LMFDB - Embedded newform 490.3.h.b.19.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [490,3,Mod(19,490)] 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("490.19"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(490, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	490.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,16,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$13.3515329537$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 42x^{14} + 1322x^{12} + 17616x^{10} + 175407x^{8} + 205392x^{6} + 203018x^{4} + 23226x^{2} + 2401 $ x^16 + 42x^14 + 1322x^12 + 17616x^10 + 175407x^8 + 205392x^6 + 203018x^4 + 23226*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.6
Root			$-0.518845 + 0.898665i$ of defining polynomial
Character	$\chi$	$=$	490.19
Dual form			490.3.h.b.129.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 + 0.707107i) q^{2} +(-0.518845 - 0.898665i) q^{3} +(1.00000 + 1.73205i) q^{4} +(2.98539 - 4.01091i) q^{5} -1.46751i q^{6} +2.82843i q^{8} +(3.96160 - 6.86169i) q^{9} +(6.49249 - 2.80135i) q^{10} +(-6.23704 - 10.8029i) q^{11} +(1.03769 - 1.79733i) q^{12} +0.748223 q^{13} +(-5.15342 - 0.601827i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(5.77534 + 10.0032i) q^{17} +(9.70390 - 5.60255i) q^{18} +(-13.0948 - 7.56027i) q^{19} +(9.93250 + 1.15994i) q^{20} -17.6410i q^{22} +(-31.4481 - 18.1566i) q^{23} +(2.54181 - 1.46751i) q^{24} +(-7.17486 - 23.9483i) q^{25} +(0.916382 + 0.529074i) q^{26} -17.5610 q^{27} +50.5846 q^{29} +(-5.88607 - 4.38111i) q^{30} +(40.4989 - 23.3820i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(-6.47211 + 11.2100i) q^{33} +16.3351i q^{34} +15.8464 q^{36} +(10.1657 + 5.86915i) q^{37} +(-10.6918 - 18.5188i) q^{38} +(-0.388211 - 0.672402i) q^{39} +(11.3446 + 8.44397i) q^{40} +12.7397i q^{41} +26.2604i q^{43} +(12.4741 - 21.6057i) q^{44} +(-15.6947 - 36.3745i) q^{45} +(-25.6773 - 44.4743i) q^{46} +(20.2244 - 35.0296i) q^{47} +4.15076 q^{48} +(8.14664 - 34.4040i) q^{50} +(5.99301 - 10.3802i) q^{51} +(0.748223 + 1.29596i) q^{52} +(-22.8390 + 13.1861i) q^{53} +(-21.5078 - 12.4175i) q^{54} +(-61.9494 - 7.23458i) q^{55} +15.6904i q^{57} +(61.9532 + 35.7687i) q^{58} +(68.4898 - 39.5426i) q^{59} +(-4.11103 - 9.52782i) q^{60} +(-45.2611 - 26.1315i) q^{61} +66.1344 q^{62} -8.00000 q^{64} +(2.23374 - 3.00106i) q^{65} +(-15.8534 + 9.15294i) q^{66} +(-30.0519 + 17.3504i) q^{67} +(-11.5507 + 20.0064i) q^{68} +37.6817i q^{69} +14.6636 q^{71} +(19.4078 + 11.2051i) q^{72} +(50.5830 + 87.6124i) q^{73} +(8.30023 + 14.3764i) q^{74} +(-17.7989 + 18.8732i) q^{75} -30.2411i q^{76} -1.09803i q^{78} +(17.8625 - 30.9387i) q^{79} +(7.92343 + 18.3635i) q^{80} +(-26.5430 - 45.9738i) q^{81} +(-9.00833 + 15.6029i) q^{82} +80.8664 q^{83} +(57.3636 + 6.69903i) q^{85} +(-18.5689 + 32.1623i) q^{86} +(-26.2455 - 45.4586i) q^{87} +(30.5551 - 17.6410i) q^{88} +(117.103 + 67.6093i) q^{89} +(6.49861 - 55.6473i) q^{90} -72.6263i q^{92} +(-42.0252 - 24.2633i) q^{93} +(49.5394 - 28.6016i) q^{94} +(-69.4166 + 29.9516i) q^{95} +(5.08362 + 2.93503i) q^{96} -91.4185 q^{97} -98.8347 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} + 6 q^{5} - 12 q^{9} - 24 q^{10} - 12 q^{11} - 28 q^{15} - 32 q^{16} + 12 q^{19} + 24 q^{24} - 42 q^{25} + 48 q^{26} - 136 q^{29} + 32 q^{30} - 84 q^{31} - 48 q^{36} + 312 q^{39} - 48 q^{40}+ \cdots + 176 q^{99}+O(q^{100}) $ 16 * q + 16 * q^4 + 6 * q^5 - 12 * q^9 - 24 * q^10 - 12 * q^11 - 28 * q^15 - 32 * q^16 + 12 * q^19 + 24 * q^24 - 42 * q^25 + 48 * q^26 - 136 * q^29 + 32 * q^30 - 84 * q^31 - 48 * q^36 + 312 * q^39 - 48 * q^40 + 24 * q^44 - 384 * q^45 - 68 * q^46 - 96 * q^50 - 76 * q^51 + 108 * q^54 + 372 * q^59 - 28 * q^60 - 348 * q^61 - 128 * q^64 - 104 * q^65 - 480 * q^66 - 384 * q^71 + 208 * q^74 + 150 * q^75 + 148 * q^79 - 24 * q^80 - 140 * q^81 + 580 * q^85 - 188 * q^86 + 912 * q^89 + 600 * q^94 - 310 * q^95 + 48 * q^96 + 176 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$3$	−0.518845	−	0.898665i	−0.172948	−	0.299555i	0.766501	−	0.642243i	$-0.221996\pi$
$3$	−0.518845	−	0.898665i	−0.172948	−	0.299555i	−0.939449	+	0.342688i	$0.888663\pi$
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	2.98539	−	4.01091i	0.597079	−	0.802183i
$5$	2.98539	−	4.01091i	0.597079	−	0.802183i
$6$		−	1.46751i		−	0.244586i
$7$		0			0
$7$		0			0
$8$			2.82843i			0.353553i
$9$	3.96160	−	6.86169i	0.440178	−	0.762410i
$10$	6.49249	−	2.80135i	0.649249	−	0.280135i
$11$	−6.23704	−	10.8029i	−0.567004	−	0.982079i	−0.996860	−	0.0791820i	$-0.974769\pi$
$11$	−6.23704	−	10.8029i	−0.567004	−	0.982079i	0.429856	−	0.902897i	$-0.358564\pi$
$12$	1.03769	−	1.79733i	0.0864741	−	0.149778i
$13$	0.748223			0.0575556			0.0287778	−	0.999586i	$-0.490838\pi$
$13$	0.748223			0.0575556			0.0287778	+	0.999586i	$0.490838\pi$
$14$		0			0
$15$	−5.15342	−	0.601827i	−0.343562	−	0.0401218i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	5.77534	+	10.0032i	0.339726	+	0.588422i	0.984381	−	0.176051i	$-0.0563324\pi$
$17$	5.77534	+	10.0032i	0.339726	+	0.588422i	−0.644655	+	0.764473i	$0.722999\pi$
$18$	9.70390	−	5.60255i	0.539106	−	0.311253i
$19$	−13.0948	−	7.56027i	−0.689198	−	0.397909i	0.114113	−	0.993468i	$-0.463597\pi$
$19$	−13.0948	−	7.56027i	−0.689198	−	0.397909i	−0.803312	+	0.595559i	$0.796931\pi$
$20$	9.93250	+	1.15994i	0.496625	+	0.0579969i
$21$		0			0
$22$		−	17.6410i		−	0.801864i
$23$	−31.4481	−	18.1566i	−1.36731	−	0.789416i	−0.376725	−	0.926325i	$-0.622950\pi$
$23$	−31.4481	−	18.1566i	−1.36731	−	0.789416i	−0.990584	+	0.136909i	$0.956283\pi$
$24$	2.54181	−	1.46751i	0.105909	−	0.0611464i
$25$	−7.17486	−	23.9483i	−0.286994	−	0.957932i
$26$	0.916382	+	0.529074i	0.0352455	+	0.0203490i
$27$	−17.5610			−0.650408
$28$		0			0
$29$	50.5846			1.74430			0.872148	−	0.489243i	$-0.162727\pi$
$29$	50.5846			1.74430			0.872148	+	0.489243i	$0.162727\pi$
$30$	−5.88607	−	4.38111i	−0.196202	−	0.146037i
$31$	40.4989	−	23.3820i	1.30642	−	0.754259i	0.324919	−	0.945742i	$-0.394663\pi$
$31$	40.4989	−	23.3820i	1.30642	−	0.754259i	0.981496	+	0.191483i	$0.0613296\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$	−6.47211	+	11.2100i	−0.196125	+	0.339698i
$34$			16.3351i			0.480445i
$35$		0			0
$36$	15.8464			0.440178
$37$	10.1657	+	5.86915i	0.274748	+	0.158626i	0.631043	−	0.775748i	$-0.282627\pi$
$37$	10.1657	+	5.86915i	0.274748	+	0.158626i	−0.356296	+	0.934373i	$0.615960\pi$
$38$	−10.6918	−	18.5188i	−0.281364	−	0.487337i
$39$	−0.388211	−	0.672402i	−0.00995414	−	0.0172411i
$40$	11.3446	+	8.44397i	0.283614	+	0.211099i
$41$			12.7397i			0.310724i	0.987858	+	0.155362i	$0.0496545\pi$
$41$			12.7397i			0.310724i	−0.987858	+	0.155362i	$0.950346\pi$
$42$		0			0
$43$			26.2604i			0.610706i	0.952239	+	0.305353i	$0.0987745\pi$
$43$			26.2604i			0.610706i	−0.952239	+	0.305353i	$0.901226\pi$
$44$	12.4741	−	21.6057i	0.283502	−	0.491040i
$45$	−15.6947	−	36.3745i	−0.348772	−	0.808322i
$46$	−25.6773	−	44.4743i	−0.558201	−	0.966833i
$47$	20.2244	−	35.0296i	0.430305	−	0.745311i	−0.566594	−	0.823997i	$-0.691739\pi$
$47$	20.2244	−	35.0296i	0.430305	−	0.745311i	0.996899	+	0.0786862i	$0.0250725\pi$
$48$	4.15076			0.0864741
$49$		0			0
$50$	8.14664	−	34.4040i	0.162933	−	0.688079i
$51$	5.99301	−	10.3802i	0.117510	−	0.203533i
$52$	0.748223	+	1.29596i	0.0143889	+	0.0249223i
$53$	−22.8390	+	13.1861i	−0.430924	+	0.248794i	−0.699740	−	0.714398i	$-0.746701\pi$
$53$	−22.8390	+	13.1861i	−0.430924	+	0.248794i	0.268816	+	0.963191i	$0.413368\pi$
$54$	−21.5078	−	12.4175i	−0.398292	−	0.229954i
$55$	−61.9494	−	7.23458i	−1.12635	−	0.131538i
$56$		0			0
$57$			15.6904i			0.275270i
$58$	61.9532	+	35.7687i	1.06816	+	0.616702i
$59$	68.4898	−	39.5426i	1.16084	−	0.670214i	0.209338	−	0.977843i	$-0.432869\pi$
$59$	68.4898	−	39.5426i	1.16084	−	0.670214i	0.951506	+	0.307630i	$0.0995358\pi$
$60$	−4.11103	−	9.52782i	−0.0685171	−	0.158797i
$61$	−45.2611	−	26.1315i	−0.741985	−	0.428385i	0.0808056	−	0.996730i	$-0.474251\pi$
$61$	−45.2611	−	26.1315i	−0.741985	−	0.428385i	−0.822791	+	0.568345i	$0.807584\pi$
$62$	66.1344			1.06668
$63$		0			0
$64$	−8.00000			−0.125000
$65$	2.23374	−	3.00106i	0.0343652	−	0.0461701i
$66$	−15.8534	+	9.15294i	−0.240202	+	0.138681i
$67$	−30.0519	+	17.3504i	−0.448535	+	0.258962i	−0.707211	−	0.707002i	$-0.750047\pi$
