LMFDB - Embedded newform 720.2.cu.e.113.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(113,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))

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

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

chi := DirichletCharacter("720.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cu (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			113.12
Character	$\chi$	$=$	720.113
Dual form			720.2.cu.e.497.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.985769 + 1.42417i) q^{3} +(2.06252 + 0.863710i) q^{5} +(-2.64986 - 0.710029i) q^{7} +(-1.05652 + 2.80780i) q^{9} +O(q^{10})$	\(q+(0.985769 + 1.42417i) q^{3} +(2.06252 + 0.863710i) q^{5} +(-2.64986 - 0.710029i) q^{7} +(-1.05652 + 2.80780i) q^{9} +(0.765403 - 0.441906i) q^{11} +(1.35352 - 0.362674i) q^{13} +(0.803103 + 3.78880i) q^{15} +(3.83033 + 3.83033i) q^{17} +4.46618i q^{19} +(-1.60095 - 4.47378i) q^{21} +(1.01575 + 3.79082i) q^{23} +(3.50801 + 3.56284i) q^{25} +(-5.04027 + 1.26318i) q^{27} +(-0.874378 - 1.51447i) q^{29} +(-2.74056 + 4.74679i) q^{31} +(1.38386 + 0.654447i) q^{33} +(-4.85215 - 3.75316i) q^{35} +(4.41426 - 4.41426i) q^{37} +(1.85077 + 1.57013i) q^{39} +(-5.85416 - 3.37990i) q^{41} +(1.28815 - 4.80743i) q^{43} +(-4.60422 + 4.87864i) q^{45} +(2.90134 - 10.8280i) q^{47} +(0.455456 + 0.262958i) q^{49} +(-1.67922 + 9.23087i) q^{51} +(-6.79105 + 6.79105i) q^{53} +(1.96034 - 0.250355i) q^{55} +(-6.36060 + 4.40262i) q^{57} +(4.02430 - 6.97029i) q^{59} +(-4.25649 - 7.37246i) q^{61} +(4.79325 - 6.69014i) q^{63} +(3.10491 + 0.421023i) q^{65} +(3.87853 + 14.4749i) q^{67} +(-4.39748 + 5.18347i) q^{69} -11.1410i q^{71} +(10.1583 + 10.1583i) q^{73} +(-1.61601 + 8.50814i) q^{75} +(-2.34198 + 0.627531i) q^{77} +(8.28119 - 4.78115i) q^{79} +(-6.76753 - 5.93300i) q^{81} +(-4.49329 - 1.20397i) q^{83} +(4.59186 + 11.2085i) q^{85} +(1.29492 - 2.73818i) q^{87} -11.3300 q^{89} -3.84415 q^{91} +(-9.46179 + 0.776214i) q^{93} +(-3.85749 + 9.21161i) q^{95} +(11.0528 + 2.96160i) q^{97} +(0.432122 + 2.61598i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q - 12 q^{15} + 16 q^{21} - 24 q^{23} + 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} + 36 q^{47} - 24 q^{51} - 40 q^{57} + 12 q^{61} + 44 q^{63} - 72 q^{65} + 36 q^{75} - 48 q^{77} - 20 q^{81} + 60 q^{83} + 24 q^{85} + 40 q^{87} - 84 q^{93} + 60 q^{95} + 24 q^{97}+O(q^{100}) $ 72 * q - 12 * q^15 + 16 * q^21 - 24 * q^23 + 12 * q^27 + 12 * q^33 + 12 * q^41 - 16 * q^45 + 36 * q^47 - 24 * q^51 - 40 * q^57 + 12 * q^61 + 44 * q^63 - 72 * q^65 + 36 * q^75 - 48 * q^77 - 20 * q^81 + 60 * q^83 + 24 * q^85 + 40 * q^87 - 84 * q^93 + 60 * q^95 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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
$3$	0.985769	+	1.42417i	0.569134	+	0.822245i
$3$	0.985769	+	1.42417i	0.569134	+	0.822245i
$4$		0			0
$5$	2.06252	+	0.863710i	0.922389	+	0.386263i
$5$	2.06252	+	0.863710i	0.922389	+	0.386263i
$6$		0			0
$7$	−2.64986	−	0.710029i	−1.00155	−	0.268366i	−0.279458	−	0.960158i	$-0.590155\pi$
$7$	−2.64986	−	0.710029i	−1.00155	−	0.268366i	−0.722096	+	0.691792i	$0.756821\pi$
$8$		0			0
$9$	−1.05652	+	2.80780i	−0.352173	+	0.935935i
$10$		0			0
$11$	0.765403	−	0.441906i	0.230778	−	0.133240i	−0.380153	−	0.924924i	$-0.624129\pi$
$11$	0.765403	−	0.441906i	0.230778	−	0.133240i	0.610931	+	0.791684i	$0.290795\pi$
$12$		0			0
$13$	1.35352	−	0.362674i	0.375399	−	0.100588i	−0.0661862	−	0.997807i	$-0.521083\pi$
$13$	1.35352	−	0.362674i	0.375399	−	0.100588i	0.441585	+	0.897220i	$0.354416\pi$
$14$		0			0
$15$	0.803103	+	3.78880i	0.207360	+	0.978265i
$16$		0			0
$17$	3.83033	+	3.83033i	0.928992	+	0.928992i	0.997641	−	0.0686484i	$-0.0218687\pi$
$17$	3.83033	+	3.83033i	0.928992	+	0.928992i	−0.0686484	+	0.997641i	$0.521869\pi$
$18$		0			0
$19$			4.46618i			1.02461i	0.858803	+	0.512306i	$0.171209\pi$
$19$			4.46618i			1.02461i	−0.858803	+	0.512306i	$0.828791\pi$
$20$		0			0
$21$	−1.60095	−	4.47378i	−0.349356	−	0.976259i
$22$		0			0
$23$	1.01575	+	3.79082i	0.211798	+	0.790440i	0.987269	+	0.159058i	$0.0508456\pi$
$23$	1.01575	+	3.79082i	0.211798	+	0.790440i	−0.775471	+	0.631383i	$0.782488\pi$
$24$		0			0
$25$	3.50801	+	3.56284i	0.701602	+	0.712569i
$26$		0			0
$27$	−5.04027	+	1.26318i	−0.970001	+	0.243100i
$28$		0			0
$29$	−0.874378	−	1.51447i	−0.162368	−	0.281229i	0.773350	−	0.633980i	$-0.218580\pi$
$29$	−0.874378	−	1.51447i	−0.162368	−	0.281229i	−0.935717	+	0.352750i	$0.885246\pi$
$30$		0			0
$31$	−2.74056	+	4.74679i	−0.492219	+	0.852548i	−0.999960	−	0.00896169i	$-0.997147\pi$
$31$	−2.74056	+	4.74679i	−0.492219	+	0.852548i	0.507741	+	0.861510i	$0.330481\pi$
$32$		0			0
$33$	1.38386	+	0.654447i	0.240899	+	0.113925i
$34$		0			0
$35$	−4.85215	−	3.75316i	−0.820163	−	0.634400i
$36$		0			0
$37$	4.41426	−	4.41426i	0.725699	−	0.725699i	−0.244061	−	0.969760i	$-0.578480\pi$
$37$	4.41426	−	4.41426i	0.725699	−	0.725699i	0.969760	+	0.244061i	$0.0784796\pi$
$38$		0			0
$39$	1.85077	+	1.57013i	0.296360	+	0.251422i
$40$		0			0
$41$	−5.85416	−	3.37990i	−0.914266	−	0.527852i	−0.0324645	−	0.999473i	$-0.510336\pi$
$41$	−5.85416	−	3.37990i	−0.914266	−	0.527852i	−0.881801	+	0.471621i	$0.843669\pi$
$42$		0			0
$43$	1.28815	−	4.80743i	0.196441	−	0.733127i	−0.795449	−	0.606021i	$-0.792765\pi$
$43$	1.28815	−	4.80743i	0.196441	−	0.733127i	0.991889	−	0.127105i	$-0.0405687\pi$
$44$		0			0
$45$	−4.60422	+	4.87864i	−0.686357	+	0.727265i
$46$		0			0
$47$	2.90134	−	10.8280i	0.423205	−	1.57942i	−0.344608	−	0.938747i	$-0.611988\pi$
$47$	2.90134	−	10.8280i	0.423205	−	1.57942i	0.767813	−	0.640674i	$-0.221345\pi$
$48$		0			0
$49$	0.455456	+	0.262958i	0.0650651	+	0.0375654i
$50$		0			0
$51$	−1.67922	+	9.23087i	−0.235138	+	1.29258i
$52$		0			0
$53$	−6.79105	+	6.79105i	−0.932823	+	0.932823i	−0.997881	−	0.0650586i	$-0.979277\pi$
$53$	−6.79105	+	6.79105i	−0.932823	+	0.932823i	0.0650586	+	0.997881i	$0.479277\pi$
$54$		0			0
$55$	1.96034	−	0.250355i	0.264332	−	0.0337579i
$56$		0			0
$57$	−6.36060	+	4.40262i	−0.842482	+	0.583142i
$58$		0			0
$59$	4.02430	−	6.97029i	0.523919	−	0.907455i	−0.475693	−	0.879611i	$-0.657803\pi$
$59$	4.02430	−	6.97029i	0.523919	−	0.907455i	0.999612	−	0.0278435i	$-0.00886401\pi$
$60$		0			0
$61$	−4.25649	−	7.37246i	−0.544988	−	0.943947i	−0.998608	−	0.0527517i	$-0.983201\pi$
$61$	−4.25649	−	7.37246i	−0.544988	−	0.943947i	0.453620	−	0.891195i	$-0.350133\pi$
$62$		0			0
$63$	4.79325	−	6.69014i	0.603893	−	0.842878i
$64$		0			0
$65$	3.10491	+	0.421023i	0.385117	+	0.0522215i
$66$		0			0
$67$	3.87853	+	14.4749i	0.473837	+	1.76839i	0.625784	+	0.779996i	$0.284779\pi$
$67$	3.87853	+	14.4749i	0.473837	+	1.76839i	−0.151947	+	0.988389i	$0.548554\pi$
$68$		0			0
$69$	−4.39748	+	5.18347i	−0.529394	+	0.624016i
$70$		0			0
$71$		−	11.1410i		−	1.32219i	−0.750302	−	0.661095i	$-0.770092\pi$
$71$		−	11.1410i		−	1.32219i	0.750302	−	0.661095i	$-0.229908\pi$
