LMFDB - Embedded newform 1890.2.t.c.1151.2

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			1151.2
Character	$\chi$	$=$	1890.1151
Dual form			1890.2.t.c.1601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(2.63859 + 0.194573i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(2.63859 + 0.194573i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} -2.09116i q^{11} +(-0.413776 - 0.238893i) q^{13} +(-2.18780 - 1.48780i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.44100 - 2.49589i) q^{17} +(4.03431 - 2.32921i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.04558 + 1.81100i) q^{22} +2.02764i q^{23} +1.00000 q^{25} +(0.238893 + 0.413776i) q^{26} +(1.15079 + 2.38237i) q^{28} +(-2.74938 + 1.58735i) q^{29} +(-4.59333 + 2.65196i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.49589 + 1.44100i) q^{34} +(-2.63859 - 0.194573i) q^{35} +(-1.93169 - 3.34578i) q^{37} -4.65842 q^{38} +1.00000i q^{40} +(4.03898 - 6.99572i) q^{41} +(-2.96902 - 5.14250i) q^{43} +(1.81100 - 1.04558i) q^{44} +(1.01382 - 1.75599i) q^{46} +(-0.0525367 + 0.0909962i) q^{47} +(6.92428 + 1.02680i) q^{49} +(-0.866025 - 0.500000i) q^{50} -0.477787i q^{52} +(4.27164 + 2.46623i) q^{53} +2.09116i q^{55} +(0.194573 - 2.63859i) q^{56} +3.17471 q^{58} +(-1.40971 - 2.44169i) q^{59} +(3.71793 + 2.14655i) q^{61} +5.30392 q^{62} -1.00000 q^{64} +(0.413776 + 0.238893i) q^{65} +(-2.73588 - 4.73867i) q^{67} +2.88201 q^{68} +(2.18780 + 1.48780i) q^{70} +10.8486i q^{71} +(5.64929 + 3.26162i) q^{73} +3.86338i q^{74} +(4.03431 + 2.32921i) q^{76} +(0.406885 - 5.51772i) q^{77} +(7.81773 - 13.5407i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-6.99572 + 4.03898i) q^{82} +(-5.58951 - 9.68132i) q^{83} +(-1.44100 + 2.49589i) q^{85} +5.93804i q^{86} -2.09116 q^{88} +(6.59060 + 11.4153i) q^{89} +(-1.04530 - 0.710851i) q^{91} +(-1.75599 + 1.01382i) q^{92} +(0.0909962 - 0.0525367i) q^{94} +(-4.03431 + 2.32921i) q^{95} +(7.98211 - 4.60847i) q^{97} +(-5.48321 - 4.35137i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	2.63859	+	0.194573i	0.997292	+	0.0735418i
$7$	2.63859	+	0.194573i	0.997292	+	0.0735418i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$		−	2.09116i		−	0.630509i	−0.949007	−	0.315255i	$-0.897910\pi$
$11$		−	2.09116i		−	0.630509i	0.949007	−	0.315255i	$-0.102090\pi$
$12$		0			0
$13$	−0.413776	−	0.238893i	−0.114761	−	0.0662571i	0.441521	−	0.897251i	$-0.354439\pi$
$13$	−0.413776	−	0.238893i	−0.114761	−	0.0662571i	−0.556282	+	0.830994i	$0.687772\pi$
$14$	−2.18780	−	1.48780i	−0.584713	−	0.397631i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.44100	−	2.49589i	0.349495	−	0.605343i	−0.636665	−	0.771141i	$-0.719687\pi$
$17$	1.44100	−	2.49589i	0.349495	−	0.605343i	0.986160	+	0.165798i	$0.0530198\pi$
$18$		0			0
$19$	4.03431	−	2.32921i	0.925535	−	0.534358i	0.0401380	−	0.999194i	$-0.487220\pi$
$19$	4.03431	−	2.32921i	0.925535	−	0.534358i	0.885397	+	0.464837i	$0.153887\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	−1.04558	+	1.81100i	−0.222919	+	0.386107i
$23$			2.02764i			0.422792i	0.977401	+	0.211396i	$0.0678009\pi$
$23$			2.02764i			0.422792i	−0.977401	+	0.211396i	$0.932199\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	0.238893	+	0.413776i	0.0468509	+	0.0811481i
$27$		0			0
$28$	1.15079	+	2.38237i	0.217478	+	0.450226i
$29$	−2.74938	+	1.58735i	−0.510547	+	0.294764i	−0.733058	−	0.680166i	$-0.761908\pi$
$29$	−2.74938	+	1.58735i	−0.510547	+	0.294764i	0.222512	+	0.974930i	$0.428574\pi$
$30$		0			0
$31$	−4.59333	+	2.65196i	−0.824987	+	0.476306i	−0.852133	−	0.523325i	$-0.824691\pi$
$31$	−4.59333	+	2.65196i	−0.824987	+	0.476306i	0.0271462	+	0.999631i	$0.491358\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	−2.49589	+	1.44100i	−0.428042	+	0.247130i
$35$	−2.63859	−	0.194573i	−0.446003	−	0.0328889i
$36$		0			0
$37$	−1.93169	−	3.34578i	−0.317568	−	0.550043i	0.662412	−	0.749140i	$-0.269533\pi$
$37$	−1.93169	−	3.34578i	−0.317568	−	0.550043i	−0.979980	+	0.199096i	$0.936199\pi$
$38$	−4.65842			−0.755696
$39$		0			0
$40$			1.00000i			0.158114i
$41$	4.03898	−	6.99572i	0.630783	−	1.09255i	−0.356609	−	0.934254i	$-0.616067\pi$
$41$	4.03898	−	6.99572i	0.630783	−	1.09255i	0.987392	−	0.158294i	$-0.0505995\pi$
$42$		0			0
$43$	−2.96902	−	5.14250i	−0.452772	−	0.784224i	0.545785	−	0.837925i	$-0.316231\pi$
$43$	−2.96902	−	5.14250i	−0.452772	−	0.784224i	−0.998557	+	0.0537015i	$0.982898\pi$
$44$	1.81100	−	1.04558i	0.273019	−	0.157627i
$45$		0			0
$46$	1.01382	−	1.75599i	0.149479	−	0.258906i
$47$	−0.0525367	+	0.0909962i	−0.00766326	+	0.0132732i	−0.869832	−	0.493349i	$-0.835773\pi$
$47$	−0.0525367	+	0.0909962i	−0.00766326	+	0.0132732i	0.862168	+	0.506622i	$0.169106\pi$
$48$		0			0
$49$	6.92428	+	1.02680i	0.989183	+	0.146685i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$		0			0
$52$		−	0.477787i		−	0.0662571i
$53$	4.27164	+	2.46623i	0.586755	+	0.338763i	0.763813	−	0.645437i	$-0.223325\pi$
$53$	4.27164	+	2.46623i	0.586755	+	0.338763i	−0.177058	+	0.984200i	$0.556658\pi$
$54$		0			0
$55$			2.09116i			0.281972i
$56$	0.194573	−	2.63859i	0.0260010	−	0.352596i
$57$		0			0
$58$	3.17471			0.416860
$59$	−1.40971	−	2.44169i	−0.183529	−	0.317881i	0.759551	−	0.650448i	$-0.225419\pi$
$59$	−1.40971	−	2.44169i	−0.183529	−	0.317881i	−0.943080	+	0.332567i	$0.892085\pi$
$60$		0			0
$61$	3.71793	+	2.14655i	0.476033	+	0.274838i	0.718762	−	0.695256i	$-0.244709\pi$
$61$	3.71793	+	2.14655i	0.476033	+	0.274838i	−0.242729	+	0.970094i	$0.578043\pi$
$62$	5.30392			0.673599
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.413776	+	0.238893i	0.0513226	+	0.0296311i
$66$		0			0
$67$	−2.73588	−	4.73867i	−0.334240	−	0.578921i	0.649098	−	0.760705i	$-0.275146\pi$
$67$	−2.73588	−	4.73867i	−0.334240	−	0.578921i	−0.983339	+	0.181783i	$0.941813\pi$
$68$	2.88201			0.349495
$69$		0			0
$70$	2.18780	+	1.48780i	0.261492	+	0.177826i
$71$			10.8486i			1.28750i	0.765238	+	0.643748i	$0.222621\pi$
$71$			10.8486i			1.28750i	−0.765238	+	0.643748i	$0.777379\pi$
$72$		0			0
$73$	5.64929	+	3.26162i	0.661199	+	0.381744i	0.792734	−	0.609568i	$-0.208657\pi$
$73$	5.64929	+	3.26162i	0.661199	+	0.381744i	−0.131535	+	0.991312i	$0.541990\pi$
$74$			3.86338i			0.449109i
$75$		0			0
$76$	4.03431	+	2.32921i	0.462767	+	0.267179i
$77$	0.406885	−	5.51772i	0.0463688	−	0.628802i
$78$		0			0
$79$	7.81773	−	13.5407i	0.879563	−	1.52345i	0.0277423	−	0.999615i	$-0.491168\pi$
$79$	7.81773	−	13.5407i	0.879563	−	1.52345i	0.851821	−	0.523833i	$-0.175498\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	−6.99572	+	4.03898i	−0.772548	+	0.446031i
$83$	−5.58951	−	9.68132i	−0.613529	−	1.06266i	−0.990641	−	0.136495i	$-0.956416\pi$
$83$	−5.58951	−	9.68132i	−0.613529	−	1.06266i	0.377112	−	0.926168i	$-0.376917\pi$
$84$		0			0
$85$	−1.44100	+	2.49589i	−0.156299	+	0.270718i
$86$			5.93804i			0.640316i
$87$		0			0
$88$	−2.09116			−0.222919
$89$	6.59060	+	11.4153i	0.698602	+	1.21001i	0.968951	+	0.247252i	$0.0795276\pi$
$89$	6.59060	+	11.4153i	0.698602	+	1.21001i	−0.270349	+	0.962762i	$0.587139\pi$
