LMFDB - Embedded newform 780.2.cc.b.121.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [780,2,Mod(121,780)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(780, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("780.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	780.cc (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.22833135766$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.1
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	780.121
Dual form			780.2.cc.b.361.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} -1.00000i q^{5} +(-2.18034 + 1.25882i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.590770 + 0.341081i) q^{11} +(-3.08725 - 1.86250i) q^{13} +(0.866025 + 0.500000i) q^{15} +(-2.39778 - 4.15307i) q^{17} +(5.65099 - 3.26260i) q^{19} -2.51764i q^{21} +(3.68715 - 6.38633i) q^{23} -1.00000 q^{25} +1.00000 q^{27} +(-2.31431 + 4.00851i) q^{29} +0.600398i q^{31} +(-0.590770 + 0.341081i) q^{33} +(1.25882 + 2.18034i) q^{35} +(-8.85666 - 5.11339i) q^{37} +(3.15660 - 1.74238i) q^{39} +(-1.31431 - 0.758819i) q^{41} +(-3.47323 - 6.01581i) q^{43} +(-0.866025 + 0.500000i) q^{45} -4.73910i q^{47} +(-0.330749 + 0.572874i) q^{49} +4.79555 q^{51} +10.3631 q^{53} +(0.341081 - 0.590770i) q^{55} +6.52520i q^{57} +(8.19868 - 4.73351i) q^{59} +(-5.66158 - 9.80614i) q^{61} +(2.18034 + 1.25882i) q^{63} +(-1.86250 + 3.08725i) q^{65} +(-3.81225 - 2.20100i) q^{67} +(3.68715 + 6.38633i) q^{69} +(0.291069 - 0.168049i) q^{71} -4.50354i q^{73} +(0.500000 - 0.866025i) q^{75} -1.71744 q^{77} -9.19615 q^{79} +(-0.500000 + 0.866025i) q^{81} +10.0392i q^{83} +(-4.15307 + 2.39778i) q^{85} +(-2.31431 - 4.00851i) q^{87} +(11.2869 + 6.51652i) q^{89} +(9.07579 + 0.174599i) q^{91} +(-0.519960 - 0.300199i) q^{93} +(-3.26260 - 5.65099i) q^{95} +(7.97021 - 4.60160i) q^{97} -0.682163i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 4 q^{9} - 12 q^{11} + 4 q^{17} + 12 q^{19} + 4 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 12 q^{33} + 8 q^{35} - 24 q^{37} - 16 q^{43} - 4 q^{49} - 8 q^{51} + 16 q^{53} + 4 q^{55} + 24 q^{59}+ \cdots + 48 q^{97}+O(q^{100}) $ 8 * q - 4 * q^3 - 4 * q^9 - 12 * q^11 + 4 * q^17 + 12 * q^19 + 4 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 12 * q^33 + 8 * q^35 - 24 * q^37 - 16 * q^43 - 4 * q^49 - 8 * q^51 + 16 * q^53 + 4 * q^55 + 24 * q^59 + 8 * q^61 + 24 * q^67 + 4 * q^69 - 12 * q^71 + 4 * q^75 - 8 * q^77 - 32 * q^79 - 4 * q^81 - 8 * q^87 - 12 * q^89 + 8 * q^91 - 24 * q^93 - 12 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/780\mathbb{Z}\right)^\times$.

$n$	$157$	$301$	$391$	$521$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−2.18034	+	1.25882i	−0.824091	+	0.475789i	−0.851825	−	0.523826i	$-0.824504\pi$
$7$	−2.18034	+	1.25882i	−0.824091	+	0.475789i	0.0277345	+	0.999615i	$0.491171\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	0.590770	+	0.341081i	0.178124	+	0.102840i	0.586411	−	0.810014i	$-0.300540\pi$
$11$	0.590770	+	0.341081i	0.178124	+	0.102840i	−0.408287	+	0.912854i	$0.633874\pi$
$12$		0			0
$13$	−3.08725	−	1.86250i	−0.856248	−	0.516565i
$13$	−3.08725	−	1.86250i	−0.856248	−	0.516565i
$14$		0			0
$15$	0.866025	+	0.500000i	0.223607	+	0.129099i
$16$		0			0
$17$	−2.39778	−	4.15307i	−0.581546	−	1.00727i	−0.995296	−	0.0968774i	$-0.969115\pi$
$17$	−2.39778	−	4.15307i	−0.581546	−	1.00727i	0.413750	−	0.910391i	$-0.364219\pi$
$18$		0			0
$19$	5.65099	−	3.26260i	1.29643	−	0.748492i	0.316641	−	0.948545i	$-0.397445\pi$
$19$	5.65099	−	3.26260i	1.29643	−	0.748492i	0.979785	+	0.200053i	$0.0641116\pi$
$20$		0			0
$21$		−	2.51764i		−	0.549394i
$22$		0			0
$23$	3.68715	−	6.38633i	0.768823	−	1.33164i	−0.169378	−	0.985551i	$-0.554176\pi$
$23$	3.68715	−	6.38633i	0.768823	−	1.33164i	0.938201	−	0.346090i	$-0.112491\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−2.31431	+	4.00851i	−0.429757	+	0.744361i	−0.996851	−	0.0792916i	$-0.974734\pi$
$29$	−2.31431	+	4.00851i	−0.429757	+	0.744361i	0.567094	+	0.823653i	$0.308067\pi$
$30$		0			0
$31$			0.600398i			0.107835i	0.998545	+	0.0539174i	$0.0171708\pi$
$31$			0.600398i			0.107835i	−0.998545	+	0.0539174i	$0.982829\pi$
$32$		0			0
$33$	−0.590770	+	0.341081i	−0.102840	+	0.0593746i
$34$		0			0
$35$	1.25882	+	2.18034i	0.212779	+	0.368544i
$36$		0			0
$37$	−8.85666	−	5.11339i	−1.45603	−	0.840636i	−0.457213	−	0.889357i	$-0.651152\pi$
$37$	−8.85666	−	5.11339i	−1.45603	−	0.840636i	−0.998812	+	0.0487209i	$0.984486\pi$
$38$		0			0
$39$	3.15660	−	1.74238i	0.505460	−	0.279005i
$40$		0			0
$41$	−1.31431	−	0.758819i	−0.205261	−	0.118508i	0.393846	−	0.919176i	$-0.371144\pi$
$41$	−1.31431	−	0.758819i	−0.205261	−	0.118508i	−0.599107	+	0.800669i	$0.704478\pi$
$42$		0			0
$43$	−3.47323	−	6.01581i	−0.529663	−	0.917403i	−0.999401	−	0.0345974i	$-0.988985\pi$
$43$	−3.47323	−	6.01581i	−0.529663	−	0.917403i	0.469738	−	0.882806i	$-0.344348\pi$
$44$		0			0
$45$	−0.866025	+	0.500000i	−0.129099	+	0.0745356i
$46$		0			0
$47$		−	4.73910i		−	0.691269i	−0.938369	−	0.345634i	$-0.887664\pi$
$47$		−	4.73910i		−	0.691269i	0.938369	−	0.345634i	$-0.112336\pi$
$48$		0			0
$49$	−0.330749	+	0.572874i	−0.0472499	+	0.0818392i
$50$		0			0
$51$	4.79555			0.671512
$52$		0			0
$53$	10.3631			1.42348			0.711739	−	0.702444i	$-0.247908\pi$
$53$	10.3631			1.42348			0.711739	+	0.702444i	$0.247908\pi$
$54$		0			0
$55$	0.341081	−	0.590770i	0.0459914	−	0.0796594i
$56$		0			0
$57$			6.52520i			0.864284i
$58$		0			0
$59$	8.19868	−	4.73351i	1.06738	−	0.616251i	0.139914	−	0.990164i	$-0.455318\pi$
$59$	8.19868	−	4.73351i	1.06738	−	0.616251i	0.927464	+	0.373913i	$0.121984\pi$
$60$		0			0
$61$	−5.66158	−	9.80614i	−0.724891	−	1.25555i	−0.959019	−	0.283342i	$-0.908557\pi$
$61$	−5.66158	−	9.80614i	−0.724891	−	1.25555i	0.234128	−	0.972206i	$-0.424777\pi$
$62$		0			0
$63$	2.18034	+	1.25882i	0.274697	+	0.158596i
$64$		0			0
$65$	−1.86250	+	3.08725i	−0.231015	+	0.382926i
$66$		0			0
$67$	−3.81225	−	2.20100i	−0.465740	−	0.268895i	0.248715	−	0.968577i	$-0.419992\pi$
$67$	−3.81225	−	2.20100i	−0.465740	−	0.268895i	−0.714455	+	0.699682i	$0.753325\pi$
$68$		0			0
$69$	3.68715	+	6.38633i	0.443880	+	0.768823i
$70$		0			0
$71$	0.291069	−	0.168049i	0.0345435	−	0.0199437i	−0.482629	−	0.875825i	$-0.660318\pi$
$71$	0.291069	−	0.168049i	0.0345435	−	0.0199437i	0.517172	+	0.855881i	$0.326985\pi$
$72$		0			0
$73$		−	4.50354i		−	0.527100i	−0.964646	−	0.263550i	$-0.915107\pi$
