LMFDB - Embedded newform 456.2.bm.b.89.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(41,456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 9, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("456.41"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bm (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			89.8
Character	$\chi$	$=$	456.89
Dual form			456.2.bm.b.41.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.20462 + 1.24454i) q^{3} +(1.70062 - 0.299865i) q^{5} +(1.13747 - 1.97015i) q^{7} +(-0.0977739 + 2.99841i) q^{9} +(2.36730 - 1.36676i) q^{11} +(0.405512 + 1.11413i) q^{13} +(2.42180 + 1.75527i) q^{15} +(-5.05418 - 6.02334i) q^{17} +(1.37777 + 4.13543i) q^{19} +(3.82215 - 0.957659i) q^{21} +(4.39335 + 0.774666i) q^{23} +(-1.89627 + 0.690186i) q^{25} +(-3.84943 + 3.49026i) q^{27} +(-3.61452 - 3.03294i) q^{29} +(2.36577 + 1.36588i) q^{31} +(4.55269 + 1.29978i) q^{33} +(1.34362 - 3.69157i) q^{35} +11.4585i q^{37} +(-0.898099 + 1.84679i) q^{39} +(-6.52964 - 2.37659i) q^{41} +(-0.346684 - 1.96614i) q^{43} +(0.732842 + 5.12847i) q^{45} +(-2.74268 + 3.26860i) q^{47} +(0.912338 + 1.58022i) q^{49} +(1.40793 - 13.5460i) q^{51} +(-0.919456 + 5.21449i) q^{53} +(3.61603 - 3.03421i) q^{55} +(-3.48703 + 6.69632i) q^{57} +(3.56459 - 2.99105i) q^{59} +(2.38649 - 13.5345i) q^{61} +(5.79610 + 3.60322i) q^{63} +(1.02371 + 1.77312i) q^{65} +(1.79402 - 2.13803i) q^{67} +(4.32822 + 6.40089i) q^{69} +(-1.40518 - 7.96915i) q^{71} +(-11.7489 - 4.27624i) q^{73} +(-3.14326 - 1.52858i) q^{75} -6.21858i q^{77} +(-2.44606 + 6.72050i) q^{79} +(-8.98088 - 0.586332i) q^{81} +(-8.58466 - 4.95636i) q^{83} +(-10.4014 - 8.72784i) q^{85} +(-0.579502 - 8.15198i) q^{87} +(4.25172 - 1.54750i) q^{89} +(2.65627 + 0.468372i) q^{91} +(1.14996 + 4.58967i) q^{93} +(3.58313 + 6.61965i) q^{95} +(-4.14485 - 4.93964i) q^{97} +(3.86664 + 7.23176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{9} + 3 q^{13} - 3 q^{15} - 6 q^{17} + 3 q^{19} + 6 q^{25} + 3 q^{27} + 6 q^{29} + 24 q^{35} + 18 q^{39} + 3 q^{41} - 21 q^{43} + 63 q^{45} - 18 q^{47} - 30 q^{49} + 33 q^{51} - 36 q^{53} + 18 q^{55}+ \cdots - 39 q^{99}+O(q^{100}) $ 60 * q - 6 * q^9 + 3 * q^13 - 3 * q^15 - 6 * q^17 + 3 * q^19 + 6 * q^25 + 3 * q^27 + 6 * q^29 + 24 * q^35 + 18 * q^39 + 3 * q^41 - 21 * q^43 + 63 * q^45 - 18 * q^47 - 30 * q^49 + 33 * q^51 - 36 * q^53 + 18 * q^55 - 24 * q^57 - 21 * q^59 - 6 * q^61 - 24 * q^63 + 24 * q^65 - 48 * q^67 - 21 * q^69 + 36 * q^71 - 57 * q^73 - 36 * q^79 + 6 * q^81 - 36 * q^83 + 6 * q^85 + 72 * q^87 - 24 * q^89 - 18 * q^91 + 108 * q^93 + 30 * q^95 + 15 * q^97 - 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.20462	+	1.24454i	0.695489	+	0.718537i
$3$	1.20462	+	1.24454i	0.695489	+	0.718537i
$4$		0			0
$5$	1.70062	−	0.299865i	0.760541	−	0.134104i	0.220090	−	0.975480i	$-0.429365\pi$
$5$	1.70062	−	0.299865i	0.760541	−	0.134104i	0.540451	+	0.841376i	$0.318254\pi$
$6$		0			0
$7$	1.13747	−	1.97015i	0.429922	−	0.744647i	−0.566944	−	0.823756i	$-0.691874\pi$
$7$	1.13747	−	1.97015i	0.429922	−	0.744647i	0.996866	+	0.0791096i	$0.0252077\pi$
$8$		0			0
$9$	−0.0977739	+	2.99841i	−0.0325913	+	0.999469i
$10$		0			0
$11$	2.36730	−	1.36676i	0.713767	−	0.412094i	−0.0986870	−	0.995119i	$-0.531464\pi$
$11$	2.36730	−	1.36676i	0.713767	−	0.412094i	0.812454	+	0.583025i	$0.198131\pi$
$12$		0			0
$13$	0.405512	+	1.11413i	0.112469	+	0.309005i	0.983138	−	0.182863i	$-0.0585365\pi$
$13$	0.405512	+	1.11413i	0.112469	+	0.309005i	−0.870670	+	0.491868i	$0.836314\pi$
$14$		0			0
$15$	2.42180	+	1.75527i	0.625306	+	0.453209i
$16$		0			0
$17$	−5.05418	−	6.02334i	−1.22582	−	1.46087i	−0.843747	−	0.536742i	$-0.819655\pi$
$17$	−5.05418	−	6.02334i	−1.22582	−	1.46087i	−0.382072	−	0.924132i	$-0.624789\pi$
$18$		0			0
$19$	1.37777	+	4.13543i	0.316082	+	0.948732i
$19$	1.37777	+	4.13543i	0.316082	+	0.948732i
$20$		0			0
$21$	3.82215	−	0.957659i	0.834062	−	0.208978i
$22$		0			0
$23$	4.39335	+	0.774666i	0.916077	+	0.161529i	0.611761	−	0.791042i	$-0.290461\pi$
$23$	4.39335	+	0.774666i	0.916077	+	0.161529i	0.304315	+	0.952571i	$0.401572\pi$
$24$		0			0
$25$	−1.89627	+	0.690186i	−0.379254	+	0.138037i
$26$		0			0
$27$	−3.84943	+	3.49026i	−0.740822	+	0.671701i
$28$		0			0
$29$	−3.61452	−	3.03294i	−0.671200	−	0.563204i	0.242220	−	0.970221i	$-0.422124\pi$
$29$	−3.61452	−	3.03294i	−0.671200	−	0.563204i	−0.913420	+	0.407018i	$0.866569\pi$
$30$		0			0
$31$	2.36577	+	1.36588i	0.424905	+	0.245319i	0.697174	−	0.716902i	$-0.254441\pi$
$31$	2.36577	+	1.36588i	0.424905	+	0.245319i	−0.272269	+	0.962221i	$0.587774\pi$
$32$		0			0
$33$	4.55269	+	1.29978i	0.792522	+	0.226262i
$34$		0			0
$35$	1.34362	−	3.69157i	0.227113	−	0.623988i
$36$		0			0
$37$			11.4585i			1.88376i	0.335949	+	0.941880i	$0.390943\pi$
$37$			11.4585i			1.88376i	−0.335949	+	0.941880i	$0.609057\pi$
$38$		0			0
$39$	−0.898099	+	1.84679i	−0.143811	+	0.295722i
$40$		0			0
$41$	−6.52964	−	2.37659i	−1.01976	−	0.371162i	−0.222586	−	0.974913i	$-0.571450\pi$
$41$	−6.52964	−	2.37659i	−1.01976	−	0.371162i	−0.797173	+	0.603751i	$0.793672\pi$
$42$		0			0
$43$	−0.346684	−	1.96614i	−0.0528688	−	0.299834i	0.946896	−	0.321541i	$-0.104201\pi$
$43$	−0.346684	−	1.96614i	−0.0528688	−	0.299834i	−0.999764	+	0.0217074i	$0.993090\pi$
$44$		0			0
$45$	0.732842	+	5.12847i	0.109246	+	0.764507i
$46$		0			0
$47$	−2.74268	+	3.26860i	−0.400061	+	0.476774i	−0.928039	−	0.372484i	$-0.878506\pi$
$47$	−2.74268	+	3.26860i	−0.400061	+	0.476774i	0.527978	+	0.849258i	$0.322951\pi$
$48$		0			0
$49$	0.912338	+	1.58022i	0.130334	+	0.225745i
$50$		0			0
$51$	1.40793	−	13.5460i	0.197149	−	1.89682i
$52$		0			0
$53$	−0.919456	+	5.21449i	−0.126297	+	0.716266i	0.854232	+	0.519892i	$0.174028\pi$
$53$	−0.919456	+	5.21449i	−0.126297	+	0.716266i	−0.980529	+	0.196374i	$0.937083\pi$
$54$		0			0
$55$	3.61603	−	3.03421i	0.487586	−	0.409133i
$56$		0			0
$57$	−3.48703	+	6.69632i	−0.461868	+	0.886949i
$58$		0			0
$59$	3.56459	−	2.99105i	0.464070	−	0.389401i	−0.380556	−	0.924758i	$-0.624267\pi$
$59$	3.56459	−	2.99105i	0.464070	−	0.389401i	0.844626	+	0.535357i	$0.179823\pi$
$60$		0			0
$61$	2.38649	−	13.5345i	0.305559	−	1.73291i	−0.315301	−	0.948992i	$-0.602105\pi$
$61$	2.38649	−	13.5345i	0.305559	−	1.73291i	0.620860	−	0.783921i	$-0.286783\pi$
$62$		0			0
$63$	5.79610	+	3.60322i	0.730240	+	0.453963i
$64$		0			0
$65$	1.02371	+	1.77312i	0.126976	+	0.219928i
$66$		0			0
$67$	1.79402	−	2.13803i	0.219175	−	0.261202i	−0.645242	−	0.763978i	$-0.723243\pi$
$67$	1.79402	−	2.13803i	0.219175	−	0.261202i	0.864417	+	0.502776i	$0.167688\pi$
$68$		0			0
$69$	4.32822	+	6.40089i	0.521056	+	0.770577i
$70$		0			0
$71$	−1.40518	−	7.96915i	−0.166764	−	0.945764i	−0.947227	−	0.320563i	$-0.896128\pi$
$71$	−1.40518	−	7.96915i	−0.166764	−	0.945764i	0.780464	−	0.625201i	$-0.214983\pi$
$72$		0			0
$73$	−11.7489	−	4.27624i	−1.37510	−	0.500496i	−0.454412	−	0.890792i	$-0.650151\pi$
