LMFDB - Embedded newform 1890.2.r.b.89.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1890,2,Mod(89,1890)] 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([1, 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("1890.89"); 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:traces = [48,24] 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			89.1
Character	$\chi$	$=$	1890.89
Dual form			1890.2.r.b.1529.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.23138 - 0.144779i) q^{5} +(2.37108 + 1.17388i) q^{7} -1.00000 q^{8} +(-0.990306 - 2.00482i) q^{10} -0.745990i q^{11} +(-1.67087 - 2.89402i) q^{13} +(0.168925 + 2.64035i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.20138 - 2.42567i) q^{17} +(6.50055 + 3.75309i) q^{19} +(1.24107 - 1.86004i) q^{20} +(0.646046 - 0.372995i) q^{22} -1.86701 q^{23} +(4.95808 + 0.646111i) q^{25} +(1.67087 - 2.89402i) q^{26} +(-2.20215 + 1.46647i) q^{28} +(0.644047 + 0.371841i) q^{29} +(-4.33139 - 2.50073i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.20138 + 2.42567i) q^{34} +(-5.12081 - 2.96266i) q^{35} +(5.78366 + 3.33920i) q^{37} +7.50618i q^{38} +(2.23138 + 0.144779i) q^{40} +(0.849794 + 1.47189i) q^{41} +(7.64047 + 4.41123i) q^{43} +(0.646046 + 0.372995i) q^{44} +(-0.933507 - 1.61688i) q^{46} +(-10.0544 + 5.80494i) q^{47} +(4.24400 + 5.56673i) q^{49} +(1.91949 + 4.61688i) q^{50} +3.34173 q^{52} +(2.94339 + 5.09811i) q^{53} +(-0.108003 + 1.66458i) q^{55} +(-2.37108 - 1.17388i) q^{56} +0.743681i q^{58} +(2.33158 - 4.03841i) q^{59} +(-1.48312 + 0.856279i) q^{61} -5.00146i q^{62} +1.00000 q^{64} +(3.30934 + 6.69956i) q^{65} +(3.92576 + 2.26654i) q^{67} +4.85133i q^{68} +(0.00533076 - 5.91608i) q^{70} -4.17217i q^{71} +(5.10736 + 8.84620i) q^{73} +6.67839i q^{74} +(-6.50055 + 3.75309i) q^{76} +(0.875705 - 1.76880i) q^{77} +(3.10806 + 5.38333i) q^{79} +(0.990306 + 2.00482i) q^{80} +(-0.849794 + 1.47189i) q^{82} +(-2.26849 - 1.30971i) q^{83} +(-9.72604 + 4.80431i) q^{85} +8.82245i q^{86} +0.745990i q^{88} +(7.58595 - 13.1393i) q^{89} +(-0.564503 - 8.82335i) q^{91} +(0.933507 - 1.61688i) q^{92} +(-10.0544 - 5.80494i) q^{94} +(-13.9618 - 9.31570i) q^{95} +(-2.32004 + 4.01843i) q^{97} +(-2.69893 + 6.45877i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8} - 3 q^{14} - 24 q^{16} + 6 q^{22} + 6 q^{23} - 3 q^{28} + 3 q^{29} + 24 q^{32} - 18 q^{35} - 3 q^{41} + 6 q^{44} + 3 q^{46} - 6 q^{49} + 18 q^{50} + 42 q^{55} - 9 q^{61}+ \cdots - 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 - 18 * 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 + 33 * q^65 - 33 * q^67 - 6 * 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

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
$10$	−0.990306	−	2.00482i	−0.313162	−	0.633979i
$11$		−	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	0.535714	−	0.844400i	$-0.320043\pi$
$13$	−1.67087	−	2.89402i	−0.463415	−	0.802658i	−0.999128	+	0.0417418i	$0.986709\pi$
$14$	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	0.105175	−	0.994454i	$-0.466460\pi$
$17$	4.20138	−	2.42567i	1.01898	−	0.588311i	0.913810	+	0.406143i	$0.133127\pi$
$18$		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	$0.336494\pi$
$20$	1.24107	−	1.86004i	0.277512	−	0.415917i
$21$		0			0
$22$	0.646046	−	0.372995i	0.137738	−	0.0795228i
$23$	−1.86701			−0.389299			−0.194650	−	0.980873i	$-0.562357\pi$
$23$	−1.86701			−0.389299			−0.194650	+	0.980873i	$0.562357\pi$
$24$		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
$35$	−5.12081	−	2.96266i	−0.865575	−	0.500780i
$36$		0			0
$37$	5.78366	+	3.33920i	0.950827	+	0.548960i	0.893338	−	0.449386i	$-0.148357\pi$
$37$	5.78366	+	3.33920i	0.950827	+	0.548960i	0.0574896	+	0.998346i	$0.481690\pi$
