LMFDB - Embedded newform 220.2.u.a.173.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(13,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 2]))

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

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

chi := DirichletCharacter("220.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.u (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			173.3
Character	$\chi$	$=$	220.173
Dual form			220.2.u.a.117.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.140599 + 0.275942i) q^{3} +(-2.21755 + 0.287183i) q^{5} +(-4.33567 + 2.20914i) q^{7} +(1.70698 + 2.34946i) q^{9} +O(q^{10})$	\(q+(-0.140599 + 0.275942i) q^{3} +(-2.21755 + 0.287183i) q^{5} +(-4.33567 + 2.20914i) q^{7} +(1.70698 + 2.34946i) q^{9} +(0.966488 + 3.17268i) q^{11} +(-0.338672 + 2.13829i) q^{13} +(0.232540 - 0.652293i) q^{15} +(-0.703440 - 4.44135i) q^{17} +(-0.954041 - 2.93624i) q^{19} -1.50700i q^{21} +(1.36205 + 1.36205i) q^{23} +(4.83505 - 1.27369i) q^{25} +(-1.80597 + 0.286037i) q^{27} +(-1.12411 + 3.45966i) q^{29} +(-5.27085 + 3.82950i) q^{31} +(-1.01136 - 0.179383i) q^{33} +(8.98015 - 6.14400i) q^{35} +(-1.75776 - 3.44980i) q^{37} +(-0.542427 - 0.394096i) q^{39} +(8.15531 - 2.64982i) q^{41} +(-6.47304 + 6.47304i) q^{43} +(-4.46004 - 4.71982i) q^{45} +(2.48598 + 1.26667i) q^{47} +(9.80329 - 13.4931i) q^{49} +(1.32446 + 0.430342i) q^{51} +(11.7922 + 1.86770i) q^{53} +(-3.05437 - 6.75802i) q^{55} +(0.944368 + 0.149573i) q^{57} +(0.864681 + 0.280952i) q^{59} +(-2.74194 + 3.77396i) q^{61} +(-12.5912 - 6.41553i) q^{63} +(0.136941 - 4.83902i) q^{65} +(-6.07207 + 6.07207i) q^{67} +(-0.567351 + 0.184344i) q^{69} +(12.1159 + 8.80269i) q^{71} +(2.22376 + 4.36438i) q^{73} +(-0.328342 + 1.51327i) q^{75} +(-11.1993 - 11.6206i) q^{77} +(6.75665 - 4.90899i) q^{79} +(-2.51725 + 7.74730i) q^{81} +(-2.28793 + 0.362373i) q^{83} +(2.83539 + 9.64689i) q^{85} +(-0.796617 - 0.796617i) q^{87} -0.430440i q^{89} +(-3.25540 - 10.0191i) q^{91} +(-0.315640 - 1.99287i) q^{93} +(2.95887 + 6.23726i) q^{95} +(-1.55943 + 9.84586i) q^{97} +(-5.80430 + 7.68642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7}+O(q^{10}) $ 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7	$ 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7} - 16 q^{15} + 10 q^{17} + 16 q^{23} - 26 q^{25} - 10 q^{27} + 16 q^{31} + 28 q^{33} - 34 q^{37} - 20 q^{41} - 56 q^{45} - 2 q^{47} - 80 q^{51} + 6 q^{53} - 18 q^{55} - 120 q^{57} - 40 q^{61} - 50 q^{63} - 72 q^{67} + 4 q^{71} - 20 q^{73} + 20 q^{75} - 36 q^{77} + 100 q^{81} + 40 q^{85} - 8 q^{91} - 14 q^{93} + 50 q^{95} + 6 q^{97}+O(q^{100}) $ 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7 - 16 * q^15 + 10 * q^17 + 16 * q^23 - 26 * q^25 - 10 * q^27 + 16 * q^31 + 28 * q^33 - 34 * q^37 - 20 * q^41 - 56 * q^45 - 2 * q^47 - 80 * q^51 + 6 * q^53 - 18 * q^55 - 120 * q^57 - 40 * q^61 - 50 * q^63 - 72 * q^67 + 4 * q^71 - 20 * q^73 + 20 * q^75 - 36 * q^77 + 100 * q^81 + 40 * q^85 - 8 * q^91 - 14 * q^93 + 50 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$	−0.140599	+	0.275942i	−0.0811751	+	0.159315i	−0.928026	−	0.372515i	$-0.878496\pi$
$3$	−0.140599	+	0.275942i	−0.0811751	+	0.159315i	0.846851	+	0.531830i	$0.178496\pi$
$4$		0			0
$5$	−2.21755	+	0.287183i	−0.991718	+	0.128432i
$5$	−2.21755	+	0.287183i	−0.991718	+	0.128432i
$6$		0			0
$7$	−4.33567	+	2.20914i	−1.63873	+	0.834975i	−0.641007	+	0.767535i	$0.721483\pi$
$7$	−4.33567	+	2.20914i	−1.63873	+	0.834975i	−0.997723	+	0.0674404i	$0.978517\pi$
$8$		0			0
$9$	1.70698	+	2.34946i	0.568993	+	0.783152i
$10$		0			0
$11$	0.966488	+	3.17268i	0.291407	+	0.956599i
$11$	0.966488	+	3.17268i	0.291407	+	0.956599i
$12$		0			0
$13$	−0.338672	+	2.13829i	−0.0939307	+	0.593055i	0.895160	+	0.445745i	$0.147061\pi$
$13$	−0.338672	+	2.13829i	−0.0939307	+	0.593055i	−0.989090	+	0.147309i	$0.952939\pi$
$14$		0			0
$15$	0.232540	−	0.652293i	0.0600416	−	0.168421i
$16$		0			0
$17$	−0.703440	−	4.44135i	−0.170609	−	1.07718i	−0.913222	−	0.407463i	$-0.866413\pi$
$17$	−0.703440	−	4.44135i	−0.170609	−	1.07718i	0.742612	−	0.669721i	$-0.233587\pi$
$18$		0			0
$19$	−0.954041	−	2.93624i	−0.218872	−	0.673619i	−0.998856	−	0.0478193i	$-0.984773\pi$
$19$	−0.954041	−	2.93624i	−0.218872	−	0.673619i	0.779984	−	0.625799i	$-0.215227\pi$
$20$		0			0
$21$		−	1.50700i		−	0.328854i
$22$		0			0
$23$	1.36205	+	1.36205i	0.284008	+	0.284008i	0.834705	−	0.550697i	$-0.185638\pi$
$23$	1.36205	+	1.36205i	0.284008	+	0.284008i	−0.550697	+	0.834705i	$0.685638\pi$
$24$		0			0
$25$	4.83505	−	1.27369i	0.967010	−	0.254737i
$26$		0			0
$27$	−1.80597	+	0.286037i	−0.347558	+	0.0550478i
$28$		0			0
$29$	−1.12411	+	3.45966i	−0.208743	+	0.642443i	0.790796	+	0.612079i	$0.209667\pi$
$29$	−1.12411	+	3.45966i	−0.208743	+	0.642443i	−0.999539	+	0.0303641i	$0.990333\pi$
$30$		0			0
$31$	−5.27085	+	3.82950i	−0.946673	+	0.687798i	−0.950018	−	0.312196i	$-0.898935\pi$
$31$	−5.27085	+	3.82950i	−0.946673	+	0.687798i	0.00334443	+	0.999994i	$0.498935\pi$
$32$		0			0
$33$	−1.01136	−	0.179383i	−0.176056	−	0.0312265i
$34$		0			0
$35$	8.98015	−	6.14400i	1.51792	−	1.03853i
$36$		0			0
$37$	−1.75776	−	3.44980i	−0.288974	−	0.567144i	0.700190	−	0.713957i	$-0.253099\pi$
$37$	−1.75776	−	3.44980i	−0.288974	−	0.567144i	−0.989164	+	0.146813i	$0.953099\pi$
$38$		0			0
$39$	−0.542427	−	0.394096i	−0.0868578	−	0.0631059i
$40$		0			0
$41$	8.15531	−	2.64982i	1.27364	−	0.413832i	0.407307	−	0.913291i	$-0.366468\pi$
$41$	8.15531	−	2.64982i	1.27364	−	0.413832i	0.866338	+	0.499459i	$0.166468\pi$
$42$		0			0
$43$	−6.47304	+	6.47304i	−0.987129	+	0.987129i	−0.999918	−	0.0127891i	$-0.995929\pi$
$43$	−6.47304	+	6.47304i	−0.987129	+	0.987129i	0.0127891	+	0.999918i	$0.495929\pi$
$44$		0			0
$45$	−4.46004	−	4.71982i	−0.664863	−	0.703589i
$46$		0			0
$47$	2.48598	+	1.26667i	0.362617	+	0.184763i	0.625801	−	0.779983i	$-0.284772\pi$
$47$	2.48598	+	1.26667i	0.362617	+	0.184763i	−0.263183	+	0.964746i	$0.584772\pi$
$48$		0			0
$49$	9.80329	−	13.4931i	1.40047	−	1.92758i
$50$		0			0
$51$	1.32446	+	0.430342i	0.185461	+	0.0602599i
$52$		0			0
$53$	11.7922	+	1.86770i	1.61978	+	0.256548i	0.899431	−	0.437063i	$-0.143981\pi$
$53$	11.7922	+	1.86770i	1.61978	+	0.256548i	0.720350	+	0.693611i	$0.243981\pi$
$54$		0			0
$55$	−3.05437	−	6.75802i	−0.411852	−	0.911251i
$56$		0			0
$57$	0.944368	+	0.149573i	0.125085	+	0.0198115i
$58$		0			0
$59$	0.864681	+	0.280952i	0.112572	+	0.0365768i	0.364761	−	0.931101i	$-0.381151\pi$
$59$	0.864681	+	0.280952i	0.112572	+	0.0365768i	−0.252189	+	0.967678i	$0.581151\pi$
$60$		0			0
$61$	−2.74194	+	3.77396i	−0.351070	+	0.483206i	−0.947634	−	0.319359i	$-0.896532\pi$
$61$	−2.74194	+	3.77396i	−0.351070	+	0.483206i	0.596564	+	0.802566i	$0.296532\pi$
$62$		0			0
$63$	−12.5912	−	6.41553i	−1.58634	−	0.808280i
$64$		0			0
$65$	0.136941	−	4.83902i	0.0169854	−	0.600207i
$66$		0			0
$67$	−6.07207	+	6.07207i	−0.741822	+	0.741822i	−0.972928	−	0.231107i	$-0.925765\pi$
$67$	−6.07207	+	6.07207i	−0.741822	+	0.741822i	0.231107	+	0.972928i	$0.425765\pi$
