LMFDB - Embedded newform 648.2.t.a.397.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] 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("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, 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:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			397.4
Character	$\chi$	$=$	648.397
Dual form			648.2.t.a.253.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24359 + 0.673416i) q^{2} +(1.09302 - 1.67490i) q^{4} +(-1.55117 - 1.84861i) q^{5} +(-1.49685 + 0.544810i) q^{7} +(-0.231362 + 2.81895i) q^{8} +(3.17390 + 1.25433i) q^{10} +(0.102391 - 0.122025i) q^{11} +(3.39140 - 0.597995i) q^{13} +(1.49458 - 1.68552i) q^{14} +(-1.61061 - 3.66141i) q^{16} +(1.43581 + 2.48690i) q^{17} +(-3.75621 - 2.16865i) q^{19} +(-4.79171 + 0.577486i) q^{20} +(-0.0451590 + 0.220701i) q^{22} +(-2.14748 - 0.781619i) q^{23} +(-0.142997 + 0.810974i) q^{25} +(-3.81480 + 3.02748i) q^{26} +(-0.723589 + 3.10257i) q^{28} +(-8.60509 - 1.51731i) q^{29} +(-6.69129 - 2.43543i) q^{31} +(4.46858 + 3.46868i) q^{32} +(-3.46028 - 2.12578i) q^{34} +(3.32901 + 1.92201i) q^{35} +(-5.14590 + 2.97099i) q^{37} +(6.13158 + 0.167414i) q^{38} +(5.57002 - 3.94497i) q^{40} +(1.74706 + 9.90807i) q^{41} +(-7.59829 + 9.05529i) q^{43} +(-0.0924647 - 0.304872i) q^{44} +(3.19694 - 0.474136i) q^{46} +(-3.66367 + 1.33347i) q^{47} +(-3.41856 + 2.86851i) q^{49} +(-0.368294 - 1.10481i) q^{50} +(2.70529 - 6.33388i) q^{52} -9.80805i q^{53} -0.384404 q^{55} +(-1.18948 - 4.34560i) q^{56} +(11.7230 - 3.90790i) q^{58} +(-1.72220 - 2.05244i) q^{59} +(-0.492702 - 1.35369i) q^{61} +(9.96127 - 1.47735i) q^{62} +(-7.89294 - 1.30440i) q^{64} +(-6.36609 - 5.34178i) q^{65} +(0.225321 - 0.0397302i) q^{67} +(5.73470 + 0.313390i) q^{68} +(-5.43423 - 0.148374i) q^{70} +(-2.82317 - 4.88987i) q^{71} +(7.14574 - 12.3768i) q^{73} +(4.39867 - 7.16002i) q^{74} +(-7.73789 + 3.92091i) q^{76} +(-0.0867843 + 0.238438i) q^{77} +(-2.18269 + 12.3786i) q^{79} +(-4.27021 + 8.65685i) q^{80} +(-8.84487 - 11.1451i) q^{82} +(-11.1079 - 1.95862i) q^{83} +(2.37013 - 6.51187i) q^{85} +(3.35117 - 16.3779i) q^{86} +(0.320294 + 0.316868i) q^{88} +(3.73417 - 6.46777i) q^{89} +(-4.75063 + 2.74278i) q^{91} +(-3.65638 + 2.74250i) q^{92} +(3.65812 - 4.12546i) q^{94} +(1.81753 + 10.3077i) q^{95} +(5.17680 + 4.34385i) q^{97} +(2.31958 - 5.86936i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−1.24359	+	0.673416i	−0.879349	+	0.476177i
$2$	−1.24359	+	0.673416i	−0.879349	+	0.476177i
$3$		0			0
$3$		0			0
$4$	1.09302	−	1.67490i	0.546511	−	0.837452i
$5$	−1.55117	−	1.84861i	−0.693704	−	0.826724i	0.298095	−	0.954536i	$-0.403649\pi$
$5$	−1.55117	−	1.84861i	−0.693704	−	0.826724i	−0.991798	+	0.127812i	$0.959204\pi$
$6$		0			0
$7$	−1.49685	+	0.544810i	−0.565757	+	0.205919i	−0.609034	−	0.793144i	$-0.708443\pi$
$7$	−1.49685	+	0.544810i	−0.565757	+	0.205919i	0.0432765	+	0.999063i	$0.486220\pi$
$8$	−0.231362	+	2.81895i	−0.0817989	+	0.996649i
$9$		0			0
$10$	3.17390	+	1.25433i	1.00367	+	0.396653i
$11$	0.102391	−	0.122025i	0.0308722	−	0.0367920i	−0.750387	−	0.660998i	$-0.770133\pi$
$11$	0.102391	−	0.122025i	0.0308722	−	0.0367920i	0.781260	+	0.624206i	$0.214577\pi$
$12$		0			0
$13$	3.39140	−	0.597995i	0.940604	−	0.165854i	0.317735	−	0.948180i	$-0.397078\pi$
$13$	3.39140	−	0.597995i	0.940604	−	0.165854i	0.622869	+	0.782326i	$0.285967\pi$
$14$	1.49458	−	1.68552i	0.399445	−	0.450475i
$15$		0			0
$16$	−1.61061	−	3.66141i	−0.402651	−	0.915353i
$17$	1.43581	+	2.48690i	0.348236	+	0.603163i	0.985936	−	0.167122i	$-0.0534474\pi$
$17$	1.43581	+	2.48690i	0.348236	+	0.603163i	−0.637700	+	0.770285i	$0.720114\pi$
$18$		0			0
$19$	−3.75621	−	2.16865i	−0.861733	−	0.497522i	0.00285908	−	0.999996i	$-0.499090\pi$
$19$	−3.75621	−	2.16865i	−0.861733	−	0.497522i	−0.864592	+	0.502474i	$0.832423\pi$
$20$	−4.79171	+	0.577486i	−1.07146	+	0.129130i
$21$		0			0
$22$	−0.0451590	+	0.220701i	−0.00962792	+	0.0470537i
$23$	−2.14748	−	0.781619i	−0.447781	−	0.162979i	0.108280	−	0.994120i	$-0.465466\pi$
$23$	−2.14748	−	0.781619i	−0.447781	−	0.162979i	−0.556061	+	0.831142i	$0.687688\pi$
$24$		0			0
$25$	−0.142997	+	0.810974i	−0.0285993	+	0.162195i
$26$	−3.81480	+	3.02748i	−0.748144	+	0.593737i
$27$		0			0
$28$	−0.723589	+	3.10257i	−0.136746	+	0.586331i
$29$	−8.60509	−	1.51731i	−1.59793	−	0.281757i	−0.697440	−	0.716643i	$-0.745678\pi$
$29$	−8.60509	−	1.51731i	−1.59793	−	0.281757i	−0.900486	+	0.434886i	$0.856789\pi$
$30$		0			0
$31$	−6.69129	−	2.43543i	−1.20179	−	0.437416i	−0.337942	−	0.941167i	$-0.609731\pi$
$31$	−6.69129	−	2.43543i	−1.20179	−	0.437416i	−0.863849	+	0.503751i	$0.831953\pi$
$32$	4.46858	+	3.46868i	0.789941	+	0.613182i
$33$		0			0
$34$	−3.46028	−	2.12578i	−0.593433	−	0.364569i
$35$	3.32901	+	1.92201i	0.562706	+	0.324878i
$36$		0			0
$37$	−5.14590	+	2.97099i	−0.845981	+	0.488427i	−0.859293	−	0.511484i	$-0.829096\pi$
$37$	−5.14590	+	2.97099i	−0.845981	+	0.488427i	0.0133118	+	0.999911i	$0.495763\pi$
$38$	6.13158	+	0.167414i	0.994673	+	0.0271582i
$39$		0			0
$40$	5.57002	−	3.94497i	0.880698	−	0.623754i
$41$	1.74706	+	9.90807i	0.272845	+	1.54738i	0.745725	+	0.666254i	$0.232103\pi$
$41$	1.74706	+	9.90807i	0.272845	+	1.54738i	−0.472880	+	0.881127i	$0.656786\pi$
$42$		0			0
$43$	−7.59829	+	9.05529i	−1.15873	+	1.38092i	−0.247567	+	0.968871i	$0.579631\pi$
$43$	−7.59829	+	9.05529i	−1.15873	+	1.38092i	−0.911162	+	0.412048i	$0.864813\pi$
$44$	−0.0924647	−	0.304872i	−0.0139396	−	0.0459612i
$45$		0			0
$46$	3.19694	−	0.474136i	0.471363	−	0.0699075i
$47$	−3.66367	+	1.33347i	−0.534402	+	0.194506i	−0.595103	−	0.803650i	$-0.702889\pi$
$47$	−3.66367	+	1.33347i	−0.534402	+	0.194506i	0.0607009	+	0.998156i	$0.480666\pi$
$48$		0			0
$49$	−3.41856	+	2.86851i	−0.488366	+	0.409788i
$50$	−0.368294	−	1.10481i	−0.0520846	−	0.156244i
$51$		0			0
$52$	2.70529	−	6.33388i	0.375156	−	0.878352i
$53$		−	9.80805i		−	1.34724i	−0.739078	−	0.673620i	$-0.764738\pi$
$53$		−	9.80805i		−	1.34724i	0.739078	−	0.673620i	$-0.235262\pi$
$54$		0			0
$55$	−0.384404			−0.0518330
$56$	−1.18948	−	4.34560i	−0.158950	−	0.580705i
$57$		0			0
$58$	11.7230	−	3.90790i	1.53930	−	0.513132i
$59$	−1.72220	−	2.05244i	−0.224212	−	0.267205i	0.642198	−	0.766539i	$-0.278023\pi$
$59$	−1.72220	−	2.05244i	−0.224212	−	0.267205i	−0.866410	+	0.499334i	$0.833578\pi$
$60$		0			0
$61$	−0.492702	−	1.35369i	−0.0630841	−	0.173322i	0.904146	−	0.427224i	$-0.140508\pi$
$61$	−0.492702	−	1.35369i	−0.0630841	−	0.173322i	−0.967230	+	0.253902i	$0.918286\pi$
$62$	9.96127	−	1.47735i	1.26508	−	0.187624i
$63$		0			0
$64$	−7.89294	−	1.30440i	−0.986618	−	0.163050i
$65$	−6.36609	−	5.34178i	−0.789616	−	0.662566i
$66$		0			0
$67$	0.225321	−	0.0397302i	0.0275273	−	0.00485381i	−0.159868	−	0.987138i	$-0.551107\pi$
$67$	0.225321	−	0.0397302i	0.0275273	−	0.00485381i	0.187395	+	0.982285i	$0.439996\pi$
$68$	5.73470	+	0.313390i	0.695435	+	0.0380041i
$69$		0			0
$70$	−5.43423	−	0.148374i	−0.649515	−	0.0177341i
$71$	−2.82317	−	4.88987i	−0.335048	−	0.580320i	0.648446	−	0.761261i	$-0.275419\pi$
$71$	−2.82317	−	4.88987i	−0.335048	−	0.580320i	−0.983494	+	0.180940i	$0.942086\pi$
$72$		0			0
$73$	7.14574	−	12.3768i	0.836346	−	1.44859i	−0.0565836	−	0.998398i	$-0.518021\pi$
$73$	7.14574	−	12.3768i	0.836346	−	1.44859i	0.892930	−	0.450196i	$-0.148646\pi$
$74$	4.39867	−	7.16002i	0.511335	−	0.832335i
$75$		0			0
$76$	−7.73789	+	3.92091i	−0.887597	+	0.449759i
$77$	−0.0867843	+	0.238438i	−0.00988999	+	0.0271725i
$78$		0			0
$79$	−2.18269	+	12.3786i	−0.245572	+	1.39271i	0.573590	+	0.819143i	$0.305550\pi$
$79$	−2.18269	+	12.3786i	−0.245572	+	1.39271i	−0.819161	+	0.573563i	$0.805561\pi$
