LMFDB - Embedded newform 1920.2.y.l.223.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1920,2,Mod(223,1920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [20,0,20,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 3 x^{18} - 6 x^{17} + 2 x^{16} + 4 x^{14} + 20 x^{13} - 24 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 3x^18 - 6x^17 + 2x^16 + 4x^14 + 20x^13 - 24x^12 + 40x^11 - 124x^10 + 80x^9 - 96x^8 + 160x^7 + 64x^6 + 128x^4 - 768x^3 + 768x^2 - 1024*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.4
Root			$-0.257862 - 1.39051i$ of defining polynomial
Character	$\chi$	$=$	1920.223
Dual form			1920.2.y.l.1567.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{3} +(-0.778677 - 2.09611i) q^{5} +(-2.44055 + 2.44055i) q^{7} +1.00000 q^{9} +(0.181897 + 0.181897i) q^{11} +4.59597i q^{13} +(-0.778677 - 2.09611i) q^{15} +(4.20448 - 4.20448i) q^{17} +(-4.75798 - 4.75798i) q^{19} +(-2.44055 + 2.44055i) q^{21} +(-5.75492 - 5.75492i) q^{23} +(-3.78732 + 3.26438i) q^{25} +1.00000 q^{27} +(0.851917 - 0.851917i) q^{29} -4.78620i q^{31} +(0.181897 + 0.181897i) q^{33} +(7.01605 + 3.21525i) q^{35} -3.97976i q^{37} +4.59597i q^{39} -7.99664i q^{41} +4.44648i q^{43} +(-0.778677 - 2.09611i) q^{45} +(-2.46569 - 2.46569i) q^{47} -4.91254i q^{49} +(4.20448 - 4.20448i) q^{51} +4.94396 q^{53} +(0.239637 - 0.522915i) q^{55} +(-4.75798 - 4.75798i) q^{57} +(-5.89705 + 5.89705i) q^{59} +(-7.88576 - 7.88576i) q^{61} +(-2.44055 + 2.44055i) q^{63} +(9.63365 - 3.57878i) q^{65} -7.54264i q^{67} +(-5.75492 - 5.75492i) q^{69} -6.34716 q^{71} +(-4.78916 + 4.78916i) q^{73} +(-3.78732 + 3.26438i) q^{75} -0.887858 q^{77} -3.83743 q^{79} +1.00000 q^{81} -6.25327 q^{83} +(-12.0870 - 5.53910i) q^{85} +(0.851917 - 0.851917i) q^{87} -5.02517 q^{89} +(-11.2167 - 11.2167i) q^{91} -4.78620i q^{93} +(-6.26830 + 13.6782i) q^{95} +(-2.96112 + 2.96112i) q^{97} +(0.181897 + 0.181897i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} - 4 q^{7} + 20 q^{9} - 8 q^{11} + 12 q^{17} - 16 q^{19} - 4 q^{21} - 16 q^{23} + 4 q^{25} + 20 q^{27} - 8 q^{33} + 28 q^{35} + 12 q^{51} - 8 q^{53} - 4 q^{55} - 16 q^{57} + 16 q^{59} + 12 q^{61}+ \cdots - 8 q^{99}+O(q^{100}) $ 20 * q + 20 * q^3 - 4 * q^7 + 20 * q^9 - 8 * q^11 + 12 * q^17 - 16 * q^19 - 4 * q^21 - 16 * q^23 + 4 * q^25 + 20 * q^27 - 8 * q^33 + 28 * q^35 + 12 * q^51 - 8 * q^53 - 4 * q^55 - 16 * q^57 + 16 * q^59 + 12 * q^61 - 4 * q^63 + 4 * q^65 - 16 * q^69 - 20 * q^73 + 4 * q^75 + 48 * q^79 + 20 * q^81 + 24 * q^83 - 4 * q^85 + 40 * q^89 + 24 * q^91 - 72 * q^95 - 28 * q^97 - 8 * 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
$5$	−0.778677	−	2.09611i	−0.348235	−	0.937407i
$5$	−0.778677	−	2.09611i	−0.348235	−	0.937407i
$6$		0			0
$7$	−2.44055	+	2.44055i	−0.922440	+	0.922440i	−0.997201	−	0.0747612i	$-0.976181\pi$
$7$	−2.44055	+	2.44055i	−0.922440	+	0.922440i	0.0747612	+	0.997201i	$0.476181\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	0.181897	+	0.181897i	0.0548441	+	0.0548441i	0.733997	−	0.679153i	$-0.237653\pi$
$11$	0.181897	+	0.181897i	0.0548441	+	0.0548441i	−0.679153	+	0.733997i	$0.737653\pi$
$12$		0			0
$13$			4.59597i			1.27469i	0.770577	+	0.637347i	$0.219968\pi$
$13$			4.59597i			1.27469i	−0.770577	+	0.637347i	$0.780032\pi$
$14$		0			0
$15$	−0.778677	−	2.09611i	−0.201054	−	0.541212i
$16$		0			0
$17$	4.20448	−	4.20448i	1.01974	−	1.01974i	0.0199338	−	0.999801i	$-0.493654\pi$
$17$	4.20448	−	4.20448i	1.01974	−	1.01974i	0.999801	−	0.0199338i	$-0.00634553\pi$
$18$		0			0
$19$	−4.75798	−	4.75798i	−1.09155	−	1.09155i	−0.995363	−	0.0961919i	$-0.969334\pi$
$19$	−4.75798	−	4.75798i	−1.09155	−	1.09155i	−0.0961919	−	0.995363i	$-0.530666\pi$
$20$		0			0
$21$	−2.44055	+	2.44055i	−0.532571	+	0.532571i
$22$		0			0
$23$	−5.75492	−	5.75492i	−1.19998	−	1.19998i	−0.974171	−	0.225813i	$-0.927496\pi$
$23$	−5.75492	−	5.75492i	−1.19998	−	1.19998i	−0.225813	−	0.974171i	$-0.572504\pi$
$24$		0			0
$25$	−3.78732	+	3.26438i	−0.757465	+	0.652876i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	0.851917	−	0.851917i	0.158197	−	0.158197i	−0.623570	−	0.781767i	$-0.714318\pi$
$29$	0.851917	−	0.851917i	0.158197	−	0.158197i	0.781767	+	0.623570i	$0.214318\pi$
$30$		0			0
$31$		−	4.78620i		−	0.859626i	−0.902918	−	0.429813i	$-0.858579\pi$
$31$		−	4.78620i		−	0.859626i	0.902918	−	0.429813i	$-0.141421\pi$
$32$		0			0
$33$	0.181897	+	0.181897i	0.0316643	+	0.0316643i
$34$		0			0
$35$	7.01605	+	3.21525i	1.18593	+	0.543476i
$36$		0			0
$37$		−	3.97976i		−	0.654268i	−0.944978	−	0.327134i	$-0.893917\pi$
$37$		−	3.97976i		−	0.654268i	0.944978	−	0.327134i	$-0.106083\pi$
$38$		0			0
$39$			4.59597i			0.735945i
$40$		0			0
$41$		−	7.99664i		−	1.24887i	−0.781079	−	0.624433i	$-0.785330\pi$
$41$		−	7.99664i		−	1.24887i	0.781079	−	0.624433i	$-0.214670\pi$
$42$		0			0
$43$			4.44648i			0.678081i	0.940772	+	0.339041i	$0.110102\pi$
$43$			4.44648i			0.678081i	−0.940772	+	0.339041i	$0.889898\pi$
$44$		0			0
$45$	−0.778677	−	2.09611i	−0.116078	−	0.312469i
$46$		0			0
$47$	−2.46569	−	2.46569i	−0.359657	−	0.359657i	0.504029	−	0.863687i	$-0.331850\pi$
$47$	−2.46569	−	2.46569i	−0.359657	−	0.359657i	−0.863687	+	0.504029i	$0.831850\pi$
$48$		0			0
$49$		−	4.91254i		−	0.701792i
$50$		0			0
$51$	4.20448	−	4.20448i	0.588744	−	0.588744i
$52$		0			0
$53$	4.94396			0.679106			0.339553	−	0.940587i	$-0.389724\pi$
$53$	4.94396			0.679106			0.339553	+	0.940587i	$0.389724\pi$
$54$		0			0
$55$	0.239637	−	0.522915i	0.0323126	−	0.0705099i
$56$		0			0
$57$	−4.75798	−	4.75798i	−0.630209	−	0.630209i
$58$		0			0
$59$	−5.89705	+	5.89705i	−0.767731	+	0.767731i	−0.977707	−	0.209976i	$-0.932662\pi$
$59$	−5.89705	+	5.89705i	−0.767731	+	0.767731i	0.209976	+	0.977707i	$0.432662\pi$
$60$		0			0
$61$	−7.88576	−	7.88576i	−1.00967	−	1.00967i	−0.999953	−	0.00971590i	$-0.996907\pi$
$61$	−7.88576	−	7.88576i	−1.00967	−	1.00967i	−0.00971590	−	0.999953i	$-0.503093\pi$
$62$		0			0
$63$	−2.44055	+	2.44055i	−0.307480	+	0.307480i
$64$		0			0
$65$	9.63365	−	3.57878i	1.19491	−	0.443893i
$66$		0			0
$67$		−	7.54264i		−	0.921480i	−0.887535	−	0.460740i	$-0.847584\pi$
$67$		−	7.54264i		−	0.921480i	0.887535	−	0.460740i	$-0.152416\pi$
$68$		0			0
$69$	−5.75492	−	5.75492i	−0.692811	−	0.692811i
$70$		0			0
$71$	−6.34716			−0.753269			−0.376635	−	0.926362i	$-0.622919\pi$
$71$	−6.34716			−0.753269			−0.376635	+	0.926362i	$0.622919\pi$
$72$		0			0
