LMFDB - Embedded newform 432.2.y.e.37.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(37,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("432.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.11
Character	$\chi$	$=$	432.37
Dual form			432.2.y.e.397.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.704761 + 1.22610i) q^{2} +(-1.00662 + 1.72821i) q^{4} +(-2.53632 + 0.679606i) q^{5} +(0.614293 - 0.354662i) q^{7} +(-2.82838 - 0.0162452i) q^{8} +O(q^{10})$	\(q+(0.704761 + 1.22610i) q^{2} +(-1.00662 + 1.72821i) q^{4} +(-2.53632 + 0.679606i) q^{5} +(0.614293 - 0.354662i) q^{7} +(-2.82838 - 0.0162452i) q^{8} +(-2.62076 - 2.63082i) q^{10} +(-0.973103 + 3.63167i) q^{11} +(0.139092 + 0.519100i) q^{13} +(0.867779 + 0.503230i) q^{14} +(-1.97341 - 3.47932i) q^{16} -6.08347 q^{17} +(-1.86732 + 1.86732i) q^{19} +(1.37863 - 5.06741i) q^{20} +(-5.13858 + 1.36634i) q^{22} +(-4.94479 - 2.85488i) q^{23} +(1.64095 - 0.947401i) q^{25} +(-0.538439 + 0.536382i) q^{26} +(-0.00543207 + 1.41864i) q^{28} +(9.68396 + 2.59481i) q^{29} +(2.14190 - 3.70987i) q^{31} +(2.87519 - 4.87168i) q^{32} +(-4.28739 - 7.45892i) q^{34} +(-1.31701 + 1.31701i) q^{35} +(3.75493 + 3.75493i) q^{37} +(-3.60553 - 0.973500i) q^{38} +(7.18473 - 1.88098i) q^{40} +(1.57053 + 0.906743i) q^{41} +(-2.31189 + 8.62809i) q^{43} +(-5.29673 - 5.33745i) q^{44} +(0.0154594 - 8.07480i) q^{46} +(2.95451 + 5.11737i) q^{47} +(-3.24843 + 5.62645i) q^{49} +(2.31808 + 1.34427i) q^{50} +(-1.03713 - 0.282158i) q^{52} +(8.56219 + 8.56219i) q^{53} -9.87242i q^{55} +(-1.74322 + 0.993140i) q^{56} +(3.64339 + 13.7022i) q^{58} +(5.19620 - 1.39232i) q^{59} +(0.655507 + 0.175643i) q^{61} +(6.05818 + 0.0115986i) q^{62} +(7.99947 + 0.0918952i) q^{64} +(-0.705566 - 1.22208i) q^{65} +(-1.96451 - 7.33165i) q^{67} +(6.12377 - 10.5135i) q^{68} +(-2.54297 - 0.686607i) q^{70} -2.51212i q^{71} +7.36013i q^{73} +(-1.95758 + 7.25023i) q^{74} +(-1.34743 - 5.10681i) q^{76} +(0.690245 + 2.57603i) q^{77} +(0.0143249 + 0.0248115i) q^{79} +(7.36978 + 7.48353i) q^{80} +(-0.00491010 + 2.56465i) q^{82} +(-14.9332 - 4.00134i) q^{83} +(15.4297 - 4.13436i) q^{85} +(-12.2082 + 3.24614i) q^{86} +(2.81130 - 10.2559i) q^{88} -1.86690i q^{89} +(0.269548 + 0.269548i) q^{91} +(9.91138 - 5.67185i) q^{92} +(-4.19216 + 7.22904i) q^{94} +(3.46709 - 6.00517i) q^{95} +(5.66064 + 9.80452i) q^{97} +(-9.18793 - 0.0175906i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.704761	+	1.22610i	0.498341	+	0.866981i
$2$	0.704761	+	1.22610i	0.498341	+	0.866981i
$3$		0			0
$3$		0			0
$4$	−1.00662	+	1.72821i	−0.503312	+	0.864105i
$5$	−2.53632	+	0.679606i	−1.13428	+	0.303929i	−0.776648	−	0.629934i	$-0.783082\pi$
$5$	−2.53632	+	0.679606i	−1.13428	+	0.303929i	−0.357630	+	0.933863i	$0.616415\pi$
$6$		0			0
$7$	0.614293	−	0.354662i	0.232181	−	0.134050i	−0.379397	−	0.925234i	$-0.623868\pi$
$7$	0.614293	−	0.354662i	0.232181	−	0.134050i	0.611578	+	0.791184i	$0.290535\pi$
$8$	−2.82838	−	0.0162452i	−0.999984	−	0.00574355i
$9$		0			0
$10$	−2.62076	−	2.63082i	−0.828758	−	0.831938i
$11$	−0.973103	+	3.63167i	−0.293402	+	1.09499i	0.649077	+	0.760723i	$0.275155\pi$
$11$	−0.973103	+	3.63167i	−0.293402	+	1.09499i	−0.942478	+	0.334267i	$0.891511\pi$
$12$		0			0
$13$	0.139092	+	0.519100i	0.0385773	+	0.143972i	0.982528	−	0.186113i	$-0.0595891\pi$
$13$	0.139092	+	0.519100i	0.0385773	+	0.143972i	−0.943951	+	0.330085i	$0.892922\pi$
$14$	0.867779	+	0.503230i	0.231924	+	0.134494i
$15$		0			0
$16$	−1.97341	−	3.47932i	−0.493353	−	0.869829i
$17$	−6.08347			−1.47546			−0.737729	−	0.675096i	$-0.764102\pi$
$17$	−6.08347			−1.47546			−0.737729	+	0.675096i	$0.764102\pi$
$18$		0			0
$19$	−1.86732	+	1.86732i	−0.428392	+	0.428392i	−0.888080	−	0.459688i	$-0.847961\pi$
$19$	−1.86732	+	1.86732i	−0.428392	+	0.428392i	0.459688	+	0.888080i	$0.347961\pi$
$20$	1.37863	−	5.06741i	0.308270	−	1.13311i
$21$		0			0
$22$	−5.13858	+	1.36634i	−1.09555	+	0.291305i
$23$	−4.94479	−	2.85488i	−1.03106	−	0.595283i	−0.113772	−	0.993507i	$-0.536293\pi$
$23$	−4.94479	−	2.85488i	−1.03106	−	0.595283i	−0.917288	+	0.398224i	$0.869627\pi$
$24$		0			0
$25$	1.64095	−	0.947401i	0.328189	−	0.189480i
$26$	−0.538439	+	0.536382i	−0.105597	+	0.105193i
$27$		0			0
$28$	−0.00543207	+	1.41864i	−0.00102656	+	0.268097i
$29$	9.68396	+	2.59481i	1.79827	+	0.481844i	0.993705	−	0.112026i	$-0.0357340\pi$
$29$	9.68396	+	2.59481i	1.79827	+	0.481844i	0.804561	+	0.593870i	$0.202401\pi$
$30$		0			0
$31$	2.14190	−	3.70987i	0.384696	−	0.666313i	−0.607031	−	0.794678i	$-0.707640\pi$
$31$	2.14190	−	3.70987i	0.384696	−	0.666313i	0.991727	+	0.128365i	$0.0409730\pi$
$32$	2.87519	−	4.87168i	0.508267	−	0.861199i
$33$		0			0
$34$	−4.28739	−	7.45892i	−0.735282	−	1.27919i
$35$	−1.31701	+	1.31701i	−0.222616	+	0.222616i
$36$		0			0
$37$	3.75493	+	3.75493i	0.617307	+	0.617307i	0.944840	−	0.327533i	$-0.106217\pi$
$37$	3.75493	+	3.75493i	0.617307	+	0.617307i	−0.327533	+	0.944840i	$0.606217\pi$
$38$	−3.60553	−	0.973500i	−0.584894	−	0.157923i
$39$		0			0
$40$	7.18473	−	1.88098i	1.13601	−	0.297409i
$41$	1.57053	+	0.906743i	0.245275	+	0.141610i	0.617599	−	0.786493i	$-0.288106\pi$
$41$	1.57053	+	0.906743i	0.245275	+	0.141610i	−0.372324	+	0.928103i	$0.621439\pi$
$42$		0			0
$43$	−2.31189	+	8.62809i	−0.352560	+	1.31577i	0.530968	+	0.847392i	$0.321828\pi$
$43$	−2.31189	+	8.62809i	−0.352560	+	1.31577i	−0.883528	+	0.468379i	$0.844838\pi$
$44$	−5.29673	−	5.33745i	−0.798513	−	0.804651i
$45$		0			0
$46$	0.0154594	−	8.07480i	0.00227937	−	1.19056i
$47$	2.95451	+	5.11737i	0.430960	+	0.746445i	0.996956	−	0.0779629i	$-0.0248416\pi$
$47$	2.95451	+	5.11737i	0.430960	+	0.746445i	−0.565996	+	0.824408i	$0.691508\pi$
$48$		0			0
$49$	−3.24843	+	5.62645i	−0.464061	+	0.803778i
$50$	2.31808	+	1.34427i	0.327826	+	0.190108i
$51$		0			0
$52$	−1.03713	−	0.282158i	−0.143824	−	0.0391283i
$53$	8.56219	+	8.56219i	1.17611	+	1.17611i	0.980728	+	0.195380i	$0.0625939\pi$
$53$	8.56219	+	8.56219i	1.17611	+	1.17611i	0.195380	+	0.980728i	$0.437406\pi$
$54$		0			0
$55$		−	9.87242i		−	1.33120i
$56$	−1.74322	+	0.993140i	−0.232947	+	0.132714i
$57$		0			0
$58$	3.64339	+	13.7022i	0.478400	+	1.79919i
$59$	5.19620	−	1.39232i	0.676487	−	0.181264i	0.0958118	−	0.995399i	$-0.469455\pi$
$59$	5.19620	−	1.39232i	0.676487	−	0.181264i	0.580675	+	0.814135i	$0.302789\pi$
$60$		0			0
$61$	0.655507	+	0.175643i	0.0839291	+	0.0224887i	0.300539	−	0.953769i	$-0.402833\pi$
$61$	0.655507	+	0.175643i	0.0839291	+	0.0224887i	−0.216610	+	0.976258i	$0.569500\pi$
$62$	6.05818	+	0.0115986i	0.769390	+	0.00147302i
$63$		0			0
$64$	7.99947	+	0.0918952i	0.999934	+	0.0114869i
$65$	−0.705566	−	1.22208i	−0.0875147	−	0.151580i
$66$		0			0
$67$	−1.96451	−	7.33165i	−0.240003	−	0.895703i	−0.975829	−	0.218533i	$-0.929873\pi$
$67$	−1.96451	−	7.33165i	−0.240003	−	0.895703i	0.735826	−	0.677170i	$-0.236794\pi$
$68$	6.12377	−	10.5135i	0.742617	−	1.27495i
$69$		0			0
$70$	−2.54297	−	0.686607i	−0.303943	−	0.0820652i
$71$		−	2.51212i		−	0.298134i	−0.988827	−	0.149067i	$-0.952373\pi$
$71$		−	2.51212i		−	0.298134i	0.988827	−	0.149067i	$-0.0476271\pi$
$72$		0			0
$73$			7.36013i			0.861437i	0.902486	+	0.430719i	$0.141740\pi$
$73$			7.36013i			0.861437i	−0.902486	+	0.430719i	$0.858260\pi$
$74$	−1.95758	+	7.25023i	−0.227564	+	0.842822i
$75$		0			0
$76$	−1.34743	−	5.10681i	−0.154561	−	0.585791i
$77$	0.690245	+	2.57603i	0.0786608	+	0.293566i
$78$		0			0
$79$	0.0143249	+	0.0248115i	0.00161168	+	0.00279151i	0.866830	−	0.498604i	$-0.166154\pi$
$79$	0.0143249	+	0.0248115i	0.00161168	+	0.00279151i	−0.865218	+	0.501395i	$0.832820\pi$
$80$	7.36978	+	7.48353i	0.823966	+	0.836684i
$81$		0			0
