LMFDB - Embedded newform 756.2.bx.a.41.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(41,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 17, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("756.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bx (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.2
Character	$\chi$	$=$	756.41
Dual form			756.2.bx.a.461.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70123 - 0.325320i) q^{3} +(2.96273 + 2.48603i) q^{5} +(1.79607 + 1.94271i) q^{7} +(2.78833 + 1.10688i) q^{9} +O(q^{10})$	\(q+(-1.70123 - 0.325320i) q^{3} +(2.96273 + 2.48603i) q^{5} +(1.79607 + 1.94271i) q^{7} +(2.78833 + 1.10688i) q^{9} +(0.338747 + 0.403702i) q^{11} +(0.435661 + 0.0768188i) q^{13} +(-4.23152 - 5.19313i) q^{15} +(-1.02179 + 1.76979i) q^{17} +(-3.49064 + 2.01532i) q^{19} +(-2.42352 - 3.88929i) q^{21} +(-2.55771 - 7.02725i) q^{23} +(1.72921 + 9.80683i) q^{25} +(-4.38349 - 2.79016i) q^{27} +(0.159050 - 0.0280448i) q^{29} +(1.87661 + 5.15593i) q^{31} +(-0.444952 - 0.796990i) q^{33} +(0.491636 + 10.2208i) q^{35} +(2.57564 - 4.46114i) q^{37} +(-0.716167 - 0.272415i) q^{39} +(-1.01692 + 5.76725i) q^{41} +(4.81951 - 4.04405i) q^{43} +(5.50934 + 10.2113i) q^{45} +(2.82049 + 1.02658i) q^{47} +(-0.548267 + 6.97850i) q^{49} +(2.31403 - 2.67840i) q^{51} +12.0204i q^{53} +2.03820i q^{55} +(6.59398 - 2.29294i) q^{57} +(-5.93331 - 4.97864i) q^{59} +(4.00630 - 11.0072i) q^{61} +(2.85768 + 7.40497i) q^{63} +(1.09977 + 1.31066i) q^{65} +(-1.79309 + 10.1691i) q^{67} +(2.06514 + 12.7870i) q^{69} +(-4.73069 - 2.73126i) q^{71} +(11.8488 - 6.84090i) q^{73} +(0.248582 - 17.2462i) q^{75} +(-0.175865 + 1.38316i) q^{77} +(1.51105 + 8.56961i) q^{79} +(6.54961 + 6.17273i) q^{81} +(-1.20343 - 6.82497i) q^{83} +(-7.42702 + 2.70321i) q^{85} +(-0.279703 - 0.00403157i) q^{87} +(0.396843 + 0.687352i) q^{89} +(0.633241 + 0.984337i) q^{91} +(-1.51520 - 9.38190i) q^{93} +(-15.3520 - 2.70696i) q^{95} +(6.78774 + 8.08932i) q^{97} +(0.497687 + 1.50061i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.70123	−	0.325320i	−0.982203	−	0.187823i
$3$	−1.70123	−	0.325320i	−0.982203	−	0.187823i
$4$		0			0
$5$	2.96273	+	2.48603i	1.32497	+	1.11179i	0.985224	+	0.171270i	$0.0547870\pi$
$5$	2.96273	+	2.48603i	1.32497	+	1.11179i	0.339750	+	0.940516i	$0.389657\pi$
$6$		0			0
$7$	1.79607	+	1.94271i	0.678851	+	0.734276i
$7$	1.79607	+	1.94271i	0.678851	+	0.734276i
$8$		0			0
$9$	2.78833	+	1.10688i	0.929445	+	0.368961i
$10$		0			0
$11$	0.338747	+	0.403702i	0.102136	+	0.121721i	0.814691	−	0.579895i	$-0.196907\pi$
$11$	0.338747	+	0.403702i	0.102136	+	0.121721i	−0.712555	+	0.701616i	$0.752462\pi$
$12$		0			0
$13$	0.435661	+	0.0768188i	0.120831	+	0.0213057i	0.233736	−	0.972300i	$-0.424905\pi$
$13$	0.435661	+	0.0768188i	0.120831	+	0.0213057i	−0.112906	+	0.993606i	$0.536016\pi$
$14$		0			0
$15$	−4.23152	−	5.19313i	−1.09257	−	1.34086i
$16$		0			0
$17$	−1.02179	+	1.76979i	−0.247820	+	0.429236i	−0.962921	−	0.269785i	$-0.913047\pi$
$17$	−1.02179	+	1.76979i	−0.247820	+	0.429236i	0.715101	+	0.699021i	$0.246381\pi$
$18$		0			0
$19$	−3.49064	+	2.01532i	−0.800807	+	0.462346i	−0.843753	−	0.536731i	$-0.819659\pi$
$19$	−3.49064	+	2.01532i	−0.800807	+	0.462346i	0.0429464	+	0.999077i	$0.486326\pi$
$20$		0			0
$21$	−2.42352	−	3.88929i	−0.528855	−	0.848712i
$22$		0			0
$23$	−2.55771	−	7.02725i	−0.533320	−	1.46528i	−0.855097	−	0.518468i	$-0.826502\pi$
$23$	−2.55771	−	7.02725i	−0.533320	−	1.46528i	0.321777	−	0.946815i	$-0.395720\pi$
$24$		0			0
$25$	1.72921	+	9.80683i	0.345842	+	1.96137i
$26$		0			0
$27$	−4.38349	−	2.79016i	−0.843604	−	0.536966i
$28$		0			0
$29$	0.159050	−	0.0280448i	0.0295348	−	0.00520778i	−0.158861	−	0.987301i	$-0.550782\pi$
$29$	0.159050	−	0.0280448i	0.0295348	−	0.00520778i	0.188396	+	0.982093i	$0.439671\pi$
$30$		0			0
$31$	1.87661	+	5.15593i	0.337048	+	0.926033i	0.986227	+	0.165397i	$0.0528905\pi$
$31$	1.87661	+	5.15593i	0.337048	+	0.926033i	−0.649179	+	0.760636i	$0.724887\pi$
$32$		0			0
$33$	−0.444952	−	0.796990i	−0.0774562	−	0.138738i
$34$		0			0
$35$	0.491636	+	10.2208i	0.0831017	+	1.72763i
$36$		0			0
$37$	2.57564	−	4.46114i	0.423433	−	0.733407i	−0.572840	−	0.819667i	$-0.694158\pi$
$37$	2.57564	−	4.46114i	0.423433	−	0.733407i	0.996273	+	0.0862605i	$0.0274917\pi$
$38$		0			0
$39$	−0.716167	−	0.272415i	−0.114679	−	0.0436214i
$40$		0			0
$41$	−1.01692	+	5.76725i	−0.158816	+	0.900693i	0.796397	+	0.604775i	$0.206737\pi$
$41$	−1.01692	+	5.76725i	−0.158816	+	0.900693i	−0.955213	+	0.295918i	$0.904374\pi$
$42$		0			0
$43$	4.81951	−	4.04405i	0.734969	−	0.616712i	−0.196512	−	0.980501i	$-0.562962\pi$
$43$	4.81951	−	4.04405i	0.734969	−	0.616712i	0.931481	+	0.363789i	$0.118517\pi$
$44$		0			0
$45$	5.50934	+	10.2113i	0.821284	+	1.52221i
$46$		0			0
$47$	2.82049	+	1.02658i	0.411411	+	0.149741i	0.539430	−	0.842030i	$-0.318640\pi$
$47$	2.82049	+	1.02658i	0.411411	+	0.149741i	−0.128019	+	0.991772i	$0.540862\pi$
$48$		0			0
$49$	−0.548267	+	6.97850i	−0.0783238	+	0.996928i
$50$		0			0
$51$	2.31403	−	2.67840i	0.324030	−	0.375051i
$52$		0			0
$53$			12.0204i			1.65112i	0.564312	+	0.825562i	$0.309142\pi$
$53$			12.0204i			1.65112i	−0.564312	+	0.825562i	$0.690858\pi$
$54$		0			0
$55$			2.03820i			0.274830i
$56$		0			0
$57$	6.59398	−	2.29294i	0.873394	−	0.303707i
$58$		0			0
$59$	−5.93331	−	4.97864i	−0.772451	−	0.648164i	0.168884	−	0.985636i	$-0.445984\pi$
$59$	−5.93331	−	4.97864i	−0.772451	−	0.648164i	−0.941336	+	0.337472i	$0.890428\pi$
$60$		0			0
$61$	4.00630	−	11.0072i	0.512954	−	1.40933i	−0.365189	−	0.930933i	$-0.618996\pi$
$61$	4.00630	−	11.0072i	0.512954	−	1.40933i	0.878144	−	0.478397i	$-0.158782\pi$
$62$		0			0
$63$	2.85768	+	7.40497i	0.360034	+	0.932939i
$64$		0			0
$65$	1.09977	+	1.31066i	0.136410	+	0.162567i
$66$		0			0
$67$	−1.79309	+	10.1691i	−0.219061	+	1.24236i	0.654657	+	0.755926i	$0.272813\pi$
$67$	−1.79309	+	10.1691i	−0.219061	+	1.24236i	−0.873718	+	0.486432i	$0.838298\pi$
$68$		0			0
$69$	2.06514	+	12.7870i	0.248613	+	1.53938i
$70$		0			0
$71$	−4.73069	−	2.73126i	−0.561430	−	0.324141i	0.192290	−	0.981338i	$-0.438409\pi$
$71$	−4.73069	−	2.73126i	−0.561430	−	0.324141i	−0.753719	+	0.657197i	$0.771742\pi$
$72$		0			0
$73$	11.8488	−	6.84090i	1.38680	−	0.800667i	0.393843	−	0.919178i	$-0.371145\pi$
$73$	11.8488	−	6.84090i	1.38680	−	0.800667i	0.992953	+	0.118511i	$0.0378120\pi$
$74$		0			0
$75$	0.248582	−	17.2462i	0.0287038	−	1.99142i
$76$		0			0
$77$	−0.175865	+	1.38316i	−0.0200417	+	0.157626i
$78$		0			0
$79$	1.51105	+	8.56961i	0.170007	+	0.964157i	0.943751	+	0.330658i	$0.107271\pi$
$79$	1.51105	+	8.56961i	0.170007	+	0.964157i	−0.773744	+	0.633499i	$0.781618\pi$
$80$		0			0
$81$	6.54961	+	6.17273i	0.727735	+	0.685858i
$82$		0			0
