LMFDB - Embedded newform 441.2.w.a.62.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(62,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.62"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.w (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			62.15
Character	$\chi$	$=$	441.62
Dual form			441.2.w.a.377.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.61687 - 0.369040i) q^{2} +(0.676145 - 0.325614i) q^{4} +(1.24446 + 1.56050i) q^{5} +(0.123672 + 2.64286i) q^{7} +(-1.62019 + 1.29205i) q^{8} +(2.58801 + 2.06387i) q^{10} +(2.40273 - 0.548408i) q^{11} +(1.35794 - 0.309940i) q^{13} +(1.17528 + 4.22752i) q^{14} +(-3.07863 + 3.86047i) q^{16} +(-0.767970 - 0.369835i) q^{17} -4.70463i q^{19} +(1.34955 + 0.649911i) q^{20} +(3.68252 - 1.77341i) q^{22} +(2.52474 + 5.24267i) q^{23} +(0.226121 - 0.990699i) q^{25} +(2.08123 - 1.00227i) q^{26} +(0.944173 + 1.74669i) q^{28} +(0.0840694 - 0.174572i) q^{29} -7.85760i q^{31} +(-1.75480 + 3.64388i) q^{32} +(-1.37819 - 0.314564i) q^{34} +(-3.97027 + 3.48191i) q^{35} +(-2.46389 - 1.18655i) q^{37} +(-1.73620 - 7.60678i) q^{38} +(-4.03250 - 0.920391i) q^{40} +(-4.44530 - 5.57423i) q^{41} +(7.98148 - 10.0085i) q^{43} +(1.44603 - 1.15317i) q^{44} +(6.01693 + 7.54500i) q^{46} +(0.467248 + 2.04715i) q^{47} +(-6.96941 + 0.653696i) q^{49} -1.68528i q^{50} +(0.817242 - 0.651729i) q^{52} +(4.06653 + 8.44425i) q^{53} +(3.84588 + 3.06699i) q^{55} +(-3.61509 - 4.12213i) q^{56} +(0.0715054 - 0.313285i) q^{58} +(-8.03149 + 10.0712i) q^{59} +(-0.510260 + 1.05957i) q^{61} +(-2.89977 - 12.7047i) q^{62} +(0.704949 - 3.08858i) q^{64} +(2.17355 + 1.73335i) q^{65} +2.43390 q^{67} -0.639683 q^{68} +(-5.13445 + 7.09499i) q^{70} +(1.39482 + 2.89637i) q^{71} +(-9.99800 - 2.28198i) q^{73} +(-4.42168 - 1.00922i) q^{74} +(-1.53190 - 3.18101i) q^{76} +(1.74652 + 6.28226i) q^{77} -6.60146 q^{79} -9.85548 q^{80} +(-9.24459 - 7.37232i) q^{82} +(3.17998 - 13.9324i) q^{83} +(-0.378578 - 1.65866i) q^{85} +(9.21150 - 19.1279i) q^{86} +(-3.18430 + 3.99298i) q^{88} +(0.346714 - 1.51906i) q^{89} +(0.987068 + 3.55051i) q^{91} +(3.41418 + 2.72272i) q^{92} +(1.51096 + 3.13754i) q^{94} +(7.34156 - 5.85470i) q^{95} +0.726497i q^{97} +(-11.0274 + 3.62894i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70}+ \cdots - 112 q^{94}+O(q^{100}) $ 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{11}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.61687	−	0.369040i	1.14330	−	0.260951i	0.391396	−	0.920222i	$-0.371992\pi$
$2$	1.61687	−	0.369040i	1.14330	−	0.260951i	0.751905	+	0.659271i	$0.229135\pi$
$3$		0			0
$3$		0			0
$4$	0.676145	−	0.325614i	0.338073	−	0.162807i
$5$	1.24446	+	1.56050i	0.556537	+	0.697876i	0.977913	−	0.209010i	$-0.0670242\pi$
$5$	1.24446	+	1.56050i	0.556537	+	0.697876i	−0.421376	+	0.906886i	$0.638453\pi$
$6$		0			0
$7$	0.123672	+	2.64286i	0.0467437	+	0.998907i
$7$	0.123672	+	2.64286i	0.0467437	+	0.998907i
$8$	−1.62019	+	1.29205i	−0.572822	+	0.456810i
$9$		0			0
$10$	2.58801	+	2.06387i	0.818401	+	0.652653i
$11$	2.40273	−	0.548408i	0.724451	−	0.165351i	0.155633	−	0.987815i	$-0.450258\pi$
$11$	2.40273	−	0.548408i	0.724451	−	0.165351i	0.568817	+	0.822464i	$0.307401\pi$
$12$		0			0
$13$	1.35794	−	0.309940i	0.376624	−	0.0859620i	−0.0300184	−	0.999549i	$-0.509557\pi$
$13$	1.35794	−	0.309940i	0.376624	−	0.0859620i	0.406643	+	0.913587i	$0.366699\pi$
$14$	1.17528	+	4.22752i	0.314108	+	1.12985i
$15$		0			0
$16$	−3.07863	+	3.86047i	−0.769656	+	0.965119i
$17$	−0.767970	−	0.369835i	−0.186260	−	0.0896982i	0.338429	−	0.940992i	$-0.390104\pi$
$17$	−0.767970	−	0.369835i	−0.186260	−	0.0896982i	−0.524690	+	0.851294i	$0.675819\pi$
$18$		0			0
$19$		−	4.70463i		−	1.07932i	−0.841884	−	0.539658i	$-0.818554\pi$
$19$		−	4.70463i		−	1.07932i	0.841884	−	0.539658i	$-0.181446\pi$
$20$	1.34955	+	0.649911i	0.301769	+	0.145324i
$21$		0			0
$22$	3.68252	−	1.77341i	0.785117	−	0.378092i
$23$	2.52474	+	5.24267i	0.526444	+	1.09317i	0.979454	+	0.201667i	$0.0646359\pi$
$23$	2.52474	+	5.24267i	0.526444	+	1.09317i	−0.453010	+	0.891506i	$0.649650\pi$
$24$		0			0
$25$	0.226121	−	0.990699i	0.0452241	−	0.198140i
$26$	2.08123	−	1.00227i	0.408163	−	0.196561i
$27$		0			0
$28$	0.944173	+	1.74669i	0.178432	+	0.330093i
$29$	0.0840694	−	0.174572i	0.0156113	−	0.0324172i	−0.893017	−	0.450022i	$-0.851416\pi$
$29$	0.0840694	−	0.174572i	0.0156113	−	0.0324172i	0.908629	+	0.417605i	$0.137130\pi$
$30$		0			0
$31$		−	7.85760i		−	1.41127i	−0.708577	−	0.705633i	$-0.750663\pi$
$31$		−	7.85760i		−	1.41127i	0.708577	−	0.705633i	$-0.249337\pi$
$32$	−1.75480	+	3.64388i	−0.310208	+	0.644153i
$33$		0			0
$34$	−1.37819	−	0.314564i	−0.236358	−	0.0539472i
$35$	−3.97027	+	3.48191i	−0.671098	+	0.588550i
$36$		0			0
$37$	−2.46389	−	1.18655i	−0.405061	−	0.195067i	0.220249	−	0.975444i	$-0.429313\pi$
$37$	−2.46389	−	1.18655i	−0.405061	−	0.195067i	−0.625310	+	0.780377i	$0.715027\pi$
$38$	−1.73620	−	7.60678i	−0.281649	−	1.23398i
$39$		0			0
$40$	−4.03250	−	0.920391i	−0.637594	−	0.145527i
$41$	−4.44530	−	5.57423i	−0.694239	−	0.870548i	0.302339	−	0.953200i	$-0.402232\pi$
$41$	−4.44530	−	5.57423i	−0.694239	−	0.870548i	−0.996578	+	0.0826521i	$0.973661\pi$
$42$		0			0
$43$	7.98148	−	10.0085i	1.21716	−	1.52628i	0.438636	−	0.898665i	$-0.355462\pi$
$43$	7.98148	−	10.0085i	1.21716	−	1.52628i	0.778528	−	0.627610i	$-0.215967\pi$
$44$	1.44603	−	1.15317i	0.217997	−	0.173846i
$45$		0			0
$46$	6.01693	+	7.54500i	0.887149	+	1.11245i
$47$	0.467248	+	2.04715i	0.0681552	+	0.298607i	0.997505	−	0.0705924i	$-0.0224890\pi$
$47$	0.467248	+	2.04715i	0.0681552	+	0.298607i	−0.929350	+	0.369200i	$0.879632\pi$
$48$		0			0
$49$	−6.96941	+	0.653696i	−0.995630	+	0.0933851i
$50$		−	1.68528i		−	0.238335i
$51$		0			0
$52$	0.817242	−	0.651729i	0.113331	−	0.0903785i
$53$	4.06653	+	8.44425i	0.558581	+	1.15991i	0.968783	+	0.247911i	$0.0797442\pi$
$53$	4.06653	+	8.44425i	0.558581	+	1.15991i	−0.410201	+	0.911995i	$0.634542\pi$
$54$		0			0
$55$	3.84588	+	3.06699i	0.518579	+	0.413553i
$56$	−3.61509	−	4.12213i	−0.483087	−	0.550843i
$57$		0			0
$58$	0.0715054	−	0.313285i	0.00938911	−	0.0411364i
$59$	−8.03149	+	10.0712i	−1.04561	+	1.31115i	−0.0968013	+	0.995304i	$0.530861\pi$
$59$	−8.03149	+	10.0712i	−1.04561	+	1.31115i	−0.948809	+	0.315850i	$0.897710\pi$
$60$		0			0
$61$	−0.510260	+	1.05957i	−0.0653321	+	0.135664i	−0.931078	−	0.364821i	$-0.881130\pi$
$61$	−0.510260	+	1.05957i	−0.0653321	+	0.135664i	0.865746	+	0.500484i	$0.166845\pi$
$62$	−2.89977	−	12.7047i	−0.368271	−	1.61350i
$63$		0			0
$64$	0.704949	−	3.08858i	0.0881186	−	0.386073i
$65$	2.17355	+	1.73335i	0.269596	+	0.214996i
$66$		0			0
$67$	2.43390			0.297348			0.148674	−	0.988886i	$-0.452499\pi$
$67$	2.43390			0.297348			0.148674	+	0.988886i	$0.452499\pi$
$68$	−0.639683			−0.0775730
$69$		0			0
$70$	−5.13445	+	7.09499i	−0.613685	+	0.848014i
$71$	1.39482	+	2.89637i	0.165534	+	0.343736i	0.967192	−	0.254048i	$-0.0817622\pi$
$71$	1.39482	+	2.89637i	0.165534	+	0.343736i	−0.801657	+	0.597784i	$0.796048\pi$
$72$		0			0
$73$	−9.99800	−	2.28198i	−1.17018	−	0.267085i	−0.407095	−	0.913386i	$-0.633458\pi$
$73$	−9.99800	−	2.28198i	−1.17018	−	0.267085i	−0.763083	+	0.646301i	$0.776315\pi$
$74$	−4.42168	−	1.00922i	−0.514010	−	0.117319i
$75$		0			0
$76$	−1.53190	−	3.18101i	−0.175720	−	0.364887i
$77$	1.74652	+	6.28226i	0.199034	+	0.715930i
$78$		0			0
$79$	−6.60146			−0.742722			−0.371361	−	0.928489i	$-0.621109\pi$
