LMFDB - Embedded newform 504.2.bu.a.41.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(41,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bu (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			41.8
Character	$\chi$	$=$	504.41
Dual form			504.2.bu.a.209.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.01807 - 1.40126i) q^{3} +(-1.60290 + 2.77631i) q^{5} +(-1.96276 - 1.77414i) q^{7} +(-0.927062 + 2.85317i) q^{9} +(4.13786 - 2.38899i) q^{11} +(0.861773 + 0.497545i) q^{13} +(5.52220 - 0.580396i) q^{15} +6.51262 q^{17} +5.38881i q^{19} +(-0.487805 + 4.55654i) q^{21} +(6.56926 + 3.79276i) q^{23} +(-2.63860 - 4.57019i) q^{25} +(4.94184 - 1.60567i) q^{27} +(-2.93665 + 1.69548i) q^{29} +(-3.51256 - 2.02798i) q^{31} +(-7.56023 - 3.36605i) q^{33} +(8.07168 - 2.60545i) q^{35} +6.29763 q^{37} +(-0.180156 - 1.71410i) q^{39} +(3.48897 - 6.04307i) q^{41} +(3.81364 + 6.60542i) q^{43} +(-6.43528 - 7.14716i) q^{45} +(-3.78098 - 6.54884i) q^{47} +(0.704849 + 6.96442i) q^{49} +(-6.63031 - 9.12588i) q^{51} +7.77397i q^{53} +15.3173i q^{55} +(7.55112 - 5.48619i) q^{57} +(2.25630 - 3.90802i) q^{59} +(-5.26324 + 3.03873i) q^{61} +(6.88152 - 3.95534i) q^{63} +(-2.76268 + 1.59503i) q^{65} +(0.493196 - 0.854240i) q^{67} +(-1.37332 - 13.0665i) q^{69} +3.20090i q^{71} +2.63782i q^{73} +(-3.71774 + 8.35014i) q^{75} +(-12.3600 - 2.65212i) q^{77} +(-7.96386 - 13.7938i) q^{79} +(-7.28111 - 5.29012i) q^{81} +(4.49071 + 7.77813i) q^{83} +(-10.4391 + 18.0811i) q^{85} +(5.36552 + 2.38890i) q^{87} +4.42081 q^{89} +(-0.808738 - 2.50547i) q^{91} +(0.734311 + 6.98663i) q^{93} +(-14.9610 - 8.63774i) q^{95} +(3.13726 - 1.81130i) q^{97} +(2.98014 + 14.0207i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9} + 8 q^{15} - 4 q^{21} + 12 q^{23} - 24 q^{25} - 36 q^{29} + 32 q^{39} + 12 q^{43} + 6 q^{49} + 24 q^{51} + 28 q^{57} - 14 q^{63} + 36 q^{65} - 60 q^{77} - 12 q^{79} - 36 q^{81} - 12 q^{91}+ \cdots + 44 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 - 4 * q^21 + 12 * q^23 - 24 * q^25 - 36 * q^29 + 32 * q^39 + 12 * q^43 + 6 * q^49 + 24 * q^51 + 28 * q^57 - 14 * q^63 + 36 * q^65 - 60 * q^77 - 12 * q^79 - 36 * q^81 - 12 * q^91 + 16 * q^93 - 108 * q^95 + 44 * q^99

Character values

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

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

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
$3$	−1.01807	−	1.40126i	−0.587784	−	0.809018i
$3$	−1.01807	−	1.40126i	−0.587784	−	0.809018i
$4$		0			0
$5$	−1.60290	+	2.77631i	−0.716840	+	1.24160i	0.245405	+	0.969421i	$0.421079\pi$
$5$	−1.60290	+	2.77631i	−0.716840	+	1.24160i	−0.962245	+	0.272183i	$0.912254\pi$
$6$		0			0
$7$	−1.96276	−	1.77414i	−0.741853	−	0.670562i
$7$	−1.96276	−	1.77414i	−0.741853	−	0.670562i
$8$		0			0
$9$	−0.927062	+	2.85317i	−0.309021	+	0.951055i
$10$		0			0
$11$	4.13786	−	2.38899i	1.24761	−	0.720308i	0.276978	−	0.960876i	$-0.410667\pi$
$11$	4.13786	−	2.38899i	1.24761	−	0.720308i	0.970632	+	0.240568i	$0.0773337\pi$
$12$		0			0
$13$	0.861773	+	0.497545i	0.239013	+	0.137994i	0.614723	−	0.788743i	$-0.289268\pi$
$13$	0.861773	+	0.497545i	0.239013	+	0.137994i	−0.375710	+	0.926737i	$0.622601\pi$
$14$		0			0
$15$	5.52220	−	0.580396i	1.42583	−	0.149858i
$16$		0			0
$17$	6.51262			1.57954			0.789771	−	0.613401i	$-0.210199\pi$
$17$	6.51262			1.57954			0.789771	+	0.613401i	$0.210199\pi$
$18$		0			0
$19$			5.38881i			1.23628i	0.786069	+	0.618138i	$0.212113\pi$
$19$			5.38881i			1.23628i	−0.786069	+	0.618138i	$0.787887\pi$
$20$		0			0
$21$	−0.487805	+	4.55654i	−0.106448	+	0.994318i
$22$		0			0
$23$	6.56926	+	3.79276i	1.36978	+	0.790846i	0.990900	−	0.134598i	$-0.0429745\pi$
$23$	6.56926	+	3.79276i	1.36978	+	0.790846i	0.378884	+	0.925444i	$0.376308\pi$
$24$		0			0
$25$	−2.63860	−	4.57019i	−0.527720	−	0.914038i
$26$		0			0
$27$	4.94184	−	1.60567i	0.951058	−	0.309011i
$28$		0			0
$29$	−2.93665	+	1.69548i	−0.545322	+	0.314842i	−0.747233	−	0.664562i	$-0.768618\pi$
$29$	−2.93665	+	1.69548i	−0.545322	+	0.314842i	0.201911	+	0.979404i	$0.435285\pi$
$30$		0			0
$31$	−3.51256	−	2.02798i	−0.630874	−	0.364235i	0.150217	−	0.988653i	$-0.452003\pi$
$31$	−3.51256	−	2.02798i	−0.630874	−	0.364235i	−0.781090	+	0.624418i	$0.785336\pi$
$32$		0			0
$33$	−7.56023	−	3.36605i	−1.31607	−	0.585954i
$34$		0			0
$35$	8.07168	−	2.60545i	1.36436	−	0.440402i
$36$		0			0
$37$	6.29763			1.03532			0.517662	−	0.855585i	$-0.326802\pi$
$37$	6.29763			1.03532			0.517662	+	0.855585i	$0.326802\pi$
$38$		0			0
$39$	−0.180156	−	1.71410i	−0.0288481	−	0.274476i
$40$		0			0
$41$	3.48897	−	6.04307i	0.544885	−	0.943769i	−0.453729	−	0.891140i	$-0.649906\pi$
$41$	3.48897	−	6.04307i	0.544885	−	0.943769i	0.998614	−	0.0526294i	$-0.0167602\pi$
$42$		0			0
$43$	3.81364	+	6.60542i	0.581575	+	1.00732i	0.995293	+	0.0969121i	$0.0308966\pi$
$43$	3.81364	+	6.60542i	0.581575	+	1.00732i	−0.413718	+	0.910405i	$0.635770\pi$
$44$		0			0
$45$	−6.43528	−	7.14716i	−0.959315	−	1.06544i
$46$		0			0
$47$	−3.78098	−	6.54884i	−0.551512	−	0.955247i	−0.998166	−	0.0605399i	$-0.980718\pi$
$47$	−3.78098	−	6.54884i	−0.551512	−	0.955247i	0.446654	−	0.894707i	$-0.352616\pi$
$48$		0			0
$49$	0.704849	+	6.96442i	0.100693	+	0.994918i
$50$		0			0
$51$	−6.63031	−	9.12588i	−0.928430	−	1.27788i
$52$		0			0
$53$			7.77397i			1.06784i	0.845536	+	0.533919i	$0.179281\pi$
$53$			7.77397i			1.06784i	−0.845536	+	0.533919i	$0.820719\pi$
$54$		0			0
$55$			15.3173i			2.06538i
$56$		0			0
$57$	7.55112	−	5.48619i	1.00017	−	0.726663i
$58$		0			0
$59$	2.25630	−	3.90802i	0.293745	−	0.508781i	−0.680947	−	0.732333i	$-0.738432\pi$
$59$	2.25630	−	3.90802i	0.293745	−	0.508781i	0.974692	+	0.223551i	$0.0717650\pi$
$60$		0			0
$61$	−5.26324	+	3.03873i	−0.673889	+	0.389070i	−0.797548	−	0.603255i	$-0.793870\pi$
$61$	−5.26324	+	3.03873i	−0.673889	+	0.389070i	0.123660	+	0.992325i	$0.460537\pi$
$62$		0			0
$63$	6.88152	−	3.95534i	0.866990	−	0.498326i
$64$		0			0
$65$	−2.76268	+	1.59503i	−0.342668	+	0.197839i
$66$		0			0
$67$	0.493196	−	0.854240i	0.0602534	−	0.104362i	−0.834325	−	0.551273i	$-0.814142\pi$
$67$	0.493196	−	0.854240i	0.0602534	−	0.104362i	0.894579	+	0.446911i	$0.147476\pi$
$68$		0			0
$69$	−1.37332	−	13.0665i	−0.165329	−	1.57303i
$70$		0			0
$71$			3.20090i			0.379877i	0.981796	+	0.189939i	$0.0608289\pi$
$71$			3.20090i			0.379877i	−0.981796	+	0.189939i	$0.939171\pi$
$72$		0			0
$73$			2.63782i			0.308733i	0.988014	+	0.154367i	$0.0493337\pi$
$73$			2.63782i			0.308733i	−0.988014	+	0.154367i	$0.950666\pi$
$74$		0			0
$75$	−3.71774	+	8.35014i	−0.429288	+	0.964192i
$76$		0			0
$77$	−12.3600	−	2.65212i	−1.40856	−	0.302237i
$78$		0			0
$79$	−7.96386	−	13.7938i	−0.896005	−	1.55193i	−0.832556	−	0.553941i	$-0.813123\pi$
