LMFDB - Embedded newform 484.2.e.d.245.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [484,2,Mod(9,484)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(484, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("484.9"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	484.e (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,4,0,-2,0,-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:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			245.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	484.245
Dual form			484.2.e.d.81.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.118034 - 0.363271i) q^{3} +(-0.500000 - 0.363271i) q^{5} +(-0.881966 + 2.71441i) q^{7} +(2.30902 - 1.67760i) q^{9} +(3.73607 - 2.71441i) q^{13} +(-0.0729490 + 0.224514i) q^{15} +(3.73607 + 2.71441i) q^{17} +(0.881966 + 2.71441i) q^{19} +1.09017 q^{21} +6.47214 q^{23} +(-1.42705 - 4.39201i) q^{25} +(-1.80902 - 1.31433i) q^{27} +(-1.97214 + 6.06961i) q^{29} +(4.73607 - 3.44095i) q^{31} +(1.42705 - 1.03681i) q^{35} +(1.50000 - 4.61653i) q^{37} +(-1.42705 - 1.03681i) q^{39} +(-1.97214 - 6.06961i) q^{41} -1.76393 q^{45} +(1.11803 + 3.44095i) q^{47} +(-0.927051 - 0.673542i) q^{49} +(0.545085 - 1.67760i) q^{51} +(-5.73607 + 4.16750i) q^{53} +(0.881966 - 0.640786i) q^{57} +(-3.11803 + 9.59632i) q^{59} +(3.73607 + 2.71441i) q^{61} +(2.51722 + 7.74721i) q^{63} -2.85410 q^{65} -4.94427 q^{67} +(-0.763932 - 2.35114i) q^{69} +(6.97214 + 5.06555i) q^{71} +(3.73607 - 11.4984i) q^{73} +(-1.42705 + 1.03681i) q^{75} +(-11.2082 + 8.14324i) q^{79} +(2.38197 - 7.33094i) q^{81} +(-12.9721 - 9.42481i) q^{83} +(-0.881966 - 2.71441i) q^{85} +2.43769 q^{87} -8.47214 q^{89} +(4.07295 + 12.5352i) q^{91} +(-1.80902 - 1.31433i) q^{93} +(0.545085 - 1.67760i) q^{95} +(-4.50000 + 3.26944i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 2 q^{5} - 8 q^{7} + 7 q^{9} + 6 q^{13} - 7 q^{15} + 6 q^{17} + 8 q^{19} - 18 q^{21} + 8 q^{23} + q^{25} - 5 q^{27} + 10 q^{29} + 10 q^{31} - q^{35} + 6 q^{37} + q^{39} + 10 q^{41} - 16 q^{45}+ \cdots - 18 q^{97}+O(q^{100}) $ 4 * q + 4 * q^3 - 2 * q^5 - 8 * q^7 + 7 * q^9 + 6 * q^13 - 7 * q^15 + 6 * q^17 + 8 * q^19 - 18 * q^21 + 8 * q^23 + q^25 - 5 * q^27 + 10 * q^29 + 10 * q^31 - q^35 + 6 * q^37 + q^39 + 10 * q^41 - 16 * q^45 + 3 * q^49 - 9 * q^51 - 14 * q^53 + 8 * q^57 - 8 * q^59 + 6 * q^61 - 19 * q^63 + 2 * q^65 + 16 * q^67 - 12 * q^69 + 10 * q^71 + 6 * q^73 + q^75 - 18 * q^79 + 14 * q^81 - 34 * q^83 - 8 * q^85 + 50 * q^87 - 16 * q^89 + 23 * q^91 - 5 * q^93 - 9 * q^95 - 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.118034	−	0.363271i	−0.0681470	−	0.209735i	0.911184	−	0.412000i	$-0.135170\pi$
$3$	−0.118034	−	0.363271i	−0.0681470	−	0.209735i	−0.979331	+	0.202265i	$0.935170\pi$
$4$		0			0
$5$	−0.500000	−	0.363271i	−0.223607	−	0.162460i	0.470342	−	0.882484i	$-0.344131\pi$
$5$	−0.500000	−	0.363271i	−0.223607	−	0.162460i	−0.693949	+	0.720024i	$0.744131\pi$
$6$		0			0
$7$	−0.881966	+	2.71441i	−0.333352	+	1.02595i	0.634176	+	0.773188i	$0.281339\pi$
$7$	−0.881966	+	2.71441i	−0.333352	+	1.02595i	−0.967528	+	0.252763i	$0.918661\pi$
$8$		0			0
$9$	2.30902	−	1.67760i	0.769672	−	0.559200i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	3.73607	−	2.71441i	1.03620	−	0.752843i	0.0666589	−	0.997776i	$-0.478766\pi$
$13$	3.73607	−	2.71441i	1.03620	−	0.752843i	0.969540	+	0.244933i	$0.0787661\pi$
$14$		0			0
$15$	−0.0729490	+	0.224514i	−0.0188354	+	0.0579693i
$16$		0			0
$17$	3.73607	+	2.71441i	0.906130	+	0.658342i	0.940033	−	0.341083i	$-0.110794\pi$
$17$	3.73607	+	2.71441i	0.906130	+	0.658342i	−0.0339034	+	0.999425i	$0.510794\pi$
$18$		0			0
$19$	0.881966	+	2.71441i	0.202337	+	0.622729i	0.999812	+	0.0193774i	$0.00616839\pi$
$19$	0.881966	+	2.71441i	0.202337	+	0.622729i	−0.797475	+	0.603352i	$0.793832\pi$
$20$		0			0
$21$	1.09017			0.237895
$22$		0			0
$23$	6.47214			1.34953			0.674767	−	0.738031i	$-0.264244\pi$
$23$	6.47214			1.34953			0.674767	+	0.738031i	$0.264244\pi$
$24$		0			0
$25$	−1.42705	−	4.39201i	−0.285410	−	0.878402i
$26$		0			0
$27$	−1.80902	−	1.31433i	−0.348145	−	0.252942i
$28$		0			0
$29$	−1.97214	+	6.06961i	−0.366216	+	1.12710i	0.582999	+	0.812473i	$0.301879\pi$
$29$	−1.97214	+	6.06961i	−0.366216	+	1.12710i	−0.949216	+	0.314626i	$0.898121\pi$
$30$		0			0
$31$	4.73607	−	3.44095i	0.850623	−	0.618014i	−0.0746948	−	0.997206i	$-0.523798\pi$
$31$	4.73607	−	3.44095i	0.850623	−	0.618014i	0.925318	+	0.379193i	$0.123798\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.42705	−	1.03681i	0.241216	−	0.175253i
$36$		0			0
$37$	1.50000	−	4.61653i	0.246598	−	0.758952i	−0.748771	−	0.662829i	$-0.769356\pi$
$37$	1.50000	−	4.61653i	0.246598	−	0.758952i	0.995369	−	0.0961233i	$-0.0306443\pi$
$38$		0			0
$39$	−1.42705	−	1.03681i	−0.228511	−	0.166023i
$40$		0			0
$41$	−1.97214	−	6.06961i	−0.307996	−	0.947914i	−0.978542	−	0.206046i	$-0.933940\pi$
$41$	−1.97214	−	6.06961i	−0.307996	−	0.947914i	0.670546	−	0.741868i	$-0.266060\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	−1.76393			−0.262951
$46$		0			0
$47$	1.11803	+	3.44095i	0.163082	+	0.501915i	0.998890	−	0.0471073i	$-0.0150003\pi$
$47$	1.11803	+	3.44095i	0.163082	+	0.501915i	−0.835808	+	0.549022i	$0.815000\pi$
$48$		0			0
$49$	−0.927051	−	0.673542i	−0.132436	−	0.0962203i
$50$		0			0
$51$	0.545085	−	1.67760i	0.0763272	−	0.234911i
$52$		0			0
$53$	−5.73607	+	4.16750i	−0.787910	+	0.572450i	−0.907342	−	0.420393i	$-0.861892\pi$
$53$	−5.73607	+	4.16750i	−0.787910	+	0.572450i	0.119433	+	0.992842i	$0.461892\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.881966	−	0.640786i	0.116819	−	0.0848742i
$58$		0			0
$59$	−3.11803	+	9.59632i	−0.405933	+	1.24933i	0.514180	+	0.857682i	$0.328096\pi$
$59$	−3.11803	+	9.59632i	−0.405933	+	1.24933i	−0.920113	+	0.391652i	$0.871904\pi$
$60$		0			0
$61$	3.73607	+	2.71441i	0.478354	+	0.347545i	0.800688	−	0.599081i	$-0.204467\pi$
$61$	3.73607	+	2.71441i	0.478354	+	0.347545i	−0.322334	+	0.946626i	$0.604467\pi$
$62$		0			0
$63$	2.51722	+	7.74721i	0.317140	+	0.976057i
$64$		0			0
$65$	−2.85410			−0.354008
$66$		0			0
$67$	−4.94427			−0.604039			−0.302019	−	0.953302i	$-0.597661\pi$
$67$	−4.94427			−0.604039			−0.302019	+	0.953302i	$0.597661\pi$
$68$		0			0
$69$	−0.763932	−	2.35114i	−0.0919666	−	0.283044i
$70$		0			0
$71$	6.97214	+	5.06555i	0.827440	+	0.601171i	0.918834	−	0.394644i	$-0.129132\pi$
$71$	6.97214	+	5.06555i	0.827440	+	0.601171i	−0.0913937	+	0.995815i	$0.529132\pi$
$72$		0			0
$73$	3.73607	−	11.4984i	0.437274	−	1.34579i	−0.453465	−	0.891274i	$-0.649812\pi$
$73$	3.73607	−	11.4984i	0.437274	−	1.34579i	0.890739	−	0.454516i	$-0.150188\pi$
$74$		0			0
