LMFDB - Embedded newform 459.2.y.a.62.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(44,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([40, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.44"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.y (of order $48$, degree $16$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			62.10
Character	$\chi$	$=$	459.62
Dual form			459.2.y.a.422.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.613881 + 0.800025i) q^{2} +(0.254448 - 0.949612i) q^{4} +(-3.54737 - 0.232507i) q^{5} +(0.00291938 + 0.0445412i) q^{7} +(2.77921 - 1.15119i) q^{8} +(-1.99165 - 2.98072i) q^{10} +(-4.54544 - 3.98625i) q^{11} +(-3.51137 - 0.940868i) q^{13} +(-0.0338419 + 0.0296785i) q^{14} +(0.924284 + 0.533636i) q^{16} +(3.77050 + 1.66834i) q^{17} +(-2.46918 - 1.02277i) q^{19} +(-1.12341 + 3.30947i) q^{20} +(0.398737 - 6.08355i) q^{22} +(-2.31805 - 6.82875i) q^{23} +(7.57258 + 0.996950i) q^{25} +(-1.40284 - 3.38676i) q^{26} +(0.0430397 + 0.00856112i) q^{28} +(-0.0353157 + 0.0174158i) q^{29} +(2.74702 + 3.13237i) q^{31} +(-0.644819 - 4.89788i) q^{32} +(0.979919 + 4.04065i) q^{34} -0.158683i q^{35} +(-1.01343 - 5.09486i) q^{37} +(-0.697541 - 2.60326i) q^{38} +(-10.1266 + 3.43751i) q^{40} +(-2.12104 + 4.30104i) q^{41} +(-0.107266 + 0.814765i) q^{43} +(-4.94197 + 3.30212i) q^{44} +(4.04017 - 6.04654i) q^{46} +(1.62385 - 0.435110i) q^{47} +(6.93814 - 0.913423i) q^{49} +(3.85108 + 6.67026i) q^{50} +(-1.78692 + 3.09503i) q^{52} +(-1.17550 + 2.83792i) q^{53} +(15.1976 + 15.1976i) q^{55} +(0.0593888 + 0.120429i) q^{56} +(-0.0356127 - 0.0175622i) q^{58} +(7.99901 + 6.13786i) q^{59} +(-0.0920527 + 0.00603345i) q^{61} +(-0.819636 + 4.12059i) q^{62} +(5.03194 - 5.03194i) q^{64} +(12.2374 + 4.15403i) q^{65} +(-5.04699 + 2.91388i) q^{67} +(2.54367 - 3.15600i) q^{68} +(0.126950 - 0.0974124i) q^{70} +(-5.65982 + 1.12581i) q^{71} +(-6.75916 - 4.51633i) q^{73} +(3.45389 - 3.93840i) q^{74} +(-1.59951 + 2.08452i) q^{76} +(0.164282 - 0.214097i) q^{77} +(3.54731 - 4.04493i) q^{79} +(-3.15471 - 2.10791i) q^{80} +(-4.74300 + 0.943442i) q^{82} +(-4.62326 + 3.54755i) q^{83} +(-12.9875 - 6.79490i) q^{85} +(-0.717681 + 0.414353i) q^{86} +(-17.2217 - 5.84597i) q^{88} +(12.7569 - 12.7569i) q^{89} +(0.0316563 - 0.159147i) q^{91} +(-7.07449 + 0.463687i) q^{92} +(1.34495 + 1.03202i) q^{94} +(8.52129 + 4.20223i) q^{95} +(1.60641 + 3.25748i) q^{97} +(4.98995 + 4.98995i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{16}\right)$

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 $

$2$	0.613881	+	0.800025i	0.434079	+	0.565703i	0.958258	−	0.285905i	$-0.0922943\pi$
$2$	0.613881	+	0.800025i	0.434079	+	0.565703i	−0.524179	+	0.851608i	$0.675628\pi$
$3$		0			0
$3$		0			0
$4$	0.254448	−	0.949612i	0.127224	−	0.474806i
$5$	−3.54737	−	0.232507i	−1.58643	−	0.103980i	−0.753536	−	0.657407i	$-0.771653\pi$
$5$	−3.54737	−	0.232507i	−1.58643	−	0.103980i	−0.832898	+	0.553426i	$0.813320\pi$
$6$		0			0
$7$	0.00291938	+	0.0445412i	0.00110342	+	0.0168350i	0.998375	−	0.0569833i	$-0.0181482\pi$
$7$	0.00291938	+	0.0445412i	0.00110342	+	0.0168350i	−0.997272	+	0.0738183i	$0.976482\pi$
$8$	2.77921	−	1.15119i	0.982600	−	0.407006i
$9$		0			0
$10$	−1.99165	−	2.98072i	−0.629816	−	0.942586i
$11$	−4.54544	−	3.98625i	−1.37050	−	1.20190i	−0.956539	−	0.291606i	$-0.905811\pi$
$11$	−4.54544	−	3.98625i	−1.37050	−	1.20190i	−0.413964	−	0.910293i	$-0.635856\pi$
$12$		0			0
$13$	−3.51137	−	0.940868i	−0.973878	−	0.260950i	−0.263414	−	0.964683i	$-0.584848\pi$
$13$	−3.51137	−	0.940868i	−0.973878	−	0.260950i	−0.710464	+	0.703733i	$0.751515\pi$
$14$	−0.0338419	+	0.0296785i	−0.00904462	+	0.00793192i
$15$		0			0
$16$	0.924284	+	0.533636i	0.231071	+	0.133409i
$17$	3.77050	+	1.66834i	0.914479	+	0.404632i
$17$	3.77050	+	1.66834i	0.914479	+	0.404632i
$18$		0			0
$19$	−2.46918	−	1.02277i	−0.566468	−	0.234639i	0.0810227	−	0.996712i	$-0.474181\pi$
$19$	−2.46918	−	1.02277i	−0.566468	−	0.234639i	−0.647490	+	0.762074i	$0.724181\pi$
$20$	−1.12341	+	3.30947i	−0.251203	+	0.740020i
$21$		0			0
$22$	0.398737	−	6.08355i	0.0850110	−	1.29702i
$23$	−2.31805	−	6.82875i	−0.483347	−	1.42389i	−0.866020	−	0.500010i	$-0.833330\pi$
$23$	−2.31805	−	6.82875i	−0.483347	−	1.42389i	0.382673	−	0.923884i	$-0.375004\pi$
$24$		0			0
$25$	7.57258	+	0.996950i	1.51452	+	0.199390i
$26$	−1.40284	−	3.38676i	−0.275120	−	0.664198i
$27$		0			0
$28$	0.0430397	+	0.00856112i	0.00813373	+	0.00161790i
$29$	−0.0353157	+	0.0174158i	−0.00655796	+	0.00323403i	−0.445565	−	0.895250i	$-0.646997\pi$
$29$	−0.0353157	+	0.0174158i	−0.00655796	+	0.00323403i	0.439007	+	0.898484i	$0.355330\pi$
$30$		0			0
$31$	2.74702	+	3.13237i	0.493379	+	0.562591i	0.943924	−	0.330163i	$-0.107104\pi$
$31$	2.74702	+	3.13237i	0.493379	+	0.562591i	−0.450545	+	0.892754i	$0.648770\pi$
$32$	−0.644819	−	4.89788i	−0.113989	−	0.865832i
$33$		0			0
$34$	0.979919	+	4.04065i	0.168055	+	0.692966i
$35$		−	0.158683i		−	0.0268223i
$36$		0			0
$37$	−1.01343	−	5.09486i	−0.166607	−	0.837589i	−0.970180	−	0.242384i	$-0.922071\pi$
$37$	−1.01343	−	5.09486i	−0.166607	−	0.837589i	0.803574	−	0.595205i	$-0.202929\pi$
$38$	−0.697541	−	2.60326i	−0.113156	−	0.422304i
$39$		0			0
$40$	−10.1266	+	3.43751i	−1.60115	+	0.543517i
$41$	−2.12104	+	4.30104i	−0.331250	+	0.671709i	−0.997240	−	0.0742521i	$-0.976343\pi$
$41$	−2.12104	+	4.30104i	−0.331250	+	0.671709i	0.665989	+	0.745962i	$0.268010\pi$
$42$		0			0
$43$	−0.107266	+	0.814765i	−0.0163579	+	0.124251i	−0.997675	−	0.0681444i	$-0.978292\pi$
$43$	−0.107266	+	0.814765i	−0.0163579	+	0.124251i	0.981318	+	0.192395i	$0.0616255\pi$
$44$	−4.94197	+	3.30212i	−0.745030	+	0.497813i
$45$		0			0
$46$	4.04017	−	6.04654i	0.595690	−	0.891513i
$47$	1.62385	−	0.435110i	0.236863	−	0.0634673i	−0.138435	−	0.990372i	$-0.544207\pi$
$47$	1.62385	−	0.435110i	0.236863	−	0.0634673i	0.375298	+	0.926904i	$0.377540\pi$
$48$		0			0
$49$	6.93814	−	0.913423i	0.991163	−	0.130489i
$50$	3.85108	+	6.67026i	0.544625	+	0.943318i
$51$		0			0
$52$	−1.78692	+	3.09503i	−0.247801	+	0.429204i
$53$	−1.17550	+	2.83792i	−0.161468	+	0.389818i	−0.983820	−	0.179161i	$-0.942662\pi$
$53$	−1.17550	+	2.83792i	−0.161468	+	0.389818i	0.822352	+	0.568979i	$0.192662\pi$
$54$		0			0
$55$	15.1976	+	15.1976i	2.04924	+	2.04924i
$56$	0.0593888	+	0.120429i	0.00793616	+	0.0160929i
$57$		0			0
$58$	−0.0356127	−	0.0175622i	−0.00467617	−	0.00230603i
$59$	7.99901	+	6.13786i	1.04138	+	0.799081i	0.979993	−	0.199033i	$-0.0637801\pi$
$59$	7.99901	+	6.13786i	1.04138	+	0.799081i	0.0613898	+	0.998114i	$0.480447\pi$
$60$		0			0
$61$	−0.0920527	+	0.00603345i	−0.0117861	+	0.000772504i	−0.0712951	−	0.997455i	$-0.522713\pi$
$61$	−0.0920527	+	0.00603345i	−0.0117861	+	0.000772504i	0.0595089	+	0.998228i	$0.481047\pi$
$62$	−0.819636	+	4.12059i	−0.104094	+	0.523315i
$63$		0			0
$64$	5.03194	−	5.03194i	0.628992	−	0.628992i
$65$	12.2374	+	4.15403i	1.51786	+	0.515244i
$66$		0			0
$67$	−5.04699	+	2.91388i	−0.616588	+	0.355987i	−0.775539	−	0.631299i	$-0.782522\pi$
$67$	−5.04699	+	2.91388i	−0.616588	+	0.355987i	0.158951	+	0.987286i	$0.449189\pi$
$68$	2.54367	−	3.15600i	0.308466	−	0.382721i
$69$		0			0
$70$	0.126950	−	0.0974124i	0.0151735	−	0.0116430i
$71$	−5.65982	+	1.12581i	−0.671697	+	0.133609i	−0.519144	−	0.854687i	$-0.673749\pi$
$71$	−5.65982	+	1.12581i	−0.671697	+	0.133609i	−0.152552	+	0.988295i	$0.548749\pi$
$72$		0			0
$73$	−6.75916	−	4.51633i	−0.791100	−	0.528596i	0.0931267	−	0.995654i	$-0.470314\pi$
$73$	−6.75916	−	4.51633i	−0.791100	−	0.528596i	−0.884227	+	0.467058i	$0.845314\pi$
$74$	3.45389	−	3.93840i	0.401506	−	0.457830i
$75$		0			0
$76$	−1.59951	+	2.08452i	−0.183476	+	0.239111i
$77$	0.164282	−	0.214097i	0.0187217	−	0.0243986i
$78$		0			0
