LMFDB - Embedded newform 1890.2.r.a.89.22

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			89.22
Character	$\chi$	$=$	1890.89
Dual form			1890.2.r.a.1529.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.05173 + 0.889037i) q^{5} +(-0.970835 - 2.46119i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.05173 + 0.889037i) q^{5} +(-0.970835 - 2.46119i) q^{7} +1.00000 q^{8} +(-0.255938 - 2.22137i) q^{10} +2.28847i q^{11} +(-2.02055 - 3.49969i) q^{13} +(-1.64604 + 2.07137i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(5.58838 - 3.22645i) q^{17} +(-0.177623 - 0.102551i) q^{19} +(-1.79580 + 1.33234i) q^{20} +(1.98187 - 1.14423i) q^{22} +2.00850 q^{23} +(3.41923 + 3.64814i) q^{25} +(-2.02055 + 3.49969i) q^{26} +(2.61687 + 0.389830i) q^{28} +(-2.95397 - 1.70547i) q^{29} +(-0.844461 - 0.487550i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-5.58838 - 3.22645i) q^{34} +(0.196198 - 5.91283i) q^{35} +(-7.40520 - 4.27539i) q^{37} +0.205102i q^{38} +(2.05173 + 0.889037i) q^{40} +(-1.15662 - 2.00333i) q^{41} +(2.12736 + 1.22823i) q^{43} +(-1.98187 - 1.14423i) q^{44} +(-1.00425 - 1.73941i) q^{46} +(4.13773 - 2.38892i) q^{47} +(-5.11496 + 4.77883i) q^{49} +(1.44977 - 4.78520i) q^{50} +4.04110 q^{52} +(-2.35928 - 4.08640i) q^{53} +(-2.03453 + 4.69532i) q^{55} +(-0.970835 - 2.46119i) q^{56} +3.41095i q^{58} +(4.53573 - 7.85612i) q^{59} +(9.33757 - 5.39105i) q^{61} +0.975100i q^{62} +1.00000 q^{64} +(-1.03427 - 8.97678i) q^{65} +(5.24087 + 3.02582i) q^{67} +6.45290i q^{68} +(-5.21876 + 2.78650i) q^{70} +11.0359i q^{71} +(-7.78631 - 13.4863i) q^{73} +8.55079i q^{74} +(0.177623 - 0.102551i) q^{76} +(5.63236 - 2.22172i) q^{77} +(3.61701 + 6.26485i) q^{79} +(-0.255938 - 2.22137i) q^{80} +(-1.15662 + 2.00333i) q^{82} +(9.91029 + 5.72171i) q^{83} +(14.3343 - 1.65154i) q^{85} -2.45646i q^{86} +2.28847i q^{88} +(5.08916 - 8.81469i) q^{89} +(-6.65180 + 8.37059i) q^{91} +(-1.00425 + 1.73941i) q^{92} +(-4.13773 - 2.38892i) q^{94} +(-0.273264 - 0.368321i) q^{95} +(4.24029 - 7.34440i) q^{97} +(6.69607 + 2.04027i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.05173	+	0.889037i	0.917563	+	0.397590i
$5$	2.05173	+	0.889037i	0.917563	+	0.397590i
$6$		0			0
$7$	−0.970835	−	2.46119i	−0.366941	−	0.930244i
$7$	−0.970835	−	2.46119i	−0.366941	−	0.930244i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.255938	−	2.22137i	−0.0809348	−	0.702460i
$11$			2.28847i			0.689998i	0.938603	+	0.344999i	$0.112121\pi$
$11$			2.28847i			0.689998i	−0.938603	+	0.344999i	$0.887879\pi$
$12$		0			0
$13$	−2.02055	−	3.49969i	−0.560399	−	0.970640i	−0.997461	−	0.0712086i	$-0.977314\pi$
$13$	−2.02055	−	3.49969i	−0.560399	−	0.970640i	0.437062	−	0.899431i	$-0.356019\pi$
$14$	−1.64604	+	2.07137i	−0.439923	+	0.553596i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	5.58838	−	3.22645i	1.35538	−	0.782529i	0.366383	−	0.930464i	$-0.380596\pi$
$17$	5.58838	−	3.22645i	1.35538	−	0.782529i	0.988997	+	0.147935i	$0.0472626\pi$
$18$		0			0
$19$	−0.177623	−	0.102551i	−0.0407496	−	0.0235268i	0.479487	−	0.877549i	$-0.340823\pi$
$19$	−0.177623	−	0.102551i	−0.0407496	−	0.0235268i	−0.520236	+	0.854022i	$0.674156\pi$
$20$	−1.79580	+	1.33234i	−0.401552	+	0.297919i
$21$		0			0
$22$	1.98187	−	1.14423i	0.422536	−	0.243951i
$23$	2.00850			0.418800			0.209400	−	0.977830i	$-0.432849\pi$
$23$	2.00850			0.418800			0.209400	+	0.977830i	$0.432849\pi$
$24$		0			0
$25$	3.41923	+	3.64814i	0.683845	+	0.729627i
$26$	−2.02055	+	3.49969i	−0.396262	+	0.686346i
$27$		0			0
$28$	2.61687	+	0.389830i	0.494543	+	0.0736709i
$29$	−2.95397	−	1.70547i	−0.548538	−	0.316698i	0.199994	−	0.979797i	$-0.435908\pi$
$29$	−2.95397	−	1.70547i	−0.548538	−	0.316698i	−0.748532	+	0.663099i	$0.769241\pi$
$30$		0			0
$31$	−0.844461	−	0.487550i	−0.151670	−	0.0875665i	0.422244	−	0.906482i	$-0.361242\pi$
$31$	−0.844461	−	0.487550i	−0.151670	−	0.0875665i	−0.573914	+	0.818915i	$0.694576\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−5.58838	−	3.22645i	−0.958399	−	0.553332i
$35$	0.196198	−	5.91283i	0.0331636	−	0.999450i
$36$		0			0
$37$	−7.40520	−	4.27539i	−1.21741	−	0.702870i	−0.253045	−	0.967455i	$-0.581432\pi$
$37$	−7.40520	−	4.27539i	−1.21741	−	0.702870i	−0.964363	+	0.264584i	$0.914765\pi$
$38$			0.205102i			0.0332719i
$39$		0			0
$40$	2.05173	+	0.889037i	0.324408	+	0.140569i
$41$	−1.15662	−	2.00333i	−0.180634	−	0.312867i	0.761463	−	0.648209i	$-0.224482\pi$
$41$	−1.15662	−	2.00333i	−0.180634	−	0.312867i	−0.942097	+	0.335342i	$0.891148\pi$
$42$		0			0
$43$	2.12736	+	1.22823i	0.324419	+	0.187303i	0.653360	−	0.757047i	$-0.273359\pi$
$43$	2.12736	+	1.22823i	0.324419	+	0.187303i	−0.328942	+	0.944350i	$0.606692\pi$
$44$	−1.98187	−	1.14423i	−0.298778	−	0.172500i
$45$		0			0
$46$	−1.00425	−	1.73941i	−0.148068	−	0.256462i
$47$	4.13773	−	2.38892i	0.603550	−	0.348460i	−0.166887	−	0.985976i	$-0.553371\pi$
$47$	4.13773	−	2.38892i	0.603550	−	0.348460i	0.770437	+	0.637516i	$0.220038\pi$
$48$		0			0
$49$	−5.11496	+	4.77883i	−0.730708	+	0.682690i
$50$	1.44977	−	4.78520i	0.205028	−	0.676730i
$51$		0			0
$52$	4.04110			0.560399
$53$	−2.35928	−	4.08640i	−0.324072	−	0.561310i	0.657252	−	0.753671i	$-0.271719\pi$
$53$	−2.35928	−	4.08640i	−0.324072	−	0.561310i	−0.981324	+	0.192361i	$0.938385\pi$
$54$		0			0
$55$	−2.03453	+	4.69532i	−0.274336	+	0.633117i
$56$	−0.970835	−	2.46119i	−0.129733	−	0.328891i
$57$		0			0
$58$			3.41095i			0.447879i
$59$	4.53573	−	7.85612i	0.590502	−	1.02278i	−0.403663	−	0.914908i	$-0.632263\pi$
$59$	4.53573	−	7.85612i	0.590502	−	1.02278i	0.994165	−	0.107872i	$-0.0344036\pi$
$60$		0			0
$61$	9.33757	−	5.39105i	1.19555	−	0.690253i	0.235993	−	0.971755i	$-0.424166\pi$
$61$	9.33757	−	5.39105i	1.19555	−	0.690253i	0.959561	+	0.281501i	$0.0908324\pi$
$62$			0.975100i			0.123838i
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.03427	−	8.97678i	−0.128286	−	1.11343i
$66$		0			0
$67$	5.24087	+	3.02582i	0.640274	+	0.369662i	0.784720	−	0.619850i	$-0.212807\pi$
$67$	5.24087	+	3.02582i	0.640274	+	0.369662i	−0.144446	+	0.989513i	$0.546140\pi$
$68$			6.45290i			0.782529i
$69$		0			0
$70$	−5.21876	+	2.78650i	−0.623761	+	0.333050i
$71$			11.0359i			1.30973i	0.755748	+	0.654863i	$0.227274\pi$
$71$			11.0359i			1.30973i	−0.755748	+	0.654863i	$0.772726\pi$
$72$		0			0
$73$	−7.78631	−	13.4863i	−0.911318	−	1.57845i	−0.812204	−	0.583373i	$-0.801732\pi$
$73$	−7.78631	−	13.4863i	−0.911318	−	1.57845i	−0.0991142	−	0.995076i	$-0.531601\pi$
$74$			8.55079i			0.994009i
$75$		0			0
$76$	0.177623	−	0.102551i	0.0203748	−	0.0117634i
$77$	5.63236	−	2.22172i	0.641867	−	0.253189i
$78$		0			0
$79$	3.61701	+	6.26485i	0.406946	+	0.704851i	0.994546	−	0.104301i	$-0.0332605\pi$
$79$	3.61701	+	6.26485i	0.406946	+	0.704851i	−0.587600	+	0.809151i	$0.699927\pi$
$80$	−0.255938	−	2.22137i	−0.0286148	−	0.248357i
$81$		0			0
$82$	−1.15662	+	2.00333i	−0.127728	+	0.221231i
$83$	9.91029	+	5.72171i	1.08780	+	0.628039i	0.932989	−	0.359906i	$-0.117191\pi$
$83$	9.91029	+	5.72171i	1.08780	+	0.628039i	0.154807	+	0.987945i	$0.450524\pi$
$84$		0			0
$85$	14.3343	−	1.65154i	1.55477	−	0.179135i
$86$		−	2.45646i		−	0.264887i
$87$		0			0
$88$			2.28847i			0.243951i
$89$	5.08916	−	8.81469i	0.539450	−	0.934355i	−0.459483	−	0.888186i	$-0.651965\pi$
