LMFDB - Embedded newform 1008.2.cc.b.209.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(209,1008)] 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("1008.209"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cc (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.1
Root			$-1.69547 - 0.354107i$ of defining polynomial
Character	$\chi$	$=$	1008.209
Dual form			1008.2.cc.b.545.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.69547 + 0.354107i) q^{3} +(-0.895175 - 1.55049i) q^{5} +(2.30191 - 1.30430i) q^{7} +(2.74922 - 1.20075i) q^{9} +(2.07976 + 1.20075i) q^{11} +(-4.23601 + 2.44566i) q^{13} +(2.06678 + 2.31181i) q^{15} +3.66466 q^{17} -3.01701i q^{19} +(-3.44095 + 3.02653i) q^{21} +(-3.26178 + 1.88319i) q^{23} +(0.897324 - 1.55421i) q^{25} +(-4.23601 + 3.00935i) q^{27} +(-5.68202 - 3.28052i) q^{29} +(4.02408 - 2.32330i) q^{31} +(-3.95136 - 1.29938i) q^{33} +(-4.08292 - 2.40150i) q^{35} +9.36404 q^{37} +(6.31599 - 5.64654i) q^{39} +(-4.04094 - 6.99911i) q^{41} +(3.48127 - 6.02973i) q^{43} +(-4.32278 - 3.18775i) q^{45} +(-2.56802 + 4.44794i) q^{47} +(3.59758 - 6.00478i) q^{49} +(-6.21332 + 1.29768i) q^{51} -4.29953i q^{55} +(1.06834 + 5.11524i) q^{57} +(-7.29501 - 12.6353i) q^{59} +(9.81058 + 5.66414i) q^{61} +(4.76230 - 6.34984i) q^{63} +(7.58394 + 4.37859i) q^{65} +(0.285115 + 0.493834i) q^{67} +(4.86340 - 4.34791i) q^{69} -5.96254i q^{71} -12.3814i q^{73} +(-0.971027 + 2.95286i) q^{75} +(6.35358 + 0.0513786i) q^{77} +(1.51831 - 2.62979i) q^{79} +(6.11639 - 6.60226i) q^{81} +(7.00270 - 12.1290i) q^{83} +(-3.28052 - 5.68202i) q^{85} +(10.7953 + 3.54997i) q^{87} -3.74863 q^{89} +(-6.56103 + 11.1547i) q^{91} +(-6.00000 + 5.36404i) q^{93} +(-4.67784 + 2.70075i) q^{95} +(4.77256 + 2.75544i) q^{97} +(7.15953 + 0.803848i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7} + 12 q^{9} + 12 q^{11} + 18 q^{21} + 48 q^{23} - 8 q^{25} - 12 q^{29} - 8 q^{37} + 36 q^{39} - 4 q^{43} - 8 q^{49} - 12 q^{51} + 48 q^{57} - 24 q^{63} + 84 q^{65} + 28 q^{67} + 78 q^{77}+ \cdots + 72 q^{99}+O(q^{100}) $ 16 * q - 2 * q^7 + 12 * q^9 + 12 * q^11 + 18 * q^21 + 48 * q^23 - 8 * q^25 - 12 * q^29 - 8 * q^37 + 36 * q^39 - 4 * q^43 - 8 * q^49 - 12 * q^51 + 48 * q^57 - 24 * q^63 + 84 * q^65 + 28 * q^67 + 78 * q^77 + 4 * q^79 + 36 * q^81 - 12 * q^85 - 24 * q^91 - 96 * q^93 - 12 * q^95 + 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−1.69547	+	0.354107i	−0.978878	+	0.204444i
$3$	−1.69547	+	0.354107i	−0.978878	+	0.204444i
$4$		0			0
$5$	−0.895175	−	1.55049i	−0.400334	−	0.693399i	0.593432	−	0.804884i	$-0.297773\pi$
$5$	−0.895175	−	1.55049i	−0.400334	−	0.693399i	−0.993766	+	0.111485i	$0.964439\pi$
$6$		0			0
$7$	2.30191	−	1.30430i	0.870040	−	0.492981i
$7$	2.30191	−	1.30430i	0.870040	−	0.492981i
$8$		0			0
$9$	2.74922	−	1.20075i	0.916406	−	0.400251i
$10$		0			0
$11$	2.07976	+	1.20075i	0.627072	+	0.362040i	0.779617	−	0.626256i	$-0.215414\pi$
$11$	2.07976	+	1.20075i	0.627072	+	0.362040i	−0.152545	+	0.988297i	$0.548747\pi$
$12$		0			0
$13$	−4.23601	+	2.44566i	−1.17486	+	0.678305i	−0.954820	−	0.297186i	$-0.903952\pi$
$13$	−4.23601	+	2.44566i	−1.17486	+	0.678305i	−0.220039	+	0.975491i	$0.570618\pi$
$14$		0			0
$15$	2.06678	+	2.31181i	0.533640	+	0.596908i
$16$		0			0
$17$	3.66466			0.888812			0.444406	−	0.895826i	$-0.353415\pi$
$17$	3.66466			0.888812			0.444406	+	0.895826i	$0.353415\pi$
$18$		0			0
$19$		−	3.01701i		−	0.692150i	−0.938207	−	0.346075i	$-0.887514\pi$
$19$		−	3.01701i		−	0.692150i	0.938207	−	0.346075i	$-0.112486\pi$
$20$		0			0
$21$	−3.44095	+	3.02653i	−0.750877	+	0.660442i
$22$		0			0
$23$	−3.26178	+	1.88319i	−0.680129	+	0.392673i	−0.799904	−	0.600128i	$-0.795116\pi$
$23$	−3.26178	+	1.88319i	−0.680129	+	0.392673i	0.119775	+	0.992801i	$0.461783\pi$
$24$		0			0
$25$	0.897324	−	1.55421i	0.179465	−	0.310842i
$26$		0			0
$27$	−4.23601	+	3.00935i	−0.815221	+	0.579150i
$28$		0			0
$29$	−5.68202	−	3.28052i	−1.05512	−	0.609176i	−0.131045	−	0.991376i	$-0.541833\pi$
$29$	−5.68202	−	3.28052i	−1.05512	−	0.609176i	−0.924080	+	0.382200i	$0.875167\pi$
$30$		0			0
$31$	4.02408	−	2.32330i	0.722746	−	0.417278i	−0.0930163	−	0.995665i	$-0.529651\pi$
$31$	4.02408	−	2.32330i	0.722746	−	0.417278i	0.815763	+	0.578387i	$0.196318\pi$
$32$		0			0
$33$	−3.95136	−	1.29938i	−0.687844	−	0.226193i
$34$		0			0
$35$	−4.08292	−	2.40150i	−0.690140	−	0.405928i
$36$		0			0
$37$	9.36404			1.53944			0.769719	−	0.638382i	$-0.220396\pi$
$37$	9.36404			1.53944			0.769719	+	0.638382i	$0.220396\pi$
$38$		0			0
$39$	6.31599	−	5.64654i	1.01137	−	0.904170i
$40$		0			0
$41$	−4.04094	−	6.99911i	−0.631088	−	1.09308i	−0.987330	−	0.158683i	$-0.949275\pi$
$41$	−4.04094	−	6.99911i	−0.631088	−	1.09308i	0.356241	−	0.934394i	$-0.384058\pi$
$42$		0			0
$43$	3.48127	−	6.02973i	0.530888	−	0.919526i	−0.468462	−	0.883484i	$-0.655192\pi$
$43$	3.48127	−	6.02973i	0.530888	−	0.919526i	0.999350	−	0.0360419i	$-0.0114750\pi$
$44$		0			0
$45$	−4.32278	−	3.18775i	−0.644402	−	0.475201i
$46$		0			0
$47$	−2.56802	+	4.44794i	−0.374584	+	0.648799i	−0.990265	−	0.139197i	$-0.955548\pi$
$47$	−2.56802	+	4.44794i	−0.374584	+	0.648799i	0.615680	+	0.787996i	$0.288881\pi$
$48$		0			0
$49$	3.59758	−	6.00478i	0.513940	−	0.857826i
$50$		0			0
$51$	−6.21332	+	1.29768i	−0.870039	+	0.181712i
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$		−	4.29953i		−	0.579749i
$56$		0			0
$57$	1.06834	+	5.11524i	0.141506	+	0.677530i
$58$		0			0
$59$	−7.29501	−	12.6353i	−0.949729	−	1.64498i	−0.745994	−	0.665953i	$-0.768025\pi$
$59$	−7.29501	−	12.6353i	−0.949729	−	1.64498i	−0.203735	−	0.979026i	$-0.565308\pi$
$60$		0			0
$61$	9.81058	+	5.66414i	1.25612	+	0.725219i	0.972317	−	0.233665i	$-0.0750718\pi$
$61$	9.81058	+	5.66414i	1.25612	+	0.725219i	0.283799	+	0.958884i	$0.408405\pi$
$62$		0			0
$63$	4.76230	−	6.34984i	0.599994	−	0.800005i
$64$		0			0
$65$	7.58394	+	4.37859i	0.940672	+	0.543097i
$66$		0			0
$67$	0.285115	+	0.493834i	0.0348324	+	0.0603315i	0.882916	−	0.469531i	$-0.155577\pi$
$67$	0.285115	+	0.493834i	0.0348324	+	0.0603315i	−0.848084	+	0.529862i	$0.822244\pi$
$68$		0			0
$69$	4.86340	−	4.34791i	0.585484	−	0.523427i
$70$		0			0
$71$		−	5.96254i		−	0.707623i	−0.935317	−	0.353811i	$-0.884885\pi$
$71$		−	5.96254i		−	0.707623i	0.935317	−	0.353811i	$-0.115115\pi$
$72$		0			0
$73$		−	12.3814i		−	1.44913i	−0.689204	−	0.724567i	$-0.742040\pi$
$73$		−	12.3814i		−	1.44913i	0.689204	−	0.724567i	$-0.257960\pi$
$74$		0			0
$75$	−0.971027	+	2.95286i	−0.112125	+	0.340967i
$76$		0			0
$77$	6.35358	+	0.0513786i	0.724057	+	0.00585514i
$78$		0			0
$79$	1.51831	−	2.62979i	0.170824	−	0.295875i	−0.767884	−	0.640588i	$-0.778691\pi$
$79$	1.51831	−	2.62979i	0.170824	−	0.295875i	0.938708	+	0.344713i	$0.112024\pi$
$80$		0			0
$81$	6.11639	−	6.60226i	0.679599	−	0.733584i
$82$		0			0
