LMFDB - Embedded newform 342.2.u.a.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(55,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("342.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.u (of order $9$, degree $6$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			289.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	342.289
Dual form			342.2.u.a.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(-0.907604 + 0.761570i) q^{5} +(-0.266044 + 0.460802i) q^{7} +(-0.500000 - 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(-0.907604 + 0.761570i) q^{5} +(-0.266044 + 0.460802i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.11334 - 0.405223i) q^{10} +(0.939693 + 1.62760i) q^{11} +(-0.673648 + 3.82045i) q^{13} +(0.407604 - 0.342020i) q^{14} +(0.173648 + 0.984808i) q^{16} +(1.09240 + 0.397600i) q^{17} +(-3.93969 + 1.86516i) q^{19} -1.18479 q^{20} +(-0.326352 - 1.85083i) q^{22} +(5.13429 + 4.30818i) q^{23} +(-0.624485 + 3.54163i) q^{25} +(1.93969 - 3.35965i) q^{26} +(-0.500000 + 0.181985i) q^{28} +(-3.77972 + 1.37570i) q^{29} +(0.979055 - 1.69577i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-0.890530 - 0.747243i) q^{34} +(-0.109470 - 0.620838i) q^{35} +6.88713 q^{37} +(4.34002 - 0.405223i) q^{38} +(1.11334 + 0.405223i) q^{40} +(1.56031 + 8.84894i) q^{41} +(1.85844 - 1.55942i) q^{43} +(-0.326352 + 1.85083i) q^{44} +(-3.35117 - 5.80439i) q^{46} +(1.91875 - 0.698367i) q^{47} +(3.35844 + 5.81699i) q^{49} +(1.79813 - 3.11446i) q^{50} +(-2.97178 + 2.49362i) q^{52} +(-9.93629 - 8.33754i) q^{53} +(-2.09240 - 0.761570i) q^{55} +0.532089 q^{56} +4.02229 q^{58} +(-2.51842 - 0.916629i) q^{59} +(-8.69253 - 7.29390i) q^{61} +(-1.50000 + 1.25865i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-2.29813 - 3.98048i) q^{65} +(10.4966 - 3.82045i) q^{67} +(0.581252 + 1.00676i) q^{68} +(-0.109470 + 0.620838i) q^{70} +(-4.65136 + 3.90295i) q^{71} +(-0.0569038 - 0.322718i) q^{73} +(-6.47178 - 2.35554i) q^{74} +(-4.21688 - 1.10359i) q^{76} -1.00000 q^{77} +(-2.80154 - 15.8883i) q^{79} +(-0.907604 - 0.761570i) q^{80} +(1.56031 - 8.84894i) q^{82} +(5.78699 - 10.0234i) q^{83} +(-1.29426 + 0.471073i) q^{85} +(-2.27972 + 0.829748i) q^{86} +(0.939693 - 1.62760i) q^{88} +(0.618089 - 3.50535i) q^{89} +(-1.58125 - 1.32683i) q^{91} +(1.16385 + 6.60051i) q^{92} -2.04189 q^{94} +(2.15523 - 4.69318i) q^{95} +(-5.52481 - 2.01087i) q^{97} +(-1.16637 - 6.61484i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q - 9 * q^5 + 3 * q^7 - 3 * q^8	$ 6 q - 9 q^{5} + 3 q^{7} - 3 q^{8} - 3 q^{13} + 6 q^{14} + 3 q^{17} - 18 q^{19} - 3 q^{22} + 21 q^{23} + 9 q^{25} + 6 q^{26} - 3 q^{28} + 3 q^{29} + 9 q^{31} + 12 q^{34} - 18 q^{35} - 18 q^{37} + 6 q^{38} + 15 q^{41} + 3 q^{43} - 3 q^{44} + 6 q^{46} + 9 q^{47} + 12 q^{49} - 3 q^{50} - 3 q^{52} - 12 q^{53} - 9 q^{55} - 6 q^{56} + 12 q^{58} - 27 q^{59} + 3 q^{61} - 9 q^{62} - 3 q^{64} + 21 q^{67} + 6 q^{68} - 18 q^{70} - 39 q^{71} + 36 q^{73} - 24 q^{74} - 9 q^{76} - 6 q^{77} - 45 q^{79} - 9 q^{80} + 15 q^{82} + 27 q^{83} - 18 q^{85} + 12 q^{86} + 30 q^{89} - 12 q^{91} + 3 q^{92} - 6 q^{94} - 6 q^{97} + 12 q^{98}+O(q^{100}) $ 6 * q - 9 * q^5 + 3 * q^7 - 3 * q^8 - 3 * q^13 + 6 * q^14 + 3 * q^17 - 18 * q^19 - 3 * q^22 + 21 * q^23 + 9 * q^25 + 6 * q^26 - 3 * q^28 + 3 * q^29 + 9 * q^31 + 12 * q^34 - 18 * q^35 - 18 * q^37 + 6 * q^38 + 15 * q^41 + 3 * q^43 - 3 * q^44 + 6 * q^46 + 9 * q^47 + 12 * q^49 - 3 * q^50 - 3 * q^52 - 12 * q^53 - 9 * q^55 - 6 * q^56 + 12 * q^58 - 27 * q^59 + 3 * q^61 - 9 * q^62 - 3 * q^64 + 21 * q^67 + 6 * q^68 - 18 * q^70 - 39 * q^71 + 36 * q^73 - 24 * q^74 - 9 * q^76 - 6 * q^77 - 45 * q^79 - 9 * q^80 + 15 * q^82 + 27 * q^83 - 18 * q^85 + 12 * q^86 + 30 * q^89 - 12 * q^91 + 3 * q^92 - 6 * q^94 - 6 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$		0			0
$3$		0			0
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.907604	+	0.761570i	−0.405893	+	0.340584i	−0.822766	−	0.568380i	$-0.807570\pi$
$5$	−0.907604	+	0.761570i	−0.405893	+	0.340584i	0.416873	+	0.908965i	$0.363126\pi$
$6$		0			0
$7$	−0.266044	+	0.460802i	−0.100555	+	0.174167i	−0.911914	−	0.410382i	$-0.865395\pi$
$7$	−0.266044	+	0.460802i	−0.100555	+	0.174167i	0.811358	+	0.584549i	$0.198729\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$		0			0
$10$	1.11334	−	0.405223i	0.352069	−	0.128143i
$11$	0.939693	+	1.62760i	0.283328	+	0.490738i	0.972202	−	0.234142i	$-0.0752282\pi$
$11$	0.939693	+	1.62760i	0.283328	+	0.490738i	−0.688874	+	0.724881i	$0.741895\pi$
$12$		0			0
$13$	−0.673648	+	3.82045i	−0.186836	+	1.05960i	0.736737	+	0.676180i	$0.236366\pi$
$13$	−0.673648	+	3.82045i	−0.186836	+	1.05960i	−0.923573	+	0.383422i	$0.874745\pi$
$14$	0.407604	−	0.342020i	0.108937	−	0.0914087i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	1.09240	+	0.397600i	0.264945	+	0.0964321i	0.471077	−	0.882092i	$-0.343865\pi$
$17$	1.09240	+	0.397600i	0.264945	+	0.0964321i	−0.206132	+	0.978524i	$0.566088\pi$
$18$		0			0
$19$	−3.93969	+	1.86516i	−0.903827	+	0.427897i
$19$	−3.93969	+	1.86516i	−0.903827	+	0.427897i
$20$	−1.18479			−0.264928
$21$		0			0
$22$	−0.326352	−	1.85083i	−0.0695784	−	0.394599i
$23$	5.13429	+	4.30818i	1.07057	+	0.898317i	0.995104	−	0.0988312i	$-0.0315104\pi$
$23$	5.13429	+	4.30818i	1.07057	+	0.898317i	0.0754683	+	0.997148i	$0.475955\pi$
$24$		0			0
$25$	−0.624485	+	3.54163i	−0.124897	+	0.708326i
$26$	1.93969	−	3.35965i	0.380405	−	0.658881i
$27$		0			0
$28$	−0.500000	+	0.181985i	−0.0944911	+	0.0343920i
$29$	−3.77972	+	1.37570i	−0.701875	+	0.255462i	−0.668211	−	0.743971i	$-0.732940\pi$
$29$	−3.77972	+	1.37570i	−0.701875	+	0.255462i	−0.0336640	+	0.999433i	$0.510718\pi$
$30$		0			0
$31$	0.979055	−	1.69577i	0.175844	−	0.304570i	−0.764609	−	0.644494i	$-0.777068\pi$
$31$	0.979055	−	1.69577i	0.175844	−	0.304570i	0.940453	+	0.339924i	$0.110401\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$		0			0
$34$	−0.890530	−	0.747243i	−0.152725	−	0.128151i
$35$	−0.109470	−	0.620838i	−0.0185039	−	0.104941i
$36$		0			0
$37$	6.88713			1.13224			0.566118	−	0.824324i	$-0.308445\pi$
$37$	6.88713			1.13224			0.566118	+	0.824324i	$0.308445\pi$
$38$	4.34002	−	0.405223i	0.704045	−	0.0657358i
$39$		0			0
$40$	1.11334	+	0.405223i	0.176035	+	0.0640714i
$41$	1.56031	+	8.84894i	0.243679	+	1.38197i	0.823540	+	0.567258i	$0.191996\pi$
$41$	1.56031	+	8.84894i	0.243679	+	1.38197i	−0.579861	+	0.814715i	$0.696893\pi$
$42$		0			0
$43$	1.85844	−	1.55942i	0.283410	−	0.237809i	−0.489989	−	0.871728i	$-0.662999\pi$
$43$	1.85844	−	1.55942i	0.283410	−	0.237809i	0.773399	+	0.633919i	$0.218555\pi$
$44$	−0.326352	+	1.85083i	−0.0491994	+	0.279024i
$45$		0			0
$46$	−3.35117	−	5.80439i	−0.494103	−	0.855811i
$47$	1.91875	−	0.698367i	0.279878	−	0.101867i	−0.198267	−	0.980148i	$-0.563531\pi$
$47$	1.91875	−	0.698367i	0.279878	−	0.101867i	0.478145	+	0.878281i	$0.341309\pi$
$48$		0			0
$49$	3.35844	+	5.81699i	0.479777	+	0.830999i
$50$	1.79813	−	3.11446i	0.254294	−	0.440451i
$51$		0			0
$52$	−2.97178	+	2.49362i	−0.412112	+	0.345803i
$53$	−9.93629	−	8.33754i	−1.36485	−	1.14525i	−0.974450	−	0.224605i	$-0.927891\pi$
$53$	−9.93629	−	8.33754i	−1.36485	−	1.14525i	−0.390404	−	0.920643i	$-0.627665\pi$
$54$		0			0
$55$	−2.09240	−	0.761570i	−0.282139	−	0.102690i
$56$	0.532089			0.0711034
$57$		0			0
$58$	4.02229			0.528152
$59$	−2.51842	−	0.916629i	−0.327870	−	0.119335i	0.172840	−	0.984950i	$-0.444706\pi$
$59$	−2.51842	−	0.916629i	−0.327870	−	0.119335i	−0.500710	+	0.865615i	$0.666928\pi$
$60$		0			0
$61$	−8.69253	−	7.29390i	−1.11296	−	0.933888i	−0.114737	−	0.993396i	$-0.536603\pi$
$61$	−8.69253	−	7.29390i	−1.11296	−	0.933888i	−0.998228	+	0.0595075i	$0.981047\pi$
$62$	−1.50000	+	1.25865i	−0.190500	+	0.159849i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.29813	−	3.98048i	−0.285048	−	0.493718i
$66$		0			0
