LMFDB - Embedded newform 585.2.bf.a.244.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,2,Mod(199,585)] 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("585.199"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			244.2
Root			$-0.228425 - 1.39564i$ of defining polynomial
Character	$\chi$	$=$	585.244
Dual form			585.2.bf.a.199.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.228425 - 0.395644i) q^{2} +(0.895644 - 1.55130i) q^{4} +(2.18890 - 0.456850i) q^{5} +(-0.866025 + 1.50000i) q^{7} -1.73205 q^{8} +(-0.680750 - 0.761669i) q^{10} +(2.29129 - 1.32288i) q^{11} +(3.46410 - 1.00000i) q^{13} +0.791288 q^{14} +(-1.39564 - 2.41733i) q^{16} +(3.96863 + 2.29129i) q^{17} +(-1.50000 - 0.866025i) q^{19} +(1.25176 - 3.80482i) q^{20} +(-1.04678 - 0.604356i) q^{22} +(-3.96863 + 2.29129i) q^{23} +(4.58258 - 2.00000i) q^{25} +(-1.18693 - 1.14213i) q^{26} +(1.55130 + 2.68693i) q^{28} +(-2.29129 - 3.96863i) q^{29} -6.20520i q^{31} +(-2.36965 + 4.10436i) q^{32} -2.09355i q^{34} +(-1.21037 + 3.67900i) q^{35} +(3.96863 + 6.87386i) q^{37} +0.791288i q^{38} +(-3.79129 + 0.791288i) q^{40} +(-2.29129 + 1.32288i) q^{41} +(-9.16478 - 5.29129i) q^{43} -4.73930i q^{44} +(1.81307 + 1.04678i) q^{46} -1.82740 q^{47} +(2.00000 + 3.46410i) q^{49} +(-1.83806 - 1.35622i) q^{50} +(1.55130 - 6.26951i) q^{52} -7.58258i q^{53} +(4.41105 - 3.94242i) q^{55} +(1.50000 - 2.59808i) q^{56} +(-1.04678 + 1.81307i) q^{58} +(12.0826 + 6.97588i) q^{59} +(0.708712 - 1.22753i) q^{61} +(-2.45505 + 1.41742i) q^{62} -3.41742 q^{64} +(7.12573 - 3.77148i) q^{65} +(-0.504525 - 0.873864i) q^{67} +(7.10895 - 4.10436i) q^{68} +(1.73205 - 0.361500i) q^{70} +(-6.08258 - 3.51178i) q^{71} +(1.81307 - 3.14033i) q^{74} +(-2.68693 + 1.55130i) q^{76} +4.58258i q^{77} +6.00000 q^{79} +(-4.15928 - 4.65369i) q^{80} +(1.04678 + 0.604356i) q^{82} +6.01450 q^{83} +(9.73371 + 3.20233i) q^{85} +4.83465i q^{86} +(-3.96863 + 2.29129i) q^{88} +(-8.29129 + 4.78698i) q^{89} +(-1.50000 + 6.06218i) q^{91} +8.20871i q^{92} +(0.417424 + 0.723000i) q^{94} +(-3.67900 - 1.21037i) q^{95} +(-5.70068 + 9.87386i) q^{97} +(0.913701 - 1.58258i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 4 q^{10} - 12 q^{14} - 2 q^{16} - 12 q^{19} - 24 q^{20} + 18 q^{26} - 6 q^{35} - 12 q^{40} + 42 q^{46} + 16 q^{49} + 12 q^{50} - 14 q^{55} + 12 q^{56} + 60 q^{59} + 24 q^{61} - 64 q^{64}+ \cdots + 6 q^{95}+O(q^{100}) $ 8 * q - 2 * q^4 - 4 * q^10 - 12 * q^14 - 2 * q^16 - 12 * q^19 - 24 * q^20 + 18 * q^26 - 6 * q^35 - 12 * q^40 + 42 * q^46 + 16 * q^49 + 12 * q^50 - 14 * q^55 + 12 * q^56 + 60 * q^59 + 24 * q^61 - 64 * q^64 + 24 * q^65 - 12 * q^71 + 42 * q^74 + 6 * q^76 + 48 * q^79 - 18 * q^80 + 42 * q^85 - 48 * q^89 - 12 * q^91 + 40 * q^94 + 6 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.228425	−	0.395644i	−0.161521	−	0.279763i	0.773893	−	0.633316i	$-0.218307\pi$
$2$	−0.228425	−	0.395644i	−0.161521	−	0.279763i	−0.935414	+	0.353553i	$0.884973\pi$
$3$		0			0
$3$		0			0
$4$	0.895644	−	1.55130i	0.447822	−	0.775650i
$5$	2.18890	−	0.456850i	0.978906	−	0.204310i
$5$	2.18890	−	0.456850i	0.978906	−	0.204310i
$6$		0			0
$7$	−0.866025	+	1.50000i	−0.327327	+	0.566947i	−0.981981	−	0.188982i	$-0.939481\pi$
$7$	−0.866025	+	1.50000i	−0.327327	+	0.566947i	0.654654	+	0.755929i	$0.272814\pi$
$8$	−1.73205			−0.612372
$9$		0			0
$10$	−0.680750	−	0.761669i	−0.215272	−	0.240861i
$11$	2.29129	−	1.32288i	0.690849	−	0.398862i	−0.113081	−	0.993586i	$-0.536072\pi$
$11$	2.29129	−	1.32288i	0.690849	−	0.398862i	0.803930	+	0.594724i	$0.202739\pi$
$12$		0			0
$13$	3.46410	−	1.00000i	0.960769	−	0.277350i
$13$	3.46410	−	1.00000i	0.960769	−	0.277350i
$14$	0.791288			0.211481
$15$		0			0
$16$	−1.39564	−	2.41733i	−0.348911	−	0.604332i
$17$	3.96863	+	2.29129i	0.962533	+	0.555719i	0.896952	−	0.442128i	$-0.145776\pi$
$17$	3.96863	+	2.29129i	0.962533	+	0.555719i	0.0655816	+	0.997847i	$0.479110\pi$
$18$		0			0
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	0.317970	−	0.948101i	$-0.396999\pi$
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	−0.662094	+	0.749421i	$0.730332\pi$
$20$	1.25176	−	3.80482i	0.279903	−	0.850783i
$21$		0			0
$22$	−1.04678	−	0.604356i	−0.223173	−	0.128849i
$23$	−3.96863	+	2.29129i	−0.827516	+	0.477767i	−0.853001	−	0.521909i	$-0.825220\pi$
$23$	−3.96863	+	2.29129i	−0.827516	+	0.477767i	0.0254855	+	0.999675i	$0.491887\pi$
$24$		0			0
$25$	4.58258	−	2.00000i	0.916515	−	0.400000i
$26$	−1.18693	−	1.14213i	−0.232776	−	0.223989i
$27$		0			0
$28$	1.55130	+	2.68693i	0.293168	+	0.507782i
$29$	−2.29129	−	3.96863i	−0.425481	−	0.736956i	0.570984	−	0.820961i	$-0.306562\pi$
$29$	−2.29129	−	3.96863i	−0.425481	−	0.736956i	−0.996465	+	0.0840058i	$0.973229\pi$
$30$		0			0
$31$		−	6.20520i		−	1.11449i	−0.830349	−	0.557244i	$-0.811859\pi$
$31$		−	6.20520i		−	1.11449i	0.830349	−	0.557244i	$-0.188141\pi$
$32$	−2.36965	+	4.10436i	−0.418899	+	0.725555i
$33$		0			0
$34$		−	2.09355i		−	0.359041i
$35$	−1.21037	+	3.67900i	−0.204590	+	0.621864i
$36$		0			0
$37$	3.96863	+	6.87386i	0.652438	+	1.13006i	0.982529	+	0.186107i	$0.0595872\pi$
$37$	3.96863	+	6.87386i	0.652438	+	1.13006i	−0.330091	+	0.943949i	$0.607080\pi$
$38$			0.791288i			0.128364i
$39$		0			0
$40$	−3.79129	+	0.791288i	−0.599455	+	0.125114i
$41$	−2.29129	+	1.32288i	−0.357839	+	0.206598i	−0.668132	−	0.744042i	$-0.732906\pi$
$41$	−2.29129	+	1.32288i	−0.357839	+	0.206598i	0.310293	+	0.950641i	$0.399573\pi$
$42$		0			0
$43$	−9.16478	−	5.29129i	−1.39762	−	0.806914i	−0.403473	−	0.914991i	$-0.632197\pi$
$43$	−9.16478	−	5.29129i	−1.39762	−	0.806914i	−0.994142	+	0.108078i	$0.965531\pi$
$44$		−	4.73930i		−	0.714477i
$45$		0			0
$46$	1.81307	+	1.04678i	0.267322	+	0.154339i
$47$	−1.82740			−0.266554			−0.133277	−	0.991079i	$-0.542550\pi$
$47$	−1.82740			−0.266554			−0.133277	+	0.991079i	$0.542550\pi$
$48$		0			0
$49$	2.00000	+	3.46410i	0.285714	+	0.494872i
$50$	−1.83806	−	1.35622i	−0.259941	−	0.191798i
$51$		0			0
$52$	1.55130	−	6.26951i	0.215127	−	0.869424i
$53$		−	7.58258i		−	1.04155i	−0.853695	−	0.520773i	$-0.825644\pi$
$53$		−	7.58258i		−	1.04155i	0.853695	−	0.520773i	$-0.174356\pi$
$54$		0			0
$55$	4.41105	−	3.94242i	0.594785	−	0.531596i
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$		0			0
$58$	−1.04678	+	1.81307i	−0.137448	+	0.238068i
$59$	12.0826	+	6.97588i	1.57302	+	0.908182i	0.995796	+	0.0915940i	$0.0291962\pi$
$59$	12.0826	+	6.97588i	1.57302	+	0.908182i	0.577221	+	0.816588i	$0.304137\pi$
$60$		0			0
$61$	0.708712	−	1.22753i	0.0907413	−	0.157169i	−0.817082	−	0.576522i	$-0.804410\pi$
$61$	0.708712	−	1.22753i	0.0907413	−	0.157169i	0.907823	+	0.419353i	$0.137743\pi$
$62$	−2.45505	+	1.41742i	−0.311792	+	0.180013i
$63$		0			0
$64$	−3.41742			−0.427178
$65$	7.12573	−	3.77148i	0.883837	−	0.467794i
$66$		0			0
$67$	−0.504525	−	0.873864i	−0.0616376	−	0.106759i	0.833560	−	0.552429i	$-0.186299\pi$
$67$	−0.504525	−	0.873864i	−0.0616376	−	0.106759i	−0.895198	+	0.445670i	$0.852966\pi$
$68$	7.10895	−	4.10436i	0.862087	−	0.497726i
$69$		0			0
$70$	1.73205	−	0.361500i	0.207020	−	0.0432075i
$71$	−6.08258	−	3.51178i	−0.721869	−	0.416771i	0.0935712	−	0.995613i	$-0.470172\pi$
$71$	−6.08258	−	3.51178i	−0.721869	−	0.416771i	−0.815440	+	0.578841i	$0.803505\pi$
$72$		0			0
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	1.81307	−	3.14033i	0.210765	−	0.365056i
$75$		0			0
$76$	−2.68693	+	1.55130i	−0.308212	+	0.177946i
$77$			4.58258i			0.522233i
$78$		0			0
