LMFDB - Embedded newform 756.2.ck.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (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			5.7
Character	$\chi$	$=$	756.5
Dual form			756.2.ck.a.605.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33105 - 1.10829i) q^{3} +(0.180656 - 1.02455i) q^{5} +(-1.77393 - 1.96295i) q^{7} +(0.543390 + 2.95038i) q^{9} +O(q^{10})$	\(q+(-1.33105 - 1.10829i) q^{3} +(0.180656 - 1.02455i) q^{5} +(-1.77393 - 1.96295i) q^{7} +(0.543390 + 2.95038i) q^{9} +(-3.15289 + 0.555939i) q^{11} +(-3.61991 + 4.31404i) q^{13} +(-1.37596 + 1.16351i) q^{15} +4.20835 q^{17} -4.25097i q^{19} +(0.185685 + 4.57881i) q^{21} +(-4.31087 + 5.13749i) q^{23} +(3.68139 + 1.33992i) q^{25} +(2.54659 - 4.52933i) q^{27} +(-2.19872 - 2.62033i) q^{29} +(2.78840 + 7.66106i) q^{31} +(4.81279 + 2.75433i) q^{33} +(-2.33161 + 1.46287i) q^{35} +(3.98796 + 6.90735i) q^{37} +(9.59948 - 1.73030i) q^{39} +(-5.69481 - 4.77851i) q^{41} +(-3.83125 - 1.39446i) q^{43} +(3.12098 - 0.0237272i) q^{45} +(6.45334 + 2.34882i) q^{47} +(-0.706311 + 6.96427i) q^{49} +(-5.60152 - 4.66407i) q^{51} +(-10.0687 + 5.81318i) q^{53} +3.33073i q^{55} +(-4.71130 + 5.65825i) q^{57} +(1.63882 + 1.37513i) q^{59} +(-2.63335 + 7.23508i) q^{61} +(4.82749 - 6.30042i) q^{63} +(3.76600 + 4.48814i) q^{65} +(-1.85427 + 10.5161i) q^{67} +(11.4318 - 2.06057i) q^{69} +(-14.4695 - 8.35397i) q^{71} +(-5.08376 - 2.93511i) q^{73} +(-3.41510 - 5.86355i) q^{75} +(6.68430 + 5.20275i) q^{77} +(-0.736951 - 4.17946i) q^{79} +(-8.40946 + 3.20641i) q^{81} +(-0.806976 + 0.677133i) q^{83} +(0.760264 - 4.31167i) q^{85} +(0.0225205 + 5.92461i) q^{87} -3.70603 q^{89} +(14.8897 - 0.547140i) q^{91} +(4.77918 - 13.2876i) q^{93} +(-4.35534 - 0.767963i) q^{95} +(1.71054 - 4.69967i) q^{97} +(-3.35348 - 9.00012i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−1.33105	−	1.10829i	−0.768482	−	0.639871i
$3$	−1.33105	−	1.10829i	−0.768482	−	0.639871i
$4$		0			0
$5$	0.180656	−	1.02455i	0.0807919	−	0.458194i	−0.917394	−	0.397981i	$-0.869711\pi$
$5$	0.180656	−	1.02455i	0.0807919	−	0.458194i	0.998186	−	0.0602126i	$-0.0191779\pi$
$6$		0			0
$7$	−1.77393	−	1.96295i	−0.670484	−	0.741924i
$7$	−1.77393	−	1.96295i	−0.670484	−	0.741924i
$8$		0			0
$9$	0.543390	+	2.95038i	0.181130	+	0.983459i
$10$		0			0
$11$	−3.15289	+	0.555939i	−0.950632	+	0.167622i	−0.627399	−	0.778698i	$-0.715881\pi$
$11$	−3.15289	+	0.555939i	−0.950632	+	0.167622i	−0.323232	+	0.946320i	$0.604769\pi$
$12$		0			0
$13$	−3.61991	+	4.31404i	−1.00398	+	1.19650i	−0.0235337	+	0.999723i	$0.507492\pi$
$13$	−3.61991	+	4.31404i	−1.00398	+	1.19650i	−0.980448	+	0.196776i	$0.936953\pi$
$14$		0			0
$15$	−1.37596	+	1.16351i	−0.355272	+	0.300417i
$16$		0			0
$17$	4.20835			1.02067			0.510337	−	0.859975i	$-0.329521\pi$
$17$	4.20835			1.02067			0.510337	+	0.859975i	$0.329521\pi$
$18$		0			0
$19$		−	4.25097i		−	0.975238i	−0.873056	−	0.487619i	$-0.837865\pi$
$19$		−	4.25097i		−	0.975238i	0.873056	−	0.487619i	$-0.162135\pi$
$20$		0			0
$21$	0.185685	+	4.57881i	0.0405197	+	0.999179i
$22$		0			0
$23$	−4.31087	+	5.13749i	−0.898878	+	1.07124i	0.0982241	+	0.995164i	$0.468684\pi$
$23$	−4.31087	+	5.13749i	−0.898878	+	1.07124i	−0.997102	+	0.0760766i	$0.975761\pi$
$24$		0			0
$25$	3.68139	+	1.33992i	0.736279	+	0.267983i
$26$		0			0
$27$	2.54659	−	4.52933i	0.490092	−	0.871671i
$28$		0			0
$29$	−2.19872	−	2.62033i	−0.408292	−	0.486583i	0.522238	−	0.852800i	$-0.325097\pi$
$29$	−2.19872	−	2.62033i	−0.408292	−	0.486583i	−0.930530	+	0.366217i	$0.880653\pi$
$30$		0			0
$31$	2.78840	+	7.66106i	0.500811	+	1.37597i	0.890484	+	0.455014i	$0.150366\pi$
$31$	2.78840	+	7.66106i	0.500811	+	1.37597i	−0.389673	+	0.920953i	$0.627412\pi$
$32$		0			0
$33$	4.81279	+	2.75433i	0.837800	+	0.479467i
$34$		0			0
$35$	−2.33161	+	1.46287i	−0.394114	+	0.247270i
$36$		0			0
$37$	3.98796	+	6.90735i	0.655617	+	1.13556i	0.981739	+	0.190234i	$0.0609245\pi$
$37$	3.98796	+	6.90735i	0.655617	+	1.13556i	−0.326122	+	0.945328i	$0.605742\pi$
$38$		0			0
$39$	9.59948	−	1.73030i	1.53715	−	0.277069i
$40$		0			0
$41$	−5.69481	−	4.77851i	−0.889379	−	0.746278i	0.0787062	−	0.996898i	$-0.474921\pi$
$41$	−5.69481	−	4.77851i	−0.889379	−	0.746278i	−0.968086	+	0.250620i	$0.919366\pi$
$42$		0			0
$43$	−3.83125	−	1.39446i	−0.584260	−	0.212653i	0.0329429	−	0.999457i	$-0.489512\pi$
$43$	−3.83125	−	1.39446i	−0.584260	−	0.212653i	−0.617203	+	0.786804i	$0.711734\pi$
$44$		0			0
$45$	3.12098	−	0.0237272i	0.465249	−	0.00353705i
$46$		0			0
$47$	6.45334	+	2.34882i	0.941317	+	0.342611i	0.766686	−	0.642023i	$-0.221905\pi$
$47$	6.45334	+	2.34882i	0.941317	+	0.342611i	0.174631	+	0.984634i	$0.444127\pi$
$48$		0			0
$49$	−0.706311	+	6.96427i	−0.100902	+	0.994896i
$50$		0			0
$51$	−5.60152	−	4.66407i	−0.784370	−	0.653100i
$52$		0			0
$53$	−10.0687	+	5.81318i	−1.38305	+	0.798502i	−0.992519	−	0.122089i	$-0.961041\pi$
$53$	−10.0687	+	5.81318i	−1.38305	+	0.798502i	−0.390527	+	0.920591i	$0.627707\pi$
$54$		0			0
$55$			3.33073i			0.449116i
$56$		0			0
$57$	−4.71130	+	5.65825i	−0.624027	+	0.749453i
$58$		0			0
$59$	1.63882	+	1.37513i	0.213356	+	0.179027i	0.743202	−	0.669067i	$-0.233306\pi$
$59$	1.63882	+	1.37513i	0.213356	+	0.179027i	−0.529846	+	0.848094i	$0.677750\pi$
$60$		0			0
$61$	−2.63335	+	7.23508i	−0.337166	+	0.926357i	0.649028	+	0.760765i	$0.275176\pi$
$61$	−2.63335	+	7.23508i	−0.337166	+	0.926357i	−0.986194	+	0.165593i	$0.947046\pi$
$62$		0			0
$63$	4.82749	−	6.30042i	0.608207	−	0.793779i
$64$		0			0
$65$	3.76600	+	4.48814i	0.467115	+	0.556686i
$66$		0			0
$67$	−1.85427	+	10.5161i	−0.226535	+	1.28475i	0.633193	+	0.773994i	$0.281744\pi$
$67$	−1.85427	+	10.5161i	−0.226535	+	1.28475i	−0.859728	+	0.510752i	$0.829367\pi$
$68$		0			0
$69$	11.4318	−	2.06057i	1.37623	−	0.248064i
$70$		0			0
$71$	−14.4695	−	8.35397i	−1.71721	−	0.991434i	−0.923911	−	0.382607i	$-0.875026\pi$
$71$	−14.4695	−	8.35397i	−1.71721	−	0.991434i	−0.793303	−	0.608827i	$-0.791640\pi$
$72$		0			0
$73$	−5.08376	−	2.93511i	−0.595009	−	0.343529i	0.172066	−	0.985085i	$-0.444956\pi$
$73$	−5.08376	−	2.93511i	−0.595009	−	0.343529i	−0.767076	+	0.641557i	$0.778289\pi$
$74$		0			0
$75$	−3.41510	−	5.86355i	−0.394342	−	0.677064i
$76$		0			0
$77$	6.68430	+	5.20275i	0.761746	+	0.592908i
$78$		0			0
$79$	−0.736951	−	4.17946i	−0.0829135	−	0.470226i	−0.997787	−	0.0664859i	$-0.978821\pi$
$79$	−0.736951	−	4.17946i	−0.0829135	−	0.470226i	0.914874	−	0.403740i	$-0.132290\pi$
$80$		0			0
$81$	−8.40946	+	3.20641i	−0.934384	+	0.356268i
$82$		0			0
$83$	−0.806976	+	0.677133i	−0.0885771	+	0.0743251i	−0.686001	−	0.727601i	$-0.740635\pi$
$83$	−0.806976	+	0.677133i	−0.0885771	+	0.0743251i	0.597424	+	0.801926i	$0.296191\pi$
$84$		0			0