$73$		−	4.50354i		−	0.527100i	0.964646	−	0.263550i	$-0.0848933\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$	−1.71744			−0.195720
$78$		0			0
$79$	−9.19615			−1.03465			−0.517324	−	0.855790i	$-0.673072\pi$
$79$	−9.19615			−1.03465			−0.517324	+	0.855790i	$0.673072\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			10.0392i			1.10194i	0.834524	+	0.550972i	$0.185743\pi$
$83$			10.0392i			1.10194i	−0.834524	+	0.550972i	$0.814257\pi$
$84$		0			0
$85$	−4.15307	+	2.39778i	−0.450464	+	0.260075i
$86$		0			0
$87$	−2.31431	−	4.00851i	−0.248120	−	0.429757i
$88$		0			0
$89$	11.2869	+	6.51652i	1.19641	+	0.690750i	0.959754	−	0.280843i	$-0.0906141\pi$
$89$	11.2869	+	6.51652i	1.19641	+	0.690750i	0.236660	+	0.971593i	$0.423947\pi$
$90$		0			0
$91$	9.07579	+	0.174599i	0.951402	+	0.0183030i
$92$		0			0
$93$	−0.519960	−	0.300199i	−0.0539174	−	0.0311292i
$94$		0			0
$95$	−3.26260	−	5.65099i	−0.334736	−	0.579779i
$96$		0			0
$97$	7.97021	−	4.60160i	0.809252	−	0.467222i	−0.0374442	−	0.999299i	$-0.511922\pi$
$97$	7.97021	−	4.60160i	0.809252	−	0.467222i	0.846696	+	0.532077i	$0.178588\pi$
$98$		0			0
$99$		−	0.682163i		−	0.0685599i
$100$		0			0
$101$	−7.33279	+	12.7008i	−0.729640	+	1.26377i	0.227396	+	0.973802i	$0.426979\pi$
$101$	−7.33279	+	12.7008i	−0.729640	+	1.26377i	−0.957036	+	0.289971i	$0.906354\pi$
$102$		0			0
$103$	4.97569			0.490269			0.245135	−	0.969489i	$-0.421168\pi$
$103$	4.97569			0.490269			0.245135	+	0.969489i	$0.421168\pi$
$104$		0			0
$105$	−2.51764			−0.245696
$106$		0			0
$107$	−2.86394	+	4.96050i	−0.276868	+	0.479549i	−0.970605	−	0.240679i	$-0.922630\pi$
$107$	−2.86394	+	4.96050i	−0.276868	+	0.479549i	0.693737	+	0.720229i	$0.255963\pi$
$108$		0			0
$109$		−	5.45465i		−	0.522461i	−0.965276	−	0.261230i	$-0.915872\pi$
$109$		−	5.45465i		−	0.522461i	0.965276	−	0.261230i	$-0.0841282\pi$
$110$		0			0
$111$	8.85666	−	5.11339i	0.840636	−	0.485342i
$112$		0			0
$113$	−4.36773	−	7.56512i	−0.410881	−	0.711667i	0.584105	−	0.811678i	$-0.301446\pi$
$113$	−4.36773	−	7.56512i	−0.410881	−	0.711667i	−0.994986	+	0.100011i	$0.968112\pi$
$114$		0			0
$115$	−6.38633	−	3.68715i	−0.595528	−	0.343828i
$116$		0			0
$117$	−0.0693504	+	3.60488i	−0.00641144	+	0.333272i
$118$		0			0
$119$	10.4559	+	6.03674i	0.958494	+	0.553387i
$120$		0			0
$121$	−5.26733	−	9.12328i	−0.478848	−	0.829389i
$122$		0			0
$123$	1.31431	−	0.758819i	0.118508	−	0.0684204i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−11.0294	+	19.1035i	−0.978704	+	1.69516i	−0.311576	+	0.950221i	$0.600857\pi$
$127$	−11.0294	+	19.1035i	−0.978704	+	1.69516i	−0.667128	+	0.744943i	$0.732477\pi$
$128$		0			0
$129$	6.94646			0.611602
$130$		0			0
$131$	−7.85666			−0.686439			−0.343220	−	0.939255i	$-0.611517\pi$
$131$	−7.85666			−0.686439			−0.343220	+	0.939255i	$0.611517\pi$
$132$		0			0
$133$	−8.21405	+	14.2271i	−0.712248	+	1.23365i
$134$		0			0
$135$		−	1.00000i		−	0.0860663i
$136$		0			0
$137$	−13.1725	+	7.60514i	−1.12540	+	0.649751i	−0.942774	−	0.333431i	$-0.891794\pi$
$137$	−13.1725	+	7.60514i	−1.12540	+	0.649751i	−0.182627	+	0.983182i	$0.558460\pi$
$138$		0			0
$139$	6.77792	+	11.7397i	0.574895	+	0.995748i	0.996053	+	0.0887606i	$0.0282906\pi$
$139$	6.77792	+	11.7397i	0.574895	+	0.995748i	−0.421158	+	0.906987i	$0.638376\pi$
$140$		0			0
$141$	4.10418	+	2.36955i	0.345634	+	0.199552i
$142$		0			0
$143$	−1.18859	−	2.15331i	−0.0993948	−	0.180069i
$144$		0			0
$145$	4.00851	+	2.31431i	0.332888	+	0.192193i
$146$		0			0
$147$	−0.330749	−	0.572874i	−0.0272797	−	0.0472499i
$148$		0			0
$149$	7.14760	−	4.12667i	0.585554	−	0.338070i	−0.177783	−	0.984070i	$-0.556893\pi$
$149$	7.14760	−	4.12667i	0.585554	−	0.338070i	0.763338	+	0.646000i	$0.223559\pi$
$150$		0			0
$151$		−	3.83307i		−	0.311931i	−0.987763	−	0.155965i	$-0.950151\pi$
$151$		−	3.83307i		−	0.311931i	0.987763	−	0.155965i	$-0.0498489\pi$
$152$		0			0
$153$	−2.39778	+	4.15307i	−0.193849	+	0.335756i
$154$		0			0
$155$	0.600398			0.0482252
$156$		0			0
$157$	−21.8654			−1.74505			−0.872524	−	0.488572i	$-0.837518\pi$
$157$	−21.8654			−1.74505			−0.872524	+	0.488572i	$0.837518\pi$
$158$		0			0
$159$	−5.18154	+	8.97469i	−0.410923	+	0.711739i
$160$		0			0
$161$			18.5658i			1.46319i
$162$		0			0
$163$	−6.94402	+	4.00913i	−0.543897	+	0.314019i	−0.746657	−	0.665209i	$-0.768342\pi$
$163$	−6.94402	+	4.00913i	−0.543897	+	0.314019i	0.202760	+	0.979229i	$0.435009\pi$
$164$		0			0
$165$	0.341081	+	0.590770i	0.0265531	+	0.0459914i
$166$		0			0
$167$	7.76368	+	4.48236i	0.600771	+	0.346856i	0.769345	−	0.638834i	$-0.220583\pi$
$167$	7.76368	+	4.48236i	0.600771	+	0.346856i	−0.168574	+	0.985689i	$0.553916\pi$
$168$		0			0
$169$	6.06218	+	11.5000i	0.466321	+	0.884615i
$170$		0			0
$171$	−5.65099	−	3.26260i	−0.432142	−	0.249497i
$172$		0			0
$173$	5.97652	+	10.3516i	0.454386	+	0.787020i	0.998653	−	0.0518925i	$-0.0165253\pi$
$173$	5.97652	+	10.3516i	0.454386	+	0.787020i	−0.544267	+	0.838912i	$0.683192\pi$
$174$		0			0
$175$	2.18034	−	1.25882i	0.164818	−	0.0951578i
$176$		0			0
$177$			9.46702i			0.711585i
$178$		0			0
$179$	9.60426	−	16.6351i	0.717856	−	1.24336i	−0.243991	−	0.969777i	$-0.578457\pi$
$179$	9.60426	−	16.6351i	0.717856	−	1.24336i	0.961848	−	0.273586i	$-0.0882098\pi$
$180$		0			0
$181$	−14.2526			−1.05939			−0.529694	−	0.848189i	$-0.677693\pi$
$181$	−14.2526			−1.05939			−0.529694	+	0.848189i	$0.677693\pi$
$182$		0			0
$183$	11.3232			0.837032
$184$		0			0
$185$	−5.11339	+	8.85666i	−0.375944	+	0.651154i
$186$		0			0
$187$		−	3.27135i		−	0.239225i
$188$		0			0
$189$	−2.18034	+	1.25882i	−0.158596	+	0.0915656i
$190$		0			0
$191$	4.84058	+	8.38414i	0.350252	+	0.606655i	0.986294	−	0.165000i	$-0.0527625\pi$
$191$	4.84058	+	8.38414i	0.350252	+	0.606655i	−0.636041	+	0.771655i	$0.719429\pi$
$192$		0			0
$193$	11.1428	+	6.43331i	0.802078	+	0.463080i	0.844197	−	0.536033i	$-0.180078\pi$
$193$	11.1428	+	6.43331i	0.802078	+	0.463080i	−0.0421193	+	0.999113i	$0.513411\pi$
$194$		0			0
$195$	−1.74238	−	3.15660i	−0.124775	−	0.226049i
$196$		0			0
$197$	−14.6883	−	8.48030i	−1.04650	−	0.604196i	−0.124831	−	0.992178i	$-0.539839\pi$
$197$	−14.6883	−	8.48030i	−1.04650	−	0.604196i	−0.921667	+	0.387982i	$0.873172\pi$
$198$		0			0
$199$	−1.30260	−	2.25617i	−0.0923391	−	0.159936i	0.816156	−	0.577832i	$-0.196101\pi$
$199$	−1.30260	−	2.25617i	−0.0923391	−	0.159936i	−0.908495	+	0.417896i	$0.862768\pi$
$200$		0			0
$201$	3.81225	−	2.20100i	0.268895	−	0.155247i
$202$		0			0
$203$		−	11.6532i		−	0.817895i
$204$		0			0
$205$	−0.758819	+	1.31431i	−0.0529982	+	0.0917956i
$206$		0			0