$82$	−0.00491010	+	2.56465i	−0.000542230	+	0.283219i
$83$	−14.9332	−	4.00134i	−1.63913	−	0.439204i	−0.682590	−	0.730802i	$-0.739146\pi$
$83$	−14.9332	−	4.00134i	−1.63913	−	0.439204i	−0.956541	+	0.291598i	$0.905813\pi$
$84$		0			0
$85$	15.4297	−	4.13436i	1.67358	−	0.448435i
$86$	−12.2082	+	3.24614i	−1.31644	+	0.350040i
$87$		0			0
$88$	2.81130	−	10.2559i	0.299686	−	1.09329i
$89$		−	1.86690i		−	0.197891i	−0.995093	−	0.0989453i	$-0.968453\pi$
$89$		−	1.86690i		−	0.197891i	0.995093	−	0.0989453i	$-0.0315469\pi$
$90$		0			0
$91$	0.269548	+	0.269548i	0.0282563	+	0.0282563i
$92$	9.91138	−	5.67185i	1.03333	−	0.591331i
$93$		0			0
$94$	−4.19216	+	7.22904i	−0.432389	+	0.745619i
$95$	3.46709	−	6.00517i	0.355715	−	0.616117i
$96$		0			0
$97$	5.66064	+	9.80452i	0.574751	+	0.995498i	0.996069	+	0.0885851i	$0.0282345\pi$
$97$	5.66064	+	9.80452i	0.574751	+	0.995498i	−0.421317	+	0.906913i	$0.638432\pi$
$98$	−9.18793	−	0.0175906i	−0.928121	−	0.00177691i
$99$		0			0
$100$	−0.0145106	+	3.78958i	−0.00145106	+	0.378958i
$101$	0.0837506	−	0.312562i	0.00833350	−	0.0311010i	−0.961634	−	0.274336i	$-0.911542\pi$
$101$	0.0837506	−	0.312562i	0.00833350	−	0.0311010i	0.969967	+	0.243235i	$0.0782086\pi$
$102$		0			0
$103$	−14.1155	−	8.14959i	−1.39084	−	0.803003i	−0.397434	−	0.917631i	$-0.630099\pi$
$103$	−14.1155	−	8.14959i	−1.39084	−	0.803003i	−0.993408	+	0.114628i	$0.963432\pi$
$104$	−0.384973	−	1.47047i	−0.0377497	−	0.144191i
$105$		0			0
$106$	−4.46378	+	16.5324i	−0.433560	+	1.60577i
$107$	−6.25131	−	6.25131i	−0.604337	−	0.604337i	0.337123	−	0.941461i	$-0.390546\pi$
$107$	−6.25131	−	6.25131i	−0.604337	−	0.604337i	−0.941461	+	0.337123i	$0.890546\pi$
$108$		0			0
$109$	−6.40184	+	6.40184i	−0.613185	+	0.613185i	−0.943775	−	0.330590i	$-0.892752\pi$
$109$	−6.40184	+	6.40184i	−0.613185	+	0.613185i	0.330590	+	0.943775i	$0.392752\pi$
$110$	12.1045	−	6.95769i	1.15412	−	0.663390i
$111$		0			0
$112$	−2.44624	−	1.43742i	−0.231147	−	0.135824i
$113$	0.984349	−	1.70494i	0.0925997	−	0.160387i	−0.816005	−	0.578045i	$-0.803816\pi$
$113$	0.984349	−	1.70494i	0.0925997	−	0.160387i	0.908604	+	0.417658i	$0.137149\pi$
$114$		0			0
$115$	14.4818	+	3.88038i	1.35043	+	0.361848i
$116$	−14.2325	+	14.1239i	−1.32145	+	1.31137i
$117$		0			0
$118$	5.36919	+	5.38979i	0.494274	+	0.496170i
$119$	−3.73703	+	2.15758i	−0.342573	+	0.197785i
$120$		0			0
$121$	−2.71581	−	1.56798i	−0.246892	−	0.142543i
$122$	0.246621	+	0.927501i	0.0223280	+	0.0839720i
$123$		0			0
$124$	4.25535	+	7.43609i	0.382142	+	0.667781i
$125$	5.76548	−	5.76548i	0.515680	−	0.515680i
$126$		0			0
$127$	10.0479			0.891606			0.445803	−	0.895131i	$-0.352918\pi$
$127$	10.0479			0.891606			0.445803	+	0.895131i	$0.352918\pi$
$128$	5.52504	+	9.87289i	0.488349	+	0.872648i
$129$		0			0
$130$	1.00113	−	1.72636i	0.0878048	−	0.151412i
$131$	1.08874	+	4.06323i	0.0951236	+	0.355006i	0.997038	−	0.0769084i	$-0.0245049\pi$
$131$	1.08874	+	4.06323i	0.0951236	+	0.355006i	−0.901915	+	0.431914i	$0.857838\pi$
$132$		0			0
$133$	−0.484813	+	1.80935i	−0.0420387	+	0.156890i
$134$	7.60480	−	7.57574i	0.656955	−	0.654444i
$135$		0			0
$136$	17.2064	+	0.0988273i	1.47543	+	0.00847437i
$137$	19.6597	−	11.3505i	1.67964	−	0.969742i	0.717756	−	0.696295i	$-0.245169\pi$
$137$	19.6597	−	11.3505i	1.67964	−	0.969742i	0.961887	−	0.273447i	$-0.0881639\pi$
$138$		0			0
$139$	10.5641	−	2.83063i	0.896032	−	0.240091i	0.218720	−	0.975788i	$-0.429812\pi$
$139$	10.5641	−	2.83063i	0.896032	−	0.240091i	0.677311	+	0.735697i	$0.263145\pi$
$140$	−0.950337	−	3.60182i	−0.0803182	−	0.304409i
$141$		0			0
$142$	3.08011	−	1.77045i	0.258477	−	0.148573i
$143$	−2.02055			−0.168967
$144$		0			0
$145$	−26.3251			−2.18618
$146$	−9.02422	+	5.18713i	−0.746850	+	0.429290i
$147$		0			0
$148$	−10.2691	+	2.70950i	−0.844115	+	0.222719i
$149$	0.633078	−	0.169633i	0.0518638	−	0.0138969i	−0.232794	−	0.972526i	$-0.574787\pi$
$149$	0.633078	−	0.169633i	0.0518638	−	0.0138969i	0.284658	+	0.958629i	$0.408120\pi$
$150$		0			0
$151$	−4.98859	+	2.88016i	−0.405965	+	0.234384i	−0.689055	−	0.724709i	$-0.741974\pi$
$151$	−4.98859	+	2.88016i	−0.405965	+	0.234384i	0.283089	+	0.959094i	$0.408641\pi$
$152$	5.31183	−	5.25116i	0.430846	−	0.425925i
$153$		0			0
$154$	−2.67200	+	2.66179i	−0.215316	+	0.214493i
$155$	−2.91129	+	10.8651i	−0.233840	+	0.872704i
$156$		0			0
$157$	−2.02462	−	7.55600i	−0.161583	−	0.603035i	−0.998451	−	0.0556311i	$-0.982283\pi$
$157$	−2.02462	−	7.55600i	−0.161583	−	0.603035i	0.836869	−	0.547404i	$-0.184384\pi$
$158$	−0.0203256	+	0.0350499i	−0.00161702	+	0.00278842i
$159$		0			0
$160$	−3.98160	+	14.3102i	−0.314773	+	1.13132i
$161$	−4.05007			−0.319190
$162$		0			0
$163$	−16.3912	+	16.3912i	−1.28386	+	1.28386i	−0.345408	+	0.938453i	$0.612259\pi$
$163$	−16.3912	+	16.3912i	−1.28386	+	1.28386i	−0.938453	+	0.345408i	$0.887741\pi$
$164$	−3.14797	+	1.80145i	−0.245815	+	0.140669i
$165$		0			0
$166$	−5.61830	−	21.1295i	−0.436065	−	1.63997i
$167$	5.76658	+	3.32934i	0.446232	+	0.257632i	0.706237	−	0.707975i	$-0.250391\pi$
$167$	5.76658	+	3.32934i	0.446232	+	0.257632i	−0.260006	+	0.965607i	$0.583724\pi$
$168$		0			0
$169$	11.0082	−	6.35559i	0.846786	−	0.488892i
$170$	15.9433	+	16.0045i	1.22280	+	1.22749i
$171$		0			0
$172$	−12.5839	−	12.6807i	−0.959516	−	0.966892i
$173$	−8.52795	−	2.28506i	−0.648368	−	0.173730i	−0.0803771	−	0.996765i	$-0.525612\pi$
$173$	−8.52795	−	2.28506i	−0.648368	−	0.173730i	−0.567991	+	0.823035i	$0.692279\pi$
$174$		0			0
$175$	0.672015	−	1.16396i	0.0507995	−	0.0879874i
$176$	14.5561	−	3.78105i	1.09720	−	0.285008i
$177$		0			0
$178$	2.28900	−	1.31572i	0.171567	−	0.0986171i
$179$	−6.98378	+	6.98378i	−0.521993	+	0.521993i	−0.918173	−	0.396180i	$-0.870336\pi$
$179$	−6.98378	+	6.98378i	−0.521993	+	0.521993i	0.396180	+	0.918173i	$0.370336\pi$
$180$		0			0
$181$	−10.1061	−	10.1061i	−0.751179	−	0.751179i	0.223520	−	0.974699i	$-0.428245\pi$
$181$	−10.1061	−	10.1061i	−0.751179	−	0.751179i	−0.974699	+	0.223520i	$0.928245\pi$
$182$	−0.140525	+	0.520459i	−0.0104164	+	0.0385790i
$183$		0			0
$184$	13.9394	+	8.15501i	1.02762	+	0.601195i
$185$	−12.0756	−	6.97184i	−0.887815	−	0.512580i
$186$		0			0
$187$	5.91985	−	22.0932i	0.432902	−	1.61561i
$188$	−11.8180	−	0.0452519i	−0.861914	−	0.00330033i
$189$		0			0
$190$	9.80638	+	0.0187746i	0.711430	+	0.00136205i
$191$	−2.87467	−	4.97907i	−0.208004	−	0.360273i	0.743082	−	0.669200i	$-0.233363\pi$
$191$	−2.87467	−	4.97907i	−0.208004	−	0.360273i	−0.951086	+	0.308928i	$0.900030\pi$
$192$		0			0
$193$	−4.45531	+	7.71683i	−0.320701	+	0.555470i	−0.980633	−	0.195856i	$-0.937252\pi$
$193$	−4.45531	+	7.71683i	−0.320701	+	0.555470i	0.659932	+	0.751325i	$0.270585\pi$
$194$	−8.03189	+	13.8503i	−0.576656	+	0.994396i
$195$		0			0
$196$	−6.45372	−	11.2777i	−0.460980	−	0.805549i
$197$	6.76280	+	6.76280i	0.481830	+	0.481830i	0.905716	−	0.423886i	$-0.139334\pi$
$197$	6.76280	+	6.76280i	0.481830	+	0.481830i	−0.423886	+	0.905716i	$0.639334\pi$
$198$		0			0
$199$		−	4.46794i		−	0.316724i	−0.987381	−	0.158362i	$-0.949379\pi$
$199$		−	4.46794i		−	0.316724i	0.987381	−	0.158362i	$-0.0506213\pi$
$200$	−4.65661	+	2.65295i	−0.329272	+	0.187592i
$201$		0			0
$202$	0.442255	−	0.117595i	0.0311169	−	0.00827394i
$203$	6.86907	−	1.84056i	0.482114	−	0.129182i
$204$		0			0
$205$	−4.59959	−	1.23246i	−0.321249	−	0.0860785i
$206$	0.0441308	−	23.0505i	0.00307474	−	1.60600i
$207$		0			0
$208$	1.53162	−	1.50834i	0.106199	−	0.104585i
$209$	−4.96439	−	8.59858i	−0.343394	−	0.594776i
$210$		0			0
$211$	2.42340	+	9.04426i	0.166834	+	0.622633i	0.997799	+	0.0663083i	$0.0211221\pi$
$211$	2.42340	+	9.04426i	0.166834	+	0.622633i	−0.830965	+	0.556324i	$0.812211\pi$
