LMFDB - Embedded newform 630.2.p.a.307.1

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)

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")

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);

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			307.1
Root			$0.382683 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	630.307
Dual form			630.2.p.a.433.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.23044 + 0.158513i) q^{5} +(-2.14065 + 1.55487i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.68925 + 1.46508i) q^{10} +2.82843 q^{11} +(-2.83730 - 2.83730i) q^{13} +(2.61313 + 0.414214i) q^{14} -1.00000 q^{16} +(1.53073 - 1.53073i) q^{17} +7.07401 q^{19} +(-0.158513 - 2.23044i) q^{20} +(-2.00000 - 2.00000i) q^{22} +(2.41421 - 2.41421i) q^{23} +(4.94975 - 0.707107i) q^{25} +4.01254i q^{26} +(-1.55487 - 2.14065i) q^{28} -4.82843i q^{29} -3.69552i q^{31} +(0.707107 + 0.707107i) q^{32} -2.16478 q^{34} +(4.52814 - 3.80736i) q^{35} +(5.41421 + 5.41421i) q^{37} +(-5.00208 - 5.00208i) q^{38} +(-1.46508 + 1.68925i) q^{40} -1.53073i q^{41} +(4.00000 - 4.00000i) q^{43} +2.82843i q^{44} -3.41421 q^{46} +(-2.61313 + 2.61313i) q^{47} +(2.16478 - 6.65685i) q^{49} +(-4.00000 - 3.00000i) q^{50} +(2.83730 - 2.83730i) q^{52} +(-0.242641 + 0.242641i) q^{53} +(-6.30864 + 0.448342i) q^{55} +(-0.414214 + 2.61313i) q^{56} +(-3.41421 + 3.41421i) q^{58} +3.82683 q^{59} +10.3212i q^{61} +(-2.61313 + 2.61313i) q^{62} -1.00000i q^{64} +(6.77817 + 5.87868i) q^{65} +(-6.48528 - 6.48528i) q^{67} +(1.53073 + 1.53073i) q^{68} +(-5.89409 - 0.509666i) q^{70} +3.41421 q^{71} +(-4.77791 - 4.77791i) q^{73} -7.65685i q^{74} +7.07401i q^{76} +(-6.05468 + 4.39782i) q^{77} -9.07107i q^{79} +(2.23044 - 0.158513i) q^{80} +(-1.08239 + 1.08239i) q^{82} +(-5.45042 - 5.45042i) q^{83} +(-3.17157 + 3.65685i) q^{85} -5.65685 q^{86} +(2.00000 - 2.00000i) q^{88} +16.9469 q^{89} +(10.4853 + 1.66205i) q^{91} +(2.41421 + 2.41421i) q^{92} +3.69552 q^{94} +(-15.7782 + 1.12132i) q^{95} +(11.0866 - 11.0866i) q^{97} +(-6.23784 + 3.17637i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.23044	+	0.158513i	−0.997484	+	0.0708890i
$5$	−2.23044	+	0.158513i	−0.997484	+	0.0708890i
$6$		0			0
$7$	−2.14065	+	1.55487i	−0.809091	+	0.587684i
$7$	−2.14065	+	1.55487i	−0.809091	+	0.587684i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	1.68925	+	1.46508i	0.534187	+	0.463298i
$11$	2.82843			0.852803			0.426401	−	0.904534i	$-0.359781\pi$
$11$	2.82843			0.852803			0.426401	+	0.904534i	$0.359781\pi$
$12$		0			0
$13$	−2.83730	−	2.83730i	−0.786925	−	0.786925i	0.194064	−	0.980989i	$-0.437833\pi$
$13$	−2.83730	−	2.83730i	−0.786925	−	0.786925i	−0.980989	+	0.194064i	$0.937833\pi$
$14$	2.61313	+	0.414214i	0.698387	+	0.110703i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.53073	−	1.53073i	0.371257	−	0.371257i	−0.496678	−	0.867935i	$-0.665447\pi$
$17$	1.53073	−	1.53073i	0.371257	−	0.371257i	0.867935	+	0.496678i	$0.165447\pi$
$18$		0			0
$19$	7.07401			1.62289			0.811445	−	0.584429i	$-0.198682\pi$
$19$	7.07401			1.62289			0.811445	+	0.584429i	$0.198682\pi$
$20$	−0.158513	−	2.23044i	−0.0354445	−	0.498742i
$21$		0			0
$22$	−2.00000	−	2.00000i	−0.426401	−	0.426401i
$23$	2.41421	−	2.41421i	0.503398	−	0.503398i	−0.409094	−	0.912492i	$-0.634155\pi$
$23$	2.41421	−	2.41421i	0.503398	−	0.503398i	0.912492	+	0.409094i	$0.134155\pi$
$24$		0			0
$25$	4.94975	−	0.707107i	0.989949	−	0.141421i
$26$			4.01254i			0.786925i
$27$		0			0
$28$	−1.55487	−	2.14065i	−0.293842	−	0.404545i
$29$		−	4.82843i		−	0.896616i	−0.893879	−	0.448308i	$-0.852027\pi$
$29$		−	4.82843i		−	0.896616i	0.893879	−	0.448308i	$-0.147973\pi$
$30$		0			0
$31$		−	3.69552i		−	0.663735i	−0.943326	−	0.331867i	$-0.892321\pi$
$31$		−	3.69552i		−	0.663735i	0.943326	−	0.331867i	$-0.107679\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	−2.16478			−0.371257
$35$	4.52814	−	3.80736i	0.765395	−	0.643561i
$36$		0			0
$37$	5.41421	+	5.41421i	0.890091	+	0.890091i	0.994531	−	0.104440i	$-0.0333050\pi$
$37$	5.41421	+	5.41421i	0.890091	+	0.890091i	−0.104440	+	0.994531i	$0.533305\pi$
$38$	−5.00208	−	5.00208i	−0.811445	−	0.811445i
$39$		0			0
$40$	−1.46508	+	1.68925i	−0.231649	+	0.267093i
$41$		−	1.53073i		−	0.239060i	−0.992831	−	0.119530i	$-0.961861\pi$
$41$		−	1.53073i		−	0.239060i	0.992831	−	0.119530i	$-0.0381388\pi$
$42$		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
$46$	−3.41421			−0.503398
$47$	−2.61313	+	2.61313i	−0.381164	+	0.381164i	−0.871521	−	0.490358i	$-0.836866\pi$
$47$	−2.61313	+	2.61313i	−0.381164	+	0.381164i	0.490358	+	0.871521i	$0.336866\pi$
$48$		0			0
$49$	2.16478	−	6.65685i	0.309255	−	0.950979i
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$		0			0
$52$	2.83730	−	2.83730i	0.393462	−	0.393462i
$53$	−0.242641	+	0.242641i	−0.0333293	+	0.0333293i	−0.723575	−	0.690246i	$-0.757502\pi$
$53$	−0.242641	+	0.242641i	−0.0333293	+	0.0333293i	0.690246	+	0.723575i	$0.257502\pi$
$54$		0			0
$55$	−6.30864	+	0.448342i	−0.850657	+	0.0604544i
$56$	−0.414214	+	2.61313i	−0.0553516	+	0.349194i
$57$		0			0
$58$	−3.41421	+	3.41421i	−0.448308	+	0.448308i
$59$	3.82683			0.498211			0.249106	−	0.968476i	$-0.419863\pi$
$59$	3.82683			0.498211			0.249106	+	0.968476i	$0.419863\pi$
$60$		0			0
$61$			10.3212i			1.32149i	0.750609	+	0.660746i	$0.229760\pi$
$61$			10.3212i			1.32149i	−0.750609	+	0.660746i	$0.770240\pi$
$62$	−2.61313	+	2.61313i	−0.331867	+	0.331867i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	6.77817	+	5.87868i	0.840729	+	0.729160i
$66$		0			0
$67$	−6.48528	−	6.48528i	−0.792303	−	0.792303i	0.189565	−	0.981868i	$-0.439292\pi$
$67$	−6.48528	−	6.48528i	−0.792303	−	0.792303i	−0.981868	+	0.189565i	$0.939292\pi$
$68$	1.53073	+	1.53073i	0.185629	+	0.185629i
$69$		0			0
$70$	−5.89409	−	0.509666i	−0.704478	−	0.0609167i
$71$	3.41421			0.405193			0.202596	−	0.979262i	$-0.435062\pi$
$71$	3.41421			0.405193			0.202596	+	0.979262i	$0.435062\pi$
$72$		0			0
$73$	−4.77791	−	4.77791i	−0.559212	−	0.559212i	0.369871	−	0.929083i	$-0.379402\pi$
$73$	−4.77791	−	4.77791i	−0.559212	−	0.559212i	−0.929083	+	0.369871i	$0.879402\pi$
$74$		−	7.65685i		−	0.890091i
$75$		0			0
$76$			7.07401i			0.811445i
$77$	−6.05468	+	4.39782i	−0.689995	+	0.501179i
$78$		0			0
$79$		−	9.07107i		−	1.02057i	−0.860004	−	0.510287i	$-0.829539\pi$
$79$		−	9.07107i		−	1.02057i	0.860004	−	0.510287i	$-0.170461\pi$
$80$	2.23044	−	0.158513i	0.249371	−	0.0177223i
$81$		0			0
$82$	−1.08239	+	1.08239i	−0.119530	+	0.119530i
$83$	−5.45042	−	5.45042i	−0.598262	−	0.598262i	0.341588	−	0.939850i	$-0.389035\pi$
$83$	−5.45042	−	5.45042i	−0.598262	−	0.598262i	−0.939850	+	0.341588i	$0.889035\pi$
$84$		0			0
$85$	−3.17157	+	3.65685i	−0.344005	+	0.396642i
$86$	−5.65685			−0.609994
$87$		0			0
$88$	2.00000	−	2.00000i	0.213201	−	0.213201i
$89$	16.9469			1.79636			0.898182	−	0.439625i	$-0.144889\pi$
$89$	16.9469			1.79636			0.898182	+	0.439625i	$0.144889\pi$
$90$		0			0
$91$	10.4853	+	1.66205i	1.09916	+	0.174230i