$90$		0			0
$91$	−1.04530	−	0.710851i	−0.109577	−	0.0745174i
$92$	−1.75599	+	1.01382i	−0.183074	+	0.105698i
$93$		0			0
$94$	0.0909962	−	0.0525367i	0.00938554	−	0.00541874i
$95$	−4.03431	+	2.32921i	−0.413912	+	0.238972i
$96$		0			0
$97$	7.98211	−	4.60847i	0.810460	−	0.467920i	−0.0366553	−	0.999328i	$-0.511670\pi$
$97$	7.98211	−	4.60847i	0.810460	−	0.467920i	0.847116	+	0.531408i	$0.178337\pi$
$98$	−5.48321	−	4.35137i	−0.553887	−	0.439555i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−18.8631			−1.87695			−0.938475	−	0.345347i	$-0.887761\pi$
$101$	−18.8631			−1.87695			−0.938475	+	0.345347i	$0.887761\pi$
$102$		0			0
$103$		−	10.1578i		−	1.00087i	−0.865773	−	0.500437i	$-0.833173\pi$
$103$		−	10.1578i		−	1.00087i	0.865773	−	0.500437i	$-0.166827\pi$
$104$	−0.238893	+	0.413776i	−0.0234254	+	0.0405740i
$105$		0			0
$106$	−2.46623	−	4.27164i	−0.239542	−	0.414898i
$107$	15.8802	−	9.16843i	1.53520	−	0.886346i	0.536086	−	0.844163i	$-0.319902\pi$
$107$	15.8802	−	9.16843i	1.53520	−	0.886346i	0.999110	−	0.0421823i	$-0.0134310\pi$
$108$		0			0
$109$	7.08626	−	12.2738i	0.678741	−	1.17561i	−0.296619	−	0.954996i	$-0.595859\pi$
$109$	7.08626	−	12.2738i	0.678741	−	1.17561i	0.975360	−	0.220618i	$-0.0708074\pi$
$110$	1.04558	−	1.81100i	0.0996923	−	0.172672i
$111$		0			0
$112$	−1.48780	+	2.18780i	−0.140584	+	0.206727i
$113$	−6.91284	−	3.99113i	−0.650305	−	0.375454i	0.138268	−	0.990395i	$-0.455847\pi$
$113$	−6.91284	−	3.99113i	−0.650305	−	0.375454i	−0.788573	+	0.614941i	$0.789180\pi$
$114$		0			0
$115$		−	2.02764i		−	0.189078i
$116$	−2.74938	−	1.58735i	−0.255273	−	0.147382i
$117$		0			0
$118$			2.81942i			0.259549i
$119$	4.28785	−	6.30525i	0.393067	−	0.578001i
$120$		0			0
$121$	6.62704			0.602458
$122$	−2.14655	−	3.71793i	−0.194340	−	0.336606i
$123$		0			0
$124$	−4.59333	−	2.65196i	−0.412493	−	0.238153i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	0.449694			0.0399039			0.0199520	−	0.999801i	$-0.493649\pi$
$127$	0.449694			0.0399039			0.0199520	+	0.999801i	$0.493649\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−0.238893	−	0.413776i	−0.0209523	−	0.0362905i
$131$	10.4428			0.912392			0.456196	−	0.889879i	$-0.349212\pi$
$131$	10.4428			0.912392			0.456196	+	0.889879i	$0.349212\pi$
$132$		0			0
$133$	11.0981	−	5.36086i	0.962326	−	0.464845i
$134$			5.47175i			0.472687i
$135$		0			0
$136$	−2.49589	−	1.44100i	−0.214021	−	0.123565i
$137$		−	17.4349i		−	1.48956i	−0.667310	−	0.744780i	$-0.732554\pi$
$137$		−	17.4349i		−	1.48956i	0.667310	−	0.744780i	$-0.267446\pi$
$138$		0			0
$139$	11.1168	+	6.41827i	0.942912	+	0.544390i	0.890872	−	0.454255i	$-0.150094\pi$
$139$	11.1168	+	6.41827i	0.942912	+	0.544390i	0.0520399	+	0.998645i	$0.483428\pi$
$140$	−1.15079	−	2.38237i	−0.0972593	−	0.201347i
$141$		0			0
$142$	5.42432	−	9.39519i	0.455198	−	0.788427i
$143$	−0.499565	+	0.865272i	−0.0417757	+	0.0723577i
$144$		0			0
$145$	2.74938	−	1.58735i	0.228323	−	0.131823i
$146$	−3.26162	−	5.64929i	−0.269933	−	0.467538i
$147$		0			0
$148$	1.93169	−	3.34578i	0.158784	−	0.275022i
$149$			1.19092i			0.0975637i	0.998809	+	0.0487818i	$0.0155339\pi$
$149$			1.19092i			0.0975637i	−0.998809	+	0.0487818i	$0.984466\pi$
$150$		0			0
$151$	1.58349			0.128863			0.0644314	−	0.997922i	$-0.479477\pi$
$151$	1.58349			0.128863			0.0644314	+	0.997922i	$0.479477\pi$
$152$	−2.32921	−	4.03431i	−0.188924	−	0.327226i
$153$		0			0
$154$	−3.11123	+	4.57504i	−0.250710	+	0.368667i
$155$	4.59333	−	2.65196i	0.368945	−	0.213011i
$156$		0			0
$157$	−14.5680	+	8.41085i	−1.16266	+	0.671259i	−0.951939	−	0.306288i	$-0.900913\pi$
$157$	−14.5680	+	8.41085i	−1.16266	+	0.671259i	−0.210716	+	0.977547i	$0.567580\pi$
$158$	−13.5407	+	7.81773i	−1.07724	+	0.621945i
$159$		0			0
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	−0.394524	+	5.35010i	−0.0310929	+	0.421647i
$162$		0			0
$163$	−5.01637	−	8.68860i	−0.392912	−	0.680544i	0.599920	−	0.800060i	$-0.295199\pi$
$163$	−5.01637	−	8.68860i	−0.392912	−	0.680544i	−0.992832	+	0.119516i	$0.961866\pi$
$164$	8.07796			0.630783
$165$		0			0
$166$			11.1790i			0.867661i
$167$	−7.17037	+	12.4194i	−0.554860	+	0.961045i	0.443055	+	0.896495i	$0.353895\pi$
$167$	−7.17037	+	12.4194i	−0.554860	+	0.961045i	−0.997914	+	0.0645506i	$0.979439\pi$
$168$		0			0
$169$	−6.38586	−	11.0606i	−0.491220	−	0.850818i
$170$	2.49589	−	1.44100i	0.191426	−	0.110520i
$171$		0			0
$172$	2.96902	−	5.14250i	0.226386	−	0.392112i
$173$	8.06316	−	13.9658i	0.613031	−	1.06180i	−0.377696	−	0.925930i	$-0.623284\pi$
$173$	8.06316	−	13.9658i	0.613031	−	1.06180i	0.990727	−	0.135870i	$-0.0433831\pi$
$174$		0			0
$175$	2.63859	+	0.194573i	0.199458	+	0.0147084i
$176$	1.81100	+	1.04558i	0.136509	+	0.0788137i
$177$		0			0
$178$		−	13.1812i		−	0.987973i
$179$	−0.0837491	−	0.0483526i	−0.00625970	−	0.00361404i	0.496867	−	0.867827i	$-0.334484\pi$
$179$	−0.0837491	−	0.0483526i	−0.00625970	−	0.00361404i	−0.503127	+	0.864213i	$0.667817\pi$
$180$		0			0
$181$			20.0938i			1.49356i	0.665072	+	0.746779i	$0.268401\pi$
$181$			20.0938i			1.49356i	−0.665072	+	0.746779i	$0.731599\pi$
$182$	0.549832	+	1.13827i	0.0407562	+	0.0843738i
$183$		0			0
$184$	2.02764			0.149479
$185$	1.93169	+	3.34578i	0.142021	+	0.245987i
$186$		0			0
$187$	−5.21932	−	3.01338i	−0.381674	−	0.220360i
$188$	−0.105073			−0.00766326
$189$		0			0
$190$	4.65842			0.337957
$191$	3.05974	+	1.76654i	0.221395	+	0.127822i	0.606596	−	0.795010i	$-0.292535\pi$
$191$	3.05974	+	1.76654i	0.221395	+	0.127822i	−0.385201	+	0.922833i	$0.625868\pi$
$192$		0			0
$193$	−12.6572	−	21.9229i	−0.911084	−	1.57804i	−0.812535	−	0.582912i	$-0.801913\pi$
$193$	−12.6572	−	21.9229i	−0.911084	−	1.57804i	−0.0985491	−	0.995132i	$-0.531420\pi$
$194$	−9.21695			−0.661738
$195$		0			0
$196$	2.57291	+	6.51000i	0.183779	+	0.465000i
$197$		−	9.01088i		−	0.641999i	−0.947079	−	0.320999i	$-0.895981\pi$
$197$		−	9.01088i		−	0.641999i	0.947079	−	0.320999i	$-0.104019\pi$
$198$		0			0
$199$	−12.3893	−	7.15296i	−0.878254	−	0.507060i	−0.00817145	−	0.999967i	$-0.502601\pi$
$199$	−12.3893	−	7.15296i	−0.878254	−	0.507060i	−0.870082	+	0.492907i	$0.835934\pi$
$200$		−	1.00000i		−	0.0707107i
$201$		0			0
$202$	16.3359	+	9.43156i	1.14939	+	0.663602i
$203$	−7.56333	+	3.65342i	−0.530842	+	0.256420i
$204$		0			0
$205$	−4.03898	+	6.99572i	−0.282095	+	0.488602i
$206$	−5.07888	+	8.79688i	−0.353863	+	0.612908i
$207$		0			0
$208$	0.413776	−	0.238893i	0.0286902	−	0.0165643i
$209$	−4.87076	−	8.43640i	−0.336917	−	0.583558i
$210$		0			0
$211$	−0.442791	+	0.766937i	−0.0304830	+	0.0527981i	−0.880864	−	0.473369i	$-0.843038\pi$
$211$	−0.442791	+	0.766937i	−0.0304830	+	0.0527981i	0.850381	+	0.526167i	$0.176371\pi$
$212$			4.93246i			0.338763i
$213$		0			0
$214$	−18.3369			−1.25348
$215$	2.96902	+	5.14250i	0.202486	+	0.350715i
$216$		0			0
$217$	−12.6359	+	6.10369i	−0.857781	+	0.414346i
$218$	−12.2738	+	7.08626i	−0.831284	+	0.479942i
$219$		0			0
$220$	−1.81100	+	1.04558i	−0.122098	+	0.0704931i
$221$	−1.19251	+	0.688493i	−0.0802166	+	0.0463131i
$222$		0			0
