LMFDB - Embedded newform 234.2.y.a.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(11,234)]

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([2, 7]))

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

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

chi := DirichletCharacter("234.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (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			11.9
Character	$\chi$	$=$	234.11
Dual form			234.2.y.a.149.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.25339 - 1.19541i) q^{3} -1.00000i q^{4} +(-0.670386 - 0.179629i) q^{5} +(-1.73157 + 0.0409976i) q^{6} +(-4.43374 - 1.18802i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.141980 + 2.99664i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.25339 - 1.19541i) q^{3} -1.00000i q^{4} +(-0.670386 - 0.179629i) q^{5} +(-1.73157 + 0.0409976i) q^{6} +(-4.43374 - 1.18802i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.141980 + 2.99664i) q^{9} +(-0.601052 + 0.347017i) q^{10} +(-1.59115 - 1.59115i) q^{11} +(-1.19541 + 1.25339i) q^{12} +(3.60547 + 0.0239902i) q^{13} +(-3.97518 + 2.29507i) q^{14} +(0.625525 + 1.02653i) q^{15} -1.00000 q^{16} +(2.32181 - 4.02149i) q^{17} +(2.21934 + 2.01855i) q^{18} +(-2.81042 + 0.753050i) q^{19} +(-0.179629 + 0.670386i) q^{20} +(4.13704 + 6.78919i) q^{21} -2.25023 q^{22} +(2.37251 - 4.10931i) q^{23} +(0.0409976 + 1.73157i) q^{24} +(-3.91298 - 2.25916i) q^{25} +(2.56642 - 2.53249i) q^{26} +(3.40426 - 3.92569i) q^{27} +(-1.18802 + 4.43374i) q^{28} -4.88226i q^{29} +(1.16818 + 0.283556i) q^{30} +(-1.74651 + 6.51808i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.0922541 + 3.89642i) q^{33} +(-1.20186 - 4.48539i) q^{34} +(2.75891 + 1.59286i) q^{35} +(2.99664 - 0.141980i) q^{36} +(3.44953 + 0.924299i) q^{37} +(-1.45478 + 2.51976i) q^{38} +(-4.49039 - 4.34009i) q^{39} +(0.347017 + 0.601052i) q^{40} +(-1.48606 - 5.54605i) q^{41} +(7.72601 + 1.87535i) q^{42} +(4.59562 - 2.65328i) q^{43} +(-1.59115 + 1.59115i) q^{44} +(0.443103 - 2.03441i) q^{45} +(-1.22810 - 4.58334i) q^{46} +(11.6601 - 3.12430i) q^{47} +(1.25339 + 1.19541i) q^{48} +(12.1845 + 7.03470i) q^{49} +(-4.36436 + 1.16943i) q^{50} +(-7.71746 + 2.26498i) q^{51} +(0.0239902 - 3.60547i) q^{52} +5.06576i q^{53} +(-0.368703 - 5.18305i) q^{54} +(0.780869 + 1.35250i) q^{55} +(2.29507 + 3.97518i) q^{56} +(4.42276 + 2.41575i) q^{57} +(-3.45228 - 3.45228i) q^{58} +(3.79710 + 3.79710i) q^{59} +(1.02653 - 0.625525i) q^{60} +(-1.56055 - 2.70295i) q^{61} +(3.37401 + 5.84395i) q^{62} +(2.93055 - 13.4550i) q^{63} +1.00000i q^{64} +(-2.41275 - 0.663731i) q^{65} +(2.82042 + 2.68995i) q^{66} +(-12.6377 + 3.38625i) q^{67} +(-4.02149 - 2.32181i) q^{68} +(-7.88601 + 2.31445i) q^{69} +(3.07717 - 0.824524i) q^{70} +(-4.16970 - 15.5615i) q^{71} +(2.01855 - 2.21934i) q^{72} +(-5.55110 + 5.55110i) q^{73} +(3.09276 - 1.78561i) q^{74} +(2.20387 + 7.50923i) q^{75} +(0.753050 + 2.81042i) q^{76} +(5.16444 + 8.94507i) q^{77} +(-6.24409 + 0.106275i) q^{78} +(-1.55400 + 2.69161i) q^{79} +(0.670386 + 0.179629i) q^{80} +(-8.95968 + 0.850926i) q^{81} +(-4.97245 - 2.87085i) q^{82} +(2.45977 + 9.17998i) q^{83} +(6.78919 - 4.13704i) q^{84} +(-2.27888 + 2.27888i) q^{85} +(1.37344 - 5.12575i) q^{86} +(-5.83631 + 6.11938i) q^{87} +2.25023i q^{88} +(-0.648204 + 2.41913i) q^{89} +(-1.12522 - 1.75186i) q^{90} +(-15.9572 - 4.38972i) q^{91} +(-4.10931 - 2.37251i) q^{92} +(9.98086 - 6.08190i) q^{93} +(6.03569 - 10.4541i) q^{94} +2.01934 q^{95} +(1.73157 - 0.0409976i) q^{96} +(-0.317765 + 1.18591i) q^{97} +(13.5900 - 3.64143i) q^{98} +(4.54220 - 4.99402i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.25339	−	1.19541i	−0.723646	−	0.690171i
$3$	−1.25339	−	1.19541i	−0.723646	−	0.690171i
$4$		−	1.00000i		−	0.500000i
$5$	−0.670386	−	0.179629i	−0.299806	−	0.0803327i	0.105780	−	0.994390i	$-0.466266\pi$
$5$	−0.670386	−	0.179629i	−0.299806	−	0.0803327i	−0.405586	+	0.914057i	$0.632933\pi$
$6$	−1.73157	+	0.0409976i	−0.706909	+	0.0167372i
$7$	−4.43374	−	1.18802i	−1.67579	−	0.449028i	−0.709131	−	0.705077i	$-0.750912\pi$
$7$	−4.43374	−	1.18802i	−1.67579	−	0.449028i	−0.966664	+	0.256049i	$0.917579\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.141980	+	2.99664i	0.0473267	+	0.998879i
$10$	−0.601052	+	0.347017i	−0.190069	+	0.109736i
$11$	−1.59115	−	1.59115i	−0.479751	−	0.479751i	0.425301	−	0.905052i	$-0.360168\pi$
$11$	−1.59115	−	1.59115i	−0.479751	−	0.479751i	−0.905052	+	0.425301i	$0.860168\pi$
$12$	−1.19541	+	1.25339i	−0.345086	+	0.361823i
$13$	3.60547	+	0.0239902i	0.999978	+	0.00665368i
$13$	3.60547	+	0.0239902i	0.999978	+	0.00665368i
$14$	−3.97518	+	2.29507i	−1.06241	+	0.613383i
$15$	0.625525	+	1.02653i	0.161510	+	0.265050i
$16$	−1.00000			−0.250000
$17$	2.32181	−	4.02149i	0.563121	−	0.975354i	−0.434101	−	0.900864i	$-0.642934\pi$
$17$	2.32181	−	4.02149i	0.563121	−	0.975354i	0.997222	−	0.0744895i	$-0.0237327\pi$
$18$	2.21934	+	2.01855i	0.523103	+	0.475776i
$19$	−2.81042	+	0.753050i	−0.644755	+	0.172762i	−0.566356	−	0.824160i	$-0.691647\pi$
$19$	−2.81042	+	0.753050i	−0.644755	+	0.172762i	−0.0783988	+	0.996922i	$0.524981\pi$
$20$	−0.179629	+	0.670386i	−0.0401663	+	0.149903i
$21$	4.13704	+	6.78919i	0.902776	+	1.48152i
$22$	−2.25023			−0.479751
$23$	2.37251	−	4.10931i	0.494703	−	0.856851i	−0.505278	−	0.862957i	$-0.668610\pi$
$23$	2.37251	−	4.10931i	0.494703	−	0.856851i	0.999981	+	0.00610531i	$0.00194339\pi$
$24$	0.0409976	+	1.73157i	0.00836860	+	0.353454i
$25$	−3.91298	−	2.25916i	−0.782595	−	0.451832i
$26$	2.56642	−	2.53249i	0.503316	−	0.496662i
$27$	3.40426	−	3.92569i	0.655150	−	0.755499i
$28$	−1.18802	+	4.43374i	−0.224514	+	0.837897i
$29$		−	4.88226i		−	0.906613i	−0.891355	−	0.453307i	$-0.850244\pi$
$29$		−	4.88226i		−	0.906613i	0.891355	−	0.453307i	$-0.149756\pi$
$30$	1.16818	+	0.283556i	0.213280	+	0.0517700i
$31$	−1.74651	+	6.51808i	−0.313683	+	1.17068i	0.611526	+	0.791224i	$0.290556\pi$
$31$	−1.74651	+	6.51808i	−0.313683	+	1.17068i	−0.925209	+	0.379457i	$0.876111\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.0922541	+	3.89642i	0.0160594	+	0.678280i
$34$	−1.20186	−	4.48539i	−0.206116	−	0.769237i
$35$	2.75891	+	1.59286i	0.466341	+	0.269242i
$36$	2.99664	−	0.141980i	0.499440	−	0.0236633i
$37$	3.44953	+	0.924299i	0.567099	+	0.151954i	0.530966	−	0.847393i	$-0.321829\pi$
$37$	3.44953	+	0.924299i	0.567099	+	0.151954i	0.0361333	+	0.999347i	$0.488496\pi$
$38$	−1.45478	+	2.51976i	−0.235997	+	0.408758i
$39$	−4.49039	−	4.34009i	−0.719038	−	0.694971i
$40$	0.347017	+	0.601052i	0.0548682	+	0.0950346i
$41$	−1.48606	−	5.54605i	−0.232083	−	0.866147i	−0.979442	−	0.201726i	$-0.935345\pi$
$41$	−1.48606	−	5.54605i	−0.232083	−	0.866147i	0.747358	−	0.664421i	$-0.231322\pi$
$42$	7.72601	+	1.87535i	1.19215	+	0.289374i
$43$	4.59562	−	2.65328i	0.700826	−	0.404622i	−0.106829	−	0.994277i	$-0.534070\pi$
$43$	4.59562	−	2.65328i	0.700826	−	0.404622i	0.807655	+	0.589655i	$0.200736\pi$
$44$	−1.59115	+	1.59115i	−0.239875	+	0.239875i
$45$	0.443103	−	2.03441i	0.0660539	−	0.303272i
$46$	−1.22810	−	4.58334i	−0.181074	−	0.675777i
$47$	11.6601	−	3.12430i	1.70080	−	0.455727i	0.727656	−	0.685943i	$-0.240610\pi$
$47$	11.6601	−	3.12430i	1.70080	−	0.455727i	0.973140	+	0.230216i	$0.0739433\pi$