$67$	−30.0519	+	17.3504i	−0.448535	+	0.258962i	0.258676	+	0.965964i	$0.416714\pi$
$68$	−11.5507	+	20.0064i	−0.169863	+	0.294211i
$69$			37.6817i			0.546112i
$70$		0			0
$71$	14.6636			0.206530			0.103265	−	0.994654i	$-0.467071\pi$
$71$	14.6636			0.206530			0.103265	+	0.994654i	$0.467071\pi$
$72$	19.4078	+	11.2051i	0.269553	+	0.155626i
$73$	50.5830	+	87.6124i	0.692918	+	1.20017i	0.970877	+	0.239577i	$0.0770086\pi$
$73$	50.5830	+	87.6124i	0.692918	+	1.20017i	−0.277959	+	0.960593i	$0.589658\pi$
$74$	8.30023	+	14.3764i	0.112165	+	0.194276i
$75$	−17.7989	+	18.8732i	−0.237318	+	0.251643i
$76$		−	30.2411i		−	0.397909i
$77$		0			0
$78$		−	1.09803i		−	0.0140773i
$79$	17.8625	−	30.9387i	0.226107	−	0.391629i	−0.730544	−	0.682866i	$-0.760733\pi$
$79$	17.8625	−	30.9387i	0.226107	−	0.391629i	0.956651	+	0.291237i	$0.0940667\pi$
$80$	7.92343	+	18.3635i	0.0990429	+	0.229544i
$81$	−26.5430	−	45.9738i	−0.327691	−	0.567577i
$82$	−9.00833	+	15.6029i	−0.109858	+	0.190279i
$83$	80.8664			0.974293			0.487147	−	0.873320i	$-0.338038\pi$
$83$	80.8664			0.974293			0.487147	+	0.873320i	$0.338038\pi$
$84$		0			0
$85$	57.3636	+	6.69903i	0.674865	+	0.0788122i
$86$	−18.5689	+	32.1623i	−0.215917	+	0.373980i
$87$	−26.2455	−	45.4586i	−0.301673	−	0.522512i
$88$	30.5551	−	17.6410i	0.347217	−	0.200466i
$89$	117.103	+	67.6093i	1.31576	+	0.759655i	0.983044	−	0.183372i	$-0.0587012\pi$
$89$	117.103	+	67.6093i	1.31576	+	0.759655i	0.332717	+	0.943027i	$0.392035\pi$
$90$	6.49861	−	55.6473i	0.0722068	−	0.618304i
$91$		0			0
$92$		−	72.6263i		−	0.789416i
$93$	−42.0252	−	24.2633i	−0.451884	−	0.260895i
$94$	49.5394	−	28.6016i	0.527014	−	0.304272i
$95$	−69.4166	+	29.9516i	−0.730701	+	0.315280i
$96$	5.08362	+	2.93503i	0.0529543	+	0.0305732i
$97$	−91.4185			−0.942459			−0.471230	−	0.882011i	$-0.656190\pi$
$97$	−91.4185			−0.942459			−0.471230	+	0.882011i	$0.656190\pi$
$98$		0			0
$99$	−98.8347			−0.998330
$100$	34.3048	−	36.3755i	0.343048	−	0.363755i
$101$	−76.2197	+	44.0054i	−0.754650	+	0.435698i	−0.827372	−	0.561655i	$-0.810165\pi$
$101$	−76.2197	+	44.0054i	−0.754650	+	0.435698i	0.0727215	+	0.997352i	$0.476832\pi$
$102$	14.6798	−	8.47539i	0.143920	−	0.0830921i
$103$	−56.2976	+	97.5104i	−0.546579	+	0.946703i	0.451927	+	0.892055i	$0.350737\pi$
$103$	−56.2976	+	97.5104i	−0.546579	+	0.946703i	−0.998506	+	0.0546475i	$0.982596\pi$
$104$			2.11629i			0.0203490i
$105$		0			0
$106$	−37.2959			−0.351848
$107$	−2.48799	−	1.43644i	−0.0232523	−	0.0134247i	0.488329	−	0.872660i	$-0.337607\pi$
$107$	−2.48799	−	1.43644i	−0.0232523	−	0.0134247i	−0.511581	+	0.859235i	$0.670940\pi$
$108$	−17.5610	−	30.4166i	−0.162602	−	0.281635i
$109$	42.6084	+	73.8000i	0.390903	+	0.677064i	0.992569	−	0.121684i	$-0.0388294\pi$
$109$	42.6084	+	73.8000i	0.390903	+	0.677064i	−0.601666	+	0.798748i	$0.705496\pi$
$110$	−70.7566	−	52.6654i	−0.643242	−	0.478776i
$111$		−	12.1807i		−	0.109736i
$112$		0			0
$113$			211.525i			1.87190i	0.352132	+	0.935950i	$0.385457\pi$
$113$			211.525i			1.87190i	−0.352132	+	0.935950i	$0.614543\pi$
$114$	−11.0948	+	19.2168i	−0.0973228	+	0.168568i
$115$	−166.709	+	71.9311i	−1.44965	+	0.625488i
$116$	50.5846	+	87.6150i	0.436074	+	0.755302i
$117$	2.96416	−	5.13408i	0.0253347	−	0.0438810i
$118$	111.843			0.947825
$119$		0			0
$120$	1.70223	−	14.5761i	0.0141852	−	0.121467i
$121$	−17.3014	+	29.9668i	−0.142986	+	0.247660i
$122$	−36.9555	−	64.0088i	−0.302914	−	0.524663i
$123$	11.4487	−	6.60993i	0.0930791	−	0.0537392i
$124$	80.9977	+	46.7641i	0.653208	+	0.377130i
$125$	−117.474	−	42.7173i	−0.939795	−	0.341739i
$126$		0			0
$127$			52.2434i			0.411366i	0.978619	+	0.205683i	$0.0659415\pi$
$127$			52.2434i			0.411366i	−0.978619	+	0.205683i	$0.934058\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$	23.5993	−	13.6250i	0.182940	−	0.105621i
$130$	4.85783	−	2.09604i	0.0373679	−	0.0161234i
$131$	−81.3342	−	46.9583i	−0.620872	−	0.358461i	0.156336	−	0.987704i	$-0.450032\pi$
$131$	−81.3342	−	46.9583i	−0.620872	−	0.358461i	−0.777208	+	0.629243i	$0.783365\pi$
$132$	−25.8884			−0.196125
$133$		0			0
$134$	−49.0745			−0.366227
$135$	−52.4265	+	70.4357i	−0.388345	+	0.521746i
$136$	−28.2933	+	16.3351i	−0.208039	+	0.120111i
$137$	101.185	−	58.4189i	0.738573	−	0.426415i	−0.0829771	−	0.996551i	$-0.526443\pi$
$137$	101.185	−	58.4189i	0.738573	−	0.426415i	0.821550	+	0.570136i	$0.193109\pi$
$138$	−26.6450	+	46.1505i	−0.193080	+	0.334424i
$139$			67.8796i			0.488342i	0.969732	+	0.244171i	$0.0785159\pi$
$139$			67.8796i			0.488342i	−0.969732	+	0.244171i	$0.921484\pi$
$140$		0			0
$141$	−41.9732			−0.297682
$142$	17.9592	+	10.3687i	0.126473	+	0.0730193i
$143$	−4.66670	−	8.08296i	−0.0326343	−	0.0565242i
$144$	15.8464	+	27.4468i	0.110044	+	0.190603i
$145$	151.015	−	202.890i	1.04148	−	1.39924i
$146$			143.070i			0.979934i
$147$		0			0
$148$			23.4766i			0.158626i
$149$	−86.0779	+	149.091i	−0.577704	+	1.00061i	0.418038	+	0.908430i	$0.362718\pi$
$149$	−86.0779	+	149.091i	−0.577704	+	1.00061i	−0.995742	+	0.0921836i	$0.970615\pi$
$150$	−35.1445	+	10.5292i	−0.234296	+	0.0701947i
$151$	55.1081	+	95.4500i	0.364954	+	0.632119i	0.988769	−	0.149453i	$-0.0477514\pi$
$151$	55.1081	+	95.4500i	0.364954	+	0.632119i	−0.623815	+	0.781572i	$0.714418\pi$
$152$	21.3837	−	37.0376i	0.140682	−	0.243668i
$153$	91.5184			0.598159
$154$		0			0
$155$	27.1217	−	232.242i	0.174979	−	1.49834i
$156$	0.776423	−	1.34480i	0.00497707	−	0.00862054i
$157$	102.082	+	176.811i	0.650201	+	1.12618i	0.983074	+	0.183210i	$0.0586488\pi$
$157$	102.082	+	176.811i	0.650201	+	1.12618i	−0.332873	+	0.942972i	$0.608018\pi$
$158$	43.7539	−	25.2613i	0.276924	−	0.159882i
$159$	23.6997	+	13.6830i	0.149055	+	0.0860569i
$160$	−3.28080	+	28.0934i	−0.0205050	+	0.175583i
$161$		0			0
$162$		−	75.0748i		−	0.463425i
$163$	−84.7593	−	48.9358i	−0.519996	−	0.300220i	0.216937	−	0.976186i	$-0.430393\pi$
$163$	−84.7593	−	48.9358i	−0.519996	−	0.300220i	−0.736933	+	0.675966i	$0.763727\pi$
$164$	−22.0658	+	12.7397i	−0.134548	+	0.0776811i
$165$	25.6406	+	59.4254i	0.155398	+	0.360154i
$166$	99.0407	+	57.1811i	0.596630	+	0.344465i
$167$	−97.1736			−0.581878			−0.290939	−	0.956742i	$-0.593968\pi$
$167$	−97.1736			−0.581878			−0.290939	+	0.956742i	$0.593968\pi$
$168$		0			0
$169$	−168.440			−0.996687
$170$	65.5188	+	48.7668i	0.385405	+	0.286863i
$171$	−103.752	+	59.9015i	−0.606740	+	0.350301i
$172$	−45.4843	+	26.2604i	−0.264444	+	0.152677i
$173$	−30.9286	+	53.5699i	−0.178778	+	0.309652i	−0.941462	−	0.337118i	$-0.890548\pi$
$173$	−30.9286	+	53.5699i	−0.178778	+	0.309652i	0.762684	+	0.646771i	$0.223881\pi$
$174$		−	74.2336i		−	0.426630i
$175$		0			0
$176$	49.8963			0.283502
$177$	−71.0711	−	41.0329i	−0.401532	−	0.231824i
$178$	95.6140	+	165.608i	0.537157	+	0.930383i
$179$	112.111	+	194.181i	0.626316	+	1.08481i	0.988285	+	0.152622i	$0.0487715\pi$
$179$	112.111	+	194.181i	0.626316	+	1.08481i	−0.361968	+	0.932190i	$0.617895\pi$
$180$	47.3077	−	63.5586i	0.262821	−	0.353103i
$181$		−	329.246i		−	1.81904i	−0.415659	−	0.909520i	$-0.636449\pi$
$181$		−	329.246i		−	1.81904i	0.415659	−	0.909520i	$-0.363551\pi$
$182$		0			0
$183$			54.2327i			0.296354i
$184$	51.3545	−	88.9486i	0.279101	−	0.483416i
$185$	53.8892	−	23.2519i	0.291293	−	0.125686i
$186$	−34.3135	−	59.4327i	−0.184481	−	0.319530i
$187$	72.0421	−	124.781i	0.385252	−	0.667275i
$188$	80.8974			0.430305
$189$		0			0
$190$	−106.197	−	12.4019i	−0.558930	−	0.0652730i
$191$	33.1175	−	57.3612i	0.173390	−	0.300320i	−0.766213	−	0.642587i	$-0.777861\pi$
$191$	33.1175	−	57.3612i	0.173390	−	0.300320i	0.939603	+	0.342266i	$0.111195\pi$
$192$	4.15076	+	7.18932i	0.0216185	+	0.0374444i
$193$	219.500	−	126.728i	1.13730	−	0.656623i	0.191543	−	0.981484i	$-0.438651\pi$
$193$	219.500	−	126.728i	1.13730	−	0.656623i	0.945762	+	0.324861i	$0.105318\pi$
$194$	−111.964	−	64.6427i	−0.577136	−	0.333210i
$195$	−3.85591	−	0.450301i	−0.0197739	−	0.00230924i
$196$		0			0
$197$		−	191.330i		−	0.971217i	−0.874176	−	0.485608i	$-0.838598\pi$
$197$		−	191.330i		−	0.971217i	0.874176	−	0.485608i	$-0.161402\pi$
$198$	−121.047	−	69.8867i	−0.611350	−	0.352963i
$199$	−195.609	+	112.935i	−0.982960	+	0.567512i	−0.903162	−	0.429299i	$-0.858761\pi$
$199$	−195.609	+	112.935i	−0.982960	+	0.567512i	−0.0797973	+	0.996811i	$0.525427\pi$
$200$	67.7360	−	20.2936i	0.338680	−	0.101468i
$201$	31.1845	+	18.0044i	0.155147	+	0.0895740i