$83$	7.00270	−	12.1290i	0.768646	−	1.33133i	−0.169651	−	0.985504i	$-0.554264\pi$
$83$	7.00270	−	12.1290i	0.768646	−	1.33133i	0.938297	−	0.345830i	$-0.112403\pi$
$84$		0			0
$85$	−3.28052	−	5.68202i	−0.355822	−	0.616302i
$86$		0			0
$87$	10.7953	+	3.54997i	1.15738	+	0.380596i
$88$		0			0
$89$	−3.74863			−0.397354			−0.198677	−	0.980065i	$-0.563664\pi$
$89$	−3.74863			−0.397354			−0.198677	+	0.980065i	$0.563664\pi$
$90$		0			0
$91$	−6.56103	+	11.1547i	−0.687783	+	1.16934i
$92$		0			0
$93$	−6.00000	+	5.36404i	−0.622171	+	0.556225i
$94$		0			0
$95$	−4.67784	+	2.70075i	−0.479936	+	0.277091i
$96$		0			0
$97$	4.77256	+	2.75544i	0.484580	+	0.279772i	0.722323	−	0.691556i	$-0.243074\pi$
$97$	4.77256	+	2.75544i	0.484580	+	0.279772i	−0.237743	+	0.971328i	$0.576408\pi$
$98$		0			0
$99$	7.15953	+	0.803848i	0.719560	+	0.0807897i
$100$		0			0
$101$	−0.125162	+	0.216787i	−0.0124541	+	0.0215711i	−0.872185	−	0.489176i	$-0.837298\pi$
$101$	−0.125162	+	0.216787i	−0.0124541	+	0.0215711i	0.859731	+	0.510747i	$0.170631\pi$
$102$		0			0
$103$	−0.145433	+	0.0839657i	−0.0143299	+	0.00827339i	−0.507148	−	0.861859i	$-0.669300\pi$
$103$	−0.145433	+	0.0839657i	−0.0143299	+	0.00827339i	0.492818	+	0.870132i	$0.335967\pi$
$104$		0			0
$105$	7.77285	+	2.62588i	0.758552	+	0.256260i
$106$		0			0
$107$			7.99080i			0.772500i	0.922394	+	0.386250i	$0.126230\pi$
$107$			7.99080i			0.772500i	−0.922394	+	0.386250i	$0.873770\pi$
$108$		0			0
$109$	−18.9533			−1.81540			−0.907700	−	0.419619i	$-0.862164\pi$
$109$	−18.9533			−1.81540			−0.907700	+	0.419619i	$0.862164\pi$
$110$		0			0
$111$	−15.8764	+	3.31587i	−1.50692	+	0.314728i
$112$		0			0
$113$	−1.00418	+	0.579764i	−0.0944653	+	0.0545396i	−0.546488	−	0.837467i	$-0.684036\pi$
$113$	−1.00418	+	0.579764i	−0.0944653	+	0.0545396i	0.452023	+	0.892006i	$0.350702\pi$
$114$		0			0
$115$	5.83973	+	3.37157i	0.544558	+	0.314401i
$116$		0			0
$117$	−8.70908	+	11.8101i	−0.805155	+	1.09184i
$118$		0			0
$119$	8.43573	−	4.77984i	0.773302	−	0.438167i
$120$		0			0
$121$	−2.61639	−	4.53172i	−0.237854	−	0.411974i
$122$		0			0
$123$	9.32971	+	10.4358i	0.841231	+	0.940968i
$124$		0			0
$125$	−12.1648			−1.08805
$126$		0			0
$127$	−1.40150			−0.124363			−0.0621817	−	0.998065i	$-0.519806\pi$
$127$	−1.40150			−0.124363			−0.0621817	+	0.998065i	$0.519806\pi$
$128$		0			0
$129$	−3.76721	+	11.4560i	−0.331684	+	1.00864i
$130$		0			0
$131$	5.24589	+	9.08614i	0.458335	+	0.793860i	0.998873	−	0.0474597i	$-0.0151126\pi$
$131$	5.24589	+	9.08614i	0.458335	+	0.793860i	−0.540538	+	0.841320i	$0.681779\pi$
$132$		0			0
$133$	−3.93510	−	6.94489i	−0.341216	−	0.602198i
$134$		0			0
$135$	8.45794	+	3.87399i	0.727943	+	0.333420i
$136$		0			0
$137$	−4.08812	−	2.36028i	−0.349272	−	0.201652i	0.315093	−	0.949061i	$-0.397964\pi$
$137$	−4.08812	−	2.36028i	−0.349272	−	0.201652i	−0.664365	+	0.747409i	$0.731298\pi$
$138$		0			0
$139$	2.04707	−	1.18187i	0.173630	−	0.100245i	−0.410666	−	0.911786i	$-0.634704\pi$
$139$	2.04707	−	1.18187i	0.173630	−	0.100245i	0.584296	+	0.811540i	$0.301371\pi$
$140$		0			0
$141$	2.77895	−	8.45070i	0.234030	−	0.711677i
$142$		0			0
$143$	−11.7465			−0.982295
$144$		0			0
$145$			11.7465i			0.975497i
$146$		0			0
$147$	−3.97325	+	11.4548i	−0.327708	+	0.944779i
$148$		0			0
$149$	−15.0377	+	8.68202i	−1.23194	+	0.711259i	−0.967433	−	0.253126i	$-0.918541\pi$
$149$	−15.0377	+	8.68202i	−1.23194	+	0.711259i	−0.264503	+	0.964385i	$0.585208\pi$
$150$		0			0
$151$	−5.61639	+	9.72787i	−0.457055	+	0.791643i	−0.998804	−	0.0488977i	$-0.984429\pi$
$151$	−5.61639	+	9.72787i	−0.457055	+	0.791643i	0.541749	+	0.840541i	$0.317762\pi$
$152$		0			0
$153$	10.0750	−	4.40035i	0.814512	−	0.355748i
$154$		0			0
$155$	−7.20451	−	4.15953i	−0.578680	−	0.334101i
$156$		0			0
$157$	11.9885	−	6.92154i	0.956783	−	0.552399i	0.0616014	−	0.998101i	$-0.480379\pi$
$157$	11.9885	−	6.92154i	0.956783	−	0.552399i	0.895181	+	0.445702i	$0.147046\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.05208	+	8.58930i	−0.398159	+	0.676931i
$162$		0			0
$163$	4.33577			0.339604			0.169802	−	0.985478i	$-0.445687\pi$
$163$	4.33577			0.339604			0.169802	+	0.985478i	$0.445687\pi$
$164$		0			0
$165$	1.52249	+	7.28972i	0.118526	+	0.567504i
$166$		0			0
$167$	6.20756	+	10.7518i	0.480355	+	0.832000i	0.999746	−	0.0225370i	$-0.00717435\pi$
$167$	6.20756	+	10.7518i	0.480355	+	0.832000i	−0.519391	+	0.854537i	$0.673841\pi$
$168$		0			0
$169$	5.46254	−	9.46139i	0.420195	−	0.727799i
$170$		0			0
$171$	−3.62268	−	8.29442i	−0.277033	−	0.634290i
$172$		0			0
$173$	8.70908	−	15.0846i	0.662139	−	1.14686i	−0.317913	−	0.948120i	$-0.602982\pi$
$173$	8.70908	−	15.0846i	0.662139	−	1.14686i	0.980052	−	0.198739i	$-0.0636846\pi$
$174$		0			0
$175$	0.0383954	−	4.74804i	0.00290242	−	0.358918i
$176$		0			0
$177$	16.8427	+	18.8396i	1.26597	+	1.41607i
$178$		0			0
$179$		−	13.1221i		−	0.980789i	−0.871501	−	0.490395i	$-0.836853\pi$
$179$		−	13.1221i		−	0.980789i	0.871501	−	0.490395i	$-0.163147\pi$
$180$		0			0
$181$			13.3577i			0.992873i	0.868073	+	0.496437i	$0.165359\pi$
$181$			13.3577i			0.992873i	−0.868073	+	0.496437i	$0.834641\pi$
$182$		0			0
$183$	−18.6392	−	6.12937i	−1.37785	−	0.453096i
$184$		0			0
$185$	−8.38245	−	14.5188i	−0.616290	−	1.06745i
$186$		0			0
$187$	7.62164	+	4.40035i	0.557349	+	0.321786i
$188$		0			0
$189$	−5.82581	+	12.4523i	−0.423765	+	0.905772i
$190$		0			0
$191$	8.01361	+	4.62666i	0.579845	+	0.334774i	0.761072	−	0.648668i	$-0.224674\pi$
$191$	8.01361	+	4.62666i	0.579845	+	0.334774i	−0.181227	+	0.983441i	$0.558007\pi$
$192$		0			0
$193$	12.2801	+	21.2698i	0.883941	+	1.53103i	0.846923	+	0.531716i	$0.178452\pi$
$193$	12.2801	+	21.2698i	0.883941	+	1.53103i	0.0370176	+	0.999315i	$0.488214\pi$
$194$		0			0
$195$	−14.4088	−	4.73823i	−1.03184	−	0.339312i
$196$		0			0
$197$		−	12.4861i		−	0.889598i	−0.895630	−	0.444799i	$-0.853275\pi$
$197$		−	12.4861i		−	0.889598i	0.895630	−	0.444799i	$-0.146725\pi$
$198$		0			0
$199$		−	0.179145i		−	0.0126993i	−0.999980	−	0.00634964i	$-0.997979\pi$
$199$		−	0.179145i		−	0.0126993i	0.999980	−	0.00634964i	$-0.00202117\pi$
$200$		0			0
$201$	−0.658274	−	0.736319i	−0.0464311	−	0.0519359i
$202$		0			0
$203$	−17.3583	−	0.140369i	−1.21831	−	0.00985198i
$204$		0			0
$205$	−7.23469	+	12.5309i	−0.505293	+	0.875193i
$206$		0			0
$207$	−6.70610	+	9.09390i	−0.466107	+	0.632069i
$208$		0			0
$209$	3.62268	−	6.27467i	0.250586	−	0.434028i
$210$		0			0
$211$	−7.56103	−	13.0961i	−0.520523	−	0.901572i	−0.999715	−	0.0238622i	$-0.992404\pi$
$211$	−7.56103	−	13.0961i	−0.520523	−	0.901572i	0.479192	−	0.877710i	$-0.340930\pi$
$212$		0			0
$213$	2.11137	+	10.1093i	0.144669	+	0.692677i
$214$		0			0
$215$	−12.4654			−0.850131
$216$		0			0
$217$	6.23278	−	10.5967i	0.423109	−	0.719348i
$218$		0			0
$219$	4.38434	+	20.9923i	0.296266	+	1.41853i
$220$		0			0