$92$	2.41421	+	2.41421i	0.251699	+	0.251699i
$93$		0			0
$94$	3.69552			0.381164
$95$	−15.7782	+	1.12132i	−1.61881	+	0.115045i
$96$		0			0
$97$	11.0866	−	11.0866i	1.12567	−	1.12567i	0.134796	−	0.990873i	$-0.456962\pi$
$97$	11.0866	−	11.0866i	1.12567	−	1.12567i	0.990873	−	0.134796i	$-0.0430378\pi$
$98$	−6.23784	+	3.17637i	−0.630117	+	0.320862i
$99$		0			0
$100$	0.707107	+	4.94975i	0.0707107	+	0.494975i
$101$		−	11.8519i		−	1.17931i	−0.807655	−	0.589655i	$-0.799264\pi$
$101$		−	11.8519i		−	1.17931i	0.807655	−	0.589655i	$-0.200736\pi$
$102$		0			0
$103$	−1.97908	−	1.97908i	−0.195004	−	0.195004i	0.602850	−	0.797854i	$-0.294032\pi$
$103$	−1.97908	−	1.97908i	−0.195004	−	0.195004i	−0.797854	+	0.602850i	$0.794032\pi$
$104$	−4.01254			−0.393462
$105$		0			0
$106$	0.343146			0.0333293
$107$	−7.65685	−	7.65685i	−0.740216	−	0.740216i	0.232403	−	0.972619i	$-0.425341\pi$
$107$	−7.65685	−	7.65685i	−0.740216	−	0.740216i	−0.972619	+	0.232403i	$0.925341\pi$
$108$		0			0
$109$			16.1421i			1.54614i	0.634323	+	0.773068i	$0.281279\pi$
$109$			16.1421i			1.54614i	−0.634323	+	0.773068i	$0.718721\pi$
$110$	4.77791	+	4.14386i	0.455556	+	0.395102i
$111$		0			0
$112$	2.14065	−	1.55487i	0.202273	−	0.146921i
$113$	−6.82843	+	6.82843i	−0.642364	+	0.642364i	−0.951136	−	0.308772i	$-0.900082\pi$
$113$	−6.82843	+	6.82843i	−0.642364	+	0.642364i	0.308772	+	0.951136i	$0.400082\pi$
$114$		0			0
$115$	−5.00208	+	5.76745i	−0.466446	+	0.537817i
$116$	4.82843			0.448308
$117$		0			0
$118$	−2.70598	−	2.70598i	−0.249106	−	0.249106i
$119$	−0.896683	+	5.65685i	−0.0821988	+	0.518563i
$120$		0			0
$121$	−3.00000			−0.272727
$122$	7.29818	−	7.29818i	0.660746	−	0.660746i
$123$		0			0
$124$	3.69552			0.331867
$125$	−10.9280	+	2.36176i	−0.977434	+	0.211242i
$126$		0			0
$127$	6.41421	+	6.41421i	0.569169	+	0.569169i	0.931896	−	0.362726i	$-0.118154\pi$
$127$	6.41421	+	6.41421i	0.569169	+	0.569169i	−0.362726	+	0.931896i	$0.618154\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−0.636039	−	8.94975i	−0.0557843	−	0.784945i
$131$			16.8925i			1.47590i	0.674855	+	0.737951i	$0.264206\pi$
$131$			16.8925i			1.47590i	−0.674855	+	0.737951i	$0.735794\pi$
$132$		0			0
$133$	−15.1430	+	10.9991i	−1.31306	+	0.953746i
$134$			9.17157i			0.792303i
$135$		0			0
$136$		−	2.16478i		−	0.185629i
$137$	13.8284	+	13.8284i	1.18144	+	1.18144i	0.979371	+	0.202071i	$0.0647673\pi$
$137$	13.8284	+	13.8284i	1.18144	+	1.18144i	0.202071	+	0.979371i	$0.435233\pi$
$138$		0			0
$139$	5.09494			0.432147			0.216073	−	0.976377i	$-0.430675\pi$
$139$	5.09494			0.432147			0.216073	+	0.976377i	$0.430675\pi$
$140$	3.80736	+	4.52814i	0.321781	+	0.382697i
$141$		0			0
$142$	−2.41421	−	2.41421i	−0.202596	−	0.202596i
$143$	−8.02509	−	8.02509i	−0.671091	−	0.671091i
$144$		0			0
$145$	0.765367	+	10.7695i	0.0635603	+	0.894361i
$146$			6.75699i			0.559212i
$147$		0			0
$148$	−5.41421	+	5.41421i	−0.445046	+	0.445046i
$149$			5.31371i			0.435316i	0.976025	+	0.217658i	$0.0698417\pi$
$149$			5.31371i			0.435316i	−0.976025	+	0.217658i	$0.930158\pi$
$150$		0			0
$151$	−3.17157			−0.258099			−0.129049	−	0.991638i	$-0.541193\pi$
$151$	−3.17157			−0.258099			−0.129049	+	0.991638i	$0.541193\pi$
$152$	5.00208	−	5.00208i	0.405722	−	0.405722i
$153$		0			0
$154$	7.39104	+	1.17157i	0.595587	+	0.0944080i
$155$	0.585786	+	8.24264i	0.0470515	+	0.662065i
$156$		0			0
$157$	−1.17525	+	1.17525i	−0.0937949	+	0.0937949i	−0.752447	−	0.658652i	$-0.771127\pi$
$157$	−1.17525	+	1.17525i	−0.0937949	+	0.0937949i	0.658652	+	0.752447i	$0.271127\pi$
$158$	−6.41421	+	6.41421i	−0.510287	+	0.510287i
$159$		0			0
$160$	−1.68925	−	1.46508i	−0.133547	−	0.115824i
$161$	−1.41421	+	8.92177i	−0.111456	+	0.703134i
$162$		0			0
$163$	2.34315	−	2.34315i	0.183529	−	0.183529i	−0.609362	−	0.792892i	$-0.708575\pi$
$163$	2.34315	−	2.34315i	0.183529	−	0.183529i	0.792892	+	0.609362i	$0.208575\pi$
$164$	1.53073			0.119530
$165$		0			0
$166$			7.70806i			0.598262i
$167$	11.5349	−	11.5349i	0.892597	−	0.892597i	−0.102170	−	0.994767i	$-0.532579\pi$
$167$	11.5349	−	11.5349i	0.892597	−	0.892597i	0.994767	+	0.102170i	$0.0325785\pi$
$168$		0			0
$169$			3.10051i			0.238500i
$170$	4.82843	−	0.343146i	0.370323	−	0.0263181i
$171$		0			0
$172$	4.00000	+	4.00000i	0.304997	+	0.304997i
$173$	8.56628	+	8.56628i	0.651282	+	0.651282i	0.953302	−	0.302019i	$-0.0976607\pi$
$173$	8.56628	+	8.56628i	0.651282	+	0.651282i	−0.302019	+	0.953302i	$0.597661\pi$
$174$		0			0
$175$	−9.49623	+	9.20986i	−0.717848	+	0.696200i
$176$	−2.82843			−0.213201
$177$		0			0
$178$	−11.9832	−	11.9832i	−0.898182	−	0.898182i
$179$			2.34315i			0.175135i	0.996159	+	0.0875675i	$0.0279093\pi$
$179$			2.34315i			0.175135i	−0.996159	+	0.0875675i	$0.972091\pi$
$180$		0			0
$181$		−	10.1355i		−	0.753364i	−0.926343	−	0.376682i	$-0.877065\pi$
$181$		−	10.1355i		−	0.753364i	0.926343	−	0.376682i	$-0.122935\pi$
$182$	−6.23897	−	8.58946i	−0.462463	−	0.636693i
$183$		0			0
$184$		−	3.41421i		−	0.251699i
$185$	−12.9343	−	11.2179i	−0.950950	−	0.824754i
$186$		0			0
$187$	4.32957	−	4.32957i	0.316609	−	0.316609i
$188$	−2.61313	−	2.61313i	−0.190582	−	0.190582i
$189$		0			0
$190$	11.9497	+	10.3640i	0.866926	+	0.751881i
$191$	−10.2426			−0.741131			−0.370566	−	0.928806i	$-0.620836\pi$
$191$	−10.2426			−0.741131			−0.370566	+	0.928806i	$0.620836\pi$
$192$		0			0
$193$	−0.242641	+	0.242641i	−0.0174657	+	0.0174657i	−0.715786	−	0.698320i	$-0.753931\pi$
$193$	−0.242641	+	0.242641i	−0.0174657	+	0.0174657i	0.698320	+	0.715786i	$0.253931\pi$
$194$	−15.6788			−1.12567
$195$		0			0
$196$	6.65685	+	2.16478i	0.475490	+	0.154627i
$197$	−3.41421	−	3.41421i	−0.243253	−	0.243253i	0.574942	−	0.818194i	$-0.305025\pi$
$197$	−3.41421	−	3.41421i	−0.243253	−	0.243253i	−0.818194	+	0.574942i	$0.805025\pi$
$198$		0			0
$199$	15.9414			1.13006			0.565028	−	0.825072i	$-0.308866\pi$
$199$	15.9414			1.13006			0.565028	+	0.825072i	$0.308866\pi$
$200$	3.00000	−	4.00000i	0.212132	−	0.282843i
$201$		0			0
$202$	−8.38057	+	8.38057i	−0.589655	+	0.589655i
$203$	7.50756	+	10.3360i	0.526927	+	0.725444i
$204$		0			0
$205$	0.242641	+	3.41421i	0.0169468	+	0.238459i
$206$			2.79884i			0.195004i
$207$		0			0
$208$	2.83730	+	2.83730i	0.196731	+	0.196731i
$209$	20.0083			1.38400
$210$		0			0
$211$	−21.6569			−1.49092			−0.745460	−	0.666551i	$-0.767770\pi$
$211$	−21.6569			−1.49092			−0.745460	+	0.666551i	$0.767770\pi$
$212$	−0.242641	−	0.242641i	−0.0166646	−	0.0166646i
$213$		0			0
$214$			10.8284i			0.740216i
$215$	−8.28772	+	9.55582i	−0.565218	+	0.651702i
$216$		0			0
$217$	5.74603	+	7.91082i	0.390066	+	0.537021i
$218$	11.4142	−	11.4142i	0.773068	−	0.773068i
$219$		0			0
$220$	−0.448342	−	6.30864i	−0.0302272	−	0.425329i
$221$	−8.68629			−0.584303
$222$		0			0
$223$	−5.86030	−	5.86030i	−0.392435	−	0.392435i	0.483120	−	0.875554i	$-0.339504\pi$
$223$	−5.86030	−	5.86030i	−0.392435	−	0.392435i	−0.875554	+	0.483120i	$0.839504\pi$
$224$	−2.61313	−	0.414214i	−0.174597	−	0.0276758i
$225$		0			0
$226$	9.65685			0.642364