$79$	−6.60146			−0.742722			−0.371361	+	0.928489i	$0.621109\pi$
$80$	−9.85548			−1.10188
$81$		0			0
$82$	−9.24459	−	7.37232i	−1.02089	−	0.814136i
$83$	3.17998	−	13.9324i	0.349048	−	1.52928i	−0.430300	−	0.902686i	$-0.641592\pi$
$83$	3.17998	−	13.9324i	0.349048	−	1.52928i	0.779347	−	0.626592i	$-0.215551\pi$
$84$		0			0
$85$	−0.378578	−	1.65866i	−0.0410626	−	0.179907i
$86$	9.21150	−	19.1279i	0.993301	−	2.06261i
$87$		0			0
$88$	−3.18430	+	3.99298i	−0.339447	+	0.425653i
$89$	0.346714	−	1.51906i	0.0367517	−	0.161020i	−0.953222	−	0.302271i	$-0.902255\pi$
$89$	0.346714	−	1.51906i	0.0367517	−	0.161020i	0.989974	+	0.141251i	$0.0451125\pi$
$90$		0			0
$91$	0.987068	+	3.55051i	0.103473	+	0.372194i
$92$	3.41418	+	2.72272i	0.355953	+	0.283863i
$93$		0			0
$94$	1.51096	+	3.13754i	0.155844	+	0.323613i
$95$	7.34156	−	5.85470i	0.753229	−	0.600680i
$96$		0			0
$97$			0.726497i			0.0737646i	0.999320	+	0.0368823i	$0.0117427\pi$
$97$			0.726497i			0.0737646i	−0.999320	+	0.0368823i	$0.988257\pi$
$98$	−11.0274	+	3.62894i	−1.11394	+	0.366578i
$99$		0			0
$100$	−0.169695	−	0.743484i	−0.0169695	−	0.0743484i
$101$	−10.0260	−	12.5722i	−0.997623	−	1.25098i	−0.967878	−	0.251422i	$-0.919102\pi$
$101$	−10.0260	−	12.5722i	−0.997623	−	1.25098i	−0.0297450	−	0.999558i	$-0.509470\pi$
$102$		0			0
$103$	4.26687	−	3.40272i	0.420427	−	0.335280i	−0.390317	−	0.920681i	$-0.627634\pi$
$103$	4.26687	−	3.40272i	0.420427	−	0.335280i	0.810744	+	0.585401i	$0.199063\pi$
$104$	−1.79965	+	2.25669i	−0.176470	+	0.221287i
$105$		0			0
$106$	9.69133	+	12.1525i	0.941305	+	1.18036i
$107$	10.2888	+	2.34836i	0.994659	+	0.227025i	0.688721	−	0.725027i	$-0.258173\pi$
$107$	10.2888	+	2.34836i	0.994659	+	0.227025i	0.305939	+	0.952051i	$0.401030\pi$
$108$		0			0
$109$	4.04543	+	17.7242i	0.387482	+	1.69767i	0.673286	+	0.739382i	$0.264882\pi$
$109$	4.04543	+	17.7242i	0.387482	+	1.69767i	−0.285804	+	0.958288i	$0.592261\pi$
$110$	7.35014	+	3.53964i	0.700808	+	0.337491i
$111$		0			0
$112$	−10.5834	−	7.65894i	−1.00004	−	0.723702i
$113$	0.975368	+	0.222621i	0.0917549	+	0.0209425i	0.268152	−	0.963377i	$-0.413587\pi$
$113$	0.975368	+	0.222621i	0.0917549	+	0.0209425i	−0.176397	+	0.984319i	$0.556444\pi$
$114$		0			0
$115$	−5.03926	+	10.4641i	−0.469913	+	0.975784i
$116$		−	0.145410i		−	0.0135010i
$117$		0			0
$118$	−9.26921	+	19.2477i	−0.853300	+	1.77190i
$119$	0.882445	−	2.07538i	0.0808936	−	0.190249i
$120$		0			0
$121$	−4.43829	+	2.13737i	−0.403481	+	0.194306i
$122$	−0.434002	+	1.90149i	−0.0392927	+	0.172153i
$123$		0			0
$124$	−2.55855	−	5.31288i	−0.229764	−	0.477111i
$125$	10.8188	−	5.21008i	0.967666	−	0.466003i
$126$		0			0
$127$	−4.17799	−	2.01201i	−0.370737	−	0.178537i	0.239233	−	0.970962i	$-0.423104\pi$
$127$	−4.17799	−	2.01201i	−0.370737	−	0.178537i	−0.609970	+	0.792425i	$0.708818\pi$
$128$		−	13.3428i		−	1.17935i
$129$		0			0
$130$	4.15403	+	2.00048i	0.364333	+	0.175454i
$131$	1.46906	−	1.84214i	0.128352	−	0.160949i	−0.713503	−	0.700652i	$-0.752892\pi$
$131$	1.46906	−	1.84214i	0.128352	−	0.160949i	0.841855	+	0.539704i	$0.181464\pi$
$132$		0			0
$133$	12.4337	−	0.581831i	1.07814	−	0.0504512i
$134$	3.93530	−	0.898208i	0.339959	−	0.0775933i
$135$		0			0
$136$	1.72210	−	0.393058i	0.147669	−	0.0337045i
$137$	3.70151	+	2.95185i	0.316241	+	0.252194i	0.768726	−	0.639578i	$-0.220891\pi$
$137$	3.70151	+	2.95185i	0.316241	+	0.252194i	−0.452485	+	0.891772i	$0.649462\pi$
$138$		0			0
$139$	7.55824	−	6.02749i	0.641081	−	0.511245i	−0.248139	−	0.968724i	$-0.579819\pi$
$139$	7.55824	−	6.02749i	0.641081	−	0.511245i	0.889220	+	0.457479i	$0.151248\pi$
$140$	−1.55072	+	3.64706i	−0.131060	+	0.308232i
$141$		0			0
$142$	3.32412	+	4.16831i	0.278954	+	0.349797i
$143$	3.09278	−	1.48941i	0.258632	−	0.124550i
$144$		0			0
$145$	0.377040	−	0.0860569i	0.0313115	−	0.00714664i
$146$	−17.0076			−1.40756
$147$		0			0
$148$	−2.05231			−0.168698
$149$	−12.0757	+	2.75620i	−0.989279	+	0.225797i	−0.686393	−	0.727230i	$-0.740807\pi$
$149$	−12.0757	+	2.75620i	−0.989279	+	0.225797i	−0.302886	+	0.953027i	$0.597950\pi$
$150$		0			0
$151$	16.5050	−	7.94839i	1.34316	−	0.646831i	0.382343	−	0.924020i	$-0.375117\pi$
$151$	16.5050	−	7.94839i	1.34316	−	0.646831i	0.960815	+	0.277189i	$0.0894029\pi$
$152$	6.07864	+	7.62237i	0.493043	+	0.618256i
$153$		0			0
$154$	5.14230	+	9.51307i	0.414378	+	0.766585i
$155$	12.2618	−	9.77843i	0.984889	−	0.785423i
$156$		0			0
$157$	−3.90479	−	3.11397i	−0.311636	−	0.248522i	0.455164	−	0.890408i	$-0.349581\pi$
$157$	−3.90479	−	3.11397i	−0.311636	−	0.248522i	−0.766800	+	0.641886i	$0.778152\pi$
$158$	−10.6737	+	2.43621i	−0.849155	+	0.193814i
$159$		0			0
$160$	−7.87004	+	1.79629i	−0.622182	+	0.142009i
$161$	−13.5434	+	7.32090i	−1.06737	+	0.576968i
$162$		0			0
$163$	0.282487	−	0.354228i	0.0221261	−	0.0277453i	−0.770645	−	0.637264i	$-0.780066\pi$
$163$	0.282487	−	0.354228i	0.0221261	−	0.0277453i	0.792771	+	0.609519i	$0.208637\pi$
$164$	−4.82072	−	2.32154i	−0.376435	−	0.181281i
$165$		0			0
$166$		−	23.7004i		−	1.83951i
$167$	17.3199	+	8.34084i	1.34026	+	0.645433i	0.960144	−	0.279507i	$-0.0901710\pi$
$167$	17.3199	+	8.34084i	1.34026	+	0.645433i	0.380113	+	0.924940i	$0.375885\pi$
$168$		0			0
$169$	−9.96466	+	4.79873i	−0.766513	+	0.369133i
$170$	−1.22422	−	2.54213i	−0.0938937	−	0.194972i
$171$		0			0
$172$	2.13774	−	9.36605i	0.163001	−	0.714155i
$173$	−3.04260	+	1.46524i	−0.231325	+	0.111400i	−0.545956	−	0.837814i	$-0.683833\pi$
$173$	−3.04260	+	1.46524i	−0.231325	+	0.111400i	0.314631	+	0.949214i	$0.398119\pi$
$174$		0			0
$175$	2.64624	+	0.475083i	0.200037	+	0.0359129i
$176$	−5.28000	+	10.9640i	−0.397995	+	0.826444i
$177$		0			0
$178$		−	2.58407i		−	0.193684i
$179$	−6.38764	+	13.2641i	−0.477435	+	0.991404i	0.513629	+	0.858013i	$0.328301\pi$
$179$	−6.38764	+	13.2641i	−0.477435	+	0.991404i	−0.991063	+	0.133391i	$0.957413\pi$
$180$		0			0
$181$	16.0470	+	3.66261i	1.19276	+	0.272240i	0.772412	−	0.635122i	$-0.219050\pi$
$181$	16.0470	+	3.66261i	1.19276	+	0.272240i	0.420350	+	0.907362i	$0.361907\pi$
$182$	2.90624	+	5.37645i	0.215425	+	0.398529i
$183$		0			0
$184$	−10.8644	−	5.23200i	−0.800931	−	0.385708i
$185$	−1.21460	−	5.32150i	−0.0892990	−	0.391245i
$186$		0			0
$187$	−2.04805	−	0.467453i	−0.149768	−	0.0341836i
$188$	0.982509	+	1.23203i	0.0716568	+	0.0898548i
$189$		0			0
$190$	9.70975	−	12.1756i	0.704419	−	0.883313i
$191$	2.77212	−	2.21069i	0.200583	−	0.159960i	−0.518047	−	0.855352i	$-0.673341\pi$
$191$	2.77212	−	2.21069i	0.200583	−	0.159960i	0.718630	+	0.695392i	$0.244769\pi$
$192$		0			0
$193$	−3.07600	−	3.85718i	−0.221415	−	0.277646i	0.658700	−	0.752405i	$-0.271106\pi$
$193$	−3.07600	−	3.85718i	−0.221415	−	0.277646i	−0.880116	+	0.474760i	$0.842535\pi$
$194$	0.268107	+	1.17465i	0.0192489	+	0.0843351i
$195$		0			0
$196$	−4.49948	+	2.71133i	−0.321392	+	0.193667i
$197$			19.9041i			1.41811i	0.705153	+	0.709055i	$0.250878\pi$
$197$			19.9041i			1.41811i	−0.705153	+	0.709055i	$0.749122\pi$
$198$		0			0
$199$	−17.4557	+	13.9205i	−1.23740	+	0.986797i	−0.237523	+	0.971382i	$0.576336\pi$
$199$	−17.4557	+	13.9205i	−1.23740	+	0.986797i	−0.999881	+	0.0154153i	$0.995093\pi$
$200$	0.913680	+	1.89728i	0.0646069	+	0.134158i
$201$		0			0
$202$	−20.8504	−	16.6276i	−1.46703	−	1.16992i
$203$	0.471766	+	0.200594i	0.0331115	+	0.0140789i
$204$		0			0
$205$	3.16660	−	13.8738i	0.221165	−	0.968985i
$206$	5.64324	−	7.07640i	0.393183	−	0.493036i
$207$		0			0
$208$	−2.98406	+	6.19647i	−0.206908	+	0.429648i