$221$	−15.5236	+	8.96254i	−1.04423	+	0.602885i
$222$		0			0
$223$	7.27049	+	4.19762i	0.486868	+	0.281093i	0.723274	−	0.690561i	$-0.242636\pi$
$223$	7.27049	+	4.19762i	0.486868	+	0.281093i	−0.236406	+	0.971654i	$0.575970\pi$
$224$		0			0
$225$	0.600717	−	5.35033i	0.0400478	−	0.356688i
$226$		0			0
$227$	−1.21261	+	2.10030i	−0.0804836	+	0.139402i	−0.903458	−	0.428677i	$-0.858980\pi$
$227$	−1.21261	+	2.10030i	−0.0804836	+	0.139402i	0.822974	+	0.568079i	$0.192313\pi$
$228$		0			0
$229$	1.74915	−	1.00987i	0.115587	−	0.0667344i	−0.441092	−	0.897462i	$-0.645409\pi$
$229$	1.74915	−	1.00987i	0.115587	−	0.0667344i	0.556679	+	0.830728i	$0.312075\pi$
$230$		0			0
$231$	−10.7905	+	2.16273i	−0.709961	+	0.142297i
$232$		0			0
$233$			12.7289i			0.833899i	0.908930	+	0.416950i	$0.136901\pi$
$233$			12.7289i			0.833899i	−0.908930	+	0.416950i	$0.863099\pi$
$234$		0			0
$235$	9.19531			0.599836
$236$		0			0
$237$	−1.64302	+	4.99637i	−0.106726	+	0.324549i
$238$		0			0
$239$	−15.1117	+	8.72474i	−0.977494	+	0.564356i	−0.901513	−	0.432753i	$-0.857542\pi$
$239$	−15.1117	+	8.72474i	−0.977494	+	0.564356i	−0.0759814	+	0.997109i	$0.524209\pi$
$240$		0			0
$241$	9.90142	+	5.71659i	0.637807	+	0.368238i	0.783769	−	0.621052i	$-0.213295\pi$
$241$	9.90142	+	5.71659i	0.637807	+	0.368238i	−0.145963	+	0.989290i	$0.546628\pi$
$242$		0			0
$243$	−8.03223	+	13.3598i	−0.515268	+	0.857029i
$244$		0			0
$245$	−12.5308	−	0.202676i	−0.800564	−	0.0129485i
$246$		0			0
$247$	7.37859	+	12.7801i	0.469489	+	0.813178i
$248$		0			0
$249$	−7.57788	+	23.0441i	−0.480228	+	1.46036i
$250$		0			0
$251$	27.3560			1.72669			0.863347	−	0.504611i	$-0.168364\pi$
$251$	27.3560			1.72669			0.863347	+	0.504611i	$0.168364\pi$
$252$		0			0
$253$	−9.04499			−0.568653
$254$		0			0
$255$	7.57405	+	8.47203i	0.474305	+	0.530539i
$256$		0			0
$257$	1.74837	+	3.02826i	0.109060	+	0.188898i	0.915390	−	0.402569i	$-0.131883\pi$
$257$	1.74837	+	3.02826i	0.109060	+	0.188898i	−0.806330	+	0.591466i	$0.798549\pi$
$258$		0			0
$259$	21.5552	−	12.2136i	1.33937	−	0.758914i
$260$		0			0
$261$	−19.5602	−	2.19615i	−1.21075	−	0.135938i
$262$		0			0
$263$	8.35150	+	4.82174i	0.514976	+	0.297321i	0.734877	−	0.678201i	$-0.237240\pi$
$263$	8.35150	+	4.82174i	0.514976	+	0.297321i	−0.219901	+	0.975522i	$0.570573\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	6.35568	−	1.32741i	0.388961	−	0.0812365i
$268$		0			0
$269$	−6.91107			−0.421376			−0.210688	−	0.977553i	$-0.567570\pi$
$269$	−6.91107			−0.421376			−0.210688	+	0.977553i	$0.567570\pi$
$270$		0			0
$271$		−	20.6312i		−	1.25326i	−0.779318	−	0.626629i	$-0.784434\pi$
$271$		−	20.6312i		−	1.25326i	0.779318	−	0.626629i	$-0.215566\pi$
$272$		0			0
$273$	7.17404	−	21.2358i	0.434193	−	1.28525i
$274$		0			0
$275$	3.73244	−	2.15493i	0.225075	−	0.129947i
$276$		0			0
$277$	7.75718	−	13.4358i	0.466084	−	0.807281i	−0.533166	−	0.846011i	$-0.678998\pi$
$277$	7.75718	−	13.4358i	0.466084	−	0.807281i	0.999250	+	0.0387296i	$0.0123311\pi$
$278$		0			0
$279$	8.27336	−	11.2192i	0.495313	−	0.671675i
$280$		0			0
$281$	11.7759	+	6.79883i	0.702492	+	0.405584i	0.808275	−	0.588805i	$-0.200401\pi$
$281$	11.7759	+	6.79883i	0.702492	+	0.405584i	−0.105783	+	0.994389i	$0.533735\pi$
$282$		0			0
$283$	4.71796	−	2.72392i	0.280454	−	0.161920i	−0.353175	−	0.935557i	$-0.614898\pi$
$283$	4.71796	−	2.72392i	0.280454	−	0.161920i	0.633629	+	0.773637i	$0.281565\pi$
$284$		0			0
$285$	6.97477	−	6.23549i	0.413150	−	0.369359i
$286$		0			0
$287$	−18.4308	−	10.8407i	−1.08794	−	0.639907i
$288$		0			0
$289$	−3.57023			−0.210014
$290$		0			0
$291$	−9.06743	−	2.98176i	−0.531542	−	0.174794i
$292$		0			0
$293$	12.2311	+	21.1849i	0.714550	+	1.23764i	0.963133	+	0.269026i	$0.0867017\pi$
$293$	12.2311	+	21.1849i	0.714550	+	1.23764i	−0.248583	+	0.968610i	$0.579965\pi$
$294$		0			0
$295$	−13.0606	+	22.6216i	−0.760418	+	1.31708i
$296$		0			0
$297$	−12.4234	+	1.17234i	−0.720878	+	0.0680260i
$298$		0			0
$299$	9.21130	−	15.9544i	0.532703	−	0.922670i
$300$		0			0
$301$	0.148959	−	18.4205i	0.00858585	−	1.06174i
$302$		0			0
$303$	0.135442	−	0.411876i	0.00778097	−	0.0236617i
$304$		0			0
$305$		−	20.2816i		−	1.16132i
$306$		0			0
$307$			31.2223i			1.78195i	0.454053	+	0.890975i	$0.349978\pi$
$307$			31.2223i			1.78195i	−0.454053	+	0.890975i	$0.650022\pi$
$308$		0			0
$309$	0.216844	−	0.193860i	0.0123358	−	0.0110283i
$310$		0			0
$311$	5.45501	+	9.44836i	0.309325	+	0.535767i	0.978215	−	0.207594i	$-0.0665634\pi$
$311$	5.45501	+	9.44836i	0.309325	+	0.535767i	−0.668889	+	0.743362i	$0.733230\pi$
$312$		0			0
$313$	2.96532	+	1.71203i	0.167610	+	0.0967694i	0.581458	−	0.813576i	$-0.302482\pi$
$313$	2.96532	+	1.71203i	0.167610	+	0.0967694i	−0.413849	+	0.910346i	$0.635816\pi$
$314$		0			0
$315$	−14.1084	−	1.69968i	−0.794921	−	0.0957662i
$316$		0			0
$317$	16.4953	+	9.52357i	0.926468	+	0.534897i	0.885693	−	0.464272i	$-0.153684\pi$
$317$	16.4953	+	9.52357i	0.926468	+	0.534897i	0.0407755	+	0.999168i	$0.487017\pi$
$318$		0			0
$319$	−7.87817	−	13.6454i	−0.441093	−	0.763995i
$320$		0			0
$321$	−2.82960	−	13.5481i	−0.157933	−	0.756183i
$322$		0			0
$323$		−	11.0563i		−	0.615191i
$324$		0			0
$325$			8.77821i			0.486927i
$326$		0			0
$327$	32.1348	−	6.71150i	1.77706	−	0.371147i
$328$		0			0
$329$	−0.109882	+	13.5882i	−0.00605801	+	0.749144i
$330$		0			0
$331$	0.0366251	−	0.0634366i	0.00201310	−	0.00348679i	−0.865017	−	0.501742i	$-0.832693\pi$
$331$	0.0366251	−	0.0634366i	0.00201310	−	0.00348679i	0.867030	+	0.498256i	$0.166026\pi$
$332$		0			0
$333$	25.7438	−	11.2439i	1.41075	−	0.616161i
$334$		0			0
$335$	0.510456	−	0.884136i	0.0278892	−	0.0483055i
$336$		0			0
$337$	1.11639	+	1.93364i	0.0608136	+	0.105332i	0.894829	−	0.446408i	$-0.147297\pi$
$337$	1.11639	+	1.93364i	0.0608136	+	0.105332i	−0.834016	+	0.551741i	$0.813964\pi$
$338$		0			0
$339$	1.49726	−	1.33856i	0.0813198	−	0.0727004i
$340$		0			0
$341$	11.1589			0.604286
$342$		0			0
$343$	0.449242	−	18.5148i	0.0242568	−	0.999706i
$344$		0			0
$345$	−11.0950	−	3.64850i	−0.597333	−	0.196429i
$346$		0			0
$347$	−27.5751	+	15.9205i	−1.48031	+	0.854656i	−0.999751	−	0.0223084i	$-0.992898\pi$
$347$	−27.5751	+	15.9205i	−1.48031	+	0.854656i	−0.480556	+	0.876964i	$0.659565\pi$
$348$		0			0
$349$	−12.7613	−	7.36772i	−0.683095	−	0.394385i	0.117925	−	0.993022i	$-0.462376\pi$
$349$	−12.7613	−	7.36772i	−0.683095	−	0.394385i	−0.801020	+	0.598637i	$0.795709\pi$
$350$		0			0
$351$	10.5839	−	23.1075i	0.564929	−	1.23339i
$352$		0			0
$353$	−1.07979	+	1.87025i	−0.0574713	+	0.0995431i	−0.893330	−	0.449402i	$-0.851637\pi$
$353$	−1.07979	+	1.87025i	−0.0574713	+	0.0995431i	0.835858	+	0.548945i	$0.184970\pi$
$354$		0			0
$355$	−9.24484	+	5.33751i	−0.490665	+	0.283286i
$356$		0			0
$357$	−12.6099	+	11.0912i	−0.667388	+	0.587009i
$358$		0			0
$359$			32.6448i			1.72293i	0.507820	+	0.861463i	$0.330451\pi$
