LMFDB - Embedded newform 460.2.x.a.337.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(17,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 14]))

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

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

chi := DirichletCharacter("460.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			337.4
Character	$\chi$	$=$	460.337
Dual form			460.2.x.a.273.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70940 - 0.637574i) q^{3} +(-0.291100 + 2.21704i) q^{5} +(3.58772 - 0.780461i) q^{7} +(0.248309 + 0.215161i) q^{9} +O(q^{10})$	\(q+(-1.70940 - 0.637574i) q^{3} +(-0.291100 + 2.21704i) q^{5} +(3.58772 - 0.780461i) q^{7} +(0.248309 + 0.215161i) q^{9} +(-4.20017 + 0.603893i) q^{11} +(-0.264746 + 1.21702i) q^{13} +(1.91113 - 3.60422i) q^{15} +(-2.65078 + 4.85454i) q^{17} +(7.45964 + 2.19035i) q^{19} +(-6.63047 - 0.953317i) q^{21} +(1.97124 + 4.37198i) q^{23} +(-4.83052 - 1.29076i) q^{25} +(2.33580 + 4.27769i) q^{27} +(2.02005 + 6.87967i) q^{29} +(2.42828 - 5.31720i) q^{31} +(7.56481 + 1.64562i) q^{33} +(0.685928 + 8.18131i) q^{35} +(0.219927 + 3.07497i) q^{37} +(1.22850 - 1.91158i) q^{39} +(1.02099 + 1.17829i) q^{41} +(-3.93792 + 10.5580i) q^{43} +(-0.549304 + 0.487878i) q^{45} +(1.35669 + 1.35669i) q^{47} +(5.89521 - 2.69225i) q^{49} +(7.62638 - 6.60830i) q^{51} +(-1.04997 - 4.82663i) q^{53} +(-0.116186 - 9.48773i) q^{55} +(-11.3550 - 8.50027i) q^{57} +(-7.60492 - 11.8335i) q^{59} +(-3.61911 - 1.65279i) q^{61} +(1.05879 + 0.578143i) q^{63} +(-2.62111 - 0.941225i) q^{65} +(8.22002 + 10.9807i) q^{67} +(-0.582184 - 8.73029i) q^{69} +(2.02551 - 14.0878i) q^{71} +(-5.82928 + 3.18303i) q^{73} +(7.43435 + 5.28625i) q^{75} +(-14.5977 + 5.44467i) q^{77} +(2.48387 - 1.59629i) q^{79} +(-1.40575 - 9.77719i) q^{81} +(-1.99694 + 0.142824i) q^{83} +(-9.99106 - 7.29004i) q^{85} +(0.933216 - 13.0481i) q^{87} +(3.10847 + 6.80661i) q^{89} +4.57294i q^{91} +(-7.54102 + 7.54102i) q^{93} +(-7.02759 + 15.9007i) q^{95} +(-4.48751 - 0.320953i) q^{97} +(-1.17288 - 0.753762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{22}\right)$

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
$3$	−1.70940	−	0.637574i	−0.986924	−	0.368104i	−0.196393	−	0.980525i	$-0.562923\pi$
$3$	−1.70940	−	0.637574i	−0.986924	−	0.368104i	−0.790531	+	0.612422i	$0.790196\pi$
$4$		0			0
$5$	−0.291100	+	2.21704i	−0.130184	+	0.991490i
$5$	−0.291100	+	2.21704i	−0.130184	+	0.991490i
$6$		0			0
$7$	3.58772	−	0.780461i	1.35603	−	0.294987i	0.524948	−	0.851134i	$-0.324085\pi$
$7$	3.58772	−	0.780461i	1.35603	−	0.294987i	0.831084	+	0.556147i	$0.187721\pi$
$8$		0			0
$9$	0.248309	+	0.215161i	0.0827698	+	0.0717204i
$10$		0			0
$11$	−4.20017	+	0.603893i	−1.26640	+	0.182081i	−0.742585	−	0.669752i	$-0.766400\pi$
$11$	−4.20017	+	0.603893i	−1.26640	+	0.182081i	−0.523814	+	0.851833i	$0.675491\pi$
$12$		0			0
$13$	−0.264746	+	1.21702i	−0.0734273	+	0.337540i	−0.999175	−	0.0406009i	$-0.987073\pi$
$13$	−0.264746	+	1.21702i	−0.0734273	+	0.337540i	0.925748	+	0.378141i	$0.123436\pi$
$14$		0			0
$15$	1.91113	−	3.60422i	0.493453	−	0.930604i
$16$		0			0
$17$	−2.65078	+	4.85454i	−0.642908	+	1.17740i	0.329509	+	0.944152i	$0.393117\pi$
$17$	−2.65078	+	4.85454i	−0.642908	+	1.17740i	−0.972418	+	0.233246i	$0.925065\pi$
$18$		0			0
$19$	7.45964	+	2.19035i	1.71136	+	0.502500i	0.983142	−	0.182846i	$-0.0585309\pi$
$19$	7.45964	+	2.19035i	1.71136	+	0.502500i	0.728218	+	0.685346i	$0.240349\pi$
$20$		0			0
$21$	−6.63047	−	0.953317i	−1.44689	−	0.208031i
$22$		0			0
$23$	1.97124	+	4.37198i	0.411032	+	0.911621i
$23$	1.97124	+	4.37198i	0.411032	+	0.911621i
$24$		0			0
$25$	−4.83052	−	1.29076i	−0.966104	−	0.258152i
$26$		0			0
$27$	2.33580	+	4.27769i	0.449524	+	0.823242i
$28$		0			0
$29$	2.02005	+	6.87967i	0.375114	+	1.27752i	0.903526	+	0.428534i	$0.140970\pi$
$29$	2.02005	+	6.87967i	0.375114	+	1.27752i	−0.528411	+	0.848989i	$0.677212\pi$
$30$		0			0
$31$	2.42828	−	5.31720i	0.436132	−	0.954996i	−0.556160	−	0.831075i	$-0.687726\pi$
$31$	2.42828	−	5.31720i	0.436132	−	0.954996i	0.992292	−	0.123921i	$-0.0395470\pi$
$32$		0			0
$33$	7.56481	+	1.64562i	1.31686	+	0.286466i
$34$		0			0
$35$	0.685928	+	8.18131i	0.115943	+	1.38289i
$36$		0			0
$37$	0.219927	+	3.07497i	0.0361557	+	0.505523i	0.982973	+	0.183751i	$0.0588239\pi$
$37$	0.219927	+	3.07497i	0.0361557	+	0.505523i	−0.946817	+	0.321772i	$0.895722\pi$
$38$		0			0
$39$	1.22850	−	1.91158i	0.196717	−	0.306097i
$40$		0			0
$41$	1.02099	+	1.17829i	0.159452	+	0.184017i	0.829854	−	0.557981i	$-0.188424\pi$
$41$	1.02099	+	1.17829i	0.159452	+	0.184017i	−0.670402	+	0.741998i	$0.733878\pi$
$42$		0			0
$43$	−3.93792	+	10.5580i	−0.600527	+	1.61008i	0.179100	+	0.983831i	$0.442681\pi$
$43$	−3.93792	+	10.5580i	−0.600527	+	1.61008i	−0.779627	+	0.626244i	$0.784591\pi$
$44$		0			0
$45$	−0.549304	+	0.487878i	−0.0818854	+	0.0727286i
$46$		0			0
$47$	1.35669	+	1.35669i	0.197893	+	0.197893i	0.799096	−	0.601203i	$-0.205312\pi$
$47$	1.35669	+	1.35669i	0.197893	+	0.197893i	−0.601203	+	0.799096i	$0.705312\pi$
$48$		0			0
$49$	5.89521	−	2.69225i	0.842173	−	0.384608i
$50$		0			0
$51$	7.62638	−	6.60830i	1.06791	−	0.925347i
$52$		0			0
$53$	−1.04997	−	4.82663i	−0.144224	−	0.662989i	−0.991312	−	0.131535i	$-0.958009\pi$
$53$	−1.04997	−	4.82663i	−0.144224	−	0.662989i	0.847087	−	0.531454i	$-0.178354\pi$
$54$		0			0
$55$	−0.116186	−	9.48773i	−0.0156665	−	1.27933i
$56$		0			0
$57$	−11.3550	−	8.50027i	−1.50401	−	1.12589i
$58$		0			0
$59$	−7.60492	−	11.8335i	−0.990077	−	1.54059i	−0.833200	−	0.552971i	$-0.813494\pi$
$59$	−7.60492	−	11.8335i	−0.990077	−	1.54059i	−0.156877	−	0.987618i	$-0.550142\pi$
$60$		0			0
$61$	−3.61911	−	1.65279i	−0.463379	−	0.211618i	0.170024	−	0.985440i	$-0.445615\pi$
$61$	−3.61911	−	1.65279i	−0.463379	−	0.211618i	−0.633403	+	0.773822i	$0.718343\pi$
$62$		0			0
$63$	1.05879	+	0.578143i	0.133395	+	0.0728392i
$64$		0			0
$65$	−2.62111	−	0.941225i	−0.325108	−	0.116745i
$66$		0			0
$67$	8.22002	+	10.9807i	1.00424	+	1.34150i	0.939107	+	0.343624i	$0.111655\pi$
$67$	8.22002	+	10.9807i	1.00424	+	1.34150i	0.0651278	+	0.997877i	$0.479254\pi$
$68$		0			0
$69$	−0.582184	−	8.73029i	−0.0700867	−	1.05100i
$70$		0			0
$71$	2.02551	−	14.0878i	0.240384	−	1.67191i	−0.409832	−	0.912161i	$-0.634413\pi$
$71$	2.02551	−	14.0878i	0.240384	−	1.67191i	0.650217	−	0.759749i	$-0.274678\pi$
$72$		0			0
$73$	−5.82928	+	3.18303i	−0.682266	+	0.372545i	−0.782701	−	0.622398i	$-0.786158\pi$
$73$	−5.82928	+	3.18303i	−0.682266	+	0.372545i	0.100435	+	0.994944i	$0.467977\pi$
$74$		0			0
$75$	7.43435	+	5.28625i	0.858445	+	0.610403i
$76$		0			0
$77$	−14.5977	+	5.44467i	−1.66357	+	0.620478i
$78$		0			0
$79$	2.48387	−	1.59629i	0.279458	−	0.179597i	−0.393402	−	0.919366i	$-0.628702\pi$
$79$	2.48387	−	1.59629i	0.279458	−	0.179597i	0.672860	+	0.739770i	$0.265066\pi$
