LMFDB - Embedded newform 666.2.bs.b.35.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(17,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

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

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

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			35.1
Character	$\chi$	$=$	666.35
Dual form			666.2.bs.b.647.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-1.84075 + 3.94750i) q^{5} +(-3.67900 + 1.33905i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})$	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-1.84075 + 3.94750i) q^{5} +(-3.67900 + 1.33905i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.17779 - 3.77205i) q^{10} +(2.86818 + 4.96784i) q^{11} +(1.89482 - 1.32677i) q^{13} +(3.78171 - 1.01331i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-3.36098 - 2.35339i) q^{17} +(-0.289320 - 3.30694i) q^{19} +(-2.49826 + 3.56788i) q^{20} +(-2.42429 - 5.19892i) q^{22} +(-1.45306 - 5.42289i) q^{23} +(-8.98045 - 10.7025i) q^{25} +(-2.00324 + 1.15657i) q^{26} +(-3.85563 + 0.679852i) q^{28} +(-1.08112 + 4.03480i) q^{29} +(-2.05220 + 2.05220i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(3.14308 + 2.63736i) q^{34} +(1.48623 - 16.9877i) q^{35} +(5.51857 + 2.55839i) q^{37} +3.31957i q^{38} +(2.79971 - 3.33657i) q^{40} +(-0.194339 + 1.10215i) q^{41} +(1.69966 + 1.69966i) q^{43} +(1.96195 + 5.39042i) q^{44} +(0.974893 + 5.52889i) q^{46} +(-5.78943 - 3.34253i) q^{47} +(6.37970 - 5.35320i) q^{49} +(8.01350 + 11.4445i) q^{50} +(2.09642 - 0.977578i) q^{52} +(1.63084 - 4.48070i) q^{53} +(-24.8902 + 2.17761i) q^{55} +(3.90021 - 0.341225i) q^{56} +(1.42866 - 3.92522i) q^{58} +(-4.06356 + 1.89487i) q^{59} +(4.71983 + 6.74061i) q^{61} +(2.22326 - 1.86553i) q^{62} +(0.866025 + 0.500000i) q^{64} +(1.74952 + 9.92203i) q^{65} +(-1.07909 - 2.96478i) q^{67} +(-2.90126 - 2.90126i) q^{68} +(-2.96115 + 16.7935i) q^{70} +(-8.12409 + 9.68192i) q^{71} +2.97976i q^{73} +(-5.27459 - 3.02963i) q^{74} +(0.289320 - 3.30694i) q^{76} +(-17.2042 - 14.4361i) q^{77} +(-1.74384 - 0.813164i) q^{79} +(-3.07986 + 3.07986i) q^{80} +(0.289659 - 1.08102i) q^{82} +(4.73697 - 0.835255i) q^{83} +(15.4767 - 8.93549i) q^{85} +(-1.54506 - 1.84133i) q^{86} +(-1.48468 - 5.54091i) q^{88} +(-6.34470 - 13.6062i) q^{89} +(-5.19444 + 7.41842i) q^{91} +(-0.489308 - 5.59282i) q^{92} +(5.47608 + 3.83439i) q^{94} +(13.5867 + 4.94515i) q^{95} +(0.604645 - 0.162014i) q^{97} +(-6.82198 + 4.77680i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) $ 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{19}{36}\right)$

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 $

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$		0			0
$3$		0			0
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−1.84075	+	3.94750i	−0.823208	+	1.76538i	−0.206040	+	0.978544i	$0.566058\pi$
$5$	−1.84075	+	3.94750i	−0.823208	+	1.76538i	−0.617168	+	0.786832i	$0.711720\pi$
$6$		0			0
$7$	−3.67900	+	1.33905i	−1.39053	+	0.506112i	−0.925354	−	0.379105i	$-0.876232\pi$
$7$	−3.67900	+	1.33905i	−1.39053	+	0.506112i	−0.465178	+	0.885217i	$0.654010\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$		0			0
$10$	2.17779	−	3.77205i	0.688678	−	1.19283i
$11$	2.86818	+	4.96784i	0.864790	+	1.49786i	0.867255	+	0.497864i	$0.165882\pi$
$11$	2.86818	+	4.96784i	0.864790	+	1.49786i	−0.00246513	+	0.999997i	$0.500785\pi$
$12$		0			0
$13$	1.89482	−	1.32677i	0.525528	−	0.367979i	−0.280502	−	0.959853i	$-0.590501\pi$
$13$	1.89482	−	1.32677i	0.525528	−	0.367979i	0.806030	+	0.591875i	$0.201612\pi$
$14$	3.78171	−	1.01331i	1.01070	−	0.270817i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−3.36098	−	2.35339i	−0.815158	−	0.570780i	0.0899572	−	0.995946i	$-0.471327\pi$
$17$	−3.36098	−	2.35339i	−0.815158	−	0.570780i	−0.905116	+	0.425166i	$0.860216\pi$
$18$		0			0
$19$	−0.289320	−	3.30694i	−0.0663745	−	0.758664i	−0.954334	−	0.298742i	$-0.903433\pi$
$19$	−0.289320	−	3.30694i	−0.0663745	−	0.758664i	0.887959	−	0.459922i	$-0.152123\pi$
$20$	−2.49826	+	3.56788i	−0.558628	+	0.797803i
$21$		0			0
$22$	−2.42429	−	5.19892i	−0.516861	−	1.10841i
$23$	−1.45306	−	5.42289i	−0.302983	−	1.13075i	−0.934667	−	0.355524i	$-0.884303\pi$
$23$	−1.45306	−	5.42289i	−0.302983	−	1.13075i	0.631684	−	0.775226i	$-0.282364\pi$
$24$		0			0
$25$	−8.98045	−	10.7025i	−1.79609	−	2.14050i
$26$	−2.00324	+	1.15657i	−0.392868	+	0.226823i
$27$		0			0
$28$	−3.85563	+	0.679852i	−0.728646	+	0.128480i
$29$	−1.08112	+	4.03480i	−0.200759	+	0.749244i	0.789941	+	0.613183i	$0.210111\pi$
$29$	−1.08112	+	4.03480i	−0.200759	+	0.749244i	−0.990700	+	0.136061i	$0.956556\pi$
$30$		0			0
$31$	−2.05220	+	2.05220i	−0.368587	+	0.368587i	−0.866962	−	0.498375i	$-0.833930\pi$
$31$	−2.05220	+	2.05220i	−0.368587	+	0.368587i	0.498375	+	0.866962i	$0.333930\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$		0			0
$34$	3.14308	+	2.63736i	0.539034	+	0.452304i
$35$	1.48623	−	16.9877i	0.251219	−	2.87145i
$36$		0			0
$37$	5.51857	+	2.55839i	0.907248	+	0.420597i
$37$	5.51857	+	2.55839i	0.907248	+	0.420597i
$38$			3.31957i			0.538505i
$39$		0			0
$40$	2.79971	−	3.33657i	0.442674	−	0.527558i
$41$	−0.194339	+	1.10215i	−0.0303507	+	0.172127i	−0.996215	−	0.0869202i	$-0.972297\pi$
$41$	−0.194339	+	1.10215i	−0.0303507	+	0.172127i	0.965865	+	0.259047i	$0.0834086\pi$
$42$		0			0
$43$	1.69966	+	1.69966i	0.259196	+	0.259196i	0.824727	−	0.565531i	$-0.191329\pi$
$43$	1.69966	+	1.69966i	0.259196	+	0.259196i	−0.565531	+	0.824727i	$0.691329\pi$
$44$	1.96195	+	5.39042i	0.295776	+	0.812637i
$45$		0			0
$46$	0.974893	+	5.52889i	0.143740	+	0.815191i
$47$	−5.78943	−	3.34253i	−0.844475	−	0.487558i	0.0143076	−	0.999898i	$-0.495446\pi$
$47$	−5.78943	−	3.34253i	−0.844475	−	0.487558i	−0.858783	+	0.512340i	$0.828779\pi$
$48$		0			0
$49$	6.37970	−	5.35320i	0.911385	−	0.764743i
$50$	8.01350	+	11.4445i	1.13328	+	1.61849i
$51$		0			0
$52$	2.09642	−	0.977578i	0.290721	−	0.135566i
$53$	1.63084	−	4.48070i	0.224013	−	0.615471i	−0.775868	−	0.630896i	$-0.782688\pi$
$53$	1.63084	−	4.48070i	0.224013	−	0.615471i	0.999881	+	0.0154242i	$0.00490987\pi$
$54$		0			0
$55$	−24.8902	+	2.17761i	−3.35619	+	0.293628i
$56$	3.90021	−	0.341225i	0.521188	−	0.0455980i
$57$		0			0
$58$	1.42866	−	3.92522i	0.187593	−	0.515407i
$59$	−4.06356	+	1.89487i	−0.529031	+	0.246691i	−0.668733	−	0.743502i	$-0.733163\pi$
$59$	−4.06356	+	1.89487i	−0.529031	+	0.246691i	0.139702	+	0.990194i	$0.455385\pi$
$60$		0			0
$61$	4.71983	+	6.74061i	0.604312	+	0.863047i	0.998430	−	0.0560127i	$-0.0178387\pi$
$61$	4.71983	+	6.74061i	0.604312	+	0.863047i	−0.394118	+	0.919060i	$0.628950\pi$
$62$	2.22326	−	1.86553i	0.282354	−	0.236923i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	1.74952	+	9.92203i	0.217002	+	1.23068i
$66$		0			0
$67$	−1.07909	−	2.96478i	−0.131832	−	0.362205i	0.856160	−	0.516711i	$-0.172844\pi$
$67$	−1.07909	−	2.96478i	−0.131832	−	0.362205i	−0.987992	+	0.154506i	$0.950621\pi$
$68$	−2.90126	−	2.90126i	−0.351830	−	0.351830i
$69$		0			0
$70$	−2.96115	+	16.7935i	−0.353925	+	2.00721i
$71$	−8.12409	+	9.68192i	−0.964152	+	1.14903i	0.0246342	+	0.999697i	$0.492158\pi$
$71$	−8.12409	+	9.68192i	−0.964152	+	1.14903i	−0.988787	+	0.149335i	$0.952287\pi$
$72$		0			0
$73$			2.97976i			0.348755i	0.984679	+	0.174377i	$0.0557913\pi$
$73$			2.97976i			0.348755i	−0.984679	+	0.174377i	$0.944209\pi$
$74$	−5.27459	−	3.02963i	−0.613159	−	0.352188i
$75$		0			0
$76$	0.289320	−	3.30694i	0.0331872	−	0.379332i
$77$	−17.2042	−	14.4361i	−1.96060	−	1.64514i
$78$		0			0
$79$	−1.74384	−	0.813164i	−0.196197	−	0.0914882i	0.322037	−	0.946727i	$-0.395633\pi$