$48$	1.25339	+	1.19541i	0.180911	+	0.172543i
$49$	12.1845	+	7.03470i	1.74064	+	1.00496i
$50$	−4.36436	+	1.16943i	−0.617213	+	0.165382i
$51$	−7.71746	+	2.26498i	−1.08066	+	0.317161i
$52$	0.0239902	−	3.60547i	0.00332684	−	0.499989i
$53$			5.06576i			0.695835i	0.937525	+	0.347918i	$0.113111\pi$
$53$			5.06576i			0.695835i	−0.937525	+	0.347918i	$0.886889\pi$
$54$	−0.368703	−	5.18305i	−0.0501741	−	0.705324i
$55$	0.780869	+	1.35250i	0.105292	+	0.182372i
$56$	2.29507	+	3.97518i	0.306692	+	0.531206i
$57$	4.42276	+	2.41575i	0.585810	+	0.319973i
$58$	−3.45228	−	3.45228i	−0.453307	−	0.453307i
$59$	3.79710	+	3.79710i	0.494341	+	0.494341i	0.909671	−	0.415330i	$-0.136334\pi$
$59$	3.79710	+	3.79710i	0.494341	+	0.494341i	−0.415330	+	0.909671i	$0.636334\pi$
$60$	1.02653	−	0.625525i	0.132525	−	0.0807549i
$61$	−1.56055	−	2.70295i	−0.199808	−	0.346078i	0.748658	−	0.662956i	$-0.230699\pi$
$61$	−1.56055	−	2.70295i	−0.199808	−	0.346078i	−0.948466	+	0.316879i	$0.897365\pi$
$62$	3.37401	+	5.84395i	0.428499	+	0.742182i
$63$	2.93055	−	13.4550i	0.369215	−	1.69517i
$64$			1.00000i			0.125000i
$65$	−2.41275	−	0.663731i	−0.299265	−	0.0823257i
$66$	2.82042	+	2.68995i	0.347170	+	0.331110i
$67$	−12.6377	+	3.38625i	−1.54393	+	0.413696i	−0.927535	−	0.373737i	$-0.878076\pi$
$67$	−12.6377	+	3.38625i	−1.54393	+	0.413696i	−0.616400	+	0.787433i	$0.711410\pi$
$68$	−4.02149	−	2.32181i	−0.487677	−	0.281560i
$69$	−7.88601	+	2.31445i	−0.949364	+	0.278627i
$70$	3.07717	−	0.824524i	0.367792	−	0.0985495i
$71$	−4.16970	−	15.5615i	−0.494852	−	1.84681i	−0.530857	−	0.847461i	$-0.678130\pi$
$71$	−4.16970	−	15.5615i	−0.494852	−	1.84681i	0.0360054	−	0.999352i	$-0.488537\pi$
$72$	2.01855	−	2.21934i	0.237888	−	0.261552i
$73$	−5.55110	+	5.55110i	−0.649707	+	0.649707i	−0.952922	−	0.303215i	$-0.901940\pi$
$73$	−5.55110	+	5.55110i	−0.649707	+	0.649707i	0.303215	+	0.952922i	$0.401940\pi$
$74$	3.09276	−	1.78561i	0.359526	−	0.207573i
$75$	2.20387	+	7.50923i	0.254481	+	0.867091i
$76$	0.753050	+	2.81042i	0.0863808	+	0.322378i
$77$	5.16444	+	8.94507i	0.588542	+	1.01939i
$78$	−6.24409	+	0.106275i	−0.707004	+	0.0120333i
$79$	−1.55400	+	2.69161i	−0.174839	+	0.302829i	−0.940105	−	0.340884i	$-0.889274\pi$
$79$	−1.55400	+	2.69161i	−0.174839	+	0.302829i	0.765267	+	0.643713i	$0.222607\pi$
$80$	0.670386	+	0.179629i	0.0749514	+	0.0200832i
$81$	−8.95968	+	0.850926i	−0.995520	+	0.0945473i
$82$	−4.97245	−	2.87085i	−0.549115	−	0.317032i
$83$	2.45977	+	9.17998i	0.269995	+	1.00763i	0.959122	+	0.282993i	$0.0913274\pi$
$83$	2.45977	+	9.17998i	0.269995	+	1.00763i	−0.689127	+	0.724640i	$0.742006\pi$
$84$	6.78919	−	4.13704i	0.740761	−	0.451388i
$85$	−2.27888	+	2.27888i	−0.247180	+	0.247180i
$86$	1.37344	−	5.12575i	0.148102	−	0.552724i
$87$	−5.83631	+	6.11938i	−0.625719	+	0.656067i
$88$			2.25023i			0.239875i
$89$	−0.648204	+	2.41913i	−0.0687095	+	0.256427i	−0.991733	−	0.128315i	$-0.959043\pi$
$89$	−0.648204	+	2.41913i	−0.0687095	+	0.256427i	0.923024	+	0.384743i	$0.125710\pi$
$90$	−1.12522	−	1.75186i	−0.118609	−	0.184663i
$91$	−15.9572	−	4.38972i	−1.67277	−	0.460168i
$92$	−4.10931	−	2.37251i	−0.428426	−	0.247352i
$93$	9.98086	−	6.08190i	1.03497	−	0.630664i
$94$	6.03569	−	10.4541i	0.622534	−	1.07826i
$95$	2.01934			0.207180
$96$	1.73157	−	0.0409976i	0.176727	−	0.00418430i
$97$	−0.317765	+	1.18591i	−0.0322641	+	0.120411i	−0.980180	−	0.198110i	$-0.936520\pi$
$97$	−0.317765	+	1.18591i	−0.0322641	+	0.120411i	0.947916	+	0.318521i	$0.103186\pi$
$98$	13.5900	−	3.64143i	1.37280	−	0.367840i
$99$	4.54220	−	4.99402i	0.456508	−	0.501918i
$100$	−2.25916	+	3.91298i	−0.225916	+	0.391298i
$101$	−3.76440			−0.374572			−0.187286	−	0.982305i	$-0.559969\pi$
$101$	−3.76440			−0.374572			−0.187286	+	0.982305i	$0.559969\pi$
$102$	−3.85549	+	7.05866i	−0.381750	+	0.698911i
$103$	13.1567	−	7.59604i	1.29637	−	0.748460i	0.316596	−	0.948561i	$-0.397460\pi$
$103$	13.1567	−	7.59604i	1.29637	−	0.748460i	0.979775	+	0.200100i	$0.0641268\pi$
$104$	−2.53249	−	2.56642i	−0.248331	−	0.251658i
$105$	−1.55387	−	5.29451i	−0.151643	−	0.516691i
$106$	3.58203	+	3.58203i	0.347918	+	0.347918i
$107$	−4.73458	+	2.73351i	−0.457709	+	0.264259i	−0.711081	−	0.703111i	$-0.751794\pi$
$107$	−4.73458	+	2.73351i	−0.457709	+	0.264259i	0.253371	+	0.967369i	$0.418461\pi$
$108$	−3.92569	−	3.40426i	−0.377749	−	0.327575i
$109$	5.10130	+	5.10130i	0.488616	+	0.488616i	0.907869	−	0.419253i	$-0.137708\pi$
$109$	5.10130	+	5.10130i	0.488616	+	0.488616i	−0.419253	+	0.907869i	$0.637708\pi$
$110$	1.50852	+	0.404207i	0.143832	+	0.0385397i
$111$	−3.21869	−	5.28212i	−0.305505	−	0.501356i
$112$	4.43374	+	1.18802i	0.418949	+	0.112257i
$113$		−	0.472893i		−	0.0444861i	−0.999753	−	0.0222430i	$-0.992919\pi$
$113$		−	0.472893i		−	0.0444861i	0.999753	−	0.0222430i	$-0.00708076\pi$
$114$	4.83556	−	1.41918i	0.452891	−	0.132918i
$115$	−2.32865	+	2.32865i	−0.217148	+	0.217148i
$116$	−4.88226			−0.453307
$117$	0.440015	+	10.8077i	0.0406794	+	0.999172i
$118$	5.36992			0.494341
$119$	−15.0719	+	15.0719i	−1.38164	+	1.38164i
$120$	0.283556	−	1.16818i	0.0258850	−	0.106640i
$121$		−	5.93646i		−	0.539678i
$122$	−3.01475	−	0.807800i	−0.272943	−	0.0731348i
$123$	−4.76720	+	8.72782i	−0.429844	+	0.786961i
$124$	6.51808	+	1.74651i	0.585341	+	0.156842i
$125$	4.67118	+	4.67118i	0.417803	+	0.417803i
$126$	−7.44189	−	11.5863i	−0.662976	−	1.03219i
$127$	−0.377096	+	0.217716i	−0.0334618	+	0.0193192i	−0.516638	−	0.856204i	$-0.672817\pi$
$127$	−0.377096	+	0.217716i	−0.0334618	+	0.0193192i	0.483176	+	0.875523i	$0.339483\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−8.93188	−	2.16806i	−0.786408	−	0.190887i
$130$	−2.17540	+	1.23674i	−0.190795	+	0.108469i
$131$	−9.02321	+	5.20955i	−0.788361	+	0.455161i	−0.839385	−	0.543537i	$-0.817085\pi$
$131$	−9.02321	+	5.20955i	−0.788361	+	0.455161i	0.0510241	+	0.998697i	$0.483751\pi$
$132$	3.89642	−	0.0922541i	0.339140	−	0.00802969i
$133$	13.3553			1.15805
$134$	−6.54173	+	11.3306i	−0.565119	+	0.978815i
$135$	−2.98734	+	2.02022i	−0.257109	+	0.173873i
$136$	−4.48539	+	1.20186i	−0.384619	+	0.103058i
$137$	1.97943	−	7.38734i	0.169114	−	0.631143i	−0.828365	−	0.560188i	$-0.810729\pi$
$137$	1.97943	−	7.38734i	0.169114	−	0.631143i	0.997480	−	0.0709549i	$-0.0226046\pi$
$138$	−3.93969	+	7.21281i	−0.335369	+	0.613996i
$139$	11.1732			0.947702			0.473851	−	0.880605i	$-0.342863\pi$
$139$	11.1732			0.947702			0.473851	+	0.880605i	$0.342863\pi$
$140$	1.59286	−	2.75891i	0.134621	−	0.233171i
$141$	−18.3495	−	10.0226i	−1.54530	−	0.844055i
$142$	−13.9521	−	8.05524i	−1.17083	−	0.675980i
$143$	−5.69869	−	5.77503i	−0.476548	−	0.482932i
$144$	−0.141980	−	2.99664i	−0.0118317	−	0.249720i
$145$	−0.876997	+	3.27300i	−0.0728307	+	0.271808i
$146$			7.85044i			0.649707i
$147$	−6.86253	−	23.3827i	−0.566012	−	1.92857i
$148$	0.924299	−	3.44953i	0.0759769	−	0.283550i
$149$	−5.23203	+	5.23203i	−0.428625	+	0.428625i	−0.888160	−	0.459535i	$-0.848016\pi$
$149$	−5.23203	+	5.23203i	−0.428625	+	0.428625i	0.459535	+	0.888160i	$0.348016\pi$
$150$	6.86820	+	3.75146i	0.560786	+	0.306305i
$151$	−3.70881	−	13.8415i	−0.301818	−	1.12640i	−0.935650	−	0.352930i	$-0.885185\pi$
$151$	−3.70881	−	13.8415i	−0.301818	−	1.12640i	0.633831	−	0.773471i	$-0.281481\pi$
$152$	2.51976	+	1.45478i	0.204379	+	0.117998i