$212$	−23.4162	+	6.17834i	−1.60823	+	0.424330i
$213$		0			0
$214$	3.25903	−	12.0704i	0.222783	−	0.825115i
$215$		−	23.4548i		−	1.59960i
$216$		0			0
$217$		−	3.03860i		−	0.206273i
$218$	−12.3610	−	3.33751i	−0.837195	−	0.226044i
$219$		0			0
$220$	17.0616	+	9.93782i	1.15029	+	0.670008i
$221$	−0.846164	−	3.15793i	−0.0569192	−	0.212425i
$222$		0			0
$223$	−5.66067	−	9.80457i	−0.379067	−	0.656562i	0.611860	−	0.790966i	$-0.290422\pi$
$223$	−5.66067	−	9.80457i	−0.379067	−	0.656562i	−0.990927	+	0.134403i	$0.957088\pi$
$224$	0.0384100	−	4.01236i	0.00256638	−	0.268087i
$225$		0			0
$226$	2.78415	+	0.00533034i	0.185199	+	0.000354569i
$227$	−7.92726	−	2.12410i	−0.526151	−	0.140982i	−0.0140406	−	0.999901i	$-0.504469\pi$
$227$	−7.92726	−	2.12410i	−0.526151	−	0.140982i	−0.512110	+	0.858920i	$0.671136\pi$
$228$		0			0
$229$	14.7077	−	3.94091i	0.971912	−	0.260423i	0.262277	−	0.964993i	$-0.415527\pi$
$229$	14.7077	−	3.94091i	0.971912	−	0.260423i	0.709635	+	0.704570i	$0.248860\pi$
$230$	5.44847	+	20.4908i	0.359262	+	1.35112i
$231$		0			0
$232$	−27.3478	−	7.49643i	−1.79547	−	0.492164i
$233$			7.40495i			0.485114i	0.970137	+	0.242557i	$0.0779862\pi$
$233$			7.40495i			0.485114i	−0.970137	+	0.242557i	$0.922014\pi$
$234$		0			0
$235$	−10.9714	−	10.9714i	−0.715695	−	0.715695i
$236$	−2.82441	+	10.3817i	−0.183853	+	0.675788i
$237$		0			0
$238$	−5.27911	−	3.06139i	−0.342194	−	0.198440i
$239$	2.17384	−	3.76519i	0.140614	−	0.243550i	−0.787114	−	0.616807i	$-0.788426\pi$
$239$	2.17384	−	3.76519i	0.140614	−	0.243550i	0.927728	+	0.373257i	$0.121759\pi$
$240$		0			0
$241$	−10.5773	−	18.3203i	−0.681341	−	1.18012i	−0.974572	−	0.224075i	$-0.928064\pi$
$241$	−10.5773	−	18.3203i	−0.681341	−	1.18012i	0.293231	−	0.956042i	$-0.405269\pi$
$242$	0.00849074	−	4.43490i	0.000545805	−	0.285086i
$243$		0			0
$244$	−0.963397	+	0.956048i	−0.0616752	+	0.0612047i
$245$	4.41530	−	16.4781i	0.282083	−	1.05275i
$246$		0			0
$247$	−1.22905	−	0.709595i	−0.0782029	−	0.0451504i
$248$	−6.11836	+	10.4581i	−0.388516	+	0.664092i
$249$		0			0
$250$	11.1323	+	3.00575i	0.704069	+	0.190100i
$251$	9.06294	+	9.06294i	0.572048	+	0.572048i	0.932700	−	0.360653i	$-0.117446\pi$
$251$	9.06294	+	9.06294i	0.572048	+	0.572048i	−0.360653	+	0.932700i	$0.617446\pi$
$252$		0			0
$253$	15.1798	−	15.1798i	0.954344	−	0.954344i
$254$	7.08136	+	12.3197i	0.444324	+	0.773005i
$255$		0			0
$256$	−8.21128	+	13.7323i	−0.513205	+	0.858266i
$257$	−5.53555	+	9.58785i	−0.345298	+	0.598074i	−0.985408	−	0.170210i	$-0.945556\pi$
$257$	−5.53555	+	9.58785i	−0.345298	+	0.598074i	0.640110	+	0.768283i	$0.278889\pi$
$258$		0			0
$259$	3.63836	+	0.974895i	0.226077	+	0.0605770i
$260$	2.82224	+	0.0108066i	0.175028	+	0.000670195i
$261$		0			0
$262$	−4.21461	+	4.19850i	−0.260380	+	0.259384i
$263$	20.4693	−	11.8180i	1.26219	−	0.728726i	0.288693	−	0.957422i	$-0.406779\pi$
$263$	20.4693	−	11.8180i	1.26219	−	0.728726i	0.973498	+	0.228695i	$0.0734460\pi$
$264$		0			0
$265$	−27.5354	−	15.8976i	−1.69149	−	0.976580i
$266$	−2.56011	+	0.680730i	−0.156971	+	0.0417382i
$267$		0			0
$268$	14.6481	+	3.98514i	0.894778	+	0.243431i
$269$	−9.76907	+	9.76907i	−0.595631	+	0.595631i	−0.939147	−	0.343516i	$-0.888382\pi$
$269$	−9.76907	+	9.76907i	−0.595631	+	0.595631i	0.343516	+	0.939147i	$0.388382\pi$
$270$		0			0
$271$	−6.14441			−0.373246			−0.186623	−	0.982432i	$-0.559754\pi$
$271$	−6.14441			−0.373246			−0.186623	+	0.982432i	$0.559754\pi$
$272$	12.0052	+	21.1663i	0.727922	+	1.28340i
$273$		0			0
$274$	27.7723	+	16.1053i	1.67778	+	0.972956i
$275$	1.84384	+	6.88130i	0.111188	+	0.414958i
$276$		0			0
$277$	−5.40336	+	20.1656i	−0.324657	+	1.21164i	0.590000	+	0.807403i	$0.299128\pi$
$277$	−5.40336	+	20.1656i	−0.324657	+	1.21164i	−0.914656	+	0.404232i	$0.867539\pi$
$278$	10.9158	+	10.9576i	0.654684	+	0.657195i
$279$		0			0
$280$	3.74641	−	3.70362i	0.223891	−	0.221334i
$281$	−9.92135	+	5.72809i	−0.591858	+	0.341709i	−0.765832	−	0.643041i	$-0.777673\pi$
$281$	−9.92135	+	5.72809i	−0.591858	+	0.341709i	0.173974	+	0.984750i	$0.444339\pi$
$282$		0			0
$283$	2.24944	−	0.602736i	0.133715	−	0.0358289i	−0.191341	−	0.981524i	$-0.561284\pi$
$283$	2.24944	−	0.602736i	0.133715	−	0.0358289i	0.325056	+	0.945695i	$0.394617\pi$
$284$	4.34148	+	2.52877i	0.257619	+	0.150055i
$285$		0			0
$286$	−1.42400	−	2.47739i	−0.0842031	−	0.146491i
$287$	1.28635			0.0759308
$288$		0			0
$289$	20.0086			1.17698
$290$	−18.5529	−	32.2771i	−1.08946	−	1.89538i
$291$		0			0
$292$	−12.7198	−	7.40888i	−0.744372	−	0.433572i
$293$	−17.3162	+	4.63987i	−1.01162	+	0.271064i	−0.726308	−	0.687369i	$-0.758765\pi$
$293$	−17.3162	+	4.63987i	−1.01162	+	0.271064i	−0.285317	+	0.958433i	$0.592099\pi$
$294$		0			0
$295$	−12.2330	+	7.06273i	−0.712233	+	0.411208i
$296$	−10.5594	−	10.6814i	−0.613751	−	0.620842i
$297$		0			0
$298$	0.654155	+	0.656664i	0.0378942	+	0.0380395i
$299$	0.794183	−	2.96393i	0.0459288	−	0.171409i
$300$		0			0
$301$	1.63988	+	6.12011i	0.0945210	+	0.352757i
$302$	−7.04712	−	4.08666i	−0.405516	−	0.235161i
$303$		0			0
$304$	10.1820	+	2.81200i	0.583977	+	0.161279i
$305$	−1.78195			−0.102034
$306$		0			0
$307$	−2.88202	+	2.88202i	−0.164486	+	0.164486i	−0.784551	−	0.620065i	$-0.787106\pi$
$307$	−2.88202	+	2.88202i	−0.164486	+	0.164486i	0.620065	+	0.784551i	$0.287106\pi$
$308$	−5.14674	−	1.40021i	−0.293263	−	0.0797843i
$309$		0			0
$310$	−15.3734	+	4.08776i	−0.873150	+	0.232169i
$311$	21.4929	+	12.4089i	1.21875	+	0.703646i	0.964651	−	0.263532i	$-0.0848874\pi$
$311$	21.4929	+	12.4089i	1.21875	+	0.703646i	0.254100	+	0.967178i	$0.418221\pi$
$312$		0			0
$313$	−3.81457	+	2.20234i	−0.215612	+	0.124484i	−0.603917	−	0.797047i	$-0.706394\pi$
$313$	−3.81457	+	2.20234i	−0.215612	+	0.124484i	0.388305	+	0.921531i	$0.373061\pi$
$314$	7.83751	−	7.80756i	0.442296	−	0.440606i
$315$		0			0
$316$	−0.0572993		0.000219403i	−0.00322334		1.23424e-5i
$317$	−10.0113	−	2.68252i	−0.562291	−	0.150665i	−0.0335323	−	0.999438i	$-0.510676\pi$
$317$	−10.0113	−	2.68252i	−0.562291	−	0.150665i	−0.528759	+	0.848772i	$0.677342\pi$
$318$		0			0
$319$	−18.8470	+	32.6439i	−1.05523	+	1.82771i
$320$	−20.3517	+	5.20341i	−1.13769	+	0.290880i
$321$		0			0
$322$	−2.85433	−	4.96577i	−0.159066	−	0.276732i
$323$	11.3598	−	11.3598i	0.632076	−	0.632076i
$324$		0			0
$325$	0.720039	+	0.720039i	0.0399406	+	0.0399406i
$326$	−31.6491	−	8.54533i	−1.75288	−	0.473282i
$327$		0			0
$328$	−4.42731	−	2.59013i	−0.244457	−	0.143016i
$329$	3.62987	+	2.09571i	0.200121	+	0.115540i
$330$		0			0
$331$	−6.40595	+	23.9073i	−0.352103	+	1.31407i	0.531988	+	0.846752i	$0.321445\pi$
$331$	−6.40595	+	23.9073i	−0.352103	+	1.31407i	−0.884091	+	0.467314i	$0.845222\pi$
$332$	21.9473	−	21.7798i	1.20451	−	1.19532i
$333$		0			0
$334$	−0.0180287	+	9.41677i	−0.000986485	+	0.515263i
$335$	9.96526	+	17.2603i	0.544461	+	0.943033i
$336$		0			0
$337$	4.48386	−	7.76627i	0.244251	−	0.423056i	−0.717670	−	0.696384i	$-0.754791\pi$
$337$	4.48386	−	7.76627i	0.244251	−	0.423056i	0.961921	+	0.273328i	$0.0881245\pi$
$338$	15.5507	+	9.01796i	0.845848	+	0.490512i
$339$		0			0
$340$	−8.38683	+	30.8274i	−0.454840	+	1.67185i
$341$	11.3887	+	11.3887i	0.616735	+	0.616735i
$342$		0			0
$343$			9.57365i			0.516928i
$344$	6.67907	−	24.3660i	0.360111	−	1.31372i
$345$		0			0
$346$	−3.20846	−	12.0665i	−0.172488	−	0.648699i
$347$	−10.4118	+	2.78983i	−0.558935	+	0.149766i	−0.527217	−	0.849731i	$-0.676764\pi$
$347$	−10.4118	+	2.78983i	−0.558935	+	0.149766i	−0.0317179	+	0.999497i	$0.510098\pi$
$348$		0			0
$349$	22.1889	+	5.94549i	1.18774	+	0.318255i	0.797993	−	0.602666i	$-0.205895\pi$
$349$	22.1889	+	5.94549i	1.18774	+	0.318255i	0.389749	+	0.920921i	$0.372562\pi$