$73$	−4.78916	+	4.78916i	−0.560529	+	0.560529i	−0.929458	−	0.368929i	$-0.879725\pi$
$73$	−4.78916	+	4.78916i	−0.560529	+	0.560529i	0.368929	+	0.929458i	$0.379725\pi$
$74$		0			0
$75$	−3.78732	+	3.26438i	−0.437322	+	0.376938i
$76$		0			0
$77$	−0.887858			−0.101181
$78$		0			0
$79$	−3.83743			−0.431745			−0.215872	−	0.976422i	$-0.569260\pi$
$79$	−3.83743			−0.431745			−0.215872	+	0.976422i	$0.569260\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−6.25327			−0.686385			−0.343193	−	0.939265i	$-0.611508\pi$
$83$	−6.25327			−0.686385			−0.343193	+	0.939265i	$0.611508\pi$
$84$		0			0
$85$	−12.0870	−	5.53910i	−1.31101	−	0.600800i
$86$		0			0
$87$	0.851917	−	0.851917i	0.0913351	−	0.0913351i
$88$		0			0
$89$	−5.02517			−0.532667			−0.266333	−	0.963881i	$-0.585812\pi$
$89$	−5.02517			−0.532667			−0.266333	+	0.963881i	$0.585812\pi$
$90$		0			0
$91$	−11.2167	−	11.2167i	−1.17583	−	1.17583i
$92$		0			0
$93$		−	4.78620i		−	0.496306i
$94$		0			0
$95$	−6.26830	+	13.6782i	−0.643114	+	1.40335i
$96$		0			0
$97$	−2.96112	+	2.96112i	−0.300656	+	0.300656i	−0.841270	−	0.540615i	$-0.818192\pi$
$97$	−2.96112	+	2.96112i	−0.300656	+	0.300656i	0.540615	+	0.841270i	$0.318192\pi$
$98$		0			0
$99$	0.181897	+	0.181897i	0.0182814	+	0.0182814i
$100$		0			0
$101$	−0.596631	+	0.596631i	−0.0593670	+	0.0593670i	−0.736167	−	0.676800i	$-0.763366\pi$
$101$	−0.596631	+	0.596631i	−0.0593670	+	0.0593670i	0.676800	+	0.736167i	$0.263366\pi$
$102$		0			0
$103$	9.06195	+	9.06195i	0.892901	+	0.892901i	0.994795	−	0.101894i	$-0.0324904\pi$
$103$	9.06195	+	9.06195i	0.892901	+	0.892901i	−0.101894	+	0.994795i	$0.532490\pi$
$104$		0			0
$105$	7.01605	+	3.21525i	0.684696	+	0.313776i
$106$		0			0
$107$	5.89771			0.570153			0.285076	−	0.958505i	$-0.407981\pi$
$107$	5.89771			0.570153			0.285076	+	0.958505i	$0.407981\pi$
$108$		0			0
$109$	3.65602	−	3.65602i	0.350183	−	0.350183i	−0.509995	−	0.860178i	$-0.670353\pi$
$109$	3.65602	−	3.65602i	0.350183	−	0.350183i	0.860178	+	0.509995i	$0.170353\pi$
$110$		0			0
$111$		−	3.97976i		−	0.377742i
$112$		0			0
$113$	−6.39894	−	6.39894i	−0.601962	−	0.601962i	0.338871	−	0.940833i	$-0.389955\pi$
$113$	−6.39894	−	6.39894i	−0.601962	−	0.601962i	−0.940833	+	0.338871i	$0.889955\pi$
$114$		0			0
$115$	−7.58170	+	16.5442i	−0.706997	+	1.54275i
$116$		0			0
$117$			4.59597i			0.424898i
$118$		0			0
$119$			20.5224i			1.88129i
$120$		0			0
$121$		−	10.9338i		−	0.993984i
$122$		0			0
$123$		−	7.99664i		−	0.721033i
$124$		0			0
$125$	9.79159	+	5.39673i	0.875787	+	0.482699i
$126$		0			0
$127$	−6.86114	−	6.86114i	−0.608827	−	0.608827i	0.333812	−	0.942640i	$-0.391665\pi$
$127$	−6.86114	−	6.86114i	−0.608827	−	0.608827i	−0.942640	+	0.333812i	$0.891665\pi$
$128$		0			0
$129$			4.44648i			0.391491i
$130$		0			0
$131$	−1.09665	+	1.09665i	−0.0958148	+	0.0958148i	−0.753389	−	0.657575i	$-0.771582\pi$
$131$	−1.09665	+	1.09665i	−0.0958148	+	0.0958148i	0.657575	+	0.753389i	$0.271582\pi$
$132$		0			0
$133$	23.2241			2.01379
$134$		0			0
$135$	−0.778677	−	2.09611i	−0.0670179	−	0.180404i
$136$		0			0
$137$	12.2428	+	12.2428i	1.04598	+	1.04598i	0.998891	+	0.0470863i	$0.0149936\pi$
$137$	12.2428	+	12.2428i	1.04598	+	1.04598i	0.0470863	+	0.998891i	$0.485006\pi$
$138$		0			0
$139$	−3.39535	+	3.39535i	−0.287990	+	0.287990i	−0.836285	−	0.548295i	$-0.815277\pi$
$139$	−3.39535	+	3.39535i	−0.287990	+	0.287990i	0.548295	+	0.836285i	$0.315277\pi$
$140$		0			0
$141$	−2.46569	−	2.46569i	−0.207648	−	0.207648i
$142$		0			0
$143$	−0.835995	+	0.835995i	−0.0699094	+	0.0699094i
$144$		0			0
$145$	−2.44908	−	1.12234i	−0.203385	−	0.0932053i
$146$		0			0
$147$		−	4.91254i		−	0.405180i
$148$		0			0
$149$	−7.84547	−	7.84547i	−0.642726	−	0.642726i	0.308499	−	0.951225i	$-0.400173\pi$
$149$	−7.84547	−	7.84547i	−0.642726	−	0.642726i	−0.951225	+	0.308499i	$0.900173\pi$
$150$		0			0
$151$	−3.19389			−0.259915			−0.129957	−	0.991520i	$-0.541484\pi$
$151$	−3.19389			−0.259915			−0.129957	+	0.991520i	$0.541484\pi$
$152$		0			0
$153$	4.20448	−	4.20448i	0.339912	−	0.339912i
$154$		0			0
$155$	−10.0324	+	3.72690i	−0.805820	+	0.299352i
$156$		0			0
$157$	17.6595			1.40938			0.704691	−	0.709514i	$-0.251085\pi$
$157$	17.6595			1.40938			0.704691	+	0.709514i	$0.251085\pi$
$158$		0			0
$159$	4.94396			0.392082
$160$		0			0
$161$	28.0903			2.21383
$162$		0			0
$163$	−8.01355			−0.627669			−0.313835	−	0.949478i	$-0.601614\pi$
$163$	−8.01355			−0.627669			−0.313835	+	0.949478i	$0.601614\pi$
$164$		0			0
$165$	0.239637	−	0.522915i	0.0186557	−	0.0407089i
$166$		0			0
$167$	8.45631	−	8.45631i	0.654369	−	0.654369i	−0.299673	−	0.954042i	$-0.596878\pi$
$167$	8.45631	−	8.45631i	0.654369	−	0.654369i	0.954042	+	0.299673i	$0.0968776\pi$
$168$		0			0
$169$	−8.12298			−0.624845
$170$		0			0
$171$	−4.75798	−	4.75798i	−0.363852	−	0.363852i
$172$		0			0
$173$			5.11465i			0.388860i	0.980916	+	0.194430i	$0.0622857\pi$
$173$			5.11465i			0.388860i	−0.980916	+	0.194430i	$0.937714\pi$
$174$		0			0
$175$	1.27627	−	17.2100i	0.0964767	−	1.30096i
$176$		0			0
$177$	−5.89705	+	5.89705i	−0.443250	+	0.443250i
$178$		0			0
$179$	4.67625	+	4.67625i	0.349519	+	0.349519i	0.859930	−	0.510411i	$-0.170507\pi$
$179$	4.67625	+	4.67625i	0.349519	+	0.349519i	−0.510411	+	0.859930i	$0.670507\pi$
$180$		0			0
$181$	5.45166	−	5.45166i	0.405219	−	0.405219i	−0.474849	−	0.880067i	$-0.657497\pi$
$181$	5.45166	−	5.45166i	0.405219	−	0.405219i	0.880067	+	0.474849i	$0.157497\pi$
$182$		0			0
$183$	−7.88576	−	7.88576i	−0.582932	−	0.582932i
$184$		0			0
$185$	−8.34199	+	3.09895i	−0.613316	+	0.227839i
$186$		0			0
$187$	1.52957			0.111853
$188$		0			0
$189$	−2.44055	+	2.44055i	−0.177524	+	0.177524i
$190$		0			0
$191$			14.1293i			1.02236i	0.859474	+	0.511179i	$0.170791\pi$
$191$			14.1293i			1.02236i	−0.859474	+	0.511179i	$0.829209\pi$
$192$		0			0
$193$	−6.89094	−	6.89094i	−0.496021	−	0.496021i	0.414176	−	0.910197i	$-0.364070\pi$
$193$	−6.89094	−	6.89094i	−0.496021	−	0.496021i	−0.910197	+	0.414176i	$0.864070\pi$
$194$		0			0
$195$	9.63365	−	3.57878i	0.689880	−	0.256282i
$196$		0			0
$197$		−	21.6079i		−	1.53950i	−0.638345	−	0.769750i	$-0.720381\pi$
$197$		−	21.6079i		−	1.53950i	0.638345	−	0.769750i	$-0.279619\pi$
$198$		0			0
$199$			8.16771i			0.578994i	0.957179	+	0.289497i	$0.0934880\pi$
$199$			8.16771i			0.578994i	−0.957179	+	0.289497i	$0.906512\pi$
$200$		0			0
$201$		−	7.54264i		−	0.532017i
$202$		0			0
$203$			4.15829i			0.291855i
$204$		0			0