$80$		0			0
$81$	−1.40575	−	9.77719i	−0.156194	−	1.08635i
$82$		0			0
$83$	−1.99694	+	0.142824i	−0.219192	+	0.0156769i	−0.180503	−	0.983574i	$-0.557773\pi$
$83$	−1.99694	+	0.142824i	−0.219192	+	0.0156769i	−0.0386889	+	0.999251i	$0.512318\pi$
$84$		0			0
$85$	−9.99106	−	7.29004i	−1.08368	−	0.790715i
$86$		0			0
$87$	0.933216	−	13.0481i	0.100051	−	1.39890i
$88$		0			0
$89$	3.10847	+	6.80661i	0.329498	+	0.721499i	0.999788	−	0.0206000i	$-0.00655765\pi$
$89$	3.10847	+	6.80661i	0.329498	+	0.721499i	−0.670290	+	0.742099i	$0.733830\pi$
$90$		0			0
$91$			4.57294i			0.479375i
$92$		0			0
$93$	−7.54102	+	7.54102i	−0.781967	+	0.781967i
$94$		0			0
$95$	−7.02759	+	15.9007i	−0.721015	+	1.63138i
$96$		0			0
$97$	−4.48751	−	0.320953i	−0.455638	−	0.0325878i	−0.158365	−	0.987381i	$-0.550622\pi$
$97$	−4.48751	−	0.320953i	−0.455638	−	0.0325878i	−0.297272	+	0.954793i	$0.596077\pi$
$98$		0			0
$99$	−1.17288	−	0.753762i	−0.117878	−	0.0757559i
$100$		0			0
$101$	0.252635	−	0.291556i	0.0251381	−	0.0290109i	−0.743041	−	0.669246i	$-0.766617\pi$
$101$	0.252635	−	0.291556i	0.0251381	−	0.0290109i	0.768179	+	0.640235i	$0.221163\pi$
$102$		0			0
$103$	6.35830	−	8.49370i	0.626502	−	0.836909i	−0.369217	−	0.929343i	$-0.620374\pi$
$103$	6.35830	−	8.49370i	0.626502	−	0.836909i	0.995719	+	0.0924345i	$0.0294649\pi$
$104$		0			0
$105$	4.04367	−	14.4225i	0.394622	−	1.40749i
$106$		0			0
$107$	0.426623	+	1.14382i	0.0412432	+	0.110577i	0.955939	−	0.293567i	$-0.0948422\pi$
$107$	0.426623	+	1.14382i	0.0412432	+	0.110577i	−0.914695	+	0.404144i	$0.867570\pi$
$108$		0			0
$109$	−11.8718	+	3.48586i	−1.13711	+	0.333885i	−0.795498	−	0.605956i	$-0.792791\pi$
$109$	−11.8718	+	3.48586i	−1.13711	+	0.333885i	−0.341611	+	0.939842i	$0.610972\pi$
$110$		0			0
$111$	1.58458	−	5.39659i	0.150402	−	0.512222i
$112$		0			0
$113$	16.1774	−	12.1103i	1.52184	−	1.13924i	0.574731	−	0.818343i	$-0.305107\pi$
$113$	16.1774	−	12.1103i	1.52184	−	1.13924i	0.947114	−	0.320896i	$-0.103984\pi$
$114$		0			0
$115$	−10.2667	+	3.09764i	−0.957373	+	0.288856i
$116$		0			0
$117$	−0.327594	+	0.245234i	−0.0302861	+	0.0226719i
$118$		0			0
$119$	−5.72148	+	19.4856i	−0.524487	+	1.78624i
$120$		0			0
$121$	6.72232	−	1.97385i	0.611120	−	0.179441i
$122$		0			0
$123$	−0.994040	−	2.66512i	−0.0896296	−	0.240306i
$124$		0			0
$125$	4.26783	−	10.3337i	0.381726	−	0.924275i
$126$		0			0
$127$	3.04014	−	4.06116i	0.269769	−	0.360369i	−0.645115	−	0.764085i	$-0.723191\pi$
$127$	3.04014	−	4.06116i	0.269769	−	0.360369i	0.914884	+	0.403716i	$0.132282\pi$
$128$		0			0
$129$	13.4630	−	15.5371i	1.18535	−	1.36797i
$130$		0			0
$131$	3.83934	+	2.46740i	0.335445	+	0.215577i	0.697509	−	0.716576i	$-0.254292\pi$
$131$	3.83934	+	2.46740i	0.335445	+	0.215577i	−0.362064	+	0.932153i	$0.617928\pi$
$132$		0			0
$133$	28.4726	+	2.03640i	2.46889	+	0.176578i
$134$		0			0
$135$	−10.1638	+	3.93331i	−0.874757	+	0.338526i
$136$		0			0
$137$	−0.830844	+	0.830844i	−0.0709838	+	0.0709838i	−0.741707	−	0.670724i	$-0.765984\pi$
$137$	−0.830844	+	0.830844i	−0.0709838	+	0.0709838i	0.670724	+	0.741707i	$0.265984\pi$
$138$		0			0
$139$		−	18.6383i		−	1.58088i	−0.612540	−	0.790439i	$-0.709852\pi$
$139$		−	18.6383i		−	1.58088i	0.612540	−	0.790439i	$-0.290148\pi$
$140$		0			0
$141$	−1.45414	−	3.18412i	−0.122460	−	0.268151i
$142$		0			0
$143$	0.377029	−	5.27156i	0.0315288	−	0.440830i
$144$		0			0
$145$	−15.8405	+	2.47587i	−1.31548	+	0.205609i
$146$		0			0
$147$	−11.7938	+	0.843510i	−0.972737	+	0.0695715i
$148$		0			0
$149$	2.12617	+	14.7879i	0.174183	+	1.21147i	0.869928	+	0.493179i	$0.164165\pi$
$149$	2.12617	+	14.7879i	0.174183	+	1.21147i	−0.695745	+	0.718289i	$0.744925\pi$
$150$		0			0
$151$	0.210782	−	0.135461i	0.0171532	−	0.0110237i	−0.532036	−	0.846722i	$-0.678573\pi$
$151$	0.210782	−	0.135461i	0.0171532	−	0.0110237i	0.549189	+	0.835698i	$0.314937\pi$
$152$		0			0
$153$	−1.70272	+	0.635083i	−0.137657	+	0.0513434i
$154$		0			0
$155$	11.0816	+	6.93143i	0.890092	+	0.556746i
$156$		0			0
$157$	8.42012	−	4.59773i	0.671998	−	0.366939i	−0.106741	−	0.994287i	$-0.534041\pi$
$157$	8.42012	−	4.59773i	0.671998	−	0.366939i	0.778739	+	0.627348i	$0.215860\pi$
$158$		0			0
$159$	−1.28252	+	8.92010i	−0.101710	+	0.707410i
$160$		0			0
$161$	10.4844	+	14.1470i	0.826289	+	1.11494i
$162$		0			0
$163$	−7.57427	−	10.1180i	−0.593263	−	0.792506i	0.398962	−	0.916968i	$-0.369371\pi$
$163$	−7.57427	−	10.1180i	−0.593263	−	0.792506i	−0.992224	+	0.124462i	$0.960280\pi$
$164$		0			0
$165$	−5.85053	+	16.2924i	−0.455463	+	1.26836i
$166$		0			0
$167$	−4.15516	−	2.26889i	−0.321536	−	0.175572i	0.310373	−	0.950615i	$-0.399546\pi$
$167$	−4.15516	−	2.26889i	−0.321536	−	0.175572i	−0.631908	+	0.775043i	$0.717728\pi$
$168$		0			0
$169$	10.4142	+	4.75599i	0.801090	+	0.365846i
$170$		0			0
$171$	1.38102	+	2.14891i	0.105609	+	0.164331i
$172$		0			0
$173$	0.702348	+	0.525771i	0.0533986	+	0.0399737i	0.625644	−	0.780109i	$-0.284836\pi$
$173$	0.702348	+	0.525771i	0.0533986	+	0.0399737i	−0.572245	+	0.820083i	$0.693927\pi$
$174$		0			0
$175$	−18.3380	−	0.860851i	−1.38622	−	0.0650742i
$176$		0			0
$177$	5.45515	+	25.0769i	0.410034	+	1.88490i
$178$		0			0
$179$	11.2759	−	9.77063i	0.842801	−	0.730291i	−0.122209	−	0.992504i	$-0.538998\pi$
$179$	11.2759	−	9.77063i	0.842801	−	0.730291i	0.965010	+	0.262213i	$0.0844524\pi$
$180$		0			0
$181$	−5.95622	+	2.72011i	−0.442722	+	0.202185i	−0.624288	−	0.781194i	$-0.714611\pi$
$181$	−5.95622	+	2.72011i	−0.442722	+	0.202185i	0.181566	+	0.983379i	$0.441884\pi$
$182$		0			0
$183$	5.13273	+	5.13273i	0.379423	+	0.379423i
$184$		0			0
$185$	−6.88136	−	0.407539i	−0.505928	−	0.0299629i
$186$		0			0
$187$	8.20210	−	21.9907i	0.599797	−	1.60812i
$188$		0			0
$189$	11.7188	+	13.5242i	0.852414	+	0.983739i
$190$		0			0
$191$	−1.25448	+	1.95201i	−0.0907711	+	0.141243i	−0.883670	−	0.468111i	$-0.844935\pi$
$191$	−1.25448	+	1.95201i	−0.0907711	+	0.141243i	0.792898	+	0.609354i	$0.208571\pi$
$192$		0			0
$193$	0.482008	+	6.73935i	0.0346957	+	0.485109i	0.984859	+	0.173357i	$0.0554613\pi$
$193$	0.482008	+	6.73935i	0.0346957	+	0.485109i	−0.950163	+	0.311752i	$0.899084\pi$
$194$		0			0
$195$	3.88043	+	3.28008i	0.277883	+	0.234892i
$196$		0			0
$197$	−1.28765	−	0.280112i	−0.0917414	−	0.0199571i	0.166460	−	0.986048i	$-0.446766\pi$
$197$	−1.28765	−	0.280112i	−0.0917414	−	0.0199571i	−0.258202	+	0.966091i	$0.583130\pi$
$198$		0			0
$199$	−6.47956	+	14.1882i	−0.459324	+	1.00578i	0.528318	+	0.849047i	$0.322823\pi$
$199$	−6.47956	+	14.1882i	−0.459324	+	1.00578i	−0.987641	+	0.156732i	$0.949904\pi$
$200$		0			0
$201$	−7.05034	−	24.0112i	−0.497293	−	1.69362i
$202$		0			0
$203$	12.6167	+	23.1058i	0.885519	+	1.62171i
$204$		0			0
$205$	−2.90952	+	1.92058i	−0.203209	+	0.134139i
$206$		0			0
$207$	−0.451203	+	1.50974i	−0.0313608	+	0.104934i
