LMFDB - Embedded newform 297.2.t.a.8.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(8,297)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("297.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.t (of order $30$, degree $8$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			8.5
Character	$\chi$	$=$	297.8
Dual form			297.2.t.a.260.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0386735 - 0.367954i) q^{2} +(1.82240 - 0.387363i) q^{4} +(2.36345 + 0.248408i) q^{5} +(1.17198 - 1.05526i) q^{7} +(-0.441671 - 1.35932i) q^{8} -0.879247i q^{10} +(-3.26686 - 0.572386i) q^{11} +(-2.49300 + 5.59938i) q^{13} +(-0.433611 - 0.390425i) q^{14} +(2.92099 - 1.30051i) q^{16} +(-0.887473 - 0.644787i) q^{17} +(-0.534855 + 0.173785i) q^{19} +(4.40337 - 0.462813i) q^{20} +(-0.0842709 + 1.22419i) q^{22} +(4.81854 - 2.78199i) q^{23} +(0.633436 + 0.134641i) q^{25} +(2.15673 + 0.700764i) q^{26} +(1.72705 - 2.37708i) q^{28} +(0.496707 + 0.551649i) q^{29} +(-5.78029 - 2.57355i) q^{31} +(-2.02077 - 3.50008i) q^{32} +(-0.202930 + 0.351486i) q^{34} +(3.03205 - 2.20291i) q^{35} +(1.32443 - 4.07617i) q^{37} +(0.0846296 + 0.190081i) q^{38} +(-0.706199 - 3.32241i) q^{40} +(-8.13175 + 9.03123i) q^{41} +(7.35471 + 4.24624i) q^{43} +(-6.17525 + 0.222344i) q^{44} +(-1.20999 - 1.66541i) q^{46} +(0.160007 - 0.752776i) q^{47} +(-0.471726 + 4.48817i) q^{49} +(0.0250445 - 0.238282i) q^{50} +(-2.37426 + 11.1700i) q^{52} +(2.66042 + 3.66175i) q^{53} +(-7.57886 - 2.16432i) q^{55} +(-1.95207 - 1.12703i) q^{56} +(0.183772 - 0.204100i) q^{58} +(-0.00233571 - 0.0109886i) q^{59} +(-2.33096 - 5.23542i) q^{61} +(-0.723404 + 2.22641i) q^{62} +(3.96382 - 2.87988i) q^{64} +(-7.28302 + 12.6146i) q^{65} +(-0.738332 - 1.27883i) q^{67} +(-1.86710 - 0.831285i) q^{68} +(-0.927831 - 1.03046i) q^{70} +(-4.89992 + 6.74417i) q^{71} +(-14.9894 - 4.87035i) q^{73} +(-1.55106 - 0.329689i) q^{74} +(-0.907402 + 0.523889i) q^{76} +(-4.43271 + 2.77655i) q^{77} +(-3.16382 + 0.332531i) q^{79} +(7.22666 - 2.34809i) q^{80} +(3.63756 + 2.64284i) q^{82} +(9.48546 - 4.22320i) q^{83} +(-1.93732 - 1.74437i) q^{85} +(1.27799 - 2.87041i) q^{86} +(0.664820 + 4.69353i) q^{88} +9.01115i q^{89} +(2.98703 + 9.19313i) q^{91} +(7.70368 - 6.93642i) q^{92} +(-0.283175 - 0.0297629i) q^{94} +(-1.30727 + 0.277869i) q^{95} +(-0.579063 - 5.50942i) q^{97} +1.66968 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) $ 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.0386735	−	0.367954i	−0.0273463	−	0.260183i	−0.999650	−	0.0264611i	$-0.991576\pi$
$2$	−0.0386735	−	0.367954i	−0.0273463	−	0.260183i	0.972304	−	0.233722i	$-0.0750905\pi$
$3$		0			0
$3$		0			0
$4$	1.82240	−	0.387363i	0.911200	−	0.193682i
$5$	2.36345	+	0.248408i	1.05697	+	0.111092i	0.617031	−	0.786939i	$-0.288335\pi$
$5$	2.36345	+	0.248408i	1.05697	+	0.111092i	0.439934	+	0.898030i	$0.355002\pi$
$6$		0			0
$7$	1.17198	−	1.05526i	0.442967	−	0.398850i	−0.417238	−	0.908797i	$-0.637002\pi$
$7$	1.17198	−	1.05526i	0.442967	−	0.398850i	0.860205	+	0.509948i	$0.170335\pi$
$8$	−0.441671	−	1.35932i	−0.156154	−	0.480594i
$9$		0			0
$10$		−	0.879247i		−	0.278042i
$11$	−3.26686	−	0.572386i	−0.984995	−	0.172581i
$11$	−3.26686	−	0.572386i	−0.984995	−	0.172581i
$12$		0			0
$13$	−2.49300	+	5.59938i	−0.691435	+	1.55299i	0.135553	+	0.990770i	$0.456719\pi$
$13$	−2.49300	+	5.59938i	−0.691435	+	1.55299i	−0.826989	+	0.562219i	$0.809948\pi$
$14$	−0.433611	−	0.390425i	−0.115887	−	0.104345i
$15$		0			0
$16$	2.92099	−	1.30051i	0.730248	−	0.325127i
$17$	−0.887473	−	0.644787i	−0.215244	−	0.156384i	0.474939	−	0.880019i	$-0.342470\pi$
$17$	−0.887473	−	0.644787i	−0.215244	−	0.156384i	−0.690183	+	0.723635i	$0.742470\pi$
$18$		0			0
$19$	−0.534855	+	0.173785i	−0.122704	+	0.0398690i	−0.369725	−	0.929141i	$-0.620548\pi$
$19$	−0.534855	+	0.173785i	−0.122704	+	0.0398690i	0.247021	+	0.969010i	$0.420548\pi$
$20$	4.40337	−	0.462813i	0.984624	−	0.103488i
$21$		0			0
$22$	−0.0842709	+	1.22419i	−0.0179666	+	0.260998i
$23$	4.81854	−	2.78199i	1.00474	−	0.580085i	0.0950898	−	0.995469i	$-0.469686\pi$
$23$	4.81854	−	2.78199i	1.00474	−	0.580085i	0.909646	+	0.415384i	$0.136353\pi$
$24$		0			0
$25$	0.633436	+	0.134641i	0.126687	+	0.0269282i
$26$	2.15673	+	0.700764i	0.422969	+	0.137431i
$27$		0			0
$28$	1.72705	−	2.37708i	0.326382	−	0.449227i
$29$	0.496707	+	0.551649i	0.0922363	+	0.102439i	0.787496	−	0.616320i	$-0.211377\pi$
$29$	0.496707	+	0.551649i	0.0922363	+	0.102439i	−0.695260	+	0.718759i	$0.744711\pi$
$30$		0			0
$31$	−5.78029	−	2.57355i	−1.03817	−	0.462223i	−0.184388	−	0.982854i	$-0.559030\pi$
$31$	−5.78029	−	2.57355i	−1.03817	−	0.462223i	−0.853782	+	0.520630i	$0.825697\pi$
$32$	−2.02077	−	3.50008i	−0.357225	−	0.618732i
$33$		0			0
$34$	−0.202930	+	0.351486i	−0.0348023	+	0.0602793i
$35$	3.03205	−	2.20291i	0.512510	−	0.372360i
$36$		0			0
$37$	1.32443	−	4.07617i	0.217735	−	0.670118i	−0.781214	−	0.624264i	$-0.785399\pi$
$37$	1.32443	−	4.07617i	0.217735	−	0.670118i	0.998948	−	0.0458543i	$-0.0146010\pi$
$38$	0.0846296	+	0.190081i	0.0137287	+	0.0308352i
$39$		0			0
$40$	−0.706199	−	3.32241i	−0.111660	−	0.525319i
$41$	−8.13175	+	9.03123i	−1.26997	+	1.41044i	−0.400614	+	0.916247i	$0.631203\pi$
$41$	−8.13175	+	9.03123i	−1.26997	+	1.41044i	−0.869352	+	0.494194i	$0.835463\pi$
$42$		0			0
$43$	7.35471	+	4.24624i	1.12158	+	0.647546i	0.941804	−	0.336162i	$-0.109129\pi$
$43$	7.35471	+	4.24624i	1.12158	+	0.647546i	0.179778	+	0.983707i	$0.442462\pi$
$44$	−6.17525	+	0.222344i	−0.930954	+	0.0335197i
$45$		0			0
$46$	−1.20999	−	1.66541i	−0.178404	−	0.245552i
$47$	0.160007	−	0.752776i	0.0233395	−	0.109804i	−0.964936	−	0.262486i	$-0.915458\pi$
$47$	0.160007	−	0.752776i	0.0233395	−	0.109804i	0.988275	+	0.152682i	$0.0487911\pi$
$48$		0			0
$49$	−0.471726	+	4.48817i	−0.0673894	+	0.641167i
$50$	0.0250445	−	0.238282i	0.00354183	−	0.0336982i
$51$		0			0
$52$	−2.37426	+	11.1700i	−0.329251	+	1.54900i
$53$	2.66042	+	3.66175i	0.365437	+	0.502981i	0.951653	−	0.307174i	$-0.0993833\pi$
$53$	2.66042	+	3.66175i	0.365437	+	0.502981i	−0.586217	+	0.810154i	$0.699383\pi$
$54$		0			0
$55$	−7.57886	−	2.16432i	−1.02193	−	0.291837i
$56$	−1.95207	−	1.12703i	−0.260856	−	0.150605i
$57$		0			0
$58$	0.183772	−	0.204100i	0.0241305	−	0.0267996i
$59$	−0.00233571	−	0.0109886i	−0.000304083	−	0.00143060i	0.977995	−	0.208627i	$-0.0668994\pi$
$59$	−0.00233571	−	0.0109886i	−0.000304083	−	0.00143060i	−0.978299	+	0.207196i	$0.933566\pi$
$60$		0			0
$61$	−2.33096	−	5.23542i	−0.298449	−	0.670327i	0.700617	−	0.713537i	$-0.252908\pi$
$61$	−2.33096	−	5.23542i	−0.298449	−	0.670327i	−0.999066	+	0.0432102i	$0.986241\pi$
$62$	−0.723404	+	2.22641i	−0.0918724	+	0.282754i
$63$		0			0
$64$	3.96382	−	2.87988i	0.495477	−	0.359985i
$65$	−7.28302	+	12.6146i	−0.903347	+	1.56464i
$66$		0			0
$67$	−0.738332	−	1.27883i	−0.0902017	−	0.156234i	0.817394	−	0.576079i	$-0.195418\pi$
$67$	−0.738332	−	1.27883i	−0.0902017	−	0.156234i	−0.907596	+	0.419845i	$0.862084\pi$
$68$	−1.86710	−	0.831285i	−0.226419	−	0.100808i
$69$		0			0
$70$	−0.927831	−	1.03046i	−0.110897	−	0.123164i
$71$	−4.89992	+	6.74417i	−0.581514	+	0.800385i	−0.993860	−	0.110642i	$-0.964709\pi$
$71$	−4.89992	+	6.74417i	−0.581514	+	0.800385i	0.412346	+	0.911027i	$0.364709\pi$
$72$		0			0
$73$	−14.9894	−	4.87035i	−1.75438	−	0.570031i	−0.757783	−	0.652507i	$-0.773717\pi$
$73$	−14.9894	−	4.87035i	−1.75438	−	0.570031i	−0.996593	+	0.0824752i	$0.973717\pi$
$74$	−1.55106	−	0.329689i	−0.180308	−	0.0383256i
$75$		0			0
$76$	−0.907402	+	0.523889i	−0.104086	+	0.0600941i
$77$	−4.43271	+	2.77655i	−0.505155	+	0.316417i
$78$		0			0
$79$	−3.16382	+	0.332531i	−0.355957	+	0.0374126i	−0.280820	−	0.959761i	$-0.590606\pi$
