LMFDB - Embedded newform 220.2.u.a.217.4

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			217.4
Character	$\chi$	$=$	220.217
Dual form			220.2.u.a.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.275942 + 0.140599i) q^{3} +(-0.412133 - 2.19776i) q^{5} +(-2.20914 - 4.33567i) q^{7} +(-1.70698 - 2.34946i) q^{9} +O(q^{10})$	\(q+(0.275942 + 0.140599i) q^{3} +(-0.412133 - 2.19776i) q^{5} +(-2.20914 - 4.33567i) q^{7} +(-1.70698 - 2.34946i) q^{9} +(0.966488 + 3.17268i) q^{11} +(2.13829 + 0.338672i) q^{13} +(0.195279 - 0.664400i) q^{15} +(4.44135 - 0.703440i) q^{17} +(0.954041 + 2.93624i) q^{19} -1.50700i q^{21} +(1.36205 - 1.36205i) q^{23} +(-4.66029 + 1.81154i) q^{25} +(-0.286037 - 1.80597i) q^{27} +(1.12411 - 3.45966i) q^{29} +(-5.27085 + 3.82950i) q^{31} +(-0.179383 + 1.01136i) q^{33} +(-8.61831 + 6.64202i) q^{35} +(3.44980 - 1.75776i) q^{37} +(0.542427 + 0.394096i) q^{39} +(8.15531 - 2.64982i) q^{41} +(6.47304 + 6.47304i) q^{43} +(-4.46004 + 4.71982i) q^{45} +(-1.26667 + 2.48598i) q^{47} +(-9.80329 + 13.4931i) q^{49} +(1.32446 + 0.430342i) q^{51} +(1.86770 - 11.7922i) q^{53} +(6.57447 - 3.43167i) q^{55} +(-0.149573 + 0.944368i) q^{57} +(-0.864681 - 0.280952i) q^{59} +(-2.74194 + 3.77396i) q^{61} +(-6.41553 + 12.5912i) q^{63} +(-0.136941 - 4.83902i) q^{65} +(-6.07207 - 6.07207i) q^{67} +(0.567351 - 0.184344i) q^{69} +(12.1159 + 8.80269i) q^{71} +(4.36438 - 2.22376i) q^{73} +(-1.54067 - 0.155355i) q^{75} +(11.6206 - 11.1993i) q^{77} +(-6.75665 + 4.90899i) q^{79} +(-2.51725 + 7.74730i) q^{81} +(0.362373 + 2.28793i) q^{83} +(-3.37642 - 9.47110i) q^{85} +(0.796617 - 0.796617i) q^{87} +0.430440i q^{89} +(-3.25540 - 10.0191i) q^{91} +(-1.99287 + 0.315640i) q^{93} +(6.05995 - 3.30687i) q^{95} +(-9.84586 - 1.55943i) q^{97} +(5.80430 - 7.68642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

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

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
$3$	0.275942	+	0.140599i	0.159315	+	0.0811751i	0.531830	−	0.846851i	$-0.321504\pi$
$3$	0.275942	+	0.140599i	0.159315	+	0.0811751i	−0.372515	+	0.928026i	$0.621504\pi$
$4$		0			0
$5$	−0.412133	−	2.19776i	−0.184312	−	0.982868i
$5$	−0.412133	−	2.19776i	−0.184312	−	0.982868i
$6$		0			0
$7$	−2.20914	−	4.33567i	−0.834975	−	1.63873i	−0.767535	−	0.641007i	$-0.778517\pi$
$7$	−2.20914	−	4.33567i	−0.834975	−	1.63873i	−0.0674404	−	0.997723i	$-0.521483\pi$
$8$		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
$13$	2.13829	+	0.338672i	0.593055	+	0.0939307i	0.445745	−	0.895160i	$-0.352939\pi$
$13$	2.13829	+	0.338672i	0.593055	+	0.0939307i	0.147309	+	0.989090i	$0.452939\pi$
$14$		0			0
$15$	0.195279	−	0.664400i	0.0504208	−	0.171547i
$16$		0			0
$17$	4.44135	−	0.703440i	1.07718	−	0.170609i	0.407463	−	0.913222i	$-0.366413\pi$
$17$	4.44135	−	0.703440i	1.07718	−	0.170609i	0.669721	+	0.742612i	$0.266413\pi$
$18$		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	$-0.685638\pi$
$23$	1.36205	−	1.36205i	0.284008	−	0.284008i	0.834705	+	0.550697i	$0.185638\pi$
$24$		0			0
$25$	−4.66029	+	1.81154i	−0.932059	+	0.362308i
$26$		0			0
$27$	−0.286037	−	1.80597i	−0.0550478	−	0.347558i
$28$		0			0
$29$	1.12411	−	3.45966i	0.208743	−	0.642443i	−0.790796	−	0.612079i	$-0.790333\pi$
$29$	1.12411	−	3.45966i	0.208743	−	0.642443i	0.999539	−	0.0303641i	$-0.00966669\pi$
$30$		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
$33$	−0.179383	+	1.01136i	−0.0312265	+	0.176056i
$34$		0			0
$35$	−8.61831	+	6.64202i	−1.45676	+	1.12271i
$36$		0			0
$37$	3.44980	−	1.75776i	0.567144	−	0.288974i	−0.146813	−	0.989164i	$-0.546901\pi$
$37$	3.44980	−	1.75776i	0.567144	−	0.288974i	0.713957	+	0.700190i	$0.246901\pi$
$38$		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	$-0.00407102\pi$
$43$	6.47304	+	6.47304i	0.987129	+	0.987129i	−0.0127891	+	0.999918i	$0.504071\pi$
$44$		0			0
$45$	−4.46004	+	4.71982i	−0.664863	+	0.703589i
$46$		0			0
$47$	−1.26667	+	2.48598i	−0.184763	+	0.362617i	−0.964746	−	0.263183i	$-0.915228\pi$
$47$	−1.26667	+	2.48598i	−0.184763	+	0.362617i	0.779983	+	0.625801i	$0.215228\pi$
$48$		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
$53$	1.86770	−	11.7922i	0.256548	−	1.61978i	−0.437063	−	0.899431i	$-0.643981\pi$
$53$	1.86770	−	11.7922i	0.256548	−	1.61978i	0.693611	−	0.720350i	$-0.256019\pi$
$54$		0			0
$55$	6.57447	−	3.43167i	0.886501	−	0.462727i
$56$		0			0
$57$	−0.149573	+	0.944368i	−0.0198115	+	0.125085i
$58$		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
$63$	−6.41553	+	12.5912i	−0.808280	+	1.58634i
$64$		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	$-0.425765\pi$
$67$	−6.07207	−	6.07207i	−0.741822	−	0.741822i	−0.972928	+	0.231107i	$0.925765\pi$
$68$		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
$73$	4.36438	−	2.22376i	0.510812	−	0.260272i	−0.179533	−	0.983752i	$-0.557459\pi$
$73$	4.36438	−	2.22376i	0.510812	−	0.260272i	0.690345	+	0.723480i	$0.257459\pi$
