LMFDB - Embedded newform 1890.2.bi.a.899.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1890,2,Mod(719,1890)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1890, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1890.719"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bi (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			899.7
Character	$\chi$	$=$	1890.899
Dual form			1890.2.bi.a.719.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.24107 + 1.86004i) q^{5} +(2.20215 + 1.46647i) q^{7} -1.00000 q^{8} +(1.24107 - 1.86004i) q^{10} +(-0.646046 + 0.372995i) q^{11} +(1.67087 + 2.89402i) q^{13} +(-2.20215 - 1.46647i) q^{14} +1.00000 q^{16} +(4.20138 + 2.42567i) q^{17} +(6.50055 - 3.75309i) q^{19} +(-1.24107 + 1.86004i) q^{20} +(0.646046 - 0.372995i) q^{22} +(0.933507 - 1.61688i) q^{23} +(-1.91949 - 4.61688i) q^{25} +(-1.67087 - 2.89402i) q^{26} +(2.20215 + 1.46647i) q^{28} +(0.644047 + 0.371841i) q^{29} -5.00146i q^{31} -1.00000 q^{32} +(-4.20138 - 2.42567i) q^{34} +(-5.46071 + 2.27609i) q^{35} +(-5.78366 + 3.33920i) q^{37} +(-6.50055 + 3.75309i) q^{38} +(1.24107 - 1.86004i) q^{40} +(-0.849794 - 1.47189i) q^{41} +(7.64047 + 4.41123i) q^{43} +(-0.646046 + 0.372995i) q^{44} +(-0.933507 + 1.61688i) q^{46} +11.6099i q^{47} +(2.69893 + 6.45877i) q^{49} +(1.91949 + 4.61688i) q^{50} +(1.67087 + 2.89402i) q^{52} +(2.94339 - 5.09811i) q^{53} +(0.108003 - 1.66458i) q^{55} +(-2.20215 - 1.46647i) q^{56} +(-0.644047 - 0.371841i) q^{58} +4.66316 q^{59} +1.71256i q^{61} +5.00146i q^{62} +1.00000 q^{64} +(-7.45666 - 0.483811i) q^{65} -4.53308i q^{67} +(4.20138 + 2.42567i) q^{68} +(5.46071 - 2.27609i) q^{70} -4.17217i q^{71} +(-5.10736 + 8.84620i) q^{73} +(5.78366 - 3.33920i) q^{74} +(6.50055 - 3.75309i) q^{76} +(-1.96968 - 0.126017i) q^{77} -6.21613 q^{79} +(-1.24107 + 1.86004i) q^{80} +(0.849794 + 1.47189i) q^{82} +(2.26849 + 1.30971i) q^{83} +(-9.72604 + 4.80431i) q^{85} +(-7.64047 - 4.41123i) q^{86} +(0.646046 - 0.372995i) q^{88} +(-7.58595 - 13.1393i) q^{89} +(-0.564503 + 8.82335i) q^{91} +(0.933507 - 1.61688i) q^{92} -11.6099i q^{94} +(-1.08673 + 16.7491i) q^{95} +(2.32004 - 4.01843i) q^{97} +(-2.69893 - 6.45877i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} + 48 q^{4} + 3 q^{7} - 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} + 6 q^{22} - 3 q^{23} - 18 q^{25} + 3 q^{28} + 3 q^{29} - 48 q^{32} + 12 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49}+ \cdots - 3 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 + 48 * q^4 + 3 * q^7 - 48 * q^8 - 6 * q^11 - 3 * q^14 + 48 * q^16 + 6 * q^22 - 3 * q^23 - 18 * q^25 + 3 * q^28 + 3 * q^29 - 48 * q^32 + 12 * q^35 + 3 * q^41 - 6 * q^44 + 3 * q^46 + 3 * q^49 + 18 * q^50 - 42 * q^55 - 3 * q^56 - 3 * q^58 + 48 * q^64 - 12 * q^65 - 12 * q^70 - 18 * q^73 + 12 * q^77 - 3 * q^82 - 9 * q^83 - 33 * q^85 + 6 * q^88 + 33 * q^89 - 3 * q^92 - 24 * q^97 - 3 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.24107	+	1.86004i	−0.555023	+	0.831835i
$5$	−1.24107	+	1.86004i	−0.555023	+	0.831835i
$6$		0			0
$7$	2.20215	+	1.46647i	0.832335	+	0.554274i
$7$	2.20215	+	1.46647i	0.832335	+	0.554274i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.24107	−	1.86004i	0.392461	−	0.588196i
$11$	−0.646046	+	0.372995i	−0.194790	+	0.112462i	−0.594223	−	0.804300i	$-0.702540\pi$
$11$	−0.646046	+	0.372995i	−0.194790	+	0.112462i	0.399433	+	0.916762i	$0.369207\pi$
$12$		0			0
$13$	1.67087	+	2.89402i	0.463415	+	0.802658i	0.999128	−	0.0417418i	$-0.0132907\pi$
$13$	1.67087	+	2.89402i	0.463415	+	0.802658i	−0.535714	+	0.844400i	$0.679957\pi$
$14$	−2.20215	−	1.46647i	−0.588549	−	0.391931i
$15$		0			0
$16$	1.00000			0.250000
$17$	4.20138	+	2.42567i	1.01898	+	0.588311i	0.913810	−	0.406143i	$-0.133127\pi$
$17$	4.20138	+	2.42567i	1.01898	+	0.588311i	0.105175	+	0.994454i	$0.466460\pi$
$18$		0			0
$19$	6.50055	−	3.75309i	1.49133	−	0.861018i	0.491377	−	0.870947i	$-0.336494\pi$
$19$	6.50055	−	3.75309i	1.49133	−	0.861018i	0.999951	+	0.00992860i	$0.00316042\pi$
$20$	−1.24107	+	1.86004i	−0.277512	+	0.415917i
$21$		0			0
$22$	0.646046	−	0.372995i	0.137738	−	0.0795228i
$23$	0.933507	−	1.61688i	0.194650	−	0.337143i	−0.752136	−	0.659008i	$-0.770976\pi$
$23$	0.933507	−	1.61688i	0.194650	−	0.337143i	0.946786	+	0.321865i	$0.104310\pi$
$24$		0			0
$25$	−1.91949	−	4.61688i	−0.383898	−	0.923375i
$26$	−1.67087	−	2.89402i	−0.327684	−	0.567565i
$27$		0			0
$28$	2.20215	+	1.46647i	0.416167	+	0.277137i
$29$	0.644047	+	0.371841i	0.119597	+	0.0690491i	0.558605	−	0.829434i	$-0.311337\pi$
$29$	0.644047	+	0.371841i	0.119597	+	0.0690491i	−0.439008	+	0.898483i	$0.644670\pi$
$30$		0			0
$31$		−	5.00146i		−	0.898289i	−0.893459	−	0.449145i	$-0.851729\pi$
$31$		−	5.00146i		−	0.898289i	0.893459	−	0.449145i	$-0.148271\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−4.20138	−	2.42567i	−0.720531	−	0.415999i
$35$	−5.46071	+	2.27609i	−0.923029	+	0.384730i
$36$		0			0
$37$	−5.78366	+	3.33920i	−0.950827	+	0.548960i	−0.893338	−	0.449386i	$-0.851643\pi$
$37$	−5.78366	+	3.33920i	−0.950827	+	0.548960i	−0.0574896	+	0.998346i	$0.518310\pi$
$38$	−6.50055	+	3.75309i	−1.05453	+	0.608832i
$39$		0			0
$40$	1.24107	−	1.86004i	0.196230	−	0.294098i
$41$	−0.849794	−	1.47189i	−0.132716	−	0.229870i	0.792007	−	0.610512i	$-0.209036\pi$
$41$	−0.849794	−	1.47189i	−0.132716	−	0.229870i	−0.924722	+	0.380642i	$0.875703\pi$
$42$		0			0
$43$	7.64047	+	4.41123i	1.16516	+	0.672706i	0.952535	−	0.304428i	$-0.0984654\pi$
$43$	7.64047	+	4.41123i	1.16516	+	0.672706i	0.212625	+	0.977134i	$0.431799\pi$
$44$	−0.646046	+	0.372995i	−0.0973951	+	0.0562311i
$45$		0			0
$46$	−0.933507	+	1.61688i	−0.137638	+	0.238396i
$47$			11.6099i			1.69347i	0.532011	+	0.846737i	$0.321436\pi$
$47$			11.6099i			1.69347i	−0.532011	+	0.846737i	$0.678564\pi$
$48$		0			0
$49$	2.69893	+	6.45877i	0.385562	+	0.922682i
$50$	1.91949	+	4.61688i	0.271457	+	0.652925i
$51$		0			0
$52$	1.67087	+	2.89402i	0.231707	+	0.401329i
$53$	2.94339	−	5.09811i	0.404306	−	0.700279i	−0.589934	−	0.807451i	$-0.700846\pi$
$53$	2.94339	−	5.09811i	0.404306	−	0.700279i	0.994240	+	0.107172i	$0.0341797\pi$
$54$		0			0
$55$	0.108003	−	1.66458i	0.0145632	−	0.224452i
$56$	−2.20215	−	1.46647i	−0.294275	−	0.195965i
$57$		0			0
$58$	−0.644047	−	0.371841i	−0.0845675	−	0.0488251i
$59$	4.66316			0.607091			0.303546	−	0.952817i	$-0.401829\pi$
$59$	4.66316			0.607091			0.303546	+	0.952817i	$0.401829\pi$
$60$		0			0
$61$			1.71256i			0.219270i	0.993972	+	0.109635i	$0.0349683\pi$
$61$			1.71256i			0.219270i	−0.993972	+	0.109635i	$0.965032\pi$
$62$			5.00146i			0.635187i
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.45666	−	0.483811i	−0.924885	−	0.0600094i
$66$		0			0
$67$		−	4.53308i		−	0.553804i	−0.960898	−	0.276902i	$-0.910692\pi$
$67$		−	4.53308i		−	0.553804i	0.960898	−	0.276902i	$-0.0893077\pi$
$68$	4.20138	+	2.42567i	0.509492	+	0.294155i
$69$		0			0
$70$	5.46071	−	2.27609i	0.652680	−	0.272045i
$71$		−	4.17217i		−	0.495145i	−0.968869	−	0.247573i	$-0.920367\pi$
$71$		−	4.17217i		−	0.495145i	0.968869	−	0.247573i	$-0.0796329\pi$
$72$		0			0
$73$	−5.10736	+	8.84620i	−0.597771	+	1.03537i	0.395378	+	0.918518i	$0.370613\pi$
$73$	−5.10736	+	8.84620i	−0.597771	+	1.03537i	−0.993149	+	0.116851i	$0.962720\pi$
$74$	5.78366	−	3.33920i	0.672337	−	0.388174i
$75$		0			0
$76$	6.50055	−	3.75309i	0.745664	−	0.430509i