$79$	3.54731	−	4.04493i	0.399104	−	0.455091i	−0.517028	−	0.855969i	$-0.672962\pi$
$79$	3.54731	−	4.04493i	0.399104	−	0.455091i	0.916131	+	0.400878i	$0.131295\pi$
$80$	−3.15471	−	2.10791i	−0.352707	−	0.235671i
$81$		0			0
$82$	−4.74300	+	0.943442i	−0.523777	+	0.104186i
$83$	−4.62326	+	3.54755i	−0.507468	+	0.389394i	−0.830521	−	0.556987i	$-0.811957\pi$
$83$	−4.62326	+	3.54755i	−0.507468	+	0.389394i	0.323053	+	0.946381i	$0.395291\pi$
$84$		0			0
$85$	−12.9875	−	6.79490i	−1.40869	−	0.737011i
$86$	−0.717681	+	0.414353i	−0.0773895	+	0.0446809i
$87$		0			0
$88$	−17.2217	−	5.84597i	−1.83584	−	0.623182i
$89$	12.7569	−	12.7569i	1.35223	−	1.35223i	0.469070	−	0.883161i	$-0.344589\pi$
$89$	12.7569	−	12.7569i	1.35223	−	1.35223i	0.883161	−	0.469070i	$-0.155411\pi$
$90$		0			0
$91$	0.0316563	−	0.159147i	0.00331848	−	0.0166832i
$92$	−7.07449	+	0.463687i	−0.737566	+	0.0483427i
$93$		0			0
$94$	1.34495	+	1.03202i	0.138721	+	0.106444i
$95$	8.52129	+	4.20223i	0.874266	+	0.431140i
$96$		0			0
$97$	1.60641	+	3.25748i	0.163106	+	0.330746i	0.963047	−	0.269332i	$-0.0868028\pi$
$97$	1.60641	+	3.25748i	0.163106	+	0.330746i	−0.799941	+	0.600078i	$0.795136\pi$
$98$	4.98995	+	4.98995i	0.504061	+	0.504061i
$99$		0			0
$100$	2.87354	−	6.93735i	0.287354	−	0.693735i
$101$	2.53423	−	4.38941i	0.252165	−	0.436763i	−0.711956	−	0.702224i	$-0.752191\pi$
$101$	2.53423	−	4.38941i	0.252165	−	0.436763i	0.964122	+	0.265461i	$0.0855240\pi$
$102$		0			0
$103$	−0.363059	−	0.628837i	−0.0357733	−	0.0619611i	0.847584	−	0.530661i	$-0.178056\pi$
$103$	−0.363059	−	0.628837i	−0.0357733	−	0.0619611i	−0.883358	+	0.468699i	$0.844723\pi$
$104$	−10.8419	+	1.42737i	−1.06314	+	0.139965i
$105$		0			0
$106$	−2.99202	+	0.801710i	−0.290611	+	0.0778690i
$107$	1.35228	−	2.02383i	0.130730	−	0.195651i	−0.760330	−	0.649537i	$-0.774963\pi$
$107$	1.35228	−	2.02383i	0.130730	−	0.195651i	0.891060	+	0.453886i	$0.149963\pi$
$108$		0			0
$109$	−7.52425	+	5.02754i	−0.720692	+	0.481551i	−0.861031	−	0.508552i	$-0.830181\pi$
$109$	−7.52425	+	5.02754i	−0.720692	+	0.481551i	0.140339	+	0.990104i	$0.455181\pi$
$110$	−2.82894	+	21.4879i	−0.269729	+	2.04879i
$111$		0			0
$112$	−0.0210704	+	0.0427266i	−0.00199097	+	0.00403728i
$113$	0.159798	−	0.0542442i	0.0150326	−	0.00510287i	−0.313913	−	0.949452i	$-0.601640\pi$
$113$	0.159798	−	0.0542442i	0.0150326	−	0.00510287i	0.328946	+	0.944349i	$0.393307\pi$
$114$		0			0
$115$	6.63526	+	24.7631i	0.618741	+	2.30917i
$116$	0.00755223	+	0.0379676i	0.000701207	+	0.00352520i
$117$		0			0
$118$			10.1673i			0.935978i
$119$	−0.0633024	+	0.172813i	−0.00580292	+	0.0158417i
$120$		0			0
$121$	3.33510	+	25.3326i	0.303191	+	2.30297i
$122$	−0.0613363	−	0.0699406i	−0.00555312	−	0.00633213i
$123$		0			0
$124$	3.67351	−	1.81158i	0.329891	−	0.162684i
$125$	−9.19761	−	1.82952i	−0.822659	−	0.163637i
$126$		0			0
$127$	−5.60153	−	13.5233i	−0.497055	−	1.20000i	−0.951062	−	0.309000i	$-0.900006\pi$
$127$	−5.60153	−	13.5233i	−0.497055	−	1.20000i	0.454007	−	0.890998i	$-0.349994\pi$
$128$	−2.68108	−	0.352971i	−0.236977	−	0.0311986i
$129$		0			0
$130$	4.18896	+	12.3403i	0.367396	+	1.08231i
$131$	1.09065	−	16.6401i	0.0952905	−	1.45385i	−0.635949	−	0.771731i	$-0.719391\pi$
$131$	1.09065	−	16.6401i	0.0952905	−	1.45385i	0.731239	−	0.682121i	$-0.238942\pi$
$132$		0			0
$133$	0.0383467	−	0.112966i	0.00332508	−	0.00979538i
$134$	−5.42943	−	2.24894i	−0.469031	−	0.194279i
$135$		0			0
$136$	12.3996	+	0.296129i	1.06325	+	0.0253929i
$137$	7.73940	+	4.46834i	0.661221	+	0.381756i	0.792742	−	0.609557i	$-0.208653\pi$
$137$	7.73940	+	4.46834i	0.661221	+	0.381756i	−0.131521	+	0.991313i	$0.541986\pi$
$138$		0			0
$139$	8.24871	−	7.23393i	0.699647	−	0.613574i	−0.233802	−	0.972284i	$-0.575117\pi$
$139$	8.24871	−	7.23393i	0.699647	−	0.613574i	0.933449	+	0.358710i	$0.116783\pi$
$140$	−0.150687	−	0.0403765i	−0.0127354	−	0.00341244i
$141$		0			0
$142$	−4.37513	−	3.83688i	−0.367152	−	0.321984i
$143$	12.2102	+	18.2738i	1.02107	+	1.52813i
$144$		0			0
$145$	0.129327	−	0.0535691i	0.0107400	−	0.00444867i
$146$	−0.536144	−	8.17998i	−0.0443716	−	0.676980i
$147$		0			0
$148$	−5.09600	−	0.334010i	−0.418889	−	0.0274554i
$149$	−2.41458	+	9.01133i	−0.197810	+	0.738237i	0.793712	+	0.608294i	$0.208146\pi$
$149$	−2.41458	+	9.01133i	−0.197810	+	0.738237i	−0.991522	+	0.129942i	$0.958521\pi$
$150$		0			0
$151$	−5.43656	−	7.08506i	−0.442421	−	0.576574i	0.517911	−	0.855435i	$-0.326710\pi$
$151$	−5.43656	−	7.08506i	−0.442421	−	0.576574i	−0.960332	+	0.278860i	$0.910043\pi$
$152$	−8.03975			−0.652110
$153$		0			0
$154$	0.272132			0.0219291
$155$	−9.01640	−	11.7504i	−0.724215	−	0.943815i
$156$		0			0
$157$	2.65070	−	9.89256i	0.211549	−	0.789512i	−0.775804	−	0.630974i	$-0.782655\pi$
$157$	2.65070	−	9.89256i	0.211549	−	0.789512i	0.987353	−	0.158538i	$-0.0506780\pi$
$158$	5.41367	+	0.354831i	0.430689	+	0.0282288i
$159$		0			0
$160$	1.14862	+	17.5246i	0.0908064	+	1.38544i
$161$	0.297393	−	0.123184i	0.0234379	−	0.00970829i
$162$		0			0
$163$	1.34058	+	2.00633i	0.105003	+	0.157148i	0.880250	−	0.474510i	$-0.157375\pi$
$163$	1.34058	+	2.00633i	0.105003	+	0.157148i	−0.775247	+	0.631658i	$0.782375\pi$
$164$	3.54463	+	3.10855i	0.276789	+	0.242737i
$165$		0			0
$166$	−5.67626	−	1.52095i	−0.440563	−	0.118048i
$167$	8.20662	−	7.19701i	0.635047	−	0.556921i	−0.280136	−	0.959960i	$-0.590379\pi$
$167$	8.20662	−	7.19701i	0.635047	−	0.556921i	0.915183	+	0.403039i	$0.132046\pi$
$168$		0			0
$169$	0.186131	+	0.107463i	0.0143178	+	0.00826638i
$170$	−2.53666	−	14.5615i	−0.194553	−	1.11682i
$171$		0			0
$172$	0.746417	+	0.309176i	0.0569138	+	0.0235745i
$173$	0.337612	−	0.994572i	0.0256681	−	0.0756159i	−0.933341	−	0.358991i	$-0.883121\pi$
$173$	0.337612	−	0.994572i	0.0256681	−	0.0756159i	0.959009	+	0.283375i	$0.0914542\pi$
$174$		0			0
$175$	−0.0222980	+	0.340202i	−0.00168557	+	0.0257169i
$176$	−2.07408	−	6.11004i	−0.156340	−	0.460561i
$177$		0			0
$178$	18.0371	+	2.37463i	1.35194	+	0.177986i
$179$	−3.32973	−	8.03868i	−0.248876	−	0.600839i	0.749233	−	0.662306i	$-0.230422\pi$
$179$	−3.32973	−	8.03868i	−0.248876	−	0.600839i	−0.998109	+	0.0614667i	$0.980422\pi$
$180$		0			0
$181$	−11.3744	−	2.26251i	−0.845453	−	0.168171i	−0.246687	−	0.969095i	$-0.579342\pi$
$181$	−11.3744	−	2.26251i	−0.845453	−	0.168171i	−0.598766	+	0.800924i	$0.704342\pi$
$182$	0.146755	−	0.0723715i	0.0108782	−	0.00536453i
$183$		0			0
$184$	−14.3035	−	16.3100i	−1.05447	−	1.20239i
$185$	2.41042	+	18.3090i	0.177218	+	1.34610i
$186$		0			0
$187$	−10.4882	−	22.6135i	−0.766970	−	1.65366i
$188$		−	1.65274i		−	0.120539i
$189$		0			0
$190$	1.86916	+	9.39691i	0.135603	+	0.681724i
$191$	−5.55024	−	20.7138i	−0.401602	−	1.49880i	−0.810238	−	0.586100i	$-0.800662\pi$
$191$	−5.55024	−	20.7138i	−0.401602	−	1.49880i	0.408637	−	0.912697i	$-0.366004\pi$
$192$		0			0
$193$	0.503524	−	0.170923i	0.0362444	−	0.0123033i	−0.303258	−	0.952908i	$-0.598075\pi$
$193$	0.503524	−	0.170923i	0.0362444	−	0.0123033i	0.339503	+	0.940605i	$0.389741\pi$
$194$	−1.61992	+	3.28487i	−0.116303	+	0.235840i
$195$		0			0
$196$	0.897996	−	6.82096i	0.0641426	−	0.487211i
$197$	−6.66381	+	4.45262i	−0.474777	+	0.317236i	−0.769834	−	0.638244i	$-0.779661\pi$
$197$	−6.66381	+	4.45262i	−0.474777	+	0.317236i	0.295057	+	0.955480i	$0.404661\pi$
$198$		0			0
$199$	1.66134	−	2.48637i	0.117769	−	0.176254i	−0.767902	−	0.640568i	$-0.778699\pi$
$199$	1.66134	−	2.48637i	0.117769	−	0.176254i	0.885671	+	0.464314i	$0.153699\pi$
$200$	22.1935	−	5.94673i	1.56932	−	0.420497i
$201$		0			0
$202$	5.06735	−	0.667130i	0.356538	−	0.0469391i
$203$	−0.000878819	−	0.00152216i	−6.16810e−5	−	0.000106835i
$204$		0			0
$205$	8.52414	−	14.7642i	0.595352	−	1.03118i
$206$	0.280210	−	0.676487i	0.0195232	−	0.0471331i
$207$		0			0
$208$	−2.74342	−	2.74342i	−0.190222	−	0.190222i