$67$	10.4966	−	3.82045i	1.28236	−	0.466742i	0.391150	−	0.920327i	$-0.372077\pi$
$67$	10.4966	−	3.82045i	1.28236	−	0.466742i	0.891213	+	0.453585i	$0.149855\pi$
$68$	0.581252	+	1.00676i	0.0704871	+	0.122087i
$69$		0			0
$70$	−0.109470	+	0.620838i	−0.0130842	+	0.0742043i
$71$	−4.65136	+	3.90295i	−0.552015	+	0.463195i	−0.875623	−	0.482996i	$-0.839549\pi$
$71$	−4.65136	+	3.90295i	−0.552015	+	0.463195i	0.323608	+	0.946191i	$0.395104\pi$
$72$		0			0
$73$	−0.0569038	−	0.322718i	−0.00666009	−	0.0377712i	0.981297	−	0.192502i	$-0.0616601\pi$
$73$	−0.0569038	−	0.322718i	−0.00666009	−	0.0377712i	−0.987957	+	0.154731i	$0.950549\pi$
$74$	−6.47178	−	2.35554i	−0.752329	−	0.273825i
$75$		0			0
$76$	−4.21688	−	1.10359i	−0.483709	−	0.126590i
$77$	−1.00000			−0.113961
$78$		0			0
$79$	−2.80154	−	15.8883i	−0.315198	−	1.78757i	−0.571109	−	0.820874i	$-0.693487\pi$
$79$	−2.80154	−	15.8883i	−0.315198	−	1.78757i	0.255912	−	0.966700i	$-0.417624\pi$
$80$	−0.907604	−	0.761570i	−0.101473	−	0.0851461i
$81$		0			0
$82$	1.56031	−	8.84894i	0.172307	−	0.977202i
$83$	5.78699	−	10.0234i	0.635205	−	1.10021i	−0.351267	−	0.936275i	$-0.614249\pi$
$83$	5.78699	−	10.0234i	0.635205	−	1.10021i	0.986472	−	0.163931i	$-0.0524175\pi$
$84$		0			0
$85$	−1.29426	+	0.471073i	−0.140383	+	0.0510951i
$86$	−2.27972	+	0.829748i	−0.245828	+	0.0894741i
$87$		0			0
$88$	0.939693	−	1.62760i	0.100172	−	0.173502i
$89$	0.618089	−	3.50535i	0.0655173	−	0.371567i	−0.934366	−	0.356314i	$-0.884033\pi$
$89$	0.618089	−	3.50535i	0.0655173	−	0.371567i	0.999884	−	0.0152532i	$-0.00485542\pi$
$90$		0			0
$91$	−1.58125	−	1.32683i	−0.165760	−	0.139089i
$92$	1.16385	+	6.60051i	0.121340	+	0.688151i
$93$		0			0
$94$	−2.04189			−0.210605
$95$	2.15523	−	4.69318i	0.221122	−	0.481510i
$96$		0			0
$97$	−5.52481	−	2.01087i	−0.560960	−	0.204173i	0.0459494	−	0.998944i	$-0.485369\pi$
$97$	−5.52481	−	2.01087i	−0.560960	−	0.204173i	−0.606909	+	0.794771i	$0.707591\pi$
$98$	−1.16637	−	6.61484i	−0.117822	−	0.668199i
$99$		0			0
$100$	−2.75490	+	2.31164i	−0.275490	+	0.231164i
$101$	−2.19594	+	12.4538i	−0.218504	+	1.23920i	0.656218	+	0.754572i	$0.272155\pi$
$101$	−2.19594	+	12.4538i	−0.218504	+	1.23920i	−0.874722	+	0.484626i	$0.838956\pi$
$102$		0			0
$103$	−1.48158	−	2.56617i	−0.145985	−	0.252853i	0.783755	−	0.621070i	$-0.213302\pi$
$103$	−1.48158	−	2.56617i	−0.145985	−	0.252853i	−0.929740	+	0.368217i	$0.879968\pi$
$104$	3.64543	−	1.32683i	0.357464	−	0.130106i
$105$		0			0
$106$	6.48545	+	11.2331i	0.629923	+	1.09106i
$107$	9.55690	−	16.5530i	0.923901	−	1.60024i	0.130581	−	0.991438i	$-0.458316\pi$
$107$	9.55690	−	16.5530i	0.923901	−	1.60024i	0.793320	−	0.608805i	$-0.208351\pi$
$108$		0			0
$109$	−12.5719	+	10.5491i	−1.20417	+	1.01042i	−0.204670	+	0.978831i	$0.565612\pi$
$109$	−12.5719	+	10.5491i	−1.20417	+	1.01042i	−0.999501	+	0.0315888i	$0.989943\pi$
$110$	1.70574	+	1.43128i	0.162636	+	0.136468i
$111$		0			0
$112$	−0.500000	−	0.181985i	−0.0472456	−	0.0171960i
$113$	5.73648			0.539643			0.269821	−	0.962910i	$-0.413035\pi$
$113$	5.73648			0.539643			0.269821	+	0.962910i	$0.413035\pi$
$114$		0			0
$115$	−7.94087			−0.740490
$116$	−3.77972	−	1.37570i	−0.350938	−	0.127731i
$117$		0			0
$118$	2.05303	+	1.72270i	0.188997	+	0.158587i
$119$	−0.473841	+	0.397600i	−0.0434369	+	0.0364479i
$120$		0			0
$121$	3.73396	−	6.46740i	0.339451	−	0.587946i
$122$	5.67365	+	9.82705i	0.513668	+	0.889699i
$123$		0			0
$124$	1.84002	−	0.669713i	0.165239	−	0.0601420i
$125$	−5.09240	−	8.82029i	−0.455478	−	0.788911i
$126$		0			0
$127$	−0.327696	+	1.85846i	−0.0290783	+	0.164911i	−0.995889	−	0.0905828i	$-0.971127\pi$
$127$	−0.327696	+	1.85846i	−0.0290783	+	0.164911i	0.966811	+	0.255494i	$0.0822381\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$		0			0
$130$	0.798133	+	4.52644i	0.0700009	+	0.396995i
$131$	10.0569	+	3.66041i	0.878676	+	0.319812i	0.741675	−	0.670759i	$-0.234032\pi$
$131$	10.0569	+	3.66041i	0.878676	+	0.319812i	0.137001	+	0.990571i	$0.456254\pi$
$132$		0			0
$133$	0.188663	−	2.31164i	0.0163592	−	0.200444i
$134$	−11.1702			−0.964962
$135$		0			0
$136$	−0.201867	−	1.14484i	−0.0173099	−	0.0981695i
$137$	8.62314	+	7.23567i	0.736725	+	0.618185i	0.931956	−	0.362572i	$-0.118101\pi$
$137$	8.62314	+	7.23567i	0.736725	+	0.618185i	−0.195231	+	0.980757i	$0.562546\pi$
$138$		0			0
$139$	−2.11334	+	11.9854i	−0.179251	+	1.01658i	0.753870	+	0.657023i	$0.228185\pi$
$139$	−2.11334	+	11.9854i	−0.179251	+	1.01658i	−0.933122	+	0.359561i	$0.882926\pi$
$140$	0.315207	−	0.545955i	0.0266399	−	0.0461416i
$141$		0			0
$142$	5.70574	−	2.07672i	0.478815	−	0.174274i
$143$	−6.85117	+	2.49362i	−0.572923	+	0.208527i
$144$		0			0
$145$	2.38279	−	4.12711i	0.197880	−	0.342738i
$146$	−0.0569038	+	0.322718i	−0.00470939	+	0.0267083i
$147$		0			0
$148$	5.27584	+	4.42696i	0.433672	+	0.363894i
$149$	2.84002	+	16.1066i	0.232664	+	1.31950i	0.847478	+	0.530830i	$0.178120\pi$
$149$	2.84002	+	16.1066i	0.232664	+	1.31950i	−0.614815	+	0.788672i	$0.710769\pi$
$150$		0			0
$151$	20.5226			1.67010			0.835052	−	0.550170i	$-0.185437\pi$
$151$	20.5226			1.67010			0.835052	+	0.550170i	$0.185437\pi$
$152$	3.58512	+	2.47929i	0.290792	+	0.201097i
$153$		0			0
$154$	0.939693	+	0.342020i	0.0757226	+	0.0275608i
$155$	0.402856	+	2.28471i	0.0323582	+	0.183512i
$156$		0			0
$157$	−2.45084	+	2.05650i	−0.195598	+	0.164126i	−0.735327	−	0.677713i	$-0.762971\pi$
$157$	−2.45084	+	2.05650i	−0.195598	+	0.164126i	0.539729	+	0.841839i	$0.318527\pi$
$158$	−2.80154	+	15.8883i	−0.222878	+	1.26401i
$159$		0			0
$160$	0.592396	+	1.02606i	0.0468330	+	0.0811172i
$161$	−3.35117	+	1.21972i	−0.264109	+	0.0961278i
$162$		0			0
$163$	12.0039	+	20.7913i	0.940216	+	1.62850i	0.765058	+	0.643961i	$0.222710\pi$
$163$	12.0039	+	20.7913i	0.940216	+	1.62850i	0.175157	+	0.984540i	$0.443957\pi$
$164$	−4.49273	+	7.78163i	−0.350823	+	0.607643i
$165$		0			0
$166$	−8.86618	+	7.43961i	−0.688149	+	0.577426i
$167$	−2.80406	−	2.35289i	−0.216985	−	0.182072i	0.527816	−	0.849359i	$-0.323011\pi$
$167$	−2.80406	−	2.35289i	−0.216985	−	0.182072i	−0.744801	+	0.667287i	$0.767456\pi$
$168$		0			0
$169$	−1.92602	−	0.701015i	−0.148156	−	0.0539242i
$170$	1.37733			0.105636
$171$		0			0
$172$	2.42602			0.184982
$173$	−5.01114	−	1.82391i	−0.380990	−	0.138669i	0.144424	−	0.989516i	$-0.453867\pi$
$173$	−5.01114	−	1.82391i	−0.380990	−	0.138669i	−0.525414	+	0.850847i	$0.676089\pi$
$174$		0			0
$175$	−1.46585	−	1.23000i	−0.110808	−	0.0929789i
$176$	−1.43969	+	1.20805i	−0.108521	+	0.0910599i
$177$		0			0
$178$	−1.77972	+	3.08256i	−0.133395	+	0.231047i
$179$	−12.6284	−	21.8730i	−0.943888	−	1.63486i	−0.757963	−	0.652297i	$-0.773805\pi$
$179$	−12.6284	−	21.8730i	−0.943888	−	1.63486i	−0.185924	−	0.982564i	$-0.559528\pi$
$180$		0			0
$181$	16.2626	−	5.91912i	1.20879	−	0.439965i	0.342508	−	0.939515i	$-0.388724\pi$
$181$	16.2626	−	5.91912i	1.20879	−	0.439965i	0.866285	+	0.499550i	$0.166501\pi$
$182$	1.03209	+	1.78763i	0.0765035	+	0.132508i
$183$		0			0
$184$	1.16385	−	6.60051i	0.0858000	−	0.486596i
$185$	−6.25078	+	5.24503i	−0.459567	+	0.385622i
$186$		0			0
$187$	0.379385	+	2.15160i	0.0277434	+	0.157341i
$188$	1.91875	+	0.698367i	0.139939	+	0.0509337i
$189$		0			0
$190$	−3.63041	+	3.67301i	−0.263378	+	0.266468i
$191$	15.1780			1.09824			0.549120	−	0.835743i	$-0.314963\pi$
$191$	15.1780			1.09824			0.549120	+	0.835743i	$0.314963\pi$
$192$		0			0
$193$	2.25877	+	12.8101i	0.162590	+	0.922093i	0.951515	+	0.307603i	$0.0995269\pi$
$193$	2.25877	+	12.8101i	0.162590	+	0.922093i	−0.788925	+	0.614490i	$0.789362\pi$
$194$	4.50387	+	3.77920i	0.323359	+	0.271330i
$195$		0			0
$196$	−1.16637	+	6.61484i	−0.0833124	+	0.472488i
$197$	−4.47431	+	7.74973i	−0.318781	+	0.552145i	−0.980234	−	0.197842i	$-0.936607\pi$
$197$	−4.47431	+	7.74973i	−0.318781	+	0.552145i	0.661453	+	0.749987i	$0.269940\pi$
$198$		0			0