$79$	−1.74384	−	0.813164i	−0.196197	−	0.0914882i	−0.518234	+	0.855239i	$0.673410\pi$
$80$	−3.07986	+	3.07986i	−0.344339	+	0.344339i
$81$		0			0
$82$	0.289659	−	1.08102i	0.0319874	−	0.119379i
$83$	4.73697	−	0.835255i	0.519949	−	0.0916811i	0.0924864	−	0.995714i	$-0.470519\pi$
$83$	4.73697	−	0.835255i	0.519949	−	0.0916811i	0.427463	+	0.904033i	$0.359407\pi$
$84$		0			0
$85$	15.4767	−	8.93549i	1.67869	−	0.969190i
$86$	−1.54506	−	1.84133i	−0.166608	−	0.198556i
$87$		0			0
$88$	−1.48468	−	5.54091i	−0.158268	−	0.590663i
$89$	−6.34470	−	13.6062i	−0.672537	−	1.44226i	−0.885236	−	0.465142i	$-0.846003\pi$
$89$	−6.34470	−	13.6062i	−0.672537	−	1.44226i	0.212700	−	0.977118i	$-0.431774\pi$
$90$		0			0
$91$	−5.19444	+	7.41842i	−0.544525	+	0.777662i
$92$	−0.489308	−	5.59282i	−0.0510139	−	0.583092i
$93$		0			0
$94$	5.47608	+	3.83439i	0.564815	+	0.395487i
$95$	13.5867	+	4.94515i	1.39397	+	0.507362i
$96$		0			0
$97$	0.604645	−	0.162014i	0.0613924	−	0.0164500i	−0.227992	−	0.973663i	$-0.573216\pi$
$97$	0.604645	−	0.162014i	0.0613924	−	0.0164500i	0.289385	+	0.957213i	$0.406549\pi$
$98$	−6.82198	+	4.77680i	−0.689124	+	0.482530i
$99$		0			0
$100$	−6.98555	−	12.0993i	−0.698555	−	1.20993i
$101$	−3.36300	+	5.82488i	−0.334631	+	0.579597i	−0.983414	−	0.181376i	$-0.941945\pi$
$101$	−3.36300	+	5.82488i	−0.334631	+	0.579597i	0.648783	+	0.760973i	$0.275278\pi$
$102$		0			0
$103$	−8.74752	−	2.34389i	−0.861918	−	0.230950i	−0.199328	−	0.979933i	$-0.563876\pi$
$103$	−8.74752	−	2.34389i	−0.861918	−	0.230950i	−0.662590	+	0.748982i	$0.730543\pi$
$104$	−2.17365	+	0.791142i	−0.213144	+	0.0775779i
$105$		0			0
$106$	−2.01515	+	4.32151i	−0.195729	+	0.419742i
$107$	−18.3954	−	3.24361i	−1.77835	−	0.313572i	−0.814532	−	0.580118i	$-0.803006\pi$
$107$	−18.3954	−	3.24361i	−1.77835	−	0.313572i	−0.963822	+	0.266546i	$0.914117\pi$
$108$		0			0
$109$	3.10795	+	0.271910i	0.297688	+	0.0260443i	0.235021	−	0.971990i	$-0.424484\pi$
$109$	3.10795	+	0.271910i	0.297688	+	0.0260443i	0.0626664	+	0.998035i	$0.480040\pi$
$110$	24.9852			2.38225
$111$		0			0
$112$	−3.91511			−0.369943
$113$	4.70645	+	0.411761i	0.442746	+	0.0387352i	0.306349	−	0.951919i	$-0.400892\pi$
$113$	4.70645	+	0.411761i	0.442746	+	0.0387352i	0.136396	+	0.990654i	$0.456448\pi$
$114$		0			0
$115$	24.0815	+	4.24623i	2.24562	+	0.395963i
$116$	−1.76533	+	3.78577i	−0.163907	+	0.351500i
$117$		0			0
$118$	4.21325	−	1.53350i	0.387861	−	0.141170i
$119$	15.5164	+	4.15760i	1.42238	+	0.381126i
$120$		0			0
$121$	−10.9530	+	18.9711i	−0.995724	+	1.72464i
$122$	−4.11439	−	7.12632i	−0.372499	−	0.645187i
$123$		0			0
$124$	−2.37739	+	1.66466i	−0.213496	+	0.149491i
$125$	37.7430	−	10.1132i	3.37583	−	0.904552i
$126$		0			0
$127$	1.18049	+	0.429662i	0.104751	+	0.0381263i	0.393864	−	0.919169i	$-0.371138\pi$
$127$	1.18049	+	0.429662i	0.104751	+	0.0381263i	−0.289113	+	0.957295i	$0.593360\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$		0			0
$130$	−0.878103	−	10.0368i	−0.0770147	−	0.880282i
$131$	8.00831	−	11.4371i	0.699690	−	0.999260i	−0.299293	−	0.954161i	$-0.596751\pi$
$131$	8.00831	−	11.4371i	0.699690	−	0.999260i	0.998983	−	0.0450991i	$-0.0143604\pi$
$132$		0			0
$133$	5.49255	+	11.7788i	0.476265	+	1.02135i
$134$	0.816587	+	3.04754i	0.0705423	+	0.263268i
$135$		0			0
$136$	2.63736	+	3.14308i	0.226152	+	0.269517i
$137$	15.4661	−	8.92937i	1.32136	−	0.762887i	0.337414	−	0.941356i	$-0.390448\pi$
$137$	15.4661	−	8.92937i	1.32136	−	0.762887i	0.983946	+	0.178469i	$0.0571144\pi$
$138$		0			0
$139$	−15.1475	+	2.67091i	−1.28479	+	0.226544i	−0.774014	−	0.633168i	$-0.781754\pi$
$139$	−15.1475	+	2.67091i	−1.28479	+	0.226544i	−0.510779	+	0.859712i	$0.670643\pi$
$140$	4.41354	−	16.4715i	0.373012	−	1.39210i
$141$		0			0
$142$	8.93701	−	8.93701i	0.749977	−	0.749977i
$143$	12.0259	+	5.60775i	1.00565	+	0.468943i
$144$		0			0
$145$	−13.9373	−	11.6948i	−1.15743	−	0.971199i
$146$	0.259704	−	2.96842i	0.0214932	−	0.245669i
$147$		0			0
$148$	4.99047	+	3.47781i	0.410214	+	0.285875i
$149$			13.4177i			1.09922i	0.835420	+	0.549612i	$0.185224\pi$
$149$			13.4177i			1.09922i	−0.835420	+	0.549612i	$0.814776\pi$
$150$		0			0
$151$	−3.99383	+	4.75966i	−0.325013	+	0.387336i	−0.903666	−	0.428238i	$-0.859134\pi$
$151$	−3.99383	+	4.75966i	−0.325013	+	0.387336i	0.578652	+	0.815574i	$0.303579\pi$
$152$	−0.576437	+	3.26914i	−0.0467552	+	0.265162i
$153$		0			0
$154$	15.8806	+	15.8806i	1.27969	+	1.27969i
$155$	−4.32348	−	11.8787i	−0.347270	−	0.954117i
$156$		0			0
$157$	4.02699	+	22.8382i	0.321389	+	1.82269i	0.533924	+	0.845532i	$0.320717\pi$
$157$	4.02699	+	22.8382i	0.321389	+	1.82269i	−0.212536	+	0.977153i	$0.568172\pi$
$158$	1.66633	+	0.962056i	0.132566	+	0.0765370i
$159$		0			0
$160$	3.33657	−	2.79971i	0.263779	−	0.221337i
$161$	12.6073	+	18.0051i	0.993595	+	1.41900i
$162$		0			0
$163$	−7.11810	+	3.31922i	−0.557533	+	0.259982i	−0.680896	−	0.732380i	$-0.738410\pi$
$163$	−7.11810	+	3.31922i	−0.557533	+	0.259982i	0.123364	+	0.992362i	$0.460632\pi$
$164$	−0.382773	+	1.05166i	−0.0298896	+	0.0821210i
$165$		0			0
$166$	−4.79174	+	0.419223i	−0.371911	+	0.0325380i
$167$	−0.0516878	+	0.00452210i	−0.00399972	+	0.000349930i	−0.0891554	−	0.996018i	$-0.528417\pi$
$167$	−0.0516878	+	0.00452210i	−0.00399972	+	0.000349930i	0.0851557	+	0.996368i	$0.472861\pi$
$168$		0			0
$169$	−2.61623	+	7.18804i	−0.201249	+	0.552927i
$170$	−16.1966	+	7.55260i	−1.24222	+	0.579258i
$171$		0			0
$172$	1.37870	+	1.96898i	0.105125	+	0.150134i
$173$	−16.5969	+	13.9264i	−1.26184	+	1.05881i	−0.266351	+	0.963876i	$0.585818\pi$
$173$	−16.5969	+	13.9264i	−1.26184	+	1.05881i	−0.995484	+	0.0949295i	$0.969737\pi$
$174$		0			0
$175$	47.3702	+	27.3492i	3.58085	+	2.06741i
$176$	0.996110	+	5.64922i	0.0750846	+	0.425826i
$177$		0			0
$178$	5.13469	+	14.1074i	0.384861	+	1.05740i
$179$	−16.3531	−	16.3531i	−1.22229	−	1.22229i	−0.966817	−	0.255468i	$-0.917770\pi$
$179$	−16.3531	−	16.3531i	−1.22229	−	1.22229i	−0.255468	−	0.966817i	$-0.582230\pi$
$180$		0			0
$181$	2.66835	−	15.1330i	0.198337	−	1.12483i	−0.709249	−	0.704958i	$-0.750966\pi$
$181$	2.66835	−	15.1330i	0.198337	−	1.12483i	0.907586	−	0.419867i	$-0.137923\pi$
$182$	5.82123	−	6.93747i	0.431498	−	0.514240i
$183$		0			0
$184$			5.61418i			0.413883i
$185$	−20.2576	+	17.0752i	−1.48937	+	1.25539i
$186$		0			0
$187$	2.05133	−	23.4468i	0.150008	−	1.71460i
$188$	−5.12105	−	4.29707i	−0.373491	−	0.313396i
$189$		0			0
$190$	−13.1040	−	6.11049i	−0.950664	−	0.443302i
$191$	−3.99095	+	3.99095i	−0.288775	+	0.288775i	−0.836596	−	0.547821i	$-0.815458\pi$
$191$	−3.99095	+	3.99095i	−0.288775	+	0.288775i	0.547821	+	0.836596i	$0.315458\pi$
$192$		0			0
$193$	2.74950	−	10.2613i	0.197913	−	0.738622i	−0.793580	−	0.608466i	$-0.791785\pi$
$193$	2.74950	−	10.2613i	0.197913	−	0.738622i	0.991493	−	0.130157i	$-0.0415480\pi$
$194$	−0.616465	+	0.108699i	−0.0442596	+	0.00780416i
$195$		0			0
$196$	7.21235	−	4.16405i	0.515168	−	0.297432i
$197$	16.8099	+	20.0333i	1.19766	+	1.42731i	0.877249	+	0.480036i	$0.159376\pi$
$197$	16.8099	+	20.0333i	1.19766	+	1.42731i	0.320410	+	0.947279i	$0.396179\pi$
$198$		0			0
$199$	−2.85814	−	10.6667i	−0.202608	−	0.756144i	−0.990165	−	0.139903i	$-0.955321\pi$
$199$	−2.85814	−	10.6667i	−0.202608	−	0.756144i	0.787557	−	0.616242i	$-0.211346\pi$
$200$	5.90444	+	12.6621i	0.417507	+	0.895347i
$201$		0			0
$202$	3.85787	−	5.50961i	0.271439	−	0.387655i
$203$	−1.42534	−	16.2917i	−0.100039	−	1.14345i
$204$		0			0
$205$	−3.99301	−	2.79594i	−0.278884	−	0.195277i
$206$	8.50995	+	3.09737i	0.592916	+	0.215804i
$207$		0			0