$350$	1.90074	+	0.00363902i	0.101599	+	0.000194514i
$351$		0			0
$352$	14.8945	+	15.1824i	0.793878	+	0.809224i
$353$	−6.69259	−	11.5919i	−0.356211	−	0.616975i	0.631114	−	0.775690i	$-0.282598\pi$
$353$	−6.69259	−	11.5919i	−0.356211	−	0.616975i	−0.987324	+	0.158715i	$0.949265\pi$
$354$		0			0
$355$	1.70725	+	6.37156i	0.0906116	+	0.338167i
$356$	3.22639	+	1.87926i	0.170998	+	0.0996008i
$357$		0			0
$358$	−13.4847	−	3.64090i	−0.712688	−	0.192427i
$359$		−	25.8640i		−	1.36505i	−0.730863	−	0.682525i	$-0.760882\pi$
$359$		−	25.8640i		−	1.36505i	0.730863	−	0.682525i	$-0.239118\pi$
$360$		0			0
$361$			12.0262i			0.632960i
$362$	5.26866	−	19.5134i	0.276915	−	1.02560i
$363$		0			0
$364$	−0.737170	+	0.194502i	−0.0386382	+	0.0101947i
$365$	−5.00198	−	18.6677i	−0.261816	−	0.977110i
$366$		0			0
$367$	−7.91603	−	13.7110i	−0.413213	−	0.715707i	0.582026	−	0.813170i	$-0.302260\pi$
$367$	−7.91603	−	13.7110i	−0.413213	−	0.715707i	−0.995239	+	0.0974639i	$0.968927\pi$
$368$	−0.174902	+	22.8384i	−0.00911739	+	1.19053i
$369$		0			0
$370$	0.0377532	−	19.7193i	0.00196269	−	1.02516i
$371$	8.29638	+	2.22301i	0.430726	+	0.115413i
$372$		0			0
$373$	3.74735	−	1.00410i	0.194030	−	0.0519902i	−0.160495	−	0.987037i	$-0.551309\pi$
$373$	3.74735	−	1.00410i	0.194030	−	0.0519902i	0.354525	+	0.935046i	$0.384642\pi$
$374$	31.2604	−	8.31209i	1.61644	−	0.429808i
$375$		0			0
$376$	−8.27336	−	14.5219i	−0.426666	−	0.748908i
$377$			5.38786i			0.277489i
$378$		0			0
$379$	17.2803	+	17.2803i	0.887628	+	0.887628i	0.994295	−	0.106667i	$-0.0340179\pi$
$379$	17.2803	+	17.2803i	0.887628	+	0.887628i	−0.106667	+	0.994295i	$0.534018\pi$
$380$	6.88813	+	12.0368i	0.353354	+	0.617475i
$381$		0			0
$382$	4.07887	−	7.03367i	0.208693	−	0.359874i
$383$	−4.26860	+	7.39343i	−0.218115	+	0.377787i	−0.954232	−	0.299068i	$-0.903324\pi$
$383$	−4.26860	+	7.39343i	−0.218115	+	0.377787i	0.736117	+	0.676855i	$0.236658\pi$
$384$		0			0
$385$	−3.50137	−	6.06455i	−0.178446	−	0.309078i
$386$	−12.6015	−	0.0241259i	−0.641400	−	0.00122798i
$387$		0			0
$388$	−22.6424	−	0.0866994i	−1.14949	−	0.00440149i
$389$	−8.03854	+	30.0002i	−0.407570	+	1.52107i	0.391696	+	0.920095i	$0.371889\pi$
$389$	−8.03854	+	30.0002i	−0.407570	+	1.52107i	−0.799266	+	0.600977i	$0.794778\pi$
$390$		0			0
$391$	30.0815	+	17.3676i	1.52129	+	0.878316i
$392$	9.27920	−	15.8610i	0.468670	−	0.801099i
$393$		0			0
$394$	−3.52569	+	13.0580i	−0.177622	+	0.657853i
$395$	−0.0531947	−	0.0531947i	−0.00267651	−	0.00267651i
$396$		0			0
$397$	16.6870	−	16.6870i	0.837495	−	0.837495i	−0.151033	−	0.988529i	$-0.548260\pi$
$397$	16.6870	−	16.6870i	0.837495	−	0.837495i	0.988529	+	0.151033i	$0.0482601\pi$
$398$	5.47813	−	3.14883i	0.274594	−	0.157837i
$399$		0			0
$400$	−6.53457	−	3.83976i	−0.326729	−	0.191988i
$401$	−8.76727	+	15.1854i	−0.437817	+	0.758321i	−0.997521	−	0.0703717i	$-0.977581\pi$
$401$	−8.76727	+	15.1854i	−0.437817	+	0.758321i	0.559704	+	0.828693i	$0.310915\pi$
$402$		0			0
$403$	2.22371	+	0.595842i	0.110771	+	0.0296810i
$404$	0.455866	+	0.459371i	0.0226802	+	0.0228545i
$405$		0			0
$406$	7.09775	+	7.12498i	0.352256	+	0.353607i
$407$	−17.2906	+	9.98273i	−0.857063	+	0.494826i
$408$		0			0
$409$	−0.805810	−	0.465235i	−0.0398447	−	0.0230044i	0.479945	−	0.877298i	$-0.340656\pi$
$409$	−0.805810	−	0.465235i	−0.0398447	−	0.0230044i	−0.519790	+	0.854294i	$0.673990\pi$
$410$	−1.73050	−	6.50813i	−0.0854633	−	0.321413i
$411$		0			0
$412$	28.2932	−	16.1910i	1.39391	−	0.797672i
$413$	2.69818	−	2.69818i	0.132769	−	0.132769i
$414$		0			0
$415$	40.5947			1.99272
$416$	2.92880	+	0.814898i	0.143596	+	0.0399537i
$417$		0			0
$418$	7.04398	−	12.1468i	0.344532	−	0.594118i
$419$	4.12510	+	15.3951i	0.201525	+	0.752100i	0.990481	+	0.137651i	$0.0439551\pi$
$419$	4.12510	+	15.3951i	0.201525	+	0.752100i	−0.788956	+	0.614449i	$0.789378\pi$
$420$		0			0
$421$	−2.10519	+	7.85668i	−0.102601	+	0.382911i	−0.998062	−	0.0622284i	$-0.980179\pi$
$421$	−2.10519	+	7.85668i	−0.102601	+	0.382911i	0.895461	+	0.445140i	$0.146846\pi$
$422$	−9.38122	+	9.34537i	−0.456671	+	0.454925i
$423$		0			0
$424$	−24.0780	−	24.3562i	−1.16933	−	1.18284i
$425$	−9.98266	+	5.76349i	−0.484230	+	0.279570i
$426$		0			0
$427$	0.464967	−	0.124588i	0.0225013	−	0.00602922i
$428$	17.0963	−	4.51085i	0.826381	−	0.218040i
$429$		0			0
$430$	28.7578	−	16.5300i	1.38683	−	0.797148i
$431$	10.8262			0.521480			0.260740	−	0.965409i	$-0.416034\pi$
$431$	10.8262			0.521480			0.260740	+	0.965409i	$0.416034\pi$
$432$		0			0
$433$	20.5356			0.986879			0.493440	−	0.869780i	$-0.335739\pi$
$433$	20.5356			0.986879			0.493440	+	0.869780i	$0.335739\pi$
$434$	3.72561	−	2.14148i	0.178835	−	0.102794i
$435$		0			0
$436$	−4.61947	−	17.5080i	−0.221232	−	0.838479i
$437$	14.5645	−	3.90254i	0.696714	−	0.186684i
$438$		0			0
$439$	24.8927	−	14.3718i	1.18806	−	0.685928i	0.230196	−	0.973144i	$-0.426063\pi$
$439$	24.8927	−	14.3718i	1.18806	−	0.685928i	0.957866	+	0.287216i	$0.0927298\pi$
$440$	−0.160379	+	27.9229i	−0.00764579	+	1.33117i
$441$		0			0
$442$	3.27558	−	3.26306i	0.155803	−	0.155208i
$443$	−3.34900	+	12.4986i	−0.159116	+	0.593827i	0.839602	+	0.543202i	$0.182788\pi$
$443$	−3.34900	+	12.4986i	−0.159116	+	0.593827i	−0.998718	+	0.0506256i	$0.983878\pi$
$444$		0			0
$445$	1.26875	+	4.73506i	0.0601447	+	0.224463i
$446$	8.03193	−	13.8504i	0.380323	−	0.655836i
$447$		0			0
$448$	4.94661	−	2.78066i	0.233705	−	0.131374i
$449$	30.1067			1.42082			0.710412	−	0.703786i	$-0.248509\pi$
$449$	30.1067			1.42082			0.710412	+	0.703786i	$0.248509\pi$
$450$		0			0
$451$	−4.82127	+	4.82127i	−0.227025	+	0.227025i
$452$	1.95563	+	3.41740i	0.0919849	+	0.160741i
$453$		0			0
$454$	−2.98247	−	11.2166i	−0.139974	−	0.526420i
$455$	−0.866848	−	0.500475i	−0.0406385	−	0.0234626i
$456$		0			0
$457$	2.00099	−	1.15527i	0.0936026	−	0.0540415i	−0.452468	−	0.891781i	$-0.649456\pi$
$457$	2.00099	−	1.15527i	0.0936026	−	0.0540415i	0.546071	+	0.837739i	$0.316123\pi$
$458$	15.1973	+	15.2556i	0.710125	+	0.712850i
$459$		0			0
$460$	−21.2838	+	21.1215i	−0.992364	+	0.984794i
$461$	16.9043	+	4.52950i	0.787313	+	0.210960i	0.630007	−	0.776590i	$-0.283052\pi$
$461$	16.9043	+	4.52950i	0.787313	+	0.210960i	0.157307	+	0.987550i	$0.449719\pi$
$462$		0			0
$463$	10.2591	−	17.7694i	0.476783	−	0.825812i	−0.522863	−	0.852417i	$-0.675136\pi$
$463$	10.2591	−	17.7694i	0.476783	−	0.825812i	0.999646	+	0.0266044i	$0.00846944\pi$
$464$	−10.0823	−	38.8142i	−0.468059	−	1.80190i
$465$		0			0
$466$	−9.07918	+	5.21872i	−0.420585	+	0.241752i
$467$	−6.49068	+	6.49068i	−0.300353	+	0.300353i	−0.841152	−	0.540799i	$-0.818122\pi$
$467$	−6.49068	+	6.49068i	−0.300353	+	0.300353i	0.540799	+	0.841152i	$0.318122\pi$
$468$		0			0
$469$	−3.80704	−	3.80704i	−0.175793	−	0.175793i
$470$	5.71978	−	21.1842i	0.263834	−	0.977155i
$471$		0			0
$472$	−14.7194	+	3.85359i	−0.677517	+	0.177376i
$473$	−29.0847	−	16.7920i	−1.33731	−	0.772099i
$474$		0			0
$475$	−1.29507	+	4.83327i	−0.0594220	+	0.221766i
$476$	0.0330458	−	8.63025i	0.00151465	−	0.395567i
$477$		0			0
$478$	6.14853	+	0.0117715i	0.281227	+	0.000538417i
$479$	−10.0990	−	17.4920i	−0.461436	−	0.799231i	0.537597	−	0.843202i	$-0.319332\pi$
$479$	−10.0990	−	17.4920i	−0.461436	−	0.799231i	−0.999033	+	0.0439712i	$0.985999\pi$
$480$		0			0
$481$	−1.42690	+	2.47146i	−0.0650610	+	0.112689i
$482$	15.0081	−	25.8802i	0.683599	−	1.17881i
$483$		0			0
$484$	5.44360	−	3.11513i	0.247436	−	0.141597i
$485$	−21.0204	−	21.0204i	−0.954489	−	0.954489i
$486$		0			0
$487$			1.65695i			0.0750836i	0.999295	+	0.0375418i	$0.0119527\pi$
$487$			1.65695i			0.0750836i	−0.999295	+	0.0375418i	$0.988047\pi$
