LMFDB - Embedded newform 504.2.cx.a.185.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(185,504)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			185.18
Character	$\chi$	$=$	504.185
Dual form			504.2.cx.a.425.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.994080 + 1.41838i) q^{3} -1.58600 q^{5} +(-1.06431 + 2.42224i) q^{7} +(-1.02361 + 2.81997i) q^{9} +O(q^{10})$	\(q+(0.994080 + 1.41838i) q^{3} -1.58600 q^{5} +(-1.06431 + 2.42224i) q^{7} +(-1.02361 + 2.81997i) q^{9} -3.95252i q^{11} +(5.09214 + 2.93995i) q^{13} +(-1.57662 - 2.24956i) q^{15} +(-3.19652 + 5.53653i) q^{17} +(-6.37856 + 3.68267i) q^{19} +(-4.49367 + 0.898299i) q^{21} +2.43102i q^{23} -2.48459 q^{25} +(-5.01734 + 1.35141i) q^{27} +(4.34058 - 2.50604i) q^{29} +(0.855353 - 0.493838i) q^{31} +(5.60618 - 3.92912i) q^{33} +(1.68800 - 3.84168i) q^{35} +(0.183332 + 0.317540i) q^{37} +(0.892030 + 10.1451i) q^{39} +(5.58681 - 9.67664i) q^{41} +(1.26688 + 2.19430i) q^{43} +(1.62345 - 4.47248i) q^{45} +(-0.543280 + 0.940989i) q^{47} +(-4.73448 - 5.15604i) q^{49} +(-11.0305 + 0.969878i) q^{51} +(6.89030 + 3.97812i) q^{53} +6.26871i q^{55} +(-11.5642 - 5.38637i) q^{57} +(-2.73420 - 4.73577i) q^{59} +(12.4765 + 7.20330i) q^{61} +(-5.74120 - 5.48075i) q^{63} +(-8.07615 - 4.66277i) q^{65} +(5.70501 + 9.88137i) q^{67} +(-3.44811 + 2.41663i) q^{69} -9.65277i q^{71} +(7.64694 + 4.41497i) q^{73} +(-2.46988 - 3.52410i) q^{75} +(9.57394 + 4.20672i) q^{77} +(5.30654 - 9.19120i) q^{79} +(-6.90445 - 5.77309i) q^{81} +(2.96819 + 5.14105i) q^{83} +(5.06969 - 8.78096i) q^{85} +(7.86941 + 3.66540i) q^{87} +(4.70952 + 8.15712i) q^{89} +(-12.5409 + 9.20535i) q^{91} +(1.55074 + 0.722301i) q^{93} +(10.1164 - 5.84072i) q^{95} +(10.4826 - 6.05213i) q^{97} +(11.1460 + 4.04583i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{9}+O(q^{10}) $ 48 * q + 2 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.994080	+	1.41838i	0.573933	+	0.818903i
$3$	0.994080	+	1.41838i	0.573933	+	0.818903i
$4$		0			0
$5$	−1.58600			−0.709283			−0.354641	−	0.935002i	$-0.615397\pi$
$5$	−1.58600			−0.709283			−0.354641	+	0.935002i	$0.615397\pi$
$6$		0			0
$7$	−1.06431	+	2.42224i	−0.402272	+	0.915520i
$7$	−1.06431	+	2.42224i	−0.402272	+	0.915520i
$8$		0			0
$9$	−1.02361	+	2.81997i	−0.341203	+	0.939990i
$10$		0			0
$11$		−	3.95252i		−	1.19173i	−0.803085	−	0.595865i	$-0.796809\pi$
$11$		−	3.95252i		−	1.19173i	0.803085	−	0.595865i	$-0.203191\pi$
$12$		0			0
$13$	5.09214	+	2.93995i	1.41231	+	0.815395i	0.995605	−	0.0936493i	$-0.0298532\pi$
$13$	5.09214	+	2.93995i	1.41231	+	0.815395i	0.416700	+	0.909044i	$0.363187\pi$
$14$		0			0
$15$	−1.57662	−	2.24956i	−0.407080	−	0.580833i
$16$		0			0
$17$	−3.19652	+	5.53653i	−0.775269	+	1.34281i	0.159374	+	0.987218i	$0.449053\pi$
$17$	−3.19652	+	5.53653i	−0.775269	+	1.34281i	−0.934643	+	0.355588i	$0.884281\pi$
$18$		0			0
$19$	−6.37856	+	3.68267i	−1.46334	+	0.844862i	−0.999164	−	0.0408799i	$-0.986984\pi$
$19$	−6.37856	+	3.68267i	−1.46334	+	0.844862i	−0.464179	+	0.885741i	$0.653651\pi$
$20$		0			0
$21$	−4.49367	+	0.898299i	−0.980599	+	0.196025i
$22$		0			0
$23$			2.43102i			0.506903i	0.967348	+	0.253451i	$0.0815658\pi$
$23$			2.43102i			0.506903i	−0.967348	+	0.253451i	$0.918434\pi$
$24$		0			0
$25$	−2.48459			−0.496918
$26$		0			0
$27$	−5.01734	+	1.35141i	−0.965587	+	0.260079i
$28$		0			0
$29$	4.34058	−	2.50604i	0.806026	−	0.465359i	−0.0395477	−	0.999218i	$-0.512592\pi$
$29$	4.34058	−	2.50604i	0.806026	−	0.465359i	0.845574	+	0.533858i	$0.179258\pi$
$30$		0			0
$31$	0.855353	−	0.493838i	0.153626	−	0.0886960i	−0.421216	−	0.906960i	$-0.638397\pi$
$31$	0.855353	−	0.493838i	0.153626	−	0.0886960i	0.574842	+	0.818264i	$0.305063\pi$
$32$		0			0
$33$	5.60618	−	3.92912i	0.975910	−	0.683972i
$34$		0			0
$35$	1.68800	−	3.84168i	0.285325	−	0.649362i
$36$		0			0
$37$	0.183332	+	0.317540i	0.0301396	+	0.0522033i	0.880702	−	0.473671i	$-0.157071\pi$
$37$	0.183332	+	0.317540i	0.0301396	+	0.0522033i	−0.850562	+	0.525874i	$0.823738\pi$
$38$		0			0
$39$	0.892030	+	10.1451i	0.142839	+	1.62452i
$40$		0			0
$41$	5.58681	−	9.67664i	0.872513	−	1.51124i	0.0131240	−	0.999914i	$-0.495822\pi$
$41$	5.58681	−	9.67664i	0.872513	−	1.51124i	0.859389	−	0.511323i	$-0.170844\pi$
$42$		0			0
$43$	1.26688	+	2.19430i	0.193197	+	0.334627i	0.946308	−	0.323266i	$-0.104781\pi$
$43$	1.26688	+	2.19430i	0.193197	+	0.334627i	−0.753111	+	0.657894i	$0.771448\pi$
$44$		0			0
$45$	1.62345	−	4.47248i	0.242009	−	0.666718i
$46$		0			0
$47$	−0.543280	+	0.940989i	−0.0792456	+	0.137257i	−0.902925	−	0.429799i	$-0.858584\pi$
$47$	−0.543280	+	0.940989i	−0.0792456	+	0.137257i	0.823679	+	0.567056i	$0.191918\pi$
$48$		0			0
$49$	−4.73448	−	5.15604i	−0.676354	−	0.736577i
$50$		0			0
$51$	−11.0305	+	0.969878i	−1.54458	+	0.135810i
$52$		0			0
$53$	6.89030	+	3.97812i	0.946455	+	0.546436i	0.891978	−	0.452079i	$-0.149317\pi$
$53$	6.89030	+	3.97812i	0.946455	+	0.546436i	0.0544773	+	0.998515i	$0.482651\pi$
$54$		0			0
$55$			6.26871i			0.845273i
$56$		0			0
$57$	−11.5642	−	5.38637i	−1.53172	−	0.713442i
$58$		0			0
$59$	−2.73420	−	4.73577i	−0.355963	−	0.616545i	0.631320	−	0.775523i	$-0.282514\pi$
$59$	−2.73420	−	4.73577i	−0.355963	−	0.616545i	−0.987282	+	0.158977i	$0.949180\pi$
$60$		0			0
$61$	12.4765	+	7.20330i	1.59745	+	0.922288i	0.991976	+	0.126423i	$0.0403496\pi$
$61$	12.4765	+	7.20330i	1.59745	+	0.922288i	0.605473	+	0.795865i	$0.292984\pi$
$62$		0			0
$63$	−5.74120	−	5.48075i	−0.723323	−	0.690510i
$64$		0			0
$65$	−8.07615	−	4.66277i	−1.00172	−	0.578345i
$66$		0			0
$67$	5.70501	+	9.88137i	0.696978	+	1.20720i	0.969509	+	0.245055i	$0.0788060\pi$
$67$	5.70501	+	9.88137i	0.696978	+	1.20720i	−0.272531	+	0.962147i	$0.587861\pi$
$68$		0			0
$69$	−3.44811	+	2.41663i	−0.415104	+	0.290928i
$70$		0			0
$71$		−	9.65277i		−	1.14557i	−0.819705	−	0.572787i	$-0.805862\pi$
$71$		−	9.65277i		−	1.14557i	0.819705	−	0.572787i	$-0.194138\pi$
$72$		0			0
$73$	7.64694	+	4.41497i	0.895007	+	0.516733i	0.875577	−	0.483079i	$-0.160481\pi$
$73$	7.64694	+	4.41497i	0.895007	+	0.516733i	0.0194302	+	0.999811i	$0.493815\pi$
$74$		0			0
$75$	−2.46988	−	3.52410i	−0.285198	−	0.406928i
$76$		0			0
$77$	9.57394	+	4.20672i	1.09105	+	0.479400i
$78$		0			0
$79$	5.30654	−	9.19120i	0.597032	−	1.03409i	−0.396224	−	0.918154i	$-0.629680\pi$
$79$	5.30654	−	9.19120i	0.597032	−	1.03409i	0.993257	−	0.115937i	$-0.0369869\pi$
$80$		0			0
$81$	−6.90445	−	5.77309i	−0.767161	−	0.641454i
$82$		0			0
$83$	2.96819	+	5.14105i	0.325801	+	0.564303i	0.981674	−	0.190568i	$-0.0610328\pi$
$83$	2.96819	+	5.14105i	0.325801	+	0.564303i	−0.655873	+	0.754871i	$0.727699\pi$
