LMFDB - Embedded newform 297.2.t.a.62.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(8,297)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			62.5
Character	$\chi$	$=$	297.62
Dual form			297.2.t.a.206.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.337994 + 0.150485i) q^{2} +(-1.24667 + 1.38456i) q^{4} +(0.966595 - 2.17101i) q^{5} +(0.327889 - 1.54259i) q^{7} +(0.441671 - 1.35932i) q^{8} +0.879247i q^{10} +(-2.12913 - 2.54299i) q^{11} +(6.09571 + 0.640685i) q^{13} +(0.121313 + 0.570731i) q^{14} +(-0.334222 - 3.17991i) q^{16} +(0.887473 - 0.644787i) q^{17} +(-0.534855 - 0.173785i) q^{19} +(1.80088 + 4.04484i) q^{20} +(1.10232 + 0.539115i) q^{22} +(4.81854 - 2.78199i) q^{23} +(-0.433320 - 0.481251i) q^{25} +(-2.15673 + 0.700764i) q^{26} +(1.72705 + 2.37708i) q^{28} +(0.726096 + 0.154337i) q^{29} +(0.661384 - 6.29265i) q^{31} +(2.02077 + 3.50008i) q^{32} +(-0.202930 + 0.351486i) q^{34} +(-3.03205 - 2.20291i) q^{35} +(1.32443 + 4.07617i) q^{37} +(0.206930 - 0.0217492i) q^{38} +(-2.52419 - 2.27279i) q^{40} +(-11.8871 + 2.52669i) q^{41} +(-7.35471 - 4.24624i) q^{43} +(6.17525 + 0.222344i) q^{44} +(-1.20999 + 1.66541i) q^{46} +(-0.571919 + 0.514959i) q^{47} +(4.12273 + 1.83556i) q^{49} +(0.218881 + 0.0974520i) q^{50} +(-8.48639 + 7.64118i) q^{52} +(-2.66042 + 3.66175i) q^{53} +(-7.57886 + 2.16432i) q^{55} +(-1.95207 - 1.12703i) q^{56} +(-0.268642 + 0.0571016i) q^{58} +(0.00834859 + 0.00751710i) q^{59} +(5.69949 - 0.599041i) q^{61} +(0.723404 + 2.22641i) q^{62} +(3.96382 + 2.87988i) q^{64} +(7.28302 - 12.6146i) q^{65} +(-0.738332 - 1.27883i) q^{67} +(-0.213635 + 2.03260i) q^{68} +(1.35632 + 0.288295i) q^{70} +(4.89992 + 6.74417i) q^{71} +(-14.9894 + 4.87035i) q^{73} +(-1.06105 - 1.17842i) q^{74} +(0.907402 - 0.523889i) q^{76} +(-4.62092 + 2.45057i) q^{77} +(1.29393 + 2.90621i) q^{79} +(-7.22666 - 2.34809i) q^{80} +(3.63756 - 2.64284i) q^{82} +(1.08533 + 10.3262i) q^{83} +(-0.542011 - 2.54996i) q^{85} +(3.12484 + 0.328434i) q^{86} +(-4.39713 + 1.77101i) q^{88} +9.01115i q^{89} +(2.98703 - 9.19313i) q^{91} +(-2.15528 + 10.1398i) q^{92} +(0.115812 - 0.260118i) q^{94} +(-0.894277 + 0.993195i) q^{95} +(5.06083 - 2.25323i) q^{97} -1.66968 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.337994	+	0.150485i	−0.238998	+	0.106409i	−0.522741	−	0.852492i	$-0.675090\pi$
$2$	−0.337994	+	0.150485i	−0.238998	+	0.106409i	0.283743	+	0.958900i	$0.408424\pi$
$3$		0			0
$3$		0			0
$4$	−1.24667	+	1.38456i	−0.623333	+	0.692282i
$5$	0.966595	−	2.17101i	0.432275	−	0.970905i	−0.557750	−	0.830009i	$-0.688335\pi$
$5$	0.966595	−	2.17101i	0.432275	−	0.970905i	0.990024	−	0.140896i	$-0.0449982\pi$
$6$		0			0
$7$	0.327889	−	1.54259i	0.123930	−	0.583046i	−0.871730	−	0.489986i	$-0.837002\pi$
$7$	0.327889	−	1.54259i	0.123930	−	0.583046i	0.995661	−	0.0930598i	$-0.0296648\pi$
$8$	0.441671	−	1.35932i	0.156154	−	0.480594i
$9$		0			0
$10$			0.879247i			0.278042i
$11$	−2.12913	−	2.54299i	−0.641957	−	0.766741i
$11$	−2.12913	−	2.54299i	−0.641957	−	0.766741i
$12$		0			0
$13$	6.09571	+	0.640685i	1.69065	+	0.177694i	0.900390	−	0.435084i	$-0.143281\pi$
$13$	6.09571	+	0.640685i	1.69065	+	0.177694i	0.790255	+	0.612778i	$0.209948\pi$
$14$	0.121313	+	0.570731i	0.0324221	+	0.152534i
$15$		0			0
$16$	−0.334222	−	3.17991i	−0.0835554	−	0.794977i
$17$	0.887473	−	0.644787i	0.215244	−	0.156384i	−0.474939	−	0.880019i	$-0.657530\pi$
$17$	0.887473	−	0.644787i	0.215244	−	0.156384i	0.690183	+	0.723635i	$0.257530\pi$
$18$		0			0
$19$	−0.534855	−	0.173785i	−0.122704	−	0.0398690i	0.247021	−	0.969010i	$-0.420548\pi$
$19$	−0.534855	−	0.173785i	−0.122704	−	0.0398690i	−0.369725	+	0.929141i	$0.620548\pi$
$20$	1.80088	+	4.04484i	0.402688	+	0.904453i
$21$		0			0
$22$	1.10232	+	0.539115i	0.235015	+	0.114940i
$23$	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
$25$	−0.433320	−	0.481251i	−0.0866641	−	0.0962502i
$26$	−2.15673	+	0.700764i	−0.422969	+	0.137431i
$27$		0			0
$28$	1.72705	+	2.37708i	0.326382	+	0.449227i
$29$	0.726096	+	0.154337i	0.134833	+	0.0286596i	0.274834	−	0.961492i	$-0.411377\pi$
$29$	0.726096	+	0.154337i	0.134833	+	0.0286596i	−0.140001	+	0.990151i	$0.544711\pi$
$30$		0			0
$31$	0.661384	−	6.29265i	0.118788	−	1.13019i	−0.758982	−	0.651111i	$-0.774303\pi$
$31$	0.661384	−	6.29265i	0.118788	−	1.13019i	0.877770	−	0.479082i	$-0.159030\pi$
$32$	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	0.998948	+	0.0458543i	$0.0146010\pi$
$37$	1.32443	+	4.07617i	0.217735	+	0.670118i	−0.781214	+	0.624264i	$0.785399\pi$
$38$	0.206930	−	0.0217492i	0.0335685	−	0.00352819i
$39$		0			0
$40$	−2.52419	−	2.27279i	−0.399109	−	0.359360i
$41$	−11.8871	+	2.52669i	−1.85646	+	0.394603i	−0.993800	−	0.111181i	$-0.964537\pi$
$41$	−11.8871	+	2.52669i	−1.85646	+	0.394603i	−0.862660	+	0.505784i	$0.831203\pi$
$42$		0			0
$43$	−7.35471	−	4.24624i	−1.12158	−	0.647546i	−0.179778	−	0.983707i	$-0.557538\pi$
$43$	−7.35471	−	4.24624i	−1.12158	−	0.647546i	−0.941804	+	0.336162i	$0.890871\pi$
$44$	6.17525	+	0.222344i	0.930954	+	0.0335197i
$45$		0			0
$46$	−1.20999	+	1.66541i	−0.178404	+	0.245552i
$47$	−0.571919	+	0.514959i	−0.0834230	+	0.0751144i	−0.709787	−	0.704416i	$-0.751209\pi$
$47$	−0.571919	+	0.514959i	−0.0834230	+	0.0751144i	0.626364	+	0.779531i	$0.284542\pi$
$48$		0			0
$49$	4.12273	+	1.83556i	0.588962	+	0.262223i
$50$	0.218881	+	0.0974520i	0.0309544	+	0.0137818i
$51$		0			0
$52$	−8.48639	+	7.64118i	−1.17685	+	1.05964i
$53$	−2.66042	+	3.66175i	−0.365437	+	0.502981i	−0.951653	−	0.307174i	$-0.900617\pi$
$53$	−2.66042	+	3.66175i	−0.365437	+	0.502981i	0.586217	+	0.810154i	$0.300617\pi$
$54$		0			0
$55$	−7.57886	+	2.16432i	−1.02193	+	0.291837i
$56$	−1.95207	−	1.12703i	−0.260856	−	0.150605i
$57$		0			0
$58$	−0.268642	+	0.0571016i	−0.0352744	+	0.00749780i
$59$	0.00834859	+	0.00751710i	0.00108689	+	0.000978643i	0.669674	−	0.742655i	$-0.266434\pi$
$59$	0.00834859	+	0.00751710i	0.00108689	+	0.000978643i	−0.668587	+	0.743634i	$0.733101\pi$
$60$		0			0
$61$	5.69949	−	0.599041i	0.729745	−	0.0766993i	0.267633	−	0.963521i	$-0.413759\pi$
$61$	5.69949	−	0.599041i	0.729745	−	0.0766993i	0.462112	+	0.886822i	$0.347092\pi$
$62$	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	$0.862084\pi$
$68$	−0.213635	+	2.03260i	−0.0259070	+	0.246489i
$69$		0			0
$70$	1.35632	+	0.288295i	0.162111	+	0.0344578i
$71$	4.89992	+	6.74417i	0.581514	+	0.800385i	0.993860	−	0.110642i	$-0.0352906\pi$
$71$	4.89992	+	6.74417i	0.581514	+	0.800385i	−0.412346	+	0.911027i	$0.635291\pi$
$72$		0			0
$73$	−14.9894	+	4.87035i	−1.75438	+	0.570031i	−0.996593	−	0.0824752i	$-0.973717\pi$
$73$	−14.9894	+	4.87035i	−1.75438	+	0.570031i	−0.757783	+	0.652507i	$0.773717\pi$
$74$	−1.06105	−	1.17842i	−0.123345	−	0.136988i
$75$		0			0
$76$	0.907402	−	0.523889i	0.104086	−	0.0600941i
$77$	−4.62092	+	2.45057i	−0.526603	+	0.279268i
$78$		0			0
$79$	1.29393	+	2.90621i	0.145578	+	0.326974i	0.971587	−	0.236683i	$-0.0760604\pi$