$38$			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	0.952535	−	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
$47$	−10.0544	+	5.80494i	−1.46659	+	0.846737i	−0.999302	−	0.0373667i	$-0.988103\pi$
$47$	−10.0544	+	5.80494i	−1.46659	+	0.846737i	−0.467290	+	0.884104i	$0.654770\pi$
$48$		0			0
$49$	4.24400	+	5.56673i	0.606285	+	0.795247i
$50$	1.91949	+	4.61688i	0.271457	+	0.652925i
$51$		0			0
$52$	3.34173			0.463415
$53$	2.94339	+	5.09811i	0.404306	+	0.700279i	0.994240	−	0.107172i	$-0.0341797\pi$
$53$	2.94339	+	5.09811i	0.404306	+	0.700279i	−0.589934	+	0.807451i	$0.700846\pi$
$54$		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
$65$	3.30934	+	6.69956i	0.410473	+	0.830978i
$66$		0			0
$67$	3.92576	+	2.26654i	0.479608	+	0.276902i	0.720253	−	0.693711i	$-0.244026\pi$
$67$	3.92576	+	2.26654i	0.479608	+	0.276902i	−0.240645	+	0.970613i	$0.577359\pi$
$68$			4.85133i			0.588311i
$69$		0			0
$70$	0.00533076	−	5.91608i	0.000637148	−	0.707106i
$71$		−	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	$0.0372802\pi$
$73$	5.10736	+	8.84620i	0.597771	+	1.03537i	−0.395378	+	0.918518i	$0.629387\pi$
$74$			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	$0.719622\pi$
$80$	0.990306	+	2.00482i	0.110720	+	0.224145i
$81$		0			0
$82$	−0.849794	+	1.47189i	−0.0938441	+	0.162543i
$83$	−2.26849	−	1.30971i	−0.248999	−	0.143760i	0.370307	−	0.928910i	$-0.379253\pi$
$83$	−2.26849	−	1.30971i	−0.248999	−	0.143760i	−0.619306	+	0.785150i	$0.712586\pi$
$84$		0			0
$85$	−9.72604	+	4.80431i	−1.05494	+	0.521100i
$86$			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
$95$	−13.9618	−	9.31570i	−1.43245	−	0.955771i
$96$		0			0
$97$	−2.32004	+	4.01843i	−0.235565	+	0.408010i	−0.959437	−	0.281924i	$-0.909027\pi$
$97$	−2.32004	+	4.01843i	−0.235565	+	0.408010i	0.723872	+	0.689934i	$0.242361\pi$
$98$	−2.69893	+	6.45877i	−0.272633	+	0.652435i
$99$		0			0
$100$	−3.03859	+	3.97077i	−0.303859	+	0.397077i
$101$	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	$-0.606650\pi$
$103$	−6.67426			−0.657635			−0.328817	+	0.944394i	$0.606650\pi$
$104$	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	$0.396135\pi$
$107$	−6.82770	+	11.8259i	−0.660058	+	1.14325i	−0.980600	+	0.196020i	$0.937198\pi$
$108$		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	$0.997148\pi$
$110$	−1.49557	+	0.738758i	−0.142597	+	0.0704378i
$111$		0			0
$112$	−0.168925	−	2.64035i	−0.0159619	−	0.249490i
$113$	10.0641	+	17.4316i	0.946754	+	1.63983i	0.752201	+	0.658934i	$0.228992\pi$
$113$	10.0641	+	17.4316i	0.946754	+	1.63983i	0.194553	+	0.980892i	$0.437674\pi$
$114$		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	$-0.970032\pi$
$127$		−	2.11883i		−	0.188015i	0.995571	−	0.0940077i	$-0.0299678\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−4.14732	+	6.21575i	−0.363744	+	0.545157i
$131$	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	$-0.655819\pi$
$137$	−11.0072			−0.940405			−0.470202	+	0.882559i	$0.655819\pi$
$138$		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	$0.0818543\pi$
$140$	5.12614	−	2.95342i	0.433238	−	0.249610i
$141$		0			0
$142$	3.61321	−	2.08609i	0.303213	−	0.175060i
$143$	−2.15891	+	1.24645i	−0.180537	+	0.104233i
$144$		0			0
$145$	−1.38328	−	0.922960i	−0.114875	−	0.0766477i
$146$	−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
$155$	9.30292	+	6.20717i	0.747228	+	0.498572i
$156$		0			0
$157$	3.52158	−	6.09956i	0.281053	−	0.486798i	−0.690591	−	0.723245i	$-0.742650\pi$
$157$	3.52158	−	6.09956i	0.281053	−	0.486798i	0.971644	+	0.236447i	$0.0759830\pi$
$158$	−3.10806	+	5.38333i	−0.247264	+	0.428274i
$159$		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	$-0.426617\pi$
$163$	−6.38815	−	3.68820i	−0.500359	−	0.288882i	−0.728862	+	0.684661i	$0.759950\pi$
$164$	−1.69959			−0.132716
$165$		0			0
