LMFDB - Embedded newform 900.2.bj.f.127.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

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

Embedding invariants

Embedding label			127.14
Character	$\chi$	$=$	900.127
Dual form			900.2.bj.f.163.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.262182 + 1.38970i) q^{2} +(-1.86252 - 0.728708i) q^{4} +(-0.583536 + 2.15858i) q^{5} +(-0.889008 + 0.889008i) q^{7} +(1.50100 - 2.39729i) q^{8} +O(q^{10})$	\(q+(-0.262182 + 1.38970i) q^{2} +(-1.86252 - 0.728708i) q^{4} +(-0.583536 + 2.15858i) q^{5} +(-0.889008 + 0.889008i) q^{7} +(1.50100 - 2.39729i) q^{8} +(-2.84679 - 1.37688i) q^{10} +(3.50723 + 4.82729i) q^{11} +(3.23824 - 0.512887i) q^{13} +(-1.00237 - 1.46853i) q^{14} +(2.93797 + 2.71447i) q^{16} +(-0.313606 + 0.615487i) q^{17} +(1.16061 + 3.57200i) q^{19} +(2.65983 - 3.59518i) q^{20} +(-7.62801 + 3.60836i) q^{22} +(-1.68898 - 0.267508i) q^{23} +(-4.31897 - 2.51922i) q^{25} +(-0.136251 + 4.63464i) q^{26} +(2.30362 - 1.00797i) q^{28} +(-8.00770 - 2.60186i) q^{29} +(-4.87146 + 1.58283i) q^{31} +(-4.54257 + 3.37120i) q^{32} +(-0.773119 - 0.597187i) q^{34} +(-1.40023 - 2.43777i) q^{35} +(-1.22564 - 7.73839i) q^{37} +(-5.26830 + 0.676388i) q^{38} +(4.29886 + 4.63895i) q^{40} +(-8.56195 - 6.22062i) q^{41} +(5.55076 + 5.55076i) q^{43} +(-3.01461 - 11.5467i) q^{44} +(0.814576 - 2.27704i) q^{46} +(4.53317 + 8.89684i) q^{47} +5.41933i q^{49} +(4.63332 - 5.34157i) q^{50} +(-6.40503 - 1.40447i) q^{52} +(2.43953 + 4.78785i) q^{53} +(-12.4667 + 4.75375i) q^{55} +(0.796803 + 3.46561i) q^{56} +(5.71528 - 10.4461i) q^{58} +(-7.86506 - 5.71430i) q^{59} +(0.117440 - 0.0853253i) q^{61} +(-0.922450 - 7.18485i) q^{62} +(-3.49397 - 7.19668i) q^{64} +(-0.782521 + 7.28930i) q^{65} +(6.40031 + 3.26112i) q^{67} +(1.03261 - 0.917829i) q^{68} +(3.75487 - 1.30676i) q^{70} +(-7.03596 - 2.28612i) q^{71} +(-0.769583 + 4.85896i) q^{73} +(11.0754 + 0.325598i) q^{74} +(0.441280 - 7.49868i) q^{76} +(-7.40945 - 1.17354i) q^{77} +(0.528568 - 1.62677i) q^{79} +(-7.57382 + 4.75786i) q^{80} +(10.8896 - 10.2676i) q^{82} +(-1.79597 + 3.52479i) q^{83} +(-1.14558 - 1.03610i) q^{85} +(-9.16918 + 6.25856i) q^{86} +(16.8368 - 1.16206i) q^{88} +(0.274839 + 0.378283i) q^{89} +(-2.42286 + 3.33478i) q^{91} +(2.95083 + 1.72901i) q^{92} +(-13.5524 + 3.96714i) q^{94} +(-8.38773 + 0.420890i) q^{95} +(1.79474 - 0.914467i) q^{97} +(-7.53123 - 1.42085i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8}+O(q^{10}) $ 240 * q - 12 * q^8	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.262182	+	1.38970i	−0.185391	+	0.982665i
$2$	−0.262182	+	1.38970i	−0.185391	+	0.982665i
$3$		0			0
$3$		0			0
$4$	−1.86252	−	0.728708i	−0.931260	−	0.364354i
$5$	−0.583536	+	2.15858i	−0.260965	+	0.965348i
$5$	−0.583536	+	2.15858i	−0.260965	+	0.965348i
$6$		0			0
$7$	−0.889008	+	0.889008i	−0.336013	+	0.336013i	−0.854865	−	0.518851i	$-0.826360\pi$
$7$	−0.889008	+	0.889008i	−0.336013	+	0.336013i	0.518851	+	0.854865i	$0.326360\pi$
$8$	1.50100	−	2.39729i	0.530685	−	0.847569i
$9$		0			0
$10$	−2.84679	−	1.37688i	−0.900233	−	0.435408i
$11$	3.50723	+	4.82729i	1.05747	+	1.45548i	0.882149	+	0.470971i	$0.156096\pi$
$11$	3.50723	+	4.82729i	1.05747	+	1.45548i	0.175321	+	0.984511i	$0.443904\pi$
$12$		0			0
$13$	3.23824	−	0.512887i	0.898126	−	0.142249i	0.309732	−	0.950824i	$-0.399761\pi$
$13$	3.23824	−	0.512887i	0.898126	−	0.142249i	0.588394	+	0.808575i	$0.299761\pi$
$14$	−1.00237	−	1.46853i	−0.267895	−	0.392482i
$15$		0			0
$16$	2.93797	+	2.71447i	0.734492	+	0.678617i
$17$	−0.313606	+	0.615487i	−0.0760607	+	0.149277i	−0.925905	−	0.377756i	$-0.876696\pi$
$17$	−0.313606	+	0.615487i	−0.0760607	+	0.149277i	0.849844	+	0.527034i	$0.176696\pi$
$18$		0			0
$19$	1.16061	+	3.57200i	0.266263	+	0.819474i	0.991400	+	0.130869i	$0.0417766\pi$
$19$	1.16061	+	3.57200i	0.266263	+	0.819474i	−0.725136	+	0.688605i	$0.758223\pi$
$20$	2.65983	−	3.59518i	0.594755	−	0.803907i
$21$		0			0
$22$	−7.62801	+	3.60836i	−1.62630	+	0.769305i
$23$	−1.68898	−	0.267508i	−0.352177	−	0.0557793i	−0.0221601	−	0.999754i	$-0.507054\pi$
$23$	−1.68898	−	0.267508i	−0.352177	−	0.0557793i	−0.330017	+	0.943975i	$0.607054\pi$
$24$		0			0
$25$	−4.31897	−	2.51922i	−0.863794	−	0.503845i
$26$	−0.136251	+	4.63464i	−0.0267210	+	0.908929i
$27$		0			0
$28$	2.30362	−	1.00797i	0.435344	−	0.190488i
$29$	−8.00770	−	2.60186i	−1.48699	−	0.483153i	−0.550799	−	0.834638i	$-0.685677\pi$
$29$	−8.00770	−	2.60186i	−1.48699	−	0.483153i	−0.936194	+	0.351484i	$0.885677\pi$
$30$		0			0
$31$	−4.87146	+	1.58283i	−0.874940	+	0.284285i	−0.711855	−	0.702327i	$-0.752144\pi$
$31$	−4.87146	+	1.58283i	−0.874940	+	0.284285i	−0.163085	+	0.986612i	$0.552144\pi$
$32$	−4.54257	+	3.37120i	−0.803021	+	0.595950i
$33$		0			0
$34$	−0.773119	−	0.597187i	−0.132589	−	0.102417i
$35$	−1.40023	−	2.43777i	−0.236682	−	0.412058i
$36$		0			0
$37$	−1.22564	−	7.73839i	−0.201494	−	1.27218i	−0.856337	−	0.516418i	$-0.827265\pi$
$37$	−1.22564	−	7.73839i	−0.201494	−	1.27218i	0.654843	−	0.755765i	$-0.272735\pi$
$38$	−5.26830	+	0.676388i	−0.854631	+	0.109725i
$39$		0			0
$40$	4.29886	+	4.63895i	0.679709	+	0.733482i
$41$	−8.56195	−	6.22062i	−1.33715	−	0.971497i	−0.999544	−	0.0302103i	$-0.990382\pi$
$41$	−8.56195	−	6.22062i	−1.33715	−	0.971497i	−0.337608	−	0.941287i	$-0.609618\pi$
$42$		0			0
$43$	5.55076	+	5.55076i	0.846482	+	0.846482i	0.989692	−	0.143210i	$-0.0457424\pi$
$43$	5.55076	+	5.55076i	0.846482	+	0.846482i	−0.143210	+	0.989692i	$0.545742\pi$
$44$	−3.01461	−	11.5467i	−0.454469	−	1.74073i
$45$		0			0
$46$	0.814576	−	2.27704i	0.120103	−	0.335731i
$47$	4.53317	+	8.89684i	0.661230	+	1.29774i	0.941239	+	0.337740i	$0.109663\pi$
$47$	4.53317	+	8.89684i	0.661230	+	1.29774i	−0.280009	+	0.959997i	$0.590337\pi$
$48$		0			0
$49$			5.41933i			0.774190i
$50$	4.63332	−	5.34157i	0.655250	−	0.755412i
$51$		0			0
$52$	−6.40503	−	1.40447i	−0.888218	−	0.194765i
$53$	2.43953	+	4.78785i	0.335096	+	0.657662i	0.995656	−	0.0931109i	$-0.0296811\pi$
$53$	2.43953	+	4.78785i	0.335096	+	0.657662i	−0.660560	+	0.750773i	$0.729681\pi$
$54$		0			0
$55$	−12.4667	+	4.75375i	−1.68101	+	0.640996i
$56$	0.796803	+	3.46561i	0.106477	+	0.463112i
$57$		0			0
$58$	5.71528	−	10.4461i	0.750453	−	1.37164i
$59$	−7.86506	−	5.71430i	−1.02394	−	0.743938i	−0.0568557	−	0.998382i	$-0.518108\pi$
$59$	−7.86506	−	5.71430i	−1.02394	−	0.743938i	−0.967087	+	0.254444i	$0.918108\pi$
$60$		0			0
$61$	0.117440	−	0.0853253i	0.0150367	−	0.0109248i	−0.580242	−	0.814444i	$-0.697042\pi$
$61$	0.117440	−	0.0853253i	0.0150367	−	0.0109248i	0.595278	+	0.803520i	$0.297042\pi$
$62$	−0.922450	−	7.18485i	−0.117151	−	0.912476i
$63$		0			0
$64$	−3.49397	−	7.19668i	−0.436747	−	0.899585i
$65$	−0.782521	+	7.28930i	−0.0970598	+	0.904126i
$66$		0			0
$67$	6.40031	+	3.26112i	0.781923	+	0.398409i	0.798913	−	0.601446i	$-0.205409\pi$
$67$	6.40031	+	3.26112i	0.781923	+	0.398409i	−0.0169907	+	0.999856i	$0.505409\pi$
$68$	1.03261	−	0.917829i	0.125222	−	0.111303i
$69$		0			0
$70$	3.75487	−	1.30676i	0.448793	−	0.156187i
$71$	−7.03596	−	2.28612i	−0.835015	−	0.271313i	−0.139859	−	0.990171i	$-0.544665\pi$
$71$	−7.03596	−	2.28612i	−0.835015	−	0.271313i	−0.695156	+	0.718859i	$0.744665\pi$
$72$		0			0
$73$	−0.769583	+	4.85896i	−0.0900729	+	0.568698i	0.900836	+	0.434160i	$0.142955\pi$
$73$	−0.769583	+	4.85896i	−0.0900729	+	0.568698i	−0.990909	+	0.134538i	$0.957045\pi$
$74$	11.0754	+	0.325598i	1.28748	+	0.0378500i
$75$		0			0
$76$	0.441280	−	7.49868i	0.0506183	−	0.860158i
$77$	−7.40945	−	1.17354i	−0.844386	−	0.133738i
$78$		0			0
$79$	0.528568	−	1.62677i	0.0594686	−	0.183026i	−0.916909	−	0.399096i	$-0.869324\pi$
