LMFDB - Embedded newform 441.2.bb.c.415.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(37,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([0, 32])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			415.1
Character	$\chi$	$=$	441.415
Dual form			441.2.bb.c.424.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0998595 + 1.33253i) q^{2} +(0.211992 + 0.0319527i) q^{4} +(-2.75951 - 2.56045i) q^{5} +(0.0649242 + 2.64495i) q^{7} +(-0.658443 + 2.88483i) q^{8} +(3.68744 - 3.42144i) q^{10} +(3.72186 + 2.53752i) q^{11} +(-0.0589476 + 0.0283876i) q^{13} +(-3.53097 - 0.177610i) q^{14} +(-3.36865 - 1.03909i) q^{16} +(-2.49491 + 6.35693i) q^{17} +(-1.99519 + 3.45577i) q^{19} +(-0.503181 - 0.630969i) q^{20} +(-3.75299 + 4.70610i) q^{22} +(-1.55211 - 3.95470i) q^{23} +(0.685332 + 9.14512i) q^{25} +(-0.0319410 - 0.0813843i) q^{26} +(-0.0707500 + 0.562784i) q^{28} +(5.59990 + 7.02205i) q^{29} +(-2.05289 - 3.55571i) q^{31} +(-0.441087 + 1.12387i) q^{32} +(-8.22168 - 3.95935i) q^{34} +(6.59311 - 7.46500i) q^{35} +(1.91661 - 0.288883i) q^{37} +(-4.40569 - 3.00375i) q^{38} +(9.20342 - 6.27479i) q^{40} +(1.34401 - 5.88848i) q^{41} +(-0.175833 - 0.770376i) q^{43} +(0.707924 + 0.656858i) q^{44} +(5.42476 - 1.67332i) q^{46} +(-0.0438639 + 0.585323i) q^{47} +(-6.99157 + 0.343443i) q^{49} -12.2546 q^{50} +(-0.0134035 + 0.00413443i) q^{52} +(3.00301 + 0.452631i) q^{53} +(-3.77330 - 16.5319i) q^{55} +(-7.67298 - 1.55426i) q^{56} +(-9.91631 + 6.76083i) q^{58} +(1.36966 - 1.27086i) q^{59} +(4.88060 - 0.735633i) q^{61} +(4.94310 - 2.38047i) q^{62} +(-7.80586 - 3.75910i) q^{64} +(0.235351 + 0.0725962i) q^{65} +(-1.53195 - 2.65342i) q^{67} +(-0.732023 + 1.26790i) q^{68} +(9.28897 + 9.53098i) q^{70} +(3.78229 - 4.74284i) q^{71} +(0.783605 + 10.4565i) q^{73} +(0.193554 + 2.58280i) q^{74} +(-0.533386 + 0.668845i) q^{76} +(-6.46999 + 10.0089i) q^{77} +(6.49358 - 11.2472i) q^{79} +(6.63527 + 11.4926i) q^{80} +(7.71238 + 2.37895i) q^{82} +(-2.60881 - 1.25634i) q^{83} +(23.1613 - 11.1539i) q^{85} +(1.04411 - 0.157374i) q^{86} +(-9.77094 + 9.06610i) q^{88} +(9.50569 - 6.48087i) q^{89} +(-0.0789112 - 0.154071i) q^{91} +(-0.202671 - 0.887960i) q^{92} +(-0.775581 - 0.116900i) q^{94} +(14.3541 - 4.42764i) q^{95} +9.43444 q^{97} +(0.240525 - 9.35079i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32}+ \cdots - 119 q^{98}+O(q^{100}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{19}{21}\right)$	$1$

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 $

$2$	−0.0998595	+	1.33253i	−0.0706113	+	0.942242i	0.843592	+	0.536985i	$0.180437\pi$
$2$	−0.0998595	+	1.33253i	−0.0706113	+	0.942242i	−0.914203	+	0.405257i	$0.867182\pi$
$3$		0			0
$3$		0			0
$4$	0.211992	+	0.0319527i	0.105996	+	0.0159763i
$5$	−2.75951	−	2.56045i	−1.23409	−	1.14507i	−0.984251	−	0.176779i	$-0.943432\pi$
$5$	−2.75951	−	2.56045i	−1.23409	−	1.14507i	−0.249838	−	0.968288i	$-0.580377\pi$
$6$		0			0
$7$	0.0649242	+	2.64495i	0.0245391	+	0.999699i
$7$	0.0649242	+	2.64495i	0.0245391	+	0.999699i
$8$	−0.658443	+	2.88483i	−0.232795	+	1.01994i
$9$		0			0
$10$	3.68744	−	3.42144i	1.16607	−	1.08196i
$11$	3.72186	+	2.53752i	1.12218	+	0.765091i	0.974599	−	0.223958i	$-0.0718980\pi$
$11$	3.72186	+	2.53752i	1.12218	+	0.765091i	0.147584	+	0.989050i	$0.452850\pi$
$12$		0			0
$13$	−0.0589476	+	0.0283876i	−0.0163491	+	0.00787332i	−0.442040	−	0.896995i	$-0.645745\pi$
$13$	−0.0589476	+	0.0283876i	−0.0163491	+	0.00787332i	0.425691	+	0.904868i	$0.360031\pi$
$14$	−3.53097	−	0.177610i	−0.943691	−	0.0474683i
$15$		0			0
$16$	−3.36865	−	1.03909i	−0.842162	−	0.259773i
$17$	−2.49491	+	6.35693i	−0.605105	+	1.54178i	0.219225	+	0.975674i	$0.429647\pi$
$17$	−2.49491	+	6.35693i	−0.605105	+	1.54178i	−0.824330	+	0.566109i	$0.808448\pi$
$18$		0			0
$19$	−1.99519	+	3.45577i	−0.457728	+	0.792809i	−0.998841	−	0.0481418i	$-0.984670\pi$
$19$	−1.99519	+	3.45577i	−0.457728	+	0.792809i	0.541112	+	0.840950i	$0.318003\pi$
$20$	−0.503181	−	0.630969i	−0.112515	−	0.141089i
$21$		0			0
$22$	−3.75299	+	4.70610i	−0.800140	+	1.00334i
$23$	−1.55211	−	3.95470i	−0.323637	−	0.824612i	−0.996402	−	0.0847563i	$-0.972989\pi$
$23$	−1.55211	−	3.95470i	−0.323637	−	0.824612i	0.672765	−	0.739856i	$-0.265106\pi$
$24$		0			0
$25$	0.685332	+	9.14512i	0.137066	+	1.82902i
$26$	−0.0319410	−	0.0813843i	−0.00626414	−	0.0159608i
$27$		0			0
$28$	−0.0707500	+	0.562784i	−0.0133705	+	0.106356i
$29$	5.59990	+	7.02205i	1.03988	+	1.30396i	0.951425	+	0.307882i	$0.0996203\pi$
$29$	5.59990	+	7.02205i	1.03988	+	1.30396i	0.0884510	+	0.996081i	$0.471808\pi$
$30$		0			0
$31$	−2.05289	−	3.55571i	−0.368710	−	0.638625i	0.620654	−	0.784085i	$-0.286867\pi$
$31$	−2.05289	−	3.55571i	−0.368710	−	0.638625i	−0.989364	+	0.145460i	$0.953534\pi$
$32$	−0.441087	+	1.12387i	−0.0779739	+	0.198674i
$33$		0			0
$34$	−8.22168	−	3.95935i	−1.41001	−	0.679023i
$35$	6.59311	−	7.46500i	1.11444	−	1.26182i
$36$		0			0
$37$	1.91661	−	0.288883i	0.315089	−	0.0474921i	0.0104061	−	0.999946i	$-0.496688\pi$
$37$	1.91661	−	0.288883i	0.315089	−	0.0474921i	0.304683	+	0.952454i	$0.401449\pi$
$38$	−4.40569	−	3.00375i	−0.714697	−	0.487272i
$39$		0			0
$40$	9.20342	−	6.27479i	1.45519	−	0.992131i
$41$	1.34401	−	5.88848i	0.209899	−	0.919626i	−0.754735	−	0.656030i	$-0.772234\pi$
$41$	1.34401	−	5.88848i	0.209899	−	0.919626i	0.964633	−	0.263596i	$-0.0849085\pi$
$42$		0			0
$43$	−0.175833	−	0.770376i	−0.0268143	−	0.117481i	0.959750	−	0.280857i	$-0.0906188\pi$
$43$	−0.175833	−	0.770376i	−0.0268143	−	0.117481i	−0.986564	+	0.163376i	$0.947762\pi$
$44$	0.707924	+	0.656858i	0.106724	+	0.0990251i
$45$		0			0
$46$	5.42476	−	1.67332i	0.799837	−	0.246717i
$47$	−0.0438639	+	0.585323i	−0.00639820	+	0.0853781i	−0.999489	−	0.0319725i	$-0.989821\pi$
$47$	−0.0438639	+	0.585323i	−0.00639820	+	0.0853781i	0.993091	+	0.117351i	$0.0374401\pi$
$48$		0			0
$49$	−6.99157	+	0.343443i	−0.998796	+	0.0490633i
$50$	−12.2546			−1.73306
$51$		0			0
$52$	−0.0134035	+	0.00413443i	−0.00185873	+	0.000573342i
$53$	3.00301	+	0.452631i	0.412496	+	0.0621737i	0.352012	−	0.935995i	$-0.385498\pi$
$53$	3.00301	+	0.452631i	0.412496	+	0.0621737i	0.0604836	+	0.998169i	$0.480736\pi$
$54$		0			0
$55$	−3.77330	−	16.5319i	−0.508792	−	2.22916i
$56$	−7.67298	−	1.55426i	−1.02535	−	0.207696i
$57$		0			0
$58$	−9.91631	+	6.76083i	−1.30208	+	0.887740i
$59$	1.36966	−	1.27086i	0.178314	−	0.165451i	−0.585966	−	0.810336i	$-0.699285\pi$
$59$	1.36966	−	1.27086i	0.178314	−	0.165451i	0.764280	+	0.644884i	$0.223094\pi$
$60$		0			0
$61$	4.88060	−	0.735633i	0.624897	−	0.0941881i	0.171042	−	0.985264i	$-0.445287\pi$
$61$	4.88060	−	0.735633i	0.624897	−	0.0941881i	0.453855	+	0.891076i	$0.350048\pi$
$62$	4.94310	−	2.38047i	0.627775	−	0.302320i
$63$		0			0
$64$	−7.80586	−	3.75910i	−0.975732	−	0.469888i
$65$	0.235351	+	0.0725962i	0.0291917	+	0.00900445i
$66$		0			0
$67$	−1.53195	−	2.65342i	−0.187158	−	0.324166i	0.757144	−	0.653248i	$-0.226594\pi$
$67$	−1.53195	−	2.65342i	−0.187158	−	0.324166i	−0.944301	+	0.329082i	$0.893261\pi$
$68$	−0.732023	+	1.26790i	−0.0887709	+	0.153756i
$69$		0			0
$70$	9.28897	+	9.53098i	1.11024	+	1.13917i
$71$	3.78229	−	4.74284i	0.448875	−	0.562871i	−0.504983	−	0.863129i	$-0.668501\pi$
$71$	3.78229	−	4.74284i	0.448875	−	0.562871i	0.953858	+	0.300258i	$0.0970728\pi$
$72$		0			0
$73$	0.783605	+	10.4565i	0.0917140	+	1.22384i	0.833239	+	0.552913i	$0.186484\pi$
$73$	0.783605	+	10.4565i	0.0917140	+	1.22384i	−0.741525	+	0.670925i	$0.765897\pi$
$74$	0.193554	+	2.58280i	0.0225002	+	0.300244i
$75$		0			0
$76$	−0.533386	+	0.668845i	−0.0611836	+	0.0767218i
$77$	−6.46999	+	10.0089i	−0.737323	+	1.14062i
$78$		0			0
