LMFDB - Embedded newform 960.2.bc.f.463.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [960,2,Mod(367,960)] 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("960.367"); 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, 3, 0, 1])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [20,0,0,0,8,0,4,0,-20,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == 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:	$\Z[a_1, \ldots, a_{11}]$
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			463.1
Root			$-0.257862 + 1.39051i$ of defining polynomial
Character	$\chi$	$=$	960.463
Dual form			960.2.bc.f.367.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{3} +(-2.09611 + 0.778677i) q^{5} +(2.44055 - 2.44055i) q^{7} -1.00000 q^{9} +(0.181897 - 0.181897i) q^{11} -4.59597 q^{13} +(-0.778677 - 2.09611i) q^{15} +(4.20448 - 4.20448i) q^{17} +(4.75798 - 4.75798i) q^{19} +(2.44055 + 2.44055i) q^{21} +(5.75492 + 5.75492i) q^{23} +(3.78732 - 3.26438i) q^{25} -1.00000i q^{27} +(0.851917 + 0.851917i) q^{29} -4.78620i q^{31} +(0.181897 + 0.181897i) q^{33} +(-3.21525 + 7.01605i) q^{35} -3.97976 q^{37} -4.59597i q^{39} +7.99664i q^{41} +4.44648 q^{43} +(2.09611 - 0.778677i) q^{45} +(-2.46569 - 2.46569i) q^{47} -4.91254i q^{49} +(4.20448 + 4.20448i) q^{51} -4.94396i q^{53} +(-0.239637 + 0.522915i) q^{55} +(4.75798 + 4.75798i) q^{57} +(5.89705 + 5.89705i) q^{59} +(7.88576 - 7.88576i) q^{61} +(-2.44055 + 2.44055i) q^{63} +(9.63365 - 3.57878i) q^{65} +7.54264 q^{67} +(-5.75492 + 5.75492i) q^{69} +6.34716 q^{71} +(4.78916 - 4.78916i) q^{73} +(3.26438 + 3.78732i) q^{75} -0.887858i q^{77} -3.83743 q^{79} +1.00000 q^{81} -6.25327i q^{83} +(-5.53910 + 12.0870i) q^{85} +(-0.851917 + 0.851917i) q^{87} +5.02517 q^{89} +(-11.2167 + 11.2167i) q^{91} +4.78620 q^{93} +(-6.26830 + 13.6782i) q^{95} +(-2.96112 + 2.96112i) q^{97} +(-0.181897 + 0.181897i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{5} + 4 q^{7} - 20 q^{9} - 8 q^{11} + 8 q^{13} + 12 q^{17} + 16 q^{19} + 4 q^{21} + 16 q^{23} - 4 q^{25} - 8 q^{33} + 12 q^{35} + 24 q^{37} + 8 q^{43} - 8 q^{45} + 12 q^{51} + 4 q^{55} + 16 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) $ 20 * q + 8 * q^5 + 4 * q^7 - 20 * q^9 - 8 * q^11 + 8 * q^13 + 12 * q^17 + 16 * q^19 + 4 * q^21 + 16 * q^23 - 4 * q^25 - 8 * q^33 + 12 * q^35 + 24 * q^37 + 8 * q^43 - 8 * q^45 + 12 * q^51 + 4 * q^55 + 16 * q^57 - 16 * q^59 - 12 * q^61 - 4 * q^63 + 4 * q^65 + 16 * q^67 - 16 * q^69 + 20 * q^73 + 8 * q^75 + 48 * q^79 + 20 * q^81 + 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 $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$		0			0
$5$	−2.09611	+	0.778677i	−0.937407	+	0.348235i
$5$	−2.09611	+	0.778677i	−0.937407	+	0.348235i
$6$		0			0
$7$	2.44055	−	2.44055i	0.922440	−	0.922440i	−0.0747612	−	0.997201i	$-0.523819\pi$
$7$	2.44055	−	2.44055i	0.922440	−	0.922440i	0.997201	+	0.0747612i	$0.0238195\pi$
$8$		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
$13$	−4.59597			−1.27469			−0.637347	−	0.770577i	$-0.719968\pi$
$13$	−4.59597			−1.27469			−0.637347	+	0.770577i	$0.719968\pi$
$14$		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	0.0961919	−	0.995363i	$-0.469334\pi$
$19$	4.75798	−	4.75798i	1.09155	−	1.09155i	0.995363	−	0.0961919i	$-0.0306662\pi$
$20$		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	$0.0725040\pi$
$23$	5.75492	+	5.75492i	1.19998	+	1.19998i	0.225813	+	0.974171i	$0.427496\pi$
$24$		0			0
$25$	3.78732	−	3.26438i	0.757465	−	0.652876i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	0.851917	+	0.851917i	0.158197	+	0.158197i	0.781767	−	0.623570i	$-0.214318\pi$
$29$	0.851917	+	0.851917i	0.158197	+	0.158197i	−0.623570	+	0.781767i	$0.714318\pi$
$30$		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
$35$	−3.21525	+	7.01605i	−0.543476	+	1.18593i
$36$		0			0
$37$	−3.97976			−0.654268			−0.327134	−	0.944978i	$-0.606083\pi$
