LMFDB - Embedded newform 720.2.q.f.241.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(241,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("720.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.q (of order $3$, degree $2$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			241.2
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	720.241
Dual form			720.2.q.f.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 1.65831i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.68614 - 2.92048i) q^{7} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 1.65831i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.68614 - 2.92048i) q^{7} +(-2.50000 - 1.65831i) q^{9} +(-2.18614 + 3.78651i) q^{11} +(3.37228 + 5.84096i) q^{13} +(-1.68614 + 0.396143i) q^{15} -1.62772 q^{17} +2.37228 q^{19} +(4.00000 + 4.25639i) q^{21} +(0.686141 + 1.18843i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(4.00000 - 3.31662i) q^{27} +(-0.686141 + 1.18843i) q^{29} +(2.37228 + 4.10891i) q^{31} +(-5.18614 - 5.51856i) q^{33} +3.37228 q^{35} -4.00000 q^{37} +(-11.3723 + 2.67181i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-2.81386 + 4.87375i) q^{43} +(0.186141 - 2.99422i) q^{45} +(-3.68614 + 6.38458i) q^{47} +(-2.18614 - 3.78651i) q^{49} +(0.813859 - 2.69927i) q^{51} -11.4891 q^{53} -4.37228 q^{55} +(-1.18614 + 3.93398i) q^{57} +(2.18614 + 3.78651i) q^{59} +(4.05842 - 7.02939i) q^{61} +(-9.05842 + 4.50506i) q^{63} +(-3.37228 + 5.84096i) q^{65} +(-3.50000 - 6.06218i) q^{67} +(-2.31386 + 0.543620i) q^{69} +6.00000 q^{71} +3.11684 q^{73} +(-1.18614 - 1.26217i) q^{75} +(7.37228 + 12.7692i) q^{77} +(1.00000 - 1.73205i) q^{79} +(3.50000 + 8.29156i) q^{81} +(3.68614 - 6.38458i) q^{83} +(-0.813859 - 1.40965i) q^{85} +(-1.62772 - 1.73205i) q^{87} +16.1168 q^{89} +22.7446 q^{91} +(-8.00000 + 1.87953i) q^{93} +(1.18614 + 2.05446i) q^{95} +(4.18614 - 7.25061i) q^{97} +(11.7446 - 5.84096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{5} + q^{7} - 10 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^5 + q^7 - 10 * q^9	$ 4 q - 2 q^{3} + 2 q^{5} + q^{7} - 10 q^{9} - 3 q^{11} + 2 q^{13} - q^{15} - 18 q^{17} - 2 q^{19} + 16 q^{21} - 3 q^{23} - 2 q^{25} + 16 q^{27} + 3 q^{29} - 2 q^{31} - 15 q^{33} + 2 q^{35} - 16 q^{37} - 34 q^{39} + 6 q^{41} - 17 q^{43} - 5 q^{45} - 9 q^{47} - 3 q^{49} + 9 q^{51} - 6 q^{55} + q^{57} + 3 q^{59} - q^{61} - 19 q^{63} - 2 q^{65} - 14 q^{67} - 15 q^{69} + 24 q^{71} - 22 q^{73} + q^{75} + 18 q^{77} + 4 q^{79} + 14 q^{81} + 9 q^{83} - 9 q^{85} - 18 q^{87} + 30 q^{89} + 68 q^{91} - 32 q^{93} - q^{95} + 11 q^{97} + 24 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^5 + q^7 - 10 * q^9 - 3 * q^11 + 2 * q^13 - q^15 - 18 * q^17 - 2 * q^19 + 16 * q^21 - 3 * q^23 - 2 * q^25 + 16 * q^27 + 3 * q^29 - 2 * q^31 - 15 * q^33 + 2 * q^35 - 16 * q^37 - 34 * q^39 + 6 * q^41 - 17 * q^43 - 5 * q^45 - 9 * q^47 - 3 * q^49 + 9 * q^51 - 6 * q^55 + q^57 + 3 * q^59 - q^61 - 19 * q^63 - 2 * q^65 - 14 * q^67 - 15 * q^69 + 24 * q^71 - 22 * q^73 + q^75 + 18 * q^77 + 4 * q^79 + 14 * q^81 + 9 * q^83 - 9 * q^85 - 18 * q^87 + 30 * q^89 + 68 * q^91 - 32 * q^93 - q^95 + 11 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.500000	+	1.65831i	−0.288675	+	0.957427i
$3$	−0.500000	+	1.65831i	−0.288675	+	0.957427i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	1.68614	−	2.92048i	0.637301	−	1.10384i	−0.348721	−	0.937226i	$-0.613384\pi$
$7$	1.68614	−	2.92048i	0.637301	−	1.10384i	0.986023	−	0.166612i	$-0.0532826\pi$
$8$		0			0
$9$	−2.50000	−	1.65831i	−0.833333	−	0.552771i
$10$		0			0
$11$	−2.18614	+	3.78651i	−0.659146	+	1.14167i	0.321691	+	0.946845i	$0.395749\pi$
$11$	−2.18614	+	3.78651i	−0.659146	+	1.14167i	−0.980837	+	0.194830i	$0.937584\pi$
$12$		0			0
$13$	3.37228	+	5.84096i	0.935303	+	1.61999i	0.774094	+	0.633071i	$0.218206\pi$
$13$	3.37228	+	5.84096i	0.935303	+	1.61999i	0.161209	+	0.986920i	$0.448461\pi$
$14$		0			0
$15$	−1.68614	+	0.396143i	−0.435360	+	0.102284i
$16$		0			0
$17$	−1.62772			−0.394780			−0.197390	−	0.980325i	$-0.563246\pi$
$17$	−1.62772			−0.394780			−0.197390	+	0.980325i	$0.563246\pi$
$18$		0			0
$19$	2.37228			0.544239			0.272119	−	0.962264i	$-0.412275\pi$
$19$	2.37228			0.544239			0.272119	+	0.962264i	$0.412275\pi$
$20$		0			0
$21$	4.00000	+	4.25639i	0.872872	+	0.928820i
$22$		0			0
$23$	0.686141	+	1.18843i	0.143070	+	0.247805i	0.928651	−	0.370954i	$-0.120969\pi$
$23$	0.686141	+	1.18843i	0.143070	+	0.247805i	−0.785581	+	0.618759i	$0.787636\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	4.00000	−	3.31662i	0.769800	−	0.638285i
$28$		0			0
$29$	−0.686141	+	1.18843i	−0.127413	+	0.220686i	−0.922674	−	0.385582i	$-0.874001\pi$
$29$	−0.686141	+	1.18843i	−0.127413	+	0.220686i	0.795261	+	0.606268i	$0.207334\pi$
$30$		0			0
$31$	2.37228	+	4.10891i	0.426074	+	0.737982i	0.996520	−	0.0833529i	$-0.0265629\pi$
$31$	2.37228	+	4.10891i	0.426074	+	0.737982i	−0.570446	+	0.821335i	$0.693230\pi$
$32$		0			0
$33$	−5.18614	−	5.51856i	−0.902791	−	0.960658i
$34$		0			0
$35$	3.37228			0.570020
$36$		0			0
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$		0			0
$39$	−11.3723	+	2.67181i	−1.82102	+	0.427833i
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	−2.81386	+	4.87375i	−0.429110	+	0.743240i	−0.996794	−	0.0800065i	$-0.974506\pi$
$43$	−2.81386	+	4.87375i	−0.429110	+	0.743240i	0.567685	+	0.823246i	$0.307839\pi$
$44$		0			0
$45$	0.186141	−	2.99422i	0.0277482	−	0.446352i
$46$		0			0
$47$	−3.68614	+	6.38458i	−0.537679	+	0.931287i	0.461350	+	0.887218i	$0.347365\pi$
$47$	−3.68614	+	6.38458i	−0.537679	+	0.931287i	−0.999029	+	0.0440687i	$0.985968\pi$
$48$		0			0
$49$	−2.18614	−	3.78651i	−0.312306	−	0.540930i
$50$		0			0
$51$	0.813859	−	2.69927i	0.113963	−	0.377973i
$52$		0			0
$53$	−11.4891			−1.57815			−0.789076	−	0.614295i	$-0.789440\pi$
$53$	−11.4891			−1.57815			−0.789076	+	0.614295i	$0.789440\pi$
$54$		0			0
$55$	−4.37228			−0.589558
$56$		0			0
$57$	−1.18614	+	3.93398i	−0.157108	+	0.521069i
$58$		0			0
$59$	2.18614	+	3.78651i	0.284611	+	0.492961i	0.972515	−	0.232841i	$-0.0748021\pi$
$59$	2.18614	+	3.78651i	0.284611	+	0.492961i	−0.687904	+	0.725802i	$0.741469\pi$
$60$		0			0
$61$	4.05842	−	7.02939i	0.519628	−	0.900022i	−0.480112	−	0.877207i	$-0.659404\pi$
$61$	4.05842	−	7.02939i	0.519628	−	0.900022i	0.999740	−	0.0228144i	$-0.00726267\pi$
$62$		0			0
$63$	−9.05842	+	4.50506i	−1.14125	+	0.567584i
$64$		0			0
$65$	−3.37228	+	5.84096i	−0.418280	+	0.724482i
$66$		0			0
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	0.569066	−	0.822292i	$-0.307305\pi$
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	−0.996659	+	0.0816792i	$0.973972\pi$
$68$		0			0
$69$	−2.31386	+	0.543620i	−0.278556	+	0.0654442i
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	3.11684			0.364799			0.182399	−	0.983225i	$-0.441614\pi$
