LMFDB - Embedded newform 1890.2.t.c.1151.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1151,1890)]

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([5, 0, 1]))

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

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

chi := DirichletCharacter("1890.1151");

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.t (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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.16
Character	$\chi$	$=$	1890.1151
Dual form			1890.2.t.c.1601.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(2.20024 - 1.46933i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(2.20024 - 1.46933i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} +4.43825i q^{11} +(-4.51990 - 2.60957i) q^{13} +(2.64013 - 0.172355i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46981 + 6.00989i) q^{17} +(-2.43077 + 1.40341i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-2.21912 + 3.84363i) q^{22} +3.48491i q^{23} +1.00000 q^{25} +(-2.60957 - 4.51990i) q^{26} +(2.37260 + 1.17080i) q^{28} +(6.40344 - 3.69703i) q^{29} +(-1.82054 + 1.05109i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-6.00989 + 3.46981i) q^{34} +(-2.20024 + 1.46933i) q^{35} +(4.36995 + 7.56898i) q^{37} -2.80681 q^{38} -1.00000i q^{40} +(-2.90122 + 5.02506i) q^{41} +(-1.02568 - 1.77653i) q^{43} +(-3.84363 + 2.21912i) q^{44} +(-1.74245 + 3.01802i) q^{46} +(-5.16742 + 8.95023i) q^{47} +(2.68214 - 6.46576i) q^{49} +(0.866025 + 0.500000i) q^{50} -5.21913i q^{52} +(4.60281 + 2.65743i) q^{53} -4.43825i q^{55} +(1.46933 + 2.20024i) q^{56} +7.39406 q^{58} +(0.534861 + 0.926406i) q^{59} +(5.23536 + 3.02264i) q^{61} -2.10218 q^{62} -1.00000 q^{64} +(4.51990 + 2.60957i) q^{65} +(-2.46400 - 4.26778i) q^{67} -6.93962 q^{68} +(-2.64013 + 0.172355i) q^{70} -11.5388i q^{71} +(13.1874 + 7.61374i) q^{73} +8.73991i q^{74} +(-2.43077 - 1.40341i) q^{76} +(6.52125 + 9.76522i) q^{77} +(-3.88551 + 6.72991i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-5.02506 + 2.90122i) q^{82} +(2.84720 + 4.93150i) q^{83} +(3.46981 - 6.00989i) q^{85} -2.05136i q^{86} -4.43825 q^{88} +(-4.16961 - 7.22198i) q^{89} +(-13.7792 + 0.899543i) q^{91} +(-3.01802 + 1.74245i) q^{92} +(-8.95023 + 5.16742i) q^{94} +(2.43077 - 1.40341i) q^{95} +(-11.4765 + 6.62595i) q^{97} +(5.55569 - 4.25845i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7}+O(q^{10}) $ 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7	$ 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7} - 16 q^{16} - 6 q^{17} - 16 q^{20} + 32 q^{25} - 12 q^{26} + 2 q^{28} - 6 q^{29} + 18 q^{31} + 2 q^{35} + 2 q^{37} + 6 q^{41} - 28 q^{43} + 6 q^{44} - 24 q^{47} + 32 q^{49} + 36 q^{53} + 6 q^{56} + 30 q^{59} + 54 q^{61} - 32 q^{64} + 4 q^{67} - 12 q^{68} - 30 q^{73} + 6 q^{77} + 4 q^{79} + 16 q^{80} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 12 q^{89} - 66 q^{91} + 18 q^{92} - 42 q^{94} + 96 q^{97} + 24 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7 - 16 * q^16 - 6 * q^17 - 16 * q^20 + 32 * q^25 - 12 * q^26 + 2 * q^28 - 6 * q^29 + 18 * q^31 + 2 * q^35 + 2 * q^37 + 6 * q^41 - 28 * q^43 + 6 * q^44 - 24 * q^47 + 32 * q^49 + 36 * q^53 + 6 * q^56 + 30 * q^59 + 54 * q^61 - 32 * q^64 + 4 * q^67 - 12 * q^68 - 30 * q^73 + 6 * q^77 + 4 * q^79 + 16 * q^80 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 12 * q^89 - 66 * q^91 + 18 * q^92 - 42 * q^94 + 96 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	2.20024	−	1.46933i	0.831614	−	0.555354i
$7$	2.20024	−	1.46933i	0.831614	−	0.555354i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$			4.43825i			1.33818i	0.743181	+	0.669091i	$0.233316\pi$
$11$			4.43825i			1.33818i	−0.743181	+	0.669091i	$0.766684\pi$
$12$		0			0
$13$	−4.51990	−	2.60957i	−1.25360	−	0.723763i	−0.281773	−	0.959481i	$-0.590923\pi$
$13$	−4.51990	−	2.60957i	−1.25360	−	0.723763i	−0.971822	+	0.235717i	$0.924256\pi$
$14$	2.64013	−	0.172355i	0.705605	−	0.0460638i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.46981	+	6.00989i	−0.841552	+	1.45761i	0.0470295	+	0.998894i	$0.485025\pi$
$17$	−3.46981	+	6.00989i	−0.841552	+	1.45761i	−0.888582	+	0.458718i	$0.848309\pi$
$18$		0			0
$19$	−2.43077	+	1.40341i	−0.557657	+	0.321963i	−0.752204	−	0.658930i	$-0.771009\pi$
$19$	−2.43077	+	1.40341i	−0.557657	+	0.321963i	0.194548	+	0.980893i	$0.437676\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	−2.21912	+	3.84363i	−0.473119	+	0.819466i
$23$			3.48491i			0.726653i	0.931662	+	0.363326i	$0.118359\pi$
$23$			3.48491i			0.726653i	−0.931662	+	0.363326i	$0.881641\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−2.60957	−	4.51990i	−0.511778	−	0.886426i
$27$		0			0
$28$	2.37260	+	1.17080i	0.448379	+	0.221261i
$29$	6.40344	−	3.69703i	1.18909	−	0.686521i	0.230990	−	0.972956i	$-0.425804\pi$
$29$	6.40344	−	3.69703i	1.18909	−	0.686521i	0.958100	+	0.286435i	$0.0924703\pi$
$30$		0			0
$31$	−1.82054	+	1.05109i	−0.326979	+	0.188781i	−0.654499	−	0.756063i	$-0.727120\pi$
$31$	−1.82054	+	1.05109i	−0.326979	+	0.188781i	0.327520	+	0.944844i	$0.393787\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−6.00989	+	3.46981i	−1.03069	+	0.595067i
$35$	−2.20024	+	1.46933i	−0.371909	+	0.248362i
$36$		0			0
$37$	4.36995	+	7.56898i	0.718416	+	1.24433i	0.961627	+	0.274359i	$0.0884658\pi$
$37$	4.36995	+	7.56898i	0.718416	+	1.24433i	−0.243211	+	0.969973i	$0.578201\pi$
$38$	−2.80681			−0.455325
$39$		0			0
$40$		−	1.00000i		−	0.158114i
$41$	−2.90122	+	5.02506i	−0.453094	+	0.784782i	−0.998576	−	0.0533403i	$-0.983013\pi$
$41$	−2.90122	+	5.02506i	−0.453094	+	0.784782i	0.545482	+	0.838122i	$0.316347\pi$
$42$		0			0
$43$	−1.02568	−	1.77653i	−0.156415	−	0.270919i	0.777158	−	0.629305i	$-0.216660\pi$
$43$	−1.02568	−	1.77653i	−0.156415	−	0.270919i	−0.933573	+	0.358386i	$0.883327\pi$
$44$	−3.84363	+	2.21912i	−0.579450	+	0.334545i
$45$		0			0
$46$	−1.74245	+	3.01802i	−0.256911	+	0.444982i
$47$	−5.16742	+	8.95023i	−0.753745	+	1.30552i	0.192251	+	0.981346i	$0.438421\pi$
$47$	−5.16742	+	8.95023i	−0.753745	+	1.30552i	−0.945996	+	0.324179i	$0.894912\pi$
$48$		0			0
$49$	2.68214	−	6.46576i	0.383163	−	0.923681i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$		−	5.21913i		−	0.723763i
$53$	4.60281	+	2.65743i	0.632245	+	0.365027i	0.781621	−	0.623754i	$-0.214393\pi$
$53$	4.60281	+	2.65743i	0.632245	+	0.365027i	−0.149376	+	0.988780i	$0.547727\pi$
$54$		0			0
$55$		−	4.43825i		−	0.598453i
$56$	1.46933	+	2.20024i	0.196347	+	0.294020i
$57$		0			0
$58$	7.39406			0.970887
$59$	0.534861	+	0.926406i	0.0696329	+	0.120608i	0.898740	−	0.438482i	$-0.144484\pi$
$59$	0.534861	+	0.926406i	0.0696329	+	0.120608i	−0.829107	+	0.559090i	$0.811151\pi$
$60$		0			0
$61$	5.23536	+	3.02264i	0.670319	+	0.387009i	0.796198	−	0.605037i	$-0.206842\pi$
$61$	5.23536	+	3.02264i	0.670319	+	0.387009i	−0.125878	+	0.992046i	$0.540175\pi$
$62$	−2.10218			−0.266977
$63$		0			0
$64$	−1.00000			−0.125000
$65$	4.51990	+	2.60957i	0.560625	+	0.323677i
$66$		0			0
$67$	−2.46400	−	4.26778i	−0.301026	−	0.521392i	0.675343	−	0.737504i	$-0.263996\pi$
$67$	−2.46400	−	4.26778i	−0.301026	−	0.521392i	−0.976369	+	0.216112i	$0.930662\pi$
$68$	−6.93962			−0.841552
$69$		0			0
$70$	−2.64013	+	0.172355i	−0.315556	+	0.0206004i
