LMFDB - Embedded newform 495.2.bj.a.217.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [495,2,Mod(28,495)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(495, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 15, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("495.28"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,10,0,0,2] 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			217.1
Character	$\chi$	$=$	495.217
Dual form			495.2.bj.a.73.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.380541 + 2.40264i) q^{2} +(-3.72576 - 1.21057i) q^{4} +(0.622076 - 2.14779i) q^{5} +(1.17208 + 2.30033i) q^{7} +(2.11764 - 4.15610i) q^{8} +(4.92366 + 2.31195i) q^{10} +(2.55440 + 2.11543i) q^{11} +(2.77422 + 0.439393i) q^{13} +(-5.97289 + 1.94071i) q^{14} +(2.84111 + 2.06419i) q^{16} +(0.932684 - 0.147723i) q^{17} +(1.28236 + 3.94669i) q^{19} +(-4.91777 + 7.24911i) q^{20} +(-6.05467 + 5.33231i) q^{22} +(-0.104710 + 0.104710i) q^{23} +(-4.22604 - 2.67218i) q^{25} +(-2.11141 + 6.49824i) q^{26} +(-1.58216 - 9.98937i) q^{28} +(-2.14459 + 6.60038i) q^{29} +(-7.33171 + 5.32680i) q^{31} +(0.555921 - 0.555921i) q^{32} +2.29712i q^{34} +(5.66976 - 1.08640i) q^{35} +(6.77002 - 3.44950i) q^{37} +(-9.97047 + 1.57917i) q^{38} +(-7.60911 - 7.13366i) q^{40} +(-3.27880 + 1.06535i) q^{41} +(3.91833 + 3.91833i) q^{43} +(-6.95623 - 10.9739i) q^{44} +(-0.211733 - 0.291426i) q^{46} +(-0.479999 + 0.942051i) q^{47} +(0.196744 - 0.270795i) q^{49} +(8.02848 - 9.13679i) q^{50} +(-9.80416 - 4.99547i) q^{52} +(0.644920 - 4.07187i) q^{53} +(6.13253 - 4.17038i) q^{55} +12.0424 q^{56} +(-15.0422 - 7.66441i) q^{58} +(6.16460 + 2.00300i) q^{59} +(5.59880 - 7.70609i) q^{61} +(-10.0084 - 19.6426i) q^{62} +(5.25251 + 7.22946i) q^{64} +(2.66950 - 5.68511i) q^{65} +(2.94509 + 2.94509i) q^{67} +(-3.65379 - 0.578703i) q^{68} +(0.452653 + 14.0358i) q^{70} +(1.02426 + 0.744171i) q^{71} +(1.57831 - 0.804189i) q^{73} +(5.71163 + 17.5786i) q^{74} -16.2568i q^{76} +(-1.87222 + 8.35541i) q^{77} +(-3.51271 + 2.55214i) q^{79} +(6.20085 - 4.81805i) q^{80} +(-1.31193 - 8.28320i) q^{82} +(-1.29707 - 8.18939i) q^{83} +(0.262923 - 2.09511i) q^{85} +(-10.9054 + 7.92326i) q^{86} +(14.2012 - 6.13664i) q^{88} -4.23092i q^{89} +(2.24084 + 6.89661i) q^{91} +(0.516882 - 0.263364i) q^{92} +(-2.08075 - 1.51175i) q^{94} +(9.27440 - 0.299098i) q^{95} +(-14.2460 - 2.25634i) q^{97} +(0.575755 + 0.575755i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8 + 24 * q^11 - 10 * q^13 - 8 * q^16 - 16 * q^20 + 10 * q^22 + 24 * q^23 + 16 * q^25 - 20 * q^26 + 50 * q^28 - 28 * q^31 + 10 * q^35 - 8 * q^37 - 10 * q^38 - 50 * q^40 - 40 * q^41 + 60 * q^46 + 28 * q^47 + 50 * q^50 - 50 * q^52 + 24 * q^53 - 64 * q^55 + 80 * q^56 - 50 * q^58 - 60 * q^61 - 100 * q^62 - 8 * q^67 + 30 * q^68 + 30 * q^70 - 24 * q^71 + 50 * q^73 - 70 * q^77 - 98 * q^80 - 10 * q^82 - 90 * q^83 + 30 * q^85 - 100 * q^86 + 170 * q^88 + 20 * q^91 + 68 * q^92 + 40 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.380541	+	2.40264i	−0.269083	+	1.69892i	0.369385	+	0.929276i	$0.379568\pi$
$2$	−0.380541	+	2.40264i	−0.269083	+	1.69892i	−0.638468	+	0.769648i	$0.720432\pi$
$3$		0			0
$3$		0			0
$4$	−3.72576	−	1.21057i	−1.86288	−	0.605287i
$5$	0.622076	−	2.14779i	0.278201	−	0.960523i
$5$	0.622076	−	2.14779i	0.278201	−	0.960523i
$6$		0			0
$7$	1.17208	+	2.30033i	0.443003	+	0.869443i	0.999261	+	0.0384331i	$0.0122367\pi$
$7$	1.17208	+	2.30033i	0.443003	+	0.869443i	−0.556258	+	0.831010i	$0.687763\pi$
$8$	2.11764	−	4.15610i	0.748698	−	1.46940i
$9$		0			0
$10$	4.92366	+	2.31195i	1.55700	+	0.731103i
$11$	2.55440	+	2.11543i	0.770182	+	0.637825i
$11$	2.55440	+	2.11543i	0.770182	+	0.637825i
$12$		0			0
$13$	2.77422	+	0.439393i	0.769429	+	0.121866i	0.528794	−	0.848750i	$-0.322644\pi$
$13$	2.77422	+	0.439393i	0.769429	+	0.121866i	0.240635	+	0.970616i	$0.422644\pi$
$14$	−5.97289	+	1.94071i	−1.59632	+	0.518677i
$15$		0			0
$16$	2.84111	+	2.06419i	0.710279	+	0.516048i
$17$	0.932684	−	0.147723i	0.226209	−	0.0358280i	−0.0423009	−	0.999105i	$-0.513469\pi$
$17$	0.932684	−	0.147723i	0.226209	−	0.0358280i	0.268510	+	0.963277i	$0.413469\pi$
$18$		0			0
$19$	1.28236	+	3.94669i	0.294193	+	0.905433i	0.983491	+	0.180955i	$0.0579189\pi$
$19$	1.28236	+	3.94669i	0.294193	+	0.905433i	−0.689298	+	0.724478i	$0.742081\pi$
$20$	−4.91777	+	7.24911i	−1.09965	+	1.62095i
$21$		0			0
$22$	−6.05467	+	5.33231i	−1.29086	+	1.13685i
$23$	−0.104710	+	0.104710i	−0.0218334	+	0.0218334i	−0.717939	−	0.696106i	$-0.754914\pi$
$23$	−0.104710	+	0.104710i	−0.0218334	+	0.0218334i	0.696106	+	0.717939i	$0.254914\pi$
$24$		0			0
$25$	−4.22604	−	2.67218i	−0.845208	−	0.534437i
$26$	−2.11141	+	6.49824i	−0.414081	+	1.27441i
$27$		0			0
$28$	−1.58216	−	9.98937i	−0.299000	−	1.88781i
$29$	−2.14459	+	6.60038i	−0.398241	+	1.22566i	0.528168	+	0.849140i	$0.322879\pi$
$29$	−2.14459	+	6.60038i	−0.398241	+	1.22566i	−0.926409	+	0.376520i	$0.877121\pi$
$30$		0			0
$31$	−7.33171	+	5.32680i	−1.31681	+	0.956722i	−0.316849	+	0.948476i	$0.602625\pi$
$31$	−7.33171	+	5.32680i	−1.31681	+	0.956722i	−0.999966	+	0.00824590i	$0.997375\pi$
$32$	0.555921	−	0.555921i	0.0982739	−	0.0982739i
$33$		0			0
$34$			2.29712i			0.393953i
$35$	5.66976	−	1.08640i	0.958364	−	0.183635i
$36$		0			0
$37$	6.77002	−	3.44950i	1.11298	−	0.567094i	0.201938	−	0.979398i	$-0.435276\pi$
$37$	6.77002	−	3.44950i	1.11298	−	0.567094i	0.911046	+	0.412305i	$0.135276\pi$
$38$	−9.97047	+	1.57917i	−1.61742	+	0.256175i
$39$		0			0
$40$	−7.60911	−	7.13366i	−1.20311	−	1.12793i
$41$	−3.27880	+	1.06535i	−0.512063	+	0.166379i	−0.553640	−	0.832756i	$-0.686762\pi$
$41$	−3.27880	+	1.06535i	−0.512063	+	0.166379i	0.0415772	+	0.999135i	$0.486762\pi$
$42$		0			0
$43$	3.91833	+	3.91833i	0.597540	+	0.597540i	0.939657	−	0.342117i	$-0.111144\pi$
$43$	3.91833	+	3.91833i	0.597540	+	0.597540i	−0.342117	+	0.939657i	$0.611144\pi$
$44$	−6.95623	−	10.9739i	−1.04869	−	1.65437i
$45$		0			0
$46$	−0.211733	−	0.291426i	−0.0312184	−	0.0429684i
$47$	−0.479999	+	0.942051i	−0.0700150	+	0.137412i	−0.923361	−	0.383933i	$-0.874569\pi$
$47$	−0.479999	+	0.942051i	−0.0700150	+	0.137412i	0.853346	+	0.521345i	$0.174569\pi$
$48$		0			0
$49$	0.196744	−	0.270795i	0.0281063	−	0.0386850i
$50$	8.02848	−	9.13679i	1.13540	−	1.29214i
$51$		0			0
$52$	−9.80416	−	4.99547i	−1.35959	−	0.692747i
$53$	0.644920	−	4.07187i	0.0885866	−	0.559314i	−0.902977	−	0.429690i	$-0.858623\pi$
$53$	0.644920	−	4.07187i	0.0885866	−	0.559314i	0.991563	−	0.129624i	$-0.0413771\pi$
$54$		0			0
$55$	6.13253	−	4.17038i	0.826911	−	0.562334i
$56$	12.0424			1.60924
$57$		0			0
$58$	−15.0422	−	7.66441i	−1.97514	−	1.00639i
$59$	6.16460	+	2.00300i	0.802563	+	0.260768i	0.681445	−	0.731870i	$-0.261352\pi$
$59$	6.16460	+	2.00300i	0.802563	+	0.260768i	0.121118	+	0.992638i	$0.461352\pi$
$60$		0			0
$61$	5.59880	−	7.70609i	0.716853	−	0.986663i	−0.282769	−	0.959188i	$-0.591253\pi$
$61$	5.59880	−	7.70609i	0.716853	−	0.986663i	0.999622	−	0.0274756i	$-0.00874685\pi$
$62$	−10.0084	−	19.6426i	−1.27107	−	2.49461i
$63$		0			0
$64$	5.25251	+	7.22946i	0.656564	+	0.903682i
$65$	2.66950	−	5.68511i	0.331111	−	0.705151i
$66$		0			0
$67$	2.94509	+	2.94509i	0.359801	+	0.359801i	0.863739	−	0.503939i	$-0.168116\pi$
$67$	2.94509	+	2.94509i	0.359801	+	0.359801i	−0.503939	+	0.863739i	$0.668116\pi$
$68$	−3.65379	−	0.578703i	−0.443087	−	0.0701781i
$69$		0			0
$70$	0.452653	+	14.0358i	0.0541023	+	1.67760i
$71$	1.02426	+	0.744171i	0.121558	+	0.0883168i	0.646903	−	0.762572i	$-0.276064\pi$
$71$	1.02426	+	0.744171i	0.121558	+	0.0883168i	−0.525345	+	0.850889i	$0.676064\pi$
$72$		0			0
$73$	1.57831	−	0.804189i	0.184727	−	0.0941232i	−0.359181	−	0.933268i	$-0.616944\pi$
$73$	1.57831	−	0.804189i	0.184727	−	0.0941232i	0.543908	+	0.839145i	$0.316944\pi$
$74$	5.71163	+	17.5786i	0.663964	+	2.04347i
$75$		0			0
$76$		−	16.2568i		−	1.86479i
