LMFDB - Embedded newform 1890.2.r.a.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(89,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1890.89");

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.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.0917259820$
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			89.1
Character	$\chi$	$=$	1890.89
Dual form			1890.2.r.a.1529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.23138 + 0.144779i) q^{5} +(-2.37108 - 1.17388i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.23138 + 0.144779i) q^{5} +(-2.37108 - 1.17388i) q^{7} +1.00000 q^{8} +(1.24107 + 1.86004i) q^{10} -0.745990i q^{11} +(1.67087 + 2.89402i) q^{13} +(0.168925 + 2.64035i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.20138 + 2.42567i) q^{17} +(6.50055 + 3.75309i) q^{19} +(0.990306 - 2.00482i) q^{20} +(-0.646046 + 0.372995i) q^{22} +1.86701 q^{23} +(4.95808 - 0.646111i) q^{25} +(1.67087 - 2.89402i) q^{26} +(2.20215 - 1.46647i) q^{28} +(0.644047 + 0.371841i) q^{29} +(-4.33139 - 2.50073i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.20138 + 2.42567i) q^{34} +(5.46071 + 2.27609i) q^{35} +(-5.78366 - 3.33920i) q^{37} -7.50618i q^{38} +(-2.23138 + 0.144779i) q^{40} +(0.849794 + 1.47189i) q^{41} +(-7.64047 - 4.41123i) q^{43} +(0.646046 + 0.372995i) q^{44} +(-0.933507 - 1.61688i) q^{46} +(10.0544 - 5.80494i) q^{47} +(4.24400 + 5.56673i) q^{49} +(-3.03859 - 3.97077i) q^{50} -3.34173 q^{52} +(-2.94339 - 5.09811i) q^{53} +(0.108003 + 1.66458i) q^{55} +(-2.37108 - 1.17388i) q^{56} -0.743681i q^{58} +(2.33158 - 4.03841i) q^{59} +(-1.48312 + 0.856279i) q^{61} +5.00146i q^{62} +1.00000 q^{64} +(-4.14732 - 6.21575i) q^{65} +(-3.92576 - 2.26654i) q^{67} -4.85133i q^{68} +(-0.759202 - 5.86716i) q^{70} -4.17217i q^{71} +(-5.10736 - 8.84620i) q^{73} +6.67839i q^{74} +(-6.50055 + 3.75309i) q^{76} +(-0.875705 + 1.76880i) q^{77} +(3.10806 + 5.38333i) q^{79} +(1.24107 + 1.86004i) q^{80} +(0.849794 - 1.47189i) q^{82} +(2.26849 + 1.30971i) q^{83} +(9.02367 - 6.02085i) q^{85} +8.82245i q^{86} -0.745990i q^{88} +(7.58595 - 13.1393i) q^{89} +(-0.564503 - 8.82335i) q^{91} +(-0.933507 + 1.61688i) q^{92} +(-10.0544 - 5.80494i) q^{94} +(-15.0485 - 7.43342i) q^{95} +(2.32004 - 4.01843i) q^{97} +(2.69893 - 6.45877i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8}+O(q^{10}) $ 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8	$ 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} - 3 q^{14} - 24 q^{16} - 6 q^{22} - 6 q^{23} + 3 q^{28} + 3 q^{29} - 24 q^{32} - 12 q^{35} - 3 q^{41} + 6 q^{44} + 3 q^{46} - 6 q^{49} + 18 q^{50} - 42 q^{55} - 9 q^{61} + 48 q^{64} + 21 q^{65} + 33 q^{67} + 12 q^{70} - 18 q^{73} + 6 q^{77} - 3 q^{82} - 9 q^{83} + 33 q^{85} - 33 q^{89} + 3 q^{92} - 33 q^{95} - 24 q^{97} + 3 q^{98}+O(q^{100}) $ 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 - 3 * q^14 - 24 * q^16 - 6 * q^22 - 6 * q^23 + 3 * q^28 + 3 * q^29 - 24 * q^32 - 12 * q^35 - 3 * q^41 + 6 * q^44 + 3 * q^46 - 6 * q^49 + 18 * q^50 - 42 * q^55 - 9 * q^61 + 48 * q^64 + 21 * q^65 + 33 * q^67 + 12 * q^70 - 18 * q^73 + 6 * q^77 - 3 * q^82 - 9 * q^83 + 33 * q^85 - 33 * q^89 + 3 * q^92 - 33 * q^95 - 24 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.23138	+	0.144779i	−0.997902	+	0.0647470i
$5$	−2.23138	+	0.144779i	−0.997902	+	0.0647470i
$6$		0			0
$7$	−2.37108	−	1.17388i	−0.896182	−	0.443686i
$7$	−2.37108	−	1.17388i	−0.896182	−	0.443686i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.24107	+	1.86004i	0.392461	+	0.588196i
$11$		−	0.745990i		−	0.224924i	−0.993656	−	0.112462i	$-0.964126\pi$
$11$		−	0.745990i		−	0.224924i	0.993656	−	0.112462i	$-0.0358737\pi$
$12$		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	$0.679957\pi$
$14$	0.168925	+	2.64035i	0.0451472	+	0.705664i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.20138	+	2.42567i	−1.01898	+	0.588311i	−0.913810	−	0.406143i	$-0.866873\pi$
$17$	−4.20138	+	2.42567i	−1.01898	+	0.588311i	−0.105175	+	0.994454i	$0.533540\pi$
$18$		0			0
$19$	6.50055	+	3.75309i	1.49133	+	0.861018i	0.999951	−	0.00992860i	$-0.00316042\pi$
$19$	6.50055	+	3.75309i	1.49133	+	0.861018i	0.491377	+	0.870947i	$0.336494\pi$
$20$	0.990306	−	2.00482i	0.221439	−	0.448291i
$21$		0			0
$22$	−0.646046	+	0.372995i	−0.137738	+	0.0795228i
$23$	1.86701			0.389299			0.194650	−	0.980873i	$-0.437643\pi$
$23$	1.86701			0.389299			0.194650	+	0.980873i	$0.437643\pi$
$24$		0			0
$25$	4.95808	−	0.646111i	0.991616	−	0.129222i
$26$	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
$31$	−4.33139	−	2.50073i	−0.777941	−	0.449145i	0.0577588	−	0.998331i	$-0.481605\pi$
$31$	−4.33139	−	2.50073i	−0.777941	−	0.449145i	−0.835700	+	0.549186i	$0.814938\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		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	−0.0574896	−	0.998346i	$-0.518310\pi$
$37$	−5.78366	−	3.33920i	−0.950827	−	0.548960i	−0.893338	+	0.449386i	$0.851643\pi$
$38$		−	7.50618i		−	1.21766i
$39$		0			0
$40$	−2.23138	+	0.144779i	−0.352812	+	0.0228915i
$41$	0.849794	+	1.47189i	0.132716	+	0.229870i	0.924722	−	0.380642i	$-0.124297\pi$
$41$	0.849794	+	1.47189i	0.132716	+	0.229870i	−0.792007	+	0.610512i	$0.790964\pi$
$42$		0			0
$43$	−7.64047	−	4.41123i	−1.16516	−	0.672706i	−0.212625	−	0.977134i	$-0.568201\pi$
$43$	−7.64047	−	4.41123i	−1.16516	−	0.672706i	−0.952535	+	0.304428i	$0.901535\pi$
$44$	0.646046	+	0.372995i	0.0973951	+	0.0562311i
$45$		0			0
$46$	−0.933507	−	1.61688i	−0.137638	−	0.238396i
$47$	10.0544	−	5.80494i	1.46659	−	0.846737i	0.467290	−	0.884104i	$-0.345230\pi$
$47$	10.0544	−	5.80494i	1.46659	−	0.846737i	0.999302	+	0.0373667i	$0.0118970\pi$
$48$		0			0
$49$	4.24400	+	5.56673i	0.606285	+	0.795247i
$50$	−3.03859	−	3.97077i	−0.429721	−	0.561551i
$51$		0			0
$52$	−3.34173			−0.463415
$53$	−2.94339	−	5.09811i	−0.404306	−	0.700279i	0.589934	−	0.807451i	$-0.299154\pi$
$53$	−2.94339	−	5.09811i	−0.404306	−	0.700279i	−0.994240	+	0.107172i	$0.965820\pi$
$54$		0			0
$55$	0.108003	+	1.66458i	0.0145632	+	0.224452i
$56$	−2.37108	−	1.17388i	−0.316848	−	0.156867i
$57$		0			0
$58$		−	0.743681i		−	0.0976501i
$59$	2.33158	−	4.03841i	0.303546	−	0.525757i	−0.673391	−	0.739287i	$-0.735163\pi$
$59$	2.33158	−	4.03841i	0.303546	−	0.525757i	0.976936	+	0.213530i	$0.0684962\pi$
$60$		0			0
$61$	−1.48312	+	0.856279i	−0.189894	+	0.109635i	−0.591933	−	0.805987i	$-0.701635\pi$
$61$	−1.48312	+	0.856279i	−0.189894	+	0.109635i	0.402039	+	0.915623i	$0.368302\pi$