$72$		0			0
$73$	10.1583	+	10.1583i	1.18894	+	1.18894i	0.977361	+	0.211580i	$0.0678609\pi$
$73$	10.1583	+	10.1583i	1.18894	+	1.18894i	0.211580	+	0.977361i	$0.432139\pi$
$74$		0			0
$75$	−1.61601	+	8.50814i	−0.186600	+	0.982436i
$76$		0			0
$77$	−2.34198	+	0.627531i	−0.266893	+	0.0715138i
$78$		0			0
$79$	8.28119	−	4.78115i	0.931707	−	0.537921i	0.0443558	−	0.999016i	$-0.485876\pi$
$79$	8.28119	−	4.78115i	0.931707	−	0.537921i	0.887351	+	0.461095i	$0.152543\pi$
$80$		0			0
$81$	−6.76753	−	5.93300i	−0.751948	−	0.659222i
$82$		0			0
$83$	−4.49329	−	1.20397i	−0.493203	−	0.132153i	0.00364075	−	0.999993i	$-0.498841\pi$
$83$	−4.49329	−	1.20397i	−0.493203	−	0.132153i	−0.496844	+	0.867840i	$0.665508\pi$
$84$		0			0
$85$	4.59186	+	11.2085i	0.498057	+	1.21573i
$86$		0			0
$87$	1.29492	−	2.73818i	0.138830	−	0.293563i
$88$		0			0
$89$	−11.3300			−1.20097			−0.600486	−	0.799635i	$-0.705026\pi$
$89$	−11.3300			−1.20097			−0.600486	+	0.799635i	$0.705026\pi$
$90$		0			0
$91$	−3.84415			−0.402976
$92$		0			0
$93$	−9.46179	+	0.776214i	−0.981142	+	0.0804897i
$94$		0			0
$95$	−3.85749	+	9.21161i	−0.395770	+	0.945091i
$96$		0			0
$97$	11.0528	+	2.96160i	1.12225	+	0.300705i	0.771792	−	0.635875i	$-0.219361\pi$
$97$	11.0528	+	2.96160i	1.12225	+	0.300705i	0.350454	+	0.936580i	$0.386027\pi$
$98$		0			0
$99$	0.432122	+	2.61598i	0.0434299	+	0.262916i
$100$		0			0
$101$	11.3287	−	6.54062i	1.12725	−	0.650816i	0.184005	−	0.982925i	$-0.441094\pi$
$101$	11.3287	−	6.54062i	1.12725	−	0.650816i	0.943241	+	0.332109i	$0.107760\pi$
$102$		0			0
$103$	5.22569	−	1.40022i	0.514902	−	0.137968i	0.00799468	−	0.999968i	$-0.497455\pi$
$103$	5.22569	−	1.40022i	0.514902	−	0.137968i	0.506908	+	0.862000i	$0.330789\pi$
$104$		0			0
$105$	0.562046	−	10.6100i	0.0548501	−	1.03543i
$106$		0			0
$107$	5.25184	+	5.25184i	0.507715	+	0.507715i	0.913824	−	0.406110i	$-0.133115\pi$
$107$	5.25184	+	5.25184i	0.507715	+	0.507715i	−0.406110	+	0.913824i	$0.633115\pi$
$108$		0			0
$109$		−	10.2761i		−	0.984270i	−0.870519	−	0.492135i	$-0.836217\pi$
$109$		−	10.2761i		−	0.984270i	0.870519	−	0.492135i	$-0.163783\pi$
$110$		0			0
$111$	10.6381	+	1.93521i	1.00972	+	0.183682i
$112$		0			0
$113$	−4.46206	−	16.6526i	−0.419755	−	1.56655i	−0.775116	−	0.631818i	$-0.782309\pi$
$113$	−4.46206	−	16.6526i	−0.419755	−	1.56655i	0.355361	−	0.934729i	$-0.384358\pi$
$114$		0			0
$115$	−1.17916	+	8.69596i	−0.109958	+	0.810903i
$116$		0			0
$117$	−0.411700	+	4.18359i	−0.0380617	+	0.386773i
$118$		0			0
$119$	−7.43021	−	12.8695i	−0.681127	−	1.17975i
$120$		0			0
$121$	−5.10944	+	8.84981i	−0.464494	+	0.804528i
$122$		0			0
$123$	−0.957296	−	11.6691i	−0.0863165	−	1.05217i
$124$		0			0
$125$	4.15809	+	10.3784i	0.371911	+	0.928268i
$126$		0			0
$127$	10.6609	−	10.6609i	0.946006	−	0.946006i	−0.0526093	−	0.998615i	$-0.516754\pi$
$127$	10.6609	−	10.6609i	0.946006	−	0.946006i	0.998615	+	0.0526093i	$0.0167538\pi$
$128$		0			0
$129$	8.11642	−	2.90448i	0.714611	−	0.255725i
$130$		0			0
$131$	0.743908	+	0.429496i	0.0649956	+	0.0375252i	0.532146	−	0.846653i	$-0.321386\pi$
$131$	0.743908	+	0.429496i	0.0649956	+	0.0375252i	−0.467150	+	0.884178i	$0.654719\pi$
$132$		0			0
$133$	3.17112	−	11.8348i	0.274971	−	1.02620i
$134$		0			0
$135$	−11.4867	−	1.74799i	−0.988619	−	0.150443i
$136$		0			0
$137$	3.70813	−	13.8389i	0.316807	−	1.18234i	−0.605488	−	0.795854i	$-0.707022\pi$
$137$	3.70813	−	13.8389i	0.316807	−	1.18234i	0.922295	−	0.386486i	$-0.126311\pi$
$138$		0			0
$139$	9.63362	+	5.56197i	0.817113	+	0.471760i	0.849420	−	0.527718i	$-0.176952\pi$
$139$	9.63362	+	5.56197i	0.817113	+	0.471760i	−0.0323071	+	0.999478i	$0.510285\pi$
$140$		0			0
$141$	18.2809	−	6.54187i	1.53953	−	0.550924i
$142$		0			0
$143$	0.875720	−	0.875720i	0.0732314	−	0.0732314i
$144$		0			0
$145$	−0.495365	−	3.87883i	−0.0411379	−	0.322119i
$146$		0			0
$147$	0.0744780	+	0.907862i	0.00614284	+	0.0748792i
$148$		0			0
$149$	0.728908	−	1.26251i	0.0597144	−	0.103428i	−0.834623	−	0.550822i	$-0.814314\pi$
$149$	0.728908	−	1.26251i	0.0597144	−	0.103428i	0.894337	+	0.447394i	$0.147648\pi$
$150$		0			0
$151$	−5.74576	−	9.95194i	−0.467583	−	0.809878i	0.531731	−	0.846913i	$-0.321542\pi$
$151$	−5.74576	−	9.95194i	−0.467583	−	0.809878i	−0.999314	+	0.0370357i	$0.988208\pi$
$152$		0			0
$153$	−14.8017	+	6.70801i	−1.19664	+	0.542310i
$154$		0			0
$155$	−9.75231	+	7.42331i	−0.783325	+	0.596255i
$156$		0			0
$157$	1.12353	+	4.19308i	0.0896675	+	0.334644i	0.996157	−	0.0875844i	$-0.0279147\pi$
$157$	1.12353	+	4.19308i	0.0896675	+	0.334644i	−0.906490	+	0.422228i	$0.861248\pi$
$158$		0			0
$159$	−16.3660	−	2.97720i	−1.29791	−	0.236108i
$160$		0			0
$161$		−	10.7664i		−	0.848508i
$162$		0			0
$163$	−10.7949	−	10.7949i	−0.845523	−	0.845523i	0.144048	−	0.989571i	$-0.453988\pi$
$163$	−10.7949	−	10.7949i	−0.845523	−	0.845523i	−0.989571	+	0.144048i	$0.953988\pi$
$164$		0			0
$165$	2.28899	+	2.54507i	0.178198	+	0.198133i
$166$		0			0
$167$	17.3964	−	4.66134i	1.34617	−	0.360705i	0.487451	−	0.873150i	$-0.337927\pi$
$167$	17.3964	−	4.66134i	1.34617	−	0.360705i	0.858720	+	0.512445i	$0.171260\pi$
$168$		0			0
$169$	−9.55785	+	5.51823i	−0.735219	+	0.424479i
$170$		0			0
$171$	−12.5402	−	4.71861i	−0.958971	−	0.360841i
$172$		0			0
$173$	−12.8049	−	3.43108i	−0.973542	−	0.260860i	−0.263219	−	0.964736i	$-0.584784\pi$
$173$	−12.8049	−	3.43108i	−0.973542	−	0.260860i	−0.710323	+	0.703876i	$0.751451\pi$
$174$		0			0
$175$	−6.76603	−	11.9318i	−0.511464	−	0.901962i
$176$		0			0
$177$	13.8939	−	1.13981i	1.04433	−	0.0856734i
$178$		0			0
$179$	−3.78241			−0.282711			−0.141355	−	0.989959i	$-0.545146\pi$
$179$	−3.78241			−0.282711			−0.141355	+	0.989959i	$0.545146\pi$
$180$		0			0
$181$	−23.0071			−1.71010			−0.855052	−	0.518541i	$-0.826475\pi$
$181$	−23.0071			−1.71010			−0.855052	+	0.518541i	$0.826475\pi$
$182$		0			0
$183$	6.30372	−	13.3295i	0.465984	−	0.985346i
$184$		0			0
$185$	12.9171	−	5.29187i	0.949688	−	0.389066i
$186$		0			0
$187$	4.62440	+	1.23910i	0.338169	+	0.0906122i
$188$		0			0
$189$	14.2529	+	0.231475i	1.03675	+	0.0168373i
$190$		0			0
$191$	−9.51688	+	5.49457i	−0.688617	+	0.397573i	−0.803094	−	0.595853i	$-0.796814\pi$
$191$	−9.51688	+	5.49457i	−0.688617	+	0.397573i	0.114476	+	0.993426i	$0.463481\pi$
$192$		0			0
$193$	10.5657	−	2.83107i	0.760536	−	0.203785i	0.142349	−	0.989816i	$-0.454534\pi$
$193$	10.5657	−	2.83107i	0.760536	−	0.203785i	0.618186	+	0.786031i	$0.287868\pi$
$194$		0			0
$195$	2.46112	+	4.83695i	0.176244	+	0.346381i
$196$		0			0
$197$	4.49711	+	4.49711i	0.320406	+	0.320406i	0.848923	−	0.528517i	$-0.177252\pi$
$197$	4.49711	+	4.49711i	0.320406	+	0.320406i	−0.528517	+	0.848923i	$0.677252\pi$
$198$		0			0
$199$			14.3650i			1.01831i	0.860676	+	0.509154i	$0.170042\pi$
$199$			14.3650i			1.01831i	−0.860676	+	0.509154i	$0.829958\pi$
$200$		0			0
$201$	−16.7913	+	19.7925i	−1.18437	+	1.39606i
$202$		0			0