$75$	−1.42705	+	1.03681i	−0.164782	+	0.119721i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−11.2082	+	8.14324i	−1.26102	+	0.916186i	−0.998807	−	0.0488240i	$-0.984453\pi$
$79$	−11.2082	+	8.14324i	−1.26102	+	0.916186i	−0.262214	+	0.965010i	$0.584453\pi$
$80$		0			0
$81$	2.38197	−	7.33094i	0.264663	−	0.814549i
$82$		0			0
$83$	−12.9721	−	9.42481i	−1.42388	−	1.03451i	−0.991116	−	0.132998i	$-0.957540\pi$
$83$	−12.9721	−	9.42481i	−1.42388	−	1.03451i	−0.432761	−	0.901509i	$-0.642460\pi$
$84$		0			0
$85$	−0.881966	−	2.71441i	−0.0956626	−	0.294419i
$86$		0			0
$87$	2.43769			0.261348
$88$		0			0
$89$	−8.47214			−0.898045			−0.449022	−	0.893521i	$-0.648228\pi$
$89$	−8.47214			−0.898045			−0.449022	+	0.893521i	$0.648228\pi$
$90$		0			0
$91$	4.07295	+	12.5352i	0.426961	+	1.31405i
$92$		0			0
$93$	−1.80902	−	1.31433i	−0.187586	−	0.136289i
$94$		0			0
$95$	0.545085	−	1.67760i	0.0559245	−	0.172118i
$96$		0			0
$97$	−4.50000	+	3.26944i	−0.456906	+	0.331961i	−0.792316	−	0.610111i	$-0.791125\pi$
$97$	−4.50000	+	3.26944i	−0.456906	+	0.331961i	0.335410	+	0.942072i	$0.391125\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.50000	+	3.99598i	−0.547270	+	0.397615i	−0.826778	−	0.562528i	$-0.809829\pi$
$101$	−5.50000	+	3.99598i	−0.547270	+	0.397615i	0.279508	+	0.960143i	$0.409829\pi$
$102$		0			0
$103$	−0.354102	+	1.08981i	−0.0348907	+	0.107383i	−0.966985	−	0.254833i	$-0.917980\pi$
$103$	−0.354102	+	1.08981i	−0.0348907	+	0.107383i	0.932094	+	0.362215i	$0.117980\pi$
$104$		0			0
$105$	−0.545085	−	0.396027i	−0.0531948	−	0.0386483i
$106$		0			0
$107$	−2.64590	−	8.14324i	−0.255789	−	0.787236i	−0.993673	−	0.112310i	$-0.964175\pi$
$107$	−2.64590	−	8.14324i	−0.255789	−	0.787236i	0.737885	−	0.674927i	$-0.235825\pi$
$108$		0			0
$109$	3.52786			0.337908			0.168954	−	0.985624i	$-0.445961\pi$
$109$	3.52786			0.337908			0.168954	+	0.985624i	$0.445961\pi$
$110$		0			0
$111$	−1.85410			−0.175984
$112$		0			0
$113$	−0.791796	−	2.43690i	−0.0744859	−	0.229244i	0.906881	−	0.421387i	$-0.138456\pi$
$113$	−0.791796	−	2.43690i	−0.0744859	−	0.229244i	−0.981367	+	0.192142i	$0.938456\pi$
$114$		0			0
$115$	−3.23607	−	2.35114i	−0.301765	−	0.219245i
$116$		0			0
$117$	4.07295	−	12.5352i	0.376544	−	1.15888i
$118$		0			0
$119$	−10.6631	+	7.74721i	−0.977487	+	0.710186i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−1.97214	+	1.43284i	−0.177822	+	0.129195i
$124$		0			0
$125$	−1.83688	+	5.65334i	−0.164296	+	0.505650i
$126$		0			0
$127$	−3.73607	−	2.71441i	−0.331522	−	0.240865i	0.409554	−	0.912286i	$-0.365684\pi$
$127$	−3.73607	−	2.71441i	−0.331522	−	0.240865i	−0.741076	+	0.671421i	$0.765684\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−18.4721			−1.61392			−0.806959	−	0.590607i	$-0.798888\pi$
$131$	−18.4721			−1.61392			−0.806959	+	0.590607i	$0.798888\pi$
$132$		0			0
$133$	−8.14590			−0.706339
$134$		0			0
$135$	0.427051	+	1.31433i	0.0367547	+	0.113119i
$136$		0			0
$137$	8.73607	+	6.34712i	0.746373	+	0.542271i	0.894700	−	0.446667i	$-0.147389\pi$
$137$	8.73607	+	6.34712i	0.746373	+	0.542271i	−0.148328	+	0.988938i	$0.547389\pi$
$138$		0			0
$139$	2.64590	−	8.14324i	0.224422	−	0.690700i	−0.773928	−	0.633274i	$-0.781711\pi$
$139$	2.64590	−	8.14324i	0.224422	−	0.690700i	0.998350	−	0.0574263i	$-0.0182894\pi$
$140$		0			0
$141$	1.11803	−	0.812299i	0.0941554	−	0.0684079i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	3.19098	−	2.31838i	0.264997	−	0.192531i
$146$		0			0
$147$	−0.135255	+	0.416272i	−0.0111556	+	0.0343335i
$148$		0			0
$149$	3.73607	+	2.71441i	0.306071	+	0.222373i	0.730209	−	0.683224i	$-0.239423\pi$
$149$	3.73607	+	2.71441i	0.306071	+	0.222373i	−0.424138	+	0.905598i	$0.639423\pi$
$150$		0			0
$151$	4.40983	+	13.5721i	0.358867	+	1.10448i	0.953733	+	0.300654i	$0.0972050\pi$
$151$	4.40983	+	13.5721i	0.358867	+	1.10448i	−0.594866	+	0.803825i	$0.702795\pi$
$152$		0			0
$153$	13.1803			1.06557
$154$		0			0
$155$	−3.61803			−0.290607
$156$		0			0
$157$	−0.791796	−	2.43690i	−0.0631922	−	0.194486i	0.914476	−	0.404640i	$-0.132603\pi$
$157$	−0.791796	−	2.43690i	−0.0631922	−	0.194486i	−0.977668	+	0.210155i	$0.932603\pi$
$158$		0			0
$159$	2.19098	+	1.59184i	0.173756	+	0.126241i
$160$		0			0
$161$	−5.70820	+	17.5680i	−0.449869	+	1.38456i
$162$		0			0
$163$	3.50000	−	2.54290i	0.274141	−	0.199175i	−0.442217	−	0.896908i	$-0.645808\pi$
$163$	3.50000	−	2.54290i	0.274141	−	0.199175i	0.716358	+	0.697733i	$0.245808\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.50000	+	3.99598i	−0.425603	+	0.309219i	−0.779888	−	0.625919i	$-0.784724\pi$
$167$	−5.50000	+	3.99598i	−0.425603	+	0.309219i	0.354285	+	0.935137i	$0.384724\pi$
$168$		0			0
$169$	2.57295	−	7.91872i	0.197919	−	0.609133i
$170$		0			0
$171$	6.59017	+	4.78804i	0.503963	+	0.366150i
$172$		0			0
$173$	−5.50000	−	16.9273i	−0.418157	−	1.28696i	−0.909396	−	0.415931i	$-0.863456\pi$
$173$	−5.50000	−	16.9273i	−0.418157	−	1.28696i	0.491239	−	0.871025i	$-0.336544\pi$
$174$		0			0
$175$	13.1803			0.996340
$176$		0			0
$177$	3.85410			0.289692
$178$		0			0
$179$	−0.118034	−	0.363271i	−0.00882227	−	0.0271522i	0.946548	−	0.322562i	$-0.104544\pi$
$179$	−0.118034	−	0.363271i	−0.00882227	−	0.0271522i	−0.955371	+	0.295409i	$0.904544\pi$
$180$		0			0
$181$	−0.500000	−	0.363271i	−0.0371647	−	0.0270017i	0.569048	−	0.822304i	$-0.307312\pi$
$181$	−0.500000	−	0.363271i	−0.0371647	−	0.0270017i	−0.606213	+	0.795303i	$0.707312\pi$
$182$		0			0
$183$	0.545085	−	1.67760i	0.0402938	−	0.124012i
$184$		0			0
$185$	−2.42705	+	1.76336i	−0.178440	+	0.129644i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	5.16312	−	3.75123i	0.375562	−	0.272862i
$190$		0			0
$191$	−0.937694	+	2.88593i	−0.0678492	+	0.208818i	−0.979233	−	0.202740i	$-0.935015\pi$
$191$	−0.937694	+	2.88593i	−0.0678492	+	0.208818i	0.911383	+	0.411558i	$0.135015\pi$
$192$		0			0
$193$	−1.97214	−	1.43284i	−0.141957	−	0.103138i	0.514540	−	0.857466i	$-0.327963\pi$
$193$	−1.97214	−	1.43284i	−0.141957	−	0.103138i	−0.656497	+	0.754328i	$0.727963\pi$
$194$		0			0
$195$	0.336881	+	1.03681i	0.0241246	+	0.0742477i
$196$		0			0
$197$	−14.9443			−1.06474			−0.532368	−	0.846513i	$-0.678698\pi$
$197$	−14.9443			−1.06474			−0.532368	+	0.846513i	$0.678698\pi$
$198$		0			0
$199$	16.9443			1.20115			0.600574	−	0.799569i	$-0.294939\pi$
$199$	16.9443			1.20115			0.600574	+	0.799569i	$0.294939\pi$
$200$		0			0
$201$	0.583592	+	1.79611i	0.0411634	+	0.126688i
$202$		0			0
$203$	−14.7361	−	10.7064i	−1.03427	−	0.751441i
$204$		0			0
$205$	−1.21885	+	3.75123i	−0.0851280	+	0.261997i
$206$		0			0
$207$	14.9443	−	10.8576i	1.03870	−	0.754659i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	18.6803	−	13.5721i	1.28601	−	0.934339i	0.286291	−	0.958143i	$-0.407578\pi$