$80$	−4.27021	+	8.65685i	−0.477424	+	0.967865i
$81$		0			0
$82$	−8.84487	−	11.1451i	−0.976753	−	1.23077i
$83$	−11.1079	−	1.95862i	−1.21925	−	0.214987i	−0.473248	−	0.880929i	$-0.656919\pi$
$83$	−11.1079	−	1.95862i	−1.21925	−	0.214987i	−0.746003	+	0.665942i	$0.768030\pi$
$84$		0			0
$85$	2.37013	−	6.51187i	0.257076	−	0.706311i
$86$	3.35117	−	16.3779i	0.361366	−	1.76607i
$87$		0			0
$88$	0.320294	+	0.316868i	0.0341434	+	0.0337783i
$89$	3.73417	−	6.46777i	0.395821	−	0.685582i	−0.597385	−	0.801955i	$-0.703793\pi$
$89$	3.73417	−	6.46777i	0.395821	−	0.685582i	0.993206	+	0.116373i	$0.0371268\pi$
$90$		0			0
$91$	−4.75063	+	2.74278i	−0.498001	+	0.287521i
$92$	−3.65638	+	2.74250i	−0.381204	+	0.285925i
$93$		0			0
$94$	3.65812	−	4.12546i	0.377307	−	0.425509i
$95$	1.81753	+	10.3077i	0.186474	+	1.05755i
$96$		0			0
$97$	5.17680	+	4.34385i	0.525624	+	0.441051i	0.866587	−	0.499026i	$-0.166309\pi$
$97$	5.17680	+	4.34385i	0.525624	+	0.441051i	−0.340963	+	0.940077i	$0.610753\pi$
$98$	2.31958	−	5.86936i	0.234313	−	0.592895i
$99$		0			0
$100$	1.20201	+	1.12592i	0.120201	+	0.112592i
$101$	−0.582767	−	1.60114i	−0.0579875	−	0.159319i	0.907316	−	0.420449i	$-0.138127\pi$
$101$	−0.582767	−	1.60114i	−0.0579875	−	0.159319i	−0.965304	+	0.261129i	$0.915905\pi$
$102$		0			0
$103$	9.82235	−	8.24193i	0.967825	−	0.812102i	−0.0143832	−	0.999897i	$-0.504578\pi$
$103$	9.82235	−	8.24193i	0.967825	−	0.812102i	0.982208	+	0.187795i	$0.0601340\pi$
$104$	0.901075	+	9.69852i	0.0883576	+	0.951019i
$105$		0			0
$106$	6.60490	+	12.1972i	0.641525	+	1.18469i
$107$			15.7558i			1.52317i	0.648065	+	0.761585i	$0.275579\pi$
$107$			15.7558i			1.52317i	−0.648065	+	0.761585i	$0.724421\pi$
$108$		0			0
$109$		−	4.23854i		−	0.405978i	−0.979181	−	0.202989i	$-0.934934\pi$
$109$		−	4.23854i		−	0.405978i	0.979181	−	0.202989i	$-0.0650656\pi$
$110$	0.478040	−	0.258864i	0.0455793	−	0.0246817i
$111$		0			0
$112$	4.40561	+	4.60312i	0.416291	+	0.434954i
$113$	5.72871	−	4.80696i	0.538912	−	0.452201i	−0.332254	−	0.943190i	$-0.607809\pi$
$113$	5.72871	−	4.80696i	0.538912	−	0.452201i	0.871166	+	0.490989i	$0.163365\pi$
$114$		0			0
$115$	1.88620	+	5.18228i	0.175889	+	0.483250i
$116$	−11.9469	+	12.7542i	−1.10924	+	1.18420i
$117$		0			0
$118$	3.52386	+	1.39263i	0.324397	+	0.128202i
$119$	−3.50409	−	2.94028i	−0.321220	−	0.269535i
$120$		0			0
$121$	1.90572	+	10.8079i	0.173248	+	0.982536i
$122$	1.52431	+	1.35164i	0.138005	+	0.122371i
$123$		0			0
$124$	−11.3928	+	8.54529i	−1.02311	+	0.767390i
$125$	−8.72843	+	5.03936i	−0.780695	+	0.450734i
$126$		0			0
$127$	6.92735	−	11.9985i	0.614703	−	1.06470i	−0.375734	−	0.926728i	$-0.622609\pi$
$127$	6.92735	−	11.9985i	0.614703	−	1.06470i	0.990437	−	0.137969i	$-0.0440574\pi$
$128$	10.6940	−	3.69310i	0.945222	−	0.326427i
$129$		0			0
$130$	11.5140	+	2.35595i	1.00985	+	0.206631i
$131$	1.76657	−	4.85361i	0.154346	−	0.424061i	−0.838286	−	0.545231i	$-0.816442\pi$
$131$	1.76657	−	4.85361i	0.154346	−	0.424061i	0.992632	+	0.121169i	$0.0386643\pi$
$132$		0			0
$133$	6.80399	+	1.19973i	0.589981	+	0.104030i
$134$	−0.253452	+	0.201143i	−0.0218949	+	0.0173761i
$135$		0			0
$136$	−7.34265	+	3.47211i	−0.629627	+	0.297731i
$137$	3.27446	−	18.5704i	0.279756	−	1.58658i	−0.443680	−	0.896185i	$-0.646327\pi$
$137$	3.27446	−	18.5704i	0.279756	−	1.58658i	0.723436	−	0.690391i	$-0.242562\pi$
$138$		0			0
$139$	−5.53623	+	15.2107i	−0.469577	+	1.29015i	0.448512	+	0.893777i	$0.351954\pi$
$139$	−5.53623	+	15.2107i	−0.469577	+	1.29015i	−0.918089	+	0.396375i	$0.870268\pi$
$140$	6.85786	−	3.47498i	0.579595	−	0.293689i
$141$		0			0
$142$	6.80377	+	4.17981i	0.570959	+	0.350762i
$143$	0.274279	−	0.475066i	0.0229364	−	0.0397270i
$144$		0			0
$145$	10.5430	+	18.2611i	0.875551	+	1.51650i
$146$	−0.551633	+	20.2037i	−0.0456535	+	1.67207i
$147$		0			0
$148$	−0.648466	+	11.8662i	−0.0533036	+	0.975399i
$149$	12.7731	−	2.25224i	1.04641	−	0.184511i	0.376092	−	0.926582i	$-0.377268\pi$
$149$	12.7731	−	2.25224i	1.04641	−	0.184511i	0.670321	+	0.742071i	$0.266157\pi$
$150$		0			0
$151$	2.57721	+	2.16253i	0.209730	+	0.175985i	0.741602	−	0.670841i	$-0.234067\pi$
$151$	2.57721	+	2.16253i	0.209730	+	0.175985i	−0.531871	+	0.846825i	$0.678511\pi$
$152$	6.98235	−	10.0868i	0.566344	−	0.818149i
$153$		0			0
$154$	−0.0526440	−	0.354961i	−0.00424217	−	0.0286035i
$155$	5.87716	+	16.1474i	0.472065	+	1.29699i
$156$		0			0
$157$	−0.320529	−	0.381992i	−0.0255810	−	0.0304863i	0.753102	−	0.657903i	$-0.228557\pi$
$157$	−0.320529	−	0.381992i	−0.0255810	−	0.0304863i	−0.778683	+	0.627417i	$0.784112\pi$
$158$	−5.62161	−	16.8638i	−0.447231	−	1.34161i
$159$		0			0
$160$	−0.519282	−	13.6412i	−0.0410528	−	1.07843i
$161$	3.64030			0.286896
$162$		0			0
$163$		−	11.3041i		−	0.885405i	−0.896669	−	0.442703i	$-0.854020\pi$
$163$		−	11.3041i		−	0.885405i	0.896669	−	0.442703i	$-0.145980\pi$
$164$	18.5046	+	7.90358i	1.44497	+	0.617166i
$165$		0			0
$166$	15.1326	−	5.04452i	1.17452	−	0.391531i
$167$	−10.0898	+	8.46632i	−0.780770	+	0.655144i	−0.943442	−	0.331536i	$-0.892433\pi$
$167$	−10.0898	+	8.46632i	−0.780770	+	0.655144i	0.162673	+	0.986680i	$0.447989\pi$
$168$		0			0
$169$	−1.07204	+	0.390189i	−0.0824644	+	0.0300146i
$170$	1.43773	+	9.69416i	0.110269	+	0.743508i
$171$		0			0
$172$	6.86164	+	22.6240i	0.523195	+	1.72507i
$173$	10.5281	−	12.5470i	0.800440	−	0.953928i	−0.199221	−	0.979955i	$-0.563841\pi$
$173$	10.5281	−	12.5470i	0.800440	−	0.953928i	0.999661	+	0.0260269i	$0.00828556\pi$
$174$		0			0
$175$	−0.227782	−	1.29182i	−0.0172187	−	0.0976521i
$176$	−0.611698	−	0.178363i	−0.0461085	−	0.0134446i
$177$		0			0
$178$	−0.288268	+	10.5579i	−0.0216066	+	0.791347i
$179$	5.13398	−	2.96410i	0.383731	−	0.221547i	−0.295709	−	0.955278i	$-0.595556\pi$
$179$	5.13398	−	2.96410i	0.383731	−	0.221547i	0.679441	+	0.733731i	$0.262223\pi$
$180$		0			0
$181$	1.50802	+	0.870656i	0.112090	+	0.0647154i	0.554997	−	0.831852i	$-0.312719\pi$
$181$	1.50802	+	0.870656i	0.112090	+	0.0647154i	−0.442907	+	0.896568i	$0.646053\pi$
$182$	4.06079	−	6.61003i	0.301006	−	0.489968i
$183$		0			0
$184$	2.70019	−	5.87280i	0.199061	−	0.432949i
$185$	13.4744	+	4.90427i	0.990655	+	0.360569i
$186$		0			0
$187$	0.450481	+	0.0794319i	0.0329424	+	0.00580863i
$188$	−1.77105	+	7.59381i	−0.129167	+	0.553836i
$189$		0			0
$190$	−9.20163	−	11.5946i	−0.667556	−	0.841160i
$191$	−1.88621	+	10.6972i	−0.136481	+	0.774023i	0.837336	+	0.546689i	$0.184112\pi$
$191$	−1.88621	+	10.6972i	−0.136481	+	0.774023i	−0.973817	+	0.227334i	$0.926999\pi$
$192$		0			0
$193$	−13.6021	−	4.95075i	−0.979100	−	0.356363i	−0.197609	−	0.980281i	$-0.563318\pi$
$193$	−13.6021	−	4.95075i	−0.979100	−	0.356363i	−0.781490	+	0.623918i	$0.785540\pi$
$194$	−9.36302	−	1.91582i	−0.672226	−	0.137548i
$195$		0			0
$196$	1.06792	+	8.86111i	0.0762800	+	0.632936i
$197$	−7.36911	−	4.25456i	−0.525027	−	0.303125i	0.213962	−	0.976842i	$-0.431363\pi$
$197$	−7.36911	−	4.25456i	−0.525027	−	0.303125i	−0.738989	+	0.673717i	$0.764697\pi$
$198$		0			0
$199$	−6.17939	−	10.7030i	−0.438045	−	0.758716i	0.559494	−	0.828835i	$-0.310996\pi$
$199$	−6.17939	−	10.7030i	−0.438045	−	0.758716i	−0.997539	+	0.0701183i	$0.977662\pi$
$200$	−2.25301	−	0.590729i	−0.159312	−	0.0417709i
$201$		0			0
$202$	1.80296	+	1.59871i	0.126855	+	0.112485i
$203$	13.7072	−	2.41695i	0.962057	−	0.169637i
$204$		0			0
$205$	15.6062	−	18.5987i	1.08998	−	1.29899i
$206$	−6.66471	+	16.8641i	−0.464352	+	1.17498i
$207$		0			0
$208$	−7.65171	−	11.4542i	−0.530550	−	0.794204i
$209$	−0.649234	+	0.236302i	−0.0449084	+	0.0163453i
$210$		0			0
$211$	1.13641	+	1.35433i	0.0782339	+	0.0932356i	0.803742	−	0.594978i	$-0.202839\pi$
