LMFDB - Embedded newform 630.2.p.a.307.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(307,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.p (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.4
Root			$-0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	630.307
Dual form			630.2.p.a.433.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.158513 + 2.23044i) q^{5} +(-2.47247 - 0.941740i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.46508 + 1.68925i) q^{10} -2.82843 q^{11} +(4.23671 + 4.23671i) q^{13} +(-1.08239 - 2.41421i) q^{14} -1.00000 q^{16} +(-3.69552 + 3.69552i) q^{17} -1.39942 q^{19} +(-2.23044 + 0.158513i) q^{20} +(-2.00000 - 2.00000i) q^{22} +(-0.414214 + 0.414214i) q^{23} +(-4.94975 + 0.707107i) q^{25} +5.99162i q^{26} +(0.941740 - 2.47247i) q^{28} +0.828427i q^{29} -1.53073i q^{31} +(-0.707107 - 0.707107i) q^{32} -5.22625 q^{34} +(1.70858 - 5.66399i) q^{35} +(2.58579 + 2.58579i) q^{37} +(-0.989538 - 0.989538i) q^{38} +(-1.68925 - 1.46508i) q^{40} +3.69552i q^{41} +(4.00000 - 4.00000i) q^{43} -2.82843i q^{44} -0.585786 q^{46} +(1.08239 - 1.08239i) q^{47} +(5.22625 + 4.65685i) q^{49} +(-4.00000 - 3.00000i) q^{50} +(-4.23671 + 4.23671i) q^{52} +(8.24264 - 8.24264i) q^{53} +(-0.448342 - 6.30864i) q^{55} +(2.41421 - 1.08239i) q^{56} +(-0.585786 + 0.585786i) q^{58} -9.23880 q^{59} +6.43996i q^{61} +(1.08239 - 1.08239i) q^{62} -1.00000i q^{64} +(-8.77817 + 10.1213i) q^{65} +(10.4853 + 10.4853i) q^{67} +(-3.69552 - 3.69552i) q^{68} +(5.21319 - 2.79690i) q^{70} +0.585786 q^{71} +(-4.14386 - 4.14386i) q^{73} +3.65685i q^{74} -1.39942i q^{76} +(6.99321 + 2.66364i) q^{77} +5.07107i q^{79} +(-0.158513 - 2.23044i) q^{80} +(-2.61313 + 2.61313i) q^{82} +(5.31911 + 5.31911i) q^{83} +(-8.82843 - 7.65685i) q^{85} +5.65685 q^{86} +(2.00000 - 2.00000i) q^{88} +11.3492 q^{89} +(-6.48528 - 14.4650i) q^{91} +(-0.414214 - 0.414214i) q^{92} +1.53073 q^{94} +(-0.221825 - 3.12132i) q^{95} +(4.59220 - 4.59220i) q^{97} +(0.402625 + 6.98841i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7} - 8 q^{16} - 16 q^{22} + 8 q^{23} + 8 q^{28} + 8 q^{35} + 32 q^{37} + 32 q^{43} - 16 q^{46} - 32 q^{50} + 32 q^{53} + 8 q^{56} - 16 q^{58} - 8 q^{65} + 16 q^{67} - 24 q^{70} + 16 q^{71} + 16 q^{77}+ \cdots - 32 q^{98}+O(q^{100}) $ 8 * q - 8 * q^7 - 8 * q^16 - 16 * q^22 + 8 * q^23 + 8 * q^28 + 8 * q^35 + 32 * q^37 + 32 * q^43 - 16 * q^46 - 32 * q^50 + 32 * q^53 + 8 * q^56 - 16 * q^58 - 8 * q^65 + 16 * q^67 - 24 * q^70 + 16 * q^71 + 16 * q^77 - 48 * q^85 + 16 * q^88 + 16 * q^91 + 8 * q^92 - 64 * q^95 - 32 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	0.158513	+	2.23044i	0.0708890	+	0.997484i
$5$	0.158513	+	2.23044i	0.0708890	+	0.997484i
$6$		0			0
$7$	−2.47247	−	0.941740i	−0.934507	−	0.355944i
$7$	−2.47247	−	0.941740i	−0.934507	−	0.355944i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−1.46508	+	1.68925i	−0.463298	+	0.534187i
$11$	−2.82843			−0.852803			−0.426401	−	0.904534i	$-0.640219\pi$
$11$	−2.82843			−0.852803			−0.426401	+	0.904534i	$0.640219\pi$
$12$		0			0
$13$	4.23671	+	4.23671i	1.17505	+	1.17505i	0.980989	+	0.194064i	$0.0621670\pi$
$13$	4.23671	+	4.23671i	1.17505	+	1.17505i	0.194064	+	0.980989i	$0.437833\pi$
$14$	−1.08239	−	2.41421i	−0.289281	−	0.645226i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−3.69552	+	3.69552i	−0.896295	+	0.896295i	−0.995106	−	0.0988114i	$-0.968496\pi$
$17$	−3.69552	+	3.69552i	−0.896295	+	0.896295i	0.0988114	+	0.995106i	$0.468496\pi$
$18$		0			0
$19$	−1.39942			−0.321048			−0.160524	−	0.987032i	$-0.551318\pi$
$19$	−1.39942			−0.321048			−0.160524	+	0.987032i	$0.551318\pi$
$20$	−2.23044	+	0.158513i	−0.498742	+	0.0354445i
$21$		0			0
$22$	−2.00000	−	2.00000i	−0.426401	−	0.426401i
$23$	−0.414214	+	0.414214i	−0.0863695	+	0.0863695i	−0.748972	−	0.662602i	$-0.769452\pi$
$23$	−0.414214	+	0.414214i	−0.0863695	+	0.0863695i	0.662602	+	0.748972i	$0.269452\pi$
$24$		0			0
$25$	−4.94975	+	0.707107i	−0.989949	+	0.141421i
$26$			5.99162i			1.17505i
$27$		0			0
$28$	0.941740	−	2.47247i	0.177972	−	0.467254i
$29$			0.828427i			0.153835i	0.997037	+	0.0769175i	$0.0245078\pi$
$29$			0.828427i			0.153835i	−0.997037	+	0.0769175i	$0.975492\pi$
$30$		0			0
$31$		−	1.53073i		−	0.274928i	−0.990507	−	0.137464i	$-0.956105\pi$
$31$		−	1.53073i		−	0.274928i	0.990507	−	0.137464i	$-0.0438951\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	−5.22625			−0.896295
$35$	1.70858	−	5.66399i	0.288802	−	0.957389i
$36$		0			0
$37$	2.58579	+	2.58579i	0.425101	+	0.425101i	0.886956	−	0.461855i	$-0.152816\pi$
$37$	2.58579	+	2.58579i	0.425101	+	0.425101i	−0.461855	+	0.886956i	$0.652816\pi$
$38$	−0.989538	−	0.989538i	−0.160524	−	0.160524i
$39$		0			0
$40$	−1.68925	−	1.46508i	−0.267093	−	0.231649i
$41$			3.69552i			0.577143i	0.957458	+	0.288571i	$0.0931803\pi$
$41$			3.69552i			0.577143i	−0.957458	+	0.288571i	$0.906820\pi$
$42$		0			0
$43$	4.00000	−	4.00000i	0.609994	−	0.609994i	−0.332950	−	0.942944i	$-0.608044\pi$
$43$	4.00000	−	4.00000i	0.609994	−	0.609994i	0.942944	+	0.332950i	$0.108044\pi$
$44$		−	2.82843i		−	0.426401i
$45$		0			0
$46$	−0.585786			−0.0863695
$47$	1.08239	−	1.08239i	0.157883	−	0.157883i	−0.623745	−	0.781628i	$-0.714390\pi$
$47$	1.08239	−	1.08239i	0.157883	−	0.157883i	0.781628	+	0.623745i	$0.214390\pi$
$48$		0			0
$49$	5.22625	+	4.65685i	0.746607	+	0.665265i
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$		0			0
$52$	−4.23671	+	4.23671i	−0.587527	+	0.587527i
$53$	8.24264	−	8.24264i	1.13221	−	1.13221i	0.142405	−	0.989808i	$-0.454516\pi$
$53$	8.24264	−	8.24264i	1.13221	−	1.13221i	0.989808	−	0.142405i	$-0.0454837\pi$
$54$		0			0
$55$	−0.448342	−	6.30864i	−0.0604544	−	0.850657i
$56$	2.41421	−	1.08239i	0.322613	−	0.144641i
$57$		0			0
$58$	−0.585786	+	0.585786i	−0.0769175	+	0.0769175i
$59$	−9.23880			−1.20279			−0.601394	−	0.798952i	$-0.705388\pi$
$59$	−9.23880			−1.20279			−0.601394	+	0.798952i	$0.705388\pi$
$60$		0			0
$61$			6.43996i			0.824552i	0.911059	+	0.412276i	$0.135266\pi$
$61$			6.43996i			0.824552i	−0.911059	+	0.412276i	$0.864734\pi$
$62$	1.08239	−	1.08239i	0.137464	−	0.137464i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−8.77817	+	10.1213i	−1.08880	+	1.25540i
$66$		0			0
$67$	10.4853	+	10.4853i	1.28098	+	1.28098i	0.940110	+	0.340871i	$0.110722\pi$
$67$	10.4853	+	10.4853i	1.28098	+	1.28098i	0.340871	+	0.940110i	$0.389278\pi$
$68$	−3.69552	−	3.69552i	−0.448147	−	0.448147i
$69$		0			0
$70$	5.21319	−	2.79690i	0.623096	−	0.334293i
$71$	0.585786			0.0695201			0.0347600	−	0.999396i	$-0.488933\pi$
$71$	0.585786			0.0695201			0.0347600	+	0.999396i	$0.488933\pi$
$72$		0			0
$73$	−4.14386	−	4.14386i	−0.485002	−	0.485002i	0.421723	−	0.906725i	$-0.361426\pi$
$73$	−4.14386	−	4.14386i	−0.485002	−	0.485002i	−0.906725	+	0.421723i	$0.861426\pi$
$74$			3.65685i			0.425101i
$75$		0			0
$76$		−	1.39942i		−	0.160524i
$77$	6.99321	+	2.66364i	0.796950	+	0.303550i
$78$		0			0
$79$			5.07107i			0.570540i	0.958447	+	0.285270i	$0.0920832\pi$
$79$			5.07107i			0.570540i	−0.958447	+	0.285270i	$0.907917\pi$
$80$	−0.158513	−	2.23044i	−0.0177223	−	0.249371i
$81$		0			0
