LMFDB - Embedded newform 1920.2.bc.h.1183.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(607,1920)]

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, 1]))

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

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

chi := DirichletCharacter("1920.607");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.bc (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:	$\Z[a_1, \ldots, a_{17}]$
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			1183.3
Root			$0.264658 - 1.38923i$ of defining polynomial
Character	$\chi$	$=$	1920.1183
Dual form			1920.2.bc.h.607.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{3} +(-2.00000 - 1.00000i) q^{5} +(3.24914 - 3.24914i) q^{7} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{3} +(-2.00000 - 1.00000i) q^{5} +(3.24914 - 3.24914i) q^{7} -1.00000 q^{9} +(-3.24914 + 3.24914i) q^{11} +(1.00000 - 2.00000i) q^{15} +(-0.0586332 + 0.0586332i) q^{17} +(4.30777 - 4.30777i) q^{19} +(3.24914 + 3.24914i) q^{21} +(-4.30777 - 4.30777i) q^{23} +(3.00000 + 4.00000i) q^{25} -1.00000i q^{27} +(-1.00000 - 1.00000i) q^{29} +6.49828i q^{31} +(-3.24914 - 3.24914i) q^{33} +(-9.74742 + 3.24914i) q^{35} -1.88273 q^{37} -4.00000i q^{41} -4.61555 q^{43} +(2.00000 + 1.00000i) q^{45} +(-6.80605 - 6.80605i) q^{47} -14.1138i q^{49} +(-0.0586332 - 0.0586332i) q^{51} -9.11383i q^{53} +(9.74742 - 3.24914i) q^{55} +(4.30777 + 4.30777i) q^{57} +(-1.36641 - 1.36641i) q^{59} +(2.05863 - 2.05863i) q^{61} +(-3.24914 + 3.24914i) q^{63} -12.3810 q^{67} +(4.30777 - 4.30777i) q^{69} -8.99656 q^{71} +(1.11727 - 1.11727i) q^{73} +(-4.00000 + 3.00000i) q^{75} +21.1138i q^{77} -8.99656 q^{79} +1.00000 q^{81} +4.99656i q^{83} +(0.175899 - 0.0586332i) q^{85} +(1.00000 - 1.00000i) q^{87} +4.11727 q^{89} -6.49828 q^{93} +(-12.9233 + 4.30777i) q^{95} +(9.99656 - 9.99656i) q^{97} +(3.24914 - 3.24914i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 12 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 6 * q - 12 * q^5 + 2 * q^7 - 6 * q^9	$ 6 q - 12 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^{29} - 2 q^{33} - 6 q^{35} - 8 q^{37} + 4 q^{43} + 12 q^{45} + 10 q^{47} - 2 q^{51} + 6 q^{55} + 10 q^{57} + 6 q^{59} + 14 q^{61} - 2 q^{63} - 36 q^{67} + 10 q^{69} + 16 q^{71} + 10 q^{73} - 24 q^{75} + 16 q^{79} + 6 q^{81} + 6 q^{85} + 6 q^{87} + 28 q^{89} - 4 q^{93} - 30 q^{95} - 10 q^{97} + 2 q^{99}+O(q^{100}) $ 6 * q - 12 * 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^29 - 2 * q^33 - 6 * q^35 - 8 * q^37 + 4 * q^43 + 12 * q^45 + 10 * q^47 - 2 * q^51 + 6 * q^55 + 10 * q^57 + 6 * q^59 + 14 * q^61 - 2 * q^63 - 36 * q^67 + 10 * q^69 + 16 * q^71 + 10 * q^73 - 24 * q^75 + 16 * q^79 + 6 * q^81 + 6 * q^85 + 6 * q^87 + 28 * q^89 - 4 * q^93 - 30 * q^95 - 10 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$		0			0
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		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	−0.999797	−	0.0201443i	$-0.993587\pi$
$11$	−3.24914	+	3.24914i	−0.979653	+	0.979653i	0.0201443	+	0.999797i	$0.493587\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		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	$-0.503712\pi$
$19$	4.30777	−	4.30777i	0.988271	−	0.988271i	0.999932	+	0.0116609i	$0.00371188\pi$
$20$		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
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−1.00000	−	1.00000i	−0.185695	−	0.185695i	0.608137	−	0.793832i	$-0.291917\pi$
$29$	−1.00000	−	1.00000i	−0.185695	−	0.185695i	−0.793832	+	0.608137i	$0.791917\pi$
$30$		0			0
$31$			6.49828i			1.16713i	0.812068	+	0.583563i	$0.198342\pi$
$31$			6.49828i			1.16713i	−0.812068	+	0.583563i	$0.801658\pi$
$32$		0			0
$33$	−3.24914	−	3.24914i	−0.565603	−	0.565603i
$34$		0			0
$35$	−9.74742	+	3.24914i	−1.64761	+	0.549205i
$36$		0			0
$37$	−1.88273			−0.309520			−0.154760	−	0.987952i	$-0.549460\pi$
$37$	−1.88273			−0.309520			−0.154760	+	0.987952i	$0.549460\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	4.00000i		−	0.624695i	−0.949968	−	0.312348i	$-0.898885\pi$
$41$		−	4.00000i		−	0.624695i	0.949968	−	0.312348i	$-0.101115\pi$
$42$		0			0
$43$	−4.61555			−0.703864			−0.351932	−	0.936025i	$-0.614475\pi$
$43$	−4.61555			−0.703864			−0.351932	+	0.936025i	$0.614475\pi$
$44$		0			0
$45$	2.00000	+	1.00000i	0.298142	+	0.149071i
$46$		0			0
$47$	−6.80605	−	6.80605i	−0.992765	−	0.992765i	0.00720889	−	0.999974i	$-0.497705\pi$
$47$	−6.80605	−	6.80605i	−0.992765	−	0.992765i	−0.999974	+	0.00720889i	$0.997705\pi$
$48$		0			0
$49$		−	14.1138i		−	2.01626i
$50$		0			0