$208$		0			0
$209$	−32.6545	−	4.69501i	−2.25876	−	0.324761i
$210$		0			0
$211$	−0.379891	−	0.111546i	−0.0261527	−	0.00767914i	0.268630	−	0.963243i	$-0.413429\pi$
$211$	−0.379891	−	0.111546i	−0.0261527	−	0.00767914i	−0.294783	+	0.955564i	$0.595247\pi$
$212$		0			0
$213$	−12.4444	+	22.7902i	−0.852677	+	1.56156i
$214$		0			0
$215$	−22.2611	−	11.8039i	−1.51819	−	0.805022i
$216$		0			0
$217$	4.56214	−	20.9718i	0.309698	−	1.42366i
$218$		0			0
$219$	11.9940	−	1.72448i	0.810480	−	0.116529i
$220$		0			0
$221$	−5.20627	−	4.51126i	−0.350212	−	0.303460i
$222$		0			0
$223$	−8.30225	+	1.80604i	−0.555959	+	0.120942i	−0.481762	−	0.876302i	$-0.660003\pi$
$223$	−8.30225	+	1.80604i	−0.555959	+	0.120942i	−0.0741973	+	0.997244i	$0.523639\pi$
$224$		0			0
$225$	−0.921742	−	1.35985i	−0.0614495	−	0.0906566i
$226$		0			0
$227$	−1.78928	−	0.667368i	−0.118759	−	0.0442948i	0.289382	−	0.957214i	$-0.406550\pi$
$227$	−1.78928	−	0.667368i	−0.118759	−	0.0442948i	−0.408141	+	0.912919i	$0.633823\pi$
$228$		0			0
$229$	24.4689			1.61695			0.808476	−	0.588529i	$-0.200293\pi$
$229$	24.4689			1.61695			0.808476	+	0.588529i	$0.200293\pi$
$230$		0			0
$231$	28.4248			1.87021
$232$		0			0
$233$	−3.83672	−	1.43102i	−0.251352	−	0.0937494i	0.220630	−	0.975358i	$-0.429189\pi$
$233$	−3.83672	−	1.43102i	−0.251352	−	0.0937494i	−0.471982	+	0.881608i	$0.656461\pi$
$234$		0			0
$235$	−3.40276	+	2.61290i	−0.221972	+	0.170447i
$236$		0			0
$237$	−5.26370	+	1.14505i	−0.341914	+	0.0743788i
$238$		0			0
$239$	6.05311	+	5.24505i	0.391543	+	0.339274i	0.828279	−	0.560316i	$-0.189320\pi$
$239$	6.05311	+	5.24505i	0.391543	+	0.339274i	−0.436736	+	0.899590i	$0.643866\pi$
$240$		0			0
$241$	−8.67906	+	1.24786i	−0.559067	+	0.0803817i	−0.416055	−	0.909339i	$-0.636588\pi$
$241$	−8.67906	+	1.24786i	−0.559067	+	0.0803817i	−0.143012	+	0.989721i	$0.545679\pi$
$242$		0			0
$243$	−0.722652	+	3.32198i	−0.0463581	+	0.213105i
$244$		0			0
$245$	4.25274	+	13.8536i	0.271697	+	0.885076i
$246$		0			0
$247$	−4.64060	+	8.49862i	−0.295274	+	0.540755i
$248$		0			0
$249$	3.50463	+	1.02905i	0.222097	+	0.0652136i
$250$		0			0
$251$	−21.7283	−	3.12405i	−1.37148	−	0.197188i	−0.583109	−	0.812394i	$-0.698164\pi$
$251$	−21.7283	−	3.12405i	−1.37148	−	0.197188i	−0.788366	+	0.615206i	$0.789073\pi$
$252$		0			0
$253$	−10.9198	−	17.1726i	−0.686519	−	1.07963i
$254$		0			0
$255$	12.4308	+	18.8317i	0.778448	+	1.17928i
$256$		0			0
$257$	1.12427	+	2.05894i	0.0701299	+	0.128433i	0.910392	−	0.413748i	$-0.135780\pi$
$257$	1.12427	+	2.05894i	0.0701299	+	0.128433i	−0.840262	+	0.542181i	$0.817599\pi$
$258$		0			0
$259$	3.18893	+	10.8605i	0.198151	+	0.674839i
$260$		0			0
$261$	−0.978640	+	2.14292i	−0.0605763	+	0.132644i
$262$		0			0
$263$	18.9761	+	4.12801i	1.17012	+	0.254544i	0.755312	−	0.655366i	$-0.227485\pi$
$263$	18.9761	+	4.12801i	1.17012	+	0.254544i	0.414807	+	0.909909i	$0.363849\pi$
$264$		0			0
$265$	11.0065	−	0.922792i	0.676123	−	0.0566866i
$266$		0			0
$267$	−0.973916	−	13.6171i	−0.0596027	−	0.833354i
$268$		0			0
$269$	−1.11377	+	1.73306i	−0.0679079	+	0.105667i	−0.873547	−	0.486740i	$-0.838186\pi$
$269$	−1.11377	+	1.73306i	−0.0679079	+	0.105667i	0.805639	+	0.592407i	$0.201822\pi$
$270$		0			0
$271$	−5.41528	−	6.24957i	−0.328955	−	0.379634i	0.567046	−	0.823686i	$-0.308086\pi$
$271$	−5.41528	−	6.24957i	−0.328955	−	0.379634i	−0.896001	+	0.444052i	$0.853541\pi$
$272$		0			0
$273$	2.91559	−	7.81700i	0.176460	−	0.473107i
$274$		0			0
$275$	21.0685	+	2.50429i	1.27048	+	0.151014i
$276$		0			0
$277$	9.89523	+	9.89523i	0.594547	+	0.594547i	0.938856	−	0.344309i	$-0.111887\pi$
$277$	9.89523	+	9.89523i	0.594547	+	0.594547i	−0.344309	+	0.938856i	$0.611887\pi$
$278$		0			0
$279$	1.74702	−	0.797837i	0.104591	−	0.0477653i
$280$		0			0
$281$	−3.91434	+	3.39179i	−0.233510	+	0.202337i	−0.763754	−	0.645508i	$-0.776646\pi$
$281$	−3.91434	+	3.39179i	−0.233510	+	0.202337i	0.530244	+	0.847845i	$0.322100\pi$
$282$		0			0
$283$	−3.74575	−	17.2189i	−0.222661	−	1.02356i	−0.943736	−	0.330701i	$-0.892715\pi$
$283$	−3.74575	−	17.2189i	−0.222661	−	1.02356i	0.721074	−	0.692858i	$-0.243649\pi$
$284$		0			0
$285$	22.1509	−	22.7001i	1.31210	−	1.34464i
$286$		0			0
$287$	4.58264	+	3.43052i	0.270505	+	0.202497i
$288$		0			0
$289$	−7.34903	−	11.4353i	−0.432296	−	0.672666i
$290$		0			0
$291$	7.46633	+	3.40976i	0.437684	+	0.199884i
$292$		0			0
$293$	11.0712	+	6.04531i	0.646784	+	0.353171i	0.768922	−	0.639342i	$-0.220793\pi$
$293$	11.0712	+	6.04531i	0.646784	+	0.353171i	−0.122138	+	0.992513i	$0.538975\pi$
$294$		0			0
$295$	28.4491	−	13.4157i	1.65637	−	0.781091i
$296$		0			0
$297$	−12.3940	−	16.5565i	−0.719173	−	0.960703i
$298$		0			0
$299$	−5.84265	+	1.24157i	−0.337889	+	0.0718019i
$300$		0			0
$301$	−5.88808	+	40.9525i	−0.339383	+	2.36046i
$302$		0			0
$303$	−0.617744	+	0.337314i	−0.0354885	+	0.0193782i
$304$		0			0
$305$	4.71782	−	7.54257i	0.270142	−	0.431886i
$306$		0			0
$307$	−26.3728	+	9.83653i	−1.50517	+	0.561400i	−0.960751	−	0.277412i	$-0.910523\pi$
$307$	−26.3728	+	9.83653i	−1.50517	+	0.561400i	−0.544421	+	0.838812i	$0.683251\pi$
$308$		0			0
$309$	−16.2843	+	10.4653i	−0.926380	+	0.595348i
$310$		0			0
$311$	3.06230	+	21.2987i	0.173647	+	1.20774i	0.871098	+	0.491109i	$0.163408\pi$
$311$	3.06230	+	21.2987i	0.173647	+	1.20774i	−0.697451	+	0.716632i	$0.745683\pi$
$312$		0			0
$313$	−3.27535	+	0.234258i	−0.185134	+	0.0132410i	−0.163598	−	0.986527i	$-0.552310\pi$
$313$	−3.27535	+	0.234258i	−0.185134	+	0.0132410i	−0.0215356	+	0.999768i	$0.506856\pi$
$314$		0			0
$315$	−1.58998	+	2.17908i	−0.0895852	+	0.122777i
$316$		0			0
$317$	−1.28520	+	17.9695i	−0.0721842	+	1.00927i	0.824289	+	0.566169i	$0.191575\pi$
$317$	−1.28520	+	17.9695i	−0.0721842	+	1.00927i	−0.896473	+	0.443098i	$0.853879\pi$
$318$		0			0
$319$	−12.6392	−	27.6759i	−0.707657	−	1.54955i
$320$		0			0
$321$		−	2.22725i		−	0.124313i
$322$		0			0
$323$	−30.4070	+	30.4070i	−1.69189	+	1.69189i
$324$		0			0
$325$	2.84974	−	5.53710i	0.158075	−	0.307143i
$326$		0			0
$327$	22.5161	+	1.61038i	1.24514	+	0.0890545i
$328$		0			0
$329$	5.92626	+	3.80858i	0.326726	+	0.209974i
$330$		0			0
$331$	16.2601	−	18.7652i	0.893736	−	1.03143i	−0.105578	−	0.994411i	$-0.533669\pi$
$331$	16.2601	−	18.7652i	0.893736	−	1.03143i	0.999315	−	0.0370157i	$-0.0117852\pi$
$332$		0			0
$333$	−0.607006	+	0.810865i	−0.0332637	+	0.0444351i
$334$		0			0
$335$	−26.7374	+	15.0276i	−1.46082	+	0.821047i
$336$		0			0
$337$	12.1168	+	32.4865i	0.660047	+	1.76965i	0.638173	+	0.769893i	$0.279690\pi$
$337$	12.1168	+	32.4865i	0.660047	+	1.76965i	0.0218737	+	0.999761i	$0.493037\pi$
$338$		0			0
$339$	−35.3750	+	10.3870i	−1.92130	+	0.564146i
$340$		0			0
$341$	−6.98818	+	23.7996i	−0.378431	+	1.28882i
$342$		0			0
$343$	−1.52585	+	1.14224i	−0.0823883	+	0.0616751i
$344$		0			0
$345$	19.5249	+	1.25066i	1.05118	+	0.0673334i