$211$	1.13641	+	1.35433i	0.0782339	+	0.0932356i	−0.725508	+	0.688214i	$0.758395\pi$
$212$	−16.4275	−	10.7204i	−1.12825	−	0.736281i
$213$		0			0
$214$	−10.6102	−	19.5937i	−0.725299	−	1.33940i
$215$	28.5259			1.94545
$216$		0			0
$217$	11.3427			0.769994
$218$	2.85430	+	5.27100i	0.193318	+	0.356997i
$219$		0			0
$220$	−0.420162	+	0.643840i	−0.0283273	+	0.0434077i
$221$	6.35657	+	7.57546i	0.427589	+	0.509581i
$222$		0			0
$223$	−2.82725	+	1.02903i	−0.189327	+	0.0689092i	−0.434944	−	0.900458i	$-0.643232\pi$
$223$	−2.82725	+	1.02903i	−0.189327	+	0.0689092i	0.245617	+	0.969367i	$0.421009\pi$
$224$	−8.57859	−	2.75758i	−0.573181	−	0.184249i
$225$		0			0
$226$	−3.88707	+	9.83568i	−0.258564	+	0.654260i
$227$	−3.65533	+	4.35626i	−0.242613	+	0.289135i	−0.873586	−	0.486670i	$-0.838211\pi$
$227$	−3.65533	+	4.35626i	−0.242613	+	0.289135i	0.630973	+	0.775805i	$0.282656\pi$
$228$		0			0
$229$	−21.4459	+	3.78149i	−1.41718	+	0.249888i	−0.829185	−	0.558974i	$-0.811195\pi$
$229$	−21.4459	+	3.78149i	−1.41718	+	0.249888i	−0.587998	+	0.808862i	$0.700084\pi$
$230$	−5.83548	−	5.17443i	−0.384780	−	0.341192i
$231$		0			0
$232$	6.26811	−	23.9063i	0.411522	−	1.56952i
$233$	11.7482	+	20.3485i	0.769650	+	1.33307i	0.937753	+	0.347303i	$0.112903\pi$
$233$	11.7482	+	20.3485i	0.769650	+	1.33307i	−0.168103	+	0.985769i	$0.553764\pi$
$234$		0			0
$235$	8.14804	+	4.70427i	0.531520	+	0.306873i
$236$	−5.32005	+	0.641160i	−0.346306	+	0.0417360i
$237$		0			0
$238$	6.33768	+	1.29679i	0.410811	+	0.0840583i
$239$	−21.9880	−	8.00297i	−1.42228	−	0.517669i	−0.487574	−	0.873082i	$-0.662118\pi$
$239$	−21.9880	−	8.00297i	−1.42228	−	0.517669i	−0.934710	+	0.355413i	$0.884340\pi$
$240$		0			0
$241$	0.682320	−	3.86963i	0.0439521	−	0.249265i	−0.954913	−	0.296884i	$-0.904052\pi$
$241$	0.682320	−	3.86963i	0.0439521	−	0.249265i	0.998866	+	0.0476196i	$0.0151635\pi$
$242$	−9.64814	−	12.1572i	−0.620206	−	0.781496i
$243$		0			0
$244$	−2.80583	−	0.654382i	−0.179625	−	0.0418925i
$245$	10.6055	+	1.87004i	0.677562	+	0.119472i
$246$		0			0
$247$	−14.0356	−	5.10855i	−0.893066	−	0.325049i
$248$	8.41347	−	18.2989i	0.534256	−	1.16198i
$249$		0			0
$250$	7.46099	−	12.1448i	0.471874	−	0.768102i
$251$	−0.431970	−	0.249398i	−0.0272657	−	0.0157419i	0.486305	−	0.873789i	$-0.338344\pi$
$251$	−0.431970	−	0.249398i	−0.0272657	−	0.0157419i	−0.513571	+	0.858047i	$0.671678\pi$
$252$		0			0
$253$	−0.315261	+	0.182016i	−0.0198203	+	0.0114433i
$254$	−0.534774	+	19.5862i	−0.0335547	+	1.22895i
$255$		0			0
$256$	−10.8119	+	11.7942i	−0.675744	+	0.737137i
$257$	−0.156179	−	0.885735i	−0.00974218	−	0.0552506i	0.979549	−	0.201205i	$-0.0644858\pi$
$257$	−0.156179	−	0.885735i	−0.00974218	−	0.0552506i	−0.989291	+	0.145955i	$0.953375\pi$
$258$		0			0
$259$	6.08403	−	7.25067i	0.378043	−	0.450535i
$260$	−15.9052	+	4.82390i	−0.986401	+	0.299165i
$261$		0			0
$262$	1.07161	+	7.22552i	0.0662044	+	0.446394i
$263$	9.42004	−	3.42861i	0.580864	−	0.211417i	−0.0348423	−	0.999393i	$-0.511093\pi$
$263$	9.42004	−	3.42861i	0.580864	−	0.211417i	0.615707	+	0.787976i	$0.288871\pi$
$264$		0			0
$265$	−18.1313	+	15.2139i	−1.11380	+	0.934585i
$266$	−9.26928	+	3.08995i	−0.568336	+	0.189457i
$267$		0			0
$268$	0.179737	−	0.420817i	0.0109792	−	0.0257055i
$269$			1.04059i			0.0634460i	0.999497	+	0.0317230i	$0.0100994\pi$
$269$			1.04059i			0.0634460i	−0.999497	+	0.0317230i	$0.989901\pi$
$270$		0			0
$271$	−30.0408			−1.82485			−0.912423	−	0.409248i	$-0.865791\pi$
$271$	−30.0408			−1.82485			−0.912423	+	0.409248i	$0.865791\pi$
$272$	6.79305	−	9.26253i	0.411889	−	0.561623i
$273$		0			0
$274$	8.43352	+	25.2990i	0.509488	+	1.52837i
$275$	0.0843178	+	0.100486i	0.00508456	+	0.00605954i
$276$		0			0
$277$	6.71914	+	18.4607i	0.403714	+	1.10920i	0.960437	+	0.278497i	$0.0898363\pi$
$277$	6.71914	+	18.4607i	0.403714	+	1.10920i	−0.556723	+	0.830698i	$0.687941\pi$
$278$	−3.35832	−	22.6440i	−0.201418	−	1.35810i
$279$		0			0
$280$	−6.18825	+	8.93964i	−0.369818	+	0.534245i
$281$	−21.2698	−	17.8475i	−1.26885	−	1.06469i	−0.994681	−	0.103008i	$-0.967153\pi$
$281$	−21.2698	−	17.8475i	−1.26885	−	1.06469i	−0.274167	−	0.961682i	$-0.588402\pi$
$282$		0			0
$283$	24.5768	−	4.33356i	1.46094	−	0.257603i	0.614007	−	0.789301i	$-0.289557\pi$
$283$	24.5768	−	4.33356i	1.46094	−	0.257603i	0.846934	+	0.531698i	$0.178446\pi$
$284$	−11.2758	−	0.616201i	−0.669098	−	0.0365648i
$285$		0			0
$286$	−0.0211737	+	0.775490i	−0.00125203	+	0.0458557i
$287$	−8.01310	−	13.8791i	−0.472999	−	0.819258i
$288$		0			0
$289$	4.37687	−	7.58097i	0.257463	−	0.445939i
$290$	−25.4085	−	15.6094i	−1.49204	−	0.916615i
$291$		0			0
$292$	−12.9195	−	25.4965i	−0.756055	−	1.49207i
$293$	−2.79279	+	7.67312i	−0.163156	+	0.448268i	−0.994149	−	0.108015i	$-0.965551\pi$
$293$	−2.79279	+	7.67312i	−0.163156	+	0.448268i	0.830993	+	0.556283i	$0.187773\pi$
$294$		0			0
$295$	−1.12274	+	6.36736i	−0.0653683	+	0.370722i
$296$	−7.18449	−	15.1934i	−0.417590	−	0.883099i
$297$		0			0
$298$	−14.3678	+	11.4025i	−0.832303	+	0.660527i
$299$	−7.75036	−	1.36660i	−0.448215	−	0.0790324i
$300$		0			0
$301$	6.44011	−	17.6941i	0.371202	−	1.01987i
$302$	−4.66127	−	0.953769i	−0.268226	−	0.0548832i
$303$		0			0
$304$	−1.89055	+	17.2459i	−0.108430	+	0.989118i
$305$	−1.73818	+	3.01061i	−0.0995278	+	0.172387i
$306$		0			0
$307$	16.1236	−	9.30896i	0.920222	−	0.531290i	0.0365160	−	0.999333i	$-0.488374\pi$
$307$	16.1236	−	9.30896i	0.920222	−	0.531290i	0.883706	+	0.468043i	$0.155041\pi$
$308$	0.304503	+	0.405973i	0.0173507	+	0.0231325i
$309$		0			0
$310$	−18.1826	−	16.1229i	−1.03271	−	0.915718i
$311$	0.851609	+	4.82971i	0.0482903	+	0.273868i	0.999386	−	0.0350274i	$-0.0111518\pi$
$311$	0.851609	+	4.82971i	0.0482903	+	0.273868i	−0.951096	+	0.308895i	$0.900041\pi$
$312$		0			0
$313$	−7.88890	−	6.61958i	−0.445907	−	0.374161i	0.392007	−	0.919962i	$-0.371781\pi$
$313$	−7.88890	−	6.61958i	−0.445907	−	0.374161i	−0.837914	+	0.545802i	$0.816225\pi$
$314$	0.655845	+	0.259191i	0.0370115	+	0.0146270i
$315$		0			0
$316$	18.3473	+	17.1859i	1.03212	+	0.966783i
$317$	7.72259	+	21.2177i	0.433744	+	1.19170i	0.943497	+	0.331381i	$0.107515\pi$
$317$	7.72259	+	21.2177i	0.433744	+	1.19170i	−0.509753	+	0.860321i	$0.670263\pi$
$318$		0			0
$319$	−1.06624	+	0.894680i	−0.0596979	+	0.0500925i
$320$	9.83196	+	16.6143i	0.549623	+	0.928769i
$321$		0			0
$322$	−4.52703	+	2.45143i	−0.252282	+	0.136613i
$323$		−	12.4551i		−	0.693020i
$324$		0			0
$325$			2.83585i			0.157304i
$326$	7.61236	+	14.0576i	0.421609	+	0.778581i
$327$		0			0
$328$	−28.3345	+	2.63252i	−1.56451	+	0.145356i
$329$	4.75749	−	3.99201i	0.262289	−	0.220087i
$330$		0			0
$331$	−8.06296	−	22.1528i	−0.443180	−	1.21763i	−0.937389	−	0.348284i	$-0.886764\pi$
$331$	−8.06296	−	22.1528i	−0.443180	−	1.21763i	0.494209	−	0.869343i	$-0.335458\pi$
$332$	−15.4217	+	16.4639i	−0.846375	+	0.903572i
$333$		0			0
$334$	6.84616	−	17.3232i	0.374605	−	0.947885i
$335$	−0.422957	−	0.354903i	−0.0231086	−	0.0193904i
$336$		0			0
$337$	−5.70981	−	32.3820i	−0.311033	−	1.76396i	−0.593649	−	0.804724i	$-0.702313\pi$
$337$	−5.70981	−	32.3820i	−0.311033	−	1.76396i	0.282615	−	0.959233i	$-0.408798\pi$
$338$	1.07041	−	1.20716i	0.0582227	−	0.0656609i
$339$		0			0
$340$	−8.31615	−	11.0873i	−0.451007	−	0.601296i
$341$	−0.982316	+	0.567140i	−0.0531954	+	0.0307124i
$342$		0			0
$343$	9.12950	−	15.8128i	0.492947	−	0.853809i
$344$	−23.7684	−	23.5143i	−1.28151	−	1.26780i
$345$		0			0
$346$	−4.64336	+	22.6931i	−0.249628	+	1.21999i
$347$	−0.288638	+	0.793027i	−0.0154949	+	0.0425719i	−0.947199	−	0.320646i	$-0.896100\pi$
$347$	−0.288638	+	0.793027i	−0.0154949	+	0.0425719i	0.931704	+	0.363218i	$0.118322\pi$
$348$		0			0
$349$	13.8072	+	2.43459i	0.739085	+	0.130321i	0.530501	−	0.847684i	$-0.322004\pi$