$208$	2.23433	−	0.598686i	0.154923	−	0.0415114i
$209$	15.5985	−	10.9222i	1.07897	−	0.755505i
$210$		0			0
$211$	8.94870	+	15.4996i	0.616054	+	1.06704i	0.990199	+	0.139667i	$0.0446031\pi$
$211$	8.94870	+	15.4996i	0.616054	+	1.06704i	−0.374144	+	0.927370i	$0.622064\pi$
$212$	2.38413	−	4.12943i	0.163743	−	0.283611i
$213$		0			0
$214$	18.0427	+	4.83454i	1.23338	+	0.330482i
$215$	−9.83807	+	3.58076i	−0.670951	+	0.244206i
$216$		0			0
$217$	4.80206	−	10.2981i	0.325985	−	0.699078i
$218$	−3.07243	−	0.541751i	−0.208091	−	0.0366920i
$219$		0			0
$220$	−24.8902	−	2.17761i	−1.67809	−	0.146814i
$221$	−9.49085			−0.638423
$222$		0			0
$223$	−0.702379			−0.0470348			−0.0235174	−	0.999723i	$-0.507487\pi$
$223$	−0.702379			−0.0470348			−0.0235174	+	0.999723i	$0.507487\pi$
$224$	3.90021	+	0.341225i	0.260594	+	0.0227990i
$225$		0			0
$226$	−4.65265	−	0.820388i	−0.309490	−	0.0545714i
$227$	−9.86083	+	21.1466i	−0.654486	+	1.40355i	0.246260	+	0.969204i	$0.420798\pi$
$227$	−9.86083	+	21.1466i	−0.654486	+	1.40355i	−0.900746	+	0.434346i	$0.856979\pi$
$228$		0			0
$229$	−19.7156	+	7.17590i	−1.30284	+	0.474197i	−0.897922	−	0.440154i	$-0.854924\pi$
$229$	−19.7156	+	7.17590i	−1.30284	+	0.474197i	−0.404922	+	0.914351i	$0.632701\pi$
$230$	−23.6198	−	6.32891i	−1.55745	−	0.417316i
$231$		0			0
$232$	2.08857	−	3.61750i	0.137121	−	0.237501i
$233$	−4.49339	−	7.78278i	−0.294372	−	0.509867i	0.680467	−	0.732779i	$-0.261777\pi$
$233$	−4.49339	−	7.78278i	−0.294372	−	0.509867i	−0.974839	+	0.222912i	$0.928444\pi$
$234$		0			0
$235$	23.8515	−	16.7010i	1.55590	−	1.08945i
$236$	−4.33087	+	1.16045i	−0.281916	+	0.0755390i
$237$		0			0
$238$	−15.0950	−	5.49412i	−0.978461	−	0.356131i
$239$	−0.261773	−	0.183295i	−0.0169327	−	0.0118564i	0.565079	−	0.825036i	$-0.308846\pi$
$239$	−0.261773	−	0.183295i	−0.0169327	−	0.0118564i	−0.582012	+	0.813180i	$0.697734\pi$
$240$		0			0
$241$	0.0536205	+	0.612886i	0.00345400	+	0.0394794i	0.997726	−	0.0673989i	$-0.0214700\pi$
$241$	0.0536205	+	0.612886i	0.00345400	+	0.0394794i	−0.994272	+	0.106878i	$0.965914\pi$
$242$	12.5647	−	17.9443i	0.807691	−	1.15350i
$243$		0			0
$244$	3.47763	+	7.45780i	0.222632	+	0.477437i
$245$	9.38834	+	35.0378i	0.599799	+	2.23848i
$246$		0			0
$247$	−4.93574	−	5.88219i	−0.314054	−	0.374275i
$248$	2.51343	−	1.45113i	0.159603	−	0.0921467i
$249$		0			0
$250$	−38.4808	+	6.78520i	−2.43374	+	0.429133i
$251$	1.78917	−	6.67729i	0.112932	−	0.421467i	−0.886192	−	0.463318i	$-0.846659\pi$
$251$	1.78917	−	6.67729i	0.112932	−	0.421467i	0.999124	+	0.0418510i	$0.0133255\pi$
$252$		0			0
$253$	22.7724	−	22.7724i	1.43169	−	1.43169i
$254$	−1.13855	−	0.530913i	−0.0714388	−	0.0333125i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	0.266151	−	3.04212i	0.0166021	−	0.189762i	−0.983365	−	0.181641i	$-0.941859\pi$
$257$	0.266151	−	3.04212i	0.0166021	−	0.189762i	0.999967	−	0.00812171i	$-0.00258525\pi$
$258$		0			0
$259$	−23.7286	−	2.02270i	−1.47443	−	0.125685i
$260$			10.0751i			0.624831i
$261$		0			0
$262$	−8.97465	+	10.6956i	−0.554455	+	0.660774i
$263$	−2.05610	+	11.6607i	−0.126785	+	0.719031i	0.853447	+	0.521179i	$0.174508\pi$
$263$	−2.05610	+	11.6607i	−0.126785	+	0.719031i	−0.980232	+	0.197852i	$0.936604\pi$
$264$		0			0
$265$	14.6856	+	14.6856i	0.902128	+	0.902128i
$266$	−4.44506	−	12.2127i	−0.272544	−	0.748809i
$267$		0			0
$268$	−0.547868	−	3.10712i	−0.0334664	−	0.189797i
$269$	13.5079	+	7.79880i	0.823592	+	0.475501i	0.851654	−	0.524105i	$-0.175600\pi$
$269$	13.5079	+	7.79880i	0.823592	+	0.475501i	−0.0280612	+	0.999606i	$0.508933\pi$
$270$		0			0
$271$	7.28409	−	6.11208i	0.442477	−	0.371282i	−0.394158	−	0.919042i	$-0.628964\pi$
$271$	7.28409	−	6.11208i	0.442477	−	0.371282i	0.836635	+	0.547760i	$0.184519\pi$
$272$	−2.35339	−	3.36098i	−0.142695	−	0.203790i
$273$		0			0
$274$	−16.1855	+	7.54743i	−0.977803	+	0.455957i
$275$	27.4107	−	75.3102i	1.65292	−	4.54137i
$276$		0			0
$277$	8.44052	−	0.738450i	0.507142	−	0.0443692i	0.169286	−	0.985567i	$-0.445854\pi$
$277$	8.44052	−	0.738450i	0.507142	−	0.0443692i	0.337856	+	0.941198i	$0.390298\pi$
$278$	15.3226	−	1.34056i	0.918990	−	0.0804012i
$279$		0			0
$280$	−5.83233	+	16.0242i	−0.348548	+	0.957629i
$281$	5.62403	−	2.62253i	0.335502	−	0.156447i	−0.247565	−	0.968871i	$-0.579630\pi$
$281$	5.62403	−	2.62253i	0.335502	−	0.156447i	0.583067	+	0.812424i	$0.301853\pi$
$282$		0			0
$283$	−5.84313	−	8.34485i	−0.347338	−	0.496050i	0.607032	−	0.794677i	$-0.292360\pi$
$283$	−5.84313	−	8.34485i	−0.347338	−	0.496050i	−0.954370	+	0.298628i	$0.903471\pi$
$284$	−9.68192	+	8.12409i	−0.574516	+	0.482076i
$285$		0			0
$286$	−11.4913	−	6.63453i	−0.679497	−	0.392308i
$287$	−0.760860	−	4.31505i	−0.0449121	−	0.254709i
$288$		0			0
$289$	−0.0565554	−	0.155385i	−0.00332679	−	0.00914027i
$290$	12.8650	+	12.8650i	0.755459	+	0.755459i
$291$		0			0
$292$	−0.517431	+	2.93449i	−0.0302803	+	0.171728i
$293$	−21.3283	+	25.4181i	−1.24601	+	1.48494i	−0.434430	+	0.900706i	$0.643050\pi$
$293$	−21.3283	+	25.4181i	−1.24601	+	1.48494i	−0.811584	+	0.584236i	$0.801394\pi$
$294$		0			0
$295$		−	19.5289i		−	1.13702i
$296$	−4.66837	−	3.89953i	−0.271343	−	0.226656i
$297$		0			0
$298$	1.16943	−	13.3667i	0.0677434	−	0.774311i
$299$	−9.94818	−	8.34751i	−0.575318	−	0.482749i
$300$		0			0
$301$	−8.52899	−	3.97713i	−0.491603	−	0.229238i
$302$	4.39347	−	4.39347i	0.252816	−	0.252816i
$303$		0			0
$304$	0.859168	−	3.20646i	0.0492767	−	0.183903i
$305$	−35.2966	+	6.22374i	−2.02108	+	0.356370i
$306$		0			0
$307$	16.3107	−	9.41698i	0.930901	−	0.537456i	0.0438043	−	0.999040i	$-0.486052\pi$
$307$	16.3107	−	9.41698i	0.930901	−	0.537456i	0.887096	+	0.461584i	$0.152719\pi$
$308$	−14.4361	−	17.2042i	−0.822571	−	0.980302i
$309$		0			0
$310$	3.27173	+	12.2103i	0.185822	+	0.693497i
$311$	3.89407	+	8.35086i	0.220812	+	0.473534i	0.985241	−	0.171175i	$-0.0547564\pi$
$311$	3.89407	+	8.35086i	0.220812	+	0.473534i	−0.764428	+	0.644709i	$0.776979\pi$
$312$		0			0
$313$	−17.9421	+	25.6240i	−1.01415	+	1.44835i	−0.124217	+	0.992255i	$0.539642\pi$
$313$	−17.9421	+	25.6240i	−1.01415	+	1.44835i	−0.889930	+	0.456097i	$0.849247\pi$
$314$	−2.02119	−	23.1023i	−0.114062	−	1.30374i
$315$		0			0
$316$	−1.57614	−	1.10362i	−0.0886648	−	0.0620837i
$317$	−6.03335	−	2.19596i	−0.338867	−	0.123337i	0.166981	−	0.985960i	$-0.446598\pi$
$317$	−6.03335	−	2.19596i	−0.338867	−	0.123337i	−0.505848	+	0.862623i	$0.668820\pi$
$318$		0			0
$319$	−23.1451	+	6.20171i	−1.29588	+	0.347229i
$320$	−3.56788	+	2.49826i	−0.199451	+	0.139657i
$321$		0			0
$322$	−10.9901	−	19.0354i	−0.612453	−	1.06080i
$323$	−6.81010	+	11.7954i	−0.378924	+	0.656316i
$324$		0			0
$325$	−31.2160	−	8.36431i	−1.73155	−	0.463968i
$326$	7.38030	−	2.68621i	0.408757	−	0.148775i
$327$		0			0
$328$	0.472975	−	1.01430i	0.0261157	−	0.0560053i
$329$	25.7751	+	4.54485i	1.42103	+	0.250566i
$330$		0			0
$331$	14.4240	+	1.26193i	0.792813	+	0.0693621i	0.476365	−	0.879248i	$-0.341954\pi$
$331$	14.4240	+	1.26193i	0.792813	+	0.0693621i	0.316448	+	0.948610i	$0.397510\pi$
$332$	4.81004			0.263985
$333$		0			0
$334$	0.0518852			0.00283903
$335$	13.6898	+	1.19770i	0.747953	+	0.0654374i
$336$		0			0
$337$	13.7777	+	2.42938i	0.750518	+	0.132337i	0.535806	−	0.844341i	$-0.320008\pi$
$337$	13.7777	+	2.42938i	0.750518	+	0.132337i	0.214711	+	0.976678i	$0.431119\pi$
$338$	3.23276	−	6.93267i	0.175839	−	0.377088i
$339$		0			0
$340$	16.7932	−	6.11223i	0.910740	−	0.331482i
$341$	−16.0811	−	4.30892i	−0.870842	−	0.233341i
$342$		0			0
$343$	−2.59984	+	4.50305i	−0.140378	+	0.243142i
$344$	−1.20184	−	2.08165i	−0.0647990	−	0.112235i
$345$		0			0
$346$	17.7475	−	12.4269i	0.954110	−	0.668075i