$203$	1.24167	+	4.63396i	0.0871479	+	0.325240i
$204$		0			0
$205$	−9.15509	−	12.0274i	−0.639419	−	0.840031i
$206$		0			0
$207$	−11.7170	−	1.15305i	−0.814390	−	0.0801428i
$208$		0			0
$209$	1.97363	+	3.41843i	0.136519	+	0.236458i
$210$		0			0
$211$	−0.167767	+	0.290581i	−0.0115496	+	0.0200044i	−0.871742	−	0.489964i	$-0.837010\pi$
$211$	−0.167767	+	0.290581i	−0.0115496	+	0.0200044i	0.860193	+	0.509969i	$0.170343\pi$
$212$		0			0
$213$	15.8666	−	10.9824i	1.08716	−	0.752504i
$214$		0			0
$215$	6.80906	−	8.80286i	0.464374	−	0.600350i
$216$		0			0
$217$	10.6325	−	10.6325i	0.721778	−	0.721778i
$218$		0			0
$219$	−4.45341	+	24.4809i	−0.300934	+	1.65427i
$220$		0			0
$221$	6.57359	+	3.79527i	0.442188	+	0.255297i
$222$		0			0
$223$	−2.22007	+	8.28540i	−0.148667	+	0.554832i	0.850898	+	0.525331i	$0.176058\pi$
$223$	−2.22007	+	8.28540i	−0.148667	+	0.554832i	−0.999565	+	0.0295007i	$0.990608\pi$
$224$		0			0
$225$	−13.7101	+	6.08560i	−0.914003	+	0.405706i
$226$		0			0
$227$	−4.57688	+	17.0812i	−0.303778	+	1.13372i	0.630214	+	0.776422i	$0.282967\pi$
$227$	−4.57688	+	17.0812i	−0.303778	+	1.13372i	−0.933992	+	0.357294i	$0.883699\pi$
$228$		0			0
$229$	4.82045	+	2.78309i	0.318544	+	0.183912i	0.650743	−	0.759298i	$-0.274457\pi$
$229$	4.82045	+	2.78309i	0.318544	+	0.183912i	−0.332199	+	0.943209i	$0.607791\pi$
$230$		0			0
$231$	−3.20236	−	2.71677i	−0.210700	−	0.178751i
$232$		0			0
$233$	12.1252	−	12.1252i	0.794347	−	0.794347i	−0.187851	−	0.982198i	$-0.560152\pi$
$233$	12.1252	−	12.1252i	0.794347	−	0.794347i	0.982198	+	0.187851i	$0.0601521\pi$
$234$		0			0
$235$	15.3363	−	19.8270i	1.00043	−	1.29337i
$236$		0			0
$237$	14.9725	+	7.08072i	0.972569	+	0.459942i
$238$		0			0
$239$	0.849620	−	1.47159i	0.0549574	−	0.0951889i	−0.837238	−	0.546839i	$-0.815831\pi$
$239$	0.849620	−	1.47159i	0.0549574	−	0.0951889i	0.892195	+	0.451650i	$0.149164\pi$
$240$		0			0
$241$	−3.86365	−	6.69204i	−0.248880	−	0.431072i	0.714336	−	0.699803i	$-0.246729\pi$
$241$	−3.86365	−	6.69204i	−0.248880	−	0.431072i	−0.963215	+	0.268731i	$0.913396\pi$
$242$		0			0
$243$	1.77837	−	15.4867i	0.114083	−	0.993471i
$244$		0			0
$245$	0.712270	+	0.935738i	0.0455052	+	0.0597821i
$246$		0			0
$247$	1.61977	+	6.04506i	0.103063	+	0.384638i
$248$		0			0
$249$	−2.71468	−	7.58605i	−0.172036	−	0.480747i
$250$		0			0
$251$		−	8.29943i		−	0.523855i	−0.965088	−	0.261928i	$-0.915642\pi$
$251$		−	8.29943i		−	0.523855i	0.965088	−	0.261928i	$-0.0843582\pi$
$252$		0			0
$253$	2.45264	+	2.45264i	0.154196	+	0.154196i
$254$		0			0
$255$	−11.4362	+	17.5885i	−0.716164	+	1.10144i
$256$		0			0
$257$	−7.35423	+	1.97056i	−0.458744	+	0.122920i	−0.480788	−	0.876837i	$-0.659649\pi$
$257$	−7.35423	+	1.97056i	−0.458744	+	0.122920i	0.0220439	+	0.999757i	$0.492983\pi$
$258$		0			0
$259$	−14.8314	+	8.56293i	−0.921580	+	0.532074i
$260$		0			0
$261$	5.17612	−	0.855019i	0.320394	−	0.0529243i
$262$		0			0
$263$	−2.77517	−	0.743605i	−0.171124	−	0.0458527i	0.172239	−	0.985055i	$-0.444900\pi$
$263$	−2.77517	−	0.743605i	−0.171124	−	0.0458527i	−0.343364	+	0.939202i	$0.611566\pi$
$264$		0			0
$265$	−19.8722	+	8.14121i	−1.22074	+	0.500111i
$266$		0			0
$267$	−11.1687	−	16.1358i	−0.683514	−	0.987493i
$268$		0			0
$269$	−23.8609			−1.45483			−0.727413	−	0.686200i	$-0.759277\pi$
$269$	−23.8609			−1.45483			−0.727413	+	0.686200i	$0.759277\pi$
$270$		0			0
$271$	20.4742			1.24372			0.621859	−	0.783129i	$-0.286378\pi$
$271$	20.4742			1.24372			0.621859	+	0.783129i	$0.286378\pi$
$272$		0			0
$273$	−3.78944	−	5.47472i	−0.229347	−	0.331345i
$274$		0			0
$275$	4.25948	+	1.17680i	0.256857	+	0.0709638i
$276$		0			0
$277$	−0.0780948	−	0.0209254i	−0.00469226	−	0.00125729i	0.256472	−	0.966552i	$-0.417440\pi$
$277$	−0.0780948	−	0.0209254i	−0.00469226	−	0.00125729i	−0.261164	+	0.965294i	$0.584106\pi$
$278$		0			0
$279$	−10.4326	−	12.7100i	−0.624583	−	0.760929i
$280$		0			0
$281$	17.1783	−	9.91792i	1.02477	−	0.591654i	0.109291	−	0.994010i	$-0.465142\pi$
$281$	17.1783	−	9.91792i	1.02477	−	0.591654i	0.915483	+	0.402356i	$0.131809\pi$
$282$		0			0
$283$	−15.1034	+	4.04694i	−0.897803	+	0.240565i	−0.678072	−	0.734995i	$-0.737184\pi$
$283$	−15.1034	+	4.04694i	−0.897803	+	0.240565i	−0.219730	+	0.975561i	$0.570518\pi$
$284$		0			0
$285$	−16.9215	+	3.58680i	−1.00234	+	0.212464i
$286$		0			0
$287$	13.1129	+	13.1129i	0.774029	+	0.774029i
$288$		0			0
$289$			12.3429i			0.726054i
$290$		0			0
$291$	6.67773	+	18.6606i	0.391455	+	1.09390i
$292$		0			0
$293$	−5.44532	−	20.3222i	−0.318119	−	1.18724i	−0.921051	−	0.389443i	$-0.872668\pi$
$293$	−5.44532	−	20.3222i	−0.318119	−	1.18724i	0.602932	−	0.797793i	$-0.293999\pi$
$294$		0			0
$295$	14.3205	−	10.9006i	0.833773	−	0.634656i
$296$		0			0
$297$	−3.29963	+	3.19417i	−0.191464	+	0.185345i
$298$		0			0
$299$	2.74966	+	4.76256i	0.159017	+	0.275426i
$300$		0			0
$301$	−6.82683	+	11.8244i	−0.393492	+	0.681548i
$302$		0			0
$303$	20.4824	+	9.68643i	1.17668	+	0.556471i
$304$		0			0
$305$	−2.41145	−	18.8823i	−0.138079	−	1.08119i
$306$		0			0
$307$	13.6057	−	13.6057i	0.776518	−	0.776518i	−0.202719	−	0.979237i	$-0.564978\pi$
$307$	13.6057	−	13.6057i	0.776518	−	0.776518i	0.979237	+	0.202719i	$0.0649778\pi$
$308$		0			0
$309$	7.14547	+	6.06197i	0.406492	+	0.344854i
$310$		0			0
$311$	−5.94616	−	3.43302i	−0.337176	−	0.194669i	0.321847	−	0.946792i	$-0.395696\pi$
$311$	−5.94616	−	3.43302i	−0.337176	−	0.194669i	−0.659022	+	0.752123i	$0.729030\pi$
$312$		0			0
$313$	−2.87818	+	10.7415i	−0.162684	+	0.607146i	0.835640	+	0.549278i	$0.185097\pi$
$313$	−2.87818	+	10.7415i	−0.162684	+	0.607146i	−0.998324	+	0.0578684i	$0.981570\pi$
$314$		0			0
$315$	15.6645	−	9.65859i	0.882597	−	0.544200i
$316$		0			0
$317$	−4.55850	+	17.0126i	−0.256031	+	0.955520i	0.711483	+	0.702703i	$0.248024\pi$
$317$	−4.55850	+	17.0126i	−0.256031	+	0.955520i	−0.967514	+	0.252817i	$0.918643\pi$
$318$		0			0
$319$	−1.33850	−	0.772785i	−0.0749418	−	0.0432676i
$320$		0			0
$321$	−2.30241	+	12.6566i	−0.128508	+	0.706424i
$322$		0			0
$323$	−17.1070	+	17.1070i	−0.951857	+	0.951857i
$324$		0			0
$325$	6.04031	+	3.55011i	0.335056	+	0.196925i
$326$		0			0
$327$	14.6349	−	10.1298i	0.809311	−	0.560182i
$328$		0			0
$329$	−15.3763	+	26.6326i	−0.847725	+	1.46830i
$330$		0			0
$331$	−11.0665	−	19.1677i	−0.608269	−	1.05355i	−0.991526	−	0.129910i	$-0.958531\pi$
$331$	−11.0665	−	19.1677i	−0.608269	−	1.05355i	0.383257	−	0.923642i	$-0.374802\pi$
$332$		0			0
$333$	7.73062	+	17.0581i	0.423636	+	0.934779i
$334$		0			0
$335$	−4.50252	+	33.2047i	−0.245999	+	1.81416i
$336$		0			0
$337$	−4.91267	−	18.3343i	−0.267610	−	0.998735i	−0.960633	−	0.277820i	$-0.910388\pi$
$337$	−4.91267	−	18.3343i	−0.267610	−	0.998735i	0.693023	−	0.720916i	$-0.256278\pi$
$338$		0			0
$339$	19.3176	−	22.7704i	1.04919	−	1.23672i
$340$		0			0
$341$			4.84427i			0.262332i
$342$		0			0
$343$	12.5587	+	12.5587i	0.678104	+	0.678104i
$344$		0			0
$345$	−13.5469	+	6.89288i	−0.729341	+	0.371100i