$79$	1.29393	+	2.90621i	0.145578	+	0.326974i	−0.826008	+	0.563658i	$0.809394\pi$
$80$	−7.22666	−	2.34809i	−0.807965	−	0.262524i
$81$		0			0
$82$	3.63756	−	2.64284i	0.401701	−	0.291853i
$83$	1.08533	+	10.3262i	0.119131	+	1.13345i	0.876814	+	0.480830i	$0.159665\pi$
$83$	1.08533	+	10.3262i	0.119131	+	1.13345i	−0.757683	+	0.652623i	$0.773669\pi$
$84$		0			0
$85$	−0.542011	−	2.54996i	−0.0587893	−	0.276582i
$86$	3.12484	+	0.328434i	0.336961	+	0.0354160i
$87$		0			0
$88$	−4.39713	+	1.77101i	−0.468735	+	0.188791i
$89$			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
$92$	−2.15528	+	10.1398i	−0.224703	+	1.05715i
$93$		0			0
$94$	0.115812	−	0.260118i	0.0119451	−	0.0268292i
$95$	−0.894277	+	0.993195i	−0.0917508	+	0.101900i
$96$		0			0
$97$	5.06083	−	2.25323i	0.513849	−	0.228781i	−0.133395	−	0.991063i	$-0.542588\pi$
$97$	5.06083	−	2.25323i	0.513849	−	0.228781i	0.647245	+	0.762282i	$0.275921\pi$
$98$	−1.66968			−0.168664
$99$		0			0
$100$	1.20653			0.120653
$101$	−8.89337	+	3.95958i	−0.884924	+	0.393993i	−0.798309	−	0.602248i	$-0.794272\pi$
$101$	−8.89337	+	3.95958i	−0.884924	+	0.393993i	−0.0866149	+	0.996242i	$0.527605\pi$
$102$		0			0
$103$	1.26663	−	1.40674i	0.124805	−	0.138610i	−0.677504	−	0.735519i	$-0.736938\pi$
$103$	1.26663	−	1.40674i	0.124805	−	0.138610i	0.802309	+	0.596910i	$0.203605\pi$
$104$	3.56320	−	8.00308i	0.349400	−	0.784766i
$105$		0			0
$106$	0.348169	−	1.63801i	0.0338171	−	0.159097i
$107$	3.79203	−	11.6707i	0.366590	−	1.12825i	−0.582390	−	0.812910i	$-0.697882\pi$
$107$	3.79203	−	11.6707i	0.366590	−	1.12825i	0.948980	−	0.315337i	$-0.102118\pi$
$108$		0			0
$109$		−	8.79322i		−	0.842238i	−0.907005	−	0.421119i	$-0.861638\pi$
$109$		−	8.79322i		−	0.842238i	0.907005	−	0.421119i	$-0.138362\pi$
$110$	2.23592	−	1.87203i	0.213186	−	0.178491i
$111$		0			0
$112$	−5.01489	−	0.527087i	−0.473863	−	0.0498050i
$113$	0.00964498	+	0.0453760i	0.000907323	+	0.00426862i	0.978599	−	0.205777i	$-0.0659721\pi$
$113$	0.00964498	+	0.0453760i	0.000907323	+	0.00426862i	−0.977692	+	0.210046i	$0.932639\pi$
$114$		0			0
$115$	−1.38214	−	13.1502i	−0.128885	−	1.22626i
$116$	−1.11889	+	0.812920i	−0.103886	+	0.0754777i
$117$		0			0
$118$	−0.00395298	−	0.00128440i	−0.000363902	−	0.000118239i
$119$	−0.703652	−	1.58043i	−0.0645037	−	0.144878i
$120$		0			0
$121$	−1.93360	+	10.8287i	−0.175782	+	0.984429i
$122$	−1.83625	+	1.06016i	−0.166246	+	0.0959823i
$123$		0			0
$124$	7.88805	+	8.76056i	0.708368	+	0.786722i
$125$	9.83712	−	3.19627i	0.879859	−	0.285883i
$126$		0			0
$127$	3.88014	+	5.34055i	0.344307	+	0.473898i	0.945693	−	0.325061i	$-0.105385\pi$
$127$	3.88014	+	5.34055i	0.344307	+	0.473898i	−0.601386	+	0.798958i	$0.705385\pi$
$128$	−9.67958	−	2.05746i	−0.855562	−	0.181855i
$129$		0			0
$130$	−0.563320	+	5.35963i	−0.0494064	+	0.470071i
$131$	−3.94169	−	6.82720i	−0.344387	−	0.596495i	0.640855	−	0.767662i	$-0.278580\pi$
$131$	−3.94169	−	6.82720i	−0.344387	−	0.596495i	−0.985242	+	0.171166i	$0.945246\pi$
$132$		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
$137$	17.5613	−	1.84577i	1.50036	−	0.157695i	0.681558	−	0.731764i	$-0.261303\pi$
$137$	17.5613	−	1.84577i	1.50036	−	0.157695i	0.818806	+	0.574070i	$0.194636\pi$
$138$		0			0
$139$	10.4649	+	9.42265i	0.887622	+	0.799219i	0.980512	−	0.196458i	$-0.0629438\pi$
$139$	10.4649	+	9.42265i	0.887622	+	0.799219i	−0.0928899	+	0.995676i	$0.529610\pi$
$140$	6.83003	−	1.45177i	0.577243	−	0.122697i
$141$		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
$146$	4.33342	−	3.90183i	0.358636	−	0.322918i
$147$		0			0
$148$	−7.29484	−	3.24787i	−0.599632	−	0.266973i
$149$	13.0135	+	5.79399i	1.06611	+	0.474662i	0.863370	−	0.504571i	$-0.168349\pi$
$149$	13.0135	+	5.79399i	1.06611	+	0.474662i	0.202738	+	0.979233i	$0.435016\pi$
$150$		0			0
$151$	1.91451	−	1.72383i	0.155801	−	0.140284i	−0.587544	−	0.809192i	$-0.699905\pi$
$151$	1.91451	−	1.72383i	0.155801	−	0.140284i	0.743345	+	0.668909i	$0.233238\pi$
$152$	−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
$157$	−5.56928	+	1.18379i	−0.444477	+	0.0944766i	−0.424713	−	0.905328i	$-0.639625\pi$
$157$	−5.56928	+	1.18379i	−0.444477	+	0.0944766i	−0.0197644	+	0.999805i	$0.506292\pi$
$158$	−0.874682	−	0.787567i	−0.0695859	−	0.0626555i
$159$		0			0
$160$	9.55197	−	1.00395i	0.755150	−	0.0793694i
$161$	−2.71153	−	8.34524i	−0.213699	−	0.657697i
$162$		0			0
$163$	6.92500	+	5.03131i	0.542408	+	0.394083i	0.824979	−	0.565164i	$-0.191187\pi$
$163$	6.92500	+	5.03131i	0.542408	+	0.394083i	−0.282570	+	0.959247i	$0.591187\pi$
$164$	11.3209	−	19.6085i	0.884017	−	1.53116i
$165$		0			0
$166$	−1.92078	−	3.32689i	−0.149081	−	0.258217i
$167$	0.318847	−	3.03363i	0.0246731	−	0.234749i	−0.975235	−	0.221173i	$-0.929012\pi$
$167$	0.318847	−	3.03363i	0.0246731	−	0.234749i	0.999908	−	0.0135767i	$-0.00432173\pi$
$168$		0			0
$169$	24.0313	+	5.10800i	1.84856	+	0.392923i
$170$	0.566927	+	0.780308i	0.0434813	+	0.0598469i
$171$		0			0
$172$	15.0481	−	4.88941i	1.14740	−	0.372814i
$173$	7.61135	+	8.45326i	0.578680	+	0.642690i	0.959416	−	0.281994i	$-0.0909959\pi$
$173$	7.61135	+	8.45326i	0.578680	+	0.642690i	−0.380736	+	0.924684i	$0.624329\pi$
$174$		0			0
$175$	−0.884456	+	0.510641i	−0.0668586	+	0.0386008i
$176$	−7.37487	+	7.62036i	−0.555902	+	0.574406i
$177$		0			0
$178$	−1.35604	−	3.04572i	−0.101640	−	0.228286i
$179$	10.1952	+	3.31261i	0.762023	+	0.247596i	0.664147	−	0.747602i	$-0.268795\pi$
$179$	10.1952	+	3.31261i	0.762023	+	0.247596i	0.0978766	+	0.995199i	$0.468795\pi$
$180$		0			0
$181$	14.3857	−	10.4518i	1.06928	−	0.776879i	0.0934987	−	0.995619i	$-0.470195\pi$
$181$	14.3857	−	10.4518i	1.06928	−	0.776879i	0.975783	+	0.218741i	$0.0701949\pi$
$182$	0.373827	+	3.55673i	0.0277099	+	0.263642i
$183$		0			0
$184$	−1.65341	−	7.77869i	−0.121891	−	0.573453i
$185$	10.1296	+	1.06466i	0.744742	+	0.0782756i
$186$		0			0
$187$	−3.52923	−	0.884000i	−0.258083	−	0.0646445i
$188$		−	1.43384i		−	0.104574i
$189$		0			0
$190$	0.152800	−	0.470269i	0.0110853	−	0.0341169i
$191$	−4.25097	+	19.9992i	−0.307589	+	1.44709i	0.504425	+	0.863456i	$0.331705\pi$
$191$	−4.25097	+	19.9992i	−0.307589	+	1.44709i	−0.812014	+	0.583638i	$0.801629\pi$
$192$		0			0
$193$	−6.21457	+	13.9581i	−0.447334	+	1.00473i	0.539350	+	0.842082i	$0.318670\pi$
$193$	−6.21457	+	13.9581i	−0.447334	+	1.00473i	−0.986684	+	0.162648i	$0.947997\pi$
$194$	−1.37146	+	1.52316i	−0.0984648	+	0.109356i
$195$		0			0
$196$	−7.68112	+	3.41985i	−0.548651	+	0.244275i
$197$	−13.1024			−0.933507			−0.466754	−	0.884387i	$-0.654576\pi$
$197$	−13.1024			−0.933507			−0.466754	+	0.884387i	$0.654576\pi$
$198$		0			0
$199$	−4.72311			−0.334812			−0.167406	−	0.985888i	$-0.553539\pi$
$199$	−4.72311			−0.334812			−0.167406	+	0.985888i	$0.553539\pi$
$200$	−0.845562	+	0.376468i	−0.0597902	+	0.0266203i
$201$		0			0
$202$	2.41005	−	2.67663i	0.169571	−	0.188327i
$203$	0.476157	−	1.06947i	0.0334197	−	0.0750618i
$204$		0			0
$205$	−6.00459	+	28.2494i	−0.419379	+	1.97302i
$206$	−0.216422	+	0.666078i	−0.0150788	+	0.0464078i