$202$	−124.466			−0.616169
$203$		0			0
$204$	23.9720			0.117510
$205$	51.0979	+	38.0330i	0.249258	+	0.185527i
$206$	−137.900	+	79.6169i	−0.669420	+	0.386490i
$207$	−249.170	+	143.858i	−1.20372	+	0.694967i
$208$	−1.49645	+	2.59192i	−0.00719445	+	0.0124612i
$209$			188.615i			0.902463i
$210$		0			0
$211$	−186.816			−0.885386			−0.442693	−	0.896673i	$-0.645977\pi$
$211$	−186.816			−0.885386			−0.442693	+	0.896673i	$0.645977\pi$
$212$	−45.6779	−	26.3722i	−0.215462	−	0.124397i
$213$	−7.60814	−	13.1777i	−0.0357190	−	0.0618670i
$214$	−2.03144	−	3.51855i	−0.00949270	−	0.0164418i
$215$	105.328	+	78.3975i	0.489898	+	0.364640i
$216$		−	49.6701i		−	0.229954i
$217$		0			0
$218$			120.515i			0.552821i
$219$	52.4894	−	90.9144i	0.239678	−	0.415134i
$220$	−49.4187	−	114.534i	−0.224631	−	0.520610i
$221$	4.32124	+	7.48461i	0.0195531	+	0.0338670i
$222$	8.61306	−	14.9183i	0.0387976	−	0.0671994i
$223$	194.106			0.870431			0.435215	−	0.900326i	$-0.356672\pi$
$223$	194.106			0.870431			0.435215	+	0.900326i	$0.356672\pi$
$224$		0			0
$225$	−192.750	−	45.6419i	−0.856666	−	0.202853i
$226$	−149.571	+	259.064i	−0.661817	+	1.14630i
$227$	−175.878	−	304.630i	−0.774795	−	1.34198i	−0.934910	−	0.354886i	$-0.884520\pi$
$227$	−175.878	−	304.630i	−0.774795	−	1.34198i	0.160115	−	0.987098i	$-0.448814\pi$
$228$	−27.1766	+	15.6904i	−0.119196	+	0.0688176i
$229$	−162.993	−	94.1041i	−0.711760	−	0.410935i	0.0999523	−	0.994992i	$-0.468131\pi$
$229$	−162.993	−	94.1041i	−0.711760	−	0.410935i	−0.811712	+	0.584057i	$0.801464\pi$
$230$	−255.039	−	29.7840i	−1.10887	−	0.129496i
$231$		0			0
$232$			143.075i			0.616702i
$233$	272.001	+	157.040i	1.16739	+	0.673991i	0.953063	−	0.302772i	$-0.0979120\pi$
$233$	272.001	+	157.040i	1.16739	+	0.673991i	0.214324	+	0.976763i	$0.431245\pi$
$234$	7.26068	−	4.19196i	0.0310286	−	0.0179143i
$235$	−80.1231	−	185.695i	−0.340949	−	0.790193i
$236$	136.980	+	79.0852i	0.580422	+	0.335107i
$237$	−37.0714			−0.156419
$238$		0			0
$239$	336.269			1.40699			0.703493	−	0.710703i	$-0.251623\pi$
$239$	336.269			1.40699			0.703493	+	0.710703i	$0.251623\pi$
$240$	12.3916	−	16.6483i	0.0516318	−	0.0693680i
$241$	331.276	−	191.262i	1.37459	−	0.793619i	0.383086	−	0.923713i	$-0.374861\pi$
$241$	331.276	−	191.262i	1.37459	−	0.793619i	0.991502	+	0.130094i	$0.0415279\pi$
$242$	−42.3795	+	24.4678i	−0.175122	+	0.101107i
$243$	−106.568	+	184.581i	−0.438551	+	0.759593i
$244$		−	104.526i		−	0.428385i
$245$		0			0
$246$	18.6957			0.0759988
$247$	−9.79781	−	5.65677i	−0.0396672	−	0.0229019i
$248$	66.1344	+	114.548i	0.266671	+	0.461887i
$249$	−41.9571	−	72.6718i	−0.168502	−	0.291855i
$250$	−113.670	−	135.385i	−0.454682	−	0.541539i
$251$			302.072i			1.20347i	0.798695	+	0.601736i	$0.205524\pi$
$251$			302.072i			1.20347i	−0.798695	+	0.601736i	$0.794476\pi$
$252$		0			0
$253$			452.973i			1.79041i
$254$	−36.9417	+	63.9849i	−0.145440	+	0.251909i
$255$	−23.7426	−	55.0264i	−0.0931082	−	0.215790i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−102.339	+	177.257i	−0.398208	+	0.689717i	−0.993505	−	0.113789i	$-0.963701\pi$
$257$	−102.339	+	177.257i	−0.398208	+	0.689717i	0.595297	+	0.803506i	$0.297034\pi$
$258$	38.5375			0.149370
$259$		0			0
$260$	7.43173	+	0.867892i	0.0285836	+	0.00333805i
$261$	200.396	−	347.096i	0.767800	−	1.32987i
$262$	−66.4091	−	115.024i	−0.253470	−	0.439023i
$263$	−84.3776	+	48.7155i	−0.320828	+	0.185230i	−0.651761	−	0.758424i	$-0.725970\pi$
$263$	−84.3776	+	48.7155i	−0.320828	+	0.185230i	0.330934	+	0.943654i	$0.392636\pi$
$264$	−31.7067	−	18.3059i	−0.120101	−	0.0693405i
$265$	−15.2950	+	130.971i	−0.0577171	+	0.494229i
$266$		0			0
$267$		−	140.315i		−	0.525524i
$268$	−60.1037	−	34.7009i	−0.224268	−	0.129481i
$269$	−83.6084	+	48.2713i	−0.310812	+	0.179447i	−0.647290	−	0.762244i	$-0.724098\pi$
$269$	−83.6084	+	48.2713i	−0.310812	+	0.179447i	0.336478	+	0.941691i	$0.390764\pi$
$270$	−114.015	+	49.1947i	−0.422277	+	0.182202i
$271$	72.4056	+	41.8034i	0.267179	+	0.154256i	0.627605	−	0.778532i	$-0.284035\pi$
$271$	72.4056	+	41.8034i	0.267179	+	0.154256i	−0.360426	+	0.932788i	$0.617369\pi$
$272$	−46.2027			−0.169863
$273$		0			0
$274$	165.234			0.603043
$275$	−213.961	+	226.876i	−0.778038	+	0.825002i
$276$	−65.2667	+	37.6817i	−0.236473	+	0.136528i
$277$	334.055	−	192.867i	1.20598	−	0.696271i	0.244098	−	0.969750i	$-0.421508\pi$
$277$	334.055	−	192.867i	1.20598	−	0.696271i	0.961878	+	0.273480i	$0.0881747\pi$
$278$	−47.9981	+	83.1352i	−0.172655	+	0.299047i
$279$		−	370.521i		−	1.32803i
$280$		0			0
$281$	243.459			0.866402			0.433201	−	0.901297i	$-0.357384\pi$
$281$	243.459			0.866402			0.433201	+	0.901297i	$0.357384\pi$
$282$	−51.4064	−	29.6795i	−0.182292	−	0.105247i
$283$	51.4153	+	89.0540i	0.181680	+	0.314678i	0.942453	−	0.334340i	$-0.108513\pi$
$283$	51.4153	+	89.0540i	0.181680	+	0.314678i	−0.760773	+	0.649018i	$0.775180\pi$
$284$	14.6636	+	25.3981i	0.0516324	+	0.0894300i
$285$	62.9329	+	46.8420i	0.220817	+	0.164358i
$286$		−	13.1994i		−	0.0461518i
$287$		0			0
$288$			44.8204i			0.155626i
$289$	77.7909	−	134.738i	0.269173	−	0.466221i
$290$	328.420	−	141.705i	1.13248	−	0.488639i
$291$	47.4320	+	82.1547i	0.162997	+	0.282318i
$292$	−101.166	+	175.225i	−0.346459	+	0.600085i
$293$	440.610			1.50379			0.751894	−	0.659284i	$-0.229141\pi$
$293$	440.610			1.50379			0.751894	+	0.659284i	$0.229141\pi$
$294$		0			0
$295$	45.8670	−	392.757i	0.155481	−	1.33138i
$296$	−16.6005	+	28.7528i	−0.0560827	+	0.0971380i
$297$	109.529	+	189.709i	0.368784	+	0.638752i
$298$	−210.847	+	121.733i	−0.707540	+	0.408499i
$299$	−23.5302	−	13.5852i	−0.0786963	−	0.0454353i
$300$	−50.4883	−	11.9553i	−0.168294	−	0.0398510i
$301$		0			0
$302$			155.869i			0.516123i
$303$	79.0923	+	45.6640i	0.261031	+	0.150706i
$304$	52.3791	−	30.2411i	0.172300	−	0.0994772i
$305$	−239.933	+	103.526i	−0.786667	+	0.339428i
$306$	112.087	+	64.7133i	0.366296	+	0.211481i
$307$	247.192			0.805185			0.402592	−	0.915379i	$-0.368109\pi$
$307$	247.192			0.805185			0.402592	+	0.915379i	$0.368109\pi$
$308$		0			0
$309$	116.839			0.378119
$310$	197.437	−	265.259i	0.636894	−	0.855675i
$311$	369.117	−	213.110i	1.18687	−	0.685240i	0.229276	−	0.973361i	$-0.426364\pi$
$311$	369.117	−	213.110i	1.18687	−	0.685240i	0.957594	+	0.288121i	$0.0930307\pi$
$312$	1.90184	−	1.09803i	0.00609564	−	0.00351932i
$313$	−66.9870	+	116.025i	−0.214016	+	0.370686i	−0.952968	−	0.303072i	$-0.901988\pi$
$313$	−66.9870	+	116.025i	−0.214016	+	0.370686i	0.738952	+	0.673758i	$0.235321\pi$
$314$			288.730i			0.919523i
$315$		0			0
$316$	71.4499			0.226107
$317$	278.831	+	160.983i	0.879593	+	0.507833i	0.870524	−	0.492126i	$-0.163780\pi$
$317$	278.831	+	160.983i	0.879593	+	0.507833i	0.00906850	+	0.999959i	$0.497113\pi$
$318$	19.3508	+	33.5165i	0.0608514	+	0.105398i
$319$	−315.498	−	546.459i	−0.989022	−	1.71304i
$320$	−23.8831	+	32.0873i	−0.0746348	+	0.100273i
$321$			2.98116i			0.00928711i
$322$		0			0
$323$		−	174.652i		−	0.540720i
$324$	53.0859	−	91.9475i	0.163845	−	0.283789i
$325$	−5.36840	−	17.9187i	−0.0165181	−	0.0551344i
$326$	−69.2057	−	119.868i	−0.212287	−	0.367693i
$327$	44.2143	−	76.5814i	0.135212	−	0.234194i
$328$	−36.0333			−0.109858
$329$		0			0
$330$	−10.6168	+	90.9116i	−0.0321723	+	0.275490i
$331$	117.402	−	203.347i	0.354690	−	0.614342i	−0.632375	−	0.774663i	$-0.717920\pi$
$331$	117.402	−	203.347i	0.354690	−	0.614342i	0.987065	+	0.160321i	$0.0512530\pi$
$332$	80.8664	+	140.065i	0.243573	+	0.421881i
$333$	80.5446	−	46.5025i	0.241876	−	0.139647i
$334$	−119.013	−	68.7121i	−0.356326	−	0.205725i
$335$	−20.1254	+	172.333i	−0.0600759	+	0.514428i
$336$		0			0
$337$		−	217.706i		−	0.646012i	−0.946397	−	0.323006i	$-0.895307\pi$
$337$		−	217.706i		−	0.646012i	0.946397	−	0.323006i	$-0.104693\pi$
$338$	−206.296	−	119.105i	−0.610344	−	0.352382i
$339$	190.090	−	109.748i	0.560737	−	0.323742i
$340$	45.7605	+	106.056i	0.134590	+	0.311928i
$341$	−505.186	−	291.669i	−1.48148	−	0.855335i
$342$	−169.427			−0.495401
$343$		0			0
$344$	−74.2755			−0.215917
$345$	151.138	+	112.495i	0.438082	+	0.326072i
$346$	−75.7593	+	43.7396i	−0.218957	+	0.126415i
$347$	−161.281	+	93.1157i	−0.464787	+	0.268345i	−0.714055	−	0.700090i	$-0.753143\pi$
$347$	−161.281	+	93.1157i	−0.464787	+	0.268345i	0.249268	+	0.968435i	$0.419810\pi$
$348$	52.4911	−	90.9172i	0.150836	−	0.261256i