$71$		−	11.5388i		−	1.36940i	−0.728825	−	0.684700i	$-0.759933\pi$
$71$		−	11.5388i		−	1.36940i	0.728825	−	0.684700i	$-0.240067\pi$
$72$		0			0
$73$	13.1874	+	7.61374i	1.54347	+	0.891121i	0.998616	+	0.0525873i	$0.0167468\pi$
$73$	13.1874	+	7.61374i	1.54347	+	0.891121i	0.544850	+	0.838533i	$0.316587\pi$
$74$			8.73991i			1.01599i
$75$		0			0
$76$	−2.43077	−	1.40341i	−0.278828	−	0.160982i
$77$	6.52125	+	9.76522i	0.743165	+	1.11285i
$78$		0			0
$79$	−3.88551	+	6.72991i	−0.437155	+	0.757174i	−0.997469	−	0.0711063i	$-0.977347\pi$
$79$	−3.88551	+	6.72991i	−0.437155	+	0.757174i	0.560314	+	0.828280i	$0.310680\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	−5.02506	+	2.90122i	−0.554925	+	0.320386i
$83$	2.84720	+	4.93150i	0.312521	+	0.541302i	0.978907	−	0.204304i	$-0.0654933\pi$
$83$	2.84720	+	4.93150i	0.312521	+	0.541302i	−0.666387	+	0.745606i	$0.732160\pi$
$84$		0			0
$85$	3.46981	−	6.00989i	0.376354	−	0.651864i
$86$		−	2.05136i		−	0.221204i
$87$		0			0
$88$	−4.43825			−0.473119
$89$	−4.16961	−	7.22198i	−0.441978	−	0.765528i	0.555858	−	0.831277i	$-0.312390\pi$
$89$	−4.16961	−	7.22198i	−0.441978	−	0.765528i	−0.997836	+	0.0657488i	$0.979056\pi$
$90$		0			0
$91$	−13.7792	+	0.899543i	−1.44445	+	0.0942977i
$92$	−3.01802	+	1.74245i	−0.314650	+	0.181663i
$93$		0			0
$94$	−8.95023	+	5.16742i	−0.923145	+	0.532978i
$95$	2.43077	−	1.40341i	0.249392	−	0.143986i
$96$		0			0
$97$	−11.4765	+	6.62595i	−1.16526	+	0.672763i	−0.952559	−	0.304354i	$-0.901559\pi$
$97$	−11.4765	+	6.62595i	−1.16526	+	0.672763i	−0.212701	+	0.977117i	$0.568226\pi$
$98$	5.55569	−	4.25845i	0.561209	−	0.430168i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−18.1043			−1.80144			−0.900721	−	0.434399i	$-0.856961\pi$
$101$	−18.1043			−1.80144			−0.900721	+	0.434399i	$0.856961\pi$
$102$		0			0
$103$		−	9.83724i		−	0.969292i	−0.874710	−	0.484646i	$-0.838948\pi$
$103$		−	9.83724i		−	0.969292i	0.874710	−	0.484646i	$-0.161052\pi$
$104$	2.60957	−	4.51990i	0.255889	−	0.443213i
$105$		0			0
$106$	2.65743	+	4.60281i	0.258113	+	0.447064i
$107$	−10.4663	+	6.04270i	−1.01181	+	0.584170i	−0.911722	−	0.410809i	$-0.865246\pi$
$107$	−10.4663	+	6.04270i	−1.01181	+	0.584170i	−0.100090	+	0.994978i	$0.531913\pi$
$108$		0			0
$109$	−1.65320	+	2.86343i	−0.158348	+	0.274267i	−0.934273	−	0.356558i	$-0.883950\pi$
$109$	−1.65320	+	2.86343i	−0.158348	+	0.274267i	0.775925	+	0.630825i	$0.217283\pi$
$110$	2.21912	−	3.84363i	0.211585	−	0.366476i
$111$		0			0
$112$	0.172355	+	2.64013i	0.0162860	+	0.249469i
$113$	−2.79421	−	1.61324i	−0.262857	−	0.151760i	0.362780	−	0.931875i	$-0.381828\pi$
$113$	−2.79421	−	1.61324i	−0.262857	−	0.151760i	−0.625637	+	0.780114i	$0.715161\pi$
$114$		0			0
$115$		−	3.48491i		−	0.324969i
$116$	6.40344	+	3.69703i	0.594545	+	0.343260i
$117$		0			0
$118$			1.06972i			0.0984758i
$119$	1.19608	+	18.3215i	0.109644	+	1.67953i
$120$		0			0
$121$	−8.69804			−0.790731
$122$	3.02264	+	5.23536i	0.273657	+	0.473987i
$123$		0			0
$124$	−1.82054	−	1.05109i	−0.163489	−	0.0943907i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	4.10553			0.364307			0.182154	−	0.983270i	$-0.441693\pi$
$127$	4.10553			0.364307			0.182154	+	0.983270i	$0.441693\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	2.60957	+	4.51990i	0.228874	+	0.396422i
$131$	19.4136			1.69618			0.848089	−	0.529854i	$-0.177753\pi$
$131$	19.4136			1.69618			0.848089	+	0.529854i	$0.177753\pi$
$132$		0			0
$133$	−3.28622	+	6.65943i	−0.284951	+	0.577446i
$134$		−	4.92801i		−	0.425715i
$135$		0			0
$136$	−6.00989	−	3.46981i	−0.515343	−	0.297534i
$137$		−	9.19632i		−	0.785695i	−0.919604	−	0.392847i	$-0.871490\pi$
$137$		−	9.19632i		−	0.785695i	0.919604	−	0.392847i	$-0.128510\pi$
$138$		0			0
$139$	−8.90078	−	5.13887i	−0.754954	−	0.435873i	0.0725271	−	0.997366i	$-0.476894\pi$
$139$	−8.90078	−	5.13887i	−0.754954	−	0.435873i	−0.827481	+	0.561494i	$0.810227\pi$
$140$	−2.37260	−	1.17080i	−0.200521	−	0.0989508i
$141$		0			0
$142$	5.76938	−	9.99286i	0.484156	−	0.838582i
$143$	11.5819	−	20.0604i	0.968527	−	1.67754i
$144$		0			0
$145$	−6.40344	+	3.69703i	−0.531777	+	0.307021i
$146$	7.61374	+	13.1874i	0.630118	+	1.09140i
$147$		0			0
$148$	−4.36995	+	7.56898i	−0.359208	+	0.622166i
$149$		−	15.3288i		−	1.25578i	−0.778302	−	0.627890i	$-0.783919\pi$
$149$		−	15.3288i		−	1.25578i	0.778302	−	0.627890i	$-0.216081\pi$
$150$		0			0
$151$	5.74675			0.467664			0.233832	−	0.972277i	$-0.424873\pi$
$151$	5.74675			0.467664			0.233832	+	0.972277i	$0.424873\pi$
$152$	−1.40341	−	2.43077i	−0.113831	−	0.197161i
$153$		0			0
$154$	0.764954	+	11.7176i	0.0616417	+	0.944228i
$155$	1.82054	−	1.05109i	0.146229	−	0.0844256i
$156$		0			0
$157$	6.17457	−	3.56489i	0.492784	−	0.284509i	−0.232945	−	0.972490i	$-0.574836\pi$
$157$	6.17457	−	3.56489i	0.492784	−	0.284509i	0.725729	+	0.687981i	$0.241503\pi$
$158$	−6.72991	+	3.88551i	−0.535403	+	0.309115i
$159$		0			0
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	5.12047	+	7.66764i	0.403550	+	0.604295i
$162$		0			0
$163$	−1.11012	−	1.92279i	−0.0869517	−	0.150605i	0.819270	−	0.573409i	$-0.194379\pi$
$163$	−1.11012	−	1.92279i	−0.0869517	−	0.150605i	−0.906221	+	0.422804i	$0.861046\pi$
$164$	−5.80244			−0.453094
$165$		0			0
$166$			5.69440i			0.441971i
$167$	−7.27271	+	12.5967i	−0.562779	+	0.974762i	0.434473	+	0.900685i	$0.356935\pi$
$167$	−7.27271	+	12.5967i	−0.562779	+	0.974762i	−0.997252	+	0.0740777i	$0.976399\pi$
$168$		0			0
$169$	7.11967	+	12.3316i	0.547667	+	0.948587i
$170$	6.00989	−	3.46981i	0.460937	−	0.266122i
$171$		0			0
$172$	1.02568	−	1.77653i	0.0782075	−	0.135459i
$173$	1.25357	−	2.17125i	0.0953073	−	0.165077i	−0.814430	−	0.580262i	$-0.802950\pi$
$173$	1.25357	−	2.17125i	0.0953073	−	0.165077i	0.909737	+	0.415185i	$0.136283\pi$
$174$		0			0
$175$	2.20024	−	1.46933i	0.166323	−	0.111071i
$176$	−3.84363	−	2.21912i	−0.289725	−	0.167273i
$177$		0			0
$178$		−	8.33922i		−	0.625051i
$179$	−6.45012	−	3.72398i	−0.482105	−	0.278343i	0.239188	−	0.970973i	$-0.423119\pi$
$179$	−6.45012	−	3.72398i	−0.482105	−	0.278343i	−0.721293	+	0.692630i	$0.756452\pi$
$180$		0			0
$181$		−	6.18571i		−	0.459780i	−0.973217	−	0.229890i	$-0.926163\pi$
$181$		−	6.18571i		−	0.459780i	0.973217	−	0.229890i	$-0.0738367\pi$
$182$	−12.3829	−	6.11057i	−0.917882	−	0.452946i
$183$		0			0
$184$	−3.48491			−0.256911
$185$	−4.36995	−	7.56898i	−0.321285	−	0.556482i
$186$		0			0
$187$	−26.6734	−	15.3999i	−1.95055	−	1.12615i
$188$	−10.3348			−0.753745
$189$		0			0
$190$	2.80681			0.203627
$191$	19.9088	+	11.4944i	1.44055	+	0.831704i	0.997886	−	0.0649822i	$-0.0206991\pi$
$191$	19.9088	+	11.4944i	1.44055	+	0.831704i	0.442667	+	0.896686i	$0.354032\pi$
$192$		0			0
$193$	5.44323	+	9.42795i	0.391812	+	0.678638i	0.992689	−	0.120703i	$-0.0385150\pi$
$193$	5.44323	+	9.42795i	0.391812	+	0.678638i	−0.600877	+	0.799342i	$0.705182\pi$
$194$	−13.2519			−0.951431
$195$		0			0
$196$	6.94059	−	0.910079i	0.495756	−	0.0650057i
$197$		−	7.07434i		−	0.504026i	−0.967724	−	0.252013i	$-0.918907\pi$
$197$		−	7.07434i		−	0.504026i	0.967724	−	0.252013i	$-0.0810926\pi$
$198$		0			0
$199$	15.9968	+	9.23577i	1.13398	+	0.654706i	0.944934	−	0.327261i	$-0.106126\pi$
$199$	15.9968	+	9.23577i	1.13398	+	0.654706i	0.189051	+	0.981967i	$0.439459\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	−15.6788	−	9.05213i	−1.10315	−	0.636906i