$347$	−24.4686	+	6.55635i	−1.31354	+	0.351963i	−0.846556	−	0.532300i	$-0.821328\pi$
$347$	−24.4686	+	6.55635i	−1.31354	+	0.351963i	−0.466988	+	0.884263i	$0.654661\pi$
$348$		0			0
$349$	−19.5804	−	7.12669i	−1.04812	−	0.381483i	−0.240165	−	0.970732i	$-0.577201\pi$
$349$	−19.5804	−	7.12669i	−1.04812	−	0.381483i	−0.807951	+	0.589249i	$0.799424\pi$
$350$	−44.8063	−	31.3737i	−2.39500	−	1.67700i
$351$		0			0
$352$	−0.499958	−	5.71454i	−0.0266478	−	0.304586i
$353$	−5.11858	+	7.31009i	−0.272435	+	0.389077i	−0.931934	−	0.362628i	$-0.881879\pi$
$353$	−5.11858	+	7.31009i	−0.272435	+	0.389077i	0.659499	+	0.751705i	$0.270768\pi$
$354$		0			0
$355$	−23.2649	−	49.8918i	−1.23477	−	2.64798i
$356$	−3.88561	−	14.5013i	−0.205937	−	0.768566i
$357$		0			0
$358$	14.8656	+	17.7161i	0.785670	+	0.936325i
$359$	−11.1457	+	6.43499i	−0.588249	+	0.339626i	−0.764405	−	0.644736i	$-0.776967\pi$
$359$	−11.1457	+	6.43499i	−0.588249	+	0.339626i	0.176156	+	0.984362i	$0.443634\pi$
$360$		0			0
$361$	7.85921	−	1.38579i	0.413643	−	0.0729364i
$362$	−3.97712	+	14.8428i	−0.209033	+	0.780122i
$363$		0			0
$364$	−6.40372	+	6.40372i	−0.335646	+	0.335646i
$365$	−11.7626	−	5.48500i	−0.615683	−	0.287098i
$366$		0			0
$367$	−13.7935	−	11.5742i	−0.720017	−	0.604166i	0.207373	−	0.978262i	$-0.433509\pi$
$367$	−13.7935	−	11.5742i	−0.720017	−	0.604166i	−0.927390	+	0.374096i	$0.877953\pi$
$368$	0.489308	−	5.59282i	0.0255070	−	0.291546i
$369$		0			0
$370$	21.6687	−	15.2447i	1.12650	−	0.792532i
$371$			18.6683i			0.969208i
$372$		0			0
$373$	−19.2215	+	22.9073i	−0.995250	+	1.18609i	−0.0127335	+	0.999919i	$0.504053\pi$
$373$	−19.2215	+	22.9073i	−0.995250	+	1.18609i	−0.982517	+	0.186174i	$0.940391\pi$
$374$	−4.08704	+	23.1788i	−0.211336	+	1.19855i
$375$		0			0
$376$	4.72705	+	4.72705i	0.243779	+	0.243779i
$377$	3.30471	+	9.07961i	0.170201	+	0.467624i
$378$		0			0
$379$	3.85160	+	21.8435i	0.197843	+	1.12203i	0.908311	+	0.418296i	$0.137372\pi$
$379$	3.85160	+	21.8435i	0.197843	+	1.12203i	−0.710467	+	0.703730i	$0.751516\pi$
$380$	12.5216	+	7.22933i	0.642343	+	0.370857i
$381$		0			0
$382$	4.32359	−	3.62793i	0.221214	−	0.185621i
$383$	−6.06729	−	8.66499i	−0.310024	−	0.442760i	0.633658	−	0.773613i	$-0.281553\pi$
$383$	−6.06729	−	8.66499i	−0.310024	−	0.442760i	−0.943682	+	0.330853i	$0.892664\pi$
$384$		0			0
$385$	88.6550	−	41.3405i	4.51828	−	2.10691i
$386$	−3.63336	+	9.98259i	−0.184933	+	0.508100i
$387$		0			0
$388$	0.623592	−	0.0545573i	0.0316581	−	0.00276973i
$389$	32.7100	−	2.86175i	1.65846	−	0.145096i	0.780930	−	0.624618i	$-0.214745\pi$
$389$	32.7100	−	2.86175i	1.65846	−	0.145096i	0.877530	+	0.479522i	$0.159190\pi$
$390$		0			0
$391$	−7.87844	+	21.6458i	−0.398430	+	1.09468i
$392$	−7.54783	+	3.51961i	−0.381223	+	0.177767i
$393$		0			0
$394$	−15.0000	−	21.4222i	−0.755687	−	1.07923i
$395$	6.41993	−	5.38696i	0.323022	−	0.271047i
$396$		0			0
$397$	−20.1086	−	11.6097i	−1.00922	−	0.582673i	−0.0982566	−	0.995161i	$-0.531327\pi$
$397$	−20.1086	−	11.6097i	−1.00922	−	0.582673i	−0.910963	+	0.412488i	$0.864660\pi$
$398$	1.91760	+	10.8752i	0.0961205	+	0.545127i
$399$		0			0
$400$	−4.77840	−	13.1285i	−0.238920	−	0.656427i
$401$	−3.80249	−	3.80249i	−0.189887	−	0.189887i	0.605760	−	0.795647i	$-0.292869\pi$
$401$	−3.80249	−	3.80249i	−0.189887	−	0.189887i	−0.795647	+	0.605760i	$0.792869\pi$
$402$		0			0
$403$	−1.16576	+	6.61135i	−0.0580706	+	0.329335i
$404$	−4.32339	+	5.15241i	−0.215096	+	0.256342i
$405$		0			0
$406$			16.3539i			0.811633i
$407$	3.11859	+	34.7533i	0.154583	+	1.72266i
$408$		0			0
$409$	−0.899624	+	10.2827i	−0.0444835	+	0.508449i	0.940968	+	0.338495i	$0.109918\pi$
$409$	−0.899624	+	10.2827i	−0.0444835	+	0.508449i	−0.985452	+	0.169955i	$0.945638\pi$
$410$	3.73414	+	3.13331i	0.184416	+	0.154743i
$411$		0			0
$412$	−8.20761	−	3.82727i	−0.404360	−	0.188556i
$413$	12.4125	−	12.4125i	0.610781	−	0.610781i
$414$		0			0
$415$	−5.42240	+	20.2367i	−0.266175	+	0.993378i
$416$	−2.27800	+	0.401674i	−0.111688	+	0.0196937i
$417$		0			0
$418$	−16.4911	+	9.52114i	−0.806606	+	0.465694i
$419$	7.84921	+	9.35432i	0.383459	+	0.456989i	0.922903	−	0.385033i	$-0.125810\pi$
$419$	7.84921	+	9.35432i	0.383459	+	0.456989i	−0.539444	+	0.842022i	$0.681365\pi$
$420$		0			0
$421$	−2.24997	−	8.39701i	−0.109657	−	0.409245i	0.889175	−	0.457568i	$-0.151279\pi$
$421$	−2.24997	−	8.39701i	−0.109657	−	0.409245i	−0.998832	+	0.0483222i	$0.984613\pi$
$422$	−7.56377	−	16.2206i	−0.368199	−	0.789605i
$423$		0			0
$424$	−2.73496	+	3.90593i	−0.132821	+	0.189689i
$425$	4.99607	+	57.1054i	0.242345	+	2.77002i
$426$		0			0
$427$	−26.3903	−	18.4787i	−1.27711	−	0.894245i
$428$	−17.5527	−	6.38867i	−0.848443	−	0.308808i
$429$		0			0
$430$	10.1127	−	2.70969i	0.487679	−	0.130673i
$431$	−19.1848	+	13.4333i	−0.924100	+	0.647062i	−0.935672	−	0.352871i	$-0.885205\pi$
$431$	−19.1848	+	13.4333i	−0.924100	+	0.647062i	0.0115720	+	0.999933i	$0.496316\pi$
$432$		0			0
$433$	−1.91324	−	3.31383i	−0.0919444	−	0.159252i	0.816385	−	0.577508i	$-0.195975\pi$
$433$	−1.91324	−	3.31383i	−0.0919444	−	0.159252i	−0.908329	+	0.418256i	$0.862642\pi$
$434$	−5.68133	+	9.84035i	−0.272712	+	0.472352i
$435$		0			0
$436$	3.01352	+	0.807469i	0.144321	+	0.0386708i
$437$	−17.5127	+	6.37412i	−0.837748	+	0.304915i
$438$		0			0
$439$	−14.7539	+	31.6398i	−0.704165	+	1.51009i	0.149218	+	0.988804i	$0.452324\pi$
$439$	−14.7539	+	31.6398i	−0.704165	+	1.51009i	−0.853384	+	0.521283i	$0.825454\pi$
$440$	24.6057	+	4.33864i	1.17303	+	0.206837i
$441$		0			0
$442$	9.45473	+	0.827182i	0.449716	+	0.0393450i
$443$	3.27081			0.155401			0.0777005	−	0.996977i	$-0.475242\pi$
$443$	3.27081			0.155401			0.0777005	+	0.996977i	$0.475242\pi$
$444$		0			0
$445$	65.3896			3.09977
$446$	0.699706	+	0.0612163i	0.0331320	+	0.00289868i
$447$		0			0
$448$	−3.85563	−	0.679852i	−0.182162	−	0.0321200i
$449$	7.15551	−	15.3450i	0.337689	−	0.724177i	−0.661990	−	0.749513i	$-0.730288\pi$
$449$	7.15551	−	15.3450i	0.337689	−	0.724177i	0.999679	+	0.0253358i	$0.00806549\pi$
$450$		0			0
$451$	−6.03272	+	2.19573i	−0.284070	+	0.103393i
$452$	4.56345	+	1.22277i	0.214647	+	0.0575144i
$453$		0			0
$454$	11.6664	−	20.2067i	0.547529	−	0.948348i
$455$	−19.7226	−	34.1605i	−0.924608	−	1.60147i
$456$		0			0
$457$	−7.80738	+	5.46679i	−0.365214	+	0.255726i	−0.741750	−	0.670676i	$-0.766004\pi$
$457$	−7.80738	+	5.46679i	−0.365214	+	0.255726i	0.376536	+	0.926402i	$0.377115\pi$
$458$	20.2660	−	5.43026i	0.946969	−	0.253739i
$459$		0			0
$460$	22.9783	+	8.36343i	1.07137	+	0.389947i
$461$	1.14368	+	0.800816i	0.0532667	+	0.0372977i	0.599907	−	0.800070i	$-0.295204\pi$
$461$	1.14368	+	0.800816i	0.0532667	+	0.0372977i	−0.546640	+	0.837368i	$0.684093\pi$
$462$		0			0
$463$	2.19697	+	25.1115i	0.102102	+	1.16703i	0.858463	+	0.512875i	$0.171420\pi$
$463$	2.19697	+	25.1115i	0.102102	+	1.16703i	−0.756361	+	0.654154i	$0.773025\pi$
$464$	−2.39591	+	3.42171i	−0.111227	+	0.158849i
$465$		0			0
$466$	3.79798	+	8.14479i	0.175938	+	0.377300i
$467$	−5.79741	−	21.6362i	−0.268272	−	1.00120i	−0.960217	−	0.279254i	$-0.909913\pi$
$467$	−5.79741	−	21.6362i	−0.268272	−	1.00120i	0.691945	−	0.721950i	$-0.256754\pi$
$468$		0			0
$469$	7.93995	+	9.46246i	0.366633	+	0.436936i
$470$	−25.2164	+	14.5587i	−1.16314	+	0.671541i
$471$		0			0
$472$	4.41553	−	0.778577i	0.203241	−	0.0358369i
$473$	−3.56871	+	13.3186i	−0.164089	+	0.612390i
$474$		0			0
$475$	−32.7942	+	32.7942i	−1.50470	+	1.50470i
$476$	14.5587	+	6.78882i	0.667296	+	0.311165i
$477$		0			0
$478$	0.244801	+	0.205413i	0.0111970	+	0.00939536i
$479$	1.36262	−	15.5748i	0.0622595	−	0.711629i	−0.899354	−	0.437221i	$-0.855963\pi$
