LMFDB - Embedded newform 880.2.cm.b.833.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(17,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 5, 18]))

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

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

chi := DirichletCharacter("880.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cm (of order $20$, degree $8$, not 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:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 220)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			833.4
Character	$\chi$	$=$	880.833
Dual form			880.2.cm.b.337.4

$q$-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 $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{10}\right)$	$1$

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
$3$	0.140599	−	0.275942i	0.0811751	−	0.159315i	−0.846851	−	0.531830i	$-0.821504\pi$
$3$	0.140599	−	0.275942i	0.0811751	−	0.159315i	0.928026	+	0.372515i	$0.121504\pi$
$4$		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	$-0.278517\pi$
$7$	4.33567	−	2.20914i	1.63873	−	0.834975i	0.997723	−	0.0674404i	$-0.0214832\pi$
$8$		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	$0.0152272\pi$
$19$	0.954041	+	2.93624i	0.218872	+	0.673619i	−0.779984	+	0.625799i	$0.784773\pi$
$20$		0			0
$21$		−	1.50700i		−	0.328854i
$22$		0			0
$23$	−1.36205	−	1.36205i	−0.284008	−	0.284008i	0.550697	−	0.834705i	$-0.314362\pi$
$23$	−1.36205	−	1.36205i	−0.284008	−	0.284008i	−0.834705	+	0.550697i	$0.814362\pi$
$24$		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	−0.00334443	−	0.999994i	$-0.501065\pi$
$31$	5.27085	−	3.82950i	0.946673	−	0.687798i	0.950018	+	0.312196i	$0.101065\pi$
$32$		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	−0.0127891	−	0.999918i	$-0.504071\pi$
$43$	6.47304	−	6.47304i	0.987129	−	0.987129i	0.999918	+	0.0127891i	$0.00407102\pi$
$44$		0			0
$45$	−4.46004	−	4.71982i	−0.664863	−	0.703589i
$46$		0			0
$47$	−2.48598	−	1.26667i	−0.362617	−	0.184763i	0.263183	−	0.964746i	$-0.415228\pi$
$47$	−2.48598	−	1.26667i	−0.362617	−	0.184763i	−0.625801	+	0.779983i	$0.715228\pi$
$48$		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	0.252189	−	0.967678i	$-0.418849\pi$
$59$	−0.864681	−	0.280952i	−0.112572	−	0.0365768i	−0.364761	+	0.931101i	$0.618849\pi$
$60$		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	−0.231107	−	0.972928i	$-0.574235\pi$
$67$	6.07207	−	6.07207i	0.741822	−	0.741822i	0.972928	+	0.231107i	$0.0742346\pi$
$68$		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	$-0.951634\pi$
$71$	−12.1159	−	8.80269i	−1.43789	−	1.04469i	−0.449411	−	0.893325i	$-0.648366\pi$
$72$		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	−0.898966	−	0.438018i	$-0.855681\pi$
$79$	−6.75665	+	4.90899i	−0.760182	+	0.552305i	0.138784	+	0.990323i	$0.455681\pi$
$80$		0			0
$81$	−2.51725	+	7.74730i	−0.279694	+	0.860811i
$82$		0			0
$83$	2.28793	−	0.362373i	0.251133	−	0.0397756i	−0.0295986	−	0.999562i	$-0.509423\pi$
$83$	2.28793	−	0.362373i	0.251133	−	0.0397756i	0.280732	+	0.959786i	$0.409423\pi$
$84$		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	−0.857815	−	0.513959i	$-0.828178\pi$
$103$	−9.60312	+	4.89304i	−0.946224	+	0.482125i	−0.0884092	+	0.996084i	$0.528178\pi$
$104$		0			0
$105$	0.432784	+	3.34184i	0.0422354	+	0.326130i
$106$		0			0
$107$	1.37786	−	2.70419i	0.133202	−	0.261424i	−0.814765	−	0.579791i	$-0.803134\pi$
$107$	1.37786	−	2.70419i	0.133202	−	0.261424i	0.947968	+	0.318367i	$0.103134\pi$