$207$		0			0
$208$		−	19.5979i		−	1.35887i
$209$	0.696843	+	1.73014i	0.0482016	+	0.119676i
$210$		0			0
$211$	−19.4298	−	2.04215i	−1.33760	−	0.140588i	−0.591439	−	0.806350i	$-0.701440\pi$
$211$	−19.4298	−	2.04215i	−1.33760	−	0.140588i	−0.746164	+	0.665762i	$0.768107\pi$
$212$	−1.75327	−	8.24851i	−0.120415	−	0.566510i
$213$		0			0
$214$	0.474574	+	4.51527i	0.0324412	+	0.308657i
$215$	−16.3277	+	11.8627i	−1.11354	+	0.809032i
$216$		0			0
$217$	−9.49015	−	3.08354i	−0.644233	−	0.209324i
$218$	1.32325	+	2.97206i	0.0896215	+	0.201293i
$219$		0			0
$220$	6.45168	−	13.1916i	0.434972	−	0.889378i
$221$	5.82288	−	3.36184i	0.391689	−	0.226142i
$222$		0			0
$223$	−10.9936	−	12.2097i	−0.736188	−	0.817620i	0.252502	−	0.967596i	$-0.418747\pi$
$223$	−10.9936	−	12.2097i	−0.736188	−	0.817620i	−0.988689	+	0.149977i	$0.952080\pi$
$224$	6.06179	−	1.96959i	0.405020	−	0.131599i
$225$		0			0
$226$	−0.0100884	−	0.0138854i	−0.000671067	−	0.000923645i
$227$	−26.5714	−	5.64793i	−1.76361	−	0.374866i	−0.791824	−	0.610749i	$-0.790869\pi$
$227$	−26.5714	−	5.64793i	−1.76361	−	0.374866i	−0.971781	+	0.235883i	$0.924202\pi$
$228$		0			0
$229$	0.453169	−	4.31161i	0.0299462	−	0.284919i	−0.969293	−	0.245910i	$-0.920913\pi$
$229$	0.453169	−	4.31161i	0.0299462	−	0.284919i	0.999239	−	0.0390091i	$-0.0124201\pi$
$230$	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	$-0.174506\pi$
$233$	9.48697	+	6.89268i	0.621512	+	0.451555i	−0.231937	+	0.972731i	$0.574506\pi$
$234$		0			0
$235$	0.565165	+	1.73940i	0.0368673	+	0.113466i
$236$	−0.0208158	+	0.00218783i	−0.00135499	+	0.000142416i
$237$		0			0
$238$	0.475661	+	0.428287i	0.0308325	+	0.0277617i
$239$	−17.5498	+	3.73031i	−1.13520	+	0.241294i	−0.736926	−	0.675973i	$-0.763724\pi$
$239$	−17.5498	+	3.73031i	−1.13520	+	0.241294i	−0.398273	+	0.917267i	$0.630390\pi$
$240$		0			0
$241$	−2.31388	−	1.33592i	−0.149050	−	0.0860541i	0.423620	−	0.905840i	$-0.360759\pi$
$241$	−2.31388	−	1.33592i	−0.149050	−	0.0860541i	−0.572670	+	0.819786i	$0.694092\pi$
$242$	−0.976011	−	3.95102i	−0.0627404	−	0.253982i
$243$		0			0
$244$	−6.27595	+	8.63811i	−0.401777	+	0.552998i
$245$	7.97003	−	7.17625i	0.509186	−	0.458474i
$246$		0			0
$247$	−3.14898	−	1.40201i	−0.200365	−	0.0892081i
$248$	−8.26164	−	3.67832i	−0.524615	−	0.233574i
$249$		0			0
$250$	−2.84390	+	2.56066i	−0.179864	+	0.161950i
$251$	7.98861	−	10.9954i	0.504237	−	0.694022i	−0.478697	−	0.877980i	$-0.658891\pi$
$251$	7.98861	−	10.9954i	0.504237	−	0.694022i	0.982934	+	0.183958i	$0.0588909\pi$
$252$		0			0
$253$	−17.3339	−	6.33030i	−1.08977	−	0.397982i
$254$	−2.11514	−	1.22118i	−0.132716	−	0.0766234i
$255$		0			0
$256$	−6.00371	+	1.27613i	−0.375232	+	0.0797580i
$257$	−3.53361	−	3.18168i	−0.220421	−	0.198468i	0.551521	−	0.834161i	$-0.314048\pi$
$257$	−3.53361	−	3.18168i	−0.220421	−	0.198468i	−0.771942	+	0.635693i	$0.780714\pi$
$258$		0			0
$259$	6.72214	−	0.706526i	0.417694	−	0.0439014i
$260$	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	$0.360137\pi$
$263$	−9.26116	+	16.0408i	−0.571067	+	0.989118i	−0.996457	+	0.0841073i	$0.973196\pi$
$264$		0			0
$265$	5.37815	+	9.31523i	0.330377	+	0.572230i
$266$	0.0342997	−	0.326340i	0.00210305	−	0.0200092i
$267$		0			0
$268$	2.69108	+	0.572006i	0.164384	+	0.0349408i
$269$	12.6954	+	17.4737i	0.774049	+	1.06539i	0.995914	+	0.0903100i	$0.0287858\pi$
$269$	12.6954	+	17.4737i	0.774049	+	1.06539i	−0.221864	+	0.975078i	$0.571214\pi$
$270$		0			0
$271$	−0.869236	+	0.282432i	−0.0528023	+	0.0171565i	−0.335299	−	0.942112i	$-0.608837\pi$
$271$	−0.869236	+	0.282432i	−0.0528023	+	0.0171565i	0.282497	+	0.959268i	$0.408837\pi$
$272$	−2.34697	−	2.60658i	−0.142306	−	0.158047i
$273$		0			0
$274$	−5.65786	+	3.26657i	−0.341804	+	0.197341i
$275$	−0.301221	+	2.12658i	−0.0181643	+	0.128237i
$276$		0			0
$277$	6.02500	+	13.5324i	0.362007	+	0.813081i	0.999105	+	0.0422984i	$0.0134680\pi$
$277$	6.02500	+	13.5324i	0.362007	+	0.813081i	−0.637098	+	0.770783i	$0.719865\pi$
$278$	−4.95505	−	1.60999i	−0.297184	−	0.0965610i
$279$		0			0
$280$	−4.33365	+	3.14858i	−0.258985	+	0.188164i
$281$	0.192078	+	1.82750i	0.0114584	+	0.109020i	0.998756	−	0.0498615i	$-0.0158780\pi$
$281$	0.192078	+	1.82750i	0.0114584	+	0.109020i	−0.987298	+	0.158881i	$0.949211\pi$
$282$		0			0
$283$	2.50950	+	11.8063i	0.149174	+	0.701810i	0.987625	+	0.156833i	$0.0501284\pi$
$283$	2.50950	+	11.8063i	0.149174	+	0.701810i	−0.838451	+	0.544977i	$0.816538\pi$
$284$	−15.4463	−	1.62347i	−0.916569	−	0.0963353i
$285$		0			0
$286$	6.37399	+	3.99252i	0.376902	+	0.236083i
$287$			19.1655i			1.13130i
$288$		0			0
$289$	−4.88143	+	15.0235i	−0.287143	+	0.883735i
$290$	−0.135700	+	0.638418i	−0.00796857	+	0.0374892i
$291$		0			0
$292$	11.9435	−	26.8255i	0.698939	−	1.56984i
$293$	11.4299	−	12.6942i	0.667743	−	0.741604i	−0.310155	−	0.950686i	$-0.600381\pi$
$293$	11.4299	−	12.6942i	0.667743	−	0.741604i	0.977898	+	0.209082i	$0.0670475\pi$
$294$		0			0
$295$	0.0243894	−	0.0108589i	0.00142001	−	0.000632227i
$296$	6.12580			0.356055
$297$		0			0
$298$	−5.27040			−0.305306
$299$	31.1548	−	13.8710i	1.80173	−	0.802182i
$300$		0			0
$301$	−8.96175	+	9.95303i	−0.516547	+	0.573683i
$302$	−0.387683	+	0.870751i	−0.0223087	+	0.0501061i
$303$		0			0
$304$	−0.373859	+	1.75887i	−0.0214423	+	0.100878i
$305$	4.20858	−	12.9527i	0.240983	−	0.741668i
$306$		0			0
$307$			16.6906i			0.952585i	0.879287	+	0.476293i	$0.158020\pi$
$307$			16.6906i			0.952585i	−0.879287	+	0.476293i	$0.841980\pi$
$308$	2.36778	−	9.45300i	0.134917	−	0.538635i
$309$		0			0
$310$	5.53279	+	0.581520i	0.314242	+	0.0330281i
$311$	6.14285	+	28.8998i	0.348329	+	1.63876i	0.708383	+	0.705828i	$0.249425\pi$
$311$	6.14285	+	28.8998i	0.348329	+	1.63876i	−0.360054	+	0.932932i	$0.617242\pi$
$312$		0			0
$313$	−1.68745	−	16.0551i	−0.0953806	−	0.907486i	−0.932671	−	0.360728i	$-0.882528\pi$
$313$	−1.68745	−	16.0551i	−0.0953806	−	0.907486i	0.837291	−	0.546758i	$-0.184138\pi$
$314$	1.70424	−	1.23821i	0.0961761	−	0.0698760i
$315$		0			0
$316$	−5.63693	−	1.83155i	−0.317102	−	0.103033i
$317$	−3.41021	−	7.65946i	−0.191536	−	0.430198i	0.792093	−	0.610400i	$-0.208991\pi$
$317$	−3.41021	−	7.65946i	−0.191536	−	0.430198i	−0.983630	+	0.180202i	$0.942325\pi$
$318$		0			0
$319$	−1.15348	−	2.17506i	−0.0645823	−	0.121780i
$320$	10.0837	−	5.82181i	0.563694	−	0.325449i
$321$		0			0
$322$	2.17232	+	2.41260i	0.121058	+	0.134449i
$323$	−0.586723	+	0.190638i	−0.0326462	+	0.0106074i
$324$		0			0
$325$	−2.33306	−	3.21119i	−0.129415	−	0.178125i
$326$	−3.09775	−	0.658447i	−0.171568	−	0.0364680i
$327$		0			0
$328$	−1.81562	+	17.2745i	−0.100251	+	0.953822i
$329$	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
$335$	−3.49002	+	0.366816i	−0.190680	+	0.0200413i
$336$		0			0
$337$	−16.5118	−	14.8673i	−0.899457	−	0.809875i	0.0829642	−	0.996553i	$-0.473561\pi$
$337$	−16.5118	−	14.8673i	−0.899457	−	0.809875i	−0.982421	+	0.186678i	$0.940228\pi$
$338$	−8.89111	+	1.88986i	−0.483613	+	0.102795i