$153$	12.3806	+	6.38664i	1.00091	+	0.516329i
$154$	9.97693	+	2.67331i	0.803964	+	0.215421i
$155$	2.34168	−	4.05590i	0.188088	−	0.325778i
$156$	−4.34009	+	4.49039i	−0.347486	+	0.359519i
$157$	−2.86104	−	4.95546i	−0.228336	−	0.395489i	0.728979	−	0.684536i	$-0.239995\pi$
$157$	−2.86104	−	4.95546i	−0.228336	−	0.395489i	−0.957315	+	0.289047i	$0.906662\pi$
$158$	0.804409	+	3.00210i	0.0639954	+	0.238834i
$159$	6.05567	−	6.34938i	0.480246	−	0.503538i
$160$	0.601052	−	0.347017i	0.0475173	−	0.0274341i
$161$	−15.4010	+	15.4010i	−1.21377	+	1.21377i
$162$	−5.73376	+	6.93715i	−0.450487	+	0.545034i
$163$	−1.44621	−	5.39731i	−0.113276	−	0.422750i	0.885877	−	0.463921i	$-0.153558\pi$
$163$	−1.44621	−	5.39731i	−0.113276	−	0.422750i	−0.999152	+	0.0411708i	$0.986891\pi$
$164$	−5.54605	+	1.48606i	−0.433074	+	0.116042i
$165$	0.638066	−	2.62868i	0.0496734	−	0.204642i
$166$	8.23054	+	4.75191i	0.638814	+	0.368819i
$167$	23.6549	−	6.33832i	1.83047	−	0.490474i	0.832495	−	0.554033i	$-0.186912\pi$
$167$	23.6549	−	6.33832i	1.83047	−	0.490474i	0.997978	+	0.0635593i	$0.0202452\pi$
$168$	1.87535	−	7.72601i	0.144687	−	0.596075i
$169$	12.9988	+	0.172992i	0.999911	+	0.0133071i
$170$			3.22283i			0.247180i
$171$	−2.65564	−	8.31490i	−0.203082	−	0.635856i
$172$	−2.65328	−	4.59562i	−0.202311	−	0.350413i
$173$	−5.29699	−	9.17465i	−0.402722	−	0.697536i	0.591331	−	0.806429i	$-0.298603\pi$
$173$	−5.29699	−	9.17465i	−0.402722	−	0.697536i	−0.994053	+	0.108893i	$0.965269\pi$
$174$	0.200161	+	8.45396i	0.0151742	+	0.640893i
$175$	14.6652	+	14.6652i	1.10858	+	1.10858i
$176$	1.59115	+	1.59115i	0.119938	+	0.119938i
$177$	−0.220154	−	9.29836i	−0.0165478	−	0.698908i
$178$	1.25223	+	2.16893i	0.0938590	+	0.162569i
$179$	−6.22591	−	10.7836i	−0.465346	−	0.806003i	0.533871	−	0.845566i	$-0.320737\pi$
$179$	−6.22591	−	10.7836i	−0.465346	−	0.806003i	−0.999217	+	0.0395630i	$0.987403\pi$
$180$	−2.03441	−	0.443103i	−0.151636	−	0.0330269i
$181$			18.4465i			1.37112i	0.728018	+	0.685558i	$0.240442\pi$
$181$			18.4465i			1.37112i	−0.728018	+	0.685558i	$0.759558\pi$
$182$	−14.3875	+	8.17945i	−1.06647	+	0.606301i
$183$	−1.27516	+	5.25336i	−0.0942627	+	0.388339i
$184$	−4.58334	+	1.22810i	−0.337889	+	0.0905370i
$185$	−2.14648	−	1.23927i	−0.157813	−	0.0911132i
$186$	2.75698	−	11.3581i	0.202151	−	0.832815i
$187$	−10.0932	+	2.70445i	−0.738084	+	0.197769i
$188$	−3.12430	−	11.6601i	−0.227863	−	0.850398i
$189$	−19.7574	+	13.3611i	−1.43714	+	0.971880i
$190$	1.42789	−	1.42789i	0.103590	−	0.103590i
$191$	7.37477	−	4.25783i	0.533620	−	0.308085i	−0.208870	−	0.977944i	$-0.566978\pi$
$191$	7.37477	−	4.25783i	0.533620	−	0.308085i	0.742489	+	0.669858i	$0.233645\pi$
$192$	1.19541	−	1.25339i	0.0862714	−	0.0904557i
$193$	−4.89947	−	18.2851i	−0.352671	−	1.31619i	−0.883390	−	0.468639i	$-0.844744\pi$
$193$	−4.89947	−	18.2851i	−0.352671	−	1.31619i	0.530718	−	0.847548i	$-0.321922\pi$
$194$	0.613875	+	1.06326i	0.0440736	+	0.0763378i
$195$	2.23069	+	3.71614i	0.159743	+	0.266119i
$196$	7.03470	−	12.1845i	0.502478	−	0.870318i
$197$	−16.8453	−	4.51369i	−1.20018	−	0.321587i	−0.397278	−	0.917698i	$-0.630045\pi$
$197$	−16.8453	−	4.51369i	−1.20018	−	0.321587i	−0.802902	+	0.596111i	$0.796712\pi$
$198$	−0.319488	−	6.74313i	−0.0227050	−	0.479213i
$199$	20.0170	+	11.5568i	1.41897	+	0.819243i	0.996208	−	0.0869986i	$-0.0277276\pi$
$199$	20.0170	+	11.5568i	1.41897	+	0.819243i	0.422761	+	0.906241i	$0.361061\pi$
$200$	1.16943	+	4.36436i	0.0826909	+	0.308607i
$201$	19.8879	+	10.8629i	1.40278	+	0.766210i
$202$	−2.66184	+	2.66184i	−0.187286	+	0.187286i
$203$	−5.80020	+	21.6467i	−0.407095	+	1.51930i
$204$	2.26498	+	7.71746i	0.158580	+	0.540331i
$205$			3.98493i			0.278320i
$206$	3.93200	−	14.6744i	0.273955	−	1.02242i
$207$	12.6510	+	6.52613i	0.879304	+	0.453597i
$208$	−3.60547	−	0.0239902i	−0.249994	−	0.00166342i
$209$	5.67003	+	3.27359i	0.392204	+	0.226439i
$210$	−4.84254	−	2.64503i	−0.334167	−	0.182524i
$211$	5.19424	−	8.99669i	0.357586	−	0.619358i	−0.629971	−	0.776619i	$-0.716933\pi$
$211$	5.19424	−	8.99669i	0.357586	−	0.619358i	0.987557	+	0.157261i	$0.0502665\pi$
$212$	5.06576			0.347918
$213$	−13.3762	+	24.4892i	−0.916520	+	1.67797i
$214$	−1.41497	+	5.28074i	−0.0967254	+	0.360984i
$215$	−3.55745	+	0.953215i	−0.242616	+	0.0650087i
$216$	−5.18305	+	0.368703i	−0.352662	+	0.0250870i
$217$	15.4872	−	26.8246i	1.05134	−	1.82097i
$218$	7.21433			0.488616
$219$	13.5935	−	0.321849i	0.918567	−	0.0217485i
$220$	1.35250	−	0.780869i	0.0911858	−	0.0526462i
$221$	8.46768	−	14.4437i	0.569598	−	0.971585i
$222$	−6.01098	−	1.45906i	−0.403431	−	0.0979258i
$223$	11.2191	+	11.2191i	0.751283	+	0.751283i	0.974719	−	0.223435i	$-0.0717271\pi$
$223$	11.2191	+	11.2191i	0.751283	+	0.751283i	−0.223435	+	0.974719i	$0.571727\pi$
$224$	3.97518	−	2.29507i	0.265603	−	0.153346i
$225$	6.21432	−	12.0465i	0.414288	−	0.803102i
$226$	−0.334386	−	0.334386i	−0.0222430	−	0.0222430i
$227$	6.15723	+	1.64982i	0.408669	+	0.109503i	0.457296	−	0.889314i	$-0.348818\pi$
$227$	6.15723	+	1.64982i	0.408669	+	0.109503i	−0.0486270	+	0.998817i	$0.515485\pi$
$228$	2.41575	−	4.42276i	0.159987	−	0.292905i
$229$	12.3575	+	3.31118i	0.816606	+	0.218809i	0.642862	−	0.765982i	$-0.277747\pi$
$229$	12.3575	+	3.31118i	0.816606	+	0.218809i	0.173744	+	0.984791i	$0.444414\pi$
$230$			3.29321i			0.217148i
$231$	4.21998	−	17.3853i	0.277654	−	1.14387i
$232$	−3.45228	+	3.45228i	−0.226653	+	0.226653i
$233$	18.2644			1.19654			0.598271	−	0.801294i	$-0.295855\pi$
$233$	18.2644			1.19654			0.598271	+	0.801294i	$0.295855\pi$
$234$	7.95334	+	7.33106i	0.519926	+	0.479246i
$235$	−8.37796			−0.546518
$236$	3.79710	−	3.79710i	0.247170	−	0.247170i
$237$	5.16535	−	1.51597i	0.335525	−	0.0984726i
$238$			21.3148i			1.38164i
$239$	19.3192	+	5.17656i	1.24965	+	0.334844i	0.822203	−	0.569195i	$-0.192745\pi$
$239$	19.3192	+	5.17656i	1.24965	+	0.334844i	0.427451	+	0.904039i	$0.359412\pi$
$240$	−0.625525	−	1.02653i	−0.0403775	−	0.0662624i
$241$	−14.5426	−	3.89667i	−0.936768	−	0.251006i	−0.242030	−	0.970269i	$-0.577813\pi$
$241$	−14.5426	−	3.89667i	−0.936768	−	0.251006i	−0.694739	+	0.719262i	$0.744480\pi$
$242$	−4.19771	−	4.19771i	−0.269839	−	0.269839i
$243$	12.2472	+	9.64397i	0.785658	+	0.618661i
$244$	−2.70295	+	1.56055i	−0.173039	+	0.0999040i
$245$	−6.90465	−	6.90465i	−0.441122	−	0.441122i
$246$	2.80058	+	9.54242i	0.178559	+	0.608403i
$247$	−10.1510	+	2.64768i	−0.645890	+	0.168468i
$248$	5.84395	−	3.37401i	0.371091	−	0.214250i
$249$	7.89080	−	14.4465i	0.500059	−	0.915512i
$250$	6.60604			0.417803
$251$	−13.1431	+	22.7645i	−0.829586	+	1.43689i	0.0687771	+	0.997632i	$0.478090\pi$
$251$	−13.1431	+	22.7645i	−0.829586	+	1.43689i	−0.898363	+	0.439253i	$0.855243\pi$
$252$	−13.4550	−	2.93055i	−0.847584	−	0.184607i
$253$	−10.3136	+	2.76352i	−0.648409	+	0.173741i
$254$	−0.112698	+	0.420596i	−0.00707132	+	0.0263905i
$255$	5.58054	−	0.132128i	0.349467	−	0.00827419i
$256$	1.00000			0.0625000
$257$	6.83291	−	11.8349i	0.426225	−	0.738244i	−0.570309	−	0.821430i	$-0.693176\pi$
$257$	6.83291	−	11.8349i	0.426225	−	0.738244i	0.996534	+	0.0831866i	$0.0265098\pi$
$258$	−7.84884	+	4.78274i	−0.488648	+	0.297761i
$259$	−14.1962	−	8.19619i	−0.882110	−	0.509286i
$260$	−0.663731	+	2.41275i	−0.0411629	+	0.149632i
$261$	14.6304	−	0.693184i	0.905597	−	0.0429070i