$74$		0			0
$75$	−1.54067	−	0.155355i	−0.177901	−	0.0179388i
$76$		0			0
$77$	11.6206	−	11.1993i	1.32429	−	1.27627i
$78$		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
$83$	0.362373	+	2.28793i	0.0397756	+	0.251133i	0.999562	−	0.0295986i	$-0.00942289\pi$
$83$	0.362373	+	2.28793i	0.0397756	+	0.251133i	−0.959786	+	0.280732i	$0.909423\pi$
$84$		0			0
$85$	−3.37642	−	9.47110i	−0.366224	−	1.02728i
$86$		0			0
$87$	0.796617	−	0.796617i	0.0854063	−	0.0854063i
$88$		0			0
$89$			0.430440i			0.0456265i	0.999740	+	0.0228133i	$0.00726232\pi$
$89$			0.430440i			0.0456265i	−0.999740	+	0.0228133i	$0.992738\pi$
$90$		0			0
$91$	−3.25540	−	10.0191i	−0.341259	−	1.05029i
$92$		0			0
$93$	−1.99287	+	0.315640i	−0.206651	+	0.0327304i
$94$		0			0
$95$	6.05995	−	3.30687i	0.621738	−	0.339278i
$96$		0			0
$97$	−9.84586	−	1.55943i	−0.999696	−	0.158336i	−0.364925	−	0.931037i	$-0.618905\pi$
$97$	−9.84586	−	1.55943i	−0.999696	−	0.158336i	−0.634771	+	0.772701i	$0.718905\pi$
$98$		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
$103$	−4.89304	−	9.60312i	−0.482125	−	0.946224i	−0.996084	−	0.0884092i	$-0.971822\pi$
$103$	−4.89304	−	9.60312i	−0.482125	−	0.946224i	0.513959	−	0.857815i	$-0.328178\pi$
$104$		0			0
$105$	−3.31202	+	0.621083i	−0.323220	+	0.0606115i
$106$		0			0
$107$	−2.70419	−	1.37786i	−0.261424	−	0.133202i	0.318367	−	0.947968i	$-0.396866\pi$
$107$	−2.70419	−	1.37786i	−0.261424	−	0.133202i	−0.579791	+	0.814765i	$0.696866\pi$
$108$		0			0
$109$	16.1122			1.54327			0.771633	−	0.636068i	$-0.219440\pi$
$109$	16.1122			1.54327			0.771633	+	0.636068i	$0.219440\pi$
$110$		0			0
$111$	1.19909			0.113812
$112$		0			0
$113$	5.81102	+	2.96086i	0.546655	+	0.278534i	0.705429	−	0.708780i	$-0.250754\pi$
$113$	5.81102	+	2.96086i	0.546655	+	0.278534i	−0.158775	+	0.987315i	$0.550754\pi$
$114$		0			0
$115$	−3.55481	−	2.43212i	−0.331488	−	0.226796i
$116$		0			0
$117$	−2.85432	−	5.60193i	−0.263882	−	0.517898i
$118$		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
$123$	2.62295	+	0.415435i	0.236504	+	0.0374585i
$124$		0			0
$125$	5.90199	+	9.49561i	0.527890	+	0.849313i
$126$		0			0
$127$	12.4878	−	1.97787i	1.10811	−	0.175508i	0.424553	−	0.905403i	$-0.360431\pi$
$127$	12.4878	−	1.97787i	1.10811	−	0.175508i	0.683558	+	0.729896i	$0.260431\pi$
$128$		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
$135$	−3.85119	+	1.37294i	−0.331458	+	0.118164i
$136$		0			0
$137$	1.10578	+	6.98164i	0.0944734	+	0.596482i	0.988821	+	0.149109i	$0.0476404\pi$
$137$	1.10578	+	6.98164i	0.0944734	+	0.596482i	−0.894347	+	0.447373i	$0.852360\pi$
$138$		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
$143$	0.992133	+	7.11143i	0.0829663	+	0.594688i
$144$		0			0
$145$	−8.06679	−	1.04469i	−0.669911	−	0.0867566i
$146$		0			0
$147$	−4.60226	+	2.34497i	−0.379588	+	0.193410i
$148$		0			0
$149$	13.7221	+	9.96972i	1.12416	+	0.816751i	0.984835	−	0.173495i	$-0.0555061\pi$
$149$	13.7221	+	9.96972i	1.12416	+	0.816751i	0.139327	+	0.990246i	$0.455506\pi$
$150$		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
$157$	−9.91931	+	19.4677i	−0.791647	+	1.55369i	0.0405259	+	0.999178i	$0.487097\pi$
$157$	−9.91931	+	19.4677i	−0.791647	+	1.55369i	−0.832173	+	0.554516i	$0.812903\pi$
$158$		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
$163$	−0.772675	+	4.87848i	−0.0605206	+	0.382112i	0.938773	+	0.344536i	$0.111964\pi$
$163$	−0.772675	+	4.87848i	−0.0605206	+	0.382112i	−0.999294	+	0.0375762i	$0.988036\pi$
$164$		0			0
$165$	2.29666	−	0.0225764i	0.178795	−	0.00175757i
$166$		0			0
$167$	0.0338522	−	0.213734i	0.00261956	−	0.0165393i	−0.986344	−	0.164699i	$-0.947335\pi$
$167$	0.0338522	−	0.213734i	0.00261956	−	0.0165393i	0.988964	+	0.148159i	$0.0473349\pi$
$168$		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
$173$	−1.32259	+	2.59574i	−0.100555	+	0.197350i	−0.935803	−	0.352523i	$-0.885324\pi$
$173$	−1.32259	+	2.59574i	−0.100555	+	0.197350i	0.835248	+	0.549873i	$0.185324\pi$
$174$		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
$183$	−1.28723	+	0.655879i	−0.0951551	+	0.0484839i
$184$		0			0
$185$	−5.28492	−	6.85740i	−0.388555	−	0.504166i
$186$		0			0
$187$	6.52430	+	13.4111i	0.477104	+	0.980717i
$188$		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
$193$	1.89093	+	11.9388i	0.136112	+	0.859376i	0.957379	+	0.288833i	$0.0932673\pi$
$193$	1.89093	+	11.9388i	0.136112	+	0.859376i	−0.821268	+	0.570543i	$0.806733\pi$
$194$		0			0
$195$	0.642576	−	1.35454i	0.0460158	−	0.0970009i
$196$		0			0
$197$	−13.0200	+	13.0200i	−0.927638	+	0.927638i	−0.997553	−	0.0699150i	$-0.977727\pi$
$197$	−13.0200	+	13.0200i	−0.927638	+	0.927638i	0.0699150	+	0.997553i	$0.477727\pi$
$198$		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
$203$	−17.4833	+	2.76908i	−1.22709	+	0.194351i
$204$		0			0
$205$	−9.18474	−	16.8313i	−0.641490	−	1.17555i
$206$		0			0
$207$	−5.52508	−	0.875087i	−0.384020	−	0.0608228i