$207$	−7.37429			−0.512549
$208$		0			0
$209$	4.45125			0.307899
$210$		0			0
$211$	0.649913	−	1.12568i	0.0447418	−	0.0774951i	−0.842787	−	0.538247i	$-0.819087\pi$
$211$	0.649913	−	1.12568i	0.0447418	−	0.0774951i	0.887529	+	0.460752i	$0.152420\pi$
$212$		0			0
$213$			0.336098i			0.0230290i
$214$		0			0
$215$	−6.01581	+	3.47323i	−0.410275	+	0.236872i
$216$		0			0
$217$	−0.755793	−	1.30907i	−0.0513066	−	0.0888656i
$218$		0			0
$219$	3.90018	+	2.25177i	0.263550	+	0.152161i
$220$		0			0
$221$	−0.332573	+	17.2874i	−0.0223713	+	1.16288i
$222$		0			0
$223$	16.6814	+	9.63103i	1.11707	+	0.644941i	0.940652	−	0.339374i	$-0.110215\pi$
$223$	16.6814	+	9.63103i	1.11707	+	0.644941i	0.176420	+	0.984315i	$0.443548\pi$
$224$		0			0
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$		0			0
$227$	19.2774	−	11.1298i	1.27949	−	0.738713i	0.302734	−	0.953075i	$-0.402101\pi$
$227$	19.2774	−	11.1298i	1.27949	−	0.738713i	0.976754	+	0.214363i	$0.0687674\pi$
$228$		0			0
$229$		−	10.5393i		−	0.696456i	−0.937410	−	0.348228i	$-0.886783\pi$
$229$		−	10.5393i		−	0.696456i	0.937410	−	0.348228i	$-0.113217\pi$
$230$		0			0
$231$	0.858719	−	1.48735i	0.0564996	−	0.0978602i
$232$		0			0
$233$	28.3517			1.85738			0.928689	−	0.370859i	$-0.120937\pi$
$233$	28.3517			1.85738			0.928689	+	0.370859i	$0.120937\pi$
$234$		0			0
$235$	−4.73910			−0.309145
$236$		0			0
$237$	4.59808	−	7.96410i	0.298677	−	0.517324i
$238$		0			0
$239$		−	7.76660i		−	0.502379i	−0.967938	−	0.251190i	$-0.919178\pi$
$239$		−	7.76660i		−	0.502379i	0.967938	−	0.251190i	$-0.0808218\pi$
$240$		0			0
$241$	−0.256282	+	0.147964i	−0.0165086	+	0.00953122i	−0.508232	−	0.861220i	$-0.669701\pi$
$241$	−0.256282	+	0.147964i	−0.0165086	+	0.00953122i	0.491723	+	0.870752i	$0.336367\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	0.572874	+	0.330749i	0.0365996	+	0.0211308i
$246$		0			0
$247$	−23.5226	−	0.452525i	−1.49671	−	0.0287935i
$248$		0			0
$249$	−8.69419	−	5.01960i	−0.550972	−	0.318104i
$250$		0			0
$251$	1.07554	+	1.86288i	0.0678872	+	0.117584i	0.897971	−	0.440054i	$-0.145041\pi$
$251$	1.07554	+	1.86288i	0.0678872	+	0.117584i	−0.830084	+	0.557639i	$0.811708\pi$
$252$		0			0
$253$	4.35651	−	2.51523i	0.273892	−	0.158131i
$254$		0			0
$255$		−	4.79555i		−	0.300309i
$256$		0			0
$257$	−1.89682	+	3.28538i	−0.118320	+	0.204936i	−0.919102	−	0.394020i	$-0.871084\pi$
$257$	−1.89682	+	3.28538i	−0.118320	+	0.204936i	0.800782	+	0.598956i	$0.204418\pi$
$258$		0			0
$259$	25.7473			1.59986
$260$		0			0
$261$	4.62863			0.286505
$262$		0			0
$263$	−5.59153	+	9.68481i	−0.344788	+	0.597191i	−0.985315	−	0.170745i	$-0.945383\pi$
$263$	−5.59153	+	9.68481i	−0.344788	+	0.597191i	0.640527	+	0.767936i	$0.278716\pi$
$264$		0			0
$265$		−	10.3631i		−	0.636599i
$266$		0			0
$267$	−11.2869	+	6.51652i	−0.690750	+	0.398804i
$268$		0			0
$269$	−13.8540	−	23.9957i	−0.844690	−	1.46305i	−0.885890	−	0.463896i	$-0.846451\pi$
$269$	−13.8540	−	23.9957i	−0.844690	−	1.46305i	0.0411996	−	0.999151i	$-0.486882\pi$
$270$		0			0
$271$	27.0381	+	15.6104i	1.64245	+	0.948267i	0.979960	+	0.199194i	$0.0638322\pi$
$271$	27.0381	+	15.6104i	1.64245	+	0.948267i	0.662487	+	0.749074i	$0.269501\pi$
$272$		0			0
$273$	−4.68910	+	7.77257i	−0.283797	+	0.470417i
$274$		0			0
$275$	−0.590770	−	0.341081i	−0.0356248	−	0.0205680i
$276$		0			0
$277$	1.07520	+	1.86230i	0.0646023	+	0.111894i	0.896518	−	0.443008i	$-0.146089\pi$
$277$	1.07520	+	1.86230i	0.0646023	+	0.111894i	−0.831915	+	0.554903i	$0.812755\pi$
$278$		0			0
$279$	0.519960	−	0.300199i	0.0311292	−	0.0179725i
$280$		0			0
$281$		−	20.0311i		−	1.19496i	−0.801885	−	0.597478i	$-0.796170\pi$
$281$		−	20.0311i		−	1.19496i	0.801885	−	0.597478i	$-0.203830\pi$
$282$		0			0
$283$	8.45461	−	14.6438i	0.502574	−	0.870484i	−0.497421	−	0.867509i	$-0.665720\pi$
$283$	8.45461	−	14.6438i	0.502574	−	0.870484i	0.999996	−	0.00297501i	$-0.000946976\pi$
$284$		0			0
$285$	6.52520			0.386520
$286$		0			0
$287$	3.82086			0.225538
$288$		0			0
$289$	−2.99867	+	5.19386i	−0.176393	+	0.305521i
$290$		0			0
$291$			9.20320i			0.539501i
$292$		0			0
$293$	−10.9754	+	6.33668i	−0.641192	+	0.370193i	−0.785074	−	0.619402i	$-0.787375\pi$
$293$	−10.9754	+	6.33668i	−0.641192	+	0.370193i	0.143881	+	0.989595i	$0.454042\pi$
$294$		0			0
$295$	−4.73351	−	8.19868i	−0.275596	−	0.477346i
$296$		0			0
$297$	0.590770	+	0.341081i	0.0342800	+	0.0197915i
$298$		0			0
$299$	−23.2777	+	12.8488i	−1.34618	+	0.743068i
$300$		0			0
$301$	15.1456	+	8.74434i	0.872980	+	0.504015i
$302$		0			0
$303$	−7.33279	−	12.7008i	−0.421258	−	0.729640i
$304$		0			0
$305$	−9.80614	+	5.66158i	−0.561498	+	0.324181i
$306$		0			0
$307$			7.54738i			0.430752i	0.976531	+	0.215376i	$0.0690976\pi$
$307$			7.54738i			0.430752i	−0.976531	+	0.215376i	$0.930902\pi$
$308$		0			0
$309$	−2.48784	+	4.30907i	−0.141528	+	0.245135i
$310$		0			0
$311$	22.0924			1.25274			0.626372	−	0.779524i	$-0.284539\pi$
$311$	22.0924			1.25274			0.626372	+	0.779524i	$0.284539\pi$
$312$		0			0
$313$	−10.9392			−0.618318			−0.309159	−	0.951010i	$-0.600048\pi$
$313$	−10.9392			−0.618318			−0.309159	+	0.951010i	$0.600048\pi$
$314$		0			0
$315$	1.25882	−	2.18034i	0.0709264	−	0.122848i
$316$		0			0
$317$		−	20.9873i		−	1.17877i	−0.807854	−	0.589383i	$-0.799371\pi$
$317$		−	20.9873i		−	1.17877i	0.807854	−	0.589383i	$-0.200629\pi$
$318$		0			0
$319$	−2.73445	+	1.57874i	−0.153100	+	0.0883924i
$320$		0			0
$321$	−2.86394	−	4.96050i	−0.159850	−	0.276868i
$322$		0			0
$323$	−27.0996	−	15.6460i	−1.50786	−	0.870566i
$324$		0			0
$325$	3.08725	+	1.86250i	0.171250	+	0.103313i
$326$		0			0
$327$	4.72386	+	2.72732i	0.261230	+	0.150821i
$328$		0			0
$329$	5.96567	+	10.3328i	0.328898	+	0.569668i
$330$		0			0
$331$	12.1031	−	6.98771i	0.665245	−	0.384079i	−0.129028	−	0.991641i	$-0.541186\pi$
$331$	12.1031	−	6.98771i	0.665245	−	0.384079i	0.794272	+	0.607562i	$0.207852\pi$
$332$		0			0
$333$			10.2268i			0.560424i
$334$		0			0
$335$	−2.20100	+	3.81225i	−0.120254	+	0.208285i
$336$		0			0
$337$	−21.2954			−1.16004			−0.580018	−	0.814603i	$-0.696955\pi$
$337$	−21.2954			−1.16004			−0.580018	+	0.814603i	$0.696955\pi$
$338$		0			0
$339$	8.73545			0.474445
$340$		0			0
$341$	−0.204785	+	0.354697i	−0.0110897	+	0.0192079i
$342$		0			0
$343$		−	19.2889i		−	1.04150i
$344$		0			0
$345$	6.38633	−	3.68715i	0.343828	−	0.198509i
$346$		0			0
$347$	−11.7167	−	20.2939i	−0.628986	−	1.08944i	−0.987756	−	0.156009i	$-0.950137\pi$
$347$	−11.7167	−	20.2939i	−0.628986	−	1.08944i	0.358770	−	0.933426i	$-0.383196\pi$