$84$		0			0
$85$	5.06969	−	8.78096i	0.549885	−	0.952429i
$86$		0			0
$87$	7.86941	+	3.66540i	0.843689	+	0.392972i
$88$		0			0
$89$	4.70952	+	8.15712i	0.499208	+	0.864653i	1.00000		0.000914461i	$-0.000291082\pi$
$89$	4.70952	+	8.15712i	0.499208	+	0.864653i	−0.500792	+	0.865568i	$0.666958\pi$
$90$		0			0
$91$	−12.5409	+	9.20535i	−1.31464	+	0.964983i
$92$		0			0
$93$	1.55074	+	0.722301i	0.160804	+	0.0748992i
$94$		0			0
$95$	10.1164	−	5.84072i	1.03792	−	0.599246i
$96$		0			0
$97$	10.4826	−	6.05213i	1.06435	−	0.614501i	0.137715	−	0.990472i	$-0.456024\pi$
$97$	10.4826	−	6.05213i	1.06435	−	0.614501i	0.926631	+	0.375971i	$0.122691\pi$
$98$		0			0
$99$	11.1460	+	4.04583i	1.12021	+	0.406621i
$100$		0			0
$101$	0.0243106			0.00241900			0.00120950	−	0.999999i	$-0.499615\pi$
$101$	0.0243106			0.00241900			0.00120950	+	0.999999i	$0.499615\pi$
$102$		0			0
$103$			1.42747i			0.140653i	0.997524	+	0.0703266i	$0.0224041\pi$
$103$			1.42747i			0.140653i	−0.997524	+	0.0703266i	$0.977596\pi$
$104$		0			0
$105$	7.12698	−	1.42471i	0.695522	−	0.139037i
$106$		0			0
$107$	−10.9445	+	6.31880i	−1.05804	+	0.610862i	−0.924890	−	0.380234i	$-0.875844\pi$
$107$	−10.9445	+	6.31880i	−1.05804	+	0.610862i	−0.133153	+	0.991095i	$0.542510\pi$
$108$		0			0
$109$	0.0726028	−	0.125752i	0.00695408	−	0.0120448i	−0.862527	−	0.506010i	$-0.831120\pi$
$109$	0.0726028	−	0.125752i	0.00695408	−	0.0120448i	0.869482	+	0.493965i	$0.164453\pi$
$110$		0			0
$111$	−0.268146	+	0.575695i	−0.0254513	+	0.0546425i
$112$		0			0
$113$	−9.35867	−	5.40323i	−0.880390	−	0.508293i	−0.00960284	−	0.999954i	$-0.503057\pi$
$113$	−9.35867	−	5.40323i	−0.880390	−	0.508293i	−0.870787	+	0.491661i	$0.836390\pi$
$114$		0			0
$115$		−	3.85561i		−	0.359537i
$116$		0			0
$117$	−13.5029	+	11.3503i	−1.24835	+	1.04934i
$118$		0			0
$119$	−10.0087	−	13.6353i	−0.917496	−	1.24995i
$120$		0			0
$121$	−4.62241			−0.420219
$122$		0			0
$123$	19.2789	−	1.69513i	1.73832	−	0.152845i
$124$		0			0
$125$	11.8706			1.06174
$126$		0			0
$127$	−3.63647			−0.322685			−0.161342	−	0.986899i	$-0.551582\pi$
$127$	−3.63647			−0.322685			−0.161342	+	0.986899i	$0.551582\pi$
$128$		0			0
$129$	−1.85297	+	3.97823i	−0.163145	+	0.350263i
$130$		0			0
$131$	5.01984			0.438585			0.219293	−	0.975659i	$-0.429625\pi$
$131$	5.01984			0.438585			0.219293	+	0.975659i	$0.429625\pi$
$132$		0			0
$133$	−2.13151	−	19.3699i	−0.184825	−	1.67958i
$134$		0			0
$135$	7.95752	−	2.14334i	0.684874	−	0.184470i
$136$		0			0
$137$		−	9.30911i		−	0.795331i	−0.917531	−	0.397665i	$-0.869820\pi$
$137$		−	9.30911i		−	0.795331i	0.917531	−	0.397665i	$-0.130180\pi$
$138$		0			0
$139$	−3.82307	−	2.20725i	−0.324269	−	0.187217i	0.329025	−	0.944321i	$-0.393280\pi$
$139$	−3.82307	−	2.20725i	−0.324269	−	0.187217i	−0.653294	+	0.757105i	$0.726613\pi$
$140$		0			0
$141$	−1.87475	+	0.164841i	−0.157882	+	0.0138821i
$142$		0			0
$143$	11.6202	−	20.1268i	0.971730	−	1.68309i
$144$		0			0
$145$	−6.88418	+	3.97459i	−0.571700	+	0.330071i
$146$		0			0
$147$	2.60677	−	11.8408i	0.215003	−	0.976613i
$148$		0			0
$149$		−	2.89473i		−	0.237145i	−0.992945	−	0.118573i	$-0.962168\pi$
$149$		−	2.89473i		−	0.237145i	0.992945	−	0.118573i	$-0.0378318\pi$
$150$		0			0
$151$	2.77117			0.225515			0.112757	−	0.993623i	$-0.464032\pi$
$151$	2.77117			0.225515			0.112757	+	0.993623i	$0.464032\pi$
$152$		0			0
$153$	−12.3409	−	14.6813i	−0.997700	−	1.18691i
$154$		0			0
$155$	−1.35659	+	0.783230i	−0.108964	+	0.0629105i
$156$		0			0
$157$	0.146366	−	0.0845044i	0.0116813	−	0.00674418i	−0.494148	−	0.869378i	$-0.664520\pi$
$157$	0.146366	−	0.0845044i	0.0116813	−	0.00674418i	0.505829	+	0.862634i	$0.331187\pi$
$158$		0			0
$159$	1.20703	+	13.7276i	0.0957236	+	1.08867i
$160$		0			0
$161$	−5.88851	−	2.58736i	−0.464079	−	0.203913i
$162$		0			0
$163$	−3.55929	−	6.16487i	−0.278785	−	0.482870i	0.692298	−	0.721612i	$-0.256598\pi$
$163$	−3.55929	−	6.16487i	−0.278785	−	0.482870i	−0.971083	+	0.238742i	$0.923265\pi$
$164$		0			0
$165$	−8.89142	+	6.23160i	−0.692196	+	0.485130i
$166$		0			0
$167$	1.19494	−	2.06970i	0.0924675	−	0.160158i	−0.816081	−	0.577937i	$-0.803858\pi$
$167$	1.19494	−	2.06970i	0.0924675	−	0.160158i	0.908549	+	0.417779i	$0.137191\pi$
$168$		0			0
$169$	10.7866	+	18.6829i	0.829737	+	1.43715i
$170$		0			0
$171$	−3.85585	−	21.7570i	−0.294865	−	1.66380i
$172$		0			0
$173$	−3.57971	+	6.20023i	−0.272160	+	0.471395i	−0.969415	−	0.245429i	$-0.921071\pi$
$173$	−3.57971	+	6.20023i	−0.272160	+	0.471395i	0.697255	+	0.716823i	$0.254405\pi$
$174$		0			0
$175$	2.64438	−	6.01827i	0.199896	−	0.454939i
$176$		0			0
$177$	3.99912	−	8.58588i	0.300592	−	0.645354i
$178$		0			0
$179$	−8.02286	−	4.63200i	−0.599657	−	0.346212i	0.169250	−	0.985573i	$-0.445866\pi$
$179$	−8.02286	−	4.63200i	−0.599657	−	0.346212i	−0.768906	+	0.639361i	$0.779199\pi$
$180$		0			0
$181$			21.5541i			1.60210i	0.598595	+	0.801052i	$0.295726\pi$
$181$			21.5541i			1.60210i	−0.598595	+	0.801052i	$0.704274\pi$
$182$		0			0
$183$	2.18560	+	24.8571i	0.161565	+	1.83749i
$184$		0			0
$185$	−0.290765	−	0.503620i	−0.0213775	−	0.0370269i
$186$		0			0
$187$	21.8832	+	12.6343i	1.60026	+	0.923911i
$188$		0			0
$189$	2.06658	−	13.5915i	0.150322	−	0.988637i
$190$		0			0
$191$	2.91100	+	1.68067i	0.210633	+	0.121609i	0.601605	−	0.798793i	$-0.294528\pi$
$191$	2.91100	+	1.68067i	0.210633	+	0.121609i	−0.390973	+	0.920402i	$0.627861\pi$
$192$		0			0
$193$	−4.17845	−	7.23728i	−0.300771	−	0.520951i	0.675540	−	0.737324i	$-0.263911\pi$
$193$	−4.17845	−	7.23728i	−0.300771	−	0.520951i	−0.976311	+	0.216373i	$0.930577\pi$
$194$		0			0
$195$	−1.41476	−	16.0902i	−0.101313	−	1.15225i
$196$		0			0
$197$			5.57159i			0.396959i	0.980105	+	0.198480i	$0.0636003\pi$
$197$			5.57159i			0.396959i	−0.980105	+	0.198480i	$0.936400\pi$
$198$		0			0
$199$	−11.6605	−	6.73222i	−0.826594	−	0.477234i	0.0260910	−	0.999660i	$-0.491694\pi$
$199$	−11.6605	−	6.73222i	−0.826594	−	0.477234i	−0.852685	+	0.522425i	$0.825027\pi$
$200$		0			0
$201$	−8.34431	+	17.9148i	−0.588562	+	1.26361i
$202$		0			0
$203$	1.45048	+	13.1811i	0.101804	+	0.925134i
$204$		0			0
$205$	−8.86070	+	15.3472i	−0.618858	+	1.07189i
$206$		0			0
$207$	−6.85540	−	2.48841i	−0.476483	−	0.172957i
$208$		0			0
$209$	14.5558	+	25.2114i	1.00685	+	1.74391i
$210$		0			0
$211$	7.23362	−	12.5290i	0.497983	−	0.862532i	−0.502014	−	0.864859i	$-0.667408\pi$
$211$	7.23362	−	12.5290i	0.497983	−	0.862532i	0.999997	+	0.00232753i	$0.000740875\pi$
$212$		0			0
$213$	13.6913	−	9.59563i	0.938113	−	0.657482i
$214$		0			0
$215$	−2.00928	−	3.48017i	−0.137031	−	0.237345i
$216$		0			0