$51$	−0.0586332	−	0.0586332i	−0.00821028	−	0.00821028i
$52$		0			0
$53$		−	9.11383i		−	1.25188i	−0.779871	−	0.625940i	$-0.784715\pi$
$53$		−	9.11383i		−	1.25188i	0.779871	−	0.625940i	$-0.215285\pi$
$54$		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	$-0.290146\pi$
$59$	−1.36641	−	1.36641i	−0.177891	−	0.177891i	−0.790436	+	0.612545i	$0.790146\pi$
$60$		0			0
$61$	2.05863	−	2.05863i	0.263581	−	0.263581i	−0.562926	−	0.826507i	$-0.690324\pi$
$61$	2.05863	−	2.05863i	0.263581	−	0.263581i	0.826507	+	0.562926i	$0.190324\pi$
$62$		0			0
$63$	−3.24914	+	3.24914i	−0.409353	+	0.409353i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−12.3810			−1.51258			−0.756291	−	0.654236i	$-0.772990\pi$
$67$	−12.3810			−1.51258			−0.756291	+	0.654236i	$0.772990\pi$
$68$		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	−0.638694	−	0.769461i	$-0.720525\pi$
$73$	1.11727	−	1.11727i	0.130766	−	0.130766i	0.769461	+	0.638694i	$0.220525\pi$
$74$		0			0
$75$	−4.00000	+	3.00000i	−0.461880	+	0.346410i
$76$		0			0
$77$			21.1138i			2.40614i
$78$		0			0
$79$	−8.99656			−1.01219			−0.506096	−	0.862477i	$-0.668912\pi$
$79$	−8.99656			−1.01219			−0.506096	+	0.862477i	$0.668912\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$			4.99656i			0.548444i	0.961666	+	0.274222i	$0.0884203\pi$
$83$			4.99656i			0.548444i	−0.961666	+	0.274222i	$0.911580\pi$
$84$		0			0
$85$	0.175899	−	0.0586332i	0.0190790	−	0.00635966i
$86$		0			0
$87$	1.00000	−	1.00000i	0.107211	−	0.107211i
$88$		0			0
$89$	4.11727			0.436429			0.218215	−	0.975901i	$-0.429977\pi$
$89$	4.11727			0.436429			0.218215	+	0.975901i	$0.429977\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−6.49828			−0.673840
$94$		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	0.835830	−	0.548988i	$-0.184987\pi$
$101$	2.88273	+	2.88273i	0.286843	+	0.286843i	−0.548988	+	0.835830i	$0.684987\pi$
$102$		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
$107$		−	17.2311i		−	1.66579i	−0.553429	−	0.832896i	$-0.686681\pi$
$107$		−	17.2311i		−	1.66579i	0.553429	−	0.832896i	$-0.313319\pi$
$108$		0			0
$109$	−7.05520	−	7.05520i	−0.675765	−	0.675765i	0.283274	−	0.959039i	$-0.408579\pi$
$109$	−7.05520	−	7.05520i	−0.675765	−	0.675765i	−0.959039	+	0.283274i	$0.908579\pi$
$110$		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
$115$	4.30777	+	12.9233i	0.401702	+	1.20511i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			0.381015i			0.0349276i
$120$		0			0
$121$		−	10.1138i		−	0.919439i
$122$		0			0
$123$	4.00000			0.360668
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	7.24914	+	7.24914i	0.643257	+	0.643257i	0.951355	−	0.308098i	$-0.0996923\pi$
$127$	7.24914	+	7.24914i	0.643257	+	0.643257i	−0.308098	+	0.951355i	$0.599692\pi$
$128$		0			0
$129$		−	4.61555i		−	0.406376i
$130$		0			0
$131$	9.13187	+	9.13187i	0.797856	+	0.797856i	0.982757	−	0.184902i	$-0.0591966\pi$
$131$	9.13187	+	9.13187i	0.797856	+	0.797856i	−0.184902	+	0.982757i	$0.559197\pi$
$132$		0			0
$133$		−	27.9931i		−	2.42731i
$134$		0			0
$135$	−1.00000	+	2.00000i	−0.0860663	+	0.172133i
$136$		0			0
$137$	5.05520	+	5.05520i	0.431894	+	0.431894i	0.889272	−	0.457378i	$-0.151211\pi$
$137$	5.05520	+	5.05520i	0.431894	+	0.431894i	−0.457378	+	0.889272i	$0.651211\pi$
$138$		0			0
$139$	−6.19051	−	6.19051i	−0.525072	−	0.525072i	0.394027	−	0.919099i	$-0.371082\pi$
$139$	−6.19051	−	6.19051i	−0.525072	−	0.525072i	−0.919099	+	0.394027i	$0.871082\pi$
$140$		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
$147$	14.1138			1.16409
$148$		0			0
$149$	0.882734	−	0.882734i	0.0723164	−	0.0723164i	−0.670024	−	0.742340i	$-0.733716\pi$
$149$	0.882734	−	0.882734i	0.0723164	−	0.0723164i	0.742340	+	0.670024i	$0.233716\pi$
$150$		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
$155$	6.49828	−	12.9966i	0.521954	−	1.04391i
$156$		0			0
$157$		−	9.76547i		−	0.779369i	−0.920948	−	0.389685i	$-0.872584\pi$
$157$		−	9.76547i		−	0.779369i	0.920948	−	0.389685i	$-0.127416\pi$
$158$		0			0
$159$	9.11383			0.722774
$160$		0			0
$161$	−27.9931			−2.20617
$162$		0			0
$163$		−	20.9966i		−	1.64458i	−0.569070	−	0.822289i	$-0.692697\pi$
$163$		−	20.9966i		−	1.64458i	0.569070	−	0.822289i	$-0.307303\pi$
$164$		0			0
$165$	3.24914	+	9.74742i	0.252945	+	0.758836i
$166$		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
$173$	0.234533			0.0178312			0.00891559	−	0.999960i	$-0.497162\pi$
$173$	0.234533			0.0178312			0.00891559	+	0.999960i	$0.497162\pi$
$174$		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	$-0.662570\pi$
$179$	5.13187	−	5.13187i	0.383574	−	0.383574i	0.872388	+	0.488814i	$0.162570\pi$
