LMFDB - Embedded newform 1890.2.r.b.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.b.1529.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.05173 - 0.889037i) q^{5} +(0.970835 + 2.46119i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.05173 - 0.889037i) q^{5} +(0.970835 + 2.46119i) q^{7} -1.00000 q^{8} +(1.79580 + 1.33234i) q^{10} +2.28847i q^{11} +(2.02055 + 3.49969i) q^{13} +(-1.64604 + 2.07137i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.58838 + 3.22645i) q^{17} +(-0.177623 - 0.102551i) q^{19} +(-0.255938 + 2.22137i) q^{20} +(-1.98187 + 1.14423i) q^{22} -2.00850 q^{23} +(3.41923 - 3.64814i) q^{25} +(-2.02055 + 3.49969i) q^{26} +(-2.61687 - 0.389830i) q^{28} +(-2.95397 - 1.70547i) q^{29} +(-0.844461 - 0.487550i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.58838 - 3.22645i) q^{34} +(4.17999 + 4.18661i) q^{35} +(7.40520 + 4.27539i) q^{37} -0.205102i q^{38} +(-2.05173 + 0.889037i) q^{40} +(-1.15662 - 2.00333i) q^{41} +(-2.12736 - 1.22823i) q^{43} +(-1.98187 - 1.14423i) q^{44} +(-1.00425 - 1.73941i) q^{46} +(-4.13773 + 2.38892i) q^{47} +(-5.11496 + 4.77883i) q^{49} +(4.86899 + 1.13707i) q^{50} -4.04110 q^{52} +(2.35928 + 4.08640i) q^{53} +(2.03453 + 4.69532i) q^{55} +(-0.970835 - 2.46119i) q^{56} -3.41095i q^{58} +(4.53573 - 7.85612i) q^{59} +(9.33757 - 5.39105i) q^{61} -0.975100i q^{62} +1.00000 q^{64} +(7.25698 + 5.38409i) q^{65} +(-5.24087 - 3.02582i) q^{67} -6.45290i q^{68} +(-1.53572 + 5.71328i) q^{70} +11.0359i q^{71} +(7.78631 + 13.4863i) q^{73} +8.55079i q^{74} +(0.177623 - 0.102551i) q^{76} +(-5.63236 + 2.22172i) q^{77} +(3.61701 + 6.26485i) q^{79} +(-1.79580 - 1.33234i) q^{80} +(1.15662 - 2.00333i) q^{82} +(-9.91029 - 5.72171i) q^{83} +(-8.59743 + 11.5881i) q^{85} -2.45646i q^{86} -2.28847i q^{88} +(5.08916 - 8.81469i) q^{89} +(-6.65180 + 8.37059i) q^{91} +(1.00425 - 1.73941i) q^{92} +(-4.13773 - 2.38892i) q^{94} +(-0.455607 - 0.0524934i) q^{95} +(-4.24029 + 7.34440i) q^{97} +(-6.69607 - 2.04027i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 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}+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

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
$10$	1.79580	+	1.33234i	0.567881	+	0.421321i
$11$			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	$0.0226856\pi$
$13$	2.02055	+	3.49969i	0.560399	+	0.970640i	−0.437062	+	0.899431i	$0.643981\pi$
$14$	−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	−0.988997	−	0.147935i	$-0.952737\pi$
$17$	−5.58838	+	3.22645i	−1.35538	+	0.782529i	−0.366383	+	0.930464i	$0.619404\pi$
$18$		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	$0.674156\pi$
$20$	−0.255938	+	2.22137i	−0.0572295	+	0.496714i
$21$		0			0
$22$	−1.98187	+	1.14423i	−0.422536	+	0.243951i
$23$	−2.00850			−0.418800			−0.209400	−	0.977830i	$-0.567151\pi$
$23$	−2.00850			−0.418800			−0.209400	+	0.977830i	$0.567151\pi$
$24$		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
$35$	4.17999	+	4.18661i	0.706547	+	0.707666i
$36$		0			0
$37$	7.40520	+	4.27539i	1.21741	+	0.702870i	0.964363	−	0.264584i	$-0.0852348\pi$
$37$	7.40520	+	4.27539i	1.21741	+	0.702870i	0.253045	+	0.967455i	$0.418568\pi$
$38$		−	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	0.328942	−	0.944350i	$-0.393308\pi$
$43$	−2.12736	−	1.22823i	−0.324419	−	0.187303i	−0.653360	+	0.757047i	$0.726641\pi$
$44$	−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	−0.770437	−	0.637516i	$-0.779962\pi$
$47$	−4.13773	+	2.38892i	−0.603550	+	0.348460i	0.166887	+	0.985976i	$0.446629\pi$
$48$		0			0
$49$	−5.11496	+	4.77883i	−0.730708	+	0.682690i
$50$	4.86899	+	1.13707i	0.688579	+	0.160806i
$51$		0			0
$52$	−4.04110			−0.560399
$53$	2.35928	+	4.08640i	0.324072	+	0.561310i	0.981324	−	0.192361i	$-0.0616145\pi$
$53$	2.35928	+	4.08640i	0.324072	+	0.561310i	−0.657252	+	0.753671i	$0.728281\pi$
$54$		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