$73$	3.11684			0.364799			0.182399	+	0.983225i	$0.441614\pi$
$74$		0			0
$75$	−1.18614	−	1.26217i	−0.136964	−	0.145743i
$76$		0			0
$77$	7.37228	+	12.7692i	0.840149	+	1.45518i
$78$		0			0
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	−0.804272	−	0.594261i	$-0.797445\pi$
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	0.916781	+	0.399390i	$0.130778\pi$
$80$		0			0
$81$	3.50000	+	8.29156i	0.388889	+	0.921285i
$82$		0			0
$83$	3.68614	−	6.38458i	0.404607	−	0.700799i	−0.589669	−	0.807645i	$-0.700742\pi$
$83$	3.68614	−	6.38458i	0.404607	−	0.700799i	0.994276	+	0.106846i	$0.0340752\pi$
$84$		0			0
$85$	−0.813859	−	1.40965i	−0.0882754	−	0.152898i
$86$		0			0
$87$	−1.62772	−	1.73205i	−0.174510	−	0.185695i
$88$		0			0
$89$	16.1168			1.70838			0.854191	−	0.519959i	$-0.174053\pi$
$89$	16.1168			1.70838			0.854191	+	0.519959i	$0.174053\pi$
$90$		0			0
$91$	22.7446			2.38428
$92$		0			0
$93$	−8.00000	+	1.87953i	−0.829561	+	0.194898i
$94$		0			0
$95$	1.18614	+	2.05446i	0.121695	+	0.210783i
$96$		0			0
$97$	4.18614	−	7.25061i	0.425038	−	0.736188i	−0.571386	−	0.820682i	$-0.693594\pi$
$97$	4.18614	−	7.25061i	0.425038	−	0.736188i	0.996424	+	0.0844938i	$0.0269273\pi$
$98$		0			0
$99$	11.7446	−	5.84096i	1.18037	−	0.587039i
$100$		0			0
$101$	−1.37228	+	2.37686i	−0.136547	+	0.236507i	−0.926187	−	0.377064i	$-0.876934\pi$
$101$	−1.37228	+	2.37686i	−0.136547	+	0.236507i	0.789640	+	0.613570i	$0.210267\pi$
$102$		0			0
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	−0.927030	−	0.374987i	$-0.877647\pi$
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	0.138767	−	0.990325i	$-0.455686\pi$
$104$		0			0
$105$	−1.68614	+	5.59230i	−0.164550	+	0.545752i
$106$		0			0
$107$	−8.48913			−0.820675			−0.410337	−	0.911934i	$-0.634589\pi$
$107$	−8.48913			−0.820675			−0.410337	+	0.911934i	$0.634589\pi$
$108$		0			0
$109$	15.3723			1.47240			0.736199	−	0.676765i	$-0.236619\pi$
$109$	15.3723			1.47240			0.736199	+	0.676765i	$0.236619\pi$
$110$		0			0
$111$	2.00000	−	6.63325i	0.189832	−	0.629600i
$112$		0			0
$113$	−1.62772	−	2.81929i	−0.153123	−	0.265217i	0.779251	−	0.626712i	$-0.215600\pi$
$113$	−1.62772	−	2.81929i	−0.153123	−	0.265217i	−0.932374	+	0.361495i	$0.882266\pi$
$114$		0			0
$115$	−0.686141	+	1.18843i	−0.0639829	+	0.110822i
$116$		0			0
$117$	1.25544	−	20.1947i	0.116065	−	1.86700i
$118$		0			0
$119$	−2.74456	+	4.75372i	−0.251594	+	0.435773i
$120$		0			0
$121$	−4.05842	−	7.02939i	−0.368947	−	0.639036i
$122$		0			0
$123$	−5.05842	+	1.18843i	−0.456103	+	0.107157i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	8.11684			0.720253			0.360127	−	0.932903i	$-0.382733\pi$
$127$	8.11684			0.720253			0.360127	+	0.932903i	$0.382733\pi$
$128$		0			0
$129$	−6.67527	−	7.10313i	−0.587724	−	0.625396i
$130$		0			0
$131$	−1.37228	−	2.37686i	−0.119897	−	0.207667i	0.799830	−	0.600227i	$-0.204923\pi$
$131$	−1.37228	−	2.37686i	−0.119897	−	0.207667i	−0.919727	+	0.392560i	$0.871590\pi$
$132$		0			0
$133$	4.00000	−	6.92820i	0.346844	−	0.600751i
$134$		0			0
$135$	4.87228	+	1.80579i	0.419339	+	0.155418i
$136$		0			0
$137$	9.55842	−	16.5557i	0.816631	−	1.41445i	−0.0915197	−	0.995803i	$-0.529172\pi$
$137$	9.55842	−	16.5557i	0.816631	−	1.41445i	0.908151	−	0.418643i	$-0.137494\pi$
$138$		0			0
$139$	0.441578	+	0.764836i	0.0374542	+	0.0648725i	0.884145	−	0.467213i	$-0.154742\pi$
$139$	0.441578	+	0.764836i	0.0374542	+	0.0648725i	−0.846691	+	0.532085i	$0.821409\pi$
$140$		0			0
$141$	−8.74456	−	9.30506i	−0.736425	−	0.783628i
$142$		0			0
$143$	−29.4891			−2.46600
$144$		0			0
$145$	−1.37228			−0.113962
$146$		0			0
$147$	7.37228	−	1.73205i	0.608056	−	0.142857i
$148$		0			0
$149$	−0.941578	−	1.63086i	−0.0771371	−	0.133605i	0.824877	−	0.565313i	$-0.191245\pi$
$149$	−0.941578	−	1.63086i	−0.0771371	−	0.133605i	−0.902014	+	0.431708i	$0.857911\pi$
$150$		0			0
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	−0.994540	−	0.104357i	$-0.966722\pi$
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	0.587646	+	0.809118i	$0.300055\pi$
$152$		0			0
$153$	4.06930	+	2.69927i	0.328983	+	0.218223i
$154$		0			0
$155$	−2.37228	+	4.10891i	−0.190546	+	0.330036i
$156$		0			0
$157$	3.37228	+	5.84096i	0.269137	+	0.466160i	0.968639	−	0.248471i	$-0.0799281\pi$
$157$	3.37228	+	5.84096i	0.269137	+	0.466160i	−0.699502	+	0.714631i	$0.746595\pi$
$158$		0			0
$159$	5.74456	−	19.0526i	0.455573	−	1.51097i
$160$		0			0
$161$	4.62772			0.364715
$162$		0			0
$163$	21.4891			1.68316			0.841579	−	0.540134i	$-0.181626\pi$
$163$	21.4891			1.68316			0.841579	+	0.540134i	$0.181626\pi$
$164$		0			0
$165$	2.18614	−	7.25061i	0.170191	−	0.564459i
$166$		0			0
$167$	6.68614	+	11.5807i	0.517389	+	0.896144i	0.999796	+	0.0201970i	$0.00642933\pi$
$167$	6.68614	+	11.5807i	0.517389	+	0.896144i	−0.482407	+	0.875947i	$0.660237\pi$
$168$		0			0
$169$	−16.2446	+	28.1364i	−1.24958	+	2.16434i
$170$		0			0
$171$	−5.93070	−	3.93398i	−0.453532	−	0.300839i
$172$		0			0
$173$	−10.3723	+	17.9653i	−0.788590	+	1.36588i	0.138241	+	0.990399i	$0.455855\pi$
$173$	−10.3723	+	17.9653i	−0.788590	+	1.36588i	−0.926831	+	0.375479i	$0.877478\pi$
$174$		0			0
$175$	1.68614	+	2.92048i	0.127460	+	0.220768i
$176$		0			0
$177$	−7.37228	+	1.73205i	−0.554135	+	0.130189i
$178$		0			0
$179$	14.7446			1.10206			0.551030	−	0.834485i	$-0.314235\pi$
$179$	14.7446			1.10206			0.551030	+	0.834485i	$0.314235\pi$
$180$		0			0
$181$	20.8614			1.55062			0.775308	−	0.631583i	$-0.217595\pi$
$181$	20.8614			1.55062			0.775308	+	0.631583i	$0.217595\pi$
$182$		0			0
$183$	9.62772	+	10.2448i	0.711701	+	0.757319i
$184$		0			0
$185$	−2.00000	−	3.46410i	−0.147043	−	0.254686i
$186$		0			0
$187$	3.55842	−	6.16337i	0.260218	−	0.450710i
$188$		0			0
$189$	−2.94158	−	17.2742i	−0.213968	−	1.25651i
$190$		0			0
$191$	8.74456	−	15.1460i	0.632734	−	1.09593i	−0.354256	−	0.935148i	$-0.615266\pi$
$191$	8.74456	−	15.1460i	0.632734	−	1.09593i	0.986990	−	0.160780i	$-0.0514008\pi$
$192$		0			0
$193$	−10.5584	−	18.2877i	−0.760012	−	1.31638i	−0.942844	−	0.333235i	$-0.891860\pi$
$193$	−10.5584	−	18.2877i	−0.760012	−	1.31638i	0.182832	−	0.983144i	$-0.441474\pi$
$194$		0			0
$195$	−8.00000	−	8.51278i	−0.572892	−	0.609613i
$196$		0			0
$197$	−5.48913			−0.391084			−0.195542	−	0.980695i	$-0.562647\pi$
$197$	−5.48913			−0.391084			−0.195542	+	0.980695i	$0.562647\pi$
$198$		0			0
$199$	−13.4891			−0.956219			−0.478109	−	0.878300i	$-0.658678\pi$
$199$	−13.4891			−0.956219			−0.478109	+	0.878300i	$0.658678\pi$
$200$		0			0
$201$	11.8030	−	2.77300i	0.832518	−	0.195593i
$202$		0			0
$203$	2.31386	+	4.00772i	0.162401	+	0.281287i
$204$		0			0
$205$	−1.50000	+	2.59808i	−0.104765	+	0.181458i
$206$		0			0
$207$	0.255437	−	4.10891i	0.0177541	−	0.285589i
$208$		0			0
$209$	−5.18614	+	8.98266i	−0.358733	+	0.621344i
$210$		0			0