$346$		0			0
$347$	0.854912	−	0.229073i	0.0458941	−	0.0122973i	−0.235799	−	0.971802i	$-0.575771\pi$
$347$	0.854912	−	0.229073i	0.0458941	−	0.0122973i	0.281693	+	0.959505i	$0.409104\pi$
$348$		0			0
$349$	−28.5844	+	16.5032i	−1.53009	+	0.883395i	−0.530728	+	0.847542i	$0.678082\pi$
$349$	−28.5844	+	16.5032i	−1.53009	+	0.883395i	−0.999357	+	0.0358533i	$0.988585\pi$
$350$		0			0
$351$	−6.36398	+	3.53772i	−0.339684	+	0.188830i
$352$		0			0
$353$	13.2519	+	3.55083i	0.705326	+	0.188991i	0.593615	−	0.804749i	$-0.297700\pi$
$353$	13.2519	+	3.55083i	0.705326	+	0.188991i	0.111711	+	0.993741i	$0.464367\pi$
$354$		0			0
$355$	9.62257	−	22.9785i	0.510713	−	1.21957i
$356$		0			0
$357$	11.0039	−	23.2682i	0.582388	−	1.23149i
$358$		0			0
$359$	−4.11438			−0.217149			−0.108574	−	0.994088i	$-0.534629\pi$
$359$	−4.11438			−0.217149			−0.108574	+	0.994088i	$0.534629\pi$
$360$		0			0
$361$	−0.946788			−0.0498310
$362$		0			0
$363$	−17.6404	+	1.44716i	−0.925878	+	0.0759560i
$364$		0			0
$365$	12.1779	+	29.7256i	0.637422	+	1.55591i
$366$		0			0
$367$	−8.89755	−	2.38409i	−0.464448	−	0.124449i	0.0190037	−	0.999819i	$-0.493951\pi$
$367$	−8.89755	−	2.38409i	−0.464448	−	0.124449i	−0.483452	+	0.875371i	$0.660617\pi$
$368$		0			0
$369$	15.6751	−	12.8664i	0.816014	−	0.669798i
$370$		0			0
$371$	22.8172	−	13.1735i	1.18461	−	0.683935i
$372$		0			0
$373$	6.70036	−	1.79536i	0.346931	−	0.0929600i	−0.0811456	−	0.996702i	$-0.525858\pi$
$373$	6.70036	−	1.79536i	0.346931	−	0.0929600i	0.428077	+	0.903742i	$0.359191\pi$
$374$		0			0
$375$	−10.6816	+	16.1525i	−0.551596	+	0.834111i
$376$		0			0
$377$	−1.73274	−	1.73274i	−0.0892409	−	0.0892409i
$378$		0			0
$379$			28.1201i			1.44443i	0.691668	+	0.722216i	$0.256876\pi$
$379$			28.1201i			1.44443i	−0.691668	+	0.722216i	$0.743124\pi$
$380$		0			0
$381$	25.6922	+	4.67377i	1.31625	+	0.239444i
$382$		0			0
$383$	4.95085	+	18.4768i	0.252977	+	0.944122i	0.969205	+	0.246256i	$0.0792003\pi$
$383$	4.95085	+	18.4768i	0.252977	+	0.944122i	−0.716228	+	0.697866i	$0.754133\pi$
$384$		0			0
$385$	−5.37239	−	0.728491i	−0.273803	−	0.0371274i
$386$		0			0
$387$	12.1374	+	8.69601i	0.616978	+	0.442043i
$388$		0			0
$389$	1.75380	+	3.03767i	0.0889211	+	0.154016i	0.907055	−	0.421011i	$-0.138325\pi$
$389$	1.75380	+	3.03767i	0.0889211	+	0.154016i	−0.818134	+	0.575027i	$0.804991\pi$
$390$		0			0
$391$	−10.6295	+	18.4107i	−0.537554	+	0.931072i
$392$		0			0
$393$	0.121647	+	1.48283i	0.00613628	+	0.0747991i
$394$		0			0
$395$	21.2097	−	2.70869i	1.06717	−	0.136289i
$396$		0			0
$397$	−6.39991	+	6.39991i	−0.321202	+	0.321202i	−0.849228	−	0.528026i	$-0.822932\pi$
$397$	−6.39991	+	6.39991i	−0.321202	+	0.321202i	0.528026	+	0.849228i	$0.322932\pi$
$398$		0			0
$399$	19.9807	−	7.15014i	1.00029	−	0.357955i
$400$		0			0
$401$	3.59094	+	2.07323i	0.179323	+	0.103532i	0.586975	−	0.809605i	$-0.300319\pi$
$401$	3.59094	+	2.07323i	0.179323	+	0.103532i	−0.407652	+	0.913138i	$0.633652\pi$
$402$		0			0
$403$	−1.98786	+	7.41880i	−0.0990224	+	0.369557i
$404$		0			0
$405$	−8.83381	−	18.0821i	−0.438956	−	0.898509i
$406$		0			0
$407$	1.42800	−	5.32937i	0.0707834	−	0.264167i
$408$		0			0
$409$	27.6500	+	15.9637i	1.36720	+	0.789356i	0.990570	−	0.137006i	$-0.0437479\pi$
$409$	27.6500	+	15.9637i	1.36720	+	0.789356i	0.376635	+	0.926362i	$0.377081\pi$
$410$		0			0
$411$	23.3644	−	8.36098i	1.15248	−	0.412417i
$412$		0			0
$413$	−15.6130	+	15.6130i	−0.768263	+	0.768263i
$414$		0			0
$415$	−8.22764	−	6.36413i	−0.403879	−	0.312403i
$416$		0			0
$417$	1.57533	+	19.2027i	0.0771442	+	0.940361i
$418$		0			0
$419$	−13.0895	+	22.6717i	−0.639466	+	1.10759i	0.346085	+	0.938203i	$0.387511\pi$
$419$	−13.0895	+	22.6717i	−0.639466	+	1.10759i	−0.985550	+	0.169384i	$0.945822\pi$
$420$		0			0
$421$	−0.259922	−	0.450198i	−0.0126678	−	0.0219413i	0.859622	−	0.510931i	$-0.170699\pi$
$421$	−0.259922	−	0.450198i	−0.0126678	−	0.0219413i	−0.872290	+	0.488989i	$0.837366\pi$
$422$		0			0
$423$	27.3375	+	19.5864i	1.32919	+	0.952322i
$424$		0			0
$425$	−0.210029	+	27.0837i	−0.0101879	+	1.31375i
$426$		0			0
$427$	6.04446	+	22.5583i	0.292512	+	1.09167i
$428$		0			0
$429$	2.11043	+	0.383916i	0.101893	+	0.0185357i
$430$		0			0
$431$		−	19.8196i		−	0.954676i	−0.878720	−	0.477338i	$-0.841602\pi$
$431$		−	19.8196i		−	0.954676i	0.878720	−	0.477338i	$-0.158398\pi$
$432$		0			0
$433$	21.6940	+	21.6940i	1.04254	+	1.04254i	0.999054	+	0.0434911i	$0.0138480\pi$
$433$	21.6940	+	21.6940i	1.04254	+	1.04254i	0.0434911	+	0.999054i	$0.486152\pi$
$434$		0			0
$435$	5.03580	−	4.52912i	0.241448	−	0.217155i
$436$		0			0
$437$	−16.9305	+	4.53651i	−0.809895	+	0.217011i
$438$		0			0
$439$	−11.8104	+	6.81876i	−0.563682	+	0.325442i	−0.754622	−	0.656160i	$-0.772180\pi$
$439$	−11.8104	+	6.81876i	−0.563682	+	0.325442i	0.190940	+	0.981602i	$0.438846\pi$
$440$		0			0
$441$	−1.21953	+	1.00101i	−0.0580729	+	0.0476672i
$442$		0			0
$443$	6.60316	+	1.76931i	0.313726	+	0.0840626i	0.412246	−	0.911072i	$-0.364744\pi$
$443$	6.60316	+	1.76931i	0.313726	+	0.0840626i	−0.0985205	+	0.995135i	$0.531411\pi$
$444$		0			0
$445$	−23.3683	−	9.78579i	−1.10776	−	0.463891i
$446$		0			0
$447$	2.51656	−	0.206450i	0.119029	−	0.00976475i
$448$		0			0
$449$	28.2468			1.33305			0.666525	−	0.745482i	$-0.267781\pi$
$449$	28.2468			1.33305			0.666525	+	0.745482i	$0.267781\pi$
$450$		0			0
$451$	−5.97439			−0.281323
$452$		0			0
$453$	8.50927	−	17.9933i	0.399800	−	0.845397i
$454$		0			0
$455$	−7.92865	−	3.32023i	−0.371701	−	0.155655i
$456$		0			0
$457$	−21.7176	−	5.81920i	−1.01590	−	0.272211i	−0.287810	−	0.957687i	$-0.592927\pi$
$457$	−21.7176	−	5.81920i	−1.01590	−	0.272211i	−0.728095	+	0.685477i	$0.759594\pi$
$458$		0			0
$459$	−24.1444	−	14.4675i	−1.12696	−	0.675286i
$460$		0			0
$461$	−23.2134	+	13.4023i	−1.08116	+	0.624206i	−0.931208	−	0.364488i	$-0.881244\pi$
$461$	−23.2134	+	13.4023i	−1.08116	+	0.624206i	−0.149948	+	0.988694i	$0.547911\pi$
$462$		0			0
$463$	−25.7031	+	6.88713i	−1.19452	+	0.320072i	−0.800673	−	0.599102i	$-0.795524\pi$
$463$	−25.7031	+	6.88713i	−1.19452	+	0.320072i	−0.393852	+	0.919174i	$0.628858\pi$
$464$		0			0
$465$	−20.1856	−	6.57128i	−0.936084	−	0.304736i
$466$		0			0
$467$	−0.918499	−	0.918499i	−0.0425031	−	0.0425031i	0.685536	−	0.728039i	$-0.259568\pi$
$467$	−0.918499	−	0.918499i	−0.0425031	−	0.0425031i	−0.728039	+	0.685536i	$0.759568\pi$
$468$		0			0
$469$		−	41.1103i		−	1.89830i
$470$		0			0
$471$	−4.86411	+	5.73350i	−0.224126	+	0.264186i
$472$		0			0
$473$	−1.13848	−	4.24886i	−0.0523473	−	0.195363i
$474$		0			0
$475$	−15.9123	+	15.6674i	−0.730107	+	0.718870i
$476$		0			0
$477$	−11.8931	−	26.2428i	−0.544546	−	1.20158i
$478$		0			0
$479$	−1.07290	−	1.85832i	−0.0490222	−	0.0849089i	0.840473	−	0.541853i	$-0.182277\pi$
$479$	−1.07290	−	1.85832i	−0.0490222	−	0.0849089i	−0.889495	+	0.456944i	$0.848944\pi$
$480$		0			0
$481$	4.37384	−	7.57572i	0.199430	−	0.345423i
$482$		0			0