$82$	−2.61313	+	2.61313i	−0.288571	+	0.288571i
$83$	5.31911	+	5.31911i	0.583848	+	0.583848i	0.935958	−	0.352111i	$-0.114536\pi$
$83$	5.31911	+	5.31911i	0.583848	+	0.583848i	−0.352111	+	0.935958i	$0.614536\pi$
$84$		0			0
$85$	−8.82843	−	7.65685i	−0.957577	−	0.830502i
$86$	5.65685			0.609994
$87$		0			0
$88$	2.00000	−	2.00000i	0.213201	−	0.213201i
$89$	11.3492			1.20301			0.601506	−	0.798869i	$-0.294568\pi$
$89$	11.3492			1.20301			0.601506	+	0.798869i	$0.294568\pi$
$90$		0			0
$91$	−6.48528	−	14.4650i	−0.679842	−	1.51635i
$92$	−0.414214	−	0.414214i	−0.0431847	−	0.0431847i
$93$		0			0
$94$	1.53073			0.157883
$95$	−0.221825	−	3.12132i	−0.0227588	−	0.320241i
$96$		0			0
$97$	4.59220	−	4.59220i	0.466267	−	0.466267i	−0.434436	−	0.900703i	$-0.643052\pi$
$97$	4.59220	−	4.59220i	0.466267	−	0.466267i	0.900703	+	0.434436i	$0.143052\pi$
$98$	0.402625	+	6.98841i	0.0406713	+	0.705936i
$99$		0			0
$100$	−0.707107	−	4.94975i	−0.0707107	−	0.494975i
$101$		−	2.74444i		−	0.273082i	−0.990634	−	0.136541i	$-0.956401\pi$
$101$		−	2.74444i		−	0.273082i	0.990634	−	0.136541i	$-0.0435986\pi$
$102$		0			0
$103$	10.0042	+	10.0042i	0.985739	+	0.985739i	0.999900	−	0.0141603i	$-0.00450753\pi$
$103$	10.0042	+	10.0042i	0.985739	+	0.985739i	−0.0141603	+	0.999900i	$0.504508\pi$
$104$	−5.99162			−0.587527
$105$		0			0
$106$	11.6569			1.13221
$107$	3.65685	+	3.65685i	0.353521	+	0.353521i	0.861418	−	0.507897i	$-0.169577\pi$
$107$	3.65685	+	3.65685i	0.353521	+	0.353521i	−0.507897	+	0.861418i	$0.669577\pi$
$108$		0			0
$109$		−	12.1421i		−	1.16301i	−0.813544	−	0.581503i	$-0.802465\pi$
$109$		−	12.1421i		−	1.16301i	0.813544	−	0.581503i	$-0.197535\pi$
$110$	4.14386	−	4.77791i	0.395102	−	0.455556i
$111$		0			0
$112$	2.47247	+	0.941740i	0.233627	+	0.0889861i
$113$	−1.17157	+	1.17157i	−0.110212	+	0.110212i	−0.760062	−	0.649850i	$-0.774832\pi$
$113$	−1.17157	+	1.17157i	−0.110212	+	0.110212i	0.649850	+	0.760062i	$0.274832\pi$
$114$		0			0
$115$	−0.989538	−	0.858221i	−0.0922749	−	0.0800296i
$116$	−0.828427			−0.0769175
$117$		0			0
$118$	−6.53281	−	6.53281i	−0.601394	−	0.601394i
$119$	12.6173	−	5.65685i	1.15662	−	0.518563i
$120$		0			0
$121$	−3.00000			−0.272727
$122$	−4.55374	+	4.55374i	−0.412276	+	0.412276i
$123$		0			0
$124$	1.53073			0.137464
$125$	−2.36176	−	10.9280i	−0.211242	−	0.977434i
$126$		0			0
$127$	3.58579	+	3.58579i	0.318187	+	0.318187i	0.848071	−	0.529883i	$-0.177764\pi$
$127$	3.58579	+	3.58579i	0.318187	+	0.318187i	−0.529883	+	0.848071i	$0.677764\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	−13.3640	+	0.949747i	−1.17210	+	0.0832984i
$131$		−	14.6508i		−	1.28004i	−0.768357	−	0.640021i	$-0.778926\pi$
$131$		−	14.6508i		−	1.28004i	0.768357	−	0.640021i	$-0.221074\pi$
$132$		0			0
$133$	3.46002	+	1.31789i	0.300022	+	0.114275i
$134$			14.8284i			1.28098i
$135$		0			0
$136$		−	5.22625i		−	0.448147i
$137$	8.17157	+	8.17157i	0.698145	+	0.698145i	0.964010	−	0.265866i	$-0.0856577\pi$
$137$	8.17157	+	8.17157i	0.698145	+	0.698145i	−0.265866	+	0.964010i	$0.585658\pi$
$138$		0			0
$139$	8.60474			0.729845			0.364922	−	0.931038i	$-0.381095\pi$
$139$	8.60474			0.729845			0.364922	+	0.931038i	$0.381095\pi$
$140$	5.66399	+	1.70858i	0.478694	+	0.144401i
$141$		0			0
$142$	0.414214	+	0.414214i	0.0347600	+	0.0347600i
$143$	−11.9832	−	11.9832i	−1.00209	−	1.00209i
$144$		0			0
$145$	−1.84776	+	0.131316i	−0.153448	+	0.0109052i
$146$		−	5.86030i		−	0.485002i
$147$		0			0
$148$	−2.58579	+	2.58579i	−0.212550	+	0.212550i
$149$		−	17.3137i		−	1.41839i	−0.705010	−	0.709197i	$-0.749058\pi$
$149$		−	17.3137i		−	1.41839i	0.705010	−	0.709197i	$-0.250942\pi$
$150$		0			0
$151$	−8.82843			−0.718447			−0.359224	−	0.933252i	$-0.616958\pi$
$151$	−8.82843			−0.718447			−0.359224	+	0.933252i	$0.616958\pi$
$152$	0.989538	−	0.989538i	0.0802621	−	0.0802621i
$153$		0			0
$154$	3.06147	+	6.82843i	0.246700	+	0.550250i
$155$	3.41421	−	0.242641i	0.274236	−	0.0194894i
$156$		0			0
$157$	−10.2283	+	10.2283i	−0.816310	+	0.816310i	−0.985571	−	0.169261i	$-0.945862\pi$
$157$	−10.2283	+	10.2283i	−0.816310	+	0.816310i	0.169261	+	0.985571i	$0.445862\pi$
$158$	−3.58579	+	3.58579i	−0.285270	+	0.285270i
$159$		0			0
$160$	1.46508	−	1.68925i	0.115824	−	0.133547i
$161$	1.41421	−	0.634051i	0.111456	−	0.0499702i
$162$		0			0
$163$	13.6569	−	13.6569i	1.06969	−	1.06969i	0.0723048	−	0.997383i	$-0.476965\pi$
$163$	13.6569	−	13.6569i	1.06969	−	1.06969i	0.997383	−	0.0723048i	$-0.0230354\pi$
$164$	−3.69552			−0.288571
$165$		0			0
$166$			7.52235i			0.583848i
$167$	−1.71644	+	1.71644i	−0.132822	+	0.132822i	−0.770392	−	0.637570i	$-0.779940\pi$
$167$	−1.71644	+	1.71644i	−0.132822	+	0.132822i	0.637570	+	0.770392i	$0.279940\pi$
$168$		0			0
$169$			22.8995i			1.76150i
$170$	−0.828427	−	11.6569i	−0.0635375	−	0.894040i
$171$		0			0
$172$	4.00000	+	4.00000i	0.304997	+	0.304997i
$173$	13.2898	+	13.2898i	1.01040	+	1.01040i	0.999945	+	0.0104595i	$0.00332943\pi$
$173$	13.2898	+	13.2898i	1.01040	+	1.01040i	0.0104595	+	0.999945i	$0.496671\pi$
$174$		0			0
$175$	12.9040	+	2.91307i	0.975453	+	0.220208i
$176$	2.82843			0.213201
$177$		0			0
$178$	8.02509	+	8.02509i	0.601506	+	0.601506i
$179$			13.6569i			1.02076i	0.859949	+	0.510381i	$0.170495\pi$
$179$			13.6569i			1.02076i	−0.859949	+	0.510381i	$0.829505\pi$
$180$		0			0
$181$			8.79045i			0.653389i	0.945130	+	0.326695i	$0.105935\pi$
$181$			8.79045i			0.653389i	−0.945130	+	0.326695i	$0.894065\pi$
$182$	5.64255	−	14.8141i	0.418253	−	1.09810i
$183$		0			0
$184$		−	0.585786i		−	0.0431847i
$185$	−5.35757	+	6.17733i	−0.393896	+	0.454166i
$186$		0			0
$187$	10.4525	−	10.4525i	0.764363	−	0.764363i
$188$	1.08239	+	1.08239i	0.0789416	+	0.0789416i
$189$		0			0
$190$	2.05025	−	2.36396i	0.148741	−	0.171500i
$191$	−1.75736			−0.127158			−0.0635790	−	0.997977i	$-0.520251\pi$
$191$	−1.75736			−0.127158			−0.0635790	+	0.997977i	$0.520251\pi$
$192$		0			0
$193$	8.24264	−	8.24264i	0.593318	−	0.593318i	−0.345208	−	0.938526i	$-0.612192\pi$
$193$	8.24264	−	8.24264i	0.593318	−	0.593318i	0.938526	+	0.345208i	$0.112192\pi$
$194$	6.49435			0.466267
$195$		0			0
$196$	−4.65685	+	5.22625i	−0.332632	+	0.373304i
$197$	−0.585786	−	0.585786i	−0.0417356	−	0.0417356i	0.685931	−	0.727667i	$-0.259395\pi$
$197$	−0.585786	−	0.585786i	−0.0417356	−	0.0417356i	−0.727667	+	0.685931i	$0.759395\pi$
$198$		0			0
$199$	−28.0334			−1.98724			−0.993618	−	0.112798i	$-0.964019\pi$
$199$	−28.0334			−1.98724			−0.993618	+	0.112798i	$0.964019\pi$
$200$	3.00000	−	4.00000i	0.212132	−	0.282843i
$201$		0			0
$202$	1.94061	−	1.94061i	0.136541	−	0.136541i
$203$	0.780163	−	2.04826i	0.0547567	−	0.143760i
$204$		0			0
$205$	−8.24264	+	0.585786i	−0.575691	+	0.0409131i
$206$			14.1480i			0.985739i
$207$		0			0
$208$	−4.23671	−	4.23671i	−0.293763	−	0.293763i
$209$	3.95815			0.273791
$210$		0			0
$211$	−10.3431			−0.712052			−0.356026	−	0.934476i	$-0.615868\pi$
$211$	−10.3431			−0.712052			−0.356026	+	0.934476i	$0.615868\pi$
$212$	8.24264	+	8.24264i	0.566107	+	0.566107i
$213$		0			0
$214$			5.17157i			0.353521i
$215$	9.55582	+	8.28772i	0.651702	+	0.565218i
$216$		0			0
$217$	−1.44155	+	3.78470i	−0.0978590	+	0.256922i