$89$	5.08916	−	8.81469i	0.539450	−	0.934355i	0.998934	−	0.0461690i	$-0.0147013\pi$
$90$		0			0
$91$	−6.65180	+	8.37059i	−0.697299	+	0.877476i
$92$	−1.00425	+	1.73941i	−0.104700	+	0.181346i
$93$		0			0
$94$	−4.13773	−	2.38892i	−0.426774	−	0.246398i
$95$	−0.273264	−	0.368321i	−0.0280363	−	0.0377889i
$96$		0			0
$97$	4.24029	−	7.34440i	0.430536	−	0.745711i	−0.566383	−	0.824142i	$-0.691658\pi$
$97$	4.24029	−	7.34440i	0.430536	−	0.745711i	0.996920	+	0.0784313i	$0.0249911\pi$
$98$	6.69607	+	2.04027i	0.676405	+	0.206098i
$99$		0			0
$100$	−4.86899	+	1.13707i	−0.486899	+	0.113707i
$101$	1.51509			0.150757			0.0753785	−	0.997155i	$-0.475983\pi$
$101$	1.51509			0.150757			0.0753785	+	0.997155i	$0.475983\pi$
$102$		0			0
$103$	−18.7761			−1.85006			−0.925031	−	0.379891i	$-0.875961\pi$
$103$	−18.7761			−1.85006			−0.925031	+	0.379891i	$0.875961\pi$
$104$	−2.02055	−	3.49969i	−0.198131	−	0.343173i
$105$		0			0
$106$	−2.35928	+	4.08640i	−0.229154	+	0.396906i
$107$	9.00357	−	15.5946i	0.870408	−	1.50759i	0.00883183	−	0.999961i	$-0.497189\pi$
$107$	9.00357	−	15.5946i	0.870408	−	1.50759i	0.861576	−	0.507629i	$-0.169478\pi$
$108$		0			0
$109$	−8.13785	−	14.0952i	−0.779464	−	1.35007i	−0.932251	−	0.361813i	$-0.882158\pi$
$109$	−8.13785	−	14.0952i	−0.779464	−	1.35007i	0.152786	−	0.988259i	$-0.451175\pi$
$110$	5.08354	−	0.585706i	0.484696	−	0.0558449i
$111$		0			0
$112$	−1.64604	+	2.07137i	−0.155536	+	0.195726i
$113$	2.98673	+	5.17317i	0.280968	+	0.486651i	0.971623	−	0.236533i	$-0.0760112\pi$
$113$	2.98673	+	5.17317i	0.280968	+	0.486651i	−0.690655	+	0.723184i	$0.742678\pi$
$114$		0			0
$115$	4.12090	+	1.78563i	0.384276	+	0.166511i
$116$	2.95397	−	1.70547i	0.274269	−	0.158349i
$117$		0			0
$118$	−9.07146			−0.835096
$119$	−13.3663	−	10.6217i	−1.22529	−	0.973693i
$120$		0			0
$121$	5.76292			0.523902
$122$	−9.33757	−	5.39105i	−0.845384	−	0.488083i
$123$		0			0
$124$	0.844461	−	0.487550i	0.0758349	−	0.0437833i
$125$	3.77201	+	10.5248i	0.337379	+	0.941369i
$126$		0			0
$127$		−	11.8327i		−	1.04998i	−0.851108	−	0.524991i	$-0.824069\pi$
$127$		−	11.8327i		−	1.04998i	0.851108	−	0.524991i	$-0.175931\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−7.25698	+	5.38409i	−0.636480	+	0.472216i
$131$	2.95626			0.258290			0.129145	−	0.991626i	$-0.458777\pi$
$131$	2.95626			0.258290			0.129145	+	0.991626i	$0.458777\pi$
$132$		0			0
$133$	−0.0799547	+	0.536725i	−0.00693295	+	0.0465400i
$134$		−	6.05164i		−	0.522782i
$135$		0			0
$136$	5.58838	−	3.22645i	0.479199	−	0.276666i
$137$	−6.86183			−0.586246			−0.293123	−	0.956075i	$-0.594695\pi$
$137$	−6.86183			−0.586246			−0.293123	+	0.956075i	$0.594695\pi$
$138$		0			0
$139$	1.44024	−	0.831524i	0.122160	−	0.0705289i	−0.437675	−	0.899133i	$-0.644198\pi$
$139$	1.44024	−	0.831524i	0.122160	−	0.0705289i	0.559835	+	0.828604i	$0.310865\pi$
$140$	5.02256	+	3.12633i	0.424484	+	0.264223i
$141$		0			0
$142$	9.55741	−	5.51797i	0.802040	−	0.463058i
$143$	8.00893	−	4.62396i	0.669740	−	0.386675i
$144$		0			0
$145$	−4.54452	−	6.12536i	−0.377402	−	0.508684i
$146$	−7.78631	+	13.4863i	−0.644399	+	1.11613i
$147$		0			0
$148$	7.40520	−	4.27539i	0.608704	−	0.351435i
$149$		−	11.7251i		−	0.960557i	−0.877116	−	0.480278i	$-0.840536\pi$
$149$		−	11.7251i		−	0.960557i	0.877116	−	0.480278i	$-0.159464\pi$
$150$		0			0
$151$	3.36336			0.273706			0.136853	−	0.990591i	$-0.456301\pi$
$151$	3.36336			0.273706			0.136853	+	0.990591i	$0.456301\pi$
$152$	−0.177623	−	0.102551i	−0.0144071	−	0.00831797i
$153$		0			0
$154$	−4.74025	−	3.76691i	−0.381980	−	0.303546i
$155$	−1.29916	−	1.75108i	−0.104351	−	0.140650i
$156$		0			0
$157$	−1.29164	+	2.23719i	−0.103084	+	0.178547i	−0.912954	−	0.408063i	$-0.866204\pi$
$157$	−1.29164	+	2.23719i	−0.103084	+	0.178547i	0.809870	+	0.586610i	$0.199538\pi$
$158$	3.61701	−	6.26485i	0.287754	−	0.498405i
$159$		0			0
$160$	−1.79580	+	1.33234i	−0.141970	+	0.105330i
$161$	−1.94992	−	4.94330i	−0.153675	−	0.389587i
$162$		0			0
$163$	21.1464	+	12.2089i	1.65631	+	0.956272i	0.974395	+	0.224841i	$0.0721863\pi$
$163$	21.1464	+	12.2089i	1.65631	+	0.956272i	0.681916	+	0.731431i	$0.261147\pi$
$164$	2.31324			0.180634
$165$		0			0
$166$		−	11.4434i		−	0.888181i
$167$	0.00904075	−	0.00521968i	0.000699594	−	0.000403911i	−0.499650	−	0.866227i	$-0.666538\pi$
$167$	0.00904075	−	0.00521968i	0.000699594	−	0.000403911i	0.500350	+	0.865823i	$0.333205\pi$
$168$		0			0
$169$	−1.66523	+	2.88426i	−0.128094	+	0.221866i
$170$	−8.59743	−	11.5881i	−0.659393	−	0.888766i
$171$		0			0
$172$	−2.12736	+	1.22823i	−0.162209	+	0.0936516i
$173$	−15.7903	+	9.11652i	−1.20051	+	0.693116i	−0.960669	−	0.277695i	$-0.910429\pi$
$173$	−15.7903	+	9.11652i	−1.20051	+	0.693116i	−0.239843	+	0.970812i	$0.577096\pi$
$174$		0			0
$175$	5.65927	−	11.9571i	0.427801	−	0.903873i
$176$	1.98187	−	1.14423i	0.149389	−	0.0862498i
$177$		0			0
$178$	−10.1783			−0.762898
$179$	13.5399	−	7.81725i	1.01202	−	0.584289i	0.100236	−	0.994964i	$-0.468040\pi$
$179$	13.5399	−	7.81725i	1.01202	−	0.584289i	0.911782	+	0.410675i	$0.134707\pi$
$180$		0			0
$181$			24.3098i			1.80693i	0.428659	+	0.903467i	$0.358986\pi$
$181$			24.3098i			1.80693i	−0.428659	+	0.903467i	$0.641014\pi$
$182$	10.5750	+	1.57534i	0.783874	+	0.116772i
$183$		0			0
$184$	2.00850			0.148068
$185$	−11.3925	−	15.3555i	−0.837594	−	1.12896i
$186$		0			0
$187$	7.38362	+	12.7888i	0.539944	+	0.935210i
$188$			4.77784i			0.348460i
$189$		0			0
$190$	−0.182343	+	0.420814i	−0.0132286	+	0.0305291i
$191$	−10.3403	+	5.96997i	−0.748197	+	0.431972i	−0.825042	−	0.565071i	$-0.808849\pi$
$191$	−10.3403	+	5.96997i	−0.748197	+	0.431972i	0.0768452	+	0.997043i	$0.475515\pi$
$192$		0			0
$193$	−10.7748	−	6.22084i	−0.775588	−	0.447786i	0.0592765	−	0.998242i	$-0.481121\pi$
$193$	−10.7748	−	6.22084i	−0.775588	−	0.447786i	−0.834864	+	0.550456i	$0.814454\pi$
$194$	−8.48058			−0.608870
$195$		0			0
$196$	−1.58111	−	6.81910i	−0.112936	−	0.487078i
$197$	−23.0465			−1.64199			−0.820996	−	0.570934i	$-0.806581\pi$
$197$	−23.0465			−1.64199			−0.820996	+	0.570934i	$0.806581\pi$
$198$		0			0
$199$	−6.98847	+	4.03479i	−0.495399	+	0.286019i	−0.726812	−	0.686837i	$-0.758999\pi$
$199$	−6.98847	+	4.03479i	−0.495399	+	0.286019i	0.231412	+	0.972856i	$0.425665\pi$
$200$	3.41923	+	3.64814i	0.241776	+	0.257962i
$201$		0			0
$202$	−0.757545	−	1.31211i	−0.0533007	−	0.0923195i
$203$	−1.32969	+	8.92602i	−0.0933258	+	0.626484i
$204$		0			0
$205$	−0.592047	−	5.13858i	−0.0413504	−	0.358894i
$206$	9.38804	+	16.2606i	0.654096	+	1.13293i
$207$		0			0
$208$	−2.02055	+	3.49969i	−0.140100	+	0.242660i
$209$	0.234684	−	0.406485i	0.0162334	−	0.0281171i
$210$		0			0
$211$	−9.23801	−	16.0007i	−0.635971	−	1.10153i	−0.986309	−	0.164910i	$-0.947266\pi$
$211$	−9.23801	−	16.0007i	−0.635971	−	1.10153i	0.350338	−	0.936623i	$-0.386067\pi$
$212$	4.71857			0.324072
$213$		0			0
$214$	−18.0071			−1.23094
$215$	3.27283	+	4.41130i	0.223205	+	0.300848i
$216$		0			0
$217$	−0.380123	+	2.55171i	−0.0258044	+	0.173222i
$218$	−8.13785	+	14.0952i	−0.551165	+	0.954645i
$219$		0			0
$220$	−3.04900	−	4.10962i	−0.205564	−	0.277070i
$221$	−22.5832	−	13.0384i	−1.51911	−	0.877057i
$222$		0			0
$223$	−2.10769	+	3.65063i	−0.141142	+	0.244464i	−0.927927	−	0.372763i	$-0.878411\pi$