$68$		0			0
$69$	−0.567351	+	0.184344i	−0.0683011	+	0.0221924i
$70$		0			0
$71$	12.1159	+	8.80269i	1.43789	+	1.04469i	0.988478	+	0.151362i	$0.0483661\pi$
$71$	12.1159	+	8.80269i	1.43789	+	1.04469i	0.449411	+	0.893325i	$0.351634\pi$
$72$		0			0
$73$	2.22376	+	4.36438i	0.260272	+	0.510812i	0.983752	−	0.179533i	$-0.0574587\pi$
$73$	2.22376	+	4.36438i	0.260272	+	0.510812i	−0.723480	+	0.690345i	$0.757459\pi$
$74$		0			0
$75$	−0.328342	+	1.51327i	−0.0379137	+	0.174738i
$76$		0			0
$77$	−11.1993	−	11.6206i	−1.27627	−	1.32429i
$78$		0			0
$79$	6.75665	−	4.90899i	0.760182	−	0.552305i	−0.138784	−	0.990323i	$-0.544319\pi$
$79$	6.75665	−	4.90899i	0.760182	−	0.552305i	0.898966	+	0.438018i	$0.144319\pi$
$80$		0			0
$81$	−2.51725	+	7.74730i	−0.279694	+	0.860811i
$82$		0			0
$83$	−2.28793	+	0.362373i	−0.251133	+	0.0397756i	−0.280732	−	0.959786i	$-0.590577\pi$
$83$	−2.28793	+	0.362373i	−0.251133	+	0.0397756i	0.0295986	+	0.999562i	$0.490577\pi$
$84$		0			0
$85$	2.83539	+	9.64689i	0.307542	+	1.04635i
$86$		0			0
$87$	−0.796617	−	0.796617i	−0.0854063	−	0.0854063i
$88$		0			0
$89$		−	0.430440i		−	0.0456265i	−0.999740	−	0.0228133i	$-0.992738\pi$
$89$		−	0.430440i		−	0.0456265i	0.999740	−	0.0228133i	$-0.00726232\pi$
$90$		0			0
$91$	−3.25540	−	10.0191i	−0.341259	−	1.05029i
$92$		0			0
$93$	−0.315640	−	1.99287i	−0.0327304	−	0.206651i
$94$		0			0
$95$	2.95887	+	6.23726i	0.303574	+	0.639930i
$96$		0			0
$97$	−1.55943	+	9.84586i	−0.158336	+	0.999696i	0.772701	+	0.634771i	$0.218905\pi$
$97$	−1.55943	+	9.84586i	−0.158336	+	0.999696i	−0.931037	+	0.364925i	$0.881095\pi$
$98$		0			0
$99$	−5.80430	+	7.68642i	−0.583354	+	0.772515i
$100$		0			0
$101$	1.24290	+	1.71071i	0.123674	+	0.170222i	0.866364	−	0.499412i	$-0.166451\pi$
$101$	1.24290	+	1.71071i	0.123674	+	0.170222i	−0.742691	+	0.669635i	$0.766451\pi$
$102$		0			0
$103$	9.60312	−	4.89304i	0.946224	−	0.482125i	0.0884092	−	0.996084i	$-0.471822\pi$
$103$	9.60312	−	4.89304i	0.946224	−	0.482125i	0.857815	+	0.513959i	$0.171822\pi$
$104$		0			0
$105$	0.432784	+	3.34184i	0.0422354	+	0.326130i
$106$		0			0
$107$	−1.37786	+	2.70419i	−0.133202	+	0.261424i	−0.947968	−	0.318367i	$-0.896866\pi$
$107$	−1.37786	+	2.70419i	−0.133202	+	0.261424i	0.814765	+	0.579791i	$0.196866\pi$
$108$		0			0
$109$	−16.1122			−1.54327			−0.771633	−	0.636068i	$-0.780560\pi$
$109$	−16.1122			−1.54327			−0.771633	+	0.636068i	$0.780560\pi$
$110$		0			0
$111$	1.19909			0.113812
$112$		0			0
$113$	−2.96086	+	5.81102i	−0.278534	+	0.546655i	−0.987315	−	0.158775i	$-0.949246\pi$
$113$	−2.96086	+	5.81102i	−0.278534	+	0.546655i	0.708780	+	0.705429i	$0.249246\pi$
$114$		0			0
$115$	−3.41158	−	2.62926i	−0.318131	−	0.245180i
$116$		0			0
$117$	−5.60193	+	2.85432i	−0.517898	+	0.263882i
$118$		0			0
$119$	12.8614	+	17.7022i	1.17900	+	1.62276i
$120$		0			0
$121$	−9.13180	+	6.13271i	−0.830164	+	0.557519i
$122$		0			0
$123$	−0.415435	+	2.62295i	−0.0374585	+	0.236504i
$124$		0			0
$125$	−10.3562	+	4.21301i	−0.926285	+	0.376823i
$126$		0			0
$127$	−1.97787	−	12.4878i	−0.175508	−	1.10811i	−0.905403	−	0.424553i	$-0.860431\pi$
$127$	−1.97787	−	12.4878i	−0.175508	−	1.10811i	0.729896	−	0.683558i	$-0.239569\pi$
$128$		0			0
$129$	−0.876077	−	2.69629i	−0.0771343	−	0.237395i
$130$		0			0
$131$		−	16.0037i		−	1.39825i	−0.715000	−	0.699124i	$-0.753573\pi$
$131$		−	16.0037i		−	1.39825i	0.715000	−	0.699124i	$-0.246427\pi$
$132$		0			0
$133$	10.6230	+	10.6230i	0.921127	+	0.921127i
$134$		0			0
$135$	3.92267	−	1.15294i	0.337610	−	0.0992296i
$136$		0			0
$137$	6.98164	−	1.10578i	0.596482	−	0.0944734i	0.149109	−	0.988821i	$-0.452360\pi$
$137$	6.98164	−	1.10578i	0.596482	−	0.0944734i	0.447373	+	0.894347i	$0.352360\pi$
$138$		0			0
$139$	−3.24197	+	9.97775i	−0.274980	+	0.846301i	0.714245	+	0.699896i	$0.246770\pi$
$139$	−3.24197	+	9.97775i	−0.274980	+	0.846301i	−0.989225	+	0.146405i	$0.953230\pi$
$140$		0			0
$141$	−0.699054	+	0.507893i	−0.0588710	+	0.0427723i
$142$		0			0
$143$	−7.11143	+	0.992133i	−0.594688	+	0.0829663i
$144$		0			0
$145$	1.49922	−	7.99480i	0.124503	−	0.663932i
$146$		0			0
$147$	2.34497	+	4.60226i	0.193410	+	0.379588i
$148$		0			0
$149$	−13.7221	−	9.96972i	−1.12416	−	0.816751i	−0.139327	−	0.990246i	$-0.544494\pi$
$149$	−13.7221	−	9.96972i	−1.12416	−	0.816751i	−0.984835	+	0.173495i	$0.944494\pi$
$150$		0			0
$151$	−0.904678	+	0.293948i	−0.0736217	+	0.0239211i	−0.345596	−	0.938383i	$-0.612323\pi$
$151$	−0.904678	+	0.293948i	−0.0736217	+	0.0239211i	0.271975	+	0.962304i	$0.412323\pi$
$152$		0			0
$153$	9.23399	−	9.23399i	0.746524	−	0.746524i
$154$		0			0
$155$	10.5886	−	10.0058i	0.850498	−	0.803686i
$156$		0			0
$157$	19.4677	+	9.91931i	1.55369	+	0.791647i	0.999178	−	0.0405259i	$-0.0129033\pi$
$157$	19.4677	+	9.91931i	1.55369	+	0.791647i	0.554516	+	0.832173i	$0.312903\pi$
$158$		0			0
$159$	−2.17335	+	2.99136i	−0.172358	+	0.237230i
$160$		0			0
$161$	−8.91438	−	2.89646i	−0.702552	−	0.228273i
$162$		0			0
$163$	−4.87848	−	0.772675i	−0.382112	−	0.0605206i	−0.0375762	−	0.999294i	$-0.511964\pi$
$163$	−4.87848	−	0.772675i	−0.382112	−	0.0605206i	−0.344536	+	0.938773i	$0.611964\pi$
$164$		0			0
$165$	2.29426	+	0.107343i	0.178608	+	0.00835667i
$166$		0			0
$167$	−0.213734	−	0.0338522i	−0.0165393	−	0.00261956i	0.148159	−	0.988964i	$-0.452665\pi$
$167$	−0.213734	−	0.0338522i	−0.0165393	−	0.00261956i	−0.164699	+	0.986344i	$0.552665\pi$
$168$		0			0
$169$	7.90615	+	2.56886i	0.608165	+	0.197605i
$170$		0			0
$171$	5.27003	−	7.25357i	0.403009	−	0.554695i
$172$		0			0
$173$	−2.59574	−	1.32259i	−0.197350	−	0.100555i	0.352523	−	0.935803i	$-0.385324\pi$
$173$	−2.59574	−	1.32259i	−0.197350	−	0.100555i	−0.549873	+	0.835248i	$0.685324\pi$
$174$		0			0
$175$	−18.1495	+	16.2036i	−1.37197	+	1.22488i
$176$		0			0
$177$	−0.199100	+	0.199100i	−0.0149653	+	0.0149653i
$178$		0			0
$179$	−1.74291	+	0.566305i	−0.130271	+	0.0423277i	−0.373427	−	0.927660i	$-0.621817\pi$
$179$	−1.74291	+	0.566305i	−0.130271	+	0.0423277i	0.243156	+	0.969987i	$0.421817\pi$
$180$		0			0
$181$	−14.2403	−	10.3462i	−1.05847	−	0.769025i	−0.0846667	−	0.996409i	$-0.526983\pi$
$181$	−14.2403	−	10.3462i	−1.05847	−	0.769025i	−0.973805	+	0.227385i	$0.926983\pi$
$182$		0			0
$183$	−0.655879	−	1.28723i	−0.0484839	−	0.0951551i
$184$		0			0
$185$	4.88865	+	7.14531i	0.359421	+	0.525333i
$186$		0			0
$187$	13.4111	−	6.52430i	0.980717	−	0.477104i
$188$		0			0
$189$	7.19818	−	5.22979i	0.523591	−	0.380411i
$190$		0			0
$191$	2.05511	−	6.32499i	0.148703	−	0.457660i	−0.848766	−	0.528769i	$-0.822654\pi$
$191$	2.05511	−	6.32499i	0.148703	−	0.457660i	0.997469	+	0.0711088i	$0.0226538\pi$
$192$		0			0
$193$	−11.9388	+	1.89093i	−0.859376	+	0.136112i	−0.570543	−	0.821268i	$-0.693267\pi$
$193$	−11.9388	+	1.89093i	−0.859376	+	0.136112i	−0.288833	+	0.957379i	$0.593267\pi$
$194$		0			0
$195$	1.31604	+	0.718152i	0.0942433	+	0.0514279i
$196$		0			0
$197$	13.0200	+	13.0200i	0.927638	+	0.927638i	0.997553	−	0.0699150i	$-0.0222728\pi$