$211$	18.6803	−	13.5721i	1.28601	−	0.934339i	0.999717	+	0.0238035i	$0.00757760\pi$
$212$		0			0
$213$	1.01722	−	3.13068i	0.0696988	−	0.214511i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	5.16312	+	15.8904i	0.350495	+	1.07871i
$218$		0			0
$219$	−4.61803			−0.312058
$220$		0			0
$221$	21.3262			1.43456
$222$		0			0
$223$	−5.82624	−	17.9313i	−0.390154	−	1.20077i	−0.932672	−	0.360726i	$-0.882529\pi$
$223$	−5.82624	−	17.9313i	−0.390154	−	1.20077i	0.542518	−	0.840044i	$-0.317471\pi$
$224$		0			0
$225$	−10.6631	−	7.74721i	−0.710875	−	0.516481i
$226$		0			0
$227$	−6.59017	+	20.2825i	−0.437405	+	1.34619i	0.453197	+	0.891410i	$0.350283\pi$
$227$	−6.59017	+	20.2825i	−0.437405	+	1.34619i	−0.890602	+	0.454784i	$0.849717\pi$
$228$		0			0
$229$	13.9721	−	10.1514i	0.923305	−	0.670820i	−0.0210397	−	0.999779i	$-0.506698\pi$
$229$	13.9721	−	10.1514i	0.923305	−	0.670820i	0.944344	+	0.328958i	$0.106698\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.73607	−	2.71441i	0.244758	−	0.177827i	−0.458642	−	0.888621i	$-0.651664\pi$
$233$	3.73607	−	2.71441i	0.244758	−	0.177827i	0.703400	+	0.710794i	$0.251664\pi$
$234$		0			0
$235$	0.690983	−	2.12663i	0.0450748	−	0.138726i
$236$		0			0
$237$	4.28115	+	3.11044i	0.278091	+	0.202045i
$238$		0			0
$239$	−2.64590	−	8.14324i	−0.171149	−	0.526742i	0.828288	−	0.560303i	$-0.189315\pi$
$239$	−2.64590	−	8.14324i	−0.171149	−	0.526742i	−0.999437	+	0.0335607i	$0.989315\pi$
$240$		0			0
$241$	−3.52786			−0.227250			−0.113625	−	0.993524i	$-0.536246\pi$
$241$	−3.52786			−0.227250			−0.113625	+	0.993524i	$0.536246\pi$
$242$		0			0
$243$	−9.65248			−0.619207
$244$		0			0
$245$	0.218847	+	0.673542i	0.0139816	+	0.0430310i
$246$		0			0
$247$	10.6631	+	7.74721i	0.678478	+	0.492943i
$248$		0			0
$249$	−1.89261	+	5.82485i	−0.119939	+	0.369135i
$250$		0			0
$251$	−0.972136	+	0.706298i	−0.0613607	+	0.0445811i	−0.618043	−	0.786144i	$-0.712074\pi$
$251$	−0.972136	+	0.706298i	−0.0613607	+	0.0445811i	0.556682	+	0.830726i	$0.312074\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−0.881966	+	0.640786i	−0.0552309	+	0.0401276i
$256$		0			0
$257$	−4.97214	+	15.3027i	−0.310153	+	0.954554i	0.667550	+	0.744565i	$0.267343\pi$
$257$	−4.97214	+	15.3027i	−0.310153	+	0.954554i	−0.977704	+	0.209989i	$0.932657\pi$
$258$		0			0
$259$	11.2082	+	8.14324i	0.696444	+	0.505996i
$260$		0			0
$261$	5.62868	+	17.3233i	0.348406	+	1.07228i
$262$		0			0
$263$	29.8885			1.84301			0.921503	−	0.388371i	$-0.126962\pi$
$263$	29.8885			1.84301			0.921503	+	0.388371i	$0.126962\pi$
$264$		0			0
$265$	4.38197			0.269182
$266$		0			0
$267$	1.00000	+	3.07768i	0.0611990	+	0.188351i
$268$		0			0
$269$	10.4443	+	7.58821i	0.636798	+	0.462661i	0.858749	−	0.512397i	$-0.171242\pi$
$269$	10.4443	+	7.58821i	0.636798	+	0.462661i	−0.221950	+	0.975058i	$0.571242\pi$
$270$		0			0
$271$	−4.40983	+	13.5721i	−0.267878	+	0.824444i	0.723138	+	0.690703i	$0.242699\pi$
$271$	−4.40983	+	13.5721i	−0.267878	+	0.824444i	−0.991016	+	0.133741i	$0.957301\pi$
$272$		0			0
$273$	4.07295	−	2.95917i	0.246506	−	0.179097i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−1.97214	+	1.43284i	−0.118494	+	0.0860911i	−0.645454	−	0.763799i	$-0.723332\pi$
$277$	−1.97214	+	1.43284i	−0.118494	+	0.0860911i	0.526960	+	0.849890i	$0.323332\pi$
$278$		0			0
$279$	5.16312	−	15.8904i	0.309108	−	0.951336i
$280$		0			0
$281$	9.44427	+	6.86167i	0.563398	+	0.409333i	0.832701	−	0.553723i	$-0.186793\pi$
$281$	9.44427	+	6.86167i	0.563398	+	0.409333i	−0.269303	+	0.963056i	$0.586793\pi$
$282$		0			0
$283$	−2.64590	−	8.14324i	−0.157282	−	0.484065i	0.841103	−	0.540875i	$-0.181907\pi$
$283$	−2.64590	−	8.14324i	−0.157282	−	0.484065i	−0.998385	+	0.0568103i	$0.981907\pi$
$284$		0			0
$285$	−0.673762			−0.0399102
$286$		0			0
$287$	18.2148			1.07518
$288$		0			0
$289$	1.33688	+	4.11450i	0.0786401	+	0.242029i
$290$		0			0
$291$	1.71885	+	1.24882i	0.100761	+	0.0732069i
$292$		0			0
$293$	−1.97214	+	6.06961i	−0.115213	+	0.354590i	−0.991991	−	0.126305i	$-0.959688\pi$
$293$	−1.97214	+	6.06961i	−0.115213	+	0.354590i	0.876778	+	0.480895i	$0.159688\pi$
$294$		0			0
$295$	5.04508	−	3.66547i	0.293736	−	0.213412i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	24.1803	−	17.5680i	1.39839	−	1.01599i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	2.10081	+	1.52633i	0.120689	+	0.0876854i
$304$		0			0
$305$	−0.881966	−	2.71441i	−0.0505012	−	0.155427i
$306$		0			0
$307$	−18.4721			−1.05426			−0.527130	−	0.849785i	$-0.676732\pi$
$307$	−18.4721			−1.05426			−0.527130	+	0.849785i	$0.676732\pi$
$308$		0			0
$309$	0.437694			0.0248995
$310$		0			0
$311$	−2.40983	−	7.41669i	−0.136649	−	0.420562i	0.859194	−	0.511650i	$-0.170966\pi$
$311$	−2.40983	−	7.41669i	−0.136649	−	0.420562i	−0.995843	+	0.0910879i	$0.970966\pi$
$312$		0			0
$313$	−24.6803	−	17.9313i	−1.39502	−	1.01354i	−0.995294	−	0.0969012i	$-0.969107\pi$
$313$	−24.6803	−	17.9313i	−1.39502	−	1.01354i	−0.399721	−	0.916637i	$-0.630893\pi$
$314$		0			0
$315$	1.55573	−	4.78804i	0.0876553	−	0.269775i
$316$		0			0
$317$	−4.50000	+	3.26944i	−0.252745	+	0.183630i	−0.706943	−	0.707271i	$-0.749926\pi$
$317$	−4.50000	+	3.26944i	−0.252745	+	0.183630i	0.454197	+	0.890901i	$0.349926\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−2.64590	+	1.92236i	−0.147680	+	0.107296i
$322$		0			0
$323$	−4.07295	+	12.5352i	−0.226625	+	0.697480i
$324$		0			0
$325$	−17.2533	−	12.5352i	−0.957040	−	0.695330i
$326$		0			0
$327$	−0.416408	−	1.28157i	−0.0230274	−	0.0708711i
$328$		0			0
$329$	−10.3262			−0.569304
$330$		0			0
$331$	−12.0000			−0.659580			−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000			−0.659580			−0.329790	+	0.944054i	$0.606978\pi$
$332$		0			0
$333$	−4.28115	−	13.1760i	−0.234606	−	0.722042i
$334$		0			0
$335$	2.47214	+	1.79611i	0.135067	+	0.0981321i
$336$		0			0
$337$	1.55573	−	4.78804i	0.0847459	−	0.260821i	−0.899700	−	0.436509i	$-0.856215\pi$
$337$	1.55573	−	4.78804i	0.0847459	−	0.260821i	0.984446	+	0.175688i	$0.0562148\pi$
$338$		0			0
$339$	−0.791796	+	0.575274i	−0.0430045	+	0.0312446i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−13.5172	+	9.82084i	−0.729861	+	0.530275i
$344$		0			0
$345$	−0.472136	+	1.45309i	−0.0254189	+	0.0782315i
$346$		0			0
$347$	5.50000	+	3.99598i	0.295255	+	0.214516i	0.725544	−	0.688176i	$-0.241588\pi$
$347$	5.50000	+	3.99598i	0.295255	+	0.214516i	−0.430289	+	0.902691i	$0.641588\pi$
$348$		0			0
$349$	0.208204	+	0.640786i	0.0111449	+	0.0343005i	0.956474	−	0.291817i	$-0.0942597\pi$
$349$	0.208204	+	0.640786i	0.0111449	+	0.0343005i	−0.945329	+	0.326117i	$0.894260\pi$
$350$		0			0
$351$	−10.3262			−0.551174
$352$		0			0