$73$	−11.7489	−	4.27624i	−1.37510	−	0.500496i	−0.920690	+	0.390296i	$0.872373\pi$
$74$		0			0
$75$	−3.14326	−	1.52858i	−0.362952	−	0.176505i
$76$		0			0
$77$		−	6.21858i		−	0.708673i
$78$		0			0
$79$	−2.44606	+	6.72050i	−0.275204	+	0.756116i	0.722686	+	0.691177i	$0.242907\pi$
$79$	−2.44606	+	6.72050i	−0.275204	+	0.756116i	−0.997889	+	0.0649388i	$0.979315\pi$
$80$		0			0
$81$	−8.98088	−	0.586332i	−0.997876	−	0.0651480i
$82$		0			0
$83$	−8.58466	−	4.95636i	−0.942289	−	0.544031i	−0.0516118	−	0.998667i	$-0.516436\pi$
$83$	−8.58466	−	4.95636i	−0.942289	−	0.544031i	−0.890677	+	0.454636i	$0.849769\pi$
$84$		0			0
$85$	−10.4014	−	8.72784i	−1.12819	−	0.946667i
$86$		0			0
$87$	−0.579502	−	8.15198i	−0.0621292	−	0.873984i
$88$		0			0
$89$	4.25172	−	1.54750i	0.450682	−	0.164035i	−0.106700	−	0.994291i	$-0.534028\pi$
$89$	4.25172	−	1.54750i	0.450682	−	0.164035i	0.557381	+	0.830257i	$0.311806\pi$
$90$		0			0
$91$	2.65627	+	0.468372i	0.278452	+	0.0490987i
$92$		0			0
$93$	1.14996	+	4.58967i	0.119246	+	0.475926i
$94$		0			0
$95$	3.58313	+	6.61965i	0.367621	+	0.679162i
$96$		0			0
$97$	−4.14485	−	4.93964i	−0.420846	−	0.501545i	0.513412	−	0.858142i	$-0.328381\pi$
$97$	−4.14485	−	4.93964i	−0.420846	−	0.501545i	−0.934258	+	0.356597i	$0.883937\pi$
$98$		0			0
$99$	3.86664	+	7.23176i	0.388612	+	0.726819i
$100$		0			0
$101$	1.50177	+	4.12608i	0.149432	+	0.410561i	0.991712	−	0.128479i	$-0.0410095\pi$
$101$	1.50177	+	4.12608i	0.149432	+	0.410561i	−0.842280	+	0.539040i	$0.818787\pi$
$102$		0			0
$103$	2.26117	−	1.30549i	0.222800	−	0.128633i	−0.384446	−	0.923147i	$-0.625608\pi$
$103$	2.26117	−	1.30549i	0.222800	−	0.128633i	0.607246	+	0.794514i	$0.292274\pi$
$104$		0			0
$105$	6.21286	−	2.77475i	0.606314	−	0.270788i
$106$		0			0
$107$	3.44458	−	5.96619i	0.333000	−	0.576773i	−0.650098	−	0.759850i	$-0.725272\pi$
$107$	3.44458	−	5.96619i	0.333000	−	0.576773i	0.983099	+	0.183077i	$0.0586057\pi$
$108$		0			0
$109$	−5.43536	+	0.958401i	−0.520614	+	0.0917982i	−0.427779	−	0.903883i	$-0.640704\pi$
$109$	−5.43536	+	0.958401i	−0.520614	+	0.0917982i	−0.0928345	+	0.995682i	$0.529593\pi$
$110$		0			0
$111$	−14.2606	+	13.8031i	−1.35355	+	1.31013i
$112$		0			0
$113$	0.374354			0.0352162			0.0176081	−	0.999845i	$-0.494395\pi$
$113$	0.374354			0.0352162			0.0176081	+	0.999845i	$0.494395\pi$
$114$		0			0
$115$	7.70372			0.718375
$116$		0			0
$117$	−3.38027	+	1.10696i	−0.312506	+	0.102338i
$118$		0			0
$119$	−17.6158	+	3.10615i	−1.61484	+	0.284740i
$120$		0			0
$121$	−1.76393	+	3.05522i	−0.160357	+	0.277747i
$122$		0			0
$123$	−4.90797	−	10.9893i	−0.442537	−	0.990873i
$124$		0			0
$125$	−10.4954	+	6.05951i	−0.938735	+	0.541979i
$126$		0			0
$127$	−3.52132	−	9.67473i	−0.312466	−	0.858494i	−0.992157	−	0.124995i	$-0.960108\pi$
$127$	−3.52132	−	9.67473i	−0.312466	−	0.858494i	0.679691	−	0.733498i	$-0.262114\pi$
$128$		0			0
$129$	2.02933	−	2.79992i	0.178672	−	0.246519i
$130$		0			0
$131$	−1.53064	−	1.82414i	−0.133732	−	0.159376i	0.695022	−	0.718988i	$-0.255394\pi$
$131$	−1.53064	−	1.82414i	−0.133732	−	0.159376i	−0.828755	+	0.559612i	$0.810950\pi$
$132$		0			0
$133$	9.71458	+	1.98950i	0.842361	+	0.172512i
$134$		0			0
$135$	−5.49980	+	7.08992i	−0.473348	+	0.610203i
$136$		0			0
$137$	5.85480	+	1.03236i	0.500209	+	0.0882004i	0.418060	−	0.908420i	$-0.362710\pi$
$137$	5.85480	+	1.03236i	0.500209	+	0.0882004i	0.0821498	+	0.996620i	$0.473821\pi$
$138$		0			0
$139$	−3.58667	+	1.30544i	−0.304217	+	0.110726i	−0.489618	−	0.871937i	$-0.662864\pi$
$139$	−3.58667	+	1.30544i	−0.304217	+	0.110726i	0.185401	+	0.982663i	$0.440642\pi$
$140$		0			0
$141$	−7.37180	+	0.524042i	−0.620818	+	0.0441323i
$142$		0			0
$143$	2.48272	+	2.08325i	0.207616	+	0.174210i
$144$		0			0
$145$	−7.05641	−	4.07402i	−0.586003	−	0.338329i
$146$		0			0
$147$	−0.867624	+	3.03901i	−0.0715605	+	0.250653i
$148$		0			0
$149$	4.43285	−	12.1792i	0.363153	−	0.997755i	−0.614755	−	0.788718i	$-0.710745\pi$
$149$	4.43285	−	12.1792i	0.363153	−	0.997755i	0.977908	−	0.209037i	$-0.0670328\pi$
$150$		0			0
$151$			21.8171i			1.77545i	0.460374	+	0.887725i	$0.347715\pi$
$151$			21.8171i			1.77545i	−0.460374	+	0.887725i	$0.652285\pi$
$152$		0			0
$153$	18.5546	−	14.5656i	1.50005	−	1.17756i
$154$		0			0
$155$	4.43286	+	1.61343i	0.356056	+	0.129594i
$156$		0			0
$157$	−0.487265	−	2.76342i	−0.0388880	−	0.220545i	0.959170	−	0.282829i	$-0.0912728\pi$
$157$	−0.487265	−	2.76342i	−0.0388880	−	0.220545i	−0.998058	+	0.0622837i	$0.980162\pi$
$158$		0			0
$159$	−7.59726	+	5.13719i	−0.602502	+	0.407406i
$160$		0			0
$161$	6.52350	−	7.77440i	0.514124	−	0.612709i
$162$		0			0
$163$	−7.70552	−	13.3464i	−0.603543	−	1.04537i	−0.992280	−	0.124018i	$-0.960422\pi$
$163$	−7.70552	−	13.3464i	−0.603543	−	1.04537i	0.388737	−	0.921349i	$-0.372912\pi$
$164$		0			0
$165$	8.13216	+	0.845231i	0.633088	+	0.0658011i
$166$		0			0
$167$	−2.70822	+	15.3591i	−0.209569	+	1.18852i	0.680518	+	0.732731i	$0.261755\pi$
$167$	−2.70822	+	15.3591i	−0.209569	+	1.18852i	−0.890087	+	0.455791i	$0.849356\pi$
$168$		0			0
$169$	8.88172	−	7.45265i	0.683209	−	0.573281i
$170$		0			0
$171$	−12.5344	+	3.72677i	−0.958530	+	0.284993i
$172$		0			0
$173$	−2.65226	+	2.22551i	−0.201647	+	0.169202i	−0.738020	−	0.674779i	$-0.764239\pi$
$173$	−2.65226	+	2.22551i	−0.201647	+	0.169202i	0.536372	+	0.843982i	$0.319794\pi$
$174$		0			0
$175$	−0.797175	+	4.52100i	−0.0602608	+	0.341756i
$176$		0			0
$177$	8.01647	+	0.833207i	0.602555	+	0.0626277i
$178$		0			0
$179$	−12.7899	−	22.1528i	−0.955965	−	1.65578i	−0.732144	−	0.681150i	$-0.761480\pi$
$179$	−12.7899	−	22.1528i	−0.955965	−	1.65578i	−0.223822	−	0.974630i	$-0.571853\pi$
$180$		0			0
$181$	8.85306	−	10.5507i	0.658043	−	0.784225i	−0.329061	−	0.944309i	$-0.606732\pi$
$181$	8.85306	−	10.5507i	0.658043	−	0.784225i	0.987103	+	0.160084i	$0.0511766\pi$
$182$		0			0
$183$	19.7191	−	13.3338i	1.45768	−	0.985666i
$184$		0			0
$185$	3.43600	+	19.4865i	0.252619	+	1.43268i
$186$		0			0
$187$	−20.1972	−	7.35119i	−1.47697	−	0.537572i
$188$		0			0
$189$	2.49775	+	11.5540i	0.181684	+	0.840430i
$190$		0			0
$191$			15.3025i			1.10725i	0.832766	+	0.553625i	$0.186756\pi$
$191$			15.3025i			1.10725i	−0.832766	+	0.553625i	$0.813244\pi$
$192$		0			0
$193$	−7.10946	+	19.5331i	−0.511750	+	1.40602i	0.367661	+	0.929960i	$0.380159\pi$
$193$	−7.10946	+	19.5331i	−0.511750	+	1.40602i	−0.879411	+	0.476063i	$0.842064\pi$
$194$		0			0
$195$	−0.973539	+	3.40999i	−0.0697166	+	0.244195i
$196$		0			0
$197$	5.61056	+	3.23926i	0.399736	+	0.230788i	0.686370	−	0.727253i	$-0.259203\pi$
$197$	5.61056	+	3.23926i	0.399736	+	0.230788i	−0.286634	+	0.958040i	$0.592536\pi$
$198$		0			0
$199$	18.1261	+	15.2096i	1.28492	+	1.07818i	0.992545	+	0.121875i	$0.0388906\pi$
$199$	18.1261	+	15.2096i	1.28492	+	1.07818i	0.292377	+	0.956303i	$0.405554\pi$
$200$		0			0
$201$	4.82199	−	0.342783i	0.340117	−	0.0241780i
$202$		0			0
$203$	−10.0868	+	3.67128i	−0.707952	+	0.257673i