$208$		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
$213$	2.10562	+	4.13252i	0.144275	+	0.283155i
$214$		0			0
$215$	11.5584	−	16.8939i	0.788278	−	1.15216i
$216$		0			0
$217$	28.2475	+	14.3928i	1.91756	+	0.977048i
$218$		0			0
$219$	1.51697			0.102508
$220$		0			0
$221$	9.73512			0.654855
$222$		0			0
$223$	−21.4682	−	10.9386i	−1.43762	−	0.732503i	−0.450542	−	0.892755i	$-0.648769\pi$
$223$	−21.4682	−	10.9386i	−1.43762	−	0.732503i	−0.987076	+	0.160252i	$0.948769\pi$
$224$		0			0
$225$	12.2112	+	7.85689i	0.814077	+	0.523793i
$226$		0			0
$227$	5.48194	+	10.7589i	0.363849	+	0.714094i	0.998264	−	0.0588986i	$-0.0187589\pi$
$227$	5.48194	+	10.7589i	0.363849	+	0.714094i	−0.634415	+	0.772993i	$0.718759\pi$
$228$		0			0
$229$	8.41255	+	11.5789i	0.555917	+	0.765154i	0.990800	−	0.135333i	$-0.0432104\pi$
$229$	8.41255	+	11.5789i	0.555917	+	0.765154i	−0.434883	+	0.900487i	$0.643210\pi$
$230$		0			0
$231$	4.78122	−	1.45649i	0.314581	−	0.0958303i
$232$		0			0
$233$	−19.2940	−	3.05586i	−1.26399	−	0.200196i	−0.511778	−	0.859118i	$-0.671013\pi$
$233$	−19.2940	−	3.05586i	−1.26399	−	0.200196i	−0.752212	+	0.658921i	$0.771013\pi$
$234$		0			0
$235$	5.98562	+	1.75928i	0.390459	+	0.114763i
$236$		0			0
$237$	−2.55464	+	0.404616i	−0.165942	+	0.0262826i
$238$		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
$245$	33.6948	+	15.9843i	2.15268	+	1.02120i
$246$		0			0
$247$	1.04560	+	6.60163i	0.0665297	+	0.420052i
$248$		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
$253$	5.63777	+	3.00495i	0.354443	+	0.188920i
$254$		0			0
$255$	0.399936	−	3.08820i	0.0250450	−	0.193390i
$256$		0			0
$257$	−6.24401	+	3.18148i	−0.389491	+	0.198455i	−0.637759	−	0.770236i	$-0.720138\pi$
$257$	−6.24401	+	3.18148i	−0.389491	+	0.198455i	0.248269	+	0.968691i	$0.420138\pi$
$258$		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	$-0.410986\pi$
$263$	−11.1111	−	11.1111i	−0.685138	−	0.685138i	−0.961153	+	0.276016i	$0.910986\pi$
$264$		0			0
$265$	−26.6861	+	0.755197i	−1.63931	+	0.0463914i
$266$		0			0
$267$	−0.0605196	+	0.118776i	−0.00370374	+	0.00726899i
$268$		0			0
$269$	12.6534	−	17.4159i	0.771491	−	1.06187i	−0.224680	−	0.974433i	$-0.572134\pi$
$269$	12.6534	−	17.4159i	0.771491	−	1.06187i	0.996170	−	0.0874331i	$-0.0278664\pi$
$270$		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
$273$	0.510378	−	3.22240i	0.0308895	−	0.195028i
$274$		0			0
$275$	−10.2515	−	13.0348i	−0.618192	−	0.786027i
$276$		0			0
$277$	0.459612	−	2.90188i	0.0276154	−	0.174357i	−0.970026	−	0.243002i	$-0.921868\pi$
$277$	0.459612	−	2.90188i	0.0276154	−	0.174357i	0.997641	+	0.0686455i	$0.0218677\pi$
$278$		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
$283$	7.85147	−	15.4094i	0.466721	−	0.915992i	−0.530925	−	0.847419i	$-0.678155\pi$
$283$	7.85147	−	15.4094i	0.466721	−	0.915992i	0.997646	−	0.0685734i	$-0.0218447\pi$
$284$		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
$293$	−5.09913	+	2.59813i	−0.297894	+	0.151785i	−0.596549	−	0.802576i	$-0.703462\pi$
$293$	−5.09913	+	2.59813i	−0.297894	+	0.151785i	0.298655	+	0.954361i	$0.403462\pi$
$294$		0			0
$295$	−0.261101	+	2.01615i	−0.0152019	+	0.117385i
$296$		0			0
$297$	5.45330	−	2.65295i	0.316433	−	0.153940i
$298$		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
$303$	0.102444	+	0.646808i	0.00588528	+	0.0371582i
$304$		0			0
$305$	9.42431	+	4.47076i	0.539634	+	0.255995i
$306$		0			0
$307$	−10.6045	+	10.6045i	−0.605228	+	0.605228i	−0.941695	−	0.336467i	$-0.890768\pi$
$307$	−10.6045	+	10.6045i	−0.605228	+	0.605228i	0.336467	+	0.941695i	$0.390768\pi$
$308$		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
$313$	19.4234	−	3.07637i	1.09788	−	0.173887i	0.418890	−	0.908037i	$-0.362419\pi$
$313$	19.4234	−	3.07637i	1.09788	−	0.173887i	0.678987	+	0.734151i	$0.262419\pi$
$314$		0			0
$315$	30.3164	+	8.91054i	1.70814	+	0.502052i
$316$		0			0
$317$	6.97539	+	1.10479i	0.391777	+	0.0620514i	0.349215	−	0.937042i	$-0.386448\pi$
$317$	6.97539	+	1.10479i	0.391777	+	0.0620514i	0.0425616	+	0.999094i	$0.486448\pi$
$318$		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
$323$	6.30269	+	12.3697i	0.350691	+	0.688270i
$324$		0			0
$325$	−10.5786	+	2.29529i	−0.586794	+	0.127320i
$326$		0			0
$327$	4.44602	+	2.26536i	0.245866	+	0.125275i
$328$		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
$333$	−10.0185	−	5.10470i	−0.549012	−	0.279736i
$334$		0			0
$335$	−10.8425	+	15.8475i	−0.592386	+	0.865839i
$336$		0			0
$337$	9.20335	+	18.0626i	0.501339	+	0.983932i	0.993543	+	0.113453i	$0.0361911\pi$
$337$	9.20335	+	18.0626i	0.501339	+	0.983932i	−0.492205	+	0.870479i	$0.663809\pi$
$338$		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
$343$	46.5154	+	7.36732i	2.51160	+	0.397798i
$344$		0			0
$345$	−0.638967	−	1.17093i	−0.0344008	−	0.0630406i
$346$		0			0
$347$	−16.4176	+	2.60029i	−0.881341	+	0.139591i	−0.580672	−	0.814138i	$-0.697210\pi$