$77$	−1.96968	−	0.126017i	−0.224466	−	0.0143609i
$78$		0			0
$79$	−6.21613			−0.699369			−0.349685	−	0.936867i	$-0.613711\pi$
$79$	−6.21613			−0.699369			−0.349685	+	0.936867i	$0.613711\pi$
$80$	−1.24107	+	1.86004i	−0.138756	+	0.207959i
$81$		0			0
$82$	0.849794	+	1.47189i	0.0938441	+	0.162543i
$83$	2.26849	+	1.30971i	0.248999	+	0.143760i	0.619306	−	0.785150i	$-0.287414\pi$
$83$	2.26849	+	1.30971i	0.248999	+	0.143760i	−0.370307	+	0.928910i	$0.620747\pi$
$84$		0			0
$85$	−9.72604	+	4.80431i	−1.05494	+	0.521100i
$86$	−7.64047	−	4.41123i	−0.823893	−	0.475675i
$87$		0			0
$88$	0.646046	−	0.372995i	0.0688688	−	0.0397614i
$89$	−7.58595	−	13.1393i	−0.804109	−	1.39276i	−0.916891	−	0.399138i	$-0.869309\pi$
$89$	−7.58595	−	13.1393i	−0.804109	−	1.39276i	0.112782	−	0.993620i	$-0.464024\pi$
$90$		0			0
$91$	−0.564503	+	8.82335i	−0.0591760	+	0.924938i
$92$	0.933507	−	1.61688i	0.0973249	−	0.168572i
$93$		0			0
$94$		−	11.6099i		−	1.19747i
$95$	−1.08673	+	16.7491i	−0.111497	+	1.71842i
$96$		0			0
$97$	2.32004	−	4.01843i	0.235565	−	0.408010i	−0.723872	−	0.689934i	$-0.757639\pi$
$97$	2.32004	−	4.01843i	0.235565	−	0.408010i	0.959437	+	0.281924i	$0.0909728\pi$
$98$	−2.69893	−	6.45877i	−0.272633	−	0.652435i
$99$		0			0
$100$	−1.91949	−	4.61688i	−0.191949	−	0.461688i
$101$	5.48710	+	9.50393i	0.545986	+	0.945676i	0.998544	+	0.0539412i	$0.0171783\pi$
$101$	5.48710	+	9.50393i	0.545986	+	0.945676i	−0.452558	+	0.891735i	$0.649488\pi$
$102$		0			0
$103$	−3.33713	+	5.78008i	−0.328817	+	0.569528i	−0.982277	−	0.187433i	$-0.939983\pi$
$103$	−3.33713	+	5.78008i	−0.328817	+	0.569528i	0.653460	+	0.756961i	$0.273317\pi$
$104$	−1.67087	−	2.89402i	−0.163842	−	0.283782i
$105$		0			0
$106$	−2.94339	+	5.09811i	−0.285888	+	0.495172i
$107$	−6.82770	−	11.8259i	−0.660058	−	1.14325i	−0.980600	−	0.196020i	$-0.937198\pi$
$107$	−6.82770	−	11.8259i	−0.660058	−	1.14325i	0.320541	−	0.947234i	$-0.396135\pi$
$108$		0			0
$109$	−5.13894	+	8.90090i	−0.492221	+	0.852551i	−0.999960	−	0.00895944i	$-0.997148\pi$
$109$	−5.13894	+	8.90090i	−0.492221	+	0.852551i	0.507739	+	0.861511i	$0.330481\pi$
$110$	−0.108003	+	1.66458i	−0.0102977	+	0.158712i
$111$		0			0
$112$	2.20215	+	1.46647i	0.208084	+	0.138568i
$113$	10.0641	+	17.4316i	0.946754	+	1.63983i	0.752201	+	0.658934i	$0.228992\pi$
$113$	10.0641	+	17.4316i	0.946754	+	1.63983i	0.194553	+	0.980892i	$0.437674\pi$
$114$		0			0
$115$	1.84892	+	3.74302i	0.172412	+	0.349039i
$116$	0.644047	+	0.371841i	0.0597983	+	0.0345245i
$117$		0			0
$118$	−4.66316			−0.429278
$119$	5.69490	+	11.5029i	0.522051	+	1.05447i
$120$		0			0
$121$	−5.22175	+	9.04434i	−0.474704	+	0.822212i
$122$		−	1.71256i		−	0.155048i
$123$		0			0
$124$		−	5.00146i		−	0.449145i
$125$	10.9698	+	2.15954i	0.981168	+	0.193155i
$126$		0			0
$127$		−	2.11883i		−	0.188015i	−0.995571	−	0.0940077i	$-0.970032\pi$
$127$		−	2.11883i		−	0.188015i	0.995571	−	0.0940077i	$-0.0299678\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	7.45666	+	0.483811i	0.653992	+	0.0424330i
$131$	7.87875	−	13.6464i	0.688370	−	1.19229i	−0.283995	−	0.958826i	$-0.591660\pi$
$131$	7.87875	−	13.6464i	0.688370	−	1.19229i	0.972365	−	0.233465i	$-0.0750066\pi$
$132$		0			0
$133$	19.8190	+	1.26798i	1.71852	+	0.109948i
$134$			4.53308i			0.391599i
$135$		0			0
$136$	−4.20138	−	2.42567i	−0.360265	−	0.207999i
$137$	5.50358	+	9.53248i	0.470202	+	0.814415i	0.999419	−	0.0340720i	$-0.0108475\pi$
$137$	5.50358	+	9.53248i	0.470202	+	0.814415i	−0.529217	+	0.848487i	$0.677514\pi$
$138$		0			0
$139$	−14.5065	+	8.37531i	−1.23042	+	0.710385i	−0.967118	−	0.254328i	$-0.918146\pi$
$139$	−14.5065	+	8.37531i	−1.23042	+	0.710385i	−0.263304	+	0.964713i	$0.584812\pi$
$140$	−5.46071	+	2.27609i	−0.461515	+	0.192365i
$141$		0			0
$142$			4.17217i			0.350121i
$143$	−2.15891	−	1.24645i	−0.180537	−	0.104233i
$144$		0			0
$145$	−1.49095	+	0.736472i	−0.123816	+	0.0611607i
$146$	5.10736	−	8.84620i	0.422688	−	0.732117i
$147$		0			0
$148$	−5.78366	+	3.33920i	−0.475414	+	0.274480i
$149$	−18.6650	−	10.7762i	−1.52909	−	0.882823i	−0.999400	−	0.0346347i	$-0.988973\pi$
$149$	−18.6650	−	10.7762i	−1.52909	−	0.882823i	−0.529695	−	0.848188i	$-0.677693\pi$
$150$		0			0
$151$	7.68913	+	13.3180i	0.625732	+	1.08380i	0.988399	+	0.151881i	$0.0485332\pi$
$151$	7.68913	+	13.3180i	0.625732	+	1.08380i	−0.362666	+	0.931919i	$0.618133\pi$
$152$	−6.50055	+	3.75309i	−0.527264	+	0.304416i
$153$		0			0
$154$	1.96968	+	0.126017i	0.158721	+	0.0101547i
$155$	9.30292	+	6.20717i	0.747228	+	0.498572i
$156$		0			0
$157$	7.04317			0.562106			0.281053	−	0.959692i	$-0.409316\pi$
$157$	7.04317			0.562106			0.281053	+	0.959692i	$0.409316\pi$
$158$	6.21613			0.494529
$159$		0			0
$160$	1.24107	−	1.86004i	0.0981152	−	0.147049i
$161$	4.42683	−	2.19166i	0.348883	−	0.172727i
$162$		0			0
$163$	6.38815	−	3.68820i	0.500359	−	0.288882i	−0.228503	−	0.973543i	$-0.573383\pi$
$163$	6.38815	−	3.68820i	0.500359	−	0.288882i	0.728862	+	0.684661i	$0.240050\pi$
$164$	−0.849794	−	1.47189i	−0.0663578	−	0.114935i
$165$		0			0
$166$	−2.26849	−	1.30971i	−0.176069	−	0.101653i
$167$	−14.6090	+	8.43452i	−1.13048	+	0.652683i	−0.944055	−	0.329787i	$-0.893023\pi$
$167$	−14.6090	+	8.43452i	−1.13048	+	0.652683i	−0.186424	+	0.982469i	$0.559690\pi$
$168$		0			0
$169$	0.916415	−	1.58728i	0.0704935	−	0.122098i
$170$	9.72604	−	4.80431i	0.745953	−	0.368473i
$171$		0			0
$172$	7.64047	+	4.41123i	0.582580	+	0.336353i
$173$		−	10.2449i		−	0.778905i	−0.921046	−	0.389453i	$-0.872664\pi$
$173$		−	10.2449i		−	0.778905i	0.921046	−	0.389453i	$-0.127336\pi$
$174$		0			0
$175$	2.54351	−	12.9819i	0.192271	−	0.981342i
$176$	−0.646046	+	0.372995i	−0.0486976	+	0.0281156i
$177$		0			0
$178$	7.58595	+	13.1393i	0.568591	+	0.984829i
$179$	16.4577	+	9.50188i	1.23011	+	0.710204i	0.967053	−	0.254577i	$-0.0819362\pi$
$179$	16.4577	+	9.50188i	1.23011	+	0.710204i	0.263056	+	0.964780i	$0.415269\pi$
$180$		0			0
$181$			5.53416i			0.411351i	0.978620	+	0.205676i	$0.0659391\pi$
$181$			5.53416i			0.411351i	−0.978620	+	0.205676i	$0.934061\pi$
$182$	0.564503	−	8.82335i	0.0418437	−	0.654030i
$183$		0			0
$184$	−0.933507	+	1.61688i	−0.0688191	+	0.119198i
$185$	0.966888	−	14.9020i	0.0710870	−	1.09562i
$186$		0			0
$187$	−3.61905			−0.264651
$188$			11.6099i			0.846737i
$189$		0			0
$190$	1.08673	−	16.7491i	0.0788400	−	1.21511i
$191$			20.0241i			1.44889i	0.689330	+	0.724447i	$0.257905\pi$
$191$			20.0241i			1.44889i	−0.689330	+	0.724447i	$0.742095\pi$
$192$		0			0
$193$			19.0139i			1.36865i	0.729176	+	0.684327i	$0.239904\pi$
$193$			19.0139i			1.36865i	−0.729176	+	0.684327i	$0.760096\pi$
$194$	−2.32004	+	4.01843i	−0.166569	+	0.288506i
$195$		0			0
$196$	2.69893	+	6.45877i	0.192781	+	0.461341i
$197$	6.94184			0.494586			0.247293	−	0.968941i	$-0.420459\pi$
$197$	6.94184			0.494586			0.247293	+	0.968941i	$0.420459\pi$
$198$		0			0
$199$	−3.90645	−	2.25539i	−0.276921	−	0.159880i	0.355108	−	0.934825i	$-0.384444\pi$
$199$	−3.90645	−	2.25539i	−0.276921	−	0.159880i	−0.632029	+	0.774945i	$0.717777\pi$
$200$	1.91949	+	4.61688i	0.135728	+	0.326463i
$201$		0			0
$202$	−5.48710	−	9.50393i	−0.386071	−	0.668694i
$203$	0.872995	+	1.76332i	0.0612722	+	0.123761i
$204$		0			0
$205$	3.79242	+	0.246064i	0.264874	+	0.0171859i
$206$	3.33713	−	5.78008i	0.232509	−	0.402717i
$207$		0			0
$208$	1.67087	+	2.89402i	0.115854	+	0.200664i
$209$	−2.79977	+	4.84934i	−0.193664	+	0.335436i
$210$		0			0