$79$	6.00000			0.675053			0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000			0.675053			0.337526	+	0.941316i	$0.390410\pi$
$80$	−4.15928	−	4.65369i	−0.465022	−	0.520298i
$81$		0			0
$82$	1.04678	+	0.604356i	0.115597	+	0.0667400i
$83$	6.01450			0.660177			0.330089	−	0.943950i	$-0.392921\pi$
$83$	6.01450			0.660177			0.330089	+	0.943950i	$0.392921\pi$
$84$		0			0
$85$	9.73371	+	3.20233i	1.05577	+	0.347342i
$86$			4.83465i			0.521334i
$87$		0			0
$88$	−3.96863	+	2.29129i	−0.423057	+	0.244252i
$89$	−8.29129	+	4.78698i	−0.878875	+	0.507419i	−0.870287	−	0.492545i	$-0.836067\pi$
$89$	−8.29129	+	4.78698i	−0.878875	+	0.507419i	−0.00858752	+	0.999963i	$0.502734\pi$
$90$		0			0
$91$	−1.50000	+	6.06218i	−0.157243	+	0.635489i
$92$			8.20871i			0.855817i
$93$		0			0
$94$	0.417424	+	0.723000i	0.0430540	+	0.0745718i
$95$	−3.67900	−	1.21037i	−0.377457	−	0.124181i
$96$		0			0
$97$	−5.70068	+	9.87386i	−0.578816	+	1.00254i	0.416799	+	0.908999i	$0.363152\pi$
$97$	−5.70068	+	9.87386i	−0.578816	+	1.00254i	−0.995615	+	0.0935404i	$0.970182\pi$
$98$	0.913701	−	1.58258i	0.0922977	−	0.159864i
$99$		0			0
$100$	1.00175	−	8.90024i	0.100175	−	0.890024i
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$		0			0
$103$			3.16515i			0.311872i	0.987767	+	0.155936i	$0.0498393\pi$
$103$			3.16515i			0.311872i	−0.987767	+	0.155936i	$0.950161\pi$
$104$	−6.00000	+	1.73205i	−0.588348	+	0.169842i
$105$		0			0
$106$	−3.00000	+	1.73205i	−0.291386	+	0.168232i
$107$	−9.16478	+	5.29129i	−0.885993	+	0.511528i	−0.872630	−	0.488383i	$-0.837587\pi$
$107$	−9.16478	+	5.29129i	−0.885993	+	0.511528i	−0.0133631	+	0.999911i	$0.504254\pi$
$108$		0			0
$109$			13.1334i			1.25795i	0.777425	+	0.628976i	$0.216526\pi$
$109$			13.1334i			1.25795i	−0.777425	+	0.628976i	$0.783474\pi$
$110$	−2.56739	−	0.844656i	−0.244791	−	0.0805348i
$111$		0			0
$112$	4.83465			0.456832
$113$	−6.42368	−	3.70871i	−0.604289	−	0.348886i	0.166438	−	0.986052i	$-0.446773\pi$
$113$	−6.42368	−	3.70871i	−0.604289	−	0.348886i	−0.770727	+	0.637166i	$0.780107\pi$
$114$		0			0
$115$	−7.64016	+	6.82847i	−0.712448	+	0.636758i
$116$	−8.20871			−0.762160
$117$		0			0
$118$		−	6.37386i		−	0.586762i
$119$	−6.87386	+	3.96863i	−0.630126	+	0.363803i
$120$		0			0
$121$	−2.00000	+	3.46410i	−0.181818	+	0.314918i
$122$	−0.647551			−0.0586265
$123$		0			0
$124$	−9.62614	−	5.55765i	−0.864453	−	0.499092i
$125$	9.11710	−	6.47135i	0.815459	−	0.578815i
$126$		0			0
$127$	−15.3700	+	8.87386i	−1.36387	+	0.787428i	−0.990136	−	0.140110i	$-0.955254\pi$
$127$	−15.3700	+	8.87386i	−1.36387	+	0.787428i	−0.373729	+	0.927538i	$0.621921\pi$
$128$	5.51993	+	9.56080i	0.487897	+	0.845063i
$129$		0			0
$130$	−3.11986	−	1.95775i	−0.273630	−	0.171706i
$131$	7.58258			0.662493			0.331246	−	0.943544i	$-0.392531\pi$
$131$	7.58258			0.662493			0.331246	+	0.943544i	$0.392531\pi$
$132$		0			0
$133$	2.59808	−	1.50000i	0.225282	−	0.130066i
$134$	−0.230493	+	0.399225i	−0.0199115	+	0.0344878i
$135$		0			0
$136$	−6.87386	−	3.96863i	−0.589429	−	0.340307i
$137$	−5.24383	+	9.08258i	−0.448010	+	0.775977i	−0.998256	−	0.0590258i	$-0.981201\pi$
$137$	−5.24383	+	9.08258i	−0.448010	+	0.775977i	0.550246	+	0.835003i	$0.314534\pi$
$138$		0			0
$139$	−10.8739	+	18.8341i	−0.922309	+	1.59749i	−0.126476	+	0.991970i	$0.540367\pi$
$139$	−10.8739	+	18.8341i	−0.922309	+	1.59749i	−0.795833	+	0.605517i	$0.792967\pi$
$140$	4.62317	+	5.17272i	0.390729	+	0.437174i
$141$		0			0
$142$			3.20871i			0.269269i
$143$	6.61438	−	6.87386i	0.553122	−	0.574821i
$144$		0			0
$145$	−6.82847	−	7.64016i	−0.567074	−	0.634480i
$146$		0			0
$147$		0			0
$148$	14.2179			1.16870
$149$	14.4564	+	8.34643i	1.18432	+	0.683766i	0.957009	−	0.290057i	$-0.0936742\pi$
$149$	14.4564	+	8.34643i	1.18432	+	0.683766i	0.227308	+	0.973823i	$0.427008\pi$
$150$		0			0
$151$			9.66930i			0.786877i	0.919351	+	0.393438i	$0.128715\pi$
$151$			9.66930i			0.786877i	−0.919351	+	0.393438i	$0.871285\pi$
$152$	2.59808	+	1.50000i	0.210732	+	0.121666i
$153$		0			0
$154$	1.81307	−	1.04678i	0.146101	−	0.0843516i
$155$	−2.83485	−	13.5826i	−0.227701	−	1.09098i
$156$		0			0
$157$		−	9.16515i		−	0.731459i	−0.930721	−	0.365729i	$-0.880820\pi$
$157$		−	9.16515i		−	0.731459i	0.930721	−	0.365729i	$-0.119180\pi$
$158$	−1.37055	−	2.37386i	−0.109035	−	0.188854i
$159$		0			0
$160$	−3.31186	+	10.0666i	−0.261825	+	0.795835i
$161$		−	7.93725i		−	0.625543i
$162$		0			0
$163$	10.5353	−	18.2477i	0.825191	−	1.42927i	−0.0765827	−	0.997063i	$-0.524401\pi$
$163$	10.5353	−	18.2477i	0.825191	−	1.42927i	0.901773	−	0.432209i	$-0.142266\pi$
$164$			4.73930i			0.370077i
$165$		0			0
$166$	−1.37386	−	2.37960i	−0.106632	−	0.184693i
$167$	4.78698	+	8.29129i	0.370427	+	0.641599i	0.989631	−	0.143631i	$-0.0458779\pi$
$167$	4.78698	+	8.29129i	0.370427	+	0.641599i	−0.619204	+	0.785230i	$0.712545\pi$
$168$		0			0
$169$	11.0000	−	6.92820i	0.846154	−	0.532939i
$170$	−0.956439	−	4.58258i	−0.0733555	−	0.351468i
$171$		0			0
$172$	−16.4168	+	9.47822i	−1.25177	+	0.722707i
$173$	−14.3609	−	8.29129i	−1.09184	−	0.630375i	−0.157775	−	0.987475i	$-0.550432\pi$
$173$	−14.3609	−	8.29129i	−1.09184	−	0.630375i	−0.934066	+	0.357100i	$0.883766\pi$
$174$		0			0
$175$	−0.968627	+	8.60591i	−0.0732213	+	0.650546i
$176$	−6.39564	−	3.69253i	−0.482090	−	0.278335i
$177$		0			0
$178$	3.78788	+	2.18693i	0.283913	+	0.163917i
$179$	−9.08258	−	15.7315i	−0.678864	−	1.17583i	−0.975323	−	0.220781i	$-0.929139\pi$
$179$	−9.08258	−	15.7315i	−0.678864	−	1.17583i	0.296460	−	0.955045i	$-0.404194\pi$
$180$		0			0
$181$	8.74773			0.650213			0.325107	−	0.945677i	$-0.394600\pi$
$181$	8.74773			0.650213			0.325107	+	0.945677i	$0.394600\pi$
$182$	2.74110	−	0.791288i	0.203184	−	0.0586542i
$183$		0			0
$184$	6.87386	−	3.96863i	0.506748	−	0.292571i
$185$	11.8273	+	13.2331i	0.869557	+	0.972920i
$186$		0			0
$187$	12.1244			0.886621
$188$	−1.63670	+	2.83485i	−0.119369	+	0.206753i
$189$		0			0
$190$	0.361500	+	1.73205i	0.0262260	+	0.125656i
$191$	−8.29129	+	14.3609i	−0.599937	+	1.03912i	0.392893	+	0.919584i	$0.371474\pi$
$191$	−8.29129	+	14.3609i	−0.599937	+	1.03912i	−0.992830	+	0.119536i	$0.961859\pi$
$192$		0			0
$193$	7.43273	+	12.8739i	0.535020	+	0.926681i	0.999162	+	0.0409206i	$0.0130291\pi$
$193$	7.43273	+	12.8739i	0.535020	+	0.926681i	−0.464143	+	0.885760i	$0.653638\pi$
$194$	5.20871			0.373964
$195$		0			0
$196$	7.16515			0.511797
$197$	7.33738	+	12.7087i	0.522767	+	0.905458i	0.999649	+	0.0264912i	$0.00843339\pi$
$197$	7.33738	+	12.7087i	0.522767	+	0.905458i	−0.476882	+	0.878967i	$0.658233\pi$
$198$		0			0
$199$	5.29129	−	9.16478i	0.375089	−	0.649674i	−0.615251	−	0.788331i	$-0.710945\pi$
$199$	5.29129	−	9.16478i	0.375089	−	0.649674i	0.990340	+	0.138657i	$0.0442787\pi$
$200$	−7.93725	+	3.46410i	−0.561249	+	0.244949i
$201$		0			0
$202$	2.05583	−	3.56080i	0.144647	−	0.250537i
$203$	7.93725			0.557086
$204$		0			0
$205$	−4.41105	+	3.94242i	−0.308081	+	0.275351i
$206$	1.25227	−	0.723000i	0.0872500	−	0.0503738i
$207$		0			0
$208$	−7.25198	−	6.97822i	−0.502834	−	0.483852i
$209$	−4.58258			−0.316983
$210$		0			0
$211$	0.0825757	+	0.143025i	0.00568475	+	0.00984627i	0.868854	−	0.495069i	$-0.164857\pi$
$211$	0.0825757	+	0.143025i	0.00568475	+	0.00984627i	−0.863169	+	0.504915i	$0.831524\pi$
$212$	−11.7629	−	6.79129i	−0.807876	−	0.466428i
$213$		0			0
$214$	4.18693	+	2.41733i	0.286213	+	0.165245i
$215$	−22.4781	−	7.39517i	−1.53300	−	0.504347i
$216$		0			0
$217$	9.30780	+	5.37386i	0.631855	+	0.364802i
$218$	5.19615	−	3.00000i	0.351928	−	0.203186i
$219$		0			0
$220$	−2.16515	−	10.3739i	−0.145974	−	0.699406i