$349$	13.8072	+	2.43459i	0.739085	+	0.130321i	0.208583	+	0.978005i	$0.433115\pi$
$350$	1.15320	+	1.45309i	0.0616409	+	0.0776711i
$351$		0			0
$352$	0.880812	−	0.190117i	0.0469475	−	0.0101333i
$353$	−4.09441	+	23.2205i	−0.217923	+	1.23590i	0.657838	+	0.753159i	$0.271471\pi$
$353$	−4.09441	+	23.2205i	−0.217923	+	1.23590i	−0.875761	+	0.482744i	$0.839640\pi$
$354$		0			0
$355$	−4.66025	+	12.8039i	−0.247341	+	0.679562i
$356$	−6.75136	−	13.3238i	−0.357821	−	0.706159i
$357$		0			0
$358$	−4.38848	+	7.14342i	−0.231938	+	0.377542i
$359$	13.4957	−	23.3753i	0.712277	−	1.23370i	−0.251724	−	0.967799i	$-0.580997\pi$
$359$	13.4957	−	23.3753i	0.712277	−	1.23370i	0.964001	−	0.265900i	$-0.0856692\pi$
$360$		0			0
$361$	−0.0939335	−	0.162698i	−0.00494387	−	0.00856303i
$362$	−2.46167	−	0.0672125i	−0.129383	−	0.00353261i
$363$		0			0
$364$	−0.598655	+	10.9548i	−0.0313780	+	0.574185i
$365$	−33.9641	+	5.98879i	−1.77776	+	0.313468i
$366$		0			0
$367$	22.3181	+	18.7271i	1.16500	+	0.977547i	0.999962	−	0.00874090i	$-0.00278235\pi$
$367$	22.3181	+	18.7271i	1.16500	+	0.977547i	0.165033	+	0.986288i	$0.447227\pi$
$368$	0.596913	+	9.12170i	0.0311163	+	0.475501i
$369$		0			0
$370$	−20.0592	+	2.97496i	−1.04283	+	0.154661i
$371$	5.34353	+	14.6812i	0.277422	+	0.762211i
$372$		0			0
$373$	−0.738799	−	0.880467i	−0.0382536	−	0.0455888i	0.746578	−	0.665297i	$-0.231695\pi$
$373$	−0.738799	−	0.880467i	−0.0382536	−	0.0455888i	−0.784832	+	0.619709i	$0.787251\pi$
$374$	−0.613703	+	0.204580i	−0.0317338	+	0.0105786i
$375$		0			0
$376$	−2.91134	−	10.6362i	−0.150141	−	0.548521i
$377$	−30.0906			−1.54975
$378$		0			0
$379$		−	16.9124i		−	0.868731i	−0.900737	−	0.434365i	$-0.856973\pi$
$379$		−	16.9124i		−	0.868731i	0.900737	−	0.434365i	$-0.143027\pi$
$380$	19.2510	+	8.22237i	0.987556	+	0.421799i
$381$		0			0
$382$	−4.85801	−	14.5731i	−0.248557	−	0.745626i
$383$	−15.4572	+	12.9701i	−0.789826	+	0.662743i	−0.945702	−	0.325034i	$-0.894624\pi$
$383$	−15.4572	+	12.9701i	−0.789826	+	0.662743i	0.155876	+	0.987777i	$0.450180\pi$
$384$		0			0
$385$	0.575396	−	0.209427i	0.0293249	−	0.0106734i
$386$	20.2493	−	3.00316i	1.03066	−	0.152857i
$387$		0			0
$388$	12.9339	−	3.92272i	0.656619	−	0.199146i
$389$	18.7454	−	22.3399i	0.950428	−	1.13268i	−0.0406204	−	0.999175i	$-0.512933\pi$
$389$	18.7454	−	22.3399i	0.950428	−	1.13268i	0.991049	−	0.133502i	$-0.0426221\pi$
$390$		0			0
$391$	−1.13957	−	6.46284i	−0.0576307	−	0.326840i
$392$	−7.29526	−	10.3004i	−0.368466	−	0.520249i
$393$		0			0
$394$	12.0292	+	0.328441i	0.606023	+	0.0165466i
$395$	26.2690	−	15.1664i	1.32174	−	0.763105i
$396$		0			0
$397$	10.3158	+	5.95584i	0.517736	+	0.298915i	0.736008	−	0.676973i	$-0.236709\pi$
$397$	10.3158	+	5.95584i	0.517736	+	0.298915i	−0.218272	+	0.975888i	$0.570042\pi$
$398$	14.8922	+	9.14884i	0.746478	+	0.458590i
$399$		0			0
$400$	3.19962	−	0.782590i	0.159981	−	0.0391295i
$401$	−2.23681	−	0.814132i	−0.111701	−	0.0406558i	0.285565	−	0.958359i	$-0.407819\pi$
$401$	−2.23681	−	0.814132i	−0.111701	−	0.0406558i	−0.397266	+	0.917704i	$0.630041\pi$
$402$		0			0
$403$	−24.1492	−	4.25815i	−1.20296	−	0.212114i
$404$	−3.31873	−	0.774002i	−0.165113	−	0.0385080i
$405$		0			0
$406$	−15.4185	+	12.2363i	−0.765207	+	0.607279i
$407$	−0.164360	+	0.932134i	−0.00814705	+	0.0462042i
$408$		0			0
$409$	12.0885	+	4.39986i	0.597739	+	0.217559i	0.623130	−	0.782119i	$-0.285861\pi$
$409$	12.0885	+	4.39986i	0.597739	+	0.217559i	−0.0253911	+	0.999678i	$0.508083\pi$
$410$	−6.88298	+	33.6386i	−0.339926	+	1.66129i
$411$		0			0
$412$	−3.06840	−	25.4601i	−0.151169	−	1.25433i
$413$	3.69607	+	2.13393i	0.181872	+	0.105004i
$414$		0			0
$415$	13.6095	+	23.5724i	0.668064	+	1.15712i
$416$	17.2290	+	9.09149i	0.844721	+	0.445747i
$417$		0			0
$418$	0.648250	−	0.731066i	0.0317069	−	0.0357576i
$419$	−7.38244	+	1.30172i	−0.360656	+	0.0635933i	−0.351040	−	0.936360i	$-0.614172\pi$
$419$	−7.38244	+	1.30172i	−0.360656	+	0.0635933i	−0.00961568	+	0.999954i	$0.503061\pi$
$420$		0			0
$421$	−5.15270	+	6.14075i	−0.251127	+	0.299282i	−0.876850	−	0.480763i	$-0.840360\pi$
$421$	−5.15270	+	6.14075i	−0.251127	+	0.299282i	0.625723	+	0.780045i	$0.284804\pi$
$422$	−2.32525	−	0.918943i	−0.113192	−	0.0447335i
$423$		0			0
$424$	27.6484	+	2.26921i	1.34273	+	0.110203i
$425$	−2.22213	+	0.808790i	−0.107789	+	0.0392321i
$426$		0			0
$427$	1.47501	+	1.75784i	0.0713805	+	0.0850680i
$428$	26.3894	+	17.2214i	1.27558	+	0.832429i
$429$		0			0
$430$	−35.4745	+	19.2098i	−1.71073	+	0.926380i
$431$	4.63698			0.223356			0.111678	−	0.993744i	$-0.464378\pi$
$431$	4.63698			0.223356			0.111678	+	0.993744i	$0.464378\pi$
$432$		0			0
$433$	−0.0678381			−0.00326009			−0.00163005	−	0.999999i	$-0.500519\pi$
$433$	−0.0678381			−0.00326009			−0.00163005	+	0.999999i	$0.500519\pi$
$434$	−14.1057	+	7.63837i	−0.677094	+	0.366654i
$435$		0			0
$436$	−7.09914	−	4.63282i	−0.339987	−	0.221872i
$437$	6.37133	+	7.59305i	0.304782	+	0.363225i
$438$		0			0
$439$	12.9530	−	4.71449i	0.618211	−	0.225010i	−0.0138813	−	0.999904i	$-0.504419\pi$
$439$	12.9530	−	4.71449i	0.618211	−	0.225010i	0.632092	+	0.774893i	$0.282196\pi$
$440$	0.0889366	−	1.08361i	0.00423989	−	0.0516593i
$441$		0			0
$442$	−13.0064	−	5.14014i	−0.618651	−	0.244492i
$443$	8.58044	−	10.2258i	0.407669	−	0.485841i	−0.522673	−	0.852533i	$-0.675065\pi$
$443$	8.58044	−	10.2258i	0.407669	−	0.485841i	0.930342	+	0.366692i	$0.119510\pi$
$444$		0			0
$445$	−17.7487	+	3.12957i	−0.841369	+	0.148356i
$446$	2.82296	−	3.18361i	0.133671	−	0.150748i
$447$		0			0
$448$	12.5252	−	2.34766i	0.591761	−	0.110917i
$449$	−6.26480	−	10.8509i	−0.295654	−	0.512088i	0.679483	−	0.733692i	$-0.262204\pi$
$449$	−6.26480	−	10.8509i	−0.295654	−	0.512088i	−0.975137	+	0.221604i	$0.928871\pi$
$450$		0			0
$451$	1.38792	+	0.801316i	0.0653546	+	0.0377325i
$452$	−1.78959	−	14.8491i	−0.0841751	−	0.698445i
$453$		0			0
$454$	1.61216	−	7.87895i	0.0756622	−	0.369777i
$455$	12.4393	+	4.52755i	0.583166	+	0.212255i
$456$		0			0
$457$	3.14504	−	17.8364i	0.147119	−	0.834352i	−0.818523	−	0.574474i	$-0.805207\pi$
$457$	3.14504	−	17.8364i	0.147119	−	0.834352i	0.965642	−	0.259878i	$-0.0836822\pi$
$458$	24.1233	−	19.1446i	1.12721	−	0.894569i
$459$		0			0
$460$	10.7415	+	2.50515i	0.500824	+	0.116803i
$461$	−6.87340	−	1.21197i	−0.320126	−	0.0564469i	0.0112760	−	0.999936i	$-0.496411\pi$
$461$	−6.87340	−	1.21197i	−0.320126	−	0.0564469i	−0.331402	+	0.943490i	$0.607522\pi$
$462$		0			0
$463$	26.8210	+	9.76206i	1.24648	+	0.453681i	0.879210	−	0.476434i	$-0.158071\pi$
$463$	26.8210	+	9.76206i	1.24648	+	0.453681i	0.367269	+	0.930115i	$0.380293\pi$
$464$	8.30391	+	33.9506i	0.385499	+	1.57612i
$465$		0			0
$466$	−28.3129	−	17.3937i	−1.31157	−	0.805747i
$467$	−0.471619	−	0.272289i	−0.0218239	−	0.0126000i	0.489048	−	0.872257i	$-0.337344\pi$
$467$	−0.471619	−	0.272289i	−0.0218239	−	0.0126000i	−0.510872	+	0.859657i	$0.670677\pi$
$468$		0			0
$469$	−0.315627	+	0.182227i	−0.0145743	+	0.00841448i
$470$	−13.3007	−	0.363158i	−0.613517	−	0.0167512i
$471$		0			0
$472$	6.18418	−	4.37994i	0.284650	−	0.201603i
$473$	0.326975	+	1.85437i	0.0150343	+	0.0852640i
$474$		0			0
$475$	2.29584	−	2.73608i	0.105340	−	0.125540i
$476$	−8.75474	+	2.65522i	−0.401273	+	0.121702i
$477$		0			0
$478$	32.7333	−	4.85466i	1.49719	−	0.222047i
$479$	−7.93244	+	2.88717i	−0.362442	+	0.131918i	−0.516821	−	0.856094i	$-0.672885\pi$
$479$	−7.93244	+	2.88717i	−0.362442	+	0.131918i	0.154379	+	0.988012i	$0.450662\pi$
$480$		0			0
$481$	−15.6752	+	13.1530i	−0.714725	+	0.599726i
$482$	1.75735	+	5.27171i	0.0800449	+	0.240120i
$483$		0			0
$484$	20.1852	+	8.62137i	0.917508	+	0.391880i