$205$	−16.7618	+	6.22680i	−1.17070	+	0.434899i
$206$		0			0
$207$	−5.75492	−	5.75492i	−0.399995	−	0.399995i
$208$		0			0
$209$		−	1.73093i		−	0.119731i
$210$		0			0
$211$	9.64189	−	9.64189i	0.663775	−	0.663775i	−0.292493	−	0.956268i	$-0.594485\pi$
$211$	9.64189	−	9.64189i	0.663775	−	0.663775i	0.956268	+	0.292493i	$0.0944847\pi$
$212$		0			0
$213$	−6.34716			−0.434900
$214$		0			0
$215$	9.32029	−	3.46237i	0.635638	−	0.236132i
$216$		0			0
$217$	11.6809	+	11.6809i	0.792954	+	0.792954i
$218$		0			0
$219$	−4.78916	+	4.78916i	−0.323621	+	0.323621i
$220$		0			0
$221$	19.3237	+	19.3237i	1.29985	+	1.29985i
$222$		0			0
$223$	13.5811	−	13.5811i	0.909456	−	0.909456i	−0.0867726	−	0.996228i	$-0.527655\pi$
$223$	13.5811	−	13.5811i	0.909456	−	0.909456i	0.996228	+	0.0867726i	$0.0276553\pi$
$224$		0			0
$225$	−3.78732	+	3.26438i	−0.252488	+	0.217625i
$226$		0			0
$227$			13.3355i			0.885109i	0.896742	+	0.442554i	$0.145928\pi$
$227$			13.3355i			0.885109i	−0.896742	+	0.442554i	$0.854072\pi$
$228$		0			0
$229$	17.5166	+	17.5166i	1.15753	+	1.15753i	0.985005	+	0.172525i	$0.0551926\pi$
$229$	17.5166	+	17.5166i	1.15753	+	1.15753i	0.172525	+	0.985005i	$0.444807\pi$
$230$		0			0
$231$	−0.887858			−0.0584168
$232$		0			0
$233$	−5.53768	+	5.53768i	−0.362786	+	0.362786i	−0.864837	−	0.502052i	$-0.832579\pi$
$233$	−5.53768	+	5.53768i	−0.362786	+	0.362786i	0.502052	+	0.864837i	$0.332579\pi$
$234$		0			0
$235$	−3.24837	+	7.08831i	−0.211900	+	0.462390i
$236$		0			0
$237$	−3.83743			−0.249268
$238$		0			0
$239$	7.70031			0.498092			0.249046	−	0.968492i	$-0.419883\pi$
$239$	7.70031			0.498092			0.249046	+	0.968492i	$0.419883\pi$
$240$		0			0
$241$	−27.9273			−1.79896			−0.899478	−	0.436967i	$-0.856053\pi$
$241$	−27.9273			−1.79896			−0.899478	+	0.436967i	$0.856053\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−10.2972	+	3.82529i	−0.657865	+	0.244389i
$246$		0			0
$247$	21.8675	−	21.8675i	1.39140	−	1.39140i
$248$		0			0
$249$	−6.25327			−0.396285
$250$		0			0
$251$	10.5948	+	10.5948i	0.668740	+	0.668740i	0.957424	−	0.288684i	$-0.0932178\pi$
$251$	10.5948	+	10.5948i	0.668740	+	0.668740i	−0.288684	+	0.957424i	$0.593218\pi$
$252$		0			0
$253$		−	2.09361i		−	0.131624i
$254$		0			0
$255$	−12.0870	−	5.53910i	−0.756915	−	0.346872i
$256$		0			0
$257$	−9.86474	+	9.86474i	−0.615345	+	0.615345i	−0.944334	−	0.328989i	$-0.893292\pi$
$257$	−9.86474	+	9.86474i	−0.615345	+	0.615345i	0.328989	+	0.944334i	$0.393292\pi$
$258$		0			0
$259$	9.71279	+	9.71279i	0.603523	+	0.603523i
$260$		0			0
$261$	0.851917	−	0.851917i	0.0527323	−	0.0527323i
$262$		0			0
$263$	−5.45464	−	5.45464i	−0.336348	−	0.336348i	0.518643	−	0.854991i	$-0.326437\pi$
$263$	−5.45464	−	5.45464i	−0.336348	−	0.336348i	−0.854991	+	0.518643i	$0.826437\pi$
$264$		0			0
$265$	−3.84975	−	10.3631i	−0.236488	−	0.636599i
$266$		0			0
$267$	−5.02517			−0.307535
$268$		0			0
$269$	1.61579	−	1.61579i	0.0985164	−	0.0985164i	−0.656131	−	0.754647i	$-0.727808\pi$
$269$	1.61579	−	1.61579i	0.0985164	−	0.0985164i	0.754647	+	0.656131i	$0.227808\pi$
$270$		0			0
$271$			6.09685i			0.370357i	0.982705	+	0.185179i	$0.0592864\pi$
$271$			6.09685i			0.370357i	−0.982705	+	0.185179i	$0.940714\pi$
$272$		0			0
$273$	−11.2167	−	11.2167i	−0.678865	−	0.678865i
$274$		0			0
$275$	−1.28269	−	0.0951219i	−0.0773489	−	0.00573607i
$276$		0			0
$277$			15.5674i			0.935355i	0.883899	+	0.467678i	$0.154909\pi$
$277$			15.5674i			0.935355i	−0.883899	+	0.467678i	$0.845091\pi$
$278$		0			0
$279$		−	4.78620i		−	0.286542i
$280$		0			0
$281$		−	18.8277i		−	1.12317i	−0.827420	−	0.561583i	$-0.810192\pi$
$281$		−	18.8277i		−	1.12317i	0.827420	−	0.561583i	$-0.189808\pi$
$282$		0			0
$283$		−	16.7014i		−	0.992798i	−0.868095	−	0.496399i	$-0.834655\pi$
$283$		−	16.7014i		−	0.992798i	0.868095	−	0.496399i	$-0.165345\pi$
$284$		0			0
$285$	−6.26830	+	13.6782i	−0.371302	+	0.810224i
$286$		0			0
$287$	19.5162	+	19.5162i	1.15200	+	1.15200i
$288$		0			0
$289$		−	18.3552i		−	1.07972i
$290$		0			0
$291$	−2.96112	+	2.96112i	−0.173584	+	0.173584i
$292$		0			0
$293$	18.1368			1.05956			0.529780	−	0.848135i	$-0.322274\pi$
$293$	18.1368			1.05956			0.529780	+	0.848135i	$0.322274\pi$
$294$		0			0
$295$	16.9528	+	7.76895i	0.987027	+	0.452326i
$296$		0			0
$297$	0.181897	+	0.181897i	0.0105548	+	0.0105548i
$298$		0			0
$299$	26.4495	−	26.4495i	1.52961	−	1.52961i
$300$		0			0
$301$	−10.8518	−	10.8518i	−0.625490	−	0.625490i
$302$		0			0
$303$	−0.596631	+	0.596631i	−0.0342756	+	0.0342756i
$304$		0			0
$305$	−10.3889	+	22.6699i	−0.594869	+	1.29807i
$306$		0			0
$307$		−	24.4651i		−	1.39630i	−0.715953	−	0.698148i	$-0.754008\pi$
$307$		−	24.4651i		−	1.39630i	0.715953	−	0.698148i	$-0.245992\pi$
$308$		0			0
$309$	9.06195	+	9.06195i	0.515517	+	0.515517i
$310$		0			0
$311$	−8.97669			−0.509022			−0.254511	−	0.967070i	$-0.581914\pi$
$311$	−8.97669			−0.509022			−0.254511	+	0.967070i	$0.581914\pi$
$312$		0			0
$313$	20.1248	−	20.1248i	1.13752	−	1.13752i	0.148625	−	0.988894i	$-0.452515\pi$
$313$	20.1248	−	20.1248i	1.13752	−	1.13752i	0.988894	−	0.148625i	$-0.0474849\pi$
$314$		0			0
$315$	7.01605	+	3.21525i	0.395309	+	0.181159i
$316$		0			0
$317$	4.43451			0.249067			0.124534	−	0.992215i	$-0.460257\pi$
$317$	4.43451			0.249067			0.124534	+	0.992215i	$0.460257\pi$
$318$		0			0
$319$	0.309923			0.0173523
$320$		0			0
$321$	5.89771			0.329178
$322$		0			0
$323$	−40.0096			−2.22619
$324$		0			0
$325$	−15.0030	−	17.4064i	−0.832217	−	0.965536i
$326$		0			0
$327$	3.65602	−	3.65602i	0.202178	−	0.202178i
$328$		0			0
$329$	12.0352			0.663524
$330$		0			0
$331$	−0.546436	−	0.546436i	−0.0300348	−	0.0300348i	0.691930	−	0.721965i	$-0.256761\pi$
$331$	−0.546436	−	0.546436i	−0.0300348	−	0.0300348i	−0.721965	+	0.691930i	$0.756761\pi$
$332$		0			0
$333$		−	3.97976i		−	0.218089i
$334$		0			0
$335$	−15.8102	+	5.87328i	−0.863802	+	0.320892i
$336$		0			0
$337$	−17.8293	+	17.8293i	−0.971226	+	0.971226i	−0.999597	−	0.0283716i	$-0.990968\pi$
$337$	−17.8293	+	17.8293i	−0.971226	+	0.971226i	0.0283716	+	0.999597i	$0.490968\pi$
$338$		0			0
$339$	−6.39894	−	6.39894i	−0.347543	−	0.347543i
$340$		0			0
$341$	0.870596	−	0.870596i	0.0471454	−	0.0471454i
$342$		0			0
$343$	−5.09454	−	5.09454i	−0.275079	−	0.275079i
$344$		0			0
$345$	−7.58170	+	16.5442i	−0.408185	+	0.890707i
$346$		0			0
$347$	15.6158			0.838301			0.419151	−	0.907917i	$-0.362328\pi$
$347$	15.6158			0.838301			0.419151	+	0.907917i	$0.362328\pi$