$79$	−7.96386	−	13.7938i	−0.896005	−	1.55193i	−0.0634485	−	0.997985i	$-0.520210\pi$
$80$		0			0
$81$	−7.28111	−	5.29012i	−0.809012	−	0.587792i
$82$		0			0
$83$	4.49071	+	7.77813i	0.492919	+	0.853761i	0.999967	−	0.00815719i	$-0.00259654\pi$
$83$	4.49071	+	7.77813i	0.492919	+	0.853761i	−0.507048	+	0.861918i	$0.669263\pi$
$84$		0			0
$85$	−10.4391	+	18.0811i	−1.13228	+	1.96117i
$86$		0			0
$87$	5.36552	+	2.38890i	0.575244	+	0.256117i
$88$		0			0
$89$	4.42081			0.468605			0.234303	−	0.972164i	$-0.424719\pi$
$89$	4.42081			0.468605			0.234303	+	0.972164i	$0.424719\pi$
$90$		0			0
$91$	−0.808738	−	2.50547i	−0.0847788	−	0.262644i
$92$		0			0
$93$	0.734311	+	6.98663i	0.0761445	+	0.724480i
$94$		0			0
$95$	−14.9610	−	8.63774i	−1.53497	−	0.886213i
$96$		0			0
$97$	3.13726	−	1.81130i	0.318540	−	0.183909i	−0.332202	−	0.943208i	$-0.607791\pi$
$97$	3.13726	−	1.81130i	0.318540	−	0.183909i	0.650742	+	0.759299i	$0.274458\pi$
$98$		0			0
$99$	2.98014	+	14.0207i	0.299516	+	1.40914i
$100$		0			0
$101$	7.31084	+	12.6627i	0.727456	+	1.25999i	0.957955	+	0.286918i	$0.0926306\pi$
$101$	7.31084	+	12.6627i	0.727456	+	1.25999i	−0.230500	+	0.973072i	$0.574036\pi$
$102$		0			0
$103$	0.883186	+	0.509908i	0.0870229	+	0.0502427i	0.542880	−	0.839810i	$-0.317334\pi$
$103$	0.883186	+	0.509908i	0.0870229	+	0.0502427i	−0.455857	+	0.890053i	$0.650667\pi$
$104$		0			0
$105$	−11.8685	−	8.65799i	−1.15824	−	0.844933i
$106$		0			0
$107$			11.0089i			1.06428i	0.846658	+	0.532138i	$0.178611\pi$
$107$			11.0089i			1.06428i	−0.846658	+	0.532138i	$0.821389\pi$
$108$		0			0
$109$	−7.38735			−0.707579			−0.353790	−	0.935325i	$-0.615107\pi$
$109$	−7.38735			−0.707579			−0.353790	+	0.935325i	$0.615107\pi$
$110$		0			0
$111$	−6.41144	−	8.82462i	−0.608547	−	0.837596i
$112$		0			0
$113$	5.31062	+	3.06609i	0.499581	+	0.288433i	0.728541	−	0.685003i	$-0.240199\pi$
$113$	5.31062	+	3.06609i	0.499581	+	0.288433i	−0.228959	+	0.973436i	$0.573532\pi$
$114$		0			0
$115$	−21.0598	+	12.1589i	−1.96383	+	1.13382i
$116$		0			0
$117$	−2.21850	+	1.99753i	−0.205100	+	0.184671i
$118$		0			0
$119$	−12.7827	−	11.5543i	−1.17179	−	1.05918i
$120$		0			0
$121$	5.91457	−	10.2443i	0.537688	−	0.931303i
$122$		0			0
$123$	−12.0199	+	1.26332i	−1.08380	+	0.113910i
$124$		0			0
$125$	0.888649			0.0794832
$126$		0			0
$127$	9.47289			0.840583			0.420291	−	0.907389i	$-0.361928\pi$
$127$	9.47289			0.840583			0.420291	+	0.907389i	$0.361928\pi$
$128$		0			0
$129$	5.37336	−	12.0687i	0.473098	−	1.06259i
$130$		0			0
$131$	7.59921	−	13.1622i	0.663946	−	1.14999i	−0.315624	−	0.948884i	$-0.602214\pi$
$131$	7.59921	−	13.1622i	0.663946	−	1.14999i	0.979570	−	0.201104i	$-0.0644528\pi$
$132$		0			0
$133$	9.56050	−	10.5769i	0.829000	−	0.917136i
$134$		0			0
$135$	−3.46346	+	16.2938i	−0.298087	+	1.40235i
$136$		0			0
$137$	−2.42115	+	1.39785i	−0.206853	+	0.119427i	−0.599848	−	0.800114i	$-0.704772\pi$
$137$	−2.42115	+	1.39785i	−0.206853	+	0.119427i	0.392995	+	0.919541i	$0.371439\pi$
$138$		0			0
$139$	−8.55582	−	4.93971i	−0.725695	−	0.418980i	0.0911499	−	0.995837i	$-0.470946\pi$
$139$	−8.55582	−	4.93971i	−0.725695	−	0.418980i	−0.816845	+	0.576857i	$0.804279\pi$
$140$		0			0
$141$	−5.32733	+	11.9653i	−0.448642	+	1.00766i
$142$		0			0
$143$	4.75452			0.397593
$144$		0			0
$145$		−	10.8707i		−	0.902766i
$146$		0			0
$147$	9.04138	−	8.07796i	0.745721	−	0.666259i
$148$		0			0
$149$	20.5582	+	11.8693i	1.68419	+	0.972369i	0.958820	+	0.284013i	$0.0916658\pi$
$149$	20.5582	+	11.8693i	1.68419	+	0.972369i	0.725373	+	0.688356i	$0.241667\pi$
$150$		0			0
$151$	−6.52875	−	11.3081i	−0.531302	−	0.920242i	−0.999333	−	0.0365301i	$-0.988370\pi$
$151$	−6.52875	−	11.3081i	−0.531302	−	0.920242i	0.468030	−	0.883712i	$-0.344964\pi$
$152$		0			0
$153$	−6.03761	+	18.5816i	−0.488111	+	1.50223i
$154$		0			0
$155$	11.2606	−	6.50130i	0.904471	−	0.522197i
$156$		0			0
$157$	−0.268291	−	0.154898i	−0.0214120	−	0.0123622i	0.489256	−	0.872140i	$-0.337268\pi$
$157$	−0.268291	−	0.154898i	−0.0214120	−	0.0123622i	−0.510668	+	0.859778i	$0.670602\pi$
$158$		0			0
$159$	10.8934	−	7.91446i	0.863900	−	0.627657i
$160$		0			0
$161$	−6.16498	−	19.0991i	−0.485868	−	1.50522i
$162$		0			0
$163$	−10.5524			−0.826525			−0.413262	−	0.910612i	$-0.635611\pi$
$163$	−10.5524			−0.826525			−0.413262	+	0.910612i	$0.635611\pi$
$164$		0			0
$165$	21.4635	−	15.5941i	1.67093	−	1.21400i
$166$		0			0
$167$	3.95655	−	6.85294i	0.306167	−	0.530296i	−0.671354	−	0.741137i	$-0.734287\pi$
$167$	3.95655	−	6.85294i	0.306167	−	0.530296i	0.977520	+	0.210841i	$0.0676201\pi$
$168$		0			0
$169$	−6.00490	−	10.4008i	−0.461915	−	0.800061i
$170$		0			0
$171$	−15.3752	−	4.99576i	−1.17577	−	0.382035i
$172$		0			0
$173$	−0.931870	−	1.61405i	−0.0708487	−	0.122714i	0.828425	−	0.560100i	$-0.189237\pi$
$173$	−0.931870	−	1.61405i	−0.0708487	−	0.122714i	−0.899274	+	0.437387i	$0.855904\pi$
$174$		0			0
$175$	−2.92922	+	13.6514i	−0.221428	+	1.03195i
$176$		0			0
$177$	−7.77323	+	0.816984i	−0.584272	+	0.0614083i
$178$		0			0
$179$		−	5.50222i		−	0.411255i	−0.978630	−	0.205628i	$-0.934076\pi$
$179$		−	5.50222i		−	0.411255i	0.978630	−	0.205628i	$-0.0659236\pi$
$180$		0			0
$181$		−	11.1382i		−	0.827900i	−0.910300	−	0.413950i	$-0.864149\pi$
$181$		−	11.1382i		−	0.827900i	0.910300	−	0.413950i	$-0.135851\pi$
$182$		0			0
$183$	9.61641	+	4.28152i	0.710865	+	0.316499i
$184$		0			0
$185$	−10.0945	+	17.4842i	−0.742162	+	1.28546i
$186$		0			0
$187$	26.9483	−	15.5586i	1.97065	−	1.13776i
$188$		0			0
$189$	−12.5483	−	5.61598i	−0.912757	−	0.408503i
$190$		0			0
$191$	−3.64535	+	2.10464i	−0.263768	+	0.152287i	−0.626052	−	0.779781i	$-0.715330\pi$
$191$	−3.64535	+	2.10464i	−0.263768	+	0.152287i	0.362284	+	0.932068i	$0.381997\pi$
$192$		0			0
$193$	1.43109	−	2.47872i	0.103012	−	0.178422i	−0.809912	−	0.586551i	$-0.800485\pi$
$193$	1.43109	−	2.47872i	0.103012	−	0.178422i	0.912924	+	0.408129i	$0.133819\pi$
$194$		0			0
$195$	5.04766	+	2.24737i	0.361470	+	0.160938i
$196$		0			0
$197$		−	1.46947i		−	0.104695i	−0.998629	−	0.0523475i	$-0.983330\pi$
$197$		−	1.46947i		−	0.104695i	0.998629	−	0.0523475i	$-0.0166704\pi$
$198$		0			0
$199$			16.3790i			1.16108i	0.814232	+	0.580539i	$0.197158\pi$
$199$			16.3790i			1.16108i	−0.814232	+	0.580539i	$0.802842\pi$
$200$		0			0
$201$	−1.69912	+	0.178581i	−0.119847	+	0.0125962i
$202$		0			0
$203$	8.77195	+	1.88222i	0.615670	+	0.132106i
$204$		0			0
$205$	11.1850	+	19.3729i	0.781192	+	1.35306i
$206$		0			0
$207$	−16.9115	+	15.2271i	−1.17543	+	1.05835i
$208$		0			0
$209$	12.8738	+	22.2981i	0.890500	+	1.54239i
$210$		0			0
$211$	−5.18297	+	8.97716i	−0.356810	+	0.618013i	−0.987426	−	0.158082i	$-0.949469\pi$
