LMFDB - Embedded newform 585.2.bf.a.199.3

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			199.3
Root			$0.228425 - 1.39564i$ of defining polynomial
Character	$\chi$	$=$	585.199
Dual form			585.2.bf.a.244.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.228425 - 0.395644i) q^{2} +(0.895644 + 1.55130i) q^{4} +(-2.18890 + 0.456850i) q^{5} +(0.866025 + 1.50000i) q^{7} +1.73205 q^{8} +(-0.319250 + 0.970381i) q^{10} +(2.29129 + 1.32288i) q^{11} +(-3.46410 - 1.00000i) q^{13} +0.791288 q^{14} +(-1.39564 + 2.41733i) q^{16} +(-3.96863 + 2.29129i) q^{17} +(-1.50000 + 0.866025i) q^{19} +(-2.66919 - 2.98647i) q^{20} +(1.04678 - 0.604356i) q^{22} +(3.96863 + 2.29129i) q^{23} +(4.58258 - 2.00000i) q^{25} +(-1.18693 + 1.14213i) q^{26} +(-1.55130 + 2.68693i) q^{28} +(-2.29129 + 3.96863i) q^{29} +6.20520i q^{31} +(2.36965 + 4.10436i) q^{32} +2.09355i q^{34} +(-2.58092 - 2.88771i) q^{35} +(-3.96863 + 6.87386i) q^{37} +0.791288i q^{38} +(-3.79129 + 0.791288i) q^{40} +(-2.29129 - 1.32288i) q^{41} +(9.16478 - 5.29129i) q^{43} +4.73930i q^{44} +(1.81307 - 1.04678i) q^{46} +1.82740 q^{47} +(2.00000 - 3.46410i) q^{49} +(0.255488 - 2.26992i) q^{50} +(-1.55130 - 6.26951i) q^{52} -7.58258i q^{53} +(-5.61976 - 1.84887i) q^{55} +(1.50000 + 2.59808i) q^{56} +(1.04678 + 1.81307i) q^{58} +(12.0826 - 6.97588i) q^{59} +(0.708712 + 1.22753i) q^{61} +(2.45505 + 1.41742i) q^{62} -3.41742 q^{64} +(8.03943 + 0.606325i) q^{65} +(0.504525 - 0.873864i) q^{67} +(-7.10895 - 4.10436i) q^{68} +(-1.73205 + 0.361500i) q^{70} +(-6.08258 + 3.51178i) q^{71} +(1.81307 + 3.14033i) q^{74} +(-2.68693 - 1.55130i) q^{76} +4.58258i q^{77} +6.00000 q^{79} +(1.95057 - 5.92889i) q^{80} +(-1.04678 + 0.604356i) q^{82} -6.01450 q^{83} +(7.64016 - 6.82847i) q^{85} -4.83465i q^{86} +(3.96863 + 2.29129i) q^{88} +(-8.29129 - 4.78698i) q^{89} +(-1.50000 - 6.06218i) q^{91} +8.20871i q^{92} +(0.417424 - 0.723000i) q^{94} +(2.88771 - 2.58092i) q^{95} +(5.70068 + 9.87386i) q^{97} +(-0.913701 - 1.58258i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

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

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	$-0.781693\pi$
$2$	0.228425	−	0.395644i	0.161521	−	0.279763i	0.935414	+	0.353553i	$0.115027\pi$
$3$		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	$-0.0605189\pi$
$7$	0.866025	+	1.50000i	0.327327	+	0.566947i	−0.654654	+	0.755929i	$0.727186\pi$
$8$	1.73205			0.612372
$9$		0			0
$10$	−0.319250	+	0.970381i	−0.100956	+	0.306862i
$11$	2.29129	+	1.32288i	0.690849	+	0.398862i	0.803930	−	0.594724i	$-0.202739\pi$
$11$	2.29129	+	1.32288i	0.690849	+	0.398862i	−0.113081	+	0.993586i	$0.536072\pi$
$12$		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	$-0.854224\pi$
$17$	−3.96863	+	2.29129i	−0.962533	+	0.555719i	−0.0655816	+	0.997847i	$0.520890\pi$
$18$		0			0
$19$	−1.50000	+	0.866025i	−0.344124	+	0.198680i	−0.662094	−	0.749421i	$-0.730332\pi$
$19$	−1.50000	+	0.866025i	−0.344124	+	0.198680i	0.317970	+	0.948101i	$0.396999\pi$
$20$	−2.66919	−	2.98647i	−0.596849	−	0.667795i
$21$		0			0
$22$	1.04678	−	0.604356i	0.223173	−	0.128849i
$23$	3.96863	+	2.29129i	0.827516	+	0.477767i	0.853001	−	0.521909i	$-0.174780\pi$
$23$	3.96863	+	2.29129i	0.827516	+	0.477767i	−0.0254855	+	0.999675i	$0.508113\pi$
$24$		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	−0.996465	−	0.0840058i	$-0.973229\pi$
$29$	−2.29129	+	3.96863i	−0.425481	+	0.736956i	0.570984	+	0.820961i	$0.306562\pi$
$30$		0			0
$31$			6.20520i			1.11449i	0.830349	+	0.557244i	$0.188141\pi$
$31$			6.20520i			1.11449i	−0.830349	+	0.557244i	$0.811859\pi$
$32$	2.36965	+	4.10436i	0.418899	+	0.725555i
$33$		0			0
$34$			2.09355i			0.359041i
$35$	−2.58092	−	2.88771i	−0.436255	−	0.488112i
$36$		0			0
$37$	−3.96863	+	6.87386i	−0.652438	+	1.13006i	0.330091	+	0.943949i	$0.392920\pi$
$37$	−3.96863	+	6.87386i	−0.652438	+	1.13006i	−0.982529	+	0.186107i	$0.940413\pi$
$38$			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	0.310293	−	0.950641i	$-0.399573\pi$
$41$	−2.29129	−	1.32288i	−0.357839	−	0.206598i	−0.668132	+	0.744042i	$0.732906\pi$
$42$		0			0
$43$	9.16478	−	5.29129i	1.39762	−	0.806914i	0.403473	−	0.914991i	$-0.367803\pi$
$43$	9.16478	−	5.29129i	1.39762	−	0.806914i	0.994142	+	0.108078i	$0.0344695\pi$
$44$			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	$-0.457450\pi$
$47$	1.82740			0.266554			0.133277	+	0.991079i	$0.457450\pi$
$48$		0			0
$49$	2.00000	−	3.46410i	0.285714	−	0.494872i
$50$	0.255488	−	2.26992i	0.0361314	−	0.321015i
$51$		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
$55$	−5.61976	−	1.84887i	−0.757768	−	0.249301i
$56$	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	0.577221	−	0.816588i	$-0.304137\pi$
$59$	12.0826	−	6.97588i	1.57302	−	0.908182i	0.995796	−	0.0915940i	$-0.0291962\pi$
$60$		0			0
$61$	0.708712	+	1.22753i	0.0907413	+	0.157169i	0.907823	−	0.419353i	$-0.137743\pi$
$61$	0.708712	+	1.22753i	0.0907413	+	0.157169i	−0.817082	+	0.576522i	$0.804410\pi$
$62$	2.45505	+	1.41742i	0.311792	+	0.180013i
$63$		0			0
$64$	−3.41742			−0.427178