$223$	0.0602532	−	0.0347872i	0.00403485	−	0.00232952i	−0.497981	−	0.867188i	$-0.665925\pi$
$223$	0.0602532	−	0.0347872i	0.00403485	−	0.00232952i	0.502016	+	0.864858i	$0.332592\pi$
$224$	2.38237	−	1.15079i	0.159179	−	0.0768903i
$225$		0			0
$226$	3.99113	+	6.91284i	0.265486	+	0.459835i
$227$	18.3801			1.21993			0.609964	−	0.792429i	$-0.291184\pi$
$227$	18.3801			1.21993			0.609964	+	0.792429i	$0.291184\pi$
$228$		0			0
$229$		−	16.0697i		−	1.06192i	−0.847398	−	0.530958i	$-0.821832\pi$
$229$		−	16.0697i		−	1.06192i	0.847398	−	0.530958i	$-0.178168\pi$
$230$	−1.01382	+	1.75599i	−0.0668492	+	0.115786i
$231$		0			0
$232$	1.58735	+	2.74938i	0.104215	+	0.180506i
$233$	22.4677	−	12.9717i	1.47191	−	0.849808i	0.472408	−	0.881380i	$-0.343385\pi$
$233$	22.4677	−	12.9717i	1.47191	−	0.849808i	0.999501	+	0.0315722i	$0.0100514\pi$
$234$		0			0
$235$	0.0525367	−	0.0909962i	0.00342711	−	0.00593593i
$236$	1.40971	−	2.44169i	0.0917643	−	0.158941i
$237$		0			0
$238$	−6.86601	+	3.31658i	−0.445058	+	0.214982i
$239$	8.46444	+	4.88695i	0.547519	+	0.316110i	0.748121	−	0.663563i	$-0.230956\pi$
$239$	8.46444	+	4.88695i	0.547519	+	0.316110i	−0.200602	+	0.979673i	$0.564290\pi$
$240$		0			0
$241$			25.6104i			1.64971i	0.565345	+	0.824854i	$0.308743\pi$
$241$			25.6104i			1.64971i	−0.565345	+	0.824854i	$0.691257\pi$
$242$	−5.73918	−	3.31352i	−0.368929	−	0.213001i
$243$		0			0
$244$			4.29310i			0.274838i
$245$	−6.92428	−	1.02680i	−0.442376	−	0.0655997i
$246$		0			0
$247$	−2.22573			−0.141620
$248$	2.65196	+	4.59333i	0.168400	+	0.291677i
$249$		0			0
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	8.02626			0.506613			0.253307	−	0.967386i	$-0.418482\pi$
$251$	8.02626			0.506613			0.253307	+	0.967386i	$0.418482\pi$
$252$		0			0
$253$	4.24012			0.266574
$254$	−0.389447	−	0.224847i	−0.0244361	−	0.0141082i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.25239			0.0781216			0.0390608	−	0.999237i	$-0.487563\pi$
$257$	1.25239			0.0781216			0.0390608	+	0.999237i	$0.487563\pi$
$258$		0			0
$259$	−4.44593	−	9.20400i	−0.276257	−	0.571908i
$260$			0.477787i			0.0296311i
$261$		0			0
$262$	−9.04374	−	5.22140i	−0.558724	−	0.322579i
$263$			7.23219i			0.445956i	0.974824	+	0.222978i	$0.0715778\pi$
$263$			7.23219i			0.445956i	−0.974824	+	0.222978i	$0.928422\pi$
$264$		0			0
$265$	−4.27164	−	2.46623i	−0.262405	−	0.151499i
$266$	−12.2917	−	0.906405i	−0.753649	−	0.0555753i
$267$		0			0
$268$	2.73588	−	4.73867i	0.167120	−	0.289461i
$269$	−5.65912	+	9.80188i	−0.345043	+	0.597631i	−0.985362	−	0.170478i	$-0.945469\pi$
$269$	−5.65912	+	9.80188i	−0.345043	+	0.597631i	0.640319	+	0.768109i	$0.278802\pi$
$270$		0			0
$271$	3.52208	−	2.03347i	0.213951	−	0.123525i	−0.389195	−	0.921155i	$-0.627247\pi$
$271$	3.52208	−	2.03347i	0.213951	−	0.123525i	0.603146	+	0.797631i	$0.293914\pi$
$272$	1.44100	+	2.49589i	0.0873737	+	0.151336i
$273$		0			0
$274$	−8.71743	+	15.0990i	−0.526639	+	0.912165i
$275$		−	2.09116i		−	0.126102i
$276$		0			0
$277$	−3.69051			−0.221741			−0.110871	−	0.993835i	$-0.535364\pi$
$277$	−3.69051			−0.221741			−0.110871	+	0.993835i	$0.535364\pi$
$278$	−6.41827	−	11.1168i	−0.384942	−	0.666739i
$279$		0			0
$280$	−0.194573	+	2.63859i	−0.0116280	+	0.157686i
$281$	−21.3133	+	12.3052i	−1.27144	+	0.734068i	−0.975260	−	0.221063i	$-0.929047\pi$
$281$	−21.3133	+	12.3052i	−1.27144	+	0.734068i	−0.296184	+	0.955131i	$0.595714\pi$
$282$		0			0
$283$	−1.56082	+	0.901139i	−0.0927810	+	0.0535671i	−0.545673	−	0.837998i	$-0.683726\pi$
$283$	−1.56082	+	0.901139i	−0.0927810	+	0.0535671i	0.452892	+	0.891566i	$0.350392\pi$
$284$	−9.39519	+	5.42432i	−0.557502	+	0.321874i
$285$		0			0
$286$	0.865272	−	0.499565i	0.0511646	−	0.0295399i
$287$	12.0184	−	17.6729i	0.709423	−	1.04320i
$288$		0			0
$289$	4.34701	+	7.52924i	0.255707	+	0.442897i
$290$	−3.17471			−0.186425
$291$		0			0
$292$			6.52324i			0.381744i
$293$	11.8910	−	20.5959i	0.694682	−	1.20322i	−0.275606	−	0.961271i	$-0.588879\pi$
$293$	11.8910	−	20.5959i	0.694682	−	1.20322i	0.970288	−	0.241953i	$-0.0777881\pi$
$294$		0			0
$295$	1.40971	+	2.44169i	0.0820765	+	0.142161i
$296$	−3.34578	+	1.93169i	−0.194470	+	0.112277i
$297$		0			0
$298$	0.595458	−	1.03136i	0.0344940	−	0.0597453i
$299$	0.484389	−	0.838987i	0.0280130	−	0.0485199i
$300$		0			0
$301$	−6.83343	−	14.1466i	−0.393872	−	0.815398i
$302$	−1.37135	−	0.791747i	−0.0789121	−	0.0455599i
$303$		0			0
$304$			4.65842i			0.267179i
$305$	−3.71793	−	2.14655i	−0.212888	−	0.122911i
$306$		0			0
$307$		−	5.99873i		−	0.342366i	−0.985239	−	0.171183i	$-0.945241\pi$
$307$		−	5.99873i		−	0.342366i	0.985239	−	0.171183i	$-0.0547589\pi$
$308$	4.98192	−	2.40649i	0.283871	−	0.137122i
$309$		0			0
$310$	−5.30392			−0.301243
$311$	11.8641	+	20.5493i	0.672753	+	1.16524i	0.977120	+	0.212688i	$0.0682217\pi$
$311$	11.8641	+	20.5493i	0.672753	+	1.16524i	−0.304367	+	0.952555i	$0.598445\pi$
$312$		0			0
$313$	2.56825	+	1.48278i	0.145166	+	0.0838116i	0.570824	−	0.821073i	$-0.306624\pi$
$313$	2.56825	+	1.48278i	0.145166	+	0.0838116i	−0.425658	+	0.904884i	$0.639957\pi$
$314$	16.8217			0.949304
$315$		0			0
$316$	15.6355			0.879563
$317$	11.2152	+	6.47508i	0.629906	+	0.363677i	0.780716	−	0.624886i	$-0.214855\pi$
$317$	11.2152	+	6.47508i	0.629906	+	0.363677i	−0.150809	+	0.988563i	$0.548188\pi$
$318$		0			0
$319$	3.31942	+	5.74940i	0.185852	+	0.321904i
$320$	1.00000			0.0559017
$321$		0			0
$322$	3.01672	−	4.43606i	0.168115	−	0.247212i
$323$		−	13.4256i		−	0.747021i
$324$		0			0
$325$	−0.413776	−	0.238893i	−0.0229521	−	0.0132514i
$326$			10.0327i			0.555662i
$327$		0			0
$328$	−6.99572	−	4.03898i	−0.386274	−	0.223015i
$329$	−0.156328	+	0.229879i	−0.00861864	+	0.0126736i
$330$		0			0
$331$	−17.0020	+	29.4483i	−0.934514	+	1.61863i	−0.159016	+	0.987276i	$0.550832\pi$
$331$	−17.0020	+	29.4483i	−0.934514	+	1.61863i	−0.775498	+	0.631350i	$0.782501\pi$
$332$	5.58951	−	9.68132i	0.306764	−	0.531332i
$333$		0			0
$334$	12.4194	−	7.17037i	0.679562	−	0.392345i
$335$	2.73588	+	4.73867i	0.149477	+	0.258901i
$336$		0			0
$337$	11.3157	−	19.5993i	0.616403	−	1.06764i	−0.373734	−	0.927536i	$-0.621923\pi$
$337$	11.3157	−	19.5993i	0.616403	−	1.06764i	0.990137	−	0.140105i	$-0.0447440\pi$
$338$			12.7717i			0.694690i
$339$		0			0
$340$	−2.88201			−0.156299
$341$	5.54568	+	9.60541i	0.300316	+	0.520162i
$342$		0			0
$343$	18.0705	+	4.05658i	0.975717	+	0.219035i
$344$	−5.14250	+	2.96902i	−0.277265	+	0.160079i
$345$		0			0
$346$	−13.9658	+	8.06316i	−0.750806	+	0.433478i
$347$	−11.0660	+	6.38896i	−0.594054	+	0.342977i	−0.766699	−	0.642007i	$-0.778102\pi$
$347$	−11.0660	+	6.38896i	−0.594054	+	0.342977i	0.172645	+	0.984984i	$0.444769\pi$
$348$		0			0
$349$	−3.95316	+	2.28236i	−0.211608	+	0.122172i	−0.602058	−	0.798452i	$-0.705653\pi$
$349$	−3.95316	+	2.28236i	−0.211608	+	0.122172i	0.390451	+	0.920624i	$0.372319\pi$
$350$	−2.18780	−	1.48780i	−0.116943	−	0.0795262i
$351$		0			0
$352$	−1.04558	−	1.81100i	−0.0557297	−	0.0965266i
$353$	−15.9021			−0.846384			−0.423192	−	0.906040i	$-0.639090\pi$
