LMFDB - Embedded newform 960.2.y.f.847.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [960,2,Mod(847,960)] 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("960.847"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(960, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.y (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,20,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.66563859404$
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			847.7
Root			$-0.257862 - 1.39051i$ of defining polynomial
Character	$\chi$	$=$	960.847
Dual form			960.2.y.f.943.7

$q$-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 $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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	$-0.0238195\pi$
$7$	2.44055	+	2.44055i	0.922440	+	0.922440i	−0.0747612	+	0.997201i	$0.523819\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	0.181897	−	0.181897i	0.0548441	−	0.0548441i	−0.679153	−	0.733997i	$-0.737653\pi$
$11$	0.181897	−	0.181897i	0.0548441	−	0.0548441i	0.733997	+	0.679153i	$0.237653\pi$
$12$		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	0.999801	+	0.0199338i	$0.00634553\pi$
$17$	4.20448	+	4.20448i	1.01974	+	1.01974i	0.0199338	+	0.999801i	$0.493654\pi$
$18$		0			0
$19$	−4.75798	+	4.75798i	−1.09155	+	1.09155i	−0.0961919	+	0.995363i	$0.530666\pi$
$19$	−4.75798	+	4.75798i	−1.09155	+	1.09155i	−0.995363	+	0.0961919i	$0.969334\pi$
$20$		0			0
$21$	2.44055	+	2.44055i	0.532571	+	0.532571i
$22$		0			0
$23$	5.75492	−	5.75492i	1.19998	−	1.19998i	0.225813	−	0.974171i	$-0.427496\pi$
$23$	5.75492	−	5.75492i	1.19998	−	1.19998i	0.974171	−	0.225813i	$-0.0725040\pi$
$24$		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	$-0.285682\pi$
$29$	−0.851917	−	0.851917i	−0.158197	−	0.158197i	−0.781767	+	0.623570i	$0.785682\pi$
$30$		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	$0.214670\pi$
$41$			7.99664i			1.24887i	−0.781079	+	0.624433i	$0.785330\pi$
$42$		0			0
$43$		−	4.44648i		−	0.678081i	−0.940772	−	0.339041i	$-0.889898\pi$
$43$		−	4.44648i		−	0.678081i	0.940772	−	0.339041i	$-0.110102\pi$
$44$		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	$-0.668150\pi$
$47$	2.46569	−	2.46569i	0.359657	−	0.359657i	0.863687	+	0.504029i	$0.168150\pi$
$48$		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	$-0.610276\pi$
$53$	−4.94396			−0.679106			−0.339553	+	0.940587i	$0.610276\pi$
$54$		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	0.209976	−	0.977707i	$-0.432662\pi$
$59$	−5.89705	−	5.89705i	−0.767731	−	0.767731i	−0.977707	+	0.209976i	$0.932662\pi$
$60$		0			0
$61$	7.88576	−	7.88576i	1.00967	−	1.00967i	0.00971590	−	0.999953i	$-0.496907\pi$
$61$	7.88576	−	7.88576i	1.00967	−	1.00967i	0.999953	−	0.00971590i	$-0.00309271\pi$
$62$		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	$0.152416\pi$
$67$			7.54264i			0.921480i	−0.887535	+	0.460740i	$0.847584\pi$
$68$		0			0
$69$	5.75492	−	5.75492i	0.692811	−	0.692811i
$70$		0			0
$71$	6.34716			0.753269			0.376635	−	0.926362i	$-0.377081\pi$
$71$	6.34716			0.753269			0.376635	+	0.926362i	$0.377081\pi$
$72$		0			0
$73$	−4.78916	−	4.78916i	−0.560529	−	0.560529i	0.368929	−	0.929458i	$-0.379725\pi$
$73$	−4.78916	−	4.78916i	−0.560529	−	0.560529i	−0.929458	+	0.368929i	$0.879725\pi$
$74$		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	$-0.430740\pi$
$79$	3.83743			0.431745			0.215872	+	0.976422i	$0.430740\pi$