$65$	7.25698	+	5.38409i	0.900118	+	0.667815i
$66$		0			0
$67$	−5.24087	−	3.02582i	−0.640274	−	0.369662i	0.144446	−	0.989513i	$-0.453860\pi$
$67$	−5.24087	−	3.02582i	−0.640274	−	0.369662i	−0.784720	+	0.619850i	$0.787193\pi$
$68$		−	6.45290i		−	0.782529i
$69$		0			0
$70$	−1.53572	+	5.71328i	−0.183553	+	0.682868i
$71$			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	$0.198268\pi$
$73$	7.78631	+	13.4863i	0.911318	+	1.57845i	0.0991142	+	0.995076i	$0.468399\pi$
$74$			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	$0.699927\pi$
$80$	−1.79580	−	1.33234i	−0.200776	−	0.148960i
$81$		0			0
$82$	1.15662	−	2.00333i	0.127728	−	0.221231i
$83$	−9.91029	−	5.72171i	−1.08780	−	0.628039i	−0.154807	−	0.987945i	$-0.549476\pi$
$83$	−9.91029	−	5.72171i	−1.08780	−	0.628039i	−0.932989	+	0.359906i	$0.882809\pi$
$84$		0			0
$85$	−8.59743	+	11.5881i	−0.932522	+	1.25691i
$86$		−	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
$95$	−0.455607	−	0.0524934i	−0.0467443	−	0.00538571i
$96$		0			0
$97$	−4.24029	+	7.34440i	−0.430536	+	0.745711i	−0.996920	−	0.0784313i	$-0.975009\pi$
$97$	−4.24029	+	7.34440i	−0.430536	+	0.745711i	0.566383	+	0.824142i	$0.308342\pi$
$98$	−6.69607	−	2.04027i	−0.676405	−	0.206098i
$99$		0			0
$100$	1.44977	+	4.78520i	0.144977	+	0.478520i
$101$	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	$-0.124039\pi$
$103$	18.7761			1.85006			0.925031	+	0.379891i	$0.124039\pi$
$104$	−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	$0.502811\pi$
$107$	−9.00357	+	15.5946i	−0.870408	+	1.50759i	−0.861576	+	0.507629i	$0.830522\pi$
$108$		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	$-0.451175\pi$
$110$	−3.04900	+	4.10962i	−0.290711	+	0.391837i
$111$		0			0
$112$	1.64604	−	2.07137i	0.155536	−	0.195726i
$113$	−2.98673	−	5.17317i	−0.280968	−	0.486651i	0.690655	−	0.723184i	$-0.257322\pi$
$113$	−2.98673	−	5.17317i	−0.280968	−	0.486651i	−0.971623	+	0.236533i	$0.923989\pi$
$114$		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	$0.175931\pi$
$127$			11.8327i			1.04998i	−0.851108	+	0.524991i	$0.824069\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.03427	+	8.97678i	−0.0907116	+	0.787316i
$131$	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	$-0.405305\pi$
$137$	6.86183			0.586246			0.293123	+	0.956075i	$0.405305\pi$
$138$		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	$0.310865\pi$
$140$	−5.71570	+	1.52667i	−0.483065	+	0.129027i
$141$		0			0
$142$	−9.55741	+	5.51797i	−0.802040	+	0.463058i
$143$	−8.00893	+	4.62396i	−0.669740	+	0.386675i
$144$		0			0
$145$	−7.57698	−	0.872991i	−0.629234	−	0.0724980i
$146$	−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
$155$	−2.16606	−	0.249565i	−0.173982	−	0.0200456i
$156$		0			0
$157$	1.29164	−	2.23719i	0.103084	−	0.178547i	−0.809870	−	0.586610i	$-0.800462\pi$
$157$	1.29164	−	2.23719i	0.103084	−	0.178547i	0.912954	+	0.408063i	$0.133796\pi$
$158$	−3.61701	+	6.26485i	−0.287754	+	0.498405i
$159$		0			0
$160$	0.255938	−	2.22137i	0.0202337	−	0.175615i
$161$	−1.94992	−	4.94330i	−0.153675	−	0.389587i
$162$		0			0
$163$	−21.1464	−	12.2089i	−1.65631	−	0.956272i	−0.974395	−	0.224841i	$-0.927814\pi$
$163$	−21.1464	−	12.2089i	−1.65631	−	0.956272i	−0.681916	−	0.731431i	$-0.738853\pi$
$164$	2.31324			0.180634
$165$		0			0
$166$		−	11.4434i		−	0.888181i
$167$	−0.00904075	+	0.00521968i	−0.000699594	+	0.000403911i	−0.500350	−	0.865823i	$-0.666795\pi$
$167$	−0.00904075	+	0.00521968i	−0.000699594	+	0.000403911i	0.499650	+	0.866227i	$0.333462\pi$
$168$		0			0
$169$	−1.66523	+	2.88426i	−0.128094	+	0.221866i
$170$	−14.3343	−	1.65154i	−1.09939	−	0.126668i
$171$		0			0
$172$	2.12736	−	1.22823i	0.162209	−	0.0936516i
$173$	15.7903	−	9.11652i	1.20051	−	0.693116i	0.239843	−	0.970812i	$-0.422904\pi$
$173$	15.7903	−	9.11652i	1.20051	−	0.693116i	0.960669	+	0.277695i	$0.0895706\pi$
$174$		0			0
$175$	12.2983	+	4.87364i	0.929662	+	0.368413i
$176$	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