$203$	8.65698	−	17.5431i	0.607601	−	1.23129i
$204$		0			0
$205$	2.90122	−	5.02506i	0.202630	−	0.350965i
$206$	4.91862	−	8.51930i	0.342697	−	0.593568i
$207$		0			0
$208$	4.51990	−	2.60957i	0.313399	−	0.180941i
$209$	−6.22866	−	10.7884i	−0.430845	−	0.746246i
$210$		0			0
$211$	−3.88575	+	6.73032i	−0.267506	+	0.463334i	−0.968217	−	0.250111i	$-0.919533\pi$
$211$	−3.88575	+	6.73032i	−0.267506	+	0.463334i	0.700711	+	0.713445i	$0.252866\pi$
$212$			5.31487i			0.365027i
$213$		0			0
$214$	−12.0854			−0.826141
$215$	1.02568	+	1.77653i	0.0699509	+	0.121159i
$216$		0			0
$217$	−2.46124	+	4.98763i	−0.167080	+	0.338582i
$218$	−2.86343	+	1.65320i	−0.193936	+	0.111969i
$219$		0			0
$220$	3.84363	−	2.21912i	0.259138	−	0.149613i
$221$	31.3664	−	18.1094i	2.10993	−	1.21817i
$222$		0			0
$223$	1.25245	−	0.723100i	0.0838699	−	0.0484223i	−0.457479	−	0.889221i	$-0.651247\pi$
$223$	1.25245	−	0.723100i	0.0838699	−	0.0484223i	0.541348	+	0.840798i	$0.317914\pi$
$224$	−1.17080	+	2.37260i	−0.0782275	+	0.158526i
$225$		0			0
$226$	−1.61324	−	2.79421i	−0.107311	−	0.185868i
$227$	8.46455			0.561812			0.280906	−	0.959735i	$-0.409365\pi$
$227$	8.46455			0.561812			0.280906	+	0.959735i	$0.409365\pi$
$228$		0			0
$229$		−	13.7837i		−	0.910853i	−0.890273	−	0.455427i	$-0.849487\pi$
$229$		−	13.7837i		−	0.910853i	0.890273	−	0.455427i	$-0.150513\pi$
$230$	1.74245	−	3.01802i	0.114894	−	0.199002i
$231$		0			0
$232$	3.69703	+	6.40344i	0.242722	+	0.420406i
$233$	−16.7359	+	9.66250i	−1.09641	+	0.633011i	−0.935275	−	0.353921i	$-0.884848\pi$
$233$	−16.7359	+	9.66250i	−1.09641	+	0.633011i	−0.161133	+	0.986933i	$0.551515\pi$
$234$		0			0
$235$	5.16742	−	8.95023i	0.337085	−	0.583848i
$236$	−0.534861	+	0.926406i	−0.0348165	+	0.0603039i
$237$		0			0
$238$	−8.12492	+	16.4649i	−0.526660	+	1.06726i
$239$	7.14170	+	4.12327i	0.461958	+	0.266712i	0.712867	−	0.701299i	$-0.247396\pi$
$239$	7.14170	+	4.12327i	0.461958	+	0.266712i	−0.250909	+	0.968011i	$0.580729\pi$
$240$		0			0
$241$		−	23.9106i		−	1.54022i	−0.637914	−	0.770108i	$-0.720203\pi$
$241$		−	23.9106i		−	1.54022i	0.637914	−	0.770108i	$-0.279797\pi$
$242$	−7.53272	−	4.34902i	−0.484222	−	0.279566i
$243$		0			0
$244$			6.04527i			0.387009i
$245$	−2.68214	+	6.46576i	−0.171356	+	0.413083i
$246$		0			0
$247$	14.6491			0.932101
$248$	−1.05109	−	1.82054i	−0.0667443	−	0.115605i
$249$		0			0
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	21.8070			1.37644			0.688222	−	0.725500i	$-0.258391\pi$
$251$	21.8070			1.37644			0.688222	+	0.725500i	$0.258391\pi$
$252$		0			0
$253$	−15.4669			−0.972394
$254$	3.55550	+	2.05277i	0.223092	+	0.128802i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.0751			0.628471			0.314235	−	0.949345i	$-0.398252\pi$
$257$	10.0751			0.628471			0.314235	+	0.949345i	$0.398252\pi$
$258$		0			0
$259$	20.7363	+	10.2327i	1.28849	+	0.635829i
$260$			5.21913i			0.323677i
$261$		0			0
$262$	16.8127	+	9.70682i	1.03869	+	0.599690i
$263$			1.97563i			0.121823i	0.998143	+	0.0609113i	$0.0194007\pi$
$263$			1.97563i			0.121823i	−0.998143	+	0.0609113i	$0.980599\pi$
$264$		0			0
$265$	−4.60281	−	2.65743i	−0.282748	−	0.163245i
$266$	−6.17567	+	4.12413i	−0.378654	+	0.252867i
$267$		0			0
$268$	2.46400	−	4.26778i	0.150513	−	0.260696i
$269$	−4.12540	+	7.14541i	−0.251530	+	0.435663i	−0.963947	−	0.266093i	$-0.914267\pi$
$269$	−4.12540	+	7.14541i	−0.251530	+	0.435663i	0.712417	+	0.701756i	$0.247600\pi$
$270$		0			0
$271$	24.8880	−	14.3691i	1.51184	−	0.872859i	0.511932	−	0.859026i	$-0.328930\pi$
$271$	24.8880	−	14.3691i	1.51184	−	0.872859i	0.999904	−	0.0138328i	$-0.00440326\pi$
$272$	−3.46981	−	6.00989i	−0.210388	−	0.364403i
$273$		0			0
$274$	4.59816	−	7.96425i	0.277785	−	0.481138i
$275$			4.43825i			0.267636i
$276$		0			0
$277$	20.4226			1.22707			0.613537	−	0.789666i	$-0.289746\pi$
$277$	20.4226			1.22707			0.613537	+	0.789666i	$0.289746\pi$
$278$	−5.13887	−	8.90078i	−0.308209	−	0.533833i
$279$		0			0
$280$	−1.46933	−	2.20024i	−0.0878092	−	0.131490i
$281$	1.53417	−	0.885754i	0.0915209	−	0.0528396i	−0.453541	−	0.891235i	$-0.649839\pi$
$281$	1.53417	−	0.885754i	0.0915209	−	0.0528396i	0.545062	+	0.838396i	$0.316506\pi$
$282$		0			0
$283$	2.09766	−	1.21108i	0.124693	−	0.0719915i	−0.436356	−	0.899774i	$-0.643731\pi$
$283$	2.09766	−	1.21108i	0.124693	−	0.0719915i	0.561049	+	0.827783i	$0.310398\pi$
$284$	9.99286	−	5.76938i	0.592967	−	0.342350i
$285$		0			0
$286$	20.0604	−	11.5819i	1.18620	−	0.684852i
$287$	1.00008	+	15.3192i	0.0590328	+	0.904263i
$288$		0			0
$289$	−15.5792	−	26.9839i	−0.916421	−	1.58729i
$290$	−7.39406			−0.434194
$291$		0			0
$292$			15.2275i			0.891121i
$293$	5.58519	−	9.67384i	0.326290	−	0.565152i	−0.655482	−	0.755211i	$-0.727535\pi$
$293$	5.58519	−	9.67384i	0.326290	−	0.565152i	0.981773	+	0.190059i	$0.0608679\pi$
$294$		0			0
$295$	−0.534861	−	0.926406i	−0.0311408	−	0.0539374i
$296$	−7.56898	+	4.36995i	−0.439938	+	0.253998i
$297$		0			0
$298$	7.66438	−	13.2751i	0.443985	−	0.769005i
$299$	9.09409	−	15.7514i	0.525925	−	0.910929i
$300$		0			0
$301$	−4.86706	−	2.40174i	−0.280533	−	0.138434i
$302$	4.97683	+	2.87338i	0.286384	+	0.165344i
$303$		0			0
$304$		−	2.80681i		−	0.160982i
$305$	−5.23536	−	3.02264i	−0.299776	−	0.173076i
$306$		0			0
$307$			2.48600i			0.141884i	0.997480	+	0.0709419i	$0.0226005\pi$
$307$			2.48600i			0.141884i	−0.997480	+	0.0709419i	$0.977400\pi$
$308$	−5.19631	+	10.5302i	−0.296087	+	0.600013i
$309$		0			0
$310$	2.10218			0.119396
$311$	3.31033	+	5.73365i	0.187711	+	0.325126i	0.944487	−	0.328549i	$-0.106560\pi$
$311$	3.31033	+	5.73365i	0.187711	+	0.325126i	−0.756775	+	0.653675i	$0.773226\pi$
$312$		0			0
$313$	−22.1815	−	12.8065i	−1.25377	−	0.723866i	−0.281916	−	0.959439i	$-0.590970\pi$
$313$	−22.1815	−	12.8065i	−1.25377	−	0.723866i	−0.971857	+	0.235573i	$0.924303\pi$
$314$	7.12978			0.402357
$315$		0			0
$316$	−7.77103			−0.437155
$317$	16.9737	+	9.79975i	0.953336	+	0.550409i	0.894116	−	0.447836i	$-0.147805\pi$
$317$	16.9737	+	9.79975i	0.953336	+	0.550409i	0.0592204	+	0.998245i	$0.481139\pi$
$318$		0			0
$319$	16.4083	+	28.4201i	0.918690	+	1.59122i
$320$	1.00000			0.0559017
$321$		0			0
$322$	0.600641	+	9.20061i	0.0334724	+	0.512730i
$323$		−	19.4782i		−	1.08380i
$324$		0			0
$325$	−4.51990	−	2.60957i	−0.250719	−	0.144753i
$326$		−	2.22025i		−	0.122968i
$327$		0			0
$328$	−5.02506	−	2.90122i	−0.277462	−	0.160193i
$329$	1.78126	+	27.2853i	0.0982040	+	1.50429i
$330$		0			0
$331$	11.3343	−	19.6316i	0.622991	−	1.07905i	−0.365934	−	0.930641i	$-0.619251\pi$
$331$	11.3343	−	19.6316i	0.622991	−	1.07905i	0.988926	−	0.148412i	$-0.0474161\pi$
$332$	−2.84720	+	4.93150i	−0.156260	+	0.270651i
$333$		0			0
$334$	−12.5967	+	7.27271i	−0.689261	+	0.397945i
$335$	2.46400	+	4.26778i	0.134623	+	0.233174i
$336$		0			0
$337$	−9.56790	+	16.5721i	−0.521196	+	0.902739i	0.478500	+	0.878088i	$0.341181\pi$
$337$	−9.56790	+	16.5721i	−0.521196	+	0.902739i	−0.999696	+	0.0246511i	$0.992153\pi$
$338$			14.2393i			0.774518i
$339$		0			0
$340$	6.93962			0.376354
$341$	−4.66500	−	8.08001i	−0.252624	−	0.437557i
$342$		0			0
$343$	−3.59897	−	18.1672i	−0.194326	−	0.980937i
$344$	1.77653	−	1.02568i	0.0957843	−	0.0553011i
$345$		0			0
$346$	2.17125	−	1.25357i	0.116727	−	0.0673924i
$347$	−0.443672	+	0.256154i	−0.0238176	+	0.0137511i	−0.511862	−	0.859068i	$-0.671044\pi$