$199$	4.23308	−	1.54071i	0.300075	−	0.109218i	−0.187595	−	0.982246i	$-0.560069\pi$
$199$	4.23308	−	1.54071i	0.300075	−	0.109218i	0.487670	+	0.873028i	$0.337847\pi$
$200$	3.37939	−	1.23000i	0.238959	−	0.0869738i
$201$		0			0
$202$	6.32295	−	10.9517i	0.444881	−	0.770557i
$203$	0.371644	−	2.10770i	0.0260843	−	0.147932i
$204$		0			0
$205$	−8.15523	−	6.84305i	−0.569586	−	0.477939i
$206$	0.514548	+	2.91815i	0.0358503	+	0.203317i
$207$		0			0
$208$	−3.87939			−0.268987
$209$	−6.73783	−	4.65955i	−0.466065	−	0.322308i
$210$		0			0
$211$	6.01754	+	2.19021i	0.414265	+	0.150780i	0.540740	−	0.841190i	$-0.318144\pi$
$211$	6.01754	+	2.19021i	0.414265	+	0.150780i	−0.126475	+	0.991970i	$0.540366\pi$
$212$	−2.25237	−	12.7738i	−0.154694	−	0.877311i
$213$		0			0
$214$	−14.6420	+	12.2861i	−1.00091	+	0.839862i
$215$	−0.499123	+	2.83067i	−0.0340399	+	0.193050i
$216$		0			0
$217$	0.520945	+	0.902302i	0.0353640	+	0.0612523i
$218$	15.4217	−	5.61305i	1.04449	−	0.380164i
$219$		0			0
$220$	−1.11334	−	1.92836i	−0.0750614	−	0.130010i
$221$	−2.25490	+	3.90560i	−0.151681	+	0.262719i
$222$		0			0
$223$	2.48886	−	2.08840i	0.166666	−	0.139849i	−0.555640	−	0.831423i	$-0.687527\pi$
$223$	2.48886	−	2.08840i	0.166666	−	0.139849i	0.722306	+	0.691574i	$0.243082\pi$
$224$	0.407604	+	0.342020i	0.0272342	+	0.0228522i
$225$		0			0
$226$	−5.39053	−	1.96199i	−0.358573	−	0.130510i
$227$	11.7023			0.776711			0.388356	−	0.921510i	$-0.373043\pi$
$227$	11.7023			0.776711			0.388356	+	0.921510i	$0.373043\pi$
$228$		0			0
$229$	−22.9067			−1.51372			−0.756860	−	0.653578i	$-0.773267\pi$
$229$	−22.9067			−1.51372			−0.756860	+	0.653578i	$0.773267\pi$
$230$	7.46198	+	2.71594i	0.492028	+	0.179084i
$231$		0			0
$232$	3.08125	+	2.58548i	0.202294	+	0.169745i
$233$	2.45084	−	2.05650i	0.160560	−	0.134726i	−0.558968	−	0.829189i	$-0.688803\pi$
$233$	2.45084	−	2.05650i	0.160560	−	0.134726i	0.719528	+	0.694463i	$0.244358\pi$
$234$		0			0
$235$	−1.20961	+	2.09510i	−0.0789061	+	0.136669i
$236$	−1.34002	−	2.32099i	−0.0872280	−	0.151083i
$237$		0			0
$238$	0.581252	−	0.211558i	0.0376770	−	0.0137133i
$239$	3.08647	+	5.34592i	0.199647	+	0.345799i	0.948414	−	0.317035i	$-0.102687\pi$
$239$	3.08647	+	5.34592i	0.199647	+	0.345799i	−0.748767	+	0.662833i	$0.769354\pi$
$240$		0			0
$241$	0.266922	−	1.51379i	0.0171939	−	0.0975117i	−0.975003	−	0.222191i	$-0.928679\pi$
$241$	0.266922	−	1.51379i	0.0171939	−	0.0975117i	0.992197	+	0.124679i	$0.0397902\pi$
$242$	−5.72075	+	4.80028i	−0.367744	+	0.308574i
$243$		0			0
$244$	−1.97044	−	11.1749i	−0.126144	−	0.715400i
$245$	−7.47818	−	2.72183i	−0.477763	−	0.173892i
$246$		0			0
$247$	−4.47178	−	16.3079i	−0.284533	−	1.03764i
$248$	−1.95811			−0.124340
$249$		0			0
$250$	1.76857	+	10.0301i	0.111854	+	0.634357i
$251$	−13.7456	−	11.5339i	−0.867612	−	0.728013i	0.0959815	−	0.995383i	$-0.469401\pi$
$251$	−13.7456	−	11.5339i	−0.867612	−	0.728013i	−0.963594	+	0.267370i	$0.913845\pi$
$252$		0			0
$253$	−2.18732	+	12.4049i	−0.137516	+	0.779889i
$254$	0.943563	−	1.63430i	0.0592044	−	0.102545i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	27.6386	−	10.0596i	1.72405	−	0.627503i	0.725871	−	0.687831i	$-0.241437\pi$
$257$	27.6386	−	10.0596i	1.72405	−	0.627503i	0.998179	+	0.0603277i	$0.0192146\pi$
$258$		0			0
$259$	−1.83228	+	3.17360i	−0.113852	+	0.197198i
$260$	0.798133	−	4.52644i	0.0494981	−	0.280718i
$261$		0			0
$262$	−8.19846	−	6.87933i	−0.506503	−	0.425006i
$263$	−1.85504	−	10.5204i	−0.114386	−	0.648718i	−0.987052	−	0.160400i	$-0.948722\pi$
$263$	−1.85504	−	10.5204i	−0.114386	−	0.648718i	0.872666	−	0.488318i	$-0.162389\pi$
$264$		0			0
$265$	15.3678			0.944038
$266$	−0.967911	+	2.10770i	−0.0593464	+	0.129231i
$267$		0			0
$268$	10.4966	+	3.82045i	0.641182	+	0.233371i
$269$	3.57310	+	20.2641i	0.217856	+	1.23552i	0.875882	+	0.482526i	$0.160281\pi$
$269$	3.57310	+	20.2641i	0.217856	+	1.23552i	−0.658026	+	0.752995i	$0.728608\pi$
$270$		0			0
$271$	1.43763	−	1.20632i	0.0873300	−	0.0732786i	−0.598078	−	0.801438i	$-0.704069\pi$
$271$	1.43763	−	1.20632i	0.0873300	−	0.0732786i	0.685408	+	0.728160i	$0.259624\pi$
$272$	−0.201867	+	1.14484i	−0.0122400	+	0.0694163i
$273$		0			0
$274$	−5.62836	−	9.74860i	−0.340021	−	0.588934i
$275$	−6.35117	+	2.31164i	−0.382990	+	0.139397i
$276$		0			0
$277$	−2.43629	−	4.21978i	−0.146382	−	0.253542i	0.783505	−	0.621385i	$-0.213430\pi$
$277$	−2.43629	−	4.21978i	−0.146382	−	0.253542i	−0.929888	+	0.367843i	$0.880096\pi$
$278$	6.08512	−	10.5397i	0.364961	−	0.632132i
$279$		0			0
$280$	−0.482926	+	0.405223i	−0.0288603	+	0.0242167i
$281$	0.309278	+	0.259515i	0.0184500	+	0.0154814i	0.651966	−	0.758248i	$-0.273944\pi$
$281$	0.309278	+	0.259515i	0.0184500	+	0.0154814i	−0.633516	+	0.773730i	$0.718389\pi$
$282$		0			0
$283$	−16.5287	−	6.01595i	−0.982528	−	0.357611i	−0.199706	−	0.979856i	$-0.563999\pi$
$283$	−16.5287	−	6.01595i	−0.982528	−	0.357611i	−0.782823	+	0.622245i	$0.786221\pi$
$284$	−6.07192			−0.360302
$285$		0			0
$286$	7.29086			0.431118
$287$	−4.49273	−	1.63522i	−0.265197	−	0.0965239i
$288$		0			0
$289$	−11.9875	−	10.0587i	−0.705148	−	0.591689i
$290$	−3.65064	+	3.06325i	−0.214373	+	0.179880i
$291$		0			0
$292$	0.163848	−	0.283793i	0.00958848	−	0.0166077i
$293$	−6.58765	−	11.4101i	−0.384855	−	0.666588i	0.606894	−	0.794782i	$-0.292415\pi$
$293$	−6.58765	−	11.4101i	−0.384855	−	0.666588i	−0.991749	+	0.128195i	$0.959082\pi$
$294$		0			0
$295$	2.98380	−	1.08602i	0.173724	−	0.0632303i
$296$	−3.44356	−	5.96443i	−0.200153	−	0.346675i
$297$		0			0
$298$	2.84002	−	16.1066i	0.164518	−	0.933028i
$299$	−19.9179	+	16.7131i	−1.15188	+	0.966542i
$300$		0			0
$301$	0.224155	+	1.27125i	0.0129201	+	0.0732735i
$302$	−19.2849	−	7.01914i	−1.10972	−	0.403906i
$303$		0			0
$304$	−2.52094	−	3.55596i	−0.144586	−	0.203948i
$305$	13.4442			0.769812
$306$		0			0
$307$	2.93494	+	16.6449i	0.167506	+	0.949975i	0.946443	+	0.322872i	$0.104648\pi$
$307$	2.93494	+	16.6449i	0.167506	+	0.949975i	−0.778937	+	0.627103i	$0.784241\pi$
$308$	−0.766044	−	0.642788i	−0.0436494	−	0.0366262i
$309$		0			0
$310$	0.402856	−	2.28471i	0.0228807	−	0.129763i
$311$	−1.19072	+	2.06239i	−0.0675197	+	0.116947i	−0.897809	−	0.440385i	$-0.854842\pi$
$311$	−1.19072	+	2.06239i	−0.0675197	+	0.116947i	0.830289	+	0.557333i	$0.188175\pi$
$312$		0			0
$313$	28.0621	−	10.2138i	1.58616	−	0.577317i	0.609632	−	0.792685i	$-0.291317\pi$
$313$	28.0621	−	10.2138i	1.58616	−	0.577317i	0.976533	+	0.215368i	$0.0690951\pi$
$314$	3.00640	−	1.09424i	0.169661	−	0.0617515i
$315$		0			0
$316$	8.06670	−	13.9719i	0.453788	−	0.785983i
$317$	1.21941	−	6.91560i	0.0684888	−	0.388419i	−0.931224	−	0.364448i	$-0.881258\pi$
$317$	1.21941	−	6.91560i	0.0684888	−	0.388419i	0.999713	−	0.0239714i	$-0.00763107\pi$
$318$		0			0
$319$	−5.79086	−	4.85911i	−0.324226	−	0.272058i
$320$	−0.205737	−	1.16679i	−0.0115011	−	0.0652257i
$321$		0			0
$322$	3.56624			0.198739
$323$	−5.04529	+	0.471073i	−0.280728	+	0.0262112i
$324$		0			0
$325$	−13.1099	−	4.77163i	−0.727208	−	0.264682i
$326$	−4.16890	−	23.6430i	−0.230894	−	1.30947i
$327$		0			0
$328$	6.88326	−	5.77574i	0.380064	−	0.318912i
$329$	−0.188663	+	1.06996i	−0.0104013	+	0.0589888i
$330$		0			0
$331$	−13.5993	−	23.5546i	−0.747483	−	1.29468i	−0.949026	−	0.315199i	$-0.897929\pi$
$331$	−13.5993	−	23.5546i	−0.747483	−	1.29468i	0.201543	−	0.979480i	$-0.435404\pi$
$332$	10.8760	−	3.95853i	0.596897	−	0.217253i
$333$		0			0
$334$	1.83022	+	3.17004i	0.100145	+	0.173457i
$335$	−6.61721	+	11.4613i	−0.361537	+	0.626200i
$336$		0			0
$337$	−8.59286	+	7.21027i	−0.468083	+	0.392768i	−0.846095	−	0.533032i	$-0.821052\pi$
$337$	−8.59286	+	7.21027i	−0.468083	+	0.392768i	0.378012	+	0.925801i	$0.376608\pi$
$338$	1.57011	+	1.31748i	0.0854026	+	0.0716613i
$339$		0			0
$340$	−1.29426	−	0.471073i	−0.0701913	−	0.0255475i
$341$	3.68004			0.199286
$342$		0			0
$343$	−7.29860			−0.394087