$166$		−	2.61943i		−	0.203307i
$167$	14.6090	−	8.43452i	1.13048	−	0.652683i	0.186424	−	0.982469i	$-0.440310\pi$
$167$	14.6090	−	8.43452i	1.13048	−	0.652683i	0.944055	+	0.329787i	$0.106977\pi$
$168$		0			0
$169$	0.916415	−	1.58728i	0.0704935	−	0.122098i
$170$	−9.02367	−	6.02085i	−0.692084	−	0.461778i
$171$		0			0
$172$	−7.64047	+	4.41123i	−0.582580	+	0.336353i
$173$	8.87235	−	5.12245i	0.674552	−	0.389453i	−0.123247	−	0.992376i	$-0.539331\pi$
$173$	8.87235	−	5.12245i	0.674552	−	0.389453i	0.797799	+	0.602923i	$0.205997\pi$
$174$		0			0
$175$	10.9975	+	7.35218i	0.831334	+	0.555773i
$176$	−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
$185$	−12.4221	−	8.28835i	−0.913289	−	0.609372i
$186$		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	−0.228056	−	0.973648i	$-0.573237\pi$
$193$	−16.4666	−	9.50697i	−1.18529	−	0.684327i	−0.957232	+	0.289321i	$0.906570\pi$
$194$	−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	$-0.420459\pi$
$197$	6.94184			0.494586			0.247293	+	0.968941i	$0.420459\pi$
$198$		0			0
$199$	−3.90645	+	2.25539i	−0.276921	+	0.159880i	−0.632029	−	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
$205$	−1.68311	−	3.40736i	−0.117554	−	0.237981i
$206$	−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
$215$	−16.4101	−	10.9493i	−1.11916	−	0.746735i
$216$		0			0
$217$	−7.33450	−	11.0140i	−0.497898	−	0.747677i
$218$	5.13894	−	8.90090i	0.348053	−	0.602845i
$219$		0			0
$220$	−1.38757	−	0.925826i	−0.0935500	−	0.0624192i
$221$	−14.0399	−	8.10593i	−0.944425	−	0.545264i
$222$		0			0
$223$	−10.7610	+	18.6387i	−0.720612	+	1.24814i	0.240143	+	0.970738i	$0.422806\pi$
$223$	−10.7610	+	18.6387i	−0.720612	+	1.24814i	−0.960755	+	0.277399i	$0.910528\pi$
$224$	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	$-0.914161\pi$
$227$		−	8.02790i		−	0.532831i	0.963858	−	0.266415i	$-0.0858393\pi$
$228$		0			0
$229$		−	19.2674i		−	1.27322i	−0.771185	−	0.636612i	$-0.780335\pi$
$229$		−	19.2674i		−	1.27322i	0.771185	−	0.636612i	$-0.219665\pi$
$230$	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	−0.884164	−	0.467176i	$-0.845271\pi$
$233$	−0.572350	+	0.991339i	−0.0374959	+	0.0649448i	0.846668	+	0.532121i	$0.178605\pi$
$234$		0			0
$235$	23.2757	−	11.4973i	1.51834	−	0.750003i
$236$	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
$245$	−8.66401	−	13.0359i	−0.553523	−	0.832834i
$246$		0			0
$247$		−	25.0837i		−	1.59603i
$248$	4.33139	+	2.50073i	0.275044	+	0.158797i
$249$		0			0
$250$	−3.61468	−	10.5799i	−0.228612	−	0.669131i
$251$	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	$0.0702406\pi$
$257$			7.01785i			0.437762i	−0.975752	+	0.218881i	$0.929759\pi$
$258$		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	$-0.473965\pi$
$263$	2.64989			0.163399			0.0816996	+	0.996657i	$0.473965\pi$
$264$		0			0
$265$	−5.82972	−	11.8019i	−0.358117	−	0.724987i
$266$	−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	$-0.795519\pi$
$277$		−	19.9426i		−	1.19823i	0.800662	−	0.599116i	$-0.204481\pi$
$278$	14.5065	+	8.37531i	0.870040	+	0.502318i
$279$		0			0
$280$	5.12081	+	2.96266i	0.306027	+	0.177053i
$281$	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	−0.704454	−	0.709750i	$-0.748808\pi$
$283$	4.41483	−	7.64671i	0.262434	−	0.454550i	0.966888	+	0.255200i	$0.0821413\pi$
$284$	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	−0.733093	−	0.680129i	$-0.761924\pi$
$293$	−8.74058	+	5.04638i	−0.510630	+	0.294812i	0.222463	+	0.974941i	$0.428590\pi$
$294$		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
$299$	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
$305$	3.43336	−	1.69596i	0.196594	−	0.0971101i
$306$		0			0
$307$	10.7285			0.612306			0.306153	−	0.951982i	$-0.400958\pi$
$307$	10.7285			0.612306			0.306153	+	0.951982i	$0.400958\pi$