$185$	18.9945	+	2.18847i	1.39650	+	0.160900i
$186$		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	0.834864	−	0.550456i	$-0.185546\pi$
$193$	10.7748	+	6.22084i	0.775588	+	0.447786i	−0.0592765	+	0.998242i	$0.518879\pi$
$194$	−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	$-0.193419\pi$
$197$	23.0465			1.64199			0.820996	+	0.570934i	$0.193419\pi$
$198$		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
$205$	−4.15411	−	3.08202i	−0.290136	−	0.215257i
$206$	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
$215$	−5.45671	−	0.628702i	−0.372145	−	0.0428771i
$216$		0			0
$217$	0.380123	−	2.55171i	0.0258044	−	0.173222i
$218$	8.13785	−	14.0952i	0.551165	−	0.954645i
$219$		0			0
$220$	−5.08354	−	0.585706i	−0.342732	−	0.0394883i
$221$	−22.5832	−	13.0384i	−1.51911	−	0.877057i
$222$		0			0
$223$	2.10769	−	3.65063i	0.141142	−	0.244464i	−0.786785	−	0.617227i	$-0.788256\pi$
$223$	2.10769	−	3.65063i	0.141142	−	0.244464i	0.927927	+	0.372763i	$0.121589\pi$
$224$	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	$0.211410\pi$
$227$			18.5740i			1.23280i	−0.787433	+	0.616400i	$0.788590\pi$
$228$		0			0
$229$			1.57155i			0.103851i	0.998651	+	0.0519256i	$0.0165359\pi$
$229$			1.57155i			0.103851i	−0.998651	+	0.0519256i	$0.983464\pi$
$230$	−3.60685	−	2.67599i	−0.237829	−	0.176450i
$231$		0			0
$232$	2.95397	+	1.70547i	0.193937	+	0.111970i
$233$	−3.77904	+	6.54549i	−0.247573	+	0.428809i	−0.962852	−	0.270030i	$-0.912966\pi$
$233$	−3.77904	+	6.54549i	−0.247573	+	0.428809i	0.715279	+	0.698839i	$0.246300\pi$
$234$		0			0
$235$	−6.36569	+	8.58003i	−0.415252	+	0.559699i
$236$	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
$245$	−6.24598	+	14.3523i	−0.399041	+	0.916933i
$246$		0			0
$247$		−	0.828835i		−	0.0527375i
$248$	0.844461	+	0.487550i	0.0536233	+	0.0309594i
$249$		0			0
$250$	11.0008	−	1.99575i	0.695750	−	0.126222i
$251$	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	$-0.800999\pi$
$257$		−	18.7643i		−	1.17049i	0.810858	−	0.585243i	$-0.199001\pi$
$258$		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	$-0.471014\pi$
$263$	2.94944			0.181870			0.0909351	+	0.995857i	$0.471014\pi$
$264$		0			0
$265$	8.47358	+	6.28671i	0.520528	+	0.386190i
$266$	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	$-0.923198\pi$
$277$		−	7.95373i		−	0.477893i	0.971033	−	0.238947i	$-0.0768021\pi$
$278$	1.44024	+	0.831524i	0.0863799	+	0.0498715i
$279$		0			0
$280$	−4.17999	−	4.18661i	−0.249802	−	0.250198i
$281$	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	$-0.486957\pi$
$283$	14.9011	−	25.8095i	0.885780	−	1.53422i	0.844817	−	0.535055i	$-0.179709\pi$
$284$	−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	−0.434361	−	0.900739i	$-0.643026\pi$
$293$	2.19993	−	1.27013i	0.128522	−	0.0742019i	0.562882	+	0.826537i	$0.309692\pi$
$294$		0			0
$295$	2.32173	−	20.1511i	0.135177	−	1.17324i
$296$	−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
$305$	14.3654	−	19.3625i	0.822559	−	1.10869i
$306$		0			0
$307$	−8.06299			−0.460179			−0.230089	−	0.973169i	$-0.573902\pi$
$307$	−8.06299			−0.460179			−0.230089	+	0.973169i	$0.573902\pi$
$308$	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	0.915143	−	0.403130i	$-0.132078\pi$
$313$	1.91868	+	3.32326i	0.108450	+	0.187842i	−0.806692	+	0.590972i	$0.798744\pi$
$314$	2.58329			0.145783
$315$		0			0
$316$	−7.23402			−0.406946
$317$	−8.66445	−	15.0073i	−0.486644	−	0.842892i	0.513238	−	0.858246i	$-0.328446\pi$
$317$	−8.66445	−	15.0073i	−0.486644	−	0.842892i	−0.999882	+	0.0153543i	$0.995112\pi$
$318$		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
$325$	19.6761	+	4.59500i	1.09143	+	0.254885i
$326$		−	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
$335$	−13.4429	−	1.54885i	−0.734466	−	0.0846224i
$336$		0			0
$337$	−1.58895	+	0.917381i	−0.0865557	+	0.0499729i	−0.542653	−	0.839957i	$-0.682580\pi$