$344$	−2.27972	−	0.829748i	−0.122914	−	0.0447370i
$345$		0			0
$346$	4.08512	+	3.42782i	0.219618	+	0.184281i
$347$	−1.48293	+	1.24432i	−0.0796076	+	0.0667987i	−0.681723	−	0.731610i	$-0.738769\pi$
$347$	−1.48293	+	1.24432i	−0.0796076	+	0.0667987i	0.602115	+	0.798409i	$0.294325\pi$
$348$		0			0
$349$	−7.19846	+	12.4681i	−0.385325	+	0.667402i	−0.991814	−	0.127689i	$-0.959244\pi$
$349$	−7.19846	+	12.4681i	−0.385325	+	0.667402i	0.606489	+	0.795092i	$0.292577\pi$
$350$	0.956767	+	1.65717i	0.0511413	+	0.0885794i
$351$		0			0
$352$	1.76604	−	0.642788i	0.0941305	−	0.0342607i
$353$	7.86184	+	13.6171i	0.418444	+	0.724766i	0.995783	−	0.0917384i	$-0.0292424\pi$
$353$	7.86184	+	13.6171i	0.418444	+	0.724766i	−0.577339	+	0.816504i	$0.695909\pi$
$354$		0			0
$355$	1.24922	−	7.08467i	0.0663016	−	0.376015i
$356$	2.72668	−	2.28796i	0.144514	−	0.121262i
$357$		0			0
$358$	4.38578	+	24.8730i	0.231796	+	1.31458i
$359$	14.5817	+	5.30731i	0.769594	+	0.280109i	0.696826	−	0.717240i	$-0.254595\pi$
$359$	14.5817	+	5.30731i	0.769594	+	0.280109i	0.0727672	+	0.997349i	$0.476817\pi$
$360$		0			0
$361$	12.0424	−	14.6963i	0.633808	−	0.773490i
$362$	−17.3063			−0.909601
$363$		0			0
$364$	−0.358441	−	2.03282i	−0.0187874	−	0.106549i
$365$	0.297418	+	0.249563i	0.0155676	+	0.0130627i
$366$		0			0
$367$	−2.73396	+	15.5050i	−0.142711	+	0.809356i	0.826465	+	0.562988i	$0.190348\pi$
$367$	−2.73396	+	15.5050i	−0.142711	+	0.809356i	−0.969176	+	0.246368i	$0.920763\pi$
$368$	−3.35117	+	5.80439i	−0.174692	+	0.302575i
$369$		0			0
$370$	7.66772	−	2.79082i	0.398626	−	0.145088i
$371$	6.48545	−	2.36051i	0.336708	−	0.122552i
$372$		0			0
$373$	14.8143	−	25.6592i	0.767057	−	1.32858i	−0.172095	−	0.985080i	$-0.555054\pi$
$373$	14.8143	−	25.6592i	0.767057	−	1.32858i	0.939152	−	0.343501i	$-0.111613\pi$
$374$	0.379385	−	2.15160i	0.0196175	−	0.111257i
$375$		0			0
$376$	−1.56418	−	1.31250i	−0.0806663	−	0.0676871i
$377$	−2.70961	−	15.3669i	−0.139552	−	0.791438i
$378$		0			0
$379$	4.72462			0.242688			0.121344	−	0.992611i	$-0.461280\pi$
$379$	4.72462			0.242688			0.121344	+	0.992611i	$0.461280\pi$
$380$	4.66772	−	2.20983i	0.239449	−	0.113362i
$381$		0			0
$382$	−14.2626	−	5.19118i	−0.729740	−	0.265604i
$383$	0.910130	+	5.16160i	0.0465055	+	0.263746i	0.999191	−	0.0402115i	$-0.0128032\pi$
$383$	0.910130	+	5.16160i	0.0465055	+	0.263746i	−0.952686	+	0.303957i	$0.901692\pi$
$384$		0			0
$385$	0.907604	−	0.761570i	0.0462558	−	0.0388132i
$386$	2.25877	−	12.8101i	0.114968	−	0.652018i
$387$		0			0
$388$	−2.93969	−	5.09170i	−0.149240	−	0.258492i
$389$	−14.1677	+	5.15663i	−0.718332	+	0.261451i	−0.675217	−	0.737619i	$-0.735950\pi$
$389$	−14.1677	+	5.15663i	−0.718332	+	0.261451i	−0.0431144	+	0.999070i	$0.513728\pi$
$390$		0			0
$391$	3.89574	+	6.74763i	0.197016	+	0.341242i
$392$	3.35844	−	5.81699i	0.169627	−	0.293802i
$393$		0			0
$394$	6.85504	−	5.75206i	0.345352	−	0.289785i
$395$	14.6427	+	12.2867i	0.736756	+	0.618212i
$396$		0			0
$397$	13.6677	+	4.97464i	0.685963	+	0.249670i	0.661406	−	0.750028i	$-0.269960\pi$
$397$	13.6677	+	4.97464i	0.685963	+	0.249670i	0.0245573	+	0.999698i	$0.492182\pi$
$398$	−4.50475			−0.225803
$399$		0			0
$400$	−3.59627			−0.179813
$401$	2.68257	+	0.976376i	0.133961	+	0.0487579i	0.408131	−	0.912923i	$-0.366181\pi$
$401$	2.68257	+	0.976376i	0.133961	+	0.0487579i	−0.274170	+	0.961681i	$0.588403\pi$
$402$		0			0
$403$	5.81908	+	4.88279i	0.289869	+	0.243229i
$404$	−9.68732	+	8.12863i	−0.481962	+	0.404414i
$405$		0			0
$406$	−1.07011	+	1.85348i	−0.0531085	+	0.0919867i
$407$	6.47178	+	11.2095i	0.320794	+	0.555632i
$408$		0			0
$409$	−32.1634	+	11.7065i	−1.59038	+	0.578851i	−0.977428	−	0.211269i	$-0.932240\pi$
$409$	−32.1634	+	11.7065i	−1.59038	+	0.578851i	−0.612952	+	0.790120i	$0.710018\pi$
$410$	5.32295	+	9.21962i	0.262882	+	0.455324i
$411$		0			0
$412$	0.514548	−	2.91815i	0.0253500	−	0.143767i
$413$	1.09240	−	0.916629i	0.0537533	−	0.0451044i
$414$		0			0
$415$	2.38120	+	13.5044i	0.116888	+	0.662907i
$416$	3.64543	+	1.32683i	0.178732	+	0.0650531i
$417$		0			0
$418$	4.73783	+	6.68302i	0.231735	+	0.326877i
$419$	7.91891			0.386864			0.193432	−	0.981114i	$-0.438038\pi$
$419$	7.91891			0.386864			0.193432	+	0.981114i	$0.438038\pi$
$420$		0			0
$421$	2.81480	+	15.9635i	0.137185	+	0.778014i	0.973313	+	0.229480i	$0.0737026\pi$
$421$	2.81480	+	15.9635i	0.137185	+	0.778014i	−0.836129	+	0.548534i	$0.815186\pi$
$422$	−4.90554	−	4.11624i	−0.238798	−	0.200375i
$423$		0			0
$424$	−2.25237	+	12.7738i	−0.109385	+	0.620353i
$425$	−2.09034	+	3.62057i	−0.101396	+	0.175623i
$426$		0			0
$427$	5.67365	−	2.06504i	0.274567	−	0.0999342i
$428$	17.9611	−	6.53731i	0.868183	−	0.315993i
$429$		0			0
$430$	1.43717	−	2.48925i	0.0693063	−	0.120042i
$431$	−4.41622	+	25.0456i	−0.212722	+	1.20641i	0.672094	+	0.740466i	$0.265395\pi$
$431$	−4.41622	+	25.0456i	−0.212722	+	1.20641i	−0.884816	+	0.465940i	$0.845716\pi$
$432$		0			0
$433$	9.07604	+	7.61570i	0.436167	+	0.365987i	0.834273	−	0.551352i	$-0.185888\pi$
$433$	9.07604	+	7.61570i	0.436167	+	0.365987i	−0.398106	+	0.917339i	$0.630332\pi$
$434$	−0.180922	−	1.02606i	−0.00868454	−	0.0492525i
$435$		0			0
$436$	−16.4115			−0.785967
$437$	−28.2629	−	7.39663i	−1.35200	−	0.353829i
$438$		0			0
$439$	−24.3002	−	8.84457i	−1.15979	−	0.422128i	−0.310766	−	0.950486i	$-0.600586\pi$
$439$	−24.3002	−	8.84457i	−1.15979	−	0.422128i	−0.849022	+	0.528358i	$0.822808\pi$
$440$	0.386659	+	2.19285i	0.0184333	+	0.104540i
$441$		0			0
$442$	3.45471	−	2.89884i	0.164324	−	0.137884i
$443$	−0.160282	+	0.909006i	−0.00761524	+	0.0431882i	−0.988379	−	0.152012i	$-0.951425\pi$
$443$	−0.160282	+	0.909006i	−0.00761524	+	0.0431882i	0.980763	+	0.195201i	$0.0625358\pi$
$444$		0			0
$445$	2.10859	+	3.65219i	0.0999569	+	0.173130i
$446$	−3.05303	+	1.11121i	−0.144565	+	0.0526175i
$447$		0			0
$448$	−0.266044	−	0.460802i	−0.0125694	−	0.0217709i
$449$	4.67230	−	8.09267i	0.220500	−	0.381917i	−0.734460	−	0.678652i	$-0.762565\pi$
$449$	4.67230	−	8.09267i	0.220500	−	0.381917i	0.954960	+	0.296735i	$0.0958979\pi$
$450$		0			0
$451$	−12.9363	+	10.8548i	−0.609146	+	0.511134i
$452$	4.39440	+	3.68734i	0.206695	+	0.173438i
$453$		0			0
$454$	−10.9966	−	4.00243i	−0.516096	−	0.187844i
$455$	2.44562			0.114653
$456$		0			0
$457$	30.9009			1.44548			0.722740	−	0.691120i	$-0.242882\pi$
$457$	30.9009			1.44548			0.722740	+	0.691120i	$0.242882\pi$
$458$	21.5253	+	7.83456i	1.00581	+	0.366085i
$459$		0			0
$460$	−6.08306	−	5.10430i	−0.283624	−	0.237989i
$461$	22.7422	−	19.0829i	1.05921	−	0.888781i	0.0651765	−	0.997874i	$-0.479239\pi$
$461$	22.7422	−	19.0829i	1.05921	−	0.888781i	0.994032	+	0.109093i	$0.0347945\pi$
$462$		0			0
$463$	5.91534	−	10.2457i	0.274909	−	0.476157i	−0.695203	−	0.718814i	$-0.744685\pi$
$463$	5.91534	−	10.2457i	0.274909	−	0.476157i	0.970112	+	0.242657i	$0.0780188\pi$
$464$	−2.01114	−	3.48340i	−0.0933650	−	0.161713i
$465$		0			0
$466$	−3.00640	+	1.09424i	−0.139269	+	0.0506896i
$467$	19.1591	+	33.1845i	0.886577	+	1.53560i	0.843895	+	0.536508i	$0.180257\pi$
$467$	19.1591	+	33.1845i	0.886577	+	1.53560i	0.0426825	+	0.999089i	$0.486410\pi$
$468$		0			0
$469$	−1.03209	+	5.85327i	−0.0476574	+	0.270279i
$470$	1.85323	−	1.55504i	0.0854829	−	0.0717287i
$471$		0			0
$472$	0.465385	+	2.63933i	0.0214211	+	0.121485i
$473$	4.28446	+	1.55942i	0.197000	+	0.0717021i
$474$		0			0
$475$	−4.14543	−	15.1177i	−0.190205	−	0.693648i
$476$	−0.618555			−0.0283514
$477$		0			0
$478$	−1.07192	−	6.07915i	−0.0490284	−	0.278054i
$479$	−28.5612	−	23.9657i	−1.30500	−	1.09502i	−0.989259	−	0.146176i	$-0.953304\pi$
$479$	−28.5612	−	23.9657i	−1.30500	−	1.09502i	−0.315738	−	0.948846i	$-0.602252\pi$
$480$		0			0
$481$	−4.63950	+	26.3119i	−0.211543	+	1.19972i
$482$	−0.768571	+	1.33120i	−0.0350074	+	0.0606347i
$483$		0			0
$484$	7.01754	−	2.55418i	0.318979	−	0.116099i
$485$	6.54576	−	2.38246i	0.297228	−	0.108182i