$211$	3.92397	+	6.79652i	0.270137	+	0.467892i	0.968897	−	0.247465i	$-0.0795976\pi$
$211$	3.92397	+	6.79652i	0.270137	+	0.467892i	−0.698759	+	0.715357i	$0.746264\pi$
$212$	2.94339	−	5.09811i	0.202153	−	0.350140i
$213$		0			0
$214$	6.82770	+	11.8259i	0.466732	+	0.808403i
$215$	−17.6874	+	8.73693i	−1.20627	+	0.595854i
$216$		0			0
$217$	7.33450	−	11.0140i	0.497898	−	0.747677i
$218$	5.13894	−	8.90090i	0.348053	−	0.602845i
$219$		0			0
$220$	0.108003	−	1.66458i	0.00728159	−	0.112226i
$221$			16.2119i			1.09053i
$222$		0			0
$223$	10.7610	−	18.6387i	0.720612	−	1.24814i	−0.240143	−	0.970738i	$-0.577194\pi$
$223$	10.7610	−	18.6387i	0.720612	−	1.24814i	0.960755	−	0.277399i	$-0.0894725\pi$
$224$	−2.20215	−	1.46647i	−0.147137	−	0.0979827i
$225$		0			0
$226$	−10.0641	−	17.4316i	−0.669456	−	1.15953i
$227$	6.95237	−	4.01395i	0.461445	−	0.266415i	−0.251207	−	0.967933i	$-0.580827\pi$
$227$	6.95237	−	4.01395i	0.461445	−	0.266415i	0.712652	+	0.701518i	$0.247494\pi$
$228$		0			0
$229$	−16.6860	−	9.63368i	−1.10264	−	0.636612i	−0.165730	−	0.986171i	$-0.552998\pi$
$229$	−16.6860	−	9.63368i	−1.10264	−	0.636612i	−0.936914	+	0.349560i	$0.886331\pi$
$230$	−1.84892	−	3.74302i	−0.121914	−	0.246808i
$231$		0			0
$232$	−0.644047	−	0.371841i	−0.0422837	−	0.0244125i
$233$	−0.572350	−	0.991339i	−0.0374959	−	0.0649448i	0.846668	−	0.532121i	$-0.178605\pi$
$233$	−0.572350	−	0.991339i	−0.0374959	−	0.0649448i	−0.884164	+	0.467176i	$0.845271\pi$
$234$		0			0
$235$	−21.5948	−	14.4087i	−1.40869	−	0.939918i
$236$	4.66316			0.303546
$237$		0			0
$238$	−5.69490	−	11.5029i	−0.369145	−	0.745621i
$239$	−10.1997	+	5.88880i	−0.659764	+	0.380915i	−0.792187	−	0.610279i	$-0.791058\pi$
$239$	−10.1997	+	5.88880i	−0.659764	+	0.380915i	0.132423	+	0.991193i	$0.457724\pi$
$240$		0			0
$241$	19.9120	−	11.4962i	1.28265	−	0.740536i	0.305314	−	0.952252i	$-0.401238\pi$
$241$	19.9120	−	11.4962i	1.28265	−	0.740536i	0.977331	+	0.211716i	$0.0679051\pi$
$242$	5.22175	−	9.04434i	0.335667	−	0.581392i
$243$		0			0
$244$			1.71256i			0.109635i
$245$	−15.3631	−	2.99567i	−0.981515	−	0.191387i
$246$		0			0
$247$	21.7231	+	12.5418i	1.38221	+	0.798017i
$248$			5.00146i			0.317593i
$249$		0			0
$250$	−10.9698	−	2.15954i	−0.693791	−	0.136581i
$251$	−1.44964			−0.0915002			−0.0457501	−	0.998953i	$-0.514568\pi$
$251$	−1.44964			−0.0915002			−0.0457501	+	0.998953i	$0.514568\pi$
$252$		0			0
$253$			1.39277i			0.0875630i
$254$			2.11883i			0.132947i
$255$		0			0
$256$	1.00000			0.0625000
$257$	6.07764	+	3.50893i	0.379113	+	0.218881i	0.677432	−	0.735585i	$-0.263093\pi$
$257$	6.07764	+	3.50893i	0.379113	+	0.218881i	−0.298319	+	0.954466i	$0.596426\pi$
$258$		0			0
$259$	−17.6333	−	1.12815i	−1.09568	−	0.0700998i
$260$	−7.45666	−	0.483811i	−0.462442	−	0.0300047i
$261$		0			0
$262$	−7.87875	+	13.6464i	−0.486751	+	0.843077i
$263$	−1.32494	−	2.29487i	−0.0816996	−	0.141508i	0.822281	−	0.569082i	$-0.192701\pi$
$263$	−1.32494	−	2.29487i	−0.0816996	−	0.141508i	−0.903980	+	0.427575i	$0.859368\pi$
$264$		0			0
$265$	5.82972	+	11.8019i	0.358117	+	0.724987i
$266$	−19.8190	−	1.26798i	−1.21518	−	0.0777451i
$267$		0			0
$268$		−	4.53308i		−	0.276902i
$269$	11.9338	−	20.6700i	0.727618	−	1.26027i	−0.230269	−	0.973127i	$-0.573961\pi$
$269$	11.9338	−	20.6700i	0.727618	−	1.26027i	0.957887	−	0.287145i	$-0.0927060\pi$
$270$		0			0
$271$	−16.9678	+	9.79635i	−1.03072	+	0.595086i	−0.917190	−	0.398449i	$-0.869549\pi$
$271$	−16.9678	+	9.79635i	−1.03072	+	0.595086i	−0.113528	+	0.993535i	$0.536215\pi$
$272$	4.20138	+	2.42567i	0.254746	+	0.147078i
$273$		0			0
$274$	−5.50358	−	9.53248i	−0.332483	−	0.575878i
$275$	2.96215	+	2.26676i	0.178624	+	0.136691i
$276$		0			0
$277$	−17.2708	+	9.97128i	−1.03770	+	0.599116i	−0.919181	−	0.393835i	$-0.871148\pi$
$277$	−17.2708	+	9.97128i	−1.03770	+	0.599116i	−0.118519	+	0.992952i	$0.537815\pi$
$278$	14.5065	−	8.37531i	0.870040	−	0.502318i
$279$		0			0
$280$	5.46071	−	2.27609i	0.326340	−	0.136023i
$281$	2.03902	+	1.17723i	0.121638	+	0.0702277i	0.559584	−	0.828773i	$-0.310961\pi$
$281$	2.03902	+	1.17723i	0.121638	+	0.0702277i	−0.437947	+	0.899001i	$0.644294\pi$
$282$		0			0
$283$	8.82966			0.524869			0.262434	−	0.964950i	$-0.415475\pi$
$283$	8.82966			0.524869			0.262434	+	0.964950i	$0.415475\pi$
$284$		−	4.17217i		−	0.247573i
$285$		0			0
$286$	2.15891	+	1.24645i	0.127659	+	0.0737041i
$287$	0.287103	−	4.48751i	0.0169472	−	0.264889i
$288$		0			0
$289$	3.26772	+	5.65986i	0.192219	+	0.332933i
$290$	1.49095	−	0.736472i	0.0875513	−	0.0432471i
$291$		0			0
$292$	−5.10736	+	8.84620i	−0.298886	+	0.517685i
$293$	8.74058	−	5.04638i	0.510630	−	0.294812i	−0.222463	−	0.974941i	$-0.571410\pi$
$293$	8.74058	−	5.04638i	0.510630	−	0.294812i	0.733093	+	0.680129i	$0.238076\pi$
$294$		0			0
$295$	−5.78731	+	8.67366i	−0.336950	+	0.505000i
$296$	5.78366	−	3.33920i	0.336168	−	0.194087i
$297$		0			0
$298$	18.6650	+	10.7762i	1.08123	+	0.624250i
$299$	6.23906			0.360814
$300$		0			0
$301$	10.3565	+	20.9187i	0.596940	+	1.20573i
$302$	−7.68913	−	13.3180i	−0.442460	−	0.766363i
$303$		0			0
$304$	6.50055	−	3.75309i	0.372832	−	0.215255i
$305$	−3.18542	−	2.12540i	−0.182397	−	0.121700i
$306$		0			0
$307$	−10.7285			−0.612306			−0.306153	−	0.951982i	$-0.599042\pi$
$307$	−10.7285			−0.612306			−0.306153	+	0.951982i	$0.599042\pi$
$308$	−1.96968	−	0.126017i	−0.112233	−	0.00718046i
$309$		0			0
$310$	−9.30292	−	6.20717i	−0.528370	−	0.352543i
$311$	4.99022			0.282969			0.141485	−	0.989940i	$-0.454812\pi$
$311$	4.99022			0.282969			0.141485	+	0.989940i	$0.454812\pi$
$312$		0			0
$313$	−20.1068			−1.13651			−0.568253	−	0.822854i	$-0.692380\pi$
$313$	−20.1068			−1.13651			−0.568253	+	0.822854i	$0.692380\pi$
$314$	−7.04317			−0.397469
$315$		0			0
$316$	−6.21613			−0.349685
$317$	−26.0102			−1.46088			−0.730440	−	0.682977i	$-0.760685\pi$
$317$	−26.0102			−1.46088			−0.730440	+	0.682977i	$0.760685\pi$
$318$		0			0
$319$	−0.554779			−0.0310616
$320$	−1.24107	+	1.86004i	−0.0693779	+	0.103979i
$321$		0			0
$322$	−4.42683	+	2.19166i	−0.246698	+	0.122136i
$323$	36.4150			2.02619
$324$		0			0
$325$	10.1541	−	13.2692i	0.563251	−	0.736045i
$326$	−6.38815	+	3.68820i	−0.353807	+	0.204271i
$327$		0			0
$328$	0.849794	+	1.47189i	0.0469220	+	0.0812713i
$329$	−17.0255	+	25.5667i	−0.938648	+	1.40954i
$330$		0			0
$331$	13.3980			0.736418			0.368209	−	0.929743i	$-0.379971\pi$
$331$	13.3980			0.736418			0.368209	+	0.929743i	$0.379971\pi$
$332$	2.26849	+	1.30971i	0.124500	+	0.0718798i
$333$		0			0
$334$	14.6090	−	8.43452i	0.799370	−	0.461516i
$335$	8.43171	+	5.62587i	0.460673	+	0.307374i
$336$		0			0
$337$	−7.18391	+	4.14763i	−0.391333	+	0.225936i	−0.682737	−	0.730664i	$-0.739211\pi$
$337$	−7.18391	+	4.14763i	−0.391333	+	0.225936i	0.291405	+	0.956600i	$0.405877\pi$
$338$	−0.916415	+	1.58728i	−0.0498464	+	0.0863366i
$339$		0			0
$340$	−9.72604	+	4.80431i	−0.527469	+	0.260550i
$341$	1.86552	+	3.23118i	0.101024	+	0.174978i
$342$		0			0
$343$	−3.52815	+	18.1811i	−0.190502	+	0.981687i
$344$	−7.64047	−	4.41123i	−0.411946	−	0.237837i
$345$		0			0
$346$			10.2449i			0.550769i
$347$	−16.4408			−0.882591			−0.441295	−	0.897362i	$-0.645481\pi$
$347$	−16.4408			−0.882591			−0.441295	+	0.897362i	$0.645481\pi$
$348$		0			0
$349$	−26.2420	−	15.1508i	−1.40470	−	0.811004i	−0.409830	−	0.912162i	$-0.634412\pi$
$349$	−26.2420	−	15.1508i	−1.40470	−	0.811004i	−0.994870	+	0.101158i	$0.967745\pi$