$485$		−	16.3079i		−	0.740505i
$486$		0			0
$487$	−15.0013			−0.679775			−0.339888	−	0.940466i	$-0.610389\pi$
$487$	−15.0013			−0.679775			−0.339888	+	0.940466i	$0.610389\pi$
$488$	3.92997	−	1.07571i	0.177901	−	0.0486951i
$489$		0			0
$490$	−14.4482	+	4.81637i	−0.652704	+	0.217581i
$491$	−9.43399	−	11.2430i	−0.425750	−	0.507389i	0.509941	−	0.860209i	$-0.329667\pi$
$491$	−9.43399	−	11.2430i	−0.425750	−	0.507389i	−0.935691	+	0.352820i	$0.885223\pi$
$492$		0			0
$493$	−8.58191	−	23.5786i	−0.386510	−	1.06193i
$494$	20.8947	−	3.09888i	0.940098	−	0.139425i
$495$		0			0
$496$	1.85991	+	28.4221i	0.0835124	+	1.27619i
$497$	6.88991	+	5.78132i	0.309055	+	0.259328i
$498$		0			0
$499$	17.0588	−	3.00792i	0.763655	−	0.134653i	0.221762	−	0.975101i	$-0.428819\pi$
$499$	17.0588	−	3.00792i	0.763655	−	0.134653i	0.541892	+	0.840448i	$0.317708\pi$
$500$	−1.09992	+	20.1274i	−0.0491900	+	0.900125i
$501$		0			0
$502$	0.705142	+	0.0192529i	0.0314720	+	0.000859300i
$503$	2.40445	+	4.16463i	0.107209	+	0.185692i	0.914639	−	0.404272i	$-0.132475\pi$
$503$	2.40445	+	4.16463i	0.107209	+	0.185692i	−0.807429	+	0.589964i	$0.799142\pi$
$504$		0			0
$505$	−2.05591	+	3.56095i	−0.0914870	+	0.158460i
$506$	0.269482	−	0.438655i	0.0119800	−	0.0195006i
$507$		0			0
$508$	−12.5246	−	24.7173i	−0.555690	−	1.09665i
$509$	−10.1785	+	27.9653i	−0.451155	+	1.23954i	0.480757	+	0.876854i	$0.340362\pi$
$509$	−10.1785	+	27.9653i	−0.451155	+	1.23954i	−0.931912	+	0.362685i	$0.881860\pi$
$510$		0			0
$511$	−3.95313	+	22.4193i	−0.174876	+	0.991772i
$512$	5.50316	−	21.9480i	0.243208	−	0.969974i
$513$		0			0
$514$	0.790690	+	0.996316i	0.0348759	+	0.0439456i
$515$	−30.4722	−	5.37308i	−1.34277	−	0.236766i
$516$		0			0
$517$	−0.212412	+	0.583597i	−0.00934187	+	0.0256666i
$518$	−2.68332	+	13.1139i	−0.117898	+	0.576193i
$519$		0			0
$520$	16.5311	−	16.7098i	0.724936	−	0.732772i
$521$	−15.3931	+	26.6615i	−0.674382	+	1.16806i	0.302267	+	0.953223i	$0.402256\pi$
$521$	−15.3931	+	26.6615i	−0.674382	+	1.16806i	−0.976649	+	0.214840i	$0.931077\pi$
$522$		0			0
$523$	−20.1716	+	11.6461i	−0.882042	+	0.509247i	−0.871331	−	0.490695i	$-0.836743\pi$
$523$	−20.1716	+	11.6461i	−0.882042	+	0.509247i	−0.0107111	+	0.999943i	$0.503410\pi$
$524$	−6.19842	−	8.26393i	−0.270779	−	0.361011i
$525$		0			0
$526$	−9.40576	+	10.6074i	−0.410111	+	0.462504i
$527$	−3.55077	−	20.1374i	−0.154674	−	0.877200i
$528$		0			0
$529$	−13.6183	−	11.4271i	−0.592099	−	0.496830i
$530$	12.3025	−	31.1298i	0.534387	−	1.35219i
$531$		0			0
$532$	9.44634	−	10.0847i	0.409551	−	0.437227i
$533$	11.8499	+	32.5574i	0.513278	+	1.41022i
$534$		0			0
$535$	29.1263	−	24.4399i	1.25924	−	1.05663i
$536$	0.0598665	+	0.644361i	0.00258584	+	0.0278321i
$537$		0			0
$538$	−0.700751	−	1.29407i	−0.0302115	−	0.0557912i
$539$			0.710862i			0.0306190i
$540$		0			0
$541$			29.0030i			1.24694i	0.781848	+	0.623469i	$0.214277\pi$
$541$			29.0030i			1.24694i	−0.781848	+	0.623469i	$0.785723\pi$
$542$	37.3583	−	20.2299i	1.60468	−	0.868950i
$543$		0			0
$544$	−2.21022	+	16.0933i	−0.0947625	+	0.689995i
$545$	−7.83541	+	6.57469i	−0.335632	+	0.281629i
$546$		0			0
$547$	3.84045	+	10.5516i	0.164206	+	0.451152i	0.994319	−	0.106443i	$-0.0339463\pi$
$547$	3.84045	+	10.5516i	0.164206	+	0.451152i	−0.830113	+	0.557596i	$0.811724\pi$
$548$	−27.5246	−	25.7823i	−1.17579	−	1.10136i
$549$		0			0
$550$	−0.172526	−	0.0681823i	−0.00735651	−	0.00290730i
$551$	29.0320	+	24.3607i	1.23681	+	1.03780i
$552$		0			0
$553$	−3.47684	−	19.7182i	−0.147850	−	0.838501i
$554$	−20.7876	−	18.4327i	−0.883179	−	0.783131i
$555$		0			0
$556$	19.4252	+	25.8983i	0.823811	+	1.09833i
$557$	−2.53413	+	1.46308i	−0.107374	+	0.0619927i	−0.552726	−	0.833363i	$-0.686412\pi$
$557$	−2.53413	+	1.46308i	−0.107374	+	0.0619927i	0.445351	+	0.895356i	$0.353079\pi$
$558$		0			0
$559$	−20.3538	+	35.2538i	−0.860874	+	1.49108i
$560$	1.67553	−	15.2845i	0.0708043	−	0.645887i
$561$		0			0
$562$	38.4696	+	7.87148i	1.62274	+	0.332038i
$563$	2.96778	−	8.15390i	0.125077	−	0.343646i	−0.861312	−	0.508077i	$-0.830357\pi$
$563$	2.96778	−	8.15390i	0.125077	−	0.343646i	0.986389	+	0.164431i	$0.0525788\pi$
$564$		0			0
$565$	−17.7724	−	3.13375i	−0.747690	−	0.131838i
$566$	−27.6452	+	21.9396i	−1.16201	+	0.922190i
$567$		0			0
$568$	14.4375	−	6.82703i	0.605782	−	0.286456i
$569$	1.80356	−	10.2285i	0.0756093	−	0.428802i	−0.923381	−	0.383884i	$-0.874586\pi$
$569$	1.80356	−	10.2285i	0.0756093	−	0.428802i	0.998991	−	0.0449179i	$-0.0143026\pi$
$570$		0			0
$571$	1.71537	−	4.71295i	0.0717862	−	0.197231i	−0.898611	−	0.438747i	$-0.855422\pi$
$571$	1.71537	−	4.71295i	0.0717862	−	0.197231i	0.970397	+	0.241516i	$0.0776447\pi$
$572$	−0.495896	−	0.978649i	−0.0207345	−	0.0409194i
$573$		0			0
$574$	19.3114	+	11.8637i	0.806043	+	0.495183i
$575$	0.940956	−	1.62978i	0.0392406	−	0.0679667i
$576$		0			0
$577$	4.43057	+	7.67398i	0.184447	+	0.319472i	0.943390	−	0.331685i	$-0.107617\pi$
$577$	4.43057	+	7.67398i	0.184447	+	0.319472i	−0.758943	+	0.651157i	$0.774284\pi$
$578$	−0.337884	+	12.3751i	−0.0140541	+	0.514735i
$579$		0			0
$580$	42.1093	+	2.30119i	1.74849	+	0.0955515i
$581$	17.6940	−	3.11993i	0.734070	−	0.129436i
$582$		0			0
$583$	−1.19683	−	1.00426i	−0.0495677	−	0.0415922i
$584$	33.2363	+	23.0070i	1.37533	+	0.952037i
$585$		0			0
$586$	−1.69412	−	11.4229i	−0.0699836	−	0.471876i
$587$	0.553940	+	1.52194i	0.0228636	+	0.0628171i	0.950599	−	0.310420i	$-0.100470\pi$
$587$	0.553940	+	1.52194i	0.0228636	+	0.0628171i	−0.927736	+	0.373238i	$0.878248\pi$
$588$		0			0
$589$	19.8523	+	23.6590i	0.817999	+	0.974854i
$590$	−2.89166	−	8.67445i	−0.119048	−	0.357121i
$591$		0			0
$592$	19.1660	+	14.0562i	0.787719	+	0.577706i
$593$	16.7535			0.687984			0.343992	−	0.938973i	$-0.388221\pi$
$593$	16.7535			0.687984			0.343992	+	0.938973i	$0.388221\pi$
$594$		0			0
$595$			11.0386i			0.452538i
$596$	10.1890	−	23.8555i	0.417357	−	0.977158i
$597$		0			0
$598$	10.5585	−	3.51973i	0.431771	−	0.143933i
$599$	31.3875	−	26.3372i	1.28246	−	1.07611i	0.289557	−	0.957161i	$-0.406492\pi$
$599$	31.3875	−	26.3372i	1.28246	−	1.07611i	0.992900	−	0.118949i	$-0.0379524\pi$
$600$		0			0
$601$	−8.03176	+	2.92332i	−0.327622	+	0.119245i	−0.500594	−	0.865682i	$-0.666885\pi$
$601$	−8.03176	+	2.92332i	−0.327622	+	0.119245i	0.172972	+	0.984927i	$0.444663\pi$
$602$	3.90662	+	26.3410i	0.159222	+	1.07358i
$603$		0			0
$604$	6.43898	−	1.95288i	0.261998	−	0.0794614i
$605$	17.0235	−	20.2878i	0.692103	−	0.824817i
$606$		0			0
$607$	4.22098	+	23.9383i	0.171324	+	0.971627i	0.942302	+	0.334765i	$0.108657\pi$
$607$	4.22098	+	23.9383i	0.171324	+	0.971627i	−0.770978	+	0.636862i	$0.780232\pi$
$608$	−9.26258	−	22.7199i	−0.375647	−	0.921413i
$609$		0			0
$610$	0.134183	−	4.91448i	0.00543291	−	0.198981i
$611$	−11.6276	+	6.71318i	−0.470401	+	0.271586i
$612$		0			0
$613$	14.3628	+	8.29237i	0.580108	+	0.334926i	0.761176	−	0.648545i	$-0.224622\pi$
$613$	14.3628	+	8.29237i	0.580108	+	0.334926i	−0.181068	+	0.983471i	$0.557955\pi$
$614$	−13.7823	+	22.4344i	−0.556208	+	0.905378i
$615$		0			0
$616$	−0.652066	−	0.299806i	−0.0262725	−	0.0120795i
$617$	17.6023	+	6.40672i	0.708642	+	0.257925i	0.671096	−	0.741370i	$-0.265824\pi$
$617$	17.6023	+	6.40672i	0.708642	+	0.257925i	0.0375461	+	0.999295i	$0.488046\pi$
$618$		0			0
$619$	−4.87939	−	0.860368i	−0.196119	−	0.0345811i	0.0747256	−	0.997204i	$-0.476192\pi$
$619$	−4.87939	−	0.860368i	−0.196119	−	0.0345811i	−0.270845	+	0.962623i	$0.587303\pi$
$620$	33.4691	+	7.80575i	1.34415	+	0.313486i
$621$		0			0
$622$	−4.31146	−	5.43269i	−0.172874	−	0.217831i
$623$	−2.06579	+	11.7157i	−0.0827643	+	0.469380i
$624$		0			0
$625$	26.7242	+	9.72681i	1.06897	+	0.389072i