$339$		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
$344$	−9.02038	+	8.12199i	−0.486346	+	0.437908i
$345$		0			0
$346$	−3.84468	−	1.71176i	−0.206691	−	0.0920249i
$347$	10.9569	+	4.87831i	0.588195	+	0.261881i	0.679181	−	0.733971i	$-0.262335\pi$
$347$	10.9569	+	4.87831i	0.588195	+	0.261881i	−0.0909858	+	0.995852i	$0.529002\pi$
$348$		0			0
$349$	7.55592	−	6.80338i	0.404459	−	0.364176i	−0.441649	−	0.897188i	$-0.645606\pi$
$349$	7.55592	−	6.80338i	0.404459	−	0.364176i	0.846108	+	0.533011i	$0.178940\pi$
$350$	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
$355$	19.3779	−	4.11890i	1.02847	−	0.218608i
$356$	−12.4765	−	11.2339i	−0.661254	−	0.595395i
$357$		0			0
$358$	−3.94441	+	0.414574i	−0.208469	+	0.0219109i
$359$	−2.51158	−	7.72985i	−0.132556	−	0.407966i	0.862646	−	0.505809i	$-0.168806\pi$
$359$	−2.51158	−	7.72985i	−0.132556	−	0.407966i	−0.995202	+	0.0978426i	$0.968806\pi$
$360$		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
$365$	−3.91511	+	37.2498i	−0.204926	+	1.94974i
$366$		0			0
$367$	−37.1245	−	7.89105i	−1.93788	−	0.411910i	−0.997400	−	0.0720664i	$-0.977041\pi$
$367$	−37.1245	−	7.89105i	−1.93788	−	0.411910i	−0.940482	−	0.339843i	$-0.889626\pi$
$368$	−10.4569	−	14.3927i	−0.545105	−	0.750272i
$369$		0			0
$370$	−3.58396	+	1.16450i	−0.186321	+	0.0605394i
$371$	4.77628	+	5.30460i	0.247972	+	0.275401i
$372$		0			0
$373$	5.61495	−	3.24179i	0.290731	−	0.167854i	−0.347540	−	0.937665i	$-0.612983\pi$
$373$	5.61495	−	3.24179i	0.290731	−	0.167854i	0.638272	+	0.769811i	$0.279650\pi$
$374$	1.32589	−	0.232309i	0.0685601	−	0.0120124i
$375$		0			0
$376$	0.447395	+	1.00487i	0.0230727	+	0.0518220i
$377$	4.32719	+	1.40599i	0.222862	+	0.0724121i
$378$		0			0
$379$	−10.0492	+	7.30119i	−0.516194	+	0.375037i	−0.815168	−	0.579224i	$-0.803356\pi$
$379$	−10.0492	+	7.30119i	−0.516194	+	0.375037i	0.298974	+	0.954261i	$0.403356\pi$
$380$	−0.260277	−	2.47637i	−0.0133519	−	0.127035i
$381$		0			0
$382$	−1.57278	−	7.39934i	−0.0804703	−	0.378583i
$383$	−14.1924	−	1.49168i	−0.725199	−	0.0762214i	−0.265266	−	0.964175i	$-0.585460\pi$
$383$	−14.1924	−	1.49168i	−0.725199	−	0.0762214i	−0.459933	+	0.887954i	$0.652126\pi$
$384$		0			0
$385$	0.853644	+	12.4008i	0.0435057	+	0.632002i
$386$		−	5.65297i		−	0.287729i
$387$		0			0
$388$	−3.18943	+	9.81606i	−0.161919	+	0.498335i
$389$	−2.23906	+	10.5339i	−0.113525	+	0.534092i	0.884226	+	0.467059i	$0.154687\pi$
$389$	−2.23906	+	10.5339i	−0.113525	+	0.534092i	−0.997751	+	0.0670327i	$0.978647\pi$
$390$		0			0
$391$	2.48254	−	5.57587i	0.125547	−	0.281984i
$392$	4.31601	−	4.79342i	0.217992	−	0.242104i
$393$		0			0
$394$	4.42854	−	1.97171i	0.223106	−	0.0993334i
$395$	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	$0.387135\pi$
$398$	1.59639	−	0.710757i	0.0800196	−	0.0356270i
$399$		0			0
$400$	−1.38551	+	1.53876i	−0.0692754	+	0.0769381i
$401$	14.5838	−	32.7557i	0.728279	−	1.63574i	−0.0428651	−	0.999081i	$-0.513649\pi$
$401$	14.5838	−	32.7557i	0.728279	−	1.63574i	0.771144	−	0.636661i	$-0.219685\pi$
$402$		0			0
$403$	8.06321	−	37.9344i	0.401657	−	1.88965i
$404$	5.60477	−	17.2497i	0.278848	−	0.858206i
$405$		0			0
$406$			0.433128i			0.0214958i
$407$	7.54578	−	12.0467i	0.374031	−	0.597133i
$408$		0			0
$409$	15.6291	+	1.64268i	0.772809	+	0.0812255i	0.482720	−	0.875774i	$-0.339649\pi$
$409$	15.6291	+	1.64268i	0.772809	+	0.0812255i	0.290088	+	0.957000i	$0.406315\pi$
$410$	−2.22159	−	10.4517i	−0.109716	−	0.516174i
$411$		0			0
$412$	0.368649	+	3.50746i	0.0181620	+	0.172800i
$413$	0.0143332	−	0.0104137i	0.000705293	−	0.000512425i
$414$		0			0
$415$	23.4675	+	7.62504i	1.15197	+	0.374298i
$416$	10.0756	+	22.6301i	0.493996	+	1.10953i
$417$		0			0
$418$	−0.495889	−	0.479914i	−0.0242547	−	0.0234734i
$419$	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
$421$	−8.12421	−	9.02285i	−0.395950	−	0.439747i	0.511898	−	0.859046i	$-0.328942\pi$
$421$	−8.12421	−	9.02285i	−0.395950	−	0.439747i	−0.907848	+	0.419299i	$0.862276\pi$
$422$	6.87448	−	2.23365i	0.334644	−	0.108733i
$423$		0			0
$424$	3.80248	+	5.23367i	0.184665	+	0.254169i
$425$	−0.694864	−	0.147698i	−0.0337059	−	0.00716440i
$426$		0			0
$427$	0.944721	−	8.98842i	0.0457183	−	0.434980i
$428$	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	$-0.511905\pi$
$431$	−20.7468	−	15.0734i	−0.999336	−	0.726060i	−0.961946	+	0.273240i	$0.911905\pi$
$432$		0			0
$433$	−0.399073	−	1.22822i	−0.0191782	−	0.0590245i	0.941009	−	0.338380i	$-0.109879\pi$
$433$	−0.399073	−	1.22822i	−0.0191782	−	0.0590245i	−0.960188	+	0.279356i	$0.909879\pi$
$434$	3.67164	−	0.385905i	0.176244	−	0.0185240i
$435$		0			0
$436$	12.1748	+	10.9622i	0.583066	+	0.524995i
$437$	−3.06069	+	0.650569i	−0.146413	+	0.0311210i
$438$		0			0
$439$	7.78450	+	4.49438i	0.371534	+	0.214505i	0.674128	−	0.738614i	$-0.264519\pi$
$439$	7.78450	+	4.49438i	0.371534	+	0.214505i	−0.302595	+	0.953119i	$0.597853\pi$
$440$	−0.405354	+	11.2581i	−0.0193245	+	0.536707i
$441$		0			0
$442$	−1.46220	+	2.01254i	−0.0695495	+	0.0957267i
$443$	−10.6597	+	9.59804i	−0.506458	+	0.456017i	−0.882314	−	0.470661i	$-0.844015\pi$
$443$	−10.6597	+	9.59804i	−0.506458	+	0.456017i	0.375856	+	0.926678i	$0.377349\pi$
$444$		0			0
$445$	19.5633	+	8.71013i	0.927388	+	0.412900i
$446$	5.55315	+	2.47242i	0.262949	+	0.117073i
$447$		0			0
$448$	5.74218	−	5.17028i	0.271293	−	0.244273i
$449$	8.37515	−	11.5274i	0.395248	−	0.544012i	−0.564296	−	0.825573i	$-0.690852\pi$
$449$	8.37515	−	11.5274i	0.395248	−	0.544012i	0.959543	+	0.281561i	$0.0908522\pi$
$450$		0			0
$451$	31.7346	+	24.8492i	1.49433	+	1.17011i
$452$	−0.0748501	−	0.0432147i	−0.00352065	−	0.00203265i
$453$		0			0
$454$	9.83091	−	2.08963i	0.461388	−	0.0980710i
$455$	−17.0711	−	15.3709i	−0.800307	−	0.720599i
$456$		0			0
$457$	−25.8336	+	2.71522i	−1.20845	+	0.127013i	−0.687248	−	0.726423i	$-0.741182\pi$
$457$	−25.8336	+	2.71522i	−1.20845	+	0.127013i	−0.521198	+	0.853436i	$0.674515\pi$
$458$	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	−0.697816	−	0.716277i	$-0.745845\pi$
$461$	5.82733	−	10.0932i	0.271406	−	0.470089i	0.969222	+	0.246188i	$0.0791781\pi$
$462$		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	$0.976130\pi$
$464$	0.248099	−	2.36050i	0.0115177	−	0.109583i
$465$		0			0
$466$	−4.24379	−	0.902044i	−0.196590	−	0.0417864i
$467$	−1.77499	−	2.44307i	−0.0821369	−	0.113052i	0.765971	−	0.642875i	$-0.222258\pi$
$467$	−1.77499	−	2.44307i	−0.0821369	−	0.113052i	−0.848108	+	0.529823i	$0.822258\pi$
$468$		0			0
$469$	−2.21481	+	0.719634i	−0.102270	+	0.0332296i
$470$	−0.452776	−	0.502858i	−0.0208850	−	0.0231951i
$471$		0			0
$472$	0.0139055	−	0.00802835i	0.000640053	−	0.000369535i
$473$	4.86098	+	27.7437i	0.223508	+	1.27566i
$474$		0			0
$475$	0.148129	+	0.332704i	0.00679664	+	0.0152655i
$476$	3.06542	+	0.996017i	0.140503	+	0.0456523i
$477$		0			0
$478$	5.37036	−	3.90180i	0.245635	−	0.178464i
$479$	−4.04360	−	38.4723i	−0.184757	−	1.75784i	−0.557751	−	0.830009i	$-0.688335\pi$