$211$	−9.37228	−	16.2333i	−0.645214	−	1.11754i	−0.984252	−	0.176771i	$-0.943435\pi$
$211$	−9.37228	−	16.2333i	−0.645214	−	1.11754i	0.339037	−	0.940773i	$-0.389899\pi$
$212$		0			0
$213$	−3.00000	+	9.94987i	−0.205557	+	0.681754i
$214$		0			0
$215$	−5.62772			−0.383807
$216$		0			0
$217$	16.0000			1.08615
$218$		0			0
$219$	−1.55842	+	5.16870i	−0.105308	+	0.349268i
$220$		0			0
$221$	−5.48913	−	9.50744i	−0.369239	−	0.639540i
$222$		0			0
$223$	3.31386	−	5.73977i	0.221912	−	0.384364i	−0.733476	−	0.679715i	$-0.762103\pi$
$223$	3.31386	−	5.73977i	0.221912	−	0.384364i	0.955389	+	0.295351i	$0.0954368\pi$
$224$		0			0
$225$	2.68614	−	1.33591i	0.179076	−	0.0890605i
$226$		0			0
$227$	9.55842	−	16.5557i	0.634415	−	1.09884i	−0.352224	−	0.935916i	$-0.614574\pi$
$227$	9.55842	−	16.5557i	0.634415	−	1.09884i	0.986639	−	0.162923i	$-0.0520922\pi$
$228$		0			0
$229$	−6.31386	−	10.9359i	−0.417232	−	0.722666i	0.578428	−	0.815733i	$-0.303666\pi$
$229$	−6.31386	−	10.9359i	−0.417232	−	0.722666i	−0.995660	+	0.0930670i	$0.970333\pi$
$230$		0			0
$231$	−24.8614	+	5.84096i	−1.63576	+	0.384307i
$232$		0			0
$233$	7.11684			0.466240			0.233120	−	0.972448i	$-0.425107\pi$
$233$	7.11684			0.466240			0.233120	+	0.972448i	$0.425107\pi$
$234$		0			0
$235$	−7.37228			−0.480915
$236$		0			0
$237$	2.37228	+	2.52434i	0.154096	+	0.163973i
$238$		0			0
$239$	−1.62772	−	2.81929i	−0.105288	−	0.182365i	0.808568	−	0.588403i	$-0.200243\pi$
$239$	−1.62772	−	2.81929i	−0.105288	−	0.182365i	−0.913856	+	0.406038i	$0.866910\pi$
$240$		0			0
$241$	6.24456	−	10.8159i	0.402248	−	0.696713i	−0.591749	−	0.806122i	$-0.701562\pi$
$241$	6.24456	−	10.8159i	0.402248	−	0.696713i	0.993997	+	0.109409i	$0.0348958\pi$
$242$		0			0
$243$	−15.5000	+	1.65831i	−0.994325	+	0.106381i
$244$		0			0
$245$	2.18614	−	3.78651i	0.139667	−	0.241911i
$246$		0			0
$247$	8.00000	+	13.8564i	0.509028	+	0.881662i
$248$		0			0
$249$	8.74456	+	9.30506i	0.554164	+	0.589684i
$250$		0			0
$251$	24.6060			1.55312			0.776558	−	0.630046i	$-0.216964\pi$
$251$	24.6060			1.55312			0.776558	+	0.630046i	$0.216964\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$		0			0
$255$	2.74456	−	0.644810i	0.171871	−	0.0403796i
$256$		0			0
$257$	−2.18614	−	3.78651i	−0.136368	−	0.236196i	0.789751	−	0.613427i	$-0.210210\pi$
$257$	−2.18614	−	3.78651i	−0.136368	−	0.236196i	−0.926119	+	0.377231i	$0.876876\pi$
$258$		0			0
$259$	−6.74456	+	11.6819i	−0.419087	+	0.725880i
$260$		0			0
$261$	3.68614	−	1.83324i	0.228166	−	0.113475i
$262$		0			0
$263$	−8.74456	+	15.1460i	−0.539213	+	0.933944i	0.459734	+	0.888057i	$0.347945\pi$
$263$	−8.74456	+	15.1460i	−0.539213	+	0.933944i	−0.998947	+	0.0458872i	$0.985389\pi$
$264$		0			0
$265$	−5.74456	−	9.94987i	−0.352886	−	0.611216i
$266$		0			0
$267$	−8.05842	+	26.7268i	−0.493167	+	1.63565i
$268$		0			0
$269$	−1.37228			−0.0836695			−0.0418347	−	0.999125i	$-0.513320\pi$
$269$	−1.37228			−0.0836695			−0.0418347	+	0.999125i	$0.513320\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		0			0
$273$	−11.3723	+	37.7176i	−0.688282	+	2.28277i
$274$		0			0
$275$	−2.18614	−	3.78651i	−0.131829	−	0.228335i
$276$		0			0
$277$	−8.37228	+	14.5012i	−0.503042	+	0.871294i	0.496952	+	0.867778i	$0.334452\pi$
$277$	−8.37228	+	14.5012i	−0.503042	+	0.871294i	−0.999994	+	0.00351574i	$0.998881\pi$
$278$		0			0
$279$	0.883156	−	14.2063i	0.0528732	−	0.850507i
$280$		0			0
$281$	0.686141	−	1.18843i	0.0409317	−	0.0708958i	−0.844834	−	0.535029i	$-0.820301\pi$
$281$	0.686141	−	1.18843i	0.0409317	−	0.0708958i	0.885765	+	0.464133i	$0.153634\pi$
$282$		0			0
$283$	−1.56930	−	2.71810i	−0.0932850	−	0.161574i	0.815607	−	0.578607i	$-0.196403\pi$
$283$	−1.56930	−	2.71810i	−0.0932850	−	0.161574i	−0.908892	+	0.417033i	$0.863070\pi$
$284$		0			0
$285$	−4.00000	+	0.939764i	−0.236940	+	0.0556668i
$286$		0			0
$287$	10.1168			0.597178
$288$		0			0
$289$	−14.3505			−0.844149
$290$		0			0
$291$	9.93070	+	10.5672i	0.582148	+	0.619462i
$292$		0			0
$293$	−13.1168	−	22.7190i	−0.766294	−	1.32726i	−0.939560	−	0.342385i	$-0.888765\pi$
$293$	−13.1168	−	22.7190i	−0.766294	−	1.32726i	0.173265	−	0.984875i	$-0.444568\pi$
$294$		0			0
$295$	−2.18614	+	3.78651i	−0.127282	+	0.220459i
$296$		0			0
$297$	3.81386	+	22.3966i	0.221303	+	1.29958i
$298$		0			0
$299$	−4.62772	+	8.01544i	−0.267628	+	0.463545i
$300$		0			0
$301$	9.48913	+	16.4356i	0.546944	+	0.947335i
$302$		0			0
$303$	−3.25544	−	3.46410i	−0.187020	−	0.199007i
$304$		0			0
$305$	8.11684			0.464769
$306$		0			0
$307$	−1.23369			−0.0704103			−0.0352051	−	0.999380i	$-0.511208\pi$
$307$	−1.23369			−0.0704103			−0.0352051	+	0.999380i	$0.511208\pi$
$308$		0			0
$309$	26.9783	−	6.33830i	1.53474	−	0.360573i
$310$		0			0
$311$	−10.3723	−	17.9653i	−0.588158	−	1.01872i	−0.994474	−	0.104987i	$-0.966520\pi$
$311$	−10.3723	−	17.9653i	−0.588158	−	1.01872i	0.406315	−	0.913733i	$-0.366813\pi$
$312$		0			0
$313$	−1.81386	+	3.14170i	−0.102525	+	0.177579i	−0.912724	−	0.408576i	$-0.866026\pi$
$313$	−1.81386	+	3.14170i	−0.102525	+	0.177579i	0.810199	+	0.586155i	$0.199359\pi$
$314$		0			0
$315$	−8.43070	−	5.59230i	−0.475016	−	0.315090i
$316$		0			0
$317$	−1.37228	+	2.37686i	−0.0770750	+	0.133498i	−0.901987	−	0.431764i	$-0.857891\pi$
$317$	−1.37228	+	2.37686i	−0.0770750	+	0.133498i	0.824912	+	0.565262i	$0.191225\pi$
$318$		0			0
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$		0			0
$321$	4.24456	−	14.0776i	0.236908	−	0.785736i
$322$		0			0
$323$	−3.86141			−0.214854
$324$		0			0
$325$	−6.74456			−0.374121
$326$		0			0
$327$	−7.68614	+	25.4920i	−0.425045	+	1.40971i
$328$		0			0
$329$	12.4307	+	21.5306i	0.685327	+	1.18702i
$330$		0			0
$331$	8.11684	−	14.0588i	0.446142	−	0.772741i	−0.551989	−	0.833851i	$-0.686131\pi$
$331$	8.11684	−	14.0588i	0.446142	−	0.772741i	0.998131	+	0.0611107i	$0.0194643\pi$
$332$		0			0
$333$	10.0000	+	6.63325i	0.547997	+	0.363500i
$334$		0			0
$335$	3.50000	−	6.06218i	0.191225	−	0.331212i
$336$		0			0
$337$	1.18614	+	2.05446i	0.0646132	+	0.111913i	0.896522	−	0.442999i	$-0.146085\pi$
$337$	1.18614	+	2.05446i	0.0646132	+	0.111913i	−0.831909	+	0.554912i	$0.812752\pi$
$338$		0			0
$339$	5.48913	−	1.28962i	0.298128	−	0.0700426i
$340$		0			0
$341$	−20.7446			−1.12338
$342$		0			0
$343$	8.86141			0.478471
$344$		0			0
$345$	−1.62772	−	1.73205i	−0.0876334	−	0.0932505i
$346$		0			0
$347$	−2.44158	−	4.22894i	−0.131071	−	0.227021i	0.793019	−	0.609197i	$-0.208508\pi$
$347$	−2.44158	−	4.22894i	−0.131071	−	0.227021i	−0.924090	+	0.382176i	$0.875175\pi$
$348$		0			0
$349$	−9.05842	+	15.6896i	−0.484886	+	0.839848i	−0.999849	−	0.0173648i	$-0.994472\pi$
$349$	−9.05842	+	15.6896i	−0.484886	+	0.839848i	0.514963	+	0.857212i	$0.327806\pi$
$350$		0			0
$351$	32.8614	+	12.1793i	1.75401	+	0.650081i
$352$		0			0
$353$	10.6753	−	18.4901i	0.568187	−	0.984129i	−0.428558	−	0.903514i	$-0.640978\pi$