$217$	0.285831	+	2.59747i	0.0194035	+	0.176328i
$218$		0			0
$219$	1.33958	+	15.2351i	0.0905202	+	1.02949i
$220$		0			0
$221$	−32.5542	+	18.7952i	−2.18983	+	1.26430i
$222$		0			0
$223$	−18.3399	+	10.5885i	−1.22813	+	0.709060i	−0.966638	−	0.256146i	$-0.917547\pi$
$223$	−18.3399	+	10.5885i	−1.22813	+	0.709060i	−0.261490	+	0.965206i	$0.584214\pi$
$224$		0			0
$225$	2.54325	−	7.00647i	0.169550	−	0.467098i
$226$		0			0
$227$	8.47672			0.562620			0.281310	−	0.959617i	$-0.409231\pi$
$227$	8.47672			0.562620			0.281310	+	0.959617i	$0.409231\pi$
$228$		0			0
$229$		−	19.7783i		−	1.30699i	−0.756932	−	0.653494i	$-0.773303\pi$
$229$		−	19.7783i		−	1.30699i	0.756932	−	0.653494i	$-0.226697\pi$
$230$		0			0
$231$	3.55055	+	17.7613i	0.233609	+	1.16861i
$232$		0			0
$233$	−23.7957	+	13.7385i	−1.55891	+	0.900037i	−0.561548	+	0.827444i	$0.689794\pi$
$233$	−23.7957	+	13.7385i	−1.55891	+	0.900037i	−0.997362	+	0.0725933i	$0.976873\pi$
$234$		0			0
$235$	0.861645	−	1.49241i	0.0562075	−	0.0973543i
$236$		0			0
$237$	18.3117	−	1.61009i	1.18948	−	0.104587i
$238$		0			0
$239$	0.979306	+	0.565402i	0.0633460	+	0.0365728i	0.531339	−	0.847160i	$-0.321689\pi$
$239$	0.979306	+	0.565402i	0.0633460	+	0.0365728i	−0.467992	+	0.883732i	$0.655023\pi$
$240$		0			0
$241$		−	1.45825i		−	0.0939339i	−0.998896	−	0.0469669i	$-0.985044\pi$
$241$		−	1.45825i		−	0.0939339i	0.998896	−	0.0469669i	$-0.0149555\pi$
$242$		0			0
$243$	1.32485	−	15.5321i	0.0849894	−	0.996382i
$244$		0			0
$245$	7.50890	+	8.17750i	0.479726	+	0.522441i
$246$		0			0
$247$	−43.3074			−2.75558
$248$		0			0
$249$	−4.34135	+	9.32063i	−0.275122	+	0.590671i
$250$		0			0
$251$	1.61932			0.102210			0.0511052	−	0.998693i	$-0.483726\pi$
$251$	1.61932			0.102210			0.0511052	+	0.998693i	$0.483726\pi$
$252$		0			0
$253$	9.60865			0.604091
$254$		0			0
$255$	17.4944	−	1.53823i	1.09554	−	0.0963277i
$256$		0			0
$257$	8.95518			0.558609			0.279305	−	0.960203i	$-0.409896\pi$
$257$	8.95518			0.558609			0.279305	+	0.960203i	$0.409896\pi$
$258$		0			0
$259$	−0.964280	+	0.106112i	−0.0599174	+	0.00659345i
$260$		0			0
$261$	2.62389	+	14.8055i	0.162415	+	0.916438i
$262$		0			0
$263$			2.71686i			0.167529i	0.996486	+	0.0837643i	$0.0266943\pi$
$263$			2.71686i			0.167529i	−0.996486	+	0.0837643i	$0.973306\pi$
$264$		0			0
$265$	−10.9280	−	6.30931i	−0.671304	−	0.387578i
$266$		0			0
$267$	−6.88827	+	14.7887i	−0.421555	+	0.905055i
$268$		0			0
$269$	−8.87918	+	15.3792i	−0.541373	+	0.937686i	0.457452	+	0.889234i	$0.348762\pi$
$269$	−8.87918	+	15.3792i	−0.541373	+	0.937686i	−0.998826	+	0.0484519i	$0.984571\pi$
$270$		0			0
$271$	2.76570	−	1.59678i	0.168004	−	0.0969973i	−0.413640	−	0.910440i	$-0.635743\pi$
$271$	2.76570	−	1.59678i	0.168004	−	0.0969973i	0.581644	+	0.813443i	$0.302410\pi$
$272$		0			0
$273$	−25.5233	−	8.63689i	−1.54474	−	0.522728i
$274$		0			0
$275$			9.82039i			0.592192i
$276$		0			0
$277$	6.63542			0.398684			0.199342	−	0.979930i	$-0.436120\pi$
$277$	6.63542			0.398684			0.199342	+	0.979930i	$0.436120\pi$
$278$		0			0
$279$	0.517063	+	2.91757i	0.0309557	+	0.174670i
$280$		0			0
$281$	−6.88306	+	3.97394i	−0.410609	+	0.237065i	−0.691051	−	0.722806i	$-0.742852\pi$
$281$	−6.88306	+	3.97394i	−0.410609	+	0.237065i	0.280442	+	0.959871i	$0.409519\pi$
$282$		0			0
$283$	21.9793	−	12.6898i	1.30653	−	0.754328i	0.325019	−	0.945708i	$-0.394629\pi$
$283$	21.9793	−	12.6898i	1.30653	−	0.754328i	0.981516	+	0.191379i	$0.0612960\pi$
$284$		0			0
$285$	18.3409	+	8.54280i	1.08642	+	0.506032i
$286$		0			0
$287$	17.4930	+	23.8315i	1.03258	+	1.40673i
$288$		0			0
$289$	−11.9354	−	20.6728i	−0.702085	−	1.21605i
$290$		0			0
$291$	19.0048	+	8.85201i	1.11408	+	0.518914i
$292$		0			0
$293$	4.29543	−	7.43990i	0.250942	−	0.434644i	−0.712844	−	0.701323i	$-0.752593\pi$
$293$	4.29543	−	7.43990i	0.250942	−	0.434644i	0.963785	+	0.266679i	$0.0859265\pi$
$294$		0			0
$295$	4.33645	+	7.51096i	0.252478	+	0.437305i
$296$		0			0
$297$	5.34148	+	19.8311i	0.309944	+	1.15072i
$298$		0			0
$299$	−7.14707	+	12.3791i	−0.413326	+	0.715901i
$300$		0			0
$301$	−6.66347	+	0.733263i	−0.384076	+	0.0422646i
$302$		0			0
$303$	0.0241667	+	0.0344817i	0.00138834	+	0.00198092i
$304$		0			0
$305$	−19.7878	−	11.4245i	−1.13304	−	0.654163i
$306$		0			0
$307$			24.2144i			1.38199i	0.722861	+	0.690994i	$0.242827\pi$
$307$			24.2144i			1.38199i	−0.722861	+	0.690994i	$0.757173\pi$
$308$		0			0
$309$	−2.02470	+	1.41902i	−0.115181	+	0.0807255i
$310$		0			0
$311$	12.7009	+	21.9986i	0.720201	+	1.24742i	0.960919	+	0.276830i	$0.0892837\pi$
$311$	12.7009	+	21.9986i	0.720201	+	1.24742i	−0.240718	+	0.970595i	$0.577383\pi$
$312$		0			0
$313$	−20.0407	−	11.5705i	−1.13276	−	0.654002i	−0.188136	−	0.982143i	$-0.560245\pi$
$313$	−20.0407	−	11.5705i	−1.13276	−	0.654002i	−0.944629	+	0.328141i	$0.893578\pi$
$314$		0			0
$315$	9.10557	+	8.69249i	0.513040	+	0.489767i
$316$		0			0
$317$	5.22166	+	3.01472i	0.293277	+	0.169324i	0.639419	−	0.768859i	$-0.279175\pi$
$317$	5.22166	+	3.01472i	0.293277	+	0.169324i	−0.346142	+	0.938182i	$0.612508\pi$
$318$		0			0
$319$	−9.90516	−	17.1562i	−0.554583	−	0.960565i
$320$		0			0
$321$	−19.8422	−	9.24205i	−1.10748	−	0.515841i
$322$		0			0
$323$		−	47.0868i		−	2.61998i
$324$		0			0
$325$	−12.6519	−	7.30457i	−0.701800	−	0.405184i
$326$		0			0
$327$	0.250537	−	0.0220289i	0.0138547	−	0.00121820i
$328$		0			0
$329$	−1.70108	−	2.31746i	−0.0937836	−	0.127766i
$330$		0			0
$331$	8.70940	−	15.0851i	0.478712	−	0.829153i	−0.520990	−	0.853563i	$-0.674437\pi$
$331$	8.70940	−	15.0851i	0.478712	−	0.829153i	0.999702	+	0.0244093i	$0.00777048\pi$
$332$		0			0
$333$	−1.08311	+	0.191954i	−0.0593542	+	0.0105190i
$334$		0			0
$335$	−9.04818	−	15.6719i	−0.494355	−	0.856247i
$336$		0			0
$337$	−0.760462	+	1.31716i	−0.0414250	+	0.0717502i	−0.885995	−	0.463696i	$-0.846523\pi$
$337$	−0.760462	+	1.31716i	−0.0414250	+	0.0717502i	0.844570	+	0.535446i	$0.179856\pi$
$338$		0			0
$339$	−1.63943	−	18.6454i	−0.0890418	−	1.01268i
$340$		0			0
$341$	−1.95191	−	3.38080i	−0.105702	−	0.183081i
$342$		0			0
$343$	17.5281	−	5.98040i	0.946429	−	0.322911i
$344$		0			0
$345$	5.46872	−	3.83278i	0.294426	−	0.206350i
$346$		0			0
$347$	−19.0030	+	10.9714i	−1.02013	+	0.588975i	−0.914143	−	0.405392i	$-0.867135\pi$
$347$	−19.0030	+	10.9714i	−1.02013	+	0.588975i	−0.105992	+	0.994367i	$0.533802\pi$
$348$		0			0
$349$	4.95655	−	2.86167i	0.265318	−	0.153182i	−0.361440	−	0.932395i	$-0.617715\pi$
$349$	4.95655	−	2.86167i	0.265318	−	0.153182i	0.626758	+	0.779214i	$0.284381\pi$
$350$		0			0
$351$	−29.5221	−	7.86915i	−1.57577	−	0.420024i
$352$		0			0