$83$	−1.20343	−	6.82497i	−0.132093	−	0.749138i	−0.976840	−	0.213972i	$-0.931360\pi$
$83$	−1.20343	−	6.82497i	−0.132093	−	0.749138i	0.844747	−	0.535166i	$-0.179751\pi$
$84$		0			0
$85$	−7.42702	+	2.70321i	−0.805573	+	0.293205i
$86$		0			0
$87$	−0.279703	−	0.00403157i	−0.0299873	−	0.000432230i
$88$		0			0
$89$	0.396843	+	0.687352i	0.0420652	+	0.0728591i	0.886291	−	0.463128i	$-0.153273\pi$
$89$	0.396843	+	0.687352i	0.0420652	+	0.0728591i	−0.844226	+	0.535987i	$0.819940\pi$
$90$		0			0
$91$	0.633241	+	0.984337i	0.0663817	+	0.103187i
$92$		0			0
$93$	−1.51520	−	9.38190i	−0.157119	−	0.972858i
$94$		0			0
$95$	−15.3520	−	2.70696i	−1.57508	−	0.277729i
$96$		0			0
$97$	6.78774	+	8.08932i	0.689191	+	0.821346i	0.991258	−	0.131941i	$-0.0421210\pi$
$97$	6.78774	+	8.08932i	0.689191	+	0.821346i	−0.302067	+	0.953287i	$0.597677\pi$
$98$		0			0
$99$	0.497687	+	1.50061i	0.0500194	+	0.150817i
$100$		0			0
$101$	−17.9577	−	6.53606i	−1.78686	−	0.650363i	−0.999423	−	0.0339631i	$-0.989187\pi$
$101$	−17.9577	−	6.53606i	−1.78686	−	0.650363i	−0.787434	−	0.616400i	$-0.788591\pi$
$102$		0			0
$103$	0.424547	−	0.505955i	0.0418319	−	0.0498533i	−0.744723	−	0.667374i	$-0.767418\pi$
$103$	0.424547	−	0.505955i	0.0418319	−	0.0498533i	0.786555	+	0.617521i	$0.211863\pi$
$104$		0			0
$105$	2.48865	−	17.5479i	0.242867	−	1.71250i
$106$		0			0
$107$			10.2820i			0.993994i	0.867752	+	0.496997i	$0.165564\pi$
$107$			10.2820i			0.993994i	−0.867752	+	0.496997i	$0.834436\pi$
$108$		0			0
$109$	4.90699			0.470004			0.235002	−	0.971995i	$-0.424490\pi$
$109$	4.90699			0.470004			0.235002	+	0.971995i	$0.424490\pi$
$110$		0			0
$111$	−5.83304	+	6.75149i	−0.553648	+	0.640824i
$112$		0			0
$113$	4.14212	−	4.93639i	0.389658	−	0.464376i	−0.535180	−	0.844738i	$-0.679756\pi$
$113$	4.14212	−	4.93639i	0.389658	−	0.464376i	0.924838	+	0.380362i	$0.124201\pi$
$114$		0			0
$115$	9.89213	−	27.1784i	0.922446	−	2.53440i
$116$		0			0
$117$	1.12974	+	0.696423i	0.104444	+	0.0643843i
$118$		0			0
$119$	−5.27338	+	1.19362i	−0.483410	+	0.109419i
$120$		0			0
$121$	1.86190	−	10.5594i	0.169264	−	0.959944i
$122$		0			0
$123$	3.60621	−	9.48057i	0.325161	−	0.854834i
$124$		0			0
$125$	−9.58794	+	16.6068i	−0.857572	+	1.48536i
$126$		0			0
$127$	−1.86687	−	3.23351i	−0.165658	−	0.286928i	0.771231	−	0.636556i	$-0.219641\pi$
$127$	−1.86687	−	3.23351i	−0.165658	−	0.286928i	−0.936889	+	0.349628i	$0.886308\pi$
$128$		0			0
$129$	−9.51469	+	5.31196i	−0.837722	+	0.467692i
$130$		0			0
$131$	14.9954	−	5.45789i	1.31016	−	0.476858i	0.409866	−	0.912146i	$-0.365575\pi$
$131$	14.9954	−	5.45789i	1.31016	−	0.476858i	0.900292	+	0.435287i	$0.143353\pi$
$132$		0			0
$133$	−10.1846	−	3.16165i	−0.883118	−	0.274150i
$134$		0			0
$135$	−6.05070	−	19.1640i	−0.520762	−	1.64937i
$136$		0			0
$137$	−10.2530	+	1.80788i	−0.875972	+	0.154458i	−0.593516	−	0.804823i	$-0.702260\pi$
$137$	−10.2530	+	1.80788i	−0.875972	+	0.154458i	−0.282457	+	0.959280i	$0.591149\pi$
$138$		0			0
$139$	−4.25631	−	11.6941i	−0.361015	−	0.991881i	−0.978671	−	0.205433i	$-0.934140\pi$
$139$	−4.25631	−	11.6941i	−0.361015	−	0.991881i	0.617656	−	0.786448i	$-0.288082\pi$
$140$		0			0
$141$	−4.46433	−	2.66400i	−0.375964	−	0.224349i
$142$		0			0
$143$	0.116567	+	0.201900i	0.00974780	+	0.0168837i
$144$		0			0
$145$	0.540942	+	0.312313i	0.0449228	+	0.0259362i
$146$		0			0
$147$	3.20297	−	11.6936i	0.264176	−	0.964474i
$148$		0			0
$149$	−18.4810	−	3.25869i	−1.51402	−	0.266963i	−0.645941	−	0.763388i	$-0.723535\pi$
$149$	−18.4810	−	3.25869i	−1.51402	−	0.266963i	−0.868080	+	0.496425i	$0.834646\pi$
$150$		0			0
$151$	2.64538	−	2.21974i	0.215278	−	0.180639i	−0.528772	−	0.848764i	$-0.677347\pi$
$151$	2.64538	−	2.21974i	0.215278	−	0.180639i	0.744049	+	0.668125i	$0.232903\pi$
$152$		0			0
$153$	−4.80803	+	3.80375i	−0.388706	+	0.307515i
$154$		0			0
$155$	−7.25791	+	19.9409i	−0.582969	+	1.60170i
$156$		0			0
$157$	6.61942	−	7.88872i	0.528288	−	0.629589i	−0.434232	−	0.900801i	$-0.642980\pi$
$157$	6.61942	−	7.88872i	0.528288	−	0.629589i	0.962519	+	0.271212i	$0.0874246\pi$
$158$		0			0
$159$	3.91046	−	20.4493i	0.310120	−	1.62174i
$160$		0			0
$161$	9.05811	−	17.5903i	0.713879	−	1.38631i
$162$		0			0
$163$	17.1535			1.34357			0.671784	−	0.740747i	$-0.265528\pi$
$163$	17.1535			1.34357			0.671784	+	0.740747i	$0.265528\pi$
$164$		0			0
$165$	0.663065	−	3.46743i	0.0516196	−	0.269939i
$166$		0			0
$167$	−2.20956	−	1.85404i	−0.170981	−	0.143470i	0.553282	−	0.832994i	$-0.313375\pi$
$167$	−2.20956	−	1.85404i	−0.170981	−	0.143470i	−0.724263	+	0.689524i	$0.757820\pi$
$168$		0			0
$169$	−12.0321	−	4.37933i	−0.925547	−	0.336871i
$170$		0			0
$171$	−11.9638	+	1.75565i	−0.914893	+	0.134258i
$172$		0			0
$173$	−2.70496	+	2.26973i	−0.205654	+	0.172565i	−0.739798	−	0.672829i	$-0.765079\pi$
$173$	−2.70496	+	2.26973i	−0.205654	+	0.172565i	0.534143	+	0.845394i	$0.320634\pi$
$174$		0			0
$175$	−15.9461	+	20.9731i	−1.20541	+	1.58542i
$176$		0			0
$177$	8.47425	+	10.4000i	0.636964	+	0.781713i
$178$		0			0
$179$	−19.6692	−	11.3560i	−1.47014	−	0.848788i	−0.470705	−	0.882290i	$-0.656001\pi$
$179$	−19.6692	−	11.3560i	−1.47014	−	0.848788i	−0.999439	+	0.0335025i	$0.989334\pi$
$180$		0			0
$181$	0.231419	−	0.133610i	0.0172012	−	0.00993112i	−0.491375	−	0.870948i	$-0.663505\pi$
$181$	0.231419	−	0.133610i	0.0172012	−	0.00993112i	0.508576	+	0.861017i	$0.330172\pi$
$182$		0			0
$183$	−10.3965	+	17.4224i	−0.768530	+	1.28790i
$184$		0			0
$185$	18.7214	−	6.81405i	1.37643	−	0.500979i
$186$		0			0
$187$	−1.06059	+	0.187011i	−0.0775583	+	0.0136756i
$188$		0			0
$189$	−2.45258	−	13.5272i	−0.178399	−	0.983958i
$190$		0			0
$191$	7.83537	−	1.38159i	0.566947	−	0.0999681i	0.117175	−	0.993111i	$-0.462616\pi$
$191$	7.83537	−	1.38159i	0.566947	−	0.0999681i	0.449773	+	0.893143i	$0.351505\pi$
$192$		0			0
$193$	9.18165	−	3.34185i	0.660909	−	0.240551i	0.0102804	−	0.999947i	$-0.496728\pi$
$193$	9.18165	−	3.34185i	0.660909	−	0.240551i	0.650629	+	0.759396i	$0.274505\pi$
$194$		0			0
$195$	−1.44458	−	2.58750i	−0.103448	−	0.185295i
$196$		0			0
$197$	19.2864	−	11.1350i	1.37410	−	0.793336i	0.382657	−	0.923890i	$-0.375009\pi$
$197$	19.2864	−	11.1350i	1.37410	−	0.793336i	0.991441	+	0.130555i	$0.0416758\pi$
$198$		0			0
$199$	21.6887	+	12.5220i	1.53747	+	0.887660i	0.998986	+	0.0450256i	$0.0143369\pi$
$199$	21.6887	+	12.5220i	1.53747	+	0.887660i	0.538486	+	0.842634i	$0.318996\pi$
$200$		0			0
$201$	6.35868	−	16.7167i	0.448506	−	1.17910i
$202$		0			0
$203$	0.340148	+	0.258618i	0.0238737	+	0.0181514i
$204$		0			0
$205$	−17.3504	+	14.5587i	−1.21181	+	1.01683i
$206$		0			0
$207$	0.646603	−	22.4254i	0.0449420	−	1.55867i
$208$		0			0
$209$	−1.99603	−	0.726496i	−0.138068	−	0.0502527i
$210$		0			0
