LMFDB - Embedded newform 1710.2.t.c.1189.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(919,1710)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1710.919");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} + \cdots + 1024 $ x^20 - 49x^16 - 8x^15 + 72x^13 + 2145x^12 - 648x^11 + 32x^10 - 7056x^9 - 11968x^8 + 10368x^7 + 9344x^6 + 18176x^5 + 56320x^4 + 28160x^3 + 8192x^2 + 4096*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1189.6
Root			$-0.372041 - 0.0996880i$ of defining polynomial
Character	$\chi$	$=$	1710.1189
Dual form			1710.2.t.c.919.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.05825 - 0.873846i) q^{5} +2.32136i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.05825 - 0.873846i) q^{5} +2.32136i q^{7} +1.00000i q^{8} +(-1.34557 - 1.78590i) q^{10} +2.85165 q^{11} +(5.20277 - 3.00382i) q^{13} +(-1.16068 + 2.01036i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.79487 - 2.19097i) q^{17} +(-2.63121 + 3.47516i) q^{19} +(-0.272353 - 2.21942i) q^{20} +(2.46960 + 1.42582i) q^{22} +(4.36172 - 2.51824i) q^{23} +(3.47279 + 3.59719i) q^{25} +6.00764 q^{26} +(-2.01036 + 1.16068i) q^{28} +(4.41039 + 7.63902i) q^{29} -0.685205 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.19097 - 3.79487i) q^{34} +(2.02851 - 4.77794i) q^{35} +7.79872i q^{37} +(-4.01627 + 1.69397i) q^{38} +(0.873846 - 2.05825i) q^{40} +(-2.58128 + 4.47091i) q^{41} +(2.24057 + 1.29360i) q^{43} +(1.42582 + 2.46960i) q^{44} +5.03648 q^{46} +(-6.83132 + 3.94406i) q^{47} +1.61129 q^{49} +(1.20893 + 4.85165i) q^{50} +(5.20277 + 3.00382i) q^{52} +(4.86905 - 2.81115i) q^{53} +(-5.86941 - 2.49190i) q^{55} -2.32136 q^{56} +8.82078i q^{58} +(0.724643 - 1.25512i) q^{59} +(5.40264 + 9.35765i) q^{61} +(-0.593405 - 0.342602i) q^{62} -1.00000 q^{64} +(-13.3335 + 1.63620i) q^{65} +(5.89514 - 3.40356i) q^{67} -4.38194i q^{68} +(4.14571 - 3.12356i) q^{70} +(-1.15149 + 1.99443i) q^{71} +(-5.38195 - 3.10727i) q^{73} +(-3.89936 + 6.75389i) q^{74} +(-4.32518 - 0.541114i) q^{76} +6.61970i q^{77} +(2.00683 - 3.47593i) q^{79} +(1.78590 - 1.34557i) q^{80} +(-4.47091 + 2.58128i) q^{82} +12.2192i q^{83} +(5.89622 + 7.82569i) q^{85} +(1.29360 + 2.24057i) q^{86} +2.85165i q^{88} +(4.34444 + 7.52479i) q^{89} +(6.97295 + 12.0775i) q^{91} +(4.36172 + 2.51824i) q^{92} -7.88813 q^{94} +(8.45244 - 4.85348i) q^{95} +(5.79684 + 3.34681i) q^{97} +(1.39542 + 0.805646i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4}+O(q^{10}) $ 20 * q + 10 * q^4	$ 20 q + 10 q^{4} - 2 q^{10} - 12 q^{11} - 10 q^{14} - 10 q^{16} + 6 q^{19} + 14 q^{25} - 8 q^{29} + 40 q^{31} + 12 q^{34} - 2 q^{35} + 2 q^{40} + 14 q^{41} - 6 q^{44} + 44 q^{46} - 8 q^{49} + 8 q^{50} - 20 q^{56} - 8 q^{59} + 16 q^{61} - 20 q^{64} - 40 q^{65} + 8 q^{70} + 4 q^{71} - 26 q^{74} + 8 q^{79} - 16 q^{85} + 20 q^{86} + 2 q^{89} - 44 q^{91} - 32 q^{94} + 80 q^{95}+O(q^{100}) $ 20 * q + 10 * q^4 - 2 * q^10 - 12 * q^11 - 10 * q^14 - 10 * q^16 + 6 * q^19 + 14 * q^25 - 8 * q^29 + 40 * q^31 + 12 * q^34 - 2 * q^35 + 2 * q^40 + 14 * q^41 - 6 * q^44 + 44 * q^46 - 8 * q^49 + 8 * q^50 - 20 * q^56 - 8 * q^59 + 16 * q^61 - 20 * q^64 - 40 * q^65 + 8 * q^70 + 4 * q^71 - 26 * q^74 + 8 * q^79 - 16 * q^85 + 20 * q^86 + 2 * q^89 - 44 * q^91 - 32 * q^94 + 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.05825	−	0.873846i	−0.920477	−	0.390796i
$5$	−2.05825	−	0.873846i	−0.920477	−	0.390796i
$6$		0			0
$7$			2.32136i			0.877391i	0.898636	+	0.438696i	$0.144559\pi$
$7$			2.32136i			0.877391i	−0.898636	+	0.438696i	$0.855441\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.34557	−	1.78590i	−0.425508	−	0.564750i
$11$	2.85165			0.859804			0.429902	−	0.902875i	$-0.358548\pi$
$11$	2.85165			0.859804			0.429902	+	0.902875i	$0.358548\pi$
$12$		0			0
$13$	5.20277	−	3.00382i	1.44299	−	0.833110i	0.444941	−	0.895560i	$-0.353224\pi$
$13$	5.20277	−	3.00382i	1.44299	−	0.833110i	0.998048	+	0.0624492i	$0.0198911\pi$
$14$	−1.16068	+	2.01036i	−0.310205	+	0.537290i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.79487	−	2.19097i	−0.920391	−	0.531388i	−0.0366311	−	0.999329i	$-0.511663\pi$
$17$	−3.79487	−	2.19097i	−0.920391	−	0.531388i	−0.883760	+	0.467941i	$0.844996\pi$
$18$		0			0
$19$	−2.63121	+	3.47516i	−0.603641	+	0.797256i
$19$	−2.63121	+	3.47516i	−0.603641	+	0.797256i
$20$	−0.272353	−	2.21942i	−0.0608999	−	0.496277i
$21$		0			0
$22$	2.46960	+	1.42582i	0.526520	+	0.303987i
$23$	4.36172	−	2.51824i	0.909481	−	0.525089i	0.0292169	−	0.999573i	$-0.490699\pi$
$23$	4.36172	−	2.51824i	0.909481	−	0.525089i	0.880264	+	0.474484i	$0.157365\pi$
$24$		0			0
$25$	3.47279	+	3.59719i	0.694558	+	0.719437i
$26$	6.00764			1.17820
$27$		0			0
$28$	−2.01036	+	1.16068i	−0.379922	+	0.219348i
$29$	4.41039	+	7.63902i	0.818989	+	1.41853i	0.906428	+	0.422360i	$0.138798\pi$
$29$	4.41039	+	7.63902i	0.818989	+	1.41853i	−0.0874397	+	0.996170i	$0.527869\pi$
$30$		0			0
$31$	−0.685205			−0.123066			−0.0615332	−	0.998105i	$-0.519599\pi$
$31$	−0.685205			−0.123066			−0.0615332	+	0.998105i	$0.519599\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−2.19097	−	3.79487i	−0.375748	−	0.650815i
$35$	2.02851	−	4.77794i	0.342881	−	0.807619i
$36$		0			0
$37$			7.79872i			1.28210i	0.767499	+	0.641050i	$0.221501\pi$
$37$			7.79872i			1.28210i	−0.767499	+	0.641050i	$0.778499\pi$
$38$	−4.01627	+	1.69397i	−0.651526	+	0.274799i
$39$		0			0
$40$	0.873846	−	2.05825i	0.138167	−	0.325438i
$41$	−2.58128	+	4.47091i	−0.403128	+	0.698239i	−0.994102	−	0.108452i	$-0.965410\pi$
$41$	−2.58128	+	4.47091i	−0.403128	+	0.698239i	0.590973	+	0.806691i	$0.298744\pi$
$42$		0			0
$43$	2.24057	+	1.29360i	0.341684	+	0.197271i	0.661017	−	0.750371i	$-0.270125\pi$
$43$	2.24057	+	1.29360i	0.341684	+	0.197271i	−0.319332	+	0.947643i	$0.603459\pi$
$44$	1.42582	+	2.46960i	0.214951	+	0.372306i
$45$		0			0
$46$	5.03648			0.742588
$47$	−6.83132	+	3.94406i	−0.996450	+	0.575301i	−0.907196	−	0.420708i	$-0.861782\pi$
$47$	−6.83132	+	3.94406i	−0.996450	+	0.575301i	−0.0892540	+	0.996009i	$0.528448\pi$
$48$		0			0
$49$	1.61129			0.230184
$50$	1.20893	+	4.85165i	0.170968	+	0.686127i
$51$		0			0
$52$	5.20277	+	3.00382i	0.721495	+	0.416555i
$53$	4.86905	−	2.81115i	0.668815	−	0.386141i	−0.126812	−	0.991927i	$-0.540475\pi$
$53$	4.86905	−	2.81115i	0.668815	−	0.386141i	0.795628	+	0.605786i	$0.207141\pi$
$54$		0			0
$55$	−5.86941	−	2.49190i	−0.791430	−	0.336008i
$56$	−2.32136			−0.310205
$57$		0			0
$58$			8.82078i			1.15822i
$59$	0.724643	−	1.25512i	0.0943405	−	0.163403i	−0.814993	−	0.579471i	$-0.803259\pi$
$59$	0.724643	−	1.25512i	0.0943405	−	0.163403i	0.909333	+	0.416069i	$0.136592\pi$
$60$		0			0
$61$	5.40264	+	9.35765i	0.691737	+	1.19812i	0.971268	+	0.237987i	$0.0764876\pi$
$61$	5.40264	+	9.35765i	0.691737	+	1.19812i	−0.279531	+	0.960137i	$0.590179\pi$
$62$	−0.593405	−	0.342602i	−0.0753625	−	0.0435105i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−13.3335	+	1.63620i	−1.65382	+	0.202945i
$66$		0			0
$67$	5.89514	−	3.40356i	0.720206	−	0.415811i	−0.0946224	−	0.995513i	$-0.530164\pi$
$67$	5.89514	−	3.40356i	0.720206	−	0.415811i	0.814829	+	0.579702i	$0.196831\pi$
$68$		−	4.38194i		−	0.531388i
$69$		0			0
$70$	4.14571	−	3.12356i	0.495507	−	0.373337i
$71$	−1.15149	+	1.99443i	−0.136656	+	0.236696i	−0.926229	−	0.376961i	$-0.876969\pi$