$347$	−16.4176	+	2.60029i	−0.881341	+	0.139591i	−0.300669	+	0.953728i	$0.597210\pi$
$348$		0			0
$349$	−8.36963	−	25.7591i	−0.448016	−	1.37885i	−0.879142	−	0.476560i	$-0.841883\pi$
$349$	−8.36963	−	25.7591i	−0.448016	−	1.37885i	0.431126	−	0.902292i	$-0.358117\pi$
$350$		0			0
$351$		−	3.95855i		−	0.211292i
$352$		0			0
$353$	15.0281	−	15.0281i	0.799867	−	0.799867i	−0.183207	−	0.983074i	$-0.558648\pi$
$353$	15.0281	−	15.0281i	0.799867	−	0.799867i	0.983074	+	0.183207i	$0.0586479\pi$
$354$		0			0
$355$	14.3529	−	30.2556i	0.761770	−	1.60580i
$356$		0			0
$357$	−1.06008	−	6.69310i	−0.0561055	−	0.354236i
$358$		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
$363$	−3.38210	+	0.408346i	−0.177514	+	0.0214326i
$364$		0			0
$365$	−6.68600	−	8.67537i	−0.349961	−	0.454090i
$366$		0			0
$367$	−15.0965	+	7.69206i	−0.788032	+	0.401522i	−0.801204	−	0.598391i	$-0.795807\pi$
$367$	−15.0965	+	7.69206i	−0.788032	+	0.401522i	0.0131721	+	0.999913i	$0.495807\pi$
$368$		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	$-0.440589\pi$
$373$	−15.3939	−	15.3939i	−0.797068	−	0.797068i	−0.982632	+	0.185564i	$0.940589\pi$
$374$		0			0
$375$	0.293529	+	3.45005i	0.0151578	+	0.178160i
$376$		0			0
$377$	3.57537	−	7.01706i	0.184141	−	0.361397i
$378$		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
$383$	−5.61460	+	35.4492i	−0.286893	+	1.81137i	0.250589	+	0.968094i	$0.419376\pi$
$383$	−5.61460	+	35.4492i	−0.286893	+	1.81137i	−0.537482	+	0.843275i	$0.680624\pi$
$384$		0			0
$385$	−29.4025	−	20.9237i	−1.49849	−	1.06637i
$386$		0			0
$387$	4.15877	−	26.2575i	0.211402	−	1.33474i
$388$		0			0
$389$	−3.47743	−	1.12989i	−0.176313	−	0.0572875i	0.219530	−	0.975606i	$-0.429548\pi$
$389$	−3.47743	−	1.12989i	−0.176313	−	0.0572875i	−0.395843	+	0.918318i	$0.629548\pi$
$390$		0			0
$391$	5.09123	−	7.00747i	0.257474	−	0.354383i
$392$		0			0
$393$	2.25011	−	4.41609i	0.113503	−	0.222762i
$394$		0			0
$395$	13.5734	+	12.8263i	0.682953	+	0.645362i
$396$		0			0
$397$	−1.57131	−	1.57131i	−0.0788616	−	0.0788616i	0.666576	−	0.745437i	$-0.267759\pi$
$397$	−1.57131	−	1.57131i	−0.0788616	−	0.0788616i	−0.745437	+	0.666576i	$0.767759\pi$
$398$		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
$403$	−12.5676	+	6.40349i	−0.626035	+	0.318981i
$404$		0			0
$405$	18.0641	+	2.33939i	0.897614	+	0.116245i
$406$		0			0
$407$	8.91101	+	9.24627i	0.441702	+	0.458320i
$408$		0			0
$409$	−3.62215	+	2.63164i	−0.179104	+	0.130126i	−0.673725	−	0.738982i	$-0.735307\pi$
$409$	−3.62215	+	2.63164i	−0.179104	+	0.130126i	0.494621	+	0.869109i	$0.335307\pi$
$410$		0			0
$411$	−0.676482	+	2.08200i	−0.0333684	+	0.102697i
$412$		0			0
$413$	0.692082	+	4.36963i	0.0340551	+	0.215016i
$414$		0			0
$415$	4.87898	−	1.73934i	0.239500	−	0.0853809i
$416$		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
$423$	8.00288	−	1.26753i	0.389113	−	0.0616295i
$424$		0			0
$425$	−19.4237	+	11.3239i	−0.942186	+	0.549290i
$426$		0			0
$427$	22.4200	+	3.55098i	1.08498	+	0.171844i
$428$		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
$433$	−3.11176	−	6.10717i	−0.149542	−	0.293492i	0.804068	−	0.594537i	$-0.202665\pi$
$433$	−3.11176	−	6.10717i	−0.149542	−	0.293492i	−0.953610	+	0.301045i	$0.902665\pi$
$434$		0			0
$435$	−2.07908	−	1.42246i	−0.0996844	−	0.0682017i
$436$		0			0
$437$	5.29876	+	2.69986i	0.253474	+	0.129152i
$438$		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
$443$	−22.3198	−	11.3725i	−1.06045	−	0.540324i	−0.165367	−	0.986232i	$-0.552881\pi$
$443$	−22.3198	−	11.3725i	−1.06045	−	0.540324i	−0.895079	+	0.445908i	$0.852881\pi$
$444$		0			0
$445$	0.946003	−	0.177398i	0.0448448	−	0.00840949i
$446$		0			0
$447$	2.38478	+	4.68039i	0.112796	+	0.221375i
$448$		0			0
$449$	21.3897	+	29.4404i	1.00944	+	1.38938i	0.919348	+	0.393444i	$0.128717\pi$
$449$	21.3897	+	29.4404i	1.00944	+	1.38938i	0.0900935	+	0.995933i	$0.471283\pi$
$450$		0			0
$451$	16.2890	+	23.3132i	0.767021	+	1.09777i
$452$		0			0
$453$	−0.290968	−	0.0460847i	−0.0136708	−	0.00216525i
$454$		0			0
$455$	−20.6779	+	11.2838i	−0.969395	+	0.528992i
$456$		0			0
$457$	27.6037	−	4.37199i	1.29124	−	0.204513i	0.527236	−	0.849719i	$-0.323228\pi$
$457$	27.6037	−	4.37199i	1.29124	−	0.204513i	0.764009	+	0.645206i	$0.223228\pi$
$458$		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	$-0.741024\pi$
$463$	0.857939	−	0.857939i	0.0398718	−	0.0398718i	0.726762	+	0.686890i	$0.241024\pi$
$464$		0			0
$465$	1.51503	+	4.24977i	0.0702579	+	0.197079i
$466$		0			0
$467$	−3.37244	−	21.2927i	−0.156058	−	0.985310i	−0.934078	−	0.357070i	$-0.883776\pi$
$467$	−3.37244	−	21.2927i	−0.156058	−	0.985310i	0.778020	−	0.628240i	$-0.216224\pi$
$468$		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
$473$	−14.2808	+	26.7930i	−0.656631	+	1.23194i
$474$		0			0
$475$	−9.76522	−	11.9554i	−0.448059	−	0.548553i
$476$		0			0
$477$	−30.8933	+	15.7409i	−1.41451	+	0.720728i