$211$	20.3108	+	17.0428i	1.39825	+	1.17327i	0.961868	+	0.273514i	$0.0881859\pi$
$211$	20.3108	+	17.0428i	1.39825	+	1.17327i	0.436385	+	0.899760i	$0.356258\pi$
$212$		0			0
$213$	7.15943	+	6.18548i	0.490556	+	0.423822i
$214$		0			0
$215$	24.3326			1.65947
$216$		0			0
$217$	−6.64598	+	12.9061i	−0.451159	+	0.876125i
$218$		0			0
$219$	−22.3829	+	7.78327i	−1.51250	+	0.525945i
$220$		0			0
$221$	−0.581105	+	0.692535i	−0.0390894	+	0.0465849i
$222$		0			0
$223$	8.14058	−	22.3660i	0.545133	−	1.49774i	−0.295073	−	0.955475i	$-0.595344\pi$
$223$	8.14058	−	22.3660i	0.545133	−	1.49774i	0.840206	−	0.542267i	$-0.182434\pi$
$224$		0			0
$225$	−6.03342	+	29.2588i	−0.402228	+	1.95058i
$226$		0			0
$227$	4.32319	−	3.62758i	0.286940	−	0.240771i	−0.487944	−	0.872875i	$-0.662253\pi$
$227$	4.32319	−	3.62758i	0.286940	−	0.240771i	0.774884	+	0.632104i	$0.217808\pi$
$228$		0			0
$229$	−6.27922	−	1.10720i	−0.414943	−	0.0731656i	−0.0377204	−	0.999288i	$-0.512010\pi$
$229$	−6.27922	−	1.10720i	−0.414943	−	0.0731656i	−0.377222	+	0.926123i	$0.623121\pi$
$230$		0			0
$231$	0.749158	−	2.29586i	0.0492909	−	0.151057i
$232$		0			0
$233$	18.5054	+	10.6841i	1.21233	+	0.699937i	0.963266	−	0.268550i	$-0.0865445\pi$
$233$	18.5054	+	10.6841i	1.21233	+	0.699937i	0.249062	+	0.968488i	$0.419878\pi$
$234$		0			0
$235$	5.80427	+	10.0533i	0.378629	+	0.655804i
$236$		0			0
$237$	0.217221	−	15.0704i	0.0141100	−	0.978929i
$238$		0			0
$239$	8.05528	+	22.1317i	0.521053	+	1.43158i	0.869350	+	0.494197i	$0.164538\pi$
$239$	8.05528	+	22.1317i	0.521053	+	1.43158i	−0.348297	+	0.937384i	$0.613240\pi$
$240$		0			0
$241$	−4.93118	+	0.869500i	−0.317645	+	0.0560094i	−0.330198	−	0.943912i	$-0.607115\pi$
$241$	−4.93118	+	0.869500i	−0.317645	+	0.0560094i	0.0125525	+	0.999921i	$0.496004\pi$
$242$		0			0
$243$	−9.13426	−	12.6319i	−0.585963	−	0.810338i
$244$		0			0
$245$	−18.9731	+	19.3124i	−1.21215	+	1.23382i
$246$		0			0
$247$	−1.67555	+	0.609850i	−0.106613	+	0.0388038i
$248$		0			0
$249$	−0.172998	+	12.0023i	−0.0109633	+	0.760616i
$250$		0			0
$251$	1.53539	+	2.65938i	0.0969132	+	0.167859i	0.910405	−	0.413717i	$-0.135770\pi$
$251$	1.53539	+	2.65938i	0.0969132	+	0.167859i	−0.813492	+	0.581576i	$0.802436\pi$
$252$		0			0
$253$	1.97050	−	3.41301i	0.123884	−	0.214574i
$254$		0			0
$255$	13.5144	−	2.18262i	0.846307	−	0.136681i
$256$		0			0
$257$	4.81703	−	27.3187i	0.300478	−	1.70410i	−0.343583	−	0.939122i	$-0.611641\pi$
$257$	4.81703	−	27.3187i	0.300478	−	1.70410i	0.644061	−	0.764974i	$-0.277248\pi$
$258$		0			0
$259$	13.2927	−	3.00879i	0.825971	−	0.186957i
$260$		0			0
$261$	0.474526	+	0.0978515i	0.0293724	+	0.00605686i
$262$		0			0
$263$	0.139169	−	0.382363i	0.00858152	−	0.0235775i	−0.935328	−	0.353782i	$-0.884895\pi$
$263$	0.139169	−	0.382363i	0.00858152	−	0.0235775i	0.943909	+	0.330204i	$0.107118\pi$
$264$		0			0
$265$	−29.8830	+	35.6131i	−1.83570	+	2.18770i
$266$		0			0
$267$	−0.451510	−	1.29844i	−0.0276319	−	0.0794633i
$268$		0			0
$269$	−16.0290			−0.977306			−0.488653	−	0.872478i	$-0.662512\pi$
$269$	−16.0290			−0.977306			−0.488653	+	0.872478i	$0.662512\pi$
$270$		0			0
$271$			2.09570i			0.127305i	0.997972	+	0.0636523i	$0.0202749\pi$
$271$			2.09570i			0.127305i	−0.997972	+	0.0636523i	$0.979725\pi$
$272$		0			0
$273$	−0.757061	−	1.88058i	−0.0458194	−	0.113818i
$274$		0			0
$275$	−3.37328	+	4.02012i	−0.203416	+	0.242422i
$276$		0			0
$277$	−17.1546	−	6.24377i	−1.03072	−	0.375152i	−0.229366	−	0.973340i	$-0.573665\pi$
$277$	−17.1546	−	6.24377i	−1.03072	−	0.375152i	−0.801355	+	0.598189i	$0.795887\pi$
$278$		0			0
$279$	−0.474416	+	16.4536i	−0.0284025	+	0.985054i
$280$		0			0
$281$	1.89410	+	2.25730i	0.112992	+	0.134659i	0.819576	−	0.572970i	$-0.194209\pi$
$281$	1.89410	+	2.25730i	0.112992	+	0.134659i	−0.706584	+	0.707630i	$0.749765\pi$
$282$		0			0
$283$	−27.9044	−	4.92030i	−1.65875	−	0.292482i	−0.735739	−	0.677265i	$-0.763165\pi$
$283$	−27.9044	−	4.92030i	−1.65875	−	0.292482i	−0.923007	+	0.384784i	$0.874276\pi$
$284$		0			0
$285$	25.2365	+	9.59945i	1.49488	+	0.568622i
$286$		0			0
$287$	−13.0306	+	8.38280i	−0.769170	+	0.494821i
$288$		0			0
$289$	6.41191	+	11.1057i	0.377171	+	0.653279i
$290$		0			0
$291$	−8.91586	−	15.9699i	−0.522657	−	0.936174i
$292$		0			0
$293$	15.3690	−	5.59385i	0.897865	−	0.326796i	0.148468	−	0.988917i	$-0.452566\pi$
$293$	15.3690	−	5.59385i	0.897865	−	0.326796i	0.749397	+	0.662121i	$0.230344\pi$
$294$		0			0
$295$	−5.20178	−	29.5008i	−0.302859	−	1.71760i
$296$		0			0
$297$	−0.358499	−	2.71478i	−0.0208022	−	0.157528i
$298$		0			0
$299$	−0.574470	−	3.25798i	−0.0332225	−	0.188414i
$300$		0			0
$301$	16.5126	+	2.09953i	0.951772	+	0.121015i
$302$		0			0
$303$	28.4238	+	16.9613i	1.63290	+	0.974402i
$304$		0			0
$305$	39.2339	−	22.6517i	2.24652	−	1.29703i
$306$		0			0
$307$	24.9496	+	14.4047i	1.42395	+	0.822118i	0.996634	−	0.0819833i	$-0.0261254\pi$
$307$	24.9496	+	14.4047i	1.42395	+	0.822118i	0.427317	+	0.904102i	$0.359459\pi$
$308$		0			0
$309$	−0.886847	+	0.722630i	−0.0504510	+	0.0411090i
$310$		0			0
$311$	−0.551909	+	3.13003i	−0.0312959	+	0.177488i	−0.996449	−	0.0841979i	$-0.973167\pi$
$311$	−0.551909	+	3.13003i	−0.0312959	+	0.177488i	0.965153	+	0.261686i	$0.0842783\pi$
$312$		0			0
$313$	1.37077	+	1.63362i	0.0774804	+	0.0923376i	0.803392	−	0.595450i	$-0.203026\pi$
$313$	1.37077	+	1.63362i	0.0774804	+	0.0923376i	−0.725912	+	0.687788i	$0.758582\pi$
$314$		0			0
$315$	−9.94242	+	29.0432i	−0.560192	+	1.63640i
$316$		0			0
$317$	7.88509	−	21.6641i	0.442871	−	1.21678i	−0.494725	−	0.869050i	$-0.664731\pi$
$317$	7.88509	−	21.6641i	0.442871	−	1.21678i	0.937596	−	0.347727i	$-0.113047\pi$
$318$		0			0
$319$	0.0651993	+	0.0547087i	0.00365046	+	0.00306310i
$320$		0			0
$321$	3.34492	−	17.4919i	0.186695	−	0.976303i
$322$		0			0
$323$		−	8.23690i		−	0.458314i
$324$		0			0
$325$			4.40529i			0.244362i
$326$		0			0
$327$	−8.34789	−	1.59634i	−0.461640	−	0.0882778i
$328$		0			0
$329$	3.07146	+	7.32321i	0.169335	+	0.403741i
$330$		0			0
$331$	−27.5488	−	10.0269i	−1.51422	−	0.551130i	−0.554521	−	0.832170i	$-0.687098\pi$
$331$	−27.5488	−	10.0269i	−1.51422	−	0.551130i	−0.959696	+	0.281040i	$0.909321\pi$
$332$		0			0
$333$	12.1197	−	9.58821i	0.664156	−	0.525431i
$334$		0			0
$335$	−30.5932	+	25.6708i	−1.67149	+	1.40254i
$336$		0			0
$337$	2.98036	−	16.9025i	0.162351	−	0.920735i	−0.789404	−	0.613874i	$-0.789610\pi$
$337$	2.98036	−	16.9025i	0.162351	−	0.920735i	0.951754	−	0.306861i	$-0.0992787\pi$
$338$		0			0
$339$	−8.65258	+	7.05039i	−0.469944	+	0.382925i
$340$		0			0
$341$	−1.44577	+	2.50414i	−0.0782928	+	0.135607i
$342$		0			0
$343$	−14.5419	+	11.4687i	−0.785191	+	0.619254i
$344$		0			0
$345$	−25.6704	+	43.0185i	−1.38205	+	2.31604i
$346$		0			0
$347$	−8.98798	−	24.6943i	−0.482500	−	1.32566i	−0.907343	−	0.420391i	$-0.861893\pi$