$197$	13.0200	+	13.0200i	0.927638	+	0.927638i	−0.0699150	+	0.997553i	$0.522273\pi$
$198$		0			0
$199$		−	11.7192i		−	0.830750i	−0.909650	−	0.415375i	$-0.863650\pi$
$199$		−	11.7192i		−	0.830750i	0.909650	−	0.415375i	$-0.136350\pi$
$200$		0			0
$201$	−0.821809	−	2.52927i	−0.0579660	−	0.178401i
$202$		0			0
$203$	−2.76908	−	17.4833i	−0.194351	−	1.22709i
$204$		0			0
$205$	−17.3238	+	8.21817i	−1.20995	+	0.573982i
$206$		0			0
$207$	−0.875087	+	5.52508i	−0.0608228	+	0.384020i
$208$		0			0
$209$	8.39367	−	5.86470i	0.580602	−	0.405670i
$210$		0			0
$211$	9.50297	+	13.0797i	0.654211	+	0.900445i	0.999273	−	0.0381354i	$-0.0121418\pi$
$211$	9.50297	+	13.0797i	0.654211	+	0.900445i	−0.345061	+	0.938580i	$0.612142\pi$
$212$		0			0
$213$	−4.13252	+	2.10562i	−0.283155	+	0.144275i
$214$		0			0
$215$	12.4953	−	16.2132i	0.852175	−	1.10573i
$216$		0			0
$217$	14.3928	−	28.2475i	0.977048	−	1.91756i
$218$		0			0
$219$	−1.51697			−0.102508
$220$		0			0
$221$	9.73512			0.654855
$222$		0			0
$223$	10.9386	−	21.4682i	0.732503	−	1.43762i	−0.160252	−	0.987076i	$-0.551231\pi$
$223$	10.9386	−	21.4682i	0.732503	−	1.43762i	0.892755	−	0.450542i	$-0.148769\pi$
$224$		0			0
$225$	11.2458	+	9.18559i	0.749720	+	0.612373i
$226$		0			0
$227$	10.7589	−	5.48194i	0.714094	−	0.363849i	−0.0588986	−	0.998264i	$-0.518759\pi$
$227$	10.7589	−	5.48194i	0.714094	−	0.363849i	0.772993	+	0.634415i	$0.218759\pi$
$228$		0			0
$229$	−8.41255	−	11.5789i	−0.555917	−	0.765154i	0.434883	−	0.900487i	$-0.356790\pi$
$229$	−8.41255	−	11.5789i	−0.555917	−	0.765154i	−0.990800	+	0.135333i	$0.956790\pi$
$230$		0			0
$231$	4.78122	−	1.45649i	0.314581	−	0.0958303i
$232$		0			0
$233$	3.05586	−	19.2940i	0.200196	−	1.26399i	−0.658921	−	0.752212i	$-0.728987\pi$
$233$	3.05586	−	19.2940i	0.200196	−	1.26399i	0.859118	−	0.511778i	$-0.171013\pi$
$234$		0			0
$235$	−5.87655	−	2.09497i	−0.383344	−	0.136661i
$236$		0			0
$237$	0.404616	+	2.55464i	0.0262826	+	0.165942i
$238$		0			0
$239$	1.44128	+	4.43580i	0.0932286	+	0.286928i	0.986788	−	0.162017i	$-0.0517999\pi$
$239$	1.44128	+	4.43580i	0.0932286	+	0.286928i	−0.893559	+	0.448945i	$0.851800\pi$
$240$		0			0
$241$			6.09988i			0.392928i	0.980511	+	0.196464i	$0.0629458\pi$
$241$			6.09988i			0.392928i	−0.980511	+	0.196464i	$0.937054\pi$
$242$		0			0
$243$	−5.66267	−	5.66267i	−0.363260	−	0.363260i
$244$		0			0
$245$	−17.8643	+	32.7369i	−1.14131	+	2.09148i
$246$		0			0
$247$	6.60163	−	1.04560i	0.420052	−	0.0665297i
$248$		0			0
$249$	0.221688	−	0.682286i	0.0140489	−	0.0432381i
$250$		0			0
$251$	7.88833	−	5.73121i	0.497907	−	0.361750i	−0.310310	−	0.950635i	$-0.600433\pi$
$251$	7.88833	−	5.73121i	0.497907	−	0.361750i	0.808217	+	0.588885i	$0.200433\pi$
$252$		0			0
$253$	−3.00495	+	5.63777i	−0.188920	+	0.354443i
$254$		0			0
$255$	−3.06064	−	0.573943i	−0.191664	−	0.0359417i
$256$		0			0
$257$	3.18148	+	6.24401i	0.198455	+	0.389491i	0.968691	−	0.248269i	$-0.0798615\pi$
$257$	3.18148	+	6.24401i	0.198455	+	0.389491i	−0.770236	+	0.637759i	$0.779862\pi$
$258$		0			0
$259$	15.2422	+	11.0741i	0.947102	+	0.688110i
$260$		0			0
$261$	−10.0472	+	3.26452i	−0.621904	+	0.202069i
$262$		0			0
$263$	11.1111	−	11.1111i	0.685138	−	0.685138i	−0.276016	−	0.961153i	$-0.589014\pi$
$263$	11.1111	−	11.1111i	0.685138	−	0.685138i	0.961153	+	0.276016i	$0.0890141\pi$
$264$		0			0
$265$	−26.6861	−	0.755197i	−1.63931	−	0.0463914i
$266$		0			0
$267$	0.118776	+	0.0605196i	0.00726899	+	0.00370374i
$268$		0			0
$269$	−12.6534	+	17.4159i	−0.771491	+	1.06187i	0.224680	+	0.974433i	$0.427866\pi$
$269$	−12.6534	+	17.4159i	−0.771491	+	1.06187i	−0.996170	+	0.0874331i	$0.972134\pi$
$270$		0			0
$271$	−12.7174	−	4.13215i	−0.772529	−	0.251010i	−0.103882	−	0.994590i	$-0.533126\pi$
$271$	−12.7174	−	4.13215i	−0.772529	−	0.251010i	−0.668647	+	0.743580i	$0.733126\pi$
$272$		0			0
$273$	3.22240	+	0.510378i	0.195028	+	0.0308895i
$274$		0			0
$275$	8.71402	+	14.1091i	0.525475	+	0.850809i
$276$		0			0
$277$	−2.90188	−	0.459612i	−0.174357	−	0.0276154i	0.0686455	−	0.997641i	$-0.478132\pi$
$277$	−2.90188	−	0.459612i	−0.174357	−	0.0276154i	−0.243002	+	0.970026i	$0.578132\pi$
$278$		0			0
$279$	−17.9945	−	5.84676i	−1.07730	−	0.350037i
$280$		0			0
$281$	−16.4633	+	22.6598i	−0.982120	+	1.35177i	−0.0464401	+	0.998921i	$0.514788\pi$
$281$	−16.4633	+	22.6598i	−0.982120	+	1.35177i	−0.935680	+	0.352851i	$0.885212\pi$
$282$		0			0
$283$	15.4094	+	7.85147i	0.915992	+	0.466721i	0.847419	−	0.530925i	$-0.178155\pi$
$283$	15.4094	+	7.85147i	0.915992	+	0.466721i	0.0685734	+	0.997646i	$0.478155\pi$
$284$		0			0
$285$	−2.13714	−	0.0604794i	−0.126593	−	0.00358249i
$286$		0			0
$287$	−29.5049	+	29.5049i	−1.74162	+	1.74162i
$288$		0			0
$289$	−3.06277	+	0.995153i	−0.180163	+	0.0585384i
$290$		0			0
$291$	−2.49763	−	1.81464i	−0.146414	−	0.106376i
$292$		0			0
$293$	−2.59813	−	5.09913i	−0.151785	−	0.297894i	0.802576	−	0.596549i	$-0.203462\pi$
$293$	−2.59813	−	5.09913i	−0.151785	−	0.297894i	−0.954361	+	0.298655i	$0.903462\pi$
$294$		0			0
$295$	−1.99816	−	0.374703i	−0.116337	−	0.0218160i
$296$		0			0
$297$	−2.65295	−	5.45330i	−0.153940	−	0.316433i
$298$		0			0
$299$	−3.37375	+	2.45118i	−0.195109	+	0.141755i
$300$		0			0
$301$	13.7652	−	42.3648i	0.793411	−	2.44187i
$302$		0			0
$303$	−0.646808	+	0.102444i	−0.0371582	+	0.00588528i
$304$		0			0
$305$	4.99658	−	9.15639i	0.286103	−	0.524293i
$306$		0			0
$307$	10.6045	+	10.6045i	0.605228	+	0.605228i	0.941695	−	0.336467i	$-0.109232\pi$
$307$	10.6045	+	10.6045i	0.605228	+	0.605228i	−0.336467	+	0.941695i	$0.609232\pi$
$308$		0			0
$309$			3.33786i			0.189884i
$310$		0			0
$311$	−1.94555	−	5.98778i	−0.110322	−	0.339536i	0.880621	−	0.473822i	$-0.157126\pi$
$311$	−1.94555	−	5.98778i	−0.110322	−	0.339536i	−0.990943	+	0.134286i	$0.957126\pi$
$312$		0			0
$313$	3.07637	+	19.4234i	0.173887	+	1.09788i	0.908037	+	0.418890i	$0.137581\pi$
$313$	3.07637	+	19.4234i	0.173887	+	1.09788i	−0.734151	+	0.678987i	$0.762419\pi$
$314$		0			0
$315$	29.7640	+	10.6108i	1.67701	+	0.597849i
$316$		0			0
$317$	1.10479	−	6.97539i	0.0620514	−	0.391777i	−0.937042	−	0.349215i	$-0.886448\pi$
$317$	1.10479	−	6.97539i	0.0620514	−	0.391777i	0.999094	−	0.0425616i	$-0.0135519\pi$
$318$		0			0
$319$	−12.0628	−	0.222729i	−0.675390	−	0.0124704i
$320$		0			0
$321$	−0.552475	−	0.760416i	−0.0308361	−	0.0424423i
$322$		0			0
$323$	−12.3697	+	6.30269i	−0.688270	+	0.350691i
$324$		0			0
$325$	1.08601	+	10.7701i	0.0602412	+	0.597418i
$326$		0			0
$327$	2.26536	−	4.44602i	0.125275	−	0.245866i
$328$		0			0
$329$	−13.5766			−0.748504
$330$		0			0
$331$	6.35394			0.349244			0.174622	−	0.984636i	$-0.444130\pi$
$331$	6.35394			0.349244			0.174622	+	0.984636i	$0.444130\pi$
$332$		0			0
$333$	5.10470	−	10.0185i	0.279736	−	0.549012i
$334$		0			0
$335$	11.7213	−	15.2089i	0.640404	−	0.830952i
$336$		0			0
$337$	18.0626	−	9.20335i	0.983932	−	0.501339i	0.113453	−	0.993543i	$-0.463809\pi$
$337$	18.0626	−	9.20335i	0.983932	−	0.501339i	0.870479	+	0.492205i	$0.163809\pi$
$338$		0			0
$339$	−1.18721	−	1.63405i	−0.0644803	−	0.0887495i