$79$	0.528568	−	1.62677i	0.0594686	−	0.183026i	0.976378	+	0.216070i	$0.0693241\pi$
$80$	−7.57382	+	4.75786i	−0.846779	+	0.531945i
$81$		0			0
$82$	10.8896	−	10.2676i	1.20255	−	1.13386i
$83$	−1.79597	+	3.52479i	−0.197133	+	0.386896i	−0.968320	−	0.249713i	$-0.919664\pi$
$83$	−1.79597	+	3.52479i	−0.197133	+	0.386896i	0.771187	+	0.636609i	$0.219664\pi$
$84$		0			0
$85$	−1.14558	−	1.03610i	−0.124256	−	0.112381i
$86$	−9.16918	+	6.25856i	−0.988738	+	0.674878i
$87$		0			0
$88$	16.8368	−	1.16206i	1.79481	−	0.123876i
$89$	0.274839	+	0.378283i	0.0291329	+	0.0400980i	0.823335	−	0.567556i	$-0.192111\pi$
$89$	0.274839	+	0.378283i	0.0291329	+	0.0400980i	−0.794202	+	0.607654i	$0.792111\pi$
$90$		0			0
$91$	−2.42286	+	3.33478i	−0.253985	+	0.349580i
$92$	2.95083	+	1.72901i	0.307645	+	0.180262i
$93$		0			0
$94$	−13.5524	+	3.96714i	−1.39783	+	0.409179i
$95$	−8.38773	+	0.420890i	−0.860563	+	0.0431824i
$96$		0			0
$97$	1.79474	−	0.914467i	0.182228	−	0.0928500i	−0.360496	−	0.932761i	$-0.617393\pi$
$97$	1.79474	−	0.914467i	0.182228	−	0.0928500i	0.542725	+	0.839911i	$0.317393\pi$
$98$	−7.53123	−	1.42085i	−0.760769	−	0.143528i
$99$		0			0
$100$	6.20839	+	7.83938i	0.620839	+	0.783938i
$101$	17.6890			1.76012			0.880059	−	0.474863i	$-0.157503\pi$
$101$	17.6890			1.76012			0.880059	+	0.474863i	$0.157503\pi$
$102$		0			0
$103$	1.62899	−	0.830010i	0.160509	−	0.0817834i	−0.371891	−	0.928277i	$-0.621290\pi$
$103$	1.62899	−	0.830010i	0.160509	−	0.0817834i	0.532400	+	0.846493i	$0.321290\pi$
$104$	3.63107	−	8.53284i	0.356056	−	0.836713i
$105$		0			0
$106$	−7.29327	+	2.13492i	−0.708385	+	0.207362i
$107$	1.33025	−	1.33025i	0.128600	−	0.128600i	−0.639877	−	0.768477i	$-0.721015\pi$
$107$	1.33025	−	1.33025i	0.128600	−	0.128600i	0.768477	+	0.639877i	$0.221015\pi$
$108$		0			0
$109$	−0.298615	+	0.411008i	−0.0286021	+	0.0393674i	−0.823079	−	0.567928i	$-0.807745\pi$
$109$	−0.298615	+	0.411008i	−0.0286021	+	0.0393674i	0.794476	+	0.607295i	$0.207745\pi$
$110$	−3.33773	−	18.5713i	−0.318241	−	1.77070i
$111$		0			0
$112$	−5.02506	+	0.198693i	−0.474824	+	0.0187747i
$113$	14.6234	−	2.31612i	1.37566	−	0.217883i	0.575563	−	0.817757i	$-0.304783\pi$
$113$	14.6234	−	2.31612i	1.37566	−	0.217883i	0.800094	+	0.599875i	$0.204783\pi$
$114$		0			0
$115$	1.56302	−	3.48970i	0.145752	−	0.325417i
$116$	13.0185	+	10.6813i	1.20874	+	0.991734i
$117$		0			0
$118$	10.0032	−	9.43187i	0.920872	−	0.868274i
$119$	−0.268374	−	0.825971i	−0.0246018	−	0.0757166i
$120$		0			0
$121$	−7.60287	+	23.3992i	−0.691170	+	2.12720i
$122$	0.0877856	+	0.185577i	0.00794774	+	0.0168014i
$123$		0			0
$124$	10.2266	+	0.601812i	0.918377	+	0.0540444i
$125$	7.95823	−	7.85280i	0.711806	−	0.702376i
$126$		0			0
$127$	0.348876	−	2.20271i	0.0309577	−	0.195459i	−0.967363	−	0.253396i	$-0.918452\pi$
$127$	0.348876	−	2.20271i	0.0309577	−	0.195459i	0.998320	+	0.0579371i	$0.0184523\pi$
$128$	10.9173	−	2.96873i	0.964959	−	0.262401i
$129$		0			0
$130$	−9.92476	−	2.99859i	−0.870459	−	0.262994i
$131$	2.72290	−	0.884725i	0.237901	−	0.0772988i	−0.187640	−	0.982238i	$-0.560084\pi$
$131$	2.72290	−	0.884725i	0.237901	−	0.0772988i	0.425541	+	0.904939i	$0.360084\pi$
$132$		0			0
$133$	−4.20734	−	2.14374i	−0.364822	−	0.185886i
$134$	−6.21002	+	8.03949i	−0.536464	+	0.694506i
$135$		0			0
$136$	1.00477	+	1.67565i	0.0861587	+	0.143686i
$137$	0.0950840	+	0.600336i	0.00812357	+	0.0512902i	0.991417	−	0.130737i	$-0.0417342\pi$
$137$	0.0950840	+	0.600336i	0.00812357	+	0.0512902i	−0.983294	+	0.182027i	$0.941734\pi$
$138$		0			0
$139$	−16.0216	+	11.6404i	−1.35894	+	0.987325i	−0.360424	+	0.932789i	$0.617368\pi$
$139$	−16.0216	+	11.6404i	−1.35894	+	0.987325i	−0.998512	+	0.0545363i	$0.982632\pi$
$140$	0.831537	+	5.56075i	0.0702777	+	0.469969i
$141$		0			0
$142$	5.02172	−	9.17848i	0.421414	−	0.770241i
$143$	13.8331	+	13.8331i	1.15678	+	1.15678i
$144$		0			0
$145$	10.2891	−	15.7670i	0.854465	−	1.30938i
$146$	−6.55071	−	2.34342i	−0.542141	−	0.193943i
$147$		0			0
$148$	−3.35625	+	15.3060i	−0.275882	+	1.25815i
$149$		−	9.98736i		−	0.818197i	−0.912490	−	0.409098i	$-0.865843\pi$
$149$		−	9.98736i		−	0.818197i	0.912490	−	0.409098i	$-0.134157\pi$
$150$		0			0
$151$		−	17.9578i		−	1.46139i	−0.682707	−	0.730693i	$-0.739197\pi$
$151$		−	17.9578i		−	1.46139i	0.682707	−	0.730693i	$-0.260803\pi$
$152$	10.3052	+	2.57927i	0.835863	+	0.209206i
$153$		0			0
$154$	3.57350	−	9.98922i	0.287961	−	0.804954i
$155$	−0.574005	−	11.4391i	−0.0461052	−	0.918810i
$156$		0			0
$157$	−4.92861	−	4.92861i	−0.393346	−	0.393346i	0.482532	−	0.875878i	$-0.339717\pi$
$157$	−4.92861	−	4.92861i	−0.393346	−	0.393346i	−0.875878	+	0.482532i	$0.839717\pi$
$158$	2.12213	+	1.16106i	0.168828	+	0.0923690i
$159$		0			0
$160$	−4.62627	−	11.7727i	−0.365739	−	0.930718i
$161$	1.73933	−	1.26370i	0.137079	−	0.0995935i
$162$		0			0
$163$	1.20062	+	7.58039i	0.0940395	+	0.593742i	0.989037	+	0.147670i	$0.0471774\pi$
$163$	1.20062	+	7.58039i	0.0940395	+	0.593742i	−0.894997	+	0.446072i	$0.852823\pi$
$164$	11.4138	+	17.8252i	0.891267	+	1.39191i
$165$		0			0
$166$	−4.42752	−	3.41999i	−0.343642	−	0.265443i
$167$	14.7520	+	7.51654i	1.14155	+	0.581648i	0.919384	−	0.393362i	$-0.128688\pi$
$167$	14.7520	+	7.51654i	1.14155	+	0.581648i	0.222164	+	0.975009i	$0.428688\pi$
$168$		0			0
$169$	−2.14059	+	0.695521i	−0.164661	+	0.0535016i
$170$	1.74022	−	1.32036i	0.133469	−	0.101267i
$171$		0			0
$172$	−6.29352	−	14.3833i	−0.479876	−	1.09671i
$173$	2.89459	−	18.2757i	0.220072	−	1.38948i	−0.592008	−	0.805932i	$-0.701664\pi$
$173$	2.89459	−	18.2757i	0.220072	−	1.38948i	0.812079	−	0.583547i	$-0.198336\pi$
$174$		0			0
$175$	6.07921	−	1.59999i	0.459545	−	0.120948i
$176$	−2.79939	+	23.7027i	−0.211012	+	1.78666i
$177$		0			0
$178$	−0.597758	+	0.282764i	−0.0448038	+	0.0211941i
$179$	−4.10815	+	12.6436i	−0.307058	+	0.945026i	0.671844	+	0.740693i	$0.265503\pi$
$179$	−4.10815	+	12.6436i	−0.307058	+	0.945026i	−0.978901	+	0.204333i	$0.934497\pi$
$180$		0			0
$181$	4.57691	+	14.0863i	0.340199	+	1.04702i	0.964104	+	0.265524i	$0.0855450\pi$
$181$	4.57691	+	14.0863i	0.340199	+	1.04702i	−0.623905	+	0.781500i	$0.714455\pi$
$182$	−3.99911	−	4.24136i	−0.296434	−	0.314391i
$183$		0			0
$184$	−3.17646	+	3.64744i	−0.234172	+	0.268893i
$185$	17.4192	+	1.86998i	1.28068	+	0.137484i
$186$		0			0
$187$	−4.07102	+	0.644786i	−0.297703	+	0.0471515i
$188$	−1.95992	−	19.8739i	−0.142942	−	1.44945i
$189$		0			0
$190$	1.61420	−	11.7668i	0.117107	−	0.853651i
$191$	9.05720	−	12.4662i	0.655356	−	0.902021i	−0.343960	−	0.938984i	$-0.611769\pi$
$191$	9.05720	−	12.4662i	0.655356	−	0.902021i	0.999317	+	0.0369636i	$0.0117686\pi$
$192$		0			0
$193$	−9.28313	+	9.28313i	−0.668215	+	0.668215i	−0.957303	−	0.289088i	$-0.906648\pi$
$193$	−9.28313	+	9.28313i	−0.668215	+	0.668215i	0.289088	+	0.957303i	$0.406648\pi$
$194$	0.800283	+	2.73391i	0.0574570	+	0.196283i
$195$		0			0
$196$	3.94911	−	10.0936i	0.282079	−	0.720973i
$197$	−18.4968	+	9.42459i	−1.31784	+	0.671474i	−0.964516	−	0.264026i	$-0.914950\pi$
$197$	−18.4968	+	9.42459i	−1.31784	+	0.671474i	−0.353327	+	0.935500i	$0.614950\pi$
$198$		0			0
$199$	5.43755			0.385457			0.192729	−	0.981252i	$-0.438266\pi$
$199$	5.43755			0.385457			0.192729	+	0.981252i	$0.438266\pi$
$200$	−12.5221	+	6.57245i	−0.885446	+	0.464742i
$201$		0			0
$202$	−4.63774	+	24.5823i	−0.326310	+	1.72961i
$203$	9.43199	−	4.80584i	0.661996	−	0.337304i
$204$		0			0
$205$	18.4239	−	14.8517i	1.28678	−	1.03729i
$206$	0.726372	+	2.48141i	0.0506088	+	0.172888i
$207$		0			0
$208$	10.9061	+	7.28325i	0.756199	+	0.505003i
$209$	−13.1726	+	18.1305i	−0.911165	+	1.25411i
$210$		0			0
$211$	6.08035	+	8.36889i	0.418589	+	0.576138i	0.965287	−	0.261192i	$-0.0841155\pi$