$308$	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	$-0.974286\pi$
$313$	−10.0534	−	17.4130i	−0.568253	−	0.984243i	0.428486	−	0.903548i	$-0.359047\pi$
$314$	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	$0.0940181\pi$
$317$	13.0051	+	22.5255i	0.730440	+	1.26516i	−0.226256	+	0.974068i	$0.572649\pi$
$318$		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
$325$	−6.41442	−	15.4284i	−0.355808	−	0.855812i
$326$		−	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
$335$	−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	$0.405877\pi$
$338$	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	−0.556490	−	0.830854i	$-0.687852\pi$
$347$	8.22042	−	14.2382i	0.441295	−	0.764346i	0.997786	+	0.0665078i	$0.0211857\pi$
$348$		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	$0.365588\pi$
$350$	−0.868416	+	13.2002i	−0.0464188	+	0.705582i
$351$		0			0
$352$	−0.646046	−	0.372995i	−0.0344344	−	0.0198807i
$353$		−	12.4615i		−	0.663257i	−0.943410	−	0.331629i	$-0.892402\pi$
$353$		−	12.4615i		−	0.663257i	0.943410	−	0.331629i	$-0.107598\pi$
$354$		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
$365$	−10.1157	−	20.4786i	−0.529480	−	1.07190i
$366$		0			0
$367$	−35.4401			−1.84996			−0.924978	−	0.380020i	$-0.875917\pi$
$367$	−35.4401			−1.84996			−0.924978	+	0.380020i	$0.875917\pi$
$368$	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	$0.228077\pi$
$373$			25.3686i			1.31353i	−0.754093	+	0.656767i	$0.771923\pi$
$374$	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	$0.284947\pi$
$380$	15.0485	−	7.43342i	0.771973	−	0.381326i
$381$		0			0
$382$	17.3414	+	10.0121i	0.887263	+	0.512262i
$383$			13.1254i			0.670674i	0.942098	+	0.335337i	$0.108850\pi$
$383$			13.1254i			0.670674i	−0.942098	+	0.335337i	$0.891150\pi$
$384$		0			0
$385$	−2.21011	+	3.82007i	−0.112638	+	0.194689i
$386$		−	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
$395$	−6.15587	−	12.4622i	−0.309735	−	0.627042i
$396$		0			0
$397$	18.0143	−	31.2016i	0.904111	−	1.56597i	0.0820040	−	0.996632i	$-0.473868\pi$
$397$	18.0143	−	31.2016i	0.904111	−	1.56597i	0.822107	−	0.569334i	$-0.192799\pi$
$398$	−3.90645	−	2.25539i	−0.195812	−	0.113052i
$399$		0			0
$400$	−1.91949	−	4.61688i	−0.0959745	−	0.230844i
$401$		−	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	$0.795667\pi$
$410$	2.10931	−	3.16130i	0.104171	−	0.156125i
$411$		0			0
$412$	3.33713	−	5.78008i	0.164409	−	0.284764i
$413$	10.2690	−	6.83838i	0.505303	−	0.336495i
$414$		0			0
$415$	4.87224	+	3.25089i	0.239169	+	0.159580i
$416$	−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
$425$	22.3980	−	9.31209i	1.08646	−	0.451703i
$426$		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	$-0.593152\pi$
$433$	−12.0060			−0.576972			−0.288486	+	0.957484i	$0.593152\pi$
$434$	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	0.784349	−	0.620320i	$-0.212997\pi$
$443$	−3.05270	−	5.28743i	−0.145038	−	0.251213i	−0.929387	+	0.369106i	$0.879664\pi$
$444$		0			0
$445$	−18.8294	+	28.2203i	−0.892599	+	1.33777i
$446$	−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
$455$	−0.0178140	+	19.7699i	−0.000835132	+	0.926829i
$456$		0			0
$457$	−28.7983	+	16.6267i	−1.34713	+	0.777765i	−0.987842	−	0.155462i	$-0.950313\pi$
$457$	−28.7983	+	16.6267i	−1.34713	+	0.777765i	−0.359287	+	0.933227i	$0.616980\pi$
$458$	16.6860	−	9.63368i	0.779687	−	0.450152i
$459$		0			0
$460$	−2.31710	+	3.47272i	−0.108035	+	0.161916i
$461$	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	−0.563514	−	0.826106i	$-0.690551\pi$
$463$	−2.79388	+	1.61305i	−0.129843	+	0.0749647i	0.433672	+	0.901071i	$0.357218\pi$
$464$		−	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	$-0.920098\pi$
$467$	−36.0480	−	20.8123i	−1.66810	−	0.963080i	−0.699443	−	0.714688i	$-0.746569\pi$