$353$	10.6753	−	18.4901i	0.568187	−	0.984129i	0.996745	−	0.0806147i	$-0.0256883\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$		0			0
$357$	−6.51087	−	6.92820i	−0.344592	−	0.366679i
$358$		0			0
$359$	17.4891			0.923041			0.461520	−	0.887130i	$-0.347304\pi$
$359$	17.4891			0.923041			0.461520	+	0.887130i	$0.347304\pi$
$360$		0			0
$361$	−13.3723			−0.703804
$362$		0			0
$363$	13.6861	−	3.21543i	0.718336	−	0.168767i
$364$		0			0
$365$	1.55842	+	2.69927i	0.0815715	+	0.141286i
$366$		0			0
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	−0.995697	−	0.0926670i	$-0.970461\pi$
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	0.578101	+	0.815966i	$0.303794\pi$
$368$		0			0
$369$	0.558422	−	8.98266i	0.0290703	−	0.467619i
$370$		0			0
$371$	−19.3723	+	33.5538i	−1.00576	+	1.74203i
$372$		0			0
$373$	7.74456	+	13.4140i	0.400998	+	0.694549i	0.993847	−	0.110765i	$-0.0353300\pi$
$373$	7.74456	+	13.4140i	0.400998	+	0.694549i	−0.592848	+	0.805314i	$0.701997\pi$
$374$		0			0
$375$	0.500000	−	1.65831i	0.0258199	−	0.0856349i
$376$		0			0
$377$	−9.25544			−0.476679
$378$		0			0
$379$	−17.8614			−0.917479			−0.458739	−	0.888571i	$-0.651699\pi$
$379$	−17.8614			−0.917479			−0.458739	+	0.888571i	$0.651699\pi$
$380$		0			0
$381$	−4.05842	+	13.4603i	−0.207919	+	0.689590i
$382$		0			0
$383$	−11.4891	−	19.8997i	−0.587067	−	1.01683i	−0.994614	−	0.103646i	$-0.966949\pi$
$383$	−11.4891	−	19.8997i	−0.587067	−	1.01683i	0.407547	−	0.913184i	$-0.366384\pi$
$384$		0			0
$385$	−7.37228	+	12.7692i	−0.375726	+	0.650777i
$386$		0			0
$387$	15.1168	−	7.51811i	0.768432	−	0.382167i
$388$		0			0
$389$	2.31386	−	4.00772i	0.117317	−	0.203200i	−0.801386	−	0.598147i	$-0.795904\pi$
$389$	2.31386	−	4.00772i	0.117317	−	0.203200i	0.918704	+	0.394947i	$0.129237\pi$
$390$		0			0
$391$	−1.11684	−	1.93443i	−0.0564812	−	0.0978284i
$392$		0			0
$393$	4.62772	−	1.08724i	0.233438	−	0.0548440i
$394$		0			0
$395$	2.00000			0.100631
$396$		0			0
$397$	22.7446			1.14152			0.570758	−	0.821118i	$-0.306649\pi$
$397$	22.7446			1.14152			0.570758	+	0.821118i	$0.306649\pi$
$398$		0			0
$399$	9.48913	+	10.0974i	0.475050	+	0.505500i
$400$		0			0
$401$	0.558422	+	0.967215i	0.0278863	+	0.0483004i	0.879632	−	0.475655i	$-0.157789\pi$
$401$	0.558422	+	0.967215i	0.0278863	+	0.0483004i	−0.851745	+	0.523956i	$0.824456\pi$
$402$		0			0
$403$	−16.0000	+	27.7128i	−0.797017	+	1.38047i
$404$		0			0
$405$	−5.43070	+	7.17687i	−0.269854	+	0.356622i
$406$		0			0
$407$	8.74456	−	15.1460i	0.433452	−	0.750761i
$408$		0			0
$409$	−8.93070	−	15.4684i	−0.441595	−	0.764865i	0.556213	−	0.831040i	$-0.312254\pi$
$409$	−8.93070	−	15.4684i	−0.441595	−	0.764865i	−0.997808	+	0.0661749i	$0.978920\pi$
$410$		0			0
$411$	22.6753	+	24.1287i	1.11849	+	1.19018i
$412$		0			0
$413$	14.7446			0.725532
$414$		0			0
$415$	7.37228			0.361891
$416$		0			0
$417$	−1.48913	+	0.349857i	−0.0729228	+	0.0171325i
$418$		0			0
$419$	12.8614	+	22.2766i	0.628321	+	1.08828i	0.987889	+	0.155165i	$0.0495908\pi$
$419$	12.8614	+	22.2766i	0.628321	+	1.08828i	−0.359568	+	0.933119i	$0.617076\pi$
$420$		0			0
$421$	−15.2337	+	26.3855i	−0.742445	+	1.28595i	0.208935	+	0.977930i	$0.433000\pi$
$421$	−15.2337	+	26.3855i	−0.742445	+	1.28595i	−0.951379	+	0.308022i	$0.900333\pi$
$422$		0			0
$423$	19.8030	−	9.84868i	0.962854	−	0.478859i
$424$		0			0
$425$	0.813859	−	1.40965i	0.0394780	−	0.0683779i
$426$		0			0
$427$	−13.6861	−	23.7051i	−0.662319	−	1.14717i
$428$		0			0
$429$	14.7446	−	48.9022i	0.711874	−	2.36102i
$430$		0			0
$431$	−8.23369			−0.396603			−0.198301	−	0.980141i	$-0.563542\pi$
$431$	−8.23369			−0.396603			−0.198301	+	0.980141i	$0.563542\pi$
$432$		0			0
$433$	6.37228			0.306232			0.153116	−	0.988208i	$-0.451069\pi$
$433$	6.37228			0.306232			0.153116	+	0.988208i	$0.451069\pi$
$434$		0			0
$435$	0.686141	−	2.27567i	0.0328979	−	0.109110i
$436$		0			0
$437$	1.62772	+	2.81929i	0.0778643	+	0.134865i
$438$		0			0
$439$	−9.11684	+	15.7908i	−0.435123	+	0.753656i	−0.997306	−	0.0733577i	$-0.976629\pi$
$439$	−9.11684	+	15.7908i	−0.435123	+	0.753656i	0.562182	+	0.827013i	$0.309962\pi$
$440$		0			0
$441$	−0.813859	+	13.0916i	−0.0387552	+	0.623408i
$442$		0			0
$443$	−1.75544	+	3.04051i	−0.0834033	+	0.144459i	−0.904710	−	0.426029i	$-0.859912\pi$
$443$	−1.75544	+	3.04051i	−0.0834033	+	0.144459i	0.821306	+	0.570487i	$0.193246\pi$
$444$		0			0
$445$	8.05842	+	13.9576i	0.382006	+	0.661654i
$446$		0			0
$447$	3.17527	−	0.746000i	0.150185	−	0.0352846i
$448$		0			0
$449$	9.86141			0.465389			0.232694	−	0.972550i	$-0.425246\pi$
$449$	9.86141			0.465389			0.232694	+	0.972550i	$0.425246\pi$
$450$		0			0
$451$	−13.1168			−0.617648
$452$		0			0
$453$	−11.8614	−	12.6217i	−0.557297	−	0.593019i
$454$		0			0
$455$	11.3723	+	19.6974i	0.533141	+	0.923427i
$456$		0			0
$457$	−6.44158	+	11.1571i	−0.301324	+	0.521909i	−0.976436	−	0.215806i	$-0.930762\pi$
$457$	−6.44158	+	11.1571i	−0.301324	+	0.521909i	0.675112	+	0.737715i	$0.264095\pi$
$458$		0			0
$459$	−6.51087	+	5.39853i	−0.303902	+	0.251982i
$460$		0			0
$461$	−0.941578	+	1.63086i	−0.0438537	+	0.0759568i	−0.887119	−	0.461541i	$-0.847297\pi$
$461$	−0.941578	+	1.63086i	−0.0438537	+	0.0759568i	0.843265	+	0.537497i	$0.180630\pi$
$462$		0			0
$463$	10.0000	+	17.3205i	0.464739	+	0.804952i	0.999190	−	0.0402476i	$-0.0128147\pi$
$463$	10.0000	+	17.3205i	0.464739	+	0.804952i	−0.534450	+	0.845200i	$0.679481\pi$
$464$		0			0
$465$	−5.62772	−	5.98844i	−0.260979	−	0.277707i
$466$		0			0
$467$	−43.1168			−1.99521			−0.997605	−	0.0691713i	$-0.977964\pi$
$467$	−43.1168			−1.99521			−0.997605	+	0.0691713i	$0.977964\pi$
$468$		0			0
$469$	−23.6060			−1.09002
$470$		0			0
$471$	−11.3723	+	2.67181i	−0.524007	+	0.123111i
$472$		0			0
$473$	−12.3030	−	21.3094i	−0.565692	−	0.979807i
$474$		0			0
$475$	−1.18614	+	2.05446i	−0.0544239	+	0.0942649i
$476$		0			0
$477$	28.7228	+	19.0526i	1.31513	+	0.872357i
$478$		0			0
$479$	−0.255437	+	0.442430i	−0.0116712	+	0.0202152i	−0.871802	−	0.489858i	$-0.837048\pi$
$479$	−0.255437	+	0.442430i	−0.0116712	+	0.0202152i	0.860131	+	0.510074i	$0.170382\pi$
$480$		0			0
$481$	−13.4891	−	23.3639i	−0.615051	−	1.06530i
$482$		0			0
$483$	−2.31386	+	7.67420i	−0.105284	+	0.349188i
$484$		0			0
$485$	8.37228			0.380166
$486$		0			0
$487$	12.7446			0.577511			0.288756	−	0.957403i	$-0.406758\pi$
$487$	12.7446			0.577511			0.288756	+	0.957403i	$0.406758\pi$
$488$		0			0
$489$	−10.7446	+	35.6357i	−0.485886	+	1.61150i
$490$		0			0
$491$	−18.3030	−	31.7017i	−0.826002	−	1.43068i	−0.901151	−	0.433505i	$-0.857277\pi$
$491$	−18.3030	−	31.7017i	−0.826002	−	1.43068i	0.0751489	−	0.997172i	$-0.476057\pi$
$492$		0			0
$493$	1.11684	−	1.93443i	0.0503001	−	0.0871224i
$494$		0			0
$495$	10.9307	+	7.25061i	0.491299	+	0.325891i
$496$		0			0
$497$	10.1168	−	17.5229i	0.453802	−	0.786009i
$498$		0			0