$79$	−3.16382	+	0.332531i	−0.355957	+	0.0374126i	−0.0751377	+	0.997173i	$0.523940\pi$
$80$	7.22666	−	2.34809i	0.807965	−	0.262524i
$81$		0			0
$82$	3.63756	+	2.64284i	0.401701	+	0.291853i
$83$	9.48546	−	4.22320i	1.04116	−	0.463556i	0.186346	−	0.982484i	$-0.440335\pi$
$83$	9.48546	−	4.22320i	1.04116	−	0.463556i	0.854818	+	0.518928i	$0.173669\pi$
$84$		0			0
$85$	−1.93732	−	1.74437i	−0.210132	−	0.189204i
$86$	1.27799	−	2.87041i	0.137809	−	0.309524i
$87$		0			0
$88$	0.664820	+	4.69353i	0.0708700	+	0.500332i
$89$			9.01115i			0.955180i	0.878583	+	0.477590i	$0.158489\pi$
$89$			9.01115i			0.955180i	−0.878583	+	0.477590i	$0.841511\pi$
$90$		0			0
$91$	2.98703	+	9.19313i	0.313126	+	0.963702i
$92$	7.70368	−	6.93642i	0.803164	−	0.723172i
$93$		0			0
$94$	−0.283175	−	0.0297629i	−0.0292073	−	0.00306981i
$95$	−1.30727	+	0.277869i	−0.134123	+	0.0285087i
$96$		0			0
$97$	−0.579063	−	5.50942i	−0.0587950	−	0.559397i	−0.983778	−	0.179389i	$-0.942588\pi$
$97$	−0.579063	−	5.50942i	−0.0587950	−	0.559397i	0.924983	−	0.380008i	$-0.124079\pi$
$98$	1.66968			0.168664
$99$		0			0
$100$	1.20653			0.120653
$101$	−1.01759	−	9.68168i	−0.101254	−	0.963363i	−0.920717	−	0.390231i	$-0.872395\pi$
$101$	−1.01759	−	9.68168i	−0.101254	−	0.963363i	0.819463	−	0.573132i	$-0.194272\pi$
$102$		0			0
$103$	−1.85159	+	0.393567i	−0.182442	+	0.0387793i	−0.298227	−	0.954495i	$-0.596395\pi$
$103$	−1.85159	+	0.393567i	−0.182442	+	0.0387793i	0.115785	+	0.993274i	$0.463062\pi$
$104$	8.71247	+	0.915717i	0.854328	+	0.0897934i
$105$		0			0
$106$	1.24447	−	1.12053i	0.120874	−	0.108835i
$107$	−3.79203	−	11.6707i	−0.366590	−	1.12825i	−0.948980	−	0.315337i	$-0.897882\pi$
$107$	−3.79203	−	11.6707i	−0.366590	−	1.12825i	0.582390	−	0.812910i	$-0.302118\pi$
$108$		0			0
$109$			8.79322i			0.842238i	0.907005	+	0.421119i	$0.138362\pi$
$109$			8.79322i			0.842238i	−0.907005	+	0.421119i	$0.861638\pi$
$110$	−0.503269	+	2.87238i	−0.0479848	+	0.273870i
$111$		0			0
$112$	2.05098	−	4.60657i	0.193799	−	0.435280i
$113$	−0.0344743	−	0.0310408i	−0.00324307	−	0.00292007i	0.667507	−	0.744603i	$-0.267361\pi$
$113$	−0.0344743	−	0.0310408i	−0.00324307	−	0.00292007i	−0.670751	+	0.741683i	$0.734028\pi$
$114$		0			0
$115$	12.0794	−	5.37811i	1.12641	−	0.501512i
$116$	1.11889	+	0.812920i	0.103886	+	0.0754777i
$117$		0			0
$118$	−0.00395298	+	0.00128440i	−0.000363902	+	0.000118239i
$119$	−1.72052	+	0.180834i	−0.157720	+	0.0165770i
$120$		0			0
$121$	10.3447	+	3.73981i	0.940432	+	0.339983i
$122$	−1.83625	+	1.06016i	−0.166246	+	0.0959823i
$123$		0			0
$124$	−11.5309	−	2.45097i	−1.03551	−	0.220103i
$125$	−9.83712	−	3.19627i	−0.879859	−	0.285883i
$126$		0			0
$127$	3.88014	−	5.34055i	0.344307	−	0.473898i	−0.601386	−	0.798958i	$-0.705385\pi$
$127$	3.88014	−	5.34055i	0.344307	−	0.473898i	0.945693	+	0.325061i	$0.105385\pi$
$128$	−6.62160	−	7.35403i	−0.585272	−	0.650011i
$129$		0			0
$130$	4.92324	+	2.19197i	0.431797	+	0.192248i
$131$	3.94169	+	6.82720i	0.344387	+	0.596495i	0.985242	−	0.171166i	$-0.0547536\pi$
$131$	3.94169	+	6.82720i	0.344387	+	0.596495i	−0.640855	+	0.767662i	$0.721420\pi$
$132$		0			0
$133$	−0.443452	+	0.768082i	−0.0384522	+	0.0666011i
$134$	−0.441997	+	0.321129i	−0.0381827	+	0.0277414i
$135$		0			0
$136$	−0.484503	+	1.49115i	−0.0415458	+	0.127865i
$137$	7.18217	+	16.1314i	0.613614	+	1.37820i	0.906562	+	0.422072i	$0.138697\pi$
$137$	7.18217	+	16.1314i	0.613614	+	1.37820i	−0.292948	+	0.956128i	$0.594636\pi$
$138$		0			0
$139$	2.92780	+	13.7742i	0.248333	+	1.16831i	0.908726	+	0.417393i	$0.137056\pi$
$139$	2.92780	+	13.7742i	0.248333	+	1.16831i	−0.660393	+	0.750920i	$0.729610\pi$
$140$	4.67228	−	5.18910i	0.394880	−	0.438559i
$141$		0			0
$142$	2.67104	+	1.54213i	0.224149	+	0.129412i
$143$	11.3493	−	16.8654i	0.949077	−	1.41036i
$144$		0			0
$145$	1.03691	+	1.42718i	0.0861105	+	0.118521i
$146$	−1.21237	+	5.70376i	−0.100337	+	0.472047i
$147$		0			0
$148$	0.834680	−	7.94145i	0.0686103	−	0.652783i
$149$	1.48901	−	14.1670i	0.121985	−	1.16061i	−0.746672	−	0.665193i	$-0.768349\pi$
$149$	1.48901	−	14.1670i	0.121985	−	1.16061i	0.868657	−	0.495415i	$-0.164984\pi$
$150$		0			0
$151$	0.535628	−	2.51993i	0.0435888	−	0.205069i	−0.950964	−	0.309301i	$-0.899905\pi$
$151$	0.535628	−	2.51993i	0.0435888	−	0.205069i	0.994553	+	0.104232i	$0.0332383\pi$
$152$	0.472460	+	0.650285i	0.0383216	+	0.0527451i
$153$		0			0
$154$	1.19307	+	1.52366i	0.0961405	+	0.122780i
$155$	−13.0221	−	7.51832i	−1.04596	−	0.603886i
$156$		0			0
$157$	3.80983	−	4.23125i	0.304058	−	0.337690i	−0.571681	−	0.820476i	$-0.693708\pi$
$157$	3.80983	−	4.23125i	0.304058	−	0.337690i	0.875738	+	0.482786i	$0.160375\pi$
$158$	0.244712	+	1.15128i	0.0194683	+	0.0915909i
$159$		0			0
$160$	−3.90654	−	8.77423i	−0.308839	−	0.693663i
$161$	2.71153	−	8.34524i	0.213699	−	0.657697i
$162$		0			0
$163$	6.92500	−	5.03131i	0.542408	−	0.394083i	−0.282570	−	0.959247i	$-0.591187\pi$
$163$	6.92500	−	5.03131i	0.542408	−	0.394083i	0.824979	+	0.565164i	$0.191187\pi$
$164$	−11.3209	+	19.6085i	−0.884017	+	1.53116i
$165$		0			0
$166$	−1.92078	−	3.32689i	−0.149081	−	0.258217i
$167$	2.78662	+	1.24068i	0.215635	+	0.0960071i	0.511712	−	0.859157i	$-0.329012\pi$
$167$	2.78662	+	1.24068i	0.215635	+	0.0960071i	−0.296076	+	0.955164i	$0.595678\pi$
$168$		0			0
$169$	−16.4393	−	18.2577i	−1.26456	−	1.40444i
$170$	−0.566927	+	0.780308i	−0.0434813	+	0.0598469i
$171$		0			0
$172$	15.0481	+	4.88941i	1.14740	+	0.372814i
$173$	11.1264	+	2.36499i	0.845926	+	0.179807i	0.610432	−	0.792069i	$-0.290996\pi$
$173$	11.1264	+	2.36499i	0.845926	+	0.179807i	0.235494	+	0.971876i	$0.424329\pi$
$174$		0			0
$175$	0.884456	−	0.510641i	0.0668586	−	0.0386008i
$176$	−10.2869	+	2.57665i	−0.775401	+	0.194222i
$177$		0			0
$178$	3.31569	−	0.348493i	0.248521	−	0.0261207i
$179$	−10.1952	+	3.31261i	−0.762023	+	0.247596i	−0.664147	−	0.747602i	$-0.731205\pi$
$179$	−10.1952	+	3.31261i	−0.762023	+	0.247596i	−0.0978766	+	0.995199i	$0.531205\pi$
$180$		0			0
$181$	14.3857	+	10.4518i	1.06928	+	0.776879i	0.975783	−	0.218741i	$-0.0701949\pi$
$181$	14.3857	+	10.4518i	1.06928	+	0.776879i	0.0934987	+	0.995619i	$0.470195\pi$
$182$	3.26713	−	1.45462i	0.242176	−	0.107824i
$183$		0			0
$184$	−5.90984	−	5.32124i	−0.435679	−	0.392287i
$185$	4.14277	−	9.30481i	0.304582	−	0.684103i
$186$		0			0
$187$	2.53018	+	2.61441i	0.185025	+	0.191184i
$188$		−	1.43384i		−	0.104574i
$189$		0			0
$190$	0.152800	+	0.470269i	0.0110853	+	0.0341169i
$191$	15.1944	−	13.6811i	1.09943	−	0.989927i	0.0994383	−	0.995044i	$-0.468295\pi$
$191$	15.1944	−	13.6811i	1.09943	−	0.989927i	0.999987	+	0.00511682i	$0.00162874\pi$
$192$		0			0
$193$	15.1954	+	1.59710i	1.09379	+	0.114962i	0.634199	−	0.773170i	$-0.281330\pi$
$193$	15.1954	+	1.59710i	1.09379	+	0.114962i	0.459589	+	0.888132i	$0.347997\pi$
$194$	−2.00482	+	0.426138i	−0.143938	+	0.0305949i
$195$		0			0
$196$	0.878879	+	8.36197i	0.0627770	+	0.597284i
$197$	13.1024			0.933507			0.466754	−	0.884387i	$-0.345424\pi$
$197$	13.1024			0.933507			0.466754	+	0.884387i	$0.345424\pi$
$198$		0			0
$199$	−4.72311			−0.334812			−0.167406	−	0.985888i	$-0.553539\pi$
$199$	−4.72311			−0.334812			−0.167406	+	0.985888i	$0.553539\pi$
$200$	−0.0967497	−	0.920512i	−0.00684124	−	0.0650900i
$201$		0			0
$202$	−3.52306	+	0.748850i	−0.247882	+	0.0526889i
$203$	1.16426	+	0.122369i	0.0817153	+	0.00858862i
$204$		0			0
$205$	−21.4624	+	19.3248i	−1.49900	+	1.34970i
$206$	0.216422	+	0.666078i	0.0150788	+	0.0464078i
$207$		0			0
$208$			19.5979i			1.35887i
$209$	1.84677	−	0.261587i	0.127744	−	0.0180944i
$210$		0			0
$211$	7.94634	−	17.8478i	0.547049	−	1.22869i	−0.402600	−	0.915376i	$-0.631893\pi$
$211$	7.94634	−	17.8478i	0.547049	−	1.22869i	0.949649	−	0.313316i	$-0.101440\pi$