$71$	−1.15149	+	1.99443i	−0.136656	+	0.236696i	0.789573	+	0.613657i	$0.210302\pi$
$72$		0			0
$73$	−5.38195	−	3.10727i	−0.629909	−	0.363678i	0.150808	−	0.988563i	$-0.451813\pi$
$73$	−5.38195	−	3.10727i	−0.629909	−	0.363678i	−0.780717	+	0.624885i	$0.785146\pi$
$74$	−3.89936	+	6.75389i	−0.453291	+	0.785123i
$75$		0			0
$76$	−4.32518	−	0.541114i	−0.496132	−	0.0620700i
$77$			6.61970i			0.754385i
$78$		0			0
$79$	2.00683	−	3.47593i	0.225786	−	0.391072i	−0.730769	−	0.682625i	$-0.760838\pi$
$79$	2.00683	−	3.47593i	0.225786	−	0.391072i	0.956555	+	0.291552i	$0.0941718\pi$
$80$	1.78590	−	1.34557i	0.199669	−	0.150440i
$81$		0			0
$82$	−4.47091	+	2.58128i	−0.493729	+	0.285055i
$83$			12.2192i			1.34123i	0.741806	+	0.670614i	$0.233969\pi$
$83$			12.2192i			1.34123i	−0.741806	+	0.670614i	$0.766031\pi$
$84$		0			0
$85$	5.89622	+	7.82569i	0.639535	+	0.848815i
$86$	1.29360	+	2.24057i	0.139492	+	0.241607i
$87$		0			0
$88$			2.85165i			0.303987i
$89$	4.34444	+	7.52479i	0.460510	+	0.797626i	0.998986	−	0.0450142i	$-0.0143333\pi$
$89$	4.34444	+	7.52479i	0.460510	+	0.797626i	−0.538477	+	0.842640i	$0.681000\pi$
$90$		0			0
$91$	6.97295	+	12.0775i	0.730964	+	1.26607i
$92$	4.36172	+	2.51824i	0.454740	+	0.262545i
$93$		0			0
$94$	−7.88813			−0.813598
$95$	8.45244	−	4.85348i	0.867202	−	0.497956i
$96$		0			0
$97$	5.79684	+	3.34681i	0.588580	+	0.339817i	0.764536	−	0.644581i	$-0.222968\pi$
$97$	5.79684	+	3.34681i	0.588580	+	0.339817i	−0.175956	+	0.984398i	$0.556302\pi$
$98$	1.39542	+	0.805646i	0.140959	+	0.0813825i
$99$		0			0
$100$	−1.37886	+	4.80612i	−0.137886	+	0.480612i
$101$	7.02206	+	12.1626i	0.698721	+	1.21022i	0.968910	+	0.247413i	$0.0795805\pi$
$101$	7.02206	+	12.1626i	0.698721	+	1.21022i	−0.270189	+	0.962807i	$0.587086\pi$
$102$		0			0
$103$		−	14.0958i		−	1.38890i	−0.719542	−	0.694449i	$-0.755648\pi$
$103$		−	14.0958i		−	1.38890i	0.719542	−	0.694449i	$-0.244352\pi$
$104$	3.00382	+	5.20277i	0.294549	+	0.510174i
$105$		0			0
$106$	5.62229			0.546085
$107$		−	16.7729i		−	1.62150i	−0.585395	−	0.810748i	$-0.699060\pi$
$107$		−	16.7729i		−	1.62150i	0.585395	−	0.810748i	$-0.300940\pi$
$108$		0			0
$109$	4.45191	−	7.71093i	0.426416	−	0.738573i	−0.570136	−	0.821550i	$-0.693109\pi$
$109$	4.45191	−	7.71093i	0.426416	−	0.738573i	0.996551	+	0.0829770i	$0.0264428\pi$
$110$	−3.83710	−	5.09275i	−0.365854	−	0.485575i
$111$		0			0
$112$	−2.01036	−	1.16068i	−0.189961	−	0.109674i
$113$			11.8870i			1.11824i	0.829087	+	0.559120i	$0.188861\pi$
$113$			11.8870i			1.11824i	−0.829087	+	0.559120i	$0.811139\pi$
$114$		0			0
$115$	−11.1781	+	1.37170i	−1.04236	+	0.127912i
$116$	−4.41039	+	7.63902i	−0.409494	+	0.709265i
$117$		0			0
$118$	1.25512	−	0.724643i	0.115543	−	0.0667088i
$119$	5.08602	−	8.80925i	0.466235	−	0.807543i
$120$		0			0
$121$	−2.86810			−0.260737
$122$			10.8053i			0.978264i
$123$		0			0
$124$	−0.342602	−	0.593405i	−0.0307666	−	0.0532893i
$125$	−4.00448	−	10.4386i	−0.358172	−	0.933656i
$126$		0			0
$127$	−7.72660	+	4.46095i	−0.685625	+	0.395846i	−0.801971	−	0.597363i	$-0.796215\pi$
$127$	−7.72660	+	4.46095i	−0.685625	+	0.395846i	0.116346	+	0.993209i	$0.462882\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−12.3652	−	5.24975i	−1.08450	−	0.460434i
$131$	−0.0274319	+	0.0475134i	−0.00239673	+	0.00415127i	−0.867221	−	0.497923i	$-0.834096\pi$
$131$	−0.0274319	+	0.0475134i	−0.00239673	+	0.00415127i	0.864825	+	0.502074i	$0.167430\pi$
$132$		0			0
$133$	−8.06710	−	6.10798i	−0.699506	−	0.529629i
$134$	6.80712			0.588046
$135$		0			0
$136$	2.19097	−	3.79487i	0.187874	−	0.325407i
$137$	15.5732	−	8.99119i	1.33051	−	0.768169i	0.345131	−	0.938555i	$-0.387835\pi$
$137$	15.5732	−	8.99119i	1.33051	−	0.768169i	0.985377	+	0.170386i	$0.0545013\pi$
$138$		0			0
$139$	−10.3327	−	17.8967i	−0.876405	−	1.51798i	−0.855258	−	0.518202i	$-0.826601\pi$
$139$	−10.3327	−	17.8967i	−0.876405	−	1.51798i	−0.0211474	−	0.999776i	$-0.506732\pi$
$140$	5.15207	−	0.632228i	0.435429	−	0.0534330i
$141$		0			0
$142$	−1.99443	+	1.15149i	−0.167369	+	0.0966306i
$143$	14.8365	−	8.56584i	1.24069	−	0.716312i
$144$		0			0
$145$	−2.40236	−	19.5770i	−0.199505	−	1.62578i
$146$	−3.10727	−	5.38195i	−0.257159	−	0.445413i
$147$		0			0
$148$	−6.75389	+	3.89936i	−0.555166	+	0.320525i
$149$	1.92651	−	3.33682i	0.157826	−	0.273363i	−0.776258	−	0.630415i	$-0.782885\pi$
$149$	1.92651	−	3.33682i	0.157826	−	0.273363i	0.934084	+	0.357052i	$0.116218\pi$
$150$		0			0
$151$	7.77324			0.632577			0.316289	−	0.948663i	$-0.397563\pi$
$151$	7.77324			0.632577			0.316289	+	0.948663i	$0.397563\pi$
$152$	−3.47516	−	2.63121i	−0.281873	−	0.213419i
$153$		0			0
$154$	−3.30985	+	5.73283i	−0.266715	+	0.461964i
$155$	1.41032	+	0.598763i	0.113280	+	0.0480938i
$156$		0			0
$157$	−16.6929	−	9.63765i	−1.33224	−	0.769169i	−0.346596	−	0.938014i	$-0.612663\pi$
$157$	−16.6929	−	9.63765i	−1.33224	−	0.769169i	−0.985642	+	0.168846i	$0.945996\pi$
$158$	3.47593	−	2.00683i	0.276530	−	0.159655i
$159$		0			0
$160$	2.21942	−	0.272353i	0.175461	−	0.0215314i
$161$	5.84574	+	10.1251i	0.460709	+	0.797971i
$162$		0			0
$163$		−	15.9168i		−	1.24670i	−0.781944	−	0.623348i	$-0.785772\pi$
$163$		−	15.9168i		−	1.24670i	0.781944	−	0.623348i	$-0.214228\pi$
$164$	−5.16256			−0.403128
$165$		0			0
$166$	−6.10958	+	10.5821i	−0.474196	+	0.821331i
$167$	−16.4675	+	9.50754i	−1.27430	+	0.735716i	−0.975794	−	0.218693i	$-0.929821\pi$
$167$	−16.4675	+	9.50754i	−1.27430	+	0.735716i	−0.298503	+	0.954409i	$0.596487\pi$
$168$		0			0
$169$	11.5459	−	19.9981i	0.888146	−	1.53831i
$170$	1.19343	+	9.72536i	0.0915321	+	0.745901i
$171$		0			0
$172$			2.58719i			0.197271i
$173$	−12.3792	−	7.14712i	−0.941172	−	0.543386i	−0.0508444	−	0.998707i	$-0.516191\pi$
$173$	−12.3792	−	7.14712i	−0.941172	−	0.543386i	−0.890327	+	0.455321i	$0.849525\pi$
$174$		0			0
$175$	−8.35036	+	8.06159i	−0.631228	+	0.609399i
$176$	−1.42582	+	2.46960i	−0.107476	+	0.186153i
$177$		0			0
$178$			8.68888i			0.651259i
$179$	6.66682			0.498301			0.249151	−	0.968465i	$-0.419849\pi$
$179$	6.66682			0.498301			0.249151	+	0.968465i	$0.419849\pi$
$180$		0			0
$181$	−3.06793	−	5.31382i	−0.228038	−	0.394973i	0.729189	−	0.684313i	$-0.239898\pi$
$181$	−3.06793	−	5.31382i	−0.228038	−	0.394973i	−0.957226	+	0.289340i	$0.906564\pi$
$182$			13.9459i			1.03374i
$183$		0			0
$184$	2.51824	+	4.36172i	0.185647	+	0.321550i
$185$	6.81487	−	16.0517i	0.501039	−	1.18014i
$186$		0			0
$187$	−10.8216	−	6.24787i	−0.791356	−	0.456890i
$188$	−6.83132	−	3.94406i	−0.498225	−	0.287650i
$189$		0			0
$190$	9.74677	+	0.0229835i	0.707105	+	0.00166740i
$191$	18.8448			1.36356			0.681780	−	0.731557i	$-0.261206\pi$
$191$	18.8448			1.36356			0.681780	+	0.731557i	$0.261206\pi$
$192$		0			0
$193$	14.3105	+	8.26218i	1.03009	+	0.594725i	0.917012	−	0.398861i	$-0.130594\pi$
$193$	14.3105	+	8.26218i	1.03009	+	0.594725i	0.113082	+	0.993586i	$0.463928\pi$
$194$	3.34681	+	5.79684i	0.240287	+	0.416189i
$195$		0			0
$196$	0.805646	+	1.39542i	0.0575461	+	0.0996728i
$197$		−	6.90254i		−	0.491786i	−0.969297	−	0.245893i	$-0.920919\pi$
$197$		−	6.90254i		−	0.491786i	0.969297	−	0.245893i	$-0.0790811\pi$
$198$		0			0
$199$	3.26514	+	5.65540i	0.231460	+	0.400900i	0.958238	−	0.285972i	$-0.0923164\pi$
$199$	3.26514	+	5.65540i	0.231460	+	0.400900i	−0.726778	+	0.686872i	$0.758983\pi$
$200$	−3.59719	+	3.47279i	−0.254359	+	0.245563i
$201$		0			0
