LMFDB - Embedded newform 1920.2.y.h.223.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(223,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("1920.223");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.y (of order $4$, 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:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.3
Root			$0.264658 - 1.38923i$ of defining polynomial
Character	$\chi$	$=$	1920.223
Dual form			1920.2.y.h.1567.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{3} +(-1.00000 + 2.00000i) q^{5} +(3.24914 - 3.24914i) q^{7} +1.00000 q^{9} +(-3.24914 - 3.24914i) q^{11} +(-1.00000 + 2.00000i) q^{15} +(-0.0586332 + 0.0586332i) q^{17} +(-4.30777 - 4.30777i) q^{19} +(3.24914 - 3.24914i) q^{21} +(-4.30777 - 4.30777i) q^{23} +(-3.00000 - 4.00000i) q^{25} +1.00000 q^{27} +(1.00000 - 1.00000i) q^{29} -6.49828i q^{31} +(-3.24914 - 3.24914i) q^{33} +(3.24914 + 9.74742i) q^{35} +1.88273i q^{37} +4.00000i q^{41} -4.61555i q^{43} +(-1.00000 + 2.00000i) q^{45} +(6.80605 + 6.80605i) q^{47} -14.1138i q^{49} +(-0.0586332 + 0.0586332i) q^{51} -9.11383 q^{53} +(9.74742 - 3.24914i) q^{55} +(-4.30777 - 4.30777i) q^{57} +(1.36641 - 1.36641i) q^{59} +(2.05863 + 2.05863i) q^{61} +(3.24914 - 3.24914i) q^{63} +12.3810i q^{67} +(-4.30777 - 4.30777i) q^{69} -8.99656 q^{71} +(-1.11727 + 1.11727i) q^{73} +(-3.00000 - 4.00000i) q^{75} -21.1138 q^{77} +8.99656 q^{79} +1.00000 q^{81} +4.99656 q^{83} +(-0.0586332 - 0.175899i) q^{85} +(1.00000 - 1.00000i) q^{87} -4.11727 q^{89} -6.49828i q^{93} +(12.9233 - 4.30777i) q^{95} +(9.99656 - 9.99656i) q^{97} +(-3.24914 - 3.24914i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} - 6 q^{5} + 2 q^{7} + 6 q^{9} - 2 q^{11} - 6 q^{15} - 2 q^{17} - 10 q^{19} + 2 q^{21} - 10 q^{23} - 18 q^{25} + 6 q^{27} + 6 q^{29} - 2 q^{33} + 2 q^{35} - 6 q^{45} - 10 q^{47} - 2 q^{51}+ \cdots - 2 q^{99}+O(q^{100}) $ 6 * q + 6 * q^3 - 6 * q^5 + 2 * q^7 + 6 * q^9 - 2 * q^11 - 6 * q^15 - 2 * q^17 - 10 * q^19 + 2 * q^21 - 10 * q^23 - 18 * q^25 + 6 * q^27 + 6 * q^29 - 2 * q^33 + 2 * q^35 - 6 * q^45 - 10 * q^47 - 2 * q^51 + 12 * q^53 + 6 * q^55 - 10 * q^57 - 6 * q^59 + 14 * q^61 + 2 * q^63 - 10 * q^69 + 16 * q^71 - 10 * q^73 - 18 * q^75 - 60 * q^77 - 16 * q^79 + 6 * q^81 - 40 * q^83 - 2 * q^85 + 6 * q^87 - 28 * q^89 + 30 * q^95 - 10 * q^97 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$		0			0
$7$	3.24914	−	3.24914i	1.22806	−	1.22806i	0.263363	−	0.964697i	$-0.415168\pi$
$7$	3.24914	−	3.24914i	1.22806	−	1.22806i	0.964697	−	0.263363i	$-0.0848316\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−3.24914	−	3.24914i	−0.979653	−	0.979653i	0.0201443	−	0.999797i	$-0.493587\pi$
$11$	−3.24914	−	3.24914i	−0.979653	−	0.979653i	−0.999797	+	0.0201443i	$0.993587\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		0			0
$15$	−1.00000	+	2.00000i	−0.258199	+	0.516398i
$16$		0			0
$17$	−0.0586332	+	0.0586332i	−0.0142206	+	0.0142206i	−0.714181	−	0.699961i	$-0.753201\pi$
$17$	−0.0586332	+	0.0586332i	−0.0142206	+	0.0142206i	0.699961	+	0.714181i	$0.253201\pi$
$18$		0			0
$19$	−4.30777	−	4.30777i	−0.988271	−	0.988271i	0.0116609	−	0.999932i	$-0.496288\pi$
$19$	−4.30777	−	4.30777i	−0.988271	−	0.988271i	−0.999932	+	0.0116609i	$0.996288\pi$
$20$		0			0
$21$	3.24914	−	3.24914i	0.709021	−	0.709021i
$22$		0			0
$23$	−4.30777	−	4.30777i	−0.898233	−	0.898233i	0.0970469	−	0.995280i	$-0.469060\pi$
$23$	−4.30777	−	4.30777i	−0.898233	−	0.898233i	−0.995280	+	0.0970469i	$0.969060\pi$
$24$		0			0
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	1.00000	−	1.00000i	0.185695	−	0.185695i	−0.608137	−	0.793832i	$-0.708083\pi$
$29$	1.00000	−	1.00000i	0.185695	−	0.185695i	0.793832	+	0.608137i	$0.208083\pi$
$30$		0			0
$31$		−	6.49828i		−	1.16713i	−0.812068	−	0.583563i	$-0.801658\pi$
$31$		−	6.49828i		−	1.16713i	0.812068	−	0.583563i	$-0.198342\pi$
$32$		0			0
$33$	−3.24914	−	3.24914i	−0.565603	−	0.565603i
$34$		0			0
$35$	3.24914	+	9.74742i	0.549205	+	1.64761i
$36$		0			0
$37$			1.88273i			0.309520i	0.987952	+	0.154760i	$0.0494604\pi$
$37$			1.88273i			0.309520i	−0.987952	+	0.154760i	$0.950540\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			4.00000i			0.624695i	0.949968	+	0.312348i	$0.101115\pi$
$41$			4.00000i			0.624695i	−0.949968	+	0.312348i	$0.898885\pi$
$42$		0			0
$43$		−	4.61555i		−	0.703864i	−0.936025	−	0.351932i	$-0.885525\pi$
$43$		−	4.61555i		−	0.703864i	0.936025	−	0.351932i	$-0.114475\pi$
$44$		0			0
$45$	−1.00000	+	2.00000i	−0.149071	+	0.298142i
$46$		0			0
$47$	6.80605	+	6.80605i	0.992765	+	0.992765i	0.999974	−	0.00720889i	$-0.00229468\pi$
$47$	6.80605	+	6.80605i	0.992765	+	0.992765i	−0.00720889	+	0.999974i	$0.502295\pi$
$48$		0			0
$49$		−	14.1138i		−	2.01626i
$50$		0			0
$51$	−0.0586332	+	0.0586332i	−0.00821028	+	0.00821028i
$52$		0			0
$53$	−9.11383			−1.25188			−0.625940	−	0.779871i	$-0.715285\pi$
$53$	−9.11383			−1.25188			−0.625940	+	0.779871i	$0.715285\pi$
$54$		0			0
$55$	9.74742	−	3.24914i	1.31434	−	0.438114i
$56$		0			0
$57$	−4.30777	−	4.30777i	−0.570579	−	0.570579i
$58$		0			0
$59$	1.36641	−	1.36641i	0.177891	−	0.177891i	−0.612545	−	0.790436i	$-0.709854\pi$
$59$	1.36641	−	1.36641i	0.177891	−	0.177891i	0.790436	+	0.612545i	$0.209854\pi$
$60$		0			0
$61$	2.05863	+	2.05863i	0.263581	+	0.263581i	0.826507	−	0.562926i	$-0.190324\pi$
$61$	2.05863	+	2.05863i	0.263581	+	0.263581i	−0.562926	+	0.826507i	$0.690324\pi$
$62$		0			0
$63$	3.24914	−	3.24914i	0.409353	−	0.409353i
$64$		0			0
$65$		0			0
$66$		0			0
$67$			12.3810i			1.51258i	0.654236	+	0.756291i	$0.272990\pi$
$67$			12.3810i			1.51258i	−0.654236	+	0.756291i	$0.727010\pi$
$68$		0			0
$69$	−4.30777	−	4.30777i	−0.518595	−	0.518595i
$70$		0			0
$71$	−8.99656			−1.06770			−0.533848	−	0.845581i	$-0.679254\pi$
$71$	−8.99656			−1.06770			−0.533848	+	0.845581i	$0.679254\pi$
$72$		0			0
$73$	−1.11727	+	1.11727i	−0.130766	+	0.130766i	−0.769461	−	0.638694i	$-0.779475\pi$
$73$	−1.11727	+	1.11727i	−0.130766	+	0.130766i	0.638694	+	0.769461i	$0.279475\pi$
$74$		0			0
$75$	−3.00000	−	4.00000i	−0.346410	−	0.461880i
$76$		0			0
$77$	−21.1138			−2.40614
$78$		0			0
$79$	8.99656			1.01219			0.506096	−	0.862477i	$-0.331088\pi$