$359$			32.6448i			1.72293i	−0.507820	+	0.861463i	$0.669549\pi$
$360$		0			0
$361$	9.89765			0.520929
$362$		0			0
$363$	6.04071	+	6.75690i	0.317055	+	0.354645i
$364$		0			0
$365$	−19.1972	+	11.0835i	−1.00483	+	0.580138i
$366$		0			0
$367$	−25.7212	−	14.8501i	−1.34264	−	0.775171i	−0.355442	−	0.934698i	$-0.615670\pi$
$367$	−25.7212	−	14.8501i	−1.34264	−	0.775171i	−0.987194	+	0.159527i	$0.949003\pi$
$368$		0			0
$369$	−19.5136	−	14.3899i	−1.01584	−	0.749109i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	1.00836	+	1.74653i	0.0522109	+	0.0904320i	0.890950	−	0.454102i	$-0.150040\pi$
$373$	1.00836	+	1.74653i	0.0522109	+	0.0904320i	−0.838739	+	0.544534i	$0.816707\pi$
$374$		0			0
$375$	20.6250	−	4.30763i	1.06507	−	0.222445i
$376$		0			0
$377$	32.0921			1.65283
$378$		0			0
$379$	18.8709			0.969332			0.484666	−	0.874699i	$-0.338941\pi$
$379$	18.8709			0.969332			0.484666	+	0.874699i	$0.338941\pi$
$380$		0			0
$381$	2.37620	−	0.496282i	0.121737	−	0.0254253i
$382$		0			0
$383$	0.418256	+	0.724440i	0.0213719	+	0.0370172i	0.876514	−	0.481377i	$-0.159863\pi$
$383$	0.418256	+	0.724440i	0.0213719	+	0.0370172i	−0.855142	+	0.518394i	$0.826530\pi$
$384$		0			0
$385$	−5.60790	−	9.89714i	−0.285805	−	0.504405i
$386$		0			0
$387$	2.33055	−	20.7572i	0.118468	−	1.05515i
$388$		0			0
$389$	21.4964	+	12.4109i	1.08991	+	0.629260i	0.933552	−	0.358441i	$-0.116692\pi$
$389$	21.4964	+	12.4109i	1.08991	+	0.629260i	0.156357	+	0.987701i	$0.450025\pi$
$390$		0			0
$391$	−11.9533	+	6.90127i	−0.604507	+	0.349012i
$392$		0			0
$393$	−12.1117	−	13.5477i	−0.610954	−	0.683389i
$394$		0			0
$395$	−5.43662			−0.273546
$396$		0			0
$397$		−	3.03390i		−	0.152267i	−0.997098	−	0.0761336i	$-0.975742\pi$
$397$		−	3.03390i		−	0.152267i	0.997098	−	0.0761336i	$-0.0242575\pi$
$398$		0			0
$399$	9.13106	+	10.3814i	0.457125	+	0.519719i
$400$		0			0
$401$	11.3251	−	6.53854i	0.565548	−	0.326519i	−0.189822	−	0.981819i	$-0.560791\pi$
$401$	11.3251	−	6.53854i	0.565548	−	0.326519i	0.755369	+	0.655300i	$0.227458\pi$
$402$		0			0
$403$	−11.3640	+	19.6831i	−0.566083	+	0.980485i
$404$		0			0
$405$	−15.7120	−	3.57322i	−0.780733	−	0.177555i
$406$		0			0
$407$	19.4750	+	11.2439i	0.965339	+	0.557339i
$408$		0			0
$409$	4.82124	−	2.78354i	0.238395	−	0.137637i	−0.376044	−	0.926602i	$-0.622716\pi$
$409$	4.82124	−	2.78354i	0.238395	−	0.137637i	0.614439	+	0.788965i	$0.289382\pi$
$410$		0			0
$411$	7.76707	+	2.55414i	0.383121	+	0.125987i
$412$		0			0
$413$	−33.2728	−	19.5705i	−1.63725	−	0.963000i
$414$		0			0
$415$	−25.0746			−1.23086
$416$		0			0
$417$	−3.05223	+	2.72871i	−0.149468	+	0.133625i
$418$		0			0
$419$	−8.19938	−	14.2017i	−0.400566	−	0.693800i	0.593228	−	0.805034i	$-0.297853\pi$
$419$	−8.19938	−	14.2017i	−0.400566	−	0.693800i	−0.993794	+	0.111234i	$0.964520\pi$
$420$		0			0
$421$	−7.72892	+	13.3869i	−0.376684	+	0.652437i	−0.990578	−	0.136952i	$-0.956269\pi$
$421$	−7.72892	+	13.3869i	−0.376684	+	0.652437i	0.613893	+	0.789389i	$0.289603\pi$
$422$		0			0
$423$	−1.71917	+	15.3119i	−0.0835889	+	0.744491i
$424$		0			0
$425$	3.28839	−	5.69566i	0.159510	−	0.276280i
$426$		0			0
$427$	29.9708	+	0.242361i	1.45039	+	0.0117287i
$428$		0			0
$429$	19.9159	−	4.15953i	0.961547	−	0.200824i
$430$		0			0
$431$		−	25.0266i		−	1.20549i	−0.797935	−	0.602744i	$-0.794074\pi$
$431$		−	25.0266i		−	1.20549i	0.797935	−	0.602744i	$-0.205926\pi$
$432$		0			0
$433$		−	2.25168i		−	0.108209i	−0.998535	−	0.0541044i	$-0.982770\pi$
$433$		−	2.25168i		−	0.108209i	0.998535	−	0.0541044i	$-0.0172304\pi$
$434$		0			0
$435$	−4.15953	−	19.9159i	−0.199434	−	0.954893i
$436$		0			0
$437$	5.68161	+	9.84084i	0.271788	+	0.470751i
$438$		0			0
$439$	−16.2293	−	9.37000i	−0.774583	−	0.447206i	0.0599239	−	0.998203i	$-0.480914\pi$
$439$	−16.2293	−	9.37000i	−0.774583	−	0.447206i	−0.834507	+	0.550997i	$0.814248\pi$
$440$		0			0
$441$	2.68027	−	20.8283i	0.127632	−	0.991822i
$442$		0			0
$443$	1.04314	+	0.602256i	0.0495610	+	0.0286141i	0.524576	−	0.851364i	$-0.324224\pi$
$443$	1.04314	+	0.602256i	0.0495610	+	0.0286141i	−0.475015	+	0.879978i	$0.657557\pi$
$444$		0			0
$445$	3.35568	+	5.81221i	0.159074	+	0.275525i
$446$		0			0
$447$	22.4216	−	20.0450i	1.06050	−	0.948097i
$448$		0			0
$449$		−	26.8022i		−	1.26487i	−0.774612	−	0.632436i	$-0.782055\pi$
$449$		−	26.8022i		−	1.26487i	0.774612	−	0.632436i	$-0.217945\pi$
$450$		0			0
$451$		−	19.4087i		−	0.913918i
$452$		0			0
$453$	6.07770	−	18.4821i	0.285555	−	0.868364i
$454$		0			0
$455$	23.1686	+	0.187354i	1.08616	+	0.00878331i
$456$		0			0
$457$	−6.92442	+	11.9934i	−0.323911	+	0.561030i	−0.981291	−	0.192529i	$-0.938331\pi$
$457$	−6.92442	+	11.9934i	−0.323911	+	0.561030i	0.657381	+	0.753559i	$0.271664\pi$
$458$		0			0
$459$	−15.5236	+	11.0283i	−0.724578	+	0.514755i
$460$		0			0
$461$	2.40241	−	4.16110i	0.111892	−	0.193802i	−0.804641	−	0.593761i	$-0.797642\pi$
$461$	2.40241	−	4.16110i	0.111892	−	0.193802i	0.916533	+	0.399959i	$0.130976\pi$
$462$		0			0
$463$	−10.5194	−	18.2201i	−0.488877	−	0.846760i	0.511041	−	0.859556i	$-0.329260\pi$
$463$	−10.5194	−	18.2201i	−0.488877	−	0.846760i	−0.999918	+	0.0127960i	$0.995927\pi$
$464$		0			0
$465$	13.6879	+	4.50118i	0.634763	+	0.208737i
$466$		0			0
$467$	−5.82302			−0.269457			−0.134729	−	0.990883i	$-0.543016\pi$
$467$	−5.82302			−0.269457			−0.134729	+	0.990883i	$0.543016\pi$
$468$		0			0
$469$	1.30042	+	0.764885i	0.0600478	+	0.0353191i
$470$		0			0
$471$	−17.8751	+	15.9804i	−0.823640	+	0.736339i
$472$		0			0
$473$	14.4804	−	8.36028i	0.665811	−	0.384406i
$474$		0			0
$475$	−4.68907	−	2.70724i	−0.215149	−	0.124217i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−13.4781	+	23.3447i	−0.615828	+	1.06665i	0.374411	+	0.927263i	$0.377845\pi$
$479$	−13.4781	+	23.3447i	−0.615828	+	1.06665i	−0.990239	+	0.139382i	$0.955488\pi$
$480$		0			0
$481$	−39.6662	+	22.9013i	−1.80862	+	1.04421i
$482$		0			0
$483$	5.52410	−	16.3518i	0.251355	−	0.744035i
$484$		0			0
$485$		−	9.86639i		−	0.448010i
$486$		0			0
$487$	13.6268			0.617487			0.308744	−	0.951145i	$-0.400091\pi$
$487$	13.6268			0.617487			0.308744	+	0.951145i	$0.400091\pi$
$488$		0			0
$489$	−7.35116	+	1.53533i	−0.332431	+	0.0694299i
$490$		0			0
$491$	33.7430	−	19.4815i	1.52280	−	0.879188i	0.523162	−	0.852234i	$-0.324752\pi$
$491$	33.7430	−	19.4815i	1.52280	−	0.879188i	0.999637	−	0.0269544i	$-0.00858088\pi$
$492$		0			0
$493$	−20.8227	−	12.0220i	−0.937807	−	0.541443i
$494$		0			0
$495$	−5.16267	−	11.8203i	−0.232045	−	0.531285i
$496$		0			0
$497$	−7.77696	−	13.7252i	−0.348844	−	0.615660i
$498$		0			0
$499$	13.0048	+	22.5250i	0.582176	+	1.00836i	0.995221	+	0.0976483i	$0.0311320\pi$
$499$	13.0048	+	22.5250i	0.582176	+	1.00836i	−0.413045	+	0.910711i	$0.635535\pi$
$500$		0			0
$501$	−14.3320	−	16.0312i	−0.640307	−	0.716221i
$502$		0			0
