LMFDB - Embedded newform 504.2.cx.a.425.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(185,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.185"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cx (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			425.13
Character	$\chi$	$=$	504.425
Dual form			504.2.cx.a.185.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.149059 + 1.72562i) q^{3} -2.22094 q^{5} +(-2.45091 + 0.996507i) q^{7} +(-2.95556 + 0.514438i) q^{9} -1.17296i q^{11} +(3.12404 - 1.80366i) q^{13} +(-0.331050 - 3.83251i) q^{15} +(-3.71178 - 6.42899i) q^{17} +(-3.05231 - 1.76225i) q^{19} +(-2.08493 - 4.08082i) q^{21} +5.81246i q^{23} -0.0674336 q^{25} +(-1.32828 - 5.02351i) q^{27} +(-6.04430 - 3.48968i) q^{29} +(6.88517 + 3.97516i) q^{31} +(2.02410 - 0.174840i) q^{33} +(5.44333 - 2.21318i) q^{35} +(-5.54350 + 9.60163i) q^{37} +(3.57811 + 5.12207i) q^{39} +(-0.809022 - 1.40127i) q^{41} +(0.904302 - 1.56630i) q^{43} +(6.56412 - 1.14254i) q^{45} +(-4.26476 - 7.38679i) q^{47} +(5.01395 - 4.88471i) q^{49} +(10.5407 - 7.36343i) q^{51} +(-9.62611 + 5.55764i) q^{53} +2.60508i q^{55} +(2.58602 - 5.52983i) q^{57} +(-2.00138 + 3.46649i) q^{59} +(-7.09004 + 4.09344i) q^{61} +(6.73119 - 4.20608i) q^{63} +(-6.93830 + 4.00583i) q^{65} +(-4.96334 + 8.59676i) q^{67} +(-10.0301 + 0.866397i) q^{69} +3.67194i q^{71} +(6.92803 - 3.99990i) q^{73} +(-0.0100516 - 0.116365i) q^{75} +(1.16887 + 2.87483i) q^{77} +(2.25993 + 3.91432i) q^{79} +(8.47071 - 3.04091i) q^{81} +(-0.390969 + 0.677179i) q^{83} +(8.24363 + 14.2784i) q^{85} +(5.12092 - 10.9504i) q^{87} +(1.75440 - 3.03870i) q^{89} +(-5.85938 + 7.53375i) q^{91} +(-5.83334 + 12.4738i) q^{93} +(6.77900 + 3.91386i) q^{95} +(-3.49226 - 2.01626i) q^{97} +(0.603418 + 3.46677i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61}+ \cdots - 64 q^{99}+O(q^{100}) $ 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	0.149059	+	1.72562i	0.0860590	+	0.996290i
$3$	0.149059	+	1.72562i	0.0860590	+	0.996290i
$4$		0			0
$5$	−2.22094			−0.993234			−0.496617	−	0.867970i	$-0.665425\pi$
$5$	−2.22094			−0.993234			−0.496617	+	0.867970i	$0.665425\pi$
$6$		0			0
$7$	−2.45091	+	0.996507i	−0.926358	+	0.376644i
$7$	−2.45091	+	0.996507i	−0.926358	+	0.376644i
$8$		0			0
$9$	−2.95556	+	0.514438i	−0.985188	+	0.171479i
$10$		0			0
$11$		−	1.17296i		−	0.353662i	−0.984241	−	0.176831i	$-0.943415\pi$
$11$		−	1.17296i		−	0.353662i	0.984241	−	0.176831i	$-0.0565846\pi$
$12$		0			0
$13$	3.12404	−	1.80366i	0.866453	−	0.500247i	0.000284763	−	1.00000i	$-0.499909\pi$
$13$	3.12404	−	1.80366i	0.866453	−	0.500247i	0.866168	+	0.499753i	$0.166576\pi$
$14$		0			0
$15$	−0.331050	−	3.83251i	−0.0854767	−	0.989549i
$16$		0			0
$17$	−3.71178	−	6.42899i	−0.900238	−	1.55926i	−0.827185	−	0.561930i	$-0.810059\pi$
$17$	−3.71178	−	6.42899i	−0.900238	−	1.55926i	−0.0730533	−	0.997328i	$-0.523274\pi$
$18$		0			0
$19$	−3.05231	−	1.76225i	−0.700249	−	0.404289i	0.107191	−	0.994238i	$-0.465814\pi$
$19$	−3.05231	−	1.76225i	−0.700249	−	0.404289i	−0.807440	+	0.589950i	$0.799148\pi$
$20$		0			0
$21$	−2.08493	−	4.08082i	−0.454969	−	0.890508i
$22$		0			0
$23$			5.81246i			1.21198i	0.795472	+	0.605991i	$0.207223\pi$
$23$			5.81246i			1.21198i	−0.795472	+	0.605991i	$0.792777\pi$
$24$		0			0
$25$	−0.0674336			−0.0134867
$26$		0			0
$27$	−1.32828	−	5.02351i	−0.255628	−	0.966775i
$28$		0			0
$29$	−6.04430	−	3.48968i	−1.12240	−	0.648017i	−0.180387	−	0.983596i	$-0.557735\pi$
$29$	−6.04430	−	3.48968i	−1.12240	−	0.648017i	−0.942012	+	0.335579i	$0.891068\pi$
$30$		0			0
$31$	6.88517	+	3.97516i	1.23661	+	0.713959i	0.968400	−	0.249400i	$-0.0802335\pi$
$31$	6.88517	+	3.97516i	1.23661	+	0.713959i	0.268213	+	0.963360i	$0.413567\pi$
$32$		0			0
$33$	2.02410	−	0.174840i	0.352350	−	0.0304358i
$34$		0			0
$35$	5.44333	−	2.21318i	0.920090	−	0.374096i
$36$		0			0
$37$	−5.54350	+	9.60163i	−0.911346	+	1.57850i	−0.0991818	+	0.995069i	$0.531623\pi$
$37$	−5.54350	+	9.60163i	−0.911346	+	1.57850i	−0.812164	+	0.583429i	$0.801711\pi$
$38$		0			0
$39$	3.57811	+	5.12207i	0.572957	+	0.820187i
$40$		0			0
$41$	−0.809022	−	1.40127i	−0.126348	−	0.218841i	0.795911	−	0.605414i	$-0.206992\pi$
$41$	−0.809022	−	1.40127i	−0.126348	−	0.218841i	−0.922259	+	0.386572i	$0.873659\pi$
$42$		0			0
$43$	0.904302	−	1.56630i	0.137905	−	0.238858i	−0.788799	−	0.614652i	$-0.789297\pi$
$43$	0.904302	−	1.56630i	0.137905	−	0.238858i	0.926703	+	0.375794i	$0.122630\pi$
$44$		0			0
$45$	6.56412	−	1.14254i	0.978522	−	0.170319i
$46$		0			0
$47$	−4.26476	−	7.38679i	−0.622080	−	1.07747i	−0.989098	−	0.147260i	$-0.952955\pi$
$47$	−4.26476	−	7.38679i	−0.622080	−	1.07747i	0.367018	−	0.930214i	$-0.380379\pi$
$48$		0			0
$49$	5.01395	−	4.88471i	0.716278	−	0.697815i
$50$		0			0
$51$	10.5407	−	7.36343i	1.47600	−	1.03109i
$52$		0			0
$53$	−9.62611	+	5.55764i	−1.32225	+	0.763400i	−0.984087	−	0.177688i	$-0.943138\pi$
$53$	−9.62611	+	5.55764i	−1.32225	+	0.763400i	−0.338161	+	0.941088i	$0.609805\pi$
$54$		0			0
$55$			2.60508i			0.351269i
$56$		0			0
$57$	2.58602	−	5.52983i	0.342526	−	0.732444i
$58$		0			0
$59$	−2.00138	+	3.46649i	−0.260557	+	0.451298i	−0.966390	−	0.257080i	$-0.917240\pi$
$59$	−2.00138	+	3.46649i	−0.260557	+	0.451298i	0.705833	+	0.708378i	$0.250573\pi$
$60$		0			0
$61$	−7.09004	+	4.09344i	−0.907787	+	0.524111i	−0.879718	−	0.475495i	$-0.842269\pi$
$61$	−7.09004	+	4.09344i	−0.907787	+	0.524111i	−0.0280684	+	0.999606i	$0.508936\pi$
$62$		0			0
$63$	6.73119	−	4.20608i	0.848050	−	0.529917i
$64$		0			0
$65$	−6.93830	+	4.00583i	−0.860590	+	0.496862i
$66$		0			0
$67$	−4.96334	+	8.59676i	−0.606369	+	1.05026i	0.385465	+	0.922723i	$0.374041\pi$
$67$	−4.96334	+	8.59676i	−0.606369	+	1.05026i	−0.991834	+	0.127539i	$0.959292\pi$
$68$		0			0
$69$	−10.0301	+	0.866397i	−1.20749	+	0.104302i
$70$		0			0
$71$			3.67194i			0.435779i	0.975973	+	0.217890i	$0.0699172\pi$
$71$			3.67194i			0.435779i	−0.975973	+	0.217890i	$0.930083\pi$
$72$		0			0
$73$	6.92803	−	3.99990i	0.810865	−	0.468153i	−0.0363913	−	0.999338i	$-0.511586\pi$
$73$	6.92803	−	3.99990i	0.810865	−	0.468153i	0.847256	+	0.531185i	$0.178253\pi$
$74$		0			0
$75$	−0.0100516	−	0.116365i	−0.00116065	−	0.0134367i
$76$		0			0
$77$	1.16887	+	2.87483i	0.133205	+	0.327618i
$78$		0			0
$79$	2.25993	+	3.91432i	0.254262	+	0.440395i	0.964695	−	0.263370i	$-0.0848340\pi$
$79$	2.25993	+	3.91432i	0.254262	+	0.440395i	−0.710433	+	0.703765i	$0.751501\pi$
$80$		0			0
$81$	8.47071	−	3.04091i	0.941190	−	0.337879i
$82$		0			0
$83$	−0.390969	+	0.677179i	−0.0429145	+	0.0743300i	−0.886685	−	0.462374i	$-0.846998\pi$