$62$			5.00146i			0.635187i
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.14732	−	6.21575i	−0.514412	−	0.770969i
$66$		0			0
$67$	−3.92576	−	2.26654i	−0.479608	−	0.276902i	0.240645	−	0.970613i	$-0.422641\pi$
$67$	−3.92576	−	2.26654i	−0.479608	−	0.276902i	−0.720253	+	0.693711i	$0.755974\pi$
$68$		−	4.85133i		−	0.588311i
$69$		0			0
$70$	−0.759202	−	5.86716i	−0.0907420	−	0.701260i
$71$		−	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	−0.993149	−	0.116851i	$-0.962720\pi$
$73$	−5.10736	−	8.84620i	−0.597771	−	1.03537i	0.395378	−	0.918518i	$-0.370613\pi$
$74$			6.67839i			0.776347i
$75$		0			0
$76$	−6.50055	+	3.75309i	−0.745664	+	0.430509i
$77$	−0.875705	+	1.76880i	−0.0997958	+	0.201573i
$78$		0			0
$79$	3.10806	+	5.38333i	0.349685	+	0.605672i	0.986193	−	0.165598i	$-0.0529554\pi$
$79$	3.10806	+	5.38333i	0.349685	+	0.605672i	−0.636509	+	0.771269i	$0.719622\pi$
$80$	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
$85$	9.02367	−	6.02085i	0.978755	−	0.653052i
$86$			8.82245i			0.951349i
$87$		0			0
$88$		−	0.745990i		−	0.0795228i
$89$	7.58595	−	13.1393i	0.804109	−	1.39276i	−0.112782	−	0.993620i	$-0.535976\pi$
$89$	7.58595	−	13.1393i	0.804109	−	1.39276i	0.916891	−	0.399138i	$-0.130691\pi$
$90$		0			0
$91$	−0.564503	−	8.82335i	−0.0591760	−	0.924938i
$92$	−0.933507	+	1.61688i	−0.0973249	+	0.168572i
$93$		0			0
$94$	−10.0544	−	5.80494i	−1.03704	−	0.598734i
$95$	−15.0485	−	7.43342i	−1.54395	−	0.762653i
$96$		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
$101$	10.9742			1.09197			0.545986	−	0.837794i	$-0.316155\pi$
$101$	10.9742			1.09197			0.545986	+	0.837794i	$0.316155\pi$
$102$		0			0
$103$	6.67426			0.657635			0.328817	−	0.944394i	$-0.393350\pi$
$103$	6.67426			0.657635			0.328817	+	0.944394i	$0.393350\pi$
$104$	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	−0.320541	−	0.947234i	$-0.603865\pi$
$107$	6.82770	−	11.8259i	0.660058	−	1.14325i	0.980600	−	0.196020i	$-0.0628018\pi$
$108$		0			0
$109$	−5.13894	−	8.90090i	−0.492221	−	0.852551i	0.507739	−	0.861511i	$-0.330481\pi$
$109$	−5.13894	−	8.90090i	−0.492221	−	0.852551i	−0.999960	+	0.00895944i	$0.997148\pi$
$110$	1.38757	−	0.925826i	0.132300	−	0.0882740i
$111$		0			0
$112$	0.168925	+	2.64035i	0.0159619	+	0.249490i
$113$	−10.0641	−	17.4316i	−0.946754	−	1.63983i	−0.752201	−	0.658934i	$-0.771008\pi$
$113$	−10.0641	−	17.4316i	−0.946754	−	1.63983i	−0.194553	−	0.980892i	$-0.562326\pi$
$114$		0			0
$115$	−4.16601	+	0.270304i	−0.388483	+	0.0252060i
$116$	−0.644047	+	0.371841i	−0.0597983	+	0.0345245i
$117$		0			0
$118$	−4.66316			−0.429278
$119$	12.8092	−	0.819513i	1.17422	−	0.0751246i
$120$		0			0
$121$	10.4435			0.949409
$122$	1.48312	+	0.856279i	0.134275	+	0.0775238i
$123$		0			0
$124$	4.33139	−	2.50073i	0.388971	−	0.224572i
$125$	−10.9698	+	2.15954i	−0.981168	+	0.193155i
$126$		0			0
$127$			2.11883i			0.188015i	0.995571	+	0.0940077i	$0.0299678\pi$
$127$			2.11883i			0.188015i	−0.995571	+	0.0940077i	$0.970032\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−3.30934	+	6.69956i	−0.290248	+	0.587590i
$131$	15.7575			1.37674			0.688370	−	0.725360i	$-0.258327\pi$
$131$	15.7575			1.37674			0.688370	+	0.725360i	$0.258327\pi$
$132$		0			0
$133$	−11.0076	−	16.5297i	−0.954480	−	1.43331i
$134$			4.53308i			0.391599i
$135$		0			0
$136$	−4.20138	+	2.42567i	−0.360265	+	0.207999i
$137$	11.0072			0.940405			0.470202	−	0.882559i	$-0.344181\pi$
$137$	11.0072			0.940405			0.470202	+	0.882559i	$0.344181\pi$
$138$		0			0
$139$	14.5065	−	8.37531i	1.23042	−	0.710385i	0.263304	−	0.964713i	$-0.415188\pi$
$139$	14.5065	−	8.37531i	1.23042	−	0.710385i	0.967118	+	0.254328i	$0.0818543\pi$
$140$	−4.70151	+	3.59107i	−0.397350	+	0.303501i
$141$		0			0
$142$	−3.61321	+	2.08609i	−0.303213	+	0.175060i
$143$	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
$149$			21.5525i			1.76565i	0.469705	+	0.882823i	$0.344360\pi$
$149$			21.5525i			1.76565i	−0.469705	+	0.882823i	$0.655640\pi$
$150$		0			0
$151$	−15.3783			−1.25146			−0.625732	−	0.780038i	$-0.715200\pi$
$151$	−15.3783			−1.25146			−0.625732	+	0.780038i	$0.715200\pi$
$152$	6.50055	+	3.75309i	0.527264	+	0.304416i
$153$		0			0
$154$	1.96968	−	0.126017i	0.158721	−	0.0101547i
$155$	10.0270	+	4.95298i	0.805390	+	0.397833i
$156$		0			0
$157$	−3.52158	+	6.09956i	−0.281053	+	0.486798i	−0.971644	−	0.236447i	$-0.924017\pi$
$157$	−3.52158	+	6.09956i	−0.281053	+	0.486798i	0.690591	+	0.723245i	$0.257350\pi$
$158$	3.10806	−	5.38333i	0.247264	−	0.428274i
$159$		0			0
$160$	0.990306	−	2.00482i	0.0782906	−	0.158495i
$161$	−4.42683	−	2.19166i	−0.348883	−	0.172727i
$162$		0			0
$163$	6.38815	+	3.68820i	0.500359	+	0.288882i	0.728862	−	0.684661i	$-0.240050\pi$
$163$	6.38815	+	3.68820i	0.500359	+	0.288882i	−0.228503	+	0.973543i	$0.573383\pi$
$164$	−1.69959			−0.132716
$165$		0			0
$166$		−	2.61943i		−	0.203307i
$167$	−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
$173$	−8.87235	+	5.12245i	−0.674552	+	0.389453i	−0.797799	−	0.602923i	$-0.794003\pi$
$173$	−8.87235	+	5.12245i	−0.674552	+	0.389453i	0.123247	+	0.992376i	$0.460669\pi$
$174$		0			0
$175$	−12.5144	−	4.28823i	−0.946002	−	0.324159i
$176$	−0.646046	+	0.372995i	−0.0486976	+	0.0281156i
$177$		0			0
$178$	−15.1719			−1.13718
$179$	−16.4577	+	9.50188i	−1.23011	+	0.710204i	−0.967053	−	0.254577i	$-0.918064\pi$
$179$	−16.4577	+	9.50188i	−1.23011	+	0.710204i	−0.263056	+	0.964780i	$0.584731\pi$
$180$		0			0
$181$		−	5.53416i		−	0.411351i	−0.978620	−	0.205676i	$-0.934061\pi$
$181$		−	5.53416i		−	0.411351i	0.978620	−	0.205676i	$-0.0659391\pi$
$182$	−7.35899	+	4.90055i	−0.545485	+	0.363253i
$183$		0			0
$184$	1.86701			0.137638
$185$	13.3890	+	6.61365i	0.984376	+	0.486245i
$186$		0			0
$187$	1.80952	+	3.13419i	0.132325	+	0.229194i
$188$			11.6099i			0.846737i
$189$		0			0
$190$	1.08673	+	16.7491i	0.0788400	+	1.21511i
$191$	17.3414	−	10.0121i	1.25478	−	0.724447i	0.282725	−	0.959201i	$-0.408762\pi$
$191$	17.3414	−	10.0121i	1.25478	−	0.724447i	0.972055	+	0.234754i	$0.0754283\pi$
$192$		0			0
$193$	16.4666	+	9.50697i	1.18529	+	0.684327i	0.957232	−	0.289321i	$-0.0934296\pi$
$193$	16.4666	+	9.50697i	1.18529	+	0.684327i	0.228056	+	0.973648i	$0.426763\pi$
$194$	−4.64008			−0.333139
$195$		0			0
$196$	−6.94293	+	0.892045i	−0.495923	+	0.0637175i
$197$	−6.94184			−0.494586			−0.247293	−	0.968941i	$-0.579541\pi$
$197$	−6.94184			−0.494586			−0.247293	+	0.968941i	$0.579541\pi$
$198$		0			0
$199$	−3.90645	+	2.25539i	−0.276921	+	0.159880i	−0.632029	−	0.774945i	$-0.717777\pi$