$348$		0			0
$349$	−13.2104	−	7.62701i	−0.707135	−	0.408264i	0.102865	−	0.994695i	$-0.467199\pi$
$349$	−13.2104	−	7.62701i	−0.707135	−	0.408264i	−0.809999	+	0.586431i	$0.800533\pi$
$350$		0			0
$351$	−3.08725	−	1.86250i	−0.164785	−	0.0994130i
$352$		0			0
$353$	19.9325	+	11.5080i	1.06090	+	0.612510i	0.925680	−	0.378306i	$-0.123493\pi$
$353$	19.9325	+	11.5080i	1.06090	+	0.612510i	0.135217	+	0.990816i	$0.456827\pi$
$354$		0			0
$355$	−0.168049	−	0.291069i	−0.00891910	−	0.0154483i
$356$		0			0
$357$	−10.4559	+	6.03674i	−0.553387	+	0.319498i
$358$		0			0
$359$			2.03111i			0.107198i	0.998563	+	0.0535990i	$0.0170693\pi$
$359$			2.03111i			0.107198i	−0.998563	+	0.0535990i	$0.982931\pi$
$360$		0			0
$361$	11.7891	−	20.4194i	0.620480	−	1.07470i
$362$		0			0
$363$	10.5347			0.552926
$364$		0			0
$365$	−4.50354			−0.235726
$366$		0			0
$367$	−13.0719	+	22.6412i	−0.682348	+	1.18186i	0.291915	+	0.956444i	$0.405708\pi$
$367$	−13.0719	+	22.6412i	−0.682348	+	1.18186i	−0.974262	+	0.225417i	$0.927626\pi$
$368$		0			0
$369$			1.51764i			0.0790051i
$370$		0			0
$371$	−22.5950	+	13.0452i	−1.17308	+	0.677275i
$372$		0			0
$373$	−5.12680	−	8.87988i	−0.265456	−	0.459783i	0.702227	−	0.711953i	$-0.252189\pi$
$373$	−5.12680	−	8.87988i	−0.265456	−	0.459783i	−0.967683	+	0.252170i	$0.918856\pi$
$374$		0			0
$375$	−0.866025	−	0.500000i	−0.0447214	−	0.0258199i
$376$		0			0
$377$	14.6107	−	8.06484i	0.752490	−	0.415360i
$378$		0			0
$379$	−13.0013	−	7.50632i	−0.667833	−	0.385574i	0.127422	−	0.991849i	$-0.459330\pi$
$379$	−13.0013	−	7.50632i	−0.667833	−	0.385574i	−0.795255	+	0.606275i	$0.792663\pi$
$380$		0			0
$381$	−11.0294	−	19.1035i	−0.565055	−	0.978704i
$382$		0			0
$383$	6.60256	−	3.81199i	0.337375	−	0.194784i	−0.321736	−	0.946830i	$-0.604266\pi$
$383$	6.60256	−	3.81199i	0.337375	−	0.194784i	0.659111	+	0.752046i	$0.270933\pi$
$384$		0			0
$385$			1.71744i			0.0875288i
$386$		0			0
$387$	−3.47323	+	6.01581i	−0.176554	+	0.305801i
$388$		0			0
$389$	4.91824			0.249364			0.124682	−	0.992197i	$-0.460209\pi$
$389$	4.91824			0.249364			0.124682	+	0.992197i	$0.460209\pi$
$390$		0			0
$391$	−35.3638			−1.78843
$392$		0			0
$393$	3.92833	−	6.80406i	0.198158	−	0.343220i
$394$		0			0
$395$			9.19615i			0.462709i
$396$		0			0
$397$	16.9432	−	9.78215i	0.850353	−	0.490952i	−0.0104167	−	0.999946i	$-0.503316\pi$
$397$	16.9432	−	9.78215i	0.850353	−	0.490952i	0.860770	+	0.508994i	$0.169982\pi$
$398$		0			0
$399$	−8.21405	−	14.2271i	−0.411217	−	0.712248i
$400$		0			0
$401$	−6.23851	−	3.60181i	−0.311536	−	0.179866i	0.336077	−	0.941834i	$-0.390900\pi$
$401$	−6.23851	−	3.60181i	−0.311536	−	0.179866i	−0.647614	+	0.761969i	$0.724233\pi$
$402$		0			0
$403$	1.11824	−	1.85358i	0.0557036	−	0.0923333i
$404$		0			0
$405$	0.866025	+	0.500000i	0.0430331	+	0.0248452i
$406$		0			0
$407$	−3.48817	−	6.04168i	−0.172902	−	0.299475i
$408$		0			0
$409$	24.6051	−	14.2057i	1.21664	−	0.702429i	0.252444	−	0.967611i	$-0.418766\pi$
$409$	24.6051	−	14.2057i	1.21664	−	0.702429i	0.964198	+	0.265182i	$0.0854322\pi$
$410$		0			0
$411$		−	15.2103i		−	0.750268i
$412$		0			0
$413$	−11.9173	+	20.6413i	−0.586410	+	1.01569i
$414$		0			0
$415$	10.0392			0.492805
$416$		0			0
$417$	−13.5558			−0.663832
$418$		0			0
$419$	17.7177	−	30.6879i	0.865564	−	1.49920i	−0.000921968	−	1.00000i	$-0.500293\pi$
$419$	17.7177	−	30.6879i	0.865564	−	1.49920i	0.866486	−	0.499201i	$-0.166373\pi$
$420$		0			0
$421$		−	24.9625i		−	1.21660i	−0.793708	−	0.608299i	$-0.791852\pi$
$421$		−	24.9625i		−	1.21660i	0.793708	−	0.608299i	$-0.208148\pi$
$422$		0			0
$423$	−4.10418	+	2.36955i	−0.199552	+	0.115211i
$424$		0			0
$425$	2.39778	+	4.15307i	0.116309	+	0.201454i
$426$		0			0
$427$	24.6883	+	14.2538i	1.19475	+	0.689790i
$428$		0			0
$429$	2.45912	+	0.0473082i	0.118727	+	0.00228406i
$430$		0			0
$431$	−0.463797	−	0.267773i	−0.0223403	−	0.0128982i	0.488788	−	0.872402i	$-0.337439\pi$
$431$	−0.463797	−	0.267773i	−0.0223403	−	0.0128982i	−0.511129	+	0.859504i	$0.670772\pi$
$432$		0			0
$433$	6.34967	+	10.9980i	0.305146	+	0.528528i	0.977294	−	0.211889i	$-0.0679615\pi$
$433$	6.34967	+	10.9980i	0.305146	+	0.528528i	−0.672148	+	0.740417i	$0.734628\pi$
$434$		0			0
$435$	−4.00851	+	2.31431i	−0.192193	+	0.110963i
$436$		0			0
$437$		−	48.1188i		−	2.30183i
$438$		0			0
$439$	−6.71752	+	11.6351i	−0.320610	+	0.555312i	−0.980614	−	0.195949i	$-0.937221\pi$
$439$	−6.71752	+	11.6351i	−0.320610	+	0.555312i	0.660004	+	0.751262i	$0.270554\pi$
$440$		0			0
$441$	0.661498			0.0314999
$442$		0			0
$443$	−1.83564			−0.0872138			−0.0436069	−	0.999049i	$-0.513885\pi$
$443$	−1.83564			−0.0872138			−0.0436069	+	0.999049i	$0.513885\pi$
$444$		0			0
$445$	6.51652	−	11.2869i	0.308913	−	0.535052i
$446$		0			0
$447$			8.25334i			0.390369i
$448$		0			0
$449$	7.49598	−	4.32780i	0.353757	−	0.204242i	−0.312582	−	0.949891i	$-0.601194\pi$
$449$	7.49598	−	4.32780i	0.353757	−	0.204242i	0.666339	+	0.745649i	$0.267860\pi$
$450$		0			0
$451$	−0.517638	−	0.896575i	−0.0243746	−	0.0422181i
$452$		0			0
$453$	3.31954	+	1.91654i	0.155965	+	0.0900467i
$454$		0			0
$455$	0.174599	−	9.07579i	0.00818533	−	0.425480i
$456$		0			0
$457$	32.3298	+	18.6656i	1.51232	+	0.873141i	0.999896	+	0.0144108i	$0.00458726\pi$
$457$	32.3298	+	18.6656i	1.51232	+	0.873141i	0.512428	+	0.858730i	$0.328746\pi$
$458$		0			0
$459$	−2.39778	−	4.15307i	−0.111919	−	0.193849i
$460$		0			0
$461$	−22.0005	+	12.7020i	−1.02466	+	0.591590i	−0.915451	−	0.402429i	$-0.868166\pi$
$461$	−22.0005	+	12.7020i	−1.02466	+	0.591590i	−0.109212	+	0.994018i	$0.534833\pi$
$462$		0			0
$463$			22.2244i			1.03285i	0.856331	+	0.516427i	$0.172738\pi$
$463$			22.2244i			1.03285i	−0.856331	+	0.516427i	$0.827262\pi$
$464$		0			0
$465$	−0.300199	+	0.519960i	−0.0139214	+	0.0241126i
$466$		0			0
$467$	2.97104			0.137483			0.0687417	−	0.997634i	$-0.478102\pi$
$467$	2.97104			0.137483			0.0687417	+	0.997634i	$0.478102\pi$
$468$		0			0
$469$	11.0827			0.511750
$470$		0			0
$471$	10.9327	−	18.9360i	0.503752	−	0.872524i
$472$		0			0
$473$		−	4.73862i		−	0.217882i
$474$		0			0
$475$	−5.65099	+	3.26260i	−0.259285	+	0.149698i
$476$		0			0
$477$	−5.18154	−	8.97469i	−0.237246	−	0.410923i
$478$		0			0
$479$	15.6262	+	9.02178i	0.713979	+	0.412216i	0.812533	−	0.582916i	$-0.198088\pi$
$479$	15.6262	+	9.02178i	0.713979	+	0.412216i	−0.0985537	+	0.995132i	$0.531422\pi$
$480$		0			0
$481$	17.8190	+	32.2818i	0.812475	+	1.47192i
$482$		0			0
$483$	−16.0785	−	9.28290i	−0.731595	−	0.422387i