$180$		0			0
$181$	−0.0586332	−	0.0586332i	−0.00435817	−	0.00435817i	0.704924	−	0.709283i	$-0.250981\pi$
$181$	−0.0586332	−	0.0586332i	−0.00435817	−	0.00435817i	−0.709283	+	0.704924i	$0.750981\pi$
$182$		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
$187$		−	0.381015i		−	0.0278626i
$188$		0			0
$189$	−3.24914	−	3.24914i	−0.236340	−	0.236340i
$190$		0			0
$191$		−	20.6155i		−	1.49169i	−0.666120	−	0.745844i	$-0.732046\pi$
$191$		−	20.6155i		−	1.49169i	0.666120	−	0.745844i	$-0.267954\pi$
$192$		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
$197$	14.8793			1.06011			0.530053	−	0.847965i	$-0.322172\pi$
$197$	14.8793			1.06011			0.530053	+	0.847965i	$0.322172\pi$
$198$		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
$203$	−6.49828			−0.456090
$204$		0			0
$205$	−4.00000	+	8.00000i	−0.279372	+	0.558744i
$206$		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	0.329759	−	0.944065i	$-0.393033\pi$
$211$	−8.92332	−	8.92332i	−0.614307	−	0.614307i	−0.944065	+	0.329759i	$0.893033\pi$
$212$		0			0
$213$		−	8.99656i		−	0.616434i
$214$		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	−0.993470	−	0.114095i	$-0.963603\pi$
$223$	−13.1319	+	13.1319i	−0.879375	+	0.879375i	0.114095	+	0.993470i	$0.463603\pi$
$224$		0			0
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$		0			0
$227$	1.50172			0.0996726			0.0498363	−	0.998757i	$-0.484130\pi$
$227$	1.50172			0.0996726			0.0498363	+	0.998757i	$0.484130\pi$
$228$		0			0
$229$	−7.05520	+	7.05520i	−0.466220	+	0.466220i	−0.900688	−	0.434467i	$-0.856937\pi$
$229$	−7.05520	+	7.05520i	−0.466220	+	0.466220i	0.434467	+	0.900688i	$0.356937\pi$
$230$		0			0
$231$	−21.1138			−1.38919
$232$		0			0
$233$	9.05520	−	9.05520i	0.593226	−	0.593226i	−0.345276	−	0.938501i	$-0.612215\pi$
$233$	9.05520	−	9.05520i	0.593226	−	0.593226i	0.938501	+	0.345276i	$0.112215\pi$
$234$		0			0
$235$	6.80605	+	20.4182i	0.443978	+	1.33193i
$236$		0			0
$237$		−	8.99656i		−	0.584390i
$238$		0			0
$239$	−16.9966			−1.09942			−0.549708	−	0.835357i	$-0.685261\pi$
$239$	−16.9966			−1.09942			−0.549708	+	0.835357i	$0.685261\pi$
$240$		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
$243$			1.00000i			0.0641500i
$244$		0			0
$245$	−14.1138	+	28.2277i	−0.901699	+	1.80340i
$246$		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	−0.897854	−	0.440293i	$-0.854875\pi$
$251$	−7.24914	+	7.24914i	−0.457562	+	0.457562i	0.440293	+	0.897854i	$0.354875\pi$
$252$		0			0
$253$	27.9931			1.75991
$254$		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
$267$			4.11727i			0.251973i
$268$		0			0
$269$	17.8793	+	17.8793i	1.09012	+	1.09012i	0.995515	+	0.0946050i	$0.0301588\pi$
$269$	17.8793	+	17.8793i	1.09012	+	1.09012i	0.0946050	+	0.995515i	$0.469841\pi$
$270$		0			0
$271$		−	18.4983i		−	1.12369i	−0.827242	−	0.561845i	$-0.810092\pi$
$271$		−	18.4983i		−	1.12369i	0.827242	−	0.561845i	$-0.189908\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−22.7440	−	3.24914i	−1.37151	−	0.195931i
$276$		0			0
$277$	16.1104			0.967980			0.483990	−	0.875074i	$-0.339187\pi$
$277$	16.1104			0.967980			0.483990	+	0.875074i	$0.339187\pi$
$278$		0			0
$279$		−	6.49828i		−	0.389042i
$280$		0			0
$281$			10.1173i			0.603546i	0.953380	+	0.301773i	$0.0975784\pi$
$281$			10.1173i			0.603546i	−0.953380	+	0.301773i	$0.902422\pi$
$282$		0			0
$283$	−5.61211			−0.333605			−0.166803	−	0.985990i	$-0.553344\pi$
$283$	−5.61211			−0.333605			−0.166803	+	0.985990i	$0.553344\pi$
$284$		0			0
$285$	−4.30777	−	12.9233i	−0.255170	−	0.765511i
$286$		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
$293$			20.2277i			1.18171i	0.806777	+	0.590856i	$0.201210\pi$
$293$			20.2277i			1.18171i	−0.806777	+	0.590856i	$0.798790\pi$
$294$		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
$307$	20.6155			1.17659			0.588296	−	0.808646i	$-0.299799\pi$
$307$	20.6155			1.17659			0.588296	+	0.808646i	$0.299799\pi$
$308$		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	−0.617220	−	0.786790i	$-0.711741\pi$
$313$	3.00000	−	3.00000i	0.169570	−	0.169570i	0.786790	+	0.617220i	$0.211741\pi$
$314$		0			0
$315$	9.74742	−	3.24914i	0.549205	−	0.183068i
$316$		0			0
$317$			1.11383i			0.0625588i	0.999511	+	0.0312794i	$0.00995817\pi$
$317$			1.11383i			0.0625588i	−0.999511	+	0.0312794i	$0.990042\pi$
$318$		0			0
$319$	6.49828			0.363834
$320$		0			0
$321$	17.2311			0.961746
$322$		0			0
$323$			0.505157i			0.0281077i
$324$		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	−0.417984	−	0.908454i	$-0.637263\pi$
$331$	8.92332	−	8.92332i	0.490470	−	0.490470i	0.908454	+	0.417984i	$0.137263\pi$