$37$	−3.97976			−0.654268			−0.327134	+	0.944978i	$0.606083\pi$
$38$		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
$43$	4.44648			0.678081			0.339041	−	0.940772i	$-0.389898\pi$
$43$	4.44648			0.678081			0.339041	+	0.940772i	$0.389898\pi$
$44$		0			0
$45$	2.09611	−	0.778677i	0.312469	−	0.116078i
$46$		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
$53$		−	4.94396i		−	0.679106i	−0.940587	−	0.339553i	$-0.889724\pi$
$53$		−	4.94396i		−	0.679106i	0.940587	−	0.339553i	$-0.110276\pi$
$54$		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	$-0.0673385\pi$
$59$	5.89705	+	5.89705i	0.767731	+	0.767731i	−0.209976	+	0.977707i	$0.567338\pi$
$60$		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
$67$	7.54264			0.921480			0.460740	−	0.887535i	$-0.347584\pi$
$67$	7.54264			0.921480			0.460740	+	0.887535i	$0.347584\pi$
$68$		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	$-0.620275\pi$
$73$	4.78916	−	4.78916i	0.560529	−	0.560529i	0.929458	+	0.368929i	$0.120275\pi$
$74$		0			0
$75$	3.26438	+	3.78732i	0.376938	+	0.437322i
$76$		0			0
$77$		−	0.887858i		−	0.101181i
$78$		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
$83$		−	6.25327i		−	0.686385i	−0.939265	−	0.343193i	$-0.888492\pi$
$83$		−	6.25327i		−	0.686385i	0.939265	−	0.343193i	$-0.111508\pi$
$84$		0			0
$85$	−5.53910	+	12.0870i	−0.600800	+	1.31101i
$86$		0			0
$87$	−0.851917	+	0.851917i	−0.0913351	+	0.0913351i
$88$		0			0
$89$	5.02517			0.532667			0.266333	−	0.963881i	$-0.414188\pi$
$89$	5.02517			0.532667			0.266333	+	0.963881i	$0.414188\pi$
$90$		0			0
$91$	−11.2167	+	11.2167i	−1.17583	+	1.17583i
$92$		0			0
$93$	4.78620			0.496306
$94$		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	$-0.236634\pi$
$101$	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	0.101894	−	0.994795i	$-0.467510\pi$
$103$	−9.06195	−	9.06195i	−0.892901	−	0.892901i	−0.994795	+	0.101894i	$0.967510\pi$
$104$		0			0
$105$	−7.01605	−	3.21525i	−0.684696	−	0.313776i
$106$		0			0
$107$		−	5.89771i		−	0.570153i	−0.958505	−	0.285076i	$-0.907981\pi$
$107$		−	5.89771i		−	0.570153i	0.958505	−	0.285076i	$-0.0920190\pi$
$108$		0			0
$109$	3.65602	+	3.65602i	0.350183	+	0.350183i	0.860178	−	0.509995i	$-0.170353\pi$
$109$	3.65602	+	3.65602i	0.350183	+	0.350183i	−0.509995	+	0.860178i	$0.670353\pi$
$110$		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
$115$	−16.5442	−	7.58170i	−1.54275	−	0.706997i
$116$		0			0
$117$	4.59597			0.424898
$118$		0			0
$119$		−	20.5224i		−	1.88129i
$120$		0			0
$121$			10.9338i			0.993984i
$122$		0			0
$123$	−7.99664			−0.721033
$124$		0			0
$125$	−5.39673	+	9.79159i	−0.482699	+	0.875787i
$126$		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	0.657575	−	0.753389i	$-0.271582\pi$
$131$	−1.09665	−	1.09665i	−0.0958148	−	0.0958148i	−0.753389	+	0.657575i	$0.771582\pi$
$132$		0			0
$133$		−	23.2241i		−	2.01379i
$134$		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	$-0.985006\pi$
$137$	−12.2428	−	12.2428i	−1.04598	−	1.04598i	−0.0470863	−	0.998891i	$-0.514994\pi$
$138$		0			0
$139$	3.39535	+	3.39535i	0.287990	+	0.287990i	0.836285	−	0.548295i	$-0.184723\pi$
$139$	3.39535	+	3.39535i	0.287990	+	0.287990i	−0.548295	+	0.836285i	$0.684723\pi$
$140$		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
$147$	4.91254			0.405180
$148$		0			0
$149$	−7.84547	+	7.84547i	−0.642726	+	0.642726i	−0.951225	−	0.308499i	$-0.900173\pi$
$149$	−7.84547	+	7.84547i	−0.642726	+	0.642726i	0.308499	+	0.951225i	$0.400173\pi$
$150$		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
$155$	3.72690	+	10.0324i	0.299352	+	0.805820i
$156$		0			0
$157$			17.6595i			1.40938i	0.709514	+	0.704691i	$0.248915\pi$
$157$			17.6595i			1.40938i	−0.709514	+	0.704691i	$0.751085\pi$
$158$		0			0
$159$	4.94396			0.392082
$160$		0			0
$161$	28.0903			2.21383
$162$		0			0
$163$		−	8.01355i		−	0.627669i	−0.949478	−	0.313835i	$-0.898386\pi$