$83$	−0.390969	+	0.677179i	−0.0429145	+	0.0743300i	0.843770	+	0.536704i	$0.180331\pi$
$84$		0			0
$85$	8.24363	+	14.2784i	0.894147	+	1.54871i
$86$		0			0
$87$	5.12092	−	10.9504i	0.549021	−	1.17400i
$88$		0			0
$89$	1.75440	−	3.03870i	0.185966	−	0.322102i	−0.757936	−	0.652329i	$-0.773792\pi$
$89$	1.75440	−	3.03870i	0.185966	−	0.322102i	0.943901	+	0.330227i	$0.107125\pi$
$90$		0			0
$91$	−5.85938	+	7.53375i	−0.614230	+	0.789752i
$92$		0			0
$93$	−5.83334	+	12.4738i	−0.604889	+	1.29347i
$94$		0			0
$95$	6.77900	+	3.91386i	0.695511	+	0.401553i
$96$		0			0
$97$	−3.49226	−	2.01626i	−0.354585	−	0.204720i	0.312118	−	0.950043i	$-0.398962\pi$
$97$	−3.49226	−	2.01626i	−0.354585	−	0.204720i	−0.666703	+	0.745324i	$0.732295\pi$
$98$		0			0
$99$	0.603418	+	3.46677i	0.0606458	+	0.348424i
$100$		0			0
$101$	2.27809			0.226678			0.113339	−	0.993556i	$-0.463845\pi$
$101$	2.27809			0.226678			0.113339	+	0.993556i	$0.463845\pi$
$102$		0			0
$103$			8.87303i			0.874285i	0.899392	+	0.437143i	$0.144010\pi$
$103$			8.87303i			0.874285i	−0.899392	+	0.437143i	$0.855990\pi$
$104$		0			0
$105$	4.63050	+	9.06324i	0.451890	+	0.884482i
$106$		0			0
$107$	−0.574764	−	0.331840i	−0.0555646	−	0.0320802i	0.471960	−	0.881620i	$-0.343547\pi$
$107$	−0.574764	−	0.331840i	−0.0555646	−	0.0320802i	−0.527525	+	0.849540i	$0.676880\pi$
$108$		0			0
$109$	−8.03435	−	13.9159i	−0.769551	−	1.33290i	−0.937807	−	0.347158i	$-0.887147\pi$
$109$	−8.03435	−	13.9159i	−0.769551	−	1.33290i	0.168256	−	0.985743i	$-0.446187\pi$
$110$		0			0
$111$	−17.3951	−	8.13480i	−1.65107	−	0.772121i
$112$		0			0
$113$	−4.86666	+	2.80977i	−0.457817	+	0.264321i	−0.711126	−	0.703065i	$-0.751814\pi$
$113$	−4.86666	+	2.80977i	−0.457817	+	0.264321i	0.253309	+	0.967385i	$0.418481\pi$
$114$		0			0
$115$		−	12.9091i		−	1.20378i
$116$		0			0
$117$	−8.30542	+	6.93797i	−0.767836	+	0.641416i
$118$		0			0
$119$	15.5038	+	12.0581i	1.42123	+	1.10536i
$120$		0			0
$121$	9.62415			0.874923
$122$		0			0
$123$	2.29747	−	1.60494i	0.207156	−	0.144713i
$124$		0			0
$125$	11.2545			1.00663
$126$		0			0
$127$	7.74425			0.687191			0.343595	−	0.939118i	$-0.388355\pi$
$127$	7.74425			0.687191			0.343595	+	0.939118i	$0.388355\pi$
$128$		0			0
$129$	2.83764	+	1.32702i	0.249840	+	0.116837i
$130$		0			0
$131$	−15.6259			−1.36524			−0.682619	−	0.730774i	$-0.739159\pi$
$131$	−15.6259			−1.36524			−0.682619	+	0.730774i	$0.739159\pi$
$132$		0			0
$133$	9.23705	+	1.27748i	0.800954	+	0.110771i
$134$		0			0
$135$	2.95003	+	11.1569i	0.253898	+	0.960234i
$136$		0			0
$137$			1.07565i			0.0918991i	0.998944	+	0.0459496i	$0.0146313\pi$
$137$			1.07565i			0.0918991i	−0.998944	+	0.0459496i	$0.985369\pi$
$138$		0			0
$139$	5.81776	−	3.35889i	0.493456	−	0.284897i	−0.232551	−	0.972584i	$-0.574707\pi$
$139$	5.81776	−	3.35889i	0.493456	−	0.284897i	0.726007	+	0.687687i	$0.241374\pi$
$140$		0			0
$141$	12.1111	−	8.46045i	1.01994	−	0.712498i
$142$		0			0
$143$	−2.11563	−	3.66439i	−0.176918	−	0.306431i
$144$		0			0
$145$	13.4240	+	7.75036i	1.11480	+	0.643633i
$146$		0			0
$147$	9.17654	+	7.92408i	0.756868	+	0.653567i
$148$		0			0
$149$		−	17.5635i		−	1.43886i	−0.694565	−	0.719430i	$-0.744403\pi$
$149$		−	17.5635i		−	1.43886i	0.694565	−	0.719430i	$-0.255597\pi$
$150$		0			0
$151$	1.69606			0.138023			0.0690115	−	0.997616i	$-0.478015\pi$
$151$	1.69606			0.138023			0.0690115	+	0.997616i	$0.478015\pi$
$152$		0			0
$153$	14.2777	+	17.0918i	1.15428	+	1.38179i
$154$		0			0
$155$	−15.2915	−	8.82858i	−1.22825	−	0.709128i
$156$		0			0
$157$	6.82630	+	3.94116i	0.544798	+	0.314539i	0.747021	−	0.664800i	$-0.231483\pi$
$157$	6.82630	+	3.94116i	0.544798	+	0.314539i	−0.202223	+	0.979339i	$0.564817\pi$
$158$		0			0
$159$	−11.0253	−	15.7826i	−0.874360	−	1.25165i
$160$		0			0
$161$	−5.79216	−	14.2458i	−0.456486	−	1.12273i
$162$		0			0
$163$	−5.69385	+	9.86204i	−0.445977	+	0.772455i	−0.998120	−	0.0612949i	$-0.980477\pi$
$163$	−5.69385	+	9.86204i	−0.445977	+	0.772455i	0.552143	+	0.833750i	$0.313810\pi$
$164$		0			0
$165$	−4.49539	+	0.388310i	−0.349966	+	0.0302299i
$166$		0			0
$167$	8.05638	+	13.9541i	0.623422	+	1.07980i	0.988844	+	0.148956i	$0.0475913\pi$
$167$	8.05638	+	13.9541i	0.623422	+	1.07980i	−0.365422	+	0.930842i	$0.619075\pi$
$168$		0			0
$169$	0.00641296	−	0.0111076i	0.000493305	−	0.000854429i
$170$		0			0
$171$	9.92788	+	3.63823i	0.759204	+	0.278222i
$172$		0			0
$173$	3.45182	+	5.97872i	0.262437	+	0.454554i	0.966889	−	0.255198i	$-0.0821405\pi$
$173$	3.45182	+	5.97872i	0.262437	+	0.454554i	−0.704452	+	0.709752i	$0.748807\pi$
$174$		0			0
$175$	0.165274	−	0.0671981i	0.0124935	−	0.00507970i
$176$		0			0
$177$	−6.28018	−	2.93692i	−0.472047	−	0.220752i
$178$		0			0
$179$	−5.28759	+	3.05279i	−0.395213	+	0.228176i	−0.684416	−	0.729091i	$-0.739943\pi$
$179$	−5.28759	+	3.05279i	−0.395213	+	0.228176i	0.289203	+	0.957268i	$0.406610\pi$
$180$		0			0
$181$		−	5.46329i		−	0.406083i	−0.979170	−	0.203041i	$-0.934917\pi$
$181$		−	5.46329i		−	0.406083i	0.979170	−	0.203041i	$-0.0650826\pi$
$182$		0			0
$183$	−8.12057	−	11.6246i	−0.600290	−	0.859315i
$184$		0			0
$185$	12.3118	−	21.3246i	0.905180	−	1.56782i
$186$		0			0
$187$	−7.54097	+	4.35378i	−0.551451	+	0.318380i
$188$		0			0
$189$	8.26147	+	10.9885i	0.600933	+	0.799299i
$190$		0			0
$191$	5.21032	−	3.00818i	0.377005	−	0.217664i	−0.299509	−	0.954093i	$-0.596823\pi$
$191$	5.21032	−	3.00818i	0.377005	−	0.217664i	0.676515	+	0.736429i	$0.263490\pi$
$192$		0			0
$193$	2.89017	−	5.00592i	0.208039	−	0.360334i	−0.743058	−	0.669227i	$-0.766625\pi$
$193$	2.89017	−	5.00592i	0.208039	−	0.360334i	0.951097	+	0.308893i	$0.0999586\pi$
$194$		0			0
$195$	−7.94677	−	11.3758i	−0.569080	−	0.814638i
$196$		0			0
$197$			7.95354i			0.566666i	0.959022	+	0.283333i	$0.0914402\pi$
$197$			7.95354i			0.566666i	−0.959022	+	0.283333i	$0.908560\pi$
$198$		0			0
$199$	−15.5229	+	8.96214i	−1.10039	+	0.635309i	−0.936323	−	0.351141i	$-0.885794\pi$
$199$	−15.5229	+	8.96214i	−1.10039	+	0.635309i	−0.164065	+	0.986450i	$0.552461\pi$
$200$		0			0
$201$	−15.5746	−	7.28345i	−1.09855	−	0.513735i
$202$		0			0
$203$	18.2915	+	2.52971i	1.28382	+	0.177551i
$204$		0			0
$205$	1.79679	+	3.11213i	0.125493	+	0.217360i
$206$		0			0
$207$	−2.99015	−	17.1791i	−0.207830	−	1.19403i
$208$		0			0
$209$	−2.06706	+	3.58026i	−0.142982	+	0.247651i
$210$		0			0
$211$	−4.00200	−	6.93166i	−0.275509	−	0.477195i	0.694755	−	0.719247i	$-0.255513\pi$
$211$	−4.00200	−	6.93166i	−0.275509	−	0.477195i	−0.970263	+	0.242052i	$0.922180\pi$
$212$		0			0
$213$	−6.33639	+	0.547334i	−0.434162	+	0.0375027i