$499$	7.55842	+	13.0916i	0.338361	+	0.586059i	0.984125	−	0.177479i	$-0.0567940\pi$
$499$	7.55842	+	13.0916i	0.338361	+	0.586059i	−0.645763	+	0.763538i	$0.723461\pi$
$500$		0			0
$501$	−22.5475	+	5.29734i	−1.00735	+	0.236668i
$502$		0			0
$503$	6.86141			0.305935			0.152967	−	0.988231i	$-0.451117\pi$
$503$	6.86141			0.305935			0.152967	+	0.988231i	$0.451117\pi$
$504$		0			0
$505$	−2.74456			−0.122131
$506$		0			0
$507$	−38.5367	−	41.0068i	−1.71147	−	1.82117i
$508$		0			0
$509$	21.1753	+	36.6766i	0.938577	+	1.62566i	0.768127	+	0.640297i	$0.221189\pi$
$509$	21.1753	+	36.6766i	0.938577	+	1.62566i	0.170450	+	0.985366i	$0.445478\pi$
$510$		0			0
$511$	5.25544	−	9.10268i	0.232487	−	0.402679i
$512$		0			0
$513$	9.48913	−	7.86797i	0.418955	−	0.347379i
$514$		0			0
$515$	8.00000	−	13.8564i	0.352522	−	0.610586i
$516$		0			0
$517$	−16.1168	−	27.9152i	−0.708818	−	1.22771i
$518$		0			0
$519$	−24.6060	−	26.1831i	−1.08008	−	1.14931i
$520$		0			0
$521$	−6.76631			−0.296438			−0.148219	−	0.988955i	$-0.547354\pi$
$521$	−6.76631			−0.296438			−0.148219	+	0.988955i	$0.547354\pi$
$522$		0			0
$523$	−6.11684			−0.267471			−0.133735	−	0.991017i	$-0.542697\pi$
$523$	−6.11684			−0.267471			−0.133735	+	0.991017i	$0.542697\pi$
$524$		0			0
$525$	−5.68614	+	1.33591i	−0.248164	+	0.0583038i
$526$		0			0
$527$	−3.86141	−	6.68815i	−0.168206	−	0.291340i
$528$		0			0
$529$	10.5584	−	18.2877i	0.459062	−	0.795118i
$530$		0			0
$531$	0.813859	−	13.0916i	0.0353185	−	0.568126i
$532$		0			0
$533$	−10.1168	+	17.5229i	−0.438209	+	0.759001i
$534$		0			0
$535$	−4.24456	−	7.35180i	−0.183508	−	0.317846i
$536$		0			0
$537$	−7.37228	+	24.4511i	−0.318137	+	1.05514i
$538$		0			0
$539$	19.1168			0.823421
$540$		0			0
$541$	27.3723			1.17683			0.588413	−	0.808560i	$-0.299753\pi$
$541$	27.3723			1.17683			0.588413	+	0.808560i	$0.299753\pi$
$542$		0			0
$543$	−10.4307	+	34.5947i	−0.447624	+	1.48460i
$544$		0			0
$545$	7.68614	+	13.3128i	0.329238	+	0.570257i
$546$		0			0
$547$	−14.7337	+	25.5195i	−0.629967	+	1.09113i	0.357591	+	0.933878i	$0.383598\pi$
$547$	−14.7337	+	25.5195i	−0.629967	+	1.09113i	−0.987558	+	0.157256i	$0.949735\pi$
$548$		0			0
$549$	−21.8030	+	10.8434i	−0.930529	+	0.462783i
$550$		0			0
$551$	−1.62772	+	2.81929i	−0.0693431	+	0.120106i
$552$		0			0
$553$	−3.37228	−	5.84096i	−0.143404	−	0.248383i
$554$		0			0
$555$	6.74456	−	1.58457i	0.286291	−	0.0672614i
$556$		0			0
$557$	−44.2337			−1.87424			−0.937121	−	0.349005i	$-0.886520\pi$
$557$	−44.2337			−1.87424			−0.937121	+	0.349005i	$0.886520\pi$
$558$		0			0
$559$	−37.9565			−1.60539
$560$		0			0
$561$	8.44158	+	8.98266i	0.356404	+	0.379248i
$562$		0			0
$563$	−20.3614	−	35.2670i	−0.858131	−	1.48633i	−0.873710	−	0.486448i	$-0.838292\pi$
$563$	−20.3614	−	35.2670i	−0.858131	−	1.48633i	0.0155787	−	0.999879i	$-0.495041\pi$
$564$		0			0
$565$	1.62772	−	2.81929i	0.0684786	−	0.118608i
$566$		0			0
$567$	30.1168	+	3.75906i	1.26479	+	0.157865i
$568$		0			0
$569$	15.3030	−	26.5055i	0.641534	−	1.11117i	−0.343556	−	0.939132i	$-0.611631\pi$
$569$	15.3030	−	26.5055i	0.641534	−	1.11117i	0.985090	−	0.172038i	$-0.0550352\pi$
$570$		0			0
$571$	4.30298	+	7.45299i	0.180074	+	0.311898i	0.941906	−	0.335878i	$-0.109033\pi$
$571$	4.30298	+	7.45299i	0.180074	+	0.311898i	−0.761831	+	0.647775i	$0.775700\pi$
$572$		0			0
$573$	20.7446	+	22.0742i	0.866617	+	0.922164i
$574$		0			0
$575$	−1.37228			−0.0572281
$576$		0			0
$577$	−41.1168			−1.71172			−0.855858	−	0.517210i	$-0.826970\pi$
$577$	−41.1168			−1.71172			−0.855858	+	0.517210i	$0.826970\pi$
$578$		0			0
$579$	35.6060	−	8.36530i	1.47973	−	0.347650i
$580$		0			0
$581$	−12.4307	−	21.5306i	−0.515712	−	0.893240i
$582$		0			0
$583$	25.1168	−	43.5036i	1.04023	−	1.80174i
$584$		0			0
$585$	18.1168	−	9.01011i	0.749039	−	0.372522i
$586$		0			0
$587$	13.5000	−	23.3827i	0.557205	−	0.965107i	−0.440524	−	0.897741i	$-0.645207\pi$
$587$	13.5000	−	23.3827i	0.557205	−	0.965107i	0.997728	−	0.0673658i	$-0.0214594\pi$
$588$		0			0
$589$	5.62772	+	9.74749i	0.231886	+	0.401639i
$590$		0			0
$591$	2.74456	−	9.10268i	0.112896	−	0.374434i
$592$		0			0
$593$	−19.7228			−0.809919			−0.404959	−	0.914335i	$-0.632714\pi$
$593$	−19.7228			−0.809919			−0.404959	+	0.914335i	$0.632714\pi$
$594$		0			0
$595$	−5.48913			−0.225032
$596$		0			0
$597$	6.74456	−	22.3692i	0.276037	−	0.915510i
$598$		0			0
$599$	−1.88316	−	3.26172i	−0.0769437	−	0.133270i	0.824986	−	0.565153i	$-0.191183\pi$
$599$	−1.88316	−	3.26172i	−0.0769437	−	0.133270i	−0.901930	+	0.431883i	$0.857849\pi$
$600$		0			0
$601$	0.930703	−	1.61203i	0.0379642	−	0.0657559i	−0.846419	−	0.532517i	$-0.821246\pi$
$601$	0.930703	−	1.61203i	0.0379642	−	0.0657559i	0.884383	+	0.466762i	$0.154579\pi$
$602$		0			0
$603$	−1.30298	+	20.9595i	−0.0530616	+	0.853538i
$604$		0			0
$605$	4.05842	−	7.02939i	0.164998	−	0.285785i
$606$		0			0
$607$	9.05842	+	15.6896i	0.367670	+	0.636823i	0.989201	−	0.146567i	$-0.0468223\pi$
$607$	9.05842	+	15.6896i	0.367670	+	0.636823i	−0.621531	+	0.783390i	$0.713489\pi$
$608$		0			0
$609$	−7.80298	+	1.83324i	−0.316193	+	0.0742867i
$610$		0			0
$611$	−49.7228			−2.01157
$612$		0			0
$613$	34.2337			1.38269			0.691343	−	0.722527i	$-0.257019\pi$
$613$	34.2337			1.38269			0.691343	+	0.722527i	$0.257019\pi$
$614$		0			0
$615$	−3.55842	−	3.78651i	−0.143489	−	0.152687i
$616$		0			0
$617$	2.44158	+	4.22894i	0.0982942	+	0.170251i	0.910979	−	0.412453i	$-0.135328\pi$
$617$	2.44158	+	4.22894i	0.0982942	+	0.170251i	−0.812684	+	0.582704i	$0.801995\pi$
$618$		0			0
$619$	−10.4416	+	18.0853i	−0.419682	+	0.726911i	−0.995907	−	0.0903798i	$-0.971192\pi$
$619$	−10.4416	+	18.0853i	−0.419682	+	0.726911i	0.576225	+	0.817291i	$0.304525\pi$
$620$		0			0
$621$	6.68614	+	2.47805i	0.268306	+	0.0994408i
$622$		0			0
$623$	27.1753	−	47.0689i	1.08875	−	1.88578i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−12.3030	−	13.0916i	−0.491334	−	0.522827i
$628$		0			0
$629$	6.51087			0.259606
$630$		0			0
$631$	23.7228			0.944390			0.472195	−	0.881494i	$-0.343462\pi$
$631$	23.7228			0.944390			0.472195	+	0.881494i	$0.343462\pi$
$632$		0			0
$633$	31.6060	−	7.42554i	1.25622	−	0.295139i
$634$		0			0
$635$	4.05842	+	7.02939i	0.161054	+	0.278953i
$636$		0			0
$637$	14.7446	−	25.5383i	0.584201	−	1.01187i
$638$		0			0
$639$	−15.0000	−	9.94987i	−0.593391	−	0.393611i
$640$		0			0
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	−0.167247	−	0.985915i	$-0.553488\pi$
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	0.937451	−	0.348117i	$-0.113179\pi$
$642$		0			0
$643$	5.50000	+	9.52628i	0.216899	+	0.375680i	0.953858	−	0.300257i	$-0.0970725\pi$
$643$	5.50000	+	9.52628i	0.216899	+	0.375680i	−0.736959	+	0.675937i	$0.763739\pi$
$644$		0			0
$645$	2.81386	−	9.33252i	0.110796	−	0.367467i
$646$		0			0
$647$	39.0951			1.53699			0.768493	−	0.639858i	$-0.221007\pi$