$202$			14.0441i			0.988141i
$203$	−17.7329	+	10.2381i	−1.24461	+	0.718573i
$204$		0			0
$205$	9.21980	−	6.94661i	0.643939	−	0.485172i
$206$	7.04788	−	12.2073i	0.491049	−	0.850522i
$207$		0			0
$208$			6.00764i			0.416555i
$209$	−7.50328	+	9.90993i	−0.519013	+	0.685484i
$210$		0			0
$211$	−11.1943	+	19.3891i	−0.770648	+	1.33480i	0.166560	+	0.986031i	$0.446734\pi$
$211$	−11.1943	+	19.3891i	−0.770648	+	1.33480i	−0.937208	+	0.348771i	$0.886599\pi$
$212$	4.86905	+	2.81115i	0.334408	+	0.193070i
$213$		0			0
$214$	8.38645	−	14.5258i	0.573286	−	0.992960i
$215$	−3.48126	−	4.62046i	−0.237420	−	0.315113i
$216$		0			0
$217$		−	1.59061i		−	0.107977i
$218$	7.71093	−	4.45191i	0.522250	−	0.301521i
$219$		0			0
$220$	−0.776654	−	6.32900i	−0.0523620	−	0.426701i
$221$	−26.3251			−1.77082
$222$		0			0
$223$	−1.62511	−	0.938256i	−0.108825	−	0.0628302i	0.444600	−	0.895729i	$-0.353346\pi$
$223$	−1.62511	−	0.938256i	−0.108825	−	0.0628302i	−0.553425	+	0.832899i	$0.686679\pi$
$224$	−1.16068	−	2.01036i	−0.0775512	−	0.134323i
$225$		0			0
$226$	−5.94352	+	10.2945i	−0.395357	+	0.684779i
$227$			20.3703i			1.35203i	0.736890	+	0.676013i	$0.236294\pi$
$227$			20.3703i			1.35203i	−0.736890	+	0.676013i	$0.763706\pi$
$228$		0			0
$229$	−10.7813			−0.712449			−0.356224	−	0.934400i	$-0.615936\pi$
$229$	−10.7813			−0.712449			−0.356224	+	0.934400i	$0.615936\pi$
$230$	−10.3663	−	4.40110i	−0.683536	−	0.290200i
$231$		0			0
$232$	−7.63902	+	4.41039i	−0.501526	+	0.289556i
$233$	−11.7576	−	6.78823i	−0.770263	−	0.444711i	0.0627056	−	0.998032i	$-0.480027\pi$
$233$	−11.7576	−	6.78823i	−0.770263	−	0.444711i	−0.832968	+	0.553321i	$0.813360\pi$
$234$		0			0
$235$	17.5071	−	2.14835i	1.14203	−	0.140143i
$236$	1.44929			0.0943405
$237$		0			0
$238$	8.80925	−	5.08602i	0.571019	−	0.329678i
$239$	−2.08081			−0.134596			−0.0672981	−	0.997733i	$-0.521438\pi$
$239$	−2.08081			−0.134596			−0.0672981	+	0.997733i	$0.521438\pi$
$240$		0			0
$241$	−8.51317	−	14.7453i	−0.548382	−	0.949825i	−0.998386	−	0.0567985i	$-0.981911\pi$
$241$	−8.51317	−	14.7453i	−0.548382	−	0.949825i	0.450004	−	0.893027i	$-0.351423\pi$
$242$	−2.48385	−	1.43405i	−0.159668	−	0.0921843i
$243$		0			0
$244$	−5.40264	+	9.35765i	−0.345869	+	0.599062i
$245$	−3.31644	−	1.40802i	−0.211880	−	0.0899551i
$246$		0			0
$247$	−3.25082	+	25.9842i	−0.206845	+	1.65333i
$248$		−	0.685205i		−	0.0435105i
$249$		0			0
$250$	1.75131	−	11.0423i	0.110763	−	0.698378i
$251$	−9.62571	−	16.6722i	−0.607569	−	1.05234i	−0.991640	−	0.129037i	$-0.958811\pi$
$251$	−9.62571	−	16.6722i	−0.607569	−	1.05234i	0.384070	−	0.923304i	$-0.374522\pi$
$252$		0			0
$253$	12.4381	−	7.18113i	0.781976	−	0.451474i
$254$	−8.92191			−0.559810
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.3212	−	8.84568i	0.955708	−	0.551779i	0.0608589	−	0.998146i	$-0.480616\pi$
$257$	15.3212	−	8.84568i	0.955708	−	0.551779i	0.894850	+	0.446368i	$0.147283\pi$
$258$		0			0
$259$	−18.1036			−1.12490
$260$	−8.08373	−	10.7290i	−0.501332	−	0.665387i
$261$		0			0
$262$	−0.0475134	+	0.0274319i	−0.00293539	+	0.00169475i
$263$	−9.98291	−	5.76364i	−0.615573	−	0.355401i	0.159570	−	0.987187i	$-0.448989\pi$
$263$	−9.98291	−	5.76364i	−0.615573	−	0.355401i	−0.775143	+	0.631785i	$0.782322\pi$
$264$		0			0
$265$	−12.4782	+	1.53125i	−0.766532	+	0.0940637i
$266$	−3.93232	−	9.32321i	−0.241106	−	0.571643i
$267$		0			0
$268$	5.89514	+	3.40356i	0.360103	+	0.207906i
$269$	−10.2776	+	17.8013i	−0.626635	+	1.08536i	0.361587	+	0.932338i	$0.382235\pi$
$269$	−10.2776	+	17.8013i	−0.626635	+	1.08536i	−0.988222	+	0.153025i	$0.951098\pi$
$270$		0			0
$271$	12.9912	−	22.5014i	0.789159	−	1.36686i	−0.137324	−	0.990526i	$-0.543850\pi$
$271$	12.9912	−	22.5014i	0.789159	−	1.36686i	0.926483	−	0.376337i	$-0.122816\pi$
$272$	3.79487	−	2.19097i	0.230098	−	0.132847i
$273$		0			0
$274$	17.9824			1.08636
$275$	9.90317	+	10.2579i	0.597184	+	0.618575i
$276$		0			0
$277$		−	4.14296i		−	0.248926i	−0.992224	−	0.124463i	$-0.960279\pi$
$277$		−	4.14296i		−	0.248926i	0.992224	−	0.124463i	$-0.0397208\pi$
$278$		−	20.6653i		−	1.23942i
$279$		0			0
$280$	4.77794	+	2.02851i	0.285536	+	0.121227i
$281$	4.29844	+	7.44511i	0.256423	+	0.444138i	0.965281	−	0.261213i	$-0.0841226\pi$
$281$	4.29844	+	7.44511i	0.256423	+	0.444138i	−0.708858	+	0.705351i	$0.750789\pi$
$282$		0			0
$283$	−12.4490	−	7.18742i	−0.740015	−	0.427248i	0.0820596	−	0.996627i	$-0.473850\pi$
$283$	−12.4490	−	7.18742i	−0.740015	−	0.427248i	−0.822075	+	0.569379i	$0.807184\pi$
$284$	−2.30297			−0.136656
$285$		0			0
$286$	17.1317			1.01302
$287$	−10.3786	−	5.99208i	−0.612628	−	0.353701i
$288$		0			0
$289$	1.10069	+	1.90644i	0.0647462	+	0.112144i
$290$	7.70800	−	18.1554i	0.452629	−	1.06612i
$291$		0			0
$292$		−	6.21454i		−	0.363678i
$293$		−	8.47490i		−	0.495109i	−0.968874	−	0.247554i	$-0.920373\pi$
$293$		−	8.47490i		−	0.495109i	0.968874	−	0.247554i	$-0.0796269\pi$
$294$		0			0
$295$	−2.58828	+	1.95012i	−0.150695	+	0.113541i
$296$	−7.79872			−0.453291
$297$		0			0
$298$	3.33682	−	1.92651i	0.193297	−	0.111600i
$299$	15.1287	−	26.2037i	0.874914	−	1.51540i
$300$		0			0
$301$	−3.00290	+	5.20118i	−0.173084	+	0.299791i
$302$	6.73182	+	3.88662i	0.387373	+	0.223650i
$303$		0			0
$304$	−1.69397	−	4.01627i	−0.0971560	−	0.230349i
$305$	−2.94285	−	23.9814i	−0.168507	−	1.37317i
$306$		0			0
$307$	18.6780	+	10.7838i	1.06601	+	0.615462i	0.927089	−	0.374841i	$-0.122303\pi$
$307$	18.6780	+	10.7838i	1.06601	+	0.615462i	0.138922	+	0.990303i	$0.455636\pi$
$308$	−5.73283	+	3.30985i	−0.326658	+	0.188596i
$309$		0			0
$310$	0.921994	+	1.22371i	0.0523657	+	0.0695018i
$311$	−6.25433			−0.354650			−0.177325	−	0.984152i	$-0.556744\pi$
$311$	−6.25433			−0.354650			−0.177325	+	0.984152i	$0.556744\pi$
$312$		0			0
$313$	15.3732	−	8.87575i	0.868947	−	0.501687i	0.00194901	−	0.999998i	$-0.499380\pi$
$313$	15.3732	−	8.87575i	0.868947	−	0.501687i	0.866998	+	0.498311i	$0.166046\pi$
$314$	−9.63765	−	16.6929i	−0.543884	−	0.942035i
$315$		0			0
$316$	4.01365			0.225786
$317$	−0.640437	+	0.369757i	−0.0359705	+	0.0207676i	−0.517877	−	0.855455i	$-0.673278\pi$
$317$	−0.640437	+	0.369757i	−0.0359705	+	0.0207676i	0.481907	+	0.876222i	$0.339944\pi$
$318$		0			0
$319$	12.5769	+	21.7838i	0.704170	+	1.21966i
$320$	2.05825	+	0.873846i	0.115060	+	0.0488495i
$321$		0			0
$322$			11.6915i			0.651540i
$323$	17.5991	−	7.42288i	0.979238	−	0.413020i
$324$		0			0
$325$	28.8734	+	8.28370i	1.60161	+	0.459497i
$326$	7.95838	−	13.7843i	0.440774	−	0.763442i
$327$		0			0
$328$	−4.47091	−	2.58128i	−0.246865	−	0.142527i
$329$	−9.15559	−	15.8579i	−0.504764	−	0.874277i
$330$		0			0
$331$	−4.54461			−0.249794			−0.124897	−	0.992170i	$-0.539860\pi$
$331$	−4.54461			−0.249794			−0.124897	+	0.992170i	$0.539860\pi$
$332$	−10.5821	+	6.10958i	−0.580769	+	0.335307i
$333$		0			0
$334$	−19.0151			−1.04046
$335$	−15.1079	+	1.85394i	−0.825431	+	0.101291i
$336$		0			0
$337$	17.9486	+	10.3626i	0.977722	+	0.564488i	0.901582	−	0.432609i	$-0.142407\pi$
$337$	17.9486	+	10.3626i	0.977722	+	0.564488i	0.0761405	+	0.997097i	$0.475740\pi$
$338$	19.9981	−	11.5459i	1.08775	−	0.628014i
$339$		0			0
$340$	−3.82914	+	9.01912i	−0.207664	+	0.489131i
$341$	−1.95396			−0.105813
$342$		0			0
$343$			19.9899i			1.07935i
$344$	−1.29360	+	2.24057i	−0.0697460	+	0.120804i
$345$		0			0
$346$	−7.14712	−	12.3792i	−0.384232	−	0.665509i