$214$		0			0
$215$	−2.00840	+	3.47865i	−0.136972	+	0.237242i
$216$		0			0
$217$	−20.8362	−	2.88164i	−1.41446	−	0.195618i
$218$		0			0
$219$	7.93501	+	11.3590i	0.536198	+	0.767568i
$220$		0			0
$221$	−23.1915	−	13.3896i	−1.56003	−	0.900682i
$222$		0			0
$223$	−14.2405	−	8.22177i	−0.953616	−	0.550570i	−0.0594134	−	0.998233i	$-0.518923\pi$
$223$	−14.2405	−	8.22177i	−0.953616	−	0.550570i	−0.894202	+	0.447663i	$0.852256\pi$
$224$		0			0
$225$	0.199304	−	0.0346904i	0.0132869	−	0.00231269i
$226$		0			0
$227$	−15.9930			−1.06149			−0.530746	−	0.847531i	$-0.678088\pi$
$227$	−15.9930			−1.06149			−0.530746	+	0.847531i	$0.678088\pi$
$228$		0			0
$229$		−	15.4612i		−	1.02170i	−0.859669	−	0.510851i	$-0.829330\pi$
$229$		−	15.4612i		−	1.02170i	0.859669	−	0.510851i	$-0.170670\pi$
$230$		0			0
$231$	−4.78665	+	2.44555i	−0.314939	+	0.160905i
$232$		0			0
$233$	16.5268	+	9.54175i	1.08271	+	0.625101i	0.931625	−	0.363421i	$-0.118391\pi$
$233$	16.5268	+	9.54175i	1.08271	+	0.625101i	0.151081	+	0.988521i	$0.451725\pi$
$234$		0			0
$235$	9.47178	+	16.4056i	0.617871	+	1.07018i
$236$		0			0
$237$	−6.41778	+	4.48326i	−0.416880	+	0.291219i
$238$		0			0
$239$	7.37626	−	4.25868i	0.477130	−	0.275471i	−0.242089	−	0.970254i	$-0.577833\pi$
$239$	7.37626	−	4.25868i	0.477130	−	0.275471i	0.719220	+	0.694783i	$0.244499\pi$
$240$		0			0
$241$		−	22.6376i		−	1.45821i	−0.684400	−	0.729107i	$-0.739936\pi$
$241$		−	22.6376i		−	1.45821i	0.684400	−	0.729107i	$-0.260064\pi$
$242$		0			0
$243$	6.51010	+	14.1640i	0.417623	+	0.908620i
$244$		0			0
$245$	−11.1357	+	10.8486i	−0.711431	+	0.693093i
$246$		0			0
$247$	−12.7141			−0.808976
$248$		0			0
$249$	−1.22683	−	0.573727i	−0.0777474	−	0.0363585i
$250$		0			0
$251$	7.74235			0.488693			0.244346	−	0.969688i	$-0.421427\pi$
$251$	7.74235			0.488693			0.244346	+	0.969688i	$0.421427\pi$
$252$		0			0
$253$	6.81781			0.428632
$254$		0			0
$255$	−23.4103	+	16.3537i	−1.46601	+	1.02411i
$256$		0			0
$257$	−23.7890			−1.48392			−0.741958	−	0.670447i	$-0.766103\pi$
$257$	−23.7890			−1.48392			−0.741958	+	0.670447i	$0.766103\pi$
$258$		0			0
$259$	4.01855	−	29.0569i	0.249700	−	1.80551i
$260$		0			0
$261$	19.6595	+	7.20455i	1.21690	+	0.445950i
$262$		0			0
$263$		−	20.5341i		−	1.26619i	−0.774075	−	0.633094i	$-0.781785\pi$
$263$		−	20.5341i		−	1.26619i	0.774075	−	0.633094i	$-0.218215\pi$
$264$		0			0
$265$	21.3790	−	12.3432i	1.31330	−	0.758235i
$266$		0			0
$267$	5.50517	+	2.57448i	0.336911	+	0.157556i
$268$		0			0
$269$	6.17188	+	10.6900i	0.376306	+	0.651782i	0.990522	−	0.137357i	$-0.0438607\pi$
$269$	6.17188	+	10.6900i	0.376306	+	0.651782i	−0.614215	+	0.789138i	$0.710527\pi$
$270$		0			0
$271$	−25.3900	−	14.6589i	−1.54233	−	0.890467i	−0.998691	−	0.0511505i	$-0.983711\pi$
$271$	−25.3900	−	14.6589i	−1.54233	−	0.890467i	−0.543643	−	0.839317i	$-0.682955\pi$
$272$		0			0
$273$	−13.8738	−	8.98812i	−0.839682	−	0.543986i
$274$		0			0
$275$			0.0790972i			0.00476974i
$276$		0			0
$277$	−2.48230			−0.149147			−0.0745735	−	0.997216i	$-0.523760\pi$
$277$	−2.48230			−0.149147			−0.0745735	+	0.997216i	$0.523760\pi$
$278$		0			0
$279$	−22.3945	−	8.20683i	−1.34073	−	0.491330i
$280$		0			0
$281$	20.0970	+	11.6030i	1.19889	+	0.692178i	0.960307	−	0.278944i	$-0.0899845\pi$
$281$	20.0970	+	11.6030i	1.19889	+	0.692178i	0.238581	+	0.971123i	$0.423318\pi$
$282$		0			0
$283$	−23.6425	−	13.6500i	−1.40540	−	0.811408i	−0.410460	−	0.911879i	$-0.634632\pi$
$283$	−23.6425	−	13.6500i	−1.40540	−	0.811408i	−0.994940	+	0.100471i	$0.967965\pi$
$284$		0			0
$285$	−5.74338	+	12.2814i	−0.340209	+	0.727488i
$286$		0			0
$287$	3.37922	+	2.62819i	0.199469	+	0.155137i
$288$		0			0
$289$	−19.0546	+	33.0035i	−1.12086	+	1.94138i
$290$		0			0
$291$	2.95875	−	6.32687i	0.173445	−	0.370888i
$292$		0			0
$293$	4.15628	+	7.19888i	0.242812	+	0.420563i	0.961514	−	0.274755i	$-0.0885968\pi$
$293$	4.15628	+	7.19888i	0.242812	+	0.420563i	−0.718702	+	0.695318i	$0.755263\pi$
$294$		0			0
$295$	4.44494	−	7.69886i	0.258794	−	0.448245i
$296$		0			0
$297$	−5.89240	+	1.55803i	−0.341912	+	0.0904058i
$298$		0			0
$299$	10.4837	+	18.1584i	0.606290	+	1.05012i
$300$		0			0
$301$	−0.655539	+	4.74000i	−0.0377846	+	0.273209i
$302$		0			0
$303$	0.339569	+	3.93113i	0.0195077	+	0.225837i
$304$		0			0
$305$	15.7465	−	9.09127i	0.901645	−	0.520565i
$306$		0			0
$307$		−	22.4908i		−	1.28362i	−0.766864	−	0.641810i	$-0.778184\pi$
$307$		−	22.4908i		−	1.28362i	0.766864	−	0.641810i	$-0.221816\pi$
$308$		0			0
$309$	−15.3115	+	1.32260i	−0.871042	+	0.0752401i
$310$		0			0
$311$	4.83900	−	8.38139i	0.274394	−	0.475265i	−0.695588	−	0.718441i	$-0.744856\pi$
$311$	4.83900	−	8.38139i	0.274394	−	0.475265i	0.969982	+	0.243176i	$0.0781893\pi$
$312$		0			0
$313$	21.2150	−	12.2485i	1.19914	−	0.692324i	0.238776	−	0.971075i	$-0.423254\pi$
$313$	21.2150	−	12.2485i	1.19914	−	0.692324i	0.960363	+	0.278751i	$0.0899204\pi$
$314$		0			0
$315$	−14.9495	+	9.34145i	−0.842312	+	0.526331i
$316$		0			0
$317$	7.95548	−	4.59310i	0.446824	−	0.257974i	−0.259664	−	0.965699i	$-0.583612\pi$
$317$	7.95548	−	4.59310i	0.446824	−	0.257974i	0.706488	+	0.707725i	$0.250278\pi$
$318$		0			0
$319$	−4.09327	+	7.08975i	−0.229179	+	0.396950i
$320$		0			0
$321$	0.486958	−	1.04129i	0.0271794	−	0.0581192i
$322$		0			0
$323$			26.1644i			1.45582i
$324$		0			0
$325$	−0.210665	+	0.121628i	−0.0116856	+	0.00674668i
$326$		0			0
$327$	22.8160	−	15.9386i	1.26173	−	0.881404i
$328$		0			0
$329$	17.8136	+	13.8545i	0.982093	+	0.763823i
$330$		0			0
$331$	−12.8599	−	22.2739i	−0.706842	−	1.22429i	−0.966023	−	0.258457i	$-0.916786\pi$
$331$	−12.8599	−	22.2739i	−0.706842	−	1.22429i	0.259181	−	0.965829i	$-0.416547\pi$
$332$		0			0
$333$	11.4447	−	31.2300i	0.627167	−	1.71139i
$334$		0			0
$335$	11.0233	−	19.0929i	0.602266	−	1.04316i
$336$		0			0
$337$	8.80657	+	15.2534i	0.479724	+	0.830907i	0.999730	−	0.0232560i	$-0.00740329\pi$
$337$	8.80657	+	15.2534i	0.479724	+	0.830907i	−0.520005	+	0.854163i	$0.674070\pi$
$338$		0			0
$339$	−5.57402	−	7.97921i	−0.302739	−	0.433371i
$340$		0			0
$341$	4.66272	−	8.07606i	0.252500	−	0.437343i
$342$		0			0
$343$	−7.42110	+	16.9684i	−0.400702	+	0.916209i
$344$		0			0
$345$	22.2763	−	1.92421i	1.19932	−	0.103596i
$346$		0			0
$347$	7.23389	+	4.17649i	0.388335	+	0.224206i	0.681439	−	0.731875i	$-0.261355\pi$
$347$	7.23389	+	4.17649i	0.388335	+	0.224206i	−0.293103	+	0.956081i	$0.594688\pi$
$348$		0			0
$349$	−16.4062	−	9.47211i	−0.878203	−	0.507031i	−0.00813729	−	0.999967i	$-0.502590\pi$
$349$	−16.4062	−	9.47211i	−0.878203	−	0.507031i	−0.870065	+	0.492936i	$0.835924\pi$