$227$	−1.94061	+	1.94061i	−0.128803	+	0.128803i	−0.768569	−	0.639766i	$-0.779031\pi$
$227$	−1.94061	+	1.94061i	−0.128803	+	0.128803i	0.639766	+	0.768569i	$0.279031\pi$
$228$		0			0
$229$	7.52235			0.497091			0.248546	−	0.968620i	$-0.420047\pi$
$229$	7.52235			0.497091			0.248546	+	0.968620i	$0.420047\pi$
$230$	7.61521	−	0.541196i	0.502132	−	0.0356854i
$231$		0			0
$232$	−3.41421	−	3.41421i	−0.224154	−	0.224154i
$233$	−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
$235$	5.41421	−	6.24264i	0.353184	−	0.407225i
$236$			3.82683i			0.249106i
$237$		0			0
$238$	4.63405	−	3.36595i	0.300381	−	0.218182i
$239$		−	10.4853i		−	0.678236i	−0.940744	−	0.339118i	$-0.889871\pi$
$239$		−	10.4853i		−	0.678236i	0.940744	−	0.339118i	$-0.110129\pi$
$240$		0			0
$241$			5.86030i			0.377495i	0.982026	+	0.188748i	$0.0604428\pi$
$241$			5.86030i			0.377495i	−0.982026	+	0.188748i	$0.939557\pi$
$242$	2.12132	+	2.12132i	0.136364	+	0.136364i
$243$		0			0
$244$	−10.3212			−0.660746
$245$	−3.77323	+	15.1909i	−0.241063	+	0.970509i
$246$		0			0
$247$	−20.0711	−	20.0711i	−1.27709	−	1.27709i
$248$	−2.61313	−	2.61313i	−0.165934	−	0.165934i
$249$		0			0
$250$	9.39731	+	6.05728i	0.594338	+	0.383096i
$251$		−	28.7988i		−	1.81776i	−0.417055	−	0.908881i	$-0.636938\pi$
$251$		−	28.7988i		−	1.81776i	0.417055	−	0.908881i	$-0.363062\pi$
$252$		0			0
$253$	6.82843	−	6.82843i	0.429300	−	0.429300i
$254$		−	9.07107i		−	0.569169i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−3.24718	+	3.24718i	−0.202553	+	0.202553i	−0.801093	−	0.598540i	$-0.795748\pi$
$257$	−3.24718	+	3.24718i	−0.202553	+	0.202553i	0.598540	+	0.801093i	$0.295748\pi$
$258$		0			0
$259$	−20.0083	−	3.17157i	−1.24326	−	0.197072i
$260$	−5.87868	+	6.77817i	−0.364580	+	0.420365i
$261$		0			0
$262$	11.9448	−	11.9448i	0.737951	−	0.737951i
$263$	16.5858	−	16.5858i	1.02272	−	1.02272i	0.0229877	−	0.999736i	$-0.492682\pi$
$263$	16.5858	−	16.5858i	1.02272	−	1.02272i	0.999736	−	0.0229877i	$-0.00731784\pi$
$264$		0			0
$265$	0.502734	−	0.579658i	0.0308827	−	0.0356081i
$266$	18.4853	+	2.93015i	1.13341	+	0.179659i
$267$		0			0
$268$	6.48528	−	6.48528i	0.396152	−	0.396152i
$269$	−12.6717			−0.772606			−0.386303	−	0.922372i	$-0.626248\pi$
$269$	−12.6717			−0.772606			−0.386303	+	0.922372i	$0.626248\pi$
$270$		0			0
$271$		−	13.8854i		−	0.843477i	−0.906717	−	0.421739i	$-0.861420\pi$
$271$		−	13.8854i		−	0.843477i	0.906717	−	0.421739i	$-0.138580\pi$
$272$	−1.53073	+	1.53073i	−0.0928144	+	0.0928144i
$273$		0			0
$274$		−	19.5563i		−	1.18144i
$275$	14.0000	−	2.00000i	0.844232	−	0.120605i
$276$		0			0
$277$	−10.2426	−	10.2426i	−0.615421	−	0.615421i	0.328933	−	0.944353i	$-0.393311\pi$
$277$	−10.2426	−	10.2426i	−0.615421	−	0.615421i	−0.944353	+	0.328933i	$0.893311\pi$
$278$	−3.60266	−	3.60266i	−0.216073	−	0.216073i
$279$		0			0
$280$	0.509666	−	5.89409i	0.0304584	−	0.352239i
$281$	−5.65685			−0.337460			−0.168730	−	0.985662i	$-0.553967\pi$
$281$	−5.65685			−0.337460			−0.168730	+	0.985662i	$0.553967\pi$
$282$		0			0
$283$	0.224171	+	0.224171i	0.0133256	+	0.0133256i	0.713738	−	0.700413i	$-0.247001\pi$
$283$	0.224171	+	0.224171i	0.0133256	+	0.0133256i	−0.700413	+	0.713738i	$0.747001\pi$
$284$			3.41421i			0.202596i
$285$		0			0
$286$			11.3492i			0.671091i
$287$	2.38009	+	3.27677i	0.140492	+	0.193422i
$288$		0			0
$289$			12.3137i			0.724336i
$290$	7.07401	−	8.15640i	0.415400	−	0.478960i
$291$		0			0
$292$	4.77791	−	4.77791i	0.279606	−	0.279606i
$293$	2.07193	+	2.07193i	0.121043	+	0.121043i	0.765034	−	0.643990i	$-0.222722\pi$
$293$	2.07193	+	2.07193i	0.121043	+	0.121043i	−0.643990	+	0.765034i	$0.722722\pi$
$294$		0			0
$295$	−8.53553	+	0.606602i	−0.496958	+	0.0353177i
$296$	7.65685			0.445046
$297$		0			0
$298$	3.75736	−	3.75736i	0.217658	−	0.217658i
$299$	−13.6997			−0.792273
$300$		0			0
$301$	−2.34315	+	14.7821i	−0.135057	+	0.852024i
$302$	2.24264	+	2.24264i	0.129049	+	0.129049i
$303$		0			0
$304$	−7.07401			−0.405722
$305$	−1.63604	−	23.0208i	−0.0936793	−	1.31817i
$306$		0			0
$307$	4.18232	−	4.18232i	0.238698	−	0.238698i	−0.577613	−	0.816311i	$-0.696016\pi$
$307$	4.18232	−	4.18232i	0.238698	−	0.238698i	0.816311	+	0.577613i	$0.196016\pi$
$308$	−4.39782	−	6.05468i	−0.250589	−	0.344997i
$309$		0			0
$310$	5.41421	−	6.24264i	0.307507	−	0.354558i
$311$		−	23.0698i		−	1.30817i	−0.756422	−	0.654084i	$-0.773054\pi$
$311$		−	23.0698i		−	1.30817i	0.756422	−	0.654084i	$-0.226946\pi$
$312$		0			0
$313$	5.86030	+	5.86030i	0.331244	+	0.331244i	0.853059	−	0.521815i	$-0.174745\pi$
$313$	5.86030	+	5.86030i	0.331244	+	0.331244i	−0.521815	+	0.853059i	$0.674745\pi$
$314$	1.66205			0.0937949
$315$		0			0
$316$	9.07107			0.510287
$317$	−2.10051	−	2.10051i	−0.117976	−	0.117976i	0.645654	−	0.763630i	$-0.276585\pi$
$317$	−2.10051	−	2.10051i	−0.117976	−	0.117976i	−0.763630	+	0.645654i	$0.776585\pi$
$318$		0			0
$319$		−	13.6569i		−	0.764637i
$320$	0.158513	+	2.23044i	0.00886113	+	0.124686i
$321$		0			0
$322$	7.30864	−	5.30864i	0.407295	−	0.295839i
$323$	10.8284	−	10.8284i	0.602510	−	0.602510i
$324$		0			0
$325$	−16.0502	−	12.0376i	−0.890303	−	0.667728i
$326$	−3.31371			−0.183529
$327$		0			0
$328$	−1.08239	−	1.08239i	−0.0597651	−	0.0597651i
$329$	1.53073	−	9.65685i	0.0843921	−	0.532400i
$330$		0			0
$331$	0.686292			0.0377220			0.0188610	−	0.999822i	$-0.493996\pi$
$331$	0.686292			0.0377220			0.0188610	+	0.999822i	$0.493996\pi$
$332$	5.45042	−	5.45042i	0.299131	−	0.299131i
$333$		0			0
$334$	−16.3128			−0.892597
$335$	15.4930	+	13.4370i	0.846476	+	0.734144i
$336$		0			0
$337$	12.2426	+	12.2426i	0.666899	+	0.666899i	0.956997	−	0.290098i	$-0.0936879\pi$
$337$	12.2426	+	12.2426i	0.666899	+	0.666899i	−0.290098	+	0.956997i	$0.593688\pi$
$338$	2.19239	−	2.19239i	0.119250	−	0.119250i
$339$		0			0
$340$	−3.65685	−	3.17157i	−0.198321	−	0.172003i
$341$		−	10.4525i		−	0.566035i
$342$		0			0
$343$	5.71646	+	17.6160i	0.308660	+	0.951172i
$344$		−	5.65685i		−	0.304997i
$345$		0			0
$346$		−	12.1146i		−	0.651282i
$347$	−17.3137	−	17.3137i	−0.929449	−	0.929449i	0.0682216	−	0.997670i	$-0.478268\pi$
$347$	−17.3137	−	17.3137i	−0.929449	−	0.929449i	−0.997670	+	0.0682216i	$0.978268\pi$
$348$		0			0
$349$	24.9176			1.33381			0.666903	−	0.745145i	$-0.267620\pi$
$349$	24.9176			1.33381			0.666903	+	0.745145i	$0.267620\pi$
$350$	13.2272	+	0.202493i	0.707024	+	0.0108237i
$351$		0			0
$352$	2.00000	+	2.00000i	0.106600	+	0.106600i
$353$	−5.67459	−	5.67459i	−0.302028	−	0.302028i	0.539779	−	0.841807i	$-0.318508\pi$
$353$	−5.67459	−	5.67459i	−0.302028	−	0.302028i	−0.841807	+	0.539779i	$0.818508\pi$
$354$		0			0
$355$	−7.61521	+	0.541196i	−0.404173	+	0.0287237i
$356$			16.9469i			0.898182i
$357$		0			0
$358$	1.65685	−	1.65685i	0.0875675	−	0.0875675i
$359$		−	16.9706i		−	0.895672i	−0.894116	−	0.447836i	$-0.852195\pi$
$359$		−	16.9706i		−	0.895672i	0.894116	−	0.447836i	$-0.147805\pi$
$360$		0			0
$361$	31.0416			1.63377
$362$	−7.16687	+	7.16687i	−0.376682	+	0.376682i
$363$		0			0
$364$	−1.66205	+	10.4853i	−0.0871151	+	0.549578i