$349$		−	81.7368i		−	0.234203i	−0.993120	−	0.117101i	$-0.962640\pi$
$349$		−	81.7368i		−	0.234203i	0.993120	−	0.117101i	$-0.0373603\pi$
$350$		0			0
$351$	−13.1396			−0.0374347
$352$	61.1103	+	35.2820i	0.173609	+	0.100233i
$353$	53.9682	+	93.4757i	0.152884	+	0.264804i	0.932287	−	0.361720i	$-0.117810\pi$
$353$	53.9682	+	93.4757i	0.152884	+	0.264804i	−0.779402	+	0.626524i	$0.784477\pi$
$354$	−58.0293	−	100.510i	−0.163925	−	0.283926i
$355$	43.7767	−	58.8145i	0.123315	−	0.165675i
$356$			270.437i			0.759655i
$357$		0			0
$358$			317.097i			0.885745i
$359$	−301.930	+	522.957i	−0.841029	+	1.45671i	0.0479959	+	0.998848i	$0.484717\pi$
$359$	−301.930	+	522.957i	−0.841029	+	1.45671i	−0.889025	+	0.457858i	$0.848617\pi$
$360$	102.883	−	44.3914i	0.285785	−	0.123309i
$361$	−66.1847	−	114.635i	−0.183337	−	0.317549i
$362$	232.812	−	403.243i	0.643128	−	1.11393i
$363$	35.9069			0.0989169
$364$		0			0
$365$	502.416	+	58.6732i	1.37648	+	0.160748i
$366$	−38.3483	+	66.4213i	−0.104777	+	0.181479i
$367$	−271.765	−	470.710i	−0.740503	−	1.28259i	−0.952266	−	0.305268i	$-0.901254\pi$
$367$	−271.765	−	470.710i	−0.740503	−	1.28259i	0.211763	−	0.977321i	$-0.432080\pi$
$368$	125.792	−	72.6263i	0.341827	−	0.197354i
$369$	87.4159	+	50.4696i	0.236900	+	0.136774i
$370$	82.4421	+	9.62775i	0.222816	+	0.0260210i
$371$		0			0
$372$		−	97.0531i		−	0.260895i
$373$	−72.1316	−	41.6452i	−0.193382	−	0.111649i	0.400183	−	0.916435i	$-0.368947\pi$
$373$	−72.1316	−	41.6452i	−0.193382	−	0.111649i	−0.593565	+	0.804786i	$0.702280\pi$
$374$	176.466	−	101.883i	0.471835	−	0.272414i
$375$	22.5623	+	127.734i	0.0601663	+	0.340623i
$376$	99.0787	+	57.2031i	0.263507	+	0.152136i
$377$	37.8485			0.100394
$378$		0			0
$379$	−30.4409			−0.0803189			−0.0401595	−	0.999193i	$-0.512787\pi$
$379$	−30.4409			−0.0803189			−0.0401595	+	0.999193i	$0.512787\pi$
$380$	−121.294	−	90.2815i	−0.319196	−	0.237583i
$381$	46.9493	−	27.1062i	0.123227	−	0.0711449i
$382$	81.1209	−	46.8352i	0.212358	−	0.122605i
$383$	−147.759	+	255.925i	−0.385793	+	0.668213i	−0.991879	−	0.127186i	$-0.959405\pi$
$383$	−147.759	+	255.925i	−0.385793	+	0.668213i	0.606086	+	0.795399i	$0.292739\pi$
$384$			11.7401i			0.0305732i
$385$		0			0
$386$	358.442			0.928605
$387$	180.191	+	104.033i	0.465609	+	0.268819i
$388$	−91.4185	−	158.342i	−0.235615	−	0.408097i
$389$	−214.388	−	371.330i	−0.551125	−	0.954577i	−0.998194	−	0.0600771i	$-0.980865\pi$
$389$	−214.388	−	371.330i	−0.551125	−	0.954577i	0.447069	−	0.894500i	$-0.352468\pi$
$390$	−4.40410	−	3.27804i	−0.0112926	−	0.00840524i
$391$		−	419.441i		−	1.07274i
$392$		0			0
$393$			97.4563i			0.247980i
$394$	135.291	−	234.330i	0.343377	−	0.594746i
$395$	−70.7660	−	164.009i	−0.179154	−	0.415213i
$396$	−98.8347	−	171.187i	−0.249582	−	0.432290i
$397$	160.392	−	277.807i	0.404009	−	0.699765i	−0.590196	−	0.807260i	$-0.700950\pi$
$397$	160.392	−	277.807i	0.404009	−	0.699765i	0.994206	+	0.107495i	$0.0342830\pi$
$398$	−319.428			−0.802583
$399$		0			0
$400$	97.3091	+	23.0422i	0.243273	+	0.0576054i
$401$	118.854	−	205.861i	0.296394	−	0.513370i	−0.678914	−	0.734218i	$-0.737549\pi$
$401$	118.854	−	205.861i	0.296394	−	0.513370i	0.975308	+	0.220848i	$0.0708824\pi$
$402$	25.4620	+	44.1015i	0.0633384	+	0.109705i
$403$	30.3022	−	17.4950i	0.0751915	−	0.0434119i
$404$	−152.439	−	88.0109i	−0.377325	−	0.217849i
$405$	−263.638	−	30.7882i	−0.650958	−	0.0760202i
$406$		0			0
$407$		−	146.425i		−	0.359765i
$408$	29.3596	+	16.9508i	0.0719598	+	0.0415460i
$409$	−171.560	+	99.0500i	−0.419461	+	0.242176i	−0.694847	−	0.719158i	$-0.744528\pi$
$409$	−171.560	+	99.0500i	−0.419461	+	0.242176i	0.275386	+	0.961334i	$0.411194\pi$
$410$	35.6884	+	82.7124i	0.0870450	+	0.201738i
$411$	−104.998	−	60.6207i	−0.255470	−	0.147496i
$412$	−225.191			−0.546579
$413$		0			0
$414$	−406.892			−0.982831
$415$	241.418	−	324.348i	0.581730	−	0.781561i
$416$	−3.66553	+	2.11629i	−0.00881137	+	0.00508725i
$417$	61.0010	−	35.2189i	0.146285	−	0.0844579i
$418$	−133.371	+	231.005i	−0.319069	+	0.552644i
$419$		−	56.6448i		−	0.135190i	−0.997713	−	0.0675952i	$-0.978467\pi$
$419$		−	56.6448i		−	0.135190i	0.997713	−	0.0675952i	$-0.0215326\pi$
$420$		0			0
$421$	−220.350			−0.523396			−0.261698	−	0.965150i	$-0.584282\pi$
$421$	−220.350			−0.523396			−0.261698	+	0.965150i	$0.584282\pi$
$422$	−228.802	−	132.099i	−0.542186	−	0.313031i
$423$	−160.242	−	277.547i	−0.378822	−	0.656139i
$424$	−37.2959	−	64.5983i	−0.0879619	−	0.152355i
$425$	198.122	−	210.081i	0.466169	−	0.494308i
$426$		−	21.5191i		−	0.0505142i
$427$		0			0
$428$		−	5.74577i		−	0.0134247i
$429$	−4.84258	+	8.38760i	−0.0112881	+	0.0195515i
$430$	73.5646	+	170.495i	0.171080	+	0.396500i
$431$	136.661	+	236.704i	0.317079	+	0.549197i	0.979877	−	0.199601i	$-0.0639646\pi$
$431$	136.661	+	236.704i	0.317079	+	0.549197i	−0.662798	+	0.748798i	$0.730631\pi$
$432$	35.1220	−	60.8332i	0.0813010	−	0.140818i
$433$	−201.926			−0.466342			−0.233171	−	0.972436i	$-0.574910\pi$
$433$	−201.926			−0.466342			−0.233171	+	0.972436i	$0.574910\pi$
$434$		0			0
$435$	−260.684	−	30.4432i	−0.599273	−	0.0699843i
$436$	−85.2169	+	147.600i	−0.195452	+	0.338532i
$437$	274.537	+	475.512i	0.628231	+	1.08813i
$438$	128.572	−	74.2313i	0.293544	−	0.169478i
$439$	527.183	+	304.370i	1.20087	+	0.693325i	0.960749	−	0.277418i	$-0.0894786\pi$
$439$	527.183	+	304.370i	1.20087	+	0.693325i	0.240124	+	0.970742i	$0.422812\pi$
$440$	20.4625	−	175.219i	0.0465056	−	0.398226i
$441$		0			0
$442$			12.2223i			0.0276523i
$443$	−674.954	−	389.685i	−1.52360	−	0.879650i	−0.999610	−	0.0279237i	$-0.991110\pi$
$443$	−674.954	−	389.685i	−1.52360	−	0.879650i	−0.523988	−	0.851726i	$-0.675556\pi$
$444$	21.0976	−	12.1807i	0.0475171	−	0.0274340i
$445$	620.773	−	267.849i	1.39499	−	0.601907i
$446$	237.730	+	137.254i	0.533028	+	0.307744i
$447$	178.644			0.399652
$448$		0			0
$449$	−8.03323			−0.0178914			−0.00894569	−	0.999960i	$-0.502848\pi$
$449$	−8.03323			−0.0178914			−0.00894569	+	0.999960i	$0.502848\pi$
$450$	−203.796	−	192.194i	−0.452879	−	0.427099i
$451$	137.625	−	79.4580i	0.305156	−	0.176182i
$452$	−366.372	+	211.525i	−0.810557	+	0.467975i
$453$	57.1850	−	99.0474i	0.126236	−	0.218648i
$454$		−	497.459i		−	1.09573i
$455$		0			0
$456$	−44.3792			−0.0973228
$457$	−432.413	−	249.654i	−0.946200	−	0.546289i	−0.0543016	−	0.998525i	$-0.517293\pi$
$457$	−432.413	−	249.654i	−0.946200	−	0.546289i	−0.891898	+	0.452236i	$0.850627\pi$
$458$	−133.083	−	230.507i	−0.290575	−	0.503290i
$459$	−101.421	−	175.666i	−0.220960	−	0.382715i
$460$	−291.298	−	216.818i	−0.633256	−	0.471343i
$461$			690.386i			1.49758i	0.662805	+	0.748792i	$0.269366\pi$
$461$			690.386i			1.49758i	−0.662805	+	0.748792i	$0.730634\pi$
$462$		0			0
$463$		−	615.045i		−	1.32839i	−0.747559	−	0.664195i	$-0.768774\pi$
$463$		−	615.045i		−	1.32839i	0.747559	−	0.664195i	$-0.231226\pi$
$464$	−101.169	+	175.230i	−0.218037	+	0.377651i
$465$	−222.780	+	96.1242i	−0.479096	+	0.206719i
$466$	222.088	+	384.668i	0.476584	+	0.825467i
$467$	−23.9340	+	41.4549i	−0.0512506	+	0.0887686i	−0.890513	−	0.454959i	$-0.849654\pi$
$467$	−23.9340	+	41.4549i	−0.0512506	+	0.0887686i	0.839262	+	0.543727i	$0.182987\pi$
$468$	11.8566			0.0253347
$469$		0			0
$470$	33.1760	−	284.085i	0.0705873	−	0.604436i
$471$	105.929	−	183.474i	0.224902	−	0.389542i
$472$	111.843	+	193.718i	0.236956	+	0.410420i
$473$	283.687	−	163.787i	0.599762	−	0.346273i
$474$	−45.4030	−	26.2134i	−0.0957869	−	0.0553026i
$475$	−87.1025	+	367.841i	−0.183374	+	0.774403i
$476$		0			0
$477$			208.952i			0.438054i
$478$	411.844	+	237.778i	0.861599	+	0.497444i
$479$	−116.614	+	67.3269i	−0.243452	+	0.140557i	−0.616762	−	0.787149i	$-0.711556\pi$
$479$	−116.614	+	67.3269i	−0.243452	+	0.140557i	0.373310	+	0.927707i	$0.378223\pi$
$480$	26.9487	−	11.6277i	0.0561432	−	0.0242245i
$481$	7.60619	+	4.39143i	0.0158133	+	0.00912980i
$482$	540.971			1.12235
$483$		0			0
$484$	−69.2054			−0.142986
$485$	−272.920	+	366.672i	−0.562722	+	0.756025i
$486$	−261.037	+	150.710i	−0.537113	+	0.310103i
$487$	−386.964	+	223.414i	−0.794588	+	0.458755i	−0.841575	−	0.540140i	$-0.818371\pi$
$487$	−386.964	+	223.414i	−0.794588	+	0.458755i	0.0469875	+	0.998895i	$0.485038\pi$
$488$	73.9110	−	128.018i	0.151457	−	0.262331i
$489$			101.560i			0.207690i
$490$		0			0
$491$	−119.125			−0.242617			−0.121309	−	0.992615i	$-0.538709\pi$