$80$		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	0.540615	−	0.841270i	$-0.318192\pi$
$97$	−2.96112	−	2.96112i	−0.300656	−	0.300656i	−0.841270	+	0.540615i	$0.818192\pi$
$98$		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	$-0.236634\pi$
$101$	0.596631	+	0.596631i	0.0593670	+	0.0593670i	−0.676800	+	0.736167i	$0.736634\pi$
$102$		0			0
$103$	−9.06195	+	9.06195i	−0.892901	+	0.892901i	−0.994795	−	0.101894i	$-0.967510\pi$
$103$	−9.06195	+	9.06195i	−0.892901	+	0.892901i	0.101894	+	0.994795i	$0.467510\pi$
$104$		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	$-0.329647\pi$
$109$	−3.65602	−	3.65602i	−0.350183	−	0.350183i	−0.860178	+	0.509995i	$0.829647\pi$
$110$		0			0
$111$		−	3.97976i		−	0.377742i
$112$		0			0
$113$	−6.39894	+	6.39894i	−0.601962	+	0.601962i	−0.940833	−	0.338871i	$-0.889955\pi$
$113$	−6.39894	+	6.39894i	−0.601962	+	0.601962i	0.338871	+	0.940833i	$0.389955\pi$
$114$		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	$-0.608335\pi$
$127$	6.86114	−	6.86114i	0.608827	−	0.608827i	0.942640	+	0.333812i	$0.108335\pi$
$128$		0			0
$129$		−	4.44648i		−	0.391491i
$130$		0			0
$131$	−1.09665	−	1.09665i	−0.0958148	−	0.0958148i	0.657575	−	0.753389i	$-0.271582\pi$
$131$	−1.09665	−	1.09665i	−0.0958148	−	0.0958148i	−0.753389	+	0.657575i	$0.771582\pi$
$132$		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	0.0470863	−	0.998891i	$-0.485006\pi$
$137$	12.2428	−	12.2428i	1.04598	−	1.04598i	0.998891	−	0.0470863i	$-0.0149936\pi$
$138$		0			0
$139$	−3.39535	−	3.39535i	−0.287990	−	0.287990i	0.548295	−	0.836285i	$-0.315277\pi$
$139$	−3.39535	−	3.39535i	−0.287990	−	0.287990i	−0.836285	+	0.548295i	$0.815277\pi$
$140$		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	$-0.599827\pi$
$149$	7.84547	−	7.84547i	0.642726	−	0.642726i	0.951225	+	0.308499i	$0.0998266\pi$
$150$		0			0
$151$	3.19389			0.259915			0.129957	−	0.991520i	$-0.458516\pi$
$151$	3.19389			0.259915			0.129957	+	0.991520i	$0.458516\pi$
$152$		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	$-0.748915\pi$
$157$	−17.6595			−1.40938			−0.704691	+	0.709514i	$0.748915\pi$
$158$		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	$-0.403122\pi$
$167$	−8.45631	−	8.45631i	−0.654369	−	0.654369i	−0.954042	+	0.299673i	$0.903122\pi$
$168$		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	−0.510411	−	0.859930i	$-0.670507\pi$
$179$	4.67625	−	4.67625i	0.349519	−	0.349519i	0.859930	+	0.510411i	$0.170507\pi$
$180$		0			0
$181$	−5.45166	−	5.45166i	−0.405219	−	0.405219i	0.474849	−	0.880067i	$-0.342503\pi$
$181$	−5.45166	−	5.45166i	−0.405219	−	0.405219i	−0.880067	+	0.474849i	$0.842503\pi$
$182$		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	−0.910197	−	0.414176i	$-0.864070\pi$
$193$	−6.89094	+	6.89094i	−0.496021	+	0.496021i	0.414176	+	0.910197i	$0.364070\pi$
$194$		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	0.956268	−	0.292493i	$-0.0944847\pi$
$211$	9.64189	+	9.64189i	0.663775	+	0.663775i	−0.292493	+	0.956268i	$0.594485\pi$
$212$		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	$-0.472345\pi$
$223$	−13.5811	−	13.5811i	−0.909456	−	0.909456i	−0.996228	+	0.0867726i	$0.972345\pi$
$224$		0			0
$225$	−3.78732	−	3.26438i	−0.252488	−	0.217625i
$226$		0			0
$227$		−	13.3355i		−	0.885109i	−0.896742	−	0.442554i	$-0.854072\pi$
$227$		−	13.3355i		−	0.885109i	0.896742	−	0.442554i	$-0.145928\pi$