$484$		0			0
$485$	−4.60160	−	7.97021i	−0.208948	−	0.361908i
$486$		0			0
$487$	31.9312	−	18.4355i	1.44694	−	0.835393i	0.448644	−	0.893710i	$-0.351907\pi$
$487$	31.9312	−	18.4355i	1.44694	−	0.835393i	0.998298	+	0.0583177i	$0.0185736\pi$
$488$		0			0
$489$		−	8.01826i		−	0.362598i
$490$		0			0
$491$	−6.24668	+	10.8196i	−0.281909	+	0.488280i	−0.971855	−	0.235580i	$-0.924301\pi$
$491$	−6.24668	+	10.8196i	−0.281909	+	0.488280i	0.689946	+	0.723861i	$0.257634\pi$
$492$		0			0
$493$	22.1968			0.999695
$494$		0			0
$495$	−0.682163			−0.0306609
$496$		0			0
$497$	−0.423086	+	0.732806i	−0.0189780	+	0.0328709i
$498$		0			0
$499$			25.2232i			1.12914i	0.825384	+	0.564572i	$0.190959\pi$
$499$			25.2232i			1.12914i	−0.825384	+	0.564572i	$0.809041\pi$
$500$		0			0
$501$	−7.76368	+	4.48236i	−0.346856	+	0.200257i
$502$		0			0
$503$	−21.1455	−	36.6251i	−0.942833	−	1.63303i	−0.760033	−	0.649884i	$-0.774817\pi$
$503$	−21.1455	−	36.6251i	−0.942833	−	1.63303i	−0.182800	−	0.983150i	$-0.558516\pi$
$504$		0			0
$505$	12.7008	+	7.33279i	0.565177	+	0.326305i
$506$		0			0
$507$	−12.9904	−	0.500000i	−0.576923	−	0.0222058i
$508$		0			0
$509$	−32.0972	−	18.5313i	−1.42268	−	0.821387i	−0.426157	−	0.904649i	$-0.640133\pi$
$509$	−32.0972	−	18.5313i	−1.42268	−	0.821387i	−0.996528	+	0.0832618i	$0.973466\pi$
$510$		0			0
$511$	5.66914	+	9.81925i	0.250788	+	0.434378i
$512$		0			0
$513$	5.65099	−	3.26260i	0.249497	−	0.144047i
$514$		0			0
$515$		−	4.97569i		−	0.219255i
$516$		0			0
$517$	1.61642	−	2.79972i	0.0710900	−	0.123131i
$518$		0			0
$519$	−11.9530			−0.524680
$520$		0			0
$521$	−15.6983			−0.687754			−0.343877	−	0.939015i	$-0.611740\pi$
$521$	−15.6983			−0.687754			−0.343877	+	0.939015i	$0.611740\pi$
$522$		0			0
$523$	−11.8549	+	20.5333i	−0.518378	+	0.897858i	0.481394	+	0.876505i	$0.340131\pi$
$523$	−11.8549	+	20.5333i	−0.518378	+	0.897858i	−0.999772	+	0.0213532i	$0.993203\pi$
$524$		0			0
$525$			2.51764i			0.109879i
$526$		0			0
$527$	2.49350	−	1.43962i	0.108618	−	0.0627109i
$528$		0			0
$529$	−15.6901	−	27.1761i	−0.682178	−	1.18157i
$530$		0			0
$531$	−8.19868	−	4.73351i	−0.355792	−	0.205417i
$532$		0			0
$533$	2.64431	+	4.79057i	0.114538	+	0.207503i
$534$		0			0
$535$	4.96050	+	2.86394i	0.214461	+	0.123819i
$536$		0			0
$537$	9.60426	+	16.6351i	0.414454	+	0.717856i
$538$		0			0
$539$	−0.390794	+	0.225625i	−0.0168327	+	0.00971835i
$540$		0			0
$541$		−	33.9788i		−	1.46086i	−0.682987	−	0.730431i	$-0.739319\pi$
$541$		−	33.9788i		−	1.46086i	0.682987	−	0.730431i	$-0.260681\pi$
$542$		0			0
$543$	7.12630	−	12.3431i	0.305819	−	0.529694i
$544$		0			0
$545$	−5.45465			−0.233652
$546$		0			0
$547$	−11.5043			−0.491888			−0.245944	−	0.969284i	$-0.579098\pi$
$547$	−11.5043			−0.491888			−0.245944	+	0.969284i	$0.579098\pi$
$548$		0			0
$549$	−5.66158	+	9.80614i	−0.241630	+	0.418516i
$550$		0			0
$551$			30.2027i			1.28668i
$552$		0			0
$553$	20.0507	−	11.5763i	0.852644	−	0.492274i
$554$		0			0
$555$	−5.11339	−	8.85666i	−0.217051	−	0.375944i
$556$		0			0
$557$	11.4808	+	6.62845i	0.486458	+	0.280856i	0.723104	−	0.690739i	$-0.242715\pi$
$557$	11.4808	+	6.62845i	0.486458	+	0.280856i	−0.236646	+	0.971596i	$0.576048\pi$
$558$		0			0
$559$	−0.481740	+	25.0412i	−0.0203754	+	1.05913i
$560$		0			0
$561$	2.83307	+	1.63567i	0.119612	+	0.0690582i
$562$		0			0
$563$	−19.1263	−	33.1277i	−0.806077	−	1.39617i	−0.915562	−	0.402177i	$-0.868254\pi$
$563$	−19.1263	−	33.1277i	−0.806077	−	1.39617i	0.109485	−	0.993988i	$-0.465080\pi$
$564$		0			0
$565$	−7.56512	+	4.36773i	−0.318267	+	0.183752i
$566$		0			0
$567$		−	2.51764i		−	0.105731i
$568$		0			0
$569$	1.68122	−	2.91196i	0.0704803	−	0.122076i	−0.828632	−	0.559794i	$-0.810880\pi$
$569$	1.68122	−	2.91196i	0.0704803	−	0.122076i	0.899112	+	0.437719i	$0.144213\pi$
$570$		0			0
$571$	11.7625			0.492246			0.246123	−	0.969239i	$-0.420843\pi$
$571$	11.7625			0.492246			0.246123	+	0.969239i	$0.420843\pi$
$572$		0			0
$573$	−9.68117			−0.404437
$574$		0			0
$575$	−3.68715	+	6.38633i	−0.153765	+	0.266328i
$576$		0			0
$577$			9.86954i			0.410874i	0.978670	+	0.205437i	$0.0658616\pi$
$577$			9.86954i			0.410874i	−0.978670	+	0.205437i	$0.934138\pi$
$578$		0			0
$579$	−11.1428	+	6.43331i	−0.463080	+	0.267359i
$580$		0			0
$581$	−12.6375	−	21.8888i	−0.524293	−	0.908102i
$582$		0			0
$583$	6.12220	+	3.53465i	0.253556	+	0.146390i
$584$		0			0
$585$	3.60488	+	0.0693504i	0.149044	+	0.00286728i
$586$		0			0
$587$	23.5364	+	13.5888i	0.971453	+	0.560869i	0.899679	−	0.436552i	$-0.143801\pi$
$587$	23.5364	+	13.5888i	0.971453	+	0.560869i	0.0717740	+	0.997421i	$0.477134\pi$
$588$		0			0
$589$	1.95886	+	3.39285i	0.0807134	+	0.139800i
$590$		0			0
$591$	14.6883	−	8.48030i	0.604196	−	0.348833i
$592$		0			0
$593$			44.1747i			1.81404i	0.421090	+	0.907019i	$0.361648\pi$
$593$			44.1747i			1.81404i	−0.421090	+	0.907019i	$0.638352\pi$
$594$		0			0
$595$	6.03674	−	10.4559i	0.247482	−	0.428651i
$596$		0			0
$597$	2.60521			0.106624
$598$		0			0
$599$	16.1581			0.660203			0.330101	−	0.943945i	$-0.392917\pi$
$599$	16.1581			0.660203			0.330101	+	0.943945i	$0.392917\pi$
$600$		0			0
$601$	7.11685	−	12.3267i	0.290302	−	0.502819i	−0.683579	−	0.729877i	$-0.739577\pi$
$601$	7.11685	−	12.3267i	0.290302	−	0.502819i	0.973881	+	0.227058i	$0.0729108\pi$
$602$		0			0
$603$			4.40201i			0.179264i
$604$		0			0
$605$	−9.12328	+	5.26733i	−0.370914	+	0.214147i
$606$		0			0
$607$	3.96336	+	6.86475i	0.160868	+	0.278631i	0.935180	−	0.354172i	$-0.115237\pi$
$607$	3.96336	+	6.86475i	0.160868	+	0.278631i	−0.774312	+	0.632804i	$0.781904\pi$
$608$		0			0
$609$	10.0920	+	5.82660i	0.408947	+	0.236106i
$610$		0			0
$611$	−8.82658	+	14.6308i	−0.357085	+	0.591897i
$612$		0			0
$613$	−16.9541	−	9.78846i	−0.684770	−	0.395352i	0.116880	−	0.993146i	$-0.462711\pi$
$613$	−16.9541	−	9.78846i	−0.684770	−	0.395352i	−0.801650	+	0.597794i	$0.796044\pi$
$614$		0			0
$615$	−0.758819	−	1.31431i	−0.0305985	−	0.0529982i
$616$		0			0
$617$	26.3970	−	15.2403i	1.06270	−	0.613552i	0.136525	−	0.990637i	$-0.456407\pi$
$617$	26.3970	−	15.2403i	1.06270	−	0.613552i	0.926179	+	0.377084i	$0.123073\pi$
$618$		0			0
$619$			36.7094i			1.47548i	0.675087	+	0.737738i	$0.264106\pi$
$619$			36.7094i			1.47548i	−0.675087	+	0.737738i	$0.735894\pi$
$620$		0			0
$621$	3.68715	−	6.38633i	0.147960	−	0.256274i
$622$		0			0
$623$	−32.8125			−1.31460
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−2.22562	+	3.85490i	−0.0888829	+	0.153950i
$628$		0			0
