153	−	0.674912i
$446$	5.85878	+	1.08704i	0.277421	+	0.0514726i
$447$		0			0
$448$	−2.04343	+	0.661323i	−0.0965429	+	0.0312446i
$449$		−	20.1223i		−	0.949629i	−0.880086	−	0.474814i	$-0.842515\pi$
$449$		−	20.1223i		−	0.949629i	0.880086	−	0.474814i	$-0.157485\pi$
$450$		0			0
$451$			52.5194i			2.47304i
$452$	−22.1017	−	24.5655i	−1.03957	−	1.15547i
$453$		0			0
$454$	2.66915	−	14.3859i	0.125270	−	0.675163i
$455$	1.00008	−	0.159926i	0.0468847	−	0.00749746i
$456$		0			0
$457$	5.50274	−	5.50274i	0.257407	−	0.257407i	−0.566591	−	0.823999i	$-0.691738\pi$
$457$	5.50274	−	5.50274i	0.257407	−	0.257407i	0.823999	+	0.566591i	$0.191738\pi$
$458$	2.30436	+	0.0607887i	0.107675	+	0.00284047i
$459$		0			0
$460$	−13.9302	+	9.06823i	−0.649499	+	0.422808i
$461$	−1.99209	−	1.44734i	−0.0927808	−	0.0674092i	0.540428	−	0.841390i	$-0.318262\pi$
$461$	−1.99209	−	1.44734i	−0.0927808	−	0.0674092i	−0.633209	+	0.773981i	$0.718262\pi$
$462$		0			0
$463$	−5.26029	+	33.2122i	−0.244467	+	1.54350i	0.494151	+	0.869376i	$0.335479\pi$
$463$	−5.26029	+	33.2122i	−0.244467	+	1.54350i	−0.738617	+	0.674125i	$0.764521\pi$
$464$	−6.61362	−	11.4757i	−0.307030	−	0.532745i
$465$		0			0
$466$	4.19857	−	0.551925i	0.194495	−	0.0255674i
$467$	−9.58390	+	4.88324i	−0.443490	+	0.225969i	−0.661452	−	0.749988i	$-0.730059\pi$
$467$	−9.58390	+	4.88324i	−0.443490	+	0.225969i	0.217962	+	0.975957i	$0.430059\pi$
$468$		0			0
$469$	−1.86151	−	0.604841i	−0.0859565	−	0.0279290i
$470$	−2.33870	−	7.85788i	−0.107876	−	0.362457i
$471$		0			0
$472$	10.1956	+	4.23009i	0.469289	+	0.194706i
$473$	0.00990292	+	0.0625246i	0.000455337	+	0.00287488i
$474$		0			0
$475$	2.87158	−	0.942507i	0.131757	−	0.0432452i
$476$	2.50289	−	1.62402i	0.114720	−	0.0744368i
$477$		0			0
$478$	−17.7338	−	25.8136i	−0.811125	−	1.18068i
$479$	−7.08607	−	21.8087i	−0.323771	−	0.996464i	−0.971992	−	0.235012i	$-0.924487\pi$
$479$	−7.08607	−	21.8087i	−0.323771	−	0.996464i	0.648221	−	0.761452i	$-0.275513\pi$
$480$		0			0
$481$	1.24188	−	3.82210i	0.0566247	−	0.174273i
$482$	0.102942	−	0.0304710i	0.00468886	−	0.00138792i
$483$		0			0
$484$	7.05549	−	18.3589i	0.320704	−	0.834495i
$485$	1.85999	−	1.35560i	0.0844577	−	0.0615547i
$486$		0			0
$487$	16.6355	+	2.63480i	0.753826	+	0.119394i	0.521509	−	0.853246i	$-0.325369\pi$
$487$	16.6355	+	2.63480i	0.753826	+	0.119394i	0.232317	+	0.972640i	$0.425369\pi$
$488$	−2.59782	+	32.7648i	−0.117598	+	1.48319i
$489$		0			0
$490$	−15.1011	−	15.8719i	−0.682197	−	0.717021i
$491$	−6.71450	−	9.24172i	−0.303021	−	0.417073i	0.630168	−	0.776459i	$-0.282986\pi$
$491$	−6.71450	−	9.24172i	−0.303021	−	0.417073i	−0.933189	+	0.359386i	$0.882986\pi$
$492$		0			0
$493$	13.0104	+	13.0104i	0.585959	+	0.585959i
$494$	−1.04631	+	0.992526i	−0.0470757	+	0.0446558i
$495$		0			0
$496$	2.86649	−	27.0708i	0.128709	−	1.21552i
$497$	−3.17107	−	1.61574i	−0.142242	−	0.0724759i
$498$		0			0
$499$	−41.8728			−1.87448			−0.937242	−	0.348679i	$-0.886630\pi$
$499$	−41.8728			−1.87448			−0.937242	+	0.348679i	$0.886630\pi$
$500$	19.4104	+	11.1012i	0.868060	+	0.496459i
$501$		0			0
$502$	−14.1416	+	39.9100i	−0.631169	+	1.78127i
$503$	−21.0178	−	10.7091i	−0.937139	−	0.477496i	−0.0824263	−	0.996597i	$-0.526267\pi$
$503$	−21.0178	−	10.7091i	−0.937139	−	0.477496i	−0.854713	+	0.519101i	$0.826267\pi$
$504$		0			0
$505$	6.74072	−	13.2783i	0.299958	−	0.590877i
$506$	17.4063	−	16.5115i	0.773802	−	0.734026i
$507$		0			0
$508$	−1.38664	+	2.39958i	−0.0615223	+	0.106464i
$509$	22.3651	+	30.7830i	0.991318	+	1.36443i	0.930504	+	0.366282i	$0.119370\pi$
$509$	22.3651	+	30.7830i	0.991318	+	1.36443i	0.0608138	+	0.998149i	$0.480630\pi$
$510$		0			0
$511$	0.776968	−	1.06941i	0.0343711	−	0.0473077i
$512$	22.5607	−	1.73596i	0.997053	−	0.0767194i
$513$		0			0
$514$	26.7007	−	12.7292i	1.17772	−	0.561461i
$515$	27.1458	−	19.7845i	1.19619	−	0.871807i
$516$		0			0
$517$	5.37240	+	10.5439i	0.236278	+	0.463722i
$518$	0.867235	−	0.256704i	0.0381041	−	0.0112789i
$519$		0			0
$520$	−10.6379	−	0.827492i	−0.466502	−	0.0362879i
$521$	−2.57819	−	7.93486i	−0.112953	−	0.347632i	0.878562	−	0.477629i	$-0.158504\pi$