$228$		0			0
$229$	−17.5166	+	17.5166i	−1.15753	+	1.15753i	−0.172525	+	0.985005i	$0.555193\pi$
$229$	−17.5166	+	17.5166i	−1.15753	+	1.15753i	−0.985005	+	0.172525i	$0.944807\pi$
$230$		0			0
$231$	0.887858			0.0584168
$232$		0			0
$233$	−5.53768	−	5.53768i	−0.362786	−	0.362786i	0.502052	−	0.864837i	$-0.332579\pi$
$233$	−5.53768	−	5.53768i	−0.362786	−	0.362786i	−0.864837	+	0.502052i	$0.832579\pi$
$234$		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	$-0.580117\pi$
$239$	−7.70031			−0.498092			−0.249046	+	0.968492i	$0.580117\pi$
$240$		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	−0.288684	−	0.957424i	$-0.593218\pi$
$251$	10.5948	−	10.5948i	0.668740	−	0.668740i	0.957424	+	0.288684i	$0.0932178\pi$
$252$		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	0.328989	−	0.944334i	$-0.393292\pi$
$257$	−9.86474	−	9.86474i	−0.615345	−	0.615345i	−0.944334	+	0.328989i	$0.893292\pi$
$258$		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	$-0.673563\pi$
$263$	5.45464	−	5.45464i	0.336348	−	0.336348i	0.854991	+	0.518643i	$0.173563\pi$
$264$		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	$-0.272192\pi$
$269$	−1.61579	−	1.61579i	−0.0985164	−	0.0985164i	−0.754647	+	0.656131i	$0.772192\pi$
$270$		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	$0.189808\pi$
$281$			18.8277i			1.12317i	−0.827420	+	0.561583i	$0.810192\pi$
$282$		0			0
$283$			16.7014i			0.992798i	0.868095	+	0.496399i	$0.165345\pi$
$283$			16.7014i			0.992798i	−0.868095	+	0.496399i	$0.834655\pi$
$284$		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	$-0.677726\pi$
$293$	−18.1368			−1.05956			−0.529780	+	0.848135i	$0.677726\pi$
$294$		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	$0.245992\pi$
$307$			24.4651i			1.39630i	−0.715953	+	0.698148i	$0.754008\pi$
$308$		0			0
$309$	−9.06195	+	9.06195i	−0.515517	+	0.515517i
$310$		0			0
$311$	8.97669			0.509022			0.254511	−	0.967070i	$-0.418086\pi$
$311$	8.97669			0.509022			0.254511	+	0.967070i	$0.418086\pi$
$312$		0			0
$313$	20.1248	+	20.1248i	1.13752	+	1.13752i	0.988894	+	0.148625i	$0.0474849\pi$
$313$	20.1248	+	20.1248i	1.13752	+	1.13752i	0.148625	+	0.988894i	$0.452515\pi$
$314$		0			0
$315$	7.01605	−	3.21525i	0.395309	−	0.181159i
$316$		0			0
$317$	−4.43451			−0.249067			−0.124534	−	0.992215i	$-0.539743\pi$
$317$	−4.43451			−0.249067			−0.124534	+	0.992215i	$0.539743\pi$
$318$		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	−0.721965	−	0.691930i	$-0.756761\pi$
$331$	−0.546436	+	0.546436i	−0.0300348	+	0.0300348i	0.691930	+	0.721965i	$0.256761\pi$
$332$		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	0.0283716	−	0.999597i	$-0.490968\pi$
$337$	−17.8293	−	17.8293i	−0.971226	−	0.971226i	−0.999597	+	0.0283716i	$0.990968\pi$
$338$		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	$-0.307088\pi$
$349$	−4.71294	−	4.71294i	−0.252278	−	0.252278i	−0.821904	+	0.569626i	$0.807088\pi$
$350$		0			0
$351$			4.59597i			0.245315i
$352$		0			0
$353$	19.3304	−	19.3304i	1.02885	−	1.02885i	0.0292825	−	0.999571i	$-0.490678\pi$
$353$	19.3304	−	19.3304i	1.02885	−	1.02885i	0.999571	−	0.0292825i	$-0.00932226\pi$
$354$		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	$-0.994393\pi$
$367$	−18.8168	+	18.8168i	−0.982231	+	0.982231i	0.0176142	+	0.999845i	$0.494393\pi$
$368$		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	$-0.191448\pi$
