LMFDB - Embedded newform 234.2.z.a.227.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, 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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.2
Character	$\chi$	$=$	234.227
Dual form			234.2.z.a.167.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-1.15524 + 1.29051i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.817032 - 3.04921i) q^{5} +(-0.947539 - 1.44989i) q^{6} +(-2.08075 - 2.08075i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.330837 - 2.98170i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.15524 + 1.29051i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.817032 - 3.04921i) q^{5} +(-0.947539 - 1.44989i) q^{6} +(-2.08075 - 2.08075i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.330837 - 2.98170i) q^{9} +(2.73384 + 1.57838i) q^{10} +(-0.842637 - 0.225784i) q^{11} +(1.64572 - 0.539995i) q^{12} +(-0.0715101 - 3.60484i) q^{13} +(2.54838 - 1.47131i) q^{14} +(2.99116 + 4.57696i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.80087 + 3.11920i) q^{17} +(2.96573 + 0.452158i) q^{18} +(-4.90132 - 1.31331i) q^{19} +(-2.23217 + 2.23217i) q^{20} +(5.08899 - 0.281462i) q^{21} +(0.436181 - 0.755487i) q^{22} +3.73515 q^{23} +(0.0956502 + 1.72941i) q^{24} +(-4.29998 - 2.48260i) q^{25} +(3.50052 + 0.863928i) q^{26} +(4.23011 + 3.01764i) q^{27} +(0.761606 + 2.84235i) q^{28} +(7.44735 - 4.29973i) q^{29} +(-5.19517 + 1.70464i) q^{30} +(-4.96612 - 1.33067i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.26482 - 0.826597i) q^{33} +(-3.47902 + 0.932200i) q^{34} +(-8.04466 + 4.64459i) q^{35} +(-1.20434 + 2.74765i) q^{36} +(-5.77159 + 1.54649i) q^{37} +(2.53711 - 4.39440i) q^{38} +(4.73470 + 4.07218i) q^{39} +(-1.57838 - 2.73384i) q^{40} +(-7.72453 - 7.72453i) q^{41} +(-1.04526 + 4.98844i) q^{42} -6.33580i q^{43} +(0.616853 + 0.616853i) q^{44} +(-9.36213 - 1.42736i) q^{45} +(-0.966728 + 3.60788i) q^{46} +(1.63674 + 6.10838i) q^{47} +(-1.69524 - 0.355213i) q^{48} +1.65902i q^{49} +(3.51092 - 3.51092i) q^{50} +(-6.10581 - 1.27939i) q^{51} +(-1.74049 + 3.15764i) q^{52} +6.73100i q^{53} +(-4.00965 + 3.30496i) q^{54} +(-1.37692 + 2.38490i) q^{55} -2.94262 q^{56} +(7.35704 - 4.80802i) q^{57} +(2.22570 + 8.30644i) q^{58} +(1.42714 + 5.32616i) q^{59} +(-0.301946 - 5.45934i) q^{60} +6.36898 q^{61} +(2.57066 - 4.45251i) q^{62} +(-5.51578 + 6.89256i) q^{63} -1.00000i q^{64} +(-11.0503 - 2.72722i) q^{65} +(0.471071 + 1.43567i) q^{66} +(5.85124 - 5.85124i) q^{67} -3.60175i q^{68} +(-4.31500 + 4.82025i) q^{69} +(-2.40422 - 8.97266i) q^{70} +(1.65986 - 6.19468i) q^{71} +(-2.34232 - 1.87444i) q^{72} +(10.6419 + 10.6419i) q^{73} -5.97519i q^{74} +(8.17134 - 2.68118i) q^{75} +(3.58802 + 3.58802i) q^{76} +(1.28351 + 2.22311i) q^{77} +(-5.15885 + 3.51941i) q^{78} +(-1.30671 + 2.26329i) q^{79} +(3.04921 - 0.817032i) q^{80} +(-8.78109 + 1.97291i) q^{81} +(9.46058 - 5.46207i) q^{82} +(11.0800 - 2.96889i) q^{83} +(-4.54793 - 2.30074i) q^{84} +(10.9825 - 2.94274i) q^{85} +(6.11991 + 1.63983i) q^{86} +(-3.05464 + 14.5781i) q^{87} +(-0.755487 + 0.436181i) q^{88} +(-2.10194 - 7.84455i) q^{89} +(3.80182 - 8.67369i) q^{90} +(-7.35197 + 7.64956i) q^{91} +(-3.23474 - 1.86758i) q^{92} +(7.45431 - 4.87159i) q^{93} -6.32386 q^{94} +(-8.00907 + 13.8721i) q^{95} +(0.781868 - 1.54554i) q^{96} +(-11.9612 + 11.9612i) q^{97} +(-1.60249 - 0.429386i) q^{98} +(-0.394445 + 2.58719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7}+O(q^{10}) $ 56 * q - 8 * q^7	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−1.15524	+	1.29051i	−0.666979	+	0.745077i
$3$	−1.15524	+	1.29051i	−0.666979	+	0.745077i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.817032	−	3.04921i	0.365388	−	1.36365i	−0.501506	−	0.865154i	$-0.667221\pi$
$5$	0.817032	−	3.04921i	0.365388	−	1.36365i	0.866894	−	0.498492i	$-0.166113\pi$
$6$	−0.947539	−	1.44989i	−0.386831	−	0.591913i
$7$	−2.08075	−	2.08075i	−0.786449	−	0.786449i	0.194462	−	0.980910i	$-0.437704\pi$
$7$	−2.08075	−	2.08075i	−0.786449	−	0.786449i	−0.980910	+	0.194462i	$0.937704\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.330837	−	2.98170i	−0.110279	−	0.993901i
$10$	2.73384	+	1.57838i	0.864517	+	0.499129i
$11$	−0.842637	−	0.225784i	−0.254064	−	0.0680764i	0.129539	−	0.991574i	$-0.458650\pi$
$11$	−0.842637	−	0.225784i	−0.254064	−	0.0680764i	−0.383603	+	0.923498i	$0.625317\pi$
$12$	1.64572	−	0.539995i	0.475079	−	0.155883i
$13$	−0.0715101	−	3.60484i	−0.0198333	−	0.999803i
$13$	−0.0715101	−	3.60484i	−0.0198333	−	0.999803i
$14$	2.54838	−	1.47131i	0.681084	−	0.393224i
$15$	2.99116	+	4.57696i	0.772315	+	1.18176i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.80087	+	3.11920i	0.436776	+	0.756518i	0.997439	−	0.0715262i	$-0.0227870\pi$
$17$	1.80087	+	3.11920i	0.436776	+	0.756518i	−0.560663	+	0.828044i	$0.689454\pi$
$18$	2.96573	+	0.452158i	0.699029	+	0.106575i
$19$	−4.90132	−	1.31331i	−1.12444	−	0.301293i	−0.351761	−	0.936090i	$-0.614417\pi$
$19$	−4.90132	−	1.31331i	−1.12444	−	0.301293i	−0.772679	+	0.634797i	$0.781084\pi$
$20$	−2.23217	+	2.23217i	−0.499129	+	0.499129i
$21$	5.08899	−	0.281462i	1.11051	−	0.0614201i
$22$	0.436181	−	0.755487i	0.0929941	−	0.161070i
$23$	3.73515			0.778833			0.389416	−	0.921062i	$-0.372677\pi$
$23$	3.73515			0.778833			0.389416	+	0.921062i	$0.372677\pi$
$24$	0.0956502	+	1.72941i	0.0195245	+	0.353014i
$25$	−4.29998	−	2.48260i	−0.859997	−	0.496519i
$26$	3.50052	+	0.863928i	0.686508	+	0.169430i
$27$	4.23011	+	3.01764i	0.814086	+	0.580744i
$28$	0.761606	+	2.84235i	0.143930	+	0.537154i
$29$	7.44735	−	4.29973i	1.38294	−	0.798439i	0.390431	−	0.920632i	$-0.372326\pi$
$29$	7.44735	−	4.29973i	1.38294	−	0.798439i	0.992506	+	0.122193i	$0.0389925\pi$
$30$	−5.19517	+	1.70464i	−0.948504	+	0.311223i
$31$	−4.96612	−	1.33067i	−0.891942	−	0.238995i	−0.216390	−	0.976307i	$-0.569428\pi$
$31$	−4.96612	−	1.33067i	−0.891942	−	0.238995i	−0.675553	+	0.737312i	$0.736095\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	1.26482	−	0.826597i	0.220178	−	0.143892i
$34$	−3.47902	+	0.932200i	−0.596647	+	0.159871i
$35$	−8.04466	+	4.64459i	−1.35980	+	0.785079i
$36$	−1.20434	+	2.74765i	−0.200723	+	0.457941i
$37$	−5.77159	+	1.54649i	−0.948844	+	0.254242i	−0.699872	−	0.714269i	$-0.746760\pi$
$37$	−5.77159	+	1.54649i	−0.948844	+	0.254242i	−0.248972	+	0.968511i	$0.580093\pi$
$38$	2.53711	−	4.39440i	0.411574	−	0.712867i
$39$	4.73470	+	4.07218i	0.758159	+	0.652070i
$40$	−1.57838	−	2.73384i	−0.249565	−	0.432258i
$41$	−7.72453	−	7.72453i	−1.20637	−	1.20637i	−0.972194	−	0.234175i	$-0.924761\pi$
$41$	−7.72453	−	7.72453i	−1.20637	−	1.20637i	−0.234175	−	0.972194i	$-0.575239\pi$
$42$	−1.04526	+	4.98844i	−0.161287	+	0.769732i
$43$		−	6.33580i		−	0.966200i	−0.875565	−	0.483100i	$-0.839511\pi$
$43$		−	6.33580i		−	0.966200i	0.875565	−	0.483100i	$-0.160489\pi$
$44$	0.616853	+	0.616853i	0.0929941	+	0.0929941i
$45$	−9.36213	−	1.42736i	−1.39562	−	0.212778i
$46$	−0.966728	+	3.60788i	−0.142536	+	0.531953i
$47$	1.63674	+	6.10838i	0.238742	+	0.890999i	0.976426	+	0.215852i	$0.0692529\pi$
$47$	1.63674	+	6.10838i	0.238742	+	0.890999i	−0.737684	+	0.675146i	$0.764080\pi$
$48$	−1.69524	−	0.355213i	−0.244686	−	0.0512705i
$49$			1.65902i			0.237003i