$629$			49.0431i			1.95548i
$630$		0			0
$631$	−5.94414	+	3.43185i	−0.236633	+	0.136620i	−0.613628	−	0.789595i	$-0.710291\pi$
$631$	−5.94414	+	3.43185i	−0.236633	+	0.136620i	0.376996	+	0.926215i	$0.376957\pi$
$632$		0			0
$633$	0.649913	+	1.12568i	0.0258317	+	0.0447418i
$634$		0			0
$635$	19.1035	+	11.0294i	0.758101	+	0.437690i
$636$		0			0
$637$	2.08808	−	1.15258i	0.0827329	−	0.0456670i
$638$		0			0
$639$	−0.291069	−	0.168049i	−0.0115145	−	0.00664791i
$640$		0			0
$641$	7.31212	+	12.6650i	0.288812	+	0.500236i	0.973526	−	0.228575i	$-0.0734066\pi$
$641$	7.31212	+	12.6650i	0.288812	+	0.500236i	−0.684715	+	0.728811i	$0.740073\pi$
$642$		0			0
$643$	18.5342	−	10.7007i	0.730919	−	0.421996i	−0.0878394	−	0.996135i	$-0.527996\pi$
$643$	18.5342	−	10.7007i	0.730919	−	0.421996i	0.818758	+	0.574138i	$0.194663\pi$
$644$		0			0
$645$		−	6.94646i		−	0.273517i
$646$		0			0
$647$	−7.37395	+	12.7721i	−0.289900	+	0.502122i	−0.973786	−	0.227468i	$-0.926955\pi$
$647$	−7.37395	+	12.7721i	−0.289900	+	0.502122i	0.683886	+	0.729589i	$0.260289\pi$
$648$		0			0
$649$	6.45805			0.253501
$650$		0			0
$651$	1.51159			0.0592437
$652$		0			0
$653$	6.96066	−	12.0562i	0.272392	−	0.471796i	−0.697082	−	0.716991i	$-0.745519\pi$
$653$	6.96066	−	12.0562i	0.272392	−	0.471796i	0.969474	+	0.245195i	$0.0788520\pi$
$654$		0			0
$655$			7.85666i			0.306985i
$656$		0			0
$657$	−3.90018	+	2.25177i	−0.152161	+	0.0878499i
$658$		0			0
$659$	−1.60229	−	2.77524i	−0.0624162	−	0.108108i	0.833129	−	0.553079i	$-0.186547\pi$
$659$	−1.60229	−	2.77524i	−0.0624162	−	0.108108i	−0.895545	+	0.444971i	$0.853214\pi$
$660$		0			0
$661$	−26.8607	−	15.5080i	−1.04476	−	0.603192i	−0.123582	−	0.992334i	$-0.539438\pi$
$661$	−26.8607	−	15.5080i	−1.04476	−	0.603192i	−0.921178	+	0.389142i	$0.872771\pi$
$662$		0			0
$663$	−14.8051	−	8.93173i	−0.574981	−	0.346880i
$664$		0			0
$665$	14.2271	+	8.21405i	0.551705	+	0.318527i
$666$		0			0
$667$	17.0664	+	29.5599i	0.660815	+	1.14456i
$668$		0			0
$669$	−16.6814	+	9.63103i	−0.644941	+	0.372357i
$670$		0			0
$671$		−	7.72424i		−	0.298191i
$672$		0			0
$673$	9.74082	−	16.8716i	0.375481	−	0.650352i	−0.614918	−	0.788591i	$-0.710811\pi$
$673$	9.74082	−	16.8716i	0.375481	−	0.650352i	0.990399	+	0.138239i	$0.0441442\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	44.0602			1.69337			0.846685	−	0.532095i	$-0.178595\pi$
$677$	44.0602			1.69337			0.846685	+	0.532095i	$0.178595\pi$
$678$		0			0
$679$	−11.5852	+	20.0661i	−0.444598	+	0.770066i
$680$		0			0
$681$			22.2597i			0.852992i
$682$		0			0
$683$	15.1167	−	8.72765i	0.578426	−	0.333954i	−0.182082	−	0.983283i	$-0.558284\pi$
$683$	15.1167	−	8.72765i	0.578426	−	0.333954i	0.760507	+	0.649329i	$0.224950\pi$
$684$		0			0
$685$	7.60514	+	13.1725i	0.290578	+	0.503295i
$686$		0			0
$687$	9.12730	+	5.26965i	0.348228	+	0.201050i
$688$		0			0
$689$	−31.9934	−	19.3013i	−1.21885	−	0.735319i
$690$		0			0
$691$	26.4277	+	15.2580i	1.00536	+	0.580443i	0.909829	−	0.414984i	$-0.136213\pi$
$691$	26.4277	+	15.2580i	1.00536	+	0.580443i	0.0955281	+	0.995427i	$0.469546\pi$
$692$		0			0
$693$	0.858719	+	1.48735i	0.0326201	+	0.0564996i
$694$		0			0
$695$	11.7397	−	6.77792i	0.445312	−	0.257101i
$696$		0			0
$697$			7.27792i			0.275671i
$698$		0			0
$699$	−14.1758	+	24.5533i	−0.536179	+	0.928689i
$700$		0			0
$701$	−26.9510			−1.01792			−0.508962	−	0.860789i	$-0.669971\pi$
$701$	−26.9510			−1.01792			−0.508962	+	0.860789i	$0.669971\pi$
$702$		0			0
$703$	−66.7318			−2.51684
$704$		0			0
$705$	2.36955	−	4.10418i	0.0892424	−	0.154572i
$706$		0			0
$707$		−	36.9226i		−	1.38862i
$708$		0			0
$709$	−0.508972	+	0.293855i	−0.0191148	+	0.0110360i	−0.509527	−	0.860455i	$-0.670180\pi$
$709$	−0.508972	+	0.293855i	−0.0191148	+	0.0110360i	0.490412	+	0.871491i	$0.336846\pi$
$710$		0			0
$711$	4.59808	+	7.96410i	0.172441	+	0.298677i
$712$		0			0
$713$	3.83434	+	2.21376i	0.143597	+	0.0829058i
$714$		0			0
$715$	−2.15331	+	1.18859i	−0.0805293	+	0.0444507i
$716$		0			0
$717$	6.72607	+	3.88330i	0.251190	+	0.145024i
$718$		0			0
$719$	−4.67083	−	8.09011i	−0.174192	−	0.301710i	0.765689	−	0.643211i	$-0.222398\pi$
$719$	−4.67083	−	8.09011i	−0.174192	−	0.301710i	−0.939882	+	0.341501i	$0.889065\pi$
$720$		0			0
$721$	−10.8487	+	6.26349i	−0.404026	+	0.233265i
$722$		0			0
$723$		−	0.295929i		−	0.0110057i
$724$		0			0
$725$	2.31431	−	4.00851i	0.0859514	−	0.148872i
$726$		0			0
$727$	−6.51180			−0.241509			−0.120755	−	0.992682i	$-0.538531\pi$
$727$	−6.51180			−0.241509			−0.120755	+	0.992682i	$0.538531\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−16.6561	+	28.8492i	−0.616047	+	1.06702i
$732$		0			0
$733$			20.7661i			0.767014i	0.923538	+	0.383507i	$0.125284\pi$
$733$			20.7661i			0.767014i	−0.923538	+	0.383507i	$0.874716\pi$
$734$		0			0
$735$	−0.572874	+	0.330749i	−0.0211308	+	0.0121999i
$736$		0			0
$737$	−1.50144	−	2.60057i	−0.0553063	−	0.0957934i
$738$		0			0
$739$	−37.4028	−	21.5945i	−1.37588	−	0.794367i	−0.384223	−	0.923240i	$-0.625531\pi$
$739$	−37.4028	−	21.5945i	−1.37588	−	0.794367i	−0.991661	+	0.128874i	$0.958864\pi$
$740$		0			0
$741$	12.1532	−	20.1449i	0.446459	−	0.740042i
$742$		0			0
$743$	8.44574	+	4.87615i	0.309844	+	0.178889i	0.646857	−	0.762612i	$-0.276083\pi$
$743$	8.44574	+	4.87615i	0.309844	+	0.178889i	−0.337013	+	0.941500i	$0.609416\pi$
$744$		0			0
$745$	−4.12667	−	7.14760i	−0.151189	−	0.261868i
$746$		0			0
$747$	8.69419	−	5.01960i	0.318104	−	0.183657i
$748$		0			0
$749$		−	14.4207i		−	0.526923i
$750$		0			0
$751$	20.1431	−	34.8888i	0.735031	−	1.27311i	−0.219679	−	0.975572i	$-0.570501\pi$
$751$	20.1431	−	34.8888i	0.735031	−	1.27311i	0.954710	−	0.297539i	$-0.0961658\pi$
$752$		0			0
$753$	−2.15107			−0.0783894
$754$		0			0
$755$	−3.83307			−0.139500
$756$		0			0
$757$	−4.06486	+	7.04055i	−0.147740	+	0.255893i	−0.930392	−	0.366567i	$-0.880533\pi$
$757$	−4.06486	+	7.04055i	−0.147740	+	0.255893i	0.782652	+	0.622460i	$0.213867\pi$
$758$		0			0
$759$			5.03047i			0.182594i
$760$		0			0
$761$	12.1452	−	7.01203i	0.440263	−	0.254186i	−0.263446	−	0.964674i	$-0.584859\pi$
$761$	12.1452	−	7.01203i	0.440263	−	0.254186i	0.703709	+	0.710488i	$0.251526\pi$
$762$		0			0
$763$	6.86642	+	11.8930i	0.248581	+	0.430555i
$764$		0			0
$765$	4.15307	+	2.39778i	0.150155	+	0.0866918i
$766$		0			0
$767$	−34.1275	−	0.656541i	−1.23227	−	0.0237063i
$768$		0			0
$769$	31.2076	+	18.0177i	1.12538	+	0.649736i	0.942768	−	0.333450i	$-0.108213\pi$
$769$	31.2076	+	18.0177i	1.12538	+	0.649736i	0.182607	+	0.983186i	$0.441546\pi$