$347$	−8.98798	−	24.6943i	−0.482500	−	1.32566i	0.424843	−	0.905267i	$-0.360329\pi$
$348$		0			0
$349$	−20.9044	+	3.68602i	−1.11899	+	0.197308i	−0.702397	−	0.711786i	$-0.747887\pi$
$349$	−20.9044	+	3.68602i	−1.11899	+	0.197308i	−0.416592	+	0.909094i	$0.636776\pi$
$350$		0			0
$351$	−1.69538	−	1.55230i	−0.0904927	−	0.0828556i
$352$		0			0
$353$	−5.37900	−	30.5059i	−0.286296	−	1.62366i	−0.700621	−	0.713534i	$-0.747093\pi$
$353$	−5.37900	−	30.5059i	−0.286296	−	1.62366i	0.414325	−	0.910129i	$-0.364018\pi$
$354$		0			0
$355$	−7.22577	−	19.8526i	−0.383504	−	1.05367i
$356$		0			0
$357$	9.35952	−	0.315082i	0.495359	−	0.0166759i
$358$		0			0
$359$	5.58490	−	3.22445i	0.294760	−	0.170180i	−0.345327	−	0.938483i	$-0.612232\pi$
$359$	5.58490	−	3.22445i	0.294760	−	0.170180i	0.640086	+	0.768303i	$0.278899\pi$
$360$		0			0
$361$	−1.37697	+	2.38499i	−0.0724724	+	0.125526i
$362$		0			0
$363$	−6.60269	+	17.3582i	−0.346551	+	0.911068i
$364$		0			0
$365$	52.1115	+	9.18866i	2.72764	+	0.480956i
$366$		0			0
$367$	1.21743	+	1.45088i	0.0635493	+	0.0757352i	0.796883	−	0.604134i	$-0.206481\pi$
$367$	1.21743	+	1.45088i	0.0635493	+	0.0757352i	−0.733333	+	0.679869i	$0.762036\pi$
$368$		0			0
$369$	−9.21920	+	14.9554i	−0.479932	+	0.778547i
$370$		0			0
$371$	−23.3521	+	21.5894i	−1.21238	+	1.12087i
$372$		0			0
$373$	−20.5013	−	17.2027i	−1.06152	−	0.890720i	−0.0672618	−	0.997735i	$-0.521426\pi$
$373$	−20.5013	−	17.2027i	−1.06152	−	0.890720i	−0.994257	+	0.107015i	$0.965871\pi$
$374$		0			0
$375$	21.7138	−	25.1328i	1.12129	−	1.29785i
$376$		0			0
$377$	0.0714462			0.00367967
$378$		0			0
$379$	−34.2398			−1.75878			−0.879389	−	0.476104i	$-0.842049\pi$
$379$	−34.2398			−1.75878			−0.879389	+	0.476104i	$0.842049\pi$
$380$		0			0
$381$	2.12404	+	6.10826i	0.108818	+	0.312936i
$382$		0			0
$383$	−7.21930	−	6.05771i	−0.368889	−	0.309534i	0.439433	−	0.898275i	$-0.355179\pi$
$383$	−7.21930	−	6.05771i	−0.368889	−	0.309534i	−0.808322	+	0.588741i	$0.799624\pi$
$384$		0			0
$385$	−3.95963	+	3.66074i	−0.201801	+	0.186569i
$386$		0			0
$387$	17.9147	−	5.94153i	0.910656	−	0.302025i
$388$		0			0
$389$	−3.40981	−	4.06365i	−0.172884	−	0.206035i	0.672644	−	0.739966i	$-0.265159\pi$
$389$	−3.40981	−	4.06365i	−0.172884	−	0.206035i	−0.845528	+	0.533931i	$0.820714\pi$
$390$		0			0
$391$	15.0502	+	2.65375i	0.761120	+	0.134206i
$392$		0			0
$393$	−27.2862	+	4.40679i	−1.37641	+	0.222293i
$394$		0			0
$395$	−16.8274	+	29.1460i	−0.846681	+	1.46649i
$396$		0			0
$397$	22.2739	−	12.8599i	1.11790	−	0.645418i	0.177033	−	0.984205i	$-0.443350\pi$
$397$	22.2739	−	12.8599i	1.11790	−	0.645418i	0.940863	+	0.338787i	$0.110017\pi$
$398$		0			0
$399$	16.2978	+	8.69193i	0.815909	+	0.435141i
$400$		0			0
$401$	−2.53667	−	6.96944i	−0.126675	−	0.348037i	0.860101	−	0.510123i	$-0.170400\pi$
$401$	−2.53667	−	6.96944i	−0.126675	−	0.348037i	−0.986777	+	0.162086i	$0.948178\pi$
$402$		0			0
$403$	0.421492	+	2.39040i	0.0209960	+	0.119074i
$404$		0			0
$405$	4.05919	+	34.5707i	0.201703	+	1.71783i
$406$		0			0
$407$	2.67346	−	0.471403i	0.132519	−	0.0233666i
$408$		0			0
$409$	5.51677	+	15.1572i	0.272787	+	0.749475i	0.998132	+	0.0610902i	$0.0194577\pi$
$409$	5.51677	+	15.1572i	0.272787	+	0.749475i	−0.725346	+	0.688385i	$0.758320\pi$
$410$		0			0
$411$	18.0308	+	0.259891i	0.889393	+	0.0128195i
$412$		0			0
$413$	−0.984575	−	20.4687i	−0.0484478	−	1.00720i
$414$		0			0
$415$	13.4016	−	23.2123i	0.657861	−	1.13945i
$416$		0			0
$417$	3.43661	+	21.2790i	0.168292	+	1.04204i
$418$		0			0
$419$	3.79439	−	21.5190i	0.185368	−	1.05127i	−0.740114	−	0.672481i	$-0.765228\pi$
$419$	3.79439	−	21.5190i	0.185368	−	1.05127i	0.925482	−	0.378792i	$-0.123660\pi$
$420$		0			0
$421$	21.7924	−	18.2860i	1.06210	−	0.891205i	0.0677839	−	0.997700i	$-0.478407\pi$
$421$	21.7924	−	18.2860i	1.06210	−	0.891205i	0.994313	+	0.106495i	$0.0339627\pi$
$422$		0			0
$423$	6.72817	+	5.98439i	0.327135	+	0.290971i
$424$		0			0
$425$	−19.1229	−	6.96016i	−0.927596	−	0.337617i
$426$		0			0
$427$	28.5795	−	11.9866i	1.38306	−	0.580074i
$428$		0			0
$429$	−0.132624	−	0.381398i	−0.00640317	−	0.0184141i
$430$		0			0
$431$			35.9184i			1.73013i	0.501662	+	0.865064i	$0.332722\pi$
$431$			35.9184i			1.73013i	−0.501662	+	0.865064i	$0.667278\pi$
$432$		0			0
$433$			20.0480i			0.963447i	0.876323	+	0.481724i	$0.159989\pi$
$433$			20.0480i			0.963447i	−0.876323	+	0.481724i	$0.840011\pi$
$434$		0			0
$435$	−0.818663	−	0.707294i	−0.0392519	−	0.0339122i
$436$		0			0
$437$	23.0902	+	19.3750i	1.10455	+	0.926831i
$438$		0			0
$439$	−1.50467	+	4.13404i	−0.0718138	+	0.197307i	−0.970407	−	0.241477i	$-0.922368\pi$
$439$	−1.50467	+	4.13404i	−0.0718138	+	0.197307i	0.898593	+	0.438783i	$0.144590\pi$
$440$		0			0
$441$	−9.25314	+	18.8515i	−0.440626	+	0.897691i
$442$		0			0
$443$	15.0733	+	17.9636i	0.716152	+	0.853477i	0.994251	−	0.107076i	$-0.0341487\pi$
$443$	15.0733	+	17.9636i	0.716152	+	0.853477i	−0.278099	+	0.960553i	$0.589704\pi$
$444$		0			0
$445$	−0.533037	+	3.02300i	−0.0252684	+	0.143304i
$446$		0			0
$447$	30.3802	+	11.5560i	1.43693	+	0.546580i
$448$		0			0
$449$	3.97274	+	2.29366i	0.187485	+	0.108245i	0.590805	−	0.806815i	$-0.298810\pi$
$449$	3.97274	+	2.29366i	0.187485	+	0.108245i	−0.403320	+	0.915059i	$0.632144\pi$
$450$		0			0
$451$	−2.67273	+	1.54310i	−0.125854	+	0.0726618i
$452$		0			0
$453$	−5.22251	+	2.91568i	−0.245375	+	0.136990i
$454$		0			0
$455$	−0.570964	+	4.49058i	−0.0267672	+	0.210522i
$456$		0			0
$457$	1.49961	+	8.50469i	0.0701487	+	0.397833i	0.999584	+	0.0288474i	$0.00918368\pi$
$457$	1.49961	+	8.50469i	0.0701487	+	0.397833i	−0.929435	+	0.368985i	$0.879705\pi$
$458$		0			0
$459$	9.41698	−	4.90690i	0.439547	−	0.229034i
$460$		0			0
$461$	−1.10346	−	6.25802i	−0.0513932	−	0.291465i	0.948269	−	0.317469i	$-0.102833\pi$
$461$	−1.10346	−	6.25802i	−0.0513932	−	0.291465i	−0.999662	+	0.0260038i	$0.991722\pi$
$462$		0			0
$463$	5.00316	−	1.82100i	0.232517	−	0.0846291i	−0.223134	−	0.974788i	$-0.571629\pi$
$463$	5.00316	−	1.82100i	0.232517	−	0.0846291i	0.455651	+	0.890159i	$0.349407\pi$
$464$		0			0
$465$	18.8345	−	31.5629i	0.873430	−	1.46369i
$466$		0			0
$467$	7.53405	+	13.0494i	0.348634	+	0.603852i	0.986007	−	0.166703i	$-0.0533122\pi$
$467$	7.53405	+	13.0494i	0.348634	+	0.603852i	−0.637373	+	0.770556i	$0.719979\pi$
$468$		0			0
$469$	−22.9762	+	14.7810i	−1.06094	+	0.682524i
$470$		0			0
$471$	−13.8275	+	11.2671i	−0.637137	+	0.519159i
$472$		0			0
$473$	3.26519	+	0.575741i	0.150133	+	0.0264726i
$474$		0			0
$475$	−25.7999	−	30.7472i	−1.18378	−	1.41078i
$476$		0			0
$477$	−13.3051	+	33.5168i	−0.609201	+	1.53463i
$478$		0			0
$479$	8.09837	+	2.94757i	0.370024	+	0.134678i	0.520338	−	0.853961i	$-0.325806\pi$