$50$	3.51092	−	3.51092i	0.496519	−	0.496519i
$51$	−6.10581	−	1.27939i	−0.854984	−	0.179150i
$52$	−1.74049	+	3.15764i	−0.241363	+	0.437886i
$53$			6.73100i			0.924574i	0.886730	+	0.462287i	$0.152971\pi$
$53$			6.73100i			0.924574i	−0.886730	+	0.462287i	$0.847029\pi$
$54$	−4.00965	+	3.30496i	−0.545644	+	0.449747i
$55$	−1.37692	+	2.38490i	−0.185664	+	0.321580i
$56$	−2.94262			−0.393224
$57$	7.35704	−	4.80802i	0.974464	−	0.636838i
$58$	2.22570	+	8.30644i	0.292249	+	1.09069i
$59$	1.42714	+	5.32616i	0.185798	+	0.693407i	0.994458	+	0.105131i	$0.0335263\pi$
$59$	1.42714	+	5.32616i	0.185798	+	0.693407i	−0.808660	+	0.588276i	$0.799807\pi$
$60$	−0.301946	−	5.45934i	−0.0389810	−	0.704798i
$61$	6.36898			0.815464			0.407732	−	0.913102i	$-0.366320\pi$
$61$	6.36898			0.815464			0.407732	+	0.913102i	$0.366320\pi$
$62$	2.57066	−	4.45251i	0.326474	−	0.565469i
$63$	−5.51578	+	6.89256i	−0.694923	+	0.868380i
$64$		−	1.00000i		−	0.125000i
$65$	−11.0503	−	2.72722i	−1.37062	−	0.338270i
$66$	0.471071	+	1.43567i	0.0579848	+	0.176718i
$67$	5.85124	−	5.85124i	0.714842	−	0.714842i	−0.252702	−	0.967544i	$-0.581319\pi$
$67$	5.85124	−	5.85124i	0.714842	−	0.714842i	0.967544	+	0.252702i	$0.0813192\pi$
$68$		−	3.60175i		−	0.436776i
$69$	−4.31500	+	4.82025i	−0.519465	+	0.580290i
$70$	−2.40422	−	8.97266i	−0.287359	−	1.07244i
$71$	1.65986	−	6.19468i	0.196989	−	0.735174i	−0.794754	−	0.606932i	$-0.792400\pi$
$71$	1.65986	−	6.19468i	0.196989	−	0.735174i	0.991743	−	0.128242i	$-0.0409333\pi$
$72$	−2.34232	−	1.87444i	−0.276045	−	0.220905i
$73$	10.6419	+	10.6419i	1.24555	+	1.24555i	0.957667	+	0.287878i	$0.0929498\pi$
$73$	10.6419	+	10.6419i	1.24555	+	1.24555i	0.287878	+	0.957667i	$0.407050\pi$
$74$		−	5.97519i		−	0.694602i
$75$	8.17134	−	2.68118i	0.943545	−	0.309596i
$76$	3.58802	+	3.58802i	0.411574	+	0.411574i
$77$	1.28351	+	2.22311i	0.146270	+	0.253347i
$78$	−5.15885	+	3.51941i	−0.584125	+	0.398495i
$79$	−1.30671	+	2.26329i	−0.147016	+	0.254640i	−0.930123	−	0.367247i	$-0.880300\pi$
$79$	−1.30671	+	2.26329i	−0.147016	+	0.254640i	0.783107	+	0.621887i	$0.213634\pi$
$80$	3.04921	−	0.817032i	0.340912	−	0.0913470i
$81$	−8.78109	+	1.97291i	−0.975677	+	0.219212i
$82$	9.46058	−	5.46207i	1.04475	−	0.603185i
$83$	11.0800	−	2.96889i	1.21619	−	0.325878i	0.407004	−	0.913426i	$-0.366573\pi$
$83$	11.0800	−	2.96889i	1.21619	−	0.325878i	0.809189	+	0.587548i	$0.199907\pi$
$84$	−4.54793	−	2.30074i	−0.496220	−	0.251032i
$85$	10.9825	−	2.94274i	1.19122	−	0.319185i
$86$	6.11991	+	1.63983i	0.659927	+	0.176827i
$87$	−3.05464	+	14.5781i	−0.327491	+	1.56294i
$88$	−0.755487	+	0.436181i	−0.0805352	+	0.0464970i
$89$	−2.10194	−	7.84455i	−0.222805	−	0.831521i	−0.983272	−	0.182144i	$-0.941696\pi$
$89$	−2.10194	−	7.84455i	−0.222805	−	0.831521i	0.760467	−	0.649377i	$-0.224970\pi$
$90$	3.80182	−	8.67369i	0.400747	−	0.914287i
$91$	−7.35197	+	7.64956i	−0.770696	+	0.801892i
$92$	−3.23474	−	1.86758i	−0.337244	−	0.194708i
$93$	7.45431	−	4.87159i	0.772976	−	0.505161i
$94$	−6.32386			−0.652256
$95$	−8.00907	+	13.8721i	−0.821714	+	1.42325i
$96$	0.781868	−	1.54554i	0.0797991	−	0.157741i
$97$	−11.9612	+	11.9612i	−1.21448	+	1.21448i	−0.244941	+	0.969538i	$0.578769\pi$
$97$	−11.9612	+	11.9612i	−1.21448	+	1.21448i	−0.969538	+	0.244941i	$0.921231\pi$
$98$	−1.60249	−	0.429386i	−0.161876	−	0.0433745i
$99$	−0.394445	+	2.58719i	−0.0396432	+	0.260022i
$100$	2.48260	+	4.29998i	0.248260	+	0.429998i
$101$	2.58133	+	4.47099i	0.256851	+	0.444880i	0.965397	−	0.260786i	$-0.0839815\pi$
$101$	2.58133	+	4.47099i	0.256851	+	0.444880i	−0.708545	+	0.705665i	$0.750648\pi$
$102$	2.81609	−	5.56663i	0.278835	−	0.551178i
$103$	7.99184	−	4.61409i	0.787459	−	0.454640i	−0.0516081	−	0.998667i	$-0.516435\pi$
$103$	7.99184	−	4.61409i	0.787459	−	0.454640i	0.839067	+	0.544028i	$0.183101\pi$
$104$	−2.59957	−	2.49844i	−0.254909	−	0.244992i
$105$	3.29963	−	15.7473i	0.322011	−	1.53678i
$106$	−6.50165	−	1.74211i	−0.631496	−	0.169209i
$107$	−0.210437	−	0.121496i	−0.0203437	−	0.0117454i	0.489794	−	0.871838i	$-0.337072\pi$
$107$	−0.210437	−	0.121496i	−0.0203437	−	0.0117454i	−0.510137	+	0.860093i	$0.670405\pi$
$108$	−2.15457	−	4.72841i	−0.207323	−	0.454991i
$109$	2.87971	−	2.87971i	0.275827	−	0.275827i	−0.555614	−	0.831440i	$-0.687517\pi$
$109$	2.87971	−	2.87971i	0.275827	−	0.275827i	0.831440	+	0.555614i	$0.187517\pi$
$110$	−1.94726	−	1.94726i	−0.185664	−	0.185664i
$111$	4.67181	−	9.23488i	0.443429	−	0.876536i
$112$	0.761606	−	2.84235i	0.0719650	−	0.268577i
$113$	2.64736	+	1.52846i	0.249043	+	0.143785i	0.619326	−	0.785134i	$-0.287406\pi$
$113$	2.64736	+	1.52846i	0.249043	+	0.143785i	−0.370283	+	0.928919i	$0.620739\pi$
$114$	2.74005	+	8.35076i	0.256629	+	0.782121i
$115$	3.05174	−	11.3892i	0.284576	−	1.06205i
$116$	−8.59946			−0.798439
$117$	−10.7249	+	1.40584i	−0.991518	+	0.129970i
$118$	−5.51405			−0.507609
$119$	2.74311	−	10.2374i	0.251461	−	0.938464i
$120$	5.35147	+	1.12132i	0.488520	+	0.102362i
$121$	−8.86722	−	5.11949i	−0.806111	−	0.465408i
$122$	−1.64841	+	6.15196i	−0.149240	+	0.556972i
$123$	18.8923	−	1.04490i	1.70346	−	0.0942152i
$124$	3.63546	+	3.63546i	0.326474	+	0.326474i
$125$	0.0776933	−	0.0776933i	0.00694910	−	0.00694910i
$126$	−5.23011	−	7.11176i	−0.465935	−	0.633566i
$127$	16.5577	+	9.55958i	1.46926	+	0.848276i	0.999406	−	0.0344705i	$-0.0109745\pi$
$127$	16.5577	+	9.55958i	1.46926	+	0.848276i	0.469851	+	0.882746i	$0.344308\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	8.17642	+	7.31937i	0.719893	+	0.644435i
$130$	5.49433	−	9.96794i	0.481885	−	0.874246i
$131$	−10.6970	+	6.17593i	−0.934603	+	0.539593i	−0.888264	−	0.459332i	$-0.848089\pi$
$131$	−10.6970	+	6.17593i	−0.934603	+	0.539593i	−0.0463386	+	0.998926i	$0.514755\pi$
$132$	−1.50867	+	0.0834416i	−0.131313	+	0.00726266i
$133$	7.46576	+	12.9311i	0.647363	+	1.12127i
$134$	4.13745	+	7.16627i	0.357421	+	0.619072i
$135$	12.6575	−	10.4330i	1.08939	−	0.897928i
$136$	3.47902	+	0.932200i	0.298323	+	0.0799355i
$137$	−4.91649	+	4.91649i	−0.420044	+	0.420044i	−0.885219	−	0.465175i	$-0.845991\pi$
$137$	−4.91649	+	4.91649i	−0.420044	+	0.420044i	0.465175	+	0.885219i	$0.345991\pi$
$138$	−3.53920	−	5.41554i	−0.301277	−	0.461002i
$139$	2.84060	−	4.92006i	0.240937	−	0.417314i	−0.720045	−	0.693928i	$-0.755879\pi$
$139$	2.84060	−	4.92006i	0.240937	−	0.417314i	0.960981	+	0.276613i	$0.0892121\pi$
$140$	9.28918			0.785079
$141$	−9.77375	−	4.94443i	−0.823099	−	0.416396i
$142$	5.55400	+	3.20660i	0.466081	+	0.269092i
$143$	−0.753658	+	3.05372i	−0.0630240	+	0.255365i
$144$	2.41681	−	1.77736i	0.201401	−	0.148114i
$145$	−7.02603	−	26.2215i	−0.583480	−	2.17758i
$146$	−13.0337	+	7.52499i	−1.07867	+	0.622773i
$147$	−2.14098	−	1.91657i	−0.176585	−	0.158076i
$148$	5.77159	+	1.54649i	0.474422	+	0.127121i
$149$	20.0748	−	5.37903i	1.64459	−	0.440668i	0.686502	−	0.727128i	$-0.259145\pi$
$149$	20.0748	−	5.37903i	1.64459	−	0.440668i	0.958092	+	0.286461i	$0.0924787\pi$
$150$	0.474922	+	8.58684i	0.0387772	+	0.701113i
$151$	7.11970	−	1.90772i	0.579393	−	0.155248i	0.0427921	−	0.999084i	$-0.486375\pi$
$151$	7.11970	−	1.90772i	0.579393	−	0.155248i	0.536601	+	0.843836i	$0.319708\pi$
$152$	−4.39440	+	2.53711i	−0.356433	+	0.205787i
$153$	8.70474	−	6.40161i	0.703737	−	0.517540i