$647$	39.0951			1.53699			0.768493	+	0.639858i	$0.221007\pi$
$648$		0			0
$649$	−19.1168			−0.750402
$650$		0			0
$651$	−8.00000	+	26.5330i	−0.313545	+	1.03991i
$652$		0			0
$653$	−9.86141	−	17.0805i	−0.385907	−	0.668410i	0.605988	−	0.795474i	$-0.292778\pi$
$653$	−9.86141	−	17.0805i	−0.385907	−	0.668410i	−0.991895	+	0.127064i	$0.959445\pi$
$654$		0			0
$655$	1.37228	−	2.37686i	0.0536195	−	0.0928716i
$656$		0			0
$657$	−7.79211	−	5.16870i	−0.303999	−	0.201650i
$658$		0			0
$659$	8.74456	−	15.1460i	0.340640	−	0.590005i	−0.643912	−	0.765100i	$-0.722690\pi$
$659$	8.74456	−	15.1460i	0.340640	−	0.590005i	0.984552	+	0.175094i	$0.0560230\pi$
$660$		0			0
$661$	6.11684	+	10.5947i	0.237918	+	0.412085i	0.960117	−	0.279600i	$-0.0902018\pi$
$661$	6.11684	+	10.5947i	0.237918	+	0.412085i	−0.722199	+	0.691685i	$0.756868\pi$
$662$		0			0
$663$	18.5109	−	4.34896i	0.718903	−	0.168900i
$664$		0			0
$665$	8.00000			0.310227
$666$		0			0
$667$	−1.88316			−0.0729161
$668$		0			0
$669$	7.86141	+	8.36530i	0.303940	+	0.323421i
$670$		0			0
$671$	17.7446	+	30.7345i	0.685021	+	1.18649i
$672$		0			0
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	−0.753420	−	0.657539i	$-0.771597\pi$
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	0.946156	+	0.323711i	$0.104931\pi$
$674$		0			0
$675$	0.872281	+	5.12241i	0.0335741	+	0.197162i
$676$		0			0
$677$	−6.86141	+	11.8843i	−0.263705	+	0.456751i	−0.967224	−	0.253926i	$-0.918278\pi$
$677$	−6.86141	+	11.8843i	−0.263705	+	0.456751i	0.703518	+	0.710677i	$0.251611\pi$
$678$		0			0
$679$	−14.1168	−	24.4511i	−0.541755	−	0.938347i
$680$		0			0
$681$	22.6753	+	24.1287i	0.868918	+	0.924613i
$682$		0			0
$683$	30.0951			1.15156			0.575778	−	0.817606i	$-0.304699\pi$
$683$	30.0951			1.15156			0.575778	+	0.817606i	$0.304699\pi$
$684$		0			0
$685$	19.1168			0.730417
$686$		0			0
$687$	21.2921	−	5.00239i	0.812345	−	0.190853i
$688$		0			0
$689$	−38.7446	−	67.1076i	−1.47605	−	2.55659i
$690$		0			0
$691$	−18.1168	+	31.3793i	−0.689197	+	1.19372i	0.282901	+	0.959149i	$0.408703\pi$
$691$	−18.1168	+	31.3793i	−0.689197	+	1.19372i	−0.972098	+	0.234575i	$0.924630\pi$
$692$		0			0
$693$	2.74456	−	44.1485i	0.104257	−	1.67706i
$694$		0			0
$695$	−0.441578	+	0.764836i	−0.0167500	+	0.0290119i
$696$		0			0
$697$	−2.44158	−	4.22894i	−0.0924814	−	0.160182i
$698$		0			0
$699$	−3.55842	+	11.8020i	−0.134592	+	0.446391i
$700$		0			0
$701$	42.8614			1.61885			0.809426	−	0.587221i	$-0.199778\pi$
$701$	42.8614			1.61885			0.809426	+	0.587221i	$0.199778\pi$
$702$		0			0
$703$	−9.48913			−0.357889
$704$		0			0
$705$	3.68614	−	12.2255i	0.138828	−	0.460441i
$706$		0			0
$707$	4.62772	+	8.01544i	0.174043	+	0.301452i
$708$		0			0
$709$	−1.43070	+	2.47805i	−0.0537312	+	0.0930652i	−0.891640	−	0.452745i	$-0.850445\pi$
$709$	−1.43070	+	2.47805i	−0.0537312	+	0.0930652i	0.837909	+	0.545810i	$0.183778\pi$
$710$		0			0
$711$	−5.37228	+	2.67181i	−0.201476	+	0.100201i
$712$		0			0
$713$	−3.25544	+	5.63858i	−0.121917	+	0.211167i
$714$		0			0
$715$	−14.7446	−	25.5383i	−0.551415	−	0.955079i
$716$		0			0
$717$	5.48913	−	1.28962i	0.204995	−	0.0481618i
$718$		0			0
$719$	3.76631			0.140460			0.0702299	−	0.997531i	$-0.477627\pi$
$719$	3.76631			0.140460			0.0702299	+	0.997531i	$0.477627\pi$
$720$		0			0
$721$	−53.9565			−2.00945
$722$		0			0
$723$	14.8139	+	15.7634i	0.550933	+	0.586247i
$724$		0			0
$725$	−0.686141	−	1.18843i	−0.0254826	−	0.0441372i
$726$		0			0
$727$	9.05842	−	15.6896i	0.335958	−	0.581897i	−0.647710	−	0.761887i	$-0.724273\pi$
$727$	9.05842	−	15.6896i	0.335958	−	0.581897i	0.983668	+	0.179990i	$0.0576066\pi$
$728$		0			0
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$		0			0
$731$	4.58017	−	7.93309i	0.169404	−	0.293416i
$732$		0			0
$733$	0.116844	+	0.202380i	0.00431573	+	0.00747506i	0.868175	−	0.496258i	$-0.165293\pi$
$733$	0.116844	+	0.202380i	0.00431573	+	0.00747506i	−0.863859	+	0.503733i	$0.831960\pi$
$734$		0			0
$735$	5.18614	+	5.51856i	0.191294	+	0.203555i
$736$		0			0
$737$	30.6060			1.12739
$738$		0			0
$739$	41.1168			1.51251			0.756254	−	0.654278i	$-0.227028\pi$
$739$	41.1168			1.51251			0.756254	+	0.654278i	$0.227028\pi$
$740$		0			0
$741$	−26.9783	+	6.33830i	−0.991071	+	0.232843i
$742$		0			0
$743$	3.94158	+	6.82701i	0.144602	+	0.250459i	0.929225	−	0.369516i	$-0.120476\pi$
$743$	3.94158	+	6.82701i	0.144602	+	0.250459i	−0.784622	+	0.619974i	$0.787143\pi$
$744$		0			0
$745$	0.941578	−	1.63086i	0.0344967	−	0.0597501i
$746$		0			0
$747$	−19.8030	+	9.84868i	−0.724553	+	0.360345i
$748$		0			0
$749$	−14.3139	+	24.7923i	−0.523017	+	0.905892i
$750$		0			0
$751$	8.11684	+	14.0588i	0.296188	+	0.513012i	0.975261	−	0.221059i	$-0.0709512\pi$
$751$	8.11684	+	14.0588i	0.296188	+	0.513012i	−0.679073	+	0.734071i	$0.737618\pi$
$752$		0			0
$753$	−12.3030	+	40.8044i	−0.448346	+	1.48699i
$754$		0			0
$755$	−10.0000			−0.363937
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$		0			0
$759$	3.00000	−	9.94987i	0.108893	−	0.361158i
$760$		0			0
$761$	25.5475	+	44.2496i	0.926098	+	1.60405i	0.789786	+	0.613383i	$0.210192\pi$
$761$	25.5475	+	44.2496i	0.926098	+	1.60405i	0.136312	+	0.990666i	$0.456475\pi$
$762$		0			0
$763$	25.9198	−	44.8945i	0.938361	−	1.62529i
$764$		0			0
$765$	−0.302985	+	4.87375i	−0.0109544	+	0.176211i
$766$		0			0
$767$	−14.7446	+	25.5383i	−0.532395	+	0.922136i
$768$		0			0
$769$	23.4307	+	40.5832i	0.844933	+	1.46347i	0.885680	+	0.464297i	$0.153693\pi$
$769$	23.4307	+	40.5832i	0.844933	+	1.46347i	−0.0407468	+	0.999170i	$0.512974\pi$
$770$		0			0
$771$	7.37228	−	1.73205i	0.265506	−	0.0623783i
$772$		0			0
$773$	3.25544			0.117090			0.0585450	−	0.998285i	$-0.481354\pi$
$773$	3.25544			0.117090			0.0585450	+	0.998285i	$0.481354\pi$
$774$		0			0
$775$	−4.74456			−0.170430
$776$		0			0
$777$	−16.0000	−	17.0256i	−0.573997	−	0.610788i
$778$		0			0
$779$	3.55842	+	6.16337i	0.127494	+	0.220826i
$780$		0			0
$781$	−13.1168	+	22.7190i	−0.469358	+	0.812951i
$782$		0			0
$783$	1.19702	+	7.02939i	0.0427778	+	0.251210i
$784$		0			0
$785$	−3.37228	+	5.84096i	−0.120362	+	0.208473i
$786$		0			0
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	0.500953	−	0.865474i	$-0.332983\pi$
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	−0.999999	+	0.00110111i	$0.999650\pi$
$788$		0			0
$789$	−20.7446	−	22.0742i	−0.738526	−	0.785863i
$790$		0			0
$791$	−10.9783			−0.390342
$792$		0			0
$793$	54.7446			1.94404
$794$		0			0
$795$	19.3723	−	4.55134i	0.687064	−	0.161419i
$796$		0			0
$797$	−7.37228	−	12.7692i	−0.261140	−	0.452307i	0.705405	−	0.708804i	$-0.250765\pi$
$797$	−7.37228	−	12.7692i	−0.261140	−	0.452307i	−0.966545	+	0.256497i	$0.917432\pi$
$798$		0			0
$799$	6.00000	−	10.3923i	0.212265	−	0.367653i
$800$		0			0
$801$	−40.2921	−	26.7268i	−1.42365	−	0.944344i
$802$		0			0
$803$	−6.81386	+	11.8020i	−0.240456	+	0.416482i
$804$		0			0