$479$	8.09837	+	2.94757i	0.370024	+	0.134678i	−0.150314	+	0.988638i	$0.548028\pi$
$480$		0			0
$481$	1.46481	−	1.74569i	0.0667894	−	0.0795965i
$482$		0			0
$483$	−21.1324	+	26.9783i	−0.961556	+	1.22756i
$484$		0			0
$485$			40.8410i			1.85449i
$486$		0			0
$487$	27.0332			1.22499			0.612495	−	0.790475i	$-0.290166\pi$
$487$	27.0332			1.22499			0.612495	+	0.790475i	$0.290166\pi$
$488$		0			0
$489$	−29.1820	−	5.58038i	−1.31966	−	0.252354i
$490$		0			0
$491$	12.7073	−	15.1440i	0.573474	−	0.683440i	−0.398866	−	0.917009i	$-0.630596\pi$
$491$	12.7073	−	15.1440i	0.573474	−	0.683440i	0.972340	+	0.233569i	$0.0750405\pi$
$492$		0			0
$493$	−0.112882	+	0.310140i	−0.00508394	+	0.0139680i
$494$		0			0
$495$	−2.25605	+	5.68317i	−0.101402	+	0.255440i
$496$		0			0
$497$	−3.19058	−	14.0959i	−0.143117	−	0.632288i
$498$		0			0
$499$	3.66923	−	20.8092i	0.164257	−	0.931549i	−0.785570	−	0.618773i	$-0.787630\pi$
$499$	3.66923	−	20.8092i	0.164257	−	0.931549i	0.949827	−	0.312776i	$-0.101259\pi$
$500$		0			0
$501$	3.15580	+	3.87296i	0.140991	+	0.173031i
$502$		0			0
$503$	1.01476	−	1.75761i	0.0452458	−	0.0783681i	−0.842516	−	0.538672i	$-0.818926\pi$
$503$	1.01476	−	1.75761i	0.0452458	−	0.0783681i	0.887761	+	0.460304i	$0.152260\pi$
$504$		0			0
$505$	−36.9550	−	64.0079i	−1.64448	−	2.84831i
$506$		0			0
$507$	19.0446	+	11.3645i	0.845802	+	0.504715i
$508$		0			0
$509$	−26.7901	+	9.75081i	−1.18745	+	0.432197i	−0.858828	−	0.512264i	$-0.828807\pi$
$509$	−26.7901	+	9.75081i	−1.18745	+	0.432197i	−0.328624	+	0.944461i	$0.606585\pi$
$510$		0			0
$511$	34.5712	+	10.7321i	1.52934	+	0.474758i
$512$		0			0
$513$	20.9242	+	0.905292i	0.923828	+	0.0399696i
$514$		0			0
$515$	2.51564	−	0.443575i	0.110852	−	0.0195462i
$516$		0			0
$517$	0.541001	+	1.48639i	0.0237932	+	0.0653713i
$518$		0			0
$519$	5.34014	−	2.98135i	0.234406	−	0.130867i
$520$		0			0
$521$	−6.77514	−	11.7349i	−0.296824	−	0.514115i	0.678583	−	0.734523i	$-0.262594\pi$
$521$	−6.77514	−	11.7349i	−0.296824	−	0.514115i	−0.975408	+	0.220409i	$0.929261\pi$
$522$		0			0
$523$	4.44184	+	2.56450i	0.194228	+	0.112138i	0.593960	−	0.804494i	$-0.297564\pi$
$523$	4.44184	+	2.56450i	0.194228	+	0.112138i	−0.399732	+	0.916632i	$0.630897\pi$
$524$		0			0
$525$	33.9508	−	30.4924i	1.48174	−	1.33080i
$526$		0			0
$527$	−11.0424	−	1.94707i	−0.481014	−	0.0848157i
$528$		0			0
$529$	−25.2214	+	21.1632i	−1.09658	+	0.920141i
$530$		0			0
$531$	−11.0333	−	20.4496i	−0.478804	−	0.887437i
$532$		0			0
$533$	−0.886067	+	2.43445i	−0.0383798	+	0.105448i
$534$		0			0
$535$	−25.5612	+	30.4627i	−1.10511	+	1.31702i
$536$		0			0
$537$	29.7674	+	25.7179i	1.28456	+	1.10981i
$538$		0			0
$539$	−3.00296	+	2.14260i	−0.129347	+	0.0922885i
$540$		0			0
$541$	19.8658			0.854097			0.427048	−	0.904229i	$-0.359553\pi$
$541$	19.8658			0.854097			0.427048	+	0.904229i	$0.359553\pi$
$542$		0			0
$543$	−0.437161	+	0.152015i	−0.0187604	+	0.00652358i
$544$		0			0
$545$	14.5381	+	12.1989i	0.622744	+	0.522544i
$546$		0			0
$547$	−15.5559	−	5.66188i	−0.665122	−	0.242085i	−0.0126758	−	0.999920i	$-0.504035\pi$
$547$	−15.5559	−	5.66188i	−0.665122	−	0.242085i	−0.652446	+	0.757835i	$0.726257\pi$
$548$		0			0
$549$	23.3546	−	26.2573i	0.996751	−	1.12063i
$550$		0			0
$551$	−0.498666	+	0.418430i	−0.0212439	+	0.0178257i
$552$		0			0
$553$	−13.9343	+	18.3272i	−0.592548	+	0.779350i
$554$		0			0
$555$	−34.0661	+	5.50178i	−1.44603	+	0.233537i
$556$		0			0
$557$	−25.1633	−	14.5281i	−1.06620	−	0.615574i	−0.139063	−	0.990284i	$-0.544409\pi$
$557$	−25.1633	−	14.5281i	−1.06620	−	0.615574i	−0.927142	+	0.374710i	$0.877742\pi$
$558$		0			0
$559$	2.41033	−	1.39161i	0.101946	−	0.0588587i
$560$		0			0
$561$	1.86515	+	0.0268837i	0.0787465	+	0.00113503i
$562$		0			0
$563$	2.56115	−	0.932182i	0.107940	−	0.0392868i	−0.287486	−	0.957785i	$-0.592819\pi$
$563$	2.56115	−	0.932182i	0.107940	−	0.0392868i	0.395425	+	0.918498i	$0.370597\pi$
$564$		0			0
$565$	24.5440	−	4.32777i	1.03257	−	0.182071i
$566$		0			0
$567$	−0.228270	+	23.8107i	−0.00958643	+	0.999954i
$568$		0			0
$569$	31.2049	−	5.50227i	1.30818	−	0.230667i	0.524275	−	0.851549i	$-0.324336\pi$
$569$	31.2049	−	5.50227i	1.30818	−	0.230667i	0.783904	+	0.620882i	$0.213225\pi$
$570$		0			0
$571$	−8.83590	+	3.21601i	−0.369771	+	0.134586i	−0.520220	−	0.854032i	$-0.674150\pi$
$571$	−8.83590	+	3.21601i	−0.369771	+	0.134586i	0.150449	+	0.988618i	$0.451928\pi$
$572$		0			0
$573$	−13.7792	−	0.198610i	−0.575634	−	0.00829704i
$574$		0			0
$575$	64.4923	−	37.2346i	2.68951	−	1.55279i
$576$		0			0
$577$	−4.00443	−	2.31196i	−0.166707	−	0.0962481i	0.414325	−	0.910129i	$-0.364018\pi$
$577$	−4.00443	−	2.31196i	−0.166707	−	0.0962481i	−0.581032	+	0.813881i	$0.697351\pi$
$578$		0			0
$579$	−16.7072	+	2.69826i	−0.694328	+	0.112136i
$580$		0			0
$581$	11.0975	−	14.5960i	0.460403	−	0.605546i
$582$		0			0
$583$	−4.85265	+	4.07186i	−0.200976	+	0.168639i
$584$		0			0
$585$	1.61579	+	4.87188i	0.0668046	+	0.201427i
$586$		0			0
$587$	−9.10676	−	3.31459i	−0.375876	−	0.136808i	0.147172	−	0.989111i	$-0.452983\pi$
$587$	−9.10676	−	3.31459i	−0.375876	−	0.136808i	−0.523048	+	0.852303i	$0.675205\pi$
$588$		0			0
$589$	−16.9414	−	14.2155i	−0.698058	−	0.585740i
$590$		0			0
$591$	−36.4329	+	12.6689i	−1.49865	+	0.521129i
$592$		0			0
$593$	−1.01328			−0.0416104			−0.0208052	−	0.999784i	$-0.506623\pi$
$593$	−1.01328			−0.0416104			−0.0208052	+	0.999784i	$0.506623\pi$
$594$		0			0
$595$	−18.5910	−	9.57340i	−0.762157	−	0.392471i
$596$		0			0
$597$	−32.8237	−	28.3585i	−1.34339	−	1.16064i
$598$		0			0
$599$	−12.1760	+	14.5108i	−0.497498	+	0.592895i	−0.955108	−	0.296258i	$-0.904261\pi$
$599$	−12.1760	+	14.5108i	−0.497498	+	0.592895i	0.457610	+	0.889153i	$0.348706\pi$
$600$		0			0
$601$	−6.74204	+	18.5236i	−0.275014	+	0.755593i	0.722895	+	0.690957i	$0.242811\pi$
$601$	−6.74204	+	18.5236i	−0.275014	+	0.755593i	−0.997909	+	0.0646360i	$0.979411\pi$
$602$		0			0
$603$	−16.2558	+	26.3702i	−0.661987	+	1.07388i
$604$		0			0
$605$	31.7672	−	26.6559i	1.29152	−	1.08372i
$606$		0			0
$607$	6.65045	+	1.17265i	0.269933	+	0.0475966i	0.306976	−	0.951717i	$-0.400683\pi$
$607$	6.65045	+	1.17265i	0.269933	+	0.0475966i	−0.0370430	+	0.999314i	$0.511794\pi$
$608$		0			0
$609$	−0.494534	−	0.550624i	−0.0200395	−	0.0223124i
$610$		0			0
$611$	1.14992	+	0.663906i	0.0465207	+	0.0268588i
$612$		0			0
$613$	−2.23959	−	3.87908i	−0.0904561	−	0.156675i	0.817247	−	0.576288i	$-0.195499\pi$
$613$	−2.23959	−	3.87908i	−0.0904561	−	0.156675i	−0.907703	+	0.419613i	$0.862166\pi$
$614$		0			0
$615$	34.2532	−	19.1232i	1.38122	−	0.771123i
$616$		0			0
$617$	−12.2280	−	33.5960i	−0.492279	−	1.35252i	−0.898590	−	0.438790i	$-0.855407\pi$
$617$	−12.2280	−	33.5960i	−0.492279	−	1.35252i	0.406311	−	0.913735i	$-0.366815\pi$
$618$		0			0