$479$	−4.04360	−	38.4723i	−0.184757	−	1.75784i	0.372994	−	0.927834i	$-0.378331\pi$
$480$		0			0
$481$	5.46179	+	25.6957i	0.249036	+	1.17162i
$482$	0.983114	+	0.103329i	0.0447796	+	0.00470653i
$483$		0			0
$484$	−12.5825	−	16.1770i	−0.571932	−	0.735318i
$485$		−	13.1651i		−	0.597795i
$486$		0			0
$487$	−3.79422	+	11.6774i	−0.171933	+	0.529154i	−0.999480	−	0.0322416i	$-0.989735\pi$
$487$	−3.79422	+	11.6774i	−0.171933	+	0.529154i	0.827548	+	0.561396i	$0.189735\pi$
$488$	1.70301	−	8.01204i	0.0770917	−	0.362688i
$489$		0			0
$490$	−1.61391	+	3.62490i	−0.0729090	+	0.163756i
$491$	24.4022	−	27.1014i	1.10125	−	1.22307i	0.128383	−	0.991725i	$-0.459021\pi$
$491$	24.4022	−	27.1014i	1.10125	−	1.22307i	0.972872	−	0.231343i	$-0.0743119\pi$
$492$		0			0
$493$	0.743905	−	0.331208i	0.0335038	−	0.0149168i
$494$	1.27532			0.0573793
$495$		0			0
$496$	−20.2311			−0.908403
$497$	12.0101	−	5.34726i	0.538729	−	0.239857i
$498$		0			0
$499$	16.2473	−	18.0445i	0.727329	−	0.807781i	−0.260144	−	0.965570i	$-0.583770\pi$
$499$	16.2473	−	18.0445i	0.727329	−	0.807781i	0.987473	+	0.157789i	$0.0504366\pi$
$500$	−7.83816	+	17.6048i	−0.350533	+	0.787311i
$501$		0			0
$502$	−1.04547	+	4.91854i	−0.0466616	+	0.219525i
$503$	−6.87821	+	21.1689i	−0.306684	+	0.943876i	0.672359	+	0.740225i	$0.265281\pi$
$503$	−6.87821	+	21.1689i	−0.306684	+	0.943876i	−0.979043	+	0.203652i	$0.934719\pi$
$504$		0			0
$505$			23.1349i			1.02949i
$506$	6.81137	−	0.468881i	0.302802	−	0.0208443i
$507$		0			0
$508$	−12.2316	−	1.28559i	−0.542689	−	0.0570389i
$509$	−5.89189	−	27.7192i	−0.261153	−	1.22863i	−0.891753	−	0.452522i	$-0.850524\pi$
$509$	−5.89189	−	27.7192i	−0.261153	−	1.22863i	0.630600	−	0.776108i	$-0.282809\pi$
$510$		0			0
$511$	2.59812	+	24.7195i	0.114934	+	1.09353i
$512$	17.8490	−	12.9680i	0.788820	−	0.573111i
$513$		0			0
$514$	1.67314	+	0.543635i	0.0737989	+	0.0239787i
$515$	−1.82972	−	4.10961i	−0.0806270	−	0.181091i
$516$		0			0
$517$	2.52723	+	0.357971i	0.111147	+	0.0157436i
$518$	−2.16573	+	1.25038i	−0.0951565	+	0.0549386i
$519$		0			0
$520$	−13.9306	−	15.4715i	−0.610896	−	0.678469i
$521$	14.9548	−	4.85911i	0.655182	−	0.212882i	0.0374843	−	0.999297i	$-0.488066\pi$
$521$	14.9548	−	4.85911i	0.655182	−	0.212882i	0.617698	+	0.786416i	$0.288066\pi$
$522$		0			0
$523$	8.59617	+	11.8316i	0.375884	+	0.517360i	0.954488	−	0.298248i	$-0.0964023\pi$
$523$	8.59617	+	11.8316i	0.375884	+	0.517360i	−0.578604	+	0.815609i	$0.696402\pi$
$524$	14.3667	+	3.05373i	0.627610	+	0.133403i
$525$		0			0
$526$	0.716324	−	6.81536i	0.0312332	−	0.297164i
$527$	−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
$533$	−74.0794	+	7.78606i	−3.20873	+	0.337252i
$534$		0			0
$535$	−21.6718	−	19.5134i	−0.936953	−	0.843636i
$536$	−2.06444	+	0.438811i	−0.0891704	+	0.0189538i
$537$		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	−0.521497	−	0.853253i	$-0.674626\pi$
$541$	10.4934	−	14.4429i	0.451146	−	0.620950i	0.972643	+	0.232303i	$0.0746262\pi$
$542$	0.251295	−	0.226267i	0.0107941	−	0.00971901i
$543$		0			0
$544$	4.05018	+	1.80326i	0.173650	+	0.0773141i
$545$	−19.0902	−	8.49949i	−0.817733	−	0.364078i
$546$		0			0
$547$	−3.35413	+	3.02008i	−0.143412	+	0.129129i	−0.737715	−	0.675113i	$-0.764095\pi$
$547$	−3.35413	+	3.02008i	−0.143412	+	0.129129i	0.594302	+	0.804242i	$0.297428\pi$
$548$	−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
$553$	4.90737	−	1.04309i	0.208683	−	0.0443569i
$554$	−4.07283	−	3.66719i	−0.173038	−	0.155804i
$555$		0			0
$556$	−26.0925	+	2.74243i	−1.10657	+	0.116305i
$557$	8.48770	+	26.1225i	0.359635	+	1.10684i	0.953273	+	0.302111i	$0.0976914\pi$
$557$	8.48770	+	26.1225i	0.359635	+	1.10684i	−0.593637	+	0.804733i	$0.702309\pi$
$558$		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
$563$	−1.09423	+	10.4109i	−0.0461162	+	0.438766i	0.946965	+	0.321337i	$0.104132\pi$
$563$	−1.09423	+	10.4109i	−0.0461162	+	0.438766i	−0.993081	+	0.117430i	$0.962535\pi$
$564$		0			0
$565$	0.107835	+	0.0229210i	0.00453664	+	0.000964292i
$566$	−2.62486	−	3.61281i	−0.110331	−	0.151858i
$567$		0			0
$568$	11.3317	−	3.68188i	0.475466	−	0.154488i
$569$	24.8077	+	27.5518i	1.03999	+	1.15503i	0.987694	+	0.156398i	$0.0499884\pi$
$569$	24.8077	+	27.5518i	1.03999	+	1.15503i	0.0522995	+	0.998631i	$0.483345\pi$
$570$		0			0
$571$	5.32451	−	3.07411i	0.222824	−	0.128647i	−0.384433	−	0.923153i	$-0.625603\pi$
$571$	5.32451	−	3.07411i	0.222824	−	0.128647i	0.607257	+	0.794505i	$0.292270\pi$
$572$	37.5001	+	5.31173i	1.56796	+	0.222095i
$573$		0			0
$574$	−2.88412	−	6.47784i	−0.120381	−	0.270380i
$575$	−3.42681	−	1.11344i	−0.142908	−	0.0464335i
$576$		0			0
$577$	−8.59300	+	6.24318i	−0.357731	+	0.259907i	−0.752105	−	0.659043i	$-0.770961\pi$
$577$	−8.59300	+	6.24318i	−0.357731	+	0.259907i	0.394374	+	0.918950i	$0.370961\pi$
$578$	−0.610912	−	5.81244i	−0.0254106	−	0.241766i
$579$		0			0
$580$	0.683344	+	3.21488i	0.0283743	+	0.133491i
$581$	16.2851	+	1.71163i	0.675619	+	0.0710104i
$582$		0			0
$583$	14.9762	−	1.03093i	0.620250	−	0.0426968i
$584$			22.5266i			0.932155i
$585$		0			0
$586$	−1.95296	+	6.01061i	−0.0806762	+	0.248296i
$587$	−1.30614	+	6.14489i	−0.0539100	+	0.253627i	−0.996847	−	0.0793437i	$-0.974718\pi$
$587$	−1.30614	+	6.14489i	−0.0539100	+	0.253627i	0.942937	+	0.332970i	$0.108051\pi$
$588$		0			0
$589$	−1.44731	+	3.25071i	−0.0596354	+	0.133943i
$590$	−0.00660939	+	0.00734047i	−0.000272104	+	0.000302202i
$591$		0			0
$592$	12.5192	−	5.57390i	0.514535	−	0.229086i
$593$	−13.2967			−0.546030			−0.273015	−	0.962010i	$-0.588021\pi$
$593$	−13.2967			−0.546030			−0.273015	+	0.962010i	$0.588021\pi$
$594$		0			0
$595$	−4.11127			−0.168546
$596$	−24.2456	+	10.7949i	−0.993140	+	0.442175i
$597$		0			0
$598$	−8.44278	+	9.37665i	−0.345251	+	0.383440i
$599$	−14.2316	+	31.9648i	−0.581489	+	1.30605i	0.348103	+	0.937456i	$0.386826\pi$
$599$	−14.2316	+	31.9648i	−0.581489	+	1.30605i	−0.929592	+	0.368590i	$0.879841\pi$
$600$		0			0
$601$	1.09690	−	5.16050i	0.0447434	−	0.210501i	−0.950097	−	0.311955i	$-0.899016\pi$
$601$	1.09690	−	5.16050i	0.0447434	−	0.210501i	0.994840	+	0.101454i	$0.0323494\pi$
$602$	1.53124	−	4.71268i	0.0624087	−	0.192074i
$603$		0			0
$604$			4.79981i			0.195301i
$605$	21.6402	+	14.6649i	0.879801	+	0.596211i
$606$		0			0
$607$	20.6851	+	2.17409i	0.839580	+	0.0882435i	0.514550	−	0.857460i	$-0.327959\pi$
$607$	20.6851	+	2.17409i	0.839580	+	0.0882435i	0.325030	+	0.945704i	$0.394626\pi$
$608$	−0.472559	−	2.22321i	−0.0191648	−	0.0901632i
$609$		0			0
$610$	0.526705	+	5.01126i	0.0213256	+	0.202900i
$611$	−3.81618	+	2.77262i	−0.154386	+	0.112168i
$612$		0			0
$613$	−25.6016	−	8.31845i	−1.03404	−	0.335979i	−0.257652	−	0.966238i	$-0.582949\pi$
$613$	−25.6016	−	8.31845i	−1.03404	−	0.335979i	−0.776385	+	0.630259i	$0.782949\pi$
$614$	−2.51169	−	5.64134i	−0.101363	−	0.227666i
$615$		0			0
$616$	1.29019	+	7.36368i	0.0519832	+	0.296691i
$617$	−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