$262$	−2.69666	+	10.0641i	−0.166600	+	0.621761i
$263$		−	4.79600i		−	0.295734i	−0.989007	−	0.147867i	$-0.952759\pi$
$263$		−	4.79600i		−	0.295734i	0.989007	−	0.147867i	$-0.0472408\pi$
$264$	2.68995	−	2.82042i	0.165555	−	0.173585i
$265$	0.909959	−	3.39601i	0.0558983	−	0.208615i
$266$	9.44363	−	9.44363i	0.579026	−	0.579026i
$267$	3.70431	−	2.25725i	0.226700	−	0.138141i
$268$	3.38625	+	12.6377i	0.206848	+	0.771967i
$269$	21.5499	+	12.4418i	1.31392	+	0.758591i	0.982743	−	0.184978i	$-0.0592214\pi$
$269$	21.5499	+	12.4418i	1.31392	+	0.758591i	0.331176	+	0.943569i	$0.392555\pi$
$270$	−0.683856	+	3.54088i	−0.0416181	+	0.215491i
$271$	−0.766787	−	0.205460i	−0.0465790	−	0.0124808i	0.235454	−	0.971885i	$-0.424342\pi$
$271$	−0.766787	−	0.205460i	−0.0465790	−	0.0124808i	−0.282033	+	0.959405i	$0.591009\pi$
$272$	−2.32181	+	4.02149i	−0.140780	+	0.243838i
$273$	14.7531	+	24.5775i	0.892898	+	1.48750i
$274$	−3.82397	−	6.62331i	−0.231015	−	0.400129i
$275$	2.63148	+	9.82081i	0.158684	+	0.592217i
$276$	2.31445	+	7.88601i	0.139313	+	0.474682i
$277$	28.5357	−	16.4751i	1.71455	−	0.989893i	0.786366	−	0.617760i	$-0.211960\pi$
$277$	28.5357	−	16.4751i	1.71455	−	0.989893i	0.928179	−	0.372133i	$-0.121373\pi$
$278$	7.90068	−	7.90068i	0.473851	−	0.473851i
$279$	−19.7803	−	4.30823i	−1.18422	−	0.257927i
$280$	−0.824524	−	3.07717i	−0.0492747	−	0.183896i
$281$	−17.5706	+	4.70802i	−1.04817	+	0.280857i	−0.741496	−	0.670957i	$-0.765883\pi$
$281$	−17.5706	+	4.70802i	−1.04817	+	0.280857i	−0.306676	+	0.951814i	$0.599217\pi$
$282$	−20.0621	+	5.88797i	−1.19468	+	0.350624i
$283$	−21.1331	−	12.2012i	−1.25624	−	0.725288i	−0.283895	−	0.958856i	$-0.591627\pi$
$283$	−21.1331	−	12.2012i	−1.25624	−	0.725288i	−0.972341	+	0.233568i	$0.924960\pi$
$284$	−15.5615	+	4.16970i	−0.923406	+	0.247426i
$285$	−2.53102	−	2.41394i	−0.149925	−	0.142989i
$286$	−8.11314	−	0.0539834i	−0.479740	−	0.00319211i
$287$			26.3552i			1.55570i
$288$	−2.21934	−	2.01855i	−0.130776	−	0.118944i
$289$	−2.28157	−	3.95179i	−0.134210	−	0.232458i
$290$	1.69423	+	2.93449i	0.0994886	+	0.172319i
$291$	1.81594	−	1.10656i	0.106452	−	0.0648674i
$292$	5.55110	+	5.55110i	0.324853	+	0.324853i
$293$	2.57215	+	2.57215i	0.150266	+	0.150266i	0.778237	−	0.627971i	$-0.216114\pi$
$293$	2.57215	+	2.57215i	0.150266	+	0.150266i	−0.627971	+	0.778237i	$0.716114\pi$
$294$	−21.3866	−	11.6815i	−1.24729	−	0.681279i
$295$	−1.86345	−	3.22760i	−0.108494	−	0.187918i
$296$	−1.78561	−	3.09276i	−0.103786	−	0.179763i
$297$	−11.6631	+	0.829666i	−0.676760	+	0.0481421i
$298$			7.39921i			0.428625i
$299$	8.65261	−	14.7591i	0.500394	−	0.853541i
$300$	7.50923	−	2.20387i	0.433546	−	0.127240i
$301$	−23.5279	+	6.30429i	−1.35613	+	0.363373i
$302$	−12.4099	−	7.16486i	−0.714110	−	0.412291i
$303$	4.71827	+	4.50002i	0.271058	+	0.258519i
$304$	2.81042	−	0.753050i	0.161189	−	0.0431904i
$305$	0.560641	+	2.09234i	0.0321022	+	0.119807i
$306$	13.2704	−	4.23836i	0.758620	−	0.242291i
$307$	10.8993	−	10.8993i	0.622055	−	0.622055i	−0.324001	−	0.946057i	$-0.605028\pi$
$307$	10.8993	−	10.8993i	0.622055	−	0.622055i	0.946057	+	0.324001i	$0.105028\pi$
$308$	8.94507	−	5.16444i	0.509693	−	0.294271i
$309$	−25.5709	−	6.20690i	−1.45468	−	0.353098i
$310$	−1.21214	−	4.52377i	−0.0688450	−	0.256933i
$311$	−5.37895	−	9.31661i	−0.305012	−	0.528296i	0.672252	−	0.740322i	$-0.265327\pi$
$311$	−5.37895	−	9.31661i	−0.305012	−	0.528296i	−0.977264	+	0.212026i	$0.931994\pi$
$312$	0.106275	+	6.24409i	0.00601664	+	0.353502i
$313$	6.34655	−	10.9926i	0.358728	−	0.621336i	−0.629020	−	0.777389i	$-0.716544\pi$
$313$	6.34655	−	10.9926i	0.358728	−	0.621336i	0.987749	+	0.156053i	$0.0498771\pi$
$314$	−5.52710	−	1.48098i	−0.311912	−	0.0835766i
$315$	−4.38151	+	8.49361i	−0.246870	+	0.478561i
$316$	2.69161	+	1.55400i	0.151415	+	0.0874193i
$317$	−6.74033	−	25.1552i	−0.378574	−	1.41286i	−0.848051	−	0.529914i	$-0.822224\pi$
$317$	−6.74033	−	25.1552i	−0.378574	−	1.41286i	0.469477	−	0.882945i	$-0.344443\pi$
$318$	−0.207684	−	8.77169i	−0.0116463	−	0.491892i
$319$	−7.76843	+	7.76843i	−0.434948	+	0.434948i
$320$	0.179629	−	0.670386i	0.0100416	−	0.0374757i
$321$	9.20196	+	2.23362i	0.513603	+	0.124668i
$322$			21.7803i			1.21377i
$323$	−3.49687	+	13.0505i	−0.194571	+	0.726150i
$324$	0.850926	+	8.95968i	0.0472737	+	0.497760i
$325$	−14.0539	−	8.23920i	−0.779572	−	0.457029i
$326$	−4.83910	−	2.79386i	−0.268013	−	0.154737i
$327$	−0.295770	−	12.4921i	−0.0163561	−	0.690814i
$328$	−2.87085	+	4.97245i	−0.158516	+	0.274558i
$329$	−55.4094			−3.05482
$330$	−1.40758	−	2.30994i	−0.0774845	−	0.127158i
$331$	−5.24463	+	19.5732i	−0.288271	+	1.07584i	0.658145	+	0.752891i	$0.271341\pi$
$331$	−5.24463	+	19.5732i	−0.288271	+	1.07584i	−0.946416	+	0.322950i	$0.895325\pi$
$332$	9.17998	−	2.45977i	0.503817	−	0.134997i
$333$	−2.28002	+	10.4682i	−0.124945	+	0.573655i
$334$	12.2447	−	21.2084i	0.670000	−	1.16047i
$335$	9.08037			0.496114
$336$	−4.13704	−	6.78919i	−0.225694	−	0.370381i
$337$	−6.82932	+	3.94291i	−0.372017	+	0.214784i	−0.674339	−	0.738422i	$-0.735571\pi$
$337$	−6.82932	+	3.94291i	−0.372017	+	0.214784i	0.302322	+	0.953206i	$0.402238\pi$
$338$	9.31390	−	9.06925i	0.506609	−	0.493302i
$339$	−0.565302	+	0.592720i	−0.0307030	+	0.0321922i
$340$	2.27888	+	2.27888i	0.123590	+	0.123590i
$341$	13.1502	−	7.59229i	0.712125	−	0.411146i
$342$	−7.75735	−	4.00170i	−0.419469	−	0.216387i
$343$	−22.9453	−	22.9453i	−1.23893	−	1.23893i
$344$	−5.12575	−	1.37344i	−0.276362	−	0.0740510i
$345$	5.70241	−	0.135014i	0.307008	−	0.00726890i
$346$	−10.2330	−	2.74192i	−0.550129	−	0.147407i
$347$			16.9956i			0.912370i	0.889885	+	0.456185i	$0.150784\pi$
$347$			16.9956i			0.912370i	−0.889885	+	0.456185i	$0.849216\pi$
$348$	6.11938	+	5.83631i	0.328033	+	0.312859i
$349$	−10.2799	+	10.2799i	−0.550269	+	0.550269i	−0.926518	−	0.376250i	$-0.877214\pi$
$349$	−10.2799	+	10.2799i	−0.550269	+	0.550269i	0.376250	+	0.926518i	$0.377214\pi$
$350$	20.7397			1.10858
$351$	12.3681	−	14.0723i	0.660163	−	0.751123i
$352$	2.25023			0.119938
$353$	−6.02030	+	6.02030i	−0.320428	+	0.320428i	−0.848931	−	0.528503i	$-0.822754\pi$
$353$	−6.02030	+	6.02030i	−0.320428	+	0.320428i	0.528503	+	0.848931i	$0.322754\pi$
$354$	−6.73061	−	6.41926i	−0.357728	−	0.341180i
$355$			11.1812i			0.593438i
$356$	2.41913	+	0.648204i	0.128214	+	0.0343548i
$357$	36.9080	−	0.873857i	1.95338	−	0.0462494i
$358$	−12.0275	−	3.22277i	−0.635674	−	0.170328i
$359$	2.80645	+	2.80645i	0.148119	+	0.148119i	0.777277	−	0.629158i	$-0.216600\pi$
$359$	2.80645	+	2.80645i	0.148119	+	0.148119i	−0.629158	+	0.777277i	$0.716600\pi$
$360$	−1.75186	+	1.12522i	−0.0923314	+	0.0593044i
$361$	−9.12309	+	5.26722i	−0.480163	+	0.277222i
$362$	13.0436	+	13.0436i	0.685558	+	0.685558i
$363$	−7.09652	+	7.44071i	−0.372471	+	0.390536i
$364$	−4.38972	+	15.9572i	−0.230084	+	0.836385i
$365$	4.71852	−	2.72424i	0.246979	−	0.142593i
$366$	2.81301	+	4.61636i	0.147038	+	0.241301i
$367$	−24.3581			−1.27148			−0.635742	−	0.771901i	$-0.719306\pi$
$367$	−24.3581			−1.27148			−0.635742	+	0.771901i	$0.719306\pi$
$368$	−2.37251	+	4.10931i	−0.123676	+	0.214213i
$369$	16.4085	−	5.24061i	0.854193	−	0.272815i
$370$	−2.39409	+	0.641495i	−0.124463	+	0.0333497i
$371$	6.01820	−	22.4602i	0.312449	−	1.16608i
$372$	−6.08190	−	9.98086i	−0.315332	−	0.517483i