$365$	11.4142	+	9.89949i	0.597447	+	0.518163i
$366$		0			0
$367$	−7.39104	+	7.39104i	−0.385809	+	0.385809i	−0.873190	−	0.487381i	$-0.837952\pi$
$367$	−7.39104	+	7.39104i	−0.385809	+	0.385809i	0.487381	+	0.873190i	$0.337952\pi$
$368$	−2.41421	+	2.41421i	−0.125850	+	0.125850i
$369$		0			0
$370$	1.21371	+	17.0782i	0.0630977	+	0.887852i
$371$	0.142136	−	0.896683i	0.00737931	−	0.0465535i
$372$		0			0
$373$	−0.928932	+	0.928932i	−0.0480983	+	0.0480983i	−0.730747	−	0.682649i	$-0.760828\pi$
$373$	−0.928932	+	0.928932i	−0.0480983	+	0.0480983i	0.682649	+	0.730747i	$0.260828\pi$
$374$	−6.12293			−0.316609
$375$		0			0
$376$			3.69552i			0.190582i
$377$	−13.6997	+	13.6997i	−0.705569	+	0.705569i
$378$		0			0
$379$		−	22.1421i		−	1.13737i	−0.822557	−	0.568683i	$-0.807453\pi$
$379$		−	22.1421i		−	1.13737i	0.822557	−	0.568683i	$-0.192547\pi$
$380$	−1.12132	−	15.7782i	−0.0575225	−	0.809403i
$381$		0			0
$382$	7.24264	+	7.24264i	0.370566	+	0.370566i
$383$	10.9008	+	10.9008i	0.557007	+	0.557007i	0.928454	−	0.371447i	$-0.121138\pi$
$383$	10.9008	+	10.9008i	0.557007	+	0.557007i	−0.371447	+	0.928454i	$0.621138\pi$
$384$		0			0
$385$	12.8075	−	10.7688i	0.652731	−	0.548831i
$386$	0.343146			0.0174657
$387$		0			0
$388$	11.0866	+	11.0866i	0.562835	+	0.562835i
$389$			28.1421i			1.42686i	0.700725	+	0.713431i	$0.252860\pi$
$389$			28.1421i			1.42686i	−0.700725	+	0.713431i	$0.747140\pi$
$390$		0			0
$391$		−	7.39104i		−	0.373781i
$392$	−3.17637	−	6.23784i	−0.160431	−	0.315059i
$393$		0			0
$394$			4.82843i			0.243253i
$395$	1.43788	+	20.2325i	0.0723476	+	1.01801i
$396$		0			0
$397$	−15.7716	+	15.7716i	−0.791554	+	0.791554i	−0.981747	−	0.190192i	$-0.939089\pi$
$397$	−15.7716	+	15.7716i	−0.791554	+	0.791554i	0.190192	+	0.981747i	$0.439089\pi$
$398$	−11.2723	−	11.2723i	−0.565028	−	0.565028i
$399$		0			0
$400$	−4.94975	+	0.707107i	−0.247487	+	0.0353553i
$401$	28.2426			1.41037			0.705185	−	0.709023i	$-0.250864\pi$
$401$	28.2426			1.41037			0.705185	+	0.709023i	$0.250864\pi$
$402$		0			0
$403$	−10.4853	+	10.4853i	−0.522309	+	0.522309i
$404$	11.8519			0.589655
$405$		0			0
$406$	2.00000	−	12.6173i	0.0992583	−	0.626185i
$407$	15.3137	+	15.3137i	0.759072	+	0.759072i
$408$		0			0
$409$	−23.3324			−1.15371			−0.576857	−	0.816845i	$-0.695721\pi$
$409$	−23.3324			−1.15371			−0.576857	+	0.816845i	$0.695721\pi$
$410$	2.24264	−	2.58579i	0.110756	−	0.127703i
$411$		0			0
$412$	1.97908	−	1.97908i	0.0975020	−	0.0975020i
$413$	−8.19192	+	5.95021i	−0.403098	+	0.292791i
$414$		0			0
$415$	13.0208	+	11.2929i	0.639167	+	0.554346i
$416$		−	4.01254i		−	0.196731i
$417$		0			0
$418$	−14.1480	−	14.1480i	−0.692002	−	0.692002i
$419$	−24.2835			−1.18633			−0.593163	−	0.805082i	$-0.702121\pi$
$419$	−24.2835			−1.18633			−0.593163	+	0.805082i	$0.702121\pi$
$420$		0			0
$421$	−21.7990			−1.06242			−0.531209	−	0.847241i	$-0.678262\pi$
$421$	−21.7990			−1.06242			−0.531209	+	0.847241i	$0.678262\pi$
$422$	15.3137	+	15.3137i	0.745460	+	0.745460i
$423$		0			0
$424$			0.343146i			0.0166646i
$425$	6.49435	−	8.65914i	0.315022	−	0.420030i
$426$		0			0
$427$	−16.0481	−	22.0941i	−0.776620	−	1.06921i
$428$	7.65685	−	7.65685i	0.370108	−	0.370108i
$429$		0			0
$430$	12.6173	−	0.896683i	0.608460	−	0.0432419i
$431$	5.65685			0.272481			0.136241	−	0.990676i	$-0.456498\pi$
$431$	5.65685			0.272481			0.136241	+	0.990676i	$0.456498\pi$
$432$		0			0
$433$	4.32957	+	4.32957i	0.208066	+	0.208066i	0.803445	−	0.595379i	$-0.202998\pi$
$433$	4.32957	+	4.32957i	0.208066	+	0.208066i	−0.595379	+	0.803445i	$0.702998\pi$
$434$	1.53073	−	9.65685i	0.0734776	−	0.463544i
$435$		0			0
$436$	−16.1421			−0.773068
$437$	17.0782	−	17.0782i	0.816960	−	0.816960i
$438$		0			0
$439$	−18.7402			−0.894422			−0.447211	−	0.894428i	$-0.647583\pi$
$439$	−18.7402			−0.894422			−0.447211	+	0.894428i	$0.647583\pi$
$440$	−4.14386	+	4.77791i	−0.197551	+	0.227778i
$441$		0			0
$442$	6.14214	+	6.14214i	0.292152	+	0.292152i
$443$	−24.1421	+	24.1421i	−1.14703	+	1.14703i	−0.159893	+	0.987134i	$0.551115\pi$
$443$	−24.1421	+	24.1421i	−1.14703	+	1.14703i	−0.987134	+	0.159893i	$0.948885\pi$
$444$		0			0
$445$	−37.7990	+	2.68629i	−1.79184	+	0.127342i
$446$			8.28772i			0.392435i
$447$		0			0
$448$	1.55487	+	2.14065i	0.0734605	+	0.101136i
$449$		−	14.3431i		−	0.676895i	−0.940985	−	0.338447i	$-0.890098\pi$
$449$		−	14.3431i		−	0.676895i	0.940985	−	0.338447i	$-0.109902\pi$
$450$		0			0
$451$		−	4.32957i		−	0.203871i
$452$	−6.82843	−	6.82843i	−0.321182	−	0.321182i
$453$		0			0
$454$	2.74444			0.128803
$455$	−23.6503	−	2.04506i	−1.10874	−	0.0958737i
$456$		0			0
$457$	9.65685	+	9.65685i	0.451729	+	0.451729i	0.895928	−	0.444199i	$-0.146512\pi$
$457$	9.65685	+	9.65685i	0.451729	+	0.451729i	−0.444199	+	0.895928i	$0.646512\pi$
$458$	−5.31911	−	5.31911i	−0.248546	−	0.248546i
$459$		0			0
$460$	−5.76745	−	5.00208i	−0.268909	−	0.233223i
$461$		−	11.9288i		−	0.555582i	−0.960642	−	0.277791i	$-0.910398\pi$
$461$		−	11.9288i		−	0.555582i	0.960642	−	0.277791i	$-0.0896022\pi$
$462$		0			0
$463$	20.9706	−	20.9706i	0.974585	−	0.974585i	−0.0251002	−	0.999685i	$-0.507990\pi$
$463$	20.9706	−	20.9706i	0.974585	−	0.974585i	0.999685	+	0.0251002i	$0.00799049\pi$
$464$			4.82843i			0.224154i
$465$		0			0
$466$	4.24264			0.196537
$467$	13.3442	−	13.3442i	0.617496	−	0.617496i	−0.327393	−	0.944888i	$-0.606170\pi$
$467$	13.3442	−	13.3442i	0.617496	−	0.617496i	0.944888	+	0.327393i	$0.106170\pi$
$468$		0			0
$469$	23.9665	+	3.79899i	1.10667	+	0.175421i
$470$	−8.24264	+	0.585786i	−0.380205	+	0.0270203i
$471$		0			0
$472$	2.70598	−	2.70598i	0.124553	−	0.124553i
$473$	11.3137	−	11.3137i	0.520205	−	0.520205i
$474$		0			0
$475$	35.0146	−	5.00208i	1.60658	−	0.229511i
$476$	−5.65685	−	0.896683i	−0.259281	−	0.0410994i
$477$		0			0
$478$	−7.41421	+	7.41421i	−0.339118	+	0.339118i
$479$	4.59220			0.209823			0.104912	−	0.994482i	$-0.466544\pi$
$479$	4.59220			0.209823			0.104912	+	0.994482i	$0.466544\pi$
$480$		0			0
$481$		−	30.7235i		−	1.40087i
$482$	4.14386	−	4.14386i	0.188748	−	0.188748i
$483$		0			0
$484$		−	3.00000i		−	0.136364i
$485$	−22.9706	+	26.4853i	−1.04304	+	1.20263i
$486$		0			0
$487$	20.8995	+	20.8995i	0.947047	+	0.947047i	0.998667	−	0.0516203i	$-0.0164385\pi$
$487$	20.8995	+	20.8995i	0.947047	+	0.947047i	−0.0516203	+	0.998667i	$0.516439\pi$
$488$	7.29818	+	7.29818i	0.330373	+	0.330373i
$489$		0			0
$490$	13.4096	−	8.07349i	0.605786	−	0.364723i
$491$	−30.8284			−1.39127			−0.695634	−	0.718397i	$-0.744876\pi$
$491$	−30.8284			−1.39127			−0.695634	+	0.718397i	$0.744876\pi$
$492$		0			0
$493$	−7.39104	−	7.39104i	−0.332876	−	0.332876i
$494$			28.3848i			1.27709i
$495$		0			0
$496$			3.69552i			0.165934i
$497$	−7.30864	+	5.30864i	−0.327837	+	0.238125i
$498$		0			0
$499$			24.4853i			1.09611i	0.836442	+	0.548056i	$0.184632\pi$
$499$			24.4853i			1.09611i	−0.836442	+	0.548056i	$0.815368\pi$
$500$	−2.36176	−	10.9280i	−0.105621	−	0.488717i
$501$		0			0
$502$	−20.3638	+	20.3638i	−0.908881	+	0.908881i