$468$		0			0
$469$	6.64763	+	9.98253i	0.306959	+	0.460950i
$470$	21.5948	+	14.4087i	0.996095	+	0.664622i
$471$		0			0
$472$	−2.33158	+	4.03841i	−0.107320	+	0.185883i
$473$	3.29073	−	5.69971i	0.151308	−	0.262073i
$474$		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
$479$	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
$485$	5.75867	−	8.63074i	0.261488	−	0.391902i
$486$		0			0
$487$	9.17108	−	5.29492i	0.415581	−	0.239936i	−0.277604	−	0.960696i	$-0.589540\pi$
$487$	9.17108	−	5.29492i	0.415581	−	0.239936i	0.693185	+	0.720760i	$0.256207\pi$
$488$	1.48312	−	0.856279i	0.0671376	−	0.0387619i
$489$		0			0
$490$	6.95742	−	14.0212i	0.314304	−	0.633414i
$491$	−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	$0.604982\pi$
$500$	7.35511	−	8.42035i	0.328931	−	0.376570i
$501$		0			0
$502$	0.724818	+	1.25542i	0.0323502	+	0.0560322i
$503$			33.2244i			1.48140i	0.671833	+	0.740702i	$0.265507\pi$
$503$			33.2244i			1.48140i	−0.671833	+	0.740702i	$0.734493\pi$
$504$		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
$520$	−3.30934	−	6.69956i	−0.145124	−	0.293795i
$521$	−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	$0.401581\pi$
$523$	−15.3867	+	26.6505i	−0.672813	+	1.16535i	−0.977103	+	0.212766i	$0.931753\pi$
$524$	−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
$530$	7.30592	−	10.9497i	0.317349	−	0.475623i
$531$		0			0
$532$	−19.8190	+	1.26798i	−0.859262	+	0.0549741i
$533$	2.83978	−	4.91865i	0.123005	−	0.213050i
$534$		0			0
$535$	16.9473	−	25.3996i	0.732696	−	1.09812i
$536$	−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
$545$	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
$550$	3.44414	−	1.43192i	0.146859	−	0.0610573i
$551$	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	0.971954	−	0.235172i	$-0.0755652\pi$
$557$	6.66281	+	11.5403i	0.282312	+	0.488979i	−0.689642	+	0.724151i	$0.742232\pi$
$558$		0			0
$559$		−	29.4823i		−	1.24697i
$560$	−0.00533076	+	5.91608i	−0.000225266	+	0.250000i
$561$		0			0
$562$			2.35446i			0.0993170i
$563$	−8.13242	−	4.69526i	−0.342741	−	0.197881i	0.318743	−	0.947841i	$-0.396739\pi$
$563$	−8.13242	−	4.69526i	−0.342741	−	0.197881i	−0.661483	+	0.749960i	$0.730073\pi$
$564$		0			0
$565$	−19.9331	−	40.3535i	−0.838594	−	1.69768i
$566$	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	0.629209	−	0.777236i	$-0.283379\pi$
$577$	−8.61149	−	14.9155i	−0.358501	−	0.620942i	−0.987711	+	0.156293i	$0.950045\pi$
$578$	6.53545			0.271839
$579$		0			0
$580$	1.49095	−	0.736472i	0.0619081	−	0.0305803i
$581$	−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	0.0696932	−	0.997568i	$-0.477798\pi$
$587$	−18.3983	−	10.6223i	−0.759380	−	0.438428i	−0.829073	+	0.559140i	$0.811131\pi$
$588$		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	0.386102	−	0.922456i	$-0.373821\pi$
$593$	−5.35047	−	3.08910i	−0.219718	−	0.126854i	−0.605819	+	0.795602i	$0.707155\pi$
$594$		0			0
$595$	−28.7009	−	0.0258613i	−1.17662	−	0.00106021i
$596$	−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	$-0.411800\pi$
$607$	13.4794			0.547111			0.273555	+	0.961856i	$0.411800\pi$
$608$	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	$-0.737153\pi$
$613$	−9.41875	+	5.43792i	−0.380420	+	0.219636i	0.297581	+	0.954697i	$0.403820\pi$
$614$	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	0.880051	−	0.474879i	$-0.157508\pi$
$617$	0.714583	+	1.23769i	0.0287680	+	0.0498277i	−0.851283	+	0.524707i	$0.824175\pi$
$618$		0			0
$619$			22.2859i			0.895747i	0.894097	+	0.447873i	$0.147818\pi$
$619$			22.2859i			0.895747i	−0.894097	+	0.447873i	$0.852182\pi$
$620$	−10.0270	+	4.95298i	−0.402695	+	0.198916i
$621$		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
$640$	−0.990306	−	2.00482i	−0.0391453	−	0.0792474i