$373$	−9.25807			−0.479365			−0.239682	−	0.970851i	$-0.577043\pi$
$373$	−9.25807			−0.479365			−0.239682	+	0.970851i	$0.577043\pi$
$374$	−5.22460	+	9.04927i	−0.270158	+	0.467927i
$375$	−0.270832	−	11.4388i	−0.0139857	−	0.590697i
$376$	−10.4541	−	6.03569i	−0.539130	−	0.311267i
$377$	0.117126	−	17.6029i	0.00603231	−	0.906593i
$378$	−4.52282	+	23.4183i	−0.232629	+	1.20451i
$379$	−3.58050	+	13.3626i	−0.183918	+	0.686391i	0.810942	+	0.585127i	$0.198955\pi$
$379$	−3.58050	+	13.3626i	−0.183918	+	0.686391i	−0.994860	+	0.101264i	$0.967711\pi$
$380$		−	2.01934i		−	0.103590i
$381$	0.732909	+	0.177901i	0.0375481	+	0.00911414i
$382$	2.20401	−	8.22549i	0.112767	−	0.420853i
$383$	12.5916	−	12.5916i	0.643398	−	0.643398i	−0.307991	−	0.951389i	$-0.599657\pi$
$383$	12.5916	−	12.5916i	0.643398	−	0.643398i	0.951389	+	0.307991i	$0.0996567\pi$
$384$	−0.0409976	−	1.73157i	−0.00209215	−	0.0883636i
$385$	−1.85537	−	6.92433i	−0.0945584	−	0.352897i
$386$	−16.3939	−	9.46505i	−0.834430	−	0.481758i
$387$	8.60342	+	13.3947i	0.437336	+	0.680891i
$388$	1.18591	+	0.317765i	0.0602057	+	0.0161321i
$389$	7.46970	−	12.9379i	0.378729	−	0.655978i	−0.612149	−	0.790743i	$-0.709695\pi$
$389$	7.46970	−	12.9379i	0.378729	−	0.655978i	0.990878	+	0.134765i	$0.0430279\pi$
$390$	4.20504	+	1.05038i	0.212931	+	0.0531879i
$391$	−11.0170	−	19.0821i	−0.557155	−	0.965021i
$392$	−3.64143	−	13.5900i	−0.183920	−	0.686398i
$393$	17.5372	+	4.25684i	0.884633	+	0.214729i
$394$	−15.1031	+	8.71978i	−0.760884	+	0.439296i
$395$	1.52527	−	1.52527i	0.0767447	−	0.0767447i
$396$	−4.99402	−	4.54220i	−0.250959	−	0.228254i
$397$	0.691339	+	2.58011i	0.0346973	+	0.129492i	0.981102	−	0.193491i	$-0.0619810\pi$
$397$	0.691339	+	2.58011i	0.0346973	+	0.129492i	−0.946405	+	0.322983i	$0.895314\pi$
$398$	22.3261	−	5.98226i	1.11911	−	0.299864i
$399$	−16.7394	−	15.9651i	−0.838019	−	0.799254i
$400$	3.91298	+	2.25916i	0.195649	+	0.112958i
$401$	−0.0650204	+	0.0174222i	−0.00324697	+	0.000870022i	−0.260442	−	0.965489i	$-0.583868\pi$
$401$	−0.0650204	+	0.0174222i	−0.00324697	+	0.000870022i	0.257195	+	0.966359i	$0.417202\pi$
$402$	21.7441	−	6.38162i	1.08450	−	0.318287i
$403$	−6.45338	+	23.4588i	−0.321466	+	1.16857i
$404$			3.76440i			0.187286i
$405$	6.15930	+	1.03897i	0.306058	+	0.0516270i
$406$	11.2051	+	19.4079i	0.556101	+	0.963196i
$407$	−4.01803	−	6.95943i	−0.199166	−	0.344966i
$408$	7.05866	+	3.85549i	0.349456	+	0.190875i
$409$	−14.4433	−	14.4433i	−0.714173	−	0.714173i	0.253233	−	0.967405i	$-0.418506\pi$
$409$	−14.4433	−	14.4433i	−0.714173	−	0.714173i	−0.967405	+	0.253233i	$0.918506\pi$
$410$	2.81777	+	2.81777i	0.139160	+	0.139160i
$411$	−11.3119	+	6.89300i	−0.557976	+	0.340006i
$412$	−7.59604	−	13.1567i	−0.374230	−	0.648186i
$413$	−12.3243	−	21.3464i	−0.606441	−	1.05039i
$414$	13.5603	−	4.33093i	0.666450	−	0.212853i
$415$		−	6.59597i		−	0.323784i
$416$	−2.56642	+	2.53249i	−0.125829	+	0.124166i
$417$	−14.0045	−	13.3566i	−0.685801	−	0.654077i
$418$	6.32410	−	1.69454i	0.309322	−	0.0828825i
$419$	−19.8836	−	11.4798i	−0.971378	−	0.560826i	−0.0717221	−	0.997425i	$-0.522849\pi$
$419$	−19.8836	−	11.4798i	−0.971378	−	0.560826i	−0.899656	+	0.436599i	$0.856183\pi$
$420$	−5.29451	+	1.55387i	−0.258346	+	0.0758213i
$421$	10.9066	−	2.92242i	0.531556	−	0.142430i	0.0169495	−	0.999856i	$-0.494605\pi$
$421$	10.9066	−	2.92242i	0.531556	−	0.142430i	0.514607	+	0.857426i	$0.327938\pi$
$422$	−2.68874	−	10.0345i	−0.130886	−	0.488472i
$423$	11.0179	+	34.4974i	0.535709	+	1.67732i
$424$	3.58203	−	3.58203i	0.173959	−	0.173959i
$425$	−18.1703	+	10.4907i	−0.881391	+	0.508871i
$426$	7.85809	+	26.7748i	0.380726	+	1.29725i
$427$	3.70792	+	13.8381i	0.179439	+	0.669674i
$428$	2.73351	+	4.73458i	0.132129	+	0.228855i
$429$	0.239144	+	14.0507i	0.0115460	+	0.678372i
$430$	−1.84147	+	3.18952i	−0.0888036	+	0.153812i
$431$	8.79469	+	2.35653i	0.423625	+	0.113510i	0.464332	−	0.885661i	$-0.346294\pi$
$431$	8.79469	+	2.35653i	0.423625	+	0.113510i	−0.0407069	+	0.999171i	$0.512961\pi$
$432$	−3.40426	+	3.92569i	−0.163788	+	0.188875i
$433$	19.6096	+	11.3216i	0.942379	+	0.544083i	0.890705	−	0.454581i	$-0.150211\pi$
$433$	19.6096	+	11.3216i	0.942379	+	0.544083i	0.0516737	+	0.998664i	$0.483544\pi$
$434$	−8.01675	−	29.9189i	−0.384816	−	1.43615i
$435$	5.01180	−	3.05398i	0.240298	−	0.146427i
$436$	5.10130	−	5.10130i	0.244308	−	0.244308i
$437$	−3.57325	+	13.3355i	−0.170931	+	0.637925i
$438$	9.38451	−	9.83967i	0.448409	−	0.470158i
$439$			21.3894i			1.02086i	0.859920	+	0.510430i	$0.170514\pi$
$439$			21.3894i			1.02086i	−0.859920	+	0.510430i	$0.829486\pi$
$440$	0.404207	−	1.50852i	0.0192698	−	0.0719160i
$441$	−19.3505	+	37.5112i	−0.921452	+	1.78625i
$442$	−4.22565	−	16.2008i	−0.200994	−	0.770592i
$443$	27.1059	+	15.6496i	1.28784	+	0.743535i	0.978269	−	0.207341i	$-0.0664811\pi$
$443$	27.1059	+	15.6496i	1.28784	+	0.743535i	0.309571	+	0.950876i	$0.399814\pi$
$444$	−5.28212	+	3.21869i	−0.250678	+	0.152752i
$445$	0.869094	−	1.50532i	0.0411990	−	0.0713588i
$446$	15.8661			0.751283
$447$	12.8122	−	0.303350i	0.605997	−	0.0143480i
$448$	1.18802	−	4.43374i	0.0561285	−	0.209474i
$449$	12.7731	−	3.42254i	0.602800	−	0.161520i	0.0555034	−	0.998458i	$-0.482324\pi$
$449$	12.7731	−	3.42254i	0.602800	−	0.161520i	0.547297	+	0.836939i	$0.315657\pi$
$450$	−4.12400	−	12.9124i	−0.194407	−	0.608695i
$451$	−6.46007	+	11.1892i	−0.304193	+	0.526877i
$452$	−0.472893			−0.0222430
$453$	−11.8977	+	21.7823i	−0.559000	+	1.02342i
$454$	5.52042	−	3.18721i	0.259086	−	0.149583i
$455$	9.90896	+	5.80919i	0.464539	+	0.272339i
$456$	−1.41918	−	4.83556i	−0.0664590	−	0.226446i
$457$	8.28185	+	8.28185i	0.387409	+	0.387409i	0.873762	−	0.486354i	$-0.161673\pi$
$457$	8.28185	+	8.28185i	0.387409	+	0.387409i	−0.486354	+	0.873762i	$0.661673\pi$
$458$	11.0794	−	6.39671i	0.517707	−	0.298898i
$459$	−7.88306	−	22.8049i	−0.367950	−	1.06444i
$460$	2.32865	+	2.32865i	0.108574	+	0.108574i
$461$	7.07647	+	1.89613i	0.329584	+	0.0883118i	0.419817	−	0.907609i	$-0.362094\pi$
$461$	7.07647	+	1.89613i	0.329584	+	0.0883118i	−0.0902326	+	0.995921i	$0.528761\pi$
$462$	−9.30929	−	15.2772i	−0.433107	−	0.710762i
$463$	−14.1615	−	3.79457i	−0.658142	−	0.176349i	−0.0857346	−	0.996318i	$-0.527324\pi$
$463$	−14.1615	−	3.79457i	−0.658142	−	0.176349i	−0.572407	+	0.819969i	$0.693990\pi$
$464$			4.88226i			0.226653i
$465$	−7.78351	+	2.28437i	−0.360952	+	0.105935i
$466$	12.9149	−	12.9149i	0.598271	−	0.598271i
$467$	−18.0118			−0.833488			−0.416744	−	0.909024i	$-0.636829\pi$
$467$	−18.0118			−0.833488			−0.416744	+	0.909024i	$0.636829\pi$
$468$	10.8077	−	0.440015i	0.499586	−	0.0203397i
$469$	60.0549			2.77308
$470$	−5.92411	+	5.92411i	−0.273259	+	0.273259i
$471$	−2.33782	+	9.63125i	−0.107721	+	0.443785i
$472$		−	5.36992i		−	0.247170i
$473$	−11.5341	−	3.09056i	−0.530339	−	0.142104i
$474$	2.58050	−	4.72440i	0.118526	−	0.216999i
$475$	12.6984	+	3.40252i	0.582641	+	0.156118i
$476$	15.0719	+	15.0719i	0.690818	+	0.690818i
$477$	−15.1802	+	0.719237i	−0.695056	+	0.0329316i
$478$	17.3211	−	10.0003i	0.792249	−	0.457405i
$479$	−5.08536	−	5.08536i	−0.232356	−	0.232356i	0.581319	−	0.813675i	$-0.302537\pi$
$479$	−5.08536	−	5.08536i	−0.232356	−	0.232356i	−0.813675	+	0.581319i	$0.802537\pi$
$480$	−1.16818	−	0.283556i	−0.0533199	−	0.0129425i