$486$		0			0
$487$	−16.4893	+	28.5603i	−0.747203	+	1.29419i	0.201956	+	0.979395i	$0.435270\pi$
$487$	−16.4893	+	28.5603i	−0.747203	+	1.29419i	−0.949159	+	0.314798i	$0.898063\pi$
$488$	−1.97044	+	11.1749i	−0.0891975	+	0.505864i
$489$		0			0
$490$	6.09627	+	5.11538i	0.275401	+	0.231089i
$491$	−3.07027	−	17.4124i	−0.138559	−	0.785809i	−0.972315	−	0.233675i	$-0.924925\pi$
$491$	−3.07027	−	17.4124i	−0.138559	−	0.785809i	0.833755	−	0.552134i	$-0.186186\pi$
$492$		0			0
$493$	−4.67593			−0.210593
$494$	−1.37551	+	16.8538i	−0.0618873	+	0.758289i
$495$		0			0
$496$	1.84002	+	0.669713i	0.0826194	+	0.0300710i
$497$	−0.561023	−	3.18172i	−0.0251653	−	0.142720i
$498$		0			0
$499$	20.7781	−	17.4349i	0.930157	−	0.780494i	−0.0456890	−	0.998956i	$-0.514548\pi$
$499$	20.7781	−	17.4349i	0.930157	−	0.780494i	0.975846	+	0.218462i	$0.0701039\pi$
$500$	1.76857	−	10.0301i	0.0790929	−	0.448558i
$501$		0			0
$502$	8.97178	+	15.5396i	0.400430	+	0.693565i
$503$	0.536837	−	0.195393i	0.0239364	−	0.00871212i	−0.330024	−	0.943972i	$-0.607057\pi$
$503$	0.536837	−	0.195393i	0.0239364	−	0.00871212i	0.353961	+	0.935260i	$0.384835\pi$
$504$		0			0
$505$	−7.49138	−	12.9755i	−0.333362	−	0.577400i
$506$	6.29813	−	10.9087i	0.279986	−	0.484950i
$507$		0			0
$508$	−1.44562	+	1.21302i	−0.0641391	+	0.0538191i
$509$	−31.0638	−	26.0656i	−1.37688	−	1.15534i	−0.970352	−	0.241698i	$-0.922296\pi$
$509$	−31.0638	−	26.0656i	−1.37688	−	1.15534i	−0.406526	−	0.913639i	$-0.633260\pi$
$510$		0			0
$511$	0.163848	+	0.0596358i	0.00724821	+	0.00263813i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−29.4124			−1.29733
$515$	3.29901	+	1.20074i	0.145372	+	0.0529110i
$516$		0			0
$517$	2.93969	+	2.46669i	0.129288	+	0.108485i
$518$	2.80722	−	2.35554i	0.123342	−	0.103496i
$519$		0			0
$520$	−2.29813	+	3.98048i	−0.100780	+	0.174556i
$521$	9.44996	+	16.3678i	0.414010	+	0.717087i	0.995324	−	0.0965927i	$-0.0307944\pi$
$521$	9.44996	+	16.3678i	0.414010	+	0.717087i	−0.581314	+	0.813680i	$0.697461\pi$
$522$		0			0
$523$	4.45589	−	1.62181i	0.194842	−	0.0709168i	−0.242756	−	0.970087i	$-0.578051\pi$
$523$	4.45589	−	1.62181i	0.194842	−	0.0709168i	0.437598	+	0.899171i	$0.355829\pi$
$524$	5.35117	+	9.26849i	0.233767	+	0.404896i
$525$		0			0
$526$	−1.85504	+	10.5204i	−0.0808835	+	0.458713i
$527$	1.74376	−	1.46318i	0.0759592	−	0.0637373i
$528$		0			0
$529$	3.80659	+	21.5882i	0.165504	+	0.938619i
$530$	−14.4410	−	5.25611i	−0.627279	−	0.228311i
$531$		0			0
$532$	1.63041	−	1.64955i	0.0706875	−	0.0715169i
$533$	−34.8580			−1.50987
$534$		0			0
$535$	3.93242	+	22.3019i	0.170013	+	0.964193i
$536$	−8.55690	−	7.18009i	−0.369602	−	0.310133i
$537$		0			0
$538$	3.57310	−	20.2641i	0.154047	−	0.873646i
$539$	−6.31180	+	10.9324i	−0.271869	+	0.470890i
$540$		0			0
$541$	26.6506	−	9.70004i	1.14580	−	0.417037i	0.301796	−	0.953373i	$-0.402414\pi$
$541$	26.6506	−	9.70004i	1.14580	−	0.417037i	0.844005	+	0.536335i	$0.180192\pi$
$542$	−1.76352	+	0.641868i	−0.0757496	+	0.0275706i
$543$		0			0
$544$	0.581252	−	1.00676i	0.0249210	−	0.0431644i
$545$	3.37645	−	19.1488i	0.144631	−	0.820244i
$546$		0			0
$547$	−5.27063	−	4.42258i	−0.225356	−	0.189096i	0.523118	−	0.852260i	$-0.324769\pi$
$547$	−5.27063	−	4.42258i	−0.225356	−	0.189096i	−0.748474	+	0.663164i	$0.769213\pi$
$548$	1.95471	+	11.0857i	0.0835010	+	0.473557i
$549$		0			0
$550$	6.75877			0.288195
$551$	12.3250	−	12.4696i	0.525063	−	0.531224i
$552$		0			0
$553$	8.06670	+	2.93604i	0.343031	+	0.124853i
$554$	0.846114	+	4.79855i	0.0359480	+	0.203871i
$555$		0			0
$556$	−9.32295	+	7.82288i	−0.395381	+	0.331764i
$557$	2.45929	−	13.9473i	0.104204	−	0.590968i	−0.887332	−	0.461131i	$-0.847444\pi$
$557$	2.45929	−	13.9473i	0.104204	−	0.590968i	0.991535	−	0.129836i	$-0.0414452\pi$
$558$		0			0
$559$	4.70574	+	8.15058i	0.199031	+	0.344733i
$560$	0.592396	−	0.215615i	0.0250333	−	0.00911138i
$561$		0			0
$562$	−0.201867	−	0.349643i	−0.00851523	−	0.0147488i
$563$	−18.1275	+	31.3977i	−0.763982	+	1.32326i	0.176801	+	0.984247i	$0.443425\pi$
$563$	−18.1275	+	31.3977i	−0.763982	+	1.32326i	−0.940783	+	0.339009i	$0.889908\pi$
$564$		0			0
$565$	−5.20645	+	4.36873i	−0.219037	+	0.183794i
$566$	13.4743	+	11.3063i	0.566367	+	0.475239i
$567$		0			0
$568$	5.70574	+	2.07672i	0.239407	+	0.0871372i
$569$	30.2918			1.26990			0.634949	−	0.772554i	$-0.281021\pi$
$569$	30.2918			1.26990			0.634949	+	0.772554i	$0.281021\pi$
$570$		0			0
$571$	3.39094			0.141906			0.0709532	−	0.997480i	$-0.477396\pi$
$571$	3.39094			0.141906			0.0709532	+	0.997480i	$0.477396\pi$
$572$	−6.85117	−	2.49362i	−0.286462	−	0.104264i
$573$		0			0
$574$	3.66250	+	3.07321i	0.152870	+	0.128273i
$575$	−18.4643	+	15.4934i	−0.770013	+	0.646117i
$576$		0			0
$577$	11.1514	−	19.3147i	0.464237	−	0.804082i	−0.534930	−	0.844897i	$-0.679662\pi$
$577$	11.1514	−	19.3147i	0.464237	−	0.804082i	0.999167	+	0.0408143i	$0.0129952\pi$
$578$	7.82429	+	13.5521i	0.325448	+	0.563692i
$579$		0			0
$580$	4.47818	−	1.62992i	0.185946	−	0.0676789i
$581$	3.07919	+	5.33332i	0.127746	+	0.221263i
$582$		0			0
$583$	4.23308	−	24.0070i	0.175316	−	0.994268i
$584$	−0.251030	+	0.210639i	−0.0103877	+	0.00871630i
$585$		0			0
$586$	2.28787	+	12.9751i	0.0945109	+	0.535998i
$587$	−27.0164	−	9.83315i	−1.11508	−	0.405858i	−0.282228	−	0.959347i	$-0.591074\pi$
$587$	−27.0164	−	9.83315i	−1.11508	−	0.405858i	−0.832856	+	0.553490i	$0.813296\pi$
$588$		0			0
$589$	−0.694288	+	8.50692i	−0.0286076	+	0.350522i
$590$	−3.17530			−0.130725
$591$		0			0
$592$	1.19594	+	6.78250i	0.0491527	+	0.278759i
$593$	−9.02094	−	7.56947i	−0.370446	−	0.310841i	0.438492	−	0.898735i	$-0.355513\pi$
$593$	−9.02094	−	7.56947i	−0.370446	−	0.310841i	−0.808938	+	0.587894i	$0.799957\pi$
$594$		0			0
$595$	0.127260	−	0.721726i	0.00521714	−	0.0295879i
$596$	−8.17752	+	14.1639i	−0.334964	+	0.580175i
$597$		0			0
$598$	24.4329	−	8.89284i	0.999135	−	0.363655i
$599$	−20.3268	+	7.39836i	−0.830531	+	0.302289i	−0.722077	−	0.691813i	$-0.756812\pi$
$599$	−20.3268	+	7.39836i	−0.830531	+	0.302289i	−0.108454	+	0.994101i	$0.534590\pi$
$600$		0			0
$601$	13.0967	−	22.6842i	0.534227	−	0.925308i	−0.464973	−	0.885325i	$-0.653936\pi$
$601$	13.0967	−	22.6842i	0.534227	−	0.925308i	0.999200	−	0.0399835i	$-0.0127305\pi$
$602$	0.224155	−	1.27125i	0.00913589	−	0.0518122i
$603$		0			0
$604$	15.7212	+	13.1917i	0.639687	+	0.536761i
$605$	1.53643	+	8.71351i	0.0624646	+	0.354254i
$606$		0			0
$607$	−13.2249			−0.536783			−0.268392	−	0.963310i	$-0.586492\pi$
$607$	−13.2249			−0.536783			−0.268392	+	0.963310i	$0.586492\pi$
$608$	1.15270	+	4.20372i	0.0467483	+	0.170483i
$609$		0			0
$610$	−12.6334	−	4.59818i	−0.511512	−	0.186175i
$611$	1.37551	+	7.80093i	0.0556474	+	0.315592i
$612$		0			0
$613$	−4.30722	+	3.61419i	−0.173967	+	0.145976i	−0.725614	−	0.688102i	$-0.758444\pi$
$613$	−4.30722	+	3.61419i	−0.173967	+	0.145976i	0.551647	+	0.834078i	$0.314000\pi$
$614$	2.93494	−	16.6449i	0.118445	−	0.671733i
$615$		0			0
$616$	0.500000	+	0.866025i	0.0201456	+	0.0348932i
$617$	8.90673	−	3.24178i	0.358571	−	0.130509i	−0.156452	−	0.987686i	$-0.550006\pi$
$617$	8.90673	−	3.24178i	0.358571	−	0.130509i	0.515023	+	0.857176i	$0.327783\pi$
$618$		0			0
$619$	7.37464	+	12.7732i	0.296412	+	0.513400i	0.975312	−	0.220830i	$-0.0708766\pi$
$619$	7.37464	+	12.7732i	0.296412	+	0.513400i	−0.678901	+	0.734230i	$0.737543\pi$
$620$	−1.15998	+	2.00914i	−0.0465858	+	0.0806890i
$621$		0			0
$622$	1.82429	−	1.53076i	0.0731475	−	0.0613780i
$623$	1.45084	+	1.21740i	0.0581266	+	0.0487740i
$624$		0			0
$625$	−5.55778	−	2.02287i	−0.222311	−	0.0809147i
$626$	−29.8631			−1.19357
$627$		0			0
$628$	−3.19934			−0.127668
$629$	7.52347	+	2.73832i	0.299980	+	0.109184i
$630$		0			0
$631$	19.1518	+	16.0703i	0.762422	+	0.639748i	0.938756	−	0.344582i	$-0.111979\pi$
$631$	19.1518	+	16.0703i	0.762422	+	0.639748i	−0.176334	+	0.984330i	$0.556424\pi$