$204$		0			0
$205$	−11.8171	−	2.08367i	−0.825342	−	0.145530i
$206$		0			0
$207$	−2.75232	+	13.0973i	−0.191299	+	0.910326i
$208$		0			0
$209$	8.91373	+	7.90671i	0.616575	+	0.546919i
$210$		0			0
$211$	10.4139	+	12.4108i	0.716925	+	0.854398i	0.994328	−	0.106356i	$-0.0339182\pi$
$211$	10.4139	+	12.4108i	0.716925	+	0.854398i	−0.277403	+	0.960754i	$0.589474\pi$
$212$		0			0
$213$	8.22524	−	11.3486i	0.563584	−	0.777594i
$214$		0			0
$215$	−1.17916	−	3.23970i	−0.0804178	−	0.220946i
$216$		0			0
$217$	5.38197	−	3.10728i	0.365352	−	0.210936i
$218$		0			0
$219$	−8.83098	−	19.7732i	−0.596742	−	1.33615i
$220$		0			0
$221$	4.66128	−	8.07357i	0.313551	−	0.543087i
$222$		0			0
$223$	27.2136	−	4.79849i	1.82236	−	0.321331i	0.845298	−	0.534295i	$-0.179423\pi$
$223$	27.2136	−	4.79849i	1.82236	−	0.321331i	0.977060	+	0.212965i	$0.0683119\pi$
$224$		0			0
$225$	−1.88405	−	5.75328i	−0.125604	−	0.383552i
$226$		0			0
$227$	18.7680			1.24568			0.622838	−	0.782351i	$-0.285979\pi$
$227$	18.7680			1.24568			0.622838	+	0.782351i	$0.285979\pi$
$228$		0			0
$229$	17.6129			1.16389			0.581947	−	0.813227i	$-0.302291\pi$
$229$	17.6129			1.16389			0.581947	+	0.813227i	$0.302291\pi$
$230$		0			0
$231$	7.73929	−	7.49104i	0.509208	−	0.492874i
$232$		0			0
$233$	23.7313	−	4.18447i	1.55469	−	0.274134i	0.670731	−	0.741701i	$-0.265981\pi$
$233$	23.7313	−	4.18447i	1.55469	−	0.274134i	0.883957	+	0.467567i	$0.154869\pi$
$234$		0			0
$235$	−3.68412	+	6.38108i	−0.240325	+	0.416256i
$236$		0			0
$237$	−11.3105	+	5.05143i	−0.734698	+	0.328126i
$238$		0			0
$239$	−5.92338	+	3.41987i	−0.383152	+	0.221213i	−0.679189	−	0.733964i	$-0.737668\pi$
$239$	−5.92338	+	3.41987i	−0.383152	+	0.221213i	0.296037	+	0.955176i	$0.404335\pi$
$240$		0			0
$241$	4.39799	+	12.0834i	0.283299	+	0.778359i	0.996963	+	0.0778705i	$0.0248121\pi$
$241$	4.39799	+	12.0834i	0.283299	+	0.778359i	−0.713664	+	0.700488i	$0.752966\pi$
$242$		0			0
$243$	−10.0888	−	11.8834i	−0.647200	−	0.762320i
$244$		0			0
$245$	2.02539	+	2.41377i	0.129398	+	0.154210i
$246$		0			0
$247$	−4.04872	+	3.21198i	−0.257614	+	0.204373i
$248$		0			0
$249$	−4.17287	−	16.6545i	−0.264445	−	1.05544i
$250$		0			0
$251$	20.4899	+	3.61293i	1.29331	+	0.228046i	0.777624	−	0.628730i	$-0.216425\pi$
$251$	20.4899	+	3.61293i	1.29331	+	0.228046i	0.515689	+	0.856776i	$0.327536\pi$
$252$		0			0
$253$	11.4592	−	4.17079i	0.720431	−	0.262215i
$254$		0			0
$255$	−1.66762	−	23.4588i	−0.104430	−	1.46905i
$256$		0			0
$257$	−14.1602	−	11.8818i	−0.883287	−	0.741166i	0.0835651	−	0.996502i	$-0.473369\pi$
$257$	−14.1602	−	11.8818i	−0.883287	−	0.741166i	−0.966852	+	0.255336i	$0.917814\pi$
$258$		0			0
$259$	22.5749	+	13.0336i	1.40274	+	0.809870i
$260$		0			0
$261$	9.44741	−	10.5413i	0.584780	−	0.652488i
$262$		0			0
$263$	0.446655	−	1.22717i	0.0275419	−	0.0756707i	−0.925160	−	0.379578i	$-0.876069\pi$
$263$	0.446655	−	1.22717i	0.0275419	−	0.0756707i	0.952702	+	0.303907i	$0.0982914\pi$
$264$		0			0
$265$			9.14359i			0.561686i
$266$		0			0
$267$	7.04765	+	3.42730i	0.431309	+	0.209747i
$268$		0			0
$269$	5.32181	+	1.93698i	0.324476	+	0.118100i	0.499122	−	0.866532i	$-0.333656\pi$
$269$	5.32181	+	1.93698i	0.324476	+	0.118100i	−0.174646	+	0.984631i	$0.555878\pi$
$270$		0			0
$271$	−1.92559	−	10.9206i	−0.116971	−	0.663378i	−0.985755	−	0.168186i	$-0.946209\pi$
$271$	−1.92559	−	10.9206i	−0.116971	−	0.663378i	0.868784	−	0.495192i	$-0.164902\pi$
$272$		0			0
$273$	2.61689	+	3.87005i	0.158381	+	0.234226i
$274$		0			0
$275$	−3.54572	+	4.22563i	−0.213815	+	0.254815i
$276$		0			0
$277$	−15.1132	−	26.1769i	−0.908067	−	1.57282i	−0.816747	−	0.576996i	$-0.804225\pi$
$277$	−15.1132	−	26.1769i	−0.908067	−	1.57282i	−0.0913202	−	0.995822i	$-0.529109\pi$
$278$		0			0
$279$	−4.32677	+	6.95999i	−0.259037	+	0.416684i
$280$		0			0
$281$	−2.59528	+	14.7186i	−0.154822	+	0.878037i	0.804127	+	0.594458i	$0.202633\pi$
$281$	−2.59528	+	14.7186i	−0.154822	+	0.878037i	−0.958949	+	0.283580i	$0.908478\pi$
$282$		0			0
$283$	−8.57356	+	7.19407i	−0.509645	+	0.427643i	−0.861004	−	0.508598i	$-0.830164\pi$
$283$	−8.57356	+	7.19407i	−0.509645	+	0.427643i	0.351359	+	0.936241i	$0.385720\pi$
$284$		0			0
$285$	−3.92212	+	12.4335i	−0.232326	+	0.736499i
$286$		0			0
$287$	−12.1095	+	10.1611i	−0.714801	+	0.599789i
$288$		0			0
$289$	−7.78384	+	44.1443i	−0.457873	+	2.59673i
$290$		0			0
$291$	1.15462	−	11.1088i	0.0676850	−	0.651212i
$292$		0			0
$293$	14.9865	+	25.9574i	0.875520	+	1.51645i	0.856208	+	0.516632i	$0.172814\pi$
$293$	14.9865	+	25.9574i	0.875520	+	1.51645i	0.0193121	+	0.999814i	$0.493852\pi$
$294$		0			0
$295$	5.16511	−	6.15553i	0.300724	−	0.358389i
$296$		0			0
$297$	−4.34239	+	13.5237i	−0.251971	+	0.784727i
$298$		0			0
$299$	0.918472	+	5.20891i	0.0531166	+	0.301239i
$300$		0			0
$301$	−4.26794	−	1.55340i	−0.246000	−	0.0895366i
$302$		0			0
$303$	−3.32602	+	6.83939i	−0.191075	+	0.392913i
$304$		0			0
$305$		−	23.7327i		−	1.35893i
$306$		0			0
$307$	−3.30994	+	9.09398i	−0.188908	+	0.519021i	−0.997602	−	0.0692087i	$-0.977953\pi$
$307$	−3.30994	+	9.09398i	−0.188908	+	0.519021i	0.808694	+	0.588229i	$0.200175\pi$
$308$		0			0
$309$	4.34859	+	1.24150i	0.247382	+	0.0706267i
$310$		0			0
$311$	18.3990	+	10.6227i	1.04331	+	0.602357i	0.920770	−	0.390106i	$-0.127562\pi$
$311$	18.3990	+	10.6227i	1.04331	+	0.602357i	0.122543	+	0.992463i	$0.460895\pi$
$312$		0			0
$313$	−12.8192	−	10.7566i	−0.724586	−	0.608000i	0.204064	−	0.978958i	$-0.434585\pi$
$313$	−12.8192	−	10.7566i	−0.724586	−	0.608000i	−0.928650	+	0.370958i	$0.879029\pi$
$314$		0			0
$315$	10.9374	+	4.38966i	0.616255	+	0.247329i
$316$		0			0
$317$	−16.0860	+	5.85481i	−0.903478	+	0.328839i	−0.751646	−	0.659567i	$-0.770740\pi$
$317$	−16.0860	+	5.85481i	−0.903478	+	0.328839i	−0.151832	+	0.988406i	$0.548517\pi$
$318$		0			0
$319$	−12.7020	−	2.23970i	−0.711174	−	0.125399i
$320$		0			0
$321$	11.5746	−	2.90007i	0.646031	−	0.161866i
$322$		0			0
$323$	17.9456	−	29.2000i	0.998519	−	1.62473i
$324$		0			0
$325$	−1.53792	−	1.83282i	−0.0853085	−	0.101667i
$326$		0			0
$327$	−7.74033	−	5.61003i	−0.428041	−	0.310236i
$328$		0			0
$329$	3.31992	+	9.12142i	0.183033	+	0.502880i
$330$		0			0
$331$	−1.99575	+	1.15225i	−0.109696	+	0.0633333i	−0.553844	−	0.832620i	$-0.686840\pi$
$331$	−1.99575	+	1.15225i	−0.109696	+	0.0633333i	0.444148	+	0.895953i	$0.353506\pi$
$332$		0			0
$333$	−34.3571	−	1.12034i	−1.88276	−	0.0613942i
$334$		0			0
$335$	2.40983	−	4.17395i	0.131663	−	0.228047i
$336$		0			0
$337$	−0.881977	+	0.155516i	−0.0480443	+	0.00847151i	−0.197619	−	0.980279i	$-0.563321\pi$
$337$	−0.881977	+	0.155516i	−0.0480443	+	0.00847151i	0.149574	+	0.988750i	$0.452210\pi$
$338$		0			0
$339$	0.450954	+	0.465899i	0.0244925	+	0.0253042i
$340$		0			0
$341$	7.46731			0.404378
$342$		0			0
$343$	20.0756			1.08398
$344$		0			0
$345$	9.28006	+	9.58760i	0.499622	+	0.516179i
$346$		0			0