$65$	8.03943	+	0.606325i	0.997168	+	0.0752054i
$66$		0			0
$67$	0.504525	−	0.873864i	0.0616376	−	0.106759i	−0.833560	−	0.552429i	$-0.813701\pi$
$67$	0.504525	−	0.873864i	0.0616376	−	0.106759i	0.895198	+	0.445670i	$0.147034\pi$
$68$	−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	−0.815440	−	0.578841i	$-0.803505\pi$
$71$	−6.08258	+	3.51178i	−0.721869	+	0.416771i	0.0935712	+	0.995613i	$0.470172\pi$
$72$		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	$0.390410\pi$
$80$	1.95057	−	5.92889i	0.218080	−	0.662870i
$81$		0			0
$82$	−1.04678	+	0.604356i	−0.115597	+	0.0667400i
$83$	−6.01450			−0.660177			−0.330089	−	0.943950i	$-0.607079\pi$
$83$	−6.01450			−0.660177			−0.330089	+	0.943950i	$0.607079\pi$
$84$		0			0
$85$	7.64016	−	6.82847i	0.828691	−	0.740652i
$86$		−	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	−0.00858752	−	0.999963i	$-0.502734\pi$
$89$	−8.29129	−	4.78698i	−0.878875	−	0.507419i	−0.870287	+	0.492545i	$0.836067\pi$
$90$		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
$95$	2.88771	−	2.58092i	0.296273	−	0.264797i
$96$		0			0
$97$	5.70068	+	9.87386i	0.578816	+	1.00254i	0.995615	+	0.0935404i	$0.0298184\pi$
$97$	5.70068	+	9.87386i	0.578816	+	1.00254i	−0.416799	+	0.908999i	$0.636848\pi$
$98$	−0.913701	−	1.58258i	−0.0922977	−	0.159864i
$99$		0			0
$100$	7.20696	+	5.31767i	0.720696	+	0.531767i
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$		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	$-0.162413\pi$
$107$	9.16478	+	5.29129i	0.885993	+	0.511528i	0.0133631	+	0.999911i	$0.495746\pi$
$108$		0			0
$109$		−	13.1334i		−	1.25795i	−0.777425	−	0.628976i	$-0.783474\pi$
$109$		−	13.1334i		−	1.25795i	0.777425	−	0.628976i	$-0.216526\pi$
$110$	−2.01519	+	1.80110i	−0.192141	+	0.171728i
$111$		0			0
$112$	−4.83465			−0.456832
$113$	6.42368	−	3.70871i	0.604289	−	0.348886i	−0.166438	−	0.986052i	$-0.553227\pi$
$113$	6.42368	−	3.70871i	0.604289	−	0.348886i	0.770727	+	0.637166i	$0.219893\pi$
$114$		0			0
$115$	−9.73371	−	3.20233i	−0.907673	−	0.298619i
$116$	−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	$-0.0447455\pi$
$127$	15.3700	+	8.87386i	1.36387	+	0.787428i	0.373729	+	0.927538i	$0.378079\pi$
$128$	−5.51993	+	9.56080i	−0.487897	+	0.845063i
$129$		0			0
$130$	2.07630	−	3.04225i	0.182103	−	0.266823i
$131$	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	$-0.0187994\pi$
$137$	5.24383	+	9.08258i	0.448010	+	0.775977i	−0.550246	+	0.835003i	$0.685466\pi$
$138$		0			0
$139$	−10.8739	−	18.8341i	−0.922309	−	1.59749i	−0.795833	−	0.605517i	$-0.792967\pi$
$139$	−10.8739	−	18.8341i	−0.922309	−	1.59749i	−0.126476	−	0.991970i	$-0.540367\pi$
$140$	2.16812	−	6.59014i	0.183239	−	0.556968i
$141$		0			0
$142$			3.20871i			0.269269i
$143$	−6.61438	−	6.87386i	−0.553122	−	0.574821i
$144$		0			0
$145$	3.20233	−	9.73371i	0.265939	−	0.808340i
$146$		0			0
$147$		0			0
$148$	−14.2179			−1.16870
$149$	14.4564	−	8.34643i	1.18432	−	0.683766i	0.227308	−	0.973823i	$-0.427008\pi$
$149$	14.4564	−	8.34643i	1.18432	−	0.683766i	0.957009	+	0.290057i	$0.0936742\pi$
$150$		0			0
$151$		−	9.66930i		−	0.786877i	−0.919351	−	0.393438i	$-0.871285\pi$
$151$		−	9.66930i		−	0.786877i	0.919351	−	0.393438i	$-0.128715\pi$
$152$	−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
$160$	−7.06201	−	7.90145i	−0.558301	−	0.624665i
$161$			7.93725i			0.625543i
$162$		0			0
$163$	−10.5353	−	18.2477i	−0.825191	−	1.42927i	−0.901773	−	0.432209i	$-0.857734\pi$
$163$	−10.5353	−	18.2477i	−0.825191	−	1.42927i	0.0765827	−	0.997063i	$-0.475599\pi$
$164$		−	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	$-0.954122\pi$
$167$	−4.78698	+	8.29129i	−0.370427	+	0.641599i	0.619204	+	0.785230i	$0.287455\pi$
$168$		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	$-0.449568\pi$
$173$	14.3609	−	8.29129i	1.09184	−	0.630375i	0.934066	+	0.357100i	$0.116234\pi$
$174$		0			0
$175$	6.96863	+	5.14181i	0.526779	+	0.388685i
$176$	−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	0.296460	+	0.955045i	$0.404194\pi$
$179$	−9.08258	+	15.7315i	−0.678864	+	1.17583i	−0.975323	+	0.220781i	$0.929139\pi$
$180$		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
$185$	5.54661	−	16.8593i	0.407795	−	1.23952i
$186$		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	−0.992830	−	0.119536i	$-0.961859\pi$
$191$	−8.29129	−	14.3609i	−0.599937	−	1.03912i	0.392893	−	0.919584i	$-0.371474\pi$
$192$		0			0
$193$	−7.43273	+	12.8739i	−0.535020	+	0.926681i	0.464143	+	0.885760i	$0.346362\pi$
$193$	−7.43273	+	12.8739i	−0.535020	+	0.926681i	−0.999162	+	0.0409206i	$0.986971\pi$
$194$	5.20871			0.373964
$195$		0			0
$196$	7.16515			0.511797
$197$	−7.33738	+	12.7087i	−0.522767	+	0.905458i	0.476882	+	0.878967i	$0.341767\pi$
$197$	−7.33738	+	12.7087i	−0.522767	+	0.905458i	−0.999649	+	0.0264912i	$0.991567\pi$
$198$		0			0
$199$	5.29129	+	9.16478i	0.375089	+	0.649674i	0.990340	−	0.138657i	$-0.0442787\pi$
$199$	5.29129	+	9.16478i	0.375089	+	0.649674i	−0.615251	+	0.788331i	$0.710945\pi$
$200$	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
$205$	5.61976	+	1.84887i	0.392501	+	0.129131i