$373$	31.8481			1.64903			0.824515	+	0.565840i	$0.191448\pi$
$374$		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	0.346790	−	0.937943i	$-0.387272\pi$
$379$	−11.5085	−	11.5085i	−0.591153	−	0.591153i	−0.937943	+	0.346790i	$0.887272\pi$
$380$		0			0
$381$	6.86114	−	6.86114i	0.351507	−	0.351507i
$382$		0			0
$383$	−19.7097	−	19.7097i	−1.00712	−	1.00712i	−0.999974	−	0.00714591i	$-0.997725\pi$
$383$	−19.7097	−	19.7097i	−1.00712	−	1.00712i	−0.00714591	−	0.999974i	$-0.502275\pi$
$384$		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	$-0.659329\pi$
$389$	7.83824	−	7.83824i	0.397414	−	0.397414i	0.877320	+	0.479906i	$0.159329\pi$
$390$		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	$-0.290095\pi$
$397$	24.4147			1.22534			0.612670	+	0.790339i	$0.290095\pi$
$398$		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	−0.662769	−	0.748824i	$-0.730619\pi$
$419$	1.76149	−	1.76149i	0.0860546	−	0.0860546i	0.748824	+	0.662769i	$0.230619\pi$
$420$		0			0
$421$	15.1301	+	15.1301i	0.737397	+	0.737397i	0.972074	−	0.234677i	$-0.0754031\pi$
$421$	15.1301	+	15.1301i	0.737397	+	0.737397i	−0.234677	+	0.972074i	$0.575403\pi$
$422$		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	0.217448	−	0.976072i	$-0.430227\pi$
$433$	24.8355	−	24.8355i	1.19352	−	1.19352i	0.976072	−	0.217448i	$-0.0697734\pi$
$434$		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	$-0.991099\pi$
$443$		−	1.17693i		−	0.0559176i	0.999609	−	0.0279588i	$-0.00890072\pi$
$444$		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	$0.142538\pi$
$449$			18.3494i			0.865962i	−0.901403	+	0.432981i	$0.857462\pi$
$450$		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	−0.144987	−	0.989434i	$-0.546314\pi$
$457$	18.0522	−	18.0522i	0.844446	−	0.844446i	0.989434	+	0.144987i	$0.0463141\pi$
$458$		0			0
$459$	4.20448	+	4.20448i	0.196248	+	0.196248i
$460$		0			0
$461$	23.5968	−	23.5968i	1.09901	−	1.09901i	0.104487	−	0.994526i	$-0.466680\pi$
$461$	23.5968	−	23.5968i	1.09901	−	1.09901i	0.994526	−	0.104487i	$-0.0333199\pi$
$462$		0			0
$463$	20.2744	+	20.2744i	0.942231	+	0.942231i	0.998420	−	0.0561894i	$-0.0178951\pi$
$463$	20.2744	+	20.2744i	0.942231	+	0.942231i	−0.0561894	+	0.998420i	$0.517895\pi$
$464$		0			0
$465$	−10.0324	−	3.72690i	−0.465240	−	0.172831i
$466$		0			0
$467$		−	14.3565i		−	0.664340i	−0.943220	−	0.332170i	$-0.892219\pi$
$467$		−	14.3565i		−	0.664340i	0.943220	−	0.332170i	$-0.107781\pi$
$468$		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	$-0.467689\pi$
$479$	4.43555			0.202665			0.101333	+	0.994853i	$0.467689\pi$
$480$		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	−0.999984	−	0.00568049i	$-0.998192\pi$
$487$	−22.1931	−	22.1931i	−1.00566	−	1.00566i	−0.00568049	−	0.999984i	$-0.501808\pi$
$488$		0			0
$489$	−8.01355			−0.362385
$490$		0			0
$491$	−20.7625	+	20.7625i	−0.936997	+	0.936997i	−0.998130	−	0.0611325i	$-0.980529\pi$
$491$	−20.7625	+	20.7625i	−0.936997	+	0.936997i	0.0611325	+	0.998130i	$0.480529\pi$
$492$		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	−0.867672	−	0.497137i	$-0.834385\pi$
$499$	−8.27712	+	8.27712i	−0.370535	+	0.370535i	0.497137	+	0.867672i	$0.334385\pi$
$500$		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	$-0.854731\pi$
$503$	−10.2485	+	10.2485i	−0.456958	+	0.456958i	0.440698	+	0.897656i	$0.354731\pi$
$504$		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	0.982841	+	0.184455i	$0.0590518\pi$