$347$	−20.9177	+	3.68835i	−1.12292	+	0.198001i	−0.704122	−	0.710079i	$-0.748659\pi$
$347$	−20.9177	+	3.68835i	−1.12292	+	0.198001i	−0.418797	+	0.908080i	$0.637548\pi$
$348$		0			0
$349$	−1.90514	+	3.29981i	−0.101980	+	0.176635i	−0.912500	−	0.409076i	$-0.865851\pi$
$349$	−1.90514	+	3.29981i	−0.101980	+	0.176635i	0.810520	+	0.585711i	$0.199184\pi$
$350$		0			0
$351$	−5.44960	−	2.87343i	−0.290878	−	0.153373i
$352$		0			0
$353$	−26.4683	+	15.2815i	−1.40877	+	0.813352i	−0.995269	−	0.0971532i	$-0.969026\pi$
$353$	−26.4683	+	15.2815i	−1.40877	+	0.813352i	−0.413498	+	0.910505i	$0.635693\pi$
$354$		0			0
$355$	−4.77934	−	13.1311i	−0.253661	−	0.696928i
$356$		0			0
$357$	−25.0862	−	18.1819i	−1.32770	−	0.962290i
$358$		0			0
$359$	−10.6079	−	12.6420i	−0.559862	−	0.667218i	0.409655	−	0.912240i	$-0.365649\pi$
$359$	−10.6079	−	12.6420i	−0.559862	−	0.667218i	−0.969517	+	0.245023i	$0.921205\pi$
$360$		0			0
$361$	−15.2035	+	11.3953i	−0.800185	+	0.599753i
$362$		0			0
$363$	−5.92722	+	1.48509i	−0.311098	+	0.0779472i
$364$		0			0
$365$	−21.2627	−	3.74918i	−1.11294	−	0.196241i
$366$		0			0
$367$	−21.3217	+	7.76048i	−1.11299	+	0.405094i	−0.832088	−	0.554644i	$-0.812854\pi$
$367$	−21.3217	+	7.76048i	−1.11299	+	0.405094i	−0.280898	+	0.959738i	$0.590632\pi$
$368$		0			0
$369$	7.76442	−	19.3461i	0.404200	−	1.00712i
$370$		0			0
$371$	9.22748	+	7.74278i	0.479067	+	0.401985i
$372$		0			0
$373$	13.8874	+	8.01792i	0.719064	+	0.415152i	0.814408	−	0.580292i	$-0.197062\pi$
$373$	13.8874	+	8.01792i	0.719064	+	0.415152i	−0.0953438	+	0.995444i	$0.530395\pi$
$374$		0			0
$375$	−20.1843	−	5.76253i	−1.04231	−	0.297576i
$376$		0			0
$377$	1.91338	−	5.25696i	0.0985439	−	0.270747i
$378$		0			0
$379$		−	12.2124i		−	0.627310i	−0.949537	−	0.313655i	$-0.898446\pi$
$379$		−	12.2124i		−	0.627310i	0.949537	−	0.313655i	$-0.101554\pi$
$380$		0			0
$381$	7.79877	−	16.0368i	0.399543	−	0.821591i
$382$		0			0
$383$	−10.3260	−	3.75835i	−0.527633	−	0.192043i	0.0644484	−	0.997921i	$-0.479471\pi$
$383$	−10.3260	−	3.75835i	−0.527633	−	0.192043i	−0.592081	+	0.805879i	$0.701693\pi$
$384$		0			0
$385$	−1.86474	−	10.5754i	−0.0950358	−	0.538975i
$386$		0			0
$387$	5.92919	−	0.847262i	0.301398	−	0.0430687i
$388$		0			0
$389$	−2.99194	+	3.56565i	−0.151697	+	0.180786i	−0.836541	−	0.547904i	$-0.815426\pi$
$389$	−2.99194	+	3.56565i	−0.151697	+	0.180786i	0.684844	+	0.728690i	$0.259870\pi$
$390$		0			0
$391$	−17.5387	−	30.3779i	−0.886970	−	1.53628i
$392$		0			0
$393$	0.426384	−	4.10234i	0.0215082	−	0.206936i
$394$		0			0
$395$	−2.14458	+	12.1625i	−0.107906	+	0.611963i
$396$		0			0
$397$	25.5841	−	21.4676i	1.28403	−	1.07743i	0.291355	−	0.956615i	$-0.405894\pi$
$397$	25.5841	−	21.4676i	1.28403	−	1.07743i	0.992675	−	0.120814i	$-0.0385506\pi$
$398$		0			0
$399$	9.22637	+	14.4868i	0.461896	+	0.725247i
$400$		0			0
$401$	−6.59413	+	5.53314i	−0.329295	+	0.276312i	−0.792413	−	0.609985i	$-0.791175\pi$
$401$	−6.59413	+	5.53314i	−0.329295	+	0.276312i	0.463117	+	0.886297i	$0.346731\pi$
$402$		0			0
$403$	−0.562424	+	3.18966i	−0.0280163	+	0.158888i
$404$		0			0
$405$	−15.4489	+	1.69593i	−0.767662	+	0.0842713i
$406$		0			0
$407$	15.6610	+	27.1256i	0.776286	+	1.34457i
$408$		0			0
$409$	24.7880	−	29.5412i	1.22569	−	1.46072i	0.381757	−	0.924263i	$-0.375319\pi$
$409$	24.7880	−	29.5412i	1.22569	−	1.46072i	0.843930	−	0.536454i	$-0.180237\pi$
$410$		0			0
$411$	5.76800	+	8.53015i	0.284515	+	0.420761i
$412$		0			0
$413$	−1.83821	−	10.4250i	−0.0904523	−	0.512981i
$414$		0			0
$415$	−16.0855	−	5.85464i	−0.789606	−	0.287393i
$416$		0			0
$417$	−5.94526	−	2.89120i	−0.291140	−	0.141583i
$418$		0			0
$419$			13.5426i			0.661599i	0.943701	+	0.330800i	$0.107318\pi$
$419$			13.5426i			0.661599i	−0.943701	+	0.330800i	$0.892682\pi$
$420$		0			0
$421$	3.77353	−	10.3677i	0.183911	−	0.505291i	−0.813137	−	0.582072i	$-0.802242\pi$
$421$	3.77353	−	10.3677i	0.183911	−	0.505291i	0.997048	+	0.0767815i	$0.0244644\pi$
$422$		0			0
$423$	−9.53242	−	8.54325i	−0.463482	−	0.415387i
$424$		0			0
$425$	13.7413	+	7.93356i	0.666552	+	0.384834i
$426$		0			0
$427$	−23.9504	−	20.0968i	−1.15904	−	0.972551i
$428$		0			0
$429$	0.398045	+	5.59938i	0.0192178	+	0.270341i
$430$		0			0
$431$	28.3609	−	10.3225i	1.36610	−	0.497219i	0.448163	−	0.893952i	$-0.352078\pi$
$431$	28.3609	−	10.3225i	1.36610	−	0.497219i	0.917934	+	0.396733i	$0.129856\pi$
$432$		0			0
$433$	5.90393	+	1.04102i	0.283725	+	0.0500284i	0.313700	−	0.949522i	$-0.398432\pi$
$433$	5.90393	+	1.04102i	0.283725	+	0.0500284i	−0.0299746	+	0.999551i	$0.509543\pi$
$434$		0			0
$435$	−3.43001	−	13.6897i	−0.164456	−	0.656369i
$436$		0			0
$437$	2.84944	+	19.2357i	0.136307	+	0.920168i
$438$		0			0
$439$	9.38099	+	11.1798i	0.447730	+	0.533584i	0.941950	−	0.335753i	$-0.108991\pi$
$439$	9.38099	+	11.1798i	0.447730	+	0.533584i	−0.494220	+	0.869337i	$0.664546\pi$
$440$		0			0
$441$	−4.82733	+	2.58106i	−0.229873	+	0.122907i
$442$		0			0
$443$	10.1225	+	27.8113i	0.480934	+	1.32135i	0.908694	+	0.417462i	$0.137080\pi$
$443$	10.1225	+	27.8113i	0.480934	+	1.32135i	−0.427761	+	0.903892i	$0.640697\pi$
$444$		0			0
$445$	6.76653	−	3.90666i	0.320764	−	0.185193i
$446$		0			0
$447$	20.4974	−	9.15440i	0.969493	−	0.432988i
$448$		0			0
$449$	2.00340	−	3.46999i	0.0945464	−	0.163759i	−0.814873	−	0.579640i	$-0.803193\pi$
$449$	2.00340	−	3.46999i	0.0945464	−	0.163759i	0.909419	+	0.415881i	$0.136527\pi$
$450$		0			0
$451$	−18.7058	+	3.29835i	−0.880824	+	0.155313i
$452$		0			0
$453$	−27.1523	+	26.2813i	−1.27573	+	1.23481i
$454$		0			0
$455$	4.65775			0.218359
$456$		0			0
$457$	−24.2985			−1.13663			−0.568317	−	0.822810i	$-0.692405\pi$
$457$	−24.2985			−1.13663			−0.568317	+	0.822810i	$0.692405\pi$
$458$		0			0
$459$	40.4787	+	5.54598i	1.88938	+	0.258864i
$460$		0			0
$461$	−0.557098	+	0.0982314i	−0.0259466	+	0.00457509i	−0.186606	−	0.982435i	$-0.559749\pi$
$461$	−0.557098	+	0.0982314i	−0.0259466	+	0.00457509i	0.160660	+	0.987010i	$0.448638\pi$
$462$		0			0
$463$	11.3553	−	19.6679i	0.527724	−	0.914045i	−0.471753	−	0.881731i	$-0.656379\pi$
$463$	11.3553	−	19.6679i	0.527724	−	0.914045i	0.999478	−	0.0323149i	$-0.0102879\pi$
$464$		0			0
$465$	3.33193	+	7.46045i	0.154515	+	0.345970i
$466$		0			0
$467$	−15.2952	+	8.83071i	−0.707779	+	0.408636i	−0.810238	−	0.586101i	$-0.800662\pi$
$467$	−15.2952	+	8.83071i	−0.707779	+	0.408636i	0.102459	+	0.994737i	$0.467329\pi$
$468$		0			0
$469$	−2.17161	−	5.96644i	−0.100275	−	0.275504i
$470$		0			0
$471$	2.85222	−	3.93530i	0.131424	−	0.181329i
$472$		0			0
$473$	−3.50795	−	4.18061i	−0.161296	−	0.192225i
$474$		0			0
$475$	−5.46684	−	6.89098i	−0.250836	−	0.316180i
$476$		0			0
$477$	−15.5453	−	3.26674i	−0.711769	−	0.149574i
$478$		0			0
$479$	−18.8260	−	3.31954i	−0.860183	−	0.151674i	−0.273879	−	0.961764i	$-0.588307\pi$
$479$	−18.8260	−	3.31954i	−0.860183	−	0.151674i	−0.586305	+	0.810091i	$0.699418\pi$
$480$		0			0
$481$	−12.7663	+	4.64654i	−0.582092	+	0.211864i
$482$		0			0