$479$	1.36262	−	15.5748i	0.0622595	−	0.711629i	0.961613	−	0.274408i	$-0.0884818\pi$
$480$		0			0
$481$	13.8511	−	2.47416i	0.631555	−	0.112812i
$482$		−	0.615227i		−	0.0280228i
$483$		0			0
$484$	−14.0809	+	16.7809i	−0.640039	+	0.762769i
$485$	−0.473449	+	2.68506i	−0.0214982	+	0.121922i
$486$		0			0
$487$	−4.58534	−	4.58534i	−0.207782	−	0.207782i	0.595542	−	0.803324i	$-0.296937\pi$
$487$	−4.58534	−	4.58534i	−0.207782	−	0.207782i	−0.803324	+	0.595542i	$0.796937\pi$
$488$	−2.81441	−	7.73251i	−0.127402	−	0.350035i
$489$		0			0
$490$	−6.29887	−	35.7227i	−0.284554	−	1.61379i
$491$	6.84043	+	3.94933i	0.308704	+	0.178231i	0.646347	−	0.763044i	$-0.276296\pi$
$491$	6.84043	+	3.94933i	0.308704	+	0.178231i	−0.337642	+	0.941275i	$0.609629\pi$
$492$		0			0
$493$	13.1291	−	11.0166i	0.591304	−	0.496163i
$494$	4.40429	+	6.28998i	0.198158	+	0.283000i
$495$		0			0
$496$	−2.63034	+	1.22655i	−0.118106	+	0.0550735i
$497$	16.9240	−	46.4983i	0.759146	−	2.08574i
$498$		0			0
$499$	−3.67262	+	0.321312i	−0.164409	+	0.0143839i	−0.169063	−	0.985605i	$-0.554074\pi$
$499$	−3.67262	+	0.321312i	−0.164409	+	0.0143839i	0.00465401	+	0.999989i	$0.498519\pi$
$500$	38.9257	−	3.40556i	1.74081	−	0.152301i
$501$		0			0
$502$	−2.36433	+	6.49595i	−0.105525	+	0.289928i
$503$	12.1815	−	5.68032i	0.543146	−	0.253273i	−0.131626	−	0.991299i	$-0.542020\pi$
$503$	12.1815	−	5.68032i	0.543146	−	0.253273i	0.674772	+	0.738026i	$0.264242\pi$
$504$		0			0
$505$	−16.8033	−	23.9976i	−0.747736	−	1.06788i
$506$	−24.6705	+	20.7010i	−1.09674	+	0.920272i
$507$		0			0
$508$	1.08794	+	0.628124i	0.0482697	+	0.0278685i
$509$	−3.21069	−	18.2087i	−0.142311	−	0.807087i	−0.969487	−	0.245144i	$-0.921165\pi$
$509$	−3.21069	−	18.2087i	−0.142311	−	0.807087i	0.827175	−	0.561944i	$-0.189946\pi$
$510$		0			0
$511$	−3.99004	−	10.9626i	−0.176509	−	0.484955i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−0.530277	+	3.00735i	−0.0233895	+	0.132649i
$515$	25.3545	−	30.2163i	1.11725	−	1.33149i
$516$		0			0
$517$		−	38.3480i		−	1.68654i
$518$	23.4621	+	4.08309i	1.03086	+	0.179401i
$519$		0			0
$520$	0.878103	−	10.0368i	0.0385073	−	0.440141i
$521$	−4.79830	−	4.02625i	−0.210217	−	0.176393i	0.531599	−	0.846996i	$-0.321591\pi$
$521$	−4.79830	−	4.02625i	−0.210217	−	0.176393i	−0.741817	+	0.670603i	$0.766036\pi$
$522$		0			0
$523$	−19.9529	−	9.30419i	−0.872479	−	0.406844i	−0.0657998	−	0.997833i	$-0.520960\pi$
$523$	−19.9529	−	9.30419i	−0.872479	−	0.406844i	−0.806680	+	0.590989i	$0.798738\pi$
$524$	9.87267	−	9.87267i	0.431290	−	0.431290i
$525$		0			0
$526$	3.06457	−	11.4371i	0.133622	−	0.498683i
$527$	11.7271	−	2.06780i	0.510839	−	0.0900746i
$528$		0			0
$529$	−7.37773	+	4.25953i	−0.320771	+	0.185197i
$530$	−13.3498	−	15.9096i	−0.579877	−	0.691070i
$531$		0			0
$532$	3.36374	+	12.5536i	0.145837	+	0.544270i
$533$	1.09406	+	2.34622i	0.0473890	+	0.101626i
$534$		0			0
$535$	46.6655	−	66.6453i	2.01753	−	2.88133i
$536$	0.274981	+	3.14304i	0.0118774	+	0.135759i
$537$		0			0
$538$	−12.7768	−	8.94642i	−0.550847	−	0.385707i
$539$	44.8920	+	16.3394i	1.93364	+	0.703786i
$540$		0			0
$541$	20.8060	−	5.57494i	0.894519	−	0.239686i	0.217858	−	0.975981i	$-0.430093\pi$
$541$	20.8060	−	5.57494i	0.894519	−	0.239686i	0.676661	+	0.736295i	$0.263426\pi$
$542$	−7.78907	+	5.45397i	−0.334569	+	0.234268i
$543$		0			0
$544$	2.05150	+	3.55331i	0.0879574	+	0.152347i
$545$	−6.79432	+	11.7681i	−0.291037	+	0.504091i
$546$		0			0
$547$	−18.4975	−	4.95640i	−0.790898	−	0.211920i	−0.159314	−	0.987228i	$-0.550928\pi$
$547$	−18.4975	−	4.95640i	−0.790898	−	0.211920i	−0.631584	+	0.775308i	$0.717595\pi$
$548$	16.7817	−	6.10805i	0.716880	−	0.260923i
$549$		0			0
$550$	−33.8701	+	72.6346i	−1.44422	+	3.09715i
$551$	13.6556	+	2.40786i	0.581749	+	0.102578i
$552$		0			0
$553$	7.50445	+	0.656554i	0.319121	+	0.0279195i
$554$	−8.47276			−0.359973
$555$		0			0
$556$	−15.3812			−0.652307
$557$	19.4594	+	1.70248i	0.824521	+	0.0721362i	0.491603	−	0.870820i	$-0.336411\pi$
$557$	19.4594	+	1.70248i	0.824521	+	0.0721362i	0.332918	+	0.942956i	$0.391967\pi$
$558$		0			0
$559$	5.47561	+	0.965497i	0.231593	+	0.0408362i
$560$	7.20674	−	15.4549i	0.304540	−	0.653089i
$561$		0			0
$562$	−5.83120	+	2.12238i	−0.245974	+	0.0895273i
$563$	24.7298	+	6.62634i	1.04224	+	0.279267i	0.739041	−	0.673661i	$-0.235279\pi$
$563$	24.7298	+	6.62634i	1.04224	+	0.279267i	0.303198	+	0.952928i	$0.401946\pi$
$564$		0			0
$565$	−10.2888	+	17.8208i	−0.432854	+	0.749725i
$566$	5.09359	+	8.82236i	0.214100	+	0.370831i
$567$		0			0
$568$	10.3531	−	7.24934i	0.434408	−	0.304176i
$569$	7.09278	−	1.90051i	0.297345	−	0.0796733i	−0.107062	−	0.994252i	$-0.534144\pi$
$569$	7.09278	−	1.90051i	0.297345	−	0.0796733i	0.404407	+	0.914579i	$0.367478\pi$
$570$		0			0
$571$	40.0387	+	14.5729i	1.67557	+	0.609857i	0.992692	−	0.120677i	$-0.0385066\pi$
$571$	40.0387	+	14.5729i	1.67557	+	0.609857i	0.682876	+	0.730534i	$0.260729\pi$
$572$	10.8694	+	7.61082i	0.454471	+	0.318224i
$573$		0			0
$574$	0.381883	+	4.36494i	0.0159395	+	0.182189i
$575$	−44.9892	+	64.2513i	−1.87618	+	2.67946i
$576$		0			0
$577$	10.4394	+	22.3874i	0.434599	+	0.932002i	0.994627	+	0.103527i	$0.0330129\pi$
$577$	10.4394	+	22.3874i	0.434599	+	0.932002i	−0.560027	+	0.828474i	$0.689209\pi$
$578$	0.0427975	+	0.159722i	0.00178014	+	0.00664358i
$579$		0			0
$580$	−11.6948	−	13.9373i	−0.485599	−	0.578715i
$581$	−16.3089	+	9.41592i	−0.676605	+	0.390638i
$582$		0			0
$583$	26.9370	−	4.74971i	1.11561	−	0.196713i
$584$	0.771220	−	2.87823i	0.0319133	−	0.119102i
$585$		0			0
$586$	23.4625	−	23.4625i	0.969227	−	0.969227i
$587$	−22.9752	−	10.7135i	−0.948288	−	0.442194i	−0.113974	−	0.993484i	$-0.536358\pi$
$587$	−22.9752	−	10.7135i	−0.948288	−	0.442194i	−0.834314	+	0.551290i	$0.814136\pi$
$588$		0			0
$589$	7.38025	+	6.19277i	0.304098	+	0.255169i
$590$	−1.70205	+	19.4546i	−0.0700725	+	0.800932i
$591$		0			0
$592$	4.31074	+	4.29157i	0.177170	+	0.176382i
$593$		−	13.6948i		−	0.562380i	−0.959652	−	0.281190i	$-0.909271\pi$
$593$		−	13.6948i		−	0.562380i	0.959652	−	0.281190i	$-0.0907291\pi$
$594$		0			0
$595$	−44.9738	+	53.5977i	−1.84375	+	2.19729i
$596$	−2.32997	+	13.2139i	−0.0954391	+	0.541262i
$597$		0			0
$598$	9.18279	+	9.18279i	0.375512	+	0.375512i
$599$	−0.736719	−	2.02412i	−0.0301015	−	0.0827033i	0.923732	−	0.383040i	$-0.125123\pi$
$599$	−0.736719	−	2.02412i	−0.0301015	−	0.0827033i	−0.953833	+	0.300337i	$0.902901\pi$
$600$		0			0
$601$	−5.19357	−	29.4542i	−0.211850	−	1.20146i	−0.886290	−	0.463131i	$-0.846726\pi$
$601$	−5.19357	−	29.4542i	−0.211850	−	1.20146i	0.674440	−	0.738330i	$-0.264385\pi$
$602$	8.14991	+	4.70535i	0.332165	+	0.191776i
$603$		0			0
$604$	−4.75966	+	3.99383i	−0.193668	+	0.162507i
$605$	−54.7267	−	78.1578i	−2.22496	−	3.17757i
$606$		0			0
$607$	13.4382	−	6.26634i	0.545440	−	0.254343i	−0.130310	−	0.991473i	$-0.541597\pi$
$607$	13.4382	−	6.26634i	0.545440	−	0.254343i	0.675751	+	0.737130i	$0.263820\pi$
$608$	−1.13536	+	3.11938i	−0.0460449	+	0.126507i
$609$		0			0
$610$	35.7047	−	3.12376i	1.44564	−	0.126477i
$611$	−15.4047	+	1.34773i	−0.623206	+	0.0545235i
$612$		0			0
$613$	−12.0211	+	33.0278i	−0.485530	+	1.33398i	0.419161	+	0.907912i	$0.362324\pi$
$613$	−12.0211	+	33.0278i	−0.485530	+	1.33398i	−0.904690	+	0.426069i	$0.859898\pi$
$614$	−17.0694	+	7.95958i	−0.688864	+	0.321222i
$615$		0			0
$616$	12.8817	+	18.3970i	0.519018	+	0.741234i
$617$	0.745154	−	0.625258i	0.0299988	−	0.0251719i	−0.627665	−	0.778484i	$-0.715989\pi$
$617$	0.745154	−	0.625258i	0.0299988	−	0.0251719i	0.657664	+	0.753312i	$0.271545\pi$
$618$		0			0