$353$	−15.9021			−0.846384			−0.423192	+	0.906040i	$0.639090\pi$
$354$		0			0
$355$		−	10.8486i		−	0.575786i
$356$	−6.59060	+	11.4153i	−0.349301	+	0.605007i
$357$		0			0
$358$	0.0483526	+	0.0837491i	0.00255551	+	0.00442628i
$359$	17.0237	−	9.82867i	0.898479	−	0.518737i	0.0217726	−	0.999763i	$-0.493069\pi$
$359$	17.0237	−	9.82867i	0.898479	−	0.518737i	0.876706	+	0.481026i	$0.159736\pi$
$360$		0			0
$361$	1.35045	−	2.33904i	0.0710761	−	0.123107i
$362$	10.0469	−	17.4017i	0.528052	−	0.914614i
$363$		0			0
$364$	0.0929646	−	1.26068i	0.00487267	−	0.0660777i
$365$	−5.64929	−	3.26162i	−0.295697	−	0.170721i
$366$		0			0
$367$			21.9998i			1.14838i	0.818721	+	0.574191i	$0.194683\pi$
$367$			21.9998i			1.14838i	−0.818721	+	0.574191i	$0.805317\pi$
$368$	−1.75599	−	1.01382i	−0.0915371	−	0.0528490i
$369$		0			0
$370$		−	3.86338i		−	0.200847i
$371$	10.7912	+	7.33852i	0.560253	+	0.380997i
$372$		0			0
$373$	−23.3319			−1.20808			−0.604041	−	0.796954i	$-0.706444\pi$
$373$	−23.3319			−1.20808			−0.604041	+	0.796954i	$0.706444\pi$
$374$	3.01338	+	5.21932i	0.155818	+	0.269885i
$375$		0			0
$376$	0.0909962	+	0.0525367i	0.00469277	+	0.00270937i
$377$	1.51683			0.0781210
$378$		0			0
$379$	−20.3159			−1.04356			−0.521780	−	0.853080i	$-0.674732\pi$
$379$	−20.3159			−1.04356			−0.521780	+	0.853080i	$0.674732\pi$
$380$	−4.03431	−	2.32921i	−0.206956	−	0.119486i
$381$		0			0
$382$	−1.76654	−	3.05974i	−0.0903841	−	0.156550i
$383$	3.82312			0.195352			0.0976762	−	0.995218i	$-0.468859\pi$
$383$	3.82312			0.195352			0.0976762	+	0.995218i	$0.468859\pi$
$384$		0			0
$385$	−0.406885	+	5.51772i	−0.0207368	+	0.281209i
$386$			25.3144i			1.28847i
$387$		0			0
$388$	7.98211	+	4.60847i	0.405230	+	0.233960i
$389$		−	19.3426i		−	0.980711i	−0.871522	−	0.490356i	$-0.836867\pi$
$389$		−	19.3426i		−	0.980711i	0.871522	−	0.490356i	$-0.163133\pi$
$390$		0			0
$391$	5.06077	+	2.92184i	0.255934	+	0.147764i
$392$	1.02680	−	6.92428i	0.0518611	−	0.349729i
$393$		0			0
$394$	−4.50544	+	7.80365i	−0.226981	+	0.393142i
$395$	−7.81773	+	13.5407i	−0.393353	+	0.681307i
$396$		0			0
$397$	−26.2370	+	15.1479i	−1.31680	+	0.760253i	−0.983212	−	0.182467i	$-0.941592\pi$
$397$	−26.2370	+	15.1479i	−1.31680	+	0.760253i	−0.333585	+	0.942720i	$0.608258\pi$
$398$	7.15296	+	12.3893i	0.358546	+	0.621019i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$			33.0679i			1.65133i	0.564159	+	0.825666i	$0.309200\pi$
$401$			33.0679i			1.65133i	−0.564159	+	0.825666i	$0.690800\pi$
$402$		0			0
$403$	2.53415			0.126235
$404$	−9.43156	−	16.3359i	−0.469238	−	0.812743i
$405$		0			0
$406$	8.37674	+	0.617714i	0.415731	+	0.0306566i
$407$	−6.99658	+	4.03948i	−0.346808	+	0.200229i
$408$		0			0
$409$	−14.7421	+	8.51133i	−0.728948	+	0.420858i	−0.818037	−	0.575165i	$-0.804938\pi$
$409$	−14.7421	+	8.51133i	−0.728948	+	0.420858i	0.0890894	+	0.996024i	$0.471604\pi$
$410$	6.99572	−	4.03898i	0.345494	−	0.199471i
$411$		0			0
$412$	8.79688	−	5.07888i	0.433391	−	0.250219i
$413$	−3.24456	−	6.71690i	−0.159654	−	0.330517i
$414$		0			0
$415$	5.58951	+	9.68132i	0.274378	+	0.475237i
$416$	−0.477787			−0.0234254
$417$		0			0
$418$			9.74152i			0.476473i
$419$	3.89228	−	6.74162i	0.190150	−	0.329350i	−0.755150	−	0.655552i	$-0.772436\pi$
$419$	3.89228	−	6.74162i	0.190150	−	0.329350i	0.945300	+	0.326203i	$0.105769\pi$
$420$		0			0
$421$	15.4668	+	26.7894i	0.753808	+	1.30563i	0.945965	+	0.324269i	$0.105118\pi$
$421$	15.4668	+	26.7894i	0.753808	+	1.30563i	−0.192157	+	0.981364i	$0.561548\pi$
$422$	0.766937	−	0.442791i	0.0373339	−	0.0215547i
$423$		0			0
$424$	2.46623	−	4.27164i	0.119771	−	0.207449i
$425$	1.44100	−	2.49589i	0.0698990	−	0.121069i
$426$		0			0
$427$	9.39243	+	6.38727i	0.454532	+	0.309102i
$428$	15.8802	+	9.16843i	0.767598	+	0.443173i
$429$		0			0
$430$		−	5.93804i		−	0.286358i
$431$	−17.0026	−	9.81647i	−0.818988	−	0.472843i	0.0310795	−	0.999517i	$-0.490105\pi$
$431$	−17.0026	−	9.81647i	−0.818988	−	0.472843i	−0.850067	+	0.526674i	$0.823439\pi$
$432$		0			0
$433$			35.9562i			1.72794i	0.503540	+	0.863972i	$0.332031\pi$
$433$			35.9562i			1.72794i	−0.503540	+	0.863972i	$0.667969\pi$
$434$	13.9949	+	1.03200i	0.671775	+	0.0495377i
$435$		0			0
$436$	14.1725			0.678741
$437$	4.72280	+	8.18012i	0.225922	+	0.391308i
$438$		0			0
$439$	21.0814	+	12.1713i	1.00616	+	0.580906i	0.910065	−	0.414467i	$-0.136032\pi$
$439$	21.0814	+	12.1713i	1.00616	+	0.580906i	0.0960937	+	0.995372i	$0.469365\pi$
$440$	2.09116			0.0996923
$441$		0			0
$442$	1.37699			0.0654966
$443$	5.14619	+	2.97116i	0.244503	+	0.141164i	0.617245	−	0.786771i	$-0.288249\pi$
$443$	5.14619	+	2.97116i	0.244503	+	0.141164i	−0.372742	+	0.927935i	$0.621582\pi$
$444$		0			0
$445$	−6.59060	−	11.4153i	−0.312424	−	0.541135i
$446$	−0.0695744			−0.00329444
$447$		0			0
$448$	−2.63859	−	0.194573i	−0.124662	−	0.00919273i
$449$		−	3.59042i		−	0.169442i	−0.996405	−	0.0847211i	$-0.973000\pi$
$449$		−	3.59042i		−	0.169442i	0.996405	−	0.0847211i	$-0.0269999\pi$
$450$		0			0
$451$	−14.6292	−	8.44617i	−0.688862	−	0.397715i
$452$		−	7.98226i		−	0.375454i
$453$		0			0
$454$	−15.9176	−	9.19003i	−0.747050	−	0.431310i
$455$	1.04530	+	0.710851i	0.0490045	+	0.0333252i
$456$		0			0
$457$	−6.72945	+	11.6558i	−0.314791	+	0.545233i	−0.979393	−	0.201964i	$-0.935268\pi$
$457$	−6.72945	+	11.6558i	−0.314791	+	0.545233i	0.664602	+	0.747197i	$0.268601\pi$
$458$	−8.03486	+	13.9168i	−0.375444	+	0.650288i
$459$		0			0
$460$	1.75599	−	1.01382i	0.0818733	−	0.0472695i
$461$	−13.5633	−	23.4924i	−0.631708	−	1.09415i	−0.987202	−	0.159472i	$-0.949021\pi$
$461$	−13.5633	−	23.4924i	−0.631708	−	1.09415i	0.355495	−	0.934678i	$-0.384312\pi$
$462$		0			0
$463$	−15.9746	+	27.6688i	−0.742403	+	1.28588i	0.208995	+	0.977917i	$0.432981\pi$
$463$	−15.9746	+	27.6688i	−0.742403	+	1.28588i	−0.951398	+	0.307963i	$0.900353\pi$
$464$		−	3.17471i		−	0.147382i
$465$		0			0
$466$	−25.9435			−1.20181
$467$	18.4026	+	31.8743i	0.851572	+	1.47497i	0.879789	+	0.475364i	$0.157684\pi$
$467$	18.4026	+	31.8743i	0.851572	+	1.47497i	−0.0282177	+	0.999602i	$0.508983\pi$
$468$		0			0
$469$	−6.29682	−	13.0357i	−0.290760	−	0.601934i
$470$	−0.0909962	+	0.0525367i	−0.00419734	+	0.00242334i
$471$		0			0
$472$	−2.44169	+	1.40971i	−0.112388	+	0.0648872i
$473$	−10.7538	+	6.20871i	−0.494460	+	0.285477i
$474$		0			0
$475$	4.03431	−	2.32921i	0.185107	−	0.106872i
$476$	7.60443	+	0.560762i	0.348549	+	0.0257025i
$477$		0			0
$478$	−4.88695	−	8.46444i	−0.223524	−	0.387155i
$479$	17.6491			0.806406			0.403203	−	0.915110i	$-0.367897\pi$
$479$	17.6491			0.806406			0.403203	+	0.915110i	$0.367897\pi$
$480$		0			0
$481$			1.84587i			0.0841645i
$482$	12.8052	−	22.1792i	0.583260	−	1.01024i
$483$		0			0
$484$	3.31352	+	5.73918i	0.150614	+	0.260872i
$485$	−7.98211	+	4.60847i	−0.362449	+	0.209260i
$486$		0			0
$487$	5.44521	−	9.43137i	0.246746	−	0.427376i	−0.715875	−	0.698228i	$-0.753972\pi$
$487$	5.44521	−	9.43137i	0.246746	−	0.427376i	0.962621	+	0.270852i	$0.0873054\pi$
$488$	2.14655	−	3.71793i	0.0971698	−	0.168303i
$489$		0			0
$490$	5.48321	+	4.35137i	0.247706	+	0.196575i