$503$	22.8072	+	22.8072i	1.01692	+	1.01692i	0.999854	+	0.0170666i	$0.00543274\pi$
$503$	22.8072	+	22.8072i	1.01692	+	1.01692i	0.0170666	+	0.999854i	$0.494567\pi$
$504$		0			0
$505$	1.87868	+	26.4350i	0.0836001	+	1.17634i
$506$	−9.65685			−0.429300
$507$		0			0
$508$	−6.41421	+	6.41421i	−0.284585	+	0.284585i
$509$	−1.66205			−0.0736691			−0.0368345	−	0.999321i	$-0.511727\pi$
$509$	−1.66205			−0.0736691			−0.0368345	+	0.999321i	$0.511727\pi$
$510$		0			0
$511$	17.6569	+	2.79884i	0.781093	+	0.123813i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	4.59220			0.202553
$515$	4.72792	+	4.10051i	0.208337	+	0.180690i
$516$		0			0
$517$	−7.39104	+	7.39104i	−0.325057	+	0.325057i
$518$	11.9054	+	16.3907i	0.523092	+	0.720164i
$519$		0			0
$520$	8.94975	−	0.636039i	0.392472	−	0.0278922i
$521$			36.8464i			1.61427i	0.590367	+	0.807135i	$0.298983\pi$
$521$			36.8464i			1.61427i	−0.590367	+	0.807135i	$0.701017\pi$
$522$		0			0
$523$	−6.84984	−	6.84984i	−0.299523	−	0.299523i	0.541304	−	0.840827i	$-0.317931\pi$
$523$	−6.84984	−	6.84984i	−0.299523	−	0.299523i	−0.840827	+	0.541304i	$0.817931\pi$
$524$	−16.8925			−0.737951
$525$		0			0
$526$	−23.4558			−1.02272
$527$	−5.65685	−	5.65685i	−0.246416	−	0.246416i
$528$		0			0
$529$			11.3431i			0.493180i
$530$	−0.765367	+	0.0543929i	−0.0332454	+	0.00236268i
$531$		0			0
$532$	−10.9991	−	15.1430i	−0.476873	−	0.656532i
$533$	−4.34315	+	4.34315i	−0.188123	+	0.188123i
$534$		0			0
$535$	18.2919	+	15.8645i	0.790827	+	0.685881i
$536$	−9.17157			−0.396152
$537$		0			0
$538$	8.96023	+	8.96023i	0.386303	+	0.386303i
$539$	6.12293	−	18.8284i	0.263733	−	0.810998i
$540$		0			0
$541$	−22.9706			−0.987582			−0.493791	−	0.869581i	$-0.664389\pi$
$541$	−22.9706			−0.987582			−0.493791	+	0.869581i	$0.664389\pi$
$542$	−9.81845	+	9.81845i	−0.421739	+	0.421739i
$543$		0			0
$544$	2.16478			0.0928144
$545$	−2.55873	−	36.0041i	−0.109604	−	1.54225i
$546$		0			0
$547$	14.6274	+	14.6274i	0.625423	+	0.625423i	0.946913	−	0.321490i	$-0.104184\pi$
$547$	14.6274	+	14.6274i	0.625423	+	0.625423i	−0.321490	+	0.946913i	$0.604184\pi$
$548$	−13.8284	+	13.8284i	−0.590721	+	0.590721i
$549$		0			0
$550$	−11.3137	−	8.48528i	−0.482418	−	0.361814i
$551$		−	34.1563i		−	1.45511i
$552$		0			0
$553$	14.1043	+	19.4180i	0.599776	+	0.825737i
$554$			14.4853i			0.615421i
$555$		0			0
$556$			5.09494i			0.216073i
$557$	1.27208	+	1.27208i	0.0538997	+	0.0538997i	0.733543	−	0.679643i	$-0.237865\pi$
$557$	1.27208	+	1.27208i	0.0538997	+	0.0538997i	−0.679643	+	0.733543i	$0.737865\pi$
$558$		0			0
$559$	−22.6984			−0.960039
$560$	−4.52814	+	3.80736i	−0.191349	+	0.160890i
$561$		0			0
$562$	4.00000	+	4.00000i	0.168730	+	0.168730i
$563$	32.0844	+	32.0844i	1.35220	+	1.35220i	0.883200	+	0.468997i	$0.155385\pi$
$563$	32.0844	+	32.0844i	1.35220	+	1.35220i	0.468997	+	0.883200i	$0.344615\pi$
$564$		0			0
$565$	14.1480	−	16.3128i	0.595212	−	0.686285i
$566$		−	0.317025i		−	0.0133256i
$567$		0			0
$568$	2.41421	−	2.41421i	0.101298	−	0.101298i
$569$			1.41421i			0.0592869i	0.999561	+	0.0296435i	$0.00943719\pi$
$569$			1.41421i			0.0592869i	−0.999561	+	0.0296435i	$0.990563\pi$
$570$		0			0
$571$	25.4558			1.06529			0.532647	−	0.846338i	$-0.321197\pi$
$571$	25.4558			1.06529			0.532647	+	0.846338i	$0.321197\pi$
$572$	8.02509	−	8.02509i	0.335546	−	0.335546i
$573$		0			0
$574$	0.634051	−	4.00000i	0.0264648	−	0.166957i
$575$	10.2426	−	13.6569i	0.427148	−	0.569530i
$576$		0			0
$577$	−4.40649	+	4.40649i	−0.183445	+	0.183445i	−0.792855	−	0.609410i	$-0.791406\pi$
$577$	−4.40649	+	4.40649i	−0.183445	+	0.183445i	0.609410	+	0.792855i	$0.291406\pi$
$578$	8.70711	−	8.70711i	0.362168	−	0.362168i
$579$		0			0
$580$	−10.7695	+	0.765367i	−0.447180	+	0.0317801i
$581$	20.1421	+	3.19278i	0.835637	+	0.132459i
$582$		0			0
$583$	−0.686292	+	0.686292i	−0.0284233	+	0.0284233i
$584$	−6.75699			−0.279606
$585$		0			0
$586$		−	2.93015i		−	0.121043i
$587$	−5.58174	+	5.58174i	−0.230383	+	0.230383i	−0.812853	−	0.582470i	$-0.802087\pi$
$587$	−5.58174	+	5.58174i	−0.230383	+	0.230383i	0.582470	+	0.812853i	$0.302087\pi$
$588$		0			0
$589$		−	26.1421i		−	1.07717i
$590$	6.46447	+	5.60660i	0.266138	+	0.230820i
$591$		0			0
$592$	−5.41421	−	5.41421i	−0.222523	−	0.222523i
$593$	−18.6633	−	18.6633i	−0.766410	−	0.766410i	0.211063	−	0.977473i	$-0.432308\pi$
$593$	−18.6633	−	18.6633i	−0.766410	−	0.766410i	−0.977473	+	0.211063i	$0.932308\pi$
$594$		0			0
$595$	1.10332	−	12.7594i	0.0452316	−	0.523085i
$596$	−5.31371			−0.217658
$597$		0			0
$598$	9.68714	+	9.68714i	0.396136	+	0.396136i
$599$			46.5269i			1.90104i	0.310666	+	0.950519i	$0.399448\pi$
$599$			46.5269i			1.90104i	−0.310666	+	0.950519i	$0.600552\pi$
$600$		0			0
$601$		−	19.1116i		−	0.779580i	−0.920904	−	0.389790i	$-0.872548\pi$
$601$		−	19.1116i		−	0.779580i	0.920904	−	0.389790i	$-0.127452\pi$
$602$	12.1094	−	8.79565i	0.493541	−	0.358484i
$603$		0			0
$604$		−	3.17157i		−	0.129049i
$605$	6.69133	−	0.475538i	0.272041	−	0.0193334i
$606$		0			0
$607$	−0.262632	+	0.262632i	−0.0106599	+	0.0106599i	−0.712417	−	0.701757i	$-0.752399\pi$
$607$	−0.262632	+	0.262632i	−0.0106599	+	0.0106599i	0.701757	+	0.712417i	$0.252399\pi$
$608$	5.00208	+	5.00208i	0.202861	+	0.202861i
$609$		0			0
$610$	−15.1213	+	17.4350i	−0.612244	+	0.705924i
$611$	14.8284			0.599894
$612$		0			0
$613$	0.100505	−	0.100505i	0.00405936	−	0.00405936i	−0.705074	−	0.709134i	$-0.749086\pi$
$613$	0.100505	−	0.100505i	0.00405936	−	0.00405936i	0.709134	+	0.705074i	$0.249086\pi$
$614$	−5.91470			−0.238698
$615$		0			0
$616$	−1.17157	+	7.39104i	−0.0472040	+	0.297793i
$617$	11.5147	+	11.5147i	0.463565	+	0.463565i	0.899822	−	0.436257i	$-0.143696\pi$
$617$	11.5147	+	11.5147i	0.463565	+	0.463565i	−0.436257	+	0.899822i	$0.643696\pi$
$618$		0			0
$619$	−34.9217			−1.40362			−0.701811	−	0.712363i	$-0.747625\pi$
$619$	−34.9217			−1.40362			−0.701811	+	0.712363i	$0.747625\pi$
$620$	−8.24264	+	0.585786i	−0.331032	+	0.0235257i
$621$		0			0
$622$	−16.3128	+	16.3128i	−0.654084	+	0.654084i
$623$	−36.2773	+	26.3501i	−1.45342	+	1.05569i
$624$		0			0
$625$	24.0000	−	7.00000i	0.960000	−	0.280000i
$626$		−	8.28772i		−	0.331244i
$627$		0			0
$628$	−1.17525	−	1.17525i	−0.0468975	−	0.0468975i
$629$	16.5754			0.660906
$630$		0			0
$631$	−29.3553			−1.16862			−0.584309	−	0.811531i	$-0.698634\pi$
$631$	−29.3553			−1.16862			−0.584309	+	0.811531i	$0.698634\pi$
$632$	−6.41421	−	6.41421i	−0.255144	−	0.255144i
$633$		0			0
$634$			2.97056i			0.117976i
$635$	−15.3233	−	13.2898i	−0.608085	−	0.527390i
$636$		0			0
$637$	−25.0296	+	12.7453i	−0.991709	+	0.504989i
$638$	−9.65685	+	9.65685i	−0.382319	+	0.382319i
$639$		0			0
$640$	1.46508	−	1.68925i	0.0579122	−	0.0667733i
$641$	−5.21320			−0.205909			−0.102955	−	0.994686i	$-0.532830\pi$
$641$	−5.21320			−0.205909			−0.102955	+	0.994686i	$0.532830\pi$
$642$		0			0
$643$	27.0439	+	27.0439i	1.06651	+	1.06651i	0.997625	+	0.0688814i	$0.0219430\pi$
$643$	27.0439	+	27.0439i	1.06651	+	1.06651i	0.0688814	+	0.997625i	$0.478057\pi$