$340$		0			0
$341$	−17.2440	−	13.0216i	−0.933815	−	0.705158i
$342$		0			0
$343$	−7.36732	+	46.5154i	−0.397798	+	2.51160i
$344$		0			0
$345$	1.20519	−	0.571725i	0.0648852	−	0.0307806i
$346$		0			0
$347$	2.60029	+	16.4176i	0.139591	+	0.881341i	0.953728	+	0.300669i	$0.0972101\pi$
$347$	2.60029	+	16.4176i	0.139591	+	0.881341i	−0.814138	+	0.580672i	$0.802790\pi$
$348$		0			0
$349$	8.36963	+	25.7591i	0.448016	+	1.37885i	0.879142	+	0.476560i	$0.158117\pi$
$349$	8.36963	+	25.7591i	0.448016	+	1.37885i	−0.431126	+	0.902292i	$0.641883\pi$
$350$		0			0
$351$		−	3.95855i		−	0.211292i
$352$		0			0
$353$	15.0281	+	15.0281i	0.799867	+	0.799867i	0.983074	−	0.183207i	$-0.0586479\pi$
$353$	15.0281	+	15.0281i	0.799867	+	0.799867i	−0.183207	+	0.983074i	$0.558648\pi$
$354$		0			0
$355$	−29.3955	−	16.0409i	−1.56015	−	0.851365i
$356$		0			0
$357$	−6.69310	+	1.06008i	−0.354236	+	0.0561055i
$358$		0			0
$359$	−0.0866807	+	0.266776i	−0.00457483	+	0.0140799i	−0.953318	−	0.301969i	$-0.902356\pi$
$359$	−0.0866807	+	0.266776i	−0.00457483	+	0.0140799i	0.948743	+	0.316048i	$0.102356\pi$
$360$		0			0
$361$	7.66003	−	5.56534i	0.403160	−	0.292913i
$362$		0			0
$363$	−0.408346	−	3.38210i	−0.0214326	−	0.177514i
$364$		0			0
$365$	−6.18468	−	9.03960i	−0.323721	−	0.473154i
$366$		0			0
$367$	7.69206	+	15.0965i	0.401522	+	0.788032i	0.999913	−	0.0131721i	$-0.00419294\pi$
$367$	7.69206	+	15.0965i	0.401522	+	0.788032i	−0.598391	+	0.801204i	$0.704193\pi$
$368$		0			0
$369$	20.1466	+	14.6373i	1.04879	+	0.761990i
$370$		0			0
$371$	−55.2530	+	17.9528i	−2.86859	+	0.932063i
$372$		0			0
$373$	15.3939	−	15.3939i	0.797068	−	0.797068i	−0.185564	−	0.982632i	$-0.559411\pi$
$373$	15.3939	−	15.3939i	0.797068	−	0.797068i	0.982632	+	0.185564i	$0.0594111\pi$
$374$		0			0
$375$	0.293529	−	3.45005i	0.0151578	−	0.178160i
$376$		0			0
$377$	−7.01706	−	3.57537i	−0.361397	−	0.184141i
$378$		0			0
$379$	−3.73639	+	5.14270i	−0.191925	+	0.264163i	−0.894125	−	0.447818i	$-0.852201\pi$
$379$	−3.73639	+	5.14270i	−0.191925	+	0.264163i	0.702200	+	0.711980i	$0.252201\pi$
$380$		0			0
$381$	3.72399	+	1.21000i	0.190786	+	0.0619900i
$382$		0			0
$383$	−35.4492	−	5.61460i	−1.81137	−	0.286893i	−0.843275	−	0.537482i	$-0.819376\pi$
$383$	−35.4492	−	5.61460i	−1.81137	−	0.286893i	−0.968094	+	0.250589i	$0.919376\pi$
$384$		0			0
$385$	28.1722	+	22.5530i	1.43579	+	1.14941i
$386$		0			0
$387$	−26.2575	−	4.15877i	−1.33474	−	0.211402i
$388$		0			0
$389$	3.47743	+	1.12989i	0.176313	+	0.0572875i	0.395843	−	0.918318i	$-0.370452\pi$
$389$	3.47743	+	1.12989i	0.176313	+	0.0572875i	−0.219530	+	0.975606i	$0.570452\pi$
$390$		0			0
$391$	5.09123	−	7.00747i	0.257474	−	0.354383i
$392$		0			0
$393$	4.41609	+	2.25011i	0.222762	+	0.113503i
$394$		0			0
$395$	−13.5734	+	12.8263i	−0.682953	+	0.645362i
$396$		0			0
$397$	−1.57131	+	1.57131i	−0.0788616	+	0.0788616i	−0.745437	−	0.666576i	$-0.767759\pi$
$397$	−1.57131	+	1.57131i	−0.0788616	+	0.0788616i	0.666576	+	0.745437i	$0.267759\pi$
$398$		0			0
$399$	−4.42490	+	1.43774i	−0.221522	+	0.0719769i
$400$		0			0
$401$	3.09984	+	2.25217i	0.154799	+	0.112468i	0.662488	−	0.749072i	$-0.269500\pi$
$401$	3.09984	+	2.25217i	0.154799	+	0.112468i	−0.507690	+	0.861540i	$0.669500\pi$
$402$		0			0
$403$	−6.40349	−	12.5676i	−0.318981	−	0.626035i
$404$		0			0
$405$	3.35723	−	17.9029i	0.166822	−	0.889604i
$406$		0			0
$407$	9.24627	−	8.91101i	0.458320	−	0.441702i
$408$		0			0
$409$	3.62215	−	2.63164i	0.179104	−	0.130126i	−0.494621	−	0.869109i	$-0.664693\pi$
$409$	3.62215	−	2.63164i	0.179104	−	0.130126i	0.673725	+	0.738982i	$0.264693\pi$
$410$		0			0
$411$	−0.676482	+	2.08200i	−0.0333684	+	0.102697i
$412$		0			0
$413$	−4.36963	+	0.692082i	−0.215016	+	0.0340551i
$414$		0			0
$415$	4.96953	−	1.46064i	0.243945	−	0.0716998i
$416$		0			0
$417$	−2.29746	−	2.29746i	−0.112507	−	0.112507i
$418$		0			0
$419$		−	33.4847i		−	1.63584i	−0.575334	−	0.817918i	$-0.695128\pi$
$419$		−	33.4847i		−	1.63584i	0.575334	−	0.817918i	$-0.304872\pi$
$420$		0			0
$421$	7.06395	+	21.7406i	0.344276	+	1.05957i	0.961970	+	0.273154i	$0.0880669\pi$
$421$	7.06395	+	21.7406i	0.344276	+	1.05957i	−0.617694	+	0.786418i	$0.711933\pi$
$422$		0			0
$423$	1.26753	+	8.00288i	0.0616295	+	0.389113i
$424$		0			0
$425$	−9.05805	−	20.5782i	−0.439380	−	0.998188i
$426$		0			0
$427$	3.55098	−	22.4200i	0.171844	−	1.08498i
$428$		0			0
$429$	0.726092	−	2.10184i	0.0350561	−	0.101478i
$430$		0			0
$431$	14.9266	+	20.5447i	0.718989	+	0.989604i	0.999557	+	0.0297697i	$0.00947738\pi$
$431$	14.9266	+	20.5447i	0.718989	+	0.989604i	−0.280567	+	0.959834i	$0.590523\pi$
$432$		0			0
$433$	6.10717	−	3.11176i	0.293492	−	0.149542i	−0.301045	−	0.953610i	$-0.597335\pi$
$433$	6.10717	−	3.11176i	0.293492	−	0.149542i	0.594537	+	0.804068i	$0.297335\pi$
$434$		0			0
$435$	1.99531	+	1.53776i	0.0956679	+	0.0737300i
$436$		0			0
$437$	2.69986	−	5.29876i	0.129152	−	0.253474i
$438$		0			0
$439$	34.6192			1.65229			0.826143	−	0.563461i	$-0.190531\pi$
$439$	34.6192			1.65229			0.826143	+	0.563461i	$0.190531\pi$
$440$		0			0
$441$	48.4354			2.30645
$442$		0			0
$443$	11.3725	−	22.3198i	0.540324	−	1.06045i	−0.445908	−	0.895079i	$-0.647119\pi$
$443$	11.3725	−	22.3198i	0.540324	−	1.06045i	0.986232	−	0.165367i	$-0.0528807\pi$
$444$		0			0
$445$	0.123615	+	0.954521i	0.00585991	+	0.0452487i
$446$		0			0
$447$	4.68039	−	2.38478i	0.221375	−	0.112796i
$448$		0			0
$449$	−21.3897	−	29.4404i	−1.00944	−	1.38938i	−0.919348	−	0.393444i	$-0.871283\pi$
$449$	−21.3897	−	29.4404i	−1.00944	−	1.38938i	−0.0900935	−	0.995933i	$-0.528717\pi$
$450$		0			0
$451$	16.2890	+	23.3132i	0.767021	+	1.09777i
$452$		0			0
$453$	0.0460847	−	0.290968i	0.00216525	−	0.0136708i
$454$		0			0
$455$	10.0963	+	21.2830i	0.473323	+	0.997760i
$456$		0			0
$457$	−4.37199	−	27.6037i	−0.204513	−	1.29124i	−0.849719	−	0.527236i	$-0.823228\pi$
$457$	−4.37199	−	27.6037i	−0.204513	−	1.29124i	0.645206	−	0.764009i	$-0.276772\pi$
$458$		0			0
$459$	2.54078	+	7.81971i	0.118593	+	0.364993i
$460$		0			0
$461$		−	11.5248i		−	0.536764i	−0.963312	−	0.268382i	$-0.913511\pi$
$461$		−	11.5248i		−	0.536764i	0.963312	−	0.268382i	$-0.0864890\pi$
$462$		0			0
$463$	0.857939	+	0.857939i	0.0398718	+	0.0398718i	0.726762	−	0.686890i	$-0.241024\pi$
$463$	0.857939	+	0.857939i	0.0398718	+	0.0398718i	−0.686890	+	0.726762i	$0.741024\pi$
$464$		0			0
$465$	1.27227	+	4.32865i	0.0590000	+	0.200736i
$466$		0			0
$467$	−21.2927	+	3.37244i	−0.985310	+	0.156058i	−0.628240	−	0.778020i	$-0.716224\pi$
$467$	−21.2927	+	3.37244i	−0.985310	+	0.156058i	−0.357070	+	0.934078i	$0.616224\pi$
$468$		0			0
$469$	12.9125	−	39.7406i	0.596243	−	1.83505i
$470$		0			0
$471$	−5.47431	+	3.97732i	−0.252243	+	0.183265i
$472$		0			0
$473$	−26.7930	−	14.2808i	−1.23194	−	0.656631i
$474$		0			0
$475$	−8.35268	−	12.9817i	−0.383247	−	0.595641i
$476$		0			0
$477$	15.7409	+	30.8933i	0.720728	+	1.41451i
$478$		0			0
$479$	−0.932642	−	0.677604i	−0.0426135	−	0.0309605i	0.566275	−	0.824217i	$-0.308384\pi$
$479$	−0.932642	−	0.677604i	−0.0426135	−	0.0309605i	−0.608888	+	0.793256i	$0.708384\pi$