$483$	17.5339	−	1.24644i	0.797821	−	0.0567150i
$484$		0			0
$485$	−8.53005	−	7.15756i	−0.387330	−	0.325008i
$486$		0			0
$487$	−0.536606	−	0.309810i	−0.0243159	−	0.0140388i	0.487793	−	0.872959i	$-0.337802\pi$
$487$	−0.536606	−	0.309810i	−0.0243159	−	0.0140388i	−0.512109	+	0.858921i	$0.671136\pi$
$488$		0			0
$489$	7.32787	−	25.6672i	0.331378	−	1.16071i
$490$		0			0
$491$	−10.0111	+	27.5052i	−0.451793	+	1.24129i	0.479667	+	0.877450i	$0.340757\pi$
$491$	−10.0111	+	27.5052i	−0.451793	+	1.24129i	−0.931461	+	0.363842i	$0.881465\pi$
$492$		0			0
$493$			37.1005i			1.67092i
$494$		0			0
$495$	8.74425	+	11.1390i	0.393025	+	0.500661i
$496$		0			0
$497$	−17.2988	−	6.29623i	−0.775956	−	0.282425i
$498$		0			0
$499$	−1.69657	−	9.62174i	−0.0759490	−	0.430728i	−0.998945	−	0.0459190i	$-0.985378\pi$
$499$	−1.69657	−	9.62174i	−0.0759490	−	0.430728i	0.922996	−	0.384809i	$-0.125733\pi$
$500$		0			0
$501$	−22.3774	+	15.1314i	−0.999750	+	0.676021i
$502$		0			0
$503$	15.8295	−	18.8649i	0.705803	−	0.841143i	−0.287367	−	0.957821i	$-0.592780\pi$
$503$	15.8295	−	18.8649i	0.705803	−	0.841143i	0.993170	+	0.116677i	$0.0372244\pi$
$504$		0			0
$505$	3.79121	+	6.56657i	0.168707	+	0.292209i
$506$		0			0
$507$	19.9743	+	2.07606i	0.887088	+	0.0922011i
$508$		0			0
$509$	4.54614	−	25.7825i	0.201504	−	1.14279i	−0.701342	−	0.712825i	$-0.747416\pi$
$509$	4.54614	−	25.7825i	0.201504	−	1.14279i	0.902847	−	0.429963i	$-0.141473\pi$
$510$		0			0
$511$	−21.7888	+	18.2830i	−0.963879	+	0.808791i
$512$		0			0
$513$	−19.7373	−	11.1103i	−0.871425	−	0.490530i
$514$		0			0
$515$	3.45392	−	2.89818i	0.152198	−	0.127709i
$516$		0			0
$517$	−2.02535	+	11.4863i	−0.0890748	+	0.505169i
$518$		0			0
$519$	−5.96471	−	0.619953i	−0.261822	−	0.0272129i
$520$		0			0
$521$	−2.06261	−	3.57254i	−0.0903645	−	0.156516i	0.817300	−	0.576212i	$-0.195470\pi$
$521$	−2.06261	−	3.57254i	−0.0903645	−	0.156516i	−0.907665	+	0.419696i	$0.862137\pi$
$522$		0			0
$523$	19.4644	−	23.1968i	0.851119	−	1.01432i	−0.148558	−	0.988904i	$-0.547463\pi$
$523$	19.4644	−	23.1968i	0.851119	−	1.01432i	0.999677	−	0.0254208i	$-0.00809255\pi$
$524$		0			0
$525$	−6.58688	+	4.45398i	−0.287475	+	0.194388i
$526$		0			0
$527$	−3.72988	−	21.1532i	−0.162476	−	0.921449i
$528$		0			0
$529$	−2.91152	−	1.05971i	−0.126588	−	0.0460742i
$530$		0			0
$531$	8.61985	+	10.9805i	0.374070	+	0.476515i
$532$		0			0
$533$		−	8.23863i		−	0.356855i
$534$		0			0
$535$	4.06887	−	11.1791i	0.175913	−	0.483316i
$536$		0			0
$537$	12.1631	−	42.6034i	0.524877	−	1.83847i
$538$		0			0
$539$	4.31955	+	2.49390i	0.186056	+	0.107420i
$540$		0			0
$541$	15.8434	+	13.2942i	0.681162	+	0.571563i	0.916346	−	0.400388i	$-0.131125\pi$
$541$	15.8434	+	13.2942i	0.681162	+	0.571563i	−0.235183	+	0.971951i	$0.575569\pi$
$542$		0			0
$543$	23.7953	−	1.69155i	1.02116	−	0.0725912i
$544$		0			0
$545$	−8.95610	+	3.25975i	−0.383637	+	0.139633i
$546$		0			0
$547$	−21.7347	−	3.83242i	−0.929310	−	0.163862i	−0.311550	−	0.950230i	$-0.600848\pi$
$547$	−21.7347	−	3.83242i	−0.929310	−	0.163862i	−0.617759	+	0.786367i	$0.711959\pi$
$548$		0			0
$549$	40.3485	+	8.47900i	1.72203	+	0.361875i
$550$		0			0
$551$	7.56255	−	19.1263i	0.322175	−	0.814807i
$552$		0			0
$553$	10.4581	+	12.4635i	0.444723	+	0.530000i
$554$		0			0
$555$	−20.1127	+	27.7501i	−0.853737	+	1.17793i
$556$		0			0
$557$	−4.12552	−	11.3348i	−0.174804	−	0.480269i	0.821090	−	0.570799i	$-0.193366\pi$
$557$	−4.12552	−	11.3348i	−0.174804	−	0.480269i	−0.995894	+	0.0905293i	$0.971144\pi$
$558$		0			0
$559$	2.04996	−	1.18355i	0.0867041	−	0.0500587i
$560$		0			0
$561$	−15.1811	−	33.9917i	−0.640948	−	1.43513i
$562$		0			0
$563$	17.3789	−	30.1011i	0.732434	−	1.26861i	−0.223407	−	0.974725i	$-0.571718\pi$
$563$	17.3789	−	30.1011i	0.732434	−	1.26861i	0.955840	−	0.293887i	$-0.0949489\pi$
$564$		0			0
$565$	0.636633	−	0.112256i	0.0267834	−	0.00472263i
$566$		0			0
$567$	−11.3706	+	17.0268i	−0.477521	+	0.715056i
$568$		0			0
$569$	0.922002			0.0386523			0.0193262	−	0.999813i	$-0.493848\pi$
$569$	0.922002			0.0386523			0.0193262	+	0.999813i	$0.493848\pi$
$570$		0			0
$571$	31.1356			1.30298			0.651492	−	0.758655i	$-0.274143\pi$
$571$	31.1356			1.30298			0.651492	+	0.758655i	$0.274143\pi$
$572$		0			0
$573$	−19.0446	+	18.4337i	−0.795600	+	0.770080i
$574$		0			0
$575$	−8.86565	+	1.56325i	−0.369723	+	0.0651921i
$576$		0			0
$577$	−11.5819	+	20.0604i	−0.482159	+	0.835124i	−0.999790	−	0.0204802i	$-0.993481\pi$
$577$	−11.5819	+	20.0604i	−0.482159	+	0.835124i	0.517631	+	0.855604i	$0.326814\pi$
$578$		0			0
$579$	−32.8740	+	14.6819i	−1.36620	+	0.610161i
$580$		0			0
$581$	−19.5295	+	11.2754i	−0.810222	+	0.467782i
$582$		0			0
$583$	4.95034	+	13.6009i	0.205022	+	0.563293i
$584$		0			0
$585$	−5.41663	+	2.89614i	−0.223950	+	0.119741i
$586$		0			0
$587$	−26.7727	−	31.9065i	−1.10503	−	1.31692i	−0.943990	−	0.329974i	$-0.892960\pi$
$587$	−26.7727	−	31.9065i	−1.10503	−	1.31692i	−0.161038	−	0.986948i	$-0.551484\pi$
$588$		0			0
$589$	−2.38901	+	11.6653i	−0.0984373	+	0.480661i
$590$		0			0
$591$	2.72721	+	10.8847i	0.112182	+	0.447735i
$592$		0			0
$593$	−37.1913	−	6.55783i	−1.52726	−	0.269298i	−0.653981	−	0.756511i	$-0.726902\pi$
$593$	−37.1913	−	6.55783i	−1.52726	−	0.269298i	−0.873283	+	0.487214i	$0.838013\pi$
$594$		0			0
$595$	−29.0264	+	10.5648i	−1.18997	+	0.433113i
$596$		0			0
$597$	2.90608	+	40.8804i	0.118938	+	1.67312i
$598$		0			0
$599$	36.3437	+	30.4960i	1.48496	+	1.24603i	0.900681	+	0.434481i	$0.143068\pi$
$599$	36.3437	+	30.4960i	1.48496	+	1.24603i	0.584282	+	0.811551i	$0.301376\pi$
$600$		0			0
$601$	28.2909	+	16.3338i	1.15401	+	0.666268i	0.949861	−	0.312672i	$-0.101224\pi$
$601$	28.2909	+	16.3338i	1.15401	+	0.666268i	0.204149	+	0.978940i	$0.434557\pi$
$602$		0			0
$603$	6.23528	+	5.58825i	0.253920	+	0.227571i
$604$		0			0
$605$	−2.08362	+	5.72471i	−0.0847113	+	0.232742i
$606$		0			0
$607$		−	12.9568i		−	0.525898i	−0.964810	−	0.262949i	$-0.915305\pi$
$607$		−	12.9568i		−	0.525898i	0.964810	−	0.262949i	$-0.0846951\pi$
$608$		0			0
$609$	−16.7198	−	8.13090i	−0.677520	−	0.329481i
$610$		0			0
$611$	−4.75385	−	1.73026i	−0.192320	−	0.0699987i
$612$		0			0
$613$	−2.25785	−	12.8049i	−0.0911939	−	0.517186i	−0.995847	−	0.0910384i	$-0.970981\pi$
$613$	−2.25785	−	12.8049i	−0.0911939	−	0.517186i	0.904653	−	0.426148i	$-0.140130\pi$
$614$		0			0
$615$	−11.6419	−	17.2169i	−0.469447	−	0.694253i
$616$		0			0
$617$	−11.8376	+	14.1075i	−0.476565	+	0.567948i	−0.949748	−	0.313016i	$-0.898661\pi$
$617$	−11.8376	+	14.1075i	−0.476565	+	0.567948i	0.473183	+	0.880964i	$0.343105\pi$
$618$		0			0
$619$	22.3471	+	38.7063i	0.898205	+	1.55574i	0.829787	+	0.558080i	$0.188462\pi$
$619$	22.3471	+	38.7063i	0.898205	+	1.55574i	0.0684178	+	0.997657i	$0.478205\pi$
$620$		0			0
$621$	−19.6157	+	12.3519i	−0.787149	+	0.495665i
$622$		0			0
$623$	1.78738	−	10.1368i	0.0716101	−	0.406121i
$624$		0			0
$625$	−8.30235	+	6.96650i	−0.332094	+	0.278660i