$350$	−2.54351	+	12.9819i	−0.135956	+	0.693913i
$351$		0			0
$352$	0.646046	−	0.372995i	0.0344344	−	0.0198807i
$353$	10.7919	−	6.23074i	0.574398	−	0.331629i	−0.184506	−	0.982831i	$-0.559069\pi$
$353$	10.7919	−	6.23074i	0.574398	−	0.331629i	0.758904	+	0.651203i	$0.225735\pi$
$354$		0			0
$355$	7.76040	+	5.17796i	0.411879	+	0.274817i
$356$	−7.58595	−	13.1393i	−0.402055	−	0.696379i
$357$		0			0
$358$	−16.4577	−	9.50188i	−0.869818	−	0.502190i
$359$	−1.01914	+	0.588399i	−0.0537880	+	0.0310545i	−0.526653	−	0.850080i	$-0.676553\pi$
$359$	−1.01914	+	0.588399i	−0.0537880	+	0.0310545i	0.472865	+	0.881135i	$0.343220\pi$
$360$		0			0
$361$	18.6714	−	32.3398i	0.982705	−	1.70210i
$362$		−	5.53416i		−	0.290869i
$363$		0			0
$364$	−0.564503	+	8.82335i	−0.0295880	+	0.462469i
$365$	−10.1157	−	20.4786i	−0.529480	−	1.07190i
$366$		0			0
$367$	−17.7200	−	30.6920i	−0.924978	−	1.60211i	−0.791596	−	0.611045i	$-0.790749\pi$
$367$	−17.7200	−	30.6920i	−0.924978	−	1.60211i	−0.133383	−	0.991065i	$-0.542584\pi$
$368$	0.933507	−	1.61688i	0.0486624	−	0.0842858i
$369$		0			0
$370$	−0.966888	+	14.9020i	−0.0502661	+	0.774718i
$371$	13.9580	−	6.91040i	0.724664	−	0.358770i
$372$		0			0
$373$	−21.9698	−	12.6843i	−1.13755	−	0.656767i	−0.191730	−	0.981448i	$-0.561410\pi$
$373$	−21.9698	−	12.6843i	−1.13755	−	0.656767i	−0.945824	+	0.324680i	$0.894743\pi$
$374$	3.61905			0.187136
$375$		0			0
$376$		−	11.6099i		−	0.598734i
$377$			2.48518i			0.127993i
$378$		0			0
$379$	24.3494			1.25075			0.625373	−	0.780326i	$-0.284947\pi$
$379$	24.3494			1.25075			0.625373	+	0.780326i	$0.284947\pi$
$380$	−1.08673	+	16.7491i	−0.0557483	+	0.859212i
$381$		0			0
$382$		−	20.0241i		−	1.02452i
$383$	11.3669	+	6.56268i	0.580821	+	0.335337i	0.761460	−	0.648212i	$-0.224483\pi$
$383$	11.3669	+	6.56268i	0.580821	+	0.335337i	−0.180639	+	0.983550i	$0.557816\pi$
$384$		0			0
$385$	2.67890	−	3.50728i	0.136530	−	0.178748i
$386$		−	19.0139i		−	0.967784i
$387$		0			0
$388$	2.32004	−	4.01843i	0.117782	−	0.204005i
$389$	−16.7387	+	9.66411i	−0.848688	+	0.489990i	−0.860208	−	0.509944i	$-0.829666\pi$
$389$	−16.7387	+	9.66411i	−0.848688	+	0.489990i	0.0115202	+	0.999934i	$0.496333\pi$
$390$		0			0
$391$	7.84404	−	4.52876i	0.396690	−	0.229029i
$392$	−2.69893	−	6.45877i	−0.136317	−	0.326217i
$393$		0			0
$394$	−6.94184			−0.349725
$395$	7.71465	−	11.5622i	0.388166	−	0.581760i
$396$		0			0
$397$	−18.0143	−	31.2016i	−0.904111	−	1.56597i	−0.822107	−	0.569334i	$-0.807201\pi$
$397$	−18.0143	−	31.2016i	−0.904111	−	1.56597i	−0.0820040	−	0.996632i	$-0.526132\pi$
$398$	3.90645	+	2.25539i	0.195812	+	0.113052i
$399$		0			0
$400$	−1.91949	−	4.61688i	−0.0959745	−	0.230844i
$401$	2.72857	+	1.57534i	0.136258	+	0.0786688i	0.566580	−	0.824007i	$-0.308266\pi$
$401$	2.72857	+	1.57534i	0.136258	+	0.0786688i	−0.430321	+	0.902676i	$0.641600\pi$
$402$		0			0
$403$	14.4744	−	8.35677i	0.721019	−	0.416281i
$404$	5.48710	+	9.50393i	0.272993	+	0.472838i
$405$		0			0
$406$	−0.872995	−	1.76332i	−0.0433260	−	0.0875123i
$407$	2.49101	−	4.31455i	0.123475	−	0.213864i
$408$		0			0
$409$		−	15.9469i		−	0.788525i	−0.918998	−	0.394262i	$-0.871000\pi$
$409$		−	15.9469i		−	0.788525i	0.918998	−	0.394262i	$-0.129000\pi$
$410$	−3.79242	−	0.246064i	−0.187294	−	0.0121522i
$411$		0			0
$412$	−3.33713	+	5.78008i	−0.164409	+	0.284764i
$413$	10.2690	+	6.83838i	0.505303	+	0.336495i
$414$		0			0
$415$	−5.25147	+	2.59403i	−0.257785	+	0.127336i
$416$	−1.67087	−	2.89402i	−0.0819209	−	0.141891i
$417$		0			0
$418$	2.79977	−	4.84934i	0.136941	−	0.237189i
$419$	−17.4629	−	30.2467i	−0.853120	−	1.47765i	−0.878378	−	0.477966i	$-0.841374\pi$
$419$	−17.4629	−	30.2467i	−0.853120	−	1.47765i	0.0252584	−	0.999681i	$-0.491959\pi$
$420$		0			0
$421$	18.6679	−	32.3338i	0.909818	−	1.57585i	0.0955030	−	0.995429i	$-0.469554\pi$
$421$	18.6679	−	32.3338i	0.909818	−	1.57585i	0.814315	−	0.580423i	$-0.197113\pi$
$422$	−3.92397	−	6.79652i	−0.191016	−	0.330849i
$423$		0			0
$424$	−2.94339	+	5.09811i	−0.142944	+	0.247586i
$425$	3.13450	−	24.0533i	0.152046	−	1.16676i
$426$		0			0
$427$	−2.51141	+	3.77131i	−0.121536	+	0.182506i
$428$	−6.82770	−	11.8259i	−0.330029	−	0.571627i
$429$		0			0
$430$	17.6874	−	8.73693i	0.852963	−	0.421332i
$431$	7.75117	+	4.47514i	0.373361	+	0.215560i	0.674926	−	0.737886i	$-0.264176\pi$
$431$	7.75117	+	4.47514i	0.373361	+	0.215560i	−0.301565	+	0.953446i	$0.597509\pi$
$432$		0			0
$433$	12.0060			0.576972			0.288486	−	0.957484i	$-0.406848\pi$
$433$	12.0060			0.576972			0.288486	+	0.957484i	$0.406848\pi$
$434$	−7.33450	+	11.0140i	−0.352067	+	0.528688i
$435$		0			0
$436$	−5.13894	+	8.90090i	−0.246110	+	0.426276i
$437$		−	14.0142i		−	0.670388i
$438$		0			0
$439$			32.7739i			1.56422i	0.623144	+	0.782108i	$0.285855\pi$
$439$			32.7739i			1.56422i	−0.623144	+	0.782108i	$0.714145\pi$
$440$	−0.108003	+	1.66458i	−0.00514886	+	0.0793559i
$441$		0			0
$442$		−	16.2119i		−	0.771119i
$443$	6.10539			0.290076			0.145038	−	0.989426i	$-0.453670\pi$
$443$	6.10539			0.290076			0.145038	+	0.989426i	$0.453670\pi$
$444$		0			0
$445$	33.8542	+	2.19657i	1.60484	+	0.104127i
$446$	−10.7610	+	18.6387i	−0.509550	+	0.882566i
$447$		0			0
$448$	2.20215	+	1.46647i	0.104042	+	0.0692842i
$449$		−	4.39667i		−	0.207492i	−0.994604	−	0.103746i	$-0.966917\pi$
$449$		−	4.39667i		−	0.207492i	0.994604	−	0.103746i	$-0.0330828\pi$
$450$		0			0
$451$	1.09801	+	0.633938i	0.0517034	+	0.0298510i
$452$	10.0641	+	17.4316i	0.473377	+	0.819913i
$453$		0			0
$454$	−6.95237	+	4.01395i	−0.326291	+	0.188384i
$455$	−15.7112	−	12.0004i	−0.736552	−	0.562587i
$456$		0			0
$457$		−	33.2534i		−	1.55553i	−0.628555	−	0.777765i	$-0.716353\pi$
$457$		−	33.2534i		−	1.55553i	0.628555	−	0.777765i	$-0.283647\pi$
$458$	16.6860	+	9.63368i	0.779687	+	0.450152i
$459$		0			0
$460$	1.84892	+	3.74302i	0.0862062	+	0.174519i
$461$	−6.22235	+	10.7774i	−0.289804	+	0.501955i	−0.973763	−	0.227566i	$-0.926923\pi$
$461$	−6.22235	+	10.7774i	−0.289804	+	0.501955i	0.683959	+	0.729520i	$0.260257\pi$
$462$		0			0
$463$	−2.79388	+	1.61305i	−0.129843	+	0.0749647i	−0.563514	−	0.826106i	$-0.690551\pi$
$463$	−2.79388	+	1.61305i	−0.129843	+	0.0749647i	0.433672	+	0.901071i	$0.357218\pi$
$464$	0.644047	+	0.371841i	0.0298991	+	0.0172623i
$465$		0			0
$466$	0.572350	+	0.991339i	0.0265136	+	0.0459229i
$467$	−36.0480	+	20.8123i	−1.66810	+	0.963080i	−0.699443	+	0.714688i	$0.746569\pi$
$467$	−36.0480	+	20.8123i	−1.66810	+	0.963080i	−0.968660	+	0.248392i	$0.920098\pi$
$468$		0			0
$469$	6.64763	−	9.98253i	0.306959	−	0.460950i
$470$	21.5948	+	14.4087i	0.996095	+	0.664622i
$471$		0			0
$472$	−4.66316			−0.214639
$473$	−6.58146			−0.302616
$474$		0			0
$475$	−29.8053	−	22.8082i	−1.36756	−	1.04651i
$476$	5.69490	+	11.5029i	0.261025	+	0.527234i
$477$		0			0
$478$	10.1997	−	5.88880i	0.466523	−	0.269347i
$479$	11.5051	+	19.9275i	0.525683	+	0.910509i	0.999552	+	0.0299141i	$0.00952336\pi$
$479$	11.5051	+	19.9275i	0.525683	+	0.910509i	−0.473870	+	0.880595i	$0.657143\pi$
$480$		0			0
$481$	−19.3274	−	11.1587i	−0.881255	−	0.508793i
$482$	−19.9120	+	11.4962i	−0.906967	+	0.523638i
$483$		0			0
$484$	−5.22175	+	9.04434i	−0.237352	+	0.411106i
$485$	4.59510	+	9.30252i	0.208653	+	0.422406i
$486$		0			0
$487$	−9.17108	−	5.29492i	−0.415581	−	0.239936i	0.277604	−	0.960696i	$-0.410460\pi$
$487$	−9.17108	−	5.29492i	−0.415581	−	0.239936i	−0.693185	+	0.720760i	$0.743793\pi$