$644$	−8.92177	−	1.41421i	−0.351567	−	0.0557278i
$645$		0			0
$646$	−15.3137			−0.602510
$647$	−20.7193	+	20.7193i	−0.814560	+	0.814560i	−0.985314	−	0.170754i	$-0.945380\pi$
$647$	−20.7193	+	20.7193i	−0.814560	+	0.814560i	0.170754	+	0.985314i	$0.445380\pi$
$648$		0			0
$649$	10.8239			0.424876
$650$	2.83730	+	19.8611i	0.111288	+	0.779016i
$651$		0			0
$652$	2.34315	+	2.34315i	0.0917647	+	0.0917647i
$653$	16.7279	−	16.7279i	0.654614	−	0.654614i	−0.299486	−	0.954101i	$-0.596815\pi$
$653$	16.7279	−	16.7279i	0.654614	−	0.654614i	0.954101	+	0.299486i	$0.0968153\pi$
$654$		0			0
$655$	−2.67767	−	37.6777i	−0.104625	−	1.47219i
$656$			1.53073i			0.0597651i
$657$		0			0
$658$	−7.91082	+	5.74603i	−0.308396	+	0.224004i
$659$			18.3431i			0.714548i	0.934000	+	0.357274i	$0.116294\pi$
$659$			18.3431i			0.714548i	−0.934000	+	0.357274i	$0.883706\pi$
$660$		0			0
$661$			0.208239i			0.00809958i	0.999992	+	0.00404979i	$0.00128909\pi$
$661$			0.208239i			0.00809958i	−0.999992	+	0.00404979i	$0.998711\pi$
$662$	−0.485281	−	0.485281i	−0.0188610	−	0.0188610i
$663$		0			0
$664$	−7.70806			−0.299131
$665$	32.0321	−	26.9333i	1.24215	−	1.04443i
$666$		0			0
$667$	−11.6569	−	11.6569i	−0.451355	−	0.451355i
$668$	11.5349	+	11.5349i	0.446299	+	0.446299i
$669$		0			0
$670$	−1.45381	−	20.4567i	−0.0561656	−	0.790310i
$671$			29.1927i			1.12697i
$672$		0			0
$673$	16.7990	−	16.7990i	0.647553	−	0.647553i	−0.304848	−	0.952401i	$-0.598606\pi$
$673$	16.7990	−	16.7990i	0.647553	−	0.647553i	0.952401	+	0.304848i	$0.0986055\pi$
$674$		−	17.3137i		−	0.666899i
$675$		0			0
$676$	−3.10051			−0.119250
$677$	−30.7394	+	30.7394i	−1.18141	+	1.18141i	−0.202032	+	0.979379i	$0.564754\pi$
$677$	−30.7394	+	30.7394i	−1.18141	+	1.18141i	−0.979379	+	0.202032i	$0.935246\pi$
$678$		0			0
$679$	−6.49435	+	40.9706i	−0.249230	+	1.57231i
$680$	0.343146	+	4.82843i	0.0131590	+	0.185162i
$681$		0			0
$682$	−7.39104	+	7.39104i	−0.283017	+	0.283017i
$683$	2.68629	−	2.68629i	0.102788	−	0.102788i	−0.653843	−	0.756631i	$-0.726844\pi$
$683$	2.68629	−	2.68629i	0.102788	−	0.102788i	0.756631	+	0.653843i	$0.226844\pi$
$684$		0			0
$685$	−33.0355	−	28.6515i	−1.26222	−	1.09472i
$686$	8.41421	−	16.4985i	0.321256	−	0.629916i
$687$		0			0
$688$	−4.00000	+	4.00000i	−0.152499	+	0.152499i
$689$	1.37689			0.0524552
$690$		0			0
$691$			12.5629i			0.477915i	0.971030	+	0.238958i	$0.0768057\pi$
$691$			12.5629i			0.477915i	−0.971030	+	0.238958i	$0.923194\pi$
$692$	−8.56628	+	8.56628i	−0.325641	+	0.325641i
$693$		0			0
$694$			24.4853i			0.929449i
$695$	−11.3640	+	0.807612i	−0.431060	+	0.0306345i
$696$		0			0
$697$	−2.34315	−	2.34315i	−0.0887530	−	0.0887530i
$698$	−17.6194	−	17.6194i	−0.666903	−	0.666903i
$699$		0			0
$700$	−9.20986	−	9.49623i	−0.348100	−	0.358924i
$701$	−49.1127			−1.85496			−0.927481	−	0.373872i	$-0.878030\pi$
$701$	−49.1127			−1.85496			−0.927481	+	0.373872i	$0.878030\pi$
$702$		0			0
$703$	38.3002	+	38.3002i	1.44452	+	1.44452i
$704$		−	2.82843i		−	0.106600i
$705$		0			0
$706$			8.02509i			0.302028i
$707$	18.4281	+	25.3708i	0.693062	+	0.954169i
$708$		0			0
$709$		−	18.6863i		−	0.701778i	−0.936417	−	0.350889i	$-0.885879\pi$
$709$		−	18.6863i		−	0.701778i	0.936417	−	0.350889i	$-0.114121\pi$
$710$	5.76745	+	5.00208i	0.216448	+	0.187725i
$711$		0			0
$712$	11.9832	−	11.9832i	0.449091	−	0.449091i
$713$	−8.92177	−	8.92177i	−0.334123	−	0.334123i
$714$		0			0
$715$	19.1716	+	16.6274i	0.716976	+	0.621830i
$716$	−2.34315			−0.0875675
$717$		0			0
$718$	−12.0000	+	12.0000i	−0.447836	+	0.447836i
$719$	−9.44703			−0.352315			−0.176157	−	0.984362i	$-0.556367\pi$
$719$	−9.44703			−0.352315			−0.176157	+	0.984362i	$0.556367\pi$
$720$		0			0
$721$	7.31371	+	1.15932i	0.272377	+	0.0431752i
$722$	−21.9497	−	21.9497i	−0.816885	−	0.816885i
$723$		0			0
$724$	10.1355			0.376682
$725$	−3.41421	−	23.8995i	−0.126801	−	0.887605i
$726$		0			0
$727$	18.6633	−	18.6633i	0.692183	−	0.692183i	−0.270528	−	0.962712i	$-0.587198\pi$
$727$	18.6633	−	18.6633i	0.692183	−	0.692183i	0.962712	+	0.270528i	$0.0871984\pi$
$728$	8.58946	−	6.23897i	0.318347	−	0.231231i
$729$		0			0
$730$	−1.07107	−	15.0711i	−0.0396420	−	0.557805i
$731$		−	12.2459i		−	0.452930i
$732$		0			0
$733$	12.3387	+	12.3387i	0.455741	+	0.455741i	0.897255	−	0.441513i	$-0.145558\pi$
$733$	12.3387	+	12.3387i	0.455741	+	0.455741i	−0.441513	+	0.897255i	$0.645558\pi$
$734$	10.4525			0.385809
$735$		0			0
$736$	3.41421			0.125850
$737$	−18.3431	−	18.3431i	−0.675678	−	0.675678i
$738$		0			0
$739$			1.65685i			0.0609484i	0.999536	+	0.0304742i	$0.00970174\pi$
$739$			1.65685i			0.0609484i	−0.999536	+	0.0304742i	$0.990298\pi$
$740$	11.2179	−	12.9343i	0.412377	−	0.475475i
$741$		0			0
$742$	−0.734556	+	0.533546i	−0.0269664	+	0.0195871i
$743$	21.0416	−	21.0416i	0.771943	−	0.771943i	−0.206503	−	0.978446i	$-0.566208\pi$
$743$	21.0416	−	21.0416i	0.771943	−	0.771943i	0.978446	+	0.206503i	$0.0662084\pi$
$744$		0			0
$745$	−0.842290	−	11.8519i	−0.0308591	−	0.434221i
$746$	1.31371			0.0480983
$747$		0			0
$748$	4.32957	+	4.32957i	0.158305	+	0.158305i
$749$	28.2960	+	4.48528i	1.03391	+	0.163889i
$750$		0			0
$751$	14.4853			0.528575			0.264288	−	0.964444i	$-0.414863\pi$
$751$	14.4853			0.528575			0.264288	+	0.964444i	$0.414863\pi$
$752$	2.61313	−	2.61313i	0.0952909	−	0.0952909i
$753$		0			0
$754$	19.3743			0.705569
$755$	7.07401	−	0.502734i	0.257450	−	0.0182964i
$756$		0			0
$757$	−11.8995	−	11.8995i	−0.432494	−	0.432494i	0.456982	−	0.889476i	$-0.348931\pi$
$757$	−11.8995	−	11.8995i	−0.432494	−	0.432494i	−0.889476	+	0.456982i	$0.848931\pi$
$758$	−15.6569	+	15.6569i	−0.568683	+	0.568683i
$759$		0			0
$760$	−10.3640	+	11.9497i	−0.375940	+	0.433463i
$761$			32.3630i			1.17316i	0.809892	+	0.586579i	$0.199525\pi$
$761$			32.3630i			1.17316i	−0.809892	+	0.586579i	$0.800475\pi$
$762$		0			0
$763$	−25.0989	−	34.5547i	−0.908640	−	1.25096i
$764$		−	10.2426i		−	0.370566i
$765$		0			0
$766$		−	15.4161i		−	0.557007i
$767$	−10.8579	−	10.8579i	−0.392055	−	0.392055i
$768$		0			0
$769$	−20.2710			−0.730989			−0.365495	−	0.930813i	$-0.619100\pi$
$769$	−20.2710			−0.730989			−0.365495	+	0.930813i	$0.619100\pi$
$770$	−16.6710	−	1.44155i	−0.600781	−	0.0519500i
$771$		0			0
$772$	−0.242641	−	0.242641i	−0.00873283	−	0.00873283i
$773$	−1.49227	−	1.49227i	−0.0536733	−	0.0536733i	0.679761	−	0.733434i	$-0.262084\pi$
$773$	−1.49227	−	1.49227i	−0.0536733	−	0.0536733i	−0.733434	+	0.679761i	$0.762084\pi$
$774$		0			0
$775$	−2.61313	−	18.2919i	−0.0938663	−	0.657064i
$776$		−	15.6788i		−	0.562835i
$777$		0			0
$778$	19.8995	−	19.8995i	0.713431	−	0.713431i
$779$		−	10.8284i		−	0.387969i
$780$		0			0
$781$	9.65685			0.345549
$782$	−5.22625	+	5.22625i	−0.186890	+	0.186890i
$783$		0			0
$784$	−2.16478	+	6.65685i	−0.0773137	+	0.237745i
$785$	2.43503	−	2.80761i	0.0869099	−	0.100208i
$786$		0			0
$787$	−3.97408	+	3.97408i	−0.141661	+	0.141661i	−0.774381	−	0.632720i	$-0.781938\pi$
$787$	−3.97408	+	3.97408i	−0.141661	+	0.141661i	0.632720	+	0.774381i	$0.281938\pi$