$223$	−2.10769	+	3.65063i	−0.141142	+	0.244464i	0.786785	+	0.617227i	$0.211744\pi$
$224$	2.61687	+	0.389830i	0.174847	+	0.0260466i
$225$		0			0
$226$	2.98673	−	5.17317i	0.198674	−	0.344114i
$227$		−	18.5740i		−	1.23280i	−0.787433	−	0.616400i	$-0.788590\pi$
$227$		−	18.5740i		−	1.23280i	0.787433	−	0.616400i	$-0.211410\pi$
$228$		0			0
$229$			1.57155i			0.103851i	0.998651	+	0.0519256i	$0.0165359\pi$
$229$			1.57155i			0.103851i	−0.998651	+	0.0519256i	$0.983464\pi$
$230$	−0.514051	−	4.46162i	−0.0338955	−	0.294190i
$231$		0			0
$232$	−2.95397	−	1.70547i	−0.193937	−	0.111970i
$233$	3.77904	−	6.54549i	0.247573	−	0.428809i	−0.715279	−	0.698839i	$-0.753700\pi$
$233$	3.77904	−	6.54549i	0.247573	−	0.428809i	0.962852	+	0.270030i	$0.0870336\pi$
$234$		0			0
$235$	10.6134	−	1.22283i	0.692340	−	0.0797688i
$236$	4.53573	+	7.85612i	0.295251	+	0.511390i
$237$		0			0
$238$	−2.51553	+	16.8864i	−0.163058	+	1.09458i
$239$	−14.4459	+	8.34037i	−0.934430	+	0.539494i	−0.888210	−	0.459438i	$-0.848051\pi$
$239$	−14.4459	+	8.34037i	−0.934430	+	0.539494i	−0.0462202	+	0.998931i	$0.514718\pi$
$240$		0			0
$241$		−	28.3707i		−	1.82751i	−0.406260	−	0.913757i	$-0.633167\pi$
$241$		−	28.3707i		−	1.82751i	0.406260	−	0.913757i	$-0.366833\pi$
$242$	−2.88146	−	4.99084i	−0.185227	−	0.320823i
$243$		0			0
$244$			10.7821i			0.690253i
$245$	−14.7431	+	5.25750i	−0.941902	+	0.335889i
$246$		0			0
$247$			0.828835i			0.0527375i
$248$	−0.844461	−	0.487550i	−0.0536233	−	0.0309594i
$249$		0			0
$250$	7.22876	−	8.52907i	0.457187	−	0.539426i
$251$	9.95552			0.628387			0.314193	−	0.949359i	$-0.398266\pi$
$251$	9.95552			0.628387			0.314193	+	0.949359i	$0.398266\pi$
$252$		0			0
$253$			4.59638i			0.288972i
$254$	−10.2474	+	5.91635i	−0.642980	+	0.371225i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$			18.7643i			1.17049i	0.810858	+	0.585243i	$0.199001\pi$
$257$			18.7643i			1.17049i	−0.810858	+	0.585243i	$0.800999\pi$
$258$		0			0
$259$	−3.33335	+	22.3763i	−0.207124	+	1.39040i
$260$	8.29125	+	3.59268i	0.514202	+	0.222809i
$261$		0			0
$262$	−1.47813	−	2.56020i	−0.0913192	−	0.158170i
$263$	−2.94944			−0.181870			−0.0909351	−	0.995857i	$-0.528986\pi$
$263$	−2.94944			−0.181870			−0.0909351	+	0.995857i	$0.528986\pi$
$264$		0			0
$265$	−1.20766	−	10.4817i	−0.0741861	−	0.643885i
$266$	0.504795	−	0.199120i	0.0309510	−	0.0122088i
$267$		0			0
$268$	−5.24087	+	3.02582i	−0.320137	+	0.184831i
$269$	13.8077	+	23.9156i	0.841869	+	1.45816i	0.888313	+	0.459239i	$0.151878\pi$
$269$	13.8077	+	23.9156i	0.841869	+	1.45816i	−0.0464436	+	0.998921i	$0.514789\pi$
$270$		0			0
$271$	12.8142	+	7.39828i	0.778407	+	0.449413i	0.835865	−	0.548935i	$-0.184966\pi$
$271$	12.8142	+	7.39828i	0.778407	+	0.449413i	−0.0574587	+	0.998348i	$0.518300\pi$
$272$	−5.58838	−	3.22645i	−0.338845	−	0.195632i
$273$		0			0
$274$	3.43092	+	5.94252i	0.207269	+	0.359001i
$275$	−8.34863	+	7.82478i	−0.503442	+	0.471852i
$276$		0			0
$277$			7.95373i			0.477893i	0.971033	+	0.238947i	$0.0768021\pi$
$277$			7.95373i			0.477893i	−0.971033	+	0.238947i	$0.923198\pi$
$278$	−1.44024	−	0.831524i	−0.0863799	−	0.0498715i
$279$		0			0
$280$	0.196198	−	5.91283i	0.0117251	−	0.353359i
$281$	12.9850	+	7.49690i	0.774621	+	0.447228i	0.834521	−	0.550977i	$-0.185745\pi$
$281$	12.9850	+	7.49690i	0.774621	+	0.447228i	−0.0598996	+	0.998204i	$0.519078\pi$
$282$		0			0
$283$	−14.9011	+	25.8095i	−0.885780	+	1.53422i	−0.0409630	+	0.999161i	$0.513043\pi$
$283$	−14.9011	+	25.8095i	−0.885780	+	1.53422i	−0.844817	+	0.535055i	$0.820291\pi$
$284$	−9.55741	−	5.51797i	−0.567128	−	0.327431i
$285$		0			0
$286$	−8.00893	−	4.62396i	−0.473578	−	0.273420i
$287$	−3.80769	+	4.79157i	−0.224761	+	0.282838i
$288$		0			0
$289$	12.3200	−	21.3388i	0.724704	−	1.25522i
$290$	−3.03246	+	6.99835i	−0.178072	+	0.410957i
$291$		0			0
$292$	15.5726			0.911318
$293$	−2.19993	+	1.27013i	−0.128522	+	0.0742019i	−0.562882	−	0.826537i	$-0.690308\pi$
$293$	−2.19993	+	1.27013i	−0.128522	+	0.0742019i	0.434361	+	0.900739i	$0.356974\pi$
$294$		0			0
$295$	16.2905	−	12.0862i	0.948469	−	0.703688i
$296$	−7.40520	−	4.27539i	−0.430418	−	0.248502i
$297$		0			0
$298$	−10.1542	+	5.86255i	−0.588219	+	0.339608i
$299$	−4.05826	−	7.02912i	−0.234695	−	0.406504i
$300$		0			0
$301$	0.957600	−	6.42825i	0.0551952	−	0.370518i
$302$	−1.68168	−	2.91276i	−0.0967699	−	0.167610i
$303$		0			0
$304$			0.205102i			0.0117634i
$305$	23.9511	−	2.75955i	1.37143	−	0.158012i
$306$		0			0
$307$	8.06299			0.460179			0.230089	−	0.973169i	$-0.426098\pi$
$307$	8.06299			0.460179			0.230089	+	0.973169i	$0.426098\pi$
$308$	−0.892112	+	5.98863i	−0.0508328	+	0.341234i
$309$		0			0
$310$	−0.866900	+	2.00065i	−0.0492366	+	0.113629i
$311$	0.381813	−	0.661319i	0.0216506	−	0.0374999i	−0.854997	−	0.518633i	$-0.826441\pi$
$311$	0.381813	−	0.661319i	0.0216506	−	0.0374999i	0.876648	+	0.481133i	$0.159775\pi$
$312$		0			0
$313$	−1.91868	−	3.32326i	−0.108450	−	0.187842i	0.806692	−	0.590972i	$-0.201256\pi$
$313$	−1.91868	−	3.32326i	−0.108450	−	0.187842i	−0.915143	+	0.403130i	$0.867922\pi$
$314$	2.58329			0.145783
$315$		0			0
$316$	−7.23402			−0.406946
$317$	8.66445	+	15.0073i	0.486644	+	0.842892i	0.999882	−	0.0153543i	$-0.00488761\pi$
$317$	8.66445	+	15.0073i	0.486644	+	0.842892i	−0.513238	+	0.858246i	$0.671554\pi$
$318$		0			0
$319$	3.90292	−	6.76005i	0.218521	−	0.378490i
$320$	2.05173	+	0.889037i	0.114695	+	0.0496987i
$321$		0			0
$322$	−3.30606	+	4.16033i	−0.184240	+	0.231846i
$323$	−1.32350			−0.0736416
$324$		0			0
$325$	5.85864	−	19.3375i	0.324979	−	1.07265i
$326$		−	24.4177i		−	1.35237i
$327$		0			0
$328$	−1.15662	−	2.00333i	−0.0638638	−	0.110615i
$329$	−9.89665	−	7.86452i	−0.545620	−	0.433585i
$330$		0			0
$331$	2.47937	+	4.29439i	0.136278	+	0.236041i	0.926085	−	0.377315i	$-0.123153\pi$
$331$	2.47937	+	4.29439i	0.136278	+	0.236041i	−0.789807	+	0.613356i	$0.789819\pi$
$332$	−9.91029	+	5.72171i	−0.543898	+	0.314020i
$333$		0			0
$334$	−0.00904075	−	0.00521968i	−0.000494688	−	0.000285608i
$335$	8.06281	+	10.8675i	0.440518	+	0.593755i
$336$		0			0
$337$	1.58895	−	0.917381i	0.0865557	−	0.0499729i	−0.456097	−	0.889930i	$-0.650753\pi$
$337$	1.58895	−	0.917381i	0.0865557	−	0.0499729i	0.542653	+	0.839957i	$0.317420\pi$
$338$	3.33046			0.181153
$339$		0			0
$340$	−5.73687	+	13.2396i	−0.311125	+	0.718020i
$341$	1.11574	−	1.93252i	0.0604208	−	0.104652i
$342$		0			0
$343$	16.7274	+	7.94946i	0.903195	+	0.429230i
$344$	2.12736	+	1.22823i	0.114699	+	0.0662217i
$345$		0			0
$346$	15.7903	+	9.11652i	0.848890	+	0.490107i
$347$	−3.39243	+	5.87586i	−0.182115	+	0.315433i	−0.942601	−	0.333922i	$-0.891628\pi$
$347$	−3.39243	+	5.87586i	−0.182115	+	0.315433i	0.760486	+	0.649355i	$0.224961\pi$
$348$		0			0
$349$	11.4343	+	6.60159i	0.612064	+	0.353375i	0.773773	−	0.633463i	$-0.218367\pi$
$349$	11.4343	+	6.60159i	0.612064	+	0.353375i	−0.161709	+	0.986838i	$0.551701\pi$
$350$	−13.1848	+	1.07749i	−0.704757	+	0.0575942i
$351$		0			0
$352$	−1.98187	−	1.14423i	−0.105634	−	0.0609878i
$353$			31.0211i			1.65109i	0.564340	+	0.825543i	$0.309131\pi$
$353$			31.0211i			1.65109i	−0.564340	+	0.825543i	$0.690869\pi$
$354$		0			0
$355$	−9.81137	+	22.6428i	−0.520733	+	1.20176i