$108$		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	$0.139569\pi$
$127$	1.97787	+	12.4878i	0.175508	+	1.10811i	−0.729896	+	0.683558i	$0.760431\pi$
$128$		0			0
$129$	−0.876077	−	2.69629i	−0.0771343	−	0.237395i
$130$		0			0
$131$			16.0037i			1.39825i	0.715000	+	0.699124i	$0.246427\pi$
$131$			16.0037i			1.39825i	−0.715000	+	0.699124i	$0.753573\pi$
$132$		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	$-0.753230\pi$
$139$	3.24197	−	9.97775i	0.274980	−	0.846301i	0.989225	−	0.146405i	$-0.0467704\pi$
$140$		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	−0.271975	−	0.962304i	$-0.587677\pi$
$151$	0.904678	−	0.293948i	0.0736217	−	0.0239211i	0.345596	+	0.938383i	$0.387677\pi$
$152$		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	0.344536	−	0.938773i	$-0.388036\pi$
$163$	4.87848	+	0.772675i	0.382112	+	0.0605206i	0.0375762	+	0.999294i	$0.488036\pi$
$164$		0			0
$165$	2.29426	+	0.107343i	0.178608	+	0.00835667i
$166$		0			0
$167$	0.213734	+	0.0338522i	0.0165393	+	0.00261956i	0.164699	−	0.986344i	$-0.447335\pi$
$167$	0.213734	+	0.0338522i	0.0165393	+	0.00261956i	−0.148159	+	0.988964i	$0.547335\pi$
$168$		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	−0.243156	−	0.969987i	$-0.578183\pi$
$179$	1.74291	−	0.566305i	0.130271	−	0.0423277i	0.373427	+	0.927660i	$0.378183\pi$
$180$		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	−0.997469	−	0.0711088i	$-0.977346\pi$
$191$	−2.05511	+	6.32499i	−0.148703	+	0.457660i	0.848766	+	0.528769i	$0.177346\pi$
$192$		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	$0.136350\pi$
$199$			11.7192i			0.830750i	−0.909650	+	0.415375i	$0.863650\pi$
$200$		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	0.345061	−	0.938580i	$-0.387858\pi$
$211$	−9.50297	−	13.0797i	−0.654211	−	0.900445i	−0.999273	+	0.0381354i	$0.987858\pi$
$212$		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	$0.448769\pi$
$223$	−10.9386	+	21.4682i	−0.732503	+	1.43762i	−0.892755	+	0.450542i	$0.851231\pi$
$224$		0			0
$225$	11.2458	+	9.18559i	0.749720	+	0.612373i
$226$		0			0
$227$	−10.7589	+	5.48194i	−0.714094	+	0.363849i	−0.772993	−	0.634415i	$-0.781241\pi$
$227$	−10.7589	+	5.48194i	−0.714094	+	0.363849i	0.0588986	+	0.998264i	$0.481241\pi$
$228$		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	0.893559	−	0.448945i	$-0.148200\pi$
$239$	−1.44128	−	4.43580i	−0.0932286	−	0.286928i	−0.986788	+	0.162017i	$0.948200\pi$
$240$		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	−0.808217	−	0.588885i	$-0.799567\pi$
$251$	−7.88833	+	5.73121i	−0.497907	+	0.361750i	0.310310	+	0.950635i	$0.399567\pi$
$252$		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	−0.961153	−	0.276016i	$-0.910986\pi$
$263$	−11.1111	+	11.1111i	−0.685138	+	0.685138i	0.276016	+	0.961153i	$0.410986\pi$
$264$		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	0.668647	−	0.743580i	$-0.266874\pi$
$271$	12.7174	+	4.13215i	0.772529	+	0.251010i	0.103882	+	0.994590i	$0.466874\pi$
$272$		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	−0.0685734	−	0.997646i	$-0.521845\pi$
$283$	−15.4094	−	7.85147i	−0.915992	−	0.466721i	−0.847419	+	0.530925i	$0.821845\pi$
$284$		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	0.336467	−	0.941695i	$-0.390768\pi$
$307$	−10.6045	−	10.6045i	−0.605228	−	0.605228i	−0.941695	+	0.336467i	$0.890768\pi$
$308$		0			0
$309$			3.33786i			0.189884i
$310$		0			0
$311$	1.94555	+	5.98778i	0.110322	+	0.339536i	0.990943	−	0.134286i	$-0.0428741\pi$