$483$	15.3331	−	10.6131i	0.697681	−	0.482915i
$484$		0			0
$485$	20.2388	+	15.6548i	0.918996	+	0.710849i
$486$		0			0
$487$	−17.2421	+	17.2421i	−0.781316	+	0.781316i	−0.980053	−	0.198737i	$-0.936316\pi$
$487$	−17.2421	+	17.2421i	−0.781316	+	0.781316i	0.198737	+	0.980053i	$0.436316\pi$
$488$		0			0
$489$	4.73250	−	26.0151i	0.214011	−	1.17644i
$490$		0			0
$491$	−8.57448	−	4.95048i	−0.386961	−	0.223412i	0.293882	−	0.955842i	$-0.405053\pi$
$491$	−8.57448	−	4.95048i	−0.386961	−	0.223412i	−0.680843	+	0.732430i	$0.738386\pi$
$492$		0			0
$493$	2.45175	−	9.15007i	0.110421	−	0.412098i
$494$		0			0
$495$	−1.36819	+	5.76876i	−0.0614955	+	0.259286i
$496$		0			0
$497$	−7.91041	+	29.5221i	−0.354830	+	1.32425i
$498$		0			0
$499$	−7.91417	−	4.56925i	−0.354287	−	0.204548i	0.312285	−	0.949989i	$-0.398906\pi$
$499$	−7.91417	−	4.56925i	−0.354287	−	0.204548i	−0.666572	+	0.745441i	$0.732239\pi$
$500$		0			0
$501$	23.7873	+	20.1804i	1.06274	+	0.901593i
$502$		0			0
$503$	−10.7908	+	10.7908i	−0.481138	+	0.481138i	−0.905495	−	0.424357i	$-0.860500\pi$
$503$	−10.7908	+	10.7908i	−0.481138	+	0.481138i	0.424357	+	0.905495i	$0.360500\pi$
$504$		0			0
$505$	29.0149	−	3.70549i	1.29115	−	0.164892i
$506$		0			0
$507$	−17.2807	−	8.17230i	−0.767464	−	0.362945i
$508$		0			0
$509$	5.74497	−	9.95058i	0.254641	−	0.441052i	−0.710157	−	0.704044i	$-0.751376\pi$
$509$	5.74497	−	9.95058i	0.254641	−	0.441052i	0.964798	+	0.262992i	$0.0847092\pi$
$510$		0			0
$511$	−19.7054	−	34.1308i	−0.871718	−	1.50986i
$512$		0			0
$513$	−5.64161	−	22.5108i	−0.249083	−	0.993876i
$514$		0			0
$515$	11.9875	+	1.62549i	0.528232	+	0.0716277i
$516$		0			0
$517$	−2.56424	−	9.56988i	−0.112775	−	0.420883i
$518$		0			0
$519$	−7.73629	−	21.6187i	−0.339585	−	0.948954i
$520$		0			0
$521$			9.40066i			0.411850i	0.978568	+	0.205925i	$0.0660203\pi$
$521$			9.40066i			0.411850i	−0.978568	+	0.205925i	$0.933980\pi$
$522$		0			0
$523$	−1.46556	−	1.46556i	−0.0640843	−	0.0640843i	0.674338	−	0.738423i	$-0.264429\pi$
$523$	−1.46556	−	1.46556i	−0.0640843	−	0.0640843i	−0.738423	+	0.674338i	$0.764429\pi$
$524$		0			0
$525$	10.3232	−	21.3980i	0.450542	−	0.933886i
$526$		0			0
$527$	−28.6790	+	7.68452i	−1.24928	+	0.334743i
$528$		0			0
$529$	6.58002	−	3.79898i	0.286088	−	0.165173i
$530$		0			0
$531$	15.3195	+	18.6637i	0.664808	+	0.809936i
$532$		0			0
$533$	−9.14951	−	2.45160i	−0.396309	−	0.106191i
$534$		0			0
$535$	6.29598	+	15.3681i	0.272199	+	0.664422i
$536$		0			0
$537$	−3.72858	−	5.38680i	−0.160900	−	0.232457i
$538$		0			0
$539$	0.464810			0.0200208
$540$		0			0
$541$	−7.78309			−0.334621			−0.167311	−	0.985904i	$-0.553508\pi$
$541$	−7.78309			−0.334621			−0.167311	+	0.985904i	$0.553508\pi$
$542$		0			0
$543$	−22.6797	−	32.7660i	−0.973279	−	1.40612i
$544$		0			0
$545$	8.87555	−	21.1947i	0.380187	−	0.907880i
$546$		0			0
$547$	−34.6694	−	9.28964i	−1.48236	−	0.397196i	−0.575208	−	0.818007i	$-0.695079\pi$
$547$	−34.6694	−	9.28964i	−1.48236	−	0.397196i	−0.907148	+	0.420811i	$0.861746\pi$
$548$		0			0
$549$	25.1975	−	4.16225i	1.07540	−	0.177641i
$550$		0			0
$551$	6.76388	−	3.90513i	0.288151	−	0.166364i
$552$		0			0
$553$	−25.3388	+	6.78950i	−1.07751	+	0.288719i
$554$		0			0
$555$	20.2699	+	13.1796i	0.860407	+	0.559445i
$556$		0			0
$557$	6.17130	+	6.17130i	0.261486	+	0.261486i	0.825658	−	0.564171i	$-0.190804\pi$
$557$	6.17130	+	6.17130i	0.261486	+	0.261486i	−0.564171	+	0.825658i	$0.690804\pi$
$558$		0			0
$559$		−	6.97413i		−	0.294974i
$560$		0			0
$561$	2.79389	+	7.80739i	0.117958	+	0.329628i
$562$		0			0
$563$	−9.65058	−	36.0164i	−0.406723	−	1.51791i	−0.800855	−	0.598858i	$-0.795621\pi$
$563$	−9.65058	−	36.0164i	−0.406723	−	1.51791i	0.394132	−	0.919054i	$-0.371045\pi$
$564$		0			0
$565$	5.17993	−	38.2004i	0.217921	−	1.60710i
$566$		0			0
$567$	13.7204	+	20.5268i	0.576204	+	0.862044i
$568$		0			0
$569$	−8.78087	−	15.2089i	−0.368113	−	0.637591i	0.621157	−	0.783686i	$-0.286663\pi$
$569$	−8.78087	−	15.2089i	−0.368113	−	0.637591i	−0.989271	+	0.146095i	$0.953329\pi$
$570$		0			0
$571$	3.87707	−	6.71529i	0.162250	−	0.281026i	−0.773425	−	0.633888i	$-0.781458\pi$
$571$	3.87707	−	6.71529i	0.162250	−	0.281026i	0.935675	+	0.352862i	$0.114791\pi$
$572$		0			0
$573$	−17.2067	−	8.13728i	−0.718818	−	0.339940i
$574$		0			0
$575$	−9.94284	+	16.9172i	−0.414645	+	0.705495i
$576$		0			0
$577$	21.1946	−	21.1946i	0.882344	−	0.882344i	−0.111428	−	0.993772i	$-0.535542\pi$
$577$	21.1946	−	21.1946i	0.882344	−	0.882344i	0.993772	+	0.111428i	$0.0355425\pi$
$578$		0			0
$579$	14.4473	+	12.2566i	0.600408	+	0.509366i
$580$		0			0
$581$	11.0518	+	6.38073i	0.458504	+	0.264717i
$582$		0			0
$583$	−2.19689	+	8.19890i	−0.0909858	+	0.339564i
$584$		0			0
$585$	−4.46255	+	8.27316i	−0.184504	+	0.342053i
$586$		0			0
$587$	1.98989	−	7.42638i	0.0821317	−	0.306520i	−0.912624	−	0.408800i	$-0.865947\pi$
$587$	1.98989	−	7.42638i	0.0821317	−	0.306520i	0.994756	+	0.102281i	$0.0326139\pi$
$588$		0			0
$589$	−21.2000	−	12.2398i	−0.873532	−	0.504334i
$590$		0			0
$591$	−1.97154	+	10.8378i	−0.0810982	+	0.445806i
$592$		0			0
$593$	2.97136	−	2.97136i	0.122019	−	0.122019i	−0.643460	−	0.765479i	$-0.722502\pi$
$593$	2.97136	−	2.97136i	0.122019	−	0.122019i	0.765479	+	0.643460i	$0.222502\pi$
$594$		0			0
$595$	−4.20948	−	32.9612i	−0.172572	−	1.35128i
$596$		0			0
$597$	−20.4582	+	14.1606i	−0.837298	+	0.579553i
$598$		0			0
$599$	5.40103	−	9.35485i	0.220680	−	0.382229i	−0.734335	−	0.678788i	$-0.762506\pi$
$599$	5.40103	−	9.35485i	0.220680	−	0.382229i	0.955015	+	0.296559i	$0.0958390\pi$
$600$		0			0
$601$	13.2730	+	22.9895i	0.541418	+	0.937763i	0.998823	+	0.0485045i	$0.0154455\pi$
$601$	13.2730	+	22.9895i	0.541418	+	0.937763i	−0.457405	+	0.889258i	$0.651221\pi$
$602$		0			0
$603$	−44.7403	−	4.40282i	−1.82197	−	0.179297i
$604$		0			0
$605$	−18.1820	+	13.8399i	−0.739204	+	0.562671i
$606$		0			0
$607$	−8.19313	−	30.5772i	−0.332549	−	1.24109i	−0.906502	−	0.422201i	$-0.861258\pi$
$607$	−8.19313	−	30.5772i	−0.332549	−	1.24109i	0.573953	−	0.818888i	$-0.305409\pi$
$608$		0			0
$609$	−5.37555	+	6.33636i	−0.217828	+	0.256762i
$610$		0			0
$611$		−	15.7081i		−	0.635482i
$612$		0			0
$613$	15.6780	+	15.6780i	0.633228	+	0.633228i	0.948876	−	0.315648i	$-0.102222\pi$
$613$	15.6780	+	15.6780i	0.633228	+	0.633228i	−0.315648	+	0.948876i	$0.602222\pi$
$614$		0			0
$615$	8.10428	−	24.8947i	0.326796	−	1.00385i
$616$		0			0
$617$	−6.01563	+	1.61188i	−0.242180	+	0.0648920i	−0.377867	−	0.925860i	$-0.623342\pi$
$617$	−6.01563	+	1.61188i	−0.242180	+	0.0648920i	0.135687	+	0.990752i	$0.456676\pi$
$618$		0			0
$619$	12.1759	−	7.02976i	0.489391	−	0.282550i	−0.234931	−	0.972012i	$-0.575486\pi$
$619$	12.1759	−	7.02976i	0.489391	−	0.282550i	0.724322	+	0.689462i	$0.242153\pi$
$620$		0			0
$621$	−9.90814	−	17.8237i	−0.397600	−	0.715240i
$622$		0			0
$623$	30.0228	+	8.04459i	1.20284	+	0.322300i
$624$		0			0
$625$	−0.387717	+	24.9970i	−0.0155087	+	0.999880i
$626$		0			0