$212$	6.26678	+	5.64263i	0.430404	+	0.387538i
$213$		0			0
$214$	−4.14762	+	1.84664i	−0.283526	+	0.126234i
$215$	16.3277	+	11.8627i	1.11354	+	0.809032i
$216$		0			0
$217$	−9.49015	+	3.08354i	−0.644233	+	0.209324i
$218$	3.23550	−	0.340065i	0.219136	−	0.0230321i
$219$		0			0
$220$	−14.6501	−	1.00848i	−0.987710	−	0.0679920i
$221$	5.82288	−	3.36184i	0.391689	−	0.226142i
$222$		0			0
$223$	16.0707	+	3.41593i	1.07617	+	0.228748i	0.711712	−	0.702471i	$-0.247920\pi$
$223$	16.0707	+	3.41593i	1.07617	+	0.228748i	0.364461	+	0.931219i	$0.381253\pi$
$224$	−6.06179	−	1.96959i	−0.405020	−	0.131599i
$225$		0			0
$226$	−0.0100884	+	0.0138854i	−0.000671067	+	0.000923645i
$227$	−18.1769	−	20.1875i	−1.20645	−	1.33989i	−0.924836	−	0.380366i	$-0.875798\pi$
$227$	−18.1769	−	20.1875i	−1.20645	−	1.33989i	−0.281610	−	0.959529i	$-0.590869\pi$
$228$		0			0
$229$	−3.96055	−	1.76335i	−0.261720	−	0.116525i	0.271682	−	0.962387i	$-0.412420\pi$
$229$	−3.96055	−	1.76335i	−0.261720	−	0.116525i	−0.533402	+	0.845862i	$0.679087\pi$
$230$	−2.44605	−	4.23669i	−0.161288	−	0.279359i
$231$		0			0
$232$	0.530489	−	0.918835i	0.0348283	−	0.0603244i
$233$	−9.48697	+	6.89268i	−0.621512	+	0.451555i	−0.853449	−	0.521176i	$-0.825494\pi$
$233$	−9.48697	+	6.89268i	−0.621512	+	0.451555i	0.231937	+	0.972731i	$0.425494\pi$
$234$		0			0
$235$	0.565165	−	1.73940i	0.0368673	−	0.113466i
$236$	−0.00851319	−	0.0191209i	−0.000554161	−	0.00124467i
$237$		0			0
$238$	0.133077	+	0.626078i	0.00862610	+	0.0405826i
$239$	−12.0054	+	13.3334i	−0.776566	+	0.862464i	−0.993513	−	0.113719i	$-0.963724\pi$
$239$	−12.0054	+	13.3334i	−0.776566	+	0.862464i	0.216947	+	0.976183i	$0.430390\pi$
$240$		0			0
$241$	2.31388	+	1.33592i	0.149050	+	0.0860541i	0.572670	−	0.819786i	$-0.305908\pi$
$241$	2.31388	+	1.33592i	0.149050	+	0.0860541i	−0.423620	+	0.905840i	$0.639241\pi$
$242$	0.976011	−	3.95102i	0.0627404	−	0.253982i
$243$		0			0
$244$	−6.27595	−	8.63811i	−0.401777	−	0.552998i
$245$	−2.22980	+	10.4904i	−0.142456	+	0.670205i
$246$		0			0
$247$	0.360308	−	3.42810i	0.0229258	−	0.218125i
$248$	−0.945302	+	8.99395i	−0.0600268	+	0.571116i
$249$		0			0
$250$	−0.795646	+	3.74322i	−0.0503211	+	0.236742i
$251$	−7.98861	−	10.9954i	−0.504237	−	0.694022i	0.478697	−	0.877980i	$-0.341109\pi$
$251$	−7.98861	−	10.9954i	−0.504237	−	0.694022i	−0.982934	+	0.183958i	$0.941109\pi$
$252$		0			0
$253$	−17.3339	+	6.33030i	−1.08977	+	0.397982i
$254$	−2.11514	−	1.22118i	−0.132716	−	0.0766234i
$255$		0			0
$256$	4.10701	−	4.56130i	0.256688	−	0.285081i
$257$	0.988609	+	4.65104i	0.0616677	+	0.290124i	0.998165	−	0.0605507i	$-0.0192857\pi$
$257$	0.988609	+	4.65104i	0.0616677	+	0.290124i	−0.936497	+	0.350675i	$0.885952\pi$
$258$		0			0
$259$	−2.74920	−	6.17481i	−0.170827	−	0.383684i
$260$	−8.38616	+	25.8099i	−0.520088	+	1.60066i
$261$		0			0
$262$	2.35966	−	1.71439i	0.145780	−	0.105915i
$263$	9.26116	−	16.0408i	0.571067	−	0.989118i	−0.425389	−	0.905010i	$-0.639863\pi$
$263$	9.26116	−	16.0408i	0.571067	−	0.989118i	0.996457	−	0.0841073i	$-0.0268039\pi$
$264$		0			0
$265$	5.37815	+	9.31523i	0.330377	+	0.572230i
$266$	0.299769	+	0.133466i	0.0183800	+	0.00818330i
$267$		0			0
$268$	−1.84091	−	2.04454i	−0.112451	−	0.124890i
$269$	−12.6954	+	17.4737i	−0.774049	+	1.06539i	0.221864	+	0.975078i	$0.428786\pi$
$269$	−12.6954	+	17.4737i	−0.774049	+	1.06539i	−0.995914	+	0.0903100i	$0.971214\pi$
$270$		0			0
$271$	−0.869236	−	0.282432i	−0.0528023	−	0.0171565i	0.282497	−	0.959268i	$-0.408837\pi$
$271$	−0.869236	−	0.282432i	−0.0528023	−	0.0171565i	−0.335299	+	0.942112i	$0.608837\pi$
$272$	−3.43085	−	0.729250i	−0.208026	−	0.0442173i
$273$		0			0
$274$	5.65786	−	3.26657i	0.341804	−	0.197341i
$275$	−1.99228	−	0.802423i	−0.120139	−	0.0483879i
$276$		0			0
$277$	−14.7319	+	1.54838i	−0.885153	+	0.0930333i	−0.536184	−	0.844101i	$-0.680135\pi$
$277$	−14.7319	+	1.54838i	−0.885153	+	0.0930333i	−0.348969	+	0.937134i	$0.613468\pi$
$278$	4.95505	−	1.60999i	0.297184	−	0.0965610i
$279$		0			0
$280$	−4.33365	−	3.14858i	−0.258985	−	0.188164i
$281$	1.67870	−	0.747406i	0.100143	−	0.0445865i	−0.356054	−	0.934465i	$-0.615878\pi$
$281$	1.67870	−	0.747406i	0.100143	−	0.0445865i	0.456197	+	0.889879i	$0.349211\pi$
$282$		0			0
$283$	8.96978	+	8.07643i	0.533198	+	0.480094i	0.891190	−	0.453631i	$-0.149872\pi$
$283$	8.96978	+	8.07643i	0.533198	+	0.480094i	−0.357991	+	0.933725i	$0.616538\pi$
$284$	−6.31718	+	14.1886i	−0.374856	+	0.841940i
$285$		0			0
$286$	−6.64462	−	3.52378i	−0.392905	−	0.208365i
$287$			19.1655i			1.13130i
$288$		0			0
$289$	−4.88143	−	15.0235i	−0.287143	−	0.883735i
$290$	0.485036	−	0.436728i	0.0284823	−	0.0256456i
$291$		0			0
$292$	−29.2033	−	3.06939i	−1.70899	−	0.179622i
$293$	16.7085	−	3.55150i	0.976120	−	0.207481i	0.307879	−	0.951426i	$-0.400381\pi$
$293$	16.7085	−	3.55150i	0.976120	−	0.207481i	0.668241	+	0.743945i	$0.267048\pi$
$294$		0			0
$295$	−0.00279065	−	0.0265513i	−0.000162478	−	0.00154587i
$296$	−6.12580			−0.356055
$297$		0			0
$298$	−5.27040			−0.305306
$299$	3.56475	+	33.9164i	0.206155	+	1.96143i
$300$		0			0
$301$	13.1005	−	2.78459i	0.755098	−	0.160501i
$302$	−0.947934	−	0.0996319i	−0.0545475	−	0.00573317i
$303$		0			0
$304$	−1.33630	+	1.20321i	−0.0766419	+	0.0690087i
$305$	−4.20858	−	12.9527i	−0.240983	−	0.741668i
$306$		0			0
$307$		−	16.6906i		−	0.952585i	−0.879287	−	0.476293i	$-0.841980\pi$
$307$		−	16.6906i		−	0.952585i	0.879287	−	0.476293i	$-0.158020\pi$
$308$	−7.00265	+	6.77706i	−0.399013	+	0.386159i
$309$		0			0
$310$	−2.26279	+	5.08230i	−0.128518	+	0.288655i
$311$	−21.9566	−	19.7698i	−1.24504	−	1.12104i	−0.987969	−	0.154650i	$-0.950575\pi$
$311$	−21.9566	−	19.7698i	−1.24504	−	1.12104i	−0.257074	−	0.966392i	$-0.582758\pi$
$312$		0			0
$313$	14.7478	−	6.56615i	0.833596	−	0.371141i	0.0548610	−	0.998494i	$-0.482528\pi$
$313$	14.7478	−	6.56615i	0.833596	−	0.371141i	0.778735	+	0.627353i	$0.215862\pi$
$314$	−1.70424	−	1.23821i	−0.0961761	−	0.0698760i
$315$		0			0
$316$	−5.63693	+	1.83155i	−0.317102	+	0.103033i
$317$	−8.33839	+	0.876400i	−0.468331	+	0.0492235i	−0.335755	−	0.941949i	$-0.608991\pi$
$317$	−8.33839	+	0.876400i	−0.468331	+	0.0492235i	−0.132576	+	0.991173i	$0.542325\pi$
$318$		0			0
$319$	−1.30692	−	2.08647i	−0.0731733	−	0.116820i
$320$	10.0837	−	5.82181i	0.563694	−	0.325449i
$321$		0			0
$322$	−3.17553	−	0.674980i	−0.176965	−	0.0376152i
$323$	0.586723	+	0.190638i	0.0326462	+	0.0106074i
$324$		0			0
$325$	−2.33306	+	3.21119i	−0.129415	+	0.178125i
$326$	−2.11911	−	2.35351i	−0.117366	−	0.130349i
$327$		0			0
$328$	15.8679	+	7.06486i	0.876160	+	0.390092i
$329$	−0.606846	−	1.05109i	−0.0334565	−	0.0579484i
$330$		0			0
$331$	0.503541	−	0.872158i	0.0276771	−	0.0479381i	−0.851855	−	0.523778i	$-0.824522\pi$
$331$	0.503541	−	0.872158i	0.0276771	−	0.0479381i	0.879532	+	0.475839i	$0.157856\pi$
$332$	15.6504	−	11.3707i	0.858927	−	0.624047i
$333$		0			0
$334$	0.348746	−	1.07333i	0.0190826	−	0.0587301i
$335$	−1.42734	−	3.20585i	−0.0779838	−	0.175154i
$336$		0			0
$337$	−4.61956	−	21.7333i	−0.251644	−	1.18389i	−0.904522	−	0.426427i	$-0.859772\pi$
$337$	−4.61956	−	21.7333i	−0.251644	−	1.18389i	0.652878	−	0.757463i	$-0.273561\pi$
$338$	−6.08223	+	6.75500i	−0.330829	+	0.367423i
$339$		0			0
$340$	−4.20629	−	2.42850i	−0.228118	−	0.131704i
$341$	17.4103	+	11.7160i	0.942822	+	0.634456i
$342$		0			0
$343$	10.6721	+	14.6889i	0.576240	+	0.793126i
$344$	2.52366	−	11.8729i	0.136067	−	0.640143i
$345$		0			0
$346$	0.439911	−	4.18547i	0.0236498	−	0.225012i
$347$	1.25369	−	11.9281i	0.0673017	−	0.640333i	−0.907926	−	0.419130i	$-0.862335\pi$
$347$	1.25369	−	11.9281i	0.0673017	−	0.640333i	0.975228	−	0.221203i	$-0.0709982\pi$
$348$		0			0