$209$	7.14650	+	14.4917i	0.494334	+	1.00241i
$210$		0			0
$211$	10.8516	+	5.35143i	0.747056	+	0.368407i	0.775633	−	0.631184i	$-0.217431\pi$
$211$	10.8516	+	5.35143i	0.747056	+	0.368407i	−0.0285766	+	0.999592i	$0.509097\pi$
$212$	2.39582	+	1.83837i	0.164545	+	0.126260i
$213$		0			0
$214$	2.44926	−	0.160533i	0.167428	−	0.0109738i
$215$	0.569951	−	2.86534i	0.0388703	−	0.195414i
$216$		0			0
$217$	−0.131500	+	0.131500i	−0.00892680	+	0.00892680i
$218$	−8.64115	−	2.93327i	−0.585252	−	0.198666i
$219$		0			0
$220$	18.2988	−	10.5648i	1.23370	−	0.712279i
$221$	−11.6699	−	9.40570i	−0.785003	−	0.632696i
$222$		0			0
$223$	6.20019	−	4.75757i	0.415195	−	0.318590i	−0.379953	−	0.925006i	$-0.624060\pi$
$223$	6.20019	−	4.75757i	0.415195	−	0.318590i	0.795148	+	0.606415i	$0.207393\pi$
$224$	0.216275	−	0.0430198i	0.0144505	−	0.00287438i
$225$		0			0
$226$	0.141494	+	0.0945431i	0.00941203	+	0.00628892i
$227$	−3.90357	+	4.45117i	−0.259089	+	0.295435i	−0.866730	−	0.498777i	$-0.833783\pi$
$227$	−3.90357	+	4.45117i	−0.259089	+	0.295435i	0.607641	+	0.794212i	$0.292116\pi$
$228$		0			0
$229$	8.45010	−	11.0124i	0.558398	−	0.727719i	−0.425795	−	0.904820i	$-0.640005\pi$
$229$	8.45010	−	11.0124i	0.558398	−	0.727719i	0.984193	+	0.177101i	$0.0566720\pi$
$230$	−15.7378	+	20.5100i	−1.03772	+	1.35239i
$231$		0			0
$232$	−0.0781010	+	0.0890571i	−0.00512758	+	0.00584688i
$233$	12.5770	+	8.40367i	0.823946	+	0.550543i	0.894553	−	0.446961i	$-0.147494\pi$
$233$	12.5770	+	8.40367i	0.823946	+	0.550543i	−0.0706075	+	0.997504i	$0.522494\pi$
$234$		0			0
$235$	−5.86158	+	1.16594i	−0.382367	+	0.0760576i
$236$	7.86391	−	6.03419i	0.511897	−	0.392793i
$237$		0			0
$238$	−0.177115	+	0.0554430i	−0.0114806	+	0.00359383i
$239$	4.27091	−	2.46581i	0.276262	−	0.159500i	−0.355468	−	0.934689i	$-0.615678\pi$
$239$	4.27091	−	2.46581i	0.276262	−	0.159500i	0.631730	+	0.775188i	$0.282345\pi$
$240$		0			0
$241$	−14.1988	−	4.81984i	−0.914624	−	0.310473i	−0.175843	−	0.984418i	$-0.556265\pi$
$241$	−14.1988	−	4.81984i	−0.914624	−	0.310473i	−0.738781	+	0.673945i	$0.764598\pi$
$242$	−18.2194	+	18.2194i	−1.17119	+	1.17119i
$243$		0			0
$244$	−0.0176932	+	0.0889495i	−0.00113269	+	0.00569441i
$245$	−24.8246	+	1.62709i	−1.58598	+	0.103951i
$246$		0			0
$247$	7.70789	+	5.91447i	0.490441	+	0.376329i
$248$	11.2405	+	5.54320i	0.713772	+	0.351993i
$249$		0			0
$250$	−4.18257	−	8.48142i	−0.264529	−	0.536412i
$251$	2.57518	+	2.57518i	0.162544	+	0.162544i	0.783693	−	0.621149i	$-0.213334\pi$
$251$	2.57518	+	2.57518i	0.162544	+	0.162544i	−0.621149	+	0.783693i	$0.713334\pi$
$252$		0			0
$253$	−16.6845	+	40.2800i	−1.04895	+	2.53238i
$254$	7.38030	−	12.7830i	0.463081	−	0.802080i
$255$		0			0
$256$	−8.47971	−	14.6873i	−0.529982	−	0.917956i
$257$	−18.8702	+	2.48431i	−1.17709	+	0.154967i	−0.693586	−	0.720374i	$-0.743970\pi$
$257$	−18.8702	+	2.48431i	−1.17709	+	0.154967i	−0.483506	+	0.875341i	$0.660637\pi$
$258$		0			0
$259$	0.223972	−	0.0600132i	0.0139170	−	0.00372904i
$260$	7.05849	−	10.5638i	0.437749	−	0.655138i
$261$		0			0
$262$	13.9820	−	9.34249i	0.863812	−	0.577181i
$263$	1.63423	−	12.4132i	0.100771	−	0.765434i	−0.864213	−	0.503126i	$-0.832183\pi$
$263$	1.63423	−	12.4132i	0.100771	−	0.765434i	0.964984	−	0.262308i	$-0.0844835\pi$
$264$		0			0
$265$	4.82979	−	9.79384i	0.296691	−	0.601631i
$266$	0.113916	−	0.0386692i	0.00698462	−	0.00237096i
$267$		0			0
$268$	1.48286	+	5.53412i	0.0905802	+	0.338050i
$269$	3.23153	+	16.2460i	0.197030	+	0.990536i	0.945066	+	0.326879i	$0.105997\pi$
$269$	3.23153	+	16.2460i	0.197030	+	0.990536i	−0.748036	+	0.663658i	$0.769003\pi$
$270$		0			0
$271$		−	21.3512i		−	1.29699i	−0.761218	−	0.648496i	$-0.775398\pi$
$271$		−	21.3512i		−	1.29699i	0.761218	−	0.648496i	$-0.224602\pi$
$272$	2.59472	+	3.55409i	0.157328	+	0.215499i
$273$		0			0
$274$	1.17628	+	8.93474i	0.0710617	+	0.539767i
$275$	−30.4467	−	34.7178i	−1.83600	−	2.09356i
$276$		0			0
$277$	28.3672	−	13.9891i	1.70442	−	0.840526i	0.714376	−	0.699762i	$-0.246711\pi$
$277$	28.3672	−	13.9891i	1.70442	−	0.840526i	0.990043	−	0.140764i	$-0.0449559\pi$
$278$	10.8510	+	2.15841i	0.650803	+	0.129453i
$279$		0			0
$280$	−0.182674	−	0.441014i	−0.0109168	−	0.0263556i
$281$	−2.66328	−	0.350628i	−0.158878	−	0.0209167i	0.0506674	−	0.998716i	$-0.483865\pi$
$281$	−2.66328	−	0.350628i	−0.158878	−	0.0209167i	−0.209546	+	0.977799i	$0.567198\pi$
$282$		0			0
$283$	1.15252	+	3.39522i	0.0685102	+	0.201825i	0.975793	−	0.218697i	$-0.0701805\pi$
$283$	1.15252	+	3.39522i	0.0685102	+	0.201825i	−0.907283	+	0.420521i	$0.861847\pi$
$284$	−0.371047	+	5.66109i	−0.0220176	+	0.335924i
$285$		0			0
$286$	−7.12392	+	20.9864i	−0.421247	+	1.24095i
$287$	−0.197765	−	0.0819171i	−0.0116737	−	0.00483541i
$288$		0			0
$289$	11.4333	+	12.5810i	0.672545	+	0.740056i
$290$	0.122248	+	0.0705800i	0.00717866	+	0.00414460i
$291$		0			0
$292$	−6.00861	+	5.26941i	−0.351627	+	0.308369i
$293$	10.4050	+	2.78802i	0.607868	+	0.162878i	0.549607	−	0.835423i	$-0.314778\pi$
$293$	10.4050	+	2.78802i	0.607868	+	0.162878i	0.0582617	+	0.998301i	$0.481444\pi$
$294$		0			0
$295$	−26.9484	−	23.6331i	−1.56900	−	1.37597i
$296$	−8.68167	−	12.9930i	−0.504612	−	0.755205i
$297$		0			0
$298$	−8.69155	+	3.60016i	−0.503488	+	0.208551i
$299$	1.71457	+	26.1592i	0.0991559	+	1.51283i
$300$		0			0
$301$	−0.0366037	−	0.00239914i	−0.00210980	−	0.000138284i
$302$	2.33083	−	8.69877i	0.134124	−	0.500558i
$303$		0			0
$304$	−1.73644	−	2.26297i	−0.0995914	−	0.129790i
$305$	0.327948			0.0187783
$306$		0			0
$307$	1.09298			0.0623795			0.0311897	−	0.999513i	$-0.490070\pi$
$307$	1.09298			0.0623795			0.0311897	+	0.999513i	$0.490070\pi$
$308$	−0.161508	−	0.210481i	−0.00920275	−	0.0119933i
$309$		0			0
$310$	3.86562	−	14.4267i	0.219552	−	0.819381i
$311$	33.0715	+	2.16762i	1.87531	+	0.122915i	0.960030	−	0.279897i	$-0.0903003\pi$
$311$	33.0715	+	2.16762i	1.87531	+	0.122915i	0.915283	+	0.402811i	$0.131967\pi$
$312$		0			0
$313$	0.269319	+	4.10902i	0.0152228	+	0.232255i	0.998690	+	0.0511690i	$0.0162947\pi$
$313$	0.269319	+	4.10902i	0.0152228	+	0.232255i	−0.983467	+	0.181086i	$0.942039\pi$
$314$	9.54151	−	3.95222i	0.538459	−	0.223037i
$315$		0			0
$316$	−2.93851	−	4.39779i	−0.165304	−	0.247395i
$317$	−15.5326	−	13.6217i	−0.872395	−	0.765070i	0.100835	−	0.994903i	$-0.467849\pi$
$317$	−15.5326	−	13.6217i	−0.872395	−	0.765070i	−0.973230	+	0.229833i	$0.926182\pi$
$318$		0			0
$319$	0.229949	+	0.0616147i	0.0128747	+	0.00344976i
$320$	−19.0201	+	16.6802i	−1.06326	+	0.932452i
$321$		0			0
$322$	0.281115	+	0.162302i	0.0156659	+	0.00904471i
$323$	−7.60369	−	7.97576i	−0.423081	−	0.443783i
$324$		0			0
$325$	−25.6521	−	10.6255i	−1.42292	−	0.589394i
$326$	−0.782152	+	2.30415i	−0.0433194	+	0.127615i
$327$		0			0
$328$	−0.943512	+	14.3952i	−0.0520967	+	0.794842i
$329$	0.0241210	+	0.0710580i	0.00132983	+	0.00391756i
$330$		0			0
$331$	14.3095	+	1.88388i	0.786522	+	0.103548i	0.513080	−	0.858341i	$-0.328504\pi$
$331$	14.3095	+	1.88388i	0.786522	+	0.103548i	0.273442	+	0.961888i	$0.411838\pi$
$332$	2.19242	+	5.29297i	0.120325	+	0.290489i
$333$		0			0
$334$	10.7957	+	2.14739i	0.590713	+	0.117500i
$335$	18.5811	−	9.16317i	1.01519	−	0.500637i
$336$		0			0
$337$	17.9342	+	20.4500i	0.976939	+	1.11399i	0.993467	+	0.114122i	$0.0364054\pi$
$337$	17.9342	+	20.4500i	0.976939	+	1.11399i	−0.0165281	+	0.999863i	$0.505261\pi$
$338$	0.0282894	+	0.214879i	0.00153874	+	0.0116879i
$339$		0			0
$340$	−9.75715	+	10.6041i	−0.529156	+	0.575088i
$341$		−	25.1883i		−	1.36402i
$342$		0			0
$343$	0.121897	+	0.612820i	0.00658184	+	0.0330891i
$344$	0.639833	+	2.38789i	0.0344975	+	0.128746i
$345$		0			0
$346$	1.00294	−	0.340451i	0.0539181	−	0.0183027i
$347$	14.3684	−	29.1361i	0.771334	−	1.56411i	−0.0533894	−	0.998574i	$-0.517002\pi$