$481$	12.4150	+	3.41529i	0.566075	+	0.155724i
$482$	−13.0385	+	7.52778i	−0.593887	+	0.342881i
$483$	37.7141	−	0.892942i	1.71605	−	0.0406303i
$484$	−5.93646			−0.269839
$485$	0.426050	−	0.737940i	0.0193459	−	0.0335082i
$486$	15.4794	−	1.84076i	0.702160	−	0.0834985i
$487$	0.324094	−	0.0868407i	0.0146861	−	0.00393513i	−0.251469	−	0.967865i	$-0.580913\pi$
$487$	0.324094	−	0.0868407i	0.0146861	−	0.00393513i	0.266155	+	0.963930i	$0.414247\pi$
$488$	−0.807800	+	3.01475i	−0.0365674	+	0.136471i
$489$	−4.63935	+	8.49376i	−0.209799	+	0.384101i
$490$	−9.76464			−0.441122
$491$	−1.96382	+	3.40144i	−0.0886260	+	0.153505i	−0.906931	−	0.421280i	$-0.861581\pi$
$491$	−1.96382	+	3.40144i	−0.0886260	+	0.153505i	0.818305	+	0.574785i	$0.194914\pi$
$492$	8.72782	+	4.76720i	0.393481	+	0.214922i
$493$	−19.6339	−	11.3357i	−0.884269	−	0.510533i
$494$	−5.30562	+	9.05001i	−0.238711	+	0.407179i
$495$	−3.94210	+	2.53201i	−0.177184	+	0.113805i
$496$	1.74651	−	6.51808i	0.0784208	−	0.292670i
$497$			73.9493i			3.31708i
$498$	−4.63561	−	15.7949i	−0.207726	−	0.707786i
$499$	−5.25372	+	19.6072i	−0.235189	+	0.877737i	0.742875	+	0.669431i	$0.233462\pi$
$499$	−5.25372	+	19.6072i	−0.235189	+	0.877737i	−0.978064	+	0.208307i	$0.933205\pi$
$500$	4.67118	−	4.67118i	0.208901	−	0.208901i
$501$	−37.2258	−	20.3330i	−1.66313	−	0.908411i
$502$	6.80338	+	25.3906i	0.303650	+	1.13324i
$503$	24.7833	+	14.3086i	1.10503	+	0.637991i	0.937538	−	0.347882i	$-0.113099\pi$
$503$	24.7833	+	14.3086i	1.10503	+	0.637991i	0.167494	+	0.985873i	$0.446432\pi$
$504$	−11.5863	+	7.44189i	−0.516096	+	0.331488i
$505$	2.52360	+	0.676198i	0.112299	+	0.0300904i
$506$	−5.33870	+	9.24691i	−0.237334	+	0.411075i
$507$	−16.0858	−	15.7558i	−0.714398	−	0.699740i
$508$	0.217716	+	0.377096i	0.00965960	+	0.0167309i
$509$	−4.15448	−	15.5047i	−0.184144	−	0.687235i	−0.994812	−	0.101729i	$-0.967562\pi$
$509$	−4.15448	−	15.5047i	−0.184144	−	0.687235i	0.810668	−	0.585506i	$-0.199104\pi$
$510$	3.85261	−	4.03946i	0.170596	−	0.178870i
$511$	31.2069	−	18.0173i	1.38051	−	0.797039i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−6.61117	+	13.5964i	−0.291890	+	0.600296i
$514$	−3.53697	−	13.2002i	−0.156009	−	0.582235i
$515$	−10.1846	+	2.72894i	−0.448785	+	0.120252i
$516$	−2.16806	+	8.93188i	−0.0954435	+	0.393204i
$517$	−23.5242	−	13.5817i	−1.03459	−	0.597323i
$518$	−15.8338	+	4.24266i	−0.695698	+	0.186412i
$519$	−4.32829	+	17.8315i	−0.189991	+	0.782716i
$520$	1.23674	+	2.17540i	0.0542347	+	0.0953976i
$521$		−	19.3205i		−	0.846448i	−0.906025	−	0.423224i	$-0.860898\pi$
$521$		−	19.3205i		−	0.846448i	0.906025	−	0.423224i	$-0.139102\pi$
$522$	9.85508	−	10.8354i	0.431345	−	0.474252i
$523$	4.17667	+	7.23421i	0.182633	+	0.316330i	0.942776	−	0.333426i	$-0.108205\pi$
$523$	4.17667	+	7.23421i	0.182633	+	0.316330i	−0.760143	+	0.649755i	$0.774871\pi$
$524$	5.20955	+	9.02321i	0.227580	+	0.394181i
$525$	−0.850278	−	35.9122i	−0.0371092	−	1.56734i
$526$	−3.39129	−	3.39129i	−0.147867	−	0.147867i
$527$	22.1573	+	22.1573i	0.965187	+	0.965187i
$528$	−0.0922541	−	3.89642i	−0.00401484	−	0.169570i
$529$	0.242357	+	0.419774i	0.0105372	+	0.0182510i
$530$	−1.75791	−	3.04478i	−0.0763585	−	0.132257i
$531$	−10.8394	+	11.9177i	−0.470392	+	0.517183i
$532$		−	13.3553i		−	0.579026i
$533$	−5.22489	−	20.0318i	−0.226315	−	0.867672i
$534$	1.02323	−	4.21546i	0.0442795	−	0.182421i
$535$	3.66502	−	0.982038i	0.158452	−	0.0424572i
$536$	11.3306	+	6.54173i	0.489408	+	0.282560i
$537$	−5.08733	+	20.9586i	−0.219535	+	0.904429i
$538$	24.0358	−	6.44036i	1.03625	−	0.277664i
$539$	−8.19405	−	30.5806i	−0.352943	−	1.31720i
$540$	2.02022	+	2.98734i	0.0869364	+	0.128555i
$541$	18.5480	−	18.5480i	0.797443	−	0.797443i	−0.185249	−	0.982692i	$-0.559309\pi$
$541$	18.5480	−	18.5480i	0.797443	−	0.797443i	0.982692	+	0.185249i	$0.0593092\pi$
$542$	−0.687482	+	0.396918i	−0.0295299	+	0.0170491i
$543$	22.0511	−	23.1207i	0.946305	−	0.992202i
$544$	1.20186	+	4.48539i	0.0515291	+	0.192309i
$545$	−2.50350	−	4.33618i	−0.107238	−	0.185742i
$546$	27.8109	+	6.94689i	1.19020	+	0.297299i
$547$	−11.1826	+	19.3688i	−0.478133	+	0.828151i	−0.999686	−	0.0250681i	$-0.992020\pi$
$547$	−11.1826	+	19.3688i	−0.478133	+	0.828151i	0.521552	+	0.853219i	$0.325353\pi$
$548$	−7.38734	−	1.97943i	−0.315572	−	0.0845572i
$549$	7.87820	−	5.06017i	0.336234	−	0.215963i
$550$	8.80510	+	5.08363i	0.375451	+	0.216767i
$551$	3.67659	+	13.7212i	0.156628	+	0.584544i
$552$	7.21281	+	3.93969i	0.306998	+	0.167684i
$553$	10.0877	−	10.0877i	0.428972	−	0.428972i
$554$	8.52814	−	31.8275i	0.362326	−	1.35222i
$555$	1.20894	+	4.11923i	0.0513168	+	0.174851i
$556$		−	11.1732i		−	0.473851i
$557$	−3.13004	+	11.6815i	−0.132624	+	0.494959i	−0.999996	−	0.00270033i	$-0.999140\pi$
$557$	−3.13004	+	11.6815i	−0.132624	+	0.494959i	0.867372	+	0.497660i	$0.165807\pi$
$558$	−17.0332	+	10.9404i	−0.721071	+	0.463144i
$559$	16.6330	−	9.45609i	0.703503	−	0.399950i
$560$	−2.75891	−	1.59286i	−0.116585	−	0.0673105i
$561$	15.8836	+	8.67574i	0.670606	+	0.366290i
$562$	−9.09520	+	15.7533i	−0.383658	+	0.664515i
$563$	35.1807			1.48269			0.741345	−	0.671124i	$-0.234188\pi$
$563$	35.1807			1.48269			0.741345	+	0.671124i	$0.234188\pi$
$564$	−10.0226	+	18.3495i	−0.422028	+	0.772651i
$565$	−0.0849455	+	0.317021i	−0.00357368	+	0.0133372i
$566$	−23.5710	+	6.31582i	−0.990761	+	0.265474i
$567$	40.7358	+	6.87147i	1.71074	+	0.288574i
$568$	−8.05524	+	13.9521i	−0.337990	+	0.585416i
$569$	−11.2623			−0.472141			−0.236071	−	0.971736i	$-0.575860\pi$
$569$	−11.2623			−0.472141			−0.236071	+	0.971736i	$0.575860\pi$
$570$	−3.49662	+	0.0827880i	−0.146457	+	0.00346761i
$571$	27.0909	−	15.6409i	1.13372	−	0.654553i	0.188852	−	0.982006i	$-0.439523\pi$
$571$	27.0909	−	15.6409i	1.13372	−	0.654553i	0.944868	+	0.327452i	$0.106190\pi$
$572$	−5.77503	+	5.69869i	−0.241466	+	0.238274i
$573$	−14.3333	−	3.47917i	−0.598783	−	0.145344i
$574$	18.6359	+	18.6359i	0.777848	+	0.777848i
$575$	−18.5672	+	10.7198i	−0.774305	+	0.447045i
$576$	−2.99664	+	0.141980i	−0.124860	+	0.00591584i
$577$	−26.9790	−	26.9790i	−1.12315	−	1.12315i	−0.991265	−	0.131887i	$-0.957897\pi$
$577$	−26.9790	−	26.9790i	−1.12315	−	1.12315i	−0.131887	−	0.991265i	$-0.542103\pi$
$578$	−4.40765	−	1.18103i	−0.183334	−	0.0491242i
$579$	−15.7172	+	28.7752i	−0.653186	+	1.19586i
$580$	3.27300	+	0.876997i	0.135904	+	0.0364153i
$581$		−	43.6238i		−	1.80982i
$582$	0.501611	−	2.06652i	0.0207924	−	0.0856599i
$583$	8.06040	−	8.06040i	0.333828	−	0.333828i
$584$	7.85044			0.324853
$585$	1.64640	−	7.32437i	0.0680703	−	0.302825i
$586$	3.63756			0.150266
$587$	1.61436	−	1.61436i	0.0666316	−	0.0666316i	−0.673006	−	0.739637i	$-0.734997\pi$
$587$	1.61436	−	1.61436i	0.0666316	−	0.0666316i	0.739637	+	0.673006i	$0.234997\pi$
$588$	−23.3827	+	6.86253i	−0.964285	+	0.283006i
$589$		−	19.6338i		−	0.808995i
$590$	−3.59992	−	0.964595i	−0.148206	−	0.0397117i
$591$	15.7181	+	25.7945i	0.646555	+	1.06105i
$592$	−3.44953	−	0.924299i	−0.141775	−	0.0379884i
$593$	−21.4122	−	21.4122i	−0.879295	−	0.879295i	0.114166	−	0.993462i	$-0.463580\pi$
$593$	−21.4122	−	21.4122i	−0.879295	−	0.879295i	−0.993462	+	0.114166i	$0.963580\pi$
$594$	−7.66037	+	8.83370i	−0.314309	+	0.362451i
$595$	12.8113	−	7.39662i	0.525213	−	0.303232i
$596$	5.23203	+	5.23203i	0.214312	+	0.214312i