$85$	0.760264	−	4.31167i	0.0824622	−	0.467666i
$86$		0			0
$87$	0.0225205	+	5.92461i	0.00241446	+	0.635184i
$88$		0			0
$89$	−3.70603			−0.392839			−0.196419	−	0.980520i	$-0.562931\pi$
$89$	−3.70603			−0.392839			−0.196419	+	0.980520i	$0.562931\pi$
$90$		0			0
$91$	14.8897	−	0.547140i	1.56087	−	0.0573559i
$92$		0			0
$93$	4.77918	−	13.2876i	0.495577	−	1.37786i
$94$		0			0
$95$	−4.35534	−	0.767963i	−0.446848	−	0.0787914i
$96$		0			0
$97$	1.71054	−	4.69967i	0.173679	−	0.477179i	−0.822059	−	0.569402i	$-0.807175\pi$
$97$	1.71054	−	4.69967i	0.173679	−	0.477179i	0.995738	+	0.0922225i	$0.0293971\pi$
$98$		0			0
$99$	−3.35348	−	9.00012i	−0.337037	−	0.904546i
$100$		0			0
$101$	5.71563	−	4.79598i	0.568726	−	0.477218i	−0.312497	−	0.949919i	$-0.601165\pi$
$101$	5.71563	−	4.79598i	0.568726	−	0.477218i	0.881223	+	0.472701i	$0.156721\pi$
$102$		0			0
$103$	17.0739	+	3.01059i	1.68234	+	0.296643i	0.931474	−	0.363808i	$-0.118523\pi$
$103$	17.0739	+	3.01059i	1.68234	+	0.296643i	0.750870	+	0.660450i	$0.229635\pi$
$104$		0			0
$105$	4.72478	+	0.636947i	0.461091	+	0.0621597i
$106$		0			0
$107$	−11.6596	−	6.73167i	−1.12718	−	0.650775i	−0.183952	−	0.982935i	$-0.558889\pi$
$107$	−11.6596	−	6.73167i	−1.12718	−	0.650775i	−0.943223	+	0.332160i	$0.892223\pi$
$108$		0			0
$109$	3.21351	+	5.56596i	0.307798	+	0.533122i	0.977880	−	0.209165i	$-0.0670746\pi$
$109$	3.21351	+	5.56596i	0.307798	+	0.533122i	−0.670082	+	0.742287i	$0.733741\pi$
$110$		0			0
$111$	2.34717	−	13.6138i	0.222783	−	1.29217i
$112$		0			0
$113$	4.24375	+	11.6596i	0.399218	+	1.09684i	0.962666	+	0.270691i	$0.0872522\pi$
$113$	4.24375	+	11.6596i	0.399218	+	1.09684i	−0.563448	+	0.826151i	$0.690526\pi$
$114$		0			0
$115$	4.48484	+	5.34483i	0.418214	+	0.498408i
$116$		0			0
$117$	−14.6951	−	8.33589i	−1.35856	−	0.770654i
$118$		0			0
$119$	−7.46533	−	8.26076i	−0.684346	−	0.757262i
$120$		0			0
$121$	−0.704983	+	0.256593i	−0.0640894	+	0.0233266i
$122$		0			0
$123$	2.28410	+	12.6719i	0.205951	+	1.14259i
$124$		0			0
$125$	4.63877	−	8.03459i	0.414905	−	0.718636i
$126$		0			0
$127$	0.751871	+	1.30228i	0.0667178	+	0.115559i	0.897455	−	0.441107i	$-0.145414\pi$
$127$	0.751871	+	1.30228i	0.0667178	+	0.115559i	−0.830737	+	0.556665i	$0.812081\pi$
$128$		0			0
$129$	3.55412	+	6.10223i	0.312923	+	0.537271i
$130$		0			0
$131$	−11.0025	−	9.23223i	−0.961297	−	0.806624i	0.0198667	−	0.999803i	$-0.493676\pi$
$131$	−11.0025	−	9.23223i	−0.961297	−	0.806624i	−0.981164	+	0.193179i	$0.938120\pi$
$132$		0			0
$133$	−8.34441	+	7.54094i	−0.723553	+	0.653882i
$134$		0			0
$135$	−4.18048	−	3.42737i	−0.359798	−	0.294981i
$136$		0			0
$137$	−0.192260	+	0.528231i	−0.0164259	+	0.0451298i	−0.947635	−	0.319357i	$-0.896533\pi$
$137$	−0.192260	+	0.528231i	−0.0164259	+	0.0451298i	0.931209	+	0.364486i	$0.118755\pi$
$138$		0			0
$139$	−19.7935	−	3.49013i	−1.67886	−	0.296029i	−0.748627	−	0.662991i	$-0.769287\pi$
$139$	−19.7935	−	3.49013i	−1.67886	−	0.296029i	−0.930236	+	0.366962i	$0.880398\pi$
$140$		0			0
$141$	−5.98655	−	10.2786i	−0.504158	−	0.865612i
$142$		0			0
$143$	9.01482	−	15.6141i	0.753858	−	1.30572i
$144$		0			0
$145$	−3.08188	+	1.77932i	−0.255936	+	0.147765i
$146$		0			0
$147$	8.65857	−	8.48700i	0.714147	−	0.699996i
$148$		0			0
$149$	−6.70021	−	18.4087i	−0.548903	−	1.50810i	−0.835194	−	0.549956i	$-0.814645\pi$
$149$	−6.70021	−	18.4087i	−0.548903	−	1.50810i	0.286291	−	0.958143i	$-0.407578\pi$
$150$		0			0
$151$	0.856796	+	4.85913i	0.0697250	+	0.395430i	0.999619	+	0.0276026i	$0.00878728\pi$
$151$	0.856796	+	4.85913i	0.0697250	+	0.395430i	−0.929894	+	0.367828i	$0.880102\pi$
$152$		0			0
$153$	2.28677	+	12.4162i	0.184875	+	1.00379i
$154$		0			0
$155$	8.35290	−	1.47284i	0.670921	−	0.118301i
$156$		0			0
$157$	8.43876	−	10.0569i	0.673487	−	0.802630i	−0.315768	−	0.948837i	$-0.602262\pi$
$157$	8.43876	−	10.0569i	0.673487	−	0.802630i	0.989254	+	0.146207i	$0.0467064\pi$
$158$		0			0
$159$	19.8447	+	3.42143i	1.57379	+	0.271337i
$160$		0			0
$161$	17.7318	−	0.651576i	1.39746	−	0.0513514i
$162$		0			0
$163$	−2.70825	+	4.69083i	−0.212127	+	0.367414i	−0.952380	−	0.304914i	$-0.901372\pi$
$163$	−2.70825	+	4.69083i	−0.212127	+	0.367414i	0.740253	+	0.672328i	$0.234706\pi$
$164$		0			0
$165$	3.69141	−	4.43337i	0.287376	−	0.345138i
$166$		0			0
$167$	−17.6448	+	6.42219i	−1.36540	+	0.496964i	−0.917719	−	0.397231i	$-0.869971\pi$
$167$	−17.6448	+	6.42219i	−1.36540	+	0.496964i	−0.447678	+	0.894195i	$0.647749\pi$
$168$		0			0
$169$	−3.24977	−	18.4304i	−0.249982	−	1.41772i
$170$		0			0
$171$	12.5420	−	2.30993i	0.959107	−	0.176645i
$172$		0			0
$173$	−0.770078	+	0.646172i	−0.0585479	+	0.0491276i	−0.671592	−	0.740921i	$-0.734389\pi$
$173$	−0.770078	+	0.646172i	−0.0585479	+	0.0491276i	0.613044	+	0.790049i	$0.289945\pi$
$174$		0			0
$175$	−3.90037	−	9.60330i	−0.294840	−	0.725941i
$176$		0			0
$177$	−0.657306	−	3.64666i	−0.0494062	−	0.274100i
$178$		0			0
$179$		−	26.0886i		−	1.94995i	−0.222307	−	0.974977i	$-0.571359\pi$
$179$		−	26.0886i		−	1.94995i	0.222307	−	0.974977i	$-0.428641\pi$
$180$		0			0
$181$	0.793323	−	0.458026i	0.0589673	−	0.0340448i	−0.470227	−	0.882546i	$-0.655828\pi$
$181$	0.793323	−	0.458026i	0.0589673	−	0.0340448i	0.529194	+	0.848501i	$0.322494\pi$
$182$		0			0
$183$	11.5237	−	6.71174i	0.851856	−	0.496146i
$184$		0			0
$185$	7.79739	−	2.83802i	0.573275	−	0.208655i
$186$		0			0
$187$	−13.2684	+	2.33959i	−0.970285	+	0.171087i
$188$		0			0
$189$	−13.4083	+	3.03592i	−0.975312	+	0.220831i
$190$		0			0
$191$	−6.34061	+	1.11802i	−0.458790	+	0.0808971i	−0.398267	−	0.917270i	$-0.630388\pi$
$191$	−6.34061	+	1.11802i	−0.458790	+	0.0808971i	−0.0605236	+	0.998167i	$0.519277\pi$
$192$		0			0
$193$	−9.14158	+	3.32726i	−0.658026	+	0.239502i	−0.649384	−	0.760461i	$-0.724973\pi$
$193$	−9.14158	+	3.32726i	−0.658026	+	0.239502i	−0.00864188	+	0.999963i	$0.502751\pi$
$194$		0			0
$195$	−0.0385735	−	10.1478i	−0.00276231	−	0.726696i
$196$		0			0
$197$	−8.98992	+	5.19033i	−0.640505	+	0.369796i	−0.784809	−	0.619738i	$-0.787239\pi$
$197$	−8.98992	+	5.19033i	−0.640505	+	0.369796i	0.144304	+	0.989533i	$0.453906\pi$
$198$		0			0
$199$		−	2.58419i		−	0.183188i	−0.995796	−	0.0915941i	$-0.970804\pi$
$199$		−	2.58419i		−	0.183188i	0.995796	−	0.0915941i	$-0.0291962\pi$
$200$		0			0
$201$	14.1230	−	11.9424i	0.996160	−	0.842351i
$202$		0			0
$203$	−1.24318	+	8.96426i	−0.0872544	+	0.629168i
$204$		0			0
$205$	−5.92463	+	4.97136i	−0.413794	+	0.347215i
$206$		0			0
$207$	−17.5000	−	9.92702i	−1.21634	−	0.689976i
$208$		0			0
$209$	2.36328	+	13.4028i	0.163471	+	0.927092i
$210$		0			0
$211$	−13.6574	+	4.97088i	−0.940213	+	0.342210i	−0.766250	−	0.642542i	$-0.777880\pi$
$211$	−13.6574	+	4.97088i	−0.940213	+	0.342210i	−0.173963	+	0.984752i	$0.555657\pi$