$221$	16.0390	+	3.96863i	1.07890	+	0.266959i
$222$		0			0
$223$	−4.33013	−	7.50000i	−0.289967	−	0.502237i	0.683835	−	0.729637i	$-0.260311\pi$
$223$	−4.33013	−	7.50000i	−0.289967	−	0.502237i	−0.973801	+	0.227400i	$0.926978\pi$
$224$	−4.10436	−	7.10895i	−0.274234	−	0.474987i
$225$		0			0
$226$			3.38865i			0.225410i
$227$	−0.409175	+	0.708712i	−0.0271579	+	0.0470389i	−0.879285	−	0.476296i	$-0.841979\pi$
$227$	−0.409175	+	0.708712i	−0.0271579	+	0.0470389i	0.852127	+	0.523335i	$0.175312\pi$
$228$		0			0
$229$		−	26.2668i		−	1.73576i	−0.496774	−	0.867880i	$-0.665482\pi$
$229$		−	26.2668i		−	1.73576i	0.496774	−	0.867880i	$-0.334518\pi$
$230$	4.44685	+	1.46299i	0.293216	+	0.0964665i
$231$		0			0
$232$	3.96863	+	6.87386i	0.260553	+	0.451291i
$233$		−	2.83485i		−	0.185717i	−0.995679	−	0.0928586i	$-0.970400\pi$
$233$		−	2.83485i		−	0.185717i	0.995679	−	0.0928586i	$-0.0296004\pi$
$234$		0			0
$235$	−4.00000	+	0.834849i	−0.260931	+	0.0544595i
$236$	21.6434	−	12.4958i	1.40886	−	0.813408i
$237$		0			0
$238$	3.14033	+	1.81307i	0.203557	+	0.117524i
$239$			0.190700i			0.0123354i	0.999981	+	0.00616769i	$0.00196325\pi$
$239$			0.190700i			0.0123354i	−0.999981	+	0.00616769i	$0.998037\pi$
$240$		0			0
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	0.450910	−	0.892570i	$-0.351100\pi$
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	−0.547533	+	0.836784i	$0.684433\pi$
$242$	1.82740			0.117470
$243$		0			0
$244$	−1.26951	−	2.19885i	−0.0812719	−	0.140767i
$245$	5.96038	+	6.66888i	0.380795	+	0.426059i
$246$		0			0
$247$	−6.06218	−	1.50000i	−0.385727	−	0.0954427i
$248$			10.7477i			0.682481i
$249$		0			0
$250$	−4.64293	−	2.12891i	−0.293644	−	0.134644i
$251$	−0.0825757	+	0.143025i	−0.00521213	+	0.00902768i	−0.868620	−	0.495479i	$-0.834992\pi$
$251$	−0.0825757	+	0.143025i	−0.00521213	+	0.00902768i	0.863408	+	0.504507i	$0.168326\pi$
$252$		0			0
$253$	−6.06218	+	10.5000i	−0.381126	+	0.660129i
$254$	7.02178	+	4.05403i	0.440586	+	0.254372i
$255$		0			0
$256$	−0.895644	+	1.55130i	−0.0559777	+	0.0969563i
$257$	−15.7315	+	9.08258i	−0.981303	+	0.566556i	−0.902663	−	0.430348i	$-0.858391\pi$
$257$	−15.7315	+	9.08258i	−0.981303	+	0.566556i	−0.0786397	+	0.996903i	$0.525058\pi$
$258$		0			0
$259$	−13.7477			−0.854242
$260$	0.531418	−	14.4320i	0.0329571	−	0.895037i
$261$		0			0
$262$	−1.73205	−	3.00000i	−0.107006	−	0.185341i
$263$	−7.79423	+	4.50000i	−0.480613	+	0.277482i	−0.720672	−	0.693276i	$-0.756167\pi$
$263$	−7.79423	+	4.50000i	−0.480613	+	0.277482i	0.240059	+	0.970758i	$0.422833\pi$
$264$		0			0
$265$	−3.46410	−	16.5975i	−0.212798	−	1.01958i
$266$	−1.18693	−	0.685275i	−0.0727755	−	0.0420169i
$267$		0			0
$268$	−1.80750			−0.110411
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	−0.541533	−	0.840679i	$-0.682156\pi$
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	0.998816	+	0.0486418i	$0.0154893\pi$
$270$		0			0
$271$	7.50000	−	4.33013i	0.455593	−	0.263036i	−0.254597	−	0.967047i	$-0.581943\pi$
$271$	7.50000	−	4.33013i	0.455593	−	0.263036i	0.710189	+	0.704011i	$0.248609\pi$
$272$		−	12.7913i		−	0.775586i
$273$		0			0
$274$	4.79129			0.289452
$275$	7.85425	−	10.6448i	0.473629	−	0.641903i
$276$		0			0
$277$	−6.42368	−	3.70871i	−0.385961	−	0.222835i	0.294447	−	0.955668i	$-0.404864\pi$
$277$	−6.42368	−	3.70871i	−0.385961	−	0.222835i	−0.680409	+	0.732833i	$0.738198\pi$
$278$	9.93545			0.595889
$279$		0			0
$280$	2.09642	−	6.37221i	0.125285	−	0.380812i
$281$			3.65480i			0.218027i	0.994040	+	0.109014i	$0.0347692\pi$
$281$			3.65480i			0.218027i	−0.994040	+	0.109014i	$0.965231\pi$
$282$		0			0
$283$	−24.0302	+	13.8739i	−1.42845	+	0.824716i	−0.996998	−	0.0774209i	$-0.975331\pi$
$283$	−24.0302	+	13.8739i	−1.42845	+	0.824716i	−0.431451	+	0.902136i	$0.641998\pi$
$284$	−10.8956	+	6.29060i	−0.646538	+	0.373279i
$285$		0			0
$286$	−4.23049	−	1.04678i	−0.250154	−	0.0618971i
$287$		−	4.58258i		−	0.270501i
$288$		0			0
$289$	2.00000	+	3.46410i	0.117647	+	0.203771i
$290$	−1.46299	+	4.44685i	−0.0859096	+	0.261128i
$291$		0			0
$292$		0			0
$293$	9.06943	−	15.7087i	0.529842	−	0.917713i	−0.469552	−	0.882905i	$-0.655585\pi$
$293$	9.06943	−	15.7087i	0.529842	−	0.917713i	0.999394	−	0.0348081i	$-0.0110820\pi$
$294$		0			0
$295$	29.6345	+	9.74958i	1.72539	+	0.567642i
$296$	−6.87386	−	11.9059i	−0.399535	−	0.692015i
$297$		0			0
$298$		−	7.62614i		−	0.441770i
$299$	−11.4564	+	11.9059i	−0.662543	+	0.688535i
$300$		0			0
$301$	15.8739	−	9.16478i	0.914954	−	0.528249i
$302$	3.82560	−	2.20871i	0.220139	−	0.127097i
$303$		0			0
$304$			4.83465i			0.277286i
$305$	0.990505	−	3.01071i	0.0567162	−	0.172393i
$306$		0			0
$307$	24.2487			1.38395			0.691974	−	0.721923i	$-0.256741\pi$
$307$	24.2487			1.38395			0.691974	+	0.721923i	$0.256741\pi$
$308$	7.10895	+	4.10436i	0.405070	+	0.233867i
$309$		0			0
$310$	−4.72631	+	4.22419i	−0.268437	+	0.239918i
$311$	−7.58258			−0.429968			−0.214984	−	0.976618i	$-0.568970\pi$
$311$	−7.58258			−0.429968			−0.214984	+	0.976618i	$0.568970\pi$
$312$		0			0
$313$		−	3.25227i		−	0.183829i	−0.995767	−	0.0919147i	$-0.970701\pi$
$313$		−	3.25227i		−	0.183829i	0.995767	−	0.0919147i	$-0.0292987\pi$
$314$	−3.62614	+	2.09355i	−0.204635	+	0.118146i
$315$		0			0
$316$	5.37386	−	9.30780i	0.302303	−	0.523605i
$317$	0.190700			0.0107108			0.00535540	−	0.999986i	$-0.498295\pi$
$317$	0.190700			0.0107108			0.00535540	+	0.999986i	$0.498295\pi$
$318$		0			0
$319$	−10.5000	−	6.06218i	−0.587887	−	0.339417i
$320$	−7.48040	+	1.56125i	−0.418167	+	0.0872766i
$321$		0			0
$322$	−3.14033	+	1.81307i	−0.175004	+	0.101038i
$323$	−3.96863	−	6.87386i	−0.220820	−	0.382472i
$324$		0			0
$325$	13.8745	−	11.5108i	0.769619	−	0.638503i
$326$	−9.62614			−0.533142
$327$		0			0
$328$	3.96863	−	2.29129i	0.219131	−	0.126515i
$329$	1.58258	−	2.74110i	0.0872502	−	0.151122i
$330$		0			0
$331$	−3.87386	−	2.23658i	−0.212927	−	0.122933i	0.389744	−	0.920923i	$-0.372563\pi$
$331$	−3.87386	−	2.23658i	−0.212927	−	0.122933i	−0.602671	+	0.797990i	$0.705897\pi$
$332$	5.38685	−	9.33030i	0.295642	−	0.512067i
$333$		0			0
$334$	2.18693	−	3.78788i	0.119664	−	0.207263i
$335$	−1.50358	−	1.68231i	−0.0821494	−	0.0919143i
$336$		0			0
$337$		−	30.7477i		−	1.67494i	−0.546487	−	0.837468i	$-0.684035\pi$
$337$		−	30.7477i		−	1.67494i	0.546487	−	0.837468i	$-0.315965\pi$
$338$	−5.25378	−	2.76951i	−0.285768	−	0.150641i
$339$		0			0
$340$	13.6857	−	12.2318i	0.742212	−	0.663360i
$341$	−8.20871	−	14.2179i	−0.444527	−	0.769943i
$342$		0			0
$343$	−19.0526			−1.02874
$344$	15.8739	+	9.16478i	0.855861	+	0.494132i
$345$		0			0
$346$			7.57575i			0.407275i
$347$	18.4726	+	10.6652i	0.991660	+	0.572535i	0.905770	−	0.423769i	$-0.139293\pi$
$347$	18.4726	+	10.6652i	0.991660	+	0.572535i	0.0858901	+	0.996305i	$0.472627\pi$
$348$		0			0
$349$	2.12614	−	1.22753i	0.113809	−	0.0657079i	−0.442015	−	0.897008i	$-0.645736\pi$
$349$	2.12614	−	1.22753i	0.113809	−	0.0657079i	0.555824	+	0.831300i	$0.312403\pi$
$350$	3.62614	−	1.58258i	0.193825	−	0.0845922i
$351$		0			0
$352$			12.5390i			0.668332i
$353$	−3.41643	−	5.91742i	−0.181838	−	0.314953i	0.760668	−	0.649141i	$-0.224871\pi$
$353$	−3.41643	−	5.91742i	−0.181838	−	0.314953i	−0.942506	+	0.334188i	$0.891538\pi$
$354$		0			0
$355$	−14.9185	−	4.90811i	−0.791792	−	0.260495i
$356$			17.1497i			0.908933i
$357$		0			0
$358$	−4.14938	+	7.18693i	−0.219301	+	0.379841i
$359$		−	19.5293i		−	1.03072i	−0.856975	−	0.515359i	$-0.827659\pi$
$359$		−	19.5293i		−	1.03072i	0.856975	−	0.515359i	$-0.172341\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$	−1.99820	−	3.46099i	−0.105023	−	0.181905i