$347$	−0.443672	+	0.256154i	−0.0238176	+	0.0137511i	0.488044	+	0.872819i	$0.337711\pi$
$348$		0			0
$349$	−1.14174	+	0.659186i	−0.0611161	+	0.0352854i	−0.530247	−	0.847843i	$-0.677901\pi$
$349$	−1.14174	+	0.659186i	−0.0611161	+	0.0352854i	0.469131	+	0.883129i	$0.344567\pi$
$350$	2.64013	−	0.172355i	0.141121	−	0.00921276i
$351$		0			0
$352$	−2.21912	−	3.84363i	−0.118280	−	0.204866i
$353$	−12.3002			−0.654672			−0.327336	−	0.944908i	$-0.606151\pi$
$353$	−12.3002			−0.654672			−0.327336	+	0.944908i	$0.606151\pi$
$354$		0			0
$355$			11.5388i			0.612414i
$356$	4.16961	−	7.22198i	0.220989	−	0.382764i
$357$		0			0
$358$	−3.72398	−	6.45012i	−0.196819	−	0.340900i
$359$	−20.6370	+	11.9148i	−1.08918	+	0.628837i	−0.933357	−	0.358948i	$-0.883135\pi$
$359$	−20.6370	+	11.9148i	−1.08918	+	0.628837i	−0.155820	+	0.987785i	$0.549802\pi$
$360$		0			0
$361$	−5.56091	+	9.63178i	−0.292679	+	0.506936i
$362$	3.09285	−	5.35698i	0.162557	−	0.281557i
$363$		0			0
$364$	−7.66863	−	11.4834i	−0.401945	−	0.601892i
$365$	−13.1874	−	7.61374i	−0.690259	−	0.398521i
$366$		0			0
$367$			30.1194i			1.57222i	0.618087	+	0.786110i	$0.287908\pi$
$367$			30.1194i			1.57222i	−0.618087	+	0.786110i	$0.712092\pi$
$368$	−3.01802	−	1.74245i	−0.157325	−	0.0908316i
$369$		0			0
$370$		−	8.73991i		−	0.454366i
$371$	14.0319	−	0.916043i	0.728502	−	0.0475586i
$372$		0			0
$373$	36.8547			1.90826			0.954131	−	0.299389i	$-0.0967829\pi$
$373$	36.8547			1.90826			0.954131	+	0.299389i	$0.0967829\pi$
$374$	−15.3999	−	26.6734i	−0.796308	−	1.37925i
$375$		0			0
$376$	−8.95023	−	5.16742i	−0.461573	−	0.266489i
$377$	−38.5906			−1.98752
$378$		0			0
$379$	−3.10706			−0.159599			−0.0797994	−	0.996811i	$-0.525428\pi$
$379$	−3.10706			−0.159599			−0.0797994	+	0.996811i	$0.525428\pi$
$380$	2.43077	+	1.40341i	0.124696	+	0.0719932i
$381$		0			0
$382$	11.4944	+	19.9088i	0.588103	+	1.01863i
$383$	11.1938			0.571979			0.285990	−	0.958233i	$-0.407678\pi$
$383$	11.1938			0.571979			0.285990	+	0.958233i	$0.407678\pi$
$384$		0			0
$385$	−6.52125	−	9.76522i	−0.332354	−	0.497682i
$386$			10.8865i			0.554106i
$387$		0			0
$388$	−11.4765	−	6.62595i	−0.582630	−	0.336382i
$389$		−	22.9992i		−	1.16610i	−0.812435	−	0.583052i	$-0.801858\pi$
$389$		−	22.9992i		−	1.16610i	0.812435	−	0.583052i	$-0.198142\pi$
$390$		0			0
$391$	−20.9439	−	12.0920i	−1.05918	−	0.611517i
$392$	6.46576	+	2.68214i	0.326570	+	0.135469i
$393$		0			0
$394$	3.53717	−	6.12656i	0.178200	−	0.308652i
$395$	3.88551	−	6.72991i	0.195501	−	0.338618i
$396$		0			0
$397$	−6.76832	+	3.90769i	−0.339692	+	0.196121i	−0.660136	−	0.751146i	$-0.729501\pi$
$397$	−6.76832	+	3.90769i	−0.339692	+	0.196121i	0.320444	+	0.947268i	$0.396168\pi$
$398$	9.23577	+	15.9968i	0.462947	+	0.801848i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	11.6348i		−	0.581015i	−0.956873	−	0.290507i	$-0.906176\pi$
$401$		−	11.6348i		−	0.581015i	0.956873	−	0.290507i	$-0.0938241\pi$
$402$		0			0
$403$	10.9716			0.546532
$404$	−9.05213	−	15.6788i	−0.450360	−	0.780047i
$405$		0			0
$406$	16.2687	−	10.8643i	0.807403	−	0.539186i
$407$	−33.5930	+	19.3949i	−1.66514	+	0.961371i
$408$		0			0
$409$	24.2276	−	13.9878i	1.19798	−	0.691653i	0.237874	−	0.971296i	$-0.423549\pi$
$409$	24.2276	−	13.9878i	1.19798	−	0.691653i	0.960104	+	0.279643i	$0.0902161\pi$
$410$	5.02506	−	2.90122i	0.248170	−	0.143281i
$411$		0			0
$412$	8.51930	−	4.91862i	0.419716	−	0.242323i
$413$	2.53802	+	1.25243i	0.124888	+	0.0616281i
$414$		0			0
$415$	−2.84720	−	4.93150i	−0.139764	−	0.242078i
$416$	5.21913			0.255889
$417$		0			0
$418$		−	12.4573i		−	0.609307i
$419$	−1.60593	+	2.78155i	−0.0784549	+	0.135888i	−0.902583	−	0.430515i	$-0.858332\pi$
$419$	−1.60593	+	2.78155i	−0.0784549	+	0.135888i	0.824129	+	0.566403i	$0.191665\pi$
$420$		0			0
$421$	3.72961	+	6.45987i	0.181770	+	0.314835i	0.942483	−	0.334253i	$-0.108484\pi$
$421$	3.72961	+	6.45987i	0.181770	+	0.314835i	−0.760713	+	0.649088i	$0.775151\pi$
$422$	−6.73032	+	3.88575i	−0.327627	+	0.189155i
$423$		0			0
$424$	−2.65743	+	4.60281i	−0.129056	+	0.223532i
$425$	−3.46981	+	6.00989i	−0.168310	+	0.291522i
$426$		0			0
$427$	15.9603	−	1.04193i	0.772374	−	0.0504226i
$428$	−10.4663	−	6.04270i	−0.505906	−	0.292085i
$429$		0			0
$430$			2.05136i			0.0989256i
$431$	12.2228	+	7.05686i	0.588753	+	0.339917i	0.764604	−	0.644500i	$-0.222934\pi$
$431$	12.2228	+	7.05686i	0.588753	+	0.339917i	−0.175851	+	0.984417i	$0.556268\pi$
$432$		0			0
$433$			17.9235i			0.861348i	0.902508	+	0.430674i	$0.141724\pi$
$433$			17.9235i			0.861348i	−0.902508	+	0.430674i	$0.858276\pi$
$434$	−4.62531	+	3.08880i	−0.222022	+	0.148267i
$435$		0			0
$436$	−3.30640			−0.158348
$437$	−4.89073	−	8.47100i	−0.233956	−	0.405223i
$438$		0			0
$439$	33.6745	+	19.4420i	1.60719	+	0.927914i	0.989994	+	0.141109i	$0.0450667\pi$
$439$	33.6745	+	19.4420i	1.60719	+	0.927914i	0.617201	+	0.786806i	$0.288267\pi$
$440$	4.43825			0.211585
$441$		0			0
$442$	36.2188			1.72275
$443$	−23.5754	−	13.6113i	−1.12010	−	0.646692i	−0.178676	−	0.983908i	$-0.557181\pi$
$443$	−23.5754	−	13.6113i	−1.12010	−	0.646692i	−0.941427	+	0.337216i	$0.890515\pi$
$444$		0			0
$445$	4.16961	+	7.22198i	0.197659	+	0.342355i
$446$	1.44620			0.0684795
$447$		0			0
$448$	−2.20024	+	1.46933i	−0.103952	+	0.0694193i
$449$			16.5846i			0.782674i	0.920248	+	0.391337i	$0.127987\pi$
$449$			16.5846i			0.782674i	−0.920248	+	0.391337i	$0.872013\pi$
$450$		0			0
$451$	−22.3024	−	12.8763i	−1.05018	−	0.606322i
$452$		−	3.22647i		−	0.151760i
$453$		0			0
$454$	7.33052	+	4.23228i	0.344038	+	0.198631i
$455$	13.7792	−	0.899543i	0.645979	−	0.0421712i
$456$		0			0
$457$	−8.76829	+	15.1871i	−0.410163	+	0.710424i	−0.994907	−	0.100794i	$-0.967862\pi$
$457$	−8.76829	+	15.1871i	−0.410163	+	0.710424i	0.584744	+	0.811218i	$0.301195\pi$
$458$	6.89186	−	11.9370i	0.322035	−	0.557782i
$459$		0			0
$460$	3.01802	−	1.74245i	0.140716	−	0.0812423i
$461$	−17.8733	−	30.9575i	−0.832444	−	1.44184i	−0.896095	−	0.443863i	$-0.853608\pi$
$461$	−17.8733	−	30.9575i	−0.832444	−	1.44184i	0.0636506	−	0.997972i	$-0.479726\pi$
$462$		0			0
$463$	10.2703	−	17.7886i	0.477299	−	0.826707i	−0.522362	−	0.852724i	$-0.674949\pi$
$463$	10.2703	−	17.7886i	0.477299	−	0.826707i	0.999661	+	0.0260170i	$0.00828242\pi$
$464$			7.39406i			0.343260i
$465$		0			0
$466$	−19.3250			−0.895213
$467$	−3.54772	−	6.14483i	−0.164169	−	0.284349i	0.772191	−	0.635390i	$-0.219161\pi$
$467$	−3.54772	−	6.14483i	−0.164169	−	0.284349i	−0.936360	+	0.351042i	$0.885827\pi$
$468$		0			0
$469$	−11.6922	−	5.76972i	−0.539895	−	0.266421i
$470$	8.95023	−	5.16742i	0.412843	−	0.238355i
$471$		0			0
$472$	−0.926406	+	0.534861i	−0.0426413	+	0.0246190i
$473$	7.88470	−	4.55223i	0.362539	−	0.209312i
$474$		0			0
$475$	−2.43077	+	1.40341i	−0.111531	+	0.0643926i
$476$	−15.2689	+	10.1966i	−0.699847	+	0.467360i
$477$		0			0
$478$	4.12327	+	7.14170i	0.188594	+	0.326654i
$479$	−17.3106			−0.790942			−0.395471	−	0.918478i	$-0.629419\pi$
$479$	−17.3106			−0.790942			−0.395471	+	0.918478i	$0.629419\pi$
$480$		0			0
$481$		−	45.6147i		−	2.07985i
$482$	11.9553	−	20.7072i	0.544548	−	0.943185i
$483$		0			0
$484$	−4.34902	−	7.53272i	−0.197683	−	0.342396i
$485$	11.4765	−	6.62595i	0.521120	−	0.300869i
$486$		0			0