$348$		0			0
$349$	4.71294	−	4.71294i	0.252278	−	0.252278i	−0.569626	−	0.821904i	$-0.692912\pi$
$349$	4.71294	−	4.71294i	0.252278	−	0.252278i	0.821904	+	0.569626i	$0.192912\pi$
$350$		0			0
$351$			4.59597i			0.245315i
$352$		0			0
$353$	19.3304	+	19.3304i	1.02885	+	1.02885i	0.999571	+	0.0292825i	$0.00932226\pi$
$353$	19.3304	+	19.3304i	1.02885	+	1.02885i	0.0292825	+	0.999571i	$0.490678\pi$
$354$		0			0
$355$	4.94239	+	13.3043i	0.262315	+	0.706120i
$356$		0			0
$357$			20.5224i			1.08616i
$358$		0			0
$359$		−	17.4634i		−	0.921685i	−0.887482	−	0.460842i	$-0.847547\pi$
$359$		−	17.4634i		−	0.921685i	0.887482	−	0.460842i	$-0.152453\pi$
$360$		0			0
$361$			26.2767i			1.38298i
$362$		0			0
$363$		−	10.9338i		−	0.573877i
$364$		0			0
$365$	13.7678	+	6.30938i	0.720639	+	0.330248i
$366$		0			0
$367$	18.8168	+	18.8168i	0.982231	+	0.982231i	0.999845	−	0.0176142i	$-0.00560705\pi$
$367$	18.8168	+	18.8168i	0.982231	+	0.982231i	−0.0176142	+	0.999845i	$0.505607\pi$
$368$		0			0
$369$		−	7.99664i		−	0.416289i
$370$		0			0
$371$	−12.0660	+	12.0660i	−0.626435	+	0.626435i
$372$		0			0
$373$	−31.8481			−1.64903			−0.824515	−	0.565840i	$-0.808552\pi$
$373$	−31.8481			−1.64903			−0.824515	+	0.565840i	$0.808552\pi$
$374$		0			0
$375$	9.79159	+	5.39673i	0.505636	+	0.278686i
$376$		0			0
$377$	3.91539	+	3.91539i	0.201653	+	0.201653i
$378$		0			0
$379$	−11.5085	+	11.5085i	−0.591153	+	0.591153i	−0.937943	−	0.346790i	$-0.887272\pi$
$379$	−11.5085	+	11.5085i	−0.591153	+	0.591153i	0.346790	+	0.937943i	$0.387272\pi$
$380$		0			0
$381$	−6.86114	−	6.86114i	−0.351507	−	0.351507i
$382$		0			0
$383$	19.7097	−	19.7097i	1.00712	−	1.00712i	0.00714591	−	0.999974i	$-0.497725\pi$
$383$	19.7097	−	19.7097i	1.00712	−	1.00712i	0.999974	−	0.00714591i	$-0.00227463\pi$
$384$		0			0
$385$	0.691355	+	1.86104i	0.0352347	+	0.0948476i
$386$		0			0
$387$			4.44648i			0.226027i
$388$		0			0
$389$	−7.83824	−	7.83824i	−0.397414	−	0.397414i	0.479906	−	0.877320i	$-0.340671\pi$
$389$	−7.83824	−	7.83824i	−0.397414	−	0.397414i	−0.877320	+	0.479906i	$0.840671\pi$
$390$		0			0
$391$	−48.3928			−2.44733
$392$		0			0
$393$	−1.09665	+	1.09665i	−0.0553187	+	0.0553187i
$394$		0			0
$395$	2.98812	+	8.04366i	0.150349	+	0.404721i
$396$		0			0
$397$	−24.4147			−1.22534			−0.612670	−	0.790339i	$-0.709905\pi$
$397$	−24.4147			−1.22534			−0.612670	+	0.790339i	$0.709905\pi$
$398$		0			0
$399$	23.2241			1.16266
$400$		0			0
$401$	14.7988			0.739016			0.369508	−	0.929228i	$-0.379526\pi$
$401$	14.7988			0.739016			0.369508	+	0.929228i	$0.379526\pi$
$402$		0			0
$403$	21.9972			1.09576
$404$		0			0
$405$	−0.778677	−	2.09611i	−0.0386928	−	0.104156i
$406$		0			0
$407$	0.723907	−	0.723907i	0.0358827	−	0.0358827i
$408$		0			0
$409$	−19.2953			−0.954092			−0.477046	−	0.878878i	$-0.658292\pi$
$409$	−19.2953			−0.954092			−0.477046	+	0.878878i	$0.658292\pi$
$410$		0			0
$411$	12.2428	+	12.2428i	0.603895	+	0.603895i
$412$		0			0
$413$		−	28.7841i		−	1.41637i
$414$		0			0
$415$	4.86928	+	13.1075i	0.239023	+	0.643423i
$416$		0			0
$417$	−3.39535	+	3.39535i	−0.166271	+	0.166271i
$418$		0			0
$419$	1.76149	+	1.76149i	0.0860546	+	0.0860546i	0.748824	−	0.662769i	$-0.230619\pi$
$419$	1.76149	+	1.76149i	0.0860546	+	0.0860546i	−0.662769	+	0.748824i	$0.730619\pi$
$420$		0			0
$421$	−15.1301	+	15.1301i	−0.737397	+	0.737397i	−0.972074	−	0.234677i	$-0.924597\pi$
$421$	−15.1301	+	15.1301i	−0.737397	+	0.737397i	0.234677	+	0.972074i	$0.424597\pi$
$422$		0			0
$423$	−2.46569	−	2.46569i	−0.119886	−	0.119886i
$424$		0			0
$425$	−2.19870	+	29.6487i	−0.106653	+	1.43817i
$426$		0			0
$427$	38.4912			1.86272
$428$		0			0
$429$	−0.835995	+	0.835995i	−0.0403622	+	0.0403622i
$430$		0			0
$431$			35.7121i			1.72019i	0.510133	+	0.860095i	$0.329596\pi$
$431$			35.7121i			1.72019i	−0.510133	+	0.860095i	$0.670404\pi$
$432$		0			0
$433$	24.8355	+	24.8355i	1.19352	+	1.19352i	0.976072	+	0.217448i	$0.0697734\pi$
$433$	24.8355	+	24.8355i	1.19352	+	1.19352i	0.217448	+	0.976072i	$0.430227\pi$
$434$		0			0
$435$	−2.44908	−	1.12234i	−0.117424	−	0.0538121i
$436$		0			0
$437$			54.7636i			2.61970i
$438$		0			0
$439$			4.09956i			0.195661i	0.995203	+	0.0978307i	$0.0311904\pi$
$439$			4.09956i			0.195661i	−0.995203	+	0.0978307i	$0.968810\pi$
$440$		0			0
$441$		−	4.91254i		−	0.233931i
$442$		0			0
$443$			1.17693i			0.0559176i	0.999609	+	0.0279588i	$0.00890072\pi$
$443$			1.17693i			0.0559176i	−0.999609	+	0.0279588i	$0.991099\pi$
$444$		0			0
$445$	3.91298	+	10.5333i	0.185493	+	0.499326i
$446$		0			0
$447$	−7.84547	−	7.84547i	−0.371078	−	0.371078i
$448$		0			0
$449$		−	18.3494i		−	0.865962i	−0.901403	−	0.432981i	$-0.857462\pi$
$449$		−	18.3494i		−	0.865962i	0.901403	−	0.432981i	$-0.142538\pi$
$450$		0			0
$451$	1.45457	−	1.45457i	0.0684929	−	0.0684929i
$452$		0			0
$453$	−3.19389			−0.150062
$454$		0			0
$455$	−14.7772	+	32.2456i	−0.692766	+	1.51170i
$456$		0			0
$457$	18.0522	+	18.0522i	0.844446	+	0.844446i	0.989434	−	0.144987i	$-0.0463141\pi$
$457$	18.0522	+	18.0522i	0.844446	+	0.844446i	−0.144987	+	0.989434i	$0.546314\pi$
$458$		0			0
$459$	4.20448	−	4.20448i	0.196248	−	0.196248i
$460$		0			0
$461$	−23.5968	−	23.5968i	−1.09901	−	1.09901i	−0.994526	−	0.104487i	$-0.966680\pi$
$461$	−23.5968	−	23.5968i	−1.09901	−	1.09901i	−0.104487	−	0.994526i	$-0.533320\pi$
$462$		0			0
$463$	−20.2744	+	20.2744i	−0.942231	+	0.942231i	−0.998420	−	0.0561894i	$-0.982105\pi$
$463$	−20.2744	+	20.2744i	−0.942231	+	0.942231i	0.0561894	+	0.998420i	$0.482105\pi$
$464$		0			0
$465$	−10.0324	+	3.72690i	−0.465240	+	0.172831i
$466$		0			0
$467$			14.3565i			0.664340i	0.943220	+	0.332170i	$0.107781\pi$
$467$			14.3565i			0.664340i	−0.943220	+	0.332170i	$0.892219\pi$
$468$		0			0
$469$	18.4082	+	18.4082i	0.850010	+	0.850010i
$470$		0			0
$471$	17.6595			0.813707
$472$		0			0
$473$	−0.808802	+	0.808802i	−0.0371888	+	0.0371888i
$474$		0			0
$475$	33.5518	+	2.48815i	1.53946	+	0.114164i
$476$		0			0
$477$	4.94396			0.226369
$478$		0			0
$479$	−4.43555			−0.202665			−0.101333	−	0.994853i	$-0.532311\pi$
$479$	−4.43555			−0.202665			−0.101333	+	0.994853i	$0.532311\pi$
$480$		0			0
$481$	18.2909			0.833991
$482$		0			0
$483$	28.0903			1.27815
$484$		0			0
$485$	8.51257	+	3.90106i	0.386536	+	0.177138i
$486$		0			0
$487$	22.1931	−	22.1931i	1.00566	−	1.00566i	0.00568049	−	0.999984i	$-0.498192\pi$
$487$	22.1931	−	22.1931i	1.00566	−	1.00566i	0.999984	−	0.00568049i	$-0.00180817\pi$