$154$	−2.47956	+	0.664396i	−0.199809	+	0.0535386i
$155$	−8.11497	+	14.0555i	−0.651810	+	1.12897i
$156$	−2.06428	−	5.89396i	−0.165275	−	0.471894i
$157$	−5.21020	−	9.02434i	−0.415819	−	0.720220i	0.579695	−	0.814834i	$-0.303172\pi$
$157$	−5.21020	−	9.02434i	−0.415819	−	0.720220i	−0.995514	+	0.0946134i	$0.969838\pi$
$158$	−1.84797	−	1.84797i	−0.147016	−	0.147016i
$159$	−8.68643	−	7.77593i	−0.688879	−	0.616671i
$160$			3.15677i			0.249565i
$161$	−7.77191	−	7.77191i	−0.612512	−	0.612512i
$162$	0.367028	−	8.99251i	0.0288364	−	0.706519i
$163$	1.76529	−	6.58816i	0.138268	−	0.516025i	−0.861695	−	0.507427i	$-0.830597\pi$
$163$	1.76529	−	6.58816i	0.138268	−	0.516025i	0.999963	−	0.00859756i	$-0.00273672\pi$
$164$	2.82738	+	10.5519i	0.220781	+	0.823966i
$165$	−1.48706	−	4.53207i	−0.115768	−	0.352821i
$166$			11.4709i			0.890315i
$167$	−9.73117	+	9.73117i	−0.753021	+	0.753021i	−0.975042	−	0.222021i	$-0.928735\pi$
$167$	−9.73117	+	9.73117i	−0.753021	+	0.753021i	0.222021	+	0.975042i	$0.428735\pi$
$168$	3.39944	−	3.79748i	0.262272	−	0.292982i
$169$	−12.9898	+	0.515565i	−0.999213	+	0.0396588i
$170$			11.3699i			0.872030i
$171$	−2.29435	+	15.0488i	−0.175453	+	1.15081i
$172$	−3.16790	+	5.48696i	−0.241550	+	0.418377i
$173$	4.06007			0.308682			0.154341	−	0.988018i	$-0.450675\pi$
$173$	4.06007			0.308682			0.154341	+	0.988018i	$0.450675\pi$
$174$	−13.2908	−	6.72364i	−1.00757	−	0.509718i
$175$	3.78152	+	14.1128i	0.285856	+	1.06683i
$176$	−0.225784	−	0.842637i	−0.0170191	−	0.0635161i
$177$	−8.52216	−	4.31126i	−0.640565	−	0.324054i
$178$	8.12128			0.608715
$179$	9.70640	−	16.8120i	0.725490	−	1.25659i	−0.233282	−	0.972409i	$-0.574946\pi$
$179$	9.70640	−	16.8120i	0.725490	−	1.25659i	0.958772	−	0.284177i	$-0.0917203\pi$
$180$	7.39416	+	5.91719i	0.551128	+	0.441041i
$181$			0.0982851i			0.00730547i	0.999993	+	0.00365274i	$0.00116270\pi$
$181$			0.0982851i			0.00730547i	−0.999993	+	0.00365274i	$0.998837\pi$
$182$	−5.48608	−	9.08131i	−0.406655	−	0.673152i
$183$	−7.35770	+	8.21923i	−0.543897	+	0.607583i
$184$	2.64115	−	2.64115i	0.194708	−	0.194708i
$185$			18.8623i			1.38678i
$186$	2.77628	+	8.46117i	0.203567	+	0.620403i
$187$	−0.813216	−	3.03496i	−0.0594682	−	0.221938i
$188$	1.63674	−	6.10838i	0.119371	−	0.445499i
$189$	−2.52286	−	15.0807i	−0.183511	−	1.09696i
$190$	−11.3265	−	11.3265i	−0.821714	−	0.821714i
$191$			12.6972i			0.918735i	0.888246	+	0.459367i	$0.151924\pi$
$191$			12.6972i			0.918735i	−0.888246	+	0.459367i	$0.848076\pi$
$192$	1.29051	+	1.15524i	0.0931346	+	0.0833723i
$193$	16.7784	+	16.7784i	1.20774	+	1.20774i	0.971758	+	0.235981i	$0.0758303\pi$
$193$	16.7784	+	16.7784i	1.20774	+	1.20774i	0.235981	+	0.971758i	$0.424170\pi$
$194$	−8.45787	−	14.6495i	−0.607240	−	1.05177i
$195$	16.2853	−	11.1100i	1.16621	−	0.795602i
$196$	0.829510	−	1.43675i	0.0592507	−	0.102625i
$197$	5.16169	−	1.38307i	0.367755	−	0.0985397i	−0.0702085	−	0.997532i	$-0.522366\pi$
$197$	5.16169	−	1.38307i	0.367755	−	0.0985397i	0.437964	+	0.898993i	$0.355700\pi$
$198$	−2.39694	−	1.05062i	−0.170343	−	0.0746642i
$199$	−7.44445	+	4.29806i	−0.527723	+	0.304681i	−0.740089	−	0.672509i	$-0.765217\pi$
$199$	−7.44445	+	4.29806i	−0.527723	+	0.304681i	0.212366	+	0.977190i	$0.431883\pi$
$200$	−4.79601	+	1.28509i	−0.339129	+	0.0908694i
$201$	0.791496	+	14.3107i	0.0558278	+	1.00940i
$202$	−4.98674	+	1.33619i	−0.350866	+	0.0940142i
$203$	−24.4427	−	6.54940i	−1.71554	−	0.459678i
$204$	4.64809	+	4.16088i	0.325432	+	0.291320i
$205$	−29.8649	+	17.2425i	−2.08585	+	1.20427i
$206$	2.38843	+	8.91374i	0.166410	+	0.621050i
$207$	−1.23572	−	11.1371i	−0.0858888	−	0.774082i
$208$	3.08613	−	1.86435i	0.213985	−	0.129269i
$209$	3.83351	+	2.21328i	0.265169	+	0.153096i
$210$	14.3568	+	7.26291i	0.990711	+	0.501189i
$211$	−9.74147			−0.670630			−0.335315	−	0.942106i	$-0.608843\pi$
$211$	−9.74147			−0.670630			−0.335315	+	0.942106i	$0.608843\pi$
$212$	3.36550	−	5.82922i	0.231144	−	0.400352i
$213$	6.07677	+	9.29842i	0.416373	+	0.637117i
$214$	0.171821	−	0.171821i	0.0117454	−	0.0117454i
$215$	−19.3191	−	5.17655i	−1.31755	−	0.353038i
$216$	5.12493	−	0.857352i	0.348708	−	0.0583354i
$217$	7.56446	+	13.1020i	0.513509	+	0.889424i
$218$	2.03627	+	3.52692i	0.137913	+	0.238873i
$219$	−26.0276	+	1.43953i	−1.75878	+	0.0972747i
$220$	2.38490	−	1.37692i	0.160790	−	0.0928321i
$221$	11.1155	−	6.71492i	0.747706	−	0.451694i
$222$	7.71105	+	6.90279i	0.517532	+	0.463285i
$223$	−18.3352	−	4.91290i	−1.22782	−	0.328992i	−0.414087	−	0.910237i	$-0.635899\pi$
$223$	−18.3352	−	4.91290i	−1.22782	−	0.328992i	−0.813729	+	0.581245i	$0.802566\pi$
$224$	2.54838	+	1.47131i	0.170271	+	0.0983061i
$225$	−5.97977	+	13.6426i	−0.398651	+	0.909507i
$226$	−2.16156	+	2.16156i	−0.143785	+	0.143785i
$227$	−10.9382	−	10.9382i	−0.725991	−	0.725991i	0.243827	−	0.969819i	$-0.421597\pi$
$227$	−10.9382	−	10.9382i	−0.725991	−	0.725991i	−0.969819	+	0.243827i	$0.921597\pi$
$228$	−8.77540	+	0.485351i	−0.581165	+	0.0321431i
$229$	3.92348	−	14.6426i	0.259271	−	0.967612i	−0.706394	−	0.707819i	$-0.749679\pi$
$229$	3.92348	−	14.6426i	0.259271	−	0.967612i	0.965664	−	0.259792i	$-0.0836542\pi$
$230$	10.2113	+	5.89551i	0.673314	+	0.388738i
$231$	−4.35172	−	0.911841i	−0.286322	−	0.0599948i
$232$	2.22570	−	8.30644i	0.146125	−	0.545344i
$233$	11.5129			0.754237			0.377118	−	0.926165i	$-0.376915\pi$
$233$	11.5129			0.754237			0.377118	+	0.926165i	$0.376915\pi$
$234$	1.41788	−	10.7233i	0.0926896	−	0.701005i
$235$	19.9630			1.30224
$236$	1.42714	−	5.32616i	0.0928989	−	0.346704i
$237$	−1.41123	−	4.30097i	−0.0916695	−	0.279378i
$238$	9.17863	+	5.29929i	0.594963	+	0.343502i
$239$	1.04280	−	3.89177i	0.0674528	−	0.251737i	−0.923963	−	0.382481i	$-0.875070\pi$
$239$	1.04280	−	3.89177i	0.0674528	−	0.251737i	0.991416	+	0.130743i	$0.0417364\pi$
$240$	−2.46818	+	4.87890i	−0.159320	+	0.314932i
$241$	10.4725	+	10.4725i	0.674591	+	0.674591i	0.958771	−	0.284180i	$-0.0917212\pi$
$241$	10.4725	+	10.4725i	0.674591	+	0.674591i	−0.284180	+	0.958771i	$0.591721\pi$
$242$	7.24006	−	7.24006i	0.465408	−	0.465408i
$243$	7.59822	−	13.6113i	0.487426	−	0.873164i
$244$	−5.51569	−	3.18449i	−0.353106	−	0.203866i
$245$	5.05869	+	1.35547i	0.323188	+	0.0865980i
$246$	−3.88039	+	18.5190i	−0.247405	+	1.18073i
$247$	−4.38376	+	17.7624i	−0.278932	+	1.13019i
$248$	−4.45251	+	2.57066i	−0.282734	+	0.163237i
$249$	−8.96874	+	17.7287i	−0.568371	+	1.12351i
$250$	0.0549375	+	0.0951545i	0.00347455	+	0.00601810i
$251$	−1.98281	−	3.43432i	−0.125154	−	0.216772i	0.796639	−	0.604455i	$-0.206609\pi$
$251$	−1.98281	−	3.43432i	−0.125154	−	0.216772i	−0.921793	+	0.387682i	$0.873276\pi$
$252$	8.22309	−	3.21124i	0.518006	−	0.202289i
$253$	−3.14737	−	0.843337i	−0.197874	−	0.0530201i
$254$	−13.5193	+	13.5193i	−0.848276	+	0.848276i
$255$	−8.88975	+	17.5726i	−0.556698	+	1.10044i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.8559			−0.864307			−0.432153	−	0.901800i	$-0.642246\pi$
$257$	−13.8559			−0.864307			−0.432153	+	0.901800i	$0.642246\pi$
$258$	−9.18618	+	6.00342i	−0.571907	+	0.373756i
$259$	15.2271	+	8.79137i	0.946165	+	0.546269i
$260$	8.20625	+	7.88701i	0.508930	+	0.489132i
$261$	−15.2844	−	20.7833i	−0.946078	−	1.28645i
$262$	−3.19690	−	11.9310i	−0.197505	−	0.737098i