$521$	−2.57819	−	7.93486i	−0.112953	−	0.347632i	−0.991515	+	0.129996i	$0.958504\pi$
$522$		0			0
$523$	32.5180	−	5.15034i	1.42191	−	0.225209i	0.602365	−	0.798221i	$-0.294225\pi$
$523$	32.5180	−	5.15034i	1.42191	−	0.225209i	0.819547	+	0.573012i	$0.194225\pi$
$524$	−21.6415	−	33.3532i	−0.945412	−	1.45704i
$525$		0			0
$526$	17.8259	−	32.8160i	0.777245	−	1.43085i
$527$	5.91572	+	37.3504i	0.257693	+	1.62701i
$528$		0			0
$529$	−8.73626	+	2.83858i	−0.379837	+	0.123417i
$530$	−9.00497	−	30.2561i	−0.391151	−	1.31424i
$531$		0			0
$532$	−0.317443	−	0.0676032i	−0.0137629	−	0.00293097i
$533$	−17.2962	+	8.81284i	−0.749180	+	0.381726i
$534$		0			0
$535$	34.1668	−	11.1578i	1.47716	−	0.482393i
$536$	17.5758	+	10.7845i	0.759160	+	0.465821i
$537$		0			0
$538$	−16.7746	−	12.8767i	−0.723203	−	0.555156i
$539$	25.5827	+	18.5869i	1.10193	+	0.800596i
$540$		0			0
$541$	−7.48590	+	5.43883i	−0.321844	+	0.233833i	−0.736962	−	0.675934i	$-0.763740\pi$
$541$	−7.48590	+	5.43883i	−0.321844	+	0.233833i	0.415118	+	0.909768i	$0.363740\pi$
$542$	12.4555	+	0.328576i	0.535011	+	0.0141136i
$543$		0			0
$544$	−29.6403	+	10.4639i	−1.27082	+	0.448634i
$545$	−14.6324	+	2.33991i	−0.626784	+	0.100231i
$546$		0			0
$547$	6.35363	−	12.4697i	0.271662	−	0.533166i	−0.714361	−	0.699777i	$-0.753283\pi$
$547$	6.35363	−	12.4697i	0.271662	−	0.533166i	0.986023	+	0.166611i	$0.0532825\pi$
$548$	5.71055	−	5.13780i	0.243943	−	0.219476i
$549$		0			0
$550$	−30.4540	−	10.6889i	−1.29856	−	0.455776i
$551$		−	2.00153i		−	0.0852679i
$552$		0			0
$553$	−1.64547	+	3.22941i	−0.0699723	+	0.137328i
$554$	12.6270	+	2.34282i	0.536472	+	0.0995367i
$555$		0			0
$556$	9.56162	+	35.7399i	0.405503	+	1.51571i
$557$	−2.87624	+	2.87624i	−0.121870	+	0.121870i	−0.765411	−	0.643541i	$-0.777464\pi$
$557$	−2.87624	+	2.87624i	−0.121870	+	0.121870i	0.643541	+	0.765411i	$0.277464\pi$
$558$		0			0
$559$	−0.0189295	+	0.0137531i	−0.000800630	+	0.000581692i
$560$	−1.20213	−	2.07872i	−0.0507993	−	0.0878418i
$561$		0			0
$562$	−24.7838	+	32.2860i	−1.04544	+	1.36190i
$563$	−3.30793	+	20.8854i	−0.139412	+	0.880216i	0.814507	+	0.580153i	$0.197007\pi$
$563$	−3.30793	+	20.8854i	−0.139412	+	0.880216i	−0.953920	+	0.300062i	$0.902993\pi$
$564$		0			0
$565$	21.6712	−	29.9215i	0.911713	−	1.25881i
$566$	3.30416	+	25.1352i	0.138884	+	1.05651i
$567$		0			0
$568$	28.4971	+	24.3675i	1.19571	+	1.02244i
$569$	−3.40048	−	1.10488i	−0.142556	−	0.0463192i	0.236870	−	0.971541i	$-0.423878\pi$
$569$	−3.40048	−	1.10488i	−0.142556	−	0.0463192i	−0.379426	+	0.925222i	$0.623878\pi$
$570$		0			0
$571$	10.6049	−	3.44576i	0.443803	−	0.144200i	−0.0785864	−	0.996907i	$-0.525041\pi$
$571$	10.6049	−	3.44576i	0.443803	−	0.144200i	0.522390	+	0.852707i	$0.325041\pi$
$572$	15.3174	−	1.60391i	0.640451	−	0.0670630i
$573$		0			0
$574$	−3.83884	−	2.08529i	−0.160230	−	0.0870381i
$575$	−13.1798	−	13.1014i	−0.549635	−	0.546367i
$576$		0			0
$577$	−38.4820	+	6.09495i	−1.60203	+	0.253736i	−0.892535	−	0.450979i	$-0.851075\pi$
$577$	−38.4820	+	6.09495i	−1.60203	+	0.253736i	−0.709491	+	0.704714i	$0.751075\pi$
$578$	16.1748	−	11.1120i	0.672785	−	0.462200i
$579$		0			0
$580$	10.9939	−	9.92089i	0.456495	−	0.411943i
$581$	−0.626072	+	1.92685i	−0.0259738	+	0.0799393i
$582$		0			0
$583$	20.6860	+	40.5986i	0.856727	+	1.68142i
$584$	−10.5948	+	9.03814i	−0.438415	+	0.374001i
$585$		0			0
$586$	−1.06755	−	2.23929i	−0.0441002	−	0.0925041i
$587$	−15.7614	−	2.49636i	−0.650542	−	0.103036i	−0.177563	−	0.984109i	$-0.556821\pi$
$587$	−15.7614	−	2.49636i	−0.650542	−	0.103036i	−0.472979	+	0.881074i	$0.656821\pi$
$588$		0			0
$589$	2.41796	−	3.32804i	0.0996303	−	0.137129i
$590$	−2.23326	+	12.1374i	−0.0919419	+	0.499689i
$591$		0			0
$592$	−9.51574	+	0.491299i	−0.391094	+	0.0201923i
$593$	−6.24575	−	6.24575i	−0.256482	−	0.256482i	0.567140	−	0.823622i	$-0.308050\pi$
$593$	−6.24575	−	6.24575i	−0.256482	−	0.256482i	−0.823622	+	0.567140i	$0.808050\pi$
$594$		0			0
$595$	2.36226	+	2.35523i	0.0968433	+	0.0965550i
$596$	−24.0872	+	29.7216i	−0.986650	+	1.21745i
$597$		0			0
$598$	8.35852	+	2.96173i	0.341805	+	0.121114i