$619$	−22.6201	+	3.98854i	−0.909179	+	0.160313i	−0.608630	−	0.793454i	$-0.708281\pi$
$619$	−22.6201	+	3.98854i	−0.909179	+	0.160313i	−0.300548	+	0.953767i	$0.597170\pi$
$620$		0			0
$621$	−8.39545	+	37.9403i	−0.336898	+	1.52249i
$622$		0			0
$623$	−0.622570	+	2.00548i	−0.0249427	+	0.0803480i
$624$		0			0
$625$	−22.9036	+	8.33624i	−0.916145	+	0.333450i
$626$		0			0
$627$	3.15935	+	1.88528i	0.126172	+	0.0752908i
$628$		0			0
$629$	5.26351	+	9.11666i	0.209870	+	0.363505i
$630$		0			0
$631$	11.8477	−	20.5208i	0.471649	−	0.816919i	−0.527825	−	0.849353i	$-0.676992\pi$
$631$	11.8477	−	20.5208i	0.471649	−	0.816919i	0.999474	+	0.0324337i	$0.0103258\pi$
$632$		0			0
$633$	−29.0089	−	35.6011i	−1.15300	−	1.41502i
$634$		0			0
$635$	2.50757	−	14.2211i	0.0995098	−	0.564348i
$636$		0			0
$637$	−0.774938	+	2.99814i	−0.0307042	+	0.118791i
$638$		0			0
$639$	−10.1675	−	12.8520i	−0.402222	−	0.508417i
$640$		0			0
$641$	3.54522	−	9.74042i	0.140028	−	0.384723i	−0.849779	−	0.527139i	$-0.823265\pi$
$641$	3.54522	−	9.74042i	0.140028	−	0.384723i	0.989807	+	0.142416i	$0.0454869\pi$
$642$		0			0
$643$	−22.5352	+	26.8565i	−0.888703	+	1.05912i	0.109176	+	0.994022i	$0.465179\pi$
$643$	−22.5352	+	26.8565i	−0.888703	+	1.05912i	−0.997879	+	0.0650928i	$0.979266\pi$
$644$		0			0
$645$	−41.3952	−	7.91586i	−1.62993	−	0.311687i
$646$		0			0
$647$	41.8249			1.64431			0.822154	−	0.569265i	$-0.192772\pi$
$647$	41.8249			1.64431			0.822154	+	0.569265i	$0.192772\pi$
$648$		0			0
$649$		−	4.08179i		−	0.160224i
$650$		0			0
$651$	15.5049	−	19.7941i	0.607686	−	0.775794i
$652$		0			0
$653$	5.71332	−	6.80888i	0.223580	−	0.266452i	−0.642581	−	0.766218i	$-0.722136\pi$
$653$	5.71332	−	6.80888i	0.223580	−	0.266452i	0.866160	+	0.499766i	$0.166581\pi$
$654$		0			0
$655$	57.9959	+	21.1088i	2.26609	+	0.824789i
$656$		0			0
$657$	40.6105	−	5.95948i	1.58437	−	0.232502i
$658$		0			0
$659$	12.6768	+	15.1076i	0.493818	+	0.588509i	0.954184	−	0.299220i	$-0.0967264\pi$
$659$	12.6768	+	15.1076i	0.493818	+	0.588509i	−0.460366	+	0.887729i	$0.652282\pi$
$660$		0			0
$661$	−35.7231	−	6.29895i	−1.38947	−	0.245001i	−0.571659	−	0.820491i	$-0.693700\pi$
$661$	−35.7231	−	6.29895i	−1.38947	−	0.245001i	−0.817809	+	0.575490i	$0.804811\pi$
$662$		0			0
$663$	1.21389	−	0.989112i	0.0471434	−	0.0384139i
$664$		0			0
$665$	−22.3143	−	34.6863i	−0.865313	−	1.34508i
$666$		0			0
$667$	−0.603881	−	1.04595i	−0.0233824	−	0.0404995i
$668$		0			0
$669$	−21.1251	+	35.4014i	−0.816742	+	1.36870i
$670$		0			0
$671$	5.80076	−	2.11130i	0.223936	−	0.0815060i
$672$		0			0
$673$	−5.46796	−	31.0103i	−0.210774	−	1.19536i	−0.888091	−	0.459668i	$-0.847968\pi$
$673$	−5.46796	−	31.0103i	−0.210774	−	1.19536i	0.677317	−	0.735692i	$-0.263143\pi$
$674$		0			0
$675$	19.7827	−	47.8130i	0.761435	−	1.84032i
$676$		0			0
$677$	−3.28571	−	18.6342i	−0.126280	−	0.716170i	−0.980539	−	0.196323i	$-0.937100\pi$
$677$	−3.28571	−	18.6342i	−0.126280	−	0.716170i	0.854259	−	0.519847i	$-0.174011\pi$
$678$		0			0
$679$	−3.52396	+	27.7156i	−0.135237	+	1.06363i
$680$		0			0
$681$	−8.53484	+	4.76492i	−0.327056	+	0.182592i
$682$		0			0
$683$	−34.0145	+	19.6383i	−1.30153	+	0.751438i	−0.980666	−	0.195688i	$-0.937306\pi$
$683$	−34.0145	+	19.6383i	−1.30153	+	0.751438i	−0.320863	+	0.947126i	$0.603973\pi$
$684$		0			0
$685$	−34.8713	−	20.1330i	−1.33236	−	0.769241i
$686$		0			0
$687$	10.3222	+	3.92635i	0.393816	+	0.149799i
$688$		0			0
$689$	−0.923390	+	5.23680i	−0.0351784	+	0.199506i
$690$		0			0
$691$	5.86756	+	6.99268i	0.223212	+	0.266014i	0.866015	−	0.500017i	$-0.166673\pi$
$691$	5.86756	+	6.99268i	0.223212	+	0.266014i	−0.642803	+	0.766032i	$0.722229\pi$
$692$		0			0
$693$	−2.02138	+	3.66206i	−0.0767857	+	0.139110i
$694$		0			0
$695$	16.4616	−	45.2278i	0.624423	−	1.71559i
$696$		0			0
$697$	−9.16772	−	7.69263i	−0.347252	−	0.291379i
$698$		0			0
$699$	−28.0061	−	24.1962i	−1.05929	−	0.915184i
$700$		0			0
$701$			48.6132i			1.83610i	0.396469	+	0.918048i	$0.370235\pi$
$701$			48.6132i			1.83610i	−0.396469	+	0.918048i	$0.629765\pi$
$702$		0			0
$703$			20.7629i			0.783089i
$704$		0			0
$705$	−6.60384	−	18.9912i	−0.248715	−	0.715248i
$706$		0			0
$707$	−19.5556	−	46.6259i	−0.735463	−	1.75355i
$708$		0			0
$709$	15.1822	+	5.52587i	0.570179	+	0.207528i	0.610990	−	0.791639i	$-0.290772\pi$
$709$	15.1822	+	5.52587i	0.570179	+	0.207528i	−0.0408102	+	0.999167i	$0.512994\pi$
$710$		0			0
$711$	−5.27224	+	25.5675i	−0.197725	+	0.958856i
$712$		0			0
$713$	31.4322	−	26.3748i	1.17715	−	0.987743i
$714$		0			0
$715$	−0.156572	+	0.887963i	−0.00585545	+	0.0332079i
$716$		0			0
$717$	−6.50397	−	40.2716i	−0.242895	−	1.50397i
$718$		0			0
$719$	5.26374	−	9.11707i	0.196305	−	0.340009i	−0.751023	−	0.660276i	$-0.770439\pi$
$719$	5.26374	−	9.11707i	0.196305	−	0.340009i	0.947327	+	0.320267i	$0.103773\pi$
$720$		0			0
$721$	1.74544	−	0.0839583i	0.0650037	−	0.00312677i
$722$		0			0
$723$	8.67191	+	0.124995i	0.322512	+	0.00464860i
$724$		0			0
$725$	0.550061	+	1.51128i	0.0204287	+	0.0561275i
$726$		0			0
$727$	41.5663	−	7.32927i	1.54161	−	0.271827i	0.662726	−	0.748862i	$-0.269400\pi$
$727$	41.5663	−	7.32927i	1.54161	−	0.271827i	0.878884	+	0.477035i	$0.158288\pi$
$728$		0			0
$729$	11.4300	+	24.4613i	0.423334	+	0.905974i
$730$		0			0
$731$	2.23259	+	12.6617i	0.0825754	+	0.468309i
$732$		0			0
$733$	−6.35155	−	17.4508i	−0.234600	−	0.644558i	−0.999999	−	0.00100281i	$-0.999681\pi$
$733$	−6.35155	−	17.4508i	−0.234600	−	0.644558i	0.765399	−	0.643555i	$-0.222541\pi$
$734$		0			0
$735$	38.5602	−	26.6824i	1.42232	−	0.984196i
$736$		0			0
$737$	−4.71271	+	2.72088i	−0.173595	+	0.100225i
$738$		0			0
$739$	2.22752	−	3.85819i	0.0819408	−	0.141926i	−0.822143	−	0.569281i	$-0.807221\pi$
$739$	2.22752	−	3.85819i	0.0819408	−	0.141926i	0.904084	+	0.427356i	$0.140555\pi$
$740$		0			0
$741$	3.04888	−	0.492403i	0.112003	−	0.0180889i
$742$		0			0
$743$	−9.18232	−	1.61909i	−0.336867	−	0.0593987i	0.00265623	−	0.999996i	$-0.499154\pi$
$743$	−9.18232	−	1.61909i	−0.336867	−	0.0593987i	−0.339523	+	0.940598i	$0.610266\pi$
$744$		0			0
$745$	−46.6530	−	55.5989i	−1.70923	−	2.03698i
$746$		0			0
$747$	4.19890	−	20.3624i	0.153630	−	0.745020i
$748$		0			0
$749$	−19.9749	+	18.4671i	−0.729866	+	0.674773i
$750$		0			0
$751$	−25.2029	−	21.1478i	−0.919668	−	0.771693i	0.0542659	−	0.998527i	$-0.482718\pi$
$751$	−25.2029	−	21.1478i	−0.919668	−	0.771693i	−0.973933	+	0.226834i	$0.927163\pi$
$752$		0			0
$753$	−1.74690	−	5.02370i	−0.0636606	−	0.183074i
$754$		0			0
$755$	13.3559			0.486070
$756$		0			0
$757$	−8.61580			−0.313147			−0.156573	−	0.987666i	$-0.550045\pi$
$757$	−8.61580			−0.313147			−0.156573	+	0.987666i	$0.550045\pi$
$758$		0			0
$759$	−4.46259	+	5.16526i	−0.161982	+	0.187487i
$760$		0			0