$347$	14.3684	−	29.1361i	0.771334	−	1.56411i	0.824723	−	0.565537i	$-0.191331\pi$
$348$		0			0
$349$	−3.60538	+	27.3856i	−0.192992	+	1.46592i	0.571137	+	0.820855i	$0.306502\pi$
$349$	−3.60538	+	27.3856i	−0.192992	+	1.46592i	−0.764129	+	0.645064i	$0.776831\pi$
$350$	−0.285859	+	0.191005i	−0.0152798	+	0.0102096i
$351$		0			0
$352$	−16.5932	+	24.8335i	−0.884420	+	1.32363i
$353$	−25.5043	+	6.83386i	−1.35746	+	0.363729i	−0.862882	−	0.505406i	$-0.831343\pi$
$353$	−25.5043	+	6.83386i	−1.35746	+	0.363729i	−0.494575	+	0.869135i	$0.664676\pi$
$354$		0			0
$355$	20.3392	−	2.67771i	1.07950	−	0.142118i
$356$	−8.86816	−	15.3601i	−0.470011	−	0.814084i
$357$		0			0
$358$	4.38709	−	7.59866i	0.231865	−	0.401602i
$359$	3.39378	−	8.19330i	0.179117	−	0.432426i	−0.808665	−	0.588269i	$-0.799810\pi$
$359$	3.39378	−	8.19330i	0.179117	−	0.432426i	0.987782	+	0.155843i	$0.0498095\pi$
$360$		0			0
$361$	−8.38425	−	8.38425i	−0.441276	−	0.441276i
$362$	−5.17246	−	10.4887i	−0.271859	−	0.551275i
$363$		0			0
$364$	−0.143073	−	0.0705559i	−0.00749907	−	0.00369813i
$365$	22.9272	+	17.5927i	1.20006	+	0.920842i
$366$		0			0
$367$	−37.0294	+	2.42703i	−1.93292	+	0.126690i	−0.982737	−	0.185008i	$-0.940769\pi$
$367$	−37.0294	+	2.42703i	−1.93292	+	0.126690i	−0.950181	+	0.311698i	$0.899102\pi$
$368$	1.50153	−	7.54870i	0.0782727	−	0.393503i
$369$		0			0
$370$	−13.1679	+	13.1679i	−0.684568	+	0.684568i
$371$	−0.129836	−	0.0440733i	−0.00674074	−	0.00228817i
$372$		0			0
$373$	−12.4589	+	7.19313i	−0.645096	+	0.372446i	−0.786575	−	0.617495i	$-0.788148\pi$
$373$	−12.4589	+	7.19313i	−0.645096	+	0.372446i	0.141479	+	0.989941i	$0.454814\pi$
$374$	11.6529	−	22.2728i	0.602556	−	1.15170i
$375$		0			0
$376$	4.01214	−	3.07862i	0.206910	−	0.158768i
$377$	0.140392	−	0.0279258i	0.00723057	−	0.00143825i
$378$		0			0
$379$	13.9109	+	9.29500i	0.714557	+	0.477452i	0.858944	−	0.512069i	$-0.171121\pi$
$379$	13.9109	+	9.29500i	0.714557	+	0.477452i	−0.144387	+	0.989521i	$0.546121\pi$
$380$	6.15872	−	7.02267i	0.315936	−	0.360255i
$381$		0			0
$382$	13.1644	−	17.1561i	0.673547	−	0.877784i
$383$	−22.2673	+	29.0193i	−1.13780	+	1.48282i	−0.286547	+	0.958066i	$0.592508\pi$
$383$	−22.2673	+	29.0193i	−1.13780	+	1.48282i	−0.851257	+	0.524749i	$0.824159\pi$
$384$		0			0
$385$	−0.632550	+	0.721285i	−0.0322377	+	0.0367601i
$386$	0.445846	+	0.297905i	0.0226930	+	0.0151630i
$387$		0			0
$388$	3.50209	−	0.696608i	0.177791	−	0.0353649i
$389$	−14.0093	+	10.7497i	−0.710300	+	0.545033i	−0.899508	−	0.436904i	$-0.856075\pi$
$389$	−14.0093	+	10.7497i	−0.710300	+	0.545033i	0.189207	+	0.981937i	$0.439408\pi$
$390$		0			0
$391$	2.65250	−	29.6151i	0.134143	−	1.49770i
$392$	18.2310	−	10.5257i	0.920806	−	0.531628i
$393$		0			0
$394$	−7.65299	−	2.59784i	−0.385552	−	0.130877i
$395$	−13.5241	+	13.5241i	−0.680472	+	0.680472i
$396$		0			0
$397$	−3.93979	+	19.8067i	−0.197732	+	0.994068i	0.746650	+	0.665217i	$0.231661\pi$
$397$	−3.93979	+	19.8067i	−0.197732	+	0.994068i	−0.944382	+	0.328850i	$0.893339\pi$
$398$	3.00902	−	0.197222i	0.150829	−	0.00988584i
$399$		0			0
$400$	6.46721	+	4.96247i	0.323361	+	0.248123i
$401$	−12.5872	−	6.20733i	−0.628576	−	0.309979i	0.0999553	−	0.994992i	$-0.468130\pi$
$401$	−12.5872	−	6.20733i	−0.628576	−	0.309979i	−0.728531	+	0.685013i	$0.759797\pi$
$402$		0			0
$403$	−6.69864	−	13.5835i	−0.333683	−	0.676642i
$404$	−3.52341	−	3.52341i	−0.175296	−	0.175296i
$405$		0			0
$406$	0.000678275	−	0.00163750i	3.36622e−5	−	8.12678e-5i
$407$	−15.7029	+	27.1982i	−0.778362	+	1.34816i
$408$		0			0
$409$	2.43755	+	4.22196i	0.120529	+	0.208762i	0.919976	−	0.391974i	$-0.128208\pi$
$409$	2.43755	+	4.22196i	0.120529	+	0.208762i	−0.799447	+	0.600736i	$0.794874\pi$
$410$	17.0446	−	2.24396i	0.841771	−	0.110821i
$411$		0			0
$412$	−0.689531	+	0.184759i	−0.0339707	+	0.00910243i
$413$	−0.250035	+	0.374204i	−0.0123034	+	0.0184134i
$414$		0			0
$415$	17.2253	−	11.5096i	0.845555	−	0.564982i
$416$	−2.34407	+	17.8050i	−0.114927	+	0.872960i
$417$		0			0
$418$	−7.20660	+	14.6135i	−0.352486	+	0.714771i
$419$	−25.2196	+	8.56091i	−1.23206	+	0.418228i	−0.860150	−	0.510041i	$-0.829630\pi$
$419$	−25.2196	+	8.56091i	−1.23206	+	0.418228i	−0.371909	+	0.928269i	$0.621297\pi$
$420$		0			0
$421$	−8.60215	−	32.1037i	−0.419243	−	1.56464i	−0.776182	−	0.630509i	$-0.782846\pi$
$421$	−8.60215	−	32.1037i	−0.419243	−	1.56464i	0.356939	−	0.934128i	$-0.383820\pi$
$422$	2.38033	+	11.9667i	0.115872	+	0.582530i
$423$		0			0
$424$			9.24039i			0.448753i
$425$	26.8891	+	16.3927i	1.30432	+	0.795161i
$426$		0			0
$427$	−0.000537474	−	0.00408252i	−2.60102e−5	−	0.000197567i
$428$	−1.57777	−	1.79910i	−0.0762645	−	0.0869630i
$429$		0			0
$430$	2.64222	−	1.30300i	0.127419	−	0.0628363i
$431$	−19.7216	−	3.92286i	−0.949955	−	0.188958i	−0.304291	−	0.952579i	$-0.598419\pi$
$431$	−19.7216	−	3.92286i	−0.949955	−	0.188958i	−0.645664	+	0.763622i	$0.723419\pi$
$432$		0			0
$433$	1.73656	+	4.19243i	0.0834538	+	0.201475i	0.960098	−	0.279664i	$-0.0902231\pi$
$433$	1.73656	+	4.19243i	0.0834538	+	0.201475i	−0.876644	+	0.481139i	$0.840223\pi$
$434$	−0.185929	−	0.0244780i	−0.00892486	−	0.00117498i
$435$		0			0
$436$	2.85969	+	8.42436i	0.136954	+	0.403454i
$437$	−1.26055	+	19.2322i	−0.0603001	+	0.920001i
$438$		0			0
$439$	0.571654	−	1.68404i	0.0272836	−	0.0803748i	−0.932435	−	0.361337i	$-0.882320\pi$
$439$	0.571654	−	1.68404i	0.0272836	−	0.0803748i	0.959719	+	0.280962i	$0.0906536\pi$
$440$	59.7325	+	24.7420i	2.84763	+	1.17953i
$441$		0			0
$442$	0.360864	−	15.1102i	0.0171646	−	0.718718i
$443$	26.7176	+	15.4254i	1.26939	+	0.732883i	0.974873	−	0.222763i	$-0.0715077\pi$
$443$	26.7176	+	15.4254i	1.26939	+	0.732883i	0.294518	+	0.955646i	$0.404841\pi$
$444$		0			0
$445$	−48.2197	+	42.2875i	−2.28583	+	2.00462i
$446$	7.61235	+	2.03972i	0.360455	+	0.0965837i
$447$		0			0
$448$	0.238818	+	0.209438i	0.0112831	+	0.00989502i
$449$	19.7458	+	29.5517i	0.931861	+	1.39463i	0.918804	+	0.394714i	$0.129156\pi$
$449$	19.7458	+	29.5517i	0.931861	+	1.39463i	0.0130574	+	0.999915i	$0.495844\pi$
$450$		0			0
$451$	26.7861	−	11.0952i	1.26131	−	0.522450i
$452$	−0.0108506	−	0.165549i	−0.000510371	−	0.00778676i
$453$		0			0
$454$	−5.95737	−	0.390467i	−0.279593	−	0.0183255i
$455$	−0.149300	+	0.557194i	−0.00699928	+	0.0261217i
$456$		0			0
$457$	3.70468	+	4.82804i	0.173298	+	0.225846i	0.871925	−	0.489640i	$-0.162872\pi$
$457$	3.70468	+	4.82804i	0.173298	+	0.225846i	−0.698627	+	0.715486i	$0.746205\pi$
$458$	13.9975			0.654061
$459$		0			0
$460$	25.2037			1.17513
$461$	23.4323	+	30.5376i	1.09135	+	1.42228i	0.897374	+	0.441270i	$0.145472\pi$
$461$	23.4323	+	30.5376i	1.09135	+	1.42228i	0.193976	+	0.981006i	$0.437861\pi$
$462$		0			0
$463$	−5.04899	+	18.8431i	−0.234646	+	0.875712i	0.743662	+	0.668556i	$0.233087\pi$
$463$	−5.04899	+	18.8431i	−0.234646	+	0.875712i	−0.978308	+	0.207156i	$0.933579\pi$
$464$	−0.0419354	−	0.00274859i	−0.00194680	−	0.000127600i
$465$		0			0
$466$	0.997621	+	15.2208i	0.0462139	+	0.705088i
$467$	1.38122	−	0.572119i	0.0639152	−	0.0264745i	−0.350497	−	0.936564i	$-0.613987\pi$
$467$	1.38122	−	0.572119i	0.0639152	−	0.0264745i	0.414412	+	0.910089i	$0.363987\pi$
$468$		0			0
$469$	−0.144522	−	0.216292i	−0.00667340	−	0.00998744i
$470$	−4.53109	−	3.97366i	−0.209004	−	0.183291i
$471$		0			0
$472$	29.2968	+	7.85004i	1.34849	+	0.361328i
$473$	3.73543	−	3.27588i	0.171755	−	0.150625i
$474$		0			0
$475$	−17.6784	−	10.2066i	−0.811140	−	0.468312i
$476$	0.147998	+	0.104085i	0.00678348	+	0.00477071i
$477$		0			0
$478$	4.59454	+	1.90312i	0.210149	+	0.0870467i
$479$	0.891901	−	2.62746i	0.0407520	−	0.120052i	−0.924650	−	0.380819i	$-0.875642\pi$
$479$	0.891901	−	2.62746i	0.0407520	−	0.120052i	0.965402	+	0.260767i	$0.0839755\pi$
$480$		0			0