$478$		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
$487$	−2.71050	+	5.31965i	−0.122824	+	0.241056i	−0.944229	−	0.329289i	$-0.893191\pi$
$487$	−2.71050	+	5.31965i	−0.122824	+	0.241056i	0.821405	+	0.570346i	$0.193191\pi$
$488$		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
$493$	2.55891	−	16.1563i	0.115247	−	0.727644i
$494$		0			0
$495$	−19.2851	−	9.58862i	−0.866799	−	0.430977i
$496$		0			0
$497$	11.4000	−	71.9768i	0.511360	−	3.22860i
$498$		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
$503$	−4.90996	+	9.63633i	−0.218924	+	0.429663i	−0.974182	−	0.225765i	$-0.927512\pi$
$503$	−4.90996	+	9.63633i	−0.218924	+	0.429663i	0.755258	+	0.655428i	$0.227512\pi$
$504$		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	−0.502946	−	0.864318i	$-0.667750\pi$
$509$	−9.06512	+	2.94543i	−0.401804	+	0.130554i	0.101142	+	0.994872i	$0.467750\pi$
$510$		0			0
$511$	−19.2830	−	14.0099i	−0.853030	−	0.619763i
$512$		0			0
$513$	5.02985	−	2.56284i	0.222073	−	0.113152i
$514$		0			0
$515$	−19.0888	+	14.7115i	−0.841152	+	0.648265i
$516$		0			0
$517$	−9.11144	−	1.61607i	−0.400720	−	0.0710747i
$518$		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
$523$	−0.368170	−	2.32454i	−0.0160990	−	0.101645i	0.978330	−	0.207050i	$-0.0663862\pi$
$523$	−0.368170	−	2.32454i	−0.0160990	−	0.101645i	−0.994429	+	0.105405i	$0.966386\pi$
$524$		0			0
$525$	2.72998	+	7.02305i	0.119146	+	0.306511i
$526$		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
$533$	18.3358	−	2.90411i	0.794213	−	0.125791i
$534$		0			0
$535$	−1.91371	+	6.51103i	−0.0827368	+	0.281496i
$536$		0			0
$537$	0.560564	+	0.0887846i	0.0241901	+	0.00383134i
$538$		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
$543$	−2.47482	−	4.85712i	−0.106205	−	0.208439i
$544$		0			0
$545$	−6.64036	−	35.4107i	−0.284442	−	1.51683i
$546$		0			0
$547$	5.52296	+	2.81409i	0.236145	+	0.120322i	0.568059	−	0.822988i	$-0.307694\pi$
$547$	5.52296	+	2.81409i	0.236145	+	0.120322i	−0.331914	+	0.943310i	$0.607694\pi$
$548$		0			0
$549$	13.5472			0.578181
$550$		0			0
$551$	11.2308			0.478450
$552$		0			0
$553$	36.2101	+	18.4500i	1.53981	+	0.784573i
$554$		0			0
$555$	−0.494183	−	2.63530i	−0.0209769	−	0.111862i
$556$		0			0
$557$	8.82946	+	17.3288i	0.374116	+	0.734245i	0.998916	−	0.0465401i	$-0.0148195\pi$
$557$	8.82946	+	17.3288i	0.374116	+	0.734245i	−0.624800	+	0.780785i	$0.714820\pi$
$558$		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
$563$	0.602546	+	0.0954339i	0.0253943	+	0.00402206i	0.169119	−	0.985596i	$-0.445908\pi$
$563$	0.602546	+	0.0954339i	0.0253943	+	0.00402206i	−0.143724	+	0.989618i	$0.545908\pi$
$564$		0			0
$565$	4.11235	−	13.9915i	0.173008	−	0.588626i
$566$		0			0
$567$	39.1507	−	6.20086i	1.64417	−	0.260412i
$568$		0			0
$569$	−10.4094	−	32.0369i	−0.436385	−	1.34306i	−0.891660	−	0.452705i	$-0.850459\pi$
$569$	−10.4094	−	32.0369i	−0.436385	−	1.34306i	0.455275	−	0.890351i	$-0.349541\pi$
$570$		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
$575$	−3.88015	+	8.81498i	−0.161814	+	0.367610i
$576$		0			0
$577$	−3.64966	−	23.0431i	−0.151937	−	0.959295i	−0.939373	−	0.342898i	$-0.888592\pi$
$577$	−3.64966	−	23.0431i	−0.151937	−	0.959295i	0.787435	−	0.616397i	$-0.211408\pi$
$578$		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
$583$	39.2179	−	5.47139i	1.62424	−	0.226602i
$584$		0			0
$585$	−11.1353	+	8.58185i	−0.460389	+	0.354816i
$586$		0			0
$587$	25.5396	−	13.0131i	1.05413	−	0.537108i	0.161026	−	0.986950i	$-0.448520\pi$
$587$	25.5396	−	13.0131i	1.05413	−	0.537108i	0.893108	+	0.449842i	$0.148520\pi$
$588$		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	$-0.324814\pi$
$593$	−8.01991	−	8.01991i	−0.329338	−	0.329338i	−0.852335	+	0.522996i	$0.824814\pi$
$594$		0			0
$595$	−33.6046	+	35.5620i	−1.37766	+	1.45790i
$596$		0			0
$597$	−1.64771	+	3.23381i	−0.0674362	+	0.132351i
$598$		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
$603$	−3.90116	+	24.6310i	−0.158868	+	1.00305i
$604$		0			0
$605$	17.2417	+	17.5420i	0.700977	+	0.713184i
$606$		0			0
$607$	4.53083	−	28.6065i	0.183901	−	1.16110i	−0.707104	−	0.707109i	$-0.749999\pi$
$607$	4.53083	−	28.6065i	0.183901	−	1.16110i	0.891005	−	0.453994i	$-0.150001\pi$
$608$		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
$613$	0.870774	−	1.70899i	0.0351702	−	0.0690254i	−0.872753	−	0.488163i	$-0.837667\pi$
$613$	0.870774	−	1.70899i	0.0351702	−	0.0690254i	0.907923	+	0.419137i	$0.137667\pi$
$614$		0			0
$615$	−0.167980	−	5.93584i	−0.00677360	−	0.239356i
$616$		0			0
$617$	−22.8666	−	22.8666i	−0.920576	−	0.920576i	0.0764940	−	0.997070i	$-0.475627\pi$
$617$	−22.8666	−	22.8666i	−0.920576	−	0.920576i	−0.997070	+	0.0764940i	$0.975627\pi$
$618$		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
$623$	1.86625	−	0.950900i	0.0747696	−	0.0380970i
$624$		0			0
$625$	18.4367	−	16.8846i	0.737466	−	0.675384i
$626$		0			0