$209$	−2.58005	−	11.3040i	−0.178466	−	0.781911i
$210$		0			0
$211$	4.87397	−	21.3543i	0.335538	−	1.47009i	−0.472696	−	0.881226i	$-0.656719\pi$
$211$	4.87397	−	21.3543i	0.335538	−	1.47009i	0.808234	−	0.588862i	$-0.200424\pi$
$212$	5.49914	+	4.38542i	0.377682	+	0.301192i
$213$		0			0
$214$	17.5024			1.19644
$215$	25.5508			1.74255
$216$		0			0
$217$	20.7665	−	0.971766i	1.40972	−	0.0659678i
$218$	13.0819	+	27.1648i	0.886017	+	1.83983i
$219$		0			0
$220$	3.59903	+	0.821455i	0.242647	+	0.0553825i
$221$	−1.15748	−	0.264188i	−0.0778607	−	0.0177712i
$222$		0			0
$223$	−4.60807	−	9.56875i	−0.308579	−	0.640771i	0.687790	−	0.725910i	$-0.258581\pi$
$223$	−4.60807	−	9.56875i	−0.308579	−	0.640771i	−0.996369	+	0.0851386i	$0.972867\pi$
$224$	−9.84729	−	4.18705i	−0.657950	−	0.279759i
$225$		0			0
$226$	1.65920			0.110368
$227$	−14.4562			−0.959490			−0.479745	−	0.877408i	$-0.659271\pi$
$227$	−14.4562			−0.959490			−0.479745	+	0.877408i	$0.659271\pi$
$228$		0			0
$229$	6.88002	+	5.48663i	0.454644	+	0.362567i	0.823875	−	0.566771i	$-0.191808\pi$
$229$	6.88002	+	5.48663i	0.454644	+	0.362567i	−0.369231	+	0.929338i	$0.620379\pi$
$230$	−4.28615	+	18.7788i	−0.282620	+	1.23824i
$231$		0			0
$232$	0.0893485	+	0.391461i	0.00586601	+	0.0257007i
$233$	1.43613	−	2.98216i	0.0940841	−	0.195368i	−0.848616	−	0.529010i	$-0.822563\pi$
$233$	1.43613	−	2.98216i	0.0940841	−	0.195368i	0.942700	+	0.333642i	$0.108278\pi$
$234$		0			0
$235$	−2.61310	+	3.27673i	−0.170460	+	0.213750i
$236$	−2.15114	+	9.42474i	−0.140027	+	0.613498i
$237$		0			0
$238$	0.660903	−	3.68127i	0.0428400	−	0.238622i
$239$	−18.8587	−	15.0393i	−1.21987	−	0.972810i	−0.219869	−	0.975529i	$-0.570563\pi$
$239$	−18.8587	−	15.0393i	−1.21987	−	0.972810i	−0.999996	+	0.00271895i	$0.999135\pi$
$240$		0			0
$241$	9.80881	+	20.3682i	0.631841	+	1.31203i	0.933487	+	0.358611i	$0.116750\pi$
$241$	9.80881	+	20.3682i	0.631841	+	1.31203i	−0.301646	+	0.953420i	$0.597536\pi$
$242$	−6.38737	+	5.09376i	−0.410596	+	0.327439i
$243$		0			0
$244$			0.882569i			0.0565007i
$245$	−9.69321	−	10.0623i	−0.619277	−	0.642854i
$246$		0			0
$247$	−1.45815	−	6.38859i	−0.0927801	−	0.406496i
$248$	10.1524	+	12.7308i	0.644681	+	0.808404i
$249$		0			0
$250$	15.5699	−	12.4166i	0.984729	−	0.785295i
$251$	3.42386	−	4.29339i	0.216112	−	0.270996i	−0.661944	−	0.749553i	$-0.730268\pi$
$251$	3.42386	−	4.29339i	0.216112	−	0.270996i	0.878057	+	0.478557i	$0.158840\pi$
$252$		0			0
$253$	8.94139	+	11.2121i	0.562140	+	0.704902i
$254$	−7.49779	−	1.71132i	−0.470453	−	0.107378i
$255$		0			0
$256$	−3.51414	−	15.3964i	−0.219634	−	0.962277i
$257$	−19.0231	−	9.16104i	−1.18663	−	0.571450i	−0.266792	−	0.963754i	$-0.585964\pi$
$257$	−19.0231	−	9.16104i	−1.18663	−	0.571450i	−0.919835	+	0.392304i	$0.871678\pi$
$258$		0			0
$259$	2.83116	−	6.65846i	0.175920	−	0.413737i
$260$	2.03404	+	0.464257i	0.126146	+	0.0287920i
$261$		0			0
$262$	1.69545	−	3.52065i	0.104745	−	0.217506i
$263$			22.1586i			1.36636i	0.730252	+	0.683178i	$0.239403\pi$
$263$			22.1586i			1.36636i	−0.730252	+	0.683178i	$0.760597\pi$
$264$		0			0
$265$	−8.11661	+	16.8543i	−0.498599	+	1.03535i
$266$	19.8889	−	5.52927i	1.21947	−	0.339022i
$267$		0			0
$268$	1.64567	−	0.792513i	0.100525	−	0.0484104i
$269$	−2.41640	+	10.5870i	−0.147331	+	0.645498i	0.846290	+	0.532723i	$0.178831\pi$
$269$	−2.41640	+	10.5870i	−0.147331	+	0.645498i	−0.993621	+	0.112775i	$0.964026\pi$
$270$		0			0
$271$	14.0530	+	29.1814i	0.853661	+	1.77265i	0.588622	+	0.808408i	$0.299670\pi$
$271$	14.0530	+	29.1814i	0.853661	+	1.77265i	0.265039	+	0.964238i	$0.414615\pi$
$272$	3.79203	−	1.82615i	0.229926	−	0.110726i
$273$		0			0
$274$	7.07421	+	3.40676i	0.427369	+	0.205810i
$275$		−	2.50439i		−	0.151020i
$276$		0			0
$277$	−21.1898	−	10.2045i	−1.27317	−	0.613128i	−0.329546	−	0.944139i	$-0.606896\pi$
$277$	−21.1898	−	10.2045i	−1.27317	−	0.613128i	−0.943627	+	0.331012i	$0.892610\pi$
$278$	9.99631	−	12.5350i	0.599539	−	0.751798i
$279$		0			0
$280$	1.93376	−	10.7712i	0.115564	−	0.643699i
$281$	6.15580	−	1.40502i	0.367224	−	0.0838165i	−0.0349268	−	0.999390i	$-0.511120\pi$
$281$	6.15580	−	1.40502i	0.367224	−	0.0838165i	0.402151	+	0.915573i	$0.368263\pi$
$282$		0			0
$283$	16.3965	−	3.74238i	0.974668	−	0.222462i	0.294608	−	0.955618i	$-0.404811\pi$
$283$	16.3965	−	3.74238i	0.974668	−	0.222462i	0.680060	+	0.733156i	$0.261954\pi$
$284$	1.88620	+	1.50419i	0.111925	+	0.0892575i
$285$		0			0
$286$	4.45098	−	3.54954i	0.263192	−	0.209889i
$287$	14.1821	−	12.4377i	0.837145	−	0.734173i
$288$		0			0
$289$	−10.1463	−	12.7231i	−0.596843	−	0.748417i
$290$	0.577867	−	0.278286i	0.0339335	−	0.0163415i
$291$		0			0
$292$	−7.50315	+	1.71254i	−0.439089	+	0.100219i
$293$	−20.5047			−1.19790			−0.598948	−	0.800788i	$-0.704415\pi$
$293$	−20.5047			−1.19790			−0.598948	+	0.800788i	$0.704415\pi$
$294$		0			0
$295$	−25.7109			−1.49694
$296$	5.52504	−	1.26106i	0.321137	−	0.0732974i
$297$		0			0
$298$	−18.5077	+	8.91284i	−1.07212	+	0.516307i
$299$	5.05335	+	6.33670i	0.292243	+	0.366461i
$300$		0			0
$301$	27.4380	+	19.8562i	1.58150	+	1.14449i
$302$	23.7532	−	18.9425i	1.36684	−	1.09002i
$303$		0			0
$304$	18.1621	+	14.4838i	1.04167	+	0.830702i
$305$	−2.28845	+	0.522323i	−0.131036	+	0.0299081i
$306$		0			0
$307$	−24.1636	+	5.51519i	−1.37909	+	0.314769i	−0.846853	−	0.531826i	$-0.821506\pi$
$307$	−24.1636	+	5.51519i	−1.37909	+	0.314769i	−0.532238	+	0.846595i	$0.678649\pi$
$308$	3.22649	+	3.67903i	0.183846	+	0.209632i
$309$		0			0
$310$	16.2171	−	20.3356i	0.921067	−	1.15498i
$311$	26.8403	+	12.9256i	1.52197	+	0.732944i	0.993266	−	0.115860i	$-0.0369624\pi$
$311$	26.8403	+	12.9256i	1.52197	+	0.732944i	0.528708	+	0.848804i	$0.322677\pi$
$312$		0			0
$313$			20.0324i			1.13230i	0.824303	+	0.566149i	$0.191567\pi$
$313$			20.0324i			1.13230i	−0.824303	+	0.566149i	$0.808433\pi$
$314$	−7.46273	−	3.59386i	−0.421146	−	0.202813i
$315$		0			0
$316$	−4.46355	+	2.14953i	−0.251094	+	0.120921i
$317$	4.49995	+	9.34425i	0.252742	+	0.524825i	0.988279	−	0.152660i	$-0.0487840\pi$
$317$	4.49995	+	9.34425i	0.252742	+	0.524825i	−0.735536	+	0.677485i	$0.763070\pi$
$318$		0			0
$319$	0.106260	−	0.465554i	0.00594940	−	0.0260660i
$320$	5.69701	−	2.74353i	0.318472	−	0.153368i
$321$		0			0
$322$	−19.1962	+	16.8350i	−1.06976	+	0.938179i
$323$	−1.73994	+	3.61302i	−0.0968127	+	0.201034i
$324$		0			0
$325$		−	1.41539i		−	0.0785118i
$326$	0.326021	−	0.676991i	0.0180567	−	0.0374950i
$327$		0			0
$328$	14.4044	+	3.28771i	0.795351	+	0.181534i
$329$	−5.35254	+	1.48805i	−0.295095	+	0.0820387i
$330$		0			0
$331$	9.12925	+	4.39641i	0.501789	+	0.241649i	0.667616	−	0.744506i	$-0.267315\pi$
$331$	9.12925	+	4.39641i	0.501789	+	0.241649i	−0.165827	+	0.986155i	$0.553029\pi$
$332$	−2.38646	−	10.4558i	−0.130974	−	0.573835i
$333$		0			0
$334$	31.0822	+	7.09431i	1.70074	+	0.388183i
$335$	3.02888	+	3.79810i	0.165485	+	0.207512i
$336$		0			0
$337$	−1.16913	+	1.46605i	−0.0636868	+	0.0798607i	−0.812655	−	0.582746i	$-0.801978\pi$
$337$	−1.16913	+	1.46605i	−0.0636868	+	0.0798607i	0.748968	+	0.662606i	$0.230550\pi$
$338$	−14.3407	+	11.4363i	−0.780029	+	0.622052i
$339$		0			0
$340$	−0.796057	−	0.998224i	−0.0431723	−	0.0541363i
$341$	−4.30917	−	18.8797i	−0.233354	−	1.02239i
$342$		0			0
$343$	−2.58955	−	18.3383i	−0.139822	−	0.990177i
$344$			26.5281i			1.43030i
$345$		0			0
$346$	−4.37876	+	3.49195i	−0.235404	+	0.187728i
$347$	−2.10351	−	4.36797i	−0.112922	−	0.234485i	0.836847	−	0.547437i	$-0.184396\pi$