$488$		−	1.71256i		−	0.0775238i
$489$		0			0
$490$	15.3631	+	2.99567i	0.694036	+	0.135331i
$491$	−2.99490	+	1.72911i	−0.135158	+	0.0780336i	−0.566054	−	0.824368i	$-0.691531\pi$
$491$	−2.99490	+	1.72911i	−0.135158	+	0.0780336i	0.430896	+	0.902401i	$0.358197\pi$
$492$		0			0
$493$	1.80392	+	3.12449i	0.0812446	+	0.140720i
$494$	−21.7231	−	12.5418i	−0.977368	−	0.564283i
$495$		0			0
$496$		−	5.00146i		−	0.224572i
$497$	6.11836	−	9.18775i	0.274446	−	0.412127i
$498$		0			0
$499$	7.23460	−	12.5307i	0.323865	−	0.560951i	−0.657417	−	0.753527i	$-0.728351\pi$
$499$	7.23460	−	12.5307i	0.323865	−	0.560951i	0.981282	+	0.192576i	$0.0616843\pi$
$500$	10.9698	+	2.15954i	0.490584	+	0.0965776i
$501$		0			0
$502$	1.44964			0.0647004
$503$		−	33.2244i		−	1.48140i	−0.671833	−	0.740702i	$-0.734493\pi$
$503$		−	33.2244i		−	1.48140i	0.671833	−	0.740702i	$-0.265507\pi$
$504$		0			0
$505$	−24.4876	−	1.58883i	−1.08968	−	0.0707019i
$506$		−	1.39277i		−	0.0619164i
$507$		0			0
$508$		−	2.11883i		−	0.0940077i
$509$	20.9146	−	36.2251i	0.927023	−	1.60565i	0.138748	−	0.990328i	$-0.455692\pi$
$509$	20.9146	−	36.2251i	0.927023	−	1.60565i	0.788275	−	0.615323i	$-0.210974\pi$
$510$		0			0
$511$	−24.2199	+	11.9909i	−1.07142	+	0.530445i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−6.07764	−	3.50893i	−0.268073	−	0.154772i
$515$	−6.60956	−	13.3807i	−0.291252	−	0.589623i
$516$		0			0
$517$	−4.33043	−	7.50052i	−0.190452	−	0.329872i
$518$	17.6333	+	1.12815i	0.774763	+	0.0495680i
$519$		0			0
$520$	7.45666	+	0.483811i	0.326996	+	0.0212165i
$521$	11.1096	−	19.2425i	0.486722	−	0.843027i	−0.513161	−	0.858292i	$-0.671526\pi$
$521$	11.1096	−	19.2425i	0.486722	−	0.843027i	0.999883	+	0.0152648i	$0.00485914\pi$
$522$		0			0
$523$	15.3867	+	26.6505i	0.672813	+	1.16535i	0.977103	+	0.212766i	$0.0682473\pi$
$523$	15.3867	+	26.6505i	0.672813	+	1.16535i	−0.304291	+	0.952579i	$0.598419\pi$
$524$	7.87875	−	13.6464i	0.344185	−	0.596146i
$525$		0			0
$526$	1.32494	+	2.29487i	0.0577703	+	0.100061i
$527$	12.1319	−	21.0130i	0.528473	−	0.915343i
$528$		0			0
$529$	9.75713	+	16.8998i	0.424223	+	0.734776i
$530$	−5.82972	−	11.8019i	−0.253227	−	0.512643i
$531$		0			0
$532$	19.8190	+	1.26798i	0.859262	+	0.0549741i
$533$	2.83978	−	4.91865i	0.123005	−	0.213050i
$534$		0			0
$535$	30.4703	+	1.97701i	1.31735	+	0.0854735i
$536$			4.53308i			0.195799i
$537$		0			0
$538$	−11.9338	+	20.6700i	−0.514504	+	0.891147i
$539$	−4.15272	−	3.16598i	−0.178871	−	0.136368i
$540$		0			0
$541$	2.61686	+	4.53253i	0.112508	+	0.194869i	0.916781	−	0.399391i	$-0.130778\pi$
$541$	2.61686	+	4.53253i	0.112508	+	0.194869i	−0.804273	+	0.594260i	$0.797445\pi$
$542$	16.9678	−	9.79635i	0.728828	−	0.420789i
$543$		0			0
$544$	−4.20138	−	2.42567i	−0.180133	−	0.104000i
$545$	−10.1782	−	20.6053i	−0.435988	−	0.882632i
$546$		0			0
$547$	−3.57961	−	2.06669i	−0.153053	−	0.0883652i	0.421518	−	0.906820i	$-0.361498\pi$
$547$	−3.57961	−	2.06669i	−0.153053	−	0.0883652i	−0.574571	+	0.818455i	$0.694831\pi$
$548$	5.50358	+	9.53248i	0.235101	+	0.407207i
$549$		0			0
$550$	−2.96215	−	2.26676i	−0.126307	−	0.0966548i
$551$	5.58221			0.237810
$552$		0			0
$553$	−13.6889	−	9.11577i	−0.582109	−	0.387642i
$554$	17.2708	−	9.97128i	0.733765	−	0.423639i
$555$		0			0
$556$	−14.5065	+	8.37531i	−0.615211	+	0.355192i
$557$	6.66281	−	11.5403i	0.282312	−	0.488979i	−0.689642	−	0.724151i	$-0.742232\pi$
$557$	6.66281	−	11.5403i	0.282312	−	0.488979i	0.971954	+	0.235172i	$0.0755652\pi$
$558$		0			0
$559$			29.4823i			1.24697i
$560$	−5.46071	+	2.27609i	−0.230757	+	0.0961825i
$561$		0			0
$562$	−2.03902	−	1.17723i	−0.0860110	−	0.0496585i
$563$		−	9.39051i		−	0.395763i	−0.980226	−	0.197881i	$-0.936594\pi$
$563$		−	9.39051i		−	0.395763i	0.980226	−	0.197881i	$-0.0634061\pi$
$564$		0			0
$565$	−44.9137	−	2.91414i	−1.88953	−	0.122599i
$566$	−8.82966			−0.371138
$567$		0			0
$568$			4.17217i			0.175060i
$569$		−	34.6834i		−	1.45400i	−0.686635	−	0.727002i	$-0.740913\pi$
$569$		−	34.6834i		−	1.45400i	0.686635	−	0.727002i	$-0.259087\pi$
$570$		0			0
$571$	11.4946			0.481034			0.240517	−	0.970645i	$-0.422683\pi$
$571$	11.4946			0.481034			0.240517	+	0.970645i	$0.422683\pi$
$572$	−2.15891	−	1.24645i	−0.0902687	−	0.0521167i
$573$		0			0
$574$	−0.287103	+	4.48751i	−0.0119835	+	0.187305i
$575$	−9.25680	−	1.20630i	−0.386035	−	0.0503061i
$576$		0			0
$577$	8.61149	−	14.9155i	0.358501	−	0.620942i	−0.629209	−	0.777236i	$-0.716621\pi$
$577$	8.61149	−	14.9155i	0.358501	−	0.620942i	0.987711	+	0.156293i	$0.0499546\pi$
$578$	−3.26772	−	5.65986i	−0.135919	−	0.235419i
$579$		0			0
$580$	−1.49095	+	0.736472i	−0.0619081	+	0.0305803i
$581$	3.07490	+	6.21086i	0.127568	+	0.257670i
$582$		0			0
$583$			4.39148i			0.181877i
$584$	5.10736	−	8.84620i	0.211344	−	0.366059i
$585$		0			0
$586$	−8.74058	+	5.04638i	−0.361070	+	0.208464i
$587$	18.3983	+	10.6223i	0.759380	+	0.438428i	0.829073	−	0.559140i	$-0.188869\pi$
$587$	18.3983	+	10.6223i	0.759380	+	0.438428i	−0.0696932	+	0.997568i	$0.522202\pi$
$588$		0			0
$589$	−18.7710	−	32.5122i	−0.773444	−	1.33964i
$590$	5.78731	−	8.67366i	0.238260	−	0.357089i
$591$		0			0
$592$	−5.78366	+	3.33920i	−0.237707	+	0.137240i
$593$	−5.35047	+	3.08910i	−0.219718	+	0.126854i	−0.605819	−	0.795602i	$-0.707155\pi$
$593$	−5.35047	+	3.08910i	−0.219718	+	0.126854i	0.386102	+	0.922456i	$0.373821\pi$
$594$		0			0
$595$	−28.4636	−	3.68315i	−1.16689	−	0.150994i
$596$	−18.6650	−	10.7762i	−0.764547	−	0.441412i
$597$		0			0
$598$	−6.23906			−0.255134
$599$			20.2605i			0.827821i	0.910318	+	0.413911i	$0.135837\pi$
$599$			20.2605i			0.827821i	−0.910318	+	0.413911i	$0.864163\pi$
$600$		0			0
$601$	−1.81095	−	1.04555i	−0.0738700	−	0.0426489i	0.462610	−	0.886562i	$-0.346913\pi$
$601$	−1.81095	−	1.04555i	−0.0738700	−	0.0426489i	−0.536480	+	0.843913i	$0.680246\pi$
$602$	−10.3565	−	20.9187i	−0.422100	−	0.852583i
$603$		0			0
$604$	7.68913	+	13.3180i	0.312866	+	0.541900i
$605$	−10.3423	−	20.9373i	−0.420473	−	0.851223i
$606$		0			0
$607$	6.73968	−	11.6735i	0.273555	−	0.473812i	−0.696214	−	0.717834i	$-0.745134\pi$
$607$	6.73968	−	11.6735i	0.273555	−	0.473812i	0.969770	+	0.244022i	$0.0784670\pi$
$608$	−6.50055	+	3.75309i	−0.263632	+	0.152208i
$609$		0			0
$610$	3.18542	+	2.12540i	0.128974	+	0.0860551i
$611$	−33.5993	+	19.3985i	−1.35928	+	0.784781i
$612$		0			0
$613$	9.41875	+	5.43792i	0.380420	+	0.219636i	0.678001	−	0.735061i	$-0.262847\pi$
$613$	9.41875	+	5.43792i	0.380420	+	0.219636i	−0.297581	+	0.954697i	$0.596180\pi$
$614$	10.7285			0.432965
$615$		0			0
$616$	1.96968	+	0.126017i	0.0793605	+	0.00507735i
$617$	0.714583	+	1.23769i	0.0287680	+	0.0498277i	0.880051	−	0.474879i	$-0.157508\pi$
$617$	0.714583	+	1.23769i	0.0287680	+	0.0498277i	−0.851283	+	0.524707i	$0.824175\pi$
$618$		0			0
$619$	−19.3002	+	11.1430i	−0.775739	+	0.447873i	−0.834918	−	0.550374i	$-0.814485\pi$
$619$	−19.3002	+	11.1430i	−0.775739	+	0.447873i	0.0591788	+	0.998247i	$0.481152\pi$
$620$	9.30292	+	6.20717i	0.373614	+	0.249286i
$621$		0			0
$622$	−4.99022			−0.200089
$623$	2.56292	−	40.0592i	0.102681	−	1.60494i
$624$		0			0
$625$	−17.6311	+	17.7241i	−0.705244	+	0.708964i
$626$	20.1068			0.803631
$627$		0			0
$628$	7.04317			0.281053
$629$	−32.3991			−1.29184
$630$		0			0
$631$	13.9478			0.555255			0.277627	−	0.960689i	$-0.410452\pi$
$631$	13.9478			0.555255			0.277627	+	0.960689i	$0.410452\pi$