$206$	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	−0.863169	−	0.504915i	$-0.831524\pi$
$211$	0.0825757	−	0.143025i	0.00568475	−	0.00984627i	0.868854	+	0.495069i	$0.164857\pi$
$212$	11.7629	−	6.79129i	0.807876	−	0.466428i
$213$		0			0
$214$	4.18693	−	2.41733i	0.286213	−	0.165245i
$215$	−17.6435	+	15.7690i	−1.20327	+	1.07544i
$216$		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	$-0.739689\pi$
$223$	4.33013	−	7.50000i	0.289967	−	0.502237i	0.973801	+	0.227400i	$0.0730224\pi$
$224$	−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	$-0.158021\pi$
$227$	0.409175	+	0.708712i	0.0271579	+	0.0470389i	−0.852127	+	0.523335i	$0.824688\pi$
$228$		0			0
$229$			26.2668i			1.73576i	0.496774	+	0.867880i	$0.334518\pi$
$229$			26.2668i			1.73576i	−0.496774	+	0.867880i	$0.665482\pi$
$230$	−3.49041	+	3.11959i	−0.230151	+	0.205700i
$231$		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	$-0.998037\pi$
$239$		−	0.190700i		−	0.0123354i	0.999981	−	0.00616769i	$-0.00196325\pi$
$240$		0			0
$241$	−1.50000	+	0.866025i	−0.0966235	+	0.0557856i	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−1.50000	+	0.866025i	−0.0966235	+	0.0557856i	0.450910	+	0.892570i	$0.351100\pi$
$242$	−1.82740			−0.117470
$243$		0			0
$244$	−1.26951	+	2.19885i	−0.0812719	+	0.140767i
$245$	−2.79523	+	8.49628i	−0.178580	+	0.542807i
$246$		0			0
$247$	6.06218	−	1.50000i	0.385727	−	0.0954427i
$248$			10.7477i			0.682481i
$249$		0			0
$250$	0.477776	+	5.08535i	0.0302172	+	0.321626i
$251$	−0.0825757	−	0.143025i	−0.00521213	−	0.00902768i	0.863408	−	0.504507i	$-0.168326\pi$
$251$	−0.0825757	−	0.143025i	−0.00521213	−	0.00902768i	−0.868620	+	0.495479i	$0.834992\pi$
$252$		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	$-0.141609\pi$
$257$	15.7315	+	9.08258i	0.981303	+	0.566556i	0.0786397	+	0.996903i	$0.474942\pi$
$258$		0			0
$259$	−13.7477			−0.854242
$260$	6.25987	+	13.0146i	0.388221	+	0.807132i
$261$		0			0
$262$	1.73205	−	3.00000i	0.107006	−	0.185341i
$263$	7.79423	+	4.50000i	0.480613	+	0.277482i	0.720672	−	0.693276i	$-0.243833\pi$
$263$	7.79423	+	4.50000i	0.480613	+	0.277482i	−0.240059	+	0.970758i	$0.577167\pi$
$264$		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	0.998816	−	0.0486418i	$-0.0154893\pi$
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	−0.541533	+	0.840679i	$0.682156\pi$
$270$		0			0
$271$	7.50000	+	4.33013i	0.455593	+	0.263036i	0.710189	−	0.704011i	$-0.248609\pi$
$271$	7.50000	+	4.33013i	0.455593	+	0.263036i	−0.254597	+	0.967047i	$0.581943\pi$
$272$		−	12.7913i		−	0.775586i
$273$		0			0
$274$	4.79129			0.289452
$275$	13.1458	+	1.47960i	0.792719	+	0.0892234i
$276$		0			0
$277$	6.42368	−	3.70871i	0.385961	−	0.222835i	−0.294447	−	0.955668i	$-0.595136\pi$
$277$	6.42368	−	3.70871i	0.385961	−	0.222835i	0.680409	+	0.732833i	$0.261802\pi$
$278$	−9.93545			−0.595889
$279$		0			0
$280$	−4.47028	−	5.00166i	−0.267151	−	0.298906i
$281$		−	3.65480i		−	0.218027i	−0.994040	−	0.109014i	$-0.965231\pi$
$281$		−	3.65480i		−	0.218027i	0.994040	−	0.109014i	$-0.0347692\pi$
$282$		0			0
$283$	24.0302	+	13.8739i	1.42845	+	0.824716i	0.996998	−	0.0774209i	$-0.0246685\pi$
$283$	24.0302	+	13.8739i	1.42845	+	0.824716i	0.431451	+	0.902136i	$0.358002\pi$
$284$	−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
$290$	−3.11959	−	3.49041i	−0.183189	−	0.204964i
$291$		0			0
$292$		0			0
$293$	−9.06943	−	15.7087i	−0.529842	−	0.917713i	−0.999394	−	0.0348081i	$-0.988918\pi$
$293$	−9.06943	−	15.7087i	−0.529842	−	0.917713i	0.469552	−	0.882905i	$-0.344415\pi$
$294$		0			0
$295$	−23.2606	+	20.7894i	−1.35429	+	1.21041i
$296$	−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
$305$	−2.11210	−	2.36316i	−0.120938	−	0.135314i
$306$		0			0
$307$	−24.2487			−1.38395			−0.691974	−	0.721923i	$-0.743259\pi$
$307$	−24.2487			−1.38395			−0.691974	+	0.721923i	$0.743259\pi$
$308$	−7.10895	+	4.10436i	−0.405070	+	0.233867i
$309$		0			0
$310$	−6.02141	−	1.98101i	−0.341993	−	0.112514i
$311$	−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	$-0.501705\pi$
$317$	−0.190700			−0.0107108			−0.00535540	+	0.999986i	$0.501705\pi$
$318$		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
$325$	−17.8745	+	2.34563i	−0.991499	+	0.130112i
$326$	−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	−0.602671	−	0.797990i	$-0.705897\pi$
$331$	−3.87386	+	2.23658i	−0.212927	+	0.122933i	0.389744	+	0.920923i	$0.372563\pi$
$332$	−5.38685	−	9.33030i	−0.295642	−	0.512067i
$333$		0			0
$334$	2.18693	+	3.78788i	0.119664	+	0.207263i
$335$	−0.705131	+	2.14329i	−0.0385254	+	0.117101i
$336$		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
$340$	17.4359	+	5.73630i	0.945593	+	0.311095i
$341$	−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	$-0.860707\pi$
$347$	−18.4726	+	10.6652i	−0.991660	+	0.572535i	−0.0858901	+	0.996305i	$0.527373\pi$
$348$		0			0
$349$	2.12614	+	1.22753i	0.113809	+	0.0657079i	0.555824	−	0.831300i	$-0.312403\pi$
$349$	2.12614	+	1.22753i	0.113809	+	0.0657079i	−0.442015	+	0.897008i	$0.645736\pi$
