LMFDB - Embedded newform 459.2.y.a.422.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			422.1
Character	$\chi$	$=$	459.422
Dual form			459.2.y.a.62.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.45899 + 1.90139i) q^{2} +(-0.969004 - 3.61637i) q^{4} +(0.502973 - 0.0329666i) q^{5} +(0.0485612 - 0.740900i) q^{7} +(3.86148 + 1.59948i) q^{8} +(-0.671150 + 1.00445i) q^{10} +(-0.767594 + 0.673162i) q^{11} +(-5.20440 + 1.39452i) q^{13} +(1.33789 + 1.17330i) q^{14} +(-2.19038 + 1.26462i) q^{16} +(-3.71857 - 1.78107i) q^{17} +(-3.37354 + 1.39737i) q^{19} +(-0.606603 - 1.78699i) q^{20} +(-0.160033 - 2.44163i) q^{22} +(0.172029 - 0.506782i) q^{23} +(-4.70533 + 0.619468i) q^{25} +(4.94165 - 11.9302i) q^{26} +(-2.72643 + 0.542320i) q^{28} +(-5.67976 - 2.80095i) q^{29} +(-0.677946 + 0.773049i) q^{31} +(-0.299892 + 2.27790i) q^{32} +(8.81188 - 4.47190i) q^{34} -0.374254i q^{35} +(2.20919 - 11.1064i) q^{37} +(2.26502 - 8.45317i) q^{38} +(1.99495 + 0.677194i) q^{40} +(2.96507 + 6.01257i) q^{41} +(0.384182 + 2.91815i) q^{43} +(3.17821 + 2.12361i) q^{44} +(0.712603 + 1.06649i) q^{46} +(-11.4370 - 3.06452i) q^{47} +(6.39354 + 0.841725i) q^{49} +(5.68718 - 9.85048i) q^{50} +(10.0862 + 17.4698i) q^{52} +(3.30651 + 7.98262i) q^{53} +(-0.363887 + 0.363887i) q^{55} +(1.37257 - 2.78330i) q^{56} +(13.6124 - 6.71290i) q^{58} +(6.97647 - 5.35323i) q^{59} +(6.35837 + 0.416750i) q^{61} +(-0.480754 - 2.41691i) q^{62} +(-7.47053 - 7.47053i) q^{64} +(-2.57170 + 0.872975i) q^{65} +(-8.82398 - 5.09452i) q^{67} +(-2.83771 + 15.1736i) q^{68} +(0.711604 + 0.546033i) q^{70} +(-4.19907 - 0.835247i) q^{71} +(2.65455 - 1.77371i) q^{73} +(17.8943 + 20.4046i) q^{74} +(8.32238 + 10.8459i) q^{76} +(0.461470 + 0.601400i) q^{77} +(-6.82883 - 7.78679i) q^{79} +(-1.06001 + 0.708279i) q^{80} +(-15.7583 - 3.13452i) q^{82} +(-1.02986 - 0.790239i) q^{83} +(-1.92906 - 0.773243i) q^{85} +(-6.10907 - 3.52707i) q^{86} +(-4.04075 + 1.37165i) q^{88} +(-2.39586 - 2.39586i) q^{89} +(0.780465 + 3.92366i) q^{91} +(-1.99941 - 0.131048i) q^{92} +(22.5133 - 17.2750i) q^{94} +(-1.65074 + 0.814053i) q^{95} +(-7.04839 + 14.2927i) q^{97} +(-10.9286 + 10.9286i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Character values

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

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{16}\right)$

Coefficient data

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

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

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

$2$	−1.45899	+	1.90139i	−1.03166	+	1.34449i	−0.0945260	+	0.995522i	$0.530134\pi$
$2$	−1.45899	+	1.90139i	−1.03166	+	1.34449i	−0.937136	+	0.348965i	$0.886533\pi$
$3$		0			0
$3$		0			0
$4$	−0.969004	−	3.61637i	−0.484502	−	1.80819i
$5$	0.502973	−	0.0329666i	0.224936	−	0.0147431i	0.0474819	−	0.998872i	$-0.484880\pi$
$5$	0.502973	−	0.0329666i	0.224936	−	0.0147431i	0.177455	+	0.984129i	$0.443214\pi$
$6$		0			0
$7$	0.0485612	−	0.740900i	0.0183544	−	0.280034i	−0.978809	−	0.204773i	$-0.934354\pi$
$7$	0.0485612	−	0.740900i	0.0183544	−	0.280034i	0.997164	−	0.0752609i	$-0.0239790\pi$
$8$	3.86148	+	1.59948i	1.36524	+	0.565500i
$9$		0			0
$10$	−0.671150	+	1.00445i	−0.212236	+	0.317634i
$11$	−0.767594	+	0.673162i	−0.231438	+	0.202966i	−0.767208	−	0.641398i	$-0.778355\pi$
$11$	−0.767594	+	0.673162i	−0.231438	+	0.202966i	0.535770	+	0.844364i	$0.320021\pi$
$12$		0			0
$13$	−5.20440	+	1.39452i	−1.44344	+	0.386769i	−0.893737	−	0.448591i	$-0.851926\pi$
$13$	−5.20440	+	1.39452i	−1.44344	+	0.386769i	−0.549704	+	0.835360i	$0.685259\pi$
$14$	1.33789	+	1.17330i	0.357567	+	0.313578i
$15$		0			0
$16$	−2.19038	+	1.26462i	−0.547596	+	0.316155i
$17$	−3.71857	−	1.78107i	−0.901886	−	0.431973i
$17$	−3.71857	−	1.78107i	−0.901886	−	0.431973i
$18$		0			0
$19$	−3.37354	+	1.39737i	−0.773944	+	0.320578i	−0.734469	−	0.678643i	$-0.762569\pi$
$19$	−3.37354	+	1.39737i	−0.773944	+	0.320578i	−0.0394751	+	0.999221i	$0.512569\pi$
$20$	−0.606603	−	1.78699i	−0.135641	−	0.399584i
$21$		0			0
$22$	−0.160033	−	2.44163i	−0.0341192	−	0.520558i
$23$	0.172029	−	0.506782i	0.0358706	−	0.105671i	−0.927520	−	0.373774i	$-0.878063\pi$
$23$	0.172029	−	0.506782i	0.0358706	−	0.105671i	0.963390	+	0.268103i	$0.0863968\pi$
$24$		0			0
$25$	−4.70533	+	0.619468i	−0.941066	+	0.123894i
$26$	4.94165	−	11.9302i	0.969137	−	2.33970i
$27$		0			0
$28$	−2.72643	+	0.542320i	−0.515246	+	0.102489i
$29$	−5.67976	−	2.80095i	−1.05471	−	0.520123i	−0.169600	−	0.985513i	$-0.554247\pi$
$29$	−5.67976	−	2.80095i	−1.05471	−	0.520123i	−0.885106	+	0.465390i	$0.845914\pi$
$30$		0			0
$31$	−0.677946	+	0.773049i	−0.121763	+	0.138844i	−0.809509	−	0.587107i	$-0.800267\pi$
$31$	−0.677946	+	0.773049i	−0.121763	+	0.138844i	0.687747	+	0.725951i	$0.258600\pi$
$32$	−0.299892	+	2.27790i	−0.0530139	+	0.402680i
$33$		0			0
$34$	8.81188	−	4.47190i	1.51122	−	0.766925i
$35$		−	0.374254i		−	0.0632604i
$36$		0			0
$37$	2.20919	−	11.1064i	0.363189	−	1.82587i	−0.176856	−	0.984237i	$-0.556593\pi$
$37$	2.20919	−	11.1064i	0.363189	−	1.82587i	0.540045	−	0.841636i	$-0.318407\pi$
$38$	2.26502	−	8.45317i	0.367435	−	1.37129i
$39$		0			0
$40$	1.99495	+	0.677194i	0.315429	+	0.107074i
$41$	2.96507	+	6.01257i	0.463067	+	0.939006i	0.995698	+	0.0926589i	$0.0295366\pi$
$41$	2.96507	+	6.01257i	0.463067	+	0.939006i	−0.532631	+	0.846347i	$0.678797\pi$
$42$		0			0
$43$	0.384182	+	2.91815i	0.0585872	+	0.445014i	0.995448	+	0.0953104i	$0.0303844\pi$
$43$	0.384182	+	2.91815i	0.0585872	+	0.445014i	−0.936860	+	0.349704i	$0.886282\pi$
$44$	3.17821	+	2.12361i	0.479133	+	0.320146i
$45$		0			0
$46$	0.712603	+	1.06649i	0.105068	+	0.157245i
$47$	−11.4370	−	3.06452i	−1.66825	−	0.447007i	−0.703614	−	0.710583i	$-0.748431\pi$
$47$	−11.4370	−	3.06452i	−1.66825	−	0.447007i	−0.964639	+	0.263576i	$0.915098\pi$
$48$		0			0
$49$	6.39354	+	0.841725i	0.913363	+	0.120246i
$50$	5.68718	−	9.85048i	0.804288	−	1.39307i
$51$		0			0
$52$	10.0862	+	17.4698i	1.39870	+	2.42262i
$53$	3.30651	+	7.98262i	0.454184	+	1.09650i	0.970716	+	0.240230i	$0.0772228\pi$
$53$	3.30651	+	7.98262i	0.454184	+	1.09650i	−0.516532	+	0.856268i	$0.672777\pi$
$54$		0			0
$55$	−0.363887	+	0.363887i	−0.0490666	+	0.0490666i
$56$	1.37257	−	2.78330i	0.183417	−	0.371934i
$57$		0			0
$58$	13.6124	−	6.71290i	1.78740	−	0.881447i
$59$	6.97647	−	5.35323i	0.908259	−	0.696932i	−0.0450319	−	0.998986i	$-0.514339\pi$
$59$	6.97647	−	5.35323i	0.908259	−	0.696932i	0.953291	+	0.302054i	$0.0976723\pi$
$60$		0			0
$61$	6.35837	+	0.416750i	0.814106	+	0.0533593i	0.466767	−	0.884380i	$-0.345419\pi$
$61$	6.35837	+	0.416750i	0.814106	+	0.0533593i	0.347339	+	0.937740i	$0.387085\pi$
$62$	−0.480754	−	2.41691i	−0.0610558	−	0.306948i
$63$		0			0
$64$	−7.47053	−	7.47053i	−0.933817	−	0.933817i
$65$	−2.57170	+	0.872975i	−0.318980	+	0.108279i
$66$		0			0
$67$	−8.82398	−	5.09452i	−1.07802	−	0.622395i	−0.147659	−	0.989038i	$-0.547174\pi$
$67$	−8.82398	−	5.09452i	−1.07802	−	0.622395i	−0.930362	+	0.366643i	$0.880507\pi$
$68$	−2.83771	+	15.1736i	−0.344122	+	1.84007i
$69$		0			0
$70$	0.711604	+	0.546033i	0.0850529	+	0.0652634i
$71$	−4.19907	−	0.835247i	−0.498338	−	0.0991255i	−0.0604793	−	0.998169i	$-0.519263\pi$
$71$	−4.19907	−	0.835247i	−0.498338	−	0.0991255i	−0.437858	+	0.899044i	$0.644263\pi$
$72$		0			0
$73$	2.65455	−	1.77371i	0.310691	−	0.207597i	−0.390442	−	0.920627i	$-0.627678\pi$
$73$	2.65455	−	1.77371i	0.310691	−	0.207597i	0.701133	+	0.713030i	$0.252678\pi$
$74$	17.8943	+	20.4046i	2.08018	+	2.37199i
$75$		0			0
$76$	8.32238	+	10.8459i	0.954642	+	1.24411i
$77$	0.461470	+	0.601400i	0.0525894	+	0.0685359i
$78$		0			0
$79$	−6.82883	−	7.78679i	−0.768304	−	0.876083i	0.226899	−	0.973918i	$-0.427141\pi$