$79$	6.49358	−	11.2472i	0.730585	−	1.26541i	−0.226049	−	0.974116i	$-0.572581\pi$
$79$	6.49358	−	11.2472i	0.730585	−	1.26541i	0.956634	−	0.291294i	$-0.0940858\pi$
$80$	6.63527	+	11.4926i	0.741845	+	1.28491i
$81$		0			0
$82$	7.71238	+	2.37895i	0.851690	+	0.262711i
$83$	−2.60881	−	1.25634i	−0.286354	−	0.137901i	0.285193	−	0.958470i	$-0.407942\pi$
$83$	−2.60881	−	1.25634i	−0.286354	−	0.137901i	−0.571547	+	0.820569i	$0.693657\pi$
$84$		0			0
$85$	23.1613	−	11.1539i	2.51220	−	1.20981i
$86$	1.04411	−	0.157374i	0.112589	−	0.0169701i
$87$		0			0
$88$	−9.77094	+	9.06610i	−1.04159	+	0.966450i
$89$	9.50569	−	6.48087i	1.00760	−	0.686971i	0.0573173	−	0.998356i	$-0.481745\pi$
$89$	9.50569	−	6.48087i	1.00760	−	0.686971i	0.950284	+	0.311385i	$0.100793\pi$
$90$		0			0
$91$	−0.0789112	−	0.154071i	−0.00827214	−	0.0161510i
$92$	−0.202671	−	0.887960i	−0.0211299	−	0.0925762i
$93$		0			0
$94$	−0.775581	−	0.116900i	−0.0799951	−	0.0120573i
$95$	14.3541	−	4.42764i	1.47270	−	0.454267i
$96$		0			0
$97$	9.43444			0.957922			0.478961	−	0.877836i	$-0.341013\pi$
$97$	9.43444			0.957922			0.478961	+	0.877836i	$0.341013\pi$
$98$	0.240525	−	9.35079i	0.0242967	−	0.944572i
$99$		0			0
$100$	−0.146926	+	1.96059i	−0.0146926	+	0.196059i
$101$	2.02096	−	0.623382i	0.201093	−	0.0620289i	−0.192573	−	0.981283i	$-0.561683\pi$
$101$	2.02096	−	0.623382i	0.201093	−	0.0620289i	0.393665	+	0.919254i	$0.371207\pi$
$102$		0			0
$103$	4.79710	+	4.45106i	0.472672	+	0.438576i	0.880190	−	0.474621i	$-0.157415\pi$
$103$	4.79710	+	4.45106i	0.472672	+	0.438576i	−0.407518	+	0.913197i	$0.633606\pi$
$104$	−0.0430798	−	0.188745i	−0.00422433	−	0.0185080i
$105$		0			0
$106$	−0.903025	+	3.95641i	−0.0877095	+	0.384281i
$107$	−12.3936	+	8.44979i	−1.19813	+	0.816872i	−0.987021	−	0.160590i	$-0.948660\pi$
$107$	−12.3936	+	8.44979i	−1.19813	+	0.816872i	−0.211110	+	0.977462i	$0.567708\pi$
$108$		0			0
$109$	−3.43593	−	2.34257i	−0.329102	−	0.224378i	0.387484	−	0.921876i	$-0.373344\pi$
$109$	−3.43593	−	2.34257i	−0.329102	−	0.224378i	−0.716586	+	0.697498i	$0.754296\pi$
$110$	22.4061	−	3.37718i	2.13634	−	0.322001i
$111$		0			0
$112$	2.52964	−	8.97738i	0.239028	−	0.848283i
$113$	−12.2623	−	5.90522i	−1.15354	−	0.555516i	−0.243446	−	0.969915i	$-0.578278\pi$
$113$	−12.2623	−	5.90522i	−1.15354	−	0.555516i	−0.910096	+	0.414398i	$0.863992\pi$
$114$		0			0
$115$	−5.84276	+	14.8871i	−0.544840	+	1.38823i
$116$	0.962762	+	1.66755i	0.0893902	+	0.154828i
$117$		0			0
$118$	1.55668	+	1.95202i	0.143304	+	0.179698i
$119$	−16.9758	−	6.18621i	−1.55617	−	0.567089i
$120$		0			0
$121$	3.39447	+	8.64897i	0.308588	+	0.786270i
$122$	0.492880	+	6.57702i	0.0446232	+	0.595455i
$123$		0			0
$124$	−0.321583	−	0.819379i	−0.0288790	−	0.0735824i
$125$	9.78907	−	12.2751i	0.875561	−	1.09792i
$126$		0			0
$127$	−2.01055	−	2.52115i	−0.178407	−	0.223716i	0.684585	−	0.728933i	$-0.259984\pi$
$127$	−2.01055	−	2.52115i	−0.178407	−	0.223716i	−0.862992	+	0.505218i	$0.831412\pi$
$128$	4.58128	−	7.93501i	0.404932	−	0.701363i
$129$		0			0
$130$	−0.120239	+	0.306364i	−0.0105456	+	0.0268699i
$131$	8.96036	+	2.76390i	0.782870	+	0.241483i	0.660325	−	0.750980i	$-0.270418\pi$
$131$	8.96036	+	2.76390i	0.782870	+	0.241483i	0.122545	+	0.992463i	$0.460895\pi$
$132$		0			0
$133$	−9.26990	−	5.05283i	−0.803802	−	0.438136i
$134$	3.68874	−	1.77640i	0.318659	−	0.153458i
$135$		0			0
$136$	−16.6959	−	11.3831i	−1.43166	−	0.976090i
$137$	5.83694	−	5.41589i	0.498684	−	0.462711i	−0.390275	−	0.920698i	$-0.627620\pi$
$137$	5.83694	−	5.41589i	0.498684	−	0.462711i	0.888959	+	0.457988i	$0.151430\pi$
$138$		0			0
$139$	−2.20355	+	9.65438i	−0.186903	+	0.818874i	0.791334	+	0.611383i	$0.209387\pi$
$139$	−2.20355	+	9.65438i	−0.186903	+	0.818874i	−0.978237	+	0.207490i	$0.933470\pi$
$140$	1.63621	−	1.37186i	0.138285	−	0.115943i
$141$		0			0
$142$	5.94229	+	5.51363i	0.498665	+	0.462694i
$143$	−0.291429	−	0.0439258i	−0.0243705	−	0.00367326i
$144$		0			0
$145$	2.52664	−	33.7156i	0.209826	−	2.79993i
$146$	−14.0118			−1.15963
$147$		0			0
$148$	0.415538			0.0341570
$149$	0.369028	−	4.92434i	0.0302320	−	0.403418i	−0.961474	−	0.274894i	$-0.911357\pi$
$149$	0.369028	−	4.92434i	0.0302320	−	0.403418i	0.991706	−	0.128524i	$-0.0410238\pi$
$150$		0			0
$151$	14.1090	+	2.12659i	1.14818	+	0.173060i	0.695440	−	0.718584i	$-0.255210\pi$
$151$	14.1090	+	2.12659i	1.14818	+	0.173060i	0.452737	+	0.891644i	$0.350448\pi$
$152$	−8.65558	−	8.03121i	−0.702061	−	0.651417i
$153$		0			0
$154$	−12.6911	−	9.62095i	−1.02268	−	0.775278i
$155$	−3.43925	+	15.0683i	−0.276247	+	1.21032i
$156$		0			0
$157$	−5.68342	+	5.27344i	−0.453586	+	0.420867i	−0.873595	−	0.486653i	$-0.838217\pi$
$157$	−5.68342	+	5.27344i	−0.453586	+	0.420867i	0.420009	+	0.907520i	$0.362027\pi$
$158$	14.3388	+	9.77604i	1.14074	+	0.777740i
$159$		0			0
$160$	4.09480	−	1.97195i	0.323722	−	0.155896i
$161$	10.3592	−	4.36201i	0.816422	−	0.343774i
$162$		0			0
$163$	3.65640	+	1.12785i	0.286391	+	0.0883399i	0.434622	−	0.900613i	$-0.356882\pi$
$163$	3.65640	+	1.12785i	0.286391	+	0.0883399i	−0.148231	+	0.988953i	$0.547358\pi$
$164$	0.473072	−	1.20537i	0.0369407	−	0.0941234i
$165$		0			0
$166$	1.93462	−	3.35086i	0.150156	−	0.260077i
$167$	10.3140	+	12.9333i	0.798121	+	1.00081i	0.999772	+	0.0213544i	$0.00679785\pi$
$167$	10.3140	+	12.9333i	0.798121	+	1.00081i	−0.201651	+	0.979457i	$0.564631\pi$
$168$		0			0
$169$	−8.10270	+	10.1605i	−0.623284	+	0.781574i
$170$	12.5501	+	31.9770i	0.962545	+	2.45253i
$171$		0			0
$172$	−0.0126597	−	0.168932i	−0.000965294	−	0.0128809i
$173$	−4.33512	−	11.0457i	−0.329593	−	0.839789i	−0.995588	−	0.0938329i	$-0.970088\pi$
$173$	−4.33512	−	11.0457i	−0.329593	−	0.839789i	0.665995	−	0.745956i	$-0.268007\pi$
$174$		0			0
$175$	−24.1439	+	2.40641i	−1.82511	+	0.181908i
$176$	−9.90092	−	12.4154i	−0.746310	−	0.935843i
$177$		0			0
$178$	7.68673	+	13.3138i	0.576145	+	0.997912i
$179$	−2.99699	+	7.63620i	−0.224006	+	0.570757i	−0.998053	−	0.0623708i	$-0.980134\pi$
$179$	−2.99699	+	7.63620i	−0.224006	+	0.570757i	0.774048	+	0.633127i	$0.218229\pi$
$180$		0			0
$181$	8.89213	+	4.28223i	0.660947	+	0.318295i	0.734116	−	0.679024i	$-0.237597\pi$
$181$	8.89213	+	4.28223i	0.660947	+	0.318295i	−0.0731687	+	0.997320i	$0.523311\pi$
$182$	0.213184	−	0.0897662i	0.0158022	−	0.00665392i
$183$		0			0
$184$	12.4306	−	1.87361i	0.916396	−	0.138124i
$185$	−6.02857	−	4.11021i	−0.443230	−	0.302189i
$186$		0			0
$187$	−25.4166	+	17.3287i	−1.85864	+	1.26720i
$188$	−0.0280014	+	0.122682i	−0.00204221	+	0.00894753i
$189$		0			0
$190$	4.46659	+	19.5694i	0.324040	+	1.41971i
$191$	−5.93523	−	5.50709i	−0.429458	−	0.398479i	0.435608	−	0.900136i	$-0.356533\pi$
$191$	−5.93523	−	5.50709i	−0.429458	−	0.398479i	−0.865066	+	0.501657i	$0.832724\pi$
$192$		0			0
$193$	23.6034	−	7.28070i	1.69901	−	0.524076i	0.714537	−	0.699598i	$-0.246637\pi$
$193$	23.6034	−	7.28070i	1.69901	−	0.524076i	0.984476	+	0.175522i	$0.0561613\pi$
$194$	−0.942118	+	12.5717i	−0.0676401	+	0.902595i
$195$		0			0
$196$	−1.49313	−	0.150592i	−0.106652	−	0.0107566i
$197$	1.40734			0.100269			0.0501345	−	0.998742i	$-0.484035\pi$
$197$	1.40734			0.100269			0.0501345	+	0.998742i	$0.484035\pi$
$198$		0			0
$199$	18.3110	−	5.64819i	1.29803	−	0.400390i	0.432676	−	0.901549i	$-0.357569\pi$
$199$	18.3110	−	5.64819i	1.29803	−	0.400390i	0.865355	+	0.501160i	$0.167093\pi$
$200$	−26.8333	−	4.04447i	−1.89740	−	0.285988i
$201$		0			0
$202$	0.628865	+	2.75524i	0.0442468	+	0.193858i
$203$	−18.2094	+	15.2674i	−1.27805	+	1.07156i
$204$		0			0
$205$	−18.7859	+	12.8080i	−1.31207	+	0.894552i
$206$	−6.41021	+	5.94781i	−0.446621	+	0.414403i
$207$		0			0
$208$	0.228071	−	0.0343761i	0.0158139	−	0.00238356i
$209$	−16.1949	+	7.79906i	−1.12023	+	0.539472i