$212$		0			0
$213$	10.0010	+	27.1560i	0.685259	+	1.86070i
$214$		0			0
$215$	−2.12084	+	3.67340i	−0.144640	+	0.250524i
$216$		0			0
$217$	10.0918	−	19.0637i	0.685077	−	1.29413i
$218$		0			0
$219$	3.51379	+	9.54106i	0.237440	+	0.644725i
$220$		0			0
$221$	−15.2338	+	18.1550i	−1.02474	+	1.22124i
$222$		0			0
$223$	10.4953	−	1.85061i	0.702818	−	0.123926i	0.189192	−	0.981940i	$-0.439413\pi$
$223$	10.4953	−	1.85061i	0.702818	−	0.123926i	0.513626	+	0.858014i	$0.328302\pi$
$224$		0			0
$225$	−1.95283	+	11.5896i	−0.130189	+	0.772640i
$226$		0			0
$227$	3.60603	+	20.4508i	0.239341	+	1.35737i	0.833276	+	0.552857i	$0.186462\pi$
$227$	3.60603	+	20.4508i	0.239341	+	1.35737i	−0.593936	+	0.804513i	$0.702427\pi$
$228$		0			0
$229$	4.57450	+	12.5683i	0.302291	+	0.830539i	0.994101	+	0.108459i	$0.0345916\pi$
$229$	4.57450	+	12.5683i	0.302291	+	0.830539i	−0.691810	+	0.722080i	$0.743186\pi$
$230$		0			0
$231$	−3.13098	−	14.3333i	−0.206004	−	0.943059i
$232$		0			0
$233$	13.0930	−	7.55926i	0.857752	−	0.495223i	−0.00550680	−	0.999985i	$-0.501753\pi$
$233$	13.0930	−	7.55926i	0.857752	−	0.495223i	0.863259	+	0.504761i	$0.168420\pi$
$234$		0			0
$235$	3.57233	−	6.18745i	0.233033	−	0.403625i
$236$		0			0
$237$	−3.65113	+	6.37982i	−0.237166	+	0.414414i
$238$		0			0
$239$	10.9911	+	1.93803i	0.710955	+	0.125361i	0.517418	−	0.855733i	$-0.326893\pi$
$239$	10.9911	+	1.93803i	0.710955	+	0.125361i	0.193536	+	0.981093i	$0.438004\pi$
$240$		0			0
$241$	1.42884	−	3.92570i	0.0920396	−	0.252877i	−0.885128	−	0.465348i	$-0.845929\pi$
$241$	1.42884	−	3.92570i	0.0920396	−	0.252877i	0.977167	+	0.212472i	$0.0681513\pi$
$242$		0			0
$243$	14.7470	+	5.05222i	0.946023	+	0.324100i
$244$		0			0
$245$	7.00766	+	1.98179i	0.447703	+	0.126612i
$246$		0			0
$247$	18.3388	+	15.3881i	1.16687	+	0.979122i
$248$		0			0
$249$	1.82459	−	0.00693559i	0.115628	−	0.000439525i
$250$		0			0
$251$	−5.12996	−	8.88536i	−0.323800	−	0.560839i	0.657468	−	0.753482i	$-0.271627\pi$
$251$	−5.12996	−	8.88536i	−0.323800	−	0.560839i	−0.981269	+	0.192643i	$0.938294\pi$
$252$		0			0
$253$	10.7355	−	18.5945i	0.674938	−	1.16903i
$254$		0			0
$255$	−5.79053	+	4.89646i	−0.362617	+	0.306628i
$256$		0			0
$257$	−19.1202	+	6.95920i	−1.19269	+	0.434103i	−0.860667	−	0.509169i	$-0.829953\pi$
$257$	−19.1202	+	6.95920i	−1.19269	+	0.434103i	−0.332022	+	0.943272i	$0.607731\pi$
$258$		0			0
$259$	6.48437	−	20.0813i	0.402919	−	1.24779i
$260$		0			0
$261$	6.53620	−	7.91091i	0.404581	−	0.489673i
$262$		0			0
$263$	14.8895	+	17.7446i	0.918123	+	1.09418i	0.995269	+	0.0971568i	$0.0309748\pi$
$263$	14.8895	+	17.7446i	0.918123	+	1.09418i	−0.0771459	+	0.997020i	$0.524581\pi$
$264$		0			0
$265$	4.13693	+	11.3661i	0.254130	+	0.698216i
$266$		0			0
$267$	4.93292	+	4.10736i	0.301890	+	0.251366i
$268$		0			0
$269$	6.90423	+	11.9585i	0.420958	+	0.729121i	0.996033	−	0.0889793i	$-0.0283605\pi$
$269$	6.90423	+	11.9585i	0.420958	+	0.729121i	−0.575075	+	0.818101i	$0.695027\pi$
$270$		0			0
$271$	17.5834	+	10.1518i	1.06812	+	0.616678i	0.927667	−	0.373410i	$-0.121811\pi$
$271$	17.5834	+	10.1518i	1.06812	+	0.616678i	0.140451	+	0.990088i	$0.455145\pi$
$272$		0			0
$273$	−20.4253	−	15.7738i	−1.23620	−	0.954676i
$274$		0			0
$275$	−12.3519	−	2.17798i	−0.744850	−	0.131337i
$276$		0			0
$277$	−12.1880	+	10.2270i	−0.732308	+	0.614479i	−0.930760	−	0.365631i	$-0.880853\pi$
$277$	−12.1880	+	10.2270i	−0.732308	+	0.614479i	0.198452	+	0.980111i	$0.436409\pi$
$278$		0			0
$279$	−21.0878	+	12.3898i	−1.26250	+	0.741756i
$280$		0			0
$281$	7.50502	−	20.6199i	0.447712	−	1.23008i	−0.486601	−	0.873625i	$-0.661763\pi$
$281$	7.50502	−	20.6199i	0.447712	−	1.23008i	0.934313	−	0.356454i	$-0.116015\pi$
$282$		0			0
$283$	0.867207	+	0.152912i	0.0515501	+	0.00908967i	0.199364	−	0.979926i	$-0.436112\pi$
$283$	0.867207	+	0.152912i	0.0515501	+	0.00908967i	−0.147814	+	0.989015i	$0.547224\pi$
$284$		0			0
$285$	4.94605	+	5.84917i	0.292978	+	0.346475i
$286$		0			0
$287$	0.722259	+	19.6554i	0.0426336	+	1.16022i
$288$		0			0
$289$	0.710180			0.0417753
$290$		0			0
$291$	−7.48541	+	4.35973i	−0.438803	+	0.255572i
$292$		0			0
$293$	2.51485	−	14.2624i	0.146919	−	0.833221i	−0.818887	−	0.573955i	$-0.805408\pi$
$293$	2.51485	−	14.2624i	0.146919	−	0.833221i	0.965806	−	0.259266i	$-0.0834805\pi$
$294$		0			0
$295$	1.70496	−	1.43063i	0.0992665	−	0.0832945i
$296$		0			0
$297$	−5.51109	+	15.6962i	−0.319786	+	0.910788i
$298$		0			0
$299$	−6.55839	−	37.1945i	−0.379282	−	2.15101i
$300$		0			0
$301$	4.05914	+	9.99422i	0.233965	+	0.576057i
$302$		0			0
$303$	−12.9231	+	0.0491232i	−0.742414	+	0.00282206i
$304$		0			0
$305$	6.93699	+	4.00507i	0.397211	+	0.229330i
$306$		0			0
$307$	9.66111	+	5.57784i	0.551388	+	0.318344i	0.749682	−	0.661798i	$-0.230207\pi$
$307$	9.66111	+	5.57784i	0.551388	+	0.318344i	−0.198293	+	0.980143i	$0.563540\pi$
$308$		0			0
$309$	−19.3896	−	22.9301i	−1.10304	−	1.30445i
$310$		0			0
$311$	−2.01607	+	11.4337i	−0.114321	+	0.648347i	0.872763	+	0.488144i	$0.162326\pi$
$311$	−2.01607	+	11.4337i	−0.114321	+	0.648347i	−0.987084	+	0.160203i	$0.948785\pi$
$312$		0			0
$313$	−10.2513	−	12.2170i	−0.579435	−	0.690544i	0.394104	−	0.919066i	$-0.371055\pi$
$313$	−10.2513	−	12.2170i	−0.579435	−	0.690544i	−0.973539	+	0.228522i	$0.926611\pi$
$314$		0			0
$315$	−5.58299	−	6.08423i	−0.314566	−	0.342807i
$316$		0			0
$317$	−8.44013	+	23.1891i	−0.474045	+	1.30243i	0.440431	+	0.897787i	$0.354826\pi$
$317$	−8.44013	+	23.1891i	−0.474045	+	1.30243i	−0.914476	+	0.404641i	$0.867396\pi$
$318$		0			0
$319$	8.38906	+	7.03925i	0.469697	+	0.394123i
$320$		0			0
$321$	8.05887	+	21.8824i	0.449802	+	1.22136i
$322$		0			0
$323$		−	17.8895i		−	0.995400i
$324$		0			0
$325$	−19.1068	+	11.0313i	−1.05985	+	0.611906i
$326$		0			0
$327$	1.89135	−	10.9701i	0.104592	−	0.606646i
$328$		0			0
$329$	−6.83719	−	16.8342i	−0.376947	−	0.928101i
$330$		0			0
$331$	6.47121	+	2.35533i	0.355690	+	0.129460i	0.513684	−	0.857980i	$-0.328280\pi$
$331$	6.47121	+	2.35533i	0.355690	+	0.129460i	−0.157994	+	0.987440i	$0.550503\pi$
$332$		0			0
$333$	−18.2123	+	15.5194i	−0.998026	+	0.850456i
$334$		0			0
$335$	10.4393	+	3.79960i	0.570360	+	0.207594i
$336$		0			0
$337$	2.78612	+	2.33783i	0.151770	+	0.127350i	0.715511	−	0.698602i	$-0.246194\pi$
$337$	2.78612	+	2.33783i	0.151770	+	0.127350i	−0.563741	+	0.825951i	$0.690638\pi$
$338$		0			0
$339$	7.27357	−	20.2228i	0.395046	−	1.09835i
$340$		0			0
$341$	−13.0506	−	22.6043i	−0.706729	−	1.22409i
$342$		0			0
$343$	14.9234	−	10.9677i	0.805790	−	0.592201i
$344$		0			0
$345$	−0.0459364	−	12.0847i	−0.00247313	−	0.650620i
$346$		0			0
$347$	6.90040	+	18.9587i	0.370433	+	1.01776i	0.975195	+	0.221349i	$0.0710461\pi$