$619$	24.9661	+	27.7277i	1.00347	+	1.11447i	0.993421	+	0.114520i	$0.0365329\pi$
$619$	24.9661	+	27.7277i	1.00347	+	1.11447i	0.0100515	+	0.999949i	$0.496800\pi$
$620$	26.6438	−	8.65710i	1.07004	−	0.347678i
$621$		0			0
$622$	−6.42524	−	8.84358i	−0.257629	−	0.354595i
$623$	13.9005	+	2.95465i	0.556914	+	0.118376i
$624$		0			0
$625$	2.90783	−	27.6662i	0.116313	−	1.10665i
$626$	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	−0.999328	−	0.0366537i	$-0.988330\pi$
$631$	−5.33541	−	16.4207i	−0.212399	−	0.653698i	0.786929	−	0.617044i	$-0.211670\pi$
$632$	4.52198	−	0.475279i	0.179875	−	0.0189056i
$633$		0			0
$634$	2.30526	+	2.07567i	0.0915537	+	0.0824354i
$635$	15.3449	−	3.26166i	0.608944	−	0.129435i
$636$		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
$641$	7.01171	−	6.31337i	0.276946	−	0.249363i	−0.518939	−	0.854811i	$-0.673673\pi$
$641$	7.01171	−	6.31337i	0.276946	−	0.249363i	0.795885	+	0.605448i	$0.207006\pi$
$642$		0			0
$643$	7.46251	+	3.32252i	0.294293	+	0.131028i	0.548572	−	0.836103i	$-0.315172\pi$
$643$	7.46251	+	3.32252i	0.294293	+	0.131028i	−0.254279	+	0.967131i	$0.581838\pi$
$644$	14.9349	+	6.64944i	0.588517	+	0.262025i
$645$		0			0
$646$	0.169621	−	0.152727i	0.00667365	−	0.00600898i
$647$	−12.6621	+	17.4279i	−0.497799	+	0.685162i	−0.981803	−	0.189904i	$-0.939182\pi$
$647$	−12.6621	+	17.4279i	−0.497799	+	0.685162i	0.484003	+	0.875066i	$0.339182\pi$
$648$		0			0
$649$	0.00134068	−	0.0372353i	5.26264e−5	−	0.00146161i
$650$	1.27180	+	0.734273i	0.0498840	+	0.0288005i
$651$		0			0
$652$	−15.5993	+	3.31574i	−0.610917	+	0.129854i
$653$	−33.9745	−	30.5908i	−1.32953	−	1.19711i	−0.963874	−	0.266358i	$-0.914180\pi$
$653$	−33.9745	−	30.5908i	−1.32953	−	1.19711i	−0.365651	−	0.930752i	$-0.619154\pi$
$654$		0			0
$655$	−18.6319	+	1.95829i	−0.728010	+	0.0765169i
$656$	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	−0.916595	−	0.399816i	$-0.869074\pi$
$659$	−2.87636	+	4.98200i	−0.112047	+	0.194071i	0.804548	+	0.593887i	$0.202407\pi$
$660$		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	$-0.364393\pi$
$662$	−0.0389474	+	0.370560i	−0.00151373	+	0.0144022i
$663$		0			0
$664$	14.5161	+	3.08549i	0.563333	+	0.119740i
$665$	1.23887	+	1.70516i	0.0480415	+	0.0661234i
$666$		0			0
$667$	3.92809	−	1.27631i	0.152096	−	0.0494190i
$668$	3.80276	+	4.22339i	0.147133	+	0.163408i
$669$		0			0
$670$	1.12441	−	0.649177i	0.0434396	−	0.0250799i
$671$	−13.6583	−	13.2183i	−0.527273	−	0.510287i
$672$		0			0
$673$	−0.526783	−	1.18317i	−0.0203060	−	0.0456080i	0.903108	−	0.429414i	$-0.141280\pi$
$673$	−0.526783	−	1.18317i	−0.0203060	−	0.0456080i	−0.923414	+	0.383806i	$0.874613\pi$
$674$	7.81821	+	2.54029i	0.301146	+	0.0978484i
$675$		0			0
$676$	−37.0313	+	26.9048i	−1.42428	+	1.03480i
$677$	−2.18984	−	20.8349i	−0.0841623	−	0.800750i	−0.952451	−	0.304691i	$-0.901447\pi$
$677$	−2.18984	−	20.8349i	−0.0841623	−	0.800750i	0.868289	−	0.496059i	$-0.165220\pi$
$678$		0			0
$679$	−1.81643	−	8.54562i	−0.0697081	−	0.327951i
$680$	−3.70561	−	0.389476i	−0.142104	−	0.0149357i
$681$		0			0
$682$	4.12151	−	6.57993i	0.157821	−	0.251958i
$683$		−	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
$686$	−1.39666	+	6.57076i	−0.0533246	+	0.250873i
$687$		0			0
$688$	−11.0445	+	24.8065i	−0.421069	+	0.945737i
$689$	−18.5632	+	20.6165i	−0.707201	+	0.785426i
$690$		0			0
$691$	−26.3548	+	11.7339i	−1.00258	+	0.446378i	−0.841322	−	0.540534i	$-0.818222\pi$
$691$	−26.3548	+	11.7339i	−1.00258	+	0.446378i	−0.161260	+	0.986912i	$0.551556\pi$
$692$	−21.1929			−0.805633
$693$		0			0
$694$	−4.43747			−0.168444
$695$	30.5720	−	13.6115i	1.15966	−	0.516315i
$696$		0			0
$697$	−8.92034	+	9.90704i	−0.337882	+	0.375256i
$698$	−1.53005	+	3.43655i	−0.0579134	+	0.130076i
$699$		0			0
$700$	0.395607	−	1.86118i	0.0149525	−	0.0703461i
$701$	1.64023	−	5.04812i	0.0619507	−	0.190665i	−0.915291	−	0.402793i	$-0.868039\pi$
$701$	1.64023	−	5.04812i	0.0619507	−	0.190665i	0.977242	+	0.212128i	$0.0680395\pi$
$702$		0			0
$703$		−	2.41032i		−	0.0909071i
$704$	−1.11597	−	16.2116i	−0.0420599	−	0.610998i
$705$		0			0
$706$	−1.69815	−	0.178483i	−0.0639107	−	0.00671728i
$707$	3.19200	+	15.0172i	0.120047	+	0.564779i
$708$		0			0
$709$	3.01787	+	28.7131i	0.113339	+	1.07834i	0.892353	+	0.451338i	$0.149053\pi$
$709$	3.01787	+	28.7131i	0.113339	+	1.07834i	−0.779014	+	0.627006i	$0.784280\pi$
$710$	−5.92979	+	4.30824i	−0.222541	+	0.161685i
$711$		0			0
$712$	12.2491	+	3.97997i	0.459054	+	0.149156i
$713$	−14.3192	−	32.1614i	−0.536257	−	1.20445i
$714$		0			0
$715$	−47.5852	+	8.33740i	−1.77959	+	0.311801i
$716$	−17.2965	+	9.98615i	−0.646401	+	0.373200i
$717$		0			0
$718$	2.01213	+	2.23469i	0.0750919	+	0.0833980i
$719$	35.5978	−	11.5664i	1.32757	−	0.431355i	0.442484	−	0.896776i	$-0.354097\pi$
$719$	35.5978	−	11.5664i	1.32757	−	0.431355i	0.885089	+	0.465422i	$0.154097\pi$
$720$		0			0
$721$	−1.75471	−	2.41515i	−0.0653488	−	0.0899449i
$722$	6.76157	+	1.43722i	0.251639	+	0.0534876i
$723$		0			0
$724$	−3.46296	+	32.9479i	−0.128700	+	1.22450i
$725$	−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
$731$	−9.26502	+	0.973793i	−0.342679	+	0.0360170i
$732$		0			0
$733$	3.94813	+	3.55491i	0.145827	+	0.131304i	0.738816	−	0.673907i	$-0.235385\pi$
$733$	3.94813	+	3.55491i	0.145827	+	0.131304i	−0.592988	+	0.805211i	$0.702052\pi$
$734$	13.7354	−	2.91954i	0.506981	−	0.107762i
$735$		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	−0.737140	−	0.675740i	$-0.763824\pi$
$739$	3.62411	−	4.98816i	0.133315	−	0.183492i	0.870455	+	0.492247i	$0.163824\pi$
$740$	−14.1023	+	12.6978i	−0.518411	+	0.466780i
$741$		0			0
$742$	−2.41262	−	1.07417i	−0.0885700	−	0.0394339i
$743$	−6.10349	−	2.71745i	−0.223915	−	0.0996935i	0.291713	−	0.956506i	$-0.405775\pi$
$743$	−6.10349	−	2.71745i	−0.223915	−	0.0996935i	−0.515628	+	0.856812i	$0.672441\pi$
$744$		0			0
$745$	25.1576	−	22.6520i	0.921703	−	0.829905i
$746$	−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
$751$	27.7224	−	5.89257i	1.01160	−	0.215023i	0.327845	−	0.944731i	$-0.393677\pi$
$751$	27.7224	−	5.89257i	1.01160	−	0.215023i	0.683759	+	0.729708i	$0.260344\pi$
$752$	1.82867	+	1.64654i	0.0666847	+	0.0600431i
$753$		0			0
$754$	−1.67415	+	0.175960i	−0.0609688	+	0.00640808i
$755$	−1.89190	−	5.82267i	−0.0688533	−	0.211909i
$756$		0			0
$757$	10.7918	+	7.84073i	0.392236	+	0.284976i	0.766371	−	0.642398i	$-0.222060\pi$
$757$	10.7918	+	7.84073i	0.392236	+	0.284976i	−0.374135	+	0.927374i	$0.622060\pi$
$758$	2.29786	−	3.98002i	0.0834621	−	0.144561i
$759$		0			0
$760$	0.955098	+	1.65428i	0.0346450	+	0.0600070i
$761$	0.0581249	−	0.553022i	0.00210703	−	0.0200470i	−0.993418	−	0.114547i	$-0.963458\pi$
$761$	0.0581249	−	0.553022i	0.00210703	−	0.0200470i	0.995525	+	0.0944996i	$0.0301251\pi$
$762$		0			0
$763$	−13.5644	−	2.88320i	−0.491063	−	0.104379i
$764$	−22.3907	−	30.8181i	−0.810066	−	1.11496i
$765$		0			0
$766$	5.02143	−	1.63156i	0.181432	−	0.0589507i
$767$	0.0460744	+	0.0511709i	0.00166365	+	0.00184767i