$347$	−10.7406	−	6.20108i	−0.576585	−	0.332891i	0.183190	−	0.983077i	$-0.441358\pi$
$347$	−10.7406	−	6.20108i	−0.576585	−	0.332891i	−0.759775	+	0.650186i	$0.774691\pi$
$348$		0			0
$349$	14.4163			0.771684			0.385842	−	0.922565i	$-0.373911\pi$
$349$	14.4163			0.771684			0.385842	+	0.922565i	$0.373911\pi$
$350$	−11.2624	+	2.80636i	−0.602002	+	0.150006i
$351$		0			0
$352$	−2.46960	+	1.42582i	−0.131630	+	0.0759967i
$353$			35.6707i			1.89856i	0.314430	+	0.949281i	$0.398187\pi$
$353$			35.6707i			1.89856i	−0.314430	+	0.949281i	$0.601813\pi$
$354$		0			0
$355$	4.11287	−	3.09882i	0.218289	−	0.164468i
$356$	−4.34444	+	7.52479i	−0.230255	+	0.398813i
$357$		0			0
$358$	5.77363	+	3.33341i	0.305146	+	0.176176i
$359$	−1.15286	+	1.99682i	−0.0608457	+	0.105388i	−0.894844	−	0.446380i	$-0.852713\pi$
$359$	−1.15286	+	1.99682i	−0.0608457	+	0.105388i	0.833998	+	0.551768i	$0.186046\pi$
$360$		0			0
$361$	−5.15348	−	18.2877i	−0.271236	−	0.962513i
$362$		−	6.13587i		−	0.322494i
$363$		0			0
$364$	−6.97295	+	12.0775i	−0.365482	+	0.633033i
$365$	8.36212	+	11.0985i	0.437693	+	0.580923i
$366$		0			0
$367$	−9.47038	+	5.46773i	−0.494350	+	0.285413i	−0.726377	−	0.687296i	$-0.758797\pi$
$367$	−9.47038	+	5.46773i	−0.494350	+	0.285413i	0.232027	+	0.972709i	$0.425464\pi$
$368$			5.03648i			0.262545i
$369$		0			0
$370$	13.9277	−	10.4937i	0.724067	−	0.545544i
$371$	6.52568	+	11.3028i	0.338796	+	0.586813i
$372$		0			0
$373$		−	23.3847i		−	1.21082i	−0.795915	−	0.605408i	$-0.793010\pi$
$373$		−	23.3847i		−	1.21082i	0.795915	−	0.605408i	$-0.206990\pi$
$374$	−6.24787	−	10.8216i	−0.323070	−	0.559573i
$375$		0			0
$376$	−3.94406	−	6.83132i	−0.203400	−	0.352298i
$377$	45.8925	+	26.4960i	2.36358	+	1.36462i
$378$		0			0
$379$	−23.2493			−1.19424			−0.597118	−	0.802154i	$-0.703687\pi$
$379$	−23.2493			−1.19424			−0.597118	+	0.802154i	$0.703687\pi$
$380$	8.42946	+	4.89329i	0.432422	+	0.251020i
$381$		0			0
$382$	16.3200	+	9.42238i	0.835006	+	0.482091i
$383$	−17.9351	−	10.3548i	−0.916441	−	0.529107i	−0.0339428	−	0.999424i	$-0.510806\pi$
$383$	−17.9351	−	10.3548i	−0.916441	−	0.529107i	−0.882498	+	0.470317i	$0.844140\pi$
$384$		0			0
$385$	5.78460	−	13.6250i	0.294810	−	0.694394i
$386$	8.26218	+	14.3105i	0.420534	+	0.728386i
$387$		0			0
$388$			6.69361i			0.339817i
$389$	−18.1887	−	31.5037i	−0.922203	−	1.59730i	−0.795999	−	0.605297i	$-0.793054\pi$
$389$	−18.1887	−	31.5037i	−0.922203	−	1.59730i	−0.126203	−	0.992004i	$-0.540279\pi$
$390$		0			0
$391$	−22.0695			−1.11610
$392$			1.61129i			0.0813825i
$393$		0			0
$394$	3.45127	−	5.97778i	0.173873	−	0.301156i
$395$	−7.16797	+	5.40067i	−0.360660	+	0.271737i
$396$		0			0
$397$	28.6128	+	16.5196i	1.43604	+	0.829096i	0.997571	−	0.0696530i	$-0.0221892\pi$
$397$	28.6128	+	16.5196i	1.43604	+	0.829096i	0.438464	+	0.898749i	$0.355523\pi$
$398$			6.53029i			0.327334i
$399$		0			0
$400$	−4.85165	+	1.20893i	−0.242582	+	0.0604465i
$401$	10.5982	−	18.3566i	0.529249	−	0.916685i	−0.470170	−	0.882576i	$-0.655807\pi$
$401$	10.5982	−	18.3566i	0.529249	−	0.916685i	0.999418	−	0.0341092i	$-0.0108594\pi$
$402$		0			0
$403$	−3.56496	+	2.05823i	−0.177583	+	0.102528i
$404$	−7.02206	+	12.1626i	−0.349361	+	0.605110i
$405$		0			0
$406$	−20.4762			−1.01622
$407$			22.2392i			1.10236i
$408$		0			0
$409$	−5.26086	−	9.11207i	−0.260133	−	0.450563i	0.706144	−	0.708068i	$-0.250433\pi$
$409$	−5.26086	−	9.11207i	−0.260133	−	0.450563i	−0.966277	+	0.257505i	$0.917100\pi$
$410$	11.4579	−	1.40604i	0.565865	−	0.0694392i
$411$		0			0
$412$	12.2073	−	7.04788i	0.601410	−	0.347224i
$413$	2.91358	+	1.68216i	0.143368	+	0.0827735i
$414$		0			0
$415$	10.6777	−	25.1501i	0.524146	−	1.23457i
$416$	−3.00382	+	5.20277i	−0.147275	+	0.255087i
$417$		0			0
$418$	−11.4530	+	4.83061i	−0.560185	+	0.236273i
$419$	26.3874			1.28911			0.644555	−	0.764558i	$-0.277043\pi$
$419$	26.3874			1.28911			0.644555	+	0.764558i	$0.277043\pi$
$420$		0			0
$421$	−4.24202	+	7.34740i	−0.206743	+	0.358090i	−0.950687	−	0.310152i	$-0.899620\pi$
$421$	−4.24202	+	7.34740i	−0.206743	+	0.358090i	0.743943	+	0.668243i	$0.232953\pi$
$422$	−19.3891	+	11.1943i	−0.943847	+	0.544931i
$423$		0			0
$424$	2.81115	+	4.86905i	0.136521	+	0.236462i
$425$	−5.29745	−	21.2596i	−0.256964	−	1.03124i
$426$		0			0
$427$	−21.7225	+	12.5415i	−1.05122	+	0.606924i
$428$	14.5258	−	8.38645i	0.702129	−	0.405374i
$429$		0			0
$430$	−0.704628	−	5.74206i	−0.0339802	−	0.276907i
$431$	−9.83833	−	17.0405i	−0.473896	−	0.820811i	0.525658	−	0.850696i	$-0.323819\pi$
$431$	−9.83833	−	17.0405i	−0.473896	−	0.820811i	−0.999553	+	0.0298849i	$0.990486\pi$
$432$		0			0
$433$	−12.0899	+	6.98010i	−0.581003	+	0.335442i	−0.761532	−	0.648127i	$-0.775552\pi$
$433$	−12.0899	+	6.98010i	−0.581003	+	0.335442i	0.180529	+	0.983570i	$0.442219\pi$
$434$	0.795303	−	1.37751i	0.0381758	−	0.0661224i
$435$		0			0
$436$	8.90382			0.426416
$437$	−2.72531	+	21.7837i	−0.130369	+	1.04205i
$438$		0			0
$439$	10.2610	−	17.7725i	0.489729	−	0.848236i	−0.510201	−	0.860055i	$-0.670429\pi$
$439$	10.2610	−	17.7725i	0.489729	−	0.848236i	0.999930	+	0.0118193i	$0.00376230\pi$
$440$	2.49190	−	5.86941i	0.118797	−	0.279813i
$441$		0			0
$442$	−22.7982	−	13.1626i	−1.08440	−	0.626079i
$443$	20.4256	−	11.7927i	0.970450	−	0.560290i	0.0710768	−	0.997471i	$-0.477356\pi$
$443$	20.4256	−	11.7927i	0.970450	−	0.560290i	0.899374	+	0.437181i	$0.144023\pi$
$444$		0			0
$445$	−2.36644	−	19.2843i	−0.112180	−	0.914162i
$446$	−0.938256	−	1.62511i	−0.0444277	−	0.0769510i
$447$		0			0
$448$		−	2.32136i		−	0.109674i
$449$	28.2500			1.33320			0.666601	−	0.745415i	$-0.267749\pi$
$449$	28.2500			1.33320			0.666601	+	0.745415i	$0.267749\pi$
$450$		0			0
$451$	−7.36090	+	12.7495i	−0.346611	+	0.600349i
$452$	−10.2945	+	5.94352i	−0.484212	+	0.279560i
$453$		0			0
$454$	−10.1852	+	17.6412i	−0.478013	+	0.827943i
$455$	−3.79820	−	30.9518i	−0.178063	−	1.45104i
$456$		0			0
$457$			31.6784i			1.48185i	0.671587	+	0.740926i	$0.265613\pi$
$457$			31.6784i			1.48185i	−0.671587	+	0.740926i	$0.734387\pi$
$458$	−9.33688	−	5.39065i	−0.436284	−	0.251889i
$459$		0			0
$460$	−6.77695	−	8.99463i	−0.315977	−	0.419377i
$461$	−0.595751	+	1.03187i	−0.0277469	+	0.0480590i	−0.879565	−	0.475778i	$-0.842167\pi$
$461$	−0.595751	+	1.03187i	−0.0277469	+	0.0480590i	0.851819	+	0.523837i	$0.175500\pi$
$462$		0			0
$463$		−	19.8469i		−	0.922366i	−0.887305	−	0.461183i	$-0.847425\pi$
$463$		−	19.8469i		−	0.922366i	0.887305	−	0.461183i	$-0.152575\pi$
$464$	−8.82078			−0.409494
$465$		0			0
$466$	−6.78823	−	11.7576i	−0.314458	−	0.544658i
$467$			14.2451i			0.659184i	0.944123	+	0.329592i	$0.106911\pi$
$467$			14.2451i			0.659184i	−0.944123	+	0.329592i	$0.893089\pi$
$468$		0			0
$469$	7.90089	+	13.6847i	0.364829	+	0.631903i
$470$	16.2357	+	6.89300i	0.748899	+	0.317951i
$471$		0			0
$472$	1.25512	+	0.724643i	0.0577715	+	0.0333544i
$473$	6.38933	+	3.68888i	0.293782	+	0.169615i
$474$		0			0
$475$	−21.6384	+	2.60355i	−0.992839	+	0.119459i
$476$	10.1720			0.466235
$477$		0			0
$478$	−1.80203	−	1.04040i	−0.0824231	−	0.0475870i
$479$	−14.3482	−	24.8519i	−0.655588	−	1.13551i	−0.981746	−	0.190196i	$-0.939088\pi$
$479$	−14.3482	−	24.8519i	−0.655588	−	1.13551i	0.326159	−	0.945315i	$-0.394246\pi$
$480$		0			0
$481$	23.4260	+	40.5749i	1.06813	+	1.85006i
$482$		−	17.0263i		−	0.775529i
$483$		0			0