$347$	−2.10351	−	4.36797i	−0.112922	−	0.234485i	−0.949769	+	0.312952i	$0.898682\pi$
$348$		0			0
$349$	−24.5577	−	19.5841i	−1.31454	−	1.04831i	−0.994910	−	0.100770i	$-0.967869\pi$
$349$	−24.5577	−	19.5841i	−1.31454	−	1.04831i	−0.319632	−	0.947542i	$-0.603559\pi$
$350$	4.45396	−	0.208422i	0.238074	−	0.0111406i
$351$		0			0
$352$	−2.21798	+	9.71762i	−0.118219	+	0.517951i
$353$	12.0119	−	15.0624i	0.639328	−	0.801691i	−0.351591	−	0.936154i	$-0.614359\pi$
$353$	12.0119	−	15.0624i	0.639328	−	0.801691i	0.990919	+	0.134462i	$0.0429307\pi$
$354$		0			0
$355$	−2.78399	+	5.78101i	−0.147759	+	0.306824i
$356$	−0.260197	−	1.14000i	−0.0137904	−	0.0604197i
$357$		0			0
$358$	−5.43302	+	23.8036i	−0.287144	+	1.25806i
$359$	13.8395	+	11.0366i	0.730420	+	0.582491i	0.916496	−	0.400045i	$-0.131005\pi$
$359$	13.8395	+	11.0366i	0.730420	+	0.582491i	−0.186075	+	0.982535i	$0.559577\pi$
$360$		0			0
$361$	−3.13354			−0.164923
$362$	27.2975			1.43473
$363$		0			0
$364$	1.82350	+	2.07925i	0.0955772	+	0.108983i
$365$	−8.88105	−	18.4417i	−0.464855	−	0.965282i
$366$		0			0
$367$	−27.7535	−	6.33455i	−1.44872	−	0.330661i	−0.575426	−	0.817854i	$-0.695164\pi$
$367$	−27.7535	−	6.33455i	−1.44872	−	0.330661i	−0.873294	+	0.487193i	$0.838021\pi$
$368$	−28.0119	−	6.39354i	−1.46022	−	0.333286i
$369$		0			0
$370$	−3.92770	−	8.15595i	−0.204191	−	0.424008i
$371$	−21.8140	+	11.7916i	−1.13253	+	0.612189i
$372$		0			0
$373$	−15.1007			−0.781884			−0.390942	−	0.920415i	$-0.627851\pi$
$373$	−15.1007			−0.781884			−0.390942	+	0.920415i	$0.627851\pi$
$374$	−3.48394			−0.180150
$375$		0			0
$376$	−3.40206	−	2.71305i	−0.175448	−	0.139915i
$377$	0.0600541	−	0.263114i	0.00309294	−	0.0135511i
$378$		0			0
$379$	2.76701	+	12.1231i	0.142132	+	0.622721i	0.994938	+	0.100493i	$0.0320419\pi$
$379$	2.76701	+	12.1231i	0.142132	+	0.622721i	−0.852806	+	0.522228i	$0.825101\pi$
$380$	3.05759	−	6.34915i	0.156851	−	0.325704i
$381$		0			0
$382$	3.66632	−	4.59742i	0.187585	−	0.235225i
$383$	5.38704	−	23.6021i	0.275265	−	1.20601i	−0.628440	−	0.777858i	$-0.716306\pi$
$383$	5.38704	−	23.6021i	0.275265	−	1.20601i	0.903705	−	0.428156i	$-0.140836\pi$
$384$		0			0
$385$	−7.62999	+	10.5434i	−0.388860	+	0.537343i
$386$	−6.39695	−	5.10140i	−0.325596	−	0.259654i
$387$		0			0
$388$	0.236558	+	0.491218i	0.0120094	+	0.0249378i
$389$	0.741770	−	0.591542i	0.0376092	−	0.0299924i	−0.604505	−	0.796601i	$-0.706629\pi$
$389$	0.741770	−	0.591542i	0.0376092	−	0.0299924i	0.642114	+	0.766609i	$0.278058\pi$
$390$		0			0
$391$		−	4.95995i		−	0.250836i
$392$	10.4471	−	10.0640i	0.527660	−	0.508307i
$393$		0			0
$394$	7.34543	+	32.1824i	0.370057	+	1.62133i
$395$	−8.21522	−	10.3016i	−0.413353	−	0.518328i
$396$		0			0
$397$	−16.0461	+	12.7963i	−0.805330	+	0.642229i	−0.937104	−	0.349051i	$-0.886504\pi$
$397$	−16.0461	+	12.7963i	−0.805330	+	0.642229i	0.131774	+	0.991280i	$0.457933\pi$
$398$	−23.0865	+	28.9495i	−1.15722	+	1.45111i
$399$		0			0
$400$	3.12843	+	3.92292i	0.156421	+	0.196146i
$401$	−28.8491	−	6.58461i	−1.44065	−	0.328820i	−0.570377	−	0.821383i	$-0.693203\pi$
$401$	−28.8491	−	6.58461i	−1.44065	−	0.328820i	−0.870276	+	0.492564i	$0.836060\pi$
$402$		0			0
$403$	−2.43539	−	10.6701i	−0.121315	−	0.531517i
$404$	−10.8727	−	5.23602i	−0.540937	−	0.260502i
$405$		0			0
$406$	0.836813	+	0.150234i	0.0415303	+	0.00745599i
$407$	−6.57078	−	1.49974i	−0.325701	−	0.0743392i
$408$		0			0
$409$	−12.2144	+	25.3634i	−0.603962	+	1.25414i	0.344956	+	0.938619i	$0.387894\pi$
$409$	−12.2144	+	25.3634i	−0.603962	+	1.25414i	−0.948918	+	0.315521i	$0.897821\pi$
$410$		−	23.6007i		−	1.16555i
$411$		0			0
$412$	1.77705	−	3.69008i	0.0875490	−	0.181797i
$413$	−27.6099	−	19.9806i	−1.35860	−	0.983179i
$414$		0			0
$415$	25.6988	−	12.3759i	1.26150	−	0.607509i
$416$	−1.25352	+	5.49205i	−0.0614591	+	0.269270i
$417$		0			0
$418$	−8.34323	−	17.3249i	−0.408081	−	0.847389i
$419$	16.8705	−	8.12440i	0.824178	−	0.396903i	0.0262493	−	0.999655i	$-0.491644\pi$
$419$	16.8705	−	8.12440i	0.824178	−	0.396903i	0.797928	+	0.602752i	$0.205929\pi$
$420$		0			0
$421$	−22.2346	−	10.7076i	−1.08365	−	0.521858i	−0.195168	−	0.980770i	$-0.562525\pi$
$421$	−22.2346	−	10.7076i	−1.08365	−	0.521858i	−0.888482	+	0.458911i	$0.848240\pi$
$422$		−	36.3258i		−	1.76831i
$423$		0			0
$424$	−17.4990	−	8.42706i	−0.849825	−	0.409254i
$425$	−0.540049	+	0.677200i	−0.0261962	+	0.0328490i
$426$		0			0
$427$	−2.86339	−	1.21751i	−0.138569	−	0.0589193i
$428$	7.72141	−	1.76236i	0.373228	−	0.0851869i
$429$		0			0
$430$	41.3123	−	9.42926i	1.99226	−	0.454720i
$431$	15.8922	+	12.6736i	0.765500	+	0.610466i	0.926416	−	0.376502i	$-0.122873\pi$
$431$	15.8922	+	12.6736i	0.765500	+	0.610466i	−0.160916	+	0.986968i	$0.551445\pi$
$432$		0			0
$433$	22.1422	−	17.6578i	1.06409	−	0.848580i	0.0751872	−	0.997169i	$-0.476045\pi$
$433$	22.1422	−	17.6578i	1.06409	−	0.848580i	0.988899	+	0.148589i	$0.0474731\pi$
$434$	33.2182	−	9.23491i	1.59452	−	0.443290i
$435$		0			0
$436$	8.50655	+	10.6669i	0.407390	+	0.510851i
$437$	24.6648	−	11.8780i	1.17988	−	0.568200i
$438$		0			0
$439$	6.77204	−	1.54567i	0.323212	−	0.0737710i	−0.0578366	−	0.998326i	$-0.518420\pi$
$439$	6.77204	−	1.54567i	0.323212	−	0.0737710i	0.381048	+	0.924555i	$0.375563\pi$
$440$	−10.1938			−0.485968
$441$		0			0
$442$	−1.96900			−0.0936556
$443$	−40.3342	+	9.20601i	−1.91633	+	0.437391i	−0.917083	+	0.398695i	$0.869463\pi$
$443$	−40.3342	+	9.20601i	−1.91633	+	0.437391i	−0.999251	+	0.0386957i	$0.987680\pi$
$444$		0			0
$445$	2.80195	−	1.34935i	0.132825	−	0.0639653i
$446$	−10.9819	−	13.7709i	−0.520009	−	0.652070i
$447$		0			0
$448$	8.24987	+	1.48111i	0.389770	+	0.0699758i
$449$	−9.76889	+	7.79043i	−0.461022	+	0.367653i	−0.826286	−	0.563251i	$-0.809550\pi$
$449$	−9.76889	+	7.79043i	−0.461022	+	0.367653i	0.365263	+	0.930904i	$0.380979\pi$
$450$		0			0
$451$	−13.7378	−	10.9555i	−0.646888	−	0.515876i
$452$	0.731979	−	0.167069i	0.0344294	−	0.00785829i
$453$		0			0
$454$	−23.3738	+	5.33491i	−1.09699	+	0.250380i
$455$	−4.31220	+	5.95876i	−0.202159	+	0.279351i
$456$		0			0
$457$	20.7195	−	25.9814i	0.969216	−	1.21536i	−0.00731325	−	0.999973i	$-0.502328\pi$
$457$	20.7195	−	25.9814i	0.969216	−	1.21536i	0.976529	−	0.215385i	$-0.0691007\pi$
$458$	13.1489	+	6.33217i	0.614407	+	0.295883i
$459$		0			0
$460$			8.71612i			0.406391i
$461$	5.58333	+	2.68879i	0.260042	+	0.125229i	0.559363	−	0.828923i	$-0.311046\pi$
$461$	5.58333	+	2.68879i	0.260042	+	0.125229i	−0.299321	+	0.954152i	$0.596760\pi$
$462$		0			0
$463$	−21.5815	+	10.3931i	−1.00298	+	0.483009i	−0.861948	−	0.506996i	$-0.830756\pi$
$463$	−21.5815	+	10.3931i	−1.00298	+	0.483009i	−0.141031	+	0.990005i	$0.545042\pi$
$464$	0.415112	+	0.861990i	0.0192711	+	0.0400169i
$465$		0			0
$466$	1.22150	−	5.35176i	0.0565851	−	0.247915i
$467$	−22.1418	+	10.6629i	−1.02460	+	0.493421i	−0.869216	−	0.494433i	$-0.835376\pi$
$467$	−22.1418	+	10.6629i	−1.02460	+	0.493421i	−0.155384	+	0.987854i	$0.549661\pi$
$468$		0			0
$469$	0.301006	+	6.43246i	0.0138991	+	0.297023i
$470$	−3.01581	+	6.26239i	−0.139109	+	0.288862i
$471$		0			0
$472$		−	26.6943i		−	1.22870i
$473$	13.6886	−	28.4247i	0.629404	−	1.30697i
$474$		0			0
$475$	−4.66087	−	1.06381i	−0.213855	−	0.0488111i
$476$	−0.0791110	−	1.69059i	−0.00362605	−	0.0774882i
$477$		0			0
$478$	−36.0421	−	17.3570i	−1.64853	−	0.793890i
$479$	−1.64374	−	7.20168i	−0.0751042	−	0.329053i	0.923393	−	0.383856i	$-0.125404\pi$