$626$	14.2683	+	2.91951i	0.570275	+	0.116687i
$627$		0			0
$628$	−0.990145	+	0.119330i	−0.0395111	+	0.00476179i
$629$	−14.7771	−	8.53157i	−0.589202	−	0.340176i
$630$		0			0
$631$	−2.46788	−	4.27449i	−0.0982447	−	0.170165i	0.812713	−	0.582664i	$-0.197989\pi$
$631$	−2.46788	−	4.27449i	−0.0982447	−	0.170165i	−0.910958	+	0.412499i	$0.864656\pi$
$632$	−34.3898	−	9.01684i	−1.36795	−	0.358670i
$633$		0			0
$634$	−23.8920	−	21.1855i	−0.948874	−	0.841384i
$635$	−32.9261	+	5.80576i	−1.30663	+	0.230394i
$636$		0			0
$637$	−9.87834	+	11.7725i	−0.391394	+	0.466445i
$638$	0.723469	−	1.83064i	0.0286424	−	0.0724755i
$639$		0			0
$640$	−23.4153	−	14.0404i	−0.925569	−	0.554994i
$641$	−1.74409	+	0.634798i	−0.0688875	+	0.0250730i	−0.376234	−	0.926525i	$-0.622781\pi$
$641$	−1.74409	+	0.634798i	−0.0688875	+	0.0250730i	0.307347	+	0.951598i	$0.400559\pi$
$642$		0			0
$643$	−21.2761	−	25.3559i	−0.839048	−	0.999938i	−0.999916	−	0.0129623i	$-0.995874\pi$
$643$	−21.2761	−	25.3559i	−0.839048	−	0.999938i	0.160868	−	0.986976i	$-0.448571\pi$
$644$	3.97893	−	6.09715i	0.156792	−	0.240261i
$645$		0			0
$646$	8.38746	+	15.4890i	0.330000	+	0.609407i
$647$	−8.85391			−0.348083			−0.174042	−	0.984738i	$-0.555683\pi$
$647$	−8.85391			−0.348083			−0.174042	+	0.984738i	$0.555683\pi$
$648$		0			0
$649$	−0.426789			−0.0167529
$650$	−1.90970	−	3.52662i	−0.0749047	−	0.138326i
$651$		0			0
$652$	−18.9333	−	12.3556i	−0.741484	−	0.483884i
$653$	6.38975	+	7.61501i	0.250050	+	0.297998i	0.876439	−	0.481512i	$-0.159912\pi$
$653$	6.38975	+	7.61501i	0.250050	+	0.297998i	−0.626389	+	0.779511i	$0.715468\pi$
$654$		0			0
$655$	−11.7127	+	4.26306i	−0.457652	+	0.166572i
$656$	33.4637	−	22.3547i	1.30654	−	0.872804i
$657$		0			0
$658$	−3.22808	+	8.16819i	−0.125844	+	0.318429i
$659$	27.1973	−	32.4125i	1.05946	−	1.26261i	0.0958197	−	0.995399i	$-0.469453\pi$
$659$	27.1973	−	32.4125i	1.05946	−	1.26261i	0.963637	−	0.267213i	$-0.0861028\pi$
$660$		0			0
$661$	−49.7307	+	8.76886i	−1.93430	+	0.341069i	−0.999886	−	0.0151198i	$-0.995187\pi$
$661$	−49.7307	+	8.76886i	−1.93430	+	0.341069i	−0.934414	+	0.356189i	$0.884076\pi$
$662$	24.9450	+	22.1192i	0.969516	+	0.859688i
$663$		0			0
$664$	8.09121	−	30.8595i	0.314000	−	1.19758i
$665$	−8.33631	−	14.4389i	−0.323268	−	0.559917i
$666$		0			0
$667$	17.2933	+	9.98430i	0.669600	+	0.386594i
$668$	3.15193	+	26.1533i	0.121952	+	1.01190i
$669$		0			0
$670$	0.764981	+	0.156527i	0.0295538	+	0.00604717i
$671$	−0.215633	−	0.0784840i	−0.00832442	−	0.00302984i
$672$		0			0
$673$	2.52619	−	14.3267i	0.0973775	−	0.552255i	−0.896615	−	0.442810i	$-0.853981\pi$
$673$	2.52619	−	14.3267i	0.0973775	−	0.552255i	0.993993	−	0.109445i	$-0.0349074\pi$
$674$	28.9072	+	36.4247i	1.11346	+	1.40303i
$675$		0			0
$676$	−0.518230	+	2.22204i	−0.0199319	+	0.0854632i
$677$	−39.3485	−	6.93820i	−1.51229	−	0.266657i	−0.644890	−	0.764276i	$-0.723097\pi$
$677$	−39.3485	−	6.93820i	−1.51229	−	0.266657i	−0.867396	+	0.497619i	$0.834208\pi$
$678$		0			0
$679$	−10.1155	−	3.68173i	−0.388197	−	0.141292i
$680$	17.8083	+	8.18786i	0.682916	+	0.313990i
$681$		0			0
$682$	0.839675	−	1.36680i	0.0321528	−	0.0523373i
$683$	−16.3031	−	9.41260i	−0.623821	−	0.360163i	0.154534	−	0.987987i	$-0.450612\pi$
$683$	−16.3031	−	9.41260i	−0.623821	−	0.360163i	−0.778355	+	0.627824i	$0.783946\pi$
$684$		0			0
$685$	−39.4087	+	22.7526i	−1.50573	+	0.869333i
$686$	−0.704774	+	25.8125i	−0.0269084	+	0.985526i
$687$		0			0
$688$	45.3930	+	13.2360i	1.73059	+	0.504617i
$689$	−5.86516	−	33.2630i	−0.223445	−	1.26722i
$690$		0			0
$691$	−7.33473	+	8.74119i	−0.279026	+	0.332531i	−0.887297	−	0.461199i	$-0.847419\pi$
$691$	−7.33473	+	8.74119i	−0.279026	+	0.332531i	0.608270	+	0.793730i	$0.291864\pi$
$692$	−9.50745	−	31.3477i	−0.361419	−	1.19166i
$693$		0			0
$694$	−0.175090	−	1.18057i	−0.00664632	−	0.0448139i
$695$	36.7062	−	13.3600i	1.39235	−	0.506773i
$696$		0			0
$697$	−22.1320	+	18.5709i	−0.838307	+	0.703423i
$698$	−18.8100	+	6.27039i	−0.711969	+	0.237338i
$699$		0			0
$700$	−2.41264	−	1.03047i	−0.0911891	−	0.0389481i
$701$			29.8398i			1.12704i	0.826104	+	0.563518i	$0.190552\pi$
$701$			29.8398i			1.12704i	−0.826104	+	0.563518i	$0.809448\pi$
$702$		0			0
$703$	25.7721			0.972013
$704$	−0.967340	+	0.829580i	−0.0364580	+	0.0312660i
$705$		0			0
$706$	−10.5453	−	31.6340i	−0.396878	−	1.19056i
$707$	1.74463	+	2.07917i	0.0656137	+	0.0781954i
$708$		0			0
$709$	−0.897749	−	2.46655i	−0.0337157	−	0.0926331i	0.921693	−	0.387921i	$-0.126807\pi$
$709$	−0.897749	−	2.46655i	−0.0337157	−	0.0926331i	−0.955408	+	0.295288i	$0.904584\pi$
$710$	−2.82694	−	19.0611i	−0.106093	−	0.715351i
$711$		0			0
$712$	17.3684	+	12.0228i	0.650907	+	0.450574i
$713$	12.4658	+	10.4601i	0.466849	+	0.391733i
$714$		0			0
$715$	−1.30367	+	0.229871i	−0.0487543	+	0.00859670i
$716$	0.646963	−	11.8387i	0.0241781	−	0.442435i
$717$		0			0
$718$	−1.04184	+	38.1574i	−0.0388809	+	1.42402i
$719$	6.54404	+	11.3346i	0.244051	+	0.422709i	0.961864	−	0.273526i	$-0.0881901\pi$
$719$	6.54404	+	11.3346i	0.244051	+	0.422709i	−0.717813	+	0.696236i	$0.754857\pi$
$720$		0			0
$721$	−10.2123	+	17.6883i	−0.380327	+	0.658746i
$722$	0.226378	+	0.139072i	0.00842491	+	0.00517574i
$723$		0			0
$724$	3.10657	−	1.57414i	0.115455	−	0.0585026i
$725$	2.46100	−	6.76154i	0.0913992	−	0.251117i
$726$		0			0
$727$	6.97054	−	39.5319i	0.258523	−	1.46616i	−0.528342	−	0.849031i	$-0.677186\pi$
$727$	6.97054	−	39.5319i	0.258523	−	1.46616i	0.786865	−	0.617125i	$-0.211703\pi$
$728$	−6.63263	−	14.0263i	−0.245822	−	0.519851i
$729$		0			0
$730$	38.2044	−	30.3196i	1.41401	−	1.12218i
$731$	−33.4294	−	5.89450i	−1.23643	−	0.218016i
$732$		0			0
$733$	0.696450	−	1.91348i	0.0257240	−	0.0706760i	−0.926166	−	0.377116i	$-0.876916\pi$
$733$	0.696450	−	1.91348i	0.0257240	−	0.0706760i	0.951890	+	0.306440i	$0.0991380\pi$
$734$	−40.3657	−	8.25944i	−1.48992	−	0.304862i
$735$		0			0
$736$	−6.88501	−	10.9417i	−0.253785	−	0.403315i
$737$	0.0182229	−	0.0315629i	0.000671248	−	0.00116264i
$738$		0			0
$739$	30.6990	−	17.7241i	1.12928	−	0.651990i	0.185526	−	0.982639i	$-0.440601\pi$
$739$	30.6990	−	17.7241i	1.12928	−	0.651990i	0.943754	+	0.330649i	$0.107268\pi$
$740$	22.9419	−	17.2078i	0.843363	−	0.632571i
$741$		0			0
$742$	−16.5317	−	14.6590i	−0.606898	−	0.538148i
$743$	−9.22773	−	52.3330i	−0.338532	−	1.91991i	−0.389106	−	0.921193i	$-0.627216\pi$
$743$	−9.22773	−	52.3330i	−0.338532	−	1.91991i	0.0505739	−	0.998720i	$-0.483895\pi$
$744$		0			0
$745$	−23.9767	−	20.1189i	−0.878440	−	0.737099i
$746$	1.51168	+	0.597419i	0.0553466	+	0.0218731i
$747$		0			0
$748$	0.625426	−	0.667691i	0.0228678	−	0.0244132i
$749$	−8.58392	−	23.5841i	−0.313649	−	0.861745i
$750$		0			0
$751$	6.58894	−	5.52878i	0.240434	−	0.201748i	−0.514606	−	0.857427i	$-0.672062\pi$
$751$	6.58894	−	5.52878i	0.240434	−	0.201748i	0.755040	+	0.655679i	$0.227617\pi$
$752$	10.7831	+	11.2665i	0.393220	+	0.410848i
$753$		0			0
$754$	37.4203	−	20.2635i	1.36277	−	0.737953i
$755$		−	8.11871i		−	0.295470i
$756$		0			0
$757$			21.7216i			0.789484i	0.918792	+	0.394742i	$0.129166\pi$
$757$			21.7216i			0.789484i	−0.918792	+	0.394742i	$0.870834\pi$
$758$	11.3891	+	21.0320i	0.413670	+	0.763918i
$759$		0			0
$760$	−29.4774	+	2.73870i	−1.06926	+	0.0993430i
$761$	0.341041	−	0.286168i	0.0123627	−	0.0103736i	−0.636585	−	0.771206i	$-0.719654\pi$
$761$	0.341041	−	0.286168i	0.0123627	−	0.0103736i	0.648948	+	0.760833i	$0.275209\pi$
$762$		0			0
$763$	2.30920	+	6.34447i	0.0835986	+	0.229685i
$764$	15.8551	+	14.8515i	0.573618	+	0.537308i
$765$		0			0
$766$	10.4881	−	26.5386i	0.378951	−	0.958880i
$767$	−7.06802	−	5.93077i	−0.255211	−	0.214148i
$768$		0			0