$805$	2.31386	+	4.00772i	0.0815528	+	0.141254i
$806$		0			0
$807$	0.686141	−	2.27567i	0.0241533	−	0.0801074i
$808$		0			0
$809$	39.3505			1.38349			0.691746	−	0.722141i	$-0.256842\pi$
$809$	39.3505			1.38349			0.691746	+	0.722141i	$0.256842\pi$
$810$		0			0
$811$	−3.62772			−0.127386			−0.0636932	−	0.997970i	$-0.520288\pi$
$811$	−3.62772			−0.127386			−0.0636932	+	0.997970i	$0.520288\pi$
$812$		0			0
$813$	4.00000	−	13.2665i	0.140286	−	0.465276i
$814$		0			0
$815$	10.7446	+	18.6101i	0.376366	+	0.651884i
$816$		0			0
$817$	−6.67527	+	11.5619i	−0.233538	+	0.404500i
$818$		0			0
$819$	−56.8614	−	37.7176i	−1.98690	−	1.31796i
$820$		0			0
$821$	11.9198	−	20.6457i	0.416005	−	0.720542i	−0.579528	−	0.814952i	$-0.696763\pi$
$821$	11.9198	−	20.6457i	0.416005	−	0.720542i	0.995533	+	0.0944104i	$0.0300966\pi$
$822$		0			0
$823$	−12.5475	−	21.7330i	−0.437380	−	0.757564i	0.560107	−	0.828421i	$-0.310760\pi$
$823$	−12.5475	−	21.7330i	−0.437380	−	0.757564i	−0.997487	+	0.0708562i	$0.977427\pi$
$824$		0			0
$825$	7.37228	−	1.73205i	0.256670	−	0.0603023i
$826$		0			0
$827$	−36.8614			−1.28180			−0.640898	−	0.767626i	$-0.721438\pi$
$827$	−36.8614			−1.28180			−0.640898	+	0.767626i	$0.721438\pi$
$828$		0			0
$829$	−50.1168			−1.74063			−0.870315	−	0.492496i	$-0.836085\pi$
$829$	−50.1168			−1.74063			−0.870315	+	0.492496i	$0.836085\pi$
$830$		0			0
$831$	−19.8614	−	21.1345i	−0.688985	−	0.733147i
$832$		0			0
$833$	3.55842	+	6.16337i	0.123292	+	0.213548i
$834$		0			0
$835$	−6.68614	+	11.5807i	−0.231383	+	0.400768i
$836$		0			0
$837$	23.1168	+	8.56768i	0.799035	+	0.296142i
$838$		0			0
$839$	4.88316	−	8.45787i	0.168585	−	0.291998i	−0.769337	−	0.638843i	$-0.779413\pi$
$839$	4.88316	−	8.45787i	0.168585	−	0.291998i	0.937923	+	0.346844i	$0.112747\pi$
$840$		0			0
$841$	13.5584	+	23.4839i	0.467532	+	0.809789i
$842$		0			0
$843$	1.62772	+	1.73205i	0.0560616	+	0.0596550i
$844$		0			0
$845$	−32.4891			−1.11766
$846$		0			0
$847$	−27.3723			−0.940523
$848$		0			0
$849$	5.29211	−	1.24333i	0.181625	−	0.0426711i
$850$		0			0
$851$	−2.74456	−	4.75372i	−0.0940824	−	0.162955i
$852$		0			0
$853$	18.1168	−	31.3793i	0.620309	−	1.07441i	−0.369119	−	0.929382i	$-0.620341\pi$
$853$	18.1168	−	31.3793i	0.620309	−	1.07441i	0.989428	−	0.145024i	$-0.0463261\pi$
$854$		0			0
$855$	0.441578	−	7.10313i	0.0151016	−	0.242922i
$856$		0			0
$857$	−0.255437	+	0.442430i	−0.00872557	+	0.0151131i	−0.870355	−	0.492424i	$-0.836111\pi$
$857$	−0.255437	+	0.442430i	−0.00872557	+	0.0151131i	0.861630	+	0.507538i	$0.169444\pi$
$858$		0			0
$859$	−8.55842	−	14.8236i	−0.292010	−	0.505775i	0.682275	−	0.731095i	$-0.260991\pi$
$859$	−8.55842	−	14.8236i	−0.292010	−	0.505775i	−0.974285	+	0.225320i	$0.927657\pi$
$860$		0			0
$861$	−5.05842	+	16.7769i	−0.172391	+	0.571755i
$862$		0			0
$863$	2.39403			0.0814938			0.0407469	−	0.999170i	$-0.487026\pi$
$863$	2.39403			0.0814938			0.0407469	+	0.999170i	$0.487026\pi$
$864$		0			0
$865$	−20.7446			−0.705336
$866$		0			0
$867$	7.17527	−	23.7977i	0.243685	−	0.808211i
$868$		0			0
$869$	4.37228	+	7.57301i	0.148319	+	0.256897i
$870$		0			0
$871$	23.6060	−	40.8867i	0.799858	−	1.38539i
$872$		0			0
$873$	−22.4891	+	11.1846i	−0.761142	+	0.378541i
$874$		0			0
$875$	−1.68614	+	2.92048i	−0.0570020	+	0.0987303i
$876$		0			0
$877$	−17.9783	−	31.1392i	−0.607082	−	1.05150i	−0.991719	−	0.128429i	$-0.959006\pi$
$877$	−17.9783	−	31.1392i	−0.607082	−	1.05150i	0.384636	−	0.923068i	$-0.374327\pi$
$878$		0			0
$879$	44.2337	−	10.3923i	1.49197	−	0.350524i
$880$		0			0
$881$	−24.3505			−0.820390			−0.410195	−	0.911998i	$-0.634539\pi$
$881$	−24.3505			−0.820390			−0.410195	+	0.911998i	$0.634539\pi$
$882$		0			0
$883$	44.7228			1.50504			0.752521	−	0.658568i	$-0.228837\pi$
$883$	44.7228			1.50504			0.752521	+	0.658568i	$0.228837\pi$
$884$		0			0
$885$	−5.18614	−	5.51856i	−0.174330	−	0.185504i
$886$		0			0
$887$	9.86141	+	17.0805i	0.331114	+	0.573506i	0.982730	−	0.185043i	$-0.0592423\pi$
$887$	9.86141	+	17.0805i	0.331114	+	0.573506i	−0.651617	+	0.758548i	$0.725909\pi$
$888$		0			0
$889$	13.6861	−	23.7051i	0.459018	−	0.795043i
$890$		0			0
$891$	−39.0475	−	4.87375i	−1.30814	−	0.163277i
$892$		0			0
$893$	−8.74456	+	15.1460i	−0.292626	+	0.506842i
$894$		0			0
$895$	7.37228	+	12.7692i	0.246428	+	0.426826i
$896$		0			0
$897$	−10.9783	−	11.6819i	−0.366553	−	0.390048i
$898$		0			0
$899$	−6.51087			−0.217150
$900$		0			0
$901$	18.7011			0.623023
$902$		0			0
$903$	−32.0000	+	7.51811i	−1.06489	+	0.250187i
$904$		0			0
$905$	10.4307	+	18.0665i	0.346728	+	0.600551i
$906$		0			0
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	−0.918265	−	0.395966i	$-0.870410\pi$
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	0.802049	+	0.597258i	$0.203743\pi$
$908$		0			0
$909$	7.37228	−	3.66648i	0.244523	−	0.121610i
$910$		0			0
$911$	−21.0000	+	36.3731i	−0.695761	+	1.20509i	0.274162	+	0.961683i	$0.411599\pi$
$911$	−21.0000	+	36.3731i	−0.695761	+	1.20509i	−0.969923	+	0.243410i	$0.921734\pi$
$912$		0			0
$913$	16.1168	+	27.9152i	0.533390	+	0.923858i
$914$		0			0
$915$	−4.05842	+	13.4603i	−0.134167	+	0.444983i
$916$		0			0
$917$	−9.25544			−0.305641
$918$		0			0
$919$	26.4674			0.873078			0.436539	−	0.899685i	$-0.356204\pi$
$919$	26.4674			0.873078			0.436539	+	0.899685i	$0.356204\pi$
$920$		0			0
$921$	0.616844	−	2.04584i	0.0203257	−	0.0674127i
$922$		0			0
$923$	20.2337	+	35.0458i	0.666000	+	1.15355i
$924$		0			0
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$		0			0
$927$	−2.97825	+	47.9075i	−0.0978186	+	1.57349i
$928$		0			0
$929$	−25.9783	+	44.9956i	−0.852319	+	1.47626i	0.0267916	+	0.999641i	$0.491471\pi$
$929$	−25.9783	+	44.9956i	−0.852319	+	1.47626i	−0.879110	+	0.476618i	$0.841862\pi$
$930$		0			0
$931$	−5.18614	−	8.98266i	−0.169969	−	0.294395i
$932$		0			0
$933$	34.9783	−	8.21782i	1.14514	−	0.269039i
$934$		0			0
$935$	7.11684			0.232746
$936$		0			0
$937$	39.7228			1.29769			0.648844	−	0.760922i	$-0.275253\pi$
$937$	39.7228			1.29769			0.648844	+	0.760922i	$0.275253\pi$
$938$		0			0
$939$	−4.30298	−	4.57879i	−0.140423	−	0.149423i
$940$		0			0
$941$	−21.6861	−	37.5615i	−0.706948	−	1.22447i	−0.965984	−	0.258602i	$-0.916738\pi$
$941$	−21.6861	−	37.5615i	−0.706948	−	1.22447i	0.259036	−	0.965868i	$-0.416595\pi$
$942$		0			0
$943$	−2.05842	+	3.56529i	−0.0670314	+	0.116102i
$944$		0			0
$945$	13.4891	−	11.1846i	0.438801	−	0.363835i
$946$		0			0
$947$	−17.3614	+	30.0708i	−0.564170	+	0.977171i	0.432956	+	0.901415i	$0.357470\pi$
$947$	−17.3614	+	30.0708i	−0.564170	+	0.977171i	−0.997126	+	0.0757561i	$0.975863\pi$
$948$		0			0
$949$	10.5109	+	18.2054i	0.341197	+	0.590971i
$950$		0			0
$951$	−3.25544	−	3.46410i	−0.105565	−	0.112331i
$952$		0			0
$953$	2.13859			0.0692758			0.0346379	−	0.999400i	$-0.488972\pi$
$953$	2.13859			0.0692758			0.0346379	+	0.999400i	$0.488972\pi$
$954$		0			0