$353$	3.84540			0.204670			0.102335	−	0.994750i	$-0.467369\pi$
$353$	3.84540			0.204670			0.102335	+	0.994750i	$0.467369\pi$
$354$		0			0
$355$			15.3093i			0.812535i
$356$		0			0
$357$	9.39063	−	27.7508i	0.497005	−	1.46873i
$358$		0			0
$359$	−10.8763	+	6.27946i	−0.574031	+	0.331417i	−0.758758	−	0.651373i	$-0.774193\pi$
$359$	−10.8763	+	6.27946i	−0.574031	+	0.331417i	0.184727	+	0.982790i	$0.440860\pi$
$360$		0			0
$361$	17.6241	−	30.5258i	0.927582	−	1.60662i
$362$		0			0
$363$	−4.59505	−	6.55634i	−0.241177	−	0.344119i
$364$		0			0
$365$	−12.1281	−	7.00215i	−0.634813	−	0.366509i
$366$		0			0
$367$		−	1.22224i		−	0.0638006i	−0.999491	−	0.0319003i	$-0.989844\pi$
$367$		−	1.22224i		−	0.0638006i	0.999491	−	0.0319003i	$-0.0101559\pi$
$368$		0			0
$369$	21.5691	+	25.6597i	1.12284	+	1.33579i
$370$		0			0
$371$	−16.9694	+	12.4560i	−0.881006	+	0.646683i
$372$		0			0
$373$	13.1525			0.681010			0.340505	−	0.940243i	$-0.389402\pi$
$373$	13.1525			0.681010			0.340505	+	0.940243i	$0.389402\pi$
$374$		0			0
$375$	11.8003	+	16.8370i	0.609366	+	0.869460i
$376$		0			0
$377$	29.4705			1.51781
$378$		0			0
$379$	22.9852			1.18067			0.590336	−	0.807157i	$-0.298995\pi$
$379$	22.9852			1.18067			0.590336	+	0.807157i	$0.298995\pi$
$380$		0			0
$381$	−3.61495	−	5.15790i	−0.185199	−	0.264247i
$382$		0			0
$383$	−27.9366			−1.42749			−0.713746	−	0.700404i	$-0.753003\pi$
$383$	−27.9366			−1.42749			−0.713746	+	0.700404i	$0.753003\pi$
$384$		0			0
$385$	−15.1843	−	6.67187i	−0.773864	−	0.340030i
$386$		0			0
$387$	−7.48464	+	1.32646i	−0.380466	+	0.0674276i
$388$		0			0
$389$			14.3116i			0.725627i	0.931862	+	0.362814i	$0.118184\pi$
$389$			14.3116i			0.725627i	−0.931862	+	0.362814i	$0.881816\pi$
$390$		0			0
$391$	−13.4594	−	7.77080i	−0.680672	−	0.392986i
$392$		0			0
$393$	4.99012	+	7.12004i	0.251718	+	0.359159i
$394$		0			0
$395$	−8.41619	+	14.5773i	−0.423465	+	0.733462i
$396$		0			0
$397$	−3.97038	+	2.29230i	−0.199267	+	0.115047i	−0.596314	−	0.802751i	$-0.703369\pi$
$397$	−3.97038	+	2.29230i	−0.199267	+	0.115047i	0.397046	+	0.917799i	$0.370035\pi$
$398$		0			0
$399$	25.3550	−	22.2785i	1.26934	−	1.11532i
$400$		0			0
$401$			11.0739i			0.553003i	0.961013	+	0.276502i	$0.0891751\pi$
$401$			11.0739i			0.553003i	−0.961013	+	0.276502i	$0.910825\pi$
$402$		0			0
$403$	5.80744			0.289289
$404$		0			0
$405$	10.9505	+	9.15614i	0.544134	+	0.454972i
$406$		0			0
$407$	1.25508	−	0.724623i	0.0622122	−	0.0359182i
$408$		0			0
$409$	5.31691	−	3.06972i	0.262904	−	0.151788i	−0.362754	−	0.931885i	$-0.618164\pi$
$409$	5.31691	−	3.06972i	0.262904	−	0.151788i	0.625659	+	0.780097i	$0.284830\pi$
$410$		0			0
$411$	13.2039	−	9.25400i	0.651298	−	0.456466i
$412$		0			0
$413$	14.3812	−	1.58254i	0.707653	−	0.0778718i
$414$		0			0
$415$	−4.70756	−	8.15372i	−0.231085	−	0.400251i
$416$		0			0
$417$	−0.669718	−	7.61676i	−0.0327962	−	0.372994i
$418$		0			0
$419$	−8.83059	+	15.2950i	−0.431402	+	0.747211i	−0.996994	−	0.0774744i	$-0.975314\pi$
$419$	−8.83059	+	15.2950i	−0.431402	+	0.747211i	0.565592	+	0.824685i	$0.308648\pi$
$420$		0			0
$421$	11.3569	+	19.6707i	0.553501	+	0.958693i	0.998018	+	0.0629223i	$0.0200420\pi$
$421$	11.3569	+	19.6707i	0.553501	+	0.958693i	−0.444517	+	0.895770i	$0.646625\pi$
$422$		0			0
$423$	−2.09745	−	2.49524i	−0.101982	−	0.121323i
$424$		0			0
$425$	7.94204	−	13.7560i	0.385245	−	0.667265i
$426$		0			0
$427$	−30.7270	+	22.5545i	−1.48698	+	1.09149i
$428$		0			0
$429$	40.0989	−	3.52577i	1.93599	−	0.170226i
$430$		0			0
$431$	18.4152	+	10.6320i	0.887031	+	0.512128i	0.872970	−	0.487773i	$-0.162191\pi$
$431$	18.4152	+	10.6320i	0.887031	+	0.512128i	0.0140610	+	0.999901i	$0.495524\pi$
$432$		0			0
$433$			16.1075i			0.774079i	0.922063	+	0.387039i	$0.126502\pi$
$433$			16.1075i			0.774079i	−0.922063	+	0.387039i	$0.873498\pi$
$434$		0			0
$435$	−12.4809	−	5.81334i	−0.598414	−	0.278728i
$436$		0			0
$437$	−8.95263	−	15.5064i	−0.428262	−	0.741772i
$438$		0			0
$439$	−11.2480	−	6.49401i	−0.536836	−	0.309942i	0.206960	−	0.978349i	$-0.433643\pi$
$439$	−11.2480	−	6.49401i	−0.536836	−	0.309942i	−0.743796	+	0.668407i	$0.766976\pi$
$440$		0			0
$441$	19.3861	−	8.07332i	0.923148	−	0.384444i
$442$		0			0
$443$	15.4357	+	8.91183i	0.733374	+	0.423414i	0.819655	−	0.572857i	$-0.194165\pi$
$443$	15.4357	+	8.91183i	0.733374	+	0.423414i	−0.0862809	+	0.996271i	$0.527498\pi$
$444$		0			0
$445$	−7.46931	−	12.9372i	−0.354079	−	0.613284i
$446$		0			0
$447$	4.10582	−	2.87759i	0.194199	−	0.136105i
$448$		0			0
$449$		−	5.71118i		−	0.269527i	−0.990878	−	0.134764i	$-0.956972\pi$
$449$		−	5.71118i		−	0.269527i	0.990878	−	0.134764i	$-0.0430275\pi$
$450$		0			0
$451$	−38.2471	−	22.0820i	−1.80099	−	1.03980i
$452$		0			0
$453$	2.75476	+	3.93057i	0.129430	+	0.184674i
$454$		0			0
$455$	19.8899	−	14.5997i	0.932452	−	0.684446i
$456$		0			0
$457$	4.75884	−	8.24255i	0.222609	−	0.385570i	−0.732990	−	0.680239i	$-0.761876\pi$
$457$	4.75884	−	8.24255i	0.222609	−	0.385570i	0.955599	+	0.294669i	$0.0952093\pi$
$458$		0			0
$459$	8.55589	−	32.0985i	0.399355	−	1.49823i
$460$		0			0
$461$	−20.1348	−	34.8746i	−0.937773	−	1.62427i	−0.769613	−	0.638510i	$-0.779551\pi$
$461$	−20.1348	−	34.8746i	−0.937773	−	1.62427i	−0.168160	−	0.985760i	$-0.553782\pi$
$462$		0			0
$463$	6.92014	−	11.9860i	0.321606	−	0.557038i	−0.659213	−	0.751956i	$-0.729111\pi$
$463$	6.92014	−	11.9860i	0.321606	−	0.557038i	0.980820	+	0.194917i	$0.0624439\pi$
$464$		0			0
$465$	−2.45948	−	1.14557i	−0.114056	−	0.0531247i
$466$		0			0
$467$	−10.5793	−	18.3238i	−0.489549	−	0.847924i	0.510378	−	0.859950i	$-0.329505\pi$
$467$	−10.5793	−	18.3238i	−0.489549	−	0.847924i	−0.999928	+	0.0120256i	$0.996172\pi$
$468$		0			0
$469$	−30.0070	+	3.30203i	−1.38559	+	0.152474i
$470$		0			0
$471$	0.265359	+	0.123598i	0.0122271	+	0.00569511i
$472$		0			0
$473$	8.67301	−	5.00736i	0.398785	−	0.230239i
$474$		0			0
$475$	15.8481	−	9.14992i	0.727162	−	0.419827i
$476$		0			0
$477$	−18.2711	+	15.3584i	−0.836578	+	0.703213i
$478$		0			0
$479$	−2.34127			−0.106975			−0.0534876	−	0.998569i	$-0.517034\pi$
$479$	−2.34127			−0.106975			−0.0534876	+	0.998569i	$0.517034\pi$
$480$		0			0
$481$			2.15594i			0.0983026i
$482$		0			0
$483$	−2.18378	−	10.9242i	−0.0993656	−	0.497068i
$484$		0			0
$485$	−16.6254	+	9.59871i	−0.754923	+	0.435855i
$486$		0			0
$487$	−8.83818	+	15.3082i	−0.400496	+	0.693679i	−0.993786	−	0.111310i	$-0.964495\pi$
$487$	−8.83818	+	15.3082i	−0.400496	+	0.693679i	0.593290	+	0.804989i	$0.297829\pi$
$488$		0			0
$489$	5.20591	−	11.1768i	0.235419	−	0.505432i
$490$		0			0
$491$	2.01875	+	1.16553i	0.0911051	+	0.0525995i	0.544860	−	0.838527i	$-0.316583\pi$