$481$	−1.23506	+	18.8434i	−0.0563140	+	0.859185i
$482$	−4.86037	−	14.3182i	−0.221384	−	0.652175i
$483$		0			0
$484$	24.9048	+	3.27878i	1.13204	+	0.149035i
$485$	−4.94115	−	11.9290i	−0.224366	−	0.541667i
$486$		0			0
$487$	−20.5857	−	4.09475i	−0.932828	−	0.185551i	−0.294795	−	0.955560i	$-0.595252\pi$
$487$	−20.5857	−	4.09475i	−0.932828	−	0.185551i	−0.638033	+	0.770009i	$0.720252\pi$
$488$	−0.248888	+	0.122738i	−0.0112666	+	0.00555609i
$489$		0			0
$490$	−16.5410	−	18.8614i	−0.747247	−	0.852072i
$491$	−3.11766	−	23.6810i	−0.140698	−	1.06871i	−0.905471	−	0.424408i	$-0.860482\pi$
$491$	−3.11766	−	23.6810i	−0.140698	−	1.06871i	0.764773	−	0.644300i	$-0.222851\pi$
$492$		0			0
$493$	−0.162213	+	0.00674744i	−0.00730571	+	0.000303890i
$494$			9.79728i			0.440801i
$495$		0			0
$496$	0.867479	+	4.36111i	0.0389509	+	0.195820i
$497$	−0.0666679	−	0.248808i	−0.00299047	−	0.0111606i
$498$		0			0
$499$	2.07387	−	0.703983i	0.0928390	−	0.0315146i	−0.274633	−	0.961549i	$-0.588557\pi$
$499$	2.07387	−	0.703983i	0.0928390	−	0.0315146i	0.367473	+	0.930034i	$0.380223\pi$
$500$	−4.07764	+	8.26864i	−0.182358	+	0.369785i
$501$		0			0
$502$	−0.479354	+	3.64106i	−0.0213946	+	0.162508i
$503$	−13.6455	+	9.11766i	−0.608425	+	0.406536i	−0.821262	−	0.570551i	$-0.806730\pi$
$503$	−13.6455	+	9.11766i	−0.608425	+	0.406536i	0.212837	+	0.977088i	$0.431730\pi$
$504$		0			0
$505$	−10.0104	+	14.9817i	−0.445458	+	0.666675i
$506$	−42.4673	+	11.3791i	−1.88790	+	0.505862i
$507$		0			0
$508$	−14.2672	+	1.87831i	−0.633004	+	0.0833365i
$509$	2.71304	+	4.69913i	0.120254	+	0.208285i	0.919868	−	0.392229i	$-0.128296\pi$
$509$	2.71304	+	4.69913i	0.120254	+	0.208285i	−0.799614	+	0.600514i	$0.794963\pi$
$510$		0			0
$511$	0.181430	−	0.314246i	0.00802598	−	0.0139014i
$512$	4.47495	−	10.8035i	0.197767	−	0.477451i
$513$		0			0
$514$	−13.5716	−	13.5716i	−0.598616	−	0.598616i
$515$	1.14170	+	2.31513i	0.0503092	+	0.102017i
$516$		0			0
$517$	−9.11559	−	4.49531i	−0.400903	−	0.197703i
$518$	0.185504	+	0.142342i	0.00815059	+	0.00625417i
$519$		0			0
$520$	38.7923	−	2.54258i	1.70116	−	0.111500i
$521$	−5.58058	+	28.0555i	−0.244490	+	1.22913i	0.642116	+	0.766607i	$0.278057\pi$
$521$	−5.58058	+	28.0555i	−0.244490	+	1.22913i	−0.886606	+	0.462525i	$0.846943\pi$
$522$		0			0
$523$	6.31889	−	6.31889i	0.276306	−	0.276306i	−0.555326	−	0.831632i	$-0.687407\pi$
$523$	6.31889	−	6.31889i	0.276306	−	0.276306i	0.831632	+	0.555326i	$0.187407\pi$
$524$	−15.5241	−	5.26973i	−0.678175	−	0.230209i
$525$		0			0
$526$	10.9341	−	6.31282i	0.476751	−	0.275252i
$527$	5.13175	+	16.3936i	0.223542	+	0.714115i
$528$		0			0
$529$	−23.0114	+	17.6573i	−1.00050	+	0.767707i
$530$	10.8002	−	2.14830i	0.469132	−	0.0933161i
$531$		0			0
$532$	−0.0975164	−	0.0651584i	−0.00422787	−	0.00282498i
$533$	11.4944	−	13.1069i	0.497880	−	0.567723i
$534$		0			0
$535$	−5.26761	+	6.86488i	−0.227739	+	0.296795i
$536$	−10.6722	+	13.9083i	−0.460970	+	0.600748i
$537$		0			0
$538$	−11.0134	+	12.5584i	−0.474823	+	0.541432i
$539$	−35.1780	−	23.5052i	−1.51523	−	1.01244i
$540$		0			0
$541$	24.1708	−	4.80786i	1.03918	−	0.206706i	0.354127	−	0.935197i	$-0.384778\pi$
$541$	24.1708	−	4.80786i	1.03918	−	0.206706i	0.685055	+	0.728491i	$0.259778\pi$
$542$	17.0815	−	13.1071i	0.733712	−	0.562997i
$543$		0			0
$544$	5.74006	−	19.5432i	0.246103	−	0.837909i
$545$	27.8603	−	16.0851i	1.19340	−	0.689011i
$546$		0			0
$547$	38.8821	+	13.1987i	1.66248	+	0.564335i	0.985202	−	0.171396i	$-0.0548277\pi$
$547$	38.8821	+	13.1987i	1.66248	+	0.564335i	0.677274	+	0.735731i	$0.263161\pi$
$548$	6.21246	−	6.21246i	0.265383	−	0.265383i
$549$		0			0
$550$	9.08446	−	45.6707i	0.387363	−	1.94740i
$551$	0.105013	−	0.00688291i	0.00447370	−	0.000293222i
$552$		0			0
$553$	0.190522	+	0.146193i	0.00810182	+	0.00621674i
$554$	28.6057	+	14.1068i	1.21534	+	0.599340i
$555$		0			0
$556$	−4.77056	−	9.67374i	−0.202317	−	0.410258i
$557$	−4.89600	−	4.89600i	−0.207450	−	0.207450i	0.595733	−	0.803183i	$-0.296862\pi$
$557$	−4.89600	−	4.89600i	−0.207450	−	0.207450i	−0.803183	+	0.595733i	$0.796862\pi$
$558$		0			0
$559$	1.14324	−	2.76002i	0.0483537	−	0.116736i
$560$	0.0846789	−	0.146668i	0.00357834	−	0.00619786i
$561$		0			0
$562$	−1.35443	−	2.34594i	−0.0571331	−	0.0989574i
$563$	−26.2295	+	3.45318i	−1.10544	+	0.145534i	−0.661081	−	0.750314i	$-0.729902\pi$
$563$	−26.2295	+	3.45318i	−1.10544	+	0.145534i	−0.444360	+	0.895848i	$0.646569\pi$
$564$		0			0
$565$	−0.579477	+	0.155270i	−0.0243788	+	0.00653227i
$566$	−2.00875	+	3.00630i	−0.0844339	+	0.126364i
$567$		0			0
$568$	−14.4338	+	9.64436i	−0.605629	+	0.404668i
$569$	1.38486	−	10.5191i	0.0580565	−	0.440983i	−0.937588	−	0.347749i	$-0.886946\pi$
$569$	1.38486	−	10.5191i	0.0580565	−	0.440983i	0.995644	−	0.0932340i	$-0.0297205\pi$
$570$		0			0
$571$	13.8278	−	28.0400i	0.578676	−	1.17344i	−0.388999	−	0.921238i	$-0.627179\pi$
$571$	13.8278	−	28.0400i	0.578676	−	1.17344i	0.967675	−	0.252201i	$-0.0811544\pi$
$572$	20.4599	−	6.94520i	0.855472	−	0.290394i
$573$		0			0
$574$	−0.0558686	−	0.208505i	−0.00233191	−	0.00870281i
$575$	−10.7457	−	54.0223i	−0.448127	−	2.25289i
$576$		0			0
$577$			2.52465i			0.105103i	0.998618	+	0.0525513i	$0.0167353\pi$
$577$			2.52465i			0.105103i	−0.998618	+	0.0525513i	$0.983265\pi$
$578$	−3.04641	+	16.8701i	−0.126714	+	0.701704i
$579$		0			0
$580$	−0.0179628	−	0.136441i	−0.000745866	−	0.00566542i
$581$	−0.171509	−	0.195569i	−0.00711540	−	0.00811355i
$582$		0			0
$583$	16.6558	−	8.21374i	0.689814	−	0.340178i
$584$	−23.9843	−	4.77077i	−0.992476	−	0.197416i
$585$		0			0
$586$	4.15696	+	10.0358i	0.171723	+	0.414575i
$587$	22.0477	+	2.90263i	0.910004	+	0.119804i	0.570971	−	0.820970i	$-0.306567\pi$
$587$	22.0477	+	2.90263i	0.910004	+	0.119804i	0.339033	+	0.940775i	$0.389900\pi$
$588$		0			0
$589$	−3.57918	−	10.5439i	−0.147478	−	0.434455i
$590$	2.36398	−	36.0673i	0.0973233	−	1.48487i
$591$		0			0
$592$	1.78210	−	5.24990i	0.0732439	−	0.215769i
$593$	−33.8563	−	14.0237i	−1.39031	−	0.575885i	−0.443092	−	0.896476i	$-0.646119\pi$
$593$	−33.8563	−	14.0237i	−1.39031	−	0.575885i	−0.947218	+	0.320591i	$0.896119\pi$
$594$		0			0
$595$	0.264737	−	0.598314i	0.0108532	−	0.0245285i
$596$	7.94288	+	4.58582i	0.325353	+	0.187843i
$597$		0			0
$598$	−19.8755	+	17.4303i	−0.812769	+	0.712780i
$599$	17.4913	+	4.68679i	0.714677	+	0.191497i	0.597795	−	0.801649i	$-0.296044\pi$
$599$	17.4913	+	4.68679i	0.714677	+	0.191497i	0.116882	+	0.993146i	$0.462710\pi$
$600$		0			0
$601$	18.6627	+	16.3667i	0.761267	+	0.667613i	0.949237	−	0.314562i	$-0.101857\pi$
$601$	18.6627	+	16.3667i	0.761267	+	0.667613i	−0.187970	+	0.982175i	$0.560191\pi$
$602$	−0.0205510	−	0.0307567i	−0.000837595	−	0.00125355i
$603$		0			0
$604$	−8.11138	+	3.35985i	−0.330048	+	0.136710i
$605$	−5.94084	−	90.6398i	−0.241530	−	3.68503i
$606$		0			0
$607$	−23.4864	−	1.53938i	−0.953283	−	0.0624815i	−0.419182	−	0.907902i	$-0.637683\pi$
$607$	−23.4864	−	1.53938i	−0.953283	−	0.0624815i	−0.534101	+	0.845421i	$0.679350\pi$
$608$	−3.41722	+	12.7532i	−0.138586	+	0.517212i
$609$		0			0
$610$	0.201321	+	0.262367i	0.00815125	+	0.0106229i
$611$	−6.11132			−0.247238
$612$		0			0
$613$	−17.8940			−0.722732			−0.361366	−	0.932424i	$-0.617689\pi$
$613$	−17.8940			−0.722732			−0.361366	+	0.932424i	$0.617689\pi$
$614$	0.670957	+	0.874408i	0.0270776	+	0.0352882i
$615$		0			0
$616$	0.210110	−	0.784140i	0.00846556	−	0.0315939i
$617$	−28.8136	−	1.88854i	−1.15999	−	0.0760299i	−0.526776	−	0.850004i	$-0.676599\pi$
$617$	−28.8136	−	1.88854i	−1.15999	−	0.0760299i	−0.633217	+	0.773974i	$0.718266\pi$
$618$		0			0
$619$	1.16740	+	17.8110i	0.0469217	+	0.715887i	0.954911	+	0.296893i	$0.0959504\pi$
$619$	1.16740	+	17.8110i	0.0469217	+	0.715887i	−0.907989	+	0.418994i	$0.862383\pi$