$77$	−1.87222	+	8.35541i	−0.213359	+	0.952187i
$78$		0			0
$79$	−3.51271	+	2.55214i	−0.395211	+	0.287138i	−0.767588	−	0.640944i	$-0.778543\pi$
$79$	−3.51271	+	2.55214i	−0.395211	+	0.287138i	0.372376	+	0.928082i	$0.378543\pi$
$80$	6.20085	−	4.81805i	0.693276	−	0.538674i
$81$		0			0
$82$	−1.31193	−	8.28320i	−0.144878	−	0.914726i
$83$	−1.29707	−	8.18939i	−0.142372	−	0.898902i	−0.950687	−	0.310152i	$-0.899620\pi$
$83$	−1.29707	−	8.18939i	−0.142372	−	0.898902i	0.808315	−	0.588750i	$-0.200380\pi$
$84$		0			0
$85$	0.262923	−	2.09511i	0.0285180	−	0.227246i
$86$	−10.9054	+	7.92326i	−1.17596	+	0.854388i
$87$		0			0
$88$	14.2012	−	6.13664i	1.51385	−	0.654168i
$89$		−	4.23092i		−	0.448477i	−0.974534	−	0.224238i	$-0.928011\pi$
$89$		−	4.23092i		−	0.448477i	0.974534	−	0.224238i	$-0.0719894\pi$
$90$		0			0
$91$	2.24084	+	6.89661i	0.234904	+	0.722961i
$92$	0.516882	−	0.263364i	0.0538886	−	0.0274576i
$93$		0			0
$94$	−2.08075	−	1.51175i	−0.214613	−	0.155926i
$95$	9.27440	−	0.299098i	0.951534	−	0.0306868i
$96$		0			0
$97$	−14.2460	−	2.25634i	−1.44646	−	0.229097i	−0.616691	−	0.787205i	$-0.711527\pi$
$97$	−14.2460	−	2.25634i	−1.44646	−	0.229097i	−0.829768	+	0.558109i	$0.811527\pi$
$98$	0.575755	+	0.575755i	0.0581600	+	0.0581600i
$99$		0			0
$100$	12.5104	+	15.0719i	1.25104	+	1.50719i
$101$	−1.13747	−	1.56559i	−0.113182	−	0.155782i	0.748668	−	0.662946i	$-0.230694\pi$
$101$	−1.13747	−	1.56559i	−0.113182	−	0.155782i	−0.861850	+	0.507164i	$0.830694\pi$
$102$		0			0
$103$	−0.780525	−	1.53187i	−0.0769075	−	0.150939i	0.849351	−	0.527829i	$-0.176994\pi$
$103$	−0.780525	−	1.53187i	−0.0769075	−	0.150939i	−0.926258	+	0.376889i	$0.876994\pi$
$104$	7.70094	−	10.5994i	0.755139	−	1.03936i
$105$		0			0
$106$	9.53782	+	3.09903i	0.926395	+	0.301004i
$107$	−3.70571	−	1.88816i	−0.358245	−	0.182535i	0.265600	−	0.964083i	$-0.414430\pi$
$107$	−3.70571	−	1.88816i	−0.358245	−	0.182535i	−0.623844	+	0.781549i	$0.714430\pi$
$108$		0			0
$109$	−3.22321			−0.308728			−0.154364	−	0.988014i	$-0.549333\pi$
$109$	−3.22321			−0.308728			−0.154364	+	0.988014i	$0.549333\pi$
$110$	7.68624	+	16.3213i	0.732855	+	1.55617i
$111$		0			0
$112$	−1.41832	+	8.95489i	−0.134018	+	0.846157i
$113$	9.93758	+	5.06345i	0.934849	+	0.476329i	0.853928	−	0.520391i	$-0.174214\pi$
$113$	9.93758	+	5.06345i	0.934849	+	0.476329i	0.0809210	+	0.996721i	$0.474214\pi$
$114$		0			0
$115$	0.159757	+	0.290032i	0.0148974	+	0.0270456i
$116$	15.9805	−	21.9953i	1.48375	−	2.04221i
$117$		0			0
$118$	−7.15838	+	14.0491i	−0.658982	+	1.29333i
$119$	1.43299	+	1.97234i	0.131362	+	0.180804i
$120$		0			0
$121$	2.04995	+	10.8073i	0.186359	+	0.982482i
$122$	16.3844	+	16.3844i	1.48337	+	1.48337i
$123$		0			0
$124$	33.7647	−	10.9708i	3.03216	−	0.985209i
$125$	−8.36822	+	7.41437i	−0.748477	+	0.663161i
$126$		0			0
$127$	−2.34580	+	0.371538i	−0.208156	+	0.0329687i	−0.259641	−	0.965705i	$-0.583604\pi$
$127$	−2.34580	+	0.371538i	−0.208156	+	0.0329687i	0.0514856	+	0.998674i	$0.483604\pi$
$128$	−17.9676	+	9.15495i	−1.58813	+	0.809191i
$129$		0			0
$130$	12.6434	+	8.57727i	1.10890	+	0.752276i
$131$		−	3.12466i		−	0.273003i	−0.990640	−	0.136501i	$-0.956414\pi$
$131$		−	3.12466i		−	0.273003i	0.990640	−	0.136501i	$-0.0435858\pi$
$132$		0			0
$133$	−7.57567	+	7.57567i	−0.656894	+	0.656894i
$134$	−8.19674	+	5.95528i	−0.708090	+	0.514458i
$135$		0			0
$136$	1.36114	−	4.18915i	0.116716	−	0.359216i
$137$	−2.58679	−	16.3323i	−0.221004	−	1.39537i	−0.809621	−	0.586953i	$-0.800327\pi$
$137$	−2.58679	−	16.3323i	−0.221004	−	1.39537i	0.588617	−	0.808412i	$-0.299673\pi$
$138$		0			0
$139$	1.33510	−	4.10901i	0.113242	−	0.348522i	−0.878335	−	0.478046i	$-0.841345\pi$
$139$	1.33510	−	4.10901i	0.113242	−	0.348522i	0.991576	+	0.129524i	$0.0413451\pi$
$140$	−22.4393	−	2.81599i	−1.89647	−	0.237995i
$141$		0			0
$142$	−2.17775	+	2.17775i	−0.182753	+	0.182753i
$143$	6.15696	+	6.99103i	0.514871	+	0.584619i
$144$		0			0
$145$	12.8422	+	8.71208i	1.06648	+	0.723499i
$146$	1.33157	+	4.09814i	0.110201	+	0.339164i
$147$		0			0
$148$	−29.3994	+	4.65640i	−2.41661	+	0.382754i
$149$	−6.83188	−	4.96365i	−0.559689	−	0.406638i	0.271656	−	0.962394i	$-0.412429\pi$
$149$	−6.83188	−	4.96365i	−0.559689	−	0.406638i	−0.831345	+	0.555756i	$0.812429\pi$
$150$		0			0
$151$	11.3483	−	3.68729i	0.923513	−	0.300068i	0.191606	−	0.981472i	$-0.438630\pi$
$151$	11.3483	−	3.68729i	0.923513	−	0.300068i	0.731907	+	0.681404i	$0.238630\pi$
$152$	19.1184	+	3.02806i	1.55071	+	0.245608i
$153$		0			0
$154$	−19.3626	−	7.67785i	−1.56028	−	0.618699i
$155$	6.87999	+	19.0607i	0.552614	+	1.53099i
$156$		0			0
$157$	0.618117	−	1.21312i	0.0493311	−	0.0968177i	−0.865025	−	0.501729i	$-0.832698\pi$
$157$	0.618117	−	1.21312i	0.0493311	−	0.0968177i	0.914356	+	0.404911i	$0.132698\pi$
$158$	−4.79514	−	9.41098i	−0.381481	−	0.748698i
$159$		0			0
$160$	−0.848179	−	1.53983i	−0.0670544	−	0.121734i
$161$	−0.363594	−	0.118139i	−0.0286552	−	0.00931064i
$162$		0			0
$163$	3.58914	−	22.6610i	0.281123	−	1.77494i	−0.292939	−	0.956131i	$-0.594633\pi$
$163$	3.58914	−	22.6610i	0.281123	−	1.77494i	0.574062	−	0.818812i	$-0.305367\pi$
$164$	13.5057			1.05462
$165$		0			0
$166$	20.1698			1.56548
$167$	2.24646	−	14.1836i	0.173836	−	1.09756i	−0.734282	−	0.678845i	$-0.762481\pi$
$167$	2.24646	−	14.1836i	0.173836	−	1.09756i	0.908118	−	0.418714i	$-0.137519\pi$
$168$		0			0
$169$	−4.86053	−	1.57928i	−0.373887	−	0.121483i
$170$	4.93374	+	1.42898i	0.378401	+	0.109598i
$171$		0			0
$172$	−9.85535	−	19.3422i	−0.751464	−	1.47483i
$173$	10.1247	−	19.8708i	0.769766	−	1.51075i	−0.0876641	−	0.996150i	$-0.527940\pi$
$173$	10.1247	−	19.8708i	0.769766	−	1.51075i	0.857430	−	0.514601i	$-0.172060\pi$
$174$		0			0
$175$	1.19366	−	12.8533i	0.0902321	−	0.971618i
$176$	2.89071	+	11.2829i	0.217896	+	0.850484i
$177$		0			0
$178$	10.1654	+	1.61004i	0.761928	+	0.120678i
$179$	4.15441	−	1.34985i	0.310516	−	0.100893i	−0.149614	−	0.988745i	$-0.547803\pi$
$179$	4.15441	−	1.34985i	0.310516	−	0.100893i	0.460129	+	0.887852i	$0.347803\pi$
$180$		0			0
$181$	−7.63694	−	5.54857i	−0.567650	−	0.412422i	0.266601	−	0.963807i	$-0.414099\pi$
$181$	−7.63694	−	5.54857i	−0.567650	−	0.412422i	−0.834251	+	0.551385i	$0.814099\pi$
$182$	−17.4228	+	2.75950i	−1.29147	+	0.204548i
$183$		0			0
$184$	0.213446	+	0.656920i	0.0157355	+	0.0484287i
$185$	−3.19734	−	16.6865i	−0.235073	−	1.22681i
$186$		0			0
$187$	2.69495	+	1.59568i	0.197074	+	0.116688i
$188$	2.92879	−	2.92879i	0.213604	−	0.213604i
$189$		0			0
$190$	−2.81067	+	22.3969i	−0.203907	+	1.62484i
$191$	2.00020	−	6.15597i	0.144729	−	0.445430i	−0.852247	−	0.523140i	$-0.824761\pi$
$191$	2.00020	−	6.15597i	0.144729	−	0.445430i	0.996976	+	0.0777092i	$0.0247606\pi$
$192$		0			0
$193$	0.157473	+	0.994245i	0.0113352	+	0.0715674i	0.992707	−	0.120548i	$-0.0384652\pi$
$193$	0.157473	+	0.994245i	0.0113352	+	0.0715674i	−0.981372	+	0.192115i	$0.938465\pi$
$194$	10.8424	−	33.3693i	0.778436	−	2.39578i
$195$		0			0
$196$	−1.06084	+	0.770746i	−0.0757744	+	0.0550533i
$197$	−17.3425	+	17.3425i	−1.23560	+	1.23560i	−0.273821	+	0.961781i	$0.588287\pi$
$197$	−17.3425	+	17.3425i	−1.23560	+	1.23560i	−0.961781	+	0.273821i	$0.911713\pi$
$198$		0			0
$199$		−	3.25580i		−	0.230797i	−0.993319	−	0.115399i	$-0.963185\pi$
$199$		−	3.25580i		−	0.230797i	0.993319	−	0.115399i	$-0.0368146\pi$
$200$	−20.0551	+	11.9051i	−1.41811	+	0.841819i
$201$		0			0
$202$	4.19440	−	2.13715i	0.295117	−	0.150370i
$203$	−17.6967	+	2.80288i	−1.24206	+	0.196723i
$204$		0			0
$205$	0.248483	+	7.70492i	0.0173548	+	0.538135i
$206$	3.97755	−	1.29238i	0.277129	−	0.0900447i
$207$		0			0
$208$	6.97487	+	6.97487i	0.483621	+	0.483621i
$209$	−5.07327	+	12.7942i	−0.350926	+	0.884991i
$210$		0			0
$211$	−14.6014	−	20.0971i	−1.00520	−	1.38354i	−0.922080	−	0.387000i	$-0.873511\pi$
$211$	−14.6014	−	20.0971i	−1.00520	−	1.38354i	−0.0831208	−	0.996539i	$-0.526489\pi$