$599$	−19.3797			−0.791832			−0.395916	−	0.918287i	$-0.629573\pi$
$599$	−19.3797			−0.791832			−0.395916	+	0.918287i	$0.629573\pi$
$600$		0			0
$601$	21.8893			0.892883			0.446441	−	0.894813i	$-0.352691\pi$
$601$	21.8893			0.892883			0.446441	+	0.894813i	$0.352691\pi$
$602$	−0.00496336	−	0.00175870i	−0.000202291	−	7.16793e-5i
$603$		0			0
$604$	−0.994286	+	1.22687i	−0.0404569	+	0.0499206i
$605$	21.7238	+	3.40753i	0.883199	+	0.138536i
$606$		0			0
$607$	−26.4147	−	26.4147i	−1.07214	−	1.07214i	−0.997187	−	0.0749533i	$-0.976119\pi$
$607$	−26.4147	−	26.4147i	−1.07214	−	1.07214i	−0.0749533	−	0.997187i	$-0.523881\pi$
$608$	3.08482	+	1.47506i	0.125106	+	0.0598214i
$609$		0			0
$610$	−36.4265	+	4.84370i	−1.47487	+	0.196116i
$611$	−2.57093	+	3.53858i	−0.104009	+	0.143156i
$612$		0			0
$613$	−23.7116	−	3.75555i	−0.957703	−	0.151685i	−0.342032	−	0.939688i	$-0.611115\pi$
$613$	−23.7116	−	3.75555i	−0.957703	−	0.151685i	−0.615671	+	0.788003i	$0.711115\pi$
$614$	−10.0561	−	21.0937i	−0.405833	−	0.851270i
$615$		0			0
$616$	2.24946	+	2.63689i	0.0906334	+	0.106243i
$617$	−19.1096	−	37.5048i	−0.769325	−	1.50989i	−0.857900	−	0.513816i	$-0.828231\pi$
$617$	−19.1096	−	37.5048i	−0.769325	−	1.50989i	0.0885751	−	0.996070i	$-0.471769\pi$
$618$		0			0
$619$	0.176865	−	0.544334i	0.00710880	−	0.0218786i	−0.947439	−	0.319936i	$-0.896339\pi$
$619$	0.176865	−	0.544334i	0.00710880	−	0.0218786i	0.954548	+	0.298057i	$0.0963386\pi$
$620$	30.2651	−	3.21474i	1.21547	−	0.129107i
$621$		0			0
$622$	6.56976	−	4.51339i	0.263423	−	0.180971i
$623$	−1.89632	+	0.300347i	−0.0759744	+	0.0120332i
$624$		0			0
$625$	−7.58352	+	23.8221i	−0.303341	+	0.952882i
$626$	22.2910	+	12.1086i	0.890928	+	0.483958i
$627$		0			0
$628$	2.77565	−	0.290645i	0.110761	−	0.0115980i
$629$	12.5887	−	4.09030i	0.501943	−	0.163091i
$630$		0			0
$631$	12.1577	+	3.95028i	0.483991	+	0.157258i	0.540842	−	0.841124i	$-0.318106\pi$
$631$	12.1577	+	3.95028i	0.483991	+	0.157258i	−0.0568504	+	0.998383i	$0.518106\pi$
$632$	24.8158	−	29.0213i	0.987118	−	1.15441i
$633$		0			0
$634$	1.68596	+	12.8253i	0.0669579	+	0.509359i
$635$	−2.94831	−	0.953109i	−0.117000	−	0.0378230i
$636$		0			0
$637$	−1.82840	+	11.5441i	−0.0724438	+	0.457392i
$638$	−13.0152	+	16.9550i	−0.515277	+	0.671253i
$639$		0			0
$640$	7.18832	+	24.2555i	0.284143	+	0.958782i
$641$	0.248557	−	0.180587i	0.00981740	−	0.00713276i	−0.582866	−	0.812568i	$-0.698069\pi$
$641$	0.248557	−	0.180587i	0.00981740	−	0.00713276i	0.592683	+	0.805436i	$0.298069\pi$
$642$		0			0
$643$	−16.7114	+	16.7114i	−0.659034	+	0.659034i	−0.955152	−	0.296117i	$-0.904308\pi$
$643$	−16.7114	+	16.7114i	−0.659034	+	0.659034i	0.296117	+	0.955152i	$0.404308\pi$
$644$	0.515773	+	1.92788i	0.0203243	+	0.0759691i
$645$		0			0
$646$	−4.67031	−	0.866527i	−0.183751	−	0.0340931i
$647$	0.506217	−	0.993506i	0.0199014	−	0.0390588i	−0.880842	−	0.473411i	$-0.843023\pi$
$647$	0.506217	−	0.993506i	0.0199014	−	0.0390588i	0.900743	+	0.434352i	$0.143023\pi$
$648$		0			0
$649$		−	17.8132i		−	0.699229i
$650$	−1.59007	−	11.8230i	−0.0623676	−	0.463737i
$651$		0			0
$652$	11.2160	−	10.0911i	0.439253	−	0.395197i
$653$	−7.76292	+	15.2356i	−0.303786	+	0.596214i	−0.991551	−	0.129720i	$-0.958592\pi$
$653$	−7.76292	+	15.2356i	−0.303786	+	0.596214i	0.687764	+	0.725934i	$0.258592\pi$
$654$		0			0
$655$	31.3855	−	31.4792i	1.22633	−	1.22999i
$656$	34.1793	+	30.8232i	1.33448	+	1.20344i
$657$		0			0
$658$	−0.984008	−	0.0259581i	−0.0383606	−	0.00101195i
$659$	19.1442	−	13.9091i	0.745752	−	0.541820i	−0.148755	−	0.988874i	$-0.547527\pi$
$659$	19.1442	−	13.9091i	0.745752	−	0.541820i	0.894507	+	0.447054i	$0.147527\pi$
$660$		0			0
$661$	11.9962	+	8.71577i	0.466599	+	0.339004i	0.796115	−	0.605146i	$-0.206885\pi$
$661$	11.9962	+	8.71577i	0.466599	+	0.339004i	−0.329515	+	0.944150i	$0.606885\pi$
$662$	8.34416	+	6.40527i	0.324305	+	0.248948i
$663$		0			0
$664$	11.1631	−	18.1928i	0.433212	−	0.706016i
$665$	−0.000540897	−	0.362870i	−2.09751e−5	−	0.0140715i
$666$		0			0
$667$	−10.9657	+	5.58730i	−0.424594	+	0.216341i
$668$	38.4662	+	8.19183i	1.48830	+	0.316951i