$620$	−13.4525	+	5.57222i	−0.540267	+	0.223786i
$621$		0			0
$622$	18.5678	+	27.7887i	0.744501	+	1.11422i
$623$	0.605451	+	0.530966i	0.0242569	+	0.0212727i
$624$		0			0
$625$	−4.68638	−	1.25571i	−0.187455	−	0.0502284i
$626$	−3.12199	+	2.73791i	−0.124780	+	0.109429i
$627$		0			0
$628$	−8.71963	−	5.03428i	−0.347951	−	0.200890i
$629$	4.67883	−	20.9009i	0.186557	−	0.833373i
$630$		0			0
$631$	−25.8159	−	10.6933i	−1.02772	−	0.425694i	−0.195829	−	0.980638i	$-0.562740\pi$
$631$	−25.8159	−	10.6933i	−1.02772	−	0.425694i	−0.831888	+	0.554944i	$0.812740\pi$
$632$	5.20225	−	15.3253i	0.206934	−	0.609609i
$633$		0			0
$634$	1.36255	−	20.7885i	0.0541138	−	0.825617i
$635$	16.7265	+	49.2746i	0.663770	+	1.95540i
$636$		0			0
$637$	−25.2218	−	3.32051i	−0.999322	−	0.131563i
$638$	0.0918680	+	0.221789i	0.00363709	+	0.00878071i
$639$		0			0
$640$	9.42874	+	1.87549i	0.372704	+	0.0741354i
$641$	37.7631	−	18.6227i	1.49155	−	0.735553i	0.500095	−	0.865971i	$-0.333299\pi$
$641$	37.7631	−	18.6227i	1.49155	−	0.735553i	0.991459	+	0.130418i	$0.0416319\pi$
$642$		0			0
$643$	15.2754	+	17.4183i	0.602403	+	0.686909i	0.970008	−	0.243073i	$-0.0781555\pi$
$643$	15.2754	+	17.4183i	0.602403	+	0.686909i	−0.367605	+	0.929982i	$0.619822\pi$
$644$	−0.0413063	−	0.313752i	−0.00162770	−	0.0123636i
$645$		0			0
$646$	1.71305	−	10.9793i	0.0673990	−	0.431975i
$647$			19.0689i			0.749678i	0.927090	+	0.374839i	$0.122302\pi$
$647$			19.0689i			0.749678i	−0.927090	+	0.374839i	$0.877698\pi$
$648$		0			0
$649$	−11.8920	−	59.7853i	−0.466803	−	2.34678i
$650$	−7.24671	−	27.0451i	−0.284239	−	1.06080i
$651$		0			0
$652$	2.24634	−	0.762530i	0.0879735	−	0.0298630i
$653$	−13.7091	+	27.7993i	−0.536479	+	1.08787i	0.444862	+	0.895599i	$0.353253\pi$
$653$	−13.7091	+	27.7993i	−0.536479	+	1.08787i	−0.981341	+	0.192273i	$0.938414\pi$
$654$		0			0
$655$	−7.73789	+	58.7751i	−0.302344	+	2.29653i
$656$	−4.25563	+	2.84352i	−0.166154	+	0.111021i
$657$		0			0
$658$	−0.0420408	+	0.0629185i	−0.00163892	+	0.00245282i
$659$	20.1217	−	5.39159i	0.783829	−	0.210026i	0.155357	−	0.987858i	$-0.450347\pi$
$659$	20.1217	−	5.39159i	0.783829	−	0.210026i	0.628472	+	0.777832i	$0.283681\pi$
$660$		0			0
$661$	18.4937	−	2.43474i	0.719321	−	0.0947004i	0.238026	−	0.971259i	$-0.423500\pi$
$661$	18.4937	−	2.43474i	0.719321	−	0.0947004i	0.481295	+	0.876558i	$0.340166\pi$
$662$	7.27718	+	12.6045i	0.282836	+	0.489886i
$663$		0			0
$664$	−8.76512	+	15.1816i	−0.340152	+	0.589161i
$665$	−0.162296	+	0.391816i	−0.00629355	+	0.0151940i
$666$		0			0
$667$	0.200792	+	0.200792i	0.00777468	+	0.00777468i
$668$	−4.74621	−	9.62437i	−0.183637	−	0.372378i
$669$		0			0
$670$	18.7373	+	9.24022i	0.723886	+	0.356981i
$671$	0.442471	+	0.339520i	0.0170814	+	0.0131070i
$672$		0			0
$673$	33.6834	−	2.20773i	1.29840	−	0.0851017i	0.599531	−	0.800351i	$-0.295354\pi$
$673$	33.6834	−	2.20773i	1.29840	−	0.0851017i	0.698869	+	0.715250i	$0.253687\pi$
$674$	−5.35108	+	26.9017i	−0.206116	+	1.03621i
$675$		0			0
$676$	0.149409	−	0.149409i	0.00574649	−	0.00574649i
$677$	−42.1399	−	14.3046i	−1.61957	−	0.549769i	−0.643164	−	0.765729i	$-0.722379\pi$
$677$	−42.1399	−	14.3046i	−1.61957	−	0.549769i	−0.976402	+	0.215960i	$0.930712\pi$
$678$		0			0
$679$	−0.140402	+	0.0810611i	−0.00538813	+	0.00311084i
$680$	−43.9171	−	3.93347i	−1.68414	−	0.150842i
$681$		0			0
$682$	20.1513	−	15.4626i	0.771632	−	0.592094i
$683$	30.5882	−	6.08436i	1.17042	−	0.232812i	0.428655	−	0.903468i	$-0.358987\pi$
$683$	30.5882	−	6.08436i	1.17042	−	0.232812i	0.741768	+	0.670656i	$0.233987\pi$
$684$		0			0
$685$	−26.4156	−	17.6504i	−1.00929	−	0.674385i
$686$	−0.415440	+	0.473719i	−0.0158616	+	0.0180867i
$687$		0			0
$688$	−0.533932	+	0.695834i	−0.0203560	+	0.0265284i
$689$	6.79773	−	8.85897i	0.258973	−	0.337500i
$690$		0			0
$691$	−1.10645	+	1.26166i	−0.0420912	+	0.0479958i	−0.772502	−	0.635012i	$-0.780995\pi$
$691$	−1.10645	+	1.26166i	−0.0420912	+	0.0479958i	0.730411	+	0.683008i	$0.239329\pi$
$692$	−0.858553	−	0.573667i	−0.0326373	−	0.0218075i
$693$		0			0
$694$	32.1301	−	6.39107i	1.21964	−	0.242602i
$695$	−30.9432	+	23.7436i	−1.17374	+	0.900645i
$696$		0			0
$697$	−15.1730	+	12.6784i	−0.574717	+	0.480230i
$698$	−24.1224	+	13.9271i	−0.913048	+	0.527149i
$699$		0			0
$700$	0.317386	+	0.107738i	0.0119961	+	0.00407212i
$701$	−31.7515	+	31.7515i	−1.19924	+	1.19924i	−0.224844	+	0.974395i	$0.572187\pi$
$701$	−31.7515	+	31.7515i	−1.19924	+	1.19924i	−0.974395	+	0.224844i	$0.927813\pi$
$702$		0			0
$703$	−2.70851	+	13.6166i	−0.102153	+	0.513560i
$704$	−42.9309	+	2.81384i	−1.61802	+	0.106051i
$705$		0			0
$706$	−21.1238	−	16.2089i	−0.795007	−	0.610030i
$707$	0.202908	+	0.100063i	0.00763114	+	0.00376326i
$708$		0			0
$709$	−13.2765	−	26.9220i	−0.498608	−	1.01108i	−0.990122	−	0.140207i	$-0.955223\pi$
$709$	−13.2765	−	26.9220i	−0.498608	−	1.01108i	0.491515	−	0.870869i	$-0.336443\pi$
$710$	14.6281	+	14.6281i	0.548983	+	0.548983i
$711$		0			0
$712$	20.7686	−	50.1398i	0.778335	−	1.87907i
$713$	15.0225	−	26.0197i	0.562596	−	0.974445i
$714$		0			0
$715$	−39.0653	−	67.6631i	−1.46096	−	2.53046i
$716$	−8.48087	+	1.11653i	−0.316945	+	0.0417266i
$717$		0			0
$718$	8.63821	−	2.31460i	0.322375	−	0.0863802i
$719$	−8.11589	+	12.1463i	−0.302672	+	0.452980i	−0.951363	−	0.308071i	$-0.900316\pi$
$719$	−8.11589	+	12.1463i	−0.302672	+	0.452980i	0.648692	+	0.761051i	$0.275316\pi$
$720$		0			0
$721$	0.0269492	−	0.0180069i	0.00100364	−	0.000670612i
$722$	1.56068	−	11.8545i	0.0580825	−	0.441180i
$723$		0			0
$724$	−5.04270	+	10.2256i	−0.187410	+	0.380031i
$725$	−0.284794	+	0.0966744i	−0.0105770	+	0.00359040i
$726$		0			0
$727$	3.03341	+	11.3208i	0.112503	+	0.419867i	0.999088	−	0.0426988i	$-0.0135956\pi$
$727$	3.03341	+	11.3208i	0.112503	+	0.419867i	−0.886585	+	0.462566i	$0.846929\pi$
$728$	−0.0952285	−	0.478746i	−0.00352940	−	0.0177435i
$729$		0			0
$730$			29.1421i			1.07860i
$731$	−1.76375	+	2.89311i	−0.0652347	+	0.107006i
$732$		0			0
$733$	−3.54452	−	26.9233i	−0.130920	−	0.994435i	−0.923212	−	0.384292i	$-0.874446\pi$
$733$	−3.54452	−	26.9233i	−0.130920	−	0.994435i	0.792292	−	0.610142i	$-0.208888\pi$
$734$	−24.6733	−	28.1345i	−0.910708	−	1.03846i
$735$		0			0
$736$	−31.9517	+	15.7568i	−1.17776	+	0.580805i
$737$	34.5563	+	6.87367i	1.27290	+	0.253195i
$738$		0			0
$739$	15.1973	+	36.6896i	0.559044	+	1.34965i	0.910524	+	0.413455i	$0.135678\pi$
$739$	15.1973	+	36.6896i	0.559044	+	1.34965i	−0.351481	+	0.936195i	$0.614322\pi$
$740$	17.9998	+	2.36971i	0.661685	+	0.0871124i
$741$		0			0
$742$	−0.0444440	−	0.130928i	−0.00163159	−	0.00480651i
$743$	0.545324	−	8.32003i	0.0200060	−	0.305232i	−0.976116	−	0.217250i	$-0.930291\pi$
$743$	0.545324	−	8.32003i	0.0200060	−	0.305232i	0.996122	−	0.0879825i	$-0.0280420\pi$
$744$		0			0
$745$	10.6606	−	31.4051i	0.390575	−	1.15060i
$746$	−13.4029	−	5.55168i	−0.490717	−	0.203262i
$747$		0			0
$748$	−24.1427	+	4.20573i	−0.882745	+	0.153777i
$749$	0.0940918	+	0.0543239i	0.00343804	+	0.00198495i
$750$		0			0
$751$	20.5314	−	18.0056i	0.749203	−	0.657034i	−0.197075	−	0.980389i	$-0.563144\pi$
$751$	20.5314	−	18.0056i	0.749203	−	0.657034i	0.946278	+	0.323355i	$0.104811\pi$
$752$	1.73309	+	0.464380i	0.0631993	+	0.0169342i
$753$		0			0
$754$	0.108525	+	0.0951742i	0.00395226	+	0.00346604i
$755$	17.6382	+	26.3974i	0.641920	+	0.960700i
$756$		0			0
$757$	19.8952	−	8.24087i	0.723104	−	0.299520i	0.00938948	−	0.999956i	$-0.497011\pi$
$757$	19.8952	−	8.24087i	0.723104	−	0.299520i	0.713715	+	0.700436i	$0.247011\pi$
$758$	1.10343	+	16.8351i	0.0400785	+	0.611479i
$759$		0			0
$760$	28.5200	+	1.86930i	1.03453	+	0.0678067i
$761$	3.50934	−	13.0970i	0.127213	−	0.474767i	−0.872695	−	0.488265i	$-0.837630\pi$
$761$	3.50934	−	13.0970i	0.127213	−	0.474767i	0.999909	+	0.0134978i	$0.00429662\pi$
$762$		0			0