$199$	−3.90645	+	2.25539i	−0.276921	+	0.159880i	0.355108	+	0.934825i	$0.384444\pi$
$200$	4.95808	−	0.646111i	0.350589	−	0.0456869i
$201$		0			0
$202$	−5.48710	−	9.50393i	−0.386071	−	0.668694i
$203$	−1.09059	−	1.63770i	−0.0765442	−	0.114944i
$204$		0			0
$205$	−2.10931	−	3.16130i	−0.147320	−	0.220795i
$206$	−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	$0.746264\pi$
$212$	5.88679			0.404306
$213$		0			0
$214$	−13.6554			−0.933464
$215$	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
$220$	−1.49557	−	0.738758i	−0.100832	−	0.0498071i
$221$	−14.0399	−	8.10593i	−0.944425	−	0.545264i
$222$		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
$227$			8.02790i			0.532831i	0.963858	+	0.266415i	$0.0858393\pi$
$227$			8.02790i			0.532831i	−0.963858	+	0.266415i	$0.914161\pi$
$228$		0			0
$229$		−	19.2674i		−	1.27322i	−0.771185	−	0.636612i	$-0.780335\pi$
$229$		−	19.2674i		−	1.27322i	0.771185	−	0.636612i	$-0.219665\pi$
$230$	2.31710	+	3.47272i	0.152785	+	0.228984i
$231$		0			0
$232$	0.644047	+	0.371841i	0.0422837	+	0.0244125i
$233$	0.572350	−	0.991339i	0.0374959	−	0.0649448i	−0.846668	−	0.532121i	$-0.821395\pi$
$233$	0.572350	−	0.991339i	0.0374959	−	0.0649448i	0.884164	+	0.467176i	$0.154729\pi$
$234$		0			0
$235$	−21.5948	+	14.4087i	−1.40869	+	0.939918i
$236$	2.33158	+	4.03841i	0.151773	+	0.262878i
$237$		0			0
$238$	−7.11434	−	10.6834i	−0.461154	−	0.692500i
$239$	−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
$241$		−	22.9924i		−	1.48107i	−0.672017	−	0.740536i	$-0.734572\pi$
$241$		−	22.9924i		−	1.48107i	0.672017	−	0.740536i	$-0.265428\pi$
$242$	−5.22175	−	9.04434i	−0.335667	−	0.581392i
$243$		0			0
$244$		−	1.71256i		−	0.109635i
$245$	−10.2759	−	11.8070i	−0.656503	−	0.754323i
$246$		0			0
$247$			25.0837i			1.59603i
$248$	−4.33139	−	2.50073i	−0.275044	−	0.158797i
$249$		0			0
$250$	7.35511	+	8.42035i	0.465178	+	0.532550i
$251$	1.44964			0.0915002			0.0457501	−	0.998953i	$-0.485432\pi$
$251$	1.44964			0.0915002			0.0457501	+	0.998953i	$0.485432\pi$
$252$		0			0
$253$		−	1.39277i		−	0.0875630i
$254$	1.83496	−	1.05941i	0.115135	−	0.0664735i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		−	7.01785i		−	0.437762i	−0.975752	−	0.218881i	$-0.929759\pi$
$257$		−	7.01785i		−	0.437762i	0.975752	−	0.218881i	$-0.0702406\pi$
$258$		0			0
$259$	9.79366	+	14.7068i	0.608549	+	0.913838i
$260$	7.45666	−	0.483811i	0.462442	−	0.0300047i
$261$		0			0
$262$	−7.87875	−	13.6464i	−0.486751	−	0.843077i
$263$	−2.64989			−0.163399			−0.0816996	−	0.996657i	$-0.526035\pi$
$263$	−2.64989			−0.163399			−0.0816996	+	0.996657i	$0.526035\pi$
$264$		0			0
$265$	7.30592	+	10.9497i	0.448799	+	0.672632i
$266$	−8.81138	+	17.7977i	−0.540260	+	1.09125i
$267$		0			0
$268$	3.92576	−	2.26654i	0.239804	−	0.138451i
$269$	−11.9338	−	20.6700i	−0.727618	−	1.26027i	−0.957887	−	0.287145i	$-0.907294\pi$
$269$	−11.9338	−	20.6700i	−0.727618	−	1.26027i	0.230269	−	0.973127i	$-0.426039\pi$
$270$		0			0
$271$	−16.9678	−	9.79635i	−1.03072	−	0.595086i	−0.113528	−	0.993535i	$-0.536215\pi$
$271$	−16.9678	−	9.79635i	−1.03072	−	0.595086i	−0.917190	+	0.398449i	$0.869549\pi$
$272$	4.20138	+	2.42567i	0.254746	+	0.147078i
$273$		0			0
$274$	−5.50358	−	9.53248i	−0.332483	−	0.575878i
$275$	−0.481992	−	3.69868i	−0.0290652	−	0.223039i
$276$		0			0
$277$			19.9426i			1.19823i	0.800662	+	0.599116i	$0.204481\pi$
$277$			19.9426i			1.19823i	−0.800662	+	0.599116i	$0.795519\pi$
$278$	−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
$283$	−4.41483	+	7.64671i	−0.262434	+	0.454550i	−0.966888	−	0.255200i	$-0.917859\pi$
$283$	−4.41483	+	7.64671i	−0.262434	+	0.454550i	0.704454	+	0.709750i	$0.251192\pi$
$284$	3.61321	+	2.08609i	0.214404	+	0.123786i
$285$		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
$290$	0.107669	+	1.65943i	0.00632255	+	0.0974452i
$291$		0			0
$292$	10.2147			0.597771
$293$	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
$295$	−4.61795	+	9.34878i	−0.268868	+	0.544307i
$296$	−5.78366	−	3.33920i	−0.336168	−	0.194087i
$297$		0			0
$298$	18.6650	−	10.7762i	1.08123	−	0.624250i
$299$	3.11953	+	5.40319i	0.180407	+	0.312474i
$300$		0			0
$301$	12.9379	+	19.4284i	0.745726	+	1.11983i
$302$	7.68913	+	13.3180i	0.442460	+	0.766363i
$303$		0			0
$304$		−	7.50618i		−	0.430509i
$305$	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	$0.599042\pi$
$308$	−1.09397	−	1.64278i	−0.0623348	−	0.0936062i
$309$		0			0
$310$	−0.724105	−	11.1601i	−0.0411264	−	0.633854i
$311$	2.49511	−	4.32165i	0.141485	−	0.245059i	−0.786571	−	0.617500i	$-0.788146\pi$
$311$	2.49511	−	4.32165i	0.141485	−	0.245059i	0.928056	+	0.372441i	$0.121479\pi$
$312$		0			0
$313$	10.0534	+	17.4130i	0.568253	+	0.984243i	0.996739	+	0.0806942i	$0.0257137\pi$
$313$	10.0534	+	17.4130i	0.568253	+	0.984243i	−0.428486	+	0.903548i	$0.640953\pi$
$314$	7.04317			0.397469
$315$		0			0
$316$	−6.21613			−0.349685
$317$	−13.0051	−	22.5255i	−0.730440	−	1.26516i	−0.956695	−	0.291091i	$-0.905982\pi$
$317$	−13.0051	−	22.5255i	−0.730440	−	1.26516i	0.226256	−	0.974068i	$-0.427351\pi$
$318$		0			0
$319$	0.277389	−	0.480452i	0.0155308	−	0.0269002i
$320$	−2.23138	+	0.144779i	−0.124738	+	0.00809337i
$321$		0			0
$322$	0.315386	+	4.92958i	0.0175758	+	0.274715i
$323$	−36.4150			−2.02619
$324$		0			0
$325$	10.1541	+	13.2692i	0.563251	+	0.736045i
$326$		−	7.37640i		−	0.408541i
$327$		0			0
$328$	0.849794	+	1.47189i	0.0469220	+	0.0812713i
$329$	−30.6542	+	1.96120i	−1.69002	+	0.108125i
$330$		0			0
$331$	−6.69898	−	11.6030i	−0.368209	−	0.637757i	0.621076	−	0.783750i	$-0.286696\pi$
$331$	−6.69898	−	11.6030i	−0.368209	−	0.637757i	−0.989286	+	0.145993i	$0.953362\pi$
$332$	−2.26849	+	1.30971i	−0.124500	+	0.0718798i
$333$		0			0
$334$	14.6090	+	8.43452i	0.799370	+	0.461516i
$335$	9.08800	+	4.48914i	0.496531	+	0.245268i
$336$		0			0
$337$	7.18391	−	4.14763i	0.391333	−	0.225936i	−0.291405	−	0.956600i	$-0.594123\pi$
$337$	7.18391	−	4.14763i	0.391333	−	0.225936i	0.682737	+	0.730664i	$0.260789\pi$
$338$	−1.83283			−0.0996929
$339$		0			0
$340$	0.702369	+	10.8252i	0.0380913	+	0.587076i
$341$	−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
$346$	8.87235	+	5.12245i	0.476980	+	0.275385i
$347$	−8.22042	+	14.2382i	−0.441295	+	0.764346i	−0.997786	−	0.0665078i	$-0.978814\pi$
$347$	−8.22042	+	14.2382i	−0.441295	+	0.764346i	0.556490	+	0.830854i	$0.312148\pi$
$348$		0			0
$349$	26.2420	+	15.1508i	1.40470	+	0.811004i	0.994870	−	0.101158i	$-0.0322547\pi$
$349$	26.2420	+	15.1508i	1.40470	+	0.811004i	0.409830	+	0.912162i	$0.365588\pi$