$487$	−17.8900	+	30.9864i	−0.810675	+	1.40413i	0.101718	+	0.994813i	$0.467566\pi$
$487$	−17.8900	+	30.9864i	−0.810675	+	1.40413i	−0.912393	+	0.409316i	$0.865767\pi$
$488$	−3.02264	+	5.23536i	−0.136828	+	0.236994i
$489$		0			0
$490$	−5.55569	+	4.25845i	−0.250980	+	0.192377i
$491$	−24.0944	−	13.9109i	−1.08736	−	0.627789i	−0.154490	−	0.987994i	$-0.549373\pi$
$491$	−24.0944	−	13.9109i	−1.08736	−	0.627789i	−0.932873	+	0.360205i	$0.882707\pi$
$492$		0			0
$493$			51.3119i			2.31097i
$494$	12.6865	+	7.32456i	0.570793	+	0.329547i
$495$		0			0
$496$		−	2.10218i		−	0.0943907i
$497$	−16.9542	−	25.3881i	−0.760502	−	1.13881i
$498$		0			0
$499$	−10.7082			−0.479365			−0.239683	−	0.970851i	$-0.577043\pi$
$499$	−10.7082			−0.479365			−0.239683	+	0.970851i	$0.577043\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	18.8854	+	10.9035i	0.842897	+	0.486647i
$503$	−26.8197			−1.19583			−0.597916	−	0.801559i	$-0.704004\pi$
$503$	−26.8197			−1.19583			−0.597916	+	0.801559i	$0.704004\pi$
$504$		0			0
$505$	18.1043			0.805629
$506$	−13.3947	−	7.73344i	−0.595467	−	0.343793i
$507$		0			0
$508$	2.05277	+	3.55550i	0.0910768	+	0.157750i
$509$	10.7357			0.475852			0.237926	−	0.971283i	$-0.423532\pi$
$509$	10.7357			0.475852			0.237926	+	0.971283i	$0.423532\pi$
$510$		0			0
$511$	40.2025	−	2.62453i	1.77846	−	0.116102i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	8.72534	+	5.03757i	0.384858	+	0.222198i
$515$			9.83724i			0.433481i
$516$		0			0
$517$	−39.7233	−	22.9343i	−1.74703	−	1.00865i
$518$	12.8418	+	19.2299i	0.564236	+	0.844914i
$519$		0			0
$520$	−2.60957	+	4.51990i	−0.114437	+	0.198211i
$521$	3.27417	−	5.67102i	0.143444	−	0.248452i	−0.785347	−	0.619055i	$-0.787516\pi$
$521$	3.27417	−	5.67102i	0.143444	−	0.248452i	0.928791	+	0.370603i	$0.120849\pi$
$522$		0			0
$523$	27.2374	−	15.7255i	1.19101	−	0.687628i	0.232472	−	0.972603i	$-0.425319\pi$
$523$	27.2374	−	15.7255i	1.19101	−	0.687628i	0.958535	+	0.284975i	$0.0919853\pi$
$524$	9.70682	+	16.8127i	0.424045	+	0.734467i
$525$		0			0
$526$	−0.987816	+	1.71095i	−0.0430708	+	0.0746008i
$527$		−	14.5883i		−	0.635478i
$528$		0			0
$529$	10.8554			0.471975
$530$	−2.65743	−	4.60281i	−0.115432	−	0.199933i
$531$		0			0
$532$	−7.41035	+	0.483768i	−0.321279	+	0.0209740i
$533$	26.2264	−	15.1418i	1.13599	−	0.655866i
$534$		0			0
$535$	10.4663	−	6.04270i	0.452496	−	0.261249i
$536$	4.26778	−	2.46400i	0.184340	−	0.106429i
$537$		0			0
$538$	−7.14541	+	4.12540i	−0.308060	+	0.177859i
$539$	28.6967	+	11.9040i	1.23605	+	0.512742i
$540$		0			0
$541$	3.61196	+	6.25610i	0.155290	+	0.268971i	0.933165	−	0.359449i	$-0.117035\pi$
$541$	3.61196	+	6.25610i	0.155290	+	0.268971i	−0.777874	+	0.628420i	$0.783702\pi$
$542$	28.7381			1.23441
$543$		0			0
$544$		−	6.93962i		−	0.297534i
$545$	1.65320	−	2.86343i	0.0708153	−	0.122656i
$546$		0			0
$547$	−3.09371	−	5.35846i	−0.132277	−	0.229111i	0.792277	−	0.610162i	$-0.208896\pi$
$547$	−3.09371	−	5.35846i	−0.132277	−	0.229111i	−0.924554	+	0.381051i	$0.875562\pi$
$548$	7.96425	−	4.59816i	0.340216	−	0.196424i
$549$		0			0
$550$	−2.21912	+	3.84363i	−0.0946237	+	0.163893i
$551$	−10.3769	+	17.9732i	−0.442069	+	0.765686i
$552$		0			0
$553$	1.33937	+	20.5165i	0.0569560	+	0.872452i
$554$	17.6865	+	10.2113i	0.751427	+	0.433837i
$555$		0			0
$556$		−	10.2777i		−	0.435873i
$557$	−3.23352	−	1.86687i	−0.137009	−	0.0791020i	0.429929	−	0.902863i	$-0.358539\pi$
$557$	−3.23352	−	1.86687i	−0.137009	−	0.0791020i	−0.566938	+	0.823761i	$0.691872\pi$
$558$		0			0
$559$			10.7063i			0.452830i
$560$	−0.172355	−	2.64013i	−0.00728332	−	0.111566i
$561$		0			0
$562$	1.77151			0.0747265
$563$	2.05579	+	3.56073i	0.0866411	+	0.150067i	0.906089	−	0.423086i	$-0.139053\pi$
$563$	2.05579	+	3.56073i	0.0866411	+	0.150067i	−0.819448	+	0.573153i	$0.805720\pi$
$564$		0			0
$565$	2.79421	+	1.61324i	0.117553	+	0.0678693i
$566$	2.42217			0.101811
$567$		0			0
$568$	11.5388			0.484156
$569$	17.0126	+	9.82222i	0.713205	+	0.411769i	0.812246	−	0.583314i	$-0.198244\pi$
$569$	17.0126	+	9.82222i	0.713205	+	0.411769i	−0.0990419	+	0.995083i	$0.531578\pi$
$570$		0			0
$571$	21.3658	+	37.0067i	0.894132	+	1.54868i	0.834875	+	0.550440i	$0.185540\pi$
$571$	21.3658	+	37.0067i	0.894132	+	1.54868i	0.0592571	+	0.998243i	$0.481127\pi$
$572$	23.1638			0.968527
$573$		0			0
$574$	−6.79350	+	13.7669i	−0.283555	+	0.574617i
$575$			3.48491i			0.145331i
$576$		0			0
$577$	−18.1866	−	10.5000i	−0.757117	−	0.437122i	0.0711425	−	0.997466i	$-0.477335\pi$
$577$	−18.1866	−	10.5000i	−0.757117	−	0.437122i	−0.828260	+	0.560344i	$0.810669\pi$
$578$		−	31.1583i		−	1.29601i
$579$		0			0
$580$	−6.40344	−	3.69703i	−0.265888	−	0.153511i
$581$	13.5105	+	6.66702i	0.560511	+	0.276594i
$582$		0			0
$583$	−11.7943	+	20.4284i	−0.488472	+	0.846058i
$584$	−7.61374	+	13.1874i	−0.315059	+	0.545698i
$585$		0			0
$586$	9.67384	−	5.58519i	0.399623	−	0.230722i
$587$	0.432150	+	0.748507i	0.0178368	+	0.0308942i	0.874806	−	0.484473i	$-0.160989\pi$
$587$	0.432150	+	0.748507i	0.0178368	+	0.0308942i	−0.856969	+	0.515368i	$0.827655\pi$
$588$		0			0
$589$	2.95021	−	5.10991i	0.121561	−	0.210550i
$590$		−	1.06972i		−	0.0440397i
$591$		0			0
$592$	−8.73991			−0.359208
$593$	0.642454	+	1.11276i	0.0263824	+	0.0456957i	0.878915	−	0.476978i	$-0.158268\pi$
$593$	0.642454	+	1.11276i	0.0263824	+	0.0456957i	−0.852533	+	0.522674i	$0.824935\pi$
$594$		0			0
$595$	−1.19608	−	18.3215i	−0.0490344	−	0.751109i
$596$	13.2751	−	7.66438i	0.543769	−	0.313945i
$597$		0			0
$598$	15.7514	−	9.09409i	0.644124	−	0.371885i
$599$	0.953971	−	0.550775i	0.0389782	−	0.0225041i	−0.480384	−	0.877058i	$-0.659503\pi$
$599$	0.953971	−	0.550775i	0.0389782	−	0.0225041i	0.519362	+	0.854554i	$0.326169\pi$
$600$		0			0
$601$	0.162569	−	0.0938594i	0.00663134	−	0.00382860i	−0.496681	−	0.867933i	$-0.665448\pi$
$601$	0.162569	−	0.0938594i	0.00663134	−	0.00382860i	0.503312	+	0.864105i	$0.332115\pi$
$602$	−3.01413	−	4.51350i	−0.122847	−	0.183957i
$603$		0			0
$604$	2.87338	+	4.97683i	0.116916	+	0.202504i
$605$	8.69804			0.353626
$606$		0			0
$607$			2.78981i			0.113235i	0.998396	+	0.0566175i	$0.0180315\pi$
$607$			2.78981i			0.113235i	−0.998396	+	0.0566175i	$0.981968\pi$
$608$	1.40341	−	2.43077i	0.0569156	−	0.0985807i
$609$		0			0
$610$	−3.02264	−	5.23536i	−0.122383	−	0.211973i
$611$	46.7124	−	26.9694i	1.88978	−	1.09107i
$612$		0			0
$613$	15.0929	−	26.1417i	0.609598	−	1.05586i	−0.381708	−	0.924283i	$-0.624664\pi$
$613$	15.0929	−	26.1417i	0.609598	−	1.05586i	0.991307	−	0.131572i	$-0.0420026\pi$
$614$	−1.24300	+	2.15294i	−0.0501635	+	0.0868857i
$615$		0			0
$616$	−9.76522	+	6.52125i	−0.393452	+	0.262749i
$617$	−18.6357	−	10.7593i	−0.750246	−	0.433155i	0.0755367	−	0.997143i	$-0.475933\pi$
$617$	−18.6357	−	10.7593i	−0.750246	−	0.433155i	−0.825783	+	0.563988i	$0.809266\pi$
$618$		0			0
$619$		−	26.6566i		−	1.07142i	−0.844402	−	0.535710i	$-0.820044\pi$
$619$		−	26.6566i		−	1.07142i	0.844402	−	0.535710i	$-0.179956\pi$
$620$	1.82054	+	1.05109i	0.0731147	+	0.0422128i
$621$		0			0
$622$			6.62065i			0.265464i
$623$	−19.7856	−	9.76358i	−0.792694	−	0.391170i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−12.8065	−	22.1815i	−0.511851	−	0.886551i
$627$		0			0
$628$	6.17457	+	3.56489i	0.246392	+	0.142255i
$629$	−60.6516			−2.41834
$630$		0			0
$631$	−12.9441			−0.515297			−0.257648	−	0.966239i	$-0.582948\pi$