$350$		0			0
$351$	−13.2103	−	13.2979i	−0.705115	−	0.709788i
$352$		0			0
$353$	25.4971			1.35707			0.678537	−	0.734566i	$-0.262614\pi$
$353$	25.4971			1.35707			0.678537	+	0.734566i	$0.262614\pi$
$354$		0			0
$355$		−	8.15515i		−	0.432830i
$356$		0			0
$357$	−18.4967	+	28.5511i	−0.978951	+	1.51108i
$358$		0			0
$359$	−17.4128	−	10.0533i	−0.919013	−	0.530592i	−0.0356928	−	0.999363i	$-0.511364\pi$
$359$	−17.4128	−	10.0533i	−0.919013	−	0.530592i	−0.883320	+	0.468771i	$0.844697\pi$
$360$		0			0
$361$	−3.28892	−	5.69658i	−0.173101	−	0.299820i
$362$		0			0
$363$	1.43456	+	16.6077i	0.0752950	+	0.871677i
$364$		0			0
$365$	−15.3867	+	8.88353i	−0.805378	+	0.464985i
$366$		0			0
$367$			23.2850i			1.21547i	0.794140	+	0.607735i	$0.207922\pi$
$367$			23.2850i			1.21547i	−0.794140	+	0.607735i	$0.792078\pi$
$368$		0			0
$369$	3.11198	+	3.72534i	0.162003	+	0.193934i
$370$		0			0
$371$	18.0545	−	23.2138i	0.937345	−	1.20520i
$372$		0			0
$373$	−25.1249			−1.30092			−0.650460	−	0.759540i	$-0.725424\pi$
$373$	−25.1249			−1.30092			−0.650460	+	0.759540i	$0.725424\pi$
$374$		0			0
$375$	1.67757	+	19.4210i	0.0866295	+	1.00289i
$376$		0			0
$377$	−25.1768			−1.29667
$378$		0			0
$379$	32.3000			1.65914			0.829569	−	0.558404i	$-0.188586\pi$
$379$	32.3000			1.65914			0.829569	+	0.558404i	$0.188586\pi$
$380$		0			0
$381$	1.15435	+	13.3637i	0.0591390	+	0.684641i
$382$		0			0
$383$	9.54363			0.487657			0.243828	−	0.969818i	$-0.421597\pi$
$383$	9.54363			0.487657			0.243828	+	0.969818i	$0.421597\pi$
$384$		0			0
$385$	−2.59598	−	6.38483i	−0.132304	−	0.325401i
$386$		0			0
$387$	−1.86696	+	5.09450i	−0.0949028	+	0.258968i
$388$		0			0
$389$			13.6201i			0.690566i	0.938499	+	0.345283i	$0.112217\pi$
$389$			13.6201i			0.690566i	−0.938499	+	0.345283i	$0.887783\pi$
$390$		0			0
$391$	37.3682	−	21.5746i	1.88979	−	1.09107i
$392$		0			0
$393$	−2.32917	−	26.9644i	−0.117491	−	1.36017i
$394$		0			0
$395$	−5.01917	−	8.69346i	−0.252542	−	0.437415i
$396$		0			0
$397$	2.59589	+	1.49874i	0.130284	+	0.0752196i	0.563726	−	0.825962i	$-0.309368\pi$
$397$	2.59589	+	1.49874i	0.130284	+	0.0752196i	−0.433441	+	0.901182i	$0.642701\pi$
$398$		0			0
$399$	−0.827585	+	16.1301i	−0.0414311	+	0.807516i
$400$		0			0
$401$		−	13.0336i		−	0.650869i	−0.945565	−	0.325434i	$-0.894489\pi$
$401$		−	13.0336i		−	0.650869i	0.945565	−	0.325434i	$-0.105511\pi$
$402$		0			0
$403$	28.6794			1.42862
$404$		0			0
$405$	−18.8129	+	6.75367i	−0.934821	+	0.335593i
$406$		0			0
$407$	11.2624	+	6.50233i	0.558255	+	0.322309i
$408$		0			0
$409$	−28.4682	−	16.4361i	−1.40766	−	0.812714i	−0.412500	−	0.910958i	$-0.635344\pi$
$409$	−28.4682	−	16.4361i	−1.40766	−	0.812714i	−0.995162	+	0.0982431i	$0.968678\pi$
$410$		0			0
$411$	−1.85617	+	0.160335i	−0.0915582	+	0.00790875i
$412$		0			0
$413$	1.45082	−	10.4905i	0.0713903	−	0.516201i
$414$		0			0
$415$	0.868319	−	1.50397i	0.0426241	−	0.0738271i
$416$		0			0
$417$	6.66337	+	9.53861i	0.326307	+	0.467108i
$418$		0			0
$419$	11.0687	+	19.1716i	0.540742	+	0.936593i	0.998862	+	0.0477024i	$0.0151899\pi$
$419$	11.0687	+	19.1716i	0.540742	+	0.936593i	−0.458119	+	0.888891i	$0.651477\pi$
$420$		0			0
$421$	12.1963	−	21.1245i	0.594409	−	1.02955i	−0.399221	−	0.916855i	$-0.630719\pi$
$421$	12.1963	−	21.1245i	0.594409	−	1.02955i	0.993630	−	0.112692i	$-0.0359472\pi$
$422$		0			0
$423$	16.4048	+	19.6382i	0.797630	+	0.954840i
$424$		0			0
$425$	0.250298	+	0.433529i	0.0121413	+	0.0210293i
$426$		0			0
$427$	13.2979	−	17.0979i	0.643532	−	0.827427i
$428$		0			0
$429$	6.00800	−	4.19700i	0.290069	−	0.202633i
$430$		0			0
$431$	−12.2611	+	7.07897i	−0.590598	+	0.340982i	−0.765334	−	0.643634i	$-0.777426\pi$
$431$	−12.2611	+	7.07897i	−0.590598	+	0.340982i	0.174736	+	0.984615i	$0.444093\pi$
$432$		0			0
$433$			8.90220i			0.427813i	0.976854	+	0.213906i	$0.0686187\pi$
$433$			8.90220i			0.427813i	−0.976854	+	0.213906i	$0.931381\pi$
$434$		0			0
$435$	−11.3733	+	24.3201i	−0.545306	+	1.16606i
$436$		0			0
$437$	10.2430	−	17.7415i	0.489991	−	0.848689i
$438$		0			0
$439$	−13.9971	+	8.08120i	−0.668043	+	0.385695i	−0.795335	−	0.606171i	$-0.792705\pi$
$439$	−13.9971	+	8.08120i	−0.668043	+	0.385695i	0.127292	+	0.991865i	$0.459372\pi$
$440$		0			0
$441$	−12.3062	+	17.0164i	−0.586007	+	0.810306i
$442$		0			0
$443$	−15.1101	+	8.72383i	−0.717903	+	0.414482i	−0.813980	−	0.580892i	$-0.802704\pi$
$443$	−15.1101	+	8.72383i	−0.717903	+	0.414482i	0.0960772	+	0.995374i	$0.469370\pi$
$444$		0			0
$445$	−3.89640	+	6.74877i	−0.184707	+	0.319922i
$446$		0			0
$447$	30.3080	−	2.61799i	1.43352	−	0.123827i
$448$		0			0
$449$		−	9.14988i		−	0.431809i	−0.976414	−	0.215905i	$-0.930730\pi$
$449$		−	9.14988i		−	0.431809i	0.976414	−	0.215905i	$-0.0692700\pi$
$450$		0			0
$451$	−1.64364	+	0.948954i	−0.0773958	+	0.0446845i
$452$		0			0
$453$	0.252812	+	2.92676i	0.0118781	+	0.137511i
$454$		0			0
$455$	13.0133	−	16.7320i	0.610074	−	0.784408i
$456$		0			0
$457$	−7.05757	−	12.2241i	−0.330139	−	0.571818i	0.652400	−	0.757875i	$-0.273762\pi$
$457$	−7.05757	−	12.2241i	−0.330139	−	0.571818i	−0.982539	+	0.186057i	$0.940429\pi$
$458$		0			0
$459$	−27.3658	+	27.1856i	−1.27733	+	1.26892i
$460$		0			0
$461$	−17.5323	+	30.3668i	−0.816561	+	1.41432i	0.0916412	+	0.995792i	$0.470789\pi$
$461$	−17.5323	+	30.3668i	−0.816561	+	1.41432i	−0.908202	+	0.418532i	$0.862545\pi$
$462$		0			0
$463$	15.9985	+	27.7103i	0.743515	+	1.28781i	0.950885	+	0.309543i	$0.100176\pi$
$463$	15.9985	+	27.7103i	0.743515	+	1.28781i	−0.207370	+	0.978263i	$0.566490\pi$
$464$		0			0
$465$	12.9555	−	27.7034i	0.600796	−	1.28472i
$466$		0			0
$467$	−8.02671	+	13.9027i	−0.371432	+	0.643339i	−0.989786	−	0.142561i	$-0.954466\pi$
$467$	−8.02671	+	13.9027i	−0.371432	+	0.643339i	0.618354	+	0.785899i	$0.287800\pi$
$468$		0			0
$469$	3.59798	−	26.0159i	0.166139	−	1.20130i
$470$		0			0
$471$	−5.78345	+	12.3671i	−0.266487	+	0.569846i
$472$		0			0
$473$	−1.83721	−	1.06071i	−0.0844751	−	0.0487717i
$474$		0			0
$475$	0.205828	+	0.118835i	0.00944406	+	0.00545253i
$476$		0			0
$477$	25.5915	−	21.3780i	1.17176	−	0.978831i
$478$		0			0
$479$	31.4961			1.43909			0.719547	−	0.694443i	$-0.244349\pi$
$479$	31.4961			1.43909			0.719547	+	0.694443i	$0.244349\pi$
$480$		0			0
$481$			39.9945i			1.82359i
$482$		0			0
$483$	23.7196	−	12.1186i	1.07928	−	0.551413i
$484$		0			0
$485$	7.75609	+	4.47798i	0.352186	+	0.203335i
$486$		0			0
$487$	10.7924	+	18.6930i	0.489052	+	0.847062i	0.999921	−	0.0125963i	$-0.00400964\pi$
$487$	10.7924	+	18.6930i	0.489052	+	0.847062i	−0.510869	+	0.859659i	$0.670676\pi$
$488$		0			0