$632$	6.21613			0.247264
$633$		0			0
$634$	26.0102			1.03300
$635$	3.94110	+	2.62961i	0.156398	+	0.104353i
$636$		0			0
$637$	−14.1823	+	18.6025i	−0.561923	+	0.737059i
$638$	0.554779			0.0219639
$639$		0			0
$640$	1.24107	−	1.86004i	0.0490576	−	0.0735245i
$641$	−7.54412	+	4.35560i	−0.297975	+	0.172036i	−0.641533	−	0.767096i	$-0.721701\pi$
$641$	−7.54412	+	4.35560i	−0.297975	+	0.172036i	0.343558	+	0.939132i	$0.388368\pi$
$642$		0			0
$643$	21.6235	+	37.4529i	0.852746	+	1.47700i	0.878720	+	0.477337i	$0.158398\pi$
$643$	21.6235	+	37.4529i	0.852746	+	1.47700i	−0.0259739	+	0.999663i	$0.508269\pi$
$644$	4.42683	−	2.19166i	0.174442	−	0.0863634i
$645$		0			0
$646$	−36.4150			−1.43273
$647$	31.0729	+	17.9400i	1.22160	+	0.705293i	0.965260	−	0.261293i	$-0.0841487\pi$
$647$	31.0729	+	17.9400i	1.22160	+	0.705293i	0.256344	+	0.966586i	$0.417482\pi$
$648$		0			0
$649$	−3.01262	+	1.73933i	−0.118256	+	0.0682748i
$650$	−10.1541	+	13.2692i	−0.398278	+	0.520462i
$651$		0			0
$652$	6.38815	−	3.68820i	0.250179	−	0.144441i
$653$	1.94271	−	3.36488i	0.0760243	−	0.131678i	−0.825507	−	0.564392i	$-0.809111\pi$
$653$	1.94271	−	3.36488i	0.0760243	−	0.131678i	0.901531	+	0.432714i	$0.142444\pi$
$654$		0			0
$655$	15.6047	+	31.5909i	0.609728	+	1.23436i
$656$	−0.849794	−	1.47189i	−0.0331789	−	0.0574675i
$657$		0			0
$658$	17.0255	−	25.5667i	0.663725	−	0.996693i
$659$	12.1007	+	6.98632i	0.471375	+	0.272149i	0.716815	−	0.697263i	$-0.245599\pi$
$659$	12.1007	+	6.98632i	0.471375	+	0.272149i	−0.245440	+	0.969412i	$0.578932\pi$
$660$		0			0
$661$		−	44.7175i		−	1.73931i	−0.493662	−	0.869654i	$-0.664342\pi$
$661$		−	44.7175i		−	1.73931i	0.493662	−	0.869654i	$-0.335658\pi$
$662$	−13.3980			−0.520726
$663$		0			0
$664$	−2.26849	−	1.30971i	−0.0880345	−	0.0508267i
$665$	−26.9552	+	35.2904i	−1.04528	+	1.36850i
$666$		0			0
$667$	1.20244	−	0.694232i	0.0465589	−	0.0268808i
$668$	−14.6090	+	8.43452i	−0.565240	+	0.326341i
$669$		0			0
$670$	−8.43171	−	5.62587i	−0.325745	−	0.217346i
$671$	−0.638775	−	1.10639i	−0.0246596	−	0.0427118i
$672$		0			0
$673$	32.2357	+	18.6113i	1.24259	+	0.717412i	0.969622	−	0.244610i	$-0.0786598\pi$
$673$	32.2357	+	18.6113i	1.24259	+	0.717412i	0.272973	+	0.962022i	$0.411993\pi$
$674$	7.18391	−	4.14763i	0.276714	−	0.159761i
$675$		0			0
$676$	0.916415	−	1.58728i	0.0352467	−	0.0610492i
$677$			12.5830i			0.483605i	0.970325	+	0.241803i	$0.0777386\pi$
$677$			12.5830i			0.483605i	−0.970325	+	0.241803i	$0.922261\pi$
$678$		0			0
$679$	11.0020	−	5.44692i	0.422218	−	0.209033i
$680$	9.72604	−	4.80431i	0.372977	−	0.184237i
$681$		0			0
$682$	−1.86552	−	3.23118i	−0.0714345	−	0.123728i
$683$	8.98544	−	15.5632i	0.343818	−	0.595511i	−0.641320	−	0.767274i	$-0.721613\pi$
$683$	8.98544	−	15.5632i	0.343818	−	0.595511i	0.985138	+	0.171763i	$0.0549462\pi$
$684$		0			0
$685$	−24.5611	−	1.59360i	−0.938432	−	0.0608884i
$686$	3.52815	−	18.1811i	0.134705	−	0.694157i
$687$		0			0
$688$	7.64047	+	4.41123i	0.291290	+	0.168176i
$689$	19.6721			0.749446
$690$		0			0
$691$		−	44.2400i		−	1.68297i	−0.540280	−	0.841485i	$-0.681682\pi$
$691$		−	44.2400i		−	1.68297i	0.540280	−	0.841485i	$-0.318318\pi$
$692$		−	10.2449i		−	0.389453i
$693$		0			0
$694$	16.4408			0.624086
$695$	2.42513	−	37.3769i	0.0919905	−	1.41779i
$696$		0			0
$697$		−	8.24527i		−	0.312312i
$698$	26.2420	+	15.1508i	0.993273	+	0.573466i
$699$		0			0
$700$	2.54351	−	12.9819i	0.0961355	−	0.490671i
$701$		−	29.6654i		−	1.12045i	−0.828342	−	0.560223i	$-0.810716\pi$
$701$		−	29.6654i		−	1.12045i	0.828342	−	0.560223i	$-0.189284\pi$
$702$		0			0
$703$	−25.0646	+	43.4132i	−0.945330	+	1.63736i
$704$	−0.646046	+	0.372995i	−0.0243488	+	0.0140578i
$705$		0			0
$706$	−10.7919	+	6.23074i	−0.406160	+	0.234497i
$707$	−1.85382	+	28.9757i	−0.0697200	+	1.08974i
$708$		0			0
$709$	36.7363			1.37966			0.689831	−	0.723971i	$-0.257685\pi$
$709$	36.7363			1.37966			0.689831	+	0.723971i	$0.257685\pi$
$710$	−7.76040	−	5.17796i	−0.291243	−	0.194325i
$711$		0			0
$712$	7.58595	+	13.1393i	0.284296	+	0.492414i
$713$	−8.08678	−	4.66890i	−0.302852	−	0.174852i
$714$		0			0
$715$	4.99781	−	2.46873i	0.186907	−	0.0923253i
$716$	16.4577	+	9.50188i	0.615054	+	0.355102i
$717$		0			0
$718$	1.01914	−	0.588399i	0.0380339	−	0.0219589i
$719$	15.0842	+	26.1266i	0.562546	+	0.974358i	0.997273	+	0.0737961i	$0.0235114\pi$
$719$	15.0842	+	26.1266i	0.562546	+	0.974358i	−0.434727	+	0.900562i	$0.643155\pi$
$720$		0			0
$721$	−15.8252	+	7.83480i	−0.589360	+	0.291783i
$722$	−18.6714	+	32.3398i	−0.694878	+	1.20356i
$723$		0			0
$724$			5.53416i			0.205676i
$725$	0.480501	−	3.68723i	0.0178453	−	0.136940i
$726$		0			0
$727$	−2.77440	+	4.80540i	−0.102897	+	0.178222i	−0.912877	−	0.408235i	$-0.866144\pi$
$727$	−2.77440	+	4.80540i	−0.102897	+	0.178222i	0.809980	+	0.586457i	$0.199478\pi$
$728$	0.564503	−	8.82335i	0.0209219	−	0.327015i
$729$		0			0
$730$	10.1157	+	20.4786i	0.374399	+	0.757949i
$731$	21.4003	+	37.0665i	0.791520	+	1.37095i
$732$		0			0
$733$	10.1357	−	17.5555i	0.374370	−	0.648428i	−0.615863	−	0.787854i	$-0.711192\pi$
$733$	10.1357	−	17.5555i	0.374370	−	0.648428i	0.990233	+	0.139426i	$0.0445257\pi$
$734$	17.7200	+	30.6920i	0.654059	+	1.13286i
$735$		0			0
$736$	−0.933507	+	1.61688i	−0.0344095	+	0.0595991i
$737$	1.69082	+	2.92858i	0.0622820	+	0.107876i
$738$		0			0
$739$	24.5774	−	42.5693i	0.904095	−	1.56594i	0.0819667	−	0.996635i	$-0.473880\pi$
$739$	24.5774	−	42.5693i	0.904095	−	1.56594i	0.822128	−	0.569303i	$-0.192787\pi$
$740$	0.966888	−	14.9020i	0.0355435	−	0.547809i
$741$		0			0
$742$	−13.9580	+	6.91040i	−0.512415	+	0.253689i
$743$	13.5537	+	23.4757i	0.497237	+	0.861240i	0.999995	−	0.00318755i	$-0.00101463\pi$
$743$	13.5537	+	23.4757i	0.497237	+	0.861240i	−0.502758	+	0.864427i	$0.667681\pi$
$744$		0			0
$745$	43.2088	−	21.3435i	1.58305	−	0.781967i
$746$	21.9698	+	12.6843i	0.804372	+	0.464405i
$747$		0			0
$748$	−3.61905			−0.132325
$749$	2.30674	−	36.0551i	0.0842865	−	1.31742i
$750$		0			0
$751$	−20.6403	+	35.7500i	−0.753174	+	1.30454i	0.193102	+	0.981179i	$0.438145\pi$
$751$	−20.6403	+	35.7500i	−0.753174	+	1.30454i	−0.946277	+	0.323358i	$0.895188\pi$
$752$			11.6099i			0.423369i
$753$		0			0
$754$		−	2.48518i		−	0.0905050i
$755$	−34.3147	−	2.22644i	−1.24884	−	0.0810285i
$756$		0			0
$757$			37.6630i			1.36888i	0.729067	+	0.684442i	$0.239954\pi$
$757$			37.6630i			1.36888i	−0.729067	+	0.684442i	$0.760046\pi$
$758$	−24.3494			−0.884411
$759$		0			0
$760$	1.08673	−	16.7491i	0.0394200	−	0.607554i
$761$	−10.0532	+	17.4126i	−0.364427	+	0.631207i	−0.988684	−	0.150013i	$-0.952069\pi$
$761$	−10.0532	+	17.4126i	−0.364427	+	0.631207i	0.624257	+	0.781219i	$0.285402\pi$
$762$		0			0
$763$	−24.3696	+	12.0650i	−0.882239	+	0.436783i
$764$			20.0241i			0.724447i
$765$		0			0
$766$	−11.3669	−	6.56268i	−0.410702	−	0.237119i
$767$	7.79151	+	13.4953i	0.281335	+	0.487287i
$768$		0			0
$769$	24.3791	−	14.0753i	0.879134	−	0.507568i	0.00876117	−	0.999962i	$-0.497211\pi$
$769$	24.3791	−	14.0753i	0.879134	−	0.507568i	0.870373	+	0.492393i	$0.163878\pi$
$770$	−2.67890	+	3.50728i	−0.0965409	+	0.126394i
$771$		0			0
$772$			19.0139i			0.684327i
$773$	−37.3009	−	21.5357i	−1.34162	−	0.774585i	−0.354576	−	0.935027i	$-0.615375\pi$
$773$	−37.3009	−	21.5357i	−1.34162	−	0.774585i	−0.987045	+	0.160442i	$0.948708\pi$
$774$		0			0
$775$	−23.0911	+	9.60026i	−0.829458	+	0.344852i