$627$	−3.14074	+	0.438172i	−0.125429	+	0.0174989i
$628$		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
$633$	0.783267	+	4.94535i	0.0311321	+	0.196560i
$634$		0			0
$635$	−9.49351	−	26.6300i	−0.376738	−	1.05678i
$636$		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
$643$	27.2490	−	4.31582i	1.07460	−	0.170199i	0.406035	−	0.913857i	$-0.366911\pi$
$643$	27.2490	−	4.31582i	1.07460	−	0.170199i	0.668560	+	0.743658i	$0.266911\pi$
$644$		0			0
$645$	5.56473	−	3.03664i	0.219111	−	0.119567i
$646$		0			0
$647$	16.5666	+	2.62389i	0.651299	+	0.103156i	0.473337	−	0.880882i	$-0.343049\pi$
$647$	16.5666	+	2.62389i	0.651299	+	0.103156i	0.177963	+	0.984037i	$0.443049\pi$
$648$		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
$653$	3.43913	+	6.74967i	0.134583	+	0.264135i	0.948456	−	0.316908i	$-0.102645\pi$
$653$	3.43913	+	6.74967i	0.134583	+	0.264135i	−0.813873	+	0.581043i	$0.802645\pi$
$654$		0			0
$655$	−35.1723	+	6.59565i	−1.37429	+	0.257713i
$656$		0			0
$657$	−12.6745	−	6.45800i	−0.494481	−	0.251951i
$658$		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
$663$	2.68633	+	1.36875i	0.104328	+	0.0531579i
$664$		0			0
$665$	−27.7248	−	18.9686i	−1.07512	−	0.735572i
$666$		0			0
$667$	−3.18115	−	6.24335i	−0.123174	−	0.241743i
$668$		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
$673$	49.6194	+	7.85894i	1.91269	+	0.302940i	0.995441	−	0.0953786i	$-0.0304062\pi$
$673$	49.6194	+	7.85894i	1.91269	+	0.302940i	0.917247	+	0.398319i	$0.130406\pi$
$674$		0			0
$675$	4.60459	+	7.89816i	0.177231	+	0.304000i
$676$		0			0
$677$	−24.7077	+	3.91331i	−0.949594	+	0.150401i	−0.611971	−	0.790881i	$-0.709623\pi$
$677$	−24.7077	+	3.91331i	−0.949594	+	0.150401i	−0.337623	+	0.941281i	$0.609623\pi$
$678$		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	0.0997098	−	0.995017i	$-0.468209\pi$
$683$	28.6099	−	28.6099i	1.09473	−	1.09473i	0.995017	−	0.0997098i	$-0.0317914\pi$
$684$		0			0
$685$	14.8882	−	5.30761i	0.568850	−	0.202793i
$686$		0			0
$687$	0.693391	+	4.37790i	0.0264545	+	0.167027i
$688$		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
$693$	−46.1483	−	8.18520i	−1.75303	−	0.310930i
$694$		0			0
$695$	−23.2648	−	3.01290i	−0.882484	−	0.114286i
$696$		0			0
$697$	34.3565	−	17.5055i	1.30135	−	0.663069i
$698$		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
$707$	4.67134	−	9.16802i	0.175684	−	0.344799i
$708$		0			0
$709$	−17.8503	+	24.5688i	−0.670380	+	0.922699i	−0.999769	−	0.0214951i	$-0.993157\pi$
$709$	−17.8503	+	24.5688i	−0.670380	+	0.922699i	0.329389	+	0.944194i	$0.393157\pi$
$710$		0			0
$711$	23.0669	+	7.49490i	0.865077	+	0.281081i
$712$		0			0
$713$	−1.96320	+	12.3952i	−0.0735225	+	0.464203i
$714$		0			0
$715$	15.2203	−	5.11133i	0.569208	−	0.191153i
$716$		0			0
$717$	0.225962	−	1.42667i	0.00843870	−	0.0532798i
$718$		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
$723$	−0.857639	+	1.68321i	−0.0318959	+	0.0625993i
$724$		0			0
$725$	1.02862	+	18.1594i	0.0382020	+	0.674424i
$726$		0			0
$727$	−34.1964	−	34.1964i	−1.26828	−	1.26828i	−0.946979	−	0.321296i	$-0.895881\pi$
$727$	−34.1964	−	34.1964i	−1.26828	−	1.26828i	−0.321296	−	0.946979i	$-0.604119\pi$
$728$		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
$733$	−40.6692	+	20.7220i	−1.50215	+	0.765384i	−0.995317	−	0.0966600i	$-0.969184\pi$
$733$	−40.6692	+	20.7220i	−1.50215	+	0.765384i	−0.506833	+	0.862044i	$0.669184\pi$
$734$		0			0
$735$	7.05041	+	9.14821i	0.260058	+	0.337437i
$736$		0			0
$737$	13.3962	−	25.1333i	0.493454	−	0.925798i
$738$		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
$743$	−1.66544	−	10.5152i	−0.0610992	−	0.385765i	−0.999221	−	0.0394600i	$-0.987436\pi$
$743$	−1.66544	−	10.5152i	−0.0610992	−	0.385765i	0.938122	−	0.346305i	$-0.112564\pi$
$744$		0			0
$745$	16.2557	−	34.2668i	0.595563	−	1.25544i
$746$		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
$753$	2.98252	−	0.472385i	0.108689	−	0.0172147i
$754$		0			0
$755$	1.01887	+	1.86712i	0.0370806	+	0.0679514i
$756$		0			0
$757$	2.38566	+	0.377851i	0.0867082	+	0.0137332i	0.199638	−	0.979870i	$-0.436023\pi$
$757$	2.38566	+	0.377851i	0.0867082	+	0.0137332i	−0.112930	+	0.993603i	$0.536023\pi$
$758$		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
$763$	−35.5940	−	69.8571i	−1.28859	−	2.52900i
$764$		0			0
$765$	−16.4885	+	24.0997i	−0.596141	+	0.871327i
$766$		0			0
$767$	−1.75379	−	0.893599i	−0.0633256	−	0.0322660i
$768$		0			0
$769$	−17.4640			−0.629769			−0.314885	−	0.949130i	$-0.601966\pi$
$769$	−17.4640			−0.629769			−0.314885	+	0.949130i	$0.601966\pi$
$770$		0			0
$771$	−2.17030			−0.0781614
$772$		0			0
$773$	−16.2510	−	8.28029i	−0.584507	−	0.297821i	0.136621	−	0.990623i	$-0.456376\pi$
$773$	−16.2510	−	8.28029i	−0.584507	−	0.297821i	−0.721128	+	0.692802i	$0.756376\pi$
$774$		0			0
$775$	17.6264	−	27.3949i	0.633160	−	0.984055i
$776$		0			0
$777$	−2.64894	−	5.19884i	−0.0950303	−	0.186507i