$491$	−119.125			−0.242617			−0.121309	+	0.992615i	$0.538709\pi$
$492$	22.8975	+	13.2199i	0.0465395	+	0.0268696i
$493$	292.143	+	506.007i	0.592582	+	1.02638i
$494$	−7.99988	−	13.8562i	−0.0161941	−	0.0280490i
$495$	−295.060	+	396.417i	−0.596081	+	0.800843i
$496$			187.056i			0.377130i
$497$		0			0
$498$		−	118.673i		−	0.238298i
$499$	−42.1210	+	72.9558i	−0.0844109	+	0.146204i	−0.905140	−	0.425114i	$-0.860234\pi$
$499$	−42.1210	+	72.9558i	−0.0844109	+	0.146204i	0.820729	+	0.571318i	$0.193568\pi$
$500$	−43.4858	−	246.189i	−0.0869715	−	0.492378i
$501$	50.4180	+	87.3265i	0.100635	+	0.174304i
$502$	−213.597	+	369.961i	−0.425492	+	0.736973i
$503$	388.428			0.772223			0.386111	−	0.922452i	$-0.373818\pi$
$503$	388.428			0.772223			0.386111	+	0.922452i	$0.373818\pi$
$504$		0			0
$505$	−51.0436	+	437.084i	−0.101076	+	0.865513i
$506$	−320.300	+	554.776i	−0.633004	+	1.09640i
$507$	87.3943	+	151.371i	0.172375	+	0.298563i
$508$	−90.4883	+	52.2434i	−0.178127	+	0.102841i
$509$	−68.8518	−	39.7516i	−0.135269	−	0.0780975i	0.430838	−	0.902429i	$-0.358218\pi$
$509$	−68.8518	−	39.7516i	−0.135269	−	0.0780975i	−0.566107	+	0.824332i	$0.691551\pi$
$510$	9.83093	−	84.1818i	0.0192763	−	0.165062i
$511$		0			0
$512$		−	22.6274i		−	0.0441942i
$513$	229.957	+	132.766i	0.448260	+	0.258803i
$514$	−250.680	+	144.730i	−0.487703	+	0.281576i
$515$	223.035	+	516.912i	0.433078	+	1.00371i
$516$	47.1986	+	27.2501i	0.0914701	+	0.0528103i
$517$	−504.561			−0.975939
$518$		0			0
$519$	64.1885			0.123677
$520$	8.48828	+	6.31797i	0.0163236	+	0.0121499i
$521$	−69.7252	+	40.2559i	−0.133830	+	0.0772666i	−0.565420	−	0.824803i	$-0.691286\pi$
$521$	−69.7252	+	40.2559i	−0.133830	+	0.0772666i	0.431590	+	0.902070i	$0.357953\pi$
$522$	490.868	−	283.403i	0.940359	−	0.542917i
$523$	406.182	−	703.527i	0.776638	−	1.34518i	−0.157231	−	0.987562i	$-0.550257\pi$
$523$	406.182	−	703.527i	0.776638	−	1.34518i	0.933869	−	0.357615i	$-0.116410\pi$
$524$		−	187.833i		−	0.358461i
$525$		0			0
$526$	−137.788			−0.261955
$527$	467.789	+	270.078i	0.887646	+	0.512483i
$528$	−25.8884	−	44.8401i	−0.0490311	−	0.0849244i
$529$	394.822	+	683.851i	0.746355	+	1.29272i
$530$	−111.343	+	149.590i	−0.210081	+	0.282246i
$531$		−	626.608i		−	1.18005i
$532$		0			0
$533$			9.53214i			0.0178839i
$534$	99.2176	−	171.850i	0.185801	−	0.321816i
$535$	−13.1891	+	5.69078i	−0.0246525	+	0.0106370i
$536$	−49.0745	−	84.9995i	−0.0915569	−	0.158581i
$537$	116.336	−	201.500i	0.216641	−	0.375233i
$538$	−136.532			−0.253777
$539$		0			0
$540$	−174.425	−	20.3697i	−0.323009	−	0.0377217i
$541$	−141.664	+	245.370i	−0.261857	+	0.453549i	−0.966735	−	0.255779i	$-0.917668\pi$
$541$	−141.664	+	245.370i	−0.261857	+	0.453549i	0.704879	+	0.709328i	$0.251001\pi$
$542$	59.1190	+	102.397i	0.109076	+	0.188924i
$543$	−295.882	+	170.828i	−0.544903	+	0.314600i
$544$	−56.5865	−	32.6703i	−0.104019	−	0.0600556i
$545$	423.208	+	49.4231i	0.776529	+	0.0906847i
$546$		0			0
$547$			51.6110i			0.0943529i	0.998887	+	0.0471764i	$0.0150223\pi$
$547$			51.6110i			0.0943529i	−0.998887	+	0.0471764i	$0.984978\pi$
$548$	202.369	+	116.838i	0.369287	+	0.213208i
$549$	−358.613	+	207.045i	−0.653211	+	0.377131i
$550$	−422.472	+	126.572i	−0.768132	+	0.230131i
$551$	−662.393	−	382.433i	−1.20217	−	0.694070i
$552$	−106.580			−0.193080
$553$		0			0
$554$	545.510			0.984675
$555$	−48.8558	−	36.3642i	−0.0880284	−	0.0655211i
$556$	−117.571	+	67.8796i	−0.211458	+	0.122086i
$557$	204.171	−	117.878i	0.366555	−	0.211631i	−0.305397	−	0.952225i	$-0.598789\pi$
$557$	204.171	−	117.878i	0.366555	−	0.211631i	0.671953	+	0.740594i	$0.265456\pi$
$558$	261.998	−	453.794i	0.469530	−	0.813251i
$559$			19.6486i			0.0351496i
$560$		0			0
$561$	−149.515			−0.266514
$562$	298.175	+	172.151i	0.530561	+	0.306319i
$563$	−132.816	−	230.044i	−0.235907	−	0.408604i	0.723629	−	0.690190i	$-0.242473\pi$
$563$	−132.816	−	230.044i	−0.235907	−	0.408604i	−0.959536	+	0.281586i	$0.909140\pi$
$564$	−41.9732	−	72.6997i	−0.0744205	−	0.128900i
$565$	848.408	+	631.484i	1.50161	+	1.11767i
$566$			145.425i			0.256934i
$567$		0			0
$568$			41.4750i			0.0730193i
$569$	13.0381	−	22.5826i	0.0229141	−	0.0396883i	−0.854341	−	0.519713i	$-0.826039\pi$
$569$	13.0381	−	22.5826i	0.0229141	−	0.0396883i	0.877255	+	0.480025i	$0.159372\pi$
$570$	43.9544	+	101.870i	0.0771130	+	0.178719i
$571$	−147.312	−	255.152i	−0.257989	−	0.446851i	0.707714	−	0.706499i	$-0.249727\pi$
$571$	−147.312	−	255.152i	−0.257989	−	0.446851i	−0.965703	+	0.259649i	$0.916393\pi$
$572$	9.33340	−	16.1659i	0.0163171	−	0.0282621i
$573$	−68.7313			−0.119950
$574$		0			0
$575$	−209.183	+	883.399i	−0.363797	+	1.53635i
$576$	−31.6928	+	54.8935i	−0.0550222	+	0.0953013i
$577$	−287.549	−	498.049i	−0.498351	−	0.863170i	0.501647	−	0.865072i	$-0.332728\pi$
$577$	−287.549	−	498.049i	−0.498351	−	0.863170i	−0.999998	+	0.00190285i	$0.999394\pi$
$578$	190.548	−	110.013i	0.329668	−	0.190334i
$579$	−227.773	−	131.505i	−0.393389	−	0.227124i
$580$	502.431	+	58.6750i	0.866261	+	0.101164i
$581$		0			0
$582$			134.158i			0.230512i
$583$	284.895	+	164.484i	0.488671	+	0.282134i
$584$	−247.805	+	143.070i	−0.424324	+	0.244984i
$585$	−11.7432	−	27.2162i	−0.0200738	−	0.0465235i
$586$	539.635	+	311.558i	0.920878	+	0.531669i
$587$	−509.360			−0.867734			−0.433867	−	0.900977i	$-0.642851\pi$
$587$	−509.360			−0.867734			−0.433867	+	0.900977i	$0.642851\pi$
$588$		0			0
$589$	−707.098			−1.20051
$590$	333.896	−	448.594i	0.565926	−	0.760329i
$591$	−171.941	+	99.2704i	−0.290933	+	0.167970i
$592$	−40.6627	+	23.4766i	−0.0686869	+	0.0396564i
$593$	−107.373	+	185.975i	−0.181067	+	0.313618i	−0.942244	−	0.334926i	$-0.891289\pi$
$593$	−107.373	+	185.975i	−0.181067	+	0.313618i	0.761177	+	0.648544i	$0.224622\pi$
$594$			309.794i			0.521539i
$595$		0			0
$596$	−344.312			−0.577704
$597$	202.981	+	117.191i	0.340002	+	0.196300i
$598$	−19.2123	−	33.2767i	−0.0321276	−	0.0556467i
$599$	477.250	+	826.621i	0.796744	+	1.38000i	0.921726	+	0.387842i	$0.126779\pi$
$599$	477.250	+	826.621i	0.796744	+	1.38000i	−0.124982	+	0.992159i	$0.539887\pi$
$600$	−53.3816	−	50.3428i	−0.0889693	−	0.0839047i
$601$		−	851.298i		−	1.41647i	−0.705977	−	0.708234i	$-0.749492\pi$
$601$		−	851.298i		−	1.41647i	0.705977	−	0.708234i	$-0.250508\pi$
$602$		0			0
$603$			274.942i			0.455957i
$604$	−110.216	+	190.900i	−0.182477	+	0.316059i
$605$	68.5430	+	158.857i	0.113294	+	0.262574i
$606$	64.5786	+	111.853i	0.106565	+	0.184577i
$607$	−525.284	+	909.818i	−0.865377	+	1.49888i	0.00129613	+	0.999999i	$0.499587\pi$
$607$	−525.284	+	909.818i	−0.865377	+	1.49888i	−0.866673	+	0.498877i	$0.833746\pi$
$608$	85.5347			0.140682
$609$		0			0
$610$	−367.061	−	42.8661i	−0.601739	−	0.0702723i
$611$	15.1323	−	26.2100i	0.0247665	−	0.0428968i
$612$	91.5184	+	158.514i	0.149540	+	0.259011i
$613$	−876.517	+	506.057i	−1.42988	+	0.825542i	−0.997111	−	0.0759624i	$-0.975797\pi$
$613$	−876.517	+	506.057i	−1.42988	+	0.825542i	−0.432770	+	0.901504i	$0.642464\pi$
$614$	302.747	+	174.791i	0.493073	+	0.284676i
$615$	7.66710	−	65.6531i	0.0124668	−	0.106753i
$616$		0			0
$617$			706.409i			1.14491i	0.819937	+	0.572454i	$0.194009\pi$
$617$			706.409i			1.14491i	−0.819937	+	0.572454i	$0.805991\pi$
$618$	143.098	+	82.6176i	0.231550	+	0.133685i
$619$	−681.409	+	393.412i	−1.10082	+	0.635560i	−0.936437	−	0.350836i	$-0.885897\pi$
$619$	−681.409	+	393.412i	−1.10082	+	0.635560i	−0.164385	+	0.986396i	$0.552564\pi$
$620$	429.377	−	185.266i	0.692543	−	0.298816i
$621$	552.261	+	318.848i	0.889309	+	0.513443i
$622$	602.765			0.969076
$623$		0			0
$624$	3.10569			0.00497707
$625$	−522.043	+	343.652i	−0.835268	+	0.549842i
$626$	−164.084	+	94.7339i	−0.262115	+	0.151332i
$627$	169.502	−	97.8617i	0.270337	−	0.156079i
$628$	−204.163	+	353.621i	−0.325101	+	0.563091i
$629$			135.585i			0.215557i
$630$		0			0
$631$	−218.755			−0.346680			−0.173340	−	0.984862i	$-0.555456\pi$
$631$	−218.755			−0.346680			−0.173340	+	0.984862i	$0.555456\pi$
$632$	87.5079	+	50.5227i	0.138462	+	0.0799410i
$633$	96.9287	+	167.885i	0.153126	+	0.265222i
$634$	227.664	+	394.326i	0.359092	+	0.621966i
$635$	209.544	+	155.967i	0.329990	+	0.245618i
$636$			54.7322i			0.0860569i
$637$		0			0
$638$		−	892.363i		−	1.39869i
$639$	58.0914	−	100.617i	0.0909098	−	0.157460i
$640$	−51.9399	+	22.4108i	−0.0811561	+	0.0350169i