$632$	−12.3589	+	10.3704i	−0.491611	+	0.412511i
$633$		0			0
$634$	−3.51114	+	6.08148i	−0.139445	+	0.241526i
$635$	−1.11793	−	1.93631i	−0.0443636	−	0.0768399i
$636$		0			0
$637$	−24.4859	+	8.91215i	−0.970167	+	0.353112i
$638$	3.77972	+	6.54666i	0.149640	+	0.259185i
$639$		0			0
$640$	−0.205737	+	1.16679i	−0.00813247	+	0.0461215i
$641$	33.4996	−	28.1095i	1.32315	−	1.11026i	0.337528	−	0.941315i	$-0.390409\pi$
$641$	33.4996	−	28.1095i	1.32315	−	1.11026i	0.985626	−	0.168943i	$-0.0540353\pi$
$642$		0			0
$643$	−5.80912	−	32.9451i	−0.229089	−	1.29923i	−0.854712	−	0.519103i	$-0.826266\pi$
$643$	−5.80912	−	32.9451i	−0.229089	−	1.29923i	0.625622	−	0.780126i	$-0.284845\pi$
$644$	−3.35117	−	1.21972i	−0.132054	−	0.0480639i
$645$		0			0
$646$	4.90214	+	1.28293i	0.192872	+	0.0504761i
$647$	32.1266			1.26303			0.631514	−	0.775365i	$-0.282434\pi$
$647$	32.1266			1.26303			0.631514	+	0.775365i	$0.282434\pi$
$648$		0			0
$649$	−0.874638	−	4.96032i	−0.0343325	−	0.194709i
$650$	10.6873	+	8.96773i	0.419191	+	0.351743i
$651$		0			0
$652$	−4.16890	+	23.6430i	−0.163267	+	0.925932i
$653$	1.44815	−	2.50827i	0.0566704	−	0.0981561i	−0.836298	−	0.548275i	$-0.815285\pi$
$653$	1.44815	−	2.50827i	0.0566704	−	0.0981561i	0.892969	+	0.450118i	$0.148618\pi$
$654$		0			0
$655$	−11.9153	+	4.33683i	−0.465571	+	0.169454i
$656$	−8.44356	+	3.07321i	−0.329666	+	0.119989i
$657$		0			0
$658$	0.543233	−	0.940908i	0.0211774	−	0.0366804i
$659$	−3.15926	+	17.9171i	−0.123067	+	0.697950i	0.859370	+	0.511355i	$0.170856\pi$
$659$	−3.15926	+	17.9171i	−0.123067	+	0.697950i	−0.982437	+	0.186595i	$0.940255\pi$
$660$		0			0
$661$	16.4081	+	13.7680i	0.638200	+	0.535513i	0.903465	−	0.428662i	$-0.141015\pi$
$661$	16.4081	+	13.7680i	0.638200	+	0.535513i	−0.265265	+	0.964176i	$0.585459\pi$
$662$	4.72297	+	26.7853i	0.183564	+	1.04104i
$663$		0			0
$664$	−11.5740			−0.449157
$665$	1.58924	+	2.24173i	0.0616281	+	0.0869305i
$666$		0			0
$667$	−25.3329	−	9.22043i	−0.980894	−	0.357016i
$668$	−0.635630	−	3.60483i	−0.0245932	−	0.139475i
$669$		0			0
$670$	10.1382	−	8.50692i	0.391671	−	0.328651i
$671$	3.70321	−	21.0020i	0.142961	−	0.810771i
$672$		0			0
$673$	−20.3457	−	35.2398i	−0.784269	−	1.35839i	−0.929435	−	0.368987i	$-0.879705\pi$
$673$	−20.3457	−	35.2398i	−0.784269	−	1.35839i	0.145165	−	0.989407i	$-0.453629\pi$
$674$	10.5407	−	3.83650i	0.406013	−	0.147777i
$675$		0			0
$676$	−1.02481	−	1.77503i	−0.0394160	−	0.0682704i
$677$	−0.0680482	+	0.117863i	−0.00261530	+	0.00452984i	−0.867330	−	0.497733i	$-0.834166\pi$
$677$	−0.0680482	+	0.117863i	−0.00261530	+	0.00452984i	0.864715	+	0.502263i	$0.167499\pi$
$678$		0			0
$679$	2.39646	−	2.01087i	0.0919677	−	0.0771700i
$680$	1.05509	+	0.885328i	0.0404610	+	0.0339508i
$681$		0			0
$682$	−3.45811	−	1.25865i	−0.132418	−	0.0481962i
$683$	43.6459			1.67006			0.835032	−	0.550202i	$-0.185449\pi$
$683$	43.6459			1.67006			0.835032	+	0.550202i	$0.185449\pi$
$684$		0			0
$685$	−13.3369			−0.509576
$686$	6.85844	+	2.49627i	0.261856	+	0.0953080i
$687$		0			0
$688$	1.85844	+	1.55942i	0.0708524	+	0.0594522i
$689$	38.5467	−	32.3445i	1.46851	−	1.23223i
$690$		0			0
$691$	−7.93376	+	13.7417i	−0.301815	+	0.522758i	−0.976547	−	0.215304i	$-0.930926\pi$
$691$	−7.93376	+	13.7417i	−0.301815	+	0.522758i	0.674732	+	0.738062i	$0.264259\pi$
$692$	−2.66637	−	4.61830i	−0.101360	−	0.175561i
$693$		0			0
$694$	1.81908	−	0.662090i	0.0690513	−	0.0251326i
$695$	−7.20961	−	12.4874i	−0.273476	−	0.473674i
$696$		0			0
$697$	−1.81386	+	10.2869i	−0.0687050	+	0.389645i
$698$	11.0287	−	9.25417i	0.417442	−	0.350275i
$699$		0			0
$700$	−0.332282	−	1.88446i	−0.0125591	−	0.0712260i
$701$	18.0513	+	6.57013i	0.681787	+	0.248150i	0.659615	−	0.751604i	$-0.270719\pi$
$701$	18.0513	+	6.57013i	0.681787	+	0.248150i	0.0221726	+	0.999754i	$0.492942\pi$
$702$		0			0
$703$	−27.1332	+	12.8456i	−1.02335	+	0.484481i
$704$	−1.87939			−0.0708320
$705$		0			0
$706$	−2.73039	−	15.4848i	−0.102760	−	0.582779i
$707$	−5.15451	−	4.32515i	−0.193855	−	0.162664i
$708$		0			0
$709$	5.73489	−	32.5242i	0.215378	−	1.22147i	−0.664871	−	0.746959i	$-0.731513\pi$
$709$	5.73489	−	32.5242i	0.215378	−	1.22147i	0.880249	−	0.474512i	$-0.157376\pi$
$710$	−3.59698	+	6.23016i	−0.134992	+	0.233814i
$711$		0			0
$712$	−3.34477	+	1.21740i	−0.125351	+	0.0456239i
$713$	12.3324	−	4.48864i	0.461854	−	0.168101i
$714$		0			0
$715$	4.31908	−	7.48086i	0.161524	−	0.279768i
$716$	4.38578	−	24.8730i	0.163904	−	0.929548i
$717$		0			0
$718$	−11.8871	−	9.97448i	−0.443624	−	0.372244i
$719$	−6.84952	−	38.8455i	−0.255444	−	1.44869i	−0.794931	−	0.606700i	$-0.792493\pi$
$719$	−6.84952	−	38.8455i	−0.255444	−	1.44869i	0.539487	−	0.841994i	$-0.318618\pi$
$720$		0			0
$721$	1.57667			0.0587181
$722$	−16.3425	+	9.69129i	−0.608207	+	0.360672i
$723$		0			0
$724$	16.2626	+	5.91912i	0.604396	+	0.219982i
$725$	−2.51186	−	14.2455i	−0.0932881	−	0.529063i
$726$		0			0
$727$	13.9816	−	11.7319i	0.518548	−	0.435114i	−0.345577	−	0.938390i	$-0.612317\pi$
$727$	13.9816	−	11.7319i	0.518548	−	0.435114i	0.864125	+	0.503277i	$0.167872\pi$
$728$	−0.358441	+	2.03282i	−0.0132847	+	0.0753413i
$729$		0			0
$730$	−0.194126	−	0.336236i	−0.00718492	−	0.0124446i
$731$	2.65018	−	0.964586i	0.0980204	−	0.0356765i
$732$		0			0
$733$	−7.69640	−	13.3306i	−0.284273	−	0.492376i	0.688160	−	0.725559i	$-0.258419\pi$
$733$	−7.69640	−	13.3306i	−0.284273	−	0.492376i	−0.972433	+	0.233184i	$0.925086\pi$
$734$	7.87211	−	13.6349i	0.290565	−	0.503273i
$735$		0			0
$736$	5.13429	−	4.30818i	0.189252	−	0.158802i
$737$	16.0817	+	13.4942i	0.592378	+	0.497064i
$738$		0			0
$739$	−14.2618	−	5.19086i	−0.524627	−	0.190949i	0.0661104	−	0.997812i	$-0.478941\pi$
$739$	−14.2618	−	5.19086i	−0.524627	−	0.190949i	−0.590738	+	0.806864i	$0.701163\pi$
$740$	−8.15982			−0.299961
$741$		0			0
$742$	−6.90167			−0.253368
$743$	−9.27156	−	3.37457i	−0.340141	−	0.123801i	0.166302	−	0.986075i	$-0.446817\pi$
$743$	−9.27156	−	3.37457i	−0.340141	−	0.123801i	−0.506442	+	0.862274i	$0.669040\pi$
$744$		0			0
$745$	−14.8439	−	12.4555i	−0.543838	−	0.456334i
$746$	−22.6969	+	19.0449i	−0.830991	+	0.697285i
$747$		0			0
$748$	−1.09240	+	1.89209i	−0.0399420	+	0.0691815i
$749$	5.08512	+	8.80769i	0.185806	+	0.321826i
$750$		0			0
$751$	9.17024	−	3.33770i	0.334627	−	0.121794i	−0.169242	−	0.985575i	$-0.554132\pi$
$751$	9.17024	−	3.33770i	0.334627	−	0.121794i	0.503869	+	0.863780i	$0.331910\pi$
$752$	1.02094	+	1.76833i	0.0372300	+	0.0644843i
$753$		0			0
$754$	−2.70961	+	15.3669i	−0.0986781	+	0.559631i
$755$	−18.6264	+	15.6294i	−0.677883	+	0.568812i
$756$		0			0
$757$	−7.55438	−	42.8430i	−0.274569	−	1.55716i	−0.740329	−	0.672245i	$-0.765330\pi$
$757$	−7.55438	−	42.8430i	−0.274569	−	1.55716i	0.465761	−	0.884911i	$-0.345781\pi$
$758$	−4.43969	−	1.61592i	−0.161257	−	0.0586927i
$759$		0			0
$760$	−5.14203	+	0.480105i	−0.186521	+	0.0174152i
$761$	−44.7137			−1.62087			−0.810435	−	0.585828i	$-0.800769\pi$
$761$	−44.7137			−1.62087			−0.810435	+	0.585828i	$0.800769\pi$
$762$		0			0
$763$	−1.51636	−	8.59970i	−0.0548959	−	0.311330i
$764$	11.6270	+	9.75622i	0.420651	+	0.352968i
$765$		0			0
$766$	0.910130	−	5.16160i	0.0328843	−	0.186496i
$767$	5.19846	−	9.00400i	0.187706	−	0.325116i
$768$		0			0
$769$	−20.7690	+	7.55931i	−0.748951	+	0.272596i	−0.688164	−	0.725555i	$-0.741583\pi$
$769$	−20.7690	+	7.55931i	−0.748951	+	0.272596i	−0.0607865	+	0.998151i	$0.519361\pi$
$770$	−1.11334	+	0.405223i	−0.0401220	+	0.0146032i
$771$		0			0
$772$	−6.50387	+	11.2650i	−0.234079	+	0.405437i
$773$	−7.32429	+	41.5381i	−0.263436	+	1.49402i	0.510014	+	0.860166i	$0.329640\pi$
$773$	−7.32429	+	41.5381i	−0.263436	+	1.49402i	−0.773451	+	0.633857i	$0.781471\pi$
$774$		0			0
$775$	5.39440	+	4.52644i	0.193773	+	0.162594i
$776$	1.02094	+	5.79006i	0.0366498	+	0.207851i
$777$		0			0
$778$	15.0770			0.540536
$779$	−22.6518	−	31.9519i	−0.811586	−	1.14480i