$349$	2.11394	−	9.94531i	0.113157	−	0.532360i	−0.884655	−	0.466245i	$-0.845606\pi$
$349$	2.11394	−	9.94531i	0.113157	−	0.532360i	0.997812	−	0.0661146i	$-0.0210603\pi$
$350$	−0.222097	−	0.305691i	−0.0118716	−	0.0163399i
$351$		0			0
$352$	4.59818	+	12.5909i	0.245084	+	0.671099i
$353$	3.99680	+	2.30756i	0.212728	+	0.122819i	0.602579	−	0.798059i	$-0.294140\pi$
$353$	3.99680	+	2.30756i	0.212728	+	0.122819i	−0.389850	+	0.920878i	$0.627473\pi$
$354$		0			0
$355$	−13.2560	+	14.7223i	−0.703556	+	0.781378i
$356$	3.49059	+	16.4219i	0.185001	+	0.870360i
$357$		0			0
$358$	1.61317	+	3.62325i	0.0852589	+	0.191495i
$359$	2.51158	−	7.72985i	0.132556	−	0.407966i	−0.862646	−	0.505809i	$-0.831194\pi$
$359$	2.51158	−	7.72985i	0.132556	−	0.407966i	0.995202	+	0.0978426i	$0.0311942\pi$
$360$		0			0
$361$	−15.1155	+	10.9820i	−0.795550	+	0.578001i
$362$	3.28945	−	5.69749i	0.172890	−	0.299454i
$363$		0			0
$364$	9.00465	+	15.5965i	0.471972	+	0.817479i
$365$	−34.2168	−	15.2343i	−1.79099	−	0.797400i
$366$		0			0
$367$	25.3961	+	28.2052i	1.32567	+	1.47230i	0.764554	+	0.644560i	$0.222959\pi$
$367$	25.3961	+	28.2052i	1.32567	+	1.47230i	0.561111	+	0.827740i	$0.310374\pi$
$368$	10.4569	−	14.3927i	0.545105	−	0.750272i
$369$		0			0
$370$	−3.58396	−	1.16450i	−0.186321	−	0.0605394i
$371$	6.98206	+	1.48408i	0.362490	+	0.0770497i
$372$		0			0
$373$	−5.61495	+	3.24179i	−0.290731	+	0.167854i	−0.638272	−	0.769811i	$-0.720350\pi$
$373$	−5.61495	+	3.24179i	−0.290731	+	0.167854i	0.347540	+	0.937665i	$0.387017\pi$
$374$	0.864130	−	1.03210i	0.0446831	−	0.0533686i
$375$		0			0
$376$	−1.09394	+	0.114978i	−0.0564155	+	0.00592951i
$377$	−4.32719	+	1.40599i	−0.222862	+	0.0724121i
$378$		0			0
$379$	−10.0492	−	7.30119i	−0.516194	−	0.375037i	0.298974	−	0.954261i	$-0.403356\pi$
$379$	−10.0492	−	7.30119i	−0.516194	−	0.375037i	−0.815168	+	0.579224i	$0.803356\pi$
$380$	−2.27473	+	1.01278i	−0.116691	+	0.0519544i
$381$		0			0
$382$	−5.62162	−	5.06173i	−0.287627	−	0.258981i
$383$	−5.80437	+	13.0368i	−0.296590	+	0.666151i	−0.998957	−	0.0456636i	$-0.985460\pi$
$383$	−5.80437	+	13.0368i	−0.296590	+	0.666151i	0.702367	+	0.711815i	$0.252126\pi$
$384$		0			0
$385$	−11.1662	+	5.46111i	−0.569082	+	0.278324i
$386$		−	5.65297i		−	0.287729i
$387$		0			0
$388$	−3.18943	−	9.81606i	−0.161919	−	0.498335i
$389$	8.00313	−	7.20605i	0.405775	−	0.365361i	−0.440823	−	0.897594i	$-0.645313\pi$
$389$	8.00313	−	7.20605i	0.405775	−	0.365361i	0.846598	+	0.532233i	$0.178647\pi$
$390$		0			0
$391$	−6.07012	−	0.637995i	−0.306979	−	0.0322648i
$392$	6.30923	−	1.34107i	0.318664	−	0.0677342i
$393$		0			0
$394$	−0.506716	−	4.82108i	−0.0255280	−	0.242883i
$395$	−7.56012			−0.380391
$396$		0			0
$397$	13.8356			0.694387			0.347193	−	0.937794i	$-0.387135\pi$
$397$	13.8356			0.694387			0.347193	+	0.937794i	$0.387135\pi$
$398$	0.182659	+	1.73789i	0.00915589	+	0.0871125i
$399$		0			0
$400$	2.02536	−	0.430504i	0.101268	−	0.0215252i
$401$	35.6592	+	3.74793i	1.78073	+	0.187163i	0.936936	−	0.349500i	$-0.113649\pi$
$401$	35.6592	+	3.74793i	1.78073	+	0.187163i	0.843797	+	0.536663i	$0.180315\pi$
$402$		0			0
$403$	28.8206	−	25.9502i	1.43565	−	1.29267i
$404$	−5.60477	−	17.2497i	−0.278848	−	0.858206i
$405$		0			0
$406$		−	0.433128i		−	0.0214958i
$407$	−6.65986	+	12.5582i	−0.330117	+	0.622487i
$408$		0			0
$409$	−6.39194	+	14.3565i	−0.316061	+	0.709885i	−0.999803	−	0.0198391i	$-0.993685\pi$
$409$	−6.39194	+	14.3565i	−0.316061	+	0.709885i	0.683742	+	0.729724i	$0.260351\pi$
$410$	7.94068	+	7.14982i	0.392162	+	0.353104i
$411$		0			0
$412$	−3.22188	+	1.43447i	−0.158730	+	0.0706714i
$413$	−0.0143332	−	0.0104137i	−0.000705293	−	0.000512425i
$414$		0			0
$415$	23.4675	−	7.62504i	1.15197	−	0.374298i
$416$	24.6361	−	2.58935i	1.20788	−	0.126954i
$417$		0			0
$418$	−0.167673	−	0.669409i	−0.00820116	−	0.0327419i
$419$	13.1723	−	7.60505i	0.643510	−	0.371531i	−0.142455	−	0.989801i	$-0.545500\pi$
$419$	13.1723	−	7.60505i	0.643510	−	0.371531i	0.785965	+	0.618270i	$0.212166\pi$
$420$		0			0
$421$	11.8761	+	2.52435i	0.578807	+	0.123029i	0.488006	−	0.872840i	$-0.337724\pi$
$421$	11.8761	+	2.52435i	0.578807	+	0.123029i	0.0908001	+	0.995869i	$0.471058\pi$
$422$	−6.87448	−	2.23365i	−0.334644	−	0.108733i
$423$		0			0
$424$	3.80248	−	5.23367i	0.184665	−	0.254169i
$425$	−0.475342	−	0.527921i	−0.0230575	−	0.0256079i
$426$		0			0
$427$	−8.25656	−	3.67606i	−0.399563	−	0.177897i
$428$	−11.4314	−	19.7998i	−0.552557	−	0.957057i
$429$		0			0
$430$	3.73349	−	6.46660i	0.180045	−	0.311847i
$431$	20.7468	−	15.0734i	0.999336	−	0.726060i	0.0373906	−	0.999301i	$-0.488095\pi$
$431$	20.7468	−	15.0734i	0.999336	−	0.726060i	0.961946	+	0.273240i	$0.0880954\pi$
$432$		0			0
$433$	−0.399073	+	1.22822i	−0.0191782	+	0.0590245i	−0.960188	−	0.279356i	$-0.909879\pi$
$433$	−0.399073	+	1.22822i	−0.0191782	+	0.0590245i	0.941009	+	0.338380i	$0.109879\pi$
$434$	1.50162	+	3.37269i	0.0720799	+	0.161894i
$435$		0			0
$436$	3.40617	+	16.0248i	0.163126	+	0.767447i
$437$	−2.09375	+	2.32535i	−0.100158	+	0.111237i
$438$		0			0
$439$	−7.78450	−	4.49438i	−0.371534	−	0.214505i	0.302595	−	0.953119i	$-0.402147\pi$
$439$	−7.78450	−	4.49438i	−0.371534	−	0.214505i	−0.674128	+	0.738614i	$0.735481\pi$
$440$	0.405354	+	11.2581i	0.0193245	+	0.536707i
$441$		0			0
$442$	−1.46220	−	2.01254i	−0.0695495	−	0.0957267i
$443$	2.98230	−	14.0306i	0.141693	−	0.666614i	−0.848762	−	0.528776i	$-0.822651\pi$
$443$	2.98230	−	14.0306i	0.141693	−	0.666614i	0.990455	−	0.137838i	$-0.0440154\pi$
$444$		0			0
$445$	−2.23844	+	21.2974i	−0.106112	+	1.00959i
$446$	0.635396	−	6.04538i	0.0300869	−	0.286257i
$447$		0			0
$448$	1.60651	−	7.55802i	0.0759003	−	0.357083i
$449$	−8.37515	−	11.5274i	−0.395248	−	0.544012i	0.564296	−	0.825573i	$-0.309148\pi$
$449$	−8.37515	−	11.5274i	−0.395248	−	0.544012i	−0.959543	+	0.281561i	$0.909148\pi$
$450$		0			0
$451$	31.7346	−	24.8492i	1.49433	−	1.17011i
$452$	−0.0748501	−	0.0432147i	−0.00352065	−	0.00203265i
$453$		0			0
$454$	−6.72512	+	7.46901i	−0.315626	+	0.350538i
$455$	4.77604	+	22.4695i	0.223904	+	1.05339i
$456$		0			0
$457$	10.5654	+	23.7302i	0.494227	+	1.11005i	0.972725	+	0.231963i	$0.0745149\pi$
$457$	10.5654	+	23.7302i	0.494227	+	1.11005i	−0.478498	+	0.878089i	$0.658818\pi$
$458$	−0.495664	+	1.52550i	−0.0231608	+	0.0712817i
$459$		0			0
$460$	19.9303	−	14.4802i	0.929255	−	0.675143i
$461$	−5.82733	+	10.0932i	−0.271406	+	0.470089i	−0.969222	−	0.246188i	$-0.920822\pi$
$461$	−5.82733	+	10.0932i	−0.271406	+	0.470089i	0.697816	+	0.716277i	$0.254155\pi$
$462$		0			0
$463$	−9.33236	−	16.1641i	−0.433712	−	0.751211i	0.563478	−	0.826131i	$-0.309463\pi$
$463$	−9.33236	−	16.1641i	−0.433712	−	0.751211i	−0.997190	+	0.0749205i	$0.976130\pi$
$464$	2.16830	+	0.965391i	0.100661	+	0.0448171i
$465$		0			0
$466$	2.90309	+	3.22420i	0.134483	+	0.149358i
$467$	1.77499	−	2.44307i	0.0821369	−	0.113052i	−0.765971	−	0.642875i	$-0.777742\pi$
$467$	1.77499	−	2.44307i	0.0821369	−	0.113052i	0.848108	+	0.529823i	$0.177742\pi$
$468$		0			0
$469$	−2.21481	−	0.719634i	−0.102270	−	0.0332296i
$470$	−0.661876	−	0.140686i	−0.0305301	−	0.00648937i
$471$		0			0
$472$	−0.0139055	+	0.00802835i	−0.000640053	+	0.000369535i
$473$	−21.5963	−	18.0816i	−0.992999	−	0.831393i
$474$		0			0
$475$	−0.362195	+	0.0380682i	−0.0166186	+	0.00174669i
$476$	−3.06542	+	0.996017i	−0.140503	+	0.0456523i
$477$		0			0
$478$	5.37036	+	3.90180i	0.245635	+	0.178464i
$479$	−35.3397	+	15.7343i	−1.61471	+	0.718917i	−0.997684	−	0.0680220i	$-0.978331\pi$
$479$	−35.3397	+	15.7343i	−1.61471	+	0.718917i	−0.617031	+	0.786939i	$0.711665\pi$
$480$		0			0
$481$	19.5222	+	17.5779i	0.890137	+	0.801483i
$482$	0.402071	−	0.903067i	0.0183138	−	0.0411336i
$483$		0			0
$484$	20.3009	+	2.80826i	0.922770	+	0.127648i