$788$	3.41421	−	3.41421i	0.121626	−	0.121626i
$789$		0			0
$790$	13.2898	−	15.3233i	0.472830	−	0.545177i
$791$	4.00000	−	25.2346i	0.142224	−	0.897238i
$792$		0			0
$793$	29.2843	−	29.2843i	1.03991	−	1.03991i
$794$	22.3044			0.791554
$795$		0			0
$796$			15.9414i			0.565028i
$797$	11.4964	−	11.4964i	0.407225	−	0.407225i	−0.473545	−	0.880770i	$-0.657026\pi$
$797$	11.4964	−	11.4964i	0.407225	−	0.407225i	0.880770	+	0.473545i	$0.157026\pi$
$798$		0			0
$799$			8.00000i			0.283020i
$800$	4.00000	+	3.00000i	0.141421	+	0.106066i
$801$		0			0
$802$	−19.9706	−	19.9706i	−0.705185	−	0.705185i
$803$	−13.5140	−	13.5140i	−0.476898	−	0.476898i
$804$		0			0
$805$	1.74011	−	20.1237i	0.0613308	−	0.709266i
$806$	14.8284			0.522309
$807$		0			0
$808$	−8.38057	−	8.38057i	−0.294828	−	0.294828i
$809$		−	14.1005i		−	0.495747i	−0.968792	−	0.247874i	$-0.920268\pi$
$809$		−	14.1005i		−	0.495747i	0.968792	−	0.247874i	$-0.0797318\pi$
$810$		0			0
$811$			7.18280i			0.252222i	0.992016	+	0.126111i	$0.0402496\pi$
$811$			7.18280i			0.252222i	−0.992016	+	0.126111i	$0.959750\pi$
$812$	−10.3360	+	7.50756i	−0.362722	+	0.263464i
$813$		0			0
$814$		−	21.6569i		−	0.759072i
$815$	−4.85483	+	5.59767i	−0.170057	+	0.196078i
$816$		0			0
$817$	28.2960	−	28.2960i	0.989953	−	0.989953i
$818$	16.4985	+	16.4985i	0.576857	+	0.576857i
$819$		0			0
$820$	−3.41421	+	0.242641i	−0.119230	+	0.00847338i
$821$	17.5147			0.611268			0.305634	−	0.952149i	$-0.401132\pi$
$821$	17.5147			0.611268			0.305634	+	0.952149i	$0.401132\pi$
$822$		0			0
$823$	−13.6569	+	13.6569i	−0.476048	+	0.476048i	−0.903865	−	0.427817i	$-0.859283\pi$
$823$	−13.6569	+	13.6569i	−0.476048	+	0.476048i	0.427817	+	0.903865i	$0.359283\pi$
$824$	−2.79884			−0.0975020
$825$		0			0
$826$	10.0000	+	1.58513i	0.347945	+	0.0551536i
$827$	24.4853	+	24.4853i	0.851437	+	0.851437i	0.990310	−	0.138873i	$-0.0443481\pi$
$827$	24.4853	+	24.4853i	0.851437	+	0.851437i	−0.138873	+	0.990310i	$0.544348\pi$
$828$		0			0
$829$	30.7009			1.06629			0.533144	−	0.846025i	$-0.321011\pi$
$829$	30.7009			1.06629			0.533144	+	0.846025i	$0.321011\pi$
$830$	−1.22183	−	17.1924i	−0.0424102	−	0.596757i
$831$		0			0
$832$	−2.83730	+	2.83730i	−0.0983656	+	0.0983656i
$833$	−6.87616	−	13.5036i	−0.238245	−	0.467871i
$834$		0			0
$835$	−23.8995	+	27.5563i	−0.827076	+	0.953627i
$836$			20.0083i			0.692002i
$837$		0			0
$838$	17.1710	+	17.1710i	0.593163	+	0.593163i
$839$	12.8799			0.444664			0.222332	−	0.974971i	$-0.428633\pi$
$839$	12.8799			0.444664			0.222332	+	0.974971i	$0.428633\pi$
$840$		0			0
$841$	5.68629			0.196079
$842$	15.4142	+	15.4142i	0.531209	+	0.531209i
$843$		0			0
$844$		−	21.6569i		−	0.745460i
$845$	−0.491469	−	6.91550i	−0.0169071	−	0.237900i
$846$		0			0
$847$	6.42196	−	4.66460i	0.220661	−	0.160277i
$848$	0.242641	−	0.242641i	0.00833232	−	0.00833232i
$849$		0			0
$850$	−10.7151	+	1.53073i	−0.367526	+	0.0525037i
$851$	26.1421			0.896141
$852$		0			0
$853$	16.4826	+	16.4826i	0.564353	+	0.564353i	0.930541	−	0.366188i	$-0.119337\pi$
$853$	16.4826	+	16.4826i	0.564353	+	0.564353i	−0.366188	+	0.930541i	$0.619337\pi$
$854$	−4.27518	+	26.9706i	−0.146294	+	0.922914i
$855$		0			0
$856$	−10.8284			−0.370108
$857$	−35.0530	+	35.0530i	−1.19739	+	1.19739i	−0.222443	+	0.974946i	$0.571403\pi$
$857$	−35.0530	+	35.0530i	−1.19739	+	1.19739i	−0.974946	+	0.222443i	$0.928597\pi$
$858$		0			0
$859$	−45.9313			−1.56716			−0.783579	−	0.621293i	$-0.786608\pi$
$859$	−45.9313			−1.56716			−0.783579	+	0.621293i	$0.786608\pi$
$860$	−9.55582	−	8.28772i	−0.325851	−	0.282609i
$861$		0			0
$862$	−4.00000	−	4.00000i	−0.136241	−	0.136241i
$863$	33.5563	−	33.5563i	1.14227	−	1.14227i	0.154238	−	0.988034i	$-0.450708\pi$
$863$	33.5563	−	33.5563i	1.14227	−	1.14227i	0.988034	−	0.154238i	$-0.0492921\pi$
$864$		0			0
$865$	−20.4645	−	17.7487i	−0.695813	−	0.603475i
$866$		−	6.12293i		−	0.208066i
$867$		0			0
$868$	−7.91082	+	5.74603i	−0.268511	+	0.195033i
$869$		−	25.6569i		−	0.870349i
$870$		0			0
$871$			36.8013i			1.24697i
$872$	11.4142	+	11.4142i	0.386534	+	0.386534i
$873$		0			0
$874$	−24.1522			−0.816960
$875$	19.7209	−	22.0473i	0.666689	−	0.745336i
$876$		0			0
$877$	9.55635	+	9.55635i	0.322695	+	0.322695i	0.849800	−	0.527105i	$-0.176723\pi$
$877$	9.55635	+	9.55635i	0.322695	+	0.322695i	−0.527105	+	0.849800i	$0.676723\pi$
$878$	13.2513	+	13.2513i	0.447211	+	0.447211i
$879$		0			0
$880$	6.30864	−	0.448342i	0.212664	−	0.0151136i
$881$			11.7206i			0.394877i	0.980315	+	0.197439i	$0.0632623\pi$
$881$			11.7206i			0.394877i	−0.980315	+	0.197439i	$0.936738\pi$
$882$		0			0
$883$	−23.1716	+	23.1716i	−0.779786	+	0.779786i	−0.979794	−	0.200009i	$-0.935903\pi$
$883$	−23.1716	+	23.1716i	−0.779786	+	0.779786i	0.200009	+	0.979794i	$0.435903\pi$
$884$		−	8.68629i		−	0.292152i
$885$		0			0
$886$	34.1421			1.14703
$887$	41.6243	−	41.6243i	1.39761	−	1.39761i	0.590760	−	0.806847i	$-0.298828\pi$
$887$	41.6243	−	41.6243i	1.39761	−	1.39761i	0.806847	−	0.590760i	$-0.201172\pi$
$888$		0			0
$889$	−23.7038	−	3.75736i	−0.795001	−	0.126018i
$890$	28.6274	+	24.8284i	0.959593	+	0.832251i
$891$		0			0
$892$	5.86030	−	5.86030i	0.196217	−	0.196217i
$893$	−18.4853	+	18.4853i	−0.618586	+	0.618586i
$894$		0			0
$895$	−0.371418	−	5.22625i	−0.0124151	−	0.174694i
$896$	0.414214	−	2.61313i	0.0138379	−	0.0872984i
$897$		0			0
$898$	−10.1421	+	10.1421i	−0.338447	+	0.338447i
$899$	−17.8435			−0.595115
$900$		0			0
$901$			0.742837i			0.0247475i
$902$	−3.06147	+	3.06147i	−0.101936	+	0.101936i
$903$		0			0
$904$			9.65685i			0.321182i
$905$	1.60660	+	22.6066i	0.0534052	+	0.751469i
$906$		0			0
$907$	16.8284	+	16.8284i	0.558779	+	0.558779i	0.928960	−	0.370181i	$-0.120704\pi$
$907$	16.8284	+	16.8284i	0.558779	+	0.558779i	−0.370181	+	0.928960i	$0.620704\pi$
$908$	−1.94061	−	1.94061i	−0.0644015	−	0.0644015i
$909$		0			0
$910$	15.2772	+	18.1693i	0.506434	+	0.602308i
$911$	−0.142136			−0.00470916			−0.00235458	−	0.999997i	$-0.500749\pi$
$911$	−0.142136			−0.00470916			−0.00235458	+	0.999997i	$0.500749\pi$
$912$		0			0
$913$	−15.4161	−	15.4161i	−0.510199	−	0.510199i
$914$		−	13.6569i		−	0.451729i
$915$		0			0
$916$			7.52235i			0.248546i
$917$	−26.2655	−	36.1609i	−0.867364	−	1.19414i
$918$		0			0
$919$		−	28.3848i		−	0.936327i	−0.883642	−	0.468164i	$-0.844916\pi$
$919$		−	28.3848i		−	0.936327i	0.883642	−	0.468164i	$-0.155084\pi$
$920$	0.541196	+	7.61521i	0.0178427	+	0.251066i
$921$		0			0
$922$	−8.43497	+	8.43497i	−0.277791	+	0.277791i
$923$	−9.68714	−	9.68714i	−0.318856	−	0.318856i
$924$		0			0
$925$	30.6274	+	22.9706i	1.00702	+	0.755267i
$926$	−29.6569			−0.974585
$927$		0			0
$928$	3.41421	−	3.41421i	0.112077	−	0.112077i
$929$	13.7766			0.451996			0.225998	−	0.974128i	$-0.427436\pi$
$929$	13.7766			0.451996			0.225998	+	0.974128i	$0.427436\pi$
$930$		0			0
$931$	15.3137	−	47.0907i	0.501887	−	1.54333i
$932$	−3.00000	−	3.00000i	−0.0982683	−	0.0982683i
$933$		0			0
$934$	−18.8715			−0.617496
$935$	−8.97056	+	10.3431i	−0.293369	+	0.338257i
$936$		0			0