$480$		0			0
$481$	7.97198	−	2.59025i	0.363491	−	0.118105i
$482$		0			0
$483$	2.05261	−	2.05261i	0.0933970	−	0.0933970i
$484$		0			0
$485$	0.630551	−	22.2815i	0.0286318	−	1.01175i
$486$		0			0
$487$	5.31965	+	2.71050i	0.241056	+	0.122824i	0.570346	−	0.821405i	$-0.306809\pi$
$487$	5.31965	+	2.71050i	0.241056	+	0.122824i	−0.329289	+	0.944229i	$0.606809\pi$
$488$		0			0
$489$	0.899125	−	1.23754i	0.0406598	−	0.0559635i
$490$		0			0
$491$	21.5993	+	7.01804i	0.974763	+	0.316720i	0.752737	−	0.658321i	$-0.228733\pi$
$491$	21.5993	+	7.01804i	0.974763	+	0.316720i	0.222026	+	0.975041i	$0.428733\pi$
$492$		0			0
$493$	16.1563	+	2.55891i	0.727644	+	0.115247i
$494$		0			0
$495$	10.6639	−	18.7119i	0.479307	−	0.841038i
$496$		0			0
$497$	−71.9768	−	11.4000i	−3.22860	−	0.511360i
$498$		0			0
$499$	−15.1246	−	4.91428i	−0.677070	−	0.219993i	−0.0497577	−	0.998761i	$-0.515845\pi$
$499$	−15.1246	−	4.91428i	−0.677070	−	0.219993i	−0.627312	+	0.778768i	$0.715845\pi$
$500$		0			0
$501$	0.0393922	−	0.0542187i	0.00175991	−	0.00242231i
$502$		0			0
$503$	−9.63633	−	4.90996i	−0.429663	−	0.218924i	0.225765	−	0.974182i	$-0.427512\pi$
$503$	−9.63633	−	4.90996i	−0.429663	−	0.218924i	−0.655428	+	0.755258i	$0.727512\pi$
$504$		0			0
$505$	−3.24749	−	3.43664i	−0.144511	−	0.152929i
$506$		0			0
$507$	−1.82046	+	1.82046i	−0.0808493	+	0.0808493i
$508$		0			0
$509$	9.06512	−	2.94543i	0.401804	−	0.130554i	−0.101142	−	0.994872i	$-0.532250\pi$
$509$	9.06512	−	2.94543i	0.401804	−	0.130554i	0.502946	+	0.864318i	$0.332250\pi$
$510$		0			0
$511$	−19.2830	−	14.0099i	−0.853030	−	0.619763i
$512$		0			0
$513$	2.56284	+	5.02985i	0.113152	+	0.222073i
$514$		0			0
$515$	−19.8902	+	13.6084i	−0.876467	+	0.599658i
$516$		0			0
$517$	−1.61607	+	9.11144i	−0.0710747	+	0.400720i
$518$		0			0
$519$	0.729918	−	0.530316i	0.0320398	−	0.0232783i
$520$		0			0
$521$	−8.87876	+	27.3260i	−0.388986	+	1.19717i	0.544562	+	0.838721i	$0.316696\pi$
$521$	−8.87876	+	27.3260i	−0.388986	+	1.19717i	−0.933547	+	0.358454i	$0.883304\pi$
$522$		0			0
$523$	2.32454	−	0.368170i	0.101645	−	0.0160990i	−0.105405	−	0.994429i	$-0.533614\pi$
$523$	2.32454	−	0.368170i	0.101645	−	0.0160990i	0.207050	+	0.978330i	$0.433614\pi$
$524$		0			0
$525$	−1.91944	−	7.28641i	−0.0837713	−	0.318005i
$526$		0			0
$527$	20.7159	+	20.7159i	0.902397	+	0.902397i
$528$		0			0
$529$		−	19.2896i		−	0.838679i
$530$		0			0
$531$	0.815909	+	2.51111i	0.0354074	+	0.108973i
$532$		0			0
$533$	2.90411	+	18.3358i	0.125791	+	0.794213i
$534$		0			0
$535$	2.27886	−	6.39238i	0.0985239	−	0.276367i
$536$		0			0
$537$	0.0887846	−	0.560564i	0.00383134	−	0.0241901i
$538$		0			0
$539$	52.2840	+	18.0618i	2.25203	+	0.777978i
$540$		0			0
$541$	6.48751	+	8.92929i	0.278920	+	0.383900i	0.925376	−	0.379051i	$-0.123750\pi$
$541$	6.48751	+	8.92929i	0.278920	+	0.383900i	−0.646456	+	0.762951i	$0.723750\pi$
$542$		0			0
$543$	4.85712	−	2.47482i	0.208439	−	0.106205i
$544$		0			0
$545$	35.7295	−	4.62714i	1.53049	−	0.198205i
$546$		0			0
$547$	2.81409	−	5.52296i	0.120322	−	0.236145i	−0.822988	−	0.568059i	$-0.807694\pi$
$547$	2.81409	−	5.52296i	0.120322	−	0.236145i	0.943310	+	0.331914i	$0.107694\pi$
$548$		0			0
$549$	−13.5472			−0.578181
$550$		0			0
$551$	11.2308			0.478450
$552$		0			0
$553$	−18.4500	+	36.2101i	−0.784573	+	1.53981i
$554$		0			0
$555$	−2.65903	+	0.344357i	−0.112870	+	0.0146171i
$556$		0			0
$557$	17.3288	−	8.82946i	0.734245	−	0.374116i	−0.0465401	−	0.998916i	$-0.514820\pi$
$557$	17.3288	−	8.82946i	0.734245	−	0.374116i	0.780785	+	0.624800i	$0.214820\pi$
$558$		0			0
$559$	−11.6490	−	16.0335i	−0.492700	−	0.678143i
$560$		0			0
$561$	−0.0852668	+	4.61800i	−0.00359997	+	0.194972i
$562$		0			0
$563$	−0.0954339	+	0.602546i	−0.00402206	+	0.0253943i	−0.989618	−	0.143724i	$-0.954092\pi$
$563$	−0.0954339	+	0.602546i	−0.00402206	+	0.0253943i	0.985596	+	0.169119i	$0.0540921\pi$
$564$		0			0
$565$	4.89703	−	13.7365i	0.206020	−	0.577900i
$566$		0			0
$567$	−6.20086	−	39.1507i	−0.260412	−	1.64417i
$568$		0			0
$569$	10.4094	+	32.0369i	0.436385	+	1.34306i	0.891660	+	0.452705i	$0.149541\pi$
$569$	10.4094	+	32.0369i	0.436385	+	1.34306i	−0.455275	+	0.890351i	$0.650459\pi$
$570$		0			0
$571$			2.77837i			0.116271i	0.998309	+	0.0581356i	$0.0185156\pi$
$571$			2.77837i			0.116271i	−0.998309	+	0.0581356i	$0.981484\pi$
$572$		0			0
$573$	1.45638	+	1.45638i	0.0608412	+	0.0608412i
$574$		0			0
$575$	8.32043	+	4.85077i	0.346986	+	0.202291i
$576$		0			0
$577$	−23.0431	+	3.64966i	−0.959295	+	0.151937i	−0.616397	−	0.787435i	$-0.711408\pi$
$577$	−23.0431	+	3.64966i	−0.959295	+	0.151937i	−0.342898	+	0.939373i	$0.611408\pi$
$578$		0			0
$579$	1.15681	−	3.56029i	0.0480753	−	0.147961i
$580$		0			0
$581$	9.11920	−	6.62548i	0.378328	−	0.274871i
$582$		0			0
$583$	5.47139	+	39.2179i	0.226602	+	1.62424i
$584$		0			0
$585$	11.6028	−	7.93838i	0.479718	−	0.328212i
$586$		0			0
$587$	−13.0131	−	25.5396i	−0.537108	−	1.05413i	−0.986950	−	0.161026i	$-0.948520\pi$
$587$	−13.0131	−	25.5396i	−0.537108	−	1.05413i	0.449842	−	0.893108i	$-0.351480\pi$
$588$		0			0
$589$	16.2729	+	11.8230i	0.670514	+	0.487157i
$590$		0			0
$591$	−5.42338	+	1.76216i	−0.223088	+	0.0724856i
$592$		0			0
$593$	8.01991	−	8.01991i	0.329338	−	0.329338i	−0.522996	−	0.852335i	$-0.675186\pi$
$593$	8.01991	−	8.01991i	0.329338	−	0.329338i	0.852335	+	0.522996i	$0.175186\pi$
$594$		0			0
$595$	−33.6046	−	35.5620i	−1.37766	−	1.45790i
$596$		0			0
$597$	3.23381	+	1.64771i	0.132351	+	0.0674362i
$598$		0			0
$599$	−14.0073	+	19.2794i	−0.572322	+	0.787733i	−0.992827	−	0.119557i	$-0.961853\pi$
$599$	−14.0073	+	19.2794i	−0.572322	+	0.787733i	0.420506	+	0.907290i	$0.361853\pi$
$600$		0			0
$601$	−32.6897	−	10.6215i	−1.33344	−	0.433261i	−0.446351	−	0.894858i	$-0.647277\pi$
$601$	−32.6897	−	10.6215i	−1.33344	−	0.433261i	−0.887090	+	0.461597i	$0.847277\pi$
$602$		0			0
$603$	−24.6310	−	3.90116i	−1.00305	−	0.158868i
$604$		0			0
$605$	18.4890	−	16.2221i	0.751685	−	0.659522i
$606$		0			0
$607$	−28.6065	−	4.53083i	−1.16110	−	0.183901i	−0.453994	−	0.891005i	$-0.650001\pi$
$607$	−28.6065	−	4.53083i	−1.16110	−	0.183901i	−0.707109	+	0.707104i	$0.750001\pi$
$608$		0			0
$609$	5.21370	+	1.69404i	0.211270	+	0.0686458i
$610$		0			0
$611$	−3.55044	+	4.88676i	−0.143635	+	0.197697i
$612$		0			0
$613$	1.70899	+	0.870774i	0.0690254	+	0.0351702i	0.488163	−	0.872753i	$-0.337667\pi$
$613$	1.70899	+	0.870774i	0.0690254	+	0.0351702i	−0.419137	+	0.907923i	$0.637667\pi$
$614$		0			0
$615$	0.167980	−	5.93584i	0.00677360	−	0.239356i
$616$		0			0
$617$	−22.8666	+	22.8666i	−0.920576	+	0.920576i	−0.997070	−	0.0764940i	$-0.975627\pi$
$617$	−22.8666	+	22.8666i	−0.920576	+	0.920576i	0.0764940	+	0.997070i	$0.475627\pi$
$618$		0			0
$619$	−23.6638	+	7.68882i	−0.951127	+	0.309040i	−0.743173	−	0.669099i	$-0.766680\pi$
$619$	−23.6638	+	7.68882i	−0.951127	+	0.309040i	−0.207953	+	0.978139i	$0.566680\pi$
$620$		0			0
$621$	−2.84942	−	2.07022i	−0.114343	−	0.0830752i
$622$		0			0