$641$		−	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	$-0.841602\pi$
$643$	−21.6235	−	37.4529i	−0.852746	−	1.47700i	0.0259739	−	0.999663i	$-0.491731\pi$
$644$	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	0.256344	−	0.966586i	$-0.417482\pi$
$647$	31.0729	−	17.9400i	1.22160	−	0.705293i	0.965260	+	0.261293i	$0.0841487\pi$
$648$		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
$653$	−3.88543			−0.152049			−0.0760243	−	0.997106i	$-0.524223\pi$
$653$	−3.88543			−0.152049			−0.0760243	+	0.997106i	$0.524223\pi$
$654$		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
$665$	−22.1689	−	38.4777i	−0.859674	−	1.49210i
$666$		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	0.969622	−	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
$677$	−10.8972	+	6.29151i	−0.418814	+	0.241803i	−0.694570	−	0.719425i	$-0.744405\pi$
$677$	−10.8972	+	6.29151i	−0.418814	+	0.241803i	0.275756	+	0.961228i	$0.411072\pi$
$678$		0			0
$679$	−10.2182	+	6.80454i	−0.392137	+	0.261134i
$680$	9.72604	−	4.80431i	0.372977	−	0.184237i
$681$		0			0
$682$	−3.73104			−0.142869
$683$	8.98544	+	15.5632i	0.343818	+	0.595511i	0.985138	−	0.171763i	$-0.0549462\pi$
$683$	8.98544	+	15.5632i	0.343818	+	0.595511i	−0.641320	+	0.767274i	$0.721613\pi$
$684$		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
$695$	−33.5819	+	16.5882i	−1.27384	+	0.629228i
$696$		0			0
$697$	7.14061	+	4.12264i	0.270470	+	0.156156i
$698$			30.3016i			1.14693i
$699$		0			0
$700$	−11.8659	+	5.84804i	−0.448490	+	0.221035i
$701$		−	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	$-0.408982\pi$
$710$	−8.36444	+	4.13173i	−0.313912	+	0.155061i
$711$		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
$716$		−	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
$725$	2.95298	+	2.25974i	0.109671	+	0.0839247i
$726$		0			0
$727$	2.77440	−	4.80540i	0.102897	−	0.178222i	−0.809980	−	0.586457i	$-0.800522\pi$
$727$	2.77440	−	4.80540i	0.102897	−	0.178222i	0.912877	+	0.408235i	$0.133856\pi$
$728$	0.564503	+	8.82335i	0.0209219	+	0.327015i
$729$		0			0
$730$	12.6772	−	18.9998i	0.469203	−	0.703213i
$731$	42.8007			1.58304
$732$		0			0
$733$	20.2714			0.748740			0.374370	−	0.927279i	$-0.377859\pi$
$733$	20.2714			0.748740			0.374370	+	0.927279i	$0.377859\pi$
$734$	−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	$0.473880\pi$
$740$	13.3890	−	6.61365i	0.492188	−	0.243123i
$741$		0			0
$742$	−12.9636	+	8.63280i	−0.475908	+	0.316920i
$743$	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
$745$	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	$0.239954\pi$
$757$			37.6630i			1.36888i	−0.729067	+	0.684442i	$0.760046\pi$
$758$	12.1747	+	21.0872i	0.442206	+	0.765923i
$759$		0			0
$760$	13.9618	+	9.31570i	0.506448	+	0.337916i
$761$	−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	$0.502789\pi$
$770$	−4.41333	−	0.00397670i	−0.159046	−	0.000143310i
$771$		0			0
$772$	16.4666	−	9.50697i	0.592644	−	0.342163i
$773$	−37.3009	+	21.5357i	−1.34162	+	0.774585i	−0.987045	−	0.160442i	$-0.948708\pi$
$773$	−37.3009	+	21.5357i	−1.34162	+	0.774585i	−0.354576	+	0.935027i	$0.615375\pi$
$774$		0			0
$775$	−19.8596	−	15.1974i	−0.713380	−	0.545906i
$776$	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
$785$	−8.74106	+	13.1006i	−0.311982	+	0.467579i
$786$		0			0
$787$	−17.6587	+	30.5858i	−0.629466	+	1.09027i	0.358193	+	0.933648i	$0.383393\pi$
$787$	−17.6587	+	30.5858i	−0.629466	+	1.09027i	−0.987659	+	0.156620i	$0.949940\pi$
$788$	−3.47092	+	6.01181i	−0.123646	+	0.214162i
$789$		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
$794$	36.0286			1.27861
$795$		0			0
$796$		−	4.51077i		−	0.159880i
$797$	−14.2561	+	8.23077i	−0.504978	+	0.291549i	−0.730767	−	0.682627i	$-0.760837\pi$
$797$	−14.2561	+	8.23077i	−0.504978	+	0.291549i	0.225789	+	0.974176i	$0.427504\pi$