$641$	304.336	+	527.125i	0.474783	+	0.822348i	0.999583	−	0.0288778i	$-0.00919336\pi$
$641$	304.336	+	527.125i	0.474783	+	0.822348i	−0.524800	+	0.851225i	$0.675860\pi$
$642$	−2.10800	+	3.65116i	−0.00328349	+	0.00568717i
$643$	−1184.38			−1.84196			−0.920978	−	0.389614i	$-0.872608\pi$
$643$	−1184.38			−1.84196			−0.920978	+	0.389614i	$0.872608\pi$
$644$		0			0
$645$	15.8042	−	135.331i	0.0245027	−	0.209815i
$646$	123.498	−	213.905i	0.191173	−	0.331122i
$647$	113.802	+	197.111i	0.175892	+	0.304653i	0.940470	−	0.339878i	$-0.110386\pi$
$647$	113.802	+	197.111i	0.175892	+	0.304653i	−0.764578	+	0.644531i	$0.777052\pi$
$648$	130.033	−	75.0748i	0.200669	−	0.115856i
$649$	−854.347	−	493.258i	−1.31641	−	0.760027i
$650$	6.09550	−	25.7418i	0.00937769	−	0.0396028i
$651$		0			0
$652$		−	195.743i		−	0.300220i
$653$	199.761	+	115.332i	0.305912	+	0.176619i	0.645096	−	0.764102i	$-0.276817\pi$
$653$	199.761	+	115.332i	0.305912	+	0.176619i	−0.339183	+	0.940720i	$0.610151\pi$
$654$	108.303	−	62.5285i	0.165600	−	0.0956093i
$655$	−431.160	+	186.036i	−0.658260	+	0.284024i
$656$	−44.1316	−	25.4794i	−0.0672738	−	0.0388406i
$657$	801.559			1.22003
$658$		0			0
$659$	726.539			1.10249			0.551244	−	0.834344i	$-0.314153\pi$
$659$	726.539			1.10249			0.551244	+	0.834344i	$0.314153\pi$
$660$	−77.2871	+	103.836i	−0.117102	+	0.157328i
$661$	214.930	−	124.090i	0.325159	−	0.187731i	−0.328531	−	0.944493i	$-0.606553\pi$
$661$	214.930	−	124.090i	0.325159	−	0.187731i	0.653690	+	0.756763i	$0.273220\pi$
$662$	287.576	−	166.032i	0.434405	−	0.250804i
$663$	4.48411	−	7.76670i	0.00676336	−	0.0117145i
$664$			228.725i			0.344465i
$665$		0			0
$666$	131.529			0.197491
$667$	−1590.79	−	918.442i	−2.38499	−	1.37697i
$668$	−97.1736	−	168.310i	−0.145469	−	0.251960i
$669$	−100.711	−	174.436i	−0.150539	−	0.260742i
$670$	−146.507	+	196.833i	−0.218667	+	0.293781i
$671$			651.933i			0.971584i
$672$		0			0
$673$		−	835.990i		−	1.24218i	−0.783738	−	0.621092i	$-0.786689\pi$
$673$		−	835.990i		−	1.24218i	0.783738	−	0.621092i	$-0.213311\pi$
$674$	153.941	−	266.634i	0.228400	−	0.395600i
$675$	125.998	+	420.557i	0.186664	+	0.623047i
$676$	−168.440	−	291.747i	−0.249172	−	0.431578i
$677$	−189.063	+	327.468i	−0.279267	+	0.483704i	−0.971203	−	0.238255i	$-0.923425\pi$
$677$	−189.063	+	327.468i	−0.279267	+	0.483704i	0.691936	+	0.721959i	$0.256758\pi$
$678$	310.416			0.457840
$679$		0			0
$680$	−18.9477	+	162.249i	−0.0278643	+	0.238601i
$681$	−182.507	+	316.112i	−0.267999	+	0.464188i
$682$	−412.483	−	714.441i	−0.604813	−	1.04757i
$683$	167.429	−	96.6649i	0.245137	−	0.141530i	−0.372399	−	0.928073i	$-0.621465\pi$
$683$	167.429	−	96.6649i	0.245137	−	0.141530i	0.617535	+	0.786543i	$0.288131\pi$
$684$	−207.505	−	119.803i	−0.303370	−	0.175151i
$685$	67.7623	−	580.246i	0.0989231	−	0.847074i
$686$		0			0
$687$			195.302i			0.284282i
$688$	−90.9686	−	52.5207i	−0.132222	−	0.0763383i
$689$	−17.0886	+	9.86613i	−0.0248021	+	0.0143195i
$690$	105.560	+	244.648i	0.152985	+	0.354563i
$691$	−501.502	−	289.542i	−0.725763	−	0.419019i	0.0911074	−	0.995841i	$-0.470959\pi$
$691$	−501.502	−	289.542i	−0.725763	−	0.419019i	−0.816870	+	0.576822i	$0.804293\pi$
$692$	−123.714			−0.178778
$693$		0			0
$694$	−263.371			−0.379497
$695$	272.259	+	202.647i	0.391740	+	0.291579i
$696$	128.576	−	74.2336i	0.184736	−	0.106657i
$697$	−127.438	+	73.5761i	−0.182837	+	0.105561i
$698$	57.7966	−	100.107i	0.0828032	−	0.143419i
$699$		−	325.917i		−	0.466262i
$700$		0			0
$701$	−516.871			−0.737334			−0.368667	−	0.929562i	$-0.620186\pi$
$701$	−516.871			−0.737334			−0.368667	+	0.929562i	$0.620186\pi$
$702$	−16.0926	−	9.29107i	−0.0229239	−	0.0132351i
$703$	−88.7447	−	153.710i	−0.126237	−	0.218649i
$704$	49.8963	+	86.4230i	0.0708755	+	0.122760i
$705$	−125.306	+	168.351i	−0.177740	+	0.238796i
$706$			152.645i			0.216211i
$707$		0			0
$708$		−	164.132i		−	0.231824i
$709$	−29.9375	+	51.8533i	−0.0422250	+	0.0731359i	−0.886366	−	0.462986i	$-0.846778\pi$
$709$	−29.9375	+	51.8533i	−0.0422250	+	0.0731359i	0.844141	+	0.536122i	$0.180111\pi$
$710$	95.2034	−	41.0780i	0.134089	−	0.0578563i
$711$	−141.528	−	245.134i	−0.199055	−	0.344773i
$712$	−191.228	+	331.216i	−0.268579	+	0.465192i
$713$	−1698.15			−2.38170
$714$		0			0
$715$	−46.3520	−	5.41308i	−0.0648279	−	0.00757074i
$716$	−224.221	+	388.363i	−0.313158	+	0.542406i
$717$	−174.472	−	302.194i	−0.243336	−	0.421470i
$718$	−739.573	+	426.993i	−1.03005	+	0.594698i
$719$	1072.53	+	619.228i	1.49170	+	0.861235i	0.999955	−	0.00950279i	$-0.00302488\pi$
$719$	1072.53	+	619.228i	1.49170	+	0.861235i	0.491748	+	0.870738i	$0.336358\pi$
$720$	157.394	+	18.3808i	0.218603	+	0.0255289i
$721$		0			0
$722$		−	187.199i		−	0.259278i
$723$	−343.761	−	198.471i	−0.475465	−	0.274510i
$724$	570.271	−	329.246i	0.787668	−	0.454760i
$725$	−362.937	−	1211.41i	−0.500603	−	1.67092i
$726$	43.9767	+	25.3900i	0.0605740	+	0.0349724i
$727$	387.549			0.533080			0.266540	−	0.963824i	$-0.414120\pi$
$727$	387.549			0.533080			0.266540	+	0.963824i	$0.414120\pi$
$728$		0			0
$729$	−256.605			−0.351995
$730$	573.843	+	427.121i	0.786086	+	0.585098i
$731$	−262.687	+	151.663i	−0.359353	+	0.207473i
$732$	−93.9339	+	54.2327i	−0.128325	+	0.0740884i
$733$	526.551	−	912.012i	0.718350	−	1.24422i	−0.243303	−	0.969950i	$-0.578231\pi$
$733$	526.551	−	912.012i	0.718350	−	1.24422i	0.961653	−	0.274269i	$-0.0884357\pi$
$734$		−	768.667i		−	1.04723i
$735$		0			0
$736$	205.418			0.279101
$737$	374.869	+	216.431i	0.508642	+	0.293665i
$738$	71.3748	+	123.625i	0.0967138	+	0.167513i
$739$	−123.560	−	214.013i	−0.167199	−	0.289598i	0.770235	−	0.637760i	$-0.220139\pi$
$739$	−123.560	−	214.013i	−0.167199	−	0.289598i	−0.937434	+	0.348163i	$0.886806\pi$
$740$	94.1626	+	70.0869i	0.127247	+	0.0947120i
$741$			11.7399i			0.0158434i
$742$		0			0
$743$			189.686i			0.255298i	0.991819	+	0.127649i	$0.0407431\pi$
$743$			189.686i			0.255298i	−0.991819	+	0.127649i	$0.959257\pi$
$744$	68.6269	−	118.865i	0.0922405	−	0.159765i
$745$	341.016	+	790.348i	0.457740	+	1.06087i
$746$	−58.8952	−	102.010i	−0.0789480	−	0.136742i
$747$	320.360	−	554.880i	0.428862	−	0.742811i
$748$	288.168			0.385252
$749$		0			0
$750$	−62.6883	+	172.395i	−0.0835844	+	0.229860i
$751$	400.319	−	693.373i	0.533048	−	0.923267i	−0.466207	−	0.884676i	$-0.654380\pi$
$751$	400.319	−	693.373i	0.533048	−	0.923267i	0.999255	−	0.0385908i	$-0.0122869\pi$
$752$	80.8974	+	140.118i	0.107576	+	0.186328i
$753$	271.461	−	156.728i	0.360506	−	0.208138i
$754$	46.3548	+	26.7630i	0.0614785	+	0.0354946i
$755$	547.361	+	63.9219i	0.724981	+	0.0846648i
$756$		0			0
$757$			809.069i			1.06878i	0.845237	+	0.534392i	$0.179459\pi$
$757$			809.069i			1.06878i	−0.845237	+	0.534392i	$0.820541\pi$
$758$	−37.2823	−	21.5249i	−0.0491851	−	0.0283970i
$759$	407.071	−	235.023i	0.536325	−	0.309648i
$760$	−84.7160	−	196.340i	−0.111468	−	0.258342i
$761$	213.647	+	123.349i	0.280745	+	0.162088i	0.633761	−	0.773529i	$-0.281510\pi$
$761$	213.647	+	123.349i	0.280745	+	0.162088i	−0.353016	+	0.935617i	$0.614844\pi$
$762$	76.6680			0.100614
$763$		0			0
$764$	132.470			0.173390
$765$	273.218	−	367.072i	0.357148	−	0.479833i
$766$	−361.933	+	208.962i	−0.472498	+	0.272797i
$767$	51.2456	−	29.5867i	0.0668131	−	0.0385746i
$768$	−8.30151	+	14.3786i	−0.0108093	+	0.0187222i
$769$			851.221i			1.10692i	0.832876	+	0.553460i	$0.186693\pi$
$769$			851.221i			1.10692i	−0.832876	+	0.553460i	$0.813307\pi$
$770$		0			0
$771$	212.393			0.275478
$772$	439.000	+	253.457i	0.568652	+	0.328312i
$773$	−445.532	−	771.684i	−0.576368	−	0.998298i	−0.995892	−	0.0905537i	$-0.971136\pi$
$773$	−445.532	−	771.684i	−0.576368	−	0.998298i	0.419524	−	0.907744i	$-0.362197\pi$
$774$	147.125	+	254.828i	0.190084	+	0.329235i
$775$	−850.534	−	802.116i	−1.09746	−	1.03499i
$776$		−	258.571i		−	0.333210i
$777$		0			0
$778$		−	606.380i		−	0.779409i
$779$	96.3156	−	166.823i	0.123640	−	0.214151i
$780$	−3.07597	−	7.12893i	−0.00394355	−	0.00913966i
$781$	−91.4576	−	158.409i	−0.117103	−	0.202829i
$782$	296.590	−	513.709i	0.379271	−	0.656916i
$783$	−888.317			−1.13450
$784$		0			0
$785$	1013.93	+	118.408i	1.29162	+	0.150839i
$786$	−68.9120	+	119.359i	−0.0876743	+	0.151856i
$787$	245.676	+	425.522i	0.312167	+	0.540689i	0.978831	−	0.204669i	$-0.0656118\pi$
$787$	245.676	+	425.522i	0.312167	+	0.540689i	−0.666664	+	0.745358i	$0.732278\pi$