$626$		0			0
$627$	0.897424	+	20.6181i	0.0358397	+	0.823408i
$628$		0			0
$629$	69.0182	−	57.9132i	2.75194	−	2.30915i
$630$		0			0
$631$	0.664942	−	3.77107i	0.0264709	−	0.150124i	−0.968708	−	0.248205i	$-0.920159\pi$
$631$	0.664942	−	3.77107i	0.0264709	−	0.150124i	0.995178	+	0.0980810i	$0.0312704\pi$
$632$		0			0
$633$	−2.90098	+	27.9110i	−0.115304	+	1.10936i
$634$		0			0
$635$	−8.88954	−	15.3971i	−0.352771	−	0.611017i
$636$		0			0
$637$	−1.39061	+	1.65726i	−0.0550979	+	0.0656631i
$638$		0			0
$639$	24.0321	−	3.43411i	0.950697	−	0.135851i
$640$		0			0
$641$	4.27908	+	24.2679i	0.169014	+	0.958523i	0.944829	+	0.327564i	$0.106228\pi$
$641$	4.27908	+	24.2679i	0.169014	+	0.958523i	−0.775816	+	0.630960i	$0.782661\pi$
$642$		0			0
$643$	43.1808	+	15.7165i	1.70288	+	0.619799i	0.996149	−	0.0876796i	$-0.0279452\pi$
$643$	43.1808	+	15.7165i	1.70288	+	0.619799i	0.706735	+	0.707479i	$0.250167\pi$
$644$		0			0
$645$	2.61151	−	5.37013i	0.102828	−	0.211449i
$646$		0			0
$647$		−	33.9965i		−	1.33654i	−0.743918	−	0.668271i	$-0.767035\pi$
$647$		−	33.9965i		−	1.33654i	0.743918	−	0.668271i	$-0.232965\pi$
$648$		0			0
$649$	4.35041	−	11.9526i	0.170768	−	0.469182i
$650$		0			0
$651$	10.3504	+	2.95499i	0.405663	+	0.115815i
$652$		0			0
$653$	16.5918	+	9.57930i	0.649289	+	0.374867i	0.788184	−	0.615440i	$-0.211022\pi$
$653$	16.5918	+	9.57930i	0.649289	+	0.374867i	−0.138895	+	0.990307i	$0.544355\pi$
$654$		0			0
$655$	−3.15003	−	2.64319i	−0.123082	−	0.103278i
$656$		0			0
$657$	13.9706	−	34.8098i	0.545046	−	1.35806i
$658$		0			0
$659$	−36.5442	+	13.3010i	−1.42356	+	0.518133i	−0.935078	−	0.354442i	$-0.884671\pi$
$659$	−36.5442	+	13.3010i	−1.42356	+	0.518133i	−0.488480	+	0.872575i	$0.662449\pi$
$660$		0			0
$661$	16.1892	+	2.85460i	0.629688	+	0.111031i	0.479379	−	0.877608i	$-0.340862\pi$
$661$	16.1892	+	2.85460i	0.629688	+	0.111031i	0.150309	+	0.988639i	$0.451973\pi$
$662$		0			0
$663$	15.6630	−	3.92443i	0.608300	−	0.152412i
$664$		0			0
$665$	17.1174	+	0.470323i	0.663784	+	0.0182383i
$666$		0			0
$667$	−13.5303	−	16.1248i	−0.523897	−	0.624356i
$668$		0			0
$669$	38.7540	+	28.0881i	1.49832	+	1.08595i
$670$		0			0
$671$	−12.8489	−	35.3019i	−0.496025	−	1.36282i
$672$		0			0
$673$	−2.52834	+	1.45974i	−0.0974602	+	0.0562687i	−0.547938	−	0.836519i	$-0.684587\pi$
$673$	−2.52834	+	1.45974i	−0.0974602	+	0.0562687i	0.450478	+	0.892788i	$0.351254\pi$
$674$		0			0
$675$	4.89063	−	9.27530i	0.188240	−	0.357007i
$676$		0			0
$677$	1.71065	−	2.96294i	0.0657457	−	0.113875i	−0.831279	−	0.555856i	$-0.812391\pi$
$677$	1.71065	−	2.96294i	0.0657457	−	0.113875i	0.897025	+	0.441981i	$0.145724\pi$
$678$		0			0
$679$	−14.4465	+	2.54730i	−0.554405	+	0.0977565i
$680$		0			0
$681$	22.6083	+	23.3576i	0.866354	+	0.895065i
$682$		0			0
$683$	36.0864			1.38081			0.690404	−	0.723424i	$-0.257433\pi$
$683$	36.0864			1.38081			0.690404	+	0.723424i	$0.257433\pi$
$684$		0			0
$685$	10.2664			0.392258
$686$		0			0
$687$	21.2169	+	21.9200i	0.809475	+	0.836301i
$688$		0			0
$689$	−6.18249	+	1.09014i	−0.235534	+	0.0415310i
$690$		0			0
$691$	−1.37889	+	2.38830i	−0.0524553	+	0.0908553i	−0.891061	−	0.453884i	$-0.850038\pi$
$691$	−1.37889	+	2.38830i	−0.0524553	+	0.0908553i	0.838605	+	0.544739i	$0.183371\pi$
$692$		0			0
$693$	18.6458	+	0.608015i	0.708296	+	0.0230966i
$694$		0			0
$695$	−5.70811	+	3.29558i	−0.216521	+	0.125008i
$696$		0			0
$697$	18.6869	+	51.3420i	0.707819	+	1.94472i
$698$		0			0
$699$	33.7950	+	24.4939i	1.27824	+	0.926445i
$700$		0			0
$701$	−4.56617	−	5.44174i	−0.172462	−	0.205532i	0.672889	−	0.739743i	$-0.265053\pi$
$701$	−4.56617	−	5.44174i	−0.172462	−	0.205532i	−0.845351	+	0.534211i	$0.820609\pi$
$702$		0			0
$703$	−47.3857	+	15.7871i	−1.78718	+	0.595422i
$704$		0			0
$705$	−12.3795	+	3.10174i	−0.466239	+	0.116818i
$706$		0			0
$707$	9.83722	+	1.73457i	0.369967	+	0.0652351i
$708$		0			0
$709$	30.5071	−	11.1037i	1.14572	−	0.417008i	0.301743	−	0.953389i	$-0.402431\pi$
$709$	30.5071	−	11.1037i	1.14572	−	0.417008i	0.843975	+	0.536382i	$0.180209\pi$
$710$		0			0
$711$	−19.9116	−	7.99138i	−0.746745	−	0.299700i
$712$		0			0
$713$	9.33555	+	7.83346i	0.349619	+	0.293365i
$714$		0			0
$715$	4.84686	+	2.79834i	0.181262	+	0.104652i
$716$		0			0
$717$	−11.3916	−	3.25226i	−0.425427	−	0.121458i
$718$		0			0
$719$	10.5400	−	28.9585i	0.393076	−	1.07997i	−0.572513	−	0.819896i	$-0.694031\pi$
$719$	10.5400	−	28.9585i	0.393076	−	1.07997i	0.965589	−	0.260072i	$-0.0837464\pi$
$720$		0			0
$721$		−	5.93979i		−	0.221209i
$722$		0			0
$723$	−9.74036	+	20.0294i	−0.362248	+	0.744901i
$724$		0			0
$725$	8.94741	+	3.25659i	0.332299	+	0.120947i
$726$		0			0
$727$	0.123372	+	0.699679i	0.00457562	+	0.0259496i	0.987010	−	0.160658i	$-0.0513617\pi$
$727$	0.123372	+	0.699679i	0.00457562	+	0.0259496i	−0.982434	+	0.186608i	$0.940251\pi$
$728$		0			0
$729$	2.63616	−	26.8710i	0.0976354	−	0.995222i
$730$		0			0
$731$	−10.0905	+	12.0254i	−0.373212	+	0.444777i
$732$		0			0
$733$	5.28122	+	9.14735i	0.195066	+	0.337865i	0.946922	−	0.321462i	$-0.104174\pi$
$733$	5.28122	+	9.14735i	0.195066	+	0.337865i	−0.751856	+	0.659328i	$0.770841\pi$
$734$		0			0
$735$	−0.564207	+	5.42837i	−0.0208111	+	0.200228i
$736$		0			0
$737$	1.32481	−	7.51336i	0.0488000	−	0.276758i
$738$		0			0
$739$	24.9740	−	20.9557i	0.918682	−	0.770866i	−0.0550684	−	0.998483i	$-0.517538\pi$
$739$	24.9740	−	20.9557i	0.918682	−	0.770866i	0.973751	+	0.227617i	$0.0730933\pi$
$740$		0			0
$741$	−8.87462	−	1.16958i	−0.326017	−	0.0429657i
$742$		0			0
$743$	−23.8083	+	19.9775i	−0.873442	+	0.732905i	−0.964820	−	0.262912i	$-0.915317\pi$
$743$	−23.8083	+	19.9775i	−0.873442	+	0.732905i	0.0913781	+	0.995816i	$0.470873\pi$
$744$		0			0
$745$	3.88649	−	22.0414i	0.142390	−	0.807534i
$746$		0			0
$747$	15.7005	−	25.2557i	0.574452	−	0.924058i
$748$		0			0
$749$	−7.83619	−	13.5727i	−0.286328	−	0.495935i
$750$		0			0
$751$	4.33202	−	5.16270i	0.158078	−	0.188389i	−0.681192	−	0.732104i	$-0.738538\pi$
$751$	4.33202	−	5.16270i	0.158078	−	0.188389i	0.839270	+	0.543715i	$0.182983\pi$
$752$		0			0
$753$	20.1862	+	29.8528i	0.735625	+	1.08790i
$754$		0			0
$755$	6.54219	+	37.1026i	0.238095	+	1.35030i
$756$		0			0
$757$	−5.03676	−	1.83323i	−0.183064	−	0.0666300i	0.248862	−	0.968539i	$-0.419944\pi$
$757$	−5.03676	−	1.83323i	−0.183064	−	0.0666300i	−0.431926	+	0.901909i	$0.642166\pi$
$758$		0			0
$759$	18.9947	+	9.23718i	0.689463	+	0.335289i
$760$		0			0
$761$		−	20.3885i		−	0.739083i	−0.929214	−	0.369541i	$-0.879515\pi$
$761$		−	20.3885i		−	0.739083i	0.929214	−	0.369541i	$-0.120485\pi$
$762$		0			0
$763$	−4.29435	+	11.7986i	−0.155466	+	0.427139i
$764$		0			0
$765$	27.1866	−	30.3344i	0.982934	−	1.09674i
$766$		0			0
$767$	4.77791	+	2.75853i	0.172520	+	0.0996047i
$768$		0			0
$769$	−13.9535	−	11.7084i	−0.503177	−	0.422216i	0.355543	−	0.934660i	$-0.384296\pi$
$769$	−13.9535	−	11.7084i	−0.503177	−	0.422216i	−0.858721	+	0.512444i	$0.828740\pi$