$211$	6.08035	+	8.36889i	0.418589	+	0.576138i	−0.546698	+	0.837330i	$0.684115\pi$
$212$	−1.05473	−	10.6952i	−0.0724394	−	0.734548i
$213$		0			0
$214$	1.49988	+	2.19741i	0.102529	+	0.150212i
$215$	−15.2208	+	8.74271i	−1.03805	+	0.596248i
$216$		0			0
$217$	2.92361	−	5.73791i	0.198468	−	0.389515i
$218$	−0.492886	−	0.522743i	−0.0333824	−	0.0354047i
$219$		0			0
$220$	26.6836	+	0.230624i	1.79901	+	0.0155486i
$221$	−0.699857	+	2.15394i	−0.0470775	+	0.144890i
$222$		0			0
$223$	−2.70636	−	0.428646i	−0.181232	−	0.0287043i	0.0651589	−	0.997875i	$-0.479245\pi$
$223$	−2.70636	−	0.428646i	−0.181232	−	0.0287043i	−0.246390	+	0.969171i	$0.579245\pi$
$224$	1.04136	−	7.03541i	0.0695787	−	0.470073i
$225$		0			0
$226$	−0.615291	+	20.9294i	−0.0409285	+	1.39220i
$227$	−0.660098	+	4.16770i	−0.0438123	+	0.276620i	−0.999862	−	0.0165832i	$-0.994721\pi$
$227$	−0.660098	+	4.16770i	−0.0438123	+	0.276620i	0.956050	+	0.293203i	$0.0947212\pi$
$228$		0			0
$229$	−3.60946	−	1.17279i	−0.238520	−	0.0774998i	0.187318	−	0.982299i	$-0.440021\pi$
$229$	−3.60946	−	1.17279i	−0.238520	−	0.0774998i	−0.425838	+	0.904800i	$0.640021\pi$
$230$	4.43984	+	3.08706i	0.292754	+	0.203555i
$231$		0			0
$232$	−18.2570	+	15.2914i	−1.19863	+	1.00393i
$233$	16.3284	+	8.31976i	1.06971	+	0.545045i	0.897952	−	0.440093i	$-0.145055\pi$
$233$	16.3284	+	8.31976i	1.06971	+	0.545045i	0.171760	+	0.985139i	$0.445055\pi$
$234$		0			0
$235$	−21.8498	+	4.59359i	−1.42533	+	0.299653i
$236$	10.4848	+	16.3743i	0.682501	+	1.06588i
$237$		0			0
$238$	1.21821	−	0.156404i	0.0789650	−	0.0101382i
$239$	−9.01008	+	6.54621i	−0.582814	+	0.423439i	−0.839737	−	0.542993i	$-0.817291\pi$
$239$	−9.01008	+	6.54621i	−0.582814	+	0.423439i	0.256924	+	0.966432i	$0.417291\pi$
$240$		0			0
$241$	10.5335	+	7.65304i	0.678523	+	0.492976i	0.872867	−	0.487958i	$-0.162258\pi$
$241$	10.5335	+	7.65304i	0.678523	+	0.492976i	−0.194344	+	0.980933i	$0.562258\pi$
$242$	−30.5245	−	16.7005i	−1.96219	−	1.07355i
$243$		0			0
$244$	−0.280912	+	0.0733405i	−0.0179835	+	0.00469514i
$245$	−11.6981	−	3.16238i	−0.747363	−	0.202037i
$246$		0			0
$247$	5.59038	+	10.9717i	0.355707	+	0.698115i
$248$	−3.51757	+	14.0541i	−0.223366	+	0.892438i
$249$		0			0
$250$	8.82652	+	13.1184i	0.558238	+	0.829681i
$251$		−	4.07587i		−	0.257267i	−0.991692	−	0.128633i	$-0.958941\pi$
$251$		−	4.07587i		−	0.257267i	0.991692	−	0.128633i	$-0.0410590\pi$
$252$		0			0
$253$	−4.63230	−	9.09141i	−0.291230	−	0.571572i
$254$	2.96964	+	1.06234i	0.186332	+	0.0666574i
$255$		0			0
$256$	1.26332	+	15.9500i	0.0789575	+	0.996878i
$257$	14.0123	+	14.0123i	0.874061	+	0.874061i	0.992912	−	0.118851i	$-0.0379212\pi$
$257$	14.0123	+	14.0123i	0.874061	+	0.874061i	−0.118851	+	0.992912i	$0.537921\pi$
$258$		0			0
$259$	7.96909	+	5.78988i	0.495175	+	0.359766i
$260$	6.76923	−	13.0062i	0.419810	−	0.806613i
$261$		0			0
$262$	0.515603	+	4.01597i	0.0318541	+	0.248108i
$263$	1.13644	+	7.17523i	0.0700762	+	0.442444i	0.997633	+	0.0687618i	$0.0219048\pi$
$263$	1.13644	+	7.17523i	0.0700762	+	0.442444i	−0.927557	+	0.373682i	$0.878095\pi$
$264$		0			0
$265$	−11.7585	+	2.47205i	−0.722322	+	0.151857i
$266$	4.08225	−	5.28487i	0.250299	−	0.324036i
$267$		0			0
$268$	−9.54431	−	10.7379i	−0.583012	−	0.655920i
$269$	1.95436	−	0.635011i	0.119160	−	0.0387173i	−0.248830	−	0.968547i	$-0.580046\pi$
$269$	1.95436	−	0.635011i	0.119160	−	0.0387173i	0.367990	+	0.929830i	$0.380046\pi$
$270$		0			0
$271$	22.9587	+	7.45974i	1.39464	+	0.453147i	0.907455	−	0.420150i	$-0.138023\pi$
$271$	22.9587	+	7.45974i	1.39464	+	0.453147i	0.487188	+	0.873297i	$0.338023\pi$
$272$	−2.59208	+	0.957007i	−0.157168	+	0.0580270i
$273$		0			0
$274$	−0.859216	−	0.0252596i	−0.0519071	−	0.00152599i
$275$	−2.98660	−	29.6844i	−0.180099	−	1.79004i
$276$		0			0
$277$	13.6780	+	2.16637i	0.821829	+	0.130165i	0.553168	−	0.833070i	$-0.313419\pi$
$277$	13.6780	+	2.16637i	0.821829	+	0.130165i	0.268661	+	0.963235i	$0.413419\pi$
$278$	−11.9760	−	25.3171i	−0.718275	−	1.51842i
$279$		0			0
$280$	−7.94578	−	0.302345i	−0.474851	−	0.0180685i
$281$	8.63244	+	26.5679i	0.514968	+	1.58491i	0.783339	+	0.621594i	$0.213515\pi$
$281$	8.63244	+	26.5679i	0.514968	+	1.58491i	−0.268371	+	0.963316i	$0.586485\pi$
$282$		0			0
$283$	0.0314980	−	0.0618183i	0.00187236	−	0.00367472i	−0.890068	−	0.455827i	$-0.849344\pi$
$283$	0.0314980	−	0.0618183i	0.00187236	−	0.00367472i	0.891941	+	0.452152i	$0.149344\pi$
$284$	11.4387	+	9.38511i	0.678762	+	0.556904i
$285$		0			0
$286$	−22.8506	+	15.5970i	−1.35119	+	0.922273i
$287$	13.1418	−	2.08146i	0.775737	−	0.122865i
$288$		0			0
$289$	9.71187	+	13.3672i	0.571287	+	0.786309i
$290$	19.2138	+	18.4326i	1.12827	+	1.08240i
$291$		0			0
$292$	4.97413	−	8.48911i	0.291089	−	0.496787i
$293$	−13.8584	+	13.8584i	−0.809614	+	0.809614i	−0.984575	−	0.174961i	$-0.944020\pi$
$293$	−13.8584	+	13.8584i	−0.809614	+	0.809614i	0.174961	+	0.984575i	$0.444020\pi$
$294$		0			0
$295$	16.9243	−	13.6429i	0.985373	−	0.794320i
$296$	−20.3908	−	8.67714i	−1.18519	−	0.504349i
$297$		0			0
$298$	13.8794	+	2.61851i	0.804013	+	0.151686i
$299$	−5.60652			−0.324234
$300$		0			0
$301$	−9.86933			−0.568859
$302$	24.9559	+	4.70822i	1.43605	+	0.270927i
$303$		0			0
$304$	−6.28624	+	13.6449i	−0.360541	+	0.782588i
$305$	0.115651	+	0.303295i	0.00662217	+	0.0173666i
$306$		0			0
$307$	14.4642	−	14.4642i	0.825517	−	0.825517i	−0.161376	−	0.986893i	$-0.551593\pi$
$307$	14.4642	−	14.4642i	0.825517	−	0.825517i	0.986893	+	0.161376i	$0.0515932\pi$
$308$	12.9451	+	7.58508i	0.737615	+	0.432200i
$309$		0			0
$310$	16.0474	+	2.20143i	0.911430	+	0.125033i
$311$	−15.9923	−	22.0115i	−0.906840	−	1.24816i	−0.968234	−	0.250045i	$-0.919555\pi$
$311$	−15.9923	−	22.0115i	−0.906840	−	1.24816i	0.0613941	−	0.998114i	$-0.480445\pi$
$312$		0			0
$313$	33.5431	−	5.31270i	1.89597	−	0.300292i	0.904075	−	0.427374i	$-0.140561\pi$
$313$	33.5431	−	5.31270i	1.89597	−	0.300292i	0.991892	+	0.127083i	$0.0405613\pi$
$314$	8.14148	−	5.55709i	0.459450	−	0.313605i
$315$		0			0
$316$	−2.16991	+	2.64471i	−0.122067	+	0.148777i
$317$	15.3076	−	30.0429i	0.859762	−	1.68738i	0.143382	−	0.989667i	$-0.454202\pi$
$317$	15.3076	−	30.0429i	0.859762	−	1.68738i	0.716380	−	0.697711i	$-0.245798\pi$
$318$		0			0
$319$	−15.5249	−	47.7808i	−0.869229	−	2.67521i
$320$	17.5735	−	3.34251i	0.982388	−	0.186852i
$321$		0			0
$322$	1.30014	+	2.74847i	0.0724539	+	0.153166i
$323$	−2.56250	−	0.405860i	−0.142581	−	0.0225826i
$324$		0			0
$325$	−15.2779	−	5.94271i	−0.847468	−	0.329642i
$326$	−10.8492	−	0.318950i	−0.600883	−	0.0176650i
$327$		0			0
$328$	−27.7641	+	11.1883i	−1.53302	+	0.617769i
$329$	−11.9394	−	3.87934i	−0.658239	−	0.213875i
$330$		0			0
$331$	−0.541262	+	0.175867i	−0.0297505	+	0.00966651i	−0.323854	−	0.946107i	$-0.604979\pi$
$331$	−0.541262	+	0.175867i	−0.0297505	+	0.00966651i	0.294104	+	0.955773i	$0.404979\pi$
$332$	5.91357	−	5.25626i	0.324550	−	0.288474i
$333$		0			0
$334$	−14.3135	+	18.5302i	−0.783197	+	1.01393i
$335$	−10.7742	+	11.9126i	−0.588659	+	0.650857i
$336$		0			0
$337$	−3.65964	−	23.1060i	−0.199353	−	1.25867i	−0.860905	−	0.508766i	$-0.830102\pi$
$337$	−3.65964	−	23.1060i	−0.199353	−	1.25867i	0.661551	−	0.749900i	$-0.269898\pi$
$338$	−0.405339	−	3.15713i	−0.0220475	−	0.171725i
$339$		0			0
$340$	1.37865	+	2.76456i	0.0747677	+	0.149929i
$341$	−24.7261	−	17.9646i	−1.33899	−	0.972836i
$342$		0			0
$343$	−11.0409	−	11.0409i	−0.596152	−	0.596152i
$344$	21.6385	−	4.97505i	1.16667	−	0.268237i
$345$		0			0
$346$	24.6389	+	8.81419i	1.32459	+	0.473854i
$347$	−15.2550	−	29.9397i	−0.818933	−	1.60725i	−0.794281	−	0.607551i	$-0.792152\pi$
$347$	−15.2550	−	29.9397i	−0.818933	−	1.60725i	−0.0246528	−	0.999696i	$-0.507848\pi$
$348$		0			0