$332$		0			0
$333$	1.88273			0.103173
$334$		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
$347$		−	0.234533i		−	0.0125904i	−0.999980	−	0.00629519i	$-0.997996\pi$
$347$		−	0.234533i		−	0.0125904i	0.999980	−	0.00629519i	$-0.00200383\pi$
$348$		0			0
$349$	−21.1725	−	21.1725i	−1.13334	−	1.13334i	−0.989619	−	0.143717i	$-0.954094\pi$
$349$	−21.1725	−	21.1725i	−1.13334	−	1.13334i	−0.143717	−	0.989619i	$-0.545906\pi$
$350$		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
$355$	17.9931	+	8.99656i	0.954976	+	0.477488i
$356$		0			0
$357$	−0.381015			−0.0201654
$358$		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
$363$	10.1138			0.530838
$364$		0			0
$365$	−3.35180	+	1.11727i	−0.175441	+	0.0584804i
$366$		0			0
$367$	6.36297	+	6.36297i	0.332144	+	0.332144i	0.853400	−	0.521256i	$-0.174536\pi$
$367$	6.36297	+	6.36297i	0.332144	+	0.332144i	−0.521256	+	0.853400i	$0.674536\pi$
$368$		0			0
$369$			4.00000i			0.208232i
$370$		0			0
$371$	−29.6121	−	29.6121i	−1.53738	−	1.53738i
$372$		0			0
$373$			28.2277i			1.46157i	0.682606	+	0.730786i	$0.260846\pi$
$373$			28.2277i			1.46157i	−0.682606	+	0.730786i	$0.739154\pi$
$374$		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	0.999850	+	0.0173425i	$0.00552057\pi$
$379$	19.8026	+	19.8026i	1.01719	+	1.01719i	0.0173425	+	0.999850i	$0.494479\pi$
$380$		0			0
$381$	−7.24914	+	7.24914i	−0.371385	+	0.371385i
$382$		0			0
$383$	7.69223	−	7.69223i	0.393054	−	0.393054i	−0.482720	−	0.875775i	$-0.660351\pi$
$383$	7.69223	−	7.69223i	0.393054	−	0.393054i	0.875775	+	0.482720i	$0.160351\pi$
$384$		0			0
$385$	21.1138	−	42.2277i	1.07606	−	2.15212i
$386$		0			0
$387$	4.61555			0.234621
$388$		0			0
$389$	8.88273	−	8.88273i	0.450372	−	0.450372i	−0.445106	−	0.895478i	$-0.646834\pi$
$389$	8.88273	−	8.88273i	0.450372	−	0.450372i	0.895478	+	0.445106i	$0.146834\pi$
$390$		0			0
$391$	0.505157			0.0255469
$392$		0			0
$393$	−9.13187	+	9.13187i	−0.460642	+	0.460642i
$394$		0			0
$395$	17.9931	+	8.99656i	0.905332	+	0.452666i
$396$		0			0
$397$			8.11727i			0.407394i	0.979034	+	0.203697i	$0.0652957\pi$
$397$			8.11727i			0.407394i	−0.979034	+	0.203697i	$0.934704\pi$
$398$		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
$405$	−2.00000	−	1.00000i	−0.0993808	−	0.0496904i
$406$		0			0
$407$	6.11727	−	6.11727i	0.303222	−	0.303222i
$408$		0			0
$409$	2.65164			0.131115			0.0655576	−	0.997849i	$-0.479117\pi$
$409$	2.65164			0.131115			0.0655576	+	0.997849i	$0.479117\pi$
$410$		0			0
$411$	−5.05520	+	5.05520i	−0.249354	+	0.249354i
$412$		0			0
$413$	−8.87930			−0.436922
$414$		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	$-0.837580\pi$
$419$	−7.86469	+	7.86469i	−0.384215	+	0.384215i	0.488403	+	0.872618i	$0.337580\pi$
$420$		0			0
$421$	2.94480	+	2.94480i	0.143521	+	0.143521i	0.775217	−	0.631696i	$-0.217641\pi$
$421$	2.94480	+	2.94480i	0.143521	+	0.143521i	−0.631696	+	0.775217i	$0.717641\pi$
$422$		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
$427$		−	13.3776i		−	0.647386i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			28.3810i			1.36707i	0.729920	+	0.683533i	$0.239557\pi$
$431$			28.3810i			1.36707i	−0.729920	+	0.683533i	$0.760443\pi$
$432$		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
$435$	−3.00000	+	1.00000i	−0.143839	+	0.0479463i
$436$		0			0
$437$	−37.1138			−1.77540
$438$		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
$443$	−39.2603			−1.86531			−0.932657	−	0.360765i	$-0.882516\pi$
$443$	−39.2603			−1.86531			−0.932657	+	0.360765i	$0.882516\pi$
$444$		0			0
$445$	−8.23453	−	4.11727i	−0.390354	−	0.195177i
$446$		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	0.147255	−	0.989099i	$-0.452956\pi$
$457$	−17.9966	−	17.9966i	−0.841844	−	0.841844i	−0.989099	+	0.147255i	$0.952956\pi$
$458$		0			0
$459$	0.0586332	+	0.0586332i	0.00273676	+	0.00273676i
$460$		0			0
$461$	16.1138	−	16.1138i	0.750496	−	0.750496i	−0.224076	−	0.974572i	$-0.571936\pi$
$461$	16.1138	−	16.1138i	0.750496	−	0.750496i	0.974572	+	0.224076i	$0.0719363\pi$
$462$		0			0
$463$	6.86813	−	6.86813i	0.319189	−	0.319189i	−0.529267	−	0.848456i	$-0.677533\pi$
$463$	6.86813	−	6.86813i	0.319189	−	0.319189i	0.848456	+	0.529267i	$0.177533\pi$
$464$		0			0
$465$	12.9966	+	6.49828i	0.602701	+	0.301351i
$466$		0			0
$467$	−1.26719			−0.0586384			−0.0293192	−	0.999570i	$-0.509334\pi$
$467$	−1.26719			−0.0586384			−0.0293192	+	0.999570i	$0.509334\pi$
$468$		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
$475$	30.1544	+	4.30777i	1.38358	+	0.197654i
$476$		0			0
$477$			9.11383i			0.417294i
$478$		0			0