$211$	−5.18297	+	8.97716i	−0.356810	+	0.618013i	0.630616	+	0.776095i	$0.282802\pi$
$212$		0			0
$213$	4.48530	−	3.25875i	0.307328	−	0.223286i
$214$		0			0
$215$	−24.4516			−1.66759
$216$		0			0
$217$	3.29639	+	10.2122i	0.223773	+	0.693249i
$218$		0			0
$219$	3.69627	−	2.68549i	0.249771	−	0.181468i
$220$		0			0
$221$	5.61240	+	3.24032i	0.377531	+	0.217968i
$222$		0			0
$223$	−4.87592	+	2.81511i	−0.326516	+	0.188514i	−0.654293	−	0.756241i	$-0.727034\pi$
$223$	−4.87592	+	2.81511i	−0.326516	+	0.188514i	0.327777	+	0.944755i	$0.393700\pi$
$224$		0			0
$225$	15.4857	−	3.29151i	1.03238	−	0.219434i
$226$		0			0
$227$	3.52714	+	6.10919i	0.234105	+	0.405481i	0.959012	−	0.283365i	$-0.0914509\pi$
$227$	3.52714	+	6.10919i	0.234105	+	0.405481i	−0.724908	+	0.688846i	$0.758118\pi$
$228$		0			0
$229$	18.5744	+	10.7239i	1.22743	+	0.708657i	0.966492	−	0.256698i	$-0.0826346\pi$
$229$	18.5744	+	10.7239i	1.22743	+	0.708657i	0.260939	+	0.965355i	$0.415968\pi$
$230$		0			0
$231$	8.86707	+	20.0197i	0.583410	+	1.31720i
$232$		0			0
$233$		−	11.6101i		−	0.760601i	−0.924863	−	0.380300i	$-0.875821\pi$
$233$		−	11.6101i		−	0.760601i	0.924863	−	0.380300i	$-0.124179\pi$
$234$		0			0
$235$	24.2422			1.58138
$236$		0			0
$237$	−11.2210	+	25.2025i	−0.728879	+	1.63708i
$238$		0			0
$239$	5.85573	+	3.38081i	0.378776	+	0.218686i	0.677285	−	0.735720i	$-0.263156\pi$
$239$	5.85573	+	3.38081i	0.378776	+	0.218686i	−0.298510	+	0.954407i	$0.596490\pi$
$240$		0			0
$241$	2.60243	−	1.50251i	0.167637	−	0.0967854i	−0.413834	−	0.910352i	$-0.635811\pi$
$241$	2.60243	−	1.50251i	0.167637	−	0.0967854i	0.581471	+	0.813567i	$0.302477\pi$
$242$		0			0
$243$	−0.000152282		15.5885i	−9.76892e−6		1.00000i
$244$		0			0
$245$	−20.4652	−	9.20642i	−1.30747	−	0.588177i
$246$		0			0
$247$	−2.68117	+	4.64393i	−0.170599	+	0.295486i
$248$		0			0
$249$	6.32733	−	14.2113i	0.400978	−	0.900607i
$250$		0			0
$251$	−27.9921			−1.76685			−0.883424	−	0.468575i	$-0.844768\pi$
$251$	−27.9921			−1.76685			−0.883424	+	0.468575i	$0.844768\pi$
$252$		0			0
$253$	36.2435			2.27861
$254$		0			0
$255$	35.9640	−	3.77990i	2.25216	−	0.236707i
$256$		0			0
$257$	1.17693	−	2.03850i	0.0734147	−	0.127158i	−0.826981	−	0.562230i	$-0.809944\pi$
$257$	1.17693	−	2.03850i	0.0734147	−	0.127158i	0.900396	+	0.435072i	$0.143277\pi$
$258$		0			0
$259$	−12.3607	−	11.1729i	−0.768059	−	0.694249i
$260$		0			0
$261$	−2.11502	−	9.95056i	−0.130916	−	0.615924i
$262$		0			0
$263$	11.6768	−	6.74159i	0.720021	−	0.415704i	−0.0947394	−	0.995502i	$-0.530202\pi$
$263$	11.6768	−	6.74159i	0.720021	−	0.415704i	0.814760	+	0.579798i	$0.196868\pi$
$264$		0			0
$265$	−21.5830	−	12.4609i	−1.32583	−	0.765469i
$266$		0			0
$267$	−4.50070	−	6.19471i	−0.275438	−	0.379110i
$268$		0			0
$269$	11.0797			0.675543			0.337772	−	0.941228i	$-0.390327\pi$
$269$	11.0797			0.675543			0.337772	+	0.941228i	$0.390327\pi$
$270$		0			0
$271$			4.31052i			0.261845i	0.991393	+	0.130923i	$0.0417940\pi$
$271$			4.31052i			0.261845i	−0.991393	+	0.130923i	$0.958206\pi$
$272$		0			0
$273$	−2.68746	+	3.68400i	−0.162652	+	0.222966i
$274$		0			0
$275$	−21.8363	−	12.6072i	−1.31678	−	0.760242i
$276$		0			0
$277$	−4.20911	−	7.29039i	−0.252901	−	0.438037i	0.711422	−	0.702765i	$-0.248051\pi$
$277$	−4.20911	−	7.29039i	−0.252901	−	0.438037i	−0.964323	+	0.264728i	$0.914718\pi$
$278$		0			0
$279$	9.04251	−	8.14185i	0.541361	−	0.487440i
$280$		0			0
$281$	−16.1633	+	9.33189i	−0.964222	+	0.556694i	−0.897470	−	0.441076i	$-0.854597\pi$
$281$	−16.1633	+	9.33189i	−0.964222	+	0.556694i	−0.0667521	+	0.997770i	$0.521264\pi$
$282$		0			0
$283$	−23.7038	−	13.6854i	−1.40904	−	0.813512i	−0.413748	−	0.910392i	$-0.635780\pi$
$283$	−23.7038	−	13.6854i	−1.40904	−	0.813512i	−0.995296	+	0.0968797i	$0.969114\pi$
$284$		0			0
$285$	3.12764	+	29.7581i	0.185266	+	1.76272i
$286$		0			0
$287$	−17.5693	+	5.67117i	−1.03708	+	0.334759i
$288$		0			0
$289$	25.4143			1.49496
$290$		0			0
$291$	−5.73205	−	2.55209i	−0.336019	−	0.149606i
$292$		0			0
$293$	4.66210	−	8.07500i	0.272363	−	0.471747i	−0.697103	−	0.716971i	$-0.745528\pi$
$293$	4.66210	−	8.07500i	0.272363	−	0.471747i	0.969466	+	0.245224i	$0.0788615\pi$
$294$		0			0
$295$	7.23326	+	12.5284i	0.421136	+	0.729430i
$296$		0			0
$297$	16.6127	−	18.4501i	0.963967	−	1.07058i
$298$		0			0
$299$	3.77414	+	6.53700i	0.218264	+	0.378044i
$300$		0			0
$301$	4.23369	−	19.7308i	0.244026	−	1.13726i
$302$		0			0
$303$	10.3008	−	23.1360i	0.591768	−	1.32913i
$304$		0			0
$305$		−	19.4832i		−	1.11560i
$306$		0			0
$307$		−	33.6506i		−	1.92054i	−0.279069	−	0.960271i	$-0.590026\pi$
$307$		−	33.6506i		−	1.92054i	0.279069	−	0.960271i	$-0.409974\pi$
$308$		0			0
$309$	−0.184633	−	1.75670i	−0.0105034	−	0.0999350i
$310$		0			0
$311$	−7.69514	+	13.3284i	−0.436351	+	0.755783i	−0.997405	−	0.0719967i	$-0.977063\pi$
$311$	−7.69514	+	13.3284i	−0.436351	+	0.755783i	0.561053	+	0.827780i	$0.310396\pi$
$312$		0			0
$313$	27.6028	−	15.9365i	1.56020	−	0.900784i	0.562968	−	0.826479i	$-0.309659\pi$
$313$	27.6028	−	15.9365i	1.56020	−	0.900784i	0.997236	−	0.0743050i	$-0.0236738\pi$
$314$		0			0
$315$	−0.0491599	+	25.4453i	−0.00276985	+	1.43368i
$316$		0			0
$317$	17.3039	−	9.99044i	0.971886	−	0.561119i	0.0720756	−	0.997399i	$-0.477038\pi$
$317$	17.3039	−	9.99044i	0.971886	−	0.561119i	0.899811	+	0.436280i	$0.143704\pi$
$318$		0			0
$319$	−8.10096	+	14.0313i	−0.453567	+	0.785600i
$320$		0			0
$321$	15.4264	−	11.2079i	0.861018	−	0.625564i
$322$		0			0
$323$			35.0953i			1.95275i
$324$		0			0
$325$		−	5.25129i		−	0.291289i
$326$		0			0
$327$	7.52084	+	10.3516i	0.415904	+	0.572445i
$328$		0			0
$329$	−4.19742	+	19.5618i	−0.231411	+	1.07848i
$330$		0			0
$331$	4.48225	+	7.76348i	0.246367	+	0.426719i	0.962515	−	0.271229i	$-0.0874300\pi$
$331$	4.48225	+	7.76348i	0.246367	+	0.426719i	−0.716148	+	0.697948i	$0.754097\pi$
$332$		0			0
$333$	−5.83830	+	17.9682i	−0.319937	+	0.984651i
$334$		0			0
$335$	1.58109	+	2.73853i	0.0863842	+	0.149622i
$336$		0			0
$337$	−2.72022	+	4.71155i	−0.148180	+	0.256655i	−0.930555	−	0.366153i	$-0.880675\pi$
$337$	−2.72022	+	4.71155i	−0.148180	+	0.256655i	0.782375	+	0.622808i	$0.214008\pi$
$338$		0			0
$339$	−1.11020	−	10.5631i	−0.0602978	−	0.573706i
$340$		0			0
$341$	−19.3793			−1.04945
$342$		0			0
$343$	10.9724	−	14.9200i	0.592455	−	0.805604i
$344$		0			0
$345$	38.4781	+	17.1316i	2.07159	+	0.922336i
$346$		0			0
$347$	−14.0234	−	8.09639i	−0.752813	−	0.434637i	0.0738962	−	0.997266i	$-0.476457\pi$
$347$	−14.0234	−	8.09639i	−0.752813	−	0.434637i	−0.826710	+	0.562629i	$0.809790\pi$
$348$		0			0
$349$	−17.1071	+	9.87682i	−0.915725	+	0.528694i	−0.882269	−	0.470746i	$-0.843985\pi$
$349$	−17.1071	+	9.87682i	−0.915725	+	0.528694i	−0.0334560	+	0.999440i	$0.510651\pi$