$210$		0			0
$211$	−16.5702	−	7.97978i	−1.14074	−	0.549351i	−0.234499	−	0.972116i	$-0.575345\pi$
$211$	−16.5702	−	7.97978i	−1.14074	−	0.549351i	−0.906239	+	0.422766i	$0.861059\pi$
$212$	0.622153	+	0.191909i	0.0427296	+	0.0131803i
$213$		0			0
$214$	−10.0220	−	17.3586i	−0.685090	−	1.18661i
$215$	−1.48729	+	2.57607i	−0.101433	+	0.175686i
$216$		0			0
$217$	9.27142	−	5.66066i	0.629385	−	0.384270i
$218$	3.46466	−	4.34455i	0.234657	−	0.294250i
$219$		0			0
$220$	−0.271672	−	3.62521i	−0.0183161	−	0.244411i
$221$	−0.0333894	−	0.445550i	−0.00224601	−	0.0299710i
$222$		0			0
$223$	−2.25162	+	2.82344i	−0.150779	+	0.189071i	−0.851485	−	0.524379i	$-0.824297\pi$
$223$	−2.25162	+	2.82344i	−0.150779	+	0.189071i	0.700705	+	0.713451i	$0.252869\pi$
$224$	−3.00123	−	1.09369i	−0.200528	−	0.0730752i
$225$		0			0
$226$	9.09340	−	15.7502i	0.604884	−	1.04769i
$227$	−1.72495	−	2.98770i	−0.114489	−	0.198301i	0.803086	−	0.595863i	$-0.203190\pi$
$227$	−1.72495	−	2.98770i	−0.114489	−	0.198301i	−0.917575	+	0.397562i	$0.869856\pi$
$228$		0			0
$229$	−16.1532	−	4.98261i	−1.06744	−	0.329260i	−0.289224	−	0.957262i	$-0.593397\pi$
$229$	−16.1532	−	4.98261i	−1.06744	−	0.329260i	−0.778212	+	0.628001i	$0.783873\pi$
$230$	−19.2541	−	9.27228i	−1.26958	−	0.611396i
$231$		0			0
$232$	−23.9446	+	11.5311i	−1.57204	+	0.757055i
$233$	−19.0102	+	2.86532i	−1.24540	+	0.187714i	−0.738477	−	0.674279i	$-0.764455\pi$
$233$	−19.0102	+	2.86532i	−1.24540	+	0.187714i	−0.506922	+	0.861992i	$0.669217\pi$
$234$		0			0
$235$	1.61973	−	1.50289i	0.105660	−	0.0980377i
$236$	0.330964	−	0.225647i	0.0215439	−	0.0146884i
$237$		0			0
$238$	9.93852	−	22.0030i	0.644218	−	1.42624i
$239$	−1.24058	−	5.43532i	−0.0802463	−	0.351582i	0.918825	−	0.394665i	$-0.129139\pi$
$239$	−1.24058	−	5.43532i	−0.0802463	−	0.351582i	−0.999072	+	0.0430827i	$0.986282\pi$
$240$		0			0
$241$	7.31260	+	1.10220i	0.471046	+	0.0709988i	0.380276	−	0.924873i	$-0.375829\pi$
$241$	7.31260	+	1.10220i	0.471046	+	0.0709988i	0.0907702	+	0.995872i	$0.471067\pi$
$242$	−11.8640	+	3.65956i	−0.762647	+	0.235245i
$243$		0			0
$244$	1.05816			0.0677415
$245$	20.1726	+	16.9538i	1.28878	+	1.08314i
$246$		0			0
$247$	0.0195104	−	0.260348i	0.00124142	−	0.0165656i
$248$	11.6093	−	3.58100i	0.737193	−	0.227394i
$249$		0			0
$250$	15.3794	+	14.2700i	0.972681	+	0.902516i
$251$	−6.33379	−	27.7502i	−0.399785	−	1.75157i	−0.628240	−	0.778020i	$-0.716224\pi$
$251$	−6.33379	−	27.7502i	−0.399785	−	1.75157i	0.228454	−	0.973555i	$-0.426633\pi$
$252$		0			0
$253$	4.25842	−	18.6573i	0.267724	−	1.17298i
$254$	3.56028	−	2.42736i	0.223392	−	0.152306i
$255$		0			0
$256$	−4.20064	−	2.86395i	−0.262540	−	0.178997i
$257$	13.5894	−	2.04827i	0.847683	−	0.127768i	0.289185	−	0.957273i	$-0.406616\pi$
$257$	13.5894	−	2.04827i	0.847683	−	0.127768i	0.558499	+	0.829506i	$0.311378\pi$
$258$		0			0
$259$	0.888517	+	5.05060i	0.0552097	+	0.313829i
$260$	0.0475730	+	0.0229099i	0.00295035	+	0.00142081i
$261$		0			0
$262$	−4.57777	+	11.6640i	−0.282815	+	0.720602i
$263$	−2.04122	−	3.53549i	−0.125867	−	0.218008i	0.796205	−	0.605027i	$-0.206838\pi$
$263$	−2.04122	−	3.53549i	−0.125867	−	0.218008i	−0.922071	+	0.387020i	$0.873505\pi$
$264$		0			0
$265$	−7.12789	−	8.93809i	−0.437863	−	0.549063i
$266$	7.65874	−	11.8479i	0.469587	−	0.726439i
$267$		0			0
$268$	−0.239978	−	0.611454i	−0.0146590	−	0.0373505i
$269$	1.69012	+	22.5531i	0.103049	+	1.37509i	0.773811	+	0.633417i	$0.218348\pi$
$269$	1.69012	+	22.5531i	0.103049	+	1.37509i	−0.670762	+	0.741672i	$0.734033\pi$
$270$		0			0
$271$	4.33561	+	11.0469i	0.263369	+	0.671054i	0.999986	−	0.00525615i	$-0.00167309\pi$
$271$	4.33561	+	11.0469i	0.263369	+	0.671054i	−0.736617	+	0.676310i	$0.763578\pi$
$272$	15.0099	−	18.8218i	0.910109	−	1.14124i
$273$		0			0
$274$	6.63397	+	8.31874i	0.400773	+	0.502554i
$275$	−20.6552	+	35.7759i	−1.24556	+	2.15737i
$276$		0			0
$277$	5.05209	−	12.8725i	0.303551	−	0.773435i	−0.694969	−	0.719040i	$-0.744582\pi$
$277$	5.05209	−	12.8725i	0.303551	−	0.773435i	0.998519	−	0.0543951i	$-0.0173230\pi$
$278$	−12.6447	−	3.90038i	−0.758380	−	0.233929i
$279$		0			0
$280$	17.1941	+	23.9352i	1.02754	+	1.43040i
$281$	−8.30552	+	3.99973i	−0.495466	+	0.238604i	−0.664893	−	0.746939i	$-0.731523\pi$
$281$	−8.30552	+	3.99973i	−0.495466	+	0.238604i	0.169427	+	0.985543i	$0.445808\pi$
$282$		0			0
$283$	−6.20181	−	4.22832i	−0.368659	−	0.251348i	0.364793	−	0.931089i	$-0.381140\pi$
$283$	−6.20181	−	4.22832i	−0.368659	−	0.251348i	−0.733452	+	0.679741i	$0.762092\pi$
$284$	0.953362	−	0.884590i	0.0565716	−	0.0524908i
$285$		0			0
$286$	0.0876344	−	0.383952i	0.00518193	−	0.0227035i
$287$	15.6620	+	3.17253i	0.924500	+	0.187269i
$288$		0			0
$289$	−21.7241	−	20.1571i	−1.27789	−	1.18571i
$290$	44.6749	+	6.73365i	2.62340	+	0.395414i
$291$		0			0
$292$	−0.167995	+	2.24173i	−0.00983114	+	0.131187i
$293$	18.8716			1.10249			0.551246	−	0.834343i	$-0.314153\pi$
$293$	18.8716			1.10249			0.551246	+	0.834343i	$0.314153\pi$
$294$		0			0
$295$	−7.03354			−0.409508
$296$	−0.428603	+	5.71931i	−0.0249120	+	0.332428i
$297$		0			0
$298$	6.52499	+	0.983484i	0.377983	+	0.0569717i
$299$	0.203758	+	0.189059i	0.0117836	+	0.0109336i
$300$		0			0
$301$	2.02619	−	0.515087i	0.116788	−	0.0296891i
$302$	−4.24267	+	18.5884i	−0.244138	+	1.06964i
$303$		0			0
$304$	10.3120	−	9.56809i	0.591431	−	0.548768i
$305$	−15.3516	−	10.4665i	−0.879030	−	0.599313i
$306$		0			0
$307$	−12.3053	+	5.92590i	−0.702298	+	0.338209i	−0.750722	−	0.660618i	$-0.770294\pi$
$307$	−12.3053	+	5.92590i	−0.702298	+	0.338209i	0.0484241	+	0.998827i	$0.484580\pi$
$308$	−1.69140	+	1.91507i	−0.0963763	+	0.109121i
$309$		0			0
$310$	−19.7356	−	6.08762i	−1.12091	−	0.345754i
$311$	1.81450	−	4.62328i	0.102891	−	0.262162i	−0.870153	−	0.492782i	$-0.835980\pi$
$311$	1.81450	−	4.62328i	0.102891	−	0.262162i	0.973044	+	0.230620i	$0.0740753\pi$
$312$		0			0
$313$	−3.31230	+	5.73707i	−0.187222	+	0.324278i	−0.944323	−	0.329020i	$-0.893282\pi$
$313$	−3.31230	+	5.73707i	−0.187222	+	0.324278i	0.757101	+	0.653298i	$0.226615\pi$
$314$	−6.45949	−	8.09994i	−0.364530	−	0.457106i
$315$		0			0
$316$	1.73597	−	2.17683i	0.0976558	−	0.122456i
$317$	4.44722	+	11.3313i	0.249781	+	0.636432i	0.999685	−	0.0251156i	$-0.00799538\pi$
$317$	4.44722	+	11.3313i	0.249781	+	0.636432i	−0.749904	+	0.661547i	$0.769900\pi$
$318$		0			0
$319$	3.02344	+	40.3450i	0.169280	+	2.25888i
$320$	11.9153	+	30.3597i	0.666087	+	1.69716i
$321$		0			0
$322$	4.77805	+	14.2396i	0.266270	+	0.793542i
$323$	−16.9903	−	21.3052i	−0.945365	−	1.18545i
$324$		0			0
$325$	−0.300007	−	0.519627i	−0.0166414	−	0.0288237i
$326$	−1.86802	+	4.75964i	−0.103460	+	0.263612i
$327$		0			0
$328$	16.1023	+	7.75446i	0.889100	+	0.428168i
$329$	−1.55100	−	0.0780163i	−0.0855094	−	0.00430118i
$330$		0			0
$331$	11.4838	−	1.73091i	0.631208	−	0.0951393i	0.174357	−	0.984682i	$-0.444215\pi$
$331$	11.4838	−	1.73091i	0.631208	−	0.0951393i	0.456851	+	0.889543i	$0.348977\pi$
$332$	−0.512904	−	0.349692i	−0.0281493	−	0.0191918i
$333$		0			0
$334$	−18.2640	+	12.4522i	−0.999364	+	0.681355i
$335$	−2.56651	+	11.2446i	−0.140223	+	0.614358i
$336$		0			0
$337$	3.44323	+	15.0858i	0.187565	+	0.821774i	0.977896	+	0.209094i	$0.0670515\pi$
$337$	3.44323	+	15.0858i	0.187565	+	0.821774i	−0.790331	+	0.612680i	$0.790091\pi$
$338$	−12.7300	−	11.8117i	−0.692421	−	0.642473i
$339$		0			0
$340$	5.26642	−	1.62447i	0.285612	−	0.0880995i
$341$	1.38212	−	18.4431i	0.0748460	−	0.998751i
$342$		0			0
$343$	−1.36231	−	18.4701i	−0.0735581	−	0.997291i
$344$	2.33818			0.126066
$345$		0			0
$346$	15.1517	−	4.67367i	0.814558	−	0.251258i
$347$	32.5408	+	4.90474i	1.74688	+	0.263300i	0.943311	−	0.331909i	$-0.107693\pi$