$350$	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	$-0.775129\pi$
$353$	3.41643	−	5.91742i	0.181838	−	0.314953i	0.942506	+	0.334188i	$0.108462\pi$
$354$		0			0
$355$	11.7098	−	10.4658i	0.621492	−	0.555465i
$356$		−	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	$0.172341\pi$
$359$			19.5293i			1.03072i	−0.856975	+	0.515359i	$0.827659\pi$
$360$		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	$-0.347858\pi$
$367$	−1.51358	−	0.873864i	−0.0790080	−	0.0456153i	−0.538984	+	0.842316i	$0.681192\pi$
$368$	−11.0776	+	6.39564i	−0.577459	+	0.333396i
$369$		0			0
$370$	−5.40329	−	6.04556i	−0.280903	−	0.314294i
$371$	11.3739	−	6.56670i	0.590502	−	0.340926i
$372$		0			0
$373$	−11.2583	+	6.50000i	−0.582934	+	0.336557i	−0.762299	−	0.647225i	$-0.775929\pi$
$373$	−11.2583	+	6.50000i	−0.582934	+	0.336557i	0.179364	+	0.983783i	$0.442596\pi$
$374$	−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	0.243317	−	0.969947i	$-0.421765\pi$
$379$	−9.24773	−	5.33918i	−0.475024	−	0.274255i	−0.718340	+	0.695692i	$0.755098\pi$
$380$	6.59014	+	2.16812i	0.338067	+	0.111222i
$381$		0			0
$382$	−7.57575			−0.387609
$383$	11.8105	+	20.4564i	0.603490	+	1.04528i	0.992288	+	0.123952i	$0.0395570\pi$
$383$	11.8105	+	20.4564i	0.603490	+	1.04528i	−0.388798	+	0.921323i	$0.627110\pi$
$384$		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	0.999924	+	0.0122949i	$0.00391368\pi$
$397$	10.1738	+	17.6216i	0.510610	+	0.884402i	−0.489315	+	0.872107i	$0.662753\pi$
$398$	4.83465			0.242339
$399$		0			0
$400$	−1.56099	+	13.8689i	−0.0780496	+	0.693443i
$401$	25.8303	+	14.9131i	1.28990	+	0.744726i	0.978637	−	0.205596i	$-0.0659134\pi$
$401$	25.8303	+	14.9131i	1.28990	+	0.744726i	0.311267	+	0.950323i	$0.399247\pi$
$402$		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	−0.302979	−	0.952997i	$-0.597981\pi$
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	0.673830	+	0.738886i	$0.264648\pi$
$410$	2.01519	−	1.80110i	0.0995230	−	0.0889498i
$411$		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	−0.785922	−	0.618326i	$-0.787811\pi$
$419$	2.91742	−	5.05313i	0.142526	−	0.246861i	0.928447	+	0.371465i	$0.121144\pi$
$420$		0			0
$421$			5.48220i			0.267186i	0.991036	+	0.133593i	$0.0426515\pi$
$421$			5.48220i			0.267186i	−0.991036	+	0.133593i	$0.957348\pi$
$422$	−0.0377247	−	0.0653411i	−0.00183641	−	0.00318076i
$423$		0			0
$424$		−	13.1334i		−	0.637815i
$425$	−13.6040	+	18.4373i	−0.659889	+	0.894338i
$426$		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	0.312834	−	0.949808i	$-0.398722\pi$
$431$	−7.33485	−	4.23478i	−0.353307	−	0.203982i	−0.666141	+	0.745826i	$0.732055\pi$
$432$		0			0
$433$	8.44178	−	4.87386i	0.405686	−	0.234223i	−0.283248	−	0.959047i	$-0.591412\pi$
$433$	8.44178	−	4.87386i	0.405686	−	0.234223i	0.688934	+	0.724824i	$0.258079\pi$
$434$			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	−0.985520	−	0.169562i	$-0.945765\pi$
$439$	−7.24773	+	12.5534i	−0.345915	+	0.599143i	0.639604	+	0.768704i	$0.279098\pi$
$440$	−9.73371	−	3.20233i	−0.464036	−	0.152665i
$441$		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
$445$	20.3357	+	6.69034i	0.964007	+	0.317153i
$446$	−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	−0.707994	−	0.706218i	$-0.750400\pi$
$449$	−9.54356	+	5.50998i	−0.450388	+	0.260032i	0.257606	+	0.966250i	$0.417066\pi$
$450$		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
$455$	6.05286	+	12.5842i	0.283762	+	0.589958i
$456$		0			0
$457$	−0.866025	+	1.50000i	−0.0405110	+	0.0701670i	−0.885570	−	0.464506i	$-0.846232\pi$
$457$	−0.866025	+	1.50000i	−0.0405110	+	0.0701670i	0.845059	+	0.534673i	$0.179565\pi$
$458$	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	−0.998217	−	0.0596914i	$-0.980988\pi$
$461$	−31.0390	+	17.9204i	−1.44563	+	0.834635i	−0.447414	+	0.894327i	$0.647655\pi$
$462$		0			0
$463$	−39.4002			−1.83108			−0.915542	−	0.402223i	$-0.868238\pi$
$463$	−39.4002			−1.83108			−0.915542	+	0.402223i	$0.868238\pi$
$464$	−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
$470$	−0.583398	+	1.77328i	−0.0269101	+	0.0817951i
$471$		0			0
$472$	20.9276	−	12.0826i	0.963272	−	0.556146i
$473$	27.9989			1.28739
$474$		0			0
$475$	−5.14181	+	6.96863i	−0.235923	+	0.319743i
$476$		−	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	0.404880	−	0.914370i	$-0.367313\pi$
$479$	−4.03901	−	2.33193i	−0.184547	−	0.106548i	−0.589427	+	0.807821i	$0.700647\pi$
$480$		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
$485$	−16.9891	−	19.0086i	−0.771435	−	0.863134i
$486$		0			0
$487$	−5.33918	−	9.24773i	−0.241941	−	0.419055i	0.719326	−	0.694673i	$-0.244451\pi$
$487$	−5.33918	−	9.24773i	−0.241941	−	0.419055i	−0.961267	+	0.275618i	$0.911117\pi$
$488$	1.22753	+	2.12614i	0.0555675	+	0.0962457i
$489$		0			0
$490$	2.72300	+	3.04668i	0.123013	+	0.137635i
$491$	9.70871	−	16.8160i	0.438148	−	0.758895i	−0.559399	−	0.828899i	$-0.688968\pi$
$491$	9.70871	−	16.8160i	0.438148	−	0.758895i	0.997547	+	0.0700041i	$0.0223012\pi$
$492$		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	$0.00515142\pi$
$499$			0.723000i			0.0323659i	−0.999869	+	0.0161830i	$0.994849\pi$