$503$	−10.5271			−0.469378			−0.234689	−	0.972070i	$-0.575407\pi$
$503$	−10.5271			−0.469378			−0.234689	+	0.972070i	$0.575407\pi$
$504$		0			0
$505$	0.448168			0.0199432
$506$		0			0
$507$	−5.91121	+	17.9758i	−0.262526	+	0.798333i
$508$		0			0
$509$	0.469435	+	0.813086i	0.0208074	+	0.0360394i	0.876242	−	0.481872i	$-0.160043\pi$
$509$	0.469435	+	0.813086i	0.0208074	+	0.0360394i	−0.855434	+	0.517911i	$0.826710\pi$
$510$		0			0
$511$	−16.1491	−	28.5009i	−0.714395	−	1.26081i
$512$		0			0
$513$	9.07925	+	12.7801i	0.400859	+	0.564255i
$514$		0			0
$515$	0.260376	+	0.150328i	0.0114735	+	0.00662424i
$516$		0			0
$517$	−10.6818	+	6.16711i	−0.469783	+	0.271229i
$518$		0			0
$519$	−9.42442	+	28.6593i	−0.413686	+	1.25801i
$520$		0			0
$521$	−39.5054			−1.73076			−0.865382	−	0.501112i	$-0.832924\pi$
$521$	−39.5054			−1.73076			−0.865382	+	0.501112i	$0.832924\pi$
$522$		0			0
$523$			24.3292i			1.06384i	0.846794	+	0.531922i	$0.178530\pi$
$523$			24.3292i			1.06384i	−0.846794	+	0.531922i	$0.821470\pi$
$524$		0			0
$525$	1.61621	+	8.06374i	0.0705373	+	0.351930i
$526$		0			0
$527$	14.7469	−	8.51413i	0.642385	−	0.370881i
$528$		0			0
$529$	−4.40718	+	7.63346i	−0.191616	+	0.331889i
$530$		0			0
$531$	−35.2274	−	25.9777i	−1.52874	−	1.12734i
$532$		0			0
$533$	34.2349	+	19.7655i	1.48288	+	0.856141i
$534$		0			0
$535$	12.3896	−	7.15316i	0.535651	−	0.309258i
$536$		0			0
$537$	4.64661	+	22.2480i	0.200516	+	0.960073i
$538$		0			0
$539$	14.6924	−	8.16873i	0.632845	−	0.351852i
$540$		0			0
$541$	42.7281			1.83702			0.918512	−	0.395394i	$-0.129392\pi$
$541$	42.7281			1.83702			0.918512	+	0.395394i	$0.129392\pi$
$542$		0			0
$543$	−4.73007	−	22.6476i	−0.202987	−	0.971902i
$544$		0			0
$545$	16.9665	+	29.3869i	0.726767	+	1.25880i
$546$		0			0
$547$	12.2477	−	21.2136i	0.523672	−	0.907026i	−0.475949	−	0.879473i	$-0.657895\pi$
$547$	12.2477	−	21.2136i	0.523672	−	0.907026i	0.999620	−	0.0275530i	$-0.00877149\pi$
$548$		0			0
$549$	33.7727	+	3.79188i	1.44138	+	0.161833i
$550$		0			0
$551$	−9.89735	+	17.1427i	−0.421641	+	0.730304i
$552$		0			0
$553$	0.0649667	−	8.03389i	0.00276266	−	0.341636i
$554$		0			0
$555$	19.3534	+	21.6479i	0.821506	+	0.918903i
$556$		0			0
$557$			2.54431i			0.107806i	0.998546	+	0.0539030i	$0.0171662\pi$
$557$			2.54431i			0.107806i	−0.998546	+	0.0539030i	$0.982834\pi$
$558$		0			0
$559$			34.0560i			1.44042i
$560$		0			0
$561$	−14.4804	−	4.76178i	−0.611364	−	0.201043i
$562$		0			0
$563$	7.90707	+	13.6954i	0.333243	+	0.577194i	0.983146	−	0.182823i	$-0.0585236\pi$
$563$	7.90707	+	13.6954i	0.333243	+	0.577194i	−0.649902	+	0.760018i	$0.725190\pi$
$564$		0			0
$565$	1.79783	+	1.03798i	0.0756354	+	0.0436681i
$566$		0			0
$567$	5.46803	−	23.1754i	0.229635	−	0.973277i
$568$		0			0
$569$	−5.52793	−	3.19155i	−0.231743	−	0.133797i	0.379633	−	0.925137i	$-0.376050\pi$
$569$	−5.52793	−	3.19155i	−0.231743	−	0.133797i	−0.611376	+	0.791340i	$0.709384\pi$
$570$		0			0
$571$	−3.91188	−	6.77557i	−0.163707	−	0.283549i	0.772488	−	0.635029i	$-0.219012\pi$
$571$	−3.91188	−	6.77557i	−0.163707	−	0.283549i	−0.936195	+	0.351480i	$0.885678\pi$
$572$		0			0
$573$	−15.2252	−	5.00668i	−0.636040	−	0.209157i
$574$		0			0
$575$			6.75933i			0.281884i
$576$		0			0
$577$			14.3197i			0.596138i	0.954544	+	0.298069i	$0.0963425\pi$
$577$			14.3197i			0.596138i	−0.954544	+	0.298069i	$0.903657\pi$
$578$		0			0
$579$	−28.3523	−	31.7137i	−1.17828	−	1.31798i
$580$		0			0
$581$	0.299637	−	37.0536i	0.0124310	−	1.53724i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	26.1075	+	2.93126i	1.07941	+	0.121193i
$586$		0			0
$587$	2.37575	−	4.11492i	0.0980577	−	0.169841i	−0.812823	−	0.582511i	$-0.802070\pi$
$587$	2.37575	−	4.11492i	0.0980577	−	0.169841i	0.910881	+	0.412670i	$0.135404\pi$
$588$		0			0
$589$	−7.00943	−	12.1407i	−0.288819	−	0.500249i
$590$		0			0
$591$	4.42141	+	21.1698i	0.181873	+	0.870808i
$592$		0			0
$593$	3.58070			0.147042			0.0735208	−	0.997294i	$-0.476576\pi$
$593$	3.58070			0.147042			0.0735208	+	0.997294i	$0.476576\pi$
$594$		0			0
$595$	−14.9625	−	8.80071i	−0.613404	−	0.360794i
$596$		0			0
$597$	0.0634366	+	0.303735i	0.00259629	+	0.0124311i
$598$		0			0
$599$	13.0471	−	7.53277i	0.533091	−	0.307780i	−0.209183	−	0.977877i	$-0.567080\pi$
$599$	13.0471	−	7.53277i	0.533091	−	0.307780i	0.742274	+	0.670096i	$0.233747\pi$
$600$		0			0
$601$	−19.8704	−	11.4722i	−0.810530	−	0.467960i	0.0366096	−	0.999330i	$-0.488344\pi$
$601$	−19.8704	−	11.4722i	−0.810530	−	0.467960i	−0.847140	+	0.531370i	$0.821678\pi$
$602$		0			0
$603$	1.37682	+	1.01531i	0.0560683	+	0.0413464i
$604$		0			0
$605$	−4.68425	+	8.11336i	−0.190442	+	0.329855i
$606$		0			0
$607$	−21.2030	+	12.2416i	−0.860605	+	0.496870i	−0.864215	−	0.503123i	$-0.832184\pi$
$607$	−21.2030	+	12.2416i	−0.860605	+	0.496870i	0.00360990	+	0.999993i	$0.498851\pi$
$608$		0			0
$609$	29.4801	−	5.90869i	1.19459	−	0.239432i
$610$		0			0
$611$		−	25.1221i		−	1.01633i
$612$		0			0
$613$	−0.880086			−0.0355463			−0.0177732	−	0.999842i	$-0.505658\pi$
$613$	−0.880086			−0.0355463			−0.0177732	+	0.999842i	$0.505658\pi$
$614$		0			0
$615$	7.82892	−	23.8075i	0.315693	−	0.960011i
$616$		0			0
$617$	−11.7607	+	6.79005i	−0.473468	+	0.273357i	−0.717690	−	0.696362i	$-0.754801\pi$
$617$	−11.7607	+	6.79005i	−0.473468	+	0.273357i	0.244222	+	0.969719i	$0.421467\pi$
$618$		0			0
$619$	30.7325	+	17.7434i	1.23524	+	0.713169i	0.968118	−	0.250493i	$-0.0805926\pi$
$619$	30.7325	+	17.7434i	1.23524	+	0.713169i	0.267126	+	0.963662i	$0.413926\pi$
$620$		0			0
$621$	8.14977	−	17.7931i	0.327039	−	0.714012i
$622$		0			0
$623$	−8.62901	+	4.88936i	−0.345714	+	0.195888i
$624$		0			0
$625$	6.40300	+	11.0903i	0.256120	+	0.443613i
$626$		0			0
$627$	−3.92024	+	11.9213i	−0.156559	+	0.476091i
$628$		0			0
$629$	34.3161			1.36827
$630$		0			0
$631$	−26.9822			−1.07415			−0.537073	−	0.843536i	$-0.680470\pi$
$631$	−26.9822			−1.07415			−0.537073	+	0.843536i	$0.680470\pi$
$632$		0			0
$633$	17.4569	+	19.5266i	0.693849	+	0.776112i
$634$		0			0
$635$	1.25459	+	2.17302i	0.0497869	+	0.0862335i
$636$		0			0
$637$	−0.553721	+	34.2348i	−0.0219392	+	1.35643i
$638$		0			0
$639$	−7.15953	−	16.3923i	−0.283227	−	0.648470i
$640$		0			0
$641$	0.932777	+	0.538539i	0.0368425	+	0.0212710i	0.518308	−	0.855194i	$-0.326562\pi$
$641$	0.932777	+	0.538539i	0.0368425	+	0.0212710i	−0.481466	+	0.876465i	$0.659895\pi$
$642$		0			0
$643$	−33.3126	+	19.2330i	−1.31372	+	0.758477i	−0.982710	−	0.185150i	$-0.940723\pi$
$643$	−33.3126	+	19.2330i	−1.31372	+	0.758477i	−0.331010	+	0.943627i	$0.607389\pi$
$644$		0			0
$645$	21.1346	−	4.41407i	0.832175	−	0.173804i
$646$		0			0
$647$	8.95210			0.351943			0.175972	−	0.984395i	$-0.443693\pi$
$647$	8.95210			0.351943			0.175972	+	0.984395i	$0.443693\pi$
$648$		0			0
$649$		−	35.0380i		−	1.37536i
$650$		0			0
$651$	−6.81512	+	20.1734i	−0.267106	+	0.790656i