$79$	−6.82883	−	7.78679i	−0.768304	−	0.876083i	−0.995203	+	0.0978357i	$0.968808\pi$
$80$	−1.06001	+	0.708279i	−0.118513	+	0.0791880i
$81$		0			0
$82$	−15.7583	−	3.13452i	−1.74021	−	0.346149i
$83$	−1.02986	−	0.790239i	−0.113042	−	0.0867400i	0.550694	−	0.834707i	$-0.314363\pi$
$83$	−1.02986	−	0.790239i	−0.113042	−	0.0867400i	−0.663735	+	0.747967i	$0.731030\pi$
$84$		0			0
$85$	−1.92906	−	0.773243i	−0.209236	−	0.0838699i
$86$	−6.10907	−	3.52707i	−0.658758	−	0.380334i
$87$		0			0
$88$	−4.04075	+	1.37165i	−0.430746	+	0.146218i
$89$	−2.39586	−	2.39586i	−0.253961	−	0.253961i	0.568632	−	0.822592i	$-0.307473\pi$
$89$	−2.39586	−	2.39586i	−0.253961	−	0.253961i	−0.822592	+	0.568632i	$0.807473\pi$
$90$		0			0
$91$	0.780465	+	3.92366i	0.0818149	+	0.411311i
$92$	−1.99941	−	0.131048i	−0.208453	−	0.0136627i
$93$		0			0
$94$	22.5133	−	17.2750i	2.32207	−	1.78178i
$95$	−1.65074	+	0.814053i	−0.169362	+	0.0835200i
$96$		0			0
$97$	−7.04839	+	14.2927i	−0.715656	+	1.45121i	0.169316	+	0.985562i	$0.445844\pi$
$97$	−7.04839	+	14.2927i	−0.715656	+	1.45121i	−0.884972	+	0.465644i	$0.845823\pi$
$98$	−10.9286	+	10.9286i	−1.10395	+	1.10395i
$99$		0			0
$100$	6.79971	+	16.4160i	0.679971	+	1.64160i
$101$	6.54019	+	11.3279i	0.650773	+	1.12717i	0.982936	+	0.183949i	$0.0588883\pi$
$101$	6.54019	+	11.3279i	0.650773	+	1.12717i	−0.332163	+	0.943222i	$0.607778\pi$
$102$		0			0
$103$	−3.23969	+	5.61131i	−0.319216	+	0.552899i	−0.980325	−	0.197391i	$-0.936753\pi$
$103$	−3.23969	+	5.61131i	−0.319216	+	0.552899i	0.661108	+	0.750290i	$0.270086\pi$
$104$	−22.3272	−	2.93943i	−2.18936	−	0.288235i
$105$		0			0
$106$	−20.0023	−	5.35959i	−1.94279	−	0.520570i
$107$	−8.20002	−	12.2722i	−0.792726	−	1.18640i	−0.978992	−	0.203899i	$-0.934639\pi$
$107$	−8.20002	−	12.2722i	−0.792726	−	1.18640i	0.186266	−	0.982499i	$-0.440361\pi$
$108$		0			0
$109$	0.866335	+	0.578867i	0.0829798	+	0.0554454i	0.596368	−	0.802711i	$-0.296610\pi$
$109$	0.866335	+	0.578867i	0.0829798	+	0.0554454i	−0.513388	+	0.858156i	$0.671610\pi$
$110$	−0.160985	−	1.22280i	−0.0153493	−	0.116589i
$111$		0			0
$112$	0.830589	+	1.68427i	0.0784832	+	0.159148i
$113$	−4.50947	−	1.53076i	−0.424215	−	0.144002i	0.101164	−	0.994870i	$-0.467743\pi$
$113$	−4.50947	−	1.53076i	−0.424215	−	0.144002i	−0.525379	+	0.850868i	$0.676077\pi$
$114$		0			0
$115$	0.0698193	−	0.260569i	0.00651068	−	0.0242982i
$116$	−4.62556	+	23.2543i	−0.429473	+	2.15911i
$117$		0			0
$118$			21.0753i			1.94014i
$119$	−1.50017	+	2.66860i	−0.137521	+	0.244630i
$120$		0			0
$121$	−1.29973	+	9.87246i	−0.118158	+	0.897497i
$122$	−10.0692	+	11.4817i	−0.911623	+	1.03951i
$123$		0			0
$124$	3.45257	+	1.70262i	0.310050	+	0.152900i
$125$	−4.81807	+	0.958374i	−0.430941	+	0.0857195i
$126$		0			0
$127$	−2.87472	+	6.94019i	−0.255090	+	0.615843i	−0.998601	−	0.0528818i	$-0.983159\pi$
$127$	−2.87472	+	6.94019i	−0.255090	+	0.615843i	0.743510	+	0.668724i	$0.233159\pi$
$128$	20.5480	−	2.70520i	1.81621	−	0.239108i
$129$		0			0
$130$	2.09222	−	6.16348i	0.183500	−	0.540573i
$131$	−0.287829	−	4.39143i	−0.0251478	−	0.383681i	−0.991818	−	0.127657i	$-0.959254\pi$
$131$	−0.287829	−	4.39143i	−0.0251478	−	0.383681i	0.966671	−	0.256023i	$-0.0824124\pi$
$132$		0			0
$133$	0.871486	+	2.56732i	0.0755675	+	0.222615i
$134$	22.5608	−	9.34498i	1.94895	−	0.807284i
$135$		0			0
$136$	−11.5104	−	12.8253i	−0.987009	−	1.09976i
$137$	−5.46680	+	3.15626i	−0.467060	+	0.269657i	−0.715008	−	0.699116i	$-0.753577\pi$
$137$	−5.46680	+	3.15626i	−0.467060	+	0.269657i	0.247948	+	0.968773i	$0.420244\pi$
$138$		0			0
$139$	11.3931	+	9.99145i	0.966347	+	0.847463i	0.988335	−	0.152295i	$-0.0486664\pi$
$139$	11.3931	+	9.99145i	0.966347	+	0.847463i	−0.0219884	+	0.999758i	$0.507000\pi$
$140$	−1.35344	+	0.362654i	−0.114387	+	0.0306498i
$141$		0			0
$142$	7.71453	−	6.76546i	0.647389	−	0.567745i
$143$	3.05613	−	4.57383i	0.255567	−	0.382483i
$144$		0			0
$145$	−2.94911	−	1.22156i	−0.244910	−	0.101445i
$146$	−0.500435	+	7.63516i	−0.0414163	+	0.631890i
$147$		0			0
$148$	−42.3054	+	2.77284i	−3.47749	+	0.227926i
$149$	1.91554	+	7.14890i	0.156927	+	0.585661i	0.998933	+	0.0461915i	$0.0147085\pi$
$149$	1.91554	+	7.14890i	0.156927	+	0.585661i	−0.842005	+	0.539469i	$0.818625\pi$
$150$		0			0
$151$	−1.49586	+	1.94944i	−0.121731	+	0.158643i	−0.850244	−	0.526389i	$-0.823545\pi$
$151$	−1.49586	+	1.94944i	−0.121731	+	0.158643i	0.728512	+	0.685033i	$0.240212\pi$
$152$	−15.2619			−1.23790
$153$		0			0
$154$	−1.81678			−0.146400
$155$	−0.315504	+	0.411173i	−0.0253419	+	0.0330262i
$156$		0			0
$157$	−2.48072	−	9.25817i	−0.197983	−	0.738883i	−0.991474	−	0.130301i	$-0.958406\pi$
$157$	−2.48072	−	9.25817i	−0.197983	−	0.738883i	0.793491	−	0.608581i	$-0.208261\pi$
$158$	24.7689	−	1.62344i	1.97051	−	0.129154i
$159$		0			0
$160$	−0.0757428	+	1.15561i	−0.00598799	+	0.0913591i
$161$	−0.367121	−	0.152067i	−0.0289332	−	0.0119845i
$162$		0			0
$163$	3.62885	−	5.43096i	0.284234	−	0.425386i	−0.661689	−	0.749779i	$-0.730160\pi$
$163$	3.62885	−	5.43096i	0.284234	−	0.425386i	0.945922	+	0.324393i	$0.105160\pi$
$164$	18.8705	−	16.5490i	1.47354	−	1.29226i
$165$		0			0
$166$	3.00511	−	0.805217i	0.233242	−	0.0624970i
$167$	−3.06714	−	2.68981i	−0.237343	−	0.208144i	0.532409	−	0.846487i	$-0.321287\pi$
$167$	−3.06714	−	2.68981i	−0.237343	−	0.208144i	−0.769752	+	0.638343i	$0.779620\pi$
$168$		0			0
$169$	13.8828	−	8.01523i	1.06791	−	0.616556i
$170$	4.28471	−	2.53974i	0.328623	−	0.194790i
$171$		0			0
$172$	10.1809	−	4.21705i	0.776283	−	0.321547i
$173$	2.64623	+	7.79554i	0.201189	+	0.592684i	0.999960	−	0.00895141i	$-0.00284936\pi$
$173$	2.64623	+	7.79554i	0.201189	+	0.592684i	−0.798771	+	0.601635i	$0.794516\pi$
$174$		0			0
$175$	0.230468	+	3.51626i	0.0174217	+	0.265804i
$176$	0.830032	−	2.44520i	0.0625660	−	0.184314i
$177$		0			0
$178$	8.05100	−	1.05993i	0.603448	−	0.0794455i
$179$	4.54443	−	10.9712i	0.339667	−	0.820028i	−0.658081	−	0.752947i	$-0.728631\pi$
$179$	4.54443	−	10.9712i	0.339667	−	0.820028i	0.997748	−	0.0670807i	$-0.0213685\pi$
$180$		0			0
$181$	17.5732	−	3.49554i	1.30621	−	0.259821i	0.507559	−	0.861617i	$-0.330548\pi$
$181$	17.5732	−	3.49554i	1.30621	−	0.259821i	0.798650	+	0.601796i	$0.205548\pi$
$182$	−8.59911	−	4.24061i	−0.637408	−	0.314335i
$183$		0			0
$184$	1.47487	−	1.68177i	0.108729	−	0.123982i
$185$	0.745025	−	5.65903i	0.0547753	−	0.416060i
$186$		0			0
$187$	4.05330	−	1.13606i	0.296407	−	0.0830771i
$188$			44.3299i			3.23309i
$189$		0			0
$190$	0.860573	−	4.32639i	0.0624325	−	0.313869i
$191$	5.55608	−	20.7356i	0.402024	−	1.50037i	−0.407456	−	0.913225i	$-0.633584\pi$
$191$	5.55608	−	20.7356i	0.402024	−	1.50037i	0.809479	−	0.587148i	$-0.199749\pi$
$192$		0			0
$193$	8.52695	+	2.89451i	0.613783	+	0.208351i	0.610982	−	0.791645i	$-0.290775\pi$
$193$	8.52695	+	2.89451i	0.613783	+	0.208351i	0.00280156	+	0.999996i	$0.499108\pi$
$194$	−16.8925	−	34.2547i	−1.21281	−	2.45934i
$195$		0			0
$196$	−3.15137	−	23.9371i	−0.225098	−	1.70979i
$197$	15.1511	+	10.1237i	1.07947	+	0.721281i	0.962344	−	0.271836i	$-0.0876307\pi$
$197$	15.1511	+	10.1237i	1.07947	+	0.721281i	0.117130	+	0.993117i	$0.462631\pi$
$198$		0			0
$199$	13.9975	+	20.9487i	0.992255	+	1.48501i	0.870326	+	0.492476i	$0.163908\pi$
$199$	13.9975	+	20.9487i	0.992255	+	1.48501i	0.121929	+	0.992539i	$0.461092\pi$
$200$	−19.1603	−	5.13400i	−1.35484	−	0.363029i
$201$		0			0
$202$	−31.0809	−	4.09188i	−2.18685	−	0.287904i
$203$	−2.35104	+	4.07212i	−0.165011	+	0.285807i
$204$		0			0
$205$	1.68957	+	2.92642i	0.118004	+	0.204390i
$206$	−5.94263	−	14.3468i	−0.414043	−	0.999587i
$207$		0			0
$208$	9.63611	−	9.63611i	0.668144	−	0.668144i