$347$	6.90040	+	18.9587i	0.370433	+	1.01776i	−0.604762	+	0.796406i	$0.706732\pi$
$348$		0			0
$349$	−16.9430	−	20.1919i	−0.906938	−	1.08085i	−0.996393	−	0.0848561i	$-0.972957\pi$
$349$	−16.9430	−	20.1919i	−0.906938	−	1.08085i	0.0894549	−	0.995991i	$-0.471487\pi$
$350$		0			0
$351$	10.3213	+	27.3819i	0.550910	+	1.46154i
$352$		0			0
$353$	2.39086	+	0.870202i	0.127253	+	0.0463162i	0.404862	−	0.914378i	$-0.367320\pi$
$353$	2.39086	+	0.870202i	0.127253	+	0.0463162i	−0.277609	+	0.960694i	$0.589542\pi$
$354$		0			0
$355$	−11.1731	+	13.3156i	−0.593006	+	0.706717i
$356$		0			0
$357$	0.781426	+	19.2692i	0.0413574	+	1.01984i
$358$		0			0
$359$			24.1573i			1.27497i	0.770462	+	0.637486i	$0.220026\pi$
$359$			24.1573i			1.27497i	−0.770462	+	0.637486i	$0.779974\pi$
$360$		0			0
$361$	0.929290			0.0489100
$362$		0			0
$363$	1.22275	+	0.439787i	0.0641776	+	0.0230828i
$364$		0			0
$365$	−3.92559	+	4.67833i	−0.205475	+	0.244875i
$366$		0			0
$367$	−18.2957	+	3.22602i	−0.955027	+	0.168397i	−0.629383	−	0.777095i	$-0.716692\pi$
$367$	−18.2957	+	3.22602i	−0.955027	+	0.168397i	−0.325644	+	0.945492i	$0.605581\pi$
$368$		0			0
$369$	11.0039	−	19.3984i	0.572841	−	1.00984i
$370$		0			0
$371$	29.2722	+	9.45216i	1.51974	+	0.490732i
$372$		0			0
$373$	3.27355	−	18.5652i	0.169498	−	0.961271i	−0.774807	−	0.632198i	$-0.782153\pi$
$373$	3.27355	−	18.5652i	0.169498	−	0.961271i	0.944305	−	0.329073i	$-0.106736\pi$
$374$		0			0
$375$	−15.0791	+	5.55334i	−0.778681	+	0.286773i
$376$		0			0
$377$	19.2634			0.992114
$378$		0			0
$379$	−22.5186			−1.15670			−0.578352	−	0.815788i	$-0.696304\pi$
$379$	−22.5186			−1.15670			−0.578352	+	0.815788i	$0.696304\pi$
$380$		0			0
$381$	0.442524	−	2.56669i	0.0226712	−	0.131495i
$382$		0			0
$383$	0.178794	−	1.01399i	0.00913594	−	0.0518125i	−0.979899	−	0.199494i	$-0.936070\pi$
$383$	0.178794	−	1.01399i	0.00913594	−	0.0518125i	0.989035	+	0.147682i	$0.0471812\pi$
$384$		0			0
$385$	6.53805	−	5.90850i	0.333210	−	0.301125i
$386$		0			0
$387$	2.03232	−	12.0614i	0.103309	−	0.613114i
$388$		0			0
$389$	−5.57571	+	0.983148i	−0.282700	+	0.0498476i	−0.313200	−	0.949687i	$-0.601401\pi$
$389$	−5.57571	+	0.983148i	−0.282700	+	0.0498476i	0.0305004	+	0.999535i	$0.490290\pi$
$390$		0			0
$391$	−18.1416	+	21.6203i	−0.917461	+	1.09339i
$392$		0			0
$393$	4.41296	+	24.4826i	0.222604	+	1.23498i
$394$		0			0
$395$	−4.41521			−0.222153
$396$		0			0
$397$		−	15.0350i		−	0.754586i	−0.926094	−	0.377293i	$-0.876855\pi$
$397$		−	15.0350i		−	0.754586i	0.926094	−	0.377293i	$-0.123145\pi$
$398$		0			0
$399$	19.4644	−	0.789339i	0.974438	−	0.0395164i
$400$		0			0
$401$	−16.1931	+	19.2982i	−0.808646	+	0.963707i	−0.999841	−	0.0178453i	$-0.994319\pi$
$401$	−16.1931	+	19.2982i	−0.808646	+	0.963707i	0.191195	+	0.981552i	$0.438764\pi$
$402$		0			0
$403$	−43.1439	−	15.7031i	−2.14915	−	0.782227i
$404$		0			0
$405$	1.76591	+	9.19518i	0.0877490	+	0.456912i
$406$		0			0
$407$	−16.4137	−	19.5610i	−0.813595	−	0.969605i
$408$		0			0
$409$	−7.38281	−	20.2841i	−0.365056	−	1.00298i	−0.977215	−	0.212250i	$-0.931921\pi$
$409$	−7.38281	−	20.2841i	−0.365056	−	1.00298i	0.612159	−	0.790735i	$-0.290301\pi$
$410$		0			0
$411$	0.841341	−	0.490022i	0.0415003	−	0.0241710i
$412$		0			0
$413$	−0.207848	−	5.65631i	−0.0102275	−	0.278329i
$414$		0			0
$415$	0.547973	+	0.949117i	0.0268989	+	0.0465903i
$416$		0			0
$417$	22.4781	+	26.5825i	1.10076	+	1.30175i
$418$		0			0
$419$	15.5980	+	13.0883i	0.762012	+	0.639404i	0.938650	−	0.344872i	$-0.112078\pi$
$419$	15.5980	+	13.0883i	0.762012	+	0.639404i	−0.176638	+	0.984276i	$0.556522\pi$
$420$		0			0
$421$	19.3992	+	7.06073i	0.945459	+	0.344119i	0.768319	−	0.640067i	$-0.221093\pi$
$421$	19.3992	+	7.06073i	0.945459	+	0.344119i	0.177140	+	0.984186i	$0.443316\pi$
$422$		0			0
$423$	−3.42324	+	20.3161i	−0.166444	+	0.987804i
$424$		0			0
$425$	15.4926	+	5.63884i	0.751500	+	0.273524i
$426$		0			0
$427$	18.8735	−	7.66543i	0.913351	−	0.370956i
$428$		0			0
$429$	−29.3042	+	10.7922i	−1.41482	+	0.521051i
$430$		0			0
$431$	4.87013	−	2.81177i	0.234586	−	0.135438i	−0.378100	−	0.925765i	$-0.623422\pi$
$431$	4.87013	−	2.81177i	0.234586	−	0.135438i	0.612686	+	0.790327i	$0.290089\pi$
$432$		0			0
$433$			21.1008i			1.01404i	0.861934	+	0.507020i	$0.169253\pi$
$433$			21.1008i			1.01404i	−0.861934	+	0.507020i	$0.830747\pi$
$434$		0			0
$435$	6.07414	+	1.04724i	0.291232	+	0.0502115i
$436$		0			0
$437$	21.8393	+	18.3253i	1.04472	+	0.876620i
$438$		0			0
$439$	−7.62477	+	20.9489i	−0.363910	+	0.999836i	0.613723	+	0.789521i	$0.289671\pi$
$439$	−7.62477	+	20.9489i	−0.363910	+	0.999836i	−0.977634	+	0.210315i	$0.932551\pi$
$440$		0			0
$441$	−20.9310	+	1.70043i	−0.996716	+	0.0809729i
$442$		0			0
$443$	9.81811	+	11.7008i	0.466473	+	0.555920i	0.947073	−	0.321020i	$-0.104026\pi$
$443$	9.81811	+	11.7008i	0.466473	+	0.555920i	−0.480600	+	0.876940i	$0.659581\pi$
$444$		0			0
$445$	−0.669518	+	3.79703i	−0.0317382	+	0.179996i
$446$		0			0
$447$	−11.4838	+	31.9287i	−0.543166	+	1.51017i
$448$		0			0
$449$	19.7219	+	11.3864i	0.930734	+	0.537359i	0.887044	−	0.461686i	$-0.152755\pi$
$449$	19.7219	+	11.3864i	0.930734	+	0.537359i	0.0436902	+	0.999045i	$0.486089\pi$
$450$		0			0
$451$	20.6116	+	11.9001i	0.970565	+	0.560356i
$452$		0			0
$453$	4.24488	−	7.41732i	0.199442	−	0.348496i
$454$		0			0
$455$	2.12934	−	15.3541i	0.0998252	−	0.719812i
$456$		0			0
$457$	2.64733	+	15.0137i	0.123837	+	0.702313i	0.981992	+	0.188923i	$0.0604995\pi$
$457$	2.64733	+	15.0137i	0.123837	+	0.702313i	−0.858155	+	0.513390i	$0.828389\pi$
$458$		0			0
$459$	10.7169	−	19.0610i	0.500224	−	0.889692i
$460$		0			0
$461$	8.45610	−	7.09551i	0.393840	−	0.330471i	−0.424267	−	0.905537i	$-0.639468\pi$
$461$	8.45610	−	7.09551i	0.393840	−	0.330471i	0.818107	+	0.575066i	$0.195024\pi$
$462$		0			0
$463$	2.82578	−	16.0258i	0.131325	−	0.744781i	−0.846024	−	0.533145i	$-0.821010\pi$
$463$	2.82578	−	16.0258i	0.131325	−	0.744781i	0.977349	−	0.211636i	$-0.0678791\pi$
$464$		0			0
$465$	−12.7505	−	7.29700i	−0.591289	−	0.338390i
$466$		0			0
$467$	−24.4283			−1.13041			−0.565203	−	0.824952i	$-0.691202\pi$
$467$	−24.4283			−1.13041			−0.565203	+	0.824952i	$0.691202\pi$
$468$		0			0
$469$	23.9319	−	15.0150i	1.10507	−	0.693330i
$470$		0			0
$471$	−22.3784	+	4.03368i	−1.03114	+	0.185862i
$472$		0			0
$473$	12.8547	+	2.26664i	0.591061	+	0.104220i
$474$		0			0
$475$	5.69594	−	15.6495i	0.261348	−	0.718047i
$476$		0			0
$477$	−22.6223	−	26.5477i	−1.03581	−	1.21554i
$478$		0			0
$479$	14.3565	−	12.0465i	0.655964	−	0.550419i	−0.252910	−	0.967490i	$-0.581388\pi$
$479$	14.3565	−	12.0465i	0.655964	−	0.550419i	0.908874	+	0.417071i	$0.136943\pi$
$480$		0			0
$481$	−44.2346	−	7.79976i	−2.01693	−	0.355638i