$218$	8.58579	−	8.58579i	0.581503	−	0.581503i
$219$		0			0
$220$	6.30864	−	0.448342i	0.425329	−	0.0302272i
$221$	−31.3137			−2.10639
$222$		0			0
$223$	−6.75699	−	6.75699i	−0.452481	−	0.452481i	0.443696	−	0.896177i	$-0.353667\pi$
$223$	−6.75699	−	6.75699i	−0.452481	−	0.452481i	−0.896177	+	0.443696i	$0.853667\pi$
$224$	1.08239	+	2.41421i	0.0723204	+	0.161306i
$225$		0			0
$226$	−1.65685			−0.110212
$227$	−8.38057	+	8.38057i	−0.556238	+	0.556238i	−0.928234	−	0.371996i	$-0.878673\pi$
$227$	−8.38057	+	8.38057i	−0.556238	+	0.556238i	0.371996	+	0.928234i	$0.378673\pi$
$228$		0			0
$229$	−7.70806			−0.509363			−0.254682	−	0.967025i	$-0.581971\pi$
$229$	−7.70806			−0.509363			−0.254682	+	0.967025i	$0.581971\pi$
$230$	−0.0928546	−	1.30656i	−0.00612265	−	0.0861522i
$231$		0			0
$232$	−0.585786	−	0.585786i	−0.0384588	−	0.0384588i
$233$	−3.00000	+	3.00000i	−0.196537	+	0.196537i	−0.798513	−	0.601977i	$-0.794380\pi$
$233$	−3.00000	+	3.00000i	−0.196537	+	0.196537i	0.601977	+	0.798513i	$0.294380\pi$
$234$		0			0
$235$	2.58579	+	2.24264i	0.168678	+	0.146294i
$236$		−	9.23880i		−	0.601394i
$237$		0			0
$238$	12.9218	+	4.92177i	0.837594	+	0.319031i
$239$			6.48528i			0.419498i	0.977755	+	0.209749i	$0.0672647\pi$
$239$			6.48528i			0.419498i	−0.977755	+	0.209749i	$0.932735\pi$
$240$		0			0
$241$			6.75699i			0.435256i	0.976032	+	0.217628i	$0.0698319\pi$
$241$			6.75699i			0.435256i	−0.976032	+	0.217628i	$0.930168\pi$
$242$	−2.12132	−	2.12132i	−0.136364	−	0.136364i
$243$		0			0
$244$	−6.43996			−0.412276
$245$	−9.55842	+	12.3950i	−0.610665	+	0.791889i
$246$		0			0
$247$	−5.92893	−	5.92893i	−0.377249	−	0.377249i
$248$	1.08239	+	1.08239i	0.0687320	+	0.0687320i
$249$		0			0
$250$	6.05728	−	9.39731i	0.383096	−	0.594338i
$251$		−	14.0936i		−	0.889582i	−0.895634	−	0.444791i	$-0.853278\pi$
$251$		−	14.0936i		−	0.889582i	0.895634	−	0.444791i	$-0.146722\pi$
$252$		0			0
$253$	1.17157	−	1.17157i	0.0736562	−	0.0736562i
$254$			5.07107i			0.318187i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−7.83938	+	7.83938i	−0.489007	+	0.489007i	−0.907993	−	0.418986i	$-0.862386\pi$
$257$	−7.83938	+	7.83938i	−0.489007	+	0.489007i	0.418986	+	0.907993i	$0.362386\pi$
$258$		0			0
$259$	−3.95815	−	8.82843i	−0.245948	−	0.548572i
$260$	−10.1213	−	8.77817i	−0.627698	−	0.544399i
$261$		0			0
$262$	10.3596	−	10.3596i	0.640021	−	0.640021i
$263$	19.4142	−	19.4142i	1.19713	−	1.19713i	0.222110	−	0.975022i	$-0.428706\pi$
$263$	19.4142	−	19.4142i	1.19713	−	1.19713i	0.975022	−	0.222110i	$-0.0712944\pi$
$264$		0			0
$265$	19.6913	+	17.0782i	1.20963	+	1.04910i
$266$	1.51472	+	3.37849i	0.0928734	+	0.207149i
$267$		0			0
$268$	−10.4853	+	10.4853i	−0.640490	+	0.640490i
$269$	−26.8966			−1.63992			−0.819958	−	0.572424i	$-0.806003\pi$
$269$	−26.8966			−1.63992			−0.819958	+	0.572424i	$0.806003\pi$
$270$		0			0
$271$		−	18.7402i		−	1.13839i	−0.822203	−	0.569194i	$-0.807255\pi$
$271$		−	18.7402i		−	1.13839i	0.822203	−	0.569194i	$-0.192745\pi$
$272$	3.69552	−	3.69552i	0.224074	−	0.224074i
$273$		0			0
$274$			11.5563i			0.698145i
$275$	14.0000	−	2.00000i	0.844232	−	0.120605i
$276$		0			0
$277$	−1.75736	−	1.75736i	−0.105589	−	0.105589i	0.652338	−	0.757928i	$-0.273788\pi$
$277$	−1.75736	−	1.75736i	−0.105589	−	0.105589i	−0.757928	+	0.652338i	$0.773788\pi$
$278$	6.08447	+	6.08447i	0.364922	+	0.364922i
$279$		0			0
$280$	2.79690	+	5.21319i	0.167147	+	0.311548i
$281$	5.65685			0.337460			0.168730	−	0.985662i	$-0.446033\pi$
$281$	5.65685			0.337460			0.168730	+	0.985662i	$0.446033\pi$
$282$		0			0
$283$	−3.15432	−	3.15432i	−0.187505	−	0.187505i	0.607112	−	0.794617i	$-0.292328\pi$
$283$	−3.15432	−	3.15432i	−0.187505	−	0.187505i	−0.794617	+	0.607112i	$0.792328\pi$
$284$			0.585786i			0.0347600i
$285$		0			0
$286$		−	16.9469i		−	1.00209i
$287$	3.48022	−	9.13707i	0.205431	−	0.539344i
$288$		0			0
$289$		−	10.3137i		−	0.606689i
$290$	−1.39942	−	1.21371i	−0.0821766	−	0.0712714i
$291$		0			0
$292$	4.14386	−	4.14386i	0.242501	−	0.242501i
$293$	−2.38896	−	2.38896i	−0.139564	−	0.139564i	0.633873	−	0.773437i	$-0.281464\pi$
$293$	−2.38896	−	2.38896i	−0.139564	−	0.139564i	−0.773437	+	0.633873i	$0.781464\pi$
$294$		0			0
$295$	−1.46447	−	20.6066i	−0.0852645	−	1.19976i
$296$	−3.65685			−0.212550
$297$		0			0
$298$	12.2426	−	12.2426i	0.709197	−	0.709197i
$299$	−3.50981			−0.202977
$300$		0			0
$301$	−13.6569	+	6.12293i	−0.787168	+	0.352920i
$302$	−6.24264	−	6.24264i	−0.359224	−	0.359224i
$303$		0			0
$304$	1.39942			0.0802621
$305$	−14.3640	+	1.02082i	−0.822478	+	0.0584517i
$306$		0			0
$307$	−23.1626	+	23.1626i	−1.32196	+	1.32196i	−0.409776	+	0.912186i	$0.634393\pi$
$307$	−23.1626	+	23.1626i	−1.32196	+	1.32196i	−0.912186	+	0.409776i	$0.865607\pi$
$308$	−2.66364	+	6.99321i	−0.151775	+	0.398475i
$309$		0			0
$310$	2.58579	+	2.24264i	0.146863	+	0.127373i
$311$			3.43289i			0.194661i	0.995252	+	0.0973305i	$0.0310304\pi$
$311$			3.43289i			0.194661i	−0.995252	+	0.0973305i	$0.968970\pi$
$312$		0			0
$313$	6.75699	+	6.75699i	0.381927	+	0.381927i	0.871796	−	0.489869i	$-0.162955\pi$
$313$	6.75699	+	6.75699i	0.381927	+	0.381927i	−0.489869	+	0.871796i	$0.662955\pi$
$314$	−14.4650			−0.816310
$315$		0			0
$316$	−5.07107			−0.285270
$317$	−21.8995	−	21.8995i	−1.23000	−	1.23000i	−0.963963	−	0.266035i	$-0.914286\pi$
$317$	−21.8995	−	21.8995i	−1.23000	−	1.23000i	−0.266035	−	0.963963i	$-0.585714\pi$
$318$		0			0
$319$		−	2.34315i		−	0.131191i
$320$	2.23044	−	0.158513i	0.124686	−	0.00886113i
$321$		0			0
$322$	1.44834	+	0.551658i	0.0807129	+	0.0307427i
$323$	5.17157	−	5.17157i	0.287754	−	0.287754i
$324$		0			0
$325$	−23.9665	−	17.9749i	−1.32942	−	0.997066i
$326$	19.3137			1.06969
$327$		0			0
$328$	−2.61313	−	2.61313i	−0.144286	−	0.144286i
$329$	−3.69552	+	1.65685i	−0.203741	+	0.0913453i
$330$		0			0
$331$	23.3137			1.28144			0.640719	−	0.767776i	$-0.278637\pi$
$331$	23.3137			1.28144			0.640719	+	0.767776i	$0.278637\pi$
$332$	−5.31911	+	5.31911i	−0.291924	+	0.291924i
$333$		0			0
$334$	−2.42742			−0.132822
$335$	−21.7248	+	25.0489i	−1.18695	+	1.36857i
$336$		0			0
$337$	3.75736	+	3.75736i	0.204676	+	0.204676i	0.802000	−	0.597324i	$-0.203769\pi$
$337$	3.75736	+	3.75736i	0.204676	+	0.204676i	−0.597324	+	0.802000i	$0.703769\pi$
$338$	−16.1924	+	16.1924i	−0.880750	+	0.880750i
$339$		0			0
$340$	7.65685	−	8.82843i	0.415251	−	0.478789i
$341$			4.32957i			0.234459i
$342$		0			0
$343$	−8.53622	−	16.4357i	−0.460913	−	0.887445i
$344$			5.65685i			0.304997i
$345$		0			0
$346$			18.7946i			1.01040i
$347$	5.31371	+	5.31371i	0.285255	+	0.285255i	0.835200	−	0.549946i	$-0.185352\pi$
$347$	5.31371	+	5.31371i	0.285255	+	0.285255i	−0.549946	+	0.835200i	$0.685352\pi$
$348$		0			0
$349$	−2.66752			−0.142789			−0.0713945	−	0.997448i	$-0.522745\pi$
$349$	−2.66752			−0.142789			−0.0713945	+	0.997448i	$0.522745\pi$
$350$	7.06467	+	11.1844i	0.377623	+	0.597830i
$351$		0			0
$352$	2.00000	+	2.00000i	0.106600	+	0.106600i
$353$	8.47343	+	8.47343i	0.450995	+	0.450995i	0.895685	−	0.444690i	$-0.146686\pi$
$353$	8.47343	+	8.47343i	0.450995	+	0.450995i	−0.444690	+	0.895685i	$0.646686\pi$
$354$		0			0
$355$	0.0928546	+	1.30656i	0.00492821	+	0.0693452i