$479$	−1.64374	−	7.20168i	−0.0751042	−	0.329053i	−0.998497	+	0.0548029i	$0.982547\pi$
$480$		0			0
$481$	−3.71357	−	0.847598i	−0.169324	−	0.0386471i
$482$	23.3763	+	29.3129i	1.06476	+	1.33517i
$483$		0			0
$484$	−2.30497	+	2.89034i	−0.104771	+	0.131379i
$485$	−1.13370	+	0.904093i	−0.0514785	+	0.0410528i
$486$		0			0
$487$	−17.1121	−	21.4579i	−0.775424	−	0.972351i	0.224574	−	0.974457i	$-0.427901\pi$
$487$	−17.1121	−	21.4579i	−0.775424	−	0.972351i	−0.999998	+	0.00210608i	$0.999330\pi$
$488$	−0.542301	−	2.37598i	−0.0245488	−	0.107555i
$489$		0			0
$490$	−19.3861	−	12.6922i	−0.875773	−	0.573375i
$491$		−	10.8534i		−	0.489809i	−0.969547	−	0.244904i	$-0.921243\pi$
$491$		−	10.8534i		−	0.489809i	0.969547	−	0.244904i	$-0.0787566\pi$
$492$		0			0
$493$	−0.129126	+	0.102974i	−0.00581553	+	0.00463773i
$494$	−4.71530	−	9.79142i	−0.212151	−	0.440537i
$495$		0			0
$496$	30.3341	+	24.1906i	1.36204	+	1.08619i
$497$	−7.48220	+	4.04451i	−0.335622	+	0.181421i
$498$		0			0
$499$	−5.30664	+	23.2499i	−0.237558	+	1.04081i	0.705638	+	0.708572i	$0.250660\pi$
$499$	−5.30664	+	23.2499i	−0.237558	+	1.04081i	−0.943196	+	0.332236i	$0.892197\pi$
$500$	5.61863	−	7.04554i	0.251273	−	0.315086i
$501$		0			0
$502$	3.95151	−	8.20540i	0.176365	−	0.366225i
$503$	−2.00502	−	8.78455i	−0.0893993	−	0.391684i	0.910356	−	0.413827i	$-0.135808\pi$
$503$	−2.00502	−	8.78455i	−0.0893993	−	0.391684i	−0.999755	+	0.0221432i	$0.992951\pi$
$504$		0			0
$505$	7.14198	−	31.2911i	0.317814	−	1.39243i
$506$	18.5948	+	14.8289i	0.826640	+	0.659224i
$507$		0			0
$508$	−3.48007			−0.154403
$509$	−39.3676			−1.74494			−0.872469	−	0.488669i	$-0.837482\pi$
$509$	−39.3676			−1.74494			−0.872469	+	0.488669i	$0.837482\pi$
$510$		0			0
$511$	4.79447	−	26.7055i	0.212095	−	1.18138i
$512$	0.214638	+	0.445700i	0.00948574	+	0.0196973i
$513$		0			0
$514$	−34.1387	−	7.79193i	−1.50579	−	0.343687i
$515$	10.6199	+	2.42391i	0.467967	+	0.106810i
$516$		0			0
$517$	2.24534	+	4.66251i	0.0987501	+	0.205057i
$518$	2.12039	−	11.8107i	0.0931644	−	0.518932i
$519$		0			0
$520$	−5.76115			−0.252643
$521$	−29.7894			−1.30510			−0.652549	−	0.757746i	$-0.726301\pi$
$521$	−29.7894			−1.30510			−0.652549	+	0.757746i	$0.726301\pi$
$522$		0			0
$523$	5.99277	+	4.77907i	0.262045	+	0.208974i	0.745695	−	0.666288i	$-0.232118\pi$
$523$	5.99277	+	4.77907i	0.262045	+	0.208974i	−0.483650	+	0.875262i	$0.660689\pi$
$524$	0.393469	−	1.72390i	0.0171888	−	0.0753090i
$525$		0			0
$526$	8.17741	+	35.8276i	0.356552	+	1.56216i
$527$	−2.90601	+	6.03440i	−0.126588	+	0.262863i
$528$		0			0
$529$	−6.77105	+	8.49062i	−0.294393	+	0.369157i
$530$	−6.90359	+	30.2466i	−0.299873	+	1.31383i
$531$		0			0
$532$	8.21752	−	4.44199i	0.356275	−	0.192585i
$533$	−7.76412	−	6.19168i	−0.336301	−	0.268191i
$534$		0			0
$535$	9.13939	+	18.9781i	0.395130	+	0.820496i
$536$	−3.94337	+	3.14473i	−0.170328	+	0.135832i
$537$		0			0
$538$			18.0095i			0.776445i
$539$	−16.3871	+	5.39273i	−0.705844	+	0.232281i
$540$		0			0
$541$	0.673732	+	2.95181i	0.0289660	+	0.126908i	0.987344	−	0.158595i	$-0.0506964\pi$
$541$	0.673732	+	2.95181i	0.0289660	+	0.126908i	−0.958378	+	0.285503i	$0.907839\pi$
$542$	33.4911	+	41.9965i	1.43857	+	1.80390i
$543$		0			0
$544$	2.69527	−	2.14941i	0.115559	−	0.0921550i
$545$	−22.6242	+	28.3699i	−0.969115	+	1.21523i
$546$		0			0
$547$	17.7640	+	22.2753i	0.759533	+	0.952424i	0.999833	−	0.0182745i	$-0.00581729\pi$
$547$	17.7640	+	22.2753i	0.759533	+	0.952424i	−0.240300	+	0.970699i	$0.577246\pi$
$548$	3.46392	+	0.790618i	0.147971	+	0.0337735i
$549$		0			0
$550$	−0.924221	−	4.04928i	−0.0394089	−	0.172662i
$551$	−0.821296	−	0.395515i	−0.0349884	−	0.0168495i
$552$		0			0
$553$	−0.816417	−	17.4467i	−0.0347176	−	0.741910i
$554$	−38.0271	−	8.67943i	−1.61562	−	0.368754i
$555$		0			0
$556$	3.14783	−	6.53653i	0.133498	−	0.277211i
$557$		−	11.2411i		−	0.476299i	−0.971228	−	0.238150i	$-0.923459\pi$
$557$		−	11.2411i		−	0.476299i	0.971228	−	0.238150i	$-0.0765409\pi$
$558$		0			0
$559$	7.73632	−	16.0646i	0.327212	−	0.679462i
$560$	−1.21885	−	26.0466i	−0.0515057	−	1.10067i
$561$		0			0
$562$	9.43463	−	4.54348i	0.397976	−	0.191655i
$563$	−6.04365	+	26.4789i	−0.254709	+	1.11595i	0.672111	+	0.740450i	$0.265388\pi$
$563$	−6.04365	+	26.4789i	−0.254709	+	1.11595i	−0.926821	+	0.375504i	$0.877470\pi$
$564$		0			0
$565$	0.866402	+	1.79910i	0.0364498	+	0.0756888i
$566$	25.1299	−	12.1019i	1.05629	−	0.508681i
$567$		0			0
$568$	−6.00213	−	2.89047i	−0.251844	−	0.121282i
$569$			28.8622i			1.20997i	0.796238	+	0.604984i	$0.206820\pi$
$569$			28.8622i			1.20997i	−0.796238	+	0.604984i	$0.793180\pi$
$570$		0			0
$571$	18.7194	+	9.01481i	0.783384	+	0.377258i	0.782428	−	0.622742i	$-0.213981\pi$
$571$	18.7194	+	9.01481i	0.783384	+	0.377258i	0.000956678		1.00000i	$0.499695\pi$
$572$	1.60620	−	2.01411i	0.0671586	−	0.0842142i
$573$		0			0
$574$	18.3407	−	25.3439i	0.765526	−	1.05783i
$575$	5.76480	−	1.31578i	0.240409	−	0.0548718i
$576$		0			0
$577$	18.0877	−	4.12840i	0.753001	−	0.171868i	0.171242	−	0.985229i	$-0.445222\pi$
$577$	18.0877	−	4.12840i	0.753001	−	0.171868i	0.581759	+	0.813361i	$0.302365\pi$
$578$	−21.1006	−	16.8272i	−0.877671	−	0.699919i
$579$		0			0
$580$	0.226912	−	0.180957i	0.00942202	−	0.00751381i
$581$	37.2146	+	6.68118i	1.54392	+	0.277182i
$582$		0			0
$583$	14.4017	+	18.0591i	0.596457	+	0.747933i
$584$	19.1471	−	9.22074i	0.792311	−	0.381557i
$585$		0			0
$586$	−33.1534	+	7.56706i	−1.36956	+	0.312592i
$587$	10.0746			0.415823			0.207911	−	0.978148i	$-0.433333\pi$
$587$	10.0746			0.415823			0.207911	+	0.978148i	$0.433333\pi$
$588$		0			0
$589$	−36.9671			−1.52320
$590$	−41.5712	+	9.48835i	−1.71146	+	0.390629i
$591$		0			0
$592$	12.1660	−	5.85885i	0.500021	−	0.240797i
$593$	19.5733	+	24.5442i	0.803780	+	1.00791i	0.999628	+	0.0272741i	$0.00868268\pi$
$593$	19.5733	+	24.5442i	0.803780	+	1.00791i	−0.195848	+	0.980634i	$0.562746\pi$
$594$		0			0
$595$	4.33678	−	1.20566i	0.177791	−	0.0494272i
$596$	−7.26746	+	5.79561i	−0.297687	+	0.237397i
$597$		0			0
$598$	10.5091	+	8.38074i	0.429750	+	0.342714i
$599$	43.4803	−	9.92410i	1.77656	−	0.405488i	0.796570	−	0.604546i	$-0.206645\pi$
$599$	43.4803	−	9.92410i	1.77656	−	0.405488i	0.979988	+	0.199058i	$0.0637882\pi$
$600$		0			0
$601$	−13.2382	+	3.02152i	−0.539996	+	0.123251i	−0.483815	−	0.875170i	$-0.660749\pi$
$601$	−13.2382	+	3.02152i	−0.539996	+	0.123251i	−0.0561805	+	0.998421i	$0.517892\pi$
$602$	51.6915	+	21.9791i	2.10679	+	0.895802i
$603$		0			0
$604$	8.57167	−	10.7485i	0.348776	−	0.437352i
$605$	−8.85862	−	4.26608i	−0.360154	−	0.173441i
$606$		0			0
$607$		−	14.5618i		−	0.591044i	−0.955336	−	0.295522i	$-0.904507\pi$
$607$		−	14.5618i		−	0.591044i	0.955336	−	0.295522i	$-0.0954935\pi$
$608$	17.1431	+	8.25569i	0.695245	+	0.334812i
$609$		0			0
$610$	−3.50737	+	1.68906i	−0.142009	+	0.0683880i
$611$	1.26899	+	2.63508i	0.0513378	+	0.106604i
$612$		0			0
$613$	−8.91343	+	39.0523i	−0.360010	+	1.57731i	0.393153	+	0.919473i	$0.371384\pi$
$613$	−8.91343	+	39.0523i	−0.360010	+	1.57731i	−0.753163	+	0.657834i	$0.771473\pi$
$614$	−37.0342	+	17.8347i	−1.49458	+	0.719750i
$615$		0			0
$616$	−10.9467	−	7.92183i	−0.441055	−	0.319180i
$617$	16.3610	−	33.9739i	0.658668	−	1.36774i	−0.257239	−	0.966348i	$-0.582813\pi$
$617$	16.3610	−	33.9739i	0.658668	−	1.36774i	0.915907	−	0.401390i	$-0.131473\pi$
$618$		0			0
$619$		−	10.9899i		−	0.441721i	−0.975305	−	0.220860i	$-0.929113\pi$
$619$		−	10.9899i		−	0.441721i	0.975305	−	0.220860i	$-0.0708865\pi$