$212$	−7.33212	+	14.3901i	−0.503572	+	0.988316i
$213$		0			0
$214$	5.94674	−	8.18498i	0.406511	−	0.559514i
$215$	10.8533	−	5.97827i	0.740187	−	0.407715i
$216$		0			0
$217$	−20.8467	−	10.6219i	−1.41517	−	0.721064i
$218$	1.22657	−	7.74423i	0.0830735	−	0.524505i
$219$		0			0
$220$	−27.8969	+	8.11396i	−1.88081	+	0.547043i
$221$	2.65237			0.178418
$222$		0			0
$223$	17.4548	+	8.89368i	1.16886	+	0.595565i	0.927116	−	0.374774i	$-0.122280\pi$
$223$	17.4548	+	8.89368i	1.16886	+	0.595565i	0.241746	+	0.970339i	$0.422280\pi$
$224$	1.93038	+	0.627220i	0.128979	+	0.0419079i
$225$		0			0
$226$	−15.9473	+	21.9496i	−1.06080	+	1.46007i
$227$	−0.464395	−	0.911427i	−0.0308230	−	0.0604935i	0.875081	−	0.483976i	$-0.160808\pi$
$227$	−0.464395	−	0.911427i	−0.0308230	−	0.0604935i	−0.905904	+	0.423482i	$0.860808\pi$
$228$		0			0
$229$	0.0598653	+	0.0823975i	0.00395601	+	0.00544498i	0.810990	−	0.585059i	$-0.198929\pi$
$229$	0.0598653	+	0.0823975i	0.00395601	+	0.00544498i	−0.807034	+	0.590504i	$0.798929\pi$
$230$	−0.757637	+	0.273470i	−0.0499571	+	0.0180321i
$231$		0			0
$232$	22.8903	+	22.8903i	1.50282	+	1.50282i
$233$	21.1366	+	3.34771i	1.38470	+	0.219316i	0.803918	−	0.594740i	$-0.202745\pi$
$233$	21.1366	+	3.34771i	1.38470	+	0.219316i	0.580786	+	0.814056i	$0.302745\pi$
$234$		0			0
$235$	1.72474	+	1.61697i	0.112509	+	0.105479i
$236$	−20.5431	−	14.9254i	−1.33724	−	0.971562i
$237$		0			0
$238$	−5.28413	+	2.69240i	−0.342519	+	0.174522i
$239$	2.67723	+	8.23966i	0.173175	+	0.532979i	0.999545	−	0.0301483i	$-0.00959795\pi$
$239$	2.67723	+	8.23966i	0.173175	+	0.532979i	−0.826370	+	0.563128i	$0.809598\pi$
$240$		0			0
$241$		−	10.6492i		−	0.685976i	−0.939340	−	0.342988i	$-0.888561\pi$
$241$		−	10.6492i		−	0.685976i	0.939340	−	0.342988i	$-0.111439\pi$
$242$	−26.7462	+	0.812677i	−1.71931	+	0.0522408i
$243$		0			0
$244$	−30.1886	+	21.9333i	−1.93263	+	1.40414i
$245$	−0.459223	−	0.591022i	−0.0293387	−	0.0377590i
$246$		0			0
$247$	1.82339	+	11.5124i	0.116020	+	0.732518i
$248$	6.61279	+	41.7515i	0.419913	+	2.65123i
$249$		0			0
$250$	−14.6296	−	22.9273i	−0.925259	−	1.45005i
$251$	−7.59915	+	5.52110i	−0.479654	+	0.348489i	−0.801192	−	0.598408i	$-0.795800\pi$
$251$	−7.59915	+	5.52110i	−0.479654	+	0.348489i	0.321538	+	0.946897i	$0.395800\pi$
$252$		0			0
$253$	−0.488975	+	0.0459651i	−0.0307416	+	0.00288980i
$254$		−	5.77750i		−	0.362513i
$255$		0			0
$256$	−9.63584	−	29.6561i	−0.602240	−	1.85350i
$257$	16.4300	−	8.37149i	1.02487	−	0.522199i	0.141042	−	0.990004i	$-0.454955\pi$
$257$	16.4300	−	8.37149i	1.02487	−	0.522199i	0.883832	+	0.467804i	$0.154955\pi$
$258$		0			0
$259$	15.8700	+	11.5302i	0.986111	+	0.716451i
$260$	−16.8282	+	17.9498i	−1.04364	+	1.11320i
$261$		0			0
$262$	7.50744	+	1.18906i	0.463811	+	0.0734605i
$263$	11.8928	+	11.8928i	0.733342	+	0.733342i	0.971280	−	0.237938i	$-0.0764717\pi$
$263$	11.8928	+	11.8928i	0.733342	+	0.733342i	−0.237938	+	0.971280i	$0.576472\pi$
$264$		0			0
$265$	−8.34434	−	3.91817i	−0.512589	−	0.240691i
$266$	−15.3188	−	21.0845i	−0.939254	−	1.29277i
$267$		0			0
$268$	−7.40747	−	14.5380i	−0.452483	−	0.888049i
$269$	−16.7264	+	23.0219i	−1.01983	+	1.40367i	−0.107502	+	0.994205i	$0.534285\pi$
$269$	−16.7264	+	23.0219i	−1.01983	+	1.40367i	−0.912325	+	0.409467i	$0.865715\pi$
$270$		0			0
$271$	−28.2295	−	9.17232i	−1.71482	−	0.557179i	−0.723696	−	0.690118i	$-0.757558\pi$
$271$	−28.2295	−	9.17232i	−1.71482	−	0.557179i	−0.991124	+	0.132939i	$0.957558\pi$
$272$	2.95479	+	1.50554i	0.179160	+	0.0912868i
$273$		0			0
$274$	40.2251			2.43009
$275$	−5.14221	−	15.7657i	−0.310087	−	0.950708i
$276$		0			0
$277$	−1.94287	+	12.2668i	−0.116736	+	0.737041i	0.857995	+	0.513658i	$0.171710\pi$
$277$	−1.94287	+	12.2668i	−0.116736	+	0.737041i	−0.974731	+	0.223383i	$0.928290\pi$
$278$	9.36443	+	4.77141i	0.561641	+	0.286170i
$279$		0			0
$280$	7.49130	−	25.8646i	0.447691	−	1.54571i
$281$	−12.8578	+	17.6972i	−0.767032	+	1.05573i	0.229564	+	0.973294i	$0.426270\pi$
$281$	−12.8578	+	17.6972i	−0.767032	+	1.05573i	−0.996596	+	0.0824357i	$0.973730\pi$
$282$		0			0
$283$	12.3474	−	24.2332i	0.733978	−	1.44051i	−0.157532	−	0.987514i	$-0.550354\pi$
$283$	12.3474	−	24.2332i	0.733978	−	1.44051i	0.891511	−	0.453000i	$-0.149646\pi$
$284$	−2.91529	−	4.01255i	−0.172991	−	0.238101i
$285$		0			0
$286$	−19.1399	+	12.1326i	−1.13177	+	0.717416i
$287$	−6.29366	−	6.29366i	−0.371503	−	0.371503i
$288$		0			0
$289$	−15.3199	+	4.97773i	−0.901170	+	0.292808i
$290$	−25.8190	+	27.5398i	−1.51614	+	1.61719i
$291$		0			0
$292$	−6.85394	+	1.08556i	−0.401096	+	0.0635274i
$293$	−17.9201	+	9.13077i	−1.04691	+	0.533425i	−0.890838	−	0.454321i	$-0.849882\pi$
$293$	−17.9201	+	9.13077i	−1.04691	+	0.533425i	−0.156068	+	0.987746i	$0.549882\pi$
$294$		0			0
$295$	8.13689	−	11.9943i	0.473748	−	0.698334i
$296$		−	35.4416i		−	2.06000i
$297$		0			0
$298$	14.5257	−	14.5257i	0.841450	−	0.841450i
$299$	−0.336495	+	0.244478i	−0.0194600	+	0.0141385i
$300$		0			0
$301$	−4.42087	+	13.6060i	−0.254815	+	0.784239i
$302$	4.54074	+	28.6691i	0.261290	+	1.64972i
$303$		0			0
$304$	−4.50340	+	13.8600i	−0.258288	+	0.794927i
$305$	−13.0682	−	16.8188i	−0.748284	−	0.963044i
$306$		0			0
$307$	−14.6921	+	14.6921i	−0.838520	+	0.838520i	−0.988664	−	0.150144i	$-0.952026\pi$
$307$	−14.6921	+	14.6921i	−0.838520	+	0.838520i	0.150144	+	0.988664i	$0.452026\pi$
$308$	17.0903	−	28.8638i	0.973810	−	1.64467i
$309$		0			0
$310$	−48.4141	+	9.27678i	−2.74974	+	0.526886i
$311$	−7.19358	−	22.1396i	−0.407911	−	1.25542i	−0.918440	−	0.395560i	$-0.870551\pi$
$311$	−7.19358	−	22.1396i	−0.407911	−	1.25542i	0.510530	−	0.859860i	$-0.329449\pi$
$312$		0			0
$313$	13.8454	−	2.19289i	0.782587	−	0.123950i	0.247659	−	0.968847i	$-0.420339\pi$
$313$	13.8454	−	2.19289i	0.782587	−	0.123950i	0.534928	+	0.844898i	$0.320339\pi$
$314$	2.67948	+	1.94676i	0.151212	+	0.109862i
$315$		0			0
$316$	16.1771	−	5.25626i	0.910032	−	0.295687i
$317$	−29.1369	−	4.61482i	−1.63649	−	0.259194i	−0.730630	−	0.682774i	$-0.760773\pi$
$317$	−29.1369	−	4.61482i	−1.63649	−	0.259194i	−0.905859	+	0.423580i	$0.860773\pi$
$318$		0			0
$319$	−19.4408	+	12.3233i	−1.08847	+	0.689972i
$320$	18.7949	−	6.78404i	1.05066	−	0.379239i
$321$		0			0
$322$	0.422208	−	0.828629i	0.0235287	−	0.0461777i
$323$	1.77905	+	3.49158i	0.0989889	+	0.194277i
$324$		0			0
$325$	−10.5498	−	9.27011i	−0.585198	−	0.514213i
$326$	53.0803	+	17.2468i	2.93985	+	0.955215i
$327$		0			0
$328$	−2.51563	+	15.8830i	−0.138902	+	0.876994i
$329$	−2.72962			−0.150489
$330$		0			0
$331$	2.18560			0.120131			0.0600657	−	0.998194i	$-0.480869\pi$
$331$	2.18560			0.120131			0.0600657	+	0.998194i	$0.480869\pi$
$332$	−5.08128	+	32.0819i	−0.278871	+	1.76072i
$333$		0			0
$334$	33.2232	+	10.7949i	1.81789	+	0.590670i
$335$	8.15753	−	4.49338i	0.445694	−	0.245500i
$336$		0			0
$337$	−0.818095	−	1.60560i	−0.0445645	−	0.0874627i	0.867650	−	0.497175i	$-0.165629\pi$
$337$	−0.818095	−	1.60560i	−0.0445645	−	0.0874627i	−0.912215	+	0.409712i	$0.865629\pi$
$338$	5.64408	−	11.0771i	0.306997	−	0.602516i
$339$		0			0
$340$	−3.51587	+	7.48759i	−0.190675	+	0.406072i
$341$	−29.9966	−	1.90289i	−1.62441	−	0.103047i
$342$		0			0
$343$	18.7031	+	2.96227i	1.00987	+	0.159948i
$344$	24.5826	−	7.98736i	1.32540	−	0.430650i
$345$		0			0
$346$	43.8896	+	31.8877i	2.35952	+	1.71429i
$347$	21.2079	−	3.35900i	1.13850	−	0.180321i	0.441411	−	0.897305i	$-0.354478\pi$
$347$	21.2079	−	3.35900i	1.13850	−	0.180321i	0.697090	+	0.716984i	$0.254478\pi$
$348$		0			0
$349$	3.29300	+	10.1348i	0.176270	+	0.542505i	0.999689	−	0.0249295i	$-0.00793612\pi$
$349$	3.29300	+	10.1348i	0.176270	+	0.542505i	−0.823419	+	0.567434i	$0.807936\pi$
$350$	30.4276	+	7.75914i	1.62643	+	0.414744i
$351$		0			0
$352$	2.59606	−	0.244037i	0.138370	−	0.0130072i
$353$	7.73857	−	7.73857i	0.411883	−	0.411883i	−0.470511	−	0.882394i	$-0.655931\pi$
$353$	7.73857	−	7.73857i	0.411883	−	0.411883i	0.882394	+	0.470511i	$0.155931\pi$