$597$	−11.2740	−	38.4138i	−0.461414	−	1.57217i
$598$	−4.31794	−	16.5546i	−0.176574	−	0.676967i
$599$	−27.0669	+	15.6271i	−1.10593	+	0.638506i	−0.937771	−	0.347255i	$-0.887114\pi$
$599$	−27.0669	+	15.6271i	−1.10593	+	0.638506i	−0.168154	+	0.985761i	$0.553781\pi$
$600$	3.75146	−	6.86820i	0.153153	−	0.280393i
$601$	−27.8755			−1.13707			−0.568533	−	0.822661i	$-0.692489\pi$
$601$	−27.8755			−1.13707			−0.568533	+	0.822661i	$0.692489\pi$
$602$	−12.1789	+	21.0946i	−0.496377	+	0.859750i
$603$	−11.9417	−	37.3897i	−0.486302	−	1.52263i
$604$	−13.8415	+	3.70881i	−0.563201	+	0.150909i
$605$	−1.06636	+	3.97972i	−0.0433538	+	0.161799i
$606$	6.51831	−	0.154332i	0.264788	−	0.00626929i
$607$	−2.84557			−0.115498			−0.0577490	−	0.998331i	$-0.518392\pi$
$607$	−2.84557			−0.115498			−0.0577490	+	0.998331i	$0.518392\pi$
$608$	1.45478	−	2.51976i	0.0589992	−	0.102190i
$609$	33.1466	−	20.1981i	1.34317	−	0.818468i
$610$	1.87594	+	1.08308i	0.0759547	+	0.0438525i
$611$	42.1150	−	10.9849i	1.70379	−	0.444400i
$612$	6.38664	−	12.3806i	0.258165	−	0.500456i
$613$	0.202550	−	0.755928i	0.00818093	−	0.0305316i	−0.961715	−	0.274053i	$-0.911636\pi$
$613$	0.202550	−	0.755928i	0.00818093	−	0.0305316i	0.969896	+	0.243521i	$0.0783024\pi$
$614$		−	15.4139i		−	0.622055i
$615$	4.76364	−	4.99468i	0.192088	−	0.201405i
$616$	2.67331	−	9.97693i	0.107711	−	0.401982i
$617$	−19.5997	+	19.5997i	−0.789055	+	0.789055i	−0.981339	−	0.192284i	$-0.938410\pi$
$617$	−19.5997	+	19.5997i	−0.789055	+	0.789055i	0.192284	+	0.981339i	$0.438410\pi$
$618$	−22.4703	+	13.6924i	−0.903889	+	0.550791i
$619$	1.73266	+	6.46639i	0.0696417	+	0.259906i	0.991965	−	0.126513i	$-0.0403785\pi$
$619$	1.73266	+	6.46639i	0.0696417	+	0.259906i	−0.922323	+	0.386419i	$0.873712\pi$
$620$	−4.05590	−	2.34168i	−0.162889	−	0.0940440i
$621$	−8.05522	−	23.3029i	−0.323245	−	0.935114i
$622$	−10.3913	−	2.78435i	−0.416654	−	0.111642i
$623$	5.74793	−	9.95571i	0.230286	−	0.398867i
$624$	4.49039	+	4.34009i	0.179759	+	0.173743i
$625$	9.00338	+	15.5943i	0.360135	+	0.623772i
$626$	−3.28522	−	12.2606i	−0.131304	−	0.490032i
$627$	−3.19348	−	10.8811i	−0.127535	−	0.434550i
$628$	−4.95546	+	2.86104i	−0.197744	+	0.114168i
$629$	11.7262	−	11.7262i	0.467554	−	0.467554i
$630$	2.90770	+	9.10409i	0.115845	+	0.362715i
$631$	−1.16111	−	4.33331i	−0.0462230	−	0.172506i	0.938956	−	0.344038i	$-0.111795\pi$
$631$	−1.16111	−	4.33331i	−0.0462230	−	0.172506i	−0.985179	+	0.171532i	$0.945128\pi$
$632$	3.00210	−	0.804409i	0.119417	−	0.0319977i
$633$	−17.2652	+	5.06711i	−0.686229	+	0.201400i
$634$	−22.5536	−	13.0213i	−0.895717	−	0.517142i
$635$	0.291908	−	0.0782165i	0.0115840	−	0.00310393i
$636$	−6.34938	−	6.05567i	−0.251769	−	0.240123i
$637$	43.7619	+	25.6557i	1.73391	+	1.01652i
$638$			10.9862i			0.434948i
$639$	46.0402	−	14.7045i	1.82132	−	0.581701i
$640$	−0.347017	−	0.601052i	−0.0137171	−	0.0237586i
$641$	21.4910	+	37.2236i	0.848845	+	1.47024i	0.882240	+	0.470801i	$0.156035\pi$
$641$	21.4910	+	37.2236i	0.848845	+	1.47024i	−0.0333945	+	0.999442i	$0.510632\pi$
$642$	8.08617	−	4.92736i	0.319136	−	0.194467i
$643$	16.1469	+	16.1469i	0.636771	+	0.636771i	0.949758	−	0.312987i	$-0.101329\pi$
$643$	16.1469	+	16.1469i	0.636771	+	0.636771i	−0.312987	+	0.949758i	$0.601329\pi$
$644$	15.4010	+	15.4010i	0.606886	+	0.606886i
$645$	5.59836	+	3.05786i	0.220435	+	0.120403i
$646$	6.75544	+	11.7008i	0.265789	+	0.460361i
$647$	−18.2315	−	31.5780i	−0.716756	−	1.24146i	−0.962278	−	0.272067i	$-0.912293\pi$
$647$	−18.2315	−	31.5780i	−0.716756	−	1.24146i	0.245523	−	0.969391i	$-0.421040\pi$
$648$	6.93715	+	5.73376i	0.272517	+	0.225243i
$649$		−	12.0836i		−	0.474321i
$650$	−15.7636	+	4.11163i	−0.618300	+	0.161271i
$651$	−51.4779	+	15.1081i	−2.01758	+	0.592134i
$652$	−5.39731	+	1.44621i	−0.211375	+	0.0566378i
$653$	−2.93974	−	1.69726i	−0.115041	−	0.0664190i	0.441375	−	0.897323i	$-0.354491\pi$
$653$	−2.93974	−	1.69726i	−0.115041	−	0.0664190i	−0.556416	+	0.830904i	$0.687824\pi$
$654$	−9.04238	−	8.62410i	−0.353585	−	0.337229i
$655$	6.98482	−	1.87158i	0.272919	−	0.0731285i
$656$	1.48606	+	5.54605i	0.0580209	+	0.216537i
$657$	−17.4228	−	15.8465i	−0.679727	−	0.618230i
$658$	−39.1803	+	39.1803i	−1.52741	+	1.52741i
$659$	−23.7208	+	13.6952i	−0.924032	+	0.533490i	−0.884919	−	0.465745i	$-0.845786\pi$
$659$	−23.7208	+	13.6952i	−0.924032	+	0.533490i	−0.0391126	+	0.999235i	$0.512453\pi$
$660$	−2.62868	−	0.638066i	−0.102321	−	0.0248367i
$661$	11.8777	+	44.3282i	0.461990	+	1.72417i	0.666682	+	0.745342i	$0.267714\pi$
$661$	11.8777	+	44.3282i	0.461990	+	1.72417i	−0.204692	+	0.978826i	$0.565619\pi$
$662$	10.1318	+	17.5489i	0.393785	+	0.682056i
$663$	−27.8794	+	7.98118i	−1.08275	+	0.309963i
$664$	4.75191	−	8.23054i	0.184410	−	0.319407i
$665$	−8.95321	−	2.39900i	−0.347191	−	0.0930294i
$666$	5.78993	+	9.01437i	0.224355	+	0.349300i
$667$	−20.0627	−	11.5832i	−0.776833	−	0.448505i
$668$	−6.33832	−	23.6549i	−0.245237	−	0.915236i
$669$	−0.650474	−	27.4733i	−0.0251488	−	1.06218i
$670$	6.42079	−	6.42079i	0.248057	−	0.248057i
$671$	−1.81774	+	6.78389i	−0.0701730	+	0.261889i
$672$	−7.72601	−	1.87535i	−0.298037	−	0.0723434i
$673$			20.6898i			0.797535i	0.917052	+	0.398767i	$0.130562\pi$
$673$			20.6898i			0.797535i	−0.917052	+	0.398767i	$0.869438\pi$
$674$	−2.04100	+	7.61712i	−0.0786164	+	0.293401i
$675$	−22.1895	+	7.67035i	−0.854076	+	0.295232i
$676$	0.172992	−	12.9988i	0.00665353	−	0.499956i
$677$	6.49755	+	3.75136i	0.249721	+	0.144176i	0.619636	−	0.784889i	$-0.287280\pi$
$677$	6.49755	+	3.75136i	0.249721	+	0.144176i	−0.369916	+	0.929065i	$0.620613\pi$
$678$	0.0193875	+	0.818846i	0.000744572	+	0.0314476i
$679$	2.81777	−	4.88052i	0.108136	−	0.187297i
$680$	3.22283			0.123590
$681$	−5.74519	−	9.42830i	−0.220156	−	0.361293i
$682$	3.93006	−	14.6672i	0.150490	−	0.561635i
$683$	−39.9739	+	10.7110i	−1.52956	+	0.409844i	−0.922875	−	0.385100i	$-0.874167\pi$
$683$	−39.9739	+	10.7110i	−1.52956	+	0.409844i	−0.606683	+	0.794944i	$0.707500\pi$
$684$	−8.31490	+	2.65564i	−0.317928	+	0.101541i
$685$	−2.65397	+	4.59681i	−0.101403	+	0.175635i
$686$	−32.4495			−1.23893
$687$	−11.5305	−	18.9225i	−0.439918	−	0.721938i
$688$	−4.59562	+	2.65328i	−0.175206	+	0.101155i
$689$	−0.121528	+	18.2644i	−0.00462986	+	0.695820i
$690$	3.93675	−	4.12768i	0.149869	−	0.157138i
$691$	3.99681	+	3.99681i	0.152046	+	0.152046i	0.779031	−	0.626985i	$-0.215711\pi$
$691$	3.99681	+	3.99681i	0.152046	+	0.152046i	−0.626985	+	0.779031i	$0.715711\pi$
$692$	−9.17465	+	5.29699i	−0.348768	+	0.201361i
$693$	−26.0719	+	16.7460i	−0.990389	+	0.636127i
$694$	12.0177	+	12.0177i	0.456185	+	0.456185i
$695$	−7.49039	−	2.00704i	−0.284127	−	0.0761315i
$696$	8.45396	−	0.200161i	0.320446	−	0.00758708i
$697$	−25.7537	−	6.90068i	−0.975491	−	0.261382i
$698$			14.5379i			0.550269i
$699$	−22.8925	−	21.8335i	−0.865872	−	0.825819i
$700$	14.6652	−	14.6652i	0.554292	−	0.554292i
$701$	40.7022			1.53730			0.768651	−	0.639669i	$-0.220928\pi$
$701$	40.7022			1.53730			0.768651	+	0.639669i	$0.220928\pi$
$702$	−1.20500	−	18.6962i	−0.0454800	−	0.705643i
$703$	−10.3907			−0.391892
$704$	1.59115	−	1.59115i	0.0599688	−	0.0599688i
$705$	10.5009	+	10.0151i	0.395485	+	0.377191i
$706$			8.51399i			0.320428i
$707$	16.6904	+	4.47217i	0.627706	+	0.168193i
$708$	−9.29836	+	0.220154i	−0.349454	+	0.00827388i