$623$	0.950900	+	1.86625i	0.0380970	+	0.0747696i
$624$		0			0
$625$	21.7555	−	12.3167i	0.870218	−	0.492667i
$626$		0			0
$627$	0.438172	+	3.14074i	0.0174989	+	0.125429i
$628$		0			0
$629$	−14.0853	+	10.2336i	−0.561617	+	0.408039i
$630$		0			0
$631$	0.649576	−	1.99919i	0.0258592	−	0.0795864i	−0.937294	−	0.348540i	$-0.886678\pi$
$631$	0.649576	−	1.99919i	0.0258592	−	0.0795864i	0.963153	+	0.268953i	$0.0866777\pi$
$632$		0			0
$633$	−4.94535	+	0.783267i	−0.196560	+	0.0311321i
$634$		0			0
$635$	7.97230	+	27.1243i	0.316371	+	1.07639i
$636$		0			0
$637$	25.5320	+	25.5320i	1.01161	+	1.01161i
$638$		0			0
$639$			43.4917i			1.72051i
$640$		0			0
$641$	−7.27316	−	22.3845i	−0.287272	−	0.884134i	−0.985708	−	0.168461i	$-0.946120\pi$
$641$	−7.27316	−	22.3845i	−0.287272	−	0.884134i	0.698436	−	0.715673i	$-0.253880\pi$
$642$		0			0
$643$	4.31582	+	27.2490i	0.170199	+	1.07460i	0.913857	+	0.406035i	$0.133089\pi$
$643$	4.31582	+	27.2490i	0.170199	+	1.07460i	−0.743658	+	0.668560i	$0.766911\pi$
$644$		0			0
$645$	2.71707	+	5.72756i	0.106985	+	0.225522i
$646$		0			0
$647$	2.62389	−	16.5666i	0.103156	−	0.651299i	−0.880882	−	0.473337i	$-0.843049\pi$
$647$	2.62389	−	16.5666i	0.103156	−	0.651299i	0.984037	−	0.177963i	$-0.0569506\pi$
$648$		0			0
$649$	−0.0556670	+	3.01489i	−0.00218512	+	0.118345i
$650$		0			0
$651$	5.77105	+	7.94316i	0.226185	+	0.311317i
$652$		0			0
$653$	−6.74967	+	3.43913i	−0.264135	+	0.134583i	−0.581043	−	0.813873i	$-0.697355\pi$
$653$	−6.74967	+	3.43913i	−0.264135	+	0.134583i	0.316908	+	0.948456i	$0.397355\pi$
$654$		0			0
$655$	4.59599	+	35.4890i	0.179580	+	1.38667i
$656$		0			0
$657$	−6.45800	+	12.6745i	−0.251951	+	0.494481i
$658$		0			0
$659$	0.843775			0.0328688			0.0164344	−	0.999865i	$-0.494769\pi$
$659$	0.843775			0.0328688			0.0164344	+	0.999865i	$0.494769\pi$
$660$		0			0
$661$	−8.82429			−0.343225			−0.171613	−	0.985165i	$-0.554898\pi$
$661$	−8.82429			−0.343225			−0.171613	+	0.985165i	$0.554898\pi$
$662$		0			0
$663$	−1.36875	+	2.68633i	−0.0531579	+	0.104328i
$664$		0			0
$665$	−26.6077	−	20.5062i	−1.03180	−	0.795196i
$666$		0			0
$667$	−6.24335	+	3.18115i	−0.241743	+	0.123174i
$668$		0			0
$669$	4.38602	+	6.03684i	0.169573	+	0.233398i
$670$		0			0
$671$	−14.6236	−	5.05183i	−0.564539	−	0.195024i
$672$		0			0
$673$	−7.85894	+	49.6194i	−0.302940	+	1.91269i	0.0953786	+	0.995441i	$0.469594\pi$
$673$	−7.85894	+	49.6194i	−0.302940	+	1.91269i	−0.398319	+	0.917247i	$0.630406\pi$
$674$		0			0
$675$	−8.36762	+	3.68324i	−0.322070	+	0.141768i
$676$		0			0
$677$	3.91331	+	24.7077i	0.150401	+	0.949594i	0.941281	+	0.337623i	$0.109623\pi$
$677$	3.91331	+	24.7077i	0.150401	+	0.949594i	−0.790881	+	0.611971i	$0.790377\pi$
$678$		0			0
$679$	−14.9897	−	46.1335i	−0.575251	−	1.77044i
$680$		0			0
$681$			3.73959i			0.143301i
$682$		0			0
$683$	28.6099	+	28.6099i	1.09473	+	1.09473i	0.995017	+	0.0997098i	$0.0317914\pi$
$683$	28.6099	+	28.6099i	1.09473	+	1.09473i	0.0997098	+	0.995017i	$0.468209\pi$
$684$		0			0
$685$	−15.1646	+	4.45714i	−0.579408	+	0.170298i
$686$		0			0
$687$	4.37790	−	0.693391i	0.167027	−	0.0264545i
$688$		0			0
$689$	−7.98736	+	24.5826i	−0.304294	+	0.936521i
$690$		0			0
$691$	5.75944	−	4.18448i	0.219100	−	0.159185i	−0.472822	−	0.881158i	$-0.656765\pi$
$691$	5.75944	−	4.18448i	0.219100	−	0.159185i	0.691921	+	0.721973i	$0.256765\pi$
$692$		0			0
$693$	8.18520	−	46.1483i	0.310930	−	1.75303i
$694$		0			0
$695$	4.32378	−	23.0572i	0.164010	−	0.874609i
$696$		0			0
$697$	−17.5055	−	34.3565i	−0.663069	−	1.30135i
$698$		0			0
$699$	4.89436	+	3.55596i	0.185122	+	0.134499i
$700$		0			0
$701$	35.7034	−	11.6007i	1.34850	−	0.438154i	0.456312	−	0.889820i	$-0.349170\pi$
$701$	35.7034	−	11.6007i	1.34850	−	0.438154i	0.892187	+	0.451666i	$0.149170\pi$
$702$		0			0
$703$	−8.45246	+	8.45246i	−0.318790	+	0.318790i
$704$		0			0
$705$	1.40433	−	1.32703i	0.0528901	−	0.0499790i
$706$		0			0
$707$	−9.16802	−	4.67134i	−0.344799	−	0.175684i
$708$		0			0
$709$	17.8503	−	24.5688i	0.670380	−	0.922699i	−0.329389	−	0.944194i	$-0.606843\pi$
$709$	17.8503	−	24.5688i	0.670380	−	0.922699i	0.999769	+	0.0214951i	$0.00684263\pi$
$710$		0			0
$711$	23.0669	+	7.49490i	0.865077	+	0.281081i
$712$		0			0
$713$	−12.3952	−	1.96320i	−0.464203	−	0.0735225i
$714$		0			0
$715$	15.4850	−	4.24239i	0.579107	−	0.158656i
$716$		0			0
$717$	−1.42667	−	0.225962i	−0.0532798	−	0.00843870i
$718$		0			0
$719$	7.15180	+	2.32376i	0.266717	+	0.0866616i	0.439322	−	0.898329i	$-0.355219\pi$
$719$	7.15180	+	2.32376i	0.266717	+	0.0866616i	−0.172605	+	0.984991i	$0.555219\pi$
$720$		0			0
$721$	−30.8266	+	42.4292i	−1.14804	+	1.58015i
$722$		0			0
$723$	−1.68321	−	0.857639i	−0.0625993	−	0.0318959i
$724$		0			0
$725$	−1.02862	+	18.1594i	−0.0382020	+	0.674424i
$726$		0			0
$727$	−34.1964	+	34.1964i	−1.26828	+	1.26828i	−0.321296	+	0.946979i	$0.604119\pi$
$727$	−34.1964	+	34.1964i	−1.26828	+	1.26828i	−0.946979	+	0.321296i	$0.895881\pi$
$728$		0			0
$729$	−20.8832	+	6.78535i	−0.773450	+	0.251309i
$730$		0			0
$731$	33.3024	+	24.1956i	1.23173	+	0.894907i
$732$		0			0
$733$	−20.7220	−	40.6692i	−0.765384	−	1.50215i	−0.862044	−	0.506833i	$-0.830816\pi$
$733$	−20.7220	−	40.6692i	−0.765384	−	1.50215i	0.0966600	−	0.995317i	$-0.469184\pi$
$734$		0			0
$735$	−6.52177	−	9.53230i	−0.240559	−	0.351604i
$736$		0			0
$737$	−25.1333	−	13.3962i	−0.925798	−	0.493454i
$738$		0			0
$739$	23.4555	−	17.0414i	0.862826	−	0.626880i	−0.0658264	−	0.997831i	$-0.520968\pi$
$739$	23.4555	−	17.0414i	0.862826	−	0.626880i	0.928652	+	0.370951i	$0.120968\pi$
$740$		0			0
$741$	−0.639662	+	1.96868i	−0.0234986	+	0.0723211i
$742$		0			0
$743$	10.5152	−	1.66544i	0.385765	−	0.0610992i	0.0394600	−	0.999221i	$-0.487436\pi$
$743$	10.5152	−	1.66544i	0.385765	−	0.0610992i	0.346305	+	0.938122i	$0.387436\pi$
$744$		0			0
$745$	33.2927	+	18.1676i	1.21975	+	0.665609i
$746$		0			0
$747$	−4.75683	−	4.75683i	−0.174043	−	0.174043i
$748$		0			0
$749$		−	14.7684i		−	0.539625i
$750$		0			0
$751$	−12.0184	−	36.9889i	−0.438559	−	1.34975i	−0.889395	−	0.457139i	$-0.848874\pi$
$751$	−12.0184	−	36.9889i	−0.438559	−	1.34975i	0.450836	−	0.892607i	$-0.351126\pi$
$752$		0			0
$753$	0.472385	+	2.98252i	0.0172147	+	0.108689i
$754$		0			0
$755$	1.92175	−	0.911652i	0.0699397	−	0.0331784i
$756$		0			0
$757$	0.377851	−	2.38566i	0.0137332	−	0.0867082i	−0.979870	−	0.199638i	$-0.936023\pi$
$757$	0.377851	−	2.38566i	0.0137332	−	0.0867082i	0.993603	+	0.112930i	$0.0360235\pi$
$758$		0			0
$759$	−1.13320	−	1.62186i	−0.0411326	−	0.0588698i
$760$		0			0
$761$	13.4584	+	18.5238i	0.487865	+	0.671489i	0.979992	−	0.199034i	$-0.0637806\pi$
$761$	13.4584	+	18.5238i	0.487865	+	0.671489i	−0.492127	+	0.870523i	$0.663781\pi$
$762$		0			0
$763$	69.8571	−	35.5940i	2.52900	−	1.28859i
$764$		0			0
$765$	−17.8250	+	23.1287i	−0.644464	+	0.836219i
$766$		0			0
$767$	−0.893599	+	1.75379i	−0.0322660	+	0.0633256i
$768$		0			0
$769$	17.4640			0.629769			0.314885	−	0.949130i	$-0.398034\pi$
$769$	17.4640			0.629769			0.314885	+	0.949130i	$0.398034\pi$
$770$		0			0