$337$	−1.58895	+	0.917381i	−0.0865557	+	0.0499729i	0.456097	+	0.889930i	$0.349247\pi$
$338$	−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	−0.760486	−	0.649355i	$-0.775039\pi$
$347$	3.39243	−	5.87586i	0.182115	−	0.315433i	0.942601	+	0.333922i	$0.108372\pi$
$348$		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	$0.551701\pi$
$350$	1.92844	+	13.0874i	0.103079	+	0.699553i
$351$		0			0
$352$	1.98187	+	1.14423i	0.105634	+	0.0609878i
$353$		−	31.0211i		−	1.65109i	−0.564340	−	0.825543i	$-0.690869\pi$
$353$		−	31.0211i		−	1.65109i	0.564340	−	0.825543i	$-0.309131\pi$
$354$		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
$365$	27.9652	+	20.7479i	1.46377	+	1.08600i
$366$		0			0
$367$	12.3632			0.645354			0.322677	−	0.946509i	$-0.395417\pi$
$367$	12.3632			0.645354			0.322677	+	0.946509i	$0.395417\pi$
$368$	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	$-0.601973\pi$
$373$		−	36.6612i		−	1.89825i	0.314906	−	0.949123i	$-0.398027\pi$
$374$	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	$0.335004\pi$
$380$	0.273264	−	0.368321i	0.0140182	−	0.0188945i
$381$		0			0
$382$	−10.3403	−	5.96997i	−0.529055	−	0.305450i
$383$		−	8.18915i		−	0.418446i	−0.977868	−	0.209223i	$-0.932907\pi$
$383$		−	8.18915i		−	0.418446i	0.977868	−	0.209223i	$-0.0670934\pi$
$384$		0			0
$385$	−9.58091	+	9.56576i	−0.488288	+	0.487516i
$386$			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
$395$	12.9908	+	9.63815i	0.653640	+	0.484948i
$396$		0			0
$397$	−5.82466	+	10.0886i	−0.292332	+	0.506333i	−0.974361	−	0.224992i	$-0.927764\pi$
$397$	−5.82466	+	10.0886i	−0.292332	+	0.506333i	0.682029	+	0.731325i	$0.261098\pi$
$398$	−6.98847	−	4.03479i	−0.350300	−	0.202246i
$399$		0			0
$400$	−4.86899	−	1.13707i	−0.243450	−	0.0568534i
$401$		−	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	$0.698225\pi$
$410$	0.592047	−	5.13858i	0.0292391	−	0.253776i
$411$		0			0
$412$	−9.38804	+	16.2606i	−0.462516	+	0.801100i
$413$	23.7389	+	3.53633i	1.16811	+	0.174011i
$414$		0			0
$415$	−25.4201	−	2.92881i	−1.24782	−	0.143770i
$416$	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
$425$	−7.33739	+	31.4191i	−0.355916	+	1.52405i
$426$		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	$-0.693894\pi$
$433$	−23.8117			−1.14432			−0.572158	+	0.820143i	$0.693894\pi$
$434$	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	$-0.831012\pi$
$443$	−18.3040	−	31.7035i	−0.869649	−	1.50628i	−0.00729415	−	0.999973i	$-0.502322\pi$
$444$		0			0
$445$	2.60502	−	22.6099i	0.123490	−	1.07181i
$446$	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
$455$	−6.20597	+	23.0879i	−0.290940	+	1.08238i
$456$		0			0
$457$	1.65880	−	0.957706i	0.0775952	−	0.0447996i	−0.460700	−	0.887556i	$-0.652402\pi$
$457$	1.65880	−	0.957706i	0.0775952	−	0.0447996i	0.538296	+	0.842756i	$0.319068\pi$
$458$	−1.36101	+	0.785777i	−0.0635956	+	0.0367169i
$459$		0			0
$460$	0.514051	−	4.46162i	0.0239678	−	0.208024i
$461$	−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	−0.401750	−	0.915749i	$-0.631598\pi$
$463$	4.09771	−	2.36581i	0.190437	−	0.109949i	0.592187	+	0.805801i	$0.298265\pi$
$464$			3.41095i			0.158349i
$465$		0			0
$466$	−7.55808			−0.350121
$467$	29.9337	+	17.2822i	1.38517	+	0.799726i	0.992766	−	0.120068i	$-0.0383112\pi$
$467$	29.9337	+	17.2822i	1.38517	+	0.799726i	0.392401	+	0.919794i	$0.371645\pi$
$468$		0			0
$469$	2.35911	−	15.8364i	0.108933	−	0.731256i
$470$	−10.6134	−	1.22283i	−0.489558	−	0.0564050i
$471$		0			0
$472$	−4.53573	+	7.85612i	−0.208774	+	0.361607i
$473$	2.81076	−	4.86838i	0.129239	−	0.223848i
$474$		0			0
$475$	−0.981453	+	0.297349i	−0.0450322	+	0.0136433i
$476$	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
$485$	−2.17050	+	18.8385i	−0.0985576	+	0.855413i
$486$		0			0
$487$	8.25200	−	4.76429i	0.373934	−	0.215891i	−0.301242	−	0.953548i	$-0.597401\pi$
$487$	8.25200	−	4.76429i	0.373934	−	0.215891i	0.675176	+	0.737657i	$0.264068\pi$
$488$	−9.33757	+	5.39105i	−0.422692	+	0.244041i