$761$	−26.6750	−	22.3830i	−0.966969	−	0.811383i	0.0151036	−	0.999886i	$-0.495192\pi$
$761$	−26.6750	−	22.3830i	−0.966969	−	0.811383i	−0.982073	+	0.188503i	$0.939637\pi$
$762$		0			0
$763$	8.81329	+	9.53287i	0.319063	+	0.345113i
$764$		0			0
$765$	−23.7011	−	0.683387i	−0.856917	−	0.0247079i
$766$		0			0
$767$	−2.20246	−	2.62479i	−0.0795262	−	0.0947757i
$768$		0			0
$769$	39.3508	+	6.93861i	1.41903	+	0.250213i	0.829938	−	0.557856i	$-0.188376\pi$
$769$	39.3508	+	6.93861i	1.41903	+	0.250213i	0.589088	+	0.808069i	$0.299487\pi$
$770$		0			0
$771$	−17.0822	+	44.9082i	−0.615200	+	1.61733i
$772$		0			0
$773$	−15.8113	+	27.3859i	−0.568692	+	0.985003i	0.428004	+	0.903777i	$0.359217\pi$
$773$	−15.8113	+	27.3859i	−0.568692	+	0.985003i	−0.996696	+	0.0812264i	$0.974116\pi$
$774$		0			0
$775$	−47.3183	+	27.3192i	−1.69972	+	0.981336i
$776$		0			0
$777$	−23.5928	+	0.794235i	−0.846386	+	0.0284930i
$778$		0			0
$779$	−8.07315	−	22.1808i	−0.289251	−	0.794709i
$780$		0			0
$781$	−0.499886	−	2.83500i	−0.0178873	−	0.101444i
$782$		0			0
$783$	−0.775443	−	0.320840i	−0.0277121	−	0.0114659i
$784$		0			0
$785$	39.2232	−	6.91610i	1.39993	−	0.246846i
$786$		0			0
$787$	18.6226	+	51.1653i	0.663825	+	1.82385i	0.558671	+	0.829389i	$0.311311\pi$
$787$	18.6226	+	51.1653i	0.663825	+	1.82385i	0.105154	+	0.994456i	$0.466466\pi$
$788$		0			0
$789$	−0.361148	+	0.605211i	−0.0128572	+	0.0215461i
$790$		0			0
$791$	17.0295	−	0.819145i	0.605500	−	0.0291254i
$792$		0			0
$793$	2.59095	−	4.48766i	0.0920074	−	0.159361i
$794$		0			0
$795$	62.4233	−	50.8644i	2.21393	−	1.80397i
$796$		0			0
$797$	−2.68399	+	15.2217i	−0.0950718	+	0.539179i	0.899653	+	0.436605i	$0.143819\pi$
$797$	−2.68399	+	15.2217i	−0.0950718	+	0.539179i	−0.994725	+	0.102575i	$0.967292\pi$
$798$		0			0
$799$	−4.69876	+	3.94273i	−0.166230	+	0.139484i
$800$		0			0
$801$	0.345711	+	2.35582i	0.0122151	+	0.0832390i
$802$		0			0
$803$	6.77543	+	2.46605i	0.239100	+	0.0870251i
$804$		0			0
$805$	70.5668	−	29.5967i	2.48715	−	1.04315i
$806$		0			0
$807$	27.2689	+	5.21455i	0.959912	+	0.183561i
$808$		0			0
$809$		−	10.5892i		−	0.372298i	−0.982522	−	0.186149i	$-0.940399\pi$
$809$		−	10.5892i		−	0.372298i	0.982522	−	0.186149i	$-0.0596007\pi$
$810$		0			0
$811$		−	19.7910i		−	0.694955i	−0.937688	−	0.347477i	$-0.887038\pi$
$811$		−	19.7910i		−	0.694955i	0.937688	−	0.347477i	$-0.112962\pi$
$812$		0			0
$813$	0.681772	−	3.56526i	0.0239108	−	0.125039i
$814$		0			0
$815$	50.8213	+	42.6441i	1.78019	+	1.49376i
$816$		0			0
$817$	−8.67311	+	23.8292i	−0.303434	+	0.833677i
$818$		0			0
$819$	0.676141	+	3.44558i	0.0236263	+	0.120398i
$820$		0			0
$821$	13.5290	+	16.1232i	0.472165	+	0.562704i	0.948589	−	0.316512i	$-0.102512\pi$
$821$	13.5290	+	16.1232i	0.472165	+	0.562704i	−0.476424	+	0.879216i	$0.658067\pi$
$822$		0			0
$823$	−6.18334	+	35.0674i	−0.215538	+	1.22237i	0.664434	+	0.747347i	$0.268673\pi$
$823$	−6.18334	+	35.0674i	−0.215538	+	1.22237i	−0.879971	+	0.475027i	$0.842438\pi$
$824$		0			0
$825$	7.04653	−	5.74173i	0.245329	−	0.199901i
$826$		0			0
$827$	−12.2674	−	7.08260i	−0.426580	−	0.246286i	0.271309	−	0.962492i	$-0.412544\pi$
$827$	−12.2674	−	7.08260i	−0.426580	−	0.246286i	−0.697889	+	0.716206i	$0.745877\pi$
$828$		0			0
$829$	18.8774	−	10.8989i	0.655638	−	0.378533i	−0.134975	−	0.990849i	$-0.543095\pi$
$829$	18.8774	−	10.8989i	0.655638	−	0.378533i	0.790613	+	0.612316i	$0.209762\pi$
$830$		0			0
$831$	27.1526	+	16.2028i	0.941915	+	0.562069i
$832$		0			0
$833$	−11.7902	−	8.10085i	−0.408507	−	0.280678i
$834$		0			0
$835$	−1.93714	−	10.9861i	−0.0670375	−	0.380188i
$836$		0			0
$837$	6.15978	−	27.8370i	0.212913	−	0.962188i
$838$		0			0
$839$	−4.48518	−	25.4367i	−0.154846	−	0.878173i	−0.958927	−	0.283654i	$-0.908453\pi$
$839$	−4.48518	−	25.4367i	−0.154846	−	0.878173i	0.804081	−	0.594520i	$-0.202658\pi$
$840$		0			0
$841$	−27.2266	+	9.90966i	−0.938847	+	0.341713i
$842$		0			0
$843$	−2.48794	−	4.45636i	−0.0856893	−	0.153485i
$844$		0			0
$845$	−24.7608	−	42.8869i	−0.851797	−	1.47536i
$846$		0			0
$847$	23.8580	−	15.3482i	0.819769	−	0.527372i
$848$		0			0
$849$	45.8710	+	17.4484i	1.57429	+	0.598827i
$850$		0			0
$851$	−37.9373	−	6.68937i	−1.30047	−	0.229309i
$852$		0			0
$853$	6.80562	+	8.11062i	0.233020	+	0.277702i	0.869865	−	0.493289i	$-0.164206\pi$
$853$	6.80562	+	8.11062i	0.233020	+	0.277702i	−0.636845	+	0.770991i	$0.719761\pi$
$854$		0			0
$855$	−39.8101	−	24.5408i	−1.36148	−	0.839276i
$856$		0			0
$857$	4.04919	+	1.47379i	0.138318	+	0.0503436i	0.410252	−	0.911972i	$-0.365441\pi$
$857$	4.04919	+	1.47379i	0.138318	+	0.0503436i	−0.271934	+	0.962316i	$0.587663\pi$
$858$		0			0
$859$	2.43859	−	2.90620i	0.0832036	−	0.0991582i	−0.722837	−	0.691019i	$-0.757162\pi$
$859$	2.43859	−	2.90620i	0.0832036	−	0.0991582i	0.806040	+	0.591861i	$0.201607\pi$
$860$		0			0
$861$	24.8950	−	10.0219i	0.848420	−	0.341546i
$862$		0			0
$863$			23.0651i			0.785147i	0.919721	+	0.392573i	$0.128415\pi$
$863$			23.0651i			0.785147i	−0.919721	+	0.392573i	$0.871585\pi$
$864$		0			0
$865$	−13.6567			−0.464342
$866$		0			0
$867$	−7.29518	−	20.9793i	−0.247757	−	0.712494i
$868$		0			0
$869$	−2.94771	+	3.51294i	−0.0999942	+	0.119168i
$870$		0			0
$871$	−1.56236	+	4.29256i	−0.0529386	+	0.145448i
$872$		0			0
$873$	9.97256	+	30.0690i	0.337520	+	1.01768i
$874$		0			0
$875$	−49.4829	+	11.2004i	−1.67283	+	0.378641i
$876$		0			0
$877$	1.83482	−	10.4058i	0.0619573	−	0.351378i	−0.938031	−	0.346551i	$-0.887353\pi$
$877$	1.83482	−	10.4058i	0.0619573	−	0.351378i	0.999988	−	0.00482623i	$-0.00153624\pi$
$878$		0			0
$879$	−27.9659	+	4.51656i	−0.943265	+	0.152340i
$880$		0			0
$881$	−7.77385	+	13.4647i	−0.261908	+	0.453637i	−0.966749	−	0.255728i	$-0.917685\pi$
$881$	−7.77385	+	13.4647i	−0.261908	+	0.453637i	0.704841	+	0.709365i	$0.251018\pi$
$882$		0			0
$883$	19.0385	+	32.9756i	0.640696	+	1.10972i	0.985278	+	0.170962i	$0.0546876\pi$
$883$	19.0385	+	32.9756i	0.640696	+	1.10972i	−0.344581	+	0.938757i	$0.611979\pi$
$884$		0			0
$885$	−0.747780	+	51.8797i	−0.0251364	+	1.74392i
$886$		0			0
$887$	−16.5628	+	6.02837i	−0.556124	+	0.202413i	−0.604766	−	0.796404i	$-0.706733\pi$
$887$	−16.5628	+	6.02837i	−0.556124	+	0.202413i	0.0486411	+	0.998816i	$0.484511\pi$
$888$		0			0
$889$	2.92876	−	9.43441i	0.0982274	−	0.316420i
$890$		0			0
$891$	−0.273285	+	4.73508i	−0.00915540	+	0.158631i
$892$		0			0
$893$	−11.9142	+	2.10079i	−0.398693	+	0.0703003i
$894$		0			0
$895$	−30.0432	−	82.5430i	−1.00423	−	2.75911i
$896$		0			0
$897$	−0.0825828	+	5.72945i	−0.00275736	+	0.191301i
$898$		0			0
$899$	0.443071	+	0.767421i	0.0147772	+	0.0255949i
$900$		0			0
$901$	−21.2735	−	12.2822i	−0.708722	−	0.409181i
$902$		0			0
$903$	−27.4087	−	8.94366i	−0.912103	−	0.297626i
$904$		0			0