$479$	−7.00344			−0.319995			−0.159998	−	0.987117i	$-0.551149\pi$
$479$	−7.00344			−0.319995			−0.159998	+	0.987117i	$0.551149\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		−	27.9931i		−	1.27373i
$484$		0			0
$485$	−29.9897	+	9.99656i	−1.36176	+	0.453921i
$486$		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	−0.425208	−	0.905096i	$-0.639799\pi$
$491$	10.6336	−	10.6336i	0.479887	−	0.479887i	0.905096	+	0.425208i	$0.139799\pi$
$492$		0			0
$493$	0.117266			0.00528141
$494$		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	$-0.706460\pi$
$499$	4.30777	−	4.30777i	0.192842	−	0.192842i	0.796923	+	0.604081i	$0.206460\pi$
$500$		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
$507$		−	13.0000i		−	0.577350i
$508$		0			0
$509$	16.9931	+	16.9931i	0.753207	+	0.753207i	0.975076	−	0.221869i	$-0.0712159\pi$
$509$	16.9931	+	16.9931i	0.753207	+	0.753207i	−0.221869	+	0.975076i	$0.571216\pi$
$510$		0			0
$511$		−	7.26031i		−	0.321177i
$512$		0			0
$513$	−4.30777	−	4.30777i	−0.190193	−	0.190193i
$514$		0			0
$515$	5.36641	+	16.0992i	0.236472	+	0.709416i
$516$		0			0
$517$	44.2277			1.94513
$518$		0			0
$519$			0.234533i			0.0102948i
$520$		0			0
$521$		−	14.3518i		−	0.628764i	−0.949297	−	0.314382i	$-0.898203\pi$
$521$		−	14.3518i		−	0.628764i	0.949297	−	0.314382i	$-0.101797\pi$
$522$		0			0
$523$	4.38101			0.191568			0.0957842	−	0.995402i	$-0.469464\pi$
$523$	4.38101			0.191568			0.0957842	+	0.995402i	$0.469464\pi$
$524$		0			0
$525$	−3.24914	+	22.7440i	−0.141804	+	0.992629i
$526$		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	−0.357501	−	0.933913i	$-0.616371\pi$
$541$	13.4070	−	13.4070i	0.576412	−	0.576412i	0.933913	+	0.357501i	$0.116371\pi$
$542$		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
$547$	−19.3845			−0.828819			−0.414410	−	0.910090i	$-0.636012\pi$
$547$	−19.3845			−0.828819			−0.414410	+	0.910090i	$0.636012\pi$
$548$		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
$555$	−1.88273	+	3.76547i	−0.0799176	+	0.159835i
$556$		0			0
$557$			35.9931i			1.52508i	0.646942	+	0.762539i	$0.276047\pi$
$557$			35.9931i			1.52508i	−0.646942	+	0.762539i	$0.723953\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.381015			0.0160865
$562$		0			0
$563$		−	8.23453i		−	0.347044i	−0.984830	−	0.173522i	$-0.944485\pi$
$563$		−	8.23453i		−	0.347044i	0.984830	−	0.173522i	$-0.0555148\pi$
$564$		0			0
$565$	−2.05863	−	6.17590i	−0.0866073	−	0.259822i
$566$		0			0
$567$	3.24914	−	3.24914i	0.136451	−	0.136451i
$568$		0			0
$569$	15.8827			0.665839			0.332919	−	0.942955i	$-0.391966\pi$
$569$	15.8827			0.665839			0.332919	+	0.942955i	$0.391966\pi$
$570$		0			0
$571$	−22.1905	+	22.1905i	−0.928644	+	0.928644i	−0.997618	−	0.0689746i	$-0.978027\pi$
$571$	−22.1905	+	22.1905i	−0.928644	+	0.928644i	0.0689746	+	0.997618i	$0.478027\pi$
$572$		0			0
$573$	20.6155			0.861227
$574$		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
$587$			3.00344i			0.123965i	0.998077	+	0.0619826i	$0.0197423\pi$
$587$			3.00344i			0.123965i	−0.998077	+	0.0619826i	$0.980258\pi$
$588$		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
$595$	0.381015	−	0.762030i	0.0156201	−	0.0312402i
$596$		0			0
$597$	−18.4983			−0.757084
$598$		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	$-0.638604\pi$
$601$		−	44.4553i		−	1.81337i	0.421808	−	0.906685i	$-0.361396\pi$
$602$		0			0
$603$	12.3810			0.504194
$604$		0			0
$605$	−10.1138	+	20.2277i	−0.411186	+	0.822371i
$606$		0			0
$607$	22.5975	+	22.5975i	0.917204	+	0.917204i	0.996825	−	0.0796209i	$-0.0253710\pi$
$607$	22.5975	+	22.5975i	0.917204	+	0.917204i	−0.0796209	+	0.996825i	$0.525371\pi$
$608$		0			0
$609$		−	6.49828i		−	0.263324i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		−	16.1173i		−	0.650970i	−0.945547	−	0.325485i	$-0.894472\pi$
$613$		−	16.1173i		−	0.650970i	0.945547	−	0.325485i	$-0.105528\pi$
$614$		0			0
$615$	−8.00000	−	4.00000i	−0.322591	−	0.161296i
$616$		0			0
$617$	21.2897	+	21.2897i	0.857092	+	0.857092i	0.990995	−	0.133902i	$-0.0427509\pi$
$617$	21.2897	+	21.2897i	0.857092	+	0.857092i	−0.133902	+	0.990995i	$0.542751\pi$
$618$		0			0
$619$	−6.19051	−	6.19051i	−0.248817	−	0.248817i	0.571668	−	0.820485i	$-0.306297\pi$
$619$	−6.19051	−	6.19051i	−0.248817	−	0.248817i	−0.820485	+	0.571668i	$0.806297\pi$
$620$		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
$627$	−27.9931			−1.11794
$628$		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
$635$	−7.24914	−	21.7474i	−0.287673	−	0.863020i
$636$		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
$643$		−	5.46563i		−	0.215543i	−0.994176	−	0.107772i	$-0.965628\pi$