$631$	−12.9441			−0.515297			−0.257648	+	0.966239i	$0.582948\pi$
$632$	−6.72991	−	3.88551i	−0.267701	−	0.154557i
$633$		0			0
$634$	9.79975	+	16.9737i	0.389198	+	0.674110i
$635$	−4.10553			−0.162923
$636$		0			0
$637$	−28.9959	+	22.2254i	−1.14886	+	0.880602i
$638$			32.8167i			1.29922i
$639$		0			0
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$			50.1023i			1.97892i	0.144797	+	0.989461i	$0.453747\pi$
$641$			50.1023i			1.97892i	−0.144797	+	0.989461i	$0.546253\pi$
$642$		0			0
$643$	13.3473	+	7.70607i	0.526366	+	0.303898i	0.739535	−	0.673118i	$-0.235045\pi$
$643$	13.3473	+	7.70607i	0.526366	+	0.303898i	−0.213169	+	0.977015i	$0.568379\pi$
$644$	−4.08013	+	8.26828i	−0.160780	+	0.325816i
$645$		0			0
$646$	9.73910	−	16.8686i	0.383180	−	0.663687i
$647$	8.95179	−	15.5050i	0.351931	−	0.609563i	−0.634657	−	0.772794i	$-0.718858\pi$
$647$	8.95179	−	15.5050i	0.351931	−	0.609563i	0.986588	+	0.163232i	$0.0521918\pi$
$648$		0			0
$649$	−4.11162	+	2.37384i	−0.161395	+	0.0931815i
$650$	−2.60957	−	4.51990i	−0.102356	−	0.177285i
$651$		0			0
$652$	1.11012	−	1.92279i	0.0434758	−	0.0753024i
$653$			0.406480i			0.0159068i	0.999968	+	0.00795339i	$0.00253167\pi$
$653$			0.406480i			0.0159068i	−0.999968	+	0.00795339i	$0.997468\pi$
$654$		0			0
$655$	−19.4136			−0.758554
$656$	−2.90122	−	5.02506i	−0.113274	−	0.196196i
$657$		0			0
$658$	−12.1000	+	24.5204i	−0.471709	+	0.955905i
$659$	17.3817	−	10.0353i	0.677093	−	0.390920i	−0.121666	−	0.992571i	$-0.538824\pi$
$659$	17.3817	−	10.0353i	0.677093	−	0.390920i	0.798759	+	0.601651i	$0.205490\pi$
$660$		0			0
$661$	−1.06654	+	0.615764i	−0.0414834	+	0.0239505i	−0.520598	−	0.853802i	$-0.674291\pi$
$661$	−1.06654	+	0.615764i	−0.0414834	+	0.0239505i	0.479115	+	0.877752i	$0.340958\pi$
$662$	19.6316	−	11.3343i	0.763005	−	0.440521i
$663$		0			0
$664$	−4.93150	+	2.84720i	−0.191379	+	0.110493i
$665$	3.28622	−	6.65943i	0.127434	−	0.258242i
$666$		0			0
$667$	12.8838	+	22.3154i	0.498862	+	0.864055i
$668$	−14.5454			−0.562779
$669$		0			0
$670$			4.92801i			0.190386i
$671$	−13.4152	+	23.2358i	−0.517888	+	0.897009i
$672$		0			0
$673$	−12.4710	−	21.6005i	−0.480723	−	0.832637i	0.519032	−	0.854755i	$-0.326293\pi$
$673$	−12.4710	−	21.6005i	−0.480723	−	0.832637i	−0.999755	+	0.0221176i	$0.992959\pi$
$674$	−16.5721	+	9.56790i	−0.638333	+	0.368542i
$675$		0			0
$676$	−7.11967	+	12.3316i	−0.273834	+	0.474294i
$677$	−3.88825	+	6.73465i	−0.149438	+	0.258834i	−0.931020	−	0.364969i	$-0.881080\pi$
$677$	−3.88825	+	6.73465i	−0.149438	+	0.258834i	0.781582	+	0.623802i	$0.214413\pi$
$678$		0			0
$679$	−15.5154	+	31.4414i	−0.595425	+	1.20661i
$680$	6.00989	+	3.46981i	0.230469	+	0.133061i
$681$		0			0
$682$		−	9.33000i		−	0.357264i
$683$	29.8265	+	17.2203i	1.14128	+	0.658917i	0.946747	−	0.321979i	$-0.104348\pi$
$683$	29.8265	+	17.2203i	1.14128	+	0.658917i	0.194532	+	0.980896i	$0.437681\pi$
$684$		0			0
$685$			9.19632i			0.351373i
$686$	5.96680	−	17.5327i	0.227814	−	0.669403i
$687$		0			0
$688$	2.05136			0.0782075
$689$	−13.8695	−	24.0227i	−0.528386	−	0.915191i
$690$		0			0
$691$	−0.603200	−	0.348258i	−0.0229468	−	0.0132483i	0.488483	−	0.872574i	$-0.337551\pi$
$691$	−0.603200	−	0.348258i	−0.0229468	−	0.0132483i	−0.511430	+	0.859325i	$0.670884\pi$
$692$	2.50714			0.0953073
$693$		0			0
$694$	−0.512308			−0.0194470
$695$	8.90078	+	5.13887i	0.337626	+	0.194928i
$696$		0			0
$697$	−20.1333	−	34.8720i	−0.762605	−	1.32087i
$698$	−1.31837			−0.0499011
$699$		0			0
$700$	2.37260	+	1.17080i	0.0896758	+	0.0442522i
$701$		−	40.4903i		−	1.52930i	−0.644447	−	0.764649i	$-0.722912\pi$
$701$		−	40.4903i		−	1.52930i	0.644447	−	0.764649i	$-0.277088\pi$
$702$		0			0
$703$	−21.2447	−	12.2656i	−0.801259	−	0.462607i
$704$		−	4.43825i		−	0.167273i
$705$		0			0
$706$	−10.6523	−	6.15009i	−0.400903	−	0.231462i
$707$	−39.8338	+	26.6011i	−1.49810	+	1.00044i
$708$		0			0
$709$	−17.9957	+	31.1695i	−0.675844	+	1.17060i	0.300377	+	0.953820i	$0.402887\pi$
$709$	−17.9957	+	31.1695i	−0.675844	+	1.17060i	−0.976221	+	0.216776i	$0.930446\pi$
$710$	−5.76938	+	9.99286i	−0.216521	+	0.375025i
$711$		0			0
$712$	7.22198	−	4.16961i	0.270655	−	0.156263i
$713$	−3.66295	−	6.34442i	−0.137179	−	0.237600i
$714$		0			0
$715$	−11.5819	+	20.0604i	−0.433139	+	0.750218i
$716$		−	7.44796i		−	0.278343i
$717$		0			0
$718$	−23.8295			−0.889310
$719$	2.71108	+	4.69573i	0.101106	+	0.175121i	0.912141	−	0.409877i	$-0.134428\pi$
$719$	2.71108	+	4.69573i	0.101106	+	0.175121i	−0.811034	+	0.584998i	$0.801095\pi$
$720$		0			0
$721$	−14.4542	−	21.6443i	−0.538301	−	0.806077i
$722$	−9.63178	+	5.56091i	−0.358458	+	0.206956i
$723$		0			0
$724$	5.35698	−	3.09285i	0.199091	−	0.114945i
$725$	6.40344	−	3.69703i	0.237818	−	0.137304i
$726$		0			0
$727$	−28.3952	+	16.3940i	−1.05312	+	0.608020i	−0.923522	−	0.383547i	$-0.874703\pi$
$727$	−28.3952	+	16.3940i	−1.05312	+	0.608020i	−0.129600	+	0.991566i	$0.541369\pi$
$728$	−0.899543	−	13.7792i	−0.0333393	−	0.510691i
$729$		0			0
$730$	−7.61374	−	13.1874i	−0.281797	−	0.488087i
$731$	14.2357			0.526526
$732$		0			0
$733$			6.24073i			0.230507i	0.993336	+	0.115253i	$0.0367680\pi$
$733$			6.24073i			0.230507i	−0.993336	+	0.115253i	$0.963232\pi$
$734$	−15.0597	+	26.0842i	−0.555864	+	0.962784i
$735$		0			0
$736$	−1.74245	−	3.01802i	−0.0642277	−	0.111246i
$737$	18.9415	−	10.9359i	0.697718	−	0.402828i
$738$		0			0
$739$	13.1808	−	22.8298i	0.484864	−	0.839809i	−0.514985	−	0.857199i	$-0.672202\pi$
$739$	13.1808	−	22.8298i	0.484864	−	0.839809i	0.999849	+	0.0173901i	$0.00553572\pi$
$740$	4.36995	−	7.56898i	0.160643	−	0.278241i
$741$		0			0
$742$	12.6100	+	6.22266i	0.462929	+	0.228441i
$743$	32.8093	+	18.9425i	1.20366	+	0.694931i	0.961366	−	0.275273i	$-0.0887681\pi$
$743$	32.8093	+	18.9425i	1.20366	+	0.694931i	0.242290	+	0.970204i	$0.422101\pi$
$744$		0			0
$745$			15.3288i			0.561602i
$746$	31.9171	+	18.4273i	1.16857	+	0.674673i
$747$		0			0
$748$		−	30.7997i		−	1.12615i
$749$	−14.1496	+	28.6738i	−0.517015	+	1.04772i
$750$		0			0
$751$	0.439573			0.0160402			0.00802012	−	0.999968i	$-0.497447\pi$
$751$	0.439573			0.0160402			0.00802012	+	0.999968i	$0.497447\pi$
$752$	−5.16742	−	8.95023i	−0.188436	−	0.326381i
$753$		0			0
$754$	−33.4204	−	19.2953i	−1.21710	−	0.702693i
$755$	−5.74675			−0.209146
$756$		0			0
$757$	−5.35536			−0.194644			−0.0973220	−	0.995253i	$-0.531028\pi$
$757$	−5.35536			−0.194644			−0.0973220	+	0.995253i	$0.531028\pi$
$758$	−2.69079	−	1.55353i	−0.0977339	−	0.0564267i
$759$		0			0
$760$	1.40341	+	2.43077i	0.0509069	+	0.0881733i
$761$	−1.19842			−0.0434429			−0.0217214	−	0.999764i	$-0.506915\pi$
$761$	−1.19842			−0.0434429			−0.0217214	+	0.999764i	$0.506915\pi$
$762$		0			0
$763$	0.569875	+	8.72933i	0.0206308	+	0.316023i
$764$			22.9888i			0.831704i
$765$		0			0
$766$	9.69416	+	5.59692i	0.350264	+	0.202225i
$767$		−	5.58302i		−	0.201591i
$768$		0			0
$769$	37.0240	+	21.3758i	1.33512	+	0.770831i	0.986079	−	0.166277i	$-0.0531745\pi$
$769$	37.0240	+	21.3758i	1.33512	+	0.770831i	0.349040	+	0.937108i	$0.386508\pi$
$770$	−0.764954	−	11.7176i	−0.0275670	−	0.422271i
$771$		0			0
$772$	−5.44323	+	9.42795i	−0.195906	+	0.339319i
$773$	11.5098	−	19.9356i	0.413979	−	0.717032i	−0.581342	−	0.813659i	$-0.697472\pi$
$773$	11.5098	−	19.9356i	0.413979	−	0.717032i	0.995321	+	0.0966270i	$0.0308054\pi$