$489$		0			0
$490$	−15.5524	+	1.76696i	−0.702587	+	0.0798231i
$491$	−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	$0.794911\pi$
$500$	7.22876	+	8.52907i	0.323280	+	0.381432i
$501$		0			0
$502$	4.97776	+	8.62173i	0.222168	+	0.384807i
$503$		−	2.25896i		−	0.100722i	−0.998731	−	0.0503609i	$-0.983963\pi$
$503$		−	2.25896i		−	0.100722i	0.998731	−	0.0503609i	$-0.0160372\pi$
$504$		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
$520$	−7.25698	−	5.38409i	−0.318240	−	0.236108i
$521$	−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	$-0.614982\pi$
$523$	14.4859	−	25.0903i	0.633424	−	1.09712i	0.986847	−	0.161659i	$-0.0516846\pi$
$524$	−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
$530$	−1.20766	+	10.4817i	−0.0524575	+	0.455296i
$531$		0			0
$532$	0.424840	+	0.337605i	0.0184192	+	0.0146371i
$533$	4.67402	−	8.09564i	0.202454	−	0.350661i
$534$		0			0
$535$	−4.60871	+	40.0005i	−0.199252	+	1.72937i
$536$	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
$545$	−29.2278	−	21.6847i	−1.25198	−	0.928870i
$546$		0			0
$547$	12.6990	+	7.33178i	0.542971	+	0.313484i	0.746282	−	0.665630i	$-0.231837\pi$
$547$	12.6990	+	7.33178i	0.542971	+	0.313484i	−0.203311	+	0.979114i	$0.565170\pi$
$548$	−3.43092	+	5.94252i	−0.146562	+	0.253852i
$549$		0			0
$550$	−2.60214	+	11.1425i	−0.110956	+	0.475119i
$551$	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	$-0.974621\pi$
$557$	−13.3908	−	23.1936i	−0.567387	−	0.982743i	0.429436	−	0.903097i	$-0.358712\pi$
$558$		0			0
$559$		−	9.92679i		−	0.419858i
$560$	1.53572	−	5.71328i	0.0648958	−	0.241430i
$561$		0			0
$562$			14.9938i			0.632475i
$563$	16.0483	+	9.26547i	0.676354	+	0.390493i	0.798480	−	0.602022i	$-0.205638\pi$
$563$	16.0483	+	9.26547i	0.676354	+	0.390493i	−0.122126	+	0.992515i	$0.538971\pi$
$564$		0			0
$565$	−10.7271	−	7.95865i	−0.451293	−	0.334823i
$566$	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	0.839050	−	0.544055i	$-0.183112\pi$
$577$	−1.24045	−	2.14853i	−0.0516407	−	0.0894443i	−0.890690	+	0.454611i	$0.849778\pi$
$578$	24.6399			1.02489
$579$		0			0
$580$	4.54452	−	6.12536i	0.188701	−	0.254342i
$581$	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	0.285439	−	0.958397i	$-0.407860\pi$
$587$	−9.73573	−	5.62093i	−0.401837	−	0.232001i	−0.687276	+	0.726396i	$0.741194\pi$
$588$		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	−0.121649	−	0.992573i	$-0.538818\pi$
$593$	−25.3760	−	14.6508i	−1.04207	−	0.601638i	−0.920418	+	0.390935i	$0.872152\pi$
$594$		0			0
$595$	−36.8672	−	9.90982i	−1.51141	−	0.406263i
$596$	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	$-0.552834\pi$
$607$	−8.14122			−0.330442			−0.165221	+	0.986257i	$0.552834\pi$
$608$	−0.177623	+	0.102551i	−0.00720357	+	0.00415899i
$609$		0			0
$610$	23.9511	+	2.75955i	0.969750	+	0.111731i
$611$	−16.7210	−	9.65386i	−0.676458	−	0.390553i
$612$		0			0
$613$	14.5475	−	8.39900i	0.587568	−	0.339232i	−0.176567	−	0.984289i	$-0.556499\pi$
$613$	14.5475	−	8.39900i	0.587568	−	0.339232i	0.764135	+	0.645056i	$0.223166\pi$
$614$	−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	$0.0203326\pi$
$617$	13.7676	+	23.8461i	0.554262	+	0.960009i	−0.443699	+	0.896176i	$0.646334\pi$
$618$		0			0
$619$		−	9.34724i		−	0.375697i	−0.982198	−	0.187849i	$-0.939849\pi$
$619$		−	9.34724i		−	0.375697i	0.982198	−	0.187849i	$-0.0601514\pi$
$620$	1.29916	−	1.75108i	0.0521755	−	0.0703251i
$621$		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
$640$	1.79580	+	1.33234i	0.0709851	+	0.0526652i
$641$		−	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	0.544629	−	0.838677i	$-0.316670\pi$
$643$	−11.5123	−	19.9399i	−0.454001	−	0.786353i	−0.998630	+	0.0523244i	$0.983337\pi$
$644$	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	−0.759145	−	0.650922i	$-0.774383\pi$
$647$	−14.6259	+	8.44426i	−0.575003	+	0.331978i	0.184142	+	0.982900i	$0.441049\pi$
$648$		0			0
$649$	17.9785	+	10.3799i	0.705716	+	0.407445i