$489$	−17.8669	−	8.35543i	−0.807969	−	0.377846i
$490$		0			0
$491$	−28.9290	+	16.7022i	−1.30555	+	0.753758i	−0.981349	−	0.192232i	$-0.938427\pi$
$491$	−28.9290	+	16.7022i	−1.30555	+	0.753758i	−0.324197	+	0.945990i	$0.605094\pi$
$492$		0			0
$493$			51.8116i			2.33348i
$494$		0			0
$495$	−1.34015	−	7.69948i	−0.0602355	−	0.346066i
$496$		0			0
$497$	−3.65911	−	8.99960i	−0.164134	−	0.403687i
$498$		0			0
$499$	32.1443			1.43898			0.719489	−	0.694504i	$-0.244376\pi$
$499$	32.1443			1.43898			0.719489	+	0.694504i	$0.244376\pi$
$500$		0			0
$501$	−22.8786	+	15.9823i	−1.02214	+	0.714035i
$502$		0			0
$503$	−21.7295			−0.968872			−0.484436	−	0.874827i	$-0.660975\pi$
$503$	−21.7295			−0.968872			−0.484436	+	0.874827i	$0.660975\pi$
$504$		0			0
$505$	−5.05949			−0.225145
$506$		0			0
$507$	0.0201234	+	0.00941069i	0.000893713	+	0.000417943i
$508$		0			0
$509$	23.8864			1.05875			0.529373	−	0.848389i	$-0.322427\pi$
$509$	23.8864			1.05875			0.529373	+	0.848389i	$0.322427\pi$
$510$		0			0
$511$	−12.9941	+	16.7072i	−0.574824	+	0.739085i
$512$		0			0
$513$	−4.79838	+	17.6741i	−0.211854	+	0.780331i
$514$		0			0
$515$		−	19.7064i		−	0.868370i
$516$		0			0
$517$	−8.66444	+	5.00242i	−0.381062	+	0.220006i
$518$		0			0
$519$	−9.80251	+	6.84772i	−0.430283	+	0.300582i
$520$		0			0
$521$	13.5098	+	23.3996i	0.591874	+	1.02516i	0.993980	+	0.109562i	$0.0349449\pi$
$521$	13.5098	+	23.3996i	0.591874	+	1.02516i	−0.402106	+	0.915593i	$0.631722\pi$
$522$		0			0
$523$	27.2136	+	15.7118i	1.18997	+	0.687028i	0.958299	−	0.285766i	$-0.0922482\pi$
$523$	27.2136	+	15.7118i	1.18997	+	0.687028i	0.231669	+	0.972795i	$0.425582\pi$
$524$		0			0
$525$	0.140594	+	0.275184i	0.00613603	+	0.0120100i
$526$		0			0
$527$		−	59.0196i		−	2.57093i
$528$		0			0
$529$	−10.7847			−0.468899
$530$		0			0
$531$	4.13190	−	11.2750i	0.179309	−	0.489294i
$532$		0			0
$533$	−5.05483	−	2.91841i	−0.218949	−	0.126410i
$534$		0			0
$535$	1.27652	+	0.736997i	0.0551886	+	0.0318632i
$536$		0			0
$537$	−6.05613	−	8.66935i	−0.261341	−	0.374110i
$538$		0			0
$539$	−5.72959	−	5.88118i	−0.246791	−	0.253320i
$540$		0			0
$541$	−0.0969057	+	0.167846i	−0.00416630	+	0.00721624i	−0.868101	−	0.496388i	$-0.834660\pi$
$541$	−0.0969057	+	0.167846i	−0.00416630	+	0.00721624i	0.863935	+	0.503604i	$0.167993\pi$
$542$		0			0
$543$	9.42758	−	0.814350i	0.404576	−	0.0349471i
$544$		0			0
$545$	17.8438	+	30.9064i	0.764344	+	1.32388i
$546$		0			0
$547$	0.987053	−	1.70963i	0.0422033	−	0.0730983i	−0.844152	−	0.536104i	$-0.819896\pi$
$547$	0.987053	−	1.70963i	0.0422033	−	0.0730983i	0.886355	+	0.463005i	$0.153229\pi$
$548$		0			0
$549$	18.8492	−	15.7458i	0.804466	−	0.672015i
$550$		0			0
$551$	12.2994	+	21.3032i	0.523972	+	0.907547i
$552$		0			0
$553$	−9.43955	−	7.34161i	−0.401410	−	0.312197i
$554$		0			0
$555$	38.6335	+	18.0669i	1.63990	+	0.766897i
$556$		0			0
$557$	−18.3383	+	10.5876i	−0.777018	+	0.448612i	−0.835373	−	0.549684i	$-0.814748\pi$
$557$	−18.3383	+	10.5876i	−0.777018	+	0.448612i	0.0583543	+	0.998296i	$0.481415\pi$
$558$		0			0
$559$		−	6.52423i		−	0.275946i
$560$		0			0
$561$	−8.63704	−	12.3639i	−0.364656	−	0.522005i
$562$		0			0
$563$	−17.0645	+	29.5565i	−0.719182	+	1.24566i	0.242142	+	0.970241i	$0.422150\pi$
$563$	−17.0645	+	29.5565i	−0.719182	+	1.24566i	−0.961324	+	0.275419i	$0.911183\pi$
$564$		0			0
$565$	10.8085	−	6.24032i	0.454719	−	0.262532i
$566$		0			0
$567$	−17.7307	+	15.8941i	−0.744618	+	0.667491i
$568$		0			0
$569$	9.55993	−	5.51943i	0.400773	−	0.231387i	−0.286044	−	0.958216i	$-0.592340\pi$
$569$	9.55993	−	5.51943i	0.400773	−	0.231387i	0.686818	+	0.726830i	$0.259007\pi$
$570$		0			0
$571$	−20.6616	+	35.7870i	−0.864663	+	1.49764i	0.00271871	+	0.999996i	$0.499135\pi$
$571$	−20.6616	+	35.7870i	−0.864663	+	1.49764i	−0.867382	+	0.497644i	$0.834199\pi$
$572$		0			0
$573$	5.96763	+	8.54266i	0.249301	+	0.356875i
$574$		0			0
$575$		−	0.391955i		−	0.0163456i
$576$		0			0
$577$	12.5253	−	7.23151i	0.521437	−	0.301052i	−0.216085	−	0.976374i	$-0.569329\pi$
$577$	12.5253	−	7.23151i	0.521437	−	0.301052i	0.737522	+	0.675323i	$0.235996\pi$
$578$		0			0
$579$	9.06915	+	4.24117i	0.376901	+	0.176257i
$580$		0			0
$581$	0.283418	−	2.04931i	0.0117582	−	0.0850197i
$582$		0			0
$583$	6.51891	+	11.2911i	0.269986	+	0.467629i
$584$		0			0
$585$	18.4458	−	15.4088i	0.762641	−	0.637076i
$586$		0			0
$587$	−0.248251	+	0.429983i	−0.0102464	+	0.0177473i	−0.871103	−	0.491100i	$-0.836595\pi$
$587$	−0.248251	+	0.429983i	−0.0102464	+	0.0177473i	0.860857	+	0.508847i	$0.169928\pi$
$588$		0			0
$589$	−14.0105	−	24.2669i	−0.577292	−	0.999898i
$590$		0			0
$591$	−13.7248	+	1.18554i	−0.564564	+	0.0487667i
$592$		0			0
$593$	12.2302	−	21.1834i	0.502236	−	0.869898i	−0.497761	−	0.867314i	$-0.665844\pi$
$593$	12.2302	−	21.1834i	0.502236	−	0.869898i	0.999997	−	0.00258345i	$-0.000822338\pi$
$594$		0			0
$595$	−34.4329	−	26.7802i	−1.41161	−	1.09788i
$596$		0			0
$597$	−17.7791	−	25.4508i	−0.727650	−	1.04163i
$598$		0			0
$599$	16.3114	+	9.41741i	0.666467	+	0.384785i	0.794737	−	0.606954i	$-0.207609\pi$
$599$	16.3114	+	9.41741i	0.666467	+	0.384785i	−0.128270	+	0.991739i	$0.540942\pi$
$600$		0			0
$601$	−6.37572	−	3.68102i	−0.260071	−	0.150152i	0.364296	−	0.931283i	$-0.381310\pi$
$601$	−6.37572	−	3.68102i	−0.260071	−	0.150152i	−0.624367	+	0.781131i	$0.714643\pi$
$602$		0			0
$603$	10.2470	−	27.9616i	0.417289	−	1.13868i
$604$		0			0
$605$	−21.3747			−0.869003
$606$		0			0
$607$		−	28.9923i		−	1.17676i	−0.808584	−	0.588380i	$-0.799766\pi$
$607$		−	28.9923i		−	1.17676i	0.808584	−	0.588380i	$-0.200234\pi$
$608$		0			0
$609$	−1.63881	+	31.9414i	−0.0664081	+	1.29433i
$610$		0			0
$611$	−26.6466	−	15.3844i	−1.07801	−	0.622387i
$612$		0			0
$613$	12.4334	+	21.5352i	0.502179	+	0.869799i	0.999997	+	0.00251771i	$0.000801413\pi$
$613$	12.4334	+	21.5352i	0.502179	+	0.869799i	−0.497818	+	0.867282i	$0.665865\pi$
$614$		0			0
$615$	−5.10254	+	3.56447i	−0.205754	+	0.143733i
$616$		0			0
$617$	−37.4629	+	21.6292i	−1.50820	+	0.870759i	−0.508245	+	0.861213i	$0.669706\pi$
$617$	−37.4629	+	21.6292i	−1.50820	+	0.870759i	−0.999954	+	0.00954684i	$0.996961\pi$
$618$		0			0
$619$			7.45221i			0.299529i	0.988722	+	0.149765i	$0.0478516\pi$
$619$			7.45221i			0.299529i	−0.988722	+	0.149765i	$0.952148\pi$
$620$		0			0
$621$	29.1990	−	7.72057i	1.17171	−	0.309816i
$622$		0			0
$623$	−1.27178	+	9.19586i	−0.0509528	+	0.368424i
$624$		0			0
$625$	−24.6583			−0.986331
$626$		0			0
$627$	−6.48629	−	3.03331i	−0.259038	−	0.121139i
$628$		0			0
$629$	82.3050			3.28171
$630$		0			0
$631$	−9.67068			−0.384984			−0.192492	−	0.981299i	$-0.561657\pi$