$484$	−1.43405	−	2.48385i	−0.0651842	−	0.112902i
$485$	−9.00675	−	11.9541i	−0.408976	−	0.542808i
$486$		0			0
$487$		−	19.6433i		−	0.890122i	−0.895500	−	0.445061i	$-0.853182\pi$
$487$		−	19.6433i		−	0.890122i	0.895500	−	0.445061i	$-0.146818\pi$
$488$	−9.35765	+	5.40264i	−0.423601	+	0.244566i
$489$		0			0
$490$	−2.16811	−	2.87760i	−0.0979453	−	0.129997i
$491$	−4.99544	+	8.65235i	−0.225441	+	0.390475i	−0.956452	−	0.291891i	$-0.905716\pi$
$491$	−4.99544	+	8.65235i	−0.225441	+	0.390475i	0.731011	+	0.682366i	$0.239049\pi$
$492$		0			0
$493$		−	38.6521i		−	1.74080i
$494$	−15.8074	+	20.8775i	−0.711207	+	0.939324i
$495$		0			0
$496$	0.342602	−	0.593405i	0.0153833	−	0.0266446i
$497$	−4.62980	−	2.67301i	−0.207675	−	0.119901i
$498$		0			0
$499$	−7.18085	+	12.4376i	−0.321459	+	0.556784i	−0.980789	−	0.195070i	$-0.937507\pi$
$499$	−7.18085	+	12.4376i	−0.321459	+	0.556784i	0.659330	+	0.751854i	$0.270840\pi$
$500$	7.03784	−	8.68728i	0.314742	−	0.388507i
$501$		0			0
$502$		−	19.2514i		−	0.859233i
$503$	7.26003	−	4.19158i	0.323709	−	0.186893i	−0.329336	−	0.944213i	$-0.606825\pi$
$503$	7.26003	−	4.19158i	0.323709	−	0.186893i	0.653044	+	0.757320i	$0.273491\pi$
$504$		0			0
$505$	−3.82495	−	31.1698i	−0.170208	−	1.38704i
$506$	14.3623			0.638480
$507$		0			0
$508$	−7.72660	−	4.46095i	−0.342812	−	0.197923i
$509$	−5.67635	−	9.83173i	−0.251600	−	0.435784i	0.712367	−	0.701808i	$-0.247623\pi$
$509$	−5.67635	−	9.83173i	−0.251600	−	0.435784i	−0.963966	+	0.266024i	$0.914290\pi$
$510$		0			0
$511$	7.21308	−	12.4934i	0.319088	−	0.552677i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	17.6914			0.780333
$515$	−12.3175	+	29.0126i	−0.542775	+	1.27845i
$516$		0			0
$517$	−19.4805	+	11.2471i	−0.856752	+	0.494646i
$518$	−15.6782	−	9.05181i	−0.688860	−	0.397714i
$519$		0			0
$520$	−1.63620	−	13.3335i	−0.0717520	−	0.584712i
$521$	29.3742			1.28691			0.643453	−	0.765485i	$-0.277501\pi$
$521$	29.3742			1.28691			0.643453	+	0.765485i	$0.277501\pi$
$522$		0			0
$523$	−35.2243	+	20.3368i	−1.54025	+	0.889265i	−0.541429	+	0.840746i	$0.682117\pi$
$523$	−35.2243	+	20.3368i	−1.54025	+	0.889265i	−0.998822	+	0.0485186i	$0.984550\pi$
$524$	−0.0548638			−0.00239673
$525$		0			0
$526$	−5.76364	−	9.98291i	−0.251307	−	0.435276i
$527$	2.60026	+	1.50126i	0.113269	+	0.0653960i
$528$		0			0
$529$	1.18305	−	2.04911i	0.0514371	−	0.0890917i
$530$	−11.5721	−	4.91302i	−0.502659	−	0.213408i
$531$		0			0
$532$	1.25612	−	10.0403i	0.0544597	−	0.435302i
$533$			31.0148i			1.34340i
$534$		0			0
$535$	−14.6569	+	34.5228i	−0.633674	+	1.49255i
$536$	3.40356	+	5.89514i	0.147011	+	0.254631i
$537$		0			0
$538$	−17.8013	+	10.2776i	−0.767468	+	0.443098i
$539$	4.59484			0.197914
$540$		0			0
$541$	−12.6792	−	21.9610i	−0.545122	−	0.944179i	−0.998599	−	0.0529108i	$-0.983150\pi$
$541$	−12.6792	−	21.9610i	−0.545122	−	0.944179i	0.453478	−	0.891268i	$-0.350183\pi$
$542$	22.5014	−	12.9912i	0.966518	−	0.558019i
$543$		0			0
$544$	4.38194			0.187874
$545$	−15.9013	+	11.9807i	−0.681137	+	0.513199i
$546$		0			0
$547$	−27.8110	+	16.0567i	−1.18911	+	0.686535i	−0.958105	−	0.286417i	$-0.907536\pi$
$547$	−27.8110	+	16.0567i	−1.18911	+	0.686535i	−0.231009	+	0.972952i	$0.574203\pi$
$548$	15.5732	+	8.99119i	0.665254	+	0.384085i
$549$		0			0
$550$	3.44744	+	13.8352i	0.146999	+	0.589935i
$551$	−38.1515	−	4.77304i	−1.62531	−	0.203338i
$552$		0			0
$553$	8.06887	+	4.65857i	0.343123	+	0.198102i
$554$	2.07148	−	3.58791i	0.0880087	−	0.152435i
$555$		0			0
$556$	10.3327	−	17.8967i	0.438203	−	0.758989i
$557$	−6.90306	+	3.98549i	−0.292492	+	0.168870i	−0.639065	−	0.769153i	$-0.720679\pi$
$557$	−6.90306	+	3.98549i	−0.292492	+	0.168870i	0.346573	+	0.938023i	$0.387345\pi$
$558$		0			0
$559$	15.5429			0.657396
$560$	3.12356	+	4.14571i	0.131995	+	0.175188i
$561$		0			0
$562$			8.59688i			0.362637i
$563$		−	13.8459i		−	0.583537i	−0.956489	−	0.291768i	$-0.905756\pi$
$563$		−	13.8459i		−	0.583537i	0.956489	−	0.291768i	$-0.0942436\pi$
$564$		0			0
$565$	10.3874	−	24.4665i	0.437003	−	1.02931i
$566$	−7.18742	−	12.4490i	−0.302110	−	0.523270i
$567$		0			0
$568$	−1.99443	−	1.15149i	−0.0836846	−	0.0483153i
$569$	−28.6171			−1.19969			−0.599845	−	0.800117i	$-0.704771\pi$
$569$	−28.6171			−1.19969			−0.599845	+	0.800117i	$0.704771\pi$
$570$		0			0
$571$	18.2331			0.763033			0.381517	−	0.924362i	$-0.375402\pi$
$571$	18.2331			0.763033			0.381517	+	0.924362i	$0.375402\pi$
$572$	14.8365	+	8.56584i	0.620344	+	0.358156i
$573$		0			0
$574$	−5.99208	−	10.3786i	−0.250105	−	0.433194i
$575$	24.2059	+	6.94460i	1.00946	+	0.289610i
$576$		0			0
$577$			37.3878i			1.55647i	0.627970	+	0.778237i	$0.283886\pi$
$577$			37.3878i			1.55647i	−0.627970	+	0.778237i	$0.716114\pi$
$578$			2.20137i			0.0915650i
$579$		0			0
$580$	15.7530	−	11.8690i	0.654108	−	0.492834i
$581$	−28.3651			−1.17678
$582$		0			0
$583$	13.8848	−	8.01640i	0.575050	−	0.332005i
$584$	3.10727	−	5.38195i	0.128580	−	0.222707i
$585$		0			0
$586$	4.23745	−	7.33948i	0.175047	−	0.303191i
$587$	1.52408	+	0.879926i	0.0629053	+	0.0363184i	0.531123	−	0.847295i	$-0.321770\pi$
$587$	1.52408	+	0.879926i	0.0629053	+	0.0363184i	−0.468217	+	0.883613i	$0.655104\pi$
$588$		0			0
$589$	1.80292	−	2.38120i	0.0742879	−	0.0981155i
$590$	−3.21657	+	0.394717i	−0.132424	+	0.0162502i
$591$		0			0
$592$	−6.75389	−	3.89936i	−0.277583	−	0.160263i
$593$	9.65263	−	5.57295i	0.396386	−	0.228854i	−0.288537	−	0.957469i	$-0.593169\pi$
$593$	9.65263	−	5.57295i	0.396386	−	0.228854i	0.684923	+	0.728615i	$0.259836\pi$
$594$		0			0
$595$	−18.1662	+	13.6872i	−0.744743	+	0.561122i
$596$	3.85302			0.157826
$597$		0			0
$598$	26.2037	−	15.1287i	1.07155	−	0.618658i
$599$	−19.0286	−	32.9586i	−0.777489	−	1.34665i	−0.933385	−	0.358877i	$-0.883160\pi$
$599$	−19.0286	−	32.9586i	−0.777489	−	1.34665i	0.155896	−	0.987774i	$-0.450174\pi$
$600$		0			0
$601$	34.4084			1.40355			0.701775	−	0.712399i	$-0.252391\pi$
$601$	34.4084			1.40355			0.701775	+	0.712399i	$0.252391\pi$
$602$	−5.20118	+	3.00290i	−0.211984	+	0.122389i
$603$		0			0
$604$	3.88662	+	6.73182i	0.158144	+	0.273914i
$605$	5.90327	+	2.50628i	0.240002	+	0.101895i
$606$		0			0
$607$			16.1885i			0.657071i	0.944492	+	0.328536i	$0.106555\pi$
$607$			16.1885i			0.657071i	−0.944492	+	0.328536i	$0.893445\pi$
$608$	0.541114	−	4.32518i	0.0219451	−	0.175409i
$609$		0			0
$610$	9.44215	−	22.2400i	0.382301	−	0.900470i
$611$	−23.6945	+	41.0401i	−0.958578	+	1.66031i
$612$		0			0
$613$	−16.7637	−	9.67851i	−0.677078	−	0.390911i	0.121675	−	0.992570i	$-0.461173\pi$
$613$	−16.7637	−	9.67851i	−0.677078	−	0.390911i	−0.798753	+	0.601659i	$0.794507\pi$
$614$	10.7838	+	18.6780i	0.435197	+	0.753784i
$615$		0			0
$616$	−6.61970			−0.266715
$617$	7.58517	−	4.37930i	0.305367	−	0.176304i	−0.339484	−	0.940612i	$-0.610253\pi$
$617$	7.58517	−	4.37930i	0.305367	−	0.176304i	0.644852	+	0.764308i	$0.276919\pi$
$618$		0			0
$619$	36.5640			1.46963			0.734815	−	0.678268i	$-0.237269\pi$
$619$	36.5640			1.46963			0.734815	+	0.678268i	$0.237269\pi$
$620$	0.186617	+	1.52076i	0.00749473	+	0.0610750i
$621$		0			0
$622$	−5.41641	−	3.12716i	−0.217178	−	0.125388i
$623$	−17.4677	+	10.0850i	−0.699830	+	0.404047i
$624$		0			0
$625$	−0.879489	+	24.9845i	−0.0351796	+	0.999381i
$626$	17.7515			0.709492
$627$		0			0
$628$		−	19.2753i		−	0.769169i
$629$	17.0867	−	29.5951i	0.681293	−	1.18003i