$346$		0			0
$347$	0.605017	−	0.452910i	0.0324790	−	0.0243135i	−0.582915	−	0.812533i	$-0.698088\pi$
$347$	0.605017	−	0.452910i	0.0324790	−	0.0243135i	0.615394	+	0.788220i	$0.288997\pi$
$348$		0			0
$349$	1.63191	−	5.55777i	0.0873540	−	0.297501i	−0.904215	−	0.427077i	$-0.859543\pi$
$349$	1.63191	−	5.55777i	0.0873540	−	0.297501i	0.991569	+	0.129576i	$0.0413616\pi$
$350$		0			0
$351$	−5.82441	+	1.71020i	−0.310884	+	0.0912838i
$352$		0			0
$353$	−2.80624	−	7.52382i	−0.149361	−	0.400452i	0.840625	−	0.541618i	$-0.182188\pi$
$353$	−2.80624	−	7.52382i	−0.149361	−	0.400452i	−0.989986	+	0.141165i	$0.954915\pi$
$354$		0			0
$355$	30.6435	+	8.59159i	1.62639	+	0.455994i
$356$		0			0
$357$	22.2038	−	29.6608i	1.17515	−	1.56982i
$358$		0			0
$359$	19.5916	−	22.6099i	1.03401	−	1.19331i	0.0531481	−	0.998587i	$-0.483074\pi$
$359$	19.5916	−	22.6099i	1.03401	−	1.19331i	0.980859	−	0.194721i	$-0.0623801\pi$
$360$		0			0
$361$	34.8648	+	22.4063i	1.83499	+	1.17928i
$362$		0			0
$363$	−12.7496	−	0.911872i	−0.669182	−	0.0478609i
$364$		0			0
$365$	−5.35999	−	13.8503i	−0.280555	−	0.724959i
$366$		0			0
$367$	9.76221	−	9.76221i	0.509583	−	0.509583i	−0.404815	−	0.914399i	$-0.632664\pi$
$367$	9.76221	−	9.76221i	0.509583	−	0.509583i	0.914399	+	0.404815i	$0.132664\pi$
$368$		0			0
$369$			0.512257i			0.0266670i
$370$		0			0
$371$	−7.53400	−	16.4972i	−0.391146	−	0.856490i
$372$		0			0
$373$	0.221861	−	3.10203i	0.0114875	−	0.160617i	−0.988470	−	0.151416i	$-0.951617\pi$
$373$	0.221861	−	3.10203i	0.0114875	−	0.160617i	0.999958	−	0.00920087i	$-0.00292877\pi$
$374$		0			0
$375$	−13.8839	+	14.9434i	−0.716964	+	0.771675i
$376$		0			0
$377$	−8.90748	+	0.637075i	−0.458758	+	0.0328110i
$378$		0			0
$379$	−0.910714	−	6.33416i	−0.0467803	−	0.325364i	−0.999751	−	0.0223024i	$-0.992900\pi$
$379$	−0.910714	−	6.33416i	−0.0467803	−	0.325364i	0.952971	−	0.303061i	$-0.0980087\pi$
$380$		0			0
$381$	−7.78612	+	5.00384i	−0.398895	+	0.256354i
$382$		0			0
$383$	−4.28339	+	1.59762i	−0.218871	+	0.0816346i	−0.456508	−	0.889719i	$-0.650900\pi$
$383$	−4.28339	+	1.59762i	−0.218871	+	0.0816346i	0.237637	+	0.971354i	$0.423627\pi$
$384$		0			0
$385$	−7.82165	−	33.9487i	−0.398628	−	1.73019i
$386$		0			0
$387$	−3.24949	+	1.77435i	−0.165181	+	0.0901955i
$388$		0			0
$389$	1.97442	−	13.7324i	0.100107	−	0.696262i	−0.876527	−	0.481353i	$-0.840146\pi$
$389$	1.97442	−	13.7324i	0.100107	−	0.696262i	0.976634	−	0.214909i	$-0.0689454\pi$
$390$		0			0
$391$	−26.4493	−	2.01968i	−1.33760	−	0.102140i
$392$		0			0
$393$	−4.98984	−	6.66564i	−0.251704	−	0.336237i
$394$		0			0
$395$	2.81598	+	5.97153i	0.141687	+	0.300460i
$396$		0			0
$397$	1.03104	+	0.562988i	0.0517462	+	0.0282556i	0.504914	−	0.863170i	$-0.331524\pi$
$397$	1.03104	+	0.562988i	0.0517462	+	0.0282556i	−0.453168	+	0.891425i	$0.649706\pi$
$398$		0			0
$399$	−47.3728	−	21.6344i	−2.37161	−	1.08308i
$400$		0			0
$401$	−15.9120	−	24.7596i	−0.794609	−	1.23644i	−0.967843	−	0.251555i	$-0.919058\pi$
$401$	−15.9120	−	24.7596i	−0.794609	−	1.23644i	0.173234	−	0.984881i	$-0.444578\pi$
$402$		0			0
$403$	5.82824	+	4.36297i	0.290325	+	0.217335i
$404$		0			0
$405$	22.0856	−	0.270459i	1.09744	−	0.0134392i
$406$		0			0
$407$	−2.78069	−	12.7826i	−0.137833	−	0.633610i
$408$		0			0
$409$	20.4417	−	17.7128i	1.01078	−	0.875844i	0.0184936	−	0.999829i	$-0.494113\pi$
$409$	20.4417	−	17.7128i	1.01078	−	0.875844i	0.992284	+	0.123985i	$0.0395675\pi$
$410$		0			0
$411$	1.94997	−	0.890523i	0.0961851	−	0.0439262i
$412$		0			0
$413$	−36.5199	−	36.5199i	−1.79703	−	1.79703i
$414$		0			0
$415$	0.264662	−	4.46886i	0.0129918	−	0.219368i
$416$		0			0
$417$	−11.8833	+	31.8603i	−0.581927	+	1.56021i
$418$		0			0
$419$	−5.43530	−	6.27268i	−0.265532	−	0.306440i	0.607289	−	0.794481i	$-0.292257\pi$
$419$	−5.43530	−	6.27268i	−0.265532	−	0.306440i	−0.872821	+	0.488041i	$0.837712\pi$
$420$		0			0
$421$	13.8567	−	21.5614i	0.675332	−	1.05084i	−0.319329	−	0.947644i	$-0.603457\pi$
$421$	13.8567	−	21.5614i	0.675332	−	1.05084i	0.994661	−	0.103194i	$-0.0329062\pi$
$422$		0			0
$423$	0.0449716	+	0.628785i	0.00218659	+	0.0305726i
$424$		0			0
$425$	19.0707	−	20.0284i	0.925064	−	0.971522i
$426$		0			0
$427$	−14.2743	−	3.10518i	−0.690781	−	0.150270i
$428$		0			0
$429$	−4.00550	+	8.77083i	−0.193388	+	0.423460i
$430$		0			0
$431$	1.95785	+	6.66783i	0.0943064	+	0.321178i	0.993112	−	0.117169i	$-0.0373821\pi$
$431$	1.95785	+	6.66783i	0.0943064	+	0.321178i	−0.898805	+	0.438348i	$0.855564\pi$
$432$		0			0
$433$	−4.50506	−	8.25041i	−0.216500	−	0.396489i	0.746747	−	0.665108i	$-0.231615\pi$
$433$	−4.50506	−	8.25041i	−0.216500	−	0.396489i	−0.963247	+	0.268619i	$0.913433\pi$
$434$		0			0
$435$	28.6564	+	5.86727i	1.37397	+	0.281314i
$436$		0			0
$437$	5.12859	+	36.9311i	0.245334	+	1.76665i
$438$		0			0
$439$	−8.19211	−	1.17785i	−0.390988	−	0.0562156i	−0.0559825	−	0.998432i	$-0.517829\pi$
$439$	−8.19211	−	1.17785i	−0.390988	−	0.0562156i	−0.335006	+	0.942216i	$0.608738\pi$
$440$		0			0
$441$	2.04311	+	0.599910i	0.0972907	+	0.0285671i
$442$		0			0
$443$	10.1961	−	18.6728i	0.484431	−	0.887169i	−0.515117	−	0.857120i	$-0.672252\pi$
$443$	10.1961	−	18.6728i	0.484431	−	0.887169i	0.999548	−	0.0300498i	$-0.00956657\pi$
$444$		0			0
$445$	−15.9954	+	4.91020i	−0.758254	+	0.232766i
$446$		0			0
$447$	5.79387	−	26.6340i	0.274041	−	1.25975i
$448$		0			0
$449$	18.8848	−	2.71523i	0.891230	−	0.128140i	0.318538	−	0.947910i	$-0.396808\pi$
$449$	18.8848	−	2.71523i	0.891230	−	0.128140i	0.572692	+	0.819771i	$0.305899\pi$
$450$		0			0
$451$	−4.99990	−	4.33243i	−0.235436	−	0.204006i
$452$		0			0
$453$	−0.446678	+	0.0971689i	−0.0209868	+	0.00456539i
$454$		0			0
$455$	−10.1384	−	1.33118i	−0.475295	−	0.0624068i
$456$		0			0
$457$	6.02071	+	2.24561i	0.281637	+	0.105045i	0.486313	−	0.873785i	$-0.338341\pi$
$457$	6.02071	+	2.24561i	0.281637	+	0.105045i	−0.204676	+	0.978830i	$0.565614\pi$
$458$		0			0
$459$	−26.9579			−1.25829
$460$		0			0
$461$	4.43818			0.206707			0.103353	−	0.994645i	$-0.467043\pi$
$461$	4.43818			0.206707			0.103353	+	0.994645i	$0.467043\pi$
$462$		0			0
$463$	6.56503	+	2.44863i	0.305103	+	0.113798i	0.497352	−	0.867549i	$-0.334306\pi$
$463$	6.56503	+	2.44863i	0.305103	+	0.113798i	−0.192250	+	0.981346i	$0.561578\pi$
$464$		0			0
$465$	−14.5235	−	18.9139i	−0.673513	−	0.877112i
$466$		0			0
$467$	29.6946	−	6.45966i	1.37410	−	0.298917i	0.535901	−	0.844281i	$-0.319972\pi$
$467$	29.6946	−	6.45966i	1.37410	−	0.298917i	0.838200	+	0.545364i	$0.183608\pi$
$468$		0			0
$469$	38.0611	+	32.9802i	1.75750	+	1.52288i
$470$		0			0
$471$	−17.3248	+	2.49093i	−0.798283	+	0.114776i
$472$		0			0
$473$	10.1640	−	46.7234i	0.467343	−	2.14834i
$474$		0			0
$475$	−33.2067	−	20.2091i	−1.52363	−	0.927258i
$476$		0			0
$477$	0.777787	−	1.42441i	0.0356124	−	0.0652193i
$478$		0			0