$937$	−35.5014	+	35.5014i	−1.15978	+	1.15978i	−0.175256	+	0.984523i	$0.556075\pi$
$937$	−35.5014	+	35.5014i	−1.15978	+	1.15978i	−0.984523	+	0.175256i	$0.943925\pi$
$938$	−14.2606	−	19.6331i	−0.465624	−	0.641045i
$939$		0			0
$940$	6.24264	+	5.41421i	0.203612	+	0.176592i
$941$			37.7975i			1.23216i	0.787683	+	0.616081i	$0.211281\pi$
$941$			37.7975i			1.23216i	−0.787683	+	0.616081i	$0.788719\pi$
$942$		0			0
$943$	−3.69552	−	3.69552i	−0.120343	−	0.120343i
$944$	−3.82683			−0.124553
$945$		0			0
$946$	−16.0000			−0.520205
$947$	10.9706	+	10.9706i	0.356495	+	0.356495i	0.862519	−	0.506024i	$-0.168885\pi$
$947$	10.9706	+	10.9706i	0.356495	+	0.356495i	−0.506024	+	0.862519i	$0.668885\pi$
$948$		0			0
$949$			27.1127i			0.880115i
$950$	−28.2960	−	21.2220i	−0.918045	−	0.688534i
$951$		0			0
$952$	3.36595	+	4.63405i	0.109091	+	0.150190i
$953$	5.14214	−	5.14214i	0.166570	−	0.166570i	−0.618900	−	0.785470i	$-0.712421\pi$
$953$	5.14214	−	5.14214i	0.166570	−	0.166570i	0.785470	+	0.618900i	$0.212421\pi$
$954$		0			0
$955$	22.8456	−	1.62359i	0.739267	−	0.0525381i
$956$	10.4853			0.339118
$957$		0			0
$958$	−3.24718	−	3.24718i	−0.104912	−	0.104912i
$959$	−51.1032	−	8.10051i	−1.65021	−	0.261579i
$960$		0			0
$961$	17.3431			0.559456
$962$	−21.7248	+	21.7248i	−0.700435	+	0.700435i
$963$		0			0
$964$	−5.86030			−0.188748
$965$	0.502734	−	0.579658i	0.0161836	−	0.0186598i
$966$		0			0
$967$	40.2132	+	40.2132i	1.29317	+	1.29317i	0.932816	+	0.360354i	$0.117344\pi$
$967$	40.2132	+	40.2132i	1.29317	+	1.29317i	0.360354	+	0.932816i	$0.382656\pi$
$968$	−2.12132	+	2.12132i	−0.0681818	+	0.0681818i
$969$		0			0
$970$	34.9706	−	2.48528i	1.12284	−	0.0797976i
$971$		−	33.6536i		−	1.08000i	−0.841666	−	0.539998i	$-0.818425\pi$
$971$		−	33.6536i		−	1.08000i	0.841666	−	0.539998i	$-0.181575\pi$
$972$		0			0
$973$	−10.9065	+	7.92194i	−0.349646	+	0.253966i
$974$		−	29.5563i		−	0.947047i
$975$		0			0
$976$		−	10.3212i		−	0.330373i
$977$	20.1716	+	20.1716i	0.645346	+	0.645346i	0.951865	−	0.306519i	$-0.0991642\pi$
$977$	20.1716	+	20.1716i	0.645346	+	0.645346i	−0.306519	+	0.951865i	$0.599164\pi$
$978$		0			0
$979$	47.9329			1.53194
$980$	−15.1909	−	3.77323i	−0.485255	−	0.120531i
$981$		0			0
$982$	21.7990	+	21.7990i	0.695634	+	0.695634i
$983$	11.9063	+	11.9063i	0.379752	+	0.379752i	0.871013	−	0.491260i	$-0.163464\pi$
$983$	11.9063	+	11.9063i	0.379752	+	0.379752i	−0.491260	+	0.871013i	$0.663464\pi$
$984$		0			0
$985$	8.15640	+	7.07401i	0.259885	+	0.225397i
$986$			10.4525i			0.332876i
$987$		0			0
$988$	20.0711	−	20.0711i	0.638546	−	0.638546i
$989$		−	19.3137i		−	0.614140i
$990$		0			0
$991$	−35.4142			−1.12497			−0.562485	−	0.826808i	$-0.690155\pi$
$991$	−35.4142			−1.12497			−0.562485	+	0.826808i	$0.690155\pi$
$992$	2.61313	−	2.61313i	0.0829668	−	0.0829668i
$993$		0			0
$994$	8.92177	+	1.41421i	0.282981	+	0.0448561i
$995$	−35.5563	+	2.52691i	−1.12721	+	0.0801085i
$996$		0			0
$997$	−38.0760	+	38.0760i	−1.20588	+	1.20588i	−0.233531	+	0.972349i	$0.575028\pi$
$997$	−38.0760	+	38.0760i	−1.20588	+	1.20588i	−0.972349	+	0.233531i	$0.924972\pi$
$998$	17.3137	−	17.3137i	0.548056	−	0.548056i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.p.a.307.1		8
3.2	odd	2		70.2.g.a.27.3	yes	8
5.3	odd	4	inner	630.2.p.a.433.2		8
7.6	odd	2	inner	630.2.p.a.307.2		8
12.11	even	2		560.2.bj.c.97.3		8
15.2	even	4		350.2.g.a.293.1		8
15.8	even	4		70.2.g.a.13.4	yes	8
15.14	odd	2		350.2.g.a.307.2		8
21.2	odd	6		490.2.l.a.227.4		16
21.5	even	6		490.2.l.a.227.3		16
21.11	odd	6		490.2.l.a.117.1		16
21.17	even	6		490.2.l.a.117.2		16
21.20	even	2		70.2.g.a.27.4	yes	8
35.13	even	4	inner	630.2.p.a.433.1		8
60.23	odd	4		560.2.bj.c.433.2		8
84.83	odd	2		560.2.bj.c.97.2		8
105.23	even	12		490.2.l.a.423.2		16
105.38	odd	12		490.2.l.a.313.4		16
105.53	even	12		490.2.l.a.313.3		16
105.62	odd	4		350.2.g.a.293.2		8
105.68	odd	12		490.2.l.a.423.1		16
105.83	odd	4		70.2.g.a.13.3	✓	8
105.104	even	2		350.2.g.a.307.1		8
420.83	even	4		560.2.bj.c.433.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.g.a.13.3	✓	8	105.83	odd	4
70.2.g.a.13.4	yes	8	15.8	even	4
70.2.g.a.27.3	yes	8	3.2	odd	2
70.2.g.a.27.4	yes	8	21.20	even	2
350.2.g.a.293.1		8	15.2	even	4
350.2.g.a.293.2		8	105.62	odd	4
350.2.g.a.307.1		8	105.104	even	2
350.2.g.a.307.2		8	15.14	odd	2
490.2.l.a.117.1		16	21.11	odd	6
490.2.l.a.117.2		16	21.17	even	6
490.2.l.a.227.3		16	21.5	even	6
490.2.l.a.227.4		16	21.2	odd	6
490.2.l.a.313.3		16	105.53	even	12
490.2.l.a.313.4		16	105.38	odd	12
490.2.l.a.423.1		16	105.68	odd	12
490.2.l.a.423.2		16	105.23	even	12
560.2.bj.c.97.2		8	84.83	odd	2
560.2.bj.c.97.3		8	12.11	even	2
560.2.bj.c.433.2		8	60.23	odd	4
560.2.bj.c.433.3		8	420.83	even	4
630.2.p.a.307.1		8	1.1	even	1	trivial
630.2.p.a.307.2		8	7.6	odd	2	inner
630.2.p.a.433.1		8	35.13	even	4	inner
630.2.p.a.433.2		8	5.3	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.23044 + 0.158513i) q^{5} +(-2.14065 + 1.55487i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.68925 + 1.46508i) q^{10} +2.82843 q^{11} +(-2.83730 - 2.83730i) q^{13} +(2.61313 + 0.414214i) q^{14} -1.00000 q^{16} +(1.53073 - 1.53073i) q^{17} +7.07401 q^{19} +(-0.158513 - 2.23044i) q^{20} +(-2.00000 - 2.00000i) q^{22} +(2.41421 - 2.41421i) q^{23} +(4.94975 - 0.707107i) q^{25} +4.01254i q^{26} +(-1.55487 - 2.14065i) q^{28} -4.82843i q^{29} -3.69552i q^{31} +(0.707107 + 0.707107i) q^{32} -2.16478 q^{34} +(4.52814 - 3.80736i) q^{35} +(5.41421 + 5.41421i) q^{37} +(-5.00208 - 5.00208i) q^{38} +(-1.46508 + 1.68925i) q^{40} -1.53073i q^{41} +(4.00000 - 4.00000i) q^{43} +2.82843i q^{44} -3.41421 q^{46} +(-2.61313 + 2.61313i) q^{47} +(2.16478 - 6.65685i) q^{49} +(-4.00000 - 3.00000i) q^{50} +(2.83730 - 2.83730i) q^{52} +(-0.242641 + 0.242641i) q^{53} +(-6.30864 + 0.448342i) q^{55} +(-0.414214 + 2.61313i) q^{56} +(-3.41421 + 3.41421i) q^{58} +3.82683 q^{59} +10.3212i q^{61} +(-2.61313 + 2.61313i) q^{62} -1.00000i q^{64} +(6.77817 + 5.87868i) q^{65} +(-6.48528 - 6.48528i) q^{67} +(1.53073 + 1.53073i) q^{68} +(-5.89409 - 0.509666i) q^{70} +3.41421 q^{71} +(-4.77791 - 4.77791i) q^{73} -7.65685i q^{74} +7.07401i q^{76} +(-6.05468 + 4.39782i) q^{77} -9.07107i q^{79} +(2.23044 - 0.158513i) q^{80} +(-1.08239 + 1.08239i) q^{82} +(-5.45042 - 5.45042i) q^{83} +(-3.17157 + 3.65685i) q^{85} -5.65685 q^{86} +(2.00000 - 2.00000i) q^{88} +16.9469 q^{89} +(10.4853 + 1.66205i) q^{91} +(2.41421 + 2.41421i) q^{92} +3.69552 q^{94} +(-15.7782 + 1.12132i) q^{95} +(11.0866 - 11.0866i) q^{97} +(-6.23784 + 3.17637i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7} - 8 q^{16} - 16 q^{22} + 8 q^{23} + 8 q^{28} + 8 q^{35} + 32 q^{37} + 32 q^{43} - 16 q^{46} - 32 q^{50} + 32 q^{53} + 8 q^{56} - 16 q^{58} - 8 q^{65} + 16 q^{67} - 24 q^{70} + 16 q^{71} + 16 q^{77}+ \cdots - 32 q^{98}+O(q^{100}) \) 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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Database

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