$776$	−2.32004	+	4.01843i	−0.0832846	+	0.144253i
$777$		0			0
$778$	16.7387	−	9.66411i	0.600113	−	0.346475i
$779$	−11.0483	−	6.37871i	−0.395845	−	0.228541i
$780$		0			0
$781$	1.55620	+	2.69541i	0.0556852	+	0.0964495i
$782$	−7.84404	+	4.52876i	−0.280502	+	0.161948i
$783$		0			0
$784$	2.69893	+	6.45877i	0.0963904	+	0.230671i
$785$	−8.74106	+	13.1006i	−0.311982	+	0.467579i
$786$		0			0
$787$	−35.3175			−1.25893			−0.629466	−	0.777028i	$-0.716726\pi$
$787$	−35.3175			−1.25893			−0.629466	+	0.777028i	$0.716726\pi$
$788$	6.94184			0.247293
$789$		0			0
$790$	−7.71465	+	11.5622i	−0.274475	+	0.411366i
$791$	−3.40017	+	53.1457i	−0.120896	+	1.88964i
$792$		0			0
$793$	−4.95618	+	2.86145i	−0.175999	+	0.101613i
$794$	18.0143	+	31.2016i	0.639303	+	1.10730i
$795$		0			0
$796$	−3.90645	−	2.25539i	−0.138460	−	0.0799401i
$797$	14.2561	−	8.23077i	0.504978	−	0.291549i	−0.225789	−	0.974176i	$-0.572496\pi$
$797$	14.2561	−	8.23077i	0.504978	−	0.291549i	0.730767	+	0.682627i	$0.239163\pi$
$798$		0			0
$799$	−28.1617	+	48.7775i	−0.996289	+	1.72562i
$800$	1.91949	+	4.61688i	0.0678642	+	0.163231i
$801$		0			0
$802$	−2.72857	−	1.57534i	−0.0963492	−	0.0556272i
$803$		−	7.62008i		−	0.268907i
$804$		0			0
$805$	−1.41744	+	10.9541i	−0.0499583	+	0.386081i
$806$	−14.4744	+	8.35677i	−0.509838	+	0.294355i
$807$		0			0
$808$	−5.48710	−	9.50393i	−0.193035	−	0.334347i
$809$	21.2722	+	12.2815i	0.747890	+	0.431795i	0.824931	−	0.565233i	$-0.191214\pi$
$809$	21.2722	+	12.2815i	0.747890	+	0.431795i	−0.0770407	+	0.997028i	$0.524547\pi$
$810$		0			0
$811$			7.28238i			0.255719i	0.991792	+	0.127860i	$0.0408107\pi$
$811$			7.28238i			0.255719i	−0.991792	+	0.127860i	$0.959189\pi$
$812$	0.872995	+	1.76332i	0.0306361	+	0.0618806i
$813$		0			0
$814$	−2.49101	+	4.31455i	−0.0873097	+	0.151225i
$815$	−1.06795	+	16.4595i	−0.0374085	+	0.576552i
$816$		0			0
$817$	66.2230			2.31685
$818$			15.9469i			0.557571i
$819$		0			0
$820$	3.79242	+	0.246064i	0.132437	+	0.00859293i
$821$		−	6.68610i		−	0.233346i	−0.993170	−	0.116673i	$-0.962777\pi$
$821$		−	6.68610i		−	0.233346i	0.993170	−	0.116673i	$-0.0372230\pi$
$822$		0			0
$823$			11.4060i			0.397589i	0.980041	+	0.198794i	$0.0637026\pi$
$823$			11.4060i			0.397589i	−0.980041	+	0.198794i	$0.936297\pi$
$824$	3.33713	−	5.78008i	0.116254	−	0.201359i
$825$		0			0
$826$	−10.2690	−	6.83838i	−0.357303	−	0.237938i
$827$	−9.16990			−0.318868			−0.159434	−	0.987209i	$-0.550967\pi$
$827$	−9.16990			−0.318868			−0.159434	+	0.987209i	$0.550967\pi$
$828$		0			0
$829$	13.6953	+	7.90700i	0.475659	+	0.274622i	0.718605	−	0.695418i	$-0.244781\pi$
$829$	13.6953	+	7.90700i	0.475659	+	0.274622i	−0.242947	+	0.970040i	$0.578114\pi$
$830$	5.25147	−	2.59403i	0.182281	−	0.0900402i
$831$		0			0
$832$	1.67087	+	2.89402i	0.0579268	+	0.100332i
$833$	−4.32761	+	33.6825i	−0.149943	+	1.16703i
$834$		0			0
$835$	2.44228	−	37.6412i	0.0845184	−	1.30263i
$836$	−2.79977	+	4.84934i	−0.0968320	+	0.167718i
$837$		0			0
$838$	17.4629	+	30.2467i	0.603247	+	1.04485i
$839$	14.0897	−	24.4040i	0.486429	−	0.842520i	−0.513449	−	0.858120i	$-0.671633\pi$
$839$	14.0897	−	24.4040i	0.486429	−	0.842520i	0.999878	+	0.0156002i	$0.00496589\pi$
$840$		0			0
$841$	−14.2235	−	24.6358i	−0.490464	−	0.849509i
$842$	−18.6679	+	32.3338i	−0.643339	+	1.11430i
$843$		0			0
$844$	3.92397	+	6.79652i	0.135069	+	0.233946i
$845$	1.81506	+	3.67449i	0.0624401	+	0.126406i
$846$		0			0
$847$	−24.7623	+	12.2594i	−0.850844	+	0.421240i
$848$	2.94339	−	5.09811i	0.101077	−	0.175070i
$849$		0			0
$850$	−3.13450	+	24.0533i	−0.107512	+	0.825021i
$851$			12.4687i			0.427420i
$852$		0			0
$853$	4.37925	−	7.58508i	0.149943	−	0.259708i	−0.781263	−	0.624201i	$-0.785424\pi$
$853$	4.37925	−	7.58508i	0.149943	−	0.259708i	0.931206	+	0.364493i	$0.118758\pi$
$854$	2.51141	−	3.77131i	0.0859388	−	0.129051i
$855$		0			0
$856$	6.82770	+	11.8259i	0.233366	+	0.404202i
$857$	−27.6321	+	15.9534i	−0.943894	+	0.544958i	−0.891179	−	0.453652i	$-0.850121\pi$
$857$	−27.6321	+	15.9534i	−0.943894	+	0.544958i	−0.0527153	+	0.998610i	$0.516788\pi$
$858$		0			0
$859$	39.6265	+	22.8784i	1.35204	+	0.780601i	0.988535	−	0.150992i	$-0.0482466\pi$
$859$	39.6265	+	22.8784i	1.35204	+	0.780601i	0.363505	+	0.931592i	$0.381580\pi$
$860$	−17.6874	+	8.73693i	−0.603136	+	0.297927i
$861$		0			0
$862$	−7.75117	−	4.47514i	−0.264006	−	0.152424i
$863$	21.5708	+	37.3618i	0.734280	+	1.27181i	0.955039	+	0.296481i	$0.0958132\pi$
$863$	21.5708	+	37.3618i	0.734280	+	1.27181i	−0.220759	+	0.975328i	$0.570853\pi$
$864$		0			0
$865$	19.0559	+	12.7146i	0.647921	+	0.432311i
$866$	−12.0060			−0.407981
$867$		0			0
$868$	7.33450	−	11.0140i	0.248949	−	0.373839i
$869$	4.01591	−	2.31859i	0.136230	−	0.0786526i
$870$		0			0
$871$	13.1188	−	7.57417i	0.444515	−	0.256641i
$872$	5.13894	−	8.90090i	0.174026	−	0.301422i
$873$		0			0
$874$			14.0142i			0.474036i
$875$	20.9902	+	20.8425i	0.709599	+	0.704605i
$876$		0			0
$877$	15.9331	+	9.19897i	0.538022	+	0.310627i	0.744277	−	0.667871i	$-0.232794\pi$
$877$	15.9331	+	9.19897i	0.538022	+	0.310627i	−0.206255	+	0.978498i	$0.566128\pi$
$878$		−	32.7739i		−	1.10607i
$879$		0			0
$880$	0.108003	−	1.66458i	0.00364079	−	0.0561131i
$881$	8.81308			0.296920			0.148460	−	0.988918i	$-0.452568\pi$
$881$	8.81308			0.296920			0.148460	+	0.988918i	$0.452568\pi$
$882$		0			0
$883$			2.02023i			0.0679863i	0.999422	+	0.0339931i	$0.0108224\pi$
$883$			2.02023i			0.0679863i	−0.999422	+	0.0339931i	$0.989178\pi$
$884$			16.2119i			0.545264i
$885$		0			0
$886$	−6.10539			−0.205115
$887$	−28.8147	−	16.6362i	−0.967504	−	0.558589i	−0.0690297	−	0.997615i	$-0.521990\pi$
$887$	−28.8147	−	16.6362i	−0.967504	−	0.558589i	−0.898474	+	0.439026i	$0.855324\pi$
$888$		0			0
$889$	3.10720	−	4.66597i	0.104212	−	0.156492i
$890$	−33.8542	−	2.19657i	−1.13480	−	0.0736291i
$891$		0			0
$892$	10.7610	−	18.6387i	0.360306	−	0.624068i
$893$	43.5729	+	75.4705i	1.45811	+	2.52553i
$894$		0			0
$895$	−38.0991	+	18.8195i	−1.27351	+	0.629068i
$896$	−2.20215	−	1.46647i	−0.0735687	−	0.0489913i
$897$		0			0
$898$			4.39667i			0.146719i
$899$	1.85975	−	3.22118i	0.0620261	−	0.107432i
$900$		0			0
$901$	24.7326	−	14.2794i	0.823963	−	0.475715i
$902$	−1.09801	−	0.633938i	−0.0365598	−	0.0211078i
$903$		0			0
$904$	−10.0641	−	17.4316i	−0.334728	−	0.579766i
$905$	−10.2938	−	6.86828i	−0.342176	−	0.228309i
$906$		0			0
$907$	9.65915	−	5.57672i	0.320727	−	0.185172i	−0.330990	−	0.943634i	$-0.607383\pi$
$907$	9.65915	−	5.57672i	0.320727	−	0.185172i	0.651717	+	0.758463i	$0.274049\pi$
$908$	6.95237	−	4.01395i	0.230722	−	0.133208i
$909$		0			0
$910$	15.7112	+	12.0004i	0.520821	+	0.397809i
$911$	−33.9893	−	19.6237i	−1.12612	−	0.650163i	−0.183160	−	0.983083i	$-0.558633\pi$
$911$	−33.9893	−	19.6237i	−1.12612	−	0.650163i	−0.942955	+	0.332920i	$0.891966\pi$
$912$		0			0
$913$	−1.95407			−0.0646701
$914$			33.2534i			1.09993i
$915$		0			0
$916$	−16.6860	−	9.63368i	−0.551322	−	0.318306i
$917$	37.3622	−	18.4975i	1.23381	−	0.610840i
$918$		0			0
$919$	−13.5598	−	23.4863i	−0.447298	−	0.774743i	0.550911	−	0.834564i	$-0.314280\pi$
$919$	−13.5598	−	23.4863i	−0.447298	−	0.774743i	−0.998209	+	0.0598209i	$0.980947\pi$
$920$	−1.84892	−	3.74302i	−0.0609570	−	0.123404i
$921$		0			0
$922$	6.22235	−	10.7774i	0.204922	−	0.354936i
$923$	12.0744	−	6.97114i	0.397432	−	0.229458i
$924$		0			0
$925$	26.5183	+	20.2929i	0.871918	+	0.667226i
$926$	2.79388	−	1.61305i	0.0918126	−	0.0530080i