$263$	13.8744	−	8.01036i	0.855529	−	0.493940i	−0.00698346	−	0.999976i	$-0.502223\pi$
$263$	13.8744	−	8.01036i	0.855529	−	0.493940i	0.862513	+	0.506036i	$0.168890\pi$
$264$	0.309874	−	1.47886i	0.0190714	−	0.0910174i
$265$	20.5242	+	5.49945i	1.26079	+	0.337828i
$266$	−14.4227	+	3.86456i	−0.884314	+	0.236951i
$267$	12.5517	+	6.34977i	0.768153	+	0.388600i
$268$	−7.99294	+	2.14170i	−0.488246	+	0.130825i
$269$	−1.90561	+	1.10021i	−0.116187	+	0.0670808i	−0.556967	−	0.830534i	$-0.688035\pi$
$269$	−1.90561	+	1.10021i	−0.116187	+	0.0670808i	0.440780	+	0.897615i	$0.354702\pi$
$270$	6.80148	+	14.9265i	0.413925	+	0.908397i
$271$	−5.96826	+	1.59919i	−0.362546	+	0.0971439i	−0.435494	−	0.900192i	$-0.643426\pi$
$271$	−5.96826	+	1.59919i	−0.362546	+	0.0971439i	0.0729474	+	0.997336i	$0.476759\pi$
$272$	−1.80087	+	3.11920i	−0.109194	+	0.189129i
$273$	−1.37854	−	18.3249i	−0.0834331	−	1.10907i
$274$	−3.47648	−	6.02145i	−0.210022	−	0.363769i
$275$	3.06279	+	3.06279i	0.184693	+	0.184693i
$276$	6.14703	−	2.01696i	0.370007	−	0.121407i
$277$		−	20.4207i		−	1.22696i	−0.789711	−	0.613479i	$-0.789769\pi$
$277$		−	20.4207i		−	1.22696i	0.789711	−	0.613479i	$-0.210231\pi$
$278$	4.01721	+	4.01721i	0.240937	+	0.240937i
$279$	−2.32468	+	15.2477i	−0.139175	+	0.912858i
$280$	−2.40422	+	8.97266i	−0.143679	+	0.536219i
$281$	5.37665	+	20.0659i	0.320744	+	1.19703i	0.918521	+	0.395372i	$0.129384\pi$
$281$	5.37665	+	20.0659i	0.320744	+	1.19703i	−0.597777	+	0.801662i	$0.703949\pi$
$282$	7.30558	−	8.16101i	0.435041	−	0.485981i
$283$		−	24.1047i		−	1.43287i	−0.697652	−	0.716436i	$-0.745772\pi$
$283$		−	24.1047i		−	1.43287i	0.697652	−	0.716436i	$-0.254228\pi$
$284$	−4.53482	+	4.53482i	−0.269092	+	0.269092i
$285$	−8.64971	−	26.3614i	−0.512365	−	1.56152i
$286$	−2.75460	−	1.51834i	−0.162883	−	0.0897812i
$287$			32.1456i			1.89750i
$288$	1.09128	+	2.79448i	0.0643046	+	0.164666i
$289$	2.01371	−	3.48785i	0.118454	−	0.205168i
$290$	27.1465			1.59410
$291$	−1.61799	−	29.2542i	−0.0948485	−	1.71491i
$292$	−3.89522	−	14.5372i	−0.227951	−	0.850723i
$293$	−0.671035	−	2.50434i	−0.0392023	−	0.146305i	0.943551	−	0.331228i	$-0.107463\pi$
$293$	−0.671035	−	2.50434i	−0.0392023	−	0.146305i	−0.982753	+	0.184923i	$0.940796\pi$
$294$	2.40539	−	1.57199i	0.140285	−	0.0916801i
$295$	17.4066			1.01345
$296$	−2.98760	+	5.17467i	−0.173651	+	0.300772i
$297$	−2.88312	−	3.49786i	−0.167295	−	0.202967i
$298$			20.7830i			1.20393i
$299$	−0.267101	−	13.4646i	−0.0154468	−	0.778680i
$300$	−8.41717	−	1.76370i	−0.485966	−	0.101827i
$301$	−13.1832	+	13.1832i	−0.759867	+	0.759867i
$302$			7.37086i			0.424145i
$303$	−8.75191	−	1.83384i	−0.502784	−	0.105351i
$304$	−1.31331	−	4.90132i	−0.0753232	−	0.281110i
$305$	5.20366	−	19.4203i	0.297961	−	1.11200i
$306$	3.93053	+	10.0650i	0.224693	+	0.575377i
$307$	0.409589	+	0.409589i	0.0233765	+	0.0233765i	0.718698	−	0.695322i	$-0.244738\pi$
$307$	0.409589	+	0.409589i	0.0233765	+	0.0233765i	−0.695322	+	0.718698i	$0.744738\pi$
$308$		−	2.56703i		−	0.146270i
$309$	−3.27797	+	15.6439i	−0.186477	+	0.889953i
$310$	−11.4763	−	11.4763i	−0.651810	−	0.651810i
$311$	−8.67641	−	15.0280i	−0.491994	−	0.852159i	0.507963	−	0.861379i	$-0.330398\pi$
$311$	−8.67641	−	15.0280i	−0.491994	−	0.852159i	−0.999957	+	0.00921998i	$0.997065\pi$
$312$	6.22740	−	0.468474i	0.352557	−	0.0265221i
$313$	12.3328	−	21.3610i	0.697089	−	1.20739i	−0.272382	−	0.962189i	$-0.587812\pi$
$313$	12.3328	−	21.3610i	0.697089	−	1.20739i	0.969471	−	0.245205i	$-0.0788552\pi$
$314$	10.0653	−	2.69700i	0.568020	−	0.152200i
$315$	16.5102	+	22.4502i	0.930247	+	1.26492i
$316$	2.26329	−	1.30671i	0.127320	−	0.0735082i
$317$	24.1300	−	6.46561i	1.35528	−	0.363145i	0.493196	−	0.869918i	$-0.335828\pi$
$317$	24.1300	−	6.46561i	1.35528	−	0.363145i	0.862080	+	0.506773i	$0.169162\pi$
$318$	9.75919	−	6.37789i	0.547268	−	0.357654i
$319$	−7.24622	+	1.94162i	−0.405710	+	0.108710i
$320$	−3.04921	−	0.817032i	−0.170456	−	0.0456735i
$321$	0.399896	−	0.131214i	0.0223200	−	0.00732365i
$322$	9.51860	−	5.49557i	0.530451	−	0.306256i
$323$	−4.73019	−	17.6533i	−0.263195	−	0.982257i
$324$	8.59111	+	2.68196i	0.477284	+	0.148998i
$325$	−8.64188	+	15.6783i	−0.479365	+	0.869675i
$326$	5.90679	+	3.41028i	0.327147	+	0.188878i
$327$	0.389539	+	7.04307i	0.0215415	+	0.389482i
$328$	−10.9241			−0.603185
$329$	9.30436	−	16.1156i	0.512966	−	0.888483i
$330$	4.76252	−	0.263406i	0.262168	−	0.0145000i
$331$	22.7569	−	22.7569i	1.25083	−	1.25083i	0.295486	−	0.955347i	$-0.404518\pi$
$331$	22.7569	−	22.7569i	1.25083	−	1.25083i	0.955347	−	0.295486i	$-0.0954817\pi$
$332$	−11.0800	−	2.96889i	−0.608097	−	0.162939i
$333$	6.52064	+	16.6975i	0.357329	+	0.915019i
$334$	−6.88098	−	11.9182i	−0.376510	−	0.652135i
$335$	−13.0610	−	22.6223i	−0.713597	−	1.23599i
$336$	2.78825	+	4.26647i	0.152111	+	0.232755i
$337$	−25.7601	+	14.8726i	−1.40324	+	0.810161i	−0.994724	−	0.102590i	$-0.967287\pi$
$337$	−25.7601	+	14.8726i	−1.40324	+	0.810161i	−0.408516	+	0.912751i	$0.633954\pi$
$338$	2.86400	−	12.6806i	0.155781	−	0.689733i
$339$	−5.03083	+	1.65072i	−0.273237	+	0.0896546i
$340$	−10.9825	−	2.94274i	−0.595608	−	0.159593i
$341$	3.88419	+	2.24254i	0.210341	+	0.121440i
$342$	−13.9422	−	6.11108i	−0.753906	−	0.330449i
$343$	−11.1132	+	11.1132i	−0.600058	+	0.600058i
$344$	−4.48009	−	4.48009i	−0.241550	−	0.241550i
$345$	11.1724	+	17.0956i	0.601504	+	0.920397i
$346$	−1.05082	+	3.92173i	−0.0564927	+	0.210833i
$347$	29.4281	+	16.9903i	1.57978	+	0.912088i	0.994889	+	0.100978i	$0.0321972\pi$
$347$	29.4281	+	16.9903i	1.57978	+	0.912088i	0.584894	+	0.811110i	$0.301136\pi$
$348$	9.93444	−	11.0977i	0.532542	−	0.594899i
$349$	−2.12443	+	7.92850i	−0.113718	+	0.424403i	−0.999188	−	0.0402949i	$-0.987170\pi$
$349$	−2.12443	+	7.92850i	−0.113718	+	0.424403i	0.885469	+	0.464698i	$0.153837\pi$
$350$	−14.6107			−0.780974
$351$	10.5756	−	15.4647i	0.564484	−	0.825444i
$352$	0.872362			0.0464970
$353$	4.06187	−	15.1591i	0.216192	−	0.806838i	−0.769552	−	0.638584i	$-0.779521\pi$
$353$	4.06187	−	15.1591i	0.216192	−	0.806838i	0.985744	−	0.168254i	$-0.0538128\pi$
$354$	6.37005	−	7.11594i	0.338565	−	0.378208i
$355$	−17.5327	−	10.1225i	−0.930539	−	0.537247i
$356$	−2.10194	+	7.84455i	−0.111403	+	0.415760i
$357$	10.0426	+	15.3667i	0.531509	+	0.813293i
$358$	13.7269	+	13.7269i	0.725490	+	0.725490i
$359$	12.5155	−	12.5155i	0.660544	−	0.660544i	−0.294964	−	0.955508i	$-0.595308\pi$
$359$	12.5155	−	12.5155i	0.660544	−	0.660544i	0.955508	+	0.294964i	$0.0953077\pi$
$360$	−7.62932	+	5.61073i	−0.402100	+	0.295711i
$361$	5.84370	+	3.37386i	0.307563	+	0.177572i
$362$	−0.0949361	−	0.0254381i	−0.00498973	−	0.00133699i
$363$	16.8505	−	5.52900i	0.884424	−	0.290197i
$364$	10.1918	−	2.94873i	0.534194	−	0.154555i
$365$	41.1443	−	23.7547i	2.15359	−	1.24338i
$366$	−6.03486	−	9.23429i	−0.315447	−	0.482684i
$367$	−13.2121	−	22.8840i	−0.689666	−	1.19454i	−0.971946	−	0.235204i	$-0.924424\pi$
$367$	−13.2121	−	22.8840i	−0.689666	−	1.19454i	0.282280	−	0.959332i	$-0.408909\pi$
$368$	1.86758	+	3.23474i	0.0973541	+	0.168622i
$369$	−20.4767	+	25.5878i	−1.06597	+	1.33205i
$370$	−18.2196	−	4.88192i	−0.947191	−	0.253799i
$371$	14.0055	−	14.0055i	0.727130	−	0.727130i
$372$	−8.89142	+	0.491768i	−0.460999	+	0.0254970i
$373$	−11.3495	+	19.6580i	−0.587656	+	1.01785i	0.406883	+	0.913480i	$0.366616\pi$