$350$		0			0
$351$	5.05764	+	1.07507i	0.269957	+	0.0573828i
$352$		0			0
$353$	−10.3112	−	17.8596i	−0.548811	−	0.950569i	−0.998356	−	0.0573115i	$-0.981747\pi$
$353$	−10.3112	−	17.8596i	−0.548811	−	0.950569i	0.449545	−	0.893258i	$-0.351586\pi$
$354$		0			0
$355$	−8.88670	−	5.13074i	−0.471657	−	0.272311i
$356$		0			0
$357$	−3.17689	+	29.6750i	−0.168139	+	1.57057i
$358$		0			0
$359$		−	15.2442i		−	0.804557i	−0.915517	−	0.402278i	$-0.868218\pi$
$359$		−	15.2442i		−	0.804557i	0.915517	−	0.402278i	$-0.131782\pi$
$360$		0			0
$361$	−10.0392			−0.528380
$362$		0			0
$363$	−20.3764	+	2.14161i	−1.06949	+	0.112405i
$364$		0			0
$365$	−7.32340	−	4.22817i	−0.383324	−	0.221312i
$366$		0			0
$367$	2.87711	−	1.66110i	0.150184	−	0.0867087i	−0.423025	−	0.906118i	$-0.639032\pi$
$367$	2.87711	−	1.66110i	0.150184	−	0.0867087i	0.573209	+	0.819409i	$0.305698\pi$
$368$		0			0
$369$	14.0074	+	15.5569i	0.729196	+	0.809860i
$370$		0			0
$371$	13.7921	−	15.2584i	0.716051	−	0.792178i
$372$		0			0
$373$	−11.6885	+	20.2451i	−0.605208	+	1.04825i	0.386811	+	0.922159i	$0.373577\pi$
$373$	−11.6885	+	20.2451i	−0.605208	+	1.04825i	−0.992019	+	0.126092i	$0.959757\pi$
$374$		0			0
$375$	−0.904708	−	1.24523i	−0.0467189	−	0.0643033i
$376$		0			0
$377$	−3.37430			−0.173785
$378$		0			0
$379$	13.9325			0.715663			0.357832	−	0.933786i	$-0.383516\pi$
$379$	13.9325			0.715663			0.357832	+	0.933786i	$0.383516\pi$
$380$		0			0
$381$	−9.64407	−	13.2740i	−0.494081	−	0.680047i
$382$		0			0
$383$	−3.93132	+	6.80925i	−0.200881	+	0.347936i	−0.948813	−	0.315840i	$-0.897714\pi$
$383$	−3.93132	+	6.80925i	−0.200881	+	0.347936i	0.747931	+	0.663776i	$0.231047\pi$
$384$		0			0
$385$	27.1750	−	30.0642i	1.38497	−	1.53221i
$386$		0			0
$387$	−22.3818	+	4.75732i	−1.13773	+	0.241828i
$388$		0			0
$389$	−16.5208	+	9.53829i	−0.837638	+	0.483611i	−0.856461	−	0.516212i	$-0.827342\pi$
$389$	−16.5208	+	9.53829i	−0.837638	+	0.483611i	0.0188226	+	0.999823i	$0.494008\pi$
$390$		0			0
$391$	42.7831	+	24.7008i	2.16363	+	1.24917i
$392$		0			0
$393$	−26.1802	+	2.75160i	−1.32062	+	0.138800i
$394$		0			0
$395$	51.0612			2.56917
$396$		0			0
$397$		−	13.8919i		−	0.697214i	−0.937269	−	0.348607i	$-0.886655\pi$
$397$		−	13.8919i		−	0.697214i	0.937269	−	0.348607i	$-0.113345\pi$
$398$		0			0
$399$	−24.5543	−	2.62868i	−1.22925	−	0.131599i
$400$		0			0
$401$	−20.6674	−	11.9323i	−1.03208	−	0.595872i	−0.114501	−	0.993423i	$-0.536527\pi$
$401$	−20.6674	−	11.9323i	−1.03208	−	0.595872i	−0.917580	+	0.397551i	$0.869860\pi$
$402$		0			0
$403$	−2.01802	−	3.49531i	−0.100525	−	0.174114i
$404$		0			0
$405$	26.3579	−	11.7351i	1.30974	−	0.583120i
$406$		0			0
$407$	26.0587	−	15.0450i	1.29168	−	0.745753i
$408$		0			0
$409$	−20.9384	−	12.0888i	−1.03534	−	0.597753i	−0.116830	−	0.993152i	$-0.537273\pi$
$409$	−20.9384	−	12.0888i	−1.03534	−	0.597753i	−0.918510	+	0.395399i	$0.870606\pi$
$410$		0			0
$411$	4.42366	+	1.96955i	0.218203	+	0.0971507i
$412$		0			0
$413$	−11.3620	+	3.66752i	−0.559085	+	0.180467i
$414$		0			0
$415$	−28.7927			−1.41338
$416$		0			0
$417$	1.78862	+	17.0179i	0.0875891	+	0.833371i
$418$		0			0
$419$	−9.84384	+	17.0500i	−0.480903	+	0.832949i	−0.999760	−	0.0219125i	$-0.993024\pi$
$419$	−9.84384	+	17.0500i	−0.480903	+	0.832949i	0.518857	+	0.854861i	$0.326358\pi$
$420$		0			0
$421$	−18.5884	−	32.1961i	−0.905944	−	1.56914i	−0.819646	−	0.572871i	$-0.805830\pi$
$421$	−18.5884	−	32.1961i	−0.905944	−	1.56914i	−0.0862979	−	0.996269i	$-0.527504\pi$
$422$		0			0
$423$	22.1901	−	4.71657i	1.07892	−	0.229327i
$424$		0			0
$425$	−17.1842	−	29.7639i	−0.833556	−	1.44376i
$426$		0			0
$427$	15.7216	+	3.37343i	0.760822	+	0.163252i
$428$		0			0
$429$	−4.84044	−	6.66233i	−0.233699	−	0.321660i
$430$		0			0
$431$			8.86241i			0.426887i	0.976955	+	0.213444i	$0.0684680\pi$
$431$			8.86241i			0.426887i	−0.976955	+	0.213444i	$0.931532\pi$
$432$		0			0
$433$			35.2461i			1.69382i	0.531737	+	0.846910i	$0.321540\pi$
$433$			35.2461i			1.69382i	−0.531737	+	0.846910i	$0.678460\pi$
$434$		0			0
$435$	−15.2327	+	11.0672i	−0.730354	+	0.530631i
$436$		0			0
$437$	−20.4385	+	35.4004i	−0.977704	+	1.69343i
$438$		0			0
$439$	−7.51356	+	4.33796i	−0.358603	+	0.207039i	−0.668468	−	0.743741i	$-0.733049\pi$
$439$	−7.51356	+	4.33796i	−0.358603	+	0.207039i	0.309865	+	0.950781i	$0.399716\pi$
$440$		0			0
$441$	−20.5241	−	4.44540i	−0.977338	−	0.211686i
$442$		0			0
$443$	−13.7031	+	7.91148i	−0.651053	+	0.375886i	−0.788860	−	0.614574i	$-0.789328\pi$
$443$	−13.7031	+	7.91148i	−0.651053	+	0.375886i	0.137807	+	0.990459i	$0.455995\pi$
$444$		0			0
$445$	−7.08613	+	12.2735i	−0.335915	+	0.581822i
$446$		0			0
$447$	−4.29775	−	40.8912i	−0.203277	−	1.93409i
$448$		0			0
$449$		−	7.87563i		−	0.371674i	−0.982581	−	0.185837i	$-0.940500\pi$
$449$		−	7.87563i		−	0.371674i	0.982581	−	0.185837i	$-0.0594996\pi$
$450$		0			0
$451$		−	33.3405i		−	1.56994i
$452$		0			0
$453$	−9.19890	+	20.6610i	−0.432202	+	0.970737i
$454$		0			0
$455$	8.25229	+	1.77071i	0.386873	+	0.0830124i
$456$		0			0
$457$	5.53132	+	9.58053i	0.258744	+	0.448158i	0.965906	−	0.258894i	$-0.0833580\pi$
$457$	5.53132	+	9.58053i	0.258744	+	0.448158i	−0.707161	+	0.707052i	$0.750025\pi$
$458$		0			0
$459$	32.1844	−	10.4571i	1.50224	−	0.488097i
$460$		0			0
$461$	−6.73005	−	11.6568i	−0.313450	−	0.542911i	0.665657	−	0.746258i	$-0.268151\pi$
$461$	−6.73005	−	11.6568i	−0.313450	−	0.542911i	−0.979107	+	0.203347i	$0.934818\pi$
$462$		0			0
$463$	8.57103	−	14.8455i	0.398329	−	0.689927i	−0.595191	−	0.803585i	$-0.702923\pi$
$463$	8.57103	−	14.8455i	0.398329	−	0.689927i	0.993520	+	0.113658i	$0.0362568\pi$
$464$		0			0
$465$	−20.5741	−	9.16022i	−0.954100	−	0.424795i
$466$		0			0
$467$	−5.67554			−0.262633			−0.131316	−	0.991341i	$-0.541920\pi$
$467$	−5.67554			−0.262633			−0.131316	+	0.991341i	$0.541920\pi$
$468$		0			0
$469$	−2.48357	+	0.801669i	−0.114680	+	0.0370176i
$470$		0			0
$471$	0.0560871	+	0.533643i	0.00258436	+	0.0245890i
$472$		0			0
$473$	31.5606	+	18.2215i	1.45116	+	0.837826i
$474$		0			0
$475$	24.6279	−	14.2189i	1.13000	−	0.652408i
$476$		0			0
$477$	−22.1804	−	7.20695i	−1.01557	−	0.329984i
$478$		0			0
$479$	6.71476	+	11.6303i	0.306805	+	0.531402i	0.977662	−	0.210185i	$-0.0674066\pi$
$479$	6.71476	+	11.6303i	0.306805	+	0.531402i	−0.670856	+	0.741587i	$0.734073\pi$
$480$		0			0
$481$	5.42713	+	3.13335i	0.247456	+	0.142869i
$482$		0			0
$483$	−20.4864	+	28.0829i	−0.932163	+	1.27782i
$484$		0			0
$485$			11.6133i			0.527334i
$486$		0			0
$487$	−11.4841			−0.520394			−0.260197	−	0.965556i	$-0.583788\pi$
$487$	−11.4841			−0.520394			−0.260197	+	0.965556i	$0.583788\pi$
$488$		0			0
$489$	10.7431	+	14.7866i	0.485818	+	0.668673i