$491$	2.01875	+	1.16553i	0.0911051	+	0.0525995i	−0.453755	+	0.891126i	$0.649916\pi$
$492$		0			0
$493$			32.0424i			1.44312i
$494$		0			0
$495$	−17.6776	−	6.41671i	−0.794548	−	0.288409i
$496$		0			0
$497$	23.3813	+	10.2736i	1.04880	+	0.460832i
$498$		0			0
$499$	31.6088			1.41500			0.707501	−	0.706712i	$-0.249822\pi$
$499$	31.6088			1.41500			0.707501	+	0.706712i	$0.249822\pi$
$500$		0			0
$501$	4.12350	−	0.362566i	0.184224	−	0.0161983i
$502$		0			0
$503$	38.9500			1.73670			0.868348	−	0.495956i	$-0.165182\pi$
$503$	38.9500			1.73670			0.868348	+	0.495956i	$0.165182\pi$
$504$		0			0
$505$	−0.0385567			−0.00171575
$506$		0			0
$507$	−15.7768	+	33.8718i	−0.700670	+	1.50430i
$508$		0			0
$509$	13.7956			0.611477			0.305739	−	0.952115i	$-0.401097\pi$
$509$	13.7956			0.611477			0.305739	+	0.952115i	$0.401097\pi$
$510$		0			0
$511$	−18.8328	+	13.8238i	−0.833116	+	0.611530i
$512$		0			0
$513$	27.0266	−	27.0972i	1.19325	−	1.19637i
$514$		0			0
$515$		−	2.26398i		−	0.0997629i
$516$		0			0
$517$	3.71928	+	2.14733i	0.163574	+	0.0944393i
$518$		0			0
$519$	−12.3528	+	1.08614i	−0.542228	+	0.0476764i
$520$		0			0
$521$	2.27458	−	3.93969i	0.0996512	−	0.172601i	−0.811889	−	0.583812i	$-0.801561\pi$
$521$	2.27458	−	3.93969i	0.0996512	−	0.172601i	0.911540	+	0.411211i	$0.134894\pi$
$522$		0			0
$523$	32.6301	−	18.8390i	1.42681	−	0.823772i	0.429946	−	0.902855i	$-0.358533\pi$
$523$	32.6301	−	18.8390i	1.42681	−	0.823772i	0.996868	+	0.0790830i	$0.0251992\pi$
$524$		0			0
$525$	11.1649	−	2.23191i	0.487277	−	0.0974084i
$526$		0			0
$527$			6.31425i			0.275053i
$528$		0			0
$529$	17.0901			0.743050
$530$		0			0
$531$	16.1535	−	2.86278i	0.701002	−	0.124234i
$532$		0			0
$533$	56.8976	−	32.8498i	2.46451	−	1.42288i
$534$		0			0
$535$	17.3580	−	10.0216i	0.750452	−	0.433274i
$536$		0			0
$537$	−1.40543	−	15.9840i	−0.0606487	−	0.689763i
$538$		0			0
$539$	−20.3793	+	18.7131i	−0.877800	+	0.806031i
$540$		0			0
$541$	−1.53417	−	2.65727i	−0.0659593	−	0.114245i	0.831160	−	0.556034i	$-0.187677\pi$
$541$	−1.53417	−	2.65727i	−0.0659593	−	0.114245i	−0.897119	+	0.441789i	$0.854344\pi$
$542$		0			0
$543$	−30.5719	+	21.4265i	−1.31197	+	0.919500i
$544$		0			0
$545$	−0.115148	+	0.199443i	−0.00493241	+	0.00854319i
$546$		0			0
$547$	−7.22022	−	12.5058i	−0.308714	−	0.534709i	0.669367	−	0.742932i	$-0.266565\pi$
$547$	−7.22022	−	12.5058i	−0.308714	−	0.534709i	−0.978081	+	0.208223i	$0.933232\pi$
$548$		0			0
$549$	−33.0841	+	27.8099i	−1.41200	+	1.18690i
$550$		0			0
$551$	−18.4578	+	31.9698i	−0.786329	+	1.36196i
$552$		0			0
$553$	16.6155	+	22.6360i	0.706561	+	0.962581i
$554$		0			0
$555$	0.425281	−	0.913054i	0.0180522	−	0.0387570i
$556$		0			0
$557$	7.14024	+	4.12242i	0.302542	+	0.174672i	0.643584	−	0.765375i	$-0.277447\pi$
$557$	7.14024	+	4.12242i	0.302542	+	0.174672i	−0.341042	+	0.940048i	$0.610780\pi$
$558$		0			0
$559$			14.8982i			0.630128i
$560$		0			0
$561$	3.83346	+	43.5983i	0.161849	+	1.84072i
$562$		0			0
$563$	−4.68623	−	8.11678i	−0.197501	−	0.342082i	0.750217	−	0.661192i	$-0.229949\pi$
$563$	−4.68623	−	8.11678i	−0.197501	−	0.342082i	−0.947717	+	0.319111i	$0.896616\pi$
$564$		0			0
$565$	14.8429	+	8.56955i	0.624445	+	0.360524i
$566$		0			0
$567$	21.3323	−	10.5799i	0.895872	−	0.444312i
$568$		0			0
$569$	−16.5077	−	9.53072i	−0.692039	−	0.399549i	0.112337	−	0.993670i	$-0.464167\pi$
$569$	−16.5077	−	9.53072i	−0.692039	−	0.399549i	−0.804375	+	0.594121i	$0.797500\pi$
$570$		0			0
$571$	5.02208	+	8.69850i	0.210167	+	0.364021i	0.951767	−	0.306822i	$-0.0992657\pi$
$571$	5.02208	+	8.69850i	0.210167	+	0.364021i	−0.741599	+	0.670843i	$0.765932\pi$
$572$		0			0
$573$	0.509943	+	5.79963i	0.0213032	+	0.242283i
$574$		0			0
$575$		−	6.04009i		−	0.251889i
$576$		0			0
$577$	−10.1403	−	5.85453i	−0.422148	−	0.243727i	0.273848	−	0.961773i	$-0.411704\pi$
$577$	−10.1403	−	5.85453i	−0.422148	−	0.243727i	−0.695996	+	0.718046i	$0.745037\pi$
$578$		0			0
$579$	6.11151	−	13.1211i	0.253986	−	0.545293i
$580$		0			0
$581$	−15.6119	+	1.71797i	−0.647692	+	0.0712735i
$582$		0			0
$583$	15.7236	−	27.2340i	0.651204	−	1.12792i
$584$		0			0
$585$	21.4157	−	18.0017i	0.885430	−	0.744277i
$586$		0			0
$587$	−0.476262	−	0.824911i	−0.0196575	−	0.0340477i	0.856029	−	0.516927i	$-0.172924\pi$
$587$	−0.476262	−	0.824911i	−0.0196575	−	0.0340477i	−0.875687	+	0.482880i	$0.839591\pi$
$588$		0			0
$589$	−3.63728	+	6.29996i	−0.149872	+	0.259585i
$590$		0			0
$591$	−7.90263	+	5.53860i	−0.325071	+	0.227828i
$592$		0			0
$593$	−15.4339	−	26.7323i	−0.633794	−	1.09776i	−0.986769	−	0.162130i	$-0.948164\pi$
$593$	−15.4339	−	26.7323i	−0.633794	−	1.09776i	0.352976	−	0.935632i	$-0.385170\pi$
$594$		0			0
$595$	15.8738	+	21.6257i	0.650764	+	0.886567i
$596$		0			0
$597$	−2.04267	−	23.2315i	−0.0836009	−	0.950800i
$598$		0			0
$599$	35.6899	−	20.6056i	1.45825	−	0.841921i	0.459325	−	0.888268i	$-0.348091\pi$
$599$	35.6899	−	20.6056i	1.45825	−	0.841921i	0.998925	+	0.0463468i	$0.0147579\pi$
$600$		0			0
$601$	−14.3592	+	8.29029i	−0.585724	+	0.338168i	−0.763405	−	0.645920i	$-0.776474\pi$
$601$	−14.3592	+	8.29029i	−0.585724	+	0.338168i	0.177681	+	0.984088i	$0.443141\pi$
$602$		0			0
$603$	−33.7049	+	5.97331i	−1.37257	+	0.243252i
$604$		0			0
$605$	7.33116			0.298054
$606$		0			0
$607$		−	47.4652i		−	1.92655i	−0.268510	−	0.963277i	$-0.586531\pi$
$607$		−	47.4652i		−	1.92655i	0.268510	−	0.963277i	$-0.413469\pi$
$608$		0			0
$609$	−17.2540	+	15.1604i	−0.699166	+	0.614332i
$610$		0			0
$611$	−5.53292	+	3.19443i	−0.223838	+	0.129233i
$612$		0			0
$613$	7.32074	−	12.6799i	0.295682	−	0.512136i	−0.679462	−	0.733711i	$-0.737787\pi$
$613$	7.32074	−	12.6799i	0.295682	−	0.512136i	0.975143	+	0.221575i	$0.0711199\pi$
$614$		0			0
$615$	−30.5764	+	2.68849i	−1.23296	+	0.108410i
$616$		0			0
$617$	−40.1960	−	23.2072i	−1.61823	−	0.934286i	−0.987378	−	0.158383i	$-0.949372\pi$
$617$	−40.1960	−	23.2072i	−1.61823	−	0.934286i	−0.630852	−	0.775903i	$-0.717295\pi$
$618$		0			0
$619$			7.74450i			0.311278i	0.987814	+	0.155639i	$0.0497436\pi$
$619$			7.74450i			0.311278i	−0.987814	+	0.155639i	$0.950256\pi$
$620$		0			0
$621$	−3.28530	−	12.1972i	−0.131835	−	0.489459i
$622$		0			0
$623$	−24.7709	+	2.72585i	−0.992425	+	0.109209i
$624$		0			0
$625$	−6.40386			−0.256154
$626$		0			0
$627$	−21.2897	+	45.7078i	−0.850230	+	1.82540i
$628$		0			0
$629$	−2.34409			−0.0934651
$630$		0			0
$631$	24.3088			0.967718			0.483859	−	0.875146i	$-0.339235\pi$
$631$	24.3088			0.967718			0.483859	+	0.875146i	$0.339235\pi$
$632$		0			0
$633$	24.9617	−	2.19480i	0.992138	−	0.0872356i
$634$		0			0
$635$	5.76746			0.228875