$209$	1.64886	−	3.34355i	0.114054	−	0.231278i
$210$		0			0
$211$	−13.5539	+	6.68404i	−0.933088	+	0.460148i	−0.844281	−	0.535901i	$-0.819972\pi$
$211$	−13.5539	+	6.68404i	−0.933088	+	0.460148i	−0.0888071	+	0.996049i	$0.528305\pi$
$212$	25.6641	−	19.6928i	1.76262	−	1.35251i
$213$		0			0
$214$	35.2980	+	2.31355i	2.41292	+	0.158151i
$215$	0.289435	+	1.45509i	0.0197393	+	0.0992361i
$216$		0			0
$217$	0.539830	+	0.539830i	0.0366461	+	0.0366461i
$218$	−2.36463	+	0.802683i	−0.160153	+	0.0543645i
$219$		0			0
$220$	1.66856	+	0.963344i	0.112494	+	0.0649487i
$221$	21.8367	+	4.08380i	1.46889	+	0.274706i
$222$		0			0
$223$	−12.2180	−	9.37523i	−0.818180	−	0.627812i	0.112497	−	0.993652i	$-0.464115\pi$
$223$	−12.2180	−	9.37523i	−0.818180	−	0.627812i	−0.930678	+	0.365840i	$0.880782\pi$
$224$	1.67314	+	0.332808i	0.111791	+	0.0222366i
$225$		0			0
$226$	9.48984	−	6.34091i	0.631255	−	0.421791i
$227$	11.7400	+	13.3870i	0.779214	+	0.888523i	0.996150	−	0.0876626i	$-0.0279397\pi$
$227$	11.7400	+	13.3870i	0.779214	+	0.888523i	−0.216936	+	0.976186i	$0.569606\pi$
$228$		0			0
$229$	4.83506	+	6.30117i	0.319509	+	0.416393i	0.925303	−	0.379229i	$-0.123811\pi$
$229$	4.83506	+	6.30117i	0.319509	+	0.416393i	−0.605793	+	0.795622i	$0.707144\pi$
$230$	0.393579	+	0.512922i	0.0259518	+	0.0338211i
$231$		0			0
$232$	−17.4522	−	19.9004i	−1.14579	−	1.30653i
$233$	−15.3673	+	10.2681i	−1.00675	+	0.672687i	−0.945563	−	0.325440i	$-0.894488\pi$
$233$	−15.3673	+	10.2681i	−1.00675	+	0.672687i	−0.0611841	+	0.998126i	$0.519488\pi$
$234$		0			0
$235$	−5.85351	−	1.16434i	−0.381841	−	0.0759529i
$236$	−26.1195	−	20.0422i	−1.70024	−	1.30464i
$237$		0			0
$238$	−2.88532	−	6.74588i	−0.187027	−	0.437271i
$239$	−14.9969	−	8.65844i	−0.970067	−	0.560068i	−0.0708101	−	0.997490i	$-0.522558\pi$
$239$	−14.9969	−	8.65844i	−0.970067	−	0.560068i	−0.899257	+	0.437422i	$0.855892\pi$
$240$		0			0
$241$	−11.7751	+	3.99711i	−0.758501	+	0.257476i	−0.673784	−	0.738929i	$-0.735332\pi$
$241$	−11.7751	+	3.99711i	−0.758501	+	0.257476i	−0.0847170	+	0.996405i	$0.526999\pi$
$242$	−16.8751	−	16.8751i	−1.08477	−	1.08477i
$243$		0			0
$244$	−4.65417	−	23.3981i	−0.297953	−	1.49791i
$245$	3.24353	+	0.212592i	0.207221	+	0.0135820i
$246$		0			0
$247$	15.6086	−	11.9769i	0.993153	−	0.762073i
$248$	−3.85435	+	1.90075i	−0.244751	+	0.120698i
$249$		0			0
$250$	5.20727	−	10.5593i	0.329337	−	0.667829i
$251$	12.5986	−	12.5986i	0.795218	−	0.795218i	−0.187119	−	0.982337i	$-0.559915\pi$
$251$	12.5986	−	12.5986i	0.795218	−	0.795218i	0.982337	+	0.187119i	$0.0599151\pi$
$252$		0			0
$253$	0.209098	+	0.504807i	0.0131459	+	0.0317369i
$254$	−9.00184	−	15.5916i	−0.564826	−	0.978307i
$255$		0			0
$256$	−14.2708	+	24.7178i	−0.891925	+	1.54486i
$257$	11.1120	+	1.46292i	0.693147	+	0.0912545i	0.468865	−	0.883270i	$-0.344663\pi$
$257$	11.1120	+	1.46292i	0.693147	+	0.0912545i	0.224282	+	0.974524i	$0.427996\pi$
$258$		0			0
$259$	−8.12142	−	2.17613i	−0.504640	−	0.135218i
$260$	5.64900	+	8.45432i	0.350336	+	0.524315i
$261$		0			0
$262$	8.76977	+	5.85977i	0.541798	+	0.362018i
$263$	2.18215	+	16.5751i	0.134557	+	1.02206i	0.916873	+	0.399180i	$0.130705\pi$
$263$	2.18215	+	16.5751i	0.134557	+	1.02206i	−0.782316	+	0.622882i	$0.785962\pi$
$264$		0			0
$265$	1.92625	+	3.90604i	0.118328	+	0.239946i
$266$	−6.15297	−	2.08865i	−0.377263	−	0.128063i
$267$		0			0
$268$	−9.87323	+	36.8474i	−0.603104	+	2.25081i
$269$	1.87839	−	9.44333i	0.114528	−	0.575770i	−0.880319	−	0.474382i	$-0.842672\pi$
$269$	1.87839	−	9.44333i	0.114528	−	0.575770i	0.994847	−	0.101388i	$-0.0323284\pi$
$270$		0			0
$271$		−	21.5828i		−	1.31106i	−0.755168	−	0.655531i	$-0.772445\pi$
$271$		−	21.5828i		−	1.31106i	0.755168	−	0.655531i	$-0.227555\pi$
$272$	10.3975	−	0.801347i	0.630440	−	0.0485888i
$273$		0			0
$274$	1.97472	−	14.9995i	0.119297	−	0.906152i
$275$	3.19478	−	3.64295i	0.192652	−	0.219678i
$276$		0			0
$277$	−23.0315	−	11.3579i	−1.38383	−	0.682428i	−0.410502	−	0.911860i	$-0.634647\pi$
$277$	−23.0315	−	11.3579i	−1.38383	−	0.682428i	−0.973325	+	0.229432i	$0.926313\pi$
$278$	−35.6200	+	7.08526i	−2.13635	+	0.424946i
$279$		0			0
$280$	0.598610	−	1.44517i	0.0357738	−	0.0863656i
$281$	−11.5690	+	1.52308i	−0.690147	+	0.0908595i	−0.467439	−	0.884026i	$-0.654823\pi$
$281$	−11.5690	+	1.52308i	−0.690147	+	0.0908595i	−0.222708	+	0.974885i	$0.571490\pi$
$282$		0			0
$283$	0.351485	−	1.03544i	0.0208936	−	0.0615506i	−0.935983	−	0.352045i	$-0.885486\pi$
$283$	0.351485	−	1.03544i	0.0208936	−	0.0615506i	0.956877	+	0.290494i	$0.0938197\pi$
$284$	1.04835	+	15.9948i	0.0622082	+	0.949114i
$285$		0			0
$286$	4.23777	+	12.4841i	0.250585	+	0.738199i
$287$	4.59870	−	1.90485i	0.271453	−	0.112439i
$288$		0			0
$289$	10.6556	+	13.2461i	0.626798	+	0.779182i
$290$	6.62538	−	3.82517i	0.389056	−	0.224622i
$291$		0			0
$292$	−8.98667	−	7.88110i	−0.525905	−	0.461206i
$293$	−2.28133	+	0.611280i	−0.133276	+	0.0357113i	−0.324841	−	0.945769i	$-0.605311\pi$
$293$	−2.28133	+	0.611280i	−0.133276	+	0.0357113i	0.191564	+	0.981480i	$0.438644\pi$
$294$		0			0
$295$	3.33250	−	2.92252i	0.194026	−	0.170156i
$296$	26.2951	−	39.3534i	1.52837	−	2.28737i
$297$		0			0
$298$	−16.3876	−	6.78798i	−0.949310	−	0.393217i
$299$	−0.188595	+	2.87740i	−0.0109067	+	0.166404i
$300$		0			0
$301$	2.18072	−	0.142932i	0.125694	−	0.00823844i
$302$	−1.52421	−	5.68844i	−0.0877086	−	0.327333i
$303$		0			0
$304$	5.62222	−	7.32702i	0.322456	−	0.420233i
$305$	3.21183			0.183909
$306$		0			0
$307$	−31.4910			−1.79729			−0.898644	−	0.438678i	$-0.855447\pi$
$307$	−31.4910			−1.79729			−0.898644	+	0.438678i	$0.855447\pi$
$308$	1.72772	−	2.25161i	0.0984460	−	0.128297i
$309$		0			0
$310$	−0.321484	−	1.19979i	−0.0182590	−	0.0681437i
$311$	11.2499	−	0.737360i	0.637926	−	0.0418119i	0.256991	−	0.966414i	$-0.417269\pi$
$311$	11.2499	−	0.737360i	0.637926	−	0.0418119i	0.380935	+	0.924602i	$0.375602\pi$
$312$		0			0
$313$	−0.550274	+	8.39557i	−0.0311034	+	0.474545i	0.953687	+	0.300800i	$0.0972537\pi$
$313$	−0.550274	+	8.39557i	−0.0311034	+	0.474545i	−0.984791	+	0.173745i	$0.944413\pi$
$314$	21.2228	+	8.79076i	1.19767	+	0.496091i
$315$		0			0
$316$	−21.5428	+	32.2411i	−1.21188	+	1.81370i
$317$	−0.973224	+	0.853495i	−0.0546617	+	0.0479371i	−0.686241	−	0.727374i	$-0.740740\pi$
$317$	−0.973224	+	0.853495i	−0.0546617	+	0.0479371i	0.631579	+	0.775311i	$0.282407\pi$
$318$		0			0
$319$	6.24524	−	1.67341i	0.349667	−	0.0936929i
$320$	−4.00376	−	3.51120i	−0.223817	−	0.196282i
$321$		0			0
$322$	0.824764	−	0.476178i	0.0459623	−	0.0265364i
$323$	15.0336	+	0.812309i	0.836491	+	0.0451981i
$324$		0			0
$325$	23.6246	−	9.78561i	1.31045	−	0.542808i
$326$	5.03193	+	14.8236i	0.278693	+	0.821003i
$327$		0			0
$328$	1.83259	+	27.9600i	0.101188	+	1.54383i
$329$	−2.82590	+	8.32483i	−0.155797	+	0.458963i
$330$		0			0
$331$	−6.58097	+	0.866401i	−0.361723	+	0.0476217i	−0.309197	−	0.950998i	$-0.600060\pi$
$331$	−6.58097	+	0.866401i	−0.361723	+	0.0476217i	−0.0525254	+	0.998620i	$0.516727\pi$
$332$	−1.85986	+	4.49010i	−0.102073	+	0.246426i
$333$		0			0
$334$	9.58932	−	1.90744i	0.524705	−	0.104370i
$335$	−4.60617	−	2.27151i	−0.251662	−	0.124106i
$336$		0			0
$337$	−4.97913	+	5.67761i	−0.271230	+	0.309279i	−0.871380	−	0.490609i	$-0.836774\pi$
$337$	−4.97913	+	5.67761i	−0.271230	+	0.309279i	0.600150	+	0.799888i	$0.295108\pi$
$338$	−5.01475	+	38.0908i	−0.272766	+	2.07186i
$339$		0			0
$340$	−0.927068	+	7.72547i	−0.0502773	+	0.418973i
$341$		−	1.04976i		−	0.0568474i
$342$		0			0
$343$	1.94808	−	9.79366i	0.105186	−	0.528808i
$344$	−3.18400	+	11.8829i	−0.171670	+	0.640681i
$345$		0			0
$346$	−18.6832	−	6.34209i	−1.00442	−	0.340953i
$347$	12.1309	+	24.5991i	0.651223	+	1.32055i	0.932586	+	0.360949i	$0.117547\pi$