$509$	26.3354	+	26.3354i	1.16730	+	1.16730i	0.184455	+	0.982841i	$0.440948\pi$
$510$		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	$0.158827\pi$
$521$			21.8449i			0.957042i	−0.878076	+	0.478521i	$0.841173\pi$
$522$		0			0
$523$			10.0725i			0.440439i	0.975450	+	0.220220i	$0.0706774\pi$
$523$			10.0725i			0.440439i	−0.975450	+	0.220220i	$0.929323\pi$
$524$		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	$-0.791446\pi$
$541$	−4.27091	+	4.27091i	−0.183621	+	0.183621i	0.609311	+	0.792932i	$0.291446\pi$
$542$		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	$0.0247257\pi$
$547$			3.62983i			0.155200i	−0.996985	+	0.0776001i	$0.975274\pi$
$548$		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	$-0.667302\pi$
$557$	−23.6824			−1.00345			−0.501727	+	0.865026i	$0.667302\pi$
$558$		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	−0.907383	−	0.420305i	$-0.861923\pi$
$571$	−11.6390	+	11.6390i	−0.487078	+	0.487078i	0.420305	+	0.907383i	$0.361923\pi$
$572$		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	0.990070	−	0.140576i	$-0.0448954\pi$
$577$	20.4055	+	20.4055i	0.849494	+	0.849494i	−0.140576	+	0.990070i	$0.544895\pi$
$578$		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	−0.896253	−	0.443543i	$-0.853721\pi$
$593$	−11.0242	+	11.0242i	−0.452710	+	0.452710i	0.443543	+	0.896253i	$0.353721\pi$
$594$		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	$0.131824\pi$
$601$			19.7299i			0.804801i	−0.915464	+	0.402401i	$0.868176\pi$
$602$		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	$-0.856730\pi$
$607$	−11.4651	+	11.4651i	−0.465352	+	0.465352i	0.435053	+	0.900405i	$0.356730\pi$
$608$		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	$-0.535624\pi$
$613$	−5.53021			−0.223363			−0.111682	+	0.993744i	$0.535624\pi$
$614$		0			0
$615$	16.7618	+	6.22680i	0.675901	+	0.251089i
$616$		0			0
$617$	28.8633	−	28.8633i	1.16199	−	1.16199i	0.177952	−	0.984039i	$-0.443053\pi$
$617$	28.8633	−	28.8633i	1.16199	−	1.16199i	0.984039	−	0.177952i	$-0.0569472\pi$
$618$		0			0
$619$	−24.3467	−	24.3467i	−0.978577	−	0.978577i	0.0211987	−	0.999775i	$-0.493252\pi$
$619$	−24.3467	−	24.3467i	−0.978577	−	0.978577i	−0.999775	+	0.0211987i	$0.993252\pi$
$620$		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	$-0.366075\pi$
$631$	20.5195			0.816870			0.408435	+	0.912787i	$0.366075\pi$
$632$		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	$-0.485957\pi$
$647$	−24.2897	−	24.2897i	−0.954925	−	0.954925i	−0.999027	+	0.0441018i	$0.985957\pi$
$648$		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	−0.397367	−	0.917660i	$-0.630076\pi$
$659$	13.3564	−	13.3564i	0.520292	−	0.520292i	0.917660	+	0.397367i	$0.130076\pi$
$660$		0			0
$661$	22.8218	+	22.8218i	0.887664	+	0.887664i	0.994298	−	0.106635i	$-0.0340076\pi$
$661$	22.8218	+	22.8218i	0.887664	+	0.887664i	−0.106635	+	0.994298i	$0.534008\pi$
$662$		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	−0.209763	−	0.977752i	$-0.567269\pi$
$673$	19.9234	−	19.9234i	0.767989	−	0.767989i	0.977752	+	0.209763i	$0.0672693\pi$
$674$		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	$-0.998144\pi$
$683$		−	0.304845i		−	0.0116646i	0.999983	−	0.00583228i	$-0.00185648\pi$
$684$		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	0.790839	−	0.612024i	$-0.209645\pi$
$691$	4.70048	+	4.70048i	0.178815	+	0.178815i	−0.612024	+	0.790839i	$0.709645\pi$