$491$	21.5186	+	12.4238i	0.971123	+	0.560678i	0.899578	−	0.436760i	$-0.143874\pi$
$491$	21.5186	+	12.4238i	0.971123	+	0.560678i	0.0715443	+	0.997437i	$0.477207\pi$
$492$		0			0
$493$			9.14954i			0.412075i
$494$	1.92754	+	1.11287i	0.0867242	+	0.0500702i
$495$		0			0
$496$		−	5.30392i		−	0.238153i
$497$	−2.11086	+	28.6251i	−0.0946848	+	1.28401i
$498$		0			0
$499$	36.8849			1.65119			0.825597	−	0.564261i	$-0.190839\pi$
$499$	36.8849			1.65119			0.825597	+	0.564261i	$0.190839\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	−6.95095	−	4.01313i	−0.310236	−	0.179115i
$503$	−4.02007			−0.179246			−0.0896231	−	0.995976i	$-0.528566\pi$
$503$	−4.02007			−0.179246			−0.0896231	+	0.995976i	$0.528566\pi$
$504$		0			0
$505$	18.8631			0.839398
$506$	−3.67205	−	2.12006i	−0.163243	−	0.0942482i
$507$		0			0
$508$	0.224847	+	0.389447i	0.00997598	+	0.0172789i
$509$	−24.2483			−1.07479			−0.537394	−	0.843331i	$-0.680591\pi$
$509$	−24.2483			−1.07479			−0.537394	+	0.843331i	$0.680591\pi$
$510$		0			0
$511$	14.2715	+	9.70527i	0.631335	+	0.429336i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−1.08460	−	0.626193i	−0.0478395	−	0.0276202i
$515$			10.1578i			0.447605i
$516$		0			0
$517$	0.190288	+	0.109863i	0.00836885	+	0.00483176i
$518$	−0.751711	+	10.1939i	−0.0330283	+	0.447892i
$519$		0			0
$520$	0.238893	−	0.413776i	0.0104762	−	0.0181453i
$521$	−20.9866	+	36.3499i	−0.919440	+	1.59252i	−0.119173	+	0.992874i	$0.538024\pi$
$521$	−20.9866	+	36.3499i	−0.919440	+	1.59252i	−0.800267	+	0.599643i	$0.795309\pi$
$522$		0			0
$523$	−2.05664	+	1.18740i	−0.0899304	+	0.0519213i	−0.544291	−	0.838897i	$-0.683201\pi$
$523$	−2.05664	+	1.18740i	−0.0899304	+	0.0519213i	0.454360	+	0.890818i	$0.349868\pi$
$524$	5.22140	+	9.04374i	0.228098	+	0.395077i
$525$		0			0
$526$	3.61609	−	6.26326i	0.157669	−	0.273091i
$527$			15.2860i			0.665867i
$528$		0			0
$529$	18.8887			0.821247
$530$	2.46623	+	4.27164i	0.107126	+	0.185548i
$531$		0			0
$532$	10.1917	+	6.93079i	0.441865	+	0.300488i
$533$	−3.34246	+	1.92977i	−0.144778	+	0.0835877i
$534$		0			0
$535$	−15.8802	+	9.16843i	−0.686560	+	0.396386i
$536$	−4.73867	+	2.73588i	−0.204680	+	0.118172i
$537$		0			0
$538$	9.80188	−	5.65912i	0.422589	−	0.243982i
$539$	2.14720	−	14.4798i	0.0924865	−	0.623689i
$540$		0			0
$541$	−4.57807	−	7.92946i	−0.196827	−	0.340914i	0.750671	−	0.660676i	$-0.229730\pi$
$541$	−4.57807	−	7.92946i	−0.196827	−	0.340914i	−0.947498	+	0.319762i	$0.896397\pi$
$542$	−4.06694			−0.174690
$543$		0			0
$544$		−	2.88201i		−	0.123565i
$545$	−7.08626	+	12.2738i	−0.303542	+	0.525750i
$546$		0			0
$547$	−23.0072	−	39.8496i	−0.983717	−	1.70385i	−0.647505	−	0.762061i	$-0.724187\pi$
$547$	−23.0072	−	39.8496i	−0.983717	−	1.70385i	−0.336212	−	0.941786i	$-0.609146\pi$
$548$	15.0990	−	8.71743i	0.644998	−	0.372390i
$549$		0			0
$550$	−1.04558	+	1.81100i	−0.0445837	+	0.0772213i
$551$	−7.39457	+	12.8078i	−0.315019	+	0.545629i
$552$		0			0
$553$	23.2624	−	34.2072i	0.989219	−	1.45464i
$554$	3.19608	+	1.84526i	0.135788	+	0.0783974i
$555$		0			0
$556$			12.8365i			0.544390i
$557$	−16.7682	−	9.68111i	−0.710490	−	0.410202i	0.100752	−	0.994912i	$-0.467875\pi$
$557$	−16.7682	−	9.68111i	−0.710490	−	0.410202i	−0.811242	+	0.584710i	$0.801208\pi$
$558$		0			0
$559$			2.83712i			0.119997i
$560$	1.48780	−	2.18780i	0.0628710	−	0.0924513i
$561$		0			0
$562$	24.6104			1.03813
$563$	10.8619	+	18.8134i	0.457775	+	0.792889i	0.998843	−	0.0480895i	$-0.0153133\pi$
$563$	10.8619	+	18.8134i	0.457775	+	0.792889i	−0.541068	+	0.840979i	$0.681980\pi$
$564$		0			0
$565$	6.91284	+	3.99113i	0.290825	+	0.167908i
$566$	1.80228			0.0757554
$567$		0			0
$568$	10.8486			0.455198
$569$	−18.3585	−	10.5993i	−0.769629	−	0.444346i	0.0631131	−	0.998006i	$-0.479897\pi$
$569$	−18.3585	−	10.5993i	−0.769629	−	0.444346i	−0.832742	+	0.553661i	$0.813230\pi$
$570$		0			0
$571$	5.52866	+	9.57592i	0.231367	+	0.400740i	0.958211	−	0.286063i	$-0.0923468\pi$
$571$	5.52866	+	9.57592i	0.231367	+	0.400740i	−0.726843	+	0.686803i	$0.759013\pi$
$572$	−0.999130			−0.0417757
$573$		0			0
$574$	−19.2447	+	9.29602i	−0.803258	+	0.388008i
$575$			2.02764i			0.0845583i
$576$		0			0
$577$	−27.5702	−	15.9177i	−1.14776	−	0.662662i	−0.199423	−	0.979914i	$-0.563907\pi$
$577$	−27.5702	−	15.9177i	−1.14776	−	0.662662i	−0.948341	+	0.317251i	$0.897240\pi$
$578$		−	8.69402i		−	0.361624i
$579$		0			0
$580$	2.74938	+	1.58735i	0.114162	+	0.0659113i
$581$	−12.8647	−	26.6326i	−0.533717	−	1.10491i
$582$		0			0
$583$	5.15729	−	8.93269i	0.213593	−	0.369954i
$584$	3.26162	−	5.64929i	0.134967	−	0.233769i
$585$		0			0
$586$	−20.5959	+	11.8910i	−0.850808	+	0.491214i
$587$	14.7632	+	25.5706i	0.609343	+	1.05541i	0.991349	+	0.131253i	$0.0419000\pi$
$587$	14.7632	+	25.5706i	0.609343	+	1.05541i	−0.382006	+	0.924160i	$0.624767\pi$
$588$		0			0
$589$	−12.3540	+	21.3977i	−0.509036	+	0.881676i
$590$		−	2.81942i		−	0.116074i
$591$		0			0
$592$	3.86338			0.158784
$593$	10.9772	+	19.0131i	0.450780	+	0.780773i	0.998435	−	0.0559309i	$-0.0178126\pi$
$593$	10.9772	+	19.0131i	0.450780	+	0.780773i	−0.547655	+	0.836704i	$0.684479\pi$
$594$		0			0
$595$	−4.28785	+	6.30525i	−0.175785	+	0.258490i
$596$	−1.03136	+	0.595458i	−0.0422463	+	0.0243909i
$597$		0			0
$598$	−0.838987	+	0.484389i	−0.0343087	+	0.0198082i
$599$	−23.0407	+	13.3026i	−0.941418	+	0.543528i	−0.890405	−	0.455170i	$-0.849579\pi$
$599$	−23.0407	+	13.3026i	−0.941418	+	0.543528i	−0.0510136	+	0.998698i	$0.516245\pi$
$600$		0			0
$601$	−33.3026	+	19.2273i	−1.35844	+	0.784296i	−0.989414	−	0.145122i	$-0.953642\pi$
$601$	−33.3026	+	19.2273i	−1.35844	+	0.784296i	−0.369027	+	0.929419i	$0.620309\pi$
$602$	−1.15539	+	15.6680i	−0.0470900	+	0.638582i
$603$		0			0
$604$	0.791747	+	1.37135i	0.0322157	+	0.0557993i
$605$	−6.62704			−0.269427
$606$		0			0
$607$		−	23.5753i		−	0.956893i	−0.878117	−	0.478446i	$-0.841200\pi$
$607$		−	23.5753i		−	0.956893i	0.878117	−	0.478446i	$-0.158800\pi$
$608$	2.32921	−	4.03431i	0.0944620	−	0.163613i
$609$		0			0
$610$	2.14655	+	3.71793i	0.0869113	+	0.150535i
$611$	0.0434768	−	0.0251013i	0.00175888	−	0.00101549i
$612$		0			0
$613$	−7.77138	+	13.4604i	−0.313883	+	0.543661i	−0.979199	−	0.202900i	$-0.934963\pi$
$613$	−7.77138	+	13.4604i	−0.313883	+	0.543661i	0.665316	+	0.746561i	$0.268297\pi$
$614$	−2.99936	+	5.19505i	−0.121044	+	0.209655i
$615$		0			0
$616$	−5.51772	−	0.406885i	−0.222315	−	0.0163939i
$617$	11.7195	+	6.76627i	0.471810	+	0.272400i	0.716997	−	0.697076i	$-0.245516\pi$
$617$	11.7195	+	6.76627i	0.471810	+	0.272400i	−0.245187	+	0.969476i	$0.578849\pi$
$618$		0			0
$619$			23.6194i			0.949345i	0.880163	+	0.474672i	$0.157433\pi$
$619$			23.6194i			0.949345i	−0.880163	+	0.474672i	$0.842567\pi$
$620$	4.59333	+	2.65196i	0.184473	+	0.106505i
$621$		0			0
$622$		−	23.7283i		−	0.951416i
$623$	15.1688	+	31.4025i	0.607724	+	1.25811i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−1.48278	−	2.56825i	−0.0592637	−	0.102648i
$627$		0			0
$628$	−14.5680	−	8.41085i	−0.581328	−	0.335630i
$629$	−11.1343			−0.443953