$627$	−2.92288	+	6.18057i	−0.116729	+	0.246828i
$628$		0			0
$629$	33.8162			1.34834
$630$		0			0
$631$	−33.2378			−1.32318			−0.661589	−	0.749867i	$-0.730118\pi$
$631$	−33.2378			−1.32318			−0.661589	+	0.749867i	$0.730118\pi$
$632$		0			0
$633$	−0.579216	+	0.0475170i	−0.0230218	+	0.00188863i
$634$		0			0
$635$	31.1964	−	12.7805i	1.23799	−	0.507178i
$636$		0			0
$637$	0.711836	+	0.190736i	0.0282040	+	0.00755723i
$638$		0			0
$639$	31.2817	+	11.7707i	1.23748	+	0.465640i
$640$		0			0
$641$	12.3490	−	7.12970i	0.487756	−	0.281606i	−0.235887	−	0.971780i	$-0.575800\pi$
$641$	12.3490	−	7.12970i	0.487756	−	0.281606i	0.723643	+	0.690174i	$0.242466\pi$
$642$		0			0
$643$	35.0630	−	9.39510i	1.38275	−	0.370507i	0.510631	−	0.859800i	$-0.329412\pi$
$643$	35.0630	−	9.39510i	1.38275	−	0.370507i	0.872119	+	0.489293i	$0.162745\pi$
$644$		0			0
$645$	19.2489	+	1.01967i	0.757926	+	0.0401497i
$646$		0			0
$647$	11.6172	+	11.6172i	0.456718	+	0.456718i	0.897577	−	0.440858i	$-0.145326\pi$
$647$	11.6172	+	11.6172i	0.456718	+	0.456718i	−0.440858	+	0.897577i	$0.645326\pi$
$648$		0			0
$649$		−	7.11345i		−	0.279227i
$650$		0			0
$651$	25.6236	+	4.66128i	1.00427	+	0.182690i
$652$		0			0
$653$	8.43066	+	31.4636i	0.329917	+	1.23127i	0.909276	+	0.416194i	$0.136636\pi$
$653$	8.43066	+	31.4636i	0.329917	+	1.23127i	−0.579359	+	0.815073i	$0.696697\pi$
$654$		0			0
$655$	1.16337	+	1.52837i	0.0454566	+	0.0597182i
$656$		0			0
$657$	−39.2550	+	17.7901i	−1.53148	+	0.694058i
$658$		0			0
$659$	−14.2138	−	24.6190i	−0.553691	−	0.959021i	−0.998004	−	0.0631491i	$-0.979886\pi$
$659$	−14.2138	−	24.6190i	−0.553691	−	0.959021i	0.444313	−	0.895871i	$-0.353448\pi$
$660$		0			0
$661$	1.00541	−	1.74143i	0.0391060	−	0.0677336i	−0.845810	−	0.533484i	$-0.820882\pi$
$661$	1.00541	−	1.74143i	0.0391060	−	0.0677336i	0.884916	+	0.465751i	$0.154216\pi$
$662$		0			0
$663$	1.07494	+	13.1032i	0.0417472	+	0.508885i
$664$		0			0
$665$	16.7623	−	21.6706i	0.650015	−	0.840349i
$666$		0			0
$667$	4.85292	−	4.85292i	0.187906	−	0.187906i
$668$		0			0
$669$	−13.9883	+	5.00574i	−0.540819	+	0.193533i
$670$		0			0
$671$	−6.51587	−	3.76194i	−0.251542	−	0.145228i
$672$		0			0
$673$	−5.36532	+	20.0237i	−0.206818	+	0.771855i	0.782070	+	0.623191i	$0.214164\pi$
$673$	−5.36532	+	20.0237i	−0.206818	+	0.771855i	−0.988888	+	0.148664i	$0.952503\pi$
$674$		0			0
$675$	−22.1819	−	13.5264i	−0.853780	−	0.520633i
$676$		0			0
$677$	3.55998	−	13.2860i	0.136821	−	0.510623i	−0.863163	−	0.504926i	$-0.831520\pi$
$677$	3.55998	−	13.2860i	0.136821	−	0.510623i	0.999984	−	0.00569716i	$-0.00181347\pi$
$678$		0			0
$679$	−27.1857	−	15.6957i	−1.04329	−	0.602345i
$680$		0			0
$681$	−28.8382	+	10.3198i	−1.10508	+	0.395456i
$682$		0			0
$683$	−17.6518	+	17.6518i	−0.675426	+	0.675426i	−0.958962	−	0.283536i	$-0.908492\pi$
$683$	−17.6518	+	17.6518i	−0.675426	+	0.675426i	0.283536	+	0.958962i	$0.408492\pi$
$684$		0			0
$685$	19.6009	−	25.3404i	0.748913	−	0.968206i
$686$		0			0
$687$	0.788259	+	9.60861i	0.0300740	+	0.366592i
$688$		0			0
$689$	−6.72888	+	11.6548i	−0.256350	+	0.444011i
$690$		0			0
$691$	5.36784	+	9.29738i	0.204202	+	0.353689i	0.949878	−	0.312620i	$-0.101207\pi$
$691$	5.36784	+	9.29738i	0.204202	+	0.353689i	−0.745676	+	0.666309i	$0.767873\pi$
$692$		0			0
$693$	0.712360	−	7.23882i	0.0270603	−	0.274980i
$694$		0			0
$695$	15.0656	+	19.7923i	0.571472	+	0.750767i
$696$		0			0
$697$	−9.47723	−	35.3695i	−0.358976	−	1.33972i
$698$		0			0
$699$	29.2209	+	5.31569i	1.10524	+	0.201058i
$700$		0			0
$701$		−	38.4271i		−	1.45137i	−0.688026	−	0.725686i	$-0.741522\pi$
$701$		−	38.4271i		−	1.45137i	0.688026	−	0.725686i	$-0.258478\pi$
$702$		0			0
$703$	19.7149	+	19.7149i	0.743561	+	0.743561i
$704$		0			0
$705$	43.3551	+	2.29665i	1.63285	+	0.0864969i
$706$		0			0
$707$	−34.6635	+	9.28805i	−1.30365	+	0.349313i
$708$		0			0
$709$	3.01213	−	1.73906i	0.113123	−	0.0653116i	−0.442371	−	0.896832i	$-0.645863\pi$
$709$	3.01213	−	1.73906i	0.113123	−	0.0653116i	0.555494	+	0.831521i	$0.312529\pi$
$710$		0			0
$711$	4.67529	+	28.3033i	0.175337	+	1.06146i
$712$		0			0
$713$	−20.7779	−	5.56743i	−0.778139	−	0.208502i
$714$		0			0
$715$	2.56256	−	1.04983i	0.0958343	−	0.0392612i
$716$		0			0
$717$	2.93332	−	0.240640i	0.109547	−	0.00898685i
$718$		0			0
$719$	19.6808			0.733970			0.366985	−	0.930227i	$-0.380390\pi$
$719$	19.6808			0.733970			0.366985	+	0.930227i	$0.380390\pi$
$720$		0			0
$721$	−14.8416			−0.552728
$722$		0			0
$723$	5.72193	−	12.0993i	0.212801	−	0.449978i
$724$		0			0
$725$	2.32848	−	8.42804i	0.0864776	−	0.313009i
$726$		0			0
$727$	20.1645	+	5.40306i	0.747860	+	0.200388i	0.612569	−	0.790417i	$-0.290136\pi$
$727$	20.1645	+	5.40306i	0.747860	+	0.200388i	0.135291	+	0.990806i	$0.456803\pi$
$728$		0			0
$729$	23.8087	−	12.7336i	0.881805	−	0.471614i
$730$		0			0
$731$	23.3481	−	13.4800i	0.863561	−	0.498577i
$732$		0			0
$733$	11.2977	−	3.02722i	0.417291	−	0.111813i	−0.0440635	−	0.999029i	$-0.514030\pi$
$733$	11.2977	−	3.02722i	0.417291	−	0.111813i	0.461354	+	0.887216i	$0.347364\pi$
$734$		0			0
$735$	−0.630516	+	1.93681i	−0.0232569	+	0.0714405i
$736$		0			0
$737$	9.36516	+	9.36516i	0.344970	+	0.344970i
$738$		0			0
$739$		−	3.09434i		−	0.113827i	−0.998379	−	0.0569136i	$-0.981874\pi$
$739$		−	3.09434i		−	0.113827i	0.998379	−	0.0569136i	$-0.0181259\pi$
$740$		0			0
$741$	−7.01248	+	8.26586i	−0.257610	+	0.303654i
$742$		0			0
$743$	−4.79197	−	17.8839i	−0.175800	−	0.656096i	−0.996414	−	0.0846124i	$-0.973035\pi$
$743$	−4.79197	−	17.8839i	−0.175800	−	0.656096i	0.820614	−	0.571483i	$-0.193632\pi$
$744$		0			0
$745$	2.59383	−	1.97438i	0.0950305	−	0.0723358i
$746$		0			0
$747$	8.12777	−	11.3443i	0.297380	−	0.415065i
$748$		0			0
$749$	−10.1877	−	17.6456i	−0.372251	−	0.644757i
$750$		0			0
$751$	−27.1986	+	47.1093i	−0.992490	+	1.71904i	−0.390310	+	0.920684i	$0.627632\pi$
$751$	−27.1986	+	47.1093i	−0.992490	+	1.71904i	−0.602181	+	0.798360i	$0.705701\pi$
$752$		0			0
$753$	11.8198	−	8.18132i	0.430737	−	0.298144i
$754$		0			0
$755$	−3.25517	−	25.4888i	−0.118468	−	0.927632i
$756$		0			0
$757$	−23.8602	+	23.8602i	−0.867215	+	0.867215i	−0.992163	−	0.124949i	$-0.960123\pi$
$757$	−23.8602	+	23.8602i	−0.867215	+	0.867215i	0.124949	+	0.992163i	$0.460123\pi$
$758$		0			0
$759$	−1.07524	+	5.91071i	−0.0390287	+	0.214545i
$760$		0			0
$761$	8.20716	+	4.73841i	0.297509	+	0.171767i	0.641323	−	0.767271i	$-0.278386\pi$
$761$	8.20716	+	4.73841i	0.297509	+	0.171767i	−0.343814	+	0.939038i	$0.611719\pi$
$762$		0			0
$763$	−7.29631	+	27.2302i	−0.264144	+	0.985800i
$764$		0			0
$765$	−36.3225	+	1.05110i	−1.31324	+	0.0380025i
$766$		0			0
$767$	2.91902	−	10.8939i	0.105400	−	0.393357i
$768$		0			0
$769$	13.0491	+	7.53390i	0.470562	+	0.271679i	0.716475	−	0.697613i	$-0.245754\pi$
$769$	13.0491	+	7.53390i	0.470562	+	0.271679i	−0.245913	+	0.969292i	$0.579088\pi$
$770$		0			0
$771$	−10.0560	−	8.53115i	−0.362157	−	0.307242i