$349$		−	1.82016i		−	0.0974309i	−0.998813	−	0.0487154i	$-0.984487\pi$
$349$		−	1.82016i		−	0.0974309i	0.998813	−	0.0487154i	$-0.0155127\pi$
$350$	0.629641	+	8.86775i	0.0336557	+	0.474001i
$351$		0			0
$352$	−32.2056	−	10.1047i	−1.71657	−	0.538584i
$353$	−7.29751	−	14.3222i	−0.388407	−	0.762293i	0.611166	−	0.791503i	$-0.290701\pi$
$353$	−7.29751	−	14.3222i	−0.388407	−	0.762293i	−0.999573	+	0.0292100i	$0.990701\pi$
$354$		0			0
$355$	9.04052	−	13.8537i	0.479821	−	0.735277i
$356$	−0.236235	−	0.904838i	−0.0125204	−	0.0479563i
$357$		0			0
$358$	−16.4937	−	9.02401i	−0.871718	−	0.476934i
$359$	13.1872	+	9.58103i	0.695992	+	0.505668i	0.878624	−	0.477514i	$-0.158462\pi$
$359$	13.1872	+	9.58103i	0.695992	+	0.505668i	−0.182633	+	0.983181i	$0.558462\pi$
$360$		0			0
$361$	3.95914	−	2.87648i	0.208376	−	0.151394i
$362$	−20.7756	+	2.66735i	−1.09194	+	0.140193i
$363$		0			0
$364$	6.94271	−	4.44554i	0.363897	−	0.233010i
$365$	−10.0394	−	4.49659i	−0.525486	−	0.235362i
$366$		0			0
$367$	4.47934	+	2.28234i	0.233820	+	0.119137i	0.566975	−	0.823735i	$-0.308113\pi$
$367$	4.47934	+	2.28234i	0.233820	+	0.119137i	−0.333156	+	0.942872i	$0.608113\pi$
$368$	−4.23603	−	5.37061i	−0.220818	−	0.279963i
$369$		0			0
$370$	−7.16571	+	23.7171i	−0.372527	+	1.23299i
$371$	−6.42520	−	2.08768i	−0.333580	−	0.108387i
$372$		0			0
$373$	0.445750	−	2.81436i	0.0230801	−	0.145722i	−0.973457	−	0.228869i	$-0.926497\pi$
$373$	0.445750	−	2.81436i	0.0230801	−	0.145722i	0.996537	+	0.0831473i	$0.0264972\pi$
$374$	0.171291	−	5.82654i	0.00885725	−	0.301283i
$375$		0			0
$376$	28.1326	+	2.48689i	1.45083	+	0.128252i
$377$	−27.2653	−	4.31840i	−1.40424	−	0.222409i
$378$		0			0
$379$	−4.96244	+	15.2728i	−0.254903	+	0.784512i	0.738945	+	0.673765i	$0.235324\pi$
$379$	−4.96244	+	15.2728i	−0.254903	+	0.784512i	−0.993849	+	0.110746i	$0.964676\pi$
$380$	15.9290	+	5.32829i	0.817142	+	0.273336i
$381$		0			0
$382$	14.9496	+	15.8552i	0.764887	+	0.811222i
$383$	−15.1017	+	29.6388i	−0.771662	+	1.51447i	0.0837286	+	0.996489i	$0.473317\pi$
$383$	−15.1017	+	29.6388i	−0.771662	+	1.51447i	−0.855391	+	0.517983i	$0.826683\pi$
$384$		0			0
$385$	6.85687	−	15.3091i	0.349459	−	0.780225i
$386$	−10.4669	−	15.3346i	−0.532750	−	0.780512i
$387$		0			0
$388$	−4.00912	+	0.395370i	−0.203532	+	0.0200719i
$389$	11.6281	+	16.0047i	0.589569	+	0.811472i	0.994704	−	0.102785i	$-0.0327754\pi$
$389$	11.6281	+	16.0047i	0.589569	+	0.811472i	−0.405135	+	0.914257i	$0.632775\pi$
$390$		0			0
$391$	0.694322	−	0.955652i	0.0351134	−	0.0483294i
$392$	12.9917	+	8.13444i	0.656179	+	0.410851i
$393$		0			0
$394$	−8.24780	−	28.1759i	−0.415518	−	1.41948i
$395$	3.20307	+	2.09024i	0.161164	+	0.105171i
$396$		0			0
$397$	−14.4965	+	7.38633i	−0.727558	+	0.370709i	−0.778208	−	0.628007i	$-0.783871\pi$
$397$	−14.4965	+	7.38633i	−0.727558	+	0.370709i	0.0506495	+	0.998716i	$0.483871\pi$
$398$	−1.42563	+	7.55655i	−0.0714603	+	0.378775i
$399$		0			0
$400$	−5.85065	−	19.1251i	−0.292532	−	0.956256i
$401$	−1.12938			−0.0563985			−0.0281992	−	0.999602i	$-0.508977\pi$
$401$	−1.12938			−0.0563985			−0.0281992	+	0.999602i	$0.508977\pi$
$402$		0			0
$403$	−14.9631	+	7.62410i	−0.745367	+	0.379783i
$404$	−32.9461	−	12.8901i	−1.63913	−	0.641307i
$405$		0			0
$406$	4.20576	+	14.3676i	0.208728	+	0.713053i
$407$	33.0568	−	33.0568i	1.63857	−	1.63857i
$408$		0			0
$409$	−15.6753	+	21.5752i	−0.775093	+	1.06682i	0.220713	+	0.975339i	$0.429162\pi$
$409$	−15.6753	+	21.5752i	−0.775093	+	1.06682i	−0.995806	+	0.0914855i	$0.970838\pi$
$410$	15.8090	+	29.4976i	0.780750	+	1.45678i
$411$		0			0
$412$	−3.63886	+	0.358855i	−0.179274	+	0.0176795i
$413$	12.0722	−	1.91204i	0.594032	−	0.0940854i
$414$		0			0
$415$	−6.56054	−	5.93359i	−0.322044	−	0.291269i
$416$	−12.9809	+	13.2466i	−0.636441	+	0.649468i
$417$		0			0
$418$	−21.7423	−	23.0594i	−1.06345	−	1.12787i
$419$	1.24633	+	3.83581i	0.0608873	+	0.187392i	0.976874	−	0.213818i	$-0.0685899\pi$
$419$	1.24633	+	3.83581i	0.0608873	+	0.187392i	−0.915986	+	0.401210i	$0.868590\pi$
$420$		0			0
$421$	6.01598	−	18.5153i	0.293201	−	0.902380i	−0.690619	−	0.723219i	$-0.742662\pi$
$421$	6.01598	−	18.5153i	0.293201	−	0.902380i	0.983820	−	0.179161i	$-0.0573382\pi$
$422$	−13.2244	+	6.25568i	−0.643753	+	0.304522i
$423$		0			0
$424$	15.1396	+	1.33833i	0.735245	+	0.0649949i
$425$	2.90500	−	1.86822i	0.140913	−	0.0906222i
$426$		0			0
$427$	−0.0285504	+	0.180260i	−0.00138165	+	0.00872340i
$428$	−3.44698	+	1.50825i	−0.166616	+	0.0729042i
$429$		0			0
$430$	−8.15909	−	23.4446i	−0.393466	−	1.13060i
$431$	24.6627	−	8.01340i	1.18796	−	0.385992i	0.352642	−	0.935758i	$-0.385283\pi$
$431$	24.6627	−	8.01340i	1.18796	−	0.385992i	0.835318	+	0.549766i	$0.185283\pi$
$432$		0			0
$433$	19.3515	+	9.86010i	0.929976	+	0.473846i	0.852254	−	0.523129i	$-0.175235\pi$
$433$	19.3515	+	9.86010i	0.929976	+	0.473846i	0.0777221	+	0.996975i	$0.475235\pi$
$434$	7.20745	+	5.56732i	0.345969	+	0.267240i
$435$		0			0
$436$	0.855681	−	0.547908i	0.0409797	−	0.0262400i
$437$	−1.00471	−	6.34352i	−0.0480620	−	0.303452i
$438$		0			0
$439$	−8.84102	+	6.42338i	−0.421959	+	0.306571i	−0.778426	−	0.627737i	$-0.783981\pi$
$439$	−8.84102	+	6.42338i	−0.421959	+	0.306571i	0.356467	+	0.934308i	$0.383981\pi$
$440$	−7.31646	+	37.0217i	−0.348799	+	1.76494i
$441$		0			0
$442$	−2.80983	−	1.53731i	−0.133650	−	0.0731226i
$443$	11.6714	+	11.6714i	0.554527	+	0.554527i	0.927744	−	0.373217i	$-0.121745\pi$
$443$	11.6714	+	11.6714i	0.554527	+	0.554527i	−0.373217	+	0.927744i	$0.621745\pi$
$444$		0			0
$445$	−0.976935	+	0.372521i	−0.0463112	+	0.0176592i
$446$	1.30525	−	3.64865i	0.0618053	−	0.172768i
$447$		0			0
$448$	9.50407	+	3.29173i	0.449025	+	0.155520i
$449$		−	6.14595i		−	0.290045i	−0.989428	−	0.145023i	$-0.953674\pi$
$449$		−	6.14595i		−	0.290045i	0.989428	−	0.145023i	$-0.0463255\pi$
$450$		0			0
$451$		−	63.1481i		−	2.97353i
$452$	−28.9242	−	6.34239i	−1.36048	−	0.298321i
$453$		0			0
$454$	−5.61877	−	2.01003i	−0.263702	−	0.0943355i
$455$	−5.78458	−	7.17591i	−0.271185	−	0.336412i
$456$		0			0
$457$	−17.1334	−	17.1334i	−0.801466	−	0.801466i	0.181859	−	0.983325i	$-0.441789\pi$
$457$	−17.1334	−	17.1334i	−0.801466	−	0.801466i	−0.983325	+	0.181859i	$0.941789\pi$
$458$	2.57615	−	4.70858i	0.120376	−	0.220017i
$459$		0			0
$460$	−5.45413	+	5.36066i	−0.254300	+	0.249942i
$461$	−20.6031	+	14.9690i	−0.959581	+	0.697176i	−0.953053	−	0.302802i	$-0.902078\pi$
$461$	−20.6031	+	14.9690i	−0.959581	+	0.697176i	−0.00652765	+	0.999979i	$0.502078\pi$
$462$		0			0
$463$	−1.06522	−	6.72555i	−0.0495051	−	0.312563i	−0.999998	−	0.00181762i	$-0.999421\pi$
$463$	−1.06522	−	6.72555i	−0.0495051	−	0.312563i	0.950493	−	0.310745i	$-0.100579\pi$
$464$	−16.4637	−	29.3808i	−0.764309	−	1.36397i
$465$		0			0
$466$	−15.8430	+	20.5103i	−0.733912	+	0.950122i
$467$	19.1476	+	9.75620i	0.886046	+	0.451463i	0.836917	−	0.547329i	$-0.184355\pi$
$467$	19.1476	+	9.75620i	0.886046	+	0.451463i	0.0491291	+	0.998792i	$0.484355\pi$
$468$		0			0
$469$	−8.58909	+	2.79077i	−0.396607	+	0.128866i
$470$	−0.655065	−	31.5690i	−0.0302159	−	1.45617i
$471$		0			0
$472$	−25.5043	+	10.2776i	−1.17393	+	0.473066i
$473$	−7.32732	+	46.2629i	−0.336911	+	2.12717i
$474$		0			0
$475$	3.98602	−	18.3512i	0.182891	−	0.842012i
$476$	−0.102039	+	1.73395i	−0.00467696	+	0.0794757i
$477$		0			0
$478$	−6.73497	−	14.2376i	−0.308050	−	0.651212i
$479$	−8.36276	+	25.7379i	−0.382104	+	1.17600i	0.556455	+	0.830878i	$0.312161\pi$
$479$	−8.36276	+	25.7379i	−0.382104	+	1.17600i	−0.938559	+	0.345118i	$0.887839\pi$
$480$		0			0
$481$	−7.93783	−	24.4301i	−0.361934	−	1.11392i
$482$	−13.3971	+	12.6319i	−0.610222	+	0.575368i
$483$		0			0
$484$	31.2117	−	38.0413i	1.41871	−	1.72915i