$488$		0			0
$489$	−8.01355			−0.362385
$490$		0			0
$491$	−20.7625	−	20.7625i	−0.936997	−	0.936997i	0.0611325	−	0.998130i	$-0.480529\pi$
$491$	−20.7625	−	20.7625i	−0.936997	−	0.936997i	−0.998130	+	0.0611325i	$0.980529\pi$
$492$		0			0
$493$		−	7.16373i		−	0.322638i
$494$		0			0
$495$	0.239637	−	0.522915i	0.0107709	−	0.0235033i
$496$		0			0
$497$	15.4905	−	15.4905i	0.694846	−	0.694846i
$498$		0			0
$499$	−8.27712	−	8.27712i	−0.370535	−	0.370535i	0.497137	−	0.867672i	$-0.334385\pi$
$499$	−8.27712	−	8.27712i	−0.370535	−	0.370535i	−0.867672	+	0.497137i	$0.834385\pi$
$500$		0			0
$501$	8.45631	−	8.45631i	0.377800	−	0.377800i
$502$		0			0
$503$	10.2485	+	10.2485i	0.456958	+	0.456958i	0.897656	−	0.440698i	$-0.145269\pi$
$503$	10.2485	+	10.2485i	0.456958	+	0.456958i	−0.440698	+	0.897656i	$0.645269\pi$
$504$		0			0
$505$	1.71519	+	0.786019i	0.0763247	+	0.0349774i
$506$		0			0
$507$	−8.12298			−0.360754
$508$		0			0
$509$	−26.3354	+	26.3354i	−1.16730	+	1.16730i	−0.184455	+	0.982841i	$0.559052\pi$
$509$	−26.3354	+	26.3354i	−1.16730	+	1.16730i	−0.982841	+	0.184455i	$0.940948\pi$
$510$		0			0
$511$		−	23.3763i		−	1.03411i
$512$		0			0
$513$	−4.75798	−	4.75798i	−0.210070	−	0.210070i
$514$		0			0
$515$	11.9385	−	26.0512i	0.526072	−	1.14795i
$516$		0			0
$517$		−	0.897003i		−	0.0394501i
$518$		0			0
$519$			5.11465i			0.224508i
$520$		0			0
$521$		−	21.8449i		−	0.957042i	−0.878076	−	0.478521i	$-0.841173\pi$
$521$		−	21.8449i		−	0.957042i	0.878076	−	0.478521i	$-0.158827\pi$
$522$		0			0
$523$		−	10.0725i		−	0.440439i	−0.975450	−	0.220220i	$-0.929323\pi$
$523$		−	10.0725i		−	0.440439i	0.975450	−	0.220220i	$-0.0706774\pi$
$524$		0			0
$525$	1.27627	−	17.2100i	0.0557008	−	0.751107i
$526$		0			0
$527$	−20.1234	−	20.1234i	−0.876591	−	0.876591i
$528$		0			0
$529$			43.2382i			1.87992i
$530$		0			0
$531$	−5.89705	+	5.89705i	−0.255910	+	0.255910i
$532$		0			0
$533$	36.7524			1.59192
$534$		0			0
$535$	−4.59241	−	12.3622i	−0.198547	−	0.534465i
$536$		0			0
$537$	4.67625	+	4.67625i	0.201795	+	0.201795i
$538$		0			0
$539$	0.893579	−	0.893579i	0.0384892	−	0.0384892i
$540$		0			0
$541$	4.27091	+	4.27091i	0.183621	+	0.183621i	0.792932	−	0.609311i	$-0.208554\pi$
$541$	4.27091	+	4.27091i	0.183621	+	0.183621i	−0.609311	+	0.792932i	$0.708554\pi$
$542$		0			0
$543$	5.45166	−	5.45166i	0.233953	−	0.233953i
$544$		0			0
$545$	−10.5103	−	4.81654i	−0.450210	−	0.206318i
$546$		0			0
$547$		−	3.62983i		−	0.155200i	−0.996985	−	0.0776001i	$-0.975274\pi$
$547$		−	3.62983i		−	0.155200i	0.996985	−	0.0776001i	$-0.0247257\pi$
$548$		0			0
$549$	−7.88576	−	7.88576i	−0.336556	−	0.336556i
$550$		0			0
$551$	−8.10680			−0.345361
$552$		0			0
$553$	9.36543	−	9.36543i	0.398259	−	0.398259i
$554$		0			0
$555$	−8.34199	+	3.09895i	−0.354098	+	0.131543i
$556$		0			0
$557$	23.6824			1.00345			0.501727	−	0.865026i	$-0.332698\pi$
$557$	23.6824			1.00345			0.501727	+	0.865026i	$0.332698\pi$
$558$		0			0
$559$	−20.4359			−0.864346
$560$		0			0
$561$	1.52957			0.0645783
$562$		0			0
$563$	10.0778			0.424727			0.212364	−	0.977191i	$-0.431884\pi$
$563$	10.0778			0.424727			0.212364	+	0.977191i	$0.431884\pi$
$564$		0			0
$565$	−8.43015	+	18.3956i	−0.354659	+	0.773907i
$566$		0			0
$567$	−2.44055	+	2.44055i	−0.102493	+	0.102493i
$568$		0			0
$569$	17.6744			0.740950			0.370475	−	0.928842i	$-0.379195\pi$
$569$	17.6744			0.740950			0.370475	+	0.928842i	$0.379195\pi$
$570$		0			0
$571$	−11.6390	−	11.6390i	−0.487078	−	0.487078i	0.420305	−	0.907383i	$-0.361923\pi$
$571$	−11.6390	−	11.6390i	−0.487078	−	0.487078i	−0.907383	+	0.420305i	$0.861923\pi$
$572$		0			0
$573$			14.1293i			0.590258i
$574$		0			0
$575$	40.5820	+	3.00949i	1.69239	+	0.125505i
$576$		0			0
$577$	20.4055	−	20.4055i	0.849494	−	0.849494i	−0.140576	−	0.990070i	$-0.544895\pi$
$577$	20.4055	−	20.4055i	0.849494	−	0.849494i	0.990070	+	0.140576i	$0.0448954\pi$
$578$		0			0
$579$	−6.89094	−	6.89094i	−0.286378	−	0.286378i
$580$		0			0
$581$	15.2614	−	15.2614i	0.633150	−	0.633150i
$582$		0			0
$583$	0.899294	+	0.899294i	0.0372449	+	0.0372449i
$584$		0			0
$585$	9.63365	−	3.57878i	0.398302	−	0.147964i
$586$		0			0
$587$	45.2307			1.86687			0.933436	−	0.358745i	$-0.116795\pi$
$587$	45.2307			1.86687			0.933436	+	0.358745i	$0.116795\pi$
$588$		0			0
$589$	−22.7726	+	22.7726i	−0.938329	+	0.938329i
$590$		0			0
$591$		−	21.6079i		−	0.888831i
$592$		0			0
$593$	−11.0242	−	11.0242i	−0.452710	−	0.452710i	0.443543	−	0.896253i	$-0.353721\pi$
$593$	−11.0242	−	11.0242i	−0.452710	−	0.452710i	−0.896253	+	0.443543i	$0.853721\pi$
$594$		0			0
$595$	43.0172	−	15.9804i	1.76353	−	0.655131i
$596$		0			0
$597$			8.16771i			0.334282i
$598$		0			0
$599$		−	0.523855i		−	0.0214041i	−0.999943	−	0.0107021i	$-0.996593\pi$
$599$		−	0.523855i		−	0.0214041i	0.999943	−	0.0107021i	$-0.00340664\pi$
$600$		0			0
$601$		−	19.7299i		−	0.804801i	−0.915464	−	0.402401i	$-0.868176\pi$
$601$		−	19.7299i		−	0.804801i	0.915464	−	0.402401i	$-0.131824\pi$
$602$		0			0
$603$		−	7.54264i		−	0.307160i
$604$		0			0
$605$	−22.9185	+	8.51392i	−0.931768	+	0.346140i
$606$		0			0
$607$	11.4651	+	11.4651i	0.465352	+	0.465352i	0.900405	−	0.435053i	$-0.143270\pi$
$607$	11.4651	+	11.4651i	0.465352	+	0.465352i	−0.435053	+	0.900405i	$0.643270\pi$
$608$		0			0
$609$			4.15829i			0.168502i
$610$		0			0
$611$	11.3322	−	11.3322i	0.458453	−	0.458453i
$612$		0			0
$613$	5.53021			0.223363			0.111682	−	0.993744i	$-0.464376\pi$
$613$	5.53021			0.223363			0.111682	+	0.993744i	$0.464376\pi$
$614$		0			0
$615$	−16.7618	+	6.22680i	−0.675901	+	0.251089i
$616$		0			0
$617$	28.8633	+	28.8633i	1.16199	+	1.16199i	0.984039	+	0.177952i	$0.0569472\pi$
$617$	28.8633	+	28.8633i	1.16199	+	1.16199i	0.177952	+	0.984039i	$0.443053\pi$
$618$		0			0
$619$	−24.3467	+	24.3467i	−0.978577	+	0.978577i	−0.999775	−	0.0211987i	$-0.993252\pi$
$619$	−24.3467	+	24.3467i	−0.978577	+	0.978577i	0.0211987	+	0.999775i	$0.493252\pi$
$620$		0			0
$621$	−5.75492	−	5.75492i	−0.230937	−	0.230937i
$622$		0			0
$623$	12.2642	−	12.2642i	0.491353	−	0.491353i
$624$		0			0
$625$	3.68764	−	24.7265i	0.147506	−	0.989061i
$626$		0			0
$627$		−	1.73093i		−	0.0691265i
$628$		0			0
$629$	−16.7328	−	16.7328i	−0.667180	−	0.667180i
$630$		0			0
$631$	−20.5195			−0.816870			−0.408435	−	0.912787i	$-0.633925\pi$
$631$	−20.5195			−0.816870			−0.408435	+	0.912787i	$0.633925\pi$
$632$		0			0