$798$		0			0
$799$	−28.1617	+	48.7775i	−0.996289	+	1.72562i
$800$	3.03859	−	3.97077i	0.107430	−	0.140388i
$801$		0			0
$802$	2.72857	−	1.57534i	0.0963492	−	0.0556272i
$803$	6.59918	−	3.81004i	0.232880	−	0.134453i
$804$		0			0
$805$	9.56062	+	5.53132i	0.336968	+	0.194953i
$806$	−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
$815$	13.7204	+	9.15463i	0.480605	+	0.320673i
$816$		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	0.317860	−	0.948138i	$-0.397036\pi$
$823$	−9.87790	−	5.70301i	−0.344322	−	0.198794i	−0.662182	+	0.749343i	$0.730369\pi$
$824$	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	$-0.550967\pi$
$827$	−9.16990			−0.318868			−0.159434	+	0.987209i	$0.550967\pi$
$828$		0			0
$829$	13.6953	−	7.90700i	0.475659	−	0.274622i	−0.242947	−	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
$835$	−33.8193	+	16.7055i	−1.17037	+	0.578118i
$836$	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
$845$	−2.27467	+	3.40914i	−0.0782511	+	0.117278i
$846$		0			0
$847$	24.7623	+	12.2594i	0.850844	+	0.421240i
$848$	2.94339	−	5.09811i	0.101077	−	0.175070i
$849$		0			0
$850$	19.2635	+	14.7412i	0.660733	+	0.505619i
$851$	−10.7982	−	6.23433i	−0.370157	−	0.213710i
$852$		0			0
$853$	−4.37925	+	7.58508i	−0.149943	+	0.259708i	−0.931206	−	0.364493i	$-0.881242\pi$
$853$	−4.37925	+	7.58508i	−0.149943	+	0.259708i	0.781263	+	0.624201i	$0.214576\pi$
$854$	−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	$0.183454\pi$
$857$			31.9068i			1.08992i	−0.838464	+	0.544958i	$0.816546\pi$
$858$		0			0
$859$			45.7568i			1.56120i	0.625030	+	0.780601i	$0.285087\pi$
$859$			45.7568i			1.56120i	−0.625030	+	0.780601i	$0.714913\pi$
$860$	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	−0.220759	−	0.975328i	$-0.570853\pi$
$863$	21.5708	−	37.3618i	0.734280	−	1.27181i	0.955039	−	0.296481i	$-0.0958132\pi$
$864$		0			0
$865$	−20.5392	+	10.1456i	−0.698352	+	0.344960i
$866$	−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
$875$	−23.4752	−	17.9977i	−0.793605	−	0.608433i
$876$		0			0
$877$		−	18.3979i		−	0.621255i	−0.950532	−	0.310627i	$-0.899461\pi$
$877$		−	18.3979i		−	0.621255i	0.950532	−	0.310627i	$-0.100539\pi$
$878$	−28.3831	−	16.3870i	−0.957882	−	0.553034i
$879$		0			0
$880$	1.49557	−	0.738758i	0.0504158	−	0.0249035i
$881$	−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	$0.0108224\pi$
$883$			2.02023i			0.0679863i	−0.999422	+	0.0339931i	$0.989178\pi$
$884$	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	$-0.811343\pi$
$887$		−	33.2724i		−	1.11718i	0.829445	−	0.558589i	$-0.188657\pi$
$888$		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
$895$	38.0991	−	18.8195i	1.27351	−	0.629068i
$896$	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	$0.0592842\pi$
$907$			11.1534i			0.370344i	−0.982706	+	0.185172i	$0.940716\pi$
$908$	6.95237	+	4.01395i	0.230722	+	0.133208i
$909$		0			0
$910$	−17.1302	+	9.86954i	−0.567860	+	0.327172i
$911$	−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
$925$	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
$929$	−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
$935$	3.58396	+	7.25553i	0.117208	+	0.237281i
$936$		0			0
$937$	−31.2098			−1.01958			−0.509789	−	0.860299i	$-0.670277\pi$
$937$	−31.2098			−1.01958			−0.509789	+	0.860299i	$0.670277\pi$
$938$	−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	$0.0165198\pi$
$947$	16.7485	+	29.0092i	0.544252	+	0.942672i	−0.454402	+	0.890797i	$0.650147\pi$
$948$		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	$-0.547019\pi$
$953$	−9.08698			−0.294356			−0.147178	+	0.989110i	$0.547019\pi$
$954$		0			0
$955$	−40.1447	+	19.8300i	−1.29905	+	0.641684i
$956$		−	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