$652$		0			0
$653$	−9.85934	+	5.69229i	−0.385826	+	0.222757i	−0.680350	−	0.732887i	$-0.738172\pi$
$653$	−9.85934	+	5.69229i	−0.385826	+	0.222757i	0.294524	+	0.955644i	$0.404839\pi$
$654$		0			0
$655$	9.39197	−	16.2674i	0.366975	−	0.635619i
$656$		0			0
$657$	−14.8670	−	34.0392i	−0.580017	−	1.32799i
$658$		0			0
$659$	−31.4373	−	18.1503i	−1.22462	−	0.707036i	−0.258723	−	0.965952i	$-0.583302\pi$
$659$	−31.4373	−	18.1503i	−1.22462	−	0.707036i	−0.965900	+	0.258915i	$0.916635\pi$
$660$		0			0
$661$	−31.2425	+	18.0379i	−1.21519	+	0.701593i	−0.963886	−	0.266315i	$-0.914194\pi$
$661$	−31.2425	+	18.0379i	−1.21519	+	0.701593i	−0.251308	+	0.967907i	$0.580861\pi$
$662$		0			0
$663$	23.1460	−	20.6927i	0.898916	−	0.803637i
$664$		0			0
$665$	−7.24536	+	12.3182i	−0.280963	+	0.477680i
$666$		0			0
$667$	24.7114			0.956828
$668$		0			0
$669$	−13.8133	−	4.54240i	−0.534052	−	0.175619i
$670$		0			0
$671$	13.6025	+	23.5602i	0.525117	+	0.909530i
$672$		0			0
$673$	4.78512	−	8.28806i	0.184453	−	0.319481i	−0.758939	−	0.651161i	$-0.774282\pi$
$673$	4.78512	−	8.28806i	0.184453	−	0.319481i	0.943392	+	0.331680i	$0.107615\pi$
$674$		0			0
$675$	0.876091	+	9.28402i	0.0337207	+	0.357342i
$676$		0			0
$677$	7.81408	−	13.5344i	0.300320	−	0.520169i	−0.675889	−	0.737004i	$-0.736240\pi$
$677$	7.81408	−	13.5344i	0.300320	−	0.520169i	0.976208	+	0.216835i	$0.0695733\pi$
$678$		0			0
$679$	14.5799	+	0.117902i	0.559526	+	0.00452465i
$680$		0			0
$681$	1.31221	−	3.99038i	0.0502839	−	0.152912i
$682$		0			0
$683$			11.1313i			0.425926i	0.977060	+	0.212963i	$0.0683114\pi$
$683$			11.1313i			0.425926i	−0.977060	+	0.212963i	$0.931689\pi$
$684$		0			0
$685$			8.45145i			0.322913i
$686$		0			0
$687$	−2.60803	+	2.33159i	−0.0995025	+	0.0889559i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−2.61903	−	1.51210i	−0.0996324	−	0.0575228i	0.449356	−	0.893353i	$-0.351654\pi$
$691$	−2.61903	−	1.51210i	−0.0996324	−	0.0575228i	−0.548988	+	0.835830i	$0.684987\pi$
$692$		0			0
$693$	17.5291	−	7.48782i	0.665874	−	0.284439i
$694$		0			0
$695$	−3.66497	−	2.11597i	−0.139020	−	0.0802633i
$696$		0			0
$697$	−14.8087	−	25.6494i	−0.560919	−	0.971540i
$698$		0			0
$699$	−4.50739	−	21.5815i	−0.170485	−	0.816286i
$700$		0			0
$701$		−	50.1486i		−	1.89409i	−0.321103	−	0.947044i	$-0.604054\pi$
$701$		−	50.1486i		−	1.89409i	0.321103	−	0.947044i	$-0.395946\pi$
$702$		0			0
$703$		−	28.2514i		−	1.06552i
$704$		0			0
$705$	−15.5904	+	3.25612i	−0.587167	+	0.122633i
$706$		0			0
$707$	−0.00535553	+	0.662274i	−0.000201415	+	0.0249074i
$708$		0			0
$709$	1.80385	−	3.12436i	0.0677449	−	0.117338i	−0.830163	−	0.557520i	$-0.811753\pi$
$709$	1.80385	−	3.12436i	0.0677449	−	0.117338i	0.897908	+	0.440183i	$0.145086\pi$
$710$		0			0
$711$	1.01644	−	9.05299i	0.0381195	−	0.339514i
$712$		0			0
$713$	−8.75046	+	15.1562i	−0.327707	+	0.567605i
$714$		0			0
$715$	10.5152	+	18.2129i	0.393246	+	0.681123i
$716$		0			0
$717$	22.5319	−	20.1437i	0.841469	−	0.752279i
$718$		0			0
$719$	34.3161			1.27977			0.639887	−	0.768469i	$-0.278981\pi$
$719$	34.3161			1.27977			0.639887	+	0.768469i	$0.278981\pi$
$720$		0			0
$721$	−0.225257	+	0.382970i	−0.00838899	+	0.0142626i
$722$		0			0
$723$	−18.8118	−	6.18613i	−0.699619	−	0.230065i
$724$		0			0
$725$	−10.1972	+	5.88737i	−0.378716	+	0.218651i
$726$		0			0
$727$	−19.4757	−	11.2443i	−0.722315	−	0.417029i	0.0932892	−	0.995639i	$-0.470262\pi$
$727$	−19.4757	−	11.2443i	−0.722315	−	0.417029i	−0.815604	+	0.578610i	$0.803595\pi$
$728$		0			0
$729$	8.88761	−	25.4953i	0.329171	−	0.944270i
$730$		0			0
$731$	12.7577	−	22.0970i	0.471860	−	0.817285i
$732$		0			0
$733$	27.0065	−	15.5922i	0.997509	−	0.575912i	0.0899987	−	0.995942i	$-0.471314\pi$
$733$	27.0065	−	15.5922i	0.997509	−	0.575912i	0.907510	+	0.420030i	$0.137980\pi$
$734$		0			0
$735$	21.3173	−	4.09361i	0.786302	−	0.150995i
$736$		0			0
$737$			1.36941i			0.0504429i
$738$		0			0
$739$	−4.08628			−0.150316			−0.0751581	−	0.997172i	$-0.523946\pi$
$739$	−4.08628			−0.150316			−0.0751581	+	0.997172i	$0.523946\pi$
$740$		0			0
$741$	−17.0357	−	19.0554i	−0.625821	−	0.700018i
$742$		0			0
$743$	1.78246	−	1.02910i	0.0653921	−	0.0377542i	−0.466947	−	0.884285i	$-0.654646\pi$
$743$	1.78246	−	1.02910i	0.0653921	−	0.0377542i	0.532340	+	0.846531i	$0.321313\pi$
$744$		0			0
$745$	26.9227	+	15.5439i	0.986373	+	0.569483i
$746$		0			0
$747$	4.68798	−	41.7538i	0.171524	−	1.52769i
$748$		0			0
$749$	10.4224	+	18.3941i	0.380828	+	0.672106i
$750$		0			0
$751$	11.9053	+	20.6205i	0.434429	+	0.752454i	0.997249	−	0.0741262i	$-0.0236168\pi$
$751$	11.9053	+	20.6205i	0.434429	+	0.752454i	−0.562820	+	0.826580i	$0.690283\pi$
$752$		0			0
$753$	−46.3811	+	9.68693i	−1.69022	+	0.353011i
$754$		0			0
$755$	20.1106			0.731900
$756$		0			0
$757$	10.0754			0.366197			0.183098	−	0.983095i	$-0.441387\pi$
$757$	10.0754			0.366197			0.183098	+	0.983095i	$0.441387\pi$
$758$		0			0
$759$	15.3355	−	3.20289i	0.556642	−	0.116258i
$760$		0			0
$761$	13.9368	+	24.1392i	0.505207	+	0.875044i	0.999982	+	0.00602283i	$0.00191714\pi$
$761$	13.9368	+	24.1392i	0.505207	+	0.875044i	−0.494775	+	0.869021i	$0.664750\pi$
$762$		0			0
$763$	−43.6289	+	24.7209i	−1.57947	+	0.894957i
$764$		0			0
$765$	−15.8415	−	11.6820i	−0.572752	−	0.422364i
$766$		0			0
$767$	61.8035	+	35.6823i	2.23159	+	1.28841i
$768$		0			0
$769$	−6.21166	+	3.58631i	−0.223998	+	0.129326i	−0.607800	−	0.794090i	$-0.707948\pi$
$769$	−6.21166	+	3.58631i	−0.223998	+	0.129326i	0.383802	+	0.923415i	$0.374615\pi$
$770$		0			0
$771$	−4.03663	−	4.51521i	−0.145376	−	0.162611i
$772$		0			0
$773$	−2.14153			−0.0770255			−0.0385128	−	0.999258i	$-0.512262\pi$
$773$	−2.14153			−0.0770255			−0.0385128	+	0.999258i	$0.512262\pi$
$774$		0			0
$775$		−	8.33903i		−	0.299547i
$776$		0			0
$777$	−32.2212	+	28.3405i	−1.15593	+	1.01671i
$778$		0			0
$779$	−21.1164	+	12.1916i	−0.756573	+	0.436808i
$780$		0			0
$781$	7.15953	−	12.4007i	0.256188	−	0.443731i
$782$		0			0
$783$	33.9413	−	3.20289i	1.21296	−	0.114462i
$784$		0			0
$785$	−21.4635	−	12.3920i	−0.766066	−	0.442288i
$786$		0			0
$787$	−15.8961	+	9.17759i	−0.566633	+	0.327146i	−0.755804	−	0.654798i	$-0.772753\pi$
$787$	−15.8961	+	9.17759i	−0.566633	+	0.327146i	0.189170	+	0.981944i	$0.439420\pi$
$788$		0			0
$789$	−15.8671	−	5.21778i	−0.564884	−	0.185758i
$790$		0			0
$791$	−1.55534	+	2.64432i	−0.0553017	+	0.0940212i
$792$		0			0
$793$	−55.4103			−1.96768
$794$		0			0
$795$		0			0
$796$		0			0
$797$	12.4226	+	21.5166i	0.440031	+	0.762156i	0.997691	−	0.0679130i	$-0.0216340\pi$
$797$	12.4226	+	21.5166i	0.440031	+	0.762156i	−0.557660	+	0.830069i	$0.688301\pi$
$798$		0			0
$799$	−9.41094	+	16.3002i	−0.332935	+	0.576660i
$800$		0			0
$801$	−10.3058	+	4.50118i	−0.364138	+	0.159041i
$802$		0			0
$803$	14.8670	−	25.7504i	0.524645	−	0.908712i
$804$		0			0