$311$	1.94555	+	5.98778i	0.110322	+	0.339536i	−0.880621	+	0.473822i	$0.842874\pi$
$312$		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	$-0.555870\pi$
$331$	−6.35394			−0.349244			−0.174622	+	0.984636i	$0.555870\pi$
$332$		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	$-0.902790\pi$
$347$	−2.60029	−	16.4176i	−0.139591	−	0.881341i	0.814138	−	0.580672i	$-0.197210\pi$
$348$		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	−0.948743	−	0.316048i	$-0.897644\pi$
$359$	0.0866807	−	0.266776i	0.00457483	−	0.0140799i	0.953318	+	0.301969i	$0.0976438\pi$
$360$		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	0.598391	−	0.801204i	$-0.295807\pi$
$367$	−7.69206	−	15.0965i	−0.401522	−	0.788032i	−0.999913	+	0.0131721i	$0.995807\pi$
$368$		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	−0.702200	−	0.711980i	$-0.747799\pi$
$379$	3.73639	−	5.14270i	0.191925	−	0.264163i	0.894125	+	0.447818i	$0.147799\pi$
$380$		0			0
$381$	3.72399	+	1.21000i	0.190786	+	0.0619900i
$382$		0			0
$383$	35.4492	+	5.61460i	1.81137	+	0.286893i	0.968094	−	0.250589i	$-0.0806242\pi$
$383$	35.4492	+	5.61460i	1.81137	+	0.286893i	0.843275	+	0.537482i	$0.180624\pi$
$384$		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	$0.304872\pi$
$419$			33.4847i			1.63584i	−0.575334	+	0.817918i	$0.695128\pi$
$420$		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	$-0.990523\pi$
$431$	−14.9266	−	20.5447i	−0.718989	−	0.989604i	0.280567	−	0.959834i	$-0.409477\pi$
$432$		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	$-0.809469\pi$
$439$	−34.6192			−1.65229			−0.826143	+	0.563461i	$0.809469\pi$
$440$		0			0
$441$	48.4354			2.30645
$442$		0			0
$443$	−11.3725	+	22.3198i	−0.540324	+	1.06045i	0.445908	+	0.895079i	$0.352881\pi$
$443$	−11.3725	+	22.3198i	−0.540324	+	1.06045i	−0.986232	+	0.165367i	$0.947119\pi$
$444$		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	0.686890	−	0.726762i	$-0.258976\pi$
$463$	−0.857939	−	0.857939i	−0.0398718	−	0.0398718i	−0.726762	+	0.686890i	$0.758976\pi$
$464$		0			0
$465$	1.27227	+	4.32865i	0.0590000	+	0.200736i
$466$		0			0
$467$	21.2927	−	3.37244i	0.985310	−	0.156058i	0.357070	−	0.934078i	$-0.383776\pi$
$467$	21.2927	−	3.37244i	0.985310	−	0.156058i	0.628240	+	0.778020i	$0.283776\pi$
$468$		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	0.608888	−	0.793256i	$-0.291616\pi$
$479$	0.932642	+	0.677604i	0.0426135	+	0.0309605i	−0.566275	+	0.824217i	$0.691616\pi$
$480$		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	0.329289	−	0.944229i	$-0.393191\pi$
$487$	−5.31965	−	2.71050i	−0.241056	−	0.122824i	−0.570346	+	0.821405i	$0.693191\pi$
$488$		0			0
$489$	0.899125	−	1.23754i	0.0406598	−	0.0559635i
$490$		0			0
$491$	−21.5993	−	7.01804i	−0.974763	−	0.316720i	−0.222026	−	0.975041i	$-0.571267\pi$
$491$	−21.5993	−	7.01804i	−0.974763	−	0.316720i	−0.752737	+	0.658321i	$0.771267\pi$
$492$		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	0.627312	−	0.778768i	$-0.284155\pi$
$499$	15.1246	+	4.91428i	0.677070	+	0.219993i	0.0497577	+	0.998761i	$0.484155\pi$
$500$		0			0
$501$	0.0393922	−	0.0542187i	0.00175991	−	0.00242231i
$502$		0			0
$503$	9.63633	+	4.90996i	0.429663	+	0.218924i	0.655428	−	0.755258i	$-0.272488\pi$
$503$	9.63633	+	4.90996i	0.429663	+	0.218924i	−0.225765	+	0.974182i	$0.572488\pi$
$504$		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	−0.207050	−	0.978330i	$-0.566386\pi$