$500$	−18.2047	−	8.34734i	−0.814139	−	0.373305i
$501$		0			0
$502$	−0.0754495			−0.00336747
$503$	−0.143025	+	0.0825757i	−0.00637718	+	0.00368187i	−0.503185	−	0.864179i	$-0.667839\pi$
$503$	−0.143025	+	0.0825757i	−0.00637718	+	0.00368187i	0.496808	+	0.867860i	$0.334505\pi$
$504$		0			0
$505$	−6.28926	+	19.1166i	−0.279868	+	0.850678i
$506$	5.53901			0.246239
$507$		0			0
$508$			31.7913i			1.41051i
$509$	7.33485	+	4.23478i	0.325111	+	0.187703i	0.653669	−	0.756781i	$-0.273229\pi$
$509$	7.33485	+	4.23478i	0.325111	+	0.187703i	−0.328557	+	0.944484i	$0.606562\pi$
$510$		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
$520$	13.9247	+	1.05019i	0.610638	+	0.0460537i
$521$	−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	$-0.334483\pi$
$523$	−0.143025	−	0.0825757i	−0.00625406	−	0.00361078i	−0.503124	+	0.864214i	$0.667816\pi$
$524$	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
$530$	7.35799	+	2.42074i	0.319611	+	0.105150i
$531$		0			0
$532$		−	5.37386i		−	0.232987i
$533$	6.61438	+	6.87386i	0.286501	+	0.297740i
$534$		0			0
$535$	−22.4781	−	7.39517i	−0.971814	−	0.319721i
$536$	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	$-0.928284\pi$
$541$		−	10.3923i		−	0.446800i	0.974727	−	0.223400i	$-0.0717156\pi$
$542$	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
$550$	3.58822	−	4.86306i	0.153002	−	0.207362i
$551$		−	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	$-0.780856\pi$
$557$	3.87328	−	6.70871i	0.164116	−	0.284257i	0.936341	+	0.351092i	$0.114190\pi$
$558$		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	$-0.605931\pi$
$563$	7.79423	−	4.50000i	0.328488	−	0.189652i	0.655169	+	0.755482i	$0.272597\pi$
$564$		0			0
$565$	−12.3665	+	11.0527i	−0.520261	+	0.464989i
$566$	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	−0.935729	−	0.352719i	$-0.885257\pi$
$569$	−3.87386	+	6.70973i	−0.162401	+	0.281286i	0.773328	+	0.634006i	$0.218590\pi$
$570$		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
$575$	22.7691	+	2.56275i	0.949537	+	0.106874i
$576$		0			0
$577$	6.92820			0.288425			0.144212	−	0.989547i	$-0.453935\pi$
$577$	6.92820			0.288425			0.144212	+	0.989547i	$0.453935\pi$
$578$	−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	−0.0941934	−	0.995554i	$-0.530027\pi$
$587$	19.7478	−	34.2042i	0.815078	−	1.41176i	0.909272	−	0.416203i	$-0.136639\pi$
$588$		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	$-0.643107\pi$
$593$	−21.1660			−0.869184			−0.434592	+	0.900627i	$0.643107\pi$
$594$		0			0
$595$	16.8593	+	5.54661i	0.691163	+	0.227389i
$596$	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	−0.985344	−	0.170580i	$-0.945436\pi$
$601$	−8.45644	+	14.6470i	−0.344945	+	0.597463i	0.640398	+	0.768043i	$0.278769\pi$
$602$	7.25198	−	4.18693i	0.295569	−	0.170647i
$603$		0			0
$604$	15.0000	−	8.66025i	0.610341	−	0.352381i
$605$	5.96038	+	6.66888i	0.242324	+	0.271128i
$606$		0			0
$607$	−6.70973	+	3.87386i	−0.272339	+	0.157235i	−0.629950	−	0.776635i	$-0.716925\pi$
$607$	−6.70973	+	3.87386i	−0.272339	+	0.157235i	0.357611	+	0.933871i	$0.383591\pi$
$608$	−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	$-0.795193\pi$
$613$	2.95958	−	5.12614i	0.119536	−	0.207043i	0.919584	+	0.392894i	$0.128526\pi$
$614$	−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	$-0.257279\pi$
$617$	−6.97588	−	12.0826i	−0.280838	−	0.486426i	−0.971591	+	0.236664i	$0.923946\pi$
$618$		0			0
$619$		−	29.7309i		−	1.19499i	−0.801874	−	0.597493i	$-0.796164\pi$
$619$		−	29.7309i		−	1.19499i	0.801874	−	0.597493i	$-0.203836\pi$
$620$	18.5316	−	16.5629i	0.744249	−	0.665180i
$621$		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	−0.598552	−	0.801084i	$-0.704257\pi$
$631$	−5.12614	+	2.95958i	−0.204068	+	0.117819i	0.394483	+	0.918903i	$0.370924\pi$
$632$	10.3923			0.413384
$633$		0			0
$634$	−0.0435608	+	0.0754495i	−0.00173002	+	0.00299648i
$635$	−37.6974	−	12.4022i	−1.49598	−	0.492167i
$636$		0			0
$637$	−10.3923	+	10.0000i	−0.411758	+	0.396214i
$638$			5.53901i			0.219292i
$639$		0			0
$640$	7.71472	−	23.4494i	0.304951	−	0.926920i
$641$	9.08258	+	15.7315i	0.358740	+	0.621356i	0.987751	−	0.156041i	$-0.0498731\pi$
$641$	9.08258	+	15.7315i	0.358740	+	0.621356i	−0.629010	+	0.777397i	$0.716540\pi$
$642$		0			0
$643$	10.8968	+	18.8739i	0.429729	+	0.744313i	0.996849	−	0.0793227i	$-0.0252757\pi$
$643$	10.8968	+	18.8739i	0.429729	+	0.744313i	−0.567120	+	0.823635i	$0.691942\pi$
$644$	−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	$-0.511419\pi$
$647$	−23.3827	−	13.5000i	−0.919268	−	0.530740i	−0.883402	+	0.468617i	$0.844753\pi$
$648$		0			0
$649$	36.9129			1.44896
$650$	−3.15495	+	7.60774i	−0.123747	+	0.298400i
$651$		0			0
$652$	18.8718	−	32.6869i	0.739077	−	1.28012i
$653$	−37.0882	−	21.4129i	−1.45137	−	0.837951i	−0.452814	−	0.891605i	$-0.649580\pi$
$653$	−37.0882	−	21.4129i	−1.45137	−	0.837951i	−0.998560	+	0.0536545i	$0.982913\pi$
$654$		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	−0.993692	−	0.112146i	$-0.964228\pi$
$659$	−15.2477	−	26.4098i	−0.593967	−	1.02878i	0.399725	−	0.916635i	$-0.369106\pi$