$354$		0			0
$355$	2.23550	−	1.73698i	0.118648	−	0.0921891i
$356$	−5.12185	+	15.7634i	−0.271457	+	0.835460i
$357$		0			0
$358$	1.66228	+	10.4952i	0.0878544	+	0.554691i
$359$	−1.01178	+	3.11394i	−0.0533997	+	0.164347i	−0.974200	−	0.225688i	$-0.927537\pi$
$359$	−1.01178	+	3.11394i	−0.0533997	+	0.164347i	0.920800	+	0.390035i	$0.127537\pi$
$360$		0			0
$361$	1.43940	−	1.04578i	0.0757578	−	0.0550412i
$362$	16.2374	−	16.2374i	0.853418	−	0.853418i
$363$		0			0
$364$		−	28.4079i		−	1.48898i
$365$	−0.745404	−	3.89015i	−0.0390162	−	0.203620i
$366$		0			0
$367$	16.2428	−	8.27615i	0.847870	−	0.432011i	0.0246243	−	0.999697i	$-0.492161\pi$
$367$	16.2428	−	8.27615i	0.847870	−	0.432011i	0.823246	+	0.567686i	$0.192161\pi$
$368$	−0.513632	+	0.0813513i	−0.0267749	+	0.00424073i
$369$		0			0
$370$	41.3083	−	1.33219i	2.14752	−	0.0692570i
$371$	10.1225	−	3.28901i	0.525536	−	0.170757i
$372$		0			0
$373$	12.4917	+	12.4917i	0.646795	+	0.646795i	0.952217	−	0.305422i	$-0.0987976\pi$
$373$	12.4917	+	12.4917i	0.646795	+	0.646795i	−0.305422	+	0.952217i	$0.598798\pi$
$374$	−4.85939	+	5.86777i	−0.251273	+	0.303415i
$375$		0			0
$376$	2.89879	+	3.98984i	0.149494	+	0.205760i
$377$	−8.84972	+	17.3686i	−0.455784	+	0.894526i
$378$		0			0
$379$	−12.9685	+	17.8496i	−0.666146	+	0.916872i	−0.999665	−	0.0258717i	$-0.991764\pi$
$379$	−12.9685	+	17.8496i	−0.666146	+	0.916872i	0.333519	+	0.942743i	$0.391764\pi$
$380$	−34.9163	−	10.1130i	−1.79117	−	0.518785i
$381$		0			0
$382$	14.0294	+	7.14836i	0.717809	+	0.365742i
$383$	3.08015	−	19.4473i	0.157389	−	0.993712i	−0.774923	−	0.632056i	$-0.782211\pi$
$383$	3.08015	−	19.4473i	0.157389	−	0.993712i	0.932311	−	0.361656i	$-0.117789\pi$
$384$		0			0
$385$	16.7810	+	9.21884i	0.855241	+	0.469836i
$386$	−2.44874			−0.124638
$387$		0			0
$388$	50.3457	+	25.6524i	2.55591	+	1.30230i
$389$	16.2827	+	5.29057i	0.825565	+	0.268242i	0.691176	−	0.722686i	$-0.257093\pi$
$389$	16.2827	+	5.29057i	0.825565	+	0.268242i	0.134389	+	0.990929i	$0.457093\pi$
$390$		0			0
$391$	−0.0821929	+	0.113129i	−0.00415667	+	0.00572117i
$392$	−0.708818	−	1.39113i	−0.0358007	−	0.0702629i
$393$		0			0
$394$	−35.0683	−	48.2673i	−1.76671	−	2.43167i
$395$	3.29629	+	9.13221i	0.165854	+	0.459491i
$396$		0			0
$397$	5.24887	+	5.24887i	0.263433	+	0.263433i	0.826447	−	0.563014i	$-0.190358\pi$
$397$	5.24887	+	5.24887i	0.263433	+	0.263433i	−0.563014	+	0.826447i	$0.690358\pi$
$398$	7.82252	+	1.23896i	0.392107	+	0.0621037i
$399$		0			0
$400$	−6.49077	−	16.3153i	−0.324539	−	0.815767i
$401$	9.93091	+	7.21523i	0.495926	+	0.360311i	0.807459	−	0.589924i	$-0.200842\pi$
$401$	9.93091	+	7.21523i	0.495926	+	0.360311i	−0.311533	+	0.950235i	$0.600842\pi$
$402$		0			0
$403$	−22.6803	+	11.5562i	−1.12979	+	0.575655i
$404$	2.34267	+	7.21000i	0.116552	+	0.358711i
$405$		0			0
$406$		−	43.5854i		−	2.16311i
$407$	24.5905	+	5.51006i	1.21891	+	0.273124i
$408$		0			0
$409$	21.6485	−	15.7286i	1.07045	−	0.777727i	0.0944563	−	0.995529i	$-0.469889\pi$
$409$	21.6485	−	15.7286i	1.07045	−	0.777727i	0.975993	+	0.217802i	$0.0698887\pi$
$410$	−18.6067	−	2.33503i	−0.918921	−	0.115319i
$411$		0			0
$412$	1.05361	+	6.65226i	0.0519079	+	0.327733i
$413$	2.61782	+	16.5283i	0.128815	+	0.813304i
$414$		0			0
$415$	−18.3960	−	2.30858i	−0.903024	−	0.113324i
$416$	1.78651	−	1.29798i	0.0875910	−	0.0636386i
$417$		0			0
$418$	−28.8092	−	17.0580i	−1.40911	−	0.834332i
$419$			14.2401i			0.695676i	0.937555	+	0.347838i	$0.113084\pi$
$419$			14.2401i			0.695676i	−0.937555	+	0.347838i	$0.886916\pi$
$420$		0			0
$421$	−2.13413	−	6.56818i	−0.104011	−	0.320113i	0.885486	−	0.464666i	$-0.153826\pi$
$421$	−2.13413	−	6.56818i	−0.104011	−	0.320113i	−0.989497	+	0.144553i	$0.953826\pi$
$422$	53.8425	−	27.4341i	2.62101	−	1.33547i
$423$		0			0
$424$	−15.5574	−	11.3031i	−0.755532	−	0.548926i
$425$	−4.33630	−	1.86802i	−0.210342	−	0.0906123i
$426$		0			0
$427$	24.2888	+	3.84696i	1.17542	+	0.186168i
$428$	11.5209	+	11.5209i	0.556882	+	0.556882i
$429$		0			0
$430$	10.2335	+	28.3515i	0.493505	+	1.36723i
$431$	4.19638	+	5.77582i	0.202132	+	0.278211i	0.898034	−	0.439926i	$-0.144995\pi$
$431$	4.19638	+	5.77582i	0.202132	+	0.278211i	−0.695902	+	0.718137i	$0.744995\pi$
$432$		0			0
$433$	−7.62822	−	14.9712i	−0.366589	−	0.719471i	0.631864	−	0.775079i	$-0.282290\pi$
$433$	−7.62822	−	14.9712i	−0.366589	−	0.719471i	−0.998453	+	0.0556084i	$0.982290\pi$
$434$	33.4538	−	46.0451i	1.60583	−	2.21024i
$435$		0			0
$436$	12.0089	+	3.90194i	0.575124	+	0.186869i
$437$	−0.547531	−	0.278981i	−0.0261920	−	0.0133455i
$438$		0			0
$439$	0.772934			0.0368901			0.0184451	−	0.999830i	$-0.494128\pi$
$439$	0.772934			0.0368901			0.0184451	+	0.999830i	$0.494128\pi$
$440$	−4.34601	−	34.3187i	−0.207188	−	1.63608i
$441$		0			0
$442$	−1.00934	+	6.37271i	−0.0480093	+	0.303119i
$443$	−16.7419	−	8.53040i	−0.795430	−	0.405292i	0.00853887	−	0.999964i	$-0.497282\pi$
$443$	−16.7419	−	8.53040i	−0.795430	−	0.405292i	−0.803968	+	0.594672i	$0.797282\pi$
$444$		0			0
$445$	−9.08715	−	2.63196i	−0.430772	−	0.124767i
$446$	−28.0106	+	38.5533i	−1.32634	+	1.82555i
$447$		0			0
$448$	−10.4738	+	20.5560i	−0.494840	+	0.971179i
$449$	0.419317	+	0.577140i	0.0197888	+	0.0272369i	0.818797	−	0.574084i	$-0.194642\pi$
$449$	0.419317	+	0.577140i	0.0197888	+	0.0272369i	−0.799008	+	0.601320i	$0.794642\pi$
$450$		0			0
$451$	−10.6291	−	4.21474i	−0.500502	−	0.198464i
$452$	−30.8954	−	30.8954i	−1.45320	−	1.45320i
$453$		0			0
$454$	2.36655	−	0.768940i	0.111068	−	0.0360882i
$455$	16.2065	−	0.522656i	0.759772	−	0.0245025i
$456$		0			0
$457$	−19.1068	+	3.02622i	−0.893780	+	0.141561i	−0.586396	−	0.810025i	$-0.699454\pi$
$457$	−19.1068	+	3.02622i	−0.893780	+	0.141561i	−0.307384	+	0.951586i	$0.599454\pi$
$458$	−0.220753	+	0.112479i	−0.0103151	+	0.00525581i
$459$		0			0
$460$	−0.244113	−	1.27399i	−0.0113818	−	0.0594000i
$461$		−	36.5277i		−	1.70126i	−0.525761	−	0.850632i	$-0.676219\pi$
$461$		−	36.5277i		−	1.70126i	0.525761	−	0.850632i	$-0.323781\pi$
$462$		0			0
$463$	−17.1422	+	17.1422i	−0.796664	+	0.796664i	−0.982568	−	0.185904i	$-0.940479\pi$
$463$	−17.1422	+	17.1422i	−0.796664	+	0.796664i	0.185904	+	0.982568i	$0.440479\pi$
$464$	−19.7175	+	14.3256i	−0.915361	+	0.665049i
$465$		0			0
$466$	−16.0867	+	49.5097i	−0.745201	+	2.29349i
$467$	2.31832	+	14.6373i	0.107279	+	0.677333i	0.981451	+	0.191715i	$0.0614051\pi$
$467$	2.31832	+	14.6373i	0.107279	+	0.677333i	−0.874172	+	0.485617i	$0.838595\pi$
$468$		0			0
$469$	−3.32281	+	10.2266i	−0.153433	+	0.472219i
$470$	−4.54132	+	3.52860i	−0.209476	+	0.162762i
$471$		0			0
$472$	21.3791	−	21.3791i	0.984051	−	0.984051i
$473$	1.72006	+	18.2979i	0.0790885	+	0.841340i
$474$		0			0
$475$	5.12699	−	20.1056i	0.235242	−	0.922507i
$476$	−2.95131	−	9.08320i	−0.135273	−	0.416328i
$477$		0			0
$478$	−20.8157	+	3.29689i	−0.952090	+	0.150796i
$479$	−22.3176	−	16.2146i	−1.01971	−	0.740866i	−0.0534905	−	0.998568i	$-0.517035\pi$
$479$	−22.3176	−	16.2146i	−1.01971	−	0.740866i	−0.966224	+	0.257702i	$0.917035\pi$
$480$		0			0
$481$	20.2972	−	6.59495i	0.925471	−	0.300704i
$482$	25.5862	+	4.05246i	1.16542	+	0.184585i
$483$		0			0
$484$	5.44540	−	42.7471i	0.247518	−	1.94305i
$485$	−13.7082	+	29.1938i	−0.622459	+	1.32562i
$486$		0			0
$487$	17.6583	−	34.6563i	0.800174	−	1.57043i	−0.0210198	−	0.999779i	$-0.506691\pi$
$487$	17.6583	−	34.6563i	0.800174	−	1.57043i	0.821193	−	0.570650i	$-0.193309\pi$
$488$	−20.1710	−	39.5879i	−0.913099	−	1.79206i
$489$		0			0
$490$	1.59477	−	0.878440i	0.0720442	−	0.0396839i
$491$	−17.8811	−	5.80992i	−0.806962	−	0.262198i	−0.123652	−	0.992326i	$-0.539461\pi$
$491$	−17.8811	−	5.80992i	−0.806962	−	0.262198i	−0.683311	+	0.730128i	$0.739461\pi$
$492$		0			0
$493$	−1.02520	+	6.47287i	−0.0461728	+	0.291523i
$494$	−28.3541			−1.27571
$495$		0			0
$496$	−31.8258			−1.42902
$497$	−0.511323	+	3.22837i	−0.0229360	+	0.144812i
$498$		0			0