$363$		0			0
$364$	8.06080	+	7.75650i	0.422500	+	0.406551i
$365$		0			0
$366$		0			0
$367$	1.51358	−	0.873864i	0.0790080	−	0.0456153i	−0.459976	−	0.887932i	$-0.652142\pi$
$367$	1.51358	−	0.873864i	0.0790080	−	0.0456153i	0.538984	+	0.842316i	$0.318808\pi$
$368$	11.0776	+	6.39564i	0.577459	+	0.333396i
$369$		0			0
$370$	2.53397	−	7.70216i	0.131735	−	0.400416i
$371$	11.3739	+	6.56670i	0.590502	+	0.340926i
$372$		0			0
$373$	11.2583	+	6.50000i	0.582934	+	0.336557i	0.762299	−	0.647225i	$-0.224071\pi$
$373$	11.2583	+	6.50000i	0.582934	+	0.336557i	−0.179364	+	0.983783i	$0.557404\pi$
$374$	−2.76951	−	4.79693i	−0.143208	−	0.248043i
$375$		0			0
$376$	3.16515			0.163230
$377$	−11.9059	−	11.4564i	−0.613184	−	0.590037i
$378$		0			0
$379$	−9.24773	+	5.33918i	−0.475024	+	0.274255i	−0.718340	−	0.695692i	$-0.755098\pi$
$379$	−9.24773	+	5.33918i	−0.475024	+	0.274255i	0.243317	+	0.969947i	$0.421765\pi$
$380$	−5.17272	+	4.62317i	−0.265355	+	0.237164i
$381$		0			0
$382$	7.57575			0.387609
$383$	−11.8105	+	20.4564i	−0.603490	+	1.04528i	0.388798	+	0.921323i	$0.372890\pi$
$383$	−11.8105	+	20.4564i	−0.603490	+	1.04528i	−0.992288	+	0.123952i	$0.960443\pi$
$384$		0			0
$385$	2.09355	+	10.0308i	0.106697	+	0.511217i
$386$	3.39564	−	5.88143i	0.172834	−	0.299357i
$387$		0			0
$388$	10.2116	+	17.6869i	0.518413	+	0.897918i
$389$	−3.16515			−0.160480			−0.0802398	−	0.996776i	$-0.525569\pi$
$389$	−3.16515			−0.160480			−0.0802398	+	0.996776i	$0.525569\pi$
$390$		0			0
$391$	−21.0000			−1.06202
$392$	−3.46410	−	6.00000i	−0.174964	−	0.303046i
$393$		0			0
$394$	3.35208	−	5.80598i	0.168876	−	0.292501i
$395$	13.1334	−	2.74110i	0.660813	−	0.137920i
$396$		0			0
$397$	−10.1738	+	17.6216i	−0.510610	+	0.884402i	0.489315	+	0.872107i	$0.337247\pi$
$397$	−10.1738	+	17.6216i	−0.510610	+	0.884402i	−0.999924	+	0.0122949i	$0.996086\pi$
$398$	−4.83465			−0.242339
$399$		0			0
$400$	−11.2303	−	8.28629i	−0.561515	−	0.414315i
$401$	25.8303	−	14.9131i	1.28990	−	0.744726i	0.311267	−	0.950323i	$-0.399247\pi$
$401$	25.8303	−	14.9131i	1.28990	−	0.744726i	0.978637	+	0.205596i	$0.0659134\pi$
$402$		0			0
$403$	−6.20520	−	21.4955i	−0.309103	−	1.07076i
$404$	16.1216			0.802079
$405$		0			0
$406$	−1.81307	−	3.14033i	−0.0899811	−	0.155852i
$407$	18.1865	+	10.5000i	0.901473	+	0.520466i
$408$		0			0
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	0.673830	−	0.738886i	$-0.264648\pi$
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	−0.302979	+	0.952997i	$0.597981\pi$
$410$	2.56739	+	0.844656i	0.126794	+	0.0417146i
$411$		0			0
$412$	4.91010	+	2.83485i	0.241903	+	0.139663i
$413$	−20.9276	+	12.0826i	−1.02978	+	0.594545i
$414$		0			0
$415$	13.1652	−	2.74773i	0.646252	−	0.134881i
$416$	−4.10436	+	16.5876i	−0.201233	+	0.813272i
$417$		0			0
$418$	1.04678	+	1.81307i	0.0511995	+	0.0886801i
$419$	2.91742	+	5.05313i	0.142526	+	0.246861i	0.928447	−	0.371465i	$-0.121144\pi$
$419$	2.91742	+	5.05313i	0.142526	+	0.246861i	−0.785922	+	0.618326i	$0.787811\pi$
$420$		0			0
$421$		−	5.48220i		−	0.267186i	−0.991036	−	0.133593i	$-0.957348\pi$
$421$		−	5.48220i		−	0.267186i	0.991036	−	0.133593i	$-0.0426515\pi$
$422$	0.0377247	−	0.0653411i	0.00183641	−	0.00318076i
$423$		0			0
$424$			13.1334i			0.637815i
$425$	22.7691	+	2.56275i	1.10446	+	0.124311i
$426$		0			0
$427$	1.22753	+	2.12614i	0.0594041	+	0.102891i
$428$			18.9564i			0.916294i
$429$		0			0
$430$	2.20871	+	10.5826i	0.106514	+	0.510337i
$431$	−7.33485	+	4.23478i	−0.353307	+	0.203982i	−0.666141	−	0.745826i	$-0.732055\pi$
$431$	−7.33485	+	4.23478i	−0.353307	+	0.203982i	0.312834	+	0.949808i	$0.398722\pi$
$432$		0			0
$433$	−8.44178	−	4.87386i	−0.405686	−	0.234223i	0.283248	−	0.959047i	$-0.408588\pi$
$433$	−8.44178	−	4.87386i	−0.405686	−	0.234223i	−0.688934	+	0.724824i	$0.741921\pi$
$434$		−	4.91010i		−	0.235692i
$435$		0			0
$436$	20.3739	+	11.7629i	0.975731	+	0.563339i
$437$	7.93725			0.379690
$438$		0			0
$439$	−7.24773	−	12.5534i	−0.345915	−	0.599143i	0.639604	−	0.768704i	$-0.279098\pi$
$439$	−7.24773	−	12.5534i	−0.345915	−	0.599143i	−0.985520	+	0.169562i	$0.945765\pi$
$440$	−7.64016	+	6.82847i	−0.364230	+	0.325535i
$441$		0			0
$442$	−2.09355	−	7.25227i	−0.0995801	−	0.344955i
$443$		−	19.9129i		−	0.946089i	−0.881038	−	0.473045i	$-0.843155\pi$
$443$		−	19.9129i		−	0.946089i	0.881038	−	0.473045i	$-0.156845\pi$
$444$		0			0
$445$	−15.9619	+	14.2661i	−0.756666	+	0.676278i
$446$	−1.97822	+	3.42638i	−0.0936714	+	0.162244i
$447$		0			0
$448$	2.95958	−	5.12614i	0.139827	−	0.242187i
$449$	−9.54356	−	5.50998i	−0.450388	−	0.260032i	0.257606	−	0.966250i	$-0.417066\pi$
$449$	−9.54356	−	5.50998i	−0.450388	−	0.260032i	−0.707994	+	0.706218i	$0.750400\pi$
$450$		0			0
$451$	−3.50000	+	6.06218i	−0.164809	+	0.285457i
$452$	−11.5067	+	6.64337i	−0.541228	+	0.312478i
$453$		0			0
$454$	0.373864			0.0175463
$455$	−0.513844	+	13.9548i	−0.0240894	+	0.654210i
$456$		0			0
$457$	0.866025	+	1.50000i	0.0405110	+	0.0701670i	0.885570	−	0.464506i	$-0.153768\pi$
$457$	0.866025	+	1.50000i	0.0405110	+	0.0701670i	−0.845059	+	0.534673i	$0.820435\pi$
$458$	−10.3923	+	6.00000i	−0.485601	+	0.280362i
$459$		0			0
$460$	3.75015	+	17.9681i	0.174852	+	0.837765i
$461$	−31.0390	−	17.9204i	−1.44563	−	0.834635i	−0.447414	−	0.894327i	$-0.647655\pi$
$461$	−31.0390	−	17.9204i	−1.44563	−	0.834635i	−0.998217	+	0.0596914i	$0.980988\pi$
$462$		0			0
$463$	39.4002			1.83108			0.915542	−	0.402223i	$-0.131762\pi$
$463$	39.4002			1.83108			0.915542	+	0.402223i	$0.131762\pi$
$464$	−6.39564	+	11.0776i	−0.296910	+	0.514264i
$465$		0			0
$466$	−1.12159	+	0.647551i	−0.0519567	+	0.0299972i
$467$		−	24.3303i		−	1.12587i	−0.826500	−	0.562936i	$-0.809672\pi$
$467$		−	24.3303i		−	1.12587i	0.826500	−	0.562936i	$-0.190328\pi$
$468$		0			0
$469$	1.74773			0.0807025
$470$	1.24400	+	1.39188i	0.0573816	+	0.0642024i
$471$		0			0
$472$	−20.9276	−	12.0826i	−0.963272	−	0.556146i
$473$	−27.9989			−1.28739
$474$		0			0
$475$	−8.60591	−	0.968627i	−0.394866	−	0.0444437i
$476$			14.2179i			0.651677i
$477$		0			0
$478$	0.0754495	−	0.0435608i	0.00345098	−	0.00199242i
$479$	−4.03901	+	2.33193i	−0.184547	+	0.106548i	−0.589427	−	0.807821i	$-0.700647\pi$
$479$	−4.03901	+	2.33193i	−0.184547	+	0.106548i	0.404880	+	0.914370i	$0.367313\pi$
$480$		0			0
$481$	20.6216	+	19.8431i	0.940264	+	0.904769i
$482$			0.791288i			0.0360422i
$483$		0			0
$484$	3.58258	+	6.20520i	0.162844	+	0.282055i
$485$	−7.96734	+	24.2173i	−0.361778	+	1.09965i
$486$		0			0
$487$	5.33918	−	9.24773i	0.241941	−	0.419055i	−0.719326	−	0.694673i	$-0.755549\pi$
$487$	5.33918	−	9.24773i	0.241941	−	0.419055i	0.961267	+	0.275618i	$0.0888825\pi$
$488$	−1.22753	+	2.12614i	−0.0555675	+	0.0962457i
$489$		0			0
$490$	1.27700	−	3.88153i	0.0576890	−	0.175349i
$491$	9.70871	+	16.8160i	0.438148	+	0.758895i	0.997547	−	0.0700041i	$-0.0223012\pi$
$491$	9.70871	+	16.8160i	0.438148	+	0.758895i	−0.559399	+	0.828899i	$0.688968\pi$
$492$		0			0
$493$		−	21.0000i		−	0.945792i
$494$	0.791288	+	2.74110i	0.0356017	+	0.123328i
$495$		0			0
$496$	−15.0000	+	8.66025i	−0.673520	+	0.388857i
$497$	10.5353	−	6.08258i	0.472574	−	0.272841i
$498$		0			0
$499$		−	0.723000i		−	0.0323659i	−0.999869	−	0.0161830i	$-0.994849\pi$
$499$		−	0.723000i		−	0.0323659i	0.999869	−	0.0161830i	$-0.00515142\pi$
$500$	−1.87334	−	19.9394i	−0.0837781	−	0.891717i
$501$		0			0
$502$	0.0754495			0.00336747
$503$	0.143025	+	0.0825757i	0.00637718	+	0.00368187i	0.503185	−	0.864179i	$-0.332161\pi$