$788$	331.393	−	191.330i	0.420549	−	0.242804i
$789$	87.5578	+	50.5515i	0.110973	+	0.0640703i
$790$	29.3016	−	250.908i	0.0370906	−	0.317605i
$791$		0			0
$792$		−	279.547i		−	0.352963i
$793$	−33.8654	−	19.5522i	−0.0427054	−	0.0246560i
$794$	392.878	−	226.828i	0.494808	−	0.285678i
$795$	125.635	−	54.2083i	0.158031	−	0.0681866i
$796$	−391.218	−	225.870i	−0.491480	−	0.283756i
$797$	68.9206			0.0864751			0.0432375	−	0.999065i	$-0.486233\pi$
$797$	68.9206			0.0864751			0.0432375	+	0.999065i	$0.486233\pi$
$798$		0			0
$799$	467.210			0.584744
$800$	102.886	+	97.0287i	0.128607	+	0.121286i
$801$	927.828	−	535.682i	1.15834	−	0.668766i
$802$	291.132	−	168.085i	0.363007	−	0.209582i
$803$	630.977	−	1092.88i	0.785774	−	1.36100i
$804$			72.0175i			0.0895740i
$805$		0			0
$806$	49.4833			0.0613936
$807$	86.7595	+	50.0906i	0.107509	+	0.0620702i
$808$	−124.466	−	215.582i	−0.154042	−	0.266809i
$809$	19.0763	+	33.0411i	0.0235801	+	0.0408419i	0.877575	−	0.479440i	$-0.159160\pi$
$809$	19.0763	+	33.0411i	0.0235801	+	0.0408419i	−0.853995	+	0.520282i	$0.825827\pi$
$810$	−301.119	−	224.128i	−0.371752	−	0.276701i
$811$			763.676i			0.941648i	0.882227	+	0.470824i	$0.156043\pi$
$811$			763.676i			0.941648i	−0.882227	+	0.470824i	$0.843957\pi$
$812$		0			0
$813$		−	86.7579i		−	0.106713i
$814$	103.538	−	179.333i	0.127196	−	0.220310i
$815$	−449.317	+	193.870i	−0.551309	+	0.237877i
$816$	23.9720	+	41.5208i	0.0293775	+	0.0508833i
$817$	198.535	−	343.873i	0.243005	−	0.420898i
$818$	−280.156			−0.342489
$819$		0			0
$820$	−14.7773	+	126.537i	−0.0180211	+	0.154314i
$821$	204.439	−	354.099i	0.249013	−	0.431302i	−0.714240	−	0.699901i	$-0.753227\pi$
$821$	204.439	−	354.099i	0.249013	−	0.431302i	0.963252	+	0.268599i	$0.0865606\pi$
$822$	−85.7306	−	148.490i	−0.104295	−	0.180644i
$823$	133.113	−	76.8529i	0.161741	−	0.0933814i	−0.416945	−	0.908932i	$-0.636899\pi$
$823$	133.113	−	76.8529i	0.161741	−	0.0933814i	0.578686	+	0.815551i	$0.303566\pi$
$824$	−275.801	−	159.234i	−0.334710	−	0.193245i
$825$	314.898	+	74.5657i	0.381694	+	0.0903827i
$826$		0			0
$827$		−	571.706i		−	0.691301i	−0.938363	−	0.345650i	$-0.887658\pi$
$827$		−	571.706i		−	0.691301i	0.938363	−	0.345650i	$-0.112342\pi$
$828$	−498.339	−	287.716i	−0.601859	−	0.347483i
$829$	1099.69	−	634.905i	1.32652	−	0.765869i	0.341763	−	0.939786i	$-0.388976\pi$
$829$	1099.69	−	634.905i	1.32652	−	0.765869i	0.984760	+	0.173918i	$0.0556426\pi$
$830$	525.024	−	226.535i	0.632559	−	0.272934i
$831$	−346.646	−	200.136i	−0.417143	−	0.240838i
$832$	−5.98578			−0.00719445
$833$		0			0
$834$	99.6142			0.119442
$835$	−290.101	+	389.755i	−0.347427	+	0.466772i
$836$	−326.690	+	188.615i	−0.390778	+	0.225616i
$837$	−711.202	+	410.612i	−0.849703	+	0.490576i
$838$	40.0539	−	69.3754i	0.0477970	−	0.0827869i
$839$			732.075i			0.872556i	0.899812	+	0.436278i	$0.143704\pi$
$839$			732.075i			0.872556i	−0.899812	+	0.436278i	$0.856296\pi$
$840$		0			0
$841$	1717.80			2.04257
$842$	−269.872	−	155.811i	−0.320513	−	0.185048i
$843$	−126.317	−	218.788i	−0.149843	−	0.259535i
$844$	−186.816	−	323.575i	−0.221346	−	0.383383i
$845$	−502.860	+	675.599i	−0.595101	+	0.799525i
$846$		−	453.232i		−	0.535735i
$847$		0			0
$848$		−	105.489i		−	0.124397i
$849$	53.3531	−	92.4103i	0.0628423	−	0.108846i
$850$	391.199	−	117.202i	0.460234	−	0.137885i
$851$	−213.127	−	369.147i	−0.250443	−	0.433780i
$852$	15.2163	−	26.3554i	0.0178595	−	0.0309335i
$853$	193.304			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$853$	193.304			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$854$		0			0
$855$	−69.4820	+	594.972i	−0.0812655	+	0.695873i
$856$	4.06287	−	7.03710i	0.00474635	−	0.00822092i
$857$	236.907	+	410.336i	0.276438	+	0.478805i	0.970497	−	0.241113i	$-0.0775126\pi$
$857$	236.907	+	410.336i	0.276438	+	0.478805i	−0.694059	+	0.719918i	$0.744179\pi$
$858$	−11.8619	+	6.84844i	−0.0138250	+	0.00798187i
$859$	760.044	+	438.811i	0.884801	+	0.510840i	0.872238	−	0.489081i	$-0.162668\pi$
$859$	760.044	+	438.811i	0.884801	+	0.510840i	0.0125624	+	0.999921i	$0.496001\pi$
$860$	−30.4604	+	260.831i	−0.0354191	+	0.303292i
$861$		0			0
$862$			386.536i			0.448417i
$863$	782.535	+	451.797i	0.906761	+	0.523519i	0.879388	−	0.476106i	$-0.157952\pi$
$863$	782.535	+	451.797i	0.906761	+	0.523519i	0.0273737	+	0.999625i	$0.491286\pi$
$864$	86.0311	−	49.6701i	0.0995730	−	0.0574885i
$865$	122.530	+	283.979i	0.141653	+	0.328299i
$866$	−247.308	−	142.783i	−0.285575	−	0.164877i
$867$	−161.446			−0.186212
$868$		0			0
$869$	−445.636			−0.512814
$870$	−297.744	−	221.616i	−0.342235	−	0.254731i
$871$	−22.4855	+	12.9820i	−0.0258157	+	0.0149047i
$872$	−208.738	+	120.515i	−0.239378	+	0.138205i
$873$	−362.164	+	627.286i	−0.414850	+	0.718541i
$874$			776.508i			0.888453i
$875$		0			0
$876$	209.958			0.239678
$877$	−1129.07	−	651.867i	−1.28742	−	0.743292i	−0.309226	−	0.950988i	$-0.600070\pi$
$877$	−1129.07	−	651.867i	−1.28742	−	0.743292i	−0.978193	+	0.207696i	$0.933403\pi$
$878$	430.443	+	745.550i	0.490255	+	0.849146i
$879$	−228.608	−	395.961i	−0.260077	−	0.450467i
$880$	148.960	−	200.130i	0.169273	−	0.227420i
$881$		−	796.338i		−	0.903902i	−0.892043	−	0.451951i	$-0.850728\pi$
$881$		−	796.338i		−	0.903902i	0.892043	−	0.451951i	$-0.149272\pi$
$882$		0			0
$883$		−	1253.73i		−	1.41985i	−0.704276	−	0.709927i	$-0.748728\pi$
$883$		−	1253.73i		−	1.41985i	0.704276	−	0.709927i	$-0.251272\pi$
$884$	−8.64249	+	14.9692i	−0.00977657	+	0.0169335i
$885$	−376.755	+	162.561i	−0.425712	+	0.183684i
$886$	−551.097	−	954.529i	−0.622006	−	1.07735i
$887$	−489.613	+	848.034i	−0.551987	+	0.956070i	0.446144	+	0.894961i	$0.352797\pi$
$887$	−489.613	+	848.034i	−0.551987	+	0.956070i	−0.998131	+	0.0611090i	$0.980536\pi$
$888$	34.4522			0.0387976
$889$		0			0
$890$	949.686	+	110.906i	1.06706	+	0.124614i
$891$	−331.099	+	573.480i	−0.371604	+	0.643637i
$892$	194.106	+	336.202i	0.217608	+	0.376908i
$893$	−529.666	+	305.803i	−0.593132	+	0.342445i
$894$	218.794	+	126.321i	0.244736	+	0.141298i
$895$	1113.54	+	130.041i	1.24418	+	0.145298i
$896$		0			0
$897$			28.1943i			0.0314318i
$898$	−9.83866	−	5.68035i	−0.0109562	−	0.00632556i
$899$	2048.62	−	1182.77i	2.27877	−	1.31565i
$900$	−113.696	−	379.495i	−0.126329	−	0.421661i
$901$	−263.805	−	152.308i	−0.292792	−	0.169043i
$902$	224.741			0.249159
$903$		0			0
$904$	−598.282			−0.661817
$905$	−1320.58	−	982.930i	−1.45920	−	1.08611i
$906$	140.074	−	80.8718i	0.154607	−	0.0892625i
$907$	1429.61	−	825.386i	1.57620	−	0.910017i	0.580813	−	0.814037i	$-0.302735\pi$
$907$	1429.61	−	825.386i	1.57620	−	0.910017i	0.995383	−	0.0959807i	$-0.0305987\pi$
$908$	351.757	−	609.261i	0.387398	−	0.670992i
$909$			697.328i			0.767138i
$910$		0			0
$911$	−736.949			−0.808945			−0.404472	−	0.914550i	$-0.632545\pi$
$911$	−736.949			−0.808945			−0.404472	+	0.914550i	$0.632545\pi$
$912$	−54.3532	−	31.3808i	−0.0595978	−	0.0344088i
$913$	−504.367	−	873.589i	−0.552428	−	0.956833i
$914$	−353.064	−	611.525i	−0.386285	−	0.669064i
$915$	217.523	+	161.906i	0.237730	+	0.176946i
$916$		−	376.416i		−	0.410935i
$917$		0			0
$918$		−	286.862i		−	0.312485i
$919$	−432.226	+	748.637i	−0.470322	+	0.814621i	−0.999424	−	0.0339368i	$-0.989196\pi$
$919$	−432.226	+	748.637i	−0.470322	+	0.814621i	0.529102	+	0.848558i	$0.322529\pi$
$920$	−203.452	−	471.525i	−0.221143	−	0.512527i
$921$	−128.254	−	222.143i	−0.139255	−	0.241197i
$922$	−488.177	+	845.547i	−0.529476	+	0.917080i
$923$	10.9717			0.0118870
$924$		0			0
$925$	67.6190	−	285.561i	0.0731016	−	0.308714i
$926$	434.902	−	753.273i	0.469657	−	0.813470i
$927$	446.058	+	772.594i	0.481184	+	0.833435i
$928$	−247.813	+	143.075i	−0.267040	+	0.154175i
$929$	−515.059	−	297.370i	−0.554423	−	0.320096i	0.196481	−	0.980508i	$-0.437049\pi$
$929$	−515.059	−	297.370i	−0.554423	−	0.320096i	−0.750904	+	0.660411i	$0.770382\pi$
$930$	−340.818	−	39.8015i	−0.366471	−	0.0427973i
$931$		0			0
$932$			628.160i			0.673991i
$933$	−383.028	−	221.142i	−0.410534	−	0.237022i
$934$	−58.6261	+	33.8478i	−0.0627689	+	0.0362396i
$935$	−285.410	−	661.473i	−0.305251	−	0.707458i
$936$	14.5214	+	8.38391i	0.0155143	+	0.00895717i
$937$	−312.979			−0.334022			−0.167011	−	0.985955i	$-0.553412\pi$
$937$	−312.979			−0.334022			−0.167011	+	0.985955i	$0.553412\pi$
$938$		0			0
$939$	139.023			0.148055
$940$	241.511	−	324.473i	0.256926	−	0.345184i