$763$	−0.245899	−	0.320461i	−0.00890213	−	0.0116015i
$764$	−21.0823			−0.762731
$765$		0			0
$766$	−36.8856			−1.33273
$767$	−22.3125	−	29.0783i	−0.805659	−	1.04996i
$768$		0			0
$769$	−6.16375	+	23.0034i	−0.222271	+	0.829525i	0.761209	+	0.648507i	$0.224606\pi$
$769$	−6.16375	+	23.0034i	−0.222271	+	0.829525i	−0.983480	+	0.181019i	$0.942061\pi$
$770$	−0.965356	−	0.0632727i	−0.0347890	−	0.00228019i
$771$		0			0
$772$	−0.0341903	−	0.521643i	−0.00123054	−	0.0187743i
$773$	34.8872	−	14.4507i	1.25480	−	0.519757i	0.346493	−	0.938053i	$-0.387372\pi$
$773$	34.8872	−	14.4507i	1.25480	−	0.519757i	0.908311	+	0.418296i	$0.137372\pi$
$774$		0			0
$775$	17.6792	+	26.4588i	0.635056	+	0.950428i
$776$	8.21451	+	7.20393i	0.294884	+	0.258606i
$777$		0			0
$778$	−17.2001	−	4.60875i	−0.616653	−	0.165232i
$779$	9.63617	−	8.45069i	0.345252	−	0.302778i
$780$		0			0
$781$	30.2141	+	17.4441i	1.08115	+	0.624200i
$782$	25.3211	−	16.0581i	0.905481	−	0.574235i
$783$		0			0
$784$	6.90025	+	2.85818i	0.246437	+	0.102078i
$785$	−11.7031	+	34.4763i	−0.417703	+	1.23051i
$786$		0			0
$787$	2.24777	−	34.2943i	0.0801243	−	1.22246i	−0.748684	−	0.662927i	$-0.769314\pi$
$787$	2.24777	−	34.2943i	0.0801243	−	1.22246i	0.828808	−	0.559533i	$-0.189019\pi$
$788$	2.53267	+	7.46100i	0.0902225	+	0.265787i
$789$		0			0
$790$	−19.1218	−	2.51744i	−0.680324	−	0.0895664i
$791$	0.00288261	+	0.00695924i	0.000102494	+	0.000247442i
$792$		0			0
$793$	0.328907	+	0.0654237i	0.0116798	+	0.00232327i
$794$	−18.2644	+	9.00700i	−0.648179	+	0.319646i
$795$		0			0
$796$	−1.93836	−	2.21028i	−0.0687035	−	0.0783413i
$797$	−2.34507	−	17.8125i	−0.0830665	−	0.630952i	−0.981447	−	0.191734i	$-0.938589\pi$
$797$	−2.34507	−	17.8125i	−0.0830665	−	0.630952i	0.898380	−	0.439218i	$-0.144744\pi$
$798$		0			0
$799$	6.84864	+	1.06856i	0.242287	+	0.0378030i
$800$		−	37.7325i		−	1.33404i
$801$		0			0
$802$	−2.76103	−	13.8807i	−0.0974955	−	0.490143i
$803$	12.7202	+	47.4724i	0.448886	+	1.67526i
$804$		0			0
$805$	−1.08361	+	0.367835i	−0.0381921	+	0.0129645i
$806$	6.75497	−	13.6977i	0.237934	−	0.482482i
$807$		0			0
$808$	1.99012	−	15.1165i	0.0700123	−	0.531796i
$809$	33.5595	−	22.4237i	1.17989	−	0.788377i	0.198443	−	0.980112i	$-0.436412\pi$
$809$	33.5595	−	22.4237i	1.17989	−	0.788377i	0.981447	+	0.191735i	$0.0614116\pi$
$810$		0			0
$811$	27.5220	−	41.1896i	0.966429	−	1.44636i	0.0729089	−	0.997339i	$-0.476772\pi$
$811$	27.5220	−	41.1896i	0.966429	−	1.44636i	0.893520	−	0.449024i	$-0.148228\pi$
$812$	−0.00166907		0.000447227i	−5.85730e−5		1.56946e-5i
$813$		0			0
$814$	−31.3989	+	4.13374i	−1.10053	+	0.144888i
$815$	−4.28907	−	7.42889i	−0.150240	−	0.260223i
$816$		0			0
$817$	1.09817	−	1.90209i	0.0384202	−	0.0665457i
$818$	−1.88131	+	4.54188i	−0.0657784	+	0.158803i
$819$		0			0
$820$	−11.8514	−	11.8514i	−0.413867	−	0.413867i
$821$	9.05339	+	18.3585i	0.315966	+	0.640715i	0.995689	−	0.0927536i	$-0.0295669\pi$
$821$	9.05339	+	18.3585i	0.315966	+	0.640715i	−0.679724	+	0.733468i	$0.737900\pi$
$822$		0			0
$823$	3.87792	+	1.91238i	0.135176	+	0.0666613i	0.508619	−	0.860992i	$-0.330156\pi$
$823$	3.87792	+	1.91238i	0.135176	+	0.0666613i	−0.373443	+	0.927653i	$0.621823\pi$
$824$	−1.73293	−	1.32972i	−0.0603693	−	0.0463230i
$825$		0			0
$826$	−0.452864	+	0.0296823i	−0.0157572	+	0.00103278i
$827$	10.3076	−	51.8200i	0.358432	−	1.80196i	−0.208308	−	0.978063i	$-0.566796\pi$
$827$	10.3076	−	51.8200i	0.358432	−	1.80196i	0.566740	−	0.823896i	$-0.308204\pi$
$828$		0			0
$829$	28.8577	−	28.8577i	1.00227	−	1.00227i	0.00227095	−	0.999997i	$-0.499277\pi$
$829$	28.8577	−	28.8577i	1.00227	−	1.00227i	0.999997	−	0.00227095i	$-0.000722865\pi$
$830$	19.7822	+	6.71515i	0.686649	+	0.233086i
$831$		0			0
$832$	−22.4034	+	12.9346i	−0.776697	+	0.448426i
$833$	27.6841	+	8.13113i	0.959198	+	0.281727i
$834$		0			0
$835$	−30.7853	+	23.6224i	−1.06537	+	0.817487i
$836$	15.5799	−	3.09903i	0.538841	−	0.107182i
$837$		0			0
$838$	−22.3308	−	14.9210i	−0.771404	−	0.515436i
$839$	21.4617	−	24.4724i	0.740941	−	0.844881i	−0.251468	−	0.967866i	$-0.580913\pi$
$839$	21.4617	−	24.4724i	0.740941	−	0.844881i	0.992409	+	0.122985i	$0.0392466\pi$
$840$		0			0
$841$	−17.6531	+	23.0060i	−0.608729	+	0.793311i
$842$	20.4030	−	26.5898i	0.703135	−	0.916343i
$843$		0			0
$844$	7.84295	−	8.94317i	0.269966	−	0.307837i
$845$	−0.635291	−	0.424488i	−0.0218547	−	0.0146028i
$846$		0			0
$847$	−1.11861	+	0.222505i	−0.0384358	+	0.00764536i
$848$	−2.60091	+	1.99575i	−0.0893157	+	0.0685344i
$849$		0			0
$850$	3.39219	+	31.5751i	0.116351	+	1.08302i
$851$	−32.4423	+	18.7306i	−1.11211	+	0.642076i
$852$		0			0
$853$	41.5544	+	14.1058i	1.42280	+	0.482974i	0.923547	−	0.383485i	$-0.125276\pi$
$853$	41.5544	+	14.1058i	1.42280	+	0.482974i	0.499248	+	0.866459i	$0.333609\pi$
$854$	0.00293617	−	0.00293617i	0.000100474	−	0.000100474i
$855$		0			0
$856$	1.42847	−	7.18139i	0.0488240	−	0.245455i
$857$	−22.0443	+	1.44486i	−0.753020	+	0.0493555i	−0.437079	−	0.899423i	$-0.643987\pi$
$857$	−22.0443	+	1.44486i	−0.753020	+	0.0493555i	−0.315941	+	0.948779i	$0.602320\pi$
$858$		0			0
$859$	−6.16767	−	4.73262i	−0.210438	−	0.161475i	0.498165	−	0.867083i	$-0.334008\pi$
$859$	−6.16767	−	4.73262i	−0.210438	−	0.161475i	−0.708603	+	0.705607i	$0.750674\pi$
$860$	−2.57594	−	1.27031i	−0.0878387	−	0.0433173i
$861$		0			0
$862$	−8.96830	−	18.1859i	−0.305462	−	0.619415i
$863$	−0.406686	−	0.406686i	−0.0138437	−	0.0138437i	0.700151	−	0.713995i	$-0.253116\pi$
$863$	−0.406686	−	0.406686i	−0.0138437	−	0.0138437i	−0.713995	+	0.700151i	$0.753116\pi$
$864$		0			0
$865$	−1.42888	+	3.44962i	−0.0485834	+	0.117291i
$866$	−2.28801	+	3.96294i	−0.0777496	+	0.134666i
$867$		0			0
$868$	0.0914141	+	0.158334i	0.00310280	+	0.00537420i
$869$	−32.2482	+	4.24556i	−1.09395	+	0.144021i
$870$		0			0
$871$	20.4634	−	5.48316i	0.693376	−	0.185790i
$872$	−15.1238	+	22.6344i	−0.512158	+	0.766498i
$873$		0			0
$874$	−16.1601	+	10.7978i	−0.546622	+	0.365241i
$875$	0.0546375	−	0.415013i	0.00184709	−	0.0140300i
$876$		0			0
$877$	14.7602	−	29.9306i	0.498415	−	1.01069i	−0.491744	−	0.870740i	$-0.663640\pi$
$877$	14.7602	−	29.9306i	0.498415	−	1.01069i	0.990159	−	0.139946i	$-0.0446929\pi$
$878$	1.69820	−	0.576461i	0.0573115	−	0.0194546i
$879$		0			0
$880$	5.93690	+	22.1568i	0.200133	+	0.746907i
$881$	4.35402	+	21.8892i	0.146691	+	0.737465i	0.982178	+	0.187954i	$0.0601857\pi$
$881$	4.35402	+	21.8892i	0.146691	+	0.737465i	−0.835487	+	0.549510i	$0.814814\pi$
$882$		0			0
$883$			11.7962i			0.396975i	0.980103	+	0.198487i	$0.0636029\pi$
$883$			11.7962i			0.396975i	−0.980103	+	0.198487i	$0.936397\pi$
$884$	−11.9011	+	8.68862i	−0.400279	+	0.292230i
$885$		0			0
$886$	4.06070	+	30.8441i	0.136422	+	1.03623i
$887$	−14.5275	−	16.5655i	−0.487787	−	0.556215i	0.454619	−	0.890686i	$-0.349776\pi$
$887$	−14.5275	−	16.5655i	−0.487787	−	0.556215i	−0.942406	+	0.334472i	$0.891442\pi$
$888$		0			0
$889$	0.585990	−	0.288978i	0.0196535	−	0.00969202i
$890$	−63.4322	−	12.6174i	−2.12625	−	0.422938i
$891$		0			0
$892$	−2.94022	−	7.09832i	−0.0984459	−	0.237669i
$893$	−4.45459	−	0.586458i	−0.149067	−	0.0196251i
$894$		0			0
$895$	9.94276	+	29.2904i	0.332350	+	0.979071i
$896$	0.00789465	−	0.120449i	0.000263742	−	0.00402392i
$897$		0			0
$898$	−11.5205	+	33.9383i	−0.384444	+	1.13254i
$899$	−0.151566	−	0.0627805i	−0.00505499	−	0.00209385i
$900$		0			0
$901$	−9.16684	+	8.73921i	−0.305392	+	0.291145i
$902$	25.3198	+	14.6184i	0.843058	+	0.486740i
$903$		0			0
$904$	0.381668	−	0.334714i	0.0126941	−	0.0111324i
$905$	39.8232	+	10.6706i	1.32377	+	0.354703i
$906$		0			0
$907$	31.3287	+	27.4745i	1.04025	+	0.912276i	0.996230	−	0.0867547i	$-0.0276496\pi$
$907$	31.3287	+	27.4745i	1.04025	+	0.912276i	0.0440216	+	0.999031i	$0.485983\pi$