$633$	9.64189	−	9.64189i	0.383231	−	0.383231i
$634$		0			0
$635$	−9.03906	+	19.7243i	−0.358704	+	0.782734i
$636$		0			0
$637$	22.5779			0.894570
$638$		0			0
$639$	−6.34716			−0.251090
$640$		0			0
$641$	−12.4196			−0.490546			−0.245273	−	0.969454i	$-0.578878\pi$
$641$	−12.4196			−0.490546			−0.245273	+	0.969454i	$0.578878\pi$
$642$		0			0
$643$	−45.7180			−1.80294			−0.901472	−	0.432838i	$-0.857512\pi$
$643$	−45.7180			−1.80294			−0.901472	+	0.432838i	$0.857512\pi$
$644$		0			0
$645$	9.32029	−	3.46237i	0.366986	−	0.136331i
$646$		0			0
$647$	24.2897	−	24.2897i	0.954925	−	0.954925i	−0.0441018	−	0.999027i	$-0.514043\pi$
$647$	24.2897	−	24.2897i	0.954925	−	0.954925i	0.999027	+	0.0441018i	$0.0140426\pi$
$648$		0			0
$649$	−2.14532			−0.0842110
$650$		0			0
$651$	11.6809	+	11.6809i	0.457812	+	0.457812i
$652$		0			0
$653$		−	33.3219i		−	1.30399i	−0.758225	−	0.651993i	$-0.773933\pi$
$653$		−	33.3219i		−	1.30399i	0.758225	−	0.651993i	$-0.226067\pi$
$654$		0			0
$655$	3.15263	+	1.44476i	0.123184	+	0.0564514i
$656$		0			0
$657$	−4.78916	+	4.78916i	−0.186843	+	0.186843i
$658$		0			0
$659$	13.3564	+	13.3564i	0.520292	+	0.520292i	0.917660	−	0.397367i	$-0.130076\pi$
$659$	13.3564	+	13.3564i	0.520292	+	0.520292i	−0.397367	+	0.917660i	$0.630076\pi$
$660$		0			0
$661$	−22.8218	+	22.8218i	−0.887664	+	0.887664i	−0.994298	−	0.106635i	$-0.965992\pi$
$661$	−22.8218	+	22.8218i	−0.887664	+	0.887664i	0.106635	+	0.994298i	$0.465992\pi$
$662$		0			0
$663$	19.3237	+	19.3237i	0.750469	+	0.750469i
$664$		0			0
$665$	−18.0841	−	48.6803i	−0.701272	−	1.88774i
$666$		0			0
$667$	−9.80543			−0.379668
$668$		0			0
$669$	13.5811	−	13.5811i	0.525074	−	0.525074i
$670$		0			0
$671$		−	2.86880i		−	0.110749i
$672$		0			0
$673$	19.9234	+	19.9234i	0.767989	+	0.767989i	0.977752	−	0.209763i	$-0.0672693\pi$
$673$	19.9234	+	19.9234i	0.767989	+	0.767989i	−0.209763	+	0.977752i	$0.567269\pi$
$674$		0			0
$675$	−3.78732	+	3.26438i	−0.145774	+	0.125646i
$676$		0			0
$677$			3.27932i			0.126035i	0.998012	+	0.0630173i	$0.0200723\pi$
$677$			3.27932i			0.126035i	−0.998012	+	0.0630173i	$0.979928\pi$
$678$		0			0
$679$		−	14.4535i		−	0.554674i
$680$		0			0
$681$			13.3355i			0.511018i
$682$		0			0
$683$			0.304845i			0.0116646i	0.999983	+	0.00583228i	$0.00185648\pi$
$683$			0.304845i			0.0116646i	−0.999983	+	0.00583228i	$0.998144\pi$
$684$		0			0
$685$	16.1291	−	35.1955i	0.616261	−	1.34475i
$686$		0			0
$687$	17.5166	+	17.5166i	0.668300	+	0.668300i
$688$		0			0
$689$			22.7223i			0.865652i
$690$		0			0
$691$	4.70048	−	4.70048i	0.178815	−	0.178815i	−0.612024	−	0.790839i	$-0.709645\pi$
$691$	4.70048	−	4.70048i	0.178815	−	0.178815i	0.790839	+	0.612024i	$0.209645\pi$
$692$		0			0
$693$	−0.887858			−0.0337269
$694$		0			0
$695$	9.76090	+	4.47314i	0.370252	+	0.169676i
$696$		0			0
$697$	−33.6217	−	33.6217i	−1.27351	−	1.27351i
$698$		0			0
$699$	−5.53768	+	5.53768i	−0.209454	+	0.209454i
$700$		0			0
$701$	32.6716	+	32.6716i	1.23399	+	1.23399i	0.962418	+	0.271572i	$0.0875434\pi$
$701$	32.6716	+	32.6716i	1.23399	+	1.23399i	0.271572	+	0.962418i	$0.412457\pi$
$702$		0			0
$703$	−18.9356	+	18.9356i	−0.714169	+	0.714169i
$704$		0			0
$705$	−3.24837	+	7.08831i	−0.122341	+	0.266961i
$706$		0			0
$707$		−	2.91221i		−	0.109525i
$708$		0			0
$709$	−9.52932	−	9.52932i	−0.357881	−	0.357881i	0.505150	−	0.863031i	$-0.331437\pi$
$709$	−9.52932	−	9.52932i	−0.357881	−	0.357881i	−0.863031	+	0.505150i	$0.831437\pi$
$710$		0			0
$711$	−3.83743			−0.143915
$712$		0			0
$713$	−27.5442	+	27.5442i	−1.03154	+	1.03154i
$714$		0			0
$715$	2.40331	+	1.10136i	0.0898785	+	0.0411887i
$716$		0			0
$717$	7.70031			0.287573
$718$		0			0
$719$	0.471667			0.0175902			0.00879511	−	0.999961i	$-0.497200\pi$
$719$	0.471667			0.0175902			0.00879511	+	0.999961i	$0.497200\pi$
$720$		0			0
$721$	−44.2323			−1.64730
$722$		0			0
$723$	−27.9273			−1.03863
$724$		0			0
$725$	−0.445504	+	6.00747i	−0.0165456	+	0.223112i
$726$		0			0
$727$	−37.3759	+	37.3759i	−1.38620	+	1.38620i	−0.553045	+	0.833152i	$0.686534\pi$
$727$	−37.3759	+	37.3759i	−1.38620	+	1.38620i	−0.833152	+	0.553045i	$0.813466\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	18.6951	+	18.6951i	0.691463	+	0.691463i
$732$		0			0
$733$			24.0502i			0.888314i	0.895949	+	0.444157i	$0.146497\pi$
$733$			24.0502i			0.888314i	−0.895949	+	0.444157i	$0.853503\pi$
$734$		0			0
$735$	−10.2972	+	3.82529i	−0.379818	+	0.141098i
$736$		0			0
$737$	1.37199	−	1.37199i	0.0505377	−	0.0505377i
$738$		0			0
$739$	19.0456	+	19.0456i	0.700604	+	0.700604i	0.964540	−	0.263936i	$-0.0850208\pi$
$739$	19.0456	+	19.0456i	0.700604	+	0.700604i	−0.263936	+	0.964540i	$0.585021\pi$
$740$		0			0
$741$	21.8675	−	21.8675i	0.803324	−	0.803324i
$742$		0			0
$743$	−17.1881	−	17.1881i	−0.630569	−	0.630569i	0.317642	−	0.948211i	$-0.397109\pi$
$743$	−17.1881	−	17.1881i	−0.630569	−	0.630569i	−0.948211	+	0.317642i	$0.897109\pi$
$744$		0			0
$745$	−10.3358	+	22.5540i	−0.378676	+	0.826315i
$746$		0			0
$747$	−6.25327			−0.228795
$748$		0			0
$749$	−14.3936	+	14.3936i	−0.525932	+	0.525932i
$750$		0			0
$751$		−	36.8021i		−	1.34293i	−0.741037	−	0.671464i	$-0.765666\pi$
$751$		−	36.8021i		−	1.34293i	0.741037	−	0.671464i	$-0.234334\pi$
$752$		0			0
$753$	10.5948	+	10.5948i	0.386097	+	0.386097i
$754$		0			0
$755$	2.48701	+	6.69473i	0.0905114	+	0.243646i
$756$		0			0
$757$		−	2.17732i		−	0.0791360i	−0.999217	−	0.0395680i	$-0.987402\pi$
$757$		−	2.17732i		−	0.0791360i	0.999217	−	0.0395680i	$-0.0125982\pi$
$758$		0			0
$759$		−	2.09361i		−	0.0759932i
$760$		0			0
$761$			10.5601i			0.382803i	0.981512	+	0.191402i	$0.0613033\pi$
$761$			10.5601i			0.382803i	−0.981512	+	0.191402i	$0.938697\pi$
$762$		0			0
$763$			17.8454i			0.646046i
$764$		0			0
$765$	−12.0870	−	5.53910i	−0.437005	−	0.200267i
$766$		0			0
$767$	−27.1027	−	27.1027i	−0.978622	−	0.978622i
$768$		0			0
$769$			13.8582i			0.499739i	0.968279	+	0.249870i	$0.0803878\pi$
$769$			13.8582i			0.499739i	−0.968279	+	0.249870i	$0.919612\pi$
$770$		0			0
$771$	−9.86474	+	9.86474i	−0.355270	+	0.355270i
$772$		0			0
$773$	−18.6483			−0.670732			−0.335366	−	0.942088i	$-0.608860\pi$
$773$	−18.6483			−0.670732			−0.335366	+	0.942088i	$0.608860\pi$
$774$		0			0
$775$	15.6240	+	18.1269i	0.561230	+	0.651137i
$776$		0			0
$777$	9.71279	+	9.71279i	0.348444	+	0.348444i
$778$		0			0
$779$	−38.0478	+	38.0478i	−1.36321	+	1.36321i
$780$		0			0
$781$	−1.15453	−	1.15453i	−0.0413124	−	0.0413124i