$631$	−9.67068			−0.384984			−0.192492	+	0.981299i	$0.561657\pi$
$632$		0			0
$633$	11.3649	−	7.93917i	0.451715	−	0.315554i
$634$		0			0
$635$	−17.1995			−0.682541
$636$		0			0
$637$	6.85339	−	24.3035i	0.271541	−	0.962939i
$638$		0			0
$639$	−1.88899	−	10.8526i	−0.0747272	−	0.429324i
$640$		0			0
$641$		−	30.9590i		−	1.22281i	−0.791318	−	0.611404i	$-0.790605\pi$
$641$		−	30.9590i		−	1.22281i	0.791318	−	0.611404i	$-0.209395\pi$
$642$		0			0
$643$	6.99262	−	4.03719i	0.275762	−	0.159211i	−0.355741	−	0.934585i	$-0.615772\pi$
$643$	6.99262	−	4.03719i	0.275762	−	0.159211i	0.631503	+	0.775373i	$0.282438\pi$
$644$		0			0
$645$	−6.30221	−	2.94722i	−0.248149	−	0.116047i
$646$		0			0
$647$	4.54355	+	7.86966i	0.178625	+	0.309388i	0.941410	−	0.337265i	$-0.109502\pi$
$647$	4.54355	+	7.86966i	0.178625	+	0.309388i	−0.762785	+	0.646653i	$0.776168\pi$
$648$		0			0
$649$	4.06607	+	2.34755i	0.159607	+	0.0921492i
$650$		0			0
$651$	1.86680	−	36.3851i	0.0731658	−	1.42604i
$652$		0			0
$653$		−	20.5913i		−	0.805800i	−0.915244	−	0.402900i	$-0.868002\pi$
$653$		−	20.5913i		−	0.805800i	0.915244	−	0.402900i	$-0.131998\pi$
$654$		0			0
$655$	34.7041			1.35600
$656$		0			0
$657$	−18.4185	+	15.3860i	−0.718575	+	0.600265i
$658$		0			0
$659$	−41.7687	−	24.1152i	−1.62708	−	0.939395i	−0.984959	−	0.172791i	$-0.944722\pi$
$659$	−41.7687	−	24.1152i	−1.62708	−	0.939395i	−0.642121	−	0.766604i	$-0.721945\pi$
$660$		0			0
$661$	−23.8342	−	13.7607i	−0.927042	−	0.535228i	−0.0411674	−	0.999152i	$-0.513108\pi$
$661$	−23.8342	−	13.7607i	−0.927042	−	0.535228i	−0.885875	+	0.463924i	$0.846441\pi$
$662$		0			0
$663$	19.6485	−	42.0156i	0.763086	−	1.63175i
$664$		0			0
$665$	−20.5149	−	2.83720i	−0.795535	−	0.110022i
$666$		0			0
$667$	20.2836	−	35.1323i	0.785385	−	1.36033i
$668$		0			0
$669$	12.0650	−	25.7993i	0.466460	−	0.997459i
$670$		0			0
$671$	4.80146	+	8.31637i	0.185358	+	0.321050i
$672$		0			0
$673$	−17.5734	+	30.4380i	−0.677404	+	1.17330i	0.298355	+	0.954455i	$0.403562\pi$
$673$	−17.5734	+	30.4380i	−0.677404	+	1.17330i	−0.975760	+	0.218844i	$0.929771\pi$
$674$		0			0
$675$	0.0895707	+	0.338753i	0.00344758	+	0.0130386i
$676$		0			0
$677$	−21.9428	−	38.0060i	−0.843329	−	1.46069i	−0.887064	−	0.461646i	$-0.847259\pi$
$677$	−21.9428	−	38.0060i	−0.843329	−	1.46069i	0.0437349	−	0.999043i	$-0.486074\pi$
$678$		0			0
$679$	10.5684	+	1.46161i	0.405579	+	0.0560913i
$680$		0			0
$681$	−2.38389	−	27.5979i	−0.0913510	−	1.05755i
$682$		0			0
$683$	17.9331	−	10.3537i	0.686190	−	0.396172i	−0.115993	−	0.993250i	$-0.537005\pi$
$683$	17.9331	−	10.3537i	0.686190	−	0.396172i	0.802183	+	0.597078i	$0.203672\pi$
$684$		0			0
$685$		−	2.38896i		−	0.0912773i
$686$		0			0
$687$	26.6802	−	2.30462i	1.01791	−	0.0879267i
$688$		0			0
$689$	−20.0482	+	34.7246i	−0.763777	+	1.32290i
$690$		0			0
$691$	−15.8678	+	9.16129i	−0.603640	+	0.348512i	−0.770472	−	0.637474i	$-0.779980\pi$
$691$	−15.8678	+	9.16129i	−0.603640	+	0.348512i	0.166832	+	0.985985i	$0.446646\pi$
$692$		0			0
$693$	−4.93359	−	7.89544i	−0.187412	−	0.299923i
$694$		0			0
$695$	−12.9209	+	7.45988i	−0.490117	+	0.282969i
$696$		0			0
$697$	−6.00582	+	10.4024i	−0.227487	+	0.394018i
$698$		0			0
$699$	−14.0020	+	29.9413i	−0.529605	+	1.13248i
$700$		0			0
$701$			2.62840i			0.0992734i	0.998767	+	0.0496367i	$0.0158064\pi$
$701$			2.62840i			0.0992734i	−0.998767	+	0.0496367i	$0.984194\pi$
$702$		0			0
$703$	33.8410	−	19.5381i	1.27634	−	0.736894i
$704$		0			0
$705$	−26.8981	+	18.7901i	−1.01304	+	0.707677i
$706$		0			0
$707$	−5.58340	+	2.27013i	−0.209985	+	0.0853771i
$708$		0			0
$709$	8.16634	+	14.1445i	0.306693	+	0.531208i	0.977637	−	0.210300i	$-0.0674441\pi$
$709$	8.16634	+	14.1445i	0.306693	+	0.531208i	−0.670944	+	0.741508i	$0.734111\pi$
$710$		0			0
$711$	−8.69305	−	10.4064i	−0.326015	−	0.390271i
$712$		0			0
$713$	−23.1054	+	40.0198i	−0.865305	+	1.49875i
$714$		0			0
$715$	4.69869	+	8.13838i	0.175721	+	0.304358i
$716$		0			0
$717$	8.44839	+	12.0939i	0.315511	+	0.451654i
$718$		0			0
$719$	3.15485	−	5.46436i	0.117656	−	0.203786i	−0.801182	−	0.598420i	$-0.795795\pi$
$719$	3.15485	−	5.46436i	0.117656	−	0.203786i	0.918838	+	0.394634i	$0.129129\pi$
$720$		0			0
$721$	−8.84204	−	21.7470i	−0.329295	−	0.809901i
$722$		0			0
$723$	39.0640	−	3.37432i	1.45280	−	0.125492i
$724$		0			0
$725$	0.407589	+	0.235322i	0.0151375	+	0.00873962i
$726$		0			0
$727$	14.3318	+	8.27447i	0.531537	+	0.306883i	0.741642	−	0.670796i	$-0.234047\pi$
$727$	14.3318	+	8.27447i	0.531537	+	0.306883i	−0.210105	+	0.977679i	$0.567381\pi$
$728$		0			0
$729$	−23.4713	+	13.3453i	−0.869309	+	0.494269i
$730$		0			0
$731$	−13.4263			−0.496589
$732$		0			0
$733$			19.9109i			0.735425i	0.929939	+	0.367713i	$0.119859\pi$
$733$			19.9109i			0.735425i	−0.929939	+	0.367713i	$0.880141\pi$
$734$		0			0
$735$	−20.3805	−	17.5989i	−0.751747	−	0.649145i
$736$		0			0
$737$	10.0837	+	5.82183i	0.371438	+	0.214450i
$738$		0			0
$739$	−24.1545	−	41.8368i	−0.888536	−	1.53899i	−0.841606	−	0.540092i	$-0.818389\pi$
$739$	−24.1545	−	41.8368i	−0.888536	−	1.53899i	−0.0469307	−	0.998898i	$-0.514944\pi$
$740$		0			0
$741$	−1.89514	−	21.9397i	−0.0696197	−	0.805975i
$742$		0			0
$743$	−7.17819	+	4.14433i	−0.263342	+	0.152041i	−0.625858	−	0.779937i	$-0.715251\pi$
$743$	−7.17819	+	4.14433i	−0.263342	+	0.152041i	0.362516	+	0.931978i	$0.381918\pi$
$744$		0			0
$745$			39.0075i			1.42912i
$746$		0			0
$747$	0.807168	−	2.20257i	0.0295327	−	0.0805880i
$748$		0			0
$749$	1.73938	+	0.240555i	0.0635555	+	0.00878968i
$750$		0			0
$751$	−25.0229			−0.913099			−0.456549	−	0.889698i	$-0.650915\pi$
$751$	−25.0229			−0.913099			−0.456549	+	0.889698i	$0.650915\pi$
$752$		0			0
$753$	1.15406	+	13.3604i	0.0420564	+	0.486879i
$754$		0			0
$755$	−3.76683			−0.137089
$756$		0			0
$757$	−18.7744			−0.682368			−0.341184	−	0.939997i	$-0.610828\pi$
$757$	−18.7744			−0.682368			−0.341184	+	0.939997i	$0.610828\pi$
$758$		0			0
$759$	1.01625	+	11.7650i	0.0368876	+	0.427042i
$760$		0			0
$761$	23.1927			0.840733			0.420367	−	0.907354i	$-0.361901\pi$
$761$	23.1927			0.840733			0.420367	+	0.907354i	$0.361901\pi$
$762$		0			0
$763$	33.5588	+	26.1004i	1.21491	+	0.944897i
$764$		0			0
$765$	−31.7099	−	37.9598i	−1.14647	−	1.37244i
$766$		0			0
$767$			14.4393i			0.521372i
$768$		0			0
$769$	27.8202	−	16.0620i	1.00322	−	0.579210i	0.0940211	−	0.995570i	$-0.470028\pi$
$769$	27.8202	−	16.0620i	1.00322	−	0.579210i	0.909200	+	0.416360i	$0.136695\pi$
$770$		0			0
$771$	−3.54595	−	41.0509i	−0.127704	−	1.47841i
$772$		0			0