$771$	−2.17030			−0.0781614
$772$		0			0
$773$	8.28029	−	16.2510i	0.297821	−	0.584507i	−0.692802	−	0.721128i	$-0.743624\pi$
$773$	8.28029	−	16.2510i	0.297821	−	0.584507i	0.990623	+	0.136621i	$0.0436241\pi$
$774$		0			0
$775$	−20.6073	+	25.2292i	−0.740235	+	0.906261i
$776$		0			0
$777$	−5.19884	+	2.64894i	−0.186507	+	0.0950303i
$778$		0			0
$779$	−15.5610	−	21.4179i	−0.557530	−	0.767375i
$780$		0			0
$781$	−16.2183	+	46.9475i	−0.580336	+	1.67991i
$782$		0			0
$783$	1.04052	−	6.56957i	0.0371851	−	0.234777i
$784$		0			0
$785$	−46.0193	−	16.4058i	−1.64250	−	0.585546i
$786$		0			0
$787$	2.42251	+	15.2951i	0.0863530	+	0.545212i	0.992500	+	0.122248i	$0.0390103\pi$
$787$	2.42251	+	15.2951i	0.0863530	+	0.545212i	−0.906147	+	0.422964i	$0.860990\pi$
$788$		0			0
$789$	1.50380	+	4.62822i	0.0535367	+	0.164769i
$790$		0			0
$791$		−	31.7356i		−	1.12839i
$792$		0			0
$793$	−7.14121	−	7.14121i	−0.253592	−	0.253592i
$794$		0			0
$795$	3.96044	−	7.25764i	0.140462	−	0.257402i
$796$		0			0
$797$	32.1486	−	5.09184i	1.13876	−	0.180362i	0.441556	−	0.897234i	$-0.354427\pi$
$797$	32.1486	−	5.09184i	1.13876	−	0.180362i	0.697205	+	0.716871i	$0.254427\pi$
$798$		0			0
$799$	3.87698	−	11.9321i	0.137158	−	0.422128i
$800$		0			0
$801$	1.01130	−	0.734752i	0.0357325	−	0.0259612i
$802$		0			0
$803$	−11.6975	+	11.2734i	−0.412797	+	0.397830i
$804$		0			0
$805$	20.5999	+	3.86298i	0.726051	+	0.136152i
$806$		0			0
$807$	−3.02672	−	5.94026i	−0.106545	−	0.209107i
$808$		0			0
$809$	−14.4049	−	10.4658i	−0.506449	−	0.367956i	0.305026	−	0.952344i	$-0.401335\pi$
$809$	−14.4049	−	10.4658i	−0.506449	−	0.367956i	−0.811475	+	0.584388i	$0.801335\pi$
$810$		0			0
$811$	12.8704	−	4.18186i	0.451942	−	0.146845i	−0.0741968	−	0.997244i	$-0.523639\pi$
$811$	12.8704	−	4.18186i	0.451942	−	0.146845i	0.526139	+	0.850399i	$0.323639\pi$
$812$		0			0
$813$	2.92830	−	2.92830i	0.102700	−	0.102700i
$814$		0			0
$815$	11.0402	+	0.312429i	0.386720	+	0.0109439i
$816$		0			0
$817$	25.1819	+	12.8308i	0.881004	+	0.448894i
$818$		0			0
$819$	17.9825	−	24.7508i	0.628361	−	0.864864i
$820$		0			0
$821$	24.1837	+	7.85777i	0.844018	+	0.274238i	0.698938	−	0.715182i	$-0.253656\pi$
$821$	24.1837	+	7.85777i	0.844018	+	0.274238i	0.145079	+	0.989420i	$0.453656\pi$
$822$		0			0
$823$	42.8204	+	6.78208i	1.49262	+	0.236409i	0.848779	−	0.528747i	$-0.177338\pi$
$823$	42.8204	+	6.78208i	1.49262	+	0.236409i	0.643845	+	0.765156i	$0.277338\pi$
$824$		0			0
$825$	−5.11847	+	0.420834i	−0.178202	+	0.0146516i
$826$		0			0
$827$	43.5841	+	6.90305i	1.51557	+	0.240042i	0.858117	−	0.513455i	$-0.171634\pi$
$827$	43.5841	+	6.90305i	1.51557	+	0.240042i	0.657451	+	0.753497i	$0.271634\pi$
$828$		0			0
$829$	−22.2216	−	7.22022i	−0.771787	−	0.250769i	−0.103457	−	0.994634i	$-0.532990\pi$
$829$	−22.2216	−	7.22022i	−0.771787	−	0.250769i	−0.668330	+	0.743865i	$0.732990\pi$
$830$		0			0
$831$	0.534828	−	0.736128i	0.0185530	−	0.0255360i
$832$		0			0
$833$	−66.8234	−	34.0482i	−2.31529	−	1.17970i
$834$		0			0
$835$	0.483688	+	0.0136880i	0.0167387	+	0.000473694i
$836$		0			0
$837$	8.42360	−	8.42360i	0.291162	−	0.291162i
$838$		0			0
$839$	4.94488	−	1.60669i	0.170716	−	0.0554690i	−0.222412	−	0.974953i	$-0.571393\pi$
$839$	4.94488	−	1.60669i	0.170716	−	0.0554690i	0.393128	+	0.919484i	$0.371393\pi$
$840$		0			0
$841$	12.7558	+	9.26767i	0.439857	+	0.319575i
$842$		0			0
$843$	−3.93806	−	7.72888i	−0.135634	−	0.266197i
$844$		0			0
$845$	−18.2700	−	3.42607i	−0.628508	−	0.117860i
$846$		0			0
$847$	26.0445	−	46.7628i	0.894900	−	1.60679i
$848$		0			0
$849$	−4.33310	+	3.14818i	−0.148712	+	0.108045i
$850$		0			0
$851$	2.30465	−	7.09298i	0.0790024	−	0.243144i
$852$		0			0
$853$	−7.00915	+	1.11014i	−0.239989	+	0.0380105i	−0.275270	−	0.961367i	$-0.588767\pi$
$853$	−7.00915	+	1.11014i	−0.239989	+	0.0380105i	0.0352814	+	0.999377i	$0.488767\pi$
$854$		0			0
$855$	−9.60345	+	17.5986i	−0.328431	+	0.601860i
$856$		0			0
$857$	−4.48225	−	4.48225i	−0.153111	−	0.153111i	0.626395	−	0.779506i	$-0.284530\pi$
$857$	−4.48225	−	4.48225i	−0.153111	−	0.153111i	−0.779506	+	0.626395i	$0.784530\pi$
$858$		0			0
$859$		−	17.8717i		−	0.609775i	−0.952388	−	0.304887i	$-0.901381\pi$
$859$		−	17.8717i		−	0.609775i	0.952388	−	0.304887i	$-0.0986188\pi$
$860$		0			0
$861$	−3.99327	−	12.2900i	−0.136090	−	0.418843i
$862$		0			0
$863$	−6.68465	−	42.2052i	−0.227548	−	1.43668i	−0.791649	−	0.610976i	$-0.790777\pi$
$863$	−6.68465	−	42.2052i	−0.227548	−	1.43668i	0.564101	−	0.825706i	$-0.309223\pi$
$864$		0			0
$865$	6.13600	+	2.18747i	0.208630	+	0.0743760i
$866$		0			0
$867$	0.156019	−	0.985063i	0.00529867	−	0.0334545i
$868$		0			0
$869$	22.1049	+	16.6922i	0.749857	+	0.566244i
$870$		0			0
$871$	−10.9274	−	15.0403i	−0.370261	−	0.509621i
$872$		0			0
$873$	−25.7943	+	13.1429i	−0.873006	+	0.444819i
$874$		0			0
$875$	35.5939	−	41.1444i	1.20329	−	1.39094i
$876$		0			0
$877$	2.02535	−	3.97498i	0.0683913	−	0.134225i	−0.854280	−	0.519814i	$-0.826001\pi$
$877$	2.02535	−	3.97498i	0.0683913	−	0.134225i	0.922671	+	0.385588i	$0.126001\pi$
$878$		0			0
$879$	1.77236			0.0597802
$880$		0			0
$881$	−8.60710			−0.289980			−0.144990	−	0.989433i	$-0.546315\pi$
$881$	−8.60710			−0.289980			−0.144990	+	0.989433i	$0.546315\pi$
$882$		0			0
$883$	−11.4418	+	22.4558i	−0.385048	+	0.755699i	−0.999445	−	0.0332976i	$-0.989399\pi$
$883$	−11.4418	+	22.4558i	−0.385048	+	0.755699i	0.614398	+	0.788997i	$0.289399\pi$
$884$		0			0
$885$	0.384336	−	0.498692i	0.0129193	−	0.0167634i
$886$		0			0
$887$	32.6198	−	16.6206i	1.09527	−	0.558066i	0.189516	−	0.981878i	$-0.439308\pi$
$887$	32.6198	−	16.6206i	1.09527	−	0.558066i	0.905750	+	0.423812i	$0.139308\pi$
$888$		0			0
$889$	36.1626	+	49.7735i	1.21285	+	1.66935i
$890$		0			0
$891$	−27.0126	−	0.498761i	−0.904956	−	0.0167091i
$892$		0			0
$893$	1.34751	−	8.50787i	0.0450929	−	0.284705i
$894$		0			0
$895$	3.70235	−	1.75634i	0.123756	−	0.0587081i
$896$		0			0
$897$	−0.202034	−	1.27559i	−0.00674573	−	0.0425908i
$898$		0			0
$899$	−7.32375	−	22.5402i	−0.244261	−	0.751757i
$900$		0			0
$901$		−	53.6870i		−	1.78857i
$902$		0			0
$903$	9.75485	+	9.75485i	0.324621	+	0.324621i
$904$		0			0
$905$	34.5498	+	18.8536i	1.14847	+	0.626714i
$906$		0			0
$907$	−11.6098	+	1.83881i	−0.385497	+	0.0610568i	−0.346175	−	0.938170i	$-0.612520\pi$
$907$	−11.6098	+	1.83881i	−0.385497	+	0.0610568i	−0.0393219	+	0.999227i	$0.512520\pi$
$908$		0			0
$909$	−1.89763	+	5.84030i	−0.0629403	+	0.193710i
$910$		0			0
$911$	−33.4277	+	24.2866i	−1.10751	+	0.804652i	−0.982270	−	0.187474i	$-0.939970\pi$
$911$	−33.4277	+	24.2866i	−1.10751	+	0.804652i	−0.125239	+	0.992127i	$0.539970\pi$
$912$		0			0
$913$	−3.36095	−	6.90865i	−0.111231	−	0.228643i
$914$		0			0
$915$	1.82412	+	2.66615i	0.0603034	+	0.0881401i
$916$		0			0
$917$	35.3543	+	69.3868i	1.16750	+	2.29135i
$918$		0			0
$919$	−19.4520	−	14.1327i	−0.641663	−	0.466196i	0.218758	−	0.975779i	$-0.429799\pi$
$919$	−19.4520	−	14.1327i	−0.641663	−	0.466196i	−0.860421	+	0.509584i	$0.829799\pi$
$920$		0			0