$669$		0			0
$670$	−7.66763	+	21.7423i	−0.296227	+	0.839978i
$671$	50.4448	−	16.3905i	1.94740	−	0.632748i
$672$		0			0
$673$	5.11813	+	32.3146i	0.197289	+	1.24564i	0.865212	+	0.501406i	$0.167184\pi$
$673$	5.11813	+	32.3146i	0.197289	+	1.24564i	−0.667923	+	0.744231i	$0.732816\pi$
$674$	−8.07250	+	14.8608i	−0.310941	+	0.572417i
$675$		0			0
$676$	−11.0537	−	17.0356i	−0.425141	−	0.655216i
$677$	16.7410	−	2.65152i	0.643410	−	0.101906i	0.173801	−	0.984781i	$-0.444395\pi$
$677$	16.7410	−	2.65152i	0.643410	−	0.101906i	0.469609	+	0.882875i	$0.344395\pi$
$678$		0			0
$679$	−0.0853926	−	0.262811i	−0.00327707	−	0.0100858i
$680$	−18.3896	−	29.9479i	−0.705207	−	1.14845i
$681$		0			0
$682$	−42.1236	+	12.4687i	−1.61300	+	0.477451i
$683$	−10.1740	−	19.9676i	−0.389296	−	0.764037i	0.610308	−	0.792164i	$-0.291046\pi$
$683$	−10.1740	−	19.9676i	−0.389296	−	0.764037i	−0.999604	+	0.0281270i	$0.991046\pi$
$684$		0			0
$685$	6.95561	+	5.03772i	0.265760	+	0.192482i
$686$	−4.77341	+	2.27566i	−0.182250	+	0.0868853i
$687$		0			0
$688$	0.0465026	+	0.0302504i	0.00177290	+	0.00115329i
$689$	−9.89915	+	13.6250i	−0.377128	+	0.519072i
$690$		0			0
$691$	−9.13509	−	12.5734i	−0.347515	−	0.478314i	0.599102	−	0.800672i	$-0.295524\pi$
$691$	−9.13509	−	12.5734i	−0.347515	−	0.478314i	−0.946618	+	0.322359i	$0.895524\pi$
$692$	−16.8836	+	29.2171i	−0.641819	+	1.11067i
$693$		0			0
$694$	34.6760	−	32.8936i	1.31628	−	1.24862i
$695$	−36.8273	+	18.8336i	−1.39694	+	0.714400i
$696$		0			0
$697$	−56.9675	−	29.0264i	−2.15780	−	1.09945i
$698$	12.9637	−	36.5859i	0.490684	−	1.38479i
$699$		0			0
$700$	1.99047	−	1.80160i	0.0752327	−	0.0680940i
$701$	10.8238			0.408809			0.204404	−	0.978887i	$-0.434474\pi$
$701$	10.8238			0.408809			0.204404	+	0.978887i	$0.434474\pi$
$702$		0			0
$703$	−1.28295	−	0.653695i	−0.0483873	−	0.0246546i
$704$	−16.5398	−	32.5547i	−0.623367	−	1.22695i
$705$		0			0
$706$	10.9923	−	10.4273i	0.413702	−	0.392436i
$707$	−1.26425	−	1.26425i	−0.0475469	−	0.0475469i
$708$		0			0
$709$	1.47386	+	2.02859i	0.0553519	+	0.0761853i	0.835796	−	0.549041i	$-0.185007\pi$
$709$	1.47386	+	2.02859i	0.0553519	+	0.0761853i	−0.780444	+	0.625226i	$0.785007\pi$
$710$	−19.9549	+	36.8663i	−0.748895	+	1.38357i
$711$		0			0
$712$	20.1640	+	1.59874i	0.755677	+	0.0599153i
$713$	−24.9830	−	3.95692i	−0.935621	−	0.148188i
$714$		0			0
$715$	5.34535	+	16.3682i	0.199905	+	0.612138i
$716$	−1.64521	+	4.28095i	−0.0614842	+	0.159986i
$717$		0			0
$718$	−18.0252	+	5.33550i	−0.672694	+	0.199119i
$719$	−2.03075	+	6.25002i	−0.0757344	+	0.233086i	−0.981756	−	0.190145i	$-0.939104\pi$
$719$	−2.03075	+	6.25002i	−0.0757344	+	0.233086i	0.906022	+	0.423231i	$0.139104\pi$
$720$		0			0
$721$	−1.24627	−	3.83563i	−0.0464135	−	0.142846i
$722$	−14.9225	−	21.7214i	−0.555357	−	0.808386i
$723$		0			0
$724$	23.1204	−	15.0018i	0.859262	−	0.557538i
$725$	13.4233	+	9.69158i	0.498528	+	0.359936i
$726$		0			0
$727$	−4.93599	−	31.1646i	−0.183066	−	1.15583i	−0.892496	−	0.451055i	$-0.851048\pi$
$727$	−4.93599	−	31.1646i	−0.183066	−	1.15583i	0.709430	−	0.704776i	$-0.248952\pi$
$728$	−0.490940	+	1.18329i	−0.0181955	+	0.0438556i
$729$		0			0
$730$	−12.3647	−	9.46232i	−0.457638	−	0.350216i
$731$	−0.0732932	−	0.0238144i	−0.00271085	−	0.000880808i
$732$		0			0
$733$	37.4928	−	19.1035i	1.38483	−	0.705605i	0.406691	−	0.913566i	$-0.366683\pi$
$733$	37.4928	−	19.1035i	1.38483	−	0.705605i	0.978137	+	0.207961i	$0.0666826\pi$
$734$	36.5643	−	4.80657i	1.34961	−	0.177414i
$735$		0			0
$736$	−0.529997	−	21.0184i	−0.0195359	−	0.774747i
$737$	5.20569	−	32.8674i	0.191754	−	1.21069i
$738$		0			0
$739$	−22.9251	−	16.6560i	−0.843313	−	0.612702i	0.0799814	−	0.996796i	$-0.474514\pi$
$739$	−22.9251	−	16.6560i	−0.843313	−	0.612702i	−0.923294	+	0.384094i	$0.874514\pi$
$740$	−2.76857	−	10.2870i	−0.101775	−	0.378159i
$741$		0			0
$742$	−3.78884	−	0.0999495i	−0.139093	−	0.00366926i
$743$	35.9683	−	35.9683i	1.31955	−	1.31955i	0.405414	−	0.914133i	$-0.367127\pi$
$743$	35.9683	−	35.9683i	1.31955	−	1.31955i	0.914133	−	0.405414i	$-0.132873\pi$
$744$		0			0