$523$	−2.32454	+	0.368170i	−0.101645	+	0.0160990i	0.105405	+	0.994429i	$0.466386\pi$
$524$		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	−0.943310	−	0.331914i	$-0.892306\pi$
$547$	−2.81409	+	5.52296i	−0.120322	+	0.236145i	0.822988	+	0.568059i	$0.192306\pi$
$548$		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	−0.985596	−	0.169119i	$-0.945908\pi$
$563$	0.0954339	−	0.602546i	0.00402206	−	0.0253943i	0.989618	+	0.143724i	$0.0459079\pi$
$564$		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	$-0.981484\pi$
$571$		−	2.77837i		−	0.116271i	0.998309	−	0.0581356i	$-0.0185156\pi$
$572$		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	$0.0514802\pi$
$587$	13.0131	+	25.5396i	0.537108	+	1.05413i	−0.449842	+	0.893108i	$0.648520\pi$
$588$		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	−0.420506	−	0.907290i	$-0.638147\pi$
$599$	14.0073	−	19.2794i	0.572322	−	0.787733i	0.992827	+	0.119557i	$0.0381473\pi$
$600$		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	0.707109	−	0.707104i	$-0.249999\pi$
$607$	28.6065	+	4.53083i	1.16110	+	0.183901i	0.453994	+	0.891005i	$0.349999\pi$
$608$		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	0.207953	−	0.978139i	$-0.433320\pi$
$619$	23.6638	−	7.68882i	0.951127	−	0.309040i	0.743173	+	0.669099i	$0.233320\pi$
$620$		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	−0.963153	−	0.268953i	$-0.913322\pi$
$631$	−0.649576	+	1.99919i	−0.0258592	+	0.0795864i	0.937294	+	0.348540i	$0.113322\pi$
$632$		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	$-0.866911\pi$
$643$	−4.31582	−	27.2490i	−0.170199	−	1.07460i	0.743658	−	0.668560i	$-0.233089\pi$
$644$		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	$0.156951\pi$
$647$	−2.62389	+	16.5666i	−0.103156	+	0.651299i	−0.984037	+	0.177963i	$0.943049\pi$
$648$		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	$-0.505231\pi$
$659$	−0.843775			−0.0328688			−0.0164344	+	0.999865i	$0.505231\pi$
$660$		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	$-0.968209\pi$
$683$	−28.6099	−	28.6099i	−1.09473	−	1.09473i	−0.0997098	−	0.995017i	$-0.531791\pi$
$684$		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	−0.691921	−	0.721973i	$-0.743235\pi$
$691$	−5.75944	+	4.18448i	−0.219100	+	0.159185i	0.472822	+	0.881158i	$0.343235\pi$
$692$		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	0.172605	−	0.984991i	$-0.444781\pi$
$719$	−7.15180	−	2.32376i	−0.266717	−	0.0866616i	−0.439322	+	0.898329i	$0.644781\pi$
$720$		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	$-0.395881\pi$
$727$	34.1964	−	34.1964i	1.26828	−	1.26828i	0.946979	−	0.321296i	$-0.104119\pi$
$728$		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	−0.928652	−	0.370951i	$-0.879032\pi$
$739$	−23.4555	+	17.0414i	−0.862826	+	0.626880i	0.0658264	+	0.997831i	$0.479032\pi$
$740$		0			0
$741$	−0.639662	+	1.96868i	−0.0234986	+	0.0723211i
$742$		0			0
$743$	−10.5152	+	1.66544i	−0.385765	+	0.0610992i	−0.346305	−	0.938122i	$-0.612564\pi$
$743$	−10.5152	+	1.66544i	−0.385765	+	0.0610992i	−0.0394600	+	0.999221i	$0.512564\pi$
$744$		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	$0.151126\pi$
$751$	12.0184	+	36.9889i	0.438559	+	1.34975i	−0.450836	+	0.892607i	$0.648874\pi$
$752$		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	$-0.960990\pi$
$787$	−2.42251	−	15.2951i	−0.0863530	−	0.545212i	0.906147	−	0.422964i	$-0.139010\pi$
$788$		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	−0.526139	−	0.850399i	$-0.676361\pi$