$347$	32.5408	+	4.90474i	1.74688	+	0.263300i	0.803571	+	0.595209i	$0.202931\pi$
$348$		0			0
$349$	1.92813	+	8.44767i	0.103210	+	0.452194i	0.999954	+	0.00964245i	$0.00306933\pi$
$349$	1.92813	+	8.44767i	0.103210	+	0.452194i	−0.896743	+	0.442551i	$0.854074\pi$
$350$	−0.795621	−	32.4129i	−0.0425277	−	1.73254i
$351$		0			0
$352$	−4.49351	+	3.06362i	−0.239505	+	0.163292i
$353$	16.8163	−	15.6032i	0.895041	−	0.830477i	−0.0911928	−	0.995833i	$-0.529068\pi$
$353$	16.8163	−	15.6032i	0.895041	−	0.830477i	0.986234	+	0.165357i	$0.0528775\pi$
$354$		0			0
$355$	−22.5810	+	3.40354i	−1.19848	+	0.180641i
$356$	2.22221	−	1.07016i	0.117777	−	0.0567185i
$357$		0			0
$358$	−9.87621	−	4.75613i	−0.521974	−	0.251369i
$359$	9.71518	+	2.99674i	0.512747	+	0.158162i	0.540322	−	0.841458i	$-0.318302\pi$
$359$	9.71518	+	2.99674i	0.512747	+	0.158162i	−0.0275749	+	0.999620i	$0.508778\pi$
$360$		0			0
$361$	1.53842	+	2.66463i	0.0809697	+	0.140244i
$362$	−6.59417	+	11.4214i	−0.346582	+	0.600297i
$363$		0			0
$364$	−0.0118056	−	0.0351832i	−0.000618781	−	0.00184410i
$365$	24.6109	−	30.8611i	1.28819	−	1.61534i
$366$		0			0
$367$	0.330097	+	4.40484i	0.0172309	+	0.229931i	0.999170	+	0.0407336i	$0.0129695\pi$
$367$	0.330097	+	4.40484i	0.0172309	+	0.229931i	−0.981939	+	0.189197i	$0.939411\pi$
$368$	1.11921	+	14.9348i	0.0583427	+	0.778529i
$369$		0			0
$370$	6.07900	−	7.62282i	0.316032	−	0.396292i
$371$	−1.00222	+	7.97222i	−0.0520327	+	0.413897i
$372$		0			0
$373$	−17.6841	+	30.6298i	−0.915648	+	1.58595i	−0.109699	+	0.993965i	$0.534989\pi$
$373$	−17.6841	+	30.6298i	−0.915648	+	1.58595i	−0.805949	+	0.591985i	$0.798345\pi$
$374$	−20.5530	−	35.5988i	−1.06277	−	1.84077i
$375$		0			0
$376$	−1.65967	−	0.511941i	−0.0855911	−	0.0264013i
$377$	−0.529440	−	0.254965i	−0.0272676	−	0.0131314i
$378$		0			0
$379$	−0.651629	+	0.313808i	−0.0334719	+	0.0161192i	−0.450545	−	0.892754i	$-0.648770\pi$
$379$	−0.651629	+	0.313808i	−0.0334719	+	0.0161192i	0.417073	+	0.908873i	$0.363056\pi$
$380$	3.18443	−	0.479975i	0.163358	−	0.0246222i
$381$		0			0
$382$	7.93106	−	7.35895i	0.405788	−	0.376516i
$383$	2.35203	−	1.60358i	0.120183	−	0.0819393i	−0.501737	−	0.865020i	$-0.667305\pi$
$383$	2.35203	−	1.60358i	0.120183	−	0.0819393i	0.621920	+	0.783081i	$0.286353\pi$
$384$		0			0
$385$	43.4812	−	11.0535i	2.21601	−	0.563341i
$386$	7.34473	+	32.1794i	0.373837	+	1.63789i
$387$		0			0
$388$	2.00003	+	0.301456i	0.101536	+	0.0153041i
$389$	21.9466	−	6.76964i	1.11274	−	0.343234i	0.316727	−	0.948517i	$-0.397416\pi$
$389$	21.9466	−	6.76964i	1.11274	−	0.343234i	0.796011	+	0.605282i	$0.206940\pi$
$390$		0			0
$391$	29.0122			1.46721
$392$	3.61277	−	20.3956i	0.182473	−	1.03013i
$393$		0			0
$394$	−0.140537	+	1.87533i	−0.00708013	+	0.0944777i
$395$	−46.7170	+	14.4103i	−2.35059	+	0.725059i
$396$		0			0
$397$	12.2225	+	11.3409i	0.613432	+	0.569181i	0.924489	−	0.381210i	$-0.124492\pi$
$397$	12.2225	+	11.3409i	0.613432	+	0.569181i	−0.311057	+	0.950391i	$0.600683\pi$
$398$	5.69787	+	24.9640i	0.285608	+	1.25133i
$399$		0			0
$400$	7.19396	−	31.5188i	0.359698	−	1.57594i
$401$	23.4834	−	16.0107i	1.17270	−	0.799537i	0.189471	−	0.981886i	$-0.439323\pi$
$401$	23.4834	−	16.0107i	1.17270	−	0.799537i	0.983234	+	0.182350i	$0.0583703\pi$
$402$		0			0
$403$	0.221951	+	0.151324i	0.0110562	+	0.00753798i
$404$	0.448346	−	0.0675773i	0.0223060	−	0.00336209i
$405$		0			0
$406$	−18.5259	−	25.7893i	−0.919425	−	1.27990i
$407$	7.86641	+	3.78826i	0.389923	+	0.187777i
$408$		0			0
$409$	10.0565	−	25.6235i	0.497260	−	1.26700i	−0.433429	−	0.901188i	$-0.642696\pi$
$409$	10.0565	−	25.6235i	0.497260	−	1.26700i	0.930689	−	0.365811i	$-0.119208\pi$
$410$	−15.1912	−	26.3119i	−0.750238	−	1.29945i
$411$		0			0
$412$	0.874725	+	1.09687i	0.0430946	+	0.0540389i
$413$	3.45028	+	3.54017i	0.169777	+	0.174200i
$414$		0			0
$415$	3.98224	+	10.1466i	0.195480	+	0.498076i
$416$	−0.00590307	−	0.0787709i	−0.000289422	−	0.00386206i
$417$		0			0
$418$	−8.77528	−	22.3590i	−0.429213	−	1.09362i
$419$	−18.7746	+	23.5427i	−0.917201	+	1.15013i	0.0710771	+	0.997471i	$0.477356\pi$
$419$	−18.7746	+	23.5427i	−0.917201	+	1.15013i	−0.988278	+	0.152663i	$0.951215\pi$
$420$		0			0
$421$	5.08112	+	6.37152i	0.247639	+	0.310529i	0.890079	−	0.455807i	$-0.150649\pi$
$421$	5.08112	+	6.37152i	0.247639	+	0.310529i	−0.642440	+	0.766336i	$0.722078\pi$
$422$	12.2880	−	21.2834i	0.598170	−	1.03606i
$423$		0			0
$424$	−3.28308	+	8.36514i	−0.159440	+	0.406247i
$425$	−59.8448	−	18.4597i	−2.90290	−	0.895425i
$426$		0			0
$427$	2.26258	+	12.8612i	0.109494	+	0.622398i
$428$	−2.89733	+	1.39528i	−0.140048	+	0.0674435i
$429$		0			0
$430$	−3.28417	−	2.23911i	−0.158377	−	0.107980i
$431$	−13.8220	+	12.8250i	−0.665783	+	0.617756i	−0.938886	−	0.344229i	$-0.888140\pi$
$431$	−13.8220	+	12.8250i	−0.665783	+	0.617756i	0.273103	+	0.961985i	$0.411950\pi$
$432$		0			0
$433$	1.18208	−	5.17903i	0.0568071	−	0.248888i	−0.938549	−	0.345145i	$-0.887830\pi$
$433$	1.18208	−	5.17903i	0.0568071	−	0.248888i	0.995357	+	0.0962565i	$0.0306869\pi$
$434$	6.61717	+	12.9197i	0.317634	+	0.620167i
$435$		0			0
$436$	−0.653538	−	0.606395i	−0.0312988	−	0.0290410i
$437$	16.7633	+	2.52666i	0.801897	+	0.120867i
$438$		0			0
$439$	2.92560	−	39.0394i	0.139631	−	1.86325i	−0.285843	−	0.958277i	$-0.592273\pi$
$439$	2.92560	−	39.0394i	0.139631	−	1.86325i	0.425474	−	0.904971i	$-0.360108\pi$
$440$	50.1762			2.39206
$441$		0			0
$442$	0.597044			0.0283985
$443$	1.54877	−	20.6669i	0.0735842	−	0.981914i	−0.831181	−	0.556002i	$-0.812335\pi$
$443$	1.54877	−	20.6669i	0.0735842	−	0.981914i	0.904765	−	0.425911i	$-0.140046\pi$
$444$		0			0
$445$	−42.8249	−	6.45482i	−2.03010	−	0.305988i
$446$	−3.53748	−	3.28230i	−0.167504	−	0.155421i
$447$		0			0
$448$	9.43587	−	20.8902i	0.445803	−	0.986969i
$449$	−3.76595	+	16.4997i	−0.177726	+	0.778668i	0.804951	+	0.593341i	$0.202192\pi$
$449$	−3.76595	+	16.4997i	−0.177726	+	0.778668i	−0.982677	+	0.185327i	$0.940666\pi$
$450$		0			0
$451$	19.9443	−	18.5056i	0.939142	−	0.871397i
$452$	−2.41083	−	1.64367i	−0.113396	−	0.0773119i
$453$		0			0
$454$	4.15346	−	2.00020i	0.194931	−	0.0938740i
$455$	−0.176734	+	0.627206i	−0.00828540	+	0.0294039i
$456$		0			0
$457$	24.7711	+	7.64086i	1.15874	+	0.357425i	0.813769	−	0.581188i	$-0.197412\pi$
$457$	24.7711	+	7.64086i	1.15874	+	0.357425i	0.344973	+	0.938613i	$0.387888\pi$
$458$	8.25255	−	21.0271i	0.385616	−	0.982534i
$459$		0			0
$460$	−1.71430	+	2.96926i	−0.0799298	+	0.138442i
$461$	21.5679	+	27.0452i	1.00452	+	1.25962i	0.965505	+	0.260384i	$0.0838491\pi$
$461$	21.5679	+	27.0452i	1.00452	+	1.25962i	0.0390102	+	0.999239i	$0.487580\pi$
$462$		0			0
$463$	5.43211	−	6.81165i	0.252452	−	0.316564i	−0.639416	−	0.768861i	$-0.720824\pi$
$463$	5.43211	−	6.81165i	0.252452	−	0.316564i	0.891868	+	0.452297i	$0.149395\pi$
$464$	−11.5675	−	29.4736i	−0.537010	−	1.36828i
$465$		0			0
$466$	−1.91979	−	25.6178i	−0.0889325	−	1.18672i
$467$	7.20939	+	18.3692i	0.333611	+	0.850027i	0.994990	+	0.0999751i	$0.0318763\pi$
$467$	7.20939	+	18.3692i	0.333611	+	0.850027i	−0.661379	+	0.750052i	$0.730028\pi$
$468$		0			0
$469$	6.91871	−	4.22421i	0.319476	−	0.195056i
$470$	1.84090	+	2.30842i	0.0849146	+	0.106479i
$471$		0			0
$472$	2.76436	+	4.78801i	0.127240	+	0.220386i
$473$	1.30042	−	3.31341i	0.0597933	−	0.152351i
$474$		0			0
$475$	−32.9708	−	15.8779i	−1.51280	−	0.728528i
$476$	−3.40107	−	1.85385i	−0.155888	−	0.0849711i
$477$		0			0
$478$	7.36663	−	1.11034i	0.336942	−	0.0507858i
$479$	−23.1008	−	15.7499i	−1.05550	−	0.719631i	−0.0943212	−	0.995542i	$-0.530068\pi$
$479$	−23.1008	−	15.7499i	−1.05550	−	0.719631i	−0.961183	+	0.275911i	$0.911020\pi$
$480$		0			0
$481$	−0.104779	+	0.0714371i	−0.00477751	+	0.00325725i