$772$		0			0
$773$	−29.1782	+	29.1782i	−1.04947	+	1.04947i	−0.0507568	+	0.998711i	$0.516163\pi$
$773$	−29.1782	+	29.1782i	−1.04947	+	1.04947i	−0.998711	+	0.0507568i	$0.983837\pi$
$774$		0			0
$775$	−26.5260	+	6.88760i	−0.952841	+	0.247410i
$776$		0			0
$777$	−26.8154	−	12.6814i	−0.961998	−	0.454943i
$778$		0			0
$779$	15.0952	−	26.1457i	0.540843	−	0.936768i
$780$		0			0
$781$	−4.92326	−	8.52734i	−0.176168	−	0.305132i
$782$		0			0
$783$	6.32015	+	6.52883i	0.225864	+	0.233321i
$784$		0			0
$785$	−1.30429	+	9.61872i	−0.0465521	+	0.343307i
$786$		0			0
$787$	−7.77504	−	29.0169i	−0.277150	−	1.03434i	−0.954387	−	0.298574i	$-0.903489\pi$
$787$	−7.77504	−	29.0169i	−0.277150	−	1.03434i	0.677236	−	0.735766i	$-0.263177\pi$
$788$		0			0
$789$	−1.67666	−	4.68534i	−0.0596906	−	0.166803i
$790$		0			0
$791$			47.2954i			1.68163i
$792$		0			0
$793$	−8.43505	−	8.43505i	−0.299537	−	0.299537i
$794$		0			0
$795$	−31.1839	−	20.2760i	−1.10598	−	0.719117i
$796$		0			0
$797$	−7.09921	+	1.90223i	−0.251467	+	0.0673804i	−0.382350	−	0.924017i	$-0.624885\pi$
$797$	−7.09921	+	1.90223i	−0.251467	+	0.0673804i	0.130883	+	0.991398i	$0.458219\pi$
$798$		0			0
$799$	52.5878	−	30.3616i	1.86042	−	1.07412i
$800$		0			0
$801$	11.9703	−	31.8123i	0.422950	−	1.12403i
$802$		0			0
$803$	12.2642	+	3.28619i	0.432795	+	0.115967i
$804$		0			0
$805$	9.29901	−	22.2059i	0.327747	−	0.782654i
$806$		0			0
$807$	−23.5213	−	33.9820i	−0.827991	−	1.19622i
$808$		0			0
$809$	−9.95255			−0.349913			−0.174957	−	0.984576i	$-0.555979\pi$
$809$	−9.95255			−0.349913			−0.174957	+	0.984576i	$0.555979\pi$
$810$		0			0
$811$	17.0435			0.598480			0.299240	−	0.954178i	$-0.403267\pi$
$811$	17.0435			0.598480			0.299240	+	0.954178i	$0.403267\pi$
$812$		0			0
$813$	20.1828	+	29.1587i	0.707843	+	1.02264i
$814$		0			0
$815$	−12.9411	−	31.5884i	−0.453307	−	1.10649i
$816$		0			0
$817$	21.4709	+	5.75310i	0.751171	+	0.201276i
$818$		0			0
$819$	4.06142	−	10.7936i	0.141917	−	0.377160i
$820$		0			0
$821$	−20.0949	+	11.6018i	−0.701317	+	0.404905i	−0.807838	−	0.589405i	$-0.799362\pi$
$821$	−20.0949	+	11.6018i	−0.701317	+	0.404905i	0.106521	+	0.994310i	$0.466029\pi$
$822$		0			0
$823$	36.7186	−	9.83871i	1.27993	−	0.342956i	0.446102	−	0.894982i	$-0.352812\pi$
$823$	36.7186	−	9.83871i	1.27993	−	0.342956i	0.833827	+	0.552026i	$0.186145\pi$
$824$		0			0
$825$	2.52290	+	7.22628i	0.0878361	+	0.251587i
$826$		0			0
$827$	5.71693	+	5.71693i	0.198797	+	0.198797i	0.799484	−	0.600687i	$-0.205106\pi$
$827$	5.71693	+	5.71693i	0.198797	+	0.198797i	−0.600687	+	0.799484i	$0.705106\pi$
$828$		0			0
$829$			44.6644i			1.55126i	0.631189	+	0.775629i	$0.282567\pi$
$829$			44.6644i			1.55126i	−0.631189	+	0.775629i	$0.717433\pi$
$830$		0			0
$831$	−0.0471820	−	0.131848i	−0.00163673	−	0.00457375i
$832$		0			0
$833$	0.737333	+	2.75176i	0.0255471	+	0.0953430i
$834$		0			0
$835$	39.9065	+	5.41128i	1.38102	+	0.187265i
$836$		0			0
$837$	7.81710	−	27.3869i	0.270199	−	0.946631i
$838$		0			0
$839$	−10.5225	−	18.2255i	−0.363277	−	0.629215i	0.625221	−	0.780448i	$-0.285009\pi$
$839$	−10.5225	−	18.2255i	−0.363277	−	0.629215i	−0.988498	+	0.151233i	$0.951676\pi$
$840$		0			0
$841$	12.9709	−	22.4663i	0.447273	−	0.774700i
$842$		0			0
$843$	31.0587	+	14.6881i	1.06972	+	0.505885i
$844$		0			0
$845$	−24.4794	+	3.12627i	−0.842118	+	0.107547i
$846$		0			0
$847$	19.8229	−	19.8229i	0.681124	−	0.681124i
$848$		0			0
$849$	−20.6520	−	17.5204i	−0.708774	−	0.601300i
$850$		0			0
$851$	21.2174	+	12.2499i	0.727323	+	0.419920i
$852$		0			0
$853$	1.07750	−	4.02129i	0.0368929	−	0.137686i	−0.945023	−	0.327004i	$-0.893961\pi$
$853$	1.07750	−	4.02129i	0.0368929	−	0.137686i	0.981916	+	0.189318i	$0.0606276\pi$
$854$		0			0
$855$	−21.7889	−	20.5633i	−0.745164	−	0.703250i
$856$		0			0
$857$	2.32222	−	8.66663i	0.0793254	−	0.296047i	−0.914854	−	0.403785i	$-0.867694\pi$
$857$	2.32222	−	8.66663i	0.0793254	−	0.296047i	0.994179	+	0.107739i	$0.0343610\pi$
$858$		0			0
$859$	29.3253	+	16.9310i	1.00057	+	0.577677i	0.908416	−	0.418068i	$-0.137293\pi$
$859$	29.3253	+	16.9310i	1.00057	+	0.577677i	0.0921499	+	0.995745i	$0.470626\pi$
$860$		0			0
$861$	−5.74870	+	31.6013i	−0.195915	+	1.07697i
$862$		0			0
$863$	−23.6082	+	23.6082i	−0.803631	+	0.803631i	−0.983661	−	0.180030i	$-0.942380\pi$
$863$	−23.6082	+	23.6082i	−0.803631	+	0.803631i	0.180030	+	0.983661i	$0.442380\pi$
$864$		0			0
$865$	−23.4471	−	18.1364i	−0.797224	−	0.616657i
$866$		0			0
$867$	−17.5784	+	12.1673i	−0.596994	+	0.413222i
$868$		0			0
$869$	4.22563	−	7.31901i	0.143345	−	0.248280i
$870$		0			0
$871$	10.4993	+	18.1853i	0.355756	+	0.616187i
$872$		0			0
$873$	−19.9931	+	27.9052i	−0.676665	+	0.944449i
$874$		0			0
$875$	−3.64945	−	30.4536i	−0.123374	−	1.02952i
$876$		0			0
$877$	10.4930	+	39.1603i	0.354322	+	1.32235i	0.881335	+	0.472491i	$0.156645\pi$
$877$	10.4930	+	39.1603i	0.354322	+	1.32235i	−0.527013	+	0.849857i	$0.676688\pi$
$878$		0			0
$879$	23.5744	−	27.7880i	0.795146	−	0.937268i
$880$		0			0
$881$		−	55.0463i		−	1.85456i	−0.374373	−	0.927278i	$-0.622142\pi$
$881$		−	55.0463i		−	1.85456i	0.374373	−	0.927278i	$-0.377858\pi$
$882$		0			0
$883$	−24.7855	−	24.7855i	−0.834098	−	0.834098i	0.153976	−	0.988075i	$-0.450792\pi$
$883$	−24.7855	−	24.7855i	−0.834098	−	0.834098i	−0.988075	+	0.153976i	$0.950792\pi$
$884$		0			0
$885$	29.6410	+	9.64942i	0.996371	+	0.324362i
$886$		0			0
$887$	−4.54754	+	1.21851i	−0.152692	+	0.0409136i	−0.334355	−	0.942447i	$-0.608518\pi$
$887$	−4.54754	+	1.21851i	−0.152692	+	0.0409136i	0.181664	+	0.983361i	$0.441852\pi$
$888$		0			0
$889$	−35.8196	+	20.6805i	−1.20135	+	0.693601i
$890$		0			0
$891$	−7.80172	−	1.55052i	−0.261367	−	0.0519445i
$892$		0			0
$893$	48.3597	+	12.9579i	1.61829	+	0.433621i
$894$		0			0
$895$	−7.80132	−	3.26691i	−0.260769	−	0.109201i
$896$		0			0
$897$	−4.07216	+	8.61077i	−0.135965	+	0.287505i
$898$		0			0
$899$	9.58513			0.319682
$900$		0			0
$901$	−52.0240			−1.73317
$902$		0			0
$903$	−23.5697	+	1.93358i	−0.784349	+	0.0643454i
$904$		0			0
$905$	−47.4527	−	19.8715i	−1.57738	−	0.660550i
$906$		0			0
$907$	−37.0766	−	9.93464i	−1.23111	−	0.329874i	−0.416097	−	0.909320i	$-0.636602\pi$
$907$	−37.0766	−	9.93464i	−1.23111	−	0.329874i	−0.815011	+	0.579446i	$0.803269\pi$
$908$		0			0
$909$	6.39581	+	38.7190i	0.212136	+	1.28423i
$910$		0			0
$911$	−19.6058	+	11.3194i	−0.649570	+	0.375029i	−0.788291	−	0.615302i	$-0.789034\pi$
$911$	−19.6058	+	11.3194i	−0.649570	+	0.375029i	0.138721	+	0.990331i	$0.455701\pi$
$912$		0			0
$913$	−3.97122	+	1.06409i	−0.131428	+	0.0352161i
$914$		0			0
$915$	24.5144	−	22.0479i	0.810421	−	0.728880i
$916$		0			0
$917$	−1.66630	−	1.66630i	−0.0550261	−	0.0550261i
$918$		0			0
$919$			34.4135i			1.13520i	0.823306	+	0.567598i	$0.192127\pi$
$919$			34.4135i			1.13520i	−0.823306	+	0.567598i	$0.807873\pi$
$920$		0			0
$921$	32.7889	+	5.96475i	1.08043	+	0.196545i
$922$		0			0
$923$	−4.04055	−	15.0795i	−0.132996	−	0.496348i