$745$	−38.1392	−	19.3613i	−1.39731	−	0.709345i
$746$	−7.62943	+	41.1202i	−0.279333	+	1.50552i
$747$		0			0
$748$	33.9276	+	37.7098i	1.24051	+	1.37881i
$749$		−	4.31542i		−	0.157682i
$750$		0			0
$751$			4.28864i			0.156495i	0.996934	+	0.0782473i	$0.0249324\pi$
$751$			4.28864i			0.156495i	−0.996934	+	0.0782473i	$0.975068\pi$
$752$	10.0150	+	2.69183i	0.365208	+	0.0981608i
$753$		0			0
$754$	−7.76774	−	1.44122i	−0.282884	−	0.0524862i
$755$	−1.57433	−	0.799209i	−0.0572959	−	0.0290862i
$756$		0			0
$757$	12.7121	−	12.7121i	0.462030	−	0.462030i	−0.437291	−	0.899320i	$-0.644062\pi$
$757$	12.7121	−	12.7121i	0.462030	−	0.462030i	0.899320	+	0.437291i	$0.144062\pi$
$758$	−0.722167	+	27.3756i	−0.0262303	+	0.994327i
$759$		0			0
$760$	−0.889069	+	3.71812i	−0.0322499	+	0.134871i
$761$	27.1391	+	19.7177i	0.983792	+	0.714766i	0.958553	−	0.284915i	$-0.0919654\pi$
$761$	27.1391	+	19.7177i	0.983792	+	0.714766i	0.0252388	+	0.999681i	$0.491965\pi$
$762$		0			0
$763$	−0.278321	+	1.75725i	−0.0100759	+	0.0636167i
$764$	−2.80910	+	53.2061i	−0.101630	+	1.92493i
$765$		0			0
$766$	1.76968	+	13.4622i	0.0639410	+	0.486409i
$767$	5.86641	−	2.98908i	0.211824	−	0.107930i
$768$		0			0
$769$	38.5837	+	12.5366i	1.39136	+	0.452081i	0.906388	−	0.422447i	$-0.138829\pi$
$769$	38.5837	+	12.5366i	1.39136	+	0.452081i	0.484975	+	0.874528i	$0.338829\pi$
$770$	−2.35504	+	3.07740i	−0.0848696	+	0.110902i
$771$		0			0
$772$	1.92579	+	18.3913i	0.0693108	+	0.661917i
$773$	−1.29494	−	8.17594i	−0.0465758	−	0.294068i	0.953395	−	0.301725i	$-0.0975626\pi$
$773$	−1.29494	−	8.17594i	−0.0465758	−	0.294068i	−0.999971	+	0.00765730i	$0.997563\pi$
$774$		0			0
$775$	10.6116	+	32.3308i	0.381179	+	1.16136i
$776$	0.226728	+	2.90243i	0.00813906	+	0.104191i
$777$		0			0
$778$	22.5223	−	15.4727i	0.807464	−	0.554724i
$779$	2.14923	+	6.61466i	0.0770043	+	0.236995i
$780$		0			0
$781$	18.6980	−	57.5465i	0.669066	−	2.05917i
$782$	8.28986	+	28.0060i	0.296445	+	1.00149i
$783$		0			0
$784$	27.1106	−	5.74056i	0.968235	−	0.205020i
$785$	0.968630	+	2.96609i	0.0345719	+	0.105864i
$786$		0			0
$787$	−12.9653	−	2.05351i	−0.462164	−	0.0731996i	−0.0789893	−	0.996875i	$-0.525169\pi$
$787$	−12.9653	−	2.05351i	−0.462164	−	0.0731996i	−0.383175	+	0.923676i	$0.625169\pi$
$788$	−11.0479	−	24.8400i	−0.393566	−	0.884887i
$789$		0			0
$790$	37.5445	+	20.3220i	1.33577	+	0.723025i
$791$	−2.60729	−	3.58862i	−0.0927045	−	0.127597i
$792$		0			0
$793$	13.8626	+	13.8626i	0.492275	+	0.492275i
$794$	−19.1601	−	20.1984i	−0.679968	−	0.716815i
$795$		0			0
$796$	11.5201	+	9.33623i	0.408321	+	0.330914i
$797$	30.9282	+	15.7587i	1.09553	+	0.558202i	0.905831	−	0.423640i	$-0.139248\pi$
$797$	30.9282	+	15.7587i	1.09553	+	0.558202i	0.189702	+	0.981842i	$0.439248\pi$
$798$		0			0
$799$	−14.4062			−0.509653
$800$	−24.8295	+	13.5461i	−0.877855	+	0.478926i
$801$		0			0
$802$	45.2531	+	16.0348i	1.59794	+	0.566209i
$803$	20.0241	+	10.2028i	0.706634	+	0.360048i
$804$		0			0
$805$	−1.98654	+	1.01592i	−0.0700162	+	0.0358066i
$806$	−11.1747	−	11.7803i	−0.393613	−	0.414942i
$807$		0			0
$808$	9.83252	+	16.0662i	0.345907	+	0.565207i
$809$	11.2361	+	15.4652i	0.395042	+	0.543728i	0.959491	−	0.281739i	$-0.0909114\pi$
$809$	11.2361	+	15.4652i	0.395042	+	0.543728i	−0.564449	+	0.825468i	$0.690911\pi$
$810$		0			0
$811$	8.18655	−	11.2678i	0.287469	−	0.395667i	−0.640721	−	0.767774i	$-0.721365\pi$
$811$	8.18655	−	11.2678i	0.287469	−	0.395667i	0.928190	+	0.372107i	$0.121365\pi$
$812$	−0.722533	−	1.62453i	−0.0253559	−	0.0570098i
$813$		0			0
$814$	6.61713	+	13.8800i	0.231930	+	0.486495i
$815$	13.6614	+	9.89453i	0.478539	+	0.346590i
$816$		0			0
$817$	0.00380592	+	0.00746953i	0.000133152	+	0.000261326i
$818$	−5.48151	−	18.5185i	−0.191656	−	0.647482i
$819$		0			0
$820$	−25.6796	+	44.5918i	−0.896770	+	1.55721i
$821$	−5.48325	−	16.8757i	−0.191367	−	0.588967i	−1.00000		0.000653180i	$-0.999792\pi$
$821$	−5.48325	−	16.8757i	−0.191367	−	0.588967i	0.808633	−	0.588314i	$-0.200208\pi$
$822$		0			0
$823$	−8.33927	+	1.32081i	−0.290689	+	0.0460405i	−0.300076	−	0.953915i	$-0.597012\pi$