$780$		0			0
$781$	−10.7233	−	3.90295i	−0.383709	−	0.139659i
$782$	−1.35298	−	7.67312i	−0.0483824	−	0.274390i
$783$		0			0
$784$	−5.14543	+	4.31753i	−0.183765	+	0.154197i
$785$	0.658223	−	3.73297i	0.0234930	−	0.133235i
$786$		0			0
$787$	14.2396	+	24.6638i	0.507588	+	0.879169i	0.999961	+	0.00878442i	$0.00279620\pi$
$787$	14.2396	+	24.6638i	0.507588	+	0.879169i	−0.492373	+	0.870384i	$0.663870\pi$
$788$	−8.40895	+	3.06061i	−0.299556	+	0.109030i
$789$		0			0
$790$	−9.55737	−	16.5539i	−0.340036	−	0.588960i
$791$	−1.52616	+	2.64339i	−0.0542640	+	0.0939880i
$792$		0			0
$793$	33.7217	−	28.2959i	1.19749	−	1.00482i
$794$	−11.1420	−	9.34927i	−0.395416	−	0.331793i
$795$		0			0
$796$	4.23308	+	1.54071i	0.150037	+	0.0546092i
$797$	−16.6081			−0.588290			−0.294145	−	0.955761i	$-0.595035\pi$
$797$	−16.6081			−0.588290			−0.294145	+	0.955761i	$0.595035\pi$
$798$		0			0
$799$	2.37370			0.0839756
$800$	3.37939	+	1.23000i	0.119479	+	0.0434869i
$801$		0			0
$802$	−2.18685	−	1.83499i	−0.0772204	−	0.0647956i
$803$	0.471782	−	0.395872i	0.0166488	−	0.0139700i
$804$		0			0
$805$	2.11263	−	3.65917i	0.0744603	−	0.128969i
$806$	−3.79813	−	6.57856i	−0.133784	−	0.231720i
$807$		0			0
$808$	11.8833	−	4.32515i	0.418051	−	0.152158i
$809$	−6.83915	−	11.8457i	−0.240452	−	0.416474i	0.720391	−	0.693568i	$-0.243962\pi$
$809$	−6.83915	−	11.8457i	−0.240452	−	0.416474i	−0.960843	+	0.277093i	$0.910629\pi$
$810$		0			0
$811$	−0.107355	+	0.608839i	−0.00376973	+	0.0213792i	−0.986635	−	0.162948i	$-0.947900\pi$
$811$	−0.107355	+	0.608839i	−0.00376973	+	0.0213792i	0.982865	+	0.184328i	$0.0590107\pi$
$812$	1.63950	−	1.37570i	0.0575352	−	0.0482777i
$813$		0			0
$814$	−2.24763	−	12.7469i	−0.0787793	−	0.446779i
$815$	−26.7288	−	9.72849i	−0.936269	−	0.340774i
$816$		0			0
$817$	−4.41312	+	9.60991i	−0.154396	+	0.336208i
$818$	34.2276			1.19674
$819$		0			0
$820$	−1.84864	−	10.4842i	−0.0645573	−	0.366123i
$821$	−4.68210	−	3.92875i	−0.163407	−	0.137114i	0.557418	−	0.830232i	$-0.311792\pi$
$821$	−4.68210	−	3.92875i	−0.163407	−	0.137114i	−0.720824	+	0.693118i	$0.756237\pi$
$822$		0			0
$823$	5.32311	−	30.1889i	0.185552	−	1.05232i	−0.739692	−	0.672945i	$-0.765029\pi$
$823$	5.32311	−	30.1889i	0.185552	−	1.05232i	0.925244	−	0.379372i	$-0.123860\pi$
$824$	−1.48158	+	2.56617i	−0.0516133	+	0.0893969i
$825$		0			0
$826$	−1.34002	+	0.487728i	−0.0466253	+	0.0169702i
$827$	−47.6550	+	17.3450i	−1.65713	+	0.603145i	−0.989907	−	0.141717i	$-0.954738\pi$
$827$	−47.6550	+	17.3450i	−1.65713	+	0.603145i	−0.667219	+	0.744862i	$0.732515\pi$
$828$		0			0
$829$	6.50000	−	11.2583i	0.225754	−	0.391018i	−0.730791	−	0.682601i	$-0.760849\pi$
$829$	6.50000	−	11.2583i	0.225754	−	0.391018i	0.956545	+	0.291583i	$0.0941820\pi$
$830$	2.38120	−	13.5044i	0.0826525	−	0.468746i
$831$		0			0
$832$	−2.97178	−	2.49362i	−0.103028	−	0.0864507i
$833$	1.35591	+	7.68977i	0.0469797	+	0.266435i
$834$		0			0
$835$	4.33687			0.150083
$836$	−2.16637	−	7.90041i	−0.0749256	−	0.273241i
$837$		0			0
$838$	−7.44134	−	2.70843i	−0.257057	−	0.0935611i
$839$	3.73308	+	21.1713i	0.128880	+	0.730916i	0.978927	+	0.204209i	$0.0654623\pi$
$839$	3.73308	+	21.1713i	0.128880	+	0.730916i	−0.850047	+	0.526707i	$0.823427\pi$
$840$		0			0
$841$	−9.82160	+	8.24130i	−0.338676	+	0.284183i
$842$	2.81480	−	15.9635i	0.0970043	−	0.550139i
$843$		0			0
$844$	3.20187	+	5.54580i	0.110213	+	0.190894i
$845$	2.28194	−	0.830557i	0.0785010	−	0.0285720i
$846$		0			0
$847$	1.98680	+	3.44123i	0.0682671	+	0.118242i
$848$	6.48545	−	11.2331i	0.222711	−	0.385747i
$849$		0			0
$850$	3.20258	−	2.68729i	0.109848	−	0.0921731i
$851$	35.3605	+	29.6710i	1.21214	+	1.01711i
$852$		0			0
$853$	43.4397	+	15.8108i	1.48735	+	0.541351i	0.952750	−	0.303755i	$-0.0982406\pi$
$853$	43.4397	+	15.8108i	1.48735	+	0.541351i	0.534599	+	0.845106i	$0.320463\pi$
$854$	−6.03777			−0.206608
$855$		0			0
$856$	−19.1138			−0.653296
$857$	−41.0292	−	14.9334i	−1.40153	−	0.510115i	−0.472897	−	0.881118i	$-0.656792\pi$
$857$	−41.0292	−	14.9334i	−1.40153	−	0.510115i	−0.928632	+	0.371003i	$0.879014\pi$
$858$		0			0
$859$	15.4474	+	12.9619i	0.527060	+	0.442256i	0.867085	−	0.498161i	$-0.165991\pi$
$859$	15.4474	+	12.9619i	0.527060	+	0.442256i	−0.340025	+	0.940416i	$0.610436\pi$
$860$	−2.20187	+	1.84759i	−0.0750830	+	0.0630021i
$861$		0			0
$862$	12.7160	−	22.0248i	0.433109	−	0.750166i
$863$	−16.3466	−	28.3131i	−0.556444	−	0.963789i	−0.997790	−	0.0664522i	$-0.978832\pi$
$863$	−16.3466	−	28.3131i	−0.556444	−	0.963789i	0.441346	−	0.897337i	$-0.354501\pi$
$864$		0			0
$865$	5.93717	−	2.16095i	0.201870	−	0.0734746i
$866$	−5.92396	−	10.2606i	−0.201304	−	0.348670i
$867$		0			0
$868$	−0.180922	+	1.02606i	−0.00614090	+	0.0348268i
$869$	23.2271	−	19.4899i	0.787927	−	0.661149i
$870$		0			0
$871$	7.52481	+	42.6753i	0.254969	+	1.44600i
$872$	15.4217	+	5.61305i	0.522246	+	0.190082i
$873$		0			0
$874$	24.0287	+	16.6171i	0.812782	+	0.562080i
$875$	5.41921			0.183203
$876$		0			0
$877$	5.26099	+	29.8366i	0.177651	+	1.00751i	0.935039	+	0.354544i	$0.115364\pi$
$877$	5.26099	+	29.8366i	0.177651	+	1.00751i	−0.757388	+	0.652965i	$0.773525\pi$
$878$	19.8097	+	16.6223i	0.668546	+	0.560977i
$879$		0			0
$880$	0.386659	−	2.19285i	0.0130343	−	0.0739211i
$881$	11.7788	−	20.4015i	0.396839	−	0.687346i	−0.596495	−	0.802617i	$-0.703440\pi$
$881$	11.7788	−	20.4015i	0.396839	−	0.687346i	0.993334	+	0.115271i	$0.0367738\pi$
$882$		0			0
$883$	−34.6079	+	12.5962i	−1.16465	+	0.423897i	−0.850756	−	0.525561i	$-0.823855\pi$
$883$	−34.6079	+	12.5962i	−1.16465	+	0.423897i	−0.313892	+	0.949459i	$0.601633\pi$
$884$	−4.23783	+	1.54244i	−0.142534	+	0.0518780i
$885$		0			0
$886$	0.461515	−	0.799367i	0.0155049	−	0.0268552i
$887$	−0.748093	+	4.24265i	−0.0251185	+	0.142454i	−0.994788	−	0.101966i	$-0.967487\pi$
$887$	−0.748093	+	4.24265i	−0.0251185	+	0.142454i	0.969669	+	0.244420i	$0.0785977\pi$
$888$		0			0
$889$	−0.769200	−	0.645435i	−0.0257981	−	0.0216472i
$890$	−0.732307	−	4.15312i	−0.0245470	−	0.139213i
$891$		0			0
$892$	3.24897			0.108784
$893$	−6.25671	+	6.33012i	−0.209373	+	0.211830i
$894$		0			0
$895$	28.1193	+	10.2346i	0.939925	+	0.342105i
$896$	0.0923963	+	0.524005i	0.00308674	+	0.0175058i
$897$		0			0
$898$	−7.15839	+	6.00660i	−0.238878	+	0.200443i
$899$	−1.36767	+	7.75643i	−0.0456143	+	0.258691i
$900$		0			0
$901$	−7.53936	−	13.0586i	−0.251173	−	0.435044i
$902$	15.8687	−	5.77574i	0.528370	−	0.192311i
$903$		0			0
$904$	−2.86824	−	4.96794i	−0.0953963	−	0.165231i
$905$	−10.2522	+	17.7574i	−0.340795	+	0.590274i
$906$		0			0
$907$	17.8799	−	15.0030i	0.593691	−	0.498166i	−0.295720	−	0.955275i	$-0.595560\pi$
$907$	17.8799	−	15.0030i	0.593691	−	0.498166i	0.889411	+	0.457109i	$0.151115\pi$
$908$	8.96451	+	7.52211i	0.297498	+	0.249630i
$909$		0			0
$910$	−2.29813	−	0.836452i	−0.0761824	−	0.0277281i
$911$	−22.5631			−0.747547			−0.373774	−	0.927520i	$-0.621936\pi$
$911$	−22.5631			−0.747547			−0.373774	+	0.927520i	$0.621936\pi$
$912$		0			0
$913$	21.7520			0.719885
$914$	−29.0373	−	10.5687i	−0.960469	−	0.349582i
$915$		0			0
$916$	−17.5476	−	14.7242i	−0.579788	−	0.486500i
$917$	−4.36231	+	3.66041i	−0.144056	+	0.120878i
$918$		0			0
$919$	−2.12789	+	3.68561i	−0.0701926	+	0.121577i	−0.898986	−	0.437978i	$-0.855695\pi$
$919$	−2.12789	+	3.68561i	−0.0701926	+	0.121577i	0.828793	+	0.559555i	$0.189028\pi$
$920$	3.97044	+	6.87700i	0.130901	+	0.226728i
$921$		0			0
$922$	−27.8974	+	10.1538i	−0.918752	+	0.334398i
$923$	−11.7777	−	20.3995i	−0.387666	−	0.671458i
$924$		0			0
$925$	−4.30091	+	24.3917i	−0.141413	+	0.801993i
$926$	−9.06283	+	7.60462i	−0.297823	+	0.249903i
$927$		0			0
$928$	0.698463	+	3.96118i	0.0229282	+	0.130032i
$929$	55.9347	+	20.3586i	1.83516	+	0.667943i	0.991341	+	0.131311i	$0.0419187\pi$
$929$	55.9347	+	20.3586i	1.83516	+	0.667943i	0.843817	+	0.536632i	$0.180303\pi$
$930$		0			0