$350$	2.54351	+	12.9819i	0.135956	+	0.693913i
$351$		0			0
$352$	0.646046	+	0.372995i	0.0344344	+	0.0198807i
$353$			12.4615i			0.663257i	0.943410	+	0.331629i	$0.107598\pi$
$353$			12.4615i			0.663257i	−0.943410	+	0.331629i	$0.892402\pi$
$354$		0			0
$355$	0.604041	+	9.30968i	0.0320592	+	0.494107i
$356$	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	$-0.323447\pi$
$359$	1.01914	+	0.588399i	0.0537880	+	0.0310545i	−0.472865	+	0.881135i	$0.656780\pi$
$360$		0			0
$361$	18.6714	+	32.3398i	0.982705	+	1.70210i
$362$	−4.79273	+	2.76708i	−0.251900	+	0.145435i
$363$		0			0
$364$	7.92350	+	3.92280i	0.415304	+	0.205611i
$365$	12.6772	+	18.9998i	0.663554	+	0.994493i
$366$		0			0
$367$	35.4401			1.84996			0.924978	−	0.380020i	$-0.124083\pi$
$367$	35.4401			1.84996			0.924978	+	0.380020i	$0.124083\pi$
$368$	−0.933507	−	1.61688i	−0.0486624	−	0.0842858i
$369$		0			0
$370$	−0.966888	−	14.9020i	−0.0502661	−	0.774718i
$371$	0.994427	+	15.5432i	0.0516281	+	0.806963i
$372$		0			0
$373$		−	25.3686i		−	1.31353i	−0.754093	−	0.656767i	$-0.771923\pi$
$373$		−	25.3686i		−	1.31353i	0.754093	−	0.656767i	$-0.228077\pi$
$374$	1.80952	−	3.13419i	0.0935682	−	0.162065i
$375$		0			0
$376$	10.0544	−	5.80494i	0.518519	−	0.299367i
$377$			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	$0.284947\pi$
$380$	13.9618	−	9.31570i	0.716225	−	0.477885i
$381$		0			0
$382$	−17.3414	−	10.0121i	−0.887263	−	0.512262i
$383$		−	13.1254i		−	0.670674i	−0.942098	−	0.335337i	$-0.891150\pi$
$383$		−	13.1254i		−	0.670674i	0.942098	−	0.335337i	$-0.108850\pi$
$384$		0			0
$385$	1.69794	−	4.07364i	0.0865352	−	0.207612i
$386$		−	19.0139i		−	0.967784i
$387$		0			0
$388$	2.32004	+	4.01843i	0.117782	+	0.204005i
$389$		−	19.3282i		−	0.979980i	−0.871728	−	0.489990i	$-0.837000\pi$
$389$		−	19.3282i		−	0.979980i	0.871728	−	0.489990i	$-0.163000\pi$
$390$		0			0
$391$	−7.84404	+	4.52876i	−0.396690	+	0.229029i
$392$	4.24400	+	5.56673i	0.214354	+	0.281162i
$393$		0			0
$394$	3.47092	+	6.01181i	0.174862	+	0.302871i
$395$	−7.71465	−	11.5622i	−0.388166	−	0.581760i
$396$		0			0
$397$	−18.0143	+	31.2016i	−0.904111	+	1.56597i	−0.0820040	+	0.996632i	$0.526132\pi$
$397$	−18.0143	+	31.2016i	−0.904111	+	1.56597i	−0.822107	+	0.569334i	$0.807201\pi$
$398$	3.90645	+	2.25539i	0.195812	+	0.113052i
$399$		0			0
$400$	−3.03859	−	3.97077i	−0.151929	−	0.198538i
$401$		−	3.15068i		−	0.157338i	−0.996901	−	0.0786688i	$-0.974933\pi$
$401$		−	3.15068i		−	0.157338i	0.996901	−	0.0786688i	$-0.0250669\pi$
$402$		0			0
$403$		−	16.7135i		−	0.832561i
$404$	−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
$409$	−13.8104	−	7.97346i	−0.682882	−	0.394262i	0.118058	−	0.993007i	$-0.462333\pi$
$409$	−13.8104	−	7.97346i	−0.682882	−	0.394262i	−0.800940	+	0.598744i	$0.795667\pi$
$410$	−1.68311	+	3.40736i	−0.0831230	+	0.168278i
$411$		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
$416$	−3.34173			−0.163842
$417$		0			0
$418$	−5.59954			−0.273882
$419$	17.4629	+	30.2467i	0.853120	+	1.47765i	0.878378	+	0.477966i	$0.158626\pi$
$419$	17.4629	+	30.2467i	0.853120	+	1.47765i	−0.0252584	+	0.999681i	$0.508041\pi$
$420$		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
$425$	−19.2635	+	14.7412i	−0.934418	+	0.715054i
$426$		0			0
$427$	4.52176	−	0.289294i	0.218823	−	0.0139999i
$428$	6.82770	+	11.8259i	0.330029	+	0.571627i
$429$		0			0
$430$	−1.27730	−	19.6862i	−0.0615970	−	0.949353i
$431$	−7.75117	+	4.47514i	−0.373361	+	0.215560i	−0.674926	−	0.737886i	$-0.735824\pi$
$431$	−7.75117	+	4.47514i	−0.373361	+	0.215560i	0.301565	+	0.953446i	$0.402491\pi$
$432$		0			0
$433$	12.0060			0.576972			0.288486	−	0.957484i	$-0.406848\pi$
$433$	12.0060			0.576972			0.288486	+	0.957484i	$0.406848\pi$
$434$	5.87113	−	11.8588i	0.281823	−	0.569243i
$435$		0			0
$436$	10.2779			0.492221
$437$	12.1366	+	7.00708i	0.580573	+	0.335194i
$438$		0			0
$439$	−28.3831	+	16.3870i	−1.35465	+	0.782108i	−0.988897	−	0.148604i	$-0.952522\pi$
$439$	−28.3831	+	16.3870i	−1.35465	+	0.782108i	−0.365753	+	0.930712i	$0.619189\pi$
$440$	0.108003	+	1.66458i	0.00514886	+	0.0793559i
$441$		0			0
$442$			16.2119i			0.771119i
$443$	3.05270	+	5.28743i	0.145038	+	0.251213i	0.929387	−	0.369106i	$-0.120336\pi$
$443$	3.05270	+	5.28743i	0.145038	+	0.251213i	−0.784349	+	0.620320i	$0.787003\pi$
$444$		0			0
$445$	−15.0248	+	30.4169i	−0.712245	+	1.44190i
$446$	−21.5221			−1.01910
$447$		0			0
$448$	−2.37108	−	1.17388i	−0.112023	−	0.0554608i
$449$		−	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
$452$	20.1283			0.946754
$453$		0			0
$454$	6.95237	−	4.01395i	0.326291	−	0.188384i
$455$	2.53705	+	19.6065i	0.118939	+	0.919166i
$456$		0			0
$457$	28.7983	−	16.6267i	1.34713	−	0.777765i	0.359287	−	0.933227i	$-0.383020\pi$
$457$	28.7983	−	16.6267i	1.34713	−	0.777765i	0.987842	+	0.155462i	$0.0496866\pi$
$458$	−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	−0.683959	−	0.729520i	$-0.739743\pi$
$461$	6.22235	−	10.7774i	0.289804	−	0.501955i	0.973763	+	0.227566i	$0.0730766\pi$
$462$		0			0
$463$	2.79388	−	1.61305i	0.129843	−	0.0749647i	−0.433672	−	0.901071i	$-0.642782\pi$
$463$	2.79388	−	1.61305i	0.129843	−	0.0749647i	0.563514	+	0.826106i	$0.309449\pi$
$464$		−	0.743681i		−	0.0345245i
$465$		0			0
$466$	−1.14470			−0.0530272
$467$	36.0480	+	20.8123i	1.66810	+	0.963080i	0.968660	+	0.248392i	$0.0799021\pi$
$467$	36.0480	+	20.8123i	1.66810	+	0.963080i	0.699443	+	0.714688i	$0.253431\pi$
$468$		0			0
$469$	6.64763	+	9.98253i	0.306959	+	0.460950i
$470$	23.2757	+	11.4973i	1.07363	+	0.530332i
$471$		0			0
$472$	2.33158	−	4.03841i	0.107320	−	0.185883i
$473$	−3.29073	+	5.69971i	−0.151308	+	0.262073i
$474$		0			0
$475$	34.6551	+	14.4081i	1.59009	+	0.661087i
$476$	−5.69490	+	11.5029i	−0.261025	+	0.527234i
$477$		0			0
$478$	10.1997	+	5.88880i	0.466523	+	0.269347i
$479$	23.0103			1.05137			0.525683	−	0.850681i	$-0.323810\pi$
$479$	23.0103			1.05137			0.525683	+	0.850681i	$0.323810\pi$
$480$		0			0
$481$		−	22.3174i		−	1.01759i
$482$	−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	−0.693185	−	0.720760i	$-0.743793\pi$
$487$	−9.17108	+	5.29492i	−0.415581	+	0.239936i	0.277604	+	0.960696i	$0.410460\pi$
$488$	−1.48312	+	0.856279i	−0.0671376	+	0.0387619i
$489$		0			0
$490$	−5.08724	+	14.8027i	−0.229818	+	0.668718i
$491$	−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
$493$	−3.60785			−0.162489
$494$	21.7231	−	12.5418i	0.977368	−	0.564283i
$495$		0			0
$496$			5.00146i			0.224572i