$490$		0			0
$491$	−9.04656	−	5.22303i	−0.408265	−	0.235712i	0.281779	−	0.959479i	$-0.409076\pi$
$491$	−9.04656	−	5.22303i	−0.408265	−	0.235712i	−0.690044	+	0.723767i	$0.742409\pi$
$492$		0			0
$493$	−19.1253	+	11.0420i	−0.861360	+	0.497306i
$494$		0			0
$495$	−43.7028	−	14.2001i	−1.96429	−	0.638246i
$496$		0			0
$497$	5.67885	−	6.28260i	0.254731	−	0.281813i
$498$		0			0
$499$	8.43609	−	14.6117i	0.377651	−	0.654111i	−0.613069	−	0.790030i	$-0.710065\pi$
$499$	8.43609	−	14.6117i	0.377651	−	0.654111i	0.990720	+	0.135918i	$0.0433985\pi$
$500$		0			0
$501$	−13.6308	+	1.43263i	−0.608979	+	0.0640051i
$502$		0			0
$503$	−21.1129			−0.941379			−0.470690	−	0.882299i	$-0.655995\pi$
$503$	−21.1129			−0.941379			−0.470690	+	0.882299i	$0.655995\pi$
$504$		0			0
$505$	−46.8743			−2.08588
$506$		0			0
$507$	−8.46080	+	19.0032i	−0.375757	+	0.843960i
$508$		0			0
$509$	11.2232	−	19.4391i	0.497458	−	0.861622i	−0.502538	−	0.864555i	$-0.667600\pi$
$509$	11.2232	−	19.4391i	0.497458	−	0.861622i	0.999996	+	0.00293304i	$0.000933617\pi$
$510$		0			0
$511$	4.67986	−	5.17740i	0.207025	−	0.229035i
$512$		0			0
$513$	8.65265	+	26.6306i	0.382024	+	1.17577i
$514$		0			0
$515$	−2.83132	+	1.63467i	−0.124763	+	0.0720320i
$516$		0			0
$517$	−31.2903	−	18.0654i	−1.37614	−	0.794517i
$518$		0			0
$519$	−1.31299	+	2.94901i	−0.0576338	+	0.129447i
$520$		0			0
$521$	27.8533			1.22027			0.610137	−	0.792296i	$-0.291114\pi$
$521$	27.8533			1.22027			0.610137	+	0.792296i	$0.291114\pi$
$522$		0			0
$523$			3.02647i			0.132338i	0.997808	+	0.0661691i	$0.0210777\pi$
$523$			3.02647i			0.132338i	−0.997808	+	0.0661691i	$0.978922\pi$
$524$		0			0
$525$	22.1114	−	9.79352i	0.965019	−	0.427424i
$526$		0			0
$527$	−22.8760	−	13.2074i	−0.996492	−	0.575325i
$528$		0			0
$529$	17.2701	+	29.9127i	0.750873	+	1.30055i
$530$		0			0
$531$	9.05851	+	10.0606i	0.393106	+	0.436592i
$532$		0			0
$533$	6.01340	−	3.47184i	0.260469	−	0.150382i
$534$		0			0
$535$	−30.5643	−	17.6463i	−1.32141	−	0.762915i
$536$		0			0
$537$	−7.71004	+	5.60165i	−0.332713	+	0.241729i
$538$		0			0
$539$	19.5545	+	27.1339i	0.842273	+	1.16874i
$540$		0			0
$541$	−43.4800			−1.86935			−0.934677	−	0.355499i	$-0.884311\pi$
$541$	−43.4800			−1.86935			−0.934677	+	0.355499i	$0.884311\pi$
$542$		0			0
$543$	−15.6076	+	11.3395i	−0.669786	+	0.486626i
$544$		0			0
$545$	11.8412	−	20.5096i	0.507221	−	0.878533i
$546$		0			0
$547$	−20.3399	−	35.2297i	−0.869670	−	1.50631i	−0.862335	−	0.506339i	$-0.830998\pi$
$547$	−20.3399	−	35.2297i	−0.869670	−	1.50631i	−0.00733515	−	0.999973i	$-0.502335\pi$
$548$		0			0
$549$	−3.79066	−	17.8340i	−0.161781	−	0.761136i
$550$		0			0
$551$	−9.13659	−	15.8250i	−0.389232	−	0.674169i
$552$		0			0
$553$	−8.84103	+	41.2030i	−0.375959	+	1.75213i
$554$		0			0
$555$	34.7768	−	3.65512i	1.47619	−	0.155151i
$556$		0			0
$557$		−	13.6889i		−	0.580016i	−0.957024	−	0.290008i	$-0.906342\pi$
$557$		−	13.6889i		−	0.580016i	0.957024	−	0.290008i	$-0.0936580\pi$
$558$		0			0
$559$			7.58983i			0.321016i
$560$		0			0
$561$	−49.2369	−	21.9218i	−2.07879	−	0.925540i
$562$		0			0
$563$	6.70705	−	11.6169i	0.282668	−	0.489596i	−0.689373	−	0.724407i	$-0.742114\pi$
$563$	6.70705	−	11.6169i	0.282668	−	0.489596i	0.972041	+	0.234811i	$0.0754471\pi$
$564$		0			0
$565$	−17.0248	+	9.82929i	−0.716240	+	0.413521i
$566$		0			0
$567$	4.90564	+	23.3010i	0.206018	+	0.978548i
$568$		0			0
$569$	−19.6370	+	11.3374i	−0.823227	+	0.475291i	−0.851528	−	0.524309i	$-0.824324\pi$
$569$	−19.6370	+	11.3374i	−0.823227	+	0.475291i	0.0283007	+	0.999599i	$0.490990\pi$
$570$		0			0
$571$	7.77378	−	13.4646i	0.325323	−	0.563475i	−0.656255	−	0.754539i	$-0.727860\pi$
$571$	7.77378	−	13.4646i	0.325323	−	0.563475i	0.981578	+	0.191064i	$0.0611938\pi$
$572$		0			0
$573$	6.66038	+	2.96541i	0.278241	+	0.123882i
$574$		0			0
$575$		−	40.0303i		−	1.66938i
$576$		0			0
$577$			41.8101i			1.74058i	0.492541	+	0.870289i	$0.336068\pi$
$577$			41.8101i			1.74058i	−0.492541	+	0.870289i	$0.663932\pi$
$578$		0			0
$579$	−4.93028	+	0.518183i	−0.204895	+	0.0215350i
$580$		0			0
$581$	4.98532	−	23.2337i	0.206826	−	0.963898i
$582$		0			0
$583$	18.5720	+	32.1676i	0.769172	+	1.33224i
$584$		0			0
$585$	−1.98972	−	9.36107i	−0.0822648	−	0.387033i
$586$		0			0
$587$	13.3910	+	23.1939i	0.552706	+	0.957315i	0.998078	+	0.0619696i	$0.0197382\pi$
$587$	13.3910	+	23.1939i	0.552706	+	0.957315i	−0.445372	+	0.895346i	$0.646928\pi$
$588$		0			0
$589$	10.9284	−	18.9285i	0.450295	−	0.779935i
$590$		0			0
$591$	−2.05910	+	1.49602i	−0.0847002	+	0.0615381i
$592$		0			0
$593$	−28.3434			−1.16392			−0.581962	−	0.813216i	$-0.697715\pi$
$593$	−28.3434			−1.16392			−0.581962	+	0.813216i	$0.697715\pi$
$594$		0			0
$595$	52.5678	−	16.9683i	2.15507	−	0.695634i
$596$		0			0
$597$	22.9513	−	16.6750i	0.939333	−	0.682463i
$598$		0			0
$599$	−7.73785	−	4.46745i	−0.316160	−	0.182535i	0.333520	−	0.942743i	$-0.391764\pi$
$599$	−7.73785	−	4.46745i	−0.316160	−	0.182535i	−0.649680	+	0.760208i	$0.725097\pi$
$600$		0			0
$601$	−19.2085	+	11.0901i	−0.783533	+	0.452373i	−0.837681	−	0.546160i	$-0.816089\pi$
$601$	−19.2085	+	11.0901i	−0.783533	+	0.452373i	0.0541481	+	0.998533i	$0.482756\pi$
$602$		0			0
$603$	1.98007	+	2.19910i	0.0806345	+	0.0895544i
$604$		0			0
$605$	18.9610	+	32.8414i	0.770873	+	1.33519i
$606$		0			0
$607$	30.3887	+	17.5449i	1.23344	+	0.712127i	0.967746	−	0.251930i	$-0.0810652\pi$
$607$	30.3887	+	17.5449i	1.23344	+	0.712127i	0.265695	+	0.964057i	$0.414399\pi$
$608$		0			0
$609$	−6.29299	−	14.2080i	−0.255005	−	0.575738i
$610$		0			0
$611$		−	7.52482i		−	0.304422i
$612$		0			0
$613$	15.4883			0.625566			0.312783	−	0.949825i	$-0.398739\pi$
$613$	15.4883			0.625566			0.312783	+	0.949825i	$0.398739\pi$
$614$		0			0
$615$	15.7594	−	35.3961i	0.635481	−	1.42731i
$616$		0			0
$617$	36.8217	+	21.2590i	1.48239	+	0.855856i	0.999800	−	0.0199930i	$-0.00636440\pi$
$617$	36.8217	+	21.2590i	1.48239	+	0.855856i	0.482586	+	0.875849i	$0.339698\pi$
$618$		0			0
$619$	−25.9906	+	15.0057i	−1.04465	+	0.603128i	−0.921146	−	0.389216i	$-0.872746\pi$
$619$	−25.9906	+	15.0057i	−1.04465	+	0.603128i	−0.123502	+	0.992344i	$0.539413\pi$
$620$		0			0
$621$	38.5542	+	8.19518i	1.54713	+	0.328861i
$622$		0			0
$623$	−8.67699	−	7.84314i	−0.347636	−	0.314229i
$624$		0			0
$625$	11.7686	−	20.3838i	0.470743	−	0.815351i
$626$		0			0
$627$	18.1390	−	40.7406i	0.724401	−	1.62702i
$628$		0			0
$629$	41.0141			1.63534
$630$		0			0
$631$	20.6833			0.823388			0.411694	−	0.911322i	$-0.364937\pi$
$631$	20.6833			0.823388			0.411694	+	0.911322i	$0.364937\pi$
$632$		0			0
$633$	17.8560	−	1.87670i	0.709711	−	0.0745922i
$634$		0			0
$635$	−15.1841	+	26.2997i	−0.602564	+	1.04367i