$692$		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	−0.271572	+	0.962418i	$0.587543\pi$
$701$	−32.6716	+	32.6716i	−1.23399	+	1.23399i	−0.962418	+	0.271572i	$0.912457\pi$
$702$		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	$-0.668563\pi$
$709$	9.52932	−	9.52932i	0.357881	−	0.357881i	0.863031	+	0.505150i	$0.168563\pi$
$710$		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	$-0.502800\pi$
$719$	−0.471667			−0.0175902			−0.00879511	+	0.999961i	$0.502800\pi$
$720$		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	0.833152	+	0.553045i	$0.186534\pi$
$727$	37.3759	+	37.3759i	1.38620	+	1.38620i	0.553045	+	0.833152i	$0.313466\pi$
$728$		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	−0.263936	−	0.964540i	$-0.585021\pi$
$739$	19.0456	−	19.0456i	0.700604	−	0.700604i	0.964540	+	0.263936i	$0.0850208\pi$
$740$		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	$-0.602891\pi$
$743$	17.1881	−	17.1881i	0.630569	−	0.630569i	0.948211	+	0.317642i	$0.102891\pi$
$744$		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	$-0.938697\pi$
$761$		−	10.5601i		−	0.382803i	0.981512	−	0.191402i	$-0.0613033\pi$
$762$		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	$-0.919612\pi$
$769$		−	13.8582i		−	0.499739i	0.968279	−	0.249870i	$-0.0803878\pi$
$770$		0			0
$771$	−9.86474	−	9.86474i	−0.355270	−	0.355270i
$772$		0			0
$773$	18.6483			0.670732			0.335366	−	0.942088i	$-0.391140\pi$
$773$	18.6483			0.670732			0.335366	+	0.942088i	$0.391140\pi$
$774$		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	$-0.826143\pi$
$787$		−	29.1438i		−	1.03886i	0.854512	−	0.519432i	$-0.173857\pi$
$788$		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	$-0.563011\pi$
$797$	−11.1042			−0.393331			−0.196665	+	0.980471i	$0.563011\pi$
$798$		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	−0.999588	−	0.0286974i	$-0.990864\pi$
$811$	−27.6491	+	27.6491i	−0.970891	+	0.970891i	0.0286974	+	0.999588i	$0.490864\pi$
$812$		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	$-0.335104\pi$
$821$	−10.7053	−	10.7053i	−0.373616	−	0.373616i	−0.868793	+	0.495176i	$0.835104\pi$
$822$		0			0
$823$	31.2787	−	31.2787i	1.09031	−	1.09031i	0.0948116	−	0.995495i	$-0.469775\pi$
$823$	31.2787	−	31.2787i	1.09031	−	1.09031i	0.995495	−	0.0948116i	$-0.0302249\pi$
$824$		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	$-0.282176\pi$
$829$	−4.10901	−	4.10901i	−0.142712	−	0.142712i	−0.774853	+	0.632141i	$0.782176\pi$
$830$		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	$-0.609772\pi$
$853$	−19.7470			−0.676126			−0.338063	+	0.941123i	$0.609772\pi$
$854$		0			0
$855$	6.26830	+	13.6782i	0.214371	+	0.467783i
$856$		0			0
$857$	7.67020	−	7.67020i	0.262009	−	0.262009i	−0.563861	−	0.825870i	$-0.690685\pi$
$857$	7.67020	−	7.67020i	0.262009	−	0.262009i	0.825870	+	0.563861i	$0.190685\pi$
$858$		0			0
$859$	32.7389	+	32.7389i	1.11704	+	1.11704i	0.992174	+	0.124862i	$0.0398487\pi$
$859$	32.7389	+	32.7389i	1.11704	+	1.11704i	0.124862	+	0.992174i	$0.460151\pi$
$860$		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	$-0.197066\pi$
$863$	6.87701	+	6.87701i	0.234096	+	0.234096i	−0.580304	+	0.814400i	$0.697066\pi$
$864$		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	$-0.557129\pi$
$877$	−10.5732			−0.357030			−0.178515	+	0.983937i	$0.557129\pi$