$660$		0			0
$661$	15.8739	+	9.16478i	0.617422	+	0.356469i	0.775865	−	0.630900i	$-0.217314\pi$
$661$	15.8739	+	9.16478i	0.617422	+	0.356469i	−0.158443	+	0.987368i	$0.550647\pi$
$662$			2.04356i			0.0794252i
$663$		0			0
$664$	−10.4174			−0.404274
$665$	6.37221	+	2.09642i	0.247104	+	0.0812957i
$666$		0			0
$667$	−18.1865	+	10.5000i	−0.704185	+	0.406562i
$668$	−17.1497			−0.663542
$669$		0			0
$670$	0.686911	+	0.768563i	0.0265377	+	0.0296922i
$671$			3.75015i			0.144773i
$672$		0			0
$673$	20.9276	+	12.0826i	0.806701	+	0.465749i	0.845809	−	0.533486i	$-0.179118\pi$
$673$	20.9276	+	12.0826i	0.806701	+	0.465749i	−0.0391079	+	0.999235i	$0.512452\pi$
$674$	−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
$680$	13.2331	−	11.8273i	0.507468	−	0.453555i
$681$		0			0
$682$	3.75015	+	6.49545i	0.143601	+	0.248724i
$683$	16.5498	+	28.6652i	0.633262	+	1.09684i	0.986881	+	0.161452i	$0.0516177\pi$
$683$	16.5498	+	28.6652i	0.633262	+	1.09684i	−0.353619	+	0.935390i	$0.615049\pi$
$684$		0			0
$685$	−15.6276	−	17.4852i	−0.597100	−	0.668076i
$686$	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	0.789034	−	0.614349i	$-0.210581\pi$
$691$	17.1261	+	9.88778i	0.651509	+	0.376149i	−0.137525	+	0.990498i	$0.543915\pi$
$692$	25.7246	+	14.8521i	0.977901	+	0.564591i
$693$		0			0
$694$			9.74475i			0.369906i
$695$	32.4062	+	36.2582i	1.22924	+	1.37535i
$696$		0			0
$697$	12.1244			0.459243
$698$	0.971326	−	0.560795i	0.0367652	−	0.0212264i
$699$		0			0
$700$	−1.73509	+	15.4157i	−0.0655802	+	0.582658i
$701$	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	0.226299	−	0.974058i	$-0.427337\pi$
$709$	31.5000	−	18.1865i	1.18301	−	0.683010i	0.956708	+	0.291048i	$0.0940040\pi$
$710$	−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
$715$	17.6185	+	12.0244i	0.658896	+	0.449688i
$716$	−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	0.998788	−	0.0492257i	$-0.0156754\pi$
$719$	12.2477	+	21.2137i	0.456763	+	0.791137i	−0.542025	+	0.840363i	$0.682342\pi$
$720$		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
$725$	−2.56275	+	22.7691i	−0.0951780	+	0.845623i
$726$		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	$-0.638362\pi$
$733$	−22.8027			−0.842237			−0.421119	+	0.907006i	$0.638362\pi$
$734$	−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	0.203490	−	0.979077i	$-0.434772\pi$
$739$	−14.7523	−	8.51723i	−0.542671	−	0.313311i	−0.746161	+	0.665766i	$0.768105\pi$
$740$	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	$-0.799824\pi$
$743$	2.86423	−	4.96099i	0.105078	−	0.182001i	0.913770	+	0.406232i	$0.133157\pi$
$744$		0			0
$745$	−27.8306	+	24.8739i	−1.01964	+	0.911310i
$746$			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	−0.953068	−	0.302755i	$-0.902093\pi$
$751$	−5.87386	+	10.1738i	−0.214340	+	0.371248i	0.738728	+	0.674004i	$0.235427\pi$
$752$	−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	$-0.276648\pi$
$757$	8.44178	+	4.87386i	0.306822	+	0.177144i	−0.338682	+	0.940901i	$0.609981\pi$
$758$	−4.22483	+	2.43920i	−0.153453	+	0.0885959i
$759$		0			0
$760$	5.00166	−	4.47028i	0.181429	−	0.162154i
$761$	30.7087	−	17.7297i	1.11319	−	0.642701i	0.173536	−	0.984827i	$-0.444481\pi$
$761$	30.7087	−	17.7297i	1.11319	−	0.642701i	0.939654	+	0.342127i	$0.111147\pi$
$762$		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	0.236433	−	0.971648i	$-0.424022\pi$
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	−0.723255	+	0.690581i	$0.757355\pi$
$770$	−4.44685	−	1.46299i	−0.160253	−	0.0527224i
$771$		0			0
$772$	−26.6283			−0.958374
$773$	−12.0767	−	20.9174i	−0.434368	−	0.752347i	0.562876	−	0.826541i	$-0.309695\pi$
$773$	−12.0767	−	20.9174i	−0.434368	−	0.752347i	−0.997244	+	0.0741940i	$0.976362\pi$
$774$		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	$-0.260562\pi$
$787$	−8.15573	−	14.1261i	−0.290720	−	0.503542i	−0.973980	+	0.226633i	$0.927228\pi$
$788$	−26.2867			−0.936425
$789$		0			0
$790$	−1.91550	+	5.82229i	−0.0681504	+	0.207148i
$791$	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	$-0.381549\pi$
$797$	38.1727	−	22.0390i	1.35215	−	0.780662i	0.988550	+	0.150895i	$0.0482154\pi$
$798$		0			0
$799$	−7.25227	+	4.18710i	−0.256567	+	0.148129i
$800$	19.0678	+	14.0692i	0.674149	+	0.497422i
$801$		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	0.250942	−	0.968002i	$-0.419260\pi$
$809$	27.4129	−	47.4805i	0.963785	−	1.66933i	0.712843	−	0.701323i	$-0.247407\pi$
$810$		0			0
$811$		−	50.5155i		−	1.77384i	−0.461923	−	0.886920i	$-0.652840\pi$
$811$		−	50.5155i		−	1.77384i	0.461923	−	0.886920i	$-0.347160\pi$
$812$	−7.10895	−	12.3131i	−0.249475	−	0.432104i
$813$		0			0
$814$			9.59386i			0.336264i
$815$	31.3973	+	35.1294i	1.09980	+	1.23053i
$816$		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	0.200173	−	0.979761i	$-0.435850\pi$
$821$	−15.7087	−	9.06943i	−0.548238	−	0.316525i	−0.748411	+	0.663235i	$0.769183\pi$
$822$		0			0
$823$	−27.2083	+	15.7087i	−0.948421	+	0.547571i	−0.892590	−	0.450869i	$-0.851114\pi$
$823$	−27.2083	+	15.7087i	−0.948421	+	0.547571i	−0.0558311	+	0.998440i	$0.517781\pi$