$485$		−	13.1651i		−	0.597795i
$486$		0			0
$487$	−3.79422	−	11.6774i	−0.171933	−	0.529154i	0.827548	−	0.561396i	$-0.189735\pi$
$487$	−3.79422	−	11.6774i	−0.171933	−	0.529154i	−0.999480	+	0.0322416i	$0.989735\pi$
$488$	−6.08712	+	5.48087i	−0.275551	+	0.248107i
$489$		0			0
$490$	3.94621	+	0.414763i	0.178272	+	0.0187371i
$491$	35.6716	−	7.58222i	1.60984	−	0.342181i	0.686785	−	0.726861i	$-0.259021\pi$
$491$	35.6716	−	7.58222i	1.60984	−	0.342181i	0.923050	+	0.384680i	$0.125688\pi$
$492$		0			0
$493$	−0.0851181	−	0.809844i	−0.00383352	−	0.0364736i
$494$	−1.27532			−0.0573793
$495$		0			0
$496$	−20.2311			−0.908403
$497$	1.37421	+	13.0747i	0.0616417	+	0.586481i
$498$		0			0
$499$	−23.7506	+	5.04835i	−1.06322	+	0.225995i	−0.706136	−	0.708076i	$-0.749563\pi$
$499$	−23.7506	+	5.04835i	−1.06322	+	0.225995i	−0.357087	+	0.934071i	$0.616230\pi$
$500$	−19.1653	−	2.01435i	−0.857098	−	0.0900846i
$501$		0			0
$502$	−3.73685	+	3.36467i	−0.166784	+	0.150173i
$503$	6.87821	+	21.1689i	0.306684	+	0.943876i	0.979043	+	0.203652i	$0.0652810\pi$
$503$	6.87821	+	21.1689i	0.306684	+	0.943876i	−0.672359	+	0.740225i	$0.734719\pi$
$504$		0			0
$505$		−	23.1349i		−	1.02949i
$506$	2.99962	+	6.13326i	0.133349	+	0.272657i
$507$		0			0
$508$	5.00244	−	11.2357i	0.221947	−	0.498501i
$509$	21.0596	+	18.9621i	0.933448	+	0.840481i	0.987429	−	0.158061i	$-0.0505244\pi$
$509$	21.0596	+	18.9621i	0.933448	+	0.840481i	−0.0539810	+	0.998542i	$0.517191\pi$
$510$		0			0
$511$	−22.7068	+	10.1097i	−1.00449	+	0.447227i
$512$	−17.8490	−	12.9680i	−0.788820	−	0.573111i
$513$		0			0
$514$	1.67314	−	0.543635i	0.0737989	−	0.0239787i
$515$	−4.47389	+	0.470225i	−0.197143	+	0.0207206i
$516$		0			0
$517$	−0.953601	+	2.36763i	−0.0419393	+	0.104128i
$518$	−2.16573	+	1.25038i	−0.0951565	+	0.0549386i
$519$		0			0
$520$	20.3640	+	4.32850i	0.893019	+	0.189817i
$521$	−14.9548	−	4.85911i	−0.655182	−	0.212882i	−0.0374843	−	0.999297i	$-0.511934\pi$
$521$	−14.9548	−	4.85911i	−0.655182	−	0.212882i	−0.617698	+	0.786416i	$0.711934\pi$
$522$		0			0
$523$	8.59617	−	11.8316i	0.375884	−	0.517360i	−0.578604	−	0.815609i	$-0.696402\pi$
$523$	8.59617	−	11.8316i	0.375884	−	0.517360i	0.954488	+	0.298248i	$0.0964023\pi$
$524$	9.82794	+	10.9150i	0.429335	+	0.476825i
$525$		0			0
$526$	−6.26044	−	2.78733i	−0.272968	−	0.121533i
$527$	3.47046	+	6.01101i	0.151175	+	0.261844i
$528$		0			0
$529$	3.97891	−	6.89168i	0.172996	−	0.299638i
$530$	3.21959	−	2.33917i	0.139850	−	0.101607i
$531$		0			0
$532$	−0.510621	+	1.57153i	−0.0221382	+	0.0681345i
$533$	−30.2968	−	68.0477i	−1.31230	−	2.94747i
$534$		0			0
$535$	−6.06318	−	28.5250i	−0.262134	−	1.23324i
$536$	−1.41224	+	1.56846i	−0.0609997	+	0.0677470i
$537$		0			0
$538$	6.92048	+	3.99554i	0.298363	+	0.172260i
$539$	4.11003	−	14.3922i	0.177031	−	0.619916i
$540$		0			0
$541$	10.4934	+	14.4429i	0.451146	+	0.620950i	0.972643	−	0.232303i	$-0.0746262\pi$
$541$	10.4934	+	14.4429i	0.451146	+	0.620950i	−0.521497	+	0.853253i	$0.674626\pi$
$542$	−0.0703055	+	0.330762i	−0.00301988	+	0.0142074i
$543$		0			0
$544$	−0.463425	+	4.40919i	−0.0198692	+	0.189043i
$545$	−2.18431	+	20.7823i	−0.0935655	+	0.890216i
$546$		0			0
$547$	−0.938395	+	4.41480i	−0.0401229	+	0.188763i	−0.993645	−	0.112560i	$-0.964095\pi$
$547$	−0.938395	+	4.41480i	−0.0401229	+	0.188763i	0.953522	+	0.301323i	$0.0974283\pi$
$548$	19.3375	+	26.6158i	0.826058	+	1.13697i
$549$		0			0
$550$	−0.218206	+	0.764100i	−0.00930435	+	0.0325813i
$551$	−0.361535	−	0.208732i	−0.0154019	−	0.00889229i
$552$		0			0
$553$	−3.35703	+	3.72836i	−0.142756	+	0.158546i
$554$	1.13947	+	5.36077i	0.0484113	+	0.227757i
$555$		0			0
$556$	10.6712	+	23.9680i	0.452561	+	1.01647i
$557$	−8.48770	+	26.1225i	−0.359635	+	1.10684i	0.593637	+	0.804733i	$0.297691\pi$
$557$	−8.48770	+	26.1225i	−0.359635	+	1.10684i	−0.953273	+	0.302111i	$0.902309\pi$
$558$		0			0
$559$	−42.1116	+	30.5959i	−1.78113	+	1.29407i
$560$	5.99168	−	10.3779i	0.253195	−	0.438546i
$561$		0			0
$562$	−0.339933	−	0.588781i	−0.0143392	−	0.0248362i
$563$	−9.56320	−	4.25781i	−0.403041	−	0.179445i	0.195197	−	0.980764i	$-0.437465\pi$
$563$	−9.56320	−	4.25781i	−0.403041	−	0.179445i	−0.598238	+	0.801319i	$0.704132\pi$
$564$		0			0
$565$	−0.0737674	−	0.0819270i	−0.00310342	−	0.00344670i
$566$	2.62486	−	3.61281i	0.110331	−	0.151858i
$567$		0			0
$568$	11.3317	+	3.68188i	0.475466	+	0.154488i
$569$	36.2644	+	7.70823i	1.52028	+	0.323146i	0.890990	−	0.454023i	$-0.150012\pi$
$569$	36.2644	+	7.70823i	1.52028	+	0.323146i	0.629292	+	0.777169i	$0.283345\pi$
$570$		0			0
$571$	−5.32451	+	3.07411i	−0.222824	+	0.128647i	−0.607257	−	0.794505i	$-0.707730\pi$
$571$	−5.32451	+	3.07411i	−0.222824	+	0.128647i	0.384433	+	0.923153i	$0.374397\pi$
$572$	14.1499	−	35.1319i	0.591639	−	1.46894i
$573$		0			0
$574$	7.05203	−	0.741198i	0.294346	−	0.0309370i
$575$	3.42681	−	1.11344i	0.142908	−	0.0464335i
$576$		0			0
$577$	−8.59300	−	6.24318i	−0.357731	−	0.259907i	0.394374	−	0.918950i	$-0.370961\pi$
$577$	−8.59300	−	6.24318i	−0.357731	−	0.259907i	−0.752105	+	0.659043i	$0.770961\pi$
$578$	−5.33918	+	2.37715i	−0.222080	+	0.0988766i
$579$		0			0
$580$	2.44250	+	2.19923i	0.101419	+	0.0913182i
$581$	6.66022	−	14.9591i	0.276313	−	0.620608i
$582$		0			0
$583$	−6.59528	−	13.4852i	−0.273149	−	0.558501i
$584$			22.5266i			0.932155i
$585$		0			0
$586$	−1.95296	−	6.01061i	−0.0806762	−	0.248296i
$587$	4.66856	−	4.20359i	0.192692	−	0.173501i	−0.567137	−	0.823623i	$-0.691949\pi$
$587$	4.66856	−	4.20359i	0.192692	−	0.173501i	0.759829	+	0.650123i	$0.225282\pi$
$588$		0			0
$589$	3.53886	+	0.371949i	0.145816	+	0.0153259i
$590$	−0.00966173	+	0.00205366i	−0.000397767	+	8.45480e-5i
$591$		0			0
$592$	−1.43245	−	13.6289i	−0.0588735	−	0.560144i
$593$	13.2967			0.546030			0.273015	−	0.962010i	$-0.411979\pi$
$593$	13.2967			0.546030			0.273015	+	0.962010i	$0.411979\pi$
$594$		0			0
$595$	−4.11127			−0.168546
$596$	−2.77420	−	26.3948i	−0.113636	−	1.08117i
$597$		0			0
$598$	12.3418	−	2.62333i	0.504694	−	0.107276i
$599$	−34.7982	−	3.65743i	−1.42181	−	0.149439i	−0.637810	−	0.770194i	$-0.720159\pi$
$599$	−34.7982	−	3.65743i	−1.42181	−	0.149439i	−0.784004	+	0.620755i	$0.786826\pi$
$600$		0			0
$601$	3.92068	−	3.53019i	0.159928	−	0.144000i	−0.585282	−	0.810830i	$-0.699016\pi$
$601$	3.92068	−	3.53019i	0.159928	−	0.144000i	0.745210	+	0.666830i	$0.232349\pi$
$602$	−1.53124	−	4.71268i	−0.0624087	−	0.192074i
$603$		0			0
$604$		−	4.79981i		−	0.195301i
$605$	23.5203	+	11.4086i	0.956235	+	0.463824i
$606$		0			0
$607$	−8.45971	+	19.0008i	−0.343369	+	0.771220i	0.656488	+	0.754336i	$0.272041\pi$
$607$	−8.45971	+	19.0008i	−0.343369	+	0.771220i	−0.999857	+	0.0168835i	$0.994626\pi$
$608$	1.68908	+	1.52085i	0.0685012	+	0.0616788i
$609$		0			0
$610$	−4.60323	+	2.04949i	−0.186379	+	0.0829814i
$611$	3.81618	+	2.77262i	0.154386	+	0.112168i
$612$		0			0
$613$	−25.6016	+	8.31845i	−1.03404	+	0.335979i	−0.776385	−	0.630259i	$-0.782949\pi$
$613$	−25.6016	+	8.31845i	−1.03404	+	0.335979i	−0.257652	+	0.966238i	$0.582949\pi$
$614$	−6.14139	+	0.645486i	−0.247846	+	0.0260497i
$615$		0			0
$616$	5.73204	+	4.79918i	0.230950	+	0.193364i
$617$	−29.0656	+	16.7811i	−1.17014	+	0.675580i	−0.953713	−	0.300719i	$-0.902773\pi$
$617$	−29.0656	+	16.7811i	−1.17014	+	0.675580i	−0.216426	+	0.976299i	$0.569440\pi$
$618$		0			0
$619$	−36.4959	−	7.75745i	−1.46689	−	0.311798i	−0.595887	−	0.803068i	$-0.703200\pi$
$619$	−36.4959	−	7.75745i	−1.46689	−	0.311798i	−0.871007	+	0.491270i	$0.836533\pi$
$620$	−26.6438	−	8.65710i	−1.07004	−	0.347678i
$621$		0			0
$622$	−6.42524	+	8.84358i	−0.257629	+	0.354595i
$623$	9.50908	+	10.5609i	0.380973	+	0.423113i
$624$		0			0
$625$	−25.4135	−	11.3148i	−1.01654	−	0.452593i