$479$	−5.94643	−	1.74603i	−0.271699	−	0.0797781i	0.143045	−	0.989716i	$-0.454311\pi$
$479$	−5.94643	−	1.74603i	−0.271699	−	0.0797781i	−0.414744	+	0.909938i	$0.636129\pi$
$480$		0			0
$481$	−3.80052	−	0.546432i	−0.173289	−	0.0249152i
$482$		0			0
$483$	−8.90237	−	30.8675i	−0.405072	−	1.40452i
$484$		0			0
$485$	2.01788	−	9.85556i	0.0916272	−	0.447518i
$486$		0			0
$487$	17.3884	+	31.8444i	0.787942	+	1.44301i	0.893723	+	0.448619i	$0.148084\pi$
$487$	17.3884	+	31.8444i	0.787942	+	1.44301i	−0.105780	+	0.994390i	$0.533734\pi$
$488$		0			0
$489$	6.49648	+	22.1250i	0.293781	+	1.00053i
$490$		0			0
$491$	−3.54430	+	7.76094i	−0.159952	+	0.350246i	−0.972591	−	0.232521i	$-0.925303\pi$
$491$	−3.54430	+	7.76094i	−0.159952	+	0.350246i	0.812639	+	0.582767i	$0.198030\pi$
$492$		0			0
$493$	−38.7523	−	8.43006i	−1.74532	−	0.379671i
$494$		0			0
$495$	2.01254	−	2.38089i	0.0904571	−	0.107013i
$496$		0			0
$497$	−3.72797	−	52.1238i	−0.167222	−	2.33807i
$498$		0			0
$499$	−5.65482	+	8.79907i	−0.253144	+	0.393900i	−0.944446	−	0.328666i	$-0.893401\pi$
$499$	−5.65482	+	8.79907i	−0.253144	+	0.393900i	0.691302	+	0.722566i	$0.257037\pi$
$500$		0			0
$501$	5.65625	+	6.52766i	0.252703	+	0.291634i
$502$		0			0
$503$	11.0972	−	29.7527i	0.494799	−	1.32661i	−0.414342	−	0.910121i	$-0.635988\pi$
$503$	11.0972	−	29.7527i	0.494799	−	1.32661i	0.909142	−	0.416487i	$-0.136739\pi$
$504$		0			0
$505$	0.572850	+	0.644974i	0.0254915	+	0.0287010i
$506$		0			0
$507$	−14.7697	−	14.7697i	−0.655947	−	0.655947i
$508$		0			0
$509$	−10.5626	+	4.82379i	−0.468181	+	0.213811i	−0.635514	−	0.772090i	$-0.719212\pi$
$509$	−10.5626	+	4.82379i	−0.468181	+	0.213811i	0.167333	+	0.985900i	$0.446484\pi$
$510$		0			0
$511$	−18.4296	+	15.9694i	−0.815278	+	0.706442i
$512$		0			0
$513$	8.05457	+	37.0262i	0.355618	+	1.63475i
$514$		0			0
$515$	16.9800	+	16.5691i	0.748226	+	0.730123i
$516$		0			0
$517$	−6.51762	−	4.87903i	−0.286644	−	0.214579i
$518$		0			0
$519$	−0.865378	−	1.34655i	−0.0379859	−	0.0591072i
$520$		0			0
$521$	31.1056	+	14.2054i	1.36276	+	0.622351i	0.956587	−	0.291445i	$-0.0941361\pi$
$521$	31.1056	+	14.2054i	1.36276	+	0.622351i	0.406172	+	0.913797i	$0.366863\pi$
$522$		0			0
$523$	8.32223	+	4.54428i	0.363906	+	0.198708i	0.650790	−	0.759258i	$-0.274438\pi$
$523$	8.32223	+	4.54428i	0.363906	+	0.198708i	−0.286884	+	0.957965i	$0.592620\pi$
$524$		0			0
$525$	30.7981	+	13.1634i	1.34414	+	0.574496i
$526$		0			0
$527$	19.3757	+	25.8829i	0.844019	+	1.12748i
$528$		0			0
$529$	−15.2284	+	17.2365i	−0.662105	+	0.749411i
$530$		0			0
$531$	0.657736	−	4.57465i	0.0285433	−	0.198523i
$532$		0			0
$533$	−1.70430	+	0.930617i	−0.0738213	+	0.0403095i
$534$		0			0
$535$	−2.66008	+	0.612874i	−0.115005	+	0.0264968i
$536$		0			0
$537$	−25.5046	+	9.51271i	−1.10060	+	0.410504i
$538$		0			0
$539$	−23.1351	+	14.8680i	−0.996498	+	0.640410i
$540$		0			0
$541$	−0.0279214	−	0.194198i	−0.00120043	−	0.00834920i	0.989212	−	0.146488i	$-0.0467970\pi$
$541$	−0.0279214	−	0.194198i	−0.00120043	−	0.00834920i	−0.990413	+	0.138139i	$0.955888\pi$
$542$		0			0
$543$	11.9159	−	0.852239i	0.511358	−	0.0365731i
$544$		0			0
$545$	−4.27243	−	27.3349i	−0.183011	−	1.17090i
$546$		0			0
$547$	−2.68149	+	37.4921i	−0.114652	+	1.60305i	0.536367	+	0.843985i	$0.319796\pi$
$547$	−2.68149	+	37.4921i	−0.114652	+	1.60305i	−0.651019	+	0.759062i	$0.725658\pi$
$548$		0			0
$549$	−0.543041	−	1.18909i	−0.0231764	−	0.0507493i
$550$		0			0
$551$			55.7445i			2.37480i
$552$		0			0
$553$	7.66561	−	7.66561i	0.325975	−	0.325975i
$554$		0			0
$555$	11.5032	+	5.08403i	0.488283	+	0.215805i
$556$		0			0
$557$	−8.61310	−	0.616021i	−0.364949	−	0.0261017i	−0.112339	−	0.993670i	$-0.535834\pi$
$557$	−8.61310	−	0.616021i	−0.364949	−	0.0261017i	−0.252610	+	0.967568i	$0.581289\pi$
$558$		0			0
$559$	−11.8067	−	7.58769i	−0.499369	−	0.320925i
$560$		0			0
$561$	−28.0414	+	32.3615i	−1.18391	+	1.36630i
$562$		0			0
$563$	9.74292	−	13.0150i	0.410615	−	0.548518i	−0.546788	−	0.837271i	$-0.684150\pi$
$563$	9.74292	−	13.0150i	0.410615	−	0.548518i	0.957404	+	0.288753i	$0.0932407\pi$
$564$		0			0
$565$	22.1397	+	39.3913i	0.931424	+	1.65720i
$566$		0			0
$567$	−12.6742	−	33.9807i	−0.532264	−	1.42706i
$568$		0			0
$569$	−21.0561	+	6.18262i	−0.882717	+	0.259189i	−0.691515	−	0.722362i	$-0.743057\pi$
$569$	−21.0561	+	6.18262i	−0.882717	+	0.259189i	−0.191202	+	0.981551i	$0.561238\pi$
$570$		0			0
$571$	12.0172	−	40.9267i	0.502903	−	1.71273i	−0.181291	−	0.983430i	$-0.558028\pi$
$571$	12.0172	−	40.9267i	0.502903	−	1.71273i	0.684194	−	0.729300i	$-0.260154\pi$
$572$		0			0
$573$	3.38897	−	2.53695i	0.141576	−	0.105983i
$574$		0			0
$575$	−3.87895	−	23.6633i	−0.161763	−	0.986830i
$576$		0			0
$577$	12.9747	−	9.71276i	0.540145	−	0.404348i	−0.294072	−	0.955783i	$-0.595011\pi$
$577$	12.9747	−	9.71276i	0.540145	−	0.404348i	0.834217	+	0.551436i	$0.185920\pi$
$578$		0			0
$579$	3.47289	−	11.8276i	0.144328	−	0.491537i
$580$		0			0
$581$	−7.05299	+	2.07094i	−0.292607	+	0.0859172i
$582$		0			0
$583$	7.32482	+	19.6386i	0.303363	+	0.813348i
$584$		0			0
$585$	−0.448330	−	0.797676i	−0.0185362	−	0.0329798i
$586$		0			0
$587$	11.2982	−	15.0927i	0.466328	−	0.622941i	−0.504299	−	0.863529i	$-0.668249\pi$
$587$	11.2982	−	15.0927i	0.466328	−	0.622941i	0.970627	+	0.240587i	$0.0773401\pi$
$588$		0			0
$589$	29.7606	−	34.3456i	1.22627	−	1.41519i
$590$		0			0
$591$	2.02252	+	1.29980i	0.0831955	+	0.0534665i
$592$		0			0
$593$	−29.9380	−	2.14121i	−1.22940	−	0.0879288i	−0.558520	−	0.829491i	$-0.688631\pi$
$593$	−29.9380	−	2.14121i	−1.22940	−	0.0879288i	−0.670884	+	0.741562i	$0.734085\pi$
$594$		0			0
$595$	−41.5348	−	18.3570i	−1.70276	−	0.752563i
$596$		0			0
$597$	20.1222	−	20.1222i	0.823548	−	0.823548i
$598$		0			0
$599$			28.4062i			1.16065i	0.814386	+	0.580324i	$0.197074\pi$
$599$			28.4062i			1.16065i	−0.814386	+	0.580324i	$0.802926\pi$
$600$		0			0
$601$	5.65565	+	12.3841i	0.230699	+	0.505160i	0.989211	−	0.146499i	$-0.0468006\pi$
$601$	5.65565	+	12.3841i	0.230699	+	0.505160i	−0.758512	+	0.651659i	$0.774073\pi$
$602$		0			0
$603$	−0.321505	+	4.49523i	−0.0130927	+	0.183060i
$604$		0			0
$605$	2.41924	+	15.4782i	0.0983561	+	0.629280i
$606$		0			0
$607$	−18.2712	+	1.30679i	−0.741607	+	0.0530408i	−0.437030	−	0.899447i	$-0.643970\pi$
$607$	−18.2712	+	1.30679i	−0.741607	+	0.0530408i	−0.304577	+	0.952488i	$0.598515\pi$
$608$		0			0
$609$	−6.83539	−	47.5412i	−0.276984	−	1.92647i
$610$		0			0
$611$	−2.01029	+	1.29194i	−0.0813276	+	0.0522661i
$612$		0			0
$613$	−33.0156	+	12.3142i	−1.33349	+	0.497364i	−0.912267	−	0.409595i	$-0.865670\pi$
$613$	−33.0156	+	12.3142i	−1.33349	+	0.497364i	−0.421218	+	0.906959i	$0.638397\pi$
$614$		0			0
$615$	6.19805	−	1.42801i	0.249929	−	0.0575828i
$616$		0			0
$617$	25.8787	−	14.1308i	1.04184	−	0.568886i	0.135209	−	0.990817i	$-0.456829\pi$