$773$	−8.14023	−	14.0993i	−0.292784	−	0.507116i	0.681683	−	0.731647i	$-0.261248\pi$
$773$	−8.14023	−	14.0993i	−0.292784	−	0.507116i	−0.974467	+	0.224531i	$0.927915\pi$
$774$		0			0
$775$	−0.464292	−	0.268059i	−0.0166779	−	0.00962896i
$776$		0			0
$777$	50.7403	+	2.60332i	1.82030	+	0.0933938i
$778$		0			0
$779$			5.70281i			0.204324i
$780$		0			0
$781$	4.30705			0.154119
$782$		0			0
$783$	−9.50192	+	34.9989i	−0.339571	+	1.25076i
$784$		0			0
$785$	−15.1608	−	8.75308i	−0.541112	−	0.312411i
$786$		0			0
$787$	−0.799139	−	0.461383i	−0.0284862	−	0.0164465i	0.485689	−	0.874132i	$-0.338569\pi$
$787$	−0.799139	−	0.461383i	−0.0284862	−	0.0164465i	−0.514175	+	0.857685i	$0.671902\pi$
$788$		0			0
$789$	35.4342	−	3.06079i	1.26149	−	0.108967i
$790$		0			0
$791$	9.12780	−	11.7362i	0.324547	−	0.417290i
$792$		0			0
$793$	−14.7664	+	25.5761i	−0.524369	+	0.908235i
$794$		0			0
$795$	24.4864	+	35.0523i	0.868443	+	1.24318i
$796$		0			0
$797$	−2.98084	−	5.16296i	−0.105587	−	0.182881i	0.808391	−	0.588646i	$-0.200339\pi$
$797$	−2.98084	−	5.16296i	−0.105587	−	0.182881i	−0.913978	+	0.405764i	$0.867005\pi$
$798$		0			0
$799$	−31.6597	+	54.8362i	−1.12004	+	1.93997i
$800$		0			0
$801$	−3.62200	+	9.88360i	−0.127977	+	0.349220i
$802$		0			0
$803$	−4.69174	−	8.12634i	−0.165568	−	0.286772i
$804$		0			0
$805$	12.8640	+	31.6391i	0.453397	+	1.11513i
$806$		0			0
$807$	−17.5270	+	12.2438i	−0.616979	+	0.431002i
$808$		0			0
$809$	−18.0267	+	10.4077i	−0.633784	+	0.365916i	−0.782216	−	0.623007i	$-0.785911\pi$
$809$	−18.0267	+	10.4077i	−0.633784	+	0.365916i	0.148432	+	0.988923i	$0.452577\pi$
$810$		0			0
$811$			11.7101i			0.411198i	0.978636	+	0.205599i	$0.0659142\pi$
$811$			11.7101i			0.411198i	−0.978636	+	0.205599i	$0.934086\pi$
$812$		0			0
$813$	21.5112	−	45.9987i	0.754432	−	1.61324i
$814$		0			0
$815$	12.6457	−	21.9030i	0.442959	−	0.767228i
$816$		0			0
$817$	−5.52043	+	3.18722i	−0.193135	+	0.111507i
$818$		0			0
$819$	13.4421	−	25.2808i	0.469706	−	0.883382i
$820$		0			0
$821$	0.483490	−	0.279143i	0.0168739	−	0.00974215i	−0.491539	−	0.870855i	$-0.663566\pi$
$821$	0.483490	−	0.279143i	0.0168739	−	0.00974215i	0.508413	+	0.861113i	$0.330232\pi$
$822$		0			0
$823$	−20.7043	+	35.8609i	−0.721707	+	1.25003i	0.238607	+	0.971116i	$0.423309\pi$
$823$	−20.7043	+	35.8609i	−0.721707	+	1.25003i	−0.960315	+	0.278918i	$0.910024\pi$
$824$		0			0
$825$	−0.136492	+	0.0117901i	−0.00475204	+	0.000410479i
$826$		0			0
$827$		−	8.83309i		−	0.307157i	−0.988136	−	0.153578i	$-0.950920\pi$
$827$		−	8.83309i		−	0.307157i	0.988136	−	0.153578i	$-0.0490797\pi$
$828$		0			0
$829$	−7.60753	+	4.39221i	−0.264220	+	0.152548i	−0.626258	−	0.779616i	$-0.715414\pi$
$829$	−7.60753	+	4.39221i	−0.264220	+	0.152548i	0.362038	+	0.932163i	$0.382081\pi$
$830$		0			0
$831$	−0.370008	−	4.28352i	−0.0128355	−	0.148594i
$832$		0			0
$833$	−50.0143	−	14.1037i	−1.73289	−	0.488663i
$834$		0			0
$835$	−17.8927	−	30.9911i	−0.619204	−	1.07249i
$836$		0			0
$837$	10.8238	−	39.8679i	0.374126	−	1.37804i
$838$		0			0
$839$	11.6778	−	20.2265i	0.403161	−	0.698295i	−0.590944	−	0.806712i	$-0.701245\pi$
$839$	11.6778	−	20.2265i	0.403161	−	0.698295i	0.994106	+	0.108417i	$0.0345781\pi$
$840$		0			0
$841$	9.85573	+	17.0706i	0.339853	+	0.588642i
$842$		0			0
$843$	−17.0268	+	36.4095i	−0.586435	+	1.25401i
$844$		0			0
$845$	−0.0142428	+	0.0246693i	−0.000489967	+	0.000848648i
$846$		0			0
$847$	−23.5880	+	9.59054i	−0.810492	+	0.329535i
$848$		0			0
$849$	20.0307	−	42.8327i	0.687450	−	1.47001i
$850$		0			0
$851$	−55.8091	−	32.2214i	−1.91311	−	1.10453i
$852$		0			0
$853$	−13.8754	−	8.01099i	−0.475086	−	0.274291i	0.243280	−	0.969956i	$-0.421777\pi$
$853$	−13.8754	−	8.01099i	−0.475086	−	0.274291i	−0.718366	+	0.695665i	$0.755110\pi$
$854$		0			0
$855$	−22.0492	−	8.08027i	−0.754067	−	0.276340i
$856$		0			0
$857$	−16.8241			−0.574700			−0.287350	−	0.957826i	$-0.592774\pi$
$857$	−16.8241			−0.574700			−0.287350	+	0.957826i	$0.592774\pi$
$858$		0			0
$859$		−	47.5953i		−	1.62393i	−0.583705	−	0.811966i	$-0.698397\pi$
$859$		−	47.5953i		−	1.62393i	0.583705	−	0.811966i	$-0.301603\pi$
$860$		0			0
$861$	−4.03156	+	6.22301i	−0.137395	+	0.212080i
$862$		0			0
$863$	−44.7300	−	25.8249i	−1.52263	−	0.879089i	−0.999642	−	0.0267477i	$-0.991485\pi$
$863$	−44.7300	−	25.8249i	−1.52263	−	0.879089i	−0.522985	−	0.852342i	$-0.675182\pi$
$864$		0			0
$865$	−7.66628	−	13.2784i	−0.260661	−	0.451478i
$866$		0			0
$867$	−59.7919	−	27.9616i	−2.03064	−	0.949625i
$868$		0			0
$869$	4.59136	−	2.65082i	0.155751	−	0.0899230i
$870$		0			0
$871$			35.8088i			1.21334i
$872$		0			0
$873$	11.3588	+	4.16262i	0.384438	+	0.140883i
$874$		0			0
$875$	−27.5837	+	11.2151i	−0.932499	+	0.379141i
$876$		0			0
$877$	14.3056			0.483066			0.241533	−	0.970393i	$-0.422350\pi$
$877$	14.3056			0.483066			0.241533	+	0.970393i	$0.422350\pi$
$878$		0			0
$879$	−11.8030	+	8.24523i	−0.398107	+	0.278105i
$880$		0			0
$881$	−10.4054			−0.350566			−0.175283	−	0.984518i	$-0.556084\pi$
$881$	−10.4054			−0.350566			−0.175283	+	0.984518i	$0.556084\pi$
$882$		0			0
$883$	44.9042			1.51115			0.755574	−	0.655064i	$-0.227358\pi$
$883$	44.9042			1.51115			0.755574	+	0.655064i	$0.227358\pi$
$884$		0			0
$885$	13.9479	+	6.52271i	0.468853	+	0.219259i
$886$		0			0
$887$	0.948519			0.0318482			0.0159241	−	0.999873i	$-0.494931\pi$
$887$	0.948519			0.0318482			0.0159241	+	0.999873i	$0.494931\pi$
$888$		0			0
$889$	−18.9805	+	7.71720i	−0.636585	+	0.258827i
$890$		0			0
$891$	−3.56688	−	9.93584i	−0.119495	−	0.332863i
$892$		0			0
$893$			30.0624i			1.00600i
$894$		0			0
$895$	11.7434	−	6.78006i	0.392539	−	0.226632i
$896$		0			0
$897$	−29.7718	+	20.7976i	−0.994052	+	0.694413i
$898$		0			0
$899$	−27.7440	−	48.0541i	−0.925316	−	1.60269i
$900$		0			0
$901$	71.4600	+	41.2574i	2.38068	+	1.37448i
$902$		0			0
$903$	−8.27718	−	0.424676i	−0.275447	−	0.0141323i
$904$		0			0
$905$			12.1336i			0.403335i
$906$		0			0
$907$	35.0550			1.16398			0.581990	−	0.813196i	$-0.302274\pi$
$907$	35.0550			1.16398			0.581990	+	0.813196i	$0.302274\pi$
$908$		0			0
$909$	−6.73303	+	1.17194i	−0.223321	+	0.0388707i
$910$		0			0
$911$	−42.8316	−	24.7288i	−1.41907	−	0.819303i	−0.422857	−	0.906196i	$-0.638973\pi$
$911$	−42.8316	−	24.7288i	−1.41907	−	0.819303i	−0.996218	+	0.0868934i	$0.972306\pi$
$912$		0			0
$913$	0.794307	+	0.458593i	0.0262877	+	0.0151772i
$914$		0			0
$915$	18.0353	+	25.8175i	0.596228	+	0.853500i
$916$		0			0
$917$	38.2976	−	15.5713i	1.26470	−	0.514209i
$918$		0			0
$919$	8.34526	−	14.4544i	0.275285	−	0.476807i	−0.694922	−	0.719085i	$-0.744561\pi$