$782$		0			0
$783$	0.851917	−	0.851917i	0.0304450	−	0.0304450i
$784$		0			0
$785$	−13.7511	−	37.0162i	−0.490796	−	1.32117i
$786$		0			0
$787$			29.1438i			1.03886i	0.854512	+	0.519432i	$0.173857\pi$
$787$			29.1438i			1.03886i	−0.854512	+	0.519432i	$0.826143\pi$
$788$		0			0
$789$	−5.45464	−	5.45464i	−0.194190	−	0.194190i
$790$		0			0
$791$	31.2338			1.11055
$792$		0			0
$793$	36.2428	−	36.2428i	1.28702	−	1.28702i
$794$		0			0
$795$	−3.84975	−	10.3631i	−0.136537	−	0.367540i
$796$		0			0
$797$	11.1042			0.393331			0.196665	−	0.980471i	$-0.436989\pi$
$797$	11.1042			0.393331			0.196665	+	0.980471i	$0.436989\pi$
$798$		0			0
$799$	−20.7338			−0.733510
$800$		0			0
$801$	−5.02517			−0.177556
$802$		0			0
$803$	−1.74227			−0.0614834
$804$		0			0
$805$	−21.8733	−	58.8803i	−0.770932	−	2.07526i
$806$		0			0
$807$	1.61579	−	1.61579i	0.0568784	−	0.0568784i
$808$		0			0
$809$	−27.7185			−0.974531			−0.487265	−	0.873254i	$-0.662006\pi$
$809$	−27.7185			−0.974531			−0.487265	+	0.873254i	$0.662006\pi$
$810$		0			0
$811$	−27.6491	−	27.6491i	−0.970891	−	0.970891i	0.0286974	−	0.999588i	$-0.490864\pi$
$811$	−27.6491	−	27.6491i	−0.970891	−	0.970891i	−0.999588	+	0.0286974i	$0.990864\pi$
$812$		0			0
$813$			6.09685i			0.213826i
$814$		0			0
$815$	6.23997	+	16.7972i	0.218576	+	0.588382i
$816$		0			0
$817$	21.1562	−	21.1562i	0.740163	−	0.740163i
$818$		0			0
$819$	−11.2167	−	11.2167i	−0.391943	−	0.391943i
$820$		0			0
$821$	10.7053	−	10.7053i	0.373616	−	0.373616i	−0.495176	−	0.868793i	$-0.664896\pi$
$821$	10.7053	−	10.7053i	0.373616	−	0.373616i	0.868793	+	0.495176i	$0.164896\pi$
$822$		0			0
$823$	−31.2787	−	31.2787i	−1.09031	−	1.09031i	−0.995495	−	0.0948116i	$-0.969775\pi$
$823$	−31.2787	−	31.2787i	−1.09031	−	1.09031i	−0.0948116	−	0.995495i	$-0.530225\pi$
$824$		0			0
$825$	−1.28269	−	0.0951219i	−0.0446574	−	0.00331172i
$826$		0			0
$827$	−53.4550			−1.85881			−0.929406	−	0.369060i	$-0.879680\pi$
$827$	−53.4550			−1.85881			−0.929406	+	0.369060i	$0.879680\pi$
$828$		0			0
$829$	4.10901	−	4.10901i	0.142712	−	0.142712i	−0.632141	−	0.774853i	$-0.717824\pi$
$829$	4.10901	−	4.10901i	0.142712	−	0.142712i	0.774853	+	0.632141i	$0.217824\pi$
$830$		0			0
$831$			15.5674i			0.540028i
$832$		0			0
$833$	−20.6547	−	20.6547i	−0.715642	−	0.715642i
$834$		0			0
$835$	−24.3101	−	11.1406i	−0.841284	−	0.385536i
$836$		0			0
$837$		−	4.78620i		−	0.165435i
$838$		0			0
$839$			4.01939i			0.138765i	0.997590	+	0.0693824i	$0.0221029\pi$
$839$			4.01939i			0.138765i	−0.997590	+	0.0693824i	$0.977897\pi$
$840$		0			0
$841$			27.5485i			0.949947i
$842$		0			0
$843$		−	18.8277i		−	0.648461i
$844$		0			0
$845$	6.32518	+	17.0266i	0.217593	+	0.585734i
$846$		0			0
$847$	26.6845	+	26.6845i	0.916891	+	0.916891i
$848$		0			0
$849$		−	16.7014i		−	0.573192i
$850$		0			0
$851$	−22.9032	+	22.9032i	−0.785111	+	0.785111i
$852$		0			0
$853$	19.7470			0.676126			0.338063	−	0.941123i	$-0.390228\pi$
$853$	19.7470			0.676126			0.338063	+	0.941123i	$0.390228\pi$
$854$		0			0
$855$	−6.26830	+	13.6782i	−0.214371	+	0.467783i
$856$		0			0
$857$	7.67020	+	7.67020i	0.262009	+	0.262009i	0.825870	−	0.563861i	$-0.190685\pi$
$857$	7.67020	+	7.67020i	0.262009	+	0.262009i	−0.563861	+	0.825870i	$0.690685\pi$
$858$		0			0
$859$	32.7389	−	32.7389i	1.11704	−	1.11704i	0.124862	−	0.992174i	$-0.460151\pi$
$859$	32.7389	−	32.7389i	1.11704	−	1.11704i	0.992174	−	0.124862i	$-0.0398487\pi$
$860$		0			0
$861$	19.5162	+	19.5162i	0.665110	+	0.665110i
$862$		0			0
$863$	−6.87701	+	6.87701i	−0.234096	+	0.234096i	−0.814400	−	0.580304i	$-0.802934\pi$
$863$	−6.87701	+	6.87701i	−0.234096	+	0.234096i	0.580304	+	0.814400i	$0.302934\pi$
$864$		0			0
$865$	10.7209	−	3.98266i	0.364520	−	0.135415i
$866$		0			0
$867$		−	18.3552i		−	0.623376i
$868$		0			0
$869$	−0.698018	−	0.698018i	−0.0236787	−	0.0236787i
$870$		0			0
$871$	34.6658			1.17460
$872$		0			0
$873$	−2.96112	+	2.96112i	−0.100219	+	0.100219i
$874$		0			0
$875$	−37.0678	+	10.7259i	−1.25312	+	0.362600i
$876$		0			0
$877$	10.5732			0.357030			0.178515	−	0.983937i	$-0.442871\pi$
$877$	10.5732			0.357030			0.178515	+	0.983937i	$0.442871\pi$
$878$		0			0
$879$	18.1368			0.611738
$880$		0			0
$881$	−53.2314			−1.79341			−0.896705	−	0.442628i	$-0.854046\pi$
$881$	−53.2314			−1.79341			−0.896705	+	0.442628i	$0.854046\pi$
$882$		0			0
$883$	12.9838			0.436939			0.218470	−	0.975844i	$-0.429894\pi$
$883$	12.9838			0.436939			0.218470	+	0.975844i	$0.429894\pi$
$884$		0			0
$885$	16.9528	+	7.76895i	0.569860	+	0.261150i
$886$		0			0
$887$	−13.3689	+	13.3689i	−0.448884	+	0.448884i	−0.894983	−	0.446100i	$-0.852813\pi$
$887$	−13.3689	+	13.3689i	−0.448884	+	0.448884i	0.446100	+	0.894983i	$0.352813\pi$
$888$		0			0
$889$	33.4899			1.12321
$890$		0			0
$891$	0.181897	+	0.181897i	0.00609379	+	0.00609379i
$892$		0			0
$893$			23.4633i			0.785171i
$894$		0			0
$895$	6.16062	−	13.4432i	0.205927	−	0.449357i
$896$		0			0
$897$	26.4495	−	26.4495i	0.883122	−	0.883122i
$898$		0			0
$899$	−4.07744	−	4.07744i	−0.135990	−	0.135990i
$900$		0			0
$901$	20.7868	−	20.7868i	0.692508	−	0.692508i
$902$		0			0
$903$	−10.8518	−	10.8518i	−0.361127	−	0.361127i
$904$		0			0
$905$	−15.6723	−	7.18217i	−0.520966	−	0.238744i
$906$		0			0
$907$	−12.5840			−0.417846			−0.208923	−	0.977932i	$-0.566996\pi$
$907$	−12.5840			−0.417846			−0.208923	+	0.977932i	$0.566996\pi$
$908$		0			0
$909$	−0.596631	+	0.596631i	−0.0197890	+	0.0197890i
$910$		0			0
$911$		−	39.5012i		−	1.30873i	−0.756177	−	0.654367i	$-0.772935\pi$
$911$		−	39.5012i		−	1.30873i	0.756177	−	0.654367i	$-0.227065\pi$
$912$		0			0
$913$	−1.13745	−	1.13745i	−0.0376442	−	0.0376442i
$914$		0			0
$915$	−10.3889	+	22.6699i	−0.343448	+	0.749443i
$916$		0			0
$917$		−	5.35286i		−	0.176767i
$918$		0			0
$919$		−	8.49556i		−	0.280243i	−0.990134	−	0.140121i	$-0.955251\pi$
$919$		−	8.49556i		−	0.280243i	0.990134	−	0.140121i	$-0.0447492\pi$
$920$		0			0
$921$		−	24.4651i		−	0.806152i
$922$		0			0
$923$		−	29.1714i		−	0.960188i
$924$		0			0
$925$	12.9914	+	15.0726i	0.427156	+	0.495585i
$926$		0			0
$927$	9.06195	+	9.06195i	0.297634	+	0.297634i
$928$		0			0
$929$		−	36.4760i		−	1.19674i	−0.801220	−	0.598369i	$-0.795816\pi$
$929$		−	36.4760i		−	1.19674i	0.801220	−	0.598369i	$-0.204184\pi$
$930$		0			0
$931$	−23.3738	+	23.3738i	−0.766044	+	0.766044i
$932$		0			0
$933$	−8.97669			−0.293884
$934$		0			0