$163$		−	8.01355i		−	0.627669i	0.949478	−	0.313835i	$-0.101614\pi$
$164$		0			0
$165$	−0.522915	−	0.239637i	−0.0407089	−	0.0186557i
$166$		0			0
$167$	−8.45631	+	8.45631i	−0.654369	+	0.654369i	−0.954042	−	0.299673i	$-0.903122\pi$
$167$	−8.45631	+	8.45631i	−0.654369	+	0.654369i	0.299673	+	0.954042i	$0.403122\pi$
$168$		0			0
$169$	8.12298			0.624845
$170$		0			0
$171$	−4.75798	+	4.75798i	−0.363852	+	0.363852i
$172$		0			0
$173$	−5.11465			−0.388860			−0.194430	−	0.980916i	$-0.562286\pi$
$173$	−5.11465			−0.388860			−0.194430	+	0.980916i	$0.562286\pi$
$174$		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	$-0.829493\pi$
$179$	−4.67625	+	4.67625i	−0.349519	+	0.349519i	0.510411	+	0.859930i	$0.329493\pi$
$180$		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
$187$		−	1.52957i		−	0.111853i
$188$		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
$195$	3.57878	+	9.63365i	0.256282	+	0.689880i
$196$		0			0
$197$	−21.6079			−1.53950			−0.769750	−	0.638345i	$-0.779619\pi$
$197$	−21.6079			−1.53950			−0.769750	+	0.638345i	$0.779619\pi$
$198$		0			0
$199$		−	8.16771i		−	0.578994i	−0.957179	−	0.289497i	$-0.906512\pi$
$199$		−	8.16771i		−	0.578994i	0.957179	−	0.289497i	$-0.0934880\pi$
$200$		0			0
$201$			7.54264i			0.532017i
$202$		0			0
$203$	4.15829			0.291855
$204$		0			0
$205$	−6.22680	−	16.7618i	−0.434899	−	1.17070i
$206$		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
$213$			6.34716i			0.434900i
$214$		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
$227$	−13.3355			−0.885109			−0.442554	−	0.896742i	$-0.645928\pi$
$227$	−13.3355			−0.885109			−0.442554	+	0.896742i	$0.645928\pi$
$228$		0			0
$229$	17.5166	−	17.5166i	1.15753	−	1.15753i	0.172525	−	0.985005i	$-0.444807\pi$
$229$	17.5166	−	17.5166i	1.15753	−	1.15753i	0.985005	−	0.172525i	$-0.0551926\pi$
$230$		0			0
$231$	0.887858			0.0584168
$232$		0			0
$233$	5.53768	−	5.53768i	0.362786	−	0.362786i	−0.502052	−	0.864837i	$-0.667421\pi$
$233$	5.53768	−	5.53768i	0.362786	−	0.362786i	0.864837	+	0.502052i	$0.167421\pi$
$234$		0			0
$235$	7.08831	+	3.24837i	0.462390	+	0.211900i
$236$		0			0
$237$		−	3.83743i		−	0.249268i
$238$		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
$243$			1.00000i			0.0641500i
$244$		0			0
$245$	3.82529	+	10.2972i	0.244389	+	0.657865i
$246$		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
$253$	2.09361			0.131624
$254$		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	0.854991	−	0.518643i	$-0.173563\pi$
$263$	5.45464	+	5.45464i	0.336348	+	0.336348i	−0.518643	+	0.854991i	$0.673563\pi$
$264$		0			0
$265$	3.84975	+	10.3631i	0.236488	+	0.636599i
$266$		0			0
$267$			5.02517i			0.307535i
$268$		0			0
$269$	1.61579	+	1.61579i	0.0985164	+	0.0985164i	0.754647	−	0.656131i	$-0.227808\pi$
$269$	1.61579	+	1.61579i	0.0985164	+	0.0985164i	−0.656131	+	0.754647i	$0.727808\pi$
$270$		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
$275$	0.0951219	−	1.28269i	0.00573607	−	0.0773489i
$276$		0			0
$277$	15.5674			0.935355			0.467678	−	0.883899i	$-0.345091\pi$
$277$	15.5674			0.935355			0.467678	+	0.883899i	$0.345091\pi$
$278$		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
$283$	−16.7014			−0.992798			−0.496399	−	0.868095i	$-0.665345\pi$
$283$	−16.7014			−0.992798			−0.496399	+	0.868095i	$0.665345\pi$
$284$		0			0
$285$	−13.6782	−	6.26830i	−0.810224	−	0.371302i
$286$		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
$293$		−	18.1368i		−	1.05956i	−0.848135	−	0.529780i	$-0.822274\pi$
$293$		−	18.1368i		−	1.05956i	0.848135	−	0.529780i	$-0.177726\pi$
$294$		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
$307$	24.4651			1.39630			0.698148	−	0.715953i	$-0.254008\pi$
$307$	24.4651			1.39630			0.698148	+	0.715953i	$0.254008\pi$
$308$		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	−0.148625	+	0.988894i	$0.547485\pi$
$313$	−20.1248	+	20.1248i	−1.13752	+	1.13752i	−0.988894	+	0.148625i	$0.952515\pi$