$643$		−	5.46563i		−	0.215543i	0.994176	−	0.107772i	$-0.0343715\pi$
$644$		0			0
$645$	−4.61555	+	9.23109i	−0.181737	+	0.363474i
$646$		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
$653$	3.11383			0.121854			0.0609268	−	0.998142i	$-0.480594\pi$
$653$	3.11383			0.121854			0.0609268	+	0.998142i	$0.480594\pi$
$654$		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	$-0.875844\pi$
$659$	−13.9820	+	13.9820i	−0.544660	+	0.544660i	0.380232	+	0.924891i	$0.375844\pi$
$660$		0			0
$661$	−29.2897	−	29.2897i	−1.13924	−	1.13924i	−0.988587	−	0.150651i	$-0.951863\pi$
$661$	−29.2897	−	29.2897i	−1.13924	−	1.13924i	−0.150651	−	0.988587i	$-0.548137\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−27.9931	+	55.9862i	−1.08553	+	2.17105i
$666$		0			0
$667$			8.61555i			0.333595i
$668$		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
$675$	4.00000	−	3.00000i	0.153960	−	0.115470i
$676$		0			0
$677$	22.8793			0.879323			0.439661	−	0.898164i	$-0.355098\pi$
$677$	22.8793			0.879323			0.439661	+	0.898164i	$0.355098\pi$
$678$		0			0
$679$		−	64.9605i		−	2.49295i
$680$		0			0
$681$			1.50172i			0.0575460i
$682$		0			0
$683$	35.7294			1.36715			0.683573	−	0.729882i	$-0.260425\pi$
$683$	35.7294			1.36715			0.683573	+	0.729882i	$0.260425\pi$
$684$		0			0
$685$	−5.05520	−	15.1656i	−0.193149	−	0.579447i
$686$		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	0.990512	−	0.137424i	$-0.0438822\pi$
$691$	22.4250	+	22.4250i	0.853089	+	0.853089i	−0.137424	+	0.990512i	$0.543882\pi$
$692$		0			0
$693$		−	21.1138i		−	0.802048i
$694$		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	−0.542475	−	0.840072i	$-0.682513\pi$
$701$	7.87930	−	7.87930i	0.297597	−	0.297597i	0.840072	+	0.542475i	$0.182513\pi$
$702$		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
$707$	18.7328			0.704520
$708$		0			0
$709$	17.9414	−	17.9414i	0.673802	−	0.673802i	−0.284788	−	0.958590i	$-0.591923\pi$
$709$	17.9414	−	17.9414i	0.673802	−	0.673802i	0.958590	+	0.284788i	$0.0919233\pi$
$710$		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
$717$		−	16.9966i		−	0.634748i
$718$		0			0
$719$	−8.00000			−0.298350			−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000			−0.298350			−0.149175	+	0.988811i	$0.547662\pi$
$720$		0			0
$721$	−34.8724			−1.29872
$722$		0			0
$723$		−	23.9931i		−	0.892314i
$724$		0			0
$725$	1.00000	−	7.00000i	0.0371391	−	0.259973i
$726$		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
$733$	−2.35180			−0.0868657			−0.0434328	−	0.999056i	$-0.513829\pi$
$733$	−2.35180			−0.0868657			−0.0434328	+	0.999056i	$0.513829\pi$
$734$		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	$-0.654940\pi$
$739$	11.3112	−	11.3112i	0.416090	−	0.416090i	0.883853	+	0.467764i	$0.154940\pi$
$740$		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
$747$		−	4.99656i		−	0.182815i
$748$		0			0
$749$	−55.9862	−	55.9862i	−2.04569	−	2.04569i
$750$		0			0
$751$		−	5.73625i		−	0.209319i	−0.994508	−	0.104659i	$-0.966625\pi$
$751$		−	5.73625i		−	0.209319i	0.994508	−	0.104659i	$-0.0333752\pi$
$752$		0			0
$753$	−7.24914	−	7.24914i	−0.264173	−	0.264173i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	12.3449			0.448684			0.224342	−	0.974510i	$-0.427977\pi$
$757$	12.3449			0.448684			0.224342	+	0.974510i	$0.427977\pi$
$758$		0			0
$759$			27.9931i			1.01609i
$760$		0			0
$761$			31.8759i			1.15550i	0.816214	+	0.577749i	$0.196069\pi$
$761$			31.8759i			1.15550i	−0.816214	+	0.577749i	$0.803931\pi$
$762$		0			0
$763$	−45.8466			−1.65976
$764$		0			0
$765$	−0.175899	+	0.0586332i	−0.00635966	+	0.00211989i
$766$		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
$773$		−	35.5760i		−	1.27958i	−0.768550	−	0.639790i	$-0.779021\pi$
$773$		−	35.5760i		−	1.27958i	0.768550	−	0.639790i	$-0.220979\pi$
$774$		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
$787$	45.1430			1.60918			0.804588	−	0.593834i	$-0.202386\pi$
$787$	45.1430			1.60918			0.804588	+	0.593834i	$0.202386\pi$
$788$		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
$795$	−18.2277	−	9.11383i	−0.646468	−	0.323234i
$796$		0			0
$797$		−	43.3415i		−	1.53523i	−0.640909	−	0.767617i	$-0.721442\pi$
$797$		−	43.3415i		−	1.53523i	0.640909	−	0.767617i	$-0.278558\pi$
$798$		0			0
$799$	0.798121			0.0282355
$800$		0			0
$801$	−4.11727			−0.145476
$802$		0			0
$803$			7.26031i			0.256211i
$804$		0			0
$805$	55.9862	+	27.9931i	1.97326	+	0.986628i
$806$		0			0
$807$	−17.8793	+	17.8793i	−0.629381	+	0.629381i
$808$		0			0
$809$	−35.5241			−1.24896			−0.624480	−	0.781041i	$-0.714689\pi$
$809$	−35.5241			−1.24896			−0.624480	+	0.781041i	$0.714689\pi$