$79$	8.99656			1.01219			0.506096	+	0.862477i	$0.331088\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	4.99656			0.548444			0.274222	−	0.961666i	$-0.411580\pi$
$83$	4.99656			0.548444			0.274222	+	0.961666i	$0.411580\pi$
$84$		0			0
$85$	−0.0586332	−	0.175899i	−0.00635966	−	0.0190790i
$86$		0			0
$87$	1.00000	−	1.00000i	0.107211	−	0.107211i
$88$		0			0
$89$	−4.11727			−0.436429			−0.218215	−	0.975901i	$-0.570023\pi$
$89$	−4.11727			−0.436429			−0.218215	+	0.975901i	$0.570023\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		−	6.49828i		−	0.673840i
$94$		0			0
$95$	12.9233	−	4.30777i	1.32590	−	0.441968i
$96$		0			0
$97$	9.99656	−	9.99656i	1.01500	−	1.01500i	0.0151113	−	0.999886i	$-0.495190\pi$
$97$	9.99656	−	9.99656i	1.01500	−	1.01500i	0.999886	−	0.0151113i	$-0.00481026\pi$
$98$		0			0
$99$	−3.24914	−	3.24914i	−0.326551	−	0.326551i
$100$		0			0
$101$	2.88273	−	2.88273i	0.286843	−	0.286843i	−0.548988	−	0.835830i	$-0.684987\pi$
$101$	2.88273	−	2.88273i	0.286843	−	0.286843i	0.835830	+	0.548988i	$0.184987\pi$
$102$		0			0
$103$	−5.36641	−	5.36641i	−0.528768	−	0.528768i	0.391437	−	0.920205i	$-0.371978\pi$
$103$	−5.36641	−	5.36641i	−0.528768	−	0.528768i	−0.920205	+	0.391437i	$0.871978\pi$
$104$		0			0
$105$	3.24914	+	9.74742i	0.317084	+	0.951251i
$106$		0			0
$107$	17.2311			1.66579			0.832896	−	0.553429i	$-0.186681\pi$
$107$	17.2311			1.66579			0.832896	+	0.553429i	$0.186681\pi$
$108$		0			0
$109$	7.05520	−	7.05520i	0.675765	−	0.675765i	−0.283274	−	0.959039i	$-0.591421\pi$
$109$	7.05520	−	7.05520i	0.675765	−	0.675765i	0.959039	+	0.283274i	$0.0914205\pi$
$110$		0			0
$111$			1.88273i			0.178701i
$112$		0			0
$113$	2.05863	+	2.05863i	0.193660	+	0.193660i	0.797276	−	0.603616i	$-0.206274\pi$
$113$	2.05863	+	2.05863i	0.193660	+	0.193660i	−0.603616	+	0.797276i	$0.706274\pi$
$114$		0			0
$115$	12.9233	−	4.30777i	1.20511	−	0.401702i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			0.381015i			0.0349276i
$120$		0			0
$121$			10.1138i			0.919439i
$122$		0			0
$123$			4.00000i			0.360668i
$124$		0			0
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$	−7.24914	−	7.24914i	−0.643257	−	0.643257i	0.308098	−	0.951355i	$-0.400308\pi$
$127$	−7.24914	−	7.24914i	−0.643257	−	0.643257i	−0.951355	+	0.308098i	$0.900308\pi$
$128$		0			0
$129$		−	4.61555i		−	0.406376i
$130$		0			0
$131$	9.13187	−	9.13187i	0.797856	−	0.797856i	−0.184902	−	0.982757i	$-0.559197\pi$
$131$	9.13187	−	9.13187i	0.797856	−	0.797856i	0.982757	+	0.184902i	$0.0591966\pi$
$132$		0			0
$133$	−27.9931			−2.42731
$134$		0			0
$135$	−1.00000	+	2.00000i	−0.0860663	+	0.172133i
$136$		0			0
$137$	−5.05520	−	5.05520i	−0.431894	−	0.431894i	0.457378	−	0.889272i	$-0.348789\pi$
$137$	−5.05520	−	5.05520i	−0.431894	−	0.431894i	−0.889272	+	0.457378i	$0.848789\pi$
$138$		0			0
$139$	6.19051	−	6.19051i	0.525072	−	0.525072i	−0.394027	−	0.919099i	$-0.628918\pi$
$139$	6.19051	−	6.19051i	0.525072	−	0.525072i	0.919099	+	0.394027i	$0.128918\pi$
$140$		0			0
$141$	6.80605	+	6.80605i	0.573173	+	0.573173i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	1.00000	+	3.00000i	0.0830455	+	0.249136i
$146$		0			0
$147$		−	14.1138i		−	1.16409i
$148$		0			0
$149$	−0.882734	−	0.882734i	−0.0723164	−	0.0723164i	0.670024	−	0.742340i	$-0.266284\pi$
$149$	−0.882734	−	0.882734i	−0.0723164	−	0.0723164i	−0.742340	+	0.670024i	$0.766284\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		0			0
$153$	−0.0586332	+	0.0586332i	−0.00474021	+	0.00474021i
$154$		0			0
$155$	12.9966	+	6.49828i	1.04391	+	0.521954i
$156$		0			0
$157$	9.76547			0.779369			0.389685	−	0.920948i	$-0.372584\pi$
$157$	9.76547			0.779369			0.389685	+	0.920948i	$0.372584\pi$
$158$		0			0
$159$	−9.11383			−0.722774
$160$		0			0
$161$	−27.9931			−2.20617
$162$		0			0
$163$	−20.9966			−1.64458			−0.822289	−	0.569070i	$-0.807303\pi$
$163$	−20.9966			−1.64458			−0.822289	+	0.569070i	$0.807303\pi$
$164$		0			0
$165$	9.74742	−	3.24914i	0.758836	−	0.252945i
$166$		0			0
$167$	2.42504	−	2.42504i	0.187655	−	0.187655i	−0.607026	−	0.794682i	$-0.707638\pi$
$167$	2.42504	−	2.42504i	0.187655	−	0.187655i	0.794682	+	0.607026i	$0.207638\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$	−4.30777	−	4.30777i	−0.329424	−	0.329424i
$172$		0			0
$173$			0.234533i			0.0178312i	0.999960	+	0.00891559i	$0.00283796\pi$
$173$			0.234533i			0.0178312i	−0.999960	+	0.00891559i	$0.997162\pi$
$174$		0			0
$175$	−22.7440	−	3.24914i	−1.71928	−	0.245612i
$176$		0			0
$177$	1.36641	−	1.36641i	0.102705	−	0.102705i
$178$		0			0
$179$	−5.13187	−	5.13187i	−0.383574	−	0.383574i	0.488814	−	0.872388i	$-0.337430\pi$
$179$	−5.13187	−	5.13187i	−0.383574	−	0.383574i	−0.872388	+	0.488814i	$0.837430\pi$
$180$		0			0
$181$	−0.0586332	+	0.0586332i	−0.00435817	+	0.00435817i	−0.709283	−	0.704924i	$-0.750981\pi$
$181$	−0.0586332	+	0.0586332i	−0.00435817	+	0.00435817i	0.704924	+	0.709283i	$0.250981\pi$
$182$		0			0
$183$	2.05863	+	2.05863i	0.152179	+	0.152179i
$184$		0			0
$185$	−3.76547	−	1.88273i	−0.276843	−	0.138421i
$186$		0			0
$187$	0.381015			0.0278626
$188$		0			0
$189$	3.24914	−	3.24914i	0.236340	−	0.236340i
$190$		0			0
$191$			20.6155i			1.49169i	0.666120	+	0.745844i	$0.267954\pi$
$191$			20.6155i			1.49169i	−0.666120	+	0.745844i	$0.732046\pi$
$192$		0			0
$193$	13.9966	+	13.9966i	1.00749	+	1.00749i	0.999972	+	0.00752289i	$0.00239463\pi$
$193$	13.9966	+	13.9966i	1.00749	+	1.00749i	0.00752289	+	0.999972i	$0.497605\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	14.8793i		−	1.06011i	−0.847965	−	0.530053i	$-0.822172\pi$
$197$		−	14.8793i		−	1.06011i	0.847965	−	0.530053i	$-0.177828\pi$
$198$		0			0
$199$			18.4983i			1.31131i	0.755061	+	0.655654i	$0.227607\pi$
$199$			18.4983i			1.31131i	−0.755061	+	0.655654i	$0.772393\pi$
$200$		0			0
$201$			12.3810i			0.873289i
$202$		0			0
$203$		−	6.49828i		−	0.456090i
$204$		0			0
$205$	−8.00000	−	4.00000i	−0.558744	−	0.279372i
$206$		0			0
$207$	−4.30777	−	4.30777i	−0.299411	−	0.299411i
$208$		0			0
$209$			27.9931i			1.93632i
$210$		0			0
$211$	−8.92332	+	8.92332i	−0.614307	+	0.614307i	−0.944065	−	0.329759i	$-0.893033\pi$
$211$	−8.92332	+	8.92332i	−0.614307	+	0.614307i	0.329759	+	0.944065i	$0.393033\pi$
$212$		0			0
$213$	−8.99656			−0.616434