$709$	1.65798	+	0.444255i	0.0622668	+	0.0166843i	0.289818	−	0.957082i	$-0.406405\pi$
$709$	1.65798	+	0.444255i	0.0622668	+	0.0166843i	−0.227551	+	0.973766i	$0.573072\pi$
$710$	7.90632	+	7.90632i	0.296719	+	0.296719i
$711$	−8.28641	−	4.27462i	−0.310765	−	0.160311i
$712$	2.16893	−	1.25223i	0.0812843	−	0.0469295i
$713$	22.6412	+	22.6412i	0.847920	+	0.847920i
$714$	25.4800	−	26.7158i	0.953565	−	0.999815i
$715$	2.78295	+	4.89515i	0.104077	+	0.183068i
$716$	−10.7836	+	6.22591i	−0.403001	+	0.232673i
$717$	−18.0264	−	29.5826i	−0.673207	−	1.10478i
$718$	3.96892			0.148119
$719$	−10.3528	+	17.9315i	−0.386093	+	0.668732i	−0.991920	−	0.126864i	$-0.959509\pi$
$719$	−10.3528	+	17.9315i	−0.386093	+	0.668732i	0.605827	+	0.795596i	$0.292842\pi$
$720$	−0.443103	+	2.03441i	−0.0165135	+	0.0758179i
$721$	−67.3577	+	18.0484i	−2.50853	+	0.672159i
$722$	−2.72651	+	10.1755i	−0.101470	+	0.378692i
$723$	13.5694	+	22.2684i	0.504651	+	0.828171i
$724$	18.4465			0.685558
$725$	−11.0298	+	19.1042i	−0.409637	+	0.709511i
$726$	0.243381	+	10.2794i	0.00903270	+	0.381503i
$727$	38.1761	+	22.0410i	1.41587	+	0.817455i	0.995933	−	0.0900971i	$-0.0287178\pi$
$727$	38.1761	+	22.0410i	1.41587	+	0.817455i	0.419940	+	0.907552i	$0.362051\pi$
$728$	8.17945	+	14.3875i	0.303150	+	0.533234i
$729$	−3.82201	−	26.7281i	−0.141556	−	0.989930i
$730$	1.41017	−	5.26282i	0.0521927	−	0.194786i
$731$		−	24.6416i		−	0.911404i
$732$	5.25336	+	1.27516i	0.194170	+	0.0471313i
$733$	−5.25644	+	19.6173i	−0.194151	+	0.724582i	0.798334	+	0.602215i	$0.205715\pi$
$733$	−5.25644	+	19.6173i	−0.194151	+	0.724582i	−0.992485	+	0.122367i	$0.960952\pi$
$734$	−17.2238	+	17.2238i	−0.635742	+	0.635742i
$735$	0.400327	+	16.9081i	0.0147663	+	0.623665i
$736$	1.22810	+	4.58334i	0.0452685	+	0.168944i
$737$	25.4965	+	14.7204i	0.939175	+	0.542233i
$738$	7.89690	−	15.3082i	0.290689	−	0.563504i
$739$	37.8060	+	10.1301i	1.39072	+	0.372642i	0.875002	−	0.484118i	$-0.160860\pi$
$739$	37.8060	+	10.1301i	1.39072	+	0.372642i	0.515715	+	0.856760i	$0.327526\pi$
$740$	−1.23927	+	2.14648i	−0.0455566	+	0.0789063i
$741$	15.8882	+	8.81601i	0.583668	+	0.323864i
$742$	−11.6263	−	20.1373i	−0.426814	−	0.739263i
$743$	−13.6576	−	50.9709i	−0.501049	−	1.86994i	−0.493101	−	0.869972i	$-0.664137\pi$
$743$	−13.6576	−	50.9709i	−0.501049	−	1.86994i	−0.00794786	−	0.999968i	$-0.502530\pi$
$744$	−11.3581	−	2.75698i	−0.416408	−	0.101076i
$745$	4.44731	−	2.56765i	0.162937	−	0.0940716i
$746$	−6.54644	+	6.54644i	−0.239682	+	0.239682i
$747$	−27.1598	+	8.67441i	−0.993726	+	0.317380i
$748$	2.70445	+	10.0932i	0.0988845	+	0.369042i
$749$	24.2393	−	6.49491i	0.885686	−	0.237319i
$750$	−8.27995	−	7.89694i	−0.302341	−	0.288355i
$751$	−24.5558	−	14.1773i	−0.896053	−	0.517336i	−0.0201351	−	0.999797i	$-0.506410\pi$
$751$	−24.5558	−	14.1773i	−0.896053	−	0.517336i	−0.875917	+	0.482461i	$0.839743\pi$
$752$	−11.6601	+	3.12430i	−0.425199	+	0.113932i
$753$	43.6865	−	12.8214i	1.59202	−	0.467239i
$754$	−12.3643	−	12.5299i	−0.450280	−	0.456313i
$755$			9.94532i			0.361947i
$756$	13.3611	+	19.7574i	0.485940	+	0.718569i
$757$	24.6271	+	42.6555i	0.895089	+	1.55034i	0.833694	+	0.552226i	$0.186221\pi$
$757$	24.6271	+	42.6555i	0.895089	+	1.55034i	0.0613944	+	0.998114i	$0.480445\pi$
$758$	6.91700	+	11.9806i	0.251237	+	0.435155i
$759$	16.2305	+	8.86521i	0.589130	+	0.321787i
$760$	−1.42789	−	1.42789i	−0.0517949	−	0.0517949i
$761$	−18.9582	−	18.9582i	−0.687235	−	0.687235i	0.274385	−	0.961620i	$-0.411526\pi$
$761$	−18.9582	−	18.9582i	−0.687235	−	0.687235i	−0.961620	+	0.274385i	$0.911526\pi$
$762$	0.644040	−	0.392450i	0.0233311	−	0.0142170i
$763$	−16.5574	−	28.6783i	−0.599418	−	1.03822i
$764$	−4.25783	−	7.37477i	−0.154043	−	0.266810i
$765$	−7.15254	−	6.50543i	−0.258601	−	0.235204i
$766$		−	17.8071i		−	0.643398i
$767$	13.5993	+	13.7814i	0.491041	+	0.497619i
$768$	−1.25339	−	1.19541i	−0.0452279	−	0.0431357i
$769$	41.4115	−	11.0962i	1.49334	−	0.400138i	0.5

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.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.25339 - 1.19541i) q^{3} -1.00000i q^{4} +(-0.670386 - 0.179629i) q^{5} +(-1.73157 + 0.0409976i) q^{6} +(-4.43374 - 1.18802i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.141980 + 2.99664i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.25339 - 1.19541i) q^{3} -1.00000i q^{4} +(-0.670386 - 0.179629i) q^{5} +(-1.73157 + 0.0409976i) q^{6} +(-4.43374 - 1.18802i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.141980 + 2.99664i) q^{9} +(-0.601052 + 0.347017i) q^{10} +(-1.59115 - 1.59115i) q^{11} +(-1.19541 + 1.25339i) q^{12} +(3.60547 + 0.0239902i) q^{13} +(-3.97518 + 2.29507i) q^{14} +(0.625525 + 1.02653i) q^{15} -1.00000 q^{16} +(2.32181 - 4.02149i) q^{17} +(2.21934 + 2.01855i) q^{18} +(-2.81042 + 0.753050i) q^{19} +(-0.179629 + 0.670386i) q^{20} +(4.13704 + 6.78919i) q^{21} -2.25023 q^{22} +(2.37251 - 4.10931i) q^{23} +(0.0409976 + 1.73157i) q^{24} +(-3.91298 - 2.25916i) q^{25} +(2.56642 - 2.53249i) q^{26} +(3.40426 - 3.92569i) q^{27} +(-1.18802 + 4.43374i) q^{28} -4.88226i q^{29} +(1.16818 + 0.283556i) q^{30} +(-1.74651 + 6.51808i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.0922541 + 3.89642i) q^{33} +(-1.20186 - 4.48539i) q^{34} +(2.75891 + 1.59286i) q^{35} +(2.99664 - 0.141980i) q^{36} +(3.44953 + 0.924299i) q^{37} +(-1.45478 + 2.51976i) q^{38} +(-4.49039 - 4.34009i) q^{39} +(0.347017 + 0.601052i) q^{40} +(-1.48606 - 5.54605i) q^{41} +(7.72601 + 1.87535i) q^{42} +(4.59562 - 2.65328i) q^{43} +(-1.59115 + 1.59115i) q^{44} +(0.443103 - 2.03441i) q^{45} +(-1.22810 - 4.58334i) q^{46} +(11.6601 - 3.12430i) q^{47} +(1.25339 + 1.19541i) q^{48} +(12.1845 + 7.03470i) q^{49} +(-4.36436 + 1.16943i) q^{50} +(-7.71746 + 2.26498i) q^{51} +(0.0239902 - 3.60547i) q^{52} +5.06576i q^{53} +(-0.368703 - 5.18305i) q^{54} +(0.780869 + 1.35250i) q^{55} +(2.29507 + 3.97518i) q^{56} +(4.42276 + 2.41575i) q^{57} +(-3.45228 - 3.45228i) q^{58} +(3.79710 + 3.79710i) q^{59} +(1.02653 - 0.625525i) q^{60} +(-1.56055 - 2.70295i) q^{61} +(3.37401 + 5.84395i) q^{62} +(2.93055 - 13.4550i) q^{63} +1.00000i q^{64} +(-2.41275 - 0.663731i) q^{65} +(2.82042 + 2.68995i) q^{66} +(-12.6377 + 3.38625i) q^{67} +(-4.02149 - 2.32181i) q^{68} +(-7.88601 + 2.31445i) q^{69} +(3.07717 - 0.824524i) q^{70} +(-4.16970 - 15.5615i) q^{71} +(2.01855 - 2.21934i) q^{72} +(-5.55110 + 5.55110i) q^{73} +(3.09276 - 1.78561i) q^{74} +(2.20387 + 7.50923i) q^{75} +(0.753050 + 2.81042i) q^{76} +(5.16444 + 8.94507i) q^{77} +(-6.24409 + 0.106275i) q^{78} +(-1.55400 + 2.69161i) q^{79} +(0.670386 + 0.179629i) q^{80} +(-8.95968 + 0.850926i) q^{81} +(-4.97245 - 2.87085i) q^{82} +(2.45977 + 9.17998i) q^{83} +(6.78919 - 4.13704i) q^{84} +(-2.27888 + 2.27888i) q^{85} +(1.37344 - 5.12575i) q^{86} +(-5.83631 + 6.11938i) q^{87} +2.25023i q^{88} +(-0.648204 + 2.41913i) q^{89} +(-1.12522 - 1.75186i) q^{90} +(-15.9572 - 4.38972i) q^{91} +(-4.10931 - 2.37251i) q^{92} +(9.98086 - 6.08190i) q^{93} +(6.03569 - 10.4541i) q^{94} +2.01934 q^{95} +(1.73157 - 0.0409976i) q^{96} +(-0.317765 + 1.18591i) q^{97} +(13.5900 - 3.64143i) q^{98} +(4.54220 - 4.99402i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

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