$650$	5.85864	+	19.3375i	0.229795	+	0.758478i
$651$		0			0
$652$	21.1464	−	12.2089i	0.828156	−	0.478136i
$653$	−21.7662			−0.851776			−0.425888	−	0.904776i	$-0.640038\pi$
$653$	−21.7662			−0.851776			−0.425888	+	0.904776i	$0.640038\pi$
$654$		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
$665$	−0.313123	−	1.17230i	−0.0121424	−	0.0454599i
$666$		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	0.562719	−	0.826648i	$-0.309755\pi$
$673$	3.32531	+	1.91987i	0.128181	+	0.0740054i	−0.434538	+	0.900653i	$0.643088\pi$
$674$	−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	−0.204909	−	0.978781i	$-0.565690\pi$
$677$	14.0578	−	8.11628i	0.540286	−	0.311934i	0.745195	+	0.666847i	$0.232357\pi$
$678$		0			0
$679$	−22.1926	−	3.30598i	−0.851674	−	0.126872i
$680$	8.59743	−	11.5881i	0.329696	−	0.444383i
$681$		0			0
$682$	2.23148			0.0854479
$683$	−4.73579	−	8.20262i	−0.181210	−	0.313865i	0.761083	−	0.648655i	$-0.224668\pi$
$683$	−4.73579	−	8.20262i	−0.181210	−	0.313865i	−0.942293	+	0.334790i	$0.891335\pi$
$684$		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
$695$	2.21574	−	2.98649i	0.0840477	−	0.113284i
$696$		0			0
$697$	12.9273	+	7.46357i	0.489655	+	0.282703i
$698$			13.2032i			0.499748i
$699$		0			0
$700$	−10.3698	+	8.21380i	−0.391943	+	0.310452i
$701$		−	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	$0.671927\pi$
$710$	−14.7036	+	19.8183i	−0.551816	+	0.743768i
$711$		0			0
$712$	−5.08916	+	8.81469i	−0.190724	+	0.330345i
$713$	1.69610	+	0.979242i	0.0635193	+	0.0366729i
$714$		0			0
$715$	−12.3213	+	16.6074i	−0.460791	+	0.621080i
$716$			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
$725$	−16.3221	+	4.94507i	−0.606187	+	0.183655i
$726$		0			0
$727$	21.4490	−	37.1508i	0.795499	−	1.37785i	−0.127022	−	0.991900i	$-0.540542\pi$
$727$	21.4490	−	37.1508i	0.795499	−	1.37785i	0.922522	−	0.385945i	$-0.126125\pi$
$728$	6.65180	−	8.37059i	0.246532	−	0.310235i
$729$		0			0
$730$	−3.98563	+	34.5926i	−0.147515	+	1.28033i
$731$	15.8513			0.586281
$732$		0			0
$733$	−4.73892			−0.175036			−0.0875179	−	0.996163i	$-0.527894\pi$
$733$	−4.73892			−0.175036			−0.0875179	+	0.996163i	$0.527894\pi$
$734$	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	$-0.347486\pi$
$740$	−11.3925	+	15.3555i	−0.418797	+	0.564478i
$741$		0			0
$742$	−12.3479	−	1.83944i	−0.453305	−	0.0675278i
$743$	−16.2571	−	28.1581i	−0.596415	−	1.03302i	−0.993346	−	0.115173i	$-0.963258\pi$
$743$	−16.2571	−	28.1581i	−0.596415	−	1.03302i	0.396930	−	0.917849i	$-0.370075\pi$
$744$		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	$0.00756188\pi$
$757$			1.30712i			0.0475082i	−0.999718	+	0.0237541i	$0.992438\pi$
$758$	9.64531	+	16.7062i	0.350334	+	0.606795i
$759$		0			0
$760$	0.455607	+	0.0524934i	0.0165266	+	0.00190413i
$761$	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	$0.0787403\pi$
$770$	−13.0746	−	3.51443i	−0.471178	−	0.126651i
$771$		0			0
$772$	−10.7748	+	6.22084i	−0.387794	+	0.223893i
$773$	31.3729	−	18.1132i	1.12841	−	0.651486i	0.184872	−	0.982763i	$-0.440813\pi$
$773$	31.3729	−	18.1132i	1.12841	−	0.651486i	0.943534	+	0.331277i	$0.107479\pi$
$774$		0			0
$775$	−4.66605	+	1.41367i	−0.167610	+	0.0507804i
$776$	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
$785$	0.661161	−	5.73844i	0.0235979	−	0.204814i
$786$		0			0
$787$	−8.56447	+	14.8341i	−0.305290	+	0.528778i	−0.977326	−	0.211740i	$-0.932087\pi$
$787$	−8.56447	+	14.8341i	−0.305290	+	0.528778i	0.672036	+	0.740519i	$0.265420\pi$
$788$	−11.5232	+	19.9588i	−0.410498	+	0.711003i
$789$		0			0
$790$	−1.85146	+	16.0695i	−0.0658721	+	0.571726i
$791$	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	−0.975438	−	0.220275i	$-0.929305\pi$
$797$	−35.9212	+	20.7391i	−1.27239	+	0.734616i	−0.296955	+	0.954891i	$0.595971\pi$
$798$		0			0
$799$	15.4155	−	26.7004i	0.545360	−	0.944591i
$800$	−1.44977	−	4.78520i	−0.0512570	−	0.169183i
$801$		0			0