$805$	17.8401	+	0.144265i	0.628781	+	0.00508468i
$806$		0			0
$807$	11.7175	−	2.44726i	0.412475	−	0.0861475i
$808$		0			0
$809$			37.7861i			1.32849i	0.747516	+	0.664244i	$0.231246\pi$
$809$			37.7861i			1.32849i	−0.747516	+	0.664244i	$0.768754\pi$
$810$		0			0
$811$			36.5165i			1.28227i	0.767429	+	0.641134i	$0.221536\pi$
$811$			36.5165i			1.28227i	−0.767429	+	0.641134i	$0.778464\pi$
$812$		0			0
$813$	7.30565	+	34.9795i	0.256220	+	1.22679i
$814$		0			0
$815$	−3.88128	−	6.72257i	−0.135955	−	0.235481i
$816$		0			0
$817$	−18.1918	−	10.5030i	−0.636449	−	0.367454i
$818$		0			0
$819$	−4.64361	+	38.5450i	−0.162261	+	1.34687i
$820$		0			0
$821$	−5.52142	−	3.18779i	−0.192699	−	0.111255i	0.400547	−	0.916276i	$-0.368820\pi$
$821$	−5.52142	−	3.18779i	−0.192699	−	0.111255i	−0.593245	+	0.805022i	$0.702154\pi$
$822$		0			0
$823$	14.0293	+	24.2995i	0.489032	+	0.847028i	0.999920	−	0.0126187i	$-0.00401678\pi$
$823$	14.0293	+	24.2995i	0.489032	+	0.847028i	−0.510888	+	0.859647i	$0.670683\pi$
$824$		0			0
$825$	−5.56516	+	4.97529i	−0.193754	+	0.173217i
$826$		0			0
$827$		−	0.581579i		−	0.0202235i	−0.999949	−	0.0101117i	$-0.996781\pi$
$827$		−	0.581579i		−	0.0202235i	0.999949	−	0.0101117i	$-0.00321872\pi$
$828$		0			0
$829$		−	51.9246i		−	1.80342i	−0.432346	−	0.901708i	$-0.642314\pi$
$829$		−	51.9246i		−	1.80342i	0.432346	−	0.901708i	$-0.357686\pi$
$830$		0			0
$831$	−8.39433	+	25.5269i	−0.291196	+	0.885518i
$832$		0			0
$833$	13.1839	−	22.0055i	0.456796	−	0.762446i
$834$		0			0
$835$	11.1137	−	19.2495i	0.384606	−	0.666156i
$836$		0			0
$837$	−10.0544	+	21.9514i	−0.347532	+	0.758752i
$838$		0			0
$839$	3.33038	−	5.76838i	0.114977	−	0.199147i	−0.802793	−	0.596257i	$-0.796654\pi$
$839$	3.33038	−	5.76838i	0.114977	−	0.199147i	0.917771	+	0.397111i	$0.129987\pi$
$840$		0			0
$841$	7.02357	+	12.1652i	0.242192	+	0.419489i
$842$		0			0
$843$	−22.3732	−	7.35726i	−0.770574	−	0.253397i
$844$		0			0
$845$	−19.5597			−0.672874
$846$		0			0
$847$	−11.9334	−	7.01904i	−0.410038	−	0.241177i
$848$		0			0
$849$	−7.03459	+	6.28897i	−0.241427	+	0.215837i
$850$		0			0
$851$	−30.5435	+	17.6343i	−1.04702	+	0.604495i
$852$		0			0
$853$	−19.2287	−	11.1017i	−0.658378	−	0.380115i	0.133281	−	0.991078i	$-0.457449\pi$
$853$	−19.2287	−	11.1017i	−0.658378	−	0.380115i	−0.791659	+	0.610964i	$0.790782\pi$
$854$		0			0
$855$	−9.61746	+	13.0419i	−0.328910	+	0.446023i
$856$		0			0
$857$	−7.64830	+	13.2472i	−0.261261	+	0.452517i	−0.966577	−	0.256375i	$-0.917472\pi$
$857$	−7.64830	+	13.2472i	−0.261261	+	0.452517i	0.705316	+	0.708893i	$0.250805\pi$
$858$		0			0
$859$	−3.68620	+	2.12823i	−0.125772	+	0.0726143i	−0.561566	−	0.827432i	$-0.689801\pi$
$859$	−3.68620	+	2.12823i	−0.125772	+	0.0726143i	0.435794	+	0.900046i	$0.356468\pi$
$860$		0			0
$861$	35.0877	+	11.8536i	1.19578	+	0.403969i
$862$		0			0
$863$		−	23.6624i		−	0.805476i	−0.915315	−	0.402738i	$-0.868059\pi$
$863$		−	23.6624i		−	0.805476i	0.915315	−	0.402738i	$-0.131941\pi$
$864$		0			0
$865$	−31.1846			−1.06031
$866$		0			0
$867$	6.05321	−	1.26424i	0.205578	−	0.0429359i
$868$		0			0
$869$	6.31546	−	3.64623i	0.214237	−	0.123690i
$870$		0			0
$871$	−2.41551	−	1.39459i	−0.0818463	−	0.0472540i
$872$		0			0
$873$	16.4294	+	1.84464i	0.556051	+	0.0624315i
$874$		0			0
$875$	−28.0023	+	15.8666i	−0.946649	+	0.536389i
$876$		0			0
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	0.985226	−	0.171258i	$-0.0547831\pi$
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	−0.640927	+	0.767602i	$0.721450\pi$
$878$		0			0
$879$	−28.2392	−	31.5872i	−0.952484	−	1.06541i
$880$		0			0
$881$	32.4586			1.09356			0.546780	−	0.837276i	$-0.315853\pi$
$881$	32.4586			1.09356			0.546780	+	0.837276i	$0.315853\pi$
$882$		0			0
$883$	24.8311			0.835632			0.417816	−	0.908532i	$-0.362796\pi$
$883$	24.8311			0.835632			0.417816	+	0.908532i	$0.362796\pi$
$884$		0			0
$885$	14.1334	−	42.9791i	0.475088	−	1.44473i
$886$		0			0
$887$	4.86059	+	8.41879i	0.163203	+	0.282675i	0.936016	−	0.351959i	$-0.114484\pi$
$887$	4.86059	+	8.41879i	0.163203	+	0.282675i	−0.772813	+	0.634634i	$0.781151\pi$
$888$		0			0
$889$	−3.22614	+	1.82799i	−0.108201	+	0.0613088i
$890$		0			0
$891$	20.6483	−	6.38687i	0.691745	−	0.213968i
$892$		0			0
$893$	13.4195	+	7.74775i	0.449066	+	0.259269i
$894$		0			0
$895$	−20.3456	+	11.7465i	−0.680079	+	0.392644i
$896$		0			0
$897$	−9.96789	+	30.3120i	−0.332818	+	1.01209i
$898$		0			0
$899$	−30.4865			−1.01678
$900$		0			0
$901$		0			0
$902$		0			0
$903$	6.27028	+	31.2842i	0.208662	+	1.04107i
$904$		0			0
$905$	20.7110	−	11.9575i	0.688458	−	0.397481i
$906$		0			0
$907$	−8.04314	+	13.9311i	−0.267068	+	0.462575i	−0.968103	−	0.250551i	$-0.919388\pi$
$907$	−8.04314	+	13.9311i	−0.267068	+	0.462575i	0.701035	+	0.713127i	$0.252722\pi$
$908$		0			0
$909$	−0.0837902	+	0.746284i	−0.00277915	+	0.0247527i
$910$		0			0
$911$	−27.0087	−	15.5935i	−0.894838	−	0.516635i	−0.0193161	−	0.999813i	$-0.506149\pi$
$911$	−27.0087	−	15.5935i	−0.894838	−	0.516635i	−0.875522	+	0.483179i	$0.839482\pi$
$912$		0			0
$913$	29.1279	−	16.8170i	0.963993	−	0.556562i
$914$		0			0
$915$	7.18184	+	34.3868i	0.237424	+	1.13679i
$916$		0			0
$917$	23.9267	+	14.0733i	0.790128	+	0.464740i
$918$		0			0
$919$	−25.7664			−0.849955			−0.424977	−	0.905204i	$-0.639718\pi$
$919$	−25.7664			−0.849955			−0.424977	+	0.905204i	$0.639718\pi$
$920$		0			0
$921$	−11.0560	−	52.9363i	−0.364308	−	1.74431i
$922$		0			0
$923$	14.5824	+	25.2574i	0.479984	+	0.831357i
$924$		0			0
$925$	8.40258	−	14.5537i	0.276275	−	0.478522i
$926$		0			0
$927$	−0.299004	+	0.405469i	−0.00982060	+	0.0133173i
$928$		0			0
$929$	−27.3744	+	47.4138i	−0.898124	+	1.55560i	−0.0682329	+	0.997669i	$0.521736\pi$
$929$	−27.3744	+	47.4138i	−0.898124	+	1.55560i	−0.829891	+	0.557926i	$0.811597\pi$
$930$		0			0
$931$	−18.1165	−	10.8539i	−0.593744	−	0.355723i
$932$		0			0
$933$	−12.5945	−	14.0877i	−0.412326	−	0.461212i
$934$		0			0
$935$		−	15.7563i		−	0.515288i
$936$		0			0
$937$			58.2065i			1.90152i	0.309924	+	0.950761i	$0.399696\pi$
$937$			58.2065i			1.90152i	−0.309924	+	0.950761i	$0.600304\pi$
$938$		0			0
$939$	−5.63384	−	1.85265i	−0.183853	−	0.0604588i
$940$		0			0
$941$	16.6658	+	28.8660i	0.543289	+	0.941005i	0.998712	+	0.0507297i	$0.0161547\pi$
$941$	16.6658	+	28.8660i	0.543289	+	0.941005i	−0.455423	+	0.890275i	$0.650512\pi$
$942$		0			0
$943$	26.3613	+	15.2197i	0.858443	+	0.495622i
$944$		0			0
$945$	24.5223	−	2.11414i	0.797710	−	0.0687730i
$946$		0			0
$947$	6.59497	+	3.80761i	0.214308	+	0.123731i	0.603312	−	0.797505i	$-0.293847\pi$
$947$	6.59497	+	3.80761i	0.214308	+	0.123731i	−0.389004	+	0.921236i	$0.627181\pi$
$948$		0			0
$949$	30.2808	+	52.4478i	0.982955	+	1.70253i
$950$		0			0
$951$	−31.3396	−	10.3058i	−1.01626	−	0.334188i
$952$		0			0
$953$			55.7861i			1.80709i	0.428495	+	0.903544i	$0.359044\pi$