$630$		0			0
$631$	12.0437	+	20.8604i	0.479453	+	0.830437i	0.999722	−	0.0235650i	$-0.00750166\pi$
$631$	12.0437	+	20.8604i	0.479453	+	0.830437i	−0.520269	+	0.854002i	$0.674168\pi$
$632$	3.47593	+	2.00683i	0.138265	+	0.0798273i
$633$		0			0
$634$	−0.739513			−0.0293698
$635$	19.8015	−	2.42991i	0.785797	−	0.0964279i
$636$		0			0
$637$	8.38318	−	4.84003i	0.332154	−	0.191769i
$638$			25.1538i			0.995847i
$639$		0			0
$640$	1.34557	+	1.78590i	0.0531885	+	0.0705938i
$641$	12.7503	−	22.0841i	0.503605	−	0.872270i	−0.496386	−	0.868102i	$-0.665340\pi$
$641$	12.7503	−	22.0841i	0.503605	−	0.872270i	0.999991	−	0.00416788i	$-0.00132668\pi$
$642$		0			0
$643$	8.09885	+	4.67587i	0.319387	+	0.184398i	0.651119	−	0.758975i	$-0.274300\pi$
$643$	8.09885	+	4.67587i	0.319387	+	0.184398i	−0.331732	+	0.943374i	$0.607633\pi$
$644$	−5.84574	+	10.1251i	−0.230354	+	0.398985i
$645$		0			0
$646$	18.9527	+	2.37113i	0.745683	+	0.0932907i
$647$		−	2.93501i		−	0.115387i	−0.998334	−	0.0576935i	$-0.981625\pi$
$647$		−	2.93501i		−	0.115387i	0.998334	−	0.0576935i	$-0.0183746\pi$
$648$		0			0
$649$	2.06643	−	3.57916i	0.0811144	−	0.140494i
$650$	20.8633	+	21.6106i	0.818325	+	0.847638i
$651$		0			0
$652$	13.7843	−	7.95838i	0.539835	−	0.311674i
$653$		−	13.5336i		−	0.529613i	−0.964302	−	0.264806i	$-0.914692\pi$
$653$		−	13.5336i		−	0.529613i	0.964302	−	0.264806i	$-0.0853080\pi$
$654$		0			0
$655$	0.0979811	−	0.0738233i	0.00382844	−	0.00288451i
$656$	−2.58128	−	4.47091i	−0.100782	−	0.174560i
$657$		0			0
$658$		−	18.3112i		−	0.713844i
$659$	11.2236	+	19.4399i	0.437210	+	0.757270i	0.997473	−	0.0710447i	$-0.0226333\pi$
$659$	11.2236	+	19.4399i	0.437210	+	0.757270i	−0.560263	+	0.828315i	$0.689300\pi$
$660$		0			0
$661$	−4.81389	−	8.33791i	−0.187239	−	0.324307i	0.757090	−	0.653311i	$-0.226620\pi$
$661$	−4.81389	−	8.33791i	−0.187239	−	0.324307i	−0.944329	+	0.329004i	$0.893287\pi$
$662$	−3.93574	−	2.27230i	−0.152967	−	0.0883156i
$663$		0			0
$664$	−12.2192			−0.474196
$665$	11.2667	+	19.6211i	0.436903	+	0.760876i
$666$		0			0
$667$	38.4737	+	22.2128i	1.48971	+	0.860084i
$668$	−16.4675	−	9.50754i	−0.637148	−	0.367858i
$669$		0			0
$670$	−14.0108	−	5.94837i	−0.541283	−	0.229806i
$671$	15.4064	+	26.6847i	0.594758	+	1.03015i
$672$		0			0
$673$		−	3.35484i		−	0.129320i	−0.997907	−	0.0646598i	$-0.979404\pi$
$673$		−	3.35484i		−	0.129320i	0.997907	−	0.0646598i	$-0.0205962\pi$
$674$	10.3626	+	17.9486i	0.399153	+	0.691354i
$675$		0			0
$676$	23.0918			0.888146
$677$		−	18.6287i		−	0.715958i	−0.933730	−	0.357979i	$-0.883466\pi$
$677$		−	18.6287i		−	0.715958i	0.933730	−	0.357979i	$-0.116534\pi$
$678$		0			0
$679$	−7.76914	+	13.4565i	−0.298152	+	0.516415i
$680$	−7.82569	+	5.89622i	−0.300102	+	0.226110i
$681$		0			0
$682$	−1.69218	−	0.976981i	−0.0647970	−	0.0374105i
$683$			22.3842i			0.856506i	0.903659	+	0.428253i	$0.140871\pi$
$683$			22.3842i			0.856506i	−0.903659	+	0.428253i	$0.859129\pi$
$684$		0			0
$685$	−39.9104	+	4.89755i	−1.52490	+	0.187126i
$686$	−9.99495	+	17.3118i	−0.381609	+	0.660966i
$687$		0			0
$688$	−2.24057	+	1.29360i	−0.0854211	+	0.0493179i
$689$	16.8884	−	29.2515i	0.643396	−	1.11439i
$690$		0			0
$691$	−43.1700			−1.64226			−0.821132	−	0.570738i	$-0.806657\pi$
$691$	−43.1700			−1.64226			−0.821132	+	0.570738i	$0.806657\pi$
$692$		−	14.2942i		−	0.543386i
$693$		0			0
$694$	−6.20108	−	10.7406i	−0.235390	−	0.407707i
$695$	5.62826	+	45.8651i	0.213492	+	1.73976i
$696$		0			0
$697$	19.5912	−	11.3110i	0.742071	−	0.428435i
$698$	12.4848	+	7.20813i	0.472558	+	0.272832i
$699$		0			0
$700$	−11.1567	−	3.20083i	−0.421684	−	0.120980i
$701$	14.1571	−	24.5208i	0.534705	−	0.926137i	−0.464472	−	0.885588i	$-0.653756\pi$
$701$	14.1571	−	24.5208i	0.534705	−	0.926137i	0.999178	−	0.0405493i	$-0.0129108\pi$
$702$		0			0
$703$	−27.1018	−	20.5200i	−1.02216	−	0.773928i
$704$	−2.85165			−0.107476
$705$		0			0
$706$	−17.8354	+	30.8918i	−0.671243	+	1.16263i
$707$	−28.2337	+	16.3007i	−1.06184	+	0.613052i
$708$		0			0
$709$	8.52409	+	14.7642i	0.320129	+	0.554480i	0.980514	−	0.196447i	$-0.0629404\pi$
$709$	8.52409	+	14.7642i	0.320129	+	0.554480i	−0.660385	+	0.750927i	$0.729607\pi$
$710$	5.11126	−	0.627221i	0.191822	−	0.0235392i
$711$		0			0
$712$	−7.52479	+	4.34444i	−0.282003	+	0.162815i
$713$	−2.98867	+	1.72551i	−0.111927	+	0.0646208i
$714$		0			0
$715$	−38.0224	+	4.66586i	−1.42196	+	0.174493i
$716$	3.33341	+	5.77363i	0.124575	+	0.215771i
$717$		0			0
$718$	−1.99682	+	1.15286i	−0.0745205	+	0.0430244i
$719$	1.65729	−	2.87050i	0.0618063	−	0.107052i	−0.833467	−	0.552570i	$-0.813647\pi$
$719$	1.65729	−	2.87050i	0.0618063	−	0.107052i	0.895273	+	0.445518i	$0.146981\pi$
$720$		0			0
$721$	32.7213			1.21861
$722$	4.68083	−	18.4144i	0.174202	−	0.685313i
$723$		0			0
$724$	3.06793	−	5.31382i	0.114019	−	0.197486i
$725$	−12.1626	+	42.3937i	−0.451708	+	1.57446i
$726$		0			0
$727$	29.7663	+	17.1856i	1.10397	+	0.637379i	0.937261	−	0.348627i	$-0.113352\pi$
$727$	29.7663	+	17.1856i	1.10397	+	0.637379i	0.166711	+	0.986006i	$0.446685\pi$
$728$	−12.0775	+	6.97295i	−0.447622	+	0.258435i
$729$		0			0
$730$	1.69255	+	13.7927i	0.0626439	+	0.510489i
$731$	−5.66845	−	9.81805i	−0.209655	−	0.363134i
$732$		0			0
$733$			39.0068i			1.44075i	0.693585	+	0.720375i	$0.256030\pi$
$733$			39.0068i			1.44075i	−0.693585	+	0.720375i	$0.743970\pi$
$734$	−10.9355			−0.403635
$735$		0			0
$736$	−2.51824	+	4.36172i	−0.0928235	+	0.160775i
$737$	16.8109	−	9.70576i	0.619236	−	0.357516i
$738$		0			0
$739$	−4.19339	+	7.26316i	−0.154256	+	0.267180i	−0.932788	−	0.360426i	$-0.882631\pi$
$739$	−4.19339	+	7.26316i	−0.154256	+	0.267180i	0.778532	+	0.627605i	$0.215965\pi$
$740$	17.3086	−	2.12400i	0.636278	−	0.0780798i
$741$		0			0
$742$			13.0514i			0.479131i
$743$	−1.64985	−	0.952540i	−0.0605270	−	0.0349453i	0.469431	−	0.882969i	$-0.344459\pi$
$743$	−1.64985	−	0.952540i	−0.0605270	−	0.0349453i	−0.529958	+	0.848024i	$0.677792\pi$
$744$		0			0
$745$	−6.88111	+	5.18453i	−0.252104	+	0.189946i
$746$	11.6924	−	20.2518i	0.428088	−	0.741470i
$747$		0			0
$748$		−	12.4957i		−	0.456890i
$749$	38.9359			1.42269
$750$		0			0
$751$	−5.63534	−	9.76069i	−0.205636	−	0.356173i	0.744699	−	0.667401i	$-0.232593\pi$
$751$	−5.63534	−	9.76069i	−0.205636	−	0.356173i	−0.950335	+	0.311228i	$0.899260\pi$
$752$		−	7.88813i		−	0.287650i
$753$		0			0
$754$	26.4960	+	45.8925i	0.964929	+	1.67131i
$755$	−15.9993	−	6.79261i	−0.582273	−	0.247208i
$756$		0			0
$757$	−38.7692	−	22.3834i	−1.40909	−	0.813540i	−0.413792	−	0.910372i	$-0.635796\pi$
$757$	−38.7692	−	22.3834i	−1.40909	−	0.813540i	−0.995301	+	0.0968318i	$0.969129\pi$
$758$	−20.1345	−	11.6246i	−0.731317	−	0.422226i
$759$		0			0
$760$	4.85348	+	8.45244i	0.176054	+	0.306602i
$761$	33.7181			1.22228			0.611139	−	0.791523i	$-0.290711\pi$
$761$	33.7181			1.22228			0.611139	+	0.791523i	$0.290711\pi$
$762$		0			0
$763$	17.8998	+	10.3345i	0.648018	+	0.374133i
$764$	9.42238	+	16.3200i	0.340890	+	0.590439i
$765$		0			0
$766$	−10.3548	−	17.9351i	−0.374135	−	0.648021i
$767$		−	8.70680i		−	0.314384i
$768$		0			0
$769$	16.2178	+	28.0901i	0.584830	+	1.01296i	0.994897	+	0.100900i	$0.0321723\pi$
$769$	16.2178	+	28.0901i	0.584830	+	1.01296i	−0.410066	+	0.912056i	$0.634494\pi$
$770$	11.8221	−	8.90730i	0.426039	−	0.320997i
$771$		0			0
$772$			16.5244i			0.594725i