$769$	3.22004	+	18.2618i	0.116118	+	0.658536i	0.986191	+	0.165614i	$0.0529604\pi$
$769$	3.22004	+	18.2618i	0.116118	+	0.658536i	−0.870073	+	0.492923i	$0.835928\pi$
$770$	−0.574524	+	0.647922i	−0.0207044	+	0.0233495i
$771$		0			0
$772$	−23.1594	+	17.3709i	−0.833526	+	0.625192i
$773$	−1.50501	+	0.868919i	−0.0541315	+	0.0312528i	−0.526822	−	0.849976i	$-0.676616\pi$
$773$	−1.50501	+	0.868919i	−0.0541315	+	0.0312528i	0.472690	+	0.881229i	$0.343283\pi$
$774$		0			0
$775$	2.93190	−	5.07821i	0.105317	−	0.182415i
$776$	−13.4428	+	13.5881i	−0.482569	+	0.487785i
$777$		0			0
$778$	−8.26750	+	40.4050i	−0.296404	+	1.44859i
$779$	14.9248	−	41.0055i	0.534736	−	1.46918i
$780$		0			0
$781$	−0.885756	−	0.156183i	−0.0316948	−	0.00558865i
$782$	5.76934	+	7.26970i	0.206311	+	0.259964i
$783$		0			0
$784$	16.0088	+	7.89672i	0.571742	+	0.282026i
$785$	−0.208959	+	1.18507i	−0.00745808	+	0.0422969i
$786$		0			0
$787$	−12.6576	+	34.7764i	−0.451193	+	1.23964i	0.480692	+	0.876890i	$0.340386\pi$
$787$	−12.6576	+	34.7764i	−0.451193	+	1.23964i	−0.931885	+	0.362754i	$0.881837\pi$
$788$	−15.1806	+	7.69222i	−0.540785	+	0.274024i
$789$		0			0
$790$	−22.4545	+	36.5507i	−0.798896	+	1.30042i
$791$	−5.95616	+	10.3164i	−0.211777	+	0.366808i
$792$		0			0
$793$	−2.48045	−	4.29626i	−0.0880833	−	0.152565i
$794$	−16.8394	−	0.459776i	−0.597608	−	0.0163168i
$795$		0			0
$796$	−24.6807	−	1.34875i	−0.874785	−	0.0478052i
$797$	−11.7114	+	2.06503i	−0.414837	+	0.0731470i	−0.377172	−	0.926143i	$-0.623103\pi$
$797$	−11.7114	+	2.06503i	−0.414837	+	0.0731470i	−0.0376658	+	0.999290i	$0.511992\pi$
$798$		0			0
$799$	−8.57656	−	7.19659i	−0.303417	−	0.254597i
$800$	−3.45201	+	3.12790i	−0.122047	+	0.110588i
$801$		0			0
$802$	3.32992	−	0.493858i	0.117584	−	0.0174387i
$803$	−0.778620	−	2.13924i	−0.0274769	−	0.0754922i
$804$		0			0
$805$	−5.64671	−	6.72949i	−0.199021	−	0.237183i
$806$	32.8992	−	10.9671i	1.15882	−	0.386298i
$807$		0			0
$808$	4.64836	−	1.27235i	0.163529	−	0.0447610i
$809$	−13.6067			−0.478385			−0.239192	−	0.970972i	$-0.576883\pi$
$809$	−13.6067			−0.478385			−0.239192	+	0.970972i	$0.576883\pi$
$810$		0			0
$811$		−	23.1998i		−	0.814656i	−0.913282	−	0.407328i	$-0.866461\pi$
$811$		−	23.1998i		−	0.814656i	0.913282	−	0.407328i	$-0.133539\pi$
$812$	10.9341	−	25.6000i	0.383712	−	0.898385i
$813$		0			0
$814$	−0.423317	−	1.26987i	−0.0148373	−	0.0445091i
$815$	−20.8969	+	17.5346i	−0.731985	+	0.614209i
$816$		0			0
$817$	48.1785	−	17.5355i	1.68555	−	0.613491i
$818$	−17.9961	+	2.66899i	−0.629218	+	0.0933189i
$819$		0			0
$820$	−14.0932	−	46.4676i	−0.492155	−	1.62272i
$821$	−18.9516	+	22.5856i	−0.661414	+	0.788243i	−0.987588	−	0.157067i	$-0.949796\pi$
$821$	−18.9516	+	22.5856i	−0.661414	+	0.788243i	0.326174	+	0.945310i	$0.394241\pi$
$822$		0			0
$823$	2.95142	+	16.7383i	0.102880	+	0.583462i	0.992046	+	0.125877i	$0.0401744\pi$
$823$	2.95142	+	16.7383i	0.102880	+	0.583462i	−0.889166	+	0.457585i	$0.848715\pi$
$824$	20.9611	+	29.5956i	0.730213	+	1.03101i
$825$		0			0
$826$	−6.03342	−	0.164734i	−0.209929	−	0.00573183i
$827$	−44.0488	+	25.4316i	−1.53173	+	0.884343i	−0.532444	+	0.846465i	$0.678726\pi$
$827$	−44.0488	+	25.4316i	−1.53173	+	0.884343i	−0.999282	+	0.0378772i	$0.987940\pi$
$828$		0			0
$829$	−41.8595	−	24.1676i	−1.45384	−	0.839374i	−0.455143	−	0.890418i	$-0.650412\pi$
$829$	−41.8595	−	24.1676i	−1.45384	−	0.839374i	−0.998696	+	0.0510440i	$0.983745\pi$
$830$	−32.7986	−	20.1494i	−1.13846	−	0.699397i
$831$		0			0
$832$	−27.5481	+	0.296210i	−0.955059	+	0.0102692i
$833$	−12.0421	−	4.38298i	−0.417235	−	0.151861i
$834$		0			0
$835$	31.3019	+	5.51936i	1.08325	+	0.191005i
$836$	−0.313844	+	1.34569i	−0.0108545	+	0.0465416i
$837$		0			0
$838$	8.30411	−	6.59026i	0.286861	−	0.227657i
$839$	−4.93028	+	27.9610i	−0.170212	+	0.965321i	0.773314	+	0.634023i	$0.218598\pi$
$839$	−4.93028	+	27.9610i	−0.170212	+	0.965321i	−0.943526	+	0.331298i	$0.892514\pi$
$840$		0			0
$841$	44.4943	+	16.1946i	1.53429	+	0.558434i
$842$	2.27256	−	11.1065i	0.0783176	−	0.382754i
$843$		0			0
$844$	3.51049	−	0.423076i	0.120836	−	0.0145629i
$845$	2.38422	+	1.37653i	0.0820196	+	0.0473540i
$846$		0			0
$847$	−8.74084	−	15.1396i	−0.300339	−	0.520202i
$848$	−35.9113	+	15.7969i	−1.23320	+	0.542468i
$849$		0			0
$850$	2.21876	−	2.50222i	0.0761030	−	0.0858254i
$851$	13.3729	−	2.35800i	0.458417	−	0.0808313i
$852$		0			0
$853$	−17.3921	+	20.7271i	−0.595495	+	0.709684i	−0.976652	−	0.214827i	$-0.931081\pi$
$853$	−17.3921	+	20.7271i	−0.595495	+	0.709684i	0.381157	+	0.924510i	$0.375526\pi$
$854$	−3.01806	−	1.19274i	−0.103276	−	0.0408147i
$855$		0			0
$856$	−44.4148	−	3.64530i	−1.51807	−	0.124594i
$857$	−1.73329	+	0.630867i	−0.0592082	+	0.0215500i	−0.371454	−	0.928451i	$-0.621141\pi$
$857$	−1.73329	+	0.630867i	−0.0592082	+	0.0215500i	0.312246	+	0.950001i	$0.398919\pi$
$858$		0			0
$859$	−11.6792	−	13.9187i	−0.398489	−	0.474901i	0.529070	−	0.848578i	$-0.322541\pi$
$859$	−11.6792	−	13.9187i	−0.398489	−	0.474901i	−0.927559	+	0.373678i	$0.878097\pi$
$860$	31.1795	−	47.7782i	1.06321	−	1.62922i
$861$		0			0
$862$	−5.76650	+	3.12262i	−0.196408	+	0.106357i
$863$	−49.6695			−1.69077			−0.845385	−	0.534157i	$-0.820629\pi$
$863$	−49.6695			−1.69077			−0.845385	+	0.534157i	$0.820629\pi$
$864$		0			0
$865$	−39.5254			−1.34390
$866$	0.0843627	−	0.0456833i	0.00286676	−	0.00155238i
$867$		0			0
$868$	12.3979	−	18.9980i	0.420810	−	0.644833i
$869$	1.28702	+	1.53381i	0.0436592	+	0.0520310i
$870$		0			0
$871$	0.740394	−	0.269482i	0.0250873	−	0.00913103i
$872$	11.9482	+	0.980638i	0.404618	+	0.0332086i
$873$		0			0
$874$	−13.0366	−	5.15208i	−0.440969	−	0.174272i
$875$	10.3197	−	12.2985i	0.348869	−	0.415766i
$876$		0			0
$877$	22.9919	−	4.05410i	0.776382	−	0.136897i	0.228603	−	0.973520i	$-0.426584\pi$
$877$	22.9919	−	4.05410i	0.776382	−	0.136897i	0.547779	+	0.836623i	$0.315473\pi$
$878$	−12.9333	+	14.5856i	−0.436479	+	0.492240i
$879$		0			0
$880$	0.619123	+	1.40746i	0.0208706	+	0.0474455i
$881$	15.9640	+	27.6505i	0.537842	+	0.931569i	0.999020	+	0.0442614i	$0.0140935\pi$
$881$	15.9640	+	27.6505i	0.537842	+	0.931569i	−0.461178	+	0.887307i	$0.652573\pi$
$882$		0			0
$883$	−40.1101	−	23.1576i	−1.34981	−	0.779315i	−0.361590	−	0.932337i	$-0.617766\pi$
$883$	−40.1101	−	23.1576i	−1.34981	−	0.779315i	−0.988223	+	0.153023i	$0.951099\pi$
$884$	19.6360	−	2.36649i	0.660432	−	0.0795937i
$885$		0			0
$886$	−3.78434	+	18.4949i	−0.127137	+	0.621347i
$887$	32.0649	+	11.6707i	1.07663	+	0.391863i	0.818654	−	0.574288i	$-0.194721\pi$
$887$	32.0649	+	11.6707i	1.07663	+	0.391863i	0.257980	+	0.966150i	$0.416943\pi$
$888$		0			0
$889$	−3.83231	+	21.7341i	−0.128532	+	0.728939i
$890$	19.9646	−	15.8442i	0.669214	−	0.531097i
$891$		0			0
$892$	−1.36671	+	5.86013i	−0.0457609	+	0.196212i
$893$	16.6533	+	2.93643i	0.557283	+	0.0982640i
$894$		0			0
$895$	−13.4431	−	4.89290i	−0.449354	−	0.163552i
$896$	−13.9953	+	11.3542i	−0.467549	+	0.379318i
$897$		0			0
$898$	15.0980	+	9.27530i	0.503828	+	0.309521i
$899$	53.8839	+	31.1099i	1.79713	+	1.03757i
$900$		0			0
$901$	24.3917	−	14.0825i	0.812605	−	0.469158i
$902$	−2.26562	−	0.0618596i	−0.0754369	−	0.00205970i
$903$		0			0
$904$	12.2252	+	17.2611i	0.406603	+	0.574095i
$905$	−0.729690	−	4.13828i	−0.0242557	−	0.137561i
$906$		0			0
$907$	0.685743	−	0.817237i	0.0227697	−	0.0271359i	−0.754539	−	0.656255i	$-0.772140\pi$
$907$	0.685743	−	0.817237i	0.0227697	−	0.0271359i	0.777309	+	0.629119i	$0.216584\pi$
$908$	3.30095	+	10.8838i	0.109546	+	0.361192i
$909$		0			0
$910$	−18.5183	+	2.74644i	−0.613877	+	0.0910438i
$911$	−2.39685	+	0.872383i	−0.0794113	+	0.0289033i	−0.381420	−	0.924402i	$-0.624565\pi$
$911$	−2.39685	+	0.872383i	−0.0794113	+	0.0289033i	0.302009	+	0.953305i	$0.402343\pi$