$356$			11.3492i			0.601506i
$357$		0			0
$358$	−9.65685	+	9.65685i	−0.510381	+	0.510381i
$359$			16.9706i			0.895672i	0.894116	+	0.447836i	$0.147805\pi$
$359$			16.9706i			0.895672i	−0.894116	+	0.447836i	$0.852195\pi$
$360$		0			0
$361$	−17.0416			−0.896928
$362$	−6.21579	+	6.21579i	−0.326695	+	0.326695i
$363$		0			0
$364$	14.4650	−	6.48528i	0.758174	−	0.339921i
$365$	8.58579	−	9.89949i	0.449401	−	0.518163i
$366$		0			0
$367$	−3.06147	+	3.06147i	−0.159807	+	0.159807i	−0.782481	−	0.622674i	$-0.786046\pi$
$367$	−3.06147	+	3.06147i	−0.159807	+	0.159807i	0.622674	+	0.782481i	$0.286046\pi$
$368$	0.414214	−	0.414214i	0.0215924	−	0.0215924i
$369$		0			0
$370$	−8.15640	+	0.579658i	−0.424031	+	0.0301350i
$371$	−28.1421	+	12.6173i	−1.46107	+	0.655057i
$372$		0			0
$373$	−15.0711	+	15.0711i	−0.780350	+	0.780350i	−0.979890	−	0.199539i	$-0.936055\pi$
$373$	−15.0711	+	15.0711i	−0.780350	+	0.780350i	0.199539	+	0.979890i	$0.436055\pi$
$374$	14.7821			0.764363
$375$		0			0
$376$			1.53073i			0.0789416i
$377$	−3.50981	+	3.50981i	−0.180764	+	0.180764i
$378$		0			0
$379$			6.14214i			0.315500i	0.987479	+	0.157750i	$0.0504241\pi$
$379$			6.14214i			0.315500i	−0.987479	+	0.157750i	$0.949576\pi$
$380$	3.12132	−	0.221825i	0.160120	−	0.0113794i
$381$		0			0
$382$	−1.24264	−	1.24264i	−0.0635790	−	0.0635790i
$383$	−10.6382	−	10.6382i	−0.543587	−	0.543587i	0.380991	−	0.924579i	$-0.375583\pi$
$383$	−10.6382	−	10.6382i	−0.543587	−	0.543587i	−0.924579	+	0.380991i	$0.875583\pi$
$384$		0			0
$385$	−4.83259	+	16.0202i	−0.246292	+	0.816464i
$386$	11.6569			0.593318
$387$		0			0
$388$	4.59220	+	4.59220i	0.233134	+	0.233134i
$389$		−	0.142136i		−	0.00720656i	−0.999994	−	0.00360328i	$-0.998853\pi$
$389$		−	0.142136i		−	0.00720656i	0.999994	−	0.00360328i	$-0.00114696\pi$
$390$		0			0
$391$		−	3.06147i		−	0.154825i
$392$	−6.98841	+	0.402625i	−0.352968	+	0.0203356i
$393$		0			0
$394$		−	0.828427i		−	0.0417356i
$395$	−11.3107	+	0.803828i	−0.569104	+	0.0404450i
$396$		0			0
$397$	−1.12085	+	1.12085i	−0.0562540	+	0.0562540i	−0.734674	−	0.678420i	$-0.762665\pi$
$397$	−1.12085	+	1.12085i	−0.0562540	+	0.0562540i	0.678420	+	0.734674i	$0.262665\pi$
$398$	−19.8226	−	19.8226i	−0.993618	−	0.993618i
$399$		0			0
$400$	4.94975	−	0.707107i	0.247487	−	0.0353553i
$401$	19.7574			0.986635			0.493318	−	0.869849i	$-0.335784\pi$
$401$	19.7574			0.986635			0.493318	+	0.869849i	$0.335784\pi$
$402$		0			0
$403$	6.48528	−	6.48528i	0.323055	−	0.323055i
$404$	2.74444			0.136541
$405$		0			0
$406$	2.00000	−	0.896683i	0.0992583	−	0.0445016i
$407$	−7.31371	−	7.31371i	−0.362527	−	0.362527i
$408$		0			0
$409$	24.9719			1.23478			0.617392	−	0.786656i	$-0.288189\pi$
$409$	24.9719			1.23478			0.617392	+	0.786656i	$0.288189\pi$
$410$	−6.24264	−	5.41421i	−0.308302	−	0.267389i
$411$		0			0
$412$	−10.0042	+	10.0042i	−0.492870	+	0.492870i
$413$	22.8427	+	8.70054i	1.12401	+	0.428126i
$414$		0			0
$415$	−11.0208	+	12.7071i	−0.540991	+	0.623767i
$416$		−	5.99162i		−	0.293763i
$417$		0			0
$418$	2.79884	+	2.79884i	0.136895	+	0.136895i
$419$	11.5893			0.566174			0.283087	−	0.959094i	$-0.408642\pi$
$419$	11.5893			0.566174			0.283087	+	0.959094i	$0.408642\pi$
$420$		0			0
$421$	17.7990			0.867470			0.433735	−	0.901041i	$-0.357195\pi$
$421$	17.7990			0.867470			0.433735	+	0.901041i	$0.357195\pi$
$422$	−7.31371	−	7.31371i	−0.356026	−	0.356026i
$423$		0			0
$424$			11.6569i			0.566107i
$425$	15.6788	−	20.9050i	0.760531	−	1.01404i
$426$		0			0
$427$	6.06477	−	15.9226i	0.293495	−	0.770550i
$428$	−3.65685	+	3.65685i	−0.176761	+	0.176761i
$429$		0			0
$430$	0.896683	+	12.6173i	0.0432419	+	0.608460i
$431$	−5.65685			−0.272481			−0.136241	−	0.990676i	$-0.543502\pi$
$431$	−5.65685			−0.272481			−0.136241	+	0.990676i	$0.543502\pi$
$432$		0			0
$433$	10.4525	+	10.4525i	0.502315	+	0.502315i	0.912157	−	0.409841i	$-0.134416\pi$
$433$	10.4525	+	10.4525i	0.502315	+	0.502315i	−0.409841	+	0.912157i	$0.634416\pi$
$434$	−3.69552	+	1.65685i	−0.177391	+	0.0795315i
$435$		0			0
$436$	12.1421			0.581503
$437$	0.579658	−	0.579658i	0.0277288	−	0.0277288i
$438$		0			0
$439$	13.8854			0.662713			0.331357	−	0.943506i	$-0.392494\pi$
$439$	13.8854			0.662713			0.331357	+	0.943506i	$0.392494\pi$
$440$	4.77791	+	4.14386i	0.227778	+	0.197551i
$441$		0			0
$442$	−22.1421	−	22.1421i	−1.05319	−	1.05319i
$443$	4.14214	−	4.14214i	0.196799	−	0.196799i	−0.601827	−	0.798626i	$-0.705560\pi$
$443$	4.14214	−	4.14214i	0.196799	−	0.196799i	0.798626	+	0.601827i	$0.205560\pi$
$444$		0			0
$445$	1.79899	+	25.3137i	0.0852803	+	1.19998i
$446$		−	9.55582i		−	0.452481i
$447$		0			0
$448$	−0.941740	+	2.47247i	−0.0444930	+	0.116813i
$449$		−	25.6569i		−	1.21082i	−0.795913	−	0.605411i	$-0.793009\pi$
$449$		−	25.6569i		−	1.21082i	0.795913	−	0.605411i	$-0.206991\pi$
$450$		0			0
$451$		−	10.4525i		−	0.492189i
$452$	−1.17157	−	1.17157i	−0.0551062	−	0.0551062i
$453$		0			0
$454$	−11.8519			−0.556238
$455$	31.2355	−	16.7579i	1.46434	−	0.785624i
$456$		0			0
$457$	−1.65685	−	1.65685i	−0.0775044	−	0.0775044i	0.667292	−	0.744796i	$-0.267453\pi$
$457$	−1.65685	−	1.65685i	−0.0775044	−	0.0775044i	−0.744796	+	0.667292i	$0.767453\pi$
$458$	−5.45042	−	5.45042i	−0.254682	−	0.254682i
$459$		0			0
$460$	0.858221	−	0.989538i	0.0400148	−	0.0461374i
$461$			34.0250i			1.58470i	0.610064	+	0.792352i	$0.291144\pi$
$461$			34.0250i			1.58470i	−0.610064	+	0.792352i	$0.708856\pi$
$462$		0			0
$463$	−12.9706	+	12.9706i	−0.602793	+	0.602793i	−0.941053	−	0.338260i	$-0.890162\pi$
$463$	−12.9706	+	12.9706i	−0.602793	+	0.602793i	0.338260	+	0.941053i	$0.390162\pi$
$464$		−	0.828427i		−	0.0384588i
$465$		0			0
$466$	−4.24264			−0.196537
$467$	17.4337	−	17.4337i	0.806734	−	0.806734i	−0.177404	−	0.984138i	$-0.556770\pi$
$467$	17.4337	−	17.4337i	0.806734	−	0.806734i	0.984138	+	0.177404i	$0.0567701\pi$
$468$		0			0
$469$	−16.0502	−	35.7990i	−0.741128	−	1.65304i
$470$	0.242641	+	3.41421i	0.0111922	+	0.157486i
$471$		0			0
$472$	6.53281	−	6.53281i	0.300697	−	0.300697i
$473$	−11.3137	+	11.3137i	−0.520205	+	0.520205i
$474$		0			0
$475$	6.92676	−	0.989538i	0.317822	−	0.0454031i
$476$	5.65685	+	12.6173i	0.259281	+	0.578312i
$477$		0			0
$478$	−4.58579	+	4.58579i	−0.209749	+	0.209749i
$479$	−11.0866			−0.506558			−0.253279	−	0.967393i	$-0.581509\pi$
$479$	−11.0866			−0.506558			−0.253279	+	0.967393i	$0.581509\pi$
$480$		0			0
$481$			21.9105i			0.999032i
$482$	−4.77791	+	4.77791i	−0.217628	+	0.217628i
$483$		0			0
$484$		−	3.00000i		−	0.136364i
$485$	10.9706	+	9.51472i	0.498148	+	0.432041i
$486$		0			0
$487$	1.10051	+	1.10051i	0.0498686	+	0.0498686i	0.731601	−	0.681733i	$-0.238773\pi$
$487$	1.10051	+	1.10051i	0.0498686	+	0.0498686i	−0.681733	+	0.731601i	$0.738773\pi$
$488$	−4.55374	−	4.55374i	−0.206138	−	0.206138i
$489$		0			0
$490$	−15.5234	+	2.00578i	−0.701277	+	0.0906121i
$491$	−25.1716			−1.13598			−0.567989	−	0.823036i	$-0.692278\pi$
$491$	−25.1716			−1.13598			−0.567989	+	0.823036i	$0.692278\pi$
$492$		0			0
$493$	−3.06147	−	3.06147i	−0.137882	−	0.137882i
$494$		−	8.38478i		−	0.377249i
$495$		0			0
$496$			1.53073i			0.0687320i