$482$	−2.19895	+	9.63421i	−0.100159	+	0.438826i
$483$		0			0
$484$	0.443243	+	1.94198i	0.0201474	+	0.0882717i
$485$	−26.0344	−	24.1564i	−1.18216	−	1.09688i
$486$		0			0
$487$	−3.73015	+	1.15060i	−0.169029	+	0.0521387i	−0.378115	−	0.925759i	$-0.623428\pi$
$487$	−3.73015	+	1.15060i	−0.169029	+	0.0521387i	0.209085	+	0.977897i	$0.432951\pi$
$488$	−1.09143	+	14.5641i	−0.0494065	+	0.659284i
$489$		0			0
$490$	−24.6059	+	25.1877i	−1.11158	+	1.13786i
$491$	−21.1430			−0.954172			−0.477086	−	0.878857i	$-0.658307\pi$
$491$	−21.1430			−0.954172			−0.477086	+	0.878857i	$0.658307\pi$
$492$		0			0
$493$	−58.6100	+	18.0788i	−2.63966	+	0.814228i
$494$	0.344974	+	0.0519964i	0.0155211	+	0.00233943i
$495$		0			0
$496$	3.22076	+	14.1111i	0.144617	+	0.633606i
$497$	12.7902	+	9.69605i	0.573717	+	0.434927i
$498$		0			0
$499$	14.4255	−	9.83515i	0.645775	−	0.440282i	−0.195637	−	0.980676i	$-0.562677\pi$
$499$	14.4255	−	9.83515i	0.645775	−	0.440282i	0.841412	+	0.540394i	$0.181725\pi$
$500$	2.46743	−	2.28944i	0.110347	−	0.102387i
$501$		0			0
$502$	37.6105	−	5.66887i	1.67864	−	0.253014i
$503$	−25.0379	+	12.0576i	−1.11638	+	0.537622i	−0.898773	−	0.438414i	$-0.855540\pi$
$503$	−25.0379	+	12.0576i	−1.11638	+	0.537622i	−0.217610	+	0.976036i	$0.569826\pi$
$504$		0			0
$505$	−7.17298	−	3.45432i	−0.319193	−	0.153715i
$506$	24.4363	+	7.53759i	1.08632	+	0.335087i
$507$		0			0
$508$	−0.345663	−	0.598706i	−0.0153363	−	0.0265633i
$509$	9.66821	−	16.7458i	0.428536	−	0.742246i	−0.568207	−	0.822885i	$-0.692363\pi$
$509$	9.66821	−	16.7458i	0.428536	−	0.742246i	0.996743	+	0.0806394i	$0.0256962\pi$
$510$		0			0
$511$	−27.6060	+	2.75148i	−1.22122	+	0.121718i
$512$	15.6613	−	19.6387i	0.692138	−	0.867914i
$513$		0			0
$514$	1.37236	+	18.3128i	0.0605321	+	0.807745i
$515$	−1.84093	−	24.5654i	−0.0811209	−	1.08248i
$516$		0			0
$517$	−1.64852	+	2.06718i	−0.0725020	+	0.0909146i
$518$	−6.81881	+	0.679627i	−0.299601	+	0.0298611i
$519$		0			0
$520$	−0.364393	+	0.631147i	−0.0159797	+	0.0276776i
$521$	13.1734	+	22.8170i	0.577137	+	0.999631i	0.995806	+	0.0914922i	$0.0291637\pi$
$521$	13.1734	+	22.8170i	0.577137	+	0.999631i	−0.418668	+	0.908139i	$0.637503\pi$
$522$		0			0
$523$	−12.1773	−	3.75619i	−0.532475	−	0.164247i	0.0168464	−	0.999858i	$-0.494637\pi$
$523$	−12.1773	−	3.75619i	−0.532475	−	0.164247i	−0.549321	+	0.835611i	$0.685114\pi$
$524$	1.81121	+	0.872234i	0.0791232	+	0.0381037i
$525$		0			0
$526$	4.91499	−	2.36693i	0.214304	−	0.103203i
$527$	27.7252	−	4.17891i	1.20773	−	0.182036i
$528$		0			0
$529$	3.62956	−	3.36774i	0.157807	−	0.146423i
$530$	12.6221	−	8.60559i	0.548268	−	0.373803i
$531$		0			0
$532$	−1.80369	−	1.36736i	−0.0782001	−	0.0592825i
$533$	0.0879342	+	0.385265i	0.00380885	+	0.0166877i
$534$		0			0
$535$	55.8354	+	8.41583i	2.41397	+	0.363848i
$536$	8.66335	−	2.67229i	0.374200	−	0.115425i
$537$		0			0
$538$	−30.2216			−1.30294
$539$	−26.8931	−	16.4630i	−1.15837	−	0.709112i
$540$		0			0
$541$	−3.27173	+	43.6582i	−0.140663	+	1.87701i	0.266747	+	0.963766i	$0.414051\pi$
$541$	−3.27173	+	43.6582i	−0.140663	+	1.87701i	−0.407410	+	0.913245i	$0.633568\pi$
$542$	−15.1534	+	4.67419i	−0.650893	+	0.200774i
$543$		0			0
$544$	−6.04391	−	5.60793i	−0.259130	−	0.240438i
$545$	3.48342	+	15.2619i	0.149213	+	0.653746i
$546$		0			0
$547$	2.22803	−	9.76163i	0.0952636	−	0.417377i	−0.904699	−	0.426052i	$-0.859904\pi$
$547$	2.22803	−	9.76163i	0.0952636	−	0.417377i	0.999962	+	0.00867463i	$0.00276125\pi$
$548$	1.41044	−	0.961621i	0.0602510	−	0.0410784i
$549$		0			0
$550$	−45.6099	−	31.0963i	−1.94481	−	1.32595i
$551$	−35.4395	+	5.34164i	−1.50977	+	0.227562i
$552$		0			0
$553$	30.1699	+	16.4450i	1.28296	+	0.699313i
$554$	16.6486	+	8.01752i	0.707329	+	0.340632i
$555$		0			0
$556$	−0.775619	+	1.97624i	−0.0328936	+	0.0838114i
$557$	14.0927	+	24.4092i	0.597126	+	1.03425i	0.993243	+	0.116052i	$0.0370239\pi$
$557$	14.0927	+	24.4092i	0.597126	+	1.03425i	−0.396118	+	0.918200i	$0.629643\pi$
$558$		0			0
$559$	0.0322341	+	0.0404203i	0.00136336	+	0.00170960i
$560$	−29.9667	+	18.2961i	−1.26632	+	0.773153i
$561$		0			0
$562$	−4.50038	−	11.4668i	−0.189837	−	0.483697i
$563$	3.02314	+	40.3409i	0.127410	+	1.70017i	0.585023	+	0.811017i	$0.301085\pi$
$563$	3.02314	+	40.3409i	0.127410	+	1.70017i	−0.457613	+	0.889151i	$0.651295\pi$
$564$		0			0
$565$	18.7179	+	47.6925i	0.787469	+	2.00644i
$566$	6.25368	−	7.84187i	0.262862	−	0.329618i
$567$		0			0
$568$	11.1918	+	14.0341i	0.469599	+	0.588859i
$569$	−4.84199	+	8.38657i	−0.202987	+	0.351583i	−0.949489	−	0.313799i	$-0.898398\pi$
$569$	−4.84199	+	8.38657i	−0.202987	+	0.351583i	0.746503	+	0.665382i	$0.231732\pi$
$570$		0			0
$571$	−16.4533	+	41.9223i	−0.688548	+	1.75439i	−0.0327414	+	0.999464i	$0.510424\pi$
$571$	−16.4533	+	41.9223i	−0.688548	+	1.75439i	−0.655807	+	0.754929i	$0.727671\pi$
$572$	−0.0603771	−	0.0186239i	−0.00252449	−	0.000778703i
$573$		0			0
$574$	−5.79150	+	20.5533i	−0.241733	+	0.857880i
$575$	35.1025	−	16.9045i	1.46388	−	0.704966i
$576$		0			0
$577$	−25.9882	−	17.7184i	−1.08190	−	0.737629i	−0.115151	−	0.993348i	$-0.536735\pi$
$577$	−25.9882	−	17.7184i	−1.08190	−	0.737629i	−0.966751	+	0.255719i	$0.917688\pi$
$578$	29.0293	−	26.9352i	1.20746	−	1.12036i
$579$		0			0
$580$	1.61293	−	7.06672i	0.0669734	−	0.293430i
$581$	3.15358	−	6.98175i	0.130832	−	0.289652i
$582$		0			0
$583$	10.0282	+	9.30484i	0.415327	+	0.385367i
$584$	−30.6811	−	4.62443i	−1.26959	−	0.191360i
$585$		0			0
$586$	−1.88451	+	25.1470i	−0.0778484	+	1.03881i
$587$	−38.4018			−1.58501			−0.792507	−	0.609863i	$-0.791224\pi$
$587$	−38.4018			−1.58501			−0.792507	+	0.609863i	$0.791224\pi$
$588$		0			0
$589$	16.3836			0.675076
$590$	0.702365	−	9.37241i	0.0289159	−	0.385856i
$591$		0			0
$592$	−6.75657	−	1.01839i	−0.277693	−	0.0418555i
$593$	15.2351	+	14.1361i	0.625629	+	0.580499i	0.927949	−	0.372708i	$-0.121571\pi$
$593$	15.2351	+	14.1361i	0.625629	+	0.580499i	−0.302320	+	0.953207i	$0.597761\pi$
$594$		0			0
$595$	31.0053	+	60.5365i	1.27109	+	2.48175i
$596$	0.235577	−	1.03213i	0.00964961	−	0.0422777i
$597$		0			0
$598$	−0.272275	+	0.252634i	−0.0111341	+	0.0103310i
$599$	−20.3756	−	13.8919i	−0.832526	−	0.567607i	0.0703424	−	0.997523i	$-0.477591\pi$
$599$	−20.3756	−	13.8919i	−0.832526	−	0.567607i	−0.902869	+	0.429916i	$0.858543\pi$
$600$		0			0
$601$	−22.0342	+	10.6111i	−0.898794	+	0.432836i	−0.825453	−	0.564471i	$-0.809080\pi$
$601$	−22.0342	+	10.6111i	−0.898794	+	0.432836i	−0.0733409	+	0.997307i	$0.523366\pi$
$602$	0.484035	+	2.75140i	0.0197278	+	0.112139i
$603$		0			0
$604$	2.92305	+	0.901643i	0.118937	+	0.0366873i
$605$	12.7782	−	32.5582i	0.519506	−	1.32368i
$606$		0			0
$607$	6.95586	−	12.0479i	0.282330	−	0.489009i	−0.689628	−	0.724163i	$-0.742226\pi$
$607$	6.95586	−	12.0479i	0.282330	−	0.489009i	0.971958	+	0.235154i	$0.0755595\pi$
$608$	−3.00379	−	3.76664i	−0.121820	−	0.152757i
$609$		0			0
$610$	15.4800	−	19.4113i	0.626767	−	0.785941i
$611$	−0.0140303	−	0.0357485i	−0.000567604	−	0.00144623i
$612$		0			0
$613$	−2.76764	−	36.9316i	−0.111784	−	1.49165i	−0.717828	−	0.696220i	$-0.754864\pi$
$613$	−2.76764	−	36.9316i	−0.111784	−	1.49165i	0.606044	−	0.795431i	$-0.292755\pi$
$614$	−6.66766	−	16.9889i	−0.269085	−	0.685617i
$615$		0			0
$616$	−24.6138	−	25.2551i	−0.991718	−	1.01756i
$617$	12.6418	+	15.8524i	0.508941	+	0.638192i	0.968220	−	0.250100i	$-0.0804636\pi$
$617$	12.6418	+	15.8524i	0.508941	+	0.638192i	−0.459279	+	0.888292i	$0.651892\pi$
$618$		0			0
$619$	−8.66727	−	15.0122i	−0.348367	−	0.603390i	0.637592	−	0.770374i	$-0.279930\pi$
$619$	−8.66727	−	15.0122i	−0.348367	−	0.603390i	−0.985960	+	0.166984i	$0.946597\pi$
$620$	−1.21057	+	3.08448i	−0.0486176	+	0.123876i