$373$	−11.3495	+	19.6580i	−0.587656	+	1.01785i	−0.994539	+	0.104370i	$0.966718\pi$
$374$	3.14202			0.162470
$375$	0.0105096	+	0.190019i	0.000542712	+	0.00981252i
$376$	5.47662	+	3.16193i	0.282435	+	0.163064i
$377$	−16.0324	−	26.5390i	−0.825711	−	1.36683i
$378$	15.2198	+	1.46629i	0.782824	+	0.0754176i
$379$	−2.62959	−	9.81377i	−0.135073	−	0.504100i	−0.999998	−	0.00219770i	$-0.999300\pi$
$379$	−2.62959	−	9.81377i	−0.135073	−	0.504100i	0.864924	−	0.501902i	$-0.167366\pi$
$380$	13.8721	−	8.00907i	0.711625	−	0.410857i
$381$	−31.4648	+	10.3242i	−1.61199	+	0.528927i
$382$	−12.2645	−	3.28627i	−0.627508	−	0.168140i
$383$	−18.0806	+	4.84467i	−0.923874	+	0.247551i	−0.689240	−	0.724533i	$-0.742056\pi$
$383$	−18.0806	+	4.84467i	−0.923874	+	0.247551i	−0.234633	+	0.972084i	$0.575389\pi$
$384$	−1.44989	+	0.947539i	−0.0739892	+	0.0483539i
$385$	7.82740	−	2.09735i	0.398921	−	0.106891i
$386$	−20.5493	+	11.8641i	−1.04593	+	0.603869i
$387$	−18.8915	+	2.09611i	−0.960307	+	0.106551i
$388$	16.3393	−	4.37811i	0.829505	−	0.222265i
$389$	−10.9802	+	19.0182i	−0.556716	+	0.964261i	0.441051	+	0.897482i	$0.354606\pi$
$389$	−10.9802	+	19.0182i	−0.556716	+	0.964261i	−0.997768	+	0.0667792i	$0.978728\pi$
$390$	6.51646	+	18.6059i	0.329974	+	0.942145i
$391$	6.72653	+	11.6507i	0.340175	+	0.589201i
$392$	1.17310	+	1.17310i	0.0592507	+	0.0592507i
$393$	4.38753	−	20.9393i	0.221322	−	1.05625i
$394$			5.34378i			0.269216i
$395$	5.83361	+	5.83361i	0.293521	+	0.293521i
$396$	1.63519	−	2.04335i	0.0821716	−	0.102682i
$397$	0.908301	−	3.38983i	0.0455863	−	0.170130i	−0.939380	−	0.342879i	$-0.888598\pi$
$397$	0.908301	−	3.38983i	0.0455863	−	0.170130i	0.984966	+	0.172748i	$0.0552647\pi$
$398$	−2.22484	−	8.30321i	−0.111521	−	0.416202i
$399$	−25.3124	−	5.30386i	−1.26721	−	0.265525i
$400$		−	4.96519i		−	0.248260i
$401$	−1.78155	+	1.78155i	−0.0889663	+	0.0889663i	−0.750189	−	0.661223i	$-0.770038\pi$
$401$	−1.78155	+	1.78155i	−0.0889663	+	0.0889663i	0.661223	+	0.750189i	$0.270038\pi$
$402$	−14.0279	−	2.93935i	−0.699648	−	0.146601i
$403$	−4.44172	+	17.9972i	−0.221258	+	0.896507i
$404$		−	5.16265i		−	0.256851i
$405$	−1.15862	+	28.3873i	−0.0575724	+	1.41058i
$406$	12.6525	−	21.9147i	0.627932	−	1.08761i
$407$	5.21253			0.258375
$408$	−5.22212	+	3.41280i	−0.258533	+	0.168959i
$409$	4.46385	+	16.6593i	0.220723	+	0.823751i	0.984073	+	0.177765i	$0.0568867\pi$
$409$	4.46385	+	16.6593i	0.220723	+	0.823751i	−0.763350	+	0.645986i	$0.776447\pi$
$410$	−8.92537	−	33.3099i	−0.440793	−	1.64506i
$411$	−0.665053	−	12.0245i	−0.0328046	−	0.593126i
$412$	−9.22818			−0.454640
$413$	8.11288	−	14.0519i	0.399209	−	0.691450i
$414$	11.0774	+	1.68888i	0.544427	+	0.0830038i
$415$		−	36.2110i		−	1.77753i
$416$	1.00208	+	3.46350i	0.0491308	+	0.169812i
$417$	3.06782	+	9.34968i	0.150232	+	0.457856i
$418$	−3.13005	+	3.13005i	−0.153096	+	0.153096i
$419$			18.7654i			0.916750i	0.888759	+	0.458375i	$0.151568\pi$
$419$			18.7654i			0.916750i	−0.888759	+	0.458375i	$0.848432\pi$
$420$	−10.7312	+	11.9878i	−0.523631	+	0.584944i
$421$	6.19861	+	23.1335i	0.302102	+	1.12746i	0.935412	+	0.353560i	$0.115029\pi$
$421$	6.19861	+	23.1335i	0.302102	+	1.12746i	−0.633310	+	0.773898i	$0.718304\pi$
$422$	2.52128	−	9.40954i	0.122734	−	0.458049i
$423$	17.6719	−	6.90113i	0.859236	−	0.335545i
$424$	4.75954	+	4.75954i	0.231144	+	0.231144i
$425$		−	17.8834i		−	0.867471i
$426$	−10.5544	+	3.46310i	−0.511361	+	0.167788i
$427$	−13.2522	−	13.2522i	−0.641320	−	0.641320i
$428$	0.121496	+	0.210437i	0.00587271	+	0.0101718i
$429$	−3.07020	−	4.50038i	−0.148231	−	0.217281i
$430$	10.0003	−	17.3211i	0.482259	−	0.835296i
$431$	0.739992	−	0.198280i	0.0356441	−	0.00955082i	−0.240953	−	0.970537i	$-0.577460\pi$
$431$	0.739992	−	0.198280i	0.0356441	−	0.00955082i	0.276597	+	0.960986i	$0.410793\pi$
$432$	−0.498292	+	5.17221i	−0.0239741	+	0.248848i
$433$	12.3652	−	7.13904i	0.594233	−	0.343080i	−0.172537	−	0.985003i	$-0.555196\pi$
$433$	12.3652	−	7.13904i	0.594233	−	0.343080i	0.766769	+	0.641923i	$0.221863\pi$
$434$	−14.6134	+	3.91565i	−0.701467	+	0.187957i
$435$	41.9559	+	21.2250i	2.01163	+	1.01766i
$436$	−3.93376	+	1.05405i	−0.188393	+	0.0504798i
$437$	−18.3072	−	4.90539i	−0.875751	−	0.234657i
$438$	5.34594	−	25.5133i	0.255439	−	1.21907i
$439$	−10.9885	+	6.34419i	−0.524451	+	0.302792i	−0.738754	−	0.673975i	$-0.764585\pi$
$439$	−10.9885	+	6.34419i	−0.524451	+	0.302792i	0.214303	+	0.976767i	$0.431252\pi$
$440$	0.712747	+	2.66001i	0.0339789	+	0.126811i
$441$	4.94670	−	0.548865i	0.235557	−	0.0261364i
$442$	3.60922	+	12.4747i	0.171673	+	0.593359i
$443$	9.00475	+	5.19889i	0.427828	+	0.247007i	0.698421	−	0.715687i	$-0.253886\pi$
$443$	9.00475	+	5.19889i	0.427828	+	0.247007i	−0.270593	+	0.962694i	$0.587220\pi$
$444$	−8.66335	+	5.66173i	−0.411144	+	0.268694i
$445$	−25.6370			−1.21531
$446$	9.49100	−	16.4389i	0.449412	−	0.778404i
$447$	−16.2496	+	32.1209i	−0.768578	+	1.51926i
$448$	−2.08075	+	2.08075i	−0.0983061	+	0.0983061i
$449$	8.91529	+	2.38885i	0.420739	+	0.112737i	0.462976	−	0.886371i	$-0.346782\pi$
$449$	8.91529	+	2.38885i	0.420739	+	0.112737i	−0.0422369	+	0.999108i	$0.513448\pi$
$450$	−11.6301	−	9.30698i	−0.548247	−	0.438735i
$451$	4.76490	+	8.25305i	0.224370	+	0.388621i
$452$	−1.52846	−	2.64736i	−0.0718925	−	0.124521i
$453$	−5.76304	+	11.3919i	−0.270771	+	0.535239i
$454$	13.3965	−	7.73445i	0.628727	−	0.362996i
$455$	17.3183	+	28.6676i	0.811894	+	1.34396i
$456$	1.80243	−	8.60200i	0.0844064	−	0.402826i
$457$	8.40882	+	2.25314i	0.393348	+	0.105397i	0.450071	−	0.892993i	$-0.351399\pi$
$457$	8.40882	+	2.25314i	0.393348	+	0.105397i	−0.0567231	+	0.998390i	$0.518065\pi$
$458$	13.1282	+	7.57958i	0.613441	+	0.354170i
$459$	−1.79472	+	18.6290i	−0.0837704	+	0.869526i
$460$	−8.33750	+	8.33750i	−0.388738	+	0.388738i
$461$	7.38995	+	7.38995i	0.344184	+	0.344184i	0.857938	−	0.513753i	$-0.171745\pi$
$461$	7.38995	+	7.38995i	0.344184	+	0.344184i	−0.513753	+	0.857938i	$0.671745\pi$
$462$	2.00708	−	3.96744i	0.0933778	−	0.184582i
$463$	−1.45201	+	5.41897i	−0.0674806	+	0.251841i	−0.991423	−	0.130690i	$-0.958281\pi$
$463$	−1.45201	+	5.41897i	−0.0674806	+	0.251841i	0.923943	+	0.382531i	$0.124947\pi$
$464$	7.44735	+	4.29973i	0.345734	+	0.199610i
$465$	−8.76408	−	26.7100i	−0.406424	−	1.23865i
$466$	−2.97976	+	11.1206i	−0.138035	+	0.515153i
$467$	−11.8737			−0.549447			−0.274724	−	0.961523i	$-0.588586\pi$
$467$	−11.8737			−0.549447			−0.274724	+	0.961523i	$0.588586\pi$
$468$	9.99096	+	4.14496i	0.461832	+	0.191601i
$469$	−24.3499			−1.12437
$470$	−5.16680	+	19.2827i	−0.238327	+	0.889447i
$471$	17.6650	+	3.70146i	0.813962	+	0.170554i
$472$	4.77531	+	2.75702i	0.219801	+	0.126902i
$473$	−1.43052	+	5.33877i	−0.0657754	+	0.245477i
$474$	4.51967	−	0.249974i	0.207595	−	0.0114817i
$475$	17.8152	+	17.8152i	0.817417	+	0.817417i
$476$	−7.49432	+	7.49432i	−0.343502	+	0.343502i
$477$	20.0698	−	2.22686i	0.918935	−	0.101961i
$478$	3.48926	+	2.01453i	0.159595	+	0.0921423i
$479$	30.3482	+	8.13177i	1.38664	+	0.371550i	0.873530	−	0.486771i	$-0.161825\pi$
$479$	30.3482	+	8.13177i	1.38664	+	0.371550i	0.513113	+	0.858321i	$0.328492\pi$
$480$	−4.07385	−	3.64683i	−0.185945	−	0.166454i
$481$	5.98759	+	20.6951i	0.273011	+	0.943615i