$482$		0			0
$483$	−24.3241	−	18.7847i	−1.10678	−	0.854733i
$484$		0			0
$485$	−4.50604	−	2.60156i	−0.204609	−	0.118131i
$486$		0			0
$487$	−5.53657	−	9.58961i	−0.250886	−	0.434547i	0.712884	−	0.701282i	$-0.247389\pi$
$487$	−5.53657	−	9.58961i	−0.250886	−	0.434547i	−0.963770	+	0.266735i	$0.914055\pi$
$488$		0			0
$489$	8.80362	−	3.24221i	0.398113	−	0.146618i
$490$		0			0
$491$	5.05302	+	13.8831i	0.228040	+	0.626534i	0.999958	−	0.00918816i	$-0.00292472\pi$
$491$	5.05302	+	13.8831i	0.228040	+	0.626534i	−0.771918	+	0.635722i	$0.780703\pi$
$492$		0			0
$493$	−9.25297	−	11.0273i	−0.416733	−	0.496643i
$494$		0			0
$495$	−9.82692	+	1.80989i	−0.441687	+	0.0813483i
$496$		0			0
$497$	9.26956	+	43.2223i	0.415797	+	1.93878i
$498$		0			0
$499$	10.0211	−	3.64739i	0.448607	−	0.163280i	−0.107830	−	0.994169i	$-0.534390\pi$
$499$	10.0211	−	3.64739i	0.448607	−	0.163280i	0.556437	+	0.830890i	$0.312168\pi$
$500$		0			0
$501$	30.6038	+	11.0073i	1.36728	+	0.491770i
$502$		0			0
$503$	−10.1407	+	17.5643i	−0.452154	+	0.783153i	−0.998520	−	0.0543935i	$-0.982677\pi$
$503$	−10.1407	+	17.5643i	−0.452154	+	0.783153i	0.546366	+	0.837547i	$0.316011\pi$
$504$		0			0
$505$	−3.88117	−	6.72238i	−0.172710	−	0.299142i
$506$		0			0
$507$	−16.1006	+	28.1334i	−0.715051	+	1.24945i
$508$		0			0
$509$	8.85975	+	7.43421i	0.392701	+	0.329516i	0.817664	−	0.575695i	$-0.195268\pi$
$509$	8.85975	+	7.43421i	0.392701	+	0.329516i	−0.424963	+	0.905211i	$0.639713\pi$
$510$		0			0
$511$	3.25680	+	15.1858i	0.144072	+	0.671782i
$512$		0			0
$513$	−19.2540	−	10.8255i	−0.850087	−	0.477957i
$514$		0			0
$515$	6.16902	−	16.9492i	0.271840	−	0.746873i
$516$		0			0
$517$	−21.6525	−	3.81791i	−0.952274	−	0.167912i
$518$		0			0
$519$	1.74116	−	0.00661847i	0.0764284	−	0.000290519i
$520$		0			0
$521$	9.61790	−	16.6587i	0.421368	−	0.729830i	−0.574706	−	0.818360i	$-0.694884\pi$
$521$	9.61790	−	16.6587i	0.421368	−	0.729830i	0.996074	+	0.0885297i	$0.0282168\pi$
$522$		0			0
$523$	−12.5265	+	7.23220i	−0.547747	+	0.316242i	−0.748213	−	0.663459i	$-0.769088\pi$
$523$	−12.5265	+	7.23220i	−0.547747	+	0.316242i	0.200466	+	0.979701i	$0.435755\pi$
$524$		0			0
$525$	−5.45165	+	17.1052i	−0.237930	+	0.746533i
$526$		0			0
$527$	11.7346	+	32.2404i	0.511165	+	1.40441i
$528$		0			0
$529$	−3.81633	−	21.6435i	−0.165928	−	0.941022i
$530$		0			0
$531$	−3.16664	+	5.58237i	−0.137421	+	0.242254i
$532$		0			0
$533$	41.2294	−	7.26985i	1.78584	−	0.314892i
$534$		0			0
$535$	−9.00332	+	10.7297i	−0.389248	+	0.463887i
$536$		0			0
$537$	−28.9137	+	34.7252i	−1.24772	+	1.49850i
$538$		0			0
$539$	−1.64479	−	22.3502i	−0.0708463	−	0.962693i
$540$		0			0
$541$	20.7842	−	35.9992i	0.893581	−	1.54773i	0.0580304	−	0.998315i	$-0.481518\pi$
$541$	20.7842	−	35.9992i	0.893581	−	1.54773i	0.835551	−	0.549413i	$-0.185149\pi$
$542$		0			0
$543$	−1.56358	−	0.269577i	−0.0670996	−	0.0115687i
$544$		0			0
$545$	6.28315	−	2.28688i	0.269141	−	0.0979592i
$546$		0			0
$547$	−0.705826	−	4.00294i	−0.0301789	−	0.171153i	0.965993	−	0.258568i	$-0.0832506\pi$
$547$	−0.705826	−	4.00294i	−0.0301789	−	0.171153i	−0.996172	+	0.0874147i	$0.972139\pi$
$548$		0			0
$549$	−22.7772	−	3.83792i	−0.972106	−	0.163798i
$550$		0			0
$551$	−11.1389	+	9.34667i	−0.474534	+	0.398182i
$552$		0			0
$553$	−6.89674	+	8.86068i	−0.293279	+	0.376794i
$554$		0			0
$555$	−13.5241	−	4.86422i	−0.574064	−	0.206475i
$556$		0			0
$557$		−	34.5593i		−	1.46432i	−0.681131	−	0.732162i	$-0.738511\pi$
$557$		−	34.5593i		−	1.46432i	0.681131	−	0.732162i	$-0.261489\pi$
$558$		0			0
$559$	19.8845	−	11.4803i	0.841026	−	0.485567i
$560$		0			0
$561$	20.2539	+	11.5912i	0.855121	+	0.489380i
$562$		0			0
$563$	−5.25710	+	1.91343i	−0.221560	+	0.0806414i	−0.450415	−	0.892819i	$-0.648724\pi$
$563$	−5.25710	+	1.91343i	−0.221560	+	0.0806414i	0.228855	+	0.973461i	$0.426502\pi$
$564$		0			0
$565$	12.7125	−	2.24156i	0.534820	−	0.0943032i
$566$		0			0
$567$	21.2118	+	10.8193i	0.890813	+	0.454370i
$568$		0			0
$569$	−6.12310	+	1.07967i	−0.256694	+	0.0452620i	−0.300514	−	0.953777i	$-0.597158\pi$
$569$	−6.12310	+	1.07967i	−0.256694	+	0.0452620i	0.0438203	+	0.999039i	$0.486047\pi$
$570$		0			0
$571$	7.26870	−	2.64559i	0.304185	−	0.110714i	−0.185418	−	0.982660i	$-0.559364\pi$
$571$	7.26870	−	2.64559i	0.304185	−	0.110714i	0.489603	+	0.871945i	$0.337142\pi$
$572$		0			0
$573$	9.67876	+	5.53909i	0.404336	+	0.231399i
$574$		0			0
$575$	−22.7538	+	13.1369i	−0.948899	+	0.547847i
$576$		0			0
$577$		−	27.4212i		−	1.14156i	−0.821103	−	0.570781i	$-0.806641\pi$
$577$		−	27.4212i		−	1.14156i	0.821103	−	0.570781i	$-0.193359\pi$
$578$		0			0
$579$	15.8555	+	5.70276i	0.658931	+	0.236999i
$580$		0			0
$581$	2.76070	+	0.382860i	0.114533	+	0.0158837i
$582$		0			0
$583$	28.5138	−	23.9259i	1.18092	−	0.990910i
$584$		0			0
$585$	−11.1953	+	13.5499i	−0.462869	+	0.560221i
$586$		0			0
$587$	−6.31806	−	35.8315i	−0.260774	−	1.47892i	−0.780804	−	0.624776i	$-0.785190\pi$
$587$	−6.31806	−	35.8315i	−0.260774	−	1.47892i	0.520030	−	0.854148i	$-0.325921\pi$
$588$		0			0
$589$	32.5669	−	11.8534i	1.34190	−	0.488410i
$590$		0			0
$591$	17.7184	+	3.05484i	0.728838	+	0.125659i
$592$		0			0
$593$	20.9240	−	36.2414i	0.859245	−	1.48826i	−0.0134060	−	0.999910i	$-0.504267\pi$
$593$	20.9240	−	36.2414i	0.859245	−	1.48826i	0.872651	−	0.488345i	$-0.162399\pi$
$594$		0			0
$595$	−9.81223	+	6.15626i	−0.402262	+	0.252382i
$596$		0			0
$597$	−2.86403	+	3.43968i	−0.117217	+	0.140777i
$598$		0			0
$599$	7.62840	−	9.09117i	0.311688	−	0.371455i	−0.587345	−	0.809337i	$-0.699827\pi$
$599$	7.62840	−	9.09117i	0.311688	−	0.371455i	0.899033	+	0.437882i	$0.144271\pi$
$600$		0			0
$601$	−0.550033	+	0.0969857i	−0.0224363	+	0.00395613i	−0.184855	−	0.982766i	$-0.559182\pi$
$601$	−0.550033	+	0.0969857i	−0.0224363	+	0.00395613i	0.162419	+	0.986722i	$0.448070\pi$
$602$		0			0
$603$	−32.0340	+	0.243538i	−1.30453	+	0.00991765i
$604$		0			0
$605$	0.135533	+	0.768647i	0.00551021	+	0.0312499i
$606$		0			0
$607$	6.51556	+	17.9014i	0.264459	+	0.726594i	0.998854	+	0.0478715i	$0.0152438\pi$
$607$	6.51556	+	17.9014i	0.264459	+	0.726594i	−0.734395	+	0.678722i	$0.762534\pi$
$608$		0			0
$609$	11.5897	−	10.5541i	0.469640	−	0.427673i
$610$		0			0
$611$	−33.4934	+	19.3374i	−1.35500	+	0.782309i
$612$		0			0
$613$	−11.4442	+	19.8220i	−0.462227	+	0.800601i	−0.999072	−	0.0430801i	$-0.986283\pi$
$613$	−11.4442	+	19.8220i	−0.462227	+	0.800601i	0.536844	+	0.843681i	$0.319616\pi$
$614$		0			0
$615$	13.3957	−	0.0509195i	0.540166	−	0.00205327i
$616$		0			0
$617$	8.14188	+	1.43563i	0.327780	+	0.0577964i	0.335117	−	0.942177i	$-0.391224\pi$
$617$	8.14188	+	1.43563i	0.327780	+	0.0577964i	−0.00733686	+	0.999973i	$0.502335\pi$
$618$		0			0