$499$	−4.98327	−	1.61916i	−0.223082	−	0.0724837i	0.195343	−	0.980735i	$-0.437418\pi$
$499$	−4.98327	−	1.61916i	−0.223082	−	0.0724837i	−0.418425	+	0.908251i	$0.637418\pi$
$500$	40.1537	−	17.4938i	1.79573	−	0.782348i
$501$		0			0
$502$	−10.3734	−	20.3590i	−0.462990	−	0.908668i
$503$	−5.98921	+	11.7545i	−0.267046	+	0.524106i	−0.985122	−	0.171858i	$-0.945023\pi$
$503$	−5.98921	+	11.7545i	−0.267046	+	0.524106i	0.718076	+	0.695965i	$0.245023\pi$
$504$		0			0
$505$	−4.07015	+	1.46913i	−0.181119	+	0.0653754i
$506$	0.0756375	−	1.19232i	0.00336250	−	0.0530053i
$507$		0			0
$508$	9.18967	+	1.45550i	0.407726	+	0.0645774i
$509$	5.32193	−	1.72920i	0.235890	−	0.0766454i	−0.188686	−	0.982037i	$-0.560423\pi$
$509$	5.32193	−	1.72920i	0.235890	−	0.0766454i	0.424577	+	0.905392i	$0.360423\pi$
$510$		0			0
$511$	3.69980	+	2.68806i	0.163669	+	0.118913i
$512$	35.0853	−	5.55696i	1.55056	−	0.245585i
$513$		0			0
$514$	13.8614	+	42.6611i	0.611401	+	1.88170i
$515$	−3.77568	+	0.723470i	−0.166376	+	0.0318799i
$516$		0			0
$517$	−3.21895	+	1.39098i	−0.141569	+	0.0611751i
$518$	−33.7421	+	33.7421i	−1.48254	+	1.48254i
$519$		0			0
$520$	−17.9748	−	23.1337i	−0.788249	−	1.01448i
$521$	−5.89515	+	18.1434i	−0.258271	+	0.794877i	0.734896	+	0.678179i	$0.237231\pi$
$521$	−5.89515	+	18.1434i	−0.258271	+	0.794877i	−0.993168	+	0.116697i	$0.962769\pi$
$522$		0			0
$523$	5.49061	+	34.6664i	0.240088	+	1.51585i	0.753349	+	0.657621i	$0.228437\pi$
$523$	5.49061	+	34.6664i	0.240088	+	1.51585i	−0.513261	+	0.858233i	$0.671563\pi$
$524$	−3.78263	+	11.6417i	−0.165245	+	0.508572i
$525$		0			0
$526$	−33.0999	+	24.0485i	−1.44322	+	1.04856i
$527$	−6.05128	+	6.05128i	−0.263598	+	0.263598i
$528$		0			0
$529$			22.9781i			0.999047i
$530$	12.5893	−	18.5574i	0.546845	−	0.806084i
$531$		0			0
$532$	37.3961	−	19.0542i	1.62132	−	0.826106i
$533$	−9.56421	+	1.51482i	−0.414272	+	0.0656143i
$534$		0			0
$535$	−6.36060	+	6.78453i	−0.274993	+	0.293321i
$536$	18.4767	−	6.00346i	0.798074	−	0.259310i
$537$		0			0
$538$	−48.9484	−	48.9484i	−2.11031	−	2.11031i
$539$	1.07541	−	0.275523i	0.0463213	−	0.0118676i
$540$		0			0
$541$	−1.49345	−	2.05556i	−0.0642084	−	0.0883752i	0.775705	−	0.631095i	$-0.217394\pi$
$541$	−1.49345	−	2.05556i	−0.0642084	−	0.0883752i	−0.839914	+	0.542720i	$0.817394\pi$
$542$	32.7803	−	64.3350i	1.40803	−	2.76342i
$543$		0			0
$544$	0.436376	−	0.600621i	0.0187095	−	0.0257514i
$545$	−2.00508	+	6.92280i	−0.0858884	+	0.296540i
$546$		0			0
$547$	13.2087	+	6.73017i	0.564764	+	0.287761i	0.712969	−	0.701195i	$-0.247350\pi$
$547$	13.2087	+	6.73017i	0.564764	+	0.287761i	−0.148206	+	0.988957i	$0.547350\pi$
$548$	−10.1337	+	63.9819i	−0.432892	+	2.73317i
$549$		0			0
$550$	39.8362	−	6.35539i	1.69862	−	0.270995i
$551$	−28.7998			−1.22691
$552$		0			0
$553$	−9.98792	−	5.08910i	−0.424730	−	0.216411i
$554$	−28.7334	−	9.33604i	−1.22076	−	0.396650i
$555$		0			0
$556$	−9.94853	+	13.6930i	−0.421912	+	0.580712i
$557$	−5.79353	−	11.3704i	−0.245480	−	0.481781i	0.735086	−	0.677974i	$-0.237142\pi$
$557$	−5.79353	−	11.3704i	−0.245480	−	0.481781i	−0.980565	+	0.196194i	$0.937142\pi$
$558$		0			0
$559$	9.14861	+	12.5920i	0.386945	+	0.532584i
$560$	18.3510	+	8.61687i	0.775470	+	0.364129i
$561$		0			0
$562$	−37.6272	−	37.6272i	−1.58721	−	1.58721i
$563$	33.1190	+	5.24553i	1.39580	+	0.221073i	0.808594	−	0.588367i	$-0.200229\pi$
$563$	33.1190	+	5.24553i	1.39580	+	0.221073i	0.587204	+	0.809439i	$0.300229\pi$
$564$		0			0
$565$	17.0572	−	18.1940i	0.717601	−	0.765429i
$566$	53.5250	+	38.8882i	2.24982	+	1.63459i
$567$		0			0
$568$	5.26186	−	2.68105i	0.220783	−	0.112494i
$569$	−2.57065	−	7.91165i	−0.107767	−	0.331674i	0.882603	−	0.470120i	$-0.155789\pi$
$569$	−2.57065	−	7.91165i	−0.107767	−	0.331674i	−0.990370	+	0.138446i	$0.955789\pi$
$570$		0			0
$571$			45.2601i			1.89408i	0.321118	+	0.947039i	$0.395941\pi$
$571$			45.2601i			1.89408i	−0.321118	+	0.947039i	$0.604059\pi$
$572$	−14.4762	−	33.5004i	−0.605282	−	1.40072i
$573$		0			0
$574$	17.5164	−	12.7264i	0.731121	−	0.531190i
$575$	0.722310	−	0.162704i	0.0301224	−	0.00678522i
$576$		0			0
$577$	−3.58768	−	22.6517i	−0.149357	−	0.943005i	−0.942558	−	0.334044i	$-0.891587\pi$
$577$	−3.58768	−	22.6517i	−0.149357	−	0.943005i	0.793200	−	0.608961i	$-0.208413\pi$
$578$	−6.12986	−	38.7024i	−0.254969	−	1.60981i
$579$		0			0
$580$	−37.3002	−	48.0056i	−1.54881	−	1.99332i
$581$	17.3180	−	12.5823i	0.718472	−	0.522001i
$582$		0			0
$583$	10.2611	−	9.03691i	0.424972	−	0.374270i
$584$		−	8.26259i		−	0.341908i
$585$		0			0
$586$	−15.1186	−	46.5303i	−0.624545	−	1.92215i
$587$	−8.99622	+	4.58380i	−0.371314	+	0.189194i	−0.629683	−	0.776853i	$-0.716815\pi$
$587$	−8.99622	+	4.58380i	−0.371314	+	0.189194i	0.258369	+	0.966046i	$0.416815\pi$
$588$		0			0
$589$	−30.4251	−	22.1051i	−1.25365	−	0.910827i
$590$	25.7215	+	24.1143i	1.05894	+	0.992772i
$591$		0			0
$592$	26.3548	+	4.17419i	1.08318	+	0.171558i
$593$	−9.47168	−	9.47168i	−0.388955	−	0.388955i	0.485359	−	0.874315i	$-0.338689\pi$
$593$	−9.47168	−	9.47168i	−0.388955	−	0.388955i	−0.874315	+	0.485359i	$0.838689\pi$
$594$		0			0
$595$	5.12760	−	1.85082i	0.210211	−	0.0758761i
$596$	19.4451	+	26.7639i	0.796503	+	1.09629i
$597$		0			0
$598$	−0.459343	−	0.901512i	−0.0187839	−	0.0368656i
$599$	−23.5167	+	32.3680i	−0.960866	+	1.32252i	−0.0143383	+	0.999897i	$0.504564\pi$
$599$	−23.5167	+	32.3680i	−0.960866	+	1.32252i	−0.946528	+	0.322622i	$0.895436\pi$
$600$		0			0
$601$	34.5805	+	11.2359i	1.41057	+	0.458322i	0.912593	−	0.408869i	$-0.134077\pi$
$601$	34.5805	+	11.2359i	1.41057	+	0.458322i	0.497976	+	0.867191i	$0.334077\pi$
$602$	−31.0081	−	15.7994i	−1.26380	−	0.643937i
$603$		0			0
$604$	−46.7449			−1.90202
$605$	24.4871	+	2.32009i	0.995541	+	0.0943251i
$606$		0			0
$607$	−3.89991	+	24.6231i	−0.158293	+	0.999420i	0.772803	+	0.634646i	$0.218854\pi$
$607$	−3.89991	+	24.6231i	−0.158293	+	0.999420i	−0.931096	+	0.364774i	$0.881146\pi$
$608$	2.90694	+	1.48116i	0.117892	+	0.0600689i
$609$		0			0
$610$	45.3827	−	24.9980i	1.83749	−	1.01214i
$611$	−1.74555	+	2.40254i	−0.0706174	+	0.0971965i
$612$		0			0
$613$	−5.30759	+	10.4167i	−0.214372	+	0.420728i	−0.973003	−	0.230792i	$-0.925868\pi$
$613$	−5.30759	+	10.4167i	−0.214372	+	0.420728i	0.758632	+	0.651520i	$0.225868\pi$
$614$	−29.7088	−	40.8907i	−1.19895	−	1.65021i
$615$		0			0
$616$	30.7612	+	25.4748i	1.23940	+	1.02641i
$617$	−6.18386	−	6.18386i	−0.248953	−	0.248953i	0.571588	−	0.820541i	$-0.306328\pi$
$617$	−6.18386	−	6.18386i	−0.248953	−	0.248953i	−0.820541	+	0.571588i	$0.806328\pi$
$618$		0			0
$619$	−1.04489	+	0.339504i	−0.0419975	+	0.0136458i	−0.329940	−	0.944002i	$-0.607029\pi$
$619$	−1.04489	+	0.339504i	−0.0419975	+	0.0136458i	0.287943	+	0.957648i	$0.407029\pi$
$620$	−2.55884	−	79.3444i	−0.102766	−	3.18655i
$621$		0			0
$622$	55.9309	−	8.85859i	2.24263	−	0.355197i
$623$	9.73251	−	4.95896i	0.389925	−	0.198677i
$624$		0			0
$625$	10.7189	+	22.5855i	0.428755	+	0.903421i
$626$			34.1000i			1.36291i
$627$		0			0
$628$	−3.77153	+	3.77153i	−0.150501	+	0.150501i
$629$	5.80472	−	4.21737i	0.231449	−	0.168158i
$630$		0			0
$631$	−1.00765	+	3.10124i	−0.0401140	+	0.123458i	−0.969108	−	0.246636i	$-0.920675\pi$
$631$	−1.00765	+	3.10124i	−0.0401140	+	0.123458i	0.928994	+	0.370095i	$0.120675\pi$
$632$	3.16827	+	20.0037i	0.126027	+	0.795703i
$633$		0			0
$634$	22.1755	−	68.2493i	0.880703	−	2.71053i
$635$	−0.661278	+	5.26942i	−0.0262420	+	0.209110i
$636$		0			0
$637$	0.664797	−	0.664797i	0.0263402	−	0.0263402i
$638$	−22.2105	−	51.3987i	−0.879321	−	2.03490i
$639$		0			0
$640$	8.48573	+	44.2858i	0.335428	+	1.75055i
$641$	2.75407	+	8.47616i	0.108779	+	0.334788i	0.990599	−	0.136799i	$-0.0436814\pi$
$641$	2.75407	+	8.47616i	0.108779	+	0.334788i	−0.881820	+	0.471587i	$0.843681\pi$
$642$		0			0
$643$	−36.6439	+	5.80382i	−1.44509	+	0.228880i	−0.829202	−	0.558950i	$-0.811204\pi$