$214$		0			0
$215$	9.23109	+	4.61555i	0.629555	+	0.314778i
$216$		0			0
$217$	−21.1138	−	21.1138i	−1.43330	−	1.43330i
$218$		0			0
$219$	−1.11727	+	1.11727i	−0.0754979	+	0.0754979i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	13.1319	−	13.1319i	0.879375	−	0.879375i	−0.114095	−	0.993470i	$-0.536397\pi$
$223$	13.1319	−	13.1319i	0.879375	−	0.879375i	0.993470	+	0.114095i	$0.0363967\pi$
$224$		0			0
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$		0			0
$227$		−	1.50172i		−	0.0996726i	−0.998757	−	0.0498363i	$-0.984130\pi$
$227$		−	1.50172i		−	0.0996726i	0.998757	−	0.0498363i	$-0.0158700\pi$
$228$		0			0
$229$	7.05520	+	7.05520i	0.466220	+	0.466220i	0.900688	−	0.434467i	$-0.143063\pi$
$229$	7.05520	+	7.05520i	0.466220	+	0.466220i	−0.434467	+	0.900688i	$0.643063\pi$
$230$		0			0
$231$	−21.1138			−1.38919
$232$		0			0
$233$	−9.05520	+	9.05520i	−0.593226	+	0.593226i	−0.938501	−	0.345276i	$-0.887785\pi$
$233$	−9.05520	+	9.05520i	−0.593226	+	0.593226i	0.345276	+	0.938501i	$0.387785\pi$
$234$		0			0
$235$	−20.4182	+	6.80605i	−1.33193	+	0.443978i
$236$		0			0
$237$	8.99656			0.584390
$238$		0			0
$239$	16.9966			1.09942			0.549708	−	0.835357i	$-0.314739\pi$
$239$	16.9966			1.09942			0.549708	+	0.835357i	$0.314739\pi$
$240$		0			0
$241$	−23.9931			−1.54553			−0.772767	−	0.634690i	$-0.781128\pi$
$241$	−23.9931			−1.54553			−0.772767	+	0.634690i	$0.781128\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	28.2277	+	14.1138i	1.80340	+	0.901699i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	4.99656			0.316644
$250$		0			0
$251$	−7.24914	−	7.24914i	−0.457562	−	0.457562i	0.440293	−	0.897854i	$-0.354875\pi$
$251$	−7.24914	−	7.24914i	−0.457562	−	0.457562i	−0.897854	+	0.440293i	$0.854875\pi$
$252$		0			0
$253$			27.9931i			1.75991i
$254$		0			0
$255$	−0.0586332	−	0.175899i	−0.00367175	−	0.0110153i
$256$		0			0
$257$	−3.17246	+	3.17246i	−0.197893	+	0.197893i	−0.799096	−	0.601203i	$-0.794688\pi$
$257$	−3.17246	+	3.17246i	−0.197893	+	0.197893i	0.601203	+	0.799096i	$0.294688\pi$
$258$		0			0
$259$	6.11727	+	6.11727i	0.380108	+	0.380108i
$260$		0			0
$261$	1.00000	−	1.00000i	0.0618984	−	0.0618984i
$262$		0			0
$263$	20.6888	+	20.6888i	1.27573	+	1.27573i	0.943037	+	0.332689i	$0.107956\pi$
$263$	20.6888	+	20.6888i	1.27573	+	1.27573i	0.332689	+	0.943037i	$0.392044\pi$
$264$		0			0
$265$	9.11383	−	18.2277i	0.559858	−	1.11972i
$266$		0			0
$267$	−4.11727			−0.251973
$268$		0			0
$269$	−17.8793	+	17.8793i	−1.09012	+	1.09012i	−0.0946050	+	0.995515i	$0.530159\pi$
$269$	−17.8793	+	17.8793i	−1.09012	+	1.09012i	−0.995515	+	0.0946050i	$0.969841\pi$
$270$		0			0
$271$			18.4983i			1.12369i	0.827242	+	0.561845i	$0.189908\pi$
$271$			18.4983i			1.12369i	−0.827242	+	0.561845i	$0.810092\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.24914	+	22.7440i	−0.195931	+	1.37151i
$276$		0			0
$277$		−	16.1104i		−	0.967980i	−0.875074	−	0.483990i	$-0.839187\pi$
$277$		−	16.1104i		−	0.967980i	0.875074	−	0.483990i	$-0.160813\pi$
$278$		0			0
$279$		−	6.49828i		−	0.389042i
$280$		0			0
$281$		−	10.1173i		−	0.603546i	−0.953380	−	0.301773i	$-0.902422\pi$
$281$		−	10.1173i		−	0.603546i	0.953380	−	0.301773i	$-0.0975784\pi$
$282$		0			0
$283$		−	5.61211i		−	0.333605i	−0.985990	−	0.166803i	$-0.946656\pi$
$283$		−	5.61211i		−	0.333605i	0.985990	−	0.166803i	$-0.0533443\pi$
$284$		0			0
$285$	12.9233	−	4.30777i	0.765511	−	0.255170i
$286$		0			0
$287$	12.9966	+	12.9966i	0.767163	+	0.767163i
$288$		0			0
$289$			16.9931i			0.999596i
$290$		0			0
$291$	9.99656	−	9.99656i	0.586009	−	0.586009i
$292$		0			0
$293$	20.2277			1.18171			0.590856	−	0.806777i	$-0.298790\pi$
$293$	20.2277			1.18171			0.590856	+	0.806777i	$0.298790\pi$
$294$		0			0
$295$	1.36641	+	4.09922i	0.0795553	+	0.238666i
$296$		0			0
$297$	−3.24914	−	3.24914i	−0.188534	−	0.188534i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−14.9966	−	14.9966i	−0.864387	−	0.864387i
$302$		0			0
$303$	2.88273	−	2.88273i	0.165609	−	0.165609i
$304$		0			0
$305$	−6.17590	+	2.05863i	−0.353631	+	0.117877i
$306$		0			0
$307$		−	20.6155i		−	1.17659i	−0.808646	−	0.588296i	$-0.799799\pi$
$307$		−	20.6155i		−	1.17659i	0.808646	−	0.588296i	$-0.200201\pi$
$308$		0			0
$309$	−5.36641	−	5.36641i	−0.305284	−	0.305284i
$310$		0			0
$311$	−21.2311			−1.20390			−0.601952	−	0.798532i	$-0.705610\pi$
$311$	−21.2311			−1.20390			−0.601952	+	0.798532i	$0.705610\pi$
$312$		0			0
$313$	−3.00000	+	3.00000i	−0.169570	+	0.169570i	−0.786790	−	0.617220i	$-0.788259\pi$
$313$	−3.00000	+	3.00000i	−0.169570	+	0.169570i	0.617220	+	0.786790i	$0.288259\pi$
$314$		0			0
$315$	3.24914	+	9.74742i	0.183068	+	0.549205i
$316$		0			0
$317$	−1.11383			−0.0625588			−0.0312794	−	0.999511i	$-0.509958\pi$
$317$	−1.11383			−0.0625588			−0.0312794	+	0.999511i	$0.509958\pi$
$318$		0			0
$319$	−6.49828			−0.363834
$320$		0			0
$321$	17.2311			0.961746
$322$		0			0
$323$	0.505157			0.0281077
$324$		0			0
$325$		0			0
$326$		0			0
$327$	7.05520	−	7.05520i	0.390153	−	0.390153i
$328$		0			0
$329$	44.2277			2.43835
$330$		0			0
$331$	8.92332	+	8.92332i	0.490470	+	0.490470i	0.908454	−	0.417984i	$-0.137263\pi$
$331$	8.92332	+	8.92332i	0.490470	+	0.490470i	−0.417984	+	0.908454i	$0.637263\pi$
$332$		0			0
$333$			1.88273i			0.103173i
$334$		0			0
$335$	−24.7620	−	12.3810i	−1.35289	−	0.676447i
$336$		0			0
$337$	−2.00344	+	2.00344i	−0.109134	+	0.109134i	−0.759565	−	0.650431i	$-0.774588\pi$
$337$	−2.00344	+	2.00344i	−0.109134	+	0.109134i	0.650431	+	0.759565i	$0.274588\pi$
$338$		0			0
$339$	2.05863	+	2.05863i	0.111810	+	0.111810i
$340$		0			0
$341$	−21.1138	+	21.1138i	−1.14338	+	1.14338i
$342$		0			0
$343$	−23.1138	−	23.1138i	−1.24803	−	1.24803i
$344$		0			0
$345$	12.9233	−	4.30777i	0.695768	−	0.231923i
$346$		0			0
$347$	0.234533			0.0125904			0.00629519	−	0.999980i	$-0.497996\pi$
$347$	0.234533			0.0125904			0.00629519	+	0.999980i	$0.497996\pi$
$348$		0			0
$349$	21.1725	−	21.1725i	1.13334	−	1.13334i	0.143717	−	0.989619i	$-0.454094\pi$
$349$	21.1725	−	21.1725i	1.13334	−	1.13334i	0.989619	−	0.143717i	$-0.0459055\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.0586332	−	0.0586332i	−0.00312073	−	0.00312073i	0.705545	−	0.708665i	$-0.250702\pi$