$356$	5.08916	+	8.81469i	0.269725	+	0.467178i
$357$		0			0
$358$	−13.5399	−	7.81725i	−0.715605	−	0.413155i
$359$	24.9912	+	14.4287i	1.31899	+	0.761517i	0.983565	−	0.180552i	$-0.0577884\pi$
$359$	24.9912	+	14.4287i	1.31899	+	0.761517i	0.335420	+	0.942069i	$0.391122\pi$
$360$		0			0
$361$	−9.47897	−	16.4181i	−0.498893	−	0.864108i
$362$	21.0529	−	12.1549i	1.10652	−	0.638847i
$363$		0			0
$364$	−3.92324	−	9.94592i	−0.205634	−	0.521308i
$365$	−3.98563	−	34.5926i	−0.208617	−	1.81066i
$366$		0			0
$367$	−12.3632			−0.645354			−0.322677	−	0.946509i	$-0.604583\pi$
$367$	−12.3632			−0.645354			−0.322677	+	0.946509i	$0.604583\pi$
$368$	−1.00425	−	1.73941i	−0.0523501	−	0.0906730i
$369$		0			0
$370$	−7.60197	+	17.5439i	−0.395207	+	0.912066i
$371$	−7.76695	+	9.77387i	−0.403240	+	0.507434i
$372$		0			0
$373$			36.6612i			1.89825i	0.314906	+	0.949123i	$0.398027\pi$
$373$			36.6612i			1.89825i	−0.314906	+	0.949123i	$0.601973\pi$
$374$	7.38362	−	12.7888i	0.381798	−	0.661294i
$375$		0			0
$376$	4.13773	−	2.38892i	0.213387	−	0.123199i
$377$			13.7840i			0.709910i
$378$		0			0
$379$	19.2906			0.990893			0.495446	−	0.868639i	$-0.335004\pi$
$379$	19.2906			0.990893			0.495446	+	0.868639i	$0.335004\pi$
$380$	0.455607	−	0.0524934i	0.0233722	−	0.00269285i
$381$		0			0
$382$	10.3403	+	5.96997i	0.529055	+	0.305450i
$383$			8.18915i			0.418446i	0.977868	+	0.209223i	$0.0670934\pi$
$383$			8.18915i			0.418446i	−0.977868	+	0.209223i	$0.932907\pi$
$384$		0			0
$385$	13.5313	+	0.448993i	0.689619	+	0.0228828i
$386$			12.4417i			0.633265i
$387$		0			0
$388$	4.24029	+	7.34440i	0.215268	+	0.372855i
$389$		−	8.82897i		−	0.447647i	−0.974630	−	0.223823i	$-0.928146\pi$
$389$		−	8.82897i		−	0.447647i	0.974630	−	0.223823i	$-0.0718538\pi$
$390$		0			0
$391$	11.2242	−	6.48032i	0.567634	−	0.327724i
$392$	−5.11496	+	4.77883i	−0.258344	+	0.241367i
$393$		0			0
$394$	11.5232	+	19.9588i	0.580532	+	1.00551i
$395$	1.85146	+	16.0695i	0.0931572	+	0.808542i
$396$		0			0
$397$	5.82466	−	10.0886i	0.292332	−	0.506333i	−0.682029	−	0.731325i	$-0.738902\pi$
$397$	5.82466	−	10.0886i	0.292332	−	0.506333i	0.974361	+	0.224992i	$0.0722356\pi$
$398$	6.98847	+	4.03479i	0.350300	+	0.202246i
$399$		0			0
$400$	1.44977	−	4.78520i	0.0724883	−	0.239260i
$401$		−	2.64152i		−	0.131911i	−0.997823	−	0.0659557i	$-0.978990\pi$
$401$		−	2.64152i		−	0.131911i	0.997823	−	0.0659557i	$-0.0210096\pi$
$402$		0			0
$403$			3.94047i			0.196289i
$404$	−0.757545	+	1.31211i	−0.0376893	+	0.0652797i
$405$		0			0
$406$	8.39500	−	3.31147i	0.416637	−	0.164345i
$407$	9.78409	−	16.9465i	0.484979	−	0.840009i
$408$		0			0
$409$	−3.46721	−	2.00180i	−0.171443	−	0.0989824i	0.411823	−	0.911264i	$-0.364892\pi$
$409$	−3.46721	−	2.00180i	−0.171443	−	0.0989824i	−0.583266	+	0.812281i	$0.698225\pi$
$410$	−4.15411	+	3.08202i	−0.205157	+	0.152210i
$411$		0			0
$412$	9.38804	−	16.2606i	0.462516	−	0.801100i
$413$	−23.7389	−	3.53633i	−1.16811	−	0.174011i
$414$		0			0
$415$	15.2465	+	20.5500i	0.748420	+	1.00876i
$416$	4.04110			0.198131
$417$		0			0
$418$	−0.469368			−0.0229575
$419$	10.3156	+	17.8671i	0.503949	+	0.872865i	0.999990	+	0.00456603i	$0.00145342\pi$
$419$	10.3156	+	17.8671i	0.503949	+	0.872865i	−0.496040	+	0.868299i	$0.665213\pi$
$420$		0			0
$421$	−2.08360	+	3.60891i	−0.101549	+	0.175887i	−0.912323	−	0.409472i	$-0.865713\pi$
$421$	−2.08360	+	3.60891i	−0.101549	+	0.175887i	0.810774	+	0.585359i	$0.199046\pi$
$422$	−9.23801	+	16.0007i	−0.449699	+	0.778902i
$423$		0			0
$424$	−2.35928	−	4.08640i	−0.114577	−	0.198453i
$425$	30.8785	+	9.35519i	1.49782	+	0.453794i
$426$		0			0
$427$	−22.3337	−	17.7478i	−1.08080	−	0.858875i
$428$	9.00357	+	15.5946i	0.435204	+	0.753795i
$429$		0			0
$430$	2.18388	−	5.04000i	0.105316	−	0.243050i
$431$	−1.89577	+	1.09452i	−0.0913159	+	0.0527213i	−0.544963	−	0.838460i	$-0.683456\pi$
$431$	−1.89577	+	1.09452i	−0.0913159	+	0.0527213i	0.453647	+	0.891182i	$0.350123\pi$
$432$		0			0
$433$	23.8117			1.14432			0.572158	−	0.820143i	$-0.306106\pi$
$433$	23.8117			1.14432			0.572158	+	0.820143i	$0.306106\pi$
$434$	2.39991	−	0.946661i	0.115199	−	0.0454412i
$435$		0			0
$436$	16.2757			0.779464
$437$	−0.356756	−	0.205973i	−0.0170659	−	0.00985302i
$438$		0			0
$439$	12.4614	−	7.19459i	0.594750	−	0.343379i	−0.172223	−	0.985058i	$-0.555095\pi$
$439$	12.4614	−	7.19459i	0.594750	−	0.343379i	0.766973	+	0.641679i	$0.221762\pi$
$440$	−2.03453	+	4.69532i	−0.0969925	+	0.223841i
$441$		0			0
$442$			26.0768i			1.24035i
$443$	18.3040	+	31.7035i	0.869649	+	1.50628i	0.862355	+	0.506304i	$0.168988\pi$
$443$	18.3040	+	31.7035i	0.869649	+	1.50628i	0.00729415	+	0.999973i	$0.497678\pi$
$444$		0			0
$445$	18.2782	−	13.5609i	0.866470	−	0.642850i
$446$	4.21539			0.199604
$447$		0			0
$448$	−0.970835	−	2.46119i	−0.0458676	−	0.116281i
$449$		−	0.350689i		−	0.0165500i	−0.999966	−	0.00827501i	$-0.997366\pi$
$449$		−	0.350689i		−	0.0165500i	0.999966	−	0.00827501i	$-0.00263405\pi$
$450$		0			0
$451$	4.58455	−	2.64689i	0.215878	−	0.124637i
$452$	−5.97346			−0.280968
$453$		0			0
$454$	−16.0856	+	9.28700i	−0.754933	+	0.435861i
$455$	−21.0895	+	11.2605i	−0.988691	+	0.527901i
$456$		0			0
$457$	−1.65880	+	0.957706i	−0.0775952	+	0.0447996i	−0.538296	−	0.842756i	$-0.680932\pi$
$457$	−1.65880	+	0.957706i	−0.0775952	+	0.0447996i	0.460700	+	0.887556i	$0.347598\pi$
$458$	1.36101	−	0.785777i	0.0635956	−	0.0367169i
$459$		0			0
$460$	−3.60685	+	2.67599i	−0.168170	+	0.124769i
$461$	−12.2091	+	21.1468i	−0.568636	+	0.984906i	0.428065	+	0.903748i	$0.359195\pi$
$461$	−12.2091	+	21.1468i	−0.568636	+	0.984906i	−0.996701	+	0.0811583i	$0.974138\pi$
$462$		0			0
$463$	−4.09771	+	2.36581i	−0.190437	+	0.109949i	−0.592187	−	0.805801i	$-0.701735\pi$
$463$	−4.09771	+	2.36581i	−0.190437	+	0.109949i	0.401750	+	0.915749i	$0.368402\pi$
$464$			3.41095i			0.158349i
$465$		0			0
$466$	−7.55808			−0.350121
$467$	−29.9337	−	17.2822i	−1.38517	−	0.799726i	−0.392401	−	0.919794i	$-0.628355\pi$
$467$	−29.9337	−	17.2822i	−1.38517	−	0.799726i	−0.992766	+	0.120068i	$0.961689\pi$
$468$		0			0
$469$	2.35911	−	15.8364i	0.108933	−	0.731256i
$470$	−6.36569	−	8.58003i	−0.293627	−	0.395767i
$471$		0			0
$472$	4.53573	−	7.85612i	0.208774	−	0.361607i
$473$	−2.81076	+	4.86838i	−0.129239	+	0.223848i
$474$		0			0
$475$	−0.233215	−	0.998638i	−0.0107006	−	0.0458207i
$476$	15.8818	−	6.26470i	0.727943	−	0.287142i
$477$		0			0
$478$	14.4459	+	8.34037i	0.660742	+	0.381480i
$479$	41.5530			1.89861			0.949303	−	0.314364i	$-0.101791\pi$
$479$	41.5530			1.89861			0.949303	+	0.314364i	$0.101791\pi$
$480$		0			0
$481$			34.5545i			1.57555i
$482$	−24.5697	+	14.1853i	−1.11912	+	0.646124i
$483$		0			0
$484$	−2.88146	+	4.99084i	−0.130976	+	0.226856i
$485$	15.2294	−	11.2990i	0.691531	−	0.513060i
$486$		0			0
$487$	−8.25200	+	4.76429i	−0.373934	+	0.215891i	−0.675176	−	0.737657i	$-0.735932\pi$
$487$	−8.25200	+	4.76429i	−0.373934	+	0.215891i	0.301242	+	0.953548i	$0.402599\pi$
$488$	9.33757	−	5.39105i	0.422692	−	0.244041i
$489$		0			0
$490$	11.9247	+	10.1391i	0.538702	+	0.458040i
$491$	−3.87273	+	2.23592i	−0.174774	+	0.100906i	−0.584835	−	0.811152i	$-0.698841\pi$
$491$	−3.87273	+	2.23592i	−0.174774	+	0.100906i	0.410061	+	0.912058i	$0.365507\pi$
$492$		0			0
$493$	−22.0105			−0.991303