$770$		0			0
$771$	−1.89682	−	3.28538i	−0.0683121	−	0.118320i
$772$		0			0
$773$	15.9183	−	9.19044i	0.572542	−	0.330557i	−0.185622	−	0.982621i	$-0.559430\pi$
$773$	15.9183	−	9.19044i	0.572542	−	0.330557i	0.758164	+	0.652064i	$0.226097\pi$
$774$		0			0
$775$		−	0.600398i		−	0.0215669i
$776$		0			0
$777$	−12.8737	+	22.2979i	−0.461840	+	0.799931i
$778$		0			0
$779$	−9.90289			−0.354808
$780$		0			0
$781$	0.229273			0.00820404
$782$		0			0
$783$	−2.31431	+	4.00851i	−0.0827068	+	0.143252i
$784$		0			0
$785$			21.8654i			0.780409i
$786$		0			0
$787$	−2.22029	+	1.28189i	−0.0791449	+	0.0456943i	−0.539050	−	0.842274i	$-0.681217\pi$
$787$	−2.22029	+	1.28189i	−0.0791449	+	0.0456943i	0.459905	+	0.887968i	$0.347883\pi$
$788$		0			0
$789$	−5.59153	−	9.68481i	−0.199064	−	0.344788i
$790$		0			0
$791$	19.0462	+	10.9964i	0.677206	+	0.390985i
$792$		0			0
$793$	−0.785265	+	40.8187i	−0.0278856	+	1.44951i
$794$		0			0
$795$	8.97469	+	5.18154i	0.318300	+	0.183770i
$796$		0			0
$797$	14.6111	+	25.3072i	0.517552	+	0.896427i	0.999792	+	0.0203879i	$0.00649011\pi$
$797$	14.6111	+	25.3072i	0.517552	+	0.896427i	−0.482240	+	0.876039i	$0.660177\pi$
$798$		0			0
$799$	−19.6818	+	11.3633i	−0.696293	+	0.402005i
$800$		0			0
$801$		−	13.0330i		−	0.460500i
$802$		0			0
$803$	1.53607	−	2.66056i	0.0542069	−	0.0938891i
$804$		0			0
$805$	18.5658			0.654359
$806$		0			0
$807$	27.7079			0.975364
$808$		0			0
$809$	−10.5166	+	18.2154i	−0.369745	+	0.640418i	−0.989526	−	0.144358i	$-0.953888\pi$
$809$	−10.5166	+	18.2154i	−0.369745	+	0.640418i	0.619780	+	0.784776i	$0.287222\pi$
$810$		0			0
$811$			39.9501i			1.40284i	0.712750	+	0.701419i	$0.247450\pi$
$811$			39.9501i			1.40284i	−0.712750	+	0.701419i	$0.752550\pi$
$812$		0			0
$813$	−27.0381	+	15.6104i	−0.948267	+	0.547482i
$814$		0			0
$815$	4.00913	+	6.94402i	0.140434	+	0.243238i
$816$		0			0
$817$	−39.2544	−	22.6635i	−1.37334	−	0.792897i
$818$		0			0
$819$	−4.38669	−	7.94717i	−0.153283	−	0.277697i
$820$		0			0
$821$	36.6162	+	21.1404i	1.27791	+	0.737804i	0.976465	−	0.215678i	$-0.0691961\pi$
$821$	36.6162	+	21.1404i	1.27791	+	0.737804i	0.301450	+	0.953482i	$0.402529\pi$
$822$		0			0
$823$	3.91824	+	6.78658i	0.136581	+	0.236565i	0.926200	−	0.377032i	$-0.123055\pi$
$823$	3.91824	+	6.78658i	0.136581	+	0.236565i	−0.789619	+	0.613597i	$0.789722\pi$
$824$		0			0
$825$	0.590770	−	0.341081i	0.0205680	−	0.0118749i
$826$		0			0
$827$			36.0916i			1.25503i	0.778605	+	0.627515i	$0.215928\pi$
$827$			36.0916i			1.25503i	−0.778605	+	0.627515i	$0.784072\pi$
$828$		0			0
$829$	−12.7220	+	22.0351i	−0.441852	+	0.765309i	−0.997827	−	0.0658893i	$-0.979012\pi$
$829$	−12.7220	+	22.0351i	−0.441852	+	0.765309i	0.555975	+	0.831199i	$0.312345\pi$
$830$		0			0
$831$	−2.15039			−0.0745963
$832$		0			0
$833$	3.17225			0.109912
$834$		0			0
$835$	4.48236	−	7.76368i	0.155119	−	0.268673i
$836$		0			0
$837$			0.600398i			0.0207528i
$838$		0			0
$839$	−41.3763	+	23.8886i	−1.42847	+	0.824727i	−0.997000	−	0.0774010i	$-0.975338\pi$
$839$	−41.3763	+	23.8886i	−1.42847	+	0.824727i	−0.431469	+	0.902128i	$0.642004\pi$
$840$		0			0
$841$	3.78791	+	6.56085i	0.130618	+	0.226236i
$842$		0			0
$843$	17.3475	+	10.0156i	0.597478	+	0.344954i
$844$		0			0
$845$	11.5000	−	6.06218i	0.395612	−	0.208545i
$846$		0			0
$847$	22.9691	+	13.2612i	0.789228	+	0.455661i
$848$		0			0
$849$	8.45461	+	14.6438i	0.290161	+	0.502574i
$850$		0			0
$851$	−65.3116	+	37.7077i	−2.23885	+	1.29260i
$852$		0			0
$853$		−	3.49165i		−	0.119552i	−0.998212	−	0.0597759i	$-0.980961\pi$
$853$		−	3.49165i		−	0.119552i	0.998212	−	0.0597759i	$-0.0190386\pi$
$854$		0			0
$855$	−3.26260	+	5.65099i	−0.111579	+	0.193260i
$856$		0			0
$857$	24.0170			0.820404			0.410202	−	0.911995i	$-0.365458\pi$
$857$	24.0170			0.820404			0.410202	+	0.911995i	$0.365458\pi$
$858$		0			0
$859$	1.09887			0.0374928			0.0187464	−	0.999824i	$-0.494032\pi$
$859$	1.09887			0.0374928			0.0187464	+	0.999824i	$0.494032\pi$
$860$		0			0
$861$	−1.91043	+	3.30896i	−0.0651073	+	0.112769i
$862$		0			0
$863$			19.6082i			0.667472i	0.942667	+	0.333736i	$0.108309\pi$
$863$			19.6082i			0.667472i	−0.942667	+	0.333736i	$0.891691\pi$
$864$		0			0
$865$	10.3516	−	5.97652i	0.351966	−	0.203208i
$866$		0			0
$867$	−2.99867	−	5.19386i	−0.101840	−	0.176393i
$868$		0			0
$869$	−5.43281	−	3.13664i	−0.184296	−	0.106403i
$870$		0			0
$871$	7.66998	+	13.8954i	0.259887	+	0.470826i
$872$		0			0
$873$	−7.97021	−	4.60160i	−0.269751	−	0.155741i
$874$		0			0
$875$	−1.25882	−	2.18034i	−0.0425559	−	0.0737089i
$876$		0			0
$877$	30.7427	−	17.7493i	1.03811	−	0.599352i	0.118812	−	0.992917i	$-0.462091\pi$
$877$	30.7427	−	17.7493i	1.03811	−	0.599352i	0.919297	+	0.393564i	$0.128758\pi$
$878$		0			0
$879$		−	12.6734i		−	0.427462i
$880$		0			0
$881$	−6.30663	+	10.9234i	−0.212476	+	0.368019i	−0.952489	−	0.304574i	$-0.901486\pi$
$881$	−6.30663	+	10.9234i	−0.212476	+	0.368019i	0.740013	+	0.672592i	$0.234819\pi$
$882$		0			0
$883$	−16.9815			−0.571474			−0.285737	−	0.958308i	$-0.592238\pi$
$883$	−16.9815			−0.571474			−0.285737	+	0.958308i	$0.592238\pi$
$884$		0			0
$885$	9.46702			0.318230
$886$		0			0
$887$	13.4683	−	23.3278i	0.452222	−	0.783272i	−0.546302	−	0.837589i	$-0.683965\pi$
$887$	13.4683	−	23.3278i	0.452222	−	0.783272i	0.998524	+	0.0543167i	$0.0172980\pi$
$888$		0			0
$889$		−	55.5362i		−	1.86263i
$890$		0			0
$891$	−0.590770	+	0.341081i	−0.0197915	+	0.0114267i
$892$		0			0
$893$	−15.4618	−	26.7806i	−0.517409	−	0.896179i
$894$		0			0
$895$	−16.6351	−	9.60426i	−0.556049	−	0.321035i
$896$		0			0
$897$	0.511410	−	26.5835i	0.0170755	−	0.887596i
$898$		0			0
$899$	−2.40670	−	1.38951i	−0.0802680	−	0.0463427i
$900$		0			0
$901$	−24.8484	−	43.0386i	−0.827819	−	1.43382i
$902$		0			0
$903$	−15.1456	+	8.74434i	−0.504015	+	0.290993i
$904$		0			0
$905$			14.2526i			0.473773i
$906$		0			0
$907$	11.5207	−	19.9544i	0.382538	−	0.662575i	−0.608887	−	0.793257i	$-0.708384\pi$
$907$	11.5207	−	19.9544i	0.382538	−	0.662575i	0.991424	+	0.130683i	$0.0417169\pi$
$908$		0			0
$909$	14.6656			0.486427
$910$		0			0
$911$	−22.8698			−0.757709			−0.378854	−	0.925456i	$-0.623682\pi$
$911$	−22.8698			−0.757709			−0.378854	+	0.925456i	$0.623682\pi$
$912$		0			0
$913$	−3.42418	+	5.93086i	−0.113324	+	0.196283i
$914$		0			0
$915$		−	11.3232i		−	0.374332i
$916$		0			0
$917$	17.1302	−	9.89011i	0.565688	−	0.326600i
$918$		0			0
$919$	−13.9537	−	24.1686i	−0.460291	−	0.797248i	0.538684	−	0.842508i	$-0.318922\pi$