$347$	12.1309	+	24.5991i	0.651223	+	1.32055i	−0.281362	+	0.959602i	$0.590786\pi$
$348$		0			0
$349$	−1.41604	−	10.7559i	−0.0757990	−	0.575751i	−0.986631	−	0.162972i	$-0.947892\pi$
$349$	−1.41604	−	10.7559i	−0.0757990	−	0.575751i	0.910832	−	0.412778i	$-0.135442\pi$
$350$	−7.02204	−	4.69198i	−0.375344	−	0.250797i
$351$		0			0
$352$	−1.30320	−	1.95038i	−0.0694610	−	0.103956i
$353$	6.82053	+	1.82756i	0.363020	+	0.0972710i	0.435719	−	0.900083i	$-0.356494\pi$
$353$	6.82053	+	1.82756i	0.363020	+	0.0972710i	−0.0726982	+	0.997354i	$0.523161\pi$
$354$		0			0
$355$	−2.13955	−	0.281678i	−0.113556	−	0.0149499i
$356$	−6.34272	+	10.9859i	−0.336164	+	0.582253i
$357$		0			0
$358$	14.2303	+	24.6477i	0.752096	+	1.30267i
$359$	1.46983	+	3.54849i	0.0775748	+	0.187282i	0.957909	−	0.287072i	$-0.0926818\pi$
$359$	1.46983	+	3.54849i	0.0775748	+	0.187282i	−0.880334	+	0.474354i	$0.842682\pi$
$360$		0			0
$361$	−4.00687	+	4.00687i	−0.210888	+	0.210888i
$362$	−18.9928	+	38.5136i	−0.998239	+	2.02423i
$363$		0			0
$364$	13.4332	−	6.62450i	0.704088	−	0.347218i
$365$	1.27669	−	0.979641i	0.0668251	−	0.0512767i
$366$		0			0
$367$	14.8625	+	0.974142i	0.775818	+	0.0508498i	0.448168	−	0.893949i	$-0.352077\pi$
$367$	14.8625	+	0.974142i	0.775818	+	0.0508498i	0.327650	+	0.944799i	$0.393743\pi$
$368$	0.264076	+	1.32760i	0.0137659	+	0.0692059i
$369$		0			0
$370$	9.67305	+	9.67305i	0.502878	+	0.502878i
$371$	6.07490	−	2.06215i	0.315393	−	0.107061i
$372$		0			0
$373$	−3.87184	−	2.23541i	−0.200476	−	0.115745i	0.396401	−	0.918077i	$-0.370259\pi$
$373$	−3.87184	−	2.23541i	−0.200476	−	0.115745i	−0.596878	+	0.802332i	$0.703592\pi$
$374$	−3.75363	+	9.36442i	−0.194096	+	0.484223i
$375$		0			0
$376$	−39.2619	−	30.1267i	−2.02478	−	1.55367i
$377$	33.4657	+	6.65675i	1.72357	+	0.342840i
$378$		0			0
$379$	−12.0411	+	8.04562i	−0.618511	+	0.413276i	−0.824968	−	0.565180i	$-0.808807\pi$
$379$	−12.0411	+	8.04562i	−0.618511	+	0.413276i	0.206457	+	0.978456i	$0.433807\pi$
$380$	4.54349	+	5.18086i	0.233076	+	0.265772i
$381$		0			0
$382$	31.3202	+	40.8173i	1.60248	+	2.08839i
$383$	−0.898203	−	1.17056i	−0.0458961	−	0.0598129i	0.769841	−	0.638235i	$-0.220335\pi$
$383$	−0.898203	−	1.17056i	−0.0458961	−	0.0598129i	−0.815737	+	0.578422i	$0.803669\pi$
$384$		0			0
$385$	0.251933	+	0.287275i	0.0128397	+	0.0146409i
$386$	−17.9443	+	11.9900i	−0.913342	+	0.610276i
$387$		0			0
$388$	58.5178	+	11.6399i	2.97079	+	0.590927i
$389$	−30.2791	−	23.2340i	−1.53521	−	1.17801i	−0.921438	−	0.388525i	$-0.872985\pi$
$389$	−30.2791	−	23.2340i	−1.53521	−	1.17801i	−0.613772	−	0.789484i	$-0.710348\pi$
$390$		0			0
$391$	−1.54232	+	1.57811i	−0.0779985	+	0.0798085i
$392$	23.3422	+	13.4766i	1.17896	+	0.680672i
$393$		0			0
$394$	−41.3544	+	14.0379i	−2.08340	+	0.707221i
$395$	−3.69142	−	3.69142i	−0.185736	−	0.185736i
$396$		0			0
$397$	−1.08068	−	5.43296i	−0.0542379	−	0.272673i	0.944144	−	0.329533i	$-0.106891\pi$
$397$	−1.08068	−	5.43296i	−0.0542379	−	0.272673i	−0.998382	+	0.0568600i	$0.981891\pi$
$398$	−60.2539	−	3.94925i	−3.02026	−	0.197958i
$399$		0			0
$400$	9.52309	−	7.30732i	0.476154	−	0.365366i
$401$	−18.3820	+	9.06500i	−0.917953	+	0.452684i	−0.838961	−	0.544191i	$-0.816837\pi$
$401$	−18.3820	+	9.06500i	−0.917953	+	0.452684i	−0.0789918	+	0.996875i	$0.525170\pi$
$402$		0			0
$403$	2.45027	−	4.96866i	0.122057	−	0.247507i
$404$	34.6286	−	34.6286i	1.72284	−	1.72284i
$405$		0			0
$406$	−4.31256	−	10.4114i	−0.214029	−	0.516711i
$407$	5.78061	+	10.0123i	0.286534	+	0.496292i
$408$		0			0
$409$	11.6707	−	20.2142i	0.577078	−	0.999528i	−0.418735	−	0.908109i	$-0.637526\pi$
$409$	11.6707	−	20.2142i	0.577078	−	0.999528i	0.995812	−	0.0914193i	$-0.0291404\pi$
$410$	−8.02933	−	1.05708i	−0.396540	−	0.0522055i
$411$		0			0
$412$	23.4319	+	6.27855i	1.15441	+	0.309322i
$413$	−3.62743	−	5.42883i	−0.178494	−	0.267135i
$414$		0			0
$415$	−0.544044	−	0.363518i	−0.0267060	−	0.0178444i
$416$	−1.61581	−	12.2733i	−0.0792218	−	0.601750i
$417$		0			0
$418$	3.95174	+	8.01333i	0.193286	+	0.391945i
$419$	−32.7941	−	11.1321i	−1.60210	−	0.543839i	−0.629634	−	0.776892i	$-0.716795\pi$
$419$	−32.7941	−	11.1321i	−1.60210	−	0.543839i	−0.972464	+	0.233053i	$0.925128\pi$
$420$		0			0
$421$	−0.782462	+	2.92019i	−0.0381349	+	0.142321i	−0.982368	−	0.186955i	$-0.940138\pi$
$421$	−0.782462	+	2.92019i	−0.0381349	+	0.142321i	0.944234	+	0.329276i	$0.106805\pi$
$422$	7.06601	−	35.5232i	0.343968	−	1.72924i
$423$		0			0
$424$			36.1134i			1.75382i
$425$	18.6004	+	6.07699i	0.902253	+	0.294777i
$426$		0			0
$427$	0.617540	−	4.69068i	0.0298849	−	0.226998i
$428$	−36.4350	+	41.5462i	−1.76115	+	2.00821i
$429$		0			0
$430$	−3.18897	−	1.57263i	−0.153786	−	0.0758389i
$431$	−38.4058	+	7.63939i	−1.84994	+	0.367977i	−0.989845	−	0.142151i	$-0.954598\pi$
$431$	−38.4058	+	7.63939i	−1.84994	+	0.367977i	−0.860098	+	0.510128i	$0.829598\pi$
$432$		0			0
$433$	9.24045	−	22.3084i	0.444068	−	1.07207i	−0.530441	−	0.847722i	$-0.677973\pi$
$433$	9.24045	−	22.3084i	0.444068	−	1.07207i	0.974508	−	0.224352i	$-0.0720265\pi$
$434$	−1.81404	+	0.238822i	−0.0870765	+	0.0114638i
$435$		0			0
$436$	1.25392	−	3.69392i	0.0600517	−	0.176906i
$437$	0.127812	+	1.95004i	0.00611410	+	0.0932831i
$438$		0			0
$439$	−12.2201	−	35.9991i	−0.583231	−	1.71814i	−0.689952	−	0.723855i	$-0.742368\pi$
$439$	−12.2201	−	35.9991i	−0.583231	−	1.71814i	0.106720	−	0.994289i	$-0.465965\pi$
$440$	−1.98717	+	0.823114i	−0.0947347	+	0.0392404i
$441$		0			0
$442$	−39.6244	+	35.5619i	−1.88474	+	1.69151i
$443$	33.1913	−	19.1630i	1.57697	−	0.910462i	0.581687	−	0.813413i	$-0.302393\pi$
$443$	33.1913	−	19.1630i	1.57697	−	0.910462i	0.995280	−	0.0970494i	$-0.0309405\pi$
$444$		0			0
$445$	−1.28404	−	1.12607i	−0.0608692	−	0.0533808i
$446$	35.6520	−	9.55292i	1.68817	−	0.452344i
$447$		0			0
$448$	−5.89770	+	5.17214i	−0.278640	+	0.244361i
$449$	−8.96395	+	13.4155i	−0.423035	+	0.633116i	−0.980369	−	0.197172i	$-0.936824\pi$
$449$	−8.96395	+	13.4155i	−0.423035	+	0.633116i	0.557334	+	0.830288i	$0.311824\pi$
$450$		0			0
$451$	−6.32341	−	2.61924i	−0.297758	−	0.123335i
$452$	−1.16610	+	17.7912i	−0.0548487	+	0.836829i
$453$		0			0
$454$	−42.5825	+	2.79100i	−1.99849	+	0.130988i
$455$	0.521903	+	1.94777i	0.0244672	+	0.0913127i
$456$		0			0
$457$	11.9497	−	15.5731i	0.558983	−	0.728480i	−0.425306	−	0.905050i	$-0.639833\pi$
$457$	11.9497	−	15.5731i	0.558983	−	0.728480i	0.984288	+	0.176569i	$0.0565000\pi$
$458$	−19.0353			−0.889461
$459$		0			0
$460$	−1.00997			−0.0470901
$461$	8.16054	−	10.6350i	0.380074	−	0.495322i	−0.563669	−	0.826000i	$-0.690611\pi$
$461$	8.16054	−	10.6350i	0.380074	−	0.495322i	0.943744	+	0.330678i	$0.107277\pi$
$462$		0			0
$463$	0.244877	+	0.913894i	0.0113804	+	0.0424722i	0.971383	−	0.237520i	$-0.0763346\pi$
$463$	0.244877	+	0.913894i	0.0113804	+	0.0424722i	−0.960002	+	0.279993i	$0.909668\pi$
$464$	15.9830	−	1.04758i	0.741992	−	0.0486327i
$465$		0			0
$466$	2.89705	−	44.2004i	0.134203	−	2.04754i
$467$	−27.8933	−	11.5538i	−1.29075	−	0.534644i	−0.371538	−	0.928418i	$-0.621169\pi$
$467$	−27.8933	−	11.5538i	−1.29075	−	0.534644i	−0.919208	+	0.393773i	$0.871169\pi$
$468$		0			0
$469$	−4.20304	+	6.29029i	−0.194078	+	0.290459i
$470$	10.7541	−	9.43107i	0.496049	−	0.435023i
$471$		0			0
$472$	35.5018	−	9.51269i	1.63410	−	0.437857i
$473$	−2.25928	−	1.98134i	−0.103882	−	0.0911021i
$474$		0			0
$475$	15.0080	−	8.66488i	0.688614	−	0.397572i
$476$	11.1043	+	2.83931i	0.508966	+	0.130139i
$477$		0			0
$478$	38.3434	−	15.8823i	1.75379	−	0.726442i
$479$	−6.91907	−	20.3829i	−0.316140	−	0.931319i	−0.982593	−	0.185772i	$-0.940521\pi$
$479$	−6.91907	−	20.3829i	−0.316140	−	0.931319i	0.666453	−	0.745547i	$-0.267812\pi$