$811$	−12.8704	+	4.18186i	−0.451942	+	0.146845i	0.0741968	+	0.997244i	$0.476361\pi$
$812$		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	−0.643845	−	0.765156i	$-0.722662\pi$
$823$	−42.8204	−	6.78208i	−1.49262	−	0.236409i	−0.848779	+	0.528747i	$0.822662\pi$
$824$		0			0
$825$	−5.11847	+	0.420834i	−0.178202	+	0.0146516i
$826$		0			0
$827$	−43.5841	−	6.90305i	−1.51557	−	0.240042i	−0.657451	−	0.753497i	$-0.728366\pi$
$827$	−43.5841	−	6.90305i	−1.51557	−	0.240042i	−0.858117	+	0.513455i	$0.828366\pi$
$828$		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	−0.393128	−	0.919484i	$-0.628607\pi$
$839$	−4.94488	+	1.60669i	−0.170716	+	0.0554690i	0.222412	+	0.974953i	$0.428607\pi$
$840$		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	$0.0986188\pi$
$859$			17.8717i			0.609775i	−0.952388	+	0.304887i	$0.901381\pi$
$860$		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	$0.209223\pi$
$863$	6.68465	+	42.2052i	0.227548	+	1.43668i	−0.564101	+	0.825706i	$0.690777\pi$
$864$		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	−0.614398	−	0.788997i	$-0.710601\pi$
$883$	11.4418	−	22.4558i	0.385048	−	0.755699i	0.999445	+	0.0332976i	$0.0106009\pi$
$884$		0			0
$885$	0.384336	−	0.498692i	0.0129193	−	0.0167634i
$886$		0			0
$887$	−32.6198	+	16.6206i	−1.09527	+	0.558066i	−0.905750	−	0.423812i	$-0.860692\pi$
$887$	−32.6198	+	16.6206i	−1.09527	+	0.558066i	−0.189516	+	0.981878i	$0.560692\pi$
$888$		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	0.0393219	−	0.999227i	$-0.487480\pi$
$907$	11.6098	−	1.83881i	0.385497	−	0.0610568i	0.346175	+	0.938170i	$0.387480\pi$
$908$		0			0
$909$	−1.89763	+	5.84030i	−0.0629403	+	0.193710i
$910$		0			0
$911$	33.4277	−	24.2866i	1.10751	−	0.804652i	0.125239	−	0.992127i	$-0.460030\pi$
$911$	33.4277	−	24.2866i	1.10751	−	0.804652i	0.982270	+	0.187474i	$0.0600301\pi$
$912$		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	0.860421	−	0.509584i	$-0.170201\pi$
$919$	19.4520	+	14.1327i	0.641663	+	0.466196i	−0.218758	+	0.975779i	$0.570201\pi$
$920$		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	−0.984067	−	0.177801i	$-0.943102\pi$
$947$	−24.8115	+	24.8115i	−0.806266	+	0.806266i	0.177801	+	0.984067i	$0.443102\pi$
$948$		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	$-0.965308\pi$
$967$	−34.2945	−	34.2945i	−1.10284	−	1.10284i	−0.108771	−	0.994067i	$-0.534692\pi$
$968$		0			0
$969$		−	4.29948i		−	0.138119i
$970$		0			0
$971$	7.60418	+	23.4033i	0.244030	+	0.751046i	0.995795	+	0.0916148i	$0.0292029\pi$
$971$	7.60418	+	23.4033i	0.244030	+	0.751046i	−0.751765	+	0.659431i	$0.770797\pi$
$972$		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	−0.709144	−	0.705064i	$-0.750918\pi$
$983$	−17.4184	+	8.87510i	−0.555560	+	0.283072i	0.153584	+	0.988136i	$0.450918\pi$
$984$		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	$-0.604875\pi$
$991$	−20.3705			−0.647091			−0.323545	+	0.946213i	$0.604875\pi$
$992$		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	880.2.cm.b.833.4		48
4.3	odd	2		220.2.u.a.173.3	yes	48
5.2	odd	4	inner	880.2.cm.b.657.3		48
11.7	odd	10	inner	880.2.cm.b.513.3		48
20.7	even	4		220.2.u.a.217.4	yes	48
44.7	even	10		220.2.u.a.73.4	✓	48
55.7	even	20	inner	880.2.cm.b.337.4		48
220.7	odd	20		220.2.u.a.117.3	yes	48

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cm (of order \(20\), degree \(8\), not 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

Related objects

Downloads

Learn more