$905$	1.01779	+	0.179464i	0.0338324	+	0.00596557i
$906$		0			0
$907$	−33.8290	+	28.3859i	−1.12327	+	0.942538i	−0.998765	−	0.0496805i	$-0.984180\pi$
$907$	−33.8290	+	28.3859i	−1.12327	+	0.942538i	−0.124508	+	0.992219i	$0.539735\pi$
$908$		0			0
$909$	−42.8374	−	38.1018i	−1.42083	−	1.26376i
$910$		0			0
$911$	−8.64070	+	23.7401i	−0.286279	+	0.786546i	0.710300	+	0.703899i	$0.248559\pi$
$911$	−8.64070	+	23.7401i	−0.286279	+	0.786546i	−0.996579	+	0.0826462i	$0.973663\pi$
$912$		0			0
$913$	2.34760	−	2.79776i	0.0776943	−	0.0925924i
$914$		0			0
$915$	−74.1147	+	25.7721i	−2.45016	+	0.851998i
$916$		0			0
$917$	37.5360	+	19.3291i	1.23955	+	0.638302i
$918$		0			0
$919$	9.20198			0.303545			0.151773	−	0.988415i	$-0.451502\pi$
$919$	9.20198			0.303545			0.151773	+	0.988415i	$0.451502\pi$
$920$		0			0
$921$	−37.7588	−	32.6222i	−1.24420	−	1.07494i
$922$		0			0
$923$	−1.85117	−	1.55331i	−0.0609318	−	0.0511279i
$924$		0			0
$925$	48.2035	+	17.5446i	1.58492	+	0.576864i
$926$		0			0
$927$	1.74381	−	0.940848i	0.0572743	−	0.0309015i
$928$		0			0
$929$	−42.0340	+	35.2707i	−1.37909	+	1.15720i	−0.409545	+	0.912290i	$0.634312\pi$
$929$	−42.0340	+	35.2707i	−1.37909	+	1.15720i	−0.969547	+	0.244905i	$0.921243\pi$
$930$		0			0
$931$	−12.1501	−	25.4643i	−0.398203	−	0.834559i
$932$		0			0
$933$	1.95718	−	5.14534i	0.0640752	−	0.168451i
$934$		0			0
$935$	−3.60717	−	2.08260i	−0.117967	−	0.0681083i
$936$		0			0
$937$	13.9817	−	8.07236i	0.456763	−	0.263712i	−0.253919	−	0.967225i	$-0.581720\pi$
$937$	13.9817	−	8.07236i	0.456763	−	0.263712i	0.710682	+	0.703513i	$0.248386\pi$
$938$		0			0
$939$	−1.80054	−	3.22509i	−0.0587583	−	0.105247i
$940$		0			0
$941$	1.41968	−	0.516721i	0.0462802	−	0.0168446i	−0.318776	−	0.947830i	$-0.603272\pi$
$941$	1.41968	−	0.516721i	0.0462802	−	0.0168446i	0.365057	+	0.930985i	$0.381050\pi$
$942$		0			0
$943$	43.1289	−	7.60479i	1.40447	−	0.247646i
$944$		0			0
$945$	26.3626	−	46.1746i	0.857576	−	1.50206i
$946$		0			0
$947$	−21.7837	+	3.84105i	−0.707874	+	0.124817i	−0.515983	−	0.856599i	$-0.672573\pi$
$947$	−21.7837	+	3.84105i	−0.707874	+	0.124817i	−0.191891	+	0.981416i	$0.561462\pi$
$948$		0			0
$949$	5.68757	−	2.07011i	0.184626	−	0.0671985i
$950$		0			0
$951$	−20.4621	+	34.2903i	−0.663528	+	1.11194i
$952$		0			0
$953$	−15.2587	+	8.80962i	−0.494278	+	0.285371i	−0.726347	−	0.687328i	$-0.758784\pi$
$953$	−15.2587	+	8.80962i	−0.494278	+	0.285371i	0.232070	+	0.972699i	$0.425450\pi$
$954$		0			0
$955$	26.6488	+	15.3857i	0.862334	+	0.497869i
$956$		0			0
$957$	−0.0931209	−	0.114282i	−0.00301017	−	0.00369423i
$958$		0			0
$959$	−21.9273	−	16.6715i	−0.708069	−	0.538352i
$960$		0			0
$961$	0.685388	−	0.575109i	0.0221093	−	0.0185519i
$962$		0			0
$963$	−11.3809	+	28.6695i	−0.366745	+	0.923862i
$964$		0			0
$965$	35.5107	+	12.9248i	1.14313	+	0.416065i
$966$		0			0
$967$	−9.81476	−	8.23556i	−0.315621	−	0.264838i	0.471189	−	0.882032i	$-0.343825\pi$
$967$	−9.81476	−	8.23556i	−0.315621	−	0.264838i	−0.786811	+	0.617194i	$0.788269\pi$
$968$		0			0
$969$	−2.67963	+	14.0128i	−0.0860820	+	0.450157i
$970$		0			0
$971$	35.1253			1.12722			0.563612	−	0.826039i	$-0.309411\pi$
$971$	35.1253			1.12722			0.563612	+	0.826039i	$0.309411\pi$
$972$		0			0
$973$	15.0737	−	29.2722i	0.483239	−	0.938424i
$974$		0			0
$975$	1.43313	−	7.49439i	0.0458968	−	0.240013i
$976$		0			0
$977$	0.977986	−	1.16552i	0.0312885	−	0.0372882i	−0.750173	−	0.661241i	$-0.770030\pi$
$977$	0.977986	−	1.16552i	0.0312885	−	0.0372882i	0.781462	+	0.623953i	$0.214474\pi$
$978$		0			0
$979$	−0.143056	+	0.393044i	−0.00457210	+	0.0125618i
$980$		0			0
$981$	13.6823	+	5.43147i	0.436843	+	0.173413i
$982$		0			0
$983$	−11.1072	+	9.32003i	−0.354264	+	0.297263i	−0.802500	−	0.596653i	$-0.796497\pi$
$983$	−11.1072	+	9.32003i	−0.354264	+	0.297263i	0.448236	+	0.893915i	$0.352053\pi$
$984$		0			0
$985$	84.8223	+	14.9565i	2.70266	+	0.476553i
$986$		0			0
$987$	−2.84286	−	13.4576i	−0.0904893	−	0.428361i
$988$		0			0
$989$	−40.7455	−	23.5244i	−1.29563	−	0.748033i
$990$		0			0
$991$	19.4627	+	33.7104i	0.618254	+	1.07085i	0.989804	+	0.142434i	$0.0454930\pi$
$991$	19.4627	+	33.7104i	0.618254	+	1.07085i	−0.371550	+	0.928413i	$0.621174\pi$
$992$		0			0
$993$	43.6047	+	26.0202i	1.38375	+	0.825727i
$994$		0			0
$995$	33.1279	+	91.0180i	1.05022	+	2.88547i
$996$		0			0
$997$	20.6186	−	3.63561i	0.652997	−	0.115141i	0.162672	−	0.986680i	$-0.447989\pi$
$997$	20.6186	−	3.63561i	0.652997	−	0.115141i	0.490326	+	0.871539i	$0.336878\pi$
$998$		0			0
$999$	−23.7376	+	12.3689i	−0.751024	+	0.391335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bx.a.41.2	✓	144
7.6	odd	2	inner	756.2.bx.a.41.23	yes	144
27.2	odd	18	inner	756.2.bx.a.461.23	yes	144
189.83	even	18	inner	756.2.bx.a.461.2	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bx.a.41.2	✓	144	1.1	even	1	trivial
756.2.bx.a.41.23	yes	144	7.6	odd	2	inner
756.2.bx.a.461.2	yes	144	189.83	even	18	inner
756.2.bx.a.461.23	yes	144	27.2	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bx (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70123 - 0.325320i) q^{3} +(2.96273 + 2.48603i) q^{5} +(1.79607 + 1.94271i) q^{7} +(2.78833 + 1.10688i) q^{9} +O(q^{10})\)	\(q+(-1.70123 - 0.325320i) q^{3} +(2.96273 + 2.48603i) q^{5} +(1.79607 + 1.94271i) q^{7} +(2.78833 + 1.10688i) q^{9} +(0.338747 + 0.403702i) q^{11} +(0.435661 + 0.0768188i) q^{13} +(-4.23152 - 5.19313i) q^{15} +(-1.02179 + 1.76979i) q^{17} +(-3.49064 + 2.01532i) q^{19} +(-2.42352 - 3.88929i) q^{21} +(-2.55771 - 7.02725i) q^{23} +(1.72921 + 9.80683i) q^{25} +(-4.38349 - 2.79016i) q^{27} +(0.159050 - 0.0280448i) q^{29} +(1.87661 + 5.15593i) q^{31} +(-0.444952 - 0.796990i) q^{33} +(0.491636 + 10.2208i) q^{35} +(2.57564 - 4.46114i) q^{37} +(-0.716167 - 0.272415i) q^{39} +(-1.01692 + 5.76725i) q^{41} +(4.81951 - 4.04405i) q^{43} +(5.50934 + 10.2113i) q^{45} +(2.82049 + 1.02658i) q^{47} +(-0.548267 + 6.97850i) q^{49} +(2.31403 - 2.67840i) q^{51} +12.0204i q^{53} +2.03820i q^{55} +(6.59398 - 2.29294i) q^{57} +(-5.93331 - 4.97864i) q^{59} +(4.00630 - 11.0072i) q^{61} +(2.85768 + 7.40497i) q^{63} +(1.09977 + 1.31066i) q^{65} +(-1.79309 + 10.1691i) q^{67} +(2.06514 + 12.7870i) q^{69} +(-4.73069 - 2.73126i) q^{71} +(11.8488 - 6.84090i) q^{73} +(0.248582 - 17.2462i) q^{75} +(-0.175865 + 1.38316i) q^{77} +(1.51105 + 8.56961i) q^{79} +(6.54961 + 6.17273i) q^{81} +(-1.20343 - 6.82497i) q^{83} +(-7.42702 + 2.70321i) q^{85} +(-0.279703 - 0.00403157i) q^{87} +(0.396843 + 0.687352i) q^{89} +(0.633241 + 0.984337i) q^{91} +(-1.51520 - 9.38190i) q^{93} +(-15.3520 - 2.70696i) q^{95} +(6.78774 + 8.08932i) q^{97} +(0.497687 + 1.50061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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