$482$	−12.8261	+	7.40516i	−0.584213	+	0.337296i
$483$	19.0082	−	1.05130i	0.864901	−	0.0478360i
$484$	5.11949	+	8.86722i	0.232704	+	0.403056i
$485$	26.6995	+	46.2450i	1.21236	+	2.09988i
$486$	11.1809	+	10.8622i	0.507177	+	0.492718i
$487$	−25.9413	−	6.95096i	−1.17551	−	0.314978i	−0.382368	−	0.924010i	$-0.624891\pi$
$487$	−25.9413	−	6.95096i	−1.17551	−	0.314978i	−0.793145	+	0.609032i	$0.791558\pi$
$488$	4.50355	−	4.50355i	0.203866	−	0.203866i
$489$	6.46276	+	9.88905i	0.292256	+	0.447198i
$490$	−2.61857	+	4.53550i	−0.118295	+	0.204893i
$491$	2.67459			0.120702			0.0603512	−	0.998177i	$-0.480778\pi$
$491$	2.67459			0.120702			0.0603512	+	0.998177i	$0.480778\pi$
$492$	−16.8837	−	8.54124i	−0.761174	−	0.385069i
$493$	26.8235	+	15.4865i	1.20807	+	0.697478i
$494$	−16.0226	−	8.83164i	−0.720889	−	0.397354i
$495$	7.56660	+	3.31656i	0.340093	+	0.149068i
$496$	−1.33067	−	4.96612i	−0.0597488	−	0.222986i
$497$	−16.3433	+	9.43582i	−0.733098	+	0.423254i
$498$	−14.8033	−	13.2517i	−0.663353	−	0.593821i
$499$	4.32098	+	1.15780i	0.193434	+	0.0518304i	0.354235	−	0.935156i	$-0.384741\pi$
$499$	4.32098	+	1.15780i	0.193434	+	0.0518304i	−0.160802	+	0.986987i	$0.551408\pi$
$500$	−0.106131	+	0.0284377i	−0.00474633	+	0.00127177i
$501$	−1.31633	−	23.8000i	−0.0588095	−	1.06331i
$502$	3.83049	−	1.02638i	0.170963	−	0.0458094i
$503$	−35.5709	+	20.5369i	−1.58603	+	0.915694i	−0.592076	+	0.805882i	$0.701692\pi$
$503$	−35.5709	+	20.5369i	−1.58603	+	0.915694i	−0.993952	+	0.109812i	$0.964975\pi$
$504$	0.973527	+	8.77402i	0.0433643	+	0.390826i
$505$	15.7420	−	4.21805i	0.700509	−	0.187701i
$506$	1.62920	−	2.82186i	0.0724268	−	0.125447i
$507$	14.3410	−	17.3590i	0.636905	−	0.770942i
$508$	−9.55958	−	16.5577i	−0.424138	−	0.734628i
$509$	6.73502	+	6.73502i	0.298525	+	0.298525i	0.840436	−	0.541911i	$-0.182299\pi$
$509$	6.73502	+	6.73502i	0.298525	+	0.298525i	−0.541911	+	0.840436i	$0.682299\pi$
$510$	−14.6730	−	13.1350i	−0.649729	−	0.581625i
$511$		−	44.2864i		−	1.95911i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−16.7701	−	20.3458i	−0.740417	−	0.898291i
$514$	3.58617	−	13.3838i	0.158179	−	0.590333i
$515$	−7.53972	−	28.1386i	−0.332240	−	1.23994i
$516$	−3.42130	−	10.4270i	−0.150614	−	0.459022i
$517$		−	5.51669i		−	0.242624i
$518$	−12.4329	+	12.4329i	−0.546269	+	0.546269i
$519$	−4.69036	+	5.23957i	−0.205884	+	0.229991i
$520$	−9.74220	+	5.88533i	−0.427224	+	0.258089i
$521$			8.13120i			0.356234i	0.984009	+	0.178117i	$0.0570006\pi$
$521$			8.13120i			0.356234i	−0.984009	+	0.178117i	$0.942999\pi$
$522$	24.0310	−	9.38446i	1.05181	−	0.410747i
$523$	18.9364	−	32.7988i	0.828031	−	1.43419i	−0.0715491	−	0.997437i	$-0.522794\pi$
$523$	18.9364	−	32.7988i	0.828031	−	1.43419i	0.899580	−	0.436755i	$-0.143872\pi$
$524$	12.3519			0.539593
$525$	−22.5813	−	11.4236i	−0.985531	−	0.498568i
$526$	4.14647	+	15.4748i	0.180795	+	0.674735i
$527$	−4.79273	−	17.8867i	−0.208775	−	0.779158i
$528$	1.34827	+	0.682072i	0.0586758	+	0.0296834i
$529$	−9.04865			−0.393419
$530$	−10.6241	+	18.4015i	−0.461482	+	0.799310i
$531$	15.4089	−	6.01740i	0.668688	−	0.261133i
$532$		−	14.9315i		−	0.647363i
$533$	−27.2933	+	28.3981i	−1.18221	+	1.23006i
$534$	−9.38203	+	10.4806i	−0.406000	+	0.453540i
$535$	−0.542398	+	0.542398i	−0.0234499	+	0.0234499i
$536$		−	8.27490i		−	0.357421i
$537$	10.4828	+	31.9481i	0.452367	+	1.37866i
$538$	−0.569509	−	2.12544i	−0.0245533	−	0.0916341i
$539$	0.374580	−	1.39795i	0.0161343	−	0.0602140i
$540$	−16.1782	+	2.70646i	−0.696200	+	0.116468i
$541$	−9.80824	−	9.80824i	−0.421689	−	0.421689i	0.464096	−	0.885785i	$-0.346379\pi$
$541$	−9.80824	−	9.80824i	−0.421689	−	0.421689i	−0.885785	+	0.464096i	$0.846379\pi$
$542$		−	6.17880i		−	0.265402i
$543$	−0.126838	−	0.113543i	−0.00544314	−	0.00487260i
$544$	−2.54682	−	2.54682i	−0.109194	−	0.109194i
$545$	−6.42802	−	11.1337i	−0.275346	−	0.476914i
$546$	18.0573	+	3.41126i	0.772780	+	0.145988i
$547$	−18.8226	+	32.6018i	−0.804798	+	1.39395i	0.111629	+	0.993750i	$0.464393\pi$
$547$	−18.8226	+	32.6018i	−0.804798	+	1.39395i	−0.916427	+	0.400201i	$0.868940\pi$
$548$	6.71605	−	1.79956i	0.286895	−	0.0768734i
$549$	−2.10709	−	18.9904i	−0.0899284	−	0.810490i
$550$	−3.75114	+	2.16572i	−0.159949	+	0.0923467i
$551$	−42.1487	+	11.2937i	−1.79559	+	0.481128i
$552$	0.357268	+	6.45960i	0.0152063	+	0.274939i
$553$	7.42827	−	1.99040i	0.315882	−	0.0846404i
$554$	19.7248	+	5.28525i	0.838028	+	0.224549i
$555$	−24.3420	−	21.7905i	−1.03326	−	0.924956i
$556$	−4.92006	+	2.84060i	−0.208657	+	0.120468i
$557$	8.83844	+	32.9855i	0.374497	+	1.39764i	0.854079	+	0.520143i	$0.174122\pi$
$557$	8.83844	+	32.9855i	0.374497	+	1.39764i	−0.479582	+	0.877497i	$0.659212\pi$
$558$	−14.1265	−	6.19188i	−0.598023	−	0.262123i
$559$	−22.8396	+	0.453073i	−0.966010	+	0.0191630i
$560$	−8.04466	−	4.64459i	−0.339949	−	0.196270i
$561$	4.85611	+	2.45665i	0.205025	+	0.103720i
$562$	−20.7738			−0.876290
$563$	−14.7518	+	25.5508i	−0.621713	+	1.07684i	0.367454	+	0.930042i	$0.380230\pi$
$563$	−14.7518	+	25.5508i	−0.621713	+	1.07684i	−0.989167	+	0.146796i	$0.953104\pi$
$564$	5.99211	+	9.16887i	0.252313	+	0.386079i
$565$	6.82355	−	6.82355i	0.287069	−	0.287069i
$566$	23.2833	+	6.23874i	0.978670	+	0.262234i
$567$	22.3764	+	14.1661i	0.939719	+	0.594921i
$568$	−3.20660	−	5.55400i	−0.134546	−	0.233041i
$569$	7.35978	+	12.7475i	0.308538	+	0.534404i	0.978043	−	0.208404i	$-0.0668269\pi$
$569$	7.35978	+	12.7475i	0.308538	+	0.534404i	−0.669505	+	0.742808i	$0.733494\pi$
$570$	27.7019	−	1.53214i	1.16031	−	0.0641743i
$571$	−16.5923	+	9.57956i	−0.694365	+	0.400892i	−0.805245	−	0.592942i	$-0.797966\pi$
$571$	−16.5923	+	9.57956i	−0.694365	+	0.400892i	0.110880	+	0.993834i	$0.464633\pi$
$572$	2.17955	−	2.26777i	0.0911314	−	0.0948201i
$573$	−16.3858	−	14.6683i	−0.684528	−	0.612777i
$574$	−31.0503	−	8.31990i	−1.29601	−	0.347266i
$575$	−16.0611	−	9.27287i	−0.669794	−	0.386706i
$576$	−2.98170	+	0.330837i	−0.124238	+	0.0137849i
$577$	0.887796	−	0.887796i	0.0369594	−	0.0369594i	−0.688386	−	0.725345i	$-0.741680\pi$
$577$	0.887796	−	0.887796i	0.0369594	−	0.0369594i	0.725345	+	0.688386i	$0.241680\pi$
$578$	2.84782	+	2.84782i	0.118454	+	0.118454i
$579$	−41.0359	+	2.26962i	−1.70539	+	0.0943221i
$580$	−7.02603	+	26.2215i	−0.291740	+	1.08879i
$581$	−29.2323	−	16.8773i	−1.21276	−	0.700187i
$582$	28.6762	+	6.00868i	1.18867	+	0.249068i
$583$	1.51975	−	5.67179i	0.0629417	−	0.234902i
$584$	15.0500			0.622773
$585$	−4.47591	+	33.8511i	−0.185056	+	1.39957i
$586$	2.59268			0.107103
$587$	2.59294	−	9.67698i	0.107022	−	0.399412i	−0.891545	−	0.452933i	$-0.850378\pi$
$587$	2.59294	−	9.67698i	0.107022	−	0.399412i	0.998567	+	0.0535210i	$0.0170444\pi$
$588$	0.895862	+	2.73029i	0.0369447	+	0.112595i
$589$	22.5930	+	13.0441i	0.930928	+	0.537472i
$590$	−4.50515	+	16.8135i	−0.185474	+	0.692199i
$591$	−4.17813	+	8.25900i	−0.171865	+	0.339730i
$592$	−4.22510	−	4.22510i	−0.173651	−	0.173651i
$593$	−26.1095	+	26.1095i	−1.07219	+	1.07219i	−0.0750069	+	0.997183i	$0.523898\pi$
$593$	−26.1095	+	26.1095i	−1.07219	+	1.07219i	−0.997183	+	0.0750069i	$0.976102\pi$
$594$	4.12488	−	1.87956i	0.169246	−	0.0771194i
$595$	−28.9748	−	16.7286i	−1.18785	−	0.685807i
$596$	−20.0748	−	5.37903i	−0.822297	−	0.220334i
$597$	3.05345	−	14.5724i	0.124969	−	0.596410i