$497$	−1.44834	−	0.551658i	−0.0649670	−	0.0247453i
$498$		0			0
$499$			7.51472i			0.336405i	0.985752	+	0.168203i	$0.0537963\pi$
$499$			7.51472i			0.336405i	−0.985752	+	0.168203i	$0.946204\pi$
$500$	10.9280	−	2.36176i	0.488717	−	0.105621i
$501$		0			0
$502$	9.96570	−	9.96570i	0.444791	−	0.444791i
$503$	18.1062	+	18.1062i	0.807314	+	0.807314i	0.984227	−	0.176912i	$-0.0566109\pi$
$503$	18.1062	+	18.1062i	0.807314	+	0.807314i	−0.176912	+	0.984227i	$0.556611\pi$
$504$		0			0
$505$	6.12132	−	0.435029i	0.272395	−	0.0193585i
$506$	1.65685			0.0736562
$507$		0			0
$508$	−3.58579	+	3.58579i	−0.159094	+	0.159094i
$509$	14.4650			0.641152			0.320576	−	0.947223i	$-0.396124\pi$
$509$	14.4650			0.641152			0.320576	+	0.947223i	$0.396124\pi$
$510$		0			0
$511$	6.34315	+	14.1480i	0.280604	+	0.625872i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−11.0866			−0.489007
$515$	−20.7279	+	23.8995i	−0.913381	+	1.05314i
$516$		0			0
$517$	−3.06147	+	3.06147i	−0.134643	+	0.134643i
$518$	3.44381	−	9.04148i	0.151312	−	0.397260i
$519$		0			0
$520$	−0.949747	−	13.3640i	−0.0416492	−	0.586048i
$521$		−	36.6925i		−	1.60753i	−0.594947	−	0.803765i	$-0.702827\pi$
$521$		−	36.6925i		−	1.60753i	0.594947	−	0.803765i	$-0.297173\pi$
$522$		0			0
$523$	−1.75490	−	1.75490i	−0.0767366	−	0.0767366i	0.667697	−	0.744433i	$-0.267280\pi$
$523$	−1.75490	−	1.75490i	−0.0767366	−	0.0767366i	−0.744433	+	0.667697i	$0.767280\pi$
$524$	14.6508			0.640021
$525$		0			0
$526$	27.4558			1.19713
$527$	5.65685	+	5.65685i	0.246416	+	0.246416i
$528$		0			0
$529$			22.6569i			0.985081i
$530$	1.84776	+	25.9999i	0.0802615	+	1.12937i
$531$		0			0
$532$	−1.31789	+	3.46002i	−0.0571377	+	0.150011i
$533$	−15.6569	+	15.6569i	−0.678174	+	0.678174i
$534$		0			0
$535$	−7.57675	+	8.73606i	−0.327571	+	0.377693i
$536$	−14.8284			−0.640490
$537$		0			0
$538$	−19.0188	−	19.0188i	−0.819958	−	0.819958i
$539$	−14.7821	−	13.1716i	−0.636709	−	0.567340i
$540$		0			0
$541$	10.9706			0.471661			0.235831	−	0.971794i	$-0.424219\pi$
$541$	10.9706			0.471661			0.235831	+	0.971794i	$0.424219\pi$
$542$	13.2513	−	13.2513i	0.569194	−	0.569194i
$543$		0			0
$544$	5.22625			0.224074
$545$	27.0823	−	1.92468i	1.16008	−	0.0824443i
$546$		0			0
$547$	−30.6274	−	30.6274i	−1.30953	−	1.30953i	−0.921751	−	0.387783i	$-0.873241\pi$
$547$	−30.6274	−	30.6274i	−1.30953	−	1.30953i	−0.387783	−	0.921751i	$-0.626759\pi$
$548$	−8.17157	+	8.17157i	−0.349072	+	0.349072i
$549$		0			0
$550$	11.3137	+	8.48528i	0.482418	+	0.361814i
$551$		−	1.15932i		−	0.0493885i
$552$		0			0
$553$	4.77563	−	12.5381i	0.203080	−	0.533173i
$554$		−	2.48528i		−	0.105589i
$555$		0			0
$556$			8.60474i			0.364922i
$557$	26.7279	+	26.7279i	1.13250	+	1.13250i	0.989761	+	0.142738i	$0.0455906\pi$
$557$	26.7279	+	26.7279i	1.13250	+	1.13250i	0.142738	+	0.989761i	$0.454409\pi$
$558$		0			0
$559$	33.8937			1.43355
$560$	−1.70858	+	5.66399i	−0.0722006	+	0.239347i
$561$		0			0
$562$	4.00000	+	4.00000i	0.168730	+	0.168730i
$563$	3.54827	+	3.54827i	0.149542	+	0.149542i	0.777913	−	0.628372i	$-0.216278\pi$
$563$	3.54827	+	3.54827i	0.149542	+	0.149542i	−0.628372	+	0.777913i	$0.716278\pi$
$564$		0			0
$565$	−2.79884	−	2.42742i	−0.117748	−	0.102122i
$566$		−	4.46088i		−	0.187505i
$567$		0			0
$568$	−0.414214	+	0.414214i	−0.0173800	+	0.0173800i
$569$		−	1.41421i		−	0.0592869i	−0.999561	−	0.0296435i	$-0.990563\pi$
$569$		−	1.41421i		−	0.0592869i	0.999561	−	0.0296435i	$-0.00943719\pi$
$570$		0			0
$571$	−25.4558			−1.06529			−0.532647	−	0.846338i	$-0.678803\pi$
$571$	−25.4558			−1.06529			−0.532647	+	0.846338i	$0.678803\pi$
$572$	11.9832	−	11.9832i	0.501044	−	0.501044i
$573$		0			0
$574$	8.92177	−	4.00000i	0.372387	−	0.166957i
$575$	1.75736	−	2.34315i	0.0732869	−	0.0977159i
$576$		0			0
$577$	26.3170	−	26.3170i	1.09559	−	1.09559i	0.100670	−	0.994920i	$-0.467901\pi$
$577$	26.3170	−	26.3170i	1.09559	−	1.09559i	0.994920	−	0.100670i	$-0.0320986\pi$
$578$	7.29289	−	7.29289i	0.303344	−	0.303344i
$579$		0			0
$580$	−0.131316	−	1.84776i	−0.00545261	−	0.0767240i
$581$	−8.14214	−	18.1606i	−0.337793	−	0.753427i
$582$		0			0
$583$	−23.3137	+	23.3137i	−0.965555	+	0.965555i
$584$	5.86030			0.242501
$585$		0			0
$586$		−	3.37849i		−	0.139564i
$587$	16.0886	−	16.0886i	0.664049	−	0.664049i	−0.292283	−	0.956332i	$-0.594415\pi$
$587$	16.0886	−	16.0886i	0.664049	−	0.664049i	0.956332	+	0.292283i	$0.0944149\pi$
$588$		0			0
$589$			2.14214i			0.0882652i
$590$	13.5355	−	15.6066i	0.557249	−	0.642514i
$591$		0			0
$592$	−2.58579	−	2.58579i	−0.106275	−	0.106275i
$593$	−22.8841	−	22.8841i	−0.939737	−	0.939737i	0.0585480	−	0.998285i	$-0.481353\pi$
$593$	−22.8841	−	22.8841i	−0.939737	−	0.939737i	−0.998285	+	0.0585480i	$0.981353\pi$
$594$		0			0
$595$	14.6173	+	27.2455i	0.599250	+	1.11695i
$596$	17.3137			0.709197
$597$		0			0
$598$	−2.48181	−	2.48181i	−0.101489	−	0.101489i
$599$		−	18.5269i		−	0.756989i	−0.925604	−	0.378495i	$-0.876442\pi$
$599$		−	18.5269i		−	0.756989i	0.925604	−	0.378495i	$-0.123558\pi$
$600$		0			0
$601$		−	16.5754i		−	0.676126i	−0.941123	−	0.338063i	$-0.890228\pi$
$601$		−	16.5754i		−	0.676126i	0.941123	−	0.338063i	$-0.109772\pi$
$602$	−13.9864	−	5.32729i	−0.570044	−	0.217124i
$603$		0			0
$604$		−	8.82843i		−	0.359224i
$605$	−0.475538	−	6.69133i	−0.0193334	−	0.272041i
$606$		0			0
$607$	21.5391	−	21.5391i	0.874243	−	0.874243i	−0.118688	−	0.992932i	$-0.537869\pi$
$607$	21.5391	−	21.5391i	0.874243	−	0.874243i	0.992932	+	0.118688i	$0.0378689\pi$
$608$	0.989538	+	0.989538i	0.0401311	+	0.0401311i
$609$		0			0
$610$	−10.8787	−	9.43503i	−0.440465	−	0.382013i
$611$	9.17157			0.371042
$612$		0			0
$613$	19.8995	−	19.8995i	0.803733	−	0.803733i	−0.179944	−	0.983677i	$-0.557592\pi$
$613$	19.8995	−	19.8995i	0.803733	−	0.803733i	0.983677	+	0.179944i	$0.0575916\pi$
$614$	−32.7569			−1.32196
$615$		0			0
$616$	−6.82843	+	3.06147i	−0.275125	+	0.123350i
$617$	28.4853	+	28.4853i	1.14677	+	1.14677i	0.987183	+	0.159591i	$0.0510176\pi$
$617$	28.4853	+	28.4853i	1.14677	+	1.14677i	0.159591	+	0.987183i	$0.448982\pi$
$618$		0			0
$619$	0.688444			0.0276709			0.0138354	−	0.999904i	$-0.495596\pi$
$619$	0.688444			0.0276709			0.0138354	+	0.999904i	$0.495596\pi$
$620$	0.242641	+	3.41421i	0.00974468	+	0.137118i
$621$		0			0
$622$	−2.42742	+	2.42742i	−0.0973305	+	0.0973305i
$623$	−28.0606	−	10.6880i	−1.12422	−	0.428205i
$624$		0			0
$625$	24.0000	−	7.00000i	0.960000	−	0.280000i
$626$			9.55582i			0.381927i
$627$		0			0
$628$	−10.2283	−	10.2283i	−0.408155	−	0.408155i
$629$	−19.1116			−0.762031
$630$		0			0
$631$	41.3553			1.64633			0.823165	−	0.567802i	$-0.192206\pi$
$631$	41.3553			1.64633			0.823165	+	0.567802i	$0.192206\pi$
$632$	−3.58579	−	3.58579i	−0.142635	−	0.142635i
$633$		0			0
$634$		−	30.9706i		−	1.23000i
$635$	−7.42950	+	8.56628i	−0.294831	+	0.339943i
$636$		0			0
$637$	2.41237	+	41.8719i	0.0955818	+	1.65902i
$638$	1.65685	−	1.65685i	0.0655955	−	0.0655955i
$639$		0			0
$640$	1.68925	+	1.46508i	0.0667733	+	0.0579122i
$641$	37.2132			1.46983			0.734917	−	0.678158i	$-0.237221\pi$
$641$	37.2132			1.46983			0.734917	+	0.678158i	$0.237221\pi$
$642$		0			0
$643$	20.9435	+	20.9435i	0.825930	+	0.825930i	0.986951	−	0.161021i	$-0.0514787\pi$