$912$		0			0
$913$	−1.37636	+	1.15490i	−0.0455508	+	0.0382216i
$914$	8.10018	+	24.2991i	0.267930	+	0.803741i
$915$		0			0
$916$	−17.1072	+	40.0530i	−0.565237	+	1.32339i
$917$			8.22758i			0.271699i
$918$		0			0
$919$	3.85703			0.127232			0.0636159	−	0.997974i	$-0.479737\pi$
$919$	3.85703			0.127232			0.0636159	+	0.997974i	$0.479737\pi$
$920$	−15.0450	+	4.11810i	−0.496018	+	0.135770i
$921$		0			0
$922$	9.36384	−	3.12147i	0.308382	−	0.102800i
$923$	−12.4986	−	14.8952i	−0.411396	−	0.490283i
$924$		0			0
$925$	−1.67355	−	4.59804i	−0.0550259	−	0.151182i
$926$	−39.9282	+	5.92173i	−1.31212	+	0.194600i
$927$		0			0
$928$	−33.1895	−	36.6286i	−1.08950	−	1.20239i
$929$	−23.6191	−	19.8188i	−0.774919	−	0.650234i	0.167045	−	0.985949i	$-0.446578\pi$
$929$	−23.6191	−	19.8188i	−0.774919	−	0.650234i	−0.941964	+	0.335715i	$0.891022\pi$
$930$		0			0
$931$	19.0616	−	3.36108i	0.624719	−	0.110155i
$932$	46.9228	+	2.56423i	1.53701	+	0.0839942i
$933$		0			0
$934$	0.769863	+	0.0210200i	0.0251907	+	0.000687797i
$935$	−0.551933	−	0.955975i	−0.0180501	−	0.0312637i
$936$		0			0
$937$	3.69048	−	6.39210i	0.120563	−	0.208821i	−0.799427	−	0.600763i	$-0.794863\pi$
$937$	3.69048	−	6.39210i	0.120563	−	0.208821i	0.919990	+	0.391942i	$0.128197\pi$
$938$	0.269795	−	0.439164i	0.00880913	−	0.0143392i
$939$		0			0
$940$	16.7852	−	8.50531i	0.547473	−	0.277413i
$941$	13.1119	−	36.0246i	0.427435	−	1.17437i	−0.519929	−	0.854209i	$-0.674042\pi$
$941$	13.1119	−	36.0246i	0.427435	−	1.17437i	0.947364	−	0.320158i	$-0.103736\pi$
$942$		0			0
$943$	3.99256	−	22.6429i	0.130016	−	0.737355i
$944$	−4.74105	+	9.61137i	−0.154308	+	0.312823i
$945$		0			0
$946$	−1.65538	−	2.08588i	−0.0538212	−	0.0678178i
$947$	21.8272	+	3.84873i	0.709289	+	0.125067i	0.516642	−	0.856201i	$-0.327182\pi$
$947$	21.8272	+	3.84873i	0.709289	+	0.125067i	0.192647	+	0.981268i	$0.438293\pi$
$948$		0			0
$949$	16.8328	−	46.2477i	0.546416	−	1.50126i
$950$	−1.01256	+	4.94861i	−0.0328519	+	0.160554i
$951$		0			0
$952$	9.09922	−	9.19759i	0.294907	−	0.298095i
$953$	−22.3908	+	38.7819i	−0.725308	+	1.25627i	0.233540	+	0.972347i	$0.424969\pi$
$953$	−22.3908	+	38.7819i	−0.725308	+	1.25627i	−0.958847	+	0.283922i	$0.908364\pi$
$954$		0			0
$955$	22.7008	−	13.1063i	0.734580	−	0.424110i
$956$	−37.4375	+	28.0803i	−1.21082	+	0.908182i
$957$		0			0
$958$	7.92042	−	8.93228i	0.255897	−	0.288589i
$959$	5.21595	+	29.5811i	0.168432	+	0.955224i
$960$		0			0
$961$	15.0947	+	12.6659i	0.486925	+	0.408579i
$962$	10.6360	−	26.9128i	0.342918	−	0.867704i
$963$		0			0
$964$	−5.73547	−	5.37241i	−0.184727	−	0.173034i
$965$	11.9471	+	32.8244i	0.384591	+	1.05666i
$966$		0			0
$967$	32.4852	−	27.2583i	1.04465	−	0.876567i	0.0521310	−	0.998640i	$-0.483399\pi$
$967$	32.4852	−	27.2583i	1.04465	−	0.876567i	0.992521	+	0.122073i	$0.0389542\pi$
$968$	−30.9078	+	2.87160i	−0.993415	+	0.0922966i
$969$		0			0
$970$	10.9820	+	20.2803i	0.352611	+	0.651163i
$971$			9.33492i			0.299572i	0.988718	+	0.149786i	$0.0478584\pi$
$971$			9.33492i			0.299572i	−0.988718	+	0.149786i	$0.952142\pi$
$972$		0			0
$973$		−	25.7843i		−	0.826608i
$974$	18.6555	−	10.1021i	0.597760	−	0.323693i
$975$		0			0
$976$	−4.16286	+	3.98424i	−0.133250	+	0.127533i
$977$	−0.274142	+	0.230032i	−0.00877057	+	0.00735938i	−0.647162	−	0.762352i	$-0.724044\pi$
$977$	−0.274142	+	0.230032i	−0.00877057	+	0.00735938i	0.638392	+	0.769712i	$0.279600\pi$
$978$		0			0
$979$	−0.406885	−	1.11791i	−0.0130041	−	0.0357285i
$980$	14.7242	−	15.7192i	0.470348	−	0.502133i
$981$		0			0
$982$	19.3032	+	7.62865i	0.615990	+	0.243440i
$983$	6.53130	+	5.48041i	0.208316	+	0.174798i	0.740976	−	0.671531i	$-0.234363\pi$
$983$	6.53130	+	5.48041i	0.208316	+	0.174798i	−0.532660	+	0.846329i	$0.678808\pi$
$984$		0			0
$985$	3.56571	+	20.2221i	0.113613	+	0.644331i
$986$	26.5506	+	23.5429i	0.845542	+	0.749758i
$987$		0			0
$988$	−23.8976	+	17.9246i	−0.760283	+	0.570256i
$989$	23.3950	−	13.5071i	0.743917	−	0.429501i
$990$		0			0
$991$	−25.9790	+	44.9969i	−0.825249	+	1.42937i	0.0764798	+	0.997071i	$0.475632\pi$
$991$	−25.9790	+	44.9969i	−0.825249	+	1.42937i	−0.901729	+	0.432302i	$0.857701\pi$
$992$	−21.4529	−	34.0929i	−0.681129	−	1.08245i
$993$		0			0
$994$	−12.4614	−	2.54981i	−0.395253	−	0.0808750i
$995$	−10.2004	+	28.0255i	−0.323375	+	0.888467i
$996$		0			0
$997$	44.7921	+	7.89805i	1.41858	+	0.250134i	0.829755	−	0.558128i	$-0.188480\pi$
$997$	44.7921	+	7.89805i	1.41858	+	0.250134i	0.588824	+	0.808262i	$0.299591\pi$
$998$	−19.1885	+	15.2282i	−0.607401	+	0.482042i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.397.4		204
3.2	odd	2		216.2.t.a.133.31	yes	204
8.5	even	2	inner	648.2.t.a.397.26		204
12.11	even	2		864.2.bf.a.241.17		204
24.5	odd	2		216.2.t.a.133.9	yes	204
24.11	even	2		864.2.bf.a.241.18		204
27.13	even	9	inner	648.2.t.a.253.26		204
27.14	odd	18		216.2.t.a.13.9	✓	204
108.95	even	18		864.2.bf.a.337.18		204
216.13	even	18	inner	648.2.t.a.253.4		204
216.149	odd	18		216.2.t.a.13.31	yes	204
216.203	even	18		864.2.bf.a.337.17		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.9	✓	204	27.14	odd	18
216.2.t.a.13.31	yes	204	216.149	odd	18
216.2.t.a.133.9	yes	204	24.5	odd	2
216.2.t.a.133.31	yes	204	3.2	odd	2
648.2.t.a.253.4		204	216.13	even	18	inner
648.2.t.a.253.26		204	27.13	even	9	inner
648.2.t.a.397.4		204	1.1	even	1	trivial
648.2.t.a.397.26		204	8.5	even	2	inner
864.2.bf.a.241.17		204	12.11	even	2
864.2.bf.a.241.18		204	24.11	even	2
864.2.bf.a.337.17		204	216.203	even	18
864.2.bf.a.337.18		204	108.95	even	18

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.24359 + 0.673416i) q^{2} +(1.09302 - 1.67490i) q^{4} +(-1.55117 - 1.84861i) q^{5} +(-1.49685 + 0.544810i) q^{7} +(-0.231362 + 2.81895i) q^{8} +(3.17390 + 1.25433i) q^{10} +(0.102391 - 0.122025i) q^{11} +(3.39140 - 0.597995i) q^{13} +(1.49458 - 1.68552i) q^{14} +(-1.61061 - 3.66141i) q^{16} +(1.43581 + 2.48690i) q^{17} +(-3.75621 - 2.16865i) q^{19} +(-4.79171 + 0.577486i) q^{20} +(-0.0451590 + 0.220701i) q^{22} +(-2.14748 - 0.781619i) q^{23} +(-0.142997 + 0.810974i) q^{25} +(-3.81480 + 3.02748i) q^{26} +(-0.723589 + 3.10257i) q^{28} +(-8.60509 - 1.51731i) q^{29} +(-6.69129 - 2.43543i) q^{31} +(4.46858 + 3.46868i) q^{32} +(-3.46028 - 2.12578i) q^{34} +(3.32901 + 1.92201i) q^{35} +(-5.14590 + 2.97099i) q^{37} +(6.13158 + 0.167414i) q^{38} +(5.57002 - 3.94497i) q^{40} +(1.74706 + 9.90807i) q^{41} +(-7.59829 + 9.05529i) q^{43} +(-0.0924647 - 0.304872i) q^{44} +(3.19694 - 0.474136i) q^{46} +(-3.66367 + 1.33347i) q^{47} +(-3.41856 + 2.86851i) q^{49} +(-0.368294 - 1.10481i) q^{50} +(2.70529 - 6.33388i) q^{52} -9.80805i q^{53} -0.384404 q^{55} +(-1.18948 - 4.34560i) q^{56} +(11.7230 - 3.90790i) q^{58} +(-1.72220 - 2.05244i) q^{59} +(-0.492702 - 1.35369i) q^{61} +(9.96127 - 1.47735i) q^{62} +(-7.89294 - 1.30440i) q^{64} +(-6.36609 - 5.34178i) q^{65} +(0.225321 - 0.0397302i) q^{67} +(5.73470 + 0.313390i) q^{68} +(-5.43423 - 0.148374i) q^{70} +(-2.82317 - 4.88987i) q^{71} +(7.14574 - 12.3768i) q^{73} +(4.39867 - 7.16002i) q^{74} +(-7.73789 + 3.92091i) q^{76} +(-0.0867843 + 0.238438i) q^{77} +(-2.18269 + 12.3786i) q^{79} +(-4.27021 + 8.65685i) q^{80} +(-8.84487 - 11.1451i) q^{82} +(-11.1079 - 1.95862i) q^{83} +(2.37013 - 6.51187i) q^{85} +(3.35117 - 16.3779i) q^{86} +(0.320294 + 0.316868i) q^{88} +(3.73417 - 6.46777i) q^{89} +(-4.75063 + 2.74278i) q^{91} +(-3.65638 + 2.74250i) q^{92} +(3.65812 - 4.12546i) q^{94} +(1.81753 + 10.3077i) q^{95} +(5.17680 + 4.34385i) q^{97} +(2.31958 - 5.86936i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

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