$503$	0.143025	+	0.0825757i	0.00637718	+	0.00368187i	−0.496808	+	0.867860i	$0.665495\pi$
$504$		0			0
$505$	13.4109	+	15.0050i	0.596775	+	0.667712i
$506$	5.53901			0.246239
$507$		0			0
$508$			31.7913i			1.41051i
$509$	7.33485	−	4.23478i	0.325111	−	0.187703i	−0.328557	−	0.944484i	$-0.606562\pi$
$509$	7.33485	−	4.23478i	0.325111	−	0.187703i	0.653669	+	0.756781i	$0.273229\pi$
$510$		0			0
$511$		0			0
$512$	22.8981			1.01196
$513$		0			0
$514$	7.18693	+	4.14938i	0.317002	+	0.183021i
$515$	1.44600	+	6.92820i	0.0637184	+	0.305293i
$516$		0			0
$517$	−4.18710	+	2.41742i	−0.184149	+	0.106318i
$518$	3.14033	+	5.43920i	0.137978	+	0.238985i
$519$		0			0
$520$	−12.3421	+	6.53239i	−0.541238	+	0.286464i
$521$	−27.4955			−1.20460			−0.602299	−	0.798271i	$-0.705748\pi$
$521$	−27.4955			−1.20460			−0.602299	+	0.798271i	$0.705748\pi$
$522$		0			0
$523$	0.143025	−	0.0825757i	0.00625406	−	0.00361078i	−0.496870	−	0.867825i	$-0.665517\pi$
$523$	0.143025	−	0.0825757i	0.00625406	−	0.00361078i	0.503124	+	0.864214i	$0.332184\pi$
$524$	6.79129	−	11.7629i	0.296679	−	0.513863i
$525$		0			0
$526$	3.56080	+	2.05583i	0.155258	+	0.0896383i
$527$	14.2179	−	24.6261i	0.619342	−	1.07273i
$528$		0			0
$529$	−1.00000	+	1.73205i	−0.0434783	+	0.0753066i
$530$	−5.77542	+	5.16184i	−0.250868	+	0.224216i
$531$		0			0
$532$		−	5.37386i		−	0.232987i
$533$	−6.61438	+	6.87386i	−0.286501	+	0.297740i
$534$		0			0
$535$	−17.6435	+	15.7690i	−0.762794	+	0.681755i
$536$	0.873864	+	1.51358i	0.0377452	+	0.0653765i
$537$		0			0
$538$	−6.85275			−0.295443
$539$	9.16515	+	5.29150i	0.394771	+	0.227921i
$540$		0			0
$541$			10.3923i			0.446800i	0.974727	+	0.223400i	$0.0717156\pi$
$541$			10.3923i			0.446800i	−0.974727	+	0.223400i	$0.928284\pi$
$542$	−3.42638	−	1.97822i	−0.147175	−	0.0849718i
$543$		0			0
$544$	−18.8085	+	10.8591i	−0.806409	+	0.465580i
$545$	6.00000	+	28.7477i	0.257012	+	1.23142i
$546$		0			0
$547$		−	28.7477i		−	1.22916i	−0.788853	−	0.614582i	$-0.789325\pi$
$547$		−	28.7477i		−	1.22916i	0.788853	−	0.614582i	$-0.210675\pi$
$548$	9.39320	+	16.2695i	0.401258	+	0.694999i
$549$		0			0
$550$	−6.00564	−	0.675957i	−0.256081	−	0.0288229i
$551$			7.93725i			0.338138i
$552$		0			0
$553$	−5.19615	+	9.00000i	−0.220963	+	0.382719i
$554$			3.38865i			0.143970i
$555$		0			0
$556$	19.4782	+	33.7373i	0.826061	+	1.43078i
$557$	−3.87328	−	6.70871i	−0.164116	−	0.284257i	0.772225	−	0.635349i	$-0.219144\pi$
$557$	−3.87328	−	6.70871i	−0.164116	−	0.284257i	−0.936341	+	0.351092i	$0.885810\pi$
$558$		0			0
$559$	−37.0390	−	9.16478i	−1.56658	−	0.387629i
$560$	10.5826	−	2.20871i	0.447195	−	0.0933351i
$561$		0			0
$562$	1.44600	−	0.834849i	0.0609958	−	0.0352160i
$563$	−7.79423	−	4.50000i	−0.328488	−	0.189652i	0.326682	−	0.945134i	$-0.394069\pi$
$563$	−7.79423	−	4.50000i	−0.328488	−	0.189652i	−0.655169	+	0.755482i	$0.727403\pi$
$564$		0			0
$565$	−15.7551	−	5.18335i	−0.662823	−	0.218065i
$566$	10.9782	+	6.33828i	0.461449	+	0.266418i
$567$		0			0
$568$	10.5353	+	6.08258i	0.442053	+	0.255219i
$569$	−3.87386	−	6.70973i	−0.162401	−	0.281286i	0.773328	−	0.634006i	$-0.218590\pi$
$569$	−3.87386	−	6.70973i	−0.162401	−	0.281286i	−0.935729	+	0.352719i	$0.885257\pi$
$570$		0			0
$571$	−35.0780			−1.46797			−0.733985	−	0.679166i	$-0.762342\pi$
$571$	−35.0780			−1.46797			−0.733985	+	0.679166i	$0.762342\pi$
$572$	−4.73930	−	16.4174i	−0.198160	−	0.686447i
$573$		0			0
$574$	−1.81307	+	1.04678i	−0.0756760	+	0.0436916i
$575$	−13.6040	+	18.4373i	−0.567324	+	0.768887i
$576$		0			0
$577$	−6.92820			−0.288425			−0.144212	−	0.989547i	$-0.546065\pi$
$577$	−6.92820			−0.288425			−0.144212	+	0.989547i	$0.546065\pi$
$578$	0.913701	−	1.58258i	0.0380049	−	0.0658265i
$579$		0			0
$580$	−17.9681	+	3.75015i	−0.746083	+	0.155717i
$581$	−5.20871	+	9.02175i	−0.216094	+	0.374285i
$582$		0			0
$583$	−10.0308	−	17.3739i	−0.415433	−	0.719552i
$584$		0			0
$585$		0			0
$586$	−8.28674			−0.342322
$587$	−19.7478	−	34.2042i	−0.815078	−	1.41176i	−0.909272	−	0.416203i	$-0.863361\pi$
$587$	−19.7478	−	34.2042i	−0.815078	−	1.41176i	0.0941934	−	0.995554i	$-0.469973\pi$
$588$		0			0
$589$	−5.37386	+	9.30780i	−0.221426	+	0.383521i
$590$	−2.91190	−	13.9518i	−0.119881	−	0.574385i
$591$		0			0
$592$	11.0776	−	19.1869i	0.455286	−	0.788578i
$593$	21.1660			0.869184			0.434592	−	0.900627i	$-0.356893\pi$
$593$	21.1660			0.869184			0.434592	+	0.900627i	$0.356893\pi$
$594$		0			0
$595$	−13.2331	+	11.8273i	−0.542506	+	0.484870i
$596$	25.8956	−	14.9509i	1.06073	−	0.612411i
$597$		0			0
$598$	7.32743	+	1.81307i	0.299641	+	0.0741419i
$599$	15.4955			0.633127			0.316564	−	0.948571i	$-0.397471\pi$
$599$	15.4955			0.633127			0.316564	+	0.948571i	$0.397471\pi$
$600$		0			0
$601$	−8.45644	−	14.6470i	−0.344945	−	0.597463i	0.640398	−	0.768043i	$-0.278769\pi$
$601$	−8.45644	−	14.6470i	−0.344945	−	0.597463i	−0.985344	+	0.170580i	$0.945436\pi$
$602$	−7.25198	−	4.18693i	−0.295569	−	0.170647i
$603$		0			0
$604$	15.0000	+	8.66025i	0.610341	+	0.352381i
$605$	−2.79523	+	8.49628i	−0.113642	+	0.345423i
$606$		0			0
$607$	6.70973	+	3.87386i	0.272339	+	0.157235i	0.629950	−	0.776635i	$-0.283075\pi$
$607$	6.70973	+	3.87386i	0.272339	+	0.157235i	−0.357611	+	0.933871i	$0.616409\pi$
$608$	7.10895	−	4.10436i	0.288306	−	0.166454i
$609$		0			0
$610$	−1.41742	+	0.295834i	−0.0573898	+	0.0119780i
$611$	−6.33030	+	1.82740i	−0.256097	+	0.0739287i
$612$		0			0
$613$	−2.95958	−	5.12614i	−0.119536	−	0.207043i	0.800048	−	0.599936i	$-0.204807\pi$
$613$	−2.95958	−	5.12614i	−0.119536	−	0.207043i	−0.919584	+	0.392894i	$0.871474\pi$
$614$	−5.53901	−	9.59386i	−0.223536	−	0.387176i
$615$		0			0
$616$		−	7.93725i		−	0.319801i
$617$	6.97588	−	12.0826i	0.280838	−	0.486426i	−0.690753	−	0.723091i	$-0.742721\pi$
$617$	6.97588	−	12.0826i	0.280838	−	0.486426i	0.971591	+	0.236664i	$0.0760542\pi$
$618$		0			0
$619$			29.7309i			1.19499i	0.801874	+	0.597493i	$0.203836\pi$
$619$			29.7309i			1.19499i	−0.801874	+	0.597493i	$0.796164\pi$
$620$	−23.6097	−	7.76745i	−0.948187	−	0.311948i
$621$		0			0
$622$	1.73205	+	3.00000i	0.0694489	+	0.120289i
$623$		−	16.5826i		−	0.664367i
$624$		0			0
$625$	17.0000	−	18.3303i	0.680000	−	0.733212i
$626$	−1.28674	+	0.742901i	−0.0514286	+	0.0296923i
$627$		0			0
$628$	−14.2179	−	8.20871i	−0.567356	−	0.327563i
$629$			36.3731i			1.45029i
$630$		0			0
$631$	−5.12614	−	2.95958i	−0.204068	−	0.117819i	0.394483	−	0.918903i	$-0.370924\pi$
$631$	−5.12614	−	2.95958i	−0.204068	−	0.117819i	−0.598552	+	0.801084i	$0.704257\pi$
$632$	−10.3923			−0.413384
$633$		0			0
$634$	−0.0435608	−	0.0754495i	−0.00173002	−	0.00299648i
$635$	−29.5893	+	26.4458i	−1.17422	+	1.04947i
$636$		0			0
$637$	10.3923	+	10.0000i	0.411758	+	0.396214i
$638$			5.53901i			0.219292i
$639$		0			0
$640$	16.4504	+	18.4059i	0.650260	+	0.727555i
$641$	9.08258	−	15.7315i	0.358740	−	0.621356i	−0.629010	−	0.777397i	$-0.716540\pi$
$641$	9.08258	−	15.7315i	0.358740	−	0.621356i	0.987751	+	0.156041i	$0.0498731\pi$
$642$		0			0
$643$	−10.8968	+	18.8739i	−0.429729	+	0.744313i	−0.996849	−	0.0793227i	$-0.974724\pi$
$643$	−10.8968	+	18.8739i	−0.429729	+	0.744313i	0.567120	+	0.823635i	$0.308058\pi$
$644$	−12.3131	−	7.10895i	−0.485203	−	0.280132i
$645$		0			0
$646$	−1.81307	+	3.14033i	−0.0713342	+	0.123554i
$647$	23.3827	−	13.5000i	0.919268	−	0.530740i	0.0358667	−	0.999357i	$-0.488581\pi$
$647$	23.3827	−	13.5000i	0.919268	−	0.530740i	0.883402	+	0.468617i	$0.155247\pi$
$648$		0			0
$649$	36.9129			1.44896
$650$	−7.72346	−	2.86001i	−0.302939	−	0.112179i
$651$		0			0