$353$	2.94427			0.156708			0.0783539	−	0.996926i	$-0.475034\pi$
$353$	2.94427			0.156708			0.0783539	+	0.996926i	$0.475034\pi$
$354$		0			0
$355$	−1.64590	−	5.06555i	−0.0873552	−	0.268852i
$356$		0			0
$357$	4.07295	+	2.95917i	0.215563	+	0.156616i
$358$		0			0
$359$	2.64590	−	8.14324i	0.139645	−	0.429784i	−0.856638	−	0.515917i	$-0.827451\pi$
$359$	2.64590	−	8.14324i	0.139645	−	0.429784i	0.996284	+	0.0861336i	$0.0274512\pi$
$360$		0			0
$361$	8.78115	−	6.37988i	0.462166	−	0.335783i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6.04508	+	4.39201i	−0.316414	+	0.229888i
$366$		0			0
$367$	8.29837	−	25.5398i	0.433172	−	1.33317i	−0.461777	−	0.886996i	$-0.652788\pi$
$367$	8.29837	−	25.5398i	0.433172	−	1.33317i	0.894949	−	0.446169i	$-0.147212\pi$
$368$		0			0
$369$	−14.7361	−	10.7064i	−0.767129	−	0.557352i
$370$		0			0
$371$	−6.25329	−	19.2456i	−0.324655	−	0.999184i
$372$		0			0
$373$	33.4164			1.73024			0.865118	−	0.501568i	$-0.167243\pi$
$373$	33.4164			1.73024			0.865118	+	0.501568i	$0.167243\pi$
$374$		0			0
$375$	2.27051			0.117249
$376$		0			0
$377$	9.10739	+	28.0297i	0.469054	+	1.44360i
$378$		0			0
$379$	−7.97214	−	5.79210i	−0.409501	−	0.297520i	0.363899	−	0.931439i	$-0.381445\pi$
$379$	−7.97214	−	5.79210i	−0.409501	−	0.297520i	−0.773400	+	0.633919i	$0.781445\pi$
$380$		0			0
$381$	−0.545085	+	1.67760i	−0.0279255	+	0.0859460i
$382$		0			0
$383$	−25.1525	+	18.2743i	−1.28523	+	0.933775i	−0.999698	−	0.0245933i	$-0.992171\pi$
$383$	−25.1525	+	18.2743i	−1.28523	+	0.933775i	−0.285534	+	0.958369i	$0.592171\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−0.680340	+	2.09387i	−0.0344946	+	0.106163i	−0.966821	−	0.255454i	$-0.917775\pi$
$389$	−0.680340	+	2.09387i	−0.0344946	+	0.106163i	0.932327	+	0.361617i	$0.117775\pi$
$390$		0			0
$391$	24.1803	+	17.5680i	1.22285	+	0.888454i
$392$		0			0
$393$	2.18034	+	6.71040i	0.109984	+	0.338495i
$394$		0			0
$395$	8.56231			0.430816
$396$		0			0
$397$	−20.8328			−1.04557			−0.522785	−	0.852465i	$-0.675107\pi$
$397$	−20.8328			−1.04557			−0.522785	+	0.852465i	$0.675107\pi$
$398$		0			0
$399$	0.961493	+	2.95917i	0.0481348	+	0.148144i
$400$		0			0
$401$	28.9164	+	21.0090i	1.44402	+	1.04914i	0.987184	+	0.159587i	$0.0510162\pi$
$401$	28.9164	+	21.0090i	1.44402	+	1.04914i	0.456833	+	0.889553i	$0.348984\pi$
$402$		0			0
$403$	8.35410	−	25.7113i	0.416147	−	1.28077i
$404$		0			0
$405$	−3.85410	+	2.80017i	−0.191512	+	0.139142i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−11.2082	+	8.14324i	−0.554210	+	0.402657i	−0.829335	−	0.558751i	$-0.811281\pi$
$409$	−11.2082	+	8.14324i	−0.554210	+	0.402657i	0.275125	+	0.961408i	$0.411281\pi$
$410$		0			0
$411$	1.27458	−	3.92274i	0.0628702	−	0.193494i
$412$		0			0
$413$	−23.2984	−	16.9273i	−1.14644	−	0.832936i
$414$		0			0
$415$	3.06231	+	9.42481i	0.150323	+	0.462646i
$416$		0			0
$417$	−3.27051			−0.160158
$418$		0			0
$419$	−31.4164			−1.53479			−0.767396	−	0.641173i	$-0.778448\pi$
$419$	−31.4164			−1.53479			−0.767396	+	0.641173i	$0.778448\pi$
$420$		0			0
$421$	7.50000	+	23.0826i	0.365528	+	1.12498i	0.949650	+	0.313313i	$0.101439\pi$
$421$	7.50000	+	23.0826i	0.365528	+	1.12498i	−0.584122	+	0.811666i	$0.698561\pi$
$422$		0			0
$423$	8.35410	+	6.06961i	0.406190	+	0.295115i
$424$		0			0
$425$	6.59017	−	20.2825i	0.319670	−	0.983844i
$426$		0			0
$427$	−10.6631	+	7.74721i	−0.516024	+	0.374914i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−26.1525	+	19.0009i	−1.25972	+	0.915240i	−0.998744	−	0.0501047i	$-0.984044\pi$
$431$	−26.1525	+	19.0009i	−1.25972	+	0.915240i	−0.260976	+	0.965345i	$0.584044\pi$
$432$		0			0
$433$	−11.2639	+	34.6668i	−0.541310	+	1.66598i	0.188295	+	0.982112i	$0.439704\pi$
$433$	−11.2639	+	34.6668i	−0.541310	+	1.66598i	−0.729605	+	0.683868i	$0.760296\pi$
$434$		0			0
$435$	−1.21885	−	0.885544i	−0.0584392	−	0.0424586i
$436$		0			0
$437$	5.70820	+	17.5680i	0.273060	+	0.840394i
$438$		0			0
$439$	−11.4164			−0.544875			−0.272438	−	0.962173i	$-0.587830\pi$
$439$	−11.4164			−0.544875			−0.272438	+	0.962173i	$0.587830\pi$
$440$		0			0
$441$	−3.27051			−0.155739
$442$		0			0
$443$	−9.35410	−	28.7890i	−0.444427	−	1.36781i	−0.883111	−	0.469164i	$-0.844555\pi$
$443$	−9.35410	−	28.7890i	−0.444427	−	1.36781i	0.438684	−	0.898641i	$-0.355445\pi$
$444$		0			0
$445$	4.23607	+	3.07768i	0.200809	+	0.145896i
$446$		0			0
$447$	0.545085	−	1.67760i	0.0257816	−	0.0793477i
$448$		0			0
$449$	−4.50000	+	3.26944i	−0.212368	+	0.154294i	−0.688885	−	0.724871i	$-0.741899\pi$
$449$	−4.50000	+	3.26944i	−0.212368	+	0.154294i	0.476516	+	0.879166i	$0.341899\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	4.40983	−	3.20393i	0.207192	−	0.150534i
$454$		0			0
$455$	2.51722	−	7.74721i	0.118009	−	0.363195i
$456$		0			0
$457$	−11.2082	−	8.14324i	−0.524298	−	0.380925i	0.293923	−	0.955829i	$-0.405039\pi$
$457$	−11.2082	−	8.14324i	−0.524298	−	0.380925i	−0.818220	+	0.574905i	$0.805039\pi$
$458$		0			0
$459$	−3.19098	−	9.82084i	−0.148942	−	0.458397i
$460$		0			0
$461$	−37.7771			−1.75945			−0.879727	−	0.475479i	$-0.842275\pi$
$461$	−37.7771			−1.75945			−0.879727	+	0.475479i	$0.842275\pi$
$462$		0			0
$463$	−12.0000			−0.557687			−0.278844	−	0.960337i	$-0.589951\pi$
$463$	−12.0000			−0.557687			−0.278844	+	0.960337i	$0.589951\pi$
$464$		0			0
$465$	0.427051	+	1.31433i	0.0198040	+	0.0609505i
$466$		0			0
$467$	−22.9164	−	16.6497i	−1.06044	−	0.770458i	−0.0862742	−	0.996271i	$-0.527496\pi$
$467$	−22.9164	−	16.6497i	−1.06044	−	0.770458i	−0.974171	+	0.225813i	$0.927496\pi$
$468$		0			0
$469$	4.36068	−	13.4208i	0.201357	−	0.619715i
$470$		0			0
$471$	−0.791796	+	0.575274i	−0.0364840	+	0.0265072i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	10.6631	−	7.74721i	0.489257	−	0.355466i
$476$		0			0
$477$	−6.25329	+	19.2456i	−0.286318	+	0.881198i
$478$		0			0
$479$	−9.44427	−	6.86167i	−0.431520	−	0.313517i	0.350737	−	0.936474i	$-0.385931\pi$
$479$	−9.44427	−	6.86167i	−0.431520	−	0.313517i	−0.782256	+	0.622957i	$0.785931\pi$
$480$		0			0
$481$	−6.92705	−	21.3193i	−0.315846	−	0.972075i
$482$		0			0
$483$	7.05573			0.321047
$484$		0			0
$485$	3.43769			0.156098
$486$		0			0
$487$	3.40983	+	10.4944i	0.154514	+	0.475546i	0.998111	−	0.0614309i	$-0.0195664\pi$
$487$	3.40983	+	10.4944i	0.154514	+	0.475546i	−0.843597	+	0.536977i	$0.819566\pi$
$488$		0			0
$489$	−1.33688	−	0.971301i	−0.0604559	−	0.0439237i
$490$		0			0
$491$	2.64590	−	8.14324i	0.119408	−	0.367499i	−0.873433	−	0.486944i	$-0.838112\pi$
$491$	2.64590	−	8.14324i	0.119408	−	0.367499i	0.992841	+	0.119445i	$0.0381115\pi$
$492$		0			0
$493$	−23.8435	+	17.3233i	−1.07386	+	0.780202i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−19.8992	+	14.4576i	−0.892601	+	0.648512i