$480$		0			0
$481$	3.99046	+	60.8827i	0.181949	+	2.77601i
$482$	9.57968	−	28.2208i	0.436342	−	1.28542i
$483$		0			0
$484$	36.9620	−	4.86614i	1.68009	−	0.221188i
$485$	−3.07397	+	7.42122i	−0.139582	+	0.336980i
$486$		0			0
$487$	−9.83269	+	1.95584i	−0.445562	+	0.0886277i	−0.412772	−	0.910835i	$-0.635439\pi$
$487$	−9.83269	+	1.95584i	−0.445562	+	0.0886277i	−0.0327900	+	0.999462i	$0.510439\pi$
$488$	23.8861	+	11.7793i	1.08127	+	0.533226i
$489$		0			0
$490$	−5.13650	+	5.85705i	−0.232043	+	0.264595i
$491$	−0.564476	+	4.28762i	−0.0254744	+	0.193498i	−0.999450	−	0.0331544i	$-0.989445\pi$
$491$	−0.564476	+	4.28762i	−0.0254744	+	0.193498i	0.973976	+	0.226652i	$0.0727780\pi$
$492$		0			0
$493$	16.1319	+	20.5316i	0.726545	+	0.924697i
$494$			47.1523i			2.12148i
$495$		0			0
$496$	0.507349	−	2.55062i	0.0227807	−	0.114526i
$497$	−0.822746	+	3.07053i	−0.0369052	+	0.137732i
$498$		0			0
$499$	−22.1611	−	7.52269i	−0.992069	−	0.336762i	−0.222226	−	0.974995i	$-0.571332\pi$
$499$	−22.1611	−	7.52269i	−0.992069	−	0.336762i	−0.769843	+	0.638233i	$0.779665\pi$
$500$	8.13457	+	16.4953i	0.363789	+	0.737691i
$501$		0			0
$502$	5.57367	+	42.3362i	0.248765	+	1.88956i
$503$	9.17711	+	6.13195i	0.409187	+	0.273410i	0.743082	−	0.669200i	$-0.233363\pi$
$503$	9.17711	+	6.13195i	0.409187	+	0.273410i	−0.333895	+	0.942610i	$0.608363\pi$
$504$		0			0
$505$	3.66298	+	5.48204i	0.163001	+	0.243948i
$506$	−1.26491	−	0.338931i	−0.0562320	−	0.0150673i
$507$		0			0
$508$	27.8839	+	3.67099i	1.23715	+	0.162874i
$509$	13.6706	−	23.6782i	0.605939	−	1.04952i	−0.385963	−	0.922514i	$-0.626131\pi$
$509$	13.6706	−	23.6782i	0.605939	−	1.04952i	0.991902	−	0.127003i	$-0.0405358\pi$
$510$		0			0
$511$	−1.18523	−	2.05289i	−0.0524317	−	0.0908144i
$512$	−10.3147	−	24.9019i	−0.455850	−	1.10052i
$513$		0			0
$514$	−18.9939	+	18.9939i	−0.837783	+	0.837783i
$515$	−1.44449	+	2.92914i	−0.0636520	+	0.129073i
$516$		0			0
$517$	10.8419	−	5.34662i	0.476825	−	0.235144i
$518$	15.9867	−	12.2671i	0.702417	−	0.538983i
$519$		0			0
$520$	−11.3269	−	0.742402i	−0.496716	−	0.0325565i
$521$	0.254038	+	1.27713i	0.0111296	+	0.0559523i	0.985951	−	0.167035i	$-0.0534192\pi$
$521$	0.254038	+	1.27713i	0.0111296	+	0.0559523i	−0.974821	+	0.222987i	$0.928419\pi$
$522$		0			0
$523$	−4.98904	−	4.98904i	−0.218155	−	0.218155i	0.589565	−	0.807721i	$-0.299299\pi$
$523$	−4.98904	−	4.98904i	−0.218155	−	0.218155i	−0.807721	+	0.589565i	$0.799299\pi$
$524$	−15.6021	+	5.29621i	−0.681582	+	0.231366i
$525$		0			0
$526$	−34.6994	−	20.0337i	−1.51297	−	0.873511i
$527$	3.89785	−	1.66717i	0.169793	−	0.0726230i
$528$		0			0
$529$	18.0199	+	13.8271i	0.783474	+	0.601180i
$530$	−10.2373	−	2.03632i	−0.444680	−	0.0884523i
$531$		0			0
$532$	8.43990	−	5.63936i	0.365916	−	0.244497i
$533$	−23.8161	−	27.1570i	−1.03159	−	1.17630i
$534$		0			0
$535$	−4.52896	−	5.90226i	−0.195804	−	0.255177i
$536$	−25.9250	−	33.7861i	−1.11979	−	1.45934i
$537$		0			0
$538$	15.2149	+	17.3493i	0.655961	+	0.747981i
$539$	−5.47426	+	3.65778i	−0.235793	+	0.157552i
$540$		0			0
$541$	40.2772	+	8.01163i	1.73165	+	0.344447i	0.957474	−	0.288521i	$-0.0931634\pi$
$541$	40.2772	+	8.01163i	1.73165	+	0.344447i	0.774178	+	0.632968i	$0.218163\pi$
$542$	41.0374	+	31.4891i	1.76271	+	1.35257i
$543$		0			0
$544$	5.17228	−	7.93643i	0.221760	−	0.340271i
$545$	0.454827	+	0.262594i	0.0194826	+	0.0112483i
$546$		0			0
$547$	34.7372	−	11.7917i	1.48526	−	0.504176i	0.543191	−	0.839609i	$-0.317216\pi$
$547$	34.7372	−	11.7917i	1.48526	−	0.504176i	0.942064	+	0.335433i	$0.108883\pi$
$548$	16.7116	+	16.7116i	0.713883	+	0.713883i
$549$		0			0
$550$	2.26552	+	11.3896i	0.0966022	+	0.485652i
$551$	23.0749	+	1.51241i	0.983023	+	0.0644307i
$552$		0			0
$553$	−6.10085	+	4.68135i	−0.259435	+	0.199071i
$554$	55.1984	−	27.2209i	2.34516	−	1.15650i
$555$		0			0
$556$	25.0929	−	50.8833i	1.06417	−	2.15793i
$557$	−4.48661	+	4.48661i	−0.190104	+	0.190104i	−0.795741	−	0.605637i	$-0.792918\pi$
$557$	−4.48661	+	4.48661i	−0.190104	+	0.190104i	0.605637	+	0.795741i	$0.292918\pi$
$558$		0			0
$559$	−6.06884	−	14.6515i	−0.256685	−	0.619692i
$560$	0.473288	+	0.819760i	0.0200001	+	0.0346412i
$561$		0			0
$562$	13.9830	−	24.2193i	0.589838	−	1.02163i
$563$	−18.8368	−	2.47992i	−0.793878	−	0.104516i	−0.277330	−	0.960775i	$-0.589450\pi$
$563$	−18.8368	−	2.47992i	−0.793878	−	0.104516i	−0.516547	+	0.856259i	$0.672783\pi$
$564$		0			0
$565$	−2.31861	−	0.621268i	−0.0975445	−	0.0261370i
$566$	1.45597	+	2.17901i	0.0611989	+	0.0915906i
$567$		0			0
$568$	−14.8786	−	9.94159i	−0.624294	−	0.417140i
$569$	2.50333	+	19.0147i	0.104945	+	0.797138i	0.960275	+	0.279055i	$0.0900210\pi$
$569$	2.50333	+	19.0147i	0.104945	+	0.797138i	−0.855330	+	0.518084i	$0.826646\pi$
$570$		0			0
$571$	−12.4378	−	25.2214i	−0.520507	−	1.05548i	−0.985422	−	0.170128i	$-0.945582\pi$
$571$	−12.4378	−	25.2214i	−0.520507	−	1.05548i	0.464915	−	0.885355i	$-0.346085\pi$
$572$	−19.5021	−	6.62006i	−0.815422	−	0.276799i
$573$		0			0
$574$	−3.08760	+	11.5231i	−0.128874	+	0.480965i
$575$	−0.495519	+	2.49114i	−0.0206646	+	0.103888i
$576$		0			0
$577$		−	44.0005i		−	1.83176i	−0.401449	−	0.915881i	$-0.631493\pi$
$577$		−	44.0005i		−	1.83176i	0.401449	−	0.915881i	$-0.368507\pi$
$578$	−40.7324	+	0.934513i	−1.69424	+	0.0388706i
$579$		0			0
$580$	−1.55992	+	11.8488i	−0.0647722	+	0.491993i
$581$	−0.635500	+	0.724648i	−0.0263650	+	0.0300635i
$582$		0			0
$583$	−7.91166	−	3.90160i	−0.327667	−	0.161588i
$584$	13.0875	−	2.60326i	0.541564	−	0.107724i
$585$		0			0
$586$	2.16615	−	5.22955i	0.0894828	−	0.216031i
$587$	−10.6266	+	1.39901i	−0.438605	+	0.0577434i	−0.346596	−	0.938015i	$-0.612662\pi$
$587$	−10.6266	+	1.39901i	−0.438605	+	0.0577434i	−0.0920095	+	0.995758i	$0.529329\pi$
$588$		0			0
$589$	1.20685	−	3.55525i	0.0497272	−	0.146492i
$590$	0.694782	+	10.6003i	0.0286037	+	0.436408i
$591$		0			0
$592$	9.20632	+	27.1210i	0.378378	+	1.11466i
$593$	−17.9488	+	7.43464i	−0.737069	+	0.305304i	−0.719453	−	0.694541i	$-0.755608\pi$
$593$	−17.9488	+	7.43464i	−0.737069	+	0.305304i	−0.0176157	+	0.999845i	$0.505608\pi$
$594$		0			0
$595$	−0.666573	+	1.39169i	−0.0273268	+	0.0570537i
$596$	23.9969	−	13.8546i	0.982953	−	0.567508i
$597$		0			0
$598$	−5.19590	−	4.55668i	−0.212476	−	0.186337i
$599$	−15.6130	+	4.18348i	−0.637929	+	0.170932i	−0.563265	−	0.826276i	$-0.690455\pi$
$599$	−15.6130	+	4.18348i	−0.637929	+	0.170932i	−0.0746637	+	0.997209i	$0.523788\pi$
$600$		0			0
$601$	−13.0141	+	11.4131i	−0.530858	+	0.465550i	−0.882319	−	0.470653i	$-0.844019\pi$
$601$	−13.0141	+	11.4131i	−0.530858	+	0.465550i	0.351460	+	0.936203i	$0.385685\pi$
$602$	−2.90987	+	4.35493i	−0.118598	+	0.177494i
$603$		0			0
$604$	8.49941	+	3.52057i	0.345836	+	0.143250i
$605$	−0.328270	+	5.00843i	−0.0133461	+	0.203622i
$606$		0			0
$607$	−5.60520	+	0.367384i	−0.227508	+	0.0149117i	−0.178731	−	0.983898i	$-0.557199\pi$
$607$	−5.60520	+	0.367384i	−0.227508	+	0.0149117i	−0.0487772	+	0.998810i	$0.515532\pi$
$608$	−2.17137	−	8.10367i	−0.0880607	−	0.328647i
$609$		0			0
$610$	−4.68603	+	6.10695i	−0.189732	+	0.247263i
$611$	63.7961			2.58091
$612$		0			0
$613$	−24.3856			−0.984927			−0.492463	−	0.870333i	$-0.663903\pi$
$613$	−24.3856			−0.984927			−0.492463	+	0.870333i	$0.663903\pi$
$614$	45.9451	−	59.8768i	1.85419	−	2.41643i
$615$		0			0
$616$	0.820033	+	3.06040i	0.0330401	+	0.123307i
$617$	−18.3824	+	1.20485i	−0.740047	+	0.0485053i	−0.430764	−	0.902465i	$-0.641756\pi$
$617$	−18.3824	+	1.20485i	−0.740047	+	0.0485053i	−0.309283	+	0.950970i	$0.600089\pi$
$618$		0			0
$619$	−0.609409	+	9.29778i	−0.0244942	+	0.373709i	0.967961	+	0.251101i	$0.0807926\pi$
$619$	−0.609409	+	9.29778i	−0.0244942	+	0.373709i	−0.992455	+	0.122608i	$0.960874\pi$