$643$	−36.6439	+	5.80382i	−1.44509	+	0.228880i	−0.615893	+	0.787830i	$0.711204\pi$
$644$	1.21165	+	0.880315i	0.0477457	+	0.0346893i
$645$		0			0
$646$	−9.06602	+	2.94573i	−0.356698	+	0.115898i
$647$	21.7803	+	3.44966i	0.856273	+	0.135620i	0.569110	−	0.822262i	$-0.307288\pi$
$647$	21.7803	+	3.44966i	0.856273	+	0.135620i	0.287163	+	0.957882i	$0.407288\pi$
$648$		0			0
$649$	11.5097	+	18.1572i	0.451794	+	0.712734i
$650$	26.2874	−	21.8198i	1.03108	−	0.855842i
$651$		0			0
$652$	−40.8051	+	80.0844i	−1.59805	+	3.13635i
$653$	−22.0554	−	43.2861i	−0.863093	−	1.69392i	−0.708232	−	0.705980i	$-0.750507\pi$
$653$	−22.0554	−	43.2861i	−0.863093	−	1.69392i	−0.154861	−	0.987936i	$-0.549493\pi$
$654$		0			0
$655$	−6.71113	−	1.94378i	−0.262225	−	0.0759496i
$656$	−11.5145	−	3.74130i	−0.449567	−	0.146073i
$657$		0			0
$658$	1.03873	−	6.55831i	0.0404941	−	0.255669i
$659$	47.3029			1.84266			0.921329	−	0.388783i	$-0.127104\pi$
$659$	47.3029			1.84266			0.921329	+	0.388783i	$0.127104\pi$
$660$		0			0
$661$	−26.7159			−1.03913			−0.519564	−	0.854432i	$-0.673906\pi$
$661$	−26.7159			−1.03913			−0.519564	+	0.854432i	$0.673906\pi$
$662$	−0.831711	+	5.25121i	−0.0323254	+	0.204094i
$663$		0			0
$664$	−36.7826	−	11.9514i	−1.42744	−	0.463804i
$665$	11.5583	+	20.9836i	0.448213	+	0.813710i
$666$		0			0
$667$	−0.466563	−	0.915682i	−0.0180654	−	0.0354553i
$668$	−25.5401	+	50.1252i	−0.988175	+	1.93940i
$669$		0			0
$670$	7.69172	+	21.3095i	0.297157	+	0.823260i
$671$	30.6032	−	7.84061i	1.18143	−	0.302683i
$672$		0			0
$673$	13.0723	+	2.07046i	0.503902	+	0.0798102i	0.403210	−	0.915107i	$-0.367894\pi$
$673$	13.0723	+	2.07046i	0.503902	+	0.0798102i	0.100692	+	0.994918i	$0.467894\pi$
$674$	4.16900	−	1.35459i	0.160584	−	0.0521769i
$675$		0			0
$676$	16.1973	+	11.7681i	0.622975	+	0.452618i
$677$	−33.9668	+	5.37982i	−1.30545	+	0.206763i	−0.770131	−	0.637885i	$-0.779809\pi$
$677$	−33.9668	+	5.37982i	−1.30545	+	0.206763i	−0.535321	+	0.844649i	$0.679809\pi$
$678$		0			0
$679$	−11.5070	−	35.4150i	−0.441600	−	1.35910i
$680$	−8.15069	−	5.52941i	−0.312565	−	0.212043i
$681$		0			0
$682$	15.9869	−	71.3470i	0.612171	−	2.73202i
$683$	−27.9495	+	27.9495i	−1.06946	+	1.06946i	−0.0720555	+	0.997401i	$0.522956\pi$
$683$	−27.9495	+	27.9495i	−1.06946	+	1.06946i	−0.997401	+	0.0720555i	$0.977044\pi$
$684$		0			0
$685$	−36.6877	−	4.60407i	−1.40176	−	0.175912i
$686$	−14.2346	+	43.8095i	−0.543478	+	1.67265i
$687$		0			0
$688$	3.04425	+	19.2206i	0.116061	+	0.732779i
$689$	3.57830	−	11.0129i	0.136322	−	0.419557i
$690$		0			0
$691$	−2.64892	+	1.92455i	−0.100770	+	0.0732134i	−0.637029	−	0.770840i	$-0.719837\pi$
$691$	−2.64892	+	1.92455i	−0.100770	+	0.0732134i	0.536259	+	0.844053i	$0.319837\pi$
$692$	−61.7773	+	61.7773i	−2.34842	+	2.34842i
$693$		0			0
$694$			52.2333i			1.98275i
$695$	−7.99478	−	5.42364i	−0.303259	−	0.205730i
$696$		0			0
$697$	−2.90071	+	1.47799i	−0.109872	+	0.0559827i
$698$	−25.6035	+	4.05519i	−0.969106	+	0.153491i
$699$		0			0
$700$	−20.0072	+	46.4433i	−0.756199	+	1.75539i
$701$	5.55696	−	1.80557i	0.209883	−	0.0681953i	−0.202188	−	0.979347i	$-0.564805\pi$
$701$	5.55696	−	1.80557i	0.209883	−	0.0681953i	0.412072	+	0.911151i	$0.364805\pi$
$702$		0			0
$703$	22.2957	+	22.2957i	0.840897	+	0.840897i
$704$	−1.87635	+	29.5782i	−0.0707178	+	1.11477i
$705$		0			0
$706$	15.6482	+	21.5379i	0.588927	+	0.810588i
$707$	2.26817	−	4.45154i	0.0853034	−	0.167417i
$708$		0			0
$709$	−23.5016	+	32.3472i	−0.882623	+	1.21483i	0.0930647	+	0.995660i	$0.470334\pi$
$709$	−23.5016	+	32.3472i	−0.882623	+	1.21483i	−0.975688	+	0.219166i	$0.929666\pi$
$710$	3.32263	+	6.03209i	0.124696	+	0.226380i
$711$		0			0
$712$	−17.5841	−	8.95956i	−0.658993	−	0.335774i
$713$	0.209933	−	1.32547i	0.00786207	−	0.0496391i
$714$		0			0
$715$	18.8454	−	8.87494i	0.704778	−	0.331904i
$716$	−17.1125			−0.639523
$717$		0			0
$718$	−7.09665	−	3.61592i	−0.264845	−	0.134945i
$719$	19.2106	+	6.24190i	0.716434	+	0.232784i	0.644477	−	0.764624i	$-0.277075\pi$
$719$	19.2106	+	6.24190i	0.716434	+	0.232784i	0.0719577	+	0.997408i	$0.477075\pi$
$720$		0			0
$721$	2.60896	−	3.59093i	0.0971629	−	0.133733i
$722$	1.96489	+	3.85632i	0.0731258	+	0.143517i
$723$		0			0
$724$	21.7365	+	29.9177i	0.807831	+	1.11188i
$725$	26.7006	−	22.1627i	0.991634	−	0.823103i
$726$		0			0
$727$	26.5141	+	26.5141i	0.983354	+	0.983354i	0.999864	−	0.0165102i	$-0.00525558\pi$
$727$	26.5141	+	26.5141i	0.983354	+	0.983354i	−0.0165102	+	0.999864i	$0.505256\pi$
$728$	33.4083	+	5.29135i	1.23819	+	0.196111i
$729$		0			0
$730$	9.63030	−	0.310576i	0.356433	−	0.0114949i
$731$	4.23339	+	3.07574i	0.156578	+	0.113760i
$732$		0			0
$733$	28.4208	−	14.4811i	1.04975	−	0.534873i	0.158015	−	0.987437i	$-0.449490\pi$
$733$	28.4208	−	14.4811i	1.04975	−	0.534873i	0.891732	+	0.452563i	$0.149490\pi$
$734$	13.7035	+	42.1752i	0.505807	+	1.55671i
$735$		0			0
$736$			0.116420i			0.00429131i
$737$	1.29283	+	13.7531i	0.0476220	+	0.506601i
$738$		0			0
$739$	31.6871	−	23.0220i	1.16563	−	0.846879i	0.175150	−	0.984542i	$-0.443959\pi$
$739$	31.6871	−	23.0220i	1.16563	−	0.846879i	0.990479	+	0.137662i	$0.0439589\pi$
$740$	−8.28765	+	66.0404i	−0.304660	+	2.42769i
$741$		0			0
$742$	4.05027	+	25.5724i	0.148690	+	0.938793i
$743$	−1.06140	−	6.70139i	−0.0389389	−	0.245850i	0.960540	−	0.278143i	$-0.0897190\pi$
$743$	−1.06140	−	6.70139i	−0.0389389	−	0.245850i	−0.999478	+	0.0322930i	$0.989719\pi$
$744$		0			0
$745$	−14.9109	+	11.5857i	−0.546291	+	0.424467i
$746$	−34.7666	+	25.2594i	−1.27290	+	0.924814i
$747$		0			0
$748$	−8.10905	−	9.20756i	−0.296496	−	0.336662i
$749$		−	10.7374i		−	0.392337i
$750$		0			0
$751$	−6.82703	−	21.0114i	−0.249122	−	0.766718i	−0.994931	−	0.100559i	$-0.967937\pi$
$751$	−6.82703	−	21.0114i	−0.249122	−	0.766718i	0.745809	−	0.666160i	$-0.232063\pi$
$752$	−3.30830	+	1.68567i	−0.120641	+	0.0614699i
$753$		0			0
$754$	−38.3627	−	27.8722i	−1.39709	−	1.01504i
$755$	−0.860027	−	26.6676i	−0.0312996	−	0.970535i
$756$		0			0
$757$	−33.0425	−	5.23341i	−1.20095	−	0.190212i	−0.476271	−	0.879299i	$-0.658012\pi$
$757$	−33.0425	−	5.23341i	−1.20095	−	0.190212i	−0.724678	+	0.689087i	$0.758012\pi$
$758$	−37.9511	−	37.9511i	−1.37845	−	1.37845i
$759$		0			0
$760$	18.3967	−	39.1787i	0.667320	−	1.42116i
$761$	15.3149	+	21.0791i	0.555163	+	0.764117i	0.990701	−	0.136054i	$-0.0434419\pi$
$761$	15.3149	+	21.0791i	0.555163	+	0.764117i	−0.435538	+	0.900170i	$0.643442\pi$
$762$		0			0
$763$	−3.77785	−	7.41445i	−0.136767	−	0.268421i
$764$	−14.9045	+	20.5143i	−0.539227	+	0.742182i
$765$		0			0
$766$	45.5528	+	14.8010i	1.64589	+	0.534782i
$767$	16.2218	+	8.26544i	0.585736	+	0.298448i
$768$		0			0
$769$	51.2907			1.84959			0.924794	−	0.380468i	$-0.124237\pi$
$769$	51.2907			1.84959			0.924794	+	0.380468i	$0.124237\pi$
$770$	−28.5355	+	36.8107i	−1.02835	+	1.32656i
$771$		0			0
$772$	0.616901	−	3.89496i	0.0222027	−	0.140183i
$773$	−14.7145	−	7.49740i	−0.529243	−	0.269663i	0.168885	−	0.985636i	$-0.445983\pi$
$773$	−14.7145	−	7.49740i	−0.529243	−	0.269663i	−0.698128	+	0.715973i	$0.745983\pi$
$774$		0			0
$775$	45.2183	−	2.91960i	1.62429	−	0.104875i
$776$	−39.5453	+	54.4295i	−1.41960	+	1.95391i
$777$		0			0
$778$	−18.9076	+	37.1082i	−0.677869	+	1.33039i
$779$	−8.40920	−	11.5743i	−0.301291	−	0.414691i
$780$		0			0
$781$	1.04214	+	4.06766i	0.0372908	+	0.145552i
$782$	−0.240530	−	0.240530i	−0.00860135	−	0.00860135i
$783$		0			0
$784$	1.11795	−	0.363243i	0.0399267	−	0.0129730i
$785$	−2.22102	−	2.08224i	−0.0792717	−	0.0743184i
$786$		0			0
$787$	4.37316	−	0.692641i	0.155886	−	0.0246900i	−0.0780034	−	0.996953i	$-0.524854\pi$
$787$	4.37316	−	0.692641i	0.155886	−	0.0246900i	0.233890	+	0.972263i	$0.424854\pi$
$788$	85.6084	−	43.6197i	3.04967	−	1.55389i
$789$		0			0
$790$	−23.1958	+	4.44462i	−0.825270	+	0.158132i
$791$			28.7945i			1.02381i
$792$		0			0
$793$	18.9183	−	18.9183i	0.671808	−	0.671808i
$794$	−14.6086	+	10.6137i	−0.518438	+	0.376667i