$774$		0			0
$775$	−1.82054	+	1.05109i	−0.0653958	+	0.0377563i
$776$	−6.62595	−	11.4765i	−0.237858	−	0.411982i
$777$		0			0
$778$	11.4996	−	19.9179i	0.412280	−	0.714090i
$779$		−	16.2863i		−	0.583519i
$780$		0			0
$781$	51.2119			1.83251
$782$	−12.0920	−	20.9439i	−0.432408	−	0.748952i
$783$		0			0
$784$	4.25845	+	5.55569i	0.152087	+	0.198417i
$785$	−6.17457	+	3.56489i	−0.220380	+	0.127236i
$786$		0			0
$787$	45.4340	−	26.2313i	1.61955	−	0.935046i	0.632511	−	0.774552i	$-0.282024\pi$
$787$	45.4340	−	26.2313i	1.61955	−	0.935046i	0.987037	−	0.160495i	$-0.0513090\pi$
$788$	6.12656	−	3.53717i	0.218250	−	0.126007i
$789$		0			0
$790$	6.72991	−	3.88551i	0.239439	−	0.138240i
$791$	−8.51831	+	0.556098i	−0.302876	+	0.0197726i
$792$		0			0
$793$	−15.7755	−	27.3240i	−0.560206	−	0.970305i
$794$	−7.81538			−0.277358
$795$		0			0
$796$			18.4715i			0.654706i
$797$	−23.0129	+	39.8595i	−0.815158	+	1.41190i	0.0940562	+	0.995567i	$0.470017\pi$
$797$	−23.0129	+	39.8595i	−0.815158	+	1.41190i	−0.909214	+	0.416328i	$0.863317\pi$
$798$		0			0
$799$	−35.8599	−	62.1112i	−1.26863	−	2.19734i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	5.81741	−	10.0760i	0.205420	−	0.355797i
$803$	−33.7917	+	58.5289i	−1.19248	+	2.06544i
$804$		0			0
$805$	−5.12047	−	7.66764i	−0.180473	−	0.270249i
$806$	9.50165	+	5.48578i	0.334681	+	0.193228i
$807$		0			0
$808$		−	18.1043i		−	0.636906i
$809$	−6.56411	−	3.78979i	−0.230782	−	0.133242i	0.380151	−	0.924924i	$-0.375872\pi$
$809$	−6.56411	−	3.78979i	−0.230782	−	0.133242i	−0.610933	+	0.791683i	$0.709205\pi$
$810$		0			0
$811$			27.5654i			0.967951i	0.875081	+	0.483976i	$0.160808\pi$
$811$			27.5654i			0.967951i	−0.875081	+	0.483976i	$0.839192\pi$
$812$	19.5213	−	1.27440i	0.685063	−	0.0447227i
$813$		0			0
$814$	−38.7899			−1.35958
$815$	1.11012	+	1.92279i	0.0388860	+	0.0673525i
$816$		0			0
$817$	4.98639	+	2.87890i	0.174452	+	0.100720i
$818$	27.9756			0.978145
$819$		0			0
$820$	5.80244			0.202630
$821$	−27.7304	−	16.0101i	−0.967796	−	0.558757i	−0.0692324	−	0.997601i	$-0.522055\pi$
$821$	−27.7304	−	16.0101i	−0.967796	−	0.558757i	−0.898564	+	0.438843i	$0.855388\pi$
$822$		0			0
$823$	16.9369	+	29.3356i	0.590384	+	1.02258i	0.994181	+	0.107727i	$0.0343572\pi$
$823$	16.9369	+	29.3356i	0.590384	+	1.02258i	−0.403796	+	0.914849i	$0.632309\pi$
$824$	9.83724			0.342697
$825$		0			0
$826$	1.57177	+	2.35365i	0.0546890	+	0.0818939i
$827$			49.6428i			1.72625i	0.504992	+	0.863124i	$0.331495\pi$
$827$			49.6428i			1.72625i	−0.504992	+	0.863124i	$0.668505\pi$
$828$		0			0
$829$	23.6571	+	13.6584i	0.821646	+	0.474378i	0.850984	−	0.525192i	$-0.176006\pi$
$829$	23.6571	+	13.6584i	0.821646	+	0.474378i	−0.0293377	+	0.999570i	$0.509340\pi$
$830$		−	5.69440i		−	0.197656i
$831$		0			0
$832$	4.51990	+	2.60957i	0.156699	+	0.0904704i
$833$	29.5520	+	38.5543i	1.02392	+	1.33583i
$834$		0			0
$835$	7.27271	−	12.5967i	0.251683	−	0.435927i
$836$	6.22866	−	10.7884i	0.215423	−	0.373123i
$837$		0			0
$838$	−2.78155	+	1.60593i	−0.0960872	+	0.0554760i
$839$	15.8314	+	27.4209i	0.546562	+	0.946673i	0.998507	+	0.0546273i	$0.0173971\pi$
$839$	15.8314	+	27.4209i	0.546562	+	0.946673i	−0.451945	+	0.892046i	$0.649270\pi$
$840$		0			0
$841$	12.8360	−	22.2327i	0.442622	−	0.766644i
$842$			7.45922i			0.257062i
$843$		0			0
$844$	−7.77150			−0.267506
$845$	−7.11967	−	12.3316i	−0.244924	−	0.424221i
$846$		0			0
$847$	−19.1378	+	12.7803i	−0.657583	+	0.439136i
$848$	−4.60281	+	2.65743i	−0.158061	+	0.0912566i
$849$		0			0
$850$	−6.00989	+	3.46981i	−0.206137	+	0.119013i
$851$	−26.3772	+	15.2289i	−0.904198	+	0.522039i
$852$		0			0
$853$	8.23214	−	4.75283i	0.281863	−	0.162734i	−0.352403	−	0.935848i	$-0.614635\pi$
$853$	8.23214	−	4.75283i	0.281863	−	0.162734i	0.634267	+	0.773114i	$0.281302\pi$
$854$	14.3430	+	7.07782i	0.490807	+	0.242198i
$855$		0			0
$856$	−6.04270	−	10.4663i	−0.206535	−	0.357729i
$857$	3.35621			0.114646			0.0573230	−	0.998356i	$-0.481744\pi$
$857$	3.35621			0.114646			0.0573230	+	0.998356i	$0.481744\pi$
$858$		0			0
$859$			30.7525i			1.04926i	0.851330	+	0.524631i	$0.175797\pi$
$859$			30.7525i			1.04926i	−0.851330	+	0.524631i	$0.824203\pi$
$860$	−1.02568	+	1.77653i	−0.0349755	+	0.0605793i
$861$		0			0
$862$	7.05686	+	12.2228i	0.240358	+	0.416312i
$863$	−46.5984	+	26.9036i	−1.58623	+	0.915809i	−0.592307	+	0.805712i	$0.701783\pi$
$863$	−46.5984	+	26.9036i	−1.58623	+	0.915809i	−0.993921	+	0.110097i	$0.964884\pi$
$864$		0			0
$865$	−1.25357	+	2.17125i	−0.0426227	+	0.0738247i
$866$	−8.96174	+	15.5222i	−0.304532	+	0.527465i
$867$		0			0
$868$	−5.55003	+	0.362321i	−0.188380	+	0.0122980i
$869$	−29.8690	−	17.2449i	−1.01324	−	0.584992i
$870$		0			0
$871$			25.7199i			0.871487i
$872$	−2.86343	−	1.65320i	−0.0969679	−	0.0559844i
$873$		0			0
$874$		−	9.78147i		−	0.330863i
$875$	−2.20024	+	1.46933i	−0.0743818	+	0.0496724i
$876$		0			0
$877$	−50.5842			−1.70811			−0.854053	−	0.520186i	$-0.825863\pi$
$877$	−50.5842			−1.70811			−0.854053	+	0.520186i	$0.825863\pi$
$878$	19.4420	+	33.6745i	0.656135	+	1.13646i
$879$		0			0
$880$	3.84363	+	2.21912i	0.129569	+	0.0748066i
$881$	40.0580			1.34959			0.674793	−	0.738007i	$-0.264233\pi$
$881$	40.0580			1.34959			0.674793	+	0.738007i	$0.264233\pi$
$882$		0			0
$883$	−20.3605			−0.685187			−0.342593	−	0.939484i	$-0.611305\pi$
$883$	−20.3605			−0.685187			−0.342593	+	0.939484i	$0.611305\pi$
$884$	31.3664	+	18.1094i	1.05497	+	0.609085i
$885$		0			0
$886$	−13.6113	−	23.5754i	−0.457280	−	0.792032i
$887$	−25.8585			−0.868245			−0.434122	−	0.900854i	$-0.642941\pi$
$887$	−25.8585			−0.868245			−0.434122	+	0.900854i	$0.642941\pi$
$888$		0			0
$889$	9.03317	−	6.03238i	0.302963	−	0.202320i
$890$			8.33922i			0.279531i
$891$		0			0
$892$	1.25245	+	0.723100i	0.0419350	+	0.0242112i
$893$		−	29.0079i		−	0.970713i
$894$		0			0
$895$	6.45012	+	3.72398i	0.215604	+	0.124479i
$896$	−2.64013	+	0.172355i	−0.0882006	+	0.00575797i
$897$		0			0
$898$	−8.29228	+	14.3626i	−0.276717	+	0.479288i
$899$	−7.77182	+	13.4612i	−0.259205	+	0.448956i
$900$		0			0
$901$	−31.9417	+	18.4416i	−1.06413	+	0.614378i
$902$	−12.8763	−	22.3024i	−0.428735	−	0.742590i
$903$		0			0
$904$	1.61324	−	2.79421i	0.0536554	−	0.0929339i
$905$			6.18571i			0.205620i
$906$		0			0
$907$	37.0791			1.23119			0.615595	−	0.788062i	$-0.288916\pi$
$907$	37.0791			1.23119			0.615595	+	0.788062i	$0.288916\pi$
$908$	4.23228	+	7.33052i	0.140453	+	0.243272i
$909$		0			0
$910$	12.3829	+	6.11057i	0.410489	+	0.202563i
$911$	18.8303	−	10.8717i	0.623874	−	0.360194i	−0.154502	−	0.987993i	$-0.549377\pi$
$911$	18.8303	−	10.8717i	0.623874	−	0.360194i	0.778376	+	0.627799i	$0.216044\pi$
$912$		0			0
$913$	−21.8872	+	12.6366i	−0.724360	+	0.418210i
$914$	−15.1871	+	8.76829i	−0.502345	+	0.290029i
$915$		0			0
$916$	11.9370	−	6.89186i	0.394411	−	0.227713i
$917$	42.7148	−	28.5250i	1.41057	−	0.941980i
$918$		0			0
$919$	9.93377	+	17.2058i	0.327685	+	0.567567i	0.982052	−	0.188610i	$-0.0603983\pi$
$919$	9.93377	+	17.2058i	0.327685	+	0.567567i	−0.654367	+	0.756177i	$0.727065\pi$
$920$	3.48491			0.114894
$921$		0			0
$922$		−	35.7467i		−	1.17725i
$923$	−30.1112	+	52.1541i	−0.991121	+	1.71667i
$924$		0			0
$925$	4.36995	+	7.56898i	0.143683	+	0.248867i
$926$	17.7886	−	10.2703i	0.584570	−	0.337502i
$927$		0			0