$630$		0			0
$631$	29.0626			1.15696			0.578482	−	0.815695i	$-0.303645\pi$
$631$	29.0626			1.15696			0.578482	+	0.815695i	$0.303645\pi$
$632$	−13.5407	−	7.81773i	−0.538620	−	0.310973i
$633$		0			0
$634$	−6.47508	−	11.2152i	−0.257158	−	0.445411i
$635$	−0.449694			−0.0178456
$636$		0			0
$637$	−2.61980	−	2.07903i	−0.103800	−	0.0823742i
$638$		−	6.63883i		−	0.262834i
$639$		0			0
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$			5.47596i			0.216288i	0.994135	+	0.108144i	$0.0344907\pi$
$641$			5.47596i			0.216288i	−0.994135	+	0.108144i	$0.965509\pi$
$642$		0			0
$643$	22.6584	+	13.0818i	0.893560	+	0.515897i	0.875105	−	0.483933i	$-0.160792\pi$
$643$	22.6584	+	13.0818i	0.893560	+	0.515897i	0.0184548	+	0.999830i	$0.494125\pi$
$644$	−4.83058	+	2.33338i	−0.190352	+	0.0919481i
$645$		0			0
$646$	−6.71281	+	11.6269i	−0.264112	+	0.457455i
$647$	−7.13123	+	12.3517i	−0.280358	+	0.485594i	−0.971473	−	0.237151i	$-0.923786\pi$
$647$	−7.13123	+	12.3517i	−0.280358	+	0.485594i	0.691115	+	0.722745i	$0.257120\pi$
$648$		0			0
$649$	−5.10597	+	2.94793i	−0.200427	+	0.115717i
$650$	0.238893	+	0.413776i	0.00937017	+	0.0162296i
$651$		0			0
$652$	5.01637	−	8.68860i	0.196456	−	0.340272i
$653$			14.4155i			0.564123i	0.959396	+	0.282062i	$0.0910183\pi$
$653$			14.4155i			0.564123i	−0.959396	+	0.282062i	$0.908982\pi$
$654$		0			0
$655$	−10.4428			−0.408034
$656$	4.03898	+	6.99572i	0.157696	+	0.273137i
$657$		0			0
$658$	0.250324	−	0.120917i	0.00975863	−	0.00471384i
$659$	23.0675	−	13.3180i	0.898581	−	0.518796i	0.0218413	−	0.999761i	$-0.493047\pi$
$659$	23.0675	−	13.3180i	0.898581	−	0.518796i	0.876739	+	0.480966i	$0.159714\pi$
$660$		0			0
$661$	10.9321	−	6.31167i	0.425211	−	0.245496i	−0.272093	−	0.962271i	$-0.587716\pi$
$661$	10.9321	−	6.31167i	0.425211	−	0.245496i	0.697304	+	0.716775i	$0.254383\pi$
$662$	29.4483	−	17.0020i	1.14454	−	0.660801i
$663$		0			0
$664$	−9.68132	+	5.58951i	−0.375708	+	0.216915i
$665$	−11.0981	+	5.36086i	−0.430365	+	0.207885i
$666$		0			0
$667$	−3.21858	−	5.57474i	−0.124624	−	0.215855i
$668$	−14.3407			−0.554860
$669$		0			0
$670$		−	5.47175i		−	0.211392i
$671$	4.48879	−	7.77481i	0.173288	−	0.300143i
$672$		0			0
$673$	−1.51712	−	2.62772i	−0.0584805	−	0.101291i	0.835303	−	0.549790i	$-0.185292\pi$
$673$	−1.51712	−	2.62772i	−0.0584805	−	0.101291i	−0.893784	+	0.448499i	$0.851959\pi$
$674$	−19.5993	+	11.3157i	−0.754936	+	0.435863i
$675$		0			0
$676$	6.38586	−	11.0606i	0.245610	−	0.425409i
$677$	5.58739	−	9.67764i	0.214741	−	0.371942i	−0.738452	−	0.674306i	$-0.764443\pi$
$677$	5.58739	−	9.67764i	0.214741	−	0.371942i	0.953192	+	0.302365i	$0.0977760\pi$
$678$		0			0
$679$	21.9582	−	10.6068i	0.842677	−	0.407050i
$680$	2.49589	+	1.44100i	0.0957131	+	0.0552600i
$681$		0			0
$682$		−	11.0914i		−	0.424710i
$683$	−23.9631	−	13.8351i	−0.916924	−	0.529387i	−0.0342719	−	0.999413i	$-0.510911\pi$
$683$	−23.9631	−	13.8351i	−0.916924	−	0.529387i	−0.882653	+	0.470026i	$0.844245\pi$
$684$		0			0
$685$			17.4349i			0.666151i
$686$	−13.6213	−	12.5484i	−0.520062	−	0.479099i
$687$		0			0
$688$	5.93804			0.226386
$689$	−1.17833	−	2.04093i	−0.0448909	−	0.0777534i
$690$		0			0
$691$	−11.7384	−	6.77716i	−0.446549	−	0.257815i	0.259823	−	0.965656i	$-0.416336\pi$
$691$	−11.7384	−	6.77716i	−0.446549	−	0.257815i	−0.706372	+	0.707841i	$0.749669\pi$
$692$	16.1263			0.613031
$693$		0			0
$694$	12.7779			0.485043
$695$	−11.1168	−	6.41827i	−0.421683	−	0.243459i
$696$		0			0
$697$	−11.6404	−	20.1617i	−0.440911	−	0.763680i
$698$	4.56471			0.172777
$699$		0			0
$700$	1.15079	+	2.38237i	0.0434957	+	0.0900451i
$701$		−	45.4060i		−	1.71496i	−0.514516	−	0.857481i	$-0.672028\pi$
$701$		−	45.4060i		−	1.71496i	0.514516	−	0.857481i	$-0.327972\pi$
$702$		0			0
$703$	−15.5861	−	8.99862i	−0.587840	−	0.339389i
$704$			2.09116i			0.0788137i
$705$		0			0
$706$	13.7716	+	7.95106i	0.518302	+	0.299242i
$707$	−49.7720	−	3.67026i	−1.87187	−	0.138034i
$708$		0			0
$709$	10.2957	−	17.8327i	0.386663	−	0.669719i	−0.605336	−	0.795970i	$-0.706961\pi$
$709$	10.2957	−	17.8327i	0.386663	−	0.669719i	0.991998	+	0.126251i	$0.0402944\pi$
$710$	−5.42432	+	9.39519i	−0.203571	+	0.352595i
$711$		0			0
$712$	11.4153	−	6.59060i	0.427805	−	0.246993i
$713$	−5.37722	−	9.31361i	−0.201378	−	0.348798i
$714$		0			0
$715$	0.499565	−	0.865272i	0.0186827	−	0.0323594i
$716$		−	0.0967051i		−	0.00361404i
$717$		0			0
$718$	−19.6573			−0.733605
$719$	19.2776	+	33.3899i	0.718935	+	1.24523i	0.961422	+	0.275077i	$0.0887033\pi$
$719$	19.2776	+	33.3899i	0.718935	+	1.24523i	−0.242488	+	0.970155i	$0.577963\pi$
$720$		0			0
$721$	1.97643	−	26.8021i	0.0736061	−	0.998164i
$722$	−2.33904	+	1.35045i	−0.0870501	+	0.0502584i
$723$		0			0
$724$	−17.4017	+	10.0469i	−0.646729	+	0.373389i
$725$	−2.74938	+	1.58735i	−0.102109	+	0.0589529i
$726$		0			0
$727$	21.6549	−	12.5025i	0.803137	−	0.463692i	−0.0414296	−	0.999141i	$-0.513191\pi$
$727$	21.6549	−	12.5025i	0.803137	−	0.463692i	0.844567	+	0.535450i	$0.179858\pi$
$728$	−0.710851	+	1.04530i	−0.0263459	+	0.0387414i
$729$		0			0
$730$	3.26162	+	5.64929i	0.120718	+	0.209090i
$731$	−17.1135			−0.632966
$732$		0			0
$733$			49.3523i			1.82287i	0.411444	+	0.911435i	$0.365024\pi$
$733$			49.3523i			1.82287i	−0.411444	+	0.911435i	$0.634976\pi$
$734$	10.9999	−	19.0524i	0.406014	−	0.703237i
$735$		0			0
$736$	1.01382	+	1.75599i	0.0373699	+	0.0647265i
$737$	−9.90934	+	5.72116i	−0.365015	+	0.210742i
$738$		0			0
$739$	10.3267	−	17.8864i	0.379874	−	0.657961i	−0.611170	−	0.791500i	$-0.709301\pi$
$739$	10.3267	−	17.8864i	0.379874	−	0.657961i	0.991044	+	0.133539i	$0.0426340\pi$
$740$	−1.93169	+	3.34578i	−0.0710103	+	0.122993i
$741$		0			0
$742$	−5.67622	−	11.7510i	−0.208381	−	0.431391i
$743$	−7.62562	−	4.40265i	−0.279757	−	0.161518i	0.353556	−	0.935413i	$-0.384972\pi$
$743$	−7.62562	−	4.40265i	−0.279757	−	0.161518i	−0.633313	+	0.773895i	$0.718306\pi$
$744$		0			0
$745$		−	1.19092i		−	0.0436318i
$746$	20.2060	+	11.6660i	0.739796	+	0.427121i
$747$		0			0
$748$		−	6.02675i		−	0.220360i
$749$	43.6852	−	21.1018i	1.59622	−	0.771044i
$750$		0			0
$751$	42.7052			1.55833			0.779167	−	0.626816i	$-0.215642\pi$
$751$	42.7052			1.55833			0.779167	+	0.626816i	$0.215642\pi$
$752$	−0.0525367	−	0.0909962i	−0.00191581	−	0.00331829i
$753$		0			0
$754$	−1.31362	−	0.758417i	−0.0478391	−	0.0276199i
$755$	−1.58349			−0.0576292
$756$		0			0
$757$	−23.4364			−0.851811			−0.425905	−	0.904768i	$-0.640044\pi$
$757$	−23.4364			−0.851811			−0.425905	+	0.904768i	$0.640044\pi$
$758$	17.5941	+	10.1580i	0.639047	+	0.368954i
$759$		0			0
$760$	2.32921	+	4.03431i	0.0844894	+	0.146340i
$761$	7.38846			0.267832			0.133916	−	0.990993i	$-0.457245\pi$
$761$	7.38846			0.267832			0.133916	+	0.990993i	$0.457245\pi$
$762$		0			0
$763$	21.0859	−	31.0066i	0.763360	−	1.12251i
$764$			3.53308i			0.127822i
$765$		0			0
$766$	−3.31092	−	1.91156i	−0.119628	−	0.0690675i
$767$			1.34708i			0.0486403i
$768$		0			0
$769$	−41.7890	−	24.1269i	−1.50695	−	0.870038i	−0.999967	−	0.00808106i	$-0.997428\pi$