$636$		0			0
$637$	−8.95014	−	40.1744i	−0.354617	−	1.59177i
$638$		0			0
$639$	27.2205	+	9.88065i	1.07683	+	0.390873i
$640$		0			0
$641$			17.5326i			0.692495i	0.938143	+	0.346248i	$0.112544\pi$
$641$			17.5326i			0.692495i	−0.938143	+	0.346248i	$0.887456\pi$
$642$		0			0
$643$	−7.49992	−	4.33008i	−0.295768	−	0.170762i	0.344772	−	0.938686i	$-0.387956\pi$
$643$	−7.49992	−	4.33008i	−0.295768	−	0.170762i	−0.640540	+	0.767925i	$0.721290\pi$
$644$		0			0
$645$	2.93882	−	6.30948i	0.115716	−	0.248436i
$646$		0			0
$647$	−13.3349	+	23.0967i	−0.524249	+	0.908026i	0.475352	+	0.879796i	$0.342321\pi$
$647$	−13.3349	+	23.0967i	−0.524249	+	0.908026i	−0.999601	+	0.0282305i	$0.991013\pi$
$648$		0			0
$649$	−18.7182	+	10.8070i	−0.734755	+	0.424211i
$650$		0			0
$651$	−3.40006	+	2.98751i	−0.133259	+	0.117090i
$652$		0			0
$653$		−	43.8362i		−	1.71544i	−0.514116	−	0.857721i	$-0.671880\pi$
$653$		−	43.8362i		−	1.71544i	0.514116	−	0.857721i	$-0.328120\pi$
$654$		0			0
$655$	−7.96148			−0.311081
$656$		0			0
$657$	−20.2775	+	17.0450i	−0.791102	+	0.664987i
$658$		0			0
$659$	−39.3555	+	22.7219i	−1.53307	+	0.885120i	−0.533855	+	0.845576i	$0.679257\pi$
$659$	−39.3555	+	22.7219i	−1.53307	+	0.885120i	−0.999218	+	0.0395437i	$0.987410\pi$
$660$		0			0
$661$	−34.9261	+	20.1646i	−1.35847	+	0.784311i	−0.989417	−	0.145098i	$-0.953650\pi$
$661$	−34.9261	+	20.1646i	−1.35847	+	0.784311i	−0.369050	+	0.929410i	$0.620317\pi$
$662$		0			0
$663$	−59.0202	−	27.4904i	−2.29216	−	1.06764i
$664$		0			0
$665$	3.38058	+	30.7208i	0.131093	+	1.19130i
$666$		0			0
$667$	6.09223	+	10.5520i	0.235892	+	0.408577i
$668$		0			0
$669$	−33.2498	−	15.4871i	−1.28551	−	0.598764i
$670$		0			0
$671$	28.4712	−	49.3135i	1.09912	−	1.90373i
$672$		0			0
$673$	−3.85511	−	6.67724i	−0.148603	−	0.257389i	0.782108	−	0.623143i	$-0.214144\pi$
$673$	−3.85511	−	6.67724i	−0.148603	−	0.257389i	−0.930712	+	0.365754i	$0.880811\pi$
$674$		0			0
$675$	12.4660	−	3.35770i	0.479818	−	0.129238i
$676$		0			0
$677$	22.0288	−	38.1550i	0.846635	−	1.46642i	−0.0375585	−	0.999294i	$-0.511958\pi$
$677$	22.0288	−	38.1550i	0.846635	−	1.46642i	0.884194	−	0.467121i	$-0.154709\pi$
$678$		0			0
$679$	3.50294	+	31.8327i	0.134431	+	1.22163i
$680$		0			0
$681$	8.42654	+	12.0232i	0.322906	+	0.460731i
$682$		0			0
$683$	−3.75165	−	2.16602i	−0.143553	−	0.0828804i	0.426503	−	0.904486i	$-0.359745\pi$
$683$	−3.75165	−	2.16602i	−0.143553	−	0.0828804i	−0.570056	+	0.821606i	$0.693079\pi$
$684$		0			0
$685$			14.7643i			0.564114i
$686$		0			0
$687$	28.0532	−	19.6612i	1.07030	−	0.750123i
$688$		0			0
$689$	23.3909	+	40.5142i	0.891123	+	1.54347i
$690$		0			0
$691$	7.00301	+	4.04319i	0.266407	+	0.153810i	0.627254	−	0.778815i	$-0.284179\pi$
$691$	7.00301	+	4.04319i	0.266407	+	0.153810i	−0.360847	+	0.932625i	$0.617512\pi$
$692$		0			0
$693$	−21.6628	+	22.6922i	−0.822901	+	0.862005i
$694$		0			0
$695$	6.06341	+	3.50071i	0.229998	+	0.132790i
$696$		0			0
$697$	35.7167	+	61.8631i	1.35286	+	2.34323i
$698$		0			0
$699$	−43.1413	−	20.0943i	−1.63175	−	0.760035i
$700$		0			0
$701$			41.8099i			1.57914i	0.613662	+	0.789569i	$0.289696\pi$
$701$			41.8099i			1.57914i	−0.613662	+	0.789569i	$0.710304\pi$
$702$		0			0
$703$	−2.33879	−	1.35030i	−0.0882091	−	0.0509275i
$704$		0			0
$705$	2.97335	−	0.261438i	0.111983	−	0.00984632i
$706$		0			0
$707$	−0.0258741	+	0.0588861i	−0.000973095	+	0.00221464i
$708$		0			0
$709$	22.6470	−	39.2257i	0.850526	−	1.47315i	−0.0302091	−	0.999544i	$-0.509617\pi$
$709$	22.6470	−	39.2257i	0.850526	−	1.47315i	0.880735	−	0.473610i	$-0.157049\pi$
$710$		0			0
$711$	20.4871	+	24.3725i	0.768325	+	0.914039i
$712$		0			0
$713$	1.20053	+	2.07938i	0.0449602	+	0.0778734i
$714$		0			0
$715$	−18.4297	+	31.9212i	−0.689231	+	1.19378i
$716$		0			0
$717$	0.171553	+	1.95108i	0.00640676	+	0.0728646i
$718$		0			0
$719$	1.73529	+	3.00561i	0.0647155	+	0.112090i	0.896568	−	0.442907i	$-0.146053\pi$
$719$	1.73529	+	3.00561i	0.0647155	+	0.112090i	−0.831852	+	0.554997i	$0.812719\pi$
$720$		0			0
$721$	−3.45768	−	1.51928i	−0.128771	−	0.0565809i
$722$		0			0
$723$	2.06835	−	1.44961i	0.0769227	−	0.0539117i
$724$		0			0
$725$	−10.7846	+	6.22648i	−0.400529	+	0.231246i
$726$		0			0
$727$	−37.7189	+	21.7770i	−1.39892	+	0.807665i	−0.994279	−	0.106811i	$-0.965936\pi$
$727$	−37.7189	+	21.7770i	−1.39892	+	0.807665i	−0.404638	+	0.914477i	$0.632603\pi$
$728$		0			0
$729$	23.3474	−	13.5610i	0.864718	−	0.502258i
$730$		0			0
$731$	−16.1984			−0.599120
$732$		0			0
$733$			7.63755i			0.282099i	0.990003	+	0.141050i	$0.0450477\pi$
$733$			7.63755i			0.282099i	−0.990003	+	0.141050i	$0.954952\pi$
$734$		0			0
$735$	−4.13435	+	18.7796i	−0.152498	+	0.692695i
$736$		0			0
$737$	39.0563	−	22.5492i	1.43866	−	0.830610i
$738$		0			0
$739$	22.0809	−	38.2453i	0.812260	−	1.40687i	−0.0990195	−	0.995085i	$-0.531571\pi$
$739$	22.0809	−	38.2453i	0.812260	−	1.40687i	0.911279	−	0.411789i	$-0.135096\pi$
$740$		0			0
$741$	−43.0510	−	61.4264i	−1.58152	−	2.25655i
$742$		0			0
$743$	10.8720	+	6.27693i	0.398853	+	0.230278i	0.685989	−	0.727612i	$-0.259370\pi$
$743$	10.8720	+	6.27693i	0.398853	+	0.230278i	−0.287136	+	0.957890i	$0.592703\pi$
$744$		0			0
$745$			4.59105i			0.168203i
$746$		0			0
$747$	−17.5359	+	3.10777i	−0.641603	+	0.113707i
$748$		0			0
$749$	−3.65729	−	33.2353i	−0.133635	−	1.21439i
$750$		0			0
$751$	18.1150			0.661025			0.330512	−	0.943802i	$-0.392778\pi$
$751$	18.1150			0.661025			0.330512	+	0.943802i	$0.392778\pi$
$752$		0			0
$753$	1.60973	+	2.29681i	0.0586619	+	0.0837004i
$754$		0			0
$755$	−4.39509			−0.159954
$756$		0			0
$757$	39.8682			1.44903			0.724517	−	0.689257i	$-0.242063\pi$
$757$	39.8682			1.44903			0.724517	+	0.689257i	$0.242063\pi$
$758$		0			0
$759$	9.55177	+	13.6287i	0.346707	+	0.494691i
$760$		0			0
$761$	15.0569			0.545812			0.272906	−	0.962041i	$-0.412015\pi$
$761$	15.0569			0.545812			0.272906	+	0.962041i	$0.412015\pi$
$762$		0			0
$763$	0.227328	+	0.309700i	0.00822984	+	0.0112119i
$764$		0			0
$765$	19.5727	+	23.2846i	0.707651	+	0.841858i
$766$		0			0
$767$		−	32.1536i		−	1.16100i
$768$		0			0
$769$	−0.522559	−	0.301700i	−0.0188440	−	0.0108796i	0.490548	−	0.871414i	$-0.336796\pi$
$769$	−0.522559	−	0.301700i	−0.0188440	−	0.0108796i	−0.509392	+	0.860534i	$0.670130\pi$
$770$		0			0
$771$	8.90217	+	12.7019i	0.320604	+	0.457446i
$772$		0			0
$773$	1.56956	−	2.71856i	0.0564533	−	0.0977799i	−0.836418	−	0.548093i	$-0.815354\pi$
$773$	1.56956	−	2.71856i	0.0564533	−	0.0977799i	0.892871	+	0.450313i	$0.148687\pi$
$774$		0			0
$775$	−2.12520	+	1.22699i	−0.0763395	+	0.0440746i
$776$		0			0