$353$	−0.0586332	−	0.0586332i	−0.00312073	−	0.00312073i	−0.708665	+	0.705545i	$0.750702\pi$
$354$		0			0
$355$	8.99656	−	17.9931i	0.477488	−	0.954976i
$356$		0			0
$357$			0.381015i			0.0201654i
$358$		0			0
$359$			9.84664i			0.519686i	0.965651	+	0.259843i	$0.0836708\pi$
$359$			9.84664i			0.519686i	−0.965651	+	0.259843i	$0.916329\pi$
$360$		0			0
$361$			18.1138i			0.953359i
$362$		0			0
$363$			10.1138i			0.530838i
$364$		0			0
$365$	−1.11727	−	3.35180i	−0.0584804	−	0.175441i
$366$		0			0
$367$	−6.36297	−	6.36297i	−0.332144	−	0.332144i	0.521256	−	0.853400i	$-0.325464\pi$
$367$	−6.36297	−	6.36297i	−0.332144	−	0.332144i	−0.853400	+	0.521256i	$0.825464\pi$
$368$		0			0
$369$			4.00000i			0.208232i
$370$		0			0
$371$	−29.6121	+	29.6121i	−1.53738	+	1.53738i
$372$		0			0
$373$	28.2277			1.46157			0.730786	−	0.682606i	$-0.239154\pi$
$373$	28.2277			1.46157			0.730786	+	0.682606i	$0.239154\pi$
$374$		0			0
$375$	11.0000	−	2.00000i	0.568038	−	0.103280i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−19.8026	+	19.8026i	−1.01719	+	1.01719i	−0.0173425	+	0.999850i	$0.505521\pi$
$379$	−19.8026	+	19.8026i	−1.01719	+	1.01719i	−0.999850	+	0.0173425i	$0.994479\pi$
$380$		0			0
$381$	−7.24914	−	7.24914i	−0.371385	−	0.371385i
$382$		0			0
$383$	−7.69223	+	7.69223i	−0.393054	+	0.393054i	−0.875775	−	0.482720i	$-0.839649\pi$
$383$	−7.69223	+	7.69223i	−0.393054	+	0.393054i	0.482720	+	0.875775i	$0.339649\pi$
$384$		0			0
$385$	21.1138	−	42.2277i	1.07606	−	2.15212i
$386$		0			0
$387$		−	4.61555i		−	0.234621i
$388$		0			0
$389$	−8.88273	−	8.88273i	−0.450372	−	0.450372i	0.445106	−	0.895478i	$-0.353166\pi$
$389$	−8.88273	−	8.88273i	−0.450372	−	0.450372i	−0.895478	+	0.445106i	$0.853166\pi$
$390$		0			0
$391$	0.505157			0.0255469
$392$		0			0
$393$	9.13187	−	9.13187i	0.460642	−	0.460642i
$394$		0			0
$395$	−8.99656	+	17.9931i	−0.452666	+	0.905332i
$396$		0			0
$397$	−8.11727			−0.407394			−0.203697	−	0.979034i	$-0.565296\pi$
$397$	−8.11727			−0.407394			−0.203697	+	0.979034i	$0.565296\pi$
$398$		0			0
$399$	−27.9931			−1.40141
$400$		0			0
$401$	26.1104			1.30389			0.651945	−	0.758266i	$-0.273953\pi$
$401$	26.1104			1.30389			0.651945	+	0.758266i	$0.273953\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−1.00000	+	2.00000i	−0.0496904	+	0.0993808i
$406$		0			0
$407$	6.11727	−	6.11727i	0.303222	−	0.303222i
$408$		0			0
$409$	−2.65164			−0.131115			−0.0655576	−	0.997849i	$-0.520883\pi$
$409$	−2.65164			−0.131115			−0.0655576	+	0.997849i	$0.520883\pi$
$410$		0			0
$411$	−5.05520	−	5.05520i	−0.249354	−	0.249354i
$412$		0			0
$413$		−	8.87930i		−	0.436922i
$414$		0			0
$415$	−4.99656	+	9.99312i	−0.245272	+	0.490543i
$416$		0			0
$417$	6.19051	−	6.19051i	0.303150	−	0.303150i
$418$		0			0
$419$	7.86469	+	7.86469i	0.384215	+	0.384215i	0.872618	−	0.488403i	$-0.162420\pi$
$419$	7.86469	+	7.86469i	0.384215	+	0.384215i	−0.488403	+	0.872618i	$0.662420\pi$
$420$		0			0
$421$	2.94480	−	2.94480i	0.143521	−	0.143521i	−0.631696	−	0.775217i	$-0.717641\pi$
$421$	2.94480	−	2.94480i	0.143521	−	0.143521i	0.775217	+	0.631696i	$0.217641\pi$
$422$		0			0
$423$	6.80605	+	6.80605i	0.330922	+	0.330922i
$424$		0			0
$425$	0.410432	+	0.0586332i	0.0199089	+	0.00284413i
$426$		0			0
$427$	13.3776			0.647386
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	28.3810i		−	1.36707i	−0.729920	−	0.683533i	$-0.760443\pi$
$431$		−	28.3810i		−	1.36707i	0.729920	−	0.683533i	$-0.239557\pi$
$432$		0			0
$433$	12.1138	+	12.1138i	0.582153	+	0.582153i	0.935495	−	0.353341i	$-0.114954\pi$
$433$	12.1138	+	12.1138i	0.582153	+	0.582153i	−0.353341	+	0.935495i	$0.614954\pi$
$434$		0			0
$435$	1.00000	+	3.00000i	0.0479463	+	0.143839i
$436$		0			0
$437$			37.1138i			1.77540i
$438$		0			0
$439$			14.7328i			0.703159i	0.936158	+	0.351579i	$0.114355\pi$
$439$			14.7328i			0.703159i	−0.936158	+	0.351579i	$0.885645\pi$
$440$		0			0
$441$		−	14.1138i		−	0.672087i
$442$		0			0
$443$		−	39.2603i		−	1.86531i	−0.360765	−	0.932657i	$-0.617484\pi$
$443$		−	39.2603i		−	1.86531i	0.360765	−	0.932657i	$-0.382516\pi$
$444$		0			0
$445$	4.11727	−	8.23453i	0.195177	−	0.390354i
$446$		0			0
$447$	−0.882734	−	0.882734i	−0.0417519	−	0.0417519i
$448$		0			0
$449$		−	9.64820i		−	0.455327i	−0.973740	−	0.227663i	$-0.926891\pi$
$449$		−	9.64820i		−	0.455327i	0.973740	−	0.227663i	$-0.0731086\pi$
$450$		0			0
$451$	12.9966	−	12.9966i	0.611984	−	0.611984i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	17.9966	+	17.9966i	0.841844	+	0.841844i	0.989099	−	0.147255i	$-0.0470438\pi$
$457$	17.9966	+	17.9966i	0.841844	+	0.841844i	−0.147255	+	0.989099i	$0.547044\pi$
$458$		0			0
$459$	−0.0586332	+	0.0586332i	−0.00273676	+	0.00273676i
$460$		0			0
$461$	16.1138	+	16.1138i	0.750496	+	0.750496i	0.974572	−	0.224076i	$-0.0719363\pi$
$461$	16.1138	+	16.1138i	0.750496	+	0.750496i	−0.224076	+	0.974572i	$0.571936\pi$
$462$		0			0
$463$	−6.86813	+	6.86813i	−0.319189	+	0.319189i	−0.848456	−	0.529267i	$-0.822467\pi$
$463$	−6.86813	+	6.86813i	−0.319189	+	0.319189i	0.529267	+	0.848456i	$0.322467\pi$
$464$		0			0
$465$	12.9966	+	6.49828i	0.602701	+	0.301351i
$466$		0			0
$467$			1.26719i			0.0586384i	0.999570	+	0.0293192i	$0.00933393\pi$
$467$			1.26719i			0.0586384i	−0.999570	+	0.0293192i	$0.990666\pi$
$468$		0			0
$469$	40.2277	+	40.2277i	1.85754	+	1.85754i
$470$		0			0
$471$	9.76547			0.449969
$472$		0			0
$473$	−14.9966	+	14.9966i	−0.689543	+	0.689543i
$474$		0			0
$475$	−4.30777	+	30.1544i	−0.197654	+	1.38358i
$476$		0			0
$477$	−9.11383			−0.417294
$478$		0			0
$479$	7.00344			0.319995			0.159998	−	0.987117i	$-0.448851\pi$
$479$	7.00344			0.319995			0.159998	+	0.987117i	$0.448851\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−27.9931			−1.27373
$484$		0			0
$485$	9.99656	+	29.9897i	0.453921	+	1.36176i
$486$		0			0
$487$	25.2423	−	25.2423i	1.14384	−	1.14384i	0.156094	−	0.987742i	$-0.450110\pi$
$487$	25.2423	−	25.2423i	1.14384	−	1.14384i	0.987742	−	0.156094i	$-0.0498903\pi$
$488$		0			0
$489$	−20.9966			−0.949497
$490$		0			0
$491$	10.6336	+	10.6336i	0.479887	+	0.479887i	0.905096	−	0.425208i	$-0.139799\pi$
$491$	10.6336	+	10.6336i	0.479887	+	0.479887i	−0.425208	+	0.905096i	$0.639799\pi$
$492$		0			0