$619$	6.09297	+	3.51778i	0.244897	+	0.141391i	0.617425	−	0.786629i	$-0.288176\pi$
$619$	6.09297	+	3.51778i	0.244897	+	0.141391i	−0.372528	+	0.928021i	$0.621509\pi$
$620$	−2.19509	−	12.4490i	−0.0881569	−	0.499962i
$621$		0			0
$622$	−3.15143	−	8.65847i	−0.126361	−	0.347173i
$623$	41.5616	+	41.5616i	1.66513	+	1.66513i
$624$		0			0
$625$	−17.4232	+	98.8119i	−0.696928	+	3.95247i
$626$	20.1071	−	23.9627i	0.803641	−	0.957742i
$627$		0			0
$628$			23.1905i			0.925402i
$629$	−12.5269	−	21.5860i	−0.499482	−	0.860692i
$630$		0			0
$631$	−0.727482	+	8.31516i	−0.0289606	+	0.331021i	0.967869	+	0.251455i	$0.0809091\pi$
$631$	−0.727482	+	8.31516i	−0.0289606	+	0.331021i	−0.996830	+	0.0795662i	$0.974646\pi$
$632$	1.47395	+	1.23679i	0.0586308	+	0.0491971i
$633$		0			0
$634$	5.81901	+	2.71345i	0.231102	+	0.107765i
$635$	−3.86907	+	3.86907i	−0.153539	+	0.153539i
$636$		0			0
$637$	4.98592	−	18.6077i	0.197549	−	0.737264i
$638$	23.5975	−	4.16088i	0.934236	−	0.164731i
$639$		0			0
$640$	3.77205	−	2.17779i	0.149103	−	0.0860848i
$641$	9.35820	+	11.1527i	0.369627	+	0.440504i	0.918512	−	0.395394i	$-0.129392\pi$
$641$	9.35820	+	11.1527i	0.369627	+	0.440504i	−0.548885	+	0.835898i	$0.684947\pi$
$642$		0			0
$643$	−0.676534	−	2.52486i	−0.0266799	−	0.0995708i	0.951302	−	0.308260i	$-0.0997468\pi$
$643$	−0.676534	−	2.52486i	−0.0266799	−	0.0995708i	−0.977982	+	0.208690i	$0.933080\pi$
$644$	9.28922	+	19.9208i	0.366046	+	0.784989i
$645$		0			0
$646$	7.81223	−	11.1570i	0.307368	−	0.438967i
$647$	−2.29417	−	26.2225i	−0.0901930	−	1.03091i	−0.897569	−	0.440874i	$-0.854669\pi$
$647$	−2.29417	−	26.2225i	−0.0901930	−	1.03091i	0.807376	−	0.590037i	$-0.200887\pi$
$648$		0			0
$649$	−21.0685	−	14.7523i	−0.827009	−	0.579078i
$650$	30.3682	+	11.0531i	1.19114	+	0.433540i
$651$		0			0
$652$	−7.58634	+	2.03275i	−0.297104	+	0.0796088i
$653$	10.5423	−	7.38179i	0.412552	−	0.288872i	−0.348817	−	0.937191i	$-0.613417\pi$
$653$	10.5423	−	7.38179i	0.412552	−	0.288872i	0.761369	+	0.648319i	$0.224528\pi$
$654$		0			0
$655$	30.4065	+	52.6656i	1.18808	+	2.05781i
$656$	−0.559577	+	0.969216i	−0.0218478	+	0.0378415i
$657$		0			0
$658$	−25.2809	−	6.77401i	−0.985554	−	0.264078i
$659$	23.2107	−	8.44800i	0.904160	−	0.329088i	0.152242	−	0.988343i	$-0.451351\pi$
$659$	23.2107	−	8.44800i	0.904160	−	0.329088i	0.751919	+	0.659256i	$0.229129\pi$
$660$		0			0
$661$	18.1164	−	38.8507i	0.704645	−	1.51112i	−0.148204	−	0.988957i	$-0.547349\pi$
$661$	18.1164	−	38.8507i	0.704645	−	1.51112i	0.852848	−	0.522158i	$-0.174873\pi$
$662$	−14.2591	−	2.51426i	−0.554195	−	0.0977196i
$663$		0			0
$664$	−4.79174	−	0.419223i	−0.185955	−	0.0162690i
$665$	−56.6073			−2.19514
$666$		0			0
$667$	23.4512			0.908034
$668$	−0.0516878	−	0.00452210i	−0.00199986	−	0.000174965i
$669$		0			0
$670$	−13.5333	−	2.38629i	−0.522837	−	0.0921903i
$671$	−19.9490	+	42.7807i	−0.770121	+	1.65153i
$672$		0			0
$673$	−15.1518	+	5.51479i	−0.584057	+	0.212580i	−0.617114	−	0.786874i	$-0.711698\pi$
$673$	−15.1518	+	5.51479i	−0.584057	+	0.212580i	0.0330563	+	0.999453i	$0.489476\pi$
$674$	−13.5135	−	3.62093i	−0.520521	−	0.139473i
$675$		0			0
$676$	−3.82468	+	6.62454i	−0.147103	+	0.254790i
$677$	−15.5433	−	26.9218i	−0.597378	−	1.03469i	−0.993207	−	0.116365i	$-0.962876\pi$
$677$	−15.5433	−	26.9218i	−0.597378	−	1.03469i	0.395828	−	0.918325i	$-0.370458\pi$
$678$		0			0
$679$	−2.00755	+	1.40570i	−0.0770425	+	0.0539458i
$680$	−17.2620	+	4.62535i	−0.661969	+	0.177374i
$681$		0			0
$682$	15.6444	+	5.69409i	0.599054	+	0.218038i
$683$	−7.46872	−	5.22965i	−0.285783	−	0.200107i	0.421891	−	0.906646i	$-0.361366\pi$
$683$	−7.46872	−	5.22965i	−0.285783	−	0.200107i	−0.707674	+	0.706539i	$0.750255\pi$
$684$		0			0
$685$	6.77943	+	77.4892i	0.259029	+	2.96071i
$686$	2.98241	−	4.25933i	0.113869	−	0.162622i
$687$		0			0
$688$	1.01584	+	2.17848i	0.0387286	+	0.0830538i
$689$	−2.85469	−	10.6539i	−0.108755	−	0.405879i
$690$		0			0
$691$	−9.54102	−	11.3705i	−0.362957	−	0.432556i	0.553401	−	0.832915i	$-0.313330\pi$
$691$	−9.54102	−	11.3705i	−0.362957	−	0.432556i	−0.916358	+	0.400359i	$0.868885\pi$
$692$	−18.7630	+	10.8328i	−0.713262	+	0.411802i
$693$		0			0
$694$	24.9469	−	4.39882i	0.946972	−	0.166977i
$695$	17.3393	−	64.7112i	0.657717	−	2.45463i
$696$		0			0
$697$	3.24696	−	3.24696i	0.122987	−	0.122987i
$698$	18.8848	+	8.80612i	0.714799	+	0.333316i
$699$		0			0
$700$	41.9014	+	35.1595i	1.58373	+	1.32890i
$701$	−0.332401	+	3.79936i	−0.0125546	+	0.143500i	−0.999885	−	0.0151795i	$-0.995168\pi$
$701$	−0.332401	+	3.79936i	−0.0125546	+	0.143500i	0.987330	+	0.158679i	$0.0507236\pi$
$702$		0			0
$703$	6.86381	−	18.9898i	0.258874	−	0.716213i
$704$			5.73637i			0.216198i
$705$		0			0
$706$	5.73622	−	6.83616i	0.215886	−	0.257282i
$707$	4.57268	−	25.9330i	0.171973	−	0.975309i
$708$		0			0
$709$	−3.49167	−	3.49167i	−0.131133	−	0.131133i	0.638494	−	0.769627i	$-0.279558\pi$
$709$	−3.49167	−	3.49167i	−0.131133	−	0.131133i	−0.769627	+	0.638494i	$0.779558\pi$
$710$	18.8280	+	51.7296i	0.706604	+	1.94138i
$711$		0			0
$712$	2.60695	+	14.7848i	0.0976996	+	0.554082i
$713$	14.1108	+	8.14690i	0.528455	+	0.305104i
$714$		0			0
$715$	−44.2731	+	37.1496i	−1.65572	+	1.38932i
$716$	−13.2649	−	18.9443i	−0.495734	−	0.707982i
$717$		0			0
$718$	11.6642	−	5.43909i	0.435303	−	0.202985i
$719$	−9.24069	+	25.3886i	−0.344620	+	0.946835i	0.639415	+	0.768861i	$0.279176\pi$
$719$	−9.24069	+	25.3886i	−0.344620	+	0.946835i	−0.984035	+	0.177974i	$0.943046\pi$
$720$		0			0
$721$	35.3207	−	3.09016i	1.31541	−	0.115084i
$722$	−7.95009	+	0.695543i	−0.295872	+	0.0258854i
$723$		0			0
$724$	5.25563	−	14.4397i	0.195324	−	0.536648i
$725$	52.8914	−	24.6636i	1.96434	−	0.915985i
$726$		0			0
$727$	−9.80450	−	14.0023i	−0.363629	−	0.519316i	0.595095	−	0.803655i	$-0.297114\pi$
$727$	−9.80450	−	14.0023i	−0.363629	−	0.519316i	−0.958724	+	0.284340i	$0.908226\pi$
$728$	6.93747	−	5.82123i	0.257120	−	0.215749i
$729$		0			0
$730$	11.2398	+	6.48930i	0.416004	+	0.240180i
$731$	−1.71258	−	9.71250i	−0.0633419	−	0.359230i
$732$		0			0
$733$	−13.4202	−	36.8716i	−0.495685	−	1.36188i	−0.895408	−	0.445247i	$-0.853116\pi$
$733$	−13.4202	−	36.8716i	−0.495685	−	1.36188i	0.399723	−	0.916636i	$-0.369106\pi$
$734$	12.7323	+	12.7323i	0.469958	+	0.469958i
$735$		0			0
$736$	−0.974893	+	5.52889i	−0.0359350	+	0.203798i
$737$	11.6335	−	13.8643i	0.428526	−	0.510697i
$738$		0			0
$739$			31.6574i			1.16453i	0.812997	+	0.582267i	$0.197834\pi$
$739$			31.6574i			1.16453i	−0.812997	+	0.582267i	$0.802166\pi$
$740$	−22.9149	+	13.2981i	−0.842368	+	0.488848i
$741$		0			0
$742$	1.62705	−	18.5972i	0.0597308	−	0.682726i
$743$	16.3290	+	13.7017i	0.599054	+	0.502666i	0.891141	−	0.453726i	$-0.149905\pi$
$743$	16.3290	+	13.7017i	0.599054	+	0.502666i	−0.292088	+	0.956392i	$0.594350\pi$
$744$		0			0
$745$	−52.9665	−	24.6987i	−1.94054	−	0.904890i
$746$	21.1448	−	21.1448i	0.774167	−	0.774167i
$747$		0			0
$748$	6.09165	−	22.7344i	0.222733	−	0.831251i
$749$	72.0202	−	12.6991i	2.63156	−	0.464015i
$750$		0			0
$751$	7.50388	−	4.33237i	0.273821	−	0.158090i	−0.356802	−	0.934180i	$-0.616133\pi$
$751$	7.50388	−	4.33237i	0.273821	−	0.158090i	0.630623	+	0.776090i	$0.282800\pi$
$752$	−4.29707	−	5.12105i	−0.156698	−	0.186746i
$753$		0			0
$754$	−2.50079	−	9.33308i	−0.0910735	−	0.339891i
$755$	−11.4371	−	24.5270i	−0.416240	−	0.892629i
$756$		0			0
$757$	−9.97790	+	14.2499i	−0.362653	+	0.517922i	−0.958468	−	0.285200i	$-0.907940\pi$
$757$	−9.97790	+	14.2499i	−0.362653	+	0.517922i	0.595815	+	0.803121i	$0.296829\pi$
$758$	−1.93316	−	22.0961i	−0.0702154	−	0.802566i
$759$		0			0
$760$	−11.8438	−	8.29315i	−0.429621	−	0.300824i