$777$	−1.10908	−	1.26223i	−0.0397880	−	0.0452824i
$778$		0			0
$779$			82.2974i			2.94861i
$780$		0			0
$781$	−38.1528			−1.36521
$782$		0			0
$783$	−18.3915	+	18.4395i	−0.657259	+	0.658976i
$784$		0			0
$785$	−0.232137	+	0.134024i	−0.00828532	+	0.00478353i
$786$		0			0
$787$	15.9640	−	9.21682i	0.569055	−	0.328544i	−0.187717	−	0.982223i	$-0.560109\pi$
$787$	15.9640	−	9.21682i	0.569055	−	0.328544i	0.756772	+	0.653679i	$0.226775\pi$
$788$		0			0
$789$	−3.85354	+	2.70077i	−0.137190	+	0.0961501i
$790$		0			0
$791$	23.0485	−	16.9182i	0.819509	−	0.601542i
$792$		0			0
$793$	42.3547	+	73.3604i	1.50406	+	2.60510i
$794$		0			0
$795$	−1.91435	−	21.7721i	−0.0678951	−	0.772176i
$796$		0			0
$797$	−17.1802	+	29.7570i	−0.608554	+	1.05405i	0.382925	+	0.923779i	$0.374917\pi$
$797$	−17.1802	+	29.7570i	−0.608554	+	1.05405i	−0.991479	+	0.130267i	$0.958417\pi$
$798$		0			0
$799$	−3.47321	−	6.01578i	−0.122873	−	0.212823i
$800$		0			0
$801$	−27.8235	+	4.93100i	−0.983096	+	0.174228i
$802$		0			0
$803$	17.4502	−	30.2247i	0.615806	−	1.06661i
$804$		0			0
$805$	9.33920	+	4.10357i	0.329164	+	0.144632i
$806$		0			0
$807$	−30.6402	+	2.69410i	−1.07859	+	0.0948367i
$808$		0			0
$809$	−44.3399	−	25.5996i	−1.55891	−	0.900035i	−0.997362	−	0.0725881i	$-0.976874\pi$
$809$	−44.3399	−	25.5996i	−1.55891	−	0.900035i	−0.561544	−	0.827447i	$-0.689793\pi$
$810$		0			0
$811$			46.2446i			1.62387i	0.583751	+	0.811933i	$0.301585\pi$
$811$			46.2446i			1.62387i	−0.583751	+	0.811933i	$0.698415\pi$
$812$		0			0
$813$	5.01417	+	2.33549i	0.175855	+	0.0819092i
$814$		0			0
$815$	5.64505	+	9.77751i	0.197737	+	0.342491i
$816$		0			0
$817$	−16.1617	−	9.33099i	−0.565428	−	0.326450i
$818$		0			0
$819$	−13.1219	−	44.7876i	−0.458515	−	1.56500i
$820$		0			0
$821$	−7.33282	−	4.23361i	−0.255917	−	0.147754i	0.366553	−	0.930397i	$-0.380538\pi$
$821$	−7.33282	−	4.23361i	−0.255917	−	0.147754i	−0.622471	+	0.782643i	$0.713871\pi$
$822$		0			0
$823$	12.6623	+	21.9317i	0.441380	+	0.764492i	0.997792	−	0.0664144i	$-0.0211559\pi$
$823$	12.6623	+	21.9317i	0.441380	+	0.764492i	−0.556413	+	0.830906i	$0.687823\pi$
$824$		0			0
$825$	−13.9291	+	9.76226i	−0.484948	+	0.339878i
$826$		0			0
$827$			6.75531i			0.234905i	0.993078	+	0.117453i	$0.0374728\pi$
$827$			6.75531i			0.234905i	−0.993078	+	0.117453i	$0.962527\pi$
$828$		0			0
$829$	−17.0191	−	9.82599i	−0.591098	−	0.341271i	0.174434	−	0.984669i	$-0.444191\pi$
$829$	−17.0191	−	9.82599i	−0.591098	−	0.341271i	−0.765532	+	0.643398i	$0.777524\pi$
$830$		0			0
$831$	6.59614	+	9.41155i	0.228817	+	0.326483i
$832$		0			0
$833$	43.6804	−	9.73122i	1.51344	−	0.337167i
$834$		0			0
$835$	−1.89519	+	3.28256i	−0.0655856	+	0.113598i
$836$		0			0
$837$	−3.62422	+	3.63369i	−0.125271	+	0.125599i
$838$		0			0
$839$	16.6302	+	28.8044i	0.574140	+	0.994439i	0.996135	+	0.0878410i	$0.0279967\pi$
$839$	16.6302	+	28.8044i	0.574140	+	0.994439i	−0.421995	+	0.906598i	$0.638670\pi$
$840$		0			0
$841$	−1.93955	+	3.35940i	−0.0668811	+	0.115841i
$842$		0			0
$843$	−12.4789	−	5.81239i	−0.429795	−	0.200189i
$844$		0			0
$845$	−17.1076	−	29.6312i	−0.588518	−	1.01934i
$846$		0			0
$847$	4.91969	−	11.1966i	0.169043	−	0.384719i
$848$		0			0
$849$	39.8481	+	18.5604i	1.36758	+	0.636991i
$850$		0			0
$851$	−0.771946	+	0.445683i	−0.0264620	+	0.0152778i
$852$		0			0
$853$	−25.0891	+	14.4852i	−0.859035	+	0.495964i	−0.863689	−	0.504025i	$-0.831852\pi$
$853$	−25.0891	+	14.4852i	−0.859035	+	0.495964i	0.00465409	+	0.999989i	$0.498519\pi$
$854$		0			0
$855$	6.11540	+	34.5066i	0.209142	+	1.18010i
$856$		0			0
$857$	−46.6449			−1.59336			−0.796680	−	0.604401i	$-0.793412\pi$
$857$	−46.6449			−1.59336			−0.796680	+	0.604401i	$0.793412\pi$
$858$		0			0
$859$			14.7329i			0.502680i	0.967899	+	0.251340i	$0.0808712\pi$
$859$			14.7329i			0.502680i	−0.967899	+	0.251340i	$0.919129\pi$
$860$		0			0
$861$	−16.4127	+	48.5022i	−0.559345	+	1.65295i
$862$		0			0
$863$	40.0533	−	23.1248i	1.36343	−	0.787177i	0.373352	−	0.927690i	$-0.378208\pi$
$863$	40.0533	−	23.1248i	1.36343	−	0.787177i	0.990079	+	0.140513i	$0.0448751\pi$
$864$		0			0
$865$	5.67743	−	9.83360i	0.193038	−	0.334352i
$866$		0			0
$867$	17.4571	−	37.4794i	0.592874	−	1.27287i
$868$		0			0
$869$	−36.3284	−	20.9742i	−1.23236	−	0.711501i
$870$		0			0
$871$			67.0898i			2.27325i
$872$		0			0
$873$	6.33675	+	35.7556i	0.214467	+	1.21014i
$874$		0			0
$875$	−12.6340	+	28.7534i	−0.427108	+	0.972042i
$876$		0			0
$877$	−47.9408			−1.61884			−0.809422	−	0.587227i	$-0.800220\pi$
$877$	−47.9408			−1.61884			−0.809422	+	0.587227i	$0.800220\pi$
$878$		0			0
$879$	14.8226	−	1.30331i	0.499954	−	0.0439594i
$880$		0			0
$881$	22.8464			0.769715			0.384857	−	0.922976i	$-0.374251\pi$
$881$	22.8464			0.769715			0.384857	+	0.922976i	$0.374251\pi$
$882$		0			0
$883$	−9.97054			−0.335535			−0.167768	−	0.985827i	$-0.553656\pi$
$883$	−9.97054			−0.335535			−0.167768	+	0.985827i	$0.553656\pi$
$884$		0			0
$885$	−6.34261	+	13.6172i	−0.213205	+	0.457738i
$886$		0			0
$887$	14.5527			0.488633			0.244317	−	0.969696i	$-0.421436\pi$
$887$	14.5527			0.488633			0.244317	+	0.969696i	$0.421436\pi$
$888$		0			0
$889$	3.87034	−	8.80840i	0.129807	−	0.295424i
$890$		0			0
$891$	−22.8182	+	27.2900i	−0.764440	+	0.914249i
$892$		0			0
$893$		−	8.00288i		−	0.267806i
$894$		0			0
$895$	12.7243	+	7.34637i	0.425326	+	0.245562i
$896$		0			0
$897$	−24.6630	+	2.16854i	−0.823474	+	0.0724055i
$898$		0			0
$899$	2.47516	−	4.28709i	0.0825510	−	0.142983i
$900$		0			0
$901$	−44.0499	+	25.4322i	−1.46752	+	0.847270i
$902$		0			0
$903$	−7.66407	−	8.72242i	−0.255044	−	0.290264i
$904$		0			0
$905$		−	34.1849i		−	1.13634i
$906$		0			0
$907$	−21.9091			−0.727481			−0.363740	−	0.931500i	$-0.618500\pi$
$907$	−21.9091			−0.727481			−0.363740	+	0.931500i	$0.618500\pi$
$908$		0			0
$909$	−0.0248845	+	0.0685551i	−0.000825368	+	0.00227383i
$910$		0			0
$911$	44.3072	−	25.5808i	1.46796	−	0.847529i	0.468608	−	0.883406i	$-0.344756\pi$
$911$	44.3072	−	25.5808i	1.46796	−	0.847529i	0.999356	+	0.0358768i	$0.0114224\pi$
$912$		0			0
$913$	20.3201	−	11.7318i	0.672497	−	0.388266i
$914$		0			0
$915$	−3.46638	−	39.4234i	−0.114595	−	1.30330i
$916$		0			0
$917$	−5.34268	+	12.1592i	−0.176431	+	0.401534i
$918$		0			0
$919$	−28.4261	−	49.2355i	−0.937691	−	1.62413i	−0.769763	−	0.638329i	$-0.779626\pi$
$919$	−28.4261	−	49.2355i	−0.937691	−	1.62413i	−0.167928	−	0.985799i	$-0.553707\pi$
$920$		0			0
$921$	−34.3452	+	24.0710i	−1.13171	+	0.793168i
$922$		0			0
$923$	28.3786	−	49.1533i	0.934094	−	1.61790i
$924$		0			0
$925$	−0.455505	−	0.788957i	−0.0149769	−	0.0259407i
$926$		0			0