$824$			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	$-0.440020\pi$
$827$	10.7737			0.374638			0.187319	+	0.982299i	$0.440020\pi$
$828$		0			0
$829$	−16.6652	+	28.8649i	−0.578805	+	1.00252i	0.416812	+	0.908993i	$0.363147\pi$
$829$	−16.6652	+	28.8649i	−0.578805	+	1.00252i	−0.995617	+	0.0935264i	$0.970186\pi$
$830$	1.92013	−	5.83636i	0.0666487	−	0.202583i
$831$		0			0
$832$	11.8383	+	3.41742i	0.410419	+	0.118478i
$833$			18.3303i			0.635107i
$834$		0			0
$835$	6.69034	−	20.3357i	0.231529	−	0.703747i
$836$	−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	−0.981434	−	0.191800i	$-0.938567\pi$
$839$	−37.8303	+	21.8413i	−1.30605	+	0.754047i	−0.324613	+	0.945847i	$0.605234\pi$
$840$		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
$845$	−27.2431	−	10.1398i	−0.937190	−	0.348820i
$846$		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	$-0.469255\pi$
$853$	5.63310			0.192874			0.0964369	+	0.995339i	$0.469255\pi$
$854$	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	$0.227744\pi$
$860$	−40.2648	−	13.2469i	−1.37302	−	0.451715i
$861$		0			0
$862$	−3.35093	+	1.93466i	−0.114133	+	0.0658947i
$863$	13.6657			0.465186			0.232593	−	0.972574i	$-0.425279\pi$
$863$	13.6657			0.465186			0.232593	+	0.972574i	$0.425279\pi$
$864$		0			0
$865$	−27.6468	+	24.7096i	−0.940019	+	0.840152i
$866$		−	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
$875$	−17.6027	−	8.07130i	−0.595079	−	0.272860i
$876$		0			0
$877$	3.96863	+	6.87386i	0.134011	+	0.232114i	0.925219	−	0.379433i	$-0.123881\pi$
$877$	3.96863	+	6.87386i	0.134011	+	0.232114i	−0.791208	+	0.611547i	$0.790548\pi$
$878$	3.31113	+	5.73504i	0.111745	+	0.193548i
$879$		0			0
$880$	12.3125	−	11.0044i	0.415054	−	0.370959i
$881$	18.2477	−	31.6060i	0.614782	−	1.06483i	−0.375641	−	0.926765i	$-0.622578\pi$
$881$	18.2477	−	31.6060i	0.614782	−	1.06483i	0.990423	−	0.138068i	$-0.0440892\pi$
$882$		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	−0.994170	−	0.107826i	$-0.965611\pi$
$887$	−47.1944	−	27.2477i	−1.58463	−	0.914889i	−0.590465	−	0.807064i	$-0.701055\pi$
$888$		0			0
$889$			30.7400i			1.03099i
$890$	7.29219	−	6.51747i	0.244435	−	0.218466i
$891$		0			0
$892$	15.5130			0.519414
$893$	−2.74110	+	1.58258i	−0.0917275	+	0.0529589i
$894$		0			0
$895$	12.6939	−	38.5840i	0.424311	−	1.28972i
$896$	−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	$-0.366434\pi$
$907$	−5.41463	−	3.12614i	−0.179790	−	0.103802i	−0.587194	+	0.809446i	$0.699767\pi$
$908$	−0.732950	+	1.26951i	−0.0243238	+	0.0421301i
$909$		0			0
$910$	6.36150	+	0.479778i	0.210882	+	0.0159045i
$911$	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	0.835807	+	0.549023i	$0.185000\pi$
$919$	27.0826	+	46.9084i	0.893372	+	1.54737i	0.0575648	+	0.998342i	$0.481666\pi$
$920$	−16.8593	−	5.54661i	−0.555834	−	0.182866i
$921$		0			0
$922$			16.3739i			0.539244i
$923$	24.5824	−	6.08258i	0.809141	−	0.200210i
$924$		0			0
$925$	−4.43881	+	39.4373i	−0.145947	+	1.29669i
$926$	−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	−0.825346	−	0.564627i	$-0.809020\pi$
$929$	−22.8303	+	13.1811i	−0.749038	+	0.432457i	0.0763082	+	0.997084i	$0.475687\pi$
$930$		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
$940$	−4.87768	−	5.45748i	−0.159092	−	0.178003i
$941$			26.4575i			0.862490i	0.902235	+	0.431245i	$0.141926\pi$
$941$			26.4575i			0.862490i	−0.902235	+	0.431245i	$0.858074\pi$
$942$		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	$-0.758518\pi$
$947$	7.16658	−	12.4129i	0.232883	−	0.403364i	0.958655	+	0.284570i	$0.0918509\pi$
$948$		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	$-0.624900\pi$
$953$	6.99578	−	4.03901i	0.226616	−	0.130837i	0.609010	+	0.793163i	$0.291567\pi$
$954$		0			0
$955$	24.7096	+	27.6468i	0.799584	+	0.894629i
$956$	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
$965$	10.3881	−	31.5753i	0.334404	−	1.01644i
$966$		0			0
$967$	37.3821			1.20213			0.601064	−	0.799201i	$-0.294744\pi$
$967$	37.3821			1.20213			0.601064	+	0.799201i	$0.294744\pi$
$968$	−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	0.678622	−	0.734487i	$-0.262577\pi$
$971$	−9.24773	−	16.0175i	−0.296774	−	0.514027i	−0.975396	+	0.220460i	$0.929244\pi$
$972$		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	0.432258	+	0.901750i	$0.357717\pi$
$977$	−17.6542	+	30.5780i	−0.564809	+	0.978278i	−0.997067	+	0.0765281i	$0.975617\pi$
$978$		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	$-0.158576\pi$
$983$	55.0840			1.75691			0.878454	+	0.477827i	$0.158576\pi$
$984$		0			0
$985$	10.2548	−	31.1702i	0.326746	−	0.993165i
$986$	−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	−0.744124	−	0.668042i	$-0.767133\pi$
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	0.950603	+	0.310409i	$0.100466\pi$
$992$	−25.4684	+	14.7042i	−0.808621	+	0.466858i
$993$		0			0
$994$	−4.81307	+	2.77883i	−0.152661	+	0.0881390i
$995$	−15.7690	−	17.6435i	−0.499912	−	0.559336i
$996$		0			0
$997$	−0.143025	+	0.0825757i	−0.00452966	+	0.00261520i	−0.502263	−	0.864715i	$-0.667499\pi$