$498$		0			0
$499$	3.17376	−	9.76784i	0.142077	−	0.437268i	−0.854546	−	0.519375i	$-0.826165\pi$
$499$	3.17376	−	9.76784i	0.142077	−	0.437268i	0.996624	+	0.0821066i	$0.0261648\pi$
$500$		0			0
$501$	2.10081	+	1.52633i	0.0938574	+	0.0681914i
$502$		0			0
$503$	−0.465558	−	1.43284i	−0.0207582	−	0.0638872i	0.940141	−	0.340786i	$-0.110693\pi$
$503$	−0.465558	−	1.43284i	−0.0207582	−	0.0638872i	−0.960899	+	0.276899i	$0.910693\pi$
$504$		0			0
$505$	4.20163			0.186970
$506$		0			0
$507$	−3.18034			−0.141244
$508$		0			0
$509$	9.79180	+	30.1360i	0.434014	+	1.33576i	0.894094	+	0.447880i	$0.147821\pi$
$509$	9.79180	+	30.1360i	0.434014	+	1.33576i	−0.460080	+	0.887877i	$0.652179\pi$
$510$		0			0
$511$	27.9164	+	20.2825i	1.23495	+	0.897243i
$512$		0			0
$513$	1.97214	−	6.06961i	0.0870719	−	0.267980i
$514$		0			0
$515$	0.572949	−	0.416272i	0.0252472	−	0.0183431i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−5.50000	+	3.99598i	−0.241423	+	0.175404i
$520$		0			0
$521$	7.20820	−	22.1846i	0.315797	−	0.971924i	−0.659628	−	0.751592i	$-0.729286\pi$
$521$	7.20820	−	22.1846i	0.315797	−	0.971924i	0.975425	−	0.220331i	$-0.0707139\pi$
$522$		0			0
$523$	−22.2082	−	16.1352i	−0.971097	−	0.705543i	−0.0153956	−	0.999881i	$-0.504901\pi$
$523$	−22.2082	−	16.1352i	−0.971097	−	0.705543i	−0.955701	+	0.294338i	$0.904901\pi$
$524$		0			0
$525$	−1.55573	−	4.78804i	−0.0678975	−	0.208967i
$526$		0			0
$527$	27.0344			1.17764
$528$		0			0
$529$	18.8885			0.821241
$530$		0			0
$531$	8.89919	+	27.3889i	0.386192	+	1.18858i
$532$		0			0
$533$	−23.8435	−	17.3233i	−1.03277	−	0.750355i
$534$		0			0
$535$	−1.63525	+	5.03280i	−0.0706982	+	0.217587i
$536$		0			0
$537$	−0.118034	+	0.0857567i	−0.00509354	+	0.00370068i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−20.4443	+	14.8536i	−0.878968	+	0.638608i	−0.932978	−	0.359933i	$-0.882800\pi$
$541$	−20.4443	+	14.8536i	−0.878968	+	0.638608i	0.0540103	+	0.998540i	$0.482800\pi$
$542$		0			0
$543$	−0.0729490	+	0.224514i	−0.00313054	+	0.00963482i
$544$		0			0
$545$	−1.76393	−	1.28157i	−0.0755585	−	0.0548965i
$546$		0			0
$547$	−7.00658	−	21.5640i	−0.299580	−	0.922011i	−0.981645	−	0.190720i	$-0.938918\pi$
$547$	−7.00658	−	21.5640i	−0.299580	−	0.922011i	0.682065	−	0.731292i	$-0.261082\pi$
$548$		0			0
$549$	13.1803			0.562523
$550$		0			0
$551$	−18.2148			−0.775976
$552$		0			0
$553$	−12.2188	−	37.6057i	−0.519598	−	1.59916i
$554$		0			0
$555$	0.927051	+	0.673542i	0.0393511	+	0.0285903i
$556$		0			0
$557$	−3.31966	+	10.2169i	−0.140659	+	0.432902i	−0.996427	−	0.0844563i	$-0.973085\pi$
$557$	−3.31966	+	10.2169i	−0.140659	+	0.432902i	0.855769	+	0.517359i	$0.173085\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.9721	−	9.42481i	0.546710	−	0.397208i	−0.279861	−	0.960041i	$-0.590288\pi$
$563$	12.9721	−	9.42481i	0.546710	−	0.397208i	0.826571	+	0.562832i	$0.190288\pi$
$564$		0			0
$565$	−0.489357	+	1.50609i	−0.0205874	+	0.0633615i
$566$		0			0
$567$	17.7984	+	12.9313i	0.747461	+	0.543063i
$568$		0			0
$569$	10.7918	+	33.2137i	0.452416	+	1.39239i	0.874143	+	0.485669i	$0.161424\pi$
$569$	10.7918	+	33.2137i	0.452416	+	1.39239i	−0.421727	+	0.906723i	$0.638576\pi$
$570$		0			0
$571$	−18.4721			−0.773035			−0.386517	−	0.922282i	$-0.626322\pi$
$571$	−18.4721			−0.773035			−0.386517	+	0.922282i	$0.626322\pi$
$572$		0			0
$573$	1.15905			0.0484202
$574$		0			0
$575$	−9.23607	−	28.4257i	−0.385171	−	1.18543i
$576$		0			0
$577$	20.1525	+	14.6416i	0.838959	+	0.609539i	0.922080	−	0.387000i	$-0.126489\pi$
$577$	20.1525	+	14.6416i	0.838959	+	0.609539i	−0.0831210	+	0.996539i	$0.526489\pi$
$578$		0			0
$579$	−0.287731	+	0.885544i	−0.0119577	+	0.0368020i
$580$		0			0
$581$	37.0238	−	26.8994i	1.53601	−	1.11597i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−6.59017	+	4.78804i	−0.272470	+	0.197961i
$586$		0			0
$587$	−0.354102	+	1.08981i	−0.0146154	+	0.0449814i	−0.958098	−	0.286440i	$-0.907528\pi$
$587$	−0.354102	+	1.08981i	−0.0146154	+	0.0449814i	0.943483	+	0.331421i	$0.107528\pi$
$588$		0			0
$589$	13.5172	+	9.82084i	0.556967	+	0.404660i
$590$		0			0
$591$	1.76393	+	5.42882i	0.0725585	+	0.223312i
$592$		0			0
$593$	−10.5836			−0.434616			−0.217308	−	0.976103i	$-0.569728\pi$
$593$	−10.5836			−0.434616			−0.217308	+	0.976103i	$0.569728\pi$
$594$		0			0
$595$	8.14590			0.333949
$596$		0			0
$597$	−2.00000	−	6.15537i	−0.0818546	−	0.251922i
$598$		0			0
$599$	0.791796	+	0.575274i	0.0323519	+	0.0235050i	0.603844	−	0.797103i	$-0.293635\pi$
$599$	0.791796	+	0.575274i	0.0323519	+	0.0235050i	−0.571492	+	0.820608i	$0.693635\pi$
$600$		0			0
$601$	−4.15248	+	12.7800i	−0.169383	+	0.521307i	−0.999333	−	0.0365312i	$-0.988369\pi$
$601$	−4.15248	+	12.7800i	−0.169383	+	0.521307i	0.829949	+	0.557839i	$0.188369\pi$
$602$		0			0
$603$	−11.4164	+	8.29451i	−0.464912	+	0.337778i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	33.6246	−	24.4297i	1.36478	−	0.991571i	0.366656	−	0.930356i	$-0.380503\pi$
$607$	33.6246	−	24.4297i	1.36478	−	0.991571i	0.998125	−	0.0612149i	$-0.0194975\pi$
$608$		0			0
$609$	−2.14996	+	6.61691i	−0.0871209	+	0.268131i
$610$		0			0
$611$	13.5172	+	9.82084i	0.546848	+	0.397308i
$612$		0			0
$613$	9.44427	+	29.0665i	0.381451	+	1.17398i	0.939023	+	0.343856i	$0.111733\pi$
$613$	9.44427	+	29.0665i	0.381451	+	1.17398i	−0.557572	+	0.830129i	$0.688267\pi$
$614$		0			0
$615$	1.50658			0.0607511
$616$		0			0
$617$	−16.4721			−0.663143			−0.331572	−	0.943430i	$-0.607579\pi$
$617$	−16.4721			−0.663143			−0.331572	+	0.943430i	$0.607579\pi$
$618$		0			0
$619$	2.06231	+	6.34712i	0.0828911	+	0.255112i	0.983909	−	0.178669i	$-0.0571791\pi$
$619$	2.06231	+	6.34712i	0.0828911	+	0.255112i	−0.901018	+	0.433781i	$0.857179\pi$
$620$		0			0
$621$	−11.7082	−	8.50651i	−0.469834	−	0.341354i
$622$		0			0
$623$	7.47214	−	22.9969i	0.299365	−	0.921350i
$624$		0			0
$625$	−15.7082	+	11.4127i	−0.628328	+	0.456507i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	18.1353	−	13.1760i	0.723100	−	0.525363i
$630$		0			0
$631$	−5.29837	+	16.3067i	−0.210925	+	0.649160i	0.788493	+	0.615044i	$0.210862\pi$
$631$	−5.29837	+	16.3067i	−0.210925	+	0.649160i	−0.999418	+	0.0341164i	$0.989138\pi$
$632$		0			0
$633$	−7.13525	−	5.18407i	−0.283601	−	0.206048i
$634$		0			0
$635$	0.881966	+	2.71441i	0.0349998	+	0.107718i
$636$		0			0
$637$	−5.29180			−0.209669
$638$		0			0
$639$	24.5967			0.973032
$640$		0			0
$641$	4.91641	+	15.1311i	0.194186	+	0.597644i	0.999985	+	0.00545483i	$0.00173634\pi$
$641$	4.91641	+	15.1311i	0.194186	+	0.597644i	−0.805799	+	0.592190i	$0.798264\pi$
$642$		0			0
$643$	−17.2082	−	12.5025i	−0.678625	−	0.493050i	0.194276	−	0.980947i	$-0.437764\pi$