$598$	13.0750	+	3.22690i	0.534675	+	0.131958i
$599$	6.17074	−	3.56268i	0.252130	−	0.145567i	−0.368609	−	0.929584i	$-0.620166\pi$
$599$	6.17074	−	3.56268i	0.252130	−	0.145567i	0.620739	+	0.784017i	$0.286833\pi$
$600$	3.88213	−	7.67389i	0.158487	−	0.313285i
$601$	1.60598	+	2.78164i	0.0655092	+	0.113465i	0.896920	−	0.442193i	$-0.145799\pi$
$601$	1.60598	+	2.78164i	0.0655092	+	0.113465i	−0.831411	+	0.555659i	$0.812466\pi$
$602$	−9.32193	−	16.1461i	−0.379933	−	0.658064i
$603$	−19.3824	−	15.5108i	−0.789314	−	0.631650i
$604$	−7.11970	−	1.90772i	−0.289697	−	0.0776240i
$605$	−22.8552	+	22.8552i	−0.929196	+	0.929196i
$606$	4.03651	−	7.97906i	0.163972	−	0.324127i
$607$	20.6661	−	35.7948i	0.838812	−	1.45286i	−0.0520768	−	0.998643i	$-0.516584\pi$
$607$	20.6661	−	35.7948i	0.838812	−	1.45286i	0.890889	−	0.454222i	$-0.150083\pi$
$608$	5.07422			0.205787
$609$	36.6893	−	23.9774i	1.48672	−	0.971615i
$610$	17.4118	+	10.0527i	0.704982	+	0.407022i
$611$	21.9027	−	6.33698i	0.886088	−	0.256367i
$612$	−10.7393	+	1.19159i	−0.434112	+	0.0481671i
$613$	5.73651	+	21.4090i	0.231695	+	0.864699i	0.979611	+	0.200905i	$0.0643883\pi$
$613$	5.73651	+	21.4090i	0.231695	+	0.864699i	−0.747915	+	0.663794i	$0.768945\pi$
$614$	−0.501642	+	0.289623i	−0.0202446	+	0.0116882i
$615$	12.2495	−	58.4602i	0.493948	−	2.35734i
$616$	2.47956	+	0.664396i	0.0999043	+	0.0267693i
$617$	−21.5609	+	5.77723i	−0.868010	+	0.232583i	−0.665227	−	0.746641i	$-0.731665\pi$
$617$	−21.5609	+	5.77723i	−0.868010	+	0.232583i	−0.202783	+	0.979224i	$0.564999\pi$
$618$	−14.2625	−	7.21522i	−0.573721	−	0.290239i
$619$	16.0700	−	4.30594i	0.645907	−	0.173070i	0.0790293	−	0.996872i	$-0.474818\pi$
$619$	16.0700	−	4.30594i	0.645907	−	0.173070i	0.566878	+	0.823802i	$0.308151\pi$
$620$	14.0555	−	8.11497i	0.564484	−	0.325905i
$621$	15.8001	+	11.2713i	0.634037	+	0.452303i
$622$	16.7615	−	4.49124i	0.672076	−	0.180082i
$623$	−11.9489	+	20.6961i	−0.478723	+	0.829173i
$624$	−1.15926	+	6.13646i	−0.0464075	+	0.245655i
$625$	−12.5864	−	21.8003i	−0.503456	−	0.872012i
$626$	17.4412	+	17.4412i	0.697089	+	0.697089i
$627$	−7.28489	+	2.39032i	−0.290930	+	0.0954600i
$628$			10.4204i			0.415819i
$629$	−15.2177	−	15.2177i	−0.606771	−	0.606771i
$630$	−25.9584	+	10.1371i	−1.03421	+	0.403873i
$631$	−3.53536	+	13.1942i	−0.140741	+	0.525251i	0.859168	+	0.511694i	$0.170982\pi$
$631$	−3.53536	+	13.1942i	−0.140741	+	0.525251i	−0.999908	+	0.0135565i	$0.995685\pi$
$632$	0.676403	+	2.52437i	0.0269059	+	0.100414i
$633$	11.2537	−	12.5715i	0.447296	−	0.499671i
$634$			24.9812i			0.992131i
$635$	42.6773	−	42.6773i	1.69360	−	1.69360i
$636$	3.63471	+	11.0774i	0.144125	+	0.439246i
$637$	5.98051	−	0.118637i	0.236956	−	0.00470055i
$638$		−	7.50184i		−	0.297000i
$639$	−19.0198	−	2.89978i	−0.752413	−	0.114714i
$640$	1.57838	−	2.73384i	0.0623911	−	0.108065i
$641$	−22.1785			−0.876000			−0.438000	−	0.898975i	$-0.644313\pi$
$641$	−22.1785			−0.876000			−0.438000	+	0.898975i	$0.644313\pi$
$642$	0.0232422	+	0.420231i	0.000917295	+	0.0165852i
$643$	2.39351	+	8.93270i	0.0943908	+	0.352271i	0.996926	−	0.0783440i	$-0.0249632\pi$
$643$	2.39351	+	8.93270i	0.0943908	+	0.352271i	−0.902536	+	0.430615i	$0.858297\pi$
$644$	2.84471	+	10.6166i	0.112097	+	0.418353i
$645$	28.9987	−	18.9514i	1.14182	−	0.746211i
$646$	18.2761			0.719062
$647$	8.23841	−	14.2694i	0.323886	−	0.560986i	−0.657401	−	0.753541i	$-0.728344\pi$
$647$	8.23841	−	14.2694i	0.323886	−	0.560986i	0.981286	+	0.192555i	$0.0616774\pi$
$648$	−4.81411	+	7.60423i	−0.189116	+	0.298722i
$649$		−	4.81024i		−	0.188819i
$650$	−12.9074	−	12.4053i	−0.506269	−	0.486574i
$651$	−25.6471	−	5.37399i	−1.00519	−	0.210623i
$652$	−4.82287	+	4.82287i	−0.188878	+	0.188878i
$653$		−	33.8732i		−	1.32556i	−0.748813	−	0.662781i	$-0.769376\pi$
$653$		−	33.8732i		−	1.32556i	0.748813	−	0.662781i	$-0.230624\pi$
$654$	−6.90390	−	1.44661i	−0.269964	−	0.0565671i
$655$	10.0919	+	37.6633i	0.394322	+	1.47163i
$656$	2.82738	−	10.5519i	0.110390	−	0.411983i
$657$	28.2104	−	35.2518i	1.10059	−	1.37531i
$658$	13.1584	+	13.1584i	0.512966	+	0.512966i
$659$			9.62356i			0.374881i	0.982276	+	0.187440i	$0.0600191\pi$
$659$			9.62356i			0.374881i	−0.982276	+	0.187440i	$0.939981\pi$
$660$	−0.978200	+	4.66842i	−0.0380764	+	0.181718i
$661$	18.6266	+	18.6266i	0.724492	+	0.724492i	0.969517	−	0.245025i	$-0.0787961\pi$
$661$	18.6266	+	18.6266i	0.724492	+	0.724492i	−0.245025	+	0.969517i	$0.578796\pi$
$662$	16.0916	+	27.8714i	0.625417	+	1.08325i
$663$	−4.17536	+	22.1020i	−0.162157	+	0.858369i
$664$	5.73546	−	9.93410i	0.222579	−	0.385518i
$665$	45.5292	−	12.1995i	1.76555	−	0.473077i
$666$	−17.8162	+	1.97681i	−0.690366	+	0.0765999i
$667$	27.8170	−	16.0601i	1.07708	−	0.621851i
$668$	13.2930	−	3.56186i	0.514323	−	0.137812i
$669$	27.5217	−	17.9862i	1.06405	−	0.695386i
$670$	25.2319	−	6.76086i	0.974792	−	0.261195i
$671$	−5.36673	−	1.43801i	−0.207180	−	0.0555138i
$672$	−4.84274	+	1.58900i	−0.186813	+	0.0612970i
$673$	4.64587	−	2.68230i	0.179085	−	0.103395i	−0.407778	−	0.913081i	$-0.633696\pi$
$673$	4.64587	−	2.68230i	0.179085	−	0.103395i	0.586863	+	0.809686i	$0.300363\pi$
$674$	−7.69861	−	28.7316i	−0.296539	−	1.10670i
$675$	−10.6979	−	23.4775i	−0.411761	−	0.903648i
$676$	11.5073	+	6.04839i	0.442587	+	0.232631i
$677$	−6.42329	−	3.70849i	−0.246867	−	0.142529i	0.371462	−	0.928448i	$-0.378857\pi$
$677$	−6.42329	−	3.70849i	−0.246867	−	0.142529i	−0.618329	+	0.785919i	$0.712190\pi$
$678$	−0.292394	−	5.28665i	−0.0112293	−	0.203032i
$679$	49.7766			1.91025
$680$	5.68494	−	9.84661i	0.218008	−	0.377600i
$681$	26.7520	−	1.47960i	1.02514	−	0.0566985i
$682$	−3.17143	+	3.17143i	−0.121440	+	0.121440i
$683$	−17.3967	−	4.66144i	−0.665668	−	0.178365i	−0.0898653	−	0.995954i	$-0.528644\pi$
$683$	−17.3967	−	4.66144i	−0.665668	−	0.178365i	−0.575803	+	0.817589i	$0.695310\pi$
$684$	9.51135	−	11.8854i	0.363675	−	0.454451i
$685$	10.9745	+	19.0083i	0.419312	+	0.726270i
$686$	−7.85824	−	13.6109i	−0.300029	−	0.519665i
$687$	14.3639	+	21.9790i	0.548017	+	0.838553i
$688$	5.48696	−	3.16790i	0.209188	−	0.120775i
$689$	24.2642	−	0.481334i	0.924393	−	0.0183374i
$690$	−19.4047	+	6.36708i	−0.738726	+	0.242391i
$691$	−15.3897	−	4.12366i	−0.585452	−	0.156871i	−0.0460781	−	0.998938i	$-0.514672\pi$
$691$	−15.3897	−	4.12366i	−0.585452	−	0.156871i	−0.539374	+	0.842066i	$0.681339\pi$
$692$	−3.51613	−	2.03004i	−0.133663	−	0.0771704i
$693$	6.20403	−	4.56255i	0.235671	−	0.173317i
$694$	−24.0279	+	24.0279i	−0.912088	+	0.912088i
$695$	−12.6814	−	12.6814i	−0.481034	−	0.481034i
$696$	8.14832	+	12.4682i	0.308861	+	0.472607i
$697$	10.1835	−	38.0053i	0.385727	−	1.43955i
$698$	−7.10849	−	4.10409i	−0.269060	−	0.155342i
$699$	−13.3002	+	14.8576i	−0.503060	+	0.561964i
$700$	3.78152	−	14.1128i	0.142928	−	0.533415i
$701$	10.3675			0.391576			0.195788	−	0.980646i	$-0.437274\pi$
$701$	10.3675			0.391576			0.195788	+	0.980646i	$0.437274\pi$
$702$	12.2006	+	14.2178i	0.460481	+	0.536617i
$703$	30.3195			1.14352
$704$	−0.225784	+	0.842637i	−0.00850955	+	0.0317581i
$705$	−23.0620	+	25.7624i	−0.868567	+	0.970269i
$706$	13.5913	+	7.84693i	0.511515	+	0.295323i
$707$	3.93191	−	14.6741i	0.147875	−	0.551876i
$708$	5.22478	+	7.99474i	0.196359	+	0.300461i