$955$	17.4891			0.565935
$956$		0			0
$957$	10.1168	−	2.37686i	0.327031	−	0.0768330i
$958$		0			0
$959$	−32.2337	−	55.8304i	−1.04088	−	1.80286i
$960$		0			0
$961$	4.24456	−	7.35180i	0.136921	−	0.237155i
$962$		0			0
$963$	21.2228	+	14.0776i	0.683896	+	0.453645i
$964$		0			0
$965$	10.5584	−	18.2877i	0.339888	−	0.588703i
$966$		0			0
$967$	18.0584	+	31.2781i	0.580720	+	1.00584i	0.995394	+	0.0958662i	$0.0305621\pi$
$967$	18.0584	+	31.2781i	0.580720	+	1.00584i	−0.414675	+	0.909970i	$0.636105\pi$
$968$		0			0
$969$	1.93070	−	6.40342i	0.0620231	−	0.205707i
$970$		0			0
$971$	22.9783			0.737407			0.368704	−	0.929547i	$-0.379802\pi$
$971$	22.9783			0.737407			0.368704	+	0.929547i	$0.379802\pi$
$972$		0			0
$973$	2.97825			0.0954783
$974$		0			0
$975$	3.37228	−	11.1846i	0.107999	−	0.358194i
$976$		0			0
$977$	11.4416	+	19.8174i	0.366049	+	0.634015i	0.988944	−	0.148291i	$-0.0473771\pi$
$977$	11.4416	+	19.8174i	0.366049	+	0.634015i	−0.622895	+	0.782305i	$0.714044\pi$
$978$		0			0
$979$	−35.2337	+	61.0265i	−1.12607	+	1.95042i
$980$		0			0
$981$	−38.4307	−	25.4920i	−1.22700	−	0.813898i
$982$		0			0
$983$	−6.43070	+	11.1383i	−0.205108	+	0.355257i	−0.950167	−	0.311741i	$-0.899088\pi$
$983$	−6.43070	+	11.1383i	−0.205108	+	0.355257i	0.745059	+	0.666998i	$0.232421\pi$
$984$		0			0
$985$	−2.74456	−	4.75372i	−0.0874490	−	0.151466i
$986$		0			0
$987$	−41.9198	+	9.84868i	−1.33432	+	0.313487i
$988$		0			0
$989$	−7.72281			−0.245571
$990$		0			0
$991$	−16.2337			−0.515680			−0.257840	−	0.966188i	$-0.583011\pi$
$991$	−16.2337			−0.515680			−0.257840	+	0.966188i	$0.583011\pi$
$992$		0			0
$993$	19.2554	+	20.4897i	0.611053	+	0.650220i
$994$		0			0
$995$	−6.74456	−	11.6819i	−0.213817	−	0.370342i
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$		0			0
$999$	−16.0000	+	13.2665i	−0.506218	+	0.419733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.q.f.241.2		4
3.2	odd	2		2160.2.q.f.721.2		4
4.3	odd	2		90.2.e.c.61.1	yes	4
9.2	odd	6		6480.2.a.bn.1.1		2
9.4	even	3	inner	720.2.q.f.481.1		4
9.5	odd	6		2160.2.q.f.1441.2		4
9.7	even	3		6480.2.a.be.1.1		2
12.11	even	2		270.2.e.c.181.1		4
20.3	even	4		450.2.j.g.349.2		8
20.7	even	4		450.2.j.g.349.3		8
20.19	odd	2		450.2.e.j.151.2		4
36.7	odd	6		810.2.a.i.1.2		2
36.11	even	6		810.2.a.k.1.2		2
36.23	even	6		270.2.e.c.91.1		4
36.31	odd	6		90.2.e.c.31.2	✓	4
60.23	odd	4		1350.2.j.f.1099.4		8
60.47	odd	4		1350.2.j.f.1099.1		8
60.59	even	2		1350.2.e.l.451.2		4
180.7	even	12		4050.2.c.v.649.2		4
180.23	odd	12		1350.2.j.f.199.1		8
180.43	even	12		4050.2.c.v.649.3		4
180.47	odd	12		4050.2.c.ba.649.4		4
180.59	even	6		1350.2.e.l.901.2		4
180.67	even	12		450.2.j.g.49.2		8
180.79	odd	6		4050.2.a.bw.1.1		2
180.83	odd	12		4050.2.c.ba.649.1		4
180.103	even	12		450.2.j.g.49.3		8
180.119	even	6		4050.2.a.bo.1.1		2
180.139	odd	6		450.2.e.j.301.1		4
180.167	odd	12		1350.2.j.f.199.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.c.31.2	✓	4	36.31	odd	6
90.2.e.c.61.1	yes	4	4.3	odd	2
270.2.e.c.91.1		4	36.23	even	6
270.2.e.c.181.1		4	12.11	even	2
450.2.e.j.151.2		4	20.19	odd	2
450.2.e.j.301.1		4	180.139	odd	6
450.2.j.g.49.2		8	180.67	even	12
450.2.j.g.49.3		8	180.103	even	12
450.2.j.g.349.2		8	20.3	even	4
450.2.j.g.349.3		8	20.7	even	4
720.2.q.f.241.2		4	1.1	even	1	trivial
720.2.q.f.481.1		4	9.4	even	3	inner
810.2.a.i.1.2		2	36.7	odd	6
810.2.a.k.1.2		2	36.11	even	6
1350.2.e.l.451.2		4	60.59	even	2
1350.2.e.l.901.2		4	180.59	even	6
1350.2.j.f.199.1		8	180.23	odd	12
1350.2.j.f.199.4		8	180.167	odd	12
1350.2.j.f.1099.1		8	60.47	odd	4
1350.2.j.f.1099.4		8	60.23	odd	4
2160.2.q.f.721.2		4	3.2	odd	2
2160.2.q.f.1441.2		4	9.5	odd	6
4050.2.a.bo.1.1		2	180.119	even	6
4050.2.a.bw.1.1		2	180.79	odd	6
4050.2.c.v.649.2		4	180.7	even	12
4050.2.c.v.649.3		4	180.43	even	12
4050.2.c.ba.649.1		4	180.83	odd	12
4050.2.c.ba.649.4		4	180.47	odd	12
6480.2.a.be.1.1		2	9.7	even	3
6480.2.a.bn.1.1		2	9.2	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.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 1.65831i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.68614 - 2.92048i) q^{7} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 1.65831i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.68614 - 2.92048i) q^{7} +(-2.50000 - 1.65831i) q^{9} +(-2.18614 + 3.78651i) q^{11} +(3.37228 + 5.84096i) q^{13} +(-1.68614 + 0.396143i) q^{15} -1.62772 q^{17} +2.37228 q^{19} +(4.00000 + 4.25639i) q^{21} +(0.686141 + 1.18843i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(4.00000 - 3.31662i) q^{27} +(-0.686141 + 1.18843i) q^{29} +(2.37228 + 4.10891i) q^{31} +(-5.18614 - 5.51856i) q^{33} +3.37228 q^{35} -4.00000 q^{37} +(-11.3723 + 2.67181i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-2.81386 + 4.87375i) q^{43} +(0.186141 - 2.99422i) q^{45} +(-3.68614 + 6.38458i) q^{47} +(-2.18614 - 3.78651i) q^{49} +(0.813859 - 2.69927i) q^{51} -11.4891 q^{53} -4.37228 q^{55} +(-1.18614 + 3.93398i) q^{57} +(2.18614 + 3.78651i) q^{59} +(4.05842 - 7.02939i) q^{61} +(-9.05842 + 4.50506i) q^{63} +(-3.37228 + 5.84096i) q^{65} +(-3.50000 - 6.06218i) q^{67} +(-2.31386 + 0.543620i) q^{69} +6.00000 q^{71} +3.11684 q^{73} +(-1.18614 - 1.26217i) q^{75} +(7.37228 + 12.7692i) q^{77} +(1.00000 - 1.73205i) q^{79} +(3.50000 + 8.29156i) q^{81} +(3.68614 - 6.38458i) q^{83} +(-0.813859 - 1.40965i) q^{85} +(-1.62772 - 1.73205i) q^{87} +16.1168 q^{89} +22.7446 q^{91} +(-8.00000 + 1.87953i) q^{93} +(1.18614 + 2.05446i) q^{95} +(4.18614 - 7.25061i) q^{97} +(11.7446 - 5.84096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{5} + q^{7} - 10 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^5 + q^7 - 10 * q^9	\( 4 q - 2 q^{3} + 2 q^{5} + q^{7} - 10 q^{9} - 3 q^{11} + 2 q^{13} - q^{15} - 18 q^{17} - 2 q^{19} + 16 q^{21} - 3 q^{23} - 2 q^{25} + 16 q^{27} + 3 q^{29} - 2 q^{31} - 15 q^{33} + 2 q^{35} - 16 q^{37} - 34 q^{39} + 6 q^{41} - 17 q^{43} - 5 q^{45} - 9 q^{47} - 3 q^{49} + 9 q^{51} - 6 q^{55} + q^{57} + 3 q^{59} - q^{61} - 19 q^{63} - 2 q^{65} - 14 q^{67} - 15 q^{69} + 24 q^{71} - 22 q^{73} + q^{75} + 18 q^{77} + 4 q^{79} + 14 q^{81} + 9 q^{83} - 9 q^{85} - 18 q^{87} + 30 q^{89} + 68 q^{91} - 32 q^{93} - q^{95} + 11 q^{97} + 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^5 + q^7 - 10 * q^9 - 3 * q^11 + 2 * q^13 - q^15 - 18 * q^17 - 2 * q^19 + 16 * q^21 - 3 * q^23 - 2 * q^25 + 16 * q^27 + 3 * q^29 - 2 * q^31 - 15 * q^33 + 2 * q^35 - 16 * q^37 - 34 * q^39 + 6 * q^41 - 17 * q^43 - 5 * q^45 - 9 * q^47 - 3 * q^49 + 9 * q^51 - 6 * q^55 + q^57 + 3 * q^59 - q^61 - 19 * q^63 - 2 * q^65 - 14 * q^67 - 15 * q^69 + 24 * q^71 - 22 * q^73 + q^75 + 18 * q^77 + 4 * q^79 + 14 * q^81 + 9 * q^83 - 9 * q^85 - 18 * q^87 + 30 * q^89 + 68 * q^91 - 32 * q^93 - q^95 + 11 * q^97 + 24 * q^99

Introduction

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