$314$		0			0
$315$	3.21525	−	7.01605i	0.181159	−	0.395309i
$316$		0			0
$317$			4.43451i			0.249067i	0.992215	+	0.124534i	$0.0397434\pi$
$317$			4.43451i			0.249067i	−0.992215	+	0.124534i	$0.960257\pi$
$318$		0			0
$319$	0.309923			0.0173523
$320$		0			0
$321$	5.89771			0.329178
$322$		0			0
$323$		−	40.0096i		−	2.22619i
$324$		0			0
$325$	−17.4064	+	15.0030i	−0.965536	+	0.832217i
$326$		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
$333$	3.97976			0.218089
$334$		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
$347$		−	15.6158i		−	0.838301i	−0.907917	−	0.419151i	$-0.862328\pi$
$347$		−	15.6158i		−	0.838301i	0.907917	−	0.419151i	$-0.137672\pi$
$348$		0			0
$349$	4.71294	+	4.71294i	0.252278	+	0.252278i	0.821904	−	0.569626i	$-0.192912\pi$
$349$	4.71294	+	4.71294i	0.252278	+	0.252278i	−0.569626	+	0.821904i	$0.692912\pi$
$350$		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
$355$	−13.3043	+	4.94239i	−0.706120	+	0.262315i
$356$		0			0
$357$	20.5224			1.08616
$358$		0			0
$359$			17.4634i			0.921685i	0.887482	+	0.460842i	$0.152453\pi$
$359$			17.4634i			0.921685i	−0.887482	+	0.460842i	$0.847547\pi$
$360$		0			0
$361$		−	26.2767i		−	1.38298i
$362$		0			0
$363$	−10.9338			−0.573877
$364$		0			0
$365$	−6.30938	+	13.7678i	−0.330248	+	0.720639i
$366$		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
$373$			31.8481i			1.64903i	0.565840	+	0.824515i	$0.308552\pi$
$373$			31.8481i			1.64903i	−0.565840	+	0.824515i	$0.691448\pi$
$374$		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	$-0.112728\pi$
$379$	11.5085	+	11.5085i	0.591153	+	0.591153i	−0.346790	+	0.937943i	$0.612728\pi$
$380$		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
$387$	−4.44648			−0.226027
$388$		0			0
$389$	−7.83824	+	7.83824i	−0.397414	+	0.397414i	−0.877320	−	0.479906i	$-0.840671\pi$
$389$	−7.83824	+	7.83824i	−0.397414	+	0.397414i	0.479906	+	0.877320i	$0.340671\pi$
$390$		0			0
$391$	48.3928			2.44733
$392$		0			0
$393$	1.09665	−	1.09665i	0.0553187	−	0.0553187i
$394$		0			0
$395$	8.04366	−	2.98812i	0.404721	−	0.150349i
$396$		0			0
$397$		−	24.4147i		−	1.22534i	−0.790339	−	0.612670i	$-0.790095\pi$
$397$		−	24.4147i		−	1.22534i	0.790339	−	0.612670i	$-0.209905\pi$
$398$		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
$403$			21.9972i			1.09576i
$404$		0			0
$405$	−2.09611	+	0.778677i	−0.104156	+	0.0386928i
$406$		0			0
$407$	−0.723907	+	0.723907i	−0.0358827	+	0.0358827i
$408$		0			0
$409$	19.2953			0.954092			0.477046	−	0.878878i	$-0.341708\pi$
$409$	19.2953			0.954092			0.477046	+	0.878878i	$0.341708\pi$
$410$		0			0
$411$	12.2428	−	12.2428i	0.603895	−	0.603895i
$412$		0			0
$413$	28.7841			1.41637
$414$		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	$-0.769381\pi$
$419$	−1.76149	+	1.76149i	−0.0860546	+	0.0860546i	0.662769	+	0.748824i	$0.269381\pi$
$420$		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
$427$		−	38.4912i		−	1.86272i
$428$		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
$435$	1.12234	−	2.44908i	0.0538121	−	0.117424i
$436$		0			0
$437$	54.7636			2.61970
$438$		0			0
$439$		−	4.09956i		−	0.195661i	−0.995203	−	0.0978307i	$-0.968810\pi$
$439$		−	4.09956i		−	0.195661i	0.995203	−	0.0978307i	$-0.0311904\pi$
$440$		0			0
$441$			4.91254i			0.233931i
$442$		0			0
$443$	1.17693			0.0559176			0.0279588	−	0.999609i	$-0.491099\pi$
$443$	1.17693			0.0559176			0.0279588	+	0.999609i	$0.491099\pi$
$444$		0			0
$445$	−10.5333	+	3.91298i	−0.499326	+	0.185493i
$446$		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
$453$			3.19389i			0.150062i
$454$		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	$-0.453686\pi$
$457$	−18.0522	−	18.0522i	−0.844446	−	0.844446i	−0.989434	+	0.144987i	$0.953686\pi$
$458$		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	$-0.982105\pi$
$463$	−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