$810$		0			0
$811$	28.9233	−	28.9233i	1.01564	−	1.01564i	0.0157594	−	0.999876i	$-0.494983\pi$
$811$	28.9233	−	28.9233i	1.01564	−	1.01564i	0.999876	−	0.0157594i	$-0.00501657\pi$
$812$		0			0
$813$	18.4983			0.648763
$814$		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	0.451066	−	0.892491i	$-0.351044\pi$
$821$	−12.6482	−	12.6482i	−0.441425	−	0.441425i	−0.892491	+	0.451066i	$0.851044\pi$
$822$		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
$827$		−	18.2277i		−	0.633838i	−0.948453	−	0.316919i	$-0.897352\pi$
$827$		−	18.2277i		−	0.633838i	0.948453	−	0.316919i	$-0.102648\pi$
$828$		0			0
$829$	−10.8207	−	10.8207i	−0.375817	−	0.375817i	0.493773	−	0.869591i	$-0.335617\pi$
$829$	−10.8207	−	10.8207i	−0.375817	−	0.375817i	−0.869591	+	0.493773i	$0.835617\pi$
$830$		0			0
$831$			16.1104i			0.558863i
$832$		0			0
$833$	0.827538	+	0.827538i	0.0286725	+	0.0286725i
$834$		0			0
$835$	−7.27512	+	2.42504i	−0.251766	+	0.0839220i
$836$		0			0
$837$	6.49828			0.224613
$838$		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
$843$	−10.1173			−0.348457
$844$		0			0
$845$	26.0000	+	13.0000i	0.894427	+	0.447214i
$846$		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
$853$			36.1173i			1.23663i	0.785930	+	0.618316i	$0.212185\pi$
$853$			36.1173i			1.23663i	−0.785930	+	0.618316i	$0.787815\pi$
$854$		0			0
$855$	12.9233	−	4.30777i	0.441968	−	0.147323i
$856$		0			0
$857$	−8.93793	−	8.93793i	−0.305314	−	0.305314i	0.537775	−	0.843089i	$-0.319265\pi$
$857$	−8.93793	−	8.93793i	−0.305314	−	0.305314i	−0.843089	+	0.537775i	$0.819265\pi$
$858$		0			0
$859$	−39.7665	−	39.7665i	−1.35682	−	1.35682i	−0.877813	−	0.479003i	$-0.840998\pi$
$859$	−39.7665	−	39.7665i	−1.35682	−	1.35682i	−0.479003	−	0.877813i	$-0.659002\pi$
$860$		0			0
$861$	12.9966	−	12.9966i	0.442922	−	0.442922i
$862$		0			0
$863$	10.8061	−	10.8061i	0.367842	−	0.367842i	−0.498847	−	0.866690i	$-0.666243\pi$
$863$	10.8061	−	10.8061i	0.367842	−	0.367842i	0.866690	+	0.498847i	$0.166243\pi$
$864$		0			0
$865$	−0.469065	−	0.234533i	−0.0159487	−	0.00797435i
$866$		0			0
$867$	−16.9931			−0.577117
$868$		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
$875$	−42.2388	−	29.2423i	−1.42793	−	0.988569i
$876$		0			0
$877$			14.2345i			0.480666i	0.970690	+	0.240333i	$0.0772566\pi$
$877$			14.2345i			0.480666i	−0.970690	+	0.240333i	$0.922743\pi$
$878$		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
$883$			58.7552i			1.97727i	0.150341	+	0.988634i	$0.451963\pi$
$883$			58.7552i			1.97727i	−0.150341	+	0.988634i	$0.548037\pi$
$884$		0			0
$885$	−4.09922	+	1.36641i	−0.137794	+	0.0459313i
$886$		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
$893$	−58.6379			−1.96224
$894$		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
$907$		−	8.23453i		−	0.273423i	−0.990611	−	0.136712i	$-0.956347\pi$
$907$		−	8.23453i		−	0.273423i	0.990611	−	0.136712i	$-0.0436534\pi$
$908$		0			0
$909$	−2.88273	−	2.88273i	−0.0956142	−	0.0956142i
$910$		0			0
$911$			42.6087i			1.41169i	0.708367	+	0.705844i	$0.249432\pi$
$911$			42.6087i			1.41169i	−0.708367	+	0.705844i	$0.750568\pi$
$912$		0			0
$913$	−16.2345	−	16.2345i	−0.537285	−	0.537285i
$914$		0			0
$915$	−2.05863	−	6.17590i	−0.0680563	−	0.204169i
$916$		0			0
$917$	59.3415			1.95963
$918$		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
$925$	−5.64820	−	7.53093i	−0.185712	−	0.247616i
$926$		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
$933$		−	21.2311i		−	0.695075i
$934$		0			0
$935$	−0.381015	+	0.762030i	−0.0124605	+	0.0249210i
$936$		0			0
$937$	21.2277	+	21.2277i	0.693477	+	0.693477i	0.962995	−	0.269518i	$-0.0868644\pi$
$937$	21.2277	+	21.2277i	0.693477	+	0.693477i	−0.269518	+	0.962995i	$0.586864\pi$
$938$		0			0
$939$	3.00000	+	3.00000i	0.0979013	+	0.0979013i
$940$		0			0
$941$	−7.99656	+	7.99656i	−0.260680	+	0.260680i	−0.825330	−	0.564650i	$-0.809011\pi$
$941$	−7.99656	+	7.99656i	−0.260680	+	0.260680i	0.564650	+	0.825330i	$0.309011\pi$
$942$		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
$947$	41.7225			1.35580			0.677900	−	0.735155i	$-0.262890\pi$
$947$	41.7225			1.35580			0.677900	+	0.735155i	$0.262890\pi$
$948$		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	−0.303173	−	0.952936i	$-0.598046\pi$
$953$	20.0586	−	20.0586i	0.649763	−	0.649763i	0.952936	+	0.303173i	$0.0980459\pi$
$954$		0			0
$955$	−20.6155	+	41.2311i	−0.667103	+	1.33421i
$956$		0			0
$957$			6.49828i			0.210060i
$958$		0			0
$959$	32.8501			1.06078
$960$		0			0
$961$	−11.2277			−0.362182
$962$		0			0
$963$			17.2311i			0.555264i
$964$		0			0