$773$	35.2122	−	20.3298i	1.26649	−	0.731211i	0.292172	−	0.956366i	$-0.405622\pi$
$773$	35.2122	−	20.3298i	1.26649	−	0.731211i	0.974323	+	0.225155i	$0.0722888\pi$
$774$		0			0
$775$	−2.37957	−	2.46481i	−0.0854767	−	0.0885385i
$776$	−3.34681	+	5.79684i	−0.120143	+	0.208094i
$777$		0			0
$778$		−	36.3774i		−	1.30419i
$779$	−8.74524	−	20.7343i	−0.313331	−	0.742882i
$780$		0			0
$781$	−3.28363	+	5.68742i	−0.117498	+	0.203512i
$782$	−19.1128	−	11.0348i	−0.683471	−	0.394602i
$783$		0			0
$784$	−0.805646	+	1.39542i	−0.0287731	+	0.0498364i
$785$	25.9364	+	34.4237i	0.925708	+	1.22864i
$786$		0			0
$787$		−	33.0432i		−	1.17786i	−0.808183	−	0.588931i	$-0.799549\pi$
$787$		−	33.0432i		−	1.17786i	0.808183	−	0.588931i	$-0.200451\pi$
$788$	5.97778	−	3.45127i	0.212949	−	0.122946i
$789$		0			0
$790$	−8.90798	+	1.09313i	−0.316932	+	0.0388918i
$791$	−27.5941			−0.981133
$792$		0			0
$793$	56.2174	+	32.4571i	1.99634	+	1.15259i
$794$	16.5196	+	28.6128i	0.586259	+	1.01543i
$795$		0			0
$796$	−3.26514	+	5.65540i	−0.115730	+	0.200450i
$797$		−	25.1288i		−	0.890109i	−0.895504	−	0.445054i	$-0.853184\pi$
$797$		−	25.1288i		−	0.890109i	0.895504	−	0.445054i	$-0.146816\pi$
$798$		0			0
$799$	34.5653			1.22283
$800$	−4.80612	−	1.37886i	−0.169922	−	0.0487501i
$801$		0			0
$802$	18.3566	−	10.5982i	0.648194	−	0.374235i
$803$	−15.3474	−	8.86083i	−0.541599	−	0.312692i
$804$		0			0
$805$	−3.18420	−	25.9483i	−0.112228	−	0.914557i
$806$	−4.11647			−0.144996
$807$		0			0
$808$	−12.1626	+	7.02206i	−0.427878	+	0.247035i
$809$	−22.9578			−0.807152			−0.403576	−	0.914946i	$-0.632233\pi$
$809$	−22.9578			−0.807152			−0.403576	+	0.914946i	$0.632233\pi$
$810$		0			0
$811$	−27.0425	−	46.8390i	−0.949590	−	1.64474i	−0.746289	−	0.665622i	$-0.768166\pi$
$811$	−27.0425	−	46.8390i	−0.949590	−	1.64474i	−0.203301	−	0.979116i	$-0.565167\pi$
$812$	−17.7329	−	10.2381i	−0.622303	−	0.359287i
$813$		0			0
$814$	−11.1196	+	19.2597i	−0.389742	+	0.675052i
$815$	−13.9088	+	32.7607i	−0.487203	+	1.14756i
$816$		0			0
$817$	−10.3909	+	4.38263i	−0.363531	+	0.153329i
$818$		−	10.5217i		−	0.367883i
$819$		0			0
$820$	10.6258	+	4.51128i	0.371070	+	0.157541i
$821$	−5.40068	−	9.35426i	−0.188485	−	0.326466i	0.756260	−	0.654271i	$-0.227024\pi$
$821$	−5.40068	−	9.35426i	−0.188485	−	0.326466i	−0.944745	+	0.327805i	$0.893691\pi$
$822$		0			0
$823$	−29.3326	+	16.9352i	−1.02247	+	0.590324i	−0.914819	−	0.403865i	$-0.867667\pi$
$823$	−29.3326	+	16.9352i	−1.02247	+	0.590324i	−0.107652	+	0.994189i	$0.534333\pi$
$824$	14.0958			0.491049
$825$		0			0
$826$	1.68216	+	2.91358i	0.0585297	+	0.101376i
$827$	−14.8973	+	8.60097i	−0.518030	+	0.299085i	−0.736128	−	0.676842i	$-0.763348\pi$
$827$	−14.8973	+	8.60097i	−0.518030	+	0.299085i	0.218098	+	0.975927i	$0.430015\pi$
$828$		0			0
$829$	−15.3463			−0.532998			−0.266499	−	0.963835i	$-0.585867\pi$
$829$	−15.3463			−0.532998			−0.266499	+	0.963835i	$0.585867\pi$
$830$	21.8222	−	16.4418i	0.757459	−	0.570703i
$831$		0			0
$832$	−5.20277	+	3.00382i	−0.180374	+	0.104139i
$833$	−6.11464	−	3.53029i	−0.211860	−	0.122317i
$834$		0			0
$835$	42.2024	−	5.17881i	1.46048	−	0.179220i
$836$	−12.3339	−	1.54307i	−0.426577	−	0.0533680i
$837$		0			0
$838$	22.8522	+	13.1937i	0.789415	+	0.455769i
$839$	−22.5501	+	39.0579i	−0.778516	+	1.34843i	0.154281	+	0.988027i	$0.450694\pi$
$839$	−22.5501	+	39.0579i	−0.778516	+	1.34843i	−0.932797	+	0.360402i	$0.882639\pi$
$840$		0			0
$841$	−24.4030	+	42.2673i	−0.841484	+	1.45749i
$842$	−7.34740	+	4.24202i	−0.253208	+	0.146190i
$843$		0			0
$844$	−22.3886			−0.770648
$845$	−41.2396	+	31.0717i	−1.41868	+	1.06890i
$846$		0			0
$847$		−	6.65790i		−	0.228768i
$848$			5.62229i			0.193070i
$849$		0			0
$850$	6.04208	−	21.0601i	0.207242	−	0.722355i
$851$	19.6390	+	34.0158i	0.673217	+	1.16605i
$852$		0			0
$853$	11.3790	+	6.56967i	0.389609	+	0.224941i	0.681991	−	0.731361i	$-0.261114\pi$
$853$	11.3790	+	6.56967i	0.389609	+	0.224941i	−0.292381	+	0.956302i	$0.594448\pi$
$854$	−25.0829			−0.858320
$855$		0			0
$856$	16.7729			0.573286
$857$	−19.8940	−	11.4858i	−0.679566	−	0.392348i	0.120125	−	0.992759i	$-0.461670\pi$
$857$	−19.8940	−	11.4858i	−0.679566	−	0.392348i	−0.799692	+	0.600411i	$0.795004\pi$
$858$		0			0
$859$	−11.2488	−	19.4834i	−0.383803	−	0.664766i	0.607800	−	0.794090i	$-0.292052\pi$
$859$	−11.2488	−	19.4834i	−0.383803	−	0.664766i	−0.991602	+	0.129325i	$0.958719\pi$
$860$	2.26081	−	5.32509i	0.0770928	−	0.181584i
$861$		0			0
$862$		−	19.6767i		−	0.670190i
$863$		−	24.1235i		−	0.821175i	−0.911821	−	0.410587i	$-0.865324\pi$
$863$		−	24.1235i		−	0.821175i	0.911821	−	0.410587i	$-0.134676\pi$
$864$		0			0
$865$	19.2340	+	25.5281i	0.653975	+	0.867980i
$866$	−13.9602			−0.474387
$867$		0			0
$868$	1.37751	−	0.795303i	0.0467556	−	0.0269943i
$869$	5.72276	−	9.91212i	0.194131	−	0.336246i
$870$		0			0
$871$	20.4474	−	35.4159i	0.692833	−	1.20002i
$872$	7.71093	+	4.45191i	0.261125	+	0.150761i
$873$		0			0
$874$	−13.2520	+	17.5026i	−0.448256	+	0.592033i
$875$	24.2317	−	9.29584i	0.819181	−	0.314257i
$876$		0			0
$877$	1.11105	+	0.641465i	0.0375175	+	0.0216607i	0.518641	−	0.854992i	$-0.326438\pi$
$877$	1.11105	+	0.641465i	0.0375175	+	0.0216607i	−0.481124	+	0.876653i	$0.659771\pi$
$878$	17.7725	−	10.2610i	0.599793	−	0.346291i
$879$		0			0
$880$	5.09275	−	3.83710i	0.171677	−	0.129349i
$881$	18.1444			0.611301			0.305650	−	0.952144i	$-0.401126\pi$
$881$	18.1444			0.611301			0.305650	+	0.952144i	$0.401126\pi$
$882$		0			0
$883$	−39.6706	+	22.9039i	−1.33502	+	0.770776i	−0.986065	−	0.166362i	$-0.946798\pi$
$883$	−39.6706	+	22.9039i	−1.33502	+	0.770776i	−0.348958	+	0.937138i	$0.613465\pi$
$884$	−13.1626	−	22.7982i	−0.442705	−	0.766787i
$885$		0			0
$886$	23.5855			0.792369
$887$	−50.4856	+	29.1479i	−1.69514	+	0.978689i	−0.744896	+	0.667180i	$0.767501\pi$
$887$	−50.4856	+	29.1479i	−1.69514	+	0.978689i	−0.950243	+	0.311509i	$0.899166\pi$
$888$		0			0
$889$	−10.3555	−	17.9362i	−0.347312	−	0.601561i
$890$	7.59274	−	17.8839i	0.254509	−	0.599469i
$891$		0			0
$892$		−	1.87651i		−	0.0628302i
$893$	4.26837	−	34.1176i	0.142836	−	1.14170i
$894$		0			0
$895$	−13.7220	−	5.82577i	−0.458675	−	0.194734i
$896$	1.16068	−	2.01036i	0.0387756	−	0.0671613i
$897$		0			0
$898$	24.4653	+	14.1250i	0.816416	+	0.471358i
$899$	−3.02202	−	5.23429i	−0.100790	−	0.174573i
$900$		0			0
$901$	−24.6365			−0.820762
$902$	−12.7495	+	7.36090i	−0.424511	+	0.245091i
$903$		0			0
$904$	−11.8870			−0.395357
$905$	1.67112	+	13.6181i	0.0555499	+	0.452680i
$906$		0			0
$907$	27.2008	+	15.7044i	0.903187	+	0.521455i	0.878233	−	0.478233i	$-0.158723\pi$
$907$	27.2008	+	15.7044i	0.903187	+	0.521455i	0.0249542	+	0.999689i	$0.492056\pi$
$908$	−17.6412	+	10.1852i	−0.585444	+	0.338006i
$909$		0			0
$910$	12.1866	−	28.7042i	0.403981	−	0.951533i
$911$	−19.8665			−0.658206			−0.329103	−	0.944294i	$-0.606746\pi$
$911$	−19.8665			−0.658206			−0.329103	+	0.944294i	$0.606746\pi$
$912$		0			0
$913$			34.8448i			1.15319i
$914$	−15.8392	+	27.4343i	−0.523914	+	0.907445i
$915$		0			0
$916$	−5.39065	−	9.33688i	−0.178112	−	0.308499i
$917$	−0.110296	−	0.0636793i	−0.00364228	−	0.00210287i
$918$		0			0
$919$	40.8314			1.34690			0.673451	−	0.739231i	$-0.264811\pi$
$919$	40.8314			1.34690			0.673451	+	0.739231i	$0.264811\pi$
$920$	−1.37170	−	11.1781i	−0.0452235	−	0.368530i
$921$		0			0