$493$			0.117266i			0.00528141i
$494$		0			0
$495$	9.74742	−	3.24914i	0.438114	−	0.146038i
$496$		0			0
$497$	−29.2311	+	29.2311i	−1.31119	+	1.31119i
$498$		0			0
$499$	−4.30777	−	4.30777i	−0.192842	−	0.192842i	0.604081	−	0.796923i	$-0.293540\pi$
$499$	−4.30777	−	4.30777i	−0.192842	−	0.192842i	−0.796923	+	0.604081i	$0.793540\pi$
$500$		0			0
$501$	2.42504	−	2.42504i	0.108343	−	0.108343i
$502$		0			0
$503$	−13.0698	−	13.0698i	−0.582754	−	0.582754i	0.352905	−	0.935659i	$-0.385194\pi$
$503$	−13.0698	−	13.0698i	−0.582754	−	0.582754i	−0.935659	+	0.352905i	$0.885194\pi$
$504$		0			0
$505$	2.88273	+	8.64820i	0.128280	+	0.384840i
$506$		0			0
$507$	13.0000			0.577350
$508$		0			0
$509$	−16.9931	+	16.9931i	−0.753207	+	0.753207i	−0.975076	−	0.221869i	$-0.928784\pi$
$509$	−16.9931	+	16.9931i	−0.753207	+	0.753207i	0.221869	+	0.975076i	$0.428784\pi$
$510$		0			0
$511$			7.26031i			0.321177i
$512$		0			0
$513$	−4.30777	−	4.30777i	−0.190193	−	0.190193i
$514$		0			0
$515$	16.0992	−	5.36641i	0.709416	−	0.236472i
$516$		0			0
$517$		−	44.2277i		−	1.94513i
$518$		0			0
$519$			0.234533i			0.0102948i
$520$		0			0
$521$			14.3518i			0.628764i	0.949297	+	0.314382i	$0.101797\pi$
$521$			14.3518i			0.628764i	−0.949297	+	0.314382i	$0.898203\pi$
$522$		0			0
$523$			4.38101i			0.191568i	0.995402	+	0.0957842i	$0.0305359\pi$
$523$			4.38101i			0.191568i	−0.995402	+	0.0957842i	$0.969464\pi$
$524$		0			0
$525$	−22.7440	−	3.24914i	−0.992629	−	0.141804i
$526$		0			0
$527$	0.381015	+	0.381015i	0.0165973	+	0.0165973i
$528$		0			0
$529$			14.1138i			0.613645i
$530$		0			0
$531$	1.36641	−	1.36641i	0.0592970	−	0.0592970i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−17.2311	+	34.4622i	−0.744965	+	1.48993i
$536$		0			0
$537$	−5.13187	−	5.13187i	−0.221457	−	0.221457i
$538$		0			0
$539$	−45.8578	+	45.8578i	−1.97524	+	1.97524i
$540$		0			0
$541$	13.4070	+	13.4070i	0.576412	+	0.576412i	0.933913	−	0.357501i	$-0.116371\pi$
$541$	13.4070	+	13.4070i	0.576412	+	0.576412i	−0.357501	+	0.933913i	$0.616371\pi$
$542$		0			0
$543$	−0.0586332	+	0.0586332i	−0.00251619	+	0.00251619i
$544$		0			0
$545$	7.05520	+	21.1656i	0.302211	+	0.906634i
$546$		0			0
$547$			19.3845i			0.828819i	0.910090	+	0.414410i	$0.136012\pi$
$547$			19.3845i			0.828819i	−0.910090	+	0.414410i	$0.863988\pi$
$548$		0			0
$549$	2.05863	+	2.05863i	0.0878603	+	0.0878603i
$550$		0			0
$551$	−8.61555			−0.367035
$552$		0			0
$553$	29.2311	−	29.2311i	1.24303	−	1.24303i
$554$		0			0
$555$	−3.76547	−	1.88273i	−0.159835	−	0.0799176i
$556$		0			0
$557$	−35.9931			−1.52508			−0.762539	−	0.646942i	$-0.776047\pi$
$557$	−35.9931			−1.52508			−0.762539	+	0.646942i	$0.776047\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.381015			0.0160865
$562$		0			0
$563$	−8.23453			−0.347044			−0.173522	−	0.984830i	$-0.555515\pi$
$563$	−8.23453			−0.347044			−0.173522	+	0.984830i	$0.555515\pi$
$564$		0			0
$565$	−6.17590	+	2.05863i	−0.259822	+	0.0866073i
$566$		0			0
$567$	3.24914	−	3.24914i	0.136451	−	0.136451i
$568$		0			0
$569$	−15.8827			−0.665839			−0.332919	−	0.942955i	$-0.608034\pi$
$569$	−15.8827			−0.665839			−0.332919	+	0.942955i	$0.608034\pi$
$570$		0			0
$571$	−22.1905	−	22.1905i	−0.928644	−	0.928644i	0.0689746	−	0.997618i	$-0.478027\pi$
$571$	−22.1905	−	22.1905i	−0.928644	−	0.928644i	−0.997618	+	0.0689746i	$0.978027\pi$
$572$		0			0
$573$			20.6155i			0.861227i
$574$		0			0
$575$	−4.30777	+	30.1544i	−0.179647	+	1.25753i
$576$		0			0
$577$	8.00344	−	8.00344i	0.333187	−	0.333187i	−0.520608	−	0.853796i	$-0.674295\pi$
$577$	8.00344	−	8.00344i	0.333187	−	0.333187i	0.853796	+	0.520608i	$0.174295\pi$
$578$		0			0
$579$	13.9966	+	13.9966i	0.581677	+	0.581677i
$580$		0			0
$581$	16.2345	−	16.2345i	0.673522	−	0.673522i
$582$		0			0
$583$	29.6121	+	29.6121i	1.22641	+	1.22641i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.00344			−0.123965			−0.0619826	−	0.998077i	$-0.519742\pi$
$587$	−3.00344			−0.123965			−0.0619826	+	0.998077i	$0.519742\pi$
$588$		0			0
$589$	−27.9931	+	27.9931i	−1.15344	+	1.15344i
$590$		0			0
$591$		−	14.8793i		−	0.612052i
$592$		0			0
$593$	−22.0518	−	22.0518i	−0.905557	−	0.905557i	0.0903527	−	0.995910i	$-0.471201\pi$
$593$	−22.0518	−	22.0518i	−0.905557	−	0.905557i	−0.995910	+	0.0903527i	$0.971201\pi$
$594$		0			0
$595$	−0.762030	−	0.381015i	−0.0312402	−	0.0156201i
$596$		0			0
$597$			18.4983i			0.757084i
$598$		0			0
$599$			17.8466i			0.729194i	0.931165	+	0.364597i	$0.118793\pi$
$599$			17.8466i			0.729194i	−0.931165	+	0.364597i	$0.881207\pi$
$600$		0			0
$601$			44.4553i			1.81337i	0.421808	+	0.906685i	$0.361396\pi$
$601$			44.4553i			1.81337i	−0.421808	+	0.906685i	$0.638604\pi$
$602$		0			0
$603$			12.3810i			0.504194i
$604$		0			0
$605$	−20.2277	−	10.1138i	−0.822371	−	0.411186i
$606$		0			0
$607$	−22.5975	−	22.5975i	−0.917204	−	0.917204i	0.0796209	−	0.996825i	$-0.474629\pi$
$607$	−22.5975	−	22.5975i	−0.917204	−	0.917204i	−0.996825	+	0.0796209i	$0.974629\pi$
$608$		0			0
$609$		−	6.49828i		−	0.263324i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−16.1173			−0.650970			−0.325485	−	0.945547i	$-0.605528\pi$
$613$	−16.1173			−0.650970			−0.325485	+	0.945547i	$0.605528\pi$
$614$		0			0
$615$	−8.00000	−	4.00000i	−0.322591	−	0.161296i
$616$		0			0
$617$	−21.2897	−	21.2897i	−0.857092	−	0.857092i	0.133902	−	0.990995i	$-0.457249\pi$
$617$	−21.2897	−	21.2897i	−0.857092	−	0.857092i	−0.990995	+	0.133902i	$0.957249\pi$
$618$		0			0
$619$	6.19051	−	6.19051i	0.248817	−	0.248817i	−0.571668	−	0.820485i	$-0.693703\pi$
$619$	6.19051	−	6.19051i	0.248817	−	0.248817i	0.820485	+	0.571668i	$0.193703\pi$
$620$		0			0
$621$	−4.30777	−	4.30777i	−0.172865	−	0.172865i
$622$		0			0
$623$	−13.3776	+	13.3776i	−0.535961	+	0.535961i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$			27.9931i			1.11794i
$628$		0			0
$629$	−0.110391	−	0.110391i	−0.00440156	−	0.00440156i
$630$		0			0
$631$	1.46563			0.0583457			0.0291729	−	0.999574i	$-0.490713\pi$
$631$	1.46563			0.0583457			0.0291729	+	0.999574i	$0.490713\pi$
$632$		0			0
$633$	−8.92332	+	8.92332i	−0.354670	+	0.354670i
$634$		0			0
$635$	21.7474	−	7.24914i	0.863020	−	0.287673i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−8.99656			−0.355898