$620$	5.10674	−	10.6042i	0.205091	−	0.425877i
$621$		0			0
$622$	48.1674	+	10.9939i	1.93134	+	0.440815i
$623$	4.05753	+	0.728453i	0.162561	+	0.0291848i
$624$		0			0
$625$	17.0162	+	8.19455i	0.680646	+	0.327782i
$626$	7.39276	+	32.3898i	0.295474	+	1.29456i
$627$		0			0
$628$	−3.65416	−	0.834038i	−0.145817	−	0.0332817i
$629$	1.45337	+	1.82247i	0.0579496	+	0.0726665i
$630$		0			0
$631$	28.7388	−	36.0373i	1.14407	−	1.43462i	0.261027	−	0.965331i	$-0.415939\pi$
$631$	28.7388	−	36.0373i	1.14407	−	1.43462i	0.883045	−	0.469289i	$-0.155490\pi$
$632$	10.6956	−	8.52945i	0.425448	−	0.339283i
$633$		0			0
$634$	10.7242	+	13.4478i	0.425914	+	0.534080i
$635$	−2.05958	−	9.02361i	−0.0817319	−	0.358091i
$636$		0			0
$637$	−9.26142	+	3.04778i	−0.366951	+	0.120757i
$638$		−	0.791955i		−	0.0313538i
$639$		0			0
$640$	20.8214	−	16.6045i	0.823039	−	0.656352i
$641$	−5.96447	−	12.3854i	−0.235582	−	0.489192i	0.749341	−	0.662185i	$-0.230371\pi$
$641$	−5.96447	−	12.3854i	−0.235582	−	0.489192i	−0.984923	+	0.172993i	$0.944656\pi$
$642$		0			0
$643$	13.9766	+	11.1459i	0.551182	+	0.439553i	0.859062	−	0.511872i	$-0.171048\pi$
$643$	13.9766	+	11.1459i	0.551182	+	0.439553i	−0.307879	+	0.951425i	$0.599619\pi$
$644$	−6.77352	+	9.35992i	−0.266914	+	0.368833i
$645$		0			0
$646$	−1.47991	+	6.48389i	−0.0582261	+	0.255105i
$647$	2.71769	−	3.40788i	0.106844	−	0.133978i	−0.725535	−	0.688186i	$-0.758407\pi$
$647$	2.71769	−	3.40788i	0.106844	−	0.133978i	0.832378	+	0.554208i	$0.186979\pi$
$648$		0			0
$649$	−13.7744	+	28.6028i	−0.540692	+	1.12276i
$650$	−0.522336	−	2.28851i	−0.0204877	−	0.0897626i
$651$		0			0
$652$	0.0756608	−	0.331492i	0.00296311	−	0.0129822i
$653$	28.2832	+	22.5551i	1.10681	+	0.882648i	0.993826	−	0.110949i	$-0.0353890\pi$
$653$	28.2832	+	22.5551i	1.10681	+	0.882648i	0.112980	+	0.993597i	$0.463960\pi$
$654$		0			0
$655$	4.70283			0.183755
$656$	35.2046			1.37451
$657$		0			0
$658$	−8.10522	+	4.38128i	−0.315974	+	0.170800i
$659$	−9.48481	−	19.6954i	−0.369476	−	0.767224i	0.630484	−	0.776202i	$-0.282856\pi$
$659$	−9.48481	−	19.6954i	−0.369476	−	0.767224i	−0.999960	+	0.00897814i	$0.997142\pi$
$660$		0			0
$661$	−16.6330	−	3.79637i	−0.646947	−	0.147662i	−0.113558	−	0.993531i	$-0.536225\pi$
$661$	−16.6330	−	3.79637i	−0.646947	−	0.147662i	−0.533389	+	0.845870i	$0.679082\pi$
$662$	16.3833	+	3.73938i	0.636754	+	0.145335i
$663$		0			0
$664$	12.8493	+	26.6818i	0.498648	+	1.03545i
$665$	16.3811	+	18.6787i	0.635232	+	0.724327i
$666$		0			0
$667$	1.12748			0.0436561
$668$	14.4267			0.558185
$669$		0			0
$670$	6.29896	+	5.02326i	0.243350	+	0.194065i
$671$	−0.644944	+	2.82568i	−0.0248978	+	0.109084i
$672$		0			0
$673$	−0.300780	−	1.31780i	−0.0115942	−	0.0507976i	0.968800	−	0.247844i	$-0.0797221\pi$
$673$	−0.300780	−	1.31780i	−0.0115942	−	0.0507976i	−0.980394	+	0.197047i	$0.936865\pi$
$674$	−1.34931	+	2.80187i	−0.0519734	+	0.107924i
$675$		0			0
$676$	−5.17503	+	6.48928i	−0.199039	+	0.249588i
$677$	−6.85747	+	30.0445i	−0.263554	+	1.15470i	0.653811	+	0.756658i	$0.273169\pi$
$677$	−6.85747	+	30.0445i	−0.263554	+	1.15470i	−0.917365	+	0.398047i	$0.869688\pi$
$678$		0			0
$679$	−1.92003	+	0.0898474i	−0.0736840	+	0.00344803i
$680$	2.75645	+	2.19819i	0.105705	+	0.0842968i
$681$		0			0
$682$	−13.9347	−	28.9358i	−0.533589	−	1.10801i
$683$	−7.21649	+	5.75495i	−0.276131	+	0.220207i	−0.751757	−	0.659441i	$-0.770793\pi$
$683$	−7.21649	+	5.75495i	−0.276131	+	0.220207i	0.475626	+	0.879648i	$0.342222\pi$
$684$		0			0
$685$			9.44964i			0.361052i
$686$	−10.9546	−	28.6951i	−0.418247	−	1.09558i
$687$		0			0
$688$	14.0654	+	61.6246i	0.536239	+	2.34941i
$689$	8.13931	+	10.2064i	0.310083	+	0.388832i
$690$		0			0
$691$	3.61709	−	2.88453i	0.137601	−	0.109733i	−0.552271	−	0.833665i	$-0.686239\pi$
$691$	3.61709	−	2.88453i	0.137601	−	0.109733i	0.689871	+	0.723932i	$0.257667\pi$
$692$	−1.58014	+	1.98143i	−0.0600678	+	0.0753227i
$693$		0			0
$694$	−5.01306	−	6.28617i	−0.190293	−	0.238620i
$695$	18.8118	+	4.29367i	0.713572	+	0.162868i
$696$		0			0
$697$	1.35231	+	5.92487i	0.0512225	+	0.224420i
$698$	−46.9339	−	22.6022i	−1.77647	−	0.855505i
$699$		0			0
$700$	1.94394	−	0.540430i	0.0734740	−	0.0204263i
$701$	15.7508	+	3.59501i	0.594898	+	0.135782i	0.509360	−	0.860553i	$-0.329882\pi$
$701$	15.7508	+	3.59501i	0.594898	+	0.135782i	0.0855376	+	0.996335i	$0.472739\pi$
$702$		0			0
$703$	−5.58227	+	11.5917i	−0.210539	+	0.437189i
$704$		−	7.80763i		−	0.294261i
$705$		0			0
$706$	13.8630	−	28.7869i	0.521742	−	1.08341i
$707$	31.9866	−	28.0521i	1.20298	−	1.05501i
$708$		0			0
$709$	12.6766	−	6.10473i	0.476080	−	0.229268i	−0.180427	−	0.983588i	$-0.557748\pi$
$709$	12.6766	−	6.10473i	0.476080	−	0.229268i	0.656506	+	0.754321i	$0.272034\pi$
$710$	−2.36793	+	10.3746i	−0.0888667	+	0.389350i
$711$		0			0
$712$	1.40096	+	2.90913i	0.0525032	+	0.109024i
$713$	41.1948	−	19.8384i	1.54276	−	0.742953i
$714$		0			0
$715$	6.17305	+	2.97278i	0.230859	+	0.111176i
$716$			11.0484i			0.412896i
$717$		0			0
$718$	26.4496	+	12.7375i	0.987091	+	0.475358i
$719$	−8.39810	+	10.5309i	−0.313196	+	0.392736i	−0.913368	−	0.407136i	$-0.866528\pi$
$719$	−8.39810	+	10.5309i	−0.313196	+	0.392736i	0.600171	+	0.799871i	$0.295099\pi$
$720$		0			0
$721$	9.52059	+	10.8559i	0.354565	+	0.404295i
$722$	−5.06653	+	1.15640i	−0.188557	+	0.0430368i
$723$		0			0
$724$	12.0427	−	2.74866i	0.447563	−	0.102153i
$725$	−0.153938	−	0.122762i	−0.00571713	−	0.00455926i
$726$		0			0
$727$	22.1775	−	17.6860i	0.822519	−	0.655937i	−0.119001	−	0.992894i	$-0.537969\pi$
$727$	22.1775	−	17.6860i	0.822519	−	0.655937i	0.941520	+	0.336957i	$0.109398\pi$
$728$	−6.18668	−	4.47713i	−0.229294	−	0.165934i
$729$		0			0
$730$	−21.1652	−	26.5404i	−0.783361	−	0.982303i
$731$	−9.83101	+	4.73437i	−0.363613	+	0.175107i
$732$		0			0
$733$	12.9806	−	2.96274i	0.479450	−	0.109431i	0.0240359	−	0.999711i	$-0.492348\pi$
$733$	12.9806	−	2.96274i	0.479450	−	0.109431i	0.455414	+	0.890280i	$0.349491\pi$
$734$	−47.2115			−1.74261
$735$		0			0
$736$	−23.5341			−0.867478
$737$	5.84801	−	1.33477i	0.215414	−	0.0491669i
$738$		0			0
$739$	−3.30389	+	1.59107i	−0.121536	+	0.0585285i	−0.493664	−	0.869653i	$-0.664343\pi$
$739$	−3.30389	+	1.59107i	−0.121536	+	0.0585285i	0.372128	+	0.928181i	$0.378628\pi$
$740$	−2.55400	−	3.20262i	−0.0938870	−	0.117731i
$741$		0			0
$742$	−30.9189	+	27.1158i	−1.13507	+	0.995451i
$743$	14.1620	−	11.2938i	0.519555	−	0.414331i	−0.328289	−	0.944577i	$-0.606472\pi$
$743$	14.1620	−	11.2938i	0.519555	−	0.414331i	0.847844	+	0.530246i	$0.177901\pi$
$744$		0			0
$745$	−19.3287	−	15.4141i	−0.708149	−	0.564730i
$746$	−24.4159	+	5.57276i	−0.893928	+	0.204033i
$747$		0			0
$748$	−1.53699	+	0.350807i	−0.0561978	+	0.0128268i
$749$	−4.93394	+	27.4824i	−0.180282	+	1.00418i
$750$		0			0
$751$	−5.67349	+	7.11433i	−0.207028	+	0.259606i	−0.874495	−	0.485034i	$-0.838807\pi$
$751$	−5.67349	+	7.11433i	−0.207028	+	0.259606i	0.667467	+	0.744640i	$0.267379\pi$
$752$	−9.34145	−	4.49860i	−0.340648	−	0.164047i
$753$		0			0
$754$		−	0.447584i		−	0.0163001i
$755$	32.9432	+	15.8646i	1.19893	+	0.577372i
$756$		0			0
$757$	23.0567	−	11.1035i	0.838008	−	0.403564i	0.0348959	−	0.999391i	$-0.488890\pi$
$757$	23.0567	−	11.1035i	0.838008	−	0.403564i	0.803113	+	0.595827i	$0.203176\pi$
$758$	8.94781	+	18.5803i	0.324999	+	0.674867i
$759$		0			0
$760$	−4.33010	+	18.9714i	−0.157069	+	0.688165i
$761$	−25.4896	+	12.2752i	−0.923998	+	0.444974i	−0.834497	−	0.551013i	$-0.814242\pi$