$467$	−14.3565			−0.664340			−0.332170	−	0.943220i	$-0.607781\pi$
$467$	−14.3565			−0.664340			−0.332170	+	0.943220i	$0.607781\pi$
$468$		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
$475$	2.48815	−	33.5518i	0.114164	−	1.53946i
$476$		0			0
$477$			4.94396i			0.226369i
$478$		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
$483$			28.0903i			1.27815i
$484$		0			0
$485$	3.90106	−	8.51257i	0.177138	−	0.386536i
$486$		0			0
$487$	−22.1931	+	22.1931i	−1.00566	+	1.00566i	−0.00568049	+	0.999984i	$0.501808\pi$
$487$	−22.1931	+	22.1931i	−1.00566	+	1.00566i	−0.999984	+	0.00568049i	$0.998192\pi$
$488$		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
$493$	7.16373			0.322638
$494$		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	$-0.665615\pi$
$499$	8.27712	−	8.27712i	0.370535	−	0.370535i	0.867672	+	0.497137i	$0.165615\pi$
$500$		0			0
$501$	−8.45631	−	8.45631i	−0.377800	−	0.377800i
$502$		0			0
$503$	−10.2485	−	10.2485i	−0.456958	−	0.456958i	0.440698	−	0.897656i	$-0.354731\pi$
$503$	−10.2485	−	10.2485i	−0.456958	−	0.456958i	−0.897656	+	0.440698i	$0.854731\pi$
$504$		0			0
$505$	−1.71519	−	0.786019i	−0.0763247	−	0.0349774i
$506$		0			0
$507$			8.12298i			0.360754i
$508$		0			0
$509$	−26.3354	−	26.3354i	−1.16730	−	1.16730i	−0.982841	−	0.184455i	$-0.940948\pi$
$509$	−26.3354	−	26.3354i	−1.16730	−	1.16730i	−0.184455	−	0.982841i	$-0.559052\pi$
$510$		0			0
$511$		−	23.3763i		−	1.03411i
$512$		0			0
$513$	−4.75798	−	4.75798i	−0.210070	−	0.210070i
$514$		0			0
$515$	26.0512	+	11.9385i	1.14795	+	0.526072i
$516$		0			0
$517$	−0.897003			−0.0394501
$518$		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
$523$	−10.0725			−0.440439			−0.220220	−	0.975450i	$-0.570677\pi$
$523$	−10.0725			−0.440439			−0.220220	+	0.975450i	$0.570677\pi$
$524$		0			0
$525$	17.2100	+	1.27627i	0.751107	+	0.0557008i
$526$		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
$533$		−	36.7524i		−	1.59192i
$534$		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
$547$	3.62983			0.155200			0.0776001	−	0.996985i	$-0.475274\pi$
$547$	3.62983			0.155200			0.0776001	+	0.996985i	$0.475274\pi$
$548$		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
$555$	3.09895	+	8.34199i	0.131543	+	0.354098i
$556$		0			0
$557$			23.6824i			1.00345i	0.865026	+	0.501727i	$0.167302\pi$
$557$			23.6824i			1.00345i	−0.865026	+	0.501727i	$0.832698\pi$
$558$		0			0
$559$	−20.4359			−0.864346
$560$		0			0
$561$	1.52957			0.0645783
$562$		0			0
$563$			10.0778i			0.424727i	0.977191	+	0.212364i	$0.0681161\pi$
$563$			10.0778i			0.424727i	−0.977191	+	0.212364i	$0.931884\pi$
$564$		0			0
$565$	18.3956	+	8.43015i	0.773907	+	0.354659i
$566$		0			0
$567$	2.44055	−	2.44055i	0.102493	−	0.102493i
$568$		0			0
$569$	−17.6744			−0.740950			−0.370475	−	0.928842i	$-0.620805\pi$
$569$	−17.6744			−0.740950			−0.370475	+	0.928842i	$0.620805\pi$
$570$		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
$573$	−14.1293			−0.590258
$574$		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
$587$		−	45.2307i		−	1.86687i	−0.358745	−	0.933436i	$-0.616795\pi$
$587$		−	45.2307i		−	1.86687i	0.358745	−	0.933436i	$-0.383205\pi$
$588$		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
$595$	15.9804	+	43.0172i	0.655131	+	1.76353i
$596$		0			0
$597$	8.16771			0.334282
$598$		0			0
$599$			0.523855i			0.0214041i	0.999943	+	0.0107021i	$0.00340664\pi$
$599$			0.523855i			0.0214041i	−0.999943	+	0.0107021i	$0.996593\pi$
$600$		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
$603$	−7.54264			−0.307160
$604$		0			0
$605$	−8.51392	−	22.9185i	−0.346140	−	0.931768i
$606$		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
$613$		−	5.53021i		−	0.223363i	−0.993744	−	0.111682i	$-0.964376\pi$
$613$		−	5.53021i		−	0.223363i	0.993744	−	0.111682i	$-0.0356237\pi$
$614$		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	$-0.943053\pi$