$795$		0			0
$796$	−3.94138	+	12.1303i	−0.139699	+	0.429948i
$797$	−3.00692	−	18.9850i	−0.106511	−	0.672482i	−0.981948	−	0.189150i	$-0.939427\pi$
$797$	−3.00692	−	18.9850i	−0.106511	−	0.672482i	0.875437	−	0.483331i	$-0.160573\pi$
$798$		0			0
$799$	−0.308525	+	0.949542i	−0.0109148	+	0.0335924i
$800$	−3.83487	+	0.863823i	−0.135583	+	0.0305407i
$801$		0			0
$802$	−21.1147	+	21.1147i	−0.745587	+	0.745587i
$803$	5.73284	+	1.28457i	0.202308	+	0.0453316i
$804$		0			0
$805$	−0.479921	+	0.707434i	−0.0169150	+	0.0249338i
$806$	−19.1346	−	58.8903i	−0.673988	−	2.07432i
$807$		0			0
$808$	−8.91548	+	1.41207i	−0.313645	+	0.0496765i
$809$	−24.9923	−	18.1580i	−0.878683	−	0.638401i	0.0542197	−	0.998529i	$-0.482733\pi$
$809$	−24.9923	−	18.1580i	−0.878683	−	0.638401i	−0.932903	+	0.360128i	$0.882733\pi$
$810$		0			0
$811$	23.8090	−	7.73601i	0.836047	−	0.271648i	0.140456	−	0.990087i	$-0.455143\pi$
$811$	23.8090	−	7.73601i	0.836047	−	0.271648i	0.695590	+	0.718439i	$0.255143\pi$
$812$	69.3267	+	10.9803i	2.43289	+	0.385332i
$813$		0			0
$814$	−22.5964	+	56.9854i	−0.792004	+	1.99734i
$815$	−46.4383	−	21.8056i	−1.62666	−	0.763816i
$816$		0			0
$817$	−10.4397	+	20.4891i	−0.365240	+	0.716825i
$818$	29.5519	+	57.9990i	1.03326	+	2.02789i
$819$		0			0
$820$	8.40160	−	29.0075i	0.293396	−	1.01299i
$821$	21.6750	+	7.04264i	0.756463	+	0.245790i	0.661760	−	0.749716i	$-0.269810\pi$
$821$	21.6750	+	7.04264i	0.756463	+	0.245790i	0.0947032	+	0.995506i	$0.469810\pi$
$822$		0			0
$823$	2.76029	−	17.4278i	0.0962177	−	0.607495i	−0.891713	−	0.452601i	$-0.850496\pi$
$823$	2.76029	−	17.4278i	0.0962177	−	0.607495i	0.987931	−	0.154894i	$-0.0495036\pi$
$824$	−8.01946			−0.279371
$825$		0			0
$826$	−40.7077			−1.41640
$827$	2.60613	−	16.4544i	0.0906239	−	0.572177i	−0.900035	−	0.435817i	$-0.856460\pi$
$827$	2.60613	−	16.4544i	0.0906239	−	0.572177i	0.990659	−	0.136360i	$-0.0435404\pi$
$828$		0			0
$829$	−39.7855	−	12.9271i	−1.38181	−	0.448976i	−0.478544	−	0.878064i	$-0.658835\pi$
$829$	−39.7855	−	12.9271i	−1.38181	−	0.448976i	−0.903263	+	0.429087i	$0.858835\pi$
$830$	12.5471	−	43.3205i	0.435517	−	1.50368i
$831$		0			0
$832$	11.3950	+	22.3640i	0.395051	+	0.775332i
$833$	0.143498	−	0.281630i	0.00497190	−	0.00975790i
$834$		0			0
$835$	−29.0660	−	13.6482i	−1.00587	−	0.472316i
$836$	34.3901	−	41.5265i	1.18941	−	1.43622i
$837$		0			0
$838$	−34.2139	−	5.41895i	−1.18190	−	0.187195i
$839$	−49.3818	+	16.0451i	−1.70485	+	0.553939i	−0.989463	−	0.144788i	$-0.953750\pi$
$839$	−49.3818	+	16.0451i	−1.70485	+	0.553939i	−0.715388	+	0.698728i	$0.753750\pi$
$840$		0			0
$841$	−15.5042	−	11.2645i	−0.534629	−	0.388431i
$842$	16.5931	−	2.62809i	0.571836	−	0.0905699i
$843$		0			0
$844$	30.0723	+	92.5530i	1.03513	+	3.18581i
$845$	−6.41559	+	9.45698i	−0.220703	+	0.325330i
$846$		0			0
$847$	−22.4576	+	17.3825i	−0.771654	+	0.597271i
$848$	10.2374	−	10.2374i	0.351554	−	0.351554i
$849$		0			0
$850$	6.13833	−	9.70773i	0.210543	−	0.332972i
$851$	−0.347690	+	1.07008i	−0.0119187	+	0.0366819i
$852$		0			0
$853$	−2.19089	−	13.8327i	−0.0750145	−	0.473623i	−0.996386	−	0.0849401i	$-0.972930\pi$
$853$	−2.19089	−	13.8327i	−0.0750145	−	0.473623i	0.921372	−	0.388683i	$-0.127070\pi$
$854$	−18.4857	+	56.8933i	−0.632569	+	1.94685i
$855$		0			0
$856$	−15.6947	+	11.4029i	−0.536434	+	0.389742i
$857$	10.2364	−	10.2364i	0.349669	−	0.349669i	−0.510317	−	0.859986i	$-0.670472\pi$
$857$	10.2364	−	10.2364i	0.349669	−	0.349669i	0.859986	+	0.510317i	$0.170472\pi$
$858$		0			0
$859$		−	56.0426i		−	1.91215i	−0.293125	−	0.956074i	$-0.594695\pi$
$859$		−	56.0426i		−	1.91215i	0.293125	−	0.956074i	$-0.405305\pi$
$860$	−47.6739	+	9.13494i	−1.62567	+	0.311499i
$861$		0			0
$862$	−15.4741	+	7.88446i	−0.527050	+	0.268546i
$863$	17.0244	−	2.69640i	0.579518	−	0.0917867i	0.140208	−	0.990122i	$-0.455223\pi$
$863$	17.0244	−	2.69640i	0.579518	−	0.0917867i	0.439310	+	0.898335i	$0.355223\pi$
$864$		0			0
$865$	−36.3801	−	34.1069i	−1.23696	−	1.15967i
$866$	38.8733	−	12.6307i	1.32097	−	0.429209i
$867$		0			0
$868$	64.8114	+	64.8114i	2.19984	+	2.19984i
$869$	−14.3717	−	0.911700i	−0.487528	−	0.0309273i
$870$		0			0
$871$	6.87628	+	9.46438i	0.232994	+	0.320688i
$872$	−6.82560	+	13.3960i	−0.231144	+	0.453645i
$873$		0			0
$874$	0.878650	−	1.20936i	0.0297208	−	0.0409071i
$875$	−26.8637	−	10.5595i	−0.908158	−	0.356975i
$876$		0			0
$877$	6.28165	+	3.20066i	0.212116	+	0.108079i	0.556821	−	0.830633i	$-0.312021\pi$
$877$	6.28165	+	3.20066i	0.212116	+	0.108079i	−0.344705	+	0.938711i	$0.612021\pi$
$878$	−0.294133	+	1.85708i	−0.00992651	+	0.0626735i
$879$		0			0
$880$	26.0317	+	0.810196i	0.877528	+	0.0273117i
$881$	46.6330			1.57111			0.785553	−	0.618794i	$-0.212378\pi$
$881$	46.6330			1.57111			0.785553	+	0.618794i	$0.212378\pi$
$882$		0			0
$883$	9.80743	+	4.99714i	0.330046	+	0.168167i	0.611159	−	0.791508i	$-0.290704\pi$
$883$	9.80743	+	4.99714i	0.330046	+	0.168167i	−0.281113	+	0.959675i	$0.590704\pi$
$884$	−9.88212	−	3.21090i	−0.332372	−	0.107994i
$885$		0			0
$886$	26.8665	−	36.9785i	0.902597	−	1.24232i
$887$	17.6954	+	34.7292i	0.594154	+	1.16609i	0.970835	+	0.239750i	$0.0770655\pi$
$887$	17.6954	+	34.7292i	0.594154	+	1.16609i	−0.376680	+	0.926343i	$0.622934\pi$
$888$		0			0
$889$	−3.60411	−	4.96064i	−0.120878	−	0.166374i
$890$	9.78168	−	20.8316i	0.327883	−	0.698277i
$891$		0			0
$892$	−54.2662	−	54.2662i	−1.81697	−	1.81697i
$893$	−4.33351	−	0.686361i	−0.145016	−	0.0229682i
$894$		0			0
$895$	−0.314840	−	9.76254i	−0.0105240	−	0.326326i
$896$	−42.1188	−	30.6011i	−1.40709	−	1.02231i
$897$		0			0
$898$	−1.54623	+	0.787843i	−0.0515983	+	0.0262906i
$899$	−19.4354	−	59.8159i	−0.648206	−	1.99497i
$900$		0			0
$901$		−	3.89303i		−	0.129696i
$902$	14.1713	−	23.9339i	0.471852	−	0.796912i
$903$		0			0
$904$	42.0884	−	30.5790i	1.39984	−	1.01704i
$905$	−16.6679	+	12.9510i	−0.554061	+	0.430504i
$906$		0			0
$907$	−4.39815	−	27.7688i	−0.146038	−	0.922049i	−0.946509	−	0.322677i	$-0.895417\pi$
$907$	−4.39815	−	27.7688i	−0.146038	−	0.922049i	0.800471	−	0.599372i	$-0.204583\pi$
$908$	0.626877	+	3.95795i	0.0208037	+	0.131349i
$909$		0			0
$910$	−4.91148	+	39.1373i	−0.162814	+	1.29739i
$911$	−23.8530	+	17.3302i	−0.790285	+	0.574175i	−0.908048	−	0.418866i	$-0.862428\pi$
$911$	−23.8530	+	17.3302i	−0.790285	+	0.574175i	0.117763	+	0.993042i	$0.462428\pi$
$912$		0			0
$913$	14.0108	−	23.6628i	0.463689	−	0.783126i
$914$		−	47.0585i		−	1.55656i
$915$		0			0
$916$	−0.123296	−	0.379465i	−0.00407380	−	0.0125379i
$917$	7.18775	−	3.66234i	0.237360	−	0.120941i
$918$		0			0
$919$	−32.9943	−	23.9718i	−1.08838	−	0.790755i	−0.109256	−	0.994014i	$-0.534847\pi$
$919$	−32.9943	−	23.9718i	−1.08838	−	0.790755i	−0.979125	+	0.203258i	$0.934847\pi$
$920$	1.54371	−	0.0497843i	0.0508945	−	0.00164134i
$921$		0			0
$922$	87.7630	+	13.9003i	2.89032	+	0.457782i
$923$	2.51454	+	2.51454i	0.0827672	+	0.0827672i
$924$		0			0
$925$	−37.8281	−	3.51301i	−1.24378	−	0.115507i
$926$	−34.6632	−	47.7098i	−1.13910	−	1.56784i
$927$		0			0
$928$	2.47706	+	4.86151i	0.0813136	+	0.159587i
$929$	30.1380	−	41.4814i	0.988795	−	1.36096i	0.0568413	−	0.998383i	$-0.481897\pi$
$929$	30.1380	−	41.4814i	0.988795	−	1.36096i	0.931954	−	0.362577i	$-0.118103\pi$
$930$		0			0
$931$	1.32104	+	0.429233i	0.0432954	+	0.0140675i
$932$	−74.6973	−	38.0602i	−2.44679	−	1.24670i
$933$		0			0
$934$	−36.0504			−1.17960
$935$	5.10365	−	4.79556i	0.166907	−	0.156831i
$936$		0			0
$937$	0.481891	−	3.04254i	0.0157427	−	0.0993955i	−0.978566	−	0.205934i	$-0.933977\pi$
$937$	0.481891	−	3.04254i	0.0157427	−	0.0993955i	0.994309	+	0.106539i	$0.0339768\pi$
$938$	−23.3063	−	11.8752i	−0.760978	−	0.387738i
$939$		0			0
$940$	−4.46850	−	8.11236i	−0.145746	−	0.264596i
$941$	16.7138	−	23.0045i	0.544854	−	0.749927i	−0.444449	−	0.895804i	$-0.646601\pi$
$941$	16.7138	−	23.0045i	0.544854	−	0.749927i	0.989303	+	0.145877i	$0.0466005\pi$