$617$	25.8787	−	14.1308i	1.04184	−	0.568886i	0.906628	+	0.421931i	$0.138648\pi$
$618$		0			0
$619$	4.17722	−	29.0532i	0.167897	−	1.16775i	−0.715325	−	0.698792i	$-0.753721\pi$
$619$	4.17722	−	29.0532i	0.167897	−	1.16775i	0.883222	−	0.468955i	$-0.155369\pi$
$620$		0			0
$621$	−14.0976	+	18.6444i	−0.565715	+	0.748174i
$622$		0			0
$623$	16.4646	+	21.9942i	0.659642	+	0.881178i
$624$		0			0
$625$	21.6679	+	12.4701i	0.866715	+	0.498803i
$626$		0			0
$627$	52.8263	+	28.8453i	2.10968	+	1.15197i
$628$		0			0
$629$	−15.5106	−	7.08344i	−0.618447	−	0.282435i
$630$		0			0
$631$	19.5686	+	30.4494i	0.779015	+	1.21217i	0.972918	+	0.231150i	$0.0742489\pi$
$631$	19.5686	+	30.4494i	0.779015	+	1.21217i	−0.193903	+	0.981021i	$0.562115\pi$
$632$		0			0
$633$	0.578267	+	0.432886i	0.0229841	+	0.0172057i
$634$		0			0
$635$	8.11876	+	7.92232i	0.322183	+	0.314388i
$636$		0			0
$637$	1.71579	+	7.88734i	0.0679819	+	0.312508i
$638$		0			0
$639$	3.53409	−	3.06231i	0.139807	−	0.121143i
$640$		0			0
$641$	33.5782	−	15.3346i	1.32626	−	0.605682i	0.378776	−	0.925488i	$-0.376345\pi$
$641$	33.5782	−	15.3346i	1.32626	−	0.605682i	0.947483	+	0.319806i	$0.103618\pi$
$642$		0			0
$643$	−6.33697	−	6.33697i	−0.249906	−	0.249906i	0.571026	−	0.820932i	$-0.306545\pi$
$643$	−6.33697	−	6.33697i	−0.249906	−	0.249906i	−0.820932	+	0.571026i	$0.806545\pi$
$644$		0			0
$645$	30.5273	+	34.3708i	1.20201	+	1.35335i
$646$		0			0
$647$	10.2527	−	27.4886i	0.403076	−	1.08069i	−0.563906	−	0.825839i	$-0.690702\pi$
$647$	10.2527	−	27.4886i	0.403076	−	1.08069i	0.966981	−	0.254848i	$-0.0820254\pi$
$648$		0			0
$649$	39.0881	+	45.1101i	1.53434	+	1.77073i
$650$		0			0
$651$	−21.1696	+	32.9406i	−0.829703	+	1.29104i
$652$		0			0
$653$	3.31371	+	46.3318i	0.129676	+	1.81310i	0.480862	+	0.876796i	$0.340324\pi$
$653$	3.31371	+	46.3318i	0.129676	+	1.81310i	−0.351186	+	0.936306i	$0.614222\pi$
$654$		0			0
$655$	−6.58795	+	7.79372i	−0.257412	+	0.304526i
$656$		0			0
$657$	−2.13233	−	0.463860i	−0.0831901	−	0.0180969i
$658$		0			0
$659$	−8.94494	+	19.5867i	−0.348445	+	0.762989i	0.651545	+	0.758610i	$0.274121\pi$
$659$	−8.94494	+	19.5867i	−0.348445	+	0.762989i	−0.999990	+	0.00437912i	$0.998606\pi$
$660$		0			0
$661$	8.21426	+	27.9752i	0.319498	+	1.08811i	0.950085	+	0.311991i	$0.100996\pi$
$661$	8.21426	+	27.9752i	0.319498	+	1.08811i	−0.630588	+	0.776118i	$0.717186\pi$
$662$		0			0
$663$	6.02336	+	11.0310i	0.233928	+	0.428407i
$664$		0			0
$665$	−12.8032	+	62.5321i	−0.496485	+	2.42489i
$666$		0			0
$667$	−26.0958	+	22.3931i	−1.01043	+	0.867065i
$668$		0			0
$669$	15.3434	+	2.20604i	0.593209	+	0.0852906i
$670$		0			0
$671$	16.1990	+	4.75645i	0.625354	+	0.183621i
$672$		0			0
$673$	3.52587	−	6.45715i	0.135912	−	0.248905i	−0.800855	−	0.598859i	$-0.795621\pi$
$673$	3.52587	−	6.45715i	0.135912	−	0.248905i	0.936767	+	0.349954i	$0.113803\pi$
$674$		0			0
$675$	−5.76164	−	23.6784i	−0.221766	−	0.911383i
$676$		0			0
$677$	4.55209	−	20.9256i	0.174951	−	0.804238i	−0.803095	−	0.595851i	$-0.796815\pi$
$677$	4.55209	−	20.9256i	0.174951	−	0.804238i	0.978046	−	0.208387i	$-0.0668214\pi$
$678$		0			0
$679$	−16.3504	+	2.35084i	−0.627472	+	0.0902169i
$680$		0			0
$681$	2.63311	+	2.28160i	0.100901	+	0.0874312i
$682$		0			0
$683$	−25.6326	+	5.57603i	−0.980804	+	0.213361i	−0.674259	−	0.738495i	$-0.735537\pi$
$683$	−25.6326	+	5.57603i	−0.980804	+	0.213361i	−0.306545	+	0.951856i	$0.599173\pi$
$684$		0			0
$685$	−1.60016	−	2.08387i	−0.0611388	−	0.0796207i
$686$		0			0
$687$	−41.8273	−	15.6008i	−1.59581	−	0.595206i
$688$		0			0
$689$	6.15207			0.234375
$690$		0			0
$691$	17.8727			0.679909			0.339955	−	0.940442i	$-0.389588\pi$
$691$	17.8727			0.679909			0.339955	+	0.940442i	$0.389588\pi$
$692$		0			0
$693$	−4.79624	−	1.78890i	−0.182194	−	0.0679548i
$694$		0			0
$695$	41.3218	+	5.42560i	1.56743	+	0.205805i
$696$		0			0
$697$	−8.42646	+	1.83306i	−0.319175	+	0.0694323i
$698$		0			0
$699$	5.64612	+	4.89239i	0.213556	+	0.185047i
$700$		0			0
$701$	−24.1618	+	3.47394i	−0.912578	+	0.131209i	−0.582580	−	0.812773i	$-0.697957\pi$
$701$	−24.1618	+	3.47394i	−0.912578	+	0.131209i	−0.329997	+	0.943982i	$0.607048\pi$
$702$		0			0
$703$	−5.09469	+	23.4199i	−0.192150	+	0.883299i
$704$		0			0
$705$	7.48261	−	2.29698i	0.281811	−	0.0865094i
$706$		0			0
$707$	0.678836	−	1.24320i	0.0255303	−	0.0467552i
$708$		0			0
$709$	−39.0828	−	11.4758i	−1.46779	−	0.430981i	−0.552407	−	0.833574i	$-0.686291\pi$
$709$	−39.0828	−	11.4758i	−1.46779	−	0.430981i	−0.915379	+	0.402594i	$0.868109\pi$
$710$		0			0
$711$	0.960229	+	0.138060i	0.0360114	+	0.00517766i
$712$		0			0
$713$	28.0334	+	0.134924i	1.04986	+	0.00505294i
$714$		0			0
$715$	11.5775	+	2.37044i	0.432974	+	0.0886493i
$716$		0			0
$717$	−7.00310	−	12.8252i	−0.261535	−	0.478966i
$718$		0			0
$719$	11.1475	+	37.9647i	0.415730	+	1.41585i	0.855532	+	0.517751i	$0.173231\pi$
$719$	11.1475	+	37.9647i	0.415730	+	1.41585i	−0.439802	+	0.898095i	$0.644951\pi$
$720$		0			0
$721$	16.1828	−	35.4354i	0.602680	−	1.31968i
$722$		0			0
$723$	15.6316	+	3.40045i	0.581346	+	0.126464i
$724$		0			0
$725$	−0.877914	−	35.8398i	−0.0326049	−	1.33106i
$726$		0			0
$727$	1.05119	+	14.6976i	0.0389865	+	0.545102i	0.978986	+	0.203927i	$0.0653704\pi$
$727$	1.05119	+	14.6976i	0.0389865	+	0.545102i	−0.940000	+	0.341175i	$0.889175\pi$
$728$		0			0
$729$	−12.6676	+	19.7112i	−0.469170	+	0.730043i
$730$		0			0
$731$	−40.8155	−	47.1036i	−1.50962	−	1.74219i
$732$		0			0
$733$	17.3089	−	46.4070i	0.639319	−	1.71408i	−0.0589662	−	0.998260i	$-0.518780\pi$
$733$	17.3089	−	46.4070i	0.639319	−	1.71408i	0.698285	−	0.715820i	$-0.253947\pi$
$734$		0			0
$735$	1.56308	−	26.3929i	0.0576551	−	0.973516i
$736$		0			0
$737$	−41.1566	−	41.1566i	−1.51602	−	1.51602i
$738$		0			0
$739$	21.8536	−	9.98020i	0.803897	−	0.367127i	0.0292905	−	0.999571i	$-0.490675\pi$
$739$	21.8536	−	9.98020i	0.803897	−	0.367127i	0.774607	+	0.632443i	$0.217948\pi$
$740$		0			0
$741$	13.3512	−	11.5688i	0.490467	−	0.424992i
$742$		0			0
$743$	−1.14007	−	5.24080i	−0.0418250	−	0.192266i	0.951494	−	0.307667i	$-0.0995483\pi$
$743$	−1.14007	−	5.24080i	−0.0418250	−	0.192266i	−0.993319	+	0.115401i	$0.963185\pi$
$744$		0			0
$745$	−33.4042	+	0.409065i	−1.22383	+	0.0149870i
$746$		0			0
$747$	−0.526588	−	0.394199i	−0.0192669	−	0.0144230i
$748$		0			0
$749$	2.42331	+	3.77075i	0.0885459	+	0.137780i
$750$		0			0
$751$	12.2955	+	5.61514i	0.448667	+	0.204900i	0.626917	−	0.779086i	$-0.284316\pi$
$751$	12.2955	+	5.61514i	0.448667	+	0.204900i	−0.178250	+	0.983985i	$0.557044\pi$
$752$		0			0
$753$	35.1505	+	19.1936i	1.28096	+	0.699455i
$754$		0			0
$755$	0.238965	+	0.506745i	0.00869681	+	0.0184423i
$756$		0			0
$757$	−27.1653	−	36.2886i	−0.987340	−	1.31893i	−0.947510	−	0.319725i	$-0.896409\pi$
$757$	−27.1653	−	36.2886i	−0.987340	−	1.31893i	−0.0398294	−	0.999206i	$-0.512681\pi$
$758$		0			0