$617$	−28.8633	−	28.8633i	−1.16199	−	1.16199i	−0.177952	−	0.984039i	$-0.556947\pi$
$618$		0			0
$619$	24.3467	+	24.3467i	0.978577	+	0.978577i	0.999775	−	0.0211987i	$-0.00674825\pi$
$619$	24.3467	+	24.3467i	0.978577	+	0.978577i	−0.0211987	+	0.999775i	$0.506748\pi$
$620$		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
$627$	1.73093			0.0691265
$628$		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
$635$	19.7243	+	9.03906i	0.782734	+	0.358704i
$636$		0			0
$637$			22.5779i			0.894570i
$638$		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
$643$		−	45.7180i		−	1.80294i	−0.432838	−	0.901472i	$-0.642488\pi$
$643$		−	45.7180i		−	1.80294i	0.432838	−	0.901472i	$-0.357512\pi$
$644$		0			0
$645$	−3.46237	−	9.32029i	−0.136331	−	0.366986i
$646$		0			0
$647$	−24.2897	+	24.2897i	−0.954925	+	0.954925i	−0.999027	−	0.0441018i	$-0.985957\pi$
$647$	−24.2897	+	24.2897i	−0.954925	+	0.954925i	0.0441018	+	0.999027i	$0.485957\pi$
$648$		0			0
$649$	2.14532			0.0842110
$650$		0			0
$651$	11.6809	−	11.6809i	0.457812	−	0.457812i
$652$		0			0
$653$	33.3219			1.30399			0.651993	−	0.758225i	$-0.273933\pi$
$653$	33.3219			1.30399			0.651993	+	0.758225i	$0.273933\pi$
$654$		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	$-0.869924\pi$
$659$	−13.3564	+	13.3564i	−0.520292	+	0.520292i	0.397367	+	0.917660i	$0.369924\pi$
$660$		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
$667$			9.80543i			0.379668i
$668$		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
$675$	−3.26438	−	3.78732i	−0.125646	−	0.145774i
$676$		0			0
$677$	3.27932			0.126035			0.0630173	−	0.998012i	$-0.479928\pi$
$677$	3.27932			0.126035			0.0630173	+	0.998012i	$0.479928\pi$
$678$		0			0
$679$			14.4535i			0.554674i
$680$		0			0
$681$		−	13.3355i		−	0.511018i
$682$		0			0
$683$	0.304845			0.0116646			0.00583228	−	0.999983i	$-0.498144\pi$
$683$	0.304845			0.0116646			0.00583228	+	0.999983i	$0.498144\pi$
$684$		0			0
$685$	35.1955	+	16.1291i	1.34475	+	0.616261i
$686$		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
$693$			0.887858i			0.0337269i
$694$		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
$707$	2.91221			0.109525
$708$		0			0
$709$	−9.52932	+	9.52932i	−0.357881	+	0.357881i	−0.863031	−	0.505150i	$-0.831437\pi$
$709$	−9.52932	+	9.52932i	−0.357881	+	0.357881i	0.505150	+	0.863031i	$0.331437\pi$
$710$		0			0
$711$	3.83743			0.143915
$712$		0			0
$713$	27.5442	−	27.5442i	1.03154	−	1.03154i
$714$		0			0
$715$	1.10136	−	2.40331i	0.0411887	−	0.0898785i
$716$		0			0
$717$			7.70031i			0.287573i
$718$		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
$723$		−	27.9273i		−	1.03863i
$724$		0			0
$725$	6.00747	+	0.445504i	0.223112	+	0.0165456i
$726$		0			0
$727$	37.3759	−	37.3759i	1.38620	−	1.38620i	0.553045	−	0.833152i	$-0.313466\pi$
$727$	37.3759	−	37.3759i	1.38620	−	1.38620i	0.833152	−	0.553045i	$-0.186534\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	18.6951	−	18.6951i	0.691463	−	0.691463i
$732$		0			0
$733$	−24.0502			−0.888314			−0.444157	−	0.895949i	$-0.646497\pi$
$733$	−24.0502			−0.888314			−0.444157	+	0.895949i	$0.646497\pi$
$734$		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	$-0.914979\pi$
$739$	−19.0456	+	19.0456i	−0.700604	+	0.700604i	0.263936	+	0.964540i	$0.414979\pi$
$740$		0			0
$741$	−21.8675	−	21.8675i	−0.803324	−	0.803324i
$742$		0			0
$743$	17.1881	+	17.1881i	0.630569	+	0.630569i	0.948211	−	0.317642i	$-0.102891\pi$
$743$	17.1881	+	17.1881i	0.630569	+	0.630569i	−0.317642	+	0.948211i	$0.602891\pi$
$744$		0			0
$745$	10.3358	−	22.5540i	0.378676	−	0.826315i
$746$		0			0
$747$			6.25327i			0.228795i
$748$		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
$755$	−6.69473	+	2.48701i	−0.243646	+	0.0905114i
$756$		0			0
$757$	−2.17732			−0.0791360			−0.0395680	−	0.999217i	$-0.512598\pi$
$757$	−2.17732			−0.0791360			−0.0395680	+	0.999217i	$0.512598\pi$