$652$	−18.8718	−	32.6869i	−0.739077	−	1.28012i
$653$	37.0882	−	21.4129i	1.45137	−	0.837951i	0.452814	−	0.891605i	$-0.350420\pi$
$653$	37.0882	−	21.4129i	1.45137	−	0.837951i	0.998560	+	0.0536545i	$0.0170870\pi$
$654$		0			0
$655$	16.5975	−	3.46410i	0.648518	−	0.135354i
$656$	6.39564	+	3.69253i	0.249708	+	0.144169i
$657$		0			0
$658$	−1.44600			−0.0563710
$659$	−15.2477	+	26.4098i	−0.593967	+	1.02878i	0.399725	+	0.916635i	$0.369106\pi$
$659$	−15.2477	+	26.4098i	−0.593967	+	1.02878i	−0.993692	+	0.112146i	$0.964228\pi$
$660$		0			0
$661$	15.8739	−	9.16478i	0.617422	−	0.356469i	−0.158443	−	0.987368i	$-0.550647\pi$
$661$	15.8739	−	9.16478i	0.617422	−	0.356469i	0.775865	+	0.630900i	$0.217314\pi$
$662$			2.04356i			0.0794252i
$663$		0			0
$664$	−10.4174			−0.404274
$665$	5.00166	−	4.47028i	0.193956	−	0.173350i
$666$		0			0
$667$	18.1865	+	10.5000i	0.704185	+	0.406562i
$668$	17.1497			0.663542
$669$		0			0
$670$	−0.322139	+	0.979164i	−0.0124453	+	0.0378284i
$671$		−	3.75015i		−	0.144773i
$672$		0			0
$673$	−20.9276	+	12.0826i	−0.806701	+	0.465749i	−0.845809	−	0.533486i	$-0.820882\pi$
$673$	−20.9276	+	12.0826i	−0.806701	+	0.465749i	0.0391079	+	0.999235i	$0.487548\pi$
$674$	−12.1652	+	7.02355i	−0.468584	+	0.270537i
$675$		0			0
$676$	−0.895644	−	23.2695i	−0.0344478	−	0.894981i
$677$		−	2.83485i		−	0.108952i	−0.998515	−	0.0544760i	$-0.982651\pi$
$677$		−	2.83485i		−	0.108952i	0.998515	−	0.0544760i	$-0.0173489\pi$
$678$		0			0
$679$	−9.87386	−	17.1020i	−0.378924	−	0.656316i
$680$	−16.8593	−	5.54661i	−0.646524	−	0.212703i
$681$		0			0
$682$	−3.75015	+	6.49545i	−0.143601	+	0.248724i
$683$	−16.5498	+	28.6652i	−0.633262	+	1.09684i	0.353619	+	0.935390i	$0.384951\pi$
$683$	−16.5498	+	28.6652i	−0.633262	+	1.09684i	−0.986881	+	0.161452i	$0.948382\pi$
$684$		0			0
$685$	−7.32884	+	22.2765i	−0.280021	+	0.851141i
$686$	4.35208	+	7.53803i	0.166163	+	0.287803i
$687$		0			0
$688$			29.5390i			1.12616i
$689$	−7.58258	−	26.2668i	−0.288873	−	1.00069i
$690$		0			0
$691$	17.1261	−	9.88778i	0.651509	−	0.376149i	−0.137525	−	0.990498i	$-0.543915\pi$
$691$	17.1261	−	9.88778i	0.651509	−	0.376149i	0.789034	+	0.614349i	$0.210581\pi$
$692$	−25.7246	+	14.8521i	−0.977901	+	0.564591i
$693$		0			0
$694$		−	9.74475i		−	0.369906i
$695$	−15.1975	+	46.1937i	−0.576472	+	1.75223i
$696$		0			0
$697$	−12.1244			−0.459243
$698$	−0.971326	−	0.560795i	−0.0367652	−	0.0212264i
$699$		0			0
$700$	12.4828	+	9.21047i	0.471806	+	0.348123i
$701$	21.1652			0.799397			0.399698	−	0.916647i	$-0.369115\pi$
$701$	21.1652			0.799397			0.399698	+	0.916647i	$0.369115\pi$
$702$		0			0
$703$		−	13.7477i		−	0.518505i
$704$	−7.83030	+	4.52083i	−0.295116	+	0.170385i
$705$		0			0
$706$	−1.56080	+	2.70338i	−0.0587413	+	0.101743i
$707$	−15.5885			−0.586264
$708$		0			0
$709$	31.5000	+	18.1865i	1.18301	+	0.683010i	0.956708	−	0.291048i	$-0.0940040\pi$
$709$	31.5000	+	18.1865i	1.18301	+	0.683010i	0.226299	+	0.974058i	$0.427337\pi$
$710$	1.46590	+	7.02355i	0.0550143	+	0.263589i
$711$		0			0
$712$	14.3609	−	8.29129i	0.538199	−	0.310729i
$713$	14.2179	+	24.6261i	0.532465	+	0.922256i
$714$		0			0
$715$	11.3379	−	18.0680i	0.424013	−	0.675704i
$716$	−32.5390			−1.21604
$717$		0			0
$718$	−7.72665	+	4.46099i	−0.288356	+	0.166482i
$719$	12.2477	−	21.2137i	0.456763	−	0.791137i	−0.542025	−	0.840363i	$-0.682342\pi$
$719$	12.2477	−	21.2137i	0.456763	−	0.791137i	0.998788	+	0.0492257i	$0.0156754\pi$
$720$		0			0
$721$	−4.74773	−	2.74110i	−0.176815	−	0.102084i
$722$	−3.65480	+	6.33030i	−0.136018	+	0.235589i
$723$		0			0
$724$	7.83485	−	13.5704i	0.291180	−	0.504338i
$725$	−18.4373	−	13.6040i	−0.684742	−	0.505238i
$726$		0			0
$727$			15.2523i			0.565675i	0.959168	+	0.282838i	$0.0912758\pi$
$727$			15.2523i			0.565675i	−0.959168	+	0.282838i	$0.908724\pi$
$728$	2.59808	−	10.5000i	0.0962911	−	0.389156i
$729$		0			0
$730$		0			0
$731$	−24.2477	−	41.9983i	−0.896835	−	1.55336i
$732$		0			0
$733$	22.8027			0.842237			0.421119	−	0.907006i	$-0.361638\pi$
$733$	22.8027			0.842237			0.421119	+	0.907006i	$0.361638\pi$
$734$	−0.691478	−	0.399225i	−0.0255229	−	0.0147357i
$735$		0			0
$736$		−	21.7182i		−	0.800544i
$737$	−2.31203	−	1.33485i	−0.0851646	−	0.0491698i
$738$		0			0
$739$	−14.7523	+	8.51723i	−0.542671	+	0.313311i	−0.746161	−	0.665766i	$-0.768105\pi$
$739$	−14.7523	+	8.51723i	−0.542671	+	0.313311i	0.203490	+	0.979077i	$0.434772\pi$
$740$	31.1216	−	6.49545i	1.14405	−	0.238778i
$741$		0			0
$742$		−	6.00000i		−	0.220267i
$743$	−2.86423	−	4.96099i	−0.105078	−	0.182001i	0.808692	−	0.588232i	$-0.200176\pi$
$743$	−2.86423	−	4.96099i	−0.105078	−	0.182001i	−0.913770	+	0.406232i	$0.866843\pi$
$744$		0			0
$745$	35.4568	+	11.6651i	1.29904	+	0.427375i
$746$		−	5.93905i		−	0.217444i
$747$		0			0
$748$	10.8591	−	18.8085i	0.397048	−	0.687708i
$749$		−	18.3296i		−	0.669748i
$750$		0			0
$751$	−5.87386	−	10.1738i	−0.214340	−	0.371248i	0.738728	−	0.674004i	$-0.235427\pi$
$751$	−5.87386	−	10.1738i	−0.214340	−	0.371248i	−0.953068	+	0.302755i	$0.902093\pi$
$752$	2.55040	+	4.41742i	0.0930036	+	0.161087i
$753$		0			0
$754$	−1.81307	+	7.32743i	−0.0660281	+	0.266849i
$755$	4.41742	+	21.1652i	0.160767	+	0.770279i
$756$		0			0
$757$	−8.44178	+	4.87386i	−0.306822	+	0.177144i	−0.645503	−	0.763757i	$-0.723352\pi$
$757$	−8.44178	+	4.87386i	−0.306822	+	0.177144i	0.338682	+	0.940901i	$0.390019\pi$
$758$	4.22483	+	2.43920i	0.153453	+	0.0885959i
$759$		0			0
$760$	6.37221	+	2.09642i	0.231144	+	0.0760451i
$761$	30.7087	+	17.7297i	1.11319	+	0.642701i	0.939654	−	0.342127i	$-0.111147\pi$
$761$	30.7087	+	17.7297i	1.11319	+	0.642701i	0.173536	+	0.984827i	$0.444481\pi$
$762$		0			0
$763$	−19.7001	−	11.3739i	−0.713192	−	0.411762i
$764$	14.8521	+	25.7246i	0.537330	+	0.930682i
$765$		0			0
$766$	10.7913			0.389905
$767$	48.8311	+	12.0826i	1.76319	+	0.436277i
$768$		0			0
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	−0.723255	−	0.690581i	$-0.757355\pi$
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	0.236433	+	0.971648i	$0.424022\pi$
$770$	3.49041	−	3.11959i	0.125786	−	0.112422i
$771$		0			0
$772$	26.6283			0.958374
$773$	12.0767	−	20.9174i	0.434368	−	0.752347i	−0.562876	−	0.826541i	$-0.690305\pi$
$773$	12.0767	−	20.9174i	0.434368	−	0.752347i	0.997244	+	0.0741940i	$0.0236384\pi$
$774$		0			0
$775$	−12.4104	−	28.4358i	−0.445795	−	1.02144i
$776$	9.87386	−	17.1020i	0.354451	−	0.613927i
$777$		0			0
$778$	0.723000	+	1.25227i	0.0259208	+	0.0448962i
$779$	4.58258			0.164188
$780$		0			0
$781$	−18.5826			−0.664937
$782$	4.79693	+	8.30852i	0.171538	+	0.297112i
$783$		0			0
$784$	5.58258	−	9.66930i	0.199378	−	0.345332i
$785$	−4.18710	−	20.0616i	−0.149444	−	0.716030i
$786$		0			0
$787$	8.15573	−	14.1261i	0.290720	−	0.503542i	−0.683260	−	0.730175i	$-0.739438\pi$
$787$	8.15573	−	14.1261i	0.290720	−	0.503542i	0.973980	+	0.226633i	$0.0727717\pi$
$788$	26.2867			0.936425
$789$		0			0
$790$	−4.08450	−	4.57002i	−0.145320	−	0.162594i
$791$	11.1261	−	6.42368i	0.395600	−	0.228400i
$792$		0			0
$793$	1.22753	−	4.96099i	0.0435907	−	0.176170i
$794$	9.29583			0.329897
$795$		0			0
$796$	−9.47822	−	16.4168i	−0.335947	−	0.581877i
$797$	−38.1727	−	22.0390i	−1.35215	−	0.780662i	−0.363596	−	0.931557i	$-0.618451\pi$
$797$	−38.1727	−	22.0390i	−1.35215	−	0.780662i	−0.988550	+	0.150895i	$0.951785\pi$
$798$		0			0
$799$	−7.25227	−	4.18710i	−0.256567	−	0.148129i
$800$	−2.65039	+	23.5478i	−0.0937056	+	0.832541i
$801$		0			0
$802$	−11.8006	−	6.81307i	−0.416693	−	0.240578i
$803$		0			0
$804$		0			0
$805$	−3.62614	−	17.3739i	−0.127805	−	0.612348i