$488$	−1.85117	−	0.507433i	−0.0837986	−	0.0229704i
$489$		0			0
$490$	23.3155	−	6.19956i	1.05329	−	0.280067i
$491$	28.4580	−	7.62529i	1.28429	−	0.344124i	0.448801	−	0.893632i	$-0.351851\pi$
$491$	28.4580	−	7.62529i	1.28429	−	0.344124i	0.835489	+	0.549507i	$0.185185\pi$
$492$		0			0
$493$	−58.9121	−	15.7855i	−2.65327	−	0.710941i
$494$	0.00384252	−	2.00703i	0.000172883	−	0.0903007i
$495$		0			0
$496$	−17.1347	−	0.131222i	−0.769369	−	0.00589202i
$497$	−0.890955	−	1.54318i	−0.0399648	−	0.0692211i
$498$		0			0
$499$	−4.88431	−	18.2285i	−0.218652	−	0.816019i	−0.984849	−	0.173414i	$-0.944520\pi$
$499$	−4.88431	−	18.2285i	−0.218652	−	0.816019i	0.766197	−	0.642605i	$-0.222147\pi$
$500$	4.16028	+	15.7676i	0.186053	+	0.705149i
$501$		0			0
$502$	−4.72483	+	17.4992i	−0.210880	+	0.781029i
$503$			36.2450i			1.61609i	0.589124	+	0.808043i	$0.299473\pi$
$503$			36.2450i			1.61609i	−0.589124	+	0.808043i	$0.700527\pi$
$504$		0			0
$505$			0.849675i			0.0378100i
$506$	29.3100	+	7.91376i	1.30299	+	0.351809i
$507$		0			0
$508$	−10.1145	+	17.3649i	−0.448756	+	0.770441i
$509$	−2.18916	−	8.17006i	−0.0970329	−	0.362132i	0.900287	−	0.435297i	$-0.143357\pi$
$509$	−2.18916	−	8.17006i	−0.0970329	−	0.362132i	−0.997320	+	0.0731652i	$0.976690\pi$
$510$		0			0
$511$	2.61036	+	4.52127i	0.115475	+	0.200009i
$512$	−22.6241	−	0.389868i	−0.999852	−	0.0172299i
$513$		0			0
$514$	−15.6569	−	0.0299755i	−0.690595	−	0.00132216i
$515$	41.3400	+	11.0770i	1.82166	+	0.488112i
$516$		0			0
$517$	−21.4596	+	5.75009i	−0.943794	+	0.252889i
$518$	1.36886	+	5.14804i	0.0601441	+	0.226192i
$519$		0			0
$520$	1.97576	+	3.46796i	0.0866427	+	0.152080i
$521$			9.73918i			0.426681i	0.976978	+	0.213341i	$0.0684344\pi$
$521$			9.73918i			0.426681i	−0.976978	+	0.213341i	$0.931566\pi$
$522$		0			0
$523$	4.68648	+	4.68648i	0.204925	+	0.204925i	0.802106	−	0.597181i	$-0.203713\pi$
$523$	4.68648	+	4.68648i	0.204925	+	0.204925i	−0.597181	+	0.802106i	$0.703713\pi$
$524$	−8.11806	−	2.20858i	−0.354639	−	0.0964822i
$525$		0			0
$526$	28.9159	+	16.7685i	1.26079	+	0.731142i
$527$	−13.0302	+	22.5689i	−0.567603	+	0.983117i
$528$		0			0
$529$	4.80066	+	8.31498i	0.208724	+	0.361521i
$530$	0.0860868	−	44.9650i	0.00373937	−	1.95316i
$531$		0			0
$532$	−2.63891	−	2.65919i	−0.114411	−	0.115291i
$533$	−0.252242	+	0.941380i	−0.0109258	+	0.0407757i
$534$		0			0
$535$	20.1038	+	11.6069i	0.869162	+	0.501811i
$536$	5.43728	+	20.7686i	0.234855	+	0.897067i
$537$		0			0
$538$	−18.8627	−	5.09297i	−0.813228	−	0.219573i
$539$	−17.2723	−	17.2723i	−0.743972	−	0.743972i
$540$		0			0
$541$	0.808981	−	0.808981i	0.0347808	−	0.0347808i	−0.689503	−	0.724283i	$-0.742171\pi$
$541$	0.808981	−	0.808981i	0.0347808	−	0.0347808i	0.724283	+	0.689503i	$0.242171\pi$
$542$	−4.33034	−	7.53364i	−0.186004	−	0.323598i
$543$		0			0
$544$	−17.4912	+	29.6367i	−0.749927	+	1.27066i
$545$	11.8864	−	20.5879i	0.509158	−	0.881887i
$546$		0			0
$547$	14.0859	+	3.77431i	0.602271	+	0.161378i	0.547055	−	0.837096i	$-0.315749\pi$
$547$	14.0859	+	3.77431i	0.602271	+	0.161378i	0.0552156	+	0.998474i	$0.482415\pi$
$548$	−0.173847	+	45.4018i	−0.00742637	+	1.93947i
$549$		0			0
$550$	−7.13767	+	7.11039i	−0.304351	+	0.303188i
$551$	−22.9284	+	13.2377i	−0.976782	+	0.563945i
$552$		0			0
$553$	0.0175994	+	0.0101610i	0.000748402	+	0.000432090i
$554$	−28.5331	+	7.58690i	−1.21225	+	0.322336i
$555$		0			0
$556$	−5.74212	+	21.1063i	−0.243520	+	0.895106i
$557$	−1.20401	+	1.20401i	−0.0510155	+	0.0510155i	−0.732154	−	0.681139i	$-0.761485\pi$
$557$	−1.20401	+	1.20401i	−0.0510155	+	0.0510155i	0.681139	+	0.732154i	$0.261485\pi$
$558$		0			0
$559$	−4.80040			−0.203035
$560$	7.18133	+	1.98330i	0.303466	+	0.0838096i
$561$		0			0
$562$	−14.0154	−	8.12759i	−0.591203	−	0.342842i
$563$	−9.78876	−	36.5322i	−0.412547	−	1.53965i	−0.789698	−	0.613496i	$-0.789763\pi$
$563$	−9.78876	−	36.5322i	−0.412547	−	1.53965i	0.377151	−	0.926152i	$-0.376904\pi$
$564$		0			0
$565$	−1.33794	+	4.99325i	−0.0562875	+	0.210068i
$566$	2.32433	+	2.33325i	0.0976989	+	0.0980737i
$567$		0			0
$568$	−0.0408100	+	7.10524i	−0.00171235	+	0.298129i
$569$	6.58015	−	3.79905i	0.275854	−	0.159265i	−0.355691	−	0.934604i	$-0.615754\pi$
$569$	6.58015	−	3.79905i	0.275854	−	0.159265i	0.631545	+	0.775339i	$0.282421\pi$
$570$		0			0
$571$	1.00586	−	0.269518i	0.0420938	−	0.0112790i	−0.237711	−	0.971336i	$-0.576397\pi$
$571$	1.00586	−	0.269518i	0.0420938	−	0.0112790i	0.279804	+	0.960057i	$0.409730\pi$
$572$	2.03393	−	3.49193i	0.0850431	−	0.146005i
$573$		0			0
$574$	0.906569	+	1.57719i	0.0378395	+	0.0658306i
$575$	−10.8189			−0.451178
$576$		0			0
$577$	36.5164			1.52020			0.760099	−	0.649807i	$-0.225150\pi$
$577$	36.5164			1.52020			0.760099	+	0.649807i	$0.225150\pi$
$578$	14.1013	+	24.5325i	0.586537	+	1.02042i
$579$		0			0
$580$	26.4995	−	45.4953i	1.10033	−	1.88909i
$581$	−10.5925	+	2.83825i	−0.439450	+	0.117750i
$582$		0			0
$583$	−39.4269	+	22.7632i	−1.63290	+	0.942754i
$584$	0.119567	−	20.8172i	0.00494771	−	0.861423i
$585$		0			0
$586$	−17.8927	−	17.9614i	−0.739142	−	0.741977i
$587$	3.06671	−	11.4451i	0.126577	−	0.472391i	−0.873314	−	0.487157i	$-0.838034\pi$
$587$	3.06671	−	11.4451i	0.126577	−	0.472391i	0.999891	+	0.0147665i	$0.00470048\pi$
$588$		0			0
$589$	2.92791	+	10.9271i	0.120643	+	0.450244i
$590$	−17.2809	−	10.0213i	−0.711445	−	0.412571i
$591$		0			0
$592$	5.65456	−	20.4746i	0.232401	−	0.841501i
$593$	−1.44299			−0.0592563			−0.0296282	−	0.999561i	$-0.509432\pi$
$593$	−1.44299			−0.0592563			−0.0296282	+	0.999561i	$0.509432\pi$
$594$		0			0
$595$	8.01202	−	8.01202i	0.328461	−	0.328461i
$596$	−0.344111	+	1.26485i	−0.0140953	+	0.0518102i
$597$		0			0
$598$	4.19378	−	1.11512i	0.171496	−	0.0456005i
$599$	7.69747	+	4.44414i	0.314510	+	0.181583i	0.648943	−	0.760837i	$-0.275211\pi$
$599$	7.69747	+	4.44414i	0.314510	+	0.181583i	−0.334433	+	0.942420i	$0.608545\pi$
$600$		0			0
$601$	31.4648	−	18.1662i	1.28347	−	0.741015i	0.305993	−	0.952034i	$-0.401012\pi$
$601$	31.4648	−	18.1662i	1.28347	−	0.741015i	0.977482	+	0.211019i	$0.0676782\pi$
$602$	−6.34812	+	6.32386i	−0.258730	+	0.257741i
$603$		0			0
$604$	0.0441131	−	11.5206i	0.00179493	−	0.468765i
$605$	7.95379	+	2.13121i	0.323368	+	0.0866461i
$606$		0			0
$607$	−20.4864	+	35.4835i	−0.831518	+	1.44023i	0.0653163	+	0.997865i	$0.479194\pi$
$607$	−20.4864	+	35.4835i	−0.831518	+	1.44023i	−0.896834	+	0.442367i	$0.854139\pi$
$608$	3.72808	+	14.4659i	0.151194	+	0.586669i
$609$		0			0
$610$	−1.25585	−	2.18484i	−0.0508477	−	0.0884615i
$611$	−2.24547	+	2.24547i	−0.0908421	+	0.0908421i
$612$		0			0
$613$	−33.5771	−	33.5771i	−1.35616	−	1.35616i	−0.878593	−	0.477572i	$-0.841517\pi$
$613$	−33.5771	−	33.5771i	−1.35616	−	1.35616i	−0.477572	−	0.878593i	$-0.658483\pi$
$614$	−5.56477	−	1.50250i	−0.224576	−	0.0606360i
$615$		0			0
$616$	−1.91043	−	7.29721i	−0.0769734	−	0.294013i
$617$	20.8223	+	12.0218i	0.838276	+	0.483979i	0.856678	−	0.515852i	$-0.172524\pi$
$617$	20.8223	+	12.0218i	0.838276	+	0.483979i	−0.0184019	+	0.999831i	$0.505858\pi$
$618$		0			0
$619$	−1.85362	+	6.91779i	−0.0745031	+	0.278049i	−0.993120	−	0.117100i	$-0.962640\pi$
$619$	−1.85362	+	6.91779i	−0.0745031	+	0.278049i	0.918617	+	0.395149i	$0.129307\pi$
$620$	−15.8466	−	15.9684i	−0.636413	−	0.641305i
$621$		0			0
$622$	−0.0671955	+	35.0977i	−0.00269430	+	1.40729i
$623$	−0.662118	−	1.14682i	−0.0265272	−	0.0459464i
$624$		0			0
$625$	−15.4419	+	26.7461i	−0.617675	+	1.06984i
$626$	−5.38865	−	3.12491i	−0.215374	−	0.124896i
$627$		0			0
$628$	15.0964	+	4.10708i	0.602412	+	0.163891i
$629$	−22.8430	−	22.8430i	−0.910810	−	0.910810i
$630$		0			0
$631$		−	13.8491i		−	0.551325i	−0.961254	−	0.275663i	$-0.911103\pi$