$758$		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
$763$	17.8454			0.646046
$764$		0			0
$765$	5.53910	−	12.0870i	0.200267	−	0.437005i
$766$		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
$773$			18.6483i			0.670732i	0.942088	+	0.335366i	$0.108860\pi$
$773$			18.6483i			0.670732i	−0.942088	+	0.335366i	$0.891140\pi$
$774$		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
$787$	−29.1438			−1.03886			−0.519432	−	0.854512i	$-0.673857\pi$
$787$	−29.1438			−1.03886			−0.519432	+	0.854512i	$0.673857\pi$
$788$		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
$795$	−10.3631	+	3.84975i	−0.367540	+	0.136537i
$796$		0			0
$797$			11.1042i			0.393331i	0.980471	+	0.196665i	$0.0630113\pi$
$797$			11.1042i			0.393331i	−0.980471	+	0.196665i	$0.936989\pi$
$798$		0			0
$799$	−20.7338			−0.733510
$800$		0			0
$801$	−5.02517			−0.177556
$802$		0			0
$803$		−	1.74227i		−	0.0614834i
$804$		0			0
$805$	−58.8803	+	21.8733i	−2.07526	+	0.770932i
$806$		0			0
$807$	−1.61579	+	1.61579i	−0.0568784	+	0.0568784i
$808$		0			0
$809$	27.7185			0.974531			0.487265	−	0.873254i	$-0.337994\pi$
$809$	27.7185			0.974531			0.487265	+	0.873254i	$0.337994\pi$
$810$		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
$813$	−6.09685			−0.213826
$814$		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	0.995495	+	0.0948116i	$0.0302249\pi$
$823$	31.2787	+	31.2787i	1.09031	+	1.09031i	0.0948116	+	0.995495i	$0.469775\pi$
$824$		0			0
$825$	1.28269	+	0.0951219i	0.0446574	+	0.00331172i
$826$		0			0
$827$			53.4550i			1.85881i	0.369060	+	0.929406i	$0.379680\pi$
$827$			53.4550i			1.85881i	−0.369060	+	0.929406i	$0.620320\pi$
$828$		0			0
$829$	4.10901	+	4.10901i	0.142712	+	0.142712i	0.774853	−	0.632141i	$-0.217824\pi$
$829$	4.10901	+	4.10901i	0.142712	+	0.142712i	−0.632141	+	0.774853i	$0.717824\pi$
$830$		0			0
$831$			15.5674i			0.540028i
$832$		0			0
$833$	−20.6547	−	20.6547i	−0.715642	−	0.715642i
$834$		0			0
$835$	11.1406	−	24.3101i	0.385536	−	0.841284i
$836$		0			0
$837$	−4.78620			−0.165435
$838$		0			0
$839$		−	4.01939i		−	0.138765i	−0.997590	−	0.0693824i	$-0.977897\pi$
$839$		−	4.01939i		−	0.138765i	0.997590	−	0.0693824i	$-0.0221029\pi$
$840$		0			0
$841$		−	27.5485i		−	0.949947i
$842$		0			0
$843$	−18.8277			−0.648461
$844$		0			0
$845$	−17.0266	+	6.32518i	−0.585734	+	0.217593i
$846$		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
$853$		−	19.7470i		−	0.676126i	−0.941123	−	0.338063i	$-0.890228\pi$
$853$		−	19.7470i		−	0.676126i	0.941123	−	0.338063i	$-0.109772\pi$
$854$		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	$-0.309315\pi$
$857$	−7.67020	−	7.67020i	−0.262009	−	0.262009i	−0.825870	+	0.563861i	$0.809315\pi$
$858$		0			0
$859$	−32.7389	−	32.7389i	−1.11704	−	1.11704i	−0.992174	−	0.124862i	$-0.960151\pi$
$859$	−32.7389	−	32.7389i	−1.11704	−	1.11704i	−0.124862	−	0.992174i	$-0.539849\pi$
$860$		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
$867$	18.3552			0.623376
$868$		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
$875$	10.7259	+	37.0678i	0.362600	+	1.25312i
$876$		0			0
$877$			10.5732i			0.357030i	0.983937	+	0.178515i	$0.0571294\pi$
$877$			10.5732i			0.357030i	−0.983937	+	0.178515i	$0.942871\pi$
$878$		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
$883$			12.9838i			0.436939i	0.975844	+	0.218470i	$0.0701065\pi$
$883$			12.9838i			0.436939i	−0.975844	+	0.218470i	$0.929894\pi$
$884$		0			0
$885$	7.76895	−	16.9528i	0.261150	−	0.569860i
$886$		0			0
$887$	13.3689	−	13.3689i	0.448884	−	0.448884i	−0.446100	−	0.894983i	$-0.647187\pi$
$887$	13.3689	−	13.3689i	0.448884	−	0.448884i	0.894983	+	0.446100i	$0.147187\pi$
$888$		0			0
$889$	−33.4899			−1.12321
$890$		0			0
$891$	0.181897	−	0.181897i	0.00609379	−	0.00609379i
$892$		0			0
$893$	−23.4633			−0.785171
$894$		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