$709$	−16.2379	−	16.2379i	−0.609826	−	0.609826i	0.333074	−	0.942901i	$-0.391914\pi$
$709$	−16.2379	−	16.2379i	−0.609826	−	0.609826i	−0.942901	+	0.333074i	$0.891914\pi$
$710$	14.3154	−	14.3154i	0.537247	−	0.537247i
$711$	7.18076	+	3.14744i	0.269300	+	0.118038i
$712$	−7.03323	−	4.06064i	−0.263582	−	0.152179i
$713$	−18.5492	−	4.97025i	−0.694674	−	0.186137i
$714$	−17.4423	+	5.72317i	−0.652762	+	0.214184i
$715$	8.69565	+	4.79304i	0.325199	+	0.179250i
$716$	−16.8120	+	9.70640i	−0.628293	+	0.362745i
$717$	3.81769	+	5.84167i	0.142574	+	0.218161i
$718$	8.84981	+	15.3283i	0.330272	+	0.572048i
$719$	25.3323	+	43.8768i	0.944735	+	1.63633i	0.756281	+	0.654247i	$0.227014\pi$
$719$	25.3323	+	43.8768i	0.944735	+	1.63633i	0.188454	+	0.982082i	$0.439652\pi$
$720$	−3.44493	−	8.82152i	−0.128385	−	0.328759i
$721$	−26.2298	−	7.02824i	−0.976847	−	0.261745i
$722$	−4.77136	+	4.77136i	−0.177572	+	0.177572i
$723$	−25.6131	+	1.41661i	−0.952560	+	0.0526843i
$724$	0.0491425	−	0.0851174i	0.00182637	−	0.00316336i
$725$	−42.6980			−1.58576
$726$	0.979361	+	17.7074i	0.0363475	+	0.657183i
$727$	26.9809	+	15.5774i	1.00067	+	0.577734i	0.908445	−	0.418004i	$-0.137270\pi$
$727$	26.9809	+	15.5774i	1.00067	+	0.577734i	0.0922201	+	0.995739i	$0.470604\pi$
$728$	0.210427	+	10.6077i	0.00779894	+	0.393147i
$729$	8.78774	+	25.5299i	0.325472	+	0.945552i
$730$	12.2963	+	45.8905i	0.455107	+	1.69848i
$731$	19.7626	−	11.4100i	0.730948	−	0.422013i
$732$	10.4816	−	3.43921i	0.387410	−	0.127117i
$733$	−7.44254	−	1.99422i	−0.274896	−	0.0736583i	0.118737	−	0.992926i	$-0.462115\pi$
$733$	−7.44254	−	1.99422i	−0.274896	−	0.0736583i	−0.393634	+	0.919267i	$0.628782\pi$
$734$	25.5238	−	6.83908i	0.942101	−	0.252435i
$735$	−7.59326	+	4.96240i	−0.280082	+	0.183041i
$736$	−3.60788	+	0.966728i	−0.132988	+	0.0356341i
$737$	−6.25158	+	3.60935i	−0.230280	+	0.132952i
$738$	−19.4162	−	26.4016i	−0.714719	−	0.971856i
$739$	9.13725	−	2.44832i	0.336119	−	0.0900629i	−0.0868119	−	0.996225i	$-0.527668\pi$
$739$	9.13725	−	2.44832i	0.336119	−	0.0900629i	0.422931	+	0.906162i	$0.361001\pi$
$740$	9.43115	−	16.3352i	0.346696	−	0.600495i
$741$	−17.8583	−	26.1772i	−0.656040	−	0.961642i
$742$	9.90340	+	17.1532i	0.363565	+	0.629713i
$743$	3.73934	+	3.73934i	0.137183	+	0.137183i	0.772364	−	0.635181i	$-0.219074\pi$
$743$	3.73934	+	3.73934i	0.137183	+	0.137183i	−0.635181	+	0.772364i	$0.719074\pi$
$744$	1.82626	−	8.71573i	0.0669539	−	0.319534i
$745$		−	65.6071i		−	2.40366i
$746$	−16.0506	−	16.0506i	−0.587656	−	0.587656i
$747$	−12.5180	−	32.0552i	−0.458011	−	1.17284i
$748$	−0.813216	+	3.03496i	−0.0297341	+	0.110969i
$749$	0.185064	+	0.690667i	0.00676208	+	0.0252364i
$750$	−0.186264	−	0.0390290i	−0.00680140	−	0.00142514i
$751$		−	15.6205i		−	0.569999i	−0.958528	−	0.284999i	$-0.908007\pi$
$751$		−	15.6205i		−	0.569999i	0.958528	−	0.284999i	$-0.0919934\pi$
$752$	−4.47164	+	4.47164i	−0.163064	+	0.163064i
$753$	6.72265	+	1.40864i	0.244987	+	0.0513335i
$754$	29.7842	−	8.61730i	1.08468	−	0.313824i
$755$		−	23.2681i		−	0.846813i
$756$	−5.35551	+	14.3217i	−0.194778	+	0.520876i
$757$	−2.81998	+	4.88435i	−0.102494	+	0.177525i	−0.912712	−	0.408604i	$-0.866016\pi$
$757$	−2.81998	+	4.88435i	−0.102494	+	0.177525i	0.810218	+	0.586129i	$0.199349\pi$
$758$	10.1600			0.369027
$759$	4.72431	−	3.08746i	0.171482	−	0.112068i
$760$	4.14580	+	15.4723i	0.150384	+	0.561241i
$761$	4.74969	+	17.7261i	0.172176	+	0.642571i	0.997015	+	0.0772030i	$0.0245990\pi$
$761$	4.74969	+	17.7261i	0.172176	+	0.642571i	−0.824839	+	0.565367i	$0.808734\pi$
$762$	−1.82875	−	33.0648i	−0.0662487	−	1.19781i
$763$	−11.9839			−0.433847
$764$	6.34858	−	10.9961i	0.229684	−	0.397824i
$765$	−12.4078	−	31.7729i	−0.448604	−	1.14875i
$766$		−	18.7184i		−	0.676323i
$767$	19.0979	−	5.52549i	0.689586	−	0.199514i
$768$	−0.539995	−	1.64572i	−0.0194854	−	0.0593849i
$769$	14.2488	−	14.2488i	0.513824	−	0.513824i	−0.401872

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.15524 + 1.29051i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.817032 - 3.04921i) q^{5} +(-0.947539 - 1.44989i) q^{6} +(-2.08075 - 2.08075i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.330837 - 2.98170i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.15524 + 1.29051i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.817032 - 3.04921i) q^{5} +(-0.947539 - 1.44989i) q^{6} +(-2.08075 - 2.08075i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.330837 - 2.98170i) q^{9} +(2.73384 + 1.57838i) q^{10} +(-0.842637 - 0.225784i) q^{11} +(1.64572 - 0.539995i) q^{12} +(-0.0715101 - 3.60484i) q^{13} +(2.54838 - 1.47131i) q^{14} +(2.99116 + 4.57696i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.80087 + 3.11920i) q^{17} +(2.96573 + 0.452158i) q^{18} +(-4.90132 - 1.31331i) q^{19} +(-2.23217 + 2.23217i) q^{20} +(5.08899 - 0.281462i) q^{21} +(0.436181 - 0.755487i) q^{22} +3.73515 q^{23} +(0.0956502 + 1.72941i) q^{24} +(-4.29998 - 2.48260i) q^{25} +(3.50052 + 0.863928i) q^{26} +(4.23011 + 3.01764i) q^{27} +(0.761606 + 2.84235i) q^{28} +(7.44735 - 4.29973i) q^{29} +(-5.19517 + 1.70464i) q^{30} +(-4.96612 - 1.33067i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.26482 - 0.826597i) q^{33} +(-3.47902 + 0.932200i) q^{34} +(-8.04466 + 4.64459i) q^{35} +(-1.20434 + 2.74765i) q^{36} +(-5.77159 + 1.54649i) q^{37} +(2.53711 - 4.39440i) q^{38} +(4.73470 + 4.07218i) q^{39} +(-1.57838 - 2.73384i) q^{40} +(-7.72453 - 7.72453i) q^{41} +(-1.04526 + 4.98844i) q^{42} -6.33580i q^{43} +(0.616853 + 0.616853i) q^{44} +(-9.36213 - 1.42736i) q^{45} +(-0.966728 + 3.60788i) q^{46} +(1.63674 + 6.10838i) q^{47} +(-1.69524 - 0.355213i) q^{48} +1.65902i q^{49} +(3.51092 - 3.51092i) q^{50} +(-6.10581 - 1.27939i) q^{51} +(-1.74049 + 3.15764i) q^{52} +6.73100i q^{53} +(-4.00965 + 3.30496i) q^{54} +(-1.37692 + 2.38490i) q^{55} -2.94262 q^{56} +(7.35704 - 4.80802i) q^{57} +(2.22570 + 8.30644i) q^{58} +(1.42714 + 5.32616i) q^{59} +(-0.301946 - 5.45934i) q^{60} +6.36898 q^{61} +(2.57066 - 4.45251i) q^{62} +(-5.51578 + 6.89256i) q^{63} -1.00000i q^{64} +(-11.0503 - 2.72722i) q^{65} +(0.471071 + 1.43567i) q^{66} +(5.85124 - 5.85124i) q^{67} -3.60175i q^{68} +(-4.31500 + 4.82025i) q^{69} +(-2.40422 - 8.97266i) q^{70} +(1.65986 - 6.19468i) q^{71} +(-2.34232 - 1.87444i) q^{72} +(10.6419 + 10.6419i) q^{73} -5.97519i q^{74} +(8.17134 - 2.68118i) q^{75} +(3.58802 + 3.58802i) q^{76} +(1.28351 + 2.22311i) q^{77} +(-5.15885 + 3.51941i) q^{78} +(-1.30671 + 2.26329i) q^{79} +(3.04921 - 0.817032i) q^{80} +(-8.78109 + 1.97291i) q^{81} +(9.46058 - 5.46207i) q^{82} +(11.0800 - 2.96889i) q^{83} +(-4.54793 - 2.30074i) q^{84} +(10.9825 - 2.94274i) q^{85} +(6.11991 + 1.63983i) q^{86} +(-3.05464 + 14.5781i) q^{87} +(-0.755487 + 0.436181i) q^{88} +(-2.10194 - 7.84455i) q^{89} +(3.80182 - 8.67369i) q^{90} +(-7.35197 + 7.64956i) q^{91} +(-3.23474 - 1.86758i) q^{92} +(7.45431 - 4.87159i) q^{93} -6.32386 q^{94} +(-8.00907 + 13.8721i) q^{95} +(0.781868 - 1.54554i) q^{96} +(-11.9612 + 11.9612i) q^{97} +(-1.60249 - 0.429386i) q^{98} +(-0.394445 + 2.58719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7}+O(q^{10}) \) 56 * q - 8 * q^7	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

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