$640$		0			0
$641$	43.9931			1.73762			0.868812	−	0.495142i	$-0.164884\pi$
$641$	43.9931			1.73762			0.868812	+	0.495142i	$0.164884\pi$
$642$		0			0
$643$	−5.46563			−0.215543			−0.107772	−	0.994176i	$-0.534372\pi$
$643$	−5.46563			−0.215543			−0.107772	+	0.994176i	$0.534372\pi$
$644$		0			0
$645$	9.23109	+	4.61555i	0.363474	+	0.181737i
$646$		0			0
$647$	28.1836	−	28.1836i	1.10801	−	1.10801i	0.114601	−	0.993412i	$-0.463441\pi$
$647$	28.1836	−	28.1836i	1.10801	−	1.10801i	0.993412	−	0.114601i	$-0.0365591\pi$
$648$		0			0
$649$	−8.87930			−0.348543
$650$		0			0
$651$	−21.1138	−	21.1138i	−0.827516	−	0.827516i
$652$		0			0
$653$			3.11383i			0.121854i	0.998142	+	0.0609268i	$0.0194056\pi$
$653$			3.11383i			0.121854i	−0.998142	+	0.0609268i	$0.980594\pi$
$654$		0			0
$655$	9.13187	+	27.3956i	0.356812	+	1.07044i
$656$		0			0
$657$	−1.11727	+	1.11727i	−0.0435887	+	0.0435887i
$658$		0			0
$659$	13.9820	+	13.9820i	0.544660	+	0.544660i	0.924891	−	0.380232i	$-0.124156\pi$
$659$	13.9820	+	13.9820i	0.544660	+	0.544660i	−0.380232	+	0.924891i	$0.624156\pi$
$660$		0			0
$661$	−29.2897	+	29.2897i	−1.13924	+	1.13924i	−0.150651	+	0.988587i	$0.548137\pi$
$661$	−29.2897	+	29.2897i	−1.13924	+	1.13924i	−0.988587	+	0.150651i	$0.951863\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	27.9931	−	55.9862i	1.08553	−	2.17105i
$666$		0			0
$667$	−8.61555			−0.333595
$668$		0			0
$669$	13.1319	−	13.1319i	0.507708	−	0.507708i
$670$		0			0
$671$		−	13.3776i		−	0.516436i
$672$		0			0
$673$	−24.7586	−	24.7586i	−0.954374	−	0.954374i	0.0446300	−	0.999004i	$-0.485789\pi$
$673$	−24.7586	−	24.7586i	−0.954374	−	0.954374i	−0.999004	+	0.0446300i	$0.985789\pi$
$674$		0			0
$675$	−3.00000	−	4.00000i	−0.115470	−	0.153960i
$676$		0			0
$677$		−	22.8793i		−	0.879323i	−0.898164	−	0.439661i	$-0.855098\pi$
$677$		−	22.8793i		−	0.879323i	0.898164	−	0.439661i	$-0.144902\pi$
$678$		0			0
$679$		−	64.9605i		−	2.49295i
$680$		0			0
$681$		−	1.50172i		−	0.0575460i
$682$		0			0
$683$			35.7294i			1.36715i	0.729882	+	0.683573i	$0.239575\pi$
$683$			35.7294i			1.36715i	−0.729882	+	0.683573i	$0.760425\pi$
$684$		0			0
$685$	15.1656	−	5.05520i	0.579447	−	0.193149i
$686$		0			0
$687$	7.05520	+	7.05520i	0.269172	+	0.269172i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	22.4250	−	22.4250i	0.853089	−	0.853089i	−0.137424	−	0.990512i	$-0.543882\pi$
$691$	22.4250	−	22.4250i	0.853089	−	0.853089i	0.990512	+	0.137424i	$0.0438822\pi$
$692$		0			0
$693$	−21.1138			−0.802048
$694$		0			0
$695$	6.19051	+	18.5715i	0.234819	+	0.704458i
$696$		0			0
$697$	−0.234533	−	0.234533i	−0.00888356	−	0.00888356i
$698$		0			0
$699$	−9.05520	+	9.05520i	−0.342499	+	0.342499i
$700$		0			0
$701$	7.87930	+	7.87930i	0.297597	+	0.297597i	0.840072	−	0.542475i	$-0.182513\pi$
$701$	7.87930	+	7.87930i	0.297597	+	0.297597i	−0.542475	+	0.840072i	$0.682513\pi$
$702$		0			0
$703$	8.11039	−	8.11039i	0.305889	−	0.305889i
$704$		0			0
$705$	−20.4182	+	6.80605i	−0.768993	+	0.256331i
$706$		0			0
$707$		−	18.7328i		−	0.704520i
$708$		0			0
$709$	−17.9414	−	17.9414i	−0.673802	−	0.673802i	0.284788	−	0.958590i	$-0.408077\pi$
$709$	−17.9414	−	17.9414i	−0.673802	−	0.673802i	−0.958590	+	0.284788i	$0.908077\pi$
$710$		0			0
$711$	8.99656			0.337397
$712$		0			0
$713$	−27.9931	+	27.9931i	−1.04835	+	1.04835i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	16.9966			0.634748
$718$		0			0
$719$	8.00000			0.298350			0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000			0.298350			0.149175	+	0.988811i	$0.452338\pi$
$720$		0			0
$721$	−34.8724			−1.29872
$722$		0			0
$723$	−23.9931			−0.892314
$724$		0			0
$725$	−7.00000	−	1.00000i	−0.259973	−	0.0371391i
$726$		0			0
$727$	−0.281794	+	0.281794i	−0.0104512	+	0.0104512i	−0.712313	−	0.701862i	$-0.752352\pi$
$727$	−0.281794	+	0.281794i	−0.0104512	+	0.0104512i	0.701862	+	0.712313i	$0.252352\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	0.270624	+	0.270624i	0.0100094	+	0.0100094i
$732$		0			0
$733$		−	2.35180i		−	0.0868657i	−0.999056	−	0.0434328i	$-0.986171\pi$
$733$		−	2.35180i		−	0.0868657i	0.999056	−	0.0434328i	$-0.0138295\pi$
$734$		0			0
$735$	28.2277	+	14.1138i	1.04119	+	0.520596i
$736$		0			0
$737$	40.2277	−	40.2277i	1.48180	−	1.48180i
$738$		0			0
$739$	−11.3112	−	11.3112i	−0.416090	−	0.416090i	0.467764	−	0.883853i	$-0.345060\pi$
$739$	−11.3112	−	11.3112i	−0.416090	−	0.416090i	−0.883853	+	0.467764i	$0.845060\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−14.4250	−	14.4250i	−0.529203	−	0.529203i	0.391131	−	0.920335i	$-0.372084\pi$
$743$	−14.4250	−	14.4250i	−0.529203	−	0.529203i	−0.920335	+	0.391131i	$0.872084\pi$
$744$		0			0
$745$	2.64820	−	0.882734i	0.0970226	−	0.0323409i
$746$		0			0
$747$	4.99656			0.182815
$748$		0			0
$749$	55.9862	−	55.9862i	2.04569	−	2.04569i
$750$		0			0
$751$			5.73625i			0.209319i	0.994508	+	0.104659i	$0.0333752\pi$
$751$			5.73625i			0.209319i	−0.994508	+	0.104659i	$0.966625\pi$
$752$		0			0
$753$	−7.24914	−	7.24914i	−0.264173	−	0.264173i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	12.3449i		−	0.448684i	−0.974510	−	0.224342i	$-0.927977\pi$
$757$		−	12.3449i		−	0.448684i	0.974510	−	0.224342i	$-0.0720232\pi$
$758$		0			0
$759$			27.9931i			1.01609i
$760$		0			0
$761$		−	31.8759i		−	1.15550i	−0.816214	−	0.577749i	$-0.803931\pi$
$761$		−	31.8759i		−	1.15550i	0.816214	−	0.577749i	$-0.196069\pi$
$762$		0			0
$763$		−	45.8466i		−	1.65976i
$764$		0			0
$765$	−0.0586332	−	0.175899i	−0.00211989	−	0.00635966i
$766$		0			0
$767$		0			0
$768$		0			0
$769$			2.87930i			0.103830i	0.998652	+	0.0519150i	$0.0165325\pi$
$769$			2.87930i			0.103830i	−0.998652	+	0.0519150i	$0.983468\pi$
$770$		0			0
$771$	−3.17246	+	3.17246i	−0.114253	+	0.114253i
$772$		0			0
$773$	−35.5760			−1.27958			−0.639790	−	0.768550i	$-0.720979\pi$
$773$	−35.5760			−1.27958			−0.639790	+	0.768550i	$0.720979\pi$
$774$		0			0
$775$	−25.9931	+	19.4948i	−0.933701	+	0.700275i
$776$		0			0
$777$	6.11727	+	6.11727i	0.219456	+	0.219456i
$778$		0			0
$779$	17.2311	−	17.2311i	0.617368	−	0.617368i
$780$		0			0
$781$	29.2311	+	29.2311i	1.04597	+	1.04597i
$782$		0			0
$783$	1.00000	−	1.00000i	0.0357371	−	0.0357371i
$784$		0			0