$761$	38.7971	+	14.1210i	1.40640	+	0.511886i	0.930070	−	0.367383i	$-0.119746\pi$
$761$	38.7971	+	14.1210i	1.40640	+	0.511886i	0.476326	+	0.879269i	$0.341968\pi$
$762$		0			0
$763$	−11.7983	+	3.16133i	−0.427126	+	0.114448i
$764$	−4.62334	+	3.23729i	−0.167266	+	0.117121i
$765$		0			0
$766$	5.28900	+	9.16081i	0.191099	+	0.330994i
$767$	−5.18566	+	8.98183i	−0.187243	+	0.324315i
$768$		0			0
$769$	20.2189	+	5.41763i	0.729111	+	0.195365i	0.604233	−	0.796807i	$-0.293480\pi$
$769$	20.2189	+	5.41763i	0.729111	+	0.195365i	0.124878	+	0.992172i	$0.460146\pi$
$770$	−91.9207	+	33.4564i	−3.31259	+	1.20569i
$771$		0			0
$772$	4.48958	−	9.62793i	0.161583	−	0.346517i
$773$	0.877196	+	0.154673i	0.0315505	+	0.00556321i	0.189401	−	0.981900i	$-0.439345\pi$
$773$	0.877196	+	0.154673i	0.0315505	+	0.00556321i	−0.157851	+	0.987463i	$0.550456\pi$
$774$		0			0
$775$	40.3934	+	3.53396i	1.45097	+	0.126944i
$776$	−0.625974			−0.0224712
$777$		0			0
$778$	−32.8349			−1.17719
$779$	3.70097	+	0.323793i	0.132601	+	0.0116011i
$780$		0			0
$781$	−71.3996	−	12.5897i	−2.55488	−	0.450494i
$782$	9.73502	−	20.8768i	0.348124	−	0.746554i
$783$		0			0
$784$	7.82586	−	2.84838i	0.279495	−	0.101728i
$785$	−97.5664	−	26.1428i	−3.48229	−	0.933078i
$786$		0			0
$787$	−15.4356	+	26.7352i	−0.550219	+	0.953008i	0.448039	+	0.894014i	$0.352123\pi$
$787$	−15.4356	+	26.7352i	−0.550219	+	0.953008i	−0.998258	+	0.0589937i	$0.981211\pi$
$788$	13.0758	+	22.6480i	0.465807	+	0.806801i
$789$		0			0
$790$	−6.86501	+	4.80693i	−0.244246	+	0.171023i
$791$	−17.8664	+	4.78729i	−0.635256	+	0.170216i
$792$		0			0
$793$	17.8864	+	6.51013i	0.635166	+	0.231181i
$794$	19.0202	+	13.3181i	0.675001	+	0.472641i
$795$		0			0
$796$	−0.962462	−	11.0010i	−0.0341136	−	0.389920i
$797$	13.4544	−	19.2149i	0.476581	−	0.680628i	−0.506825	−	0.862049i	$-0.669181\pi$
$797$	13.4544	−	19.2149i	0.476581	−	0.680628i	0.983406	+	0.181421i	$0.0580697\pi$
$798$		0			0
$799$	11.5919	+	24.8590i	0.410093	+	0.879447i
$800$	3.61599	+	13.4950i	0.127844	+	0.477122i
$801$		0			0
$802$	3.45661	+	4.11943i	0.122057	+	0.145462i
$803$	−14.8030	+	8.54651i	−0.522386	+	0.301600i
$804$		0			0
$805$	−94.2820	+	16.6245i	−3.32300	+	0.585935i
$806$	1.73754	−	6.48459i	0.0612022	−	0.228410i
$807$		0			0
$808$	4.75600	−	4.75600i	0.167315	−	0.167315i
$809$	19.6183	+	9.14818i	0.689744	+	0.321633i	0.735697	−	0.677311i	$-0.236855\pi$
$809$	19.6183	+	9.14818i	0.689744	+	0.321633i	−0.0459532	+	0.998944i	$0.514633\pi$
$810$		0			0
$811$	−20.2698	−	17.0084i	−0.711770	−	0.597246i	0.213325	−	0.976981i	$-0.431571\pi$
$811$	−20.2698	−	17.0084i	−0.711770	−	0.597246i	−0.925095	+	0.379735i	$0.876015\pi$
$812$	1.42534	−	16.2917i	0.0500196	−	0.571727i
$813$		0			0
$814$	−0.0777729	−	34.8929i	−0.00272594	−	1.22299i
$815$		−	34.2086i		−	1.19827i
$816$		0			0
$817$	5.12893	−	6.11243i	0.179439	−	0.213847i
$818$	1.79240	−	10.1652i	0.0626698	−	0.355418i
$819$		0			0
$820$	−3.44684	−	3.44684i	−0.120369	−	0.120369i
$821$	−5.79646	−	15.9257i	−0.202298	−	0.555809i	0.796510	−	0.604626i	$-0.206677\pi$
$821$	−5.79646	−	15.9257i	−0.202298	−	0.555809i	−0.998808	+	0.0488165i	$0.984455\pi$
$822$		0			0
$823$	−4.29942	−	24.3832i	−0.149868	−	0.849945i	−0.963329	−	0.268324i	$-0.913530\pi$
$823$	−4.29942	−	24.3832i	−0.149868	−	0.849945i	0.813460	−	0.581620i	$-0.197581\pi$
$824$	7.84281	+	4.52805i	0.273217	+	0.157742i
$825$		0			0
$826$	−13.4471	+	11.2835i	−0.467885	+	0.392602i
$827$	20.1850	+	28.8272i	0.701902	+	1.00242i	0.998870	+	0.0475325i	$0.0151358\pi$
$827$	20.1850	+	28.8272i	0.701902	+	1.00242i	−0.296968	+	0.954888i	$0.595975\pi$
$828$		0			0
$829$	−19.6016	+	9.14040i	−0.680793	+	0.317459i	−0.732074	−	0.681225i	$-0.761447\pi$
$829$	−19.6016	+	9.14040i	−0.680793	+	0.317459i	0.0512807	+	0.998684i	$0.483670\pi$
$830$	7.16550	−	19.6871i	0.248718	−	0.683348i
$831$		0			0
$832$	2.30434	−	0.201604i	0.0798887	−	0.00698936i
$833$	−34.0402	+	2.97813i	−1.17942	+	0.103186i
$834$		0			0
$835$	0.0772933	−	0.212362i	0.00267484	−	0.00734908i
$836$	17.2582	−	8.04761i	0.596886	−	0.278333i
$837$		0			0
$838$	−7.00406	−	10.0028i	−0.241951	−	0.345542i
$839$	21.2281	−	17.8125i	0.732875	−	0.614955i	−0.198039	−	0.980194i	$-0.563457\pi$
$839$	21.2281	−	17.8125i	0.732875	−	0.614955i	0.930914	+	0.365239i	$0.119013\pi$
$840$		0			0
$841$	10.0039	+	5.77578i	0.344964	+	0.199165i
$842$	1.50956	+	8.56116i	0.0520230	+	0.295037i
$843$		0			0
$844$	6.12127	+	16.8181i	0.210703	+	0.578902i
$845$	−23.5590	−	23.5590i	−0.810453	−	0.810453i
$846$		0			0
$847$	14.8928	−	84.4612i	0.511722	−	2.90212i
$848$	3.06498	−	3.65270i	0.105252	−	0.125434i
$849$		0			0
$850$		−	57.3235i		−	1.96618i
$851$	5.85507	−	33.6441i	0.200709	−	1.15330i
$852$		0			0
$853$	−3.05046	+	34.8670i	−0.104446	+	1.19382i	0.745337	+	0.666688i	$0.232289\pi$
$853$	−3.05046	+	34.8670i	−0.104446	+	1.19382i	−0.849782	+	0.527133i	$0.823267\pi$
$854$	24.6793	+	20.7084i	0.844509	+	0.708627i
$855$		0			0
$856$	16.9291	+	7.89418i	0.578626	+	0.269818i
$857$	10.8471	−	10.8471i	0.370531	−	0.370531i	−0.497139	−	0.867671i	$-0.665616\pi$
$857$	10.8471	−	10.8471i	0.370531	−	0.370531i	0.867671	+	0.497139i	$0.165616\pi$
$858$		0			0
$859$	−6.64028	+	24.7818i	−0.226563	+	0.845546i	0.755209	+	0.655484i	$0.227535\pi$
$859$	−6.64028	+	24.7818i	−0.226563	+	0.845546i	−0.981772	+	0.190061i	$0.939131\pi$
$860$	−10.3104	+	1.81800i	−0.351582	+	0.0619934i
$861$		0			0
$862$	20.2826	−	11.7102i	0.690828	−	0.398850i
$863$	25.3987	+	30.2690i	0.864583	+	1.03037i	0.999221	+	0.0394749i	$0.0125685\pi$
$863$	25.3987	+	30.2690i	0.864583	+	1.03037i	−0.134638	+	0.990895i	$0.542987\pi$
$864$		0			0
$865$	−24.4239	−	91.1511i	−0.830436	−	3.09923i
$866$	1.61714	+	3.46797i	0.0549527	+	0.117846i
$867$		0			0
$868$	6.51735	−	9.30774i	0.221213	−	0.315925i
$869$	−0.961974	−	10.9954i	−0.0326327	−	0.372994i
$870$		0			0
$871$	−5.97824	−	4.18601i	−0.202565	−	0.141838i
$872$	−2.93167	−	1.06704i	−0.0992790	−	0.0361346i
$873$		0			0
$874$	18.0016	−	4.82353i	0.608915	−	0.163158i
$875$	−125.314	+	87.7461i	−4.23640	+	2.96636i
$876$		0			0
$877$	1.83360	+	3.17590i	0.0619164	+	0.107242i	0.895322	−	0.445419i	$-0.146945\pi$
$877$	1.83360	+	3.17590i	0.0619164	+	0.107242i	−0.833406	+	0.552662i	$0.813612\pi$
$878$	17.4554	−	30.2336i	0.589090	−	1.02033i
$879$		0			0
$880$	−24.1339	−	6.46665i	−0.813553	−	0.217991i
$881$	28.9780	−	10.5471i	0.976294	−	0.355342i	0.195896	−	0.980625i	$-0.437239\pi$
$881$	28.9780	−	10.5471i	0.976294	−	0.355342i	0.780398	+	0.625283i	$0.215016\pi$
$882$		0			0
$883$	−20.0074	+	42.9061i	−0.673304	+	1.44390i	0.211234	+	0.977435i	$0.432252\pi$
$883$	−20.0074	+	42.9061i	−0.673304	+	1.44390i	−0.884538	+	0.466469i	$0.845526\pi$
$884$	−9.34666	−	1.64807i	−0.314362	−	0.0554305i
$885$		0			0
$886$	−3.25837	−	0.285070i	−0.109467	−	0.00957712i
$887$	−41.1834			−1.38280			−0.691401	−	0.722471i	$-0.743006\pi$
$887$	−41.1834			−1.38280			−0.691401	+	0.722471i	$0.743006\pi$
$888$		0			0
$889$	−4.91835			−0.164956
$890$	−65.1408	−	5.69908i	−2.18353	−	0.191034i
$891$		0			0
$892$	−0.691708	−	0.121967i	−0.0231601	−	0.00408375i
$893$	−9.37854	+	20.1124i	−0.313841	+	0.673034i
$894$		0			0
$895$	94.6556	−	34.4518i	3.16399	−	1.15160i
$896$	3.78171	+	1.01331i	0.126338	+	0.0338522i
$897$		0			0
$898$	−8.46569	+	14.6630i	−0.282504	+	0.489311i
$899$	−6.06155	−	10.4989i	−0.202164	−	0.350158i
$900$		0			0
$901$	−16.0260	+	11.2216i	−0.533905	+	0.373844i
$902$	6.20113	−	1.66159i	0.206475	−	0.0553248i
$903$		0			0
$904$	−4.43951	−	1.61585i	−0.147656	−	0.0537424i
$905$	54.8256	+	38.3893i	1.82247	+	1.27610i
$906$		0			0