$621$		0			0
$622$	5.97947	+	2.87956i	0.239755	+	0.115460i
$623$	17.7588	+	24.7214i	0.711489	+	0.990440i
$624$		0			0
$625$	−13.1011	+	1.97467i	−0.524044	+	0.0789869i
$626$	−7.31406	−	4.98664i	−0.292329	−	0.199306i
$627$		0			0
$628$	−1.37334	+	0.936328i	−0.0548023	+	0.0373636i
$629$	−2.94537	+	12.9045i	−0.117440	+	0.514537i
$630$		0			0
$631$	−10.3175	−	45.2039i	−0.410733	−	1.79954i	−0.580731	−	0.814095i	$-0.697233\pi$
$631$	−10.3175	−	45.2039i	−0.410733	−	1.79954i	0.169998	−	0.985444i	$-0.445624\pi$
$632$	28.1706	+	26.1385i	1.12057	+	1.03973i
$633$		0			0
$634$	−15.5435	+	4.79453i	−0.617310	+	0.190415i
$635$	−0.907146	+	12.1050i	−0.0359990	+	0.480373i
$636$		0			0
$637$	0.402386	−	0.218719i	0.0159431	−	0.00866598i
$638$	−54.0629			−2.14037
$639$		0			0
$640$	−32.9593	+	10.1666i	−1.30283	+	0.401870i
$641$	−23.6879	−	3.57038i	−0.935616	−	0.141021i	−0.336500	−	0.941684i	$-0.609243\pi$
$641$	−23.6879	−	3.57038i	−0.935616	−	0.141021i	−0.599116	+	0.800662i	$0.704481\pi$
$642$		0			0
$643$	8.60440	+	37.6983i	0.339324	+	1.48668i	0.800481	+	0.599358i	$0.204578\pi$
$643$	8.60440	+	37.6983i	0.339324	+	1.48668i	−0.461156	+	0.887319i	$0.652565\pi$
$644$	2.33546	−	0.593706i	0.0920299	−	0.0233953i
$645$		0			0
$646$	30.0864	−	20.5126i	1.18373	−	0.807057i
$647$	−15.7584	+	14.6216i	−0.619526	+	0.574836i	−0.926225	−	0.376970i	$-0.876966\pi$
$647$	−15.7584	+	14.6216i	−0.619526	+	0.574836i	0.306699	+	0.951807i	$0.400775\pi$
$648$		0			0
$649$	8.32249	−	1.25441i	0.326686	−	0.0492401i
$650$	0.722379	−	0.347879i	0.0283340	−	0.0136449i
$651$		0			0
$652$	0.739090	+	0.355927i	0.0289450	+	0.0139392i
$653$	−10.7296	−	3.30964i	−0.419881	−	0.129516i	0.0776128	−	0.996984i	$-0.475270\pi$
$653$	−10.7296	−	3.30964i	−0.419881	−	0.129516i	−0.497494	+	0.867467i	$0.665746\pi$
$654$		0			0
$655$	−17.6493	−	30.5695i	−0.689616	−	1.19445i
$656$	−10.6461	+	18.4397i	−0.415662	+	0.719948i
$657$		0			0
$658$	0.258841	−	2.05897i	0.0100907	−	0.0802668i
$659$	25.9561	−	32.5479i	1.01111	−	1.26789i	0.0479777	−	0.998848i	$-0.484722\pi$
$659$	25.9561	−	32.5479i	1.01111	−	1.26789i	0.963129	−	0.269039i	$-0.0867062\pi$
$660$		0			0
$661$	−2.88389	−	38.4829i	−0.112170	−	1.49681i	−0.715103	−	0.699019i	$-0.753620\pi$
$661$	−2.88389	−	38.4829i	−0.112170	−	1.49681i	0.602933	−	0.797792i	$-0.293999\pi$
$662$	1.15972	+	15.4754i	0.0450739	+	0.601469i
$663$		0			0
$664$	5.34206	−	6.69873i	0.207312	−	0.259961i
$665$	12.6428	+	37.6784i	0.490268	+	1.46111i
$666$		0			0
$667$	19.0785	−	33.0449i	0.738722	−	1.27950i
$668$	1.77323	+	3.07133i	0.0686084	+	0.118833i
$669$		0			0
$670$	−14.7275	−	4.54283i	−0.568973	−	0.175505i
$671$	20.0316	+	9.64671i	0.773311	+	0.372407i
$672$		0			0
$673$	35.3237	−	17.0110i	1.36163	−	0.655726i	0.396630	−	0.917978i	$-0.370179\pi$
$673$	35.3237	−	17.0110i	1.36163	−	0.655726i	0.964999	+	0.262252i	$0.0844651\pi$
$674$	−20.4461	+	3.08175i	−0.787555	+	0.118705i
$675$		0			0
$676$	−2.04236	+	1.89504i	−0.0785524	+	0.0728860i
$677$	1.44188	−	0.983054i	0.0554158	−	0.0377818i	−0.535295	−	0.844665i	$-0.679800\pi$
$677$	1.44188	−	0.983054i	0.0554158	−	0.0377818i	0.590711	+	0.806883i	$0.298847\pi$
$678$		0			0
$679$	0.612524	+	24.9537i	0.0235065	+	0.957634i
$680$	16.9267	+	74.1606i	0.649108	+	2.84393i
$681$		0			0
$682$	24.4380	+	3.68344i	0.935780	+	0.141046i
$683$	−2.01205	+	0.620635i	−0.0769890	+	0.0237479i	−0.333010	−	0.942923i	$-0.608064\pi$
$683$	−2.01205	+	0.620635i	−0.0769890	+	0.0237479i	0.256021	+	0.966671i	$0.417588\pi$
$684$		0			0
$685$	−29.9742			−1.14525
$686$	24.7480	+	0.0290854i	0.944884	+	0.00111048i
$687$		0			0
$688$	−0.208170	+	2.77783i	−0.00793639	+	0.105904i
$689$	−0.189869	+	0.0585670i	−0.00723345	+	0.00223122i
$690$		0			0
$691$	11.1804	+	10.3739i	0.425323	+	0.394642i	0.863583	−	0.504206i	$-0.168215\pi$
$691$	11.1804	+	10.3739i	0.425323	+	0.394642i	−0.438260	+	0.898848i	$0.644405\pi$
$692$	−0.566072	−	2.48012i	−0.0215188	−	0.0942801i
$693$		0			0
$694$	−9.78523	+	42.8719i	−0.371442	+	1.62739i
$695$	30.8002	−	20.9992i	1.16832	−	0.796547i
$696$		0			0
$697$	34.0795	+	23.2350i	1.29085	+	0.880089i
$698$	−11.4493	+	1.72571i	−0.433364	+	0.0653191i
$699$		0			0
$700$	−5.19522	−	0.261323i	−0.196361	−	0.00987708i
$701$	8.18394	+	3.94118i	0.309103	+	0.148856i	0.582004	−	0.813186i	$-0.302269\pi$
$701$	8.18394	+	3.94118i	0.309103	+	0.148856i	−0.272901	+	0.962042i	$0.587983\pi$
$702$		0			0
$703$	−2.82570	+	7.19975i	−0.106573	+	0.271544i
$704$	−19.5135	−	33.7984i	−0.735442	−	1.27382i
$705$		0			0
$706$	19.1126	+	23.9664i	0.719310	+	0.901987i
$707$	1.78003	+	5.30486i	0.0669448	+	0.199510i
$708$		0			0
$709$	−16.6142	−	42.3322i	−0.623958	−	1.58982i	−0.796380	−	0.604796i	$-0.793255\pi$
$709$	−16.6142	−	42.3322i	−0.623958	−	1.58982i	0.172422	−	0.985023i	$-0.444841\pi$
$710$	−2.28040	−	30.4298i	−0.0855819	−	1.14201i
$711$		0			0
$712$	12.4372	+	31.6895i	0.466105	+	1.18762i
$713$	−10.8755	+	13.6374i	−0.407290	+	0.510725i
$714$		0			0
$715$	0.691729	+	0.867401i	0.0258692	+	0.0324390i
$716$	−0.879336	+	1.52305i	−0.0328623	+	0.0569192i
$717$		0			0
$718$	−4.96340	+	12.6465i	−0.185232	+	0.471964i
$719$	6.59364	+	2.03387i	0.245901	+	0.0758505i	0.415256	−	0.909705i	$-0.363692\pi$
$719$	6.59364	+	2.03387i	0.245901	+	0.0758505i	−0.169355	+	0.985555i	$0.554168\pi$
$720$		0			0
$721$	−11.4614	+	12.9771i	−0.426845	+	0.483292i
$722$	−3.70433	+	1.78391i	−0.137861	+	0.0663903i
$723$		0			0
$724$	1.74823	+	1.19193i	0.0649726	+	0.0442976i
$725$	−60.3797	+	56.0242i	−2.24245	+	2.08069i
$726$		0			0
$727$	−0.320126	+	1.40256i	−0.0118728	+	0.0520182i	−0.980517	−	0.196433i	$-0.937064\pi$
$727$	−0.320126	+	1.40256i	−0.0118728	+	0.0520182i	0.968645	+	0.248451i	$0.0799214\pi$
$728$	0.496425	−	0.126198i	0.0183987	−	0.00467722i
$729$		0			0
$730$	38.6658	+	35.8766i	1.43108	+	1.32785i
$731$	5.33592	+	0.804260i	0.197356	+	0.0297466i
$732$		0			0
$733$	3.72179	−	49.6639i	0.137468	−	1.83438i	−0.322648	−	0.946519i	$-0.604573\pi$
$733$	3.72179	−	49.6639i	0.137468	−	1.83438i	0.460116	−	0.887859i	$-0.347808\pi$
$734$	−5.90255			−0.217867
$735$		0			0
$736$	5.12919			0.189065
$737$	1.03139	−	13.7630i	0.0379919	−	0.506966i
$738$		0			0
$739$	44.4450	+	6.69900i	1.63493	+	0.246427i	0.901324	−	0.433145i	$-0.142596\pi$
$739$	44.4450	+	6.69900i	1.63493	+	0.246427i	0.733609	+	0.679571i	$0.237834\pi$
$740$	−1.14668	−	1.06396i	−0.0421527	−	0.0391120i
$741$		0			0
$742$	−10.5232	−	2.13159i	−0.386317	−	0.0782532i
$743$	5.01037	−	21.9519i	0.183813	−	0.805336i	−0.795980	−	0.605322i	$-0.793044\pi$
$743$	5.01037	−	21.9519i	0.183813	−	0.805336i	0.979793	−	0.200014i	$-0.0640986\pi$
$744$		0			0
$745$	−13.6269	+	12.6439i	−0.499249	+	0.463236i
$746$	−39.0492	−	26.6233i	−1.42969	−	0.974749i
$747$		0			0
$748$	−5.94181	+	2.86143i	−0.217254	+	0.104624i
$749$	−23.1540	−	32.2318i	−0.846027	−	1.17773i
$750$		0			0
$751$	−48.4830	−	14.9550i	−1.76917	−	0.545717i	−0.773100	−	0.634284i	$-0.781295\pi$
$751$	−48.4830	−	14.9550i	−1.76917	−	0.545717i	−0.996070	+	0.0885668i	$0.971771\pi$
$752$	0.755965	−	1.92617i	0.0275672	−	0.0702401i
$753$		0			0
$754$	0.392618	−	0.680035i	0.0142983	−	0.0247654i
$755$	−33.4889	−	41.9938i	−1.21879	−	1.52831i
$756$		0			0
$757$	−8.15013	+	10.2199i	−0.296222	+	0.371450i	−0.907562	−	0.419917i	$-0.862059\pi$
$757$	−8.15013	+	10.2199i	−0.296222	+	0.371450i	0.611341	+	0.791368i	$0.290631\pi$
$758$	−0.353088	−	0.899653i	−0.0128247	−	0.0326769i
$759$		0			0
$760$	3.32165	+	44.3243i	0.120489	+	1.60781i
$761$	−12.5547	−	31.9890i	−0.455109	−	1.15960i	−0.955812	−	0.293979i	$-0.905020\pi$
$761$	−12.5547	−	31.9890i	−0.455109	−	1.15960i	0.500703	−	0.865619i	$-0.333075\pi$