$494$	0.717793	−	0.414418i	0.0322950	−	0.0186455i
$495$		0			0
$496$			0.975100i			0.0437833i
$497$	27.1616	−	10.7141i	1.21836	−	0.480592i
$498$		0			0
$499$	−35.7197			−1.59903			−0.799516	−	0.600644i	$-0.794911\pi$
$499$	−35.7197			−1.59903			−0.799516	+	0.600644i	$0.794911\pi$
$500$	−11.0008	−	1.99575i	−0.491969	−	0.0892528i
$501$		0			0
$502$	−4.97776	−	8.62173i	−0.222168	−	0.384807i
$503$			2.25896i			0.100722i	0.998731	+	0.0503609i	$0.0160372\pi$
$503$			2.25896i			0.100722i	−0.998731	+	0.0503609i	$0.983963\pi$
$504$		0			0
$505$	3.10856	+	1.34697i	0.138329	+	0.0599394i
$506$	3.98058	−	2.29819i	0.176958	−	0.102167i
$507$		0			0
$508$	10.2474	+	5.91635i	0.454656	+	0.262496i
$509$	39.4144			1.74701			0.873506	−	0.486814i	$-0.161841\pi$
$509$	39.4144			1.74701			0.873506	+	0.486814i	$0.161841\pi$
$510$		0			0
$511$	−25.6331	+	32.2566i	−1.13394	+	1.42695i
$512$	1.00000			0.0441942
$513$		0			0
$514$	16.2504	−	9.38216i	0.716774	−	0.413829i
$515$	−38.5235	−	16.6926i	−1.69755	−	0.735565i
$516$		0			0
$517$	5.46696	+	9.46906i	0.240437	+	0.416449i
$518$	21.0451	−	8.30140i	0.924671	−	0.364743i
$519$		0			0
$520$	−1.03427	−	8.97678i	−0.0453558	−	0.393658i
$521$	−19.9940	−	34.6307i	−0.875954	−	1.51720i	−0.855743	−	0.517401i	$-0.826900\pi$
$521$	−19.9940	−	34.6307i	−0.875954	−	1.51720i	−0.0202106	−	0.999796i	$-0.506434\pi$
$522$		0			0
$523$	−14.4859	+	25.0903i	−0.633424	+	1.09712i	0.353422	+	0.935464i	$0.385018\pi$
$523$	−14.4859	+	25.0903i	−0.633424	+	1.09712i	−0.986847	+	0.161659i	$0.948315\pi$
$524$	−1.47813	+	2.56020i	−0.0645724	+	0.111843i
$525$		0			0
$526$	1.47472	+	2.55429i	0.0643008	+	0.111372i
$527$	−6.29222			−0.274094
$528$		0			0
$529$	−18.9659			−0.824606
$530$	−8.47358	+	6.28671i	−0.368069	+	0.273077i
$531$		0			0
$532$	−0.424840	−	0.337605i	−0.0184192	−	0.0146371i
$533$	−4.67402	+	8.09564i	−0.202454	+	0.350661i
$534$		0			0
$535$	32.3371	−	23.9915i	1.39806	−	1.03724i
$536$	5.24087	+	3.02582i	0.226371	+	0.130695i
$537$		0			0
$538$	13.8077	−	23.9156i	0.595291	−	1.03107i
$539$	−10.9362	−	11.7054i	−0.471055	−	0.504188i
$540$		0			0
$541$	2.46717	−	4.27326i	0.106072	−	0.183722i	−0.808104	−	0.589040i	$-0.799506\pi$
$541$	2.46717	−	4.27326i	0.106072	−	0.183722i	0.914176	+	0.405318i	$0.132839\pi$
$542$		−	14.7966i		−	0.635566i
$543$		0			0
$544$			6.45290i			0.276666i
$545$	−4.16557	−	36.1544i	−0.178434	−	1.54868i
$546$		0			0
$547$	−12.6990	−	7.33178i	−0.542971	−	0.313484i	0.203311	−	0.979114i	$-0.434830\pi$
$547$	−12.6990	−	7.33178i	−0.542971	−	0.313484i	−0.746282	+	0.665630i	$0.768163\pi$
$548$	3.43092	−	5.94252i	0.146562	−	0.253852i
$549$		0			0
$550$	10.9508	+	3.31774i	0.466943	+	0.141469i
$551$	0.349795	+	0.605863i	0.0149018	+	0.0258106i
$552$		0			0
$553$	11.9075	−	14.9843i	0.506358	−	0.637197i
$554$	6.88813	−	3.97687i	0.292649	−	0.168961i
$555$		0			0
$556$			1.66305i			0.0705289i
$557$	13.3908	+	23.1936i	0.567387	+	0.982743i	0.996823	+	0.0796459i	$0.0253790\pi$
$557$	13.3908	+	23.1936i	0.567387	+	0.982743i	−0.429436	+	0.903097i	$0.641288\pi$
$558$		0			0
$559$		−	9.92679i		−	0.419858i
$560$	−5.21876	+	2.78650i	−0.220533	+	0.117751i
$561$		0			0
$562$		−	14.9938i		−	0.632475i
$563$	−16.0483	−	9.26547i	−0.676354	−	0.390493i	0.122126	−	0.992515i	$-0.461029\pi$
$563$	−16.0483	−	9.26547i	−0.676354	−	0.390493i	−0.798480	+	0.602022i	$0.794362\pi$
$564$		0			0
$565$	1.52884	+	13.2693i	0.0643186	+	0.558243i
$566$	29.8023			1.25268
$567$		0			0
$568$			11.0359i			0.463058i
$569$	−20.6344	+	11.9133i	−0.865041	+	0.499431i	−0.865697	−	0.500568i	$-0.833124\pi$
$569$	−20.6344	+	11.9133i	−0.865041	+	0.499431i	0.000656372		1.00000i	$0.499791\pi$
$570$		0			0
$571$	−22.2726	+	38.5773i	−0.932079	+	1.61441i	−0.152318	+	0.988332i	$0.548674\pi$
$571$	−22.2726	+	38.5773i	−0.932079	+	1.61441i	−0.779761	+	0.626077i	$0.784660\pi$
$572$			9.24791i			0.386675i
$573$		0			0
$574$	6.05347	+	0.901771i	0.252667	+	0.0376392i
$575$	6.86750	+	7.32727i	0.286395	+	0.305568i
$576$		0			0
$577$	1.24045	+	2.14853i	0.0516407	+	0.0894443i	0.890690	−	0.454611i	$-0.150222\pi$
$577$	1.24045	+	2.14853i	0.0516407	+	0.0894443i	−0.839050	+	0.544055i	$0.816888\pi$
$578$	−24.6399			−1.02489
$579$		0			0
$580$	7.57698	−	0.872991i	0.314617	−	0.0362490i
$581$	4.46098	−	29.9460i	0.185073	−	1.24237i
$582$		0			0
$583$	9.35158	−	5.39914i	0.387303	−	0.223609i
$584$	−7.78631	−	13.4863i	−0.322200	−	0.558066i
$585$		0			0
$586$	2.19993	+	1.27013i	0.0908784	+	0.0524687i
$587$	9.73573	+	5.62093i	0.401837	+	0.232001i	0.687276	−	0.726396i	$-0.258806\pi$
$587$	9.73573	+	5.62093i	0.401837	+	0.232001i	−0.285439	+	0.958397i	$0.592140\pi$
$588$		0			0
$589$	0.0999973	+	0.173200i	0.00412032	+	0.00713660i
$590$	−18.6122	−	8.06487i	−0.766253	−	0.332025i
$591$		0			0
$592$			8.55079i			0.351435i
$593$	25.3760	+	14.6508i	1.04207	+	0.601638i	0.920418	−	0.390935i	$-0.127848\pi$
$593$	25.3760	+	14.6508i	1.04207	+	0.601638i	0.121649	+	0.992573i	$0.461182\pi$
$594$		0			0
$595$	−17.9810	−	33.6761i	−0.737150	−	1.38059i
$596$	10.1542	+	5.86255i	0.415933	+	0.240139i
$597$		0			0
$598$	−4.05826	+	7.02912i	−0.165955	+	0.287442i
$599$	−11.6918	−	6.75024i	−0.477712	−	0.275807i	0.241750	−	0.970338i	$-0.422278\pi$
$599$	−11.6918	−	6.75024i	−0.477712	−	0.275807i	−0.719463	+	0.694531i	$0.755612\pi$
$600$		0			0
$601$	13.5297	+	7.81138i	0.551889	+	0.318633i	0.749883	−	0.661570i	$-0.230110\pi$
$601$	13.5297	+	7.81138i	0.551889	+	0.318633i	−0.197995	+	0.980203i	$0.563443\pi$
$602$	−6.04582	+	2.38482i	−0.246409	+	0.0971979i
$603$		0			0
$604$	−1.68168	+	2.91276i	−0.0684266	+	0.118518i
$605$	11.8240	+	5.12345i	0.480713	+	0.208298i
$606$		0			0
$607$	8.14122			0.330442			0.165221	−	0.986257i	$-0.447166\pi$
$607$	8.14122			0.330442			0.165221	+	0.986257i	$0.447166\pi$
$608$	0.177623	−	0.102551i	0.00720357	−	0.00415899i
$609$		0			0
$610$	−14.3654	−	19.3625i	−0.581637	−	0.783963i
$611$	−16.7210	−	9.65386i	−0.676458	−	0.390553i
$612$		0			0
$613$	−14.5475	+	8.39900i	−0.587568	+	0.339232i	−0.764135	−	0.645056i	$-0.776834\pi$
$613$	−14.5475	+	8.39900i	−0.587568	+	0.339232i	0.176567	+	0.984289i	$0.443501\pi$
$614$	−4.03149	−	6.98275i	−0.162698	−	0.281801i
$615$		0			0
$616$	5.63236	−	2.22172i	0.226934	−	0.0895158i
$617$	−13.7676	−	23.8461i	−0.554262	−	0.960009i	−0.997961	−	0.0638334i	$-0.979667\pi$
$617$	−13.7676	−	23.8461i	−0.554262	−	0.960009i	0.443699	−	0.896176i	$-0.353666\pi$
$618$		0			0
$619$		−	9.34724i		−	0.375697i	−0.982198	−	0.187849i	$-0.939849\pi$
$619$		−	9.34724i		−	0.375697i	0.982198	−	0.187849i	$-0.0601514\pi$
$620$	2.16606	−	0.249565i	0.0869911	−	0.0100228i
$621$		0			0
$622$	−0.763625			−0.0306186
$623$	−26.6354	−	3.96781i	−1.06713	−	0.158967i
$624$		0			0
$625$	−1.61779	+	24.9476i	−0.0647116	+	0.997904i
$626$	−1.91868	+	3.32326i	−0.0766860	+	0.132824i
$627$		0			0
$628$	−1.29164	−	2.23719i	−0.0515421	−	0.0892736i
$629$	−55.1774			−2.20007
$630$		0			0
$631$	−45.9246			−1.82823			−0.914115	−	0.405454i	$-0.867113\pi$
$631$	−45.9246			−1.82823			−0.914115	+	0.405454i	$0.867113\pi$
$632$	3.61701	+	6.26485i	0.143877	+	0.249202i
$633$		0			0
$634$	8.66445	−	15.0073i	0.344109	−	0.596015i
$635$	10.5197	−	24.2776i	0.417462	−	0.963425i
$636$		0			0