$806$	−7.08712	+	7.36515i	−0.249633	+	0.259426i
$807$		0			0
$808$	−7.79423	−	13.5000i	−0.274200	−	0.474928i
$809$	27.4129	+	47.4805i	0.963785	+	1.66933i	0.712843	+	0.701323i	$0.247407\pi$
$809$	27.4129	+	47.4805i	0.963785	+	1.66933i	0.250942	+	0.968002i	$0.419260\pi$
$810$		0			0
$811$			50.5155i			1.77384i	0.461923	+	0.886920i	$0.347160\pi$
$811$			50.5155i			1.77384i	−0.461923	+	0.886920i	$0.652840\pi$
$812$	7.10895	−	12.3131i	0.249475	−	0.432104i
$813$		0			0
$814$		−	9.59386i		−	0.336264i
$815$	14.7243	−	44.7555i	0.515770	−	1.56772i
$816$		0			0
$817$	9.16478	+	15.8739i	0.320635	+	0.555356i
$818$		−	3.95644i		−	0.138334i
$819$		0			0
$820$	2.16515	+	10.3739i	0.0756104	+	0.362271i
$821$	−15.7087	+	9.06943i	−0.548238	+	0.316525i	−0.748411	−	0.663235i	$-0.769183\pi$
$821$	−15.7087	+	9.06943i	−0.548238	+	0.316525i	0.200173	+	0.979761i	$0.435850\pi$
$822$		0			0
$823$	27.2083	+	15.7087i	0.948421	+	0.547571i	0.892590	−	0.450869i	$-0.148886\pi$
$823$	27.2083	+	15.7087i	0.948421	+	0.547571i	0.0558311	+	0.998440i	$0.482219\pi$
$824$		−	5.48220i		−	0.190982i
$825$		0			0
$826$	9.56080	+	5.51993i	0.332663	+	0.192063i
$827$	−10.7737			−0.374638			−0.187319	−	0.982299i	$-0.559980\pi$
$827$	−10.7737			−0.374638			−0.187319	+	0.982299i	$0.559980\pi$
$828$		0			0
$829$	−16.6652	−	28.8649i	−0.578805	−	1.00252i	−0.995617	−	0.0935264i	$-0.970186\pi$
$829$	−16.6652	−	28.8649i	−0.578805	−	1.00252i	0.416812	−	0.908993i	$-0.363147\pi$
$830$	−4.09437	−	4.58106i	−0.142118	−	0.159011i
$831$		0			0
$832$	−11.8383	+	3.41742i	−0.410419	+	0.118478i
$833$			18.3303i			0.635107i
$834$		0			0
$835$	14.2661	+	15.9619i	0.493699	+	0.552384i
$836$	−4.10436	+	7.10895i	−0.141952	+	0.245868i
$837$		0			0
$838$	1.33283	−	2.30852i	0.0460417	−	0.0797466i
$839$	−37.8303	−	21.8413i	−1.30605	−	0.754047i	−0.324613	−	0.945847i	$-0.605234\pi$
$839$	−37.8303	−	21.8413i	−1.30605	−	0.754047i	−0.981434	+	0.191800i	$0.938567\pi$
$840$		0			0
$841$	4.00000	−	6.92820i	0.137931	−	0.238904i
$842$	−2.16900	+	1.25227i	−0.0747487	+	0.0431562i
$843$		0			0
$844$	0.295834			0.0101830
$845$	20.9128	−	20.1905i	0.719421	−	0.694574i
$846$		0			0
$847$	−3.46410	−	6.00000i	−0.119028	−	0.206162i
$848$	−18.3296	+	10.5826i	−0.629440	+	0.363407i
$849$		0			0
$850$	−4.18710	−	9.59386i	−0.143616	−	0.329067i
$851$	−31.5000	−	18.1865i	−1.07981	−	0.623426i
$852$		0			0
$853$	−5.63310			−0.192874			−0.0964369	−	0.995339i	$-0.530745\pi$
$853$	−5.63310			−0.192874			−0.0964369	+	0.995339i	$0.530745\pi$
$854$	0.560795	−	0.971326i	0.0191900	−	0.0332381i
$855$		0			0
$856$	15.8739	−	9.16478i	0.542557	−	0.313246i
$857$		−	4.74773i		−	0.162179i	−0.996707	−	0.0810896i	$-0.974160\pi$
$857$		−	4.74773i		−	0.162179i	0.996707	−	0.0810896i	$-0.0258400\pi$
$858$		0			0
$859$	44.2432			1.50956			0.754779	−	0.655979i	$-0.227744\pi$
$859$	44.2432			1.50956			0.754779	+	0.655979i	$0.227744\pi$
$860$	−31.6045	+	28.2469i	−1.07771	+	0.963211i
$861$		0			0
$862$	3.35093	+	1.93466i	0.114133	+	0.0658947i
$863$	−13.6657			−0.465186			−0.232593	−	0.972574i	$-0.574721\pi$
$863$	−13.6657			−0.465186			−0.232593	+	0.972574i	$0.574721\pi$
$864$		0			0
$865$	−35.2225	−	11.5880i	−1.19760	−	0.394004i
$866$			4.45325i			0.151328i
$867$		0			0
$868$	16.6730	−	9.62614i	0.565917	−	0.326732i
$869$	13.7477	−	7.93725i	0.466360	−	0.269253i
$870$		0			0
$871$	−2.62159	−	2.52263i	−0.0888292	−	0.0854759i
$872$		−	22.7477i		−	0.770335i
$873$		0			0
$874$	−1.81307	−	3.14033i	−0.0613279	−	0.106223i
$875$	1.81139	+	19.2800i	0.0612360	+	0.651783i
$876$		0			0
$877$	−3.96863	+	6.87386i	−0.134011	+	0.232114i	−0.925219	−	0.379433i	$-0.876119\pi$
$877$	−3.96863	+	6.87386i	−0.134011	+	0.232114i	0.791208	+	0.611547i	$0.209452\pi$
$878$	−3.31113	+	5.73504i	−0.111745	+	0.193548i
$879$		0			0
$880$	−15.6864	−	5.16072i	−0.528787	−	0.173968i
$881$	18.2477	+	31.6060i	0.614782	+	1.06483i	0.990423	+	0.138068i	$0.0440892\pi$
$881$	18.2477	+	31.6060i	0.614782	+	1.06483i	−0.375641	+	0.926765i	$0.622578\pi$
$882$		0			0
$883$			36.2432i			1.21968i	0.792524	+	0.609840i	$0.208766\pi$
$883$			36.2432i			1.21968i	−0.792524	+	0.609840i	$0.791234\pi$
$884$	20.5218	−	21.3269i	0.690222	−	0.717300i
$885$		0			0
$886$	−7.87841	+	4.54860i	−0.264680	+	0.152813i
$887$	47.1944	−	27.2477i	1.58463	−	0.914889i	0.590465	−	0.807064i	$-0.298945\pi$
$887$	47.1944	−	27.2477i	1.58463	−	0.914889i	0.994170	−	0.107826i	$-0.0343888\pi$
$888$		0			0
$889$		−	30.7400i		−	1.03099i
$890$	9.29039	+	3.05648i	0.311415	+	0.102454i
$891$		0			0
$892$	−15.5130			−0.519414
$893$	2.74110	+	1.58258i	0.0917275	+	0.0529589i
$894$		0			0
$895$	−27.0678	−	30.2853i	−0.904776	−	1.01233i
$896$	−19.1216			−0.638808
$897$		0			0
$898$			5.03447i			0.168002i
$899$	−24.6261	+	14.2179i	−0.821328	+	0.474194i
$900$		0			0
$901$	17.3739	−	30.0924i	0.578807	−	1.00252i
$902$	3.19795			0.106480
$903$		0			0
$904$	11.1261	+	6.42368i	0.370050	+	0.213648i
$905$	19.1479	−	3.99640i	0.636498	−	0.132845i
$906$		0			0
$907$	5.41463	−	3.12614i	0.179790	−	0.103802i	−0.407404	−	0.913248i	$-0.633566\pi$
$907$	5.41463	−	3.12614i	0.179790	−	0.103802i	0.587194	+	0.809446i	$0.300233\pi$
$908$	0.732950	+	1.26951i	0.0243238	+	0.0421301i
$909$		0			0
$910$	5.63850	−	2.98432i	0.186914	−	0.0989294i
$911$	7.91288			0.262165			0.131083	−	0.991371i	$-0.458155\pi$
$911$	7.91288			0.262165			0.131083	+	0.991371i	$0.458155\pi$
$912$		0			0
$913$	13.7810	−	7.95644i	0.456083	−	0.263320i
$914$	0.395644	−	0.685275i	0.0130867	−	0.0226669i
$915$		0			0
$916$	−40.7477	−	23.5257i	−1.34634	−	0.777311i
$917$	−6.56670	+	11.3739i	−0.216852	+	0.375598i
$918$		0			0
$919$	27.0826	−	46.9084i	0.893372	−	1.54737i	0.0575648	−	0.998342i	$-0.481666\pi$
$919$	27.0826	−	46.9084i	0.893372	−	1.54737i	0.835807	−	0.549023i	$-0.185000\pi$
$920$	13.2331	−	11.8273i	0.436284	−	0.389933i
$921$		0			0
$922$			16.3739i			0.539244i
$923$	−24.5824	−	6.08258i	−0.809141	−	0.200210i
$924$		0			0
$925$	31.9343	+	23.5627i	1.04999	+	0.774738i
$926$	−9.00000	−	15.5885i	−0.295758	−	0.512268i
$927$		0			0
$928$	21.7182			0.712935
$929$	−22.8303	−	13.1811i	−0.749038	−	0.432457i	0.0763082	−	0.997084i	$-0.475687\pi$
$929$	−22.8303	−	13.1811i	−0.749038	−	0.432457i	−0.825346	+	0.564627i	$0.809020\pi$
$930$		0			0
$931$		−	6.92820i		−	0.227063i
$932$	−4.39770	−	2.53901i	−0.144052	−	0.0831682i
$933$		0			0
$934$	−9.62614	+	5.55765i	−0.314977	+	0.181852i
$935$	26.5390	−	5.53901i	0.867919	−	0.181145i
$936$		0			0
$937$		−	31.4955i		−	1.02891i	−0.857517	−	0.514456i	$-0.827994\pi$
$937$		−	31.4955i		−	1.02891i	0.857517	−	0.514456i	$-0.172006\pi$
$938$	−0.399225	−	0.691478i	−0.0130352	−	0.0225775i
$939$		0			0
$940$	−2.28747	+	6.95293i	−0.0746092	+	0.226780i
$941$		−	26.4575i		−	0.862490i	−0.902235	−	0.431245i	$-0.858074\pi$
$941$		−	26.4575i		−	0.862490i	0.902235	−	0.431245i	$-0.141926\pi$
$942$		0			0
$943$	6.06218	−	10.5000i	0.197412	−	0.341927i
$944$		−	38.9434i		−	1.26750i
$945$		0			0
$946$	6.39564	+	11.0776i	0.207940	+	0.360163i
$947$	−7.16658	−	12.4129i	−0.232883	−	0.403364i	0.725773	−	0.687935i	$-0.241482\pi$
$947$	−7.16658	−	12.4129i	−0.232883	−	0.403364i	−0.958655	+	0.284570i	$0.908149\pi$
$948$		0			0
$949$		0			0
$950$	1.58258	+	3.62614i	0.0513455	+	0.117647i
$951$		0			0
$952$	11.9059	−	6.87386i	0.385872	−	0.222783i
$953$	−6.99578	−	4.03901i	−0.226616	−	0.130837i	0.382394	−	0.923999i	$-0.375100\pi$
$953$	−6.99578	−	4.03901i	−0.226616	−	0.130837i	−0.609010	+	0.793163i	$0.708433\pi$
$954$		0			0