$631$		−	13.8491i		−	0.551325i	0.961254	−	0.275663i	$-0.0888973\pi$
$632$	−0.0401133	−	0.0704090i	−0.00159562	−	0.00280072i
$633$		0			0
$634$	−3.76654	−	14.1654i	−0.149589	−	0.562578i
$635$	−25.4847	+	6.82860i	−1.01133	+	0.270985i
$636$		0			0
$637$	−3.37252	−	0.903663i	−0.133624	−	0.0358044i
$638$	−53.3072	−	0.102058i	−2.11045	−	0.00404052i
$639$		0			0
$640$	−20.7230	−	21.2860i	−0.819147	−	0.841403i
$641$	12.8397	+	22.2390i	0.507138	+	0.878389i	0.999966	+	0.00826230i	$0.00263000\pi$
$641$	12.8397	+	22.2390i	0.507138	+	0.878389i	−0.492828	+	0.870127i	$0.664037\pi$
$642$		0			0
$643$	−11.6011	−	43.2961i	−0.457504	−	1.70743i	−0.680619	−	0.732637i	$-0.738289\pi$
$643$	−11.6011	−	43.2961i	−0.457504	−	1.70743i	0.223115	−	0.974792i	$-0.428378\pi$
$644$	4.07690	−	6.99936i	0.160652	−	0.275814i
$645$		0			0
$646$	21.9341	+	5.92226i	0.862987	+	0.233008i
$647$			33.1472i			1.30315i	0.758584	+	0.651575i	$0.225892\pi$
$647$			33.1472i			1.30315i	−0.758584	+	0.651575i	$0.774108\pi$
$648$		0			0
$649$			20.2257i			0.793929i
$650$	−0.375382	+	1.39029i	−0.0147237	+	0.0545317i
$651$		0			0
$652$	−11.8277	−	44.8273i	−0.463207	−	1.75557i
$653$	11.5044	+	42.9351i	0.450203	+	1.68018i	0.701821	+	0.712353i	$0.252371\pi$
$653$	11.5044	+	42.9351i	0.450203	+	1.68018i	−0.251618	+	0.967827i	$0.580963\pi$
$654$		0			0
$655$	−5.52279	−	9.56575i	−0.215793	−	0.373765i
$656$	0.0555509	−	7.25373i	0.00216890	−	0.283211i
$657$		0			0
$658$	−0.0113485	+	5.92755i	−0.000442409	+	0.231080i
$659$	23.5803	+	6.31833i	0.918559	+	0.246127i	0.686970	−	0.726686i	$-0.258941\pi$
$659$	23.5803	+	6.31833i	0.918559	+	0.246127i	0.231590	+	0.972814i	$0.425607\pi$
$660$		0			0
$661$	−4.15952	+	1.11454i	−0.161787	+	0.0433506i	−0.338803	−	0.940857i	$-0.610022\pi$
$661$	−4.15952	+	1.11454i	−0.161787	+	0.0433506i	0.177017	+	0.984208i	$0.443355\pi$
$662$	−33.8274	+	8.99463i	−1.31474	+	0.349586i
$663$		0			0
$664$	42.1717	+	11.5599i	1.63658	+	0.448611i
$665$		−	4.91858i		−	0.190734i
$666$		0			0
$667$	−40.4773	−	40.4773i	−1.56729	−	1.56729i
$668$	−11.5586	+	6.61447i	−0.447215	+	0.255921i
$669$		0			0
$670$	−14.1397	+	24.3828i	−0.546265	+	0.941989i
$671$	−1.27575	+	2.20967i	−0.0492499	+	0.0853033i
$672$		0			0
$673$	−5.92537	−	10.2630i	−0.228406	−	0.395611i	0.728930	−	0.684589i	$-0.240018\pi$
$673$	−5.92537	−	10.2630i	−0.228406	−	0.395611i	−0.957336	+	0.288977i	$0.906685\pi$
$674$	12.6822	+	0.0242805i	0.488502	+	0.000935250i
$675$		0			0
$676$	−0.0973434	+	25.4222i	−0.00374398	+	0.977777i
$677$	7.27808	−	27.1622i	0.279719	−	1.04393i	−0.672893	−	0.739740i	$-0.734949\pi$
$677$	7.27808	−	27.1622i	0.279719	−	1.04393i	0.952612	−	0.304187i	$-0.0983848\pi$
$678$		0			0
$679$	6.95459	+	4.01523i	0.266892	+	0.154090i
$680$	−43.7081	+	11.4429i	−1.67613	+	0.438815i
$681$		0			0
$682$	−5.93736	+	21.9900i	−0.227353	+	0.842042i
$683$	−21.9509	−	21.9509i	−0.839928	−	0.839928i	0.148921	−	0.988849i	$-0.452420\pi$
$683$	−21.9509	−	21.9509i	−0.839928	−	0.839928i	−0.988849	+	0.148921i	$0.952420\pi$
$684$		0			0
$685$	−42.1495	+	42.1495i	−1.61045	+	1.61045i
$686$	−11.7382	+	6.74713i	−0.448167	+	0.257607i
$687$		0			0
$688$	34.5822	−	8.98299i	1.31843	−	0.342473i
$689$	−3.25369	+	5.63556i	−0.123956	+	0.214698i
$690$		0			0
$691$	−7.24099	−	1.94022i	−0.275460	−	0.0738094i	0.118444	−	0.992961i	$-0.462209\pi$
$691$	−7.24099	−	1.94022i	−0.275460	−	0.0738094i	−0.393905	+	0.919151i	$0.628876\pi$
$692$	12.5335	−	12.4379i	0.476452	−	0.472817i
$693$		0			0
$694$	−10.7584	−	10.7997i	−0.408385	−	0.409951i
$695$	−24.8702	+	14.3588i	−0.943379	+	0.544660i
$696$		0			0
$697$	−9.55425	−	5.51615i	−0.361893	−	0.208939i
$698$	8.34810	+	31.3958i	0.315980	+	1.18835i
$699$		0			0
$700$	1.33511	+	2.33306i	0.0504622	+	0.0881812i
$701$	−10.7494	+	10.7494i	−0.405998	+	0.405998i	−0.880341	−	0.474342i	$-0.842686\pi$
$701$	−10.7494	+	10.7494i	−0.405998	+	0.405998i	0.474342	+	0.880341i	$0.342686\pi$
$702$		0			0
$703$	−14.0233			−0.528899
$704$	−8.11804	+	28.9620i	−0.305960	+	1.09155i
$705$		0			0
$706$	9.49612	−	16.3753i	0.357391	−	0.616292i
$707$	−0.0594063	−	0.221707i	−0.00223421	−	0.00833817i
$708$		0			0
$709$	10.0897	−	37.6553i	0.378927	−	1.41418i	−0.468594	−	0.883414i	$-0.655239\pi$
$709$	10.0897	−	37.6553i	0.378927	−	1.41418i	0.847521	−	0.530762i	$-0.178094\pi$
$710$	−6.60894	+	6.58368i	−0.248029	+	0.247081i
$711$		0			0
$712$	−0.0303281	+	5.28030i	−0.00113659	+	0.197887i
$713$	−21.1825	+	12.2297i	−0.793289	+	0.458006i
$714$		0			0
$715$	5.12477	−	1.37318i	0.191655	−	0.0513539i
$716$	−5.03939	−	19.0995i	−0.188331	−	0.713781i
$717$		0			0
$718$	31.7117	−	18.2279i	1.18347	−	0.680260i
$719$	−5.68975			−0.212192			−0.106096	−	0.994356i	$-0.533835\pi$
$719$	−5.68975			−0.212192			−0.106096	+	0.994356i	$0.533835\pi$
$720$		0			0
$721$	−11.5614			−0.430569
$722$	−14.7453	+	8.47562i	−0.548764	+	0.315430i
$723$		0			0
$724$	27.6384	−	7.29239i	1.02717	−	0.271019i
$725$	18.3492	−	4.91665i	0.681472	−	0.182600i
$726$		0			0
$727$	26.4441	−	15.2675i	0.980759	−	0.566241i	0.0782595	−	0.996933i	$-0.475064\pi$
$727$	26.4441	−	15.2675i	0.980759	−	0.566241i	0.902499	+	0.430692i	$0.141730\pi$
$728$	−0.758006	−	0.766764i	−0.0280936	−	0.0284182i
$729$		0			0
$730$	19.3631	−	19.2891i	0.716662	−	0.713923i
$731$	14.0643	−	52.4887i	0.520187	−	1.94137i
$732$		0			0
$733$	1.12446	+	4.19653i	0.0415327	+	0.155002i	0.983578	−	0.180483i	$-0.0577662\pi$
$733$	1.12446	+	4.19653i	0.0415327	+	0.155002i	−0.942045	+	0.335486i	$0.891100\pi$
$734$	11.2321	−	19.3688i	0.414583	−	0.714914i
$735$		0			0
$736$	−28.1253	+	15.8811i	−1.03671	+	0.585386i
$737$	28.5378			1.05120
$738$		0			0
$739$	8.41621	−	8.41621i	0.309595	−	0.309595i	−0.535157	−	0.844752i	$-0.679748\pi$
$739$	8.41621	−	8.41621i	0.309595	−	0.309595i	0.844752	+	0.535157i	$0.179748\pi$
$740$	24.2044	−	13.8511i	0.889771	−	0.509177i
$741$		0			0
$742$	3.12134	+	11.7388i	0.114588	+	0.430947i
$743$	−19.8348	−	11.4516i	−0.727669	−	0.420120i	0.0899001	−	0.995951i	$-0.471345\pi$
$743$	−19.8348	−	11.4516i	−0.727669	−	0.420120i	−0.817569	+	0.575831i	$0.804679\pi$
$744$		0			0
$745$	−1.49041	+	0.860487i	−0.0546043	+	0.0315258i
$746$	3.87210	+	3.88696i	0.141768	+	0.142312i
$747$		0			0
$748$	32.2225	+	32.4703i	1.17817	+	1.18723i
$749$	−6.05724	−	1.62303i	−0.221327	−	0.0593043i
$750$		0			0
$751$	−9.44386	+	16.3572i	−0.344611	+	0.596885i	−0.985283	−	0.170930i	$-0.945323\pi$
$751$	−9.44386	+	16.3572i	−0.344611	+	0.596885i	0.640672	+	0.767815i	$0.278656\pi$
$752$	11.9745	−	20.3784i	0.436664	−	0.743123i
$753$		0			0
$754$	−6.60603	+	3.79715i	−0.240578	+	0.138284i
$755$	10.6953	−	10.6953i	0.389242	−	0.389242i
$756$		0			0
$757$	25.7838	+	25.7838i	0.937129	+	0.937129i	0.998137	−	0.0610085i	$-0.0194317\pi$
$757$	25.7838	+	25.7838i	0.937129	+	0.937129i	−0.0610085	+	0.998137i	$0.519432\pi$
$758$	−9.00882	+	33.3657i	−0.327215	+	1.21190i
$759$		0			0
$760$	−9.90379	+	16.9286i	−0.359248	+	0.614064i
$761$	8.41595	+	4.85895i	0.305078	+	0.176137i	0.644722	−	0.764417i	$-0.276973\pi$
$761$	8.41595	+	4.85895i	0.305078	+	0.176137i	−0.339644	+	0.940554i	$0.610307\pi$
$762$		0			0
$763$	−1.66211	+	6.20309i	−0.0601726	+	0.224567i
$764$	11.4986	+	0.0440289i	0.416004	+	0.00159291i
$765$		0			0
$766$	−12.0734	−	0.0231149i	−0.436230	−	0.000835174i
$767$	1.44550	+	2.50368i	0.0521940	+	0.0904027i
$768$		0			0
$769$	7.20194	−	12.4741i	0.259709	−	0.449828i	−0.706455	−	0.707758i	$-0.749707\pi$
$769$	7.20194	−	12.4741i	0.259709	−	0.449828i	0.966164	+	0.257929i	$0.0830402\pi$
$770$	4.96810	−	8.56708i	0.179038	−	0.308736i
$771$		0			0
$772$	−8.85147	−	15.4677i	−0.318571	−	0.556693i