$637$	27.0594	+	8.24493i	1.07213	+	0.326676i
$638$	−7.80583			−0.309036
$639$		0			0
$640$	−0.255938	−	2.22137i	−0.0101168	−	0.0878075i
$641$		−	18.7718i		−	0.741442i	−0.928744	−	0.370721i	$-0.879111\pi$
$641$		−	18.7718i		−	0.741442i	0.928744	−	0.370721i	$-0.120889\pi$
$642$		0			0
$643$	11.5123	+	19.9399i	0.454001	+	0.786353i	0.998630	−	0.0523244i	$-0.0166630\pi$
$643$	11.5123	+	19.9399i	0.454001	+	0.786353i	−0.544629	+	0.838677i	$0.683330\pi$
$644$	5.25598	+	0.782971i	0.207115	+	0.0308534i
$645$		0			0
$646$	0.661750	+	1.14619i	0.0260362	+	0.0450961i
$647$	14.6259	−	8.44426i	0.575003	−	0.331978i	−0.184142	−	0.982900i	$-0.558951\pi$
$647$	14.6259	−	8.44426i	0.575003	−	0.331978i	0.759145	+	0.650922i	$0.225617\pi$
$648$		0			0
$649$	17.9785	+	10.3799i	0.705716	+	0.407445i
$650$	−19.6761	+	4.59500i	−0.771759	+	0.180231i
$651$		0			0
$652$	−21.1464	+	12.2089i	−0.828156	+	0.478136i
$653$	21.7662			0.851776			0.425888	−	0.904776i	$-0.359962\pi$
$653$	21.7662			0.851776			0.425888	+	0.904776i	$0.359962\pi$
$654$		0			0
$655$	6.06546	+	2.62823i	0.236997	+	0.102693i
$656$	−1.15662	+	2.00333i	−0.0451585	+	0.0782168i
$657$		0			0
$658$	−1.86254	+	12.5030i	−0.0726095	+	0.487418i
$659$	21.0718	+	12.1658i	0.820841	+	0.473913i	0.850706	−	0.525641i	$-0.176175\pi$
$659$	21.0718	+	12.1658i	0.820841	+	0.473913i	−0.0298654	+	0.999554i	$0.509508\pi$
$660$		0			0
$661$	22.4717	+	12.9740i	0.874048	+	0.504632i	0.868691	−	0.495354i	$-0.164962\pi$
$661$	22.4717	+	12.9740i	0.874048	+	0.504632i	0.00535644	+	0.999986i	$0.498295\pi$
$662$	2.47937	−	4.29439i	0.0963633	−	0.166906i
$663$		0			0
$664$	9.91029	+	5.72171i	0.384594	+	0.222045i
$665$	−0.641215	+	1.03013i	−0.0248652	+	0.0399469i
$666$		0			0
$667$	−5.93303	−	3.42544i	−0.229728	−	0.132633i
$668$			0.0104394i			0.000403911i
$669$		0			0
$670$	5.38013	−	12.4163i	0.207853	−	0.479685i
$671$	12.3372	+	21.3687i	0.476274	+	0.824930i
$672$		0			0
$673$	−3.32531	−	1.91987i	−0.128181	−	0.0740054i	0.434538	−	0.900653i	$-0.356912\pi$
$673$	−3.32531	−	1.91987i	−0.128181	−	0.0740054i	−0.562719	+	0.826648i	$0.690245\pi$
$674$	−1.58895	−	0.917381i	−0.0612041	−	0.0353362i
$675$		0			0
$676$	−1.66523	−	2.88426i	−0.0640472	−	0.110933i
$677$	−14.0578	+	8.11628i	−0.540286	+	0.311934i	−0.745195	−	0.666847i	$-0.767643\pi$
$677$	−14.0578	+	8.11628i	−0.540286	+	0.311934i	0.204909	+	0.978781i	$0.434310\pi$
$678$		0			0
$679$	−22.1926	−	3.30598i	−0.851674	−	0.126872i
$680$	14.3343	−	1.65154i	0.549695	−	0.0633338i
$681$		0			0
$682$	−2.23148			−0.0854479
$683$	4.73579	+	8.20262i	0.181210	+	0.313865i	0.942293	−	0.334790i	$-0.108665\pi$
$683$	4.73579	+	8.20262i	0.181210	+	0.313865i	−0.761083	+	0.648655i	$0.775332\pi$
$684$		0			0
$685$	−14.0787	−	6.10043i	−0.537918	−	0.233085i
$686$	−1.47927	−	18.4611i	−0.0564789	−	0.704848i
$687$		0			0
$688$		−	2.45646i		−	0.0936516i
$689$	−9.53409	+	16.5135i	−0.363220	+	0.629115i
$690$		0			0
$691$	−13.6619	+	7.88768i	−0.519722	+	0.300062i	−0.736821	−	0.676088i	$-0.763674\pi$
$691$	−13.6619	+	7.88768i	−0.519722	+	0.300062i	0.217099	+	0.976150i	$0.430341\pi$
$692$		−	18.2330i		−	0.693116i
$693$		0			0
$694$	6.78486			0.257550
$695$	3.69425	−	0.425637i	0.140131	−	0.0161453i
$696$		0			0
$697$	−12.9273	−	7.46357i	−0.489655	−	0.282703i
$698$		−	13.2032i		−	0.499748i
$699$		0			0
$700$	7.52553	+	10.8796i	0.284438	+	0.411211i
$701$		−	3.43541i		−	0.129754i	−0.997893	−	0.0648769i	$-0.979335\pi$
$701$		−	3.43541i		−	0.129754i	0.997893	−	0.0648769i	$-0.0206655\pi$
$702$		0			0
$703$	0.876890	+	1.51882i	0.0330725	+	0.0572833i
$704$			2.28847i			0.0862498i
$705$		0			0
$706$	26.8650	−	15.5105i	1.01108	−	0.583747i
$707$	−1.47090	−	3.72893i	−0.0553190	−	0.140241i
$708$		0			0
$709$	12.9306	+	22.3965i	0.485620	+	0.841118i	0.999863	−	0.0165263i	$-0.00526071\pi$
$709$	12.9306	+	22.3965i	0.485620	+	0.841118i	−0.514244	+	0.857644i	$0.671927\pi$
$710$	24.5149	−	2.82452i	0.920030	−	0.106002i
$711$		0			0
$712$	5.08916	−	8.81469i	0.190724	−	0.330345i
$713$	−1.69610	−	0.979242i	−0.0635193	−	0.0366729i
$714$		0			0
$715$	20.5431	−	2.36689i	0.768267	−	0.0885168i
$716$			15.6345i			0.584289i
$717$		0			0
$718$		−	28.8574i		−	1.07695i
$719$	−20.8858	+	36.1753i	−0.778909	+	1.34911i	0.153663	+	0.988123i	$0.450893\pi$
$719$	−20.8858	+	36.1753i	−0.778909	+	1.34911i	−0.932571	+	0.360986i	$0.882440\pi$
$720$		0			0
$721$	18.2285	+	46.2116i	0.678864	+	1.72101i
$722$	−9.47897	+	16.4181i	−0.352771	+	0.611017i
$723$		0			0
$724$	−21.0529	−	12.1549i	−0.782425	−	0.451733i
$725$	−3.87848	−	16.6079i	−0.144043	−	0.616801i
$726$		0			0
$727$	−21.4490	+	37.1508i	−0.795499	+	1.37785i	0.127022	+	0.991900i	$0.459458\pi$
$727$	−21.4490	+	37.1508i	−0.795499	+	1.37785i	−0.922522	+	0.385945i	$0.873875\pi$
$728$	−6.65180	+	8.37059i	−0.246532	+	0.310235i
$729$		0			0
$730$	−27.9652	+	20.7479i	−1.03504	+	0.767916i
$731$	15.8513			0.586281
$732$		0			0
$733$	4.73892			0.175036			0.0875179	−	0.996163i	$-0.472106\pi$
$733$	4.73892			0.175036			0.0875179	+	0.996163i	$0.472106\pi$
$734$	6.18161	+	10.7069i	0.228167	+	0.395197i
$735$		0			0
$736$	−1.00425	+	1.73941i	−0.0370171	+	0.0641155i
$737$	−6.92448	+	11.9936i	−0.255067	+	0.441788i
$738$		0			0
$739$	−14.6252	−	25.3317i	−0.537998	−	0.931841i	−0.999012	−	0.0444475i	$-0.985847\pi$
$739$	−14.6252	−	25.3317i	−0.537998	−	0.931841i	0.461013	−	0.887393i	$-0.347486\pi$
$740$	18.9945	−	2.18847i	0.698251	−	0.0804499i
$741$		0			0
$742$	12.3479	+	1.83944i	0.453305	+	0.0675278i
$743$	16.2571	+	28.1581i	0.596415	+	1.03302i	0.993346	+	0.115173i	$0.0367421\pi$
$743$	16.2571	+	28.1581i	0.596415	+	1.03302i	−0.396930	+	0.917849i	$0.629925\pi$
$744$		0			0
$745$	10.4240	−	24.0568i	0.381907	−	0.881372i
$746$	31.7495	−	18.3306i	1.16243	−	0.671131i
$747$		0			0
$748$	−14.7672			−0.539944
$749$	−47.1224	−	7.01971i	−1.72182	−	0.256495i
$750$		0			0
$751$	−33.1956			−1.21132			−0.605662	−	0.795722i	$-0.707092\pi$
$751$	−33.1956			−1.21132			−0.605662	+	0.795722i	$0.707092\pi$
$752$	−4.13773	−	2.38892i	−0.150888	−	0.0871150i
$753$		0			0
$754$	11.9373	−	6.89198i	0.434729	−	0.250991i
$755$	6.90072	+	2.99015i	0.251143	+	0.108823i
$756$		0			0
$757$		−	1.30712i		−	0.0475082i	−0.999718	−	0.0237541i	$-0.992438\pi$
$757$		−	1.30712i		−	0.0475082i	0.999718	−	0.0237541i	$-0.00756188\pi$
$758$	−9.64531	−	16.7062i	−0.350334	−	0.606795i
$759$		0			0
$760$	−0.273264	−	0.368321i	−0.00991233	−	0.0133604i
$761$	22.7542			0.824839			0.412420	−	0.910994i	$-0.364684\pi$
$761$	22.7542			0.824839			0.412420	+	0.910994i	$0.364684\pi$
$762$		0			0
$763$	−26.7904	+	33.7129i	−0.969879	+	1.22049i
$764$		−	11.9399i		−	0.431972i
$765$		0			0
$766$	7.09201	−	4.09457i	0.256245	−	0.147943i
$767$	−36.6587			−1.32367
$768$		0			0
$769$	34.4497	−	19.8896i	1.24229	−	0.717236i	0.272729	−	0.962091i	$-0.412074\pi$
$769$	34.4497	−	19.8896i	1.24229	−	0.717236i	0.969560	+	0.244855i	$0.0787403\pi$
$770$	−6.37681	−	11.9429i	−0.229804	−	0.430394i
$771$		0			0
$772$	10.7748	−	6.22084i	0.387794	−	0.223893i
$773$	−31.3729	+	18.1132i	−1.12841	+	0.651486i	−0.943534	−	0.331277i	$-0.892521\pi$
$773$	−31.3729	+	18.1132i	−1.12841	+	0.651486i	−0.184872	+	0.982763i	$0.559187\pi$
$774$		0			0
$775$	−1.10876	−	4.74775i	−0.0398277	−	0.170544i