$643$	20.9435	+	20.9435i	0.825930	+	0.825930i	−0.161021	+	0.986951i	$0.551479\pi$
$644$	0.634051	+	1.41421i	0.0249851	+	0.0557278i
$645$		0			0
$646$	7.31371			0.287754
$647$	23.8896	−	23.8896i	0.939195	−	0.939195i	−0.0590593	−	0.998254i	$-0.518810\pi$
$647$	23.8896	−	23.8896i	0.939195	−	0.939195i	0.998254	+	0.0590593i	$0.0188101\pi$
$648$		0			0
$649$	26.1313			1.02574
$650$	−4.23671	−	29.6570i	−0.166178	−	1.16324i
$651$		0			0
$652$	13.6569	+	13.6569i	0.534844	+	0.534844i
$653$	−8.72792	+	8.72792i	−0.341550	+	0.341550i	−0.856950	−	0.515400i	$-0.827643\pi$
$653$	−8.72792	+	8.72792i	−0.341550	+	0.341550i	0.515400	+	0.856950i	$0.327643\pi$
$654$		0			0
$655$	32.6777	−	2.32233i	1.27682	−	0.0907410i
$656$		−	3.69552i		−	0.144286i
$657$		0			0
$658$	−3.78470	−	1.44155i	−0.147543	−	0.0561976i
$659$			29.6569i			1.15527i	0.816296	+	0.577634i	$0.196024\pi$
$659$			29.6569i			1.15527i	−0.816296	+	0.577634i	$0.803976\pi$
$660$		0			0
$661$		−	47.5390i		−	1.84905i	−0.381118	−	0.924526i	$-0.624461\pi$
$661$		−	47.5390i		−	1.84905i	0.381118	−	0.924526i	$-0.375539\pi$
$662$	16.4853	+	16.4853i	0.640719	+	0.640719i
$663$		0			0
$664$	−7.52235			−0.291924
$665$	−2.39101	+	7.92628i	−0.0927196	+	0.307368i
$666$		0			0
$667$	−0.343146	−	0.343146i	−0.0132867	−	0.0132867i
$668$	−1.71644	−	1.71644i	−0.0664112	−	0.0664112i
$669$		0			0
$670$	−33.0740	+	2.35049i	−1.27776	+	0.0908075i
$671$		−	18.2150i		−	0.703181i
$672$		0			0
$673$	−22.7990	+	22.7990i	−0.878836	+	0.878836i	−0.993414	−	0.114578i	$-0.963448\pi$
$673$	−22.7990	+	22.7990i	−0.878836	+	0.878836i	0.114578	+	0.993414i	$0.463448\pi$
$674$			5.31371i			0.204676i
$675$		0			0
$676$	−22.8995			−0.880750
$677$	−22.4742	+	22.4742i	−0.863754	+	0.863754i	−0.991772	−	0.128018i	$-0.959138\pi$
$677$	−22.4742	+	22.4742i	−0.863754	+	0.863754i	0.128018	+	0.991772i	$0.459138\pi$
$678$		0			0
$679$	−15.6788	+	7.02944i	−0.601695	+	0.269765i
$680$	11.6569	−	0.828427i	0.447020	−	0.0317687i
$681$		0			0
$682$	−3.06147	+	3.06147i	−0.117230	+	0.117230i
$683$	25.3137	−	25.3137i	0.968602	−	0.968602i	−0.0309197	−	0.999522i	$-0.509844\pi$
$683$	25.3137	−	25.3137i	0.968602	−	0.968602i	0.999522	+	0.0309197i	$0.00984363\pi$
$684$		0			0
$685$	−16.9309	+	19.5215i	−0.646897	+	0.745879i
$686$	5.58579	−	17.6578i	0.213266	−	0.674179i
$687$		0			0
$688$	−4.00000	+	4.00000i	−0.152499	+	0.152499i
$689$	69.8434			2.66082
$690$		0			0
$691$		−	25.1033i		−	0.954973i	−0.878639	−	0.477487i	$-0.841548\pi$
$691$		−	25.1033i		−	0.954973i	0.878639	−	0.477487i	$-0.158452\pi$
$692$	−13.2898	+	13.2898i	−0.505202	+	0.505202i
$693$		0			0
$694$			7.51472i			0.285255i
$695$	1.36396	+	19.1924i	0.0517380	+	0.728009i
$696$		0			0
$697$	−13.6569	−	13.6569i	−0.517290	−	0.517290i
$698$	−1.88622	−	1.88622i	−0.0713945	−	0.0713945i
$699$		0			0
$700$	−2.91307	+	12.9040i	−0.110104	+	0.487727i
$701$	13.1127			0.495260			0.247630	−	0.968855i	$-0.420348\pi$
$701$	13.1127			0.495260			0.247630	+	0.968855i	$0.420348\pi$
$702$		0			0
$703$	−3.61859	−	3.61859i	−0.136478	−	0.136478i
$704$			2.82843i			0.106600i
$705$		0			0
$706$			11.9832i			0.450995i
$707$	−2.58455	+	6.78556i	−0.0972020	+	0.255197i
$708$		0			0
$709$		−	41.3137i		−	1.55157i	−0.630998	−	0.775784i	$-0.717354\pi$
$709$		−	41.3137i		−	1.55157i	0.630998	−	0.775784i	$-0.282646\pi$
$710$	−0.858221	+	0.989538i	−0.0322085	+	0.0371367i
$711$		0			0
$712$	−8.02509	+	8.02509i	−0.300753	+	0.300753i
$713$	0.634051	+	0.634051i	0.0237454	+	0.0237454i
$714$		0			0
$715$	24.8284	−	28.6274i	0.928531	−	1.07060i
$716$	−13.6569			−0.510381
$717$		0			0
$718$	−12.0000	+	12.0000i	−0.447836	+	0.447836i
$719$	43.7122			1.63019			0.815094	−	0.579328i	$-0.196685\pi$
$719$	43.7122			1.63019			0.815094	+	0.579328i	$0.196685\pi$
$720$		0			0
$721$	−15.3137	−	34.1563i	−0.570312	−	1.27205i
$722$	−12.0503	−	12.0503i	−0.448464	−	0.448464i
$723$		0			0
$724$	−8.79045			−0.326695
$725$	−0.585786	−	4.10051i	−0.0217556	−	0.152289i
$726$		0			0
$727$	22.8841	−	22.8841i	0.848724	−	0.848724i	−0.141250	−	0.989974i	$-0.545112\pi$
$727$	22.8841	−	22.8841i	0.848724	−	0.848724i	0.989974	+	0.141250i	$0.0451122\pi$
$728$	14.8141	+	5.64255i	0.549048	+	0.209127i
$729$		0			0
$730$	13.0711	−	0.928932i	0.483782	−	0.0343813i
$731$			29.5641i			1.09347i
$732$		0			0
$733$	−21.9489	−	21.9489i	−0.810703	−	0.810703i	0.174037	−	0.984739i	$-0.444319\pi$
$733$	−21.9489	−	21.9489i	−0.810703	−	0.810703i	−0.984739	+	0.174037i	$0.944319\pi$
$734$	−4.32957			−0.159807
$735$		0			0
$736$	0.585786			0.0215924
$737$	−29.6569	−	29.6569i	−1.09242	−	1.09242i
$738$		0			0
$739$		−	9.65685i		−	0.355233i	−0.984100	−	0.177617i	$-0.943161\pi$
$739$		−	9.65685i		−	0.355233i	0.984100	−	0.177617i	$-0.0568387\pi$
$740$	−6.17733	−	5.35757i	−0.227083	−	0.196948i
$741$		0			0
$742$	−28.8213	−	10.9777i	−1.05806	−	0.403005i
$743$	−27.0416	+	27.0416i	−0.992061	+	0.992061i	−0.999969	−	0.00790753i	$-0.997483\pi$
$743$	−27.0416	+	27.0416i	−0.992061	+	0.992061i	0.00790753	+	0.999969i	$0.497483\pi$
$744$		0			0
$745$	38.6172	−	2.74444i	1.41483	−	0.100549i
$746$	−21.3137			−0.780350
$747$		0			0
$748$	10.4525	+	10.4525i	0.382181	+	0.382181i
$749$	−5.59767	−	12.4853i	−0.204534	−	0.456202i
$750$		0			0
$751$	−2.48528			−0.0906892			−0.0453446	−	0.998971i	$-0.514439\pi$
$751$	−2.48528			−0.0906892			−0.0453446	+	0.998971i	$0.514439\pi$
$752$	−1.08239	+	1.08239i	−0.0394708	+	0.0394708i
$753$		0			0
$754$	−4.96362			−0.180764
$755$	−1.39942	−	19.6913i	−0.0509300	−	0.716640i
$756$		0			0
$757$	7.89949	+	7.89949i	0.287112	+	0.287112i	0.835937	−	0.548825i	$-0.184925\pi$
$757$	7.89949	+	7.89949i	0.287112	+	0.287112i	−0.548825	+	0.835937i	$0.684925\pi$
$758$	−4.34315	+	4.34315i	−0.157750	+	0.157750i
$759$		0			0
$760$	2.36396	+	2.05025i	0.0857499	+	0.0743705i
$761$			26.3939i			0.956778i	0.878148	+	0.478389i	$0.158779\pi$
$761$			26.3939i			0.956778i	−0.878148	+	0.478389i	$0.841221\pi$
$762$		0			0
$763$	−11.4347	+	30.0211i	−0.413965	+	1.08684i
$764$		−	1.75736i		−	0.0635790i
$765$		0			0
$766$		−	15.0447i		−	0.543587i
$767$	−39.1421	−	39.1421i	−1.41334	−	1.41334i
$768$		0			0
$769$	17.5809			0.633984			0.316992	−	0.948428i	$-0.397327\pi$
$769$	17.5809			0.633984			0.316992	+	0.948428i	$0.397327\pi$
$770$	−14.7451	+	7.91082i	−0.531378	+	0.285086i
$771$		0			0
$772$	8.24264	+	8.24264i	0.296659	+	0.296659i
$773$	−14.6892	−	14.6892i	−0.528334	−	0.528334i	0.391741	−	0.920076i	$-0.371873\pi$
$773$	−14.6892	−	14.6892i	−0.528334	−	0.528334i	−0.920076	+	0.391741i	$0.871873\pi$
$774$		0			0
$775$	1.08239	+	7.57675i	0.0388807	+	0.272165i
$776$			6.49435i			0.233134i
$777$		0			0
$778$	0.100505	−	0.100505i	0.00360328	−	0.00360328i
$779$		−	5.17157i		−	0.185291i
$780$		0			0
$781$	−1.65685			−0.0592869
$782$	2.16478	−	2.16478i	0.0774125	−	0.0774125i
$783$		0			0
$784$	−5.22625	−	4.65685i	−0.186652	−	0.166316i
$785$	−24.4350	−	21.1924i	−0.872124	−	0.756389i
$786$		0			0
$787$	−24.3764	+	24.3764i	−0.868923	+	0.868923i	−0.992353	−	0.123430i	$-0.960611\pi$
$787$	−24.3764	+	24.3764i	−0.868923	+	0.868923i	0.123430	+	0.992353i	$0.460611\pi$