$823$	−8.33927	+	1.32081i	−0.290689	+	0.0460405i	0.00938714	+	0.999956i	$0.497012\pi$
$824$	3.30900	+	42.3599i	0.115275	+	1.47568i
$825$		0			0
$826$	1.30204	+	0.707275i	0.0453036	+	0.0246092i
$827$	8.69708	+	54.9112i	0.302427	+	1.90945i	0.404254	+	0.914647i	$0.367531\pi$
$827$	8.69708	+	54.9112i	0.302427	+	1.90945i	−0.101827	+	0.994802i	$0.532469\pi$
$828$		0			0
$829$	19.0441	−	6.18779i	0.661428	−	0.214911i	0.0409816	−	0.999160i	$-0.486952\pi$
$829$	19.0441	−	6.18779i	0.661428	−	0.214911i	0.620446	+	0.784249i	$0.286952\pi$
$830$	22.5055	+	7.93678i	0.781177	+	0.275490i
$831$		0			0
$832$	7.94582	−	10.9098i	0.275472	−	0.378228i
$833$	−34.3002	+	17.4768i	−1.18843	+	0.605536i
$834$		0			0
$835$	0.0655432	+	43.9708i	0.00226822	+	1.52167i
$836$	0.290928	−	5.51035i	0.0100620	−	0.190580i
$837$		0			0
$838$	−5.86708	+	7.64306i	−0.202675	+	0.264025i
$839$	−15.9259	−	11.5708i	−0.549822	−	0.399469i	0.277898	−	0.960611i	$-0.410362\pi$
$839$	−15.9259	−	11.5708i	−0.549822	−	0.399469i	−0.827720	+	0.561142i	$0.810362\pi$
$840$		0			0
$841$	−14.5911	+	10.6010i	−0.503140	+	0.365553i
$842$	0.478902	−	18.1540i	0.0165040	−	0.625628i
$843$		0			0
$844$	15.9623	−	4.27045i	0.549444	−	0.146995i
$845$	16.0306	−	16.0784i	0.551468	−	0.553115i
$846$		0			0
$847$	1.19860	−	2.35239i	0.0411845	−	0.0808291i
$848$	38.5618	+	10.3647i	1.32422	+	0.355924i
$849$		0			0
$850$	28.4255	−	27.1258i	0.974986	−	0.930406i
$851$			8.85366i			0.303499i
$852$		0			0
$853$	−3.78263	+	7.42382i	−0.129515	+	0.254187i	−0.946653	−	0.322255i	$-0.895559\pi$
$853$	−3.78263	+	7.42382i	−0.129515	+	0.254187i	0.817138	+	0.576442i	$0.195559\pi$
$854$	−0.804868	+	4.33799i	−0.0275420	+	0.148443i
$855$		0			0
$856$	−10.6391	+	44.2017i	−0.363637	+	1.51078i
$857$	20.2813	−	20.2813i	0.692795	−	0.692795i	−0.270051	−	0.962846i	$-0.587041\pi$
$857$	20.2813	−	20.2813i	0.692795	−	0.692795i	0.962846	+	0.270051i	$0.0870406\pi$
$858$		0			0
$859$	−7.51815	+	5.46225i	−0.256516	+	0.186370i	−0.708610	−	0.705601i	$-0.750677\pi$
$859$	−7.51815	+	5.46225i	−0.256516	+	0.186370i	0.452094	+	0.891970i	$0.350677\pi$
$860$	−0.0221635	+	0.0579289i	−0.000755771	+	0.00197536i
$861$		0			0
$862$	3.81336	+	2.92727i	0.129883	+	0.0997030i
$863$	−1.61317	+	10.1852i	−0.0549130	+	0.346707i	0.944900	+	0.327360i	$0.106159\pi$
$863$	−1.61317	+	10.1852i	−0.0549130	+	0.346707i	−0.999813	+	0.0193475i	$0.993841\pi$
$864$		0			0
$865$	−35.8984	−	11.6050i	−1.22058	−	0.394581i
$866$	−4.79682	+	0.630568i	−0.163003	+	0.0214276i
$867$		0			0
$868$	0.761136	−	3.57405i	0.0258346	−	0.121311i
$869$	−58.6051	−	19.0419i	−1.98804	−	0.645954i
$870$		0			0
$871$	11.6977	−	3.80082i	0.396363	−	0.128786i
$872$	7.18304	−	17.3129i	0.243249	−	0.586289i
$873$		0			0
$874$	1.51657	−	2.79189i	0.0512988	−	0.0944369i
$875$	2.43622	+	1.75343i	0.0823592	+	0.0592766i
$876$		0			0
$877$	−13.9619	+	2.21134i	−0.471458	+	0.0746716i	−0.387643	−	0.921810i	$-0.626711\pi$
$877$	−13.9619	+	2.21134i	−0.471458	+	0.0746716i	−0.0838154	+	0.996481i	$0.526711\pi$
$878$	−16.0474	−	23.3588i	−0.541573	−	0.788322i
$879$		0			0
$880$	31.7090	−	25.7150i	1.06891	−	0.866852i
$881$	7.58893	−	23.3563i	0.255677	−	0.786894i	−0.738018	−	0.674781i	$-0.764238\pi$
$881$	7.58893	−	23.3563i	0.255677	−	0.786894i	0.993695	−	0.112113i	$-0.0357620\pi$
$882$		0			0
$883$	−10.6317	−	20.8659i	−0.357786	−	0.702195i	0.640023	−	0.768356i	$-0.278925\pi$
$883$	−10.6317	−	20.8659i	−0.357786	−	0.702195i	−0.997809	+	0.0661610i	$0.978925\pi$
$884$	−6.72583	+	17.5011i	−0.226214	+	0.588625i
$885$		0			0
$886$	18.4627	−	8.80187i	0.620267	−	0.295705i
$887$	−9.96921	−	1.57897i	−0.334733	−	0.0530166i	−0.0131946	−	0.999913i	$-0.504200\pi$
$887$	−9.96921	−	1.57897i	−0.334733	−	0.0530166i	−0.321539	+	0.946896i	$0.604200\pi$
$888$		0			0
$889$	−0.218671	+	0.300974i	−0.00733398	+	0.0100944i
$890$	2.98089	+	22.4174i	0.0999197	+	0.751434i
$891$		0			0
$892$	−7.29634	−	4.21632i	−0.244299	−	0.141173i
$893$	1.10812	+	1.10812i	0.0370820	+	0.0370820i
$894$		0			0
$895$	−5.06558	−	0.794571i	−0.169324	−	0.0265596i
$896$	3.03626	+	0.0836310i	0.101434	+	0.00279392i
$897$		0			0