$620$	1.79268	+	0.742552i	0.0719957	+	0.0298216i
$621$		0			0
$622$	−15.0115	+	22.4664i	−0.601908	+	0.900819i
$623$	−1.89144	+	1.65875i	−0.0757789	+	0.0664563i
$624$		0			0
$625$	20.5293	−	5.50082i	0.821173	−	0.220033i
$626$	−15.1604	−	13.2953i	−0.605932	−	0.531388i
$627$		0			0
$628$	−31.0772	+	17.9424i	−1.24011	+	0.715981i
$629$	−27.9962	+	37.3651i	−1.11628	+	1.48984i
$630$		0			0
$631$	−5.45994	+	2.26158i	−0.217357	+	0.0900321i	−0.488705	−	0.872449i	$-0.662531\pi$
$631$	−5.45994	+	2.26158i	−0.217357	+	0.0900321i	0.271348	+	0.962481i	$0.412531\pi$
$632$	−13.9146	−	40.9911i	−0.553493	−	1.63054i
$633$		0			0
$634$	−0.202904	−	3.09572i	−0.00805836	−	0.122947i
$635$	−1.21711	+	3.58550i	−0.0482997	+	0.142286i
$636$		0			0
$637$	−34.4483	+	4.53521i	−1.36489	+	0.179692i
$638$	−5.92994	+	14.3161i	−0.234769	+	0.566782i
$639$		0			0
$640$	10.2459	−	2.03804i	0.405006	−	0.0805607i
$641$	14.0975	+	6.95213i	0.556819	+	0.274593i	0.698849	−	0.715270i	$-0.253696\pi$
$641$	14.0975	+	6.95213i	0.556819	+	0.274593i	−0.142030	+	0.989862i	$0.545363\pi$
$642$		0			0
$643$	−21.2118	+	24.1874i	−0.836512	+	0.953859i	−0.999463	−	0.0327755i	$-0.989565\pi$
$643$	−21.2118	+	24.1874i	−0.836512	+	0.953859i	0.162951	+	0.986634i	$0.447899\pi$
$644$	−0.194188	+	1.47500i	−0.00765206	+	0.0581232i
$645$		0			0
$646$	−23.4784	+	27.3996i	−0.923743	+	1.07802i
$647$		−	22.2315i		−	0.874010i	−0.899459	−	0.437005i	$-0.856039\pi$
$647$		−	22.2315i		−	0.874010i	0.899459	−	0.437005i	$-0.143961\pi$
$648$		0			0
$649$	−1.75150	+	8.80540i	−0.0687525	+	0.345642i
$650$	−15.8617	+	59.1967i	−0.622147	+	2.32188i
$651$		0			0
$652$	−23.1568	−	7.86066i	−0.906889	−	0.307847i
$653$	1.60076	+	3.24603i	0.0626428	+	0.127027i	0.925942	−	0.377665i	$-0.123273\pi$
$653$	1.60076	+	3.24603i	0.0626428	+	0.127027i	−0.863300	+	0.504692i	$0.831606\pi$
$654$		0			0
$655$	−0.289541	−	2.19928i	−0.0113133	−	0.0859331i
$656$	−14.0983	−	9.42016i	−0.550445	−	0.367795i
$657$		0			0
$658$	−11.7058	−	17.5190i	−0.456340	−	0.682961i
$659$	6.95540	+	1.86369i	0.270944	+	0.0725992i	0.391733	−	0.920079i	$-0.371876\pi$
$659$	6.95540	+	1.86369i	0.270944	+	0.0725992i	−0.120789	+	0.992678i	$0.538542\pi$
$660$		0			0
$661$	24.8952	+	3.27751i	0.968310	+	0.127480i	0.598060	−	0.801452i	$-0.295939\pi$
$661$	24.8952	+	3.27751i	0.968310	+	0.127480i	0.370250	+	0.928932i	$0.379272\pi$
$662$	7.95420	−	13.7771i	0.309149	−	0.535461i
$663$		0			0
$664$	−2.71281	−	4.69873i	−0.105277	−	0.182346i
$665$	0.522970	+	1.26256i	0.0202799	+	0.0489600i
$666$		0			0
$667$	−2.39656	+	2.39656i	−0.0927951	+	0.0927951i
$668$	−6.75529	+	13.6984i	−0.261370	+	0.530006i
$669$		0			0
$670$	11.0394	−	5.44403i	0.426489	−	0.210321i
$671$	−5.16119	+	3.96032i	−0.199246	+	0.152886i
$672$		0			0
$673$	−31.5469	−	2.06770i	−1.21605	−	0.0797038i	−0.556163	−	0.831073i	$-0.687727\pi$
$673$	−31.5469	−	2.06770i	−1.21605	−	0.0797038i	−0.659882	+	0.751369i	$0.729394\pi$
$674$	−3.53086	−	17.7508i	−0.136004	−	0.683737i
$675$		0			0
$676$	−42.4386	−	42.4386i	−1.63225	−	1.63225i
$677$	38.8925	−	13.2022i	1.49476	−	0.507402i	0.549999	−	0.835165i	$-0.314628\pi$
$677$	38.8925	−	13.2022i	1.49476	−	0.507402i	0.944760	+	0.327763i	$0.106295\pi$
$678$		0			0
$679$	10.2472	+	5.91623i	0.393252	+	0.227044i
$680$	−6.21223	−	6.07134i	−0.238228	−	0.232825i
$681$		0			0
$682$	1.99600	+	1.53158i	0.0764307	+	0.0586473i
$683$	−37.3073	−	7.42089i	−1.42753	−	0.283953i	−0.579961	−	0.814644i	$-0.696932\pi$
$683$	−37.3073	−	7.42089i	−1.42753	−	0.283953i	−0.847565	+	0.530692i	$0.821932\pi$
$684$		0			0
$685$	−2.64560	+	1.76774i	−0.101083	+	0.0675417i
$686$	15.7794	+	17.9929i	0.602459	+	0.686973i
$687$		0			0
$688$	−4.53186	−	5.90603i	−0.172775	−	0.225165i
$689$	−28.3403	−	36.9338i	−1.07968	−	1.40707i
$690$		0			0
$691$	−0.695421	−	0.792975i	−0.0264550	−	0.0301662i	0.738461	−	0.674296i	$-0.235553\pi$
$691$	−0.695421	−	0.792975i	−0.0264550	−	0.0301662i	−0.764916	+	0.644130i	$0.777220\pi$
$692$	25.6274	−	17.1237i	0.974207	−	0.650944i
$693$		0			0
$694$	−64.4715	−	12.8242i	−2.44731	−	0.486799i
$695$	6.05979	+	4.64984i	0.229861	+	0.176378i
$696$		0			0
$697$	−0.317018	−	27.6392i	−0.0120079	−	1.04691i
$698$	22.5172	+	13.0003i	0.852289	+	0.492069i
$699$		0			0
$700$	12.4928	−	4.24073i	0.472183	−	0.160285i
$701$	13.4241	+	13.4241i	0.507022	+	0.507022i	0.913611	−	0.406589i	$-0.133282\pi$
$701$	13.4241	+	13.4241i	0.507022	+	0.507022i	−0.406589	+	0.913611i	$0.633282\pi$
$702$		0			0
$703$	8.06685	+	40.5548i	0.304247	+	1.52955i
$704$	10.7632	+	0.705458i	0.405654	+	0.0265880i
$705$		0			0
$706$	−13.4260	+	10.3021i	−0.505294	+	0.387726i
$707$	8.71047	−	4.29553i	0.327591	−	0.161550i
$708$		0			0
$709$	−8.05113	+	16.3261i	−0.302367	+	0.613139i	−0.994033	−	0.109078i	$-0.965210\pi$
$709$	−8.05113	+	16.3261i	−0.302367	+	0.613139i	0.691666	+	0.722217i	$0.256877\pi$
$710$	3.65717	−	3.65717i	0.137251	−	0.137251i
$711$		0			0
$712$	−5.41943	−	13.0837i	−0.203102	−	0.490331i
$713$	0.275141	+	0.476558i	0.0103041	+	0.0178472i
$714$		0			0
$715$	1.38637	−	2.40126i	0.0518473	−	0.0898021i
$716$	−44.0796	−	5.80319i	−1.64733	−	0.216876i
$717$		0			0
$718$	−8.89154	−	2.38248i	−0.331829	−	0.0889134i
$719$	13.0787	+	19.5737i	0.487754	+	0.729976i	0.990955	−	0.134193i	$-0.0428444\pi$
$719$	13.0787	+	19.5737i	0.487754	+	0.729976i	−0.503201	+	0.864170i	$0.667844\pi$
$720$		0			0
$721$	4.00010	+	2.67278i	0.148971	+	0.0995395i
$722$	−1.77265	−	13.4646i	−0.0659713	−	0.501101i
$723$		0			0
$724$	−29.6697	−	60.1642i	−1.10267	−	2.23599i
$725$	28.4603	+	9.66095i	1.05699	+	0.358799i
$726$		0			0
$727$	1.11206	−	4.15025i	0.0412439	−	0.153924i	−0.942233	−	0.334958i	$-0.891278\pi$
$727$	1.11206	−	4.15025i	0.0412439	−	0.153924i	0.983477	+	0.181034i	$0.0579444\pi$
$728$	−3.26206	+	16.3995i	−0.120900	+	0.607804i
$729$		0			0
$730$			3.85678i			0.142746i
$731$	3.76883	−	11.5356i	0.139395	−	0.426660i
$732$		0			0
$733$	1.40148	−	10.6453i	0.0517647	−	0.393192i	−0.945875	−	0.324530i	$-0.894794\pi$
$733$	1.40148	−	10.6453i	0.0517647	−	0.393192i	0.997640	−	0.0686615i	$-0.0218729\pi$
$734$	−23.5365	+	26.8383i	−0.868749	+	0.990618i
$735$		0			0
$736$	1.10281	+	0.543847i	0.0406502	+	0.0200464i
$737$	10.2027	−	2.02944i	0.375820	−	0.0747553i
$738$		0			0
$739$	6.20725	−	14.9856i	0.228337	−	0.551255i	−0.767638	−	0.640884i	$-0.778568\pi$
$739$	6.20725	−	14.9856i	0.228337	−	0.551255i	0.995975	+	0.0896286i	$0.0285680\pi$
$740$	−21.1871	+	2.78933i	−0.778853	+	0.102538i
$741$		0			0
$742$	−4.94226	+	14.5594i	−0.181436	+	0.534493i
$743$	1.12085	+	17.1009i	0.0411201	+	0.627372i	0.967832	+	0.251598i	$0.0809562\pi$
$743$	1.12085	+	17.1009i	0.0411201	+	0.627372i	−0.926712	+	0.375773i	$0.877377\pi$
$744$		0			0
$745$	1.19914	+	3.53256i	0.0439332	+	0.129423i
$746$	9.89937	−	4.10045i	0.362442	−	0.150128i
$747$		0			0
$748$	−8.03609	−	13.5574i	−0.293829	−	0.495708i
$749$	−9.49068	+	5.47945i	−0.346782	+	0.200215i
$750$		0			0
$751$	−5.01816	−	4.40081i	−0.183115	−	0.160588i	0.562881	−	0.826538i	$-0.309693\pi$
$751$	−5.01816	−	4.40081i	−0.183115	−	0.160588i	−0.745996	+	0.665950i	$0.768026\pi$
$752$	28.9268	−	7.75091i	1.05485	−	0.282647i
$753$		0			0
$754$	−61.4833	+	53.9194i	−2.23909	+	1.96363i
$755$	−0.688111	+	1.02983i	−0.0250429	+	0.0374794i
$756$		0			0
$757$	9.34496	+	3.87081i	0.339648	+	0.140687i	0.545987	−	0.837794i	$-0.316155\pi$
$757$	9.34496	+	3.87081i	0.339648	+	0.140687i	−0.206339	+	0.978481i	$0.566155\pi$
$758$	2.26999	−	34.6334i	0.0824499	−	1.25794i
$759$		0			0
$760$	−7.67633	+	0.503134i	−0.278450	+	0.0182506i
$761$	3.16811	+	11.8235i	0.114844	+	0.428603i	0.999275	−	0.0380675i	$-0.0121202\pi$