$942$		0			0
$943$	0.231770	−	0.454874i	0.00754747	−	0.0148127i
$944$	13.3798	+	18.4157i	0.435474	+	0.599379i
$945$		0			0
$946$	−44.6180	−	2.83043i	−1.45065	−	0.0920252i
$947$	40.6526	+	40.6526i	1.32103	+	1.32103i	0.912941	+	0.408091i	$0.133805\pi$
$947$	40.6526	+	40.6526i	1.32103	+	1.32103i	0.408091	+	0.912941i	$0.366195\pi$
$948$		0			0
$949$	4.73193	−	1.53750i	0.153605	−	0.0499092i
$950$	46.3555	+	19.9693i	1.50397	+	0.647890i
$951$		0			0
$952$	11.2318	−	1.77894i	0.364024	−	0.0576557i
$953$	17.0501	−	8.68746i	0.552307	−	0.281414i	−0.155482	−	0.987839i	$-0.549693\pi$
$953$	17.0501	−	8.68746i	0.552307	−	0.281414i	0.707788	+	0.706424i	$0.249693\pi$
$954$		0			0
$955$	−11.9775	−	8.12549i	−0.387582	−	0.262935i
$956$		−	33.9400i		−	1.09770i
$957$		0			0
$958$	47.4507	−	47.4507i	1.53306	−	1.53306i
$959$	34.5378	−	25.0932i	1.11528	−	0.810302i
$960$		0			0
$961$	15.7997	−	48.6264i	0.509667	−	1.56859i
$962$	8.12140	+	51.2765i	0.261844	+	1.65322i
$963$		0			0
$964$	−12.8917	+	39.6764i	−0.415212	+	1.27789i
$965$	2.23340	+	0.280277i	0.0718955	+	0.00902243i
$966$		0			0
$967$	12.6930	−	12.6930i	0.408178	−	0.408178i	−0.472925	−	0.881103i	$-0.656802\pi$
$967$	12.6930	−	12.6930i	0.408178	−	0.408178i	0.881103	+	0.472925i	$0.156802\pi$
$968$	49.2572	+	14.3661i	1.58319	+	0.461745i
$969$		0			0
$970$	−64.9257	−	44.0454i	−2.08464	−	1.41421i
$971$	1.07721	+	3.31533i	0.0345695	+	0.106394i	0.966852	−	0.255336i	$-0.0821862\pi$
$971$	1.07721	+	3.31533i	0.0345695	+	0.106394i	−0.932283	+	0.361730i	$0.882186\pi$
$972$		0			0
$973$	11.0169	−	1.74491i	0.353186	−	0.0559392i
$974$	76.5471	+	55.6147i	2.45273	+	1.78201i
$975$		0			0
$976$	31.8137	−	10.3369i	1.01833	−	0.330876i
$977$	−25.5183	−	4.04170i	−0.816402	−	0.129305i	−0.265752	−	0.964042i	$-0.585620\pi$
$977$	−25.5183	−	4.04170i	−0.816402	−	0.129305i	−0.550650	+	0.834736i	$0.685620\pi$
$978$		0			0
$979$	8.95020	−	10.8075i	0.286050	−	0.345409i
$980$	0.995480	+	2.75793i	0.0317994	+	0.0880989i
$981$		0			0
$982$	20.7636	−	40.7509i	0.662595	−	1.30042i
$983$	14.1764	+	27.8228i	0.452158	+	0.887409i	0.998749	+	0.0500096i	$0.0159252\pi$
$983$	14.1764	+	27.8228i	0.452158	+	0.887409i	−0.546591	+	0.837400i	$0.684075\pi$
$984$		0			0
$985$	26.4598	+	48.0365i	0.843078	+	1.53057i
$986$	−15.1619	−	4.92639i	−0.482852	−	0.156888i
$987$		0			0
$988$	7.14313	−	45.1000i	0.227253	−	1.43482i
$989$	−0.820573			−0.0260927
$990$		0			0
$991$	−19.5868			−0.622196			−0.311098	−	0.950378i	$-0.600697\pi$
$991$	−19.5868			−0.622196			−0.311098	+	0.950378i	$0.600697\pi$
$992$	−1.11457	+	7.03714i	−0.0353877	+	0.223429i
$993$		0			0
$994$	−7.56203	−	2.45705i	−0.239853	−	0.0779330i
$995$	−6.99278	−	2.02535i	−0.221686	−	0.0642080i
$996$		0			0
$997$	12.8543	+	25.2279i	0.407098	+	0.798976i	0.999980	−	0.00631392i	$-0.00200980\pi$
$997$	12.8543	+	25.2279i	0.407098	+	0.798976i	−0.592882	+	0.805290i	$0.702010\pi$
$998$	5.78661	−	11.3569i	0.183172	−	0.359495i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bj.a.217.1		32
3.2	odd	2		55.2.l.a.52.4	yes	32
5.3	odd	4	inner	495.2.bj.a.118.4		32
11.7	odd	10	inner	495.2.bj.a.172.4		32
12.11	even	2		880.2.cm.a.657.2		32
15.2	even	4		275.2.bm.b.118.4		32
15.8	even	4		55.2.l.a.8.1	yes	32
15.14	odd	2		275.2.bm.b.107.1		32
33.2	even	10		605.2.e.b.362.15		32
33.5	odd	10		605.2.m.d.112.4		32
33.8	even	10		605.2.m.d.457.4		32
33.14	odd	10		605.2.m.c.457.1		32
33.17	even	10		605.2.m.c.112.1		32
33.20	odd	10		605.2.e.b.362.2		32
33.26	odd	10		605.2.m.e.282.4		32
33.29	even	10		55.2.l.a.7.1	✓	32
33.32	even	2		605.2.m.e.602.1		32
55.18	even	20	inner	495.2.bj.a.73.1		32
60.23	odd	4		880.2.cm.a.833.3		32
132.95	odd	10		880.2.cm.a.337.3		32
165.8	odd	20		605.2.m.d.578.4		32
165.29	even	10		275.2.bm.b.7.4		32
165.38	even	20		605.2.m.d.233.4		32
165.53	even	20		605.2.e.b.483.15		32
165.62	odd	20		275.2.bm.b.18.1		32
165.68	odd	20		605.2.e.b.483.2		32
165.83	odd	20		605.2.m.c.233.1		32
165.98	odd	4		605.2.m.e.118.4		32
165.113	even	20		605.2.m.c.578.1		32
165.128	odd	20		55.2.l.a.18.4	yes	32
165.158	even	20		605.2.m.e.403.1		32
660.623	even	20		880.2.cm.a.513.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.1	✓	32	33.29	even	10
55.2.l.a.8.1	yes	32	15.8	even	4
55.2.l.a.18.4	yes	32	165.128	odd	20
55.2.l.a.52.4	yes	32	3.2	odd	2
275.2.bm.b.7.4		32	165.29	even	10
275.2.bm.b.18.1		32	165.62	odd	20
275.2.bm.b.107.1		32	15.14	odd	2
275.2.bm.b.118.4		32	15.2	even	4
495.2.bj.a.73.1		32	55.18	even	20	inner
495.2.bj.a.118.4		32	5.3	odd	4	inner
495.2.bj.a.172.4		32	11.7	odd	10	inner
495.2.bj.a.217.1		32	1.1	even	1	trivial
605.2.e.b.362.2		32	33.20	odd	10
605.2.e.b.362.15		32	33.2	even	10
605.2.e.b.483.2		32	165.68	odd	20
605.2.e.b.483.15		32	165.53	even	20
605.2.m.c.112.1		32	33.17	even	10
605.2.m.c.233.1		32	165.83	odd	20
605.2.m.c.457.1		32	33.14	odd	10
605.2.m.c.578.1		32	165.113	even	20
605.2.m.d.112.4		32	33.5	odd	10
605.2.m.d.233.4		32	165.38	even	20
605.2.m.d.457.4		32	33.8	even	10
605.2.m.d.578.4		32	165.8	odd	20
605.2.m.e.118.4		32	165.98	odd	4
605.2.m.e.282.4		32	33.26	odd	10
605.2.m.e.403.1		32	165.158	even	20
605.2.m.e.602.1		32	33.32	even	2
880.2.cm.a.337.3		32	132.95	odd	10
880.2.cm.a.513.2		32	660.623	even	20
880.2.cm.a.657.2		32	12.11	even	2
880.2.cm.a.833.3		32	60.23	odd	4

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.380541 + 2.40264i) q^{2} +(-3.72576 - 1.21057i) q^{4} +(0.622076 - 2.14779i) q^{5} +(1.17208 + 2.30033i) q^{7} +(2.11764 - 4.15610i) q^{8} +(4.92366 + 2.31195i) q^{10} +(2.55440 + 2.11543i) q^{11} +(2.77422 + 0.439393i) q^{13} +(-5.97289 + 1.94071i) q^{14} +(2.84111 + 2.06419i) q^{16} +(0.932684 - 0.147723i) q^{17} +(1.28236 + 3.94669i) q^{19} +(-4.91777 + 7.24911i) q^{20} +(-6.05467 + 5.33231i) q^{22} +(-0.104710 + 0.104710i) q^{23} +(-4.22604 - 2.67218i) q^{25} +(-2.11141 + 6.49824i) q^{26} +(-1.58216 - 9.98937i) q^{28} +(-2.14459 + 6.60038i) q^{29} +(-7.33171 + 5.32680i) q^{31} +(0.555921 - 0.555921i) q^{32} +2.29712i q^{34} +(5.66976 - 1.08640i) q^{35} +(6.77002 - 3.44950i) q^{37} +(-9.97047 + 1.57917i) q^{38} +(-7.60911 - 7.13366i) q^{40} +(-3.27880 + 1.06535i) q^{41} +(3.91833 + 3.91833i) q^{43} +(-6.95623 - 10.9739i) q^{44} +(-0.211733 - 0.291426i) q^{46} +(-0.479999 + 0.942051i) q^{47} +(0.196744 - 0.270795i) q^{49} +(8.02848 - 9.13679i) q^{50} +(-9.80416 - 4.99547i) q^{52} +(0.644920 - 4.07187i) q^{53} +(6.13253 - 4.17038i) q^{55} +12.0424 q^{56} +(-15.0422 - 7.66441i) q^{58} +(6.16460 + 2.00300i) q^{59} +(5.59880 - 7.70609i) q^{61} +(-10.0084 - 19.6426i) q^{62} +(5.25251 + 7.22946i) q^{64} +(2.66950 - 5.68511i) q^{65} +(2.94509 + 2.94509i) q^{67} +(-3.65379 - 0.578703i) q^{68} +(0.452653 + 14.0358i) q^{70} +(1.02426 + 0.744171i) q^{71} +(1.57831 - 0.804189i) q^{73} +(5.71163 + 17.5786i) q^{74} -16.2568i q^{76} +(-1.87222 + 8.35541i) q^{77} +(-3.51271 + 2.55214i) q^{79} +(6.20085 - 4.81805i) q^{80} +(-1.31193 - 8.28320i) q^{82} +(-1.29707 - 8.18939i) q^{83} +(0.262923 - 2.09511i) q^{85} +(-10.9054 + 7.92326i) q^{86} +(14.2012 - 6.13664i) q^{88} -4.23092i q^{89} +(2.24084 + 6.89661i) q^{91} +(0.516882 - 0.263364i) q^{92} +(-2.08075 - 1.51175i) q^{94} +(9.27440 - 0.299098i) q^{95} +(-14.2460 - 2.25634i) q^{97} +(0.575755 + 0.575755i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8 + 24 * q^11 - 10 * q^13 - 8 * q^16 - 16 * q^20 + 10 * q^22 + 24 * q^23 + 16 * q^25 - 20 * q^26 + 50 * q^28 - 28 * q^31 + 10 * q^35 - 8 * q^37 - 10 * q^38 - 50 * q^40 - 40 * q^41 + 60 * q^46 + 28 * q^47 + 50 * q^50 - 50 * q^52 + 24 * q^53 - 64 * q^55 + 80 * q^56 - 50 * q^58 - 60 * q^61 - 100 * q^62 - 8 * q^67 + 30 * q^68 + 30 * q^70 - 24 * q^71 + 50 * q^73 - 70 * q^77 - 98 * q^80 - 10 * q^82 - 90 * q^83 + 30 * q^85 - 100 * q^86 + 170 * q^88 + 20 * q^91 + 68 * q^92 + 40 * q^95 - 8 * q^97

Introduction

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