$770$		0			0
$771$	−2.27024	−	31.9360i	−0.0817609	−	1.15015i
$772$		0			0
$773$	−36.5716	+	13.3110i	−1.31539	+	0.478763i	−0.901978	−	0.431781i	$-0.857885\pi$
$773$	−36.5716	+	13.3110i	−1.31539	+	0.478763i	−0.413412	+	0.910544i	$0.635663\pi$
$774$		0			0
$775$	−5.42885	−	0.957253i	−0.195010	−	0.0343855i
$776$		0			0
$777$	10.9733	+	43.7960i	0.393665	+	1.57117i
$778$		0			0
$779$	0.831907	−	30.2772i	0.0298062	−	1.08479i
$780$		0			0
$781$	−14.2184	−	16.9448i	−0.508774	−	0.606333i
$782$		0			0
$783$	24.4996	−	0.940533i	0.875544	−	0.0336119i
$784$		0			0
$785$	−1.65731	−	4.55341i	−0.0591518	−	0.162518i
$786$		0			0
$787$	8.63577	−	4.98587i	0.307832	−	0.177727i	−0.338124	−	0.941102i	$-0.609792\pi$
$787$	8.63577	−	4.98587i	0.307832	−	0.177727i	0.645956	+	0.763375i	$0.276459\pi$
$788$		0			0
$789$	2.06532	−	0.922399i	0.0735273	−	0.0328383i
$790$		0			0
$791$	0.425815	−	0.737533i	0.0151402	−	0.0262237i
$792$		0			0
$793$	16.0470	−	2.82952i	0.569845	−	0.100479i
$794$		0			0
$795$	−11.3796	+	11.0146i	−0.403592	+	0.390646i
$796$		0			0
$797$	−11.6810			−0.413764			−0.206882	−	0.978366i	$-0.566332\pi$
$797$	−11.6810			−0.413764			−0.206882	+	0.978366i	$0.566332\pi$
$798$		0			0
$799$	33.5499			1.18691
$800$		0			0
$801$	4.22433	+	12.8997i	0.149259	+	0.455788i
$802$		0			0
$803$	−33.6577	+	5.93476i	−1.18775	+	0.209433i
$804$		0			0
$805$	8.76272	−	15.1775i	0.308845	−	0.534936i
$806$		0			0
$807$	4.00011	+	8.95655i	0.140811	+	0.315285i
$808$		0			0
$809$	15.8409	−	9.14576i	0.556937	−	0.321548i	−0.194978	−	0.980808i	$-0.562464\pi$
$809$	15.8409	−	9.14576i	0.556937	−	0.321548i	0.751915	+	0.659260i	$0.229130\pi$
$810$		0			0
$811$	−9.54842	−	26.2341i	−0.335290	−	0.921203i	−0.986711	−	0.162486i	$-0.948049\pi$
$811$	−9.54842	−	26.2341i	−0.335290	−	0.921203i	0.651420	−	0.758717i	$-0.274173\pi$
$812$		0			0
$813$	11.2715	−	15.5516i	0.395309	−	0.545420i
$814$		0			0
$815$	−17.1063	−	20.3865i	−0.599207	−	0.714107i
$816$		0			0
$817$	7.65319	−	4.14257i	0.267751	−	0.144930i
$818$		0			0
$819$	−1.66408	+	7.91877i	−0.0581477	+	0.276704i
$820$		0			0
$821$	45.1994	+	7.96987i	1.57747	+	0.278150i	0.892714	−	0.450623i	$-0.148798\pi$
$821$	45.1994	+	7.96987i	1.57747	+	0.278150i	0.684755	+	0.728773i	$0.259909\pi$
$822$		0			0
$823$	−49.9436	+	18.1780i	−1.74092	+	0.633645i	−0.999309	−	0.0371801i	$-0.988162\pi$
$823$	−49.9436	+	18.1780i	−1.74092	+	0.633645i	−0.741616	+	0.670825i	$0.765940\pi$
$824$		0			0
$825$	−9.53023	+	0.677478i	−0.331800	+	0.0235868i
$826$		0			0
$827$	−17.4610	−	14.6515i	−0.607179	−	0.509484i	0.286565	−	0.958061i	$-0.407487\pi$
$827$	−17.4610	−	14.6515i	−0.607179	−	0.509484i	−0.893744	+	0.448577i	$0.851931\pi$
$828$		0			0
$829$	−7.21681	−	4.16663i	−0.250650	−	0.144713i	0.369412	−	0.929266i	$-0.379559\pi$
$829$	−7.21681	−	4.16663i	−0.250650	−	0.144713i	−0.620062	+	0.784553i	$0.712893\pi$
$830$		0			0
$831$	14.3725	−	50.3423i	0.498578	−	1.74636i
$832$		0			0
$833$	4.90705	−	13.4820i	0.170019	−	0.467124i
$834$		0			0
$835$			26.9321i			0.932024i
$836$		0			0
$837$	−13.8741	+	2.99931i	−0.479560	+	0.103671i
$838$		0			0
$839$	−26.9124	−	9.79530i	−0.929118	−	0.338171i	−0.167258	−	0.985913i	$-0.553491\pi$
$839$	−26.9124	−	9.79530i	−0.929118	−	0.338171i	−0.761860	+	0.647742i	$0.775714\pi$
$840$		0			0
$841$	−1.16978	−	6.63413i	−0.0403371	−	0.228763i
$842$		0			0
$843$	−21.4442	+	14.5004i	−0.738579	+	0.499420i
$844$		0			0
$845$	12.8697	−	15.3375i	0.442729	−	0.527624i
$846$		0			0
$847$	4.01283	+	6.95042i	0.137882	+	0.238819i
$848$		0			0
$849$	−19.2812	−	2.00403i	−0.661730	−	0.0687781i
$850$		0			0
$851$	−8.87648	+	50.3410i	−0.304282	+	1.72567i
$852$		0			0
$853$	−3.37434	+	2.83141i	−0.115535	+	0.0969457i	−0.698725	−	0.715390i	$-0.746249\pi$
$853$	−3.37434	+	2.83141i	−0.115535	+	0.0969457i	0.583190	+	0.812336i	$0.301804\pi$
$854$		0			0
$855$	−20.1987	+	10.0965i	−0.690782	+	0.345291i
$856$		0			0
$857$	24.9404	−	20.9275i	0.851947	−	0.714869i	−0.108270	−	0.994122i	$-0.534531\pi$
$857$	24.9404	−	20.9275i	0.851947	−	0.714869i	0.960218	+	0.279253i	$0.0900867\pi$
$858$		0			0
$859$	2.11844	−	12.0143i	0.0722802	−	0.409921i	−0.927103	−	0.374806i	$-0.877709\pi$
$859$	2.11844	−	12.0143i	0.0722802	−	0.409921i	0.999383	−	0.0351148i	$-0.0111797\pi$
$860$		0			0
$861$	−27.2333	−	2.83054i	−0.928107	−	0.0964645i
$862$		0			0
$863$	1.53095	+	2.65169i	0.0521143	+	0.0902646i	0.890906	−	0.454188i	$-0.150071\pi$
$863$	1.53095	+	2.65169i	0.0521143	+	0.0902646i	−0.838791	+	0.544453i	$0.816737\pi$
$864$		0			0
$865$	−3.84313	+	4.58007i	−0.130670	+	0.155727i
$866$		0			0
$867$	−64.3161	+	43.4899i	−2.18429	+	1.47699i
$868$		0			0
$869$	3.39476	+	19.2526i	0.115159	+	0.653100i
$870$		0			0
$871$	3.10955	+	1.13178i	0.105363	+	0.0383491i
$872$		0			0
$873$	15.2163	−	11.9450i	0.514994	−	0.404277i
$874$		0			0
$875$			27.5700i			0.932035i
$876$		0			0
$877$	1.79442	−	4.93014i	0.0605934	−	0.166479i	−0.905702	−	0.423915i	$-0.860655\pi$
$877$	1.79442	−	4.93014i	0.0605934	−	0.166479i	0.966295	+	0.257436i	$0.0828777\pi$
$878$		0			0
$879$	−14.2520	+	49.9201i	−0.480708	+	1.68376i
$880$		0			0
$881$	−40.9801	−	23.6599i	−1.38065	−	0.797121i	−0.388417	−	0.921484i	$-0.626978\pi$
$881$	−40.9801	−	23.6599i	−1.38065	−	0.797121i	−0.992237	+	0.124363i	$0.960311\pi$
$882$		0			0
$883$	34.0597	+	28.5794i	1.14620	+	0.961775i	0.999624	−	0.0274247i	$-0.00873064\pi$
$883$	34.0597	+	28.5794i	1.14620	+	0.961775i	0.146575	+	0.989200i	$0.453175\pi$
$884$		0			0
$885$	13.8828	−	0.986893i	0.466666	−	0.0331740i
$886$		0			0
$887$	23.2057	−	8.44619i	0.779172	−	0.283595i	0.0783444	−	0.996926i	$-0.475037\pi$
$887$	23.2057	−	8.44619i	0.779172	−	0.283595i	0.700827	+	0.713331i	$0.252814\pi$
$888$		0			0
$889$	−23.0661	−	4.06717i	−0.773611	−	0.136408i
$890$		0			0
$891$	−22.0618	+	10.8867i	−0.739098	+	0.364718i
$892$		0			0
$893$	−17.2958	−	6.83878i	−0.578783	−	0.228851i
$894$		0			0
$895$	−28.3937	−	33.8383i	−0.949097	−	1.13109i
$896$		0			0
$897$	−5.37631	+	7.41785i	−0.179510	+	0.247675i
$898$		0			0
$899$	−4.40850	−	12.1122i	−0.147032	−	0.403966i
$900$		0			0
$901$	36.0558	−	20.8168i	1.20119	−	0.693508i
$902$		0			0
$903$	−3.20797	−	7.18289i	−0.106755	−	0.239032i
$904$		0			0
$905$	11.8919	−	20.5974i	0.395301	−	0.684681i
$906$		0			0
$907$	−8.07243	+	1.42339i	−0.268041	+	0.0472628i	−0.306053	−	0.952014i	$-0.599008\pi$
$907$	−8.07243	+	1.42339i	−0.268041	+	0.0472628i	0.0380123	+	0.999277i	$0.487897\pi$
$908$		0			0
$909$	−12.5185	+	4.09950i	−0.415213	+	0.135972i
$910$		0			0
$911$	24.5898			0.814695			0.407348	−	0.913273i	$-0.366454\pi$
$911$	24.5898			0.814695			0.407348	+	0.913273i	$0.366454\pi$
$912$		0			0
$913$	−27.0966			−0.896767
$914$		0			0
$915$	29.5363	−	28.5889i	0.976440	−	0.945119i
$916$		0			0
$917$	−5.33488	+	0.940683i	−0.176173	+	0.0310641i
$918$		0			0
$919$	−18.6876	+	32.3680i	−0.616449	+	1.06772i	0.373680	+	0.927558i	$0.378096\pi$