$762$		0			0
$763$	5.97293	−	9.23996i	0.216234	−	0.334509i
$764$	−1.08226	−	1.35711i	−0.0391547	−	0.0490984i
$765$		0			0
$766$	1.90196	+	3.29428i	0.0687204	+	0.119027i
$767$	−0.0446613	+	0.113795i	−0.00161263	+	0.00410891i
$768$		0			0
$769$	−5.76738	−	2.77743i	−0.207977	−	0.100157i	0.326995	−	0.945026i	$-0.393964\pi$
$769$	−5.76738	−	2.77743i	−0.207977	−	0.100157i	−0.534973	+	0.844869i	$0.679678\pi$
$770$	10.3872	+	59.0439i	0.374328	+	2.12779i
$771$		0			0
$772$	5.23638	−	0.789258i	0.188462	−	0.0284060i
$773$	−15.1660	−	10.3400i	−0.545483	−	0.371904i	0.259002	−	0.965877i	$-0.416606\pi$
$773$	−15.1660	−	10.3400i	−0.545483	−	0.371904i	−0.804485	+	0.593973i	$0.797559\pi$
$774$		0			0
$775$	31.1105	−	21.2108i	1.11752	−	0.761914i
$776$	−6.21204	+	27.2167i	−0.222999	+	0.977023i
$777$		0			0
$778$	6.82918	+	29.9206i	0.244838	+	1.07271i
$779$	17.6677	+	16.3932i	0.633011	+	0.587348i
$780$		0			0
$781$	26.1122	−	8.05454i	0.934367	−	0.288214i
$782$	−2.89714	+	38.6596i	−0.103601	+	1.38247i
$783$		0			0
$784$	23.9090	+	6.10793i	0.853893	+	0.218140i
$785$	29.1858			1.04169
$786$		0			0
$787$	−40.4077	+	12.4641i	−1.44038	+	0.444298i	−0.913917	−	0.405900i	$-0.866958\pi$
$787$	−40.4077	+	12.4641i	−1.44038	+	0.444298i	−0.526462	+	0.850198i	$0.676482\pi$
$788$	0.298346	+	0.0449684i	0.0106281	+	0.00160193i
$789$		0			0
$790$	−14.5370	−	63.6908i	−0.517204	−	2.26602i
$791$	14.8229	−	32.8166i	0.527042	−	1.16683i
$792$		0			0
$793$	−0.266817	+	0.181913i	−0.00947494	+	0.00645991i
$794$	−16.3326	+	15.1544i	−0.579622	+	0.537811i
$795$		0			0
$796$	4.06226	−	0.612287i	0.143983	−	0.0217020i
$797$	12.2233	−	5.88642i	0.432971	−	0.208508i	−0.204687	−	0.978827i	$-0.565618\pi$
$797$	12.2233	−	5.88642i	0.432971	−	0.208508i	0.637658	+	0.770320i	$0.279903\pi$
$798$		0			0
$799$	−3.61142	−	1.73917i	−0.127763	−	0.0615274i
$800$	−10.5802	−	3.26357i	−0.374068	−	0.115385i
$801$		0			0
$802$	18.9897	+	32.8912i	0.670551	+	1.16143i
$803$	−23.6171	+	40.9060i	−0.833428	+	1.44354i
$804$		0			0
$805$	−39.7551	−	14.4873i	−1.40118	−	0.510610i
$806$	−0.223808	+	0.280646i	−0.00788329	+	0.00988534i
$807$		0			0
$808$	0.467666	+	6.24057i	0.0164524	+	0.219542i
$809$	2.66732	+	35.5929i	0.0937779	+	1.25138i	0.823373	+	0.567500i	$0.192089\pi$
$809$	2.66732	+	35.5929i	0.0937779	+	1.25138i	−0.729595	+	0.683879i	$0.760292\pi$
$810$		0			0
$811$	4.98504	−	6.25104i	0.175048	−	0.219504i	−0.686566	−	0.727068i	$-0.740883\pi$
$811$	4.98504	−	6.25104i	0.175048	−	0.219504i	0.861614	+	0.507564i	$0.169454\pi$
$812$	−4.34809	+	2.65473i	−0.152588	+	0.0931626i
$813$		0			0
$814$	−5.83351	+	10.1039i	−0.204465	+	0.354143i
$815$	−7.20205	−	12.4743i	−0.252277	−	0.436956i
$816$		0			0
$817$	3.01306	+	0.929407i	0.105414	+	0.0325158i
$818$	33.1399	+	15.9593i	1.15871	+	0.558004i
$819$		0			0
$820$	−4.39172	+	2.11494i	−0.153366	+	0.0738570i
$821$	−10.1547	+	1.53058i	−0.354402	+	0.0534174i	−0.323830	−	0.946115i	$-0.604971\pi$
$821$	−10.1547	+	1.53058i	−0.354402	+	0.0534174i	−0.0305712	+	0.999533i	$0.509733\pi$
$822$		0			0
$823$	−9.51480	+	8.82844i	−0.331665	+	0.307740i	−0.828372	−	0.560178i	$-0.810733\pi$
$823$	−9.51480	+	8.82844i	−0.331665	+	0.307740i	0.496707	+	0.867918i	$0.334542\pi$
$824$	−15.9991	+	10.9080i	−0.557357	+	0.379999i
$825$		0			0
$826$	−5.06193	+	4.24409i	−0.176127	+	0.147671i
$827$	−2.33354	−	10.2239i	−0.0811453	−	0.355521i	0.918013	−	0.396551i	$-0.129793\pi$
$827$	−2.33354	−	10.2239i	−0.0811453	−	0.355521i	−0.999158	+	0.0410305i	$0.986936\pi$
$828$		0			0
$829$	−2.85276	−	0.429984i	−0.0990803	−	0.0149340i	0.0993149	−	0.995056i	$-0.468335\pi$
$829$	−2.85276	−	0.429984i	−0.0990803	−	0.0149340i	−0.198395	+	0.980122i	$0.563573\pi$
$830$	−13.9183	+	4.29323i	−0.483111	+	0.149020i
$831$		0			0
$832$	0.566848			0.0196519
$833$	15.2601	−	45.3018i	0.528732	−	1.56961i
$834$		0			0
$835$	4.65361	−	62.0981i	0.161045	−	2.14899i
$836$	−3.68240	+	1.13587i	−0.127358	+	0.0392848i
$837$		0			0
$838$	−29.4965	−	27.3688i	−1.01894	−	0.945438i
$839$	−9.58144	−	41.9790i	−0.330788	−	1.44928i	−0.817608	−	0.575775i	$-0.804700\pi$
$839$	−9.58144	−	41.9790i	−0.330788	−	1.44928i	0.486820	−	0.873502i	$-0.338157\pi$
$840$		0			0
$841$	−11.4972	+	50.3727i	−0.396457	+	1.73699i
$842$	−8.99766	+	6.13450i	−0.310080	+	0.211409i
$843$		0			0
$844$	−3.25777	−	2.22111i	−0.112137	−	0.0764539i
$845$	48.3748	−	7.29132i	1.66414	−	0.250829i
$846$		0			0
$847$	−22.6557	+	9.53975i	−0.778461	+	0.327790i
$848$	−9.64577	−	4.64516i	−0.331237	−	0.159515i
$849$		0			0
$850$	30.5742	−	77.9017i	1.04869	−	2.67201i
$851$	−4.11723	−	7.13126i	−0.141137	−	0.244456i
$852$		0			0
$853$	7.69982	+	9.65527i	0.263637	+	0.330590i	0.895977	−	0.444101i	$-0.146477\pi$
$853$	7.69982	+	9.65527i	0.263637	+	0.330590i	−0.632340	+	0.774691i	$0.717905\pi$
$854$	−17.3639	+	1.73065i	−0.594181	+	0.0592217i
$855$		0			0
$856$	−16.2157	−	41.3170i	−0.554242	−	1.41219i
$857$	−2.21602	−	29.5707i	−0.0756977	−	1.01012i	−0.897693	−	0.440621i	$-0.854758\pi$
$857$	−2.21602	−	29.5707i	−0.0756977	−	1.01012i	0.821995	−	0.569494i	$-0.192861\pi$
$858$		0			0
$859$	−9.03533	−	23.0216i	−0.308281	−	0.785488i	−0.998106	−	0.0615120i	$-0.980408\pi$
$859$	−9.03533	−	23.0216i	−0.308281	−	0.785488i	0.689825	−	0.723976i	$-0.257687\pi$
$860$	−0.397607	+	0.498584i	−0.0135583	+	0.0170016i
$861$		0			0
$862$	−15.7094	−	19.6990i	−0.535064	−	0.670949i
$863$	15.3500	−	26.5869i	0.522518	−	0.905029i	−0.477138	−	0.878828i	$-0.658326\pi$
$863$	15.3500	−	26.5869i	0.522518	−	0.905029i	0.999657	−	0.0262003i	$-0.00834076\pi$
$864$		0			0
$865$	−16.3192	+	41.5805i	−0.554868	+	1.41378i
$866$	6.78318	+	2.09233i	0.230502	+	0.0711004i
$867$		0			0
$868$	2.14634	−	0.903769i	0.0728516	−	0.0306759i
$869$	52.7082	−	25.3829i	1.78800	−	0.861057i
$870$		0			0
$871$	0.165629	+	0.112924i	0.00561212	+	0.00382628i
$872$	9.02028	−	8.36960i	0.305465	−	0.283430i
$873$		0			0
$874$	−5.04083	+	22.0853i	−0.170509	+	0.747047i
$875$	33.1026	+	25.0947i	1.11907	+	0.848355i
$876$		0			0
$877$	−5.09060	−	4.72338i	−0.171897	−	0.159497i	0.589533	−	0.807744i	$-0.299312\pi$
$877$	−5.09060	−	4.72338i	−0.171897	−	0.159497i	−0.761430	+	0.648247i	$0.775502\pi$
$878$	51.7291	+	7.79690i	1.74577	+	0.263133i
$879$		0			0
$880$	−4.46723	+	59.6110i	−0.150590	+	2.00949i
$881$	46.0347			1.55095			0.775474	−	0.631380i	$-0.217511\pi$
$881$	46.0347			1.55095			0.775474	+	0.631380i	$0.217511\pi$
$882$		0			0
$883$	−3.48888			−0.117410			−0.0587051	−	0.998275i	$-0.518697\pi$
$883$	−3.48888			−0.117410			−0.0587051	+	0.998275i	$0.518697\pi$
$884$	0.00715824	−	0.0955201i	0.000240758	−	0.00321269i
$885$		0			0
$886$	27.3846	+	4.12757i	0.920005	+	0.138668i
$887$	−18.6764	−	17.3292i	−0.627094	−	0.581858i	0.301266	−	0.953540i	$-0.402591\pi$
$887$	−18.6764	−	17.3292i	−0.627094	−	0.581858i	−0.928360	+	0.371682i	$0.878781\pi$
$888$		0			0
$889$	6.53779	−	5.48149i	0.219270	−	0.183843i
$890$	12.8777	−	56.4210i	0.431662	−	1.89124i
$891$		0			0
$892$	−0.567542	+	0.526602i	−0.0190027	+	0.0176319i
$893$	−1.93523	−	1.31941i	−0.0647598	−	0.0441525i
$894$		0			0
$895$	27.8223	−	13.3985i	0.929997	−	0.447863i
$896$	21.2852	+	11.6021i	0.711088	+	0.387599i
$897$		0			0
$898$	−21.6103	−	6.66589i	−0.721145	−	0.222444i
$899$	13.4724	−	34.3272i	0.449330	−	1.14487i
$900$		0			0
$901$	−10.3696	+	17.9607i	−0.345462	+	0.598357i
$902$	22.6677	+	28.4244i	0.754753	+	0.946430i
$903$		0			0
$904$	25.1096	−	31.4864i	0.835132	−	1.04722i
$905$	−13.5735	−	34.5847i	−0.451198	−	1.14963i
$906$		0			0
$907$	−3.55651	−	47.4583i	−0.118092	−	1.57583i	−0.670281	−	0.742107i	$-0.733827\pi$
$907$	−3.55651	−	47.4583i	−0.118092	−	1.57583i	0.552189	−	0.833719i	$-0.313793\pi$