$965$	−13.9966	−	41.9897i	−0.450565	−	1.35170i
$966$		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	−0.990569	−	0.137015i	$-0.956249\pi$
$971$	−26.5975	+	26.5975i	−0.853554	+	0.853554i	0.137015	+	0.990569i	$0.456249\pi$
$972$		0			0
$973$	−40.2277			−1.28964
$974$		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
$987$		−	44.2277i		−	1.40778i
$988$		0			0
$989$	19.8827	+	19.8827i	0.632234	+	0.632234i
$990$		0			0
$991$		−	12.9605i		−	0.411703i	−0.978583	−	0.205851i	$-0.934004\pi$
$991$		−	12.9605i		−	0.411703i	0.978583	−	0.205851i	$-0.0659964\pi$
$992$		0			0
$993$	8.92332	+	8.92332i	0.283173	+	0.283173i
$994$		0			0
$995$	18.4983	−	36.9966i	0.586435	−	1.17287i
$996$		0			0
$997$	−22.2277			−0.703957			−0.351978	−	0.936008i	$-0.614491\pi$
$997$	−22.2277			−0.703957			−0.351978	+	0.936008i	$0.614491\pi$
$998$		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.bc.h.1183.3		6
4.3	odd	2		1920.2.bc.g.1183.1		6
5.2	odd	4		1920.2.y.h.1567.3		6
8.3	odd	2		240.2.bc.d.43.2	yes	6
8.5	even	2		960.2.bc.d.463.3		6
16.3	odd	4		1920.2.y.h.223.3		6
16.5	even	4		240.2.y.d.163.3	✓	6
16.11	odd	4		960.2.y.d.943.3		6
16.13	even	4		1920.2.y.g.223.1		6
20.7	even	4		1920.2.y.g.1567.1		6
24.11	even	2		720.2.bd.e.523.2		6
40.27	even	4		240.2.y.d.187.3	yes	6
40.37	odd	4		960.2.y.d.847.3		6
48.5	odd	4		720.2.z.e.163.1		6
80.27	even	4		960.2.bc.d.367.3		6
80.37	odd	4		240.2.bc.d.67.2	yes	6
80.67	even	4	inner	1920.2.bc.h.607.3		6
80.77	odd	4		1920.2.bc.g.607.1		6
120.107	odd	4		720.2.z.e.667.1		6
240.197	even	4		720.2.bd.e.307.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.d.163.3	✓	6	16.5	even	4
240.2.y.d.187.3	yes	6	40.27	even	4
240.2.bc.d.43.2	yes	6	8.3	odd	2
240.2.bc.d.67.2	yes	6	80.37	odd	4
720.2.z.e.163.1		6	48.5	odd	4
720.2.z.e.667.1		6	120.107	odd	4
720.2.bd.e.307.2		6	240.197	even	4
720.2.bd.e.523.2		6	24.11	even	2
960.2.y.d.847.3		6	40.37	odd	4
960.2.y.d.943.3		6	16.11	odd	4
960.2.bc.d.367.3		6	80.27	even	4
960.2.bc.d.463.3		6	8.5	even	2
1920.2.y.g.223.1		6	16.13	even	4
1920.2.y.g.1567.1		6	20.7	even	4
1920.2.y.h.223.3		6	16.3	odd	4
1920.2.y.h.1567.3		6	5.2	odd	4
1920.2.bc.g.607.1		6	80.77	odd	4
1920.2.bc.g.1183.1		6	4.3	odd	2
1920.2.bc.h.607.3		6	80.67	even	4	inner
1920.2.bc.h.1183.3		6	1.1	even	1	trivial

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.bc (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{3} +(-2.00000 - 1.00000i) q^{5} +(3.24914 - 3.24914i) q^{7} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{3} +(-2.00000 - 1.00000i) q^{5} +(3.24914 - 3.24914i) q^{7} -1.00000 q^{9} +(-3.24914 + 3.24914i) q^{11} +(1.00000 - 2.00000i) q^{15} +(-0.0586332 + 0.0586332i) q^{17} +(4.30777 - 4.30777i) q^{19} +(3.24914 + 3.24914i) q^{21} +(-4.30777 - 4.30777i) q^{23} +(3.00000 + 4.00000i) q^{25} -1.00000i q^{27} +(-1.00000 - 1.00000i) q^{29} +6.49828i q^{31} +(-3.24914 - 3.24914i) q^{33} +(-9.74742 + 3.24914i) q^{35} -1.88273 q^{37} -4.00000i q^{41} -4.61555 q^{43} +(2.00000 + 1.00000i) q^{45} +(-6.80605 - 6.80605i) q^{47} -14.1138i q^{49} +(-0.0586332 - 0.0586332i) q^{51} -9.11383i q^{53} +(9.74742 - 3.24914i) q^{55} +(4.30777 + 4.30777i) q^{57} +(-1.36641 - 1.36641i) q^{59} +(2.05863 - 2.05863i) q^{61} +(-3.24914 + 3.24914i) q^{63} -12.3810 q^{67} +(4.30777 - 4.30777i) q^{69} -8.99656 q^{71} +(1.11727 - 1.11727i) q^{73} +(-4.00000 + 3.00000i) q^{75} +21.1138i q^{77} -8.99656 q^{79} +1.00000 q^{81} +4.99656i q^{83} +(0.175899 - 0.0586332i) q^{85} +(1.00000 - 1.00000i) q^{87} +4.11727 q^{89} -6.49828 q^{93} +(-12.9233 + 4.30777i) q^{95} +(9.99656 - 9.99656i) q^{97} +(3.24914 - 3.24914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 12 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 6 * q - 12 * q^5 + 2 * q^7 - 6 * q^9	\( 6 q - 12 q^{5} + 2 q^{7} - 6 q^{9} - 2 q^{11} + 6 q^{15} - 2 q^{17} + 10 q^{19} + 2 q^{21} - 10 q^{23} + 18 q^{25} - 6 q^{29} - 2 q^{33} - 6 q^{35} - 8 q^{37} + 4 q^{43} + 12 q^{45} + 10 q^{47} - 2 q^{51} + 6 q^{55} + 10 q^{57} + 6 q^{59} + 14 q^{61} - 2 q^{63} - 36 q^{67} + 10 q^{69} + 16 q^{71} + 10 q^{73} - 24 q^{75} + 16 q^{79} + 6 q^{81} + 6 q^{85} + 6 q^{87} + 28 q^{89} - 4 q^{93} - 30 q^{95} - 10 q^{97} + 2 q^{99}+O(q^{100}) \) 6 * q - 12 * 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^29 - 2 * q^33 - 6 * q^35 - 8 * q^37 + 4 * q^43 + 12 * q^45 + 10 * q^47 - 2 * q^51 + 6 * q^55 + 10 * q^57 + 6 * q^59 + 14 * q^61 - 2 * q^63 - 36 * q^67 + 10 * q^69 + 16 * q^71 + 10 * q^73 - 24 * q^75 + 16 * q^79 + 6 * q^81 + 6 * q^85 + 6 * q^87 + 28 * q^89 - 4 * q^93 - 30 * q^95 - 10 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more