$919$	−18.6876	+	32.3680i	−0.616449	+	1.06772i	−0.990129	+	0.140163i	$0.955237\pi$
$920$		0			0
$921$	−15.3051	+	6.83544i	−0.504319	+	0.225235i
$922$		0			0
$923$	8.30888	−	4.79714i	0.273490	−	0.157900i
$924$		0			0
$925$	−7.90848	−	21.7284i	−0.260029	−	0.714424i
$926$		0			0
$927$	3.69330	+	6.90755i	0.121304	+	0.226874i
$928$		0			0
$929$	18.9324	+	22.5627i	0.621152	+	0.740260i	0.981268	−	0.192648i	$-0.0617075\pi$
$929$	18.9324	+	22.5627i	0.621152	+	0.740260i	−0.360116	+	0.932907i	$0.617263\pi$
$930$		0			0
$931$	−5.27788	+	5.95008i	−0.172975	+	0.195006i
$932$		0			0
$933$	8.94348	+	35.6947i	0.292796	+	1.16859i
$934$		0			0
$935$	−36.5522	−	6.44513i	−1.19538	−	0.210778i
$936$		0			0
$937$	−10.3758	+	3.77647i	−0.338962	+	0.123372i	−0.505892	−	0.862597i	$-0.668837\pi$
$937$	−10.3758	+	3.77647i	−0.338962	+	0.123372i	0.166931	+	0.985969i	$0.446614\pi$
$938$		0			0
$939$	−2.05526	−	28.9117i	−0.0670708	−	0.943499i
$940$		0			0
$941$	36.7707	+	30.8543i	1.19869	+	1.00582i	0.999666	+	0.0258270i	$0.00822190\pi$
$941$	36.7707	+	30.8543i	1.19869	+	1.00582i	0.199025	+	0.979994i	$0.436223\pi$
$942$		0			0
$943$	−26.8459	−	15.4995i	−0.874223	−	0.504733i
$944$		0			0
$945$	7.71236	+	18.9000i	0.250883	+	0.614817i
$946$		0			0
$947$	0.813773	−	2.23582i	0.0264441	−	0.0726545i	−0.925768	−	0.378092i	$-0.876580\pi$
$947$	0.813773	−	2.23582i	0.0264441	−	0.0726545i	0.952212	+	0.305437i	$0.0988026\pi$
$948$		0			0
$949$		−	14.8239i		−	0.481204i
$950$		0			0
$951$	−26.6641	−	12.9668i	−0.864642	−	0.420479i
$952$		0			0
$953$	−50.4055	−	18.3461i	−1.63280	−	0.594289i	−0.647037	−	0.762459i	$-0.723992\pi$
$953$	−50.4055	−	18.3461i	−1.63280	−	0.594289i	−0.985758	+	0.168170i	$0.946214\pi$
$954$		0			0
$955$	4.58869	+	26.0238i	0.148487	+	0.842109i
$956$		0			0
$957$	−12.5137	−	18.5061i	−0.404509	−	0.598218i
$958$		0			0
$959$	8.69355	−	10.3606i	0.280729	−	0.334560i
$960$		0			0
$961$	−11.7688	−	20.3841i	−0.379637	−	0.657551i
$962$		0			0
$963$	17.5523	+	10.9116i	0.565614	+	0.351621i
$964$		0			0
$965$	−6.23320	+	35.3503i	−0.200654	+	1.13797i
$966$		0			0
$967$	11.6317	−	9.76013i	0.374049	−	0.313865i	−0.436312	−	0.899796i	$-0.643716\pi$
$967$	11.6317	−	9.76013i	0.374049	−	0.313865i	0.810361	+	0.585931i	$0.199271\pi$
$968$		0			0
$969$	57.9582	−	12.8408i	1.86189	−	0.412507i
$970$		0			0
$971$	−14.2121	+	11.9253i	−0.456087	+	0.382702i	−0.841689	−	0.539963i	$-0.818438\pi$
$971$	−14.2121	+	11.9253i	−0.456087	+	0.382702i	0.385602	+	0.922665i	$0.373994\pi$
$972$		0			0
$973$	−1.50780	+	8.55117i	−0.0483379	+	0.274138i
$974$		0			0
$975$	0.428414	−	4.12186i	0.0137202	−	0.132005i
$976$		0			0
$977$	12.2070	+	21.1431i	0.390536	+	0.676429i	0.992520	−	0.122079i	$-0.0389563\pi$
$977$	12.2070	+	21.1431i	0.390536	+	0.676429i	−0.601984	+	0.798508i	$0.705623\pi$
$978$		0			0
$979$	7.95004	−	9.47448i	0.254084	−	0.302806i
$980$		0			0
$981$	−2.34224	−	16.3911i	−0.0747820	−	0.523329i
$982$		0			0
$983$	−0.779019	−	4.41804i	−0.0248468	−	0.140913i	0.969861	−	0.243660i	$-0.0783481\pi$
$983$	−0.779019	−	4.41804i	−0.0248468	−	0.140913i	−0.994708	+	0.102746i	$0.967237\pi$
$984$		0			0
$985$	10.5128	+	3.82634i	0.334965	+	0.121917i
$986$		0			0
$987$	−7.35274	+	15.1196i	−0.234040	+	0.481263i
$988$		0			0
$989$		−	8.90651i		−	0.283211i
$990$		0			0
$991$	−1.21302	+	3.33274i	−0.0385328	+	0.105868i	−0.957467	−	0.288543i	$-0.906829\pi$
$991$	−1.21302	+	3.33274i	−0.0385328	+	0.105868i	0.918934	+	0.394411i	$0.129051\pi$
$992$		0			0
$993$	−3.83815	−	1.09578i	−0.121800	−	0.0347734i
$994$		0			0
$995$	35.3864	+	20.4303i	1.12182	+	0.647685i
$996$		0			0
$997$	−31.5620	−	26.4836i	−0.999578	−	0.838746i	−0.0126521	−	0.999920i	$-0.504027\pi$
$997$	−31.5620	−	26.4836i	−0.999578	−	0.838746i	−0.986926	+	0.161174i	$0.948472\pi$
$998$		0			0
$999$	−39.9930	−	44.1085i	−1.26532	−	1.39553i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bm.b.89.8	yes	60
3.2	odd	2		456.2.bm.a.89.1	yes	60
4.3	odd	2		912.2.cc.g.545.3		60
12.11	even	2		912.2.cc.h.545.10		60
19.3	odd	18		456.2.bm.a.41.1	✓	60
57.41	even	18	inner	456.2.bm.b.41.8	yes	60
76.3	even	18		912.2.cc.h.497.10		60
228.155	odd	18		912.2.cc.g.497.3		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bm.a.41.1	✓	60	19.3	odd	18
456.2.bm.a.89.1	yes	60	3.2	odd	2
456.2.bm.b.41.8	yes	60	57.41	even	18	inner
456.2.bm.b.89.8	yes	60	1.1	even	1	trivial
912.2.cc.g.497.3		60	228.155	odd	18
912.2.cc.g.545.3		60	4.3	odd	2
912.2.cc.h.497.10		60	76.3	even	18
912.2.cc.h.545.10		60	12.11	even	2

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bm (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20462 + 1.24454i) q^{3} +(1.70062 - 0.299865i) q^{5} +(1.13747 - 1.97015i) q^{7} +(-0.0977739 + 2.99841i) q^{9} +(2.36730 - 1.36676i) q^{11} +(0.405512 + 1.11413i) q^{13} +(2.42180 + 1.75527i) q^{15} +(-5.05418 - 6.02334i) q^{17} +(1.37777 + 4.13543i) q^{19} +(3.82215 - 0.957659i) q^{21} +(4.39335 + 0.774666i) q^{23} +(-1.89627 + 0.690186i) q^{25} +(-3.84943 + 3.49026i) q^{27} +(-3.61452 - 3.03294i) q^{29} +(2.36577 + 1.36588i) q^{31} +(4.55269 + 1.29978i) q^{33} +(1.34362 - 3.69157i) q^{35} +11.4585i q^{37} +(-0.898099 + 1.84679i) q^{39} +(-6.52964 - 2.37659i) q^{41} +(-0.346684 - 1.96614i) q^{43} +(0.732842 + 5.12847i) q^{45} +(-2.74268 + 3.26860i) q^{47} +(0.912338 + 1.58022i) q^{49} +(1.40793 - 13.5460i) q^{51} +(-0.919456 + 5.21449i) q^{53} +(3.61603 - 3.03421i) q^{55} +(-3.48703 + 6.69632i) q^{57} +(3.56459 - 2.99105i) q^{59} +(2.38649 - 13.5345i) q^{61} +(5.79610 + 3.60322i) q^{63} +(1.02371 + 1.77312i) q^{65} +(1.79402 - 2.13803i) q^{67} +(4.32822 + 6.40089i) q^{69} +(-1.40518 - 7.96915i) q^{71} +(-11.7489 - 4.27624i) q^{73} +(-3.14326 - 1.52858i) q^{75} -6.21858i q^{77} +(-2.44606 + 6.72050i) q^{79} +(-8.98088 - 0.586332i) q^{81} +(-8.58466 - 4.95636i) q^{83} +(-10.4014 - 8.72784i) q^{85} +(-0.579502 - 8.15198i) q^{87} +(4.25172 - 1.54750i) q^{89} +(2.65627 + 0.468372i) q^{91} +(1.14996 + 4.58967i) q^{93} +(3.58313 + 6.61965i) q^{95} +(-4.14485 - 4.93964i) q^{97} +(3.86664 + 7.23176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{9} + 3 q^{13} - 3 q^{15} - 6 q^{17} + 3 q^{19} + 6 q^{25} + 3 q^{27} + 6 q^{29} + 24 q^{35} + 18 q^{39} + 3 q^{41} - 21 q^{43} + 63 q^{45} - 18 q^{47} - 30 q^{49} + 33 q^{51} - 36 q^{53} + 18 q^{55}+ \cdots - 39 q^{99}+O(q^{100}) \) 60 * q - 6 * q^9 + 3 * q^13 - 3 * q^15 - 6 * q^17 + 3 * q^19 + 6 * q^25 + 3 * q^27 + 6 * q^29 + 24 * q^35 + 18 * q^39 + 3 * q^41 - 21 * q^43 + 63 * q^45 - 18 * q^47 - 30 * q^49 + 33 * q^51 - 36 * q^53 + 18 * q^55 - 24 * q^57 - 21 * q^59 - 6 * q^61 - 24 * q^63 + 24 * q^65 - 48 * q^67 - 21 * q^69 + 36 * q^71 - 57 * q^73 - 36 * q^79 + 6 * q^81 - 36 * q^83 + 6 * q^85 + 72 * q^87 - 24 * q^89 - 18 * q^91 + 108 * q^93 + 30 * q^95 + 15 * q^97 - 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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