$965$	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	$0.329876\pi$
$968$	−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	$-0.574230\pi$
$977$	22.7250	−	39.3609i	0.727037	−	1.25927i	0.958130	−	0.286334i	$-0.0924366\pi$
$978$		0			0
$979$	−9.80175	−	5.65904i	−0.313265	−	0.180864i
$980$	15.6214	−	0.985300i	0.499008	−	0.0314743i
$981$		0			0
$982$	−2.99490	−	1.72911i	−0.0955713	−	0.0551781i
$983$			59.2020i			1.88825i	0.329587	+	0.944125i	$0.393091\pi$
$983$			59.2020i			1.88825i	−0.329587	+	0.944125i	$0.606909\pi$
$984$		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
$995$	9.04328	−	4.46705i	0.286691	−	0.141615i
$996$		0			0
$997$	43.8171			1.38770			0.693851	−	0.720119i	$-0.255913\pi$
$997$	43.8171			1.38770			0.693851	+	0.720119i	$0.255913\pi$
$998$	−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.b.89.1		48
3.2	odd	2		630.2.r.a.299.4	yes	48
5.4	even	2		1890.2.r.a.89.1		48
7.3	odd	6		1890.2.bi.a.899.7		48
9.4	even	3		630.2.bi.a.509.20	yes	48
9.5	odd	6		1890.2.bi.b.719.9		48
15.14	odd	2		630.2.r.b.299.21	yes	48
21.17	even	6		630.2.bi.b.479.5	yes	48
35.24	odd	6		1890.2.bi.b.899.9		48
45.4	even	6		630.2.bi.b.509.5	yes	48
45.14	odd	6		1890.2.bi.a.719.7		48
63.31	odd	6		630.2.r.b.59.21	yes	48
63.59	even	6		1890.2.r.a.1529.1		48
105.59	even	6		630.2.bi.a.479.20	yes	48
315.59	even	6	inner	1890.2.r.b.1529.1		48
315.94	odd	6		630.2.r.a.59.4	✓	48

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

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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.23138 - 0.144779i) q^{5} +(2.37108 + 1.17388i) q^{7} -1.00000 q^{8} +(-0.990306 - 2.00482i) q^{10} -0.745990i q^{11} +(-1.67087 - 2.89402i) q^{13} +(0.168925 + 2.64035i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.20138 - 2.42567i) q^{17} +(6.50055 + 3.75309i) q^{19} +(1.24107 - 1.86004i) q^{20} +(0.646046 - 0.372995i) q^{22} -1.86701 q^{23} +(4.95808 + 0.646111i) q^{25} +(1.67087 - 2.89402i) q^{26} +(-2.20215 + 1.46647i) q^{28} +(0.644047 + 0.371841i) q^{29} +(-4.33139 - 2.50073i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.20138 + 2.42567i) q^{34} +(-5.12081 - 2.96266i) q^{35} +(5.78366 + 3.33920i) q^{37} +7.50618i q^{38} +(2.23138 + 0.144779i) q^{40} +(0.849794 + 1.47189i) q^{41} +(7.64047 + 4.41123i) q^{43} +(0.646046 + 0.372995i) q^{44} +(-0.933507 - 1.61688i) q^{46} +(-10.0544 + 5.80494i) q^{47} +(4.24400 + 5.56673i) q^{49} +(1.91949 + 4.61688i) q^{50} +3.34173 q^{52} +(2.94339 + 5.09811i) q^{53} +(-0.108003 + 1.66458i) q^{55} +(-2.37108 - 1.17388i) q^{56} +0.743681i q^{58} +(2.33158 - 4.03841i) q^{59} +(-1.48312 + 0.856279i) q^{61} -5.00146i q^{62} +1.00000 q^{64} +(3.30934 + 6.69956i) q^{65} +(3.92576 + 2.26654i) q^{67} +4.85133i q^{68} +(0.00533076 - 5.91608i) q^{70} -4.17217i q^{71} +(5.10736 + 8.84620i) q^{73} +6.67839i q^{74} +(-6.50055 + 3.75309i) q^{76} +(0.875705 - 1.76880i) q^{77} +(3.10806 + 5.38333i) q^{79} +(0.990306 + 2.00482i) q^{80} +(-0.849794 + 1.47189i) q^{82} +(-2.26849 - 1.30971i) q^{83} +(-9.72604 + 4.80431i) q^{85} +8.82245i q^{86} +0.745990i q^{88} +(7.58595 - 13.1393i) q^{89} +(-0.564503 - 8.82335i) q^{91} +(0.933507 - 1.61688i) q^{92} +(-10.0544 - 5.80494i) q^{94} +(-13.9618 - 9.31570i) q^{95} +(-2.32004 + 4.01843i) q^{97} +(-2.69893 + 6.45877i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8} - 3 q^{14} - 24 q^{16} + 6 q^{22} + 6 q^{23} - 3 q^{28} + 3 q^{29} + 24 q^{32} - 18 q^{35} - 3 q^{41} + 6 q^{44} + 3 q^{46} - 6 q^{49} + 18 q^{50} + 42 q^{55} - 9 q^{61}+ \cdots - 3 q^{98}+O(q^{100}) \) 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 - 18 * 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 + 33 * q^65 - 33 * q^67 - 6 * 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more