$619$	8.59529	−	23.6154i	0.345474	−	0.949182i	−0.638303	−	0.769785i	$-0.720363\pi$
$619$	8.59529	−	23.6154i	0.345474	−	0.949182i	0.983777	−	0.179396i	$-0.0574145\pi$
$620$		0			0
$621$	12.2914	+	32.6085i	0.493237	+	1.30853i
$622$		0			0
$623$	6.57426	+	7.27474i	0.263392	+	0.291456i
$624$		0			0
$625$	7.61166	+	6.38694i	0.304466	+	0.255478i
$626$		0			0
$627$	11.7086	−	20.4590i	0.467595	−	0.817055i
$628$		0			0
$629$	16.7827	+	29.0685i	0.669171	+	1.15904i
$630$		0			0
$631$	−22.4808	+	38.9380i	−0.894948	+	1.55010i	−0.0610790	+	0.998133i	$0.519454\pi$
$631$	−22.4808	+	38.9380i	−0.894948	+	1.55010i	−0.833869	+	0.551962i	$0.813879\pi$
$632$		0			0
$633$	23.6878	+	8.51984i	0.941507	+	0.338633i
$634$		0			0
$635$	1.47008	−	0.535066i	0.0583385	−	0.0212335i
$636$		0			0
$637$	−27.4874	−	28.2571i	−1.08909	−	1.11959i
$638$		0			0
$639$	16.7848	−	47.2300i	0.663996	−	1.86839i
$640$		0			0
$641$	17.5145	+	20.8730i	0.691781	+	0.824433i	0.991570	−	0.129573i	$-0.0413606\pi$
$641$	17.5145	+	20.8730i	0.691781	+	0.824433i	−0.299789	+	0.954006i	$0.596916\pi$
$642$		0			0
$643$	2.60698	+	7.16261i	0.102809	+	0.282466i	0.980423	−	0.196902i	$-0.0630881\pi$
$643$	2.60698	+	7.16261i	0.102809	+	0.282466i	−0.877614	+	0.479368i	$0.840866\pi$
$644$		0			0
$645$	6.89413	−	2.53898i	0.271456	−	0.0999721i
$646$		0			0
$647$	19.9589	+	34.5698i	0.784665	+	1.35908i	0.929199	+	0.369580i	$0.120498\pi$
$647$	19.9589	+	34.5698i	0.784665	+	1.35908i	−0.144534	+	0.989500i	$0.546168\pi$
$648$		0			0
$649$	−5.93151	−	3.42456i	−0.232832	−	0.134426i
$650$		0			0
$651$	−34.5608	+	14.1901i	−1.35454	+	0.556154i
$652$		0			0
$653$	−9.27688	−	1.63576i	−0.363032	−	0.0640124i	−0.0108431	−	0.999941i	$-0.503452\pi$
$653$	−9.27688	−	1.63576i	−0.363032	−	0.0640124i	−0.352189	+	0.935929i	$0.614563\pi$
$654$		0			0
$655$	−11.4466	+	9.60482i	−0.447255	+	0.375291i
$656$		0			0
$657$	5.89722	−	16.5939i	0.230073	−	0.647391i
$658$		0			0
$659$	−8.23740	+	22.6321i	−0.320883	+	0.881620i	0.669443	+	0.742863i	$0.266533\pi$
$659$	−8.23740	+	22.6321i	−0.320883	+	0.881620i	−0.990327	+	0.138757i	$0.955689\pi$
$660$		0			0
$661$	11.6789	+	2.05930i	0.454256	+	0.0800975i	0.396095	−	0.918210i	$-0.370365\pi$
$661$	11.6789	+	2.05930i	0.454256	+	0.0800975i	0.0581609	+	0.998307i	$0.481476\pi$
$662$		0			0
$663$	40.3980	−	7.28169i	1.56893	−	0.282797i
$664$		0			0
$665$	6.21861	+	9.91160i	0.241147	+	0.384355i
$666$		0			0
$667$	22.9403			0.888252
$668$		0			0
$669$	−16.0208	−	9.16859i	−0.619399	−	0.354478i
$670$		0			0
$671$	4.28041	−	24.2754i	0.165243	−	0.937141i
$672$		0			0
$673$	−8.05026	+	6.75497i	−0.310315	+	0.260385i	−0.784622	−	0.619974i	$-0.787143\pi$
$673$	−8.05026	+	6.75497i	−0.310315	+	0.260385i	0.474307	+	0.880359i	$0.342699\pi$
$674$		0			0
$675$	15.4439	−	13.2620i	0.594438	−	0.510456i
$676$		0			0
$677$	−6.82193	−	38.6891i	−0.262188	−	1.48694i	−0.776924	−	0.629594i	$-0.783221\pi$
$677$	−6.82193	−	38.6891i	−0.262188	−	1.48694i	0.514736	−	0.857349i	$-0.327890\pi$
$678$		0			0
$679$	−12.2596	+	4.97921i	−0.470480	+	0.191085i
$680$		0			0
$681$	17.8656	−	31.2176i	0.684612	−	1.19626i
$682$		0			0
$683$	−29.6515	−	17.1193i	−1.13458	−	0.655051i	−0.189498	−	0.981881i	$-0.560686\pi$
$683$	−29.6515	−	17.1193i	−1.13458	−	0.655051i	−0.945083	+	0.326830i	$0.894019\pi$
$684$		0			0
$685$	0.506467	+	0.292409i	0.0193511	+	0.0111724i
$686$		0			0
$687$	7.84046	−	21.7990i	0.299132	−	0.831682i
$688$		0			0
$689$	11.3696	−	64.4801i	0.433147	−	2.45650i
$690$		0			0
$691$	4.32267	+	5.15156i	0.164442	+	0.195975i	0.841973	−	0.539520i	$-0.181394\pi$
$691$	4.32267	+	5.15156i	0.164442	+	0.195975i	−0.677531	+	0.735495i	$0.736950\pi$
$692$		0			0
$693$	−11.7179	+	22.5483i	−0.445126	+	0.856540i
$694$		0			0
$695$	−7.15164	+	19.6490i	−0.271277	+	0.745328i
$696$		0			0
$697$	−23.9657	−	20.1096i	−0.907766	−	0.761706i
$698$		0			0
$699$	−25.8053	−	4.44910i	−0.976046	−	0.168280i
$700$		0			0
$701$			6.11612i			0.231003i	0.993307	+	0.115501i	$0.0368475\pi$
$701$			6.11612i			0.231003i	−0.993307	+	0.115501i	$0.963153\pi$
$702$		0			0
$703$	29.3629	−	16.9527i	1.10744	−	0.639382i
$704$		0			0
$705$	−11.6124	+	4.27664i	−0.437350	+	0.161068i
$706$		0			0
$707$	−19.5534	−	2.71171i	−0.735382	−	0.101984i
$708$		0			0
$709$	22.4892	+	8.18540i	0.844600	+	0.307409i	0.727837	−	0.685751i	$-0.240526\pi$
$709$	22.4892	+	8.18540i	0.844600	+	0.307409i	0.116763	+	0.993160i	$0.462748\pi$
$710$		0			0
$711$	11.9305	−	4.44536i	0.447430	−	0.166714i
$712$		0			0
$713$	−51.3791	−	18.7005i	−1.92416	−	0.700337i
$714$		0			0
$715$	−14.3689	−	12.0569i	−0.537367	−	0.450904i
$716$		0			0
$717$	−12.4818	−	14.7609i	−0.466142	−	0.551257i
$718$		0			0
$719$	2.89246	+	5.00989i	0.107871	+	0.186837i	0.914907	−	0.403664i	$-0.132263\pi$
$719$	2.89246	+	5.00989i	0.107871	+	0.186837i	−0.807037	+	0.590501i	$0.798930\pi$
$720$		0			0
$721$	−24.3784	−	38.8558i	−0.907899	−	1.44707i
$722$		0			0
$723$	−6.25267	+	3.64174i	−0.232539	+	0.135438i
$724$		0			0
$725$	−4.58332	−	12.5926i	−0.170220	−	0.467676i
$726$		0			0
$727$	−27.9583	−	33.3194i	−1.03691	−	1.23575i	−0.971289	−	0.237903i	$-0.923540\pi$
$727$	−27.9583	−	33.3194i	−1.03691	−	1.23575i	−0.0656260	−	0.997844i	$-0.520904\pi$
$728$		0			0
$729$	−14.0297	−	23.0687i	−0.519620	−	0.854398i
$730$		0			0
$731$	−16.1232	−	5.86837i	−0.596339	−	0.217050i
$732$		0			0
$733$	1.57436	−	1.87625i	0.0581504	−	0.0693010i	−0.736185	−	0.676780i	$-0.763375\pi$
$733$	1.57436	−	1.87625i	0.0581504	−	0.0693010i	0.794336	+	0.607479i	$0.207819\pi$
$734$		0			0
$735$	−7.13115	−	10.4044i	−0.263037	−	0.383771i
$736$		0			0
$737$		−	34.1869i		−	1.25929i
$738$		0			0
$739$	35.8434			1.31852			0.659260	−	0.751915i	$-0.270870\pi$
$739$	35.8434			1.31852			0.659260	+	0.751915i	$0.270870\pi$
$740$		0			0
$741$	−7.35543	−	40.8071i	−0.270209	−	1.49909i
$742$		0			0
$743$	13.1744	−	15.7006i	0.483320	−	0.575999i	−0.468185	−	0.883630i	$-0.655092\pi$
$743$	13.1744	−	15.7006i	0.483320	−	0.575999i	0.951506	+	0.307632i	$0.0995364\pi$
$744$		0			0
$745$	−20.0711	+	3.53907i	−0.735348	+	0.129662i
$746$		0			0
$747$	−2.43630	−	2.01294i	−0.0891396	−	0.0736495i
$748$		0			0
$749$	7.46946	+	34.8287i	0.272928	+	1.27261i
$750$		0			0
$751$	−5.66199	+	32.1108i	−0.206609	+	1.17174i	0.688278	+	0.725447i	$0.258367\pi$
$751$	−5.66199	+	32.1108i	−0.206609	+	1.17174i	−0.894887	+	0.446292i	$0.852744\pi$
$752$		0			0
$753$	−3.01931	+	17.5123i	−0.110030	+	0.638185i
$754$		0			0
$755$	5.13322			0.186817
$756$		0			0
$757$	−16.2169			−0.589415			−0.294707	−	0.955588i	$-0.595222\pi$
$757$	−16.2169			−0.589415			−0.294707	+	0.955588i	$0.595222\pi$
$758$		0			0
$759$	−34.8977	+	12.8521i	−1.26670	+	0.466503i
$760$		0			0