$776$	4.24029	−	7.34440i	0.152218	−	0.263649i
$777$		0			0
$778$	−7.64611	+	4.41449i	−0.274126	+	0.158267i
$779$			0.474450i			0.0169989i
$780$		0			0
$781$	−25.2554			−0.903709
$782$	−11.2242	−	6.48032i	−0.401378	−	0.231736i
$783$		0			0
$784$	6.69607	+	2.04027i	0.239145	+	0.0728668i
$785$	−4.63905	+	3.44180i	−0.165575	+	0.122843i
$786$		0			0
$787$	8.56447	−	14.8341i	0.305290	−	0.528778i	−0.672036	−	0.740519i	$-0.734580\pi$
$787$	8.56447	−	14.8341i	0.305290	−	0.528778i	0.977326	+	0.211740i	$0.0679131\pi$
$788$	11.5232	−	19.9588i	0.410498	−	0.711003i
$789$		0			0
$790$	12.9908	−	9.63815i	0.462193	−	0.342910i
$791$	9.83255	−	12.3732i	0.349605	−	0.439941i
$792$		0			0
$793$	−37.7340	−	21.7858i	−1.33997	−	0.773635i
$794$	−11.6493			−0.413419
$795$		0			0
$796$		−	8.06959i		−	0.286019i
$797$	35.9212	−	20.7391i	1.27239	−	0.734616i	0.296955	−	0.954891i	$-0.404029\pi$
$797$	35.9212	−	20.7391i	1.27239	−	0.734616i	0.975438	+	0.220275i	$0.0706955\pi$
$798$		0			0
$799$	15.4155	−	26.7004i	0.545360	−	0.944591i
$800$	−4.86899	+	1.13707i	−0.172145	+	0.0402014i
$801$		0			0
$802$	−2.28763	+	1.32076i	−0.0807788	+	0.0466377i
$803$	30.8629	−	17.8187i	1.08913	−	0.628808i
$804$		0			0
$805$	0.394064	−	11.8759i	0.0138889	−	0.418570i
$806$	3.41255	−	1.97024i	0.120202	−	0.0693986i
$807$		0			0
$808$	1.51509			0.0533007
$809$	5.30390	−	3.06221i	0.186475	−	0.107661i	−0.403856	−	0.914822i	$-0.632330\pi$
$809$	5.30390	−	3.06221i	0.186475	−	0.107661i	0.590331	+	0.807161i	$0.298997\pi$
$810$		0			0
$811$			51.1448i			1.79594i	0.440059	+	0.897969i	$0.354957\pi$
$811$			51.1448i			1.79594i	−0.440059	+	0.897969i	$0.645043\pi$
$812$	−7.06531	−	5.61455i	−0.247944	−	0.197032i
$813$		0			0
$814$	−19.5682			−0.685864
$815$	32.5326	+	43.8492i	1.13957	+	1.53597i
$816$		0			0
$817$	−0.251912	−	0.436324i	−0.00881328	−	0.0152651i
$818$			4.00359i			0.139982i
$819$		0			0
$820$	4.74616	+	2.05656i	0.165743	+	0.0718182i
$821$	−7.88867	+	4.55452i	−0.275316	+	0.158954i	−0.631301	−	0.775538i	$-0.717479\pi$
$821$	−7.88867	+	4.55452i	−0.275316	+	0.158954i	0.355985	+	0.934492i	$0.384145\pi$
$822$		0			0
$823$	−38.7300	−	22.3608i	−1.35004	−	0.779449i	−0.361789	−	0.932260i	$-0.617834\pi$
$823$	−38.7300	−	22.3608i	−1.35004	−	0.779449i	−0.988255	+	0.152811i	$0.951167\pi$
$824$	−18.7761			−0.654096
$825$		0			0
$826$	8.80689	+	22.3266i	0.306431	+	0.776843i
$827$	34.3286			1.19372			0.596860	−	0.802345i	$-0.296415\pi$
$827$	34.3286			1.19372			0.596860	+	0.802345i	$0.296415\pi$
$828$		0			0
$829$	40.7898	−	23.5500i	1.41669	−	0.817925i	0.420682	−	0.907208i	$-0.361791\pi$
$829$	40.7898	−	23.5500i	1.41669	−	0.817925i	0.996006	+	0.0892828i	$0.0284575\pi$
$830$	10.1736	−	23.4788i	0.353132	−	0.814963i
$831$		0			0
$832$	−2.02055	−	3.49969i	−0.0700499	−	0.121330i
$833$	−13.1657	+	43.2091i	−0.456163	+	1.49710i
$834$		0			0
$835$	0.0231897	−	0.00267183i	0.000802513	−	9.24625e-5i
$836$	0.234684	+	0.406485i	0.00811672	+	0.0140586i
$837$		0			0
$838$	10.3156	−	17.8671i	0.356346	−	0.617209i
$839$	−7.97922	+	13.8204i	−0.275473	+	0.477134i	−0.970254	−	0.242087i	$-0.922168\pi$
$839$	−7.97922	+	13.8204i	−0.275473	+	0.477134i	0.694781	+	0.719221i	$0.255501\pi$
$840$		0			0
$841$	−8.68273	−	15.0389i	−0.299404	−	0.518583i
$842$	4.16721			0.143612
$843$		0			0
$844$	18.4760			0.635971
$845$	−5.98082	+	4.43728i	−0.205746	+	0.152647i
$846$		0			0
$847$	−5.59485	−	14.1837i	−0.192241	−	0.487357i
$848$	−2.35928	+	4.08640i	−0.0810181	+	0.140327i
$849$		0			0
$850$	−7.33739	−	31.4191i	−0.251670	−	1.07767i
$851$	−14.8733	−	8.58711i	−0.509851	−	0.294362i
$852$		0			0
$853$	−4.85434	+	8.40796i	−0.166209	+	0.287883i	−0.937084	−	0.349104i	$-0.886486\pi$
$853$	−4.85434	+	8.40796i	−0.166209	+	0.287883i	0.770875	+	0.636987i	$0.219819\pi$
$854$	−4.20318	+	28.2154i	−0.143830	+	0.965511i
$855$		0			0
$856$	9.00357	−	15.5946i	0.307736	−	0.533014i
$857$		−	31.1978i		−	1.06570i	−0.846210	−	0.532849i	$-0.821121\pi$
$857$		−	31.1978i		−	1.06570i	0.846210	−	0.532849i	$-0.178879\pi$
$858$		0			0
$859$		−	15.9449i		−	0.544031i	−0.962293	−	0.272016i	$-0.912310\pi$
$859$		−	15.9449i		−	0.544031i	0.962293	−	0.272016i	$-0.0876903\pi$
$860$	−5.45671	+	0.628702i	−0.186072	+	0.0214386i
$861$		0			0
$862$	1.89577	+	1.09452i	0.0645701	+	0.0372796i
$863$	21.8059	−	37.7689i	0.742281	−	1.28567i	−0.209174	−	0.977879i	$-0.567077\pi$
$863$	21.8059	−	37.7689i	0.742281	−	1.28567i	0.951454	−	0.307790i	$-0.0995893\pi$
$864$		0			0
$865$	−40.5024	+	4.66653i	−1.37712	+	0.158667i
$866$	−11.9058	−	20.6215i	−0.404577	−	0.700748i
$867$		0			0
$868$	−2.01979	−	1.60505i	−0.0685561	−	0.0544790i
$869$	−14.3369	+	8.27741i	−0.486346	+	0.280792i
$870$		0			0
$871$		−	24.4552i		−	0.828634i
$872$	−8.13785	−	14.0952i	−0.275582	−	0.477323i
$873$		0			0
$874$			0.411946i			0.0139343i
$875$	22.2416	−	19.5015i	0.751905	−	0.659272i
$876$		0			0
$877$		−	37.8796i		−	1.27910i	−0.768748	−	0.639552i	$-0.779120\pi$
$877$		−	37.8796i		−	1.27910i	0.768748	−	0.639552i	$-0.220880\pi$
$878$	−12.4614	−	7.19459i	−0.420552	−	0.242806i
$879$		0			0
$880$	5.08354	−	0.585706i	0.171366	−	0.0197441i
$881$	−16.7367			−0.563872			−0.281936	−	0.959433i	$-0.590977\pi$
$881$	−16.7367			−0.563872			−0.281936	+	0.959433i	$0.590977\pi$
$882$		0			0
$883$			5.43664i			0.182957i	0.995807	+	0.0914787i	$0.0291593\pi$
$883$			5.43664i			0.182957i	−0.995807	+	0.0914787i	$0.970841\pi$
$884$	22.5832	−	13.0384i	0.759554	−	0.438529i
$885$		0			0
$886$	18.3040	−	31.7035i	0.614935	−	1.06510i
$887$			38.9848i			1.30898i	0.756070	+	0.654490i	$0.227117\pi$
$887$			38.9848i			1.30898i	−0.756070	+	0.654490i	$0.772883\pi$
$888$		0			0
$889$	−29.1226	+	11.4876i	−0.976740	+	0.385282i
$890$	−20.8832	−	9.04891i	−0.700007	−	0.303320i
$891$		0			0
$892$	−2.10769	−	3.65063i	−0.0705708	−	0.122232i
$893$	−0.979943			−0.0327925
$894$		0			0
$895$	34.7301	−	4.00147i	1.16090	−	0.133754i
$896$	−1.64604	+	2.07137i	−0.0549903	+	0.0691995i
$897$		0			0
$898$	−0.303705	+	0.175344i	−0.0101348	+	0.00585132i
$899$	1.66301	+	2.88041i	0.0554644	+	0.0960671i
$900$		0			0
$901$	−26.3691	−	15.2242i	−0.878483	−	0.507192i
$902$	−4.58455	−	2.64689i	−0.152649	−	0.0881318i
$903$		0			0
$904$	2.98673	+	5.17317i	0.0993372	+	0.172057i
$905$	−21.6123	+	49.8772i	−0.718418	+	1.65798i
$906$		0			0
$907$		−	2.76265i		−	0.0917322i	−0.998948	−	0.0458661i	$-0.985395\pi$
$907$		−	2.76265i		−	0.0917322i	0.998948	−	0.0458661i	$-0.0146048\pi$
$908$	16.0856	+	9.28700i	0.533818	+	0.308200i
$909$		0			0
$910$	20.2966	+	12.6338i	0.672827	+	0.418806i
$911$	−36.0610	−	20.8198i	−1.19475	−	0.689792i	−0.235373	−	0.971905i	$-0.575631\pi$
$911$	−36.0610	−	20.8198i	−1.19475	−	0.689792i	−0.959381	+	0.282113i	$0.908965\pi$
$912$		0			0
$913$	−13.0939	+	22.6794i	−0.433346	+	0.750577i
$914$	1.65880	+	0.957706i	0.0548681	+	0.0316781i
$915$		0			0
$916$	−1.36101	−	0.785777i	−0.0449689	−	0.0259628i
$917$	−2.87004	−	7.27593i	−0.0947771	−	0.240273i
$918$		0			0
$919$	−11.8470	+	20.5196i	−0.390797	+	0.676880i	−0.992555	−	0.121798i	$-0.961134\pi$
$919$	−11.8470	+	20.5196i	−0.390797	+	0.676880i	0.601758	+	0.798679i	$0.294467\pi$
$920$	4.12090	+	1.78563i	0.135862	+	0.0588704i
$921$		0			0
$922$	24.4183			0.804172