$802$	2.28763	−	1.32076i	0.0807788	−	0.0466377i
$803$	−30.8629	+	17.8187i	−1.08913	+	0.628808i
$804$		0			0
$805$	−8.39549	−	8.40879i	−0.295902	−	0.296371i
$806$	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
$815$	−54.2409	−	6.24943i	−1.89997	−	0.218908i
$816$		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	0.988255	−	0.152811i	$-0.0488327\pi$
$823$	38.7300	+	22.3608i	1.35004	+	0.779449i	0.361789	+	0.932260i	$0.382166\pi$
$824$	−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	$-0.703585\pi$
$827$	−34.3286			−1.19372			−0.596860	+	0.802345i	$0.703585\pi$
$828$		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
$835$	−0.0139087	+	0.0187470i	−0.000481331	+	0.000648765i
$836$	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
$845$	−0.852391	+	7.39818i	−0.0293231	+	0.254505i
$846$		0			0
$847$	5.59485	+	14.1837i	0.192241	+	0.487357i
$848$	2.35928	−	4.08640i	0.0810181	−	0.140327i
$849$		0			0
$850$	−30.8785	+	9.35519i	−1.05912	+	0.320881i
$851$	−14.8733	−	8.58711i	−0.509851	−	0.294362i
$852$		0			0
$853$	4.85434	−	8.40796i	0.166209	−	0.287883i	−0.770875	−	0.636987i	$-0.780181\pi$
$853$	4.85434	−	8.40796i	0.166209	−	0.287883i	0.937084	+	0.349104i	$0.113514\pi$
$854$	−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	$0.178879\pi$
$857$			31.1978i			1.06570i	−0.846210	+	0.532849i	$0.821121\pi$
$858$		0			0
$859$		−	15.9449i		−	0.544031i	−0.962293	−	0.272016i	$-0.912310\pi$
$859$		−	15.9449i		−	0.544031i	0.962293	−	0.272016i	$-0.0876903\pi$
$860$	3.27283	−	4.41130i	0.111602	−	0.150424i
$861$		0			0
$862$	−1.89577	−	1.09452i	−0.0645701	−	0.0372796i
$863$	−21.8059	+	37.7689i	−0.742281	+	1.28567i	0.209174	+	0.977879i	$0.432923\pi$
$863$	−21.8059	+	37.7689i	−0.742281	+	1.28567i	−0.951454	+	0.307790i	$0.900411\pi$
$864$		0			0
$865$	24.2925	−	32.7428i	0.825971	−	1.11329i
$866$	−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
$875$	29.5656	−	0.934208i	0.999501	−	0.0315820i
$876$		0			0
$877$			37.8796i			1.27910i	0.768748	+	0.639552i	$0.220880\pi$
$877$			37.8796i			1.27910i	−0.768748	+	0.639552i	$0.779120\pi$
$878$	12.4614	+	7.19459i	0.420552	+	0.242806i
$879$		0			0
$880$	3.04900	−	4.10962i	0.102782	−	0.138535i
$881$	−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	$-0.970841\pi$
$883$		−	5.43664i		−	0.182957i	0.995807	−	0.0914787i	$-0.0291593\pi$
$884$	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	$-0.772883\pi$
$887$		−	38.9848i		−	1.30898i	0.756070	−	0.654490i	$-0.227117\pi$
$888$		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
$895$	20.8304	−	28.0764i	0.696284	−	0.938490i
$896$	−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	$0.0146048\pi$
$907$			2.76265i			0.0917322i	−0.998948	+	0.0458661i	$0.985395\pi$
$908$	−16.0856	−	9.28700i	−0.533818	−	0.308200i
$909$		0			0
$910$	−23.0977	+	6.16943i	−0.765682	+	0.204515i
$911$	−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
$925$	40.9173	−	12.3966i	1.34535	−	0.407599i
$926$	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
$935$	−26.5190	−	19.6749i	−0.867263	−	0.643439i
$936$		0			0
$937$	−38.6081			−1.26127			−0.630635	−	0.776079i	$-0.717206\pi$
$937$	−38.6081			−1.26127			−0.630635	+	0.776079i	$0.717206\pi$
$938$	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	$-0.979588\pi$
$947$	−17.0629	−	29.5538i	−0.554470	−	0.960369i	0.443475	−	0.896287i	$-0.353745\pi$
$948$		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	$-0.754767\pi$
$953$	−44.3067			−1.43523			−0.717617	+	0.696438i	$0.754767\pi$
$954$		0			0
$955$	−15.9080	+	21.4417i	−0.514771	+	0.693837i
$956$		−	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
$965$	27.6376	+	3.18430i	0.889686	+	0.102506i
$966$		0			0
$967$	−14.0448	+	8.10875i	−0.451649	+	0.260760i	−0.708526	−	0.705684i	$-0.750640\pi$
$967$	−14.0448	+	8.10875i	−0.451649	+	0.260760i	0.256877	+	0.966444i	$0.417306\pi$
$968$	−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	−0.927221	−	0.374516i	$-0.877809\pi$