$761$	−0.184575	+	1.04678i	−0.00669084	+	0.0379456i	−0.987970	−	0.154643i	$-0.950577\pi$
$761$	−0.184575	+	1.04678i	−0.00669084	+	0.0379456i	0.981280	+	0.192589i	$0.0616883\pi$
$762$		0			0
$763$	5.22512	−	16.1816i	0.189162	−	0.585812i
$764$		0			0
$765$	13.1342	−	0.0998524i	0.474867	−	0.00361017i
$766$		0			0
$767$	−11.8648	+	2.09208i	−0.428412	+	0.0755405i
$768$		0			0
$769$	18.2576	−	21.7586i	0.658386	−	0.784634i	−0.328767	−	0.944411i	$-0.606633\pi$
$769$	18.2576	−	21.7586i	0.658386	−	0.784634i	0.987153	+	0.159777i	$0.0510775\pi$
$770$		0			0
$771$	33.1628	+	11.9277i	1.19433	+	0.429566i
$772$		0			0
$773$	10.6270			0.382226			0.191113	−	0.981568i	$-0.438790\pi$
$773$	10.6270			0.382226			0.191113	+	0.981568i	$0.438790\pi$
$774$		0			0
$775$			31.9396i			1.14730i
$776$		0			0
$777$	−30.8870	+	19.5427i	−1.10806	+	0.701091i
$778$		0			0
$779$	−20.3133	+	24.2084i	−0.727799	+	0.867357i
$780$		0			0
$781$	50.2650	+	18.2950i	1.79862	+	0.654646i
$782$		0			0
$783$	−17.4676	+	3.28581i	−0.624241	+	0.117425i
$784$		0			0
$785$	−8.77933	−	10.4628i	−0.313348	−	0.373433i
$786$		0			0
$787$	7.40549	+	20.3464i	0.263977	+	0.725271i	0.998890	+	0.0471095i	$0.0150010\pi$
$787$	7.40549	+	20.3464i	0.263977	+	0.725271i	−0.734913	+	0.678162i	$0.762777\pi$
$788$		0			0
$789$	−0.152506	−	40.1207i	−0.00542937	−	1.42834i
$790$		0			0
$791$	15.3590	−	29.0136i	0.546104	−	1.03160i
$792$		0			0
$793$	−21.6799	−	37.5507i	−0.769877	−	1.33347i
$794$		0			0
$795$	7.09049	−	19.7138i	0.251474	−	0.699176i
$796$		0			0
$797$	−21.0090	−	17.6286i	−0.744176	−	0.624438i	0.189780	−	0.981827i	$-0.439223\pi$
$797$	−21.0090	−	17.6286i	−0.744176	−	0.624438i	−0.933956	+	0.357389i	$0.883667\pi$
$798$		0			0
$799$	27.1579	+	9.88467i	0.960777	+	0.349694i
$800$		0			0
$801$	−2.01382	−	10.9342i	−0.0711549	−	0.386341i
$802$		0			0
$803$	17.6603	+	6.42782i	0.623218	+	0.226833i
$804$		0			0
$805$	2.53579	−	18.2849i	0.0893748	−	0.644457i
$806$		0			0
$807$	4.06358	−	23.5692i	0.143045	−	0.829676i
$808$		0			0
$809$	−16.4956	+	9.52372i	−0.579953	+	0.334836i	−0.761115	−	0.648617i	$-0.775348\pi$
$809$	−16.4956	+	9.52372i	−0.579953	+	0.334836i	0.181161	+	0.983453i	$0.442014\pi$
$810$		0			0
$811$		−	38.5211i		−	1.35266i	−0.736599	−	0.676330i	$-0.763569\pi$
$811$		−	38.5211i		−	1.35266i	0.736599	−	0.676330i	$-0.236431\pi$
$812$		0			0
$813$	−12.1533	−	33.0001i	−0.426235	−	1.15736i
$814$		0			0
$815$	4.31674	+	3.62217i	0.151209	+	0.126879i
$816$		0			0
$817$	−5.92781	+	16.2865i	−0.207388	+	0.569793i
$818$		0			0
$819$	9.70518	+	43.6329i	0.339127	+	1.52466i
$820$		0			0
$821$	20.5100	+	24.4429i	0.715806	+	0.853064i	0.994216	−	0.107398i	$-0.0342520\pi$
$821$	20.5100	+	24.4429i	0.715806	+	0.853064i	−0.278410	+	0.960462i	$0.589808\pi$
$822$		0			0
$823$	2.94894	−	16.7243i	0.102794	−	0.582972i	−0.889285	−	0.457354i	$-0.848797\pi$
$823$	2.94894	−	16.7243i	0.102794	−	0.582972i	0.992079	−	0.125618i	$-0.0400915\pi$
$824$		0			0
$825$	14.0272	+	16.5885i	0.488365	+	0.577538i
$826$		0			0
$827$	26.4532	+	15.2728i	0.919869	+	0.531087i	0.883593	−	0.468255i	$-0.155117\pi$
$827$	26.4532	+	15.2728i	0.919869	+	0.531087i	0.0362760	+	0.999342i	$0.488450\pi$
$828$		0			0
$829$	−28.9574	−	16.7185i	−1.00573	−	0.580659i	−0.0957919	−	0.995401i	$-0.530538\pi$
$829$	−28.9574	−	16.7185i	−1.00573	−	0.580659i	−0.909939	+	0.414742i	$0.863872\pi$
$830$		0			0
$831$	27.5573	−	0.104751i	0.955953	−	0.00363376i
$832$		0			0
$833$	−2.97240	+	29.3081i	−0.102988	+	1.01546i
$834$		0			0
$835$	3.39222	+	19.2382i	0.117393	+	0.665767i
$836$		0			0
$837$	41.8004	+	6.88002i	1.44483	+	0.237808i
$838$		0			0
$839$	5.95109	−	4.99356i	0.205454	−	0.172397i	−0.534255	−	0.845324i	$-0.679408\pi$
$839$	5.95109	−	4.99356i	0.205454	−	0.172397i	0.739709	+	0.672927i	$0.234963\pi$
$840$		0			0
$841$	3.00403	−	17.0367i	0.103587	−	0.587472i
$842$		0			0
$843$	−32.8424	+	19.1284i	−1.13115	+	0.658816i
$844$		0			0
$845$	−19.4700			−0.669787
$846$		0			0
$847$	1.75427	+	0.928665i	0.0602775	+	0.0319093i
$848$		0			0
$849$	−0.984825	−	1.16465i	−0.0337991	−	0.0399707i
$850$		0			0
$851$	−52.6780	−	9.28855i	−1.80578	−	0.318408i
$852$		0			0
$853$	−14.7480	+	40.5198i	−0.504962	+	1.38737i	0.381413	+	0.924405i	$0.375438\pi$
$853$	−14.7480	+	40.5198i	−0.504962	+	1.38737i	−0.886375	+	0.462968i	$0.846785\pi$
$854$		0			0
$855$	−0.100864	−	13.2672i	−0.00344946	−	0.453728i
$856$		0			0
$857$	9.22291	−	7.73894i	0.315049	−	0.264357i	−0.471526	−	0.881852i	$-0.656297\pi$
$857$	9.22291	−	7.73894i	0.315049	−	0.264357i	0.786575	+	0.617495i	$0.211852\pi$
$858$		0			0
$859$	13.6766	+	2.41155i	0.466639	+	0.0822811i	0.402024	−	0.915629i	$-0.368307\pi$
$859$	13.6766	+	2.41155i	0.466639	+	0.0822811i	0.0646153	+	0.997910i	$0.479418\pi$
$860$		0			0
$861$	20.8225	−	26.9627i	0.709628	−	0.918888i
$862$		0			0
$863$	9.67586	+	5.58636i	0.329370	+	0.190162i	0.655561	−	0.755142i	$-0.272432\pi$
$863$	9.67586	+	5.58636i	0.329370	+	0.190162i	−0.326191	+	0.945304i	$0.605765\pi$
$864$		0			0
$865$	0.522918	+	0.905720i	0.0177797	+	0.0307954i
$866$		0			0
$867$	−0.945286	−	0.787085i	−0.0321036	−	0.0267308i
$868$		0			0
$869$	4.64705	+	12.7677i	0.157640	+	0.433113i
$870$		0			0
$871$	−38.6546	−	46.0667i	−1.30976	−	1.56091i
$872$		0			0
$873$	14.7953	+	2.49299i	0.500745	+	0.0843748i
$874$		0			0
$875$	−24.0004	+	5.14718i	−0.811360	+	0.174007i
$876$		0			0
$877$	36.8381	−	13.4080i	1.24394	−	0.452755i	0.365587	−	0.930777i	$-0.380868\pi$
$877$	36.8381	−	13.4080i	1.24394	−	0.452755i	0.878348	+	0.478022i	$0.158646\pi$
$878$		0			0
$879$	−19.1543	+	16.1968i	−0.646059	+	0.546306i
$880$		0			0
$881$	7.93712	−	13.7475i	0.267408	−	0.463165i	−0.700783	−	0.713374i	$-0.747166\pi$
$881$	7.93712	−	13.7475i	0.267408	−	0.463165i	0.968192	+	0.250209i	$0.0804994\pi$
$882$		0			0
$883$	2.25703	+	3.90929i	0.0759551	+	0.131558i	0.901501	−	0.432777i	$-0.142466\pi$
$883$	2.25703	+	3.90929i	0.0759551	+	0.131558i	−0.825546	+	0.564335i	$0.809133\pi$
$884$		0			0
$885$	−3.85494	+	0.0146533i	−0.129582	+	0.000492567i
$886$		0			0
$887$	7.96047	+	6.67963i	0.267286	+	0.224280i	0.766573	−	0.642157i	$-0.221960\pi$
$887$	7.96047	+	6.67963i	0.267286	+	0.224280i	−0.499287	+	0.866437i	$0.666405\pi$
$888$		0			0
$889$	1.22253	−	3.78604i	0.0410024	−	0.126980i
$890$		0			0
$891$	24.7315	−	14.7846i	0.828537	−	0.495303i
$892$		0			0
$893$	9.98477	−	27.4329i	0.334128	−	0.918008i
$894$		0			0
$895$	−26.7291	−	4.71307i	−0.893456	−	0.157540i
$896$		0			0
$897$	−32.4927	+	56.7764i	−1.08490	+	1.89571i
$898$		0			0
$899$	13.9436	−	24.1510i	0.465045	−	0.805482i
$900$		0			0
$901$	−42.3727	+	24.4639i	−1.41164	+	0.815010i
$902$		0			0
$903$	5.67357	−	17.8015i	0.188805	−	0.592397i
$904$		0			0