$761$	3.16811	+	11.8235i	0.114844	+	0.428603i	−0.884431	+	0.466670i	$0.845454\pi$
$762$		0			0
$763$	0.470953	−	0.613757i	0.0170496	−	0.0222195i
$764$	−80.3714			−2.90774
$765$		0			0
$766$	3.53617			0.127767
$767$	−28.8432	+	37.5892i	−1.04147	+	1.35727i
$768$		0			0
$769$	5.80750	+	21.6739i	0.209424	+	0.781581i	0.988055	+	0.154099i	$0.0492476\pi$
$769$	5.80750	+	21.6739i	0.209424	+	0.781581i	−0.778631	+	0.627482i	$0.784086\pi$
$770$	−0.913791	+	0.0598930i	−0.0329307	+	0.00215839i
$771$		0			0
$772$	2.20498	−	33.6414i	0.0793588	−	1.21078i
$773$	29.2000	+	12.0950i	1.05025	+	0.435029i	0.839982	−	0.542615i	$-0.182566\pi$
$773$	29.2000	+	12.0950i	1.05025	+	0.435029i	0.210270	+	0.977643i	$0.432566\pi$
$774$		0			0
$775$	2.71108	−	4.05742i	0.0973848	−	0.145747i
$776$	−50.0781	+	43.9173i	−1.79770	+	1.57654i
$777$		0			0
$778$	88.3537	−	23.6743i	3.16763	−	0.848765i
$779$	−18.4046	−	16.1404i	−0.659412	−	0.578289i
$780$		0			0
$781$	3.78544	−	2.18552i	0.135454	−	0.0782041i
$782$	−0.750379	−	5.23500i	−0.0268335	−	0.187203i
$783$		0			0
$784$	−15.0688	+	6.24169i	−0.538170	+	0.222917i
$785$	−1.55295	−	4.57483i	−0.0554270	−	0.163283i
$786$		0			0
$787$	−1.88137	−	28.7041i	−0.0670635	−	1.02319i	−0.890265	−	0.455443i	$-0.849481\pi$
$787$	−1.88137	−	28.7041i	−0.0670635	−	1.02319i	0.823202	−	0.567749i	$-0.192186\pi$
$788$	21.9294	−	64.6020i	0.781204	−	2.30135i
$789$		0			0
$790$	12.4046	−	1.63310i	0.441336	−	0.0581030i
$791$	−1.35312	+	3.26673i	−0.0481115	+	0.116152i
$792$		0			0
$793$	−33.6727	+	6.69791i	−1.19575	+	0.237850i
$794$	11.9069	+	5.87183i	0.422560	+	0.208384i
$795$		0			0
$796$	62.1947	−	70.9195i	2.20443	−	2.51368i
$797$	3.32560	−	25.2604i	0.117799	−	0.894770i	−0.825866	−	0.563866i	$-0.809313\pi$
$797$	3.32560	−	25.2604i	0.117799	−	0.894770i	0.943665	−	0.330903i	$-0.107353\pi$
$798$		0			0
$799$	37.0710	+	31.7657i	1.31148	+	1.12379i
$800$		−	10.9041i		−	0.385517i
$801$		0			0
$802$	9.58303	−	48.1771i	0.338389	−	1.70119i
$803$	−0.843619	+	3.14843i	−0.0297707	+	0.111106i
$804$		0			0
$805$	−0.189665	−	0.0643827i	−0.00668482	−	0.00226919i
$806$	5.87246	+	11.9082i	0.206848	+	0.419447i
$807$		0			0
$808$	7.13602	+	54.2034i	0.251044	+	1.90687i
$809$	−1.47986	−	0.988813i	−0.0520292	−	0.0347648i	0.529284	−	0.848445i	$-0.322461\pi$
$809$	−1.47986	−	0.988813i	−0.0520292	−	0.0347648i	−0.581313	+	0.813680i	$0.697461\pi$
$810$		0			0
$811$	27.6326	+	41.3552i	0.970314	+	1.45218i	0.890295	+	0.455383i	$0.150498\pi$
$811$	27.6326	+	41.3552i	0.970314	+	1.45218i	0.0800181	+	0.996793i	$0.474502\pi$
$812$	17.0045	+	4.55634i	0.596740	+	0.159896i
$813$		0			0
$814$	−27.4712	−	3.61665i	−0.962865	−	0.126764i
$815$	1.64618	−	2.85126i	0.0576630	−	0.0998752i
$816$		0			0
$817$	−5.37378	−	9.30767i	−0.188005	−	0.325634i
$818$	21.4077	+	51.6828i	0.748504	+	1.80705i
$819$		0			0
$820$	8.94581	−	8.94581i	0.312401	−	0.312401i
$821$	16.3205	−	33.0947i	0.569589	−	1.15501i	−0.401404	−	0.915901i	$-0.631477\pi$
$821$	16.3205	−	33.0947i	0.569589	−	1.15501i	0.970992	−	0.239111i	$-0.0768558\pi$
$822$		0			0
$823$	9.90115	−	4.88271i	0.345132	−	0.170200i	−0.261458	−	0.965215i	$-0.584203\pi$
$823$	9.90115	−	4.88271i	0.345132	−	0.170200i	0.606591	+	0.795014i	$0.292537\pi$
$824$	−21.4852	+	16.4861i	−0.748471	+	0.574322i
$825$		0			0
$826$	15.6147	+	1.02344i	0.543305	+	0.0356101i
$827$	4.01743	+	20.1970i	0.139700	+	0.702318i	0.985616	+	0.169002i	$0.0540543\pi$
$827$	4.01743	+	20.1970i	0.139700	+	0.702318i	−0.845916	+	0.533316i	$0.820946\pi$
$828$		0			0
$829$	−10.5506	−	10.5506i	−0.366437	−	0.366437i	0.499739	−	0.866176i	$-0.333429\pi$
$829$	−10.5506	−	10.5506i	−0.366437	−	0.366437i	−0.866176	+	0.499739i	$0.833429\pi$
$830$	1.48494	−	0.504071i	0.0515432	−	0.0174966i
$831$		0			0
$832$	49.2974	+	28.4619i	1.70908	+	0.986738i
$833$	−22.2757	−	14.5174i	−0.771806	−	0.502997i
$834$		0			0
$835$	−1.63137	−	1.25179i	−0.0564557	−	0.0433200i
$836$	−13.6893	−	2.72297i	−0.473454	−	0.0941758i
$837$		0			0
$838$	69.0128	−	46.1129i	2.38401	−	1.59294i
$839$	−14.6052	−	16.6541i	−0.504228	−	0.574962i	0.442593	−	0.896723i	$-0.354059\pi$
$839$	−14.6052	−	16.6541i	−0.504228	−	0.574962i	−0.946821	+	0.321761i	$0.895725\pi$
$840$		0			0
$841$	6.76031	+	8.81021i	0.233114	+	0.303800i
$842$	−4.41082	−	5.74829i	−0.152007	−	0.198099i
$843$		0			0
$844$	37.3058	+	42.5391i	1.28412	+	1.46425i
$845$	6.71844	−	4.48912i	0.231121	−	0.154430i
$846$		0			0
$847$	7.25139	+	1.44239i	0.249161	+	0.0495612i
$848$	−17.3375	−	13.3035i	−0.595372	−	0.456845i
$849$		0			0
$850$	−38.6926	+	26.5004i	−1.32714	+	0.908958i
$851$	−5.24846	−	3.03020i	−0.179915	−	0.103874i
$852$		0			0
$853$	−25.7146	+	8.72894i	−0.880452	+	0.298873i	−0.724817	−	0.688941i	$-0.758076\pi$
$853$	−25.7146	+	8.72894i	−0.880452	+	0.298873i	−0.155635	+	0.987815i	$0.549742\pi$
$854$	8.01784	+	8.01784i	0.274365	+	0.274365i
$855$		0			0
$856$	−12.0351	−	60.5046i	−0.411351	−	2.06800i
$857$	−33.3011	−	2.18267i	−1.13754	−	0.0745585i	−0.515033	−	0.857170i	$-0.672220\pi$
$857$	−33.3011	−	2.18267i	−1.13754	−	0.0745585i	−0.622510	+	0.782612i	$0.713887\pi$
$858$		0			0
$859$	−11.1148	+	8.52870i	−0.379233	+	0.290995i	−0.780735	−	0.624863i	$-0.785155\pi$
$859$	−11.1148	+	8.52870i	−0.379233	+	0.290995i	0.401502	+	0.915858i	$0.368488\pi$
$860$	4.98168	−	2.45669i	0.169874	−	0.0837725i
$861$		0			0
$862$	41.5082	−	84.1703i	1.41378	−	2.86685i
$863$	4.06464	−	4.06464i	0.138362	−	0.138362i	−0.634533	−	0.772895i	$-0.718808\pi$
$863$	4.06464	−	4.06464i	0.138362	−	0.138362i	0.772895	+	0.634533i	$0.218808\pi$
$864$		0			0
$865$	1.58798	+	3.83371i	0.0539928	+	0.130350i
$866$	28.9353	+	50.1175i	0.983263	+	1.70306i
$867$		0			0
$868$	1.42913	−	2.47533i	0.0485078	−	0.0840181i
$869$	10.4835	+	1.38018i	0.355630	+	0.0468196i
$870$		0			0
$871$	53.0279	+	14.2088i	1.79678	+	0.481446i
$872$	2.41945	+	3.62096i	0.0819329	+	0.122621i
$873$		0			0
$874$	−3.89427	−	2.60207i	−0.131726	−	0.0880163i
$875$	0.476088	+	3.61625i	0.0160947	+	0.122251i
$876$		0			0
$877$	−2.88801	−	5.85631i	−0.0975213	−	0.197754i	0.842645	−	0.538469i	$-0.180997\pi$
$877$	−2.88801	−	5.85631i	−0.0975213	−	0.197754i	−0.940166	+	0.340716i	$0.889331\pi$
$878$	86.2774	+	29.2872i	2.91172	+	0.988396i
$879$		0			0
$880$	0.336874	−	1.25723i	0.0113560	−	0.0423813i
$881$	5.82712	−	29.2949i	0.196321	−	0.986971i	−0.749431	−	0.662082i	$-0.769673\pi$
$881$	5.82712	−	29.2949i	0.196321	−	0.986971i	0.945752	−	0.324889i	$-0.105327\pi$
$882$		0			0
$883$			49.5960i			1.66904i	0.550978	+	0.834520i	$0.314255\pi$
$883$			49.5960i			1.66904i	−0.550978	+	0.834520i	$0.685745\pi$
$884$	−6.39127	−	82.9268i	−0.214962	−	2.78913i
$885$		0			0
$886$	−11.9894	+	91.0683i	−0.402791	+	3.05950i
$887$	10.0838	−	11.4984i	0.338583	−	0.386079i	−0.557344	−	0.830282i	$-0.688180\pi$
$887$	10.0838	−	11.4984i	0.338583	−	0.386079i	0.895926	+	0.444202i	$0.146513\pi$
$888$		0			0
$889$	5.00239	+	2.46691i	0.167775	+	0.0827374i
$890$	4.01450	−	0.798533i	0.134566	−	0.0267669i
$891$		0			0
$892$	−22.0650	+	53.2696i	−0.738791	+	1.78360i
$893$	42.8653	−	5.64333i	1.43443	−	0.188847i
$894$		0			0
$895$	1.92404	−	5.66805i	0.0643137	−	0.189462i
$896$	−1.00645	−	15.3554i	−0.0336230	−	0.512988i
$897$		0			0
$898$	−12.4298	−	36.6170i	−0.414788	−	1.22193i
$899$	6.01584	−	2.49184i	0.200640	−	0.0831077i
$900$		0			0
$901$	1.92212	−	35.5731i	0.0640351	−	1.18511i
$902$	14.2060	−	8.20183i	0.473008	−	0.273091i
$903$		0			0
$904$	−14.9648	−	13.1238i	−0.497722	−	0.436490i
$905$	8.72364	−	2.33749i	0.289983	−	0.0777008i
$906$		0			0
$907$	−0.239945	+	0.210426i	−0.00796724	+	0.00698708i	−0.663320	−	0.748336i	$-0.730853\pi$
$907$	−0.239945	+	0.210426i	−0.00796724	+	0.00698708i	0.655353	+	0.755323i	$0.272520\pi$