$785$	−9.76547	+	19.5309i	−0.348544	+	0.697089i
$786$		0			0
$787$		−	45.1430i		−	1.60918i	−0.593834	−	0.804588i	$-0.702386\pi$
$787$		−	45.1430i		−	1.60918i	0.593834	−	0.804588i	$-0.297614\pi$
$788$		0			0
$789$	20.6888	+	20.6888i	0.736540	+	0.736540i
$790$		0			0
$791$	13.3776			0.475652
$792$		0			0
$793$		0			0
$794$		0			0
$795$	9.11383	−	18.2277i	0.323234	−	0.646468i
$796$		0			0
$797$	43.3415			1.53523			0.767617	−	0.640909i	$-0.221442\pi$
$797$	43.3415			1.53523			0.767617	+	0.640909i	$0.221442\pi$
$798$		0			0
$799$	−0.798121			−0.0282355
$800$		0			0
$801$	−4.11727			−0.145476
$802$		0			0
$803$	7.26031			0.256211
$804$		0			0
$805$	27.9931	−	55.9862i	0.986628	−	1.97326i
$806$		0			0
$807$	−17.8793	+	17.8793i	−0.629381	+	0.629381i
$808$		0			0
$809$	35.5241			1.24896			0.624480	−	0.781041i	$-0.285311\pi$
$809$	35.5241			1.24896			0.624480	+	0.781041i	$0.285311\pi$
$810$		0			0
$811$	28.9233	+	28.9233i	1.01564	+	1.01564i	0.999876	+	0.0157594i	$0.00501657\pi$
$811$	28.9233	+	28.9233i	1.01564	+	1.01564i	0.0157594	+	0.999876i	$0.494983\pi$
$812$		0			0
$813$			18.4983i			0.648763i
$814$		0			0
$815$	20.9966	−	41.9931i	0.735477	−	1.47095i
$816$		0			0
$817$	−19.8827	+	19.8827i	−0.695609	+	0.695609i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−12.6482	+	12.6482i	−0.441425	+	0.441425i	−0.892491	−	0.451066i	$-0.851044\pi$
$821$	−12.6482	+	12.6482i	−0.441425	+	0.441425i	0.451066	+	0.892491i	$0.351044\pi$
$822$		0			0
$823$	−29.7113	−	29.7113i	−1.03567	−	1.03567i	−0.999340	−	0.0363321i	$-0.988433\pi$
$823$	−29.7113	−	29.7113i	−1.03567	−	1.03567i	−0.0363321	−	0.999340i	$-0.511567\pi$
$824$		0			0
$825$	−3.24914	+	22.7440i	−0.113121	+	0.791844i
$826$		0			0
$827$	18.2277			0.633838			0.316919	−	0.948453i	$-0.397352\pi$
$827$	18.2277			0.633838			0.316919	+	0.948453i	$0.397352\pi$
$828$		0			0
$829$	10.8207	−	10.8207i	0.375817	−	0.375817i	−0.493773	−	0.869591i	$-0.664383\pi$
$829$	10.8207	−	10.8207i	0.375817	−	0.375817i	0.869591	+	0.493773i	$0.164383\pi$
$830$		0			0
$831$		−	16.1104i		−	0.558863i
$832$		0			0
$833$	0.827538	+	0.827538i	0.0286725	+	0.0286725i
$834$		0			0
$835$	2.42504	+	7.27512i	0.0839220	+	0.251766i
$836$		0			0
$837$		−	6.49828i		−	0.224613i
$838$		0			0
$839$		−	6.84320i		−	0.236254i	−0.992999	−	0.118127i	$-0.962311\pi$
$839$		−	6.84320i		−	0.236254i	0.992999	−	0.118127i	$-0.0376889\pi$
$840$		0			0
$841$			27.0000i			0.931034i
$842$		0			0
$843$		−	10.1173i		−	0.348457i
$844$		0			0
$845$	−13.0000	+	26.0000i	−0.447214	+	0.894427i
$846$		0			0
$847$	32.8613	+	32.8613i	1.12913	+	1.12913i
$848$		0			0
$849$		−	5.61211i		−	0.192607i
$850$		0			0
$851$	8.11039	−	8.11039i	0.278021	−	0.278021i
$852$		0			0
$853$	36.1173			1.23663			0.618316	−	0.785930i	$-0.287815\pi$
$853$	36.1173			1.23663			0.618316	+	0.785930i	$0.287815\pi$
$854$		0			0
$855$	12.9233	−	4.30777i	0.441968	−	0.147323i
$856$		0			0
$857$	8.93793	+	8.93793i	0.305314	+	0.305314i	0.843089	−	0.537775i	$-0.180735\pi$
$857$	8.93793	+	8.93793i	0.305314	+	0.305314i	−0.537775	+	0.843089i	$0.680735\pi$
$858$		0			0
$859$	39.7665	−	39.7665i	1.35682	−	1.35682i	0.479003	−	0.877813i	$-0.340998\pi$
$859$	39.7665	−	39.7665i	1.35682	−	1.35682i	0.877813	−	0.479003i	$-0.159002\pi$
$860$		0			0
$861$	12.9966	+	12.9966i	0.442922	+	0.442922i
$862$		0			0
$863$	−10.8061	+	10.8061i	−0.367842	+	0.367842i	−0.866690	−	0.498847i	$-0.833757\pi$
$863$	−10.8061	+	10.8061i	−0.367842	+	0.367842i	0.498847	+	0.866690i	$0.333757\pi$
$864$		0			0
$865$	−0.469065	−	0.234533i	−0.0159487	−	0.00797435i
$866$		0			0
$867$			16.9931i			0.577117i
$868$		0			0
$869$	−29.2311	−	29.2311i	−0.991597	−	0.991597i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	9.99656	−	9.99656i	0.338332	−	0.338332i
$874$		0			0
$875$	29.2423	−	42.2388i	0.988569	−	1.42793i
$876$		0			0
$877$	−14.2345			−0.480666			−0.240333	−	0.970690i	$-0.577257\pi$
$877$	−14.2345			−0.480666			−0.240333	+	0.970690i	$0.577257\pi$
$878$		0			0
$879$	20.2277			0.682262
$880$		0			0
$881$	14.3449			0.483293			0.241646	−	0.970364i	$-0.422313\pi$
$881$	14.3449			0.483293			0.241646	+	0.970364i	$0.422313\pi$
$882$		0			0
$883$	58.7552			1.97727			0.988634	−	0.150341i	$-0.0480372\pi$
$883$	58.7552			1.97727			0.988634	+	0.150341i	$0.0480372\pi$
$884$		0			0
$885$	1.36641	+	4.09922i	0.0459313	+	0.137794i
$886$		0			0
$887$	12.3078	−	12.3078i	0.413255	−	0.413255i	−0.469616	−	0.882871i	$-0.655608\pi$
$887$	12.3078	−	12.3078i	0.413255	−	0.413255i	0.882871	+	0.469616i	$0.155608\pi$
$888$		0			0
$889$	−47.1070			−1.57992
$890$		0			0
$891$	−3.24914	−	3.24914i	−0.108850	−	0.108850i
$892$		0			0
$893$		−	58.6379i		−	1.96224i
$894$		0			0
$895$	15.3956	−	5.13187i	0.514619	−	0.171540i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.49828	−	6.49828i	−0.216730	−	0.216730i
$900$		0			0
$901$	0.534373	−	0.534373i	0.0178025	−	0.0178025i
$902$		0			0
$903$	−14.9966	−	14.9966i	−0.499054	−	0.499054i
$904$		0			0
$905$	−0.0586332	−	0.175899i	−0.00194903	−	0.00584710i
$906$		0			0
$907$	8.23453			0.273423			0.136712	−	0.990611i	$-0.456347\pi$
$907$	8.23453			0.273423			0.136712	+	0.990611i	$0.456347\pi$
$908$		0			0
$909$	2.88273	−	2.88273i	0.0956142	−	0.0956142i
$910$		0			0
$911$		−	42.6087i		−	1.41169i	−0.708367	−	0.705844i	$-0.750568\pi$
$911$		−	42.6087i		−	1.41169i	0.708367	−	0.705844i	$-0.249432\pi$
$912$		0			0
$913$	−16.2345	−	16.2345i	−0.537285	−	0.537285i
$914$		0			0
$915$	−6.17590	+	2.05863i	−0.204169	+	0.0680563i
$916$		0			0
$917$		−	59.3415i		−	1.95963i
$918$		0			0
$919$			31.2603i			1.03118i	0.856835	+	0.515591i	$0.172428\pi$
$919$			31.2603i			1.03118i	−0.856835	+	0.515591i	$0.827572\pi$
$920$		0			0
$921$		−	20.6155i		−	0.679305i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	7.53093	−	5.64820i	0.247616	−	0.185712i
$926$		0			0
$927$	−5.36641	−	5.36641i	−0.176256	−	0.176256i
$928$		0			0
$929$		−	54.5726i		−	1.79047i	−0.445596	−	0.895234i	$-0.647008\pi$
$929$		−	54.5726i		−	1.79047i	0.445596	−	0.895234i	$-0.352992\pi$
$930$		0			0
$931$	−60.7992	+	60.7992i	−1.99261	+	1.99261i
$932$		0			0
$933$	−21.2311			−0.695075
$934$		0			0
$935$	−0.381015	+	0.762030i	−0.0124605	+	0.0249210i
$936$		0			0