$931$	−24.0808	−	16.6531i	−0.789218	−	0.545784i
$932$	3.19934			0.104798
$933$		0			0
$934$	−6.65389	−	37.7361i	−0.217722	−	1.23476i
$935$	−1.98293	−	1.66387i	−0.0648486	−	0.0544144i
$936$		0			0
$937$	5.81877	−	32.9999i	0.190091	−	1.07806i	−0.729147	−	0.684357i	$-0.760083\pi$
$937$	5.81877	−	32.9999i	0.190091	−	1.07806i	0.919238	−	0.393703i	$-0.128806\pi$
$938$	2.97178	−	5.14728i	0.0970321	−	0.168065i
$939$		0			0
$940$	−2.27332	+	0.827420i	−0.0741475	+	0.0269875i
$941$	−5.19119	+	1.88944i	−0.169228	+	0.0615939i	−0.425245	−	0.905078i	$-0.639812\pi$
$941$	−5.19119	+	1.88944i	−0.169228	+	0.0615939i	0.256017	+	0.966672i	$0.417590\pi$
$942$		0			0
$943$	−30.1117	+	52.1551i	−0.980573	+	1.69840i
$944$	0.465385	−	2.63933i	0.0151470	−	0.0859028i
$945$		0			0
$946$	−3.49273	−	2.93075i	−0.113558	−	0.0952867i
$947$	2.58822	+	14.6785i	0.0841059	+	0.476988i	0.997546	+	0.0700149i	$0.0223047\pi$
$947$	2.58822	+	14.6785i	0.0841059	+	0.476988i	−0.913440	+	0.406973i	$0.866584\pi$
$948$		0			0
$949$	1.27126			0.0412668
$950$	−1.27513	+	15.6238i	−0.0413707	+	0.506903i
$951$		0			0
$952$	0.581252	+	0.211558i	0.0188385	+	0.00685665i
$953$	8.05138	+	45.6617i	0.260810	+	1.47913i	0.780707	+	0.624898i	$0.214859\pi$
$953$	8.05138	+	45.6617i	0.260810	+	1.47913i	−0.519897	+	0.854229i	$0.674030\pi$
$954$		0			0
$955$	−13.7756	+	11.5591i	−0.445768	+	0.374044i
$956$	−1.07192	+	6.07915i	−0.0346683	+	0.196614i
$957$		0			0
$958$	18.6420	+	32.2889i	0.602297	+	1.04321i
$959$	−5.62836	+	2.04855i	−0.181749	+	0.0661513i
$960$		0			0
$961$	13.5829	+	23.5263i	0.438158	+	0.758912i
$962$	13.3589	−	23.1383i	0.430708	−	0.746009i
$963$		0			0
$964$	1.17752	−	0.988055i	0.0379253	−	0.0318231i
$965$	−11.8059	−	9.90630i	−0.380045	−	0.318895i
$966$		0			0
$967$	21.8414	+	7.94961i	0.702371	+	0.255642i	0.668423	−	0.743781i	$-0.266970\pi$
$967$	21.8414	+	7.94961i	0.702371	+	0.255642i	0.0339481	+	0.999424i	$0.489192\pi$
$968$	−7.46791			−0.240028
$969$		0			0
$970$	−6.96585			−0.223660
$971$	4.63310	+	1.68631i	0.148683	+	0.0541163i	0.415290	−	0.909689i	$-0.363680\pi$
$971$	4.63310	+	1.68631i	0.148683	+	0.0541163i	−0.266606	+	0.963805i	$0.585902\pi$
$972$		0			0
$973$	−4.96064	−	4.16247i	−0.159031	−	0.133443i
$974$	25.2631	−	21.1983i	0.809482	−	0.679236i
$975$		0			0
$976$	5.67365	−	9.82705i	0.181609	−	0.314556i
$977$	16.3721	+	28.3573i	0.523790	+	0.907231i	0.999617	+	0.0276920i	$0.00881577\pi$
$977$	16.3721	+	28.3573i	0.523790	+	0.907231i	−0.475826	+	0.879539i	$0.657851\pi$
$978$		0			0
$979$	6.28611	−	2.28796i	0.200905	−	0.0731234i
$980$	−3.97906	−	6.89193i	−0.127106	−	0.220155i
$981$		0			0
$982$	−3.07027	+	17.4124i	−0.0979762	+	0.555651i
$983$	19.4886	−	16.3529i	0.621590	−	0.521576i	−0.276713	−	0.960953i	$-0.589245\pi$
$983$	19.4886	−	16.3529i	0.621590	−	0.521576i	0.898303	+	0.439377i	$0.144801\pi$
$984$		0			0
$985$	−1.84106	−	10.4412i	−0.0586611	−	0.332684i
$986$	4.39393	+	1.59926i	0.139931	+	0.0509308i
$987$		0			0
$988$	7.05690	−	15.3669i	0.224510	−	0.488888i
$989$	16.2600			0.517038
$990$		0			0
$991$	1.76311	+	9.99908i	0.0560070	+	0.317631i	0.999921	−	0.0125597i	$-0.00399797\pi$
$991$	1.76311	+	9.99908i	0.0560070	+	0.317631i	−0.943914	+	0.330191i	$0.892887\pi$
$992$	−1.50000	−	1.25865i	−0.0476250	−	0.0399622i
$993$		0			0
$994$	−0.561023	+	3.18172i	−0.0177946	+	0.100918i
$995$	−2.66860	+	4.62214i	−0.0846002	+	0.146532i
$996$		0			0
$997$	−52.4065	+	19.0744i	−1.65973	+	0.604092i	−0.990320	−	0.138801i	$-0.955675\pi$
$997$	−52.4065	+	19.0744i	−1.65973	+	0.604092i	−0.669410	+	0.742894i	$0.733453\pi$
$998$	−25.4881	+	9.27692i	−0.806813	+	0.293656i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.u.a.289.1		6
3.2	odd	2		114.2.i.d.61.1	yes	6
12.11	even	2		912.2.bo.f.289.1		6
19.5	even	9	inner	342.2.u.a.271.1		6
19.9	even	9		6498.2.a.bs.1.2		3
19.10	odd	18		6498.2.a.bn.1.2		3
57.5	odd	18		114.2.i.d.43.1	✓	6
57.29	even	18		2166.2.a.u.1.2		3
57.47	odd	18		2166.2.a.o.1.2		3
228.119	even	18		912.2.bo.f.385.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.d.43.1	✓	6	57.5	odd	18
114.2.i.d.61.1	yes	6	3.2	odd	2
342.2.u.a.271.1		6	19.5	even	9	inner
342.2.u.a.289.1		6	1.1	even	1	trivial
912.2.bo.f.289.1		6	12.11	even	2
912.2.bo.f.385.1		6	228.119	even	18
2166.2.a.o.1.2		3	57.47	odd	18
2166.2.a.u.1.2		3	57.29	even	18
6498.2.a.bn.1.2		3	19.10	odd	18
6498.2.a.bs.1.2		3	19.9	even	9

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(-0.907604 + 0.761570i) q^{5} +(-0.266044 + 0.460802i) q^{7} +(-0.500000 - 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(-0.907604 + 0.761570i) q^{5} +(-0.266044 + 0.460802i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.11334 - 0.405223i) q^{10} +(0.939693 + 1.62760i) q^{11} +(-0.673648 + 3.82045i) q^{13} +(0.407604 - 0.342020i) q^{14} +(0.173648 + 0.984808i) q^{16} +(1.09240 + 0.397600i) q^{17} +(-3.93969 + 1.86516i) q^{19} -1.18479 q^{20} +(-0.326352 - 1.85083i) q^{22} +(5.13429 + 4.30818i) q^{23} +(-0.624485 + 3.54163i) q^{25} +(1.93969 - 3.35965i) q^{26} +(-0.500000 + 0.181985i) q^{28} +(-3.77972 + 1.37570i) q^{29} +(0.979055 - 1.69577i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-0.890530 - 0.747243i) q^{34} +(-0.109470 - 0.620838i) q^{35} +6.88713 q^{37} +(4.34002 - 0.405223i) q^{38} +(1.11334 + 0.405223i) q^{40} +(1.56031 + 8.84894i) q^{41} +(1.85844 - 1.55942i) q^{43} +(-0.326352 + 1.85083i) q^{44} +(-3.35117 - 5.80439i) q^{46} +(1.91875 - 0.698367i) q^{47} +(3.35844 + 5.81699i) q^{49} +(1.79813 - 3.11446i) q^{50} +(-2.97178 + 2.49362i) q^{52} +(-9.93629 - 8.33754i) q^{53} +(-2.09240 - 0.761570i) q^{55} +0.532089 q^{56} +4.02229 q^{58} +(-2.51842 - 0.916629i) q^{59} +(-8.69253 - 7.29390i) q^{61} +(-1.50000 + 1.25865i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-2.29813 - 3.98048i) q^{65} +(10.4966 - 3.82045i) q^{67} +(0.581252 + 1.00676i) q^{68} +(-0.109470 + 0.620838i) q^{70} +(-4.65136 + 3.90295i) q^{71} +(-0.0569038 - 0.322718i) q^{73} +(-6.47178 - 2.35554i) q^{74} +(-4.21688 - 1.10359i) q^{76} -1.00000 q^{77} +(-2.80154 - 15.8883i) q^{79} +(-0.907604 - 0.761570i) q^{80} +(1.56031 - 8.84894i) q^{82} +(5.78699 - 10.0234i) q^{83} +(-1.29426 + 0.471073i) q^{85} +(-2.27972 + 0.829748i) q^{86} +(0.939693 - 1.62760i) q^{88} +(0.618089 - 3.50535i) q^{89} +(-1.58125 - 1.32683i) q^{91} +(1.16385 + 6.60051i) q^{92} -2.04189 q^{94} +(2.15523 - 4.69318i) q^{95} +(-5.52481 - 2.01087i) q^{97} +(-1.16637 - 6.61484i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q - 9 * q^5 + 3 * q^7 - 3 * q^8	\( 6 q - 9 q^{5} + 3 q^{7} - 3 q^{8} - 3 q^{13} + 6 q^{14} + 3 q^{17} - 18 q^{19} - 3 q^{22} + 21 q^{23} + 9 q^{25} + 6 q^{26} - 3 q^{28} + 3 q^{29} + 9 q^{31} + 12 q^{34} - 18 q^{35} - 18 q^{37} + 6 q^{38} + 15 q^{41} + 3 q^{43} - 3 q^{44} + 6 q^{46} + 9 q^{47} + 12 q^{49} - 3 q^{50} - 3 q^{52} - 12 q^{53} - 9 q^{55} - 6 q^{56} + 12 q^{58} - 27 q^{59} + 3 q^{61} - 9 q^{62} - 3 q^{64} + 21 q^{67} + 6 q^{68} - 18 q^{70} - 39 q^{71} + 36 q^{73} - 24 q^{74} - 9 q^{76} - 6 q^{77} - 45 q^{79} - 9 q^{80} + 15 q^{82} + 27 q^{83} - 18 q^{85} + 12 q^{86} + 30 q^{89} - 12 q^{91} + 3 q^{92} - 6 q^{94} - 6 q^{97} + 12 q^{98}+O(q^{100}) \) 6 * q - 9 * q^5 + 3 * q^7 - 3 * q^8 - 3 * q^13 + 6 * q^14 + 3 * q^17 - 18 * q^19 - 3 * q^22 + 21 * q^23 + 9 * q^25 + 6 * q^26 - 3 * q^28 + 3 * q^29 + 9 * q^31 + 12 * q^34 - 18 * q^35 - 18 * q^37 + 6 * q^38 + 15 * q^41 + 3 * q^43 - 3 * q^44 + 6 * q^46 + 9 * q^47 + 12 * q^49 - 3 * q^50 - 3 * q^52 - 12 * q^53 - 9 * q^55 - 6 * q^56 + 12 * q^58 - 27 * q^59 + 3 * q^61 - 9 * q^62 - 3 * q^64 + 21 * q^67 + 6 * q^68 - 18 * q^70 - 39 * q^71 + 36 * q^73 - 24 * q^74 - 9 * q^76 - 6 * q^77 - 45 * q^79 - 9 * q^80 + 15 * q^82 + 27 * q^83 - 18 * q^85 + 12 * q^86 + 30 * q^89 - 12 * q^91 + 3 * q^92 - 6 * q^94 - 6 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more