$636$		0			0
$637$	−2.85769	+	6.35245i	−0.113226	+	0.251693i
$638$		0			0
$639$	−9.13271	−	2.96744i	−0.361284	−	0.117390i
$640$		0			0
$641$	−25.9498	+	14.9821i	−1.02495	+	0.591758i	−0.915535	−	0.402238i	$-0.868232\pi$
$641$	−25.9498	+	14.9821i	−1.02495	+	0.591758i	−0.109419	+	0.993996i	$0.534899\pi$
$642$		0			0
$643$	28.7961	+	16.6254i	1.13561	+	0.655643i	0.945339	−	0.326090i	$-0.105731\pi$
$643$	28.7961	+	16.6254i	1.13561	+	0.655643i	0.190268	+	0.981732i	$0.439064\pi$
$644$		0			0
$645$	24.8935	+	34.2631i	0.980179	+	1.34911i
$646$		0			0
$647$	9.06135			0.356238			0.178119	−	0.984009i	$-0.442999\pi$
$647$	9.06135			0.356238			0.178119	+	0.984009i	$0.442999\pi$
$648$		0			0
$649$		−	21.5611i		−	0.846348i
$650$		0			0
$651$	10.9540	−	15.0158i	0.429321	−	0.588517i
$652$		0			0
$653$	−10.4121	−	6.01142i	−0.407456	−	0.235245i	0.282240	−	0.959344i	$-0.408923\pi$
$653$	−10.4121	−	6.01142i	−0.407456	−	0.235245i	−0.689696	+	0.724099i	$0.742256\pi$
$654$		0			0
$655$	24.3616	+	42.1955i	0.951886	+	1.64872i
$656$		0			0
$657$	−7.52613	−	2.44542i	−0.293622	−	0.0954049i
$658$		0			0
$659$	−41.1663	+	23.7674i	−1.60361	+	0.925845i	−0.612854	+	0.790196i	$0.709979\pi$
$659$	−41.1663	+	23.7674i	−1.60361	+	0.925845i	−0.990757	+	0.135649i	$0.956688\pi$
$660$		0			0
$661$	18.5254	+	10.6957i	0.720556	+	0.416013i	0.814957	−	0.579521i	$-0.196760\pi$
$661$	18.5254	+	10.6957i	0.720556	+	0.416013i	−0.0944011	+	0.995534i	$0.530094\pi$
$662$		0			0
$663$	−1.17329	−	11.1633i	−0.0455668	−	0.433547i
$664$		0			0
$665$	14.0403	+	43.4967i	0.544459	+	1.68673i
$666$		0			0
$667$	−25.7221			−0.995966
$668$		0			0
$669$	8.90874	+	3.96645i	0.344432	+	0.153352i
$670$		0			0
$671$	−14.5190	+	25.1477i	−0.560500	+	0.970815i
$672$		0			0
$673$	8.77577	+	15.2001i	0.338281	+	0.585920i	0.984109	−	0.177563i	$-0.0568213\pi$
$673$	8.77577	+	15.2001i	0.338281	+	0.585920i	−0.645829	+	0.763482i	$0.723488\pi$
$674$		0			0
$675$	−20.3778	−	18.3484i	−0.784341	−	0.706232i
$676$		0			0
$677$	−8.39862	−	14.5468i	−0.322785	−	0.559081i	0.658276	−	0.752776i	$-0.271286\pi$
$677$	−8.39862	−	14.5468i	−0.322785	−	0.559081i	−0.981062	+	0.193696i	$0.937953\pi$
$678$		0			0
$679$	−9.37117	−	2.01080i	−0.359633	−	0.0771673i
$680$		0			0
$681$	4.96968	−	11.1620i	0.190439	−	0.427730i
$682$		0			0
$683$			17.4518i			0.667773i	0.942613	+	0.333887i	$0.108360\pi$
$683$			17.4518i			0.667773i	−0.942613	+	0.333887i	$0.891640\pi$
$684$		0			0
$685$		−	8.96248i		−	0.342439i
$686$		0			0
$687$	−3.88303	−	36.9453i	−0.148147	−	1.40955i
$688$		0			0
$689$	−3.86790	+	6.69940i	−0.147355	+	0.255227i
$690$		0			0
$691$	37.8864	−	21.8737i	1.44127	−	0.832115i	0.443332	−	0.896358i	$-0.353796\pi$
$691$	37.8864	−	21.8737i	1.44127	−	0.832115i	0.997934	+	0.0642424i	$0.0204631\pi$
$692$		0			0
$693$	19.0255	−	32.8065i	0.722717	−	1.24622i
$694$		0			0
$695$	27.4283	−	15.8357i	1.04042	−	0.600684i
$696$		0			0
$697$	22.7223	−	39.3562i	0.860670	−	1.49072i
$698$		0			0
$699$	−16.2687	+	11.8199i	−0.615340	+	0.447069i
$700$		0			0
$701$		−	11.5880i		−	0.437671i	−0.975762	−	0.218836i	$-0.929774\pi$
$701$		−	11.5880i		−	0.437671i	0.975762	−	0.218836i	$-0.0702258\pi$
$702$		0			0
$703$			33.9367i			1.27995i
$704$		0			0
$705$	−24.6802	−	33.9696i	−0.929512	−	1.27937i
$706$		0			0
$707$	8.11607	−	37.8244i	0.305236	−	1.42253i
$708$		0			0
$709$	1.69813	+	2.94125i	0.0637747	+	0.110461i	0.896150	−	0.443752i	$-0.146353\pi$
$709$	1.69813	+	2.94125i	0.0637747	+	0.110461i	−0.832375	+	0.554213i	$0.813019\pi$
$710$		0			0
$711$	46.7390	−	9.93450i	1.75285	−	0.372573i
$712$		0			0
$713$	−15.3833	−	26.6446i	−0.576107	−	0.997847i
$714$		0			0
$715$	−7.62104	+	13.2000i	−0.285011	+	0.493653i
$716$		0			0
$717$	−1.22416	−	11.6473i	−0.0457170	−	0.434976i
$718$		0			0
$719$	−2.13894			−0.0797690			−0.0398845	−	0.999204i	$-0.512699\pi$
$719$	−2.13894			−0.0797690			−0.0398845	+	0.999204i	$0.512699\pi$
$720$		0			0
$721$	−0.828834	−	2.56772i	−0.0308674	−	0.0956270i
$722$		0			0
$723$	−4.75487	−	2.11702i	−0.176836	−	0.0787327i
$724$		0			0
$725$	15.4973	+	8.94737i	0.575555	+	0.332297i
$726$		0			0
$727$	−30.5447	+	17.6350i	−1.13284	+	0.654045i	−0.944647	−	0.328088i	$-0.893596\pi$
$727$	−30.5447	+	17.6350i	−1.13284	+	0.654045i	−0.188191	+	0.982132i	$0.560263\pi$
$728$		0			0
$729$	21.8436	−	15.8699i	0.809024	−	0.587776i
$730$		0			0
$731$	24.8368	+	43.0186i	0.918622	+	1.59110i
$732$		0			0
$733$	10.1611	+	5.86652i	0.375309	+	0.216685i	0.675775	−	0.737108i	$-0.263809\pi$
$733$	10.1611	+	5.86652i	0.375309	+	0.216685i	−0.300466	+	0.953792i	$0.597142\pi$
$734$		0			0
$735$	7.93444	+	38.0499i	0.292666	+	1.40349i
$736$		0			0
$737$		−	4.71296i		−	0.173604i
$738$		0			0
$739$	−37.8023			−1.39058			−0.695289	−	0.718730i	$-0.744724\pi$
$739$	−37.8023			−1.39058			−0.695289	+	0.718730i	$0.744724\pi$
$740$		0			0
$741$	9.23698	−	0.970827i	0.339329	−	0.0356642i
$742$		0			0
$743$	9.73943	+	5.62306i	0.357305	+	0.206290i	0.667898	−	0.744253i	$-0.267194\pi$
$743$	9.73943	+	5.62306i	0.357305	+	0.206290i	−0.310593	+	0.950543i	$0.600528\pi$
$744$		0			0
$745$	−65.9056	+	38.0506i	−2.41459	+	1.39407i
$746$		0			0
$747$	−26.3555	+	5.60192i	−0.964296	+	0.204963i
$748$		0			0
$749$	19.5314	−	21.6079i	0.713663	−	0.789536i
$750$		0			0
$751$	13.0985	−	22.6873i	0.477972	−	0.827871i	−0.521709	−	0.853123i	$-0.674706\pi$
$751$	13.0985	−	22.6873i	0.477972	−	0.827871i	0.999681	+	0.0252521i	$0.00803883\pi$
$752$		0			0
$753$	28.4980	+	39.2243i	1.03852	+	1.42941i
$754$		0			0
$755$	41.8598			1.52344
$756$		0			0
$757$	−0.529802			−0.0192560			−0.00962799	−	0.999954i	$-0.503065\pi$
$757$	−0.529802			−0.0192560			−0.00962799	+	0.999954i	$0.503065\pi$
$758$		0			0
$759$	−36.8985	−	50.7866i	−1.33933	−	1.84344i
$760$		0			0
$761$	24.2682	−	42.0337i	0.879721	−	1.52372i	0.0280745	−	0.999606i	$-0.491062\pi$
$761$	24.2682	−	42.0337i	0.879721	−	1.52372i	0.851647	−	0.524116i	$-0.175604\pi$
$762$		0			0
$763$	14.4996	+	13.1062i	0.524920	+	0.474476i
$764$		0			0
$765$	−41.9106	−	46.5468i	−1.51528	−	1.68290i
$766$		0			0
$767$	3.88883	−	2.24522i	0.140418	−	0.0810702i
$768$		0			0
$769$	−25.3353	−	14.6274i	−0.913615	−	0.527476i	−0.0320224	−	0.999487i	$-0.510195\pi$
$769$	−25.3353	−	14.6274i	−0.913615	−	0.527476i	−0.881592	+	0.472011i	$0.843528\pi$
$770$		0			0
$771$	−4.05466	+	0.426154i	−0.146025	+	0.0153476i
$772$		0			0
$773$	−43.5569			−1.56663			−0.783317	−	0.621623i	$-0.786474\pi$
$773$	−43.5569			−1.56663			−0.783317	+	0.621623i	$0.786474\pi$
$774$		0			0
$775$			21.4041i			0.768857i
$776$		0			0
$777$	−3.07201	+	28.6954i	−0.110208	+	1.02944i
$778$		0			0
$779$	32.5649	+	18.8014i	1.16676	+	0.673629i
$780$		0			0