$922$	−1.03187	+	0.595751i	−0.0339828	+	0.0196200i
$923$			13.8354i			0.455399i
$924$		0			0
$925$	−28.0534	+	27.0833i	−0.922391	+	0.890493i
$926$	9.92347	−	17.1880i	0.326106	−	0.564831i
$927$		0			0
$928$	−7.63902	−	4.41039i	−0.250763	−	0.144778i
$929$	−10.3109	+	17.8591i	−0.338291	+	0.585937i	−0.984111	−	0.177553i	$-0.943182\pi$
$929$	−10.3109	+	17.8591i	−0.338291	+	0.585937i	0.645821	+	0.763489i	$0.276515\pi$
$930$		0			0
$931$	−4.23964	+	5.59950i	−0.138949	+	0.183516i
$932$		−	13.5765i		−	0.444711i
$933$		0			0
$934$	−7.12255	+	12.3366i	−0.233057	+	0.403666i
$935$	16.8139	+	22.3161i	0.549875	+	0.729815i
$936$		0			0
$937$	11.5342	−	6.65926i	0.376805	−	0.217548i	−0.299622	−	0.954058i	$-0.596861\pi$
$937$	11.5342	−	6.65926i	0.376805	−	0.217548i	0.676427	+	0.736509i	$0.263527\pi$
$938$			15.8018i			0.515946i
$939$		0			0
$940$	10.6141	+	14.0874i	0.346192	+	0.459480i
$941$	−2.77725	−	4.81033i	−0.0905356	−	0.156812i	0.817201	−	0.576353i	$-0.195525\pi$
$941$	−2.77725	−	4.81033i	−0.0905356	−	0.156812i	−0.907737	+	0.419540i	$0.862191\pi$
$942$		0			0
$943$			26.0011i			0.846713i
$944$	0.724643	+	1.25512i	0.0235851	+	0.0408506i
$945$		0			0
$946$	3.68888	+	6.38933i	0.119936	+	0.207735i
$947$	1.05045	+	0.606477i	0.0341350	+	0.0197079i	0.516970	−	0.856003i	$-0.327060\pi$
$947$	1.05045	+	0.606477i	0.0341350	+	0.0197079i	−0.482835	+	0.875711i	$0.660393\pi$
$948$		0			0
$949$	−37.3347			−1.21194
$950$	−20.0412	−	8.56448i	−0.650222	−	0.277868i
$951$		0			0
$952$	8.80925	+	5.08602i	0.285510	+	0.164839i
$953$	5.12855	+	2.96097i	0.166130	+	0.0959153i	0.580760	−	0.814075i	$-0.302756\pi$
$953$	5.12855	+	2.96097i	0.166130	+	0.0959153i	−0.414630	+	0.909990i	$0.636089\pi$
$954$		0			0
$955$	−38.7872	−	16.4674i	−1.25513	−	0.532873i
$956$	−1.04040	−	1.80203i	−0.0336491	−	0.0582819i
$957$		0			0
$958$		−	28.6965i		−	0.927141i
$959$	20.8718	+	36.1510i	0.673985	+	1.16738i
$960$		0			0
$961$	−30.5305			−0.984855
$962$			46.8519i			1.51057i
$963$		0			0
$964$	8.51317	−	14.7453i	0.274191	−	0.474913i
$965$	−22.2348	−	29.5108i	−0.715762	−	0.949987i
$966$		0			0
$967$	−38.8853	−	22.4505i	−1.25047	−	0.721958i	−0.279265	−	0.960214i	$-0.590091\pi$
$967$	−38.8853	−	22.4505i	−1.25047	−	0.721958i	−0.971202	+	0.238256i	$0.923424\pi$
$968$		−	2.86810i		−	0.0921843i
$969$		0			0
$970$	−1.82302	−	14.8559i	−0.0585337	−	0.476995i
$971$	3.97050	−	6.87710i	0.127419	−	0.220697i	−0.795257	−	0.606273i	$-0.792664\pi$
$971$	3.97050	−	6.87710i	0.127419	−	0.220697i	0.922676	+	0.385576i	$0.125997\pi$
$972$		0			0
$973$	41.5447	−	23.9858i	1.33186	−	0.768950i
$974$	9.82164	−	17.0116i	0.314706	−	0.545086i
$975$		0			0
$976$	−10.8053			−0.345869
$977$			25.2607i			0.808162i	0.914723	+	0.404081i	$0.132409\pi$
$977$			25.2607i			0.808162i	−0.914723	+	0.404081i	$0.867591\pi$
$978$		0			0
$979$	12.3888	+	21.4581i	0.395948	+	0.685802i
$980$	−0.438840	−	3.57613i	−0.0140182	−	0.114235i
$981$		0			0
$982$	−8.65235	+	4.99544i	−0.276108	+	0.159411i
$983$	−9.18945	−	5.30553i	−0.293098	−	0.169220i	0.346240	−	0.938146i	$-0.387458\pi$
$983$	−9.18945	−	5.30553i	−0.293098	−	0.169220i	−0.639338	+	0.768926i	$0.720792\pi$
$984$		0			0
$985$	−6.03176	+	14.2072i	−0.192188	+	0.452678i
$986$	19.3260	−	33.4737i	0.615467	−	1.06602i
$987$		0			0
$988$	−24.1283	+	10.1768i	−0.767625	+	0.323767i
$989$	13.0303			0.414340
$990$		0			0
$991$	10.6138	−	18.3837i	0.337159	−	0.583976i	−0.646738	−	0.762712i	$-0.723867\pi$
$991$	10.6138	−	18.3837i	0.337159	−	0.583976i	0.983897	+	0.178736i	$0.0572007\pi$
$992$	0.593405	−	0.342602i	0.0188406	−	0.0108776i
$993$		0			0
$994$	−2.67301	−	4.62980i	−0.0847829	−	0.146848i
$995$	−1.77854	−	14.4935i	−0.0563836	−	0.459473i
$996$		0			0
$997$	−34.4427	+	19.8855i	−1.09081	+	0.629780i	−0.933792	−	0.357816i	$-0.883522\pi$
$997$	−34.4427	+	19.8855i	−1.09081	+	0.629780i	−0.157019	+	0.987596i	$0.550188\pi$
$998$	−12.4376	+	7.18085i	−0.393705	+	0.227306i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.t.c.1189.6		20
3.2	odd	2		570.2.q.c.49.5	✓	20
5.4	even	2	inner	1710.2.t.c.1189.4		20
15.14	odd	2		570.2.q.c.49.7	yes	20
19.7	even	3	inner	1710.2.t.c.919.4		20
57.26	odd	6		570.2.q.c.349.7	yes	20
95.64	even	6	inner	1710.2.t.c.919.6		20
285.254	odd	6		570.2.q.c.349.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.c.49.5	✓	20	3.2	odd	2
570.2.q.c.49.7	yes	20	15.14	odd	2
570.2.q.c.349.5	yes	20	285.254	odd	6
570.2.q.c.349.7	yes	20	57.26	odd	6
1710.2.t.c.919.4		20	19.7	even	3	inner
1710.2.t.c.919.6		20	95.64	even	6	inner
1710.2.t.c.1189.4		20	5.4	even	2	inner
1710.2.t.c.1189.6		20	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.05825 - 0.873846i) q^{5} +2.32136i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.05825 - 0.873846i) q^{5} +2.32136i q^{7} +1.00000i q^{8} +(-1.34557 - 1.78590i) q^{10} +2.85165 q^{11} +(5.20277 - 3.00382i) q^{13} +(-1.16068 + 2.01036i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.79487 - 2.19097i) q^{17} +(-2.63121 + 3.47516i) q^{19} +(-0.272353 - 2.21942i) q^{20} +(2.46960 + 1.42582i) q^{22} +(4.36172 - 2.51824i) q^{23} +(3.47279 + 3.59719i) q^{25} +6.00764 q^{26} +(-2.01036 + 1.16068i) q^{28} +(4.41039 + 7.63902i) q^{29} -0.685205 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.19097 - 3.79487i) q^{34} +(2.02851 - 4.77794i) q^{35} +7.79872i q^{37} +(-4.01627 + 1.69397i) q^{38} +(0.873846 - 2.05825i) q^{40} +(-2.58128 + 4.47091i) q^{41} +(2.24057 + 1.29360i) q^{43} +(1.42582 + 2.46960i) q^{44} +5.03648 q^{46} +(-6.83132 + 3.94406i) q^{47} +1.61129 q^{49} +(1.20893 + 4.85165i) q^{50} +(5.20277 + 3.00382i) q^{52} +(4.86905 - 2.81115i) q^{53} +(-5.86941 - 2.49190i) q^{55} -2.32136 q^{56} +8.82078i q^{58} +(0.724643 - 1.25512i) q^{59} +(5.40264 + 9.35765i) q^{61} +(-0.593405 - 0.342602i) q^{62} -1.00000 q^{64} +(-13.3335 + 1.63620i) q^{65} +(5.89514 - 3.40356i) q^{67} -4.38194i q^{68} +(4.14571 - 3.12356i) q^{70} +(-1.15149 + 1.99443i) q^{71} +(-5.38195 - 3.10727i) q^{73} +(-3.89936 + 6.75389i) q^{74} +(-4.32518 - 0.541114i) q^{76} +6.61970i q^{77} +(2.00683 - 3.47593i) q^{79} +(1.78590 - 1.34557i) q^{80} +(-4.47091 + 2.58128i) q^{82} +12.2192i q^{83} +(5.89622 + 7.82569i) q^{85} +(1.29360 + 2.24057i) q^{86} +2.85165i q^{88} +(4.34444 + 7.52479i) q^{89} +(6.97295 + 12.0775i) q^{91} +(4.36172 + 2.51824i) q^{92} -7.88813 q^{94} +(8.45244 - 4.85348i) q^{95} +(5.79684 + 3.34681i) q^{97} +(1.39542 + 0.805646i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4}+O(q^{10}) \) 20 * q + 10 * q^4	\( 20 q + 10 q^{4} - 2 q^{10} - 12 q^{11} - 10 q^{14} - 10 q^{16} + 6 q^{19} + 14 q^{25} - 8 q^{29} + 40 q^{31} + 12 q^{34} - 2 q^{35} + 2 q^{40} + 14 q^{41} - 6 q^{44} + 44 q^{46} - 8 q^{49} + 8 q^{50} - 20 q^{56} - 8 q^{59} + 16 q^{61} - 20 q^{64} - 40 q^{65} + 8 q^{70} + 4 q^{71} - 26 q^{74} + 8 q^{79} - 16 q^{85} + 20 q^{86} + 2 q^{89} - 44 q^{91} - 32 q^{94} + 80 q^{95}+O(q^{100}) \) 20 * q + 10 * q^4 - 2 * q^10 - 12 * q^11 - 10 * q^14 - 10 * q^16 + 6 * q^19 + 14 * q^25 - 8 * q^29 + 40 * q^31 + 12 * q^34 - 2 * q^35 + 2 * q^40 + 14 * q^41 - 6 * q^44 + 44 * q^46 - 8 * q^49 + 8 * q^50 - 20 * q^56 - 8 * q^59 + 16 * q^61 - 20 * q^64 - 40 * q^65 + 8 * q^70 + 4 * q^71 - 26 * q^74 + 8 * q^79 - 16 * q^85 + 20 * q^86 + 2 * q^89 - 44 * q^91 - 32 * q^94 + 80 * q^95

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