$497$	−4.89764	+	9.89253i	−0.219689	+	0.443741i
$498$		0			0
$499$	−14.4692			−0.647730			−0.323865	−	0.946103i	$-0.604982\pi$
$499$	−14.4692			−0.647730			−0.323865	+	0.946103i	$0.604982\pi$
$500$	3.61468	−	10.5799i	0.161653	−	0.473147i
$501$		0			0
$502$	−0.724818	−	1.25542i	−0.0323502	−	0.0560322i
$503$		−	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
$506$	−1.20618	+	0.696387i	−0.0536211	+	0.0309582i
$507$		0			0
$508$	−1.83496	−	1.05941i	−0.0814131	−	0.0470039i
$509$	41.8292			1.85405			0.927023	−	0.375005i	$-0.122359\pi$
$509$	41.8292			1.85405			0.927023	+	0.375005i	$0.122359\pi$
$510$		0			0
$511$	1.72552	+	26.9705i	0.0763327	+	1.19310i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−6.07764	+	3.50893i	−0.268073	+	0.154772i
$515$	−14.8928	+	0.966290i	−0.656255	+	0.0425798i
$516$		0			0
$517$	−4.33043	−	7.50052i	−0.190452	−	0.329872i
$518$	7.83965	−	15.8350i	0.344454	−	0.695749i
$519$		0			0
$520$	−4.14732	−	6.21575i	−0.181872	−	0.272579i
$521$	−11.1096	−	19.2425i	−0.486722	−	0.843027i	0.513161	−	0.858292i	$-0.328474\pi$
$521$	−11.1096	−	19.2425i	−0.486722	−	0.843027i	−0.999883	+	0.0152648i	$0.995141\pi$
$522$		0			0
$523$	15.3867	−	26.6505i	0.672813	−	1.16535i	−0.304291	−	0.952579i	$-0.598419\pi$
$523$	15.3867	−	26.6505i	0.672813	−	1.16535i	0.977103	−	0.212766i	$-0.0682473\pi$
$524$	−7.87875	+	13.6464i	−0.344185	+	0.596146i
$525$		0			0
$526$	1.32494	+	2.29487i	0.0577703	+	0.100061i
$527$	24.2638			1.05695
$528$		0			0
$529$	−19.5143			−0.848446
$530$	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
$535$	−13.5230	+	27.3766i	−0.584651	+	1.18359i
$536$	−3.92576	−	2.26654i	−0.169567	−	0.0978996i
$537$		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	−0.804273	−	0.594260i	$-0.797445\pi$
$541$	2.61686	−	4.53253i	0.112508	−	0.194869i	0.916781	+	0.399391i	$0.130778\pi$
$542$			19.5927i			0.841578i
$543$		0			0
$544$		−	4.85133i		−	0.207999i
$545$	12.7556	+	19.1172i	0.546388	+	0.818893i
$546$		0			0
$547$	3.57961	+	2.06669i	0.153053	+	0.0883652i	0.574571	−	0.818455i	$-0.305169\pi$
$547$	3.57961	+	2.06669i	0.153053	+	0.0883652i	−0.421518	+	0.906820i	$0.638502\pi$
$548$	−5.50358	+	9.53248i	−0.235101	+	0.407207i
$549$		0			0
$550$	−2.96215	+	2.26676i	−0.126307	+	0.0966548i
$551$	2.79110	+	4.83433i	0.118905	+	0.205950i
$552$		0			0
$553$	−1.05006	−	16.4128i	−0.0446532	−	0.697942i
$554$	17.2708	−	9.97128i	0.733765	−	0.423639i
$555$		0			0
$556$			16.7506i			0.710385i
$557$	−6.66281	−	11.5403i	−0.282312	−	0.488979i	0.689642	−	0.724151i	$-0.257768\pi$
$557$	−6.66281	−	11.5403i	−0.282312	−	0.488979i	−0.971954	+	0.235172i	$0.924435\pi$
$558$		0			0
$559$		−	29.4823i		−	1.24697i
$560$	−0.759202	−	5.86716i	−0.0320822	−	0.247933i
$561$		0			0
$562$		−	2.35446i		−	0.0993170i
$563$	8.13242	+	4.69526i	0.342741	+	0.197881i	0.661483	−	0.749960i	$-0.269927\pi$
$563$	8.13242	+	4.69526i	0.342741	+	0.197881i	−0.318743	+	0.947841i	$0.603261\pi$
$564$		0			0
$565$	24.9806	+	37.4394i	1.05094	+	1.57509i
$566$	8.82966			0.371138
$567$		0			0
$568$		−	4.17217i		−	0.175060i
$569$	−30.0367	+	17.3417i	−1.25921	+	0.727002i	−0.972920	−	0.231142i	$-0.925754\pi$
$569$	−30.0367	+	17.3417i	−1.25921	+	0.727002i	−0.286285	+	0.958144i	$0.592420\pi$
$570$		0			0
$571$	−5.74730	+	9.95461i	−0.240517	+	0.416588i	−0.960862	−	0.277029i	$-0.910650\pi$
$571$	−5.74730	+	9.95461i	−0.240517	+	0.416588i	0.720345	+	0.693616i	$0.243984\pi$
$572$			2.49290i			0.104233i
$573$		0			0
$574$	−3.74275	+	2.49240i	−0.156219	+	0.104031i
$575$	9.25680	−	1.20630i	0.386035	−	0.0503061i
$576$		0			0
$577$	8.61149	+	14.9155i	0.358501	+	0.620942i	0.987711	−	0.156293i	$-0.0499546\pi$
$577$	8.61149	+	14.9155i	0.358501	+	0.620942i	−0.629209	+	0.777236i	$0.716621\pi$
$578$	−6.53545			−0.271839
$579$		0			0
$580$	1.38328	−	0.922960i	0.0574374	−	0.0383238i
$581$	−3.84131	−	5.76837i	−0.159364	−	0.239312i
$582$		0			0
$583$	−3.80314	+	2.19574i	−0.157510	+	0.0909384i
$584$	−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
$590$	10.4053	−	0.675125i	0.428378	−	0.0277945i
$591$		0			0
$592$			6.67839i			0.274480i
$593$	5.35047	+	3.08910i	0.219718	+	0.126854i	0.605819	−	0.795602i	$-0.292845\pi$
$593$	5.35047	+	3.08910i	0.219718	+	0.126854i	−0.386102	+	0.922456i	$0.626179\pi$
$594$		0			0
$595$	−28.4636	+	3.68315i	−1.16689	+	0.150994i
$596$	−18.6650	−	10.7762i	−0.764547	−	0.441412i
$597$		0			0
$598$	3.11953	−	5.40319i	0.127567	−	0.220953i
$599$	−17.5461	−	10.1302i	−0.716914	−	0.413911i	0.0967017	−	0.995313i	$-0.469171\pi$
$599$	−17.5461	−	10.1302i	−0.716914	−	0.413911i	−0.813616	+	0.581403i	$0.802504\pi$
$600$		0			0
$601$	1.81095	+	1.04555i	0.0738700	+	0.0426489i	0.536480	−	0.843913i	$-0.319754\pi$
$601$	1.81095	+	1.04555i	0.0738700	+	0.0426489i	−0.462610	+	0.886562i	$0.653087\pi$
$602$	10.3565	−	20.9187i	0.422100	−	0.852583i
$603$		0			0
$604$	7.68913	−	13.3180i	0.312866	−	0.541900i
$605$	−23.3034	+	1.51200i	−0.947417	+	0.0614713i
$606$		0			0
$607$	−13.4794			−0.547111			−0.273555	−	0.961856i	$-0.588200\pi$
$607$	−13.4794			−0.547111			−0.273555	+	0.961856i	$0.588200\pi$
$608$	−6.50055	+	3.75309i	−0.263632	+	0.152208i
$609$		0			0
$610$	−3.43336	−	1.69596i	−0.139013	−	0.0686672i
$611$	33.5993	+	19.3985i	1.35928	+	0.784781i
$612$		0			0
$613$	9.41875	−	5.43792i	0.380420	−	0.219636i	−0.297581	−	0.954697i	$-0.596180\pi$
$613$	9.41875	−	5.43792i	0.380420	−	0.219636i	0.678001	+	0.735061i	$0.262847\pi$
$614$	5.36423	+	9.29112i	0.216483	+	0.374959i
$615$		0			0
$616$	−0.875705	+	1.76880i	−0.0352832	+	0.0712669i
$617$	−0.714583	−	1.23769i	−0.0287680	−	0.0498277i	0.851283	−	0.524707i	$-0.175825\pi$
$617$	−0.714583	−	1.23769i	−0.0287680	−	0.0498277i	−0.880051	+	0.474879i	$0.842492\pi$
$618$		0			0
$619$			22.2859i			0.895747i	0.894097	+	0.447873i	$0.147818\pi$
$619$			22.2859i			0.895747i	−0.894097	+	0.447873i	$0.852182\pi$
$620$	−9.30292	+	6.20717i	−0.373614	+	0.249286i
$621$		0			0
$622$	−4.99022			−0.200089
$623$	−33.4108	+	22.2491i	−1.33858	+	0.891393i
$624$		0			0
$625$	24.1651	−	6.40694i	0.966603	−	0.256278i
$626$	10.0534	−	17.4130i	0.401815	−	0.695965i
$627$		0			0
$628$	−3.52158	−	6.09956i	−0.140526	−	0.243399i
$629$	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	$0.410452\pi$
$632$	3.10806	+	5.38333i	0.123632	+	0.214137i
$633$		0			0
$634$	−13.0051	+	22.5255i	−0.516499	+	0.894602i
$635$	−0.306761	−	4.72790i	−0.0121734	−	0.187621i
$636$		0			0
$637$	−9.01910	+	21.5835i	−0.357350	+	0.855169i
$638$	−0.554779			−0.0219639
$639$		0			0