$643$	−17.2082	−	12.5025i	−0.678625	−	0.493050i	−0.872901	+	0.487897i	$0.837764\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	28.9164	−	21.0090i	1.13682	−	0.825949i	0.150148	−	0.988664i	$-0.452025\pi$
$647$	28.9164	−	21.0090i	1.13682	−	0.825949i	0.986673	+	0.162714i	$0.0520249\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	5.16312	−	3.75123i	0.202359	−	0.147022i
$652$		0			0
$653$	7.20820	−	22.1846i	0.282079	−	0.868149i	−0.705180	−	0.709028i	$-0.749134\pi$
$653$	7.20820	−	22.1846i	0.282079	−	0.868149i	0.987259	−	0.159121i	$-0.0508661\pi$
$654$		0			0
$655$	9.23607	+	6.71040i	0.360883	+	0.262197i
$656$		0			0
$657$	−10.6631	−	32.8177i	−0.416008	−	1.28034i
$658$		0			0
$659$	4.36068			0.169868			0.0849340	−	0.996387i	$-0.472932\pi$
$659$	4.36068			0.169868			0.0849340	+	0.996387i	$0.472932\pi$
$660$		0			0
$661$	14.3607			0.558566			0.279283	−	0.960209i	$-0.409903\pi$
$661$	14.3607			0.558566			0.279283	+	0.960209i	$0.409903\pi$
$662$		0			0
$663$	−2.51722	−	7.74721i	−0.0977608	−	0.300877i
$664$		0			0
$665$	4.07295	+	2.95917i	0.157942	+	0.114752i
$666$		0			0
$667$	−12.7639	+	39.2833i	−0.494221	+	1.52106i
$668$		0			0
$669$	−5.82624	+	4.23301i	−0.225255	+	0.163658i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	24.3885	−	17.7193i	0.940109	−	0.683029i	−0.00833769	−	0.999965i	$-0.502654\pi$
$673$	24.3885	−	17.7193i	0.940109	−	0.683029i	0.948447	+	0.316936i	$0.102654\pi$
$674$		0			0
$675$	−3.19098	+	9.82084i	−0.122821	+	0.378004i
$676$		0			0
$677$	27.9164	+	20.2825i	1.07291	+	0.779518i	0.976434	−	0.215817i	$-0.0692414\pi$
$677$	27.9164	+	20.2825i	1.07291	+	0.779518i	0.0964808	+	0.995335i	$0.469241\pi$
$678$		0			0
$679$	−4.90576	−	15.0984i	−0.188266	−	0.579423i
$680$		0			0
$681$	8.14590			0.312151
$682$		0			0
$683$	16.9443			0.648355			0.324177	−	0.945996i	$-0.394913\pi$
$683$	16.9443			0.648355			0.324177	+	0.945996i	$0.394913\pi$
$684$		0			0
$685$	−2.06231	−	6.34712i	−0.0787967	−	0.242511i
$686$		0			0
$687$	−5.33688	−	3.87747i	−0.203615	−	0.147935i
$688$		0			0
$689$	−10.1180	+	31.1401i	−0.385466	+	1.18634i
$690$		0			0
$691$	10.4443	−	7.58821i	0.397319	−	0.288669i	−0.371129	−	0.928581i	$-0.621029\pi$
$691$	10.4443	−	7.58821i	0.397319	−	0.288669i	0.768448	+	0.639912i	$0.221029\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.28115	+	3.11044i	−0.162393	+	0.117986i
$696$		0			0
$697$	9.10739	−	28.0297i	0.344967	−	1.06170i
$698$		0			0
$699$	−1.42705	−	1.03681i	−0.0539760	−	0.0392159i
$700$		0			0
$701$	−0.624612	−	1.92236i	−0.0235913	−	0.0726064i	0.938568	−	0.345095i	$-0.112153\pi$
$701$	−0.624612	−	1.92236i	−0.0235913	−	0.0726064i	−0.962159	+	0.272489i	$0.912153\pi$
$702$		0			0
$703$	13.8541			0.522517
$704$		0			0
$705$	−0.854102			−0.0321673
$706$		0			0
$707$	−5.99593	−	18.4536i	−0.225500	−	0.694019i
$708$		0			0
$709$	−6.20820	−	4.51052i	−0.233154	−	0.169396i	0.465074	−	0.885272i	$-0.346028\pi$
$709$	−6.20820	−	4.51052i	−0.233154	−	0.169396i	−0.698228	+	0.715876i	$0.746028\pi$
$710$		0			0
$711$	−12.2188	+	37.6057i	−0.458243	+	1.41033i
$712$		0			0
$713$	30.6525	−	22.2703i	1.14794	−	0.834030i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−2.64590	+	1.92236i	−0.0988129	+	0.0717918i
$718$		0			0
$719$	−1.77051	+	5.44907i	−0.0660289	+	0.203216i	−0.978628	−	0.205640i	$-0.934072\pi$
$719$	−1.77051	+	5.44907i	−0.0660289	+	0.203216i	0.912599	+	0.408856i	$0.134072\pi$
$720$		0			0
$721$	−2.64590	−	1.92236i	−0.0985384	−	0.0715923i
$722$		0			0
$723$	0.416408	+	1.28157i	0.0154864	+	0.0476622i
$724$		0			0
$725$	29.4721			1.09457
$726$		0			0
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	−6.00658	−	18.4863i	−0.222466	−	0.684679i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−4.15248	+	12.7800i	−0.153375	+	0.472040i	−0.997993	−	0.0633300i	$-0.979828\pi$
$733$	−4.15248	+	12.7800i	−0.153375	+	0.472040i	0.844617	+	0.535370i	$0.179828\pi$
$734$		0			0
$735$	0.218847	−	0.159002i	0.00807230	−	0.00586487i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−29.6803	+	21.5640i	−1.09181	+	0.793246i	−0.979704	−	0.200451i	$-0.935759\pi$
$739$	−29.6803	+	21.5640i	−1.09181	+	0.793246i	−0.112105	+	0.993696i	$0.535759\pi$
$740$		0			0
$741$	1.55573	−	4.78804i	0.0571511	−	0.175893i
$742$		0			0
$743$	−27.9164	−	20.2825i	−1.02415	−	0.744091i	−0.0570235	−	0.998373i	$-0.518161\pi$
$743$	−27.9164	−	20.2825i	−1.02415	−	0.744091i	−0.967130	+	0.254282i	$0.918161\pi$
$744$		0			0
$745$	−0.881966	−	2.71441i	−0.0323127	−	0.0994484i
$746$		0			0
$747$	−45.7639			−1.67441
$748$		0			0
$749$	24.4377			0.892934
$750$		0			0
$751$	5.59017	+	17.2048i	0.203988	+	0.627811i	0.999753	+	0.0222059i	$0.00706893\pi$
$751$	5.59017	+	17.2048i	0.203988	+	0.627811i	−0.795765	+	0.605605i	$0.792931\pi$
$752$		0			0
$753$	0.371323	+	0.269782i	0.0135318	+	0.00983140i
$754$		0			0
$755$	2.72542	−	8.38800i	0.0991884	−	0.305270i
$756$		0			0
$757$	12.7361	−	9.25330i	0.462900	−	0.336317i	−0.331768	−	0.943361i	$-0.607645\pi$
$757$	12.7361	−	9.25330i	0.462900	−	0.336317i	0.794668	+	0.607044i	$0.207645\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	37.1525	−	26.9929i	1.34678	−	0.978490i	0.347611	−	0.937639i	$-0.386993\pi$
$761$	37.1525	−	26.9929i	1.34678	−	0.978490i	0.999165	−	0.0408513i	$-0.0130070\pi$
$762$		0			0
$763$	−3.11146	+	9.57608i	−0.112642	+	0.346677i
$764$		0			0
$765$	−6.59017	−	4.78804i	−0.238268	−	0.173112i
$766$		0			0
$767$	14.3992	+	44.3161i	0.519925	+	1.60016i
$768$		0			0
$769$	−10.5836			−0.381654			−0.190827	−	0.981624i	$-0.561117\pi$
$769$	−10.5836			−0.381654			−0.190827	+	0.981624i	$0.561117\pi$
$770$		0			0
$771$	6.14590			0.221339
$772$		0			0
$773$	−3.91641	−	12.0535i	−0.140863	−	0.433533i	0.855592	−	0.517650i	$-0.173193\pi$
$773$	−3.91641	−	12.0535i	−0.140863	−	0.433533i	−0.996456	+	0.0841170i	$0.973193\pi$
$774$		0			0
$775$	−21.8713	−	15.8904i	−0.785641	−	0.570802i
$776$		0			0
$777$	1.63525	−	5.03280i	0.0586644	−	0.180551i
$778$		0			0
$779$	14.7361	−	10.7064i	0.527974	−	0.383596i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	11.5451	−	8.38800i	0.412588	−	0.299762i
$784$		0			0
$785$	−0.489357	+	1.50609i	−0.0174659	+	0.0537545i
$786$		0			0
$787$	26.1525	+	19.0009i	0.932235	+	0.677308i	0.946539	−	0.322589i	$-0.104553\pi$
$787$	26.1525	+	19.0009i	0.932235	+	0.677308i	−0.0143040	+	0.999898i	$0.504553\pi$
$788$		0			0
$789$	−3.52786	−	10.8576i	−0.125595	−	0.386543i
$790$		0			0
$791$	7.31308			0.260023
$792$		0			0
$793$	21.3262			0.757317
$794$		0			0
$795$	−0.517221	−	1.59184i	−0.0183439	−	0.0564568i
$796$		0			0
$797$	8.73607	+	6.34712i	0.309447	+	0.224827i	0.731659	−	0.681670i	$-0.238746\pi$