$759$	7.71743	+	36.3171i	0.280125	+	1.31823i
$760$		0			0
$761$	0.453637	−	3.15512i	0.0164443	−	0.114373i	−0.979946	−	0.199264i	$-0.936145\pi$
$761$	0.453637	−	3.15512i	0.0164443	−	0.114373i	0.996390	+	0.0848907i	$0.0270541\pi$
$762$		0			0
$763$	−39.8720	+	21.7718i	−1.44346	+	0.788191i
$764$		0			0
$765$	−0.912340	−	3.95987i	−0.0329857	−	0.143170i
$766$		0			0
$767$	16.4149	−	6.12245i	0.592709	−	0.221069i
$768$		0			0
$769$	20.1161	−	12.9278i	0.725405	−	0.466190i	−0.125108	−	0.992143i	$-0.539928\pi$
$769$	20.1161	−	12.9278i	0.725405	−	0.466190i	0.850513	+	0.525953i	$0.176291\pi$
$770$		0			0
$771$	−0.609098	−	4.23637i	−0.0219361	−	0.152569i
$772$		0			0
$773$	7.66890	−	0.548490i	0.275831	−	0.0197278i	0.0672615	−	0.997735i	$-0.478574\pi$
$773$	7.66890	−	0.548490i	0.275831	−	0.0197278i	0.208569	+	0.978008i	$0.433119\pi$
$774$		0			0
$775$	−18.5931	+	22.5505i	−0.667883	+	0.810038i
$776$		0			0
$777$	1.47321	−	20.5982i	0.0528511	−	0.738956i
$778$		0			0
$779$	5.03537	+	11.0259i	0.180411	+	0.395045i
$780$		0			0
$781$			60.3942i			2.16107i
$782$		0			0
$783$	−24.7107	+	24.7107i	−0.883087	+	0.883087i
$784$		0			0
$785$	7.74225	+	20.0061i	0.276333	+	0.714049i
$786$		0			0
$787$	34.0468	+	2.43508i	1.21364	+	0.0868011i	0.663438	−	0.748231i	$-0.269097\pi$
$787$	34.0468	+	2.43508i	1.21364	+	0.0868011i	0.550201	+	0.835032i	$0.314551\pi$
$788$		0			0
$789$	−29.8060	−	19.1551i	−1.06112	−	0.681940i
$790$		0			0
$791$	48.5886	−	56.0742i	1.72761	−	1.99377i
$792$		0			0
$793$	2.96962	−	3.96694i	0.105454	−	0.140870i
$794$		0			0
$795$	−19.4029	−	5.44003i	−0.688149	−	0.192938i
$796$		0			0
$797$	−4.34209	−	11.6416i	−0.153805	−	0.412366i	0.837080	−	0.547081i	$-0.184261\pi$
$797$	−4.34209	−	11.6416i	−0.153805	−	0.412366i	−0.990884	+	0.134715i	$0.956988\pi$
$798$		0			0
$799$	−10.1824	+	2.98982i	−0.360227	+	0.105772i
$800$		0			0
$801$	−0.692655	+	2.35897i	−0.0244738	+	0.0833500i
$802$		0			0
$803$	22.5618	−	16.8895i	0.796187	−	0.596018i
$804$		0			0
$805$	−34.4164	+	19.1262i	−1.21302	+	0.674110i
$806$		0			0
$807$	3.00884	−	2.25239i	0.105916	−	0.0792879i
$808$		0			0
$809$	−2.02284	+	6.88916i	−0.0711192	+	0.242210i	−0.987379	−	0.158375i	$-0.949375\pi$
$809$	−2.02284	+	6.88916i	−0.0711192	+	0.242210i	0.916260	+	0.400584i	$0.131193\pi$
$810$		0			0
$811$	−6.99102	+	2.05275i	−0.245488	+	0.0720817i	−0.402162	−	0.915569i	$-0.631741\pi$
$811$	−6.99102	+	2.05275i	−0.245488	+	0.0720817i	0.156674	+	0.987650i	$0.449923\pi$
$812$		0			0
$813$	5.27233	+	14.1357i	0.184909	+	0.495760i
$814$		0			0
$815$	24.6370	−	13.8471i	0.862995	−	0.485042i
$816$		0			0
$817$	−52.5011	+	70.1333i	−1.83678	+	2.45365i
$818$		0			0
$819$	−0.983920	+	1.13550i	−0.0343810	+	0.0396777i
$820$		0			0
$821$	−32.7352	−	21.0377i	−1.14247	−	0.734219i	−0.174342	−	0.984685i	$-0.555780\pi$
$821$	−32.7352	−	21.0377i	−1.14247	−	0.734219i	−0.968125	+	0.250466i	$0.919416\pi$
$822$		0			0
$823$	−9.52231	−	0.681049i	−0.331927	−	0.0237399i	−0.0956188	−	0.995418i	$-0.530483\pi$
$823$	−9.52231	−	0.681049i	−0.331927	−	0.0237399i	−0.236308	+	0.971678i	$0.575938\pi$
$824$		0			0
$825$	−34.4179	−	17.7136i	−1.19828	−	0.616707i
$826$		0			0
$827$	−0.228376	+	0.228376i	−0.00794143	+	0.00794143i	−0.711066	−	0.703125i	$-0.751787\pi$
$827$	−0.228376	+	0.228376i	−0.00794143	+	0.00794143i	0.703125	+	0.711066i	$0.251787\pi$
$828$		0			0
$829$		−	33.4176i		−	1.16064i	−0.814388	−	0.580320i	$-0.802927\pi$
$829$		−	33.4176i		−	1.16064i	0.814388	−	0.580320i	$-0.197073\pi$
$830$		0			0
$831$	−10.6060	−	23.2239i	−0.367918	−	0.805628i
$832$		0			0
$833$	−2.55726	+	35.7551i	−0.0886037	+	1.23884i
$834$		0			0
$835$	6.23977	−	8.55167i	0.215936	−	0.295943i
$836$		0			0
$837$	28.4173	−	2.03244i	0.982245	−	0.0702515i
$838$		0			0
$839$	−4.70767	−	32.7425i	−0.162527	−	1.13040i	−0.893850	−	0.448367i	$-0.852006\pi$
$839$	−4.70767	−	32.7425i	−0.162527	−	1.13040i	0.731323	−	0.682031i	$-0.238903\pi$
$840$		0			0
$841$	−18.8529	+	12.1160i	−0.650100	+	0.417794i
$842$		0			0
$843$	8.85370	−	3.30226i	0.304938	−	0.113736i
$844$		0			0
$845$	−13.5758	+	21.7042i	−0.467021	+	0.746646i
$846$		0			0
$847$	22.5773	−	12.3281i	0.775766	−	0.423600i
$848$		0			0
$849$	−4.57535	+	31.8223i	−0.157026	+	1.09214i
$850$		0			0
$851$	−13.0102	+	7.02303i	−0.445984	+	0.240746i
$852$		0			0
$853$	−15.9762	−	21.3417i	−0.547013	−	0.730724i	0.438797	−	0.898586i	$-0.355405\pi$
$853$	−15.9762	−	21.3417i	−0.547013	−	0.730724i	−0.985811	+	0.167862i	$0.946314\pi$
$854$		0			0
$855$	−5.16623	+	2.43623i	−0.176681	+	0.0833173i
$856$		0			0
$857$	−3.43082	−	1.87337i	−0.117195	−	0.0639931i	0.419582	−	0.907717i	$-0.362177\pi$
$857$	−3.43082	−	1.87337i	−0.117195	−	0.0639931i	−0.536777	+	0.843724i	$0.680358\pi$
$858$		0			0
$859$	32.7411	+	14.9523i	1.11711	+	0.510168i	0.886430	−	0.462862i	$-0.153177\pi$
$859$	32.7411	+	14.9523i	1.11711	+	0.510168i	0.230681	+	0.973030i	$0.425905\pi$
$860$		0			0
$861$	−5.64637	−	8.78592i	−0.192428	−	0.299423i
$862$		0			0
$863$	1.44002	+	1.07799i	0.0490189	+	0.0366951i	0.623506	−	0.781818i	$-0.285708\pi$
$863$	1.44002	+	1.07799i	0.0490189	+	0.0366951i	−0.574487	+	0.818513i	$0.694799\pi$
$864$		0			0
$865$	−1.37011	+	1.40408i	−0.0465851	+	0.0477402i
$866$		0			0
$867$	5.27159	+	24.2331i	0.179033	+	0.823000i
$868$		0			0
$869$	−9.46871	+	8.20468i	−0.321204	+	0.278325i
$870$		0			0
$871$	−15.5399	+	7.09682i	−0.526548	+	0.240467i
$872$		0			0
$873$	−1.04523	−	1.04523i	−0.0353758	−	0.0353758i
$874$		0			0
$875$	7.24672	−	40.4054i	0.244984	−	1.36595i
$876$		0			0
$877$	2.75974	−	7.39915i	0.0931898	−	0.249851i	−0.881989	−	0.471270i	$-0.843796\pi$
$877$	2.75974	−	7.39915i	0.0931898	−	0.249851i	0.975179	+	0.221418i	$0.0710686\pi$
$878$		0			0
$879$	−15.0707	−	17.3926i	−0.508323	−	0.586637i
$880$		0			0
$881$	18.5667	−	28.8904i	0.625530	−	0.973343i	−0.373426	−	0.927660i	$-0.621817\pi$
$881$	18.5667	−	28.8904i	0.625530	−	0.973343i	0.998956	−	0.0456832i	$-0.0145465\pi$
$882$		0			0
$883$	0.421628	+	5.89513i	0.0141889	+	0.198387i	0.999602	+	0.0282078i	$0.00898002\pi$
$883$	0.421628	+	5.89513i	0.0141889	+	0.198387i	−0.985413	+	0.170179i	$0.945565\pi$
$884$		0			0
$885$	−57.1845	+	4.79439i	−1.92224	+	0.161162i
$886$		0			0
$887$	6.42355	+	1.39736i	0.215682	+	0.0469187i	0.319108	−	0.947718i	$-0.396617\pi$
$887$	6.42355	+	1.39736i	0.215682	+	0.0469187i	−0.103426	+	0.994637i	$0.532980\pi$
$888$		0			0
$889$	7.73762	−	16.9430i	0.259511	−	0.568251i
$890$		0			0
$891$	11.8088	+	40.2169i	0.395608	+	1.34732i
$892$		0			0
$893$	7.14879	+	13.0920i	0.239225	+	0.438108i
$894$		0			0
$895$	18.3794	+	27.8433i	0.614357	+	0.930700i
$896$		0			0
$897$	10.7790	+	1.60278i	0.359902	+	0.0535153i
$898$		0			0
$899$	41.4858	+	5.96476i	1.38363	+	0.198936i
$900$		0			0
$901$	26.2143	+	7.69722i	0.873326	+	0.256432i
$902$		0			0