$761$	−25.4896	+	12.2752i	−0.923998	+	0.444974i	−0.0895011	+	0.995987i	$0.528527\pi$
$762$		0			0
$763$	−46.3422	+	12.8835i	−1.67770	+	0.466414i
$764$	1.15452	−	2.39739i	0.0417691	−	0.0867345i
$765$		0			0
$766$		−	40.1497i		−	1.45067i
$767$	−7.78479	+	16.1653i	−0.281093	+	0.583695i
$768$		0			0
$769$	43.6040	+	9.95234i	1.57240	+	0.358890i	0.917787	−	0.397072i	$-0.129974\pi$
$769$	43.6040	+	9.95234i	1.57240	+	0.358890i	0.654615	+	0.755963i	$0.272831\pi$
$770$	−8.44576	+	19.8631i	−0.304364	+	0.715818i
$771$		0			0
$772$	−3.33577	−	1.60642i	−0.120057	−	0.0578165i
$773$	−6.78121	−	29.7104i	−0.243903	−	1.06861i	−0.937429	−	0.348178i	$-0.886801\pi$
$773$	−6.78121	−	29.7104i	−0.243903	−	1.06861i	0.693525	−	0.720432i	$-0.256057\pi$
$774$		0			0
$775$	−7.78451	−	1.77676i	−0.279628	−	0.0638233i
$776$	−0.938674	−	1.17706i	−0.0336964	−	0.0422540i
$777$		0			0
$778$	0.981044	−	1.23019i	0.0351721	−	0.0441045i
$779$	−26.2247	+	20.9135i	−0.939597	+	0.749303i
$780$		0			0
$781$	4.93976	+	6.19427i	0.176759	+	0.221648i
$782$	−1.83042	−	8.01961i	−0.0654558	−	0.286781i
$783$		0			0
$784$	18.9326	−	28.9177i	0.676165	−	1.03278i
$785$		−	9.96861i		−	0.355795i
$786$		0			0
$787$	32.0194	−	25.5346i	1.14137	−	0.910210i	0.144515	−	0.989503i	$-0.453838\pi$
$787$	32.0194	−	25.5346i	1.14137	−	0.910210i	0.996851	+	0.0792930i	$0.0252663\pi$
$788$	6.48107	+	13.4581i	0.230879	+	0.479424i
$789$		0			0
$790$	−17.0847	−	13.6246i	−0.607845	−	0.484740i
$791$	−0.467731	+	2.60529i	−0.0166306	+	0.0926335i
$792$		0			0
$793$	−0.364499	+	1.59697i	−0.0129437	+	0.0567102i
$794$	−21.2221	+	26.6117i	−0.753144	+	0.944413i
$795$		0			0
$796$	−7.26990	+	15.0961i	−0.257675	+	0.535067i
$797$	6.88241	+	30.1538i	0.243787	+	1.06810i	0.937537	+	0.347886i	$0.113100\pi$
$797$	6.88241	+	30.1538i	0.243787	+	1.06810i	−0.693749	+	0.720216i	$0.744042\pi$
$798$		0			0
$799$	0.398274	−	1.74495i	0.0140899	−	0.0617320i
$800$	3.21319	+	2.56244i	0.113604	+	0.0905958i
$801$		0			0
$802$	−49.0752			−1.73291
$803$	−25.2740			−0.891899
$804$		0			0
$805$	−28.2784	−	12.0239i	−0.996683	−	0.423788i
$806$	−7.87542	−	16.3535i	−0.277400	−	0.576026i
$807$		0			0
$808$	32.4879	+	7.41515i	1.14292	+	0.260864i
$809$	37.9162	+	8.65413i	1.33306	+	0.304263i	0.828925	−	0.559360i	$-0.188953\pi$
$809$	37.9162	+	8.65413i	1.33306	+	0.304263i	0.504138	+	0.863623i	$0.331810\pi$
$810$		0			0
$811$	−6.71229	−	13.9382i	−0.235700	−	0.489437i	0.749247	−	0.662290i	$-0.230415\pi$
$811$	−6.71229	−	13.9382i	−0.235700	−	0.489437i	−0.984948	+	0.172854i	$0.944701\pi$
$812$	0.384299	−	0.0179832i	0.0134862	−	0.000631086i
$813$		0			0
$814$	−11.1776			−0.391774
$815$	0.904315			0.0316768
$816$		0			0
$817$	−47.0861	−	37.5499i	−1.64733	−	1.31370i
$818$	−10.3890	+	45.5170i	−0.363241	+	1.59146i
$819$		0			0
$820$	−2.37642	−	10.4118i	−0.0829881	−	0.363595i
$821$	11.4523	−	23.7809i	0.399688	−	0.829960i	−0.599866	−	0.800100i	$-0.704780\pi$
$821$	11.4523	−	23.7809i	0.399688	−	0.829960i	0.999554	−	0.0298600i	$-0.00950614\pi$
$822$		0			0
$823$	24.1231	−	30.2495i	0.840880	−	1.05443i	−0.156886	−	0.987617i	$-0.550146\pi$
$823$	24.1231	−	30.2495i	0.840880	−	1.05443i	0.997766	−	0.0668129i	$-0.0212831\pi$
$824$	−2.51663	+	11.0261i	−0.0876708	+	0.384111i
$825$		0			0
$826$	−52.0154	−	22.1168i	−1.80985	−	0.769543i
$827$	−19.5745	−	15.6101i	−0.680672	−	0.542818i	0.220981	−	0.975278i	$-0.429074\pi$
$827$	−19.5745	−	15.6101i	−0.680672	−	0.542818i	−0.901653	+	0.432460i	$0.857646\pi$
$828$		0			0
$829$	3.11101	+	6.46008i	0.108050	+	0.224368i	0.947982	−	0.318323i	$-0.103120\pi$
$829$	3.11101	+	6.46008i	0.108050	+	0.224368i	−0.839932	+	0.542691i	$0.817405\pi$
$830$	36.9845	−	29.4941i	1.28375	−	1.02376i
$831$		0			0
$832$		−	4.41259i		−	0.152979i
$833$	5.59406	+	2.07551i	0.193823	+	0.0719123i
$834$		0			0
$835$	8.53802	+	37.4075i	0.295470	+	1.29454i
$836$	−5.42522	−	6.80302i	−0.187635	−	0.235287i
$837$		0			0
$838$	24.2792	−	19.3620i	0.838711	−	0.668850i
$839$	7.64399	−	9.58526i	0.263900	−	0.330920i	−0.632173	−	0.774827i	$-0.717837\pi$
$839$	7.64399	−	9.58526i	0.263900	−	0.330920i	0.896073	+	0.443908i	$0.146408\pi$
$840$		0			0
$841$	18.0578	+	22.6438i	0.622683	+	0.780819i
$842$	−39.9021	−	9.10740i	−1.37512	−	0.313862i
$843$		0			0
$844$	−3.65774	−	16.0256i	−0.125905	−	0.551625i
$845$	−19.8890	−	9.57803i	−0.684202	−	0.329494i
$846$		0			0
$847$	−6.19766	−	11.4654i	−0.212954	−	0.393957i
$848$	−45.1181	−	10.2979i	−1.54936	−	0.353632i
$849$		0			0
$850$	−0.623276	+	1.29425i	−0.0213782	+	0.0443922i
$851$		−	15.9131i		−	0.545494i
$852$		0			0
$853$	11.9694	−	24.8547i	0.409825	−	0.851010i	−0.589248	−	0.807952i	$-0.700576\pi$
$853$	11.9694	−	24.8547i	0.409825	−	0.851010i	0.999073	−	0.0430577i	$-0.0137099\pi$
$854$	−5.07904	−	0.911846i	−0.173801	−	0.0312027i
$855$		0			0
$856$	−19.7040	+	9.48896i	−0.673470	+	0.324326i
$857$	6.66111	−	29.1842i	0.227539	−	0.996914i	−0.724100	−	0.689695i	$-0.757744\pi$
$857$	6.66111	−	29.1842i	0.227539	−	0.996914i	0.951639	−	0.307219i	$-0.0993984\pi$
$858$		0			0
$859$	21.3225	+	44.2766i	0.727513	+	1.51070i	0.854871	+	0.518840i	$0.173636\pi$
$859$	21.3225	+	44.2766i	0.727513	+	1.51070i	−0.127358	+	0.991857i	$0.540650\pi$
$860$	17.2760	−	8.31970i	0.589108	−	0.283699i
$861$		0			0
$862$	30.3727	+	14.6267i	1.03450	+	0.498188i
$863$		−	31.9261i		−	1.08678i	−0.839482	−	0.543388i	$-0.817141\pi$
$863$		−	31.9261i		−	1.08678i	0.839482	−	0.543388i	$-0.182859\pi$
$864$		0			0
$865$	−6.07289	−	2.92455i	−0.206484	−	0.0994376i
$866$	29.2846	−	36.7218i	0.995133	−	1.24786i
$867$		0			0
$868$	13.7248	−	7.41894i	0.465849	−	0.251815i
$869$	−15.8615	+	3.62029i	−0.538066	+	0.122810i
$870$		0			0
$871$	3.30508	−	0.754364i	0.111989	−	0.0255606i
$872$	−29.4550	−	23.4896i	−0.997471	−	0.795457i
$873$		0			0
$874$	35.4964	−	28.3074i	1.20068	−	0.957514i
$875$	15.1075	+	27.9483i	0.510726	+	0.944825i
$876$		0			0
$877$	32.5323	+	40.7942i	1.09854	+	1.37752i	0.919227	+	0.393728i	$0.128815\pi$
$877$	32.5323	+	40.7942i	1.09854	+	1.37752i	0.179309	+	0.983793i	$0.442614\pi$
$878$	10.3791	−	4.99831i	0.350278	−	0.168685i
$879$		0			0
$880$	−23.6801	+	5.40482i	−0.798255	+	0.182196i
$881$	−53.4246			−1.79992			−0.899960	−	0.435973i	$-0.856404\pi$
$881$	−53.4246			−1.79992			−0.899960	+	0.435973i	$0.856404\pi$
$882$		0			0
$883$	−29.9201			−1.00689			−0.503445	−	0.864027i	$-0.667935\pi$
$883$	−29.9201			−1.00689			−0.503445	+	0.864027i	$0.667935\pi$
$884$	−0.868650	+	0.198264i	−0.0292159	+	0.00666833i
$885$		0			0
$886$	−61.8178	+	29.7699i	−2.07681	+	1.00014i
$887$	20.6339	+	25.8741i	0.692818	+	0.868767i	0.996464	−	0.0840181i	$-0.0267754\pi$
$887$	20.6339	+	25.8741i	0.692818	+	0.868767i	−0.303646	+	0.952785i	$0.598204\pi$
$888$		0			0
$889$	4.80077	−	11.2907i	0.161013	−	0.378677i
$890$	4.03243	−	3.21576i	0.135168	−	0.107792i
$891$		0			0
$892$	−6.23145	−	4.96941i	−0.208644	−	0.166388i
$893$	9.63108	−	2.19823i	0.322292	−	0.0735610i
$894$		0			0
$895$	−28.6477	+	6.53865i	−0.957587	+	0.218563i
$896$	35.2632	−	1.65013i	1.17806	−	0.0551271i
$897$		0			0
$898$	−12.9201	+	16.2012i	−0.431148	+	0.540642i
$899$	−1.37172	−	0.660584i	−0.0457493	−	0.0220317i
$900$		0			0
$901$		−	7.98888i		−	0.266148i
$902$	−26.2553	−	12.6439i	−0.874206	−	0.420995i
$903$		0			0
$904$	−1.86792	+	0.899541i	−0.0621260	+	0.0299183i
$905$	14.2542	+	29.5992i	0.473827	+	0.983911i
$906$		0			0
$907$	4.95057	−	21.6899i	0.164381	−	0.720200i	−0.823796	−	0.566886i	$-0.808148\pi$