$797$	8.73607	+	6.34712i	0.309447	+	0.224827i	−0.422212	+	0.906497i	$0.638746\pi$
$798$		0			0
$799$	−5.16312	+	15.8904i	−0.182658	+	0.562164i
$800$		0			0
$801$	−19.5623	+	14.2128i	−0.691200	+	0.502186i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	9.23607	−	6.71040i	0.325529	−	0.236510i
$806$		0			0
$807$	1.52380	−	4.68977i	0.0536403	−	0.165088i
$808$		0			0
$809$	37.1525	+	26.9929i	1.30621	+	0.949018i	0.999996	−	0.00294392i	$-0.000937079\pi$
$809$	37.1525	+	26.9929i	1.30621	+	0.949018i	0.306216	+	0.951962i	$0.400937\pi$
$810$		0			0
$811$	8.77051	+	26.9929i	0.307974	+	0.947847i	0.978551	+	0.206007i	$0.0660469\pi$
$811$	8.77051	+	26.9929i	0.307974	+	0.947847i	−0.670576	+	0.741841i	$0.733953\pi$
$812$		0			0
$813$	5.45085			0.191170
$814$		0			0
$815$	−2.67376			−0.0936578
$816$		0			0
$817$		0			0
$818$		0			0
$819$	30.4336	+	22.1113i	1.06344	+	0.772632i
$820$		0			0
$821$	5.91641	−	18.2088i	0.206484	−	0.635493i	−0.793165	−	0.609007i	$-0.791568\pi$
$821$	5.91641	−	18.2088i	0.206484	−	0.635493i	0.999649	−	0.0264860i	$-0.00843173\pi$
$822$		0			0
$823$	1.20820	−	0.877812i	0.0421153	−	0.0305986i	−0.566528	−	0.824042i	$-0.691714\pi$
$823$	1.20820	−	0.877812i	0.0421153	−	0.0305986i	0.608644	+	0.793444i	$0.291714\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	12.9721	−	9.42481i	0.451085	−	0.327733i	−0.338939	−	0.940808i	$-0.610068\pi$
$827$	12.9721	−	9.42481i	0.451085	−	0.327733i	0.790024	+	0.613076i	$0.210068\pi$
$828$		0			0
$829$	−14.7918	+	45.5245i	−0.513740	+	1.58113i	0.271822	+	0.962348i	$0.412374\pi$
$829$	−14.7918	+	45.5245i	−0.513740	+	1.58113i	−0.785562	+	0.618783i	$0.787626\pi$
$830$		0			0
$831$	0.753289	+	0.547296i	0.0261313	+	0.0189855i
$832$		0			0
$833$	−1.63525	−	5.03280i	−0.0566582	−	0.174376i
$834$		0			0
$835$	4.20163			0.145403
$836$		0			0
$837$	−13.0902			−0.452462
$838$		0			0
$839$	−0.118034	−	0.363271i	−0.00407499	−	0.0125415i	0.948998	−	0.315281i	$-0.102099\pi$
$839$	−0.118034	−	0.363271i	−0.00407499	−	0.0125415i	−0.953073	+	0.302740i	$0.902099\pi$
$840$		0			0
$841$	−9.48936	−	6.89442i	−0.327219	−	0.237739i
$842$		0			0
$843$	1.37790	−	4.24074i	0.0474574	−	0.146059i
$844$		0			0
$845$	−4.16312	+	3.02468i	−0.143216	+	0.104052i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−2.64590	+	1.92236i	−0.0908070	+	0.0659751i
$850$		0			0
$851$	9.70820	−	29.8788i	0.332793	−	1.02423i
$852$		0			0
$853$	−5.50000	−	3.99598i	−0.188316	−	0.136820i	0.489632	−	0.871929i	$-0.337131\pi$
$853$	−5.50000	−	3.99598i	−0.188316	−	0.136820i	−0.677949	+	0.735109i	$0.737131\pi$
$854$		0			0
$855$	−1.55573	−	4.78804i	−0.0532048	−	0.163747i
$856$		0			0
$857$	14.9443			0.510487			0.255243	−	0.966877i	$-0.417844\pi$
$857$	14.9443			0.510487			0.255243	+	0.966877i	$0.417844\pi$
$858$		0			0
$859$	−48.9443			−1.66996			−0.834979	−	0.550283i	$-0.814520\pi$
$859$	−48.9443			−1.66996			−0.834979	+	0.550283i	$0.814520\pi$
$860$		0			0
$861$	−2.14996	−	6.61691i	−0.0732706	−	0.225504i
$862$		0			0
$863$	−21.2082	−	15.4087i	−0.721936	−	0.524517i	0.165066	−	0.986282i	$-0.447216\pi$
$863$	−21.2082	−	15.4087i	−0.721936	−	0.524517i	−0.887002	+	0.461766i	$0.847216\pi$
$864$		0			0
$865$	−3.39919	+	10.4616i	−0.115576	+	0.355706i
$866$		0			0
$867$	1.33688	−	0.971301i	0.0454029	−	0.0329871i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−18.4721	+	13.4208i	−0.625904	+	0.454746i
$872$		0			0
$873$	−4.90576	+	15.0984i	−0.166035	+	0.511003i
$874$		0			0
$875$	−13.7254	−	9.97210i	−0.464004	−	0.337119i
$876$		0			0
$877$	−13.3885	−	41.2057i	−0.452099	−	1.39142i	−0.874507	−	0.485012i	$-0.838815\pi$
$877$	−13.3885	−	41.2057i	−0.452099	−	1.39142i	0.422408	−	0.906406i	$-0.361185\pi$
$878$		0			0
$879$	2.43769			0.0822214
$880$		0			0
$881$	−19.8885			−0.670062			−0.335031	−	0.942207i	$-0.608747\pi$
$881$	−19.8885			−0.670062			−0.335031	+	0.942207i	$0.608747\pi$
$882$		0			0
$883$	16.0623	+	49.4347i	0.540540	+	1.66361i	0.731365	+	0.681986i	$0.238883\pi$
$883$	16.0623	+	49.4347i	0.540540	+	1.66361i	−0.190826	+	0.981624i	$0.561117\pi$
$884$		0			0
$885$	−1.92705	−	1.40008i	−0.0647771	−	0.0470633i
$886$		0			0
$887$	8.35410	−	25.7113i	0.280503	−	0.863300i	−0.707207	−	0.707006i	$-0.750045\pi$
$887$	8.35410	−	25.7113i	0.280503	−	0.863300i	0.987711	−	0.156294i	$-0.0499548\pi$
$888$		0			0
$889$	10.6631	−	7.74721i	0.357630	−	0.259833i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−8.35410	+	6.06961i	−0.279559	+	0.203112i
$894$		0			0
$895$	−0.0729490	+	0.224514i	−0.00243842	+	0.00750467i
$896$		0			0
$897$	−9.23607	−	6.71040i	−0.308383	−	0.224054i
$898$		0			0
$899$	11.5451	+	35.5321i	0.385050	+	1.18506i
$900$		0			0
$901$	−32.7426			−1.09082
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.118034	+	0.363271i	0.00392358	+	0.0120755i
$906$		0			0
$907$	36.3885	+	26.4378i	1.20826	+	0.877854i	0.995072	−	0.0991572i	$-0.0316147\pi$
$907$	36.3885	+	26.4378i	1.20826	+	0.877854i	0.213190	+	0.977011i	$0.431615\pi$
$908$		0			0
$909$	−5.99593	+	18.4536i	−0.198873	+	0.612067i
$910$		0			0
$911$	−14.9721	+	10.8779i	−0.496049	+	0.360401i	−0.807506	−	0.589860i	$-0.799183\pi$
$911$	−14.9721	+	10.8779i	−0.496049	+	0.360401i	0.311457	+	0.950260i	$0.399183\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−0.881966	+	0.640786i	−0.0291569	+	0.0211837i
$916$		0			0
$917$	16.2918	−	50.1410i	0.538003	−	1.65580i
$918$		0			0
$919$	−33.6246	−	24.4297i	−1.10917	−	0.805862i	−0.126640	−	0.991949i	$-0.540419\pi$
$919$	−33.6246	−	24.4297i	−1.10917	−	0.805862i	−0.982533	+	0.186087i	$0.940419\pi$
$920$		0			0
$921$	2.18034	+	6.71040i	0.0718446	+	0.221115i
$922$		0			0
$923$	39.7984			1.30998
$924$		0			0
$925$	−22.4164			−0.737047
$926$		0			0
$927$	1.01064	+	3.11044i	0.0331939	+	0.102160i
$928$		0			0
$929$	−25.1525	−	18.2743i	−0.825226	−	0.599562i	0.0929787	−	0.995668i	$-0.470361\pi$
$929$	−25.1525	−	18.2743i	−0.825226	−	0.599562i	−0.918205	+	0.396106i	$0.870361\pi$
$930$		0			0
$931$	1.01064	−	3.11044i	0.0331225	−	0.101941i
$932$		0			0
$933$	−2.40983	+	1.75084i	−0.0788943	+	0.0573201i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−11.2082	+	8.14324i	−0.366156	+	0.266028i	−0.755615	−	0.655016i	$-0.772662\pi$
$937$	−11.2082	+	8.14324i	−0.366156	+	0.266028i	0.389459	+	0.921044i	$0.372662\pi$
$938$		0			0
$939$	−3.60081	+	11.0822i	−0.117508	+	0.361653i
$940$		0			0
$941$	18.6803	+	13.5721i	0.608962	+	0.442437i	0.849049	−	0.528315i	$-0.177176\pi$
$941$	18.6803	+	13.5721i	0.608962	+	0.442437i	−0.240087	+	0.970751i	$0.577176\pi$
$942$		0			0
$943$	−12.7639	−	39.2833i	−0.415651	−	1.27924i
$944$		0			0
$945$	−3.94427			−0.128307
$946$		0			0
$947$	47.7771			1.55255			0.776273	−	0.630396i	$-0.217108\pi$