$997$	−0.143025	+	0.0825757i	−0.00452966	+	0.00261520i	0.497733	+	0.867330i	$0.334166\pi$
$998$	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.199.3		8
3.2	odd	2		65.2.l.a.4.2	✓	8
5.4	even	2	inner	585.2.bf.a.199.2		8
12.11	even	2		1040.2.df.b.849.4		8
13.10	even	6	inner	585.2.bf.a.244.2		8
15.2	even	4		325.2.n.c.251.1		4
15.8	even	4		325.2.n.b.251.2		4
15.14	odd	2		65.2.l.a.4.3	yes	8
39.2	even	12		845.2.n.d.484.2		8
39.5	even	4		845.2.n.c.529.3		8
39.8	even	4		845.2.n.d.529.1		8
39.11	even	12		845.2.n.c.484.4		8
39.17	odd	6		845.2.d.c.844.4		8
39.20	even	12		845.2.b.f.339.6		8
39.23	odd	6		65.2.l.a.49.3	yes	8
39.29	odd	6		845.2.l.c.699.2		8
39.32	even	12		845.2.b.f.339.4		8
39.35	odd	6		845.2.d.c.844.6		8
39.38	odd	2		845.2.l.c.654.3		8
60.59	even	2		1040.2.df.b.849.1		8
65.49	even	6	inner	585.2.bf.a.244.3		8
156.23	even	6		1040.2.df.b.49.1		8
195.23	even	12		325.2.n.b.101.2		4
195.29	odd	6		845.2.l.c.699.3		8
195.32	odd	12		4225.2.a.bk.1.3		4
195.44	even	4		845.2.n.d.529.2		8
195.59	even	12		845.2.b.f.339.3		8
195.62	even	12		325.2.n.c.101.1		4
195.74	odd	6		845.2.d.c.844.3		8
195.89	even	12		845.2.n.d.484.1		8
195.98	odd	12		4225.2.a.bj.1.3		4
195.119	even	12		845.2.n.c.484.3		8
195.134	odd	6		845.2.d.c.844.5		8
195.137	odd	12		4225.2.a.bk.1.2		4
195.149	even	12		845.2.b.f.339.5		8
195.164	even	4		845.2.n.c.529.4		8
195.179	odd	6		65.2.l.a.49.2	yes	8
195.188	odd	12		4225.2.a.bj.1.2		4
195.194	odd	2		845.2.l.c.654.2		8
780.179	even	6		1040.2.df.b.49.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.2	✓	8	3.2	odd	2
65.2.l.a.4.3	yes	8	15.14	odd	2
65.2.l.a.49.2	yes	8	195.179	odd	6
65.2.l.a.49.3	yes	8	39.23	odd	6
325.2.n.b.101.2		4	195.23	even	12
325.2.n.b.251.2		4	15.8	even	4
325.2.n.c.101.1		4	195.62	even	12
325.2.n.c.251.1		4	15.2	even	4
585.2.bf.a.199.2		8	5.4	even	2	inner
585.2.bf.a.199.3		8	1.1	even	1	trivial
585.2.bf.a.244.2		8	13.10	even	6	inner
585.2.bf.a.244.3		8	65.49	even	6	inner
845.2.b.f.339.3		8	195.59	even	12
845.2.b.f.339.4		8	39.32	even	12
845.2.b.f.339.5		8	195.149	even	12
845.2.b.f.339.6		8	39.20	even	12
845.2.d.c.844.3		8	195.74	odd	6
845.2.d.c.844.4		8	39.17	odd	6
845.2.d.c.844.5		8	195.134	odd	6
845.2.d.c.844.6		8	39.35	odd	6
845.2.l.c.654.2		8	195.194	odd	2
845.2.l.c.654.3		8	39.38	odd	2
845.2.l.c.699.2		8	39.29	odd	6
845.2.l.c.699.3		8	195.29	odd	6
845.2.n.c.484.3		8	195.119	even	12
845.2.n.c.484.4		8	39.11	even	12
845.2.n.c.529.3		8	39.5	even	4
845.2.n.c.529.4		8	195.164	even	4
845.2.n.d.484.1		8	195.89	even	12
845.2.n.d.484.2		8	39.2	even	12
845.2.n.d.529.1		8	39.8	even	4
845.2.n.d.529.2		8	195.44	even	4
1040.2.df.b.49.1		8	156.23	even	6
1040.2.df.b.49.4		8	780.179	even	6
1040.2.df.b.849.1		8	60.59	even	2
1040.2.df.b.849.4		8	12.11	even	2
4225.2.a.bj.1.2		4	195.188	odd	12
4225.2.a.bj.1.3		4	195.98	odd	12
4225.2.a.bk.1.2		4	195.137	odd	12
4225.2.a.bk.1.3		4	195.32	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)

\(f(q)\)	\(=\)	\(q+(0.228425 - 0.395644i) q^{2} +(0.895644 + 1.55130i) q^{4} +(-2.18890 + 0.456850i) q^{5} +(0.866025 + 1.50000i) q^{7} +1.73205 q^{8} +(-0.319250 + 0.970381i) q^{10} +(2.29129 + 1.32288i) q^{11} +(-3.46410 - 1.00000i) q^{13} +0.791288 q^{14} +(-1.39564 + 2.41733i) q^{16} +(-3.96863 + 2.29129i) q^{17} +(-1.50000 + 0.866025i) q^{19} +(-2.66919 - 2.98647i) q^{20} +(1.04678 - 0.604356i) q^{22} +(3.96863 + 2.29129i) q^{23} +(4.58258 - 2.00000i) q^{25} +(-1.18693 + 1.14213i) q^{26} +(-1.55130 + 2.68693i) q^{28} +(-2.29129 + 3.96863i) q^{29} +6.20520i q^{31} +(2.36965 + 4.10436i) q^{32} +2.09355i q^{34} +(-2.58092 - 2.88771i) q^{35} +(-3.96863 + 6.87386i) q^{37} +0.791288i q^{38} +(-3.79129 + 0.791288i) q^{40} +(-2.29129 - 1.32288i) q^{41} +(9.16478 - 5.29129i) q^{43} +4.73930i q^{44} +(1.81307 - 1.04678i) q^{46} +1.82740 q^{47} +(2.00000 - 3.46410i) q^{49} +(0.255488 - 2.26992i) q^{50} +(-1.55130 - 6.26951i) q^{52} -7.58258i q^{53} +(-5.61976 - 1.84887i) q^{55} +(1.50000 + 2.59808i) q^{56} +(1.04678 + 1.81307i) q^{58} +(12.0826 - 6.97588i) q^{59} +(0.708712 + 1.22753i) q^{61} +(2.45505 + 1.41742i) q^{62} -3.41742 q^{64} +(8.03943 + 0.606325i) q^{65} +(0.504525 - 0.873864i) q^{67} +(-7.10895 - 4.10436i) q^{68} +(-1.73205 + 0.361500i) q^{70} +(-6.08258 + 3.51178i) q^{71} +(1.81307 + 3.14033i) q^{74} +(-2.68693 - 1.55130i) q^{76} +4.58258i q^{77} +6.00000 q^{79} +(1.95057 - 5.92889i) q^{80} +(-1.04678 + 0.604356i) q^{82} -6.01450 q^{83} +(7.64016 - 6.82847i) q^{85} -4.83465i q^{86} +(3.96863 + 2.29129i) q^{88} +(-8.29129 - 4.78698i) q^{89} +(-1.50000 - 6.06218i) q^{91} +8.20871i q^{92} +(0.417424 - 0.723000i) q^{94} +(2.88771 - 2.58092i) q^{95} +(5.70068 + 9.87386i) q^{97} +(-0.913701 - 1.58258i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 4 q^{10} - 12 q^{14} - 2 q^{16} - 12 q^{19} - 24 q^{20} + 18 q^{26} - 6 q^{35} - 12 q^{40} + 42 q^{46} + 16 q^{49} + 12 q^{50} - 14 q^{55} + 12 q^{56} + 60 q^{59} + 24 q^{61} - 64 q^{64}+ \cdots + 6 q^{95}+O(q^{100}) \) 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

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