$907$	−1.45583	−	16.6402i	−0.0483400	−	0.552529i	−0.981292	−	0.192527i	$-0.938332\pi$
$907$	−1.45583	−	16.6402i	−0.0483400	−	0.552529i	0.932952	−	0.360002i	$-0.117224\pi$
$908$	−13.3831	+	19.1130i	−0.444133	+	0.634288i
$909$		0			0
$910$	16.6702	+	35.7494i	0.552613	+	1.18508i
$911$	−14.6772	−	54.7759i	−0.486276	−	1.81481i	−0.574246	−	0.818683i	$-0.694705\pi$
$911$	−14.6772	−	54.7759i	−0.486276	−	1.81481i	0.0879698	−	0.996123i	$-0.471962\pi$
$912$		0			0
$913$	17.7359	+	21.1368i	0.586973	+	0.699527i
$914$	8.25414	−	4.76553i	0.273023	−	0.157630i
$915$		0			0
$916$	−20.6622	+	3.64330i	−0.682697	+	0.120378i
$917$	−14.1478	+	52.8005i	−0.467203	+	1.74363i
$918$		0			0
$919$	20.0510	−	20.0510i	0.661420	−	0.661420i	−0.294295	−	0.955715i	$-0.595085\pi$
$919$	20.0510	−	20.0510i	0.661420	−	0.661420i	0.955715	+	0.294295i	$0.0950847\pi$
$920$	−22.1620	−	10.3343i	−0.730659	−	0.340712i
$921$		0			0
$922$	−1.06954	−	0.897448i	−0.0352233	−	0.0295559i
$923$	−2.54804	+	29.1242i	−0.0838698	+	0.958636i
$924$		0			0
$925$	−22.1781	−	82.0380i	−0.729212	−	2.69739i
$926$		−	25.2074i		−	0.828367i
$927$		0			0
$928$	2.68501	−	3.19987i	0.0881398	−	0.105041i
$929$	−9.93158	+	56.3248i	−0.325845	+	1.84796i	0.177827	+	0.984062i	$0.443093\pi$
$929$	−9.93158	+	56.3248i	−0.325845	+	1.84796i	−0.503671	+	0.863895i	$0.668018\pi$
$930$		0			0
$931$	−19.5485	−	19.5485i	−0.640676	−	0.640676i
$932$	−3.07366	−	8.44481i	−0.100681	−	0.276619i
$933$		0			0
$934$	3.88962	+	22.0592i	0.127272	+	0.721798i
$935$	88.7802	+	51.2573i	2.90342	+	1.67629i
$936$		0			0
$937$	10.0129	−	8.40182i	0.327107	−	0.274476i	−0.464413	−	0.885619i	$-0.653735\pi$
$937$	10.0129	−	8.40182i	0.327107	−	0.274476i	0.791520	+	0.611143i	$0.209290\pi$
$938$	−7.08503	−	10.1185i	−0.231334	−	0.330380i
$939$		0			0
$940$	26.3893	−	12.3055i	0.860723	−	0.401362i
$941$	−12.4081	+	34.0910i	−0.404492	+	1.11133i	0.555551	+	0.831482i	$0.312507\pi$
$941$	−12.4081	+	34.0910i	−0.404492	+	1.11133i	−0.960043	+	0.279851i	$0.909715\pi$
$942$		0			0
$943$	6.25923	−	0.547612i	0.203829	−	0.0178327i
$944$	−4.46658	+	0.390775i	−0.145375	+	0.0127187i
$945$		0			0
$946$	4.71592	−	12.9569i	0.153328	−	0.421265i
$947$	−23.9894	+	11.1864i	−0.779551	+	0.363510i	−0.771313	−	0.636456i	$-0.780400\pi$
$947$	−23.9894	+	11.1864i	−0.779551	+	0.363510i	−0.00823726	+	0.999966i	$0.502622\pi$
$948$		0			0
$949$	3.95345	+	5.64611i	0.128334	+	0.183280i
$950$	35.5277	−	29.8112i	1.15267	−	0.967204i
$951$		0			0
$952$	−13.9116	−	8.03186i	−0.450877	−	0.260314i
$953$	−0.0374736	−	0.212523i	−0.00121389	−	0.00688430i	0.984195	−	0.177089i	$-0.0566681\pi$
$953$	−0.0374736	−	0.212523i	−0.00121389	−	0.00688430i	−0.985409	+	0.170205i	$0.945557\pi$
$954$		0			0
$955$	−8.40793	−	23.1006i	−0.272074	−	0.747518i
$956$	−0.225967	−	0.225967i	−0.00730829	−	0.00730829i
$957$		0			0
$958$	−2.71486	+	15.3967i	−0.0877132	+	0.497446i
$959$	−44.9430	+	53.5610i	−1.45129	+	1.72958i
$960$		0			0
$961$			22.5769i			0.728288i
$962$	−14.0140	+	1.25755i	−0.451830	+	0.0405450i
$963$		0			0
$964$	−0.0536205	+	0.612886i	−0.00172700	+	0.0197397i
$965$	35.4452	+	29.7421i	1.14102	+	0.957431i
$966$		0			0
$967$	27.2638	+	12.7133i	0.876745	+	0.408833i	0.808265	−	0.588819i	$-0.200407\pi$
$967$	27.2638	+	12.7133i	0.876745	+	0.408833i	0.0684806	+	0.997652i	$0.478185\pi$
$968$	15.4898	−	15.4898i	0.497862	−	0.497862i
$969$		0			0
$970$	0.705666	−	2.63358i	0.0226576	−	0.0845592i
$971$	50.2831	−	8.86627i	1.61366	−	0.284532i	0.707261	−	0.706952i	$-0.249930\pi$
$971$	50.2831	−	8.86627i	1.61366	−	0.284532i	0.906400	+	0.422420i	$0.138819\pi$
$972$		0			0
$973$	52.1512	−	30.1095i	1.67189	−	0.965266i
$974$	4.16825	+	4.96753i	0.133559	+	0.159170i
$975$		0			0
$976$	2.12976	+	7.94838i	0.0681720	+	0.254422i
$977$	−24.1978	−	51.8924i	−0.774156	−	1.66018i	−0.750866	−	0.660455i	$-0.770363\pi$
$977$	−24.1978	−	51.8924i	−0.774156	−	1.66018i	−0.0232908	−	0.999729i	$-0.507414\pi$
$978$		0			0
$979$	49.3959	−	70.5447i	1.57870	−	2.25462i
$980$	3.16147	+	36.1357i	0.100989	+	1.15431i
$981$		0			0
$982$	−6.47020	−	4.53048i	−0.206472	−	0.144573i
$983$	−12.6669	−	4.61036i	−0.404010	−	0.147048i	0.132019	−	0.991247i	$-0.457854\pi$
$983$	−12.6669	−	4.61036i	−0.404010	−	0.147048i	−0.536029	+	0.844200i	$0.680076\pi$
$984$		0			0
$985$	−110.024	+	29.4809i	−3.50567	+	0.939341i
$986$	−14.0393	+	9.83041i	−0.447102	+	0.313064i
$987$		0			0
$988$	−3.83932	−	6.64990i	−0.122145	−	0.211562i
$989$	6.74737	−	11.6868i	0.214554	−	0.371618i
$990$		0			0
$991$	56.9401	+	15.2570i	1.80876	+	0.484656i	0.995289	−	0.0969486i	$-0.0309083\pi$
$991$	56.9401	+	15.2570i	1.80876	+	0.484656i	0.813472	+	0.581605i	$0.197575\pi$
$992$	2.72723	−	0.992630i	0.0865896	−	0.0315160i
$993$		0			0
$994$	−20.9122	+	44.8464i	−0.663295	+	1.42244i
$995$	47.3680	+	8.35226i	1.50167	+	0.264784i
$996$		0			0
$997$	−9.57592	−	0.837784i	−0.303272	−	0.0265329i	−0.0654960	−	0.997853i	$-0.520863\pi$
$997$	−9.57592	−	0.837784i	−0.303272	−	0.0265329i	−0.237776	+	0.971320i	$0.576419\pi$
$998$	3.68665			0.116699
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.b.35.1	✓	96
3.2	odd	2	inner	666.2.bs.b.35.8	yes	96
37.18	odd	36	inner	666.2.bs.b.647.8	yes	96
111.92	even	36	inner	666.2.bs.b.647.1	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.35.1	✓	96	1.1	even	1	trivial
666.2.bs.b.35.8	yes	96	3.2	odd	2	inner
666.2.bs.b.647.1	yes	96	111.92	even	36	inner
666.2.bs.b.647.8	yes	96	37.18	odd	36	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-1.84075 + 3.94750i) q^{5} +(-3.67900 + 1.33905i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-1.84075 + 3.94750i) q^{5} +(-3.67900 + 1.33905i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.17779 - 3.77205i) q^{10} +(2.86818 + 4.96784i) q^{11} +(1.89482 - 1.32677i) q^{13} +(3.78171 - 1.01331i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-3.36098 - 2.35339i) q^{17} +(-0.289320 - 3.30694i) q^{19} +(-2.49826 + 3.56788i) q^{20} +(-2.42429 - 5.19892i) q^{22} +(-1.45306 - 5.42289i) q^{23} +(-8.98045 - 10.7025i) q^{25} +(-2.00324 + 1.15657i) q^{26} +(-3.85563 + 0.679852i) q^{28} +(-1.08112 + 4.03480i) q^{29} +(-2.05220 + 2.05220i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(3.14308 + 2.63736i) q^{34} +(1.48623 - 16.9877i) q^{35} +(5.51857 + 2.55839i) q^{37} +3.31957i q^{38} +(2.79971 - 3.33657i) q^{40} +(-0.194339 + 1.10215i) q^{41} +(1.69966 + 1.69966i) q^{43} +(1.96195 + 5.39042i) q^{44} +(0.974893 + 5.52889i) q^{46} +(-5.78943 - 3.34253i) q^{47} +(6.37970 - 5.35320i) q^{49} +(8.01350 + 11.4445i) q^{50} +(2.09642 - 0.977578i) q^{52} +(1.63084 - 4.48070i) q^{53} +(-24.8902 + 2.17761i) q^{55} +(3.90021 - 0.341225i) q^{56} +(1.42866 - 3.92522i) q^{58} +(-4.06356 + 1.89487i) q^{59} +(4.71983 + 6.74061i) q^{61} +(2.22326 - 1.86553i) q^{62} +(0.866025 + 0.500000i) q^{64} +(1.74952 + 9.92203i) q^{65} +(-1.07909 - 2.96478i) q^{67} +(-2.90126 - 2.90126i) q^{68} +(-2.96115 + 16.7935i) q^{70} +(-8.12409 + 9.68192i) q^{71} +2.97976i q^{73} +(-5.27459 - 3.02963i) q^{74} +(0.289320 - 3.30694i) q^{76} +(-17.2042 - 14.4361i) q^{77} +(-1.74384 - 0.813164i) q^{79} +(-3.07986 + 3.07986i) q^{80} +(0.289659 - 1.08102i) q^{82} +(4.73697 - 0.835255i) q^{83} +(15.4767 - 8.93549i) q^{85} +(-1.54506 - 1.84133i) q^{86} +(-1.48468 - 5.54091i) q^{88} +(-6.34470 - 13.6062i) q^{89} +(-5.19444 + 7.41842i) q^{91} +(-0.489308 - 5.59282i) q^{92} +(5.47608 + 3.83439i) q^{94} +(13.5867 + 4.94515i) q^{95} +(0.604645 - 0.162014i) q^{97} +(-6.82198 + 4.77680i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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