$485$	0.926656	+	4.40773i	0.0420773	+	0.200145i
$486$		0			0
$487$	1.89556	−	0.300227i	0.0858958	−	0.0136046i	−0.113339	−	0.993556i	$-0.536154\pi$
$487$	1.89556	−	0.300227i	0.0858958	−	0.0136046i	0.199234	+	0.979952i	$0.436154\pi$
$488$	−0.0282710	−	0.409611i	−0.00127977	−	0.0185422i
$489$		0			0
$490$	7.46178	−	15.4277i	0.337089	−	0.696951i
$491$	22.7182	−	31.2689i	1.02526	−	1.41114i	0.116804	−	0.993155i	$-0.462735\pi$
$491$	22.7182	−	31.2689i	1.02526	−	1.41114i	0.908452	−	0.417989i	$-0.137265\pi$
$492$		0			0
$493$	4.11268	−	4.11268i	0.185226	−	0.185226i
$494$	−16.7131	+	4.89235i	−0.751958	+	0.220117i
$495$		0			0
$496$	−18.6087	−	8.57311i	−0.835557	−	0.384944i
$497$	8.28740	−	4.22264i	0.371741	−	0.189411i
$498$		0			0
$499$	6.28177			0.281211			0.140605	−	0.990066i	$-0.455095\pi$
$499$	6.28177			0.281211			0.140605	+	0.990066i	$0.455095\pi$
$500$	−20.5448	+	8.82678i	−0.918790	+	0.394746i
$501$		0			0
$502$	5.66423	+	1.06862i	0.252807	+	0.0476949i
$503$	5.14067	−	2.61930i	0.229211	−	0.116789i	−0.335614	−	0.942000i	$-0.608944\pi$
$503$	5.14067	−	2.61930i	0.229211	−	0.116789i	0.564825	+	0.825211i	$0.308944\pi$
$504$		0			0
$505$	−10.3222	+	38.1831i	−0.459330	+	1.69913i
$506$	13.8488	−	4.05390i	0.615655	−	0.180218i
$507$		0			0
$508$	−2.25492	+	3.84837i	−0.100046	+	0.170744i
$509$	6.31391	−	8.69035i	0.279859	−	0.385193i	−0.645828	−	0.763483i	$-0.723488\pi$
$509$	6.31391	−	8.69035i	0.279859	−	0.385193i	0.925687	+	0.378290i	$0.123488\pi$
$510$		0			0
$511$	−3.63549	−	5.00382i	−0.160824	−	0.221356i
$512$	−22.4970	−	2.42619i	−0.994235	−	0.107223i
$513$		0			0
$514$	−23.1466	+	15.7990i	−1.02095	+	0.696866i
$515$	0.841074	+	4.00065i	0.0370622	+	0.176290i
$516$		0			0
$517$	−27.0488	+	53.0862i	−1.18960	+	2.33473i
$518$	−10.1355	+	9.55662i	−0.445330	+	0.419894i
$519$		0			0
$520$	16.3000	+	12.8172i	0.714801	+	0.562071i
$521$	7.60669	−	23.4110i	0.333255	−	1.02565i	−0.634320	−	0.773071i	$-0.718720\pi$
$521$	7.60669	−	23.4110i	0.333255	−	1.02565i	0.967575	−	0.252584i	$-0.0812803\pi$
$522$		0			0
$523$	34.1236	+	5.40465i	1.49212	+	0.236329i	0.848574	−	0.529076i	$-0.177462\pi$
$523$	34.1236	+	5.40465i	1.49212	+	0.236329i	0.643548	+	0.765405i	$0.277462\pi$
$524$	−5.71617	−	0.336383i	−0.249712	−	0.0146950i
$525$		0			0
$526$	−10.2694	−	0.301903i	−0.447765	−	0.0131636i
$527$	0.553507	−	3.49470i	0.0241111	−	0.152232i
$528$		0			0
$529$	−19.0932	−	6.20376i	−0.830139	−	0.269729i
$530$	−0.352525	−	16.9890i	−0.0153127	−	0.737953i
$531$		0			0
$532$	6.27409	+	7.05869i	0.272016	+	0.306033i
$533$	−30.9161	−	15.7525i	−1.33912	−	0.682318i
$534$		0			0
$535$	2.09521	+	3.64770i	0.0905836	+	0.157704i
$536$	17.4247	−	10.4484i	0.752634	−	0.451303i
$537$		0			0
$538$	0.370075	+	2.88246i	0.0159550	+	0.124272i
$539$	−26.1607	+	19.0068i	−1.12682	+	0.818683i
$540$		0			0
$541$	−9.35734	−	6.79850i	−0.402303	−	0.292290i	0.368175	−	0.929756i	$-0.379983\pi$
$541$	−9.35734	−	6.79850i	−0.402303	−	0.292290i	−0.770478	+	0.637466i	$0.779983\pi$
$542$	−16.3862	+	29.9499i	−0.703846	+	1.28646i
$543$		0			0
$544$	−0.650352	−	3.85312i	−0.0278836	−	0.165201i
$545$	−0.712943	−	0.884423i	−0.0305391	−	0.0378845i
$546$		0			0
$547$	−13.5824	−	26.6569i	−0.580741	−	1.13977i	−0.975297	−	0.220897i	$-0.929102\pi$
$547$	−13.5824	−	26.6569i	−0.580741	−	1.13977i	0.394556	−	0.918872i	$-0.370898\pi$
$548$	0.260374	−	1.18743i	0.0111226	−	0.0507244i
$549$		0			0
$550$	42.0354	+	3.63225i	1.79240	+	0.154880i
$551$		−	31.6233i		−	1.34720i
$552$		0			0
$553$	0.976307	+	1.91611i	0.0415168	+	0.0814813i
$554$	−6.59672	+	18.4402i	−0.280268	+	0.783451i
$555$		0			0
$556$	38.3230	−	10.0054i	1.62526	−	0.424323i
$557$	11.3351	+	11.3351i	0.480282	+	0.480282i	0.905222	−	0.424939i	$-0.139705\pi$
$557$	11.3351	+	11.3351i	0.480282	+	0.480282i	−0.424939	+	0.905222i	$0.639705\pi$
$558$		0			0
$559$	20.8216	+	15.1278i	0.880659	+	0.639836i
$560$	2.50341	−	10.9630i	0.105788	−	0.463270i
$561$		0			0
$562$	−39.1847	+	5.03085i	−1.65291	+	0.212214i
$563$	−3.57340	−	22.5616i	−0.150601	−	0.950857i	−0.941035	−	0.338309i	$-0.890145\pi$
$563$	−3.57340	−	22.5616i	−0.150601	−	0.950857i	0.790434	−	0.612547i	$-0.209855\pi$
$564$		0			0
$565$	−3.53375	+	32.9175i	−0.148666	+	1.38485i
$566$	0.0776506	+	0.0599804i	0.00326390	+	0.00252116i
$567$		0			0
$568$	−16.0415	+	13.4357i	−0.673086	+	0.563751i
$569$	25.9715	−	8.43866i	1.08878	−	0.353767i	0.291007	−	0.956721i	$-0.406010\pi$
$569$	25.9715	−	8.43866i	1.08878	−	0.353767i	0.797776	+	0.602954i	$0.206010\pi$
$570$		0			0
$571$	29.6950	+	9.64848i	1.24270	+	0.403776i	0.855298	−	0.518136i	$-0.173374\pi$
$571$	29.6950	+	9.64848i	1.24270	+	0.403776i	0.387398	+	0.921913i	$0.373374\pi$
$572$	−15.6842	−	35.8447i	−0.655787	−	1.49874i
$573$		0			0
$574$	−0.552951	+	18.8089i	−0.0230797	+	0.785067i
$575$	6.62074	+	5.41028i	0.276104	+	0.225624i
$576$		0			0
$577$	22.2278	+	3.52054i	0.925356	+	0.146562i	0.600886	−	0.799334i	$-0.294814\pi$
$577$	22.2278	+	3.52054i	0.925356	+	0.146562i	0.324469	+	0.945896i	$0.394814\pi$
$578$	−21.1227	+	9.99192i	−0.878589	+	0.415609i
$579$		0			0
$580$	−30.6533	+	21.8686i	−1.27281	+	0.908046i
$581$	−1.53693	−	4.73020i	−0.0637628	−	0.196242i
$582$		0			0
$583$	−14.5564	+	28.5684i	−0.602862	+	1.18318i
$584$	10.4932	+	9.13823i	0.434210	+	0.378142i
$585$		0			0
$586$	−15.6255	−	22.8923i	−0.645484	−	0.945674i
$587$	−15.9467	+	2.52570i	−0.658190	+	0.104247i	−0.476590	−	0.879126i	$-0.658127\pi$
$587$	−15.9467	+	2.52570i	−0.658190	+	0.104247i	−0.181599	+	0.983373i	$0.558127\pi$
$588$		0			0
$589$	−11.3078	−	15.5638i	−0.465928	−	0.641296i
$590$	14.5222	+	27.0966i	0.597871	+	1.11555i
$591$		0			0
$592$	17.4047	−	26.0621i	0.715329	−	1.07115i
$593$	5.08886	−	5.08886i	0.208974	−	0.208974i	−0.594857	−	0.803831i	$-0.702791\pi$
$593$	5.08886	−	5.08886i	0.208974	−	0.208974i	0.803831	+	0.594857i	$0.202791\pi$
$594$		0			0
$595$	1.93953	−	0.0973243i	0.0795131	−	0.00398991i
$596$	−7.27787	+	18.6017i	−0.298113	+	0.761954i
$597$		0			0
$598$	1.46993	−	7.79137i	0.0601099	−	0.318613i
$599$	−31.4074			−1.28327			−0.641636	−	0.767009i	$-0.721744\pi$
$599$	−31.4074			−1.28327			−0.641636	+	0.767009i	$0.721744\pi$
$600$		0			0
$601$	−10.7189			−0.437232			−0.218616	−	0.975811i	$-0.570154\pi$
$601$	−10.7189			−0.437232			−0.218616	+	0.975811i	$0.570154\pi$
$602$	2.58756	−	13.7154i	0.105461	−	0.558998i
$603$		0			0
$604$	−13.0860	+	33.4468i	−0.532462	+	1.36093i
$605$	−46.0726	−	30.0657i	−1.87312	−	1.22235i
$606$		0			0
$607$	−2.32027	+	2.32027i	−0.0941769	+	0.0941769i	−0.752626	−	0.658449i	$-0.771213\pi$
$607$	−2.32027	+	2.32027i	−0.0941769	+	0.0941769i	0.658449	+	0.752626i	$0.271213\pi$
$608$	−17.3141	−	12.3134i	−0.702181	−	0.499375i
$609$		0			0
$610$	−0.451810	+	0.0812017i	−0.0182933	+	0.00328776i
$611$	19.2425	+	26.4851i	0.778470	+	1.07147i
$612$		0			0
$613$	−17.1447	+	2.71546i	−0.692469	+	0.109676i	−0.492742	−	0.870175i	$-0.664005\pi$
$613$	−17.1447	+	2.71546i	−0.692469	+	0.109676i	−0.199727	+	0.979852i	$0.564005\pi$
$614$	16.3086	+	23.8932i	0.658163	+	0.964250i
$615$		0			0
$616$	−13.9349	+	16.0011i	−0.561455	+	0.644703i
$617$	16.9930	−	33.3506i	0.684112	−	1.34264i	−0.243793	−	0.969827i	$-0.578392\pi$
$617$	16.9930	−	33.3506i	0.684112	−	1.34264i	0.927905	−	0.372817i	$-0.121608\pi$
$618$		0			0
$619$	6.63246	+	20.4126i	0.266581	+	0.820452i	0.991325	+	0.131434i	$0.0419581\pi$
$619$	6.63246	+	20.4126i	0.266581	+	0.820452i	−0.724744	+	0.689018i	$0.758042\pi$
$620$	−7.26666	+	21.7238i	−0.291836	+	0.872450i
$621$		0			0
$622$	34.7823	−	16.4534i	1.39464	−	0.659723i
$623$	−0.580631	−	0.0919629i	−0.0232625	−	0.00368442i
$624$		0			0
$625$	12.3070	+	21.7609i	0.492281	+	0.870436i