$905$	−0.325952	−	0.895546i	−0.0108350	−	0.0297690i
$906$		0			0
$907$	6.42702	+	36.4494i	0.213406	+	1.21028i	0.883652	+	0.468145i	$0.155077\pi$
$907$	6.42702	+	36.4494i	0.213406	+	1.21028i	−0.670246	+	0.742139i	$0.733812\pi$
$908$		0			0
$909$	17.2558	+	14.2572i	0.572338	+	0.472881i
$910$		0			0
$911$	14.6012	−	2.57459i	0.483760	−	0.0853000i	0.0735512	−	0.997291i	$-0.476567\pi$
$911$	14.6012	−	2.57459i	0.483760	−	0.0853000i	0.410209	+	0.911991i	$0.365456\pi$
$912$		0			0
$913$	2.16786	−	2.58356i	0.0717457	−	0.0855032i
$914$		0			0
$915$	−4.79470	−	13.0191i	−0.158508	−	0.430399i
$916$		0			0
$917$	1.39543	+	37.9748i	0.0460811	+	1.25404i
$918$		0			0
$919$	−11.8066	+	20.4496i	−0.389463	+	0.674569i	−0.992377	−	0.123237i	$-0.960673\pi$
$919$	−11.8066	+	20.4496i	−0.389463	+	0.674569i	0.602915	+	0.797806i	$0.294006\pi$
$920$		0			0
$921$	−6.67756	−	18.1317i	−0.220033	−	0.597459i
$922$		0			0
$923$	88.4177	−	32.1814i	2.91030	−	1.05926i
$924$		0			0
$925$	5.42597	+	30.7722i	0.178405	+	1.01178i
$926$		0			0
$927$	0.395409	+	52.0105i	0.0129869	+	1.70825i
$928$		0			0
$929$	−17.0376	+	14.2963i	−0.558987	+	0.469045i	−0.877971	−	0.478715i	$-0.841103\pi$
$929$	−17.0376	+	14.2963i	−0.558987	+	0.469045i	0.318984	+	0.947760i	$0.396658\pi$
$930$		0			0
$931$	29.6049	+	3.00250i	0.970261	+	0.0984031i
$932$		0			0
$933$	15.3554	−	12.9845i	0.502712	−	0.425092i
$934$		0			0
$935$			14.0169i			0.458401i
$936$		0			0
$937$	−27.4459	+	15.8459i	−0.896619	+	0.517663i	−0.876102	−	0.482126i	$-0.839865\pi$
$937$	−27.4459	+	15.8459i	−0.896619	+	0.517663i	−0.0205175	+	0.999789i	$0.506531\pi$
$938$		0			0
$939$	0.104999	+	27.6227i	0.00342652	+	0.901434i
$940$		0			0
$941$	−39.4168	+	14.3465i	−1.28495	+	0.467683i	−0.892066	−	0.451905i	$-0.850745\pi$
$941$	−39.4168	+	14.3465i	−1.28495	+	0.467683i	−0.392883	+	0.919588i	$0.628522\pi$
$942$		0			0
$943$	49.0991	−	8.65750i	1.59889	−	0.281927i
$944$		0			0
$945$	0.688161	+	14.2860i	0.0223859	+	0.464723i
$946$		0			0
$947$	17.4271	−	3.07286i	0.566303	−	0.0998546i	0.116836	−	0.993151i	$-0.462725\pi$
$947$	17.4271	−	3.07286i	0.566303	−	0.0998546i	0.449468	+	0.893297i	$0.351614\pi$
$948$		0			0
$949$	31.0649	−	11.3067i	1.00841	−	0.367032i
$950$		0			0
$951$	36.9344	−	21.5117i	1.19768	−	0.697565i
$952$		0			0
$953$	−34.8304	+	20.1094i	−1.12827	+	0.651406i	−0.943499	−	0.331376i	$-0.892487\pi$
$953$	−34.8304	+	20.1094i	−1.12827	+	0.651406i	−0.184770	+	0.982782i	$0.559154\pi$
$954$		0			0
$955$			6.69826i			0.216751i
$956$		0			0
$957$	−3.36473	−	18.6671i	−0.108766	−	0.603422i
$958$		0			0
$959$	1.37795	−	0.559651i	0.0444962	−	0.0180721i
$960$		0			0
$961$	−27.1694	+	22.7978i	−0.876431	+	0.735413i
$962$		0			0
$963$	13.5253	−	38.0581i	0.435845	−	1.22641i
$964$		0			0
$965$	1.75747	+	9.96712i	0.0565750	+	0.320853i
$966$		0			0
$967$	−45.5483	+	16.5782i	−1.46473	+	0.533120i	−0.946665	−	0.322219i	$-0.895571\pi$
$967$	−45.5483	+	16.5782i	−1.46473	+	0.533120i	−0.518069	+	0.855339i	$0.673349\pi$
$968$		0			0
$969$	−19.8268	+	23.8119i	−0.636928	+	0.764948i
$970$		0			0
$971$	6.74843	−	11.6886i	0.216567	−	0.375106i	−0.737189	−	0.675687i	$-0.763847\pi$
$971$	6.74843	−	11.6886i	0.216567	−	0.375106i	0.953756	+	0.300581i	$0.0971806\pi$
$972$		0			0
$973$	28.2615	+	45.0448i	0.906021	+	1.44407i
$974$		0			0
$975$	37.6579	+	6.49261i	1.20602	+	0.207930i
$976$		0			0
$977$	32.6477	−	38.9080i	1.04449	−	1.24478i	0.0756407	−	0.997135i	$-0.475900\pi$
$977$	32.6477	−	38.9080i	1.04449	−	1.24478i	0.968852	−	0.247642i	$-0.0796558\pi$
$978$		0			0
$979$	11.6847	−	2.06033i	0.373445	−	0.0658484i
$980$		0			0
$981$	−14.6755	+	12.5055i	−0.468552	+	0.399271i
$982$		0			0
$983$	−6.22962	−	35.3299i	−0.198694	−	1.12685i	−0.907059	−	0.421003i	$-0.861678\pi$
$983$	−6.22962	−	35.3299i	−0.198694	−	1.12685i	0.708365	−	0.705846i	$-0.249433\pi$
$984$		0			0
$985$	3.69368	+	10.1483i	0.117690	+	0.323352i
$986$		0			0
$987$	−9.55654	+	29.9848i	−0.304188	+	0.954426i
$988$		0			0
$989$	23.6800	−	13.6717i	0.752981	−	0.434734i
$990$		0			0
$991$	−10.4996	+	18.1858i	−0.333530	+	0.577691i	−0.983201	−	0.182524i	$-0.941573\pi$
$991$	−10.4996	+	18.1858i	−0.333530	+	0.577691i	0.649671	+	0.760215i	$0.274907\pi$
$992$		0			0
$993$	−6.00312	−	10.3070i	−0.190503	−	0.327084i
$994$		0			0
$995$	−2.64764	−	0.466850i	−0.0839357	−	0.0148001i
$996$		0			0
$997$	−5.54634	+	15.2385i	−0.175654	+	0.482607i	−0.996009	−	0.0892480i	$-0.971554\pi$
$997$	−5.54634	+	15.2385i	−0.175654	+	0.482607i	0.820355	+	0.571855i	$0.193776\pi$
$998$		0			0
$999$	41.4414	−	0.472598i	1.31115	−	0.0149523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.5.7	yes	144
7.3	odd	6		756.2.ca.a.437.15	yes	144
27.11	odd	18		756.2.ca.a.173.15	✓	144
189.38	even	18	inner	756.2.ck.a.605.7	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.15	✓	144	27.11	odd	18
756.2.ca.a.437.15	yes	144	7.3	odd	6
756.2.ck.a.5.7	yes	144	1.1	even	1	trivial
756.2.ck.a.605.7	yes	144	189.38	even	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.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33105 - 1.10829i) q^{3} +(0.180656 - 1.02455i) q^{5} +(-1.77393 - 1.96295i) q^{7} +(0.543390 + 2.95038i) q^{9} +O(q^{10})\)	\(q+(-1.33105 - 1.10829i) q^{3} +(0.180656 - 1.02455i) q^{5} +(-1.77393 - 1.96295i) q^{7} +(0.543390 + 2.95038i) q^{9} +(-3.15289 + 0.555939i) q^{11} +(-3.61991 + 4.31404i) q^{13} +(-1.37596 + 1.16351i) q^{15} +4.20835 q^{17} -4.25097i q^{19} +(0.185685 + 4.57881i) q^{21} +(-4.31087 + 5.13749i) q^{23} +(3.68139 + 1.33992i) q^{25} +(2.54659 - 4.52933i) q^{27} +(-2.19872 - 2.62033i) q^{29} +(2.78840 + 7.66106i) q^{31} +(4.81279 + 2.75433i) q^{33} +(-2.33161 + 1.46287i) q^{35} +(3.98796 + 6.90735i) q^{37} +(9.59948 - 1.73030i) q^{39} +(-5.69481 - 4.77851i) q^{41} +(-3.83125 - 1.39446i) q^{43} +(3.12098 - 0.0237272i) q^{45} +(6.45334 + 2.34882i) q^{47} +(-0.706311 + 6.96427i) q^{49} +(-5.60152 - 4.66407i) q^{51} +(-10.0687 + 5.81318i) q^{53} +3.33073i q^{55} +(-4.71130 + 5.65825i) q^{57} +(1.63882 + 1.37513i) q^{59} +(-2.63335 + 7.23508i) q^{61} +(4.82749 - 6.30042i) q^{63} +(3.76600 + 4.48814i) q^{65} +(-1.85427 + 10.5161i) q^{67} +(11.4318 - 2.06057i) q^{69} +(-14.4695 - 8.35397i) q^{71} +(-5.08376 - 2.93511i) q^{73} +(-3.41510 - 5.86355i) q^{75} +(6.68430 + 5.20275i) q^{77} +(-0.736951 - 4.17946i) q^{79} +(-8.40946 + 3.20641i) q^{81} +(-0.806976 + 0.677133i) q^{83} +(0.760264 - 4.31167i) q^{85} +(0.0225205 + 5.92461i) q^{87} -3.70603 q^{89} +(14.8897 - 0.547140i) q^{91} +(4.77918 - 13.2876i) q^{93} +(-4.35534 - 0.767963i) q^{95} +(1.71054 - 4.69967i) q^{97} +(-3.35348 - 9.00012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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