$908$	37.0361	−	55.4284i	1.22909	−	1.83946i
$909$		0			0
$910$	−4.46492	−	1.84943i	−0.148011	−	0.0613080i
$911$	1.06415	−	16.2358i	0.0352569	−	0.537916i	−0.943300	−	0.331941i	$-0.892297\pi$
$911$	1.06415	−	16.2358i	0.0352569	−	0.537916i	0.978557	−	0.205975i	$-0.0660367\pi$
$912$		0			0
$913$	1.32247	−	0.0866795i	0.0437675	−	0.00286867i
$914$	12.1762	+	45.4421i	0.402752	+	1.50309i
$915$		0			0
$916$	18.1022	−	23.5912i	0.598113	−	0.779476i
$917$	−3.26759			−0.107905
$918$		0			0
$919$	−32.6543			−1.07716			−0.538582	−	0.842573i	$-0.681040\pi$
$919$	−32.6543			−1.07716			−0.538582	+	0.842573i	$0.681040\pi$
$920$	0.686380	−	0.894508i	0.0226293	−	0.0294910i
$921$		0			0
$922$	8.31521	+	31.0328i	0.273847	+	1.02201i
$923$	23.0184	−	1.50871i	0.757660	−	0.0496597i
$924$		0			0
$925$	−3.51494	+	53.6276i	−0.115570	+	1.76326i
$926$	−2.09494	−	0.867754i	−0.0688441	−	0.0285162i
$927$		0			0
$928$	8.08361	−	12.0980i	0.265357	−	0.397136i
$929$	−10.6468	+	9.33703i	−0.349312	+	0.306338i	−0.815964	−	0.578103i	$-0.803793\pi$
$929$	−10.6468	+	9.33703i	−0.349312	+	0.306338i	0.466652	+	0.884441i	$0.345460\pi$
$930$		0			0
$931$	−22.7451	+	6.09453i	−0.745440	+	0.199740i
$932$	52.0244	+	45.6241i	1.70411	+	1.49447i
$933$		0			0
$934$	62.6642	−	36.1792i	2.05044	−	1.18382i
$935$	2.00125	−	0.705032i	0.0654479	−	0.0230570i
$936$		0			0
$937$	−25.9564	+	10.7515i	−0.847959	+	0.351236i	−0.763987	−	0.645232i	$-0.776761\pi$
$937$	−25.9564	+	10.7515i	−0.847959	+	0.351236i	−0.0839723	+	0.996468i	$0.526761\pi$
$938$	−5.82812	−	17.1691i	−0.190295	−	0.560591i
$939$		0			0
$940$	1.46141	+	22.2967i	0.0476658	+	0.727239i
$941$	−1.79655	+	5.29248i	−0.0585660	+	0.172530i	−0.972276	−	0.233838i	$-0.924871\pi$
$941$	−1.79655	+	5.29248i	−0.0585660	+	0.172530i	0.913710	+	0.406368i	$0.133205\pi$
$942$		0			0
$943$	3.55715	−	0.468307i	0.115837	−	0.0152502i
$944$	−8.51135	+	20.5482i	−0.277021	+	0.668787i
$945$		0			0
$946$	7.06358	−	1.40503i	0.229657	−	0.0456816i
$947$	25.5947	+	12.6219i	0.831717	+	0.410158i	0.807728	−	0.589555i	$-0.200697\pi$
$947$	25.5947	+	12.6219i	0.831717	+	0.410158i	0.0239887	+	0.999712i	$0.492363\pi$
$948$		0			0
$949$	−11.3419	+	12.9329i	−0.368172	+	0.419820i
$950$	−5.42120	+	41.1781i	−0.175887	+	1.33599i
$951$		0			0
$952$	−10.0613	+	7.90525i	−0.326087	+	0.256210i
$953$		−	37.4674i		−	1.21369i	−0.794821	−	0.606844i	$-0.792435\pi$
$953$		−	37.4674i		−	1.21369i	0.794821	−	0.606844i	$-0.207565\pi$
$954$		0			0
$955$	2.11098	−	10.6126i	0.0683096	−	0.343416i
$956$	−16.7801	+	62.6243i	−0.542709	+	2.02542i
$957$		0			0
$958$	48.8508	+	16.5826i	1.57830	+	0.535760i
$959$	2.07300	+	4.20362i	0.0669406	+	0.135742i
$960$		0			0
$961$	3.90832	+	29.6866i	0.126075	+	0.957633i
$962$	−121.584	−	81.2398i	−3.92002	−	2.61927i
$963$		0			0
$964$	25.8651	+	38.7099i	0.833060	+	1.24676i
$965$	4.38425	+	1.17476i	0.141134	+	0.0378167i
$966$		0			0
$967$	4.60784	+	0.606634i	0.148178	+	0.0195080i	0.204250	−	0.978919i	$-0.434524\pi$
$967$	4.60784	+	0.606634i	0.148178	+	0.0195080i	−0.0560721	+	0.998427i	$0.517858\pi$
$968$	−20.8097	+	36.0434i	−0.668848	+	1.15848i
$969$		0			0
$970$	−9.62576	−	16.6723i	−0.309065	−	0.535316i
$971$	17.1196	+	41.3304i	0.549394	+	1.32636i	0.917930	+	0.396742i	$0.129859\pi$
$971$	17.1196	+	41.3304i	0.549394	+	1.32636i	−0.368536	+	0.929614i	$0.620141\pi$
$972$		0			0
$973$	7.95592	−	7.95592i	0.255055	−	0.255055i
$974$	10.6270	−	21.5494i	0.340510	−	0.690486i
$975$		0			0
$976$	−14.4543	+	7.12808i	−0.462671	+	0.228164i
$977$	−23.5464	+	18.0678i	−0.753317	+	0.578040i	−0.912436	−	0.409219i	$-0.865801\pi$
$977$	−23.5464	+	18.0678i	−0.753317	+	0.578040i	0.159120	+	0.987259i	$0.449134\pi$
$978$		0			0
$979$	3.45185	+	0.226246i	0.110322	+	0.00723086i
$980$	−2.37418	−	11.9358i	−0.0758404	−	0.381276i
$981$		0			0
$982$	−7.32889	−	7.32889i	−0.233874	−	0.233874i
$983$	−27.3926	+	9.29854i	−0.873688	+	0.296577i	−0.722035	−	0.691857i	$-0.756793\pi$
$983$	−27.3926	+	9.29854i	−0.873688	+	0.296577i	−0.151653	+	0.988434i	$0.548460\pi$
$984$		0			0
$985$	7.95436	+	4.59245i	0.253447	+	0.146328i
$986$	−62.5749	+	0.717727i	−1.99279	+	0.0228571i
$987$		0			0
$988$	−58.4378	−	44.8409i	−1.85915	−	1.42658i
$989$	1.54496	+	0.307311i	0.0491268	+	0.00977193i
$990$		0			0
$991$	−15.8269	+	10.5752i	−0.502759	+	0.335933i	−0.780951	−	0.624593i	$-0.785265\pi$
$991$	−15.8269	+	10.5752i	−0.502759	+	0.335933i	0.278191	+	0.960526i	$0.410265\pi$
$992$	−1.55762	−	1.77613i	−0.0494545	−	0.0563921i
$993$		0			0
$994$	−4.63790	−	6.04424i	−0.147105	−	0.191711i
$995$	7.73097	+	10.0752i	0.245088	+	0.319405i
$996$		0			0
$997$	−21.1273	−	24.0911i	−0.669108	−	0.762972i	0.313313	−	0.949650i	$-0.398561\pi$
$997$	−21.1273	−	24.0911i	−0.669108	−	0.762972i	−0.982421	+	0.186678i	$0.940228\pi$
$998$	46.6365	−	31.1615i	1.47625	−	0.986400i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.y.a.422.1		256
3.2	odd	2		153.2.s.a.14.16	yes	256
9.2	odd	6	inner	459.2.y.a.116.1		256
9.7	even	3		153.2.s.a.65.16	yes	256
17.11	odd	16	inner	459.2.y.a.368.1		256
51.11	even	16		153.2.s.a.113.16	yes	256
153.11	even	48	inner	459.2.y.a.62.1		256
153.79	odd	48		153.2.s.a.11.16	✓	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.16	✓	256	153.79	odd	48
153.2.s.a.14.16	yes	256	3.2	odd	2
153.2.s.a.65.16	yes	256	9.7	even	3
153.2.s.a.113.16	yes	256	51.11	even	16
459.2.y.a.62.1		256	153.11	even	48	inner
459.2.y.a.116.1		256	9.2	odd	6	inner
459.2.y.a.368.1		256	17.11	odd	16	inner
459.2.y.a.422.1		256	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.45899 + 1.90139i) q^{2} +(-0.969004 - 3.61637i) q^{4} +(0.502973 - 0.0329666i) q^{5} +(0.0485612 - 0.740900i) q^{7} +(3.86148 + 1.59948i) q^{8} +(-0.671150 + 1.00445i) q^{10} +(-0.767594 + 0.673162i) q^{11} +(-5.20440 + 1.39452i) q^{13} +(1.33789 + 1.17330i) q^{14} +(-2.19038 + 1.26462i) q^{16} +(-3.71857 - 1.78107i) q^{17} +(-3.37354 + 1.39737i) q^{19} +(-0.606603 - 1.78699i) q^{20} +(-0.160033 - 2.44163i) q^{22} +(0.172029 - 0.506782i) q^{23} +(-4.70533 + 0.619468i) q^{25} +(4.94165 - 11.9302i) q^{26} +(-2.72643 + 0.542320i) q^{28} +(-5.67976 - 2.80095i) q^{29} +(-0.677946 + 0.773049i) q^{31} +(-0.299892 + 2.27790i) q^{32} +(8.81188 - 4.47190i) q^{34} -0.374254i q^{35} +(2.20919 - 11.1064i) q^{37} +(2.26502 - 8.45317i) q^{38} +(1.99495 + 0.677194i) q^{40} +(2.96507 + 6.01257i) q^{41} +(0.384182 + 2.91815i) q^{43} +(3.17821 + 2.12361i) q^{44} +(0.712603 + 1.06649i) q^{46} +(-11.4370 - 3.06452i) q^{47} +(6.39354 + 0.841725i) q^{49} +(5.68718 - 9.85048i) q^{50} +(10.0862 + 17.4698i) q^{52} +(3.30651 + 7.98262i) q^{53} +(-0.363887 + 0.363887i) q^{55} +(1.37257 - 2.78330i) q^{56} +(13.6124 - 6.71290i) q^{58} +(6.97647 - 5.35323i) q^{59} +(6.35837 + 0.416750i) q^{61} +(-0.480754 - 2.41691i) q^{62} +(-7.47053 - 7.47053i) q^{64} +(-2.57170 + 0.872975i) q^{65} +(-8.82398 - 5.09452i) q^{67} +(-2.83771 + 15.1736i) q^{68} +(0.711604 + 0.546033i) q^{70} +(-4.19907 - 0.835247i) q^{71} +(2.65455 - 1.77371i) q^{73} +(17.8943 + 20.4046i) q^{74} +(8.32238 + 10.8459i) q^{76} +(0.461470 + 0.601400i) q^{77} +(-6.82883 - 7.78679i) q^{79} +(-1.06001 + 0.708279i) q^{80} +(-15.7583 - 3.13452i) q^{82} +(-1.02986 - 0.790239i) q^{83} +(-1.92906 - 0.773243i) q^{85} +(-6.10907 - 3.52707i) q^{86} +(-4.04075 + 1.37165i) q^{88} +(-2.39586 - 2.39586i) q^{89} +(0.780465 + 3.92366i) q^{91} +(-1.99941 - 0.131048i) q^{92} +(22.5133 - 17.2750i) q^{94} +(-1.65074 + 0.814053i) q^{95} +(-7.04839 + 14.2927i) q^{97} +(-10.9286 + 10.9286i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Introduction

L-functions

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