$919$	−13.9537	−	24.1686i	−0.460291	−	0.797248i	−0.998975	+	0.0452601i	$0.985588\pi$
$920$		0			0
$921$	−6.53622	−	3.77369i	−0.215376	−	0.124347i
$922$		0			0
$923$	−1.21159	−	0.0233085i	−0.0398801	−	0.000767208i
$924$		0			0
$925$	8.85666	+	5.11339i	0.291205	+	0.168127i
$926$		0			0
$927$	−2.48784	−	4.30907i	−0.0817115	−	0.141528i
$928$		0			0
$929$	30.6659	−	17.7050i	1.00612	−	0.580882i	0.0960642	−	0.995375i	$-0.469375\pi$
$929$	30.6659	−	17.7050i	1.00612	−	0.580882i	0.910052	+	0.414494i	$0.136041\pi$
$930$		0			0
$931$			4.31641i			0.141465i
$932$		0			0
$933$	−11.0462	+	19.1326i	−0.361636	+	0.626372i
$934$		0			0
$935$	−3.27135			−0.106985
$936$		0			0
$937$	11.9030			0.388855			0.194428	−	0.980917i	$-0.437715\pi$
$937$	11.9030			0.388855			0.194428	+	0.980917i	$0.437715\pi$
$938$		0			0
$939$	5.46958	−	9.47360i	0.178493	−	0.309159i
$940$		0			0
$941$		−	5.02987i		−	0.163969i	−0.996634	−	0.0819845i	$-0.973874\pi$
$941$		−	5.02987i		−	0.163969i	0.996634	−	0.0819845i	$-0.0261258\pi$
$942$		0			0
$943$	−9.69213	+	5.59575i	−0.315619	+	0.182223i
$944$		0			0
$945$	1.25882	+	2.18034i	0.0409494	+	0.0709264i
$946$		0			0
$947$	7.70716	+	4.44973i	0.250449	+	0.144597i	0.619970	−	0.784626i	$-0.287145\pi$
$947$	7.70716	+	4.44973i	0.250449	+	0.144597i	−0.369521	+	0.929222i	$0.620478\pi$
$948$		0			0
$949$	−8.38785	+	13.9035i	−0.272281	+	0.451328i
$950$		0			0
$951$	18.1756	+	10.4937i	0.589383	+	0.340280i
$952$		0			0
$953$	0.298508	+	0.517032i	0.00966963	+	0.0167483i	0.870820	−	0.491602i	$-0.163589\pi$
$953$	0.298508	+	0.517032i	0.00966963	+	0.0167483i	−0.861150	+	0.508351i	$0.830255\pi$
$954$		0			0
$955$	8.38414	−	4.84058i	0.271304	−	0.156638i
$956$		0			0
$957$		−	3.15748i		−	0.102067i
$958$		0			0
$959$	19.1470	−	33.1636i	0.618289	−	1.07091i
$960$		0			0
$961$	30.6395			0.988372
$962$		0			0
$963$	5.72789			0.184579
$964$		0			0
$965$	6.43331	−	11.1428i	0.207096	−	0.358700i
$966$		0			0
$967$		−	33.2641i		−	1.06970i	−0.844946	−	0.534851i	$-0.820368\pi$
$967$		−	33.2641i		−	1.06970i	0.844946	−	0.534851i	$-0.179632\pi$
$968$		0			0
$969$	27.0996	−	15.6460i	0.870566	−	0.502621i
$970$		0			0
$971$	19.1490	+	33.1671i	0.614521	+	1.06438i	0.990468	+	0.137740i	$0.0439840\pi$
$971$	19.1490	+	33.1671i	0.614521	+	1.06438i	−0.375947	+	0.926641i	$0.622683\pi$
$972$		0			0
$973$	−29.5563	−	17.0643i	−0.947532	−	0.547058i
$974$		0			0
$975$	−3.15660	+	1.74238i	−0.101092	+	0.0558009i
$976$		0			0
$977$	−11.0098	−	6.35651i	−0.352235	−	0.203363i	0.313434	−	0.949610i	$-0.398520\pi$
$977$	−11.0098	−	6.35651i	−0.352235	−	0.203363i	−0.665669	+	0.746247i	$0.731854\pi$
$978$		0			0
$979$	4.44533	+	7.69953i	0.142073	+	0.246078i
$980$		0			0
$981$	−4.72386	+	2.72732i	−0.150821	+	0.0870768i
$982$		0			0
$983$		−	48.3272i		−	1.54140i	−0.637198	−	0.770700i	$-0.719907\pi$
$983$		−	48.3272i		−	1.54140i	0.637198	−	0.770700i	$-0.280093\pi$
$984$		0			0
$985$	−8.48030	+	14.6883i	−0.270205	+	0.468008i
$986$		0			0
$987$	−11.9313			−0.379779
$988$		0			0
$989$	−51.2253			−1.62887
$990$		0			0
$991$	−1.74548	+	3.02326i	−0.0554469	+	0.0960369i	−0.892417	−	0.451212i	$-0.850992\pi$
$991$	−1.74548	+	3.02326i	−0.0554469	+	0.0960369i	0.836970	+	0.547249i	$0.184325\pi$
$992$		0			0
$993$			13.9754i			0.443497i
$994$		0			0
$995$	−2.25617	+	1.30260i	−0.0715256	+	0.0412953i
$996$		0			0
$997$	−2.46671	−	4.27247i	−0.0781215	−	0.135310i	0.824318	−	0.566127i	$-0.191559\pi$
$997$	−2.46671	−	4.27247i	−0.0781215	−	0.135310i	−0.902439	+	0.430817i	$0.858226\pi$
$998$		0			0
$999$	−8.85666	−	5.11339i	−0.280212	−	0.161781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.cc.b.121.1	✓	8
3.2	odd	2		2340.2.dj.c.901.3		8
5.2	odd	4		3900.2.bw.g.2149.3		8
5.3	odd	4		3900.2.bw.l.2149.2		8
5.4	even	2		3900.2.cd.l.901.4		8
13.10	even	6	inner	780.2.cc.b.361.3	yes	8
39.23	odd	6		2340.2.dj.c.361.1		8
65.23	odd	12		3900.2.bw.g.49.3		8
65.49	even	6		3900.2.cd.l.2701.4		8
65.62	odd	12		3900.2.bw.l.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.cc.b.121.1	✓	8	1.1	even	1	trivial
780.2.cc.b.361.3	yes	8	13.10	even	6	inner
2340.2.dj.c.361.1		8	39.23	odd	6
2340.2.dj.c.901.3		8	3.2	odd	2
3900.2.bw.g.49.3		8	65.23	odd	12
3900.2.bw.g.2149.3		8	5.2	odd	4
3900.2.bw.l.49.2		8	65.62	odd	12
3900.2.bw.l.2149.2		8	5.3	odd	4
3900.2.cd.l.901.4		8	5.4	even	2
3900.2.cd.l.2701.4		8	65.49	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	780.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} -1.00000i q^{5} +(-2.18034 + 1.25882i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.590770 + 0.341081i) q^{11} +(-3.08725 - 1.86250i) q^{13} +(0.866025 + 0.500000i) q^{15} +(-2.39778 - 4.15307i) q^{17} +(5.65099 - 3.26260i) q^{19} -2.51764i q^{21} +(3.68715 - 6.38633i) q^{23} -1.00000 q^{25} +1.00000 q^{27} +(-2.31431 + 4.00851i) q^{29} +0.600398i q^{31} +(-0.590770 + 0.341081i) q^{33} +(1.25882 + 2.18034i) q^{35} +(-8.85666 - 5.11339i) q^{37} +(3.15660 - 1.74238i) q^{39} +(-1.31431 - 0.758819i) q^{41} +(-3.47323 - 6.01581i) q^{43} +(-0.866025 + 0.500000i) q^{45} -4.73910i q^{47} +(-0.330749 + 0.572874i) q^{49} +4.79555 q^{51} +10.3631 q^{53} +(0.341081 - 0.590770i) q^{55} +6.52520i q^{57} +(8.19868 - 4.73351i) q^{59} +(-5.66158 - 9.80614i) q^{61} +(2.18034 + 1.25882i) q^{63} +(-1.86250 + 3.08725i) q^{65} +(-3.81225 - 2.20100i) q^{67} +(3.68715 + 6.38633i) q^{69} +(0.291069 - 0.168049i) q^{71} -4.50354i q^{73} +(0.500000 - 0.866025i) q^{75} -1.71744 q^{77} -9.19615 q^{79} +(-0.500000 + 0.866025i) q^{81} +10.0392i q^{83} +(-4.15307 + 2.39778i) q^{85} +(-2.31431 - 4.00851i) q^{87} +(11.2869 + 6.51652i) q^{89} +(9.07579 + 0.174599i) q^{91} +(-0.519960 - 0.300199i) q^{93} +(-3.26260 - 5.65099i) q^{95} +(7.97021 - 4.60160i) q^{97} -0.682163i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 4 q^{9} - 12 q^{11} + 4 q^{17} + 12 q^{19} + 4 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 12 q^{33} + 8 q^{35} - 24 q^{37} - 16 q^{43} - 4 q^{49} - 8 q^{51} + 16 q^{53} + 4 q^{55} + 24 q^{59}+ \cdots + 48 q^{97}+O(q^{100}) \) 8 * q - 4 * q^3 - 4 * q^9 - 12 * q^11 + 4 * q^17 + 12 * q^19 + 4 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 12 * q^33 + 8 * q^35 - 24 * q^37 - 16 * q^43 - 4 * q^49 - 8 * q^51 + 16 * q^53 + 4 * q^55 + 24 * q^59 + 8 * q^61 + 24 * q^67 + 4 * q^69 - 12 * q^71 + 4 * q^75 - 8 * q^77 - 32 * q^79 - 4 * q^81 - 8 * q^87 - 12 * q^89 + 8 * q^91 - 24 * q^93 - 12 * q^95 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more