$769$	−41.7890	−	24.1269i	−1.50695	−	0.870038i	−0.506982	−	0.861957i	$-0.669239\pi$
$770$	3.11123	−	4.57504i	0.112121	−	0.164873i
$771$		0			0
$772$	12.6572	−	21.9229i	0.455542	−	0.789022i
$773$	12.6336	−	21.8821i	0.454401	−	0.787045i	−0.544253	−	0.838921i	$-0.683187\pi$
$773$	12.6336	−	21.8821i	0.454401	−	0.787045i	0.998654	+	0.0518761i	$0.0165201\pi$
$774$		0			0
$775$	−4.59333	+	2.65196i	−0.164997	+	0.0952613i
$776$	−4.60847	−	7.98211i	−0.165435	−	0.286541i
$777$		0			0
$778$	−9.67132	+	16.7512i	−0.346734	+	0.600561i
$779$		−	37.6306i		−	1.34825i
$780$		0			0
$781$	22.6863			0.811778
$782$	−2.92184	−	5.06077i	−0.104485	−	0.180973i
$783$		0			0
$784$	−4.35137	+	5.48321i	−0.155406	+	0.195829i
$785$	14.5680	−	8.41085i	0.519955	−	0.300196i
$786$		0			0
$787$	46.9696	−	27.1179i	1.67429	−	0.966649i	0.709091	−	0.705117i	$-0.249106\pi$
$787$	46.9696	−	27.1179i	1.67429	−	0.966649i	0.965195	−	0.261532i	$-0.0842278\pi$
$788$	7.80365	−	4.50544i	0.277994	−	0.160500i
$789$		0			0
$790$	13.5407	−	7.81773i	0.481757	−	0.278142i
$791$	−17.4636	−	11.8760i	−0.620933	−	0.422262i
$792$		0			0
$793$	−1.02559	−	1.77638i	−0.0364199	−	0.0630811i
$794$	30.2959			1.07516
$795$		0			0
$796$		−	14.3059i		−	0.507060i
$797$	−7.63066	+	13.2167i	−0.270292	+	0.468159i	−0.968936	−	0.247310i	$-0.920454\pi$
$797$	−7.63066	+	13.2167i	−0.270292	+	0.468159i	0.698645	+	0.715469i	$0.253787\pi$
$798$		0			0
$799$	0.151411	+	0.262252i	0.00535654	+	0.00927780i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$		0			0
$802$	16.5340	−	28.6376i	0.583834	−	1.01123i
$803$	6.82058	−	11.8136i	0.240693	−	0.416892i
$804$		0			0
$805$	0.394524	−	5.35010i	0.0139052	−	0.188566i
$806$	−2.19463	−	1.26707i	−0.0773027	−	0.0446307i
$807$		0			0
$808$			18.8631i			0.663602i
$809$	−12.9900	−	7.49978i	−0.456704	−	0.263678i	0.253953	−	0.967216i	$-0.418269\pi$
$809$	−12.9900	−	7.49978i	−0.456704	−	0.263678i	−0.710657	+	0.703538i	$0.751602\pi$
$810$		0			0
$811$		−	15.3625i		−	0.539451i	−0.962937	−	0.269726i	$-0.913067\pi$
$811$		−	15.3625i		−	0.539451i	0.962937	−	0.269726i	$-0.0869330\pi$
$812$	−6.94562	−	4.72333i	−0.243743	−	0.165756i
$813$		0			0
$814$	8.07895			0.283167
$815$	5.01637	+	8.68860i	0.175716	+	0.304348i
$816$		0			0
$817$	−23.9559	−	13.8310i	−0.838112	−	0.483884i
$818$	17.0227			0.595183
$819$		0			0
$820$	−8.07796			−0.282095
$821$	−24.2512	−	14.0014i	−0.846372	−	0.488653i	0.0130533	−	0.999915i	$-0.495845\pi$
$821$	−24.2512	−	14.0014i	−0.846372	−	0.488653i	−0.859425	+	0.511262i	$0.829178\pi$
$822$		0			0
$823$	−1.01689	−	1.76131i	−0.0354466	−	0.0613954i	0.847758	−	0.530383i	$-0.177952\pi$
$823$	−1.01689	−	1.76131i	−0.0354466	−	0.0613954i	−0.883204	+	0.468988i	$0.844619\pi$
$824$	−10.1578			−0.353863
$825$		0			0
$826$	−0.548584	+	7.43929i	−0.0190877	+	0.258846i
$827$		−	25.2422i		−	0.877758i	−0.898546	−	0.438879i	$-0.855376\pi$
$827$		−	25.2422i		−	0.877758i	0.898546	−	0.438879i	$-0.144624\pi$
$828$		0			0
$829$	−35.8687	−	20.7088i	−1.24577	−	0.719246i	−0.275508	−	0.961299i	$-0.588846\pi$
$829$	−35.8687	−	20.7088i	−1.24577	−	0.719246i	−0.970263	+	0.242053i	$0.922179\pi$
$830$		−	11.1790i		−	0.388030i
$831$		0			0
$832$	0.413776	+	0.238893i	0.0143451	+	0.00828214i
$833$	12.5407	−	15.8026i	0.434510	−	0.547529i
$834$		0			0
$835$	7.17037	−	12.4194i	0.248141	−	0.429792i
$836$	4.87076	−	8.43640i	0.168459	−	0.291779i
$837$		0			0
$838$	−6.74162	+	3.89228i	−0.232885	+	0.134456i
$839$	−7.84013	−	13.5795i	−0.270671	−	0.468817i	0.698363	−	0.715744i	$-0.253912\pi$
$839$	−7.84013	−	13.5795i	−0.270671	−	0.468817i	−0.969034	+	0.246928i	$0.920579\pi$
$840$		0			0
$841$	−9.46061	+	16.3863i	−0.326228	+	0.565043i
$842$		−	30.9337i		−	1.06605i
$843$		0			0
$844$	−0.885582			−0.0304830
$845$	6.38586	+	11.0606i	0.219680	+	0.380497i
$846$		0			0
$847$	17.4860	+	1.28945i	0.600827	+	0.0443059i
$848$	−4.27164	+	2.46623i	−0.146689	+	0.0846908i
$849$		0			0
$850$	−2.49589	+	1.44100i	−0.0856084	+	0.0494261i
$851$	6.78404	−	3.91677i	0.232554	−	0.134265i
$852$		0			0
$853$	13.0788	−	7.55104i	0.447809	−	0.258543i	−0.259095	−	0.965852i	$-0.583424\pi$
$853$	13.0788	−	7.55104i	0.447809	−	0.258543i	0.706904	+	0.707309i	$0.250091\pi$
$854$	−4.94045	−	10.2278i	−0.169059	−	0.349987i
$855$		0			0
$856$	−9.16843	−	15.8802i	−0.313371	−	0.542774i
$857$	−2.72299			−0.0930155			−0.0465077	−	0.998918i	$-0.514809\pi$
$857$	−2.72299			−0.0930155			−0.0465077	+	0.998918i	$0.514809\pi$
$858$		0			0
$859$			28.1990i			0.962136i	0.876683	+	0.481068i	$0.159751\pi$
$859$			28.1990i			0.962136i	−0.876683	+	0.481068i	$0.840249\pi$
$860$	−2.96902	+	5.14250i	−0.101243	+	0.175358i
$861$		0			0
$862$	9.81647	+	17.0026i	0.334350	+	0.579112i
$863$	−10.0634	+	5.81009i	−0.342561	+	0.197778i	−0.661404	−	0.750030i	$-0.730039\pi$
$863$	−10.0634	+	5.81009i	−0.342561	+	0.197778i	0.318843	+	0.947808i	$0.396706\pi$
$864$		0			0
$865$	−8.06316	+	13.9658i	−0.274156	+	0.474851i
$866$	17.9781	−	31.1390i	0.610920	−	1.05815i
$867$		0			0
$868$	−11.6039	−	7.89117i	−0.393862	−	0.267844i
$869$	−28.3158	−	16.3481i	−0.960548	−	0.554573i
$870$		0			0
$871$			2.61433i			0.0885832i
$872$	−12.2738	−	7.08626i	−0.415642	−	0.239971i
$873$		0			0
$874$		−	9.44559i		−	0.319502i
$875$	−2.63859	−	0.194573i	−0.0892005	−	0.00657778i
$876$		0			0
$877$	−26.9876			−0.911307			−0.455654	−	0.890157i	$-0.650594\pi$
$877$	−26.9876			−0.911307			−0.455654	+	0.890157i	$0.650594\pi$
$878$	−12.1713	−	21.0814i	−0.410762	−	0.711461i
$879$		0			0
$880$	−1.81100	−	1.04558i	−0.0610488	−	0.0352465i
$881$	3.38847			0.114160			0.0570802	−	0.998370i	$-0.481821\pi$
$881$	3.38847			0.114160			0.0570802	+	0.998370i	$0.481821\pi$
$882$		0			0
$883$	−28.0287			−0.943241			−0.471621	−	0.881802i	$-0.656331\pi$
$883$	−28.0287			−0.943241			−0.471621	+	0.881802i	$0.656331\pi$
$884$	−1.19251	−	0.688493i	−0.0401083	−	0.0231565i
$885$		0			0
$886$	−2.97116	−	5.14619i	−0.0998180	−	0.172890i
$887$	−20.1280			−0.675833			−0.337917	−	0.941176i	$-0.609722\pi$
$887$	−20.1280			−0.675833			−0.337917	+	0.941176i	$0.609722\pi$
$888$		0			0
$889$	1.18656	+	0.0874986i	0.0397959	+	0.00293461i
$890$			13.1812i			0.441835i
$891$		0			0
$892$	0.0602532	+	0.0347872i	0.00201743	+	0.00116476i
$893$			0.489476i			0.0163797i
$894$		0			0
$895$	0.0837491	+	0.0483526i	0.00279942	+	0.00161625i
$896$	2.18780	+	1.48780i	0.0730892	+	0.0497039i
$897$		0			0
$898$	−1.79521	+	3.10939i	−0.0599069	+	0.103762i
$899$	8.41921	−	14.5825i	0.280796	−	0.486353i
$900$		0			0
$901$	12.3109	−	7.10770i	0.410136	−	0.236792i
$902$	8.44617	+	14.6292i	0.281227	+	0.487099i
$903$		0			0
$904$	−3.99113	+	6.91284i	−0.132743	+	0.229918i
$905$		−	20.0938i		−	0.667939i
$906$		0			0
$907$	−33.6848			−1.11849			−0.559243	−	0.829004i	$-0.688908\pi$
$907$	−33.6848			−1.11849			−0.559243	+	0.829004i	$0.688908\pi$
$908$	9.19003	+	15.9176i	0.304982	+	0.528244i
$909$		0			0
$910$	−0.549832	−	1.13827i	−0.0182267	−	0.0377331i
$911$	34.1663	−	19.7259i	1.13198	−	0.653550i	0.187549	−	0.982255i	$-0.439946\pi$