$626$	−2.98639	−	5.17258i	−0.119360	−	0.206738i
$627$		0			0
$628$	5.30401	−	9.18682i	0.211653	−	0.366594i
$629$	−3.80365	+	2.76352i	−0.151662	+	0.110189i
$630$		0			0
$631$	−5.33541	+	16.4207i	−0.212399	+	0.653698i	0.786929	+	0.617044i	$0.211670\pi$
$631$	−5.33541	+	16.4207i	−0.212399	+	0.653698i	−0.999328	+	0.0366537i	$0.988330\pi$
$632$	1.84939	+	4.15379i	0.0735646	+	0.165229i
$633$		0			0
$634$	0.644950	+	3.03425i	0.0256142	+	0.120506i
$635$	10.4971	−	11.6583i	0.416566	−	0.462644i
$636$		0			0
$637$	−23.9550	−	13.8304i	−0.949130	−	0.547980i
$638$	−0.717182	+	0.561577i	−0.0283935	+	0.0222330i
$639$		0			0
$640$	−13.8230	−	19.0257i	−0.546402	−	0.752058i
$641$	−1.96169	+	9.22901i	−0.0774819	+	0.364524i	−0.999758	−	0.0220085i	$-0.992994\pi$
$641$	−1.96169	+	9.22901i	−0.0774819	+	0.364524i	0.922276	+	0.386532i	$0.126327\pi$
$642$		0			0
$643$	−0.853865	+	8.12398i	−0.0336732	+	0.320379i	0.964700	+	0.263353i	$0.0848284\pi$
$643$	−0.853865	+	8.12398i	−0.0336732	+	0.320379i	−0.998373	+	0.0570257i	$0.981838\pi$
$644$	1.70886	−	16.2587i	0.0673385	−	0.640683i
$645$		0			0
$646$	0.0474554	−	0.223260i	0.00186711	−	0.00878404i
$647$	12.6621	+	17.4279i	0.497799	+	0.685162i	0.981803	−	0.189904i	$-0.0608178\pi$
$647$	12.6621	+	17.4279i	0.497799	+	0.685162i	−0.484003	+	0.875066i	$0.660818\pi$
$648$		0			0
$649$	0.00134068	+	0.0372353i	5.26264e−5	+	0.00146161i
$650$	1.27180	+	0.734273i	0.0498840	+	0.0288005i
$651$		0			0
$652$	10.6712	−	11.8516i	0.417916	−	0.464143i
$653$	9.50514	+	44.7182i	0.371965	+	1.74996i	0.623229	+	0.782039i	$0.285820\pi$
$653$	9.50514	+	44.7182i	0.371965	+	1.74996i	−0.251264	+	0.967919i	$0.580846\pi$
$654$		0			0
$655$	7.62003	+	17.1149i	0.297739	+	0.668733i
$656$	−12.0076	+	36.9555i	−0.468817	+	1.44287i
$657$		0			0
$658$	−0.363284	+	0.263941i	−0.0141623	+	0.0102895i
$659$	2.87636	−	4.98200i	0.112047	−	0.194071i	−0.804548	−	0.593887i	$-0.797593\pi$
$659$	2.87636	−	4.98200i	0.112047	−	0.194071i	0.916595	+	0.399816i	$0.130926\pi$
$660$		0			0
$661$	−14.9630	−	25.9166i	−0.581991	−	1.00804i	−0.995243	−	0.0974218i	$-0.968940\pi$
$661$	−14.9630	−	25.9166i	−0.581991	−	1.00804i	0.413252	−	0.910617i	$-0.364393\pi$
$662$	−0.340388	−	0.151550i	−0.0132296	−	0.00589018i
$663$		0			0
$664$	−9.93016	−	11.0286i	−0.385365	−	0.427991i
$665$	−1.23887	+	1.70516i	−0.0480415	+	0.0661234i
$666$		0			0
$667$	3.92809	+	1.27631i	0.152096	+	0.0494190i
$668$	5.55894	+	1.18159i	0.215082	+	0.0457170i
$669$		0			0
$670$	−1.12441	+	0.649177i	−0.0434396	+	0.0250799i
$671$	4.61824	+	18.4376i	0.178285	+	0.711776i
$672$		0			0
$673$	1.28805	−	0.135380i	0.0496507	−	0.00521850i	−0.0796705	−	0.996821i	$-0.525387\pi$
$673$	1.28805	−	0.135380i	0.0496507	−	0.00521850i	0.129321	+	0.991603i	$0.458720\pi$
$674$	−7.81821	+	2.54029i	−0.301146	+	0.0978484i
$675$		0			0
$676$	−37.0313	−	26.9048i	−1.42428	−	1.03480i
$677$	−19.1385	+	8.52100i	−0.735551	+	0.327489i	−0.740096	−	0.672501i	$-0.765220\pi$
$677$	−19.1385	+	8.52100i	−0.735551	+	0.327489i	0.00454475	+	0.999990i	$0.498553\pi$
$678$		0			0
$679$	−6.49251	−	5.84588i	−0.249160	−	0.224344i
$680$	−1.51551	+	3.40389i	−0.0581172	+	0.130533i
$681$		0			0
$682$	3.63763	−	6.85930i	0.139292	−	0.262656i
$683$		−	12.7750i		−	0.488822i	−0.969672	−	0.244411i	$-0.921405\pi$
$683$		−	12.7750i		−	0.488822i	0.969672	−	0.244411i	$-0.0785945\pi$
$684$		0			0
$685$	12.9675	+	39.9099i	0.495463	+	1.52488i
$686$	4.99212	−	4.49492i	0.190600	−	0.171617i
$687$		0			0
$688$	27.0053	+	2.83837i	1.02957	+	0.108212i
$689$	−27.1360	+	5.76793i	−1.03380	+	0.219741i
$690$		0			0
$691$	3.01553	+	28.6908i	0.114716	+	1.09145i	0.888777	+	0.458340i	$0.151556\pi$
$691$	3.01553	+	28.6908i	0.114716	+	1.09145i	−0.774061	+	0.633111i	$0.781778\pi$
$692$	21.1929			0.805633
$693$		0			0
$694$	−4.43747			−0.168444
$695$	3.49807	+	33.2819i	0.132689	+	1.26245i
$696$		0			0
$697$	13.0399	−	2.77172i	0.493922	−	0.104986i
$698$	−3.74117	−	0.393213i	−0.141605	−	0.0148833i
$699$		0			0
$700$	1.41403	−	1.27320i	0.0534453	−	0.0481223i
$701$	−1.64023	−	5.04812i	−0.0619507	−	0.190665i	0.915291	−	0.402793i	$-0.131961\pi$
$701$	−1.64023	−	5.04812i	−0.0619507	−	0.190665i	−0.977242	+	0.212128i	$0.931961\pi$
$702$		0			0
$703$			2.41032i			0.0909071i
$704$	−14.5976	+	7.13934i	−0.550170	+	0.269074i
$705$		0			0
$706$	0.694504	−	1.55988i	0.0261380	−	0.0587069i
$707$	−11.4093	−	10.2729i	−0.429089	−	0.386353i
$708$		0			0
$709$	−26.3752	+	11.7430i	−0.990543	+	0.441018i	−0.837047	−	0.547131i	$-0.815720\pi$
$709$	−26.3752	+	11.7430i	−0.990543	+	0.441018i	−0.153496	+	0.988149i	$0.549053\pi$
$710$	5.92979	+	4.30824i	0.222541	+	0.161685i
$711$		0			0
$712$	12.2491	−	3.97997i	0.459054	−	0.149156i
$713$	−35.0121	+	3.67992i	−1.31122	+	0.137814i
$714$		0			0
$715$	31.0130	−	37.0413i	1.15982	−	1.38527i
$716$	−17.2965	+	9.98615i	−0.646401	+	0.373200i
$717$		0			0
$718$	−2.94136	−	0.625206i	−0.109771	−	0.0233325i
$719$	−35.5978	−	11.5664i	−1.32757	−	0.431355i	−0.442484	−	0.896776i	$-0.645903\pi$
$719$	−35.5978	−	11.5664i	−1.32757	−	0.431355i	−0.885089	+	0.465422i	$0.845903\pi$
$720$		0			0
$721$	−1.75471	+	2.41515i	−0.0653488	+	0.0899449i
$722$	4.62545	+	5.13708i	0.172141	+	0.191182i
$723$		0			0
$724$	30.2652	+	13.4749i	1.12480	+	0.500792i
$725$	0.240358	+	0.416312i	0.00892666	+	0.0154614i
$726$		0			0
$727$	−21.8970	+	37.9268i	−0.812116	+	1.40663i	0.0992641	+	0.995061i	$0.468351\pi$
$727$	−21.8970	+	37.9268i	−0.812116	+	1.40663i	−0.911380	+	0.411565i	$0.864982\pi$
$728$	11.1772	−	8.12069i	0.414253	−	0.300973i
$729$		0			0
$730$	−4.28224	+	13.1794i	−0.158493	+	0.487791i
$731$	−3.78918	−	8.51064i	−0.140148	−	0.314777i
$732$		0			0
$733$	1.10458	+	5.19663i	0.0407985	+	0.191942i	0.993827	−	0.110938i	$-0.0353854\pi$
$733$	1.10458	+	5.19663i	0.0407985	+	0.191942i	−0.953029	+	0.302880i	$0.902052\pi$
$734$	9.39607	−	10.4354i	0.346815	−	0.385177i
$735$		0			0
$736$	−19.4744	−	11.2435i	−0.717834	−	0.414442i
$737$	1.68004	+	4.60037i	0.0618852	+	0.169457i
$738$		0			0
$739$	3.62411	+	4.98816i	0.133315	+	0.183492i	0.870455	−	0.492247i	$-0.163824\pi$
$739$	3.62411	+	4.98816i	0.133315	+	0.183492i	−0.737140	+	0.675740i	$0.763824\pi$
$740$	3.94544	−	18.5619i	0.145037	−	0.682347i
$741$		0			0
$742$	0.276053	−	2.62647i	0.0101342	−	0.0964208i
$743$	−0.698365	+	6.64450i	−0.0256205	+	0.243763i	0.974215	+	0.225622i	$0.0724415\pi$
$743$	−0.698365	+	6.64450i	−0.0256205	+	0.243763i	−0.999835	+	0.0181411i	$0.994225\pi$
$744$		0			0
$745$	7.03841	−	33.1131i	0.257867	−	1.21317i
$746$	1.40998	+	1.94067i	0.0516231	+	0.0710531i
$747$		0			0
$748$	5.62373	+	3.78439i	0.205624	+	0.138371i
$749$	−16.7598	−	9.67625i	−0.612388	−	0.353563i
$750$		0			0
$751$	−18.9643	+	21.0620i	−0.692017	+	0.768563i	−0.982084	−	0.188443i	$-0.939656\pi$
$751$	−18.9643	+	21.0620i	−0.692017	+	0.768563i	0.290067	+	0.957006i	$0.406323\pi$
$752$	−0.511611	−	2.40694i	−0.0186566	−	0.0877722i
$753$		0			0
$754$	0.684687	+	1.53783i	0.0249348	+	0.0560046i
$755$	1.89190	−	5.82267i	0.0688533	−	0.211909i
$756$		0			0
$757$	10.7918	−	7.84073i	0.392236	−	0.284976i	−0.374135	−	0.927374i	$-0.622060\pi$
$757$	10.7918	−	7.84073i	0.392236	−	0.284976i	0.766371	+	0.642398i	$0.222060\pi$
$758$	−2.29786	+	3.98002i	−0.0834621	+	0.144561i
$759$		0			0
$760$	0.955098	+	1.65428i	0.0346450	+	0.0600070i
$761$	0.507993	+	0.226173i	0.0184147	+	0.00819877i	0.415923	−	0.909400i	$-0.363458\pi$
$761$	0.507993	+	0.226173i	0.0184147	+	0.00819877i	−0.397509	+	0.917598i	$0.630125\pi$
$762$		0			0
$763$	9.27911	+	10.3055i	0.335926	+	0.373084i
$764$	22.3907	−	30.8181i	0.810066	−	1.11496i
$765$		0			0
$766$	5.02143	+	1.63156i	0.181432	+	0.0589507i
$767$	0.0673525	+	0.0143162i	0.00243196	+	0.000516929i