$781$	7.64693	+	13.2449i	0.273629	+	0.473939i
$782$		0			0
$783$	−11.7901	+	13.0941i	−0.421344	+	0.467944i
$784$		0			0
$785$	0.860090	−	0.496573i	0.0306979	−	0.0177235i
$786$		0			0
$787$	8.25959	+	4.76868i	0.294423	+	0.169985i	0.639935	−	0.768429i	$-0.278961\pi$
$787$	8.25959	+	4.76868i	0.294423	+	0.169985i	−0.345512	+	0.938414i	$0.612295\pi$
$788$		0			0
$789$	−21.3345	−	9.49879i	−0.759529	−	0.338166i
$790$		0			0
$791$	−4.98380	−	15.4398i	−0.177203	−	0.548975i
$792$		0			0
$793$	−6.04762			−0.214757
$794$		0			0
$795$	4.51198	+	42.9295i	0.160024	+	1.52255i
$796$		0			0
$797$	20.4598	−	35.4374i	0.724722	−	1.25526i	−0.234366	−	0.972148i	$-0.575301\pi$
$797$	20.4598	−	35.4374i	0.724722	−	1.25526i	0.959088	−	0.283107i	$-0.0913653\pi$
$798$		0			0
$799$	−24.6241	−	42.6501i	−0.871137	−	1.50885i
$800$		0			0
$801$	−4.09837	+	12.6133i	−0.144809	+	0.445669i
$802$		0			0
$803$	6.30172	+	10.9149i	0.222383	+	0.385179i
$804$		0			0
$805$	62.9068	+	13.4981i	2.21717	+	0.475745i
$806$		0			0
$807$	−11.2800	−	15.5256i	−0.397073	−	0.546527i
$808$		0			0
$809$		−	23.7588i		−	0.835314i	−0.908605	−	0.417657i	$-0.862851\pi$
$809$		−	23.7588i		−	0.835314i	0.908605	−	0.417657i	$-0.137149\pi$
$810$		0			0
$811$			26.9638i			0.946828i	0.880840	+	0.473414i	$0.156979\pi$
$811$			26.9638i			0.946828i	−0.880840	+	0.473414i	$0.843021\pi$
$812$		0			0
$813$	6.04016	−	4.38842i	0.211838	−	0.153908i
$814$		0			0
$815$	16.9144	−	29.2966i	0.592486	−	1.02622i
$816$		0			0
$817$	−35.5953	+	20.5510i	−1.24532	+	0.718987i
$818$		0			0
$819$	7.89827	+	0.0152593i	0.275988	+	0.000533205i
$820$		0			0
$821$	31.8933	−	18.4136i	1.11308	−	0.642639i	0.173457	−	0.984841i	$-0.444506\pi$
$821$	31.8933	−	18.4136i	1.11308	−	0.642639i	0.939626	+	0.342202i	$0.111173\pi$
$822$		0			0
$823$	−2.98887	+	5.17687i	−0.104185	+	0.180454i	−0.913405	−	0.407052i	$-0.866557\pi$
$823$	−2.98887	+	5.17687i	−0.104185	+	0.180454i	0.809220	+	0.587506i	$0.199890\pi$
$824$		0			0
$825$	4.56494	+	43.4333i	0.158931	+	1.51216i
$826$		0			0
$827$			5.21366i			0.181297i	0.995883	+	0.0906484i	$0.0288939\pi$
$827$			5.21366i			0.181297i	−0.995883	+	0.0906484i	$0.971106\pi$
$828$		0			0
$829$			0.453044i			0.0157349i	0.999969	+	0.00786743i	$0.00250431\pi$
$829$			0.453044i			0.0157349i	−0.999969	+	0.00786743i	$0.997496\pi$
$830$		0			0
$831$	−5.93056	+	13.3202i	−0.205729	+	0.462072i
$832$		0			0
$833$	4.59041	+	45.3567i	0.159048	+	1.57152i
$834$		0			0
$835$	12.6839	+	21.9692i	0.438945	+	0.760276i
$836$		0			0
$837$	−20.6148	−	4.38193i	−0.712550	−	0.151462i
$838$		0			0
$839$	25.6669	+	44.4563i	0.886119	+	1.53480i	0.844426	+	0.535673i	$0.179942\pi$
$839$	25.6669	+	44.4563i	0.886119	+	1.53480i	0.0416932	+	0.999130i	$0.486725\pi$
$840$		0			0
$841$	−8.75072	+	15.1567i	−0.301749	+	0.522645i
$842$		0			0
$843$	29.5318	+	13.1485i	1.01713	+	0.452857i
$844$		0			0
$845$	38.5011			1.32448
$846$		0			0
$847$	−29.7838	+	9.61388i	−1.02338	+	0.330337i
$848$		0			0
$849$	4.95535	+	47.1479i	0.170067	+	1.61811i
$850$		0			0
$851$	41.3708	+	23.8854i	1.41817	+	0.818782i
$852$		0			0
$853$	13.7708	−	7.95059i	0.471504	−	0.272223i	−0.245365	−	0.969431i	$-0.578908\pi$
$853$	13.7708	−	7.95059i	0.471504	−	0.272223i	0.716869	+	0.697208i	$0.245575\pi$
$854$		0			0
$855$	38.5147	−	34.6785i	1.31717	−	1.18598i
$856$		0			0
$857$	7.31574	+	12.6712i	0.249901	+	0.432841i	0.963498	−	0.267715i	$-0.0862686\pi$
$857$	7.31574	+	12.6712i	0.249901	+	0.432841i	−0.713597	+	0.700556i	$0.752935\pi$
$858$		0			0
$859$	−44.0119	−	25.4103i	−1.50167	−	0.866988i	−0.999998	−	0.00192834i	$-0.999386\pi$
$859$	−44.0119	−	25.4103i	−1.50167	−	0.866988i	−0.501669	−	0.865060i	$-0.667280\pi$
$860$		0			0
$861$	25.8336	+	18.8455i	0.880405	+	0.642252i
$862$		0			0
$863$			3.00667i			0.102348i	0.998690	+	0.0511742i	$0.0162964\pi$
$863$			3.00667i			0.102348i	−0.998690	+	0.0511742i	$0.983704\pi$
$864$		0			0
$865$	5.97479			0.203149
$866$		0			0
$867$	−25.8735	−	35.6120i	−0.878711	−	1.20945i
$868$		0			0
$869$	−65.9066	−	38.0512i	−2.23573	−	1.29080i
$870$		0			0
$871$	0.850046	−	0.490774i	0.0288027	−	0.0166292i
$872$		0			0
$873$	2.25950	+	10.6303i	0.0764724	+	0.359781i
$874$		0			0
$875$	−1.74420	−	1.57659i	−0.0589648	−	0.0532984i
$876$		0			0
$877$	21.1229	−	36.5860i	0.713271	−	1.23542i	−0.250352	−	0.968155i	$-0.580546\pi$
$877$	21.1229	−	36.5860i	0.713271	−	1.23542i	0.963623	−	0.267266i	$-0.0861203\pi$
$878$		0			0
$879$	−16.0615	+	1.68810i	−0.541742	+	0.0569383i
$880$		0			0
$881$	29.4719			0.992933			0.496467	−	0.868056i	$-0.334630\pi$
$881$	29.4719			0.992933			0.496467	+	0.868056i	$0.334630\pi$
$882$		0			0
$883$	−27.1571			−0.913910			−0.456955	−	0.889490i	$-0.651060\pi$
$883$	−27.1571			−0.913910			−0.456955	+	0.889490i	$0.651060\pi$
$884$		0			0
$885$	10.1915	−	22.8904i	0.342585	−	0.769454i
$886$		0			0
$887$	5.51892	−	9.55905i	0.185307	−	0.320962i	−0.758373	−	0.651821i	$-0.774005\pi$
$887$	5.51892	−	9.55905i	0.185307	−	0.320962i	0.943680	+	0.330860i	$0.107339\pi$
$888$		0			0
$889$	−18.5930	−	16.8062i	−0.623589	−	0.563663i
$890$		0			0
$891$	−42.7663	−	4.49525i	−1.43272	−	0.150597i
$892$		0			0
$893$	35.2904	−	20.3749i	1.18095	−	0.681821i
$894$		0			0
$895$	15.2759	+	8.81953i	0.510616	+	0.294804i
$896$		0			0
$897$	5.31770	−	11.9437i	0.177553	−	0.398788i
$898$		0			0
$899$	13.7535			0.458706
$900$		0			0
$901$			50.6289i			1.68669i
$902$		0			0
$903$	−31.9582	+	14.1548i	−1.06350	+	0.471044i
$904$		0			0
$905$	30.9232	+	17.8535i	1.02792	+	0.593472i
$906$		0			0
$907$	−1.16565	−	2.01896i	−0.0387047	−	0.0670386i	0.846024	−	0.533145i	$-0.178990\pi$
$907$	−1.16565	−	2.01896i	−0.0387047	−	0.0670386i	−0.884729	+	0.466106i	$0.845657\pi$
$908$		0			0
$909$	−42.9065	+	9.11989i	−1.42312	+	0.302488i
$910$		0			0
$911$	−2.02681	+	1.17018i	−0.0671512	+	0.0387698i	−0.533200	−	0.845989i	$-0.679011\pi$
$911$	−2.02681	+	1.17018i	−0.0671512	+	0.0387698i	0.466048	+	0.884759i	$0.345677\pi$
$912$		0			0
$913$	37.1638	+	21.4565i	1.22994	+	0.710107i
$914$		0			0
$915$	−27.3010	+	19.8353i	−0.902544	+	0.655734i
$916$		0			0
$917$	−38.2670	+	12.3522i	−1.26369	+	0.407905i
$918$		0			0
$919$	3.54891			0.117068			0.0585339	−	0.998285i	$-0.481357\pi$
$919$	3.54891			0.117068			0.0585339	+	0.998285i	$0.481357\pi$
$920$		0			0
$921$	−47.1533	+	34.2587i	−1.55375	+	1.12886i
$922$		0			0
$923$	−1.59259	+	2.75845i	−0.0524208	+	0.0907955i
$924$		0			0
$925$	−16.6169	−	28.7814i	−0.546361	−	0.946326i
$926$		0			0
$927$	−2.27362	+	2.04716i	−0.0746755	+	0.0672376i
$928$		0			0
$929$	20.6699	+	35.8013i	0.678157	+	1.17460i	0.975535	+	0.219843i	$0.0705545\pi$
$929$	20.6699	+	35.8013i	0.678157	+	1.17460i	−0.297378	+	0.954760i	$0.596112\pi$