$778$		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
$783$	−6.56957	−	1.04052i	−0.234777	−	0.0371851i
$784$		0			0
$785$	46.8735	+	13.7770i	1.67299	+	0.491721i
$786$		0			0
$787$	−15.2951	+	2.42251i	−0.545212	+	0.0863530i	−0.422964	−	0.906147i	$-0.639010\pi$
$787$	−15.2951	+	2.42251i	−0.545212	+	0.0863530i	−0.122248	+	0.992500i	$0.539010\pi$
$788$		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
$795$	−7.47000	−	3.54366i	−0.264933	−	0.125681i
$796$		0			0
$797$	5.09184	+	32.1486i	0.180362	+	1.13876i	0.897234	+	0.441556i	$0.145573\pi$
$797$	5.09184	+	32.1486i	0.180362	+	1.13876i	−0.716871	+	0.697205i	$0.754427\pi$
$798$		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
$803$	11.2734	+	11.6975i	0.397830	+	0.412797i
$804$		0			0
$805$	−2.69181	+	20.7854i	−0.0948737	+	0.732589i
$806$		0			0
$807$	5.94026	−	3.02672i	0.209107	−	0.106545i
$808$		0			0
$809$	14.4049	+	10.4658i	0.506449	+	0.367956i	0.811475	−	0.584388i	$-0.198665\pi$
$809$	14.4049	+	10.4658i	0.506449	+	0.367956i	−0.305026	+	0.952344i	$0.598665\pi$
$810$		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
$817$	−12.8308	+	25.1819i	−0.448894	+	0.881004i
$818$		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
$823$	6.78208	−	42.8204i	0.236409	−	1.49262i	−0.528747	−	0.848779i	$-0.677338\pi$
$823$	6.78208	−	42.8204i	0.236409	−	1.49262i	0.765156	−	0.643845i	$-0.222662\pi$
$824$		0			0
$825$	−0.996148	−	5.03821i	−0.0346814	−	0.175408i
$826$		0			0
$827$	−6.90305	+	43.5841i	−0.240042	+	1.51557i	0.513455	+	0.858117i	$0.328366\pi$
$827$	−6.90305	+	43.5841i	−0.240042	+	1.51557i	−0.753497	+	0.657451i	$0.771634\pi$
$828$		0			0
$829$	22.2216	+	7.22022i	0.771787	+	0.250769i	0.668330	−	0.743865i	$-0.267010\pi$
$829$	22.2216	+	7.22022i	0.771787	+	0.250769i	0.103457	+	0.994634i	$0.467010\pi$
$830$		0			0
$831$	0.534828	−	0.736128i	0.0185530	−	0.0255360i
$832$		0			0
$833$	−34.0482	+	66.8234i	−1.17970	+	2.31529i
$834$		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
$843$	−7.72888	+	3.93806i	−0.266197	+	0.135634i
$844$		0			0
$845$	−2.38736	+	18.4345i	−0.0821276	+	0.634167i
$846$		0			0
$847$	46.7628	+	26.0445i	1.60679	+	0.894900i
$848$		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
$853$	1.11014	+	7.00915i	0.0380105	+	0.239989i	0.999377	−	0.0352814i	$-0.0112327\pi$
$853$	1.11014	+	7.00915i	0.0380105	+	0.239989i	−0.961367	+	0.275270i	$0.911233\pi$
$854$		0			0
$855$	−18.1136	−	8.59282i	−0.619471	−	0.293868i
$856$		0			0
$857$	4.48225	−	4.48225i	0.153111	−	0.153111i	−0.626395	−	0.779506i	$-0.715470\pi$
$857$	4.48225	−	4.48225i	0.153111	−	0.153111i	0.779506	+	0.626395i	$0.215470\pi$
$858$		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
$863$	−42.2052	+	6.68465i	−1.43668	+	0.227548i	−0.825706	−	0.564101i	$-0.809223\pi$
$863$	−42.2052	+	6.68465i	−1.43668	+	0.227548i	−0.610976	+	0.791649i	$0.709223\pi$
$864$		0			0
$865$	6.24989	+	1.83695i	0.212503	+	0.0624583i
$866$		0			0
$867$	0.985063	+	0.156019i	0.0334545	+	0.00529867i
$868$		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
$873$	13.1429	+	25.7943i	0.444819	+	0.873006i
$874$		0			0
$875$	28.1316	−	46.5662i	0.951020	−	1.57422i
$876$		0			0
$877$	3.97498	+	2.02535i	0.134225	+	0.0683913i	0.519814	−	0.854280i	$-0.326001\pi$
$877$	3.97498	+	2.02535i	0.134225	+	0.0683913i	−0.385588	+	0.922671i	$0.626001\pi$
$878$		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
$883$	22.4558	+	11.4418i	0.755699	+	0.385048i	0.788997	−	0.614398i	$-0.210601\pi$
$883$	22.4558	+	11.4418i	0.755699	+	0.385048i	−0.0332976	+	0.999445i	$0.510601\pi$
$884$		0			0
$885$	−0.355518	+	0.519629i	−0.0119506	+	0.0174672i
$886$		0			0
$887$	16.6206	+	32.6198i	0.558066	+	1.09527i	0.981878	+	0.189516i	$0.0606918\pi$
$887$	16.6206	+	32.6198i	0.558066	+	1.09527i	−0.423812	+	0.905750i	$0.639308\pi$
$888$		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
$893$	−8.50787	−	1.34751i	−0.284705	−	0.0450929i
$894$		0			0
$895$	−1.96291	−	3.59710i	−0.0656130	−	0.120238i
$896$		0			0
$897$	1.27559	−	0.202034i	0.0425908	−	0.00674573i
$898$		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
$905$	−16.8695	+	35.5607i	−0.560761	+	1.18208i
$906$		0			0
$907$	−1.83881	−	11.6098i	−0.0610568	−	0.385497i	−0.999227	−	0.0393219i	$-0.987480\pi$
$907$	−1.83881	−	11.6098i	−0.0610568	−	0.385497i	0.938170	−	0.346175i	$-0.112520\pi$
$908$		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
$913$	−6.90865	+	3.36095i	−0.228643	+	0.111231i
$914$		0			0
$915$	1.97198	+	2.55872i	0.0651915	+	0.0845887i
$916$		0			0
$917$	−69.3868	+	35.3543i	−2.29135	+	1.16750i
$918$		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
$927$	−14.2098	+	27.8883i	−0.466711	+	0.915973i
$928$		0			0
$929$	12.2209	−	16.8206i	0.400953	−	0.551865i	−0.560030	−	0.828473i	$-0.689210\pi$
$929$	12.2209	−	16.8206i	0.400953	−	0.551865i	0.960983	+	0.276608i	$0.0892102\pi$
$930$		0			0