$898$	−9.50440	+	26.8231i	−0.317166	+	0.895098i
$899$	22.5349			0.751582
$900$		0			0
$901$	−55.4697			−1.84797
$902$	24.8066	−	70.0086i	0.825970	−	2.33103i
$903$		0			0
$904$	17.8585	+	43.1853i	0.593965	+	1.43632i
$905$	21.8213	+	21.7564i	0.725365	+	0.723206i
$906$		0			0
$907$	2.65824	+	2.65824i	0.0882653	+	0.0882653i	0.749861	−	0.661596i	$-0.230120\pi$
$907$	2.65824	+	2.65824i	0.0882653	+	0.0882653i	−0.661596	+	0.749861i	$0.730120\pi$
$908$	−10.3529	+	17.9157i	−0.343574	+	0.594555i
$909$		0			0
$910$	−1.40866	−	0.259190i	−0.0466965	−	0.00859206i
$911$	−5.17032	+	7.11634i	−0.171300	+	0.235775i	−0.886032	−	0.463624i	$-0.846549\pi$
$911$	−5.17032	+	7.11634i	−0.171300	+	0.235775i	0.714732	+	0.699399i	$0.246549\pi$
$912$		0			0
$913$	−34.0211	−	5.38842i	−1.12594	−	0.178331i
$914$	−9.93430	+	4.73606i	−0.328598	+	0.156655i
$915$		0			0
$916$	−3.04300	−	1.16945i	−0.100544	−	0.0386398i
$917$	−2.42300	−	4.75540i	−0.0800145	−	0.157037i
$918$		0			0
$919$	5.44982	−	16.7728i	0.179773	−	0.553284i	−0.820046	−	0.572297i	$-0.806052\pi$
$919$	5.44982	−	16.7728i	0.179773	−	0.553284i	0.999819	+	0.0190131i	$0.00605242\pi$
$920$	22.8522	−	5.50831i	0.753416	−	0.181604i
$921$		0			0
$922$	1.97184	+	2.87023i	0.0649390	+	0.0945261i
$923$	22.0893	−	3.49860i	0.727077	−	0.115158i
$924$		0			0
$925$	10.5962	−	5.43888i	0.348400	−	0.178829i
$926$	22.6992	−	41.7874i	0.745942	−	1.37322i
$927$		0			0
$928$	3.39566	+	18.4210i	0.111468	+	0.604698i
$929$	35.1070	−	11.4069i	1.15182	−	0.374250i	0.329993	−	0.943983i	$-0.392954\pi$
$929$	35.1070	−	11.4069i	1.15182	−	0.374250i	0.821829	+	0.569734i	$0.192954\pi$
$930$		0			0
$931$	3.98270	+	1.29406i	0.130528	+	0.0424110i
$932$	−5.85741	−	1.24741i	−0.191866	−	0.0408601i
$933$		0			0
$934$	15.0819	−	1.98260i	0.493495	−	0.0648725i
$935$	−33.2667	+	45.9315i	−1.08794	+	1.50212i
$936$		0			0
$937$	6.89911	−	43.5592i	0.225384	−	1.42302i	−0.572350	−	0.820009i	$-0.693968\pi$
$937$	6.89911	−	43.5592i	0.225384	−	1.42302i	0.797734	−	0.603009i	$-0.206032\pi$
$938$	2.19572	+	1.68551i	0.0716926	+	0.0550338i
$939$		0			0
$940$	−0.594038	+	11.5792i	−0.0193754	+	0.377673i
$941$	−8.90352	+	6.46878i	−0.290246	+	0.210876i	−0.723374	−	0.690456i	$-0.757410\pi$
$941$	−8.90352	+	6.46878i	−0.290246	+	0.210876i	0.433128	+	0.901332i	$0.357410\pi$
$942$		0			0
$943$	30.2399	−	30.2399i	0.984747	−	0.984747i
$944$	−11.5927	−	10.4544i	−0.377311	−	0.340263i
$945$		0			0
$946$	0.0163318	−	0.0880231i	0.000530991	−	0.00286188i
$947$	23.8973	−	46.9012i	0.776559	−	1.52408i	−0.0734408	−	0.997300i	$-0.523398\pi$
$947$	23.8973	−	46.9012i	0.776559	−	1.52408i	0.850000	−	0.526783i	$-0.176602\pi$
$948$		0			0
$949$			8.30656i			0.269642i
$950$	−4.27301	−	0.0999751i	−0.138635	−	0.00324362i
$951$		0			0
$952$	−4.10345	+	0.982627i	−0.132993	+	0.0318471i
$953$	7.88451	−	15.4742i	0.255404	−	0.501259i	−0.727329	−	0.686289i	$-0.759238\pi$
$953$	7.88451	−	15.4742i	0.255404	−	0.501259i	0.982733	+	0.185030i	$0.0592383\pi$
$954$		0			0
$955$	−58.8217	+	9.40635i	−1.90343	+	0.304382i
$956$	11.4467	+	42.7859i	0.370211	+	1.38379i
$957$		0			0
$958$	−0.855186	+	32.4181i	−0.0276298	+	1.04738i
$959$	0.834219	−	0.606095i	0.0269383	−	0.0195718i
$960$		0			0
$961$	12.3904	+	9.00217i	0.399691	+	0.290392i
$962$	−3.46073	+	4.50830i	−0.111578	+	0.145354i
$963$		0			0
$964$	−0.151614	−	0.00800471i	−0.00488316	−	0.000257814i
$965$	−19.6531	+	6.41808i	−0.632655	+	0.206605i
$966$		0			0
$967$	−53.2482	+	27.1313i	−1.71235	+	0.872485i	−0.730476	+	0.682939i	$0.760702\pi$
$967$	−53.2482	+	27.1313i	−1.71235	+	0.872485i	−0.981872	+	0.189546i	$0.939298\pi$
$968$	−18.0765	+	21.1400i	−0.581001	+	0.679464i
$969$		0			0
$970$	−3.11967	+	0.928490i	−0.100166	+	0.0298120i
$971$	39.7349	−	12.9106i	1.27515	−	0.414322i	0.408283	−	0.912856i	$-0.366128\pi$
$971$	39.7349	−	12.9106i	1.27515	−	0.414322i	0.866871	+	0.498533i	$0.166128\pi$
$972$		0			0
$973$	0.776901	+	4.90516i	0.0249063	+	0.157252i
$974$	−20.9307	−	11.3697i	−0.670662	−	0.364308i
$975$		0			0
$976$	18.9388	−	42.4486i	0.606216	−	1.35875i
$977$	−26.2795	+	4.16226i	−0.840754	+	0.133162i	−0.561935	−	0.827181i	$-0.689943\pi$