$947$	47.7771			1.55255			0.776273	+	0.630396i	$0.217108\pi$
$948$		0			0
$949$	−17.2533	−	53.1002i	−0.560065	−	1.72370i
$950$		0			0
$951$	1.71885	+	1.24882i	0.0557374	+	0.0404956i
$952$		0			0
$953$	14.3197	−	44.0714i	0.463859	−	1.42761i	−0.396552	−	0.918012i	$-0.629793\pi$
$953$	14.3197	−	44.0714i	0.463859	−	1.42761i	0.860411	−	0.509600i	$-0.170207\pi$
$954$		0			0
$955$	1.51722	−	1.10233i	0.0490961	−	0.0356704i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−24.9336	+	18.1153i	−0.805149	+	0.584975i
$960$		0			0
$961$	1.01064	−	3.11044i	0.0326014	−	0.100337i
$962$		0			0
$963$	−19.7705	−	14.3641i	−0.637096	−	0.462877i
$964$		0			0
$965$	0.465558	+	1.43284i	0.0149868	+	0.0461248i
$966$		0			0
$967$	−44.0000			−1.41494			−0.707472	−	0.706741i	$-0.750165\pi$
$967$	−44.0000			−1.41494			−0.707472	+	0.706741i	$0.750165\pi$
$968$		0			0
$969$	5.03444			0.161730
$970$		0			0
$971$	5.59017	+	17.2048i	0.179397	+	0.552127i	0.999807	−	0.0196484i	$-0.00625469\pi$
$971$	5.59017	+	17.2048i	0.179397	+	0.552127i	−0.820410	+	0.571776i	$0.806255\pi$
$972$		0			0
$973$	19.7705	+	14.3641i	0.633813	+	0.460492i
$974$		0			0
$975$	−2.51722	+	7.74721i	−0.0806156	+	0.248109i
$976$		0			0
$977$	−28.6803	+	20.8375i	−0.917565	+	0.666650i	−0.942917	−	0.333028i	$-0.891930\pi$
$977$	−28.6803	+	20.8375i	−0.917565	+	0.666650i	0.0253515	+	0.999679i	$0.491930\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	8.14590	−	5.91834i	0.260079	−	0.188958i
$982$		0			0
$983$	−1.77051	+	5.44907i	−0.0564705	+	0.173798i	−0.975313	−	0.220825i	$-0.929125\pi$
$983$	−1.77051	+	5.44907i	−0.0564705	+	0.173798i	0.918843	+	0.394624i	$0.129125\pi$
$984$		0			0
$985$	7.47214	+	5.42882i	0.238082	+	0.172977i
$986$		0			0
$987$	1.21885	+	3.75123i	0.0387963	+	0.119403i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	24.0000			0.762385			0.381193	−	0.924496i	$-0.375513\pi$
$991$	24.0000			0.762385			0.381193	+	0.924496i	$0.375513\pi$
$992$		0			0
$993$	1.41641	+	4.35926i	0.0449483	+	0.138337i
$994$		0			0
$995$	−8.47214	−	6.15537i	−0.268585	−	0.195138i
$996$		0			0
$997$	10.7918	−	33.2137i	0.341780	−	1.05189i	−0.621506	−	0.783410i	$-0.713479\pi$
$997$	10.7918	−	33.2137i	0.341780	−	1.05189i	0.963285	−	0.268480i	$-0.0865213\pi$
$998$		0			0
$999$	−8.78115	+	6.37988i	−0.277823	+	0.201851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.e.d.245.1		4
11.2	odd	10		484.2.a.b.1.2		2
11.3	even	5		484.2.e.c.269.1		4
11.4	even	5	inner	484.2.e.d.81.1		4
11.5	even	5		484.2.e.c.9.1		4
11.6	odd	10		44.2.e.a.9.1	yes	4
11.7	odd	10		484.2.e.e.81.1		4
11.8	odd	10		44.2.e.a.5.1	✓	4
11.9	even	5		484.2.a.c.1.2		2
11.10	odd	2		484.2.e.e.245.1		4
33.2	even	10		4356.2.a.t.1.1		2
33.8	even	10		396.2.j.a.181.1		4
33.17	even	10		396.2.j.a.361.1		4
33.20	odd	10		4356.2.a.u.1.1		2
44.19	even	10		176.2.m.b.49.1		4
44.31	odd	10		1936.2.a.z.1.1		2
44.35	even	10		1936.2.a.ba.1.1		2
44.39	even	10		176.2.m.b.97.1		4
55.8	even	20		1100.2.cb.a.49.1		8
55.17	even	20		1100.2.cb.a.449.1		8
55.19	odd	10		1100.2.n.a.401.1		4
55.28	even	20		1100.2.cb.a.449.2		8
55.39	odd	10		1100.2.n.a.801.1		4
55.52	even	20		1100.2.cb.a.49.2		8
88.13	odd	10		7744.2.a.da.1.1		2
88.19	even	10		704.2.m.d.577.1		4
88.35	even	10		7744.2.a.bp.1.2		2
88.53	even	10		7744.2.a.db.1.1		2
88.61	odd	10		704.2.m.e.449.1		4
88.75	odd	10		7744.2.a.bo.1.2		2
88.83	even	10		704.2.m.d.449.1		4
88.85	odd	10		704.2.m.e.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.e.a.5.1	✓	4	11.8	odd	10
44.2.e.a.9.1	yes	4	11.6	odd	10
176.2.m.b.49.1		4	44.19	even	10
176.2.m.b.97.1		4	44.39	even	10
396.2.j.a.181.1		4	33.8	even	10
396.2.j.a.361.1		4	33.17	even	10
484.2.a.b.1.2		2	11.2	odd	10
484.2.a.c.1.2		2	11.9	even	5
484.2.e.c.9.1		4	11.5	even	5
484.2.e.c.269.1		4	11.3	even	5
484.2.e.d.81.1		4	11.4	even	5	inner
484.2.e.d.245.1		4	1.1	even	1	trivial
484.2.e.e.81.1		4	11.7	odd	10
484.2.e.e.245.1		4	11.10	odd	2
704.2.m.d.449.1		4	88.83	even	10
704.2.m.d.577.1		4	88.19	even	10
704.2.m.e.449.1		4	88.61	odd	10
704.2.m.e.577.1		4	88.85	odd	10
1100.2.n.a.401.1		4	55.19	odd	10
1100.2.n.a.801.1		4	55.39	odd	10
1100.2.cb.a.49.1		8	55.8	even	20
1100.2.cb.a.49.2		8	55.52	even	20
1100.2.cb.a.449.1		8	55.17	even	20
1100.2.cb.a.449.2		8	55.28	even	20
1936.2.a.z.1.1		2	44.31	odd	10
1936.2.a.ba.1.1		2	44.35	even	10
4356.2.a.t.1.1		2	33.2	even	10
4356.2.a.u.1.1		2	33.20	odd	10
7744.2.a.bo.1.2		2	88.75	odd	10
7744.2.a.bp.1.2		2	88.35	even	10
7744.2.a.da.1.1		2	88.13	odd	10
7744.2.a.db.1.1		2	88.53	even	10

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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.118034 - 0.363271i) q^{3} +(-0.500000 - 0.363271i) q^{5} +(-0.881966 + 2.71441i) q^{7} +(2.30902 - 1.67760i) q^{9} +(3.73607 - 2.71441i) q^{13} +(-0.0729490 + 0.224514i) q^{15} +(3.73607 + 2.71441i) q^{17} +(0.881966 + 2.71441i) q^{19} +1.09017 q^{21} +6.47214 q^{23} +(-1.42705 - 4.39201i) q^{25} +(-1.80902 - 1.31433i) q^{27} +(-1.97214 + 6.06961i) q^{29} +(4.73607 - 3.44095i) q^{31} +(1.42705 - 1.03681i) q^{35} +(1.50000 - 4.61653i) q^{37} +(-1.42705 - 1.03681i) q^{39} +(-1.97214 - 6.06961i) q^{41} -1.76393 q^{45} +(1.11803 + 3.44095i) q^{47} +(-0.927051 - 0.673542i) q^{49} +(0.545085 - 1.67760i) q^{51} +(-5.73607 + 4.16750i) q^{53} +(0.881966 - 0.640786i) q^{57} +(-3.11803 + 9.59632i) q^{59} +(3.73607 + 2.71441i) q^{61} +(2.51722 + 7.74721i) q^{63} -2.85410 q^{65} -4.94427 q^{67} +(-0.763932 - 2.35114i) q^{69} +(6.97214 + 5.06555i) q^{71} +(3.73607 - 11.4984i) q^{73} +(-1.42705 + 1.03681i) q^{75} +(-11.2082 + 8.14324i) q^{79} +(2.38197 - 7.33094i) q^{81} +(-12.9721 - 9.42481i) q^{83} +(-0.881966 - 2.71441i) q^{85} +2.43769 q^{87} -8.47214 q^{89} +(4.07295 + 12.5352i) q^{91} +(-1.80902 - 1.31433i) q^{93} +(0.545085 - 1.67760i) q^{95} +(-4.50000 + 3.26944i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 2 q^{5} - 8 q^{7} + 7 q^{9} + 6 q^{13} - 7 q^{15} + 6 q^{17} + 8 q^{19} - 18 q^{21} + 8 q^{23} + q^{25} - 5 q^{27} + 10 q^{29} + 10 q^{31} - q^{35} + 6 q^{37} + q^{39} + 10 q^{41} - 16 q^{45}+ \cdots - 18 q^{97}+O(q^{100}) \) 4 * q + 4 * q^3 - 2 * q^5 - 8 * q^7 + 7 * q^9 + 6 * q^13 - 7 * q^15 + 6 * q^17 + 8 * q^19 - 18 * q^21 + 8 * q^23 + q^25 - 5 * q^27 + 10 * q^29 + 10 * q^31 - q^35 + 6 * q^37 + q^39 + 10 * q^41 - 16 * q^45 + 3 * q^49 - 9 * q^51 - 14 * q^53 + 8 * q^57 - 8 * q^59 + 6 * q^61 - 19 * q^63 + 2 * q^65 + 16 * q^67 - 12 * q^69 + 10 * q^71 + 6 * q^73 + q^75 - 18 * q^79 + 14 * q^81 - 34 * q^83 - 8 * q^85 + 50 * q^87 - 16 * q^89 + 23 * q^91 - 5 * q^93 - 9 * q^95 - 18 * q^97

Introduction

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