$788$	0.585786	−	0.585786i	0.0208678	−	0.0208678i
$789$		0			0
$790$	−8.56628	−	7.42950i	−0.304775	−	0.264330i
$791$	4.00000	−	1.79337i	0.142224	−	0.0637648i
$792$		0			0
$793$	−27.2843	+	27.2843i	−0.968893	+	0.968893i
$794$	−1.58513			−0.0562540
$795$		0			0
$796$		−	28.0334i		−	0.993618i
$797$	16.6683	−	16.6683i	0.590421	−	0.590421i	−0.347324	−	0.937745i	$-0.612910\pi$
$797$	16.6683	−	16.6683i	0.590421	−	0.590421i	0.937745	+	0.347324i	$0.112910\pi$
$798$		0			0
$799$			8.00000i			0.283020i
$800$	4.00000	+	3.00000i	0.141421	+	0.106066i
$801$		0			0
$802$	13.9706	+	13.9706i	0.493318	+	0.493318i
$803$	11.7206	+	11.7206i	0.413611	+	0.413611i
$804$		0			0
$805$	1.63838	+	3.05382i	0.0577455	+	0.107633i
$806$	9.17157			0.323055
$807$		0			0
$808$	1.94061	+	1.94061i	0.0682705	+	0.0682705i
$809$		−	33.8995i		−	1.19184i	−0.803043	−	0.595921i	$-0.796787\pi$
$809$		−	33.8995i		−	1.19184i	0.803043	−	0.595921i	$-0.203213\pi$
$810$		0			0
$811$			50.6005i			1.77682i	0.459048	+	0.888411i	$0.348191\pi$
$811$			50.6005i			1.77682i	−0.459048	+	0.888411i	$0.651809\pi$
$812$	2.04826	+	0.780163i	0.0718800	+	0.0273784i
$813$		0			0
$814$		−	10.3431i		−	0.362527i
$815$	32.6256	+	28.2960i	1.14283	+	0.991167i
$816$		0			0
$817$	−5.59767	+	5.59767i	−0.195838	+	0.195838i
$818$	17.6578	+	17.6578i	0.617392	+	0.617392i
$819$		0			0
$820$	−0.585786	−	8.24264i	−0.0204565	−	0.287845i
$821$	34.4853			1.20354			0.601772	−	0.798668i	$-0.294461\pi$
$821$	34.4853			1.20354			0.601772	+	0.798668i	$0.294461\pi$
$822$		0			0
$823$	−2.34315	+	2.34315i	−0.0816769	+	0.0816769i	−0.746765	−	0.665088i	$-0.768394\pi$
$823$	−2.34315	+	2.34315i	−0.0816769	+	0.0816769i	0.665088	+	0.746765i	$0.268394\pi$
$824$	−14.1480			−0.492870
$825$		0			0
$826$	10.0000	+	22.3044i	0.347945	+	0.776070i
$827$	7.51472	+	7.51472i	0.261312	+	0.261312i	0.825587	−	0.564275i	$-0.190844\pi$
$827$	7.51472	+	7.51472i	0.261312	+	0.261312i	−0.564275	+	0.825587i	$0.690844\pi$
$828$		0			0
$829$	40.8589			1.41909			0.709545	−	0.704660i	$-0.248901\pi$
$829$	40.8589			1.41909			0.709545	+	0.704660i	$0.248901\pi$
$830$	−16.7782	+	1.19239i	−0.582379	+	0.0413884i
$831$		0			0
$832$	4.23671	−	4.23671i	0.146882	−	0.146882i
$833$	−36.5232	+	2.10422i	−1.26545	+	0.0729069i
$834$		0			0
$835$	−4.10051	−	3.55635i	−0.141904	−	0.123073i
$836$			3.95815i			0.136895i
$837$		0			0
$838$	8.19486	+	8.19486i	0.283087	+	0.283087i
$839$	−20.6424			−0.712654			−0.356327	−	0.934361i	$-0.615971\pi$
$839$	−20.6424			−0.712654			−0.356327	+	0.934361i	$0.615971\pi$
$840$		0			0
$841$	28.3137			0.976335
$842$	12.5858	+	12.5858i	0.433735	+	0.433735i
$843$		0			0
$844$		−	10.3431i		−	0.356026i
$845$	−51.0760	+	3.62986i	−1.75707	+	0.124871i
$846$		0			0
$847$	7.41742	+	2.82522i	0.254866	+	0.0970757i
$848$	−8.24264	+	8.24264i	−0.283053	+	0.283053i
$849$		0			0
$850$	25.8686	−	3.69552i	0.887287	−	0.126755i
$851$	−2.14214			−0.0734315
$852$		0			0
$853$	−26.7268	−	26.7268i	−0.915110	−	0.915110i	0.0815587	−	0.996669i	$-0.474010\pi$
$853$	−26.7268	−	26.7268i	−0.915110	−	0.915110i	−0.996669	+	0.0815587i	$0.974010\pi$
$854$	15.5474	−	6.97056i	0.532022	−	0.238528i
$855$		0			0
$856$	−5.17157			−0.176761
$857$	11.4580	−	11.4580i	0.391397	−	0.391397i	−0.483788	−	0.875185i	$-0.660739\pi$
$857$	11.4580	−	11.4580i	0.391397	−	0.391397i	0.875185	+	0.483788i	$0.160739\pi$
$858$		0			0
$859$	−40.6732			−1.38775			−0.693876	−	0.720094i	$-0.744099\pi$
$859$	−40.6732			−1.38775			−0.693876	+	0.720094i	$0.744099\pi$
$860$	−8.28772	+	9.55582i	−0.282609	+	0.325851i
$861$		0			0
$862$	−4.00000	−	4.00000i	−0.136241	−	0.136241i
$863$	2.44365	−	2.44365i	0.0831828	−	0.0831828i	−0.664291	−	0.747474i	$-0.731266\pi$
$863$	2.44365	−	2.44365i	0.0831828	−	0.0831828i	0.747474	+	0.664291i	$0.231266\pi$
$864$		0			0
$865$	−27.5355	+	31.7487i	−0.936236	+	1.07949i
$866$			14.7821i			0.502315i
$867$		0			0
$868$	−3.78470	−	1.44155i	−0.128461	−	0.0489295i
$869$		−	14.3431i		−	0.486558i
$870$		0			0
$871$			88.8463i			3.01044i
$872$	8.58579	+	8.58579i	0.290751	+	0.290751i
$873$		0			0
$874$	0.819760			0.0277288
$875$	−4.45199	+	29.2435i	−0.150505	+	0.988609i
$876$		0			0
$877$	−21.5563	−	21.5563i	−0.727906	−	0.727906i	0.242296	−	0.970202i	$-0.422099\pi$
$877$	−21.5563	−	21.5563i	−0.727906	−	0.727906i	−0.970202	+	0.242296i	$0.922099\pi$
$878$	9.81845	+	9.81845i	0.331357	+	0.331357i
$879$		0			0
$880$	0.448342	+	6.30864i	0.0151136	+	0.212664i
$881$			13.5140i			0.455297i	0.973743	+	0.227649i	$0.0731038\pi$
$881$			13.5140i			0.455297i	−0.973743	+	0.227649i	$0.926896\pi$
$882$		0			0
$883$	−28.8284	+	28.8284i	−0.970154	+	0.970154i	−0.999567	−	0.0294135i	$-0.990636\pi$
$883$	−28.8284	+	28.8284i	−0.970154	+	0.970154i	0.0294135	+	0.999567i	$0.490636\pi$
$884$		−	31.3137i		−	1.05319i
$885$		0			0
$886$	5.85786			0.196799
$887$	−32.5487	+	32.5487i	−1.09288	+	1.09288i	−0.0976580	+	0.995220i	$0.531135\pi$
$887$	−32.5487	+	32.5487i	−1.09288	+	1.09288i	−0.995220	+	0.0976580i	$0.968865\pi$
$888$		0			0
$889$	−5.48888	−	12.2426i	−0.184091	−	0.410605i
$890$	−16.6274	+	19.1716i	−0.557352	+	0.642633i
$891$		0			0
$892$	6.75699	−	6.75699i	0.226241	−	0.226241i
$893$	−1.51472	+	1.51472i	−0.0506881	+	0.0506881i
$894$		0			0
$895$	−30.4608	+	2.16478i	−1.01819	+	0.0723608i
$896$	−2.41421	+	1.08239i	−0.0806532	+	0.0361602i
$897$		0			0
$898$	18.1421	−	18.1421i	0.605411	−	0.605411i
$899$	1.26810			0.0422935
$900$		0			0
$901$			60.9217i			2.02959i
$902$	7.39104	−	7.39104i	0.246095	−	0.246095i
$903$		0			0
$904$		−	1.65685i		−	0.0551062i
$905$	−19.6066	+	1.39340i	−0.651745	+	0.0463181i
$906$		0			0
$907$	11.1716	+	11.1716i	0.370946	+	0.370946i	0.867822	−	0.496876i	$-0.165520\pi$
$907$	11.1716	+	11.1716i	0.370946	+	0.370946i	−0.496876	+	0.867822i	$0.665520\pi$
$908$	−8.38057	−	8.38057i	−0.278119	−	0.278119i
$909$		0			0
$910$	33.9365	+	10.2371i	1.12498	+	0.339358i
$911$	28.1421			0.932391			0.466195	−	0.884682i	$-0.345624\pi$
$911$	28.1421			0.932391			0.466195	+	0.884682i	$0.345624\pi$
$912$		0			0
$913$	−15.0447	−	15.0447i	−0.497907	−	0.497907i
$914$		−	2.34315i		−	0.0775044i
$915$		0			0
$916$		−	7.70806i		−	0.254682i
$917$	−13.7972	+	36.2236i	−0.455624	+	1.19621i
$918$		0			0
$919$			8.38478i			0.276588i	0.990391	+	0.138294i	$0.0441619\pi$
$919$			8.38478i			0.276588i	−0.990391	+	0.138294i	$0.955838\pi$
$920$	1.30656	−	0.0928546i	0.0430761	−	0.00306132i
$921$		0			0
$922$	−24.0593	+	24.0593i	−0.792352	+	0.792352i
$923$	2.48181	+	2.48181i	0.0816898	+	0.0816898i
$924$		0			0
$925$	−14.6274	−	10.9706i	−0.480947	−	0.360710i
$926$	−18.3431			−0.602793
$927$		0			0
$928$	0.585786	−	0.585786i	0.0192294	−	0.0192294i
$929$	−33.2597			−1.09121			−0.545607	−	0.838041i	$-0.683701\pi$
$929$	−33.2597			−1.09121			−0.545607	+	0.838041i	$0.683701\pi$
$930$		0			0
$931$	−7.31371	−	6.51688i	−0.239697	−	0.213582i
$932$	−3.00000	−	3.00000i	−0.0982683	−	0.0982683i
$933$		0			0
$934$	24.6549			0.806734
$935$	24.9706	+	21.6569i	0.816625	+	0.708255i
$936$		0			0
$937$	17.7666	−	17.7666i	0.580410	−	0.580410i	−0.354606	−	0.935016i	$-0.615385\pi$
$937$	17.7666	−	17.7666i	0.580410	−	0.580410i	0.935016	+	0.354606i	$0.115385\pi$