$640$	1.24107	+	1.86004i	0.0490576	+	0.0735245i
$641$		−	8.71120i		−	0.344072i	−0.985091	−	0.172036i	$-0.944965\pi$
$641$		−	8.71120i		−	0.344072i	0.985091	−	0.172036i	$-0.0550345\pi$
$642$		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	$0.508269\pi$
$644$	4.11145	−	2.73792i	0.162014	−	0.107889i
$645$		0			0
$646$	18.2075	+	31.5363i	0.716365	+	1.24078i
$647$	−31.0729	+	17.9400i	−1.22160	+	0.705293i	−0.965260	−	0.261293i	$-0.915851\pi$
$647$	−31.0729	+	17.9400i	−1.22160	+	0.705293i	−0.256344	+	0.966586i	$0.582518\pi$
$648$		0			0
$649$	−3.01262	−	1.73933i	−0.118256	−	0.0682748i
$650$	6.41442	−	15.4284i	0.251594	−	0.605150i
$651$		0			0
$652$	−6.38815	+	3.68820i	−0.250179	+	0.144441i
$653$	3.88543			0.152049			0.0760243	−	0.997106i	$-0.475777\pi$
$653$	3.88543			0.152049			0.0760243	+	0.997106i	$0.475777\pi$
$654$		0			0
$655$	−35.1609	+	2.28135i	−1.37385	+	0.0891397i
$656$	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
$661$	−38.7265	−	22.3587i	−1.50628	−	0.869654i	−0.999973	−	0.00730324i	$-0.997675\pi$
$661$	−38.7265	−	22.3587i	−1.50628	−	0.869654i	−0.506311	−	0.862351i	$-0.668991\pi$
$662$	−6.69898	+	11.6030i	−0.260363	+	0.450962i
$663$		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
$668$		−	16.8690i		−	0.652683i
$669$		0			0
$670$	−0.656293	−	10.1150i	−0.0253548	−	0.390777i
$671$	0.638775	+	1.10639i	0.0246596	+	0.0427118i
$672$		0			0
$673$	−32.2357	−	18.6113i	−1.24259	−	0.717412i	−0.272973	−	0.962022i	$-0.588007\pi$
$673$	−32.2357	−	18.6113i	−1.24259	−	0.717412i	−0.969622	+	0.244610i	$0.921340\pi$
$674$	−7.18391	−	4.14763i	−0.276714	−	0.159761i
$675$		0			0
$676$	0.916415	+	1.58728i	0.0352467	+	0.0610492i
$677$	10.8972	−	6.29151i	0.418814	−	0.241803i	−0.275756	−	0.961228i	$-0.588928\pi$
$677$	10.8972	−	6.29151i	0.418814	−	0.241803i	0.694570	+	0.719425i	$0.255595\pi$
$678$		0			0
$679$	−10.2182	+	6.80454i	−0.392137	+	0.261134i
$680$	9.02367	−	6.02085i	0.346042	−	0.230889i
$681$		0			0
$682$	3.73104			0.142869
$683$	−8.98544	−	15.5632i	−0.343818	−	0.595511i	0.641320	−	0.767274i	$-0.278387\pi$
$683$	−8.98544	−	15.5632i	−0.343818	−	0.595511i	−0.985138	+	0.171763i	$0.945054\pi$
$684$		0			0
$685$	−24.5611	+	1.59360i	−0.938432	+	0.0608884i
$686$	−13.9812	+	12.1460i	−0.533805	+	0.463737i
$687$		0			0
$688$			8.82245i			0.336353i
$689$	9.83603	−	17.0365i	0.374723	−	0.649039i
$690$		0			0
$691$	38.3130	−	22.1200i	1.45750	−	0.841485i	0.458608	−	0.888639i	$-0.348348\pi$
$691$	38.3130	−	22.1200i	1.45750	−	0.841485i	0.998888	+	0.0471537i	$0.0150151\pi$
$692$		−	10.2449i		−	0.389453i
$693$		0			0
$694$	16.4408			0.624086
$695$	−31.1568	+	20.7887i	−1.18185	+	0.788560i
$696$		0			0
$697$	−7.14061	−	4.12264i	−0.270470	−	0.156156i
$698$		−	30.3016i		−	1.14693i
$699$		0			0
$700$	9.97093	−	8.69371i	0.376866	−	0.328591i
$701$		−	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
$704$		−	0.745990i		−	0.0281156i
$705$		0			0
$706$	10.7919	−	6.23074i	0.406160	−	0.234497i
$707$	−26.0206	−	12.8824i	−0.978607	−	0.484493i
$708$		0			0
$709$	−18.3682	−	31.8146i	−0.689831	−	1.19482i	−0.971892	−	0.235425i	$-0.924352\pi$
$709$	−18.3682	−	31.8146i	−0.689831	−	1.19482i	0.282062	−	0.959396i	$-0.408982\pi$
$710$	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
$715$	−4.63689	+	3.09386i	−0.173410	+	0.115704i
$716$		−	19.0038i		−	0.710204i
$717$		0			0
$718$		−	1.17680i		−	0.0439177i
$719$	−15.0842	+	26.1266i	−0.562546	+	0.974358i	0.434727	+	0.900562i	$0.356845\pi$
$719$	−15.0842	+	26.1266i	−0.562546	+	0.974358i	−0.997273	+	0.0737961i	$0.976489\pi$
$720$		0			0
$721$	−15.8252	−	7.83480i	−0.589360	−	0.291783i
$722$	18.6714	−	32.3398i	0.694878	−	1.20356i
$723$		0			0
$724$	4.79273	+	2.76708i	0.178120	+	0.102838i
$725$	3.43349	+	1.42749i	0.127516	+	0.0530156i
$726$		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
$731$	42.8007			1.58304
$732$		0			0
$733$	−20.2714			−0.748740			−0.374370	−	0.927279i	$-0.622141\pi$
$733$	−20.2714			−0.748740			−0.374370	+	0.927279i	$0.622141\pi$
$734$	−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	0.822128	+	0.569303i	$0.192787\pi$
$739$	24.5774	+	42.5693i	0.904095	+	1.56594i	0.0819667	+	0.996635i	$0.473880\pi$
$740$	−12.4221	+	8.28835i	−0.456644	+	0.304686i
$741$		0			0
$742$	12.9636	−	8.63280i	0.475908	−	0.316920i
$743$	−13.5537	−	23.4757i	−0.497237	−	0.861240i	0.502758	−	0.864427i	$-0.332319\pi$
$743$	−13.5537	−	23.4757i	−0.497237	−	0.861240i	−0.999995	+	0.00318755i	$0.998985\pi$
$744$		0			0
$745$	−3.12033	−	48.0916i	−0.114320	−	1.76194i
$746$	−21.9698	+	12.6843i	−0.804372	+	0.464405i
$747$		0			0
$748$	−3.61905			−0.132325
$749$	−30.0712	+	20.0252i	−1.09878	+	0.731706i
$750$		0			0
$751$	41.2806			1.50635			0.753174	−	0.657821i	$-0.228522\pi$
$751$	41.2806			1.50635			0.753174	+	0.657821i	$0.228522\pi$
$752$	−10.0544	−	5.80494i	−0.366648	−	0.211684i
$753$		0			0
$754$	2.15223	−	1.24259i	0.0783797	−	0.0452525i
$755$	34.3147	−	2.22644i	1.24884	−	0.0810285i
$756$		0			0
$757$		−	37.6630i		−	1.36888i	−0.729067	−	0.684442i	$-0.760046\pi$
$757$		−	37.6630i		−	1.36888i	0.729067	−	0.684442i	$-0.239954\pi$
$758$	−12.1747	−	21.0872i	−0.442206	−	0.765923i
$759$		0			0
$760$	−15.0485	−	7.43342i	−0.545868	−	0.269638i
$761$	−20.1064			−0.728855			−0.364427	−	0.931232i	$-0.618735\pi$
$761$	−20.1064			−0.728855			−0.364427	+	0.931232i	$0.618735\pi$
$762$		0			0
$763$	1.73619	+	27.1372i	0.0628544	+	0.982433i
$764$			20.0241i			0.724447i
$765$		0			0
$766$	−11.3669	+	6.56268i	−0.410702	+	0.237119i
$767$	15.5830			0.562670
$768$		0			0
$769$	−24.3791	+	14.0753i	−0.879134	+	0.507568i	−0.870373	−	0.492393i	$-0.836122\pi$
$769$	−24.3791	+	14.0753i	−0.879134	+	0.507568i	−0.00876117	+	0.999962i	$0.502789\pi$
$770$	−4.37685	+	0.566357i	−0.157731	+	0.0204101i
$771$		0			0
$772$	−16.4666	+	9.50697i	−0.592644	+	0.342163i
$773$	37.3009	−	21.5357i	1.34162	−	0.774585i	0.354576	−	0.935027i	$-0.384625\pi$
$773$	37.3009	−	21.5357i	1.34162	−	0.774585i	0.987045	+	0.160442i	$0.0512920\pi$
$774$		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
$779$			12.7574i			0.457082i
$780$		0			0
$781$	−3.11240			−0.111370
$782$	7.84404	+	4.52876i	0.280502	+	0.161948i
$783$		0			0
$784$	2.69893	−	6.45877i	0.0963904	−	0.230671i
$785$	6.97489	−	14.1203i	0.248945	−	0.503974i
$786$		0			0
$787$	17.6587	−	30.5858i	0.629466	−	1.09027i	−0.358193	−	0.933648i	$-0.616607\pi$
$787$	17.6587	−	30.5858i	0.629466	−	1.09027i	0.987659	−	0.156620i	$-0.0500596\pi$