$907$	4.95057	−	21.6899i	0.164381	−	0.720200i	0.988177	−	0.153315i	$-0.0489948\pi$
$908$	−9.77448	+	4.70714i	−0.324377	+	0.156212i
$909$		0			0
$910$	−4.77324	+	11.2259i	−0.158231	+	0.372136i
$911$	8.61363	−	17.8864i	0.285382	−	0.592602i	−0.708162	−	0.706050i	$-0.750475\pi$
$911$	8.61363	−	17.8864i	0.285382	−	0.592602i	0.993544	+	0.113448i	$0.0361895\pi$
$912$		0			0
$913$		−	35.2197i		−	1.16560i
$914$	23.9125	−	49.6549i	0.790957	−	1.64244i
$915$		0			0
$916$	6.43842	+	1.46953i	0.212731	+	0.0485545i
$917$	5.05020	+	3.65469i	0.166772	+	0.120689i
$918$		0			0
$919$	−37.7936	−	18.2004i	−1.24670	−	0.600377i	−0.310071	−	0.950713i	$-0.600353\pi$
$919$	−37.7936	−	18.2004i	−1.24670	−	0.600377i	−0.936624	+	0.350336i	$0.886067\pi$
$920$	−5.35569	−	23.4648i	−0.176572	−	0.773612i
$921$		0			0
$922$	10.0198	+	2.28695i	0.329985	+	0.0753168i
$923$	2.79178	+	3.50078i	0.0918925	+	0.115230i
$924$		0			0
$925$	−1.73265	+	2.17267i	−0.0569691	+	0.0714370i
$926$	−31.0591	+	24.7688i	−1.02067	+	0.813953i
$927$		0			0
$928$	0.488595	+	0.612678i	0.0160389	+	0.0201121i
$929$	−8.83635	−	38.7146i	−0.289911	−	1.27018i	−0.884647	−	0.466262i	$-0.845600\pi$
$929$	−8.83635	−	38.7146i	−0.289911	−	1.27018i	0.594735	−	0.803921i	$-0.297257\pi$
$930$		0			0
$931$	3.07540	+	32.7885i	0.100792	+	1.07460i
$932$		−	2.48400i		−	0.0813661i
$933$		0			0
$934$	−31.8654	+	25.4118i	−1.04267	+	0.831499i
$935$	−1.81924	−	3.77770i	−0.0594956	−	0.123544i
$936$		0			0
$937$	21.0438	+	16.7819i	0.687471	+	0.548240i	0.903734	−	0.428095i	$-0.140815\pi$
$937$	21.0438	+	16.7819i	0.687471	+	0.548240i	−0.216262	+	0.976335i	$0.569387\pi$
$938$	2.86052	+	10.2894i	0.0933994	+	0.335960i
$939$		0			0
$940$	−0.699887	+	3.06641i	−0.0228278	+	0.100015i
$941$	−5.47593	+	6.86660i	−0.178510	+	0.223845i	−0.863034	−	0.505146i	$-0.831439\pi$
$941$	−5.47593	+	6.86660i	−0.178510	+	0.223845i	0.684524	+	0.728990i	$0.260010\pi$
$942$		0			0
$943$	18.0006	−	37.3787i	0.586181	−	1.21722i
$944$	−14.1535	−	62.0107i	−0.460658	−	2.01828i
$945$		0			0
$946$	11.6429	−	51.0108i	0.378543	−	1.65850i
$947$	−7.89215	−	6.29378i	−0.256460	−	0.204520i	0.486817	−	0.873504i	$-0.338158\pi$
$947$	−7.89215	−	6.29378i	−0.256460	−	0.204520i	−0.743277	+	0.668984i	$0.766729\pi$
$948$		0			0
$949$	−14.2839			−0.463676
$950$	−7.92862			−0.257238
$951$		0			0
$952$	1.25177	+	4.50266i	0.0405702	+	0.145932i
$953$	10.0434	+	20.8554i	0.325338	+	0.675572i	0.997921	−	0.0644502i	$-0.0205294\pi$
$953$	10.0434	+	20.8554i	0.325338	+	0.675572i	−0.672583	+	0.740022i	$0.734815\pi$
$954$		0			0
$955$	6.89955	+	1.57478i	0.223264	+	0.0509586i
$956$	−17.6482	−	4.02809i	−0.570784	−	0.130278i
$957$		0			0
$958$	−5.31542	−	11.0376i	−0.171733	−	0.356608i
$959$	−7.34356	+	10.1476i	−0.237136	+	0.327684i
$960$		0			0
$961$	−30.7418			−0.991673
$962$	−6.31716			−0.203673
$963$		0			0
$964$	13.2644	+	10.5780i	0.427216	+	0.340694i
$965$	2.19118	−	9.60017i	0.0705365	−	0.309041i
$966$		0			0
$967$	6.92235	+	30.3288i	0.222608	+	0.975308i	0.955506	+	0.294970i	$0.0953097\pi$
$967$	6.92235	+	30.3288i	0.222608	+	0.975308i	−0.732899	+	0.680338i	$0.761833\pi$
$968$	4.42926	−	9.19745i	0.142362	−	0.295617i
$969$		0			0
$970$	−1.49940	+	1.88018i	−0.0481427	+	0.0603690i
$971$	−11.0640	+	48.4747i	−0.355061	+	1.55563i	0.410255	+	0.911971i	$0.365440\pi$
$971$	−11.0640	+	48.4747i	−0.355061	+	1.55563i	−0.765316	+	0.643655i	$0.777417\pi$
$972$		0			0
$973$	16.8646	+	19.2299i	0.540653	+	0.616483i
$974$	−35.5869	−	28.3796i	−1.14028	−	0.909342i
$975$		0			0
$976$	−2.51953	−	5.23185i	−0.0806481	−	0.167468i
$977$	−6.54339	+	5.21818i	−0.209342	+	0.166944i	−0.722548	−	0.691321i	$-0.757029\pi$
$977$	−6.54339	+	5.21818i	−0.209342	+	0.166944i	0.513206	+	0.858265i	$0.328458\pi$
$978$		0			0
$979$		−	3.84002i		−	0.122728i
$980$	−9.83044	−	3.64730i	−0.314022	−	0.116509i
$981$		0			0
$982$	−4.00536	−	17.5486i	−0.127816	−	0.559999i
$983$	−15.6257	−	19.5941i	−0.498384	−	0.624953i	0.467480	−	0.884004i	$-0.345162\pi$
$983$	−15.6257	−	19.5941i	−0.498384	−	0.624953i	−0.965864	+	0.259050i	$0.916590\pi$
$984$		0			0
$985$	−31.0604	+	24.7698i	−0.989665	+	0.789232i
$986$	−0.170778	+	0.214149i	−0.00543868	+	0.00681989i
$987$		0			0
$988$	−3.06614	−	3.84482i	−0.0975470	−	0.122320i
$989$	72.6222	+	16.5755i	2.30925	+	0.527071i
$990$		0			0
$991$	5.71205	+	25.0261i	0.181449	+	0.794982i	0.980941	+	0.194305i	$0.0622451\pi$
$991$	5.71205	+	25.0261i	0.181449	+	0.794982i	−0.799492	+	0.600677i	$0.794898\pi$
$992$	28.6322	+	13.7885i	0.909072	+	0.437786i
$993$		0			0
$994$	−10.6052	+	9.30068i	−0.336375	+	0.295000i
$995$	−43.4458	−	9.91622i	−1.37732	−	0.314365i
$996$		0			0
$997$	26.2484	−	54.5053i	0.831294	−	1.72620i	0.157185	−	0.987569i	$-0.449758\pi$
$997$	26.2484	−	54.5053i	0.831294	−	1.72620i	0.674109	−	0.738632i	$-0.264528\pi$
$998$			39.5505i			1.25195i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.62.15	yes	120
3.2	odd	2	inner	441.2.w.a.62.6	✓	120
49.34	odd	14	inner	441.2.w.a.377.6	yes	120
147.83	even	14	inner	441.2.w.a.377.15	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.62.6	✓	120	3.2	odd	2	inner
441.2.w.a.62.15	yes	120	1.1	even	1	trivial
441.2.w.a.377.6	yes	120	49.34	odd	14	inner
441.2.w.a.377.15	yes	120	147.83	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.w (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61687 - 0.369040i) q^{2} +(0.676145 - 0.325614i) q^{4} +(1.24446 + 1.56050i) q^{5} +(0.123672 + 2.64286i) q^{7} +(-1.62019 + 1.29205i) q^{8} +(2.58801 + 2.06387i) q^{10} +(2.40273 - 0.548408i) q^{11} +(1.35794 - 0.309940i) q^{13} +(1.17528 + 4.22752i) q^{14} +(-3.07863 + 3.86047i) q^{16} +(-0.767970 - 0.369835i) q^{17} -4.70463i q^{19} +(1.34955 + 0.649911i) q^{20} +(3.68252 - 1.77341i) q^{22} +(2.52474 + 5.24267i) q^{23} +(0.226121 - 0.990699i) q^{25} +(2.08123 - 1.00227i) q^{26} +(0.944173 + 1.74669i) q^{28} +(0.0840694 - 0.174572i) q^{29} -7.85760i q^{31} +(-1.75480 + 3.64388i) q^{32} +(-1.37819 - 0.314564i) q^{34} +(-3.97027 + 3.48191i) q^{35} +(-2.46389 - 1.18655i) q^{37} +(-1.73620 - 7.60678i) q^{38} +(-4.03250 - 0.920391i) q^{40} +(-4.44530 - 5.57423i) q^{41} +(7.98148 - 10.0085i) q^{43} +(1.44603 - 1.15317i) q^{44} +(6.01693 + 7.54500i) q^{46} +(0.467248 + 2.04715i) q^{47} +(-6.96941 + 0.653696i) q^{49} -1.68528i q^{50} +(0.817242 - 0.651729i) q^{52} +(4.06653 + 8.44425i) q^{53} +(3.84588 + 3.06699i) q^{55} +(-3.61509 - 4.12213i) q^{56} +(0.0715054 - 0.313285i) q^{58} +(-8.03149 + 10.0712i) q^{59} +(-0.510260 + 1.05957i) q^{61} +(-2.89977 - 12.7047i) q^{62} +(0.704949 - 3.08858i) q^{64} +(2.17355 + 1.73335i) q^{65} +2.43390 q^{67} -0.639683 q^{68} +(-5.13445 + 7.09499i) q^{70} +(1.39482 + 2.89637i) q^{71} +(-9.99800 - 2.28198i) q^{73} +(-4.42168 - 1.00922i) q^{74} +(-1.53190 - 3.18101i) q^{76} +(1.74652 + 6.28226i) q^{77} -6.60146 q^{79} -9.85548 q^{80} +(-9.24459 - 7.37232i) q^{82} +(3.17998 - 13.9324i) q^{83} +(-0.378578 - 1.65866i) q^{85} +(9.21150 - 19.1279i) q^{86} +(-3.18430 + 3.99298i) q^{88} +(0.346714 - 1.51906i) q^{89} +(0.987068 + 3.55051i) q^{91} +(3.41418 + 2.72272i) q^{92} +(1.51096 + 3.13754i) q^{94} +(7.34156 - 5.85470i) q^{95} +0.726497i q^{97} +(-11.0274 + 3.62894i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70}+ \cdots - 112 q^{94}+O(q^{100}) \) 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

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