$938$	13.9645	−	36.6629i	0.455958	−	1.19709i
$939$		0			0
$940$	−2.24264	+	2.58579i	−0.0731469	+	0.0843391i
$941$		−	23.3099i		−	0.759881i	−0.925011	−	0.379940i	$-0.875944\pi$
$941$		−	23.3099i		−	0.759881i	0.925011	−	0.379940i	$-0.124056\pi$
$942$		0			0
$943$	−1.53073	−	1.53073i	−0.0498475	−	0.0498475i
$944$	9.23880			0.300697
$945$		0			0
$946$	−16.0000			−0.520205
$947$	−22.9706	−	22.9706i	−0.746443	−	0.746443i	0.227366	−	0.973809i	$-0.426989\pi$
$947$	−22.9706	−	22.9706i	−0.746443	−	0.746443i	−0.973809	+	0.227366i	$0.926989\pi$
$948$		0			0
$949$		−	35.1127i		−	1.13981i
$950$	5.59767	+	4.19825i	0.181612	+	0.136209i
$951$		0			0
$952$	−4.92177	+	12.9218i	−0.159515	+	0.418797i
$953$	−23.1421	+	23.1421i	−0.749647	+	0.749647i	−0.974413	−	0.224766i	$-0.927838\pi$
$953$	−23.1421	+	23.1421i	−0.749647	+	0.749647i	0.224766	+	0.974413i	$0.427838\pi$
$954$		0			0
$955$	−0.278564	−	3.91969i	−0.00901411	−	0.126838i
$956$	−6.48528			−0.209749
$957$		0			0
$958$	−7.83938	−	7.83938i	−0.253279	−	0.253279i
$959$	−12.5085	−	27.8995i	−0.403921	−	0.900922i
$960$		0			0
$961$	28.6569			0.924415
$962$	−15.4930	+	15.4930i	−0.499516	+	0.499516i
$963$		0			0
$964$	−6.75699			−0.217628
$965$	19.6913	+	17.0782i	0.633885	+	0.549766i
$966$		0			0
$967$	−2.21320	−	2.21320i	−0.0711718	−	0.0711718i	0.670625	−	0.741797i	$-0.266026\pi$
$967$	−2.21320	−	2.21320i	−0.0711718	−	0.0711718i	−0.741797	+	0.670625i	$0.766026\pi$
$968$	2.12132	−	2.12132i	0.0681818	−	0.0681818i
$969$		0			0
$970$	1.02944	+	14.4853i	0.0330532	+	0.465094i
$971$			18.5320i			0.594720i	0.954765	+	0.297360i	$0.0961061\pi$
$971$			18.5320i			0.594720i	−0.954765	+	0.297360i	$0.903894\pi$
$972$		0			0
$973$	−21.2750	−	8.10343i	−0.682045	−	0.259784i
$974$			1.55635i			0.0498686i
$975$		0			0
$976$		−	6.43996i		−	0.206138i
$977$	25.8284	+	25.8284i	0.826325	+	0.826325i	0.987006	−	0.160682i	$-0.0513693\pi$
$977$	25.8284	+	25.8284i	0.826325	+	0.826325i	−0.160682	+	0.987006i	$0.551369\pi$
$978$		0			0
$979$	−32.1003			−1.02593
$980$	−12.3950	−	9.55842i	−0.395945	−	0.305332i
$981$		0			0
$982$	−17.7990	−	17.7990i	−0.567989	−	0.567989i
$983$	28.7444	+	28.7444i	0.916804	+	0.916804i	0.996796	−	0.0799920i	$-0.0254895\pi$
$983$	28.7444	+	28.7444i	0.916804	+	0.916804i	−0.0799920	+	0.996796i	$0.525489\pi$
$984$		0			0
$985$	1.21371	−	1.39942i	0.0386720	−	0.0445892i
$986$		−	4.32957i		−	0.137882i
$987$		0			0
$988$	5.92893	−	5.92893i	0.188624	−	0.188624i
$989$			3.31371i			0.105370i
$990$		0			0
$991$	−32.5858			−1.03512			−0.517561	−	0.855646i	$-0.673160\pi$
$991$	−32.5858			−1.03512			−0.517561	+	0.855646i	$0.673160\pi$
$992$	−1.08239	+	1.08239i	−0.0343660	+	0.0343660i
$993$		0			0
$994$	−0.634051	−	1.41421i	−0.0201109	−	0.0448561i
$995$	−4.44365	−	62.5269i	−0.140873	−	1.98224i
$996$		0			0
$997$	0.464273	−	0.464273i	0.0147037	−	0.0147037i	−0.699717	−	0.714420i	$-0.746690\pi$
$997$	0.464273	−	0.464273i	0.0147037	−	0.0147037i	0.714420	+	0.699717i	$0.246690\pi$
$998$	−5.31371	+	5.31371i	−0.168203	+	0.168203i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.p.a.307.4		8
3.2	odd	2		70.2.g.a.27.1	yes	8
5.3	odd	4	inner	630.2.p.a.433.3		8
7.6	odd	2	inner	630.2.p.a.307.3		8
12.11	even	2		560.2.bj.c.97.4		8
15.2	even	4		350.2.g.a.293.3		8
15.8	even	4		70.2.g.a.13.2	yes	8
15.14	odd	2		350.2.g.a.307.4		8
21.2	odd	6		490.2.l.a.227.2		16
21.5	even	6		490.2.l.a.227.1		16
21.11	odd	6		490.2.l.a.117.3		16
21.17	even	6		490.2.l.a.117.4		16
21.20	even	2		70.2.g.a.27.2	yes	8
35.13	even	4	inner	630.2.p.a.433.4		8
60.23	odd	4		560.2.bj.c.433.1		8
84.83	odd	2		560.2.bj.c.97.1		8
105.23	even	12		490.2.l.a.423.4		16
105.38	odd	12		490.2.l.a.313.2		16
105.53	even	12		490.2.l.a.313.1		16
105.62	odd	4		350.2.g.a.293.4		8
105.68	odd	12		490.2.l.a.423.3		16
105.83	odd	4		70.2.g.a.13.1	✓	8
105.104	even	2		350.2.g.a.307.3		8
420.83	even	4		560.2.bj.c.433.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.g.a.13.1	✓	8	105.83	odd	4
70.2.g.a.13.2	yes	8	15.8	even	4
70.2.g.a.27.1	yes	8	3.2	odd	2
70.2.g.a.27.2	yes	8	21.20	even	2
350.2.g.a.293.3		8	15.2	even	4
350.2.g.a.293.4		8	105.62	odd	4
350.2.g.a.307.3		8	105.104	even	2
350.2.g.a.307.4		8	15.14	odd	2
490.2.l.a.117.3		16	21.11	odd	6
490.2.l.a.117.4		16	21.17	even	6
490.2.l.a.227.1		16	21.5	even	6
490.2.l.a.227.2		16	21.2	odd	6
490.2.l.a.313.1		16	105.53	even	12
490.2.l.a.313.2		16	105.38	odd	12
490.2.l.a.423.3		16	105.68	odd	12
490.2.l.a.423.4		16	105.23	even	12
560.2.bj.c.97.1		8	84.83	odd	2
560.2.bj.c.97.4		8	12.11	even	2
560.2.bj.c.433.1		8	60.23	odd	4
560.2.bj.c.433.4		8	420.83	even	4
630.2.p.a.307.3		8	7.6	odd	2	inner
630.2.p.a.307.4		8	1.1	even	1	trivial
630.2.p.a.433.3		8	5.3	odd	4	inner
630.2.p.a.433.4		8	35.13	even	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.158513 + 2.23044i) q^{5} +(-2.47247 - 0.941740i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.46508 + 1.68925i) q^{10} -2.82843 q^{11} +(4.23671 + 4.23671i) q^{13} +(-1.08239 - 2.41421i) q^{14} -1.00000 q^{16} +(-3.69552 + 3.69552i) q^{17} -1.39942 q^{19} +(-2.23044 + 0.158513i) q^{20} +(-2.00000 - 2.00000i) q^{22} +(-0.414214 + 0.414214i) q^{23} +(-4.94975 + 0.707107i) q^{25} +5.99162i q^{26} +(0.941740 - 2.47247i) q^{28} +0.828427i q^{29} -1.53073i q^{31} +(-0.707107 - 0.707107i) q^{32} -5.22625 q^{34} +(1.70858 - 5.66399i) q^{35} +(2.58579 + 2.58579i) q^{37} +(-0.989538 - 0.989538i) q^{38} +(-1.68925 - 1.46508i) q^{40} +3.69552i q^{41} +(4.00000 - 4.00000i) q^{43} -2.82843i q^{44} -0.585786 q^{46} +(1.08239 - 1.08239i) q^{47} +(5.22625 + 4.65685i) q^{49} +(-4.00000 - 3.00000i) q^{50} +(-4.23671 + 4.23671i) q^{52} +(8.24264 - 8.24264i) q^{53} +(-0.448342 - 6.30864i) q^{55} +(2.41421 - 1.08239i) q^{56} +(-0.585786 + 0.585786i) q^{58} -9.23880 q^{59} +6.43996i q^{61} +(1.08239 - 1.08239i) q^{62} -1.00000i q^{64} +(-8.77817 + 10.1213i) q^{65} +(10.4853 + 10.4853i) q^{67} +(-3.69552 - 3.69552i) q^{68} +(5.21319 - 2.79690i) q^{70} +0.585786 q^{71} +(-4.14386 - 4.14386i) q^{73} +3.65685i q^{74} -1.39942i q^{76} +(6.99321 + 2.66364i) q^{77} +5.07107i q^{79} +(-0.158513 - 2.23044i) q^{80} +(-2.61313 + 2.61313i) q^{82} +(5.31911 + 5.31911i) q^{83} +(-8.82843 - 7.65685i) q^{85} +5.65685 q^{86} +(2.00000 - 2.00000i) q^{88} +11.3492 q^{89} +(-6.48528 - 14.4650i) q^{91} +(-0.414214 - 0.414214i) q^{92} +1.53073 q^{94} +(-0.221825 - 3.12132i) q^{95} +(4.59220 - 4.59220i) q^{97} +(0.402625 + 6.98841i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7} - 8 q^{16} - 16 q^{22} + 8 q^{23} + 8 q^{28} + 8 q^{35} + 32 q^{37} + 32 q^{43} - 16 q^{46} - 32 q^{50} + 32 q^{53} + 8 q^{56} - 16 q^{58} - 8 q^{65} + 16 q^{67} - 24 q^{70} + 16 q^{71} + 16 q^{77}+ \cdots - 32 q^{98}+O(q^{100}) \) 8 * q - 8 * q^7 - 8 * q^16 - 16 * q^22 + 8 * q^23 + 8 * q^28 + 8 * q^35 + 32 * q^37 + 32 * q^43 - 16 * q^46 - 32 * q^50 + 32 * q^53 + 8 * q^56 - 16 * q^58 - 8 * q^65 + 16 * q^67 - 24 * q^70 + 16 * q^71 + 16 * q^77 - 48 * q^85 + 16 * q^88 + 16 * q^91 + 8 * q^92 - 64 * q^95 - 32 * q^98

Introduction

L-functions

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