$927$		0			0
$928$	−0.644047	−	0.371841i	−0.0211419	−	0.0122063i
$929$	−44.1075			−1.44712			−0.723559	−	0.690262i	$-0.757495\pi$
$929$	−44.1075			−1.44712			−0.723559	+	0.690262i	$0.757495\pi$
$930$		0			0
$931$	41.7849	+	31.8562i	1.36944	+	1.04405i
$932$	−0.572350	−	0.991339i	−0.0187479	−	0.0324724i
$933$		0			0
$934$	36.0480	−	20.8123i	1.17953	−	0.681000i
$935$	4.49149	−	6.73157i	0.146887	−	0.220146i
$936$		0			0
$937$	31.2098			1.01958			0.509789	−	0.860299i	$-0.329723\pi$
$937$	31.2098			1.01958			0.509789	+	0.860299i	$0.329723\pi$
$938$	−6.64763	+	9.98253i	−0.217053	+	0.325941i
$939$		0			0
$940$	−21.5948	−	14.4087i	−0.704345	−	0.469959i
$941$	−6.51025			−0.212228			−0.106114	−	0.994354i	$-0.533841\pi$
$941$	−6.51025			−0.212228			−0.106114	+	0.994354i	$0.533841\pi$
$942$		0			0
$943$	−3.17316			−0.103332
$944$	4.66316			0.151773
$945$		0			0
$946$	6.58146			0.213982
$947$	−33.4969			−1.08850			−0.544252	−	0.838922i	$-0.683186\pi$
$947$	−33.4969			−1.08850			−0.544252	+	0.838922i	$0.683186\pi$
$948$		0			0
$949$	−34.1348			−1.10806
$950$	29.8053	+	22.8082i	0.967012	+	0.739996i
$951$		0			0
$952$	−5.69490	−	11.5029i	−0.184573	−	0.372811i
$953$	−9.08698			−0.294356			−0.147178	−	0.989110i	$-0.547019\pi$
$953$	−9.08698			−0.294356			−0.147178	+	0.989110i	$0.547019\pi$
$954$		0			0
$955$	−37.2457	−	24.8513i	−1.20524	−	0.804171i
$956$	−10.1997	+	5.88880i	−0.329882	+	0.190457i
$957$		0			0
$958$	−11.5051	−	19.9275i	−0.371714	−	0.643827i
$959$	−1.85939	+	29.0628i	−0.0600427	+	0.938486i
$960$		0			0
$961$	5.98536			0.193076
$962$	19.3274	+	11.1587i	0.623141	+	0.359771i
$963$		0			0
$964$	19.9120	−	11.4962i	0.641323	−	0.370268i
$965$	−35.3667	−	23.5976i	−1.13849	−	0.759634i
$966$		0			0
$967$	0.584986	−	0.337742i	0.0188119	−	0.0108610i	−0.490565	−	0.871405i	$-0.663209\pi$
$967$	0.584986	−	0.337742i	0.0188119	−	0.0108610i	0.509376	+	0.860544i	$0.329876\pi$
$968$	5.22175	−	9.04434i	0.167833	−	0.290696i
$969$		0			0
$970$	−4.59510	−	9.30252i	−0.147540	−	0.298686i
$971$	3.90049	+	6.75585i	0.125173	+	0.216805i	0.921800	−	0.387665i	$-0.126718\pi$
$971$	3.90049	+	6.75585i	0.125173	+	0.216805i	−0.796628	+	0.604470i	$0.793385\pi$
$972$		0			0
$973$	−44.2276	−	2.82960i	−1.41787	−	0.0907129i
$974$	9.17108	+	5.29492i	0.293860	+	0.169660i
$975$		0			0
$976$			1.71256i			0.0548176i
$977$	−45.4500			−1.45407			−0.727037	−	0.686598i	$-0.759103\pi$
$977$	−45.4500			−1.45407			−0.727037	+	0.686598i	$0.759103\pi$
$978$		0			0
$979$	9.80175	+	5.65904i	0.313265	+	0.180864i
$980$	−15.3631	−	2.99567i	−0.490757	−	0.0956933i
$981$		0			0
$982$	2.99490	−	1.72911i	0.0955713	−	0.0551781i
$983$	−51.2704	+	29.6010i	−1.63527	+	0.944125i	−0.652843	+	0.757493i	$0.726424\pi$
$983$	−51.2704	+	29.6010i	−1.63527	+	0.944125i	−0.982430	+	0.186632i	$0.940243\pi$
$984$		0			0
$985$	−8.61531	+	12.9121i	−0.274507	+	0.411413i
$986$	−1.80392	−	3.12449i	−0.0574486	−	0.0995039i
$987$		0			0
$988$	21.7231	+	12.5418i	0.691103	+	0.399009i
$989$	14.2649	−	8.23582i	0.453596	−	0.261884i
$990$		0			0
$991$	−3.52175	+	6.09985i	−0.111872	+	0.193768i	−0.916525	−	0.399977i	$-0.869018\pi$
$991$	−3.52175	+	6.09985i	−0.111872	+	0.193768i	0.804653	+	0.593745i	$0.202351\pi$
$992$			5.00146i			0.158797i
$993$		0			0
$994$	−6.11836	+	9.18775i	−0.194063	+	0.291418i
$995$	9.04328	−	4.46705i	0.286691	−	0.141615i
$996$		0			0
$997$	21.9085	+	37.9467i	0.693851	+	1.20178i	0.970567	+	0.240833i	$0.0774205\pi$
$997$	21.9085	+	37.9467i	0.693851	+	1.20178i	−0.276716	+	0.960952i	$0.589246\pi$
$998$	−7.23460	+	12.5307i	−0.229007	+	0.396652i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bi.a.899.7		48
3.2	odd	2		630.2.bi.b.479.5	yes	48
5.4	even	2		1890.2.bi.b.899.9		48
7.5	odd	6		1890.2.r.b.89.1		48
9.4	even	3		630.2.r.b.59.21	yes	48
9.5	odd	6		1890.2.r.a.1529.1		48
15.14	odd	2		630.2.bi.a.479.20	yes	48
21.5	even	6		630.2.r.a.299.4	yes	48
35.19	odd	6		1890.2.r.a.89.1		48
45.4	even	6		630.2.r.a.59.4	✓	48
45.14	odd	6		1890.2.r.b.1529.1		48
63.5	even	6		1890.2.bi.b.719.9		48
63.40	odd	6		630.2.bi.a.509.20	yes	48
105.89	even	6		630.2.r.b.299.21	yes	48
315.194	even	6	inner	1890.2.bi.a.719.7		48
315.229	odd	6		630.2.bi.b.509.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.4	✓	48	45.4	even	6
630.2.r.a.299.4	yes	48	21.5	even	6
630.2.r.b.59.21	yes	48	9.4	even	3
630.2.r.b.299.21	yes	48	105.89	even	6
630.2.bi.a.479.20	yes	48	15.14	odd	2
630.2.bi.a.509.20	yes	48	63.40	odd	6
630.2.bi.b.479.5	yes	48	3.2	odd	2
630.2.bi.b.509.5	yes	48	315.229	odd	6
1890.2.r.a.89.1		48	35.19	odd	6
1890.2.r.a.1529.1		48	9.5	odd	6
1890.2.r.b.89.1		48	7.5	odd	6
1890.2.r.b.1529.1		48	45.14	odd	6
1890.2.bi.a.719.7		48	315.194	even	6	inner
1890.2.bi.a.899.7		48	1.1	even	1	trivial
1890.2.bi.b.719.9		48	63.5	even	6
1890.2.bi.b.899.9		48	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.24107 + 1.86004i) q^{5} +(2.20215 + 1.46647i) q^{7} -1.00000 q^{8} +(1.24107 - 1.86004i) q^{10} +(-0.646046 + 0.372995i) q^{11} +(1.67087 + 2.89402i) q^{13} +(-2.20215 - 1.46647i) q^{14} +1.00000 q^{16} +(4.20138 + 2.42567i) q^{17} +(6.50055 - 3.75309i) q^{19} +(-1.24107 + 1.86004i) q^{20} +(0.646046 - 0.372995i) q^{22} +(0.933507 - 1.61688i) q^{23} +(-1.91949 - 4.61688i) q^{25} +(-1.67087 - 2.89402i) q^{26} +(2.20215 + 1.46647i) q^{28} +(0.644047 + 0.371841i) q^{29} -5.00146i q^{31} -1.00000 q^{32} +(-4.20138 - 2.42567i) q^{34} +(-5.46071 + 2.27609i) q^{35} +(-5.78366 + 3.33920i) q^{37} +(-6.50055 + 3.75309i) q^{38} +(1.24107 - 1.86004i) q^{40} +(-0.849794 - 1.47189i) q^{41} +(7.64047 + 4.41123i) q^{43} +(-0.646046 + 0.372995i) q^{44} +(-0.933507 + 1.61688i) q^{46} +11.6099i q^{47} +(2.69893 + 6.45877i) q^{49} +(1.91949 + 4.61688i) q^{50} +(1.67087 + 2.89402i) q^{52} +(2.94339 - 5.09811i) q^{53} +(0.108003 - 1.66458i) q^{55} +(-2.20215 - 1.46647i) q^{56} +(-0.644047 - 0.371841i) q^{58} +4.66316 q^{59} +1.71256i q^{61} +5.00146i q^{62} +1.00000 q^{64} +(-7.45666 - 0.483811i) q^{65} -4.53308i q^{67} +(4.20138 + 2.42567i) q^{68} +(5.46071 - 2.27609i) q^{70} -4.17217i q^{71} +(-5.10736 + 8.84620i) q^{73} +(5.78366 - 3.33920i) q^{74} +(6.50055 - 3.75309i) q^{76} +(-1.96968 - 0.126017i) q^{77} -6.21613 q^{79} +(-1.24107 + 1.86004i) q^{80} +(0.849794 + 1.47189i) q^{82} +(2.26849 + 1.30971i) q^{83} +(-9.72604 + 4.80431i) q^{85} +(-7.64047 - 4.41123i) q^{86} +(0.646046 - 0.372995i) q^{88} +(-7.58595 - 13.1393i) q^{89} +(-0.564503 + 8.82335i) q^{91} +(0.933507 - 1.61688i) q^{92} -11.6099i q^{94} +(-1.08673 + 16.7491i) q^{95} +(2.32004 - 4.01843i) q^{97} +(-2.69893 - 6.45877i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} + 48 q^{4} + 3 q^{7} - 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} + 6 q^{22} - 3 q^{23} - 18 q^{25} + 3 q^{28} + 3 q^{29} - 48 q^{32} + 12 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49}+ \cdots - 3 q^{98}+O(q^{100}) \) 48 * q - 48 * q^2 + 48 * q^4 + 3 * q^7 - 48 * q^8 - 6 * q^11 - 3 * q^14 + 48 * q^16 + 6 * q^22 - 3 * q^23 - 18 * q^25 + 3 * q^28 + 3 * q^29 - 48 * q^32 + 12 * q^35 + 3 * q^41 - 6 * q^44 + 3 * q^46 + 3 * q^49 + 18 * q^50 - 42 * q^55 - 3 * q^56 - 3 * q^58 + 48 * q^64 - 12 * q^65 - 12 * q^70 - 18 * q^73 + 12 * q^77 - 3 * q^82 - 9 * q^83 - 33 * q^85 + 6 * q^88 + 33 * q^89 - 3 * q^92 - 24 * q^97 - 3 * q^98

Introduction

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