$921$	−4.41719	+	1.43523i	−0.145552	+	0.0472926i
$922$		0			0
$923$	−22.9260	+	22.9260i	−0.754619	+	0.754619i
$924$		0			0
$925$	−12.8928	−	14.4411i	−0.423914	−	0.474822i
$926$		0			0
$927$	27.8883	+	14.2098i	0.915973	+	0.466711i
$928$		0			0
$929$	−12.2209	+	16.8206i	−0.400953	+	0.551865i	−0.960983	−	0.276608i	$-0.910790\pi$
$929$	−12.2209	+	16.8206i	−0.400953	+	0.551865i	0.560030	+	0.828473i	$0.310790\pi$
$930$		0			0
$931$	−48.9716	−	15.9118i	−1.60498	−	0.521489i
$932$		0			0
$933$	1.92582	+	0.305020i	0.0630486	+	0.00998592i
$934$		0			0
$935$	−27.8661	+	18.3194i	−0.911320	+	0.599108i
$936$		0			0
$937$	6.04324	+	0.957154i	0.197424	+	0.0312689i	0.254363	−	0.967109i	$-0.418134\pi$
$937$	6.04324	+	0.957154i	0.197424	+	0.0312689i	−0.0569393	+	0.998378i	$0.518134\pi$
$938$		0			0
$939$	−5.79227	−	1.88202i	−0.189024	−	0.0614175i
$940$		0			0
$941$	15.5007	−	21.3348i	0.505307	−	0.695495i	−0.477812	−	0.878462i	$-0.658570\pi$
$941$	15.5007	−	21.3348i	0.505307	−	0.695495i	0.983119	+	0.182967i	$0.0585701\pi$
$942$		0			0
$943$	14.7172	+	7.49877i	0.479257	+	0.244193i
$944$		0			0
$945$	−14.4604	+	13.6645i	−0.470398	+	0.444506i
$946$		0			0
$947$	24.8115	−	24.8115i	0.806266	−	0.806266i	−0.177801	−	0.984067i	$-0.556898\pi$
$947$	24.8115	−	24.8115i	0.806266	−	0.806266i	0.984067	+	0.177801i	$0.0568983\pi$
$948$		0			0
$949$	−10.0854	+	3.27696i	−0.327387	+	0.106374i
$950$		0			0
$951$	1.76947	+	1.28559i	0.0573790	+	0.0416883i
$952$		0			0
$953$	14.2963	+	28.0581i	0.463103	+	0.908891i	0.997953	+	0.0639439i	$0.0203679\pi$
$953$	14.2963	+	28.0581i	0.463103	+	0.908891i	−0.534851	+	0.844947i	$0.679632\pi$
$954$		0			0
$955$	−2.74089	+	14.6162i	−0.0886930	+	0.472968i
$956$		0			0
$957$	1.75749	−	3.29733i	0.0568116	−	0.106588i
$958$		0			0
$959$	−27.8273	+	20.2177i	−0.898590	+	0.652864i
$960$		0			0
$961$	3.53731	−	10.8867i	0.114107	−	0.351184i
$962$		0			0
$963$	−8.70536	+	1.37879i	−0.280526	+	0.0444310i
$964$		0			0
$965$	25.9319	−	7.62186i	0.834778	−	0.245356i
$966$		0			0
$967$	34.2945	+	34.2945i	1.10284	+	1.10284i	0.994067	+	0.108771i	$0.0346915\pi$
$967$	34.2945	+	34.2945i	1.10284	+	1.10284i	0.108771	+	0.994067i	$0.465308\pi$
$968$		0			0
$969$		−	4.29948i		−	0.138119i
$970$		0			0
$971$	−7.60418	−	23.4033i	−0.244030	−	0.751046i	−0.995795	−	0.0916148i	$-0.970797\pi$
$971$	−7.60418	−	23.4033i	−0.244030	−	0.751046i	0.751765	−	0.659431i	$-0.229203\pi$
$972$		0			0
$973$	−7.98609	−	50.4222i	−0.256022	−	1.61646i
$974$		0			0
$975$	−3.12462	−	1.21459i	−0.100068	−	0.0388981i
$976$		0			0
$977$	4.35640	−	27.5052i	0.139373	−	0.879970i	−0.814588	−	0.580040i	$-0.803037\pi$
$977$	4.35640	−	27.5052i	0.139373	−	0.879970i	0.953961	−	0.299929i	$-0.0969631\pi$
$978$		0			0
$979$	1.36565	−	0.416015i	0.0436463	−	0.0132959i
$980$		0			0
$981$	−27.5032	−	37.8549i	−0.878108	−	1.20861i
$982$		0			0
$983$	17.4184	−	8.87510i	0.555560	−	0.283072i	−0.153584	−	0.988136i	$-0.549082\pi$
$983$	17.4184	−	8.87510i	0.555560	−	0.283072i	0.709144	+	0.705064i	$0.249082\pi$
$984$		0			0
$985$	−32.6117	−	25.1334i	−1.03909	−	0.800817i
$986$		0			0
$987$	1.90887	−	3.74636i	0.0607599	−	0.119248i
$988$		0			0
$989$	−17.6332			−0.560705
$990$		0			0
$991$	20.3705			0.647091			0.323545	−	0.946213i	$-0.395125\pi$
$991$	20.3705			0.647091			0.323545	+	0.946213i	$0.395125\pi$
$992$		0			0
$993$	−0.893360	+	1.75332i	−0.0283499	+	0.0556398i
$994$		0			0
$995$	3.36555	+	25.9878i	0.106695	+	0.823870i
$996$		0			0
$997$	−22.1155	+	11.2684i	−0.700405	+	0.356874i	−0.767656	−	0.640862i	$-0.778577\pi$
$997$	−22.1155	+	11.2684i	−0.700405	+	0.356874i	0.0672509	+	0.997736i	$0.478577\pi$
$998$		0			0
$999$	4.16123	+	5.72744i	0.131655	+	0.181208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.u.a.173.3	yes	48
4.3	odd	2		880.2.cm.b.833.4		48
5.2	odd	4	inner	220.2.u.a.217.4	yes	48
11.7	odd	10	inner	220.2.u.a.73.4	✓	48
20.7	even	4		880.2.cm.b.657.3		48
44.7	even	10		880.2.cm.b.513.3		48
55.7	even	20	inner	220.2.u.a.117.3	yes	48
220.7	odd	20		880.2.cm.b.337.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.u.a.73.4	✓	48	11.7	odd	10	inner
220.2.u.a.117.3	yes	48	55.7	even	20	inner
220.2.u.a.173.3	yes	48	1.1	even	1	trivial
220.2.u.a.217.4	yes	48	5.2	odd	4	inner
880.2.cm.b.337.4		48	220.7	odd	20
880.2.cm.b.513.3		48	44.7	even	10
880.2.cm.b.657.3		48	20.7	even	4
880.2.cm.b.833.4		48	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.140599 + 0.275942i) q^{3} +(-2.21755 + 0.287183i) q^{5} +(-4.33567 + 2.20914i) q^{7} +(1.70698 + 2.34946i) q^{9} +O(q^{10})\)	\(q+(-0.140599 + 0.275942i) q^{3} +(-2.21755 + 0.287183i) q^{5} +(-4.33567 + 2.20914i) q^{7} +(1.70698 + 2.34946i) q^{9} +(0.966488 + 3.17268i) q^{11} +(-0.338672 + 2.13829i) q^{13} +(0.232540 - 0.652293i) q^{15} +(-0.703440 - 4.44135i) q^{17} +(-0.954041 - 2.93624i) q^{19} -1.50700i q^{21} +(1.36205 + 1.36205i) q^{23} +(4.83505 - 1.27369i) q^{25} +(-1.80597 + 0.286037i) q^{27} +(-1.12411 + 3.45966i) q^{29} +(-5.27085 + 3.82950i) q^{31} +(-1.01136 - 0.179383i) q^{33} +(8.98015 - 6.14400i) q^{35} +(-1.75776 - 3.44980i) q^{37} +(-0.542427 - 0.394096i) q^{39} +(8.15531 - 2.64982i) q^{41} +(-6.47304 + 6.47304i) q^{43} +(-4.46004 - 4.71982i) q^{45} +(2.48598 + 1.26667i) q^{47} +(9.80329 - 13.4931i) q^{49} +(1.32446 + 0.430342i) q^{51} +(11.7922 + 1.86770i) q^{53} +(-3.05437 - 6.75802i) q^{55} +(0.944368 + 0.149573i) q^{57} +(0.864681 + 0.280952i) q^{59} +(-2.74194 + 3.77396i) q^{61} +(-12.5912 - 6.41553i) q^{63} +(0.136941 - 4.83902i) q^{65} +(-6.07207 + 6.07207i) q^{67} +(-0.567351 + 0.184344i) q^{69} +(12.1159 + 8.80269i) q^{71} +(2.22376 + 4.36438i) q^{73} +(-0.328342 + 1.51327i) q^{75} +(-11.1993 - 11.6206i) q^{77} +(6.75665 - 4.90899i) q^{79} +(-2.51725 + 7.74730i) q^{81} +(-2.28793 + 0.362373i) q^{83} +(2.83539 + 9.64689i) q^{85} +(-0.796617 - 0.796617i) q^{87} -0.430440i q^{89} +(-3.25540 - 10.0191i) q^{91} +(-0.315640 - 1.99287i) q^{93} +(2.95887 + 6.23726i) q^{95} +(-1.55943 + 9.84586i) q^{97} +(-5.80430 + 7.68642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7}+O(q^{10}) \) 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7	\( 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7} - 16 q^{15} + 10 q^{17} + 16 q^{23} - 26 q^{25} - 10 q^{27} + 16 q^{31} + 28 q^{33} - 34 q^{37} - 20 q^{41} - 56 q^{45} - 2 q^{47} - 80 q^{51} + 6 q^{53} - 18 q^{55} - 120 q^{57} - 40 q^{61} - 50 q^{63} - 72 q^{67} + 4 q^{71} - 20 q^{73} + 20 q^{75} - 36 q^{77} + 100 q^{81} + 40 q^{85} - 8 q^{91} - 14 q^{93} + 50 q^{95} + 6 q^{97}+O(q^{100}) \) 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7 - 16 * q^15 + 10 * q^17 + 16 * q^23 - 26 * q^25 - 10 * q^27 + 16 * q^31 + 28 * q^33 - 34 * q^37 - 20 * q^41 - 56 * q^45 - 2 * q^47 - 80 * q^51 + 6 * q^53 - 18 * q^55 - 120 * q^57 - 40 * q^61 - 50 * q^63 - 72 * q^67 + 4 * q^71 - 20 * q^73 + 20 * q^75 - 36 * q^77 + 100 * q^81 + 40 * q^85 - 8 * q^91 - 14 * q^93 + 50 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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