$768$		0			0
$769$	−28.3158	+	16.3481i	−1.02109	+	0.589528i	−0.914420	−	0.404766i	$-0.867353\pi$
$769$	−28.3158	+	16.3481i	−1.02109	+	0.589528i	−0.106672	+	0.994294i	$0.534020\pi$
$770$	−2.15465	−	4.06293i	−0.0776484	−	0.146418i
$771$		0			0
$772$	−11.5784	−	26.0056i	−0.416717	−	0.935963i
$773$	−1.30242	−	0.423182i	−0.0468448	−	0.0152208i	0.285501	−	0.958378i	$-0.407840\pi$
$773$	−1.30242	−	0.423182i	−0.0468448	−	0.0152208i	−0.332346	+	0.943158i	$0.607840\pi$
$774$		0			0
$775$	−3.31493	+	2.40844i	−0.119076	+	0.0865138i
$776$	−0.827643	−	7.87450i	−0.0297107	−	0.282678i
$777$		0			0
$778$	−0.828409	−	3.89736i	−0.0296999	−	0.139727i
$779$	6.79700	+	0.714393i	0.243528	+	0.0255958i
$780$		0			0
$781$	6.71777	−	26.8197i	0.240381	−	0.959683i
$782$			2.25820i			0.0807530i
$783$		0			0
$784$	4.45900	−	13.7234i	0.159250	−	0.490121i
$785$	−2.81323	+	13.2352i	−0.100409	+	0.472385i
$786$		0			0
$787$	3.52463	−	7.91645i	0.125640	−	0.282191i	−0.839764	−	0.542952i	$-0.817307\pi$
$787$	3.52463	−	7.91645i	0.125640	−	0.282191i	0.965403	+	0.260761i	$0.0839734\pi$
$788$	16.3343	−	18.1411i	0.581886	−	0.646250i
$789$		0			0
$790$	−2.55528	+	1.13768i	−0.0909127	+	0.0404770i
$791$	0.0731593			0.00260125
$792$		0			0
$793$	35.1262			1.24737
$794$	−4.67634	+	2.08204i	−0.165957	+	0.0738889i
$795$		0			0
$796$	5.88815	−	6.53945i	0.208700	−	0.231785i
$797$	5.48700	−	12.3240i	0.194360	−	0.436539i	−0.789907	−	0.613226i	$-0.789871\pi$
$797$	5.48700	−	12.3240i	0.194360	−	0.436539i	0.984267	+	0.176687i	$0.0565381\pi$
$798$		0			0
$799$	−0.175524	+	0.825778i	−0.00620961	+	0.0292139i
$800$	0.808775	−	2.48915i	0.0285945	−	0.0880049i
$801$		0			0
$802$			13.2659i			0.468435i
$803$	44.2996	+	27.7483i	1.56330	+	0.979216i
$804$		0			0
$805$	−20.7385	−	2.17971i	−0.730938	−	0.0768247i
$806$	2.98323	+	14.0350i	0.105080	+	0.494362i
$807$		0			0
$808$	1.45441	+	13.8378i	0.0511661	+	0.486813i
$809$	−35.6994	+	25.9371i	−1.25512	+	0.911900i	−0.998508	−	0.0546139i	$-0.982607\pi$
$809$	−35.6994	+	25.9371i	−1.25512	+	0.911900i	−0.256615	+	0.966514i	$0.582607\pi$
$810$		0			0
$811$	39.0505	+	12.6883i	1.37125	+	0.445546i	0.899782	−	0.436339i	$-0.143725\pi$
$811$	39.0505	+	12.6883i	1.37125	+	0.445546i	0.471466	+	0.881884i	$0.343725\pi$
$812$	0.887135	+	1.99254i	0.0311323	+	0.0699244i
$813$		0			0
$814$	−0.737586	+	5.20725i	−0.0258524	+	0.182514i
$815$	17.6167	−	10.1710i	0.617086	−	0.356275i
$816$		0			0
$817$	3.19577	+	3.54926i	0.111806	+	0.124173i
$818$	−5.52974	+	1.79672i	−0.193343	+	0.0628209i
$819$		0			0
$820$	−31.6274	−	43.5313i	−1.10447	−	1.52018i
$821$	−15.3738	−	3.26780i	−0.536548	−	0.114047i	−0.0683351	−	0.997662i	$-0.521769\pi$
$821$	−15.3738	−	3.26780i	−0.536548	−	0.114047i	−0.468213	+	0.883616i	$0.655102\pi$
$822$		0			0
$823$	0.594191	−	5.65335i	0.0207122	−	0.197063i	−0.979273	−	0.202546i	$-0.935078\pi$
$823$	0.594191	−	5.65335i	0.0207122	−	0.197063i	0.999985	+	0.00548245i	$0.00174513\pi$
$824$	−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	$-0.220347\pi$
$827$	11.5227	+	8.37170i	0.400682	+	0.291113i	−0.369137	+	0.929375i	$0.620347\pi$
$828$		0			0
$829$	−1.17567	−	3.61833i	−0.0408326	−	0.125670i	0.928562	−	0.371177i	$-0.121046\pi$
$829$	−1.17567	−	3.61833i	−0.0408326	−	0.125670i	−0.969395	+	0.245507i	$0.921046\pi$
$830$	−9.07932	+	0.954275i	−0.315148	+	0.0331234i
$831$		0			0
$832$	22.3172	+	20.0945i	0.773709	+	0.696651i
$833$	4.84236	−	1.02927i	0.167778	−	0.0356623i
$834$		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
$839$	2.89650	−	2.60802i	0.0999981	−	0.0900387i	−0.617615	−	0.786480i	$-0.711901\pi$
$839$	2.89650	−	2.60802i	0.0999981	−	0.0900387i	0.717613	+	0.696442i	$0.245234\pi$
$840$		0			0
$841$	−25.9894	−	11.5712i	−0.896187	−	0.399008i
$842$	4.10374	+	1.82710i	0.141424	+	0.0629661i
$843$		0			0
$844$	27.0500	−	24.3559i	0.931099	−	0.838365i
$845$	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
$850$	0.257087	−	0.0546454i	0.00881800	−	0.00187432i
$851$	17.7217	+	15.9567i	0.607491	+	0.546987i
$852$		0			0
$853$	31.5327	−	3.31423i	1.07966	−	0.113477i	0.452041	−	0.891997i	$-0.350696\pi$
$853$	31.5327	−	3.31423i	1.07966	−	0.113477i	0.627620	+	0.778520i	$0.284029\pi$
$854$	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	$0.402839\pi$
$857$	−19.7818	+	34.2630i	−0.675733	+	1.17040i	−0.976254	+	0.216628i	$0.930494\pi$
$858$		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	$0.606549\pi$
$860$	3.93043	−	37.3955i	0.134027	−	1.27518i
$861$		0			0
$862$	9.28061	+	1.97265i	0.316099	+	0.0671889i
$863$	27.4819	+	37.8256i	0.935495	+	1.28760i	0.957677	+	0.287844i	$0.0929385\pi$
$863$	27.4819	+	37.8256i	0.935495	+	1.28760i	−0.0221825	+	0.999754i	$0.507061\pi$
$864$		0			0
$865$	25.7092	−	8.35343i	0.874139	−	0.284025i
$866$	0.319713	+	0.355077i	0.0108643	+	0.0120660i
$867$		0			0
$868$	16.1004	−	9.29557i	0.546483	−	0.315512i
$869$	4.63553	−	9.47816i	0.157249	−	0.321524i
$870$		0			0
$871$	−3.68133	−	8.26841i	−0.124737	−	0.280164i
$872$	−11.9528	−	3.88371i	−0.404774	−	0.131519i
$873$		0			0
$874$	0.936595	−	0.680476i	0.0316808	−	0.0230174i
$875$	−1.70507	−	16.2227i	−0.0576421	−	0.548427i
$876$		0			0
$877$	−6.55314	−	30.8301i	−0.221284	−	1.04106i	−0.938786	−	0.344501i	$-0.888048\pi$
$877$	−6.55314	−	30.8301i	−0.221284	−	1.04106i	0.717502	−	0.696556i	$-0.245285\pi$
$878$	−3.30745	−	0.347627i	−0.111621	−	0.0117319i
$879$		0			0
$880$	9.41535	+	23.3767i	0.317392	+	0.788029i
$881$		−	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	−0.936940	−	0.349489i	$-0.886355\pi$
$883$	0.787007	−	2.42216i	0.0264849	−	0.0815122i	0.963425	+	0.267977i	$0.0863551\pi$
$884$	−2.60451	+	12.2532i	−0.0875991	+	0.412121i
$885$		0			0
$886$	2.15856	−	4.84821i	0.0725183	−	0.162879i
$887$	9.31629	−	10.3468i	0.312810	−	0.347411i	−0.566153	−	0.824300i	$-0.691569\pi$
$887$	9.31629	−	10.3468i	0.312810	−	0.347411i	0.878964	+	0.476889i	$0.158236\pi$
$888$		0			0
$889$	9.51056	−	4.23438i	0.318974	−	0.142016i
$890$	−7.92302			−0.265580
$891$		0			0
$892$	30.6104			1.02491
$893$	0.395386	−	0.176037i	0.0132311	−	0.00589086i
$894$		0			0
$895$	17.0463	−	18.9319i	0.569796	−	0.632822i
$896$	−6.34765	+	14.2570i	−0.212060	+	0.476294i
$897$		0			0
$898$	−1.09605	+	5.15653i	−0.0365758	+	0.172076i
$899$	1.45141	−	4.46699i	0.0484074	−	0.148983i
$900$		0			0
$901$			4.96511i			0.165412i
$902$	−14.4656	−	3.62332i	−0.481651	−	0.120644i
$903$		0			0
$904$	0.0659407	+	0.00693065i	0.00219315	+	0.000230510i
$905$	−8.78586	−	41.3342i	−0.292052	−	1.37400i
$906$		0			0
$907$	3.48242	+	33.1330i	0.115632	+	1.10016i	0.886359	+	0.462998i	$0.153226\pi$
$907$	3.48242	+	33.1330i	0.115632	+	1.10016i	−0.770727	+	0.637165i	$0.780107\pi$
$908$	40.9456	−	29.7487i	1.35883	−	0.987246i
$909$		0			0
$910$	8.08303	+	2.62634i	0.267950	+	0.0870622i
$911$	−2.67989	−	6.01914i	−0.0887888	−	0.199423i	0.863693	−	0.504018i	$-0.168146\pi$
$911$	−2.67989	−	6.01914i	−0.0887888	−	0.199423i	−0.952482	+	0.304595i	$0.901479\pi$