$930$		0			0
$931$	−37.5299	+	3.79829i	−1.22999	+	0.124484i
$932$		0			0
$933$	26.5107	−	2.78634i	0.867922	−	0.0912206i
$934$		0			0
$935$			99.7558i			3.26236i
$936$		0			0
$937$			1.12314i			0.0366913i	0.999832	+	0.0183457i	$0.00583993\pi$
$937$			1.12314i			0.0366913i	−0.999832	+	0.0183457i	$0.994160\pi$
$938$		0			0
$939$	−50.4328	−	22.4543i	−1.64581	−	0.732767i
$940$		0			0
$941$	20.3955	−	35.3261i	0.664875	−	1.15160i	−0.314444	−	0.949276i	$-0.601818\pi$
$941$	20.3955	−	35.3261i	0.664875	−	1.15160i	0.979319	−	0.202322i	$-0.0648486\pi$
$942$		0			0
$943$	45.8399	−	26.4657i	1.49275	−	0.861840i
$944$		0			0
$945$	35.7055	−	25.8362i	1.16150	−	0.840452i
$946$		0			0
$947$	−17.9909	+	10.3871i	−0.584626	+	0.337534i	−0.762970	−	0.646434i	$-0.776259\pi$
$947$	−17.9909	+	10.3871i	−0.584626	+	0.337534i	0.178344	+	0.983968i	$0.442926\pi$
$948$		0			0
$949$	−1.31243	+	2.27320i	−0.0426034	+	0.0737912i
$950$		0			0
$951$	−31.6159	−	14.0764i	−1.02521	−	0.456457i
$952$		0			0
$953$		−	50.6468i		−	1.64061i	−0.571926	−	0.820305i	$-0.693804\pi$
$953$		−	50.6468i		−	1.64061i	0.571926	−	0.820305i	$-0.306196\pi$
$954$		0			0
$955$		−	13.4942i		−	0.436661i
$956$		0			0
$957$	27.9088	−	2.93328i	0.902164	−	0.0948195i
$958$		0			0
$959$	7.23212	+	1.55181i	0.233537	+	0.0501107i
$960$		0			0
$961$	−7.27463	−	12.6000i	−0.234666	−	0.406453i
$962$		0			0
$963$	−31.4104	−	10.2060i	−1.01218	−	0.328883i
$964$		0			0
$965$	4.58779	+	7.94629i	0.147686	+	0.255800i
$966$		0			0
$967$	−11.1556	+	19.3220i	−0.358739	+	0.621354i	−0.987750	−	0.156042i	$-0.950127\pi$
$967$	−11.1556	+	19.3220i	−0.358739	+	0.621354i	0.629011	+	0.777396i	$0.283460\pi$
$968$		0			0
$969$	49.1776	−	35.7295i	1.57981	−	1.14780i
$970$		0			0
$971$	7.74260			0.248472			0.124236	−	0.992253i	$-0.460352\pi$
$971$	7.74260			0.248472			0.124236	+	0.992253i	$0.460352\pi$
$972$		0			0
$973$	8.02929	+	24.8747i	0.257407	+	0.797446i
$974$		0			0
$975$	−7.35842	+	5.34618i	−0.235658	+	0.171215i
$976$		0			0
$977$	−3.50084	−	2.02121i	−0.112002	−	0.0646644i	0.442953	−	0.896545i	$-0.353931\pi$
$977$	−3.50084	−	2.02121i	−0.112002	−	0.0646644i	−0.554955	+	0.831881i	$0.687264\pi$
$978$		0			0
$979$	18.2927	−	10.5613i	0.584637	−	0.337540i
$980$		0			0
$981$	6.84853	−	21.0773i	0.218657	−	0.672947i
$982$		0			0
$983$	−16.5261	−	28.6240i	−0.527100	−	0.912963i	−0.999501	−	0.0315798i	$-0.989946\pi$
$983$	−16.5261	−	28.6240i	−0.527100	−	0.912963i	0.472402	−	0.881383i	$-0.343387\pi$
$984$		0			0
$985$	4.07969	+	2.35541i	0.129990	+	0.0750496i
$986$		0			0
$987$	31.6844	−	14.0336i	1.00853	−	0.446695i
$988$		0			0
$989$			57.8569i			1.83974i
$990$		0			0
$991$	−45.7928			−1.45465			−0.727327	−	0.686291i	$-0.759238\pi$
$991$	−45.7928			−1.45465			−0.727327	+	0.686291i	$0.759238\pi$
$992$		0			0
$993$	6.31541	−	14.1846i	0.200413	−	0.450134i
$994$		0			0
$995$	−45.4733	−	26.2540i	−1.44160	−	0.832308i
$996$		0			0
$997$	43.1809	−	24.9305i	1.36755	−	0.789558i	0.376939	−	0.926238i	$-0.376977\pi$
$997$	43.1809	−	24.9305i	1.36755	−	0.789558i	0.990615	+	0.136681i	$0.0436434\pi$
$998$		0			0
$999$	31.1219	−	10.1119i	0.984654	−	0.319927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bu.a.41.8	✓	48
3.2	odd	2		1512.2.bu.a.881.21		48
4.3	odd	2		1008.2.cc.d.545.17		48
7.6	odd	2	inner	504.2.bu.a.41.17	yes	48
9.2	odd	6	inner	504.2.bu.a.209.17	yes	48
9.4	even	3		4536.2.k.a.3401.41		48
9.5	odd	6		4536.2.k.a.3401.8		48
9.7	even	3		1512.2.bu.a.1385.4		48
12.11	even	2		3024.2.cc.d.881.21		48
21.20	even	2		1512.2.bu.a.881.4		48
28.27	even	2		1008.2.cc.d.545.8		48
36.7	odd	6		3024.2.cc.d.2897.4		48
36.11	even	6		1008.2.cc.d.209.8		48
63.13	odd	6		4536.2.k.a.3401.7		48
63.20	even	6	inner	504.2.bu.a.209.8	yes	48
63.34	odd	6		1512.2.bu.a.1385.21		48
63.41	even	6		4536.2.k.a.3401.42		48
84.83	odd	2		3024.2.cc.d.881.4		48
252.83	odd	6		1008.2.cc.d.209.17		48
252.223	even	6		3024.2.cc.d.2897.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.8	✓	48	1.1	even	1	trivial
504.2.bu.a.41.17	yes	48	7.6	odd	2	inner
504.2.bu.a.209.8	yes	48	63.20	even	6	inner
504.2.bu.a.209.17	yes	48	9.2	odd	6	inner
1008.2.cc.d.209.8		48	36.11	even	6
1008.2.cc.d.209.17		48	252.83	odd	6
1008.2.cc.d.545.8		48	28.27	even	2
1008.2.cc.d.545.17		48	4.3	odd	2
1512.2.bu.a.881.4		48	21.20	even	2
1512.2.bu.a.881.21		48	3.2	odd	2
1512.2.bu.a.1385.4		48	9.7	even	3
1512.2.bu.a.1385.21		48	63.34	odd	6
3024.2.cc.d.881.4		48	84.83	odd	2
3024.2.cc.d.881.21		48	12.11	even	2
3024.2.cc.d.2897.4		48	36.7	odd	6
3024.2.cc.d.2897.21		48	252.223	even	6
4536.2.k.a.3401.7		48	63.13	odd	6
4536.2.k.a.3401.8		48	9.5	odd	6
4536.2.k.a.3401.41		48	9.4	even	3
4536.2.k.a.3401.42		48	63.41	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.01807 - 1.40126i) q^{3} +(-1.60290 + 2.77631i) q^{5} +(-1.96276 - 1.77414i) q^{7} +(-0.927062 + 2.85317i) q^{9} +(4.13786 - 2.38899i) q^{11} +(0.861773 + 0.497545i) q^{13} +(5.52220 - 0.580396i) q^{15} +6.51262 q^{17} +5.38881i q^{19} +(-0.487805 + 4.55654i) q^{21} +(6.56926 + 3.79276i) q^{23} +(-2.63860 - 4.57019i) q^{25} +(4.94184 - 1.60567i) q^{27} +(-2.93665 + 1.69548i) q^{29} +(-3.51256 - 2.02798i) q^{31} +(-7.56023 - 3.36605i) q^{33} +(8.07168 - 2.60545i) q^{35} +6.29763 q^{37} +(-0.180156 - 1.71410i) q^{39} +(3.48897 - 6.04307i) q^{41} +(3.81364 + 6.60542i) q^{43} +(-6.43528 - 7.14716i) q^{45} +(-3.78098 - 6.54884i) q^{47} +(0.704849 + 6.96442i) q^{49} +(-6.63031 - 9.12588i) q^{51} +7.77397i q^{53} +15.3173i q^{55} +(7.55112 - 5.48619i) q^{57} +(2.25630 - 3.90802i) q^{59} +(-5.26324 + 3.03873i) q^{61} +(6.88152 - 3.95534i) q^{63} +(-2.76268 + 1.59503i) q^{65} +(0.493196 - 0.854240i) q^{67} +(-1.37332 - 13.0665i) q^{69} +3.20090i q^{71} +2.63782i q^{73} +(-3.71774 + 8.35014i) q^{75} +(-12.3600 - 2.65212i) q^{77} +(-7.96386 - 13.7938i) q^{79} +(-7.28111 - 5.29012i) q^{81} +(4.49071 + 7.77813i) q^{83} +(-10.4391 + 18.0811i) q^{85} +(5.36552 + 2.38890i) q^{87} +4.42081 q^{89} +(-0.808738 - 2.50547i) q^{91} +(0.734311 + 6.98663i) q^{93} +(-14.9610 - 8.63774i) q^{95} +(3.13726 - 1.81130i) q^{97} +(2.98014 + 14.0207i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} + 8 q^{15} - 4 q^{21} + 12 q^{23} - 24 q^{25} - 36 q^{29} + 32 q^{39} + 12 q^{43} + 6 q^{49} + 24 q^{51} + 28 q^{57} - 14 q^{63} + 36 q^{65} - 60 q^{77} - 12 q^{79} - 36 q^{81} - 12 q^{91}+ \cdots + 44 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 - 4 * q^21 + 12 * q^23 - 24 * q^25 - 36 * q^29 + 32 * q^39 + 12 * q^43 + 6 * q^49 + 24 * q^51 + 28 * q^57 - 14 * q^63 + 36 * q^65 - 60 * q^77 - 12 * q^79 - 36 * q^81 - 12 * q^91 + 16 * q^93 - 108 * q^95 + 44 * q^99

Introduction

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