$626$	−1.41135	+	48.0076i	−0.0564088	+	1.91877i
$627$		0			0
$628$	5.58812	+	12.7712i	0.222990	+	0.509625i
$629$	5.14724	+	1.67244i	0.205234	+	0.0666846i
$630$		0			0
$631$	−44.1934	+	14.3593i	−1.75931	+	0.571635i	−0.997129	−	0.0757265i	$-0.975872\pi$
$631$	−44.1934	+	14.3593i	−1.75931	+	0.571635i	−0.762183	+	0.647362i	$0.775872\pi$
$632$	−3.10644	−	3.70891i	−0.123568	−	0.147533i
$633$		0			0
$634$	37.7372	+	29.1497i	1.49874	+	1.15768i
$635$	4.55116	+	2.03844i	0.180607	+	0.0808931i
$636$		0			0
$637$	2.77950	+	17.5491i	0.110128	+	0.695320i
$638$	70.4713	−	9.04768i	2.78998	−	0.358201i
$639$		0			0
$640$	0.0376250	+	25.2982i	0.00148726	+	0.999999i
$641$	34.1067	+	24.7799i	1.34713	+	0.978749i	0.999149	+	0.0412481i	$0.0131334\pi$
$641$	34.1067	+	24.7799i	1.34713	+	0.978749i	0.347983	+	0.937501i	$0.386867\pi$
$642$		0			0
$643$	16.5201	+	16.5201i	0.651489	+	0.651489i	0.953352	−	0.301862i	$-0.0976083\pi$
$643$	16.5201	+	16.5201i	0.651489	+	0.651489i	−0.301862	+	0.953352i	$0.597608\pi$
$644$	−4.16041	+	1.08620i	−0.163943	+	0.0428023i
$645$		0			0
$646$	1.23586	−	3.45469i	0.0486244	−	0.135923i
$647$	14.8096	+	29.0654i	0.582225	+	1.14268i	0.974825	+	0.222971i	$0.0715755\pi$
$647$	14.8096	+	29.0654i	0.582225	+	1.14268i	−0.392600	+	0.919709i	$0.628424\pi$
$648$		0			0
$649$		−	58.0083i		−	2.27702i
$650$	12.2642	−	19.6736i	0.481040	−	0.771664i
$651$		0			0
$652$	3.28772	−	14.9935i	0.128757	−	0.587192i
$653$	−19.1784	−	37.6397i	−0.750508	−	1.47295i	−0.876746	−	0.480954i	$-0.840290\pi$
$653$	−19.1784	−	37.6397i	−0.750508	−	1.47295i	0.126238	−	0.992000i	$-0.459710\pi$
$654$		0			0
$655$	0.320840	+	6.39388i	0.0125363	+	0.249830i
$656$	−8.26906	−	41.5171i	−0.322852	−	1.62097i
$657$		0			0
$658$	8.52141	−	15.5750i	0.332199	−	0.607178i
$659$	−4.38671	−	3.18713i	−0.170882	−	0.124153i	0.499057	−	0.866569i	$-0.333680\pi$
$659$	−4.38671	−	3.18713i	−0.170882	−	0.124153i	−0.669939	+	0.742416i	$0.733680\pi$
$660$		0			0
$661$	25.3251	−	18.3997i	0.985031	−	0.715667i	0.0262033	−	0.999657i	$-0.491658\pi$
$661$	25.3251	−	18.3997i	0.985031	−	0.715667i	0.958827	+	0.283990i	$0.0916583\pi$
$662$	−0.102492	−	0.798300i	−0.00398348	−	0.0310268i
$663$		0			0
$664$	5.75417	+	9.59618i	0.223305	+	0.372404i
$665$	7.08258	−	7.83093i	0.274651	−	0.303671i
$666$		0			0
$667$	12.8288	+	6.53662i	0.496734	+	0.253099i
$668$	−21.9986	−	24.7497i	−0.851153	−	0.957593i
$669$		0			0
$670$	−13.7301	−	18.0962i	−0.530442	−	0.699117i
$671$	0.823780	+	0.267662i	0.0318017	+	0.0103330i
$672$		0			0
$673$	−1.99690	+	12.6079i	−0.0769748	+	0.485999i	0.918842	+	0.394626i	$0.129126\pi$
$673$	−1.99690	+	12.6079i	−0.0769748	+	0.485999i	−0.995817	+	0.0913737i	$0.970874\pi$
$674$	33.0699	+	0.972203i	1.27381	+	0.0374478i
$675$		0			0
$676$	4.49373	+	0.264446i	0.172836	+	0.0101710i
$677$	6.23648	+	0.987761i	0.239687	+	0.0379627i	0.275122	−	0.961409i	$-0.411282\pi$
$677$	6.23648	+	0.987761i	0.239687	+	0.0379627i	−0.0354350	+	0.999372i	$0.511282\pi$
$678$		0			0
$679$	−0.782572	+	2.40851i	−0.0300323	+	0.0924300i
$680$	−4.20336	+	1.19109i	−0.161191	+	0.0456761i
$681$		0			0
$682$	31.4481	−	29.6518i	1.20421	−	1.13543i
$683$	−12.2876	+	24.1159i	−0.470174	+	0.922768i	0.527158	+	0.849767i	$0.323258\pi$
$683$	−12.2876	+	24.1159i	−0.470174	+	0.922768i	−0.997332	+	0.0730008i	$0.976742\pi$
$684$		0			0
$685$	−1.35136	−	0.145071i	−0.0516329	−	0.00554289i
$686$	18.2382	−	12.4488i	0.696338	−	0.475296i
$687$		0			0
$688$	1.24059	+	31.3753i	0.0472972	+	1.19617i
$689$	10.3554	+	14.2530i	0.394510	+	0.542997i
$690$		0			0
$691$	2.65374	−	3.65256i	0.100953	−	0.138950i	−0.755552	−	0.655089i	$-0.772631\pi$
$691$	2.65374	−	3.65256i	0.100953	−	0.138950i	0.856505	+	0.516139i	$0.172631\pi$
$692$	−18.7089	+	31.9296i	−0.711207	+	1.21378i
$693$		0			0
$694$	45.6067	−	13.3502i	1.73121	−	0.506768i
$695$	−15.7776	−	41.3766i	−0.598477	−	1.56950i
$696$		0			0
$697$	6.51379	−	3.31894i	0.246727	−	0.125714i
$698$	2.52947	+	0.477213i	0.0957419	+	0.0180628i
$699$		0			0
$700$	−12.4886	−	1.44996i	−0.472024	−	0.0548032i
$701$	11.3133			0.427297			0.213648	−	0.976911i	$-0.431465\pi$
$701$	11.3133			0.427297			0.213648	+	0.976911i	$0.431465\pi$
$702$		0			0
$703$	26.2191	−	13.3593i	0.988870	−	0.503855i
$704$	22.4863	−	42.1068i	0.847483	−	1.58696i
$705$		0			0
$706$	21.8168	−	6.38632i	0.821085	−	0.240352i
$707$	−15.7256	+	15.7256i	−0.591424	+	0.591424i
$708$		0			0
$709$	10.4295	−	14.3550i	0.391688	−	0.539113i	−0.566945	−	0.823755i	$-0.691875\pi$
$709$	10.4295	−	14.3550i	0.391688	−	0.539113i	0.958634	+	0.284643i	$0.0918750\pi$
$710$	16.8822	+	16.1958i	0.633576	+	0.607817i
$711$		0			0
$712$	1.31939	−	0.0910630i	0.0494462	−	0.00341273i
$713$	8.65121	−	1.37022i	0.323991	−	0.0513151i
$714$		0			0
$715$	−37.9320	+	21.7878i	−1.41858	+	0.814818i
$716$	16.8650	−	20.5553i	0.630275	−	0.768188i
$717$		0			0
$718$	−16.7722	+	15.8142i	−0.625932	+	0.590181i
$719$	−1.37168	−	4.22158i	−0.0511549	−	0.157438i	0.922216	−	0.386676i	$-0.126377\pi$
$719$	−1.37168	−	4.22158i	−0.0511549	−	0.157438i	−0.973371	+	0.229237i	$0.926377\pi$
$720$		0			0
$721$	−0.710297	+	2.18607i	−0.0264528	+	0.0814134i
$722$	2.95942	+	6.25617i	0.110138	+	0.232830i
$723$		0			0
$724$	1.74020	−	29.5712i	0.0646739	−	1.09901i
$725$	28.0304	+	31.4106i	1.04102	+	1.16656i
$726$		0			0
$727$	−5.05252	+	31.9003i	−0.187388	+	1.18312i	0.697246	+	0.716832i	$0.254408\pi$
$727$	−5.05252	+	31.9003i	−0.187388	+	1.18312i	−0.884634	+	0.466287i	$0.845592\pi$
$728$	4.35770	+	10.8138i	0.161507	+	0.400787i
$729$		0			0
$730$	8.88105	−	12.7728i	0.328702	−	0.472742i
$731$	−5.15717	+	1.67567i	−0.190745	+	0.0619767i
$732$		0			0
$733$	5.43837	+	2.77099i	0.200871	+	0.102349i	0.551532	−	0.834153i	$-0.314043\pi$
$733$	5.43837	+	2.77099i	0.200871	+	0.102349i	−0.350662	+	0.936502i	$0.614043\pi$
$734$	−4.34617	+	5.62655i	−0.160420	+	0.207680i
$735$		0			0
$736$	8.57414	−	4.47872i	0.316047	−	0.165088i
$737$	6.70499	+	42.3337i	0.246982	+	1.55938i
$738$		0			0
$739$	−32.0490	+	23.2850i	−1.17894	+	0.856551i	−0.992052	−	0.125830i	$-0.959841\pi$
$739$	−32.0490	+	23.2850i	−1.17894	+	0.856551i	−0.186889	+	0.982381i	$0.559841\pi$
$740$	−31.0809	−	16.1764i	−1.14256	−	0.594655i
$741$		0			0
$742$	4.58581	−	8.38174i	0.168350	−	0.307703i
$743$	−0.730435	−	0.730435i	−0.0267970	−	0.0267970i	0.693581	−	0.720378i	$-0.256032\pi$
$743$	−0.730435	−	0.730435i	−0.0267970	−	0.0267970i	−0.720378	+	0.693581i	$0.756032\pi$
$744$		0			0
$745$	21.5586	+	5.82799i	0.789845	+	0.213521i
$746$	3.79424	+	1.35733i	0.138917	+	0.0496955i
$747$		0			0
$748$	8.05222	+	1.76566i	0.294418	+	0.0645589i
$749$			2.36520i			0.0864226i
$750$		0			0
$751$			19.6362i			0.716534i	0.933619	+	0.358267i	$0.116632\pi$
$751$			19.6362i			0.716534i	−0.933619	+	0.358267i	$0.883368\pi$
$752$	−10.8319	+	38.4438i	−0.394998	+	1.40190i
$753$		0			0
$754$	13.1498	−	36.7583i	0.478886	−	1.33866i
$755$	38.7634	+	10.4790i	1.41075	+	0.381371i
$756$		0			0
$757$	−10.8682	−	10.8682i	−0.395011	−	0.395011i	0.481458	−	0.876469i	$-0.340107\pi$
$757$	−10.8682	−	10.8682i	−0.395011	−	0.395011i	−0.876469	+	0.481458i	$0.840107\pi$
$758$	−19.9235	−	10.9005i	−0.723655	−	0.395926i
$759$		0			0
$760$	−11.5810	+	20.7396i	−0.420088	+	0.752303i
$761$	−24.6400	+	17.9020i	−0.893198	+	0.648946i	−0.936710	−	0.350107i	$-0.886145\pi$
$761$	−24.6400	+	17.9020i	−0.893198	+	0.648946i	0.0435121	+	0.999053i	$0.486145\pi$
$762$		0			0
$763$	−0.0999185	−	0.630860i	−0.00361729	−	0.0228387i
$764$	−25.9534	+	16.6184i	−0.938962	+	0.601234i
$765$		0			0
$766$	−37.2296	−	28.7576i	−1.34516	−	1.03905i
$767$	−28.3997	−	14.4704i	−1.02545	−	0.522495i
$768$		0			0