$924$		0			0
$925$	31.2126	+	0.242048i	1.02626	+	0.00795848i
$926$		0			0
$927$	−1.58950	+	16.1521i	−0.0522060	+	0.530504i
$928$		0			0
$929$	−29.2552	−	50.6715i	−0.959832	−	1.66248i	−0.722901	−	0.690951i	$-0.757192\pi$
$929$	−29.2552	−	50.6715i	−0.959832	−	1.66248i	−0.236931	−	0.971527i	$-0.576141\pi$
$930$		0			0
$931$	−1.17442	+	2.03415i	−0.0384899	+	0.0666665i
$932$		0			0
$933$	−0.972341	−	11.8525i	−0.0318330	−	0.388034i
$934$		0			0
$935$	8.46770	+	6.54982i	0.276923	+	0.214202i
$936$		0			0
$937$	−33.6817	+	33.6817i	−1.10033	+	1.10033i	−0.105963	+	0.994370i	$0.533793\pi$
$937$	−33.6817	+	33.6817i	−1.10033	+	1.10033i	−0.994370	+	0.105963i	$0.966207\pi$
$938$		0			0
$939$	−18.1350	+	6.48963i	−0.591812	+	0.211781i
$940$		0			0
$941$	4.64011	+	2.67897i	0.151263	+	0.0873320i	0.573721	−	0.819051i	$-0.305499\pi$
$941$	4.64011	+	2.67897i	0.151263	+	0.0873320i	−0.422458	+	0.906383i	$0.638833\pi$
$942$		0			0
$943$	6.86624	−	25.6252i	0.223596	−	0.834470i
$944$		0			0
$945$	29.1971	+	12.7878i	0.949781	+	0.415988i
$946$		0			0
$947$	−8.28954	+	30.9370i	−0.269374	+	1.00532i	0.690145	+	0.723671i	$0.257547\pi$
$947$	−8.28954	+	30.9370i	−0.269374	+	1.00532i	−0.959519	+	0.281646i	$0.909120\pi$
$948$		0			0
$949$	17.4336	+	10.0653i	0.565920	+	0.326734i
$950$		0			0
$951$	−28.7224	+	10.2784i	−0.931388	+	0.333299i
$952$		0			0
$953$	−31.7285	+	31.7285i	−1.02779	+	1.02779i	−0.0281830	+	0.999603i	$0.508972\pi$
$953$	−31.7285	+	31.7285i	−1.02779	+	1.02779i	−0.999603	+	0.0281830i	$0.991028\pi$
$954$		0			0
$955$	−24.3745	+	3.11287i	−0.788741	+	0.100730i
$956$		0			0
$957$	−0.218877	−	2.66804i	−0.00707530	−	0.0862456i
$958$		0			0
$959$	−19.6521	+	34.0384i	−0.634599	+	1.09916i
$960$		0			0
$961$	0.478676	+	0.829091i	0.0154412	+	0.0267449i
$962$		0			0
$963$	−20.2948	+	9.19748i	−0.653991	+	0.296385i
$964$		0			0
$965$	24.2372	+	3.28655i	0.780224	+	0.105798i
$966$		0			0
$967$	6.48992	+	24.2207i	0.208702	+	0.778886i	0.988289	+	0.152592i	$0.0487621\pi$
$967$	6.48992	+	24.2207i	0.208702	+	0.778886i	−0.779587	+	0.626293i	$0.784571\pi$
$968$		0			0
$969$	−41.2268	−	7.49971i	−1.32439	−	0.240925i
$970$		0			0
$971$			19.3757i			0.621794i	0.950444	+	0.310897i	$0.100629\pi$
$971$			19.3757i			0.621794i	−0.950444	+	0.310897i	$0.899371\pi$
$972$		0			0
$973$	−21.5786	−	21.5786i	−0.691778	−	0.691778i
$974$		0			0
$975$	0.898389	+	12.1020i	0.0287715	+	0.387575i
$976$		0			0
$977$	47.6816	−	12.7763i	1.52547	−	0.408749i	0.603932	−	0.797036i	$-0.293600\pi$
$977$	47.6816	−	12.7763i	1.52547	−	0.408749i	0.921538	+	0.388287i	$0.126933\pi$
$978$		0			0
$979$	−8.67198	+	5.00677i	−0.277158	+	0.160017i
$980$		0			0
$981$	28.8532	+	10.8569i	0.921213	+	0.346633i
$982$		0			0
$983$	−11.0191	−	2.95256i	−0.351454	−	0.0941719i	0.0787728	−	0.996893i	$-0.474900\pi$
$983$	−11.0191	−	2.95256i	−0.351454	−	0.0941719i	−0.430227	+	0.902721i	$0.641567\pi$
$984$		0			0
$985$	5.39120	+	13.1596i	0.171778	+	0.419300i
$986$		0			0
$987$	−53.0868	+	4.35507i	−1.68977	+	0.138623i
$988$		0			0
$989$	19.5325			0.621099
$990$		0			0
$991$	25.4006			0.806876			0.403438	−	0.915007i	$-0.367815\pi$
$991$	25.4006			0.806876			0.403438	+	0.915007i	$0.367815\pi$
$992$		0			0
$993$	16.3891	−	34.6555i	0.520091	−	1.09976i
$994$		0			0
$995$	−12.4072	+	29.6282i	−0.393334	+	0.939276i
$996$		0			0
$997$	24.6160	+	6.59585i	0.779598	+	0.208893i	0.626607	−	0.779335i	$-0.284443\pi$
$997$	24.6160	+	6.59585i	0.779598	+	0.208893i	0.152990	+	0.988228i	$0.451110\pi$
$998$		0			0
$999$	−16.6730	+	27.8251i	−0.527512	+	0.880347i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cu.e.113.12		72
4.3	odd	2		360.2.bs.a.113.7	✓	72
5.2	odd	4	inner	720.2.cu.e.257.15		72
9.2	odd	6	inner	720.2.cu.e.353.15		72
12.11	even	2		1080.2.bt.a.233.3		72
20.7	even	4		360.2.bs.a.257.4	yes	72
36.7	odd	6		1080.2.bt.a.953.4		72
36.11	even	6		360.2.bs.a.353.4	yes	72
45.2	even	12	inner	720.2.cu.e.497.12		72
60.47	odd	4		1080.2.bt.a.17.4		72
180.7	even	12		1080.2.bt.a.737.3		72
180.47	odd	12		360.2.bs.a.137.7	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bs.a.113.7	✓	72	4.3	odd	2
360.2.bs.a.137.7	yes	72	180.47	odd	12
360.2.bs.a.257.4	yes	72	20.7	even	4
360.2.bs.a.353.4	yes	72	36.11	even	6
720.2.cu.e.113.12		72	1.1	even	1	trivial
720.2.cu.e.257.15		72	5.2	odd	4	inner
720.2.cu.e.353.15		72	9.2	odd	6	inner
720.2.cu.e.497.12		72	45.2	even	12	inner
1080.2.bt.a.17.4		72	60.47	odd	4
1080.2.bt.a.233.3		72	12.11	even	2
1080.2.bt.a.737.3		72	180.7	even	12
1080.2.bt.a.953.4		72	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cu (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.985769 + 1.42417i) q^{3} +(2.06252 + 0.863710i) q^{5} +(-2.64986 - 0.710029i) q^{7} +(-1.05652 + 2.80780i) q^{9} +O(q^{10})\)	\(q+(0.985769 + 1.42417i) q^{3} +(2.06252 + 0.863710i) q^{5} +(-2.64986 - 0.710029i) q^{7} +(-1.05652 + 2.80780i) q^{9} +(0.765403 - 0.441906i) q^{11} +(1.35352 - 0.362674i) q^{13} +(0.803103 + 3.78880i) q^{15} +(3.83033 + 3.83033i) q^{17} +4.46618i q^{19} +(-1.60095 - 4.47378i) q^{21} +(1.01575 + 3.79082i) q^{23} +(3.50801 + 3.56284i) q^{25} +(-5.04027 + 1.26318i) q^{27} +(-0.874378 - 1.51447i) q^{29} +(-2.74056 + 4.74679i) q^{31} +(1.38386 + 0.654447i) q^{33} +(-4.85215 - 3.75316i) q^{35} +(4.41426 - 4.41426i) q^{37} +(1.85077 + 1.57013i) q^{39} +(-5.85416 - 3.37990i) q^{41} +(1.28815 - 4.80743i) q^{43} +(-4.60422 + 4.87864i) q^{45} +(2.90134 - 10.8280i) q^{47} +(0.455456 + 0.262958i) q^{49} +(-1.67922 + 9.23087i) q^{51} +(-6.79105 + 6.79105i) q^{53} +(1.96034 - 0.250355i) q^{55} +(-6.36060 + 4.40262i) q^{57} +(4.02430 - 6.97029i) q^{59} +(-4.25649 - 7.37246i) q^{61} +(4.79325 - 6.69014i) q^{63} +(3.10491 + 0.421023i) q^{65} +(3.87853 + 14.4749i) q^{67} +(-4.39748 + 5.18347i) q^{69} -11.1410i q^{71} +(10.1583 + 10.1583i) q^{73} +(-1.61601 + 8.50814i) q^{75} +(-2.34198 + 0.627531i) q^{77} +(8.28119 - 4.78115i) q^{79} +(-6.76753 - 5.93300i) q^{81} +(-4.49329 - 1.20397i) q^{83} +(4.59186 + 11.2085i) q^{85} +(1.29492 - 2.73818i) q^{87} -11.3300 q^{89} -3.84415 q^{91} +(-9.46179 + 0.776214i) q^{93} +(-3.85749 + 9.21161i) q^{95} +(11.0528 + 2.96160i) q^{97} +(0.432122 + 2.61598i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q - 12 q^{15} + 16 q^{21} - 24 q^{23} + 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} + 36 q^{47} - 24 q^{51} - 40 q^{57} + 12 q^{61} + 44 q^{63} - 72 q^{65} + 36 q^{75} - 48 q^{77} - 20 q^{81} + 60 q^{83} + 24 q^{85} + 40 q^{87} - 84 q^{93} + 60 q^{95} + 24 q^{97}+O(q^{100}) \) 72 * q - 12 * q^15 + 16 * q^21 - 24 * q^23 + 12 * q^27 + 12 * q^33 + 12 * q^41 - 16 * q^45 + 36 * q^47 - 24 * q^51 - 40 * q^57 + 12 * q^61 + 44 * q^63 - 72 * q^65 + 36 * q^75 - 48 * q^77 - 20 * q^81 + 60 * q^83 + 24 * q^85 + 40 * q^87 - 84 * q^93 + 60 * q^95 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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