$931$	−48.9716	−	15.9118i	−1.60498	−	0.521489i
$932$		0			0
$933$	0.305020	−	1.92582i	0.00998592	−	0.0630486i
$934$		0			0
$935$	26.7855	−	19.8660i	0.875980	−	0.649688i
$936$		0			0
$937$	−0.957154	+	6.04324i	−0.0312689	+	0.197424i	−0.998378	−	0.0569393i	$-0.981866\pi$
$937$	−0.957154	+	6.04324i	−0.0312689	+	0.197424i	0.967109	+	0.254363i	$0.0818659\pi$
$938$		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
$943$	7.49877	−	14.7172i	0.244193	−	0.479257i
$944$		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	$-0.0568983\pi$
$947$	24.8115	+	24.8115i	0.806266	+	0.806266i	−0.177801	+	0.984067i	$0.556898\pi$
$948$		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
$953$	28.0581	−	14.2963i	0.908891	−	0.463103i	0.0639439	−	0.997953i	$-0.479632\pi$
$953$	28.0581	−	14.2963i	0.908891	−	0.463103i	0.844947	+	0.534851i	$0.179632\pi$
$954$		0			0
$955$	−14.7478	−	1.90991i	−0.477227	−	0.0618032i
$956$		0			0
$957$	3.29733	+	1.75749i	0.106588	+	0.0568116i
$958$		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
$963$	1.37879	+	8.70536i	0.0444310	+	0.280526i
$964$		0			0
$965$	25.4594	−	9.07619i	0.819567	−	0.292173i
$966$		0			0
$967$	−34.2945	+	34.2945i	−1.10284	+	1.10284i	−0.108771	+	0.994067i	$0.534692\pi$
$967$	−34.2945	+	34.2945i	−1.10284	+	1.10284i	−0.994067	+	0.108771i	$0.965308\pi$
$968$		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
$973$	−50.4222	+	7.98609i	−1.61646	+	0.256022i
$974$		0			0
$975$	−3.24179	−	0.853976i	−0.103820	−	0.0273491i
$976$		0			0
$977$	27.5052	+	4.35640i	0.879970	+	0.139373i	0.580040	−	0.814588i	$-0.303037\pi$
$977$	27.5052	+	4.35640i	0.879970	+	0.139373i	0.299929	+	0.953961i	$0.403037\pi$
$978$		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
$983$	−8.87510	−	17.4184i	−0.283072	−	0.555560i	0.705064	−	0.709144i	$-0.250918\pi$
$983$	−8.87510	−	17.4184i	−0.283072	−	0.555560i	−0.988136	+	0.153584i	$0.950918\pi$
$984$		0			0
$985$	33.9809	+	23.2489i	1.08272	+	0.740771i
$986$		0			0
$987$	3.74636	+	1.90887i	0.119248	+	0.0607599i
$988$		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
$993$	1.75332	+	0.893360i	0.0556398	+	0.0283499i
$994$		0			0
$995$	25.7559	−	4.82986i	0.816517	−	0.153117i
$996$		0			0
$997$	−11.2684	−	22.1155i	−0.356874	−	0.700405i	0.640862	−	0.767656i	$-0.278577\pi$
$997$	−11.2684	−	22.1155i	−0.356874	−	0.700405i	−0.997736	+	0.0672509i	$0.978577\pi$
$998$		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.217.4	yes	48
4.3	odd	2		880.2.cm.b.657.3		48
5.3	odd	4	inner	220.2.u.a.173.3	yes	48
11.7	odd	10	inner	220.2.u.a.117.3	yes	48
20.3	even	4		880.2.cm.b.833.4		48
44.7	even	10		880.2.cm.b.337.4		48
55.18	even	20	inner	220.2.u.a.73.4	✓	48
220.183	odd	20		880.2.cm.b.513.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.u.a.73.4	✓	48	55.18	even	20	inner
220.2.u.a.117.3	yes	48	11.7	odd	10	inner
220.2.u.a.173.3	yes	48	5.3	odd	4	inner
220.2.u.a.217.4	yes	48	1.1	even	1	trivial
880.2.cm.b.337.4		48	44.7	even	10
880.2.cm.b.513.3		48	220.183	odd	20
880.2.cm.b.657.3		48	4.3	odd	2
880.2.cm.b.833.4		48	20.3	even	4

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)

\(f(q)\)	\(=\)	\(q+(0.275942 + 0.140599i) q^{3} +(-0.412133 - 2.19776i) q^{5} +(-2.20914 - 4.33567i) q^{7} +(-1.70698 - 2.34946i) q^{9} +O(q^{10})\)	\(q+(0.275942 + 0.140599i) q^{3} +(-0.412133 - 2.19776i) q^{5} +(-2.20914 - 4.33567i) q^{7} +(-1.70698 - 2.34946i) q^{9} +(0.966488 + 3.17268i) q^{11} +(2.13829 + 0.338672i) q^{13} +(0.195279 - 0.664400i) q^{15} +(4.44135 - 0.703440i) q^{17} +(0.954041 + 2.93624i) q^{19} -1.50700i q^{21} +(1.36205 - 1.36205i) q^{23} +(-4.66029 + 1.81154i) q^{25} +(-0.286037 - 1.80597i) q^{27} +(1.12411 - 3.45966i) q^{29} +(-5.27085 + 3.82950i) q^{31} +(-0.179383 + 1.01136i) q^{33} +(-8.61831 + 6.64202i) q^{35} +(3.44980 - 1.75776i) q^{37} +(0.542427 + 0.394096i) q^{39} +(8.15531 - 2.64982i) q^{41} +(6.47304 + 6.47304i) q^{43} +(-4.46004 + 4.71982i) q^{45} +(-1.26667 + 2.48598i) q^{47} +(-9.80329 + 13.4931i) q^{49} +(1.32446 + 0.430342i) q^{51} +(1.86770 - 11.7922i) q^{53} +(6.57447 - 3.43167i) q^{55} +(-0.149573 + 0.944368i) q^{57} +(-0.864681 - 0.280952i) q^{59} +(-2.74194 + 3.77396i) q^{61} +(-6.41553 + 12.5912i) q^{63} +(-0.136941 - 4.83902i) q^{65} +(-6.07207 - 6.07207i) q^{67} +(0.567351 - 0.184344i) q^{69} +(12.1159 + 8.80269i) q^{71} +(4.36438 - 2.22376i) q^{73} +(-1.54067 - 0.155355i) q^{75} +(11.6206 - 11.1993i) q^{77} +(-6.75665 + 4.90899i) q^{79} +(-2.51725 + 7.74730i) q^{81} +(0.362373 + 2.28793i) q^{83} +(-3.37642 - 9.47110i) q^{85} +(0.796617 - 0.796617i) q^{87} +0.430440i q^{89} +(-3.25540 - 10.0191i) q^{91} +(-1.99287 + 0.315640i) q^{93} +(6.05995 - 3.30687i) q^{95} +(-9.84586 - 1.55943i) q^{97} +(5.80430 - 7.68642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7}+O(q^{10}) \) 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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