$912$		0			0
$913$	23.9487	−	24.7459i	0.792588	−	0.818971i
$914$	8.32303	−	4.80530i	0.275301	−	0.158945i
$915$		0			0
$916$	5.40475	+	6.00258i	0.178578	+	0.198331i
$917$	−11.8240	+	3.84186i	−0.390464	+	0.126869i
$918$		0			0
$919$	−19.1361	−	26.3386i	−0.631241	−	0.868829i	0.366869	−	0.930273i	$-0.380430\pi$
$919$	−19.1361	−	26.3386i	−0.631241	−	0.868829i	−0.998111	+	0.0614433i	$0.980430\pi$
$920$	−18.4858	−	3.92928i	−0.609458	−	0.129544i
$921$		0			0
$922$	−0.450727	+	4.28838i	−0.0148439	+	0.141230i
$923$	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
$929$	−13.9527	+	1.46649i	−0.457772	+	0.0481138i	−0.330609	−	0.943768i	$-0.607254\pi$
$929$	−13.9527	+	1.46649i	−0.457772	+	0.0481138i	−0.127164	+	0.991882i	$0.540587\pi$
$930$		0			0
$931$	−1.88607	−	1.69823i	−0.0618135	−	0.0556571i
$932$	−21.3704	+	4.54243i	−0.700012	+	0.148792i
$933$		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	0.0975008	−	0.995235i	$-0.468915\pi$
$937$	31.0358	−	42.7172i	1.01390	−	1.39551i	0.916396	−	0.400273i	$-0.131085\pi$
$938$	0.640298	−	0.576527i	0.0209065	−	0.0188243i
$939$		0			0
$940$	−3.11288	−	1.38594i	−0.101531	−	0.0452045i
$941$	2.03166	+	0.904555i	0.0662303	+	0.0294876i	0.439584	−	0.898201i	$-0.355126\pi$
$941$	2.03166	+	0.904555i	0.0662303	+	0.0294876i	−0.373354	+	0.927689i	$0.621792\pi$
$942$		0			0
$943$	−50.2495	+	45.2449i	−1.63635	+	1.47338i
$944$	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
$949$	−94.4913	+	20.0848i	−3.06732	+	0.651979i
$950$	−0.100134	−	0.0901608i	−0.00324877	−	0.00292520i
$951$		0			0
$952$	−2.45910	+	0.258462i	−0.0796999	+	0.00837679i
$953$	−6.64425	−	20.4489i	−0.215228	−	0.662404i	−0.999137	−	0.0415288i	$-0.986777\pi$
$953$	−6.64425	−	20.4489i	−0.215228	−	0.662404i	0.783909	−	0.620876i	$-0.213223\pi$
$954$		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
$959$	2.91088	−	27.6952i	0.0939972	−	0.894324i
$960$		0			0
$961$	−8.83744	−	1.87845i	−0.285079	−	0.0605953i
$962$	−5.71286	−	7.86308i	−0.184190	−	0.253516i
$963$		0			0
$964$	4.73430	−	1.53827i	0.152482	−	0.0495443i
$965$	24.2963	+	26.9838i	0.782125	+	0.868638i
$966$		0			0
$967$	−13.6754	+	7.89548i	−0.439770	+	0.253901i	−0.703500	−	0.710695i	$-0.748381\pi$
$967$	−13.6754	+	7.89548i	−0.439770	+	0.253901i	0.263730	+	0.964597i	$0.415047\pi$
$968$	13.8657	+	7.41113i	0.445661	+	0.238203i
$969$		0			0
$970$	1.98114	+	4.44972i	0.0636107	+	0.142872i
$971$	−7.29530	−	2.37039i	−0.234117	−	0.0760693i	0.189609	−	0.981860i	$-0.439278\pi$
$971$	−7.29530	−	2.37039i	−0.234117	−	0.0760693i	−0.423726	+	0.905790i	$0.639278\pi$
$972$		0			0
$973$	17.9667	−	13.0535i	0.575984	−	0.418477i
$974$	−0.474848	−	4.51787i	−0.0152151	−	0.144762i
$975$		0			0
$976$	−3.80979	−	17.9236i	−0.121948	−	0.573722i
$977$	7.43311	+	0.781252i	0.237806	+	0.0249945i	0.222682	−	0.974891i	$-0.428519\pi$
$977$	7.43311	+	0.781252i	0.237806	+	0.0249945i	0.0151245	+	0.999886i	$0.495186\pi$
$978$		0			0
$979$	22.9153	−	19.1859i	0.732375	−	0.613184i
$980$			19.9814i			0.638282i
$981$		0			0
$982$	−4.16946	+	12.8323i	−0.133053	+	0.409494i
$983$	10.3881	−	48.8720i	0.331328	−	1.55877i	−0.425376	−	0.905017i	$-0.639858\pi$
$983$	10.3881	−	48.8720i	0.331328	−	1.55877i	0.756704	−	0.653758i	$-0.226809\pi$
$984$		0			0
$985$	−12.6647	+	28.4454i	−0.403531	+	0.906346i
$986$	−0.201594	+	0.223893i	−0.00642006	+	0.00713020i
$987$		0			0
$988$	5.86690	−	2.61211i	0.186651	−	0.0831024i
$989$	−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	$0.669807\pi$
$992$	23.3613	−	10.4011i	0.741721	−	0.330236i
$993$		0			0
$994$	−3.25468	+	3.61469i	−0.103232	+	0.114651i
$995$	−4.56534	+	10.2539i	−0.144731	+	0.325071i
$996$		0			0
$997$	3.93540	−	18.5146i	0.124635	−	0.586363i	−0.870858	−	0.491534i	$-0.836436\pi$
$997$	3.93540	−	18.5146i	0.124635	−	0.586363i	0.995494	−	0.0948290i	$-0.0302304\pi$
$998$	−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.62.5		80
3.2	odd	2		99.2.p.a.29.6	✓	80
9.2	odd	6		891.2.k.a.161.10		80
9.4	even	3		99.2.p.a.95.6	yes	80
9.5	odd	6	inner	297.2.t.a.260.5		80
9.7	even	3		891.2.k.a.161.11		80
11.8	odd	10	inner	297.2.t.a.8.5		80
33.8	even	10		99.2.p.a.74.6	yes	80
99.41	even	30	inner	297.2.t.a.206.5		80
99.52	odd	30		891.2.k.a.404.10		80
99.74	even	30		891.2.k.a.404.11		80
99.85	odd	30		99.2.p.a.41.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.6	✓	80	3.2	odd	2
99.2.p.a.41.6	yes	80	99.85	odd	30
99.2.p.a.74.6	yes	80	33.8	even	10
99.2.p.a.95.6	yes	80	9.4	even	3
297.2.t.a.8.5		80	11.8	odd	10	inner
297.2.t.a.62.5		80	1.1	even	1	trivial
297.2.t.a.206.5		80	99.41	even	30	inner
297.2.t.a.260.5		80	9.5	odd	6	inner
891.2.k.a.161.10		80	9.2	odd	6
891.2.k.a.161.11		80	9.7	even	3
891.2.k.a.404.10		80	99.52	odd	30
891.2.k.a.404.11		80	99.74	even	30

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)

\(f(q)\)	\(=\)	\(q+(-0.337994 + 0.150485i) q^{2} +(-1.24667 + 1.38456i) q^{4} +(0.966595 - 2.17101i) q^{5} +(0.327889 - 1.54259i) q^{7} +(0.441671 - 1.35932i) q^{8} +0.879247i q^{10} +(-2.12913 - 2.54299i) q^{11} +(6.09571 + 0.640685i) q^{13} +(0.121313 + 0.570731i) q^{14} +(-0.334222 - 3.17991i) q^{16} +(0.887473 - 0.644787i) q^{17} +(-0.534855 - 0.173785i) q^{19} +(1.80088 + 4.04484i) q^{20} +(1.10232 + 0.539115i) q^{22} +(4.81854 - 2.78199i) q^{23} +(-0.433320 - 0.481251i) q^{25} +(-2.15673 + 0.700764i) q^{26} +(1.72705 + 2.37708i) q^{28} +(0.726096 + 0.154337i) q^{29} +(0.661384 - 6.29265i) q^{31} +(2.02077 + 3.50008i) q^{32} +(-0.202930 + 0.351486i) q^{34} +(-3.03205 - 2.20291i) q^{35} +(1.32443 + 4.07617i) q^{37} +(0.206930 - 0.0217492i) q^{38} +(-2.52419 - 2.27279i) q^{40} +(-11.8871 + 2.52669i) q^{41} +(-7.35471 - 4.24624i) q^{43} +(6.17525 + 0.222344i) q^{44} +(-1.20999 + 1.66541i) q^{46} +(-0.571919 + 0.514959i) q^{47} +(4.12273 + 1.83556i) q^{49} +(0.218881 + 0.0974520i) q^{50} +(-8.48639 + 7.64118i) q^{52} +(-2.66042 + 3.66175i) q^{53} +(-7.57886 + 2.16432i) q^{55} +(-1.95207 - 1.12703i) q^{56} +(-0.268642 + 0.0571016i) q^{58} +(0.00834859 + 0.00751710i) q^{59} +(5.69949 - 0.599041i) q^{61} +(0.723404 + 2.22641i) q^{62} +(3.96382 + 2.87988i) q^{64} +(7.28302 - 12.6146i) q^{65} +(-0.738332 - 1.27883i) q^{67} +(-0.213635 + 2.03260i) q^{68} +(1.35632 + 0.288295i) q^{70} +(4.89992 + 6.74417i) q^{71} +(-14.9894 + 4.87035i) q^{73} +(-1.06105 - 1.17842i) q^{74} +(0.907402 - 0.523889i) q^{76} +(-4.62092 + 2.45057i) q^{77} +(1.29393 + 2.90621i) q^{79} +(-7.22666 - 2.34809i) q^{80} +(3.63756 - 2.64284i) q^{82} +(1.08533 + 10.3262i) q^{83} +(-0.542011 - 2.54996i) q^{85} +(3.12484 + 0.328434i) q^{86} +(-4.39713 + 1.77101i) q^{88} +9.01115i q^{89} +(2.98703 - 9.19313i) q^{91} +(-2.15528 + 10.1398i) q^{92} +(0.115812 - 0.260118i) q^{94} +(-0.894277 + 0.993195i) q^{95} +(5.06083 - 2.25323i) q^{97} -1.66968 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 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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