$941$	−45.2375	+	26.1179i	−0.0480738	+	0.0277554i	−0.523844	−	0.851814i	$-0.675503\pi$
$941$	−45.2375	+	26.1179i	−0.0480738	+	0.0277554i	0.475770	+	0.879569i	$0.342169\pi$
$942$	259.472	−	149.806i	0.275448	−	0.159030i
$943$	231.309	−	400.639i	0.245291	−	0.424856i
$944$			316.341i			0.335107i
$945$		0			0
$946$	463.260			0.489704
$947$	487.134	+	281.247i	0.514397	+	0.296987i	0.734639	−	0.678458i	$-0.237351\pi$
$947$	487.134	+	281.247i	0.514397	+	0.296987i	−0.220242	+	0.975445i	$0.570685\pi$
$948$	−37.0714	−	64.2095i	−0.0391048	−	0.0677315i
$949$	37.8474	+	65.5536i	0.0398813	+	0.0690765i
$950$	−366.781	+	388.921i	−0.386086	+	0.409391i
$951$		−	334.101i		−	0.351315i
$952$		0			0
$953$		−	786.616i		−	0.825411i	−0.910865	−	0.412705i	$-0.864584\pi$
$953$		−	786.616i		−	0.825411i	0.910865	−	0.412705i	$-0.135416\pi$
$954$	−147.751	+	255.913i	−0.154876	+	0.268252i
$955$	−131.202	−	304.077i	−0.137384	−	0.318405i
$956$	336.269	+	582.436i	0.351746	+	0.609243i
$957$	−327.389	+	567.054i	−0.342099	+	0.592533i
$958$	−190.429			−0.198778
$959$		0			0
$960$	41.2274	+	4.81462i	0.0429452	+	0.00501523i
$961$	612.939	−	1061.64i	0.637814	−	1.10473i
$962$	6.21043	+	10.7568i	0.00645574	+	0.0111817i
$963$	−19.7129	+	11.3812i	−0.0204703	+	0.0118185i
$964$	662.551	+	382.524i	0.687294	+	0.396809i
$965$	146.997	−	1258.73i	0.152328	−	1.30438i
$966$		0			0
$967$			372.034i			0.384730i	0.981323	+	0.192365i	$0.0616157\pi$
$967$			372.034i			0.384730i	−0.981323	+	0.192365i	$0.938384\pi$
$968$	−84.7590	−	48.9356i	−0.0875609	−	0.0505533i
$969$	−156.954	+	90.6175i	−0.161975	+	0.0935165i
$970$	−593.534	+	256.096i	−0.611891	+	0.264016i
$971$	463.408	+	267.549i	0.477248	+	0.275539i	0.719269	−	0.694732i	$-0.244477\pi$
$971$	463.408	+	267.549i	0.477248	+	0.275539i	−0.242021	+	0.970271i	$0.577810\pi$
$972$	−426.272			−0.438551
$973$		0			0
$974$	−631.910			−0.648778
$975$	−13.3175	+	14.1214i	−0.0136590	+	0.0144835i
$976$	181.044	−	104.526i	0.185496	−	0.107096i
$977$	−696.209	+	401.956i	−0.712599	+	0.411419i	−0.812023	−	0.583626i	$-0.801633\pi$
$977$	−696.209	+	401.956i	−0.712599	+	0.411419i	0.0994238	+	0.995045i	$0.468300\pi$
$978$	−71.8140	+	124.385i	−0.0734294	+	0.127184i
$979$		−	1686.73i		−	1.72291i
$980$		0			0
$981$	675.191			0.688268
$982$	−145.898	−	84.2342i	−0.148572	−	0.0857782i
$983$	118.542	+	205.321i	0.120592	+	0.208872i	0.920001	−	0.391915i	$-0.128187\pi$
$983$	118.542	+	205.321i	0.120592	+	0.208872i	−0.799409	+	0.600787i	$0.794854\pi$
$984$	18.6957	+	32.3819i	0.0189997	+	0.0329084i
$985$	−767.407	−	571.194i	−0.779093	−	0.579893i
$986$			826.305i			0.838038i
$987$		0			0
$988$		−	22.6271i		−	0.0229019i
$989$	476.798	−	825.838i	0.482101	−	0.835024i
$990$	−641.683	+	276.871i	−0.648165	+	0.279668i
$991$	211.092	+	365.622i	0.213009	+	0.368942i	0.952655	−	0.304054i	$-0.0983403\pi$
$991$	211.092	+	365.622i	0.213009	+	0.368942i	−0.739646	+	0.672996i	$0.765007\pi$
$992$	−132.269	+	229.096i	−0.133335	+	0.230944i
$993$	−243.655			−0.245372
$994$		0			0
$995$	−130.997	+	1121.73i	−0.131656	+	1.12736i
$996$	83.9141	−	145.344i	0.0842511	−	0.145927i
$997$	−776.469	−	1344.88i	−0.778806	−	1.34893i	−0.932630	−	0.360833i	$-0.882492\pi$
$997$	−776.469	−	1344.88i	−0.778806	−	1.34893i	0.153825	−	0.988098i	$-0.450841\pi$
$998$	−103.175	+	59.5681i	−0.103382	+	0.0596875i
$999$	−178.519	−	103.068i	−0.178698	−	0.103171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.3.h.b.19.6		16
5.4	even	2	inner	490.3.h.b.19.3		16
7.2	even	3		490.3.d.a.489.6		16
7.3	odd	6	inner	490.3.h.b.129.3		16
7.4	even	3		70.3.h.a.59.2	yes	16
7.5	odd	6		490.3.d.a.489.3		16
7.6	odd	2		70.3.h.a.19.7	yes	16
21.11	odd	6		630.3.bc.a.199.6		16
21.20	even	2		630.3.bc.a.19.4		16
28.11	odd	6		560.3.br.b.129.6		16
28.27	even	2		560.3.br.b.369.3		16
35.4	even	6		70.3.h.a.59.7	yes	16
35.9	even	6		490.3.d.a.489.11		16
35.13	even	4		350.3.k.e.201.6		16
35.18	odd	12		350.3.k.e.101.6		16
35.19	odd	6		490.3.d.a.489.14		16
35.24	odd	6	inner	490.3.h.b.129.6		16
35.27	even	4		350.3.k.e.201.3		16
35.32	odd	12		350.3.k.e.101.3		16
35.34	odd	2		70.3.h.a.19.2	✓	16
105.74	odd	6		630.3.bc.a.199.4		16
105.104	even	2		630.3.bc.a.19.6		16
140.39	odd	6		560.3.br.b.129.3		16
140.139	even	2		560.3.br.b.369.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.h.a.19.2	✓	16	35.34	odd	2
70.3.h.a.19.7	yes	16	7.6	odd	2
70.3.h.a.59.2	yes	16	7.4	even	3
70.3.h.a.59.7	yes	16	35.4	even	6
350.3.k.e.101.3		16	35.32	odd	12
350.3.k.e.101.6		16	35.18	odd	12
350.3.k.e.201.3		16	35.27	even	4
350.3.k.e.201.6		16	35.13	even	4
490.3.d.a.489.3		16	7.5	odd	6
490.3.d.a.489.6		16	7.2	even	3
490.3.d.a.489.11		16	35.9	even	6
490.3.d.a.489.14		16	35.19	odd	6
490.3.h.b.19.3		16	5.4	even	2	inner
490.3.h.b.19.6		16	1.1	even	1	trivial
490.3.h.b.129.3		16	7.3	odd	6	inner
490.3.h.b.129.6		16	35.24	odd	6	inner
560.3.br.b.129.3		16	140.39	odd	6
560.3.br.b.129.6		16	28.11	odd	6
560.3.br.b.369.3		16	28.27	even	2
560.3.br.b.369.6		16	140.139	even	2
630.3.bc.a.19.4		16	21.20	even	2
630.3.bc.a.19.6		16	105.104	even	2
630.3.bc.a.199.4		16	105.74	odd	6
630.3.bc.a.199.6		16	21.11	odd	6

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	490.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(-0.518845 - 0.898665i) q^{3} +(1.00000 + 1.73205i) q^{4} +(2.98539 - 4.01091i) q^{5} -1.46751i q^{6} +2.82843i q^{8} +(3.96160 - 6.86169i) q^{9} +(6.49249 - 2.80135i) q^{10} +(-6.23704 - 10.8029i) q^{11} +(1.03769 - 1.79733i) q^{12} +0.748223 q^{13} +(-5.15342 - 0.601827i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(5.77534 + 10.0032i) q^{17} +(9.70390 - 5.60255i) q^{18} +(-13.0948 - 7.56027i) q^{19} +(9.93250 + 1.15994i) q^{20} -17.6410i q^{22} +(-31.4481 - 18.1566i) q^{23} +(2.54181 - 1.46751i) q^{24} +(-7.17486 - 23.9483i) q^{25} +(0.916382 + 0.529074i) q^{26} -17.5610 q^{27} +50.5846 q^{29} +(-5.88607 - 4.38111i) q^{30} +(40.4989 - 23.3820i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(-6.47211 + 11.2100i) q^{33} +16.3351i q^{34} +15.8464 q^{36} +(10.1657 + 5.86915i) q^{37} +(-10.6918 - 18.5188i) q^{38} +(-0.388211 - 0.672402i) q^{39} +(11.3446 + 8.44397i) q^{40} +12.7397i q^{41} +26.2604i q^{43} +(12.4741 - 21.6057i) q^{44} +(-15.6947 - 36.3745i) q^{45} +(-25.6773 - 44.4743i) q^{46} +(20.2244 - 35.0296i) q^{47} +4.15076 q^{48} +(8.14664 - 34.4040i) q^{50} +(5.99301 - 10.3802i) q^{51} +(0.748223 + 1.29596i) q^{52} +(-22.8390 + 13.1861i) q^{53} +(-21.5078 - 12.4175i) q^{54} +(-61.9494 - 7.23458i) q^{55} +15.6904i q^{57} +(61.9532 + 35.7687i) q^{58} +(68.4898 - 39.5426i) q^{59} +(-4.11103 - 9.52782i) q^{60} +(-45.2611 - 26.1315i) q^{61} +66.1344 q^{62} -8.00000 q^{64} +(2.23374 - 3.00106i) q^{65} +(-15.8534 + 9.15294i) q^{66} +(-30.0519 + 17.3504i) q^{67} +(-11.5507 + 20.0064i) q^{68} +37.6817i q^{69} +14.6636 q^{71} +(19.4078 + 11.2051i) q^{72} +(50.5830 + 87.6124i) q^{73} +(8.30023 + 14.3764i) q^{74} +(-17.7989 + 18.8732i) q^{75} -30.2411i q^{76} -1.09803i q^{78} +(17.8625 - 30.9387i) q^{79} +(7.92343 + 18.3635i) q^{80} +(-26.5430 - 45.9738i) q^{81} +(-9.00833 + 15.6029i) q^{82} +80.8664 q^{83} +(57.3636 + 6.69903i) q^{85} +(-18.5689 + 32.1623i) q^{86} +(-26.2455 - 45.4586i) q^{87} +(30.5551 - 17.6410i) q^{88} +(117.103 + 67.6093i) q^{89} +(6.49861 - 55.6473i) q^{90} -72.6263i q^{92} +(-42.0252 - 24.2633i) q^{93} +(49.5394 - 28.6016i) q^{94} +(-69.4166 + 29.9516i) q^{95} +(5.08362 + 2.93503i) q^{96} -91.4185 q^{97} -98.8347 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} + 6 q^{5} - 12 q^{9} - 24 q^{10} - 12 q^{11} - 28 q^{15} - 32 q^{16} + 12 q^{19} + 24 q^{24} - 42 q^{25} + 48 q^{26} - 136 q^{29} + 32 q^{30} - 84 q^{31} - 48 q^{36} + 312 q^{39} - 48 q^{40}+ \cdots + 176 q^{99}+O(q^{100}) \) 16 * q + 16 * q^4 + 6 * q^5 - 12 * q^9 - 24 * q^10 - 12 * q^11 - 28 * q^15 - 32 * q^16 + 12 * q^19 + 24 * q^24 - 42 * q^25 + 48 * q^26 - 136 * q^29 + 32 * q^30 - 84 * q^31 - 48 * q^36 + 312 * q^39 - 48 * q^40 + 24 * q^44 - 384 * q^45 - 68 * q^46 - 96 * q^50 - 76 * q^51 + 108 * q^54 + 372 * q^59 - 28 * q^60 - 348 * q^61 - 128 * q^64 - 104 * q^65 - 480 * q^66 - 384 * q^71 + 208 * q^74 + 150 * q^75 + 148 * q^79 - 24 * q^80 - 140 * q^81 + 580 * q^85 - 188 * q^86 + 912 * q^89 + 600 * q^94 - 310 * q^95 + 48 * q^96 + 176 * q^99

Introduction

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