$769$	34.1192	−	11.0860i	1.23037	−	0.399771i	0.379522	−	0.925183i	$-0.376089\pi$
$769$	34.1192	−	11.0860i	1.23037	−	0.399771i	0.850848	+	0.525411i	$0.176089\pi$
$770$	19.4773	+	13.5428i	0.701914	+	0.488047i
$771$		0			0
$772$	24.0547	−	10.5253i	0.865749	−	0.378815i
$773$	−3.98308	+	25.1482i	−0.143261	+	0.904517i	0.806430	+	0.591330i	$0.201397\pi$
$773$	−3.98308	+	25.1482i	−0.143261	+	0.904517i	−0.949691	+	0.313187i	$0.898603\pi$
$774$		0			0
$775$	25.0272	+	5.43609i	0.899003	+	0.195270i
$776$	0.501676	−	5.67513i	0.0180091	−	0.203725i
$777$		0			0
$778$	−25.2904	+	11.9634i	−0.906705	+	0.428909i
$779$	12.2830	−	37.8030i	0.440082	−	1.35443i
$780$		0			0
$781$	−13.6410	−	41.9826i	−0.488112	−	1.50225i
$782$	1.14603	+	1.21545i	0.0409819	+	0.0434645i
$783$		0			0
$784$	−14.7106	+	15.9218i	−0.525379	+	0.568636i
$785$	13.5148	−	7.76280i	0.482366	−	0.277066i
$786$		0			0
$787$	24.3154	−	3.85118i	0.866751	−	0.137280i	0.292804	−	0.956172i	$-0.405412\pi$
$787$	24.3154	−	3.85118i	0.866751	−	0.137280i	0.573947	+	0.818893i	$0.305412\pi$
$788$	41.3184	−	4.07473i	1.47191	−	0.145156i
$789$		0			0
$790$	−3.74459	+	3.90328i	−0.133226	+	0.138873i
$791$	−10.9413	+	15.0594i	−0.389028	+	0.535451i
$792$		0			0
$793$	0.336537	−	0.336537i	0.0119508	−	0.0119508i
$794$	−6.46405	−	22.0823i	−0.229400	−	0.783672i
$795$		0			0
$796$	−10.1275	−	3.96238i	−0.358961	−	0.140443i
$797$	3.79379	−	1.93303i	0.134383	−	0.0684714i	−0.385506	−	0.922705i	$-0.625973\pi$
$797$	3.79379	−	1.93303i	0.134383	−	0.0684714i	0.519889	+	0.854234i	$0.325973\pi$
$798$		0			0
$799$	−6.89752			−0.244017
$800$	28.1121	−	3.11637i	0.993912	−	0.110180i
$801$		0			0
$802$	0.296103	−	1.56950i	0.0104558	−	0.0554208i
$803$	−26.1547	+	13.3265i	−0.922979	+	0.470281i
$804$		0			0
$805$	1.71284	+	4.49191i	0.0603696	+	0.158319i
$806$	−6.67212	−	22.7931i	−0.235016	−	0.802854i
$807$		0			0
$808$	26.5512	−	42.4056i	0.934069	−	1.49182i
$809$	−1.67229	+	2.30171i	−0.0587947	+	0.0809240i	−0.837402	−	0.546588i	$-0.815927\pi$
$809$	−1.67229	+	2.30171i	−0.0587947	+	0.0809240i	0.778607	+	0.627512i	$0.215927\pi$
$810$		0			0
$811$	−24.4620	−	33.6690i	−0.858977	−	1.18228i	−0.981813	−	0.189853i	$-0.939199\pi$
$811$	−24.4620	−	33.6690i	−0.858977	−	1.18228i	0.122836	−	0.992427i	$-0.460801\pi$
$812$	−21.0693	+	2.07781i	−0.739388	+	0.0729167i
$813$		0			0
$814$	37.2721	+	54.6059i	1.30639	+	1.91394i
$815$	−17.0635	−	1.83180i	−0.597709	−	0.0641652i
$816$		0			0
$817$	−13.3850	+	26.2696i	−0.468283	+	0.919057i
$818$	−25.8732	−	27.4405i	−0.904636	−	0.959436i
$819$		0			0
$820$	−45.1375	+	14.2360i	−1.57627	+	0.497142i
$821$	0.0793176	−	0.244114i	0.00276820	−	0.00851965i	−0.949663	−	0.313274i	$-0.898574\pi$
$821$	0.0793176	−	0.244114i	0.00276820	−	0.00851965i	0.952431	+	0.304754i	$0.0985743\pi$
$822$		0			0
$823$	−42.5661	−	6.74181i	−1.48376	−	0.235005i	−0.638609	−	0.769531i	$-0.720490\pi$
$823$	−42.5661	−	6.74181i	−1.48376	−	0.235005i	−0.845152	+	0.534527i	$0.820490\pi$
$824$	0.455343	−	5.15100i	0.0158626	−	0.179444i
$825$		0			0
$826$	−0.507944	+	17.2780i	−0.0176736	+	0.601177i
$827$	−2.82535	+	17.8386i	−0.0982471	+	0.620308i	0.888604	+	0.458675i	$0.151676\pi$
$827$	−2.82535	+	17.8386i	−0.0982471	+	0.620308i	−0.986851	+	0.161632i	$0.948324\pi$
$828$		0			0
$829$	10.3078	+	3.34920i	0.358004	+	0.116323i	0.482496	−	0.875898i	$-0.339730\pi$
$829$	10.3078	+	3.34920i	0.358004	+	0.116323i	−0.124492	+	0.992221i	$0.539730\pi$
$830$	9.96596	−	7.56149i	0.345924	−	0.262463i
$831$		0			0
$832$	−15.0054	−	21.5125i	−0.520219	−	0.745813i
$833$	−3.33553	−	1.69954i	−0.115569	−	0.0588854i
$834$		0			0
$835$	−24.8334	+	27.4574i	−0.859397	+	0.950201i
$836$	37.7460	−	24.1694i	1.30547	−	0.835917i
$837$		0			0
$838$	−5.65739	+	0.726342i	−0.195431	+	0.0250911i
$839$	1.60565	−	1.16657i	0.0554332	−	0.0402746i	−0.559724	−	0.828679i	$-0.689093\pi$
$839$	1.60565	−	1.16657i	0.0554332	−	0.0402746i	0.615157	+	0.788405i	$0.289093\pi$
$840$		0			0
$841$	33.8921	+	24.6241i	1.16869	+	0.849106i
$842$	24.1534	+	13.2148i	0.832380	+	0.455411i
$843$		0			0
$844$	−5.22631	−	20.0180i	−0.179897	−	0.689049i
$845$	−0.252227	−	5.02651i	−0.00867686	−	0.172917i
$846$		0			0
$847$	−14.0431	−	27.5611i	−0.482526	−	0.947010i
$848$	−5.82921	+	20.6886i	−0.200176	+	0.710450i
$849$		0			0
$850$	1.83463	+	4.52689i	0.0629272	+	0.155271i
$851$			13.3978i			0.459272i
$852$		0			0
$853$	−15.2595	−	29.9484i	−0.522475	−	1.02542i	−0.989951	−	0.141410i	$-0.954837\pi$
$853$	−15.2595	−	29.9484i	−0.522475	−	1.02542i	0.467476	−	0.884006i	$-0.345163\pi$
$854$	−0.243022	−	0.0869374i	−0.00831603	−	0.00297494i
$855$		0			0
$856$	−1.19228	−	5.18570i	−0.0407513	−	0.177243i
$857$	7.61766	+	7.61766i	0.260214	+	0.260214i	0.825141	−	0.564927i	$-0.191096\pi$
$857$	7.61766	+	7.61766i	0.260214	+	0.260214i	−0.564927	+	0.825141i	$0.691096\pi$
$858$		0			0
$859$	−28.3958	−	20.6307i	−0.968851	−	0.703912i	−0.0136617	−	0.999907i	$-0.504349\pi$
$859$	−28.3958	−	20.6307i	−0.968851	−	0.703912i	−0.955189	+	0.295995i	$0.904349\pi$
$860$	34.7200	−	5.19192i	1.18394	−	0.177043i
$861$		0			0
$862$	4.67008	+	36.3747i	0.159064	+	1.23893i
$863$	6.01670	+	37.9879i	0.204811	+	1.29312i	0.849055	+	0.528305i	$0.177172\pi$
$863$	6.01670	+	37.9879i	0.204811	+	1.29312i	−0.644244	+	0.764820i	$0.722828\pi$
$864$		0			0
$865$	37.7606	+	16.9128i	1.28390	+	0.575052i
$866$	−18.7762	+	24.3077i	−0.638041	+	0.826008i
$867$		0			0
$868$	−9.62656	+	8.55653i	−0.326747	+	0.290427i
$869$	9.70668	−	3.15389i	0.329277	−	0.106988i
$870$		0			0
$871$	22.3983	+	7.27766i	0.758938	+	0.246594i
$872$	0.537082	+	1.33279i	0.0181879	+	0.0451340i
$873$		0			0
$874$	9.07899	+	0.266908i	0.307101	+	0.00902829i
$875$	−0.0937283	+	14.0561i	−0.00316859	+	0.475184i
$876$		0			0
$877$	34.6520	+	5.48833i	1.17011	+	0.185328i	0.711093	−	0.703098i	$-0.248200\pi$
$877$	34.6520	+	5.48833i	1.17011	+	0.185328i	0.459020	+	0.888426i	$0.348200\pi$
$878$	−6.60860	−	13.9704i	−0.223029	−	0.471480i
$879$		0			0
$880$	−49.5307	−	19.8741i	−1.66968	−	0.669956i
$881$	3.27970	+	10.0939i	0.110496	+	0.340072i	0.990981	−	0.134002i	$-0.0427830\pi$
$881$	3.27970	+	10.0939i	0.110496	+	0.340072i	−0.880485	+	0.474074i	$0.842783\pi$
$882$		0			0
$883$	3.48194	−	6.83369i	0.117177	−	0.229972i	−0.824968	−	0.565180i	$-0.808807\pi$
$883$	3.48194	−	6.83369i	0.117177	−	0.229972i	0.942144	+	0.335208i	$0.108807\pi$
$884$	2.87309	−	3.50176i	0.0966325	−	0.117777i
$885$		0			0
$886$	−19.2798	+	13.1597i	−0.647718	+	0.442110i
$887$	30.7208	−	4.86569i	1.03150	−	0.163374i	0.382339	−	0.924022i	$-0.375119\pi$
$887$	30.7208	−	4.86569i	1.03150	−	0.163374i	0.649164	+	0.760648i	$0.275119\pi$
$888$		0			0
$889$	1.64808	+	2.26838i	0.0552747	+	0.0760792i
$890$	−0.261557	−	1.45531i	−0.00876740	−	0.0487822i
$891$		0			0
$892$	4.72830	+	2.77051i	0.158315	+	0.0927636i
$893$	−26.5183	+	26.5183i	−0.887401	+	0.887401i
$894$		0			0
$895$	−24.8950	−	16.2458i	−0.832148	−	0.543036i
$896$	−7.06631	+	12.3448i	−0.236069	+	0.412409i
$897$		0			0
$898$	8.54101	+	1.61136i	0.285017	+	0.0537717i
$899$	43.1275			1.43838
$900$		0			0
$901$	−3.71191			−0.123662
$902$	87.7568	+	16.5563i	2.92198	+	0.551265i
$903$		0			0
$904$	16.3974	−	38.5331i	0.545370	−	1.28159i
$905$	−33.0772	+	1.65979i	−1.09952	+	0.0551732i
$906$		0			0
$907$	11.2357	−	11.2357i	0.373075	−	0.373075i	−0.495521	−	0.868596i	$-0.665023\pi$
$907$	11.2357	−	11.2357i	0.373075	−	0.373075i	0.868596	+	0.495521i	$0.165023\pi$
$908$	4.26648	−	7.28140i	0.141588	−	0.241642i
$909$		0			0
$910$	11.4890	−	6.15742i	0.380855	−	0.204116i
$911$	−9.83174	−	13.5322i	−0.325740	−	0.448343i	0.614469	−	0.788941i	$-0.289370\pi$
$911$	−9.83174	−	13.5322i	−0.325740	−	0.448343i	−0.940209	+	0.340598i	$0.889370\pi$