$773$	−4.99733	−	4.99733i	−0.179741	−	0.179741i	0.611502	−	0.791243i	$-0.290566\pi$
$773$	−4.99733	−	4.99733i	−0.179741	−	0.179741i	−0.791243	+	0.611502i	$0.790566\pi$
$774$		0			0
$775$		−	8.11694i		−	0.291569i
$776$	−15.8512	−	27.8229i	−0.569024	−	0.998783i
$777$		0			0
$778$	−42.4484	+	11.2870i	−1.52185	+	0.404657i
$779$	−4.62585	+	1.23949i	−0.165738	+	0.0444095i
$780$		0			0
$781$	9.12320	+	2.44456i	0.326454	+	0.0874731i
$782$	−0.0940470	+	49.1228i	−0.00336312	+	1.75663i
$783$		0			0
$784$	25.9867	+	0.199013i	0.928096	+	0.00710759i
$785$	10.2702	+	17.7885i	0.366559	+	0.634900i
$786$		0			0
$787$	−2.17639	−	8.12238i	−0.0775798	−	0.289532i	0.916226	−	0.400662i	$-0.131220\pi$
$787$	−2.17639	−	8.12238i	−0.0775798	−	0.289532i	−0.993806	+	0.111130i	$0.964553\pi$
$788$	−18.4951	+	4.87993i	−0.658862	+	0.173840i
$789$		0			0
$790$	0.0277323	−	0.102711i	0.000986670	−	0.00365430i
$791$		−	1.39644i		−	0.0496518i
$792$		0			0
$793$			0.364704i			0.0129510i
$794$	32.2202	+	8.69952i	1.14345	+	0.308734i
$795$		0			0
$796$	7.72154	+	4.49754i	0.273683	+	0.159411i
$797$	−11.0094	−	41.0878i	−0.389974	−	1.45540i	−0.830174	−	0.557504i	$-0.811759\pi$
$797$	−11.0094	−	41.0878i	−0.389974	−	1.45540i	0.440200	−	0.897900i	$-0.354908\pi$
$798$		0			0
$799$	−17.9737	−	31.1314i	−0.635864	−	1.10135i
$800$	0.102604	−	10.7181i	0.00362759	−	0.378943i
$801$		0			0
$802$	−24.7975	−	0.0474756i	−0.875632	−	0.00167642i
$803$	−26.7295	−	7.16216i	−0.943265	−	0.252747i
$804$		0			0
$805$	10.2723	−	2.75245i	0.362050	−	0.0970111i
$806$	0.836626	+	3.14641i	0.0294689	+	0.110828i
$807$		0			0
$808$	−0.241956	+	0.882682i	−0.00851199	+	0.0310527i
$809$			14.1610i			0.497874i	0.968520	+	0.248937i	$0.0800813\pi$
$809$			14.1610i			0.497874i	−0.968520	+	0.248937i	$0.919919\pi$
$810$		0			0
$811$	2.20583	+	2.20583i	0.0774570	+	0.0774570i	0.744774	−	0.667317i	$-0.232557\pi$
$811$	2.20583	+	2.20583i	0.0774570	+	0.0774570i	−0.667317	+	0.744774i	$0.732557\pi$
$812$	−3.73370	+	13.7239i	−0.131027	+	0.481616i
$813$		0			0
$814$	−24.4255	−	14.1645i	−0.856114	−	0.496465i
$815$	30.4339	−	52.7130i	1.06605	−	1.84646i
$816$		0			0
$817$	−11.7944	−	20.4284i	−0.412632	−	0.714700i
$818$	0.00251929	−	1.31588i	8.80849e−5	−	0.0460086i
$819$		0			0
$820$	6.76000	−	6.70843i	0.236070	−	0.234269i
$821$	3.66337	−	13.6719i	0.127852	−	0.477151i	−0.872073	−	0.489376i	$-0.837225\pi$
$821$	3.66337	−	13.6719i	0.127852	−	0.477151i	0.999925	+	0.0122245i	$0.00389129\pi$
$822$		0			0
$823$	−22.4132	−	12.9403i	−0.781274	−	0.451069i	0.0556074	−	0.998453i	$-0.482290\pi$
$823$	−22.4132	−	12.9403i	−0.781274	−	0.451069i	−0.836882	+	0.547384i	$0.815624\pi$
$824$	39.7916	+	23.2795i	1.38621	+	0.810978i
$825$		0			0
$826$	5.20981	+	1.40666i	0.181272	+	0.0489439i
$827$	28.2321	+	28.2321i	0.981726	+	0.981726i	0.999836	−	0.0181098i	$-0.00576485\pi$
$827$	28.2321	+	28.2321i	0.981726	+	0.981726i	−0.0181098	+	0.999836i	$0.505765\pi$
$828$		0			0
$829$	31.3884	−	31.3884i	1.09016	−	1.09016i	0.0946541	−	0.995510i	$-0.469825\pi$
$829$	31.3884	−	31.3884i	1.09016	−	1.09016i	0.995510	−	0.0946541i	$-0.0301745\pi$
$830$	28.6096	+	49.7731i	0.993053	+	1.72765i
$831$		0			0
$832$	1.06496	+	4.16530i	0.0369209	+	0.144406i
$833$	19.7617	−	34.2283i	0.684703	−	1.18594i
$834$		0			0
$835$	−16.8886	−	4.52528i	−0.584453	−	0.156604i
$836$	19.8574	+	0.0760355i	0.686784	+	0.00262974i
$837$		0			0
$838$	−15.9687	+	15.9076i	−0.551628	+	0.549520i
$839$	23.1346	−	13.3567i	0.798693	−	0.461126i	−0.0443206	−	0.999017i	$-0.514112\pi$
$839$	23.1346	−	13.3567i	0.798693	−	0.461126i	0.843014	+	0.537891i	$0.180779\pi$
$840$		0			0
$841$	61.9313	+	35.7561i	2.13556	+	1.23297i
$842$	−11.1167	+	2.95591i	−0.383107	+	0.101867i
$843$		0			0
$844$	−18.0698	−	4.91603i	−0.621989	−	0.169217i
$845$	−23.6011	+	23.6011i	−0.811902	+	0.811902i
$846$		0			0
$847$	−2.22441			−0.0764315
$848$	12.8938	−	46.6873i	0.442776	−	1.60325i
$849$		0			0
$850$	−14.1020	−	8.17782i	−0.483694	−	0.280497i
$851$	−7.84749	−	29.2872i	−0.269008	−	1.00395i
$852$		0			0
$853$	−11.8401	+	44.1878i	−0.405397	+	1.51296i	0.397927	+	0.917417i	$0.369730\pi$
$853$	−11.8401	+	44.1878i	−0.405397	+	1.51296i	−0.803323	+	0.595543i	$0.796937\pi$
$854$	0.480447	+	0.482290i	0.0164406	+	0.0165036i
$855$		0			0
$856$	17.5795	+	17.7826i	0.600856	+	0.607798i
$857$	30.8789	−	17.8279i	1.05480	−	0.608990i	0.130812	−	0.991407i	$-0.458242\pi$
$857$	30.8789	−	17.8279i	1.05480	−	0.608990i	0.923990	+	0.382417i	$0.124908\pi$
$858$		0			0
$859$	−29.1136	+	7.80095i	−0.993342	+	0.266165i	−0.718654	−	0.695368i	$-0.755241\pi$
$859$	−29.1136	+	7.80095i	−0.993342	+	0.266165i	−0.274688	+	0.961533i	$0.588575\pi$
$860$	40.5348	+	23.6102i	1.38222	+	0.805100i
$861$		0			0
$862$	7.62988	+	13.2740i	0.259875	+	0.452113i
$863$	−12.6307			−0.429956			−0.214978	−	0.976619i	$-0.568968\pi$
$863$	−12.6307			−0.429956			−0.214978	+	0.976619i	$0.568968\pi$
$864$		0			0
$865$	23.1826			0.788231
$866$	14.4727	+	25.1787i	0.491802	+	0.855606i
$867$		0			0
$868$	5.25133	+	3.05873i	0.178242	+	0.103820i
$869$	−0.104047	+	0.0278792i	−0.00352954	+	0.000945739i
$870$		0			0
$871$	3.53261	−	2.03955i	0.119698	−	0.0691076i
$872$	18.2108	−	18.0028i	0.616697	−	0.609653i
$873$		0			0
$874$	15.0494	+	15.1071i	0.509052	+	0.511005i
$875$	1.49689	−	5.58649i	0.0506043	−	0.188858i
$876$		0			0
$877$	11.4980	+	42.9110i	0.388259	+	1.44900i	0.832966	+	0.553325i	$0.186641\pi$
$877$	11.4980	+	42.9110i	0.388259	+	1.44900i	−0.444707	+	0.895676i	$0.646692\pi$
$878$	35.1646	+	20.3921i	1.18675	+	0.688201i
$879$		0			0
$880$	−34.3493	+	19.4824i	−1.15791	+	0.656750i
$881$	−42.7491			−1.44025			−0.720126	−	0.693843i	$-0.755916\pi$
$881$	−42.7491			−1.44025			−0.720126	+	0.693843i	$0.755916\pi$
$882$		0			0
$883$	9.95115	−	9.95115i	0.334883	−	0.334883i	−0.519555	−	0.854437i	$-0.673902\pi$
$883$	9.95115	−	9.95115i	0.334883	−	0.334883i	0.854437	+	0.519555i	$0.173902\pi$
$884$	6.30933	+	1.71650i	0.212206	+	0.0577321i
$885$		0			0
$886$	−17.6848	+	4.70235i	−0.594131	+	0.157978i
$887$	−44.4891	−	25.6858i	−1.49380	−	0.862445i	−0.493824	−	0.869562i	$-0.664401\pi$
$887$	−44.4891	−	25.6858i	−1.49380	−	0.862445i	−0.999975	+	0.00711642i	$0.997735\pi$
$888$		0			0
$889$	6.17234	−	3.56361i	0.207014	−	0.119519i
$890$	−4.91147	+	4.89270i	−0.164633	+	0.164004i
$891$		0			0
$892$	22.6425	+	0.0866998i	0.758127	+	0.00290292i
$893$	−15.0728	−	4.03874i	−0.504392	−	0.135151i
$894$		0			0
$895$	12.9669	−	22.4594i	0.433436	−	0.750734i
$896$	6.89553	+	4.10532i	0.230364	+	0.137149i
$897$		0			0
$898$	21.2180	+	36.9137i	0.708055	+	1.23183i
$899$	30.3684	−	30.3684i	1.01284	−	1.01284i
$900$		0			0
$901$	−52.0879	−	52.0879i	−1.73530	−	1.73530i
$902$	−9.30919	−	2.51350i	−0.309962	−	0.0836905i
$903$		0			0
$904$	−2.81181	+	4.80623i	−0.0935194	+	0.159853i
$905$	32.5004	+	18.7641i	1.08035	+	0.623741i
$906$		0			0
$907$	6.80259	−	25.3876i	0.225876	−	0.842981i	−0.756175	−	0.654369i	$-0.772934\pi$
$907$	6.80259	−	25.3876i	0.225876	−	0.842981i	0.982052	−	0.188612i	$-0.0603990\pi$
$908$	11.6507	−	11.5618i	0.386641	−	0.383692i
$909$		0			0
$910$	0.00271012	−	1.41555i	8.98396e−5	−	0.0469252i
$911$	−0.579270	−	1.00332i	−0.0191921	−	0.0332416i	0.856270	−	0.516529i	$-0.172776\pi$
$911$	−0.579270	−	1.00332i	−0.0191921	−	0.0332416i	−0.875462	+	0.483287i	$0.839443\pi$
$912$		0			0
$913$	29.0631	−	50.3387i	0.961847	−	1.66597i
$914$	2.82670	+	1.63922i	0.0934989	+	0.0542206i
$915$		0			0
$916$	−7.99440	+	29.3850i	−0.264143	+	0.970907i
$917$	2.10988	+	2.10988i	0.0696743	+	0.0696743i
$918$		0			0
$919$			43.3055i			1.42852i	0.699882	+	0.714259i	$0.253236\pi$