$928$	−3.69703	+	6.40344i	−0.121361	+	0.210203i
$929$	9.12389	−	15.8030i	0.299345	−	0.518481i	−0.676641	−	0.736313i	$-0.736565\pi$
$929$	9.12389	−	15.8030i	0.299345	−	0.518481i	0.975986	+	0.217832i	$0.0698985\pi$
$930$		0			0
$931$	2.55442	+	19.4809i	0.0837177	+	0.638461i
$932$	−16.7359	−	9.66250i	−0.548204	−	0.316506i
$933$		0			0
$934$		−	7.09543i		−	0.232170i
$935$	26.6734	+	15.3999i	0.872312	+	0.503630i
$936$		0			0
$937$			33.7791i			1.10351i	0.834005	+	0.551757i	$0.186043\pi$
$937$			33.7791i			1.10351i	−0.834005	+	0.551757i	$0.813957\pi$
$938$	−7.24087	−	10.8428i	−0.236423	−	0.354031i
$939$		0			0
$940$	10.3348			0.337085
$941$	−4.40857	−	7.63587i	−0.143715	−	0.248922i	0.785178	−	0.619271i	$-0.212572\pi$
$941$	−4.40857	−	7.63587i	−0.143715	−	0.248922i	−0.928893	+	0.370348i	$0.879238\pi$
$942$		0			0
$943$	−17.5118	−	10.1105i	−0.570264	−	0.329242i
$944$	−1.06972			−0.0348165
$945$		0			0
$946$	9.10446			0.296012
$947$	28.6235	+	16.5258i	0.930140	+	0.537017i	0.886856	−	0.462046i	$-0.152885\pi$
$947$	28.6235	+	16.5258i	0.930140	+	0.537017i	0.0432843	+	0.999063i	$0.486218\pi$
$948$		0			0
$949$	−39.7371	−	68.8267i	−1.28992	−	2.23421i
$950$	−2.80681			−0.0910649
$951$		0			0
$952$	−18.3215	+	1.19608i	−0.593803	+	0.0387651i
$953$			8.17464i			0.264803i	0.991196	+	0.132401i	$0.0422688\pi$
$953$			8.17464i			0.264803i	−0.991196	+	0.132401i	$0.957731\pi$
$954$		0			0
$955$	−19.9088	−	11.4944i	−0.644235	−	0.371949i
$956$			8.24653i			0.266712i
$957$		0			0
$958$	−14.9914	−	8.65531i	−0.484351	−	0.279640i
$959$	−13.5124	−	20.2342i	−0.436339	−	0.653395i
$960$		0			0
$961$	−13.2904	+	23.0197i	−0.428723	+	0.742570i
$962$	22.8074	−	39.5035i	0.735339	−	1.27364i
$963$		0			0
$964$	20.7072	−	11.9553i	0.666933	−	0.385054i
$965$	−5.44323	−	9.42795i	−0.175224	−	0.303496i
$966$		0			0
$967$	−16.5402	+	28.6485i	−0.531899	+	0.921275i	0.467408	+	0.884042i	$0.345188\pi$
$967$	−16.5402	+	28.6485i	−0.531899	+	0.921275i	−0.999307	+	0.0372336i	$0.988145\pi$
$968$		−	8.69804i		−	0.279566i
$969$		0			0
$970$	13.2519			0.425493
$971$	−15.3895	−	26.6554i	−0.493873	−	0.855412i	0.506102	−	0.862473i	$-0.331086\pi$
$971$	−15.3895	−	26.6554i	−0.493873	−	0.855412i	−0.999975	+	0.00706089i	$0.997752\pi$
$972$		0			0
$973$	−27.1346	+	1.77142i	−0.869894	+	0.0567890i
$974$	−30.9864	+	17.8900i	−0.992870	+	0.573234i
$975$		0			0
$976$	−5.23536	+	3.02264i	−0.167580	+	0.0967522i
$977$	−33.0891	+	19.1040i	−1.05861	+	0.611190i	−0.925048	−	0.379850i	$-0.875976\pi$
$977$	−33.0891	+	19.1040i	−1.05861	+	0.611190i	−0.133565	+	0.991040i	$0.542642\pi$
$978$		0			0
$979$	32.0529	−	18.5058i	1.02442	−	0.591447i
$980$	−6.94059	+	0.910079i	−0.221709	+	0.0290714i
$981$		0			0
$982$	−13.9109	−	24.0944i	−0.443914	−	0.768882i
$983$	26.4893			0.844877			0.422439	−	0.906391i	$-0.361174\pi$
$983$	26.4893			0.844877			0.422439	+	0.906391i	$0.361174\pi$
$984$		0			0
$985$			7.07434i			0.225407i
$986$	−25.6560	+	44.4374i	−0.817052	+	1.41518i
$987$		0			0
$988$	7.32456	+	12.6865i	0.233025	+	0.403612i
$989$	6.19105	−	3.57441i	0.196864	−	0.113659i
$990$		0			0
$991$	−19.0603	+	33.0135i	−0.605471	+	1.04871i	0.386505	+	0.922287i	$0.373682\pi$
$991$	−19.0603	+	33.0135i	−0.605471	+	1.04871i	−0.991977	+	0.126420i	$0.959651\pi$
$992$	1.05109	−	1.82054i	0.0333721	−	0.0578023i
$993$		0			0
$994$	−1.98876	−	30.4639i	−0.0630797	−	0.966255i
$995$	−15.9968	−	9.23577i	−0.507133	−	0.292794i
$996$		0			0
$997$		−	30.3486i		−	0.961149i	−0.876954	−	0.480574i	$-0.840428\pi$
$997$		−	30.3486i		−	0.961149i	0.876954	−	0.480574i	$-0.159572\pi$
$998$	−9.27358	−	5.35410i	−0.293550	−	0.169481i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.c.1151.16		32
3.2	odd	2		630.2.t.c.311.4	✓	32
7.5	odd	6		1890.2.bk.c.341.5		32
9.2	odd	6		1890.2.bk.c.521.5		32
9.7	even	3		630.2.bk.c.101.6	yes	32
21.5	even	6		630.2.bk.c.131.14	yes	32
63.47	even	6	inner	1890.2.t.c.1601.16		32
63.61	odd	6		630.2.t.c.551.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.4	✓	32	3.2	odd	2
630.2.t.c.551.4	yes	32	63.61	odd	6
630.2.bk.c.101.6	yes	32	9.7	even	3
630.2.bk.c.131.14	yes	32	21.5	even	6
1890.2.t.c.1151.16		32	1.1	even	1	trivial
1890.2.t.c.1601.16		32	63.47	even	6	inner
1890.2.bk.c.341.5		32	7.5	odd	6
1890.2.bk.c.521.5		32	9.2	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.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(2.20024 - 1.46933i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(2.20024 - 1.46933i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} +4.43825i q^{11} +(-4.51990 - 2.60957i) q^{13} +(2.64013 - 0.172355i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46981 + 6.00989i) q^{17} +(-2.43077 + 1.40341i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-2.21912 + 3.84363i) q^{22} +3.48491i q^{23} +1.00000 q^{25} +(-2.60957 - 4.51990i) q^{26} +(2.37260 + 1.17080i) q^{28} +(6.40344 - 3.69703i) q^{29} +(-1.82054 + 1.05109i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-6.00989 + 3.46981i) q^{34} +(-2.20024 + 1.46933i) q^{35} +(4.36995 + 7.56898i) q^{37} -2.80681 q^{38} -1.00000i q^{40} +(-2.90122 + 5.02506i) q^{41} +(-1.02568 - 1.77653i) q^{43} +(-3.84363 + 2.21912i) q^{44} +(-1.74245 + 3.01802i) q^{46} +(-5.16742 + 8.95023i) q^{47} +(2.68214 - 6.46576i) q^{49} +(0.866025 + 0.500000i) q^{50} -5.21913i q^{52} +(4.60281 + 2.65743i) q^{53} -4.43825i q^{55} +(1.46933 + 2.20024i) q^{56} +7.39406 q^{58} +(0.534861 + 0.926406i) q^{59} +(5.23536 + 3.02264i) q^{61} -2.10218 q^{62} -1.00000 q^{64} +(4.51990 + 2.60957i) q^{65} +(-2.46400 - 4.26778i) q^{67} -6.93962 q^{68} +(-2.64013 + 0.172355i) q^{70} -11.5388i q^{71} +(13.1874 + 7.61374i) q^{73} +8.73991i q^{74} +(-2.43077 - 1.40341i) q^{76} +(6.52125 + 9.76522i) q^{77} +(-3.88551 + 6.72991i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-5.02506 + 2.90122i) q^{82} +(2.84720 + 4.93150i) q^{83} +(3.46981 - 6.00989i) q^{85} -2.05136i q^{86} -4.43825 q^{88} +(-4.16961 - 7.22198i) q^{89} +(-13.7792 + 0.899543i) q^{91} +(-3.01802 + 1.74245i) q^{92} +(-8.95023 + 5.16742i) q^{94} +(2.43077 - 1.40341i) q^{95} +(-11.4765 + 6.62595i) q^{97} +(5.55569 - 4.25845i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7}+O(q^{10}) \) 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7	\( 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7} - 16 q^{16} - 6 q^{17} - 16 q^{20} + 32 q^{25} - 12 q^{26} + 2 q^{28} - 6 q^{29} + 18 q^{31} + 2 q^{35} + 2 q^{37} + 6 q^{41} - 28 q^{43} + 6 q^{44} - 24 q^{47} + 32 q^{49} + 36 q^{53} + 6 q^{56} + 30 q^{59} + 54 q^{61} - 32 q^{64} + 4 q^{67} - 12 q^{68} - 30 q^{73} + 6 q^{77} + 4 q^{79} + 16 q^{80} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 12 q^{89} - 66 q^{91} + 18 q^{92} - 42 q^{94} + 96 q^{97} + 24 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7 - 16 * q^16 - 6 * q^17 - 16 * q^20 + 32 * q^25 - 12 * q^26 + 2 * q^28 - 6 * q^29 + 18 * q^31 + 2 * q^35 + 2 * q^37 + 6 * q^41 - 28 * q^43 + 6 * q^44 - 24 * q^47 + 32 * q^49 + 36 * q^53 + 6 * q^56 + 30 * q^59 + 54 * q^61 - 32 * q^64 + 4 * q^67 - 12 * q^68 - 30 * q^73 + 6 * q^77 + 4 * q^79 + 16 * q^80 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 12 * q^89 - 66 * q^91 + 18 * q^92 - 42 * q^94 + 96 * q^97 + 24 * q^98

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