$788$	3.47092	−	6.01181i	0.123646	−	0.214162i
$789$		0			0
$790$	−6.15587	+	12.4622i	−0.219016	+	0.443385i
$791$	3.40017	+	53.1457i	0.120896	+	1.88964i
$792$		0			0
$793$	−4.95618	−	2.86145i	−0.175999	−	0.101613i
$794$	36.0286			1.27861
$795$		0			0
$796$		−	4.51077i		−	0.159880i
$797$	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
$803$	−6.59918	+	3.81004i	−0.232880	+	0.134453i
$804$		0			0
$805$	10.1952	+	4.24950i	0.359335	+	0.149775i
$806$	−14.4744	+	8.35677i	−0.509838	+	0.294355i
$807$		0			0
$808$	10.9742			0.386071
$809$	−21.2722	+	12.2815i	−0.747890	+	0.431795i	−0.824931	−	0.565233i	$-0.808786\pi$
$809$	−21.2722	+	12.2815i	−0.747890	+	0.431795i	0.0770407	+	0.997028i	$0.475453\pi$
$810$		0			0
$811$		−	7.28238i		−	0.255719i	−0.991792	−	0.127860i	$-0.959189\pi$
$811$		−	7.28238i		−	0.255719i	0.991792	−	0.127860i	$-0.0408107\pi$
$812$	1.96358	−	0.125627i	0.0689082	−	0.00440863i
$813$		0			0
$814$	4.98201			0.174619
$815$	−14.7883	−	7.30490i	−0.518013	−	0.255879i
$816$		0			0
$817$	−33.1115	−	57.3508i	−1.15842	−	2.00645i
$818$			15.9469i			0.557571i
$819$		0			0
$820$	3.79242	−	0.246064i	0.132437	−	0.00859293i
$821$	−5.79033	+	3.34305i	−0.202084	+	0.116673i	−0.597627	−	0.801774i	$-0.703890\pi$
$821$	−5.79033	+	3.34305i	−0.202084	+	0.116673i	0.395543	+	0.918447i	$0.370556\pi$
$822$		0			0
$823$	9.87790	+	5.70301i	0.344322	+	0.198794i	0.662182	−	0.749343i	$-0.269631\pi$
$823$	9.87790	+	5.70301i	0.344322	+	0.198794i	−0.317860	+	0.948138i	$0.602964\pi$
$824$	6.67426			0.232509
$825$		0			0
$826$	11.0567	+	5.47400i	0.384712	+	0.190465i
$827$	9.16990			0.318868			0.159434	−	0.987209i	$-0.449033\pi$
$827$	9.16990			0.318868			0.159434	+	0.987209i	$0.449033\pi$
$828$		0			0
$829$	13.6953	−	7.90700i	0.475659	−	0.274622i	−0.242947	−	0.970040i	$-0.578114\pi$
$829$	13.6953	−	7.90700i	0.475659	−	0.274622i	0.718605	+	0.695418i	$0.244781\pi$
$830$	0.379237	+	5.84493i	0.0131635	+	0.202880i
$831$		0			0
$832$	1.67087	+	2.89402i	0.0579268	+	0.100332i
$833$	−31.3337	−	13.0934i	−1.08565	−	0.453660i
$834$		0			0
$835$	31.3771	−	20.9357i	1.08585	−	0.724508i
$836$	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	−0.999878	−	0.0156002i	$-0.995034\pi$
$839$	−14.0897	+	24.4040i	−0.486429	+	0.842520i	0.513449	+	0.858120i	$0.328367\pi$
$840$		0			0
$841$	−14.2235	−	24.6358i	−0.490464	−	0.849509i
$842$	−37.3358			−1.28668
$843$		0			0
$844$	−7.84794			−0.270137
$845$	−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
$850$	22.3980	+	9.31209i	0.768246	+	0.319402i
$851$	−10.7982	−	6.23433i	−0.370157	−	0.213710i
$852$		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
$857$		−	31.9068i		−	1.08992i	−0.838464	−	0.544958i	$-0.816546\pi$
$857$		−	31.9068i		−	1.08992i	0.838464	−	0.544958i	$-0.183454\pi$
$858$		0			0
$859$			45.7568i			1.56120i	0.625030	+	0.780601i	$0.285087\pi$
$859$			45.7568i			1.56120i	−0.625030	+	0.780601i	$0.714913\pi$
$860$	−16.4101	+	10.9493i	−0.559580	+	0.373367i
$861$		0			0
$862$	7.75117	+	4.47514i	0.264006	+	0.152424i
$863$	−21.5708	+	37.3618i	−0.734280	+	1.27181i	0.220759	+	0.975328i	$0.429147\pi$
$863$	−21.5708	+	37.3618i	−0.734280	+	1.27181i	−0.955039	+	0.296481i	$0.904187\pi$
$864$		0			0
$865$	19.0559	−	12.7146i	0.647921	−	0.432311i
$866$	−6.00301	−	10.3975i	−0.203991	−	0.353322i
$867$		0			0
$868$	−13.2056	+	0.844874i	−0.448228	+	0.0286769i
$869$	4.01591	−	2.31859i	0.136230	−	0.0786526i
$870$		0			0
$871$		−	15.1483i		−	0.513282i
$872$	−5.13894	−	8.90090i	−0.174026	−	0.301422i
$873$		0			0
$874$		−	14.0142i		−	0.474036i
$875$	28.5453	+	7.75682i	0.965006	+	0.262228i
$876$		0			0
$877$			18.3979i			0.621255i	0.950532	+	0.310627i	$0.100539\pi$
$877$			18.3979i			0.621255i	−0.950532	+	0.310627i	$0.899461\pi$
$878$	28.3831	+	16.3870i	0.957882	+	0.553034i
$879$		0			0
$880$	1.38757	−	0.925826i	0.0467750	−	0.0312096i
$881$	−8.81308			−0.296920			−0.148460	−	0.988918i	$-0.547432\pi$
$881$	−8.81308			−0.296920			−0.148460	+	0.988918i	$0.547432\pi$
$882$		0			0
$883$		−	2.02023i		−	0.0679863i	−0.999422	−	0.0339931i	$-0.989178\pi$
$883$		−	2.02023i		−	0.0679863i	0.999422	−	0.0339931i	$-0.0108224\pi$
$884$	14.0399	−	8.10593i	0.472212	−	0.272632i
$885$		0			0
$886$	3.05270	−	5.28743i	0.102557	−	0.177635i
$887$			33.2724i			1.11718i	0.829445	+	0.558589i	$0.188657\pi$
$887$			33.2724i			1.11718i	−0.829445	+	0.558589i	$0.811343\pi$
$888$		0			0
$889$	2.48725	−	5.02390i	0.0834198	−	0.168496i
$890$	33.8542	−	2.19657i	1.13480	−	0.0736291i
$891$		0			0
$892$	10.7610	+	18.6387i	0.360306	+	0.624068i
$893$	87.1459			2.91623
$894$		0			0
$895$	35.3477	−	23.5850i	1.18154	−	0.788359i
$896$	0.168925	+	2.64035i	0.00564340	+	0.0882080i
$897$		0			0
$898$	−3.80762	+	2.19833i	−0.127062	+	0.0733593i
$899$	−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
$905$	0.801228	+	12.3488i	0.0266337	+	0.410488i
$906$		0			0
$907$		−	11.1534i		−	0.370344i	−0.982706	−	0.185172i	$-0.940716\pi$
$907$		−	11.1534i		−	0.370344i	0.982706	−	0.185172i	$-0.0592842\pi$
$908$	−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
$913$	0.977033	−	1.69227i	0.0323351	−	0.0560060i
$914$	−28.7983	−	16.6267i	−0.952564	−	0.549963i
$915$		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	−0.998209	−	0.0598209i	$-0.980947\pi$
$919$	−13.5598	+	23.4863i	−0.447298	+	0.774743i	0.550911	+	0.834564i	$0.314280\pi$
$920$	−4.16601	+	0.270304i	−0.137349	+	0.00891165i
$921$		0			0
$922$	−12.4447			−0.409844
$923$	12.0744	−	6.97114i	0.397432	−	0.229458i
$924$		0			0
$925$	−30.8333	−	12.8191i	−1.01379	−	0.421490i
$926$	−2.79388	−	1.61305i	−0.0918126	−	0.0530080i
$927$		0			0
$928$	−0.644047	+	0.371841i	−0.0211419	+	0.0122063i
$929$	−22.0537	−	38.1982i	−0.723559	−	1.25324i	−0.959564	−	0.281490i	$-0.909171\pi$
$929$	−22.0537	−	38.1982i	−0.723559	−	1.25324i	0.236005	−	0.971752i	$-0.424162\pi$
$930$		0			0
$931$	6.69585	+	52.1149i	0.219448	+	1.70800i
$932$	0.572350	+	0.991339i	0.0187479	+	0.0324724i
$933$		0			0
$934$		−	41.6247i		−	1.36200i
$935$	−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	$0.329723\pi$
$938$	5.32131	−	10.7483i	0.173747	−	0.350944i
$939$		0			0
$940$	−1.68086	−	25.9060i	−0.0548237	−	0.844961i
$941$	−3.25513	+	5.63804i	−0.106114	+	0.183795i	−0.914193	−	0.405280i	$-0.867174\pi$
$941$	−3.25513	+	5.63804i	−0.106114	+	0.183795i	0.808079	+	0.589074i	$0.200508\pi$
$942$		0			0
$943$	1.58658	+	2.74803i	0.0516661	+	0.0894883i
$944$	−4.66316			−0.151773
$945$		0			0
$946$	6.58146			0.213982