$923$	38.6224	−	22.2987i	1.27127	−	0.733969i
$924$		0			0
$925$	−9.72283	−	41.6337i	−0.319685	−	1.36891i
$926$	4.09771	+	2.36581i	0.134659	+	0.0777454i
$927$		0			0
$928$	2.95397	−	1.70547i	0.0969687	−	0.0559849i
$929$	3.22447	+	5.58494i	0.105791	+	0.183236i	0.914061	−	0.405576i	$-0.132929\pi$
$929$	3.22447	+	5.58494i	0.105791	+	0.183236i	−0.808270	+	0.588812i	$0.799596\pi$
$930$		0			0
$931$	1.39861	−	0.324288i	0.0458375	−	0.0106281i
$932$	3.77904	+	6.54549i	0.123787	+	0.214405i
$933$		0			0
$934$			34.5645i			1.13098i
$935$	3.77950	+	32.8036i	0.123603	+	1.07279i
$936$		0			0
$937$	38.6081			1.26127			0.630635	−	0.776079i	$-0.282794\pi$
$937$	38.6081			1.26127			0.630635	+	0.776079i	$0.282794\pi$
$938$	−14.8943	+	5.87514i	−0.486315	+	0.191830i
$939$		0			0
$940$	−4.24768	+	9.80286i	−0.138544	+	0.319734i
$941$	5.21606	−	9.03447i	0.170039	−	0.294515i	−0.768395	−	0.639976i	$-0.778944\pi$
$941$	5.21606	−	9.03447i	0.170039	−	0.294515i	0.938433	+	0.345461i	$0.112277\pi$
$942$		0			0
$943$	−2.32307	−	4.02368i	−0.0756496	−	0.131029i
$944$	−9.07146			−0.295251
$945$		0			0
$946$	5.62152			0.182771
$947$	17.0629	+	29.5538i	0.554470	+	0.960369i	0.997945	+	0.0640827i	$0.0204122\pi$
$947$	17.0629	+	29.5538i	0.554470	+	0.960369i	−0.443475	+	0.896287i	$0.646255\pi$
$948$		0			0
$949$	−31.4652	+	54.4993i	−1.02140	+	1.76912i
$950$	−0.748239	+	0.701289i	−0.0242761	+	0.0227528i
$951$		0			0
$952$	−13.3663	−	10.6217i	−0.433205	−	0.344252i
$953$	44.3067			1.43523			0.717617	−	0.696438i	$-0.245233\pi$
$953$	44.3067			1.43523			0.717617	+	0.696438i	$0.245233\pi$
$954$		0			0
$955$	−26.5230	+	3.05589i	−0.858265	+	0.0988861i
$956$		−	16.6807i		−	0.539494i
$957$		0			0
$958$	−20.7765	−	35.9860i	−0.671258	−	1.16265i
$959$	6.66171	+	16.8883i	0.215118	+	0.545352i
$960$		0			0
$961$	−15.0246	−	26.0234i	−0.484664	−	0.839463i
$962$	29.9251	−	17.2773i	0.964824	−	0.557042i
$963$		0			0
$964$	24.5697	+	14.1853i	0.791337	+	0.456879i
$965$	−16.5765	−	22.3427i	−0.533616	−	0.719237i
$966$		0			0
$967$	14.0448	−	8.10875i	0.451649	−	0.260760i	−0.256877	−	0.966444i	$-0.582694\pi$
$967$	14.0448	−	8.10875i	0.451649	−	0.260760i	0.708526	+	0.705684i	$0.249360\pi$
$968$	5.76292			0.185227
$969$		0			0
$970$	−17.3999	−	7.53955i	−0.558677	−	0.242080i
$971$	−18.1313	+	31.4043i	−0.581861	+	1.00781i	0.413397	+	0.910551i	$0.364342\pi$
$971$	−18.1313	+	31.4043i	−0.581861	+	1.00781i	−0.995259	+	0.0972627i	$0.968991\pi$
$972$		0			0
$973$	−3.44478	−	2.73744i	−0.110435	−	0.0877584i
$974$	8.25200	+	4.76429i	0.264411	+	0.152658i
$975$		0			0
$976$	−9.33757	−	5.39105i	−0.298888	−	0.172563i
$977$	4.35317	−	7.53992i	0.139270	−	0.241223i	−0.787950	−	0.615739i	$-0.788858\pi$
$977$	4.35317	−	7.53992i	0.139270	−	0.241223i	0.927221	+	0.374516i	$0.122191\pi$
$978$		0			0
$979$	20.1721	+	11.6464i	0.644704	+	0.372220i
$980$	2.81842	−	15.3966i	0.0900312	−	0.491828i
$981$		0			0
$982$	3.87273	+	2.23592i	0.123584	+	0.0713512i
$983$		−	11.1598i		−	0.355943i	−0.984036	−	0.177972i	$-0.943046\pi$
$983$		−	11.1598i		−	0.355943i	0.984036	−	0.177972i	$-0.0569535\pi$
$984$		0			0
$985$	−47.2852	−	20.4892i	−1.50663	−	0.652839i
$986$	11.0052	+	19.0616i	0.350478	+	0.607047i
$987$		0			0
$988$	−0.717793	−	0.414418i	−0.0228360	−	0.0131844i
$989$	4.27279	+	2.46689i	0.135867	+	0.0784427i
$990$		0			0
$991$	−24.4098	−	42.2790i	−0.775402	−	1.34304i	−0.934568	−	0.355785i	$-0.884214\pi$
$991$	−24.4098	−	42.2790i	−0.775402	−	1.34304i	0.159165	−	0.987252i	$-0.449120\pi$
$992$	0.844461	−	0.487550i	0.0268117	−	0.0154797i
$993$		0			0
$994$	−22.8595	−	18.1656i	−0.725058	−	0.576178i
$995$	−17.9256	+	2.06532i	−0.568279	+	0.0654749i
$996$		0			0
$997$	−17.9594			−0.568779			−0.284390	−	0.958709i	$-0.591791\pi$
$997$	−17.9594			−0.568779			−0.284390	+	0.958709i	$0.591791\pi$
$998$	17.8598	+	30.9342i	0.565343	+	0.979204i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.r.a.89.22		48
3.2	odd	2		630.2.r.b.299.15	yes	48
5.4	even	2		1890.2.r.b.89.22		48
7.3	odd	6		1890.2.bi.b.899.19		48
9.4	even	3		630.2.bi.b.509.19	yes	48
9.5	odd	6		1890.2.bi.a.719.14		48
15.14	odd	2		630.2.r.a.299.10	yes	48
21.17	even	6		630.2.bi.a.479.6	yes	48
35.24	odd	6		1890.2.bi.a.899.14		48
45.4	even	6		630.2.bi.a.509.6	yes	48
45.14	odd	6		1890.2.bi.b.719.19		48
63.31	odd	6		630.2.r.a.59.10	✓	48
63.59	even	6		1890.2.r.b.1529.22		48
105.59	even	6		630.2.bi.b.479.19	yes	48
315.59	even	6	inner	1890.2.r.a.1529.22		48
315.94	odd	6		630.2.r.b.59.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.10	✓	48	63.31	odd	6
630.2.r.a.299.10	yes	48	15.14	odd	2
630.2.r.b.59.15	yes	48	315.94	odd	6
630.2.r.b.299.15	yes	48	3.2	odd	2
630.2.bi.a.479.6	yes	48	21.17	even	6
630.2.bi.a.509.6	yes	48	45.4	even	6
630.2.bi.b.479.19	yes	48	105.59	even	6
630.2.bi.b.509.19	yes	48	9.4	even	3
1890.2.r.a.89.22		48	1.1	even	1	trivial
1890.2.r.a.1529.22		48	315.59	even	6	inner
1890.2.r.b.89.22		48	5.4	even	2
1890.2.r.b.1529.22		48	63.59	even	6
1890.2.bi.a.719.14		48	9.5	odd	6
1890.2.bi.a.899.14		48	35.24	odd	6
1890.2.bi.b.719.19		48	45.14	odd	6
1890.2.bi.b.899.19		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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.05173 + 0.889037i) q^{5} +(-0.970835 - 2.46119i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.05173 + 0.889037i) q^{5} +(-0.970835 - 2.46119i) q^{7} +1.00000 q^{8} +(-0.255938 - 2.22137i) q^{10} +2.28847i q^{11} +(-2.02055 - 3.49969i) q^{13} +(-1.64604 + 2.07137i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(5.58838 - 3.22645i) q^{17} +(-0.177623 - 0.102551i) q^{19} +(-1.79580 + 1.33234i) q^{20} +(1.98187 - 1.14423i) q^{22} +2.00850 q^{23} +(3.41923 + 3.64814i) q^{25} +(-2.02055 + 3.49969i) q^{26} +(2.61687 + 0.389830i) q^{28} +(-2.95397 - 1.70547i) q^{29} +(-0.844461 - 0.487550i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-5.58838 - 3.22645i) q^{34} +(0.196198 - 5.91283i) q^{35} +(-7.40520 - 4.27539i) q^{37} +0.205102i q^{38} +(2.05173 + 0.889037i) q^{40} +(-1.15662 - 2.00333i) q^{41} +(2.12736 + 1.22823i) q^{43} +(-1.98187 - 1.14423i) q^{44} +(-1.00425 - 1.73941i) q^{46} +(4.13773 - 2.38892i) q^{47} +(-5.11496 + 4.77883i) q^{49} +(1.44977 - 4.78520i) q^{50} +4.04110 q^{52} +(-2.35928 - 4.08640i) q^{53} +(-2.03453 + 4.69532i) q^{55} +(-0.970835 - 2.46119i) q^{56} +3.41095i q^{58} +(4.53573 - 7.85612i) q^{59} +(9.33757 - 5.39105i) q^{61} +0.975100i q^{62} +1.00000 q^{64} +(-1.03427 - 8.97678i) q^{65} +(5.24087 + 3.02582i) q^{67} +6.45290i q^{68} +(-5.21876 + 2.78650i) q^{70} +11.0359i q^{71} +(-7.78631 - 13.4863i) q^{73} +8.55079i q^{74} +(0.177623 - 0.102551i) q^{76} +(5.63236 - 2.22172i) q^{77} +(3.61701 + 6.26485i) q^{79} +(-0.255938 - 2.22137i) q^{80} +(-1.15662 + 2.00333i) q^{82} +(9.91029 + 5.72171i) q^{83} +(14.3343 - 1.65154i) q^{85} -2.45646i q^{86} +2.28847i q^{88} +(5.08916 - 8.81469i) q^{89} +(-6.65180 + 8.37059i) q^{91} +(-1.00425 + 1.73941i) q^{92} +(-4.13773 - 2.38892i) q^{94} +(-0.273264 - 0.368321i) q^{95} +(4.24029 - 7.34440i) q^{97} +(6.69607 + 2.04027i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8}+O(q^{10}) \) 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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