$935$	−1.19104	−	3.20613i	−0.0389511	−	0.104852i
$936$		0			0
$937$	−12.8804	−	12.8804i	−0.420785	−	0.420785i	0.464689	−	0.885474i	$-0.346166\pi$
$937$	−12.8804	−	12.8804i	−0.420785	−	0.420785i	−0.885474	+	0.464689i	$0.846166\pi$
$938$		0			0
$939$	20.1248	−	20.1248i	0.656747	−	0.656747i
$940$		0			0
$941$	−38.8236	−	38.8236i	−1.26561	−	1.26561i	−0.948331	−	0.317284i	$-0.897229\pi$
$941$	−38.8236	−	38.8236i	−1.26561	−	1.26561i	−0.317284	−	0.948331i	$-0.602771\pi$
$942$		0			0
$943$	−46.0200	+	46.0200i	−1.49862	+	1.49862i
$944$		0			0
$945$	7.01605	+	3.21525i	0.228232	+	0.104592i
$946$		0			0
$947$		−	28.4262i		−	0.923727i	−0.886951	−	0.461864i	$-0.847181\pi$
$947$		−	28.4262i		−	0.923727i	0.886951	−	0.461864i	$-0.152819\pi$
$948$		0			0
$949$	−22.0109	−	22.0109i	−0.714503	−	0.714503i
$950$		0			0
$951$	4.43451			0.143799
$952$		0			0
$953$	−8.00013	+	8.00013i	−0.259150	+	0.259150i	−0.824708	−	0.565559i	$-0.808661\pi$
$953$	−8.00013	+	8.00013i	−0.259150	+	0.259150i	0.565559	+	0.824708i	$0.308661\pi$
$954$		0			0
$955$	29.6164	−	11.0021i	0.958365	−	0.356021i
$956$		0			0
$957$	0.309923			0.0100184
$958$		0			0
$959$	−59.7585			−1.92970
$960$		0			0
$961$	8.09232			0.261042
$962$		0			0
$963$	5.89771			0.190051
$964$		0			0
$965$	−9.07833	+	19.8100i	−0.292242	+	0.637705i
$966$		0			0
$967$	7.65095	−	7.65095i	0.246038	−	0.246038i	−0.573304	−	0.819342i	$-0.694339\pi$
$967$	7.65095	−	7.65095i	0.246038	−	0.246038i	0.819342	+	0.573304i	$0.194339\pi$
$968$		0			0
$969$	−40.0096			−1.28529
$970$		0			0
$971$	−24.7008	−	24.7008i	−0.792686	−	0.792686i	0.189244	−	0.981930i	$-0.439396\pi$
$971$	−24.7008	−	24.7008i	−0.792686	−	0.792686i	−0.981930	+	0.189244i	$0.939396\pi$
$972$		0			0
$973$		−	16.5730i		−	0.531307i
$974$		0			0
$975$	−15.0030	−	17.4064i	−0.480481	−	0.557452i
$976$		0			0
$977$	−32.8119	+	32.8119i	−1.04975	+	1.04975i	−0.0510499	+	0.998696i	$0.516257\pi$
$977$	−32.8119	+	32.8119i	−1.04975	+	1.04975i	−0.998696	+	0.0510499i	$0.983743\pi$
$978$		0			0
$979$	−0.914065	−	0.914065i	−0.0292136	−	0.0292136i
$980$		0			0
$981$	3.65602	−	3.65602i	0.116728	−	0.116728i
$982$		0			0
$983$	6.75408	+	6.75408i	0.215422	+	0.215422i	0.806566	−	0.591144i	$-0.201324\pi$
$983$	6.75408	+	6.75408i	0.215422	+	0.215422i	−0.591144	+	0.806566i	$0.701324\pi$
$984$		0			0
$985$	−45.2925	+	16.8256i	−1.44314	+	0.536108i
$986$		0			0
$987$	12.0352			0.383086
$988$		0			0
$989$	25.5891	−	25.5891i	0.813687	−	0.813687i
$990$		0			0
$991$		−	16.3088i		−	0.518067i	−0.965868	−	0.259033i	$-0.916596\pi$
$991$		−	16.3088i		−	0.518067i	0.965868	−	0.259033i	$-0.0834039\pi$
$992$		0			0
$993$	−0.546436	−	0.546436i	−0.0173406	−	0.0173406i
$994$		0			0
$995$	17.1204	−	6.36001i	0.542753	−	0.201626i
$996$		0			0
$997$		−	18.2727i		−	0.578702i	−0.957223	−	0.289351i	$-0.906561\pi$
$997$		−	18.2727i		−	0.578702i	0.957223	−	0.289351i	$-0.0934394\pi$
$998$		0			0
$999$		−	3.97976i		−	0.125914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.y.l.223.4		20
4.3	odd	2		1920.2.y.k.223.4		20
5.2	odd	4		1920.2.bc.k.607.10		20
8.3	odd	2		960.2.y.f.943.7		20
8.5	even	2		240.2.y.f.163.9	✓	20
16.3	odd	4		240.2.bc.f.43.4	yes	20
16.5	even	4		1920.2.bc.l.1183.10		20
16.11	odd	4		1920.2.bc.k.1183.10		20
16.13	even	4		960.2.bc.f.463.1		20
20.7	even	4		1920.2.bc.l.607.10		20
24.5	odd	2		720.2.z.h.163.2		20
40.27	even	4		960.2.bc.f.367.1		20
40.37	odd	4		240.2.bc.f.67.4	yes	20
48.35	even	4		720.2.bd.h.523.7		20
80.27	even	4	inner	1920.2.y.l.1567.4		20
80.37	odd	4		1920.2.y.k.1567.4		20
80.67	even	4		240.2.y.f.187.9	yes	20
80.77	odd	4		960.2.y.f.847.7		20
120.77	even	4		720.2.bd.h.307.7		20
240.227	odd	4		720.2.z.h.667.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.f.163.9	✓	20	8.5	even	2
240.2.y.f.187.9	yes	20	80.67	even	4
240.2.bc.f.43.4	yes	20	16.3	odd	4
240.2.bc.f.67.4	yes	20	40.37	odd	4
720.2.z.h.163.2		20	24.5	odd	2
720.2.z.h.667.2		20	240.227	odd	4
720.2.bd.h.307.7		20	120.77	even	4
720.2.bd.h.523.7		20	48.35	even	4
960.2.y.f.847.7		20	80.77	odd	4
960.2.y.f.943.7		20	8.3	odd	2
960.2.bc.f.367.1		20	40.27	even	4
960.2.bc.f.463.1		20	16.13	even	4
1920.2.y.k.223.4		20	4.3	odd	2
1920.2.y.k.1567.4		20	80.37	odd	4
1920.2.y.l.223.4		20	1.1	even	1	trivial
1920.2.y.l.1567.4		20	80.27	even	4	inner
1920.2.bc.k.607.10		20	5.2	odd	4
1920.2.bc.k.1183.10		20	16.11	odd	4
1920.2.bc.l.607.10		20	20.7	even	4
1920.2.bc.l.1183.10		20	16.5	even	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(-0.778677 - 2.09611i) q^{5} +(-2.44055 + 2.44055i) q^{7} +1.00000 q^{9} +(0.181897 + 0.181897i) q^{11} +4.59597i q^{13} +(-0.778677 - 2.09611i) q^{15} +(4.20448 - 4.20448i) q^{17} +(-4.75798 - 4.75798i) q^{19} +(-2.44055 + 2.44055i) q^{21} +(-5.75492 - 5.75492i) q^{23} +(-3.78732 + 3.26438i) q^{25} +1.00000 q^{27} +(0.851917 - 0.851917i) q^{29} -4.78620i q^{31} +(0.181897 + 0.181897i) q^{33} +(7.01605 + 3.21525i) q^{35} -3.97976i q^{37} +4.59597i q^{39} -7.99664i q^{41} +4.44648i q^{43} +(-0.778677 - 2.09611i) q^{45} +(-2.46569 - 2.46569i) q^{47} -4.91254i q^{49} +(4.20448 - 4.20448i) q^{51} +4.94396 q^{53} +(0.239637 - 0.522915i) q^{55} +(-4.75798 - 4.75798i) q^{57} +(-5.89705 + 5.89705i) q^{59} +(-7.88576 - 7.88576i) q^{61} +(-2.44055 + 2.44055i) q^{63} +(9.63365 - 3.57878i) q^{65} -7.54264i q^{67} +(-5.75492 - 5.75492i) q^{69} -6.34716 q^{71} +(-4.78916 + 4.78916i) q^{73} +(-3.78732 + 3.26438i) q^{75} -0.887858 q^{77} -3.83743 q^{79} +1.00000 q^{81} -6.25327 q^{83} +(-12.0870 - 5.53910i) q^{85} +(0.851917 - 0.851917i) q^{87} -5.02517 q^{89} +(-11.2167 - 11.2167i) q^{91} -4.78620i q^{93} +(-6.26830 + 13.6782i) q^{95} +(-2.96112 + 2.96112i) q^{97} +(0.181897 + 0.181897i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} - 4 q^{7} + 20 q^{9} - 8 q^{11} + 12 q^{17} - 16 q^{19} - 4 q^{21} - 16 q^{23} + 4 q^{25} + 20 q^{27} - 8 q^{33} + 28 q^{35} + 12 q^{51} - 8 q^{53} - 4 q^{55} - 16 q^{57} + 16 q^{59} + 12 q^{61}+ \cdots - 8 q^{99}+O(q^{100}) \) 20 * q + 20 * q^3 - 4 * q^7 + 20 * q^9 - 8 * q^11 + 12 * q^17 - 16 * q^19 - 4 * q^21 - 16 * q^23 + 4 * q^25 + 20 * q^27 - 8 * q^33 + 28 * q^35 + 12 * q^51 - 8 * q^53 - 4 * q^55 - 16 * q^57 + 16 * q^59 + 12 * q^61 - 4 * q^63 + 4 * q^65 - 16 * q^69 - 20 * q^73 + 4 * q^75 + 48 * q^79 + 20 * q^81 + 24 * q^83 - 4 * q^85 + 40 * q^89 + 24 * q^91 - 72 * q^95 - 28 * q^97 - 8 * q^99

Introduction

L-functions

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