$768$		0			0
$769$	28.3158	−	16.3481i	1.02109	−	0.589528i	0.106672	−	0.994294i	$-0.465980\pi$
$769$	28.3158	−	16.3481i	1.02109	−	0.589528i	0.914420	+	0.404766i	$0.132647\pi$
$770$	2.44127	+	3.89745i	0.0879774	+	0.140454i
$771$		0			0
$772$	28.3108	−	2.97558i	1.01893	−	0.107093i
$773$	1.30242	−	0.423182i	0.0468448	−	0.0152208i	−0.285501	−	0.958378i	$-0.592160\pi$
$773$	1.30242	−	0.423182i	0.0468448	−	0.0152208i	0.332346	+	0.943158i	$0.392160\pi$
$774$		0			0
$775$	−3.31493	−	2.40844i	−0.119076	−	0.0865138i
$776$	−7.23334	+	3.22049i	−0.259662	+	0.115609i
$777$		0			0
$778$	−2.96101	−	2.66610i	−0.106157	−	0.0955844i
$779$	2.77982	−	6.24357i	0.0995972	−	0.223699i
$780$		0			0
$781$	19.8676	−	19.2276i	0.710920	−	0.688018i
$782$			2.25820i			0.0807530i
$783$		0			0
$784$	4.45900	+	13.7234i	0.159250	+	0.490121i
$785$	10.0554	−	9.05393i	0.358893	−	0.323149i
$786$		0			0
$787$	−8.61816	−	0.905805i	−0.307204	−	0.0322885i	−0.0503279	−	0.998733i	$-0.516027\pi$
$787$	−8.61816	−	0.905805i	−0.307204	−	0.0322885i	−0.256876	+	0.966444i	$0.582693\pi$
$788$	23.8778	−	5.07539i	0.850612	−	0.180803i
$789$		0			0
$790$	0.292377	+	2.78178i	0.0104023	+	0.0989712i
$791$	−0.0731593			−0.00260125
$792$		0			0
$793$	35.1262			1.24737
$794$	−0.535070	−	5.09085i	−0.0189889	−	0.180668i
$795$		0			0
$796$	−8.60740	+	1.82956i	−0.305081	+	0.0648470i
$797$	13.4164	+	1.41012i	0.475233	+	0.0499490i	0.339118	−	0.940744i	$-0.389871\pi$
$797$	13.4164	+	1.41012i	0.475233	+	0.0499490i	0.136116	+	0.990693i	$0.456538\pi$
$798$		0			0
$799$	−0.627382	+	0.564898i	−0.0221952	+	0.0199846i
$800$	−0.808775	−	2.48915i	−0.0285945	−	0.0880049i
$801$		0			0
$802$		−	13.2659i		−	0.468435i
$803$	46.1805	+	24.4905i	1.62968	+	0.864250i
$804$		0			0
$805$	8.48159	−	19.0500i	0.298937	−	0.671423i
$806$	−10.6631	−	9.60106i	−0.375590	−	0.338183i
$807$		0			0
$808$	−12.7111	+	5.65935i	−0.447175	+	0.199095i
$809$	35.6994	+	25.9371i	1.25512	+	0.911900i	0.998508	−	0.0546139i	$-0.0173928\pi$
$809$	35.6994	+	25.9371i	1.25512	+	0.911900i	0.256615	+	0.966514i	$0.417393\pi$
$810$		0			0
$811$	39.0505	−	12.6883i	1.37125	−	0.445546i	0.471466	−	0.881884i	$-0.343725\pi$
$811$	39.0505	−	12.6883i	1.37125	−	0.445546i	0.899782	+	0.436339i	$0.143725\pi$
$812$	2.16916	−	0.227988i	0.0761225	−	0.00800079i
$813$		0			0
$814$	4.87840	+	1.96486i	0.170988	+	0.0688681i
$815$	17.6167	−	10.1710i	0.617086	−	0.356275i
$816$		0			0
$817$	−4.67163	−	0.992986i	−0.163440	−	0.0347402i
$818$	5.52974	+	1.79672i	0.193343	+	0.0628209i
$819$		0			0
$820$	−31.6274	+	43.5313i	−1.10447	+	1.52018i
$821$	−10.5169	−	11.6802i	−0.367042	−	0.407641i	0.531127	−	0.847292i	$-0.321769\pi$
$821$	−10.5169	−	11.6802i	−0.367042	−	0.407641i	−0.898169	+	0.439651i	$0.855102\pi$
$822$		0			0
$823$	−5.19304	−	2.31209i	−0.181018	−	0.0805944i	0.314226	−	0.949348i	$-0.398255\pi$
$823$	−5.19304	−	2.31209i	−0.181018	−	0.0805944i	−0.495245	+	0.868754i	$0.664922\pi$
$824$	1.35278	+	2.34308i	0.0471262	+	0.0816250i
$825$		0			0
$826$	−0.00327745	+	0.00567671i	−0.000114037	+	0.000197518i
$827$	−11.5227	+	8.37170i	−0.400682	+	0.291113i	−0.769819	−	0.638263i	$-0.779653\pi$
$827$	−11.5227	+	8.37170i	−0.400682	+	0.291113i	0.369137	+	0.929375i	$0.379653\pi$
$828$		0			0
$829$	−1.17567	+	3.61833i	−0.0408326	+	0.125670i	−0.969395	−	0.245507i	$-0.921046\pi$
$829$	−1.17567	+	3.61833i	−0.0408326	+	0.125670i	0.928562	+	0.371177i	$0.121046\pi$
$830$	−3.71323	−	8.34006i	−0.128888	−	0.289488i
$831$		0			0
$832$	6.24374	+	29.3745i	0.216463	+	1.01838i
$833$	3.31256	−	3.67897i	0.114773	−	0.127469i
$834$		0			0
$835$	6.27784	+	3.62451i	0.217254	+	0.125431i
$836$	3.26422	−	1.19209i	0.112895	−	0.0412292i
$837$		0			0
$838$	−3.30773	−	4.55270i	−0.114264	−	0.157270i
$839$	−0.810360	+	3.81245i	−0.0279768	+	0.131620i	−0.989920	−	0.141630i	$-0.954766\pi$
$839$	−0.810360	+	3.81245i	−0.0279768	+	0.131620i	0.961943	+	0.273251i	$0.0880989\pi$
$840$		0			0
$841$	2.97373	−	28.2931i	0.102542	−	0.975625i
$842$	0.469552	−	4.46749i	0.0161818	−	0.153960i
$843$		0			0
$844$	7.56785	−	35.6039i	0.260496	−	1.22554i
$845$	−34.3180	−	47.2347i	−1.18058	−	1.62492i
$846$		0			0
$847$	16.0703	−	6.53338i	0.552183	−	0.224489i
$848$	12.5332	+	7.23605i	0.430392	+	0.248487i
$849$		0			0
$850$	−0.175868	+	0.195321i	−0.00603221	+	0.00669945i
$851$	−4.95804	−	23.3257i	−0.169959	−	0.799596i
$852$		0			0
$853$	−12.8962	−	28.9653i	−0.441556	−	0.991752i	−0.988028	−	0.154274i	$-0.950696\pi$
$853$	−12.8962	−	28.9653i	−0.441556	−	0.991752i	0.546472	−	0.837478i	$-0.315971\pi$
$854$	−1.03331	+	3.18020i	−0.0353592	+	0.108824i
$855$		0			0
$856$	−14.1894	+	10.3092i	−0.484984	+	0.352362i
$857$	19.7818	−	34.2630i	0.675733	−	1.17040i	−0.300522	−	0.953775i	$-0.597161\pi$
$857$	19.7818	−	34.2630i	0.675733	−	1.17040i	0.976254	−	0.216628i	$-0.0695059\pi$
$858$		0			0
$859$	19.1591	+	33.1846i	0.653701	+	1.13224i	0.982218	+	0.187746i	$0.0601181\pi$
$859$	19.1591	+	33.1846i	0.653701	+	1.13224i	−0.328516	+	0.944498i	$0.606549\pi$
$860$	34.3507	+	15.2939i	1.17135	+	0.521518i
$861$		0			0
$862$	−6.34867	−	7.05092i	−0.216237	−	0.240155i
$863$	−27.4819	+	37.8256i	−0.935495	+	1.28760i	0.0221825	+	0.999754i	$0.492939\pi$
$863$	−27.4819	+	37.8256i	−0.935495	+	1.28760i	−0.957677	+	0.287844i	$0.907061\pi$
$864$		0			0
$865$	25.7092	+	8.35343i	0.874139	+	0.284025i
$866$	0.467362	+	0.0993409i	0.0158816	+	0.00337574i
$867$		0			0
$868$	−16.1004	+	9.29557i	−0.546483	+	0.315512i
$869$	10.5261	+	0.724595i	0.357073	+	0.0245802i
$870$		0			0
$871$	9.00132	−	0.946077i	0.304998	−	0.0320566i
$872$	11.9528	−	3.88371i	0.404774	−	0.131519i
$873$		0			0
$874$	0.936595	+	0.680476i	0.0316808	+	0.0230174i
$875$	−14.9018	+	6.63471i	−0.503773	+	0.224294i
$876$		0			0
$877$	−23.4231	−	21.0902i	−0.790941	−	0.712166i	0.171046	−	0.985263i	$-0.445285\pi$
$877$	−23.4231	−	21.0902i	−0.790941	−	0.712166i	−0.961987	+	0.273097i	$0.911952\pi$
$878$	−1.35267	+	3.03815i	−0.0456505	+	0.102533i
$879$		0			0
$880$	−24.9525	+	3.53442i	−0.841149	+	0.119145i
$881$		−	42.0051i		−	1.41519i	−0.706619	−	0.707595i	$-0.749780\pi$
$881$		−	42.0051i		−	1.41519i	0.706619	−	0.707595i	$-0.250220\pi$
$882$		0			0
$883$	0.787007	+	2.42216i	0.0264849	+	0.0815122i	0.963425	−	0.267977i	$-0.0863551\pi$
$883$	0.787007	+	2.42216i	0.0264849	+	0.0815122i	−0.936940	+	0.349489i	$0.886355\pi$
$884$	9.30937	−	8.38219i	0.313108	−	0.281924i
$885$		0			0
$886$	−5.27795	−	0.554735i	−0.177316	−	0.0186367i
$887$	13.6187	−	2.89475i	0.457272	−	0.0971962i	0.0264838	−	0.999649i	$-0.491569\pi$
$887$	13.6187	−	2.89475i	0.457272	−	0.0971962i	0.430788	+	0.902453i	$0.358236\pi$
$888$		0			0
$889$	−1.08820	−	10.3536i	−0.0364972	−	0.347248i
$890$	7.92302			0.265580
$891$		0			0
$892$	30.6104			1.02491
$893$	0.0452403	+	0.430433i	0.00151391	+	0.0144039i
$894$		0			0
$895$	−24.9186	+	5.29662i	−0.832938	+	0.177047i
$896$	−15.5208	−	1.63130i	−0.518513	−	0.0544979i
$897$		0			0
$898$	−3.91766	+	3.52748i	−0.130734	+	0.117713i
$899$	−1.45141	−	4.46699i	−0.0484074	−	0.148983i
$900$		0			0
$901$		−	4.96511i		−	0.165412i
$902$	−10.3707	−	10.7159i	−0.345306	−	0.356800i
$903$		0			0
$904$	−0.0269682	+	0.0605716i	−0.000896950	+	0.00201458i
$905$	31.4035	+	28.2759i	1.04389	+	0.939922i
$906$		0			0
$907$	−30.4352	+	13.5506i	−1.01059	+	0.449941i	−0.844148	−	0.536111i	$-0.819893\pi$
$907$	−30.4352	+	13.5506i	−1.01059	+	0.449941i	−0.166437	+	0.986052i	$0.553226\pi$
$908$	−40.9456	−	29.7487i	−1.35883	−	0.987246i
$909$		0			0
$910$	8.08303	−	2.62634i	0.267950	−	0.0870622i
$911$	−6.55267	+	0.688713i	−0.217100	+	0.0228181i	−0.212454	−	0.977171i	$-0.568146\pi$
$911$	−6.55267	+	0.688713i	−0.217100	+	0.0228181i	−0.00464588	+	0.999989i	$0.501479\pi$