$919$			43.3055i			1.42852i	−0.699882	+	0.714259i	$0.746764\pi$
$920$	−40.8970	−	11.2105i	−1.34833	−	0.369598i
$921$		0			0
$922$	6.35990	+	23.9186i	0.209452	+	0.787716i
$923$	1.30404	−	0.349417i	0.0429231	−	0.0115012i
$924$		0			0
$925$	9.71906	+	2.60422i	0.319561	+	0.0856261i
$926$	29.0172	+	0.0555542i	0.953564	+	0.00182563i
$927$		0			0
$928$	40.4843	−	39.7166i	1.32896	−	1.30376i
$929$	3.69756	+	6.40436i	0.121313	+	0.210120i	0.920286	−	0.391247i	$-0.127956\pi$
$929$	3.69756	+	6.40436i	0.121313	+	0.210120i	−0.798973	+	0.601367i	$0.794623\pi$
$930$		0			0
$931$	−4.44051	−	16.5722i	−0.145532	−	0.543133i
$932$	−12.7973	−	7.45400i	−0.419189	−	0.244164i
$933$		0			0
$934$	−12.5326	−	3.38383i	−0.410079	−	0.110722i
$935$			60.0586i			1.96413i
$936$		0			0
$937$			41.4673i			1.35468i	0.735672	+	0.677338i	$0.236867\pi$
$937$			41.4673i			1.35468i	−0.735672	+	0.677338i	$0.763133\pi$
$938$	1.98475	−	7.35085i	0.0648043	−	0.240014i
$939$		0			0
$940$	30.0050	−	7.91679i	0.978654	−	0.258217i
$941$	15.4400	+	57.6229i	0.503330	+	1.87845i	0.477203	+	0.878793i	$0.341651\pi$
$941$	15.4400	+	57.6229i	0.503330	+	1.87845i	0.0261263	+	0.999659i	$0.491683\pi$
$942$		0			0
$943$	−5.17728	−	8.96732i	−0.168596	−	0.292016i
$944$	−15.0985	−	15.3316i	−0.491416	−	0.499001i
$945$		0			0
$946$	0.0909304	−	47.4950i	0.00295640	−	1.54419i
$947$	−18.9371	−	5.07419i	−0.615375	−	0.164889i	−0.0623504	−	0.998054i	$-0.519860\pi$
$947$	−18.9371	−	5.07419i	−0.615375	−	0.164889i	−0.553024	+	0.833165i	$0.686526\pi$
$948$		0			0
$949$	−3.82064	+	1.02374i	−0.124023	+	0.0332319i
$950$	−6.83877	+	1.81842i	−0.221879	+	0.0589973i
$951$		0			0
$952$	10.6048	−	6.04174i	0.343704	−	0.195814i
$953$		−	48.5032i		−	1.57117i	−0.618752	−	0.785586i	$-0.712362\pi$
$953$		−	48.5032i		−	1.57117i	0.618752	−	0.785586i	$-0.287638\pi$
$954$		0			0
$955$	10.6749	+	10.6749i	0.345431	+	0.345431i
$956$	4.31881	+	7.54698i	0.139680	+	0.244087i
$957$		0			0
$958$	14.3295	−	24.7101i	0.462966	−	0.798346i
$959$	8.05121	−	13.9451i	0.259987	−	0.450311i
$960$		0			0
$961$	6.32457	+	10.9545i	0.204018	+	0.353370i
$962$	−4.03588	−	0.00772680i	−0.130122	−	0.000249122i
$963$		0			0
$964$	42.3087	+	0.162003i	1.36267	+	0.00521776i
$965$	6.05572	−	22.6002i	0.194940	−	0.727527i
$966$		0			0
$967$	21.1523	+	12.2123i	0.680212	+	0.392721i	0.799935	−	0.600087i	$-0.204867\pi$
$967$	21.1523	+	12.2123i	0.680212	+	0.392721i	−0.119723	+	0.992807i	$0.538201\pi$
$968$	7.65589	+	4.47895i	0.246069	+	0.143959i
$969$		0			0
$970$	10.9587	−	40.5875i	0.351863	−	1.30318i
$971$	23.3101	+	23.3101i	0.748056	+	0.748056i	0.974114	−	0.226058i	$-0.0725839\pi$
$971$	23.3101	+	23.3101i	0.748056	+	0.748056i	−0.226058	+	0.974114i	$0.572584\pi$
$972$		0			0
$973$	5.48551	−	5.48551i	0.175857	−	0.175857i
$974$	−2.03158	+	1.16775i	−0.0650961	+	0.0374172i
$975$		0			0
$976$	−0.682471	−	2.62733i	−0.0218454	−	0.0840989i
$977$	2.47977	−	4.29508i	0.0793348	−	0.137412i	−0.823628	−	0.567130i	$-0.808054\pi$
$977$	2.47977	−	4.29508i	0.0793348	−	0.137412i	0.902963	+	0.429718i	$0.141387\pi$
$978$		0			0
$979$	6.77995	+	1.81668i	0.216688	+	0.0580614i
$980$	24.0331	+	24.2179i	0.767710	+	0.773611i
$981$		0			0
$982$	29.4054	+	29.5182i	0.938364	+	0.941964i
$983$	9.31801	−	5.37975i	0.297198	−	0.171588i	−0.343985	−	0.938975i	$-0.611777\pi$
$983$	9.31801	−	5.37975i	0.297198	−	0.171588i	0.641184	+	0.767388i	$0.278444\pi$
$984$		0			0
$985$	−21.7487	−	12.5566i	−0.692971	−	0.400087i
$986$	−22.1645	−	83.3569i	−0.705860	−	2.65462i
$987$		0			0
$988$	2.46353	−	1.40977i	0.0783752	−	0.0448507i
$989$	36.0640	−	36.0640i	1.14677	−	1.14677i
$990$		0			0
$991$	29.6031			0.940375			0.470187	−	0.882567i	$-0.344186\pi$
$991$	29.6031			0.940375			0.470187	+	0.882567i	$0.344186\pi$
$992$	−11.9149	−	21.1012i	−0.378300	−	0.669965i
$993$		0			0
$994$	1.26418	−	2.17997i	0.0400973	−	0.0691444i
$995$	3.03644	+	11.3322i	0.0962616	+	0.359253i
$996$		0			0
$997$	−4.19338	+	15.6499i	−0.132806	+	0.495637i	−0.999997	−	0.00233721i	$-0.999256\pi$
$997$	−4.19338	+	15.6499i	−0.132806	+	0.495637i	0.867192	+	0.497975i	$0.165923\pi$
$998$	18.9076	−	18.8354i	0.598510	−	0.596223i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.y.e.37.11		72
3.2	odd	2		144.2.x.e.85.8	yes	72
4.3	odd	2		1728.2.bc.e.1009.6		72
9.2	odd	6		144.2.x.e.133.4	yes	72
9.7	even	3	inner	432.2.y.e.181.15		72
12.11	even	2		576.2.bb.e.49.15		72
16.3	odd	4		1728.2.bc.e.145.13		72
16.13	even	4	inner	432.2.y.e.253.15		72
36.7	odd	6		1728.2.bc.e.1585.13		72
36.11	even	6		576.2.bb.e.241.12		72
48.29	odd	4		144.2.x.e.13.4	✓	72
48.35	even	4		576.2.bb.e.337.12		72
144.29	odd	12		144.2.x.e.61.8	yes	72
144.61	even	12	inner	432.2.y.e.397.11		72
144.83	even	12		576.2.bb.e.529.15		72
144.115	odd	12		1728.2.bc.e.721.6		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.4	✓	72	48.29	odd	4
144.2.x.e.61.8	yes	72	144.29	odd	12
144.2.x.e.85.8	yes	72	3.2	odd	2
144.2.x.e.133.4	yes	72	9.2	odd	6
432.2.y.e.37.11		72	1.1	even	1	trivial
432.2.y.e.181.15		72	9.7	even	3	inner
432.2.y.e.253.15		72	16.13	even	4	inner
432.2.y.e.397.11		72	144.61	even	12	inner
576.2.bb.e.49.15		72	12.11	even	2
576.2.bb.e.241.12		72	36.11	even	6
576.2.bb.e.337.12		72	48.35	even	4
576.2.bb.e.529.15		72	144.83	even	12
1728.2.bc.e.145.13		72	16.3	odd	4
1728.2.bc.e.721.6		72	144.115	odd	12
1728.2.bc.e.1009.6		72	4.3	odd	2
1728.2.bc.e.1585.13		72	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.704761 + 1.22610i) q^{2} +(-1.00662 + 1.72821i) q^{4} +(-2.53632 + 0.679606i) q^{5} +(0.614293 - 0.354662i) q^{7} +(-2.82838 - 0.0162452i) q^{8} +O(q^{10})\)	\(q+(0.704761 + 1.22610i) q^{2} +(-1.00662 + 1.72821i) q^{4} +(-2.53632 + 0.679606i) q^{5} +(0.614293 - 0.354662i) q^{7} +(-2.82838 - 0.0162452i) q^{8} +(-2.62076 - 2.63082i) q^{10} +(-0.973103 + 3.63167i) q^{11} +(0.139092 + 0.519100i) q^{13} +(0.867779 + 0.503230i) q^{14} +(-1.97341 - 3.47932i) q^{16} -6.08347 q^{17} +(-1.86732 + 1.86732i) q^{19} +(1.37863 - 5.06741i) q^{20} +(-5.13858 + 1.36634i) q^{22} +(-4.94479 - 2.85488i) q^{23} +(1.64095 - 0.947401i) q^{25} +(-0.538439 + 0.536382i) q^{26} +(-0.00543207 + 1.41864i) q^{28} +(9.68396 + 2.59481i) q^{29} +(2.14190 - 3.70987i) q^{31} +(2.87519 - 4.87168i) q^{32} +(-4.28739 - 7.45892i) q^{34} +(-1.31701 + 1.31701i) q^{35} +(3.75493 + 3.75493i) q^{37} +(-3.60553 - 0.973500i) q^{38} +(7.18473 - 1.88098i) q^{40} +(1.57053 + 0.906743i) q^{41} +(-2.31189 + 8.62809i) q^{43} +(-5.29673 - 5.33745i) q^{44} +(0.0154594 - 8.07480i) q^{46} +(2.95451 + 5.11737i) q^{47} +(-3.24843 + 5.62645i) q^{49} +(2.31808 + 1.34427i) q^{50} +(-1.03713 - 0.282158i) q^{52} +(8.56219 + 8.56219i) q^{53} -9.87242i q^{55} +(-1.74322 + 0.993140i) q^{56} +(3.64339 + 13.7022i) q^{58} +(5.19620 - 1.39232i) q^{59} +(0.655507 + 0.175643i) q^{61} +(6.05818 + 0.0115986i) q^{62} +(7.99947 + 0.0918952i) q^{64} +(-0.705566 - 1.22208i) q^{65} +(-1.96451 - 7.33165i) q^{67} +(6.12377 - 10.5135i) q^{68} +(-2.54297 - 0.686607i) q^{70} -2.51212i q^{71} +7.36013i q^{73} +(-1.95758 + 7.25023i) q^{74} +(-1.34743 - 5.10681i) q^{76} +(0.690245 + 2.57603i) q^{77} +(0.0143249 + 0.0248115i) q^{79} +(7.36978 + 7.48353i) q^{80} +(-0.00491010 + 2.56465i) q^{82} +(-14.9332 - 4.00134i) q^{83} +(15.4297 - 4.13436i) q^{85} +(-12.2082 + 3.24614i) q^{86} +(2.81130 - 10.2559i) q^{88} -1.86690i q^{89} +(0.269548 + 0.269548i) q^{91} +(9.91138 - 5.67185i) q^{92} +(-4.19216 + 7.22904i) q^{94} +(3.46709 - 6.00517i) q^{95} +(5.66064 + 9.80452i) q^{97} +(-9.18793 - 0.0175906i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Introduction

L-functions

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