$947$	−16.7485	−	29.0092i	−0.544252	−	0.942672i	−0.998654	−	0.0518752i	$-0.983480\pi$
$947$	−16.7485	−	29.0092i	−0.544252	−	0.942672i	0.454402	−	0.890797i	$-0.349853\pi$
$948$		0			0
$949$	17.0674	−	29.5616i	0.554032	−	0.959611i
$950$	−4.84983	−	37.2163i	−0.157349	−	1.20745i
$951$		0			0
$952$	12.8092	−	0.819513i	0.415150	−	0.0265606i
$953$	9.08698			0.294356			0.147178	−	0.989110i	$-0.452981\pi$
$953$	9.08698			0.294356			0.147178	+	0.989110i	$0.452981\pi$
$954$		0			0
$955$	−37.2457	+	24.8513i	−1.20524	+	0.804171i
$956$		−	11.7776i		−	0.380915i
$957$		0			0
$958$	−11.5051	−	19.9275i	−0.371714	−	0.643827i
$959$	−26.0988	−	12.9211i	−0.842774	−	0.417245i
$960$		0			0
$961$	−2.99268	−	5.18347i	−0.0965380	−	0.167209i
$962$	−19.3274	+	11.1587i	−0.623141	+	0.359771i
$963$		0			0
$964$	19.9120	+	11.4962i	0.641323	+	0.370268i
$965$	−38.1195	−	18.8296i	−1.22711	−	0.606147i
$966$		0			0
$967$	−0.584986	+	0.337742i	−0.0188119	+	0.0108610i	−0.509376	−	0.860544i	$-0.670124\pi$
$967$	−0.584986	+	0.337742i	−0.0188119	+	0.0108610i	0.490565	+	0.871405i	$0.336791\pi$
$968$	10.4435			0.335667
$969$		0			0
$970$	10.3538	−	0.671785i	0.332440	−	0.0215697i
$971$	−3.90049	+	6.75585i	−0.125173	+	0.216805i	−0.921800	−	0.387665i	$-0.873282\pi$
$971$	−3.90049	+	6.75585i	−0.125173	+	0.216805i	0.796628	+	0.604470i	$0.206615\pi$
$972$		0			0
$973$	−44.2276	+	2.82960i	−1.41787	+	0.0907129i
$974$	9.17108	+	5.29492i	0.293860	+	0.169660i
$975$		0			0
$976$	1.48312	+	0.856279i	0.0474734	+	0.0274088i
$977$	−22.7250	+	39.3609i	−0.727037	+	1.25927i	0.231093	+	0.972932i	$0.425770\pi$
$977$	−22.7250	+	39.3609i	−0.727037	+	1.25927i	−0.958130	+	0.286334i	$0.907563\pi$
$978$		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
$983$		−	59.2020i		−	1.88825i	−0.329587	−	0.944125i	$-0.606909\pi$
$983$		−	59.2020i		−	1.88825i	0.329587	−	0.944125i	$-0.393091\pi$
$984$		0			0
$985$	15.4899	−	1.00503i	0.493548	−	0.0320229i
$986$	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	0.804653	−	0.593745i	$-0.202351\pi$
$991$	−3.52175	−	6.09985i	−0.111872	−	0.193768i	−0.916525	+	0.399977i	$0.869018\pi$
$992$	4.33139	−	2.50073i	0.137522	−	0.0793983i
$993$		0			0
$994$	11.0160	−	0.704785i	0.349406	−	0.0223544i
$995$	8.39022	−	5.59819i	0.265988	−	0.177474i
$996$		0			0
$997$	−43.8171			−1.38770			−0.693851	−	0.720119i	$-0.744087\pi$
$997$	−43.8171			−1.38770			−0.693851	+	0.720119i	$0.744087\pi$
$998$	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.r.a.89.1		48
3.2	odd	2		630.2.r.b.299.21	yes	48
5.4	even	2		1890.2.r.b.89.1		48
7.3	odd	6		1890.2.bi.b.899.9		48
9.4	even	3		630.2.bi.b.509.5	yes	48
9.5	odd	6		1890.2.bi.a.719.7		48
15.14	odd	2		630.2.r.a.299.4	yes	48
21.17	even	6		630.2.bi.a.479.20	yes	48
35.24	odd	6		1890.2.bi.a.899.7		48
45.4	even	6		630.2.bi.a.509.20	yes	48
45.14	odd	6		1890.2.bi.b.719.9		48
63.31	odd	6		630.2.r.a.59.4	✓	48
63.59	even	6		1890.2.r.b.1529.1		48
105.59	even	6		630.2.bi.b.479.5	yes	48
315.59	even	6	inner	1890.2.r.a.1529.1		48
315.94	odd	6		630.2.r.b.59.21	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.4	✓	48	63.31	odd	6
630.2.r.a.299.4	yes	48	15.14	odd	2
630.2.r.b.59.21	yes	48	315.94	odd	6
630.2.r.b.299.21	yes	48	3.2	odd	2
630.2.bi.a.479.20	yes	48	21.17	even	6
630.2.bi.a.509.20	yes	48	45.4	even	6
630.2.bi.b.479.5	yes	48	105.59	even	6
630.2.bi.b.509.5	yes	48	9.4	even	3
1890.2.r.a.89.1		48	1.1	even	1	trivial
1890.2.r.a.1529.1		48	315.59	even	6	inner
1890.2.r.b.89.1		48	5.4	even	2
1890.2.r.b.1529.1		48	63.59	even	6
1890.2.bi.a.719.7		48	9.5	odd	6
1890.2.bi.a.899.7		48	35.24	odd	6
1890.2.bi.b.719.9		48	45.14	odd	6
1890.2.bi.b.899.9		48	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.23138 + 0.144779i) q^{5} +(-2.37108 - 1.17388i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.23138 + 0.144779i) q^{5} +(-2.37108 - 1.17388i) q^{7} +1.00000 q^{8} +(1.24107 + 1.86004i) q^{10} -0.745990i q^{11} +(1.67087 + 2.89402i) q^{13} +(0.168925 + 2.64035i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.20138 + 2.42567i) q^{17} +(6.50055 + 3.75309i) q^{19} +(0.990306 - 2.00482i) q^{20} +(-0.646046 + 0.372995i) q^{22} +1.86701 q^{23} +(4.95808 - 0.646111i) q^{25} +(1.67087 - 2.89402i) q^{26} +(2.20215 - 1.46647i) q^{28} +(0.644047 + 0.371841i) q^{29} +(-4.33139 - 2.50073i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.20138 + 2.42567i) q^{34} +(5.46071 + 2.27609i) q^{35} +(-5.78366 - 3.33920i) q^{37} -7.50618i q^{38} +(-2.23138 + 0.144779i) q^{40} +(0.849794 + 1.47189i) q^{41} +(-7.64047 - 4.41123i) q^{43} +(0.646046 + 0.372995i) q^{44} +(-0.933507 - 1.61688i) q^{46} +(10.0544 - 5.80494i) q^{47} +(4.24400 + 5.56673i) q^{49} +(-3.03859 - 3.97077i) q^{50} -3.34173 q^{52} +(-2.94339 - 5.09811i) q^{53} +(0.108003 + 1.66458i) q^{55} +(-2.37108 - 1.17388i) q^{56} -0.743681i q^{58} +(2.33158 - 4.03841i) q^{59} +(-1.48312 + 0.856279i) q^{61} +5.00146i q^{62} +1.00000 q^{64} +(-4.14732 - 6.21575i) q^{65} +(-3.92576 - 2.26654i) q^{67} -4.85133i q^{68} +(-0.759202 - 5.86716i) q^{70} -4.17217i q^{71} +(-5.10736 - 8.84620i) q^{73} +6.67839i q^{74} +(-6.50055 + 3.75309i) q^{76} +(-0.875705 + 1.76880i) q^{77} +(3.10806 + 5.38333i) q^{79} +(1.24107 + 1.86004i) q^{80} +(0.849794 - 1.47189i) q^{82} +(2.26849 + 1.30971i) q^{83} +(9.02367 - 6.02085i) q^{85} +8.82245i q^{86} -0.745990i q^{88} +(7.58595 - 13.1393i) q^{89} +(-0.564503 - 8.82335i) q^{91} +(-0.933507 + 1.61688i) q^{92} +(-10.0544 - 5.80494i) q^{94} +(-15.0485 - 7.43342i) q^{95} +(2.32004 - 4.01843i) q^{97} +(2.69893 - 6.45877i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8}+O(q^{10}) \) 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8	\( 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} - 3 q^{14} - 24 q^{16} - 6 q^{22} - 6 q^{23} + 3 q^{28} + 3 q^{29} - 24 q^{32} - 12 q^{35} - 3 q^{41} + 6 q^{44} + 3 q^{46} - 6 q^{49} + 18 q^{50} - 42 q^{55} - 9 q^{61} + 48 q^{64} + 21 q^{65} + 33 q^{67} + 12 q^{70} - 18 q^{73} + 6 q^{77} - 3 q^{82} - 9 q^{83} + 33 q^{85} - 33 q^{89} + 3 q^{92} - 33 q^{95} - 24 q^{97} + 3 q^{98}+O(q^{100}) \) 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 - 3 * q^14 - 24 * q^16 - 6 * q^22 - 6 * q^23 + 3 * q^28 + 3 * q^29 - 24 * q^32 - 12 * q^35 - 3 * q^41 + 6 * q^44 + 3 * q^46 - 6 * q^49 + 18 * q^50 - 42 * q^55 - 9 * q^61 + 48 * q^64 + 21 * q^65 + 33 * q^67 + 12 * q^70 - 18 * q^73 + 6 * q^77 - 3 * q^82 - 9 * q^83 + 33 * q^85 - 33 * q^89 + 3 * q^92 - 33 * q^95 - 24 * q^97 + 3 * q^98

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