$878$		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	$-0.147187\pi$
$887$	13.3689	+	13.3689i	0.448884	+	0.448884i	−0.446100	+	0.894983i	$0.647187\pi$
$888$		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	$0.204184\pi$
$929$			36.4760i			1.19674i	−0.801220	+	0.598369i	$0.795816\pi$
$930$		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	−0.885474	−	0.464689i	$-0.846166\pi$
$937$	−12.8804	+	12.8804i	−0.420785	+	0.420785i	0.464689	+	0.885474i	$0.346166\pi$
$938$		0			0
$939$	20.1248	+	20.1248i	0.656747	+	0.656747i
$940$		0			0
$941$	38.8236	−	38.8236i	1.26561	−	1.26561i	0.317284	−	0.948331i	$-0.397229\pi$
$941$	38.8236	−	38.8236i	1.26561	−	1.26561i	0.948331	−	0.317284i	$-0.102771\pi$
$942$		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	$0.152819\pi$
$947$			28.4262i			0.923727i	−0.886951	+	0.461864i	$0.847181\pi$
$948$		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	0.565559	−	0.824708i	$-0.308661\pi$
$953$	−8.00013	−	8.00013i	−0.259150	−	0.259150i	−0.824708	+	0.565559i	$0.808661\pi$
$954$		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	$-0.305661\pi$
$967$	−7.65095	−	7.65095i	−0.246038	−	0.246038i	−0.819342	+	0.573304i	$0.805661\pi$
$968$		0			0
$969$	−40.0096			−1.28529
$970$		0			0
$971$	−24.7008	+	24.7008i	−0.792686	+	0.792686i	−0.981930	−	0.189244i	$-0.939396\pi$
$971$	−24.7008	+	24.7008i	−0.792686	+	0.792686i	0.189244	+	0.981930i	$0.439396\pi$
$972$		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	−0.998696	−	0.0510499i	$-0.983743\pi$
$977$	−32.8119	−	32.8119i	−1.04975	−	1.04975i	−0.0510499	−	0.998696i	$-0.516257\pi$
$978$		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	$-0.798676\pi$
$983$	−6.75408	+	6.75408i	−0.215422	+	0.215422i	0.591144	+	0.806566i	$0.298676\pi$
$984$		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	960.2.y.f.847.7		20
4.3	odd	2		240.2.y.f.187.9	yes	20
5.3	odd	4		960.2.bc.f.463.1		20
8.3	odd	2		1920.2.y.l.1567.4		20
8.5	even	2		1920.2.y.k.1567.4		20
12.11	even	2		720.2.z.h.667.2		20
16.3	odd	4		960.2.bc.f.367.1		20
16.5	even	4		1920.2.bc.k.607.10		20
16.11	odd	4		1920.2.bc.l.607.10		20
16.13	even	4		240.2.bc.f.67.4	yes	20
20.3	even	4		240.2.bc.f.43.4	yes	20
40.3	even	4		1920.2.bc.k.1183.10		20
40.13	odd	4		1920.2.bc.l.1183.10		20
48.29	odd	4		720.2.bd.h.307.7		20
60.23	odd	4		720.2.bd.h.523.7		20
80.3	even	4	inner	960.2.y.f.943.7		20
80.13	odd	4		240.2.y.f.163.9	✓	20
80.43	even	4		1920.2.y.k.223.4		20
80.53	odd	4		1920.2.y.l.223.4		20
240.173	even	4		720.2.z.h.163.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.f.163.9	✓	20	80.13	odd	4
240.2.y.f.187.9	yes	20	4.3	odd	2
240.2.bc.f.43.4	yes	20	20.3	even	4
240.2.bc.f.67.4	yes	20	16.13	even	4
720.2.z.h.163.2		20	240.173	even	4
720.2.z.h.667.2		20	12.11	even	2
720.2.bd.h.307.7		20	48.29	odd	4
720.2.bd.h.523.7		20	60.23	odd	4
960.2.y.f.847.7		20	1.1	even	1	trivial
960.2.y.f.943.7		20	80.3	even	4	inner
960.2.bc.f.367.1		20	16.3	odd	4
960.2.bc.f.463.1		20	5.3	odd	4
1920.2.y.k.223.4		20	80.43	even	4
1920.2.y.k.1567.4		20	8.5	even	2
1920.2.y.l.223.4		20	80.53	odd	4
1920.2.y.l.1567.4		20	8.3	odd	2
1920.2.bc.k.607.10		20	16.5	even	4
1920.2.bc.k.1183.10		20	40.3	even	4
1920.2.bc.l.607.10		20	16.11	odd	4
1920.2.bc.l.1183.10		20	40.13	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.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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