$919$	8.34526	−	14.4544i	0.275285	−	0.476807i	0.970207	+	0.242278i	$0.0778945\pi$
$920$		0			0
$921$	38.8107	−	3.35245i	1.27886	−	0.110467i
$922$		0			0
$923$	6.62295	+	11.4713i	0.217997	+	0.377582i
$924$		0			0
$925$	0.373818	−	0.647472i	0.0122911	−	0.0212888i
$926$		0			0
$927$	−4.56463	−	26.2248i	−0.149922	−	0.861335i
$928$		0			0
$929$	−5.31860	−	9.21208i	−0.174498	−	0.302239i	0.765490	−	0.643448i	$-0.222497\pi$
$929$	−5.31860	−	9.21208i	−0.174498	−	0.302239i	−0.939987	+	0.341209i	$0.889163\pi$
$930$		0			0
$931$	−23.9122	+	6.07381i	−0.783692	+	0.199061i
$932$		0			0
$933$	15.1844	+	7.10097i	0.497116	+	0.232475i
$934$		0			0
$935$	16.7480	−	9.66948i	0.547719	−	0.316226i
$936$		0			0
$937$		−	26.7085i		−	0.872528i	−0.899819	−	0.436264i	$-0.856301\pi$
$937$		−	26.7085i		−	0.872528i	0.899819	−	0.436264i	$-0.143699\pi$
$938$		0			0
$939$	24.2985	+	34.7833i	0.792952	+	1.13511i
$940$		0			0
$941$	3.29534	−	5.70769i	0.107425	−	0.186065i	−0.807301	−	0.590139i	$-0.799073\pi$
$941$	3.29534	−	5.70769i	0.107425	−	0.186065i	0.914726	+	0.404074i	$0.132406\pi$
$942$		0			0
$943$	8.14481	−	4.70241i	0.265232	−	0.153131i
$944$		0			0
$945$	−18.3482	−	24.4049i	−0.596867	−	0.793891i
$946$		0			0
$947$	24.8907	−	14.3706i	0.808838	−	0.466983i	−0.0377144	−	0.999289i	$-0.512008\pi$
$947$	24.8907	−	14.3706i	0.808838	−	0.466983i	0.846552	+	0.532306i	$0.178674\pi$
$948$		0			0
$949$	14.4290	−	24.9917i	0.468384	−	0.811265i
$950$		0			0
$951$	9.11179	+	13.0435i	0.295470	+	0.422965i
$952$		0			0
$953$			18.2616i			0.591550i	0.955258	+	0.295775i	$0.0955778\pi$
$953$			18.2616i			0.591550i	−0.955258	+	0.295775i	$0.904422\pi$
$954$		0			0
$955$	−11.5718	+	6.68098i	−0.374455	+	0.216191i
$956$		0			0
$957$	−12.8444	−	6.00666i	−0.415200	−	0.194168i
$958$		0			0
$959$	−1.07189	−	2.63633i	−0.0346133	−	0.0851315i
$960$		0			0
$961$	16.1037	+	27.8925i	0.519476	+	0.899758i
$962$		0			0
$963$	1.86946	+	0.685094i	0.0602426	+	0.0220769i
$964$		0			0
$965$	−6.41889	+	11.1178i	−0.206631	+	0.357896i
$966$		0			0
$967$	12.5899	+	21.8064i	0.404865	+	0.701247i	0.994306	−	0.106565i	$-0.0339851\pi$
$967$	12.5899	+	21.8064i	0.404865	+	0.701247i	−0.589441	+	0.807812i	$0.700652\pi$
$968$		0			0
$969$	−45.1499	+	3.90003i	−1.45042	+	0.125287i
$970$		0			0
$971$	−23.7214	+	41.0866i	−0.761255	+	1.31853i	0.180949	+	0.983492i	$0.442083\pi$
$971$	−23.7214	+	41.0866i	−0.761255	+	1.31853i	−0.942204	+	0.335040i	$0.891250\pi$
$972$		0			0
$973$	−10.9117	+	14.0298i	−0.349812	+	0.449774i
$974$		0			0
$975$	−0.241285	−	0.345399i	−0.00772730	−	0.0110616i
$976$		0			0
$977$	47.9278	+	27.6711i	1.53334	+	0.885277i	0.999204	+	0.0398814i	$0.0126980\pi$
$977$	47.9278	+	27.6711i	1.53334	+	0.885277i	0.534141	+	0.845396i	$0.320635\pi$
$978$		0			0
$979$	−3.56429	−	2.05784i	−0.113915	−	0.0657690i
$980$		0			0
$981$	30.9049	+	36.9961i	0.986717	+	1.18120i
$982$		0			0
$983$	−25.3499			−0.808537			−0.404268	−	0.914640i	$-0.632474\pi$
$983$	−25.3499			−0.808537			−0.404268	+	0.914640i	$0.632474\pi$
$984$		0			0
$985$		−	17.6643i		−	0.562832i
$986$		0			0
$987$	−21.2524	+	32.8046i	−0.676472	+	1.04418i
$988$		0			0
$989$	9.10404	+	5.25622i	0.289492	+	0.167138i
$990$		0			0
$991$	−12.9683	−	22.4618i	−0.411953	−	0.713523i	0.583151	−	0.812364i	$-0.301820\pi$
$991$	−12.9683	−	22.4618i	−0.411953	−	0.713523i	−0.995103	+	0.0988413i	$0.968486\pi$
$992$		0			0
$993$	36.5196	−	25.5114i	1.15891	−	0.809580i
$994$		0			0
$995$	34.4753	−	19.9043i	1.09294	−	0.631010i
$996$		0			0
$997$			15.9283i			0.504453i	0.967668	+	0.252227i	$0.0811629\pi$
$997$			15.9283i			0.504453i	−0.967668	+	0.252227i	$0.918837\pi$
$998$		0			0
$999$	55.5972	+	15.0942i	1.75902	+	0.477559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cx.a.425.13	yes	48
3.2	odd	2		1512.2.cx.a.89.20		48
4.3	odd	2		1008.2.df.e.929.12		48
7.3	odd	6		504.2.bs.a.353.5	yes	48
9.4	even	3		1512.2.bs.a.1097.20		48
9.5	odd	6		504.2.bs.a.257.5	✓	48
12.11	even	2		3024.2.df.e.1601.20		48
21.17	even	6		1512.2.bs.a.521.20		48
28.3	even	6		1008.2.ca.e.353.20		48
36.23	even	6		1008.2.ca.e.257.20		48
36.31	odd	6		3024.2.ca.e.2609.20		48
63.31	odd	6		1512.2.cx.a.17.20		48
63.59	even	6	inner	504.2.cx.a.185.13	yes	48
84.59	odd	6		3024.2.ca.e.2033.20		48
252.31	even	6		3024.2.df.e.17.20		48
252.59	odd	6		1008.2.df.e.689.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.5	✓	48	9.5	odd	6
504.2.bs.a.353.5	yes	48	7.3	odd	6
504.2.cx.a.185.13	yes	48	63.59	even	6	inner
504.2.cx.a.425.13	yes	48	1.1	even	1	trivial
1008.2.ca.e.257.20		48	36.23	even	6
1008.2.ca.e.353.20		48	28.3	even	6
1008.2.df.e.689.12		48	252.59	odd	6
1008.2.df.e.929.12		48	4.3	odd	2
1512.2.bs.a.521.20		48	21.17	even	6
1512.2.bs.a.1097.20		48	9.4	even	3
1512.2.cx.a.17.20		48	63.31	odd	6
1512.2.cx.a.89.20		48	3.2	odd	2
3024.2.ca.e.2033.20		48	84.59	odd	6
3024.2.ca.e.2609.20		48	36.31	odd	6
3024.2.df.e.17.20		48	252.31	even	6
3024.2.df.e.1601.20		48	12.11	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.149059 + 1.72562i) q^{3} -2.22094 q^{5} +(-2.45091 + 0.996507i) q^{7} +(-2.95556 + 0.514438i) q^{9} -1.17296i q^{11} +(3.12404 - 1.80366i) q^{13} +(-0.331050 - 3.83251i) q^{15} +(-3.71178 - 6.42899i) q^{17} +(-3.05231 - 1.76225i) q^{19} +(-2.08493 - 4.08082i) q^{21} +5.81246i q^{23} -0.0674336 q^{25} +(-1.32828 - 5.02351i) q^{27} +(-6.04430 - 3.48968i) q^{29} +(6.88517 + 3.97516i) q^{31} +(2.02410 - 0.174840i) q^{33} +(5.44333 - 2.21318i) q^{35} +(-5.54350 + 9.60163i) q^{37} +(3.57811 + 5.12207i) q^{39} +(-0.809022 - 1.40127i) q^{41} +(0.904302 - 1.56630i) q^{43} +(6.56412 - 1.14254i) q^{45} +(-4.26476 - 7.38679i) q^{47} +(5.01395 - 4.88471i) q^{49} +(10.5407 - 7.36343i) q^{51} +(-9.62611 + 5.55764i) q^{53} +2.60508i q^{55} +(2.58602 - 5.52983i) q^{57} +(-2.00138 + 3.46649i) q^{59} +(-7.09004 + 4.09344i) q^{61} +(6.73119 - 4.20608i) q^{63} +(-6.93830 + 4.00583i) q^{65} +(-4.96334 + 8.59676i) q^{67} +(-10.0301 + 0.866397i) q^{69} +3.67194i q^{71} +(6.92803 - 3.99990i) q^{73} +(-0.0100516 - 0.116365i) q^{75} +(1.16887 + 2.87483i) q^{77} +(2.25993 + 3.91432i) q^{79} +(8.47071 - 3.04091i) q^{81} +(-0.390969 + 0.677179i) q^{83} +(8.24363 + 14.2784i) q^{85} +(5.12092 - 10.9504i) q^{87} +(1.75440 - 3.03870i) q^{89} +(-5.85938 + 7.53375i) q^{91} +(-5.83334 + 12.4738i) q^{93} +(6.77900 + 3.91386i) q^{95} +(-3.49226 - 2.01626i) q^{97} +(0.603418 + 3.46677i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61}+ \cdots - 64 q^{99}+O(q^{100}) \) 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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