$911$	34.1663	−	19.7259i	1.13198	−	0.653550i	0.944432	+	0.328706i	$0.106612\pi$
$912$		0			0
$913$	−20.2452	+	11.6886i	−0.670019	+	0.386836i
$914$	11.6558	−	6.72945i	0.385538	−	0.222591i
$915$		0			0
$916$	13.9168	−	8.03486i	0.459823	−	0.265479i
$917$	27.5543	+	2.03189i	0.909922	+	0.0670990i
$918$		0			0
$919$	24.5657	+	42.5490i	0.810346	+	1.40356i	0.912622	+	0.408804i	$0.134054\pi$
$919$	24.5657	+	42.5490i	0.810346	+	1.40356i	−0.102276	+	0.994756i	$0.532612\pi$
$920$	−2.02764			−0.0668492
$921$		0			0
$922$			27.1267i			0.893370i
$923$	2.59167	−	4.48890i	0.0853058	−	0.147754i
$924$		0			0
$925$	−1.93169	−	3.34578i	−0.0635135	−	0.110009i
$926$	27.6688	−	15.9746i	0.909254	−	0.524958i
$927$		0			0
$928$	−1.58735	+	2.74938i	−0.0521075	+	0.0902528i
$929$	−3.80826	+	6.59610i	−0.124945	+	0.216411i	−0.921711	−	0.387876i	$-0.873209\pi$
$929$	−3.80826	+	6.59610i	−0.124945	+	0.216411i	0.796766	+	0.604287i	$0.206542\pi$
$930$		0			0
$931$	30.3263	−	11.9857i	0.993906	−	0.392815i
$932$	22.4677	+	12.9717i	0.735955	+	0.424904i
$933$		0			0
$934$		−	36.8052i		−	1.20430i
$935$	5.21932	+	3.01338i	0.170690	+	0.0985479i
$936$		0			0
$937$			35.6260i			1.16385i	0.813243	+	0.581925i	$0.197700\pi$
$937$			35.6260i			1.16385i	−0.813243	+	0.581925i	$0.802300\pi$
$938$	−1.06466	+	14.4377i	−0.0347623	+	0.471407i
$939$		0			0
$940$	0.105073			0.00342711
$941$	−22.4863	−	38.9474i	−0.733032	−	1.26965i	−0.955581	−	0.294727i	$-0.904771\pi$
$941$	−22.4863	−	38.9474i	−0.733032	−	1.26965i	0.222550	−	0.974921i	$-0.428562\pi$
$942$		0			0
$943$	14.1848	+	8.18959i	0.461920	+	0.266690i
$944$	2.81942			0.0917643
$945$		0			0
$946$	12.4174			0.403725
$947$	−36.7624	−	21.2248i	−1.19462	−	0.689712i	−0.235266	−	0.971931i	$-0.575596\pi$
$947$	−36.7624	−	21.2248i	−1.19462	−	0.689712i	−0.959350	+	0.282219i	$0.908929\pi$
$948$		0			0
$949$	−1.55836	−	2.69916i	−0.0505865	−	0.0876183i
$950$	−4.65842			−0.151139
$951$		0			0
$952$	−6.30525	−	4.28785i	−0.204354	−	0.138970i
$953$		−	4.59106i		−	0.148719i	−0.997232	−	0.0743595i	$-0.976309\pi$
$953$		−	4.59106i		−	0.148719i	0.997232	−	0.0743595i	$-0.0236912\pi$
$954$		0			0
$955$	−3.05974	−	1.76654i	−0.0990108	−	0.0571639i
$956$			9.77390i			0.316110i
$957$		0			0
$958$	−15.2845	−	8.82453i	−0.493821	−	0.285108i
$959$	3.39236	−	46.0034i	0.109545	−	1.48553i
$960$		0			0
$961$	−1.43420	+	2.48410i	−0.0462644	+	0.0801323i
$962$	0.922936	−	1.59857i	0.0297566	−	0.0515400i
$963$		0			0
$964$	−22.1792	+	12.8052i	−0.714345	+	0.412427i
$965$	12.6572	+	21.9229i	0.407449	+	0.705723i
$966$		0			0
$967$	3.39500	−	5.88032i	0.109176	−	0.189098i	−0.806261	−	0.591560i	$-0.798512\pi$
$967$	3.39500	−	5.88032i	0.109176	−	0.189098i	0.915437	+	0.402462i	$0.131845\pi$
$968$		−	6.62704i		−	0.213001i
$969$		0			0
$970$	9.21695			0.295938
$971$	−27.3715	−	47.4087i	−0.878392	−	1.52142i	−0.853105	−	0.521739i	$-0.825284\pi$
$971$	−27.3715	−	47.4087i	−0.878392	−	1.52142i	−0.0252864	−	0.999680i	$-0.508050\pi$
$972$		0			0
$973$	28.0837	+	19.0982i	0.900323	+	0.612260i
$974$	−9.43137	+	5.44521i	−0.302201	+	0.174476i
$975$		0			0
$976$	−3.71793	+	2.14655i	−0.119008	+	0.0687094i
$977$	2.91180	−	1.68113i	0.0931566	−	0.0537840i	−0.452698	−	0.891664i	$-0.649538\pi$
$977$	2.91180	−	1.68113i	0.0931566	−	0.0537840i	0.545855	+	0.837880i	$0.316205\pi$
$978$		0			0
$979$	23.8712	−	13.7820i	0.762925	−	0.440475i
$980$	−2.57291	−	6.51000i	−0.0821885	−	0.207954i
$981$		0			0
$982$	−12.4238	−	21.5186i	−0.396459	−	0.686687i
$983$	−49.5842			−1.58149			−0.790745	−	0.612146i	$-0.790306\pi$
$983$	−49.5842			−1.58149			−0.790745	+	0.612146i	$0.790306\pi$
$984$		0			0
$985$			9.01088i			0.287111i
$986$	4.57477	−	7.92373i	0.145690	−	0.252343i
$987$		0			0
$988$	−1.11287	−	1.92754i	−0.0354050	−	0.0613233i
$989$	10.4271	−	6.02010i	0.331563	−	0.191428i
$990$		0			0
$991$	−25.0428	+	43.3755i	−0.795512	+	1.37787i	0.127001	+	0.991903i	$0.459465\pi$
$991$	−25.0428	+	43.3755i	−0.795512	+	1.37787i	−0.922513	+	0.385965i	$0.873869\pi$
$992$	−2.65196	+	4.59333i	−0.0841999	+	0.145838i
$993$		0			0
$994$	16.1406	−	23.7346i	0.511948	−	0.752816i
$995$	12.3893	+	7.15296i	0.392767	+	0.226764i
$996$		0			0
$997$			31.2926i			0.991048i	0.868594	+	0.495524i	$0.165024\pi$
$997$			31.2926i			0.991048i	−0.868594	+	0.495524i	$0.834976\pi$
$998$	−31.9432	−	18.4424i	−1.01115	−	0.583785i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.c.1151.2		32
3.2	odd	2		630.2.t.c.311.13	✓	32
7.5	odd	6		1890.2.bk.c.341.14		32
9.2	odd	6		1890.2.bk.c.521.14		32
9.7	even	3		630.2.bk.c.101.15	yes	32
21.5	even	6		630.2.bk.c.131.7	yes	32
63.47	even	6	inner	1890.2.t.c.1601.2		32
63.61	odd	6		630.2.t.c.551.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.13	✓	32	3.2	odd	2
630.2.t.c.551.13	yes	32	63.61	odd	6
630.2.bk.c.101.15	yes	32	9.7	even	3
630.2.bk.c.131.7	yes	32	21.5	even	6
1890.2.t.c.1151.2		32	1.1	even	1	trivial
1890.2.t.c.1601.2		32	63.47	even	6	inner
1890.2.bk.c.341.14		32	7.5	odd	6
1890.2.bk.c.521.14		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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(2.63859 + 0.194573i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(2.63859 + 0.194573i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} -2.09116i q^{11} +(-0.413776 - 0.238893i) q^{13} +(-2.18780 - 1.48780i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.44100 - 2.49589i) q^{17} +(4.03431 - 2.32921i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.04558 + 1.81100i) q^{22} +2.02764i q^{23} +1.00000 q^{25} +(0.238893 + 0.413776i) q^{26} +(1.15079 + 2.38237i) q^{28} +(-2.74938 + 1.58735i) q^{29} +(-4.59333 + 2.65196i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.49589 + 1.44100i) q^{34} +(-2.63859 - 0.194573i) q^{35} +(-1.93169 - 3.34578i) q^{37} -4.65842 q^{38} +1.00000i q^{40} +(4.03898 - 6.99572i) q^{41} +(-2.96902 - 5.14250i) q^{43} +(1.81100 - 1.04558i) q^{44} +(1.01382 - 1.75599i) q^{46} +(-0.0525367 + 0.0909962i) q^{47} +(6.92428 + 1.02680i) q^{49} +(-0.866025 - 0.500000i) q^{50} -0.477787i q^{52} +(4.27164 + 2.46623i) q^{53} +2.09116i q^{55} +(0.194573 - 2.63859i) q^{56} +3.17471 q^{58} +(-1.40971 - 2.44169i) q^{59} +(3.71793 + 2.14655i) q^{61} +5.30392 q^{62} -1.00000 q^{64} +(0.413776 + 0.238893i) q^{65} +(-2.73588 - 4.73867i) q^{67} +2.88201 q^{68} +(2.18780 + 1.48780i) q^{70} +10.8486i q^{71} +(5.64929 + 3.26162i) q^{73} +3.86338i q^{74} +(4.03431 + 2.32921i) q^{76} +(0.406885 - 5.51772i) q^{77} +(7.81773 - 13.5407i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-6.99572 + 4.03898i) q^{82} +(-5.58951 - 9.68132i) q^{83} +(-1.44100 + 2.49589i) q^{85} +5.93804i q^{86} -2.09116 q^{88} +(6.59060 + 11.4153i) q^{89} +(-1.04530 - 0.710851i) q^{91} +(-1.75599 + 1.01382i) q^{92} +(0.0909962 - 0.0525367i) q^{94} +(-4.03431 + 2.32921i) q^{95} +(7.98211 - 4.60847i) q^{97} +(-5.48321 - 4.35137i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7}+O(q^{10}) \) 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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