$908$	3.23363	+	4.83947i	0.107312	+	0.160603i
$909$		0			0
$910$	−0.537421	+	0.222607i	−0.0178153	+	0.00737936i
$911$	0.276446	+	4.21774i	0.00915905	+	0.139740i	0.999989	+	0.00462745i	$0.00147297\pi$
$911$	0.276446	+	4.21774i	0.00915905	+	0.139740i	−0.990830	+	0.135113i	$0.956860\pi$
$912$		0			0
$913$	35.1562	+	2.30426i	1.16350	+	0.0762598i
$914$	−1.58832	+	5.92768i	−0.0525368	+	0.196070i
$915$		0			0
$916$	−8.30738	−	10.8264i	−0.274484	−	0.357714i
$917$	0.744354			0.0245807
$918$		0			0
$919$	46.8684			1.54604			0.773022	−	0.634379i	$-0.218744\pi$
$919$	46.8684			1.54604			0.773022	+	0.634379i	$0.218744\pi$
$920$	46.9477	+	61.1835i	1.54782	+	2.01716i
$921$		0			0
$922$	−10.0462	+	37.4928i	−0.330853	+	1.23476i
$923$	20.9329	+	1.37202i	0.689016	+	0.0451605i
$924$		0			0
$925$	−2.59497	−	39.5916i	−0.0853220	−	1.30176i
$926$	−18.1744	+	7.52808i	−0.597248	+	0.247388i
$927$		0			0
$928$	0.108073	+	0.161742i	0.00354766	+	0.00530944i
$929$	11.7482	+	10.3029i	0.385446	+	0.338027i	0.830039	−	0.557706i	$-0.188318\pi$
$929$	11.7482	+	10.3029i	0.385446	+	0.338027i	−0.444593	+	0.895733i	$0.646652\pi$
$930$		0			0
$931$	−18.0657	−	4.84069i	−0.592079	−	0.158647i
$932$	11.1804	−	9.80496i	0.366227	−	0.321172i
$933$		0			0
$934$	1.30561	+	0.753796i	0.0427210	+	0.0246650i
$935$	31.9476	+	82.6571i	1.04480	+	2.70317i
$936$		0			0
$937$	39.6097	+	16.4069i	1.29399	+	0.535989i	0.920173	−	0.391512i	$-0.128048\pi$
$937$	39.6097	+	16.4069i	1.29399	+	0.535989i	0.373819	+	0.927502i	$0.378048\pi$
$938$	0.0843200	−	0.248399i	0.00275314	−	0.00811050i
$939$		0			0
$940$	−0.384275	+	5.86290i	−0.0125337	+	0.191227i
$941$	−8.02307	−	23.6352i	−0.261545	−	0.770486i	−0.995795	−	0.0916071i	$-0.970800\pi$
$941$	−8.02307	−	23.6352i	−0.261545	−	0.770486i	0.734251	−	0.678878i	$-0.237534\pi$
$942$		0			0
$943$	34.2874	+	4.51402i	1.11655	+	0.146997i
$944$	4.11798	+	9.94168i	0.134029	+	0.323574i
$945$		0			0
$946$	4.91389	+	0.977434i	0.159764	+	0.0317791i
$947$	−41.3935	+	20.4130i	−1.34511	+	0.663334i	−0.965157	−	0.261672i	$-0.915726\pi$
$947$	−41.3935	+	20.4130i	−1.34511	+	0.663334i	−0.379952	+	0.925006i	$0.624059\pi$
$948$		0			0
$949$	19.4846	+	22.2180i	0.632498	+	0.721225i
$950$	−2.68687	−	20.4088i	−0.0871736	−	0.662149i
$951$		0			0
$952$	0.0230092	+	0.553156i	0.000745732	+	0.0179279i
$953$		−	27.3799i		−	0.886922i	−0.896294	−	0.443461i	$-0.853751\pi$
$953$		−	27.3799i		−	0.886922i	0.896294	−	0.443461i	$-0.146249\pi$
$954$		0			0
$955$	14.8727	+	74.7701i	0.481269	+	2.41950i
$956$	−1.25484	−	4.68313i	−0.0405844	−	0.151463i
$957$		0			0
$958$	2.64955	−	0.899401i	0.0856031	−	0.0290583i
$959$	−0.176431	+	0.357767i	−0.00569725	+	0.0115529i
$960$		0			0
$961$	1.78066	−	13.5254i	0.0574405	−	0.436304i
$962$	−15.8334	+	10.5795i	−0.510489	+	0.341098i
$963$		0			0
$964$	−8.18982	+	12.2569i	−0.263776	+	0.394769i
$965$	−1.82593	+	0.489256i	−0.0587787	+	0.0157497i
$966$		0			0
$967$	−46.4408	+	6.11404i	−1.49343	+	0.196614i	−0.832582	−	0.553902i	$-0.813138\pi$
$967$	−46.4408	+	6.11404i	−1.49343	+	0.196614i	−0.660852	+	0.750516i	$0.729805\pi$
$968$	38.4316	+	66.5654i	1.23524	+	2.13949i
$969$		0			0
$970$	6.51021	−	11.2760i	0.209030	−	0.362051i
$971$	12.9063	−	31.1585i	0.414183	−	0.999925i	−0.569820	−	0.821770i	$-0.692987\pi$
$971$	12.9063	−	31.1585i	0.414183	−	0.999925i	0.984002	−	0.178156i	$-0.0570131\pi$
$972$		0			0
$973$	0.346289	+	0.346289i	0.0111015	+	0.0111015i
$974$	−9.36127	−	18.9828i	−0.299954	−	0.608247i
$975$		0			0
$976$	−0.0883025	−	0.0435460i	−0.00282649	−	0.00139387i
$977$	1.91476	+	1.46925i	0.0612585	+	0.0470053i	0.638937	−	0.769259i	$-0.279375\pi$
$977$	1.91476	+	1.46925i	0.0612585	+	0.0470053i	−0.577678	+	0.816265i	$0.696041\pi$
$978$		0			0
$979$	−108.838	+	7.13363i	−3.47848	+	0.227992i
$980$	−4.77145	+	23.9877i	−0.152418	+	0.766259i
$981$		0			0
$982$	17.0315	−	17.0315i	0.543497	−	0.543497i
$983$	33.6141	+	11.4104i	1.07212	+	0.363937i	0.801035	−	0.598618i	$-0.204283\pi$
$983$	33.6141	+	11.4104i	1.07212	+	0.363937i	0.271088	+	0.962555i	$0.412617\pi$
$984$		0			0
$985$	24.6743	−	14.2457i	0.786189	−	0.453906i
$986$	−0.104978	−	0.125632i	−0.00334317	−	0.00400095i
$987$		0			0
$988$	7.57771	−	5.81458i	0.241079	−	0.184987i
$989$	5.81248	−	1.15617i	0.184826	−	0.0367642i
$990$		0			0
$991$	−6.75372	−	4.51269i	−0.214539	−	0.143350i	0.443658	−	0.896196i	$-0.353681\pi$
$991$	−6.75372	−	4.51269i	−0.214539	−	0.143350i	−0.658197	+	0.752846i	$0.728681\pi$
$992$	13.5707	−	15.4744i	0.430869	−	0.491312i
$993$		0			0
$994$	0.158127	−	0.206075i	0.00501547	−	0.00653629i
$995$	−6.47150	+	8.43382i	−0.205160	+	0.267370i
$996$		0			0
$997$	−34.7445	+	39.6185i	−1.10037	+	1.25473i	−0.135845	+	0.990730i	$0.543375\pi$
$997$	−34.7445	+	39.6185i	−1.10037	+	1.25473i	−0.964523	+	0.263999i	$0.914958\pi$
$998$	1.83631	+	1.22698i	0.0581274	+	0.0388395i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.y.a.62.10		256
3.2	odd	2		153.2.s.a.11.7	✓	256
9.4	even	3		153.2.s.a.113.7	yes	256
9.5	odd	6	inner	459.2.y.a.368.10		256
17.14	odd	16	inner	459.2.y.a.116.10		256
51.14	even	16		153.2.s.a.65.7	yes	256
153.14	even	48	inner	459.2.y.a.422.10		256
153.31	odd	48		153.2.s.a.14.7	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.7	✓	256	3.2	odd	2
153.2.s.a.14.7	yes	256	153.31	odd	48
153.2.s.a.65.7	yes	256	51.14	even	16
153.2.s.a.113.7	yes	256	9.4	even	3
459.2.y.a.62.10		256	1.1	even	1	trivial
459.2.y.a.116.10		256	17.14	odd	16	inner
459.2.y.a.368.10		256	9.5	odd	6	inner
459.2.y.a.422.10		256	153.14	even	48	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.y (of order \(48\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.613881 + 0.800025i) q^{2} +(0.254448 - 0.949612i) q^{4} +(-3.54737 - 0.232507i) q^{5} +(0.00291938 + 0.0445412i) q^{7} +(2.77921 - 1.15119i) q^{8} +(-1.99165 - 2.98072i) q^{10} +(-4.54544 - 3.98625i) q^{11} +(-3.51137 - 0.940868i) q^{13} +(-0.0338419 + 0.0296785i) q^{14} +(0.924284 + 0.533636i) q^{16} +(3.77050 + 1.66834i) q^{17} +(-2.46918 - 1.02277i) q^{19} +(-1.12341 + 3.30947i) q^{20} +(0.398737 - 6.08355i) q^{22} +(-2.31805 - 6.82875i) q^{23} +(7.57258 + 0.996950i) q^{25} +(-1.40284 - 3.38676i) q^{26} +(0.0430397 + 0.00856112i) q^{28} +(-0.0353157 + 0.0174158i) q^{29} +(2.74702 + 3.13237i) q^{31} +(-0.644819 - 4.89788i) q^{32} +(0.979919 + 4.04065i) q^{34} -0.158683i q^{35} +(-1.01343 - 5.09486i) q^{37} +(-0.697541 - 2.60326i) q^{38} +(-10.1266 + 3.43751i) q^{40} +(-2.12104 + 4.30104i) q^{41} +(-0.107266 + 0.814765i) q^{43} +(-4.94197 + 3.30212i) q^{44} +(4.04017 - 6.04654i) q^{46} +(1.62385 - 0.435110i) q^{47} +(6.93814 - 0.913423i) q^{49} +(3.85108 + 6.67026i) q^{50} +(-1.78692 + 3.09503i) q^{52} +(-1.17550 + 2.83792i) q^{53} +(15.1976 + 15.1976i) q^{55} +(0.0593888 + 0.120429i) q^{56} +(-0.0356127 - 0.0175622i) q^{58} +(7.99901 + 6.13786i) q^{59} +(-0.0920527 + 0.00603345i) q^{61} +(-0.819636 + 4.12059i) q^{62} +(5.03194 - 5.03194i) q^{64} +(12.2374 + 4.15403i) q^{65} +(-5.04699 + 2.91388i) q^{67} +(2.54367 - 3.15600i) q^{68} +(0.126950 - 0.0974124i) q^{70} +(-5.65982 + 1.12581i) q^{71} +(-6.75916 - 4.51633i) q^{73} +(3.45389 - 3.93840i) q^{74} +(-1.59951 + 2.08452i) q^{76} +(0.164282 - 0.214097i) q^{77} +(3.54731 - 4.04493i) q^{79} +(-3.15471 - 2.10791i) q^{80} +(-4.74300 + 0.943442i) q^{82} +(-4.62326 + 3.54755i) q^{83} +(-12.9875 - 6.79490i) q^{85} +(-0.717681 + 0.414353i) q^{86} +(-17.2217 - 5.84597i) q^{88} +(12.7569 - 12.7569i) q^{89} +(0.0316563 - 0.159147i) q^{91} +(-7.07449 + 0.463687i) q^{92} +(1.34495 + 1.03202i) q^{94} +(8.52129 + 4.20223i) q^{95} +(1.60641 + 3.25748i) q^{97} +(4.98995 + 4.98995i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Introduction

L-functions

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