$903$	36.1753	−	66.2502i	1.20384	−	2.20467i
$904$		0			0
$905$	−4.29674	−	13.9970i	−0.142829	−	0.465276i
$906$		0			0
$907$	−8.05388	+	37.0231i	−0.267425	+	1.22933i	0.625894	+	0.779908i	$0.284734\pi$
$907$	−8.05388	+	37.0231i	−0.267425	+	1.22933i	−0.893319	+	0.449423i	$0.851630\pi$
$908$		0			0
$909$	0.125463	−	0.0180389i	0.00416135	−	0.000598312i
$910$		0			0
$911$	−10.6251	−	9.20669i	−0.352025	−	0.305031i	0.460841	−	0.887483i	$-0.347548\pi$
$911$	−10.6251	−	9.20669i	−0.352025	−	0.305031i	−0.812865	+	0.582452i	$0.802093\pi$
$912$		0			0
$913$	8.30123	−	1.80582i	0.274730	−	0.0597640i
$914$		0			0
$915$	−12.8736	+	9.88533i	−0.425588	+	0.326799i
$916$		0			0
$917$	15.7002	+	5.85588i	0.518467	+	0.193378i
$918$		0			0
$919$	−19.2557			−0.635189			−0.317594	−	0.948227i	$-0.602875\pi$
$919$	−19.2557			−0.635189			−0.317594	+	0.948227i	$0.602875\pi$
$920$		0			0
$921$	51.3532			1.69214
$922$		0			0
$923$	16.6088	+	6.19476i	0.546685	+	0.203903i
$924$		0			0
$925$	2.90669	−	15.1376i	0.0955714	−	0.497721i
$926$		0			0
$927$	3.40634	−	0.741004i	0.111879	−	0.0243378i
$928$		0			0
$929$	−2.07309	−	1.79635i	−0.0680160	−	0.0589362i	0.620189	−	0.784452i	$-0.287056\pi$
$929$	−2.07309	−	1.79635i	−0.0680160	−	0.0589362i	−0.688205	+	0.725516i	$0.741601\pi$
$930$		0			0
$931$	49.8732	−	7.17068i	1.63453	−	0.235009i
$932$		0			0
$933$	8.34483	−	38.3606i	0.273198	−	1.25587i
$934$		0			0
$935$	46.3666	+	24.5859i	1.51635	+	0.804044i
$936$		0			0
$937$	−8.47870	+	15.5276i	−0.276987	+	0.507264i	−0.978726	−	0.205170i	$-0.934225\pi$
$937$	−8.47870	+	15.5276i	−0.276987	+	0.507264i	0.701739	+	0.712434i	$0.252407\pi$
$938$		0			0
$939$	5.74825	+	1.68784i	0.187587	+	0.0550806i
$940$		0			0
$941$	−46.4210	−	6.67434i	−1.51328	−	0.217577i	−0.664889	−	0.746943i	$-0.731521\pi$
$941$	−46.4210	−	6.67434i	−1.51328	−	0.217577i	−0.848394	+	0.529365i	$0.822430\pi$
$942$		0			0
$943$	−3.13883	+	6.78644i	−0.102214	+	0.220997i
$944$		0			0
$945$	−33.3949	+	22.0441i	−1.08634	+	0.717093i
$946$		0			0
$947$	7.57550	+	13.8735i	0.246171	+	0.450828i	0.971324	−	0.237760i	$-0.0764130\pi$
$947$	7.57550	+	13.8735i	0.246171	+	0.450828i	−0.725154	+	0.688587i	$0.758231\pi$
$948$		0			0
$949$	−2.33052	−	7.93703i	−0.0756519	−	0.257647i
$950$		0			0
$951$	13.6538	−	29.8977i	0.442755	−	0.969499i
$952$		0			0
$953$	−7.75115	−	1.68616i	−0.251084	−	0.0546201i	0.0852614	−	0.996359i	$-0.472827\pi$
$953$	−7.75115	−	1.68616i	−0.251084	−	0.0546201i	−0.336346	+	0.941739i	$0.609191\pi$
$954$		0			0
$955$	−3.96251	−	3.34947i	−0.128224	−	0.108386i
$956$		0			0
$957$	3.95997	+	55.3677i	0.128008	+	1.78978i
$958$		0			0
$959$	−2.33240	+	3.62928i	−0.0753170	+	0.117196i
$960$		0			0
$961$	−2.07533	−	2.39506i	−0.0669462	−	0.0772600i
$962$		0			0
$963$	−0.140171	+	0.375814i	−0.00451696	+	0.0121104i
$964$		0			0
$965$	−15.0817	−	0.893194i	−0.485497	−	0.0287529i
$966$		0			0
$967$	−15.5704	−	15.5704i	−0.500712	−	0.500712i	0.410947	−	0.911659i	$-0.365198\pi$
$967$	−15.5704	−	15.5704i	−0.500712	−	0.500712i	−0.911659	+	0.410947i	$0.865198\pi$
$968$		0			0
$969$	71.3645	−	32.5911i	2.29256	−	1.04698i
$970$		0			0
$971$	1.06752	−	0.925015i	0.0342585	−	0.0296852i	−0.637563	−	0.770398i	$-0.720058\pi$
$971$	1.06752	−	0.925015i	0.0342585	−	0.0296852i	0.671822	+	0.740713i	$0.265512\pi$
$972$		0			0
$973$	−14.5465	−	66.8690i	−0.466338	−	2.14372i
$974$		0			0
$975$	−8.40166	+	7.64822i	−0.269069	+	0.244939i
$976$		0			0
$977$	−20.1289	−	15.0683i	−0.643982	−	0.482079i	0.226675	−	0.973971i	$-0.427215\pi$
$977$	−20.1289	−	15.0683i	−0.643982	−	0.482079i	−0.870656	+	0.491892i	$0.836306\pi$
$978$		0			0
$979$	−17.1666	−	26.7117i	−0.548646	−	0.853711i
$980$		0			0
$981$	−3.69789	−	1.68877i	−0.118065	−	0.0539183i
$982$		0			0
$983$	3.04568	+	1.66307i	0.0971422	+	0.0530436i	0.527086	−	0.849812i	$-0.323285\pi$
$983$	3.04568	+	1.66307i	0.0971422	+	0.0530436i	−0.429943	+	0.902856i	$0.641467\pi$
$984$		0			0
$985$	0.995853	−	2.77323i	0.0317305	−	0.0883626i
$986$		0			0
$987$	−7.70212	−	10.2888i	−0.245161	−	0.327497i
$988$		0			0
$989$	−53.9218	+	3.59580i	−1.71461	+	0.114340i
$990$		0			0
$991$	−2.56151	+	17.8157i	−0.0813692	+	0.565935i	0.907828	+	0.419343i	$0.137740\pi$
$991$	−2.56151	+	17.8157i	−0.0813692	+	0.565935i	−0.989197	+	0.146592i	$0.953170\pi$
$992$		0			0
$993$	−39.7593	+	21.7102i	−1.26172	+	0.688952i
$994$		0			0
$995$	−29.5697	−	18.4956i	−0.937423	−	0.586351i
$996$		0			0
$997$	−46.6631	+	17.4044i	−1.47784	+	0.551204i	−0.953787	−	0.300484i	$-0.902852\pi$
$997$	−46.6631	+	17.4044i	−1.47784	+	0.551204i	−0.524049	+	0.851688i	$0.675579\pi$
$998$		0			0
$999$	−12.6401	+	8.12329i	−0.399915	+	0.257009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.337.4	yes	240
5.3	odd	4	inner	460.2.x.a.153.9	✓	240
23.20	odd	22	inner	460.2.x.a.457.9	yes	240
115.43	even	44	inner	460.2.x.a.273.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.153.9	✓	240	5.3	odd	4	inner
460.2.x.a.273.4	yes	240	115.43	even	44	inner
460.2.x.a.337.4	yes	240	1.1	even	1	trivial
460.2.x.a.457.9	yes	240	23.20	odd	22	inner

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70940 - 0.637574i) q^{3} +(-0.291100 + 2.21704i) q^{5} +(3.58772 - 0.780461i) q^{7} +(0.248309 + 0.215161i) q^{9} +O(q^{10})\)	\(q+(-1.70940 - 0.637574i) q^{3} +(-0.291100 + 2.21704i) q^{5} +(3.58772 - 0.780461i) q^{7} +(0.248309 + 0.215161i) q^{9} +(-4.20017 + 0.603893i) q^{11} +(-0.264746 + 1.21702i) q^{13} +(1.91113 - 3.60422i) q^{15} +(-2.65078 + 4.85454i) q^{17} +(7.45964 + 2.19035i) q^{19} +(-6.63047 - 0.953317i) q^{21} +(1.97124 + 4.37198i) q^{23} +(-4.83052 - 1.29076i) q^{25} +(2.33580 + 4.27769i) q^{27} +(2.02005 + 6.87967i) q^{29} +(2.42828 - 5.31720i) q^{31} +(7.56481 + 1.64562i) q^{33} +(0.685928 + 8.18131i) q^{35} +(0.219927 + 3.07497i) q^{37} +(1.22850 - 1.91158i) q^{39} +(1.02099 + 1.17829i) q^{41} +(-3.93792 + 10.5580i) q^{43} +(-0.549304 + 0.487878i) q^{45} +(1.35669 + 1.35669i) q^{47} +(5.89521 - 2.69225i) q^{49} +(7.62638 - 6.60830i) q^{51} +(-1.04997 - 4.82663i) q^{53} +(-0.116186 - 9.48773i) q^{55} +(-11.3550 - 8.50027i) q^{57} +(-7.60492 - 11.8335i) q^{59} +(-3.61911 - 1.65279i) q^{61} +(1.05879 + 0.578143i) q^{63} +(-2.62111 - 0.941225i) q^{65} +(8.22002 + 10.9807i) q^{67} +(-0.582184 - 8.73029i) q^{69} +(2.02551 - 14.0878i) q^{71} +(-5.82928 + 3.18303i) q^{73} +(7.43435 + 5.28625i) q^{75} +(-14.5977 + 5.44467i) q^{77} +(2.48387 - 1.59629i) q^{79} +(-1.40575 - 9.77719i) q^{81} +(-1.99694 + 0.142824i) q^{83} +(-9.99106 - 7.29004i) q^{85} +(0.933216 - 13.0481i) q^{87} +(3.10847 + 6.80661i) q^{89} +4.57294i q^{91} +(-7.54102 + 7.54102i) q^{93} +(-7.02759 + 15.9007i) q^{95} +(-4.48751 - 0.320953i) q^{97} +(-1.17288 - 0.753762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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