$912$		0			0
$913$	−23.3141	+	3.69258i	−0.771583	+	0.122207i
$914$	28.3023	−	19.3182i	0.936157	−	0.638988i
$915$		0			0
$916$	5.86808	+	4.81458i	0.193887	+	0.159078i
$917$	−1.63415	+	3.20721i	−0.0539645	+	0.105911i
$918$		0			0
$919$	7.63641	+	23.5025i	0.251902	+	0.775274i	0.994424	+	0.105453i	$0.0336293\pi$
$919$	7.63641	+	23.5025i	0.251902	+	0.775274i	−0.742522	+	0.669821i	$0.766371\pi$
$920$	−6.01972	−	8.98507i	−0.198464	−	0.296229i
$921$		0			0
$922$	−15.4006	−	32.5567i	−0.507193	−	1.07220i
$923$	−23.9566	−	3.79436i	−0.788542	−	0.124893i
$924$		0			0
$925$	−14.2012	+	36.5095i	−0.466933	+	1.20043i
$926$	9.62576	+	0.282982i	0.316322	+	0.00929937i
$927$		0			0
$928$	45.1470	−	15.1765i	1.48202	−	0.498191i
$929$	39.4625	+	12.8221i	1.29472	+	0.420681i	0.873743	−	0.486389i	$-0.161686\pi$
$929$	39.4625	+	12.8221i	1.29472	+	0.420681i	0.420981	+	0.907070i	$0.361686\pi$
$930$		0			0
$931$	−19.3579	+	6.28975i	−0.634429	+	0.206138i
$932$	−24.3494	−	27.3944i	−0.797591	−	0.897333i
$933$		0			0
$934$	−18.5783	+	24.0515i	−0.607902	+	0.786990i
$935$	0.983763	−	9.16390i	0.0321725	−	0.299692i
$936$		0			0
$937$	3.66513	+	23.1407i	0.119734	+	0.755974i	0.972366	+	0.233461i	$0.0750052\pi$
$937$	3.66513	+	23.1407i	0.119734	+	0.755974i	−0.852632	+	0.522513i	$0.824995\pi$
$938$	−1.62641	−	12.6679i	−0.0531043	−	0.413623i
$939$		0			0
$940$	44.0432	+	7.36650i	1.43653	+	0.240269i
$941$	−1.45471	−	1.05691i	−0.0474222	−	0.0344543i	0.563822	−	0.825897i	$-0.309331\pi$
$941$	−1.45471	−	1.05691i	−0.0474222	−	0.0344543i	−0.611244	+	0.791442i	$0.709331\pi$
$942$		0			0
$943$	12.7969	+	12.7969i	0.416724	+	0.416724i
$944$	−7.59601	−	38.1379i	−0.247229	−	1.24128i
$945$		0			0
$946$	−62.3703	−	22.3121i	−2.02783	−	0.725428i
$947$	15.2838	+	29.9961i	0.496656	+	0.974742i	0.994225	+	0.107317i	$0.0342261\pi$
$947$	15.2838	+	29.9961i	0.496656	+	0.974742i	−0.497569	+	0.867424i	$0.665774\pi$
$948$		0			0
$949$			16.1292i			0.523575i
$950$	24.4576	+	10.3507i	0.793509	+	0.335822i
$951$		0			0
$952$	−2.38292	−	0.596416i	−0.0772309	−	0.0193299i
$953$	−25.0799	−	49.2221i	−0.812418	−	1.59446i	−0.804100	−	0.594494i	$-0.797352\pi$
$953$	−25.0799	−	49.2221i	−0.812418	−	1.59446i	−0.00831782	−	0.999965i	$-0.502648\pi$
$954$		0			0
$955$	21.6241	+	26.8252i	0.699739	+	0.868043i
$956$	21.5517	−	5.62673i	0.697033	−	0.181981i
$957$		0			0
$958$	−33.5754	−	18.3697i	−1.08477	−	0.593499i
$959$	−0.618234	−	0.449173i	−0.0199638	−	0.0145046i
$960$		0			0
$961$	−3.85379	+	2.79994i	−0.124316	+	0.0903206i
$962$	36.0317	−	4.62604i	1.16171	−	0.149150i
$963$		0			0
$964$	−14.0420	−	21.9298i	−0.452264	−	0.706312i
$965$	−14.6214	−	25.4555i	−0.470679	−	0.819441i
$966$		0			0
$967$	15.5980	+	7.94759i	0.501599	+	0.255577i	0.686434	−	0.727192i	$-0.259175\pi$
$967$	15.5980	+	7.94759i	0.501599	+	0.255577i	−0.184835	+	0.982770i	$0.559175\pi$
$968$	44.6827	+	53.3486i	1.43616	+	1.71469i
$969$		0			0
$970$	−6.36836	+	0.132145i	−0.204476	+	0.00424292i
$971$	35.6648	+	11.5882i	1.14454	+	0.371883i	0.819083	−	0.573675i	$-0.194483\pi$
$971$	35.6648	+	11.5882i	1.14454	+	0.371883i	0.325455	+	0.945558i	$0.394483\pi$
$972$		0			0
$973$	3.89495	−	24.5917i	0.124866	−	0.788375i
$974$	−0.0797568	+	2.71296i	−0.00255557	+	0.0869290i
$975$		0			0
$976$	0.576648	+	0.0681047i	0.0184581	+	0.00217998i
$977$	−7.65446	−	1.21235i	−0.244888	−	0.0387864i	0.0327839	−	0.999462i	$-0.489563\pi$
$977$	−7.65446	−	1.21235i	−0.244888	−	0.0387864i	−0.277672	+	0.960676i	$0.589563\pi$
$978$		0			0
$979$	−0.862160	+	2.65345i	−0.0275547	+	0.0848048i
$980$	19.4835	+	14.4145i	0.622377	+	0.460454i
$981$		0			0
$982$	37.4980	+	39.7695i	1.19661	+	1.26910i
$983$	19.4382	−	38.1495i	0.619981	−	1.21678i	−0.340973	−	0.940073i	$-0.610756\pi$
$983$	19.4382	−	38.1495i	0.619981	−	1.21678i	0.960954	−	0.276708i	$-0.0892436\pi$
$984$		0			0
$985$	−9.55022	−	45.4265i	−0.304295	−	1.44741i
$986$	4.63711	+	6.79365i	0.147676	+	0.216354i
$987$		0			0
$988$	−2.41700	−	24.5089i	−0.0768951	−	0.779730i
$989$	−7.89024	−	10.8600i	−0.250895	−	0.345327i
$990$		0			0
$991$	−10.1381	+	13.9539i	−0.322047	+	0.443259i	−0.939091	−	0.343670i	$-0.888330\pi$
$991$	−10.1381	+	13.9539i	−0.322047	+	0.443259i	0.617044	+	0.786929i	$0.288330\pi$
$992$	16.7929	−	23.6128i	0.533175	−	0.749707i
$993$		0			0
$994$	3.69539	+	12.6241i	0.117211	+	0.400412i
$995$	−3.17301	+	11.7374i	−0.100591	+	0.372101i
$996$		0			0
$997$	14.8156	−	7.54891i	0.469214	−	0.239076i	−0.203363	−	0.979103i	$-0.565187\pi$
$997$	14.8156	−	7.54891i	0.469214	−	0.239076i	0.672577	+	0.740027i	$0.265187\pi$
$998$	−1.64697	+	8.72976i	−0.0521339	+	0.276336i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.127.14		240
3.2	odd	2		300.2.w.a.127.17	yes	240
4.3	odd	2	inner	900.2.bj.f.127.17		240
12.11	even	2		300.2.w.a.127.14	✓	240
25.13	odd	20	inner	900.2.bj.f.163.17		240
75.38	even	20		300.2.w.a.163.14	yes	240
100.63	even	20	inner	900.2.bj.f.163.14		240
300.263	odd	20		300.2.w.a.163.17	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.14	✓	240	12.11	even	2
300.2.w.a.127.17	yes	240	3.2	odd	2
300.2.w.a.163.14	yes	240	75.38	even	20
300.2.w.a.163.17	yes	240	300.263	odd	20
900.2.bj.f.127.14		240	1.1	even	1	trivial
900.2.bj.f.127.17		240	4.3	odd	2	inner
900.2.bj.f.163.14		240	100.63	even	20	inner
900.2.bj.f.163.17		240	25.13	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.262182 + 1.38970i) q^{2} +(-1.86252 - 0.728708i) q^{4} +(-0.583536 + 2.15858i) q^{5} +(-0.889008 + 0.889008i) q^{7} +(1.50100 - 2.39729i) q^{8} +O(q^{10})\)	\(q+(-0.262182 + 1.38970i) q^{2} +(-1.86252 - 0.728708i) q^{4} +(-0.583536 + 2.15858i) q^{5} +(-0.889008 + 0.889008i) q^{7} +(1.50100 - 2.39729i) q^{8} +(-2.84679 - 1.37688i) q^{10} +(3.50723 + 4.82729i) q^{11} +(3.23824 - 0.512887i) q^{13} +(-1.00237 - 1.46853i) q^{14} +(2.93797 + 2.71447i) q^{16} +(-0.313606 + 0.615487i) q^{17} +(1.16061 + 3.57200i) q^{19} +(2.65983 - 3.59518i) q^{20} +(-7.62801 + 3.60836i) q^{22} +(-1.68898 - 0.267508i) q^{23} +(-4.31897 - 2.51922i) q^{25} +(-0.136251 + 4.63464i) q^{26} +(2.30362 - 1.00797i) q^{28} +(-8.00770 - 2.60186i) q^{29} +(-4.87146 + 1.58283i) q^{31} +(-4.54257 + 3.37120i) q^{32} +(-0.773119 - 0.597187i) q^{34} +(-1.40023 - 2.43777i) q^{35} +(-1.22564 - 7.73839i) q^{37} +(-5.26830 + 0.676388i) q^{38} +(4.29886 + 4.63895i) q^{40} +(-8.56195 - 6.22062i) q^{41} +(5.55076 + 5.55076i) q^{43} +(-3.01461 - 11.5467i) q^{44} +(0.814576 - 2.27704i) q^{46} +(4.53317 + 8.89684i) q^{47} +5.41933i q^{49} +(4.63332 - 5.34157i) q^{50} +(-6.40503 - 1.40447i) q^{52} +(2.43953 + 4.78785i) q^{53} +(-12.4667 + 4.75375i) q^{55} +(0.796803 + 3.46561i) q^{56} +(5.71528 - 10.4461i) q^{58} +(-7.86506 - 5.71430i) q^{59} +(0.117440 - 0.0853253i) q^{61} +(-0.922450 - 7.18485i) q^{62} +(-3.49397 - 7.19668i) q^{64} +(-0.782521 + 7.28930i) q^{65} +(6.40031 + 3.26112i) q^{67} +(1.03261 - 0.917829i) q^{68} +(3.75487 - 1.30676i) q^{70} +(-7.03596 - 2.28612i) q^{71} +(-0.769583 + 4.85896i) q^{73} +(11.0754 + 0.325598i) q^{74} +(0.441280 - 7.49868i) q^{76} +(-7.40945 - 1.17354i) q^{77} +(0.528568 - 1.62677i) q^{79} +(-7.57382 + 4.75786i) q^{80} +(10.8896 - 10.2676i) q^{82} +(-1.79597 + 3.52479i) q^{83} +(-1.14558 - 1.03610i) q^{85} +(-9.16918 + 6.25856i) q^{86} +(16.8368 - 1.16206i) q^{88} +(0.274839 + 0.378283i) q^{89} +(-2.42286 + 3.33478i) q^{91} +(2.95083 + 1.72901i) q^{92} +(-13.5524 + 3.96714i) q^{94} +(-8.38773 + 0.420890i) q^{95} +(1.79474 - 0.914467i) q^{97} +(-7.53123 - 1.42085i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 240 * q - 12 * q^8	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Introduction

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