$953$			55.7861i			1.80709i	−0.428495	+	0.903544i	$0.640956\pi$
$954$		0			0
$955$		−	16.5667i		−	0.536085i
$956$		0			0
$957$	18.1891	+	20.3456i	0.587970	+	0.657680i
$958$		0			0
$959$	−12.4890	−	0.100993i	−0.403291	−	0.00326125i
$960$		0			0
$961$	−4.70451	+	8.14845i	−0.151758	+	0.262853i
$962$		0			0
$963$	9.59497	+	21.9684i	0.309194	+	0.707923i
$964$		0			0
$965$	21.9857	−	38.0803i	0.707744	−	1.22585i
$966$		0			0
$967$	13.3369	+	23.1003i	0.428887	+	0.742855i	0.996775	−	0.0802517i	$-0.0255724\pi$
$967$	13.3369	+	23.1003i	0.428887	+	0.742855i	−0.567887	+	0.823106i	$0.692239\pi$
$968$		0			0
$969$	3.91512	+	18.7456i	0.125772	+	0.602197i
$970$		0			0
$971$	8.59942			0.275968			0.137984	−	0.990434i	$-0.455938\pi$
$971$	8.59942			0.275968			0.137984	+	0.990434i	$0.455938\pi$
$972$		0			0
$973$	3.17064	−	5.39057i	0.101646	−	0.172814i
$974$		0			0
$975$	−3.10842	−	14.8832i	−0.0995492	−	0.476643i
$976$		0			0
$977$	−12.7973	+	7.38854i	−0.409423	+	0.236380i	−0.690542	−	0.723293i	$-0.742628\pi$
$977$	−12.7973	+	7.38854i	−0.409423	+	0.236380i	0.281119	+	0.959673i	$0.409295\pi$
$978$		0			0
$979$	−7.79627	−	4.50118i	−0.249170	−	0.143858i
$980$		0			0
$981$	−52.1068	+	22.7583i	−1.66364	+	0.726615i
$982$		0			0
$983$	−10.2568	+	17.7652i	−0.327140	+	0.566623i	−0.981943	−	0.189176i	$-0.939418\pi$
$983$	−10.2568	+	17.7652i	−0.327140	+	0.566623i	0.654803	+	0.755800i	$0.272752\pi$
$984$		0			0
$985$	−19.3596	+	11.1772i	−0.616847	+	0.356137i
$986$		0			0
$987$	−4.62539	−	23.0773i	−0.147228	−	0.734560i
$988$		0			0
$989$			26.2236i			0.833861i
$990$		0			0
$991$	9.29294			0.295200			0.147600	−	0.989047i	$-0.452845\pi$
$991$	9.29294			0.295200			0.147600	+	0.989047i	$0.452845\pi$
$992$		0			0
$993$	−0.0396334	+	0.120524i	−0.00125773	+	0.00382471i
$994$		0			0
$995$	−0.277763	+	0.160366i	−0.00880567	+	0.00508396i
$996$		0			0
$997$	−0.0172917	−	0.00998339i	−0.000547635	−	0.000316177i	0.499726	−	0.866183i	$-0.333434\pi$
$997$	−0.0172917	−	0.00998339i	−0.000547635	−	0.000316177i	−0.500274	+	0.865867i	$0.666767\pi$
$998$		0			0
$999$	−39.6662	+	28.1797i	−1.25498	+	0.891566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cc.b.209.1		16
3.2	odd	2		3024.2.cc.b.2897.6		16
4.3	odd	2		126.2.m.a.83.8	yes	16
7.6	odd	2	inner	1008.2.cc.b.209.8		16
9.4	even	3		3024.2.cc.b.881.3		16
9.5	odd	6	inner	1008.2.cc.b.545.8		16
12.11	even	2		378.2.m.a.251.4		16
21.20	even	2		3024.2.cc.b.2897.3		16
28.3	even	6		882.2.t.b.803.3		16
28.11	odd	6		882.2.t.b.803.2		16
28.19	even	6		882.2.l.a.227.3		16
28.23	odd	6		882.2.l.a.227.2		16
28.27	even	2		126.2.m.a.83.5	yes	16
36.7	odd	6		1134.2.d.a.1133.6		16
36.11	even	6		1134.2.d.a.1133.11		16
36.23	even	6		126.2.m.a.41.5	✓	16
36.31	odd	6		378.2.m.a.125.1		16
63.13	odd	6		3024.2.cc.b.881.6		16
63.41	even	6	inner	1008.2.cc.b.545.1		16
84.11	even	6		2646.2.t.a.1979.5		16
84.23	even	6		2646.2.l.b.521.8		16
84.47	odd	6		2646.2.l.b.521.5		16
84.59	odd	6		2646.2.t.a.1979.8		16
84.83	odd	2		378.2.m.a.251.1		16
252.23	even	6		882.2.t.b.815.3		16
252.31	even	6		2646.2.l.b.1097.4		16
252.59	odd	6		882.2.l.a.509.6		16
252.67	odd	6		2646.2.l.b.1097.1		16
252.83	odd	6		1134.2.d.a.1133.14		16
252.95	even	6		882.2.l.a.509.7		16
252.103	even	6		2646.2.t.a.2285.5		16
252.131	odd	6		882.2.t.b.815.2		16
252.139	even	6		378.2.m.a.125.4		16
252.167	odd	6		126.2.m.a.41.8	yes	16
252.223	even	6		1134.2.d.a.1133.3		16
252.247	odd	6		2646.2.t.a.2285.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.5	✓	16	36.23	even	6
126.2.m.a.41.8	yes	16	252.167	odd	6
126.2.m.a.83.5	yes	16	28.27	even	2
126.2.m.a.83.8	yes	16	4.3	odd	2
378.2.m.a.125.1		16	36.31	odd	6
378.2.m.a.125.4		16	252.139	even	6
378.2.m.a.251.1		16	84.83	odd	2
378.2.m.a.251.4		16	12.11	even	2
882.2.l.a.227.2		16	28.23	odd	6
882.2.l.a.227.3		16	28.19	even	6
882.2.l.a.509.6		16	252.59	odd	6
882.2.l.a.509.7		16	252.95	even	6
882.2.t.b.803.2		16	28.11	odd	6
882.2.t.b.803.3		16	28.3	even	6
882.2.t.b.815.2		16	252.131	odd	6
882.2.t.b.815.3		16	252.23	even	6
1008.2.cc.b.209.1		16	1.1	even	1	trivial
1008.2.cc.b.209.8		16	7.6	odd	2	inner
1008.2.cc.b.545.1		16	63.41	even	6	inner
1008.2.cc.b.545.8		16	9.5	odd	6	inner
1134.2.d.a.1133.3		16	252.223	even	6
1134.2.d.a.1133.6		16	36.7	odd	6
1134.2.d.a.1133.11		16	36.11	even	6
1134.2.d.a.1133.14		16	252.83	odd	6
2646.2.l.b.521.5		16	84.47	odd	6
2646.2.l.b.521.8		16	84.23	even	6
2646.2.l.b.1097.1		16	252.67	odd	6
2646.2.l.b.1097.4		16	252.31	even	6
2646.2.t.a.1979.5		16	84.11	even	6
2646.2.t.a.1979.8		16	84.59	odd	6
2646.2.t.a.2285.5		16	252.103	even	6
2646.2.t.a.2285.8		16	252.247	odd	6
3024.2.cc.b.881.3		16	9.4	even	3
3024.2.cc.b.881.6		16	63.13	odd	6
3024.2.cc.b.2897.3		16	21.20	even	2
3024.2.cc.b.2897.6		16	3.2	odd	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.69547 + 0.354107i) q^{3} +(-0.895175 - 1.55049i) q^{5} +(2.30191 - 1.30430i) q^{7} +(2.74922 - 1.20075i) q^{9} +(2.07976 + 1.20075i) q^{11} +(-4.23601 + 2.44566i) q^{13} +(2.06678 + 2.31181i) q^{15} +3.66466 q^{17} -3.01701i q^{19} +(-3.44095 + 3.02653i) q^{21} +(-3.26178 + 1.88319i) q^{23} +(0.897324 - 1.55421i) q^{25} +(-4.23601 + 3.00935i) q^{27} +(-5.68202 - 3.28052i) q^{29} +(4.02408 - 2.32330i) q^{31} +(-3.95136 - 1.29938i) q^{33} +(-4.08292 - 2.40150i) q^{35} +9.36404 q^{37} +(6.31599 - 5.64654i) q^{39} +(-4.04094 - 6.99911i) q^{41} +(3.48127 - 6.02973i) q^{43} +(-4.32278 - 3.18775i) q^{45} +(-2.56802 + 4.44794i) q^{47} +(3.59758 - 6.00478i) q^{49} +(-6.21332 + 1.29768i) q^{51} -4.29953i q^{55} +(1.06834 + 5.11524i) q^{57} +(-7.29501 - 12.6353i) q^{59} +(9.81058 + 5.66414i) q^{61} +(4.76230 - 6.34984i) q^{63} +(7.58394 + 4.37859i) q^{65} +(0.285115 + 0.493834i) q^{67} +(4.86340 - 4.34791i) q^{69} -5.96254i q^{71} -12.3814i q^{73} +(-0.971027 + 2.95286i) q^{75} +(6.35358 + 0.0513786i) q^{77} +(1.51831 - 2.62979i) q^{79} +(6.11639 - 6.60226i) q^{81} +(7.00270 - 12.1290i) q^{83} +(-3.28052 - 5.68202i) q^{85} +(10.7953 + 3.54997i) q^{87} -3.74863 q^{89} +(-6.56103 + 11.1547i) q^{91} +(-6.00000 + 5.36404i) q^{93} +(-4.67784 + 2.70075i) q^{95} +(4.77256 + 2.75544i) q^{97} +(7.15953 + 0.803848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7} + 12 q^{9} + 12 q^{11} + 18 q^{21} + 48 q^{23} - 8 q^{25} - 12 q^{29} - 8 q^{37} + 36 q^{39} - 4 q^{43} - 8 q^{49} - 12 q^{51} + 48 q^{57} - 24 q^{63} + 84 q^{65} + 28 q^{67} + 78 q^{77}+ \cdots + 72 q^{99}+O(q^{100}) \) 16 * q - 2 * q^7 + 12 * q^9 + 12 * q^11 + 18 * q^21 + 48 * q^23 - 8 * q^25 - 12 * q^29 - 8 * q^37 + 36 * q^39 - 4 * q^43 - 8 * q^49 - 12 * q^51 + 48 * q^57 - 24 * q^63 + 84 * q^65 + 28 * q^67 + 78 * q^77 + 4 * q^79 + 36 * q^81 - 12 * q^85 - 24 * q^91 - 96 * q^93 - 12 * q^95 + 72 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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