$907$			12.5840i			0.417846i	0.977932	+	0.208923i	$0.0669957\pi$
$907$			12.5840i			0.417846i	−0.977932	+	0.208923i	$0.933004\pi$
$908$		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
$915$	−22.6699	−	10.3889i	−0.749443	−	0.343448i
$916$		0			0
$917$	−5.35286			−0.176767
$918$		0			0
$919$			8.49556i			0.280243i	0.990134	+	0.140121i	$0.0447492\pi$
$919$			8.49556i			0.280243i	−0.990134	+	0.140121i	$0.955251\pi$
$920$		0			0
$921$			24.4651i			0.806152i
$922$		0			0
$923$	−29.1714			−0.960188
$924$		0			0
$925$	−15.0726	+	12.9914i	−0.495585	+	0.427156i
$926$		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
$933$			8.97669i			0.293884i
$934$		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	$-0.153834\pi$
$937$	12.8804	+	12.8804i	0.420785	+	0.420785i	−0.464689	+	0.885474i	$0.653834\pi$
$938$		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
$947$	28.4262			0.923727			0.461864	−	0.886951i	$-0.347181\pi$
$947$	28.4262			0.923727			0.461864	+	0.886951i	$0.347181\pi$
$948$		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	$-0.691339\pi$
$953$	8.00013	−	8.00013i	0.259150	−	0.259150i	0.824708	+	0.565559i	$0.191339\pi$
$954$		0			0
$955$	−11.0021	−	29.6164i	−0.356021	−	0.958365i
$956$		0			0
$957$			0.309923i			0.0100184i
$958$		0			0
$959$	−59.7585			−1.92970
$960$		0			0
$961$	8.09232			0.261042
$962$		0			0
$963$			5.89771i			0.190051i
$964$		0			0
$965$	19.8100	+	9.07833i	0.637705	+	0.292242i
$966$		0			0
$967$	−7.65095	+	7.65095i	−0.246038	+	0.246038i	−0.819342	−	0.573304i	$-0.805661\pi$
$967$	−7.65095	+	7.65095i	−0.246038	+	0.246038i	0.573304	+	0.819342i	$0.305661\pi$
$968$		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
$973$	16.5730			0.531307
$974$		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	0.591144	−	0.806566i	$-0.298676\pi$
$983$	−6.75408	−	6.75408i	−0.215422	−	0.215422i	−0.806566	+	0.591144i	$0.798676\pi$
$984$		0			0
$985$	45.2925	−	16.8256i	1.44314	−	0.536108i
$986$		0			0
$987$		−	12.0352i		−	0.383086i
$988$		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
$995$	6.36001	+	17.1204i	0.201626	+	0.542753i
$996$		0			0
$997$	−18.2727			−0.578702			−0.289351	−	0.957223i	$-0.593439\pi$
$997$	−18.2727			−0.578702			−0.289351	+	0.957223i	$0.593439\pi$
$998$		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.bc.f.463.1		20
4.3	odd	2		240.2.bc.f.43.4	yes	20
5.2	odd	4		960.2.y.f.847.7		20
8.3	odd	2		1920.2.bc.k.1183.10		20
8.5	even	2		1920.2.bc.l.1183.10		20
12.11	even	2		720.2.bd.h.523.7		20
16.3	odd	4		960.2.y.f.943.7		20
16.5	even	4		1920.2.y.l.223.4		20
16.11	odd	4		1920.2.y.k.223.4		20
16.13	even	4		240.2.y.f.163.9	✓	20
20.7	even	4		240.2.y.f.187.9	yes	20
40.27	even	4		1920.2.y.l.1567.4		20
40.37	odd	4		1920.2.y.k.1567.4		20
48.29	odd	4		720.2.z.h.163.2		20
60.47	odd	4		720.2.z.h.667.2		20
80.27	even	4		1920.2.bc.l.607.10		20
80.37	odd	4		1920.2.bc.k.607.10		20
80.67	even	4	inner	960.2.bc.f.367.1		20
80.77	odd	4		240.2.bc.f.67.4	yes	20
240.77	even	4		720.2.bd.h.307.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.f.163.9	✓	20	16.13	even	4
240.2.y.f.187.9	yes	20	20.7	even	4
240.2.bc.f.43.4	yes	20	4.3	odd	2
240.2.bc.f.67.4	yes	20	80.77	odd	4
720.2.z.h.163.2		20	48.29	odd	4
720.2.z.h.667.2		20	60.47	odd	4
720.2.bd.h.307.7		20	240.77	even	4
720.2.bd.h.523.7		20	12.11	even	2
960.2.y.f.847.7		20	5.2	odd	4
960.2.y.f.943.7		20	16.3	odd	4
960.2.bc.f.367.1		20	80.67	even	4	inner
960.2.bc.f.463.1		20	1.1	even	1	trivial
1920.2.y.k.223.4		20	16.11	odd	4
1920.2.y.k.1567.4		20	40.37	odd	4
1920.2.y.l.223.4		20	16.5	even	4
1920.2.y.l.1567.4		20	40.27	even	4
1920.2.bc.k.607.10		20	80.37	odd	4
1920.2.bc.k.1183.10		20	8.3	odd	2
1920.2.bc.l.607.10		20	80.27	even	4
1920.2.bc.l.1183.10		20	8.5	even	2

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

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

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