$977$	−4.35317	+	7.53992i	−0.139270	+	0.241223i	0.787950	+	0.615739i	$0.211142\pi$
$978$		0			0
$979$	20.1721	+	11.6464i	0.644704	+	0.372220i
$980$	−9.30644	−	12.5853i	−0.297283	−	0.402023i
$981$		0			0
$982$	−3.87273	−	2.23592i	−0.123584	−	0.0713512i
$983$			11.1598i			0.355943i	0.984036	+	0.177972i	$0.0569535\pi$
$983$			11.1598i			0.355943i	−0.984036	+	0.177972i	$0.943046\pi$
$984$		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
$995$	−10.7514	+	14.4913i	−0.340842	+	0.459406i
$996$		0			0
$997$	17.9594			0.568779			0.284390	−	0.958709i	$-0.408209\pi$
$997$	17.9594			0.568779			0.284390	+	0.958709i	$0.408209\pi$
$998$	−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.b.89.22		48
3.2	odd	2		630.2.r.a.299.10	yes	48
5.4	even	2		1890.2.r.a.89.22		48
7.3	odd	6		1890.2.bi.a.899.14		48
9.4	even	3		630.2.bi.a.509.6	yes	48
9.5	odd	6		1890.2.bi.b.719.19		48
15.14	odd	2		630.2.r.b.299.15	yes	48
21.17	even	6		630.2.bi.b.479.19	yes	48
35.24	odd	6		1890.2.bi.b.899.19		48
45.4	even	6		630.2.bi.b.509.19	yes	48
45.14	odd	6		1890.2.bi.a.719.14		48
63.31	odd	6		630.2.r.b.59.15	yes	48
63.59	even	6		1890.2.r.a.1529.22		48
105.59	even	6		630.2.bi.a.479.6	yes	48
315.59	even	6	inner	1890.2.r.b.1529.22		48
315.94	odd	6		630.2.r.a.59.10	✓	48

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

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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.05173 - 0.889037i) q^{5} +(0.970835 + 2.46119i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.05173 - 0.889037i) q^{5} +(0.970835 + 2.46119i) q^{7} -1.00000 q^{8} +(1.79580 + 1.33234i) q^{10} +2.28847i q^{11} +(2.02055 + 3.49969i) q^{13} +(-1.64604 + 2.07137i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.58838 + 3.22645i) q^{17} +(-0.177623 - 0.102551i) q^{19} +(-0.255938 + 2.22137i) q^{20} +(-1.98187 + 1.14423i) q^{22} -2.00850 q^{23} +(3.41923 - 3.64814i) q^{25} +(-2.02055 + 3.49969i) q^{26} +(-2.61687 - 0.389830i) q^{28} +(-2.95397 - 1.70547i) q^{29} +(-0.844461 - 0.487550i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.58838 - 3.22645i) q^{34} +(4.17999 + 4.18661i) q^{35} +(7.40520 + 4.27539i) q^{37} -0.205102i q^{38} +(-2.05173 + 0.889037i) q^{40} +(-1.15662 - 2.00333i) q^{41} +(-2.12736 - 1.22823i) q^{43} +(-1.98187 - 1.14423i) q^{44} +(-1.00425 - 1.73941i) q^{46} +(-4.13773 + 2.38892i) q^{47} +(-5.11496 + 4.77883i) q^{49} +(4.86899 + 1.13707i) q^{50} -4.04110 q^{52} +(2.35928 + 4.08640i) q^{53} +(2.03453 + 4.69532i) q^{55} +(-0.970835 - 2.46119i) q^{56} -3.41095i q^{58} +(4.53573 - 7.85612i) q^{59} +(9.33757 - 5.39105i) q^{61} -0.975100i q^{62} +1.00000 q^{64} +(7.25698 + 5.38409i) q^{65} +(-5.24087 - 3.02582i) q^{67} -6.45290i q^{68} +(-1.53572 + 5.71328i) q^{70} +11.0359i q^{71} +(7.78631 + 13.4863i) q^{73} +8.55079i q^{74} +(0.177623 - 0.102551i) q^{76} +(-5.63236 + 2.22172i) q^{77} +(3.61701 + 6.26485i) q^{79} +(-1.79580 - 1.33234i) q^{80} +(1.15662 - 2.00333i) q^{82} +(-9.91029 - 5.72171i) q^{83} +(-8.59743 + 11.5881i) q^{85} -2.45646i q^{86} -2.28847i q^{88} +(5.08916 - 8.81469i) q^{89} +(-6.65180 + 8.37059i) q^{91} +(1.00425 - 1.73941i) q^{92} +(-4.13773 - 2.38892i) q^{94} +(-0.455607 - 0.0524934i) q^{95} +(-4.24029 + 7.34440i) q^{97} +(-6.69607 - 2.04027i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8}+O(q^{10}) \) 48 * q + 24 * q^2 - 24 * q^4 - 48 * q^8	\( 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8} - 3 q^{14} - 24 q^{16} + 6 q^{22} + 6 q^{23} - 3 q^{28} + 3 q^{29} + 24 q^{32} - 18 q^{35} - 3 q^{41} + 6 q^{44} + 3 q^{46} - 6 q^{49} + 18 q^{50} + 42 q^{55} - 9 q^{61} + 48 q^{64} + 33 q^{65} - 33 q^{67} - 6 q^{70} + 18 q^{73} - 6 q^{77} + 3 q^{82} + 9 q^{83} - 33 q^{85} - 33 q^{89} - 3 q^{92} - 33 q^{95} + 24 q^{97} - 3 q^{98}+O(q^{100}) \) 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

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