$977$	−26.2795	+	4.16226i	−0.840754	+	0.133162i	−0.278819	+	0.960344i	$0.589943\pi$
$978$		0			0
$979$	−10.0870	−	31.0445i	−0.322381	−	0.992186i
$980$	12.6330	+	28.2901i	0.403545	+	0.903694i
$981$		0			0
$982$	4.58530	+	15.4907i	0.146323	+	0.494329i
$983$	−1.53672	−	3.01599i	−0.0490138	−	0.0961950i	0.865200	−	0.501426i	$-0.167191\pi$
$983$	−1.53672	−	3.01599i	−0.0490138	−	0.0961950i	−0.914214	+	0.405231i	$0.867191\pi$
$984$		0			0
$985$	24.5633	−	17.9023i	0.782653	−	0.570415i
$986$	−11.1977	−	23.4882i	−0.356607	−	0.748016i
$987$		0			0
$988$	1.86354	−	0.828835i	0.0592871	−	0.0263688i
$989$	0.0302988	−	0.0417027i	0.000963446	−	0.00132607i
$990$		0			0
$991$	−29.2963	−	40.3229i	−0.930627	−	1.28090i	−0.959614	−	0.281319i	$-0.909228\pi$
$991$	−29.2963	−	40.3229i	−0.930627	−	1.28090i	0.0289870	−	0.999580i	$-0.490772\pi$
$992$	−16.6075	+	34.7316i	−0.527288	+	1.10273i
$993$		0			0
$994$	3.46389	+	3.65159i	0.109868	+	0.115821i
$995$	−7.50448	+	14.7828i	−0.237908	+	0.468647i
$996$		0			0
$997$	18.8621	+	9.61073i	0.597369	+	0.304375i	0.726407	−	0.687265i	$-0.241189\pi$
$997$	18.8621	+	9.61073i	0.597369	+	0.304375i	−0.129038	+	0.991640i	$0.541189\pi$
$998$	55.8167	+	19.7779i	1.76685	+	0.626058i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.163.4		240
3.2	odd	2		300.2.w.a.163.27	yes	240
4.3	odd	2	inner	900.2.bj.f.163.8		240
12.11	even	2		300.2.w.a.163.23	yes	240
25.2	odd	20	inner	900.2.bj.f.127.8		240
75.2	even	20		300.2.w.a.127.23	✓	240
100.27	even	20	inner	900.2.bj.f.127.4		240
300.227	odd	20		300.2.w.a.127.27	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.23	✓	240	75.2	even	20
300.2.w.a.127.27	yes	240	300.227	odd	20
300.2.w.a.163.23	yes	240	12.11	even	2
300.2.w.a.163.27	yes	240	3.2	odd	2
900.2.bj.f.127.4		240	100.27	even	20	inner
900.2.bj.f.127.8		240	25.2	odd	20	inner
900.2.bj.f.163.4		240	1.1	even	1	trivial
900.2.bj.f.163.8		240	4.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33300 - 0.472333i) q^{2} +(1.55380 + 1.25924i) q^{4} +(-1.01218 + 1.99386i) q^{5} +(0.189838 + 0.189838i) q^{7} +(-1.47645 - 2.41249i) q^{8} +(2.29101 - 2.17974i) q^{10} +(-2.68290 + 3.69270i) q^{11} +(-1.66631 - 0.263917i) q^{13} +(-0.163389 - 0.342722i) q^{14} +(0.828612 + 3.91323i) q^{16} +(-2.52266 - 4.95101i) q^{17} +(-0.186788 + 0.574876i) q^{19} +(-4.08349 + 1.82349i) q^{20} +(5.32050 - 3.65516i) q^{22} +(3.67098 - 0.581426i) q^{23} +(-2.95097 - 4.03631i) q^{25} +(2.09654 + 1.13886i) q^{26} +(0.0559189 + 0.534025i) q^{28} +(-3.14920 + 1.02324i) q^{29} +(-6.47245 - 2.10303i) q^{31} +(0.743804 - 5.60774i) q^{32} +(1.02420 + 7.79125i) q^{34} +(-0.570663 + 0.186361i) q^{35} +(-0.372643 + 2.35278i) q^{37} +(0.520523 - 0.678086i) q^{38} +(6.30461 - 0.501950i) q^{40} +(9.30874 - 6.76320i) q^{41} +(0.00980686 - 0.00980686i) q^{43} +(-8.81871 + 2.35930i) q^{44} +(-5.16806 - 0.958880i) q^{46} +(1.17702 - 2.31002i) q^{47} -6.92792i q^{49} +(2.02718 + 6.77426i) q^{50} +(-2.25678 - 2.50836i) q^{52} +(4.53201 - 8.89456i) q^{53} +(-4.64714 - 9.08702i) q^{55} +(0.177697 - 0.738270i) q^{56} +(4.68120 + 0.123490i) q^{58} +(-3.15728 + 2.29390i) q^{59} +(-9.40115 - 6.83034i) q^{61} +(7.63448 + 5.86050i) q^{62} +(-3.64021 + 7.12382i) q^{64} +(2.21282 - 3.05526i) q^{65} +(-6.49592 + 3.30984i) q^{67} +(2.31480 - 10.8695i) q^{68} +(0.848721 + 0.0211233i) q^{70} +(-12.6076 + 4.09646i) q^{71} +(-0.770226 - 4.86301i) q^{73} +(1.60803 - 2.96025i) q^{74} +(-1.01414 + 0.658032i) q^{76} +(-1.21033 + 0.191698i) q^{77} +(4.17182 + 12.8395i) q^{79} +(-8.64116 - 2.30877i) q^{80} +(-15.6031 + 4.61855i) q^{82} +(3.42602 + 6.72394i) q^{83} +(12.4250 - 0.0185208i) q^{85} +(-0.0177047 + 0.00844049i) q^{86} +(12.8698 + 1.02040i) q^{88} +(-4.20350 + 5.78562i) q^{89} +(-0.266228 - 0.366431i) q^{91} +(6.43614 + 3.71924i) q^{92} +(-2.66007 + 2.52333i) q^{94} +(-0.957159 - 0.954310i) q^{95} +(-0.917106 - 0.467289i) q^{97} +(-3.27228 + 9.23495i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58}+ \cdots - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more