$908$	−0.270211	−	0.688486i	−0.00896726	−	0.0228482i
$909$		0			0
$910$	−0.818124	−	0.298136i	−0.0271205	−	0.00988311i
$911$	33.2652	+	41.7132i	1.10212	+	1.38202i	0.916802	+	0.399342i	$0.130761\pi$
$911$	33.2652	+	41.7132i	1.10212	+	1.38202i	0.185321	+	0.982678i	$0.440667\pi$
$912$		0			0
$913$	−6.52164	−	11.2958i	−0.215835	−	0.373837i
$914$	−12.6553	+	32.2452i	−0.418601	+	1.06658i
$915$		0			0
$916$	−3.26515	−	1.57241i	−0.107884	−	0.0519540i
$917$	−6.72866	+	23.8792i	−0.222200	+	0.788560i
$918$		0			0
$919$	−43.3486	+	6.53375i	−1.42994	+	0.215529i	−0.817928	−	0.575321i	$-0.804877\pi$
$919$	−43.3486	+	6.53375i	−1.42994	+	0.215529i	−0.612011	+	0.790849i	$0.709639\pi$
$920$	−39.0996	−	26.6577i	−1.28908	−	0.878877i
$921$		0			0
$922$	−38.1924	+	26.0391i	−1.25780	+	0.857553i
$923$	−0.0883186	+	0.386949i	−0.00290704	+	0.0127366i
$924$		0			0
$925$	3.95538	+	17.3297i	0.130052	+	0.569796i
$926$	8.53430	+	7.91867i	0.280454	+	0.260224i
$927$		0			0
$928$	−10.3619	+	3.19623i	−0.340147	+	0.104922i
$929$	4.43874	−	59.2309i	0.145630	−	1.94330i	−0.151480	−	0.988460i	$-0.548404\pi$
$929$	4.43874	−	59.2309i	0.145630	−	1.94330i	0.297110	−	0.954843i	$-0.403977\pi$
$930$		0			0
$931$	12.7627	−	24.8465i	0.418279	−	0.814311i
$932$	−4.12157			−0.135006
$933$		0			0
$934$	−25.1975	+	7.77241i	−0.824488	+	0.254321i
$935$	114.506	+	17.2591i	3.74476	+	0.564432i
$936$		0			0
$937$	−5.83159	−	25.5499i	−0.190510	−	0.834678i	−0.976341	−	0.216237i	$-0.930622\pi$
$937$	−5.83159	−	25.5499i	−0.190510	−	0.834678i	0.785831	−	0.618441i	$-0.212235\pi$
$938$	4.93800	+	9.64122i	0.161231	+	0.314797i
$939$		0			0
$940$	0.391392	−	0.266846i	0.0127658	−	0.00870357i
$941$	−24.1136	+	22.3742i	−0.786082	+	0.729377i	−0.967181	−	0.254087i	$-0.918225\pi$
$941$	−24.1136	+	22.3742i	−0.786082	+	0.729377i	0.181099	+	0.983465i	$0.442034\pi$
$942$		0			0
$943$	−25.3732	+	3.82440i	−0.826266	+	0.124540i
$944$	−5.93443	+	2.85787i	−0.193149	+	0.0930157i
$945$		0			0
$946$	4.28537	+	2.06372i	0.139329	+	0.0670974i
$947$	−6.79831	−	2.09700i	−0.220915	−	0.0681434i	0.182322	−	0.983239i	$-0.441639\pi$
$947$	−6.79831	−	2.09700i	−0.220915	−	0.0681434i	−0.403237	+	0.915096i	$0.632115\pi$
$948$		0			0
$949$	−0.343026	−	0.594139i	−0.0111351	−	0.0192866i
$950$	24.4503	−	42.3491i	0.793271	−	1.37399i
$951$		0			0
$952$	29.0237	−	44.8989i	0.940665	−	1.45518i
$953$	−24.2112	+	30.3598i	−0.784277	+	0.983452i	0.215699	+	0.976460i	$0.430797\pi$
$953$	−24.2112	+	30.3598i	−0.784277	+	0.983452i	−0.999976	+	0.00699191i	$0.997774\pi$
$954$		0			0
$955$	2.27769	+	30.3937i	0.0737044	+	0.983516i
$956$	−0.0893195	−	1.19189i	−0.00288880	−	0.0385484i
$957$		0			0
$958$	23.2941	−	29.2098i	0.752597	−	0.943727i
$959$	14.7037	+	15.0868i	0.474809	+	0.487179i
$960$		0			0
$961$	7.07127	−	12.2478i	0.228105	−	0.395090i
$962$	−0.0847290	−	0.146755i	−0.00273177	−	0.00473157i
$963$		0			0
$964$	1.51500	+	0.467315i	0.0487948	+	0.0150512i
$965$	−83.7757	−	40.3442i	−2.69683	−	1.29873i
$966$		0			0
$967$	9.98184	−	4.80700i	0.320994	−	0.154583i	−0.266447	−	0.963850i	$-0.585850\pi$
$967$	9.98184	−	4.80700i	0.320994	−	0.154583i	0.587441	+	0.809267i	$0.300135\pi$
$968$	−27.1858	+	4.09761i	−0.873786	+	0.131702i
$969$		0			0
$970$	34.7889	−	32.2794i	1.11701	−	1.03643i
$971$	−9.52331	+	6.49288i	−0.305617	+	0.208366i	−0.706411	−	0.707802i	$-0.749687\pi$
$971$	−9.52331	+	6.49288i	−0.305617	+	0.208366i	0.400793	+	0.916168i	$0.368735\pi$
$972$		0			0
$973$	−25.6785	−	5.20148i	−0.823214	−	0.166752i
$974$	−1.16072	−	5.08545i	−0.0371919	−	0.162948i
$975$		0			0
$976$	−17.2054	−	2.59330i	−0.550732	−	0.0830095i
$977$	−45.2838	+	13.9682i	−1.44876	+	0.446882i	−0.916614	−	0.399773i	$-0.869089\pi$
$977$	−45.2838	+	13.9682i	−1.44876	+	0.446882i	−0.532142	+	0.846655i	$0.678613\pi$
$978$		0			0
$979$	51.8242			1.65631
$980$	3.73472	+	4.23865i	0.119301	+	0.135399i
$981$		0			0
$982$	2.11133	−	28.1738i	0.0673753	−	0.899061i
$983$	7.90001	−	2.43683i	0.251971	−	0.0777228i	−0.166197	−	0.986093i	$-0.553149\pi$
$983$	7.90001	−	2.43683i	0.251971	−	0.0777228i	0.418168	+	0.908370i	$0.362672\pi$
$984$		0			0
$985$	−3.88357	−	3.60343i	−0.123741	−	0.114815i
$986$	−18.2378	−	79.9050i	−0.580810	−	2.54469i
$987$		0			0
$988$	0.0124549	−	0.0545684i	0.000396242	−	0.00173605i
$989$	−2.77370	+	1.89107i	−0.0881984	+	0.0601326i
$990$		0			0
$991$	10.3543	+	7.05942i	0.328914	+	0.224250i	0.716505	−	0.697581i	$-0.245740\pi$
$991$	10.3543	+	7.05942i	0.328914	+	0.224250i	−0.387591	+	0.921831i	$0.626693\pi$
$992$	4.90167	−	0.738808i	0.155628	−	0.0234572i
$993$		0			0
$994$	−14.1975	+	16.0750i	−0.450318	+	0.509869i
$995$	−64.9912	−	31.2981i	−2.06036	−	0.992216i
$996$		0			0
$997$	3.97139	−	10.1189i	0.125775	−	0.320470i	−0.854092	−	0.520123i	$-0.825886\pi$
$997$	3.97139	−	10.1189i	0.125775	−	0.320470i	0.979867	+	0.199653i	$0.0639814\pi$
$998$	11.6651	+	20.2046i	0.369253	+	0.639566i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.c.415.1		48
3.2	odd	2		147.2.m.a.121.4	✓	48
49.32	even	21	inner	441.2.bb.c.424.1		48
147.32	odd	42		147.2.m.a.130.4	yes	48
147.89	even	42		7203.2.a.k.1.19		24
147.107	odd	42		7203.2.a.i.1.19		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.121.4	✓	48	3.2	odd	2
147.2.m.a.130.4	yes	48	147.32	odd	42
441.2.bb.c.415.1		48	1.1	even	1	trivial
441.2.bb.c.424.1		48	49.32	even	21	inner
7203.2.a.i.1.19		24	147.107	odd	42
7203.2.a.k.1.19		24	147.89	even	42

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0998595 + 1.33253i) q^{2} +(0.211992 + 0.0319527i) q^{4} +(-2.75951 - 2.56045i) q^{5} +(0.0649242 + 2.64495i) q^{7} +(-0.658443 + 2.88483i) q^{8} +(3.68744 - 3.42144i) q^{10} +(3.72186 + 2.53752i) q^{11} +(-0.0589476 + 0.0283876i) q^{13} +(-3.53097 - 0.177610i) q^{14} +(-3.36865 - 1.03909i) q^{16} +(-2.49491 + 6.35693i) q^{17} +(-1.99519 + 3.45577i) q^{19} +(-0.503181 - 0.630969i) q^{20} +(-3.75299 + 4.70610i) q^{22} +(-1.55211 - 3.95470i) q^{23} +(0.685332 + 9.14512i) q^{25} +(-0.0319410 - 0.0813843i) q^{26} +(-0.0707500 + 0.562784i) q^{28} +(5.59990 + 7.02205i) q^{29} +(-2.05289 - 3.55571i) q^{31} +(-0.441087 + 1.12387i) q^{32} +(-8.22168 - 3.95935i) q^{34} +(6.59311 - 7.46500i) q^{35} +(1.91661 - 0.288883i) q^{37} +(-4.40569 - 3.00375i) q^{38} +(9.20342 - 6.27479i) q^{40} +(1.34401 - 5.88848i) q^{41} +(-0.175833 - 0.770376i) q^{43} +(0.707924 + 0.656858i) q^{44} +(5.42476 - 1.67332i) q^{46} +(-0.0438639 + 0.585323i) q^{47} +(-6.99157 + 0.343443i) q^{49} -12.2546 q^{50} +(-0.0134035 + 0.00413443i) q^{52} +(3.00301 + 0.452631i) q^{53} +(-3.77330 - 16.5319i) q^{55} +(-7.67298 - 1.55426i) q^{56} +(-9.91631 + 6.76083i) q^{58} +(1.36966 - 1.27086i) q^{59} +(4.88060 - 0.735633i) q^{61} +(4.94310 - 2.38047i) q^{62} +(-7.80586 - 3.75910i) q^{64} +(0.235351 + 0.0725962i) q^{65} +(-1.53195 - 2.65342i) q^{67} +(-0.732023 + 1.26790i) q^{68} +(9.28897 + 9.53098i) q^{70} +(3.78229 - 4.74284i) q^{71} +(0.783605 + 10.4565i) q^{73} +(0.193554 + 2.58280i) q^{74} +(-0.533386 + 0.668845i) q^{76} +(-6.46999 + 10.0089i) q^{77} +(6.49358 - 11.2472i) q^{79} +(6.63527 + 11.4926i) q^{80} +(7.71238 + 2.37895i) q^{82} +(-2.60881 - 1.25634i) q^{83} +(23.1613 - 11.1539i) q^{85} +(1.04411 - 0.157374i) q^{86} +(-9.77094 + 9.06610i) q^{88} +(9.50569 - 6.48087i) q^{89} +(-0.0789112 - 0.154071i) q^{91} +(-0.202671 - 0.887960i) q^{92} +(-0.775581 - 0.116900i) q^{94} +(14.3541 - 4.42764i) q^{95} +9.43444 q^{97} +(0.240525 - 9.35079i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32}+ \cdots - 119 q^{98}+O(q^{100}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Introduction

L-functions

Modular forms

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