$955$	−11.5880	+	35.2225i	−0.374979	+	1.13977i
$956$	0.295834	+	0.170800i	0.00956794	+	0.00552406i
$957$		0			0
$958$	1.84522	+	1.06534i	0.0596165	+	0.0344196i
$959$	−9.08258	−	15.7315i	−0.293292	−	0.507996i
$960$		0			0
$961$	−7.50455			−0.242082
$962$	3.14033	−	12.6915i	0.101248	−	0.409190i
$963$		0			0
$964$	−2.68693	+	1.55130i	−0.0865402	+	0.0499640i
$965$	22.1509	+	24.7840i	0.713064	+	0.797824i
$966$		0			0
$967$	−37.3821			−1.20213			−0.601064	−	0.799201i	$-0.705256\pi$
$967$	−37.3821			−1.20213			−0.601064	+	0.799201i	$0.705256\pi$
$968$	3.46410	−	6.00000i	0.111340	−	0.192847i
$969$		0			0
$970$	11.4014	−	2.37960i	0.366075	−	0.0764044i
$971$	−9.24773	+	16.0175i	−0.296774	+	0.514027i	−0.975396	−	0.220460i	$-0.929244\pi$
$971$	−9.24773	+	16.0175i	−0.296774	+	0.514027i	0.678622	+	0.734487i	$0.262577\pi$
$972$		0			0
$973$	−18.8341	−	32.6216i	−0.603793	−	1.04580i
$974$	−4.87841			−0.156314
$975$		0			0
$976$	−3.95644			−0.126643
$977$	17.6542	+	30.5780i	0.564809	+	0.978278i	0.997067	+	0.0765281i	$0.0243835\pi$
$977$	17.6542	+	30.5780i	0.564809	+	0.978278i	−0.432258	+	0.901750i	$0.642283\pi$
$978$		0			0
$979$	−12.6652	+	21.9367i	−0.404780	+	0.701100i
$980$	15.6838	−	3.27340i	0.501001	−	0.104565i
$981$		0			0
$982$	4.43543	−	7.68239i	0.141540	−	0.245155i
$983$	−55.0840			−1.75691			−0.878454	−	0.477827i	$-0.841424\pi$
$983$	−55.0840			−1.75691			−0.878454	+	0.477827i	$0.841424\pi$
$984$		0			0
$985$	21.8668	+	24.4660i	0.696733	+	0.779553i
$986$	−8.30852	+	4.79693i	−0.264597	+	0.152765i
$987$		0			0
$988$	−7.75650	+	8.06080i	−0.246767	+	0.256448i
$989$	48.4955			1.54207
$990$		0			0
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	0.950603	−	0.310409i	$-0.100466\pi$
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	−0.744124	+	0.668042i	$0.767133\pi$
$992$	25.4684	+	14.7042i	0.808621	+	0.466858i
$993$		0			0
$994$	−4.81307	−	2.77883i	−0.152661	−	0.0881390i
$995$	7.39517	−	22.4781i	0.234443	−	0.712604i
$996$		0			0
$997$	0.143025	+	0.0825757i	0.00452966	+	0.00261520i	0.502263	−	0.864715i	$-0.332501\pi$
$997$	0.143025	+	0.0825757i	0.00452966	+	0.00261520i	−0.497733	+	0.867330i	$0.665834\pi$
$998$	−0.286051	+	0.165151i	−0.00905477	+	0.00522778i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bf.a.244.2		8
3.2	odd	2		65.2.l.a.49.3	yes	8
5.4	even	2	inner	585.2.bf.a.244.3		8
12.11	even	2		1040.2.df.b.49.1		8
13.4	even	6	inner	585.2.bf.a.199.3		8
15.2	even	4		325.2.n.c.101.1		4
15.8	even	4		325.2.n.b.101.2		4
15.14	odd	2		65.2.l.a.49.2	yes	8
39.2	even	12		845.2.b.f.339.6		8
39.5	even	4		845.2.n.c.484.4		8
39.8	even	4		845.2.n.d.484.2		8
39.11	even	12		845.2.b.f.339.4		8
39.17	odd	6		65.2.l.a.4.2	✓	8
39.20	even	12		845.2.n.c.529.3		8
39.23	odd	6		845.2.d.c.844.6		8
39.29	odd	6		845.2.d.c.844.4		8
39.32	even	12		845.2.n.d.529.1		8
39.35	odd	6		845.2.l.c.654.3		8
39.38	odd	2		845.2.l.c.699.2		8
60.59	even	2		1040.2.df.b.49.4		8
65.4	even	6	inner	585.2.bf.a.199.2		8
156.95	even	6		1040.2.df.b.849.4		8
195.2	odd	12		4225.2.a.bk.1.2		4
195.17	even	12		325.2.n.c.251.1		4
195.29	odd	6		845.2.d.c.844.5		8
195.44	even	4		845.2.n.d.484.1		8
195.59	even	12		845.2.n.d.529.2		8
195.74	odd	6		845.2.l.c.654.2		8
195.89	even	12		845.2.b.f.339.5		8
195.119	even	12		845.2.b.f.339.3		8
195.128	odd	12		4225.2.a.bj.1.2		4
195.134	odd	6		65.2.l.a.4.3	yes	8
195.149	even	12		845.2.n.c.529.4		8
195.158	odd	12		4225.2.a.bj.1.3		4
195.164	even	4		845.2.n.c.484.3		8
195.167	odd	12		4225.2.a.bk.1.3		4
195.173	even	12		325.2.n.b.251.2		4
195.179	odd	6		845.2.d.c.844.3		8
195.194	odd	2		845.2.l.c.699.3		8
780.719	even	6		1040.2.df.b.849.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.2	✓	8	39.17	odd	6
65.2.l.a.4.3	yes	8	195.134	odd	6
65.2.l.a.49.2	yes	8	15.14	odd	2
65.2.l.a.49.3	yes	8	3.2	odd	2
325.2.n.b.101.2		4	15.8	even	4
325.2.n.b.251.2		4	195.173	even	12
325.2.n.c.101.1		4	15.2	even	4
325.2.n.c.251.1		4	195.17	even	12
585.2.bf.a.199.2		8	65.4	even	6	inner
585.2.bf.a.199.3		8	13.4	even	6	inner
585.2.bf.a.244.2		8	1.1	even	1	trivial
585.2.bf.a.244.3		8	5.4	even	2	inner
845.2.b.f.339.3		8	195.119	even	12
845.2.b.f.339.4		8	39.11	even	12
845.2.b.f.339.5		8	195.89	even	12
845.2.b.f.339.6		8	39.2	even	12
845.2.d.c.844.3		8	195.179	odd	6
845.2.d.c.844.4		8	39.29	odd	6
845.2.d.c.844.5		8	195.29	odd	6
845.2.d.c.844.6		8	39.23	odd	6
845.2.l.c.654.2		8	195.74	odd	6
845.2.l.c.654.3		8	39.35	odd	6
845.2.l.c.699.2		8	39.38	odd	2
845.2.l.c.699.3		8	195.194	odd	2
845.2.n.c.484.3		8	195.164	even	4
845.2.n.c.484.4		8	39.5	even	4
845.2.n.c.529.3		8	39.20	even	12
845.2.n.c.529.4		8	195.149	even	12
845.2.n.d.484.1		8	195.44	even	4
845.2.n.d.484.2		8	39.8	even	4
845.2.n.d.529.1		8	39.32	even	12
845.2.n.d.529.2		8	195.59	even	12
1040.2.df.b.49.1		8	12.11	even	2
1040.2.df.b.49.4		8	60.59	even	2
1040.2.df.b.849.1		8	780.719	even	6
1040.2.df.b.849.4		8	156.95	even	6
4225.2.a.bj.1.2		4	195.128	odd	12
4225.2.a.bj.1.3		4	195.158	odd	12
4225.2.a.bk.1.2		4	195.2	odd	12
4225.2.a.bk.1.3		4	195.167	odd	12

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.228425 - 0.395644i) q^{2} +(0.895644 - 1.55130i) q^{4} +(2.18890 - 0.456850i) q^{5} +(-0.866025 + 1.50000i) q^{7} -1.73205 q^{8} +(-0.680750 - 0.761669i) q^{10} +(2.29129 - 1.32288i) q^{11} +(3.46410 - 1.00000i) q^{13} +0.791288 q^{14} +(-1.39564 - 2.41733i) q^{16} +(3.96863 + 2.29129i) q^{17} +(-1.50000 - 0.866025i) q^{19} +(1.25176 - 3.80482i) q^{20} +(-1.04678 - 0.604356i) q^{22} +(-3.96863 + 2.29129i) q^{23} +(4.58258 - 2.00000i) q^{25} +(-1.18693 - 1.14213i) q^{26} +(1.55130 + 2.68693i) q^{28} +(-2.29129 - 3.96863i) q^{29} -6.20520i q^{31} +(-2.36965 + 4.10436i) q^{32} -2.09355i q^{34} +(-1.21037 + 3.67900i) q^{35} +(3.96863 + 6.87386i) q^{37} +0.791288i q^{38} +(-3.79129 + 0.791288i) q^{40} +(-2.29129 + 1.32288i) q^{41} +(-9.16478 - 5.29129i) q^{43} -4.73930i q^{44} +(1.81307 + 1.04678i) q^{46} -1.82740 q^{47} +(2.00000 + 3.46410i) q^{49} +(-1.83806 - 1.35622i) q^{50} +(1.55130 - 6.26951i) q^{52} -7.58258i q^{53} +(4.41105 - 3.94242i) q^{55} +(1.50000 - 2.59808i) q^{56} +(-1.04678 + 1.81307i) q^{58} +(12.0826 + 6.97588i) q^{59} +(0.708712 - 1.22753i) q^{61} +(-2.45505 + 1.41742i) q^{62} -3.41742 q^{64} +(7.12573 - 3.77148i) q^{65} +(-0.504525 - 0.873864i) q^{67} +(7.10895 - 4.10436i) q^{68} +(1.73205 - 0.361500i) q^{70} +(-6.08258 - 3.51178i) q^{71} +(1.81307 - 3.14033i) q^{74} +(-2.68693 + 1.55130i) q^{76} +4.58258i q^{77} +6.00000 q^{79} +(-4.15928 - 4.65369i) q^{80} +(1.04678 + 0.604356i) q^{82} +6.01450 q^{83} +(9.73371 + 3.20233i) q^{85} +4.83465i q^{86} +(-3.96863 + 2.29129i) q^{88} +(-8.29129 + 4.78698i) q^{89} +(-1.50000 + 6.06218i) q^{91} +8.20871i q^{92} +(0.417424 + 0.723000i) q^{94} +(-3.67900 - 1.21037i) q^{95} +(-5.70068 + 9.87386i) q^{97} +(0.913701 - 1.58258i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 4 q^{10} - 12 q^{14} - 2 q^{16} - 12 q^{19} - 24 q^{20} + 18 q^{26} - 6 q^{35} - 12 q^{40} + 42 q^{46} + 16 q^{49} + 12 q^{50} - 14 q^{55} + 12 q^{56} + 60 q^{59} + 24 q^{61} - 64 q^{64}+ \cdots + 6 q^{95}+O(q^{100}) \) 8 * q - 2 * q^4 - 4 * q^10 - 12 * q^14 - 2 * q^16 - 12 * q^19 - 24 * q^20 + 18 * q^26 - 6 * q^35 - 12 * q^40 + 42 * q^46 + 16 * q^49 + 12 * q^50 - 14 * q^55 + 12 * q^56 + 60 * q^59 + 24 * q^61 - 64 * q^64 + 24 * q^65 - 12 * q^71 + 42 * q^74 + 6 * q^76 + 48 * q^79 - 18 * q^80 + 42 * q^85 - 48 * q^89 - 12 * q^91 + 40 * q^94 + 6 * q^95

Introduction

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