$927$	−4.02543	−	1.46117i	−0.132213	−	0.0479913i
$928$		0			0
$929$	5.15562	−	8.92980i	0.169151	−	0.292977i	−0.768971	−	0.639284i	$-0.779231\pi$
$929$	5.15562	−	8.92980i	0.169151	−	0.292977i	0.938121	+	0.346306i	$0.112564\pi$
$930$		0			0
$931$	49.1871	+	15.4526i	1.61204	+	0.506439i
$932$		0			0
$933$	−18.5767	+	39.8830i	−0.608172	+	1.30571i
$934$		0			0
$935$	−34.7069	−	20.0380i	−1.13504	−	0.655314i
$936$		0			0
$937$		−	2.65580i		−	0.0867614i	−0.999059	−	0.0433807i	$-0.986187\pi$
$937$		−	2.65580i		−	0.0867614i	0.999059	−	0.0433807i	$-0.0138128\pi$
$938$		0			0
$939$	−3.51068	−	39.9273i	−0.114567	−	1.30298i
$940$		0			0
$941$	1.43664	+	2.48834i	0.0468333	+	0.0811176i	0.888492	−	0.458893i	$-0.151754\pi$
$941$	1.43664	+	2.48834i	0.0468333	+	0.0811176i	−0.841658	+	0.540010i	$0.818420\pi$
$942$		0			0
$943$	23.5241	+	13.5816i	0.766050	+	0.442279i
$944$		0			0
$945$	−3.27760	+	21.5562i	−0.106620	+	0.701223i
$946$		0			0
$947$	−8.03333	−	4.63804i	−0.261048	−	0.150716i	0.363765	−	0.931491i	$-0.381491\pi$
$947$	−8.03333	−	4.63804i	−0.261048	−	0.150716i	−0.624813	+	0.780775i	$0.714825\pi$
$948$		0			0
$949$	25.9595	+	44.9632i	0.842682	+	1.45957i
$950$		0			0
$951$	0.914719	+	10.4032i	0.0296618	+	0.337346i
$952$		0			0
$953$		−	52.9084i		−	1.71387i	−0.515425	−	0.856935i	$-0.672366\pi$
$953$		−	52.9084i		−	1.71387i	0.515425	−	0.856935i	$-0.327634\pi$
$954$		0			0
$955$	−4.61686	−	2.66555i	−0.149398	−	0.0862551i
$956$		0			0
$957$	14.4876	−	31.1040i	0.468316	−	1.00545i
$958$		0			0
$959$	22.5489	+	9.90780i	0.728141	+	0.319940i
$960$		0			0
$961$	−15.0122	+	26.0020i	−0.484266	+	0.838773i
$962$		0			0
$963$	−6.61596	−	37.3311i	−0.213196	−	1.20298i
$964$		0			0
$965$	6.62703	+	11.4784i	0.213332	+	0.369501i
$966$		0			0
$967$	5.65450	−	9.79388i	0.181836	−	0.314950i	−0.760669	−	0.649139i	$-0.775129\pi$
$967$	5.65450	−	9.79388i	0.181836	−	0.314950i	0.942506	+	0.334189i	$0.108463\pi$
$968$		0			0
$969$	66.7870	−	46.8081i	2.14551	−	1.50369i
$970$		0			0
$971$	22.5860	+	39.1201i	0.724819	+	1.25542i	0.959048	+	0.283242i	$0.0914099\pi$
$971$	22.5860	+	39.1201i	0.724819	+	1.25542i	−0.234230	+	0.972181i	$0.575257\pi$
$972$		0			0
$973$	9.41544	−	6.91119i	0.301845	−	0.221563i
$974$		0			0
$975$	−2.21633	−	25.2065i	−0.0709794	−	0.807254i
$976$		0			0
$977$	15.2443	−	8.80132i	0.487710	−	0.281579i	−0.235914	−	0.971774i	$-0.575808\pi$
$977$	15.2443	−	8.80132i	0.487710	−	0.281579i	0.723624	+	0.690195i	$0.242475\pi$
$978$		0			0
$979$	32.2412	−	18.6145i	1.03043	−	0.594921i
$980$		0			0
$981$	0.280299	+	0.333458i	0.00894926	+	0.0106465i
$982$		0			0
$983$	−35.0841			−1.11901			−0.559504	−	0.828827i	$-0.689008\pi$
$983$	−35.0841			−1.11901			−0.559504	+	0.828827i	$0.689008\pi$
$984$		0			0
$985$		−	8.83656i		−	0.281556i
$986$		0			0
$987$	1.59603	−	4.71652i	0.0508023	−	0.150129i
$988$		0			0
$989$	−5.33438	+	3.07981i	−0.169624	+	0.0979322i
$990$		0			0
$991$	16.9731	−	29.3982i	0.539167	−	0.933865i	−0.459782	−	0.888032i	$-0.652072\pi$
$991$	16.9731	−	29.3982i	0.539167	−	0.933865i	0.998949	−	0.0458331i	$-0.0145942\pi$
$992$		0			0
$993$	30.0543	−	2.64258i	0.953744	−	0.0838598i
$994$		0			0
$995$	18.4937	+	10.6773i	0.586289	+	0.338494i
$996$		0			0
$997$		−	25.5331i		−	0.808642i	−0.914617	−	0.404321i	$-0.867508\pi$
$997$		−	25.5331i		−	0.808642i	0.914617	−	0.404321i	$-0.132492\pi$
$998$		0			0
$999$	−1.34896	−	1.34545i	−0.0426794	−	0.0425681i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cx.a.185.18	yes	48
3.2	odd	2		1512.2.cx.a.17.18		48
4.3	odd	2		1008.2.df.e.689.7		48
7.5	odd	6		504.2.bs.a.257.22	✓	48
9.2	odd	6		504.2.bs.a.353.22	yes	48
9.7	even	3		1512.2.bs.a.521.18		48
12.11	even	2		3024.2.df.e.17.18		48
21.5	even	6		1512.2.bs.a.1097.18		48
28.19	even	6		1008.2.ca.e.257.3		48
36.7	odd	6		3024.2.ca.e.2033.18		48
36.11	even	6		1008.2.ca.e.353.3		48
63.47	even	6	inner	504.2.cx.a.425.18	yes	48
63.61	odd	6		1512.2.cx.a.89.18		48
84.47	odd	6		3024.2.ca.e.2609.18		48
252.47	odd	6		1008.2.df.e.929.7		48
252.187	even	6		3024.2.df.e.1601.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.22	✓	48	7.5	odd	6
504.2.bs.a.353.22	yes	48	9.2	odd	6
504.2.cx.a.185.18	yes	48	1.1	even	1	trivial
504.2.cx.a.425.18	yes	48	63.47	even	6	inner
1008.2.ca.e.257.3		48	28.19	even	6
1008.2.ca.e.353.3		48	36.11	even	6
1008.2.df.e.689.7		48	4.3	odd	2
1008.2.df.e.929.7		48	252.47	odd	6
1512.2.bs.a.521.18		48	9.7	even	3
1512.2.bs.a.1097.18		48	21.5	even	6
1512.2.cx.a.17.18		48	3.2	odd	2
1512.2.cx.a.89.18		48	63.61	odd	6
3024.2.ca.e.2033.18		48	36.7	odd	6
3024.2.ca.e.2609.18		48	84.47	odd	6
3024.2.df.e.17.18		48	12.11	even	2
3024.2.df.e.1601.18		48	252.187	even	6

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.994080 + 1.41838i) q^{3} -1.58600 q^{5} +(-1.06431 + 2.42224i) q^{7} +(-1.02361 + 2.81997i) q^{9} +O(q^{10})\)	\(q+(0.994080 + 1.41838i) q^{3} -1.58600 q^{5} +(-1.06431 + 2.42224i) q^{7} +(-1.02361 + 2.81997i) q^{9} -3.95252i q^{11} +(5.09214 + 2.93995i) q^{13} +(-1.57662 - 2.24956i) q^{15} +(-3.19652 + 5.53653i) q^{17} +(-6.37856 + 3.68267i) q^{19} +(-4.49367 + 0.898299i) q^{21} +2.43102i q^{23} -2.48459 q^{25} +(-5.01734 + 1.35141i) q^{27} +(4.34058 - 2.50604i) q^{29} +(0.855353 - 0.493838i) q^{31} +(5.60618 - 3.92912i) q^{33} +(1.68800 - 3.84168i) q^{35} +(0.183332 + 0.317540i) q^{37} +(0.892030 + 10.1451i) q^{39} +(5.58681 - 9.67664i) q^{41} +(1.26688 + 2.19430i) q^{43} +(1.62345 - 4.47248i) q^{45} +(-0.543280 + 0.940989i) q^{47} +(-4.73448 - 5.15604i) q^{49} +(-11.0305 + 0.969878i) q^{51} +(6.89030 + 3.97812i) q^{53} +6.26871i q^{55} +(-11.5642 - 5.38637i) q^{57} +(-2.73420 - 4.73577i) q^{59} +(12.4765 + 7.20330i) q^{61} +(-5.74120 - 5.48075i) q^{63} +(-8.07615 - 4.66277i) q^{65} +(5.70501 + 9.88137i) q^{67} +(-3.44811 + 2.41663i) q^{69} -9.65277i q^{71} +(7.64694 + 4.41497i) q^{73} +(-2.46988 - 3.52410i) q^{75} +(9.57394 + 4.20672i) q^{77} +(5.30654 - 9.19120i) q^{79} +(-6.90445 - 5.77309i) q^{81} +(2.96819 + 5.14105i) q^{83} +(5.06969 - 8.78096i) q^{85} +(7.86941 + 3.66540i) q^{87} +(4.70952 + 8.15712i) q^{89} +(-12.5409 + 9.20535i) q^{91} +(1.55074 + 0.722301i) q^{93} +(10.1164 - 5.84072i) q^{95} +(10.4826 - 6.05213i) q^{97} +(11.1460 + 4.04583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9}+O(q^{10}) \) 48 * q + 2 * q^9	\( 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} - 32 q^{63} - 36 q^{65} - 12 q^{77} + 6 q^{79} + 6 q^{81} - 54 q^{87} - 18 q^{89} + 6 q^{91} + 4 q^{93} - 54 q^{95} - 64 q^{99}+O(q^{100}) \) 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

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