$937$	−21.2277	−	21.2277i	−0.693477	−	0.693477i	0.269518	−	0.962995i	$-0.413136\pi$
$937$	−21.2277	−	21.2277i	−0.693477	−	0.693477i	−0.962995	+	0.269518i	$0.913136\pi$
$938$		0			0
$939$	−3.00000	+	3.00000i	−0.0979013	+	0.0979013i
$940$		0			0
$941$	−7.99656	−	7.99656i	−0.260680	−	0.260680i	0.564650	−	0.825330i	$-0.309011\pi$
$941$	−7.99656	−	7.99656i	−0.260680	−	0.260680i	−0.825330	+	0.564650i	$0.809011\pi$
$942$		0			0
$943$	17.2311	−	17.2311i	0.561122	−	0.561122i
$944$		0			0
$945$	3.24914	+	9.74742i	0.105695	+	0.317084i
$946$		0			0
$947$		−	41.7225i		−	1.35580i	−0.735155	−	0.677900i	$-0.762890\pi$
$947$		−	41.7225i		−	1.35580i	0.735155	−	0.677900i	$-0.237110\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−1.11383			−0.0361184
$952$		0			0
$953$	−20.0586	+	20.0586i	−0.649763	+	0.649763i	−0.952936	−	0.303173i	$-0.901954\pi$
$953$	−20.0586	+	20.0586i	−0.649763	+	0.649763i	0.303173	+	0.952936i	$0.401954\pi$
$954$		0			0
$955$	−41.2311	−	20.6155i	−1.33421	−	0.667103i
$956$		0			0
$957$	−6.49828			−0.210060
$958$		0			0
$959$	−32.8501			−1.06078
$960$		0			0
$961$	−11.2277			−0.362182
$962$		0			0
$963$	17.2311			0.555264
$964$		0			0
$965$	−41.9897	+	13.9966i	−1.35170	+	0.450565i
$966$		0			0
$967$	−38.8544	+	38.8544i	−1.24947	+	1.24947i	−0.293519	+	0.955953i	$0.594826\pi$
$967$	−38.8544	+	38.8544i	−1.24947	+	1.24947i	−0.955953	+	0.293519i	$0.905174\pi$
$968$		0			0
$969$	0.505157			0.0162280
$970$		0			0
$971$	−26.5975	−	26.5975i	−0.853554	−	0.853554i	0.137015	−	0.990569i	$-0.456249\pi$
$971$	−26.5975	−	26.5975i	−0.853554	−	0.853554i	−0.990569	+	0.137015i	$0.956249\pi$
$972$		0			0
$973$		−	40.2277i		−	1.28964i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.82754	+	2.82754i	−0.0904610	+	0.0904610i	−0.750889	−	0.660428i	$-0.770375\pi$
$977$	−2.82754	+	2.82754i	−0.0904610	+	0.0904610i	0.660428	+	0.750889i	$0.270375\pi$
$978$		0			0
$979$	13.3776	+	13.3776i	0.427549	+	0.427549i
$980$		0			0
$981$	7.05520	−	7.05520i	0.225255	−	0.225255i
$982$		0			0
$983$	−13.5389	−	13.5389i	−0.431823	−	0.431823i	0.457425	−	0.889248i	$-0.348772\pi$
$983$	−13.5389	−	13.5389i	−0.431823	−	0.431823i	−0.889248	+	0.457425i	$0.848772\pi$
$984$		0			0
$985$	29.7586	+	14.8793i	0.948188	+	0.474094i
$986$		0			0
$987$	44.2277			1.40778
$988$		0			0
$989$	−19.8827	+	19.8827i	−0.632234	+	0.632234i
$990$		0			0
$991$			12.9605i			0.411703i	0.978583	+	0.205851i	$0.0659964\pi$
$991$			12.9605i			0.411703i	−0.978583	+	0.205851i	$0.934004\pi$
$992$		0			0
$993$	8.92332	+	8.92332i	0.283173	+	0.283173i
$994$		0			0
$995$	−36.9966	−	18.4983i	−1.17287	−	0.586435i
$996$		0			0
$997$			22.2277i			0.703957i	0.936008	+	0.351978i	$0.114491\pi$
$997$			22.2277i			0.703957i	−0.936008	+	0.351978i	$0.885509\pi$
$998$		0			0
$999$			1.88273i			0.0595671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.y.h.223.3		6
4.3	odd	2		1920.2.y.g.223.1		6
5.2	odd	4		1920.2.bc.h.607.3		6
8.3	odd	2		240.2.y.d.163.3	✓	6
8.5	even	2		960.2.y.d.943.3		6
16.3	odd	4		960.2.bc.d.463.3		6
16.5	even	4		1920.2.bc.g.1183.1		6
16.11	odd	4		1920.2.bc.h.1183.3		6
16.13	even	4		240.2.bc.d.43.2	yes	6
20.7	even	4		1920.2.bc.g.607.1		6
24.11	even	2		720.2.z.e.163.1		6
40.27	even	4		240.2.bc.d.67.2	yes	6
40.37	odd	4		960.2.bc.d.367.3		6
48.29	odd	4		720.2.bd.e.523.2		6
80.27	even	4	inner	1920.2.y.h.1567.3		6
80.37	odd	4		1920.2.y.g.1567.1		6
80.67	even	4		960.2.y.d.847.3		6
80.77	odd	4		240.2.y.d.187.3	yes	6
120.107	odd	4		720.2.bd.e.307.2		6
240.77	even	4		720.2.z.e.667.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.d.163.3	✓	6	8.3	odd	2
240.2.y.d.187.3	yes	6	80.77	odd	4
240.2.bc.d.43.2	yes	6	16.13	even	4
240.2.bc.d.67.2	yes	6	40.27	even	4
720.2.z.e.163.1		6	24.11	even	2
720.2.z.e.667.1		6	240.77	even	4
720.2.bd.e.307.2		6	120.107	odd	4
720.2.bd.e.523.2		6	48.29	odd	4
960.2.y.d.847.3		6	80.67	even	4
960.2.y.d.943.3		6	8.5	even	2
960.2.bc.d.367.3		6	40.37	odd	4
960.2.bc.d.463.3		6	16.3	odd	4
1920.2.y.g.223.1		6	4.3	odd	2
1920.2.y.g.1567.1		6	80.37	odd	4
1920.2.y.h.223.3		6	1.1	even	1	trivial
1920.2.y.h.1567.3		6	80.27	even	4	inner
1920.2.bc.g.607.1		6	20.7	even	4
1920.2.bc.g.1183.1		6	16.5	even	4
1920.2.bc.h.607.3		6	5.2	odd	4
1920.2.bc.h.1183.3		6	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.y (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(-1.00000 + 2.00000i) q^{5} +(3.24914 - 3.24914i) q^{7} +1.00000 q^{9} +(-3.24914 - 3.24914i) q^{11} +(-1.00000 + 2.00000i) q^{15} +(-0.0586332 + 0.0586332i) q^{17} +(-4.30777 - 4.30777i) q^{19} +(3.24914 - 3.24914i) q^{21} +(-4.30777 - 4.30777i) q^{23} +(-3.00000 - 4.00000i) q^{25} +1.00000 q^{27} +(1.00000 - 1.00000i) q^{29} -6.49828i q^{31} +(-3.24914 - 3.24914i) q^{33} +(3.24914 + 9.74742i) q^{35} +1.88273i q^{37} +4.00000i q^{41} -4.61555i q^{43} +(-1.00000 + 2.00000i) q^{45} +(6.80605 + 6.80605i) q^{47} -14.1138i q^{49} +(-0.0586332 + 0.0586332i) q^{51} -9.11383 q^{53} +(9.74742 - 3.24914i) q^{55} +(-4.30777 - 4.30777i) q^{57} +(1.36641 - 1.36641i) q^{59} +(2.05863 + 2.05863i) q^{61} +(3.24914 - 3.24914i) q^{63} +12.3810i q^{67} +(-4.30777 - 4.30777i) q^{69} -8.99656 q^{71} +(-1.11727 + 1.11727i) q^{73} +(-3.00000 - 4.00000i) q^{75} -21.1138 q^{77} +8.99656 q^{79} +1.00000 q^{81} +4.99656 q^{83} +(-0.0586332 - 0.175899i) q^{85} +(1.00000 - 1.00000i) q^{87} -4.11727 q^{89} -6.49828i q^{93} +(12.9233 - 4.30777i) q^{95} +(9.99656 - 9.99656i) q^{97} +(-3.24914 - 3.24914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} - 6 q^{5} + 2 q^{7} + 6 q^{9} - 2 q^{11} - 6 q^{15} - 2 q^{17} - 10 q^{19} + 2 q^{21} - 10 q^{23} - 18 q^{25} + 6 q^{27} + 6 q^{29} - 2 q^{33} + 2 q^{35} - 6 q^{45} - 10 q^{47} - 2 q^{51}+ \cdots - 2 q^{99}+O(q^{100}) \) 6 * q + 6 * q^3 - 6 * q^5 + 2 * q^7 + 6 * q^9 - 2 * q^11 - 6 * q^15 - 2 * q^17 - 10 * q^19 + 2 * q^21 - 10 * q^23 - 18 * q^25 + 6 * q^27 + 6 * q^29 - 2 * q^33 + 2 * q^35 - 6 * q^45 - 10 * q^47 - 2 * q^51 + 12 * q^53 + 6 * q^55 - 10 * q^57 - 6 * q^59 + 14 * q^61 + 2 * q^63 - 10 * q^69 + 16 * q^71 - 10 * q^73 - 18 * q^75 - 60 * q^77 - 16 * q^79 + 6 * q^81 - 40 * q^83 - 2 * q^85 + 6 * q^87 - 28 * q^89 + 30 * q^95 - 10 * q^97 - 2 * q^99

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