$912$		0			0
$913$	−33.4050	+	8.36725i	−1.10554	+	0.276916i
$914$	8.32303	−	4.80530i	0.275301	−	0.158945i
$915$		0			0
$916$	−7.90076	−	1.67936i	−0.261049	−	0.0554876i
$917$	11.8240	+	3.84186i	0.390464	+	0.126869i
$918$		0			0
$919$	−19.1361	+	26.3386i	−0.631241	+	0.868829i	−0.998111	−	0.0614433i	$-0.980430\pi$
$919$	−19.1361	+	26.3386i	−0.631241	+	0.868829i	0.366869	+	0.930273i	$0.380430\pi$
$920$	−12.6457	−	14.0445i	−0.416918	−	0.463034i
$921$		0			0
$922$	3.93921	+	1.75385i	0.129731	+	0.0577600i
$923$	−25.5476	−	44.2498i	−0.840910	−	1.45650i
$924$		0			0
$925$	1.38776	−	2.40367i	0.0456292	−	0.0790322i
$926$	−5.58674	+	4.05901i	−0.183592	+	0.133387i
$927$		0			0
$928$	0.927084	−	2.85327i	0.0304330	−	0.0936633i
$929$	−5.70632	−	12.8166i	−0.187218	−	0.420499i	0.795413	−	0.606068i	$-0.207254\pi$
$929$	−5.70632	−	12.8166i	−0.187218	−	0.420499i	−0.982631	+	0.185568i	$0.940587\pi$
$930$		0			0
$931$	−0.527671	−	2.48250i	−0.0172937	−	0.0813606i
$932$	−14.6191	+	16.2361i	−0.478864	+	0.531832i
$933$		0			0
$934$	−0.967583	−	0.558634i	−0.0316603	−	0.0182791i
$935$	5.33051	+	6.80753i	0.174326	+	0.222630i
$936$		0			0
$937$	31.0358	+	42.7172i	1.01390	+	1.39551i	0.916396	+	0.400273i	$0.131085\pi$
$937$	31.0358	+	42.7172i	1.01390	+	1.39551i	0.0975008	+	0.995235i	$0.468915\pi$
$938$	−0.179138	+	0.842778i	−0.00584906	+	0.0275177i
$939$		0			0
$940$	0.356178	−	3.38881i	0.0116172	−	0.110531i
$941$	0.232464	−	2.21175i	0.00757812	−	0.0721010i	−0.990079	−	0.140510i	$-0.955126\pi$
$941$	0.232464	−	2.21175i	0.00757812	−	0.0721010i	0.997657	+	0.0684093i	$0.0217924\pi$
$942$		0			0
$943$	−14.0584	+	66.1398i	−0.457806	+	2.15381i
$944$	−0.0211134	−	0.0290601i	−0.000687183	−	0.000945826i
$945$		0			0
$946$	−5.81800	+	8.64573i	−0.189159	+	0.281097i
$947$	18.9816	+	10.9590i	0.616819	+	0.356121i	0.775629	−	0.631189i	$-0.217433\pi$
$947$	18.9816	+	10.9590i	0.616819	+	0.356121i	−0.158811	+	0.987309i	$0.550766\pi$
$948$		0			0
$949$	64.6396	−	71.7895i	2.09829	−	2.33039i
$950$	0.0280147	+	0.131799i	0.000908917	+	0.00427612i
$951$		0			0
$952$	1.00572	+	2.25887i	0.0325954	+	0.0732105i
$953$	6.64425	−	20.4489i	0.215228	−	0.662404i	−0.783909	−	0.620876i	$-0.786777\pi$
$953$	6.64425	−	20.4489i	0.215228	−	0.662404i	0.999137	−	0.0415288i	$-0.0132228\pi$
$954$		0			0
$955$	39.3095	−	28.5601i	1.27203	−	0.924182i
$956$	−16.7138	+	28.9492i	−0.540564	+	0.936284i
$957$		0			0
$958$	7.15620	+	12.3949i	0.231206	+	0.400461i
$959$	25.4402	+	11.3267i	0.821506	+	0.365758i
$960$		0			0
$961$	6.04551	+	6.71422i	0.195016	+	0.216588i
$962$	5.71286	−	7.86308i	0.184190	−	0.253516i
$963$		0			0
$964$	4.73430	+	1.53827i	0.152482	+	0.0495443i
$965$	35.5168	+	7.54932i	1.14333	+	0.243021i
$966$		0			0
$967$	13.6754	−	7.89548i	0.439770	−	0.253901i	−0.263730	−	0.964597i	$-0.584953\pi$
$967$	13.6754	−	7.89548i	0.439770	−	0.253901i	0.703500	+	0.710695i	$0.251619\pi$
$968$	0.514639	−	15.7136i	0.0165411	−	0.505056i
$969$		0			0
$970$	−4.84414	+	0.509140i	−0.155536	+	0.0163475i
$971$	7.29530	−	2.37039i	0.234117	−	0.0760693i	−0.189609	−	0.981860i	$-0.560722\pi$
$971$	7.29530	−	2.37039i	0.234117	−	0.0760693i	0.423726	+	0.905790i	$0.360722\pi$
$972$		0			0
$973$	17.9667	+	13.0535i	0.575984	+	0.418477i
$974$	−4.15002	+	1.84771i	−0.132975	+	0.0592043i
$975$		0			0
$976$	−13.6174	−	12.2612i	−0.435883	−	0.392471i
$977$	3.03997	−	6.82789i	0.0972573	−	0.218444i	−0.858364	−	0.513041i	$-0.828519\pi$
$977$	3.03997	−	6.82789i	0.0972573	−	0.218444i	0.955621	+	0.294597i	$0.0951855\pi$
$978$		0			0
$979$	5.15786	−	29.4382i	0.164846	−	0.940848i
$980$			19.9814i			0.638282i
$981$		0			0
$982$	−4.16946	−	12.8323i	−0.133053	−	0.409494i
$983$	−37.1304	+	33.4323i	−1.18427	+	1.06633i	−0.187819	+	0.982204i	$0.560142\pi$
$983$	−37.1304	+	33.4323i	−1.18427	+	1.06633i	−0.996455	+	0.0841219i	$0.973191\pi$
$984$		0			0
$985$	30.9668	+	3.25474i	0.986685	+	0.103705i
$986$	−0.294694	+	0.0626391i	−0.00938496	+	0.00199484i
$987$		0			0
$988$	−0.671295	−	6.38694i	−0.0213567	−	0.203196i
$989$	47.2520			1.50252
$990$		0			0
$991$	−32.0166			−1.01704			−0.508520	−	0.861050i	$-0.669807\pi$
$991$	−32.0166			−1.01704			−0.508520	+	0.861050i	$0.669807\pi$
$992$	2.67301	+	25.4320i	0.0848682	+	0.807467i
$993$		0			0
$994$	4.75775	−	1.01129i	0.150907	−	0.0320762i
$995$	−11.1628	−	1.17326i	−0.353885	−	0.0371948i
$996$		0			0
$997$	14.0664	−	12.6655i	0.445488	−	0.401119i	−0.415623	−	0.909537i	$-0.636436\pi$
$997$	14.0664	−	12.6655i	0.445488	−	0.401119i	0.861110	+	0.508418i	$0.169770\pi$
$998$	2.77608	+	8.54390i	0.0878753	+	0.270452i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.8.5		80
3.2	odd	2		99.2.p.a.74.6	yes	80
9.2	odd	6		891.2.k.a.404.11		80
9.4	even	3		99.2.p.a.41.6	yes	80
9.5	odd	6	inner	297.2.t.a.206.5		80
9.7	even	3		891.2.k.a.404.10		80
11.7	odd	10	inner	297.2.t.a.62.5		80
33.29	even	10		99.2.p.a.29.6	✓	80
99.7	odd	30		891.2.k.a.161.11		80
99.29	even	30		891.2.k.a.161.10		80
99.40	odd	30		99.2.p.a.95.6	yes	80
99.95	even	30	inner	297.2.t.a.260.5		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.6	✓	80	33.29	even	10
99.2.p.a.41.6	yes	80	9.4	even	3
99.2.p.a.74.6	yes	80	3.2	odd	2
99.2.p.a.95.6	yes	80	99.40	odd	30
297.2.t.a.8.5		80	1.1	even	1	trivial
297.2.t.a.62.5		80	11.7	odd	10	inner
297.2.t.a.206.5		80	9.5	odd	6	inner
297.2.t.a.260.5		80	99.95	even	30	inner
891.2.k.a.161.10		80	99.29	even	30
891.2.k.a.161.11		80	99.7	odd	30
891.2.k.a.404.10		80	9.7	even	3
891.2.k.a.404.11		80	9.2	odd	6

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.t (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0386735 - 0.367954i) q^{2} +(1.82240 - 0.387363i) q^{4} +(2.36345 + 0.248408i) q^{5} +(1.17198 - 1.05526i) q^{7} +(-0.441671 - 1.35932i) q^{8} -0.879247i q^{10} +(-3.26686 - 0.572386i) q^{11} +(-2.49300 + 5.59938i) q^{13} +(-0.433611 - 0.390425i) q^{14} +(2.92099 - 1.30051i) q^{16} +(-0.887473 - 0.644787i) q^{17} +(-0.534855 + 0.173785i) q^{19} +(4.40337 - 0.462813i) q^{20} +(-0.0842709 + 1.22419i) q^{22} +(4.81854 - 2.78199i) q^{23} +(0.633436 + 0.134641i) q^{25} +(2.15673 + 0.700764i) q^{26} +(1.72705 - 2.37708i) q^{28} +(0.496707 + 0.551649i) q^{29} +(-5.78029 - 2.57355i) q^{31} +(-2.02077 - 3.50008i) q^{32} +(-0.202930 + 0.351486i) q^{34} +(3.03205 - 2.20291i) q^{35} +(1.32443 - 4.07617i) q^{37} +(0.0846296 + 0.190081i) q^{38} +(-0.706199 - 3.32241i) q^{40} +(-8.13175 + 9.03123i) q^{41} +(7.35471 + 4.24624i) q^{43} +(-6.17525 + 0.222344i) q^{44} +(-1.20999 - 1.66541i) q^{46} +(0.160007 - 0.752776i) q^{47} +(-0.471726 + 4.48817i) q^{49} +(0.0250445 - 0.238282i) q^{50} +(-2.37426 + 11.1700i) q^{52} +(2.66042 + 3.66175i) q^{53} +(-7.57886 - 2.16432i) q^{55} +(-1.95207 - 1.12703i) q^{56} +(0.183772 - 0.204100i) q^{58} +(-0.00233571 - 0.0109886i) q^{59} +(-2.33096 - 5.23542i) q^{61} +(-0.723404 + 2.22641i) q^{62} +(3.96382 - 2.87988i) q^{64} +(-7.28302 + 12.6146i) q^{65} +(-0.738332 - 1.27883i) q^{67} +(-1.86710 - 0.831285i) q^{68} +(-0.927831 - 1.03046i) q^{70} +(-4.89992 + 6.74417i) q^{71} +(-14.9894 - 4.87035i) q^{73} +(-1.55106 - 0.329689i) q^{74} +(-0.907402 + 0.523889i) q^{76} +(-4.43271 + 2.77655i) q^{77} +(-3.16382 + 0.332531i) q^{79} +(7.22666 - 2.34809i) q^{80} +(3.63756 + 2.64284i) q^{82} +(9.48546 - 4.22320i) q^{83} +(-1.93732 - 1.74437i) q^{85} +(1.27799 - 2.87041i) q^{86} +(0.664820 + 4.69353i) q^{88} +9.01115i q^{89} +(2.98703 + 9.19313i) q^{91} +(7.70368 - 6.93642i) q^{92} +(-0.283175 - 0.0297629i) q^{94} +(-1.30727 + 0.277869i) q^{95} +(-0.579063 - 5.50942i) q^{97} +1.66968 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Introduction

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